1,1,101,92,0.030000," ","int(x^3*(c*d*x+d)*(a+b*arctanh(c*x)),x)","\frac{c d a \,x^{5}}{5}+\frac{d a \,x^{4}}{4}+\frac{c d b \arctanh \left(c x \right) x^{5}}{5}+\frac{d b \arctanh \left(c x \right) x^{4}}{4}+\frac{b d \,x^{4}}{20}+\frac{b d \,x^{3}}{12 c}+\frac{b d \,x^{2}}{10 c^{2}}+\frac{b d x}{4 c^{3}}+\frac{9 d b \ln \left(c x -1\right)}{40 c^{4}}-\frac{b d \ln \left(c x +1\right)}{40 c^{4}}"," ",0,"1/5*c*d*a*x^5+1/4*d*a*x^4+1/5*c*d*b*arctanh(c*x)*x^5+1/4*d*b*arctanh(c*x)*x^4+1/20*b*d*x^4+1/12*b*d*x^3/c+1/10*b*d*x^2/c^2+1/4*b*d*x/c^3+9/40/c^4*d*b*ln(c*x-1)-1/40*b*d*ln(c*x+1)/c^4","A"
2,1,91,82,0.028000," ","int(x^2*(c*d*x+d)*(a+b*arctanh(c*x)),x)","\frac{c d a \,x^{4}}{4}+\frac{d a \,x^{3}}{3}+\frac{c d b \arctanh \left(c x \right) x^{4}}{4}+\frac{d b \arctanh \left(c x \right) x^{3}}{3}+\frac{b d \,x^{3}}{12}+\frac{b d \,x^{2}}{6 c}+\frac{b d x}{4 c^{2}}+\frac{7 d b \ln \left(c x -1\right)}{24 c^{3}}+\frac{b d \ln \left(c x +1\right)}{24 c^{3}}"," ",0,"1/4*c*d*a*x^4+1/3*d*a*x^3+1/4*c*d*b*arctanh(c*x)*x^4+1/3*d*b*arctanh(c*x)*x^3+1/12*b*d*x^3+1/6*b*d*x^2/c+1/4*b*d*x/c^2+7/24/c^3*d*b*ln(c*x-1)+1/24*b*d*ln(c*x+1)/c^3","A"
3,1,81,72,0.031000," ","int(x*(c*d*x+d)*(a+b*arctanh(c*x)),x)","\frac{c d a \,x^{3}}{3}+\frac{d a \,x^{2}}{2}+\frac{c d b \arctanh \left(c x \right) x^{3}}{3}+\frac{d b \arctanh \left(c x \right) x^{2}}{2}+\frac{b d \,x^{2}}{6}+\frac{b d x}{2 c}+\frac{5 d b \ln \left(c x -1\right)}{12 c^{2}}-\frac{b d \ln \left(c x +1\right)}{12 c^{2}}"," ",0,"1/3*c*d*a*x^3+1/2*d*a*x^2+1/3*c*d*b*arctanh(c*x)*x^3+1/2*d*b*arctanh(c*x)*x^2+1/6*b*d*x^2+1/2*b*d*x/c+5/12/c^2*d*b*ln(c*x-1)-1/12*b*d*ln(c*x+1)/c^2","A"
4,1,65,40,0.029000," ","int((c*d*x+d)*(a+b*arctanh(c*x)),x)","\frac{c d a \,x^{2}}{2}+a d x +\frac{c d b \arctanh \left(c x \right) x^{2}}{2}+d b \arctanh \left(c x \right) x +\frac{b d x}{2}+\frac{3 d b \ln \left(c x -1\right)}{4 c}+\frac{d b \ln \left(c x +1\right)}{4 c}"," ",0,"1/2*c*d*a*x^2+a*d*x+1/2*c*d*b*arctanh(c*x)*x^2+d*b*arctanh(c*x)*x+1/2*b*d*x+3/4/c*d*b*ln(c*x-1)+1/4/c*d*b*ln(c*x+1)","A"
5,1,86,54,0.047000," ","int((c*d*x+d)*(a+b*arctanh(c*x))/x,x)","d a \ln \left(c x \right)+a c d x +d b \arctanh \left(c x \right) \ln \left(c x \right)+b c d x \arctanh \left(c x \right)+\frac{d b \ln \left(c x -1\right)}{2}+\frac{d b \ln \left(c x +1\right)}{2}-\frac{d b \dilog \left(c x \right)}{2}-\frac{d b \dilog \left(c x +1\right)}{2}-\frac{d b \ln \left(c x \right) \ln \left(c x +1\right)}{2}"," ",0,"d*a*ln(c*x)+a*c*d*x+d*b*arctanh(c*x)*ln(c*x)+b*c*d*x*arctanh(c*x)+1/2*d*b*ln(c*x-1)+1/2*d*b*ln(c*x+1)-1/2*d*b*dilog(c*x)-1/2*d*b*dilog(c*x+1)-1/2*d*b*ln(c*x)*ln(c*x+1)","A"
6,1,105,64,0.054000," ","int((c*d*x+d)*(a+b*arctanh(c*x))/x^2,x)","c d a \ln \left(c x \right)-\frac{a d}{x}+c d b \arctanh \left(c x \right) \ln \left(c x \right)-\frac{d b \arctanh \left(c x \right)}{x}+c d b \ln \left(c x \right)-\frac{c d b \ln \left(c x -1\right)}{2}-\frac{c d b \ln \left(c x +1\right)}{2}-\frac{c d b \dilog \left(c x \right)}{2}-\frac{c d b \dilog \left(c x +1\right)}{2}-\frac{c d b \ln \left(c x \right) \ln \left(c x +1\right)}{2}"," ",0,"c*d*a*ln(c*x)-a*d/x+c*d*b*arctanh(c*x)*ln(c*x)-d*b*arctanh(c*x)/x+c*d*b*ln(c*x)-1/2*c*d*b*ln(c*x-1)-1/2*c*d*b*ln(c*x+1)-1/2*c*d*b*dilog(c*x)-1/2*c*d*b*dilog(c*x+1)-1/2*c*d*b*ln(c*x)*ln(c*x+1)","A"
7,1,84,52,0.040000," ","int((c*d*x+d)*(a+b*arctanh(c*x))/x^3,x)","-\frac{c d a}{x}-\frac{d a}{2 x^{2}}-\frac{c d b \arctanh \left(c x \right)}{x}-\frac{d b \arctanh \left(c x \right)}{2 x^{2}}+c^{2} d b \ln \left(c x \right)-\frac{b c d}{2 x}-\frac{3 c^{2} d b \ln \left(c x -1\right)}{4}-\frac{c^{2} d b \ln \left(c x +1\right)}{4}"," ",0,"-c*d*a/x-1/2*d*a/x^2-c*d*b*arctanh(c*x)/x-1/2*d*b*arctanh(c*x)/x^2+c^2*d*b*ln(c*x)-1/2*b*c*d/x-3/4*c^2*d*b*ln(c*x-1)-1/4*c^2*d*b*ln(c*x+1)","A"
8,1,95,84,0.041000," ","int((c*d*x+d)*(a+b*arctanh(c*x))/x^4,x)","-\frac{d a}{3 x^{3}}-\frac{c d a}{2 x^{2}}-\frac{d b \arctanh \left(c x \right)}{3 x^{3}}-\frac{c d b \arctanh \left(c x \right)}{2 x^{2}}-\frac{b c d}{6 x^{2}}-\frac{b \,c^{2} d}{2 x}+\frac{c^{3} d b \ln \left(c x \right)}{3}-\frac{5 c^{3} d b \ln \left(c x -1\right)}{12}+\frac{b \,c^{3} d \ln \left(c x +1\right)}{12}"," ",0,"-1/3*d*a/x^3-1/2*c*d*a/x^2-1/3*d*b*arctanh(c*x)/x^3-1/2*c*d*b*arctanh(c*x)/x^2-1/6*b*c*d/x^2-1/2*b*c^2*d/x+1/3*c^3*d*b*ln(c*x)-5/12*c^3*d*b*ln(c*x-1)+1/12*b*c^3*d*ln(c*x+1)","A"
9,1,105,94,0.040000," ","int((c*d*x+d)*(a+b*arctanh(c*x))/x^5,x)","-\frac{c d a}{3 x^{3}}-\frac{d a}{4 x^{4}}-\frac{c d b \arctanh \left(c x \right)}{3 x^{3}}-\frac{d b \arctanh \left(c x \right)}{4 x^{4}}-\frac{b c d}{12 x^{3}}-\frac{b \,c^{2} d}{6 x^{2}}-\frac{b \,c^{3} d}{4 x}+\frac{c^{4} d b \ln \left(c x \right)}{3}-\frac{7 c^{4} d b \ln \left(c x -1\right)}{24}-\frac{b \,c^{4} d \ln \left(c x +1\right)}{24}"," ",0,"-1/3*c*d*a/x^3-1/4*d*a/x^4-1/3*c*d*b*arctanh(c*x)/x^3-1/4*d*b*arctanh(c*x)/x^4-1/12*b*c*d/x^3-1/6*b*c^2*d/x^2-1/4*b*c^3*d/x+1/3*c^4*d*b*ln(c*x)-7/24*c^4*d*b*ln(c*x-1)-1/24*b*c^4*d*ln(c*x+1)","A"
10,1,159,137,0.030000," ","int(x^3*(c*d*x+d)^2*(a+b*arctanh(c*x)),x)","\frac{c^{2} d^{2} a \,x^{6}}{6}+\frac{2 c \,d^{2} a \,x^{5}}{5}+\frac{a \,x^{4} d^{2}}{4}+\frac{c^{2} d^{2} b \arctanh \left(c x \right) x^{6}}{6}+\frac{2 c \,d^{2} b \arctanh \left(c x \right) x^{5}}{5}+\frac{d^{2} b \arctanh \left(c x \right) x^{4}}{4}+\frac{b c \,d^{2} x^{5}}{30}+\frac{b \,d^{2} x^{4}}{10}+\frac{5 b \,d^{2} x^{3}}{36 c}+\frac{b \,d^{2} x^{2}}{5 c^{2}}+\frac{5 b \,d^{2} x}{12 c^{3}}+\frac{49 d^{2} b \ln \left(c x -1\right)}{120 c^{4}}-\frac{b \,d^{2} \ln \left(c x +1\right)}{120 c^{4}}"," ",0,"1/6*c^2*d^2*a*x^6+2/5*c*d^2*a*x^5+1/4*a*x^4*d^2+1/6*c^2*d^2*b*arctanh(c*x)*x^6+2/5*c*d^2*b*arctanh(c*x)*x^5+1/4*d^2*b*arctanh(c*x)*x^4+1/30*b*c*d^2*x^5+1/10*b*d^2*x^4+5/36*b*d^2*x^3/c+1/5*b*d^2*x^2/c^2+5/12*b*d^2*x/c^3+49/120/c^4*d^2*b*ln(c*x-1)-1/120*b*d^2*ln(c*x+1)/c^4","A"
11,1,147,125,0.030000," ","int(x^2*(c*d*x+d)^2*(a+b*arctanh(c*x)),x)","\frac{c^{2} d^{2} a \,x^{5}}{5}+\frac{c \,d^{2} a \,x^{4}}{2}+\frac{d^{2} a \,x^{3}}{3}+\frac{c^{2} d^{2} b \arctanh \left(c x \right) x^{5}}{5}+\frac{c \,d^{2} b \arctanh \left(c x \right) x^{4}}{2}+\frac{d^{2} b \arctanh \left(c x \right) x^{3}}{3}+\frac{b c \,d^{2} x^{4}}{20}+\frac{b \,d^{2} x^{3}}{6}+\frac{4 b \,d^{2} x^{2}}{15 c}+\frac{b \,d^{2} x}{2 c^{2}}+\frac{31 d^{2} b \ln \left(c x -1\right)}{60 c^{3}}+\frac{b \,d^{2} \ln \left(c x +1\right)}{60 c^{3}}"," ",0,"1/5*c^2*d^2*a*x^5+1/2*c*d^2*a*x^4+1/3*d^2*a*x^3+1/5*c^2*d^2*b*arctanh(c*x)*x^5+1/2*c*d^2*b*arctanh(c*x)*x^4+1/3*d^2*b*arctanh(c*x)*x^3+1/20*b*c*d^2*x^4+1/6*b*d^2*x^3+4/15*b*d^2*x^2/c+1/2*b*d^2*x/c^2+31/60/c^3*d^2*b*ln(c*x-1)+1/60*b*d^2*ln(c*x+1)/c^3","A"
12,1,135,113,0.028000," ","int(x*(c*d*x+d)^2*(a+b*arctanh(c*x)),x)","\frac{c^{2} d^{2} a \,x^{4}}{4}+\frac{2 c \,d^{2} a \,x^{3}}{3}+\frac{d^{2} a \,x^{2}}{2}+\frac{c^{2} d^{2} b \arctanh \left(c x \right) x^{4}}{4}+\frac{2 c \,d^{2} b \arctanh \left(c x \right) x^{3}}{3}+\frac{d^{2} b \arctanh \left(c x \right) x^{2}}{2}+\frac{b c \,d^{2} x^{3}}{12}+\frac{b \,d^{2} x^{2}}{3}+\frac{3 b \,d^{2} x}{4 c}+\frac{17 d^{2} b \ln \left(c x -1\right)}{24 c^{2}}-\frac{b \,d^{2} \ln \left(c x +1\right)}{24 c^{2}}"," ",0,"1/4*c^2*d^2*a*x^4+2/3*c*d^2*a*x^3+1/2*d^2*a*x^2+1/4*c^2*d^2*b*arctanh(c*x)*x^4+2/3*c*d^2*b*arctanh(c*x)*x^3+1/2*d^2*b*arctanh(c*x)*x^2+1/12*b*c*d^2*x^3+1/3*b*d^2*x^2+3/4*b*d^2*x/c+17/24/c^2*d^2*b*ln(c*x-1)-1/24*b*d^2*ln(c*x+1)/c^2","A"
13,1,121,63,0.028000," ","int((c*d*x+d)^2*(a+b*arctanh(c*x)),x)","\frac{c^{2} d^{2} a \,x^{3}}{3}+c \,d^{2} a \,x^{2}+a x \,d^{2}+\frac{d^{2} a}{3 c}+\frac{c^{2} d^{2} b \arctanh \left(c x \right) x^{3}}{3}+c \,d^{2} b \arctanh \left(c x \right) x^{2}+d^{2} b \arctanh \left(c x \right) x +\frac{d^{2} b \arctanh \left(c x \right)}{3 c}+\frac{c \,d^{2} b \,x^{2}}{6}+b \,d^{2} x +\frac{4 d^{2} b \ln \left(c x -1\right)}{3 c}"," ",0,"1/3*c^2*d^2*a*x^3+c*d^2*a*x^2+a*x*d^2+1/3/c*d^2*a+1/3*c^2*d^2*b*arctanh(c*x)*x^3+c*d^2*b*arctanh(c*x)*x^2+d^2*b*arctanh(c*x)*x+1/3/c*d^2*b*arctanh(c*x)+1/6*c*d^2*b*x^2+b*d^2*x+4/3/c*d^2*b*ln(c*x-1)","A"
14,1,142,104,0.049000," ","int((c*d*x+d)^2*(a+b*arctanh(c*x))/x,x)","\frac{d^{2} a \,c^{2} x^{2}}{2}+2 a c \,d^{2} x +a \,d^{2} \ln \left(c x \right)+\frac{d^{2} b \arctanh \left(c x \right) c^{2} x^{2}}{2}+2 b c \,d^{2} x \arctanh \left(c x \right)+d^{2} b \arctanh \left(c x \right) \ln \left(c x \right)-\frac{d^{2} b \dilog \left(c x \right)}{2}-\frac{d^{2} b \dilog \left(c x +1\right)}{2}-\frac{d^{2} b \ln \left(c x \right) \ln \left(c x +1\right)}{2}+\frac{b c \,d^{2} x}{2}+\frac{5 d^{2} b \ln \left(c x -1\right)}{4}+\frac{3 d^{2} b \ln \left(c x +1\right)}{4}"," ",0,"1/2*d^2*a*c^2*x^2+2*a*c*d^2*x+a*d^2*ln(c*x)+1/2*d^2*b*arctanh(c*x)*c^2*x^2+2*b*c*d^2*x*arctanh(c*x)+d^2*b*arctanh(c*x)*ln(c*x)-1/2*d^2*b*dilog(c*x)-1/2*d^2*b*dilog(c*x+1)-1/2*d^2*b*ln(c*x)*ln(c*x+1)+1/2*b*c*d^2*x+5/4*d^2*b*ln(c*x-1)+3/4*d^2*b*ln(c*x+1)","A"
15,1,123,61,0.047000," ","int((c*d*x+d)^2*(a+b*arctanh(c*x))/x^2,x)","d^{2} a \,c^{2} x +2 c \,d^{2} a \ln \left(c x \right)-\frac{d^{2} a}{x}+b \,c^{2} d^{2} x \arctanh \left(c x \right)+2 c \,d^{2} b \arctanh \left(c x \right) \ln \left(c x \right)-\frac{d^{2} b \arctanh \left(c x \right)}{x}+c \,d^{2} b \ln \left(c x \right)-c \,d^{2} b \dilog \left(c x \right)-c \,d^{2} b \dilog \left(c x +1\right)-c \,d^{2} b \ln \left(c x \right) \ln \left(c x +1\right)"," ",0,"d^2*a*c^2*x+2*c*d^2*a*ln(c*x)-d^2*a/x+b*c^2*d^2*x*arctanh(c*x)+2*c*d^2*b*arctanh(c*x)*ln(c*x)-d^2*b*arctanh(c*x)/x+c*d^2*b*ln(c*x)-c*d^2*b*dilog(c*x)-c*d^2*b*dilog(c*x+1)-c*d^2*b*ln(c*x)*ln(c*x+1)","A"
16,1,176,127,0.056000," ","int((c*d*x+d)^2*(a+b*arctanh(c*x))/x^3,x)","c^{2} d^{2} a \ln \left(c x \right)-\frac{2 c \,d^{2} a}{x}-\frac{a \,d^{2}}{2 x^{2}}+c^{2} d^{2} b \arctanh \left(c x \right) \ln \left(c x \right)-\frac{2 c \,d^{2} b \arctanh \left(c x \right)}{x}-\frac{d^{2} b \arctanh \left(c x \right)}{2 x^{2}}-\frac{b c \,d^{2}}{2 x}+2 c^{2} d^{2} b \ln \left(c x \right)-\frac{5 c^{2} d^{2} b \ln \left(c x -1\right)}{4}-\frac{3 c^{2} d^{2} b \ln \left(c x +1\right)}{4}-\frac{c^{2} d^{2} b \dilog \left(c x \right)}{2}-\frac{c^{2} d^{2} b \dilog \left(c x +1\right)}{2}-\frac{c^{2} d^{2} b \ln \left(c x \right) \ln \left(c x +1\right)}{2}"," ",0,"c^2*d^2*a*ln(c*x)-2*c*d^2*a/x-1/2*a*d^2/x^2+c^2*d^2*b*arctanh(c*x)*ln(c*x)-2*c*d^2*b*arctanh(c*x)/x-1/2*d^2*b*arctanh(c*x)/x^2-1/2*b*c*d^2/x+2*c^2*d^2*b*ln(c*x)-5/4*c^2*d^2*b*ln(c*x-1)-3/4*c^2*d^2*b*ln(c*x+1)-1/2*c^2*d^2*b*dilog(c*x)-1/2*c^2*d^2*b*dilog(c*x+1)-1/2*c^2*d^2*b*ln(c*x)*ln(c*x+1)","A"
17,1,141,73,0.043000," ","int((c*d*x+d)^2*(a+b*arctanh(c*x))/x^4,x)","-\frac{c^{2} d^{2} a}{x}-\frac{d^{2} a}{3 x^{3}}-\frac{c \,d^{2} a}{x^{2}}-\frac{c^{2} d^{2} b \arctanh \left(c x \right)}{x}-\frac{d^{2} b \arctanh \left(c x \right)}{3 x^{3}}-\frac{c \,d^{2} b \arctanh \left(c x \right)}{x^{2}}-\frac{b c \,d^{2}}{6 x^{2}}-\frac{b \,c^{2} d^{2}}{x}+\frac{4 c^{3} d^{2} b \ln \left(c x \right)}{3}-\frac{7 c^{3} d^{2} b \ln \left(c x -1\right)}{6}-\frac{c^{3} d^{2} b \ln \left(c x +1\right)}{6}"," ",0,"-c^2*d^2*a/x-1/3*d^2*a/x^3-c*d^2*a/x^2-c^2*d^2*b*arctanh(c*x)/x-1/3*d^2*b*arctanh(c*x)/x^3-c*d^2*b*arctanh(c*x)/x^2-1/6*b*c*d^2/x^2-b*c^2*d^2/x+4/3*c^3*d^2*b*ln(c*x)-7/6*c^3*d^2*b*ln(c*x-1)-1/6*c^3*d^2*b*ln(c*x+1)","A"
18,1,153,129,0.040000," ","int((c*d*x+d)^2*(a+b*arctanh(c*x))/x^5,x)","-\frac{2 c \,d^{2} a}{3 x^{3}}-\frac{c^{2} d^{2} a}{2 x^{2}}-\frac{d^{2} a}{4 x^{4}}-\frac{2 c \,d^{2} b \arctanh \left(c x \right)}{3 x^{3}}-\frac{c^{2} d^{2} b \arctanh \left(c x \right)}{2 x^{2}}-\frac{d^{2} b \arctanh \left(c x \right)}{4 x^{4}}-\frac{b c \,d^{2}}{12 x^{3}}-\frac{b \,c^{2} d^{2}}{3 x^{2}}-\frac{3 b \,c^{3} d^{2}}{4 x}+\frac{2 c^{4} d^{2} b \ln \left(c x \right)}{3}-\frac{17 c^{4} d^{2} b \ln \left(c x -1\right)}{24}+\frac{b \,c^{4} d^{2} \ln \left(c x +1\right)}{24}"," ",0,"-2/3*c*d^2*a/x^3-1/2*c^2*d^2*a/x^2-1/4*d^2*a/x^4-2/3*c*d^2*b*arctanh(c*x)/x^3-1/2*c^2*d^2*b*arctanh(c*x)/x^2-1/4*d^2*b*arctanh(c*x)/x^4-1/12*b*c*d^2/x^3-1/3*b*c^2*d^2/x^2-3/4*b*c^3*d^2/x+2/3*c^4*d^2*b*ln(c*x)-17/24*c^4*d^2*b*ln(c*x-1)+1/24*b*c^4*d^2*ln(c*x+1)","A"
19,1,165,141,0.042000," ","int((c*d*x+d)^2*(a+b*arctanh(c*x))/x^6,x)","-\frac{c^{2} d^{2} a}{3 x^{3}}-\frac{c \,d^{2} a}{2 x^{4}}-\frac{d^{2} a}{5 x^{5}}-\frac{c^{2} d^{2} b \arctanh \left(c x \right)}{3 x^{3}}-\frac{c \,d^{2} b \arctanh \left(c x \right)}{2 x^{4}}-\frac{d^{2} b \arctanh \left(c x \right)}{5 x^{5}}-\frac{b c \,d^{2}}{20 x^{4}}-\frac{b \,c^{2} d^{2}}{6 x^{3}}-\frac{4 b \,c^{3} d^{2}}{15 x^{2}}-\frac{b \,c^{4} d^{2}}{2 x}+\frac{8 c^{5} d^{2} b \ln \left(c x \right)}{15}-\frac{31 c^{5} d^{2} b \ln \left(c x -1\right)}{60}-\frac{b \,c^{5} d^{2} \ln \left(c x +1\right)}{60}"," ",0,"-1/3*c^2*d^2*a/x^3-1/2*c*d^2*a/x^4-1/5*d^2*a/x^5-1/3*c^2*d^2*b*arctanh(c*x)/x^3-1/2*c*d^2*b*arctanh(c*x)/x^4-1/5*d^2*b*arctanh(c*x)/x^5-1/20*b*c*d^2/x^4-1/6*b*c^2*d^2/x^3-4/15*b*c^3*d^2/x^2-1/2*b*c^4*d^2/x+8/15*c^5*d^2*b*ln(c*x)-31/60*c^5*d^2*b*ln(c*x-1)-1/60*b*c^5*d^2*ln(c*x+1)","A"
20,1,199,168,0.030000," ","int(x^3*(c*d*x+d)^3*(a+b*arctanh(c*x)),x)","\frac{c^{3} d^{3} a \,x^{7}}{7}+\frac{c^{2} d^{3} a \,x^{6}}{2}+\frac{3 c \,d^{3} a \,x^{5}}{5}+\frac{d^{3} a \,x^{4}}{4}+\frac{c^{3} d^{3} b \arctanh \left(c x \right) x^{7}}{7}+\frac{c^{2} d^{3} b \arctanh \left(c x \right) x^{6}}{2}+\frac{3 c \,d^{3} b \arctanh \left(c x \right) x^{5}}{5}+\frac{d^{3} b \arctanh \left(c x \right) x^{4}}{4}+\frac{b \,c^{2} d^{3} x^{6}}{42}+\frac{b c \,d^{3} x^{5}}{10}+\frac{13 b \,d^{3} x^{4}}{70}+\frac{b \,d^{3} x^{3}}{4 c}+\frac{13 b \,d^{3} x^{2}}{35 c^{2}}+\frac{3 b \,d^{3} x}{4 c^{3}}+\frac{209 d^{3} b \ln \left(c x -1\right)}{280 c^{4}}-\frac{b \,d^{3} \ln \left(c x +1\right)}{280 c^{4}}"," ",0,"1/7*c^3*d^3*a*x^7+1/2*c^2*d^3*a*x^6+3/5*c*d^3*a*x^5+1/4*d^3*a*x^4+1/7*c^3*d^3*b*arctanh(c*x)*x^7+1/2*c^2*d^3*b*arctanh(c*x)*x^6+3/5*c*d^3*b*arctanh(c*x)*x^5+1/4*d^3*b*arctanh(c*x)*x^4+1/42*b*c^2*d^3*x^6+1/10*b*c*d^3*x^5+13/70*b*d^3*x^4+1/4*b*d^3*x^3/c+13/35*b*d^3*x^2/c^2+3/4*b*d^3*x/c^3+209/280/c^4*d^3*b*ln(c*x-1)-1/280*b*d^3*ln(c*x+1)/c^4","A"
21,1,187,156,0.029000," ","int(x^2*(c*d*x+d)^3*(a+b*arctanh(c*x)),x)","\frac{c^{3} d^{3} a \,x^{6}}{6}+\frac{3 c^{2} d^{3} a \,x^{5}}{5}+\frac{3 c \,d^{3} a \,x^{4}}{4}+\frac{d^{3} a \,x^{3}}{3}+\frac{c^{3} d^{3} b \arctanh \left(c x \right) x^{6}}{6}+\frac{3 c^{2} d^{3} b \arctanh \left(c x \right) x^{5}}{5}+\frac{3 c \,d^{3} b \arctanh \left(c x \right) x^{4}}{4}+\frac{d^{3} b \arctanh \left(c x \right) x^{3}}{3}+\frac{b \,c^{2} d^{3} x^{5}}{30}+\frac{3 b c \,d^{3} x^{4}}{20}+\frac{11 b \,d^{3} x^{3}}{36}+\frac{7 b \,d^{3} x^{2}}{15 c}+\frac{11 b \,d^{3} x}{12 c^{2}}+\frac{37 d^{3} b \ln \left(c x -1\right)}{40 c^{3}}+\frac{b \,d^{3} \ln \left(c x +1\right)}{120 c^{3}}"," ",0,"1/6*c^3*d^3*a*x^6+3/5*c^2*d^3*a*x^5+3/4*c*d^3*a*x^4+1/3*d^3*a*x^3+1/6*c^3*d^3*b*arctanh(c*x)*x^6+3/5*c^2*d^3*b*arctanh(c*x)*x^5+3/4*c*d^3*b*arctanh(c*x)*x^4+1/3*d^3*b*arctanh(c*x)*x^3+1/30*b*c^2*d^3*x^5+3/20*b*c*d^3*x^4+11/36*b*d^3*x^3+7/15*b*d^3*x^2/c+11/12*b*d^3*x/c^2+37/40/c^3*d^3*b*ln(c*x-1)+1/120*b*d^3*ln(c*x+1)/c^3","A"
22,1,173,121,0.030000," ","int(x*(c*d*x+d)^3*(a+b*arctanh(c*x)),x)","\frac{c^{3} d^{3} a \,x^{5}}{5}+\frac{3 c^{2} d^{3} a \,x^{4}}{4}+c \,d^{3} a \,x^{3}+\frac{d^{3} a \,x^{2}}{2}+\frac{c^{3} d^{3} b \arctanh \left(c x \right) x^{5}}{5}+\frac{3 c^{2} d^{3} b \arctanh \left(c x \right) x^{4}}{4}+c \,d^{3} b \arctanh \left(c x \right) x^{3}+\frac{d^{3} b \arctanh \left(c x \right) x^{2}}{2}+\frac{c^{2} d^{3} b \,x^{4}}{20}+\frac{c \,d^{3} b \,x^{3}}{4}+\frac{3 d^{3} b \,x^{2}}{5}+\frac{5 b \,d^{3} x}{4 c}+\frac{49 d^{3} b \ln \left(c x -1\right)}{40 c^{2}}-\frac{d^{3} b \ln \left(c x +1\right)}{40 c^{2}}"," ",0,"1/5*c^3*d^3*a*x^5+3/4*c^2*d^3*a*x^4+c*d^3*a*x^3+1/2*d^3*a*x^2+1/5*c^3*d^3*b*arctanh(c*x)*x^5+3/4*c^2*d^3*b*arctanh(c*x)*x^4+c*d^3*b*arctanh(c*x)*x^3+1/2*d^3*b*arctanh(c*x)*x^2+1/20*c^2*d^3*b*x^4+1/4*c*d^3*b*x^3+3/5*d^3*b*x^2+5/4*b*d^3*x/c+49/40/c^2*d^3*b*ln(c*x-1)-1/40/c^2*d^3*b*ln(c*x+1)","A"
23,1,162,78,0.028000," ","int((c*d*x+d)^3*(a+b*arctanh(c*x)),x)","\frac{c^{3} d^{3} a \,x^{4}}{4}+c^{2} d^{3} a \,x^{3}+\frac{3 c \,d^{3} a \,x^{2}}{2}+a x \,d^{3}+\frac{d^{3} a}{4 c}+\frac{c^{3} d^{3} b \arctanh \left(c x \right) x^{4}}{4}+c^{2} d^{3} b \arctanh \left(c x \right) x^{3}+\frac{3 c \,d^{3} b \arctanh \left(c x \right) x^{2}}{2}+d^{3} b \arctanh \left(c x \right) x +\frac{d^{3} b \arctanh \left(c x \right)}{4 c}+\frac{c^{2} d^{3} b \,x^{3}}{12}+\frac{c \,d^{3} b \,x^{2}}{2}+\frac{7 b \,d^{3} x}{4}+\frac{2 d^{3} b \ln \left(c x -1\right)}{c}"," ",0,"1/4*c^3*d^3*a*x^4+c^2*d^3*a*x^3+3/2*c*d^3*a*x^2+a*x*d^3+1/4/c*d^3*a+1/4*c^3*d^3*b*arctanh(c*x)*x^4+c^2*d^3*b*arctanh(c*x)*x^3+3/2*c*d^3*b*arctanh(c*x)*x^2+d^3*b*arctanh(c*x)*x+1/4/c*d^3*b*arctanh(c*x)+1/12*c^2*d^3*b*x^3+1/2*c*d^3*b*x^2+7/4*b*d^3*x+2/c*d^3*b*ln(c*x-1)","B"
24,1,182,136,0.049000," ","int((c*d*x+d)^3*(a+b*arctanh(c*x))/x,x)","\frac{d^{3} a \,c^{3} x^{3}}{3}+\frac{3 d^{3} a \,c^{2} x^{2}}{2}+3 a c \,d^{3} x +d^{3} a \ln \left(c x \right)+\frac{d^{3} b \arctanh \left(c x \right) c^{3} x^{3}}{3}+\frac{3 d^{3} b \arctanh \left(c x \right) c^{2} x^{2}}{2}+3 b c \,d^{3} x \arctanh \left(c x \right)+d^{3} b \arctanh \left(c x \right) \ln \left(c x \right)-\frac{d^{3} b \dilog \left(c x \right)}{2}-\frac{d^{3} b \dilog \left(c x +1\right)}{2}-\frac{d^{3} b \ln \left(c x \right) \ln \left(c x +1\right)}{2}+\frac{b \,c^{2} d^{3} x^{2}}{6}+\frac{3 b c \,d^{3} x}{2}+\frac{29 d^{3} b \ln \left(c x -1\right)}{12}+\frac{11 d^{3} b \ln \left(c x +1\right)}{12}"," ",0,"1/3*d^3*a*c^3*x^3+3/2*d^3*a*c^2*x^2+3*a*c*d^3*x+d^3*a*ln(c*x)+1/3*d^3*b*arctanh(c*x)*c^3*x^3+3/2*d^3*b*arctanh(c*x)*c^2*x^2+3*b*c*d^3*x*arctanh(c*x)+d^3*b*arctanh(c*x)*ln(c*x)-1/2*d^3*b*dilog(c*x)-1/2*d^3*b*dilog(c*x+1)-1/2*d^3*b*ln(c*x)*ln(c*x+1)+1/6*b*c^2*d^3*x^2+3/2*b*c*d^3*x+29/12*d^3*b*ln(c*x-1)+11/12*d^3*b*ln(c*x+1)","A"
25,1,189,140,0.054000," ","int((c*d*x+d)^3*(a+b*arctanh(c*x))/x^2,x)","\frac{d^{3} a \,c^{3} x^{2}}{2}+3 d^{3} a \,c^{2} x +3 c \,d^{3} a \ln \left(c x \right)-\frac{d^{3} a}{x}+\frac{d^{3} b \arctanh \left(c x \right) c^{3} x^{2}}{2}+3 b \,c^{2} d^{3} x \arctanh \left(c x \right)+3 c \,d^{3} b \arctanh \left(c x \right) \ln \left(c x \right)-\frac{d^{3} b \arctanh \left(c x \right)}{x}-\frac{3 c \,d^{3} b \dilog \left(c x \right)}{2}-\frac{3 c \,d^{3} b \dilog \left(c x +1\right)}{2}-\frac{3 c \,d^{3} b \ln \left(c x \right) \ln \left(c x +1\right)}{2}+\frac{b \,c^{2} d^{3} x}{2}+c \,d^{3} b \ln \left(c x \right)+\frac{5 c \,d^{3} b \ln \left(c x -1\right)}{4}+\frac{3 c \,d^{3} b \ln \left(c x +1\right)}{4}"," ",0,"1/2*d^3*a*c^3*x^2+3*d^3*a*c^2*x+3*c*d^3*a*ln(c*x)-d^3*a/x+1/2*d^3*b*arctanh(c*x)*c^3*x^2+3*b*c^2*d^3*x*arctanh(c*x)+3*c*d^3*b*arctanh(c*x)*ln(c*x)-d^3*b*arctanh(c*x)/x-3/2*c*d^3*b*dilog(c*x)-3/2*c*d^3*b*dilog(c*x+1)-3/2*c*d^3*b*ln(c*x)*ln(c*x+1)+1/2*b*c^2*d^3*x+c*d^3*b*ln(c*x)+5/4*c*d^3*b*ln(c*x-1)+3/4*c*d^3*b*ln(c*x+1)","A"
26,1,200,150,0.057000," ","int((c*d*x+d)^3*(a+b*arctanh(c*x))/x^3,x)","a \,c^{3} d^{3} x +3 c^{2} d^{3} a \ln \left(c x \right)-\frac{3 c \,d^{3} a}{x}-\frac{d^{3} a}{2 x^{2}}+b \,c^{3} d^{3} x \arctanh \left(c x \right)+3 c^{2} d^{3} b \arctanh \left(c x \right) \ln \left(c x \right)-\frac{3 c \,d^{3} b \arctanh \left(c x \right)}{x}-\frac{d^{3} b \arctanh \left(c x \right)}{2 x^{2}}-\frac{3 c^{2} d^{3} b \dilog \left(c x \right)}{2}-\frac{3 c^{2} d^{3} b \dilog \left(c x +1\right)}{2}-\frac{3 c^{2} d^{3} b \ln \left(c x \right) \ln \left(c x +1\right)}{2}-\frac{b c \,d^{3}}{2 x}+3 c^{2} d^{3} b \ln \left(c x \right)-\frac{5 c^{2} d^{3} b \ln \left(c x -1\right)}{4}-\frac{3 c^{2} d^{3} b \ln \left(c x +1\right)}{4}"," ",0,"a*c^3*d^3*x+3*c^2*d^3*a*ln(c*x)-3*c*d^3*a/x-1/2*d^3*a/x^2+b*c^3*d^3*x*arctanh(c*x)+3*c^2*d^3*b*arctanh(c*x)*ln(c*x)-3*c*d^3*b*arctanh(c*x)/x-1/2*d^3*b*arctanh(c*x)/x^2-3/2*c^2*d^3*b*dilog(c*x)-3/2*c^2*d^3*b*dilog(c*x+1)-3/2*c^2*d^3*b*ln(c*x)*ln(c*x+1)-1/2*b*c*d^3/x+3*c^2*d^3*b*ln(c*x)-5/4*c^2*d^3*b*ln(c*x-1)-3/4*c^2*d^3*b*ln(c*x+1)","A"
27,1,216,158,0.057000," ","int((c*d*x+d)^3*(a+b*arctanh(c*x))/x^4,x)","c^{3} d^{3} a \ln \left(c x \right)-\frac{3 c^{2} d^{3} a}{x}-\frac{a \,d^{3}}{3 x^{3}}-\frac{3 c \,d^{3} a}{2 x^{2}}+c^{3} d^{3} b \arctanh \left(c x \right) \ln \left(c x \right)-\frac{3 c^{2} d^{3} b \arctanh \left(c x \right)}{x}-\frac{d^{3} b \arctanh \left(c x \right)}{3 x^{3}}-\frac{3 c \,d^{3} b \arctanh \left(c x \right)}{2 x^{2}}-\frac{b c \,d^{3}}{6 x^{2}}-\frac{3 b \,c^{2} d^{3}}{2 x}+\frac{10 c^{3} d^{3} b \ln \left(c x \right)}{3}-\frac{29 c^{3} d^{3} b \ln \left(c x -1\right)}{12}-\frac{11 c^{3} d^{3} b \ln \left(c x +1\right)}{12}-\frac{c^{3} d^{3} b \dilog \left(c x \right)}{2}-\frac{c^{3} d^{3} b \dilog \left(c x +1\right)}{2}-\frac{c^{3} d^{3} b \ln \left(c x \right) \ln \left(c x +1\right)}{2}"," ",0,"c^3*d^3*a*ln(c*x)-3*c^2*d^3*a/x-1/3*a*d^3/x^3-3/2*c*d^3*a/x^2+c^3*d^3*b*arctanh(c*x)*ln(c*x)-3*c^2*d^3*b*arctanh(c*x)/x-1/3*d^3*b*arctanh(c*x)/x^3-3/2*c*d^3*b*arctanh(c*x)/x^2-1/6*b*c*d^3/x^2-3/2*b*c^2*d^3/x+10/3*c^3*d^3*b*ln(c*x)-29/12*c^3*d^3*b*ln(c*x-1)-11/12*c^3*d^3*b*ln(c*x+1)-1/2*c^3*d^3*b*dilog(c*x)-1/2*c^3*d^3*b*dilog(c*x+1)-1/2*c^3*d^3*b*ln(c*x)*ln(c*x+1)","A"
28,1,181,85,0.041000," ","int((c*d*x+d)^3*(a+b*arctanh(c*x))/x^5,x)","-\frac{c^{3} d^{3} a}{x}-\frac{c \,d^{3} a}{x^{3}}-\frac{3 c^{2} d^{3} a}{2 x^{2}}-\frac{d^{3} a}{4 x^{4}}-\frac{c^{3} d^{3} b \arctanh \left(c x \right)}{x}-\frac{c \,d^{3} b \arctanh \left(c x \right)}{x^{3}}-\frac{3 c^{2} d^{3} b \arctanh \left(c x \right)}{2 x^{2}}-\frac{d^{3} b \arctanh \left(c x \right)}{4 x^{4}}-\frac{b c \,d^{3}}{12 x^{3}}-\frac{b \,c^{2} d^{3}}{2 x^{2}}-\frac{7 b \,c^{3} d^{3}}{4 x}+2 c^{4} d^{3} b \ln \left(c x \right)-\frac{15 c^{4} d^{3} b \ln \left(c x -1\right)}{8}-\frac{c^{4} d^{3} b \ln \left(c x +1\right)}{8}"," ",0,"-c^3*d^3*a/x-c*d^3*a/x^3-3/2*c^2*d^3*a/x^2-1/4*d^3*a/x^4-c^3*d^3*b*arctanh(c*x)/x-c*d^3*b*arctanh(c*x)/x^3-3/2*c^2*d^3*b*arctanh(c*x)/x^2-1/4*d^3*b*arctanh(c*x)/x^4-1/12*b*c*d^3/x^3-1/2*b*c^2*d^3/x^2-7/4*b*c^3*d^3/x+2*c^4*d^3*b*ln(c*x)-15/8*c^4*d^3*b*ln(c*x-1)-1/8*c^4*d^3*b*ln(c*x+1)","B"
29,1,193,121,0.041000," ","int((c*d*x+d)^3*(a+b*arctanh(c*x))/x^6,x)","-\frac{c^{2} d^{3} a}{x^{3}}-\frac{c^{3} d^{3} a}{2 x^{2}}-\frac{3 c \,d^{3} a}{4 x^{4}}-\frac{d^{3} a}{5 x^{5}}-\frac{c^{2} d^{3} b \arctanh \left(c x \right)}{x^{3}}-\frac{c^{3} d^{3} b \arctanh \left(c x \right)}{2 x^{2}}-\frac{3 c \,d^{3} b \arctanh \left(c x \right)}{4 x^{4}}-\frac{d^{3} b \arctanh \left(c x \right)}{5 x^{5}}-\frac{b c \,d^{3}}{20 x^{4}}-\frac{b \,c^{2} d^{3}}{4 x^{3}}-\frac{3 b \,c^{3} d^{3}}{5 x^{2}}-\frac{5 b \,c^{4} d^{3}}{4 x}+\frac{6 c^{5} d^{3} b \ln \left(c x \right)}{5}-\frac{49 c^{5} d^{3} b \ln \left(c x -1\right)}{40}+\frac{c^{5} d^{3} b \ln \left(c x +1\right)}{40}"," ",0,"-c^2*d^3*a/x^3-1/2*c^3*d^3*a/x^2-3/4*c*d^3*a/x^4-1/5*d^3*a/x^5-c^2*d^3*b*arctanh(c*x)/x^3-1/2*c^3*d^3*b*arctanh(c*x)/x^2-3/4*c*d^3*b*arctanh(c*x)/x^4-1/5*d^3*b*arctanh(c*x)/x^5-1/20*b*c*d^3/x^4-1/4*b*c^2*d^3/x^3-3/5*b*c^3*d^3/x^2-5/4*b*c^4*d^3/x+6/5*c^5*d^3*b*ln(c*x)-49/40*c^5*d^3*b*ln(c*x-1)+1/40*c^5*d^3*b*ln(c*x+1)","A"
30,1,205,172,0.040000," ","int((c*d*x+d)^3*(a+b*arctanh(c*x))/x^7,x)","-\frac{c^{3} d^{3} a}{3 x^{3}}-\frac{d^{3} a}{6 x^{6}}-\frac{3 c^{2} d^{3} a}{4 x^{4}}-\frac{3 c \,d^{3} a}{5 x^{5}}-\frac{c^{3} d^{3} b \arctanh \left(c x \right)}{3 x^{3}}-\frac{d^{3} b \arctanh \left(c x \right)}{6 x^{6}}-\frac{3 c^{2} d^{3} b \arctanh \left(c x \right)}{4 x^{4}}-\frac{3 c \,d^{3} b \arctanh \left(c x \right)}{5 x^{5}}-\frac{b c \,d^{3}}{30 x^{5}}-\frac{3 b \,c^{2} d^{3}}{20 x^{4}}-\frac{11 b \,c^{3} d^{3}}{36 x^{3}}-\frac{7 b \,c^{4} d^{3}}{15 x^{2}}-\frac{11 b \,c^{5} d^{3}}{12 x}+\frac{14 c^{6} d^{3} b \ln \left(c x \right)}{15}-\frac{37 c^{6} d^{3} b \ln \left(c x -1\right)}{40}-\frac{b \,c^{6} d^{3} \ln \left(c x +1\right)}{120}"," ",0,"-1/3*c^3*d^3*a/x^3-1/6*d^3*a/x^6-3/4*c^2*d^3*a/x^4-3/5*c*d^3*a/x^5-1/3*c^3*d^3*b*arctanh(c*x)/x^3-1/6*d^3*b*arctanh(c*x)/x^6-3/4*c^2*d^3*b*arctanh(c*x)/x^4-3/5*c*d^3*b*arctanh(c*x)/x^5-1/30*b*c*d^3/x^5-3/20*b*c^2*d^3/x^4-11/36*b*c^3*d^3/x^3-7/15*b*c^4*d^3/x^2-11/12*b*c^5*d^3/x+14/15*c^6*d^3*b*ln(c*x)-37/40*c^6*d^3*b*ln(c*x-1)-1/120*b*c^6*d^3*ln(c*x+1)","A"
31,1,237,198,0.033000," ","int(x^3*(c*d*x+d)^4*(a+b*arctanh(c*x)),x)","\frac{c^{4} d^{4} a \,x^{8}}{8}+\frac{4 c^{3} d^{4} a \,x^{7}}{7}+c^{2} d^{4} a \,x^{6}+\frac{4 c \,d^{4} a \,x^{5}}{5}+\frac{d^{4} a \,x^{4}}{4}+\frac{c^{4} d^{4} b \arctanh \left(c x \right) x^{8}}{8}+\frac{4 c^{3} d^{4} b \arctanh \left(c x \right) x^{7}}{7}+c^{2} d^{4} b \arctanh \left(c x \right) x^{6}+\frac{4 c \,d^{4} b \arctanh \left(c x \right) x^{5}}{5}+\frac{d^{4} b \arctanh \left(c x \right) x^{4}}{4}+\frac{b \,c^{3} d^{4} x^{7}}{56}+\frac{2 b \,c^{2} d^{4} x^{6}}{21}+\frac{9 b c \,d^{4} x^{5}}{40}+\frac{12 b \,d^{4} x^{4}}{35}+\frac{11 b \,d^{4} x^{3}}{24 c}+\frac{24 b \,d^{4} x^{2}}{35 c^{2}}+\frac{11 b \,d^{4} x}{8 c^{3}}+\frac{769 d^{4} b \ln \left(c x -1\right)}{560 c^{4}}-\frac{b \,d^{4} \ln \left(c x +1\right)}{560 c^{4}}"," ",0,"1/8*c^4*d^4*a*x^8+4/7*c^3*d^4*a*x^7+c^2*d^4*a*x^6+4/5*c*d^4*a*x^5+1/4*d^4*a*x^4+1/8*c^4*d^4*b*arctanh(c*x)*x^8+4/7*c^3*d^4*b*arctanh(c*x)*x^7+c^2*d^4*b*arctanh(c*x)*x^6+4/5*c*d^4*b*arctanh(c*x)*x^5+1/4*d^4*b*arctanh(c*x)*x^4+1/56*b*c^3*d^4*x^7+2/21*b*c^2*d^4*x^6+9/40*b*c*d^4*x^5+12/35*b*d^4*x^4+11/24*b*d^4*x^3/c+24/35*b*d^4*x^2/c^2+11/8*b*d^4*x/c^3+769/560/c^4*d^4*b*ln(c*x-1)-1/560*b*d^4*ln(c*x+1)/c^4","A"
32,1,225,151,0.030000," ","int(x^2*(c*d*x+d)^4*(a+b*arctanh(c*x)),x)","\frac{c^{4} d^{4} a \,x^{7}}{7}+\frac{2 c^{3} d^{4} a \,x^{6}}{3}+\frac{6 c^{2} d^{4} a \,x^{5}}{5}+c \,d^{4} a \,x^{4}+\frac{d^{4} a \,x^{3}}{3}+\frac{c^{4} d^{4} b \arctanh \left(c x \right) x^{7}}{7}+\frac{2 c^{3} d^{4} b \arctanh \left(c x \right) x^{6}}{3}+\frac{6 c^{2} d^{4} b \arctanh \left(c x \right) x^{5}}{5}+c \,d^{4} b \arctanh \left(c x \right) x^{4}+\frac{d^{4} b \arctanh \left(c x \right) x^{3}}{3}+\frac{b \,c^{3} d^{4} x^{6}}{42}+\frac{2 b \,c^{2} d^{4} x^{5}}{15}+\frac{47 b c \,d^{4} x^{4}}{140}+\frac{5 b \,d^{4} x^{3}}{9}+\frac{88 b \,d^{4} x^{2}}{105 c}+\frac{5 b \,d^{4} x}{3 c^{2}}+\frac{117 d^{4} b \ln \left(c x -1\right)}{70 c^{3}}+\frac{d^{4} b \ln \left(c x +1\right)}{210 c^{3}}"," ",0,"1/7*c^4*d^4*a*x^7+2/3*c^3*d^4*a*x^6+6/5*c^2*d^4*a*x^5+c*d^4*a*x^4+1/3*d^4*a*x^3+1/7*c^4*d^4*b*arctanh(c*x)*x^7+2/3*c^3*d^4*b*arctanh(c*x)*x^6+6/5*c^2*d^4*b*arctanh(c*x)*x^5+c*d^4*b*arctanh(c*x)*x^4+1/3*d^4*b*arctanh(c*x)*x^3+1/42*b*c^3*d^4*x^6+2/15*b*c^2*d^4*x^5+47/140*b*c*d^4*x^4+5/9*b*d^4*x^3+88/105*b*d^4*x^2/c+5/3*b*d^4*x/c^2+117/70/c^3*d^4*b*ln(c*x-1)+1/210/c^3*d^4*b*ln(c*x+1)","A"
33,1,215,137,0.030000," ","int(x*(c*d*x+d)^4*(a+b*arctanh(c*x)),x)","\frac{c^{4} d^{4} a \,x^{6}}{6}+\frac{4 c^{3} d^{4} a \,x^{5}}{5}+\frac{3 c^{2} d^{4} a \,x^{4}}{2}+\frac{4 c \,d^{4} a \,x^{3}}{3}+\frac{d^{4} a \,x^{2}}{2}+\frac{c^{4} d^{4} b \arctanh \left(c x \right) x^{6}}{6}+\frac{4 c^{3} d^{4} b \arctanh \left(c x \right) x^{5}}{5}+\frac{3 c^{2} d^{4} b \arctanh \left(c x \right) x^{4}}{2}+\frac{4 c \,d^{4} b \arctanh \left(c x \right) x^{3}}{3}+\frac{d^{4} b \arctanh \left(c x \right) x^{2}}{2}+\frac{c^{3} d^{4} b \,x^{5}}{30}+\frac{c^{2} d^{4} b \,x^{4}}{5}+\frac{5 c \,d^{4} b \,x^{3}}{9}+\frac{16 d^{4} b \,x^{2}}{15}+\frac{13 b \,d^{4} x}{6 c}+\frac{43 d^{4} b \ln \left(c x -1\right)}{20 c^{2}}-\frac{d^{4} b \ln \left(c x +1\right)}{60 c^{2}}"," ",0,"1/6*c^4*d^4*a*x^6+4/5*c^3*d^4*a*x^5+3/2*c^2*d^4*a*x^4+4/3*c*d^4*a*x^3+1/2*d^4*a*x^2+1/6*c^4*d^4*b*arctanh(c*x)*x^6+4/5*c^3*d^4*b*arctanh(c*x)*x^5+3/2*c^2*d^4*b*arctanh(c*x)*x^4+4/3*c*d^4*b*arctanh(c*x)*x^3+1/2*d^4*b*arctanh(c*x)*x^2+1/30*c^3*d^4*b*x^5+1/5*c^2*d^4*b*x^4+5/9*c*d^4*b*x^3+16/15*d^4*b*x^2+13/6*b*d^4*x/c+43/20/c^2*d^4*b*ln(c*x-1)-1/60/c^2*d^4*b*ln(c*x+1)","A"
34,1,202,95,0.028000," ","int((c*d*x+d)^4*(a+b*arctanh(c*x)),x)","\frac{c^{4} d^{4} a \,x^{5}}{5}+c^{3} d^{4} a \,x^{4}+2 c^{2} d^{4} a \,x^{3}+2 c \,d^{4} a \,x^{2}+x a \,d^{4}+\frac{d^{4} a}{5 c}+\frac{c^{4} d^{4} b \arctanh \left(c x \right) x^{5}}{5}+c^{3} d^{4} b \arctanh \left(c x \right) x^{4}+2 c^{2} d^{4} b \arctanh \left(c x \right) x^{3}+2 c \,d^{4} b \arctanh \left(c x \right) x^{2}+d^{4} b \arctanh \left(c x \right) x +\frac{d^{4} b \arctanh \left(c x \right)}{5 c}+\frac{c^{3} d^{4} b \,x^{4}}{20}+\frac{c^{2} d^{4} b \,x^{3}}{3}+\frac{11 c \,d^{4} b \,x^{2}}{10}+3 b \,d^{4} x +\frac{16 b \ln \left(c x -1\right) d^{4}}{5 c}"," ",0,"1/5*c^4*d^4*a*x^5+c^3*d^4*a*x^4+2*c^2*d^4*a*x^3+2*c*d^4*a*x^2+x*a*d^4+1/5/c*d^4*a+1/5*c^4*d^4*b*arctanh(c*x)*x^5+c^3*d^4*b*arctanh(c*x)*x^4+2*c^2*d^4*b*arctanh(c*x)*x^3+2*c*d^4*b*arctanh(c*x)*x^2+d^4*b*arctanh(c*x)*x+1/5/c*d^4*b*arctanh(c*x)+1/20*c^3*d^4*b*x^4+1/3*c^2*d^4*b*x^3+11/10*c*d^4*b*x^2+3*b*d^4*x+16/5/c*b*ln(c*x-1)*d^4","B"
35,1,222,167,0.050000," ","int((c*d*x+d)^4*(a+b*arctanh(c*x))/x,x)","\frac{d^{4} a \,c^{4} x^{4}}{4}+\frac{4 d^{4} a \,c^{3} x^{3}}{3}+3 d^{4} a \,c^{2} x^{2}+4 a c \,d^{4} x +d^{4} a \ln \left(c x \right)+\frac{d^{4} b \arctanh \left(c x \right) c^{4} x^{4}}{4}+\frac{4 d^{4} b \arctanh \left(c x \right) c^{3} x^{3}}{3}+3 d^{4} b \arctanh \left(c x \right) c^{2} x^{2}+4 b c \,d^{4} x \arctanh \left(c x \right)+d^{4} b \arctanh \left(c x \right) \ln \left(c x \right)-\frac{d^{4} b \dilog \left(c x \right)}{2}-\frac{d^{4} b \dilog \left(c x +1\right)}{2}-\frac{d^{4} b \ln \left(c x \right) \ln \left(c x +1\right)}{2}+\frac{b \,c^{3} d^{4} x^{3}}{12}+\frac{2 b \,c^{2} d^{4} x^{2}}{3}+\frac{13 b c \,d^{4} x}{4}+\frac{103 d^{4} b \ln \left(c x -1\right)}{24}+\frac{25 d^{4} b \ln \left(c x +1\right)}{24}"," ",0,"1/4*d^4*a*c^4*x^4+4/3*d^4*a*c^3*x^3+3*d^4*a*c^2*x^2+4*a*c*d^4*x+d^4*a*ln(c*x)+1/4*d^4*b*arctanh(c*x)*c^4*x^4+4/3*d^4*b*arctanh(c*x)*c^3*x^3+3*d^4*b*arctanh(c*x)*c^2*x^2+4*b*c*d^4*x*arctanh(c*x)+d^4*b*arctanh(c*x)*ln(c*x)-1/2*d^4*b*dilog(c*x)-1/2*d^4*b*dilog(c*x+1)-1/2*d^4*b*ln(c*x)*ln(c*x+1)+1/12*b*c^3*d^4*x^3+2/3*b*c^2*d^4*x^2+13/4*b*c*d^4*x+103/24*d^4*b*ln(c*x-1)+25/24*d^4*b*ln(c*x+1)","A"
36,1,229,172,0.054000," ","int((c*d*x+d)^4*(a+b*arctanh(c*x))/x^2,x)","\frac{d^{4} a \,c^{4} x^{3}}{3}+2 d^{4} a \,c^{3} x^{2}+6 a \,c^{2} d^{4} x +4 c \,d^{4} a \ln \left(c x \right)-\frac{d^{4} a}{x}+\frac{d^{4} b \arctanh \left(c x \right) c^{4} x^{3}}{3}+2 d^{4} b \arctanh \left(c x \right) c^{3} x^{2}+6 b \,c^{2} d^{4} x \arctanh \left(c x \right)+4 c \,d^{4} b \arctanh \left(c x \right) \ln \left(c x \right)-\frac{d^{4} b \arctanh \left(c x \right)}{x}-2 c \,d^{4} b \dilog \left(c x \right)-2 c \,d^{4} b \dilog \left(c x +1\right)-2 c \,d^{4} b \ln \left(c x \right) \ln \left(c x +1\right)+\frac{b \,c^{3} d^{4} x^{2}}{6}+2 b \,c^{2} d^{4} x +c \,d^{4} b \ln \left(c x \right)+\frac{11 c \,d^{4} b \ln \left(c x -1\right)}{3}+\frac{5 c \,d^{4} b \ln \left(c x +1\right)}{3}"," ",0,"1/3*d^4*a*c^4*x^3+2*d^4*a*c^3*x^2+6*a*c^2*d^4*x+4*c*d^4*a*ln(c*x)-d^4*a/x+1/3*d^4*b*arctanh(c*x)*c^4*x^3+2*d^4*b*arctanh(c*x)*c^3*x^2+6*b*c^2*d^4*x*arctanh(c*x)+4*c*d^4*b*arctanh(c*x)*ln(c*x)-d^4*b*arctanh(c*x)/x-2*c*d^4*b*dilog(c*x)-2*c*d^4*b*dilog(c*x+1)-2*c*d^4*b*ln(c*x)*ln(c*x+1)+1/6*b*c^3*d^4*x^2+2*b*c^2*d^4*x+c*d^4*b*ln(c*x)+11/3*c*d^4*b*ln(c*x-1)+5/3*c*d^4*b*ln(c*x+1)","A"
37,1,210,148,0.052000," ","int((c*d*x+d)^4*(a+b*arctanh(c*x))/x^3,x)","\frac{c^{4} d^{4} a \,x^{2}}{2}+4 a \,c^{3} d^{4} x +6 c^{2} d^{4} a \ln \left(c x \right)-\frac{4 c \,d^{4} a}{x}-\frac{d^{4} a}{2 x^{2}}+\frac{c^{4} d^{4} b \arctanh \left(c x \right) x^{2}}{2}+4 b \,c^{3} d^{4} x \arctanh \left(c x \right)+6 c^{2} d^{4} b \arctanh \left(c x \right) \ln \left(c x \right)-\frac{4 c \,d^{4} b \arctanh \left(c x \right)}{x}-\frac{d^{4} b \arctanh \left(c x \right)}{2 x^{2}}-3 c^{2} d^{4} b \dilog \left(c x \right)-3 c^{2} d^{4} b \dilog \left(c x +1\right)-3 c^{2} d^{4} b \ln \left(c x \right) \ln \left(c x +1\right)+\frac{b \,c^{3} d^{4} x}{2}+4 c^{2} d^{4} b \ln \left(c x \right)-\frac{b c \,d^{4}}{2 x}"," ",0,"1/2*c^4*d^4*a*x^2+4*a*c^3*d^4*x+6*c^2*d^4*a*ln(c*x)-4*c*d^4*a/x-1/2*d^4*a/x^2+1/2*c^4*d^4*b*arctanh(c*x)*x^2+4*b*c^3*d^4*x*arctanh(c*x)+6*c^2*d^4*b*arctanh(c*x)*ln(c*x)-4*c*d^4*b*arctanh(c*x)/x-1/2*d^4*b*arctanh(c*x)/x^2-3*c^2*d^4*b*dilog(c*x)-3*c^2*d^4*b*dilog(c*x+1)-3*c^2*d^4*b*ln(c*x)*ln(c*x+1)+1/2*b*c^3*d^4*x+4*c^2*d^4*b*ln(c*x)-1/2*b*c*d^4/x","A"
38,1,240,181,0.056000," ","int((c*d*x+d)^4*(a+b*arctanh(c*x))/x^4,x)","a \,c^{4} d^{4} x +4 c^{3} d^{4} a \ln \left(c x \right)-\frac{6 c^{2} d^{4} a}{x}-\frac{d^{4} a}{3 x^{3}}-\frac{2 c \,d^{4} a}{x^{2}}+b \,c^{4} d^{4} x \arctanh \left(c x \right)+4 c^{3} d^{4} b \arctanh \left(c x \right) \ln \left(c x \right)-\frac{6 c^{2} d^{4} b \arctanh \left(c x \right)}{x}-\frac{d^{4} b \arctanh \left(c x \right)}{3 x^{3}}-\frac{2 c \,d^{4} b \arctanh \left(c x \right)}{x^{2}}-2 c^{3} d^{4} b \dilog \left(c x \right)-2 c^{3} d^{4} b \dilog \left(c x +1\right)-2 c^{3} d^{4} b \ln \left(c x \right) \ln \left(c x +1\right)-\frac{b c \,d^{4}}{6 x^{2}}-\frac{2 b \,c^{2} d^{4}}{x}+\frac{19 c^{3} d^{4} b \ln \left(c x \right)}{3}-\frac{11 c^{3} d^{4} b \ln \left(c x -1\right)}{3}-\frac{5 c^{3} d^{4} b \ln \left(c x +1\right)}{3}"," ",0,"a*c^4*d^4*x+4*c^3*d^4*a*ln(c*x)-6*c^2*d^4*a/x-1/3*d^4*a/x^3-2*c*d^4*a/x^2+b*c^4*d^4*x*arctanh(c*x)+4*c^3*d^4*b*arctanh(c*x)*ln(c*x)-6*c^2*d^4*b*arctanh(c*x)/x-1/3*d^4*b*arctanh(c*x)/x^3-2*c*d^4*b*arctanh(c*x)/x^2-2*c^3*d^4*b*dilog(c*x)-2*c^3*d^4*b*dilog(c*x+1)-2*c^3*d^4*b*ln(c*x)*ln(c*x+1)-1/6*b*c*d^4/x^2-2*b*c^2*d^4/x+19/3*c^3*d^4*b*ln(c*x)-11/3*c^3*d^4*b*ln(c*x-1)-5/3*c^3*d^4*b*ln(c*x+1)","A"
39,1,256,189,0.057000," ","int((c*d*x+d)^4*(a+b*arctanh(c*x))/x^5,x)","c^{4} d^{4} a \ln \left(c x \right)-\frac{4 c^{3} d^{4} a}{x}-\frac{4 c \,d^{4} a}{3 x^{3}}-\frac{3 c^{2} d^{4} a}{x^{2}}-\frac{d^{4} a}{4 x^{4}}+c^{4} d^{4} b \arctanh \left(c x \right) \ln \left(c x \right)-\frac{4 c^{3} d^{4} b \arctanh \left(c x \right)}{x}-\frac{4 c \,d^{4} b \arctanh \left(c x \right)}{3 x^{3}}-\frac{3 c^{2} d^{4} b \arctanh \left(c x \right)}{x^{2}}-\frac{d^{4} b \arctanh \left(c x \right)}{4 x^{4}}-\frac{b c \,d^{4}}{12 x^{3}}-\frac{2 b \,c^{2} d^{4}}{3 x^{2}}-\frac{13 b \,c^{3} d^{4}}{4 x}+\frac{16 c^{4} d^{4} b \ln \left(c x \right)}{3}-\frac{103 c^{4} d^{4} b \ln \left(c x -1\right)}{24}-\frac{25 c^{4} d^{4} b \ln \left(c x +1\right)}{24}-\frac{c^{4} d^{4} b \dilog \left(c x \right)}{2}-\frac{c^{4} d^{4} b \dilog \left(c x +1\right)}{2}-\frac{c^{4} d^{4} b \ln \left(c x \right) \ln \left(c x +1\right)}{2}"," ",0,"c^4*d^4*a*ln(c*x)-4*c^3*d^4*a/x-4/3*c*d^4*a/x^3-3*c^2*d^4*a/x^2-1/4*d^4*a/x^4+c^4*d^4*b*arctanh(c*x)*ln(c*x)-4*c^3*d^4*b*arctanh(c*x)/x-4/3*c*d^4*b*arctanh(c*x)/x^3-3*c^2*d^4*b*arctanh(c*x)/x^2-1/4*d^4*b*arctanh(c*x)/x^4-1/12*b*c*d^4/x^3-2/3*b*c^2*d^4/x^2-13/4*b*c^3*d^4/x+16/3*c^4*d^4*b*ln(c*x)-103/24*c^4*d^4*b*ln(c*x-1)-25/24*c^4*d^4*b*ln(c*x+1)-1/2*c^4*d^4*b*dilog(c*x)-1/2*c^4*d^4*b*dilog(c*x+1)-1/2*c^4*d^4*b*ln(c*x)*ln(c*x+1)","A"
40,1,221,97,0.040000," ","int((c*d*x+d)^4*(a+b*arctanh(c*x))/x^6,x)","-\frac{c^{4} d^{4} a}{x}-\frac{2 c^{2} d^{4} a}{x^{3}}-\frac{2 c^{3} d^{4} a}{x^{2}}-\frac{c \,d^{4} a}{x^{4}}-\frac{d^{4} a}{5 x^{5}}-\frac{c^{4} d^{4} b \arctanh \left(c x \right)}{x}-\frac{2 c^{2} d^{4} b \arctanh \left(c x \right)}{x^{3}}-\frac{2 c^{3} d^{4} b \arctanh \left(c x \right)}{x^{2}}-\frac{c \,d^{4} b \arctanh \left(c x \right)}{x^{4}}-\frac{d^{4} b \arctanh \left(c x \right)}{5 x^{5}}-\frac{b c \,d^{4}}{20 x^{4}}-\frac{b \,c^{2} d^{4}}{3 x^{3}}-\frac{11 b \,c^{3} d^{4}}{10 x^{2}}-\frac{3 b \,c^{4} d^{4}}{x}+\frac{16 c^{5} d^{4} b \ln \left(c x \right)}{5}-\frac{31 c^{5} d^{4} b \ln \left(c x -1\right)}{10}-\frac{c^{5} d^{4} b \ln \left(c x +1\right)}{10}"," ",0,"-c^4*d^4*a/x-2*c^2*d^4*a/x^3-2*c^3*d^4*a/x^2-c*d^4*a/x^4-1/5*d^4*a/x^5-c^4*d^4*b*arctanh(c*x)/x-2*c^2*d^4*b*arctanh(c*x)/x^3-2*c^3*d^4*b*arctanh(c*x)/x^2-c*d^4*b*arctanh(c*x)/x^4-1/5*d^4*b*arctanh(c*x)/x^5-1/20*b*c*d^4/x^4-1/3*b*c^2*d^4/x^3-11/10*b*c^3*d^4/x^2-3*b*c^4*d^4/x+16/5*c^5*d^4*b*ln(c*x)-31/10*c^5*d^4*b*ln(c*x-1)-1/10*c^5*d^4*b*ln(c*x+1)","B"
41,1,233,133,0.040000," ","int((c*d*x+d)^4*(a+b*arctanh(c*x))/x^7,x)","-\frac{4 c^{3} d^{4} a}{3 x^{3}}-\frac{c^{4} d^{4} a}{2 x^{2}}-\frac{d^{4} a}{6 x^{6}}-\frac{3 c^{2} d^{4} a}{2 x^{4}}-\frac{4 c \,d^{4} a}{5 x^{5}}-\frac{4 c^{3} d^{4} b \arctanh \left(c x \right)}{3 x^{3}}-\frac{c^{4} d^{4} b \arctanh \left(c x \right)}{2 x^{2}}-\frac{d^{4} b \arctanh \left(c x \right)}{6 x^{6}}-\frac{3 c^{2} d^{4} b \arctanh \left(c x \right)}{2 x^{4}}-\frac{4 c \,d^{4} b \arctanh \left(c x \right)}{5 x^{5}}-\frac{b c \,d^{4}}{30 x^{5}}-\frac{b \,c^{2} d^{4}}{5 x^{4}}-\frac{5 b \,c^{3} d^{4}}{9 x^{3}}-\frac{16 b \,c^{4} d^{4}}{15 x^{2}}-\frac{13 b \,c^{5} d^{4}}{6 x}+\frac{32 c^{6} d^{4} b \ln \left(c x \right)}{15}-\frac{43 c^{6} d^{4} b \ln \left(c x -1\right)}{20}+\frac{c^{6} d^{4} b \ln \left(c x +1\right)}{60}"," ",0,"-4/3*c^3*d^4*a/x^3-1/2*c^4*d^4*a/x^2-1/6*d^4*a/x^6-3/2*c^2*d^4*a/x^4-4/5*c*d^4*a/x^5-4/3*c^3*d^4*b*arctanh(c*x)/x^3-1/2*c^4*d^4*b*arctanh(c*x)/x^2-1/6*d^4*b*arctanh(c*x)/x^6-3/2*c^2*d^4*b*arctanh(c*x)/x^4-4/5*c*d^4*b*arctanh(c*x)/x^5-1/30*b*c*d^4/x^5-1/5*b*c^2*d^4/x^4-5/9*b*c^3*d^4/x^3-16/15*b*c^4*d^4/x^2-13/6*b*c^5*d^4/x+32/15*c^6*d^4*b*ln(c*x)-43/20*c^6*d^4*b*ln(c*x-1)+1/60*c^6*d^4*b*ln(c*x+1)","A"
42,1,245,203,0.043000," ","int((c*d*x+d)^4*(a+b*arctanh(c*x))/x^8,x)","-\frac{c^{4} d^{4} a}{3 x^{3}}-\frac{d^{4} a}{7 x^{7}}-\frac{2 c \,d^{4} a}{3 x^{6}}-\frac{c^{3} d^{4} a}{x^{4}}-\frac{6 c^{2} d^{4} a}{5 x^{5}}-\frac{c^{4} d^{4} b \arctanh \left(c x \right)}{3 x^{3}}-\frac{d^{4} b \arctanh \left(c x \right)}{7 x^{7}}-\frac{2 c \,d^{4} b \arctanh \left(c x \right)}{3 x^{6}}-\frac{c^{3} d^{4} b \arctanh \left(c x \right)}{x^{4}}-\frac{6 c^{2} d^{4} b \arctanh \left(c x \right)}{5 x^{5}}-\frac{b c \,d^{4}}{42 x^{6}}-\frac{2 b \,c^{2} d^{4}}{15 x^{5}}-\frac{47 b \,c^{3} d^{4}}{140 x^{4}}-\frac{5 b \,c^{4} d^{4}}{9 x^{3}}-\frac{88 b \,c^{5} d^{4}}{105 x^{2}}-\frac{5 b \,c^{6} d^{4}}{3 x}+\frac{176 c^{7} d^{4} b \ln \left(c x \right)}{105}-\frac{117 c^{7} d^{4} b \ln \left(c x -1\right)}{70}-\frac{b \,c^{7} d^{4} \ln \left(c x +1\right)}{210}"," ",0,"-1/3*c^4*d^4*a/x^3-1/7*d^4*a/x^7-2/3*c*d^4*a/x^6-c^3*d^4*a/x^4-6/5*c^2*d^4*a/x^5-1/3*c^4*d^4*b*arctanh(c*x)/x^3-1/7*d^4*b*arctanh(c*x)/x^7-2/3*c*d^4*b*arctanh(c*x)/x^6-c^3*d^4*b*arctanh(c*x)/x^4-6/5*c^2*d^4*b*arctanh(c*x)/x^5-1/42*b*c*d^4/x^6-2/15*b*c^2*d^4/x^5-47/140*b*c^3*d^4/x^4-5/9*b*c^4*d^4/x^3-88/105*b*c^5*d^4/x^2-5/3*b*c^6*d^4/x+176/105*c^7*d^4*b*ln(c*x)-117/70*c^7*d^4*b*ln(c*x-1)-1/210*b*c^7*d^4*ln(c*x+1)","A"
43,1,253,163,0.053000," ","int(x^3*(a+b*arctanh(c*x))/(c*d*x+d),x)","\frac{a \,x^{3}}{3 c d}-\frac{a \,x^{2}}{2 c^{2} d}+\frac{a x}{c^{3} d}-\frac{a \ln \left(c x +1\right)}{c^{4} d}+\frac{b \,x^{3} \arctanh \left(c x \right)}{3 c d}-\frac{b \arctanh \left(c x \right) x^{2}}{2 c^{2} d}+\frac{b x \arctanh \left(c x \right)}{c^{3} d}-\frac{b \arctanh \left(c x \right) \ln \left(c x +1\right)}{c^{4} d}+\frac{b \ln \left(c x +1\right)^{2}}{4 c^{4} d}-\frac{b \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) \ln \left(c x +1\right)}{2 c^{4} d}+\frac{b \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{c x}{2}\right)}{2 c^{4} d}+\frac{b \dilog \left(\frac{1}{2}+\frac{c x}{2}\right)}{2 c^{4} d}+\frac{b \,x^{2}}{6 c^{2} d}-\frac{b x}{2 c^{3} d}-\frac{2 b}{3 c^{4} d}+\frac{11 b \ln \left(c x +1\right)}{12 c^{4} d}+\frac{5 b \ln \left(c x -1\right)}{12 c^{4} d}"," ",0,"1/3/c*a/d*x^3-1/2/c^2*a/d*x^2+a*x/c^3/d-1/c^4*a/d*ln(c*x+1)+1/3/c*b/d*x^3*arctanh(c*x)-1/2/c^2*b/d*arctanh(c*x)*x^2+b*x*arctanh(c*x)/c^3/d-1/c^4*b/d*arctanh(c*x)*ln(c*x+1)+1/4/c^4*b/d*ln(c*x+1)^2-1/2/c^4*b/d*ln(-1/2*c*x+1/2)*ln(c*x+1)+1/2/c^4*b/d*ln(-1/2*c*x+1/2)*ln(1/2+1/2*c*x)+1/2/c^4*b/d*dilog(1/2+1/2*c*x)+1/6*b*x^2/c^2/d-1/2*b*x/c^3/d-2/3/c^4*b/d+11/12/c^4*b/d*ln(c*x+1)+5/12/c^4*b/d*ln(c*x-1)","A"
44,1,213,135,0.050000," ","int(x^2*(a+b*arctanh(c*x))/(c*d*x+d),x)","\frac{a \,x^{2}}{2 c d}-\frac{a x}{c^{2} d}+\frac{a \ln \left(c x +1\right)}{c^{3} d}+\frac{b \arctanh \left(c x \right) x^{2}}{2 c d}-\frac{b x \arctanh \left(c x \right)}{c^{2} d}+\frac{b \arctanh \left(c x \right) \ln \left(c x +1\right)}{c^{3} d}-\frac{b \ln \left(c x +1\right)^{2}}{4 c^{3} d}+\frac{b \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) \ln \left(c x +1\right)}{2 c^{3} d}-\frac{b \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{c x}{2}\right)}{2 c^{3} d}-\frac{b \dilog \left(\frac{1}{2}+\frac{c x}{2}\right)}{2 c^{3} d}+\frac{b x}{2 c^{2} d}+\frac{b}{2 c^{3} d}-\frac{3 b \ln \left(c x +1\right)}{4 c^{3} d}-\frac{b \ln \left(c x -1\right)}{4 c^{3} d}"," ",0,"1/2/c*a/d*x^2-a*x/c^2/d+1/c^3*a/d*ln(c*x+1)+1/2/c*b/d*arctanh(c*x)*x^2-b*x*arctanh(c*x)/c^2/d+1/c^3*b/d*arctanh(c*x)*ln(c*x+1)-1/4/c^3*b/d*ln(c*x+1)^2+1/2/c^3*b/d*ln(-1/2*c*x+1/2)*ln(c*x+1)-1/2/c^3*b/d*ln(-1/2*c*x+1/2)*ln(1/2+1/2*c*x)-1/2/c^3*b/d*dilog(1/2+1/2*c*x)+1/2*b*x/c^2/d+1/2/c^3*b/d-3/4/c^3*b/d*ln(c*x+1)-1/4/c^3*b/d*ln(c*x-1)","A"
45,1,157,90,0.047000," ","int(x*(a+b*arctanh(c*x))/(c*d*x+d),x)","\frac{a x}{c d}-\frac{a \ln \left(c x +1\right)}{c^{2} d}-\frac{b \arctanh \left(c x \right) \ln \left(c x +1\right)}{c^{2} d}+\frac{b x \arctanh \left(c x \right)}{c d}+\frac{b \ln \left(c x +1\right)^{2}}{4 c^{2} d}-\frac{b \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) \ln \left(c x +1\right)}{2 c^{2} d}+\frac{b \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{c x}{2}\right)}{2 c^{2} d}+\frac{b \dilog \left(\frac{1}{2}+\frac{c x}{2}\right)}{2 c^{2} d}+\frac{b \ln \left(\left(c x -1\right) \left(c x +1\right)\right)}{2 c^{2} d}"," ",0,"a*x/c/d-1/c^2*a/d*ln(c*x+1)-1/c^2*b/d*arctanh(c*x)*ln(c*x+1)+b*x*arctanh(c*x)/c/d+1/4/c^2*b/d*ln(c*x+1)^2-1/2/c^2*b/d*ln(-1/2*c*x+1/2)*ln(c*x+1)+1/2/c^2*b/d*ln(-1/2*c*x+1/2)*ln(1/2+1/2*c*x)+1/2/c^2*b/d*dilog(1/2+1/2*c*x)+1/2/c^2*b/d*ln((c*x-1)*(c*x+1))","A"
46,1,112,49,0.045000," ","int((a+b*arctanh(c*x))/(c*d*x+d),x)","\frac{a \ln \left(c x +1\right)}{c d}+\frac{b \arctanh \left(c x \right) \ln \left(c x +1\right)}{c d}-\frac{b \ln \left(c x +1\right)^{2}}{4 c d}+\frac{b \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) \ln \left(c x +1\right)}{2 c d}-\frac{b \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{c x}{2}\right)}{2 c d}-\frac{b \dilog \left(\frac{1}{2}+\frac{c x}{2}\right)}{2 c d}"," ",0,"1/c*a/d*ln(c*x+1)+1/c*b/d*arctanh(c*x)*ln(c*x+1)-1/4/c*b/d*ln(c*x+1)^2+1/2/c*b/d*ln(-1/2*c*x+1/2)*ln(c*x+1)-1/2/c*b/d*ln(-1/2*c*x+1/2)*ln(1/2+1/2*c*x)-1/2/c*b/d*dilog(1/2+1/2*c*x)","B"
47,1,156,44,0.052000," ","int((a+b*arctanh(c*x))/x/(c*d*x+d),x)","\frac{a \ln \left(c x \right)}{d}-\frac{a \ln \left(c x +1\right)}{d}-\frac{b \arctanh \left(c x \right) \ln \left(c x +1\right)}{d}+\frac{b \arctanh \left(c x \right) \ln \left(c x \right)}{d}+\frac{b \ln \left(c x +1\right)^{2}}{4 d}-\frac{b \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) \ln \left(c x +1\right)}{2 d}+\frac{b \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{c x}{2}\right)}{2 d}+\frac{b \dilog \left(\frac{1}{2}+\frac{c x}{2}\right)}{2 d}-\frac{b \dilog \left(c x \right)}{2 d}-\frac{b \dilog \left(c x +1\right)}{2 d}-\frac{b \ln \left(c x \right) \ln \left(c x +1\right)}{2 d}"," ",0,"a/d*ln(c*x)-a/d*ln(c*x+1)-b/d*arctanh(c*x)*ln(c*x+1)+b*arctanh(c*x)/d*ln(c*x)+1/4*b/d*ln(c*x+1)^2-1/2*b/d*ln(-1/2*c*x+1/2)*ln(c*x+1)+1/2*b/d*ln(-1/2*c*x+1/2)*ln(1/2+1/2*c*x)+1/2*b/d*dilog(1/2+1/2*c*x)-1/2*b/d*dilog(c*x)-1/2*b/d*dilog(c*x+1)-1/2*b/d*ln(c*x)*ln(c*x+1)","B"
48,1,225,91,0.062000," ","int((a+b*arctanh(c*x))/x^2/(c*d*x+d),x)","-\frac{a}{d x}-\frac{c a \ln \left(c x \right)}{d}+\frac{c a \ln \left(c x +1\right)}{d}-\frac{b \arctanh \left(c x \right)}{d x}-\frac{c b \arctanh \left(c x \right) \ln \left(c x \right)}{d}+\frac{c b \arctanh \left(c x \right) \ln \left(c x +1\right)}{d}+\frac{c b \ln \left(c x \right)}{d}-\frac{c b \ln \left(c x -1\right)}{2 d}-\frac{c b \ln \left(c x +1\right)}{2 d}+\frac{c b \dilog \left(c x \right)}{2 d}+\frac{c b \dilog \left(c x +1\right)}{2 d}+\frac{c b \ln \left(c x \right) \ln \left(c x +1\right)}{2 d}-\frac{c b \ln \left(c x +1\right)^{2}}{4 d}+\frac{c b \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) \ln \left(c x +1\right)}{2 d}-\frac{c b \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{c x}{2}\right)}{2 d}-\frac{c b \dilog \left(\frac{1}{2}+\frac{c x}{2}\right)}{2 d}"," ",0,"-a/d/x-c*a/d*ln(c*x)+c*a/d*ln(c*x+1)-b/d*arctanh(c*x)/x-c*b*arctanh(c*x)/d*ln(c*x)+c*b/d*arctanh(c*x)*ln(c*x+1)+c*b/d*ln(c*x)-1/2*c*b/d*ln(c*x-1)-1/2*c*b/d*ln(c*x+1)+1/2*c*b/d*dilog(c*x)+1/2*c*b/d*dilog(c*x+1)+1/2*c*b/d*ln(c*x)*ln(c*x+1)-1/4*c*b/d*ln(c*x+1)^2+1/2*c*b/d*ln(-1/2*c*x+1/2)*ln(c*x+1)-1/2*c*b/d*ln(-1/2*c*x+1/2)*ln(1/2+1/2*c*x)-1/2*c*b/d*dilog(1/2+1/2*c*x)","B"
49,1,286,139,0.063000," ","int((a+b*arctanh(c*x))/x^3/(c*d*x+d),x)","-\frac{a}{2 d \,x^{2}}+\frac{c^{2} a \ln \left(c x \right)}{d}+\frac{c a}{d x}-\frac{c^{2} a \ln \left(c x +1\right)}{d}-\frac{b \arctanh \left(c x \right)}{2 d \,x^{2}}+\frac{c^{2} b \arctanh \left(c x \right) \ln \left(c x \right)}{d}+\frac{c b \arctanh \left(c x \right)}{d x}-\frac{c^{2} b \arctanh \left(c x \right) \ln \left(c x +1\right)}{d}-\frac{c^{2} b \dilog \left(c x \right)}{2 d}-\frac{c^{2} b \dilog \left(c x +1\right)}{2 d}-\frac{c^{2} b \ln \left(c x \right) \ln \left(c x +1\right)}{2 d}+\frac{c^{2} b \ln \left(c x +1\right)^{2}}{4 d}-\frac{c^{2} b \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) \ln \left(c x +1\right)}{2 d}+\frac{c^{2} b \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{c x}{2}\right)}{2 d}+\frac{c^{2} b \dilog \left(\frac{1}{2}+\frac{c x}{2}\right)}{2 d}-\frac{b c}{2 d x}-\frac{c^{2} b \ln \left(c x \right)}{d}+\frac{c^{2} b \ln \left(c x -1\right)}{4 d}+\frac{3 c^{2} b \ln \left(c x +1\right)}{4 d}"," ",0,"-1/2*a/d/x^2+c^2*a/d*ln(c*x)+c*a/d/x-c^2*a/d*ln(c*x+1)-1/2*b/d*arctanh(c*x)/x^2+c^2*b*arctanh(c*x)/d*ln(c*x)+c*b/d*arctanh(c*x)/x-c^2*b/d*arctanh(c*x)*ln(c*x+1)-1/2*c^2*b/d*dilog(c*x)-1/2*c^2*b/d*dilog(c*x+1)-1/2*c^2*b/d*ln(c*x)*ln(c*x+1)+1/4*c^2*b/d*ln(c*x+1)^2-1/2*c^2*b/d*ln(-1/2*c*x+1/2)*ln(c*x+1)+1/2*c^2*b/d*ln(-1/2*c*x+1/2)*ln(1/2+1/2*c*x)+1/2*c^2*b/d*dilog(1/2+1/2*c*x)-1/2*b*c/d/x-c^2*b/d*ln(c*x)+1/4*c^2*b/d*ln(c*x-1)+3/4*c^2*b/d*ln(c*x+1)","B"
50,1,328,172,0.062000," ","int((a+b*arctanh(c*x))/x^4/(c*d*x+d),x)","-\frac{a}{3 d \,x^{3}}-\frac{c^{2} a}{d x}+\frac{c a}{2 d \,x^{2}}-\frac{c^{3} a \ln \left(c x \right)}{d}+\frac{c^{3} a \ln \left(c x +1\right)}{d}-\frac{b \arctanh \left(c x \right)}{3 d \,x^{3}}-\frac{c^{2} b \arctanh \left(c x \right)}{d x}+\frac{c b \arctanh \left(c x \right)}{2 d \,x^{2}}-\frac{c^{3} b \arctanh \left(c x \right) \ln \left(c x \right)}{d}+\frac{c^{3} b \arctanh \left(c x \right) \ln \left(c x +1\right)}{d}-\frac{b c}{6 d \,x^{2}}+\frac{b \,c^{2}}{2 d x}+\frac{4 c^{3} b \ln \left(c x \right)}{3 d}-\frac{5 c^{3} b \ln \left(c x -1\right)}{12 d}-\frac{11 c^{3} b \ln \left(c x +1\right)}{12 d}+\frac{c^{3} b \dilog \left(c x \right)}{2 d}+\frac{c^{3} b \dilog \left(c x +1\right)}{2 d}+\frac{c^{3} b \ln \left(c x \right) \ln \left(c x +1\right)}{2 d}-\frac{c^{3} b \ln \left(c x +1\right)^{2}}{4 d}+\frac{c^{3} b \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) \ln \left(c x +1\right)}{2 d}-\frac{c^{3} b \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{c x}{2}\right)}{2 d}-\frac{c^{3} b \dilog \left(\frac{1}{2}+\frac{c x}{2}\right)}{2 d}"," ",0,"-1/3*a/d/x^3-c^2*a/d/x+1/2*c*a/d/x^2-c^3*a/d*ln(c*x)+c^3*a/d*ln(c*x+1)-1/3*b/d*arctanh(c*x)/x^3-c^2*b/d*arctanh(c*x)/x+1/2*c*b/d*arctanh(c*x)/x^2-c^3*b*arctanh(c*x)/d*ln(c*x)+c^3*b/d*arctanh(c*x)*ln(c*x+1)-1/6*b*c/d/x^2+1/2*b*c^2/d/x+4/3*c^3*b/d*ln(c*x)-5/12*c^3*b/d*ln(c*x-1)-11/12*c^3*b/d*ln(c*x+1)+1/2*c^3*b/d*dilog(c*x)+1/2*c^3*b/d*dilog(c*x+1)+1/2*c^3*b/d*ln(c*x)*ln(c*x+1)-1/4*c^3*b/d*ln(c*x+1)^2+1/2*c^3*b/d*ln(-1/2*c*x+1/2)*ln(c*x+1)-1/2*c^3*b/d*ln(-1/2*c*x+1/2)*ln(1/2+1/2*c*x)-1/2*c^3*b/d*dilog(1/2+1/2*c*x)","A"
51,1,265,173,0.059000," ","int(x^3*(a+b*arctanh(c*x))/(c*d*x+d)^2,x)","\frac{a \,x^{2}}{2 c^{2} d^{2}}-\frac{2 a x}{c^{3} d^{2}}+\frac{a}{c^{4} d^{2} \left(c x +1\right)}+\frac{3 a \ln \left(c x +1\right)}{c^{4} d^{2}}+\frac{b \arctanh \left(c x \right) x^{2}}{2 c^{2} d^{2}}-\frac{2 b x \arctanh \left(c x \right)}{c^{3} d^{2}}+\frac{b \arctanh \left(c x \right)}{c^{4} d^{2} \left(c x +1\right)}+\frac{3 b \arctanh \left(c x \right) \ln \left(c x +1\right)}{c^{4} d^{2}}-\frac{3 b \ln \left(c x +1\right)^{2}}{4 c^{4} d^{2}}+\frac{3 b \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) \ln \left(c x +1\right)}{2 c^{4} d^{2}}-\frac{3 b \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{c x}{2}\right)}{2 c^{4} d^{2}}-\frac{3 b \dilog \left(\frac{1}{2}+\frac{c x}{2}\right)}{2 c^{4} d^{2}}+\frac{b x}{2 c^{3} d^{2}}+\frac{b}{2 c^{4} d^{2}}+\frac{b}{2 c^{4} d^{2} \left(c x +1\right)}-\frac{3 b \ln \left(c x +1\right)}{2 c^{4} d^{2}}-\frac{b \ln \left(c x -1\right)}{2 c^{4} d^{2}}"," ",0,"1/2/c^2*a/d^2*x^2-2*a*x/c^3/d^2+1/c^4*a/d^2/(c*x+1)+3/c^4*a/d^2*ln(c*x+1)+1/2/c^2*b/d^2*arctanh(c*x)*x^2-2*b*x*arctanh(c*x)/c^3/d^2+1/c^4*b/d^2*arctanh(c*x)/(c*x+1)+3/c^4*b/d^2*arctanh(c*x)*ln(c*x+1)-3/4/c^4*b/d^2*ln(c*x+1)^2+3/2/c^4*b/d^2*ln(-1/2*c*x+1/2)*ln(c*x+1)-3/2/c^4*b/d^2*ln(-1/2*c*x+1/2)*ln(1/2+1/2*c*x)-3/2/c^4*b/d^2*dilog(1/2+1/2*c*x)+1/2*b*x/c^3/d^2+1/2/c^4*b/d^2+1/2*b/c^4/d^2/(c*x+1)-3/2/c^4*b/d^2*ln(c*x+1)-1/2/c^4*b/d^2*ln(c*x-1)","A"
52,1,216,145,0.054000," ","int(x^2*(a+b*arctanh(c*x))/(c*d*x+d)^2,x)","\frac{a x}{c^{2} d^{2}}-\frac{a}{c^{3} d^{2} \left(c x +1\right)}-\frac{2 a \ln \left(c x +1\right)}{c^{3} d^{2}}+\frac{b x \arctanh \left(c x \right)}{c^{2} d^{2}}-\frac{b \arctanh \left(c x \right)}{c^{3} d^{2} \left(c x +1\right)}-\frac{2 b \arctanh \left(c x \right) \ln \left(c x +1\right)}{c^{3} d^{2}}+\frac{b \ln \left(c x +1\right)^{2}}{2 c^{3} d^{2}}-\frac{b \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) \ln \left(c x +1\right)}{c^{3} d^{2}}+\frac{b \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{c x}{2}\right)}{c^{3} d^{2}}+\frac{b \dilog \left(\frac{1}{2}+\frac{c x}{2}\right)}{c^{3} d^{2}}-\frac{b}{2 c^{3} d^{2} \left(c x +1\right)}+\frac{3 b \ln \left(c x +1\right)}{4 c^{3} d^{2}}+\frac{b \ln \left(c x -1\right)}{4 c^{3} d^{2}}"," ",0,"a*x/c^2/d^2-1/c^3*a/d^2/(c*x+1)-2/c^3*a/d^2*ln(c*x+1)+b*x*arctanh(c*x)/c^2/d^2-1/c^3*b/d^2*arctanh(c*x)/(c*x+1)-2/c^3*b/d^2*arctanh(c*x)*ln(c*x+1)+1/2/c^3*b/d^2*ln(c*x+1)^2-1/c^3*b/d^2*ln(-1/2*c*x+1/2)*ln(c*x+1)+1/c^3*b/d^2*ln(-1/2*c*x+1/2)*ln(1/2+1/2*c*x)+1/c^3*b/d^2*dilog(1/2+1/2*c*x)-1/2*b/c^3/d^2/(c*x+1)+3/4/c^3*b/d^2*ln(c*x+1)+1/4/c^3*b/d^2*ln(c*x-1)","A"
53,1,192,100,0.056000," ","int(x*(a+b*arctanh(c*x))/(c*d*x+d)^2,x)","\frac{a}{c^{2} d^{2} \left(c x +1\right)}+\frac{a \ln \left(c x +1\right)}{c^{2} d^{2}}+\frac{b \arctanh \left(c x \right)}{c^{2} d^{2} \left(c x +1\right)}+\frac{b \arctanh \left(c x \right) \ln \left(c x +1\right)}{c^{2} d^{2}}+\frac{b}{2 c^{2} d^{2} \left(c x +1\right)}-\frac{b \ln \left(c x +1\right)}{4 c^{2} d^{2}}+\frac{b \ln \left(c x -1\right)}{4 c^{2} d^{2}}-\frac{b \ln \left(c x +1\right)^{2}}{4 c^{2} d^{2}}+\frac{b \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) \ln \left(c x +1\right)}{2 c^{2} d^{2}}-\frac{b \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{c x}{2}\right)}{2 c^{2} d^{2}}-\frac{b \dilog \left(\frac{1}{2}+\frac{c x}{2}\right)}{2 c^{2} d^{2}}"," ",0,"1/c^2*a/d^2/(c*x+1)+1/c^2*a/d^2*ln(c*x+1)+1/c^2*b/d^2*arctanh(c*x)/(c*x+1)+1/c^2*b/d^2*arctanh(c*x)*ln(c*x+1)+1/2*b/c^2/d^2/(c*x+1)-1/4/c^2*b/d^2*ln(c*x+1)+1/4/c^2*b/d^2*ln(c*x-1)-1/4/c^2*b/d^2*ln(c*x+1)^2+1/2/c^2*b/d^2*ln(-1/2*c*x+1/2)*ln(c*x+1)-1/2/c^2*b/d^2*ln(-1/2*c*x+1/2)*ln(1/2+1/2*c*x)-1/2/c^2*b/d^2*dilog(1/2+1/2*c*x)","A"
54,1,84,55,0.035000," ","int((a+b*arctanh(c*x))/(c*d*x+d)^2,x)","-\frac{a}{c \,d^{2} \left(c x +1\right)}-\frac{b \arctanh \left(c x \right)}{c \,d^{2} \left(c x +1\right)}-\frac{b \ln \left(c x -1\right)}{4 c \,d^{2}}-\frac{b}{2 c \,d^{2} \left(c x +1\right)}+\frac{b \ln \left(c x +1\right)}{4 c \,d^{2}}"," ",0,"-1/c*a/d^2/(c*x+1)-1/c*b/d^2*arctanh(c*x)/(c*x+1)-1/4/c*b/d^2*ln(c*x-1)-1/2*b/c/d^2/(c*x+1)+1/4/c*b/d^2*ln(c*x+1)","A"
55,1,221,114,0.062000," ","int((a+b*arctanh(c*x))/x/(c*d*x+d)^2,x)","\frac{a \ln \left(c x \right)}{d^{2}}+\frac{a}{d^{2} \left(c x +1\right)}-\frac{a \ln \left(c x +1\right)}{d^{2}}+\frac{b \arctanh \left(c x \right) \ln \left(c x \right)}{d^{2}}+\frac{b \arctanh \left(c x \right)}{d^{2} \left(c x +1\right)}-\frac{b \arctanh \left(c x \right) \ln \left(c x +1\right)}{d^{2}}+\frac{b \ln \left(c x +1\right)^{2}}{4 d^{2}}-\frac{b \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) \ln \left(c x +1\right)}{2 d^{2}}+\frac{b \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{c x}{2}\right)}{2 d^{2}}+\frac{b \dilog \left(\frac{1}{2}+\frac{c x}{2}\right)}{2 d^{2}}+\frac{b \ln \left(c x -1\right)}{4 d^{2}}+\frac{b}{2 d^{2} \left(c x +1\right)}-\frac{b \ln \left(c x +1\right)}{4 d^{2}}-\frac{b \dilog \left(c x \right)}{2 d^{2}}-\frac{b \dilog \left(c x +1\right)}{2 d^{2}}-\frac{b \ln \left(c x \right) \ln \left(c x +1\right)}{2 d^{2}}"," ",0,"a/d^2*ln(c*x)+a/d^2/(c*x+1)-a/d^2*ln(c*x+1)+b/d^2*arctanh(c*x)*ln(c*x)+b/d^2*arctanh(c*x)/(c*x+1)-b/d^2*arctanh(c*x)*ln(c*x+1)+1/4*b/d^2*ln(c*x+1)^2-1/2*b/d^2*ln(-1/2*c*x+1/2)*ln(c*x+1)+1/2*b/d^2*ln(-1/2*c*x+1/2)*ln(1/2+1/2*c*x)+1/2*b/d^2*dilog(1/2+1/2*c*x)+1/4*b/d^2*ln(c*x-1)+1/2*b/d^2/(c*x+1)-1/4*b/d^2*ln(c*x+1)-1/2*b/d^2*dilog(c*x)-1/2*b/d^2*dilog(c*x+1)-1/2*b/d^2*ln(c*x)*ln(c*x+1)","A"
56,1,269,167,0.063000," ","int((a+b*arctanh(c*x))/x^2/(c*d*x+d)^2,x)","-\frac{a}{d^{2} x}-\frac{2 c a \ln \left(c x \right)}{d^{2}}-\frac{c a}{d^{2} \left(c x +1\right)}+\frac{2 c a \ln \left(c x +1\right)}{d^{2}}-\frac{b \arctanh \left(c x \right)}{d^{2} x}-\frac{2 c b \arctanh \left(c x \right) \ln \left(c x \right)}{d^{2}}-\frac{c b \arctanh \left(c x \right)}{d^{2} \left(c x +1\right)}+\frac{2 c b \arctanh \left(c x \right) \ln \left(c x +1\right)}{d^{2}}+\frac{c b \ln \left(c x \right)}{d^{2}}-\frac{3 c b \ln \left(c x -1\right)}{4 d^{2}}-\frac{b c}{2 d^{2} \left(c x +1\right)}-\frac{c b \ln \left(c x +1\right)}{4 d^{2}}+\frac{c b \dilog \left(c x \right)}{d^{2}}+\frac{c b \dilog \left(c x +1\right)}{d^{2}}+\frac{c b \ln \left(c x \right) \ln \left(c x +1\right)}{d^{2}}-\frac{c b \ln \left(c x +1\right)^{2}}{2 d^{2}}+\frac{c b \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) \ln \left(c x +1\right)}{d^{2}}-\frac{c b \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{c x}{2}\right)}{d^{2}}-\frac{c b \dilog \left(\frac{1}{2}+\frac{c x}{2}\right)}{d^{2}}"," ",0,"-a/d^2/x-2*c*a/d^2*ln(c*x)-c*a/d^2/(c*x+1)+2*c*a/d^2*ln(c*x+1)-b/d^2*arctanh(c*x)/x-2*c*b/d^2*arctanh(c*x)*ln(c*x)-c*b/d^2*arctanh(c*x)/(c*x+1)+2*c*b/d^2*arctanh(c*x)*ln(c*x+1)+c*b/d^2*ln(c*x)-3/4*c*b/d^2*ln(c*x-1)-1/2*b*c/d^2/(c*x+1)-1/4*c*b/d^2*ln(c*x+1)+c*b/d^2*dilog(c*x)+c*b/d^2*dilog(c*x+1)+c*b/d^2*ln(c*x)*ln(c*x+1)-1/2*c*b/d^2*ln(c*x+1)^2+c*b/d^2*ln(-1/2*c*x+1/2)*ln(c*x+1)-c*b/d^2*ln(-1/2*c*x+1/2)*ln(1/2+1/2*c*x)-c*b/d^2*dilog(1/2+1/2*c*x)","A"
57,1,338,203,0.074000," ","int((a+b*arctanh(c*x))/x^3/(c*d*x+d)^2,x)","-\frac{a}{2 d^{2} x^{2}}+\frac{2 c a}{d^{2} x}+\frac{3 c^{2} a \ln \left(c x \right)}{d^{2}}+\frac{c^{2} a}{d^{2} \left(c x +1\right)}-\frac{3 c^{2} a \ln \left(c x +1\right)}{d^{2}}-\frac{b \arctanh \left(c x \right)}{2 d^{2} x^{2}}+\frac{2 c b \arctanh \left(c x \right)}{d^{2} x}+\frac{3 c^{2} b \arctanh \left(c x \right) \ln \left(c x \right)}{d^{2}}+\frac{c^{2} b \arctanh \left(c x \right)}{d^{2} \left(c x +1\right)}-\frac{3 c^{2} b \arctanh \left(c x \right) \ln \left(c x +1\right)}{d^{2}}-\frac{3 c^{2} b \dilog \left(c x \right)}{2 d^{2}}-\frac{3 c^{2} b \dilog \left(c x +1\right)}{2 d^{2}}-\frac{3 c^{2} b \ln \left(c x \right) \ln \left(c x +1\right)}{2 d^{2}}+\frac{3 c^{2} b \ln \left(c x +1\right)^{2}}{4 d^{2}}-\frac{3 c^{2} b \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) \ln \left(c x +1\right)}{2 d^{2}}+\frac{3 c^{2} b \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{c x}{2}\right)}{2 d^{2}}+\frac{3 c^{2} b \dilog \left(\frac{1}{2}+\frac{c x}{2}\right)}{2 d^{2}}-\frac{b c}{2 d^{2} x}-\frac{2 c^{2} b \ln \left(c x \right)}{d^{2}}+\frac{c^{2} b \ln \left(c x -1\right)}{d^{2}}+\frac{b \,c^{2}}{2 d^{2} \left(c x +1\right)}+\frac{c^{2} b \ln \left(c x +1\right)}{d^{2}}"," ",0,"-1/2*a/d^2/x^2+2*c*a/d^2/x+3*c^2*a/d^2*ln(c*x)+c^2*a/d^2/(c*x+1)-3*c^2*a/d^2*ln(c*x+1)-1/2*b/d^2*arctanh(c*x)/x^2+2*c*b/d^2*arctanh(c*x)/x+3*c^2*b/d^2*arctanh(c*x)*ln(c*x)+c^2*b/d^2*arctanh(c*x)/(c*x+1)-3*c^2*b/d^2*arctanh(c*x)*ln(c*x+1)-3/2*c^2*b/d^2*dilog(c*x)-3/2*c^2*b/d^2*dilog(c*x+1)-3/2*c^2*b/d^2*ln(c*x)*ln(c*x+1)+3/4*c^2*b/d^2*ln(c*x+1)^2-3/2*c^2*b/d^2*ln(-1/2*c*x+1/2)*ln(c*x+1)+3/2*c^2*b/d^2*ln(-1/2*c*x+1/2)*ln(1/2+1/2*c*x)+3/2*c^2*b/d^2*dilog(1/2+1/2*c*x)-1/2*b*c/d^2/x-2*c^2*b/d^2*ln(c*x)+c^2*b/d^2*ln(c*x-1)+1/2*b*c^2/d^2/(c*x+1)+c^2*b/d^2*ln(c*x+1)","A"
58,1,319,216,0.059000," ","int(x^4*(a+b*arctanh(c*x))/(c*d*x+d)^3,x)","\frac{a \,x^{2}}{2 c^{3} d^{3}}-\frac{3 a x}{c^{4} d^{3}}-\frac{a}{2 c^{5} d^{3} \left(c x +1\right)^{2}}+\frac{4 a}{c^{5} d^{3} \left(c x +1\right)}+\frac{6 a \ln \left(c x +1\right)}{c^{5} d^{3}}+\frac{b \arctanh \left(c x \right) x^{2}}{2 c^{3} d^{3}}-\frac{3 b x \arctanh \left(c x \right)}{c^{4} d^{3}}-\frac{b \arctanh \left(c x \right)}{2 c^{5} d^{3} \left(c x +1\right)^{2}}+\frac{4 b \arctanh \left(c x \right)}{c^{5} d^{3} \left(c x +1\right)}+\frac{6 b \arctanh \left(c x \right) \ln \left(c x +1\right)}{c^{5} d^{3}}-\frac{3 b \ln \left(c x +1\right)^{2}}{2 c^{5} d^{3}}+\frac{3 b \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) \ln \left(c x +1\right)}{c^{5} d^{3}}-\frac{3 b \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{c x}{2}\right)}{c^{5} d^{3}}-\frac{3 b \dilog \left(\frac{1}{2}+\frac{c x}{2}\right)}{c^{5} d^{3}}+\frac{b x}{2 c^{4} d^{3}}+\frac{b}{2 c^{5} d^{3}}-\frac{b}{8 c^{5} d^{3} \left(c x +1\right)^{2}}+\frac{15 b}{8 c^{5} d^{3} \left(c x +1\right)}-\frac{43 b \ln \left(c x +1\right)}{16 c^{5} d^{3}}-\frac{5 b \ln \left(c x -1\right)}{16 c^{5} d^{3}}"," ",0,"1/2/c^3*a/d^3*x^2-3*a*x/c^4/d^3-1/2/c^5*a/d^3/(c*x+1)^2+4/c^5*a/d^3/(c*x+1)+6/c^5*a/d^3*ln(c*x+1)+1/2/c^3*b/d^3*arctanh(c*x)*x^2-3*b*x*arctanh(c*x)/c^4/d^3-1/2/c^5*b/d^3*arctanh(c*x)/(c*x+1)^2+4/c^5*b/d^3*arctanh(c*x)/(c*x+1)+6/c^5*b/d^3*arctanh(c*x)*ln(c*x+1)-3/2/c^5*b/d^3*ln(c*x+1)^2+3/c^5*b/d^3*ln(-1/2*c*x+1/2)*ln(c*x+1)-3/c^5*b/d^3*ln(-1/2*c*x+1/2)*ln(1/2+1/2*c*x)-3/c^5*b/d^3*dilog(1/2+1/2*c*x)+1/2*b*x/c^4/d^3+1/2/c^5*b/d^3-1/8*b/c^5/d^3/(c*x+1)^2+15/8*b/c^5/d^3/(c*x+1)-43/16/c^5*b/d^3*ln(c*x+1)-5/16/c^5*b/d^3*ln(c*x-1)","A"
59,1,270,182,0.056000," ","int(x^3*(a+b*arctanh(c*x))/(c*d*x+d)^3,x)","\frac{a x}{c^{3} d^{3}}+\frac{a}{2 c^{4} d^{3} \left(c x +1\right)^{2}}-\frac{3 a}{c^{4} d^{3} \left(c x +1\right)}-\frac{3 a \ln \left(c x +1\right)}{c^{4} d^{3}}+\frac{b x \arctanh \left(c x \right)}{c^{3} d^{3}}+\frac{b \arctanh \left(c x \right)}{2 c^{4} d^{3} \left(c x +1\right)^{2}}-\frac{3 b \arctanh \left(c x \right)}{c^{4} d^{3} \left(c x +1\right)}-\frac{3 b \arctanh \left(c x \right) \ln \left(c x +1\right)}{c^{4} d^{3}}+\frac{3 b \ln \left(c x +1\right)^{2}}{4 c^{4} d^{3}}-\frac{3 b \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) \ln \left(c x +1\right)}{2 c^{4} d^{3}}+\frac{3 b \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{c x}{2}\right)}{2 c^{4} d^{3}}+\frac{3 b \dilog \left(\frac{1}{2}+\frac{c x}{2}\right)}{2 c^{4} d^{3}}+\frac{b}{8 c^{4} d^{3} \left(c x +1\right)^{2}}-\frac{11 b}{8 c^{4} d^{3} \left(c x +1\right)}+\frac{19 b \ln \left(c x +1\right)}{16 c^{4} d^{3}}-\frac{3 b \ln \left(c x -1\right)}{16 c^{4} d^{3}}"," ",0,"a*x/c^3/d^3+1/2/c^4*a/d^3/(c*x+1)^2-3/c^4*a/d^3/(c*x+1)-3/c^4*a/d^3*ln(c*x+1)+b*x*arctanh(c*x)/c^3/d^3+1/2/c^4*b/d^3*arctanh(c*x)/(c*x+1)^2-3/c^4*b/d^3*arctanh(c*x)/(c*x+1)-3/c^4*b/d^3*arctanh(c*x)*ln(c*x+1)+3/4/c^4*b/d^3*ln(c*x+1)^2-3/2/c^4*b/d^3*ln(-1/2*c*x+1/2)*ln(c*x+1)+3/2/c^4*b/d^3*ln(-1/2*c*x+1/2)*ln(1/2+1/2*c*x)+3/2/c^4*b/d^3*dilog(1/2+1/2*c*x)+1/8*b/c^4/d^3/(c*x+1)^2-11/8*b/c^4/d^3/(c*x+1)+19/16/c^4*b/d^3*ln(c*x+1)-3/16/c^4*b/d^3*ln(c*x-1)","A"
60,1,246,143,0.056000," ","int(x^2*(a+b*arctanh(c*x))/(c*d*x+d)^3,x)","-\frac{a}{2 c^{3} d^{3} \left(c x +1\right)^{2}}+\frac{2 a}{c^{3} d^{3} \left(c x +1\right)}+\frac{a \ln \left(c x +1\right)}{c^{3} d^{3}}-\frac{b \arctanh \left(c x \right)}{2 c^{3} d^{3} \left(c x +1\right)^{2}}+\frac{2 b \arctanh \left(c x \right)}{c^{3} d^{3} \left(c x +1\right)}+\frac{b \arctanh \left(c x \right) \ln \left(c x +1\right)}{c^{3} d^{3}}-\frac{b \ln \left(c x +1\right)^{2}}{4 c^{3} d^{3}}+\frac{b \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) \ln \left(c x +1\right)}{2 c^{3} d^{3}}-\frac{b \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{c x}{2}\right)}{2 c^{3} d^{3}}-\frac{b \dilog \left(\frac{1}{2}+\frac{c x}{2}\right)}{2 c^{3} d^{3}}-\frac{b}{8 c^{3} d^{3} \left(c x +1\right)^{2}}+\frac{7 b}{8 c^{3} d^{3} \left(c x +1\right)}-\frac{7 b \ln \left(c x +1\right)}{16 c^{3} d^{3}}+\frac{7 b \ln \left(c x -1\right)}{16 c^{3} d^{3}}"," ",0,"-1/2/c^3*a/d^3/(c*x+1)^2+2/c^3*a/d^3/(c*x+1)+1/c^3*a/d^3*ln(c*x+1)-1/2/c^3*b/d^3*arctanh(c*x)/(c*x+1)^2+2/c^3*b/d^3*arctanh(c*x)/(c*x+1)+1/c^3*b/d^3*arctanh(c*x)*ln(c*x+1)-1/4/c^3*b/d^3*ln(c*x+1)^2+1/2/c^3*b/d^3*ln(-1/2*c*x+1/2)*ln(c*x+1)-1/2/c^3*b/d^3*ln(-1/2*c*x+1/2)*ln(1/2+1/2*c*x)-1/2/c^3*b/d^3*dilog(1/2+1/2*c*x)-1/8*b/c^3/d^3/(c*x+1)^2+7/8*b/c^3/d^3/(c*x+1)-7/16/c^3*b/d^3*ln(c*x+1)+7/16/c^3*b/d^3*ln(c*x-1)","A"
61,1,136,69,0.039000," ","int(x*(a+b*arctanh(c*x))/(c*d*x+d)^3,x)","\frac{a}{2 c^{2} d^{3} \left(c x +1\right)^{2}}-\frac{a}{c^{2} d^{3} \left(c x +1\right)}+\frac{b \arctanh \left(c x \right)}{2 c^{2} d^{3} \left(c x +1\right)^{2}}-\frac{b \arctanh \left(c x \right)}{c^{2} d^{3} \left(c x +1\right)}-\frac{3 b \ln \left(c x -1\right)}{16 c^{2} d^{3}}+\frac{b}{8 c^{2} d^{3} \left(c x +1\right)^{2}}-\frac{3 b}{8 c^{2} d^{3} \left(c x +1\right)}+\frac{3 b \ln \left(c x +1\right)}{16 c^{2} d^{3}}"," ",0,"1/2/c^2*a/d^3/(c*x+1)^2-1/c^2*a/d^3/(c*x+1)+1/2/c^2*b/d^3*arctanh(c*x)/(c*x+1)^2-1/c^2*b/d^3*arctanh(c*x)/(c*x+1)-3/16/c^2*b/d^3*ln(c*x-1)+1/8*b/c^2/d^3/(c*x+1)^2-3/8*b/c^2/d^3/(c*x+1)+3/16/c^2*b/d^3*ln(c*x+1)","A"
62,1,100,72,0.036000," ","int((a+b*arctanh(c*x))/(c*d*x+d)^3,x)","-\frac{a}{2 c \,d^{3} \left(c x +1\right)^{2}}-\frac{b \arctanh \left(c x \right)}{2 c \,d^{3} \left(c x +1\right)^{2}}-\frac{b \ln \left(c x -1\right)}{16 c \,d^{3}}-\frac{b}{8 c \,d^{3} \left(c x +1\right)^{2}}-\frac{b}{8 c \,d^{3} \left(c x +1\right)}+\frac{b \ln \left(c x +1\right)}{16 c \,d^{3}}"," ",0,"-1/2/c*a/d^3/(c*x+1)^2-1/2/c*b/d^3*arctanh(c*x)/(c*x+1)^2-1/16/c*b/d^3*ln(c*x-1)-1/8*b/c/d^3/(c*x+1)^2-1/8*b/c/d^3/(c*x+1)+1/16/c*b/d^3*ln(c*x+1)","A"
63,1,264,147,0.063000," ","int((a+b*arctanh(c*x))/x/(c*d*x+d)^3,x)","\frac{a \ln \left(c x \right)}{d^{3}}+\frac{a}{2 d^{3} \left(c x +1\right)^{2}}+\frac{a}{d^{3} \left(c x +1\right)}-\frac{a \ln \left(c x +1\right)}{d^{3}}+\frac{b \arctanh \left(c x \right) \ln \left(c x \right)}{d^{3}}+\frac{b \arctanh \left(c x \right)}{2 d^{3} \left(c x +1\right)^{2}}+\frac{b \arctanh \left(c x \right)}{d^{3} \left(c x +1\right)}-\frac{b \arctanh \left(c x \right) \ln \left(c x +1\right)}{d^{3}}-\frac{b \dilog \left(c x \right)}{2 d^{3}}-\frac{b \dilog \left(c x +1\right)}{2 d^{3}}-\frac{b \ln \left(c x \right) \ln \left(c x +1\right)}{2 d^{3}}+\frac{b \ln \left(c x +1\right)^{2}}{4 d^{3}}-\frac{b \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) \ln \left(c x +1\right)}{2 d^{3}}+\frac{b \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{c x}{2}\right)}{2 d^{3}}+\frac{b \dilog \left(\frac{1}{2}+\frac{c x}{2}\right)}{2 d^{3}}+\frac{5 b \ln \left(c x -1\right)}{16 d^{3}}+\frac{b}{8 d^{3} \left(c x +1\right)^{2}}+\frac{5 b}{8 d^{3} \left(c x +1\right)}-\frac{5 b \ln \left(c x +1\right)}{16 d^{3}}"," ",0,"a/d^3*ln(c*x)+1/2*a/d^3/(c*x+1)^2+a/d^3/(c*x+1)-a/d^3*ln(c*x+1)+b/d^3*arctanh(c*x)*ln(c*x)+1/2*b/d^3*arctanh(c*x)/(c*x+1)^2+b/d^3*arctanh(c*x)/(c*x+1)-b/d^3*arctanh(c*x)*ln(c*x+1)-1/2*b/d^3*dilog(c*x)-1/2*b/d^3*dilog(c*x+1)-1/2*b/d^3*ln(c*x)*ln(c*x+1)+1/4*b/d^3*ln(c*x+1)^2-1/2*b/d^3*ln(-1/2*c*x+1/2)*ln(c*x+1)+1/2*b/d^3*ln(-1/2*c*x+1/2)*ln(1/2+1/2*c*x)+1/2*b/d^3*dilog(1/2+1/2*c*x)+5/16*b/d^3*ln(c*x-1)+1/8*b/d^3/(c*x+1)^2+5/8*b/d^3/(c*x+1)-5/16*b/d^3*ln(c*x+1)","A"
64,1,319,204,0.060000," ","int((a+b*arctanh(c*x))/x^2/(c*d*x+d)^3,x)","-\frac{a}{d^{3} x}-\frac{3 c a \ln \left(c x \right)}{d^{3}}-\frac{c a}{2 d^{3} \left(c x +1\right)^{2}}-\frac{2 c a}{d^{3} \left(c x +1\right)}+\frac{3 c a \ln \left(c x +1\right)}{d^{3}}-\frac{b \arctanh \left(c x \right)}{d^{3} x}-\frac{3 c b \arctanh \left(c x \right) \ln \left(c x \right)}{d^{3}}-\frac{c b \arctanh \left(c x \right)}{2 d^{3} \left(c x +1\right)^{2}}-\frac{2 c b \arctanh \left(c x \right)}{d^{3} \left(c x +1\right)}+\frac{3 c b \arctanh \left(c x \right) \ln \left(c x +1\right)}{d^{3}}+\frac{c b \ln \left(c x \right)}{d^{3}}-\frac{17 c b \ln \left(c x -1\right)}{16 d^{3}}-\frac{b c}{8 d^{3} \left(c x +1\right)^{2}}-\frac{9 b c}{8 d^{3} \left(c x +1\right)}+\frac{c b \ln \left(c x +1\right)}{16 d^{3}}+\frac{3 c b \dilog \left(c x \right)}{2 d^{3}}+\frac{3 c b \dilog \left(c x +1\right)}{2 d^{3}}+\frac{3 c b \ln \left(c x \right) \ln \left(c x +1\right)}{2 d^{3}}-\frac{3 c b \ln \left(c x +1\right)^{2}}{4 d^{3}}+\frac{3 c b \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) \ln \left(c x +1\right)}{2 d^{3}}-\frac{3 c b \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{c x}{2}\right)}{2 d^{3}}-\frac{3 c b \dilog \left(\frac{1}{2}+\frac{c x}{2}\right)}{2 d^{3}}"," ",0,"-a/d^3/x-3*c*a/d^3*ln(c*x)-1/2*c*a/d^3/(c*x+1)^2-2*c*a/d^3/(c*x+1)+3*c*a/d^3*ln(c*x+1)-b/d^3*arctanh(c*x)/x-3*c*b/d^3*arctanh(c*x)*ln(c*x)-1/2*c*b/d^3*arctanh(c*x)/(c*x+1)^2-2*c*b/d^3*arctanh(c*x)/(c*x+1)+3*c*b/d^3*arctanh(c*x)*ln(c*x+1)+c*b/d^3*ln(c*x)-17/16*c*b/d^3*ln(c*x-1)-1/8*b*c/d^3/(c*x+1)^2-9/8*b*c/d^3/(c*x+1)+1/16*c*b/d^3*ln(c*x+1)+3/2*c*b/d^3*dilog(c*x)+3/2*c*b/d^3*dilog(c*x+1)+3/2*c*b/d^3*ln(c*x)*ln(c*x+1)-3/4*c*b/d^3*ln(c*x+1)^2+3/2*c*b/d^3*ln(-1/2*c*x+1/2)*ln(c*x+1)-3/2*c*b/d^3*ln(-1/2*c*x+1/2)*ln(1/2+1/2*c*x)-3/2*c*b/d^3*dilog(1/2+1/2*c*x)","A"
65,1,394,257,0.068000," ","int((a+b*arctanh(c*x))/x^3/(c*d*x+d)^3,x)","\frac{3 c^{2} b \dilog \left(\frac{1}{2}+\frac{c x}{2}\right)}{d^{3}}-\frac{b \arctanh \left(c x \right)}{2 d^{3} x^{2}}-\frac{3 c^{2} b \dilog \left(c x \right)}{d^{3}}-\frac{3 c^{2} b \dilog \left(c x +1\right)}{d^{3}}+\frac{3 c a}{d^{3} x}+\frac{c^{2} a}{2 d^{3} \left(c x +1\right)^{2}}+\frac{3 c^{2} a}{d^{3} \left(c x +1\right)}+\frac{3 c^{2} b \ln \left(c x +1\right)^{2}}{2 d^{3}}-\frac{6 c^{2} a \ln \left(c x +1\right)}{d^{3}}+\frac{6 c^{2} a \ln \left(c x \right)}{d^{3}}+\frac{15 c^{2} b \ln \left(c x +1\right)}{16 d^{3}}+\frac{33 c^{2} b \ln \left(c x -1\right)}{16 d^{3}}-\frac{3 c^{2} b \ln \left(c x \right)}{d^{3}}-\frac{b c}{2 d^{3} x}+\frac{b \,c^{2}}{8 d^{3} \left(c x +1\right)^{2}}+\frac{13 b \,c^{2}}{8 d^{3} \left(c x +1\right)}-\frac{a}{2 d^{3} x^{2}}-\frac{3 c^{2} b \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) \ln \left(c x +1\right)}{d^{3}}-\frac{3 c^{2} b \ln \left(c x \right) \ln \left(c x +1\right)}{d^{3}}+\frac{3 c^{2} b \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{c x}{2}\right)}{d^{3}}-\frac{6 c^{2} b \arctanh \left(c x \right) \ln \left(c x +1\right)}{d^{3}}+\frac{6 c^{2} b \arctanh \left(c x \right) \ln \left(c x \right)}{d^{3}}+\frac{3 c b \arctanh \left(c x \right)}{d^{3} x}+\frac{3 c^{2} b \arctanh \left(c x \right)}{d^{3} \left(c x +1\right)}+\frac{c^{2} b \arctanh \left(c x \right)}{2 d^{3} \left(c x +1\right)^{2}}"," ",0,"3*c*a/d^3/x+1/2*c^2*a/d^3/(c*x+1)^2+3*c^2*a/d^3/(c*x+1)+3/2*c^2*b/d^3*ln(c*x+1)^2+3*c^2*b/d^3*dilog(1/2+1/2*c*x)-6*c^2*a/d^3*ln(c*x+1)+6*c^2*a/d^3*ln(c*x)-1/2*b/d^3*arctanh(c*x)/x^2+15/16*c^2*b/d^3*ln(c*x+1)+33/16*c^2*b/d^3*ln(c*x-1)-3*c^2*b/d^3*ln(c*x)-3*c^2*b/d^3*dilog(c*x)-3*c^2*b/d^3*dilog(c*x+1)-1/2*b*c/d^3/x+1/8*b*c^2/d^3/(c*x+1)^2+13/8*b*c^2/d^3/(c*x+1)-1/2*a/d^3/x^2-6*c^2*b/d^3*arctanh(c*x)*ln(c*x+1)-3*c^2*b/d^3*ln(-1/2*c*x+1/2)*ln(c*x+1)-3*c^2*b/d^3*ln(c*x)*ln(c*x+1)+6*c^2*b/d^3*arctanh(c*x)*ln(c*x)+3*c^2*b/d^3*ln(-1/2*c*x+1/2)*ln(1/2+1/2*c*x)+3*c*b/d^3*arctanh(c*x)/x+3*c^2*b/d^3*arctanh(c*x)/(c*x+1)+1/2*c^2*b/d^3*arctanh(c*x)/(c*x+1)^2","A"
66,1,95,73,0.036000," ","int((a+b*arctanh(c*x))/(c*x+1)^4,x)","-\frac{a}{3 c \left(c x +1\right)^{3}}-\frac{b \arctanh \left(c x \right)}{3 c \left(c x +1\right)^{3}}-\frac{b \ln \left(c x -1\right)}{48 c}-\frac{b}{18 c \left(c x +1\right)^{3}}-\frac{b}{24 c \left(c x +1\right)^{2}}-\frac{b}{24 c \left(c x +1\right)}+\frac{b \ln \left(c x +1\right)}{48 c}"," ",0,"-1/3/c*a/(c*x+1)^3-1/3/c*b/(c*x+1)^3*arctanh(c*x)-1/48/c*b*ln(c*x-1)-1/18*b/c/(c*x+1)^3-1/24*b/c/(c*x+1)^2-1/24*b/c/(c*x+1)+1/48/c*b*ln(c*x+1)","A"
67,1,126,39,0.054000," ","int(arctanh(a*x)/(a*c*x^2+c*x),x)","\frac{\arctanh \left(a x \right) \ln \left(a x \right)}{c}-\frac{\arctanh \left(a x \right) \ln \left(a x +1\right)}{c}+\frac{\ln \left(a x +1\right)^{2}}{4 c}-\frac{\ln \left(-\frac{a x}{2}+\frac{1}{2}\right) \ln \left(a x +1\right)}{2 c}+\frac{\ln \left(-\frac{a x}{2}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{a x}{2}\right)}{2 c}+\frac{\dilog \left(\frac{1}{2}+\frac{a x}{2}\right)}{2 c}-\frac{\dilog \left(a x \right)}{2 c}-\frac{\dilog \left(a x +1\right)}{2 c}-\frac{\ln \left(a x \right) \ln \left(a x +1\right)}{2 c}"," ",0,"1/c*arctanh(a*x)*ln(a*x)-1/c*arctanh(a*x)*ln(a*x+1)+1/4/c*ln(a*x+1)^2-1/2/c*ln(-1/2*a*x+1/2)*ln(a*x+1)+1/2/c*ln(-1/2*a*x+1/2)*ln(1/2+1/2*a*x)+1/2/c*dilog(1/2+1/2*a*x)-1/2/c*dilog(a*x)-1/2/c*dilog(a*x+1)-1/2/c*ln(a*x)*ln(a*x+1)","B"
68,1,422,240,0.059000," ","int(x^3*(c*d*x+d)*(a+b*arctanh(c*x))^2,x)","\frac{11 d \,b^{2} \ln \left(c x +1\right)}{60 c^{4}}+\frac{d a b \,x^{4}}{10}+\frac{29 d \,b^{2} \ln \left(c x -1\right)}{60 c^{4}}+\frac{c \,a^{2} d \,x^{5}}{5}+\frac{d \,b^{2} \ln \left(c x +1\right)^{2}}{80 c^{4}}+\frac{9 d \,b^{2} \ln \left(c x -1\right)^{2}}{80 c^{4}}+\frac{d \,b^{2} \arctanh \left(c x \right)^{2} x^{4}}{4}+\frac{d \,b^{2} \arctanh \left(c x \right) x^{4}}{10}-\frac{d \,b^{2} \dilog \left(\frac{1}{2}+\frac{c x}{2}\right)}{5 c^{4}}+\frac{a b d x}{2 c^{3}}+\frac{3 b^{2} d x}{10 c^{3}}+\frac{b^{2} d \,x^{2}}{12 c^{2}}+\frac{b^{2} d \,x^{3}}{30 c}+\frac{d \,b^{2} \arctanh \left(c x \right) x^{3}}{6 c}+\frac{d \,b^{2} \arctanh \left(c x \right) x^{2}}{5 c^{2}}+\frac{c d \,b^{2} \arctanh \left(c x \right)^{2} x^{5}}{5}+\frac{d a b \,x^{2}}{5 c^{2}}-\frac{d a b \ln \left(c x +1\right)}{20 c^{4}}+\frac{9 d a b \ln \left(c x -1\right)}{20 c^{4}}+\frac{d a b \,x^{3}}{6 c}-\frac{9 d \,b^{2} \ln \left(c x -1\right) \ln \left(\frac{1}{2}+\frac{c x}{2}\right)}{40 c^{4}}-\frac{d \,b^{2} \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) \ln \left(c x +1\right)}{40 c^{4}}+\frac{d \,b^{2} \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{c x}{2}\right)}{40 c^{4}}+\frac{b^{2} d x \arctanh \left(c x \right)}{2 c^{3}}+\frac{a^{2} d \,x^{4}}{4}-\frac{d \,b^{2} \arctanh \left(c x \right) \ln \left(c x +1\right)}{20 c^{4}}+\frac{9 d \,b^{2} \arctanh \left(c x \right) \ln \left(c x -1\right)}{20 c^{4}}+\frac{d a b \arctanh \left(c x \right) x^{4}}{2}+\frac{2 c d a b \arctanh \left(c x \right) x^{5}}{5}"," ",0,"11/60/c^4*d*b^2*ln(c*x+1)+1/10*d*a*b*x^4+1/4*d*b^2*arctanh(c*x)^2*x^4+1/10*d*b^2*arctanh(c*x)*x^4+29/60/c^4*d*b^2*ln(c*x-1)-1/5/c^4*d*b^2*dilog(1/2+1/2*c*x)+1/5*c*a^2*d*x^5+1/80/c^4*d*b^2*ln(c*x+1)^2+9/80/c^4*d*b^2*ln(c*x-1)^2+1/2*a*b*d*x/c^3+1/2*b^2*d*x*arctanh(c*x)/c^3+3/10*b^2*d*x/c^3+1/12*b^2*d*x^2/c^2+1/30*b^2*d*x^3/c+1/5/c^2*d*a*b*x^2-1/20/c^4*d*a*b*ln(c*x+1)+9/20/c^4*d*a*b*ln(c*x-1)+1/6/c*d*a*b*x^3-9/40/c^4*d*b^2*ln(c*x-1)*ln(1/2+1/2*c*x)-1/40/c^4*d*b^2*ln(-1/2*c*x+1/2)*ln(c*x+1)-1/20/c^4*d*b^2*arctanh(c*x)*ln(c*x+1)+9/20/c^4*d*b^2*arctanh(c*x)*ln(c*x-1)+1/40/c^4*d*b^2*ln(-1/2*c*x+1/2)*ln(1/2+1/2*c*x)+1/2*d*a*b*arctanh(c*x)*x^4+1/6/c*d*b^2*arctanh(c*x)*x^3+1/5/c^2*d*b^2*arctanh(c*x)*x^2+1/4*a^2*d*x^4+1/5*c*d*b^2*arctanh(c*x)^2*x^5+2/5*c*d*a*b*arctanh(c*x)*x^5","A"
69,1,383,210,0.063000," ","int(x^2*(c*d*x+d)*(a+b*arctanh(c*x))^2,x)","\frac{c d a b \arctanh \left(c x \right) x^{4}}{2}-\frac{d \,b^{2} \dilog \left(\frac{1}{2}+\frac{c x}{2}\right)}{3 c^{3}}+\frac{d \,b^{2} \arctanh \left(c x \right) x^{3}}{6}+\frac{d \,b^{2} \arctanh \left(c x \right)^{2} x^{3}}{3}+\frac{d a b \,x^{3}}{6}+\frac{7 d \,b^{2} \ln \left(c x -1\right)^{2}}{48 c^{3}}+\frac{d \,b^{2} \ln \left(c x +1\right)}{6 c^{3}}+\frac{d \,b^{2} \ln \left(c x -1\right)}{2 c^{3}}-\frac{d \,b^{2} \ln \left(c x +1\right)^{2}}{48 c^{3}}+\frac{c \,a^{2} d \,x^{4}}{4}+\frac{a b d x}{2 c^{2}}+\frac{b^{2} d x}{3 c^{2}}+\frac{b^{2} d \,x^{2}}{12 c}-\frac{7 d \,b^{2} \ln \left(c x -1\right) \ln \left(\frac{1}{2}+\frac{c x}{2}\right)}{24 c^{3}}+\frac{b^{2} d x \arctanh \left(c x \right)}{2 c^{2}}+\frac{d \,b^{2} \arctanh \left(c x \right) x^{2}}{3 c}+\frac{2 d a b \arctanh \left(c x \right) x^{3}}{3}+\frac{7 d \,b^{2} \arctanh \left(c x \right) \ln \left(c x -1\right)}{12 c^{3}}+\frac{d \,b^{2} \arctanh \left(c x \right) \ln \left(c x +1\right)}{12 c^{3}}+\frac{c d \,b^{2} \arctanh \left(c x \right)^{2} x^{4}}{4}+\frac{d a b \,x^{2}}{3 c}+\frac{7 d a b \ln \left(c x -1\right)}{12 c^{3}}+\frac{d a b \ln \left(c x +1\right)}{12 c^{3}}-\frac{d \,b^{2} \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{c x}{2}\right)}{24 c^{3}}+\frac{d \,b^{2} \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) \ln \left(c x +1\right)}{24 c^{3}}+\frac{a^{2} d \,x^{3}}{3}"," ",0,"1/2*c*d*a*b*arctanh(c*x)*x^4+1/6*d*a*b*x^3+7/48/c^3*d*b^2*ln(c*x-1)^2+1/6/c^3*d*b^2*ln(c*x+1)+1/2/c^3*d*b^2*ln(c*x-1)-1/3/c^3*d*b^2*dilog(1/2+1/2*c*x)+1/6*d*b^2*arctanh(c*x)*x^3+1/3*d*b^2*arctanh(c*x)^2*x^3-1/48/c^3*d*b^2*ln(c*x+1)^2+1/4*c*a^2*d*x^4+1/2*a*b*d*x/c^2+1/2*b^2*d*x*arctanh(c*x)/c^2+1/3*b^2*d*x/c^2+1/12*b^2*d*x^2/c-7/24/c^3*d*b^2*ln(c*x-1)*ln(1/2+1/2*c*x)+1/3/c*d*b^2*arctanh(c*x)*x^2+1/3/c*d*a*b*x^2+2/3*d*a*b*arctanh(c*x)*x^3+7/12/c^3*d*a*b*ln(c*x-1)+1/12/c^3*d*a*b*ln(c*x+1)-1/24/c^3*d*b^2*ln(-1/2*c*x+1/2)*ln(1/2+1/2*c*x)+7/12/c^3*d*b^2*arctanh(c*x)*ln(c*x-1)+1/12/c^3*d*b^2*arctanh(c*x)*ln(c*x+1)+1/24/c^3*d*b^2*ln(-1/2*c*x+1/2)*ln(c*x+1)+1/4*c*d*b^2*arctanh(c*x)^2*x^4+1/3*a^2*d*x^3","A"
70,1,341,178,0.060000," ","int(x*(c*d*x+d)*(a+b*arctanh(c*x))^2,x)","\frac{c \,a^{2} d \,x^{3}}{3}+\frac{a^{2} d \,x^{2}}{2}+\frac{c d \,b^{2} \arctanh \left(c x \right)^{2} x^{3}}{3}+\frac{d \,b^{2} \arctanh \left(c x \right)^{2} x^{2}}{2}+\frac{d \,b^{2} \arctanh \left(c x \right) x^{2}}{3}+\frac{b^{2} d x \arctanh \left(c x \right)}{c}+\frac{5 d \,b^{2} \arctanh \left(c x \right) \ln \left(c x -1\right)}{6 c^{2}}-\frac{d \,b^{2} \arctanh \left(c x \right) \ln \left(c x +1\right)}{6 c^{2}}+\frac{5 d \,b^{2} \ln \left(c x -1\right)^{2}}{24 c^{2}}-\frac{d \,b^{2} \dilog \left(\frac{1}{2}+\frac{c x}{2}\right)}{3 c^{2}}-\frac{5 d \,b^{2} \ln \left(c x -1\right) \ln \left(\frac{1}{2}+\frac{c x}{2}\right)}{12 c^{2}}+\frac{d \,b^{2} \ln \left(c x +1\right)^{2}}{24 c^{2}}-\frac{d \,b^{2} \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) \ln \left(c x +1\right)}{12 c^{2}}+\frac{d \,b^{2} \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{c x}{2}\right)}{12 c^{2}}+\frac{b^{2} d x}{3 c}+\frac{2 d \,b^{2} \ln \left(c x -1\right)}{3 c^{2}}+\frac{d \,b^{2} \ln \left(c x +1\right)}{3 c^{2}}+\frac{2 c d a b \arctanh \left(c x \right) x^{3}}{3}+d a b \arctanh \left(c x \right) x^{2}+\frac{d a b \,x^{2}}{3}+\frac{a b d x}{c}+\frac{5 d a b \ln \left(c x -1\right)}{6 c^{2}}-\frac{d a b \ln \left(c x +1\right)}{6 c^{2}}"," ",0,"1/3*c*a^2*d*x^3+1/2*a^2*d*x^2+1/3*c*d*b^2*arctanh(c*x)^2*x^3+1/2*d*b^2*arctanh(c*x)^2*x^2+1/3*d*b^2*arctanh(c*x)*x^2+b^2*d*x*arctanh(c*x)/c+5/6/c^2*d*b^2*arctanh(c*x)*ln(c*x-1)-1/6/c^2*d*b^2*arctanh(c*x)*ln(c*x+1)+5/24/c^2*d*b^2*ln(c*x-1)^2-1/3/c^2*d*b^2*dilog(1/2+1/2*c*x)-5/12/c^2*d*b^2*ln(c*x-1)*ln(1/2+1/2*c*x)+1/24/c^2*d*b^2*ln(c*x+1)^2-1/12/c^2*d*b^2*ln(-1/2*c*x+1/2)*ln(c*x+1)+1/12/c^2*d*b^2*ln(-1/2*c*x+1/2)*ln(1/2+1/2*c*x)+1/3*b^2*d*x/c+2/3/c^2*d*b^2*ln(c*x-1)+1/3/c^2*d*b^2*ln(c*x+1)+2/3*c*d*a*b*arctanh(c*x)*x^3+d*a*b*arctanh(c*x)*x^2+1/3*d*a*b*x^2+a*b*d*x/c+5/6/c^2*d*a*b*ln(c*x-1)-1/6/c^2*d*a*b*ln(c*x+1)","A"
71,1,296,108,0.058000," ","int((c*d*x+d)*(a+b*arctanh(c*x))^2,x)","\frac{c \,a^{2} d \,x^{2}}{2}+a^{2} d x +\frac{c d \,b^{2} \arctanh \left(c x \right)^{2} x^{2}}{2}+d \,b^{2} \arctanh \left(c x \right)^{2} x +b^{2} d x \arctanh \left(c x \right)+\frac{3 d \,b^{2} \arctanh \left(c x \right) \ln \left(c x -1\right)}{2 c}+\frac{d \,b^{2} \arctanh \left(c x \right) \ln \left(c x +1\right)}{2 c}-\frac{b^{2} \ln \left(c x +1\right)^{2} d}{8 c}+\frac{d \,b^{2} \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) \ln \left(c x +1\right)}{4 c}-\frac{d \,b^{2} \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{c x}{2}\right)}{4 c}-\frac{d \,b^{2} \dilog \left(\frac{1}{2}+\frac{c x}{2}\right)}{c}+\frac{d \,b^{2} \ln \left(c x -1\right)}{2 c}+\frac{d \,b^{2} \ln \left(c x +1\right)}{2 c}+\frac{3 d \,b^{2} \ln \left(c x -1\right)^{2}}{8 c}-\frac{3 d \,b^{2} \ln \left(c x -1\right) \ln \left(\frac{1}{2}+\frac{c x}{2}\right)}{4 c}+c d a b \arctanh \left(c x \right) x^{2}+2 d a b \arctanh \left(c x \right) x +a b d x +\frac{3 d a b \ln \left(c x -1\right)}{2 c}+\frac{d a b \ln \left(c x +1\right)}{2 c}"," ",0,"1/2*c*a^2*d*x^2+a^2*d*x+1/2*c*d*b^2*arctanh(c*x)^2*x^2+d*b^2*arctanh(c*x)^2*x+b^2*d*x*arctanh(c*x)+3/2/c*d*b^2*arctanh(c*x)*ln(c*x-1)+1/2/c*d*b^2*arctanh(c*x)*ln(c*x+1)-1/8/c*b^2*ln(c*x+1)^2*d+1/4/c*d*b^2*ln(-1/2*c*x+1/2)*ln(c*x+1)-1/4/c*d*b^2*ln(-1/2*c*x+1/2)*ln(1/2+1/2*c*x)-1/c*d*b^2*dilog(1/2+1/2*c*x)+1/2/c*d*b^2*ln(c*x-1)+1/2/c*d*b^2*ln(c*x+1)+3/8/c*d*b^2*ln(c*x-1)^2-3/4/c*d*b^2*ln(c*x-1)*ln(1/2+1/2*c*x)+c*d*a*b*arctanh(c*x)*x^2+2*d*a*b*arctanh(c*x)*x+a*b*d*x+3/2/c*d*a*b*ln(c*x-1)+1/2/c*d*a*b*ln(c*x+1)","B"
72,1,3644,187,0.457000," ","int((c*d*x+d)*(a+b*arctanh(c*x))^2/x,x)","\text{output too large to display}"," ",0,"a^2*d*c*x-d*a*b*dilog(c*x)-d*a*b*dilog(c*x+1)+2*d*b^2*arctanh(c*x)*polylog(2,-(c*x+1)/(-c^2*x^2+1)^(1/2))+d*b^2*arctanh(c*x)^2*ln(c*x)+d*b^2*arctanh(c*x)^2*ln(1-(c*x+1)/(-c^2*x^2+1)^(1/2))+2*d*b^2*arctanh(c*x)*polylog(2,(c*x+1)/(-c^2*x^2+1)^(1/2))-d*b^2*arctanh(c*x)*polylog(2,-(c*x+1)^2/(-c^2*x^2+1))-d*b^2*arctanh(c*x)*ln(1+(c*x+1)^2/(-c^2*x^2+1))-d*b^2*arctanh(c*x)^2*ln((c*x+1)^2/(-c^2*x^2+1)-1)-d*b^2*arctanh(c*x)*ln(1+I*(c*x+1)/(-c^2*x^2+1)^(1/2))-d*b^2*arctanh(c*x)*ln(1-I*(c*x+1)/(-c^2*x^2+1)^(1/2))+d*b^2*arctanh(c*x)^2*ln(1+(c*x+1)/(-c^2*x^2+1)^(1/2))+d*a*b*ln(c*x+1)+d*a*b*ln(c*x-1)-1/4*I*d*b^2*Pi*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1))*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))*polylog(2,-(c*x+1)^2/(-c^2*x^2+1))-1/2*I*d*b^2*Pi*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^2*arctanh(c*x)*ln(1-I*(c*x+1)/(-c^2*x^2+1)^(1/2))-d*b^2*dilog(1-I*(c*x+1)/(-c^2*x^2+1)^(1/2))-2*d*b^2*polylog(3,(c*x+1)/(-c^2*x^2+1)^(1/2))-d*b^2*dilog(1+I*(c*x+1)/(-c^2*x^2+1)^(1/2))+a^2*d*ln(c*x)-2*d*b^2*polylog(3,-(c*x+1)/(-c^2*x^2+1)^(1/2))+d*b^2*arctanh(c*x)^2-1/2*d*b^2*polylog(2,-(c*x+1)^2/(-c^2*x^2+1))+1/2*d*b^2*polylog(3,-(c*x+1)^2/(-c^2*x^2+1))+1/2*I*d*b^2*Pi*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1))*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))*dilog(1-I*(c*x+1)/(-c^2*x^2+1)^(1/2))+1/2*I*d*b^2*Pi*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1))*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))*arctanh(c*x)^2-1/2*I*d*b^2*Pi*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1))*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^2*arctanh(c*x)*ln(1-I*(c*x+1)/(-c^2*x^2+1)^(1/2))+1/2*I*d*b^2*Pi*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1))*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))*dilog(1+I*(c*x+1)/(-c^2*x^2+1)^(1/2))-1/2*I*d*b^2*Pi*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^2*arctanh(c*x)*ln(1+I*(c*x+1)/(-c^2*x^2+1)^(1/2))+1/2*I*d*b^2*Pi*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^2*arctanh(c*x)*ln(1+(c*x+1)^2/(-c^2*x^2+1))-1/2*I*d*b^2*Pi*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1))*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^2*arctanh(c*x)*ln(1+I*(c*x+1)/(-c^2*x^2+1)^(1/2))+1/2*I*d*b^2*Pi*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1))*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^2*arctanh(c*x)*ln(1+(c*x+1)^2/(-c^2*x^2+1))+2*d*a*b*arctanh(c*x)*c*x-1/4*I*d*b^2*Pi*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^3*polylog(2,-(c*x+1)^2/(-c^2*x^2+1))+1/2*I*d*b^2*Pi*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^3*arctanh(c*x)^2+1/2*I*d*b^2*Pi*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^3*dilog(1+I*(c*x+1)/(-c^2*x^2+1)^(1/2))-1/2*I*d*b^2*Pi*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1))*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^2*dilog(1-I*(c*x+1)/(-c^2*x^2+1)^(1/2))-1/2*I*d*b^2*Pi*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^2*dilog(1-I*(c*x+1)/(-c^2*x^2+1)^(1/2))-1/2*I*d*b^2*Pi*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1))*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^2*arctanh(c*x)^2+1/2*I*d*b^2*Pi*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^3*dilog(1-I*(c*x+1)/(-c^2*x^2+1)^(1/2))+d*b^2*arctanh(c*x)^2*c*x-d*a*b*ln(c*x)*ln(c*x+1)+2*d*a*b*arctanh(c*x)*ln(c*x)-1/2*I*d*b^2*Pi*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^2*arctanh(c*x)^2+1/2*I*d*b^2*Pi*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^3*arctanh(c*x)*ln(1-I*(c*x+1)/(-c^2*x^2+1)^(1/2))-1/2*I*d*b^2*Pi*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1))*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^2*dilog(1+I*(c*x+1)/(-c^2*x^2+1)^(1/2))-1/2*I*d*b^2*Pi*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^3*arctanh(c*x)*ln(1+(c*x+1)^2/(-c^2*x^2+1))+1/4*I*d*b^2*Pi*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^2*polylog(2,-(c*x+1)^2/(-c^2*x^2+1))-1/2*I*d*b^2*Pi*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^2*dilog(1+I*(c*x+1)/(-c^2*x^2+1)^(1/2))+1/2*I*d*b^2*Pi*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^3*arctanh(c*x)*ln(1+I*(c*x+1)/(-c^2*x^2+1)^(1/2))+1/4*I*d*b^2*Pi*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1))*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^2*polylog(2,-(c*x+1)^2/(-c^2*x^2+1))+1/2*I*d*b^2*Pi*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1))*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))*arctanh(c*x)*ln(1-I*(c*x+1)/(-c^2*x^2+1)^(1/2))+1/2*I*d*b^2*Pi*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1))*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))*arctanh(c*x)*ln(1+I*(c*x+1)/(-c^2*x^2+1)^(1/2))-1/2*I*d*b^2*Pi*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1))*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))*arctanh(c*x)*ln(1+(c*x+1)^2/(-c^2*x^2+1))","C"
73,1,3104,197,0.983000," ","int((c*d*x+d)*(a+b*arctanh(c*x))^2/x^2,x)","\text{output too large to display}"," ",0,"-a^2*d/x-1/4*c*d*b^2*dilog((c*x+1)^2/(-c^2*x^2+1))+c*a^2*d*ln(c*x)-c*d*b^2*arctanh(c*x)^2-1/4*c*d*b^2*polylog(2,-(c*x+1)^2/(-c^2*x^2+1))+1/2*c*d*b^2*polylog(3,-(c*x+1)^2/(-c^2*x^2+1))+3/4*c*d*b^2*polylog(2,(c*x+1)^2/(-c^2*x^2+1))-1/2*c*d*b^2*polylog(3,(c*x+1)^2/(-c^2*x^2+1))+1/4*c*d*b^2*dilog(1+(c*x+1)^2/(-c^2*x^2+1))-d*b^2*arctanh(c*x)^2/x-1/8*I*c*d*b^2*Pi*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1))*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^2*dilog(1+(c*x+1)^2/(-c^2*x^2+1))+1/8*I*c*d*b^2*Pi*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1))*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^2*polylog(2,-(c*x+1)^2/(-c^2*x^2+1))-1/8*I*c*d*b^2*Pi*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^2*dilog(1+(c*x+1)^2/(-c^2*x^2+1))+1/8*I*c*d*b^2*Pi*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1))*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^2*dilog((c*x+1)^2/(-c^2*x^2+1))+1/8*I*c*d*b^2*Pi*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^2*polylog(2,-(c*x+1)^2/(-c^2*x^2+1))+1/8*I*c*d*b^2*Pi*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1))*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^2*polylog(2,(c*x+1)^2/(-c^2*x^2+1))-1/4*I*c*d*b^2*Pi*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^3*arctanh(c*x)*ln(1-(c*x+1)^2/(-c^2*x^2+1))+1/8*I*c*d*b^2*Pi*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^2*polylog(2,(c*x+1)^2/(-c^2*x^2+1))+1/8*I*c*d*b^2*Pi*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^2*dilog((c*x+1)^2/(-c^2*x^2+1))-1/2*I*c*d*b^2*Pi*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^2*arctanh(c*x)^2-1/2*I*c*d*b^2*Pi*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1))*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^2*arctanh(c*x)^2-c*d*a*b*ln(c*x)*ln(c*x+1)+2*c*d*a*b*arctanh(c*x)*ln(c*x)-1/8*I*c*d*b^2*Pi*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^3*polylog(2,-(c*x+1)^2/(-c^2*x^2+1))-1/8*I*c*d*b^2*dilog((c*x+1)^2/(-c^2*x^2+1))*Pi*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^3+1/8*I*c*d*b^2*Pi*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^3*dilog(1+(c*x+1)^2/(-c^2*x^2+1))+1/2*I*c*d*b^2*Pi*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^3*arctanh(c*x)^2-1/8*I*c*d*b^2*Pi*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^3*polylog(2,(c*x+1)^2/(-c^2*x^2+1))-2*d*a*b*arctanh(c*x)/x-c*d*a*b*ln(c*x+1)-c*d*a*b*ln(c*x-1)+2*c*d*a*b*ln(c*x)-c*d*a*b*dilog(c*x)-c*d*a*b*dilog(c*x+1)+c*d*b^2*arctanh(c*x)^2*ln(1-(c*x+1)^2/(-c^2*x^2+1))+c*d*b^2*arctanh(c*x)*polylog(2,(c*x+1)^2/(-c^2*x^2+1))+3/2*c*d*b^2*arctanh(c*x)*ln(1-(c*x+1)^2/(-c^2*x^2+1))+c*d*b^2*arctanh(c*x)^2*ln(c*x)-c*d*b^2*arctanh(c*x)*polylog(2,-(c*x+1)^2/(-c^2*x^2+1))-c*d*b^2*arctanh(c*x)^2*ln((c*x+1)^2/(-c^2*x^2+1)-1)-1/4*I*c*d*b^2*Pi*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1))*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))*arctanh(c*x)*ln(1-(c*x+1)^2/(-c^2*x^2+1))+1/8*I*c*d*b^2*Pi*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1))*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))*dilog(1+(c*x+1)^2/(-c^2*x^2+1))+1/2*I*c*d*b^2*Pi*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1))*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))*arctanh(c*x)^2-1/8*I*c*d*b^2*Pi*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1))*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))*polylog(2,(c*x+1)^2/(-c^2*x^2+1))-1/8*I*c*d*b^2*Pi*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1))*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))*polylog(2,-(c*x+1)^2/(-c^2*x^2+1))-1/8*I*c*d*b^2*dilog((c*x+1)^2/(-c^2*x^2+1))*Pi*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1))*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))+1/4*I*c*d*b^2*Pi*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1))*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^2*arctanh(c*x)*ln(1-(c*x+1)^2/(-c^2*x^2+1))+1/4*I*c*d*b^2*Pi*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^2*arctanh(c*x)*ln(1-(c*x+1)^2/(-c^2*x^2+1))","C"
74,1,400,145,0.078000," ","int((c*d*x+d)*(a+b*arctanh(c*x))^2/x^3,x)","-\frac{2 c d a b \arctanh \left(c x \right)}{x}-\frac{c^{2} d \,b^{2} \arctanh \left(c x \right) \ln \left(c x +1\right)}{2}+2 c^{2} d \,b^{2} \arctanh \left(c x \right) \ln \left(c x \right)-\frac{d \,b^{2} \arctanh \left(c x \right)^{2}}{2 x^{2}}-c^{2} d \,b^{2} \dilog \left(c x +1\right)+c^{2} d \,b^{2} \dilog \left(\frac{1}{2}+\frac{c x}{2}\right)-\frac{c^{2} d \,b^{2} \ln \left(c x +1\right)}{2}+c^{2} d \,b^{2} \ln \left(c x \right)-\frac{c \,a^{2} d}{x}-c^{2} d \,b^{2} \dilog \left(c x \right)-\frac{3 c^{2} d \,b^{2} \ln \left(c x -1\right)^{2}}{8}+\frac{c^{2} d \,b^{2} \ln \left(c x +1\right)^{2}}{8}-\frac{c^{2} d \,b^{2} \ln \left(c x -1\right)}{2}-\frac{a^{2} d}{2 x^{2}}-\frac{c d \,b^{2} \arctanh \left(c x \right)}{x}-\frac{3 c^{2} d \,b^{2} \arctanh \left(c x \right) \ln \left(c x -1\right)}{2}-\frac{c d a b}{x}-c^{2} d \,b^{2} \ln \left(c x \right) \ln \left(c x +1\right)-\frac{d a b \arctanh \left(c x \right)}{x^{2}}-\frac{c d \,b^{2} \arctanh \left(c x \right)^{2}}{x}+\frac{c^{2} d \,b^{2} \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{c x}{2}\right)}{4}+\frac{3 c^{2} d \,b^{2} \ln \left(c x -1\right) \ln \left(\frac{1}{2}+\frac{c x}{2}\right)}{4}-\frac{c^{2} d \,b^{2} \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) \ln \left(c x +1\right)}{4}-\frac{c^{2} d a b \ln \left(c x +1\right)}{2}-\frac{3 c^{2} d a b \ln \left(c x -1\right)}{2}+2 c^{2} d a b \ln \left(c x \right)"," ",0,"-2*c*d*a*b*arctanh(c*x)/x-1/2*c^2*d*b^2*ln(c*x+1)+c^2*d*b^2*ln(c*x)-c^2*d*b^2*dilog(c*x)-1/2*d*b^2*arctanh(c*x)^2/x^2-c*a^2*d/x-c^2*d*b^2*dilog(c*x+1)-3/8*c^2*d*b^2*ln(c*x-1)^2+c^2*d*b^2*dilog(1/2+1/2*c*x)+1/8*c^2*d*b^2*ln(c*x+1)^2-1/2*c^2*d*b^2*ln(c*x-1)-d*a*b*arctanh(c*x)/x^2-1/2*a^2*d/x^2-c*d*a*b/x-c*d*b^2*arctanh(c*x)^2/x-c^2*d*b^2*ln(c*x)*ln(c*x+1)-c*d*b^2*arctanh(c*x)/x+1/4*c^2*d*b^2*ln(-1/2*c*x+1/2)*ln(1/2+1/2*c*x)-3/2*c^2*d*b^2*arctanh(c*x)*ln(c*x-1)-1/2*c^2*d*b^2*arctanh(c*x)*ln(c*x+1)+3/4*c^2*d*b^2*ln(c*x-1)*ln(1/2+1/2*c*x)-1/4*c^2*d*b^2*ln(-1/2*c*x+1/2)*ln(c*x+1)+2*c^2*d*b^2*arctanh(c*x)*ln(c*x)-1/2*c^2*d*a*b*ln(c*x+1)-3/2*c^2*d*a*b*ln(c*x-1)+2*c^2*d*a*b*ln(c*x)","B"
75,1,440,188,0.081000," ","int((c*d*x+d)*(a+b*arctanh(c*x))^2/x^4,x)","-\frac{c d a b \arctanh \left(c x \right)}{x^{2}}-\frac{c^{3} d \,b^{2} \dilog \left(c x +1\right)}{3}-\frac{c^{3} d \,b^{2} \dilog \left(c x \right)}{3}-\frac{d \,b^{2} \arctanh \left(c x \right)^{2}}{3 x^{3}}+\frac{c^{3} d \,b^{2} \dilog \left(\frac{1}{2}+\frac{c x}{2}\right)}{3}-\frac{5 c^{3} d \,b^{2} \ln \left(c x -1\right)^{2}}{24}+c^{3} d \,b^{2} \ln \left(c x \right)-\frac{c^{3} d \,b^{2} \ln \left(c x +1\right)^{2}}{24}-\frac{2 c^{3} d \,b^{2} \ln \left(c x -1\right)}{3}-\frac{c^{3} d \,b^{2} \ln \left(c x +1\right)}{3}-\frac{c \,a^{2} d}{2 x^{2}}-\frac{b^{2} c^{2} d}{3 x}-\frac{c^{3} d \,b^{2} \ln \left(c x \right) \ln \left(c x +1\right)}{3}-\frac{a^{2} d}{3 x^{3}}-\frac{c^{3} d \,b^{2} \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{c x}{2}\right)}{12}+\frac{2 c^{3} d a b \ln \left(c x \right)}{3}+\frac{c^{3} d a b \ln \left(c x +1\right)}{6}-\frac{5 c^{3} d a b \ln \left(c x -1\right)}{6}-\frac{c^{2} d a b}{x}-\frac{c d a b}{3 x^{2}}+\frac{5 c^{3} d \,b^{2} \ln \left(c x -1\right) \ln \left(\frac{1}{2}+\frac{c x}{2}\right)}{12}+\frac{c^{3} d \,b^{2} \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) \ln \left(c x +1\right)}{12}-\frac{c d \,b^{2} \arctanh \left(c x \right)^{2}}{2 x^{2}}-\frac{c^{2} d \,b^{2} \arctanh \left(c x \right)}{x}-\frac{c d \,b^{2} \arctanh \left(c x \right)}{3 x^{2}}-\frac{2 d a b \arctanh \left(c x \right)}{3 x^{3}}-\frac{5 c^{3} d \,b^{2} \arctanh \left(c x \right) \ln \left(c x -1\right)}{6}+\frac{c^{3} d \,b^{2} \arctanh \left(c x \right) \ln \left(c x +1\right)}{6}+\frac{2 c^{3} d \,b^{2} \arctanh \left(c x \right) \ln \left(c x \right)}{3}"," ",0,"-c*d*a*b*arctanh(c*x)/x^2-1/3*c^3*d*b^2*dilog(c*x+1)-5/24*c^3*d*b^2*ln(c*x-1)^2-1/3*c^3*d*b^2*dilog(c*x)+c^3*d*b^2*ln(c*x)-1/3*d*b^2*arctanh(c*x)^2/x^3+1/3*c^3*d*b^2*dilog(1/2+1/2*c*x)-1/24*c^3*d*b^2*ln(c*x+1)^2-2/3*c^3*d*b^2*ln(c*x-1)-1/3*c^3*d*b^2*ln(c*x+1)-1/2*c*a^2*d/x^2-1/3*b^2*c^2*d/x-1/3*c^3*d*b^2*ln(c*x)*ln(c*x+1)-1/3*a^2*d/x^3-1/12*c^3*d*b^2*ln(-1/2*c*x+1/2)*ln(1/2+1/2*c*x)+2/3*c^3*d*a*b*ln(c*x)+1/6*c^3*d*a*b*ln(c*x+1)-5/6*c^3*d*a*b*ln(c*x-1)-1/2*c*d*b^2*arctanh(c*x)^2/x^2-c^2*d*b^2*arctanh(c*x)/x-1/3*c*d*b^2*arctanh(c*x)/x^2-c^2*d*a*b/x-1/3*c*d*a*b/x^2-2/3*d*a*b*arctanh(c*x)/x^3-5/6*c^3*d*b^2*arctanh(c*x)*ln(c*x-1)+1/6*c^3*d*b^2*arctanh(c*x)*ln(c*x+1)+5/12*c^3*d*b^2*ln(c*x-1)*ln(1/2+1/2*c*x)+1/12*c^3*d*b^2*ln(-1/2*c*x+1/2)*ln(c*x+1)+2/3*c^3*d*b^2*arctanh(c*x)*ln(c*x)","B"
76,1,569,320,0.059000," ","int(x^3*(c*d*x+d)^2*(a+b*arctanh(c*x))^2,x)","\frac{d^{2} b^{2} \arctanh \left(c x \right) x^{4}}{5}+\frac{d^{2} b^{2} \arctanh \left(c x \right)^{2} x^{4}}{4}-\frac{2 d^{2} b^{2} \dilog \left(\frac{1}{2}+\frac{c x}{2}\right)}{5 c^{4}}+\frac{13 d^{2} b^{2} \ln \left(c x +1\right)}{45 c^{4}}+\frac{c^{2} d^{2} a^{2} x^{6}}{6}+\frac{2 c \,d^{2} a^{2} x^{5}}{5}+\frac{d^{2} a b \,x^{4}}{5}+\frac{d^{2} b^{2} \ln \left(c x +1\right)^{2}}{240 c^{4}}+\frac{49 d^{2} b^{2} \ln \left(c x -1\right)^{2}}{240 c^{4}}+\frac{8 d^{2} b^{2} \ln \left(c x -1\right)}{9 c^{4}}+\frac{5 a b \,d^{2} x}{6 c^{3}}+\frac{c^{2} d^{2} a b \arctanh \left(c x \right) x^{6}}{3}+\frac{b^{2} d^{2} x^{4}}{60}+\frac{3 b^{2} d^{2} x}{5 c^{3}}+\frac{31 b^{2} d^{2} x^{2}}{180 c^{2}}+\frac{b^{2} d^{2} x^{3}}{15 c}+\frac{2 c \,d^{2} b^{2} \arctanh \left(c x \right)^{2} x^{5}}{5}+\frac{2 d^{2} b^{2} \arctanh \left(c x \right) x^{2}}{5 c^{2}}+\frac{49 d^{2} b^{2} \arctanh \left(c x \right) \ln \left(c x -1\right)}{60 c^{4}}-\frac{d^{2} b^{2} \arctanh \left(c x \right) \ln \left(c x +1\right)}{60 c^{4}}+\frac{d^{2} a^{2} x^{4}}{4}-\frac{d^{2} b^{2} \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) \ln \left(c x +1\right)}{120 c^{4}}+\frac{d^{2} b^{2} \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{c x}{2}\right)}{120 c^{4}}+\frac{2 d^{2} a b \,x^{2}}{5 c^{2}}+\frac{c \,d^{2} a b \,x^{5}}{15}+\frac{5 d^{2} a b \,x^{3}}{18 c}-\frac{49 d^{2} b^{2} \ln \left(c x -1\right) \ln \left(\frac{1}{2}+\frac{c x}{2}\right)}{120 c^{4}}-\frac{d^{2} a b \ln \left(c x +1\right)}{60 c^{4}}+\frac{49 d^{2} a b \ln \left(c x -1\right)}{60 c^{4}}+\frac{5 b^{2} d^{2} x \arctanh \left(c x \right)}{6 c^{3}}+\frac{d^{2} a b \arctanh \left(c x \right) x^{4}}{2}+\frac{c \,d^{2} b^{2} \arctanh \left(c x \right) x^{5}}{15}+\frac{5 d^{2} b^{2} \arctanh \left(c x \right) x^{3}}{18 c}+\frac{c^{2} d^{2} b^{2} \arctanh \left(c x \right)^{2} x^{6}}{6}+\frac{4 c \,d^{2} a b \arctanh \left(c x \right) x^{5}}{5}"," ",0,"13/45/c^4*d^2*b^2*ln(c*x+1)-2/5/c^4*d^2*b^2*dilog(1/2+1/2*c*x)+1/5*d^2*b^2*arctanh(c*x)*x^4+1/4*d^2*b^2*arctanh(c*x)^2*x^4+1/6*c^2*d^2*a^2*x^6+2/5*c*d^2*a^2*x^5+1/5*d^2*a*b*x^4+1/240/c^4*d^2*b^2*ln(c*x+1)^2+49/240/c^4*d^2*b^2*ln(c*x-1)^2+8/9/c^4*d^2*b^2*ln(c*x-1)+5/6*a*b*d^2*x/c^3+5/6*b^2*d^2*x*arctanh(c*x)/c^3+1/60*b^2*d^2*x^4+3/5*b^2*d^2*x/c^3+31/180*b^2*d^2*x^2/c^2+1/15*b^2*d^2*x^3/c+4/5*c*d^2*a*b*arctanh(c*x)*x^5+1/3*c^2*d^2*a*b*arctanh(c*x)*x^6+1/4*d^2*a^2*x^4+1/2*d^2*a*b*arctanh(c*x)*x^4+1/15*c*d^2*b^2*arctanh(c*x)*x^5+5/18/c*d^2*b^2*arctanh(c*x)*x^3+1/6*c^2*d^2*b^2*arctanh(c*x)^2*x^6+2/5*c*d^2*b^2*arctanh(c*x)^2*x^5+2/5/c^2*d^2*b^2*arctanh(c*x)*x^2-1/120/c^4*d^2*b^2*ln(-1/2*c*x+1/2)*ln(c*x+1)+1/120/c^4*d^2*b^2*ln(-1/2*c*x+1/2)*ln(1/2+1/2*c*x)+2/5/c^2*d^2*a*b*x^2+1/15*c*d^2*a*b*x^5+5/18/c*d^2*a*b*x^3-49/120/c^4*d^2*b^2*ln(c*x-1)*ln(1/2+1/2*c*x)+49/60/c^4*d^2*b^2*arctanh(c*x)*ln(c*x-1)-1/60/c^4*d^2*b^2*arctanh(c*x)*ln(c*x+1)-1/60/c^4*d^2*a*b*ln(c*x+1)+49/60/c^4*d^2*a*b*ln(c*x-1)","A"
77,1,521,284,0.059000," ","int(x^2*(c*d*x+d)^2*(a+b*arctanh(c*x))^2,x)","\frac{d^{2} b^{2} \arctanh \left(c x \right) x^{3}}{3}+\frac{c \,d^{2} a^{2} x^{4}}{2}+\frac{d^{2} a b \,x^{3}}{3}+\frac{d^{2} b^{2} \arctanh \left(c x \right)^{2} x^{3}}{3}-\frac{8 d^{2} b^{2} \dilog \left(\frac{1}{2}+\frac{c x}{2}\right)}{15 c^{3}}+\frac{31 d^{2} b^{2} \ln \left(c x -1\right)^{2}}{120 c^{3}}+\frac{7 d^{2} b^{2} \ln \left(c x +1\right)}{20 c^{3}}+\frac{59 d^{2} b^{2} \ln \left(c x -1\right)}{60 c^{3}}+\frac{c^{2} d^{2} a^{2} x^{5}}{5}-\frac{d^{2} b^{2} \ln \left(c x +1\right)^{2}}{120 c^{3}}+c \,d^{2} a b \arctanh \left(c x \right) x^{4}+\frac{2 c^{2} d^{2} a b \arctanh \left(c x \right) x^{5}}{5}+\frac{b^{2} d^{2} x^{3}}{30}+\frac{19 b^{2} d^{2} x}{30 c^{2}}+\frac{b^{2} d^{2} x^{2}}{6 c}+\frac{c \,d^{2} b^{2} \arctanh \left(c x \right)^{2} x^{4}}{2}+\frac{d^{2} b^{2} \arctanh \left(c x \right) \ln \left(c x +1\right)}{30 c^{3}}+\frac{8 d^{2} b^{2} \arctanh \left(c x \right) x^{2}}{15 c}-\frac{31 d^{2} b^{2} \ln \left(c x -1\right) \ln \left(\frac{1}{2}+\frac{c x}{2}\right)}{60 c^{3}}+\frac{d^{2} a b \ln \left(c x +1\right)}{30 c^{3}}+\frac{31 d^{2} a b \ln \left(c x -1\right)}{30 c^{3}}+\frac{c \,d^{2} a b \,x^{4}}{10}+\frac{d^{2} b^{2} \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) \ln \left(c x +1\right)}{60 c^{3}}-\frac{d^{2} b^{2} \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{c x}{2}\right)}{60 c^{3}}+\frac{a b \,d^{2} x}{c^{2}}+\frac{d^{2} a^{2} x^{3}}{3}+\frac{8 d^{2} a b \,x^{2}}{15 c}+\frac{c \,d^{2} b^{2} \arctanh \left(c x \right) x^{4}}{10}+\frac{c^{2} d^{2} b^{2} \arctanh \left(c x \right)^{2} x^{5}}{5}+\frac{2 d^{2} a b \arctanh \left(c x \right) x^{3}}{3}+\frac{31 d^{2} b^{2} \arctanh \left(c x \right) \ln \left(c x -1\right)}{30 c^{3}}+\frac{b^{2} d^{2} x \arctanh \left(c x \right)}{c^{2}}"," ",0,"1/2*c*d^2*a^2*x^4+1/3*d^2*a*b*x^3+31/120/c^3*d^2*b^2*ln(c*x-1)^2+1/3*d^2*b^2*arctanh(c*x)^2*x^3+7/20/c^3*d^2*b^2*ln(c*x+1)+59/60/c^3*d^2*b^2*ln(c*x-1)+1/5*c^2*d^2*a^2*x^5-8/15/c^3*d^2*b^2*dilog(1/2+1/2*c*x)-1/120/c^3*d^2*b^2*ln(c*x+1)^2+1/3*d^2*b^2*arctanh(c*x)*x^3+c*d^2*a*b*arctanh(c*x)*x^4+2/5*c^2*d^2*a*b*arctanh(c*x)*x^5+1/30*b^2*d^2*x^3+19/30*b^2*d^2*x/c^2+1/6*b^2*d^2*x^2/c+1/2*c*d^2*b^2*arctanh(c*x)^2*x^4+1/30/c^3*d^2*b^2*arctanh(c*x)*ln(c*x+1)-31/60/c^3*d^2*b^2*ln(c*x-1)*ln(1/2+1/2*c*x)+1/30/c^3*d^2*a*b*ln(c*x+1)+31/30/c^3*d^2*a*b*ln(c*x-1)+8/15/c*d^2*b^2*arctanh(c*x)*x^2+1/10*c*d^2*b^2*arctanh(c*x)*x^4+1/5*c^2*d^2*b^2*arctanh(c*x)^2*x^5+1/10*c*d^2*a*b*x^4+2/3*d^2*a*b*arctanh(c*x)*x^3+1/60/c^3*d^2*b^2*ln(-1/2*c*x+1/2)*ln(c*x+1)-1/60/c^3*d^2*b^2*ln(-1/2*c*x+1/2)*ln(1/2+1/2*c*x)+31/30/c^3*d^2*b^2*arctanh(c*x)*ln(c*x-1)+a*b*d^2*x/c^2+b^2*d^2*x*arctanh(c*x)/c^2+1/3*d^2*a^2*x^3+8/15/c*d^2*a*b*x^2","A"
78,1,478,252,0.054000," ","int(x*(c*d*x+d)^2*(a+b*arctanh(c*x))^2,x)","\frac{4 c \,d^{2} a b \arctanh \left(c x \right) x^{3}}{3}+\frac{c^{2} d^{2} a b \arctanh \left(c x \right) x^{4}}{2}-\frac{2 d^{2} b^{2} \dilog \left(\frac{1}{2}+\frac{c x}{2}\right)}{3 c^{2}}+\frac{2 d^{2} b^{2} \arctanh \left(c x \right) x^{2}}{3}+\frac{d^{2} b^{2} \arctanh \left(c x \right)^{2} x^{2}}{2}+\frac{d^{2} b^{2} \ln \left(c x +1\right)^{2}}{48 c^{2}}+\frac{c^{2} d^{2} a^{2} x^{4}}{4}+\frac{2 c \,d^{2} a^{2} x^{3}}{3}+\frac{2 d^{2} a b \,x^{2}}{3}+\frac{17 d^{2} b^{2} \ln \left(c x -1\right)^{2}}{48 c^{2}}+\frac{d^{2} b^{2} \ln \left(c x +1\right)}{2 c^{2}}+\frac{7 d^{2} b^{2} \ln \left(c x -1\right)}{6 c^{2}}+\frac{3 a b \,d^{2} x}{2 c}+\frac{b^{2} d^{2} x^{2}}{12}+\frac{d^{2} a^{2} x^{2}}{2}+\frac{2 b^{2} d^{2} x}{3 c}+\frac{d^{2} b^{2} \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{c x}{2}\right)}{24 c^{2}}+\frac{3 b^{2} d^{2} x \arctanh \left(c x \right)}{2 c}+\frac{17 d^{2} b^{2} \arctanh \left(c x \right) \ln \left(c x -1\right)}{12 c^{2}}+\frac{c \,d^{2} b^{2} \arctanh \left(c x \right) x^{3}}{6}+d^{2} a b \arctanh \left(c x \right) x^{2}-\frac{d^{2} b^{2} \arctanh \left(c x \right) \ln \left(c x +1\right)}{12 c^{2}}+\frac{2 c \,d^{2} b^{2} \arctanh \left(c x \right)^{2} x^{3}}{3}+\frac{c^{2} d^{2} b^{2} \arctanh \left(c x \right)^{2} x^{4}}{4}+\frac{c \,d^{2} a b \,x^{3}}{6}-\frac{d^{2} a b \ln \left(c x +1\right)}{12 c^{2}}+\frac{17 d^{2} a b \ln \left(c x -1\right)}{12 c^{2}}-\frac{17 d^{2} b^{2} \ln \left(c x -1\right) \ln \left(\frac{1}{2}+\frac{c x}{2}\right)}{24 c^{2}}-\frac{d^{2} b^{2} \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) \ln \left(c x +1\right)}{24 c^{2}}"," ",0,"1/2*c^2*d^2*a*b*arctanh(c*x)*x^4+4/3*c*d^2*a*b*arctanh(c*x)*x^3+1/48/c^2*d^2*b^2*ln(c*x+1)^2+1/4*c^2*d^2*a^2*x^4+2/3*c*d^2*a^2*x^3+2/3*d^2*a*b*x^2-2/3/c^2*d^2*b^2*dilog(1/2+1/2*c*x)+2/3*d^2*b^2*arctanh(c*x)*x^2+1/2*d^2*b^2*arctanh(c*x)^2*x^2+17/48/c^2*d^2*b^2*ln(c*x-1)^2+1/2/c^2*d^2*b^2*ln(c*x+1)+7/6/c^2*d^2*b^2*ln(c*x-1)+3/2*a*b*d^2*x/c+3/2*b^2*d^2*x*arctanh(c*x)/c+1/12*b^2*d^2*x^2+1/2*d^2*a^2*x^2+2/3*b^2*d^2*x/c+1/24/c^2*d^2*b^2*ln(-1/2*c*x+1/2)*ln(1/2+1/2*c*x)+17/12/c^2*d^2*b^2*arctanh(c*x)*ln(c*x-1)+1/6*c*d^2*b^2*arctanh(c*x)*x^3+1/6*c*d^2*a*b*x^3+d^2*a*b*arctanh(c*x)*x^2-1/12/c^2*d^2*b^2*arctanh(c*x)*ln(c*x+1)-1/12/c^2*d^2*a*b*ln(c*x+1)+17/12/c^2*d^2*a*b*ln(c*x-1)+2/3*c*d^2*b^2*arctanh(c*x)^2*x^3+1/4*c^2*d^2*b^2*arctanh(c*x)^2*x^4-17/24/c^2*d^2*b^2*ln(c*x-1)*ln(1/2+1/2*c*x)-1/24/c^2*d^2*b^2*ln(-1/2*c*x+1/2)*ln(c*x+1)","A"
79,1,372,163,0.057000," ","int((c*d*x+d)^2*(a+b*arctanh(c*x))^2,x)","\frac{b^{2} d^{2} x}{3}+2 c \,d^{2} a b \arctanh \left(c x \right) x^{2}+\frac{2 c^{2} d^{2} a b \arctanh \left(c x \right) x^{3}}{3}-\frac{4 d^{2} b^{2} \dilog \left(\frac{1}{2}+\frac{c x}{2}\right)}{3 c}+2 b^{2} d^{2} x \arctanh \left(c x \right)+d^{2} b^{2} \arctanh \left(c x \right)^{2} x +\frac{d^{2} b^{2} \arctanh \left(c x \right)^{2}}{3 c}+c \,d^{2} a^{2} x^{2}+\frac{c^{2} d^{2} a^{2} x^{3}}{3}+\frac{5 d^{2} b^{2} \ln \left(c x +1\right)}{6 c}+\frac{7 d^{2} b^{2} \ln \left(c x -1\right)}{6 c}+\frac{2 d^{2} b^{2} \ln \left(c x -1\right)^{2}}{3 c}-\frac{d^{2} b^{2}}{3 c}+\frac{d^{2} a^{2}}{3 c}+x \,a^{2} d^{2}+2 a b \,d^{2} x +\frac{c \,d^{2} b^{2} \arctanh \left(c x \right) x^{2}}{3}+2 d^{2} a b \arctanh \left(c x \right) x +\frac{8 d^{2} b^{2} \arctanh \left(c x \right) \ln \left(c x -1\right)}{3 c}+\frac{2 d^{2} a b \arctanh \left(c x \right)}{3 c}+\frac{c^{2} d^{2} b^{2} \arctanh \left(c x \right)^{2} x^{3}}{3}+c \,d^{2} b^{2} \arctanh \left(c x \right)^{2} x^{2}+\frac{8 d^{2} a b \ln \left(c x -1\right)}{3 c}-\frac{4 d^{2} b^{2} \ln \left(c x -1\right) \ln \left(\frac{1}{2}+\frac{c x}{2}\right)}{3 c}+\frac{c \,d^{2} a b \,x^{2}}{3}"," ",0,"1/3*b^2*d^2*x+2/3*c^2*d^2*a*b*arctanh(c*x)*x^3+2*c*d^2*a*b*arctanh(c*x)*x^2+c*d^2*a^2*x^2+1/3*c^2*d^2*a^2*x^3+5/6/c*d^2*b^2*ln(c*x+1)+d^2*b^2*arctanh(c*x)^2*x+7/6/c*d^2*b^2*ln(c*x-1)+1/3/c*d^2*b^2*arctanh(c*x)^2-4/3/c*d^2*b^2*dilog(1/2+1/2*c*x)+2/3/c*d^2*b^2*ln(c*x-1)^2-1/3/c*d^2*b^2+1/3/c*d^2*a^2+x*a^2*d^2+2*a*b*d^2*x+2*b^2*d^2*x*arctanh(c*x)+2*d^2*a*b*arctanh(c*x)*x+8/3/c*d^2*a*b*ln(c*x-1)+8/3/c*d^2*b^2*arctanh(c*x)*ln(c*x-1)-4/3/c*d^2*b^2*ln(c*x-1)*ln(1/2+1/2*c*x)+2/3/c*d^2*a*b*arctanh(c*x)+1/3*c^2*d^2*b^2*arctanh(c*x)^2*x^3+c*d^2*b^2*arctanh(c*x)^2*x^2+1/3*c*d^2*b^2*arctanh(c*x)*x^2+1/3*c*d^2*a*b*x^2","B"
80,1,1082,268,1.099000," ","int((c*d*x+d)^2*(a+b*arctanh(c*x))^2/x,x)","\frac{5 d^{2} a b \ln \left(c x -1\right)}{2}+\frac{3 d^{2} a b \ln \left(c x +1\right)}{2}+\frac{d^{2} a^{2} c^{2} x^{2}}{2}+2 x \,a^{2} c \,d^{2}-d^{2} b^{2} \arctanh \left(c x \right) \polylog \left(2, -\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)-d^{2} a b \dilog \left(c x \right)-d^{2} a b \dilog \left(c x +1\right)+d^{2} b^{2} \arctanh \left(c x \right)^{2} \ln \left(c x \right)-d^{2} b^{2} \arctanh \left(c x \right)^{2} \ln \left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right)+d^{2} b^{2} \arctanh \left(c x \right)^{2} \ln \left(1-\frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)+2 d^{2} b^{2} \arctanh \left(c x \right) \polylog \left(2, \frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)+d^{2} b^{2} \arctanh \left(c x \right)^{2} \ln \left(1+\frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)+2 d^{2} b^{2} \arctanh \left(c x \right) \polylog \left(2, -\frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)-4 d^{2} b^{2} \arctanh \left(c x \right) \ln \left(1+\frac{i \left(c x +1\right)}{\sqrt{-c^{2} x^{2}+1}}\right)-4 d^{2} b^{2} \arctanh \left(c x \right) \ln \left(1-\frac{i \left(c x +1\right)}{\sqrt{-c^{2} x^{2}+1}}\right)+a b c \,d^{2} x -2 d^{2} b^{2} \polylog \left(3, \frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)-2 d^{2} b^{2} \polylog \left(3, -\frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)+\frac{d^{2} b^{2} \polylog \left(3, -\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}{2}+d^{2} b^{2} \arctanh \left(c x \right)+\frac{i d^{2} b^{2} \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right)\right) \mathrm{csgn}\left(\frac{i}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right)}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right) \arctanh \left(c x \right)^{2}}{2}+4 d^{2} a b \arctanh \left(c x \right) c x +d^{2} a b \arctanh \left(c x \right) c^{2} x^{2}+\frac{i d^{2} b^{2} \pi  \mathrm{csgn}\left(\frac{i \left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right)}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right)^{3} \arctanh \left(c x \right)^{2}}{2}-d^{2} b^{2} \ln \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)+d^{2} a^{2} \ln \left(c x \right)+\frac{3 d^{2} b^{2} \arctanh \left(c x \right)^{2}}{2}-4 d^{2} b^{2} \dilog \left(1+\frac{i \left(c x +1\right)}{\sqrt{-c^{2} x^{2}+1}}\right)-4 d^{2} b^{2} \dilog \left(1-\frac{i \left(c x +1\right)}{\sqrt{-c^{2} x^{2}+1}}\right)-\frac{i d^{2} b^{2} \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right)\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right)}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right)^{2} \arctanh \left(c x \right)^{2}}{2}-\frac{i d^{2} b^{2} \pi  \,\mathrm{csgn}\left(\frac{i}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right)}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right)^{2} \arctanh \left(c x \right)^{2}}{2}+2 d^{2} b^{2} \arctanh \left(c x \right)^{2} c x -d^{2} a b \ln \left(c x \right) \ln \left(c x +1\right)+b^{2} c \,d^{2} x \arctanh \left(c x \right)+2 d^{2} a b \arctanh \left(c x \right) \ln \left(c x \right)+\frac{d^{2} b^{2} \arctanh \left(c x \right)^{2} c^{2} x^{2}}{2}"," ",0,"5/2*d^2*a*b*ln(c*x-1)+3/2*d^2*a*b*ln(c*x+1)+1/2*d^2*a^2*c^2*x^2+2*x*a^2*c*d^2-d^2*b^2*arctanh(c*x)*polylog(2,-(c*x+1)^2/(-c^2*x^2+1))-4*d^2*b^2*arctanh(c*x)*ln(1+I*(c*x+1)/(-c^2*x^2+1)^(1/2))-4*d^2*b^2*arctanh(c*x)*ln(1-I*(c*x+1)/(-c^2*x^2+1)^(1/2))-d^2*a*b*dilog(c*x)-d^2*a*b*dilog(c*x+1)+d^2*b^2*arctanh(c*x)^2*ln(c*x)-d^2*b^2*arctanh(c*x)^2*ln((c*x+1)^2/(-c^2*x^2+1)-1)+d^2*b^2*arctanh(c*x)^2*ln(1-(c*x+1)/(-c^2*x^2+1)^(1/2))+2*d^2*b^2*arctanh(c*x)*polylog(2,(c*x+1)/(-c^2*x^2+1)^(1/2))+d^2*b^2*arctanh(c*x)^2*ln(1+(c*x+1)/(-c^2*x^2+1)^(1/2))+2*d^2*b^2*arctanh(c*x)*polylog(2,-(c*x+1)/(-c^2*x^2+1)^(1/2))+a*b*c*d^2*x+b^2*c*d^2*x*arctanh(c*x)+1/2*I*d^2*b^2*Pi*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1))*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))*arctanh(c*x)^2+1/2*I*d^2*b^2*Pi*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^3*arctanh(c*x)^2+4*d^2*a*b*arctanh(c*x)*c*x+d^2*a*b*arctanh(c*x)*c^2*x^2-2*d^2*b^2*polylog(3,(c*x+1)/(-c^2*x^2+1)^(1/2))-2*d^2*b^2*polylog(3,-(c*x+1)/(-c^2*x^2+1)^(1/2))+1/2*d^2*b^2*polylog(3,-(c*x+1)^2/(-c^2*x^2+1))+d^2*b^2*arctanh(c*x)-d^2*b^2*ln(1+(c*x+1)^2/(-c^2*x^2+1))-4*d^2*b^2*dilog(1+I*(c*x+1)/(-c^2*x^2+1)^(1/2))-4*d^2*b^2*dilog(1-I*(c*x+1)/(-c^2*x^2+1)^(1/2))+d^2*a^2*ln(c*x)+3/2*d^2*b^2*arctanh(c*x)^2-1/2*I*d^2*b^2*Pi*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1))*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^2*arctanh(c*x)^2-1/2*I*d^2*b^2*Pi*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^2*arctanh(c*x)^2+2*d^2*a*b*arctanh(c*x)*ln(c*x)-d^2*a*b*ln(c*x)*ln(c*x+1)+1/2*d^2*b^2*arctanh(c*x)^2*c^2*x^2+2*d^2*b^2*arctanh(c*x)^2*c*x","C"
81,1,6039,283,1.010000," ","int((c*d*x+d)^2*(a+b*arctanh(c*x))^2/x^2,x)","\text{output too large to display}"," ",0,"result too large to display","C"
82,1,1167,303,1.735000," ","int((c*d*x+d)^2*(a+b*arctanh(c*x))^2/x^3,x)","-\frac{i c^{2} d^{2} b^{2} \pi  \,\mathrm{csgn}\left(\frac{i}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right)}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right)^{2} \arctanh \left(c x \right)^{2}}{2}-\frac{i c^{2} d^{2} b^{2} \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right)\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right)}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right)^{2} \arctanh \left(c x \right)^{2}}{2}+\frac{i c^{2} d^{2} b^{2} \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right)\right) \mathrm{csgn}\left(\frac{i}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right)}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right) \arctanh \left(c x \right)^{2}}{2}-\frac{2 c \,d^{2} a^{2}}{x}-\frac{d^{2} a^{2}}{2 x^{2}}-c^{2} d^{2} a b \ln \left(c x \right) \ln \left(c x +1\right)+2 c^{2} d^{2} a b \arctanh \left(c x \right) \ln \left(c x \right)-\frac{4 c \,d^{2} a b \arctanh \left(c x \right)}{x}+4 c^{2} d^{2} b^{2} \arctanh \left(c x \right) \ln \left(1+\frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)-c^{2} d^{2} a b \dilog \left(c x +1\right)+c^{2} d^{2} b^{2} \arctanh \left(c x \right)^{2} \ln \left(1+\frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)+2 c^{2} d^{2} b^{2} \arctanh \left(c x \right) \polylog \left(2, -\frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)-\frac{d^{2} a b \arctanh \left(c x \right)}{x^{2}}-c^{2} d^{2} b^{2} \arctanh \left(c x \right) \polylog \left(2, -\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)+c^{2} d^{2} b^{2} \arctanh \left(c x \right)^{2} \ln \left(c x \right)-\frac{5 c^{2} d^{2} a b \ln \left(c x -1\right)}{2}-\frac{3 c^{2} d^{2} a b \ln \left(c x +1\right)}{2}-\frac{c \,d^{2} a b}{x}+4 c^{2} d^{2} a b \ln \left(c x \right)-c^{2} d^{2} b^{2} \arctanh \left(c x \right)^{2} \ln \left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right)+c^{2} d^{2} b^{2} \arctanh \left(c x \right)^{2} \ln \left(1-\frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)+2 c^{2} d^{2} b^{2} \arctanh \left(c x \right) \polylog \left(2, \frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)-\frac{2 c \,d^{2} b^{2} \arctanh \left(c x \right)^{2}}{x}-\frac{c \,d^{2} b^{2} \arctanh \left(c x \right)}{x}-c^{2} d^{2} a b \dilog \left(c x \right)-2 c^{2} d^{2} b^{2} \polylog \left(3, -\frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)+\frac{c^{2} d^{2} b^{2} \polylog \left(3, -\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}{2}-c^{2} d^{2} b^{2} \arctanh \left(c x \right)-4 c^{2} d^{2} b^{2} \dilog \left(\frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)+4 c^{2} d^{2} b^{2} \dilog \left(1+\frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)-\frac{d^{2} b^{2} \arctanh \left(c x \right)^{2}}{2 x^{2}}-\frac{3 c^{2} d^{2} b^{2} \arctanh \left(c x \right)^{2}}{2}-2 c^{2} d^{2} b^{2} \polylog \left(3, \frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)+c^{2} d^{2} b^{2} \ln \left(1+\frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)+c^{2} d^{2} b^{2} \ln \left(\frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}-1\right)+c^{2} d^{2} a^{2} \ln \left(c x \right)+\frac{i c^{2} d^{2} b^{2} \pi  \mathrm{csgn}\left(\frac{i \left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right)}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right)^{3} \arctanh \left(c x \right)^{2}}{2}"," ",0,"-1/2*I*c^2*d^2*b^2*Pi*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^2*arctanh(c*x)^2-1/2*I*c^2*d^2*b^2*Pi*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1))*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^2*arctanh(c*x)^2+1/2*I*c^2*d^2*b^2*Pi*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1))*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))*arctanh(c*x)^2-2*c*d^2*a^2/x-1/2*d^2*a^2/x^2+4*c^2*d^2*b^2*arctanh(c*x)*ln(1+(c*x+1)/(-c^2*x^2+1)^(1/2))-c^2*d^2*a*b*ln(c*x)*ln(c*x+1)+2*c^2*d^2*a*b*arctanh(c*x)*ln(c*x)-4*c*d^2*a*b*arctanh(c*x)/x-c^2*d^2*a*b*dilog(c*x+1)-5/2*c^2*d^2*a*b*ln(c*x-1)-3/2*c^2*d^2*a*b*ln(c*x+1)+c^2*d^2*b^2*arctanh(c*x)^2*ln(1+(c*x+1)/(-c^2*x^2+1)^(1/2))+2*c^2*d^2*b^2*arctanh(c*x)*polylog(2,-(c*x+1)/(-c^2*x^2+1)^(1/2))-c*d^2*a*b/x-d^2*a*b*arctanh(c*x)/x^2+4*c^2*d^2*a*b*ln(c*x)-c^2*d^2*b^2*arctanh(c*x)*polylog(2,-(c*x+1)^2/(-c^2*x^2+1))+c^2*d^2*b^2*arctanh(c*x)^2*ln(c*x)-c^2*d^2*b^2*arctanh(c*x)^2*ln((c*x+1)^2/(-c^2*x^2+1)-1)+c^2*d^2*b^2*arctanh(c*x)^2*ln(1-(c*x+1)/(-c^2*x^2+1)^(1/2))+2*c^2*d^2*b^2*arctanh(c*x)*polylog(2,(c*x+1)/(-c^2*x^2+1)^(1/2))-2*c*d^2*b^2*arctanh(c*x)^2/x-c*d^2*b^2*arctanh(c*x)/x-c^2*d^2*a*b*dilog(c*x)-2*c^2*d^2*b^2*polylog(3,-(c*x+1)/(-c^2*x^2+1)^(1/2))+1/2*c^2*d^2*b^2*polylog(3,-(c*x+1)^2/(-c^2*x^2+1))-c^2*d^2*b^2*arctanh(c*x)+c^2*d^2*b^2*ln(1+(c*x+1)/(-c^2*x^2+1)^(1/2))-4*c^2*d^2*b^2*dilog((c*x+1)/(-c^2*x^2+1)^(1/2))+4*c^2*d^2*b^2*dilog(1+(c*x+1)/(-c^2*x^2+1)^(1/2))+c^2*d^2*b^2*ln((c*x+1)/(-c^2*x^2+1)^(1/2)-1)-1/2*d^2*b^2*arctanh(c*x)^2/x^2-3/2*c^2*d^2*b^2*arctanh(c*x)^2+c^2*d^2*a^2*ln(c*x)-2*c^2*d^2*b^2*polylog(3,(c*x+1)/(-c^2*x^2+1)^(1/2))+1/2*I*c^2*d^2*b^2*Pi*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^3*arctanh(c*x)^2","C"
83,1,550,226,0.079000," ","int((c*d*x+d)^2*(a+b*arctanh(c*x))^2/x^4,x)","-\frac{2 c \,d^{2} a b \arctanh \left(c x \right)}{x^{2}}-\frac{2 c^{2} d^{2} a b \arctanh \left(c x \right)}{x}-\frac{5 c^{3} d^{2} b^{2} \ln \left(c x +1\right)}{6}-\frac{7 c^{3} d^{2} b^{2} \ln \left(c x -1\right)^{2}}{12}-\frac{c^{2} d^{2} a^{2}}{x}-\frac{4 c^{3} d^{2} b^{2} \dilog \left(c x \right)}{3}-\frac{4 c^{3} d^{2} b^{2} \dilog \left(c x +1\right)}{3}-\frac{d^{2} b^{2} \arctanh \left(c x \right)^{2}}{3 x^{3}}+\frac{4 c^{3} d^{2} b^{2} \dilog \left(\frac{1}{2}+\frac{c x}{2}\right)}{3}-\frac{c \,d^{2} a^{2}}{x^{2}}+2 c^{3} d^{2} b^{2} \ln \left(c x \right)+\frac{c^{3} d^{2} b^{2} \ln \left(c x +1\right)^{2}}{12}-\frac{7 c^{3} d^{2} b^{2} \ln \left(c x -1\right)}{6}-\frac{2 c^{2} d^{2} a b}{x}-\frac{b^{2} c^{2} d^{2}}{3 x}-\frac{d^{2} a^{2}}{3 x^{3}}-\frac{c^{3} d^{2} b^{2} \arctanh \left(c x \right) \ln \left(c x +1\right)}{3}+\frac{8 c^{3} d^{2} b^{2} \arctanh \left(c x \right) \ln \left(c x \right)}{3}-\frac{7 c^{3} d^{2} b^{2} \arctanh \left(c x \right) \ln \left(c x -1\right)}{3}-\frac{2 d^{2} a b \arctanh \left(c x \right)}{3 x^{3}}-\frac{c^{2} d^{2} b^{2} \arctanh \left(c x \right)^{2}}{x}+\frac{7 c^{3} d^{2} b^{2} \ln \left(c x -1\right) \ln \left(\frac{1}{2}+\frac{c x}{2}\right)}{6}-\frac{c^{3} d^{2} b^{2} \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) \ln \left(c x +1\right)}{6}+\frac{c^{3} d^{2} b^{2} \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{c x}{2}\right)}{6}+\frac{8 c^{3} d^{2} a b \ln \left(c x \right)}{3}-\frac{7 c^{3} d^{2} a b \ln \left(c x -1\right)}{3}-\frac{c^{3} d^{2} a b \ln \left(c x +1\right)}{3}-\frac{4 c^{3} d^{2} b^{2} \ln \left(c x \right) \ln \left(c x +1\right)}{3}-\frac{2 c^{2} d^{2} b^{2} \arctanh \left(c x \right)}{x}-\frac{c \,d^{2} b^{2} \arctanh \left(c x \right)^{2}}{x^{2}}-\frac{c \,d^{2} b^{2} \arctanh \left(c x \right)}{3 x^{2}}-\frac{c \,d^{2} a b}{3 x^{2}}"," ",0,"-2*c*d^2*a*b*arctanh(c*x)/x^2-2*c^2*d^2*a*b*arctanh(c*x)/x-4/3*c^3*d^2*b^2*dilog(c*x)-4/3*c^3*d^2*b^2*dilog(c*x+1)-5/6*c^3*d^2*b^2*ln(c*x+1)-7/12*c^3*d^2*b^2*ln(c*x-1)^2-1/3*d^2*b^2*arctanh(c*x)^2/x^3-c^2*d^2*a^2/x-c*d^2*a^2/x^2+2*c^3*d^2*b^2*ln(c*x)+4/3*c^3*d^2*b^2*dilog(1/2+1/2*c*x)+1/12*c^3*d^2*b^2*ln(c*x+1)^2-7/6*c^3*d^2*b^2*ln(c*x-1)-2*c^2*d^2*a*b/x-1/3*b^2*c^2*d^2/x-1/3*d^2*a^2/x^3-2*c^2*d^2*b^2*arctanh(c*x)/x-c*d^2*b^2*arctanh(c*x)^2/x^2-1/3*c*d^2*b^2*arctanh(c*x)/x^2-1/3*c^3*d^2*b^2*arctanh(c*x)*ln(c*x+1)+7/6*c^3*d^2*b^2*ln(c*x-1)*ln(1/2+1/2*c*x)-1/6*c^3*d^2*b^2*ln(-1/2*c*x+1/2)*ln(c*x+1)+1/6*c^3*d^2*b^2*ln(-1/2*c*x+1/2)*ln(1/2+1/2*c*x)+8/3*c^3*d^2*a*b*ln(c*x)-7/3*c^3*d^2*a*b*ln(c*x-1)-1/3*c^3*d^2*a*b*ln(c*x+1)-4/3*c^3*d^2*b^2*ln(c*x)*ln(c*x+1)+8/3*c^3*d^2*b^2*arctanh(c*x)*ln(c*x)-7/3*c^3*d^2*b^2*arctanh(c*x)*ln(c*x-1)-2/3*d^2*a*b*arctanh(c*x)/x^3-1/3*c*d^2*a*b/x^2-c^2*d^2*b^2*arctanh(c*x)^2/x","B"
84,1,662,373,0.060000," ","int(x^3*(c*d*x+d)^3*(a+b*arctanh(c*x))^2,x)","\frac{3 a b \,d^{3} x}{2 c^{3}}+\frac{2 c^{3} d^{3} a b \arctanh \left(c x \right) x^{7}}{7}+c^{2} d^{3} a b \arctanh \left(c x \right) x^{6}+\frac{6 c \,d^{3} a b \arctanh \left(c x \right) x^{5}}{5}+\frac{13 d^{3} a b \,x^{4}}{35}+\frac{353 d^{3} b^{2} \ln \left(c x -1\right)}{210 c^{4}}+\frac{209 d^{3} b^{2} \ln \left(c x -1\right)^{2}}{560 c^{4}}+\frac{d^{3} b^{2} \ln \left(c x +1\right)^{2}}{560 c^{4}}+\frac{109 d^{3} b^{2} \ln \left(c x +1\right)}{210 c^{4}}-\frac{26 d^{3} b^{2} \dilog \left(\frac{1}{2}+\frac{c x}{2}\right)}{35 c^{4}}+\frac{13 d^{3} b^{2} \arctanh \left(c x \right) x^{4}}{35}+\frac{d^{3} b^{2} \arctanh \left(c x \right)^{2} x^{4}}{4}+\frac{c^{3} d^{3} a^{2} x^{7}}{7}+\frac{c^{2} d^{3} a^{2} x^{6}}{2}+\frac{3 c \,d^{3} a^{2} x^{5}}{5}+\frac{b^{2} d^{3} x^{4}}{20}+\frac{d^{3} b^{2} \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{c x}{2}\right)}{280 c^{4}}+\frac{c \,d^{3} a b \,x^{5}}{5}+\frac{d^{3} a b \,x^{3}}{2 c}+\frac{26 d^{3} a b \,x^{2}}{35 c^{2}}+\frac{209 d^{3} a b \ln \left(c x -1\right)}{140 c^{4}}-\frac{d^{3} a b \ln \left(c x +1\right)}{140 c^{4}}+\frac{c^{2} d^{3} a b \,x^{6}}{21}+\frac{c^{3} d^{3} b^{2} \arctanh \left(c x \right)^{2} x^{7}}{7}+\frac{26 d^{3} b^{2} \arctanh \left(c x \right) x^{2}}{35 c^{2}}+\frac{3 c \,d^{3} b^{2} \arctanh \left(c x \right)^{2} x^{5}}{5}+\frac{c^{2} d^{3} b^{2} \arctanh \left(c x \right) x^{6}}{21}+\frac{d^{3} b^{2} \arctanh \left(c x \right) x^{3}}{2 c}-\frac{d^{3} b^{2} \arctanh \left(c x \right) \ln \left(c x +1\right)}{140 c^{4}}+\frac{d^{3} a b \arctanh \left(c x \right) x^{4}}{2}+\frac{d^{3} a^{2} x^{4}}{4}+\frac{3 b^{2} d^{3} x \arctanh \left(c x \right)}{2 c^{3}}+\frac{209 d^{3} b^{2} \arctanh \left(c x \right) \ln \left(c x -1\right)}{140 c^{4}}+\frac{c \,d^{3} b^{2} \arctanh \left(c x \right) x^{5}}{5}+\frac{c^{2} d^{3} b^{2} \arctanh \left(c x \right)^{2} x^{6}}{2}-\frac{209 d^{3} b^{2} \ln \left(c x -1\right) \ln \left(\frac{1}{2}+\frac{c x}{2}\right)}{280 c^{4}}-\frac{d^{3} b^{2} \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) \ln \left(c x +1\right)}{280 c^{4}}+\frac{122 b^{2} d^{3} x}{105 c^{3}}+\frac{7 b^{2} d^{3} x^{2}}{20 c^{2}}+\frac{44 b^{2} d^{3} x^{3}}{315 c}+\frac{b^{2} c \,d^{3} x^{5}}{105}"," ",0,"3/2*a*b*d^3*x/c^3+3/2*b^2*d^3*x*arctanh(c*x)/c^3+6/5*c*d^3*a*b*arctanh(c*x)*x^5+2/7*c^3*d^3*a*b*arctanh(c*x)*x^7+c^2*d^3*a*b*arctanh(c*x)*x^6+13/35*d^3*a*b*x^4-26/35/c^4*d^3*b^2*dilog(1/2+1/2*c*x)+353/210/c^4*d^3*b^2*ln(c*x-1)+209/560/c^4*d^3*b^2*ln(c*x-1)^2+1/560/c^4*d^3*b^2*ln(c*x+1)^2+109/210/c^4*d^3*b^2*ln(c*x+1)+13/35*d^3*b^2*arctanh(c*x)*x^4+1/4*d^3*b^2*arctanh(c*x)^2*x^4+1/7*c^3*d^3*a^2*x^7+1/2*c^2*d^3*a^2*x^6+3/5*c*d^3*a^2*x^5+1/20*b^2*d^3*x^4+1/280/c^4*d^3*b^2*ln(-1/2*c*x+1/2)*ln(1/2+1/2*c*x)+209/140/c^4*d^3*b^2*arctanh(c*x)*ln(c*x-1)+1/5*c*d^3*a*b*x^5+1/2/c*d^3*a*b*x^3+26/35/c^2*d^3*a*b*x^2+1/5*c*d^3*b^2*arctanh(c*x)*x^5+1/2*c^2*d^3*b^2*arctanh(c*x)^2*x^6+1/7*c^3*d^3*b^2*arctanh(c*x)^2*x^7+26/35/c^2*d^3*b^2*arctanh(c*x)*x^2+3/5*c*d^3*b^2*arctanh(c*x)^2*x^5+1/21*c^2*d^3*b^2*arctanh(c*x)*x^6+209/140/c^4*d^3*a*b*ln(c*x-1)-1/140/c^4*d^3*a*b*ln(c*x+1)+1/21*c^2*d^3*a*b*x^6+1/2/c*d^3*b^2*arctanh(c*x)*x^3-1/140/c^4*d^3*b^2*arctanh(c*x)*ln(c*x+1)+1/2*d^3*a*b*arctanh(c*x)*x^4+1/4*d^3*a^2*x^4-209/280/c^4*d^3*b^2*ln(c*x-1)*ln(1/2+1/2*c*x)-1/280/c^4*d^3*b^2*ln(-1/2*c*x+1/2)*ln(c*x+1)+122/105*b^2*d^3*x/c^3+7/20*b^2*d^3*x^2/c^2+44/315*b^2*d^3*x^3/c+1/105*b^2*c*d^3*x^5","A"
85,1,618,339,0.060000," ","int(x^2*(c*d*x+d)^3*(a+b*arctanh(c*x))^2,x)","\frac{11 a b \,d^{3} x}{6 c^{2}}+\frac{d^{3} b^{2} \arctanh \left(c x \right)^{2} x^{3}}{3}+\frac{11 d^{3} b^{2} \arctanh \left(c x \right) x^{3}}{18}-\frac{14 d^{3} b^{2} \dilog \left(\frac{1}{2}+\frac{c x}{2}\right)}{15 c^{3}}+\frac{11 d^{3} a b \,x^{3}}{18}+\frac{3 c \,d^{3} a^{2} x^{4}}{4}-\frac{d^{3} b^{2} \ln \left(c x +1\right)^{2}}{240 c^{3}}+\frac{23 d^{3} b^{2} \ln \left(c x +1\right)}{36 c^{3}}+\frac{37 d^{3} b^{2} \ln \left(c x -1\right)^{2}}{80 c^{3}}+\frac{337 d^{3} b^{2} \ln \left(c x -1\right)}{180 c^{3}}+\frac{c^{3} d^{3} a^{2} x^{6}}{6}+\frac{3 c^{2} d^{3} a^{2} x^{5}}{5}+\frac{6 c^{2} d^{3} a b \arctanh \left(c x \right) x^{5}}{5}+\frac{c^{3} d^{3} a b \arctanh \left(c x \right) x^{6}}{3}+\frac{3 c \,d^{3} a b \arctanh \left(c x \right) x^{4}}{2}+\frac{b^{2} d^{3} x^{3}}{10}+\frac{d^{3} a b \ln \left(c x +1\right)}{60 c^{3}}+\frac{37 d^{3} a b \ln \left(c x -1\right)}{20 c^{3}}+\frac{c^{2} d^{3} a b \,x^{5}}{15}+\frac{3 c \,d^{3} a b \,x^{4}}{10}+\frac{14 d^{3} a b \,x^{2}}{15 c}+\frac{11 b^{2} d^{3} x \arctanh \left(c x \right)}{6 c^{2}}+\frac{d^{3} b^{2} \arctanh \left(c x \right) \ln \left(c x +1\right)}{60 c^{3}}-\frac{37 d^{3} b^{2} \ln \left(c x -1\right) \ln \left(\frac{1}{2}+\frac{c x}{2}\right)}{40 c^{3}}+\frac{d^{3} b^{2} \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) \ln \left(c x +1\right)}{120 c^{3}}-\frac{d^{3} b^{2} \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{c x}{2}\right)}{120 c^{3}}+\frac{d^{3} a^{2} x^{3}}{3}+\frac{c^{2} d^{3} b^{2} \arctanh \left(c x \right) x^{5}}{15}+\frac{2 d^{3} a b \arctanh \left(c x \right) x^{3}}{3}+\frac{14 d^{3} b^{2} \arctanh \left(c x \right) x^{2}}{15 c}+\frac{3 c^{2} d^{3} b^{2} \arctanh \left(c x \right)^{2} x^{5}}{5}+\frac{3 c \,d^{3} b^{2} \arctanh \left(c x \right)^{2} x^{4}}{4}+\frac{3 c \,d^{3} b^{2} \arctanh \left(c x \right) x^{4}}{10}+\frac{37 d^{3} b^{2} \arctanh \left(c x \right) \ln \left(c x -1\right)}{20 c^{3}}+\frac{c^{3} d^{3} b^{2} \arctanh \left(c x \right)^{2} x^{6}}{6}+\frac{37 b^{2} d^{3} x}{30 c^{2}}+\frac{61 b^{2} d^{3} x^{2}}{180 c}+\frac{b^{2} c \,d^{3} x^{4}}{60}"," ",0,"11/6*a*b*d^3*x/c^2+11/6*b^2*d^3*x*arctanh(c*x)/c^2+11/18*d^3*a*b*x^3+3/4*c*d^3*a^2*x^4-1/240/c^3*d^3*b^2*ln(c*x+1)^2+1/3*d^3*b^2*arctanh(c*x)^2*x^3+11/18*d^3*b^2*arctanh(c*x)*x^3+23/36/c^3*d^3*b^2*ln(c*x+1)-14/15/c^3*d^3*b^2*dilog(1/2+1/2*c*x)+37/80/c^3*d^3*b^2*ln(c*x-1)^2+337/180/c^3*d^3*b^2*ln(c*x-1)+1/6*c^3*d^3*a^2*x^6+3/5*c^2*d^3*a^2*x^5+6/5*c^2*d^3*a*b*arctanh(c*x)*x^5+1/3*c^3*d^3*a*b*arctanh(c*x)*x^6+3/2*c*d^3*a*b*arctanh(c*x)*x^4+1/10*b^2*d^3*x^3+1/60/c^3*d^3*b^2*arctanh(c*x)*ln(c*x+1)+1/60/c^3*d^3*a*b*ln(c*x+1)+37/20/c^3*d^3*a*b*ln(c*x-1)+1/15*c^2*d^3*b^2*arctanh(c*x)*x^5+2/3*d^3*a*b*arctanh(c*x)*x^3+1/15*c^2*d^3*a*b*x^5+3/10*c*d^3*a*b*x^4+14/15/c*d^3*a*b*x^2+14/15/c*d^3*b^2*arctanh(c*x)*x^2+3/5*c^2*d^3*b^2*arctanh(c*x)^2*x^5+3/4*c*d^3*b^2*arctanh(c*x)^2*x^4+3/10*c*d^3*b^2*arctanh(c*x)*x^4-37/40/c^3*d^3*b^2*ln(c*x-1)*ln(1/2+1/2*c*x)+1/120/c^3*d^3*b^2*ln(-1/2*c*x+1/2)*ln(c*x+1)-1/120/c^3*d^3*b^2*ln(-1/2*c*x+1/2)*ln(1/2+1/2*c*x)+37/20/c^3*d^3*b^2*arctanh(c*x)*ln(c*x-1)+1/6*c^3*d^3*b^2*arctanh(c*x)^2*x^6+1/3*d^3*a^2*x^3+37/30*b^2*d^3*x/c^2+61/180*b^2*d^3*x^2/c+1/60*b^2*c*d^3*x^4","A"
86,1,570,258,0.061000," ","int(x*(c*d*x+d)^3*(a+b*arctanh(c*x))^2,x)","\frac{5 a b \,d^{3} x}{2 c}+\frac{d^{3} b^{2} \arctanh \left(c x \right)^{2} x^{2}}{2}+\frac{6 d^{3} b^{2} \arctanh \left(c x \right) x^{2}}{5}-\frac{6 d^{3} b^{2} \dilog \left(\frac{1}{2}+\frac{c x}{2}\right)}{5 c^{2}}+\frac{49 d^{3} b^{2} \ln \left(c x -1\right)^{2}}{80 c^{2}}+\frac{17 d^{3} b^{2} \ln \left(c x +1\right)}{20 c^{2}}+\frac{d^{3} b^{2} \ln \left(c x +1\right)^{2}}{80 c^{2}}+\frac{c^{3} d^{3} a^{2} x^{5}}{5}+\frac{3 c^{2} d^{3} a^{2} x^{4}}{4}+c \,d^{3} a^{2} x^{3}+\frac{6 d^{3} a b \,x^{2}}{5}+\frac{43 d^{3} b^{2} \ln \left(c x -1\right)}{20 c^{2}}+\frac{3 c^{2} d^{3} a b \arctanh \left(c x \right) x^{4}}{2}+\frac{2 c^{3} d^{3} a b \arctanh \left(c x \right) x^{5}}{5}+\frac{b^{2} d^{3} x^{2}}{4}+\frac{3 c^{2} d^{3} b^{2} \arctanh \left(c x \right)^{2} x^{4}}{4}+\frac{c \,d^{3} b^{2} \arctanh \left(c x \right) x^{3}}{2}+\frac{c^{3} d^{3} b^{2} \arctanh \left(c x \right)^{2} x^{5}}{5}+\frac{c^{2} d^{3} b^{2} \arctanh \left(c x \right) x^{4}}{10}+\frac{49 d^{3} b^{2} \arctanh \left(c x \right) \ln \left(c x -1\right)}{20 c^{2}}-\frac{d^{3} b^{2} \arctanh \left(c x \right) \ln \left(c x +1\right)}{20 c^{2}}+d^{3} a b \arctanh \left(c x \right) x^{2}+c \,d^{3} b^{2} \arctanh \left(c x \right)^{2} x^{3}+\frac{5 b^{2} d^{3} x \arctanh \left(c x \right)}{2 c}-\frac{49 d^{3} b^{2} \ln \left(c x -1\right) \ln \left(\frac{1}{2}+\frac{c x}{2}\right)}{40 c^{2}}-\frac{d^{3} b^{2} \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) \ln \left(c x +1\right)}{40 c^{2}}+\frac{d^{3} b^{2} \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{c x}{2}\right)}{40 c^{2}}+\frac{c^{2} d^{3} a b \,x^{4}}{10}+\frac{c \,d^{3} a b \,x^{3}}{2}-\frac{d^{3} a b \ln \left(c x +1\right)}{20 c^{2}}+\frac{49 d^{3} a b \ln \left(c x -1\right)}{20 c^{2}}+\frac{d^{3} a^{2} x^{2}}{2}+\frac{13 b^{2} d^{3} x}{10 c}+\frac{b^{2} c \,d^{3} x^{3}}{30}+2 c \,d^{3} a b \arctanh \left(c x \right) x^{3}"," ",0,"5/2*a*b*d^3*x/c+5/2*b^2*d^3*x*arctanh(c*x)/c+49/80/c^2*d^3*b^2*ln(c*x-1)^2+17/20/c^2*d^3*b^2*ln(c*x+1)+1/80/c^2*d^3*b^2*ln(c*x+1)^2+1/2*d^3*b^2*arctanh(c*x)^2*x^2+6/5*d^3*b^2*arctanh(c*x)*x^2+1/5*c^3*d^3*a^2*x^5+3/4*c^2*d^3*a^2*x^4+c*d^3*a^2*x^3+6/5*d^3*a*b*x^2-6/5/c^2*d^3*b^2*dilog(1/2+1/2*c*x)+43/20/c^2*d^3*b^2*ln(c*x-1)+3/2*c^2*d^3*a*b*arctanh(c*x)*x^4+2/5*c^3*d^3*a*b*arctanh(c*x)*x^5+2*c*d^3*a*b*arctanh(c*x)*x^3+1/4*b^2*d^3*x^2+3/4*c^2*d^3*b^2*arctanh(c*x)^2*x^4+1/2*c*d^3*b^2*arctanh(c*x)*x^3+1/5*c^3*d^3*b^2*arctanh(c*x)^2*x^5+1/10*c^2*d^3*b^2*arctanh(c*x)*x^4-49/40/c^2*d^3*b^2*ln(c*x-1)*ln(1/2+1/2*c*x)-1/40/c^2*d^3*b^2*ln(-1/2*c*x+1/2)*ln(c*x+1)+1/40/c^2*d^3*b^2*ln(-1/2*c*x+1/2)*ln(1/2+1/2*c*x)+49/20/c^2*d^3*b^2*arctanh(c*x)*ln(c*x-1)-1/20/c^2*d^3*b^2*arctanh(c*x)*ln(c*x+1)+1/10*c^2*d^3*a*b*x^4+1/2*c*d^3*a*b*x^3+d^3*a*b*arctanh(c*x)*x^2-1/20/c^2*d^3*a*b*ln(c*x+1)+49/20/c^2*d^3*a*b*ln(c*x-1)+c*d^3*b^2*arctanh(c*x)^2*x^3+1/2*d^3*a^2*x^2+13/10*b^2*d^3*x/c+1/30*b^2*c*d^3*x^3","B"
87,1,462,194,0.056000," ","int((c*d*x+d)^3*(a+b*arctanh(c*x))^2,x)","b^{2} d^{3} x +\frac{c^{3} d^{3} a b \arctanh \left(c x \right) x^{4}}{2}+d^{3} b^{2} \arctanh \left(c x \right)^{2} x +\frac{d^{3} b^{2} \arctanh \left(c x \right)^{2}}{4 c}-\frac{2 d^{3} b^{2} \dilog \left(\frac{1}{2}+\frac{c x}{2}\right)}{c}+\frac{7 b^{2} d^{3} x \arctanh \left(c x \right)}{2}+\frac{3 c \,d^{3} a^{2} x^{2}}{2}+c^{2} d^{3} a^{2} x^{3}+\frac{d^{3} b^{2} \ln \left(c x -1\right)^{2}}{c}+\frac{c^{3} d^{3} a^{2} x^{4}}{4}+\frac{7 d^{3} b^{2} \ln \left(c x -1\right)}{3 c}+\frac{4 d^{3} b^{2} \ln \left(c x +1\right)}{3 c}+3 c \,d^{3} a b \arctanh \left(c x \right) x^{2}+2 c^{2} d^{3} a b \arctanh \left(c x \right) x^{3}-\frac{13 d^{3} b^{2}}{12 c}+\frac{d^{3} a^{2}}{4 c}+\frac{4 d^{3} a b \ln \left(c x -1\right)}{c}+\frac{4 d^{3} b^{2} \arctanh \left(c x \right) \ln \left(c x -1\right)}{c}+\frac{d^{3} a b \arctanh \left(c x \right)}{2 c}+c^{2} d^{3} b^{2} \arctanh \left(c x \right)^{2} x^{3}+2 d^{3} a b \arctanh \left(c x \right) x +\frac{c^{2} d^{3} b^{2} \arctanh \left(c x \right) x^{3}}{6}+c \,d^{3} b^{2} \arctanh \left(c x \right) x^{2}+\frac{c^{3} d^{3} b^{2} \arctanh \left(c x \right)^{2} x^{4}}{4}+\frac{3 c \,d^{3} b^{2} \arctanh \left(c x \right)^{2} x^{2}}{2}+a^{2} x \,d^{3}+\frac{c^{2} d^{3} a b \,x^{3}}{6}+c \,d^{3} a b \,x^{2}-\frac{2 d^{3} b^{2} \ln \left(c x -1\right) \ln \left(\frac{1}{2}+\frac{c x}{2}\right)}{c}+\frac{7 a b \,d^{3} x}{2}+\frac{b^{2} c \,d^{3} x^{2}}{12}"," ",0,"b^2*d^3*x+1/2*c^3*d^3*a*b*arctanh(c*x)*x^4+2*c^2*d^3*a*b*arctanh(c*x)*x^3+3*c*d^3*a*b*arctanh(c*x)*x^2+3/2*c*d^3*a^2*x^2+c^2*d^3*a^2*x^3+1/c*d^3*b^2*ln(c*x-1)^2+1/4*c^3*d^3*a^2*x^4+d^3*b^2*arctanh(c*x)^2*x+7/3/c*d^3*b^2*ln(c*x-1)+1/4/c*d^3*b^2*arctanh(c*x)^2+4/3/c*d^3*b^2*ln(c*x+1)-2/c*d^3*b^2*dilog(1/2+1/2*c*x)+7/2*b^2*d^3*x*arctanh(c*x)-13/12/c*d^3*b^2+1/4/c*d^3*a^2+4/c*d^3*b^2*arctanh(c*x)*ln(c*x-1)+1/2/c*d^3*a*b*arctanh(c*x)+4/c*d^3*a*b*ln(c*x-1)+c^2*d^3*b^2*arctanh(c*x)^2*x^3+a^2*x*d^3+2*d^3*a*b*arctanh(c*x)*x+1/6*c^2*d^3*b^2*arctanh(c*x)*x^3+1/6*c^2*d^3*a*b*x^3+c*d^3*a*b*x^2+c*d^3*b^2*arctanh(c*x)*x^2+1/4*c^3*d^3*b^2*arctanh(c*x)^2*x^4+3/2*c*d^3*b^2*arctanh(c*x)^2*x^2-2/c*d^3*b^2*ln(c*x-1)*ln(1/2+1/2*c*x)+7/2*a*b*d^3*x+1/12*b^2*c*d^3*x^2","B"
88,1,1186,333,1.527000," ","int((c*d*x+d)^3*(a+b*arctanh(c*x))^2/x,x)","\frac{3 d^{3} a^{2} c^{2} x^{2}}{2}-\frac{d^{3} b^{2}}{3}+3 a b c \,d^{3} x +\frac{8 b^{2} d^{3} \arctanh \left(c x \right)}{3}+\frac{11 d^{3} b^{2} \arctanh \left(c x \right)^{2}}{6}+\frac{d^{3} b^{2} \polylog \left(3, -\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}{2}-2 d^{3} b^{2} \polylog \left(3, \frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)-2 d^{3} b^{2} \polylog \left(3, -\frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)+\frac{i d^{3} b^{2} \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right)\right) \mathrm{csgn}\left(\frac{i}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right)}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right) \arctanh \left(c x \right)^{2}}{2}+\frac{29 d^{3} a b \ln \left(c x -1\right)}{6}+\frac{11 d^{3} a b \ln \left(c x +1\right)}{6}+\frac{d^{3} a^{2} c^{3} x^{3}}{3}+\frac{b^{2} c \,d^{3} x}{3}-\frac{20 d^{3} b^{2} \dilog \left(1+\frac{i \left(c x +1\right)}{\sqrt{-c^{2} x^{2}+1}}\right)}{3}-\frac{20 d^{3} b^{2} \dilog \left(1-\frac{i \left(c x +1\right)}{\sqrt{-c^{2} x^{2}+1}}\right)}{3}+\frac{d^{3} a b \,c^{2} x^{2}}{3}-d^{3} a b \ln \left(c x \right) \ln \left(c x +1\right)-\frac{i d^{3} b^{2} \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right)\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right)}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right)^{2} \arctanh \left(c x \right)^{2}}{2}+d^{3} a^{2} \ln \left(c x \right)+3 x \,a^{2} c \,d^{3}+\frac{d^{3} b^{2} \arctanh \left(c x \right)^{2} c^{3} x^{3}}{3}+\frac{d^{3} b^{2} \arctanh \left(c x \right) c^{2} x^{2}}{3}+2 d^{3} a b \arctanh \left(c x \right) \ln \left(c x \right)+3 b^{2} c \,d^{3} x \arctanh \left(c x \right)+3 d^{3} b^{2} \arctanh \left(c x \right)^{2} c x +\frac{3 d^{3} b^{2} \arctanh \left(c x \right)^{2} c^{2} x^{2}}{2}-d^{3} a b \dilog \left(c x +1\right)+d^{3} b^{2} \arctanh \left(c x \right)^{2} \ln \left(1+\frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)+d^{3} b^{2} \arctanh \left(c x \right)^{2} \ln \left(1-\frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)+2 d^{3} b^{2} \arctanh \left(c x \right) \polylog \left(2, \frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)+d^{3} b^{2} \arctanh \left(c x \right)^{2} \ln \left(c x \right)-d^{3} b^{2} \arctanh \left(c x \right)^{2} \ln \left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right)+2 d^{3} b^{2} \arctanh \left(c x \right) \polylog \left(2, -\frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)-d^{3} b^{2} \arctanh \left(c x \right) \polylog \left(2, -\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)-d^{3} a b \dilog \left(c x \right)-\frac{20 d^{3} b^{2} \arctanh \left(c x \right) \ln \left(1+\frac{i \left(c x +1\right)}{\sqrt{-c^{2} x^{2}+1}}\right)}{3}-\frac{20 d^{3} b^{2} \arctanh \left(c x \right) \ln \left(1-\frac{i \left(c x +1\right)}{\sqrt{-c^{2} x^{2}+1}}\right)}{3}-3 d^{3} b^{2} \ln \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)-\frac{i d^{3} b^{2} \pi  \,\mathrm{csgn}\left(\frac{i}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right)}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right)^{2} \arctanh \left(c x \right)^{2}}{2}+\frac{i d^{3} b^{2} \pi  \mathrm{csgn}\left(\frac{i \left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right)}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right)^{3} \arctanh \left(c x \right)^{2}}{2}+6 d^{3} a b \arctanh \left(c x \right) c x +3 d^{3} a b \arctanh \left(c x \right) c^{2} x^{2}+\frac{2 d^{3} a b \arctanh \left(c x \right) c^{3} x^{3}}{3}"," ",0,"3/2*d^3*a^2*c^2*x^2-1/3*d^3*b^2+3*a*b*c*d^3*x+3*b^2*c*d^3*x*arctanh(c*x)-1/2*I*d^3*b^2*Pi*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1))*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^2*arctanh(c*x)^2+1/2*I*d^3*b^2*Pi*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1))*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))*arctanh(c*x)^2+29/6*d^3*a*b*ln(c*x-1)+11/6*d^3*a*b*ln(c*x+1)+1/3*d^3*a^2*c^3*x^3+1/3*b^2*c*d^3*x+8/3*b^2*d^3*arctanh(c*x)+3*d^3*b^2*arctanh(c*x)^2*c*x+1/3*d^3*a*b*c^2*x^2+3/2*d^3*b^2*arctanh(c*x)^2*c^2*x^2+1/3*d^3*b^2*arctanh(c*x)^2*c^3*x^3+1/3*d^3*b^2*arctanh(c*x)*c^2*x^2+2*d^3*a*b*arctanh(c*x)*ln(c*x)-d^3*a*b*ln(c*x)*ln(c*x+1)-1/2*I*d^3*b^2*Pi*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^2*arctanh(c*x)^2+d^3*a^2*ln(c*x)+11/6*d^3*b^2*arctanh(c*x)^2+3*x*a^2*c*d^3-d^3*a*b*dilog(c*x+1)+d^3*b^2*arctanh(c*x)^2*ln(1+(c*x+1)/(-c^2*x^2+1)^(1/2))+d^3*b^2*arctanh(c*x)^2*ln(1-(c*x+1)/(-c^2*x^2+1)^(1/2))+2*d^3*b^2*arctanh(c*x)*polylog(2,(c*x+1)/(-c^2*x^2+1)^(1/2))+d^3*b^2*arctanh(c*x)^2*ln(c*x)-20/3*d^3*b^2*arctanh(c*x)*ln(1+I*(c*x+1)/(-c^2*x^2+1)^(1/2))-20/3*d^3*b^2*arctanh(c*x)*ln(1-I*(c*x+1)/(-c^2*x^2+1)^(1/2))-d^3*b^2*arctanh(c*x)^2*ln((c*x+1)^2/(-c^2*x^2+1)-1)+2*d^3*b^2*arctanh(c*x)*polylog(2,-(c*x+1)/(-c^2*x^2+1)^(1/2))-d^3*b^2*arctanh(c*x)*polylog(2,-(c*x+1)^2/(-c^2*x^2+1))-d^3*a*b*dilog(c*x)-20/3*d^3*b^2*dilog(1+I*(c*x+1)/(-c^2*x^2+1)^(1/2))-20/3*d^3*b^2*dilog(1-I*(c*x+1)/(-c^2*x^2+1)^(1/2))+1/2*d^3*b^2*polylog(3,-(c*x+1)^2/(-c^2*x^2+1))-2*d^3*b^2*polylog(3,(c*x+1)/(-c^2*x^2+1)^(1/2))-2*d^3*b^2*polylog(3,-(c*x+1)/(-c^2*x^2+1)^(1/2))-3*d^3*b^2*ln(1+(c*x+1)^2/(-c^2*x^2+1))+6*d^3*a*b*arctanh(c*x)*c*x+3*d^3*a*b*arctanh(c*x)*c^2*x^2+2/3*d^3*a*b*arctanh(c*x)*c^3*x^3+1/2*I*d^3*b^2*Pi*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^3*arctanh(c*x)^2","C"
89,1,1270,351,1.939000," ","int((c*d*x+d)^3*(a+b*arctanh(c*x))^2/x^2,x)","\frac{d^{3} a^{2} c^{3} x^{2}}{2}+3 x \,a^{2} c^{2} d^{3}+3 c \,d^{3} a^{2} \ln \left(c x \right)-c \,d^{3} b^{2} \ln \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)+a b \,c^{2} d^{3} x -3 c \,d^{3} a b \ln \left(c x \right) \ln \left(c x +1\right)+6 c \,d^{3} a b \arctanh \left(c x \right) \ln \left(c x \right)+6 d^{3} a b \arctanh \left(c x \right) c^{2} x +d^{3} a b \arctanh \left(c x \right) c^{3} x^{2}+\frac{3 i c \,d^{3} b^{2} \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right)\right) \mathrm{csgn}\left(\frac{i}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right)}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right) \arctanh \left(c x \right)^{2}}{2}-\frac{d^{3} b^{2} \arctanh \left(c x \right)^{2}}{x}+\frac{3 c \,d^{3} b^{2} \arctanh \left(c x \right)^{2}}{2}+c \,d^{3} b^{2} \arctanh \left(c x \right)+\frac{3 c \,d^{3} b^{2} \polylog \left(3, -\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}{2}-6 c \,d^{3} b^{2} \polylog \left(3, \frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)-6 c \,d^{3} b^{2} \polylog \left(3, -\frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)-2 c \,d^{3} b^{2} \dilog \left(\frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)+b^{2} c^{2} d^{3} x \arctanh \left(c x \right)+\frac{d^{3} b^{2} \arctanh \left(c x \right)^{2} c^{3} x^{2}}{2}-3 c \,d^{3} a b \dilog \left(c x +1\right)-3 c \,d^{3} a b \dilog \left(c x \right)+3 c \,d^{3} b^{2} \arctanh \left(c x \right)^{2} \ln \left(1+\frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)+3 c \,d^{3} b^{2} \arctanh \left(c x \right)^{2} \ln \left(1-\frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)+6 c \,d^{3} b^{2} \arctanh \left(c x \right) \polylog \left(2, \frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)+3 c \,d^{3} b^{2} \arctanh \left(c x \right)^{2} \ln \left(c x \right)-\frac{2 d^{3} a b \arctanh \left(c x \right)}{x}-3 c \,d^{3} b^{2} \arctanh \left(c x \right)^{2} \ln \left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right)+6 c \,d^{3} b^{2} \arctanh \left(c x \right) \polylog \left(2, -\frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)-3 c \,d^{3} b^{2} \arctanh \left(c x \right) \polylog \left(2, -\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)+2 c \,d^{3} b^{2} \arctanh \left(c x \right) \ln \left(1+\frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)+3 d^{3} b^{2} \arctanh \left(c x \right)^{2} c^{2} x -6 c \,d^{3} b^{2} \arctanh \left(c x \right) \ln \left(1+\frac{i \left(c x +1\right)}{\sqrt{-c^{2} x^{2}+1}}\right)-6 c \,d^{3} b^{2} \arctanh \left(c x \right) \ln \left(1-\frac{i \left(c x +1\right)}{\sqrt{-c^{2} x^{2}+1}}\right)+\frac{5 c \,d^{3} a b \ln \left(c x -1\right)}{2}+\frac{3 c \,d^{3} a b \ln \left(c x +1\right)}{2}+2 c \,d^{3} a b \ln \left(c x \right)+\frac{3 i c \,d^{3} b^{2} \pi  \mathrm{csgn}\left(\frac{i \left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right)}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right)^{3} \arctanh \left(c x \right)^{2}}{2}+2 c \,d^{3} b^{2} \dilog \left(1+\frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)-6 c \,d^{3} b^{2} \dilog \left(1+\frac{i \left(c x +1\right)}{\sqrt{-c^{2} x^{2}+1}}\right)-6 c \,d^{3} b^{2} \dilog \left(1-\frac{i \left(c x +1\right)}{\sqrt{-c^{2} x^{2}+1}}\right)-\frac{d^{3} a^{2}}{x}-\frac{3 i c \,d^{3} b^{2} \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right)\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right)}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right)^{2} \arctanh \left(c x \right)^{2}}{2}-\frac{3 i c \,d^{3} b^{2} \pi  \,\mathrm{csgn}\left(\frac{i}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right)}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right)^{2} \arctanh \left(c x \right)^{2}}{2}"," ",0,"1/2*d^3*a^2*c^3*x^2+3*x*a^2*c^2*d^3-d^3*b^2*arctanh(c*x)^2/x+3/2*c*d^3*b^2*arctanh(c*x)^2+c*d^3*b^2*arctanh(c*x)-6*c*d^3*b^2*dilog(1+I*(c*x+1)/(-c^2*x^2+1)^(1/2))-6*c*d^3*b^2*dilog(1-I*(c*x+1)/(-c^2*x^2+1)^(1/2))+3/2*c*d^3*b^2*polylog(3,-(c*x+1)^2/(-c^2*x^2+1))-6*c*d^3*b^2*polylog(3,(c*x+1)/(-c^2*x^2+1)^(1/2))-6*c*d^3*b^2*polylog(3,-(c*x+1)/(-c^2*x^2+1)^(1/2))+3*c*d^3*a^2*ln(c*x)-c*d^3*b^2*ln(1+(c*x+1)^2/(-c^2*x^2+1))-2*c*d^3*b^2*dilog((c*x+1)/(-c^2*x^2+1)^(1/2))+2*c*d^3*b^2*dilog(1+(c*x+1)/(-c^2*x^2+1)^(1/2))+a*b*c^2*d^3*x+b^2*c^2*d^3*x*arctanh(c*x)+6*c*d^3*a*b*arctanh(c*x)*ln(c*x)-3*c*d^3*a*b*ln(c*x)*ln(c*x+1)+6*d^3*a*b*arctanh(c*x)*c^2*x+d^3*a*b*arctanh(c*x)*c^3*x^2+3/2*I*c*d^3*b^2*Pi*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1))*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))*arctanh(c*x)^2+1/2*d^3*b^2*arctanh(c*x)^2*c^3*x^2+5/2*c*d^3*a*b*ln(c*x-1)+3/2*c*d^3*a*b*ln(c*x+1)-3*c*d^3*a*b*dilog(c*x+1)-3*c*d^3*a*b*dilog(c*x)+2*c*d^3*a*b*ln(c*x)+3*c*d^3*b^2*arctanh(c*x)^2*ln(1+(c*x+1)/(-c^2*x^2+1)^(1/2))+3*c*d^3*b^2*arctanh(c*x)^2*ln(1-(c*x+1)/(-c^2*x^2+1)^(1/2))+6*c*d^3*b^2*arctanh(c*x)*polylog(2,(c*x+1)/(-c^2*x^2+1)^(1/2))+3*c*d^3*b^2*arctanh(c*x)^2*ln(c*x)-2*d^3*a*b*arctanh(c*x)/x-6*c*d^3*b^2*arctanh(c*x)*ln(1+I*(c*x+1)/(-c^2*x^2+1)^(1/2))-6*c*d^3*b^2*arctanh(c*x)*ln(1-I*(c*x+1)/(-c^2*x^2+1)^(1/2))-3*c*d^3*b^2*arctanh(c*x)^2*ln((c*x+1)^2/(-c^2*x^2+1)-1)+6*c*d^3*b^2*arctanh(c*x)*polylog(2,-(c*x+1)/(-c^2*x^2+1)^(1/2))-3*c*d^3*b^2*arctanh(c*x)*polylog(2,-(c*x+1)^2/(-c^2*x^2+1))+2*c*d^3*b^2*arctanh(c*x)*ln(1+(c*x+1)/(-c^2*x^2+1)^(1/2))+3*d^3*b^2*arctanh(c*x)^2*c^2*x+3/2*I*c*d^3*b^2*Pi*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^3*arctanh(c*x)^2-d^3*a^2/x-3/2*I*c*d^3*b^2*Pi*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^2*arctanh(c*x)^2-3/2*I*c*d^3*b^2*Pi*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1))*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^2*arctanh(c*x)^2","C"
90,1,1358,375,1.763000," ","int((c*d*x+d)^3*(a+b*arctanh(c*x))^2/x^3,x)","6 c^{2} d^{3} a b \ln \left(c x \right)-\frac{3 c^{2} d^{3} a b \ln \left(c x +1\right)}{2}-\frac{5 c^{2} d^{3} a b \ln \left(c x -1\right)}{2}-\frac{c \,d^{3} a b}{x}+3 c^{2} d^{3} b^{2} \arctanh \left(c x \right)^{2} \ln \left(1-\frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)+6 c^{2} d^{3} b^{2} \arctanh \left(c x \right) \polylog \left(2, \frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)+3 c^{2} d^{3} b^{2} \arctanh \left(c x \right)^{2} \ln \left(c x \right)-3 c^{2} d^{3} b^{2} \arctanh \left(c x \right)^{2} \ln \left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right)+6 c^{2} d^{3} b^{2} \arctanh \left(c x \right) \polylog \left(2, -\frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)-3 c^{2} d^{3} b^{2} \arctanh \left(c x \right) \polylog \left(2, -\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)-3 c^{2} d^{3} a b \dilog \left(c x +1\right)-3 c^{2} d^{3} a b \dilog \left(c x \right)-\frac{d^{3} a b \arctanh \left(c x \right)}{x^{2}}+c^{3} d^{3} b^{2} \arctanh \left(c x \right)^{2} x -\frac{c \,d^{3} b^{2} \arctanh \left(c x \right)}{x}-\frac{3 c \,d^{3} b^{2} \arctanh \left(c x \right)^{2}}{x}+6 c^{2} d^{3} b^{2} \arctanh \left(c x \right) \ln \left(1+\frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)+3 c^{2} d^{3} b^{2} \arctanh \left(c x \right)^{2} \ln \left(1+\frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)-2 c^{2} d^{3} b^{2} \arctanh \left(c x \right) \ln \left(1+\frac{i \left(c x +1\right)}{\sqrt{-c^{2} x^{2}+1}}\right)-2 c^{2} d^{3} b^{2} \arctanh \left(c x \right) \ln \left(1-\frac{i \left(c x +1\right)}{\sqrt{-c^{2} x^{2}+1}}\right)-\frac{3 i c^{2} d^{3} b^{2} \pi  \,\mathrm{csgn}\left(\frac{i}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right)}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right)^{2} \arctanh \left(c x \right)^{2}}{2}-\frac{3 i c^{2} d^{3} b^{2} \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right)\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right)}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right)^{2} \arctanh \left(c x \right)^{2}}{2}+\frac{3 i c^{2} d^{3} b^{2} \pi  \mathrm{csgn}\left(\frac{i \left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right)}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right)^{3} \arctanh \left(c x \right)^{2}}{2}+2 c^{3} d^{3} a b \arctanh \left(c x \right) x -\frac{6 c \,d^{3} a b \arctanh \left(c x \right)}{x}+6 c^{2} d^{3} a b \arctanh \left(c x \right) \ln \left(c x \right)-3 c^{2} d^{3} a b \ln \left(c x \right) \ln \left(c x +1\right)+\frac{3 i c^{2} d^{3} b^{2} \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right)\right) \mathrm{csgn}\left(\frac{i}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right)}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right) \arctanh \left(c x \right)^{2}}{2}-2 c^{2} d^{3} b^{2} \dilog \left(1-\frac{i \left(c x +1\right)}{\sqrt{-c^{2} x^{2}+1}}\right)-6 c^{2} d^{3} b^{2} \polylog \left(3, -\frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)-6 c^{2} d^{3} b^{2} \dilog \left(\frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)+6 c^{2} d^{3} b^{2} \dilog \left(1+\frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)-c^{2} d^{3} b^{2} \arctanh \left(c x \right)-\frac{d^{3} b^{2} \arctanh \left(c x \right)^{2}}{2 x^{2}}-\frac{3 c^{2} d^{3} b^{2} \arctanh \left(c x \right)^{2}}{2}-2 c^{2} d^{3} b^{2} \dilog \left(1+\frac{i \left(c x +1\right)}{\sqrt{-c^{2} x^{2}+1}}\right)+\frac{3 c^{2} d^{3} b^{2} \polylog \left(3, -\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}{2}-6 c^{2} d^{3} b^{2} \polylog \left(3, \frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)-\frac{d^{3} a^{2}}{2 x^{2}}+3 c^{2} d^{3} a^{2} \ln \left(c x \right)+c^{2} d^{3} b^{2} \ln \left(1+\frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)+c^{2} d^{3} b^{2} \ln \left(\frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}-1\right)+c^{3} x \,a^{2} d^{3}-\frac{3 c \,d^{3} a^{2}}{x}"," ",0,"3*c^2*d^3*b^2*arctanh(c*x)^2*ln(1-(c*x+1)/(-c^2*x^2+1)^(1/2))+6*c^2*d^3*b^2*arctanh(c*x)*polylog(2,(c*x+1)/(-c^2*x^2+1)^(1/2))+3*c^2*d^3*b^2*arctanh(c*x)^2*ln(c*x)-2*c^2*d^3*b^2*arctanh(c*x)*ln(1+I*(c*x+1)/(-c^2*x^2+1)^(1/2))-2*c^2*d^3*b^2*arctanh(c*x)*ln(1-I*(c*x+1)/(-c^2*x^2+1)^(1/2))-3*c^2*d^3*b^2*arctanh(c*x)^2*ln((c*x+1)^2/(-c^2*x^2+1)-1)+6*c^2*d^3*b^2*arctanh(c*x)*polylog(2,-(c*x+1)/(-c^2*x^2+1)^(1/2))-3*c^2*d^3*b^2*arctanh(c*x)*polylog(2,-(c*x+1)^2/(-c^2*x^2+1))-3*c^2*d^3*a*b*dilog(c*x+1)-3*c^2*d^3*a*b*dilog(c*x)+6*c^2*d^3*a*b*ln(c*x)-3/2*c^2*d^3*a*b*ln(c*x+1)-5/2*c^2*d^3*a*b*ln(c*x-1)-d^3*a*b*arctanh(c*x)/x^2-c*d^3*a*b/x+3/2*I*c^2*d^3*b^2*Pi*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1))*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))*arctanh(c*x)^2+c^3*d^3*b^2*arctanh(c*x)^2*x-c*d^3*b^2*arctanh(c*x)/x-3*c*d^3*b^2*arctanh(c*x)^2/x+6*c^2*d^3*b^2*arctanh(c*x)*ln(1+(c*x+1)/(-c^2*x^2+1)^(1/2))+3*c^2*d^3*b^2*arctanh(c*x)^2*ln(1+(c*x+1)/(-c^2*x^2+1)^(1/2))+2*c^3*d^3*a*b*arctanh(c*x)*x-6*c*d^3*a*b*arctanh(c*x)/x+6*c^2*d^3*a*b*arctanh(c*x)*ln(c*x)-3*c^2*d^3*a*b*ln(c*x)*ln(c*x+1)-3/2*I*c^2*d^3*b^2*Pi*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^2*arctanh(c*x)^2-3/2*I*c^2*d^3*b^2*Pi*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1))*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^2*arctanh(c*x)^2+3/2*I*c^2*d^3*b^2*Pi*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^3*arctanh(c*x)^2-1/2*d^3*a^2/x^2+3/2*c^2*d^3*b^2*polylog(3,-(c*x+1)^2/(-c^2*x^2+1))-6*c^2*d^3*b^2*polylog(3,(c*x+1)/(-c^2*x^2+1)^(1/2))-6*c^2*d^3*b^2*polylog(3,-(c*x+1)/(-c^2*x^2+1)^(1/2))+3*c^2*d^3*a^2*ln(c*x)-6*c^2*d^3*b^2*dilog((c*x+1)/(-c^2*x^2+1)^(1/2))+6*c^2*d^3*b^2*dilog(1+(c*x+1)/(-c^2*x^2+1)^(1/2))+c^2*d^3*b^2*ln(1+(c*x+1)/(-c^2*x^2+1)^(1/2))+c^2*d^3*b^2*ln((c*x+1)/(-c^2*x^2+1)^(1/2)-1)+c^3*x*a^2*d^3-3*c*d^3*a^2/x-c^2*d^3*b^2*arctanh(c*x)-2*c^2*d^3*b^2*dilog(1+I*(c*x+1)/(-c^2*x^2+1)^(1/2))-1/2*d^3*b^2*arctanh(c*x)^2/x^2-2*c^2*d^3*b^2*dilog(1-I*(c*x+1)/(-c^2*x^2+1)^(1/2))-3/2*c^2*d^3*b^2*arctanh(c*x)^2","C"
91,1,1337,374,2.279000," ","int((c*d*x+d)^3*(a+b*arctanh(c*x))^2/x^4,x)","-\frac{11 c^{3} d^{3} a b \ln \left(c x +1\right)}{6}-\frac{3 c^{2} d^{3} a b}{x}-\frac{c \,d^{3} a b}{3 x^{2}}-\frac{3 c^{2} d^{3} b^{2} \arctanh \left(c x \right)}{x}-\frac{3 c \,d^{3} b^{2} \arctanh \left(c x \right)^{2}}{2 x^{2}}-\frac{c \,d^{3} b^{2} \arctanh \left(c x \right)}{3 x^{2}}-\frac{3 c^{2} d^{3} b^{2} \arctanh \left(c x \right)^{2}}{x}-\frac{2 d^{3} a b \arctanh \left(c x \right)}{3 x^{3}}+c^{3} d^{3} b^{2} \arctanh \left(c x \right)^{2} \ln \left(1-\frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)+2 c^{3} d^{3} b^{2} \arctanh \left(c x \right) \polylog \left(2, \frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)+c^{3} d^{3} b^{2} \arctanh \left(c x \right)^{2} \ln \left(c x \right)-c^{3} d^{3} b^{2} \arctanh \left(c x \right)^{2} \ln \left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right)+2 c^{3} d^{3} b^{2} \arctanh \left(c x \right) \polylog \left(2, -\frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)-c^{3} d^{3} b^{2} \arctanh \left(c x \right) \polylog \left(2, -\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)+\frac{20 c^{3} d^{3} b^{2} \arctanh \left(c x \right) \ln \left(1+\frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)}{3}-c^{3} d^{3} a b \dilog \left(c x +1\right)-c^{3} d^{3} a b \dilog \left(c x \right)+c^{3} d^{3} b^{2} \arctanh \left(c x \right)^{2} \ln \left(1+\frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)-\frac{i c^{3} d^{3} b^{2} \pi  \,\mathrm{csgn}\left(\frac{i}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right)}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right)^{2} \arctanh \left(c x \right)^{2}}{2}-\frac{i c^{3} d^{3} b^{2} \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right)\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right)}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right)^{2} \arctanh \left(c x \right)^{2}}{2}-\frac{c^{3} d^{3} b^{2} \sqrt{-c^{2} x^{2}+1}}{3 \left(c x +1-\sqrt{-c^{2} x^{2}+1}\right)}+\frac{20 c^{3} d^{3} a b \ln \left(c x \right)}{3}-\frac{29 c^{3} d^{3} a b \ln \left(c x -1\right)}{6}-c^{3} d^{3} a b \ln \left(c x \right) \ln \left(c x +1\right)-\frac{3 c^{2} d^{3} a^{2}}{x}-\frac{3 c \,d^{3} a^{2}}{2 x^{2}}+c^{3} d^{3} a^{2} \ln \left(c x \right)+3 c^{3} d^{3} b^{2} \ln \left(1+\frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)+3 c^{3} d^{3} b^{2} \ln \left(\frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}-1\right)-\frac{8 b^{2} c^{3} d^{3} \arctanh \left(c x \right)}{3}-\frac{d^{3} b^{2} \arctanh \left(c x \right)^{2}}{3 x^{3}}-\frac{20 c^{3} d^{3} b^{2} \dilog \left(\frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)}{3}+\frac{20 c^{3} d^{3} b^{2} \dilog \left(1+\frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)}{3}-\frac{11 c^{3} d^{3} b^{2} \arctanh \left(c x \right)^{2}}{6}+\frac{c^{3} d^{3} b^{2} \polylog \left(3, -\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}{2}-2 c^{3} d^{3} b^{2} \polylog \left(3, \frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)-2 c^{3} d^{3} b^{2} \polylog \left(3, -\frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)+\frac{i c^{3} d^{3} b^{2} \pi  \mathrm{csgn}\left(\frac{i \left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right)}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right)^{3} \arctanh \left(c x \right)^{2}}{2}+2 c^{3} d^{3} a b \arctanh \left(c x \right) \ln \left(c x \right)-\frac{3 c \,d^{3} a b \arctanh \left(c x \right)}{x^{2}}-\frac{6 c^{2} d^{3} a b \arctanh \left(c x \right)}{x}+\frac{c^{3} d^{3} b^{2} \sqrt{-c^{2} x^{2}+1}}{3 \sqrt{-c^{2} x^{2}+1}+3 c x +3}+\frac{i c^{3} d^{3} b^{2} \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right)\right) \mathrm{csgn}\left(\frac{i}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right)}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right) \arctanh \left(c x \right)^{2}}{2}-\frac{d^{3} a^{2}}{3 x^{3}}"," ",0,"-11/6*c^3*d^3*a*b*ln(c*x+1)-3*c^2*d^3*b^2*arctanh(c*x)/x-3/2*c*d^3*b^2*arctanh(c*x)^2/x^2-1/3*c*d^3*b^2*arctanh(c*x)/x^2-3*c^2*d^3*b^2*arctanh(c*x)^2/x-2/3*d^3*a*b*arctanh(c*x)/x^3+c^3*d^3*b^2*arctanh(c*x)^2*ln(1-(c*x+1)/(-c^2*x^2+1)^(1/2))+2*c^3*d^3*b^2*arctanh(c*x)*polylog(2,(c*x+1)/(-c^2*x^2+1)^(1/2))+c^3*d^3*b^2*arctanh(c*x)^2*ln(c*x)-c^3*d^3*b^2*arctanh(c*x)^2*ln((c*x+1)^2/(-c^2*x^2+1)-1)+2*c^3*d^3*b^2*arctanh(c*x)*polylog(2,-(c*x+1)/(-c^2*x^2+1)^(1/2))-c^3*d^3*b^2*arctanh(c*x)*polylog(2,-(c*x+1)^2/(-c^2*x^2+1))-3*c^2*d^3*a*b/x-1/3*c*d^3*a*b/x^2-8/3*b^2*c^3*d^3*arctanh(c*x)-1/2*I*c^3*d^3*b^2*Pi*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^2*arctanh(c*x)^2-1/2*I*c^3*d^3*b^2*Pi*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1))*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^2*arctanh(c*x)^2+20/3*c^3*d^3*b^2*arctanh(c*x)*ln(1+(c*x+1)/(-c^2*x^2+1)^(1/2))-1/3*c^3*d^3*b^2/(c*x+1-(-c^2*x^2+1)^(1/2))*(-c^2*x^2+1)^(1/2)+1/3*c^3*d^3*b^2/((-c^2*x^2+1)^(1/2)+c*x+1)*(-c^2*x^2+1)^(1/2)-c^3*d^3*a*b*dilog(c*x+1)-c^3*d^3*a*b*dilog(c*x)+20/3*c^3*d^3*a*b*ln(c*x)+c^3*d^3*b^2*arctanh(c*x)^2*ln(1+(c*x+1)/(-c^2*x^2+1)^(1/2))-29/6*c^3*d^3*a*b*ln(c*x-1)+2*c^3*d^3*a*b*arctanh(c*x)*ln(c*x)-c^3*d^3*a*b*ln(c*x)*ln(c*x+1)-3*c*d^3*a*b*arctanh(c*x)/x^2-6*c^2*d^3*a*b*arctanh(c*x)/x-3*c^2*d^3*a^2/x-3/2*c*d^3*a^2/x^2-1/3*d^3*b^2*arctanh(c*x)^2/x^3+c^3*d^3*a^2*ln(c*x)-20/3*c^3*d^3*b^2*dilog((c*x+1)/(-c^2*x^2+1)^(1/2))+20/3*c^3*d^3*b^2*dilog(1+(c*x+1)/(-c^2*x^2+1)^(1/2))+3*c^3*d^3*b^2*ln(1+(c*x+1)/(-c^2*x^2+1)^(1/2))+3*c^3*d^3*b^2*ln((c*x+1)/(-c^2*x^2+1)^(1/2)-1)-11/6*c^3*d^3*b^2*arctanh(c*x)^2+1/2*c^3*d^3*b^2*polylog(3,-(c*x+1)^2/(-c^2*x^2+1))-2*c^3*d^3*b^2*polylog(3,(c*x+1)/(-c^2*x^2+1)^(1/2))-2*c^3*d^3*b^2*polylog(3,-(c*x+1)/(-c^2*x^2+1)^(1/2))+1/2*I*c^3*d^3*b^2*Pi*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^3*arctanh(c*x)^2+1/2*I*c^3*d^3*b^2*Pi*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1))*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))*arctanh(c*x)^2-1/3*d^3*a^2/x^3","C"
92,1,646,259,0.081000," ","int((c*d*x+d)^3*(a+b*arctanh(c*x))^2/x^5,x)","-\frac{c^{2} d^{3} a b}{x^{2}}+\frac{c^{4} d^{3} b^{2} \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{c x}{2}\right)}{8}+4 c^{4} d^{3} a b \ln \left(c x \right)-\frac{2 c^{3} d^{3} a b \arctanh \left(c x \right)}{x}-\frac{3 c^{2} d^{3} a b \arctanh \left(c x \right)}{x^{2}}-\frac{2 c \,d^{3} a b \arctanh \left(c x \right)}{x^{3}}-\frac{4 c^{4} d^{3} b^{2} \ln \left(c x +1\right)}{3}-2 c^{4} d^{3} b^{2} \dilog \left(c x \right)-2 c^{4} d^{3} b^{2} \dilog \left(c x +1\right)+2 c^{4} d^{3} b^{2} \dilog \left(\frac{1}{2}+\frac{c x}{2}\right)-\frac{d^{3} b^{2} \arctanh \left(c x \right)^{2}}{4 x^{4}}-\frac{c^{3} d^{3} a^{2}}{x}-\frac{c \,d^{3} a^{2}}{x^{3}}-\frac{3 c^{2} d^{3} a^{2}}{2 x^{2}}+\frac{c^{4} d^{3} b^{2} \ln \left(c x +1\right)^{2}}{16}+\frac{11 c^{4} d^{3} b^{2} \ln \left(c x \right)}{3}-\frac{15 c^{4} d^{3} b^{2} \ln \left(c x -1\right)^{2}}{16}-\frac{7 c^{4} d^{3} b^{2} \ln \left(c x -1\right)}{3}-\frac{b^{2} c^{2} d^{3}}{12 x^{2}}-\frac{c \,d^{3} a b}{6 x^{3}}-\frac{b^{2} c^{3} d^{3}}{x}-\frac{d^{3} a^{2}}{4 x^{4}}-\frac{3 c^{2} d^{3} b^{2} \arctanh \left(c x \right)^{2}}{2 x^{2}}-\frac{c \,d^{3} b^{2} \arctanh \left(c x \right)^{2}}{x^{3}}-\frac{c^{2} d^{3} b^{2} \arctanh \left(c x \right)}{x^{2}}-2 c^{4} d^{3} b^{2} \ln \left(c x \right) \ln \left(c x +1\right)-\frac{c^{4} d^{3} b^{2} \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) \ln \left(c x +1\right)}{8}-\frac{7 c^{3} d^{3} a b}{2 x}+\frac{15 c^{4} d^{3} b^{2} \ln \left(c x -1\right) \ln \left(\frac{1}{2}+\frac{c x}{2}\right)}{8}-\frac{c^{4} d^{3} a b \ln \left(c x +1\right)}{4}-\frac{15 c^{4} d^{3} a b \ln \left(c x -1\right)}{4}-\frac{d^{3} a b \arctanh \left(c x \right)}{2 x^{4}}+4 c^{4} d^{3} b^{2} \arctanh \left(c x \right) \ln \left(c x \right)-\frac{15 c^{4} d^{3} b^{2} \arctanh \left(c x \right) \ln \left(c x -1\right)}{4}-\frac{c^{3} d^{3} b^{2} \arctanh \left(c x \right)^{2}}{x}-\frac{c \,d^{3} b^{2} \arctanh \left(c x \right)}{6 x^{3}}-\frac{c^{4} d^{3} b^{2} \arctanh \left(c x \right) \ln \left(c x +1\right)}{4}-\frac{7 c^{3} d^{3} b^{2} \arctanh \left(c x \right)}{2 x}"," ",0,"-c^2*d^3*a*b/x^2-1/2*d^3*a*b*arctanh(c*x)/x^4+1/8*c^4*d^3*b^2*ln(-1/2*c*x+1/2)*ln(1/2+1/2*c*x)+4*c^4*d^3*a*b*ln(c*x)+4*c^4*d^3*b^2*arctanh(c*x)*ln(c*x)-15/4*c^4*d^3*b^2*arctanh(c*x)*ln(c*x-1)-2*c^3*d^3*a*b*arctanh(c*x)/x-3*c^2*d^3*a*b*arctanh(c*x)/x^2-2*c*d^3*a*b*arctanh(c*x)/x^3-4/3*c^4*d^3*b^2*ln(c*x+1)-c^3*d^3*a^2/x-c*d^3*a^2/x^3-3/2*c^2*d^3*a^2/x^2-2*c^4*d^3*b^2*dilog(c*x)-2*c^4*d^3*b^2*dilog(c*x+1)+1/16*c^4*d^3*b^2*ln(c*x+1)^2+11/3*c^4*d^3*b^2*ln(c*x)-15/16*c^4*d^3*b^2*ln(c*x-1)^2+2*c^4*d^3*b^2*dilog(1/2+1/2*c*x)-7/3*c^4*d^3*b^2*ln(c*x-1)-1/4*d^3*b^2*arctanh(c*x)^2/x^4-1/12*b^2*c^2*d^3/x^2-1/6*c*d^3*a*b/x^3-b^2*c^3*d^3/x-1/4*d^3*a^2/x^4-2*c^4*d^3*b^2*ln(c*x)*ln(c*x+1)-1/8*c^4*d^3*b^2*ln(-1/2*c*x+1/2)*ln(c*x+1)-7/2*c^3*d^3*a*b/x-c^3*d^3*b^2*arctanh(c*x)^2/x-1/6*c*d^3*b^2*arctanh(c*x)/x^3+15/8*c^4*d^3*b^2*ln(c*x-1)*ln(1/2+1/2*c*x)-1/4*c^4*d^3*b^2*arctanh(c*x)*ln(c*x+1)-1/4*c^4*d^3*a*b*ln(c*x+1)-15/4*c^4*d^3*a*b*ln(c*x-1)-7/2*c^3*d^3*b^2*arctanh(c*x)/x-3/2*c^2*d^3*b^2*arctanh(c*x)^2/x^2-c*d^3*b^2*arctanh(c*x)^2/x^3-c^2*d^3*b^2*arctanh(c*x)/x^2","B"
93,1,691,320,0.082000," ","int((c*d*x+d)^3*(a+b*arctanh(c*x))^2/x^6,x)","\frac{6 c^{5} d^{3} b^{2} \dilog \left(\frac{1}{2}+\frac{c x}{2}\right)}{5}-\frac{d^{3} b^{2} \arctanh \left(c x \right)^{2}}{5 x^{5}}-\frac{6 c^{5} d^{3} b^{2} \dilog \left(c x +1\right)}{5}-\frac{6 c^{5} d^{3} b^{2} \dilog \left(c x \right)}{5}-\frac{43 c^{5} d^{3} b^{2} \ln \left(c x -1\right)}{20}-\frac{49 c^{5} d^{3} b^{2} \ln \left(c x -1\right)^{2}}{80}-\frac{17 c^{5} d^{3} b^{2} \ln \left(c x +1\right)}{20}+3 c^{5} d^{3} b^{2} \ln \left(c x \right)-\frac{c^{5} d^{3} b^{2} \ln \left(c x +1\right)^{2}}{80}-\frac{3 c \,d^{3} a^{2}}{4 x^{4}}-\frac{c^{2} d^{3} a^{2}}{x^{3}}-\frac{c^{3} d^{3} a^{2}}{2 x^{2}}-\frac{c^{3} d^{3} a b \arctanh \left(c x \right)}{x^{2}}-\frac{3 c \,d^{3} a b \arctanh \left(c x \right)}{2 x^{4}}-\frac{2 c^{2} d^{3} a b \arctanh \left(c x \right)}{x^{3}}-\frac{b^{2} c^{2} d^{3}}{30 x^{3}}-\frac{b^{2} c^{3} d^{3}}{4 x^{2}}-\frac{13 b^{2} c^{4} d^{3}}{10 x}-\frac{d^{3} a^{2}}{5 x^{5}}+\frac{c^{5} d^{3} a b \ln \left(c x +1\right)}{20}-\frac{49 c^{5} d^{3} a b \ln \left(c x -1\right)}{20}-\frac{c^{2} d^{3} a b}{2 x^{3}}-\frac{c \,d^{3} a b}{10 x^{4}}-\frac{3 c \,d^{3} b^{2} \arctanh \left(c x \right)^{2}}{4 x^{4}}-\frac{c^{2} d^{3} b^{2} \arctanh \left(c x \right)}{2 x^{3}}-\frac{c \,d^{3} b^{2} \arctanh \left(c x \right)}{10 x^{4}}-\frac{5 c^{4} d^{3} b^{2} \arctanh \left(c x \right)}{2 x}-\frac{c^{3} d^{3} b^{2} \arctanh \left(c x \right)^{2}}{2 x^{2}}-\frac{c^{2} d^{3} b^{2} \arctanh \left(c x \right)^{2}}{x^{3}}-\frac{6 c^{3} d^{3} b^{2} \arctanh \left(c x \right)}{5 x^{2}}-\frac{2 d^{3} a b \arctanh \left(c x \right)}{5 x^{5}}-\frac{49 c^{5} d^{3} b^{2} \arctanh \left(c x \right) \ln \left(c x -1\right)}{20}+\frac{c^{5} d^{3} b^{2} \arctanh \left(c x \right) \ln \left(c x +1\right)}{20}+\frac{12 c^{5} d^{3} b^{2} \arctanh \left(c x \right) \ln \left(c x \right)}{5}-\frac{5 c^{4} d^{3} a b}{2 x}-\frac{6 c^{3} d^{3} a b}{5 x^{2}}-\frac{c^{5} d^{3} b^{2} \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{c x}{2}\right)}{40}+\frac{49 c^{5} d^{3} b^{2} \ln \left(c x -1\right) \ln \left(\frac{1}{2}+\frac{c x}{2}\right)}{40}-\frac{6 c^{5} d^{3} b^{2} \ln \left(c x \right) \ln \left(c x +1\right)}{5}+\frac{c^{5} d^{3} b^{2} \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) \ln \left(c x +1\right)}{40}+\frac{12 c^{5} d^{3} a b \ln \left(c x \right)}{5}"," ",0,"-c^3*d^3*a*b*arctanh(c*x)/x^2-3/2*c*d^3*a*b*arctanh(c*x)/x^4-2*c^2*d^3*a*b*arctanh(c*x)/x^3+6/5*c^5*d^3*b^2*dilog(1/2+1/2*c*x)-1/5*d^3*b^2*arctanh(c*x)^2/x^5-6/5*c^5*d^3*b^2*dilog(c*x+1)-6/5*c^5*d^3*b^2*dilog(c*x)-43/20*c^5*d^3*b^2*ln(c*x-1)-49/80*c^5*d^3*b^2*ln(c*x-1)^2-17/20*c^5*d^3*b^2*ln(c*x+1)+3*c^5*d^3*b^2*ln(c*x)-1/80*c^5*d^3*b^2*ln(c*x+1)^2-3/4*c*d^3*a^2/x^4-c^2*d^3*a^2/x^3-1/2*c^3*d^3*a^2/x^2-1/30*b^2*c^2*d^3/x^3-1/4*b^2*c^3*d^3/x^2-13/10*b^2*c^4*d^3/x-1/5*d^3*a^2/x^5+1/20*c^5*d^3*a*b*ln(c*x+1)-49/20*c^5*d^3*a*b*ln(c*x-1)-3/4*c*d^3*b^2*arctanh(c*x)^2/x^4-1/2*c^2*d^3*b^2*arctanh(c*x)/x^3-1/10*c*d^3*b^2*arctanh(c*x)/x^4-5/2*c^4*d^3*b^2*arctanh(c*x)/x-1/2*c^3*d^3*b^2*arctanh(c*x)^2/x^2-c^2*d^3*b^2*arctanh(c*x)^2/x^3-6/5*c^3*d^3*b^2*arctanh(c*x)/x^2-1/2*c^2*d^3*a*b/x^3-1/10*c*d^3*a*b/x^4-5/2*c^4*d^3*a*b/x-6/5*c^3*d^3*a*b/x^2-2/5*d^3*a*b*arctanh(c*x)/x^5-1/40*c^5*d^3*b^2*ln(-1/2*c*x+1/2)*ln(1/2+1/2*c*x)-49/20*c^5*d^3*b^2*arctanh(c*x)*ln(c*x-1)+49/40*c^5*d^3*b^2*ln(c*x-1)*ln(1/2+1/2*c*x)+1/20*c^5*d^3*b^2*arctanh(c*x)*ln(c*x+1)-6/5*c^5*d^3*b^2*ln(c*x)*ln(c*x+1)+1/40*c^5*d^3*b^2*ln(-1/2*c*x+1/2)*ln(c*x+1)+12/5*c^5*d^3*a*b*ln(c*x)+12/5*c^5*d^3*b^2*arctanh(c*x)*ln(c*x)","B"
94,1,736,433,0.080000," ","int((c*d*x+d)^3*(a+b*arctanh(c*x))^2/x^7,x)","-\frac{2 c^{3} d^{3} a b \arctanh \left(c x \right)}{3 x^{3}}-\frac{3 c^{2} d^{3} a b \arctanh \left(c x \right)}{2 x^{4}}-\frac{6 c \,d^{3} a b \arctanh \left(c x \right)}{5 x^{5}}-\frac{3 c^{2} d^{3} a^{2}}{4 x^{4}}-\frac{3 c \,d^{3} a^{2}}{5 x^{5}}-\frac{14 c^{6} d^{3} b^{2} \dilog \left(c x \right)}{15}-\frac{d^{3} b^{2} \arctanh \left(c x \right)^{2}}{6 x^{6}}+\frac{14 c^{6} d^{3} b^{2} \dilog \left(\frac{1}{2}+\frac{c x}{2}\right)}{15}-\frac{14 c^{6} d^{3} b^{2} \dilog \left(c x +1\right)}{15}+\frac{c^{6} d^{3} b^{2} \ln \left(c x +1\right)^{2}}{240}+\frac{113 c^{6} d^{3} b^{2} \ln \left(c x \right)}{45}-\frac{37 c^{6} d^{3} b^{2} \ln \left(c x -1\right)^{2}}{80}-\frac{c^{3} d^{3} a^{2}}{3 x^{3}}-\frac{337 c^{6} d^{3} b^{2} \ln \left(c x -1\right)}{180}-\frac{23 c^{6} d^{3} b^{2} \ln \left(c x +1\right)}{36}-\frac{b^{2} c^{2} d^{3}}{60 x^{4}}-\frac{b^{2} c^{3} d^{3}}{10 x^{3}}-\frac{61 b^{2} c^{4} d^{3}}{180 x^{2}}-\frac{37 b^{2} c^{5} d^{3}}{30 x}+\frac{37 c^{6} d^{3} b^{2} \ln \left(c x -1\right) \ln \left(\frac{1}{2}+\frac{c x}{2}\right)}{40}-\frac{d^{3} a^{2}}{6 x^{6}}+\frac{28 c^{6} d^{3} a b \ln \left(c x \right)}{15}-\frac{37 c^{6} d^{3} a b \ln \left(c x -1\right)}{20}-\frac{c^{6} d^{3} a b \ln \left(c x +1\right)}{60}-\frac{c^{3} d^{3} b^{2} \arctanh \left(c x \right)^{2}}{3 x^{3}}-\frac{14 c^{4} d^{3} b^{2} \arctanh \left(c x \right)}{15 x^{2}}-\frac{c^{6} d^{3} b^{2} \arctanh \left(c x \right) \ln \left(c x +1\right)}{60}-\frac{c \,d^{3} a b}{15 x^{5}}-\frac{11 c^{5} d^{3} a b}{6 x}-\frac{14 c^{4} d^{3} a b}{15 x^{2}}-\frac{14 c^{6} d^{3} b^{2} \ln \left(c x \right) \ln \left(c x +1\right)}{15}-\frac{c^{6} d^{3} b^{2} \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) \ln \left(c x +1\right)}{120}+\frac{c^{6} d^{3} b^{2} \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{c x}{2}\right)}{120}-\frac{11 c^{3} d^{3} a b}{18 x^{3}}-\frac{3 c^{2} d^{3} a b}{10 x^{4}}-\frac{37 c^{6} d^{3} b^{2} \arctanh \left(c x \right) \ln \left(c x -1\right)}{20}+\frac{28 c^{6} d^{3} b^{2} \arctanh \left(c x \right) \ln \left(c x \right)}{15}-\frac{3 c^{2} d^{3} b^{2} \arctanh \left(c x \right)^{2}}{4 x^{4}}-\frac{11 c^{3} d^{3} b^{2} \arctanh \left(c x \right)}{18 x^{3}}-\frac{3 c \,d^{3} b^{2} \arctanh \left(c x \right)^{2}}{5 x^{5}}-\frac{3 c^{2} d^{3} b^{2} \arctanh \left(c x \right)}{10 x^{4}}-\frac{d^{3} a b \arctanh \left(c x \right)}{3 x^{6}}-\frac{c \,d^{3} b^{2} \arctanh \left(c x \right)}{15 x^{5}}-\frac{11 c^{5} d^{3} b^{2} \arctanh \left(c x \right)}{6 x}"," ",0,"-2/3*c^3*d^3*a*b*arctanh(c*x)/x^3-3/4*c^2*d^3*a^2/x^4-3/5*c*d^3*a^2/x^5+1/240*c^6*d^3*b^2*ln(c*x+1)^2+113/45*c^6*d^3*b^2*ln(c*x)-14/15*c^6*d^3*b^2*dilog(c*x)-37/80*c^6*d^3*b^2*ln(c*x-1)^2-1/6*d^3*b^2*arctanh(c*x)^2/x^6-1/3*c^3*d^3*a^2/x^3+14/15*c^6*d^3*b^2*dilog(1/2+1/2*c*x)-337/180*c^6*d^3*b^2*ln(c*x-1)-23/36*c^6*d^3*b^2*ln(c*x+1)-14/15*c^6*d^3*b^2*dilog(c*x+1)-3/2*c^2*d^3*a*b*arctanh(c*x)/x^4-6/5*c*d^3*a*b*arctanh(c*x)/x^5-1/60*b^2*c^2*d^3/x^4-1/10*b^2*c^3*d^3/x^3-61/180*b^2*c^4*d^3/x^2-37/30*b^2*c^5*d^3/x+37/40*c^6*d^3*b^2*ln(c*x-1)*ln(1/2+1/2*c*x)-1/6*d^3*a^2/x^6-37/20*c^6*d^3*b^2*arctanh(c*x)*ln(c*x-1)+28/15*c^6*d^3*a*b*ln(c*x)+28/15*c^6*d^3*b^2*arctanh(c*x)*ln(c*x)-37/20*c^6*d^3*a*b*ln(c*x-1)-1/60*c^6*d^3*a*b*ln(c*x+1)-3/4*c^2*d^3*b^2*arctanh(c*x)^2/x^4-11/18*c^3*d^3*b^2*arctanh(c*x)/x^3-3/5*c*d^3*b^2*arctanh(c*x)^2/x^5-3/10*c^2*d^3*b^2*arctanh(c*x)/x^4-1/15*c*d^3*a*b/x^5-11/6*c^5*d^3*a*b/x-14/15*c^4*d^3*a*b/x^2-1/3*d^3*a*b*arctanh(c*x)/x^6-1/15*c*d^3*b^2*arctanh(c*x)/x^5-11/6*c^5*d^3*b^2*arctanh(c*x)/x-1/3*c^3*d^3*b^2*arctanh(c*x)^2/x^3-14/15*c^4*d^3*b^2*arctanh(c*x)/x^2-1/60*c^6*d^3*b^2*arctanh(c*x)*ln(c*x+1)-14/15*c^6*d^3*b^2*ln(c*x)*ln(c*x+1)-1/120*c^6*d^3*b^2*ln(-1/2*c*x+1/2)*ln(c*x+1)+1/120*c^6*d^3*b^2*ln(-1/2*c*x+1/2)*ln(1/2+1/2*c*x)-11/18*c^3*d^3*a*b/x^3-3/10*c^2*d^3*a*b/x^4","A"
95,1,1298,309,2.194000," ","int(x^3*(a+b*arctanh(c*x))^2/(c*d*x+d),x)","-\frac{a b x}{c^{3} d}+\frac{b^{2} x}{3 c^{3} d}-\frac{a^{2} x^{2}}{2 c^{2} d}+\frac{a^{2} x}{c^{3} d}+\frac{a^{2} x^{3}}{3 c d}+\frac{b^{2} \ln \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}{c^{4} d}+\frac{i b^{2} \pi  \,\mathrm{csgn}\left(\frac{i \left(c x +1\right)}{\sqrt{-c^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{c^{2} x^{2}-1}\right)^{2} \arctanh \left(c x \right)^{2}}{c^{4} d}+\frac{i b^{2} \pi  \mathrm{csgn}\left(\frac{i \left(c x +1\right)}{\sqrt{-c^{2} x^{2}+1}}\right)^{2} \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{c^{2} x^{2}-1}\right) \arctanh \left(c x \right)^{2}}{2 c^{4} d}+\frac{i b^{2} \pi  \,\mathrm{csgn}\left(\frac{i}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{\left(c^{2} x^{2}-1\right) \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}\right)^{2} \arctanh \left(c x \right)^{2}}{2 c^{4} d}-\frac{i b^{2} \pi  \,\mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{c^{2} x^{2}-1}\right) \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{\left(c^{2} x^{2}-1\right) \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}\right)^{2} \arctanh \left(c x \right)^{2}}{2 c^{4} d}-\frac{4 a b}{3 c^{4} d}-\frac{a^{2} \ln \left(c x +1\right)}{c^{4} d}-\frac{b^{2}}{3 c^{4} d}-\frac{a b \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) \ln \left(c x +1\right)}{c^{4} d}+\frac{a b \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{c x}{2}\right)}{c^{4} d}-\frac{2 a b \arctanh \left(c x \right) \ln \left(c x +1\right)}{c^{4} d}+\frac{2 a b \,x^{3} \arctanh \left(c x \right)}{3 c d}-\frac{a b \arctanh \left(c x \right) x^{2}}{c^{2} d}+\frac{2 a b \arctanh \left(c x \right) x}{c^{3} d}+\frac{i b^{2} \pi  \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{c^{2} x^{2}-1}\right)^{3} \arctanh \left(c x \right)^{2}}{2 c^{4} d}+\frac{i b^{2} \pi  \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{\left(c^{2} x^{2}-1\right) \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}\right)^{3} \arctanh \left(c x \right)^{2}}{2 c^{4} d}-\frac{i b^{2} \pi  \,\mathrm{csgn}\left(\frac{i}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{c^{2} x^{2}-1}\right) \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{\left(c^{2} x^{2}-1\right) \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}\right) \arctanh \left(c x \right)^{2}}{2 c^{4} d}-\frac{8 b^{2} \dilog \left(1-\frac{i \left(c x +1\right)}{\sqrt{-c^{2} x^{2}+1}}\right)}{3 c^{4} d}-\frac{8 b^{2} \dilog \left(1+\frac{i \left(c x +1\right)}{\sqrt{-c^{2} x^{2}+1}}\right)}{3 c^{4} d}-\frac{4 b^{2} \arctanh \left(c x \right)}{3 d \,c^{4}}-\frac{2 b^{2} \arctanh \left(c x \right)^{3}}{3 c^{4} d}+\frac{11 b^{2} \arctanh \left(c x \right)^{2}}{6 c^{4} d}-\frac{b^{2} \polylog \left(3, -\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}{2 c^{4} d}-\frac{b^{2} \arctanh \left(c x \right)^{2} \ln \left(c x +1\right)}{c^{4} d}+\frac{b^{2} \arctanh \left(c x \right)^{2} \ln \left(2\right)}{c^{4} d}+\frac{a b \dilog \left(\frac{1}{2}+\frac{c x}{2}\right)}{c^{4} d}-\frac{b^{2} \arctanh \left(c x \right)^{2} x^{2}}{2 c^{2} d}-\frac{8 b^{2} \arctanh \left(c x \right) \ln \left(1-\frac{i \left(c x +1\right)}{\sqrt{-c^{2} x^{2}+1}}\right)}{3 c^{4} d}-\frac{8 b^{2} \arctanh \left(c x \right) \ln \left(1+\frac{i \left(c x +1\right)}{\sqrt{-c^{2} x^{2}+1}}\right)}{3 c^{4} d}+\frac{a b \,x^{2}}{3 c^{2} d}+\frac{11 a b \ln \left(c x +1\right)}{6 c^{4} d}-\frac{b^{2} x \arctanh \left(c x \right)}{c^{3} d}+\frac{b^{2} \arctanh \left(c x \right) \polylog \left(2, -\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}{c^{4} d}+\frac{b^{2} \arctanh \left(c x \right)^{2} x}{c^{3} d}+\frac{b^{2} \arctanh \left(c x \right) x^{2}}{3 c^{2} d}+\frac{b^{2} x^{3} \arctanh \left(c x \right)^{2}}{3 c d}+\frac{2 b^{2} \arctanh \left(c x \right)^{2} \ln \left(\frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)}{c^{4} d}+\frac{a b \ln \left(c x +1\right)^{2}}{2 c^{4} d}+\frac{5 a b \ln \left(c x -1\right)}{6 c^{4} d}"," ",0,"-a*b*x/c^3/d-b^2*x*arctanh(c*x)/c^3/d+1/3*b^2*x/c^3/d-4/3*b^2*arctanh(c*x)/d/c^4-1/2/c^2*a^2/d*x^2+1/c^3*a^2/d*x+1/3/c*a^2/d*x^3+1/c^4*b^2/d*ln(1+(c*x+1)^2/(-c^2*x^2+1))-2/3/c^4*b^2/d*arctanh(c*x)^3+I/c^4*b^2/d*Pi*csgn(I*(c*x+1)/(-c^2*x^2+1)^(1/2))*csgn(I*(c*x+1)^2/(c^2*x^2-1))^2*arctanh(c*x)^2+1/2*I/c^4*b^2/d*Pi*csgn(I*(c*x+1)/(-c^2*x^2+1)^(1/2))^2*csgn(I*(c*x+1)^2/(c^2*x^2-1))*arctanh(c*x)^2+1/2*I/c^4*b^2/d*Pi*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^2*arctanh(c*x)^2-1/2*I/c^4*b^2/d*Pi*csgn(I*(c*x+1)^2/(c^2*x^2-1))*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^2*arctanh(c*x)^2+11/6/c^4*b^2/d*arctanh(c*x)^2-1/2/c^4*b^2/d*polylog(3,-(c*x+1)^2/(-c^2*x^2+1))-8/3/c^4*b^2/d*dilog(1+I*(c*x+1)/(-c^2*x^2+1)^(1/2))-8/3/c^4*b^2/d*dilog(1-I*(c*x+1)/(-c^2*x^2+1)^(1/2))-4/3/c^4*a*b/d-1/c^4*a^2/d*ln(c*x+1)-1/2*I/c^4*b^2/d*Pi*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))*csgn(I*(c*x+1)^2/(c^2*x^2-1))*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))*arctanh(c*x)^2-1/3/c^4*b^2/d-2/c^4*a*b/d*arctanh(c*x)*ln(c*x+1)-1/c^4*a*b/d*ln(-1/2*c*x+1/2)*ln(c*x+1)+1/c^4*a*b/d*ln(-1/2*c*x+1/2)*ln(1/2+1/2*c*x)+2/3/c*a*b/d*x^3*arctanh(c*x)-1/c^2*a*b/d*arctanh(c*x)*x^2+2/c^3*a*b/d*arctanh(c*x)*x+1/2*I/c^4*b^2/d*Pi*csgn(I*(c*x+1)^2/(c^2*x^2-1))^3*arctanh(c*x)^2+1/2*I/c^4*b^2/d*Pi*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^3*arctanh(c*x)^2+1/c^4*b^2/d*arctanh(c*x)*polylog(2,-(c*x+1)^2/(-c^2*x^2+1))+1/3/c^2*a*b/d*x^2+11/6/c^4*a*b/d*ln(c*x+1)+1/c^3*b^2/d*arctanh(c*x)^2*x+1/3/c^2*b^2/d*arctanh(c*x)*x^2+1/3/c*b^2/d*x^3*arctanh(c*x)^2+2/c^4*b^2/d*arctanh(c*x)^2*ln((c*x+1)/(-c^2*x^2+1)^(1/2))-1/c^4*b^2/d*arctanh(c*x)^2*ln(c*x+1)-8/3/c^4*b^2/d*arctanh(c*x)*ln(1-I*(c*x+1)/(-c^2*x^2+1)^(1/2))+1/c^4*b^2/d*arctanh(c*x)^2*ln(2)+1/2/c^4*a*b/d*ln(c*x+1)^2+5/6/c^4*a*b/d*ln(c*x-1)+1/c^4*a*b/d*dilog(1/2+1/2*c*x)-8/3/c^4*b^2/d*arctanh(c*x)*ln(1+I*(c*x+1)/(-c^2*x^2+1)^(1/2))-1/2/c^2*b^2/d*arctanh(c*x)^2*x^2","C"
96,1,1192,239,1.459000," ","int(x^2*(a+b*arctanh(c*x))^2/(c*d*x+d),x)","\frac{i b^{2} \pi  \,\mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{c^{2} x^{2}-1}\right) \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{\left(c^{2} x^{2}-1\right) \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}\right)^{2} \arctanh \left(c x \right)^{2}}{2 c^{3} d}-\frac{i b^{2} \pi  \,\mathrm{csgn}\left(\frac{i}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{\left(c^{2} x^{2}-1\right) \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}\right)^{2} \arctanh \left(c x \right)^{2}}{2 c^{3} d}-\frac{i b^{2} \pi  \mathrm{csgn}\left(\frac{i \left(c x +1\right)}{\sqrt{-c^{2} x^{2}+1}}\right)^{2} \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{c^{2} x^{2}-1}\right) \arctanh \left(c x \right)^{2}}{2 c^{3} d}-\frac{i b^{2} \pi  \,\mathrm{csgn}\left(\frac{i \left(c x +1\right)}{\sqrt{-c^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{c^{2} x^{2}-1}\right)^{2} \arctanh \left(c x \right)^{2}}{c^{3} d}+\frac{a b x}{c^{2} d}+\frac{2 b^{2} \arctanh \left(c x \right)^{3}}{3 c^{3} d}+\frac{2 b^{2} \dilog \left(1+\frac{i \left(c x +1\right)}{\sqrt{-c^{2} x^{2}+1}}\right)}{c^{3} d}+\frac{2 b^{2} \dilog \left(1-\frac{i \left(c x +1\right)}{\sqrt{-c^{2} x^{2}+1}}\right)}{c^{3} d}+\frac{a b}{c^{3} d}+\frac{a^{2} x^{2}}{2 c d}-\frac{a^{2} x}{c^{2} d}+\frac{a^{2} \ln \left(c x +1\right)}{c^{3} d}-\frac{b^{2} \ln \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}{c^{3} d}+\frac{b^{2} \arctanh \left(c x \right)}{c^{3} d}-\frac{3 b^{2} \arctanh \left(c x \right)^{2}}{2 c^{3} d}+\frac{b^{2} \polylog \left(3, -\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}{2 c^{3} d}+\frac{i b^{2} \pi  \,\mathrm{csgn}\left(\frac{i}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{c^{2} x^{2}-1}\right) \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{\left(c^{2} x^{2}-1\right) \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}\right) \arctanh \left(c x \right)^{2}}{2 c^{3} d}-\frac{i b^{2} \pi  \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{\left(c^{2} x^{2}-1\right) \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}\right)^{3} \arctanh \left(c x \right)^{2}}{2 c^{3} d}-\frac{i b^{2} \pi  \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{c^{2} x^{2}-1}\right)^{3} \arctanh \left(c x \right)^{2}}{2 c^{3} d}+\frac{a b \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) \ln \left(c x +1\right)}{c^{3} d}-\frac{a b \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{c x}{2}\right)}{c^{3} d}+\frac{a b \arctanh \left(c x \right) x^{2}}{c d}-\frac{2 a b \arctanh \left(c x \right) x}{c^{2} d}-\frac{3 a b \ln \left(c x +1\right)}{2 c^{3} d}-\frac{a b \ln \left(c x -1\right)}{2 c^{3} d}+\frac{b^{2} x \arctanh \left(c x \right)}{c^{2} d}-\frac{a b \dilog \left(\frac{1}{2}+\frac{c x}{2}\right)}{c^{3} d}-\frac{a b \ln \left(c x +1\right)^{2}}{2 c^{3} d}-\frac{2 b^{2} \arctanh \left(c x \right)^{2} \ln \left(\frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)}{c^{3} d}-\frac{b^{2} \arctanh \left(c x \right) \polylog \left(2, -\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}{c^{3} d}-\frac{b^{2} \arctanh \left(c x \right)^{2} x}{c^{2} d}+\frac{b^{2} \arctanh \left(c x \right)^{2} x^{2}}{2 c d}-\frac{b^{2} \arctanh \left(c x \right)^{2} \ln \left(2\right)}{c^{3} d}+\frac{b^{2} \arctanh \left(c x \right)^{2} \ln \left(c x +1\right)}{c^{3} d}+\frac{2 b^{2} \arctanh \left(c x \right) \ln \left(1+\frac{i \left(c x +1\right)}{\sqrt{-c^{2} x^{2}+1}}\right)}{c^{3} d}+\frac{2 b^{2} \arctanh \left(c x \right) \ln \left(1-\frac{i \left(c x +1\right)}{\sqrt{-c^{2} x^{2}+1}}\right)}{c^{3} d}+\frac{2 a b \arctanh \left(c x \right) \ln \left(c x +1\right)}{c^{3} d}"," ",0,"-I/c^3*b^2/d*Pi*csgn(I*(c*x+1)/(-c^2*x^2+1)^(1/2))*csgn(I*(c*x+1)^2/(c^2*x^2-1))^2*arctanh(c*x)^2+1/2*I/c^3*b^2/d*Pi*csgn(I*(c*x+1)^2/(c^2*x^2-1))*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^2*arctanh(c*x)^2-1/2*I/c^3*b^2/d*Pi*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^2*arctanh(c*x)^2-1/2*I/c^3*b^2/d*Pi*csgn(I*(c*x+1)/(-c^2*x^2+1)^(1/2))^2*csgn(I*(c*x+1)^2/(c^2*x^2-1))*arctanh(c*x)^2+a*b*x/c^2/d+b^2*x*arctanh(c*x)/c^2/d+1/c^3*a*b/d+1/2/c*a^2/d*x^2-1/c^2*a^2/d*x+1/c^3*a^2/d*ln(c*x+1)+1/c^3*b^2/d*arctanh(c*x)-3/2/c^3*b^2/d*arctanh(c*x)^2+1/2/c^3*b^2/d*polylog(3,-(c*x+1)^2/(-c^2*x^2+1))+2/c^3*b^2/d*dilog(1+I*(c*x+1)/(-c^2*x^2+1)^(1/2))+2/c^3*b^2/d*dilog(1-I*(c*x+1)/(-c^2*x^2+1)^(1/2))-1/c^3*b^2/d*ln(1+(c*x+1)^2/(-c^2*x^2+1))+2/3/c^3*b^2/d*arctanh(c*x)^3+1/2*I/c^3*b^2/d*Pi*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))*csgn(I*(c*x+1)^2/(c^2*x^2-1))*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))*arctanh(c*x)^2-1/2*I/c^3*b^2/d*Pi*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^3*arctanh(c*x)^2-1/2*I/c^3*b^2/d*Pi*csgn(I*(c*x+1)^2/(c^2*x^2-1))^3*arctanh(c*x)^2+1/c*a*b/d*arctanh(c*x)*x^2-2/c^2*a*b/d*arctanh(c*x)*x+2/c^3*a*b/d*arctanh(c*x)*ln(c*x+1)+1/c^3*a*b/d*ln(-1/2*c*x+1/2)*ln(c*x+1)-1/c^3*a*b/d*ln(-1/2*c*x+1/2)*ln(1/2+1/2*c*x)+2/c^3*b^2/d*arctanh(c*x)*ln(1+I*(c*x+1)/(-c^2*x^2+1)^(1/2))-1/c^3*a*b/d*dilog(1/2+1/2*c*x)-3/2/c^3*a*b/d*ln(c*x+1)-1/2/c^3*a*b/d*ln(c*x-1)+2/c^3*b^2/d*arctanh(c*x)*ln(1-I*(c*x+1)/(-c^2*x^2+1)^(1/2))-2/c^3*b^2/d*arctanh(c*x)^2*ln((c*x+1)/(-c^2*x^2+1)^(1/2))-1/c^3*b^2/d*arctanh(c*x)*polylog(2,-(c*x+1)^2/(-c^2*x^2+1))-1/2/c^3*a*b/d*ln(c*x+1)^2-1/c^2*b^2/d*arctanh(c*x)^2*x+1/2/c*b^2/d*arctanh(c*x)^2*x^2-1/c^3*b^2/d*arctanh(c*x)^2*ln(2)+1/c^3*b^2/d*arctanh(c*x)^2*ln(c*x+1)","C"
97,1,5361,170,0.572000," ","int(x*(a+b*arctanh(c*x))^2/(c*d*x+d),x)","\text{output too large to display}"," ",0,"result too large to display","C"
98,1,822,82,0.403000," ","int((a+b*arctanh(c*x))^2/(c*d*x+d),x)","\frac{a^{2} \ln \left(c x +1\right)}{c d}+\frac{b^{2} \arctanh \left(c x \right)^{2} \ln \left(c x +1\right)}{c d}-\frac{2 b^{2} \arctanh \left(c x \right)^{2} \ln \left(\frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)}{c d}+\frac{2 b^{2} \arctanh \left(c x \right)^{3}}{3 c d}-\frac{i b^{2} \pi  \mathrm{csgn}\left(\frac{i \left(c x +1\right)}{\sqrt{-c^{2} x^{2}+1}}\right)^{2} \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{c^{2} x^{2}-1}\right) \arctanh \left(c x \right)^{2}}{2 c d}-\frac{i b^{2} \pi  \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{\left(c^{2} x^{2}-1\right) \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}\right)^{3} \arctanh \left(c x \right)^{2}}{2 c d}+\frac{i b^{2} \pi  \,\mathrm{csgn}\left(\frac{i}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{c^{2} x^{2}-1}\right) \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{\left(c^{2} x^{2}-1\right) \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}\right) \arctanh \left(c x \right)^{2}}{2 c d}+\frac{i b^{2} \pi  \,\mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{c^{2} x^{2}-1}\right) \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{\left(c^{2} x^{2}-1\right) \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}\right)^{2} \arctanh \left(c x \right)^{2}}{2 c d}-\frac{i b^{2} \pi  \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{c^{2} x^{2}-1}\right)^{3} \arctanh \left(c x \right)^{2}}{2 c d}-\frac{i b^{2} \pi  \,\mathrm{csgn}\left(\frac{i}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{\left(c^{2} x^{2}-1\right) \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}\right)^{2} \arctanh \left(c x \right)^{2}}{2 c d}-\frac{i b^{2} \pi  \,\mathrm{csgn}\left(\frac{i \left(c x +1\right)}{\sqrt{-c^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{c^{2} x^{2}-1}\right)^{2} \arctanh \left(c x \right)^{2}}{c d}-\frac{b^{2} \arctanh \left(c x \right)^{2} \ln \left(2\right)}{c d}-\frac{b^{2} \arctanh \left(c x \right) \polylog \left(2, -\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}{c d}+\frac{b^{2} \polylog \left(3, -\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}{2 c d}+\frac{2 a b \arctanh \left(c x \right) \ln \left(c x +1\right)}{c d}-\frac{a b \ln \left(c x +1\right)^{2}}{2 c d}+\frac{a b \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) \ln \left(c x +1\right)}{c d}-\frac{a b \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{c x}{2}\right)}{c d}-\frac{a b \dilog \left(\frac{1}{2}+\frac{c x}{2}\right)}{c d}"," ",0,"1/c*a^2/d*ln(c*x+1)+1/c*b^2/d*arctanh(c*x)^2*ln(c*x+1)-2/c*b^2/d*arctanh(c*x)^2*ln((c*x+1)/(-c^2*x^2+1)^(1/2))+2/3/c*b^2/d*arctanh(c*x)^3-1/2*I/c*b^2/d*Pi*csgn(I*(c*x+1)/(-c^2*x^2+1)^(1/2))^2*csgn(I*(c*x+1)^2/(c^2*x^2-1))*arctanh(c*x)^2+1/2*I/c*b^2/d*Pi*csgn(I*(c*x+1)^2/(c^2*x^2-1))*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^2*arctanh(c*x)^2-1/2*I/c*b^2/d*Pi*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^2*arctanh(c*x)^2-1/2*I/c*b^2/d*Pi*csgn(I*(c*x+1)^2/(c^2*x^2-1))^3*arctanh(c*x)^2-1/2*I/c*b^2/d*Pi*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^3*arctanh(c*x)^2+1/2*I/c*b^2/d*Pi*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))*csgn(I*(c*x+1)^2/(c^2*x^2-1))*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))*arctanh(c*x)^2-I/c*b^2/d*Pi*csgn(I*(c*x+1)/(-c^2*x^2+1)^(1/2))*csgn(I*(c*x+1)^2/(c^2*x^2-1))^2*arctanh(c*x)^2-1/c*b^2/d*arctanh(c*x)^2*ln(2)-1/c*b^2/d*arctanh(c*x)*polylog(2,-(c*x+1)^2/(-c^2*x^2+1))+1/2/c*b^2/d*polylog(3,-(c*x+1)^2/(-c^2*x^2+1))+2/c*a*b/d*arctanh(c*x)*ln(c*x+1)-1/2/c*a*b/d*ln(c*x+1)^2+1/c*a*b/d*ln(-1/2*c*x+1/2)*ln(c*x+1)-1/c*a*b/d*ln(-1/2*c*x+1/2)*ln(1/2+1/2*c*x)-1/c*a*b/d*dilog(1/2+1/2*c*x)","C"
99,1,1389,75,0.354000," ","int((a+b*arctanh(c*x))^2/x/(c*d*x+d),x)","-\frac{a^{2} \ln \left(c x +1\right)}{d}-\frac{2 b^{2} \arctanh \left(c x \right)^{3}}{3 d}-\frac{2 b^{2} \polylog \left(3, \frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)}{d}-\frac{2 b^{2} \polylog \left(3, -\frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)}{d}+\frac{a^{2} \ln \left(c x \right)}{d}+\frac{i b^{2} \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right)\right) \mathrm{csgn}\left(\frac{i}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right)}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right) \arctanh \left(c x \right)^{2}}{2 d}-\frac{i b^{2} \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right)\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right)}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right)^{2} \arctanh \left(c x \right)^{2}}{2 d}-\frac{i b^{2} \pi  \,\mathrm{csgn}\left(\frac{i}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right)}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right)^{2} \arctanh \left(c x \right)^{2}}{2 d}+\frac{i b^{2} \pi  \,\mathrm{csgn}\left(\frac{i}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{\left(c^{2} x^{2}-1\right) \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}\right)^{2} \arctanh \left(c x \right)^{2}}{2 d}-\frac{i b^{2} \pi  \,\mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{c^{2} x^{2}-1}\right) \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{\left(c^{2} x^{2}-1\right) \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}\right)^{2} \arctanh \left(c x \right)^{2}}{2 d}+\frac{i b^{2} \pi  \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{c^{2} x^{2}-1}\right)^{3} \arctanh \left(c x \right)^{2}}{2 d}+\frac{i b^{2} \pi  \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{\left(c^{2} x^{2}-1\right) \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}\right)^{3} \arctanh \left(c x \right)^{2}}{2 d}+\frac{i b^{2} \pi  \mathrm{csgn}\left(\frac{i \left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right)}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right)^{3} \arctanh \left(c x \right)^{2}}{2 d}-\frac{i b^{2} \pi  \,\mathrm{csgn}\left(\frac{i}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{c^{2} x^{2}-1}\right) \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{\left(c^{2} x^{2}-1\right) \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}\right) \arctanh \left(c x \right)^{2}}{2 d}-\frac{a b \dilog \left(c x +1\right)}{d}+\frac{b^{2} \arctanh \left(c x \right)^{2} \ln \left(c x \right)}{d}+\frac{b^{2} \arctanh \left(c x \right)^{2} \ln \left(1+\frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)}{d}+\frac{b^{2} \arctanh \left(c x \right)^{2} \ln \left(1-\frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)}{d}+\frac{2 b^{2} \arctanh \left(c x \right) \polylog \left(2, \frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)}{d}+\frac{b^{2} \arctanh \left(c x \right)^{2} \ln \left(2\right)}{d}+\frac{2 b^{2} \arctanh \left(c x \right) \polylog \left(2, -\frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)}{d}-\frac{b^{2} \arctanh \left(c x \right)^{2} \ln \left(c x +1\right)}{d}+\frac{a b \dilog \left(\frac{1}{2}+\frac{c x}{2}\right)}{d}+\frac{2 b^{2} \arctanh \left(c x \right)^{2} \ln \left(\frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)}{d}-\frac{b^{2} \arctanh \left(c x \right)^{2} \ln \left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right)}{d}-\frac{a b \dilog \left(c x \right)}{d}+\frac{i b^{2} \pi  \,\mathrm{csgn}\left(\frac{i \left(c x +1\right)}{\sqrt{-c^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{c^{2} x^{2}-1}\right)^{2} \arctanh \left(c x \right)^{2}}{d}+\frac{i b^{2} \pi  \mathrm{csgn}\left(\frac{i \left(c x +1\right)}{\sqrt{-c^{2} x^{2}+1}}\right)^{2} \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{c^{2} x^{2}-1}\right) \arctanh \left(c x \right)^{2}}{2 d}+\frac{a b \ln \left(c x +1\right)^{2}}{2 d}-\frac{2 a b \arctanh \left(c x \right) \ln \left(c x +1\right)}{d}+\frac{2 a b \arctanh \left(c x \right) \ln \left(c x \right)}{d}-\frac{a b \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) \ln \left(c x +1\right)}{d}+\frac{a b \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{c x}{2}\right)}{d}-\frac{a b \ln \left(c x \right) \ln \left(c x +1\right)}{d}"," ",0,"-1/2*I*b^2/d*Pi*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1))*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^2*arctanh(c*x)^2-1/2*I*b^2/d*Pi*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^2*arctanh(c*x)^2+1/2*I*b^2/d*Pi*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^2*arctanh(c*x)^2-1/2*I*b^2/d*Pi*csgn(I*(c*x+1)^2/(c^2*x^2-1))*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^2*arctanh(c*x)^2+I*b^2/d*Pi*csgn(I*(c*x+1)/(-c^2*x^2+1)^(1/2))*csgn(I*(c*x+1)^2/(c^2*x^2-1))^2*arctanh(c*x)^2+1/2*I*b^2/d*Pi*csgn(I*(c*x+1)/(-c^2*x^2+1)^(1/2))^2*csgn(I*(c*x+1)^2/(c^2*x^2-1))*arctanh(c*x)^2-a^2/d*ln(c*x+1)-2/3*b^2/d*arctanh(c*x)^3+a^2/d*ln(c*x)-2*b^2/d*polylog(3,(c*x+1)/(-c^2*x^2+1)^(1/2))-2*b^2/d*polylog(3,-(c*x+1)/(-c^2*x^2+1)^(1/2))+1/2*I*b^2/d*Pi*csgn(I*(c*x+1)^2/(c^2*x^2-1))^3*arctanh(c*x)^2+1/2*I*b^2/d*Pi*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^3*arctanh(c*x)^2+1/2*I*b^2/d*Pi*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^3*arctanh(c*x)^2-1/2*I*b^2/d*Pi*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))*csgn(I*(c*x+1)^2/(c^2*x^2-1))*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))*arctanh(c*x)^2+1/2*I*b^2/d*Pi*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1))*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))*arctanh(c*x)^2+b^2/d*arctanh(c*x)^2*ln(1-(c*x+1)/(-c^2*x^2+1)^(1/2))+2*b^2/d*arctanh(c*x)*polylog(2,(c*x+1)/(-c^2*x^2+1)^(1/2))+b^2/d*arctanh(c*x)^2*ln(2)+2*b^2/d*arctanh(c*x)*polylog(2,-(c*x+1)/(-c^2*x^2+1)^(1/2))-b^2/d*arctanh(c*x)^2*ln(c*x+1)+a*b/d*dilog(1/2+1/2*c*x)+2*b^2/d*arctanh(c*x)^2*ln((c*x+1)/(-c^2*x^2+1)^(1/2))+1/2*a*b/d*ln(c*x+1)^2-b^2/d*arctanh(c*x)^2*ln((c*x+1)^2/(-c^2*x^2+1)-1)-a*b/d*dilog(c*x)-a*b/d*dilog(c*x+1)-2*a*b/d*arctanh(c*x)*ln(c*x+1)-a*b/d*ln(-1/2*c*x+1/2)*ln(c*x+1)+a*b/d*ln(-1/2*c*x+1/2)*ln(1/2+1/2*c*x)+2*a*b/d*arctanh(c*x)*ln(c*x)-a*b/d*ln(c*x)*ln(c*x+1)+b^2/d*arctanh(c*x)^2*ln(c*x)+b^2/d*arctanh(c*x)^2*ln(1+(c*x+1)/(-c^2*x^2+1)^(1/2))","C"
100,1,7232,160,0.949000," ","int((a+b*arctanh(c*x))^2/x^2/(c*d*x+d),x)","\text{output too large to display}"," ",0,"result too large to display","C"
101,1,1841,242,2.099000," ","int((a+b*arctanh(c*x))^2/x^3/(c*d*x+d),x)","\frac{c^{2} b^{2} \ln \left(\frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}-1\right)}{d}+\frac{c^{2} a^{2} \ln \left(c x \right)}{d}-\frac{c^{2} a^{2} \ln \left(c x +1\right)}{d}+\frac{c^{2} b^{2} \ln \left(1+\frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)}{d}+\frac{c \,a^{2}}{d x}+\frac{i c^{2} b^{2} \pi  \,\mathrm{csgn}\left(\frac{i \left(c x +1\right)}{\sqrt{-c^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{c^{2} x^{2}-1}\right)^{2} \arctanh \left(c x \right)^{2}}{d}-\frac{i c^{2} b^{2} \pi  \,\mathrm{csgn}\left(\frac{i}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right)}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right)^{2} \arctanh \left(c x \right)^{2}}{2 d}+\frac{i c^{2} b^{2} \pi  \,\mathrm{csgn}\left(\frac{i}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{\left(c^{2} x^{2}-1\right) \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}\right)^{2} \arctanh \left(c x \right)^{2}}{2 d}-\frac{i c^{2} b^{2} \pi  \,\mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{c^{2} x^{2}-1}\right) \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{\left(c^{2} x^{2}-1\right) \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}\right)^{2} \arctanh \left(c x \right)^{2}}{2 d}+\frac{i c^{2} b^{2} \pi  \mathrm{csgn}\left(\frac{i \left(c x +1\right)}{\sqrt{-c^{2} x^{2}+1}}\right)^{2} \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{c^{2} x^{2}-1}\right) \arctanh \left(c x \right)^{2}}{2 d}-\frac{i c^{2} b^{2} \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right)\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right)}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right)^{2} \arctanh \left(c x \right)^{2}}{2 d}-\frac{i c^{2} b^{2} \pi  \,\mathrm{csgn}\left(\frac{i}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{c^{2} x^{2}-1}\right) \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{\left(c^{2} x^{2}-1\right) \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}\right) \arctanh \left(c x \right)^{2}}{2 d}+\frac{i c^{2} b^{2} \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right)\right) \mathrm{csgn}\left(\frac{i}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right)}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right) \arctanh \left(c x \right)^{2}}{2 d}-\frac{c^{2} a b \ln \left(c x \right) \ln \left(c x +1\right)}{d}-\frac{c^{2} a b \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) \ln \left(c x +1\right)}{d}+\frac{c^{2} a b \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{c x}{2}\right)}{d}+\frac{2 c a b \arctanh \left(c x \right)}{d x}-\frac{2 c^{2} a b \arctanh \left(c x \right) \ln \left(c x +1\right)}{d}+\frac{2 c^{2} a b \arctanh \left(c x \right) \ln \left(c x \right)}{d}-\frac{2 c^{2} b^{2} \dilog \left(1+\frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)}{d}-\frac{2 c^{2} b^{2} \polylog \left(3, \frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)}{d}-\frac{2 c^{2} b^{2} \polylog \left(3, -\frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)}{d}+\frac{2 c^{2} b^{2} \dilog \left(\frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)}{d}-\frac{2 c^{2} b^{2} \arctanh \left(c x \right)^{3}}{3 d}-\frac{c^{2} b^{2} \arctanh \left(c x \right)}{d}+\frac{3 c^{2} b^{2} \arctanh \left(c x \right)^{2}}{2 d}-\frac{b^{2} \arctanh \left(c x \right)^{2}}{2 d \,x^{2}}-\frac{a b \arctanh \left(c x \right)}{d \,x^{2}}+\frac{c^{2} b^{2} \arctanh \left(c x \right)^{2} \ln \left(1-\frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)}{d}+\frac{i c^{2} b^{2} \pi  \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{\left(c^{2} x^{2}-1\right) \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}\right)^{3} \arctanh \left(c x \right)^{2}}{2 d}+\frac{i c^{2} b^{2} \pi  \mathrm{csgn}\left(\frac{i \left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right)}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right)^{3} \arctanh \left(c x \right)^{2}}{2 d}+\frac{i c^{2} b^{2} \pi  \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{c^{2} x^{2}-1}\right)^{3} \arctanh \left(c x \right)^{2}}{2 d}-\frac{a^{2}}{2 d \,x^{2}}+\frac{2 c^{2} b^{2} \arctanh \left(c x \right)^{2} \ln \left(\frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)}{d}-\frac{2 c^{2} b^{2} \arctanh \left(c x \right) \ln \left(1+\frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)}{d}+\frac{c^{2} b^{2} \arctanh \left(c x \right)^{2} \ln \left(1+\frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)}{d}+\frac{2 c^{2} b^{2} \arctanh \left(c x \right) \polylog \left(2, -\frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)}{d}+\frac{c^{2} a b \dilog \left(\frac{1}{2}+\frac{c x}{2}\right)}{d}+\frac{c \,b^{2} \arctanh \left(c x \right)^{2}}{d x}-\frac{c \,b^{2} \arctanh \left(c x \right)}{d x}-\frac{c^{2} b^{2} \arctanh \left(c x \right)^{2} \ln \left(c x +1\right)}{d}+\frac{c^{2} b^{2} \arctanh \left(c x \right)^{2} \ln \left(2\right)}{d}-\frac{c^{2} a b \dilog \left(c x \right)}{d}+\frac{c^{2} b^{2} \arctanh \left(c x \right)^{2} \ln \left(c x \right)}{d}+\frac{2 c^{2} b^{2} \arctanh \left(c x \right) \polylog \left(2, \frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)}{d}-\frac{c^{2} a b \dilog \left(c x +1\right)}{d}-\frac{c^{2} b^{2} \arctanh \left(c x \right)^{2} \ln \left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right)}{d}+\frac{c^{2} a b \ln \left(c x -1\right)}{2 d}+\frac{3 c^{2} a b \ln \left(c x +1\right)}{2 d}+\frac{c^{2} a b \ln \left(c x +1\right)^{2}}{2 d}-\frac{c a b}{d x}-\frac{2 c^{2} a b \ln \left(c x \right)}{d}"," ",0,"c^2*b^2/d*ln((c*x+1)/(-c^2*x^2+1)^(1/2)-1)+c^2*a^2/d*ln(c*x)-2*c^2*b^2/d*dilog(1+(c*x+1)/(-c^2*x^2+1)^(1/2))-2*c^2*b^2/d*polylog(3,(c*x+1)/(-c^2*x^2+1)^(1/2))-2*c^2*b^2/d*polylog(3,-(c*x+1)/(-c^2*x^2+1)^(1/2))+2*c^2*b^2/d*dilog((c*x+1)/(-c^2*x^2+1)^(1/2))-c^2*a^2/d*ln(c*x+1)-2/3*c^2*b^2/d*arctanh(c*x)^3+c^2*b^2/d*ln(1+(c*x+1)/(-c^2*x^2+1)^(1/2))-c^2*b^2/d*arctanh(c*x)+3/2*c^2*b^2/d*arctanh(c*x)^2-1/2*b^2/d*arctanh(c*x)^2/x^2+c*a^2/d/x-1/2*I*c^2*b^2/d*Pi*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))*csgn(I*(c*x+1)^2/(c^2*x^2-1))*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))*arctanh(c*x)^2+1/2*I*c^2*b^2/d*Pi*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1))*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))*arctanh(c*x)^2+I*c^2*b^2/d*Pi*csgn(I*(c*x+1)/(-c^2*x^2+1)^(1/2))*csgn(I*(c*x+1)^2/(c^2*x^2-1))^2*arctanh(c*x)^2-1/2*I*c^2*b^2/d*Pi*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^2*arctanh(c*x)^2+1/2*I*c^2*b^2/d*Pi*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^2*arctanh(c*x)^2-1/2*I*c^2*b^2/d*Pi*csgn(I*(c*x+1)^2/(c^2*x^2-1))*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^2*arctanh(c*x)^2+1/2*I*c^2*b^2/d*Pi*csgn(I*(c*x+1)/(-c^2*x^2+1)^(1/2))^2*csgn(I*(c*x+1)^2/(c^2*x^2-1))*arctanh(c*x)^2-1/2*I*c^2*b^2/d*Pi*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1))*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^2*arctanh(c*x)^2+2*c*a*b/d*arctanh(c*x)/x-c^2*a*b/d*ln(c*x)*ln(c*x+1)-2*c^2*a*b/d*arctanh(c*x)*ln(c*x+1)-c^2*a*b/d*ln(-1/2*c*x+1/2)*ln(c*x+1)+c^2*a*b/d*ln(-1/2*c*x+1/2)*ln(1/2+1/2*c*x)+2*c^2*a*b/d*arctanh(c*x)*ln(c*x)+1/2*I*c^2*b^2/d*Pi*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^3*arctanh(c*x)^2+1/2*I*c^2*b^2/d*Pi*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^3*arctanh(c*x)^2+1/2*I*c^2*b^2/d*Pi*csgn(I*(c*x+1)^2/(c^2*x^2-1))^3*arctanh(c*x)^2-1/2*a^2/d/x^2+c^2*b^2/d*arctanh(c*x)^2*ln(1+(c*x+1)/(-c^2*x^2+1)^(1/2))+2*c^2*b^2/d*arctanh(c*x)*polylog(2,-(c*x+1)/(-c^2*x^2+1)^(1/2))+1/2*c^2*a*b/d*ln(c*x-1)+3/2*c^2*a*b/d*ln(c*x+1)+c^2*a*b/d*dilog(1/2+1/2*c*x)+c*b^2/d*arctanh(c*x)^2/x-c*b^2/d*arctanh(c*x)/x-c^2*b^2/d*arctanh(c*x)^2*ln(c*x+1)+1/2*c^2*a*b/d*ln(c*x+1)^2-c*a*b/d/x+c^2*b^2/d*arctanh(c*x)^2*ln(2)-c^2*a*b/d*dilog(c*x)-2*c^2*a*b/d*ln(c*x)+c^2*b^2/d*arctanh(c*x)^2*ln(c*x)+2*c^2*b^2/d*arctanh(c*x)*polylog(2,(c*x+1)/(-c^2*x^2+1)^(1/2))-c^2*a*b/d*dilog(c*x+1)-c^2*b^2/d*arctanh(c*x)^2*ln((c*x+1)^2/(-c^2*x^2+1)-1)+2*c^2*b^2/d*arctanh(c*x)^2*ln((c*x+1)/(-c^2*x^2+1)^(1/2))-2*c^2*b^2/d*arctanh(c*x)*ln(1+(c*x+1)/(-c^2*x^2+1)^(1/2))-a*b/d*arctanh(c*x)/x^2+c^2*b^2/d*arctanh(c*x)^2*ln(1-(c*x+1)/(-c^2*x^2+1)^(1/2))","C"
102,1,2010,314,3.394000," ","int((a+b*arctanh(c*x))^2/x^4/(c*d*x+d),x)","\frac{i c^{3} b^{2} \pi  \,\mathrm{csgn}\left(\frac{i}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{c^{2} x^{2}-1}\right) \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{\left(c^{2} x^{2}-1\right) \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}\right) \arctanh \left(c x \right)^{2}}{2 d}-\frac{i c^{3} b^{2} \arctanh \left(c x \right)^{2} \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right)\right) \mathrm{csgn}\left(\frac{i}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right)}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right)}{2 d}-\frac{i c^{3} b^{2} \pi  \,\mathrm{csgn}\left(\frac{i \left(c x +1\right)}{\sqrt{-c^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{c^{2} x^{2}-1}\right)^{2} \arctanh \left(c x \right)^{2}}{d}+\frac{c \,a^{2}}{2 d \,x^{2}}-\frac{c^{3} b^{2} \ln \left(1+\frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)}{d}-\frac{c^{3} b^{2} \ln \left(\frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}-1\right)}{d}-\frac{c^{3} a^{2} \ln \left(c x \right)}{d}+\frac{i c^{3} b^{2} \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right)\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right)}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right)^{2} \arctanh \left(c x \right)^{2}}{2 d}+\frac{i c^{3} b^{2} \arctanh \left(c x \right)^{2} \pi  \,\mathrm{csgn}\left(\frac{i}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right)}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right)^{2}}{2 d}+\frac{i c^{3} b^{2} \pi  \,\mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{c^{2} x^{2}-1}\right) \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{\left(c^{2} x^{2}-1\right) \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}\right)^{2} \arctanh \left(c x \right)^{2}}{2 d}-\frac{i c^{3} b^{2} \pi  \,\mathrm{csgn}\left(\frac{i}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{\left(c^{2} x^{2}-1\right) \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}\right)^{2} \arctanh \left(c x \right)^{2}}{2 d}-\frac{i c^{3} b^{2} \pi  \mathrm{csgn}\left(\frac{i \left(c x +1\right)}{\sqrt{-c^{2} x^{2}+1}}\right)^{2} \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{c^{2} x^{2}-1}\right) \arctanh \left(c x \right)^{2}}{2 d}+\frac{8 c^{3} b^{2} \dilog \left(1+\frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)}{3 d}+\frac{2 c^{3} b^{2} \polylog \left(3, \frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)}{d}+\frac{2 c^{3} b^{2} \polylog \left(3, -\frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)}{d}+\frac{4 b^{2} c^{3} \arctanh \left(c x \right)}{3 d}-\frac{11 c^{3} b^{2} \arctanh \left(c x \right)^{2}}{6 d}+\frac{2 c^{3} b^{2} \arctanh \left(c x \right)^{3}}{3 d}-\frac{b^{2} \arctanh \left(c x \right)^{2}}{3 d \,x^{3}}-\frac{8 c^{3} b^{2} \dilog \left(\frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)}{3 d}+\frac{c^{3} a^{2} \ln \left(c x +1\right)}{d}-\frac{c^{2} a^{2}}{d x}-\frac{2 c^{3} a b \arctanh \left(c x \right) \ln \left(c x \right)}{d}-\frac{2 c^{2} a b \arctanh \left(c x \right)}{d x}+\frac{c a b \arctanh \left(c x \right)}{d \,x^{2}}+\frac{2 c^{3} a b \arctanh \left(c x \right) \ln \left(c x +1\right)}{d}+\frac{c^{3} a b \ln \left(c x \right) \ln \left(c x +1\right)}{d}+\frac{c^{3} a b \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) \ln \left(c x +1\right)}{d}-\frac{c^{3} a b \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{c x}{2}\right)}{d}-\frac{5 c^{3} a b \ln \left(c x -1\right)}{6 d}-\frac{c^{3} a b \ln \left(c x +1\right)^{2}}{2 d}-\frac{c^{3} b^{2} \arctanh \left(c x \right)^{2} \ln \left(2\right)}{d}+\frac{8 c^{3} b^{2} \arctanh \left(c x \right) \ln \left(1+\frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)}{3 d}-\frac{2 c^{3} b^{2} \arctanh \left(c x \right)^{2} \ln \left(\frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)}{d}-\frac{c^{3} b^{2} \arctanh \left(c x \right)^{2} \ln \left(c x \right)}{d}-\frac{c^{3} b^{2} \arctanh \left(c x \right)^{2} \ln \left(1+\frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)}{d}-\frac{2 c^{3} b^{2} \arctanh \left(c x \right) \polylog \left(2, -\frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)}{d}-\frac{c^{3} b^{2} \arctanh \left(c x \right)^{2} \ln \left(1-\frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)}{d}-\frac{2 c^{3} b^{2} \arctanh \left(c x \right) \polylog \left(2, \frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)}{d}+\frac{c^{3} b^{2} \arctanh \left(c x \right)^{2} \ln \left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right)}{d}+\frac{c^{3} b^{2} \arctanh \left(c x \right)^{2} \ln \left(c x +1\right)}{d}-\frac{c^{3} a b \dilog \left(\frac{1}{2}+\frac{c x}{2}\right)}{d}+\frac{c^{3} a b \dilog \left(c x +1\right)}{d}+\frac{c^{3} a b \dilog \left(c x \right)}{d}-\frac{c^{2} b^{2} \arctanh \left(c x \right)^{2}}{d x}+\frac{c \,b^{2} \arctanh \left(c x \right)^{2}}{2 d \,x^{2}}+\frac{c^{2} b^{2} \arctanh \left(c x \right)}{d x}-\frac{c \,b^{2} \arctanh \left(c x \right)}{3 d \,x^{2}}-\frac{2 a b \arctanh \left(c x \right)}{3 d \,x^{3}}-\frac{c^{3} b^{2} \sqrt{-c^{2} x^{2}+1}}{3 d \left(c x +1-\sqrt{-c^{2} x^{2}+1}\right)}+\frac{c^{3} b^{2} \sqrt{-c^{2} x^{2}+1}}{3 d \left(\sqrt{-c^{2} x^{2}+1}+c x +1\right)}-\frac{11 c^{3} a b \ln \left(c x +1\right)}{6 d}+\frac{8 c^{3} a b \ln \left(c x \right)}{3 d}+\frac{c^{2} a b}{d x}-\frac{c a b}{3 d \,x^{2}}-\frac{a^{2}}{3 d \,x^{3}}-\frac{i c^{3} b^{2} \pi  \mathrm{csgn}\left(\frac{i \left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right)}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right)^{3} \arctanh \left(c x \right)^{2}}{2 d}-\frac{i c^{3} b^{2} \pi  \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{\left(c^{2} x^{2}-1\right) \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}\right)^{3} \arctanh \left(c x \right)^{2}}{2 d}-\frac{i c^{3} b^{2} \pi  \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{c^{2} x^{2}-1}\right)^{3} \arctanh \left(c x \right)^{2}}{2 d}"," ",0,"1/2*c*a^2/d/x^2-c^3*b^2/d*ln(1+(c*x+1)/(-c^2*x^2+1)^(1/2))-c^3*b^2/d*ln((c*x+1)/(-c^2*x^2+1)^(1/2)-1)-c^3*a^2/d*ln(c*x)+8/3*c^3*b^2/d*dilog(1+(c*x+1)/(-c^2*x^2+1)^(1/2))+2*c^3*b^2/d*polylog(3,(c*x+1)/(-c^2*x^2+1)^(1/2))+2*c^3*b^2/d*polylog(3,-(c*x+1)/(-c^2*x^2+1)^(1/2))+1/2*I*c^3*b^2/d*Pi*csgn(I*(c*x+1)^2/(c^2*x^2-1))*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^2*arctanh(c*x)^2-1/2*I*c^3*b^2/d*Pi*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^2*arctanh(c*x)^2-1/2*I*c^3*b^2/d*Pi*csgn(I*(c*x+1)/(-c^2*x^2+1)^(1/2))^2*csgn(I*(c*x+1)^2/(c^2*x^2-1))*arctanh(c*x)^2-I*c^3*b^2/d*Pi*csgn(I*(c*x+1)/(-c^2*x^2+1)^(1/2))*csgn(I*(c*x+1)^2/(c^2*x^2-1))^2*arctanh(c*x)^2+1/2*I*c^3*b^2/d*Pi*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1))*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^2*arctanh(c*x)^2+1/2*I*c^3*b^2/d*arctanh(c*x)^2*Pi*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^2+4/3*b^2*c^3*arctanh(c*x)/d+c^3*a^2/d*ln(c*x+1)-11/6*c^3*b^2/d*arctanh(c*x)^2+2/3*c^3*b^2/d*arctanh(c*x)^3-1/3*b^2/d*arctanh(c*x)^2/x^3-c^2*a^2/d/x-8/3*c^3*b^2/d*dilog((c*x+1)/(-c^2*x^2+1)^(1/2))-2*c^3*a*b/d*arctanh(c*x)*ln(c*x)-2*c^2*a*b/d*arctanh(c*x)/x+c*a*b/d*arctanh(c*x)/x^2+c^3*a*b/d*ln(c*x)*ln(c*x+1)+2*c^3*a*b/d*arctanh(c*x)*ln(c*x+1)+c^3*a*b/d*ln(-1/2*c*x+1/2)*ln(c*x+1)-c^3*a*b/d*ln(-1/2*c*x+1/2)*ln(1/2+1/2*c*x)-5/6*c^3*a*b/d*ln(c*x-1)-1/2*c^3*a*b/d*ln(c*x+1)^2-c^3*b^2/d*arctanh(c*x)^2*ln(2)+8/3*c^3*b^2/d*arctanh(c*x)*ln(1+(c*x+1)/(-c^2*x^2+1)^(1/2))-2*c^3*b^2/d*arctanh(c*x)^2*ln((c*x+1)/(-c^2*x^2+1)^(1/2))-c^3*b^2/d*arctanh(c*x)^2*ln(c*x)-1/3*c^3*b^2/d/(c*x+1-(-c^2*x^2+1)^(1/2))*(-c^2*x^2+1)^(1/2)+1/3*c^3*b^2/d/((-c^2*x^2+1)^(1/2)+c*x+1)*(-c^2*x^2+1)^(1/2)-c^3*b^2/d*arctanh(c*x)^2*ln(1+(c*x+1)/(-c^2*x^2+1)^(1/2))-2*c^3*b^2/d*arctanh(c*x)*polylog(2,-(c*x+1)/(-c^2*x^2+1)^(1/2))-c^3*b^2/d*arctanh(c*x)^2*ln(1-(c*x+1)/(-c^2*x^2+1)^(1/2))-2*c^3*b^2/d*arctanh(c*x)*polylog(2,(c*x+1)/(-c^2*x^2+1)^(1/2))+c^3*b^2/d*arctanh(c*x)^2*ln((c*x+1)^2/(-c^2*x^2+1)-1)+c^3*b^2/d*arctanh(c*x)^2*ln(c*x+1)-c^3*a*b/d*dilog(1/2+1/2*c*x)-11/6*c^3*a*b/d*ln(c*x+1)+c^3*a*b/d*dilog(c*x+1)+c^3*a*b/d*dilog(c*x)+8/3*c^3*a*b/d*ln(c*x)-c^2*b^2/d*arctanh(c*x)^2/x+1/2*c*b^2/d*arctanh(c*x)^2/x^2+c^2*b^2/d*arctanh(c*x)/x-1/3*c*b^2/d*arctanh(c*x)/x^2+c^2*a*b/d/x-1/3*c*a*b/d/x^2-2/3*a*b/d*arctanh(c*x)/x^3+1/2*I*c^3*b^2/d*Pi*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))*csgn(I*(c*x+1)^2/(c^2*x^2-1))*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))*arctanh(c*x)^2-1/3*a^2/d/x^3-1/2*I*c^3*b^2/d*arctanh(c*x)^2*Pi*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1))*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))-1/2*I*c^3*b^2/d*Pi*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^3*arctanh(c*x)^2-1/2*I*c^3*b^2/d*Pi*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^3*arctanh(c*x)^2-1/2*I*c^3*b^2/d*Pi*csgn(I*(c*x+1)^2/(c^2*x^2-1))^3*arctanh(c*x)^2","C"
103,1,1467,378,2.309000," ","int(x^4*(a+b*arctanh(c*x))^2/(c*d*x+d)^2,x)","\frac{2 i b^{2} \arctanh \left(c x \right)^{2} \pi  \mathrm{csgn}\left(\frac{i \left(c x +1\right)}{\sqrt{-c^{2} x^{2}+1}}\right)^{2} \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{c^{2} x^{2}-1}\right)}{c^{5} d^{2}}+\frac{4 i b^{2} \arctanh \left(c x \right)^{2} \pi  \,\mathrm{csgn}\left(\frac{i \left(c x +1\right)}{\sqrt{-c^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{c^{2} x^{2}-1}\right)^{2}}{c^{5} d^{2}}-\frac{2 i b^{2} \arctanh \left(c x \right)^{2} \pi  \,\mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{c^{2} x^{2}-1}\right) \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{\left(c^{2} x^{2}-1\right) \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}\right)^{2}}{c^{5} d^{2}}+\frac{2 i b^{2} \arctanh \left(c x \right)^{2} \pi  \,\mathrm{csgn}\left(\frac{i}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{\left(c^{2} x^{2}-1\right) \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}\right)^{2}}{c^{5} d^{2}}-\frac{2 a b x}{d^{2} c^{4}}+\frac{b^{2} x}{3 d^{2} c^{4}}-\frac{b^{2}}{4 c^{5} d^{2} \left(c x +1\right)}+\frac{2 i b^{2} \pi  \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{\left(c^{2} x^{2}-1\right) \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}\right)^{3} \arctanh \left(c x \right)^{2}}{c^{5} d^{2}}+\frac{2 i b^{2} \arctanh \left(c x \right)^{2} \pi  \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{c^{2} x^{2}-1}\right)^{3}}{c^{5} d^{2}}-\frac{b^{2}}{3 c^{5} d^{2}}-\frac{7 b^{2} \arctanh \left(c x \right)}{3 c^{5} d^{2}}+\frac{29 b^{2} \arctanh \left(c x \right)^{2}}{6 c^{5} d^{2}}-\frac{8 b^{2} \arctanh \left(c x \right)^{3}}{3 c^{5} d^{2}}-\frac{2 b^{2} \polylog \left(3, -\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}{c^{5} d^{2}}-\frac{20 b^{2} \dilog \left(1-\frac{i \left(c x +1\right)}{\sqrt{-c^{2} x^{2}+1}}\right)}{3 c^{5} d^{2}}-\frac{20 b^{2} \dilog \left(1+\frac{i \left(c x +1\right)}{\sqrt{-c^{2} x^{2}+1}}\right)}{3 c^{5} d^{2}}+\frac{a^{2} x^{3}}{3 c^{2} d^{2}}-\frac{a^{2} x^{2}}{c^{3} d^{2}}+\frac{3 a^{2} x}{c^{4} d^{2}}-\frac{a^{2}}{c^{5} d^{2} \left(c x +1\right)}-\frac{4 a^{2} \ln \left(c x +1\right)}{c^{5} d^{2}}+\frac{2 b^{2} \ln \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}{c^{5} d^{2}}-\frac{7 a b}{3 c^{5} d^{2}}-\frac{2 i b^{2} \arctanh \left(c x \right)^{2} \pi  \,\mathrm{csgn}\left(\frac{i}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{c^{2} x^{2}-1}\right) \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{\left(c^{2} x^{2}-1\right) \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}\right)}{c^{5} d^{2}}-\frac{4 a b \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) \ln \left(c x +1\right)}{c^{5} d^{2}}+\frac{4 a b \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{c x}{2}\right)}{c^{5} d^{2}}+\frac{6 a b \arctanh \left(c x \right) x}{c^{4} d^{2}}+\frac{2 a b \arctanh \left(c x \right) x^{3}}{3 c^{2} d^{2}}-\frac{2 a b \arctanh \left(c x \right) x^{2}}{c^{3} d^{2}}+\frac{b^{2} \arctanh \left(c x \right) x}{2 c^{4} d^{2} \left(c x +1\right)}-\frac{2 a b \arctanh \left(c x \right)}{c^{5} d^{2} \left(c x +1\right)}-\frac{8 a b \arctanh \left(c x \right) \ln \left(c x +1\right)}{c^{5} d^{2}}-\frac{2 b^{2} x \arctanh \left(c x \right)}{d^{2} c^{4}}-\frac{4 b^{2} \arctanh \left(c x \right)^{2} \ln \left(c x +1\right)}{c^{5} d^{2}}-\frac{b^{2} \arctanh \left(c x \right)^{2} x^{2}}{c^{3} d^{2}}+\frac{3 b^{2} \arctanh \left(c x \right)^{2} x}{c^{4} d^{2}}+\frac{b^{2} \arctanh \left(c x \right) x^{2}}{3 c^{3} d^{2}}+\frac{4 b^{2} \arctanh \left(c x \right)^{2} \ln \left(2\right)}{c^{5} d^{2}}+\frac{4 a b \dilog \left(\frac{1}{2}+\frac{c x}{2}\right)}{c^{5} d^{2}}+\frac{b^{2} \arctanh \left(c x \right)^{2} x^{3}}{3 c^{2} d^{2}}-\frac{b^{2} \arctanh \left(c x \right)^{2}}{c^{5} d^{2} \left(c x +1\right)}-\frac{b^{2} \arctanh \left(c x \right)}{2 c^{5} d^{2} \left(c x +1\right)}+\frac{8 b^{2} \arctanh \left(c x \right)^{2} \ln \left(\frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)}{c^{5} d^{2}}+\frac{4 b^{2} \arctanh \left(c x \right) \polylog \left(2, -\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}{c^{5} d^{2}}-\frac{20 b^{2} \arctanh \left(c x \right) \ln \left(1-\frac{i \left(c x +1\right)}{\sqrt{-c^{2} x^{2}+1}}\right)}{3 c^{5} d^{2}}-\frac{20 b^{2} \arctanh \left(c x \right) \ln \left(1+\frac{i \left(c x +1\right)}{\sqrt{-c^{2} x^{2}+1}}\right)}{3 c^{5} d^{2}}+\frac{29 a b \ln \left(c x +1\right)}{6 c^{5} d^{2}}+\frac{11 a b \ln \left(c x -1\right)}{6 c^{5} d^{2}}+\frac{2 a b \ln \left(c x +1\right)^{2}}{c^{5} d^{2}}-\frac{a b}{c^{5} d^{2} \left(c x +1\right)}+\frac{b^{2} x}{4 c^{4} d^{2} \left(c x +1\right)}+\frac{a b \,x^{2}}{3 c^{3} d^{2}}"," ",0,"2*I/c^5*b^2/d^2*arctanh(c*x)^2*Pi*csgn(I*(c*x+1)/(-c^2*x^2+1)^(1/2))^2*csgn(I*(c*x+1)^2/(c^2*x^2-1))+4*I/c^5*b^2/d^2*arctanh(c*x)^2*Pi*csgn(I*(c*x+1)/(-c^2*x^2+1)^(1/2))*csgn(I*(c*x+1)^2/(c^2*x^2-1))^2-2*I/c^5*b^2/d^2*arctanh(c*x)^2*Pi*csgn(I*(c*x+1)^2/(c^2*x^2-1))*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^2+2*I/c^5*b^2/d^2*arctanh(c*x)^2*Pi*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^2-2*a*b*x/d^2/c^4-2*b^2*x*arctanh(c*x)/d^2/c^4+1/3*b^2*x/d^2/c^4-1/4*b^2/c^5/d^2/(c*x+1)-7/3*b^2*arctanh(c*x)/c^5/d^2+2*I/c^5*b^2/d^2*Pi*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^3*arctanh(c*x)^2+2*I/c^5*b^2/d^2*arctanh(c*x)^2*Pi*csgn(I*(c*x+1)^2/(c^2*x^2-1))^3-1/3/c^5*b^2/d^2+1/3/c^2*a^2/d^2*x^3-1/c^3*a^2/d^2*x^2+3/c^4*a^2/d^2*x-1/c^5*a^2/d^2/(c*x+1)-4/c^5*a^2/d^2*ln(c*x+1)+29/6/c^5*b^2/d^2*arctanh(c*x)^2+2/c^5*b^2/d^2*ln(1+(c*x+1)^2/(-c^2*x^2+1))-8/3/c^5*b^2/d^2*arctanh(c*x)^3-20/3/c^5*b^2/d^2*dilog(1-I*(c*x+1)/(-c^2*x^2+1)^(1/2))-20/3/c^5*b^2/d^2*dilog(1+I*(c*x+1)/(-c^2*x^2+1)^(1/2))-2/c^5*b^2/d^2*polylog(3,-(c*x+1)^2/(-c^2*x^2+1))-7/3/c^5*a*b/d^2-2*I/c^5*b^2/d^2*arctanh(c*x)^2*Pi*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))*csgn(I*(c*x+1)^2/(c^2*x^2-1))*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))+6/c^4*a*b/d^2*arctanh(c*x)*x+2/3/c^2*a*b/d^2*arctanh(c*x)*x^3-2/c^3*a*b/d^2*arctanh(c*x)*x^2+1/2/c^4*b^2/d^2*arctanh(c*x)/(c*x+1)*x-2/c^5*a*b/d^2*arctanh(c*x)/(c*x+1)-8/c^5*a*b/d^2*arctanh(c*x)*ln(c*x+1)-4/c^5*a*b/d^2*ln(-1/2*c*x+1/2)*ln(c*x+1)+4/c^5*a*b/d^2*ln(-1/2*c*x+1/2)*ln(1/2+1/2*c*x)-4/c^5*b^2/d^2*arctanh(c*x)^2*ln(c*x+1)+29/6/c^5*a*b/d^2*ln(c*x+1)+11/6/c^5*a*b/d^2*ln(c*x-1)-1/c^3*b^2/d^2*arctanh(c*x)^2*x^2+3/c^4*b^2/d^2*arctanh(c*x)^2*x+1/3/c^3*b^2/d^2*arctanh(c*x)*x^2+4/c^5*b^2/d^2*arctanh(c*x)^2*ln(2)+2/c^5*a*b/d^2*ln(c*x+1)^2+4/c^5*a*b/d^2*dilog(1/2+1/2*c*x)+1/3/c^2*b^2/d^2*arctanh(c*x)^2*x^3-1/c^5*b^2/d^2*arctanh(c*x)^2/(c*x+1)-1/2/c^5*b^2/d^2*arctanh(c*x)/(c*x+1)-20/3/c^5*b^2/d^2*arctanh(c*x)*ln(1-I*(c*x+1)/(-c^2*x^2+1)^(1/2))+8/c^5*b^2/d^2*arctanh(c*x)^2*ln((c*x+1)/(-c^2*x^2+1)^(1/2))+4/c^5*b^2/d^2*arctanh(c*x)*polylog(2,-(c*x+1)^2/(-c^2*x^2+1))-20/3/c^5*b^2/d^2*arctanh(c*x)*ln(1+I*(c*x+1)/(-c^2*x^2+1)^(1/2))-1/c^5*a*b/d^2/(c*x+1)+1/4/c^4*b^2/d^2/(c*x+1)*x+1/3/c^3*a*b/d^2*x^2","C"
104,1,1354,321,1.742000," ","int(x^3*(a+b*arctanh(c*x))^2/(c*d*x+d)^2,x)","\frac{a^{2} x^{2}}{2 c^{2} d^{2}}-\frac{2 a^{2} x}{c^{3} d^{2}}+\frac{a^{2}}{c^{4} d^{2} \left(c x +1\right)}+\frac{3 a^{2} \ln \left(c x +1\right)}{c^{4} d^{2}}-\frac{b^{2} \ln \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}{c^{4} d^{2}}+\frac{a b x}{c^{3} d^{2}}+\frac{3 i b^{2} \arctanh \left(c x \right)^{2} \pi  \,\mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{c^{2} x^{2}-1}\right) \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{\left(c^{2} x^{2}-1\right) \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}\right)^{2}}{2 c^{4} d^{2}}-\frac{3 i b^{2} \arctanh \left(c x \right)^{2} \pi  \,\mathrm{csgn}\left(\frac{i \left(c x +1\right)}{\sqrt{-c^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{c^{2} x^{2}-1}\right)^{2}}{c^{4} d^{2}}-\frac{3 i b^{2} \arctanh \left(c x \right)^{2} \pi  \mathrm{csgn}\left(\frac{i \left(c x +1\right)}{\sqrt{-c^{2} x^{2}+1}}\right)^{2} \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{c^{2} x^{2}-1}\right)}{2 c^{4} d^{2}}-\frac{3 i b^{2} \arctanh \left(c x \right)^{2} \pi  \,\mathrm{csgn}\left(\frac{i}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{\left(c^{2} x^{2}-1\right) \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}\right)^{2}}{2 c^{4} d^{2}}+\frac{b^{2}}{4 c^{4} d^{2} \left(c x +1\right)}+\frac{3 b^{2} \polylog \left(3, -\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}{2 c^{4} d^{2}}-\frac{3 b^{2} \arctanh \left(c x \right)^{2}}{c^{4} d^{2}}+\frac{2 b^{2} \arctanh \left(c x \right)^{3}}{c^{4} d^{2}}+\frac{b^{2} \arctanh \left(c x \right)}{d^{2} c^{4}}+\frac{4 b^{2} \dilog \left(1-\frac{i \left(c x +1\right)}{\sqrt{-c^{2} x^{2}+1}}\right)}{c^{4} d^{2}}+\frac{4 b^{2} \dilog \left(1+\frac{i \left(c x +1\right)}{\sqrt{-c^{2} x^{2}+1}}\right)}{c^{4} d^{2}}+\frac{3 i b^{2} \arctanh \left(c x \right)^{2} \pi  \,\mathrm{csgn}\left(\frac{i}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{c^{2} x^{2}-1}\right) \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{\left(c^{2} x^{2}-1\right) \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}\right)}{2 c^{4} d^{2}}-\frac{3 i b^{2} \pi  \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{\left(c^{2} x^{2}-1\right) \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}\right)^{3} \arctanh \left(c x \right)^{2}}{2 c^{4} d^{2}}-\frac{3 a b \ln \left(c x +1\right)^{2}}{2 c^{4} d^{2}}-\frac{3 a b \ln \left(c x +1\right)}{c^{4} d^{2}}+\frac{a b}{c^{4} d^{2} \left(c x +1\right)}-\frac{b^{2} x}{4 c^{3} d^{2} \left(c x +1\right)}+\frac{b^{2} x \arctanh \left(c x \right)}{c^{3} d^{2}}+\frac{b^{2} \arctanh \left(c x \right)^{2}}{c^{4} d^{2} \left(c x +1\right)}+\frac{b^{2} \arctanh \left(c x \right)}{2 c^{4} d^{2} \left(c x +1\right)}-\frac{6 b^{2} \arctanh \left(c x \right)^{2} \ln \left(\frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)}{c^{4} d^{2}}-\frac{3 b^{2} \arctanh \left(c x \right) \polylog \left(2, -\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}{c^{4} d^{2}}+\frac{3 b^{2} \arctanh \left(c x \right)^{2} \ln \left(c x +1\right)}{c^{4} d^{2}}-\frac{3 b^{2} \arctanh \left(c x \right)^{2} \ln \left(2\right)}{c^{4} d^{2}}-\frac{3 a b \dilog \left(\frac{1}{2}+\frac{c x}{2}\right)}{c^{4} d^{2}}-\frac{2 b^{2} \arctanh \left(c x \right)^{2} x}{c^{3} d^{2}}+\frac{b^{2} \arctanh \left(c x \right)^{2} x^{2}}{2 c^{2} d^{2}}+\frac{4 b^{2} \arctanh \left(c x \right) \ln \left(1-\frac{i \left(c x +1\right)}{\sqrt{-c^{2} x^{2}+1}}\right)}{c^{4} d^{2}}+\frac{4 b^{2} \arctanh \left(c x \right) \ln \left(1+\frac{i \left(c x +1\right)}{\sqrt{-c^{2} x^{2}+1}}\right)}{c^{4} d^{2}}+\frac{a b}{c^{4} d^{2}}-\frac{a b \ln \left(c x -1\right)}{c^{4} d^{2}}+\frac{3 a b \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) \ln \left(c x +1\right)}{c^{4} d^{2}}-\frac{3 a b \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{c x}{2}\right)}{c^{4} d^{2}}-\frac{4 a b \arctanh \left(c x \right) x}{c^{3} d^{2}}+\frac{a b \arctanh \left(c x \right) x^{2}}{c^{2} d^{2}}-\frac{b^{2} \arctanh \left(c x \right) x}{2 c^{3} d^{2} \left(c x +1\right)}+\frac{2 a b \arctanh \left(c x \right)}{c^{4} d^{2} \left(c x +1\right)}+\frac{6 a b \arctanh \left(c x \right) \ln \left(c x +1\right)}{c^{4} d^{2}}-\frac{3 i b^{2} \arctanh \left(c x \right)^{2} \pi  \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{c^{2} x^{2}-1}\right)^{3}}{2 c^{4} d^{2}}"," ",0,"1/2/c^2*a^2/d^2*x^2-2/c^3*a^2/d^2*x+1/c^4*a^2/d^2/(c*x+1)+4/c^4*b^2/d^2*dilog(1-I*(c*x+1)/(-c^2*x^2+1)^(1/2))+4/c^4*b^2/d^2*dilog(1+I*(c*x+1)/(-c^2*x^2+1)^(1/2))+3/2/c^4*b^2/d^2*polylog(3,-(c*x+1)^2/(-c^2*x^2+1))+3/c^4*a^2/d^2*ln(c*x+1)-3/c^4*b^2/d^2*arctanh(c*x)^2-1/c^4*b^2/d^2*ln(1+(c*x+1)^2/(-c^2*x^2+1))+2/c^4*b^2/d^2*arctanh(c*x)^3+a*b*x/c^3/d^2+b^2*x*arctanh(c*x)/c^3/d^2+3/2*I/c^4*b^2/d^2*arctanh(c*x)^2*Pi*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))*csgn(I*(c*x+1)^2/(c^2*x^2-1))*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))+1/4*b^2/c^4/d^2/(c*x+1)+b^2*arctanh(c*x)/d^2/c^4+3/2*I/c^4*b^2/d^2*arctanh(c*x)^2*Pi*csgn(I*(c*x+1)^2/(c^2*x^2-1))*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^2-3*I/c^4*b^2/d^2*arctanh(c*x)^2*Pi*csgn(I*(c*x+1)/(-c^2*x^2+1)^(1/2))*csgn(I*(c*x+1)^2/(c^2*x^2-1))^2-3/2*I/c^4*b^2/d^2*arctanh(c*x)^2*Pi*csgn(I*(c*x+1)/(-c^2*x^2+1)^(1/2))^2*csgn(I*(c*x+1)^2/(c^2*x^2-1))-3/2*I/c^4*b^2/d^2*arctanh(c*x)^2*Pi*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^2-3/2*I/c^4*b^2/d^2*Pi*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^3*arctanh(c*x)^2-3/2*I/c^4*b^2/d^2*arctanh(c*x)^2*Pi*csgn(I*(c*x+1)^2/(c^2*x^2-1))^3-4/c^3*a*b/d^2*arctanh(c*x)*x+1/c^2*a*b/d^2*arctanh(c*x)*x^2-1/2/c^3*b^2/d^2*arctanh(c*x)/(c*x+1)*x+1/c^4*b^2/d^2*arctanh(c*x)^2/(c*x+1)+1/2/c^4*b^2/d^2*arctanh(c*x)/(c*x+1)+4/c^4*b^2/d^2*arctanh(c*x)*ln(1-I*(c*x+1)/(-c^2*x^2+1)^(1/2))-6/c^4*b^2/d^2*arctanh(c*x)^2*ln((c*x+1)/(-c^2*x^2+1)^(1/2))-3/c^4*b^2/d^2*arctanh(c*x)*polylog(2,-(c*x+1)^2/(-c^2*x^2+1))+4/c^4*b^2/d^2*arctanh(c*x)*ln(1+I*(c*x+1)/(-c^2*x^2+1)^(1/2))+3/c^4*b^2/d^2*arctanh(c*x)^2*ln(c*x+1)-3/c^4*b^2/d^2*arctanh(c*x)^2*ln(2)-3/2/c^4*a*b/d^2*ln(c*x+1)^2-3/c^4*a*b/d^2*dilog(1/2+1/2*c*x)-3/c^4*a*b/d^2*ln(c*x+1)+1/c^4*a*b/d^2/(c*x+1)-1/4/c^3*b^2/d^2/(c*x+1)*x+1/c^4*a*b/d^2-1/c^4*a*b/d^2*ln(c*x-1)-2/c^3*b^2/d^2*arctanh(c*x)^2*x+1/2/c^2*b^2/d^2*arctanh(c*x)^2*x^2+2/c^4*a*b/d^2*arctanh(c*x)/(c*x+1)+6/c^4*a*b/d^2*arctanh(c*x)*ln(c*x+1)+3/c^4*a*b/d^2*ln(-1/2*c*x+1/2)*ln(c*x+1)-3/c^4*a*b/d^2*ln(-1/2*c*x+1/2)*ln(1/2+1/2*c*x)","C"
105,1,5542,254,0.745000," ","int(x^2*(a+b*arctanh(c*x))^2/(c*d*x+d)^2,x)","\text{output too large to display}"," ",0,"result too large to display","C"
106,1,1030,180,0.348000," ","int(x*(a+b*arctanh(c*x))^2/(c*d*x+d)^2,x)","-\frac{i b^{2} \pi  \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{\left(c^{2} x^{2}-1\right) \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}\right)^{3} \arctanh \left(c x \right)^{2}}{2 c^{2} d^{2}}+\frac{i b^{2} \arctanh \left(c x \right)^{2} \pi  \,\mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{c^{2} x^{2}-1}\right) \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{\left(c^{2} x^{2}-1\right) \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}\right) \mathrm{csgn}\left(\frac{i}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right)}{2 c^{2} d^{2}}-\frac{i b^{2} \arctanh \left(c x \right)^{2} \pi  \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{c^{2} x^{2}-1}\right)^{3}}{2 c^{2} d^{2}}-\frac{i b^{2} \arctanh \left(c x \right)^{2} \pi  \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{c^{2} x^{2}-1}\right)^{2} \mathrm{csgn}\left(\frac{i \left(c x +1\right)}{\sqrt{-c^{2} x^{2}+1}}\right)}{c^{2} d^{2}}+\frac{i b^{2} \arctanh \left(c x \right)^{2} \pi  \,\mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{c^{2} x^{2}-1}\right) \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{\left(c^{2} x^{2}-1\right) \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}\right)^{2}}{2 c^{2} d^{2}}-\frac{i b^{2} \arctanh \left(c x \right)^{2} \pi  \,\mathrm{csgn}\left(\frac{i}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{\left(c^{2} x^{2}-1\right) \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}\right)^{2}}{2 c^{2} d^{2}}-\frac{i b^{2} \arctanh \left(c x \right)^{2} \pi  \mathrm{csgn}\left(\frac{i \left(c x +1\right)}{\sqrt{-c^{2} x^{2}+1}}\right)^{2} \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{c^{2} x^{2}-1}\right)}{2 c^{2} d^{2}}+\frac{a^{2}}{c^{2} d^{2} \left(c x +1\right)}+\frac{a^{2} \ln \left(c x +1\right)}{c^{2} d^{2}}-\frac{b^{2} \arctanh \left(c x \right)^{2}}{2 c^{2} d^{2}}+\frac{2 b^{2} \arctanh \left(c x \right)^{3}}{3 c^{2} d^{2}}+\frac{b^{2} \polylog \left(3, -\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}{2 c^{2} d^{2}}+\frac{b^{2}}{4 c^{2} d^{2} \left(c x +1\right)}+\frac{2 a b \arctanh \left(c x \right) \ln \left(c x +1\right)}{c^{2} d^{2}}+\frac{2 a b \arctanh \left(c x \right)}{c^{2} d^{2} \left(c x +1\right)}+\frac{a b \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) \ln \left(c x +1\right)}{c^{2} d^{2}}-\frac{a b \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{c x}{2}\right)}{c^{2} d^{2}}-\frac{b^{2} \arctanh \left(c x \right) x}{2 c \,d^{2} \left(c x +1\right)}-\frac{a b \ln \left(c x +1\right)^{2}}{2 c^{2} d^{2}}-\frac{a b \ln \left(c x +1\right)}{2 c^{2} d^{2}}-\frac{b^{2} \arctanh \left(c x \right)^{2} \ln \left(2\right)}{c^{2} d^{2}}-\frac{a b \dilog \left(\frac{1}{2}+\frac{c x}{2}\right)}{c^{2} d^{2}}+\frac{b^{2} \arctanh \left(c x \right)^{2}}{c^{2} d^{2} \left(c x +1\right)}+\frac{b^{2} \arctanh \left(c x \right)}{2 c^{2} d^{2} \left(c x +1\right)}-\frac{2 b^{2} \arctanh \left(c x \right)^{2} \ln \left(\frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)}{c^{2} d^{2}}-\frac{b^{2} \arctanh \left(c x \right) \polylog \left(2, -\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}{c^{2} d^{2}}+\frac{b^{2} \arctanh \left(c x \right)^{2} \ln \left(c x +1\right)}{c^{2} d^{2}}+\frac{a b \ln \left(c x -1\right)}{2 c^{2} d^{2}}+\frac{a b}{c^{2} d^{2} \left(c x +1\right)}-\frac{b^{2} x}{4 c \,d^{2} \left(c x +1\right)}"," ",0,"-1/2*I/c^2*b^2/d^2*Pi*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^3*arctanh(c*x)^2+1/2*I/c^2*b^2/d^2*arctanh(c*x)^2*Pi*csgn(I*(c*x+1)^2/(c^2*x^2-1))*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))-1/2*I/c^2*b^2/d^2*arctanh(c*x)^2*Pi*csgn(I*(c*x+1)/(-c^2*x^2+1)^(1/2))^2*csgn(I*(c*x+1)^2/(c^2*x^2-1))-I/c^2*b^2/d^2*arctanh(c*x)^2*Pi*csgn(I*(c*x+1)^2/(c^2*x^2-1))^2*csgn(I*(c*x+1)/(-c^2*x^2+1)^(1/2))+1/2*I/c^2*b^2/d^2*arctanh(c*x)^2*Pi*csgn(I*(c*x+1)^2/(c^2*x^2-1))*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^2-1/2*I/c^2*b^2/d^2*arctanh(c*x)^2*Pi*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^2+1/c^2*a^2/d^2/(c*x+1)+1/c^2*a^2/d^2*ln(c*x+1)-1/2/c^2*b^2/d^2*arctanh(c*x)^2+2/3/c^2*b^2/d^2*arctanh(c*x)^3+1/2/c^2*b^2/d^2*polylog(3,-(c*x+1)^2/(-c^2*x^2+1))+1/4*b^2/c^2/d^2/(c*x+1)-1/2/c*b^2/d^2*arctanh(c*x)/(c*x+1)*x+2/c^2*a*b/d^2*arctanh(c*x)*ln(c*x+1)+1/c^2*a*b/d^2*ln(-1/2*c*x+1/2)*ln(c*x+1)-1/c^2*a*b/d^2*ln(-1/2*c*x+1/2)*ln(1/2+1/2*c*x)+2/c^2*a*b/d^2*arctanh(c*x)/(c*x+1)-1/2*I/c^2*b^2/d^2*arctanh(c*x)^2*Pi*csgn(I*(c*x+1)^2/(c^2*x^2-1))^3-1/c^2*b^2/d^2*arctanh(c*x)^2*ln(2)-1/2/c^2*a*b/d^2*ln(c*x+1)^2-1/c^2*a*b/d^2*dilog(1/2+1/2*c*x)-1/2/c^2*a*b/d^2*ln(c*x+1)+1/2/c^2*a*b/d^2*ln(c*x-1)+1/c^2*b^2/d^2*arctanh(c*x)^2/(c*x+1)+1/2/c^2*b^2/d^2*arctanh(c*x)/(c*x+1)-2/c^2*b^2/d^2*arctanh(c*x)^2*ln((c*x+1)/(-c^2*x^2+1)^(1/2))-1/c^2*b^2/d^2*arctanh(c*x)*polylog(2,-(c*x+1)^2/(-c^2*x^2+1))+1/c^2*a*b/d^2/(c*x+1)-1/4/c*b^2/d^2/(c*x+1)*x+1/c^2*b^2/d^2*arctanh(c*x)^2*ln(c*x+1)","C"
107,1,341,101,0.063000," ","int((a+b*arctanh(c*x))^2/(c*d*x+d)^2,x)","-\frac{a^{2}}{c \,d^{2} \left(c x +1\right)}-\frac{b^{2} \arctanh \left(c x \right)^{2}}{c \,d^{2} \left(c x +1\right)}-\frac{b^{2} \arctanh \left(c x \right) \ln \left(c x -1\right)}{2 c \,d^{2}}-\frac{b^{2} \arctanh \left(c x \right)}{c \,d^{2} \left(c x +1\right)}+\frac{b^{2} \arctanh \left(c x \right) \ln \left(c x +1\right)}{2 c \,d^{2}}-\frac{b^{2} \ln \left(c x -1\right)^{2}}{8 c \,d^{2}}+\frac{b^{2} \ln \left(c x -1\right) \ln \left(\frac{1}{2}+\frac{c x}{2}\right)}{4 c \,d^{2}}-\frac{b^{2} \ln \left(c x -1\right)}{4 c \,d^{2}}-\frac{b^{2}}{2 c \,d^{2} \left(c x +1\right)}+\frac{b^{2} \ln \left(c x +1\right)}{4 c \,d^{2}}-\frac{b^{2} \ln \left(c x +1\right)^{2}}{8 c \,d^{2}}+\frac{b^{2} \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) \ln \left(c x +1\right)}{4 c \,d^{2}}-\frac{b^{2} \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{c x}{2}\right)}{4 c \,d^{2}}-\frac{2 a b \arctanh \left(c x \right)}{c \,d^{2} \left(c x +1\right)}-\frac{a b \ln \left(c x -1\right)}{2 c \,d^{2}}-\frac{a b}{c \,d^{2} \left(c x +1\right)}+\frac{a b \ln \left(c x +1\right)}{2 c \,d^{2}}"," ",0,"-1/c*a^2/d^2/(c*x+1)-1/c*b^2/d^2*arctanh(c*x)^2/(c*x+1)-1/2/c*b^2/d^2*arctanh(c*x)*ln(c*x-1)-1/c*b^2/d^2*arctanh(c*x)/(c*x+1)+1/2/c*b^2/d^2*arctanh(c*x)*ln(c*x+1)-1/8/c*b^2/d^2*ln(c*x-1)^2+1/4/c*b^2/d^2*ln(c*x-1)*ln(1/2+1/2*c*x)-1/4/c*b^2/d^2*ln(c*x-1)-1/2*b^2/c/d^2/(c*x+1)+1/4/c*b^2/d^2*ln(c*x+1)-1/8/c*b^2/d^2*ln(c*x+1)^2+1/4/c*b^2/d^2*ln(-1/2*c*x+1/2)*ln(c*x+1)-1/4/c*b^2/d^2*ln(-1/2*c*x+1/2)*ln(1/2+1/2*c*x)-2/c*a*b/d^2*arctanh(c*x)/(c*x+1)-1/2/c*a*b/d^2*ln(c*x-1)-1/c*a*b/d^2/(c*x+1)+1/2/c*a*b/d^2*ln(c*x+1)","B"
108,1,1566,283,0.600000," ","int((a+b*arctanh(c*x))^2/x/(c*d*x+d)^2,x)","\frac{i b^{2} \arctanh \left(c x \right)^{2} \pi  \mathrm{csgn}\left(\frac{i \left(c x +1\right)}{\sqrt{-c^{2} x^{2}+1}}\right)^{2} \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{c^{2} x^{2}-1}\right)}{2 d^{2}}-\frac{b^{2} \arctanh \left(c x \right) c x}{2 d^{2} \left(c x +1\right)}+\frac{i b^{2} \pi  \mathrm{csgn}\left(\frac{i \left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right)}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right)^{3} \arctanh \left(c x \right)^{2}}{2 d^{2}}+\frac{i b^{2} \arctanh \left(c x \right)^{2} \pi  \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{c^{2} x^{2}-1}\right)^{3}}{2 d^{2}}+\frac{i b^{2} \pi  \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{\left(c^{2} x^{2}-1\right) \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}\right)^{3} \arctanh \left(c x \right)^{2}}{2 d^{2}}+\frac{i b^{2} \arctanh \left(c x \right)^{2} \pi  \,\mathrm{csgn}\left(\frac{i \left(c x +1\right)}{\sqrt{-c^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{c^{2} x^{2}-1}\right)^{2}}{d^{2}}-\frac{b^{2} \arctanh \left(c x \right)^{2}}{2 d^{2}}-\frac{2 b^{2} \arctanh \left(c x \right)^{3}}{3 d^{2}}-\frac{2 b^{2} \polylog \left(3, \frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)}{d^{2}}-\frac{2 b^{2} \polylog \left(3, -\frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)}{d^{2}}+\frac{a^{2}}{d^{2} \left(c x +1\right)}-\frac{a^{2} \ln \left(c x +1\right)}{d^{2}}+\frac{a^{2} \ln \left(c x \right)}{d^{2}}-\frac{a b \ln \left(c x \right) \ln \left(c x +1\right)}{d^{2}}-\frac{b^{2} c x}{4 d^{2} \left(c x +1\right)}-\frac{a b \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) \ln \left(c x +1\right)}{d^{2}}+\frac{a b \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{c x}{2}\right)}{d^{2}}+\frac{2 a b \arctanh \left(c x \right) \ln \left(c x \right)}{d^{2}}+\frac{2 a b \arctanh \left(c x \right)}{d^{2} \left(c x +1\right)}-\frac{2 a b \arctanh \left(c x \right) \ln \left(c x +1\right)}{d^{2}}+\frac{2 b^{2} \arctanh \left(c x \right) \polylog \left(2, \frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)}{d^{2}}+\frac{b^{2} \arctanh \left(c x \right)^{2} \ln \left(1-\frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)}{d^{2}}+\frac{b^{2} \arctanh \left(c x \right)^{2}}{d^{2} \left(c x +1\right)}+\frac{b^{2} \arctanh \left(c x \right)}{2 d^{2} \left(c x +1\right)}+\frac{2 b^{2} \arctanh \left(c x \right)^{2} \ln \left(\frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)}{d^{2}}+\frac{b^{2} \arctanh \left(c x \right)^{2} \ln \left(2\right)}{d^{2}}-\frac{b^{2} \arctanh \left(c x \right)^{2} \ln \left(c x +1\right)}{d^{2}}+\frac{a b \dilog \left(\frac{1}{2}+\frac{c x}{2}\right)}{d^{2}}+\frac{b^{2}}{4 d^{2} \left(c x +1\right)}+\frac{i b^{2} \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right)\right) \mathrm{csgn}\left(\frac{i}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right)}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right) \arctanh \left(c x \right)^{2}}{2 d^{2}}-\frac{i b^{2} \arctanh \left(c x \right)^{2} \pi  \,\mathrm{csgn}\left(\frac{i}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{c^{2} x^{2}-1}\right) \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{\left(c^{2} x^{2}-1\right) \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}\right)}{2 d^{2}}+\frac{a b}{d^{2} \left(c x +1\right)}+\frac{a b \ln \left(c x +1\right)^{2}}{2 d^{2}}-\frac{a b \ln \left(c x +1\right)}{2 d^{2}}+\frac{a b \ln \left(c x -1\right)}{2 d^{2}}-\frac{a b \dilog \left(c x \right)}{d^{2}}-\frac{a b \dilog \left(c x +1\right)}{d^{2}}+\frac{b^{2} \arctanh \left(c x \right)^{2} \ln \left(c x \right)}{d^{2}}-\frac{b^{2} \arctanh \left(c x \right)^{2} \ln \left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right)}{d^{2}}+\frac{b^{2} \arctanh \left(c x \right)^{2} \ln \left(1+\frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)}{d^{2}}+\frac{2 b^{2} \arctanh \left(c x \right) \polylog \left(2, -\frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)}{d^{2}}-\frac{i b^{2} \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right)\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right)}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right)^{2} \arctanh \left(c x \right)^{2}}{2 d^{2}}-\frac{i b^{2} \pi  \,\mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{c^{2} x^{2}-1}\right) \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{\left(c^{2} x^{2}-1\right) \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}\right)^{2} \arctanh \left(c x \right)^{2}}{2 d^{2}}+\frac{i b^{2} \arctanh \left(c x \right)^{2} \pi  \,\mathrm{csgn}\left(\frac{i}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{\left(c^{2} x^{2}-1\right) \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}\right)^{2}}{2 d^{2}}-\frac{i b^{2} \pi  \,\mathrm{csgn}\left(\frac{i}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right)}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right)^{2} \arctanh \left(c x \right)^{2}}{2 d^{2}}"," ",0,"1/2*I*b^2/d^2*Pi*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^3*arctanh(c*x)^2+1/2*I*b^2/d^2*arctanh(c*x)^2*Pi*csgn(I*(c*x+1)^2/(c^2*x^2-1))^3+1/2*I*b^2/d^2*Pi*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^3*arctanh(c*x)^2-1/2*b^2/d^2*arctanh(c*x)/(c*x+1)*c*x-a*b/d^2*dilog(c*x)-a*b/d^2*dilog(c*x+1)+b^2/d^2*arctanh(c*x)^2*ln(c*x)-b^2/d^2*arctanh(c*x)^2*ln((c*x+1)^2/(-c^2*x^2+1)-1)+b^2/d^2*arctanh(c*x)^2*ln(1+(c*x+1)/(-c^2*x^2+1)^(1/2))+2*b^2/d^2*arctanh(c*x)*polylog(2,-(c*x+1)/(-c^2*x^2+1)^(1/2))+2*b^2/d^2*arctanh(c*x)*polylog(2,(c*x+1)/(-c^2*x^2+1)^(1/2))+b^2/d^2*arctanh(c*x)^2*ln(1-(c*x+1)/(-c^2*x^2+1)^(1/2))+a^2/d^2/(c*x+1)-a^2/d^2*ln(c*x+1)-1/2*b^2/d^2*arctanh(c*x)^2-2/3*b^2/d^2*arctanh(c*x)^3+a^2/d^2*ln(c*x)-2*b^2/d^2*polylog(3,(c*x+1)/(-c^2*x^2+1)^(1/2))-2*b^2/d^2*polylog(3,-(c*x+1)/(-c^2*x^2+1)^(1/2))+2*a*b/d^2*arctanh(c*x)*ln(c*x)-a*b/d^2*ln(c*x)*ln(c*x+1)-1/4*b^2/d^2/(c*x+1)*c*x+2*a*b/d^2*arctanh(c*x)/(c*x+1)-2*a*b/d^2*arctanh(c*x)*ln(c*x+1)-a*b/d^2*ln(-1/2*c*x+1/2)*ln(c*x+1)+a*b/d^2*ln(-1/2*c*x+1/2)*ln(1/2+1/2*c*x)+1/4*b^2/d^2/(c*x+1)+1/2*I*b^2/d^2*Pi*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1))*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))*arctanh(c*x)^2-1/2*I*b^2/d^2*arctanh(c*x)^2*Pi*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))*csgn(I*(c*x+1)^2/(c^2*x^2-1))*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))+1/2*I*b^2/d^2*arctanh(c*x)^2*Pi*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^2-1/2*I*b^2/d^2*Pi*csgn(I*(c*x+1)^2/(c^2*x^2-1))*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^2*arctanh(c*x)^2+a*b/d^2/(c*x+1)+b^2/d^2*arctanh(c*x)^2/(c*x+1)+1/2*b^2/d^2*arctanh(c*x)/(c*x+1)+2*b^2/d^2*arctanh(c*x)^2*ln((c*x+1)/(-c^2*x^2+1)^(1/2))+b^2/d^2*arctanh(c*x)^2*ln(2)-b^2/d^2*arctanh(c*x)^2*ln(c*x+1)+1/2*a*b/d^2*ln(c*x+1)^2+a*b/d^2*dilog(1/2+1/2*c*x)-1/2*a*b/d^2*ln(c*x+1)+1/2*a*b/d^2*ln(c*x-1)-1/2*I*b^2/d^2*Pi*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1))*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^2*arctanh(c*x)^2+1/2*I*b^2/d^2*arctanh(c*x)^2*Pi*csgn(I*(c*x+1)/(-c^2*x^2+1)^(1/2))^2*csgn(I*(c*x+1)^2/(c^2*x^2-1))-1/2*I*b^2/d^2*Pi*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^2*arctanh(c*x)^2+I*b^2/d^2*arctanh(c*x)^2*Pi*csgn(I*(c*x+1)/(-c^2*x^2+1)^(1/2))*csgn(I*(c*x+1)^2/(c^2*x^2-1))^2","C"
109,1,7397,365,0.997000," ","int((a+b*arctanh(c*x))^2/x^2/(c*d*x+d)^2,x)","\text{output too large to display}"," ",0,"result too large to display","C"
110,1,2009,466,2.343000," ","int((a+b*arctanh(c*x))^2/x^3/(c*d*x+d)^2,x)","\frac{b^{2} c^{2}}{4 d^{2} \left(c x +1\right)}+\frac{3 i c^{2} b^{2} \pi  \,\mathrm{csgn}\left(\frac{i \left(c x +1\right)}{\sqrt{-c^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{c^{2} x^{2}-1}\right)^{2} \arctanh \left(c x \right)^{2}}{d^{2}}-\frac{3 i c^{2} b^{2} \pi  \,\mathrm{csgn}\left(\frac{i}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right)}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right)^{2} \arctanh \left(c x \right)^{2}}{2 d^{2}}-\frac{3 i c^{2} b^{2} \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right)\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right)}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right)^{2} \arctanh \left(c x \right)^{2}}{2 d^{2}}+\frac{3 i c^{2} b^{2} \pi  \mathrm{csgn}\left(\frac{i \left(c x +1\right)}{\sqrt{-c^{2} x^{2}+1}}\right)^{2} \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{c^{2} x^{2}-1}\right) \arctanh \left(c x \right)^{2}}{2 d^{2}}-\frac{3 i c^{2} b^{2} \pi  \,\mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{c^{2} x^{2}-1}\right) \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{\left(c^{2} x^{2}-1\right) \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}\right)^{2} \arctanh \left(c x \right)^{2}}{2 d^{2}}+\frac{3 i c^{2} b^{2} \pi  \,\mathrm{csgn}\left(\frac{i}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{\left(c^{2} x^{2}-1\right) \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}\right)^{2} \arctanh \left(c x \right)^{2}}{2 d^{2}}-\frac{3 c^{2} a b \ln \left(c x \right) \ln \left(c x +1\right)}{d^{2}}-\frac{3 c^{2} a b \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) \ln \left(c x +1\right)}{d^{2}}+\frac{3 c^{2} a b \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{c x}{2}\right)}{d^{2}}+\frac{4 c a b \arctanh \left(c x \right)}{d^{2} x}-\frac{c^{3} b^{2} \arctanh \left(c x \right) x}{2 d^{2} \left(c x +1\right)}+\frac{2 c^{2} a b \arctanh \left(c x \right)}{d^{2} \left(c x +1\right)}-\frac{6 c^{2} a b \arctanh \left(c x \right) \ln \left(c x +1\right)}{d^{2}}+\frac{6 c^{2} a b \arctanh \left(c x \right) \ln \left(c x \right)}{d^{2}}+\frac{3 i c^{2} b^{2} \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right)\right) \mathrm{csgn}\left(\frac{i}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right)}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right) \arctanh \left(c x \right)^{2}}{2 d^{2}}-\frac{3 i c^{2} b^{2} \pi  \,\mathrm{csgn}\left(\frac{i}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{c^{2} x^{2}-1}\right) \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{\left(c^{2} x^{2}-1\right) \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}\right) \arctanh \left(c x \right)^{2}}{2 d^{2}}-\frac{3 c^{2} a^{2} \ln \left(c x +1\right)}{d^{2}}+\frac{3 i c^{2} b^{2} \pi  \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{\left(c^{2} x^{2}-1\right) \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}\right)^{3} \arctanh \left(c x \right)^{2}}{2 d^{2}}+\frac{3 i c^{2} b^{2} \pi  \mathrm{csgn}\left(\frac{i \left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right)}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right)^{3} \arctanh \left(c x \right)^{2}}{2 d^{2}}+\frac{3 i c^{2} b^{2} \pi  \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{c^{2} x^{2}-1}\right)^{3} \arctanh \left(c x \right)^{2}}{2 d^{2}}+\frac{3 c^{2} b^{2} \arctanh \left(c x \right)^{2} \ln \left(1-\frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)}{d^{2}}+\frac{c^{2} b^{2} \arctanh \left(c x \right)^{2}}{d^{2} \left(c x +1\right)}+\frac{c^{2} b^{2} \arctanh \left(c x \right)}{2 d^{2} \left(c x +1\right)}-\frac{c \,b^{2} \arctanh \left(c x \right)}{d^{2} x}+\frac{6 c^{2} b^{2} \arctanh \left(c x \right)^{2} \ln \left(\frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)}{d^{2}}+\frac{3 c^{2} a b \dilog \left(\frac{1}{2}+\frac{c x}{2}\right)}{d^{2}}+\frac{3 c^{2} b^{2} \arctanh \left(c x \right)^{2} \ln \left(2\right)}{d^{2}}-\frac{a b \arctanh \left(c x \right)}{d^{2} x^{2}}-\frac{3 c^{2} a b \dilog \left(c x \right)}{d^{2}}-\frac{3 c^{2} a b \dilog \left(c x +1\right)}{d^{2}}-\frac{4 c^{2} b^{2} \arctanh \left(c x \right) \ln \left(1+\frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)}{d^{2}}+\frac{2 c \,b^{2} \arctanh \left(c x \right)^{2}}{d^{2} x}+\frac{6 c^{2} b^{2} \arctanh \left(c x \right) \polylog \left(2, \frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)}{d^{2}}+\frac{3 c^{2} b^{2} \arctanh \left(c x \right)^{2} \ln \left(c x \right)}{d^{2}}-\frac{3 c^{2} b^{2} \arctanh \left(c x \right)^{2} \ln \left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right)}{d^{2}}+\frac{3 c^{2} b^{2} \arctanh \left(c x \right)^{2} \ln \left(1+\frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)}{d^{2}}+\frac{6 c^{2} b^{2} \arctanh \left(c x \right) \polylog \left(2, -\frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)}{d^{2}}-\frac{3 c^{2} b^{2} \arctanh \left(c x \right)^{2} \ln \left(c x +1\right)}{d^{2}}+\frac{2 c^{2} a b \ln \left(c x +1\right)}{d^{2}}+\frac{2 c^{2} a b \ln \left(c x -1\right)}{d^{2}}+\frac{3 c^{2} a b \ln \left(c x +1\right)^{2}}{2 d^{2}}-\frac{c^{3} b^{2} x}{4 d^{2} \left(c x +1\right)}-\frac{4 c^{2} a b \ln \left(c x \right)}{d^{2}}+\frac{c^{2} a b}{d^{2} \left(c x +1\right)}-\frac{c a b}{d^{2} x}-\frac{a^{2}}{2 d^{2} x^{2}}+\frac{c^{2} b^{2} \ln \left(\frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}-1\right)}{d^{2}}+\frac{c^{2} b^{2} \ln \left(1+\frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)}{d^{2}}+\frac{c^{2} a^{2}}{d^{2} \left(c x +1\right)}+\frac{3 c^{2} a^{2} \ln \left(c x \right)}{d^{2}}+\frac{2 c \,a^{2}}{d^{2} x}-\frac{b^{2} c^{2} \arctanh \left(c x \right)}{d^{2}}+\frac{4 c^{2} b^{2} \dilog \left(\frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)}{d^{2}}+\frac{2 c^{2} b^{2} \arctanh \left(c x \right)^{2}}{d^{2}}-\frac{b^{2} \arctanh \left(c x \right)^{2}}{2 d^{2} x^{2}}-\frac{6 c^{2} b^{2} \polylog \left(3, \frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)}{d^{2}}-\frac{6 c^{2} b^{2} \polylog \left(3, -\frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)}{d^{2}}-\frac{4 c^{2} b^{2} \dilog \left(1+\frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)}{d^{2}}-\frac{2 c^{2} b^{2} \arctanh \left(c x \right)^{3}}{d^{2}}"," ",0,"3*I*c^2*b^2/d^2*Pi*csgn(I*(c*x+1)/(-c^2*x^2+1)^(1/2))*csgn(I*(c*x+1)^2/(c^2*x^2-1))^2*arctanh(c*x)^2-3/2*I*c^2*b^2/d^2*Pi*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^2*arctanh(c*x)^2-3/2*I*c^2*b^2/d^2*Pi*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1))*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^2*arctanh(c*x)^2+3/2*I*c^2*b^2/d^2*Pi*csgn(I*(c*x+1)/(-c^2*x^2+1)^(1/2))^2*csgn(I*(c*x+1)^2/(c^2*x^2-1))*arctanh(c*x)^2-3/2*I*c^2*b^2/d^2*Pi*csgn(I*(c*x+1)^2/(c^2*x^2-1))*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^2*arctanh(c*x)^2+3/2*I*c^2*b^2/d^2*Pi*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^2*arctanh(c*x)^2+1/4*b^2*c^2/d^2/(c*x+1)-b^2*c^2*arctanh(c*x)/d^2+4*c*a*b/d^2*arctanh(c*x)/x-1/2*c^3*b^2/d^2*arctanh(c*x)/(c*x+1)*x-3*c^2*a*b/d^2*ln(c*x)*ln(c*x+1)+2*c^2*a*b/d^2*arctanh(c*x)/(c*x+1)-6*c^2*a*b/d^2*arctanh(c*x)*ln(c*x+1)-3*c^2*a*b/d^2*ln(-1/2*c*x+1/2)*ln(c*x+1)+3*c^2*a*b/d^2*ln(-1/2*c*x+1/2)*ln(1/2+1/2*c*x)+6*c^2*a*b/d^2*arctanh(c*x)*ln(c*x)+3/2*I*c^2*b^2/d^2*Pi*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1))*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))*arctanh(c*x)^2-3/2*I*c^2*b^2/d^2*Pi*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))*csgn(I*(c*x+1)^2/(c^2*x^2-1))*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))*arctanh(c*x)^2+4*c^2*b^2/d^2*dilog((c*x+1)/(-c^2*x^2+1)^(1/2))-3*c^2*a^2/d^2*ln(c*x+1)+3/2*I*c^2*b^2/d^2*Pi*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^3*arctanh(c*x)^2+3/2*I*c^2*b^2/d^2*Pi*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^3*arctanh(c*x)^2+3/2*I*c^2*b^2/d^2*Pi*csgn(I*(c*x+1)^2/(c^2*x^2-1))^3*arctanh(c*x)^2+6*c^2*b^2/d^2*arctanh(c*x)*polylog(2,(c*x+1)/(-c^2*x^2+1)^(1/2))+2*c^2*a*b/d^2*ln(c*x+1)+2*c^2*a*b/d^2*ln(c*x-1)+3*c^2*b^2/d^2*arctanh(c*x)^2*ln(c*x)-3*c^2*b^2/d^2*arctanh(c*x)^2*ln((c*x+1)^2/(-c^2*x^2+1)-1)+3*c^2*b^2/d^2*arctanh(c*x)^2*ln(1+(c*x+1)/(-c^2*x^2+1)^(1/2))+6*c^2*b^2/d^2*arctanh(c*x)*polylog(2,-(c*x+1)/(-c^2*x^2+1)^(1/2))+3/2*c^2*a*b/d^2*ln(c*x+1)^2-1/4*c^3*b^2/d^2/(c*x+1)*x-3*c^2*b^2/d^2*arctanh(c*x)^2*ln(c*x+1)-4*c^2*a*b/d^2*ln(c*x)-4*c^2*b^2/d^2*arctanh(c*x)*ln(1+(c*x+1)/(-c^2*x^2+1)^(1/2))+2*c*b^2/d^2*arctanh(c*x)^2/x+3*c^2*b^2/d^2*arctanh(c*x)^2*ln(1-(c*x+1)/(-c^2*x^2+1)^(1/2))+c^2*b^2/d^2*arctanh(c*x)^2/(c*x+1)+1/2*c^2*b^2/d^2*arctanh(c*x)/(c*x+1)-c*b^2/d^2*arctanh(c*x)/x+6*c^2*b^2/d^2*arctanh(c*x)^2*ln((c*x+1)/(-c^2*x^2+1)^(1/2))+3*c^2*a*b/d^2*dilog(1/2+1/2*c*x)+3*c^2*b^2/d^2*arctanh(c*x)^2*ln(2)+c^2*a*b/d^2/(c*x+1)-c*a*b/d^2/x-a*b/d^2*arctanh(c*x)/x^2-3*c^2*a*b/d^2*dilog(c*x)-3*c^2*a*b/d^2*dilog(c*x+1)-1/2*a^2/d^2/x^2+c^2*b^2/d^2*ln((c*x+1)/(-c^2*x^2+1)^(1/2)-1)+c^2*b^2/d^2*ln(1+(c*x+1)/(-c^2*x^2+1)^(1/2))+2*c^2*b^2/d^2*arctanh(c*x)^2-1/2*b^2/d^2*arctanh(c*x)^2/x^2+c^2*a^2/d^2/(c*x+1)+3*c^2*a^2/d^2*ln(c*x)-6*c^2*b^2/d^2*polylog(3,(c*x+1)/(-c^2*x^2+1)^(1/2))-6*c^2*b^2/d^2*polylog(3,-(c*x+1)/(-c^2*x^2+1)^(1/2))-4*c^2*b^2/d^2*dilog(1+(c*x+1)/(-c^2*x^2+1)^(1/2))-2*c^2*b^2/d^2*arctanh(c*x)^3+2*c*a^2/d^2/x","C"
111,1,1565,390,1.998000," ","int(x^4*(a+b*arctanh(c*x))^2/(c*d*x+d)^3,x)","-\frac{6 i b^{2} \arctanh \left(c x \right)^{2} \pi  \,\mathrm{csgn}\left(\frac{i \left(c x +1\right)}{\sqrt{-c^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{c^{2} x^{2}-1}\right)^{2}}{c^{5} d^{3}}-\frac{3 i b^{2} \arctanh \left(c x \right)^{2} \pi  \,\mathrm{csgn}\left(\frac{i}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{\left(c^{2} x^{2}-1\right) \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}\right)^{2}}{c^{5} d^{3}}+\frac{3 i b^{2} \arctanh \left(c x \right)^{2} \pi  \,\mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{c^{2} x^{2}-1}\right) \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{\left(c^{2} x^{2}-1\right) \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}\right)^{2}}{c^{5} d^{3}}-\frac{3 i b^{2} \arctanh \left(c x \right)^{2} \pi  \mathrm{csgn}\left(\frac{i \left(c x +1\right)}{\sqrt{-c^{2} x^{2}+1}}\right)^{2} \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{c^{2} x^{2}-1}\right)}{c^{5} d^{3}}+\frac{a b x}{c^{4} d^{3}}-\frac{b^{2}}{64 c^{5} d^{3} \left(c x +1\right)^{2}}+\frac{7 b^{2}}{8 c^{5} d^{3} \left(c x +1\right)}+\frac{b^{2} \arctanh \left(c x \right)}{c^{5} d^{3}}-\frac{43 b^{2} \arctanh \left(c x \right)^{2}}{8 c^{5} d^{3}}+\frac{3 b^{2} \polylog \left(3, -\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}{c^{5} d^{3}}+\frac{4 b^{2} \arctanh \left(c x \right)^{3}}{c^{5} d^{3}}+\frac{6 b^{2} \dilog \left(1+\frac{i \left(c x +1\right)}{\sqrt{-c^{2} x^{2}+1}}\right)}{c^{5} d^{3}}+\frac{6 b^{2} \dilog \left(1-\frac{i \left(c x +1\right)}{\sqrt{-c^{2} x^{2}+1}}\right)}{c^{5} d^{3}}+\frac{a^{2} x^{2}}{2 c^{3} d^{3}}-\frac{3 a^{2} x}{c^{4} d^{3}}+\frac{4 a^{2}}{c^{5} d^{3} \left(c x +1\right)}-\frac{a^{2}}{2 c^{5} d^{3} \left(c x +1\right)^{2}}+\frac{6 a^{2} \ln \left(c x +1\right)}{c^{5} d^{3}}-\frac{b^{2} \ln \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}{c^{5} d^{3}}+\frac{a b}{c^{5} d^{3}}-\frac{3 i b^{2} \arctanh \left(c x \right)^{2} \pi  \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{c^{2} x^{2}-1}\right)^{3}}{c^{5} d^{3}}-\frac{3 i b^{2} \pi  \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{\left(c^{2} x^{2}-1\right) \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}\right)^{3} \arctanh \left(c x \right)^{2}}{c^{5} d^{3}}+\frac{3 i b^{2} \arctanh \left(c x \right)^{2} \pi  \,\mathrm{csgn}\left(\frac{i}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{c^{2} x^{2}-1}\right) \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{\left(c^{2} x^{2}-1\right) \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}\right)}{c^{5} d^{3}}+\frac{6 a b \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) \ln \left(c x +1\right)}{c^{5} d^{3}}-\frac{6 a b \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{c x}{2}\right)}{c^{5} d^{3}}+\frac{8 a b \arctanh \left(c x \right)}{c^{5} d^{3} \left(c x +1\right)}-\frac{7 b^{2} \arctanh \left(c x \right) x}{4 c^{4} d^{3} \left(c x +1\right)}-\frac{b^{2} \arctanh \left(c x \right) x^{2}}{16 c^{3} d^{3} \left(c x +1\right)^{2}}+\frac{b^{2} \arctanh \left(c x \right) x}{8 c^{4} d^{3} \left(c x +1\right)^{2}}+\frac{a b \arctanh \left(c x \right) x^{2}}{c^{3} d^{3}}-\frac{6 a b \arctanh \left(c x \right) x}{c^{4} d^{3}}-\frac{a b \arctanh \left(c x \right)}{c^{5} d^{3} \left(c x +1\right)^{2}}+\frac{12 a b \arctanh \left(c x \right) \ln \left(c x +1\right)}{c^{5} d^{3}}-\frac{12 b^{2} \arctanh \left(c x \right)^{2} \ln \left(\frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)}{c^{5} d^{3}}+\frac{6 b^{2} \arctanh \left(c x \right)^{2} \ln \left(c x +1\right)}{c^{5} d^{3}}+\frac{7 b^{2} \arctanh \left(c x \right)}{4 c^{5} d^{3} \left(c x +1\right)}-\frac{b^{2} \arctanh \left(c x \right)}{16 c^{5} d^{3} \left(c x +1\right)^{2}}+\frac{6 b^{2} \arctanh \left(c x \right) \ln \left(1+\frac{i \left(c x +1\right)}{\sqrt{-c^{2} x^{2}+1}}\right)}{c^{5} d^{3}}+\frac{6 b^{2} \arctanh \left(c x \right) \ln \left(1-\frac{i \left(c x +1\right)}{\sqrt{-c^{2} x^{2}+1}}\right)}{c^{5} d^{3}}-\frac{3 a b \ln \left(c x +1\right)^{2}}{c^{5} d^{3}}-\frac{43 a b \ln \left(c x +1\right)}{8 c^{5} d^{3}}-\frac{5 a b \ln \left(c x -1\right)}{8 c^{5} d^{3}}-\frac{b^{2} x^{2}}{64 c^{3} d^{3} \left(c x +1\right)^{2}}+\frac{b^{2} x}{32 c^{4} d^{3} \left(c x +1\right)^{2}}-\frac{7 b^{2} x}{8 c^{4} d^{3} \left(c x +1\right)}+\frac{b^{2} x \arctanh \left(c x \right)}{c^{4} d^{3}}-\frac{6 b^{2} \arctanh \left(c x \right)^{2} \ln \left(2\right)}{c^{5} d^{3}}-\frac{6 a b \dilog \left(\frac{1}{2}+\frac{c x}{2}\right)}{c^{5} d^{3}}+\frac{b^{2} \arctanh \left(c x \right)^{2} x^{2}}{2 c^{3} d^{3}}-\frac{3 b^{2} \arctanh \left(c x \right)^{2} x}{c^{4} d^{3}}+\frac{4 b^{2} \arctanh \left(c x \right)^{2}}{c^{5} d^{3} \left(c x +1\right)}-\frac{b^{2} \arctanh \left(c x \right)^{2}}{2 c^{5} d^{3} \left(c x +1\right)^{2}}-\frac{6 b^{2} \arctanh \left(c x \right) \polylog \left(2, -\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}{c^{5} d^{3}}-\frac{a b}{4 c^{5} d^{3} \left(c x +1\right)^{2}}+\frac{15 a b}{4 c^{5} d^{3} \left(c x +1\right)}"," ",0,"-6*I/c^5*b^2/d^3*arctanh(c*x)^2*Pi*csgn(I*(c*x+1)/(-c^2*x^2+1)^(1/2))*csgn(I*(c*x+1)^2/(c^2*x^2-1))^2-3*I/c^5*b^2/d^3*arctanh(c*x)^2*Pi*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^2+3*I/c^5*b^2/d^3*arctanh(c*x)^2*Pi*csgn(I*(c*x+1)^2/(c^2*x^2-1))*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^2-3*I/c^5*b^2/d^3*arctanh(c*x)^2*Pi*csgn(I*(c*x+1)/(-c^2*x^2+1)^(1/2))^2*csgn(I*(c*x+1)^2/(c^2*x^2-1))+a*b*x/c^4/d^3+b^2*x*arctanh(c*x)/c^4/d^3-1/64*b^2/c^5/d^3/(c*x+1)^2+7/8*b^2/c^5/d^3/(c*x+1)+b^2*arctanh(c*x)/c^5/d^3+1/2/c^3*a^2/d^3*x^2-3/c^4*a^2/d^3*x+4/c^5*a^2/d^3/(c*x+1)-1/2/c^5*a^2/d^3/(c*x+1)^2+6/c^5*a^2/d^3*ln(c*x+1)-43/8/c^5*b^2/d^3*arctanh(c*x)^2+3/c^5*b^2/d^3*polylog(3,-(c*x+1)^2/(-c^2*x^2+1))-1/c^5*b^2/d^3*ln(1+(c*x+1)^2/(-c^2*x^2+1))+6/c^5*b^2/d^3*dilog(1+I*(c*x+1)/(-c^2*x^2+1)^(1/2))+6/c^5*b^2/d^3*dilog(1-I*(c*x+1)/(-c^2*x^2+1)^(1/2))+4/c^5*b^2/d^3*arctanh(c*x)^3+1/c^5*a*b/d^3+3*I/c^5*b^2/d^3*arctanh(c*x)^2*Pi*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))*csgn(I*(c*x+1)^2/(c^2*x^2-1))*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))+8/c^5*a*b/d^3*arctanh(c*x)/(c*x+1)-7/4/c^4*b^2/d^3*arctanh(c*x)/(c*x+1)*x-1/16/c^3*b^2/d^3*arctanh(c*x)/(c*x+1)^2*x^2+1/8/c^4*b^2/d^3*arctanh(c*x)/(c*x+1)^2*x+1/c^3*a*b/d^3*arctanh(c*x)*x^2-6/c^4*a*b/d^3*arctanh(c*x)*x-1/c^5*a*b/d^3*arctanh(c*x)/(c*x+1)^2+12/c^5*a*b/d^3*arctanh(c*x)*ln(c*x+1)+6/c^5*a*b/d^3*ln(-1/2*c*x+1/2)*ln(c*x+1)-6/c^5*a*b/d^3*ln(-1/2*c*x+1/2)*ln(1/2+1/2*c*x)-6/c^5*b^2/d^3*arctanh(c*x)^2*ln(2)-3/c^5*a*b/d^3*ln(c*x+1)^2-6/c^5*a*b/d^3*dilog(1/2+1/2*c*x)-43/8/c^5*a*b/d^3*ln(c*x+1)-5/8/c^5*a*b/d^3*ln(c*x-1)+1/2/c^3*b^2/d^3*arctanh(c*x)^2*x^2-3/c^4*b^2/d^3*arctanh(c*x)^2*x+4/c^5*b^2/d^3*arctanh(c*x)^2/(c*x+1)-1/2/c^5*b^2/d^3*arctanh(c*x)^2/(c*x+1)^2-6/c^5*b^2/d^3*arctanh(c*x)*polylog(2,-(c*x+1)^2/(-c^2*x^2+1))+6/c^5*b^2/d^3*arctanh(c*x)*ln(1+I*(c*x+1)/(-c^2*x^2+1)^(1/2))+6/c^5*b^2/d^3*arctanh(c*x)*ln(1-I*(c*x+1)/(-c^2*x^2+1)^(1/2))-12/c^5*b^2/d^3*arctanh(c*x)^2*ln((c*x+1)/(-c^2*x^2+1)^(1/2))-1/64/c^3*b^2/d^3/(c*x+1)^2*x^2+1/32/c^4*b^2/d^3/(c*x+1)^2*x-7/8/c^4*b^2/d^3/(c*x+1)*x-1/4/c^5*a*b/d^3/(c*x+1)^2+15/4/c^5*a*b/d^3/(c*x+1)+6/c^5*b^2/d^3*arctanh(c*x)^2*ln(c*x+1)+7/4/c^5*b^2/d^3*arctanh(c*x)/(c*x+1)-1/16/c^5*b^2/d^3*arctanh(c*x)/(c*x+1)^2-3*I/c^5*b^2/d^3*arctanh(c*x)^2*Pi*csgn(I*(c*x+1)^2/(c^2*x^2-1))^3-3*I/c^5*b^2/d^3*Pi*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^3*arctanh(c*x)^2","C"
112,1,5750,321,0.957000," ","int(x^3*(a+b*arctanh(c*x))^2/(c*d*x+d)^3,x)","\text{output too large to display}"," ",0,"result too large to display","C"
113,1,1241,249,0.774000," ","int(x^2*(a+b*arctanh(c*x))^2/(c*d*x+d)^3,x)","-\frac{b^{2} x^{2}}{64 c \,d^{3} \left(c x +1\right)^{2}}+\frac{b^{2} \arctanh \left(c x \right) x}{8 c^{2} d^{3} \left(c x +1\right)^{2}}+\frac{a b \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) \ln \left(c x +1\right)}{c^{3} d^{3}}-\frac{a b \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{c x}{2}\right)}{c^{3} d^{3}}-\frac{a b \arctanh \left(c x \right)}{c^{3} d^{3} \left(c x +1\right)^{2}}+\frac{2 a b \arctanh \left(c x \right) \ln \left(c x +1\right)}{c^{3} d^{3}}+\frac{4 a b \arctanh \left(c x \right)}{c^{3} d^{3} \left(c x +1\right)}-\frac{b^{2} \arctanh \left(c x \right) x^{2}}{16 c \,d^{3} \left(c x +1\right)^{2}}-\frac{3 b^{2} \arctanh \left(c x \right) x}{4 c^{2} d^{3} \left(c x +1\right)}+\frac{b^{2} x}{32 c^{2} d^{3} \left(c x +1\right)^{2}}-\frac{3 b^{2} x}{8 c^{2} d^{3} \left(c x +1\right)}-\frac{a b}{4 c^{3} d^{3} \left(c x +1\right)^{2}}+\frac{7 a b}{4 c^{3} d^{3} \left(c x +1\right)}-\frac{a b \ln \left(c x +1\right)^{2}}{2 c^{3} d^{3}}-\frac{7 a b \ln \left(c x +1\right)}{8 c^{3} d^{3}}+\frac{7 a b \ln \left(c x -1\right)}{8 c^{3} d^{3}}+\frac{i b^{2} \arctanh \left(c x \right)^{2} \pi  \,\mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{c^{2} x^{2}-1}\right) \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{\left(c^{2} x^{2}-1\right) \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}\right) \mathrm{csgn}\left(\frac{i}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right)}{2 c^{3} d^{3}}-\frac{i b^{2} \arctanh \left(c x \right)^{2} \pi  \,\mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{c^{2} x^{2}-1}\right) \mathrm{csgn}\left(\frac{i \left(c x +1\right)}{\sqrt{-c^{2} x^{2}+1}}\right)^{2}}{2 c^{3} d^{3}}-\frac{i b^{2} \arctanh \left(c x \right)^{2} \pi  \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{\left(c^{2} x^{2}-1\right) \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}\right)^{2} \mathrm{csgn}\left(\frac{i}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right)}{2 c^{3} d^{3}}-\frac{i b^{2} \arctanh \left(c x \right)^{2} \pi  \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{c^{2} x^{2}-1}\right)^{2} \mathrm{csgn}\left(\frac{i \left(c x +1\right)}{\sqrt{-c^{2} x^{2}+1}}\right)}{c^{3} d^{3}}+\frac{i b^{2} \arctanh \left(c x \right)^{2} \pi  \,\mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{c^{2} x^{2}-1}\right) \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{\left(c^{2} x^{2}-1\right) \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}\right)^{2}}{2 c^{3} d^{3}}+\frac{2 a^{2}}{c^{3} d^{3} \left(c x +1\right)}-\frac{a^{2}}{2 c^{3} d^{3} \left(c x +1\right)^{2}}+\frac{a^{2} \ln \left(c x +1\right)}{c^{3} d^{3}}-\frac{b^{2}}{64 c^{3} d^{3} \left(c x +1\right)^{2}}+\frac{3 b^{2}}{8 c^{3} d^{3} \left(c x +1\right)}-\frac{7 b^{2} \arctanh \left(c x \right)^{2}}{8 c^{3} d^{3}}+\frac{b^{2} \polylog \left(3, -\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}{2 c^{3} d^{3}}+\frac{2 b^{2} \arctanh \left(c x \right)^{3}}{3 c^{3} d^{3}}-\frac{i b^{2} \arctanh \left(c x \right)^{2} \pi  \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{\left(c^{2} x^{2}-1\right) \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}\right)^{3}}{2 c^{3} d^{3}}-\frac{i b^{2} \arctanh \left(c x \right)^{2} \pi  \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{c^{2} x^{2}-1}\right)^{3}}{2 c^{3} d^{3}}-\frac{b^{2} \arctanh \left(c x \right)}{16 c^{3} d^{3} \left(c x +1\right)^{2}}-\frac{b^{2} \arctanh \left(c x \right)^{2} \ln \left(2\right)}{c^{3} d^{3}}-\frac{a b \dilog \left(\frac{1}{2}+\frac{c x}{2}\right)}{c^{3} d^{3}}+\frac{2 b^{2} \arctanh \left(c x \right)^{2}}{c^{3} d^{3} \left(c x +1\right)}-\frac{b^{2} \arctanh \left(c x \right)^{2}}{2 c^{3} d^{3} \left(c x +1\right)^{2}}-\frac{b^{2} \arctanh \left(c x \right) \polylog \left(2, -\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}{c^{3} d^{3}}-\frac{2 b^{2} \arctanh \left(c x \right)^{2} \ln \left(\frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)}{c^{3} d^{3}}+\frac{b^{2} \arctanh \left(c x \right)^{2} \ln \left(c x +1\right)}{c^{3} d^{3}}+\frac{3 b^{2} \arctanh \left(c x \right)}{4 c^{3} d^{3} \left(c x +1\right)}"," ",0,"-1/64/c*b^2/d^3/(c*x+1)^2*x^2-1/c^3*a*b/d^3*arctanh(c*x)/(c*x+1)^2+2/c^3*a*b/d^3*arctanh(c*x)*ln(c*x+1)+1/c^3*a*b/d^3*ln(-1/2*c*x+1/2)*ln(c*x+1)-1/c^3*a*b/d^3*ln(-1/2*c*x+1/2)*ln(1/2+1/2*c*x)+4/c^3*a*b/d^3*arctanh(c*x)/(c*x+1)-1/16/c*b^2/d^3*arctanh(c*x)/(c*x+1)^2*x^2-3/4/c^2*b^2/d^3*arctanh(c*x)/(c*x+1)*x+1/32/c^2*b^2/d^3/(c*x+1)^2*x-3/8/c^2*b^2/d^3/(c*x+1)*x-1/4/c^3*a*b/d^3/(c*x+1)^2+7/4/c^3*a*b/d^3/(c*x+1)-1/16/c^3*b^2/d^3*arctanh(c*x)/(c*x+1)^2-1/c^3*b^2/d^3*arctanh(c*x)^2*ln(2)-1/2/c^3*a*b/d^3*ln(c*x+1)^2-1/c^3*a*b/d^3*dilog(1/2+1/2*c*x)-7/8/c^3*a*b/d^3*ln(c*x+1)+7/8/c^3*a*b/d^3*ln(c*x-1)+2/c^3*b^2/d^3*arctanh(c*x)^2/(c*x+1)-1/2/c^3*b^2/d^3*arctanh(c*x)^2/(c*x+1)^2-1/c^3*b^2/d^3*arctanh(c*x)*polylog(2,-(c*x+1)^2/(-c^2*x^2+1))-2/c^3*b^2/d^3*arctanh(c*x)^2*ln((c*x+1)/(-c^2*x^2+1)^(1/2))+1/c^3*b^2/d^3*arctanh(c*x)^2*ln(c*x+1)+3/4/c^3*b^2/d^3*arctanh(c*x)/(c*x+1)+1/8/c^2*b^2/d^3*arctanh(c*x)/(c*x+1)^2*x+1/2*I/c^3*b^2/d^3*arctanh(c*x)^2*Pi*csgn(I*(c*x+1)^2/(c^2*x^2-1))*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))+2/c^3*a^2/d^3/(c*x+1)-1/2/c^3*a^2/d^3/(c*x+1)^2+1/c^3*a^2/d^3*ln(c*x+1)-7/8/c^3*b^2/d^3*arctanh(c*x)^2+1/2/c^3*b^2/d^3*polylog(3,-(c*x+1)^2/(-c^2*x^2+1))+2/3/c^3*b^2/d^3*arctanh(c*x)^3-1/2*I/c^3*b^2/d^3*arctanh(c*x)^2*Pi*csgn(I*(c*x+1)^2/(c^2*x^2-1))*csgn(I*(c*x+1)/(-c^2*x^2+1)^(1/2))^2-1/2*I/c^3*b^2/d^3*arctanh(c*x)^2*Pi*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^2*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))-1/2*I/c^3*b^2/d^3*arctanh(c*x)^2*Pi*csgn(I*(c*x+1)^2/(c^2*x^2-1))^3-1/2*I/c^3*b^2/d^3*arctanh(c*x)^2*Pi*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^3-I/c^3*b^2/d^3*arctanh(c*x)^2*Pi*csgn(I*(c*x+1)^2/(c^2*x^2-1))^2*csgn(I*(c*x+1)/(-c^2*x^2+1)^(1/2))+1/2*I/c^3*b^2/d^3*arctanh(c*x)^2*Pi*csgn(I*(c*x+1)^2/(c^2*x^2-1))*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^2-1/64*b^2/c^3/d^3/(c*x+1)^2+3/8*b^2/c^3/d^3/(c*x+1)","C"
114,1,460,143,0.074000," ","int(x*(a+b*arctanh(c*x))^2/(c*d*x+d)^3,x)","-\frac{a^{2}}{c^{2} d^{3} \left(c x +1\right)}+\frac{a^{2}}{2 c^{2} d^{3} \left(c x +1\right)^{2}}-\frac{b^{2} \arctanh \left(c x \right)^{2}}{c^{2} d^{3} \left(c x +1\right)}+\frac{b^{2} \arctanh \left(c x \right)^{2}}{2 c^{2} d^{3} \left(c x +1\right)^{2}}-\frac{3 b^{2} \arctanh \left(c x \right) \ln \left(c x -1\right)}{8 c^{2} d^{3}}+\frac{b^{2} \arctanh \left(c x \right)}{4 c^{2} d^{3} \left(c x +1\right)^{2}}-\frac{3 b^{2} \arctanh \left(c x \right)}{4 c^{2} d^{3} \left(c x +1\right)}+\frac{3 b^{2} \arctanh \left(c x \right) \ln \left(c x +1\right)}{8 c^{2} d^{3}}-\frac{3 b^{2} \ln \left(c x -1\right)^{2}}{32 c^{2} d^{3}}+\frac{3 b^{2} \ln \left(c x -1\right) \ln \left(\frac{1}{2}+\frac{c x}{2}\right)}{16 c^{2} d^{3}}-\frac{3 b^{2} \ln \left(c x +1\right)^{2}}{32 c^{2} d^{3}}+\frac{3 b^{2} \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) \ln \left(c x +1\right)}{16 c^{2} d^{3}}-\frac{3 b^{2} \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{c x}{2}\right)}{16 c^{2} d^{3}}-\frac{5 b^{2} \ln \left(c x -1\right)}{32 c^{2} d^{3}}+\frac{b^{2}}{16 c^{2} d^{3} \left(c x +1\right)^{2}}-\frac{5 b^{2}}{16 c^{2} d^{3} \left(c x +1\right)}+\frac{5 b^{2} \ln \left(c x +1\right)}{32 c^{2} d^{3}}-\frac{2 a b \arctanh \left(c x \right)}{c^{2} d^{3} \left(c x +1\right)}+\frac{a b \arctanh \left(c x \right)}{c^{2} d^{3} \left(c x +1\right)^{2}}-\frac{3 a b \ln \left(c x -1\right)}{8 c^{2} d^{3}}+\frac{a b}{4 c^{2} d^{3} \left(c x +1\right)^{2}}-\frac{3 a b}{4 c^{2} d^{3} \left(c x +1\right)}+\frac{3 a b \ln \left(c x +1\right)}{8 c^{2} d^{3}}"," ",0,"-1/c^2*a^2/d^3/(c*x+1)+1/2/c^2*a^2/d^3/(c*x+1)^2-1/c^2*b^2/d^3*arctanh(c*x)^2/(c*x+1)+1/2/c^2*b^2/d^3*arctanh(c*x)^2/(c*x+1)^2-3/8/c^2*b^2/d^3*arctanh(c*x)*ln(c*x-1)+1/4/c^2*b^2/d^3*arctanh(c*x)/(c*x+1)^2-3/4/c^2*b^2/d^3*arctanh(c*x)/(c*x+1)+3/8/c^2*b^2/d^3*arctanh(c*x)*ln(c*x+1)-3/32/c^2*b^2/d^3*ln(c*x-1)^2+3/16/c^2*b^2/d^3*ln(c*x-1)*ln(1/2+1/2*c*x)-3/32/c^2*b^2/d^3*ln(c*x+1)^2+3/16/c^2*b^2/d^3*ln(-1/2*c*x+1/2)*ln(c*x+1)-3/16/c^2*b^2/d^3*ln(-1/2*c*x+1/2)*ln(1/2+1/2*c*x)-5/32/c^2*b^2/d^3*ln(c*x-1)+1/16*b^2/c^2/d^3/(c*x+1)^2-5/16*b^2/c^2/d^3/(c*x+1)+5/32/c^2*b^2/d^3*ln(c*x+1)-2/c^2*a*b/d^3*arctanh(c*x)/(c*x+1)+1/c^2*a*b/d^3*arctanh(c*x)/(c*x+1)^2-3/8/c^2*a*b/d^3*ln(c*x-1)+1/4/c^2*a*b/d^3/(c*x+1)^2-3/4/c^2*a*b/d^3/(c*x+1)+3/8/c^2*a*b/d^3*ln(c*x+1)","B"
115,1,398,143,0.069000," ","int((a+b*arctanh(c*x))^2/(c*d*x+d)^3,x)","-\frac{a^{2}}{2 c \,d^{3} \left(c x +1\right)^{2}}-\frac{b^{2} \arctanh \left(c x \right)^{2}}{2 c \,d^{3} \left(c x +1\right)^{2}}-\frac{b^{2} \arctanh \left(c x \right) \ln \left(c x -1\right)}{8 c \,d^{3}}-\frac{b^{2} \arctanh \left(c x \right)}{4 c \,d^{3} \left(c x +1\right)^{2}}-\frac{b^{2} \arctanh \left(c x \right)}{4 c \,d^{3} \left(c x +1\right)}+\frac{b^{2} \arctanh \left(c x \right) \ln \left(c x +1\right)}{8 c \,d^{3}}-\frac{b^{2} \ln \left(c x -1\right)^{2}}{32 c \,d^{3}}+\frac{b^{2} \ln \left(c x -1\right) \ln \left(\frac{1}{2}+\frac{c x}{2}\right)}{16 c \,d^{3}}-\frac{b^{2} \ln \left(c x +1\right)^{2}}{32 c \,d^{3}}+\frac{b^{2} \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) \ln \left(c x +1\right)}{16 c \,d^{3}}-\frac{b^{2} \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{c x}{2}\right)}{16 c \,d^{3}}-\frac{3 b^{2} \ln \left(c x -1\right)}{32 c \,d^{3}}-\frac{b^{2}}{16 c \,d^{3} \left(c x +1\right)^{2}}-\frac{3 b^{2}}{16 c \,d^{3} \left(c x +1\right)}+\frac{3 b^{2} \ln \left(c x +1\right)}{32 c \,d^{3}}-\frac{a b \arctanh \left(c x \right)}{c \,d^{3} \left(c x +1\right)^{2}}-\frac{a b \ln \left(c x -1\right)}{8 c \,d^{3}}-\frac{a b}{4 c \,d^{3} \left(c x +1\right)^{2}}-\frac{a b}{4 c \,d^{3} \left(c x +1\right)}+\frac{a b \ln \left(c x +1\right)}{8 c \,d^{3}}"," ",0,"-1/2/c*a^2/d^3/(c*x+1)^2-1/2/c*b^2/d^3*arctanh(c*x)^2/(c*x+1)^2-1/8/c*b^2/d^3*arctanh(c*x)*ln(c*x-1)-1/4/c*b^2/d^3*arctanh(c*x)/(c*x+1)^2-1/4/c*b^2/d^3*arctanh(c*x)/(c*x+1)+1/8/c*b^2/d^3*arctanh(c*x)*ln(c*x+1)-1/32/c*b^2/d^3*ln(c*x-1)^2+1/16/c*b^2/d^3*ln(c*x-1)*ln(1/2+1/2*c*x)-1/32/c*b^2/d^3*ln(c*x+1)^2+1/16/c*b^2/d^3*ln(-1/2*c*x+1/2)*ln(c*x+1)-1/16/c*b^2/d^3*ln(-1/2*c*x+1/2)*ln(1/2+1/2*c*x)-3/32/c*b^2/d^3*ln(c*x-1)-1/16*b^2/c/d^3/(c*x+1)^2-3/16*b^2/c/d^3/(c*x+1)+3/32/c*b^2/d^3*ln(c*x+1)-1/c*a*b/d^3*arctanh(c*x)/(c*x+1)^2-1/8/c*a*b/d^3*ln(c*x-1)-1/4/c*a*b/d^3/(c*x+1)^2-1/4/c*a*b/d^3/(c*x+1)+1/8/c*a*b/d^3*ln(c*x+1)","B"
116,1,1752,342,1.013000," ","int((a+b*arctanh(c*x))^2/x/(c*d*x+d)^3,x)","-\frac{i b^{2} \arctanh \left(c x \right)^{2} \pi  \,\mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{c^{2} x^{2}-1}\right) \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{\left(c^{2} x^{2}-1\right) \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}\right)^{2}}{2 d^{3}}-\frac{3 b^{2} \arctanh \left(c x \right) c x}{4 d^{3} \left(c x +1\right)}+\frac{b^{2} \arctanh \left(c x \right) c^{2} x^{2}}{16 d^{3} \left(c x +1\right)^{2}}-\frac{b^{2} \arctanh \left(c x \right) c x}{8 d^{3} \left(c x +1\right)^{2}}+\frac{i b^{2} \arctanh \left(c x \right)^{2} \pi  \,\mathrm{csgn}\left(\frac{i}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{\left(c^{2} x^{2}-1\right) \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}\right)^{2}}{2 d^{3}}+\frac{i b^{2} \arctanh \left(c x \right)^{2} \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right)\right) \mathrm{csgn}\left(\frac{i}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right)}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right)}{2 d^{3}}-\frac{i b^{2} \arctanh \left(c x \right)^{2} \pi  \,\mathrm{csgn}\left(\frac{i}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{c^{2} x^{2}-1}\right) \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{\left(c^{2} x^{2}-1\right) \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}\right)}{2 d^{3}}+\frac{b^{2}}{64 d^{3} \left(c x +1\right)^{2}}+\frac{3 b^{2}}{8 d^{3} \left(c x +1\right)}+\frac{a^{2}}{d^{3} \left(c x +1\right)}+\frac{a^{2}}{2 d^{3} \left(c x +1\right)^{2}}-\frac{2 b^{2} \polylog \left(3, \frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)}{d^{3}}-\frac{2 b^{2} \polylog \left(3, -\frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)}{d^{3}}-\frac{5 b^{2} \arctanh \left(c x \right)^{2}}{8 d^{3}}-\frac{2 b^{2} \arctanh \left(c x \right)^{3}}{3 d^{3}}+\frac{i b^{2} \arctanh \left(c x \right)^{2} \pi  \mathrm{csgn}\left(\frac{i \left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right)}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right)^{3}}{2 d^{3}}+\frac{i b^{2} \pi  \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{\left(c^{2} x^{2}-1\right) \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}\right)^{3} \arctanh \left(c x \right)^{2}}{2 d^{3}}+\frac{i b^{2} \arctanh \left(c x \right)^{2} \pi  \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{c^{2} x^{2}-1}\right)^{3}}{2 d^{3}}-\frac{a b \dilog \left(c x +1\right)}{d^{3}}+\frac{2 b^{2} \arctanh \left(c x \right) \polylog \left(2, -\frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)}{d^{3}}+\frac{b^{2} \arctanh \left(c x \right)^{2} \ln \left(1-\frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)}{d^{3}}+\frac{b^{2} \arctanh \left(c x \right)^{2}}{d^{3} \left(c x +1\right)}+\frac{b^{2} \arctanh \left(c x \right)^{2}}{2 d^{3} \left(c x +1\right)^{2}}+\frac{b^{2} \arctanh \left(c x \right)^{2} \ln \left(2\right)}{d^{3}}+\frac{2 b^{2} \arctanh \left(c x \right)^{2} \ln \left(\frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)}{d^{3}}-\frac{b^{2} \arctanh \left(c x \right)^{2} \ln \left(c x +1\right)}{d^{3}}+\frac{3 b^{2} \arctanh \left(c x \right)}{4 d^{3} \left(c x +1\right)}+\frac{b^{2} \arctanh \left(c x \right)}{16 d^{3} \left(c x +1\right)^{2}}+\frac{a b \dilog \left(\frac{1}{2}+\frac{c x}{2}\right)}{d^{3}}+\frac{a^{2} \ln \left(c x \right)}{d^{3}}-\frac{a^{2} \ln \left(c x +1\right)}{d^{3}}-\frac{i b^{2} \arctanh \left(c x \right)^{2} \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right)\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right)}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right)^{2}}{2 d^{3}}-\frac{a b \ln \left(c x \right) \ln \left(c x +1\right)}{d^{3}}+\frac{a b}{4 d^{3} \left(c x +1\right)^{2}}+\frac{5 a b}{4 d^{3} \left(c x +1\right)}+\frac{a b \ln \left(c x +1\right)^{2}}{2 d^{3}}-\frac{5 a b \ln \left(c x +1\right)}{8 d^{3}}+\frac{5 a b \ln \left(c x -1\right)}{8 d^{3}}-\frac{b^{2} \arctanh \left(c x \right)^{2} \ln \left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right)}{d^{3}}+\frac{b^{2} \arctanh \left(c x \right)^{2} \ln \left(c x \right)}{d^{3}}+\frac{2 b^{2} \arctanh \left(c x \right) \polylog \left(2, \frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)}{d^{3}}+\frac{b^{2} \arctanh \left(c x \right)^{2} \ln \left(1+\frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)}{d^{3}}-\frac{a b \dilog \left(c x \right)}{d^{3}}-\frac{i b^{2} \arctanh \left(c x \right)^{2} \pi  \,\mathrm{csgn}\left(\frac{i}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right)}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right)^{2}}{2 d^{3}}-\frac{a b \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) \ln \left(c x +1\right)}{d^{3}}+\frac{a b \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{c x}{2}\right)}{d^{3}}+\frac{b^{2} c^{2} x^{2}}{64 d^{3} \left(c x +1\right)^{2}}-\frac{b^{2} c x}{32 d^{3} \left(c x +1\right)^{2}}-\frac{3 b^{2} c x}{8 d^{3} \left(c x +1\right)}+\frac{2 a b \arctanh \left(c x \right) \ln \left(c x \right)}{d^{3}}+\frac{2 a b \arctanh \left(c x \right)}{d^{3} \left(c x +1\right)}+\frac{a b \arctanh \left(c x \right)}{d^{3} \left(c x +1\right)^{2}}-\frac{2 a b \arctanh \left(c x \right) \ln \left(c x +1\right)}{d^{3}}+\frac{i b^{2} \arctanh \left(c x \right)^{2} \pi  \,\mathrm{csgn}\left(\frac{i \left(c x +1\right)}{\sqrt{-c^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{c^{2} x^{2}-1}\right)^{2}}{d^{3}}+\frac{i b^{2} \arctanh \left(c x \right)^{2} \pi  \mathrm{csgn}\left(\frac{i \left(c x +1\right)}{\sqrt{-c^{2} x^{2}+1}}\right)^{2} \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{c^{2} x^{2}-1}\right)}{2 d^{3}}"," ",0,"1/2*I*b^2/d^3*arctanh(c*x)^2*Pi*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^3-3/4*b^2/d^3*arctanh(c*x)/(c*x+1)*c*x+1/2*I*b^2/d^3*Pi*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^3*arctanh(c*x)^2+1/2*I*b^2/d^3*arctanh(c*x)^2*Pi*csgn(I*(c*x+1)^2/(c^2*x^2-1))^3+1/16*b^2/d^3*arctanh(c*x)/(c*x+1)^2*c^2*x^2-1/8*b^2/d^3*arctanh(c*x)/(c*x+1)^2*c*x-b^2/d^3*arctanh(c*x)^2*ln((c*x+1)^2/(-c^2*x^2+1)-1)+b^2/d^3*arctanh(c*x)^2*ln(c*x)+2*b^2/d^3*arctanh(c*x)*polylog(2,(c*x+1)/(-c^2*x^2+1)^(1/2))+b^2/d^3*arctanh(c*x)^2*ln(1+(c*x+1)/(-c^2*x^2+1)^(1/2))-a*b/d^3*dilog(c*x)-a*b/d^3*dilog(c*x+1)+2*b^2/d^3*arctanh(c*x)*polylog(2,-(c*x+1)/(-c^2*x^2+1)^(1/2))+b^2/d^3*arctanh(c*x)^2*ln(1-(c*x+1)/(-c^2*x^2+1)^(1/2))-2*b^2/d^3*polylog(3,(c*x+1)/(-c^2*x^2+1)^(1/2))-2*b^2/d^3*polylog(3,-(c*x+1)/(-c^2*x^2+1)^(1/2))-1/2*I*b^2/d^3*arctanh(c*x)^2*Pi*csgn(I*(c*x+1)^2/(c^2*x^2-1))*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^2+1/2*I*b^2/d^3*arctanh(c*x)^2*Pi*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1))*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))-1/2*I*b^2/d^3*arctanh(c*x)^2*Pi*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))*csgn(I*(c*x+1)^2/(c^2*x^2-1))*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))+1/64*b^2/d^3/(c*x+1)^2+3/8*b^2/d^3/(c*x+1)+1/2*I*b^2/d^3*arctanh(c*x)^2*Pi*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^2-5/8*b^2/d^3*arctanh(c*x)^2-2/3*b^2/d^3*arctanh(c*x)^3+a^2/d^3/(c*x+1)+1/2*a^2/d^3/(c*x+1)^2+a^2/d^3*ln(c*x)-a^2/d^3*ln(c*x+1)+2*a*b/d^3*arctanh(c*x)*ln(c*x)-a*b/d^3*ln(c*x)*ln(c*x+1)+b^2/d^3*arctanh(c*x)^2/(c*x+1)+1/2*b^2/d^3*arctanh(c*x)^2/(c*x+1)^2+b^2/d^3*arctanh(c*x)^2*ln(2)+2*b^2/d^3*arctanh(c*x)^2*ln((c*x+1)/(-c^2*x^2+1)^(1/2))-b^2/d^3*arctanh(c*x)^2*ln(c*x+1)+3/4*b^2/d^3*arctanh(c*x)/(c*x+1)+1/16*b^2/d^3*arctanh(c*x)/(c*x+1)^2+1/4*a*b/d^3/(c*x+1)^2+5/4*a*b/d^3/(c*x+1)+1/2*a*b/d^3*ln(c*x+1)^2+a*b/d^3*dilog(1/2+1/2*c*x)-5/8*a*b/d^3*ln(c*x+1)+5/8*a*b/d^3*ln(c*x-1)+2*a*b/d^3*arctanh(c*x)/(c*x+1)+a*b/d^3*arctanh(c*x)/(c*x+1)^2-2*a*b/d^3*arctanh(c*x)*ln(c*x+1)-a*b/d^3*ln(-1/2*c*x+1/2)*ln(c*x+1)+a*b/d^3*ln(-1/2*c*x+1/2)*ln(1/2+1/2*c*x)+1/64*b^2/d^3/(c*x+1)^2*c^2*x^2-1/32*b^2/d^3/(c*x+1)^2*c*x-3/8*b^2/d^3/(c*x+1)*c*x-1/2*I*b^2/d^3*arctanh(c*x)^2*Pi*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1))*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^2-1/2*I*b^2/d^3*arctanh(c*x)^2*Pi*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^2+1/2*I*b^2/d^3*arctanh(c*x)^2*Pi*csgn(I*(c*x+1)/(-c^2*x^2+1)^(1/2))^2*csgn(I*(c*x+1)^2/(c^2*x^2-1))+I*b^2/d^3*arctanh(c*x)^2*Pi*csgn(I*(c*x+1)/(-c^2*x^2+1)^(1/2))*csgn(I*(c*x+1)^2/(c^2*x^2-1))^2","C"
117,1,7593,428,1.042000," ","int((a+b*arctanh(c*x))^2/x^2/(c*d*x+d)^3,x)","\text{output too large to display}"," ",0,"result too large to display","C"
118,1,386,158,0.068000," ","int((a+b*arctanh(c*x))^2/(c*x+1)^4,x)","-\frac{a^{2}}{3 c \left(c x +1\right)^{3}}-\frac{b^{2} \arctanh \left(c x \right)^{2}}{3 c \left(c x +1\right)^{3}}-\frac{b^{2} \arctanh \left(c x \right) \ln \left(c x -1\right)}{24 c}-\frac{b^{2} \arctanh \left(c x \right)}{9 c \left(c x +1\right)^{3}}-\frac{b^{2} \arctanh \left(c x \right)}{12 c \left(c x +1\right)^{2}}-\frac{b^{2} \arctanh \left(c x \right)}{12 c \left(c x +1\right)}+\frac{b^{2} \arctanh \left(c x \right) \ln \left(c x +1\right)}{24 c}-\frac{b^{2} \ln \left(c x -1\right)^{2}}{96 c}+\frac{b^{2} \ln \left(c x -1\right) \ln \left(\frac{1}{2}+\frac{c x}{2}\right)}{48 c}-\frac{b^{2} \ln \left(c x +1\right)^{2}}{96 c}+\frac{b^{2} \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) \ln \left(c x +1\right)}{48 c}-\frac{b^{2} \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{c x}{2}\right)}{48 c}-\frac{11 b^{2} \ln \left(c x -1\right)}{288 c}-\frac{b^{2}}{54 c \left(c x +1\right)^{3}}-\frac{5 b^{2}}{144 c \left(c x +1\right)^{2}}-\frac{11 b^{2}}{144 c \left(c x +1\right)}+\frac{11 b^{2} \ln \left(c x +1\right)}{288 c}-\frac{2 a b \arctanh \left(c x \right)}{3 c \left(c x +1\right)^{3}}-\frac{a b \ln \left(c x -1\right)}{24 c}-\frac{a b}{9 c \left(c x +1\right)^{3}}-\frac{a b}{12 c \left(c x +1\right)^{2}}-\frac{a b}{12 c \left(c x +1\right)}+\frac{a b \ln \left(c x +1\right)}{24 c}"," ",0,"-1/3/c*a^2/(c*x+1)^3-1/3/c*b^2/(c*x+1)^3*arctanh(c*x)^2-1/24/c*b^2*arctanh(c*x)*ln(c*x-1)-1/9/c*b^2*arctanh(c*x)/(c*x+1)^3-1/12/c*b^2*arctanh(c*x)/(c*x+1)^2-1/12/c*b^2*arctanh(c*x)/(c*x+1)+1/24/c*b^2*arctanh(c*x)*ln(c*x+1)-1/96/c*b^2*ln(c*x-1)^2+1/48/c*b^2*ln(c*x-1)*ln(1/2+1/2*c*x)-1/96/c*b^2*ln(c*x+1)^2+1/48/c*b^2*ln(-1/2*c*x+1/2)*ln(c*x+1)-1/48/c*b^2*ln(-1/2*c*x+1/2)*ln(1/2+1/2*c*x)-11/288/c*b^2*ln(c*x-1)-1/54*b^2/c/(c*x+1)^3-5/144*b^2/c/(c*x+1)^2-11/144*b^2/c/(c*x+1)+11/288/c*b^2*ln(c*x+1)-2/3/c*a*b*arctanh(c*x)/(c*x+1)^3-1/24/c*a*b*ln(c*x-1)-1/9/c*a*b/(c*x+1)^3-1/12/c*a*b/(c*x+1)^2-1/12/c*a*b/(c*x+1)+1/24/c*a*b*ln(c*x+1)","B"
119,1,717,65,0.517000," ","int(arctanh(a*x)^2/(-a*c*x^2+c*x),x)","\frac{\arctanh \left(a x \right)^{2} \ln \left(a x \right)}{c}-\frac{\arctanh \left(a x \right)^{2} \ln \left(a x -1\right)}{c}-\frac{\arctanh \left(a x \right)^{2} \ln \left(\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}-1\right)}{c}+\frac{\arctanh \left(a x \right)^{2} \ln \left(1-\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{c}+\frac{2 \arctanh \left(a x \right) \polylog \left(2, \frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{c}-\frac{2 \polylog \left(3, \frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{c}+\frac{\arctanh \left(a x \right)^{2} \ln \left(1+\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{c}+\frac{2 \arctanh \left(a x \right) \polylog \left(2, -\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{c}-\frac{2 \polylog \left(3, -\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{c}-\frac{i \arctanh \left(a x \right)^{2} \mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}-1\right)}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right)^{2} \pi}{2 c}+\frac{i \arctanh \left(a x \right)^{2} \mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right) \mathrm{csgn}\left(i \left(\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}-1\right)\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}-1\right)}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right) \pi}{2 c}+\frac{i \arctanh \left(a x \right)^{2} \mathrm{csgn}\left(\frac{i \left(\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}-1\right)}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right)^{3} \pi}{2 c}+\frac{i \arctanh \left(a x \right)^{2} \pi}{c}+\frac{i \arctanh \left(a x \right)^{2} \mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right)^{3} \pi}{c}-\frac{i \arctanh \left(a x \right)^{2} \mathrm{csgn}\left(i \left(\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}-1\right)\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}-1\right)}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right)^{2} \pi}{2 c}-\frac{i \arctanh \left(a x \right)^{2} \mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right)^{2} \pi}{c}+\frac{\arctanh \left(a x \right)^{2} \ln \left(2\right)}{c}"," ",0,"1/c*arctanh(a*x)^2*ln(a*x)-1/c*arctanh(a*x)^2*ln(a*x-1)-1/c*arctanh(a*x)^2*ln((a*x+1)^2/(-a^2*x^2+1)-1)+1/c*arctanh(a*x)^2*ln(1-(a*x+1)/(-a^2*x^2+1)^(1/2))+2/c*arctanh(a*x)*polylog(2,(a*x+1)/(-a^2*x^2+1)^(1/2))-2/c*polylog(3,(a*x+1)/(-a^2*x^2+1)^(1/2))+1/c*arctanh(a*x)^2*ln(1+(a*x+1)/(-a^2*x^2+1)^(1/2))+2/c*arctanh(a*x)*polylog(2,-(a*x+1)/(-a^2*x^2+1)^(1/2))-2/c*polylog(3,-(a*x+1)/(-a^2*x^2+1)^(1/2))+I/c*arctanh(a*x)^2*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))^3*Pi+I/c*arctanh(a*x)^2*Pi+1/2*I/c*arctanh(a*x)^2*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*((a*x+1)^2/(-a^2*x^2+1)-1))*csgn(I*((a*x+1)^2/(-a^2*x^2+1)-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))*Pi-1/2*I/c*arctanh(a*x)^2*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*((a*x+1)^2/(-a^2*x^2+1)-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*Pi+1/2*I/c*arctanh(a*x)^2*csgn(I*((a*x+1)^2/(-a^2*x^2+1)-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^3*Pi-I/c*arctanh(a*x)^2*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*Pi-1/2*I/c*arctanh(a*x)^2*csgn(I*((a*x+1)^2/(-a^2*x^2+1)-1))*csgn(I*((a*x+1)^2/(-a^2*x^2+1)-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*Pi+1/c*arctanh(a*x)^2*ln(2)","C"
120,1,963,288,0.586000," ","int((c*x+1)^3*(a+b*arctanh(c*x))^3,x)","-\frac{b^{3}}{4 c}+\frac{a^{3}}{4 c}+b^{3} \arctanh \left(c x \right)^{3} x +\frac{21 b^{3} \arctanh \left(c x \right)^{2} x}{4}+\frac{b^{3} \arctanh \left(c x \right)^{3}}{4 c}+\frac{4 b^{3} \arctanh \left(c x \right)^{2}}{c}+\frac{3 b^{3} \polylog \left(3, -\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}{c}+\frac{11 b^{3} \arctanh \left(c x \right)}{4 c}+\frac{21 x \,a^{2} b}{4}+\frac{c^{3} x^{4} a^{3}}{4}+c^{2} x^{3} a^{3}+\frac{3 c \,x^{2} a^{3}}{2}-\frac{3 b^{3} \ln \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}{c}-\frac{13 a \,b^{2}}{4 c}+\frac{c \,x^{2} a \,b^{2}}{4}+\frac{c^{2} a^{2} b \,x^{3}}{4}-\frac{6 a \,b^{2} \ln \left(c x -1\right) \ln \left(\frac{1}{2}+\frac{c x}{2}\right)}{c}+\frac{12 a \,b^{2} \arctanh \left(c x \right) \ln \left(c x -1\right)}{c}+\frac{3 c^{3} a \,b^{2} \arctanh \left(c x \right)^{2} x^{4}}{4}+3 c^{2} a \,b^{2} \arctanh \left(c x \right)^{2} x^{3}+\frac{c^{2} a \,b^{2} \arctanh \left(c x \right) x^{3}}{2}+\frac{3 c^{3} a^{2} b \arctanh \left(c x \right) x^{4}}{4}+3 c^{2} a^{2} b \arctanh \left(c x \right) x^{3}+3 c a \,b^{2} \arctanh \left(c x \right) x^{2}+\frac{9 c \,a^{2} b \arctanh \left(c x \right) x^{2}}{2}+\frac{9 c a \,b^{2} \arctanh \left(c x \right)^{2} x^{2}}{2}-\frac{6 i b^{3} \pi  \arctanh \left(c x \right)^{2}}{c}+3 x a \,b^{2}-\frac{6 i b^{3} \pi  \mathrm{csgn}\left(\frac{i}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right)^{3} \arctanh \left(c x \right)^{2}}{c}+\frac{6 i b^{3} \pi  \mathrm{csgn}\left(\frac{i}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right)^{2} \arctanh \left(c x \right)^{2}}{c}+3 b^{3} x \arctanh \left(c x \right)-\frac{11 b^{3} \dilog \left(1-\frac{i \left(c x +1\right)}{\sqrt{-c^{2} x^{2}+1}}\right)}{c}-\frac{11 b^{3} \dilog \left(1+\frac{i \left(c x +1\right)}{\sqrt{-c^{2} x^{2}+1}}\right)}{c}+3 a \,b^{2} \arctanh \left(c x \right)^{2} x +3 a^{2} b \arctanh \left(c x \right) x +\frac{21 a \,b^{2} \arctanh \left(c x \right) x}{2}-\frac{11 b^{3} \arctanh \left(c x \right) \ln \left(1+\frac{i \left(c x +1\right)}{\sqrt{-c^{2} x^{2}+1}}\right)}{c}-\frac{11 b^{3} \arctanh \left(c x \right) \ln \left(1-\frac{i \left(c x +1\right)}{\sqrt{-c^{2} x^{2}+1}}\right)}{c}+c^{2} b^{3} \arctanh \left(c x \right)^{3} x^{3}+\frac{c^{3} b^{3} \arctanh \left(c x \right)^{3} x^{4}}{4}+\frac{c^{2} b^{3} \arctanh \left(c x \right)^{2} x^{3}}{4}+\frac{3 c \,b^{3} \arctanh \left(c x \right)^{2} x^{2}}{2}-\frac{6 b^{3} \arctanh \left(c x \right) \polylog \left(2, -\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}{c}+\frac{6 b^{3} \arctanh \left(c x \right)^{2} \ln \left(c x -1\right)}{c}+\frac{3 a^{2} b \arctanh \left(c x \right)}{4 c}+\frac{3 a \,b^{2} \arctanh \left(c x \right)^{2}}{4 c}-\frac{6 a \,b^{2} \dilog \left(\frac{1}{2}+\frac{c x}{2}\right)}{c}-\frac{6 b^{3} \arctanh \left(c x \right)^{2} \ln \left(2\right)}{c}+\frac{c \,b^{3} \arctanh \left(c x \right) x^{2}}{4}+\frac{3 c \,b^{3} \arctanh \left(c x \right)^{3} x^{2}}{2}+\frac{6 a^{2} b \ln \left(c x -1\right)}{c}+\frac{7 a \,b^{2} \ln \left(c x -1\right)}{c}+\frac{4 a \,b^{2} \ln \left(c x +1\right)}{c}+\frac{3 a \,b^{2} \ln \left(c x -1\right)^{2}}{c}+\frac{3 c \,a^{2} b \,x^{2}}{2}+a^{3} x +\frac{b^{3} x}{4}"," ",0,"-1/4/c*b^3+1/4/c*a^3+21/4*x*a^2*b+b^3*arctanh(c*x)^3*x+21/4*b^3*arctanh(c*x)^2*x+1/4*c^3*x^4*a^3+c^2*x^3*a^3+3/2*c*x^2*a^3+1/4/c*b^3*arctanh(c*x)^3+4/c*b^3*arctanh(c*x)^2-11/c*b^3*dilog(1-I*(c*x+1)/(-c^2*x^2+1)^(1/2))-11/c*b^3*dilog(1+I*(c*x+1)/(-c^2*x^2+1)^(1/2))-3/c*b^3*ln(1+(c*x+1)^2/(-c^2*x^2+1))+3/c*b^3*polylog(3,-(c*x+1)^2/(-c^2*x^2+1))-13/4/c*a*b^2+1/4*c*x^2*a*b^2+1/4*c^2*a^2*b*x^3+c^2*b^3*arctanh(c*x)^3*x^3+1/4*c^3*b^3*arctanh(c*x)^3*x^4+1/4*c^2*b^3*arctanh(c*x)^2*x^3+3/2*c*b^3*arctanh(c*x)^2*x^2-11/c*b^3*arctanh(c*x)*ln(1+I*(c*x+1)/(-c^2*x^2+1)^(1/2))-6/c*b^3*arctanh(c*x)*polylog(2,-(c*x+1)^2/(-c^2*x^2+1))-11/c*b^3*arctanh(c*x)*ln(1-I*(c*x+1)/(-c^2*x^2+1)^(1/2))+6/c*b^3*arctanh(c*x)^2*ln(c*x-1)+12/c*a*b^2*arctanh(c*x)*ln(c*x-1)-6/c*a*b^2*ln(c*x-1)*ln(1/2+1/2*c*x)+3/4*c^3*a*b^2*arctanh(c*x)^2*x^4+3*c^2*a*b^2*arctanh(c*x)^2*x^3+1/2*c^2*a*b^2*arctanh(c*x)*x^3+3/4*c^3*a^2*b*arctanh(c*x)*x^4+3*c^2*a^2*b*arctanh(c*x)*x^3+3*c*a*b^2*arctanh(c*x)*x^2+9/2*c*a^2*b*arctanh(c*x)*x^2-6*I/c*b^3*Pi*arctanh(c*x)^2+11/4*b^3*arctanh(c*x)/c+3*b^3*x*arctanh(c*x)+3*x*a*b^2-6*I/c*b^3*Pi*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))^3*arctanh(c*x)^2+6*I/c*b^3*Pi*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))^2*arctanh(c*x)^2+3/4/c*a^2*b*arctanh(c*x)+6/c*a^2*b*ln(c*x-1)+3/4/c*a*b^2*arctanh(c*x)^2+7/c*a*b^2*ln(c*x-1)+4/c*a*b^2*ln(c*x+1)+3/c*a*b^2*ln(c*x-1)^2-6/c*a*b^2*dilog(1/2+1/2*c*x)-6/c*b^3*arctanh(c*x)^2*ln(2)+1/4*c*b^3*arctanh(c*x)*x^2+3/2*c*b^3*arctanh(c*x)^3*x^2+3*a*b^2*arctanh(c*x)^2*x+3*a^2*b*arctanh(c*x)*x+21/2*a*b^2*arctanh(c*x)*x+3/2*c*a^2*b*x^2+9/2*c*a*b^2*arctanh(c*x)^2*x^2+a^3*x+1/4*b^3*x","C"
121,1,811,232,0.504000," ","int((c*x+1)^2*(a+b*arctanh(c*x))^3,x)","\frac{a^{3}}{3 c}+b^{3} \arctanh \left(c x \right)^{3} x +3 b^{3} \arctanh \left(c x \right)^{2} x +\frac{b^{3} \arctanh \left(c x \right)^{3}}{3 c}+\frac{5 b^{3} \arctanh \left(c x \right)^{2}}{2 c}+\frac{2 b^{3} \polylog \left(3, -\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}{c}+\frac{b^{3} \arctanh \left(c x \right)}{c}+3 x \,a^{2} b +\frac{c^{2} x^{3} a^{3}}{3}+c \,x^{2} a^{3}-\frac{b^{3} \ln \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}{c}-\frac{a \,b^{2}}{c}-\frac{4 a \,b^{2} \ln \left(c x -1\right) \ln \left(\frac{1}{2}+\frac{c x}{2}\right)}{c}+\frac{8 a \,b^{2} \arctanh \left(c x \right) \ln \left(c x -1\right)}{c}+c^{2} a \,b^{2} \arctanh \left(c x \right)^{2} x^{3}+c^{2} a^{2} b \arctanh \left(c x \right) x^{3}+c a \,b^{2} \arctanh \left(c x \right) x^{2}+3 c \,a^{2} b \arctanh \left(c x \right) x^{2}+3 c a \,b^{2} \arctanh \left(c x \right)^{2} x^{2}-\frac{4 i b^{3} \pi  \arctanh \left(c x \right)^{2}}{c}+x a \,b^{2}-\frac{4 i b^{3} \pi  \mathrm{csgn}\left(\frac{i}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right)^{3} \arctanh \left(c x \right)^{2}}{c}+\frac{4 i b^{3} \pi  \mathrm{csgn}\left(\frac{i}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right)^{2} \arctanh \left(c x \right)^{2}}{c}+b^{3} x \arctanh \left(c x \right)-\frac{6 b^{3} \dilog \left(1-\frac{i \left(c x +1\right)}{\sqrt{-c^{2} x^{2}+1}}\right)}{c}-\frac{6 b^{3} \dilog \left(1+\frac{i \left(c x +1\right)}{\sqrt{-c^{2} x^{2}+1}}\right)}{c}+3 a \,b^{2} \arctanh \left(c x \right)^{2} x +3 a^{2} b \arctanh \left(c x \right) x +6 a \,b^{2} \arctanh \left(c x \right) x -\frac{6 b^{3} \arctanh \left(c x \right) \ln \left(1+\frac{i \left(c x +1\right)}{\sqrt{-c^{2} x^{2}+1}}\right)}{c}-\frac{6 b^{3} \arctanh \left(c x \right) \ln \left(1-\frac{i \left(c x +1\right)}{\sqrt{-c^{2} x^{2}+1}}\right)}{c}+\frac{c^{2} b^{3} \arctanh \left(c x \right)^{3} x^{3}}{3}+\frac{c \,b^{3} \arctanh \left(c x \right)^{2} x^{2}}{2}-\frac{4 b^{3} \arctanh \left(c x \right) \polylog \left(2, -\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}{c}+\frac{4 b^{3} \arctanh \left(c x \right)^{2} \ln \left(c x -1\right)}{c}+\frac{a^{2} b \arctanh \left(c x \right)}{c}+\frac{a \,b^{2} \arctanh \left(c x \right)^{2}}{c}-\frac{4 a \,b^{2} \dilog \left(\frac{1}{2}+\frac{c x}{2}\right)}{c}-\frac{4 b^{3} \arctanh \left(c x \right)^{2} \ln \left(2\right)}{c}+c \,b^{3} \arctanh \left(c x \right)^{3} x^{2}+\frac{4 a^{2} b \ln \left(c x -1\right)}{c}+\frac{7 a \,b^{2} \ln \left(c x -1\right)}{2 c}+\frac{5 a \,b^{2} \ln \left(c x +1\right)}{2 c}+\frac{2 a \,b^{2} \ln \left(c x -1\right)^{2}}{c}+\frac{c \,a^{2} b \,x^{2}}{2}+a^{3} x"," ",0,"1/3/c*a^3+3*x*a^2*b+b^3*arctanh(c*x)^3*x+3*b^3*arctanh(c*x)^2*x+1/3*c^2*x^3*a^3+c*x^2*a^3+1/3/c*b^3*arctanh(c*x)^3+5/2/c*b^3*arctanh(c*x)^2-6/c*b^3*dilog(1-I*(c*x+1)/(-c^2*x^2+1)^(1/2))-6/c*b^3*dilog(1+I*(c*x+1)/(-c^2*x^2+1)^(1/2))-1/c*b^3*ln(1+(c*x+1)^2/(-c^2*x^2+1))+2/c*b^3*polylog(3,-(c*x+1)^2/(-c^2*x^2+1))-1/c*a*b^2+1/3*c^2*b^3*arctanh(c*x)^3*x^3+1/2*c*b^3*arctanh(c*x)^2*x^2-6/c*b^3*arctanh(c*x)*ln(1+I*(c*x+1)/(-c^2*x^2+1)^(1/2))-4/c*b^3*arctanh(c*x)*polylog(2,-(c*x+1)^2/(-c^2*x^2+1))-6/c*b^3*arctanh(c*x)*ln(1-I*(c*x+1)/(-c^2*x^2+1)^(1/2))+4/c*b^3*arctanh(c*x)^2*ln(c*x-1)+8/c*a*b^2*arctanh(c*x)*ln(c*x-1)-4/c*a*b^2*ln(c*x-1)*ln(1/2+1/2*c*x)+c^2*a*b^2*arctanh(c*x)^2*x^3+c^2*a^2*b*arctanh(c*x)*x^3+c*a*b^2*arctanh(c*x)*x^2+3*c*a^2*b*arctanh(c*x)*x^2+b^3*arctanh(c*x)/c+b^3*x*arctanh(c*x)+x*a*b^2-4*I/c*b^3*Pi*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))^3*arctanh(c*x)^2+4*I/c*b^3*Pi*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))^2*arctanh(c*x)^2+1/c*a^2*b*arctanh(c*x)+4/c*a^2*b*ln(c*x-1)+1/c*a*b^2*arctanh(c*x)^2+7/2/c*a*b^2*ln(c*x-1)+5/2/c*a*b^2*ln(c*x+1)+2/c*a*b^2*ln(c*x-1)^2-4/c*a*b^2*dilog(1/2+1/2*c*x)-4/c*b^3*arctanh(c*x)^2*ln(2)+c*b^3*arctanh(c*x)^3*x^2+3*a*b^2*arctanh(c*x)^2*x+3*a^2*b*arctanh(c*x)*x+6*a*b^2*arctanh(c*x)*x+1/2*c*a^2*b*x^2+3*c*a*b^2*arctanh(c*x)^2*x^2-4*I/c*b^3*Pi*arctanh(c*x)^2+a^3*x","C"
122,1,6440,181,0.797000," ","int((c*x+1)*(a+b*arctanh(c*x))^3,x)","\text{output too large to display}"," ",0,"result too large to display","C"
123,1,1491,105,0.455000," ","int((a+b*arctanh(c*x))^3/(c*x+1),x)","\frac{3 i a \,b^{2} \arctanh \left(c x \right)^{2} \mathrm{csgn}\left(\frac{i}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{c^{2} x^{2}-1}\right) \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{\left(c^{2} x^{2}-1\right) \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}\right) \pi}{2 c}-\frac{3 b^{3} \polylog \left(4, -\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}{4 c}+\frac{b^{3} \arctanh \left(c x \right)^{4}}{2 c}+\frac{a^{3} \ln \left(c x +1\right)}{c}+\frac{i b^{3} \arctanh \left(c x \right)^{3} \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{c^{2} x^{2}-1}\right) \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{\left(c^{2} x^{2}-1\right) \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}\right)^{2} \pi}{2 c}-\frac{i b^{3} \arctanh \left(c x \right)^{3} \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{c^{2} x^{2}-1}\right) \mathrm{csgn}\left(\frac{i \left(c x +1\right)}{\sqrt{-c^{2} x^{2}+1}}\right)^{2} \pi}{2 c}-\frac{3 i a \,b^{2} \arctanh \left(c x \right)^{2} \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{c^{2} x^{2}-1}\right)^{3} \pi}{2 c}-\frac{3 i a \,b^{2} \arctanh \left(c x \right)^{2} \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{\left(c^{2} x^{2}-1\right) \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}\right)^{3} \pi}{2 c}-\frac{i b^{3} \arctanh \left(c x \right)^{3} \mathrm{csgn}\left(\frac{i}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{\left(c^{2} x^{2}-1\right) \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}\right)^{2} \pi}{2 c}-\frac{i b^{3} \arctanh \left(c x \right)^{3} \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{c^{2} x^{2}-1}\right)^{2} \mathrm{csgn}\left(\frac{i \left(c x +1\right)}{\sqrt{-c^{2} x^{2}+1}}\right) \pi}{c}-\frac{3 i a \,b^{2} \arctanh \left(c x \right)^{2} \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{c^{2} x^{2}-1}\right)^{2} \mathrm{csgn}\left(\frac{i \left(c x +1\right)}{\sqrt{-c^{2} x^{2}+1}}\right) \pi}{c}+\frac{3 i a \,b^{2} \arctanh \left(c x \right)^{2} \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{c^{2} x^{2}-1}\right) \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{\left(c^{2} x^{2}-1\right) \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}\right)^{2} \pi}{2 c}-\frac{3 i a \,b^{2} \arctanh \left(c x \right)^{2} \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{c^{2} x^{2}-1}\right) \mathrm{csgn}\left(\frac{i \left(c x +1\right)}{\sqrt{-c^{2} x^{2}+1}}\right)^{2} \pi}{2 c}+\frac{i b^{3} \arctanh \left(c x \right)^{3} \mathrm{csgn}\left(\frac{i}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{c^{2} x^{2}-1}\right) \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{\left(c^{2} x^{2}-1\right) \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}\right) \pi}{2 c}-\frac{3 i a \,b^{2} \arctanh \left(c x \right)^{2} \mathrm{csgn}\left(\frac{i}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{\left(c^{2} x^{2}-1\right) \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}\right)^{2} \pi}{2 c}-\frac{i b^{3} \arctanh \left(c x \right)^{3} \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{\left(c^{2} x^{2}-1\right) \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}\right)^{3} \pi}{2 c}-\frac{i b^{3} \arctanh \left(c x \right)^{3} \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{c^{2} x^{2}-1}\right)^{3} \pi}{2 c}-\frac{b^{3} \arctanh \left(c x \right)^{3} \ln \left(2\right)}{c}-\frac{3 a^{2} b \dilog \left(\frac{1}{2}+\frac{c x}{2}\right)}{2 c}-\frac{3 a^{2} b \ln \left(c x +1\right)^{2}}{4 c}+\frac{3 a^{2} b \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) \ln \left(c x +1\right)}{2 c}-\frac{3 a^{2} b \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{c x}{2}\right)}{2 c}-\frac{3 a \,b^{2} \arctanh \left(c x \right)^{2} \ln \left(2\right)}{c}+\frac{3 a^{2} b \ln \left(c x +1\right) \arctanh \left(c x \right)}{c}+\frac{3 a \,b^{2} \ln \left(c x +1\right) \arctanh \left(c x \right)^{2}}{c}-\frac{6 a \,b^{2} \arctanh \left(c x \right)^{2} \ln \left(\frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)}{c}-\frac{3 a \,b^{2} \arctanh \left(c x \right) \polylog \left(2, -\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}{c}+\frac{3 a \,b^{2} \polylog \left(3, -\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}{2 c}+\frac{3 b^{3} \arctanh \left(c x \right) \polylog \left(3, -\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}{2 c}+\frac{b^{3} \ln \left(c x +1\right) \arctanh \left(c x \right)^{3}}{c}-\frac{2 b^{3} \arctanh \left(c x \right)^{3} \ln \left(\frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)}{c}-\frac{3 b^{3} \arctanh \left(c x \right)^{2} \polylog \left(2, -\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}{2 c}+\frac{2 a \,b^{2} \arctanh \left(c x \right)^{3}}{c}"," ",0,"3/2*I/c*a*b^2*arctanh(c*x)^2*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))*csgn(I*(c*x+1)^2/(c^2*x^2-1))*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))*Pi-3*I/c*a*b^2*arctanh(c*x)^2*csgn(I*(c*x+1)^2/(c^2*x^2-1))^2*csgn(I*(c*x+1)/(-c^2*x^2+1)^(1/2))*Pi+3/2*I/c*a*b^2*arctanh(c*x)^2*csgn(I*(c*x+1)^2/(c^2*x^2-1))*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^2*Pi-3/2*I/c*a*b^2*arctanh(c*x)^2*csgn(I*(c*x+1)^2/(c^2*x^2-1))*csgn(I*(c*x+1)/(-c^2*x^2+1)^(1/2))^2*Pi+1/2*I/c*b^3*arctanh(c*x)^3*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))*csgn(I*(c*x+1)^2/(c^2*x^2-1))*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))*Pi-3/2*I/c*a*b^2*arctanh(c*x)^2*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^2*Pi+a^3/c*ln(c*x+1)-3/4/c*b^3*polylog(4,-(c*x+1)^2/(-c^2*x^2+1))+1/2/c*b^3*arctanh(c*x)^4-1/2*I/c*b^3*arctanh(c*x)^3*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^3*Pi-1/2*I/c*b^3*arctanh(c*x)^3*csgn(I*(c*x+1)^2/(c^2*x^2-1))^3*Pi-1/c*b^3*arctanh(c*x)^3*ln(2)-3/4/c*a^2*b*ln(c*x+1)^2-3/2/c*a^2*b*dilog(1/2+1/2*c*x)+2/c*a*b^2*arctanh(c*x)^3+3/2/c*a*b^2*polylog(3,-(c*x+1)^2/(-c^2*x^2+1))+3/2/c*b^3*arctanh(c*x)*polylog(3,-(c*x+1)^2/(-c^2*x^2+1))+1/c*b^3*ln(c*x+1)*arctanh(c*x)^3-2/c*b^3*arctanh(c*x)^3*ln((c*x+1)/(-c^2*x^2+1)^(1/2))-3/2/c*b^3*arctanh(c*x)^2*polylog(2,-(c*x+1)^2/(-c^2*x^2+1))+1/2*I/c*b^3*arctanh(c*x)^3*csgn(I*(c*x+1)^2/(c^2*x^2-1))*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^2*Pi-1/2*I/c*b^3*arctanh(c*x)^3*csgn(I*(c*x+1)^2/(c^2*x^2-1))*csgn(I*(c*x+1)/(-c^2*x^2+1)^(1/2))^2*Pi-3/2*I/c*a*b^2*arctanh(c*x)^2*csgn(I*(c*x+1)^2/(c^2*x^2-1))^3*Pi-3/2*I/c*a*b^2*arctanh(c*x)^2*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^3*Pi-1/2*I/c*b^3*arctanh(c*x)^3*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^2*Pi-I/c*b^3*arctanh(c*x)^3*csgn(I*(c*x+1)^2/(c^2*x^2-1))^2*csgn(I*(c*x+1)/(-c^2*x^2+1)^(1/2))*Pi-3/c*a*b^2*arctanh(c*x)^2*ln(2)+3/c*a^2*b*ln(c*x+1)*arctanh(c*x)+3/2/c*a^2*b*ln(-1/2*c*x+1/2)*ln(c*x+1)-3/2/c*a^2*b*ln(-1/2*c*x+1/2)*ln(1/2+1/2*c*x)+3/c*a*b^2*ln(c*x+1)*arctanh(c*x)^2-6/c*a*b^2*arctanh(c*x)^2*ln((c*x+1)/(-c^2*x^2+1)^(1/2))-3/c*a*b^2*arctanh(c*x)*polylog(2,-(c*x+1)^2/(-c^2*x^2+1))","C"
124,1,1895,127,0.698000," ","int((a+b*arctanh(c*x))^3/(c*x+1)^2,x)","-\frac{3 i b^{3} \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{c^{2} x^{2}-1}\right) \mathrm{csgn}\left(\frac{i \left(c x +1\right)}{\sqrt{-c^{2} x^{2}+1}}\right)^{2} \arctanh \left(c x \right)^{2} \pi  x}{8 \left(c x +1\right)}+\frac{3 a \,b^{2} \ln \left(c x -1\right) \ln \left(\frac{1}{2}+\frac{c x}{2}\right)}{4 c}-\frac{3 a \,b^{2} \arctanh \left(c x \right) \ln \left(c x -1\right)}{2 c}-\frac{3 i b^{3} \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{c^{2} x^{2}-1}\right) \mathrm{csgn}\left(\frac{i \left(c x +1\right)}{\sqrt{-c^{2} x^{2}+1}}\right)^{2} \arctanh \left(c x \right)^{2} \pi}{8 c \left(c x +1\right)}-\frac{3 i b^{3} \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{\left(c^{2} x^{2}-1\right) \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}\right)^{2} \mathrm{csgn}\left(\frac{i}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right) \arctanh \left(c x \right)^{2} \pi}{8 c \left(c x +1\right)}-\frac{3 i b^{3} \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{\left(c^{2} x^{2}-1\right) \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}\right)^{2} \mathrm{csgn}\left(\frac{i}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right) \arctanh \left(c x \right)^{2} \pi  x}{8 \left(c x +1\right)}-\frac{3 i b^{3} \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{c^{2} x^{2}-1}\right)^{2} \mathrm{csgn}\left(\frac{i \left(c x +1\right)}{\sqrt{-c^{2} x^{2}+1}}\right) \arctanh \left(c x \right)^{2} \pi  x}{4 \left(c x +1\right)}+\frac{3 i b^{3} \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{\left(c^{2} x^{2}-1\right) \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}\right)^{2} \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{c^{2} x^{2}-1}\right) \arctanh \left(c x \right)^{2} \pi  x}{8 \left(c x +1\right)}-\frac{3 i b^{3} \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{c^{2} x^{2}-1}\right)^{2} \mathrm{csgn}\left(\frac{i \left(c x +1\right)}{\sqrt{-c^{2} x^{2}+1}}\right) \arctanh \left(c x \right)^{2} \pi}{4 c \left(c x +1\right)}+\frac{3 i b^{3} \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{\left(c^{2} x^{2}-1\right) \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}\right)^{2} \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{c^{2} x^{2}-1}\right) \arctanh \left(c x \right)^{2} \pi}{8 c \left(c x +1\right)}-\frac{3 b^{3}}{8 c \left(c x +1\right)}+\frac{3 b^{3} \arctanh \left(c x \right)^{2} \ln \left(c x +1\right)}{4 c}+\frac{3 i b^{3} \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{\left(c^{2} x^{2}-1\right) \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}\right) \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{c^{2} x^{2}-1}\right) \mathrm{csgn}\left(\frac{i}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right) \arctanh \left(c x \right)^{2} \pi  x}{8 \left(c x +1\right)}+\frac{3 i b^{3} \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{\left(c^{2} x^{2}-1\right) \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}\right) \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{c^{2} x^{2}-1}\right) \mathrm{csgn}\left(\frac{i}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right) \arctanh \left(c x \right)^{2} \pi}{8 c \left(c x +1\right)}+\frac{b^{3} \arctanh \left(c x \right)^{3} x}{2 c x +2}+\frac{3 b^{3} x}{8 \left(c x +1\right)}+\frac{3 a^{2} b \ln \left(c x +1\right)}{4 c}-\frac{a^{3}}{c \left(c x +1\right)}-\frac{3 a \,b^{2} \arctanh \left(c x \right)}{c \left(c x +1\right)}-\frac{3 a \,b^{2} \arctanh \left(c x \right)^{2}}{c \left(c x +1\right)}-\frac{3 a^{2} b \arctanh \left(c x \right)}{c \left(c x +1\right)}+\frac{3 a \,b^{2} \arctanh \left(c x \right) \ln \left(c x +1\right)}{2 c}-\frac{3 a^{2} b}{2 c \left(c x +1\right)}-\frac{3 b^{3} \arctanh \left(c x \right)^{2} \ln \left(\frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)}{2 c}-\frac{3 b^{3} \arctanh \left(c x \right)^{2}}{4 c \left(c x +1\right)}-\frac{3 b^{3} \arctanh \left(c x \right)}{4 c \left(c x +1\right)}+\frac{3 b^{3} \arctanh \left(c x \right)^{2} x}{4 \left(c x +1\right)}+\frac{3 b^{3} \arctanh \left(c x \right) x}{4 \left(c x +1\right)}-\frac{b^{3} \arctanh \left(c x \right)^{3}}{2 c \left(c x +1\right)}-\frac{3 b^{3} \arctanh \left(c x \right)^{2} \ln \left(c x -1\right)}{4 c}-\frac{3 a^{2} b \ln \left(c x -1\right)}{4 c}-\frac{3 a \,b^{2} \ln \left(c x -1\right)}{4 c}+\frac{3 a \,b^{2} \ln \left(c x +1\right)}{4 c}-\frac{3 a \,b^{2} \ln \left(c x -1\right)^{2}}{8 c}-\frac{3 a \,b^{2}}{2 c \left(c x +1\right)}-\frac{3 i b^{3} \mathrm{csgn}\left(\frac{i}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right)^{2} \arctanh \left(c x \right)^{2} \pi  x}{4 \left(c x +1\right)}-\frac{3 i b^{3} \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{c^{2} x^{2}-1}\right)^{3} \arctanh \left(c x \right)^{2} \pi  x}{8 \left(c x +1\right)}-\frac{3 i b^{3} \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{c^{2} x^{2}-1}\right)^{3} \arctanh \left(c x \right)^{2} \pi}{8 c \left(c x +1\right)}-\frac{3 i b^{3} \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{\left(c^{2} x^{2}-1\right) \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}\right)^{3} \arctanh \left(c x \right)^{2} \pi}{8 c \left(c x +1\right)}+\frac{3 i b^{3} \mathrm{csgn}\left(\frac{i}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right)^{3} \arctanh \left(c x \right)^{2} \pi}{4 c \left(c x +1\right)}-\frac{3 i b^{3} \mathrm{csgn}\left(\frac{i}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right)^{2} \arctanh \left(c x \right)^{2} \pi}{4 c \left(c x +1\right)}-\frac{3 i b^{3} \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{\left(c^{2} x^{2}-1\right) \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}\right)^{3} \arctanh \left(c x \right)^{2} \pi  x}{8 \left(c x +1\right)}+\frac{3 i b^{3} \mathrm{csgn}\left(\frac{i}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right)^{3} \arctanh \left(c x \right)^{2} \pi  x}{4 \left(c x +1\right)}+\frac{3 a \,b^{2} \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) \ln \left(c x +1\right)}{4 c}-\frac{3 a \,b^{2} \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{c x}{2}\right)}{4 c}+\frac{3 i b^{3} \arctanh \left(c x \right)^{2} \pi  x}{4 \left(c x +1\right)}+\frac{3 i b^{3} \arctanh \left(c x \right)^{2} \pi}{4 c \left(c x +1\right)}-\frac{3 a \,b^{2} \ln \left(c x +1\right)^{2}}{8 c}"," ",0,"3/8*I*b^3/(c*x+1)*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))*csgn(I*(c*x+1)^2/(c^2*x^2-1))*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))*arctanh(c*x)^2*Pi*x-3/8*I/c*b^3/(c*x+1)*csgn(I*(c*x+1)^2/(c^2*x^2-1))^3*arctanh(c*x)^2*Pi-3/8*I/c*b^3/(c*x+1)*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^3*arctanh(c*x)^2*Pi-3/4/c*b^3*arctanh(c*x)^2*ln(c*x-1)-3/2/c*a*b^2*arctanh(c*x)*ln(c*x-1)+3/4/c*a*b^2*ln(c*x-1)*ln(1/2+1/2*c*x)-3/8*I*b^3/(c*x+1)*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^2*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))*arctanh(c*x)^2*Pi*x-3/4*I*b^3/(c*x+1)*csgn(I*(c*x+1)^2/(c^2*x^2-1))^2*csgn(I*(c*x+1)/(-c^2*x^2+1)^(1/2))*arctanh(c*x)^2*Pi*x+3/8*I*b^3/(c*x+1)*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^2*csgn(I*(c*x+1)^2/(c^2*x^2-1))*arctanh(c*x)^2*Pi*x-3/4*I/c*b^3/(c*x+1)*csgn(I*(c*x+1)^2/(c^2*x^2-1))^2*csgn(I*(c*x+1)/(-c^2*x^2+1)^(1/2))*arctanh(c*x)^2*Pi+3/8*I/c*b^3/(c*x+1)*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^2*csgn(I*(c*x+1)^2/(c^2*x^2-1))*arctanh(c*x)^2*Pi-3/8*I/c*b^3/(c*x+1)*csgn(I*(c*x+1)^2/(c^2*x^2-1))*csgn(I*(c*x+1)/(-c^2*x^2+1)^(1/2))^2*arctanh(c*x)^2*Pi-3/8*I/c*b^3/(c*x+1)*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^2*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))*arctanh(c*x)^2*Pi-3/8*I*b^3/(c*x+1)*csgn(I*(c*x+1)^2/(c^2*x^2-1))*csgn(I*(c*x+1)/(-c^2*x^2+1)^(1/2))^2*arctanh(c*x)^2*Pi*x-3/8*b^3/c/(c*x+1)+3/8*I/c*b^3/(c*x+1)*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))*csgn(I*(c*x+1)^2/(c^2*x^2-1))*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))*arctanh(c*x)^2*Pi+3/8*b^3/(c*x+1)*x+3/4/c*a^2*b*ln(c*x+1)-3/2/c*b^3*arctanh(c*x)^2*ln((c*x+1)/(-c^2*x^2+1)^(1/2))-1/c*a^3/(c*x+1)-3/c*a*b^2/(c*x+1)*arctanh(c*x)-3/c*a*b^2/(c*x+1)*arctanh(c*x)^2-3/c*a^2*b/(c*x+1)*arctanh(c*x)-3/2/c*a^2*b/(c*x+1)-3/4/c*a^2*b*ln(c*x-1)-3/4/c*a*b^2*ln(c*x-1)+3/4/c*a*b^2*ln(c*x+1)-3/8/c*a*b^2*ln(c*x-1)^2-3/4/c*b^3*arctanh(c*x)^2/(c*x+1)-3/4/c*b^3/(c*x+1)*arctanh(c*x)-3/2/c*a*b^2/(c*x+1)+3/4*b^3/(c*x+1)*arctanh(c*x)^2*x+3/4*b^3/(c*x+1)*arctanh(c*x)*x+1/2*b^3/(c*x+1)*arctanh(c*x)^3*x-1/2/c*b^3/(c*x+1)*arctanh(c*x)^3+3/4*I/c*b^3/(c*x+1)*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))^3*arctanh(c*x)^2*Pi-3/4*I/c*b^3/(c*x+1)*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))^2*arctanh(c*x)^2*Pi-3/8*I*b^3/(c*x+1)*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^3*arctanh(c*x)^2*Pi*x+3/4*I*b^3/(c*x+1)*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))^3*arctanh(c*x)^2*Pi*x-3/4*I*b^3/(c*x+1)*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))^2*arctanh(c*x)^2*Pi*x-3/8*I*b^3/(c*x+1)*csgn(I*(c*x+1)^2/(c^2*x^2-1))^3*arctanh(c*x)^2*Pi*x+3/2/c*a*b^2*arctanh(c*x)*ln(c*x+1)+3/4/c*a*b^2*ln(-1/2*c*x+1/2)*ln(c*x+1)-3/4/c*a*b^2*ln(-1/2*c*x+1/2)*ln(1/2+1/2*c*x)+3/4*I*b^3/(c*x+1)*arctanh(c*x)^2*Pi*x+3/4*I/c*b^3/(c*x+1)*arctanh(c*x)^2*Pi+3/4/c*b^3*arctanh(c*x)^2*ln(c*x+1)-3/8/c*a*b^2*ln(c*x+1)^2","C"
125,1,2752,188,0.832000," ","int((a+b*arctanh(c*x))^3/(c*x+1)^3,x)","\text{Expression too large to display}"," ",0,"1/4*b^3/(c*x+1)^2*arctanh(c*x)^3*x+9/16*b^3/(c*x+1)^2*arctanh(c*x)^2*x+3/32*b^3/(c*x+1)^2*arctanh(c*x)*x-3/16/c*a*b^2/(c*x+1)^2-3/8/c*a^2*b/(c*x+1)^2+45/256*c*b^3/(c*x+1)^2*x^2-3/8/c*b^3/(c*x+1)^2*arctanh(c*x)^3-27/64/c*b^3/(c*x+1)^2*arctanh(c*x)-3/32/c*b^3*arctanh(c*x)^2/(c*x+1)^2-3/16/c*b^3*arctanh(c*x)^2*ln(c*x-1)-3/8/c*a*b^2*arctanh(c*x)*ln(c*x-1)+3/16/c*a*b^2*ln(c*x-1)*ln(1/2+1/2*c*x)-51/256*b^3/c/(c*x+1)^2-3/4/c*a*b^2/(c*x+1)^2*arctanh(c*x)+3/16/c*a^2*b*ln(c*x+1)-3/8/c*b^3*arctanh(c*x)^2*ln((c*x+1)/(-c^2*x^2+1)^(1/2))+3/128*b^3/(c*x+1)^2*x-1/2/c*a^3/(c*x+1)^2+21/64*c*b^3/(c*x+1)^2*arctanh(c*x)*x^2-3/4/c*a*b^2/(c*x+1)*arctanh(c*x)-3/2/c*a*b^2/(c*x+1)^2*arctanh(c*x)^2-3/8/c*a^2*b/(c*x+1)-3/16*I*b^3/(c*x+1)^2*arctanh(c*x)^2*Pi*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^2*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))*x-3/32*I*c*b^3/(c*x+1)^2*arctanh(c*x)^2*Pi*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^3*x^2+3/16*I*c*b^3/(c*x+1)^2*arctanh(c*x)^2*Pi*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))^3*x^2-3/16*I*c*b^3/(c*x+1)^2*arctanh(c*x)^2*Pi*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))^2*x^2-3/32*I*c*b^3/(c*x+1)^2*arctanh(c*x)^2*Pi*csgn(I*(c*x+1)^2/(c^2*x^2-1))^3*x^2-3/16*I/c*b^3/(c*x+1)^2*Pi*arctanh(c*x)^2*csgn(I*(c*x+1)/(-c^2*x^2+1)^(1/2))*csgn(I*(c*x+1)^2/(c^2*x^2-1))^2+3/32*I/c*b^3/(c*x+1)^2*Pi*arctanh(c*x)^2*csgn(I*(c*x+1)^2/(c^2*x^2-1))*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^2-3/32*I/c*b^3/(c*x+1)^2*Pi*arctanh(c*x)^2*csgn(I*(c*x+1)/(-c^2*x^2+1)^(1/2))^2*csgn(I*(c*x+1)^2/(c^2*x^2-1))-3/32*I/c*b^3/(c*x+1)^2*Pi*arctanh(c*x)^2*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^2-3/8*I*b^3/(c*x+1)^2*arctanh(c*x)^2*Pi*csgn(I*(c*x+1)^2/(c^2*x^2-1))^2*csgn(I*(c*x+1)/(-c^2*x^2+1)^(1/2))*x+3/16*I*b^3/(c*x+1)^2*arctanh(c*x)^2*Pi*csgn(I*(c*x+1)^2/(c^2*x^2-1))*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^2*x-3/16*I*b^3/(c*x+1)^2*arctanh(c*x)^2*Pi*csgn(I*(c*x+1)^2/(c^2*x^2-1))*csgn(I*(c*x+1)/(-c^2*x^2+1)^(1/2))^2*x-3/16/c*a^2*b*ln(c*x-1)-9/32/c*a*b^2*ln(c*x-1)+9/32/c*a*b^2*ln(c*x+1)-3/32/c*a*b^2*ln(c*x-1)^2-3/8/c*b^3*arctanh(c*x)^2/(c*x+1)-9/16/c*a*b^2/(c*x+1)+3/32*I*c*b^3/(c*x+1)^2*arctanh(c*x)^2*Pi*csgn(I*(c*x+1)^2/(c^2*x^2-1))*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))*x^2+3/16*I/c*b^3/(c*x+1)^2*Pi*arctanh(c*x)^2+3/8*I*b^3/(c*x+1)^2*arctanh(c*x)^2*Pi*x-3/8*I*b^3/(c*x+1)^2*arctanh(c*x)^2*Pi*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))^2*x-3/32*I/c*b^3/(c*x+1)^2*Pi*arctanh(c*x)^2*csgn(I*(c*x+1)^2/(c^2*x^2-1))^3-3/32*I/c*b^3/(c*x+1)^2*Pi*arctanh(c*x)^2*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^3+3/16*I/c*b^3/(c*x+1)^2*Pi*arctanh(c*x)^2*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))^3-3/16*I/c*b^3/(c*x+1)^2*Pi*arctanh(c*x)^2*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))^2+3/16*I*c*b^3/(c*x+1)^2*arctanh(c*x)^2*Pi*x^2-3/16*I*b^3/(c*x+1)^2*arctanh(c*x)^2*Pi*csgn(I*(c*x+1)^2/(c^2*x^2-1))^3*x-3/16*I*b^3/(c*x+1)^2*arctanh(c*x)^2*Pi*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^3*x+3/8*I*b^3/(c*x+1)^2*arctanh(c*x)^2*Pi*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))^3*x+3/8/c*a*b^2*arctanh(c*x)*ln(c*x+1)+3/16/c*a*b^2*ln(-1/2*c*x+1/2)*ln(c*x+1)-3/16/c*a*b^2*ln(-1/2*c*x+1/2)*ln(1/2+1/2*c*x)+3/16/c*b^3*arctanh(c*x)^2*ln(c*x+1)-3/32/c*a*b^2*ln(c*x+1)^2+1/8*c*b^3/(c*x+1)^2*arctanh(c*x)^3*x^2-3/32*I*c*b^3/(c*x+1)^2*arctanh(c*x)^2*Pi*csgn(I*(c*x+1)^2/(c^2*x^2-1))*csgn(I*(c*x+1)/(-c^2*x^2+1)^(1/2))^2*x^2-3/2/c*a^2*b/(c*x+1)^2*arctanh(c*x)-3/16*I*c*b^3/(c*x+1)^2*arctanh(c*x)^2*Pi*csgn(I*(c*x+1)^2/(c^2*x^2-1))^2*csgn(I*(c*x+1)/(-c^2*x^2+1)^(1/2))*x^2+3/16*I*b^3/(c*x+1)^2*arctanh(c*x)^2*Pi*csgn(I*(c*x+1)^2/(c^2*x^2-1))*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))*x+3/32*I/c*b^3/(c*x+1)^2*Pi*arctanh(c*x)^2*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))*csgn(I*(c*x+1)^2/(c^2*x^2-1))*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))+9/32*c*b^3/(c*x+1)^2*arctanh(c*x)^2*x^2+3/32*I*c*b^3/(c*x+1)^2*arctanh(c*x)^2*Pi*csgn(I*(c*x+1)^2/(c^2*x^2-1))*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^2*x^2-3/32*I*c*b^3/(c*x+1)^2*arctanh(c*x)^2*Pi*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^2*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))*x^2","C"
126,1,3637,249,0.890000," ","int((a+b*arctanh(c*x))^3/(c*x+1)^4,x)","\text{output too large to display}"," ",0,"-139/576/c*b^3/(c*x+1)^3*arctanh(c*x)+41/192*c*b^3/(c*x+1)^3*arctanh(c*x)*x^2+1/24*c^2*b^3/(c*x+1)^3*arctanh(c*x)^3*x^3+1/8*c*b^3/(c*x+1)^3*arctanh(c*x)^3*x^2+11/96*c^2*b^3/(c*x+1)^3*arctanh(c*x)^2*x^3+85/576*c^2*b^3/(c*x+1)^3*arctanh(c*x)*x^3+11/32*c*b^3/(c*x+1)^3*arctanh(c*x)^2*x^2-1/c*a*b^2/(c*x+1)^3*arctanh(c*x)^2-1/c*a^2*b/(c*x+1)^3*arctanh(c*x)-1/3/c*a*b^2/(c*x+1)^3*arctanh(c*x)-5/96/c*b^3*arctanh(c*x)^2/(c*x+1)^3-5/48/c*a*b^2/(c*x+1)^2-1/8/c*a^2*b/(c*x+1)^2-1/8/c*b^3*arctanh(c*x)^2/(c*x+1)^2-1/16/c*b^3*arctanh(c*x)^2*ln(c*x-1)-1/8/c*a*b^2*arctanh(c*x)*ln(c*x-1)+1/16/c*a*b^2*ln(c*x-1)*ln(1/2+1/2*c*x)-737/6912*b^3/c/(c*x+1)^3+1/16*I/c*b^3/(c*x+1)^3*Pi*arctanh(c*x)^2+3/16*I*b^3/(c*x+1)^3*arctanh(c*x)^2*Pi*x-1/4/c*a*b^2/(c*x+1)^2*arctanh(c*x)+3/32*I*b^3/(c*x+1)^3*arctanh(c*x)^2*csgn(I*(c*x+1)^2/(c^2*x^2-1))*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^2*Pi*x-3/32*I*b^3/(c*x+1)^3*arctanh(c*x)^2*csgn(I*(c*x+1)^2/(c^2*x^2-1))*csgn(I*(c*x+1)/(-c^2*x^2+1)^(1/2))^2*Pi*x-3/32*I*b^3/(c*x+1)^3*arctanh(c*x)^2*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^2*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))*Pi*x-1/32*I*c^2*b^3/(c*x+1)^3*arctanh(c*x)^2*csgn(I*(c*x+1)^2/(c^2*x^2-1))^3*Pi*x^3-1/32*I*c^2*b^3/(c*x+1)^3*arctanh(c*x)^2*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^3*Pi*x^3+1/16*I*c^2*b^3/(c*x+1)^3*arctanh(c*x)^2*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))^3*Pi*x^3-3/32*I*c*b^3/(c*x+1)^3*arctanh(c*x)^2*csgn(I*(c*x+1)^2/(c^2*x^2-1))^3*Pi*x^2-3/32*I*c*b^3/(c*x+1)^3*arctanh(c*x)^2*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^3*Pi*x^2+3/16*I*c*b^3/(c*x+1)^3*arctanh(c*x)^2*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))^3*Pi*x^2-1/16*I*c^2*b^3/(c*x+1)^3*arctanh(c*x)^2*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))^2*Pi*x^3-3/16*I*c*b^3/(c*x+1)^3*arctanh(c*x)^2*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))^2*Pi*x^2-1/16*I/c*b^3/(c*x+1)^3*Pi*arctanh(c*x)^2*csgn(I*(c*x+1)/(-c^2*x^2+1)^(1/2))*csgn(I*(c*x+1)^2/(c^2*x^2-1))^2+1/32*I/c*b^3/(c*x+1)^3*Pi*arctanh(c*x)^2*csgn(I*(c*x+1)^2/(c^2*x^2-1))*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^2-1/32*I/c*b^3/(c*x+1)^3*Pi*arctanh(c*x)^2*csgn(I*(c*x+1)/(-c^2*x^2+1)^(1/2))^2*csgn(I*(c*x+1)^2/(c^2*x^2-1))-1/32*I/c*b^3/(c*x+1)^3*Pi*arctanh(c*x)^2*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^2-3/16*I*b^3/(c*x+1)^3*arctanh(c*x)^2*csgn(I*(c*x+1)^2/(c^2*x^2-1))^2*csgn(I*(c*x+1)/(-c^2*x^2+1)^(1/2))*Pi*x-1/16*I*c^2*b^3/(c*x+1)^3*arctanh(c*x)^2*csgn(I*(c*x+1)^2/(c^2*x^2-1))^2*csgn(I*(c*x+1)/(-c^2*x^2+1)^(1/2))*Pi*x^3+1/32*I*c^2*b^3/(c*x+1)^3*arctanh(c*x)^2*csgn(I*(c*x+1)^2/(c^2*x^2-1))*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^2*Pi*x^3+1/32*I/c*b^3/(c*x+1)^3*Pi*arctanh(c*x)^2*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))*csgn(I*(c*x+1)^2/(c^2*x^2-1))*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))-1/32*I*c^2*b^3/(c*x+1)^3*arctanh(c*x)^2*csgn(I*(c*x+1)^2/(c^2*x^2-1))*csgn(I*(c*x+1)/(-c^2*x^2+1)^(1/2))^2*Pi*x^3-181/2304*b^3/(c*x+1)^3*x-1/3/c*a^3/(c*x+1)^3+1/16/c*a^2*b*ln(c*x+1)-1/8/c*b^3*arctanh(c*x)^2*ln((c*x+1)/(-c^2*x^2+1)^(1/2))-1/4/c*a*b^2/(c*x+1)*arctanh(c*x)-1/8/c*a^2*b/(c*x+1)-1/16/c*a^2*b*ln(c*x-1)-11/96/c*a*b^2*ln(c*x-1)+11/96/c*a*b^2*ln(c*x+1)-1/32/c*a*b^2*ln(c*x-1)^2+11/32*b^3/(c*x+1)^3*arctanh(c*x)^2*x-23/192*b^3/(c*x+1)^3*arctanh(c*x)*x+1/8*b^3/(c*x+1)^3*arctanh(c*x)^3*x-1/8/c*b^3*arctanh(c*x)^2/(c*x+1)-11/48/c*a*b^2/(c*x+1)-1/6/c*a^2*b/(c*x+1)^3-1/18/c*a*b^2/(c*x+1)^3+575/6912*c^2*b^3*x^3/(c*x+1)^3+235/2304*c*b^3/(c*x+1)^3*x^2-7/24/c*b^3/(c*x+1)^3*arctanh(c*x)^3-1/32*I*c^2*b^3/(c*x+1)^3*arctanh(c*x)^2*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^2*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))*Pi*x^3-3/16*I*c*b^3/(c*x+1)^3*arctanh(c*x)^2*csgn(I*(c*x+1)^2/(c^2*x^2-1))^2*csgn(I*(c*x+1)/(-c^2*x^2+1)^(1/2))*Pi*x^2+3/32*I*c*b^3/(c*x+1)^3*arctanh(c*x)^2*csgn(I*(c*x+1)^2/(c^2*x^2-1))*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^2*Pi*x^2-3/32*I*c*b^3/(c*x+1)^3*arctanh(c*x)^2*csgn(I*(c*x+1)^2/(c^2*x^2-1))*csgn(I*(c*x+1)/(-c^2*x^2+1)^(1/2))^2*Pi*x^2-3/32*I*c*b^3/(c*x+1)^3*arctanh(c*x)^2*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^2*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))*Pi*x^2+3/32*I*b^3/(c*x+1)^3*arctanh(c*x)^2*csgn(I*(c*x+1)^2/(c^2*x^2-1))*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))*Pi*x-3/32*I*b^3/(c*x+1)^3*arctanh(c*x)^2*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^3*Pi*x+3/16*I*b^3/(c*x+1)^3*arctanh(c*x)^2*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))^3*Pi*x-3/16*I*b^3/(c*x+1)^3*arctanh(c*x)^2*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))^2*Pi*x-1/32*I/c*b^3/(c*x+1)^3*Pi*arctanh(c*x)^2*csgn(I*(c*x+1)^2/(c^2*x^2-1))^3-1/32*I/c*b^3/(c*x+1)^3*Pi*arctanh(c*x)^2*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^3+1/16*I/c*b^3/(c*x+1)^3*Pi*arctanh(c*x)^2*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))^3-1/16*I/c*b^3/(c*x+1)^3*Pi*arctanh(c*x)^2*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))^2+1/16*I*c^2*b^3/(c*x+1)^3*arctanh(c*x)^2*Pi*x^3+3/16*I*c*b^3/(c*x+1)^3*arctanh(c*x)^2*Pi*x^2+1/8/c*a*b^2*arctanh(c*x)*ln(c*x+1)+1/16/c*a*b^2*ln(-1/2*c*x+1/2)*ln(c*x+1)-1/16/c*a*b^2*ln(-1/2*c*x+1/2)*ln(1/2+1/2*c*x)-3/32*I*b^3/(c*x+1)^3*arctanh(c*x)^2*csgn(I*(c*x+1)^2/(c^2*x^2-1))^3*Pi*x+1/16/c*b^3*arctanh(c*x)^2*ln(c*x+1)-1/32/c*a*b^2*ln(c*x+1)^2+3/32*I*c*b^3/(c*x+1)^3*arctanh(c*x)^2*csgn(I*(c*x+1)^2/(c^2*x^2-1))*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))*Pi*x^2+1/32*I*c^2*b^3/(c*x+1)^3*arctanh(c*x)^2*csgn(I*(c*x+1)^2/(c^2*x^2-1))*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))*Pi*x^3","C"
127,1,400,291,3.013000," ","int(x^2*arctanh(a*x)^3/(a*c*x+c),x)","\frac{x^{2} \arctanh \left(a x \right)^{3}}{2 a c}-\frac{x \arctanh \left(a x \right)^{3}}{a^{2} c}+\frac{3 x \arctanh \left(a x \right)^{2}}{2 a^{2} c}-\frac{3 \arctanh \left(a x \right)^{3}}{2 a^{3} c}+\frac{3 \arctanh \left(a x \right)^{2}}{2 a^{3} c}+\frac{\arctanh \left(a x \right)^{4}}{2 a^{3} c}-\frac{\arctanh \left(a x \right)^{3} \ln \left(1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}{a^{3} c}-\frac{3 \arctanh \left(a x \right)^{2} \polylog \left(2, -\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}{2 a^{3} c}+\frac{3 \arctanh \left(a x \right) \polylog \left(3, -\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}{2 a^{3} c}-\frac{3 \polylog \left(4, -\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}{4 a^{3} c}-\frac{3 \arctanh \left(a x \right) \ln \left(1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}{a^{3} c}-\frac{3 \polylog \left(2, -\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}{2 a^{3} c}+\frac{3 \arctanh \left(a x \right)^{2} \ln \left(1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}{a^{3} c}+\frac{3 \arctanh \left(a x \right) \polylog \left(2, -\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}{a^{3} c}-\frac{3 \polylog \left(3, -\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}{2 a^{3} c}"," ",0,"1/2*x^2*arctanh(a*x)^3/a/c-x*arctanh(a*x)^3/a^2/c+3/2*x*arctanh(a*x)^2/a^2/c-3/2*arctanh(a*x)^3/a^3/c+3/2*arctanh(a*x)^2/a^3/c+1/2*arctanh(a*x)^4/a^3/c-1/a^3/c*arctanh(a*x)^3*ln(1+(a*x+1)^2/(-a^2*x^2+1))-3/2/a^3/c*arctanh(a*x)^2*polylog(2,-(a*x+1)^2/(-a^2*x^2+1))+3/2/a^3/c*arctanh(a*x)*polylog(3,-(a*x+1)^2/(-a^2*x^2+1))-3/4/a^3/c*polylog(4,-(a*x+1)^2/(-a^2*x^2+1))-3/a^3/c*arctanh(a*x)*ln(1+(a*x+1)^2/(-a^2*x^2+1))-3/2/a^3/c*polylog(2,-(a*x+1)^2/(-a^2*x^2+1))+3/a^3/c*arctanh(a*x)^2*ln(1+(a*x+1)^2/(-a^2*x^2+1))+3/a^3/c*arctanh(a*x)*polylog(2,-(a*x+1)^2/(-a^2*x^2+1))-3/2/a^3/c*polylog(3,-(a*x+1)^2/(-a^2*x^2+1))","A"
128,1,833,197,0.597000," ","int(x*arctanh(a*x)^3/(a*c*x+c),x)","\frac{x \arctanh \left(a x \right)^{3}}{a c}-\frac{\arctanh \left(a x \right)^{3} \ln \left(a x +1\right)}{a^{2} c}+\frac{2 \arctanh \left(a x \right)^{3} \ln \left(\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{a^{2} c}+\frac{3 \arctanh \left(a x \right)^{2} \polylog \left(2, -\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}{2 a^{2} c}-\frac{3 \arctanh \left(a x \right) \polylog \left(3, -\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}{2 a^{2} c}+\frac{3 \polylog \left(4, -\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}{4 a^{2} c}-\frac{3 \arctanh \left(a x \right)^{2} \ln \left(1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}{a^{2} c}-\frac{3 \arctanh \left(a x \right) \polylog \left(2, -\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}{a^{2} c}+\frac{\arctanh \left(a x \right)^{3}}{a^{2} c}-\frac{\arctanh \left(a x \right)^{4}}{2 a^{2} c}-\frac{i \pi  \,\mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right) \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{\left(a^{2} x^{2}-1\right) \left(1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}\right)^{2} \arctanh \left(a x \right)^{3}}{2 a^{2} c}+\frac{i \pi  \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{\left(a^{2} x^{2}-1\right) \left(1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}\right)^{3} \arctanh \left(a x \right)^{3}}{2 a^{2} c}+\frac{i \pi  \mathrm{csgn}\left(\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right)^{2} \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right) \arctanh \left(a x \right)^{3}}{2 a^{2} c}+\frac{i \pi  \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right)^{3} \arctanh \left(a x \right)^{3}}{2 a^{2} c}+\frac{i \pi  \,\mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{\left(a^{2} x^{2}-1\right) \left(1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}\right)^{2} \arctanh \left(a x \right)^{3}}{2 a^{2} c}+\frac{\ln \left(2\right) \arctanh \left(a x \right)^{3}}{a^{2} c}+\frac{i \pi  \,\mathrm{csgn}\left(\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right)^{2} \arctanh \left(a x \right)^{3}}{a^{2} c}-\frac{i \pi  \,\mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right) \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{\left(a^{2} x^{2}-1\right) \left(1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}\right) \arctanh \left(a x \right)^{3}}{2 a^{2} c}+\frac{3 \polylog \left(3, -\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}{2 a^{2} c}"," ",0,"x*arctanh(a*x)^3/a/c-1/a^2/c*arctanh(a*x)^3*ln(a*x+1)+2/a^2/c*arctanh(a*x)^3*ln((a*x+1)/(-a^2*x^2+1)^(1/2))+3/2/a^2/c*arctanh(a*x)^2*polylog(2,-(a*x+1)^2/(-a^2*x^2+1))-3/2/a^2/c*arctanh(a*x)*polylog(3,-(a*x+1)^2/(-a^2*x^2+1))+3/4/a^2/c*polylog(4,-(a*x+1)^2/(-a^2*x^2+1))-3/a^2/c*arctanh(a*x)^2*ln(1+(a*x+1)^2/(-a^2*x^2+1))-3/a^2/c*arctanh(a*x)*polylog(2,-(a*x+1)^2/(-a^2*x^2+1))+arctanh(a*x)^3/a^2/c-1/2*arctanh(a*x)^4/a^2/c+1/2*I/a^2/c*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*arctanh(a*x)^3+I/a^2/c*Pi*csgn(I*(a*x+1)/(-a^2*x^2+1)^(1/2))*csgn(I*(a*x+1)^2/(a^2*x^2-1))^2*arctanh(a*x)^3+1/2*I/a^2/c*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^3*arctanh(a*x)^3-1/2*I/a^2/c*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*arctanh(a*x)^3+1/2*I/a^2/c*Pi*csgn(I*(a*x+1)/(-a^2*x^2+1)^(1/2))^2*csgn(I*(a*x+1)^2/(a^2*x^2-1))*arctanh(a*x)^3+1/a^2/c*ln(2)*arctanh(a*x)^3-1/2*I/a^2/c*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*(a*x+1)^2/(a^2*x^2-1))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))*arctanh(a*x)^3+1/2*I/a^2/c*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1))^3*arctanh(a*x)^3+3/2/a^2/c*polylog(3,-(a*x+1)^2/(-a^2*x^2+1))","C"
129,1,703,98,0.283000," ","int(arctanh(a*x)^3/(a*c*x+c),x)","\frac{\arctanh \left(a x \right)^{3} \ln \left(a x +1\right)}{a c}-\frac{2 \arctanh \left(a x \right)^{3} \ln \left(\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{a c}+\frac{\arctanh \left(a x \right)^{4}}{2 a c}-\frac{3 \arctanh \left(a x \right)^{2} \polylog \left(2, -\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}{2 a c}+\frac{3 \arctanh \left(a x \right) \polylog \left(3, -\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}{2 a c}-\frac{3 \polylog \left(4, -\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}{4 a c}+\frac{i \arctanh \left(a x \right)^{3} \mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right) \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{\left(a^{2} x^{2}-1\right) \left(1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}\right) \pi}{2 a c}-\frac{i \arctanh \left(a x \right)^{3} \mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{\left(a^{2} x^{2}-1\right) \left(1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}\right)^{2} \pi}{2 a c}-\frac{i \arctanh \left(a x \right)^{3} \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right)^{3} \pi}{2 a c}-\frac{i \arctanh \left(a x \right)^{3} \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right)^{2} \mathrm{csgn}\left(\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right) \pi}{a c}+\frac{i \arctanh \left(a x \right)^{3} \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right) \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{\left(a^{2} x^{2}-1\right) \left(1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}\right)^{2} \pi}{2 a c}-\frac{i \arctanh \left(a x \right)^{3} \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right) \mathrm{csgn}\left(\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right)^{2} \pi}{2 a c}-\frac{i \arctanh \left(a x \right)^{3} \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{\left(a^{2} x^{2}-1\right) \left(1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}\right)^{3} \pi}{2 a c}-\frac{\arctanh \left(a x \right)^{3} \ln \left(2\right)}{a c}"," ",0,"1/a/c*arctanh(a*x)^3*ln(a*x+1)-2/a/c*arctanh(a*x)^3*ln((a*x+1)/(-a^2*x^2+1)^(1/2))+1/2/a/c*arctanh(a*x)^4-3/2/a/c*arctanh(a*x)^2*polylog(2,-(a*x+1)^2/(-a^2*x^2+1))+3/2/a/c*arctanh(a*x)*polylog(3,-(a*x+1)^2/(-a^2*x^2+1))-3/4/a/c*polylog(4,-(a*x+1)^2/(-a^2*x^2+1))+1/2*I/a/c*arctanh(a*x)^3*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*(a*x+1)^2/(a^2*x^2-1))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))*Pi-1/2*I/a/c*arctanh(a*x)^3*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*Pi-1/2*I/a/c*arctanh(a*x)^3*csgn(I*(a*x+1)^2/(a^2*x^2-1))^3*Pi-I/a/c*arctanh(a*x)^3*csgn(I*(a*x+1)^2/(a^2*x^2-1))^2*csgn(I*(a*x+1)/(-a^2*x^2+1)^(1/2))*Pi+1/2*I/a/c*arctanh(a*x)^3*csgn(I*(a*x+1)^2/(a^2*x^2-1))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*Pi-1/2*I/a/c*arctanh(a*x)^3*csgn(I*(a*x+1)^2/(a^2*x^2-1))*csgn(I*(a*x+1)/(-a^2*x^2+1)^(1/2))^2*Pi-1/2*I/a/c*arctanh(a*x)^3*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^3*Pi-1/a/c*arctanh(a*x)^3*ln(2)","C"
130,1,1217,87,0.343000," ","int(arctanh(a*x)^3/x/(a*c*x+c),x)","\frac{\ln \left(2\right) \arctanh \left(a x \right)^{3}}{c}-\frac{\arctanh \left(a x \right)^{3} \ln \left(\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}-1\right)}{c}+\frac{2 \arctanh \left(a x \right)^{3} \ln \left(\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{c}+\frac{\arctanh \left(a x \right)^{3} \ln \left(1+\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{c}+\frac{3 \arctanh \left(a x \right)^{2} \polylog \left(2, -\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{c}-\frac{6 \arctanh \left(a x \right) \polylog \left(3, -\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{c}+\frac{\arctanh \left(a x \right)^{3} \ln \left(1-\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{c}+\frac{3 \arctanh \left(a x \right)^{2} \polylog \left(2, \frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{c}-\frac{6 \arctanh \left(a x \right) \polylog \left(3, \frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{c}+\frac{\arctanh \left(a x \right)^{3} \ln \left(a x \right)}{c}-\frac{\arctanh \left(a x \right)^{3} \ln \left(a x +1\right)}{c}-\frac{i \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}-1\right)\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}-1\right)}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right)^{2} \arctanh \left(a x \right)^{3}}{2 c}+\frac{i \pi  \,\mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{\left(a^{2} x^{2}-1\right) \left(1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}\right)^{2} \arctanh \left(a x \right)^{3}}{2 c}-\frac{i \pi  \,\mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}-1\right)}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right)^{2} \arctanh \left(a x \right)^{3}}{2 c}+\frac{i \pi  \mathrm{csgn}\left(\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right)^{2} \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right) \arctanh \left(a x \right)^{3}}{2 c}-\frac{i \pi  \,\mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right) \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{\left(a^{2} x^{2}-1\right) \left(1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}\right)^{2} \arctanh \left(a x \right)^{3}}{2 c}+\frac{i \pi  \,\mathrm{csgn}\left(\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right)^{2} \arctanh \left(a x \right)^{3}}{c}+\frac{i \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}-1\right)\right) \mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}-1\right)}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right) \arctanh \left(a x \right)^{3}}{2 c}-\frac{i \pi  \,\mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right) \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{\left(a^{2} x^{2}-1\right) \left(1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}\right) \arctanh \left(a x \right)^{3}}{2 c}+\frac{i \pi  \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{\left(a^{2} x^{2}-1\right) \left(1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}\right)^{3} \arctanh \left(a x \right)^{3}}{2 c}+\frac{i \pi  \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right)^{3} \arctanh \left(a x \right)^{3}}{2 c}+\frac{i \pi  \mathrm{csgn}\left(\frac{i \left(\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}-1\right)}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right)^{3} \arctanh \left(a x \right)^{3}}{2 c}-\frac{\arctanh \left(a x \right)^{4}}{2 c}+\frac{6 \polylog \left(4, \frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{c}+\frac{6 \polylog \left(4, -\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{c}"," ",0,"1/c*ln(2)*arctanh(a*x)^3-1/c*arctanh(a*x)^3*ln((a*x+1)^2/(-a^2*x^2+1)-1)+2/c*arctanh(a*x)^3*ln((a*x+1)/(-a^2*x^2+1)^(1/2))-1/2/c*arctanh(a*x)^4+6/c*polylog(4,(a*x+1)/(-a^2*x^2+1)^(1/2))+6/c*polylog(4,-(a*x+1)/(-a^2*x^2+1)^(1/2))+1/c*arctanh(a*x)^3*ln(1+(a*x+1)/(-a^2*x^2+1)^(1/2))+3/c*arctanh(a*x)^2*polylog(2,-(a*x+1)/(-a^2*x^2+1)^(1/2))-6/c*arctanh(a*x)*polylog(3,-(a*x+1)/(-a^2*x^2+1)^(1/2))+1/c*arctanh(a*x)^3*ln(1-(a*x+1)/(-a^2*x^2+1)^(1/2))+3/c*arctanh(a*x)^2*polylog(2,(a*x+1)/(-a^2*x^2+1)^(1/2))-6/c*arctanh(a*x)*polylog(3,(a*x+1)/(-a^2*x^2+1)^(1/2))-1/2*I/c*Pi*csgn(I*((a*x+1)^2/(-a^2*x^2+1)-1))*csgn(I*((a*x+1)^2/(-a^2*x^2+1)-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*arctanh(a*x)^3+1/2*I/c*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*arctanh(a*x)^3-1/2*I/c*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*((a*x+1)^2/(-a^2*x^2+1)-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*arctanh(a*x)^3+1/2*I/c*Pi*csgn(I*(a*x+1)/(-a^2*x^2+1)^(1/2))^2*csgn(I*(a*x+1)^2/(a^2*x^2-1))*arctanh(a*x)^3-1/2*I/c*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*arctanh(a*x)^3+I/c*Pi*csgn(I*(a*x+1)/(-a^2*x^2+1)^(1/2))*csgn(I*(a*x+1)^2/(a^2*x^2-1))^2*arctanh(a*x)^3+1/c*arctanh(a*x)^3*ln(a*x)-1/c*arctanh(a*x)^3*ln(a*x+1)+1/2*I/c*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^3*arctanh(a*x)^3+1/2*I/c*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1))^3*arctanh(a*x)^3+1/2*I/c*Pi*csgn(I*((a*x+1)^2/(-a^2*x^2+1)-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^3*arctanh(a*x)^3+1/2*I/c*Pi*csgn(I*((a*x+1)^2/(-a^2*x^2+1)-1))*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*((a*x+1)^2/(-a^2*x^2+1)-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))*arctanh(a*x)^3-1/2*I/c*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*(a*x+1)^2/(a^2*x^2-1))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))*arctanh(a*x)^3","C"
131,1,1217,87,0.197000," ","int(arctanh(a*x)^3/(a*c*x^2+c*x),x)","\frac{\ln \left(2\right) \arctanh \left(a x \right)^{3}}{c}-\frac{\arctanh \left(a x \right)^{3} \ln \left(\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}-1\right)}{c}+\frac{2 \arctanh \left(a x \right)^{3} \ln \left(\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{c}+\frac{\arctanh \left(a x \right)^{3} \ln \left(1+\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{c}+\frac{3 \arctanh \left(a x \right)^{2} \polylog \left(2, -\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{c}-\frac{6 \arctanh \left(a x \right) \polylog \left(3, -\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{c}+\frac{\arctanh \left(a x \right)^{3} \ln \left(1-\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{c}+\frac{3 \arctanh \left(a x \right)^{2} \polylog \left(2, \frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{c}-\frac{6 \arctanh \left(a x \right) \polylog \left(3, \frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{c}+\frac{\arctanh \left(a x \right)^{3} \ln \left(a x \right)}{c}-\frac{\arctanh \left(a x \right)^{3} \ln \left(a x +1\right)}{c}-\frac{i \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}-1\right)\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}-1\right)}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right)^{2} \arctanh \left(a x \right)^{3}}{2 c}+\frac{i \pi  \,\mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{\left(a^{2} x^{2}-1\right) \left(1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}\right)^{2} \arctanh \left(a x \right)^{3}}{2 c}-\frac{i \pi  \,\mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}-1\right)}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right)^{2} \arctanh \left(a x \right)^{3}}{2 c}+\frac{i \pi  \mathrm{csgn}\left(\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right)^{2} \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right) \arctanh \left(a x \right)^{3}}{2 c}-\frac{i \pi  \,\mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right) \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{\left(a^{2} x^{2}-1\right) \left(1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}\right)^{2} \arctanh \left(a x \right)^{3}}{2 c}+\frac{i \pi  \,\mathrm{csgn}\left(\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right)^{2} \arctanh \left(a x \right)^{3}}{c}+\frac{i \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}-1\right)\right) \mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}-1\right)}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right) \arctanh \left(a x \right)^{3}}{2 c}-\frac{i \pi  \,\mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right) \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{\left(a^{2} x^{2}-1\right) \left(1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}\right) \arctanh \left(a x \right)^{3}}{2 c}+\frac{i \pi  \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{\left(a^{2} x^{2}-1\right) \left(1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}\right)^{3} \arctanh \left(a x \right)^{3}}{2 c}+\frac{i \pi  \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right)^{3} \arctanh \left(a x \right)^{3}}{2 c}+\frac{i \pi  \mathrm{csgn}\left(\frac{i \left(\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}-1\right)}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right)^{3} \arctanh \left(a x \right)^{3}}{2 c}-\frac{\arctanh \left(a x \right)^{4}}{2 c}+\frac{6 \polylog \left(4, \frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{c}+\frac{6 \polylog \left(4, -\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{c}"," ",0,"1/c*ln(2)*arctanh(a*x)^3-1/c*arctanh(a*x)^3*ln((a*x+1)^2/(-a^2*x^2+1)-1)+2/c*arctanh(a*x)^3*ln((a*x+1)/(-a^2*x^2+1)^(1/2))-1/2/c*arctanh(a*x)^4+6/c*polylog(4,(a*x+1)/(-a^2*x^2+1)^(1/2))+6/c*polylog(4,-(a*x+1)/(-a^2*x^2+1)^(1/2))+1/c*arctanh(a*x)^3*ln(1+(a*x+1)/(-a^2*x^2+1)^(1/2))+3/c*arctanh(a*x)^2*polylog(2,-(a*x+1)/(-a^2*x^2+1)^(1/2))-6/c*arctanh(a*x)*polylog(3,-(a*x+1)/(-a^2*x^2+1)^(1/2))+1/c*arctanh(a*x)^3*ln(1-(a*x+1)/(-a^2*x^2+1)^(1/2))+3/c*arctanh(a*x)^2*polylog(2,(a*x+1)/(-a^2*x^2+1)^(1/2))-6/c*arctanh(a*x)*polylog(3,(a*x+1)/(-a^2*x^2+1)^(1/2))-1/2*I/c*Pi*csgn(I*((a*x+1)^2/(-a^2*x^2+1)-1))*csgn(I*((a*x+1)^2/(-a^2*x^2+1)-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*arctanh(a*x)^3+1/2*I/c*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*arctanh(a*x)^3-1/2*I/c*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*((a*x+1)^2/(-a^2*x^2+1)-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*arctanh(a*x)^3+1/2*I/c*Pi*csgn(I*(a*x+1)/(-a^2*x^2+1)^(1/2))^2*csgn(I*(a*x+1)^2/(a^2*x^2-1))*arctanh(a*x)^3-1/2*I/c*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*arctanh(a*x)^3+I/c*Pi*csgn(I*(a*x+1)/(-a^2*x^2+1)^(1/2))*csgn(I*(a*x+1)^2/(a^2*x^2-1))^2*arctanh(a*x)^3+1/c*arctanh(a*x)^3*ln(a*x)-1/c*arctanh(a*x)^3*ln(a*x+1)+1/2*I/c*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^3*arctanh(a*x)^3+1/2*I/c*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1))^3*arctanh(a*x)^3+1/2*I/c*Pi*csgn(I*((a*x+1)^2/(-a^2*x^2+1)-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^3*arctanh(a*x)^3+1/2*I/c*Pi*csgn(I*((a*x+1)^2/(-a^2*x^2+1)-1))*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*((a*x+1)^2/(-a^2*x^2+1)-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))*arctanh(a*x)^3-1/2*I/c*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*(a*x+1)^2/(a^2*x^2-1))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))*arctanh(a*x)^3","C"
132,1,1451,183,0.783000," ","int(arctanh(a*x)^3/x^2/(a*c*x+c),x)","\frac{i a \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}-1\right)\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}-1\right)}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right)^{2} \arctanh \left(a x \right)^{3}}{2 c}+\frac{i a \pi  \,\mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right) \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{\left(a^{2} x^{2}-1\right) \left(1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}\right)^{2} \arctanh \left(a x \right)^{3}}{2 c}-\frac{i a \pi  \mathrm{csgn}\left(\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right)^{2} \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right) \arctanh \left(a x \right)^{3}}{2 c}-\frac{i a \arctanh \left(a x \right)^{3} \pi  \,\mathrm{csgn}\left(\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right)^{2}}{c}-\frac{i a \pi  \,\mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{\left(a^{2} x^{2}-1\right) \left(1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}\right)^{2} \arctanh \left(a x \right)^{3}}{2 c}+\frac{i a \pi  \,\mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}-1\right)}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right)^{2} \arctanh \left(a x \right)^{3}}{2 c}-\frac{i a \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}-1\right)\right) \mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}-1\right)}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right) \arctanh \left(a x \right)^{3}}{2 c}+\frac{i a \pi  \,\mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right) \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{\left(a^{2} x^{2}-1\right) \left(1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}\right) \arctanh \left(a x \right)^{3}}{2 c}-\frac{\arctanh \left(a x \right)^{3}}{c x}-\frac{6 a \polylog \left(3, \frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{c}-\frac{6 a \polylog \left(4, \frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{c}-\frac{6 a \polylog \left(4, -\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{c}-\frac{6 a \polylog \left(3, -\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{c}+\frac{a \arctanh \left(a x \right)^{4}}{2 c}-\frac{a \arctanh \left(a x \right)^{3}}{c}-\frac{i a \pi  \mathrm{csgn}\left(\frac{i \left(\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}-1\right)}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right)^{3} \arctanh \left(a x \right)^{3}}{2 c}-\frac{i a \pi  \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{\left(a^{2} x^{2}-1\right) \left(1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}\right)^{3} \arctanh \left(a x \right)^{3}}{2 c}-\frac{i a \arctanh \left(a x \right)^{3} \pi  \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right)^{3}}{2 c}-\frac{a \ln \left(2\right) \arctanh \left(a x \right)^{3}}{c}+\frac{3 a \arctanh \left(a x \right)^{2} \ln \left(1-\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{c}+\frac{6 a \arctanh \left(a x \right) \polylog \left(2, \frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{c}+\frac{3 a \arctanh \left(a x \right)^{2} \ln \left(1+\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{c}+\frac{6 a \arctanh \left(a x \right) \polylog \left(2, -\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{c}-\frac{a \arctanh \left(a x \right)^{3} \ln \left(a x \right)}{c}+\frac{a \arctanh \left(a x \right)^{3} \ln \left(a x +1\right)}{c}-\frac{3 a \arctanh \left(a x \right)^{2} \polylog \left(2, \frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{c}+\frac{6 a \arctanh \left(a x \right) \polylog \left(3, \frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{c}-\frac{2 a \arctanh \left(a x \right)^{3} \ln \left(\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{c}+\frac{a \arctanh \left(a x \right)^{3} \ln \left(\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}-1\right)}{c}-\frac{a \arctanh \left(a x \right)^{3} \ln \left(1+\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{c}-\frac{3 a \arctanh \left(a x \right)^{2} \polylog \left(2, -\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{c}+\frac{6 a \arctanh \left(a x \right) \polylog \left(3, -\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{c}-\frac{a \arctanh \left(a x \right)^{3} \ln \left(1-\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{c}"," ",0,"-I*a/c*arctanh(a*x)^3*Pi*csgn(I*(a*x+1)/(-a^2*x^2+1)^(1/2))*csgn(I*(a*x+1)^2/(a^2*x^2-1))^2-1/2*I*a/c*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*arctanh(a*x)^3-1/2*I*a/c*Pi*csgn(I*((a*x+1)^2/(-a^2*x^2+1)-1))*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*((a*x+1)^2/(-a^2*x^2+1)-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))*arctanh(a*x)^3+1/2*I*a/c*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*(a*x+1)^2/(a^2*x^2-1))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))*arctanh(a*x)^3+1/2*I*a/c*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*((a*x+1)^2/(-a^2*x^2+1)-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*arctanh(a*x)^3+1/2*I*a/c*Pi*csgn(I*((a*x+1)^2/(-a^2*x^2+1)-1))*csgn(I*((a*x+1)^2/(-a^2*x^2+1)-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*arctanh(a*x)^3+1/2*I*a/c*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*arctanh(a*x)^3-1/2*I*a/c*Pi*csgn(I*(a*x+1)/(-a^2*x^2+1)^(1/2))^2*csgn(I*(a*x+1)^2/(a^2*x^2-1))*arctanh(a*x)^3-arctanh(a*x)^3/c/x-6*a/c*polylog(3,(a*x+1)/(-a^2*x^2+1)^(1/2))-6*a/c*polylog(4,(a*x+1)/(-a^2*x^2+1)^(1/2))-6*a/c*polylog(4,-(a*x+1)/(-a^2*x^2+1)^(1/2))-6*a/c*polylog(3,-(a*x+1)/(-a^2*x^2+1)^(1/2))+1/2*a*arctanh(a*x)^4/c-a*arctanh(a*x)^3/c-1/2*I*a/c*Pi*csgn(I*((a*x+1)^2/(-a^2*x^2+1)-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^3*arctanh(a*x)^3-1/2*I*a/c*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^3*arctanh(a*x)^3-1/2*I*a/c*arctanh(a*x)^3*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1))^3-3*a/c*arctanh(a*x)^2*polylog(2,(a*x+1)/(-a^2*x^2+1)^(1/2))+6*a/c*arctanh(a*x)*polylog(3,(a*x+1)/(-a^2*x^2+1)^(1/2))-2*a/c*arctanh(a*x)^3*ln((a*x+1)/(-a^2*x^2+1)^(1/2))+a/c*arctanh(a*x)^3*ln((a*x+1)^2/(-a^2*x^2+1)-1)-a/c*arctanh(a*x)^3*ln(1+(a*x+1)/(-a^2*x^2+1)^(1/2))-3*a/c*arctanh(a*x)^2*polylog(2,-(a*x+1)/(-a^2*x^2+1)^(1/2))+6*a/c*arctanh(a*x)*polylog(3,-(a*x+1)/(-a^2*x^2+1)^(1/2))-a/c*arctanh(a*x)^3*ln(1-(a*x+1)/(-a^2*x^2+1)^(1/2))-a/c*ln(2)*arctanh(a*x)^3+3*a/c*arctanh(a*x)^2*ln(1-(a*x+1)/(-a^2*x^2+1)^(1/2))+6*a/c*arctanh(a*x)*polylog(2,(a*x+1)/(-a^2*x^2+1)^(1/2))+3*a/c*arctanh(a*x)^2*ln(1+(a*x+1)/(-a^2*x^2+1)^(1/2))+6*a/c*arctanh(a*x)*polylog(2,-(a*x+1)/(-a^2*x^2+1)^(1/2))-a/c*arctanh(a*x)^3*ln(a*x)+a/c*arctanh(a*x)^3*ln(a*x+1)","C"
133,1,664,287,4.374000," ","int(arctanh(a*x)^3/x^3/(a*c*x+c),x)","\frac{a \arctanh \left(a x \right)^{3}}{c x}-\frac{3 a \arctanh \left(a x \right)^{2}}{2 c x}-\frac{\arctanh \left(a x \right)^{3}}{2 c \,x^{2}}-\frac{a^{2} \arctanh \left(a x \right)^{4}}{2 c}+\frac{6 a^{2} \polylog \left(4, \frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{c}+\frac{6 a^{2} \polylog \left(4, -\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{c}-\frac{3 a^{2} \arctanh \left(a x \right)^{2}}{2 c}+\frac{3 a^{2} \polylog \left(2, \frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{c}+\frac{3 a^{2} \polylog \left(2, -\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{c}+\frac{3 a^{2} \arctanh \left(a x \right)^{3}}{2 c}+\frac{6 a^{2} \polylog \left(3, \frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{c}+\frac{6 a^{2} \polylog \left(3, -\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{c}+\frac{3 a^{2} \arctanh \left(a x \right)^{2} \polylog \left(2, \frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{c}-\frac{6 a^{2} \arctanh \left(a x \right) \polylog \left(3, \frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{c}+\frac{a^{2} \arctanh \left(a x \right)^{3} \ln \left(1+\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{c}+\frac{3 a^{2} \arctanh \left(a x \right)^{2} \polylog \left(2, -\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{c}-\frac{6 a^{2} \arctanh \left(a x \right) \polylog \left(3, -\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{c}+\frac{3 a^{2} \arctanh \left(a x \right) \ln \left(1-\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{c}+\frac{3 a^{2} \arctanh \left(a x \right) \ln \left(1+\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{c}-\frac{3 a^{2} \arctanh \left(a x \right)^{2} \ln \left(1-\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{c}-\frac{6 a^{2} \arctanh \left(a x \right) \polylog \left(2, \frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{c}-\frac{3 a^{2} \arctanh \left(a x \right)^{2} \ln \left(1+\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{c}-\frac{6 a^{2} \arctanh \left(a x \right) \polylog \left(2, -\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{c}+\frac{a^{2} \arctanh \left(a x \right)^{3} \ln \left(1-\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{c}"," ",0,"a*arctanh(a*x)^3/c/x-3/2*a*arctanh(a*x)^2/c/x-1/2*arctanh(a*x)^3/c/x^2-1/2*a^2*arctanh(a*x)^4/c+6*a^2/c*polylog(4,(a*x+1)/(-a^2*x^2+1)^(1/2))+6*a^2/c*polylog(4,-(a*x+1)/(-a^2*x^2+1)^(1/2))-3/2*a^2*arctanh(a*x)^2/c+3*a^2/c*polylog(2,(a*x+1)/(-a^2*x^2+1)^(1/2))+3*a^2/c*polylog(2,-(a*x+1)/(-a^2*x^2+1)^(1/2))+3/2*a^2*arctanh(a*x)^3/c+6*a^2/c*polylog(3,(a*x+1)/(-a^2*x^2+1)^(1/2))+6*a^2/c*polylog(3,-(a*x+1)/(-a^2*x^2+1)^(1/2))+3*a^2/c*arctanh(a*x)^2*polylog(2,(a*x+1)/(-a^2*x^2+1)^(1/2))-6*a^2/c*arctanh(a*x)*polylog(3,(a*x+1)/(-a^2*x^2+1)^(1/2))+a^2/c*arctanh(a*x)^3*ln(1+(a*x+1)/(-a^2*x^2+1)^(1/2))+3*a^2/c*arctanh(a*x)^2*polylog(2,-(a*x+1)/(-a^2*x^2+1)^(1/2))-6*a^2/c*arctanh(a*x)*polylog(3,-(a*x+1)/(-a^2*x^2+1)^(1/2))+3*a^2/c*arctanh(a*x)*ln(1-(a*x+1)/(-a^2*x^2+1)^(1/2))+3*a^2/c*arctanh(a*x)*ln(1+(a*x+1)/(-a^2*x^2+1)^(1/2))-3*a^2/c*arctanh(a*x)^2*ln(1-(a*x+1)/(-a^2*x^2+1)^(1/2))-6*a^2/c*arctanh(a*x)*polylog(2,(a*x+1)/(-a^2*x^2+1)^(1/2))-3*a^2/c*arctanh(a*x)^2*ln(1+(a*x+1)/(-a^2*x^2+1)^(1/2))-6*a^2/c*arctanh(a*x)*polylog(2,-(a*x+1)/(-a^2*x^2+1)^(1/2))+a^2/c*arctanh(a*x)^3*ln(1-(a*x+1)/(-a^2*x^2+1)^(1/2))","B"
134,1,496,378,1.983000," ","int(x^2*arctanh(a*x)^4/(-a*c*x+c),x)","-\frac{x^{2} \arctanh \left(a x \right)^{4}}{2 a c}-\frac{x \arctanh \left(a x \right)^{4}}{a^{2} c}-\frac{2 x \arctanh \left(a x \right)^{3}}{a^{2} c}-\frac{\arctanh \left(a x \right)^{4}}{2 a^{3} c}-\frac{2 \arctanh \left(a x \right)^{3}}{a^{3} c}+\frac{\arctanh \left(a x \right)^{4} \ln \left(1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}{a^{3} c}+\frac{2 \arctanh \left(a x \right)^{3} \polylog \left(2, -\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}{a^{3} c}-\frac{3 \arctanh \left(a x \right)^{2} \polylog \left(3, -\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}{a^{3} c}+\frac{3 \arctanh \left(a x \right) \polylog \left(4, -\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}{a^{3} c}-\frac{3 \polylog \left(5, -\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}{2 a^{3} c}+\frac{6 \arctanh \left(a x \right)^{2} \ln \left(1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}{a^{3} c}+\frac{6 \arctanh \left(a x \right) \polylog \left(2, -\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}{a^{3} c}-\frac{3 \polylog \left(3, -\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}{a^{3} c}+\frac{4 \arctanh \left(a x \right)^{3} \ln \left(1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}{a^{3} c}+\frac{6 \arctanh \left(a x \right)^{2} \polylog \left(2, -\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}{a^{3} c}-\frac{6 \arctanh \left(a x \right) \polylog \left(3, -\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}{a^{3} c}+\frac{3 \polylog \left(4, -\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}{a^{3} c}"," ",0,"-1/2*x^2*arctanh(a*x)^4/a/c-x*arctanh(a*x)^4/a^2/c-2*x*arctanh(a*x)^3/a^2/c-1/2*arctanh(a*x)^4/a^3/c-2*arctanh(a*x)^3/a^3/c+1/a^3/c*arctanh(a*x)^4*ln(1+(a*x+1)^2/(-a^2*x^2+1))+2/a^3/c*arctanh(a*x)^3*polylog(2,-(a*x+1)^2/(-a^2*x^2+1))-3/a^3/c*arctanh(a*x)^2*polylog(3,-(a*x+1)^2/(-a^2*x^2+1))+3/a^3/c*arctanh(a*x)*polylog(4,-(a*x+1)^2/(-a^2*x^2+1))-3/2/a^3/c*polylog(5,-(a*x+1)^2/(-a^2*x^2+1))+6/a^3/c*arctanh(a*x)^2*ln(1+(a*x+1)^2/(-a^2*x^2+1))+6/a^3/c*arctanh(a*x)*polylog(2,-(a*x+1)^2/(-a^2*x^2+1))-3/a^3/c*polylog(3,-(a*x+1)^2/(-a^2*x^2+1))+4/a^3/c*arctanh(a*x)^3*ln(1+(a*x+1)^2/(-a^2*x^2+1))+6/a^3/c*arctanh(a*x)^2*polylog(2,-(a*x+1)^2/(-a^2*x^2+1))-6/a^3/c*arctanh(a*x)*polylog(3,-(a*x+1)^2/(-a^2*x^2+1))+3/a^3/c*polylog(4,-(a*x+1)^2/(-a^2*x^2+1))","A"
135,1,454,259,0.420000," ","int(x*arctanh(a*x)^4/(-a*c*x+c),x)","-\frac{x \arctanh \left(a x \right)^{4}}{a c}-\frac{\arctanh \left(a x \right)^{4} \ln \left(a x -1\right)}{a^{2} c}+\frac{2 \arctanh \left(a x \right)^{3} \polylog \left(2, -\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}{a^{2} c}-\frac{3 \arctanh \left(a x \right)^{2} \polylog \left(3, -\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}{a^{2} c}+\frac{3 \arctanh \left(a x \right) \polylog \left(4, -\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}{a^{2} c}-\frac{3 \polylog \left(5, -\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}{2 a^{2} c}+\frac{i \pi  \mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right)^{3} \arctanh \left(a x \right)^{4}}{a^{2} c}-\frac{i \pi  \mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right)^{2} \arctanh \left(a x \right)^{4}}{a^{2} c}-\frac{\arctanh \left(a x \right)^{4}}{a^{2} c}+\frac{4 \arctanh \left(a x \right)^{3} \ln \left(1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}{a^{2} c}+\frac{6 \arctanh \left(a x \right)^{2} \polylog \left(2, -\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}{a^{2} c}-\frac{6 \arctanh \left(a x \right) \polylog \left(3, -\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}{a^{2} c}+\frac{3 \polylog \left(4, -\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}{a^{2} c}+\frac{\ln \left(2\right) \arctanh \left(a x \right)^{4}}{a^{2} c}+\frac{i \pi  \arctanh \left(a x \right)^{4}}{a^{2} c}"," ",0,"-x*arctanh(a*x)^4/a/c-1/a^2/c*arctanh(a*x)^4*ln(a*x-1)+2/a^2/c*arctanh(a*x)^3*polylog(2,-(a*x+1)^2/(-a^2*x^2+1))-3/a^2/c*arctanh(a*x)^2*polylog(3,-(a*x+1)^2/(-a^2*x^2+1))+3/a^2/c*arctanh(a*x)*polylog(4,-(a*x+1)^2/(-a^2*x^2+1))-3/2/a^2/c*polylog(5,-(a*x+1)^2/(-a^2*x^2+1))+I/a^2/c*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))^3*arctanh(a*x)^4-I/a^2/c*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*arctanh(a*x)^4-arctanh(a*x)^4/a^2/c+4/a^2/c*arctanh(a*x)^3*ln(1+(a*x+1)^2/(-a^2*x^2+1))+6/a^2/c*arctanh(a*x)^2*polylog(2,-(a*x+1)^2/(-a^2*x^2+1))-6/a^2/c*arctanh(a*x)*polylog(3,-(a*x+1)^2/(-a^2*x^2+1))+3/a^2/c*polylog(4,-(a*x+1)^2/(-a^2*x^2+1))+1/a^2/c*ln(2)*arctanh(a*x)^4+I/a^2/c*Pi*arctanh(a*x)^4","C"
136,1,285,129,0.355000," ","int(arctanh(a*x)^4/(-a*c*x+c),x)","-\frac{\arctanh \left(a x \right)^{4} \ln \left(a x -1\right)}{a c}+\frac{i \arctanh \left(a x \right)^{4} \pi  \mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right)^{3}}{a c}-\frac{i \arctanh \left(a x \right)^{4} \pi  \mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right)^{2}}{a c}+\frac{i \arctanh \left(a x \right)^{4} \pi}{a c}+\frac{\arctanh \left(a x \right)^{4} \ln \left(2\right)}{a c}+\frac{2 \arctanh \left(a x \right)^{3} \polylog \left(2, -\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}{a c}-\frac{3 \arctanh \left(a x \right)^{2} \polylog \left(3, -\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}{a c}+\frac{3 \arctanh \left(a x \right) \polylog \left(4, -\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}{a c}-\frac{3 \polylog \left(5, -\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}{2 a c}"," ",0,"-1/a/c*arctanh(a*x)^4*ln(a*x-1)+I/a/c*arctanh(a*x)^4*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))^3-I/a/c*arctanh(a*x)^4*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))^2+I/a/c*arctanh(a*x)^4*Pi+1/a/c*arctanh(a*x)^4*ln(2)+2/a/c*arctanh(a*x)^3*polylog(2,-(a*x+1)^2/(-a^2*x^2+1))-3/a/c*arctanh(a*x)^2*polylog(3,-(a*x+1)^2/(-a^2*x^2+1))+3/a/c*arctanh(a*x)*polylog(4,-(a*x+1)^2/(-a^2*x^2+1))-3/2/a/c*polylog(5,-(a*x+1)^2/(-a^2*x^2+1))","C"
137,1,843,116,0.455000," ","int(arctanh(a*x)^4/x/(-a*c*x+c),x)","\frac{\arctanh \left(a x \right)^{4} \ln \left(a x \right)}{c}-\frac{\arctanh \left(a x \right)^{4} \ln \left(a x -1\right)}{c}-\frac{\arctanh \left(a x \right)^{4} \ln \left(\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}-1\right)}{c}+\frac{\arctanh \left(a x \right)^{4} \ln \left(1-\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{c}+\frac{4 \arctanh \left(a x \right)^{3} \polylog \left(2, \frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{c}-\frac{12 \arctanh \left(a x \right)^{2} \polylog \left(3, \frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{c}+\frac{24 \arctanh \left(a x \right) \polylog \left(4, \frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{c}-\frac{24 \polylog \left(5, \frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{c}+\frac{\arctanh \left(a x \right)^{4} \ln \left(1+\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{c}+\frac{4 \arctanh \left(a x \right)^{3} \polylog \left(2, -\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{c}-\frac{12 \arctanh \left(a x \right)^{2} \polylog \left(3, -\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{c}+\frac{24 \arctanh \left(a x \right) \polylog \left(4, -\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{c}-\frac{24 \polylog \left(5, -\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{c}-\frac{i \arctanh \left(a x \right)^{4} \mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}-1\right)}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right)^{2} \pi}{2 c}+\frac{i \arctanh \left(a x \right)^{4} \mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right) \mathrm{csgn}\left(i \left(\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}-1\right)\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}-1\right)}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right) \pi}{2 c}-\frac{i \arctanh \left(a x \right)^{4} \mathrm{csgn}\left(i \left(\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}-1\right)\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}-1\right)}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right)^{2} \pi}{2 c}+\frac{i \arctanh \left(a x \right)^{4} \mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right)^{3} \pi}{c}+\frac{i \arctanh \left(a x \right)^{4} \mathrm{csgn}\left(\frac{i \left(\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}-1\right)}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right)^{3} \pi}{2 c}-\frac{i \arctanh \left(a x \right)^{4} \mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right)^{2} \pi}{c}+\frac{i \arctanh \left(a x \right)^{4} \pi}{c}+\frac{\arctanh \left(a x \right)^{4} \ln \left(2\right)}{c}"," ",0,"1/c*arctanh(a*x)^4*ln(a*x)-1/c*arctanh(a*x)^4*ln(a*x-1)-1/c*arctanh(a*x)^4*ln((a*x+1)^2/(-a^2*x^2+1)-1)+1/c*arctanh(a*x)^4*ln(1-(a*x+1)/(-a^2*x^2+1)^(1/2))+4/c*arctanh(a*x)^3*polylog(2,(a*x+1)/(-a^2*x^2+1)^(1/2))-12/c*arctanh(a*x)^2*polylog(3,(a*x+1)/(-a^2*x^2+1)^(1/2))+24/c*arctanh(a*x)*polylog(4,(a*x+1)/(-a^2*x^2+1)^(1/2))-24/c*polylog(5,(a*x+1)/(-a^2*x^2+1)^(1/2))+1/c*arctanh(a*x)^4*ln(1+(a*x+1)/(-a^2*x^2+1)^(1/2))+4/c*arctanh(a*x)^3*polylog(2,-(a*x+1)/(-a^2*x^2+1)^(1/2))-12/c*arctanh(a*x)^2*polylog(3,-(a*x+1)/(-a^2*x^2+1)^(1/2))+24/c*arctanh(a*x)*polylog(4,-(a*x+1)/(-a^2*x^2+1)^(1/2))-24/c*polylog(5,-(a*x+1)/(-a^2*x^2+1)^(1/2))+1/2*I/c*arctanh(a*x)^4*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*((a*x+1)^2/(-a^2*x^2+1)-1))*csgn(I*((a*x+1)^2/(-a^2*x^2+1)-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))*Pi-1/2*I/c*arctanh(a*x)^4*csgn(I*((a*x+1)^2/(-a^2*x^2+1)-1))*csgn(I*((a*x+1)^2/(-a^2*x^2+1)-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*Pi-1/2*I/c*arctanh(a*x)^4*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*((a*x+1)^2/(-a^2*x^2+1)-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*Pi+I/c*arctanh(a*x)^4*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))^3*Pi+1/2*I/c*arctanh(a*x)^4*csgn(I*((a*x+1)^2/(-a^2*x^2+1)-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^3*Pi-I/c*arctanh(a*x)^4*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*Pi+I/c*arctanh(a*x)^4*Pi+1/c*arctanh(a*x)^4*ln(2)","C"
138,1,843,116,0.332000," ","int(arctanh(a*x)^4/(-a*c*x^2+c*x),x)","\frac{\arctanh \left(a x \right)^{4} \ln \left(a x \right)}{c}-\frac{\arctanh \left(a x \right)^{4} \ln \left(a x -1\right)}{c}-\frac{\arctanh \left(a x \right)^{4} \ln \left(\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}-1\right)}{c}+\frac{\arctanh \left(a x \right)^{4} \ln \left(1-\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{c}+\frac{4 \arctanh \left(a x \right)^{3} \polylog \left(2, \frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{c}-\frac{12 \arctanh \left(a x \right)^{2} \polylog \left(3, \frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{c}+\frac{24 \arctanh \left(a x \right) \polylog \left(4, \frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{c}-\frac{24 \polylog \left(5, \frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{c}+\frac{\arctanh \left(a x \right)^{4} \ln \left(1+\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{c}+\frac{4 \arctanh \left(a x \right)^{3} \polylog \left(2, -\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{c}-\frac{12 \arctanh \left(a x \right)^{2} \polylog \left(3, -\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{c}+\frac{24 \arctanh \left(a x \right) \polylog \left(4, -\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{c}-\frac{24 \polylog \left(5, -\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{c}-\frac{i \arctanh \left(a x \right)^{4} \mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}-1\right)}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right)^{2} \pi}{2 c}+\frac{i \arctanh \left(a x \right)^{4} \mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right) \mathrm{csgn}\left(i \left(\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}-1\right)\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}-1\right)}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right) \pi}{2 c}-\frac{i \arctanh \left(a x \right)^{4} \mathrm{csgn}\left(i \left(\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}-1\right)\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}-1\right)}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right)^{2} \pi}{2 c}+\frac{i \arctanh \left(a x \right)^{4} \mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right)^{3} \pi}{c}+\frac{i \arctanh \left(a x \right)^{4} \mathrm{csgn}\left(\frac{i \left(\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}-1\right)}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right)^{3} \pi}{2 c}-\frac{i \arctanh \left(a x \right)^{4} \mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right)^{2} \pi}{c}+\frac{i \arctanh \left(a x \right)^{4} \pi}{c}+\frac{\arctanh \left(a x \right)^{4} \ln \left(2\right)}{c}"," ",0,"1/c*arctanh(a*x)^4*ln(a*x)-1/c*arctanh(a*x)^4*ln(a*x-1)-1/c*arctanh(a*x)^4*ln((a*x+1)^2/(-a^2*x^2+1)-1)+1/c*arctanh(a*x)^4*ln(1-(a*x+1)/(-a^2*x^2+1)^(1/2))+4/c*arctanh(a*x)^3*polylog(2,(a*x+1)/(-a^2*x^2+1)^(1/2))-12/c*arctanh(a*x)^2*polylog(3,(a*x+1)/(-a^2*x^2+1)^(1/2))+24/c*arctanh(a*x)*polylog(4,(a*x+1)/(-a^2*x^2+1)^(1/2))-24/c*polylog(5,(a*x+1)/(-a^2*x^2+1)^(1/2))+1/c*arctanh(a*x)^4*ln(1+(a*x+1)/(-a^2*x^2+1)^(1/2))+4/c*arctanh(a*x)^3*polylog(2,-(a*x+1)/(-a^2*x^2+1)^(1/2))-12/c*arctanh(a*x)^2*polylog(3,-(a*x+1)/(-a^2*x^2+1)^(1/2))+24/c*arctanh(a*x)*polylog(4,-(a*x+1)/(-a^2*x^2+1)^(1/2))-24/c*polylog(5,-(a*x+1)/(-a^2*x^2+1)^(1/2))+1/2*I/c*arctanh(a*x)^4*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*((a*x+1)^2/(-a^2*x^2+1)-1))*csgn(I*((a*x+1)^2/(-a^2*x^2+1)-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))*Pi-1/2*I/c*arctanh(a*x)^4*csgn(I*((a*x+1)^2/(-a^2*x^2+1)-1))*csgn(I*((a*x+1)^2/(-a^2*x^2+1)-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*Pi-1/2*I/c*arctanh(a*x)^4*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*((a*x+1)^2/(-a^2*x^2+1)-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*Pi+I/c*arctanh(a*x)^4*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))^3*Pi+1/2*I/c*arctanh(a*x)^4*csgn(I*((a*x+1)^2/(-a^2*x^2+1)-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^3*Pi-I/c*arctanh(a*x)^4*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*Pi+I/c*arctanh(a*x)^4*Pi+1/c*arctanh(a*x)^4*ln(2)","C"
139,1,583,237,1.031000," ","int(arctanh(a*x)^4/x^2/(-a*c*x+c),x)","-\frac{a \arctanh \left(a x \right)^{4}}{c}-\frac{\arctanh \left(a x \right)^{4}}{c x}+\frac{a \arctanh \left(a x \right)^{4} \ln \left(1-\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{c}+\frac{4 a \arctanh \left(a x \right)^{3} \polylog \left(2, \frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{c}-\frac{12 a \arctanh \left(a x \right)^{2} \polylog \left(3, \frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{c}+\frac{24 a \arctanh \left(a x \right) \polylog \left(4, \frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{c}-\frac{24 a \polylog \left(5, \frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{c}+\frac{a \arctanh \left(a x \right)^{4} \ln \left(1+\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{c}+\frac{4 a \arctanh \left(a x \right)^{3} \polylog \left(2, -\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{c}-\frac{12 a \arctanh \left(a x \right)^{2} \polylog \left(3, -\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{c}+\frac{24 a \arctanh \left(a x \right) \polylog \left(4, -\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{c}-\frac{24 a \polylog \left(5, -\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{c}+\frac{4 a \arctanh \left(a x \right)^{3} \ln \left(1-\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{c}+\frac{12 a \arctanh \left(a x \right)^{2} \polylog \left(2, \frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{c}-\frac{24 a \arctanh \left(a x \right) \polylog \left(3, \frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{c}+\frac{24 a \polylog \left(4, \frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{c}+\frac{4 a \arctanh \left(a x \right)^{3} \ln \left(1+\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{c}+\frac{12 a \arctanh \left(a x \right)^{2} \polylog \left(2, -\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{c}-\frac{24 a \arctanh \left(a x \right) \polylog \left(3, -\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{c}+\frac{24 a \polylog \left(4, -\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{c}"," ",0,"-a*arctanh(a*x)^4/c-arctanh(a*x)^4/c/x+a/c*arctanh(a*x)^4*ln(1-(a*x+1)/(-a^2*x^2+1)^(1/2))+4*a/c*arctanh(a*x)^3*polylog(2,(a*x+1)/(-a^2*x^2+1)^(1/2))-12*a/c*arctanh(a*x)^2*polylog(3,(a*x+1)/(-a^2*x^2+1)^(1/2))+24*a/c*arctanh(a*x)*polylog(4,(a*x+1)/(-a^2*x^2+1)^(1/2))-24*a/c*polylog(5,(a*x+1)/(-a^2*x^2+1)^(1/2))+a/c*arctanh(a*x)^4*ln(1+(a*x+1)/(-a^2*x^2+1)^(1/2))+4*a/c*arctanh(a*x)^3*polylog(2,-(a*x+1)/(-a^2*x^2+1)^(1/2))-12*a/c*arctanh(a*x)^2*polylog(3,-(a*x+1)/(-a^2*x^2+1)^(1/2))+24*a/c*arctanh(a*x)*polylog(4,-(a*x+1)/(-a^2*x^2+1)^(1/2))-24*a/c*polylog(5,-(a*x+1)/(-a^2*x^2+1)^(1/2))+4*a/c*arctanh(a*x)^3*ln(1-(a*x+1)/(-a^2*x^2+1)^(1/2))+12*a/c*arctanh(a*x)^2*polylog(2,(a*x+1)/(-a^2*x^2+1)^(1/2))-24*a/c*arctanh(a*x)*polylog(3,(a*x+1)/(-a^2*x^2+1)^(1/2))+24*a/c*polylog(4,(a*x+1)/(-a^2*x^2+1)^(1/2))+4*a/c*arctanh(a*x)^3*ln(1+(a*x+1)/(-a^2*x^2+1)^(1/2))+12*a/c*arctanh(a*x)^2*polylog(2,-(a*x+1)/(-a^2*x^2+1)^(1/2))-24*a/c*arctanh(a*x)*polylog(3,-(a*x+1)/(-a^2*x^2+1)^(1/2))+24*a/c*polylog(4,-(a*x+1)/(-a^2*x^2+1)^(1/2))","B"
140,1,858,374,2.003000," ","int(arctanh(a*x)^4/x^3/(-a*c*x+c),x)","\frac{24 a^{2} \arctanh \left(a x \right) \polylog \left(4, \frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{c}-\frac{a^{2} \arctanh \left(a x \right)^{4}}{2 c}-\frac{\arctanh \left(a x \right)^{4}}{2 c \,x^{2}}-\frac{24 a^{2} \polylog \left(5, \frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{c}-\frac{24 a^{2} \polylog \left(5, -\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{c}+\frac{24 a^{2} \polylog \left(4, -\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{c}+\frac{12 a^{2} \arctanh \left(a x \right)^{2} \polylog \left(2, \frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{c}-\frac{24 a^{2} \arctanh \left(a x \right) \polylog \left(3, \frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{c}+\frac{12 a^{2} \arctanh \left(a x \right)^{2} \polylog \left(2, -\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{c}-\frac{2 a \arctanh \left(a x \right)^{3}}{c x}-\frac{a \arctanh \left(a x \right)^{4}}{c x}+\frac{a^{2} \arctanh \left(a x \right)^{4} \ln \left(1+\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{c}+\frac{4 a^{2} \arctanh \left(a x \right)^{3} \polylog \left(2, -\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{c}+\frac{6 a^{2} \arctanh \left(a x \right)^{2} \ln \left(1+\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{c}+\frac{12 a^{2} \arctanh \left(a x \right) \polylog \left(2, -\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{c}+\frac{a^{2} \arctanh \left(a x \right)^{4} \ln \left(1-\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{c}+\frac{4 a^{2} \arctanh \left(a x \right)^{3} \polylog \left(2, \frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{c}-\frac{12 a^{2} \arctanh \left(a x \right)^{2} \polylog \left(3, \frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{c}+\frac{24 a^{2} \arctanh \left(a x \right) \polylog \left(4, -\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{c}+\frac{4 a^{2} \arctanh \left(a x \right)^{3} \ln \left(1-\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{c}+\frac{6 a^{2} \arctanh \left(a x \right)^{2} \ln \left(1-\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{c}-\frac{12 a^{2} \arctanh \left(a x \right)^{2} \polylog \left(3, -\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{c}+\frac{12 a^{2} \arctanh \left(a x \right) \polylog \left(2, \frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{c}+\frac{4 a^{2} \arctanh \left(a x \right)^{3} \ln \left(1+\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{c}-\frac{24 a^{2} \arctanh \left(a x \right) \polylog \left(3, -\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{c}+\frac{24 a^{2} \polylog \left(4, \frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{c}-\frac{2 a^{2} \arctanh \left(a x \right)^{3}}{c}-\frac{12 a^{2} \polylog \left(3, \frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{c}-\frac{12 a^{2} \polylog \left(3, -\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{c}"," ",0,"-1/2*a^2*arctanh(a*x)^4/c-1/2*arctanh(a*x)^4/c/x^2-2*a^2*arctanh(a*x)^3/c-2*a*arctanh(a*x)^3/c/x-a*arctanh(a*x)^4/c/x-24*a^2/c*polylog(5,(a*x+1)/(-a^2*x^2+1)^(1/2))-24*a^2/c*polylog(5,-(a*x+1)/(-a^2*x^2+1)^(1/2))-12*a^2/c*polylog(3,-(a*x+1)/(-a^2*x^2+1)^(1/2))-12*a^2/c*polylog(3,(a*x+1)/(-a^2*x^2+1)^(1/2))+24*a^2/c*polylog(4,(a*x+1)/(-a^2*x^2+1)^(1/2))+24*a^2/c*polylog(4,-(a*x+1)/(-a^2*x^2+1)^(1/2))+a^2/c*arctanh(a*x)^4*ln(1+(a*x+1)/(-a^2*x^2+1)^(1/2))+4*a^2/c*arctanh(a*x)^3*polylog(2,-(a*x+1)/(-a^2*x^2+1)^(1/2))+6*a^2/c*arctanh(a*x)^2*ln(1+(a*x+1)/(-a^2*x^2+1)^(1/2))+12*a^2/c*arctanh(a*x)*polylog(2,-(a*x+1)/(-a^2*x^2+1)^(1/2))+a^2/c*arctanh(a*x)^4*ln(1-(a*x+1)/(-a^2*x^2+1)^(1/2))+4*a^2/c*arctanh(a*x)^3*polylog(2,(a*x+1)/(-a^2*x^2+1)^(1/2))-12*a^2/c*arctanh(a*x)^2*polylog(3,(a*x+1)/(-a^2*x^2+1)^(1/2))+24*a^2/c*arctanh(a*x)*polylog(4,-(a*x+1)/(-a^2*x^2+1)^(1/2))+4*a^2/c*arctanh(a*x)^3*ln(1-(a*x+1)/(-a^2*x^2+1)^(1/2))+12*a^2/c*arctanh(a*x)^2*polylog(2,(a*x+1)/(-a^2*x^2+1)^(1/2))+6*a^2/c*arctanh(a*x)^2*ln(1-(a*x+1)/(-a^2*x^2+1)^(1/2))-12*a^2/c*arctanh(a*x)^2*polylog(3,-(a*x+1)/(-a^2*x^2+1)^(1/2))+12*a^2/c*arctanh(a*x)*polylog(2,(a*x+1)/(-a^2*x^2+1)^(1/2))-24*a^2/c*arctanh(a*x)*polylog(3,(a*x+1)/(-a^2*x^2+1)^(1/2))+4*a^2/c*arctanh(a*x)^3*ln(1+(a*x+1)/(-a^2*x^2+1)^(1/2))+12*a^2/c*arctanh(a*x)^2*polylog(2,-(a*x+1)/(-a^2*x^2+1)^(1/2))-24*a^2/c*arctanh(a*x)*polylog(3,-(a*x+1)/(-a^2*x^2+1)^(1/2))+24*a^2/c*arctanh(a*x)*polylog(4,(a*x+1)/(-a^2*x^2+1)^(1/2))","B"
141,0,0,18,0.692000," ","int(x/(a*c*x+c)/arctanh(a*x),x)","\int \frac{x}{\left(a c x +c \right) \arctanh \left(a x \right)}\, dx"," ",0,"int(x/(a*c*x+c)/arctanh(a*x),x)","F"
142,0,0,17,0.344000," ","int(1/(a*c*x+c)/arctanh(a*x),x)","\int \frac{1}{\left(a c x +c \right) \arctanh \left(a x \right)}\, dx"," ",0,"int(1/(a*c*x+c)/arctanh(a*x),x)","F"
143,0,0,20,0.353000," ","int(1/x/(a*c*x+c)/arctanh(a*x),x)","\int \frac{1}{x \left(a c x +c \right) \arctanh \left(a x \right)}\, dx"," ",0,"int(1/x/(a*c*x+c)/arctanh(a*x),x)","F"
144,0,0,18,0.707000," ","int(x/(a*c*x+c)/arctanh(a*x)^2,x)","\int \frac{x}{\left(a c x +c \right) \arctanh \left(a x \right)^{2}}\, dx"," ",0,"int(x/(a*c*x+c)/arctanh(a*x)^2,x)","F"
145,0,0,17,0.263000," ","int(1/(a*c*x+c)/arctanh(a*x)^2,x)","\int \frac{1}{\left(a c x +c \right) \arctanh \left(a x \right)^{2}}\, dx"," ",0,"int(1/(a*c*x+c)/arctanh(a*x)^2,x)","F"
146,0,0,20,0.296000," ","int(1/x/(a*c*x+c)/arctanh(a*x)^2,x)","\int \frac{1}{x \left(a c x +c \right) \arctanh \left(a x \right)^{2}}\, dx"," ",0,"int(1/x/(a*c*x+c)/arctanh(a*x)^2,x)","F"
147,1,381,257,0.073000," ","int(x^3*(a+b*arctanh(c*x))/(e*x+d),x)","\frac{a \,x^{3}}{3 e}-\frac{a \,x^{2} d}{2 e^{2}}+\frac{a \,d^{2} x}{e^{3}}-\frac{a \,d^{3} \ln \left(c x e +c d \right)}{e^{4}}+\frac{b \arctanh \left(c x \right) x^{3}}{3 e}-\frac{b \arctanh \left(c x \right) x^{2} d}{2 e^{2}}+\frac{b \,d^{2} x \arctanh \left(c x \right)}{e^{3}}-\frac{b \arctanh \left(c x \right) d^{3} \ln \left(c x e +c d \right)}{e^{4}}+\frac{b \,d^{3} \ln \left(c x e +c d \right) \ln \left(\frac{c x e +e}{-c d +e}\right)}{2 e^{4}}+\frac{b \,d^{3} \dilog \left(\frac{c x e +e}{-c d +e}\right)}{2 e^{4}}-\frac{b \,d^{3} \ln \left(c x e +c d \right) \ln \left(\frac{c x e -e}{-c d -e}\right)}{2 e^{4}}-\frac{b \,d^{3} \dilog \left(\frac{c x e -e}{-c d -e}\right)}{2 e^{4}}-\frac{b d x}{2 c \,e^{2}}-\frac{2 b \,d^{2}}{3 c \,e^{3}}+\frac{b \,x^{2}}{6 c e}+\frac{b \ln \left(c x e +e \right) d^{2}}{2 c \,e^{3}}+\frac{b \ln \left(c x e +e \right) d}{4 c^{2} e^{2}}+\frac{b \ln \left(c x e +e \right)}{6 c^{3} e}+\frac{b \ln \left(c x e -e \right) d^{2}}{2 c \,e^{3}}-\frac{b \ln \left(c x e -e \right) d}{4 c^{2} e^{2}}+\frac{b \ln \left(c x e -e \right)}{6 c^{3} e}"," ",0,"1/3*a*x^3/e-1/2*a/e^2*x^2*d+a*d^2*x/e^3-a*d^3/e^4*ln(c*e*x+c*d)+1/3*b*arctanh(c*x)*x^3/e-1/2*b*arctanh(c*x)/e^2*x^2*d+b*d^2*x*arctanh(c*x)/e^3-b*arctanh(c*x)*d^3/e^4*ln(c*e*x+c*d)+1/2*b/e^4*d^3*ln(c*e*x+c*d)*ln((c*e*x+e)/(-c*d+e))+1/2*b/e^4*d^3*dilog((c*e*x+e)/(-c*d+e))-1/2*b/e^4*d^3*ln(c*e*x+c*d)*ln((c*e*x-e)/(-c*d-e))-1/2*b/e^4*d^3*dilog((c*e*x-e)/(-c*d-e))-1/2*b*d*x/c/e^2-2/3/c*b*d^2/e^3+1/6*b*x^2/c/e+1/2/c*b/e^3*ln(c*e*x+e)*d^2+1/4/c^2*b/e^2*ln(c*e*x+e)*d+1/6/c^3*b/e*ln(c*e*x+e)+1/2/c*b/e^3*ln(c*e*x-e)*d^2-1/4/c^2*b/e^2*ln(c*e*x-e)*d+1/6/c^3*b/e*ln(c*e*x-e)","A"
148,1,298,202,0.060000," ","int(x^2*(a+b*arctanh(c*x))/(e*x+d),x)","\frac{a \,x^{2}}{2 e}-\frac{a d x}{e^{2}}+\frac{a \,d^{2} \ln \left(c x e +c d \right)}{e^{3}}+\frac{b \arctanh \left(c x \right) x^{2}}{2 e}-\frac{b d x \arctanh \left(c x \right)}{e^{2}}+\frac{b \arctanh \left(c x \right) d^{2} \ln \left(c x e +c d \right)}{e^{3}}+\frac{b x}{2 c e}+\frac{b d}{2 c \,e^{2}}-\frac{b \ln \left(c x e +e \right) d}{2 c \,e^{2}}-\frac{b \ln \left(c x e +e \right)}{4 c^{2} e}-\frac{b \ln \left(c x e -e \right) d}{2 c \,e^{2}}+\frac{b \ln \left(c x e -e \right)}{4 c^{2} e}-\frac{b \,d^{2} \ln \left(c x e +c d \right) \ln \left(\frac{c x e +e}{-c d +e}\right)}{2 e^{3}}-\frac{b \,d^{2} \dilog \left(\frac{c x e +e}{-c d +e}\right)}{2 e^{3}}+\frac{b \,d^{2} \ln \left(c x e +c d \right) \ln \left(\frac{c x e -e}{-c d -e}\right)}{2 e^{3}}+\frac{b \,d^{2} \dilog \left(\frac{c x e -e}{-c d -e}\right)}{2 e^{3}}"," ",0,"1/2*a*x^2/e-a*d*x/e^2+a*d^2/e^3*ln(c*e*x+c*d)+1/2*b*arctanh(c*x)*x^2/e-b*d*x*arctanh(c*x)/e^2+b*arctanh(c*x)*d^2/e^3*ln(c*e*x+c*d)+1/2*b*x/c/e+1/2/c*b*d/e^2-1/2/c*b/e^2*ln(c*e*x+e)*d-1/4/c^2*b/e*ln(c*e*x+e)-1/2/c*b/e^2*ln(c*e*x-e)*d+1/4/c^2*b/e*ln(c*e*x-e)-1/2*b/e^3*d^2*ln(c*e*x+c*d)*ln((c*e*x+e)/(-c*d+e))-1/2*b/e^3*d^2*dilog((c*e*x+e)/(-c*d+e))+1/2*b/e^3*d^2*ln(c*e*x+c*d)*ln((c*e*x-e)/(-c*d-e))+1/2*b/e^3*d^2*dilog((c*e*x-e)/(-c*d-e))","A"
149,1,217,150,0.053000," ","int(x*(a+b*arctanh(c*x))/(e*x+d),x)","\frac{a x}{e}-\frac{a d \ln \left(c x e +c d \right)}{e^{2}}+\frac{b x \arctanh \left(c x \right)}{e}-\frac{b \arctanh \left(c x \right) d \ln \left(c x e +c d \right)}{e^{2}}+\frac{b d \ln \left(c x e +c d \right) \ln \left(\frac{c x e +e}{-c d +e}\right)}{2 e^{2}}+\frac{b d \dilog \left(\frac{c x e +e}{-c d +e}\right)}{2 e^{2}}-\frac{b d \ln \left(c x e +c d \right) \ln \left(\frac{c x e -e}{-c d -e}\right)}{2 e^{2}}-\frac{b d \dilog \left(\frac{c x e -e}{-c d -e}\right)}{2 e^{2}}+\frac{b \ln \left(c^{2} d^{2}-2 c d \left(c x e +c d \right)+\left(c x e +c d \right)^{2}-e^{2}\right)}{2 c e}"," ",0,"a*x/e-a*d/e^2*ln(c*e*x+c*d)+b*x*arctanh(c*x)/e-b*arctanh(c*x)*d/e^2*ln(c*e*x+c*d)+1/2*b/e^2*d*ln(c*e*x+c*d)*ln((c*e*x+e)/(-c*d+e))+1/2*b/e^2*d*dilog((c*e*x+e)/(-c*d+e))-1/2*b/e^2*d*ln(c*e*x+c*d)*ln((c*e*x-e)/(-c*d-e))-1/2*b/e^2*d*dilog((c*e*x-e)/(-c*d-e))+1/2/c*b/e*ln(c^2*d^2-2*c*d*(c*e*x+c*d)+(c*e*x+c*d)^2-e^2)","A"
150,1,148,110,0.050000," ","int((a+b*arctanh(c*x))/(e*x+d),x)","\frac{a \ln \left(c x e +c d \right)}{e}+\frac{b \ln \left(c x e +c d \right) \arctanh \left(c x \right)}{e}-\frac{b \ln \left(c x e +c d \right) \ln \left(\frac{c x e +e}{-c d +e}\right)}{2 e}-\frac{b \dilog \left(\frac{c x e +e}{-c d +e}\right)}{2 e}+\frac{b \ln \left(c x e +c d \right) \ln \left(\frac{c x e -e}{-c d -e}\right)}{2 e}+\frac{b \dilog \left(\frac{c x e -e}{-c d -e}\right)}{2 e}"," ",0,"a*ln(c*e*x+c*d)/e+b*ln(c*e*x+c*d)/e*arctanh(c*x)-1/2*b/e*ln(c*e*x+c*d)*ln((c*e*x+e)/(-c*d+e))-1/2*b/e*dilog((c*e*x+e)/(-c*d+e))+1/2*b/e*ln(c*e*x+c*d)*ln((c*e*x-e)/(-c*d-e))+1/2*b/e*dilog((c*e*x-e)/(-c*d-e))","A"
151,1,210,140,0.062000," ","int((a+b*arctanh(c*x))/x/(e*x+d),x)","\frac{a \ln \left(c x \right)}{d}-\frac{a \ln \left(c x e +c d \right)}{d}+\frac{b \arctanh \left(c x \right) \ln \left(c x \right)}{d}-\frac{b \arctanh \left(c x \right) \ln \left(c x e +c d \right)}{d}+\frac{b \ln \left(c x e +c d \right) \ln \left(\frac{c x e +e}{-c d +e}\right)}{2 d}+\frac{b \dilog \left(\frac{c x e +e}{-c d +e}\right)}{2 d}-\frac{b \ln \left(c x e +c d \right) \ln \left(\frac{c x e -e}{-c d -e}\right)}{2 d}-\frac{b \dilog \left(\frac{c x e -e}{-c d -e}\right)}{2 d}-\frac{b \dilog \left(c x \right)}{2 d}-\frac{b \dilog \left(c x +1\right)}{2 d}-\frac{b \ln \left(c x \right) \ln \left(c x +1\right)}{2 d}"," ",0,"a/d*ln(c*x)-a/d*ln(c*e*x+c*d)+b*arctanh(c*x)/d*ln(c*x)-b*arctanh(c*x)/d*ln(c*e*x+c*d)+1/2*b/d*ln(c*e*x+c*d)*ln((c*e*x+e)/(-c*d+e))+1/2*b/d*dilog((c*e*x+e)/(-c*d+e))-1/2*b/d*ln(c*e*x+c*d)*ln((c*e*x-e)/(-c*d-e))-1/2*b/d*dilog((c*e*x-e)/(-c*d-e))-1/2*b/d*dilog(c*x)-1/2*b/d*dilog(c*x+1)-1/2*b/d*ln(c*x)*ln(c*x+1)","A"
152,1,279,192,0.069000," ","int((a+b*arctanh(c*x))/x^2/(e*x+d),x)","-\frac{a}{d x}-\frac{a e \ln \left(c x \right)}{d^{2}}+\frac{a e \ln \left(c x e +c d \right)}{d^{2}}-\frac{b \arctanh \left(c x \right)}{d x}-\frac{b \arctanh \left(c x \right) e \ln \left(c x \right)}{d^{2}}+\frac{b \arctanh \left(c x \right) e \ln \left(c x e +c d \right)}{d^{2}}+\frac{c b \ln \left(c x \right)}{d}-\frac{c b \ln \left(c x -1\right)}{2 d}-\frac{c b \ln \left(c x +1\right)}{2 d}+\frac{b e \dilog \left(c x \right)}{2 d^{2}}+\frac{b e \dilog \left(c x +1\right)}{2 d^{2}}+\frac{b e \ln \left(c x \right) \ln \left(c x +1\right)}{2 d^{2}}-\frac{b \ln \left(c x e +c d \right) \ln \left(\frac{c x e +e}{-c d +e}\right) e}{2 d^{2}}-\frac{b \dilog \left(\frac{c x e +e}{-c d +e}\right) e}{2 d^{2}}+\frac{b \ln \left(c x e +c d \right) \ln \left(\frac{c x e -e}{-c d -e}\right) e}{2 d^{2}}+\frac{b \dilog \left(\frac{c x e -e}{-c d -e}\right) e}{2 d^{2}}"," ",0,"-a/d/x-a/d^2*e*ln(c*x)+a/d^2*e*ln(c*e*x+c*d)-b*arctanh(c*x)/d/x-b*arctanh(c*x)/d^2*e*ln(c*x)+b*arctanh(c*x)/d^2*e*ln(c*e*x+c*d)+c*b/d*ln(c*x)-1/2*c*b/d*ln(c*x-1)-1/2*c*b/d*ln(c*x+1)+1/2*b/d^2*e*dilog(c*x)+1/2*b/d^2*e*dilog(c*x+1)+1/2*b/d^2*e*ln(c*x)*ln(c*x+1)-1/2*b/d^2*ln(c*e*x+c*d)*ln((c*e*x+e)/(-c*d+e))*e-1/2*b/d^2*dilog((c*e*x+e)/(-c*d+e))*e+1/2*b/d^2*ln(c*e*x+c*d)*ln((c*e*x-e)/(-c*d-e))*e+1/2*b/d^2*dilog((c*e*x-e)/(-c*d-e))*e","A"
153,1,367,248,0.069000," ","int((a+b*arctanh(c*x))/x^3/(e*x+d),x)","-\frac{a}{2 d \,x^{2}}+\frac{a \,e^{2} \ln \left(c x \right)}{d^{3}}+\frac{a e}{d^{2} x}-\frac{a \,e^{2} \ln \left(c x e +c d \right)}{d^{3}}-\frac{b \arctanh \left(c x \right)}{2 d \,x^{2}}+\frac{b \arctanh \left(c x \right) e^{2} \ln \left(c x \right)}{d^{3}}+\frac{b \arctanh \left(c x \right) e}{d^{2} x}-\frac{b \arctanh \left(c x \right) e^{2} \ln \left(c x e +c d \right)}{d^{3}}-\frac{b \,e^{2} \dilog \left(c x \right)}{2 d^{3}}-\frac{b \,e^{2} \dilog \left(c x +1\right)}{2 d^{3}}-\frac{b \,e^{2} \ln \left(c x \right) \ln \left(c x +1\right)}{2 d^{3}}+\frac{b \,e^{2} \ln \left(c x e +c d \right) \ln \left(\frac{c x e +e}{-c d +e}\right)}{2 d^{3}}+\frac{b \,e^{2} \dilog \left(\frac{c x e +e}{-c d +e}\right)}{2 d^{3}}-\frac{b \,e^{2} \ln \left(c x e +c d \right) \ln \left(\frac{c x e -e}{-c d -e}\right)}{2 d^{3}}-\frac{b \,e^{2} \dilog \left(\frac{c x e -e}{-c d -e}\right)}{2 d^{3}}-\frac{b c}{2 d x}-\frac{c b e \ln \left(c x \right)}{d^{2}}-\frac{c^{2} b \ln \left(c x -1\right)}{4 d}+\frac{c b \ln \left(c x -1\right) e}{2 d^{2}}+\frac{c^{2} b \ln \left(c x +1\right)}{4 d}+\frac{c b \ln \left(c x +1\right) e}{2 d^{2}}"," ",0,"-1/2*a/d/x^2+a/d^3*e^2*ln(c*x)+a/d^2*e/x-a/d^3*e^2*ln(c*e*x+c*d)-1/2*b*arctanh(c*x)/d/x^2+b*arctanh(c*x)/d^3*e^2*ln(c*x)+b*arctanh(c*x)/d^2*e/x-b*arctanh(c*x)/d^3*e^2*ln(c*e*x+c*d)-1/2*b/d^3*e^2*dilog(c*x)-1/2*b/d^3*e^2*dilog(c*x+1)-1/2*b/d^3*e^2*ln(c*x)*ln(c*x+1)+1/2*b/d^3*e^2*ln(c*e*x+c*d)*ln((c*e*x+e)/(-c*d+e))+1/2*b/d^3*e^2*dilog((c*e*x+e)/(-c*d+e))-1/2*b/d^3*e^2*ln(c*e*x+c*d)*ln((c*e*x-e)/(-c*d-e))-1/2*b/d^3*e^2*dilog((c*e*x-e)/(-c*d-e))-1/2*b*c/d/x-c*b/d^2*e*ln(c*x)-1/4*c^2*b/d*ln(c*x-1)+1/2*c*b/d^2*ln(c*x-1)*e+1/4*c^2*b/d*ln(c*x+1)+1/2*c*b/d^2*ln(c*x+1)*e","A"
154,1,1656,375,4.583000," ","int(x^2*(a+b*arctanh(c*x))^2/(e*x+d),x)","\frac{a b x}{c e}-\frac{i b^{2} d^{2} \pi  \,\mathrm{csgn}\left(\frac{i}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(\left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right) e +c d \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)\right)}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right)^{2} \arctanh \left(c x \right)^{2}}{2 e^{3}}-\frac{i b^{2} d^{2} \pi  \,\mathrm{csgn}\left(i \left(\left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right) e +c d \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)\right)\right) \mathrm{csgn}\left(\frac{i \left(\left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right) e +c d \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)\right)}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right)^{2} \arctanh \left(c x \right)^{2}}{2 e^{3}}+\frac{i b^{2} d^{2} \pi  \,\mathrm{csgn}\left(\frac{i}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right) \mathrm{csgn}\left(i \left(\left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right) e +c d \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)\right)\right) \mathrm{csgn}\left(\frac{i \left(\left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right) e +c d \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)\right)}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right) \arctanh \left(c x \right)^{2}}{2 e^{3}}-\frac{b^{2} \ln \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}{c^{2} e}+\frac{a^{2} d^{2} \ln \left(c x e +c d \right)}{e^{3}}-\frac{a^{2} d x}{e^{2}}+\frac{b^{2} \arctanh \left(c x \right)}{c^{2} e}-\frac{b^{2} \arctanh \left(c x \right)^{2}}{2 c^{2} e}+\frac{b^{2} \arctanh \left(c x \right)^{2} x^{2}}{2 e}+\frac{b^{2} d^{2} \polylog \left(3, -\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}{2 e^{3}}+\frac{a^{2} x^{2}}{2 e}-\frac{a b \ln \left(c x e +e \right)}{2 c^{2} e}+\frac{a b \ln \left(c x e -e \right)}{2 c^{2} e}+\frac{a b d}{c \,e^{2}}+\frac{b^{2} x \arctanh \left(c x \right)}{c e}-\frac{b^{2} \arctanh \left(c x \right)^{2} d}{c \,e^{2}}+\frac{a b \arctanh \left(c x \right) x^{2}}{e}-\frac{a b \,d^{2} \dilog \left(\frac{c x e +e}{-c d +e}\right)}{e^{3}}+\frac{a b \,d^{2} \dilog \left(\frac{c x e -e}{-c d -e}\right)}{e^{3}}-\frac{b^{2} d^{2} \polylog \left(3, \frac{\left(c d +e \right) \left(c x +1\right)^{2}}{\left(-c^{2} x^{2}+1\right) \left(-c d +e \right)}\right)}{2 e^{2} \left(c d +e \right)}-\frac{b^{2} d^{2} \arctanh \left(c x \right)^{2} \ln \left(\left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right) e +c d \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)\right)}{e^{3}}+\frac{b^{2} \arctanh \left(c x \right)^{2} d^{2} \ln \left(c x e +c d \right)}{e^{3}}-\frac{b^{2} d^{2} \arctanh \left(c x \right) \polylog \left(2, -\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}{e^{3}}-\frac{b^{2} \arctanh \left(c x \right)^{2} d x}{e^{2}}+\frac{2 b^{2} \dilog \left(1+\frac{i \left(c x +1\right)}{\sqrt{-c^{2} x^{2}+1}}\right) d}{c \,e^{2}}+\frac{2 b^{2} \dilog \left(1-\frac{i \left(c x +1\right)}{\sqrt{-c^{2} x^{2}+1}}\right) d}{c \,e^{2}}+\frac{c \,b^{2} d^{3} \arctanh \left(c x \right)^{2} \ln \left(1-\frac{\left(c d +e \right) \left(c x +1\right)^{2}}{\left(-c^{2} x^{2}+1\right) \left(-c d +e \right)}\right)}{e^{3} \left(c d +e \right)}+\frac{c \,b^{2} d^{3} \arctanh \left(c x \right) \polylog \left(2, \frac{\left(c d +e \right) \left(c x +1\right)^{2}}{\left(-c^{2} x^{2}+1\right) \left(-c d +e \right)}\right)}{e^{3} \left(c d +e \right)}+\frac{i b^{2} d^{2} \pi  \mathrm{csgn}\left(\frac{i \left(\left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right) e +c d \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)\right)}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right)^{3} \arctanh \left(c x \right)^{2}}{2 e^{3}}+\frac{b^{2} d^{2} \arctanh \left(c x \right)^{2} \ln \left(1-\frac{\left(c d +e \right) \left(c x +1\right)^{2}}{\left(-c^{2} x^{2}+1\right) \left(-c d +e \right)}\right)}{e^{2} \left(c d +e \right)}+\frac{b^{2} d^{2} \arctanh \left(c x \right) \polylog \left(2, \frac{\left(c d +e \right) \left(c x +1\right)^{2}}{\left(-c^{2} x^{2}+1\right) \left(-c d +e \right)}\right)}{e^{2} \left(c d +e \right)}+\frac{2 a b \arctanh \left(c x \right) d^{2} \ln \left(c x e +c d \right)}{e^{3}}-\frac{c \,b^{2} d^{3} \polylog \left(3, \frac{\left(c d +e \right) \left(c x +1\right)^{2}}{\left(-c^{2} x^{2}+1\right) \left(-c d +e \right)}\right)}{2 e^{3} \left(c d +e \right)}-\frac{2 a b \arctanh \left(c x \right) d x}{e^{2}}+\frac{2 b^{2} \ln \left(1+\frac{i \left(c x +1\right)}{\sqrt{-c^{2} x^{2}+1}}\right) \arctanh \left(c x \right) d}{c \,e^{2}}+\frac{2 b^{2} \ln \left(1-\frac{i \left(c x +1\right)}{\sqrt{-c^{2} x^{2}+1}}\right) \arctanh \left(c x \right) d}{c \,e^{2}}+\frac{a b \,d^{2} \ln \left(c x e +c d \right) \ln \left(\frac{c x e -e}{-c d -e}\right)}{e^{3}}-\frac{a b \,d^{2} \ln \left(c x e +c d \right) \ln \left(\frac{c x e +e}{-c d +e}\right)}{e^{3}}-\frac{a b \ln \left(c x e +e \right) d}{c \,e^{2}}-\frac{a b \ln \left(c x e -e \right) d}{c \,e^{2}}"," ",0,"a*b*x/c/e+b^2*x*arctanh(c*x)/c/e-1/2*I*b^2/e^3*d^2*Pi*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))*csgn(I*(((c*x+1)^2/(-c^2*x^2+1)-1)*e+c*d*(1+(c*x+1)^2/(-c^2*x^2+1)))/(1+(c*x+1)^2/(-c^2*x^2+1)))^2*arctanh(c*x)^2-1/2*I*b^2/e^3*d^2*Pi*csgn(I*(((c*x+1)^2/(-c^2*x^2+1)-1)*e+c*d*(1+(c*x+1)^2/(-c^2*x^2+1))))*csgn(I*(((c*x+1)^2/(-c^2*x^2+1)-1)*e+c*d*(1+(c*x+1)^2/(-c^2*x^2+1)))/(1+(c*x+1)^2/(-c^2*x^2+1)))^2*arctanh(c*x)^2+1/2*I*b^2/e^3*d^2*Pi*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))*csgn(I*(((c*x+1)^2/(-c^2*x^2+1)-1)*e+c*d*(1+(c*x+1)^2/(-c^2*x^2+1))))*csgn(I*(((c*x+1)^2/(-c^2*x^2+1)-1)*e+c*d*(1+(c*x+1)^2/(-c^2*x^2+1)))/(1+(c*x+1)^2/(-c^2*x^2+1)))*arctanh(c*x)^2+1/c^2*b^2*arctanh(c*x)/e-1/c^2*b^2/e*ln(1+(c*x+1)^2/(-c^2*x^2+1))-1/2/c^2*b^2*arctanh(c*x)^2/e+1/2*b^2*arctanh(c*x)^2*x^2/e+1/2*b^2*d^2/e^3*polylog(3,-(c*x+1)^2/(-c^2*x^2+1))+a^2*d^2/e^3*ln(c*e*x+c*d)-a^2*d/e^2*x+1/2*a^2*x^2/e+2/c*b^2/e^2*dilog(1+I*(c*x+1)/(-c^2*x^2+1)^(1/2))*d+2/c*b^2/e^2*dilog(1-I*(c*x+1)/(-c^2*x^2+1)^(1/2))*d-1/c*b^2/e^2*arctanh(c*x)^2*d-1/2/c^2*a*b/e*ln(c*e*x+e)+1/2/c^2*a*b/e*ln(c*e*x-e)+a*b*arctanh(c*x)*x^2/e-a*b/e^3*d^2*dilog((c*e*x+e)/(-c*d+e))+a*b/e^3*d^2*dilog((c*e*x-e)/(-c*d-e))-1/2*b^2*d^2/e^2/(c*d+e)*polylog(3,(c*d+e)*(c*x+1)^2/(-c^2*x^2+1)/(-c*d+e))-b^2*d^2/e^3*arctanh(c*x)^2*ln(((c*x+1)^2/(-c^2*x^2+1)-1)*e+c*d*(1+(c*x+1)^2/(-c^2*x^2+1)))+b^2*arctanh(c*x)^2*d^2/e^3*ln(c*e*x+c*d)+1/c*a*b*d/e^2-b^2*d^2/e^3*arctanh(c*x)*polylog(2,-(c*x+1)^2/(-c^2*x^2+1))-b^2*arctanh(c*x)^2*d/e^2*x+c*b^2*d^3/e^3/(c*d+e)*arctanh(c*x)^2*ln(1-(c*d+e)*(c*x+1)^2/(-c^2*x^2+1)/(-c*d+e))+c*b^2*d^3/e^3/(c*d+e)*arctanh(c*x)*polylog(2,(c*d+e)*(c*x+1)^2/(-c^2*x^2+1)/(-c*d+e))+1/2*I*b^2/e^3*d^2*Pi*csgn(I*(((c*x+1)^2/(-c^2*x^2+1)-1)*e+c*d*(1+(c*x+1)^2/(-c^2*x^2+1)))/(1+(c*x+1)^2/(-c^2*x^2+1)))^3*arctanh(c*x)^2+a*b/e^3*d^2*ln(c*e*x+c*d)*ln((c*e*x-e)/(-c*d-e))+b^2*d^2/e^2/(c*d+e)*arctanh(c*x)^2*ln(1-(c*d+e)*(c*x+1)^2/(-c^2*x^2+1)/(-c*d+e))+b^2*d^2/e^2/(c*d+e)*arctanh(c*x)*polylog(2,(c*d+e)*(c*x+1)^2/(-c^2*x^2+1)/(-c*d+e))+2*a*b*arctanh(c*x)*d^2/e^3*ln(c*e*x+c*d)-a*b/e^3*d^2*ln(c*e*x+c*d)*ln((c*e*x+e)/(-c*d+e))-1/2*c*b^2*d^3/e^3/(c*d+e)*polylog(3,(c*d+e)*(c*x+1)^2/(-c^2*x^2+1)/(-c*d+e))-1/c*a*b/e^2*ln(c*e*x+e)*d-1/c*a*b/e^2*ln(c*e*x-e)*d+2/c*b^2/e^2*ln(1+I*(c*x+1)/(-c^2*x^2+1)^(1/2))*arctanh(c*x)*d+2/c*b^2/e^2*ln(1-I*(c*x+1)/(-c^2*x^2+1)^(1/2))*arctanh(c*x)*d-2*a*b*arctanh(c*x)*d/e^2*x","C"
155,1,13923,275,1.632000," ","int(x*(a+b*arctanh(c*x))^2/(e*x+d),x)","\text{output too large to display}"," ",0,"result too large to display","C"
156,1,1170,184,0.368000," ","int((a+b*arctanh(c*x))^2/(e*x+d),x)","\frac{a^{2} \ln \left(c x e +c d \right)}{e}+\frac{b^{2} \ln \left(c x e +c d \right) \arctanh \left(c x \right)^{2}}{e}-\frac{b^{2} \arctanh \left(c x \right)^{2} \ln \left(\left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right) e +c d \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)\right)}{e}-\frac{i b^{2} \arctanh \left(c x \right)^{2} \mathrm{csgn}\left(\frac{i \left(\left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right) e +c d \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)\right)}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right)^{2} \mathrm{csgn}\left(i \left(\left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right) e +c d \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)\right)\right) \pi}{2 e}+\frac{i b^{2} \arctanh \left(c x \right)^{2} \mathrm{csgn}\left(\frac{i \left(\left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right) e +c d \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)\right)}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right) \mathrm{csgn}\left(i \left(\left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right) e +c d \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)\right)\right) \mathrm{csgn}\left(\frac{i}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right) \pi}{2 e}-\frac{i b^{2} \arctanh \left(c x \right)^{2} \mathrm{csgn}\left(\frac{i \left(\left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right) e +c d \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)\right)}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right)^{2} \mathrm{csgn}\left(\frac{i}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right) \pi}{2 e}+\frac{i b^{2} \arctanh \left(c x \right)^{2} \mathrm{csgn}\left(\frac{i \left(\left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right) e +c d \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)\right)}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right)^{3} \pi}{2 e}-\frac{b^{2} \arctanh \left(c x \right) \polylog \left(2, -\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}{e}+\frac{b^{2} \polylog \left(3, -\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}{2 e}+\frac{b^{2} \arctanh \left(c x \right)^{2} \ln \left(1-\frac{\left(c d +e \right) \left(c x +1\right)^{2}}{\left(-c^{2} x^{2}+1\right) \left(-c d +e \right)}\right)}{c d +e}+\frac{b^{2} \arctanh \left(c x \right) \polylog \left(2, \frac{\left(c d +e \right) \left(c x +1\right)^{2}}{\left(-c^{2} x^{2}+1\right) \left(-c d +e \right)}\right)}{c d +e}-\frac{b^{2} \polylog \left(3, \frac{\left(c d +e \right) \left(c x +1\right)^{2}}{\left(-c^{2} x^{2}+1\right) \left(-c d +e \right)}\right)}{2 \left(c d +e \right)}+\frac{c \,b^{2} d \arctanh \left(c x \right)^{2} \ln \left(1-\frac{\left(c d +e \right) \left(c x +1\right)^{2}}{\left(-c^{2} x^{2}+1\right) \left(-c d +e \right)}\right)}{e \left(c d +e \right)}+\frac{c \,b^{2} d \arctanh \left(c x \right) \polylog \left(2, \frac{\left(c d +e \right) \left(c x +1\right)^{2}}{\left(-c^{2} x^{2}+1\right) \left(-c d +e \right)}\right)}{e \left(c d +e \right)}-\frac{c \,b^{2} d \polylog \left(3, \frac{\left(c d +e \right) \left(c x +1\right)^{2}}{\left(-c^{2} x^{2}+1\right) \left(-c d +e \right)}\right)}{2 e \left(c d +e \right)}+\frac{2 a b \ln \left(c x e +c d \right) \arctanh \left(c x \right)}{e}-\frac{a b \ln \left(c x e +c d \right) \ln \left(\frac{c x e +e}{-c d +e}\right)}{e}-\frac{a b \dilog \left(\frac{c x e +e}{-c d +e}\right)}{e}+\frac{a b \ln \left(c x e +c d \right) \ln \left(\frac{c x e -e}{-c d -e}\right)}{e}+\frac{a b \dilog \left(\frac{c x e -e}{-c d -e}\right)}{e}"," ",0,"a^2*ln(c*e*x+c*d)/e+b^2*ln(c*e*x+c*d)/e*arctanh(c*x)^2-b^2/e*arctanh(c*x)^2*ln(((c*x+1)^2/(-c^2*x^2+1)-1)*e+c*d*(1+(c*x+1)^2/(-c^2*x^2+1)))-1/2*I*b^2/e*arctanh(c*x)^2*csgn(I*(((c*x+1)^2/(-c^2*x^2+1)-1)*e+c*d*(1+(c*x+1)^2/(-c^2*x^2+1)))/(1+(c*x+1)^2/(-c^2*x^2+1)))^2*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))*Pi+1/2*I*b^2/e*arctanh(c*x)^2*csgn(I*(((c*x+1)^2/(-c^2*x^2+1)-1)*e+c*d*(1+(c*x+1)^2/(-c^2*x^2+1)))/(1+(c*x+1)^2/(-c^2*x^2+1)))*csgn(I*(((c*x+1)^2/(-c^2*x^2+1)-1)*e+c*d*(1+(c*x+1)^2/(-c^2*x^2+1))))*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))*Pi-1/2*I*b^2/e*arctanh(c*x)^2*csgn(I*(((c*x+1)^2/(-c^2*x^2+1)-1)*e+c*d*(1+(c*x+1)^2/(-c^2*x^2+1)))/(1+(c*x+1)^2/(-c^2*x^2+1)))^2*csgn(I*(((c*x+1)^2/(-c^2*x^2+1)-1)*e+c*d*(1+(c*x+1)^2/(-c^2*x^2+1))))*Pi+1/2*I*b^2/e*arctanh(c*x)^2*csgn(I*(((c*x+1)^2/(-c^2*x^2+1)-1)*e+c*d*(1+(c*x+1)^2/(-c^2*x^2+1)))/(1+(c*x+1)^2/(-c^2*x^2+1)))^3*Pi-b^2/e*arctanh(c*x)*polylog(2,-(c*x+1)^2/(-c^2*x^2+1))+1/2*b^2/e*polylog(3,-(c*x+1)^2/(-c^2*x^2+1))+b^2/(c*d+e)*arctanh(c*x)^2*ln(1-(c*d+e)*(c*x+1)^2/(-c^2*x^2+1)/(-c*d+e))+b^2/(c*d+e)*arctanh(c*x)*polylog(2,(c*d+e)*(c*x+1)^2/(-c^2*x^2+1)/(-c*d+e))-1/2*b^2/(c*d+e)*polylog(3,(c*d+e)*(c*x+1)^2/(-c^2*x^2+1)/(-c*d+e))+c*b^2/e*d/(c*d+e)*arctanh(c*x)^2*ln(1-(c*d+e)*(c*x+1)^2/(-c^2*x^2+1)/(-c*d+e))+c*b^2/e*d/(c*d+e)*arctanh(c*x)*polylog(2,(c*d+e)*(c*x+1)^2/(-c^2*x^2+1)/(-c*d+e))-1/2*c*b^2/e*d/(c*d+e)*polylog(3,(c*d+e)*(c*x+1)^2/(-c^2*x^2+1)/(-c*d+e))+2*a*b*ln(c*e*x+c*d)/e*arctanh(c*x)-a*b/e*ln(c*e*x+c*d)*ln((c*e*x+e)/(-c*d+e))-a*b/e*dilog((c*e*x+e)/(-c*d+e))+a*b/e*ln(c*e*x+c*d)*ln((c*e*x-e)/(-c*d-e))+a*b/e*dilog((c*e*x-e)/(-c*d-e))","C"
157,1,1799,311,0.436000," ","int((a+b*arctanh(c*x))^2/x/(e*x+d),x)","\frac{a b \dilog \left(\frac{c x e +e}{-c d +e}\right)}{d}-\frac{a b \dilog \left(\frac{c x e -e}{-c d -e}\right)}{d}-\frac{a b \dilog \left(c x \right)}{d}-\frac{a b \dilog \left(c x +1\right)}{d}+\frac{b^{2} \arctanh \left(c x \right)^{2} \ln \left(c x \right)}{d}-\frac{b^{2} \arctanh \left(c x \right)^{2} \ln \left(c x e +c d \right)}{d}+\frac{b^{2} \arctanh \left(c x \right)^{2} \ln \left(\left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right) e +c d \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)\right)}{d}-\frac{b^{2} \arctanh \left(c x \right)^{2} \ln \left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right)}{d}+\frac{b^{2} \arctanh \left(c x \right)^{2} \ln \left(1-\frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)}{d}+\frac{2 b^{2} \arctanh \left(c x \right) \polylog \left(2, \frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)}{d}+\frac{b^{2} \arctanh \left(c x \right)^{2} \ln \left(1+\frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)}{d}+\frac{2 b^{2} \arctanh \left(c x \right) \polylog \left(2, -\frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)}{d}+\frac{a^{2} \ln \left(c x \right)}{d}-\frac{a^{2} \ln \left(c x e +c d \right)}{d}-\frac{2 b^{2} \polylog \left(3, \frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)}{d}-\frac{2 b^{2} \polylog \left(3, -\frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)}{d}+\frac{i b^{2} \pi  \arctanh \left(c x \right)^{2} \mathrm{csgn}\left(i \left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right)\right) \mathrm{csgn}\left(\frac{i}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right)}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right)}{2 d}-\frac{i b^{2} \pi  \arctanh \left(c x \right)^{2} \mathrm{csgn}\left(\frac{i}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right) \mathrm{csgn}\left(i \left(\left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right) e +c d \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)\right)\right) \mathrm{csgn}\left(\frac{i \left(\left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right) e +c d \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)\right)}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right)}{2 d}-\frac{b^{2} e \arctanh \left(c x \right)^{2} \ln \left(1-\frac{\left(c d +e \right) \left(c x +1\right)^{2}}{\left(-c^{2} x^{2}+1\right) \left(-c d +e \right)}\right)}{d \left(c d +e \right)}-\frac{b^{2} e \arctanh \left(c x \right) \polylog \left(2, \frac{\left(c d +e \right) \left(c x +1\right)^{2}}{\left(-c^{2} x^{2}+1\right) \left(-c d +e \right)}\right)}{d \left(c d +e \right)}+\frac{i b^{2} \pi  \arctanh \left(c x \right)^{2} \mathrm{csgn}\left(\frac{i \left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right)}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right)^{3}}{2 d}-\frac{i b^{2} \pi  \arctanh \left(c x \right)^{2} \mathrm{csgn}\left(\frac{i \left(\left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right) e +c d \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)\right)}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right)^{3}}{2 d}+\frac{b^{2} c \polylog \left(3, \frac{\left(c d +e \right) \left(c x +1\right)^{2}}{\left(-c^{2} x^{2}+1\right) \left(-c d +e \right)}\right)}{2 c d +2 e}-\frac{b^{2} c \arctanh \left(c x \right)^{2} \ln \left(1-\frac{\left(c d +e \right) \left(c x +1\right)^{2}}{\left(-c^{2} x^{2}+1\right) \left(-c d +e \right)}\right)}{c d +e}-\frac{b^{2} c \arctanh \left(c x \right) \polylog \left(2, \frac{\left(c d +e \right) \left(c x +1\right)^{2}}{\left(-c^{2} x^{2}+1\right) \left(-c d +e \right)}\right)}{c d +e}+\frac{b^{2} e \polylog \left(3, \frac{\left(c d +e \right) \left(c x +1\right)^{2}}{\left(-c^{2} x^{2}+1\right) \left(-c d +e \right)}\right)}{2 d \left(c d +e \right)}+\frac{2 a b \arctanh \left(c x \right) \ln \left(c x \right)}{d}-\frac{2 a b \arctanh \left(c x \right) \ln \left(c x e +c d \right)}{d}+\frac{a b \ln \left(c x e +c d \right) \ln \left(\frac{c x e +e}{-c d +e}\right)}{d}-\frac{a b \ln \left(c x e +c d \right) \ln \left(\frac{c x e -e}{-c d -e}\right)}{d}-\frac{a b \ln \left(c x \right) \ln \left(c x +1\right)}{d}-\frac{i b^{2} \pi  \arctanh \left(c x \right)^{2} \mathrm{csgn}\left(i \left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right)\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right)}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right)^{2}}{2 d}-\frac{i b^{2} \pi  \arctanh \left(c x \right)^{2} \mathrm{csgn}\left(\frac{i}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right)}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right)^{2}}{2 d}+\frac{i b^{2} \pi  \arctanh \left(c x \right)^{2} \mathrm{csgn}\left(\frac{i}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(\left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right) e +c d \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)\right)}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right)^{2}}{2 d}+\frac{i b^{2} \pi  \arctanh \left(c x \right)^{2} \mathrm{csgn}\left(i \left(\left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right) e +c d \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)\right)\right) \mathrm{csgn}\left(\frac{i \left(\left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right) e +c d \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)\right)}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right)^{2}}{2 d}"," ",0,"1/2*b^2*c/(c*d+e)*polylog(3,(c*d+e)*(c*x+1)^2/(-c^2*x^2+1)/(-c*d+e))+a*b/d*dilog((c*e*x+e)/(-c*d+e))-a*b/d*dilog((c*e*x-e)/(-c*d-e))-a*b/d*dilog(c*x)-a*b/d*dilog(c*x+1)+b^2*arctanh(c*x)^2/d*ln(c*x)-b^2*arctanh(c*x)^2/d*ln(c*e*x+c*d)+b^2*arctanh(c*x)^2/d*ln(((c*x+1)^2/(-c^2*x^2+1)-1)*e+c*d*(1+(c*x+1)^2/(-c^2*x^2+1)))-b^2*arctanh(c*x)^2/d*ln((c*x+1)^2/(-c^2*x^2+1)-1)+b^2/d*arctanh(c*x)^2*ln(1-(c*x+1)/(-c^2*x^2+1)^(1/2))+2*b^2/d*arctanh(c*x)*polylog(2,(c*x+1)/(-c^2*x^2+1)^(1/2))+b^2/d*arctanh(c*x)^2*ln(1+(c*x+1)/(-c^2*x^2+1)^(1/2))+2*b^2/d*arctanh(c*x)*polylog(2,-(c*x+1)/(-c^2*x^2+1)^(1/2))+a^2/d*ln(c*x)-a^2/d*ln(c*e*x+c*d)-2*b^2/d*polylog(3,(c*x+1)/(-c^2*x^2+1)^(1/2))-2*b^2/d*polylog(3,-(c*x+1)/(-c^2*x^2+1)^(1/2))+1/2*I*b^2/d*Pi*arctanh(c*x)^2*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1))*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))-1/2*I*b^2/d*Pi*arctanh(c*x)^2*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))*csgn(I*(((c*x+1)^2/(-c^2*x^2+1)-1)*e+c*d*(1+(c*x+1)^2/(-c^2*x^2+1))))*csgn(I*(((c*x+1)^2/(-c^2*x^2+1)-1)*e+c*d*(1+(c*x+1)^2/(-c^2*x^2+1)))/(1+(c*x+1)^2/(-c^2*x^2+1)))-b^2/d*e/(c*d+e)*arctanh(c*x)^2*ln(1-(c*d+e)*(c*x+1)^2/(-c^2*x^2+1)/(-c*d+e))-b^2/d*e/(c*d+e)*arctanh(c*x)*polylog(2,(c*d+e)*(c*x+1)^2/(-c^2*x^2+1)/(-c*d+e))+1/2*I*b^2/d*Pi*arctanh(c*x)^2*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^3-1/2*I*b^2/d*Pi*arctanh(c*x)^2*csgn(I*(((c*x+1)^2/(-c^2*x^2+1)-1)*e+c*d*(1+(c*x+1)^2/(-c^2*x^2+1)))/(1+(c*x+1)^2/(-c^2*x^2+1)))^3-1/2*I*b^2/d*Pi*arctanh(c*x)^2*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^2+1/2*I*b^2/d*Pi*arctanh(c*x)^2*csgn(I*(((c*x+1)^2/(-c^2*x^2+1)-1)*e+c*d*(1+(c*x+1)^2/(-c^2*x^2+1))))*csgn(I*(((c*x+1)^2/(-c^2*x^2+1)-1)*e+c*d*(1+(c*x+1)^2/(-c^2*x^2+1)))/(1+(c*x+1)^2/(-c^2*x^2+1)))^2-1/2*I*b^2/d*Pi*arctanh(c*x)^2*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1))*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^2+1/2*I*b^2/d*Pi*arctanh(c*x)^2*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))*csgn(I*(((c*x+1)^2/(-c^2*x^2+1)-1)*e+c*d*(1+(c*x+1)^2/(-c^2*x^2+1)))/(1+(c*x+1)^2/(-c^2*x^2+1)))^2-b^2*c/(c*d+e)*arctanh(c*x)^2*ln(1-(c*d+e)*(c*x+1)^2/(-c^2*x^2+1)/(-c*d+e))-b^2*c/(c*d+e)*arctanh(c*x)*polylog(2,(c*d+e)*(c*x+1)^2/(-c^2*x^2+1)/(-c*d+e))+1/2*b^2/d*e/(c*d+e)*polylog(3,(c*d+e)*(c*x+1)^2/(-c^2*x^2+1)/(-c*d+e))+2*a*b*arctanh(c*x)/d*ln(c*x)-2*a*b*arctanh(c*x)/d*ln(c*e*x+c*d)+a*b/d*ln(c*e*x+c*d)*ln((c*e*x+e)/(-c*d+e))-a*b/d*ln(c*e*x+c*d)*ln((c*e*x-e)/(-c*d-e))-a*b/d*ln(c*x)*ln(c*x+1)","C"
158,1,26776,404,3.772000," ","int((a+b*arctanh(c*x))^2/x^2/(e*x+d),x)","\text{output too large to display}"," ",0,"result too large to display","C"
159,1,1507,267,0.183000," ","int(arctanh(c*x)^2/x/(e*x+d),x)","\frac{\arctanh \left(c x \right)^{2} \ln \left(c x \right)}{d}-\frac{\arctanh \left(c x \right)^{2} \ln \left(c x e +c d \right)}{d}+\frac{\arctanh \left(c x \right)^{2} \ln \left(\left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right) e +c d \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)\right)}{d}-\frac{\arctanh \left(c x \right)^{2} \ln \left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right)}{d}+\frac{\arctanh \left(c x \right)^{2} \ln \left(1-\frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)}{d}+\frac{2 \arctanh \left(c x \right) \polylog \left(2, \frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)}{d}-\frac{2 \polylog \left(3, \frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)}{d}+\frac{\arctanh \left(c x \right)^{2} \ln \left(1+\frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)}{d}+\frac{2 \arctanh \left(c x \right) \polylog \left(2, -\frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)}{d}-\frac{2 \polylog \left(3, -\frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right)}{d}+\frac{i \pi  \arctanh \left(c x \right)^{2} \mathrm{csgn}\left(\frac{i}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(\left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right) e +c d \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)\right)}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right)^{2}}{2 d}+\frac{i \pi  \arctanh \left(c x \right)^{2} \mathrm{csgn}\left(\frac{i \left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right)}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right)^{3}}{2 d}+\frac{i \pi  \arctanh \left(c x \right)^{2} \mathrm{csgn}\left(i \left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right)\right) \mathrm{csgn}\left(\frac{i}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right)}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right)}{2 d}-\frac{i \pi  \arctanh \left(c x \right)^{2} \mathrm{csgn}\left(\frac{i \left(\left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right) e +c d \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)\right)}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right)^{3}}{2 d}+\frac{i \pi  \arctanh \left(c x \right)^{2} \mathrm{csgn}\left(i \left(\left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right) e +c d \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)\right)\right) \mathrm{csgn}\left(\frac{i \left(\left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right) e +c d \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)\right)}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right)^{2}}{2 d}-\frac{i \pi  \arctanh \left(c x \right)^{2} \mathrm{csgn}\left(\frac{i}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right)}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right)^{2}}{2 d}-\frac{i \pi  \arctanh \left(c x \right)^{2} \mathrm{csgn}\left(i \left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right)\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right)}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right)^{2}}{2 d}-\frac{i \pi  \arctanh \left(c x \right)^{2} \mathrm{csgn}\left(\frac{i}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right) \mathrm{csgn}\left(i \left(\left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right) e +c d \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)\right)\right) \mathrm{csgn}\left(\frac{i \left(\left(\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}-1\right) e +c d \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)\right)}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right)}{2 d}-\frac{e \arctanh \left(c x \right)^{2} \ln \left(1-\frac{\left(c d +e \right) \left(c x +1\right)^{2}}{\left(-c^{2} x^{2}+1\right) \left(-c d +e \right)}\right)}{d \left(c d +e \right)}-\frac{e \arctanh \left(c x \right) \polylog \left(2, \frac{\left(c d +e \right) \left(c x +1\right)^{2}}{\left(-c^{2} x^{2}+1\right) \left(-c d +e \right)}\right)}{d \left(c d +e \right)}+\frac{e \polylog \left(3, \frac{\left(c d +e \right) \left(c x +1\right)^{2}}{\left(-c^{2} x^{2}+1\right) \left(-c d +e \right)}\right)}{2 d \left(c d +e \right)}-\frac{c \arctanh \left(c x \right)^{2} \ln \left(1-\frac{\left(c d +e \right) \left(c x +1\right)^{2}}{\left(-c^{2} x^{2}+1\right) \left(-c d +e \right)}\right)}{c d +e}-\frac{c \arctanh \left(c x \right) \polylog \left(2, \frac{\left(c d +e \right) \left(c x +1\right)^{2}}{\left(-c^{2} x^{2}+1\right) \left(-c d +e \right)}\right)}{c d +e}+\frac{c \polylog \left(3, \frac{\left(c d +e \right) \left(c x +1\right)^{2}}{\left(-c^{2} x^{2}+1\right) \left(-c d +e \right)}\right)}{2 c d +2 e}"," ",0,"arctanh(c*x)^2/d*ln(c*x)-arctanh(c*x)^2/d*ln(c*e*x+c*d)+arctanh(c*x)^2/d*ln(((c*x+1)^2/(-c^2*x^2+1)-1)*e+c*d*(1+(c*x+1)^2/(-c^2*x^2+1)))-arctanh(c*x)^2/d*ln((c*x+1)^2/(-c^2*x^2+1)-1)+1/d*arctanh(c*x)^2*ln(1-(c*x+1)/(-c^2*x^2+1)^(1/2))+2/d*arctanh(c*x)*polylog(2,(c*x+1)/(-c^2*x^2+1)^(1/2))-2/d*polylog(3,(c*x+1)/(-c^2*x^2+1)^(1/2))+1/d*arctanh(c*x)^2*ln(1+(c*x+1)/(-c^2*x^2+1)^(1/2))+2/d*arctanh(c*x)*polylog(2,-(c*x+1)/(-c^2*x^2+1)^(1/2))-2/d*polylog(3,-(c*x+1)/(-c^2*x^2+1)^(1/2))+1/2*I/d*Pi*arctanh(c*x)^2*csgn(I*(((c*x+1)^2/(-c^2*x^2+1)-1)*e+c*d*(1+(c*x+1)^2/(-c^2*x^2+1))))*csgn(I*(((c*x+1)^2/(-c^2*x^2+1)-1)*e+c*d*(1+(c*x+1)^2/(-c^2*x^2+1)))/(1+(c*x+1)^2/(-c^2*x^2+1)))^2-1/2*I/d*Pi*arctanh(c*x)^2*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))*csgn(I*(((c*x+1)^2/(-c^2*x^2+1)-1)*e+c*d*(1+(c*x+1)^2/(-c^2*x^2+1))))*csgn(I*(((c*x+1)^2/(-c^2*x^2+1)-1)*e+c*d*(1+(c*x+1)^2/(-c^2*x^2+1)))/(1+(c*x+1)^2/(-c^2*x^2+1)))-1/2*I/d*Pi*arctanh(c*x)^2*csgn(I*(((c*x+1)^2/(-c^2*x^2+1)-1)*e+c*d*(1+(c*x+1)^2/(-c^2*x^2+1)))/(1+(c*x+1)^2/(-c^2*x^2+1)))^3+1/2*I/d*Pi*arctanh(c*x)^2*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))*csgn(I*(((c*x+1)^2/(-c^2*x^2+1)-1)*e+c*d*(1+(c*x+1)^2/(-c^2*x^2+1)))/(1+(c*x+1)^2/(-c^2*x^2+1)))^2-1/2*I/d*Pi*arctanh(c*x)^2*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^2-1/2*I/d*Pi*arctanh(c*x)^2*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1))*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^2+1/2*I/d*Pi*arctanh(c*x)^2*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^3+1/2*I/d*Pi*arctanh(c*x)^2*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1))*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))*csgn(I*((c*x+1)^2/(-c^2*x^2+1)-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))-1/d*e/(c*d+e)*arctanh(c*x)^2*ln(1-(c*d+e)*(c*x+1)^2/(-c^2*x^2+1)/(-c*d+e))-1/d*e/(c*d+e)*arctanh(c*x)*polylog(2,(c*d+e)*(c*x+1)^2/(-c^2*x^2+1)/(-c*d+e))+1/2/d*e/(c*d+e)*polylog(3,(c*d+e)*(c*x+1)^2/(-c^2*x^2+1)/(-c*d+e))-c/(c*d+e)*arctanh(c*x)^2*ln(1-(c*d+e)*(c*x+1)^2/(-c^2*x^2+1)/(-c*d+e))-c/(c*d+e)*arctanh(c*x)*polylog(2,(c*d+e)*(c*x+1)^2/(-c^2*x^2+1)/(-c*d+e))+1/2*c/(c*d+e)*polylog(3,(c*d+e)*(c*x+1)^2/(-c^2*x^2+1)/(-c*d+e))","C"
160,0,0,20,0.801000," ","int(1/(e*x+d)/(a+b*arctan(c*x)),x)","\int \frac{1}{\left(e x +d \right) \left(a +b \arctan \left(c x \right)\right)}\, dx"," ",0,"int(1/(e*x+d)/(a+b*arctan(c*x)),x)","F"
161,1,67,60,0.025000," ","int(x^4*(-a^2*x^2+1)*arctanh(a*x),x)","-\frac{a^{2} x^{7} \arctanh \left(a x \right)}{7}+\frac{x^{5} \arctanh \left(a x \right)}{5}-\frac{x^{6} a}{42}+\frac{x^{4}}{70 a}+\frac{x^{2}}{35 a^{3}}+\frac{\ln \left(a x -1\right)}{35 a^{5}}+\frac{\ln \left(a x +1\right)}{35 a^{5}}"," ",0,"-1/7*a^2*x^7*arctanh(a*x)+1/5*x^5*arctanh(a*x)-1/42*x^6*a+1/70*x^4/a+1/35*x^2/a^3+1/35/a^5*ln(a*x-1)+1/35/a^5*ln(a*x+1)","A"
162,1,65,51,0.030000," ","int(x^3*(-a^2*x^2+1)*arctanh(a*x),x)","-\frac{a^{2} x^{6} \arctanh \left(a x \right)}{6}+\frac{x^{4} \arctanh \left(a x \right)}{4}-\frac{a \,x^{5}}{30}+\frac{x^{3}}{36 a}+\frac{x}{12 a^{3}}+\frac{\ln \left(a x -1\right)}{24 a^{4}}-\frac{\ln \left(a x +1\right)}{24 a^{4}}"," ",0,"-1/6*a^2*x^6*arctanh(a*x)+1/4*x^4*arctanh(a*x)-1/30*a*x^5+1/36*x^3/a+1/12*x/a^3+1/24/a^4*ln(a*x-1)-1/24/a^4*ln(a*x+1)","A"
163,1,59,52,0.026000," ","int(x^2*(-a^2*x^2+1)*arctanh(a*x),x)","-\frac{a^{2} x^{5} \arctanh \left(a x \right)}{5}+\frac{x^{3} \arctanh \left(a x \right)}{3}-\frac{x^{4} a}{20}+\frac{x^{2}}{15 a}+\frac{\ln \left(a x -1\right)}{15 a^{3}}+\frac{\ln \left(a x +1\right)}{15 a^{3}}"," ",0,"-1/5*a^2*x^5*arctanh(a*x)+1/3*x^3*arctanh(a*x)-1/20*x^4*a+1/15*x^2/a+1/15/a^3*ln(a*x-1)+1/15/a^3*ln(a*x+1)","A"
164,1,57,34,0.026000," ","int(x*(-a^2*x^2+1)*arctanh(a*x),x)","-\frac{a^{2} \arctanh \left(a x \right) x^{4}}{4}+\frac{\arctanh \left(a x \right) x^{2}}{2}-\frac{x^{3} a}{12}+\frac{x}{4 a}+\frac{\ln \left(a x -1\right)}{8 a^{2}}-\frac{\ln \left(a x +1\right)}{8 a^{2}}"," ",0,"-1/4*a^2*arctanh(a*x)*x^4+1/2*arctanh(a*x)*x^2-1/12*x^3*a+1/4*x/a+1/8/a^2*ln(a*x-1)-1/8/a^2*ln(a*x+1)","A"
165,1,48,56,0.026000," ","int((-a^2*x^2+1)*arctanh(a*x),x)","-\frac{a^{2} \arctanh \left(a x \right) x^{3}}{3}+x \arctanh \left(a x \right)-\frac{a \,x^{2}}{6}+\frac{\ln \left(a x -1\right)}{3 a}+\frac{\ln \left(a x +1\right)}{3 a}"," ",0,"-1/3*a^2*arctanh(a*x)*x^3+x*arctanh(a*x)-1/6*a*x^2+1/3/a*ln(a*x-1)+1/3/a*ln(a*x+1)","A"
166,1,69,38,0.048000," ","int((-a^2*x^2+1)*arctanh(a*x)/x,x)","-\frac{a^{2} x^{2} \arctanh \left(a x \right)}{2}+\arctanh \left(a x \right) \ln \left(a x \right)-\frac{a x}{2}-\frac{\ln \left(a x -1\right)}{4}+\frac{\ln \left(a x +1\right)}{4}-\frac{\dilog \left(a x \right)}{2}-\frac{\dilog \left(a x +1\right)}{2}-\frac{\ln \left(a x \right) \ln \left(a x +1\right)}{2}"," ",0,"-1/2*a^2*x^2*arctanh(a*x)+arctanh(a*x)*ln(a*x)-1/2*a*x-1/4*ln(a*x-1)+1/4*ln(a*x+1)-1/2*dilog(a*x)-1/2*dilog(a*x+1)-1/2*ln(a*x)*ln(a*x+1)","A"
167,1,45,38,0.033000," ","int((-a^2*x^2+1)*arctanh(a*x)/x^2,x)","-a^{2} x \arctanh \left(a x \right)-\frac{\arctanh \left(a x \right)}{x}+a \ln \left(a x \right)-a \ln \left(a x -1\right)-a \ln \left(a x +1\right)"," ",0,"-a^2*x*arctanh(a*x)-arctanh(a*x)/x+a*ln(a*x)-a*ln(a*x-1)-a*ln(a*x+1)","A"
168,1,87,46,0.052000," ","int((-a^2*x^2+1)*arctanh(a*x)/x^3,x)","-a^{2} \arctanh \left(a x \right) \ln \left(a x \right)-\frac{\arctanh \left(a x \right)}{2 x^{2}}-\frac{a}{2 x}-\frac{a^{2} \ln \left(a x -1\right)}{4}+\frac{a^{2} \ln \left(a x +1\right)}{4}+\frac{a^{2} \dilog \left(a x \right)}{2}+\frac{a^{2} \dilog \left(a x +1\right)}{2}+\frac{a^{2} \ln \left(a x \right) \ln \left(a x +1\right)}{2}"," ",0,"-a^2*arctanh(a*x)*ln(a*x)-1/2*arctanh(a*x)/x^2-1/2*a/x-1/4*a^2*ln(a*x-1)+1/4*a^2*ln(a*x+1)+1/2*a^2*dilog(a*x)+1/2*a^2*dilog(a*x+1)+1/2*a^2*ln(a*x)*ln(a*x+1)","A"
169,1,59,50,0.038000," ","int((-a^2*x^2+1)*arctanh(a*x)/x^4,x)","\frac{a^{2} \arctanh \left(a x \right)}{x}-\frac{\arctanh \left(a x \right)}{3 x^{3}}-\frac{a}{6 x^{2}}-\frac{2 a^{3} \ln \left(a x \right)}{3}+\frac{a^{3} \ln \left(a x -1\right)}{3}+\frac{a^{3} \ln \left(a x +1\right)}{3}"," ",0,"a^2*arctanh(a*x)/x-1/3*arctanh(a*x)/x^3-1/6*a/x^2-2/3*a^3*ln(a*x)+1/3*a^3*ln(a*x-1)+1/3*a^3*ln(a*x+1)","A"
170,1,59,36,0.036000," ","int((-a^2*x^2+1)*arctanh(a*x)/x^5,x)","\frac{a^{2} \arctanh \left(a x \right)}{2 x^{2}}-\frac{\arctanh \left(a x \right)}{4 x^{4}}+\frac{a^{3}}{4 x}-\frac{a}{12 x^{3}}+\frac{a^{4} \ln \left(a x -1\right)}{8}-\frac{a^{4} \ln \left(a x +1\right)}{8}"," ",0,"1/2*a^2*arctanh(a*x)/x^2-1/4*arctanh(a*x)/x^4+1/4*a^3/x-1/12*a/x^3+1/8*a^4*ln(a*x-1)-1/8*a^4*ln(a*x+1)","A"
171,1,68,59,0.037000," ","int((-a^2*x^2+1)*arctanh(a*x)/x^6,x)","\frac{a^{2} \arctanh \left(a x \right)}{3 x^{3}}-\frac{\arctanh \left(a x \right)}{5 x^{5}}-\frac{a}{20 x^{4}}+\frac{a^{3}}{15 x^{2}}-\frac{2 a^{5} \ln \left(a x \right)}{15}+\frac{a^{5} \ln \left(a x -1\right)}{15}+\frac{a^{5} \ln \left(a x +1\right)}{15}"," ",0,"1/3*a^2*arctanh(a*x)/x^3-1/5*arctanh(a*x)/x^5-1/20*a/x^4+1/15*a^3/x^2-2/15*a^5*ln(a*x)+1/15*a^5*ln(a*x-1)+1/15*a^5*ln(a*x+1)","A"
172,1,225,138,0.056000," ","int(x^4*(-a^2*x^2+1)*arctanh(a*x)^2,x)","-\frac{a^{2} x^{7} \arctanh \left(a x \right)^{2}}{7}+\frac{x^{5} \arctanh \left(a x \right)^{2}}{5}-\frac{a \,x^{6} \arctanh \left(a x \right)}{21}+\frac{x^{4} \arctanh \left(a x \right)}{35 a}+\frac{2 x^{2} \arctanh \left(a x \right)}{35 a^{3}}+\frac{2 \arctanh \left(a x \right) \ln \left(a x -1\right)}{35 a^{5}}+\frac{2 \arctanh \left(a x \right) \ln \left(a x +1\right)}{35 a^{5}}+\frac{\ln \left(a x -1\right)^{2}}{70 a^{5}}-\frac{2 \dilog \left(\frac{1}{2}+\frac{a x}{2}\right)}{35 a^{5}}-\frac{\ln \left(a x -1\right) \ln \left(\frac{1}{2}+\frac{a x}{2}\right)}{35 a^{5}}-\frac{\ln \left(a x +1\right)^{2}}{70 a^{5}}-\frac{\ln \left(-\frac{a x}{2}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{a x}{2}\right)}{35 a^{5}}+\frac{\ln \left(-\frac{a x}{2}+\frac{1}{2}\right) \ln \left(a x +1\right)}{35 a^{5}}-\frac{x^{5}}{105}-\frac{2 x^{3}}{315 a^{2}}+\frac{4 x}{105 a^{4}}+\frac{2 \ln \left(a x -1\right)}{105 a^{5}}-\frac{2 \ln \left(a x +1\right)}{105 a^{5}}"," ",0,"-1/7*a^2*x^7*arctanh(a*x)^2+1/5*x^5*arctanh(a*x)^2-1/21*a*x^6*arctanh(a*x)+1/35*x^4*arctanh(a*x)/a+2/35*x^2*arctanh(a*x)/a^3+2/35/a^5*arctanh(a*x)*ln(a*x-1)+2/35/a^5*arctanh(a*x)*ln(a*x+1)+1/70/a^5*ln(a*x-1)^2-2/35/a^5*dilog(1/2+1/2*a*x)-1/35/a^5*ln(a*x-1)*ln(1/2+1/2*a*x)-1/70/a^5*ln(a*x+1)^2-1/35/a^5*ln(-1/2*a*x+1/2)*ln(1/2+1/2*a*x)+1/35/a^5*ln(-1/2*a*x+1/2)*ln(a*x+1)-1/105*x^5-2/315*x^3/a^2+4/105*x/a^4+2/105/a^5*ln(a*x-1)-2/105/a^5*ln(a*x+1)","A"
173,1,205,98,0.056000," ","int(x^3*(-a^2*x^2+1)*arctanh(a*x)^2,x)","-\frac{a^{2} x^{6} \arctanh \left(a x \right)^{2}}{6}+\frac{x^{4} \arctanh \left(a x \right)^{2}}{4}-\frac{a \,x^{5} \arctanh \left(a x \right)}{15}+\frac{x^{3} \arctanh \left(a x \right)}{18 a}+\frac{x \arctanh \left(a x \right)}{6 a^{3}}+\frac{\arctanh \left(a x \right) \ln \left(a x -1\right)}{12 a^{4}}-\frac{\arctanh \left(a x \right) \ln \left(a x +1\right)}{12 a^{4}}+\frac{\ln \left(a x -1\right)^{2}}{48 a^{4}}-\frac{\ln \left(a x -1\right) \ln \left(\frac{1}{2}+\frac{a x}{2}\right)}{24 a^{4}}+\frac{\ln \left(a x +1\right)^{2}}{48 a^{4}}+\frac{\ln \left(-\frac{a x}{2}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{a x}{2}\right)}{24 a^{4}}-\frac{\ln \left(-\frac{a x}{2}+\frac{1}{2}\right) \ln \left(a x +1\right)}{24 a^{4}}-\frac{x^{4}}{60}-\frac{x^{2}}{180 a^{2}}+\frac{7 \ln \left(a x -1\right)}{90 a^{4}}+\frac{7 \ln \left(a x +1\right)}{90 a^{4}}"," ",0,"-1/6*a^2*x^6*arctanh(a*x)^2+1/4*x^4*arctanh(a*x)^2-1/15*a*x^5*arctanh(a*x)+1/18*x^3*arctanh(a*x)/a+1/6*x*arctanh(a*x)/a^3+1/12/a^4*arctanh(a*x)*ln(a*x-1)-1/12/a^4*arctanh(a*x)*ln(a*x+1)+1/48/a^4*ln(a*x-1)^2-1/24/a^4*ln(a*x-1)*ln(1/2+1/2*a*x)+1/48/a^4*ln(a*x+1)^2+1/24/a^4*ln(-1/2*a*x+1/2)*ln(1/2+1/2*a*x)-1/24/a^4*ln(-1/2*a*x+1/2)*ln(a*x+1)-1/60*x^4-1/180*x^2/a^2+7/90/a^4*ln(a*x-1)+7/90/a^4*ln(a*x+1)","B"
174,1,205,118,0.056000," ","int(x^2*(-a^2*x^2+1)*arctanh(a*x)^2,x)","-\frac{a^{2} x^{5} \arctanh \left(a x \right)^{2}}{5}+\frac{x^{3} \arctanh \left(a x \right)^{2}}{3}-\frac{a \,x^{4} \arctanh \left(a x \right)}{10}+\frac{2 x^{2} \arctanh \left(a x \right)}{15 a}+\frac{2 \arctanh \left(a x \right) \ln \left(a x -1\right)}{15 a^{3}}+\frac{2 \arctanh \left(a x \right) \ln \left(a x +1\right)}{15 a^{3}}+\frac{\ln \left(a x -1\right)^{2}}{30 a^{3}}-\frac{2 \dilog \left(\frac{1}{2}+\frac{a x}{2}\right)}{15 a^{3}}-\frac{\ln \left(a x -1\right) \ln \left(\frac{1}{2}+\frac{a x}{2}\right)}{15 a^{3}}-\frac{\ln \left(a x +1\right)^{2}}{30 a^{3}}+\frac{\ln \left(-\frac{a x}{2}+\frac{1}{2}\right) \ln \left(a x +1\right)}{15 a^{3}}-\frac{\ln \left(-\frac{a x}{2}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{a x}{2}\right)}{15 a^{3}}-\frac{x^{3}}{30}+\frac{x}{30 a^{2}}+\frac{\ln \left(a x -1\right)}{60 a^{3}}-\frac{\ln \left(a x +1\right)}{60 a^{3}}"," ",0,"-1/5*a^2*x^5*arctanh(a*x)^2+1/3*x^3*arctanh(a*x)^2-1/10*a*x^4*arctanh(a*x)+2/15*x^2*arctanh(a*x)/a+2/15/a^3*arctanh(a*x)*ln(a*x-1)+2/15/a^3*arctanh(a*x)*ln(a*x+1)+1/30/a^3*ln(a*x-1)^2-2/15/a^3*dilog(1/2+1/2*a*x)-1/15/a^3*ln(a*x-1)*ln(1/2+1/2*a*x)-1/30/a^3*ln(a*x+1)^2+1/15/a^3*ln(-1/2*a*x+1/2)*ln(a*x+1)-1/15/a^3*ln(-1/2*a*x+1/2)*ln(1/2+1/2*a*x)-1/30*x^3+1/30*x/a^2+1/60/a^3*ln(a*x-1)-1/60/a^3*ln(a*x+1)","A"
175,1,185,85,0.056000," ","int(x*(-a^2*x^2+1)*arctanh(a*x)^2,x)","-\frac{a^{2} \arctanh \left(a x \right)^{2} x^{4}}{4}+\frac{\arctanh \left(a x \right)^{2} x^{2}}{2}-\frac{a \arctanh \left(a x \right) x^{3}}{6}+\frac{x \arctanh \left(a x \right)}{2 a}+\frac{\arctanh \left(a x \right) \ln \left(a x -1\right)}{4 a^{2}}-\frac{\arctanh \left(a x \right) \ln \left(a x +1\right)}{4 a^{2}}+\frac{\ln \left(a x -1\right)^{2}}{16 a^{2}}-\frac{\ln \left(a x -1\right) \ln \left(\frac{1}{2}+\frac{a x}{2}\right)}{8 a^{2}}+\frac{\ln \left(a x +1\right)^{2}}{16 a^{2}}-\frac{\ln \left(-\frac{a x}{2}+\frac{1}{2}\right) \ln \left(a x +1\right)}{8 a^{2}}+\frac{\ln \left(-\frac{a x}{2}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{a x}{2}\right)}{8 a^{2}}-\frac{x^{2}}{12}+\frac{\ln \left(a x -1\right)}{6 a^{2}}+\frac{\ln \left(a x +1\right)}{6 a^{2}}"," ",0,"-1/4*a^2*arctanh(a*x)^2*x^4+1/2*arctanh(a*x)^2*x^2-1/6*a*arctanh(a*x)*x^3+1/2*x*arctanh(a*x)/a+1/4/a^2*arctanh(a*x)*ln(a*x-1)-1/4/a^2*arctanh(a*x)*ln(a*x+1)+1/16/a^2*ln(a*x-1)^2-1/8/a^2*ln(a*x-1)*ln(1/2+1/2*a*x)+1/16/a^2*ln(a*x+1)^2-1/8/a^2*ln(-1/2*a*x+1/2)*ln(a*x+1)+1/8/a^2*ln(-1/2*a*x+1/2)*ln(1/2+1/2*a*x)-1/12*x^2+1/6/a^2*ln(a*x-1)+1/6/a^2*ln(a*x+1)","B"
176,1,182,101,0.054000," ","int((-a^2*x^2+1)*arctanh(a*x)^2,x)","-\frac{a^{2} \arctanh \left(a x \right)^{2} x^{3}}{3}+x \arctanh \left(a x \right)^{2}-\frac{a \arctanh \left(a x \right) x^{2}}{3}+\frac{2 \arctanh \left(a x \right) \ln \left(a x -1\right)}{3 a}+\frac{2 \arctanh \left(a x \right) \ln \left(a x +1\right)}{3 a}-\frac{x}{3}-\frac{\ln \left(a x -1\right)}{6 a}+\frac{\ln \left(a x +1\right)}{6 a}+\frac{\ln \left(a x -1\right)^{2}}{6 a}-\frac{2 \dilog \left(\frac{1}{2}+\frac{a x}{2}\right)}{3 a}-\frac{\ln \left(a x -1\right) \ln \left(\frac{1}{2}+\frac{a x}{2}\right)}{3 a}-\frac{\ln \left(a x +1\right)^{2}}{6 a}+\frac{\ln \left(-\frac{a x}{2}+\frac{1}{2}\right) \ln \left(a x +1\right)}{3 a}-\frac{\ln \left(-\frac{a x}{2}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{a x}{2}\right)}{3 a}"," ",0,"-1/3*a^2*arctanh(a*x)^2*x^3+x*arctanh(a*x)^2-1/3*a*arctanh(a*x)*x^2+2/3/a*arctanh(a*x)*ln(a*x-1)+2/3/a*arctanh(a*x)*ln(a*x+1)-1/3*x-1/6/a*ln(a*x-1)+1/6/a*ln(a*x+1)+1/6/a*ln(a*x-1)^2-2/3/a*dilog(1/2+1/2*a*x)-1/3/a*ln(a*x-1)*ln(1/2+1/2*a*x)-1/6/a*ln(a*x+1)^2+1/3/a*ln(-1/2*a*x+1/2)*ln(a*x+1)-1/3/a*ln(-1/2*a*x+1/2)*ln(1/2+1/2*a*x)","A"
177,1,663,136,1.064000," ","int((-a^2*x^2+1)*arctanh(a*x)^2/x,x)","-\frac{a^{2} x^{2} \arctanh \left(a x \right)^{2}}{2}+\arctanh \left(a x \right)^{2} \ln \left(a x \right)-\arctanh \left(a x \right)^{2} \ln \left(\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}-1\right)+\arctanh \left(a x \right)^{2} \ln \left(1-\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)+2 \arctanh \left(a x \right) \polylog \left(2, \frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)-2 \polylog \left(3, \frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)+\arctanh \left(a x \right)^{2} \ln \left(1+\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)+2 \arctanh \left(a x \right) \polylog \left(2, -\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)-2 \polylog \left(3, -\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)-\arctanh \left(a x \right) \polylog \left(2, -\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)+\frac{\polylog \left(3, -\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}{2}-\left(a x +1\right) \arctanh \left(a x \right)+\frac{\arctanh \left(a x \right)^{2}}{2}+\ln \left(1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)-\frac{i \arctanh \left(a x \right)^{2} \pi  \,\mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}-1\right)}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right)^{2}}{2}+\frac{i \arctanh \left(a x \right)^{2} \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}-1\right)\right) \mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}-1\right)}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right)}{2}+\frac{i \arctanh \left(a x \right)^{2} \pi  \mathrm{csgn}\left(\frac{i \left(\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}-1\right)}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right)^{3}}{2}-\frac{i \arctanh \left(a x \right)^{2} \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}-1\right)\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}-1\right)}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right)^{2}}{2}"," ",0,"-1/2*a^2*x^2*arctanh(a*x)^2+arctanh(a*x)^2*ln(a*x)-arctanh(a*x)^2*ln((a*x+1)^2/(-a^2*x^2+1)-1)+arctanh(a*x)^2*ln(1-(a*x+1)/(-a^2*x^2+1)^(1/2))+2*arctanh(a*x)*polylog(2,(a*x+1)/(-a^2*x^2+1)^(1/2))-2*polylog(3,(a*x+1)/(-a^2*x^2+1)^(1/2))+arctanh(a*x)^2*ln(1+(a*x+1)/(-a^2*x^2+1)^(1/2))+2*arctanh(a*x)*polylog(2,-(a*x+1)/(-a^2*x^2+1)^(1/2))-2*polylog(3,-(a*x+1)/(-a^2*x^2+1)^(1/2))-arctanh(a*x)*polylog(2,-(a*x+1)^2/(-a^2*x^2+1))+1/2*polylog(3,-(a*x+1)^2/(-a^2*x^2+1))-(a*x+1)*arctanh(a*x)+1/2*arctanh(a*x)^2+ln(1+(a*x+1)^2/(-a^2*x^2+1))+1/2*I*arctanh(a*x)^2*Pi*csgn(I*((a*x+1)^2/(-a^2*x^2+1)-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^3-1/2*I*arctanh(a*x)^2*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*((a*x+1)^2/(-a^2*x^2+1)-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2+1/2*I*arctanh(a*x)^2*Pi*csgn(I*((a*x+1)^2/(-a^2*x^2+1)-1))*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*((a*x+1)^2/(-a^2*x^2+1)-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))-1/2*I*arctanh(a*x)^2*Pi*csgn(I*((a*x+1)^2/(-a^2*x^2+1)-1))*csgn(I*((a*x+1)^2/(-a^2*x^2+1)-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2","C"
178,1,170,93,0.061000," ","int((-a^2*x^2+1)*arctanh(a*x)^2/x^2,x)","-a^{2} x \arctanh \left(a x \right)^{2}-\frac{\arctanh \left(a x \right)^{2}}{x}+2 a \arctanh \left(a x \right) \ln \left(a x \right)-2 a \arctanh \left(a x \right) \ln \left(a x -1\right)-2 a \arctanh \left(a x \right) \ln \left(a x +1\right)-a \dilog \left(a x \right)-a \dilog \left(a x +1\right)-a \ln \left(a x \right) \ln \left(a x +1\right)-\frac{a \ln \left(a x -1\right)^{2}}{2}+2 a \dilog \left(\frac{1}{2}+\frac{a x}{2}\right)+a \ln \left(a x -1\right) \ln \left(\frac{1}{2}+\frac{a x}{2}\right)+\frac{a \ln \left(a x +1\right)^{2}}{2}-a \ln \left(-\frac{a x}{2}+\frac{1}{2}\right) \ln \left(a x +1\right)+a \ln \left(-\frac{a x}{2}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{a x}{2}\right)"," ",0,"-a^2*x*arctanh(a*x)^2-arctanh(a*x)^2/x+2*a*arctanh(a*x)*ln(a*x)-2*a*arctanh(a*x)*ln(a*x-1)-2*a*arctanh(a*x)*ln(a*x+1)-a*dilog(a*x)-a*dilog(a*x+1)-a*ln(a*x)*ln(a*x+1)-1/2*a*ln(a*x-1)^2+2*a*dilog(1/2+1/2*a*x)+a*ln(a*x-1)*ln(1/2+1/2*a*x)+1/2*a*ln(a*x+1)^2-a*ln(-1/2*a*x+1/2)*ln(a*x+1)+a*ln(-1/2*a*x+1/2)*ln(1/2+1/2*a*x)","A"
179,1,741,162,1.686000," ","int((-a^2*x^2+1)*arctanh(a*x)^2/x^3,x)","-a^{2} \arctanh \left(a x \right)^{2} \ln \left(a x \right)-\frac{\arctanh \left(a x \right)^{2}}{2 x^{2}}+\frac{a^{2} \arctanh \left(a x \right)^{2}}{2}-\frac{i a^{2} \arctanh \left(a x \right)^{2} \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}-1\right)\right) \mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}-1\right)}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right)}{2}+a^{2} \ln \left(1+\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)-a^{2} \arctanh \left(a x \right)-\frac{a \arctanh \left(a x \right)}{x}+a^{2} \ln \left(\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}-1\right)-\frac{i a^{2} \arctanh \left(a x \right)^{2} \pi  \mathrm{csgn}\left(\frac{i \left(\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}-1\right)}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right)^{3}}{2}+\frac{i a^{2} \arctanh \left(a x \right)^{2} \pi  \,\mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}-1\right)}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right)^{2}}{2}+\frac{i a^{2} \arctanh \left(a x \right)^{2} \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}-1\right)\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}-1\right)}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right)^{2}}{2}+a^{2} \arctanh \left(a x \right)^{2} \ln \left(\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}-1\right)-a^{2} \arctanh \left(a x \right)^{2} \ln \left(1-\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)-2 a^{2} \arctanh \left(a x \right) \polylog \left(2, \frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)+2 a^{2} \polylog \left(3, \frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)-a^{2} \arctanh \left(a x \right)^{2} \ln \left(1+\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)-2 a^{2} \arctanh \left(a x \right) \polylog \left(2, -\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)+2 a^{2} \polylog \left(3, -\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)+a^{2} \arctanh \left(a x \right) \polylog \left(2, -\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)-\frac{a^{2} \polylog \left(3, -\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}{2}"," ",0,"-a^2*arctanh(a*x)^2*ln(a*x)-1/2*arctanh(a*x)^2/x^2+1/2*a^2*arctanh(a*x)^2-1/2*I*a^2*arctanh(a*x)^2*Pi*csgn(I*((a*x+1)^2/(-a^2*x^2+1)-1))*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*((a*x+1)^2/(-a^2*x^2+1)-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))+a^2*ln(1+(a*x+1)/(-a^2*x^2+1)^(1/2))-a^2*arctanh(a*x)-a*arctanh(a*x)/x+a^2*ln((a*x+1)/(-a^2*x^2+1)^(1/2)-1)-1/2*I*a^2*arctanh(a*x)^2*Pi*csgn(I*((a*x+1)^2/(-a^2*x^2+1)-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^3+1/2*I*a^2*arctanh(a*x)^2*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*((a*x+1)^2/(-a^2*x^2+1)-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2+1/2*I*a^2*arctanh(a*x)^2*Pi*csgn(I*((a*x+1)^2/(-a^2*x^2+1)-1))*csgn(I*((a*x+1)^2/(-a^2*x^2+1)-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2+a^2*arctanh(a*x)^2*ln((a*x+1)^2/(-a^2*x^2+1)-1)-a^2*arctanh(a*x)^2*ln(1-(a*x+1)/(-a^2*x^2+1)^(1/2))-2*a^2*arctanh(a*x)*polylog(2,(a*x+1)/(-a^2*x^2+1)^(1/2))+2*a^2*polylog(3,(a*x+1)/(-a^2*x^2+1)^(1/2))-a^2*arctanh(a*x)^2*ln(1+(a*x+1)/(-a^2*x^2+1)^(1/2))-2*a^2*arctanh(a*x)*polylog(2,-(a*x+1)/(-a^2*x^2+1)^(1/2))+2*a^2*polylog(3,-(a*x+1)/(-a^2*x^2+1)^(1/2))+a^2*arctanh(a*x)*polylog(2,-(a*x+1)^2/(-a^2*x^2+1))-1/2*a^2*polylog(3,-(a*x+1)^2/(-a^2*x^2+1))","C"
180,1,237,102,0.070000," ","int((-a^2*x^2+1)*arctanh(a*x)^2/x^4,x)","\frac{a^{2} \arctanh \left(a x \right)^{2}}{x}-\frac{\arctanh \left(a x \right)^{2}}{3 x^{3}}-\frac{a \arctanh \left(a x \right)}{3 x^{2}}-\frac{4 a^{3} \arctanh \left(a x \right) \ln \left(a x \right)}{3}+\frac{2 a^{3} \arctanh \left(a x \right) \ln \left(a x -1\right)}{3}+\frac{2 a^{3} \arctanh \left(a x \right) \ln \left(a x +1\right)}{3}-\frac{a^{2}}{3 x}-\frac{a^{3} \ln \left(a x -1\right)}{6}+\frac{a^{3} \ln \left(a x +1\right)}{6}+\frac{2 a^{3} \dilog \left(a x \right)}{3}+\frac{2 a^{3} \dilog \left(a x +1\right)}{3}+\frac{2 a^{3} \ln \left(a x \right) \ln \left(a x +1\right)}{3}+\frac{a^{3} \ln \left(a x -1\right)^{2}}{6}-\frac{2 a^{3} \dilog \left(\frac{1}{2}+\frac{a x}{2}\right)}{3}-\frac{a^{3} \ln \left(a x -1\right) \ln \left(\frac{1}{2}+\frac{a x}{2}\right)}{3}-\frac{a^{3} \ln \left(a x +1\right)^{2}}{6}-\frac{a^{3} \ln \left(-\frac{a x}{2}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{a x}{2}\right)}{3}+\frac{a^{3} \ln \left(-\frac{a x}{2}+\frac{1}{2}\right) \ln \left(a x +1\right)}{3}"," ",0,"a^2*arctanh(a*x)^2/x-1/3*arctanh(a*x)^2/x^3-1/3*a*arctanh(a*x)/x^2-4/3*a^3*arctanh(a*x)*ln(a*x)+2/3*a^3*arctanh(a*x)*ln(a*x-1)+2/3*a^3*arctanh(a*x)*ln(a*x+1)-1/3*a^2/x-1/6*a^3*ln(a*x-1)+1/6*a^3*ln(a*x+1)+2/3*a^3*dilog(a*x)+2/3*a^3*dilog(a*x+1)+2/3*a^3*ln(a*x)*ln(a*x+1)+1/6*a^3*ln(a*x-1)^2-2/3*a^3*dilog(1/2+1/2*a*x)-1/3*a^3*ln(a*x-1)*ln(1/2+1/2*a*x)-1/6*a^3*ln(a*x+1)^2-1/3*a^3*ln(-1/2*a*x+1/2)*ln(1/2+1/2*a*x)+1/3*a^3*ln(-1/2*a*x+1/2)*ln(a*x+1)","B"
181,1,199,77,0.066000," ","int((-a^2*x^2+1)*arctanh(a*x)^2/x^5,x)","\frac{a^{2} \arctanh \left(a x \right)^{2}}{2 x^{2}}-\frac{\arctanh \left(a x \right)^{2}}{4 x^{4}}+\frac{a^{3} \arctanh \left(a x \right)}{2 x}-\frac{a \arctanh \left(a x \right)}{6 x^{3}}+\frac{a^{4} \arctanh \left(a x \right) \ln \left(a x -1\right)}{4}-\frac{a^{4} \arctanh \left(a x \right) \ln \left(a x +1\right)}{4}+\frac{a^{4} \ln \left(a x -1\right)^{2}}{16}-\frac{a^{4} \ln \left(a x -1\right) \ln \left(\frac{1}{2}+\frac{a x}{2}\right)}{8}+\frac{a^{4} \ln \left(a x +1\right)^{2}}{16}+\frac{a^{4} \ln \left(-\frac{a x}{2}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{a x}{2}\right)}{8}-\frac{a^{4} \ln \left(-\frac{a x}{2}+\frac{1}{2}\right) \ln \left(a x +1\right)}{8}-\frac{a^{2}}{12 x^{2}}-\frac{a^{4} \ln \left(a x \right)}{3}+\frac{a^{4} \ln \left(a x -1\right)}{6}+\frac{a^{4} \ln \left(a x +1\right)}{6}"," ",0,"1/2*a^2*arctanh(a*x)^2/x^2-1/4*arctanh(a*x)^2/x^4+1/2*a^3*arctanh(a*x)/x-1/6*a*arctanh(a*x)/x^3+1/4*a^4*arctanh(a*x)*ln(a*x-1)-1/4*a^4*arctanh(a*x)*ln(a*x+1)+1/16*a^4*ln(a*x-1)^2-1/8*a^4*ln(a*x-1)*ln(1/2+1/2*a*x)+1/16*a^4*ln(a*x+1)^2+1/8*a^4*ln(-1/2*a*x+1/2)*ln(1/2+1/2*a*x)-1/8*a^4*ln(-1/2*a*x+1/2)*ln(a*x+1)-1/12*a^2/x^2-1/3*a^4*ln(a*x)+1/6*a^4*ln(a*x-1)+1/6*a^4*ln(a*x+1)","B"
182,1,258,123,0.069000," ","int((-a^2*x^2+1)*arctanh(a*x)^2/x^6,x)","\frac{a^{2} \arctanh \left(a x \right)^{2}}{3 x^{3}}-\frac{\arctanh \left(a x \right)^{2}}{5 x^{5}}-\frac{a \arctanh \left(a x \right)}{10 x^{4}}+\frac{2 a^{3} \arctanh \left(a x \right)}{15 x^{2}}-\frac{4 a^{5} \arctanh \left(a x \right) \ln \left(a x \right)}{15}+\frac{2 a^{5} \arctanh \left(a x \right) \ln \left(a x -1\right)}{15}+\frac{2 a^{5} \arctanh \left(a x \right) \ln \left(a x +1\right)}{15}-\frac{a^{2}}{30 x^{3}}+\frac{a^{4}}{30 x}+\frac{a^{5} \ln \left(a x -1\right)}{60}-\frac{a^{5} \ln \left(a x +1\right)}{60}+\frac{2 a^{5} \dilog \left(a x \right)}{15}+\frac{2 a^{5} \dilog \left(a x +1\right)}{15}+\frac{2 a^{5} \ln \left(a x \right) \ln \left(a x +1\right)}{15}+\frac{a^{5} \ln \left(a x -1\right)^{2}}{30}-\frac{2 a^{5} \dilog \left(\frac{1}{2}+\frac{a x}{2}\right)}{15}-\frac{a^{5} \ln \left(a x -1\right) \ln \left(\frac{1}{2}+\frac{a x}{2}\right)}{15}-\frac{a^{5} \ln \left(a x +1\right)^{2}}{30}+\frac{a^{5} \ln \left(-\frac{a x}{2}+\frac{1}{2}\right) \ln \left(a x +1\right)}{15}-\frac{a^{5} \ln \left(-\frac{a x}{2}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{a x}{2}\right)}{15}"," ",0,"1/3*a^2*arctanh(a*x)^2/x^3-1/5*arctanh(a*x)^2/x^5-1/10*a*arctanh(a*x)/x^4+2/15*a^3*arctanh(a*x)/x^2-4/15*a^5*arctanh(a*x)*ln(a*x)+2/15*a^5*arctanh(a*x)*ln(a*x-1)+2/15*a^5*arctanh(a*x)*ln(a*x+1)-1/30*a^2/x^3+1/30*a^4/x+1/60*a^5*ln(a*x-1)-1/60*a^5*ln(a*x+1)+2/15*a^5*dilog(a*x)+2/15*a^5*dilog(a*x+1)+2/15*a^5*ln(a*x)*ln(a*x+1)+1/30*a^5*ln(a*x-1)^2-2/15*a^5*dilog(1/2+1/2*a*x)-1/15*a^5*ln(a*x-1)*ln(1/2+1/2*a*x)-1/30*a^5*ln(a*x+1)^2+1/15*a^5*ln(-1/2*a*x+1/2)*ln(a*x+1)-1/15*a^5*ln(-1/2*a*x+1/2)*ln(1/2+1/2*a*x)","B"
183,1,829,147,1.334000," ","int((-a^2*x^2+1)*arctanh(a*x)^3,x)","-\frac{a^{2} \arctanh \left(a x \right)^{3} x^{3}}{3}+x \arctanh \left(a x \right)^{3}-\frac{a \arctanh \left(a x \right)^{2} x^{2}}{2}+\frac{\arctanh \left(a x \right)^{2} \ln \left(a x -1\right)}{a}+\frac{\arctanh \left(a x \right)^{2} \ln \left(a x +1\right)}{a}-\frac{2 \arctanh \left(a x \right)^{2} \ln \left(\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{a}+\frac{i \arctanh \left(a x \right)^{2} \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right) \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{\left(a^{2} x^{2}-1\right) \left(1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}\right)^{2} \pi}{2 a}+\frac{i \arctanh \left(a x \right)^{2} \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right) \mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{\left(a^{2} x^{2}-1\right) \left(1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}\right) \pi}{2 a}-\frac{i \arctanh \left(a x \right)^{2} \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{\left(a^{2} x^{2}-1\right) \left(1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}\right)^{3} \pi}{2 a}-\frac{i \arctanh \left(a x \right)^{2} \pi}{a}-\frac{i \arctanh \left(a x \right)^{2} \mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{\left(a^{2} x^{2}-1\right) \left(1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}\right)^{2} \pi}{2 a}-\frac{i \arctanh \left(a x \right)^{2} \mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right)^{3} \pi}{a}+\frac{i \arctanh \left(a x \right)^{2} \mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right)^{2} \pi}{a}-\frac{i \arctanh \left(a x \right)^{2} \mathrm{csgn}\left(\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right)^{2} \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right) \pi}{2 a}-\frac{i \arctanh \left(a x \right)^{2} \mathrm{csgn}\left(\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right)^{2} \pi}{a}-\frac{i \arctanh \left(a x \right)^{2} \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right)^{3} \pi}{2 a}+\frac{2 \arctanh \left(a x \right)^{3}}{3 a}-\frac{2 \arctanh \left(a x \right)^{2} \ln \left(2\right)}{a}-x \arctanh \left(a x \right)+\frac{\arctanh \left(a x \right)^{2}}{2 a}-\frac{\arctanh \left(a x \right)}{a}+\frac{\ln \left(1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}{a}-\frac{2 \arctanh \left(a x \right) \polylog \left(2, -\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}{a}+\frac{\polylog \left(3, -\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}{a}"," ",0,"-1/3*a^2*arctanh(a*x)^3*x^3+x*arctanh(a*x)^3-1/2*a*arctanh(a*x)^2*x^2+1/a*arctanh(a*x)^2*ln(a*x-1)+1/a*arctanh(a*x)^2*ln(a*x+1)-2/a*arctanh(a*x)^2*ln((a*x+1)/(-a^2*x^2+1)^(1/2))-1/2*I/a*arctanh(a*x)^2*csgn(I*(a*x+1)^2/(a^2*x^2-1))^3*Pi-I/a*arctanh(a*x)^2*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))^3*Pi-1/2*I/a*arctanh(a*x)^2*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^3*Pi-1/2*I/a*arctanh(a*x)^2*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*Pi+I/a*arctanh(a*x)^2*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*Pi-I/a*arctanh(a*x)^2*Pi+1/2*I/a*arctanh(a*x)^2*csgn(I*(a*x+1)^2/(a^2*x^2-1))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*Pi-1/2*I/a*arctanh(a*x)^2*csgn(I*(a*x+1)/(-a^2*x^2+1)^(1/2))^2*csgn(I*(a*x+1)^2/(a^2*x^2-1))*Pi-I/a*arctanh(a*x)^2*csgn(I*(a*x+1)/(-a^2*x^2+1)^(1/2))*csgn(I*(a*x+1)^2/(a^2*x^2-1))^2*Pi+1/2*I/a*arctanh(a*x)^2*csgn(I*(a*x+1)^2/(a^2*x^2-1))*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))*Pi+2/3*arctanh(a*x)^3/a-2/a*arctanh(a*x)^2*ln(2)-x*arctanh(a*x)+1/2*arctanh(a*x)^2/a-arctanh(a*x)/a+1/a*ln(1+(a*x+1)^2/(-a^2*x^2+1))-2/a*arctanh(a*x)*polylog(2,-(a*x+1)^2/(-a^2*x^2+1))+1/a*polylog(3,-(a*x+1)^2/(-a^2*x^2+1))","C"
184,1,251,156,0.057000," ","int(x*arctanh(1/2*x*2^(1/2))/(-x^2+1),x)","-\frac{\ln \left(x^{2}-1\right) \arctanh \left(\frac{x \sqrt{2}}{2}\right)}{2}-\frac{\ln \left(\frac{x \sqrt{2}}{2}-1\right) \ln \left(x^{2}-1\right)}{4}+\frac{\ln \left(\frac{x \sqrt{2}}{2}-1\right) \ln \left(\frac{\sqrt{2}-x \sqrt{2}}{-2+\sqrt{2}}\right)}{4}+\frac{\ln \left(\frac{x \sqrt{2}}{2}-1\right) \ln \left(\frac{\sqrt{2}+x \sqrt{2}}{2+\sqrt{2}}\right)}{4}+\frac{\dilog \left(\frac{\sqrt{2}-x \sqrt{2}}{-2+\sqrt{2}}\right)}{4}+\frac{\dilog \left(\frac{\sqrt{2}+x \sqrt{2}}{2+\sqrt{2}}\right)}{4}+\frac{\ln \left(\frac{x \sqrt{2}}{2}+1\right) \ln \left(x^{2}-1\right)}{4}-\frac{\ln \left(\frac{x \sqrt{2}}{2}+1\right) \ln \left(\frac{\sqrt{2}-x \sqrt{2}}{2+\sqrt{2}}\right)}{4}-\frac{\ln \left(\frac{x \sqrt{2}}{2}+1\right) \ln \left(\frac{\sqrt{2}+x \sqrt{2}}{-2+\sqrt{2}}\right)}{4}-\frac{\dilog \left(\frac{\sqrt{2}-x \sqrt{2}}{2+\sqrt{2}}\right)}{4}-\frac{\dilog \left(\frac{\sqrt{2}+x \sqrt{2}}{-2+\sqrt{2}}\right)}{4}"," ",0,"-1/2*ln(x^2-1)*arctanh(1/2*x*2^(1/2))-1/4*ln(1/2*x*2^(1/2)-1)*ln(x^2-1)+1/4*ln(1/2*x*2^(1/2)-1)*ln((2^(1/2)-x*2^(1/2))/(-2+2^(1/2)))+1/4*ln(1/2*x*2^(1/2)-1)*ln((2^(1/2)+x*2^(1/2))/(2+2^(1/2)))+1/4*dilog((2^(1/2)-x*2^(1/2))/(-2+2^(1/2)))+1/4*dilog((2^(1/2)+x*2^(1/2))/(2+2^(1/2)))+1/4*ln(1/2*x*2^(1/2)+1)*ln(x^2-1)-1/4*ln(1/2*x*2^(1/2)+1)*ln((2^(1/2)-x*2^(1/2))/(2+2^(1/2)))-1/4*ln(1/2*x*2^(1/2)+1)*ln((2^(1/2)+x*2^(1/2))/(-2+2^(1/2)))-1/4*dilog((2^(1/2)-x*2^(1/2))/(2+2^(1/2)))-1/4*dilog((2^(1/2)+x*2^(1/2))/(-2+2^(1/2)))","A"
185,0,0,20,0.653000," ","int(x*(-a^2*x^2+1)/arctanh(a*x),x)","\int \frac{x \left(-a^{2} x^{2}+1\right)}{\arctanh \left(a x \right)}\, dx"," ",0,"int(x*(-a^2*x^2+1)/arctanh(a*x),x)","F"
186,0,0,19,0.620000," ","int((-a^2*x^2+1)/arctanh(a*x),x)","\int \frac{-a^{2} x^{2}+1}{\arctanh \left(a x \right)}\, dx"," ",0,"int((-a^2*x^2+1)/arctanh(a*x),x)","F"
187,0,0,22,0.644000," ","int((-a^2*x^2+1)/x/arctanh(a*x),x)","\int \frac{-a^{2} x^{2}+1}{x \arctanh \left(a x \right)}\, dx"," ",0,"int((-a^2*x^2+1)/x/arctanh(a*x),x)","F"
188,0,0,20,0.645000," ","int(x*(-a^2*x^2+1)/arctanh(a*x)^2,x)","\int \frac{x \left(-a^{2} x^{2}+1\right)}{\arctanh \left(a x \right)^{2}}\, dx"," ",0,"int(x*(-a^2*x^2+1)/arctanh(a*x)^2,x)","F"
189,0,0,19,0.615000," ","int((-a^2*x^2+1)/arctanh(a*x)^2,x)","\int \frac{-a^{2} x^{2}+1}{\arctanh \left(a x \right)^{2}}\, dx"," ",0,"int((-a^2*x^2+1)/arctanh(a*x)^2,x)","F"
190,0,0,22,0.635000," ","int((-a^2*x^2+1)/x/arctanh(a*x)^2,x)","\int \frac{-a^{2} x^{2}+1}{x \arctanh \left(a x \right)^{2}}\, dx"," ",0,"int((-a^2*x^2+1)/x/arctanh(a*x)^2,x)","F"
191,0,0,19,0.621000," ","int((-a^2*x^2+1)/arctanh(a*x)^3,x)","\int \frac{-a^{2} x^{2}+1}{\arctanh \left(a x \right)^{3}}\, dx"," ",0,"int((-a^2*x^2+1)/arctanh(a*x)^3,x)","F"
192,1,87,80,0.029000," ","int(x^4*(-a^2*x^2+1)^2*arctanh(a*x),x)","\frac{a^{4} x^{9} \arctanh \left(a x \right)}{9}-\frac{2 a^{2} x^{7} \arctanh \left(a x \right)}{7}+\frac{x^{5} \arctanh \left(a x \right)}{5}+\frac{a^{3} x^{8}}{72}-\frac{11 x^{6} a}{378}+\frac{2 x^{4}}{315 a}+\frac{4 x^{2}}{315 a^{3}}+\frac{4 \ln \left(a x -1\right)}{315 a^{5}}+\frac{4 \ln \left(a x +1\right)}{315 a^{5}}"," ",0,"1/9*a^4*x^9*arctanh(a*x)-2/7*a^2*x^7*arctanh(a*x)+1/5*x^5*arctanh(a*x)+1/72*a^3*x^8-11/378*x^6*a+2/315*x^4/a+4/315*x^2/a^3+4/315/a^5*ln(a*x-1)+4/315/a^5*ln(a*x+1)","A"
193,1,85,71,0.029000," ","int(x^3*(-a^2*x^2+1)^2*arctanh(a*x),x)","\frac{a^{4} x^{8} \arctanh \left(a x \right)}{8}-\frac{a^{2} x^{6} \arctanh \left(a x \right)}{3}+\frac{x^{4} \arctanh \left(a x \right)}{4}+\frac{a^{3} x^{7}}{56}-\frac{a \,x^{5}}{24}+\frac{x^{3}}{72 a}+\frac{x}{24 a^{3}}+\frac{\ln \left(a x -1\right)}{48 a^{4}}-\frac{\ln \left(a x +1\right)}{48 a^{4}}"," ",0,"1/8*a^4*x^8*arctanh(a*x)-1/3*a^2*x^6*arctanh(a*x)+1/4*x^4*arctanh(a*x)+1/56*a^3*x^7-1/24*a*x^5+1/72*x^3/a+1/24*x/a^3+1/48/a^4*ln(a*x-1)-1/48/a^4*ln(a*x+1)","A"
194,1,79,72,0.031000," ","int(x^2*(-a^2*x^2+1)^2*arctanh(a*x),x)","\frac{a^{4} x^{7} \arctanh \left(a x \right)}{7}-\frac{2 a^{2} x^{5} \arctanh \left(a x \right)}{5}+\frac{x^{3} \arctanh \left(a x \right)}{3}+\frac{x^{6} a^{3}}{42}-\frac{9 x^{4} a}{140}+\frac{4 x^{2}}{105 a}+\frac{4 \ln \left(a x -1\right)}{105 a^{3}}+\frac{4 \ln \left(a x +1\right)}{105 a^{3}}"," ",0,"1/7*a^4*x^7*arctanh(a*x)-2/5*a^2*x^5*arctanh(a*x)+1/3*x^3*arctanh(a*x)+1/42*x^6*a^3-9/140*x^4*a+4/105*x^2/a+4/105/a^3*ln(a*x-1)+4/105/a^3*ln(a*x+1)","A"
195,1,77,42,0.027000," ","int(x*(-a^2*x^2+1)^2*arctanh(a*x),x)","\frac{a^{4} \arctanh \left(a x \right) x^{6}}{6}-\frac{a^{2} \arctanh \left(a x \right) x^{4}}{2}+\frac{\arctanh \left(a x \right) x^{2}}{2}+\frac{a^{3} x^{5}}{30}-\frac{x^{3} a}{9}+\frac{x}{6 a}+\frac{\ln \left(a x -1\right)}{12 a^{2}}-\frac{\ln \left(a x +1\right)}{12 a^{2}}"," ",0,"1/6*a^4*arctanh(a*x)*x^6-1/2*a^2*arctanh(a*x)*x^4+1/2*arctanh(a*x)*x^2+1/30*a^3*x^5-1/9*x^3*a+1/6*x/a+1/12/a^2*ln(a*x-1)-1/12/a^2*ln(a*x+1)","A"
196,1,68,92,0.031000," ","int((-a^2*x^2+1)^2*arctanh(a*x),x)","\frac{a^{4} \arctanh \left(a x \right) x^{5}}{5}-\frac{2 a^{2} \arctanh \left(a x \right) x^{3}}{3}+x \arctanh \left(a x \right)+\frac{x^{4} a^{3}}{20}-\frac{7 a \,x^{2}}{30}+\frac{4 \ln \left(a x -1\right)}{15 a}+\frac{4 \ln \left(a x +1\right)}{15 a}"," ",0,"1/5*a^4*arctanh(a*x)*x^5-2/3*a^2*arctanh(a*x)*x^3+x*arctanh(a*x)+1/20*x^4*a^3-7/30*a*x^2+4/15/a*ln(a*x-1)+4/15/a*ln(a*x+1)","A"
197,1,89,58,0.049000," ","int((-a^2*x^2+1)^2*arctanh(a*x)/x,x)","\frac{a^{4} x^{4} \arctanh \left(a x \right)}{4}-a^{2} x^{2} \arctanh \left(a x \right)+\arctanh \left(a x \right) \ln \left(a x \right)-\frac{\dilog \left(a x \right)}{2}-\frac{\dilog \left(a x +1\right)}{2}-\frac{\ln \left(a x \right) \ln \left(a x +1\right)}{2}+\frac{x^{3} a^{3}}{12}-\frac{3 a x}{4}-\frac{3 \ln \left(a x -1\right)}{8}+\frac{3 \ln \left(a x +1\right)}{8}"," ",0,"1/4*a^4*x^4*arctanh(a*x)-a^2*x^2*arctanh(a*x)+arctanh(a*x)*ln(a*x)-1/2*dilog(a*x)-1/2*dilog(a*x+1)-1/2*ln(a*x)*ln(a*x+1)+1/12*x^3*a^3-3/4*a*x-3/8*ln(a*x-1)+3/8*ln(a*x+1)","A"
198,1,65,58,0.035000," ","int((-a^2*x^2+1)^2*arctanh(a*x)/x^2,x)","\frac{a^{4} x^{3} \arctanh \left(a x \right)}{3}-2 a^{2} x \arctanh \left(a x \right)-\frac{\arctanh \left(a x \right)}{x}+\frac{x^{2} a^{3}}{6}+a \ln \left(a x \right)-\frac{4 a \ln \left(a x -1\right)}{3}-\frac{4 a \ln \left(a x +1\right)}{3}"," ",0,"1/3*a^4*x^3*arctanh(a*x)-2*a^2*x*arctanh(a*x)-arctanh(a*x)/x+1/6*x^2*a^3+a*ln(a*x)-4/3*a*ln(a*x-1)-4/3*a*ln(a*x+1)","A"
199,1,80,54,0.051000," ","int((-a^2*x^2+1)^2*arctanh(a*x)/x^3,x)","\frac{a^{4} x^{2} \arctanh \left(a x \right)}{2}-2 a^{2} \arctanh \left(a x \right) \ln \left(a x \right)-\frac{\arctanh \left(a x \right)}{2 x^{2}}+a^{2} \dilog \left(a x \right)+a^{2} \dilog \left(a x +1\right)+a^{2} \ln \left(a x \right) \ln \left(a x +1\right)+\frac{a^{3} x}{2}-\frac{a}{2 x}"," ",0,"1/2*a^4*x^2*arctanh(a*x)-2*a^2*arctanh(a*x)*ln(a*x)-1/2*arctanh(a*x)/x^2+a^2*dilog(a*x)+a^2*dilog(a*x+1)+a^2*ln(a*x)*ln(a*x+1)+1/2*a^3*x-1/2*a/x","A"
200,1,69,60,0.038000," ","int((-a^2*x^2+1)^2*arctanh(a*x)/x^4,x)","a^{4} x \arctanh \left(a x \right)+\frac{2 a^{2} \arctanh \left(a x \right)}{x}-\frac{\arctanh \left(a x \right)}{3 x^{3}}-\frac{a}{6 x^{2}}-\frac{5 a^{3} \ln \left(a x \right)}{3}+\frac{4 a^{3} \ln \left(a x -1\right)}{3}+\frac{4 a^{3} \ln \left(a x +1\right)}{3}"," ",0,"a^4*x*arctanh(a*x)+2*a^2*arctanh(a*x)/x-1/3*arctanh(a*x)/x^3-1/6*a/x^2-5/3*a^3*ln(a*x)+4/3*a^3*ln(a*x-1)+4/3*a^3*ln(a*x+1)","A"
201,1,105,65,0.053000," ","int((-a^2*x^2+1)^2*arctanh(a*x)/x^5,x)","a^{4} \arctanh \left(a x \right) \ln \left(a x \right)+\frac{a^{2} \arctanh \left(a x \right)}{x^{2}}-\frac{\arctanh \left(a x \right)}{4 x^{4}}-\frac{a^{4} \dilog \left(a x \right)}{2}-\frac{a^{4} \dilog \left(a x +1\right)}{2}-\frac{a^{4} \ln \left(a x \right) \ln \left(a x +1\right)}{2}-\frac{a}{12 x^{3}}+\frac{3 a^{3}}{4 x}+\frac{3 a^{4} \ln \left(a x -1\right)}{8}-\frac{3 a^{4} \ln \left(a x +1\right)}{8}"," ",0,"a^4*arctanh(a*x)*ln(a*x)+a^2*arctanh(a*x)/x^2-1/4*arctanh(a*x)/x^4-1/2*a^4*dilog(a*x)-1/2*a^4*dilog(a*x+1)-1/2*a^4*ln(a*x)*ln(a*x+1)-1/12*a/x^3+3/4*a^3/x+3/8*a^4*ln(a*x-1)-3/8*a^4*ln(a*x+1)","A"
202,1,80,71,0.037000," ","int((-a^2*x^2+1)^2*arctanh(a*x)/x^6,x)","-\frac{a^{4} \arctanh \left(a x \right)}{x}+\frac{2 a^{2} \arctanh \left(a x \right)}{3 x^{3}}-\frac{\arctanh \left(a x \right)}{5 x^{5}}-\frac{a}{20 x^{4}}+\frac{7 a^{3}}{30 x^{2}}+\frac{8 a^{5} \ln \left(a x \right)}{15}-\frac{4 a^{5} \ln \left(a x -1\right)}{15}-\frac{4 a^{5} \ln \left(a x +1\right)}{15}"," ",0,"-a^4*arctanh(a*x)/x+2/3*a^2*arctanh(a*x)/x^3-1/5*arctanh(a*x)/x^5-1/20*a/x^4+7/30*a^3/x^2+8/15*a^5*ln(a*x)-4/15*a^5*ln(a*x-1)-4/15*a^5*ln(a*x+1)","A"
203,1,259,172,0.056000," ","int(x^4*(-a^2*x^2+1)^2*arctanh(a*x)^2,x)","\frac{a^{4} x^{9} \arctanh \left(a x \right)^{2}}{9}-\frac{2 a^{2} x^{7} \arctanh \left(a x \right)^{2}}{7}+\frac{x^{5} \arctanh \left(a x \right)^{2}}{5}+\frac{a^{3} x^{8} \arctanh \left(a x \right)}{36}-\frac{11 a \,x^{6} \arctanh \left(a x \right)}{189}+\frac{4 x^{4} \arctanh \left(a x \right)}{315 a}+\frac{8 x^{2} \arctanh \left(a x \right)}{315 a^{3}}+\frac{8 \arctanh \left(a x \right) \ln \left(a x -1\right)}{315 a^{5}}+\frac{8 \arctanh \left(a x \right) \ln \left(a x +1\right)}{315 a^{5}}+\frac{a^{2} x^{7}}{252}-\frac{23 x^{5}}{3780}-\frac{67 x^{3}}{11340 a^{2}}+\frac{29 x}{3780 a^{4}}+\frac{29 \ln \left(a x -1\right)}{7560 a^{5}}-\frac{29 \ln \left(a x +1\right)}{7560 a^{5}}+\frac{2 \ln \left(a x -1\right)^{2}}{315 a^{5}}-\frac{8 \dilog \left(\frac{1}{2}+\frac{a x}{2}\right)}{315 a^{5}}-\frac{4 \ln \left(a x -1\right) \ln \left(\frac{1}{2}+\frac{a x}{2}\right)}{315 a^{5}}-\frac{2 \ln \left(a x +1\right)^{2}}{315 a^{5}}-\frac{4 \ln \left(-\frac{a x}{2}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{a x}{2}\right)}{315 a^{5}}+\frac{4 \ln \left(-\frac{a x}{2}+\frac{1}{2}\right) \ln \left(a x +1\right)}{315 a^{5}}"," ",0,"1/9*a^4*x^9*arctanh(a*x)^2-2/7*a^2*x^7*arctanh(a*x)^2+1/5*x^5*arctanh(a*x)^2+1/36*a^3*x^8*arctanh(a*x)-11/189*a*x^6*arctanh(a*x)+4/315*x^4*arctanh(a*x)/a+8/315*x^2*arctanh(a*x)/a^3+8/315/a^5*arctanh(a*x)*ln(a*x-1)+8/315/a^5*arctanh(a*x)*ln(a*x+1)+1/252*a^2*x^7-23/3780*x^5-67/11340*x^3/a^2+29/3780*x/a^4+29/7560/a^5*ln(a*x-1)-29/7560/a^5*ln(a*x+1)+2/315/a^5*ln(a*x-1)^2-8/315/a^5*dilog(1/2+1/2*a*x)-4/315/a^5*ln(a*x-1)*ln(1/2+1/2*a*x)-2/315/a^5*ln(a*x+1)^2-4/315/a^5*ln(-1/2*a*x+1/2)*ln(1/2+1/2*a*x)+4/315/a^5*ln(-1/2*a*x+1/2)*ln(a*x+1)","A"
204,1,239,132,0.056000," ","int(x^3*(-a^2*x^2+1)^2*arctanh(a*x)^2,x)","\frac{a^{4} x^{8} \arctanh \left(a x \right)^{2}}{8}-\frac{a^{2} x^{6} \arctanh \left(a x \right)^{2}}{3}+\frac{x^{4} \arctanh \left(a x \right)^{2}}{4}+\frac{a^{3} x^{7} \arctanh \left(a x \right)}{28}-\frac{a \,x^{5} \arctanh \left(a x \right)}{12}+\frac{x^{3} \arctanh \left(a x \right)}{36 a}+\frac{x \arctanh \left(a x \right)}{12 a^{3}}+\frac{\arctanh \left(a x \right) \ln \left(a x -1\right)}{24 a^{4}}-\frac{\arctanh \left(a x \right) \ln \left(a x +1\right)}{24 a^{4}}+\frac{\ln \left(a x -1\right)^{2}}{96 a^{4}}-\frac{\ln \left(a x -1\right) \ln \left(\frac{1}{2}+\frac{a x}{2}\right)}{48 a^{4}}+\frac{\ln \left(a x +1\right)^{2}}{96 a^{4}}+\frac{\ln \left(-\frac{a x}{2}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{a x}{2}\right)}{48 a^{4}}-\frac{\ln \left(-\frac{a x}{2}+\frac{1}{2}\right) \ln \left(a x +1\right)}{48 a^{4}}+\frac{a^{2} x^{6}}{168}-\frac{x^{4}}{84}-\frac{5 x^{2}}{504 a^{2}}+\frac{2 \ln \left(a x -1\right)}{63 a^{4}}+\frac{2 \ln \left(a x +1\right)}{63 a^{4}}"," ",0,"1/8*a^4*x^8*arctanh(a*x)^2-1/3*a^2*x^6*arctanh(a*x)^2+1/4*x^4*arctanh(a*x)^2+1/28*a^3*x^7*arctanh(a*x)-1/12*a*x^5*arctanh(a*x)+1/36*x^3*arctanh(a*x)/a+1/12*x*arctanh(a*x)/a^3+1/24/a^4*arctanh(a*x)*ln(a*x-1)-1/24/a^4*arctanh(a*x)*ln(a*x+1)+1/96/a^4*ln(a*x-1)^2-1/48/a^4*ln(a*x-1)*ln(1/2+1/2*a*x)+1/96/a^4*ln(a*x+1)^2+1/48/a^4*ln(-1/2*a*x+1/2)*ln(1/2+1/2*a*x)-1/48/a^4*ln(-1/2*a*x+1/2)*ln(a*x+1)+1/168*a^2*x^6-1/84*x^4-5/504*x^2/a^2+2/63/a^4*ln(a*x-1)+2/63/a^4*ln(a*x+1)","A"
205,1,239,152,0.055000," ","int(x^2*(-a^2*x^2+1)^2*arctanh(a*x)^2,x)","\frac{a^{4} x^{7} \arctanh \left(a x \right)^{2}}{7}-\frac{2 a^{2} x^{5} \arctanh \left(a x \right)^{2}}{5}+\frac{x^{3} \arctanh \left(a x \right)^{2}}{3}+\frac{a^{3} x^{6} \arctanh \left(a x \right)}{21}-\frac{9 a \,x^{4} \arctanh \left(a x \right)}{70}+\frac{8 x^{2} \arctanh \left(a x \right)}{105 a}+\frac{8 \arctanh \left(a x \right) \ln \left(a x -1\right)}{105 a^{3}}+\frac{8 \arctanh \left(a x \right) \ln \left(a x +1\right)}{105 a^{3}}+\frac{x^{5} a^{2}}{105}-\frac{17 x^{3}}{630}-\frac{x}{210 a^{2}}-\frac{\ln \left(a x -1\right)}{420 a^{3}}+\frac{\ln \left(a x +1\right)}{420 a^{3}}+\frac{2 \ln \left(a x -1\right)^{2}}{105 a^{3}}-\frac{8 \dilog \left(\frac{1}{2}+\frac{a x}{2}\right)}{105 a^{3}}-\frac{4 \ln \left(a x -1\right) \ln \left(\frac{1}{2}+\frac{a x}{2}\right)}{105 a^{3}}-\frac{2 \ln \left(a x +1\right)^{2}}{105 a^{3}}-\frac{4 \ln \left(-\frac{a x}{2}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{a x}{2}\right)}{105 a^{3}}+\frac{4 \ln \left(-\frac{a x}{2}+\frac{1}{2}\right) \ln \left(a x +1\right)}{105 a^{3}}"," ",0,"1/7*a^4*x^7*arctanh(a*x)^2-2/5*a^2*x^5*arctanh(a*x)^2+1/3*x^3*arctanh(a*x)^2+1/21*a^3*x^6*arctanh(a*x)-9/70*a*x^4*arctanh(a*x)+8/105*x^2*arctanh(a*x)/a+8/105/a^3*arctanh(a*x)*ln(a*x-1)+8/105/a^3*arctanh(a*x)*ln(a*x+1)+1/105*x^5*a^2-17/630*x^3-1/210*x/a^2-1/420/a^3*ln(a*x-1)+1/420/a^3*ln(a*x+1)+2/105/a^3*ln(a*x-1)^2-8/105/a^3*dilog(1/2+1/2*a*x)-4/105/a^3*ln(a*x-1)*ln(1/2+1/2*a*x)-2/105/a^3*ln(a*x+1)^2-4/105/a^3*ln(-1/2*a*x+1/2)*ln(1/2+1/2*a*x)+4/105/a^3*ln(-1/2*a*x+1/2)*ln(a*x+1)","A"
206,1,219,124,0.054000," ","int(x*(-a^2*x^2+1)^2*arctanh(a*x)^2,x)","\frac{a^{4} \arctanh \left(a x \right)^{2} x^{6}}{6}-\frac{a^{2} \arctanh \left(a x \right)^{2} x^{4}}{2}+\frac{\arctanh \left(a x \right)^{2} x^{2}}{2}+\frac{a^{3} \arctanh \left(a x \right) x^{5}}{15}-\frac{2 a \arctanh \left(a x \right) x^{3}}{9}+\frac{x \arctanh \left(a x \right)}{3 a}+\frac{\arctanh \left(a x \right) \ln \left(a x -1\right)}{6 a^{2}}-\frac{\arctanh \left(a x \right) \ln \left(a x +1\right)}{6 a^{2}}+\frac{\ln \left(a x -1\right)^{2}}{24 a^{2}}-\frac{\ln \left(a x -1\right) \ln \left(\frac{1}{2}+\frac{a x}{2}\right)}{12 a^{2}}+\frac{\ln \left(a x +1\right)^{2}}{24 a^{2}}+\frac{\ln \left(-\frac{a x}{2}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{a x}{2}\right)}{12 a^{2}}-\frac{\ln \left(-\frac{a x}{2}+\frac{1}{2}\right) \ln \left(a x +1\right)}{12 a^{2}}+\frac{a^{2} x^{4}}{60}-\frac{7 x^{2}}{90}+\frac{4 \ln \left(a x -1\right)}{45 a^{2}}+\frac{4 \ln \left(a x +1\right)}{45 a^{2}}"," ",0,"1/6*a^4*arctanh(a*x)^2*x^6-1/2*a^2*arctanh(a*x)^2*x^4+1/2*arctanh(a*x)^2*x^2+1/15*a^3*arctanh(a*x)*x^5-2/9*a*arctanh(a*x)*x^3+1/3*x*arctanh(a*x)/a+1/6/a^2*arctanh(a*x)*ln(a*x-1)-1/6/a^2*arctanh(a*x)*ln(a*x+1)+1/24/a^2*ln(a*x-1)^2-1/12/a^2*ln(a*x-1)*ln(1/2+1/2*a*x)+1/24/a^2*ln(a*x+1)^2+1/12/a^2*ln(-1/2*a*x+1/2)*ln(1/2+1/2*a*x)-1/12/a^2*ln(-1/2*a*x+1/2)*ln(a*x+1)+1/60*a^2*x^4-7/90*x^2+4/45/a^2*ln(a*x-1)+4/45/a^2*ln(a*x+1)","A"
207,1,216,151,0.054000," ","int((-a^2*x^2+1)^2*arctanh(a*x)^2,x)","\frac{a^{4} \arctanh \left(a x \right)^{2} x^{5}}{5}-\frac{2 a^{2} \arctanh \left(a x \right)^{2} x^{3}}{3}+x \arctanh \left(a x \right)^{2}+\frac{a^{3} \arctanh \left(a x \right) x^{4}}{10}-\frac{7 a \arctanh \left(a x \right) x^{2}}{15}+\frac{8 \arctanh \left(a x \right) \ln \left(a x -1\right)}{15 a}+\frac{8 \arctanh \left(a x \right) \ln \left(a x +1\right)}{15 a}+\frac{x^{3} a^{2}}{30}-\frac{11 x}{30}-\frac{11 \ln \left(a x -1\right)}{60 a}+\frac{11 \ln \left(a x +1\right)}{60 a}+\frac{2 \ln \left(a x -1\right)^{2}}{15 a}-\frac{8 \dilog \left(\frac{1}{2}+\frac{a x}{2}\right)}{15 a}-\frac{4 \ln \left(a x -1\right) \ln \left(\frac{1}{2}+\frac{a x}{2}\right)}{15 a}-\frac{2 \ln \left(a x +1\right)^{2}}{15 a}-\frac{4 \ln \left(-\frac{a x}{2}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{a x}{2}\right)}{15 a}+\frac{4 \ln \left(-\frac{a x}{2}+\frac{1}{2}\right) \ln \left(a x +1\right)}{15 a}"," ",0,"1/5*a^4*arctanh(a*x)^2*x^5-2/3*a^2*arctanh(a*x)^2*x^3+x*arctanh(a*x)^2+1/10*a^3*arctanh(a*x)*x^4-7/15*a*arctanh(a*x)*x^2+8/15/a*arctanh(a*x)*ln(a*x-1)+8/15/a*arctanh(a*x)*ln(a*x+1)+1/30*x^3*a^2-11/30*x-11/60/a*ln(a*x-1)+11/60/a*ln(a*x+1)+2/15/a*ln(a*x-1)^2-8/15/a*dilog(1/2+1/2*a*x)-4/15/a*ln(a*x-1)*ln(1/2+1/2*a*x)-2/15/a*ln(a*x+1)^2-4/15/a*ln(-1/2*a*x+1/2)*ln(1/2+1/2*a*x)+4/15/a*ln(-1/2*a*x+1/2)*ln(a*x+1)","A"
208,1,728,170,1.798000," ","int((-a^2*x^2+1)^2*arctanh(a*x)^2/x,x)","-a^{2} x^{2} \arctanh \left(a x \right)^{2}-\frac{i \arctanh \left(a x \right)^{2} \pi  \,\mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}-1\right)}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right)^{2}}{2}-\frac{1}{12}+\frac{3 \arctanh \left(a x \right)^{2}}{4}+\frac{a^{4} x^{4} \arctanh \left(a x \right)^{2}}{4}+\frac{a^{2} x^{2}}{12}-\frac{i \arctanh \left(a x \right)^{2} \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}-1\right)\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}-1\right)}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right)^{2}}{2}+\frac{i \arctanh \left(a x \right)^{2} \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}-1\right)\right) \mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}-1\right)}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right)}{2}-2 \polylog \left(3, \frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)+\frac{i \arctanh \left(a x \right)^{2} \pi  \mathrm{csgn}\left(\frac{i \left(\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}-1\right)}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right)^{3}}{2}+\arctanh \left(a x \right)^{2} \ln \left(a x \right)-\arctanh \left(a x \right)^{2} \ln \left(\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}-1\right)+\arctanh \left(a x \right)^{2} \ln \left(1-\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)+2 \arctanh \left(a x \right) \polylog \left(2, \frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)+\arctanh \left(a x \right)^{2} \ln \left(1+\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)+2 \arctanh \left(a x \right) \polylog \left(2, -\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)-\arctanh \left(a x \right) \polylog \left(2, -\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)-\left(a x +1\right) \arctanh \left(a x \right)-2 \polylog \left(3, -\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)+\frac{4 \ln \left(1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}{3}+\frac{\polylog \left(3, -\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}{2}+\frac{\left(a^{2} x^{2}-4 a x +7\right) \left(a x +1\right) \arctanh \left(a x \right)}{6}+\frac{\left(a x -3\right) \left(a x +1\right) \arctanh \left(a x \right)}{2}"," ",0,"-a^2*x^2*arctanh(a*x)^2-1/2*I*arctanh(a*x)^2*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*((a*x+1)^2/(-a^2*x^2+1)-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2-1/12+3/4*arctanh(a*x)^2+1/4*a^4*x^4*arctanh(a*x)^2+1/12*a^2*x^2+1/2*I*arctanh(a*x)^2*Pi*csgn(I*((a*x+1)^2/(-a^2*x^2+1)-1))*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*((a*x+1)^2/(-a^2*x^2+1)-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))+1/2*I*arctanh(a*x)^2*Pi*csgn(I*((a*x+1)^2/(-a^2*x^2+1)-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^3-2*polylog(3,(a*x+1)/(-a^2*x^2+1)^(1/2))-1/2*I*arctanh(a*x)^2*Pi*csgn(I*((a*x+1)^2/(-a^2*x^2+1)-1))*csgn(I*((a*x+1)^2/(-a^2*x^2+1)-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2+arctanh(a*x)^2*ln(a*x)-arctanh(a*x)^2*ln((a*x+1)^2/(-a^2*x^2+1)-1)+arctanh(a*x)^2*ln(1-(a*x+1)/(-a^2*x^2+1)^(1/2))+2*arctanh(a*x)*polylog(2,(a*x+1)/(-a^2*x^2+1)^(1/2))+arctanh(a*x)^2*ln(1+(a*x+1)/(-a^2*x^2+1)^(1/2))+2*arctanh(a*x)*polylog(2,-(a*x+1)/(-a^2*x^2+1)^(1/2))-arctanh(a*x)*polylog(2,-(a*x+1)^2/(-a^2*x^2+1))-(a*x+1)*arctanh(a*x)-2*polylog(3,-(a*x+1)/(-a^2*x^2+1)^(1/2))+4/3*ln(1+(a*x+1)^2/(-a^2*x^2+1))+1/2*polylog(3,-(a*x+1)^2/(-a^2*x^2+1))+1/6*(a^2*x^2-4*a*x+7)*(a*x+1)*arctanh(a*x)+1/2*(a*x-3)*(a*x+1)*arctanh(a*x)","C"
209,1,222,142,0.064000," ","int((-a^2*x^2+1)^2*arctanh(a*x)^2/x^2,x)","\frac{a^{4} x^{3} \arctanh \left(a x \right)^{2}}{3}-2 a^{2} x \arctanh \left(a x \right)^{2}-\frac{\arctanh \left(a x \right)^{2}}{x}+\frac{a^{3} x^{2} \arctanh \left(a x \right)}{3}+2 a \arctanh \left(a x \right) \ln \left(a x \right)-\frac{8 a \arctanh \left(a x \right) \ln \left(a x -1\right)}{3}-\frac{8 a \arctanh \left(a x \right) \ln \left(a x +1\right)}{3}+\frac{a^{2} x}{3}+\frac{a \ln \left(a x -1\right)}{6}-\frac{a \ln \left(a x +1\right)}{6}-a \dilog \left(a x \right)-a \dilog \left(a x +1\right)-a \ln \left(a x \right) \ln \left(a x +1\right)-\frac{2 a \ln \left(a x -1\right)^{2}}{3}+\frac{8 a \dilog \left(\frac{1}{2}+\frac{a x}{2}\right)}{3}+\frac{4 a \ln \left(a x -1\right) \ln \left(\frac{1}{2}+\frac{a x}{2}\right)}{3}+\frac{2 a \ln \left(a x +1\right)^{2}}{3}+\frac{4 a \ln \left(-\frac{a x}{2}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{a x}{2}\right)}{3}-\frac{4 a \ln \left(-\frac{a x}{2}+\frac{1}{2}\right) \ln \left(a x +1\right)}{3}"," ",0,"1/3*a^4*x^3*arctanh(a*x)^2-2*a^2*x*arctanh(a*x)^2-arctanh(a*x)^2/x+1/3*a^3*x^2*arctanh(a*x)+2*a*arctanh(a*x)*ln(a*x)-8/3*a*arctanh(a*x)*ln(a*x-1)-8/3*a*arctanh(a*x)*ln(a*x+1)+1/3*a^2*x+1/6*a*ln(a*x-1)-1/6*a*ln(a*x+1)-a*dilog(a*x)-a*dilog(a*x+1)-a*ln(a*x)*ln(a*x+1)-2/3*a*ln(a*x-1)^2+8/3*a*dilog(1/2+1/2*a*x)+4/3*a*ln(a*x-1)*ln(1/2+1/2*a*x)+2/3*a*ln(a*x+1)^2+4/3*a*ln(-1/2*a*x+1/2)*ln(1/2+1/2*a*x)-4/3*a*ln(-1/2*a*x+1/2)*ln(a*x+1)","A"
210,1,774,158,1.876000," ","int((-a^2*x^2+1)^2*arctanh(a*x)^2/x^3,x)","4 a^{2} \polylog \left(3, -\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)-a^{2} \polylog \left(3, -\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)-a^{2} \ln \left(1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)+a^{2} \ln \left(1+\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)+a^{2} \ln \left(\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}-1\right)-2 a^{2} \arctanh \left(a x \right)^{2} \ln \left(a x \right)+2 a^{2} \arctanh \left(a x \right)^{2} \ln \left(\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}-1\right)-2 a^{2} \arctanh \left(a x \right)^{2} \ln \left(1+\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)-2 a^{2} \arctanh \left(a x \right)^{2} \ln \left(1-\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)-4 a^{2} \arctanh \left(a x \right) \polylog \left(2, \frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)-4 a^{2} \arctanh \left(a x \right) \polylog \left(2, -\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)+2 a^{2} \arctanh \left(a x \right) \polylog \left(2, -\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)-i a^{2} \arctanh \left(a x \right)^{2} \pi  \mathrm{csgn}\left(\frac{i \left(\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}-1\right)}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right)^{3}-\frac{a \arctanh \left(a x \right)}{x}+i a^{2} \pi  \arctanh \left(a x \right)^{2} \mathrm{csgn}\left(i \left(\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}-1\right)\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}-1\right)}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right)^{2}+i a^{2} \pi  \,\mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}-1\right)}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right)^{2} \arctanh \left(a x \right)^{2}+4 a^{2} \polylog \left(3, \frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)-i a^{2} \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}-1\right)\right) \mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}-1\right)}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right) \arctanh \left(a x \right)^{2}+a^{3} x \arctanh \left(a x \right)+\frac{a^{4} x^{2} \arctanh \left(a x \right)^{2}}{2}-\frac{\arctanh \left(a x \right)^{2}}{2 x^{2}}"," ",0,"4*a^2*polylog(3,-(a*x+1)/(-a^2*x^2+1)^(1/2))-a^2*polylog(3,-(a*x+1)^2/(-a^2*x^2+1))-a^2*ln(1+(a*x+1)^2/(-a^2*x^2+1))+a^2*ln(1+(a*x+1)/(-a^2*x^2+1)^(1/2))+a^2*ln((a*x+1)/(-a^2*x^2+1)^(1/2)-1)-2*a^2*arctanh(a*x)^2*ln(a*x)+2*a^2*arctanh(a*x)^2*ln((a*x+1)^2/(-a^2*x^2+1)-1)-2*a^2*arctanh(a*x)^2*ln(1+(a*x+1)/(-a^2*x^2+1)^(1/2))-2*a^2*arctanh(a*x)^2*ln(1-(a*x+1)/(-a^2*x^2+1)^(1/2))-4*a^2*arctanh(a*x)*polylog(2,(a*x+1)/(-a^2*x^2+1)^(1/2))-4*a^2*arctanh(a*x)*polylog(2,-(a*x+1)/(-a^2*x^2+1)^(1/2))+2*a^2*arctanh(a*x)*polylog(2,-(a*x+1)^2/(-a^2*x^2+1))+I*a^2*Pi*arctanh(a*x)^2*csgn(I*((a*x+1)^2/(-a^2*x^2+1)-1))*csgn(I*((a*x+1)^2/(-a^2*x^2+1)-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2-a*arctanh(a*x)/x+I*a^2*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*((a*x+1)^2/(-a^2*x^2+1)-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*arctanh(a*x)^2-I*a^2*arctanh(a*x)^2*Pi*csgn(I*((a*x+1)^2/(-a^2*x^2+1)-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^3+4*a^2*polylog(3,(a*x+1)/(-a^2*x^2+1)^(1/2))-I*a^2*Pi*csgn(I*((a*x+1)^2/(-a^2*x^2+1)-1))*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*((a*x+1)^2/(-a^2*x^2+1)-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))*arctanh(a*x)^2+a^3*x*arctanh(a*x)+1/2*a^4*x^2*arctanh(a*x)^2-1/2*arctanh(a*x)^2/x^2","C"
211,1,249,153,0.069000," ","int((-a^2*x^2+1)^2*arctanh(a*x)^2/x^4,x)","a^{4} x \arctanh \left(a x \right)^{2}+\frac{2 a^{2} \arctanh \left(a x \right)^{2}}{x}-\frac{\arctanh \left(a x \right)^{2}}{3 x^{3}}-\frac{a \arctanh \left(a x \right)}{3 x^{2}}-\frac{10 a^{3} \arctanh \left(a x \right) \ln \left(a x \right)}{3}+\frac{8 a^{3} \arctanh \left(a x \right) \ln \left(a x -1\right)}{3}+\frac{8 a^{3} \arctanh \left(a x \right) \ln \left(a x +1\right)}{3}-\frac{a^{2}}{3 x}-\frac{a^{3} \ln \left(a x -1\right)}{6}+\frac{a^{3} \ln \left(a x +1\right)}{6}+\frac{5 a^{3} \dilog \left(a x \right)}{3}+\frac{5 a^{3} \dilog \left(a x +1\right)}{3}+\frac{5 a^{3} \ln \left(a x \right) \ln \left(a x +1\right)}{3}+\frac{2 a^{3} \ln \left(a x -1\right)^{2}}{3}-\frac{8 a^{3} \dilog \left(\frac{1}{2}+\frac{a x}{2}\right)}{3}-\frac{4 a^{3} \ln \left(a x -1\right) \ln \left(\frac{1}{2}+\frac{a x}{2}\right)}{3}-\frac{2 a^{3} \ln \left(a x +1\right)^{2}}{3}-\frac{4 a^{3} \ln \left(-\frac{a x}{2}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{a x}{2}\right)}{3}+\frac{4 a^{3} \ln \left(-\frac{a x}{2}+\frac{1}{2}\right) \ln \left(a x +1\right)}{3}"," ",0,"a^4*x*arctanh(a*x)^2+2*a^2*arctanh(a*x)^2/x-1/3*arctanh(a*x)^2/x^3-1/3*a*arctanh(a*x)/x^2-10/3*a^3*arctanh(a*x)*ln(a*x)+8/3*a^3*arctanh(a*x)*ln(a*x-1)+8/3*a^3*arctanh(a*x)*ln(a*x+1)-1/3*a^2/x-1/6*a^3*ln(a*x-1)+1/6*a^3*ln(a*x+1)+5/3*a^3*dilog(a*x)+5/3*a^3*dilog(a*x+1)+5/3*a^3*ln(a*x)*ln(a*x+1)+2/3*a^3*ln(a*x-1)^2-8/3*a^3*dilog(1/2+1/2*a*x)-4/3*a^3*ln(a*x-1)*ln(1/2+1/2*a*x)-2/3*a^3*ln(a*x+1)^2-4/3*a^3*ln(-1/2*a*x+1/2)*ln(1/2+1/2*a*x)+4/3*a^3*ln(-1/2*a*x+1/2)*ln(a*x+1)","A"
212,1,927,196,2.755000," ","int((-a^2*x^2+1)^2*arctanh(a*x)^2/x^5,x)","\frac{3 a^{3} \arctanh \left(a x \right)}{2 x}+\frac{a^{2} \arctanh \left(a x \right)^{2}}{x^{2}}-\frac{a \arctanh \left(a x \right)}{6 x^{3}}+a^{4} \arctanh \left(a x \right)^{2} \ln \left(a x \right)-a^{4} \arctanh \left(a x \right)^{2} \ln \left(\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}-1\right)+a^{4} \arctanh \left(a x \right)^{2} \ln \left(1-\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)+2 a^{4} \arctanh \left(a x \right) \polylog \left(2, \frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)+a^{4} \arctanh \left(a x \right)^{2} \ln \left(1+\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)+2 a^{4} \arctanh \left(a x \right) \polylog \left(2, -\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)-a^{4} \arctanh \left(a x \right) \polylog \left(2, -\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)+\frac{i a^{4} \arctanh \left(a x \right)^{2} \pi  \mathrm{csgn}\left(\frac{i \left(\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}-1\right)}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right)^{3}}{2}+\frac{a^{4}}{24 \sqrt{-a^{2} x^{2}+1}-24}-\frac{i a^{4} \arctanh \left(a x \right)^{2} \pi  \,\mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}-1\right)}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right)^{2}}{2}-\frac{i a^{4} \arctanh \left(a x \right)^{2} \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}-1\right)\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}-1\right)}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right)^{2}}{2}-\frac{3 a^{4} \arctanh \left(a x \right)^{2}}{4}-\frac{\arctanh \left(a x \right)^{2}}{4 x^{4}}-2 a^{4} \polylog \left(3, \frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)+\frac{4 a^{4} \arctanh \left(a x \right)}{3}-2 a^{4} \polylog \left(3, -\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)+\frac{a^{4} \polylog \left(3, -\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}{2}+\frac{a^{4} \sqrt{-a^{2} x^{2}+1}}{12 \sqrt{-a^{2} x^{2}+1}+12 a x +12}+\frac{a^{5} x}{24 \sqrt{-a^{2} x^{2}+1}+24}-\frac{a^{4} \sqrt{-a^{2} x^{2}+1}}{12 \left(a x +1-\sqrt{-a^{2} x^{2}+1}\right)}-\frac{a^{5} x}{24 \left(\sqrt{-a^{2} x^{2}+1}-1\right)}+\frac{i a^{4} \arctanh \left(a x \right)^{2} \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}-1\right)\right) \mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}-1\right)}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right)}{2}-\frac{4 a^{4} \ln \left(1+\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{3}-\frac{4 a^{4} \ln \left(\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}-1\right)}{3}-\frac{a^{4}}{24 \left(\sqrt{-a^{2} x^{2}+1}+1\right)}"," ",0,"-3/4*a^4*arctanh(a*x)^2-1/4*arctanh(a*x)^2/x^4+a^2*arctanh(a*x)^2/x^2-2*a^4*polylog(3,(a*x+1)/(-a^2*x^2+1)^(1/2))-1/6*a*arctanh(a*x)/x^3+3/2*a^3*arctanh(a*x)/x-1/2*I*a^4*arctanh(a*x)^2*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*((a*x+1)^2/(-a^2*x^2+1)-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2-1/2*I*a^4*arctanh(a*x)^2*Pi*csgn(I*((a*x+1)^2/(-a^2*x^2+1)-1))*csgn(I*((a*x+1)^2/(-a^2*x^2+1)-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2+4/3*a^4*arctanh(a*x)+1/2*I*a^4*arctanh(a*x)^2*Pi*csgn(I*((a*x+1)^2/(-a^2*x^2+1)-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^3+a^4*arctanh(a*x)^2*ln(a*x)-a^4*arctanh(a*x)^2*ln((a*x+1)^2/(-a^2*x^2+1)-1)+a^4*arctanh(a*x)^2*ln(1-(a*x+1)/(-a^2*x^2+1)^(1/2))+2*a^4*arctanh(a*x)*polylog(2,(a*x+1)/(-a^2*x^2+1)^(1/2))+a^4*arctanh(a*x)^2*ln(1+(a*x+1)/(-a^2*x^2+1)^(1/2))+2*a^4*arctanh(a*x)*polylog(2,-(a*x+1)/(-a^2*x^2+1)^(1/2))-a^4*arctanh(a*x)*polylog(2,-(a*x+1)^2/(-a^2*x^2+1))-1/12*a^4/(a*x+1-(-a^2*x^2+1)^(1/2))*(-a^2*x^2+1)^(1/2)+1/12*a^4/((-a^2*x^2+1)^(1/2)+a*x+1)*(-a^2*x^2+1)^(1/2)-1/24*a^5/((-a^2*x^2+1)^(1/2)-1)*x+1/24*a^5/((-a^2*x^2+1)^(1/2)+1)*x+1/2*I*a^4*arctanh(a*x)^2*Pi*csgn(I*((a*x+1)^2/(-a^2*x^2+1)-1))*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*((a*x+1)^2/(-a^2*x^2+1)-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))-4/3*a^4*ln(1+(a*x+1)/(-a^2*x^2+1)^(1/2))-2*a^4*polylog(3,-(a*x+1)/(-a^2*x^2+1)^(1/2))+1/2*a^4*polylog(3,-(a*x+1)^2/(-a^2*x^2+1))-4/3*a^4*ln((a*x+1)/(-a^2*x^2+1)^(1/2)-1)+1/24*a^4/((-a^2*x^2+1)^(1/2)-1)-1/24*a^4/((-a^2*x^2+1)^(1/2)+1)","C"
213,1,272,137,0.071000," ","int((-a^2*x^2+1)^2*arctanh(a*x)^2/x^6,x)","-\frac{a^{4} \arctanh \left(a x \right)^{2}}{x}+\frac{2 a^{2} \arctanh \left(a x \right)^{2}}{3 x^{3}}-\frac{\arctanh \left(a x \right)^{2}}{5 x^{5}}-\frac{a \arctanh \left(a x \right)}{10 x^{4}}+\frac{7 a^{3} \arctanh \left(a x \right)}{15 x^{2}}+\frac{16 a^{5} \arctanh \left(a x \right) \ln \left(a x \right)}{15}-\frac{8 a^{5} \arctanh \left(a x \right) \ln \left(a x -1\right)}{15}-\frac{8 a^{5} \arctanh \left(a x \right) \ln \left(a x +1\right)}{15}-\frac{a^{2}}{30 x^{3}}+\frac{11 a^{4}}{30 x}+\frac{11 a^{5} \ln \left(a x -1\right)}{60}-\frac{11 a^{5} \ln \left(a x +1\right)}{60}-\frac{8 a^{5} \dilog \left(a x \right)}{15}-\frac{8 a^{5} \dilog \left(a x +1\right)}{15}-\frac{8 a^{5} \ln \left(a x \right) \ln \left(a x +1\right)}{15}-\frac{2 a^{5} \ln \left(a x -1\right)^{2}}{15}+\frac{8 a^{5} \dilog \left(\frac{1}{2}+\frac{a x}{2}\right)}{15}+\frac{4 a^{5} \ln \left(a x -1\right) \ln \left(\frac{1}{2}+\frac{a x}{2}\right)}{15}+\frac{2 a^{5} \ln \left(a x +1\right)^{2}}{15}-\frac{4 a^{5} \ln \left(-\frac{a x}{2}+\frac{1}{2}\right) \ln \left(a x +1\right)}{15}+\frac{4 a^{5} \ln \left(-\frac{a x}{2}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{a x}{2}\right)}{15}"," ",0,"-a^4*arctanh(a*x)^2/x+2/3*a^2*arctanh(a*x)^2/x^3-1/5*arctanh(a*x)^2/x^5-1/10*a*arctanh(a*x)/x^4+7/15*a^3*arctanh(a*x)/x^2+16/15*a^5*arctanh(a*x)*ln(a*x)-8/15*a^5*arctanh(a*x)*ln(a*x-1)-8/15*a^5*arctanh(a*x)*ln(a*x+1)-1/30*a^2/x^3+11/30*a^4/x+11/60*a^5*ln(a*x-1)-11/60*a^5*ln(a*x+1)-8/15*a^5*dilog(a*x)-8/15*a^5*dilog(a*x+1)-8/15*a^5*ln(a*x)*ln(a*x+1)-2/15*a^5*ln(a*x-1)^2+8/15*a^5*dilog(1/2+1/2*a*x)+4/15*a^5*ln(a*x-1)*ln(1/2+1/2*a*x)+2/15*a^5*ln(a*x+1)^2-4/15*a^5*ln(-1/2*a*x+1/2)*ln(a*x+1)+4/15*a^5*ln(-1/2*a*x+1/2)*ln(1/2+1/2*a*x)","A"
214,1,233,97,0.067000," ","int((-a^2*x^2+1)^2*arctanh(a*x)^2/x^7,x)","-\frac{a^{4} \arctanh \left(a x \right)^{2}}{2 x^{2}}+\frac{a^{2} \arctanh \left(a x \right)^{2}}{2 x^{4}}-\frac{\arctanh \left(a x \right)^{2}}{6 x^{6}}-\frac{a \arctanh \left(a x \right)}{15 x^{5}}+\frac{2 a^{3} \arctanh \left(a x \right)}{9 x^{3}}-\frac{a^{5} \arctanh \left(a x \right)}{3 x}-\frac{a^{6} \arctanh \left(a x \right) \ln \left(a x -1\right)}{6}+\frac{a^{6} \arctanh \left(a x \right) \ln \left(a x +1\right)}{6}-\frac{a^{6} \ln \left(a x -1\right)^{2}}{24}+\frac{a^{6} \ln \left(a x -1\right) \ln \left(\frac{1}{2}+\frac{a x}{2}\right)}{12}-\frac{a^{6} \ln \left(a x +1\right)^{2}}{24}-\frac{a^{6} \ln \left(-\frac{a x}{2}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{a x}{2}\right)}{12}+\frac{a^{6} \ln \left(-\frac{a x}{2}+\frac{1}{2}\right) \ln \left(a x +1\right)}{12}-\frac{a^{2}}{60 x^{4}}+\frac{7 a^{4}}{90 x^{2}}+\frac{8 a^{6} \ln \left(a x \right)}{45}-\frac{4 a^{6} \ln \left(a x -1\right)}{45}-\frac{4 a^{6} \ln \left(a x +1\right)}{45}"," ",0,"-1/2*a^4*arctanh(a*x)^2/x^2+1/2*a^2*arctanh(a*x)^2/x^4-1/6*arctanh(a*x)^2/x^6-1/15*a*arctanh(a*x)/x^5+2/9*a^3*arctanh(a*x)/x^3-1/3*a^5*arctanh(a*x)/x-1/6*a^6*arctanh(a*x)*ln(a*x-1)+1/6*a^6*arctanh(a*x)*ln(a*x+1)-1/24*a^6*ln(a*x-1)^2+1/12*a^6*ln(a*x-1)*ln(1/2+1/2*a*x)-1/24*a^6*ln(a*x+1)^2-1/12*a^6*ln(-1/2*a*x+1/2)*ln(1/2+1/2*a*x)+1/12*a^6*ln(-1/2*a*x+1/2)*ln(a*x+1)-1/60*a^2/x^4+7/90*a^4/x^2+8/45*a^6*ln(a*x)-4/45*a^6*ln(a*x-1)-4/45*a^6*ln(a*x+1)","B"
215,1,292,157,0.072000," ","int((-a^2*x^2+1)^2*arctanh(a*x)^2/x^8,x)","-\frac{a^{4} \arctanh \left(a x \right)^{2}}{3 x^{3}}-\frac{\arctanh \left(a x \right)^{2}}{7 x^{7}}+\frac{2 a^{2} \arctanh \left(a x \right)^{2}}{5 x^{5}}-\frac{a \arctanh \left(a x \right)}{21 x^{6}}+\frac{9 a^{3} \arctanh \left(a x \right)}{70 x^{4}}-\frac{8 a^{5} \arctanh \left(a x \right)}{105 x^{2}}+\frac{16 a^{7} \arctanh \left(a x \right) \ln \left(a x \right)}{105}-\frac{8 a^{7} \arctanh \left(a x \right) \ln \left(a x -1\right)}{105}-\frac{8 a^{7} \arctanh \left(a x \right) \ln \left(a x +1\right)}{105}-\frac{8 a^{7} \dilog \left(a x \right)}{105}-\frac{8 a^{7} \dilog \left(a x +1\right)}{105}-\frac{8 a^{7} \ln \left(a x \right) \ln \left(a x +1\right)}{105}-\frac{2 a^{7} \ln \left(a x -1\right)^{2}}{105}+\frac{8 a^{7} \dilog \left(\frac{1}{2}+\frac{a x}{2}\right)}{105}+\frac{4 a^{7} \ln \left(a x -1\right) \ln \left(\frac{1}{2}+\frac{a x}{2}\right)}{105}+\frac{2 a^{7} \ln \left(a x +1\right)^{2}}{105}+\frac{4 a^{7} \ln \left(-\frac{a x}{2}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{a x}{2}\right)}{105}-\frac{4 a^{7} \ln \left(-\frac{a x}{2}+\frac{1}{2}\right) \ln \left(a x +1\right)}{105}+\frac{a^{6}}{210 x}-\frac{a^{2}}{105 x^{5}}+\frac{17 a^{4}}{630 x^{3}}+\frac{a^{7} \ln \left(a x -1\right)}{420}-\frac{a^{7} \ln \left(a x +1\right)}{420}"," ",0,"-1/3*a^4*arctanh(a*x)^2/x^3-1/7*arctanh(a*x)^2/x^7+2/5*a^2*arctanh(a*x)^2/x^5-1/21*a*arctanh(a*x)/x^6+9/70*a^3*arctanh(a*x)/x^4-8/105*a^5*arctanh(a*x)/x^2+16/105*a^7*arctanh(a*x)*ln(a*x)-8/105*a^7*arctanh(a*x)*ln(a*x-1)-8/105*a^7*arctanh(a*x)*ln(a*x+1)-8/105*a^7*dilog(a*x)-8/105*a^7*dilog(a*x+1)-8/105*a^7*ln(a*x)*ln(a*x+1)-2/105*a^7*ln(a*x-1)^2+8/105*a^7*dilog(1/2+1/2*a*x)+4/105*a^7*ln(a*x-1)*ln(1/2+1/2*a*x)+2/105*a^7*ln(a*x+1)^2+4/105*a^7*ln(-1/2*a*x+1/2)*ln(1/2+1/2*a*x)-4/105*a^7*ln(-1/2*a*x+1/2)*ln(a*x+1)+1/210*a^6/x-1/105*a^2/x^5+17/630*a^4/x^3+1/420*a^7*ln(a*x-1)-1/420*a^7*ln(a*x+1)","A"
216,1,253,144,0.071000," ","int((-a^2*x^2+1)^2*arctanh(a*x)^2/x^9,x)","-\frac{\arctanh \left(a x \right)^{2}}{8 x^{8}}-\frac{a^{4} \arctanh \left(a x \right)^{2}}{4 x^{4}}+\frac{a^{2} \arctanh \left(a x \right)^{2}}{3 x^{6}}-\frac{a \arctanh \left(a x \right)}{28 x^{7}}+\frac{a^{3} \arctanh \left(a x \right)}{12 x^{5}}-\frac{a^{5} \arctanh \left(a x \right)}{36 x^{3}}-\frac{a^{7} \arctanh \left(a x \right)}{12 x}-\frac{a^{8} \arctanh \left(a x \right) \ln \left(a x -1\right)}{24}+\frac{a^{8} \arctanh \left(a x \right) \ln \left(a x +1\right)}{24}-\frac{a^{8} \ln \left(a x -1\right)^{2}}{96}+\frac{a^{8} \ln \left(a x -1\right) \ln \left(\frac{1}{2}+\frac{a x}{2}\right)}{48}-\frac{a^{8} \ln \left(a x +1\right)^{2}}{96}-\frac{a^{8} \ln \left(-\frac{a x}{2}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{a x}{2}\right)}{48}+\frac{a^{8} \ln \left(-\frac{a x}{2}+\frac{1}{2}\right) \ln \left(a x +1\right)}{48}-\frac{a^{2}}{168 x^{6}}+\frac{a^{4}}{84 x^{4}}+\frac{5 a^{6}}{504 x^{2}}+\frac{4 a^{8} \ln \left(a x \right)}{63}-\frac{2 a^{8} \ln \left(a x -1\right)}{63}-\frac{2 a^{8} \ln \left(a x +1\right)}{63}"," ",0,"-1/8*arctanh(a*x)^2/x^8-1/4*a^4*arctanh(a*x)^2/x^4+1/3*a^2*arctanh(a*x)^2/x^6-1/28*a*arctanh(a*x)/x^7+1/12*a^3*arctanh(a*x)/x^5-1/36*a^5*arctanh(a*x)/x^3-1/12*a^7*arctanh(a*x)/x-1/24*a^8*arctanh(a*x)*ln(a*x-1)+1/24*a^8*arctanh(a*x)*ln(a*x+1)-1/96*a^8*ln(a*x-1)^2+1/48*a^8*ln(a*x-1)*ln(1/2+1/2*a*x)-1/96*a^8*ln(a*x+1)^2-1/48*a^8*ln(-1/2*a*x+1/2)*ln(1/2+1/2*a*x)+1/48*a^8*ln(-1/2*a*x+1/2)*ln(a*x+1)-1/168*a^2/x^6+1/84*a^4/x^4+5/504*a^6/x^2+4/63*a^8*ln(a*x)-2/63*a^8*ln(a*x-1)-2/63*a^8*ln(a*x+1)","A"
217,1,883,223,2.464000," ","int((-a^2*x^2+1)^2*arctanh(a*x)^3,x)","\frac{8 \arctanh \left(a x \right)^{3}}{15 a}-\frac{1}{20 a}+\frac{4 i \arctanh \left(a x \right)^{2} \mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right)^{2} \pi}{5 a}+\frac{\ln \left(1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}{a}-\frac{2 a^{2} \arctanh \left(a x \right)^{3} x^{3}}{3}-\frac{8 \arctanh \left(a x \right)^{2} \ln \left(\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{5 a}+\frac{a \,x^{2}}{20}-\frac{2 i \arctanh \left(a x \right)^{2} \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{\left(a^{2} x^{2}-1\right) \left(1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}\right)^{3} \pi}{5 a}+\frac{2 i \arctanh \left(a x \right)^{2} \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right) \mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{\left(a^{2} x^{2}-1\right) \left(1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}\right) \pi}{5 a}-\frac{7 a \arctanh \left(a x \right)^{2} x^{2}}{10}+\frac{4 \arctanh \left(a x \right)^{2} \ln \left(a x -1\right)}{5 a}+\frac{4 \arctanh \left(a x \right)^{2} \ln \left(a x +1\right)}{5 a}-\frac{8 \arctanh \left(a x \right)^{2} \ln \left(2\right)}{5 a}-\frac{8 \arctanh \left(a x \right) \polylog \left(2, -\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}{5 a}+\frac{a^{4} \arctanh \left(a x \right)^{3} x^{5}}{5}+\frac{a^{2} \arctanh \left(a x \right) x^{3}}{10}+\frac{3 a^{3} \arctanh \left(a x \right)^{2} x^{4}}{20}-\frac{2 i \arctanh \left(a x \right)^{2} \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right)^{3} \pi}{5 a}-\frac{4 i \arctanh \left(a x \right)^{2} \mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right)^{3} \pi}{5 a}+\frac{2 i \arctanh \left(a x \right)^{2} \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right) \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{\left(a^{2} x^{2}-1\right) \left(1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}\right)^{2} \pi}{5 a}-\frac{4 i \arctanh \left(a x \right)^{2} \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right)^{2} \mathrm{csgn}\left(\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right) \pi}{5 a}-\frac{2 i \arctanh \left(a x \right)^{2} \mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{\left(a^{2} x^{2}-1\right) \left(1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}\right)^{2} \pi}{5 a}-\frac{2 i \arctanh \left(a x \right)^{2} \mathrm{csgn}\left(\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right)^{2} \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right) \pi}{5 a}+\frac{4 \polylog \left(3, -\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}{5 a}-\frac{\arctanh \left(a x \right)}{a}+\frac{11 \arctanh \left(a x \right)^{2}}{20 a}+x \arctanh \left(a x \right)^{3}-\frac{11 x \arctanh \left(a x \right)}{10}-\frac{4 i \arctanh \left(a x \right)^{2} \pi}{5 a}"," ",0,"-2/3*a^2*arctanh(a*x)^3*x^3-7/10*a*arctanh(a*x)^2*x^2-1/20/a+1/a*ln(1+(a*x+1)^2/(-a^2*x^2+1))+4/5/a*polylog(3,-(a*x+1)^2/(-a^2*x^2+1))+1/20*a*x^2-arctanh(a*x)/a+4/5/a*arctanh(a*x)^2*ln(a*x-1)+4/5/a*arctanh(a*x)^2*ln(a*x+1)-8/5/a*arctanh(a*x)^2*ln((a*x+1)/(-a^2*x^2+1)^(1/2))+11/20*arctanh(a*x)^2/a+8/15*arctanh(a*x)^3/a+x*arctanh(a*x)^3-11/10*x*arctanh(a*x)-8/5/a*arctanh(a*x)^2*ln(2)-8/5/a*arctanh(a*x)*polylog(2,-(a*x+1)^2/(-a^2*x^2+1))+2/5*I/a*arctanh(a*x)^2*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*(a*x+1)^2/(a^2*x^2-1))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))*Pi-4/5*I/a*arctanh(a*x)^2*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))^3*Pi-2/5*I/a*arctanh(a*x)^2*csgn(I*(a*x+1)^2/(a^2*x^2-1))^3*Pi-2/5*I/a*arctanh(a*x)^2*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^3*Pi+4/5*I/a*arctanh(a*x)^2*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*Pi+2/5*I/a*arctanh(a*x)^2*csgn(I*(a*x+1)^2/(a^2*x^2-1))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*Pi-4/5*I/a*arctanh(a*x)^2*csgn(I*(a*x+1)^2/(a^2*x^2-1))^2*csgn(I*(a*x+1)/(-a^2*x^2+1)^(1/2))*Pi-2/5*I/a*arctanh(a*x)^2*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*Pi-2/5*I/a*arctanh(a*x)^2*csgn(I*(a*x+1)^2/(a^2*x^2-1))*csgn(I*(a*x+1)/(-a^2*x^2+1)^(1/2))^2*Pi+1/5*a^4*arctanh(a*x)^3*x^5+1/10*a^2*arctanh(a*x)*x^3+3/20*a^3*arctanh(a*x)^2*x^4-4/5*I/a*arctanh(a*x)^2*Pi","C"
218,0,0,22,0.784000," ","int(x*(-a^2*x^2+1)^2/arctanh(a*x),x)","\int \frac{x \left(-a^{2} x^{2}+1\right)^{2}}{\arctanh \left(a x \right)}\, dx"," ",0,"int(x*(-a^2*x^2+1)^2/arctanh(a*x),x)","F"
219,0,0,21,0.758000," ","int((-a^2*x^2+1)^2/arctanh(a*x),x)","\int \frac{\left(-a^{2} x^{2}+1\right)^{2}}{\arctanh \left(a x \right)}\, dx"," ",0,"int((-a^2*x^2+1)^2/arctanh(a*x),x)","F"
220,0,0,24,0.948000," ","int((-a^2*x^2+1)^2/x/arctanh(a*x),x)","\int \frac{\left(-a^{2} x^{2}+1\right)^{2}}{x \arctanh \left(a x \right)}\, dx"," ",0,"int((-a^2*x^2+1)^2/x/arctanh(a*x),x)","F"
221,0,0,22,0.795000," ","int(x*(-a^2*x^2+1)^2/arctanh(a*x)^2,x)","\int \frac{x \left(-a^{2} x^{2}+1\right)^{2}}{\arctanh \left(a x \right)^{2}}\, dx"," ",0,"int(x*(-a^2*x^2+1)^2/arctanh(a*x)^2,x)","F"
222,0,0,21,0.883000," ","int((-a^2*x^2+1)^2/arctanh(a*x)^2,x)","\int \frac{\left(-a^{2} x^{2}+1\right)^{2}}{\arctanh \left(a x \right)^{2}}\, dx"," ",0,"int((-a^2*x^2+1)^2/arctanh(a*x)^2,x)","F"
223,0,0,24,0.913000," ","int((-a^2*x^2+1)^2/x/arctanh(a*x)^2,x)","\int \frac{\left(-a^{2} x^{2}+1\right)^{2}}{x \arctanh \left(a x \right)^{2}}\, dx"," ",0,"int((-a^2*x^2+1)^2/x/arctanh(a*x)^2,x)","F"
224,1,88,128,0.028000," ","int((-a^2*x^2+1)^3*arctanh(a*x),x)","-\frac{a^{6} \arctanh \left(a x \right) x^{7}}{7}+\frac{3 a^{4} \arctanh \left(a x \right) x^{5}}{5}-a^{2} \arctanh \left(a x \right) x^{3}+x \arctanh \left(a x \right)-\frac{a^{5} x^{6}}{42}+\frac{4 x^{4} a^{3}}{35}-\frac{19 a \,x^{2}}{70}+\frac{8 \ln \left(a x -1\right)}{35 a}+\frac{8 \ln \left(a x +1\right)}{35 a}"," ",0,"-1/7*a^6*arctanh(a*x)*x^7+3/5*a^4*arctanh(a*x)*x^5-a^2*arctanh(a*x)*x^3+x*arctanh(a*x)-1/42*a^5*x^6+4/35*x^4*a^3-19/70*a*x^2+8/35/a*ln(a*x-1)+8/35/a*ln(a*x+1)","A"
225,1,250,201,0.056000," ","int((-a^2*x^2+1)^3*arctanh(a*x)^2,x)","-\frac{a^{6} \arctanh \left(a x \right)^{2} x^{7}}{7}+\frac{3 a^{4} \arctanh \left(a x \right)^{2} x^{5}}{5}-a^{2} \arctanh \left(a x \right)^{2} x^{3}+x \arctanh \left(a x \right)^{2}-\frac{a^{5} \arctanh \left(a x \right) x^{6}}{21}+\frac{8 a^{3} \arctanh \left(a x \right) x^{4}}{35}-\frac{19 a \arctanh \left(a x \right) x^{2}}{35}+\frac{16 \arctanh \left(a x \right) \ln \left(a x -1\right)}{35 a}+\frac{16 \arctanh \left(a x \right) \ln \left(a x +1\right)}{35 a}+\frac{4 \ln \left(a x -1\right)^{2}}{35 a}-\frac{16 \dilog \left(\frac{1}{2}+\frac{a x}{2}\right)}{35 a}-\frac{8 \ln \left(a x -1\right) \ln \left(\frac{1}{2}+\frac{a x}{2}\right)}{35 a}-\frac{4 \ln \left(a x +1\right)^{2}}{35 a}+\frac{8 \ln \left(-\frac{a x}{2}+\frac{1}{2}\right) \ln \left(a x +1\right)}{35 a}-\frac{8 \ln \left(-\frac{a x}{2}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{a x}{2}\right)}{35 a}-\frac{a^{4} x^{5}}{105}+\frac{19 x^{3} a^{2}}{315}-\frac{38 x}{105}-\frac{19 \ln \left(a x -1\right)}{105 a}+\frac{19 \ln \left(a x +1\right)}{105 a}"," ",0,"-1/7*a^6*arctanh(a*x)^2*x^7+3/5*a^4*arctanh(a*x)^2*x^5-a^2*arctanh(a*x)^2*x^3+x*arctanh(a*x)^2-1/21*a^5*arctanh(a*x)*x^6+8/35*a^3*arctanh(a*x)*x^4-19/35*a*arctanh(a*x)*x^2+16/35/a*arctanh(a*x)*ln(a*x-1)+16/35/a*arctanh(a*x)*ln(a*x+1)+4/35/a*ln(a*x-1)^2-16/35/a*dilog(1/2+1/2*a*x)-8/35/a*ln(a*x-1)*ln(1/2+1/2*a*x)-4/35/a*ln(a*x+1)^2+8/35/a*ln(-1/2*a*x+1/2)*ln(a*x+1)-8/35/a*ln(-1/2*a*x+1/2)*ln(1/2+1/2*a*x)-1/105*a^4*x^5+19/315*x^3*a^2-38/105*x-19/105/a*ln(a*x-1)+19/105/a*ln(a*x+1)","A"
226,1,932,304,5.397000," ","int((-a^2*x^2+1)^3*arctanh(a*x)^3,x)","\frac{16 \arctanh \left(a x \right)^{3}}{35 a}-\frac{a^{4} \arctanh \left(a x \right) x^{5}}{35}-\frac{29}{420 a}+\frac{24 i \arctanh \left(a x \right)^{2} \mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right)^{2} \pi}{35 a}+\frac{14 \ln \left(1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}{15 a}-a^{2} \arctanh \left(a x \right)^{3} x^{3}-\frac{48 \arctanh \left(a x \right)^{2} \ln \left(\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{35 a}+\frac{8 a \,x^{2}}{105}-\frac{12 i \arctanh \left(a x \right)^{2} \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{\left(a^{2} x^{2}-1\right) \left(1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}\right)^{3} \pi}{35 a}+\frac{12 i \arctanh \left(a x \right)^{2} \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right) \mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{\left(a^{2} x^{2}-1\right) \left(1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}\right) \pi}{35 a}-\frac{x^{4} a^{3}}{140}-\frac{57 a \arctanh \left(a x \right)^{2} x^{2}}{70}+\frac{24 \arctanh \left(a x \right)^{2} \ln \left(a x -1\right)}{35 a}+\frac{24 \arctanh \left(a x \right)^{2} \ln \left(a x +1\right)}{35 a}-\frac{48 \arctanh \left(a x \right)^{2} \ln \left(2\right)}{35 a}-\frac{48 \arctanh \left(a x \right) \polylog \left(2, -\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}{35 a}+\frac{19 a^{2} \arctanh \left(a x \right) x^{3}}{105}+\frac{12 a^{3} \arctanh \left(a x \right)^{2} x^{4}}{35}-\frac{12 i \arctanh \left(a x \right)^{2} \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right)^{3} \pi}{35 a}-\frac{24 i \arctanh \left(a x \right)^{2} \mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right)^{3} \pi}{35 a}+\frac{12 i \pi  \,\mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right) \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{\left(a^{2} x^{2}-1\right) \left(1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}\right)^{2} \arctanh \left(a x \right)^{2}}{35 a}-\frac{24 i \arctanh \left(a x \right)^{2} \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right)^{2} \mathrm{csgn}\left(\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right) \pi}{35 a}-\frac{12 i \arctanh \left(a x \right)^{2} \mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{\left(a^{2} x^{2}-1\right) \left(1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}\right)^{2} \pi}{35 a}-\frac{12 i \arctanh \left(a x \right)^{2} \mathrm{csgn}\left(\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right)^{2} \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right) \pi}{35 a}+\frac{3 a^{4} \arctanh \left(a x \right)^{3} x^{5}}{5}-\frac{a^{6} \arctanh \left(a x \right)^{3} x^{7}}{7}-\frac{a^{5} \arctanh \left(a x \right)^{2} x^{6}}{14}+\frac{24 \polylog \left(3, -\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}{35 a}-\frac{14 \arctanh \left(a x \right)}{15 a}+\frac{19 \arctanh \left(a x \right)^{2}}{35 a}+x \arctanh \left(a x \right)^{3}-\frac{38 x \arctanh \left(a x \right)}{35}-\frac{24 i \arctanh \left(a x \right)^{2} \pi}{35 a}"," ",0,"-a^2*arctanh(a*x)^3*x^3-57/70*a*arctanh(a*x)^2*x^2-1/35*a^4*arctanh(a*x)*x^5-29/420/a+14/15/a*ln(1+(a*x+1)^2/(-a^2*x^2+1))+24/35/a*polylog(3,-(a*x+1)^2/(-a^2*x^2+1))+8/105*a*x^2-14/15*arctanh(a*x)/a+24/35/a*arctanh(a*x)^2*ln(a*x-1)+24/35/a*arctanh(a*x)^2*ln(a*x+1)-48/35/a*arctanh(a*x)^2*ln((a*x+1)/(-a^2*x^2+1)^(1/2))-1/140*x^4*a^3+19/35*arctanh(a*x)^2/a+16/35*arctanh(a*x)^3/a+x*arctanh(a*x)^3-38/35*x*arctanh(a*x)-48/35/a*arctanh(a*x)^2*ln(2)-48/35/a*arctanh(a*x)*polylog(2,-(a*x+1)^2/(-a^2*x^2+1))-12/35*I/a*Pi*csgn(I*(a*x+1)/(-a^2*x^2+1)^(1/2))^2*csgn(I*(a*x+1)^2/(a^2*x^2-1))*arctanh(a*x)^2+12/35*I/a*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*arctanh(a*x)^2-12/35*I/a*arctanh(a*x)^2*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2-24/35*I/a*arctanh(a*x)^2*Pi*csgn(I*(a*x+1)/(-a^2*x^2+1)^(1/2))*csgn(I*(a*x+1)^2/(a^2*x^2-1))^2-24/35*I/a*Pi*arctanh(a*x)^2+12/35*I/a*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*(a*x+1)^2/(a^2*x^2-1))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))*arctanh(a*x)^2+3/5*a^4*arctanh(a*x)^3*x^5+19/105*a^2*arctanh(a*x)*x^3+12/35*a^3*arctanh(a*x)^2*x^4+24/35*I/a*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*arctanh(a*x)^2-24/35*I/a*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))^3*arctanh(a*x)^2-12/35*I/a*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^3*arctanh(a*x)^2-12/35*I/a*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1))^3*arctanh(a*x)^2-1/7*a^6*arctanh(a*x)^3*x^7-1/14*a^5*arctanh(a*x)^2*x^6","C"
227,1,165,77,0.056000," ","int(x^3*arctanh(a*x)/(-a^2*x^2+1),x)","-\frac{x^{2} \arctanh \left(a x \right)}{2 a^{2}}-\frac{\arctanh \left(a x \right) \ln \left(a x -1\right)}{2 a^{4}}-\frac{\arctanh \left(a x \right) \ln \left(a x +1\right)}{2 a^{4}}-\frac{x}{2 a^{3}}-\frac{\ln \left(a x -1\right)}{4 a^{4}}+\frac{\ln \left(a x +1\right)}{4 a^{4}}-\frac{\ln \left(a x -1\right)^{2}}{8 a^{4}}+\frac{\dilog \left(\frac{1}{2}+\frac{a x}{2}\right)}{2 a^{4}}+\frac{\ln \left(a x -1\right) \ln \left(\frac{1}{2}+\frac{a x}{2}\right)}{4 a^{4}}+\frac{\ln \left(a x +1\right)^{2}}{8 a^{4}}-\frac{\ln \left(-\frac{a x}{2}+\frac{1}{2}\right) \ln \left(a x +1\right)}{4 a^{4}}+\frac{\ln \left(-\frac{a x}{2}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{a x}{2}\right)}{4 a^{4}}"," ",0,"-1/2*x^2*arctanh(a*x)/a^2-1/2/a^4*arctanh(a*x)*ln(a*x-1)-1/2/a^4*arctanh(a*x)*ln(a*x+1)-1/2*x/a^3-1/4/a^4*ln(a*x-1)+1/4/a^4*ln(a*x+1)-1/8/a^4*ln(a*x-1)^2+1/2/a^4*dilog(1/2+1/2*a*x)+1/4/a^4*ln(a*x-1)*ln(1/2+1/2*a*x)+1/8/a^4*ln(a*x+1)^2-1/4/a^4*ln(-1/2*a*x+1/2)*ln(a*x+1)+1/4/a^4*ln(-1/2*a*x+1/2)*ln(1/2+1/2*a*x)","B"
228,1,145,38,0.053000," ","int(x^2*arctanh(a*x)/(-a^2*x^2+1),x)","-\frac{x \arctanh \left(a x \right)}{a^{2}}-\frac{\arctanh \left(a x \right) \ln \left(a x -1\right)}{2 a^{3}}+\frac{\arctanh \left(a x \right) \ln \left(a x +1\right)}{2 a^{3}}-\frac{\ln \left(a x -1\right)^{2}}{8 a^{3}}+\frac{\ln \left(a x -1\right) \ln \left(\frac{1}{2}+\frac{a x}{2}\right)}{4 a^{3}}-\frac{\ln \left(a x -1\right)}{2 a^{3}}-\frac{\ln \left(a x +1\right)}{2 a^{3}}-\frac{\ln \left(a x +1\right)^{2}}{8 a^{3}}+\frac{\ln \left(-\frac{a x}{2}+\frac{1}{2}\right) \ln \left(a x +1\right)}{4 a^{3}}-\frac{\ln \left(-\frac{a x}{2}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{a x}{2}\right)}{4 a^{3}}"," ",0,"-x*arctanh(a*x)/a^2-1/2/a^3*arctanh(a*x)*ln(a*x-1)+1/2/a^3*arctanh(a*x)*ln(a*x+1)-1/8/a^3*ln(a*x-1)^2+1/4/a^3*ln(a*x-1)*ln(1/2+1/2*a*x)-1/2/a^3*ln(a*x-1)-1/2/a^3*ln(a*x+1)-1/8/a^3*ln(a*x+1)^2+1/4/a^3*ln(-1/2*a*x+1/2)*ln(a*x+1)-1/4/a^3*ln(-1/2*a*x+1/2)*ln(1/2+1/2*a*x)","B"
229,1,125,50,0.051000," ","int(x*arctanh(a*x)/(-a^2*x^2+1),x)","-\frac{\arctanh \left(a x \right) \ln \left(a x -1\right)}{2 a^{2}}-\frac{\arctanh \left(a x \right) \ln \left(a x +1\right)}{2 a^{2}}-\frac{\ln \left(a x -1\right)^{2}}{8 a^{2}}+\frac{\dilog \left(\frac{1}{2}+\frac{a x}{2}\right)}{2 a^{2}}+\frac{\ln \left(a x -1\right) \ln \left(\frac{1}{2}+\frac{a x}{2}\right)}{4 a^{2}}+\frac{\ln \left(a x +1\right)^{2}}{8 a^{2}}-\frac{\ln \left(-\frac{a x}{2}+\frac{1}{2}\right) \ln \left(a x +1\right)}{4 a^{2}}+\frac{\ln \left(-\frac{a x}{2}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{a x}{2}\right)}{4 a^{2}}"," ",0,"-1/2/a^2*arctanh(a*x)*ln(a*x-1)-1/2/a^2*arctanh(a*x)*ln(a*x+1)-1/8/a^2*ln(a*x-1)^2+1/2/a^2*dilog(1/2+1/2*a*x)+1/4/a^2*ln(a*x-1)*ln(1/2+1/2*a*x)+1/8/a^2*ln(a*x+1)^2-1/4/a^2*ln(-1/2*a*x+1/2)*ln(a*x+1)+1/4/a^2*ln(-1/2*a*x+1/2)*ln(1/2+1/2*a*x)","B"
230,1,12,11,0.023000," ","int(arctanh(a*x)/(-a^2*x^2+1),x)","\frac{\arctanh \left(a x \right)^{2}}{2 a}"," ",0,"1/2*arctanh(a*x)^2/a","A"
231,1,130,41,0.056000," ","int(arctanh(a*x)/x/(-a^2*x^2+1),x)","\arctanh \left(a x \right) \ln \left(a x \right)-\frac{\arctanh \left(a x \right) \ln \left(a x -1\right)}{2}-\frac{\arctanh \left(a x \right) \ln \left(a x +1\right)}{2}-\frac{\ln \left(a x -1\right)^{2}}{8}+\frac{\dilog \left(\frac{1}{2}+\frac{a x}{2}\right)}{2}+\frac{\ln \left(a x -1\right) \ln \left(\frac{1}{2}+\frac{a x}{2}\right)}{4}+\frac{\ln \left(a x +1\right)^{2}}{8}-\frac{\left(\ln \left(a x +1\right)-\ln \left(\frac{1}{2}+\frac{a x}{2}\right)\right) \ln \left(-\frac{a x}{2}+\frac{1}{2}\right)}{4}-\frac{\dilog \left(a x \right)}{2}-\frac{\dilog \left(a x +1\right)}{2}-\frac{\ln \left(a x \right) \ln \left(a x +1\right)}{2}"," ",0,"arctanh(a*x)*ln(a*x)-1/2*arctanh(a*x)*ln(a*x-1)-1/2*arctanh(a*x)*ln(a*x+1)-1/8*ln(a*x-1)^2+1/2*dilog(1/2+1/2*a*x)+1/4*ln(a*x-1)*ln(1/2+1/2*a*x)+1/8*ln(a*x+1)^2-1/4*(ln(a*x+1)-ln(1/2+1/2*a*x))*ln(-1/2*a*x+1/2)-1/2*dilog(a*x)-1/2*dilog(a*x+1)-1/2*ln(a*x)*ln(a*x+1)","B"
232,1,132,37,0.059000," ","int(arctanh(a*x)/x^2/(-a^2*x^2+1),x)","-\frac{\arctanh \left(a x \right)}{x}-\frac{a \arctanh \left(a x \right) \ln \left(a x -1\right)}{2}+\frac{a \arctanh \left(a x \right) \ln \left(a x +1\right)}{2}-\frac{a \ln \left(a x -1\right)^{2}}{8}+\frac{a \ln \left(a x -1\right) \ln \left(\frac{1}{2}+\frac{a x}{2}\right)}{4}+a \ln \left(a x \right)-\frac{a \ln \left(a x -1\right)}{2}-\frac{a \ln \left(a x +1\right)}{2}-\frac{a \ln \left(a x +1\right)^{2}}{8}-\frac{a \ln \left(-\frac{a x}{2}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{a x}{2}\right)}{4}+\frac{a \ln \left(-\frac{a x}{2}+\frac{1}{2}\right) \ln \left(a x +1\right)}{4}"," ",0,"-arctanh(a*x)/x-1/2*a*arctanh(a*x)*ln(a*x-1)+1/2*a*arctanh(a*x)*ln(a*x+1)-1/8*a*ln(a*x-1)^2+1/4*a*ln(a*x-1)*ln(1/2+1/2*a*x)+a*ln(a*x)-1/2*a*ln(a*x-1)-1/2*a*ln(a*x+1)-1/8*a*ln(a*x+1)^2-1/4*a*ln(-1/2*a*x+1/2)*ln(1/2+1/2*a*x)+1/4*a*ln(-1/2*a*x+1/2)*ln(a*x+1)","B"
233,1,209,74,0.067000," ","int(arctanh(a*x)/x^3/(-a^2*x^2+1),x)","-\frac{\arctanh \left(a x \right)}{2 x^{2}}+a^{2} \arctanh \left(a x \right) \ln \left(a x \right)-\frac{a^{2} \arctanh \left(a x \right) \ln \left(a x -1\right)}{2}-\frac{a^{2} \arctanh \left(a x \right) \ln \left(a x +1\right)}{2}-\frac{a}{2 x}-\frac{a^{2} \ln \left(a x -1\right)}{4}+\frac{a^{2} \ln \left(a x +1\right)}{4}-\frac{a^{2} \ln \left(a x -1\right)^{2}}{8}+\frac{a^{2} \dilog \left(\frac{1}{2}+\frac{a x}{2}\right)}{2}+\frac{a^{2} \ln \left(a x -1\right) \ln \left(\frac{1}{2}+\frac{a x}{2}\right)}{4}+\frac{a^{2} \ln \left(a x +1\right)^{2}}{8}+\frac{a^{2} \ln \left(-\frac{a x}{2}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{a x}{2}\right)}{4}-\frac{a^{2} \ln \left(-\frac{a x}{2}+\frac{1}{2}\right) \ln \left(a x +1\right)}{4}-\frac{a^{2} \dilog \left(a x \right)}{2}-\frac{a^{2} \dilog \left(a x +1\right)}{2}-\frac{a^{2} \ln \left(a x \right) \ln \left(a x +1\right)}{2}"," ",0,"-1/2*arctanh(a*x)/x^2+a^2*arctanh(a*x)*ln(a*x)-1/2*a^2*arctanh(a*x)*ln(a*x-1)-1/2*a^2*arctanh(a*x)*ln(a*x+1)-1/2*a/x-1/4*a^2*ln(a*x-1)+1/4*a^2*ln(a*x+1)-1/8*a^2*ln(a*x-1)^2+1/2*a^2*dilog(1/2+1/2*a*x)+1/4*a^2*ln(a*x-1)*ln(1/2+1/2*a*x)+1/8*a^2*ln(a*x+1)^2+1/4*a^2*ln(-1/2*a*x+1/2)*ln(1/2+1/2*a*x)-1/4*a^2*ln(-1/2*a*x+1/2)*ln(a*x+1)-1/2*a^2*dilog(a*x)-1/2*a^2*dilog(a*x+1)-1/2*a^2*ln(a*x)*ln(a*x+1)","B"
234,1,812,125,0.498000," ","int(x^3*arctanh(a*x)^2/(-a^2*x^2+1),x)","-\frac{x^{2} \arctanh \left(a x \right)^{2}}{2 a^{2}}-\frac{\arctanh \left(a x \right)^{2} \ln \left(a x -1\right)}{2 a^{4}}-\frac{\arctanh \left(a x \right)^{2} \ln \left(a x +1\right)}{2 a^{4}}+\frac{\arctanh \left(a x \right)^{2} \ln \left(\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{a^{4}}+\frac{\arctanh \left(a x \right) \polylog \left(2, -\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}{a^{4}}-\frac{\polylog \left(3, -\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}{2 a^{4}}-\frac{i \arctanh \left(a x \right)^{2} \pi  \,\mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right) \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{\left(a^{2} x^{2}-1\right) \left(1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}\right)^{2}}{4 a^{4}}-\frac{i \arctanh \left(a x \right)^{2} \pi  \,\mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right) \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{\left(a^{2} x^{2}-1\right) \left(1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}\right) \mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right)}{4 a^{4}}+\frac{i \arctanh \left(a x \right)^{2} \pi  \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right)^{3}}{4 a^{4}}+\frac{i \arctanh \left(a x \right)^{2} \pi}{2 a^{4}}+\frac{i \arctanh \left(a x \right)^{2} \pi  \mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right)^{3}}{2 a^{4}}+\frac{i \arctanh \left(a x \right)^{2} \pi  \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{\left(a^{2} x^{2}-1\right) \left(1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}\right)^{3}}{4 a^{4}}+\frac{i \arctanh \left(a x \right)^{2} \pi  \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right)^{2} \mathrm{csgn}\left(\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right)}{2 a^{4}}-\frac{i \arctanh \left(a x \right)^{2} \pi  \mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right)^{2}}{2 a^{4}}+\frac{i \arctanh \left(a x \right)^{2} \pi  \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{\left(a^{2} x^{2}-1\right) \left(1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}\right)^{2} \mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right)}{4 a^{4}}+\frac{i \arctanh \left(a x \right)^{2} \pi  \,\mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right) \mathrm{csgn}\left(\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right)^{2}}{4 a^{4}}-\frac{\arctanh \left(a x \right)^{3}}{3 a^{4}}+\frac{\arctanh \left(a x \right)^{2} \ln \left(2\right)}{a^{4}}-\frac{x \arctanh \left(a x \right)}{a^{3}}+\frac{\arctanh \left(a x \right)^{2}}{2 a^{4}}-\frac{\arctanh \left(a x \right)}{a^{4}}+\frac{\ln \left(1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}{a^{4}}"," ",0,"-1/2*x^2*arctanh(a*x)^2/a^2-1/2/a^4*arctanh(a*x)^2*ln(a*x-1)-1/2/a^4*arctanh(a*x)^2*ln(a*x+1)+1/a^4*arctanh(a*x)^2*ln((a*x+1)/(-a^2*x^2+1)^(1/2))+1/a^4*arctanh(a*x)*polylog(2,-(a*x+1)^2/(-a^2*x^2+1))-1/2/a^4*polylog(3,-(a*x+1)^2/(-a^2*x^2+1))+1/4*I/a^4*arctanh(a*x)^2*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))+1/2*I/a^4*arctanh(a*x)^2*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1))^2*csgn(I*(a*x+1)/(-a^2*x^2+1)^(1/2))+1/4*I/a^4*arctanh(a*x)^2*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^3+1/2*I/a^4*arctanh(a*x)^2*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))^3-1/4*I/a^4*arctanh(a*x)^2*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))+1/4*I/a^4*arctanh(a*x)^2*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1))^3+1/2*I/a^4*arctanh(a*x)^2*Pi-1/2*I/a^4*arctanh(a*x)^2*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))^2-1/4*I/a^4*arctanh(a*x)^2*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2+1/4*I/a^4*arctanh(a*x)^2*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1))*csgn(I*(a*x+1)/(-a^2*x^2+1)^(1/2))^2-1/3*arctanh(a*x)^3/a^4+1/a^4*arctanh(a*x)^2*ln(2)-x*arctanh(a*x)/a^3+1/2*arctanh(a*x)^2/a^4-arctanh(a*x)/a^4+1/a^4*ln(1+(a*x+1)^2/(-a^2*x^2+1))","C"
235,1,5573,73,0.553000," ","int(x^2*arctanh(a*x)^2/(-a^2*x^2+1),x)","\text{output too large to display}"," ",0,"result too large to display","C"
236,1,741,74,0.524000," ","int(x*arctanh(a*x)^2/(-a^2*x^2+1),x)","-\frac{\arctanh \left(a x \right)^{2} \ln \left(a x -1\right)}{2 a^{2}}-\frac{\arctanh \left(a x \right)^{2} \ln \left(a x +1\right)}{2 a^{2}}+\frac{\arctanh \left(a x \right)^{2} \ln \left(\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{a^{2}}-\frac{\arctanh \left(a x \right)^{3}}{3 a^{2}}+\frac{\arctanh \left(a x \right) \polylog \left(2, -\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}{a^{2}}-\frac{\polylog \left(3, -\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}{2 a^{2}}+\frac{i \arctanh \left(a x \right)^{2} \pi}{2 a^{2}}-\frac{i \arctanh \left(a x \right)^{2} \pi  \,\mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right) \mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{\left(a^{2} x^{2}-1\right) \left(1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}\right)}{4 a^{2}}+\frac{i \arctanh \left(a x \right)^{2} \pi  \,\mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{\left(a^{2} x^{2}-1\right) \left(1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}\right)^{2}}{4 a^{2}}+\frac{i \arctanh \left(a x \right)^{2} \pi  \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right)^{2} \mathrm{csgn}\left(\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right)}{2 a^{2}}+\frac{i \arctanh \left(a x \right)^{2} \pi  \,\mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right) \mathrm{csgn}\left(\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right)^{2}}{4 a^{2}}-\frac{i \arctanh \left(a x \right)^{2} \pi  \,\mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right) \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{\left(a^{2} x^{2}-1\right) \left(1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}\right)^{2}}{4 a^{2}}+\frac{i \arctanh \left(a x \right)^{2} \pi  \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right)^{3}}{4 a^{2}}-\frac{i \arctanh \left(a x \right)^{2} \pi  \mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right)^{2}}{2 a^{2}}+\frac{i \arctanh \left(a x \right)^{2} \pi  \mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right)^{3}}{2 a^{2}}+\frac{i \arctanh \left(a x \right)^{2} \pi  \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{\left(a^{2} x^{2}-1\right) \left(1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}\right)^{3}}{4 a^{2}}+\frac{\arctanh \left(a x \right)^{2} \ln \left(2\right)}{a^{2}}"," ",0,"-1/2/a^2*arctanh(a*x)^2*ln(a*x-1)-1/2/a^2*arctanh(a*x)^2*ln(a*x+1)+1/a^2*arctanh(a*x)^2*ln((a*x+1)/(-a^2*x^2+1)^(1/2))-1/3*arctanh(a*x)^3/a^2+1/a^2*arctanh(a*x)*polylog(2,-(a*x+1)^2/(-a^2*x^2+1))-1/2/a^2*polylog(3,-(a*x+1)^2/(-a^2*x^2+1))-1/4*I/a^2*arctanh(a*x)^2*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2+1/4*I/a^2*arctanh(a*x)^2*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1))*csgn(I*(a*x+1)/(-a^2*x^2+1)^(1/2))^2-1/4*I/a^2*arctanh(a*x)^2*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1))*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))+1/2*I/a^2*arctanh(a*x)^2*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1))^2*csgn(I*(a*x+1)/(-a^2*x^2+1)^(1/2))+1/4*I/a^2*arctanh(a*x)^2*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2+1/4*I/a^2*arctanh(a*x)^2*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1))^3-1/2*I/a^2*arctanh(a*x)^2*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))^2+1/2*I/a^2*arctanh(a*x)^2*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))^3+1/4*I/a^2*arctanh(a*x)^2*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^3+1/2*I/a^2*arctanh(a*x)^2*Pi+1/a^2*arctanh(a*x)^2*ln(2)","C"
237,1,12,11,0.022000," ","int(arctanh(a*x)^2/(-a^2*x^2+1),x)","\frac{\arctanh \left(a x \right)^{3}}{3 a}"," ",0,"1/3*arctanh(a*x)^3/a","A"
238,1,1188,62,0.451000," ","int(arctanh(a*x)^2/x/(-a^2*x^2+1),x)","-\frac{i \pi  \,\mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right) \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{\left(a^{2} x^{2}-1\right) \left(1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}\right) \arctanh \left(a x \right)^{2}}{4}-\arctanh \left(a x \right)^{2} \ln \left(\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}-1\right)-2 \polylog \left(3, -\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)-\frac{\arctanh \left(a x \right)^{3}}{3}+\frac{i \pi  \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right)^{3} \arctanh \left(a x \right)^{2}}{4}+\frac{i \pi  \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{\left(a^{2} x^{2}-1\right) \left(1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}\right)^{3} \arctanh \left(a x \right)^{2}}{4}-2 \polylog \left(3, \frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)+2 \arctanh \left(a x \right) \polylog \left(2, -\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)+2 \arctanh \left(a x \right) \polylog \left(2, \frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)-\frac{\arctanh \left(a x \right)^{2} \ln \left(a x -1\right)}{2}-\frac{\arctanh \left(a x \right)^{2} \ln \left(a x +1\right)}{2}+\arctanh \left(a x \right)^{2} \ln \left(\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)+\arctanh \left(a x \right)^{2} \ln \left(a x \right)+\arctanh \left(a x \right)^{2} \ln \left(1-\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)+\arctanh \left(a x \right)^{2} \ln \left(1+\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)+\arctanh \left(a x \right)^{2} \ln \left(2\right)-\frac{i \pi  \mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right)^{2} \arctanh \left(a x \right)^{2}}{2}+\frac{i \pi  \mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right)^{3} \arctanh \left(a x \right)^{2}}{2}-\frac{i \arctanh \left(a x \right)^{2} \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}-1\right)\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}-1\right)}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right)^{2}}{2}+\frac{i \arctanh \left(a x \right)^{2} \pi  \mathrm{csgn}\left(\frac{i \left(\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}-1\right)}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right)^{3}}{2}+\frac{i \pi  \,\mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{\left(a^{2} x^{2}-1\right) \left(1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}\right)^{2} \arctanh \left(a x \right)^{2}}{4}-\frac{i \pi  \,\mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right) \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{\left(a^{2} x^{2}-1\right) \left(1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}\right)^{2} \arctanh \left(a x \right)^{2}}{4}-\frac{i \arctanh \left(a x \right)^{2} \pi  \,\mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}-1\right)}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right)^{2}}{2}+\frac{i \pi  \,\mathrm{csgn}\left(\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right)^{2} \arctanh \left(a x \right)^{2}}{2}+\frac{i \pi  \mathrm{csgn}\left(\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right)^{2} \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right) \arctanh \left(a x \right)^{2}}{4}+\frac{i \arctanh \left(a x \right)^{2} \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}-1\right)\right) \mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}-1\right)}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right)}{2}+\frac{i \pi  \arctanh \left(a x \right)^{2}}{2}"," ",0,"1/2*I*arctanh(a*x)^2*Pi*csgn(I*((a*x+1)^2/(-a^2*x^2+1)-1))*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*((a*x+1)^2/(-a^2*x^2+1)-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))-1/4*I*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*(a*x+1)^2/(a^2*x^2-1))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))*arctanh(a*x)^2-2*polylog(3,-(a*x+1)/(-a^2*x^2+1)^(1/2))-2*polylog(3,(a*x+1)/(-a^2*x^2+1)^(1/2))-1/3*arctanh(a*x)^3+1/2*I*arctanh(a*x)^2*Pi*csgn(I*((a*x+1)^2/(-a^2*x^2+1)-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^3+1/4*I*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1))^3*arctanh(a*x)^2+1/4*I*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*arctanh(a*x)^2-1/4*I*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*arctanh(a*x)^2-1/2*I*arctanh(a*x)^2*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*((a*x+1)^2/(-a^2*x^2+1)-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2-1/2*I*arctanh(a*x)^2*Pi*csgn(I*((a*x+1)^2/(-a^2*x^2+1)-1))*csgn(I*((a*x+1)^2/(-a^2*x^2+1)-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2+2*arctanh(a*x)*polylog(2,-(a*x+1)/(-a^2*x^2+1)^(1/2))+2*arctanh(a*x)*polylog(2,(a*x+1)/(-a^2*x^2+1)^(1/2))-1/2*arctanh(a*x)^2*ln(a*x-1)-1/2*arctanh(a*x)^2*ln(a*x+1)+arctanh(a*x)^2*ln((a*x+1)/(-a^2*x^2+1)^(1/2))+arctanh(a*x)^2*ln(a*x)-arctanh(a*x)^2*ln((a*x+1)^2/(-a^2*x^2+1)-1)+arctanh(a*x)^2*ln(1-(a*x+1)/(-a^2*x^2+1)^(1/2))+arctanh(a*x)^2*ln(1+(a*x+1)/(-a^2*x^2+1)^(1/2))+arctanh(a*x)^2*ln(2)+1/2*I*Pi*csgn(I*(a*x+1)/(-a^2*x^2+1)^(1/2))*csgn(I*(a*x+1)^2/(a^2*x^2-1))^2*arctanh(a*x)^2+1/4*I*Pi*csgn(I*(a*x+1)/(-a^2*x^2+1)^(1/2))^2*csgn(I*(a*x+1)^2/(a^2*x^2-1))*arctanh(a*x)^2+1/4*I*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^3*arctanh(a*x)^2-1/2*I*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*arctanh(a*x)^2+1/2*I*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))^3*arctanh(a*x)^2+1/2*I*Pi*arctanh(a*x)^2","C"
239,1,4449,64,0.603000," ","int(arctanh(a*x)^2/x^2/(-a^2*x^2+1),x)","\text{output too large to display}"," ",0,"-a*arctanh(a*x)^2-arctanh(a*x)^2/x+1/2*I*a*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*dilog((a*x+1)/(-a^2*x^2+1)^(1/2))+1/4*I*a*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^3*polylog(2,-(a*x+1)/(-a^2*x^2+1)^(1/2))+1/4*I*a*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1))^3*polylog(2,-(a*x+1)/(-a^2*x^2+1)^(1/2))+1/2*I*a*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))^3*dilog(1+(a*x+1)/(-a^2*x^2+1)^(1/2))-1/2*I*a*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))^3*polylog(2,(a*x+1)/(-a^2*x^2+1)^(1/2))-1/2*I*a*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*arctanh(a*x)^2-1/4*I*a*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^3*arctanh(a*x)^2+1/2*I*a*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))^3*arctanh(a*x)^2-1/2*I*a*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*dilog(1+(a*x+1)/(-a^2*x^2+1)^(1/2))-1/4*I*a*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*(a*x+1)^2/(a^2*x^2-1))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))*arctanh(a*x)*ln(1-(a*x+1)/(-a^2*x^2+1)^(1/2))+1/3*a*arctanh(a*x)^3-1/4*I*a*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^3*dilog(1+(a*x+1)/(-a^2*x^2+1)^(1/2))+1/4*I*a*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^3*polylog(2,(a*x+1)/(-a^2*x^2+1)^(1/2))-1/2*I*a*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))^3*dilog((a*x+1)/(-a^2*x^2+1)^(1/2))-1/2*I*a*Pi*arctanh(a*x)*ln(1-(a*x+1)/(-a^2*x^2+1)^(1/2))+1/4*I*a*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1))^3*arctanh(a*x)*ln(1-(a*x+1)/(-a^2*x^2+1)^(1/2))+1/4*I*a*Pi*csgn(I*(a*x+1)/(-a^2*x^2+1)^(1/2))^2*csgn(I*(a*x+1)^2/(a^2*x^2-1))*polylog(2,-(a*x+1)/(-a^2*x^2+1)^(1/2))+1/4*I*a*Pi*csgn(I*(a*x+1)/(-a^2*x^2+1)^(1/2))^2*csgn(I*(a*x+1)^2/(a^2*x^2-1))*polylog(2,(a*x+1)/(-a^2*x^2+1)^(1/2))+1/2*I*a*Pi*csgn(I*(a*x+1)/(-a^2*x^2+1)^(1/2))*csgn(I*(a*x+1)^2/(a^2*x^2-1))^2*polylog(2,(a*x+1)/(-a^2*x^2+1)^(1/2))+1/2*I*a*Pi*csgn(I*(a*x+1)/(-a^2*x^2+1)^(1/2))*csgn(I*(a*x+1)^2/(a^2*x^2-1))^2*dilog((a*x+1)/(-a^2*x^2+1)^(1/2))-1/4*I*a*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*dilog((a*x+1)/(-a^2*x^2+1)^(1/2))-1/4*I*a*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*polylog(2,(a*x+1)/(-a^2*x^2+1)^(1/2))-1/2*I*a*Pi*csgn(I*(a*x+1)/(-a^2*x^2+1)^(1/2))*csgn(I*(a*x+1)^2/(a^2*x^2-1))^2*dilog(1+(a*x+1)/(-a^2*x^2+1)^(1/2))-1/4*I*a*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*dilog(1+(a*x+1)/(-a^2*x^2+1)^(1/2))+1/4*I*a*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*dilog((a*x+1)/(-a^2*x^2+1)^(1/2))+1/2*I*a*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*arctanh(a*x)*ln(1-(a*x+1)/(-a^2*x^2+1)^(1/2))-1/2*I*a*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))^3*arctanh(a*x)*ln(1-(a*x+1)/(-a^2*x^2+1)^(1/2))+1/2*I*a*Pi*csgn(I*(a*x+1)/(-a^2*x^2+1)^(1/2))*csgn(I*(a*x+1)^2/(a^2*x^2-1))^2*polylog(2,-(a*x+1)/(-a^2*x^2+1)^(1/2))+1/4*I*a*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*polylog(2,-(a*x+1)/(-a^2*x^2+1)^(1/2))+1/4*I*a*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*dilog(1+(a*x+1)/(-a^2*x^2+1)^(1/2))-1/4*I*a*Pi*csgn(I*(a*x+1)/(-a^2*x^2+1)^(1/2))^2*csgn(I*(a*x+1)^2/(a^2*x^2-1))*dilog(1+(a*x+1)/(-a^2*x^2+1)^(1/2))+1/4*I*a*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^3*arctanh(a*x)*ln(1-(a*x+1)/(-a^2*x^2+1)^(1/2))+1/4*I*a*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*polylog(2,(a*x+1)/(-a^2*x^2+1)^(1/2))+1/4*I*a*Pi*csgn(I*(a*x+1)/(-a^2*x^2+1)^(1/2))^2*csgn(I*(a*x+1)^2/(a^2*x^2-1))*dilog((a*x+1)/(-a^2*x^2+1)^(1/2))+1/4*I*a*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*arctanh(a*x)^2-1/4*I*a*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*polylog(2,-(a*x+1)/(-a^2*x^2+1)^(1/2))-1/2*I*a*Pi*csgn(I*(a*x+1)/(-a^2*x^2+1)^(1/2))*csgn(I*(a*x+1)^2/(a^2*x^2-1))^2*arctanh(a*x)^2-1/4*I*a*Pi*csgn(I*(a*x+1)/(-a^2*x^2+1)^(1/2))^2*csgn(I*(a*x+1)^2/(a^2*x^2-1))*arctanh(a*x)^2-1/4*I*a*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*arctanh(a*x)^2-a*dilog((a*x+1)/(-a^2*x^2+1)^(1/2))+a*dilog(1+(a*x+1)/(-a^2*x^2+1)^(1/2))+a*polylog(2,(a*x+1)/(-a^2*x^2+1)^(1/2))+a*polylog(2,-(a*x+1)/(-a^2*x^2+1)^(1/2))+1/4*I*a*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1))^3*polylog(2,(a*x+1)/(-a^2*x^2+1)^(1/2))-1/4*I*a*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1))^3*arctanh(a*x)^2+1/2*I*a*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*polylog(2,-(a*x+1)/(-a^2*x^2+1)^(1/2))+1/4*I*a*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1))^3*dilog((a*x+1)/(-a^2*x^2+1)^(1/2))-1/4*I*a*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1))^3*dilog(1+(a*x+1)/(-a^2*x^2+1)^(1/2))-1/4*I*a*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*(a*x+1)^2/(a^2*x^2-1))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))*polylog(2,(a*x+1)/(-a^2*x^2+1)^(1/2))-1/4*I*a*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*arctanh(a*x)*ln(1-(a*x+1)/(-a^2*x^2+1)^(1/2))+1/4*I*a*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*(a*x+1)^2/(a^2*x^2-1))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))*arctanh(a*x)^2+1/4*I*a*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*arctanh(a*x)*ln(1-(a*x+1)/(-a^2*x^2+1)^(1/2))+1/2*I*a*Pi*csgn(I*(a*x+1)/(-a^2*x^2+1)^(1/2))*csgn(I*(a*x+1)^2/(a^2*x^2-1))^2*arctanh(a*x)*ln(1-(a*x+1)/(-a^2*x^2+1)^(1/2))-1/4*I*a*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*(a*x+1)^2/(a^2*x^2-1))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))*dilog((a*x+1)/(-a^2*x^2+1)^(1/2))+a*arctanh(a*x)*ln(1-(a*x+1)/(-a^2*x^2+1)^(1/2))+2*a*arctanh(a*x)*ln(1+(a*x+1)/(-a^2*x^2+1)^(1/2))-1/2*a*arctanh(a*x)^2*ln(a*x-1)+1/2*a*arctanh(a*x)^2*ln(a*x+1)-a*arctanh(a*x)^2*ln((a*x+1)/(-a^2*x^2+1)^(1/2))+1/4*I*a*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^3*dilog((a*x+1)/(-a^2*x^2+1)^(1/2))-1/2*I*a*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))^3*polylog(2,-(a*x+1)/(-a^2*x^2+1)^(1/2))+1/2*I*a*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*polylog(2,(a*x+1)/(-a^2*x^2+1)^(1/2))-1/4*I*a*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*(a*x+1)^2/(a^2*x^2-1))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))*polylog(2,-(a*x+1)/(-a^2*x^2+1)^(1/2))+1/4*I*a*Pi*csgn(I*(a*x+1)/(-a^2*x^2+1)^(1/2))^2*csgn(I*(a*x+1)^2/(a^2*x^2-1))*arctanh(a*x)*ln(1-(a*x+1)/(-a^2*x^2+1)^(1/2))+1/4*I*a*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*(a*x+1)^2/(a^2*x^2-1))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))*dilog(1+(a*x+1)/(-a^2*x^2+1)^(1/2))-1/2*I*a*Pi*dilog((a*x+1)/(-a^2*x^2+1)^(1/2))+1/2*I*a*Pi*arctanh(a*x)^2-1/2*I*a*Pi*polylog(2,-(a*x+1)/(-a^2*x^2+1)^(1/2))+1/2*I*a*Pi*dilog(1+(a*x+1)/(-a^2*x^2+1)^(1/2))-1/2*I*a*Pi*polylog(2,(a*x+1)/(-a^2*x^2+1)^(1/2))","C"
240,1,1360,128,0.891000," ","int(arctanh(a*x)^2/x^3/(-a^2*x^2+1),x)","\frac{i a^{2} \arctanh \left(a x \right)^{2} \pi  \mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right)^{3}}{2}+\frac{i a^{2} \arctanh \left(a x \right)^{2} \pi  \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{\left(a^{2} x^{2}-1\right) \left(1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}\right)^{3}}{4}+\frac{i a^{2} \arctanh \left(a x \right)^{2} \pi  \mathrm{csgn}\left(\frac{i \left(\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}-1\right)}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right)^{3}}{2}-\frac{i a^{2} \arctanh \left(a x \right)^{2} \pi  \mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right)^{2}}{2}+\frac{i a^{2} \arctanh \left(a x \right)^{2} \pi  \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right)^{3}}{4}-\frac{i a^{2} \arctanh \left(a x \right)^{2} \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}-1\right)\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}-1\right)}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right)^{2}}{2}+\frac{i a^{2} \arctanh \left(a x \right)^{2} \pi  \,\mathrm{csgn}\left(\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right)^{2}}{2}-\frac{i a^{2} \arctanh \left(a x \right)^{2} \pi  \,\mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right) \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{\left(a^{2} x^{2}-1\right) \left(1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}\right)^{2}}{4}+\frac{i a^{2} \arctanh \left(a x \right)^{2} \pi  \mathrm{csgn}\left(\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right)^{2} \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right)}{4}+\frac{i a^{2} \arctanh \left(a x \right)^{2} \pi  \,\mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{\left(a^{2} x^{2}-1\right) \left(1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}\right)^{2}}{4}-\frac{i a^{2} \arctanh \left(a x \right)^{2} \pi  \,\mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}-1\right)}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right)^{2}}{2}-\frac{a \arctanh \left(a x \right)}{x}+a^{2} \arctanh \left(a x \right)^{2} \ln \left(2\right)+a^{2} \arctanh \left(a x \right)^{2} \ln \left(1-\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)+a^{2} \arctanh \left(a x \right)^{2} \ln \left(1+\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)+a^{2} \arctanh \left(a x \right)^{2} \ln \left(a x \right)-a^{2} \arctanh \left(a x \right)+\frac{i a^{2} \arctanh \left(a x \right)^{2} \pi}{2}+a^{2} \ln \left(1+\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)+a^{2} \ln \left(\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}-1\right)-a^{2} \arctanh \left(a x \right)^{2} \ln \left(\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}-1\right)-\frac{a^{2} \arctanh \left(a x \right)^{2} \ln \left(a x +1\right)}{2}+a^{2} \arctanh \left(a x \right)^{2} \ln \left(\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)+\frac{i a^{2} \arctanh \left(a x \right)^{2} \pi  \,\mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right) \mathrm{csgn}\left(i \left(\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}-1\right)\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}-1\right)}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right)}{2}-2 a^{2} \polylog \left(3, \frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)-\frac{a^{2} \arctanh \left(a x \right)^{2} \ln \left(a x -1\right)}{2}+\frac{a^{2} \arctanh \left(a x \right)^{2}}{2}-\frac{\arctanh \left(a x \right)^{2}}{2 x^{2}}-2 a^{2} \polylog \left(3, -\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)-\frac{i a^{2} \arctanh \left(a x \right)^{2} \pi  \,\mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right) \mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{\left(a^{2} x^{2}-1\right) \left(1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}\right)}{4}+2 a^{2} \arctanh \left(a x \right) \polylog \left(2, \frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)+2 a^{2} \arctanh \left(a x \right) \polylog \left(2, -\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)-\frac{a^{2} \arctanh \left(a x \right)^{3}}{3}"," ",0,"2*a^2*arctanh(a*x)*polylog(2,-(a*x+1)/(-a^2*x^2+1)^(1/2))+2*a^2*arctanh(a*x)*polylog(2,(a*x+1)/(-a^2*x^2+1)^(1/2))-a*arctanh(a*x)/x+a^2*arctanh(a*x)^2*ln(2)+a^2*arctanh(a*x)^2*ln(1-(a*x+1)/(-a^2*x^2+1)^(1/2))+a^2*arctanh(a*x)^2*ln(1+(a*x+1)/(-a^2*x^2+1)^(1/2))-1/3*a^2*arctanh(a*x)^3+1/2*I*a^2*arctanh(a*x)^2*Pi*csgn(I*(a*x+1)/(-a^2*x^2+1)^(1/2))*csgn(I*(a*x+1)^2/(a^2*x^2-1))^2-1/4*I*a^2*arctanh(a*x)^2*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2+1/4*I*a^2*arctanh(a*x)^2*Pi*csgn(I*(a*x+1)/(-a^2*x^2+1)^(1/2))^2*csgn(I*(a*x+1)^2/(a^2*x^2-1))+1/4*I*a^2*arctanh(a*x)^2*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2-1/2*I*a^2*arctanh(a*x)^2*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*((a*x+1)^2/(-a^2*x^2+1)-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2-1/2*I*a^2*arctanh(a*x)^2*Pi*csgn(I*((a*x+1)^2/(-a^2*x^2+1)-1))*csgn(I*((a*x+1)^2/(-a^2*x^2+1)-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2+1/2*a^2*arctanh(a*x)^2-1/2*arctanh(a*x)^2/x^2-a^2*arctanh(a*x)-2*a^2*polylog(3,-(a*x+1)/(-a^2*x^2+1)^(1/2))-2*a^2*polylog(3,(a*x+1)/(-a^2*x^2+1)^(1/2))+a^2*ln(1+(a*x+1)/(-a^2*x^2+1)^(1/2))+1/2*I*a^2*arctanh(a*x)^2*Pi+a^2*ln((a*x+1)/(-a^2*x^2+1)^(1/2)-1)+a^2*arctanh(a*x)^2*ln(a*x)-1/2*a^2*arctanh(a*x)^2*ln(a*x-1)-a^2*arctanh(a*x)^2*ln((a*x+1)^2/(-a^2*x^2+1)-1)-1/2*a^2*arctanh(a*x)^2*ln(a*x+1)+a^2*arctanh(a*x)^2*ln((a*x+1)/(-a^2*x^2+1)^(1/2))-1/4*I*a^2*arctanh(a*x)^2*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1))*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))+1/2*I*a^2*arctanh(a*x)^2*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*((a*x+1)^2/(-a^2*x^2+1)-1))*csgn(I*((a*x+1)^2/(-a^2*x^2+1)-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))-1/2*I*a^2*arctanh(a*x)^2*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))^2+1/4*I*a^2*arctanh(a*x)^2*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1))^3+1/2*I*a^2*arctanh(a*x)^2*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))^3+1/4*I*a^2*arctanh(a*x)^2*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^3+1/2*I*a^2*arctanh(a*x)^2*Pi*csgn(I*((a*x+1)^2/(-a^2*x^2+1)-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^3","C"
241,1,248,187,3.151000," ","int(x^3*arctanh(a*x)^3/(-a^2*x^2+1),x)","-\frac{\arctanh \left(a x \right)^{4}}{4 a^{4}}-\frac{x^{2} \arctanh \left(a x \right)^{3}}{2 a^{2}}-\frac{3 x \arctanh \left(a x \right)^{2}}{2 a^{3}}+\frac{\arctanh \left(a x \right)^{3}}{2 a^{4}}-\frac{3 \arctanh \left(a x \right)^{2}}{2 a^{4}}+\frac{\arctanh \left(a x \right)^{3} \ln \left(1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}{a^{4}}+\frac{3 \arctanh \left(a x \right)^{2} \polylog \left(2, -\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}{2 a^{4}}-\frac{3 \arctanh \left(a x \right) \polylog \left(3, -\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}{2 a^{4}}+\frac{3 \polylog \left(4, -\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}{4 a^{4}}+\frac{3 \arctanh \left(a x \right) \ln \left(1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}{a^{4}}+\frac{3 \polylog \left(2, -\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}{2 a^{4}}"," ",0,"-1/4*arctanh(a*x)^4/a^4-1/2*x^2*arctanh(a*x)^3/a^2-3/2*x*arctanh(a*x)^2/a^3+1/2*arctanh(a*x)^3/a^4-3/2*arctanh(a*x)^2/a^4+1/a^4*arctanh(a*x)^3*ln(1+(a*x+1)^2/(-a^2*x^2+1))+3/2/a^4*arctanh(a*x)^2*polylog(2,-(a*x+1)^2/(-a^2*x^2+1))-3/2/a^4*arctanh(a*x)*polylog(3,-(a*x+1)^2/(-a^2*x^2+1))+3/4/a^4*polylog(4,-(a*x+1)^2/(-a^2*x^2+1))+3/a^4*arctanh(a*x)*ln(1+(a*x+1)^2/(-a^2*x^2+1))+3/2/a^4*polylog(2,-(a*x+1)^2/(-a^2*x^2+1))","A"
242,1,788,99,0.558000," ","int(x^2*arctanh(a*x)^3/(-a^2*x^2+1),x)","-\frac{x \arctanh \left(a x \right)^{3}}{a^{2}}-\frac{\arctanh \left(a x \right)^{3} \ln \left(a x -1\right)}{2 a^{3}}+\frac{\arctanh \left(a x \right)^{3} \ln \left(a x +1\right)}{2 a^{3}}-\frac{\arctanh \left(a x \right)^{3} \ln \left(\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{a^{3}}+\frac{\arctanh \left(a x \right)^{4}}{4 a^{3}}-\frac{\arctanh \left(a x \right)^{3}}{a^{3}}-\frac{3 \polylog \left(3, -\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}{2 a^{3}}-\frac{i \pi  \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{\left(a^{2} x^{2}-1\right) \left(1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}\right)^{3} \arctanh \left(a x \right)^{3}}{4 a^{3}}-\frac{i \arctanh \left(a x \right)^{3} \pi  \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right)^{3}}{4 a^{3}}+\frac{i \pi  \arctanh \left(a x \right)^{3}}{2 a^{3}}-\frac{i \pi  \mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right)^{2} \arctanh \left(a x \right)^{3}}{2 a^{3}}+\frac{i \pi  \mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right)^{3} \arctanh \left(a x \right)^{3}}{2 a^{3}}-\frac{i \pi  \mathrm{csgn}\left(\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right)^{2} \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right) \arctanh \left(a x \right)^{3}}{4 a^{3}}-\frac{i \pi  \,\mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{\left(a^{2} x^{2}-1\right) \left(1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}\right)^{2} \arctanh \left(a x \right)^{3}}{4 a^{3}}+\frac{i \pi  \,\mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right) \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{\left(a^{2} x^{2}-1\right) \left(1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}\right) \arctanh \left(a x \right)^{3}}{4 a^{3}}+\frac{i \pi  \,\mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right) \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{\left(a^{2} x^{2}-1\right) \left(1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}\right)^{2} \arctanh \left(a x \right)^{3}}{4 a^{3}}-\frac{i \arctanh \left(a x \right)^{3} \pi  \,\mathrm{csgn}\left(\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right)^{2}}{2 a^{3}}+\frac{3 \arctanh \left(a x \right)^{2} \ln \left(1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}{a^{3}}+\frac{3 \arctanh \left(a x \right) \polylog \left(2, -\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}{a^{3}}"," ",0,"-x*arctanh(a*x)^3/a^2-1/2/a^3*arctanh(a*x)^3*ln(a*x-1)+1/2/a^3*arctanh(a*x)^3*ln(a*x+1)-1/a^3*arctanh(a*x)^3*ln((a*x+1)/(-a^2*x^2+1)^(1/2))+1/4*arctanh(a*x)^4/a^3-arctanh(a*x)^3/a^3-3/2/a^3*polylog(3,-(a*x+1)^2/(-a^2*x^2+1))-1/4*I/a^3*Pi*csgn(I*(a*x+1)/(-a^2*x^2+1)^(1/2))^2*csgn(I*(a*x+1)^2/(a^2*x^2-1))*arctanh(a*x)^3+1/2*I/a^3*Pi*arctanh(a*x)^3-1/4*I/a^3*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^3*arctanh(a*x)^3-1/4*I/a^3*arctanh(a*x)^3*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1))^3+1/2*I/a^3*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))^3*arctanh(a*x)^3-1/2*I/a^3*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*arctanh(a*x)^3+1/4*I/a^3*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*arctanh(a*x)^3-1/2*I/a^3*arctanh(a*x)^3*Pi*csgn(I*(a*x+1)/(-a^2*x^2+1)^(1/2))*csgn(I*(a*x+1)^2/(a^2*x^2-1))^2+1/4*I/a^3*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*(a*x+1)^2/(a^2*x^2-1))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))*arctanh(a*x)^3-1/4*I/a^3*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*arctanh(a*x)^3+3/a^3*arctanh(a*x)^2*ln(1+(a*x+1)^2/(-a^2*x^2+1))+3/a^3*arctanh(a*x)*polylog(2,-(a*x+1)^2/(-a^2*x^2+1))","C"
243,1,776,100,0.523000," ","int(x*arctanh(a*x)^3/(-a^2*x^2+1),x)","-\frac{\arctanh \left(a x \right)^{3} \ln \left(a x -1\right)}{2 a^{2}}-\frac{\arctanh \left(a x \right)^{3} \ln \left(a x +1\right)}{2 a^{2}}+\frac{\arctanh \left(a x \right)^{3} \ln \left(\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{a^{2}}-\frac{\arctanh \left(a x \right)^{4}}{4 a^{2}}+\frac{3 \arctanh \left(a x \right)^{2} \polylog \left(2, -\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}{2 a^{2}}-\frac{3 \arctanh \left(a x \right) \polylog \left(3, -\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}{2 a^{2}}+\frac{3 \polylog \left(4, -\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}{4 a^{2}}+\frac{i \arctanh \left(a x \right)^{3} \pi}{2 a^{2}}+\frac{i \arctanh \left(a x \right)^{3} \mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{\left(a^{2} x^{2}-1\right) \left(1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}\right)^{2} \pi}{4 a^{2}}+\frac{i \arctanh \left(a x \right)^{3} \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right) \mathrm{csgn}\left(\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right)^{2} \pi}{4 a^{2}}+\frac{i \arctanh \left(a x \right)^{3} \mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right)^{3} \pi}{2 a^{2}}-\frac{i \arctanh \left(a x \right)^{3} \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right) \mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{\left(a^{2} x^{2}-1\right) \left(1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}\right) \pi}{4 a^{2}}+\frac{i \arctanh \left(a x \right)^{3} \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right)^{2} \mathrm{csgn}\left(\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right) \pi}{2 a^{2}}+\frac{i \arctanh \left(a x \right)^{3} \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{\left(a^{2} x^{2}-1\right) \left(1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}\right)^{3} \pi}{4 a^{2}}-\frac{i \arctanh \left(a x \right)^{3} \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right) \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{\left(a^{2} x^{2}-1\right) \left(1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}\right)^{2} \pi}{4 a^{2}}+\frac{i \arctanh \left(a x \right)^{3} \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right)^{3} \pi}{4 a^{2}}-\frac{i \arctanh \left(a x \right)^{3} \mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right)^{2} \pi}{2 a^{2}}+\frac{\arctanh \left(a x \right)^{3} \ln \left(2\right)}{a^{2}}"," ",0,"-1/2/a^2*arctanh(a*x)^3*ln(a*x-1)-1/2/a^2*arctanh(a*x)^3*ln(a*x+1)+1/a^2*arctanh(a*x)^3*ln((a*x+1)/(-a^2*x^2+1)^(1/2))-1/4*arctanh(a*x)^4/a^2+3/2/a^2*arctanh(a*x)^2*polylog(2,-(a*x+1)^2/(-a^2*x^2+1))-3/2/a^2*arctanh(a*x)*polylog(3,-(a*x+1)^2/(-a^2*x^2+1))+3/4/a^2*polylog(4,-(a*x+1)^2/(-a^2*x^2+1))+1/2*I/a^2*arctanh(a*x)^3*Pi+1/2*I/a^2*arctanh(a*x)^3*csgn(I*(a*x+1)^2/(a^2*x^2-1))^2*csgn(I*(a*x+1)/(-a^2*x^2+1)^(1/2))*Pi+1/4*I/a^2*arctanh(a*x)^3*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*Pi-1/2*I/a^2*arctanh(a*x)^3*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*Pi+1/2*I/a^2*arctanh(a*x)^3*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))^3*Pi-1/4*I/a^2*arctanh(a*x)^3*csgn(I*(a*x+1)^2/(a^2*x^2-1))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*Pi+1/4*I/a^2*arctanh(a*x)^3*csgn(I*(a*x+1)^2/(a^2*x^2-1))*csgn(I*(a*x+1)/(-a^2*x^2+1)^(1/2))^2*Pi-1/4*I/a^2*arctanh(a*x)^3*csgn(I*(a*x+1)^2/(a^2*x^2-1))*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))*Pi+1/4*I/a^2*arctanh(a*x)^3*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^3*Pi+1/4*I/a^2*arctanh(a*x)^3*csgn(I*(a*x+1)^2/(a^2*x^2-1))^3*Pi+1/a^2*arctanh(a*x)^3*ln(2)","C"
244,1,12,11,0.023000," ","int(arctanh(a*x)^3/(-a^2*x^2+1),x)","\frac{\arctanh \left(a x \right)^{4}}{4 a}"," ",0,"1/4*arctanh(a*x)^4/a","A"
245,1,1245,83,0.571000," ","int(arctanh(a*x)^3/x/(-a^2*x^2+1),x)","-\frac{i \pi  \,\mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right) \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{\left(a^{2} x^{2}-1\right) \left(1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}\right) \arctanh \left(a x \right)^{3}}{4}+\frac{i \arctanh \left(a x \right)^{3} \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}-1\right)\right) \mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}-1\right)}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right)}{2}+6 \polylog \left(4, \frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)+\frac{i \arctanh \left(a x \right)^{3} \pi  \mathrm{csgn}\left(\frac{i \left(\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}-1\right)}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right)^{3}}{2}+\frac{i \pi  \,\mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{\left(a^{2} x^{2}-1\right) \left(1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}\right)^{2} \arctanh \left(a x \right)^{3}}{4}+\frac{i \pi  \mathrm{csgn}\left(\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right)^{2} \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right) \arctanh \left(a x \right)^{3}}{4}+\frac{i \arctanh \left(a x \right)^{3} \pi  \,\mathrm{csgn}\left(\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right)^{2}}{2}-\frac{i \pi  \,\mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right) \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{\left(a^{2} x^{2}-1\right) \left(1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}\right)^{2} \arctanh \left(a x \right)^{3}}{4}-\frac{i \arctanh \left(a x \right)^{3} \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}-1\right)\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}-1\right)}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right)^{2}}{2}-\frac{i \arctanh \left(a x \right)^{3} \pi  \,\mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}-1\right)}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right)^{2}}{2}+\frac{i \pi  \mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right)^{3} \arctanh \left(a x \right)^{3}}{2}-\frac{i \pi  \mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right)^{2} \arctanh \left(a x \right)^{3}}{2}+\frac{i \arctanh \left(a x \right)^{3} \pi  \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right)^{3}}{4}+\frac{i \pi  \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{\left(a^{2} x^{2}-1\right) \left(1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}\right)^{3} \arctanh \left(a x \right)^{3}}{4}+6 \polylog \left(4, -\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)+\frac{i \pi  \arctanh \left(a x \right)^{3}}{2}-\frac{\arctanh \left(a x \right)^{3} \ln \left(a x -1\right)}{2}-\frac{\arctanh \left(a x \right)^{3} \ln \left(a x +1\right)}{2}+\arctanh \left(a x \right)^{3} \ln \left(\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)+\arctanh \left(a x \right)^{3} \ln \left(a x \right)-6 \arctanh \left(a x \right) \polylog \left(3, -\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)-\arctanh \left(a x \right)^{3} \ln \left(\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}-1\right)+\ln \left(2\right) \arctanh \left(a x \right)^{3}+\arctanh \left(a x \right)^{3} \ln \left(1+\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)+\arctanh \left(a x \right)^{3} \ln \left(1-\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)-6 \arctanh \left(a x \right) \polylog \left(3, \frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)+3 \arctanh \left(a x \right)^{2} \polylog \left(2, \frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)+3 \arctanh \left(a x \right)^{2} \polylog \left(2, -\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)-\frac{\arctanh \left(a x \right)^{4}}{4}"," ",0,"-1/2*arctanh(a*x)^3*ln(a*x-1)-1/2*arctanh(a*x)^3*ln(a*x+1)+arctanh(a*x)^3*ln((a*x+1)/(-a^2*x^2+1)^(1/2))+arctanh(a*x)^3*ln(a*x)-1/4*arctanh(a*x)^4+1/2*I*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))^3*arctanh(a*x)^3-1/2*I*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*arctanh(a*x)^3+1/4*I*arctanh(a*x)^3*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1))^3+1/4*I*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^3*arctanh(a*x)^3+1/2*I*arctanh(a*x)^3*Pi*csgn(I*((a*x+1)^2/(-a^2*x^2+1)-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^3-1/4*I*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*(a*x+1)^2/(a^2*x^2-1))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))*arctanh(a*x)^3+1/2*I*arctanh(a*x)^3*Pi*csgn(I*((a*x+1)^2/(-a^2*x^2+1)-1))*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*((a*x+1)^2/(-a^2*x^2+1)-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))+6*polylog(4,-(a*x+1)/(-a^2*x^2+1)^(1/2))+6*polylog(4,(a*x+1)/(-a^2*x^2+1)^(1/2))-6*arctanh(a*x)*polylog(3,-(a*x+1)/(-a^2*x^2+1)^(1/2))-arctanh(a*x)^3*ln((a*x+1)^2/(-a^2*x^2+1)-1)+ln(2)*arctanh(a*x)^3+arctanh(a*x)^3*ln(1+(a*x+1)/(-a^2*x^2+1)^(1/2))+arctanh(a*x)^3*ln(1-(a*x+1)/(-a^2*x^2+1)^(1/2))+1/2*I*Pi*arctanh(a*x)^3-6*arctanh(a*x)*polylog(3,(a*x+1)/(-a^2*x^2+1)^(1/2))+1/4*I*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*arctanh(a*x)^3+1/4*I*Pi*csgn(I*(a*x+1)/(-a^2*x^2+1)^(1/2))^2*csgn(I*(a*x+1)^2/(a^2*x^2-1))*arctanh(a*x)^3+1/2*I*arctanh(a*x)^3*Pi*csgn(I*(a*x+1)/(-a^2*x^2+1)^(1/2))*csgn(I*(a*x+1)^2/(a^2*x^2-1))^2-1/4*I*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*arctanh(a*x)^3-1/2*I*arctanh(a*x)^3*Pi*csgn(I*((a*x+1)^2/(-a^2*x^2+1)-1))*csgn(I*((a*x+1)^2/(-a^2*x^2+1)-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2-1/2*I*arctanh(a*x)^3*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*((a*x+1)^2/(-a^2*x^2+1)-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2+3*arctanh(a*x)^2*polylog(2,(a*x+1)/(-a^2*x^2+1)^(1/2))+3*arctanh(a*x)^2*polylog(2,-(a*x+1)/(-a^2*x^2+1)^(1/2))","C"
246,1,826,86,0.624000," ","int(arctanh(a*x)^3/x^2/(-a^2*x^2+1),x)","-\frac{\arctanh \left(a x \right)^{3}}{x}-\frac{a \arctanh \left(a x \right)^{3} \ln \left(a x -1\right)}{2}+\frac{a \arctanh \left(a x \right)^{3} \ln \left(a x +1\right)}{2}+3 a \arctanh \left(a x \right)^{2} \ln \left(1+\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)+6 a \arctanh \left(a x \right) \polylog \left(2, -\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)+3 a \arctanh \left(a x \right)^{2} \ln \left(1-\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)+6 a \arctanh \left(a x \right) \polylog \left(2, \frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)-a \arctanh \left(a x \right)^{3}+\frac{a \arctanh \left(a x \right)^{4}}{4}-\frac{i a \pi  \mathrm{csgn}\left(\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right)^{2} \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right) \arctanh \left(a x \right)^{3}}{4}+\frac{i a \pi  \arctanh \left(a x \right)^{3}}{2}-\frac{i a \pi  \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{\left(a^{2} x^{2}-1\right) \left(1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}\right)^{3} \arctanh \left(a x \right)^{3}}{4}-6 a \polylog \left(3, \frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)-6 a \polylog \left(3, -\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)-a \arctanh \left(a x \right)^{3} \ln \left(\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)-\frac{i a \arctanh \left(a x \right)^{3} \pi  \,\mathrm{csgn}\left(\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right)^{2}}{2}-\frac{i a \pi  \,\mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{\left(a^{2} x^{2}-1\right) \left(1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}\right)^{2} \arctanh \left(a x \right)^{3}}{4}+\frac{i a \pi  \,\mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right) \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{\left(a^{2} x^{2}-1\right) \left(1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}\right) \arctanh \left(a x \right)^{3}}{4}-\frac{i a \arctanh \left(a x \right)^{3} \pi  \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right)^{3}}{4}-\frac{i a \pi  \mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right)^{2} \arctanh \left(a x \right)^{3}}{2}+\frac{i a \pi  \mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right)^{3} \arctanh \left(a x \right)^{3}}{2}+\frac{i a \pi  \,\mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right) \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{\left(a^{2} x^{2}-1\right) \left(1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}\right)^{2} \arctanh \left(a x \right)^{3}}{4}"," ",0,"-arctanh(a*x)^3/x-1/2*a*arctanh(a*x)^3*ln(a*x-1)+1/2*a*arctanh(a*x)^3*ln(a*x+1)+3*a*arctanh(a*x)^2*ln(1+(a*x+1)/(-a^2*x^2+1)^(1/2))+6*a*arctanh(a*x)*polylog(2,-(a*x+1)/(-a^2*x^2+1)^(1/2))+3*a*arctanh(a*x)^2*ln(1-(a*x+1)/(-a^2*x^2+1)^(1/2))+6*a*arctanh(a*x)*polylog(2,(a*x+1)/(-a^2*x^2+1)^(1/2))-a*arctanh(a*x)^3+1/4*a*arctanh(a*x)^4+1/2*I*a*Pi*arctanh(a*x)^3+1/2*I*a*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))^3*arctanh(a*x)^3-1/4*I*a*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*arctanh(a*x)^3-6*a*polylog(3,(a*x+1)/(-a^2*x^2+1)^(1/2))-6*a*polylog(3,-(a*x+1)/(-a^2*x^2+1)^(1/2))-a*arctanh(a*x)^3*ln((a*x+1)/(-a^2*x^2+1)^(1/2))-1/4*I*a*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^3*arctanh(a*x)^3-1/4*I*a*arctanh(a*x)^3*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1))^3+1/4*I*a*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*arctanh(a*x)^3+1/4*I*a*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*(a*x+1)^2/(a^2*x^2-1))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))*arctanh(a*x)^3-1/2*I*a*arctanh(a*x)^3*Pi*csgn(I*(a*x+1)/(-a^2*x^2+1)^(1/2))*csgn(I*(a*x+1)^2/(a^2*x^2-1))^2-1/2*I*a*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*arctanh(a*x)^3-1/4*I*a*Pi*csgn(I*(a*x+1)/(-a^2*x^2+1)^(1/2))^2*csgn(I*(a*x+1)^2/(a^2*x^2-1))*arctanh(a*x)^3","C"
247,1,406,182,4.727000," ","int(arctanh(a*x)^3/x^3/(-a^2*x^2+1),x)","-\frac{a^{2} \arctanh \left(a x \right)^{4}}{4}+\frac{a^{2} \arctanh \left(a x \right)^{3}}{2}-\frac{3 a^{2} \arctanh \left(a x \right)^{2}}{2}-\frac{3 a \arctanh \left(a x \right)^{2}}{2 x}-\frac{\arctanh \left(a x \right)^{3}}{2 x^{2}}+a^{2} \arctanh \left(a x \right)^{3} \ln \left(1+\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)+3 a^{2} \arctanh \left(a x \right)^{2} \polylog \left(2, -\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)-6 a^{2} \arctanh \left(a x \right) \polylog \left(3, -\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)+6 a^{2} \polylog \left(4, -\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)+a^{2} \arctanh \left(a x \right)^{3} \ln \left(1-\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)+3 a^{2} \arctanh \left(a x \right)^{2} \polylog \left(2, \frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)-6 a^{2} \arctanh \left(a x \right) \polylog \left(3, \frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)+6 a^{2} \polylog \left(4, \frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)+3 a^{2} \arctanh \left(a x \right) \ln \left(1+\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)+3 a^{2} \polylog \left(2, -\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)+3 a^{2} \arctanh \left(a x \right) \ln \left(1-\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)+3 a^{2} \polylog \left(2, \frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)"," ",0,"-1/4*a^2*arctanh(a*x)^4+1/2*a^2*arctanh(a*x)^3-3/2*a^2*arctanh(a*x)^2-3/2*a*arctanh(a*x)^2/x-1/2*arctanh(a*x)^3/x^2+a^2*arctanh(a*x)^3*ln(1+(a*x+1)/(-a^2*x^2+1)^(1/2))+3*a^2*arctanh(a*x)^2*polylog(2,-(a*x+1)/(-a^2*x^2+1)^(1/2))-6*a^2*arctanh(a*x)*polylog(3,-(a*x+1)/(-a^2*x^2+1)^(1/2))+6*a^2*polylog(4,-(a*x+1)/(-a^2*x^2+1)^(1/2))+a^2*arctanh(a*x)^3*ln(1-(a*x+1)/(-a^2*x^2+1)^(1/2))+3*a^2*arctanh(a*x)^2*polylog(2,(a*x+1)/(-a^2*x^2+1)^(1/2))-6*a^2*arctanh(a*x)*polylog(3,(a*x+1)/(-a^2*x^2+1)^(1/2))+6*a^2*polylog(4,(a*x+1)/(-a^2*x^2+1)^(1/2))+3*a^2*arctanh(a*x)*ln(1+(a*x+1)/(-a^2*x^2+1)^(1/2))+3*a^2*polylog(2,-(a*x+1)/(-a^2*x^2+1)^(1/2))+3*a^2*arctanh(a*x)*ln(1-(a*x+1)/(-a^2*x^2+1)^(1/2))+3*a^2*polylog(2,(a*x+1)/(-a^2*x^2+1)^(1/2))","B"
248,1,12,11,0.036000," ","int(arctanh(a*x)^(1/2)/(-a^2*x^2+1),x)","\frac{2 \arctanh \left(a x \right)^{\frac{3}{2}}}{3 a}"," ",0,"2/3*arctanh(a*x)^(3/2)/a","A"
249,0,0,22,0.128000," ","int(x/(-a^2*x^2+1)/arctanh(a*x),x)","\int \frac{x}{\left(-a^{2} x^{2}+1\right) \arctanh \left(a x \right)}\, dx"," ",0,"int(x/(-a^2*x^2+1)/arctanh(a*x),x)","F"
250,1,10,9,0.023000," ","int(1/(-a^2*x^2+1)/arctanh(a*x),x)","\frac{\ln \left(\arctanh \left(a x \right)\right)}{a}"," ",0,"ln(arctanh(a*x))/a","A"
251,0,0,24,0.245000," ","int(1/x/(-a^2*x^2+1)/arctanh(a*x),x)","\int \frac{1}{x \left(-a^{2} x^{2}+1\right) \arctanh \left(a x \right)}\, dx"," ",0,"int(1/x/(-a^2*x^2+1)/arctanh(a*x),x)","F"
252,0,0,25,0.124000," ","int(x/(-a^2*x^2+1)/arctanh(a*x)^2,x)","\int \frac{x}{\left(-a^{2} x^{2}+1\right) \arctanh \left(a x \right)^{2}}\, dx"," ",0,"int(x/(-a^2*x^2+1)/arctanh(a*x)^2,x)","F"
253,1,12,11,0.023000," ","int(1/(-a^2*x^2+1)/arctanh(a*x)^2,x)","-\frac{1}{a \arctanh \left(a x \right)}"," ",0,"-1/a/arctanh(a*x)","A"
254,0,0,32,0.247000," ","int(1/x/(-a^2*x^2+1)/arctanh(a*x)^2,x)","\int \frac{1}{x \left(-a^{2} x^{2}+1\right) \arctanh \left(a x \right)^{2}}\, dx"," ",0,"int(1/x/(-a^2*x^2+1)/arctanh(a*x)^2,x)","F"
255,0,0,26,0.125000," ","int(x/(-a^2*x^2+1)/arctanh(a*x)^3,x)","\int \frac{x}{\left(-a^{2} x^{2}+1\right) \arctanh \left(a x \right)^{3}}\, dx"," ",0,"int(x/(-a^2*x^2+1)/arctanh(a*x)^3,x)","F"
256,1,12,11,0.024000," ","int(1/(-a^2*x^2+1)/arctanh(a*x)^3,x)","-\frac{1}{2 a \arctanh \left(a x \right)^{2}}"," ",0,"-1/2/a/arctanh(a*x)^2","A"
257,0,0,32,0.247000," ","int(1/x/(-a^2*x^2+1)/arctanh(a*x)^3,x)","\int \frac{1}{x \left(-a^{2} x^{2}+1\right) \arctanh \left(a x \right)^{3}}\, dx"," ",0,"int(1/x/(-a^2*x^2+1)/arctanh(a*x)^3,x)","F"
258,1,18,17,0.022000," ","int(arctanh(a*x)^p/(-a^2*x^2+1),x)","\frac{\arctanh \left(a x \right)^{1+p}}{a \left(1+p \right)}"," ",0,"arctanh(a*x)^(1+p)/a/(1+p)","A"
259,1,203,99,0.064000," ","int(x^3*arctanh(a*x)/(-a^2*x^2+1)^2,x)","-\frac{\arctanh \left(a x \right)}{4 a^{4} \left(a x -1\right)}+\frac{\arctanh \left(a x \right) \ln \left(a x -1\right)}{2 a^{4}}+\frac{\arctanh \left(a x \right)}{4 a^{4} \left(a x +1\right)}+\frac{\arctanh \left(a x \right) \ln \left(a x +1\right)}{2 a^{4}}+\frac{\ln \left(a x -1\right)^{2}}{8 a^{4}}-\frac{\dilog \left(\frac{1}{2}+\frac{a x}{2}\right)}{2 a^{4}}-\frac{\ln \left(a x -1\right) \ln \left(\frac{1}{2}+\frac{a x}{2}\right)}{4 a^{4}}-\frac{\ln \left(a x +1\right)^{2}}{8 a^{4}}+\frac{\ln \left(-\frac{a x}{2}+\frac{1}{2}\right) \ln \left(a x +1\right)}{4 a^{4}}-\frac{\ln \left(-\frac{a x}{2}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{a x}{2}\right)}{4 a^{4}}+\frac{1}{8 a^{4} \left(a x -1\right)}+\frac{\ln \left(a x -1\right)}{8 a^{4}}+\frac{1}{8 a^{4} \left(a x +1\right)}-\frac{\ln \left(a x +1\right)}{8 a^{4}}"," ",0,"-1/4/a^4*arctanh(a*x)/(a*x-1)+1/2/a^4*arctanh(a*x)*ln(a*x-1)+1/4/a^4*arctanh(a*x)/(a*x+1)+1/2/a^4*arctanh(a*x)*ln(a*x+1)+1/8/a^4*ln(a*x-1)^2-1/2/a^4*dilog(1/2+1/2*a*x)-1/4/a^4*ln(a*x-1)*ln(1/2+1/2*a*x)-1/8/a^4*ln(a*x+1)^2+1/4/a^4*ln(-1/2*a*x+1/2)*ln(a*x+1)-1/4/a^4*ln(-1/2*a*x+1/2)*ln(1/2+1/2*a*x)+1/8/a^4/(a*x-1)+1/8/a^4*ln(a*x-1)+1/8/a^4/(a*x+1)-1/8/a^4*ln(a*x+1)","B"
260,1,169,51,0.062000," ","int(x^2*arctanh(a*x)/(-a^2*x^2+1)^2,x)","-\frac{\arctanh \left(a x \right)}{4 a^{3} \left(a x -1\right)}+\frac{\arctanh \left(a x \right) \ln \left(a x -1\right)}{4 a^{3}}-\frac{\arctanh \left(a x \right)}{4 a^{3} \left(a x +1\right)}-\frac{\arctanh \left(a x \right) \ln \left(a x +1\right)}{4 a^{3}}+\frac{\ln \left(a x +1\right)^{2}}{16 a^{3}}+\frac{\ln \left(-\frac{a x}{2}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{a x}{2}\right)}{8 a^{3}}-\frac{\ln \left(-\frac{a x}{2}+\frac{1}{2}\right) \ln \left(a x +1\right)}{8 a^{3}}+\frac{\ln \left(a x -1\right)^{2}}{16 a^{3}}-\frac{\ln \left(a x -1\right) \ln \left(\frac{1}{2}+\frac{a x}{2}\right)}{8 a^{3}}+\frac{1}{8 a^{3} \left(a x -1\right)}-\frac{1}{8 a^{3} \left(a x +1\right)}"," ",0,"-1/4/a^3*arctanh(a*x)/(a*x-1)+1/4/a^3*arctanh(a*x)*ln(a*x-1)-1/4/a^3*arctanh(a*x)/(a*x+1)-1/4/a^3*arctanh(a*x)*ln(a*x+1)+1/16/a^3*ln(a*x+1)^2+1/8/a^3*ln(-1/2*a*x+1/2)*ln(1/2+1/2*a*x)-1/8/a^3*ln(-1/2*a*x+1/2)*ln(a*x+1)+1/16/a^3*ln(a*x-1)^2-1/8/a^3*ln(a*x-1)*ln(1/2+1/2*a*x)+1/8/a^3/(a*x-1)-1/8/a^3/(a*x+1)","B"
261,1,68,49,0.036000," ","int(x*arctanh(a*x)/(-a^2*x^2+1)^2,x)","-\frac{\arctanh \left(a x \right)}{2 a^{2} \left(a^{2} x^{2}-1\right)}+\frac{1}{8 a^{2} \left(a x -1\right)}+\frac{\ln \left(a x -1\right)}{8 a^{2}}+\frac{1}{8 a^{2} \left(a x +1\right)}-\frac{\ln \left(a x +1\right)}{8 a^{2}}"," ",0,"-1/2/a^2/(a^2*x^2-1)*arctanh(a*x)+1/8/a^2/(a*x-1)+1/8/a^2*ln(a*x-1)+1/8/a^2/(a*x+1)-1/8/a^2*ln(a*x+1)","A"
262,1,169,48,0.060000," ","int(arctanh(a*x)/(-a^2*x^2+1)^2,x)","-\frac{\arctanh \left(a x \right)}{4 a \left(a x -1\right)}-\frac{\arctanh \left(a x \right) \ln \left(a x -1\right)}{4 a}-\frac{\arctanh \left(a x \right)}{4 a \left(a x +1\right)}+\frac{\arctanh \left(a x \right) \ln \left(a x +1\right)}{4 a}-\frac{\ln \left(a x -1\right)^{2}}{16 a}+\frac{\ln \left(a x -1\right) \ln \left(\frac{1}{2}+\frac{a x}{2}\right)}{8 a}-\frac{\ln \left(a x +1\right)^{2}}{16 a}+\frac{\ln \left(-\frac{a x}{2}+\frac{1}{2}\right) \ln \left(a x +1\right)}{8 a}-\frac{\ln \left(-\frac{a x}{2}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{a x}{2}\right)}{8 a}+\frac{1}{8 a \left(a x -1\right)}-\frac{1}{8 a \left(a x +1\right)}"," ",0,"-1/4/a*arctanh(a*x)/(a*x-1)-1/4/a*arctanh(a*x)*ln(a*x-1)-1/4/a*arctanh(a*x)/(a*x+1)+1/4/a*arctanh(a*x)*ln(a*x+1)-1/16/a*ln(a*x-1)^2+1/8/a*ln(a*x-1)*ln(1/2+1/2*a*x)-1/16/a*ln(a*x+1)^2+1/8/a*ln(-1/2*a*x+1/2)*ln(a*x+1)-1/8/a*ln(-1/2*a*x+1/2)*ln(1/2+1/2*a*x)+1/8/a/(a*x-1)-1/8/a/(a*x+1)","B"
263,1,190,81,0.069000," ","int(arctanh(a*x)/x/(-a^2*x^2+1)^2,x)","\arctanh \left(a x \right) \ln \left(a x \right)-\frac{\arctanh \left(a x \right)}{4 \left(a x -1\right)}-\frac{\arctanh \left(a x \right) \ln \left(a x -1\right)}{2}+\frac{\arctanh \left(a x \right)}{4 a x +4}-\frac{\arctanh \left(a x \right) \ln \left(a x +1\right)}{2}-\frac{\dilog \left(a x \right)}{2}-\frac{\dilog \left(a x +1\right)}{2}-\frac{\ln \left(a x \right) \ln \left(a x +1\right)}{2}-\frac{\ln \left(a x -1\right)^{2}}{8}+\frac{\dilog \left(\frac{1}{2}+\frac{a x}{2}\right)}{2}+\frac{\ln \left(a x -1\right) \ln \left(\frac{1}{2}+\frac{a x}{2}\right)}{4}+\frac{\ln \left(a x +1\right)^{2}}{8}-\frac{\left(\ln \left(a x +1\right)-\ln \left(\frac{1}{2}+\frac{a x}{2}\right)\right) \ln \left(-\frac{a x}{2}+\frac{1}{2}\right)}{4}+\frac{1}{8 a x -8}+\frac{\ln \left(a x -1\right)}{8}+\frac{1}{8 a x +8}-\frac{\ln \left(a x +1\right)}{8}"," ",0,"arctanh(a*x)*ln(a*x)-1/4*arctanh(a*x)/(a*x-1)-1/2*arctanh(a*x)*ln(a*x-1)+1/4*arctanh(a*x)/(a*x+1)-1/2*arctanh(a*x)*ln(a*x+1)-1/2*dilog(a*x)-1/2*dilog(a*x+1)-1/2*ln(a*x)*ln(a*x+1)-1/8*ln(a*x-1)^2+1/2*dilog(1/2+1/2*a*x)+1/4*ln(a*x-1)*ln(1/2+1/2*a*x)+1/8*ln(a*x+1)^2-1/4*(ln(a*x+1)-ln(1/2+1/2*a*x))*ln(-1/2*a*x+1/2)+1/8/(a*x-1)+1/8*ln(a*x-1)+1/8/(a*x+1)-1/8*ln(a*x+1)","B"
264,1,180,74,0.064000," ","int(arctanh(a*x)/x^2/(-a^2*x^2+1)^2,x)","-\frac{\arctanh \left(a x \right)}{x}-\frac{a \arctanh \left(a x \right)}{4 \left(a x -1\right)}-\frac{3 a \arctanh \left(a x \right) \ln \left(a x -1\right)}{4}-\frac{a \arctanh \left(a x \right)}{4 \left(a x +1\right)}+\frac{3 a \arctanh \left(a x \right) \ln \left(a x +1\right)}{4}-\frac{3 a \ln \left(a x -1\right)^{2}}{16}+\frac{3 a \ln \left(a x -1\right) \ln \left(\frac{1}{2}+\frac{a x}{2}\right)}{8}-\frac{3 a \ln \left(a x +1\right)^{2}}{16}-\frac{3 a \ln \left(-\frac{a x}{2}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{a x}{2}\right)}{8}+\frac{3 a \ln \left(-\frac{a x}{2}+\frac{1}{2}\right) \ln \left(a x +1\right)}{8}+a \ln \left(a x \right)-\frac{a \ln \left(a x -1\right)}{2}+\frac{a}{8 a x -8}-\frac{a \ln \left(a x +1\right)}{2}-\frac{a}{8 \left(a x +1\right)}"," ",0,"-arctanh(a*x)/x-1/4*a*arctanh(a*x)/(a*x-1)-3/4*a*arctanh(a*x)*ln(a*x-1)-1/4*a*arctanh(a*x)/(a*x+1)+3/4*a*arctanh(a*x)*ln(a*x+1)-3/16*a*ln(a*x-1)^2+3/8*a*ln(a*x-1)*ln(1/2+1/2*a*x)-3/16*a*ln(a*x+1)^2-3/8*a*ln(-1/2*a*x+1/2)*ln(1/2+1/2*a*x)+3/8*a*ln(-1/2*a*x+1/2)*ln(a*x+1)+a*ln(a*x)-1/2*a*ln(a*x-1)+1/8*a/(a*x-1)-1/2*a*ln(a*x+1)-1/8*a/(a*x+1)","B"
265,1,265,113,0.072000," ","int(arctanh(a*x)/x^3/(-a^2*x^2+1)^2,x)","-\frac{\arctanh \left(a x \right)}{2 x^{2}}+2 a^{2} \arctanh \left(a x \right) \ln \left(a x \right)-\frac{a^{2} \arctanh \left(a x \right)}{4 \left(a x -1\right)}-a^{2} \arctanh \left(a x \right) \ln \left(a x -1\right)+\frac{a^{2} \arctanh \left(a x \right)}{4 a x +4}-a^{2} \arctanh \left(a x \right) \ln \left(a x +1\right)-a^{2} \dilog \left(a x \right)-a^{2} \dilog \left(a x +1\right)-a^{2} \ln \left(a x \right) \ln \left(a x +1\right)-\frac{a^{2} \ln \left(a x -1\right)^{2}}{4}+a^{2} \dilog \left(\frac{1}{2}+\frac{a x}{2}\right)+\frac{a^{2} \ln \left(a x -1\right) \ln \left(\frac{1}{2}+\frac{a x}{2}\right)}{2}+\frac{a^{2} \ln \left(a x +1\right)^{2}}{4}+\frac{a^{2} \ln \left(-\frac{a x}{2}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{a x}{2}\right)}{2}-\frac{a^{2} \ln \left(-\frac{a x}{2}+\frac{1}{2}\right) \ln \left(a x +1\right)}{2}-\frac{a}{2 x}+\frac{a^{2}}{8 a x -8}-\frac{a^{2} \ln \left(a x -1\right)}{8}+\frac{a^{2}}{8 a x +8}+\frac{a^{2} \ln \left(a x +1\right)}{8}"," ",0,"-1/2*arctanh(a*x)/x^2+2*a^2*arctanh(a*x)*ln(a*x)-1/4*a^2*arctanh(a*x)/(a*x-1)-a^2*arctanh(a*x)*ln(a*x-1)+1/4*a^2*arctanh(a*x)/(a*x+1)-a^2*arctanh(a*x)*ln(a*x+1)-a^2*dilog(a*x)-a^2*dilog(a*x+1)-a^2*ln(a*x)*ln(a*x+1)-1/4*a^2*ln(a*x-1)^2+a^2*dilog(1/2+1/2*a*x)+1/2*a^2*ln(a*x-1)*ln(1/2+1/2*a*x)+1/4*a^2*ln(a*x+1)^2+1/2*a^2*ln(-1/2*a*x+1/2)*ln(1/2+1/2*a*x)-1/2*a^2*ln(-1/2*a*x+1/2)*ln(a*x+1)-1/2*a/x+1/8*a^2/(a*x-1)-1/8*a^2*ln(a*x-1)+1/8*a^2/(a*x+1)+1/8*a^2*ln(a*x+1)","B"
266,1,907,149,0.704000," ","int(x^3*arctanh(a*x)^2/(-a^2*x^2+1)^2,x)","\frac{i \pi  \arctanh \left(a x \right)^{2} \mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right)^{2}}{2 a^{4}}-\frac{i \pi  \arctanh \left(a x \right)^{2} \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right)^{3}}{4 a^{4}}-\frac{i \pi  \arctanh \left(a x \right)^{2} \mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right)^{3}}{2 a^{4}}-\frac{\arctanh \left(a x \right)^{2}}{4 a^{4}}+\frac{\arctanh \left(a x \right)}{8 a^{4} \left(a x -1\right)}+\frac{\arctanh \left(a x \right)}{8 a^{4} \left(a x +1\right)}+\frac{\arctanh \left(a x \right)^{3}}{3 a^{4}}+\frac{\polylog \left(3, -\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}{2 a^{4}}-\frac{i \arctanh \left(a x \right)^{2} \pi  \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{\left(a^{2} x^{2}-1\right) \left(1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}\right)^{2} \mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right)}{4 a^{4}}-\frac{x}{16 a^{3} \left(a x -1\right)}-\frac{x}{16 a^{3} \left(a x +1\right)}+\frac{\arctanh \left(a x \right)^{2}}{4 a^{4} \left(a x +1\right)}+\frac{\arctanh \left(a x \right)^{2} \ln \left(a x +1\right)}{2 a^{4}}-\frac{\arctanh \left(a x \right)^{2} \ln \left(\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{a^{4}}-\frac{\arctanh \left(a x \right) \polylog \left(2, -\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}{a^{4}}-\frac{\arctanh \left(a x \right)^{2} \ln \left(2\right)}{a^{4}}-\frac{\arctanh \left(a x \right)^{2}}{4 a^{4} \left(a x -1\right)}+\frac{i \pi  \arctanh \left(a x \right)^{2} \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right) \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{\left(a^{2} x^{2}-1\right) \left(1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}\right)^{2}}{4 a^{4}}-\frac{i \pi  \arctanh \left(a x \right)^{2} \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right) \mathrm{csgn}\left(\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right)^{2}}{4 a^{4}}-\frac{i \pi  \arctanh \left(a x \right)^{2} \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right)^{2} \mathrm{csgn}\left(\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right)}{2 a^{4}}-\frac{1}{16 a^{4} \left(a x -1\right)}+\frac{1}{16 a^{4} \left(a x +1\right)}-\frac{i \arctanh \left(a x \right)^{2} \pi  \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{\left(a^{2} x^{2}-1\right) \left(1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}\right)^{3}}{4 a^{4}}+\frac{i \pi  \arctanh \left(a x \right)^{2} \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right) \mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{\left(a^{2} x^{2}-1\right) \left(1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}\right)}{4 a^{4}}+\frac{\arctanh \left(a x \right) x}{8 a^{3} \left(a x -1\right)}-\frac{\arctanh \left(a x \right) x}{8 a^{3} \left(a x +1\right)}-\frac{i \pi  \arctanh \left(a x \right)^{2}}{2 a^{4}}+\frac{\arctanh \left(a x \right)^{2} \ln \left(a x -1\right)}{2 a^{4}}"," ",0,"-1/2*I/a^4*Pi*arctanh(a*x)^2*csgn(I*(a*x+1)^2/(a^2*x^2-1))^2*csgn(I*(a*x+1)/(-a^2*x^2+1)^(1/2))+1/4*I/a^4*Pi*arctanh(a*x)^2*csgn(I*(a*x+1)^2/(a^2*x^2-1))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2-1/4*I/a^4*Pi*arctanh(a*x)^2*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2-1/4*I/a^4*Pi*arctanh(a*x)^2*csgn(I*(a*x+1)^2/(a^2*x^2-1))*csgn(I*(a*x+1)/(-a^2*x^2+1)^(1/2))^2+1/2/a^4*arctanh(a*x)^2*ln(a*x-1)+1/4/a^4*arctanh(a*x)^2/(a*x+1)+1/2/a^4*arctanh(a*x)^2*ln(a*x+1)-1/a^4*arctanh(a*x)^2*ln((a*x+1)/(-a^2*x^2+1)^(1/2))-1/a^4*arctanh(a*x)*polylog(2,-(a*x+1)^2/(-a^2*x^2+1))-1/a^4*arctanh(a*x)^2*ln(2)-1/4/a^4*arctanh(a*x)^2/(a*x-1)-1/16/a^3*x/(a*x-1)-1/16/a^3/(a*x+1)*x-1/4*I/a^4*Pi*arctanh(a*x)^2*csgn(I*(a*x+1)^2/(a^2*x^2-1))^3-1/2*I/a^4*Pi*arctanh(a*x)^2*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))^3-1/4*I/a^4*Pi*arctanh(a*x)^2*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^3+1/2*I/a^4*Pi*arctanh(a*x)^2*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))^2+1/3*arctanh(a*x)^3/a^4+1/8/a^4*arctanh(a*x)/(a*x-1)+1/8/a^4*arctanh(a*x)/(a*x+1)-1/16/a^4/(a*x-1)+1/16/a^4/(a*x+1)+1/2/a^4*polylog(3,-(a*x+1)^2/(-a^2*x^2+1))-1/4*arctanh(a*x)^2/a^4+1/4*I/a^4*Pi*arctanh(a*x)^2*csgn(I*(a*x+1)^2/(a^2*x^2-1))*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))-1/2*I/a^4*Pi*arctanh(a*x)^2+1/8/a^3*arctanh(a*x)/(a*x-1)*x-1/8/a^3*arctanh(a*x)/(a*x+1)*x","C"
267,1,1722,84,0.813000," ","int(x^2*arctanh(a*x)^2/(-a^2*x^2+1)^2,x)","\frac{i \arctanh \left(a x \right)^{2} \pi  \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right)^{2} \mathrm{csgn}\left(\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right) x^{2}}{4 a \left(a x -1\right) \left(a x +1\right)}-\frac{i \arctanh \left(a x \right)^{2} \pi  \,\mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right) \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{\left(a^{2} x^{2}-1\right) \left(1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}\right)^{2} x^{2}}{8 a \left(a x -1\right) \left(a x +1\right)}+\frac{i \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{\left(a^{2} x^{2}-1\right) \left(1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}\right) \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right) \mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right) \arctanh \left(a x \right)^{2} \pi}{8 a^{3} \left(a x -1\right) \left(a x +1\right)}+\frac{i \arctanh \left(a x \right)^{2} \pi  \,\mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right) \mathrm{csgn}\left(\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right)^{2} x^{2}}{8 a \left(a x -1\right) \left(a x +1\right)}+\frac{i \arctanh \left(a x \right)^{2} \pi  \mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right)^{2} x^{2}}{4 a \left(a x -1\right) \left(a x +1\right)}-\frac{i \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right) \mathrm{csgn}\left(\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right)^{2} \arctanh \left(a x \right)^{2} \pi}{8 a^{3} \left(a x -1\right) \left(a x +1\right)}-\frac{i \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{\left(a^{2} x^{2}-1\right) \left(1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}\right)^{2} \mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right) \arctanh \left(a x \right)^{2} \pi}{8 a^{3} \left(a x -1\right) \left(a x +1\right)}-\frac{i \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right)^{2} \mathrm{csgn}\left(\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right) \arctanh \left(a x \right)^{2} \pi}{4 a^{3} \left(a x -1\right) \left(a x +1\right)}+\frac{i \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{\left(a^{2} x^{2}-1\right) \left(1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}\right)^{2} \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right) \arctanh \left(a x \right)^{2} \pi}{8 a^{3} \left(a x -1\right) \left(a x +1\right)}+\frac{i \arctanh \left(a x \right)^{2} \pi  \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right)^{3} x^{2}}{8 a \left(a x -1\right) \left(a x +1\right)}+\frac{i \arctanh \left(a x \right)^{2} \pi  \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{\left(a^{2} x^{2}-1\right) \left(1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}\right)^{3} x^{2}}{8 a \left(a x -1\right) \left(a x +1\right)}-\frac{i \arctanh \left(a x \right)^{2} \pi  \mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right)^{3} x^{2}}{4 a \left(a x -1\right) \left(a x +1\right)}+\frac{i \arctanh \left(a x \right)^{2} \pi  \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{\left(a^{2} x^{2}-1\right) \left(1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}\right)^{2} \mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right) x^{2}}{8 a \left(a x -1\right) \left(a x +1\right)}-\frac{i \arctanh \left(a x \right)^{2} \pi  \,\mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right) \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{\left(a^{2} x^{2}-1\right) \left(1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}\right) \mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right) x^{2}}{8 a \left(a x -1\right) \left(a x +1\right)}+\frac{\arctanh \left(a x \right)^{3}}{6 a^{3} \left(a x -1\right) \left(a x +1\right)}+\frac{\arctanh \left(a x \right)}{4 a^{3} \left(a x -1\right) \left(a x +1\right)}+\frac{i \arctanh \left(a x \right)^{2} \pi}{4 a^{3} \left(a x -1\right) \left(a x +1\right)}-\frac{i \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{\left(a^{2} x^{2}-1\right) \left(1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}\right)^{3} \arctanh \left(a x \right)^{2} \pi}{8 a^{3} \left(a x -1\right) \left(a x +1\right)}+\frac{i \mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right)^{3} \arctanh \left(a x \right)^{2} \pi}{4 a^{3} \left(a x -1\right) \left(a x +1\right)}+\frac{\arctanh \left(a x \right)^{2} \ln \left(a x -1\right)}{4 a^{3}}-\frac{\arctanh \left(a x \right)^{2}}{4 a^{3} \left(a x +1\right)}-\frac{\arctanh \left(a x \right)^{2} \ln \left(a x +1\right)}{4 a^{3}}+\frac{\arctanh \left(a x \right)^{2} \ln \left(\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{2 a^{3}}-\frac{\arctanh \left(a x \right)^{2}}{4 a^{3} \left(a x -1\right)}-\frac{i \arctanh \left(a x \right)^{2} \pi  \,x^{2}}{4 a \left(a x -1\right) \left(a x +1\right)}-\frac{i \mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right)^{2} \arctanh \left(a x \right)^{2} \pi}{4 a^{3} \left(a x -1\right) \left(a x +1\right)}-\frac{\arctanh \left(a x \right)^{3} x^{2}}{6 a \left(a x -1\right) \left(a x +1\right)}-\frac{x}{4 a^{2} \left(a x -1\right) \left(a x +1\right)}-\frac{i \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right)^{3} \arctanh \left(a x \right)^{2} \pi}{8 a^{3} \left(a x -1\right) \left(a x +1\right)}+\frac{\arctanh \left(a x \right) x^{2}}{4 a \left(a x -1\right) \left(a x +1\right)}"," ",0,"-1/4*I/a^3/(a*x-1)/(a*x+1)*csgn(I*(a*x+1)^2/(a^2*x^2-1))^2*csgn(I*(a*x+1)/(-a^2*x^2+1)^(1/2))*arctanh(a*x)^2*Pi+1/8*I/a^3/(a*x-1)/(a*x+1)*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*csgn(I*(a*x+1)^2/(a^2*x^2-1))*arctanh(a*x)^2*Pi+1/8*I/a/(a*x-1)/(a*x+1)*arctanh(a*x)^2*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1))^3*x^2+1/8*I/a/(a*x-1)/(a*x+1)*arctanh(a*x)^2*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^3*x^2-1/4*I/a/(a*x-1)/(a*x+1)*arctanh(a*x)^2*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))^3*x^2+1/4*I/a/(a*x-1)/(a*x+1)*arctanh(a*x)^2*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*x^2-1/8*I/a^3/(a*x-1)/(a*x+1)*csgn(I*(a*x+1)^2/(a^2*x^2-1))*csgn(I*(a*x+1)/(-a^2*x^2+1)^(1/2))^2*arctanh(a*x)^2*Pi-1/8*I/a^3/(a*x-1)/(a*x+1)*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*arctanh(a*x)^2*Pi+1/8*I/a/(a*x-1)/(a*x+1)*arctanh(a*x)^2*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*x^2+1/4*I/a/(a*x-1)/(a*x+1)*arctanh(a*x)^2*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1))^2*csgn(I*(a*x+1)/(-a^2*x^2+1)^(1/2))*x^2-1/8*I/a/(a*x-1)/(a*x+1)*arctanh(a*x)^2*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*x^2-1/8*I/a/(a*x-1)/(a*x+1)*arctanh(a*x)^2*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*x^2+1/8*I/a^3/(a*x-1)/(a*x+1)*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*(a*x+1)^2/(a^2*x^2-1))*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*arctanh(a*x)^2*Pi+1/8*I/a/(a*x-1)/(a*x+1)*arctanh(a*x)^2*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1))*csgn(I*(a*x+1)/(-a^2*x^2+1)^(1/2))^2*x^2+1/4*I/a^3/(a*x-1)/(a*x+1)*arctanh(a*x)^2*Pi+1/4/a^3*arctanh(a*x)^2*ln(a*x-1)-1/4/a^3*arctanh(a*x)^2/(a*x+1)-1/4/a^3*arctanh(a*x)^2*ln(a*x+1)+1/2/a^3*arctanh(a*x)^2*ln((a*x+1)/(-a^2*x^2+1)^(1/2))-1/4/a^3*arctanh(a*x)^2/(a*x-1)-1/8*I/a^3/(a*x-1)/(a*x+1)*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^3*arctanh(a*x)^2*Pi+1/4*I/a^3/(a*x-1)/(a*x+1)*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))^3*arctanh(a*x)^2*Pi-1/4*I/a^3/(a*x-1)/(a*x+1)*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*arctanh(a*x)^2*Pi-1/4*I/a/(a*x-1)/(a*x+1)*arctanh(a*x)^2*Pi*x^2-1/8*I/a^3/(a*x-1)/(a*x+1)*csgn(I*(a*x+1)^2/(a^2*x^2-1))^3*arctanh(a*x)^2*Pi-1/6/a/(a*x-1)/(a*x+1)*arctanh(a*x)^3*x^2+1/4/a/(a*x-1)/(a*x+1)*arctanh(a*x)*x^2-1/4/a^2/(a*x-1)/(a*x+1)*x+1/6/a^3/(a*x-1)/(a*x+1)*arctanh(a*x)^3+1/4/a^3/(a*x-1)/(a*x+1)*arctanh(a*x)","C"
268,1,191,74,0.062000," ","int(x*arctanh(a*x)^2/(-a^2*x^2+1)^2,x)","-\frac{\arctanh \left(a x \right)^{2}}{2 a^{2} \left(a^{2} x^{2}-1\right)}+\frac{\arctanh \left(a x \right)}{4 a^{2} \left(a x -1\right)}+\frac{\arctanh \left(a x \right) \ln \left(a x -1\right)}{4 a^{2}}+\frac{\arctanh \left(a x \right)}{4 a^{2} \left(a x +1\right)}-\frac{\arctanh \left(a x \right) \ln \left(a x +1\right)}{4 a^{2}}+\frac{\ln \left(a x -1\right)^{2}}{16 a^{2}}-\frac{\ln \left(a x -1\right) \ln \left(\frac{1}{2}+\frac{a x}{2}\right)}{8 a^{2}}+\frac{\ln \left(a x +1\right)^{2}}{16 a^{2}}+\frac{\ln \left(-\frac{a x}{2}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{a x}{2}\right)}{8 a^{2}}-\frac{\ln \left(-\frac{a x}{2}+\frac{1}{2}\right) \ln \left(a x +1\right)}{8 a^{2}}-\frac{1}{8 a^{2} \left(a x -1\right)}+\frac{1}{8 a^{2} \left(a x +1\right)}"," ",0,"-1/2/a^2/(a^2*x^2-1)*arctanh(a*x)^2+1/4/a^2*arctanh(a*x)/(a*x-1)+1/4/a^2*arctanh(a*x)*ln(a*x-1)+1/4/a^2*arctanh(a*x)/(a*x+1)-1/4/a^2*arctanh(a*x)*ln(a*x+1)+1/16/a^2*ln(a*x-1)^2-1/8/a^2*ln(a*x-1)*ln(1/2+1/2*a*x)+1/16/a^2*ln(a*x+1)^2+1/8/a^2*ln(-1/2*a*x+1/2)*ln(1/2+1/2*a*x)-1/8/a^2*ln(-1/2*a*x+1/2)*ln(a*x+1)-1/8/a^2/(a*x-1)+1/8/a^2/(a*x+1)","B"
269,1,1695,78,0.806000," ","int(arctanh(a*x)^2/(-a^2*x^2+1)^2,x)","\frac{i \mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right)^{2} \arctanh \left(a x \right)^{2} \pi}{4 a \left(a x -1\right) \left(a x +1\right)}-\frac{i a \arctanh \left(a x \right)^{2} \pi  \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right)^{2} \mathrm{csgn}\left(\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right) x^{2}}{4 \left(a x -1\right) \left(a x +1\right)}-\frac{i \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{\left(a^{2} x^{2}-1\right) \left(1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}\right) \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right) \mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right) \arctanh \left(a x \right)^{2} \pi}{8 a \left(a x -1\right) \left(a x +1\right)}-\frac{i a \arctanh \left(a x \right)^{2} \pi  \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{\left(a^{2} x^{2}-1\right) \left(1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}\right)^{2} \mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right) x^{2}}{8 \left(a x -1\right) \left(a x +1\right)}+\frac{i \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{\left(a^{2} x^{2}-1\right) \left(1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}\right)^{2} \mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right) \arctanh \left(a x \right)^{2} \pi}{8 a \left(a x -1\right) \left(a x +1\right)}-\frac{i \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{\left(a^{2} x^{2}-1\right) \left(1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}\right)^{2} \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right) \arctanh \left(a x \right)^{2} \pi}{8 a \left(a x -1\right) \left(a x +1\right)}-\frac{i a \arctanh \left(a x \right)^{2} \pi  \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{\left(a^{2} x^{2}-1\right) \left(1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}\right)^{3} x^{2}}{8 \left(a x -1\right) \left(a x +1\right)}+\frac{i a \arctanh \left(a x \right)^{2} \pi  \mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right)^{3} x^{2}}{4 \left(a x -1\right) \left(a x +1\right)}-\frac{i a \arctanh \left(a x \right)^{2} \pi  \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right)^{3} x^{2}}{8 \left(a x -1\right) \left(a x +1\right)}-\frac{i a \arctanh \left(a x \right)^{2} \pi  \mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right)^{2} x^{2}}{4 \left(a x -1\right) \left(a x +1\right)}+\frac{i \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right) \mathrm{csgn}\left(\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right)^{2} \arctanh \left(a x \right)^{2} \pi}{8 a \left(a x -1\right) \left(a x +1\right)}+\frac{i \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right)^{2} \mathrm{csgn}\left(\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right) \arctanh \left(a x \right)^{2} \pi}{4 a \left(a x -1\right) \left(a x +1\right)}-\frac{\arctanh \left(a x \right)^{2} \ln \left(\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{2 a}+\frac{i a \arctanh \left(a x \right)^{2} \pi  \,\mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right) \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{\left(a^{2} x^{2}-1\right) \left(1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}\right)^{2} x^{2}}{8 \left(a x -1\right) \left(a x +1\right)}-\frac{i a \arctanh \left(a x \right)^{2} \pi  \,\mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right) \mathrm{csgn}\left(\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right)^{2} x^{2}}{8 \left(a x -1\right) \left(a x +1\right)}+\frac{i a \arctanh \left(a x \right)^{2} \pi  \,\mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right) \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{\left(a^{2} x^{2}-1\right) \left(1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}\right) \mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right) x^{2}}{8 \left(a x -1\right) \left(a x +1\right)}-\frac{\arctanh \left(a x \right)^{3}}{6 a \left(a x -1\right) \left(a x +1\right)}+\frac{\arctanh \left(a x \right)}{4 a \left(a x -1\right) \left(a x +1\right)}-\frac{i \arctanh \left(a x \right)^{2} \pi}{4 a \left(a x -1\right) \left(a x +1\right)}-\frac{\arctanh \left(a x \right)^{2} \ln \left(a x -1\right)}{4 a}-\frac{x}{4 \left(a x -1\right) \left(a x +1\right)}-\frac{i \mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right)^{3} \arctanh \left(a x \right)^{2} \pi}{4 a \left(a x -1\right) \left(a x +1\right)}+\frac{i \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right)^{3} \arctanh \left(a x \right)^{2} \pi}{8 a \left(a x -1\right) \left(a x +1\right)}+\frac{i a \arctanh \left(a x \right)^{2} \pi  \,x^{2}}{4 \left(a x -1\right) \left(a x +1\right)}+\frac{i \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{\left(a^{2} x^{2}-1\right) \left(1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}\right)^{3} \arctanh \left(a x \right)^{2} \pi}{8 a \left(a x -1\right) \left(a x +1\right)}+\frac{a \arctanh \left(a x \right)^{3} x^{2}}{6 \left(a x -1\right) \left(a x +1\right)}+\frac{a \arctanh \left(a x \right) x^{2}}{4 \left(a x -1\right) \left(a x +1\right)}+\frac{\arctanh \left(a x \right)^{2} \ln \left(a x +1\right)}{4 a}-\frac{\arctanh \left(a x \right)^{2}}{4 a \left(a x -1\right)}-\frac{\arctanh \left(a x \right)^{2}}{4 a \left(a x +1\right)}"," ",0,"-1/8*I*a/(a*x-1)/(a*x+1)*arctanh(a*x)^2*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^3*x^2+1/4*I*a/(a*x-1)/(a*x+1)*arctanh(a*x)^2*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))^3*x^2-1/8*I*a/(a*x-1)/(a*x+1)*arctanh(a*x)^2*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1))^3*x^2-1/4*I*a/(a*x-1)/(a*x+1)*arctanh(a*x)^2*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*x^2+1/8*I/a/(a*x-1)/(a*x+1)*csgn(I*(a*x+1)^2/(a^2*x^2-1))*csgn(I*(a*x+1)/(-a^2*x^2+1)^(1/2))^2*arctanh(a*x)^2*Pi+1/4*I/a/(a*x-1)/(a*x+1)*csgn(I*(a*x+1)^2/(a^2*x^2-1))^2*csgn(I*(a*x+1)/(-a^2*x^2+1)^(1/2))*arctanh(a*x)^2*Pi+1/8*I/a/(a*x-1)/(a*x+1)*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*arctanh(a*x)^2*Pi-1/8*I/a/(a*x-1)/(a*x+1)*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*csgn(I*(a*x+1)^2/(a^2*x^2-1))*arctanh(a*x)^2*Pi+1/8*I*a/(a*x-1)/(a*x+1)*arctanh(a*x)^2*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*x^2-1/8*I*a/(a*x-1)/(a*x+1)*arctanh(a*x)^2*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1))*csgn(I*(a*x+1)/(-a^2*x^2+1)^(1/2))^2*x^2-1/4*I*a/(a*x-1)/(a*x+1)*arctanh(a*x)^2*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1))^2*csgn(I*(a*x+1)/(-a^2*x^2+1)^(1/2))*x^2-1/8*I/a/(a*x-1)/(a*x+1)*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*(a*x+1)^2/(a^2*x^2-1))*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*arctanh(a*x)^2*Pi-1/8*I*a/(a*x-1)/(a*x+1)*arctanh(a*x)^2*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*x^2-1/6/a/(a*x-1)/(a*x+1)*arctanh(a*x)^3+1/4/a/(a*x-1)/(a*x+1)*arctanh(a*x)+1/8*I*a/(a*x-1)/(a*x+1)*arctanh(a*x)^2*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*x^2-1/4/a*arctanh(a*x)^2*ln(a*x-1)+1/4/a*arctanh(a*x)^2*ln(a*x+1)-1/2/a*arctanh(a*x)^2*ln((a*x+1)/(-a^2*x^2+1)^(1/2))-1/4*I/a/(a*x-1)/(a*x+1)*arctanh(a*x)^2*Pi+1/8*I/a/(a*x-1)/(a*x+1)*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^3*arctanh(a*x)^2*Pi-1/4*I/a/(a*x-1)/(a*x+1)*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))^3*arctanh(a*x)^2*Pi+1/8*I/a/(a*x-1)/(a*x+1)*csgn(I*(a*x+1)^2/(a^2*x^2-1))^3*arctanh(a*x)^2*Pi+1/4*I/a/(a*x-1)/(a*x+1)*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*arctanh(a*x)^2*Pi+1/4*I*a/(a*x-1)/(a*x+1)*arctanh(a*x)^2*Pi*x^2-1/4/(a*x-1)/(a*x+1)*x+1/6*a/(a*x-1)/(a*x+1)*arctanh(a*x)^3*x^2+1/4*a/(a*x-1)/(a*x+1)*arctanh(a*x)*x^2-1/4/a*arctanh(a*x)^2/(a*x-1)-1/4/a*arctanh(a*x)^2/(a*x+1)","C"
270,1,1290,124,0.732000," ","int(arctanh(a*x)^2/x/(-a^2*x^2+1)^2,x)","-\frac{a x +1}{16 \left(a x -1\right)}-\frac{a x -1}{16 \left(a x +1\right)}-\arctanh \left(a x \right)^{2} \ln \left(\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}-1\right)-2 \polylog \left(3, -\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)-\frac{\arctanh \left(a x \right)^{3}}{3}-\frac{\arctanh \left(a x \right) \left(a x -1\right)}{8 \left(a x +1\right)}+\frac{i \pi  \arctanh \left(a x \right)^{2}}{2}+\frac{\arctanh \left(a x \right)^{2}}{4 a x +4}-2 \polylog \left(3, \frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)+2 \arctanh \left(a x \right) \polylog \left(2, -\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)+2 \arctanh \left(a x \right) \polylog \left(2, \frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)-\frac{\arctanh \left(a x \right)^{2} \ln \left(a x +1\right)}{2}+\arctanh \left(a x \right)^{2} \ln \left(\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)-\frac{\arctanh \left(a x \right)^{2}}{4 \left(a x -1\right)}-\frac{\arctanh \left(a x \right)^{2} \ln \left(a x -1\right)}{2}+\arctanh \left(a x \right)^{2} \ln \left(2\right)+\arctanh \left(a x \right)^{2} \ln \left(a x \right)+\arctanh \left(a x \right)^{2} \ln \left(1-\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)+\arctanh \left(a x \right)^{2} \ln \left(1+\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)-\frac{i \arctanh \left(a x \right)^{2} \pi  \,\mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right) \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{\left(a^{2} x^{2}-1\right) \left(1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}\right)}{4}+\frac{i \pi  \mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right)^{3} \arctanh \left(a x \right)^{2}}{2}-\frac{i \arctanh \left(a x \right)^{2} \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}-1\right)\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}-1\right)}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right)^{2}}{2}-\frac{i \pi  \mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right)^{2} \arctanh \left(a x \right)^{2}}{2}-\frac{\arctanh \left(a x \right)^{2}}{4}+\frac{i \arctanh \left(a x \right)^{2} \pi  \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right)^{3}}{4}+\frac{i \arctanh \left(a x \right)^{2} \pi  \mathrm{csgn}\left(\frac{i \left(\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}-1\right)}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right)^{3}}{2}+\frac{\left(a x +1\right) \arctanh \left(a x \right)}{8 a x -8}+\frac{i \pi  \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{\left(a^{2} x^{2}-1\right) \left(1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}\right)^{3} \arctanh \left(a x \right)^{2}}{4}+\frac{i \arctanh \left(a x \right)^{2} \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}-1\right)\right) \mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}-1\right)}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right)}{2}+\frac{i \arctanh \left(a x \right)^{2} \pi  \mathrm{csgn}\left(\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right)^{2} \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right)}{4}-\frac{i \arctanh \left(a x \right)^{2} \pi  \,\mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}-1\right)}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right)^{2}}{2}+\frac{i \arctanh \left(a x \right)^{2} \pi  \,\mathrm{csgn}\left(\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right)^{2}}{2}+\frac{i \arctanh \left(a x \right)^{2} \pi  \,\mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{\left(a^{2} x^{2}-1\right) \left(1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}\right)^{2}}{4}-\frac{i \arctanh \left(a x \right)^{2} \pi  \,\mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right) \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{\left(a^{2} x^{2}-1\right) \left(1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}\right)^{2}}{4}"," ",0,"-1/4*arctanh(a*x)^2/(a*x-1)-1/2*arctanh(a*x)^2*ln(a*x-1)+1/4*arctanh(a*x)^2/(a*x+1)-1/2*arctanh(a*x)^2*ln(a*x+1)+arctanh(a*x)^2*ln((a*x+1)/(-a^2*x^2+1)^(1/2))-1/16*(a*x+1)/(a*x-1)-1/16*(a*x-1)/(a*x+1)-2*polylog(3,-(a*x+1)/(-a^2*x^2+1)^(1/2))-2*polylog(3,(a*x+1)/(-a^2*x^2+1)^(1/2))-1/3*arctanh(a*x)^3-1/4*arctanh(a*x)^2+1/2*I*Pi*arctanh(a*x)^2-1/8*arctanh(a*x)*(a*x-1)/(a*x+1)+1/8*(a*x+1)*arctanh(a*x)/(a*x-1)+arctanh(a*x)^2*ln(2)+arctanh(a*x)^2*ln(a*x)-arctanh(a*x)^2*ln((a*x+1)^2/(-a^2*x^2+1)-1)+arctanh(a*x)^2*ln(1-(a*x+1)/(-a^2*x^2+1)^(1/2))+arctanh(a*x)^2*ln(1+(a*x+1)/(-a^2*x^2+1)^(1/2))+2*arctanh(a*x)*polylog(2,-(a*x+1)/(-a^2*x^2+1)^(1/2))+2*arctanh(a*x)*polylog(2,(a*x+1)/(-a^2*x^2+1)^(1/2))+1/2*I*arctanh(a*x)^2*Pi*csgn(I*((a*x+1)^2/(-a^2*x^2+1)-1))*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*((a*x+1)^2/(-a^2*x^2+1)-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))-1/4*I*arctanh(a*x)^2*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*(a*x+1)^2/(a^2*x^2-1))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))-1/4*I*arctanh(a*x)^2*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2+1/4*I*arctanh(a*x)^2*Pi*csgn(I*(a*x+1)/(-a^2*x^2+1)^(1/2))^2*csgn(I*(a*x+1)^2/(a^2*x^2-1))-1/2*I*arctanh(a*x)^2*Pi*csgn(I*((a*x+1)^2/(-a^2*x^2+1)-1))*csgn(I*((a*x+1)^2/(-a^2*x^2+1)-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2+1/2*I*arctanh(a*x)^2*Pi*csgn(I*((a*x+1)^2/(-a^2*x^2+1)-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^3-1/2*I*arctanh(a*x)^2*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*((a*x+1)^2/(-a^2*x^2+1)-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2+1/2*I*arctanh(a*x)^2*Pi*csgn(I*(a*x+1)/(-a^2*x^2+1)^(1/2))*csgn(I*(a*x+1)^2/(a^2*x^2-1))^2+1/4*I*arctanh(a*x)^2*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2+1/4*I*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^3*arctanh(a*x)^2-1/2*I*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*arctanh(a*x)^2+1/2*I*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))^3*arctanh(a*x)^2+1/4*I*arctanh(a*x)^2*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1))^3","C"
271,1,4589,132,0.874000," ","int(arctanh(a*x)^2/x^2/(-a^2*x^2+1)^2,x)","\text{output too large to display}"," ",0,"-a*arctanh(a*x)^2+1/8*a*arctanh(a*x)/(a*x-1)-1/8*a*arctanh(a*x)/(a*x+1)-3/8*I*a*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*arctanh(a*x)*ln(1-(a*x+1)/(-a^2*x^2+1)^(1/2))-arctanh(a*x)^2/x+3/4*I*a*Pi*csgn(I*(a*x+1)/(-a^2*x^2+1)^(1/2))*csgn(I*(a*x+1)^2/(a^2*x^2-1))^2*polylog(2,(a*x+1)/(-a^2*x^2+1)^(1/2))+3/8*I*a*Pi*csgn(I*(a*x+1)/(-a^2*x^2+1)^(1/2))^2*csgn(I*(a*x+1)^2/(a^2*x^2-1))*dilog((a*x+1)/(-a^2*x^2+1)^(1/2))-3/8*I*a*Pi*csgn(I*(a*x+1)/(-a^2*x^2+1)^(1/2))^2*csgn(I*(a*x+1)^2/(a^2*x^2-1))*dilog(1+(a*x+1)/(-a^2*x^2+1)^(1/2))+3/8*I*a*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^3*arctanh(a*x)*ln(1-(a*x+1)/(-a^2*x^2+1)^(1/2))-3/8*I*a*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*dilog(1+(a*x+1)/(-a^2*x^2+1)^(1/2))+3/8*I*a*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*arctanh(a*x)^2+3/8*I*a*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*dilog(1+(a*x+1)/(-a^2*x^2+1)^(1/2))-3/8*I*a*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*polylog(2,(a*x+1)/(-a^2*x^2+1)^(1/2))-1/16*a^2*x/(a*x-1)+1/16/(a*x+1)*a^2*x-1/4*a*arctanh(a*x)^2/(a*x-1)-3/4*a*arctanh(a*x)^2*ln(a*x-1)-1/4*a*arctanh(a*x)^2/(a*x+1)+3/4*a*arctanh(a*x)^2*ln(a*x+1)-3/2*a*arctanh(a*x)^2*ln((a*x+1)/(-a^2*x^2+1)^(1/2))+2*a*arctanh(a*x)*ln(1+(a*x+1)/(-a^2*x^2+1)^(1/2))+a*arctanh(a*x)*ln(1-(a*x+1)/(-a^2*x^2+1)^(1/2))+3/8*I*a*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1))^3*dilog((a*x+1)/(-a^2*x^2+1)^(1/2))+3/8*I*a*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1))^3*polylog(2,(a*x+1)/(-a^2*x^2+1)^(1/2))-3/8*I*a*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^3*arctanh(a*x)^2-3/4*I*a*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*dilog(1+(a*x+1)/(-a^2*x^2+1)^(1/2))-3/4*I*a*Pi*arctanh(a*x)*ln(1-(a*x+1)/(-a^2*x^2+1)^(1/2))+3/8*I*a*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^3*polylog(2,-(a*x+1)/(-a^2*x^2+1)^(1/2))+3/8*I*a*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^3*polylog(2,(a*x+1)/(-a^2*x^2+1)^(1/2))+3/4*I*a*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*polylog(2,-(a*x+1)/(-a^2*x^2+1)^(1/2))-3/8*I*a*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^3*dilog(1+(a*x+1)/(-a^2*x^2+1)^(1/2))+3/4*I*a*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*polylog(2,(a*x+1)/(-a^2*x^2+1)^(1/2))-3/4*I*a*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))^3*polylog(2,(a*x+1)/(-a^2*x^2+1)^(1/2))-3/4*I*a*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))^3*dilog((a*x+1)/(-a^2*x^2+1)^(1/2))+3/4*I*a*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))^3*dilog(1+(a*x+1)/(-a^2*x^2+1)^(1/2))+1/2*a*arctanh(a*x)^3+a*polylog(2,-(a*x+1)/(-a^2*x^2+1)^(1/2))-a*dilog((a*x+1)/(-a^2*x^2+1)^(1/2))+a*polylog(2,(a*x+1)/(-a^2*x^2+1)^(1/2))+a*dilog(1+(a*x+1)/(-a^2*x^2+1)^(1/2))+3/8*I*a*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*dilog((a*x+1)/(-a^2*x^2+1)^(1/2))+3/8*I*a*Pi*csgn(I*(a*x+1)/(-a^2*x^2+1)^(1/2))^2*csgn(I*(a*x+1)^2/(a^2*x^2-1))*polylog(2,-(a*x+1)/(-a^2*x^2+1)^(1/2))-3/8*I*a*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*polylog(2,-(a*x+1)/(-a^2*x^2+1)^(1/2))-3/8*I*a*Pi*csgn(I*(a*x+1)/(-a^2*x^2+1)^(1/2))^2*csgn(I*(a*x+1)^2/(a^2*x^2-1))*arctanh(a*x)^2-3/4*I*a*Pi*csgn(I*(a*x+1)/(-a^2*x^2+1)^(1/2))*csgn(I*(a*x+1)^2/(a^2*x^2-1))^2*arctanh(a*x)^2+3/8*I*a*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1))^3*arctanh(a*x)*ln(1-(a*x+1)/(-a^2*x^2+1)^(1/2))+3/8*I*a*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*polylog(2,-(a*x+1)/(-a^2*x^2+1)^(1/2))-3/8*I*a*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*dilog((a*x+1)/(-a^2*x^2+1)^(1/2))-3/4*I*a*Pi*csgn(I*(a*x+1)/(-a^2*x^2+1)^(1/2))*csgn(I*(a*x+1)^2/(a^2*x^2-1))^2*dilog(1+(a*x+1)/(-a^2*x^2+1)^(1/2))+3/4*I*a*Pi*csgn(I*(a*x+1)/(-a^2*x^2+1)^(1/2))*csgn(I*(a*x+1)^2/(a^2*x^2-1))^2*dilog((a*x+1)/(-a^2*x^2+1)^(1/2))+3/8*I*a*Pi*csgn(I*(a*x+1)/(-a^2*x^2+1)^(1/2))^2*csgn(I*(a*x+1)^2/(a^2*x^2-1))*polylog(2,(a*x+1)/(-a^2*x^2+1)^(1/2))+3/8*I*a*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*polylog(2,(a*x+1)/(-a^2*x^2+1)^(1/2))+3/4*I*a*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*arctanh(a*x)*ln(1-(a*x+1)/(-a^2*x^2+1)^(1/2))-3/4*I*a*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))^3*arctanh(a*x)*ln(1-(a*x+1)/(-a^2*x^2+1)^(1/2))+3/4*I*a*Pi*csgn(I*(a*x+1)/(-a^2*x^2+1)^(1/2))*csgn(I*(a*x+1)^2/(a^2*x^2-1))^2*polylog(2,-(a*x+1)/(-a^2*x^2+1)^(1/2))-3/8*I*a*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*arctanh(a*x)^2-1/16*a/(a*x-1)-1/16*a/(a*x+1)+3/8*I*a*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1))^3*polylog(2,-(a*x+1)/(-a^2*x^2+1)^(1/2))+3/4*I*a*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*dilog((a*x+1)/(-a^2*x^2+1)^(1/2))+3/8*I*a*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^3*dilog((a*x+1)/(-a^2*x^2+1)^(1/2))+3/4*I*a*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))^3*arctanh(a*x)^2-3/4*I*a*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))^3*polylog(2,-(a*x+1)/(-a^2*x^2+1)^(1/2))-3/4*I*a*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*arctanh(a*x)^2-3/8*I*a*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1))^3*arctanh(a*x)^2-3/8*I*a*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1))^3*dilog(1+(a*x+1)/(-a^2*x^2+1)^(1/2))-3/4*I*a*Pi*polylog(2,(a*x+1)/(-a^2*x^2+1)^(1/2))-3/4*I*a*Pi*dilog((a*x+1)/(-a^2*x^2+1)^(1/2))-3/4*I*a*Pi*polylog(2,-(a*x+1)/(-a^2*x^2+1)^(1/2))+3/4*I*a*Pi*dilog(1+(a*x+1)/(-a^2*x^2+1)^(1/2))-3/8*I*a*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*(a*x+1)^2/(a^2*x^2-1))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))*polylog(2,(a*x+1)/(-a^2*x^2+1)^(1/2))+1/8*arctanh(a*x)/(a*x-1)*a^2*x+1/8*arctanh(a*x)/(a*x+1)*a^2*x+3/4*I*a*Pi*arctanh(a*x)^2+3/8*I*a*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*(a*x+1)^2/(a^2*x^2-1))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))*dilog(1+(a*x+1)/(-a^2*x^2+1)^(1/2))+3/8*I*a*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*arctanh(a*x)*ln(1-(a*x+1)/(-a^2*x^2+1)^(1/2))+3/4*I*a*Pi*csgn(I*(a*x+1)/(-a^2*x^2+1)^(1/2))*csgn(I*(a*x+1)^2/(a^2*x^2-1))^2*arctanh(a*x)*ln(1-(a*x+1)/(-a^2*x^2+1)^(1/2))-3/8*I*a*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*(a*x+1)^2/(a^2*x^2-1))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))*arctanh(a*x)*ln(1-(a*x+1)/(-a^2*x^2+1)^(1/2))+3/8*I*a*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*(a*x+1)^2/(a^2*x^2-1))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))*arctanh(a*x)^2-3/8*I*a*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*(a*x+1)^2/(a^2*x^2-1))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))*dilog((a*x+1)/(-a^2*x^2+1)^(1/2))+3/8*I*a*Pi*csgn(I*(a*x+1)/(-a^2*x^2+1)^(1/2))^2*csgn(I*(a*x+1)^2/(a^2*x^2-1))*arctanh(a*x)*ln(1-(a*x+1)/(-a^2*x^2+1)^(1/2))-3/8*I*a*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*(a*x+1)^2/(a^2*x^2-1))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))*polylog(2,-(a*x+1)/(-a^2*x^2+1)^(1/2))","C"
272,1,3040,191,2.260000," ","int(arctanh(a*x)^2/x^3/(-a^2*x^2+1)^2,x)","\text{output too large to display}"," ",0,"I*a^4*x^2/(a*x-1)/(a*x+1)*arctanh(a*x)^2*csgn(I*(a*x+1)/(-a^2*x^2+1)^(1/2))*csgn(I*(a*x+1)^2/(a^2*x^2-1))^2*Pi-I*a^4*x^2/(a*x-1)/(a*x+1)*arctanh(a*x)^2*csgn(I*((a*x+1)^2/(-a^2*x^2+1)-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*csgn(I*((a*x+1)^2/(-a^2*x^2+1)-1))*Pi+1/2*I*a^4*x^2/(a*x-1)/(a*x+1)*arctanh(a*x)^2*csgn(I*(a*x+1)/(-a^2*x^2+1)^(1/2))^2*csgn(I*(a*x+1)^2/(a^2*x^2-1))*Pi+1/2*I*a^2/(a*x-1)/(a*x+1)*arctanh(a*x)^2*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*(a*x+1)^2/(a^2*x^2-1))*Pi-I*a^2/(a*x-1)/(a*x+1)*arctanh(a*x)^2*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*((a*x+1)^2/(-a^2*x^2+1)-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*((a*x+1)^2/(-a^2*x^2+1)-1))*Pi+1/2*I*a^4*x^2/(a*x-1)/(a*x+1)*arctanh(a*x)^2*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*Pi-I*a^4*x^2/(a*x-1)/(a*x+1)*arctanh(a*x)^2*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*((a*x+1)^2/(-a^2*x^2+1)-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*Pi-1/2*I*a^4*x^2/(a*x-1)/(a*x+1)*arctanh(a*x)^2*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*csgn(I*(a*x+1)^2/(a^2*x^2-1))*Pi+4*a^2*arctanh(a*x)*polylog(2,-(a*x+1)/(-a^2*x^2+1)^(1/2))+4*a^2*arctanh(a*x)*polylog(2,(a*x+1)/(-a^2*x^2+1)^(1/2))+a^2*ln((a*x+1)/(-a^2*x^2+1)^(1/2)-1)-1/16*a^4/(a*x-1)/(a*x+1)*x^2+2/3*a^2/(a*x-1)/(a*x+1)*arctanh(a*x)^3-1/4*a^2/(a*x-1)/(a*x+1)*arctanh(a*x)^2+a^2/(a*x-1)/(a*x+1)*arctanh(a*x)-1/2*arctanh(a*x)^2/x^2-4*a^2*polylog(3,-(a*x+1)/(-a^2*x^2+1)^(1/2))-4*a^2*polylog(3,(a*x+1)/(-a^2*x^2+1)^(1/2))+I*a^4*x^2/(a*x-1)/(a*x+1)*arctanh(a*x)^2*csgn(I*((a*x+1)^2/(-a^2*x^2+1)-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^3*Pi-1/2*I*a^2/(a*x-1)/(a*x+1)*arctanh(a*x)^2*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*Pi+1/2*I*a^2/(a*x-1)/(a*x+1)*arctanh(a*x)^2*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*csgn(I*(a*x+1)^2/(a^2*x^2-1))*Pi-1/2*I*a^2/(a*x-1)/(a*x+1)*arctanh(a*x)^2*csgn(I*(a*x+1)/(-a^2*x^2+1)^(1/2))^2*csgn(I*(a*x+1)^2/(a^2*x^2-1))*Pi-I*a^2/(a*x-1)/(a*x+1)*arctanh(a*x)^2*csgn(I*(a*x+1)/(-a^2*x^2+1)^(1/2))*csgn(I*(a*x+1)^2/(a^2*x^2-1))^2*Pi+1/2*I*a^4*x^2/(a*x-1)/(a*x+1)*arctanh(a*x)^2*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^3*Pi+1/2*I*a^4*x^2/(a*x-1)/(a*x+1)*arctanh(a*x)^2*csgn(I*(a*x+1)^2/(a^2*x^2-1))^3*Pi-I*a^4*x^2/(a*x-1)/(a*x+1)*arctanh(a*x)^2*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*Pi+I*a^2/(a*x-1)/(a*x+1)*arctanh(a*x)^2*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*((a*x+1)^2/(-a^2*x^2+1)-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*Pi+I*a^2/(a*x-1)/(a*x+1)*arctanh(a*x)^2*csgn(I*((a*x+1)^2/(-a^2*x^2+1)-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*csgn(I*((a*x+1)^2/(-a^2*x^2+1)-1))*Pi+I*a^4*x^2/(a*x-1)/(a*x+1)*arctanh(a*x)^2*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))^3*Pi+I*a^4*x^2/(a*x-1)/(a*x+1)*arctanh(a*x)^2*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*((a*x+1)^2/(-a^2*x^2+1)-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*((a*x+1)^2/(-a^2*x^2+1)-1))*Pi-1/2*I*a^4*x^2/(a*x-1)/(a*x+1)*arctanh(a*x)^2*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*(a*x+1)^2/(a^2*x^2-1))*Pi-2/3*a^4*x^2/(a*x-1)/(a*x+1)*arctanh(a*x)^3+1/4*a^4*x^2/(a*x-1)/(a*x+1)*arctanh(a*x)^2-a^4*x^2/(a*x-1)/(a*x+1)*arctanh(a*x)-1/2*a^3*x/(a*x-1)/(a*x+1)*arctanh(a*x)+a/x/(a*x-1)/(a*x+1)*arctanh(a*x)-2*a^2/(a*x-1)/(a*x+1)*arctanh(a*x)^2*ln(2)-1/2*I*a^2/(a*x-1)/(a*x+1)*arctanh(a*x)^2*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^3*Pi-I*a^2/(a*x-1)/(a*x+1)*arctanh(a*x)^2*csgn(I*((a*x+1)^2/(-a^2*x^2+1)-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^3*Pi-1/2*I*a^2/(a*x-1)/(a*x+1)*arctanh(a*x)^2*csgn(I*(a*x+1)^2/(a^2*x^2-1))^3*Pi+a^2*ln(1+(a*x+1)/(-a^2*x^2+1)^(1/2))+I*a^2/(a*x-1)/(a*x+1)*arctanh(a*x)^2*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*Pi+I*a^4*x^2/(a*x-1)/(a*x+1)*arctanh(a*x)^2*Pi-I*a^2/(a*x-1)/(a*x+1)*arctanh(a*x)^2*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))^3*Pi-3/16*a^2/(a*x-1)/(a*x+1)+2*a^4*x^2/(a*x-1)/(a*x+1)*arctanh(a*x)^2*ln(2)-I*a^2/(a*x-1)/(a*x+1)*arctanh(a*x)^2*Pi+2*a^2*arctanh(a*x)^2*ln(a*x)-1/4*a^2*arctanh(a*x)^2/(a*x-1)-a^2*arctanh(a*x)^2*ln(a*x-1)-2*a^2*arctanh(a*x)^2*ln((a*x+1)^2/(-a^2*x^2+1)-1)+1/4*a^2*arctanh(a*x)^2/(a*x+1)-a^2*arctanh(a*x)^2*ln(a*x+1)+2*a^2*arctanh(a*x)^2*ln((a*x+1)/(-a^2*x^2+1)^(1/2))+2*a^2*arctanh(a*x)^2*ln(1-(a*x+1)/(-a^2*x^2+1)^(1/2))+2*a^2*arctanh(a*x)^2*ln(1+(a*x+1)/(-a^2*x^2+1)^(1/2))","C"
273,1,1015,207,0.704000," ","int(x^3*arctanh(a*x)^3/(-a^2*x^2+1)^2,x)","-\frac{3 \arctanh \left(a x \right)}{16 a^{4} \left(a x -1\right)}+\frac{3 \arctanh \left(a x \right)}{16 a^{4} \left(a x +1\right)}-\frac{3 \arctanh \left(a x \right)^{2} x}{16 a^{3} \left(a x +1\right)}-\frac{3 \arctanh \left(a x \right) x}{16 a^{3} \left(a x +1\right)}+\frac{3 \arctanh \left(a x \right)^{2} x}{16 a^{3} \left(a x -1\right)}-\frac{3 \arctanh \left(a x \right) x}{16 a^{3} \left(a x -1\right)}-\frac{i \arctanh \left(a x \right)^{3} \pi}{2 a^{4}}-\frac{i \arctanh \left(a x \right)^{3} \pi  \mathrm{csgn}\left(\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right)^{2} \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right)}{4 a^{4}}-\frac{i \arctanh \left(a x \right)^{3} \pi  \,\mathrm{csgn}\left(\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right)^{2}}{2 a^{4}}+\frac{i \arctanh \left(a x \right)^{3} \pi  \,\mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right) \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{\left(a^{2} x^{2}-1\right) \left(1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}\right)^{2}}{4 a^{4}}-\frac{i \arctanh \left(a x \right)^{3} \pi  \,\mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{\left(a^{2} x^{2}-1\right) \left(1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}\right)^{2}}{4 a^{4}}+\frac{\arctanh \left(a x \right)^{3}}{4 a^{4} \left(a x +1\right)}+\frac{\arctanh \left(a x \right)^{3} \ln \left(a x +1\right)}{2 a^{4}}+\frac{3 \arctanh \left(a x \right) \polylog \left(3, -\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}{2 a^{4}}-\frac{\arctanh \left(a x \right)^{3} \ln \left(\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{a^{4}}-\frac{3 \arctanh \left(a x \right)^{2} \polylog \left(2, -\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}{2 a^{4}}-\frac{\arctanh \left(a x \right)^{3} \ln \left(2\right)}{a^{4}}+\frac{3 \arctanh \left(a x \right)^{2}}{16 a^{4} \left(a x +1\right)}+\frac{3 \arctanh \left(a x \right)^{2}}{16 a^{4} \left(a x -1\right)}-\frac{\arctanh \left(a x \right)^{3}}{4 a^{4} \left(a x -1\right)}+\frac{\arctanh \left(a x \right)^{3} \ln \left(a x -1\right)}{2 a^{4}}-\frac{i \arctanh \left(a x \right)^{3} \pi  \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{\left(a^{2} x^{2}-1\right) \left(1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}\right)^{3}}{4 a^{4}}+\frac{i \arctanh \left(a x \right)^{3} \pi  \mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right)^{2}}{2 a^{4}}-\frac{i \arctanh \left(a x \right)^{3} \pi  \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right)^{3}}{4 a^{4}}-\frac{i \arctanh \left(a x \right)^{3} \pi  \mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right)^{3}}{2 a^{4}}-\frac{3 x}{32 a^{3} \left(a x +1\right)}+\frac{3 x}{32 a^{3} \left(a x -1\right)}+\frac{3}{32 a^{4} \left(a x -1\right)}+\frac{3}{32 a^{4} \left(a x +1\right)}-\frac{\arctanh \left(a x \right)^{3}}{4 a^{4}}+\frac{\arctanh \left(a x \right)^{4}}{4 a^{4}}-\frac{3 \polylog \left(4, -\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}{4 a^{4}}+\frac{i \arctanh \left(a x \right)^{3} \pi  \,\mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right) \mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{\left(a^{2} x^{2}-1\right) \left(1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}\right)}{4 a^{4}}"," ",0,"-1/4*I/a^4*arctanh(a*x)^3*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^3+1/2*I/a^4*arctanh(a*x)^3*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))^2-3/16/a^3*arctanh(a*x)^2/(a*x+1)*x-3/16/a^3*arctanh(a*x)/(a*x+1)*x+3/16/a^3*arctanh(a*x)^2/(a*x-1)*x-3/16/a^3*arctanh(a*x)/(a*x-1)*x-1/2*I/a^4*arctanh(a*x)^3*Pi-3/32/a^3/(a*x+1)*x+1/4/a^4*arctanh(a*x)^3/(a*x+1)+1/2/a^4*arctanh(a*x)^3*ln(a*x+1)+3/2/a^4*arctanh(a*x)*polylog(3,-(a*x+1)^2/(-a^2*x^2+1))-1/a^4*arctanh(a*x)^3*ln((a*x+1)/(-a^2*x^2+1)^(1/2))-3/2/a^4*arctanh(a*x)^2*polylog(2,-(a*x+1)^2/(-a^2*x^2+1))-1/a^4*arctanh(a*x)^3*ln(2)-1/4*I/a^4*arctanh(a*x)^3*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1))^3+3/32/a^3*x/(a*x-1)+3/16/a^4*arctanh(a*x)^2/(a*x+1)+3/16/a^4*arctanh(a*x)^2/(a*x-1)-1/4/a^4*arctanh(a*x)^3/(a*x-1)+1/2/a^4*arctanh(a*x)^3*ln(a*x-1)-1/4*arctanh(a*x)^3/a^4+1/4*arctanh(a*x)^4/a^4-1/2*I/a^4*arctanh(a*x)^3*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))^3-1/4*I/a^4*arctanh(a*x)^3*Pi*csgn(I*(a*x+1)/(-a^2*x^2+1)^(1/2))^2*csgn(I*(a*x+1)^2/(a^2*x^2-1))-1/2*I/a^4*arctanh(a*x)^3*Pi*csgn(I*(a*x+1)/(-a^2*x^2+1)^(1/2))*csgn(I*(a*x+1)^2/(a^2*x^2-1))^2+1/4*I/a^4*arctanh(a*x)^3*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2-1/4*I/a^4*arctanh(a*x)^3*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2-3/16/a^4*arctanh(a*x)/(a*x-1)+3/16/a^4*arctanh(a*x)/(a*x+1)-3/4/a^4*polylog(4,-(a*x+1)^2/(-a^2*x^2+1))+3/32/a^4/(a*x-1)+3/32/a^4/(a*x+1)+1/4*I/a^4*arctanh(a*x)^3*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1))*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))","C"
274,1,1771,109,0.818000," ","int(x^2*arctanh(a*x)^3/(-a^2*x^2+1)^2,x)","-\frac{\arctanh \left(a x \right)^{3}}{4 a^{3} \left(a x -1\right)}-\frac{\arctanh \left(a x \right)^{3}}{4 a^{3} \left(a x +1\right)}+\frac{3 x^{2}}{16 a \left(a x -1\right) \left(a x +1\right)}-\frac{i \arctanh \left(a x \right)^{3} \pi  \mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right)^{3} x^{2}}{4 a \left(a x -1\right) \left(a x +1\right)}+\frac{i \arctanh \left(a x \right)^{3} \pi  \mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right)^{2} x^{2}}{4 a \left(a x -1\right) \left(a x +1\right)}+\frac{i \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{\left(a^{2} x^{2}-1\right) \left(1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}\right)^{2} \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right) \arctanh \left(a x \right)^{3} \pi}{8 a^{3} \left(a x -1\right) \left(a x +1\right)}-\frac{i \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right) \mathrm{csgn}\left(\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right)^{2} \arctanh \left(a x \right)^{3} \pi}{8 a^{3} \left(a x -1\right) \left(a x +1\right)}-\frac{i \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{\left(a^{2} x^{2}-1\right) \left(1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}\right)^{2} \mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right) \arctanh \left(a x \right)^{3} \pi}{8 a^{3} \left(a x -1\right) \left(a x +1\right)}+\frac{i \arctanh \left(a x \right)^{3} \pi  \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right)^{3} x^{2}}{8 a \left(a x -1\right) \left(a x +1\right)}+\frac{i \arctanh \left(a x \right)^{3} \pi  \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{\left(a^{2} x^{2}-1\right) \left(1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}\right)^{3} x^{2}}{8 a \left(a x -1\right) \left(a x +1\right)}-\frac{i \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right)^{2} \mathrm{csgn}\left(\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right) \arctanh \left(a x \right)^{3} \pi}{4 a^{3} \left(a x -1\right) \left(a x +1\right)}+\frac{3}{16 a^{3} \left(a x -1\right) \left(a x +1\right)}+\frac{i \mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right)^{3} \arctanh \left(a x \right)^{3} \pi}{4 a^{3} \left(a x -1\right) \left(a x +1\right)}-\frac{i \arctanh \left(a x \right)^{3} \pi  \,x^{2}}{4 a \left(a x -1\right) \left(a x +1\right)}-\frac{i \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right)^{3} \arctanh \left(a x \right)^{3} \pi}{8 a^{3} \left(a x -1\right) \left(a x +1\right)}-\frac{i \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{\left(a^{2} x^{2}-1\right) \left(1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}\right)^{3} \arctanh \left(a x \right)^{3} \pi}{8 a^{3} \left(a x -1\right) \left(a x +1\right)}-\frac{i \mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right)^{2} \arctanh \left(a x \right)^{3} \pi}{4 a^{3} \left(a x -1\right) \left(a x +1\right)}-\frac{i \arctanh \left(a x \right)^{3} \pi  \,\mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right) \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{\left(a^{2} x^{2}-1\right) \left(1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}\right)^{2} x^{2}}{8 a \left(a x -1\right) \left(a x +1\right)}+\frac{i \arctanh \left(a x \right)^{3} \pi  \,\mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right) \mathrm{csgn}\left(\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right)^{2} x^{2}}{8 a \left(a x -1\right) \left(a x +1\right)}+\frac{i \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{\left(a^{2} x^{2}-1\right) \left(1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}\right) \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right) \mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right) \arctanh \left(a x \right)^{3} \pi}{8 a^{3} \left(a x -1\right) \left(a x +1\right)}+\frac{i \arctanh \left(a x \right)^{3} \pi  \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{\left(a^{2} x^{2}-1\right) \left(1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}\right)^{2} \mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right) x^{2}}{8 a \left(a x -1\right) \left(a x +1\right)}+\frac{i \arctanh \left(a x \right)^{3} \pi  \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right)^{2} \mathrm{csgn}\left(\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right) x^{2}}{4 a \left(a x -1\right) \left(a x +1\right)}+\frac{\arctanh \left(a x \right)^{3} \ln \left(a x -1\right)}{4 a^{3}}-\frac{\arctanh \left(a x \right)^{3} \ln \left(a x +1\right)}{4 a^{3}}+\frac{\arctanh \left(a x \right)^{3} \ln \left(\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{2 a^{3}}-\frac{i \arctanh \left(a x \right)^{3} \pi  \,\mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right) \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{\left(a^{2} x^{2}-1\right) \left(1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}\right) \mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right) x^{2}}{8 a \left(a x -1\right) \left(a x +1\right)}+\frac{\arctanh \left(a x \right)^{4}}{8 a^{3} \left(a x -1\right) \left(a x +1\right)}+\frac{3 \arctanh \left(a x \right)^{2}}{8 a^{3} \left(a x -1\right) \left(a x +1\right)}+\frac{i \arctanh \left(a x \right)^{3} \pi}{4 a^{3} \left(a x -1\right) \left(a x +1\right)}-\frac{\arctanh \left(a x \right)^{4} x^{2}}{8 a \left(a x -1\right) \left(a x +1\right)}+\frac{3 \arctanh \left(a x \right)^{2} x^{2}}{8 a \left(a x -1\right) \left(a x +1\right)}-\frac{3 \arctanh \left(a x \right) x}{4 a^{2} \left(a x -1\right) \left(a x +1\right)}"," ",0,"3/16/a/(a*x-1)/(a*x+1)*x^2+1/8/a^3/(a*x-1)/(a*x+1)*arctanh(a*x)^4+3/8/a^3/(a*x-1)/(a*x+1)*arctanh(a*x)^2-1/4*I/a^3/(a*x-1)/(a*x+1)*csgn(I*(a*x+1)^2/(a^2*x^2-1))^2*csgn(I*(a*x+1)/(-a^2*x^2+1)^(1/2))*arctanh(a*x)^3*Pi+1/8*I/a^3/(a*x-1)/(a*x+1)*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*csgn(I*(a*x+1)^2/(a^2*x^2-1))*arctanh(a*x)^3*Pi-1/8*I/a^3/(a*x-1)/(a*x+1)*csgn(I*(a*x+1)^2/(a^2*x^2-1))*csgn(I*(a*x+1)/(-a^2*x^2+1)^(1/2))^2*arctanh(a*x)^3*Pi-1/8*I/a^3/(a*x-1)/(a*x+1)*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*arctanh(a*x)^3*Pi+1/8*I/a/(a*x-1)/(a*x+1)*arctanh(a*x)^3*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1))^3*x^2+1/8*I/a/(a*x-1)/(a*x+1)*arctanh(a*x)^3*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^3*x^2-1/4*I/a/(a*x-1)/(a*x+1)*arctanh(a*x)^3*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))^3*x^2+1/4*I/a/(a*x-1)/(a*x+1)*arctanh(a*x)^3*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*x^2+3/16/a^3/(a*x-1)/(a*x+1)-1/4/a^3*arctanh(a*x)^3/(a*x-1)+1/4/a^3*arctanh(a*x)^3*ln(a*x-1)-1/4/a^3*arctanh(a*x)^3/(a*x+1)-1/4/a^3*arctanh(a*x)^3*ln(a*x+1)+1/2/a^3*arctanh(a*x)^3*ln((a*x+1)/(-a^2*x^2+1)^(1/2))-1/8*I/a/(a*x-1)/(a*x+1)*arctanh(a*x)^3*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*x^2+1/8*I/a/(a*x-1)/(a*x+1)*arctanh(a*x)^3*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1))*csgn(I*(a*x+1)/(-a^2*x^2+1)^(1/2))^2*x^2+1/8*I/a^3/(a*x-1)/(a*x+1)*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*(a*x+1)^2/(a^2*x^2-1))*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*arctanh(a*x)^3*Pi+1/8*I/a/(a*x-1)/(a*x+1)*arctanh(a*x)^3*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*x^2+1/4*I/a/(a*x-1)/(a*x+1)*arctanh(a*x)^3*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1))^2*csgn(I*(a*x+1)/(-a^2*x^2+1)^(1/2))*x^2-1/8*I/a/(a*x-1)/(a*x+1)*arctanh(a*x)^3*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*x^2+1/4*I/a^3/(a*x-1)/(a*x+1)*arctanh(a*x)^3*Pi+1/4*I/a^3/(a*x-1)/(a*x+1)*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))^3*arctanh(a*x)^3*Pi-1/4*I/a/(a*x-1)/(a*x+1)*arctanh(a*x)^3*Pi*x^2-1/8*I/a^3/(a*x-1)/(a*x+1)*csgn(I*(a*x+1)^2/(a^2*x^2-1))^3*arctanh(a*x)^3*Pi-1/8*I/a^3/(a*x-1)/(a*x+1)*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^3*arctanh(a*x)^3*Pi-1/4*I/a^3/(a*x-1)/(a*x+1)*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*arctanh(a*x)^3*Pi-1/8/a/(a*x-1)/(a*x+1)*arctanh(a*x)^4*x^2+3/8/a/(a*x-1)/(a*x+1)*arctanh(a*x)^2*x^2-3/4/a^2/(a*x-1)/(a*x+1)*arctanh(a*x)*x","C"
275,1,1708,107,0.810000," ","int(x*arctanh(a*x)^3/(-a^2*x^2+1)^2,x)","-\frac{3 i \arctanh \left(a x \right)^{2} \pi  \,\mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right) \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{\left(a^{2} x^{2}-1\right) \left(1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}\right)^{2} x^{2}}{16 \left(a x -1\right) \left(a x +1\right)}+\frac{3 i \arctanh \left(a x \right)^{2} \pi  \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{\left(a^{2} x^{2}-1\right) \left(1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}\right)^{2} \mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right) x^{2}}{16 \left(a x -1\right) \left(a x +1\right)}+\frac{3 i \arctanh \left(a x \right)^{2} \pi  \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right)^{2} \mathrm{csgn}\left(\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right) x^{2}}{8 \left(a x -1\right) \left(a x +1\right)}+\frac{3 i \arctanh \left(a x \right)^{2} \pi  \,\mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right) \mathrm{csgn}\left(\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right)^{2} x^{2}}{16 \left(a x -1\right) \left(a x +1\right)}+\frac{3 i \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{\left(a^{2} x^{2}-1\right) \left(1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}\right)^{2} \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right) \arctanh \left(a x \right)^{2} \pi}{16 a^{2} \left(a x -1\right) \left(a x +1\right)}-\frac{3 i \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{\left(a^{2} x^{2}-1\right) \left(1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}\right)^{2} \mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right) \arctanh \left(a x \right)^{2} \pi}{16 a^{2} \left(a x -1\right) \left(a x +1\right)}-\frac{3 i \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right)^{2} \mathrm{csgn}\left(\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right) \arctanh \left(a x \right)^{2} \pi}{8 a^{2} \left(a x -1\right) \left(a x +1\right)}-\frac{3 i \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right) \mathrm{csgn}\left(\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right)^{2} \arctanh \left(a x \right)^{2} \pi}{16 a^{2} \left(a x -1\right) \left(a x +1\right)}-\frac{\arctanh \left(a x \right)^{3}}{2 a^{2} \left(a^{2} x^{2}-1\right)}+\frac{3 \arctanh \left(a x \right)^{2}}{8 a^{2} \left(a x -1\right)}+\frac{3 \arctanh \left(a x \right)^{2} \ln \left(a x -1\right)}{8 a^{2}}+\frac{3 \arctanh \left(a x \right)^{2}}{8 a^{2} \left(a x +1\right)}-\frac{3 \arctanh \left(a x \right)^{2} \ln \left(a x +1\right)}{8 a^{2}}+\frac{3 \arctanh \left(a x \right)^{2} \ln \left(\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{4 a^{2}}+\frac{3 x}{8 a \left(a x -1\right) \left(a x +1\right)}+\frac{3 i \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{\left(a^{2} x^{2}-1\right) \left(1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}\right) \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right) \mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right) \arctanh \left(a x \right)^{2} \pi}{16 a^{2} \left(a x -1\right) \left(a x +1\right)}-\frac{3 i \arctanh \left(a x \right)^{2} \pi  \,\mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right) \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{\left(a^{2} x^{2}-1\right) \left(1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}\right) \mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right) x^{2}}{16 \left(a x -1\right) \left(a x +1\right)}+\frac{\arctanh \left(a x \right)^{3}}{4 a^{2} \left(a x -1\right) \left(a x +1\right)}-\frac{3 \arctanh \left(a x \right)}{8 a^{2} \left(a x -1\right) \left(a x +1\right)}-\frac{\arctanh \left(a x \right)^{3} x^{2}}{4 \left(a x -1\right) \left(a x +1\right)}-\frac{3 \arctanh \left(a x \right) x^{2}}{8 \left(a x -1\right) \left(a x +1\right)}-\frac{3 i \arctanh \left(a x \right)^{2} \pi  \,x^{2}}{8 \left(a x -1\right) \left(a x +1\right)}+\frac{3 i \arctanh \left(a x \right)^{2} \pi}{8 a^{2} \left(a x -1\right) \left(a x +1\right)}-\frac{3 i \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right)^{3} \arctanh \left(a x \right)^{2} \pi}{16 a^{2} \left(a x -1\right) \left(a x +1\right)}+\frac{3 i \mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right)^{3} \arctanh \left(a x \right)^{2} \pi}{8 a^{2} \left(a x -1\right) \left(a x +1\right)}+\frac{3 i \arctanh \left(a x \right)^{2} \pi  \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right)^{3} x^{2}}{16 \left(a x -1\right) \left(a x +1\right)}-\frac{3 i \arctanh \left(a x \right)^{2} \pi  \mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right)^{3} x^{2}}{8 \left(a x -1\right) \left(a x +1\right)}-\frac{3 i \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{\left(a^{2} x^{2}-1\right) \left(1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}\right)^{3} \arctanh \left(a x \right)^{2} \pi}{16 a^{2} \left(a x -1\right) \left(a x +1\right)}-\frac{3 i \mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right)^{2} \arctanh \left(a x \right)^{2} \pi}{8 a^{2} \left(a x -1\right) \left(a x +1\right)}+\frac{3 i \arctanh \left(a x \right)^{2} \pi  \mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right)^{2} x^{2}}{8 \left(a x -1\right) \left(a x +1\right)}+\frac{3 i \arctanh \left(a x \right)^{2} \pi  \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{\left(a^{2} x^{2}-1\right) \left(1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}\right)^{3} x^{2}}{16 \left(a x -1\right) \left(a x +1\right)}"," ",0,"3/8*I/(a*x-1)/(a*x+1)*arctanh(a*x)^2*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1))^2*csgn(I*(a*x+1)/(-a^2*x^2+1)^(1/2))*x^2+3/16*I/(a*x-1)/(a*x+1)*arctanh(a*x)^2*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1))*csgn(I*(a*x+1)/(-a^2*x^2+1)^(1/2))^2*x^2+3/16*I/a^2/(a*x-1)/(a*x+1)*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*csgn(I*(a*x+1)^2/(a^2*x^2-1))*arctanh(a*x)^2*Pi-3/16*I/a^2/(a*x-1)/(a*x+1)*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*arctanh(a*x)^2*Pi-3/8*I/a^2/(a*x-1)/(a*x+1)*csgn(I*(a*x+1)^2/(a^2*x^2-1))^2*csgn(I*(a*x+1)/(-a^2*x^2+1)^(1/2))*arctanh(a*x)^2*Pi-3/16*I/a^2/(a*x-1)/(a*x+1)*csgn(I*(a*x+1)^2/(a^2*x^2-1))*csgn(I*(a*x+1)/(-a^2*x^2+1)^(1/2))^2*arctanh(a*x)^2*Pi-3/16*I/(a*x-1)/(a*x+1)*arctanh(a*x)^2*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*x^2+3/16*I/(a*x-1)/(a*x+1)*arctanh(a*x)^2*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*x^2-1/2/a^2/(a^2*x^2-1)*arctanh(a*x)^3+3/8/a^2*arctanh(a*x)^2/(a*x-1)+3/8/a^2*arctanh(a*x)^2*ln(a*x-1)+3/8/a^2*arctanh(a*x)^2/(a*x+1)-3/8/a^2*arctanh(a*x)^2*ln(a*x+1)+3/4/a^2*arctanh(a*x)^2*ln((a*x+1)/(-a^2*x^2+1)^(1/2))+3/8/a/(a*x-1)/(a*x+1)*x+1/4/a^2/(a*x-1)/(a*x+1)*arctanh(a*x)^3-3/8/a^2/(a*x-1)/(a*x+1)*arctanh(a*x)+3/16*I/a^2/(a*x-1)/(a*x+1)*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*(a*x+1)^2/(a^2*x^2-1))*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*arctanh(a*x)^2*Pi-3/16*I/(a*x-1)/(a*x+1)*arctanh(a*x)^2*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*x^2-1/4/(a*x-1)/(a*x+1)*arctanh(a*x)^3*x^2-3/8/(a*x-1)/(a*x+1)*arctanh(a*x)*x^2+3/8*I/a^2/(a*x-1)/(a*x+1)*arctanh(a*x)^2*Pi-3/8*I/(a*x-1)/(a*x+1)*arctanh(a*x)^2*Pi*x^2-3/8*I/(a*x-1)/(a*x+1)*arctanh(a*x)^2*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))^3*x^2-3/16*I/a^2/(a*x-1)/(a*x+1)*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^3*arctanh(a*x)^2*Pi-3/16*I/a^2/(a*x-1)/(a*x+1)*csgn(I*(a*x+1)^2/(a^2*x^2-1))^3*arctanh(a*x)^2*Pi+3/8*I/a^2/(a*x-1)/(a*x+1)*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))^3*arctanh(a*x)^2*Pi-3/8*I/a^2/(a*x-1)/(a*x+1)*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*arctanh(a*x)^2*Pi+3/8*I/(a*x-1)/(a*x+1)*arctanh(a*x)^2*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*x^2+3/16*I/(a*x-1)/(a*x+1)*arctanh(a*x)^2*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^3*x^2+3/16*I/(a*x-1)/(a*x+1)*arctanh(a*x)^2*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1))^3*x^2","C"
276,1,1742,103,0.815000," ","int(arctanh(a*x)^3/(-a^2*x^2+1)^2,x)","\frac{i a \arctanh \left(a x \right)^{3} \pi  \,x^{2}}{4 \left(a x -1\right) \left(a x +1\right)}-\frac{i \mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right)^{3} \arctanh \left(a x \right)^{3} \pi}{4 a \left(a x -1\right) \left(a x +1\right)}-\frac{i \arctanh \left(a x \right)^{3} \pi}{4 a \left(a x -1\right) \left(a x +1\right)}-\frac{i a \arctanh \left(a x \right)^{3} \pi  \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right)^{3} x^{2}}{8 \left(a x -1\right) \left(a x +1\right)}-\frac{i a \arctanh \left(a x \right)^{3} \pi  \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{\left(a^{2} x^{2}-1\right) \left(1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}\right)^{3} x^{2}}{8 \left(a x -1\right) \left(a x +1\right)}+\frac{i a \arctanh \left(a x \right)^{3} \pi  \mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right)^{3} x^{2}}{4 \left(a x -1\right) \left(a x +1\right)}-\frac{i a \arctanh \left(a x \right)^{3} \pi  \mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right)^{2} x^{2}}{4 \left(a x -1\right) \left(a x +1\right)}+\frac{i \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{\left(a^{2} x^{2}-1\right) \left(1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}\right)^{2} \mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right) \arctanh \left(a x \right)^{3} \pi}{8 a \left(a x -1\right) \left(a x +1\right)}+\frac{i \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right)^{2} \mathrm{csgn}\left(\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right) \arctanh \left(a x \right)^{3} \pi}{4 a \left(a x -1\right) \left(a x +1\right)}-\frac{i \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{\left(a^{2} x^{2}-1\right) \left(1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}\right)^{2} \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right) \arctanh \left(a x \right)^{3} \pi}{8 a \left(a x -1\right) \left(a x +1\right)}+\frac{i \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right) \mathrm{csgn}\left(\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right)^{2} \arctanh \left(a x \right)^{3} \pi}{8 a \left(a x -1\right) \left(a x +1\right)}-\frac{i \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{\left(a^{2} x^{2}-1\right) \left(1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}\right) \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right) \mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right) \arctanh \left(a x \right)^{3} \pi}{8 a \left(a x -1\right) \left(a x +1\right)}-\frac{i a \arctanh \left(a x \right)^{3} \pi  \,\mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right) \mathrm{csgn}\left(\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right)^{2} x^{2}}{8 \left(a x -1\right) \left(a x +1\right)}-\frac{i a \arctanh \left(a x \right)^{3} \pi  \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{\left(a^{2} x^{2}-1\right) \left(1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}\right)^{2} \mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right) x^{2}}{8 \left(a x -1\right) \left(a x +1\right)}-\frac{i a \arctanh \left(a x \right)^{3} \pi  \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right)^{2} \mathrm{csgn}\left(\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right) x^{2}}{4 \left(a x -1\right) \left(a x +1\right)}+\frac{i a \arctanh \left(a x \right)^{3} \pi  \,\mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right) \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{\left(a^{2} x^{2}-1\right) \left(1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}\right)^{2} x^{2}}{8 \left(a x -1\right) \left(a x +1\right)}-\frac{\arctanh \left(a x \right)^{4}}{8 a \left(a x -1\right) \left(a x +1\right)}+\frac{3 \arctanh \left(a x \right)^{2}}{8 a \left(a x -1\right) \left(a x +1\right)}-\frac{3 \arctanh \left(a x \right) x}{4 \left(a x -1\right) \left(a x +1\right)}+\frac{i \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right)^{3} \arctanh \left(a x \right)^{3} \pi}{8 a \left(a x -1\right) \left(a x +1\right)}-\frac{\arctanh \left(a x \right)^{3}}{4 a \left(a x -1\right)}-\frac{\arctanh \left(a x \right)^{3} \ln \left(a x -1\right)}{4 a}-\frac{\arctanh \left(a x \right)^{3}}{4 a \left(a x +1\right)}+\frac{\arctanh \left(a x \right)^{3} \ln \left(a x +1\right)}{4 a}-\frac{\arctanh \left(a x \right)^{3} \ln \left(\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{2 a}+\frac{i a \arctanh \left(a x \right)^{3} \pi  \,\mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right) \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{\left(a^{2} x^{2}-1\right) \left(1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}\right) \mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right) x^{2}}{8 \left(a x -1\right) \left(a x +1\right)}+\frac{3}{16 \left(a x -1\right) \left(a x +1\right) a}+\frac{3 a \,x^{2}}{16 \left(a x -1\right) \left(a x +1\right)}+\frac{i \mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right)^{2} \arctanh \left(a x \right)^{3} \pi}{4 a \left(a x -1\right) \left(a x +1\right)}+\frac{i \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{\left(a^{2} x^{2}-1\right) \left(1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}\right)^{3} \arctanh \left(a x \right)^{3} \pi}{8 a \left(a x -1\right) \left(a x +1\right)}+\frac{a \arctanh \left(a x \right)^{4} x^{2}}{8 \left(a x -1\right) \left(a x +1\right)}+\frac{3 a \arctanh \left(a x \right)^{2} x^{2}}{8 \left(a x -1\right) \left(a x +1\right)}"," ",0,"-1/8*I*a/(a*x-1)/(a*x+1)*arctanh(a*x)^3*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1))^3*x^2-1/8*I*a/(a*x-1)/(a*x+1)*arctanh(a*x)^3*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^3*x^2+1/4*I*a/(a*x-1)/(a*x+1)*arctanh(a*x)^3*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))^3*x^2-1/4*I*a/(a*x-1)/(a*x+1)*arctanh(a*x)^3*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*x^2+1/8*I/a/(a*x-1)/(a*x+1)*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*arctanh(a*x)^3*Pi+1/4*I/a/(a*x-1)/(a*x+1)*csgn(I*(a*x+1)^2/(a^2*x^2-1))^2*csgn(I*(a*x+1)/(-a^2*x^2+1)^(1/2))*arctanh(a*x)^3*Pi-1/8*I/a/(a*x-1)/(a*x+1)*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*csgn(I*(a*x+1)^2/(a^2*x^2-1))*arctanh(a*x)^3*Pi+1/8*I/a/(a*x-1)/(a*x+1)*csgn(I*(a*x+1)^2/(a^2*x^2-1))*csgn(I*(a*x+1)/(-a^2*x^2+1)^(1/2))^2*arctanh(a*x)^3*Pi-1/4/a*arctanh(a*x)^3/(a*x-1)-1/4/a*arctanh(a*x)^3*ln(a*x-1)-1/4/a*arctanh(a*x)^3/(a*x+1)+1/4/a*arctanh(a*x)^3*ln(a*x+1)-1/2/a*arctanh(a*x)^3*ln((a*x+1)/(-a^2*x^2+1)^(1/2))-1/8*I/a/(a*x-1)/(a*x+1)*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*(a*x+1)^2/(a^2*x^2-1))*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*arctanh(a*x)^3*Pi-1/8*I*a/(a*x-1)/(a*x+1)*arctanh(a*x)^3*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1))*csgn(I*(a*x+1)/(-a^2*x^2+1)^(1/2))^2*x^2-1/8*I*a/(a*x-1)/(a*x+1)*arctanh(a*x)^3*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*x^2-1/4*I*a/(a*x-1)/(a*x+1)*arctanh(a*x)^3*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1))^2*csgn(I*(a*x+1)/(-a^2*x^2+1)^(1/2))*x^2+1/8*I*a/(a*x-1)/(a*x+1)*arctanh(a*x)^3*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*x^2+1/8*I*a/(a*x-1)/(a*x+1)*arctanh(a*x)^3*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*x^2+3/16/(a*x-1)/(a*x+1)/a-1/8/a/(a*x-1)/(a*x+1)*arctanh(a*x)^4+3/8/a/(a*x-1)/(a*x+1)*arctanh(a*x)^2-3/4/(a*x-1)/(a*x+1)*arctanh(a*x)*x-1/4*I/a/(a*x-1)/(a*x+1)*arctanh(a*x)^3*Pi+3/16/(a*x-1)/(a*x+1)*a*x^2+1/8*I/a/(a*x-1)/(a*x+1)*csgn(I*(a*x+1)^2/(a^2*x^2-1))^3*arctanh(a*x)^3*Pi+1/4*I*a/(a*x-1)/(a*x+1)*arctanh(a*x)^3*Pi*x^2-1/4*I/a/(a*x-1)/(a*x+1)*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))^3*arctanh(a*x)^3*Pi+1/4*I/a/(a*x-1)/(a*x+1)*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*arctanh(a*x)^3*Pi+1/8*I/a/(a*x-1)/(a*x+1)*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^3*arctanh(a*x)^3*Pi+1/8*a/(a*x-1)/(a*x+1)*arctanh(a*x)^4*x^2+3/8*a/(a*x-1)/(a*x+1)*arctanh(a*x)^2*x^2","C"
277,1,1387,173,0.739000," ","int(arctanh(a*x)^3/x/(-a^2*x^2+1)^2,x)","\frac{\arctanh \left(a x \right)^{3}}{4 a x +4}+\frac{\frac{3 a x}{32}+\frac{3}{32}}{a x -1}-\frac{i \pi  \,\mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right) \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{\left(a^{2} x^{2}-1\right) \left(1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}\right) \arctanh \left(a x \right)^{3}}{4}+\frac{i \arctanh \left(a x \right)^{3} \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}-1\right)\right) \mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}-1\right)}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right)}{2}+6 \polylog \left(4, \frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)-\frac{\arctanh \left(a x \right)^{3}}{4}+\frac{i \arctanh \left(a x \right)^{3} \pi  \mathrm{csgn}\left(\frac{i \left(\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}-1\right)}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right)^{3}}{2}+\frac{i \pi  \,\mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{\left(a^{2} x^{2}-1\right) \left(1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}\right)^{2} \arctanh \left(a x \right)^{3}}{4}+\frac{i \pi  \mathrm{csgn}\left(\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right)^{2} \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right) \arctanh \left(a x \right)^{3}}{4}+\frac{i \arctanh \left(a x \right)^{3} \pi  \,\mathrm{csgn}\left(\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right)^{2}}{2}-\frac{i \pi  \,\mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right) \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{\left(a^{2} x^{2}-1\right) \left(1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}\right)^{2} \arctanh \left(a x \right)^{3}}{4}-\frac{i \arctanh \left(a x \right)^{3} \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}-1\right)\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}-1\right)}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right)^{2}}{2}-\frac{i \arctanh \left(a x \right)^{3} \pi  \,\mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}-1\right)}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right)^{2}}{2}+\frac{i \pi  \mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right)^{3} \arctanh \left(a x \right)^{3}}{2}-\frac{i \pi  \mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right)^{2} \arctanh \left(a x \right)^{3}}{2}+\frac{i \arctanh \left(a x \right)^{3} \pi  \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right)^{3}}{4}+\frac{i \pi  \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{\left(a^{2} x^{2}-1\right) \left(1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}\right)^{3} \arctanh \left(a x \right)^{3}}{4}+6 \polylog \left(4, -\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)-\frac{3 \arctanh \left(a x \right) \left(a x -1\right)}{16 \left(a x +1\right)}-\frac{3 \left(a x +1\right) \arctanh \left(a x \right)}{16 \left(a x -1\right)}+\frac{3 \left(a x +1\right) \arctanh \left(a x \right)^{2}}{16 \left(a x -1\right)}-\frac{3 \arctanh \left(a x \right)^{2} \left(a x -1\right)}{16 \left(a x +1\right)}+\frac{i \pi  \arctanh \left(a x \right)^{3}}{2}-\frac{\arctanh \left(a x \right)^{3} \ln \left(a x -1\right)}{2}-\frac{\arctanh \left(a x \right)^{3} \ln \left(a x +1\right)}{2}+\arctanh \left(a x \right)^{3} \ln \left(\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)+\arctanh \left(a x \right)^{3} \ln \left(a x \right)-6 \arctanh \left(a x \right) \polylog \left(3, -\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)-\arctanh \left(a x \right)^{3} \ln \left(\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}-1\right)+\ln \left(2\right) \arctanh \left(a x \right)^{3}+\arctanh \left(a x \right)^{3} \ln \left(1+\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)+\arctanh \left(a x \right)^{3} \ln \left(1-\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)-6 \arctanh \left(a x \right) \polylog \left(3, \frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)+3 \arctanh \left(a x \right)^{2} \polylog \left(2, \frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)+3 \arctanh \left(a x \right)^{2} \polylog \left(2, -\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)-\frac{\arctanh \left(a x \right)^{3}}{4 \left(a x -1\right)}-\frac{3 \left(a x -1\right)}{32 \left(a x +1\right)}-\frac{\arctanh \left(a x \right)^{4}}{4}"," ",0,"3/32*(a*x+1)/(a*x-1)+1/4*I*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*arctanh(a*x)^3+3/16*(a*x+1)*arctanh(a*x)^2/(a*x-1)-3/16*arctanh(a*x)*(a*x-1)/(a*x+1)-3/16*arctanh(a*x)^2*(a*x-1)/(a*x+1)+1/2*I*Pi*arctanh(a*x)^3-1/4*arctanh(a*x)^4-1/4*arctanh(a*x)^3-3/16*(a*x+1)*arctanh(a*x)/(a*x-1)-1/4*arctanh(a*x)^3/(a*x-1)+1/4*arctanh(a*x)^3/(a*x+1)+arctanh(a*x)^3*ln(a*x)+6*polylog(4,-(a*x+1)/(-a^2*x^2+1)^(1/2))+6*polylog(4,(a*x+1)/(-a^2*x^2+1)^(1/2))-6*arctanh(a*x)*polylog(3,-(a*x+1)/(-a^2*x^2+1)^(1/2))-1/2*arctanh(a*x)^3*ln(a*x-1)-1/2*arctanh(a*x)^3*ln(a*x+1)+arctanh(a*x)^3*ln((a*x+1)/(-a^2*x^2+1)^(1/2))+1/2*I*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))^3*arctanh(a*x)^3-1/2*I*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*arctanh(a*x)^3+1/4*I*arctanh(a*x)^3*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1))^3+1/4*I*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^3*arctanh(a*x)^3+1/2*I*arctanh(a*x)^3*Pi*csgn(I*((a*x+1)^2/(-a^2*x^2+1)-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^3-6*arctanh(a*x)*polylog(3,(a*x+1)/(-a^2*x^2+1)^(1/2))-1/4*I*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*(a*x+1)^2/(a^2*x^2-1))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))*arctanh(a*x)^3+1/2*I*arctanh(a*x)^3*Pi*csgn(I*((a*x+1)^2/(-a^2*x^2+1)-1))*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*((a*x+1)^2/(-a^2*x^2+1)-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))+3*arctanh(a*x)^2*polylog(2,(a*x+1)/(-a^2*x^2+1)^(1/2))+3*arctanh(a*x)^2*polylog(2,-(a*x+1)/(-a^2*x^2+1)^(1/2))-arctanh(a*x)^3*ln((a*x+1)^2/(-a^2*x^2+1)-1)+ln(2)*arctanh(a*x)^3+arctanh(a*x)^3*ln(1+(a*x+1)/(-a^2*x^2+1)^(1/2))+arctanh(a*x)^3*ln(1-(a*x+1)/(-a^2*x^2+1)^(1/2))-3/32*(a*x-1)/(a*x+1)-1/2*I*arctanh(a*x)^3*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*((a*x+1)^2/(-a^2*x^2+1)-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2+1/4*I*Pi*csgn(I*(a*x+1)/(-a^2*x^2+1)^(1/2))^2*csgn(I*(a*x+1)^2/(a^2*x^2-1))*arctanh(a*x)^3+1/2*I*arctanh(a*x)^3*Pi*csgn(I*(a*x+1)/(-a^2*x^2+1)^(1/2))*csgn(I*(a*x+1)^2/(a^2*x^2-1))^2-1/4*I*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*arctanh(a*x)^3-1/2*I*arctanh(a*x)^3*Pi*csgn(I*((a*x+1)^2/(-a^2*x^2+1)-1))*csgn(I*((a*x+1)^2/(-a^2*x^2+1)-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2","C"
278,1,442,177,3.034000," ","int(arctanh(a*x)^3/x^2/(-a^2*x^2+1)^2,x)","\frac{3 a^{2} x}{32 \left(a x -1\right)}+\frac{3 a^{2} x}{32 \left(a x +1\right)}+\frac{3 a}{32 \left(a x -1\right)}-\frac{3 a}{32 \left(a x +1\right)}-\frac{\arctanh \left(a x \right)^{3}}{x}-\frac{3 a \arctanh \left(a x \right)}{16 \left(a x -1\right)}-\frac{3 a \arctanh \left(a x \right)}{16 \left(a x +1\right)}+6 a \arctanh \left(a x \right) \polylog \left(2, -\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)+6 a \arctanh \left(a x \right) \polylog \left(2, \frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)+\frac{3 a \arctanh \left(a x \right)^{2}}{16 \left(a x -1\right)}-\frac{3 a \arctanh \left(a x \right)^{2}}{16 \left(a x +1\right)}+3 a \arctanh \left(a x \right)^{2} \ln \left(1+\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)+3 a \arctanh \left(a x \right)^{2} \ln \left(1-\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)-\frac{a \arctanh \left(a x \right)^{3}}{8 \left(a x -1\right)}-\frac{a \arctanh \left(a x \right)^{3}}{8 \left(a x +1\right)}-6 a \polylog \left(3, -\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)-6 a \polylog \left(3, \frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)-a \arctanh \left(a x \right)^{3}+\frac{3 a \arctanh \left(a x \right)^{4}}{8}+\frac{\arctanh \left(a x \right)^{3} x \,a^{2}}{8 a x +8}+\frac{3 \arctanh \left(a x \right)^{2} x \,a^{2}}{16 \left(a x +1\right)}-\frac{3 \arctanh \left(a x \right) a^{2} x}{16 \left(a x -1\right)}+\frac{3 \arctanh \left(a x \right) a^{2} x}{16 \left(a x +1\right)}-\frac{\arctanh \left(a x \right)^{3} x \,a^{2}}{8 \left(a x -1\right)}+\frac{3 \arctanh \left(a x \right)^{2} x \,a^{2}}{16 \left(a x -1\right)}"," ",0,"-3/16*a*arctanh(a*x)/(a*x-1)-3/16*a*arctanh(a*x)/(a*x+1)-6*a*polylog(3,-(a*x+1)/(-a^2*x^2+1)^(1/2))-arctanh(a*x)^3/x+6*a*arctanh(a*x)*polylog(2,-(a*x+1)/(-a^2*x^2+1)^(1/2))+6*a*arctanh(a*x)*polylog(2,(a*x+1)/(-a^2*x^2+1)^(1/2))-6*a*polylog(3,(a*x+1)/(-a^2*x^2+1)^(1/2))+3/32*a^2*x/(a*x-1)+3/32/(a*x+1)*a^2*x+3/16*a*arctanh(a*x)^2/(a*x-1)-3/16*a*arctanh(a*x)^2/(a*x+1)-a*arctanh(a*x)^3+3/8*a*arctanh(a*x)^4+3/32*a/(a*x-1)-3/32*a/(a*x+1)-3/16*arctanh(a*x)/(a*x-1)*a^2*x+3/16*arctanh(a*x)/(a*x+1)*a^2*x-1/8/(a*x-1)*arctanh(a*x)^3*x*a^2+3/16/(a*x-1)*arctanh(a*x)^2*x*a^2+1/8/(a*x+1)*arctanh(a*x)^3*x*a^2+3/16/(a*x+1)*arctanh(a*x)^2*x*a^2+3*a*arctanh(a*x)^2*ln(1+(a*x+1)/(-a^2*x^2+1)^(1/2))+3*a*arctanh(a*x)^2*ln(1-(a*x+1)/(-a^2*x^2+1)^(1/2))-1/8*a/(a*x-1)*arctanh(a*x)^3-1/8*a/(a*x+1)*arctanh(a*x)^3","B"
279,1,672,278,6.423000," ","int(arctanh(a*x)^3/x^3/(-a^2*x^2+1)^2,x)","\frac{a^{2} \arctanh \left(a x \right)^{3}}{8 a x +8}-\frac{a^{3} \arctanh \left(a x \right)^{3} x}{8 \left(a x -1\right)}+\frac{3 a^{3} \arctanh \left(a x \right)^{2} x}{16 \left(a x -1\right)}-\frac{3 a^{3} \arctanh \left(a x \right) x}{16 \left(a x -1\right)}-\frac{a^{3} \arctanh \left(a x \right)^{3} x}{8 \left(a x +1\right)}-\frac{3 a^{3} \arctanh \left(a x \right)^{2} x}{16 \left(a x +1\right)}-\frac{3 a^{3} \arctanh \left(a x \right) x}{16 \left(a x +1\right)}-\frac{\arctanh \left(a x \right)^{3}}{2 x^{2}}-\frac{a^{2} \arctanh \left(a x \right)^{4}}{2}+12 a^{2} \polylog \left(4, \frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)+12 a^{2} \polylog \left(4, -\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)+3 a^{2} \polylog \left(2, -\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)+3 a^{2} \polylog \left(2, \frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)-12 a^{2} \arctanh \left(a x \right) \polylog \left(3, \frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)-\frac{a^{2} \arctanh \left(a x \right)^{3}}{8 \left(a x -1\right)}+\frac{3 a^{2} \arctanh \left(a x \right)^{2}}{16 \left(a x -1\right)}-\frac{3 a^{2} \arctanh \left(a x \right)}{16 \left(a x -1\right)}+\frac{3 a^{2} \arctanh \left(a x \right)^{2}}{16 \left(a x +1\right)}+\frac{3 a^{2} \arctanh \left(a x \right)}{16 \left(a x +1\right)}-\frac{3 a \arctanh \left(a x \right)^{2}}{2 x}+2 a^{2} \arctanh \left(a x \right)^{3} \ln \left(1+\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)+2 a^{2} \arctanh \left(a x \right)^{3} \ln \left(1-\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)+3 a^{2} \arctanh \left(a x \right) \ln \left(1+\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)+3 a^{2} \arctanh \left(a x \right) \ln \left(1-\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)+6 a^{2} \arctanh \left(a x \right)^{2} \polylog \left(2, -\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)+6 a^{2} \arctanh \left(a x \right)^{2} \polylog \left(2, \frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)+\frac{3 a^{3} x}{32 \left(a x -1\right)}-\frac{3 a^{3} x}{32 \left(a x +1\right)}+\frac{3 a^{2}}{32 \left(a x +1\right)}+\frac{3 a^{2}}{32 \left(a x -1\right)}+\frac{a^{2} \arctanh \left(a x \right)^{3}}{2}-\frac{3 a^{2} \arctanh \left(a x \right)^{2}}{2}-12 a^{2} \arctanh \left(a x \right) \polylog \left(3, -\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)"," ",0,"-3/16*a^3/(a*x-1)*arctanh(a*x)*x-1/8*a^3/(a*x+1)*arctanh(a*x)^3*x-3/16*a^3/(a*x+1)*arctanh(a*x)^2*x-3/16*a^3/(a*x+1)*arctanh(a*x)*x-1/8*a^3/(a*x-1)*arctanh(a*x)^3*x+3/16*a^3/(a*x-1)*arctanh(a*x)^2*x+6*a^2*arctanh(a*x)^2*polylog(2,-(a*x+1)/(-a^2*x^2+1)^(1/2))+6*a^2*arctanh(a*x)^2*polylog(2,(a*x+1)/(-a^2*x^2+1)^(1/2))-12*a^2*arctanh(a*x)*polylog(3,-(a*x+1)/(-a^2*x^2+1)^(1/2))-12*a^2*arctanh(a*x)*polylog(3,(a*x+1)/(-a^2*x^2+1)^(1/2))-1/8*a^2/(a*x-1)*arctanh(a*x)^3+3/16*a^2/(a*x-1)*arctanh(a*x)^2-3/16*a^2/(a*x-1)*arctanh(a*x)+1/8*a^2/(a*x+1)*arctanh(a*x)^3+3/16*a^2/(a*x+1)*arctanh(a*x)^2+3/16*a^2/(a*x+1)*arctanh(a*x)+3/32*a^3*x/(a*x-1)-3/32*a^3/(a*x+1)*x+1/2*a^2*arctanh(a*x)^3-3/2*a*arctanh(a*x)^2/x-1/2*arctanh(a*x)^3/x^2-1/2*a^2*arctanh(a*x)^4+3/32*a^2/(a*x+1)+3/32*a^2/(a*x-1)-3/2*a^2*arctanh(a*x)^2+12*a^2*polylog(4,(a*x+1)/(-a^2*x^2+1)^(1/2))+2*a^2*arctanh(a*x)^3*ln(1+(a*x+1)/(-a^2*x^2+1)^(1/2))+2*a^2*arctanh(a*x)^3*ln(1-(a*x+1)/(-a^2*x^2+1)^(1/2))+3*a^2*arctanh(a*x)*ln(1+(a*x+1)/(-a^2*x^2+1)^(1/2))+3*a^2*arctanh(a*x)*ln(1-(a*x+1)/(-a^2*x^2+1)^(1/2))+12*a^2*polylog(4,-(a*x+1)/(-a^2*x^2+1)^(1/2))+3*a^2*polylog(2,-(a*x+1)/(-a^2*x^2+1)^(1/2))+3*a^2*polylog(2,(a*x+1)/(-a^2*x^2+1)^(1/2))","B"
280,-2,0,77,180.000000," ","int(arctanh(a*x)^(1/2)/(-a^2*x^2+1)^2,x)","\int \frac{\sqrt{\arctanh \left(a x \right)}}{\left(-a^{2} x^{2}+1\right)^{2}}\, dx"," ",0,"int(arctanh(a*x)^(1/2)/(-a^2*x^2+1)^2,x)","F"
281,0,0,35,0.798000," ","int(x^4/(-a^2*x^2+1)^2/arctanh(a*x),x)","\int \frac{x^{4}}{\left(-a^{2} x^{2}+1\right)^{2} \arctanh \left(a x \right)}\, dx"," ",0,"int(x^4/(-a^2*x^2+1)^2/arctanh(a*x),x)","F"
282,0,0,40,0.589000," ","int(x^3/(-a^2*x^2+1)^2/arctanh(a*x),x)","\int \frac{x^{3}}{\left(-a^{2} x^{2}+1\right)^{2} \arctanh \left(a x \right)}\, dx"," ",0,"int(x^3/(-a^2*x^2+1)^2/arctanh(a*x),x)","F"
283,1,24,23,0.200000," ","int(x^2/(-a^2*x^2+1)^2/arctanh(a*x),x)","\frac{\Chi \left(2 \arctanh \left(a x \right)\right)}{2 a^{3}}-\frac{\ln \left(\arctanh \left(a x \right)\right)}{2 a^{3}}"," ",0,"1/2*Chi(2*arctanh(a*x))/a^3-1/2*ln(arctanh(a*x))/a^3","A"
284,1,13,12,0.205000," ","int(x/(-a^2*x^2+1)^2/arctanh(a*x),x)","\frac{\Shi \left(2 \arctanh \left(a x \right)\right)}{2 a^{2}}"," ",0,"1/2*Shi(2*arctanh(a*x))/a^2","A"
285,1,24,23,0.176000," ","int(1/(-a^2*x^2+1)^2/arctanh(a*x),x)","\frac{\Chi \left(2 \arctanh \left(a x \right)\right)}{2 a}+\frac{\ln \left(\arctanh \left(a x \right)\right)}{2 a}"," ",0,"1/2*Chi(2*arctanh(a*x))/a+1/2*ln(arctanh(a*x))/a","A"
286,0,0,34,0.515000," ","int(1/x/(-a^2*x^2+1)^2/arctanh(a*x),x)","\int \frac{1}{x \left(-a^{2} x^{2}+1\right)^{2} \arctanh \left(a x \right)}\, dx"," ",0,"int(1/x/(-a^2*x^2+1)^2/arctanh(a*x),x)","F"
287,0,0,60,0.596000," ","int(x^3/(-a^2*x^2+1)^2/arctanh(a*x)^2,x)","\int \frac{x^{3}}{\left(-a^{2} x^{2}+1\right)^{2} \arctanh \left(a x \right)^{2}}\, dx"," ",0,"int(x^3/(-a^2*x^2+1)^2/arctanh(a*x)^2,x)","F"
288,1,36,38,0.197000," ","int(x^2/(-a^2*x^2+1)^2/arctanh(a*x)^2,x)","\frac{\frac{1}{2 \arctanh \left(a x \right)}-\frac{\cosh \left(2 \arctanh \left(a x \right)\right)}{2 \arctanh \left(a x \right)}+\Shi \left(2 \arctanh \left(a x \right)\right)}{a^{3}}"," ",0,"1/a^3*(1/2/arctanh(a*x)-1/2/arctanh(a*x)*cosh(2*arctanh(a*x))+Shi(2*arctanh(a*x)))","A"
289,1,28,36,0.204000," ","int(x/(-a^2*x^2+1)^2/arctanh(a*x)^2,x)","\frac{-\frac{\sinh \left(2 \arctanh \left(a x \right)\right)}{2 \arctanh \left(a x \right)}+\Chi \left(2 \arctanh \left(a x \right)\right)}{a^{2}}"," ",0,"1/a^2*(-1/2*sinh(2*arctanh(a*x))/arctanh(a*x)+Chi(2*arctanh(a*x)))","A"
290,1,36,35,0.176000," ","int(1/(-a^2*x^2+1)^2/arctanh(a*x)^2,x)","\frac{-\frac{1}{2 \arctanh \left(a x \right)}-\frac{\cosh \left(2 \arctanh \left(a x \right)\right)}{2 \arctanh \left(a x \right)}+\Shi \left(2 \arctanh \left(a x \right)\right)}{a}"," ",0,"1/a*(-1/2/arctanh(a*x)-1/2/arctanh(a*x)*cosh(2*arctanh(a*x))+Shi(2*arctanh(a*x)))","A"
291,0,0,61,0.529000," ","int(1/x/(-a^2*x^2+1)^2/arctanh(a*x)^2,x)","\int \frac{1}{x \left(-a^{2} x^{2}+1\right)^{2} \arctanh \left(a x \right)^{2}}\, dx"," ",0,"int(1/x/(-a^2*x^2+1)^2/arctanh(a*x)^2,x)","F"
292,0,0,94,0.602000," ","int(x^3/(-a^2*x^2+1)^2/arctanh(a*x)^3,x)","\int \frac{x^{3}}{\left(-a^{2} x^{2}+1\right)^{2} \arctanh \left(a x \right)^{3}}\, dx"," ",0,"int(x^3/(-a^2*x^2+1)^2/arctanh(a*x)^3,x)","F"
293,1,51,62,0.201000," ","int(x^2/(-a^2*x^2+1)^2/arctanh(a*x)^3,x)","\frac{\frac{1}{4 \arctanh \left(a x \right)^{2}}-\frac{\cosh \left(2 \arctanh \left(a x \right)\right)}{4 \arctanh \left(a x \right)^{2}}-\frac{\sinh \left(2 \arctanh \left(a x \right)\right)}{2 \arctanh \left(a x \right)}+\Chi \left(2 \arctanh \left(a x \right)\right)}{a^{3}}"," ",0,"1/a^3*(1/4/arctanh(a*x)^2-1/4/arctanh(a*x)^2*cosh(2*arctanh(a*x))-1/2*sinh(2*arctanh(a*x))/arctanh(a*x)+Chi(2*arctanh(a*x)))","A"
294,1,43,69,0.204000," ","int(x/(-a^2*x^2+1)^2/arctanh(a*x)^3,x)","\frac{-\frac{\sinh \left(2 \arctanh \left(a x \right)\right)}{4 \arctanh \left(a x \right)^{2}}-\frac{\cosh \left(2 \arctanh \left(a x \right)\right)}{2 \arctanh \left(a x \right)}+\Shi \left(2 \arctanh \left(a x \right)\right)}{a^{2}}"," ",0,"1/a^2*(-1/4*sinh(2*arctanh(a*x))/arctanh(a*x)^2-1/2/arctanh(a*x)*cosh(2*arctanh(a*x))+Shi(2*arctanh(a*x)))","A"
295,1,51,56,0.178000," ","int(1/(-a^2*x^2+1)^2/arctanh(a*x)^3,x)","\frac{-\frac{1}{4 \arctanh \left(a x \right)^{2}}-\frac{\cosh \left(2 \arctanh \left(a x \right)\right)}{4 \arctanh \left(a x \right)^{2}}-\frac{\sinh \left(2 \arctanh \left(a x \right)\right)}{2 \arctanh \left(a x \right)}+\Chi \left(2 \arctanh \left(a x \right)\right)}{a}"," ",0,"1/a*(-1/4/arctanh(a*x)^2-1/4/arctanh(a*x)^2*cosh(2*arctanh(a*x))-1/2*sinh(2*arctanh(a*x))/arctanh(a*x)+Chi(2*arctanh(a*x)))","A"
296,0,0,91,0.546000," ","int(1/x/(-a^2*x^2+1)^2/arctanh(a*x)^3,x)","\int \frac{1}{x \left(-a^{2} x^{2}+1\right)^{2} \arctanh \left(a x \right)^{3}}\, dx"," ",0,"int(1/x/(-a^2*x^2+1)^2/arctanh(a*x)^3,x)","F"
297,1,68,90,0.180000," ","int(1/(-a^2*x^2+1)^2/arctanh(a*x)^4,x)","\frac{-\frac{1}{6 \arctanh \left(a x \right)^{3}}-\frac{\cosh \left(2 \arctanh \left(a x \right)\right)}{6 \arctanh \left(a x \right)^{3}}-\frac{\sinh \left(2 \arctanh \left(a x \right)\right)}{6 \arctanh \left(a x \right)^{2}}-\frac{\cosh \left(2 \arctanh \left(a x \right)\right)}{3 \arctanh \left(a x \right)}+\frac{2 \Shi \left(2 \arctanh \left(a x \right)\right)}{3}}{a}"," ",0,"1/a*(-1/6/arctanh(a*x)^3-1/6/arctanh(a*x)^3*cosh(2*arctanh(a*x))-1/6*sinh(2*arctanh(a*x))/arctanh(a*x)^2-1/3/arctanh(a*x)*cosh(2*arctanh(a*x))+2/3*Shi(2*arctanh(a*x)))","A"
298,1,83,111,0.192000," ","int(1/(-a^2*x^2+1)^2/arctanh(a*x)^5,x)","\frac{-\frac{1}{8 \arctanh \left(a x \right)^{4}}-\frac{\cosh \left(2 \arctanh \left(a x \right)\right)}{8 \arctanh \left(a x \right)^{4}}-\frac{\sinh \left(2 \arctanh \left(a x \right)\right)}{12 \arctanh \left(a x \right)^{3}}-\frac{\cosh \left(2 \arctanh \left(a x \right)\right)}{12 \arctanh \left(a x \right)^{2}}-\frac{\sinh \left(2 \arctanh \left(a x \right)\right)}{6 \arctanh \left(a x \right)}+\frac{\Chi \left(2 \arctanh \left(a x \right)\right)}{3}}{a}"," ",0,"1/a*(-1/8/arctanh(a*x)^4-1/8/arctanh(a*x)^4*cosh(2*arctanh(a*x))-1/12/arctanh(a*x)^3*sinh(2*arctanh(a*x))-1/12/arctanh(a*x)^2*cosh(2*arctanh(a*x))-1/6*sinh(2*arctanh(a*x))/arctanh(a*x)+1/3*Chi(2*arctanh(a*x)))","A"
299,1,98,144,0.184000," ","int(1/(-a^2*x^2+1)^2/arctanh(a*x)^6,x)","\frac{-\frac{1}{10 \arctanh \left(a x \right)^{5}}-\frac{\cosh \left(2 \arctanh \left(a x \right)\right)}{10 \arctanh \left(a x \right)^{5}}-\frac{\sinh \left(2 \arctanh \left(a x \right)\right)}{20 \arctanh \left(a x \right)^{4}}-\frac{\cosh \left(2 \arctanh \left(a x \right)\right)}{30 \arctanh \left(a x \right)^{3}}-\frac{\sinh \left(2 \arctanh \left(a x \right)\right)}{30 \arctanh \left(a x \right)^{2}}-\frac{\cosh \left(2 \arctanh \left(a x \right)\right)}{15 \arctanh \left(a x \right)}+\frac{2 \Shi \left(2 \arctanh \left(a x \right)\right)}{15}}{a}"," ",0,"1/a*(-1/10/arctanh(a*x)^5-1/10/arctanh(a*x)^5*cosh(2*arctanh(a*x))-1/20/arctanh(a*x)^4*sinh(2*arctanh(a*x))-1/30/arctanh(a*x)^3*cosh(2*arctanh(a*x))-1/30*sinh(2*arctanh(a*x))/arctanh(a*x)^2-1/15/arctanh(a*x)*cosh(2*arctanh(a*x))+2/15*Shi(2*arctanh(a*x)))","A"
300,1,113,165,0.183000," ","int(1/(-a^2*x^2+1)^2/arctanh(a*x)^7,x)","\frac{-\frac{1}{12 \arctanh \left(a x \right)^{6}}-\frac{\cosh \left(2 \arctanh \left(a x \right)\right)}{12 \arctanh \left(a x \right)^{6}}-\frac{\sinh \left(2 \arctanh \left(a x \right)\right)}{30 \arctanh \left(a x \right)^{5}}-\frac{\cosh \left(2 \arctanh \left(a x \right)\right)}{60 \arctanh \left(a x \right)^{4}}-\frac{\sinh \left(2 \arctanh \left(a x \right)\right)}{90 \arctanh \left(a x \right)^{3}}-\frac{\cosh \left(2 \arctanh \left(a x \right)\right)}{90 \arctanh \left(a x \right)^{2}}-\frac{\sinh \left(2 \arctanh \left(a x \right)\right)}{45 \arctanh \left(a x \right)}+\frac{2 \Chi \left(2 \arctanh \left(a x \right)\right)}{45}}{a}"," ",0,"1/a*(-1/12/arctanh(a*x)^6-1/12/arctanh(a*x)^6*cosh(2*arctanh(a*x))-1/30/arctanh(a*x)^5*sinh(2*arctanh(a*x))-1/60/arctanh(a*x)^4*cosh(2*arctanh(a*x))-1/90/arctanh(a*x)^3*sinh(2*arctanh(a*x))-1/90/arctanh(a*x)^2*cosh(2*arctanh(a*x))-1/45*sinh(2*arctanh(a*x))/arctanh(a*x)+2/45*Chi(2*arctanh(a*x)))","A"
301,1,128,197,0.180000," ","int(1/(-a^2*x^2+1)^2/arctanh(a*x)^8,x)","\frac{-\frac{1}{14 \arctanh \left(a x \right)^{7}}-\frac{\cosh \left(2 \arctanh \left(a x \right)\right)}{14 \arctanh \left(a x \right)^{7}}-\frac{\sinh \left(2 \arctanh \left(a x \right)\right)}{42 \arctanh \left(a x \right)^{6}}-\frac{\cosh \left(2 \arctanh \left(a x \right)\right)}{105 \arctanh \left(a x \right)^{5}}-\frac{\sinh \left(2 \arctanh \left(a x \right)\right)}{210 \arctanh \left(a x \right)^{4}}-\frac{\cosh \left(2 \arctanh \left(a x \right)\right)}{315 \arctanh \left(a x \right)^{3}}-\frac{\sinh \left(2 \arctanh \left(a x \right)\right)}{315 \arctanh \left(a x \right)^{2}}-\frac{2 \cosh \left(2 \arctanh \left(a x \right)\right)}{315 \arctanh \left(a x \right)}+\frac{4 \Shi \left(2 \arctanh \left(a x \right)\right)}{315}}{a}"," ",0,"1/a*(-1/14/arctanh(a*x)^7-1/14/arctanh(a*x)^7*cosh(2*arctanh(a*x))-1/42/arctanh(a*x)^6*sinh(2*arctanh(a*x))-1/105/arctanh(a*x)^5*cosh(2*arctanh(a*x))-1/210/arctanh(a*x)^4*sinh(2*arctanh(a*x))-1/315/arctanh(a*x)^3*cosh(2*arctanh(a*x))-1/315*sinh(2*arctanh(a*x))/arctanh(a*x)^2-2/315/arctanh(a*x)*cosh(2*arctanh(a*x))+4/315*Shi(2*arctanh(a*x)))","A"
302,1,136,69,0.043000," ","int(x^3*arctanh(a*x)/(-a^2*x^2+1)^3,x)","\frac{\arctanh \left(a x \right)}{16 a^{4} \left(a x -1\right)^{2}}+\frac{3 \arctanh \left(a x \right)}{16 a^{4} \left(a x -1\right)}+\frac{\arctanh \left(a x \right)}{16 a^{4} \left(a x +1\right)^{2}}-\frac{3 \arctanh \left(a x \right)}{16 a^{4} \left(a x +1\right)}-\frac{1}{64 a^{4} \left(a x -1\right)^{2}}-\frac{5}{64 a^{4} \left(a x -1\right)}-\frac{5 \ln \left(a x -1\right)}{64 a^{4}}+\frac{1}{64 a^{4} \left(a x +1\right)^{2}}-\frac{5}{64 a^{4} \left(a x +1\right)}+\frac{5 \ln \left(a x +1\right)}{64 a^{4}}"," ",0,"1/16/a^4*arctanh(a*x)/(a*x-1)^2+3/16/a^4*arctanh(a*x)/(a*x-1)+1/16/a^4*arctanh(a*x)/(a*x+1)^2-3/16/a^4*arctanh(a*x)/(a*x+1)-1/64/a^4/(a*x-1)^2-5/64/a^4/(a*x-1)-5/64/a^4*ln(a*x-1)+1/64/a^4/(a*x+1)^2-5/64/a^4/(a*x+1)+5/64/a^4*ln(a*x+1)","A"
303,1,225,90,0.064000," ","int(x^2*arctanh(a*x)/(-a^2*x^2+1)^3,x)","\frac{\arctanh \left(a x \right)}{16 a^{3} \left(a x -1\right)^{2}}+\frac{\arctanh \left(a x \right)}{16 a^{3} \left(a x -1\right)}+\frac{\arctanh \left(a x \right) \ln \left(a x -1\right)}{16 a^{3}}-\frac{\arctanh \left(a x \right)}{16 a^{3} \left(a x +1\right)^{2}}+\frac{\arctanh \left(a x \right)}{16 a^{3} \left(a x +1\right)}-\frac{\arctanh \left(a x \right) \ln \left(a x +1\right)}{16 a^{3}}+\frac{\ln \left(a x +1\right)^{2}}{64 a^{3}}+\frac{\ln \left(-\frac{a x}{2}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{a x}{2}\right)}{32 a^{3}}-\frac{\ln \left(-\frac{a x}{2}+\frac{1}{2}\right) \ln \left(a x +1\right)}{32 a^{3}}+\frac{\ln \left(a x -1\right)^{2}}{64 a^{3}}-\frac{\ln \left(a x -1\right) \ln \left(\frac{1}{2}+\frac{a x}{2}\right)}{32 a^{3}}-\frac{1}{64 a^{3} \left(a x -1\right)^{2}}-\frac{1}{64 a^{3} \left(a x -1\right)}-\frac{1}{64 a^{3} \left(a x +1\right)^{2}}+\frac{1}{64 a^{3} \left(a x +1\right)}"," ",0,"1/16/a^3*arctanh(a*x)/(a*x-1)^2+1/16/a^3*arctanh(a*x)/(a*x-1)+1/16/a^3*arctanh(a*x)*ln(a*x-1)-1/16/a^3*arctanh(a*x)/(a*x+1)^2+1/16/a^3*arctanh(a*x)/(a*x+1)-1/16/a^3*arctanh(a*x)*ln(a*x+1)+1/64/a^3*ln(a*x+1)^2+1/32/a^3*ln(-1/2*a*x+1/2)*ln(1/2+1/2*a*x)-1/32/a^3*ln(-1/2*a*x+1/2)*ln(a*x+1)+1/64/a^3*ln(a*x-1)^2-1/32/a^3*ln(a*x-1)*ln(1/2+1/2*a*x)-1/64/a^3/(a*x-1)^2-1/64/a^3/(a*x-1)-1/64/a^3/(a*x+1)^2+1/64/a^3/(a*x+1)","B"
304,1,92,67,0.035000," ","int(x*arctanh(a*x)/(-a^2*x^2+1)^3,x)","\frac{\arctanh \left(a x \right)}{4 a^{2} \left(a^{2} x^{2}-1\right)^{2}}-\frac{1}{64 a^{2} \left(a x -1\right)^{2}}+\frac{3}{64 a^{2} \left(a x -1\right)}+\frac{3 \ln \left(a x -1\right)}{64 a^{2}}+\frac{1}{64 a^{2} \left(a x +1\right)^{2}}+\frac{3}{64 a^{2} \left(a x +1\right)}-\frac{3 \ln \left(a x +1\right)}{64 a^{2}}"," ",0,"1/4/a^2/(a^2*x^2-1)^2*arctanh(a*x)-1/64/a^2/(a*x-1)^2+3/64/a^2/(a*x-1)+3/64/a^2*ln(a*x-1)+1/64/a^2/(a*x+1)^2+3/64/a^2/(a*x+1)-3/64/a^2*ln(a*x+1)","A"
305,1,225,84,0.064000," ","int(arctanh(a*x)/(-a^2*x^2+1)^3,x)","\frac{\arctanh \left(a x \right)}{16 a \left(a x -1\right)^{2}}-\frac{3 \arctanh \left(a x \right)}{16 a \left(a x -1\right)}-\frac{3 \arctanh \left(a x \right) \ln \left(a x -1\right)}{16 a}-\frac{\arctanh \left(a x \right)}{16 a \left(a x +1\right)^{2}}-\frac{3 \arctanh \left(a x \right)}{16 a \left(a x +1\right)}+\frac{3 \arctanh \left(a x \right) \ln \left(a x +1\right)}{16 a}-\frac{3 \ln \left(a x -1\right)^{2}}{64 a}+\frac{3 \ln \left(a x -1\right) \ln \left(\frac{1}{2}+\frac{a x}{2}\right)}{32 a}-\frac{3 \ln \left(a x +1\right)^{2}}{64 a}-\frac{3 \ln \left(-\frac{a x}{2}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{a x}{2}\right)}{32 a}+\frac{3 \ln \left(-\frac{a x}{2}+\frac{1}{2}\right) \ln \left(a x +1\right)}{32 a}-\frac{1}{64 a \left(a x -1\right)^{2}}+\frac{7}{64 a \left(a x -1\right)}-\frac{1}{64 a \left(a x +1\right)^{2}}-\frac{7}{64 a \left(a x +1\right)}"," ",0,"1/16/a*arctanh(a*x)/(a*x-1)^2-3/16/a*arctanh(a*x)/(a*x-1)-3/16/a*arctanh(a*x)*ln(a*x-1)-1/16/a*arctanh(a*x)/(a*x+1)^2-3/16/a*arctanh(a*x)/(a*x+1)+3/16/a*arctanh(a*x)*ln(a*x+1)-3/64/a*ln(a*x-1)^2+3/32/a*ln(a*x-1)*ln(1/2+1/2*a*x)-3/64/a*ln(a*x+1)^2-3/32/a*ln(-1/2*a*x+1/2)*ln(1/2+1/2*a*x)+3/32/a*ln(-1/2*a*x+1/2)*ln(a*x+1)-1/64/a/(a*x-1)^2+7/64/a/(a*x-1)-1/64/a/(a*x+1)^2-7/64/a/(a*x+1)","B"
306,1,234,115,0.071000," ","int(arctanh(a*x)/x/(-a^2*x^2+1)^3,x)","\arctanh \left(a x \right) \ln \left(a x \right)+\frac{\arctanh \left(a x \right)}{16 \left(a x -1\right)^{2}}-\frac{5 \arctanh \left(a x \right)}{16 \left(a x -1\right)}-\frac{\arctanh \left(a x \right) \ln \left(a x -1\right)}{2}+\frac{\arctanh \left(a x \right)}{16 \left(a x +1\right)^{2}}+\frac{5 \arctanh \left(a x \right)}{16 \left(a x +1\right)}-\frac{\arctanh \left(a x \right) \ln \left(a x +1\right)}{2}-\frac{\dilog \left(a x \right)}{2}-\frac{\dilog \left(a x +1\right)}{2}-\frac{\ln \left(a x \right) \ln \left(a x +1\right)}{2}-\frac{\ln \left(a x -1\right)^{2}}{8}+\frac{\dilog \left(\frac{1}{2}+\frac{a x}{2}\right)}{2}+\frac{\ln \left(a x -1\right) \ln \left(\frac{1}{2}+\frac{a x}{2}\right)}{4}+\frac{\ln \left(a x +1\right)^{2}}{8}-\frac{\left(\ln \left(a x +1\right)-\ln \left(\frac{1}{2}+\frac{a x}{2}\right)\right) \ln \left(-\frac{a x}{2}+\frac{1}{2}\right)}{4}-\frac{1}{64 \left(a x -1\right)^{2}}+\frac{11}{64 \left(a x -1\right)}+\frac{11 \ln \left(a x -1\right)}{64}+\frac{1}{64 \left(a x +1\right)^{2}}+\frac{11}{64 \left(a x +1\right)}-\frac{11 \ln \left(a x +1\right)}{64}"," ",0,"arctanh(a*x)*ln(a*x)+1/16*arctanh(a*x)/(a*x-1)^2-5/16*arctanh(a*x)/(a*x-1)-1/2*arctanh(a*x)*ln(a*x-1)+1/16*arctanh(a*x)/(a*x+1)^2+5/16*arctanh(a*x)/(a*x+1)-1/2*arctanh(a*x)*ln(a*x+1)-1/2*dilog(a*x)-1/2*dilog(a*x+1)-1/2*ln(a*x)*ln(a*x+1)-1/8*ln(a*x-1)^2+1/2*dilog(1/2+1/2*a*x)+1/4*ln(a*x-1)*ln(1/2+1/2*a*x)+1/8*ln(a*x+1)^2-1/4*(ln(a*x+1)-ln(1/2+1/2*a*x))*ln(-1/2*a*x+1/2)-1/64/(a*x-1)^2+11/64/(a*x-1)+11/64*ln(a*x-1)+1/64/(a*x+1)^2+11/64/(a*x+1)-11/64*ln(a*x+1)","B"
307,1,228,111,0.070000," ","int(arctanh(a*x)/x^2/(-a^2*x^2+1)^3,x)","-\frac{\arctanh \left(a x \right)}{x}+\frac{a \arctanh \left(a x \right)}{16 \left(a x -1\right)^{2}}-\frac{7 a \arctanh \left(a x \right)}{16 \left(a x -1\right)}-\frac{15 a \arctanh \left(a x \right) \ln \left(a x -1\right)}{16}-\frac{a \arctanh \left(a x \right)}{16 \left(a x +1\right)^{2}}-\frac{7 a \arctanh \left(a x \right)}{16 \left(a x +1\right)}+\frac{15 a \arctanh \left(a x \right) \ln \left(a x +1\right)}{16}-\frac{15 a \ln \left(a x -1\right)^{2}}{64}+\frac{15 a \ln \left(a x -1\right) \ln \left(\frac{1}{2}+\frac{a x}{2}\right)}{32}-\frac{15 a \ln \left(a x +1\right)^{2}}{64}+\frac{15 a \ln \left(-\frac{a x}{2}+\frac{1}{2}\right) \ln \left(a x +1\right)}{32}-\frac{15 a \ln \left(-\frac{a x}{2}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{a x}{2}\right)}{32}+a \ln \left(a x \right)-\frac{a}{64 \left(a x -1\right)^{2}}+\frac{15 a}{64 \left(a x -1\right)}-\frac{a \ln \left(a x -1\right)}{2}-\frac{a}{64 \left(a x +1\right)^{2}}-\frac{15 a}{64 \left(a x +1\right)}-\frac{a \ln \left(a x +1\right)}{2}"," ",0,"-arctanh(a*x)/x+1/16*a*arctanh(a*x)/(a*x-1)^2-7/16*a*arctanh(a*x)/(a*x-1)-15/16*a*arctanh(a*x)*ln(a*x-1)-1/16*a*arctanh(a*x)/(a*x+1)^2-7/16*a*arctanh(a*x)/(a*x+1)+15/16*a*arctanh(a*x)*ln(a*x+1)-15/64*a*ln(a*x-1)^2+15/32*a*ln(a*x-1)*ln(1/2+1/2*a*x)-15/64*a*ln(a*x+1)^2+15/32*a*ln(-1/2*a*x+1/2)*ln(a*x+1)-15/32*a*ln(-1/2*a*x+1/2)*ln(1/2+1/2*a*x)+a*ln(a*x)-1/64*a/(a*x-1)^2+15/64*a/(a*x-1)-1/2*a*ln(a*x-1)-1/64*a/(a*x+1)^2-15/64*a/(a*x+1)-1/2*a*ln(a*x+1)","B"
308,1,297,115,0.070000," ","int(x^3*arctanh(a*x)^2/(-a^2*x^2+1)^3,x)","\frac{\arctanh \left(a x \right)^{2}}{16 a^{4} \left(a x -1\right)^{2}}+\frac{3 \arctanh \left(a x \right)^{2}}{16 a^{4} \left(a x -1\right)}+\frac{\arctanh \left(a x \right)^{2}}{16 a^{4} \left(a x +1\right)^{2}}-\frac{3 \arctanh \left(a x \right)^{2}}{16 a^{4} \left(a x +1\right)}-\frac{\arctanh \left(a x \right)}{32 a^{4} \left(a x -1\right)^{2}}-\frac{5 \arctanh \left(a x \right)}{32 a^{4} \left(a x -1\right)}-\frac{5 \arctanh \left(a x \right) \ln \left(a x -1\right)}{32 a^{4}}+\frac{\arctanh \left(a x \right)}{32 a^{4} \left(a x +1\right)^{2}}-\frac{5 \arctanh \left(a x \right)}{32 a^{4} \left(a x +1\right)}+\frac{5 \arctanh \left(a x \right) \ln \left(a x +1\right)}{32 a^{4}}-\frac{5 \ln \left(a x -1\right)^{2}}{128 a^{4}}+\frac{5 \ln \left(a x -1\right) \ln \left(\frac{1}{2}+\frac{a x}{2}\right)}{64 a^{4}}-\frac{5 \ln \left(a x +1\right)^{2}}{128 a^{4}}-\frac{5 \ln \left(-\frac{a x}{2}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{a x}{2}\right)}{64 a^{4}}+\frac{5 \ln \left(-\frac{a x}{2}+\frac{1}{2}\right) \ln \left(a x +1\right)}{64 a^{4}}+\frac{1}{128 a^{4} \left(a x -1\right)^{2}}+\frac{9}{128 a^{4} \left(a x -1\right)}+\frac{1}{128 a^{4} \left(a x +1\right)^{2}}-\frac{9}{128 a^{4} \left(a x +1\right)}"," ",0,"1/16/a^4*arctanh(a*x)^2/(a*x-1)^2+3/16/a^4*arctanh(a*x)^2/(a*x-1)+1/16/a^4*arctanh(a*x)^2/(a*x+1)^2-3/16/a^4*arctanh(a*x)^2/(a*x+1)-1/32/a^4*arctanh(a*x)/(a*x-1)^2-5/32/a^4*arctanh(a*x)/(a*x-1)-5/32/a^4*arctanh(a*x)*ln(a*x-1)+1/32/a^4*arctanh(a*x)/(a*x+1)^2-5/32/a^4*arctanh(a*x)/(a*x+1)+5/32/a^4*arctanh(a*x)*ln(a*x+1)-5/128/a^4*ln(a*x-1)^2+5/64/a^4*ln(a*x-1)*ln(1/2+1/2*a*x)-5/128/a^4*ln(a*x+1)^2-5/64/a^4*ln(-1/2*a*x+1/2)*ln(1/2+1/2*a*x)+5/64/a^4*ln(-1/2*a*x+1/2)*ln(a*x+1)+1/128/a^4/(a*x-1)^2+9/128/a^4/(a*x-1)+1/128/a^4/(a*x+1)^2-9/128/a^4/(a*x+1)","B"
309,1,2571,147,0.887000," ","int(x^2*arctanh(a*x)^2/(-a^2*x^2+1)^3,x)","\text{Expression too large to display}"," ",0,"-1/16*I/a^3/(a*x-1)^2/(a*x+1)^2*Pi*arctanh(a*x)^2+1/32*I/a^3/(a*x-1)^2/(a*x+1)^2*Pi*arctanh(a*x)^2*csgn(I*(a*x+1)/(-a^2*x^2+1)^(1/2))^2*csgn(I*(a*x+1)^2/(a^2*x^2-1))+1/32*I/a^3/(a*x-1)^2/(a*x+1)^2*Pi*arctanh(a*x)^2*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2-1/32*I/a^3/(a*x-1)^2/(a*x+1)^2*Pi*arctanh(a*x)^2*csgn(I*(a*x+1)^2/(a^2*x^2-1))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2+1/32*I*a/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)^2*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^3*Pi*x^4+1/32*I*a/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)^2*csgn(I*(a*x+1)^2/(a^2*x^2-1))^3*Pi*x^4+1/16*I*a/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)^2*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*Pi*x^4+1/8*I/a/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)^2*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))^3*Pi*x^2-1/16*I/a/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)^2*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^3*Pi*x^2-1/16*I/a/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)^2*csgn(I*(a*x+1)^2/(a^2*x^2-1))^3*Pi*x^2-1/8*I/a/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)^2*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*Pi*x^2-1/16*I*a/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)^2*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))^3*Pi*x^4+1/16*I/a^3/(a*x-1)^2/(a*x+1)^2*Pi*arctanh(a*x)^2*csgn(I*(a*x+1)/(-a^2*x^2+1)^(1/2))*csgn(I*(a*x+1)^2/(a^2*x^2-1))^2+1/64/(a*x-1)^2/(a*x+1)^2*x^3+1/16*I/a/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)^2*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*(a*x+1)^2/(a^2*x^2-1))*Pi*x^2-1/32*I*a/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)^2*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*(a*x+1)^2/(a^2*x^2-1))*Pi*x^4+1/8/a^3*arctanh(a*x)^2*ln((a*x+1)/(-a^2*x^2+1)^(1/2))+1/16/a^3*arctanh(a*x)^2/(a*x-1)^2+1/16/a^3*arctanh(a*x)^2/(a*x-1)+1/16/a^3*arctanh(a*x)^2*ln(a*x-1)-1/16/a^3*arctanh(a*x)^2/(a*x+1)^2+1/16/a^3*arctanh(a*x)^2/(a*x+1)-1/16/a^3*arctanh(a*x)^2*ln(a*x+1)+1/64/a^2/(a*x-1)^2/(a*x+1)^2*x-1/24/a^3/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)^3-1/64/a^3/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)+1/32*I*a/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)^2*csgn(I*(a*x+1)^2/(a^2*x^2-1))*csgn(I*(a*x+1)/(-a^2*x^2+1)^(1/2))^2*Pi*x^4-1/16*I/a/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)^2*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*Pi*x^2+1/16*I/a/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)^2*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*csgn(I*(a*x+1)^2/(a^2*x^2-1))*Pi*x^2-1/8*I/a/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)^2*csgn(I*(a*x+1)^2/(a^2*x^2-1))^2*csgn(I*(a*x+1)/(-a^2*x^2+1)^(1/2))*Pi*x^2-1/16*I/a/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)^2*csgn(I*(a*x+1)^2/(a^2*x^2-1))*csgn(I*(a*x+1)/(-a^2*x^2+1)^(1/2))^2*Pi*x^2-1/32*I/a^3/(a*x-1)^2/(a*x+1)^2*Pi*arctanh(a*x)^2*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*(a*x+1)^2/(a^2*x^2-1))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))+1/32*I*a/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)^2*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*Pi*x^4-1/32*I*a/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)^2*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*csgn(I*(a*x+1)^2/(a^2*x^2-1))*Pi*x^4+1/16*I*a/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)^2*csgn(I*(a*x+1)^2/(a^2*x^2-1))^2*csgn(I*(a*x+1)/(-a^2*x^2+1)^(1/2))*Pi*x^4-1/16*I*a/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)^2*Pi*x^4+1/8*I/a/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)^2*Pi*x^2+1/32*I/a^3/(a*x-1)^2/(a*x+1)^2*Pi*arctanh(a*x)^2*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^3+1/32*I/a^3/(a*x-1)^2/(a*x+1)^2*Pi*arctanh(a*x)^2*csgn(I*(a*x+1)^2/(a^2*x^2-1))^3+1/16*I/a^3/(a*x-1)^2/(a*x+1)^2*Pi*arctanh(a*x)^2*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))^2-1/16*I/a^3/(a*x-1)^2/(a*x+1)^2*Pi*arctanh(a*x)^2*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))^3-1/24*a/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)^3*x^4-1/64*a/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)*x^4+1/12/a/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)^3*x^2-3/32/a/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)*x^2","C"
310,1,247,113,0.067000," ","int(x*arctanh(a*x)^2/(-a^2*x^2+1)^3,x)","\frac{\arctanh \left(a x \right)^{2}}{4 a^{2} \left(a^{2} x^{2}-1\right)^{2}}-\frac{\arctanh \left(a x \right)}{32 a^{2} \left(a x -1\right)^{2}}+\frac{3 \arctanh \left(a x \right)}{32 a^{2} \left(a x -1\right)}+\frac{3 \arctanh \left(a x \right) \ln \left(a x -1\right)}{32 a^{2}}+\frac{\arctanh \left(a x \right)}{32 a^{2} \left(a x +1\right)^{2}}+\frac{3 \arctanh \left(a x \right)}{32 a^{2} \left(a x +1\right)}-\frac{3 \arctanh \left(a x \right) \ln \left(a x +1\right)}{32 a^{2}}+\frac{3 \ln \left(a x -1\right)^{2}}{128 a^{2}}-\frac{3 \ln \left(a x -1\right) \ln \left(\frac{1}{2}+\frac{a x}{2}\right)}{64 a^{2}}+\frac{3 \ln \left(a x +1\right)^{2}}{128 a^{2}}+\frac{3 \ln \left(-\frac{a x}{2}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{a x}{2}\right)}{64 a^{2}}-\frac{3 \ln \left(-\frac{a x}{2}+\frac{1}{2}\right) \ln \left(a x +1\right)}{64 a^{2}}+\frac{1}{128 a^{2} \left(a x -1\right)^{2}}-\frac{7}{128 a^{2} \left(a x -1\right)}+\frac{1}{128 a^{2} \left(a x +1\right)^{2}}+\frac{7}{128 a^{2} \left(a x +1\right)}"," ",0,"1/4/a^2/(a^2*x^2-1)^2*arctanh(a*x)^2-1/32/a^2*arctanh(a*x)/(a*x-1)^2+3/32/a^2*arctanh(a*x)/(a*x-1)+3/32/a^2*arctanh(a*x)*ln(a*x-1)+1/32/a^2*arctanh(a*x)/(a*x+1)^2+3/32/a^2*arctanh(a*x)/(a*x+1)-3/32/a^2*arctanh(a*x)*ln(a*x+1)+3/128/a^2*ln(a*x-1)^2-3/64/a^2*ln(a*x-1)*ln(1/2+1/2*a*x)+3/128/a^2*ln(a*x+1)^2+3/64/a^2*ln(-1/2*a*x+1/2)*ln(1/2+1/2*a*x)-3/64/a^2*ln(-1/2*a*x+1/2)*ln(a*x+1)+1/128/a^2/(a*x-1)^2-7/128/a^2/(a*x-1)+1/128/a^2/(a*x+1)^2+7/128/a^2/(a*x+1)","B"
311,1,2571,135,0.867000," ","int(arctanh(a*x)^2/(-a^2*x^2+1)^3,x)","\text{Expression too large to display}"," ",0,"-3/16*I*a/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)^2*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*(a*x+1)^2/(a^2*x^2-1))*Pi*x^2+3/32*I*a^3/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)^2*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*(a*x+1)^2/(a^2*x^2-1))*Pi*x^4+3/16*I*a/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)^2*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^3*Pi*x^2+3/16*I*a/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)^2*csgn(I*(a*x+1)^2/(a^2*x^2-1))^3*Pi*x^2+3/8*I*a/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)^2*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*Pi*x^2+3/16*I*a^3/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)^2*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))^3*Pi*x^4-3/32*I*a^3/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)^2*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^3*Pi*x^4-3/32*I/a/(a*x-1)^2/(a*x+1)^2*Pi*arctanh(a*x)^2*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2+3/32*I/a/(a*x-1)^2/(a*x+1)^2*Pi*arctanh(a*x)^2*csgn(I*(a*x+1)^2/(a^2*x^2-1))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2-3/16*I/a/(a*x-1)^2/(a*x+1)^2*Pi*arctanh(a*x)^2*csgn(I*(a*x+1)/(-a^2*x^2+1)^(1/2))*csgn(I*(a*x+1)^2/(a^2*x^2-1))^2-3/32*I/a/(a*x-1)^2/(a*x+1)^2*Pi*arctanh(a*x)^2*csgn(I*(a*x+1)/(-a^2*x^2+1)^(1/2))^2*csgn(I*(a*x+1)^2/(a^2*x^2-1))+3/32*I*a^3/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)^2*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*csgn(I*(a*x+1)^2/(a^2*x^2-1))*Pi*x^4-3/16*I*a^3/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)^2*csgn(I*(a*x+1)^2/(a^2*x^2-1))^2*csgn(I*(a*x+1)/(-a^2*x^2+1)^(1/2))*Pi*x^4-3/32*I*a^3/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)^2*csgn(I*(a*x+1)^2/(a^2*x^2-1))*csgn(I*(a*x+1)/(-a^2*x^2+1)^(1/2))^2*Pi*x^4+3/32*I/a/(a*x-1)^2/(a*x+1)^2*Pi*arctanh(a*x)^2*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*(a*x+1)^2/(a^2*x^2-1))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))+3/16*I*a/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)^2*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*Pi*x^2-3/16*I*a/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)^2*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*csgn(I*(a*x+1)^2/(a^2*x^2-1))*Pi*x^2+3/8*I*a/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)^2*csgn(I*(a*x+1)^2/(a^2*x^2-1))^2*csgn(I*(a*x+1)/(-a^2*x^2+1)^(1/2))*Pi*x^2+3/16*I*a/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)^2*csgn(I*(a*x+1)^2/(a^2*x^2-1))*csgn(I*(a*x+1)/(-a^2*x^2+1)^(1/2))^2*Pi*x^2-3/32*I*a^3/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)^2*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*Pi*x^4-3/32*I*a^3/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)^2*csgn(I*(a*x+1)^2/(a^2*x^2-1))^3*Pi*x^4-3/16*I*a^3/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)^2*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*Pi*x^4-3/8*I*a/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)^2*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))^3*Pi*x^2-3/16/a*arctanh(a*x)^2*ln(a*x-1)+3/16/a*arctanh(a*x)^2*ln(a*x+1)-3/8/a*arctanh(a*x)^2*ln((a*x+1)/(-a^2*x^2+1)^(1/2))-1/4*a/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)^3*x^2-3/32*a/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)*x^2+1/8*a^3/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)^3*x^4+15/64*a^3/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)*x^4+3/16*I/a/(a*x-1)^2/(a*x+1)^2*Pi*arctanh(a*x)^2+17/64/(a*x-1)^2/(a*x+1)^2*x+1/16/a*arctanh(a*x)^2/(a*x-1)^2-3/16/a*arctanh(a*x)^2/(a*x-1)-1/16/a*arctanh(a*x)^2/(a*x+1)^2-3/16/a*arctanh(a*x)^2/(a*x+1)-3/8*I*a/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)^2*Pi*x^2+3/16*I/a/(a*x-1)^2/(a*x+1)^2*Pi*arctanh(a*x)^2*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))^3-3/32*I/a/(a*x-1)^2/(a*x+1)^2*Pi*arctanh(a*x)^2*csgn(I*(a*x+1)^2/(a^2*x^2-1))^3-3/16*I/a/(a*x-1)^2/(a*x+1)^2*Pi*arctanh(a*x)^2*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))^2+3/16*I*a^3/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)^2*Pi*x^4-3/32*I/a/(a*x-1)^2/(a*x+1)^2*Pi*arctanh(a*x)^2*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^3-15/64*a^2/(a*x-1)^2/(a*x+1)^2*x^3+1/8/a/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)^3-17/64/a/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)","C"
312,1,1392,178,0.838000," ","int(arctanh(a*x)^2/x/(-a^2*x^2+1)^3,x)","-\frac{3 \left(a x +1\right)}{32 \left(a x -1\right)}-\arctanh \left(a x \right)^{2} \ln \left(\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}-1\right)-2 \polylog \left(3, -\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)-\frac{\arctanh \left(a x \right)^{3}}{3}-\frac{\arctanh \left(a x \right)^{2} \ln \left(a x -1\right)}{2}-\frac{\arctanh \left(a x \right)^{2} \ln \left(a x +1\right)}{2}+\arctanh \left(a x \right)^{2} \ln \left(2\right)+\frac{\arctanh \left(a x \right)^{2}}{16 \left(a x -1\right)^{2}}-\frac{5 \arctanh \left(a x \right)^{2}}{16 \left(a x -1\right)}+\frac{\arctanh \left(a x \right)^{2}}{16 \left(a x +1\right)^{2}}+\frac{5 \arctanh \left(a x \right)^{2}}{16 \left(a x +1\right)}+\arctanh \left(a x \right)^{2} \ln \left(a x \right)+\arctanh \left(a x \right)^{2} \ln \left(1-\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)+\arctanh \left(a x \right)^{2} \ln \left(1+\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)+2 \arctanh \left(a x \right) \polylog \left(2, -\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)+\frac{\arctanh \left(a x \right) \left(a x -1\right)^{2}}{128 \left(a x +1\right)^{2}}-\frac{\arctanh \left(a x \right) \left(a x +1\right)^{2}}{128 \left(a x -1\right)^{2}}+\frac{i \pi  \arctanh \left(a x \right)^{2}}{2}-\frac{3 \arctanh \left(a x \right) \left(a x -1\right)}{16 \left(a x +1\right)}+\frac{3 \left(a x +1\right) \arctanh \left(a x \right)}{16 \left(a x -1\right)}-\frac{11 \arctanh \left(a x \right)^{2}}{32}+\frac{\left(a x +1\right)^{2}}{512 \left(a x -1\right)^{2}}+\frac{\left(a x -1\right)^{2}}{512 \left(a x +1\right)^{2}}-\frac{3 \left(a x -1\right)}{32 \left(a x +1\right)}-2 \polylog \left(3, \frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)+2 \arctanh \left(a x \right) \polylog \left(2, \frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)+\arctanh \left(a x \right)^{2} \ln \left(\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)+\frac{i \pi  \arctanh \left(a x \right)^{2} \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right)^{3}}{4}+\frac{i \pi  \arctanh \left(a x \right)^{2} \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{\left(a^{2} x^{2}-1\right) \left(1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}\right)^{3}}{4}-\frac{i \pi  \mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right)^{2} \arctanh \left(a x \right)^{2}}{2}+\frac{i \arctanh \left(a x \right)^{2} \pi  \mathrm{csgn}\left(\frac{i \left(\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}-1\right)}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right)^{3}}{2}+\frac{i \pi  \mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right)^{3} \arctanh \left(a x \right)^{2}}{2}-\frac{i \pi  \arctanh \left(a x \right)^{2} \mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right) \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{\left(a^{2} x^{2}-1\right) \left(1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}\right)}{4}-\frac{i \arctanh \left(a x \right)^{2} \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}-1\right)\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}-1\right)}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right)^{2}}{2}+\frac{i \arctanh \left(a x \right)^{2} \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}-1\right)\right) \mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}-1\right)}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right)}{2}-\frac{i \arctanh \left(a x \right)^{2} \pi  \,\mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}-1\right)}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right)^{2}}{2}+\frac{i \pi  \arctanh \left(a x \right)^{2} \mathrm{csgn}\left(\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right)^{2} \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right)}{4}+\frac{i \pi  \arctanh \left(a x \right)^{2} \mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{\left(a^{2} x^{2}-1\right) \left(1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}\right)^{2}}{4}+\frac{i \pi  \arctanh \left(a x \right)^{2} \mathrm{csgn}\left(\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right)^{2}}{2}-\frac{i \pi  \arctanh \left(a x \right)^{2} \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right) \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{\left(a^{2} x^{2}-1\right) \left(1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}\right)^{2}}{4}"," ",0,"-3/32*(a*x+1)/(a*x-1)-2*polylog(3,-(a*x+1)/(-a^2*x^2+1)^(1/2))-2*polylog(3,(a*x+1)/(-a^2*x^2+1)^(1/2))-1/3*arctanh(a*x)^3-11/32*arctanh(a*x)^2+1/512*(a*x+1)^2/(a*x-1)^2-1/2*arctanh(a*x)^2*ln(a*x-1)-1/2*arctanh(a*x)^2*ln(a*x+1)+arctanh(a*x)^2*ln((a*x+1)/(-a^2*x^2+1)^(1/2))+1/512*(a*x-1)^2/(a*x+1)^2+arctanh(a*x)^2*ln(2)-3/32*(a*x-1)/(a*x+1)+1/16*arctanh(a*x)^2/(a*x-1)^2-5/16*arctanh(a*x)^2/(a*x-1)+1/16*arctanh(a*x)^2/(a*x+1)^2+5/16*arctanh(a*x)^2/(a*x+1)+arctanh(a*x)^2*ln(a*x)-arctanh(a*x)^2*ln((a*x+1)^2/(-a^2*x^2+1)-1)+arctanh(a*x)^2*ln(1-(a*x+1)/(-a^2*x^2+1)^(1/2))+arctanh(a*x)^2*ln(1+(a*x+1)/(-a^2*x^2+1)^(1/2))+1/2*I*Pi*arctanh(a*x)^2-3/16*arctanh(a*x)*(a*x-1)/(a*x+1)+1/128*arctanh(a*x)*(a*x-1)^2/(a*x+1)^2-1/128*arctanh(a*x)*(a*x+1)^2/(a*x-1)^2+3/16*(a*x+1)*arctanh(a*x)/(a*x-1)+2*arctanh(a*x)*polylog(2,-(a*x+1)/(-a^2*x^2+1)^(1/2))+2*arctanh(a*x)*polylog(2,(a*x+1)/(-a^2*x^2+1)^(1/2))+1/2*I*arctanh(a*x)^2*Pi*csgn(I*((a*x+1)^2/(-a^2*x^2+1)-1))*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*((a*x+1)^2/(-a^2*x^2+1)-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))-1/4*I*Pi*arctanh(a*x)^2*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*(a*x+1)^2/(a^2*x^2-1))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))+1/2*I*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))^3*arctanh(a*x)^2+1/4*I*Pi*arctanh(a*x)^2*csgn(I*(a*x+1)^2/(a^2*x^2-1))^3+1/4*I*Pi*arctanh(a*x)^2*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^3-1/2*I*arctanh(a*x)^2*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*((a*x+1)^2/(-a^2*x^2+1)-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2-1/2*I*arctanh(a*x)^2*Pi*csgn(I*((a*x+1)^2/(-a^2*x^2+1)-1))*csgn(I*((a*x+1)^2/(-a^2*x^2+1)-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2+1/4*I*Pi*arctanh(a*x)^2*csgn(I*(a*x+1)/(-a^2*x^2+1)^(1/2))^2*csgn(I*(a*x+1)^2/(a^2*x^2-1))+1/4*I*Pi*arctanh(a*x)^2*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2+1/2*I*Pi*arctanh(a*x)^2*csgn(I*(a*x+1)/(-a^2*x^2+1)^(1/2))*csgn(I*(a*x+1)^2/(a^2*x^2-1))^2-1/4*I*Pi*arctanh(a*x)^2*csgn(I*(a*x+1)^2/(a^2*x^2-1))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2-1/2*I*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*arctanh(a*x)^2+1/2*I*arctanh(a*x)^2*Pi*csgn(I*((a*x+1)^2/(-a^2*x^2+1)-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^3","C"
313,1,4797,193,0.952000," ","int(arctanh(a*x)^2/x^2/(-a^2*x^2+1)^3,x)","\text{output too large to display}"," ",0,"-a*arctanh(a*x)^2+1/4*a*arctanh(a*x)/(a*x-1)-1/4*a*arctanh(a*x)/(a*x+1)+1/512*a/(a*x-1)^2-15/32*I*a*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*(a*x+1)^2/(a^2*x^2-1))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))*arctanh(a*x)*ln(1-(a*x+1)/(-a^2*x^2+1)^(1/2))-arctanh(a*x)^2/x+15/16*I*a*Pi*arctanh(a*x)^2+15/16*I*a*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*polylog(2,-(a*x+1)/(-a^2*x^2+1)^(1/2))+15/16*I*a*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*polylog(2,(a*x+1)/(-a^2*x^2+1)^(1/2))+15/32*I*a*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1))^3*polylog(2,-(a*x+1)/(-a^2*x^2+1)^(1/2))+15/32*I*a*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1))^3*polylog(2,(a*x+1)/(-a^2*x^2+1)^(1/2))+15/32*I*a*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^3*dilog((a*x+1)/(-a^2*x^2+1)^(1/2))-15/16*I*a*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))^3*dilog((a*x+1)/(-a^2*x^2+1)^(1/2))-15/16*I*a*Pi*arctanh(a*x)*ln(1-(a*x+1)/(-a^2*x^2+1)^(1/2))-15/16*I*a*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*dilog(1+(a*x+1)/(-a^2*x^2+1)^(1/2))+15/16*I*a*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*dilog((a*x+1)/(-a^2*x^2+1)^(1/2))+15/32*I*a*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^3*polylog(2,-(a*x+1)/(-a^2*x^2+1)^(1/2))+15/32*I*a*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1))^3*dilog((a*x+1)/(-a^2*x^2+1)^(1/2))-15/32*I*a*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1))^3*dilog(1+(a*x+1)/(-a^2*x^2+1)^(1/2))-1/8*a^2*x/(a*x-1)+1/8/(a*x+1)*a^2*x-7/16*a*arctanh(a*x)^2/(a*x-1)-7/16*a*arctanh(a*x)^2/(a*x+1)+5/8*a*arctanh(a*x)^3-15/32*I*a*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^3*arctanh(a*x)^2-1/512*a/(a*x+1)^2+15/32*I*a*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*dilog(1+(a*x+1)/(-a^2*x^2+1)^(1/2))-15/32*I*a*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*polylog(2,(a*x+1)/(-a^2*x^2+1)^(1/2))-15/16*I*a*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))^3*arctanh(a*x)*ln(1-(a*x+1)/(-a^2*x^2+1)^(1/2))+15/16*I*a*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*arctanh(a*x)*ln(1-(a*x+1)/(-a^2*x^2+1)^(1/2))+15/16*I*a*Pi*csgn(I*(a*x+1)/(-a^2*x^2+1)^(1/2))*csgn(I*(a*x+1)^2/(a^2*x^2-1))^2*dilog((a*x+1)/(-a^2*x^2+1)^(1/2))-15/16*I*a*Pi*csgn(I*(a*x+1)/(-a^2*x^2+1)^(1/2))*csgn(I*(a*x+1)^2/(a^2*x^2-1))^2*dilog(1+(a*x+1)/(-a^2*x^2+1)^(1/2))-15/32*I*a*Pi*csgn(I*(a*x+1)/(-a^2*x^2+1)^(1/2))^2*csgn(I*(a*x+1)^2/(a^2*x^2-1))*dilog(1+(a*x+1)/(-a^2*x^2+1)^(1/2))+15/16*I*a*Pi*csgn(I*(a*x+1)/(-a^2*x^2+1)^(1/2))*csgn(I*(a*x+1)^2/(a^2*x^2-1))^2*polylog(2,(a*x+1)/(-a^2*x^2+1)^(1/2))+15/32*I*a*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^3*arctanh(a*x)*ln(1-(a*x+1)/(-a^2*x^2+1)^(1/2))+15/32*I*a*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*dilog((a*x+1)/(-a^2*x^2+1)^(1/2))+15/32*I*a*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*polylog(2,(a*x+1)/(-a^2*x^2+1)^(1/2))+15/32*I*a*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*polylog(2,-(a*x+1)/(-a^2*x^2+1)^(1/2))+15/16*I*a*Pi*csgn(I*(a*x+1)/(-a^2*x^2+1)^(1/2))*csgn(I*(a*x+1)^2/(a^2*x^2-1))^2*polylog(2,-(a*x+1)/(-a^2*x^2+1)^(1/2))-15/32*I*a*Pi*csgn(I*(a*x+1)/(-a^2*x^2+1)^(1/2))^2*csgn(I*(a*x+1)^2/(a^2*x^2-1))*arctanh(a*x)^2+15/32*I*a*Pi*csgn(I*(a*x+1)/(-a^2*x^2+1)^(1/2))^2*csgn(I*(a*x+1)^2/(a^2*x^2-1))*dilog((a*x+1)/(-a^2*x^2+1)^(1/2))-15/32*I*a*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*dilog(1+(a*x+1)/(-a^2*x^2+1)^(1/2))-1/8*a/(a*x-1)-1/8*a/(a*x+1)+a*polylog(2,-(a*x+1)/(-a^2*x^2+1)^(1/2))-a*dilog((a*x+1)/(-a^2*x^2+1)^(1/2))+a*polylog(2,(a*x+1)/(-a^2*x^2+1)^(1/2))+a*dilog(1+(a*x+1)/(-a^2*x^2+1)^(1/2))+15/32*I*a*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1))^3*arctanh(a*x)*ln(1-(a*x+1)/(-a^2*x^2+1)^(1/2))+15/32*I*a*Pi*csgn(I*(a*x+1)/(-a^2*x^2+1)^(1/2))^2*csgn(I*(a*x+1)^2/(a^2*x^2-1))*polylog(2,-(a*x+1)/(-a^2*x^2+1)^(1/2))+15/32*I*a*Pi*csgn(I*(a*x+1)/(-a^2*x^2+1)^(1/2))^2*csgn(I*(a*x+1)^2/(a^2*x^2-1))*polylog(2,(a*x+1)/(-a^2*x^2+1)^(1/2))-15/16*I*a*Pi*csgn(I*(a*x+1)/(-a^2*x^2+1)^(1/2))*csgn(I*(a*x+1)^2/(a^2*x^2-1))^2*arctanh(a*x)^2-15/32*I*a*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*arctanh(a*x)^2+15/32*I*a*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*arctanh(a*x)^2-15/32*I*a*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*polylog(2,-(a*x+1)/(-a^2*x^2+1)^(1/2))-15/32*I*a*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*dilog((a*x+1)/(-a^2*x^2+1)^(1/2))-15/32*I*a*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1))^3*arctanh(a*x)^2-15/16*I*a*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))^3*polylog(2,(a*x+1)/(-a^2*x^2+1)^(1/2))-15/16*I*a*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))^3*polylog(2,-(a*x+1)/(-a^2*x^2+1)^(1/2))-15/16*I*a*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*arctanh(a*x)^2+15/16*I*a*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))^3*dilog(1+(a*x+1)/(-a^2*x^2+1)^(1/2))+15/16*I*a*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))^3*arctanh(a*x)^2-15/32*I*a*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^3*dilog(1+(a*x+1)/(-a^2*x^2+1)^(1/2))+15/32*I*a*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^3*polylog(2,(a*x+1)/(-a^2*x^2+1)^(1/2))+1/512/(a*x-1)^2*a^3*x^2-15/8*a*arctanh(a*x)^2*ln((a*x+1)/(-a^2*x^2+1)^(1/2))+2*a*arctanh(a*x)*ln(1+(a*x+1)/(-a^2*x^2+1)^(1/2))+a*arctanh(a*x)*ln(1-(a*x+1)/(-a^2*x^2+1)^(1/2))+1/4*arctanh(a*x)/(a*x-1)*a^2*x+1/4*arctanh(a*x)/(a*x+1)*a^2*x+15/16*I*a*Pi*csgn(I*(a*x+1)/(-a^2*x^2+1)^(1/2))*csgn(I*(a*x+1)^2/(a^2*x^2-1))^2*arctanh(a*x)*ln(1-(a*x+1)/(-a^2*x^2+1)^(1/2))+15/32*I*a*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*arctanh(a*x)*ln(1-(a*x+1)/(-a^2*x^2+1)^(1/2))+15/32*I*a*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*(a*x+1)^2/(a^2*x^2-1))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))*dilog(1+(a*x+1)/(-a^2*x^2+1)^(1/2))+15/32*I*a*Pi*csgn(I*(a*x+1)/(-a^2*x^2+1)^(1/2))^2*csgn(I*(a*x+1)^2/(a^2*x^2-1))*arctanh(a*x)*ln(1-(a*x+1)/(-a^2*x^2+1)^(1/2))-15/32*I*a*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*arctanh(a*x)*ln(1-(a*x+1)/(-a^2*x^2+1)^(1/2))-15/32*I*a*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*(a*x+1)^2/(a^2*x^2-1))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))*polylog(2,-(a*x+1)/(-a^2*x^2+1)^(1/2))-15/32*I*a*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*(a*x+1)^2/(a^2*x^2-1))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))*dilog((a*x+1)/(-a^2*x^2+1)^(1/2))+15/32*I*a*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*(a*x+1)^2/(a^2*x^2-1))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))*arctanh(a*x)^2-15/32*I*a*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*(a*x+1)^2/(a^2*x^2-1))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))*polylog(2,(a*x+1)/(-a^2*x^2+1)^(1/2))-15/16*I*a*Pi*polylog(2,(a*x+1)/(-a^2*x^2+1)^(1/2))-15/16*I*a*Pi*polylog(2,-(a*x+1)/(-a^2*x^2+1)^(1/2))+15/16*I*a*Pi*dilog(1+(a*x+1)/(-a^2*x^2+1)^(1/2))-15/16*I*a*Pi*dilog((a*x+1)/(-a^2*x^2+1)^(1/2))-1/128*arctanh(a*x)/(a*x+1)^2*a^3*x^2+1/64*arctanh(a*x)/(a*x+1)^2*a^2*x-1/128*arctanh(a*x)/(a*x-1)^2*a^3*x^2-1/64*arctanh(a*x)/(a*x-1)^2*a^2*x+1/256/(a*x-1)^2*a^2*x-1/512/(a*x+1)^2*a^3*x^2+1/256/(a*x+1)^2*a^2*x+1/16*a*arctanh(a*x)^2/(a*x-1)^2-1/16*a*arctanh(a*x)^2/(a*x+1)^2-15/16*a*arctanh(a*x)^2*ln(a*x-1)+15/16*a*arctanh(a*x)^2*ln(a*x+1)-1/128*a*arctanh(a*x)/(a*x-1)^2-1/128*a*arctanh(a*x)/(a*x+1)^2","C"
314,1,2634,174,0.903000," ","int(x^3*arctanh(a*x)^3/(-a^2*x^2+1)^3,x)","\text{Expression too large to display}"," ",0,"15/64*I/a^2/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)^2*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^3*x^2+15/64*I/a^2/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)^2*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1))^3*x^2+15/32*I/a^2/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)^2*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*x^2-15/128*I/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)^2*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1))*csgn(I*(a*x+1)/(-a^2*x^2+1)^(1/2))^2*x^4-15/128*I/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)^2*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*x^4+15/128*I/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)^2*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*csgn(I*(a*x+1)^2/(a^2*x^2-1))*x^4+15/128*I/a^4/(a*x-1)^2/(a*x+1)^2*Pi*arctanh(a*x)^2*csgn(I*(a*x+1)^2/(a^2*x^2-1))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2-15/64*I/a^4/(a*x-1)^2/(a*x+1)^2*Pi*arctanh(a*x)^2*csgn(I*(a*x+1)/(-a^2*x^2+1)^(1/2))*csgn(I*(a*x+1)^2/(a^2*x^2-1))^2-15/128*I/a^4/(a*x-1)^2/(a*x+1)^2*Pi*arctanh(a*x)^2*csgn(I*(a*x+1)/(-a^2*x^2+1)^(1/2))^2*csgn(I*(a*x+1)^2/(a^2*x^2-1))-15/128*I/a^4/(a*x-1)^2/(a*x+1)^2*Pi*arctanh(a*x)^2*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2-15/32*I/a^2/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)^2*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))^3*x^2+3/16/a^4*arctanh(a*x)^3/(a*x-1)-3/16/a^4*arctanh(a*x)^3/(a*x+1)+1/16/a^4*arctanh(a*x)^3/(a*x-1)^2+1/16/a^4*arctanh(a*x)^3/(a*x+1)^2-15/64/a^4*arctanh(a*x)^2*ln(a*x-1)-15/64*I/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)^2*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1))^2*csgn(I*(a*x+1)/(-a^2*x^2+1)^(1/2))*x^4+15/64*I/a^2/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)^2*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1))*csgn(I*(a*x+1)/(-a^2*x^2+1)^(1/2))^2*x^2+15/64*I/a^2/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)^2*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*x^2-15/64*I/a^2/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)^2*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*csgn(I*(a*x+1)^2/(a^2*x^2-1))*x^2+15/128*I/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)^2*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*(a*x+1)^2/(a^2*x^2-1))*x^4+15/128*I/a^4/(a*x-1)^2/(a*x+1)^2*Pi*arctanh(a*x)^2*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*(a*x+1)^2/(a^2*x^2-1))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))+15/32*I/a^2/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)^2*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1))^2*csgn(I*(a*x+1)/(-a^2*x^2+1)^(1/2))*x^2-3/64/a^4*arctanh(a*x)^2/(a*x-1)^2-15/64/a^4*arctanh(a*x)^2/(a*x-1)+3/64/a^4*arctanh(a*x)^2/(a*x+1)^2-15/64/a^4*arctanh(a*x)^2/(a*x+1)-15/64*I/a^2/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)^2*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*(a*x+1)^2/(a^2*x^2-1))*x^2+15/64/a^4*arctanh(a*x)^2*ln(a*x+1)-15/32/a^4*arctanh(a*x)^2*ln((a*x+1)/(-a^2*x^2+1)^(1/2))+15/64*I/a^4/(a*x-1)^2/(a*x+1)^2*Pi*arctanh(a*x)^2+15/64*I/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)^2*Pi*x^4-15/128*I/a^4/(a*x-1)^2/(a*x+1)^2*Pi*arctanh(a*x)^2*csgn(I*(a*x+1)^2/(a^2*x^2-1))^3-15/64*I/a^4/(a*x-1)^2/(a*x+1)^2*Pi*arctanh(a*x)^2*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))^2-15/128*I/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)^2*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1))^3*x^4-15/64*I/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)^2*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*x^4+15/64*I/a^4/(a*x-1)^2/(a*x+1)^2*Pi*arctanh(a*x)^2*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))^3-15/128*I/a^4/(a*x-1)^2/(a*x+1)^2*Pi*arctanh(a*x)^2*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^3-15/32*I/a^2/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)^2*Pi*x^2+15/64*I/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)^2*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))^3*x^4-15/128*I/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)^2*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^3*x^4-5/16/a^2/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)^3*x^2+9/128/a^2/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)*x^2-51/256/a/(a*x-1)^2/(a*x+1)^2*x^3+45/256/a^3/(a*x-1)^2/(a*x+1)^2*x+5/32/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)^3*x^4+51/256/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)*x^4+5/32/a^4/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)^3-45/256/a^4/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)","C"
315,1,2646,195,0.851000," ","int(x^2*arctanh(a*x)^3/(-a^2*x^2+1)^3,x)","\text{Expression too large to display}"," ",0,"-1/32*I*a/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)^3*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*(a*x+1)^2/(a^2*x^2-1))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))*x^4+1/16*I/a/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)^3*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*(a*x+1)^2/(a^2*x^2-1))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))*x^2+1/32*I/a^3/(a*x-1)^2/(a*x+1)^2*Pi*arctanh(a*x)^3*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2-1/16*I*a/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)^3*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))^3*x^4+1/32*I*a/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)^3*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1))^3*x^4+1/32*I*a/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)^3*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^3*x^4+1/16*I*a/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)^3*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*x^4+1/8*I/a/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)^3*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))^3*x^2-1/16*I/a/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)^3*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1))^3*x^2-1/16*I/a/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)^3*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^3*x^2-1/8*I/a/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)^3*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*x^2-1/32*I/a^3/(a*x-1)^2/(a*x+1)^2*Pi*arctanh(a*x)^3*csgn(I*(a*x+1)^2/(a^2*x^2-1))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2+1/32*I/a^3/(a*x-1)^2/(a*x+1)^2*Pi*arctanh(a*x)^3*csgn(I*(a*x+1)/(-a^2*x^2+1)^(1/2))^2*csgn(I*(a*x+1)^2/(a^2*x^2-1))+1/16*I/a^3/(a*x-1)^2/(a*x+1)^2*Pi*arctanh(a*x)^3*csgn(I*(a*x+1)/(-a^2*x^2+1)^(1/2))*csgn(I*(a*x+1)^2/(a^2*x^2-1))^2-3/1024/a^3/(a*x-1)^2/(a*x+1)^2+1/16/a^3*arctanh(a*x)^3/(a*x-1)^2+1/16/a^3*arctanh(a*x)^3/(a*x-1)+1/16/a^3*arctanh(a*x)^3*ln(a*x-1)-1/16/a^3*arctanh(a*x)^3/(a*x+1)^2+1/16/a^3*arctanh(a*x)^3/(a*x+1)-1/16/a^3*arctanh(a*x)^3*ln(a*x+1)+1/8/a^3*arctanh(a*x)^3*ln((a*x+1)/(-a^2*x^2+1)^(1/2))-1/16*I/a^3/(a*x-1)^2/(a*x+1)^2*Pi*arctanh(a*x)^3+1/16*I*a/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)^3*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1))^2*csgn(I*(a*x+1)/(-a^2*x^2+1)^(1/2))*x^4-1/32*I*a/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)^3*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*x^4+1/32*I*a/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)^3*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1))*csgn(I*(a*x+1)/(-a^2*x^2+1)^(1/2))^2*x^4-1/16*I/a/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)^3*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*x^2-1/8*I/a/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)^3*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1))^2*csgn(I*(a*x+1)/(-a^2*x^2+1)^(1/2))*x^2+1/16*I/a/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)^3*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*x^2-1/16*I/a/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)^3*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1))*csgn(I*(a*x+1)/(-a^2*x^2+1)^(1/2))^2*x^2-1/32*I/a^3/(a*x-1)^2/(a*x+1)^2*Pi*arctanh(a*x)^3*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*(a*x+1)^2/(a^2*x^2-1))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))+1/32*I*a/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)^3*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*x^4-9/64/a/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)^2*x^2+3/64/a^2/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)*x-1/32*a/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)^4*x^4-1/16*I/a^3/(a*x-1)^2/(a*x+1)^2*Pi*arctanh(a*x)^3*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))^3-1/16*I*a/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)^3*Pi*x^4+1/8*I/a/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)^3*Pi*x^2+1/32*I/a^3/(a*x-1)^2/(a*x+1)^2*Pi*arctanh(a*x)^3*csgn(I*(a*x+1)^2/(a^2*x^2-1))^3+1/32*I/a^3/(a*x-1)^2/(a*x+1)^2*Pi*arctanh(a*x)^3*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^3+1/16*I/a^3/(a*x-1)^2/(a*x+1)^2*Pi*arctanh(a*x)^3*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))^2+3/64/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)*x^3-1/32/a^3/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)^4-3/128/a^3/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)^2-3/1024*a/(a*x-1)^2/(a*x+1)^2*x^4-9/512/a/(a*x-1)^2/(a*x+1)^2*x^2-3/128*a/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)^2*x^4+1/16/a/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)^4*x^2","C"
316,1,2582,170,0.716000," ","int(x*arctanh(a*x)^3/(-a^2*x^2+1)^3,x)","\text{Expression too large to display}"," ",0,"-9/32*I/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)^2*csgn(I*(a*x+1)^2/(a^2*x^2-1))^2*csgn(I*(a*x+1)/(-a^2*x^2+1)^(1/2))*Pi*x^2-9/64*I/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)^2*csgn(I*(a*x+1)^2/(a^2*x^2-1))*csgn(I*(a*x+1)/(-a^2*x^2+1)^(1/2))^2*Pi*x^2-9/64*I/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)^2*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*Pi*x^2-9/64*I*a^2/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)^2*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))^3*Pi*x^4+9/128*I*a^2/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)^2*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^3*Pi*x^4+9/128*I*a^2/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)^2*csgn(I*(a*x+1)^2/(a^2*x^2-1))^3*Pi*x^4+9/64*I*a^2/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)^2*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*Pi*x^4+9/128*I/a^2/(a*x-1)^2/(a*x+1)^2*Pi*arctanh(a*x)^2*csgn(I*(a*x+1)/(-a^2*x^2+1)^(1/2))^2*csgn(I*(a*x+1)^2/(a^2*x^2-1))+9/128*I/a^2/(a*x-1)^2/(a*x+1)^2*Pi*arctanh(a*x)^2*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2-9/128*I/a^2/(a*x-1)^2/(a*x+1)^2*Pi*arctanh(a*x)^2*csgn(I*(a*x+1)^2/(a^2*x^2-1))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2+9/64*I/a^2/(a*x-1)^2/(a*x+1)^2*Pi*arctanh(a*x)^2*csgn(I*(a*x+1)/(-a^2*x^2+1)^(1/2))*csgn(I*(a*x+1)^2/(a^2*x^2-1))^2+9/64*I/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)^2*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*csgn(I*(a*x+1)^2/(a^2*x^2-1))*Pi*x^2-9/128*I*a^2/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)^2*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*csgn(I*(a*x+1)^2/(a^2*x^2-1))*Pi*x^4+9/64*I*a^2/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)^2*csgn(I*(a*x+1)^2/(a^2*x^2-1))^2*csgn(I*(a*x+1)/(-a^2*x^2+1)^(1/2))*Pi*x^4+9/128*I*a^2/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)^2*csgn(I*(a*x+1)^2/(a^2*x^2-1))*csgn(I*(a*x+1)/(-a^2*x^2+1)^(1/2))^2*Pi*x^4+9/64*I/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)^2*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*(a*x+1)^2/(a^2*x^2-1))*Pi*x^2-9/128*I/a^2/(a*x-1)^2/(a*x+1)^2*Pi*arctanh(a*x)^2*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*(a*x+1)^2/(a^2*x^2-1))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))+9/128*I*a^2/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)^2*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*Pi*x^4-9/128*I*a^2/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)^2*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*(a*x+1)^2/(a^2*x^2-1))*Pi*x^4-3/32*a^2/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)^3*x^4-45/256*a^2/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)*x^4+1/4/a^2/(a^2*x^2-1)^2*arctanh(a*x)^3-3/64/a^2*arctanh(a*x)^2/(a*x-1)^2+9/64/a^2*arctanh(a*x)^2/(a*x-1)+9/64/a^2*arctanh(a*x)^2*ln(a*x-1)+3/64/a^2*arctanh(a*x)^2/(a*x+1)^2+9/64/a^2*arctanh(a*x)^2/(a*x+1)-9/64/a^2*arctanh(a*x)^2*ln(a*x+1)+9/32/a^2*arctanh(a*x)^2*ln((a*x+1)/(-a^2*x^2+1)^(1/2))-9/64*I/a^2/(a*x-1)^2/(a*x+1)^2*Pi*arctanh(a*x)^2+9/32*I/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)^2*Pi*x^2+9/128*I/a^2/(a*x-1)^2/(a*x+1)^2*Pi*arctanh(a*x)^2*csgn(I*(a*x+1)^2/(a^2*x^2-1))^3+9/64*I/a^2/(a*x-1)^2/(a*x+1)^2*Pi*arctanh(a*x)^2*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))^2-9/64*I*a^2/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)^2*Pi*x^4-9/64*I/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)^2*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^3*Pi*x^2-9/64*I/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)^2*csgn(I*(a*x+1)^2/(a^2*x^2-1))^3*Pi*x^2-9/32*I/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)^2*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*Pi*x^2+9/32*I/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)^2*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))^3*Pi*x^2-9/64*I/a^2/(a*x-1)^2/(a*x+1)^2*Pi*arctanh(a*x)^2*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))^3+9/128*I/a^2/(a*x-1)^2/(a*x+1)^2*Pi*arctanh(a*x)^2*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^3+3/16/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)^3*x^2+9/128/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)*x^2-3/32/a^2/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)^3+51/256/a^2/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)+45/256*a/(a*x-1)^2/(a*x+1)^2*x^3-51/256/a/(a*x-1)^2/(a*x+1)^2*x","C"
317,1,2646,183,0.923000," ","int(arctanh(a*x)^3/(-a^2*x^2+1)^3,x)","\text{Expression too large to display}"," ",0,"-3/16*I*a^3/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)^3*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1))^2*csgn(I*(a*x+1)/(-a^2*x^2+1)^(1/2))*x^4+3/32*I*a^3/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)^3*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*x^4-3/32*I*a^3/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)^3*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1))*csgn(I*(a*x+1)/(-a^2*x^2+1)^(1/2))^2*x^4+3/16*I*a/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)^3*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*x^2+3/8*I*a/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)^3*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1))^2*csgn(I*(a*x+1)/(-a^2*x^2+1)^(1/2))*x^2-3/16*I*a/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)^3*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*x^2+3/32*a^3/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)^4*x^4+45/128*a^3/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)^2*x^4-195/1024/a/(a*x-1)^2/(a*x+1)^2+1/16/a*arctanh(a*x)^3/(a*x-1)^2-1/16/a*arctanh(a*x)^3/(a*x+1)^2+3/16*I*a^3/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)^3*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))^3*x^4-3/32*I*a^3/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)^3*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1))^3*x^4-3/32*I*a^3/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)^3*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^3*x^4-3/16*I*a^3/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)^3*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*x^4-3/8*I*a/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)^3*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))^3*x^2+3/16*I*a/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)^3*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1))^3*x^2+3/16*I*a/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)^3*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^3*x^2+3/8*I*a/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)^3*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*x^2-3/32*I/a/(a*x-1)^2/(a*x+1)^2*Pi*arctanh(a*x)^3*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2-3/16*I/a/(a*x-1)^2/(a*x+1)^2*Pi*arctanh(a*x)^3*csgn(I*(a*x+1)/(-a^2*x^2+1)^(1/2))*csgn(I*(a*x+1)^2/(a^2*x^2-1))^2+3/32*I/a/(a*x-1)^2/(a*x+1)^2*Pi*arctanh(a*x)^3*csgn(I*(a*x+1)^2/(a^2*x^2-1))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2-3/32*I/a/(a*x-1)^2/(a*x+1)^2*Pi*arctanh(a*x)^3*csgn(I*(a*x+1)/(-a^2*x^2+1)^(1/2))^2*csgn(I*(a*x+1)^2/(a^2*x^2-1))-3/16/a*arctanh(a*x)^3/(a*x-1)-3/16/a*arctanh(a*x)^3*ln(a*x-1)-3/16/a*arctanh(a*x)^3/(a*x+1)+3/16/a*arctanh(a*x)^3*ln(a*x+1)-3/8/a*arctanh(a*x)^3*ln((a*x+1)/(-a^2*x^2+1)^(1/2))+3/16*I*a/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)^3*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1))*csgn(I*(a*x+1)/(-a^2*x^2+1)^(1/2))^2*x^2-3/32*I*a^3/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)^3*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*x^4+3/32*I*a^3/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)^3*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*(a*x+1)^2/(a^2*x^2-1))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))*x^4-3/16*I*a/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)^3*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*(a*x+1)^2/(a^2*x^2-1))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))*x^2+3/32*I/a/(a*x-1)^2/(a*x+1)^2*Pi*arctanh(a*x)^3*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*(a*x+1)^2/(a^2*x^2-1))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))+3/16*I/a/(a*x-1)^2/(a*x+1)^2*Pi*arctanh(a*x)^3+3/16*I/a/(a*x-1)^2/(a*x+1)^2*Pi*arctanh(a*x)^3*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))^3-3/32*I/a/(a*x-1)^2/(a*x+1)^2*Pi*arctanh(a*x)^3*csgn(I*(a*x+1)^2/(a^2*x^2-1))^3-3/32*I/a/(a*x-1)^2/(a*x+1)^2*Pi*arctanh(a*x)^3*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^3-3/16*I/a/(a*x-1)^2/(a*x+1)^2*Pi*arctanh(a*x)^3*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))^2+3/16*I*a^3/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)^3*Pi*x^4-3/8*I*a/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)^3*Pi*x^2+189/1024*a^3/(a*x-1)^2/(a*x+1)^2*x^4-9/512*a/(a*x-1)^2/(a*x+1)^2*x^2+51/64/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)*x+3/32/a/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)^4-51/128/a/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)^2-3/16*a/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)^4*x^2-45/64*a^2/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)*x^3-9/64*a/(a*x-1)^2/(a*x+1)^2*arctanh(a*x)^2*x^2","C"
318,1,1533,249,0.855000," ","int(arctanh(a*x)^3/x/(-a^2*x^2+1)^3,x)","\frac{\arctanh \left(a x \right)^{3}}{16 \left(a x -1\right)^{2}}-\frac{5 \arctanh \left(a x \right)^{3}}{16 \left(a x -1\right)}+\frac{\arctanh \left(a x \right)^{3}}{16 \left(a x +1\right)^{2}}+\frac{5 \arctanh \left(a x \right)^{3}}{16 \left(a x +1\right)}-\frac{i \pi  \,\mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right) \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{\left(a^{2} x^{2}-1\right) \left(1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}\right) \arctanh \left(a x \right)^{3}}{4}+\frac{i \arctanh \left(a x \right)^{3} \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}-1\right)\right) \mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}-1\right)}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right)}{2}-\frac{11 \arctanh \left(a x \right)^{3}}{32}+6 \polylog \left(4, \frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)+\frac{i \arctanh \left(a x \right)^{3} \pi  \mathrm{csgn}\left(\frac{i \left(\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}-1\right)}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right)^{3}}{2}+\frac{i \pi  \,\mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{\left(a^{2} x^{2}-1\right) \left(1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}\right)^{2} \arctanh \left(a x \right)^{3}}{4}+\frac{i \pi  \mathrm{csgn}\left(\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right)^{2} \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right) \arctanh \left(a x \right)^{3}}{4}+\frac{i \arctanh \left(a x \right)^{3} \pi  \,\mathrm{csgn}\left(\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right)^{2}}{2}-\frac{i \pi  \,\mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right) \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{\left(a^{2} x^{2}-1\right) \left(1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}\right)^{2} \arctanh \left(a x \right)^{3}}{4}-\frac{i \arctanh \left(a x \right)^{3} \pi  \,\mathrm{csgn}\left(i \left(\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}-1\right)\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}-1\right)}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right)^{2}}{2}-\frac{i \arctanh \left(a x \right)^{3} \pi  \,\mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}-1\right)}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right)^{2}}{2}+\frac{i \pi  \mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right)^{3} \arctanh \left(a x \right)^{3}}{2}-\frac{i \pi  \mathrm{csgn}\left(\frac{i}{1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}}\right)^{2} \arctanh \left(a x \right)^{3}}{2}+\frac{i \arctanh \left(a x \right)^{3} \pi  \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{a^{2} x^{2}-1}\right)^{3}}{4}+\frac{i \pi  \mathrm{csgn}\left(\frac{i \left(a x +1\right)^{2}}{\left(a^{2} x^{2}-1\right) \left(1+\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}\right)}\right)^{3} \arctanh \left(a x \right)^{3}}{4}+6 \polylog \left(4, -\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)+\frac{3 \arctanh \left(a x \right) \left(a x +1\right)^{2}}{512 \left(a x -1\right)^{2}}-\frac{9 \left(a x +1\right) \arctanh \left(a x \right)}{32 \left(a x -1\right)}-\frac{3 \left(a x +1\right)^{2}}{2048 \left(a x -1\right)^{2}}-\frac{9 \left(a x -1\right)}{64 \left(a x +1\right)}-\frac{9 \arctanh \left(a x \right)^{2} \left(a x -1\right)}{32 \left(a x +1\right)}+\frac{i \pi  \arctanh \left(a x \right)^{3}}{2}-\frac{\arctanh \left(a x \right)^{3} \ln \left(a x -1\right)}{2}-\frac{\arctanh \left(a x \right)^{3} \ln \left(a x +1\right)}{2}+\arctanh \left(a x \right)^{3} \ln \left(\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)+\arctanh \left(a x \right)^{3} \ln \left(a x \right)-6 \arctanh \left(a x \right) \polylog \left(3, -\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)-\arctanh \left(a x \right)^{3} \ln \left(\frac{\left(a x +1\right)^{2}}{-a^{2} x^{2}+1}-1\right)+\ln \left(2\right) \arctanh \left(a x \right)^{3}+\arctanh \left(a x \right)^{3} \ln \left(1+\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)+\arctanh \left(a x \right)^{3} \ln \left(1-\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)-6 \arctanh \left(a x \right) \polylog \left(3, \frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)+3 \arctanh \left(a x \right)^{2} \polylog \left(2, \frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)+3 \arctanh \left(a x \right)^{2} \polylog \left(2, -\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)+\frac{3 \left(a x -1\right)^{2}}{2048 \left(a x +1\right)^{2}}+\frac{\frac{9 a x}{64}+\frac{9}{64}}{a x -1}-\frac{\arctanh \left(a x \right)^{4}}{4}-\frac{3 \arctanh \left(a x \right)^{2} \left(a x +1\right)^{2}}{256 \left(a x -1\right)^{2}}+\frac{9 \left(a x +1\right) \arctanh \left(a x \right)^{2}}{32 \left(a x -1\right)}-\frac{9 \arctanh \left(a x \right) \left(a x -1\right)}{32 \left(a x +1\right)}+\frac{3 \arctanh \left(a x \right) \left(a x -1\right)^{2}}{512 \left(a x +1\right)^{2}}+\frac{3 \arctanh \left(a x \right)^{2} \left(a x -1\right)^{2}}{256 \left(a x +1\right)^{2}}"," ",0,"9/64*(a*x+1)/(a*x-1)-1/4*arctanh(a*x)^4-11/32*arctanh(a*x)^3+6*polylog(4,-(a*x+1)/(-a^2*x^2+1)^(1/2))+6*polylog(4,(a*x+1)/(-a^2*x^2+1)^(1/2))-3/2048*(a*x+1)^2/(a*x-1)^2-9/64*(a*x-1)/(a*x+1)-6*arctanh(a*x)*polylog(3,-(a*x+1)/(-a^2*x^2+1)^(1/2))+1/2*I*Pi*arctanh(a*x)^3*csgn(I*(a*x+1)/(-a^2*x^2+1)^(1/2))*csgn(I*(a*x+1)^2/(a^2*x^2-1))^2-1/2*I*Pi*arctanh(a*x)^3*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*((a*x+1)^2/(-a^2*x^2+1)-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2-6*arctanh(a*x)*polylog(3,(a*x+1)/(-a^2*x^2+1)^(1/2))-1/2*arctanh(a*x)^3*ln(a*x-1)-1/2*arctanh(a*x)^3*ln(a*x+1)+arctanh(a*x)^3*ln((a*x+1)/(-a^2*x^2+1)^(1/2))+3/512*arctanh(a*x)*(a*x+1)^2/(a*x-1)^2-9/32*(a*x+1)*arctanh(a*x)/(a*x-1)+3*arctanh(a*x)^2*polylog(2,(a*x+1)/(-a^2*x^2+1)^(1/2))+arctanh(a*x)^3*ln(1+(a*x+1)/(-a^2*x^2+1)^(1/2))+arctanh(a*x)^3*ln(1-(a*x+1)/(-a^2*x^2+1)^(1/2))-arctanh(a*x)^3*ln((a*x+1)^2/(-a^2*x^2+1)-1)+ln(2)*arctanh(a*x)^3+3/2048*(a*x-1)^2/(a*x+1)^2+1/16*arctanh(a*x)^3/(a*x-1)^2-5/16*arctanh(a*x)^3/(a*x-1)+1/16*arctanh(a*x)^3/(a*x+1)^2+5/16*arctanh(a*x)^3/(a*x+1)+arctanh(a*x)^3*ln(a*x)+3*arctanh(a*x)^2*polylog(2,-(a*x+1)/(-a^2*x^2+1)^(1/2))+1/2*I*arctanh(a*x)^3*Pi*csgn(I*((a*x+1)^2/(-a^2*x^2+1)-1))*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*((a*x+1)^2/(-a^2*x^2+1)-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))-1/4*I*Pi*arctanh(a*x)^3*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*(a*x+1)^2/(a^2*x^2-1))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))+1/2*I*Pi*arctanh(a*x)^3-9/32*arctanh(a*x)*(a*x-1)/(a*x+1)+3/512*arctanh(a*x)*(a*x-1)^2/(a*x+1)^2+1/2*I*Pi*arctanh(a*x)^3*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))^3+1/4*I*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^3*arctanh(a*x)^3+1/4*I*Pi*arctanh(a*x)^3*csgn(I*(a*x+1)^2/(a^2*x^2-1))^3-1/2*I*Pi*arctanh(a*x)^3*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))^2+1/2*I*Pi*arctanh(a*x)^3*csgn(I*((a*x+1)^2/(-a^2*x^2+1)-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^3-9/32*arctanh(a*x)^2*(a*x-1)/(a*x+1)+3/256*arctanh(a*x)^2*(a*x-1)^2/(a*x+1)^2-3/256*arctanh(a*x)^2*(a*x+1)^2/(a*x-1)^2+9/32*(a*x+1)*arctanh(a*x)^2/(a*x-1)-1/2*I*Pi*arctanh(a*x)^3*csgn(I*((a*x+1)^2/(-a^2*x^2+1)-1))*csgn(I*((a*x+1)^2/(-a^2*x^2+1)-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2-1/4*I*Pi*arctanh(a*x)^3*csgn(I*(a*x+1)^2/(a^2*x^2-1))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2+1/4*I*Pi*arctanh(a*x)^3*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2+1/4*I*Pi*arctanh(a*x)^3*csgn(I*(a*x+1)/(-a^2*x^2+1)^(1/2))^2*csgn(I*(a*x+1)^2/(a^2*x^2-1))","C"
319,1,842,259,3.045000," ","int(arctanh(a*x)^3/x^2/(-a^2*x^2+1)^3,x)","-\frac{3 \arctanh \left(a x \right) a^{2} x}{8 \left(a x -1\right)}+\frac{3 \arctanh \left(a x \right) a^{2} x}{8 \left(a x +1\right)}-\frac{\arctanh \left(a x \right)^{3} x \,a^{2}}{4 \left(a x -1\right)}+\frac{3 \arctanh \left(a x \right)^{2} x \,a^{2}}{8 \left(a x -1\right)}+\frac{3 \arctanh \left(a x \right)^{2} x \,a^{2}}{8 \left(a x +1\right)}-\frac{3 a}{2048 \left(a x -1\right)^{2}}-\frac{3 a \arctanh \left(a x \right)}{512 \left(a x +1\right)^{2}}-\frac{3 a \arctanh \left(a x \right)^{2}}{256 \left(a x -1\right)^{2}}+3 a \arctanh \left(a x \right)^{2} \ln \left(1+\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)+3 a \arctanh \left(a x \right)^{2} \ln \left(1-\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)-\frac{a \arctanh \left(a x \right)^{3}}{4 \left(a x -1\right)}-\frac{a \arctanh \left(a x \right)^{3}}{4 \left(a x +1\right)}+\frac{3 a^{2} x}{16 \left(a x -1\right)}+\frac{3 a^{2} x}{16 \left(a x +1\right)}-\frac{3 a \arctanh \left(a x \right)}{8 \left(a x -1\right)}+6 a \arctanh \left(a x \right) \polylog \left(2, -\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)+6 a \arctanh \left(a x \right) \polylog \left(2, \frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)+\frac{3 a \arctanh \left(a x \right)^{2}}{8 \left(a x -1\right)}-\frac{3 a \arctanh \left(a x \right)^{2}}{8 \left(a x +1\right)}+\frac{a \arctanh \left(a x \right)^{3}}{64 \left(a x -1\right)^{2}}-\frac{a \arctanh \left(a x \right)^{3}}{64 \left(a x +1\right)^{2}}-\frac{3 a \arctanh \left(a x \right)^{2}}{256 \left(a x +1\right)^{2}}+\frac{3 a \arctanh \left(a x \right)}{512 \left(a x -1\right)^{2}}+\frac{\arctanh \left(a x \right)^{3} x \,a^{2}}{32 \left(a x -1\right)^{2}}-\frac{3 \arctanh \left(a x \right)^{2} x \,a^{2}}{128 \left(a x -1\right)^{2}}-\frac{\arctanh \left(a x \right)^{3} x^{2} a^{3}}{64 \left(a x +1\right)^{2}}-\frac{3 \arctanh \left(a x \right)^{2} x^{2} a^{3}}{256 \left(a x +1\right)^{2}}+\frac{\arctanh \left(a x \right)^{3} x \,a^{2}}{32 \left(a x +1\right)^{2}}+\frac{3 \arctanh \left(a x \right)^{2} x \,a^{2}}{128 \left(a x +1\right)^{2}}+\frac{\arctanh \left(a x \right)^{3} x^{2} a^{3}}{64 \left(a x -1\right)^{2}}-\frac{3 \arctanh \left(a x \right)^{2} x^{2} a^{3}}{256 \left(a x -1\right)^{2}}-\frac{3 \arctanh \left(a x \right) a^{3} x^{2}}{512 \left(a x +1\right)^{2}}+\frac{3 \arctanh \left(a x \right) a^{2} x}{256 \left(a x +1\right)^{2}}+\frac{3 \arctanh \left(a x \right) a^{3} x^{2}}{512 \left(a x -1\right)^{2}}+\frac{3 \arctanh \left(a x \right) a^{2} x}{256 \left(a x -1\right)^{2}}+\frac{3 a}{16 \left(a x -1\right)}-\frac{3 a}{16 \left(a x +1\right)}-\frac{\arctanh \left(a x \right)^{3}}{x}+\frac{\arctanh \left(a x \right)^{3} x \,a^{2}}{4 a x +4}-\frac{3 a \arctanh \left(a x \right)}{8 \left(a x +1\right)}-6 a \polylog \left(3, -\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)-6 a \polylog \left(3, \frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)-a \arctanh \left(a x \right)^{3}+\frac{15 a \arctanh \left(a x \right)^{4}}{32}-\frac{3 a^{3} x^{2}}{2048 \left(a x -1\right)^{2}}-\frac{3 a^{2} x}{1024 \left(a x -1\right)^{2}}-\frac{3 a^{3} x^{2}}{2048 \left(a x +1\right)^{2}}+\frac{3 a^{2} x}{1024 \left(a x +1\right)^{2}}-\frac{3 a}{2048 \left(a x +1\right)^{2}}"," ",0,"-3/8*a*arctanh(a*x)/(a*x-1)-3/8*a*arctanh(a*x)/(a*x+1)-6*a*polylog(3,-(a*x+1)/(-a^2*x^2+1)^(1/2))-3/2048*a/(a*x-1)^2-arctanh(a*x)^3/x+6*a*arctanh(a*x)*polylog(2,-(a*x+1)/(-a^2*x^2+1)^(1/2))+6*a*arctanh(a*x)*polylog(2,(a*x+1)/(-a^2*x^2+1)^(1/2))-6*a*polylog(3,(a*x+1)/(-a^2*x^2+1)^(1/2))+3/16*a^2*x/(a*x-1)+3/16/(a*x+1)*a^2*x+3/8*a*arctanh(a*x)^2/(a*x-1)-3/8*a*arctanh(a*x)^2/(a*x+1)-a*arctanh(a*x)^3+15/32*a*arctanh(a*x)^4+1/32/(a*x-1)^2*arctanh(a*x)^3*x*a^2-3/128/(a*x-1)^2*arctanh(a*x)^2*x*a^2-1/64/(a*x+1)^2*arctanh(a*x)^3*x^2*a^3-3/256/(a*x+1)^2*arctanh(a*x)^2*x^2*a^3+1/32/(a*x+1)^2*arctanh(a*x)^3*x*a^2+3/128/(a*x+1)^2*arctanh(a*x)^2*x*a^2+1/64/(a*x-1)^2*arctanh(a*x)^3*x^2*a^3-3/256/(a*x-1)^2*arctanh(a*x)^2*x^2*a^3-3/512*arctanh(a*x)/(a*x+1)^2*a^3*x^2+3/256*arctanh(a*x)/(a*x+1)^2*a^2*x+3/512*arctanh(a*x)/(a*x-1)^2*a^3*x^2+3/256*arctanh(a*x)/(a*x-1)^2*a^2*x+3/16*a/(a*x-1)-3/16*a/(a*x+1)+1/64*a/(a*x-1)^2*arctanh(a*x)^3-1/64*a/(a*x+1)^2*arctanh(a*x)^3-3/256*a*arctanh(a*x)^2/(a*x+1)^2-3/8*arctanh(a*x)/(a*x-1)*a^2*x+3/8*arctanh(a*x)/(a*x+1)*a^2*x+3/512*a*arctanh(a*x)/(a*x-1)^2-3/512*a*arctanh(a*x)/(a*x+1)^2-3/2048/(a*x-1)^2*a^3*x^2-3/1024/(a*x-1)^2*a^2*x-3/2048/(a*x+1)^2*a^3*x^2+3/1024/(a*x+1)^2*a^2*x-3/256*a*arctanh(a*x)^2/(a*x-1)^2-3/2048*a/(a*x+1)^2-1/4/(a*x-1)*arctanh(a*x)^3*x*a^2+3/8/(a*x-1)*arctanh(a*x)^2*x*a^2+1/4/(a*x+1)*arctanh(a*x)^3*x*a^2+3/8/(a*x+1)*arctanh(a*x)^2*x*a^2+3*a*arctanh(a*x)^2*ln(1+(a*x+1)/(-a^2*x^2+1)^(1/2))+3*a*arctanh(a*x)^2*ln(1-(a*x+1)/(-a^2*x^2+1)^(1/2))-1/4*a/(a*x-1)*arctanh(a*x)^3-1/4*a/(a*x+1)*arctanh(a*x)^3","B"
320,-2,0,126,180.000000," ","int(arctanh(a*x)^(1/2)/(-a^2*x^2+1)^3,x)","\int \frac{\sqrt{\arctanh \left(a x \right)}}{\left(-a^{2} x^{2}+1\right)^{3}}\, dx"," ",0,"int(arctanh(a*x)^(1/2)/(-a^2*x^2+1)^3,x)","F"
321,0,0,24,0.743000," ","int(x^6/(-a^2*x^2+1)^3/arctanh(a*x),x)","\int \frac{x^{6}}{\left(-a^{2} x^{2}+1\right)^{3} \arctanh \left(a x \right)}\, dx"," ",0,"int(x^6/(-a^2*x^2+1)^3/arctanh(a*x),x)","F"
322,0,0,24,0.489000," ","int(x^5/(-a^2*x^2+1)^3/arctanh(a*x),x)","\int \frac{x^{5}}{\left(-a^{2} x^{2}+1\right)^{3} \arctanh \left(a x \right)}\, dx"," ",0,"int(x^5/(-a^2*x^2+1)^3/arctanh(a*x),x)","F"
323,1,36,35,0.255000," ","int(x^4/(-a^2*x^2+1)^3/arctanh(a*x),x)","-\frac{\Chi \left(2 \arctanh \left(a x \right)\right)}{2 a^{5}}+\frac{\Chi \left(4 \arctanh \left(a x \right)\right)}{8 a^{5}}+\frac{3 \ln \left(\arctanh \left(a x \right)\right)}{8 a^{5}}"," ",0,"-1/2*Chi(2*arctanh(a*x))/a^5+1/8*Chi(4*arctanh(a*x))/a^5+3/8*ln(arctanh(a*x))/a^5","A"
324,1,24,25,0.178000," ","int(x^3/(-a^2*x^2+1)^3/arctanh(a*x),x)","\frac{\frac{\Shi \left(4 \arctanh \left(a x \right)\right)}{8}-\frac{\Shi \left(2 \arctanh \left(a x \right)\right)}{4}}{a^{4}}"," ",0,"1/a^4*(1/8*Shi(4*arctanh(a*x))-1/4*Shi(2*arctanh(a*x)))","A"
325,1,24,23,0.187000," ","int(x^2/(-a^2*x^2+1)^3/arctanh(a*x),x)","\frac{\Chi \left(4 \arctanh \left(a x \right)\right)}{8 a^{3}}-\frac{\ln \left(\arctanh \left(a x \right)\right)}{8 a^{3}}"," ",0,"1/8*Chi(4*arctanh(a*x))/a^3-1/8*ln(arctanh(a*x))/a^3","A"
326,1,24,25,0.190000," ","int(x/(-a^2*x^2+1)^3/arctanh(a*x),x)","\frac{\frac{\Shi \left(4 \arctanh \left(a x \right)\right)}{8}+\frac{\Shi \left(2 \arctanh \left(a x \right)\right)}{4}}{a^{2}}"," ",0,"1/a^2*(1/8*Shi(4*arctanh(a*x))+1/4*Shi(2*arctanh(a*x)))","A"
327,1,36,35,0.185000," ","int(1/(-a^2*x^2+1)^3/arctanh(a*x),x)","\frac{\Chi \left(2 \arctanh \left(a x \right)\right)}{2 a}+\frac{\Chi \left(4 \arctanh \left(a x \right)\right)}{8 a}+\frac{3 \ln \left(\arctanh \left(a x \right)\right)}{8 a}"," ",0,"1/2*Chi(2*arctanh(a*x))/a+1/8*Chi(4*arctanh(a*x))/a+3/8*ln(arctanh(a*x))/a","A"
328,0,0,44,0.618000," ","int(1/x/(-a^2*x^2+1)^3/arctanh(a*x),x)","\int \frac{1}{x \left(-a^{2} x^{2}+1\right)^{3} \arctanh \left(a x \right)}\, dx"," ",0,"int(1/x/(-a^2*x^2+1)^3/arctanh(a*x),x)","F"
329,0,0,97,0.508000," ","int(x^5/(-a^2*x^2+1)^3/arctanh(a*x)^2,x)","\int \frac{x^{5}}{\left(-a^{2} x^{2}+1\right)^{3} \arctanh \left(a x \right)^{2}}\, dx"," ",0,"int(x^5/(-a^2*x^2+1)^3/arctanh(a*x)^2,x)","F"
330,1,62,51,0.247000," ","int(x^4/(-a^2*x^2+1)^3/arctanh(a*x)^2,x)","\frac{-\frac{3}{8 \arctanh \left(a x \right)}+\frac{\cosh \left(2 \arctanh \left(a x \right)\right)}{2 \arctanh \left(a x \right)}-\Shi \left(2 \arctanh \left(a x \right)\right)-\frac{\cosh \left(4 \arctanh \left(a x \right)\right)}{8 \arctanh \left(a x \right)}+\frac{\Shi \left(4 \arctanh \left(a x \right)\right)}{2}}{a^{5}}"," ",0,"1/a^5*(-3/8/arctanh(a*x)+1/2/arctanh(a*x)*cosh(2*arctanh(a*x))-Shi(2*arctanh(a*x))-1/8/arctanh(a*x)*cosh(4*arctanh(a*x))+1/2*Shi(4*arctanh(a*x)))","A"
331,1,54,51,0.178000," ","int(x^3/(-a^2*x^2+1)^3/arctanh(a*x)^2,x)","\frac{-\frac{\sinh \left(4 \arctanh \left(a x \right)\right)}{8 \arctanh \left(a x \right)}+\frac{\Chi \left(4 \arctanh \left(a x \right)\right)}{2}+\frac{\sinh \left(2 \arctanh \left(a x \right)\right)}{4 \arctanh \left(a x \right)}-\frac{\Chi \left(2 \arctanh \left(a x \right)\right)}{2}}{a^{4}}"," ",0,"1/a^4*(-1/8/arctanh(a*x)*sinh(4*arctanh(a*x))+1/2*Chi(4*arctanh(a*x))+1/4*sinh(2*arctanh(a*x))/arctanh(a*x)-1/2*Chi(2*arctanh(a*x)))","A"
332,1,38,39,0.164000," ","int(x^2/(-a^2*x^2+1)^3/arctanh(a*x)^2,x)","\frac{\frac{1}{8 \arctanh \left(a x \right)}-\frac{\cosh \left(4 \arctanh \left(a x \right)\right)}{8 \arctanh \left(a x \right)}+\frac{\Shi \left(4 \arctanh \left(a x \right)\right)}{2}}{a^{3}}"," ",0,"1/a^3*(1/8/arctanh(a*x)-1/8/arctanh(a*x)*cosh(4*arctanh(a*x))+1/2*Shi(4*arctanh(a*x)))","A"
333,1,54,49,0.186000," ","int(x/(-a^2*x^2+1)^3/arctanh(a*x)^2,x)","\frac{-\frac{\sinh \left(4 \arctanh \left(a x \right)\right)}{8 \arctanh \left(a x \right)}+\frac{\Chi \left(4 \arctanh \left(a x \right)\right)}{2}-\frac{\sinh \left(2 \arctanh \left(a x \right)\right)}{4 \arctanh \left(a x \right)}+\frac{\Chi \left(2 \arctanh \left(a x \right)\right)}{2}}{a^{2}}"," ",0,"1/a^2*(-1/8/arctanh(a*x)*sinh(4*arctanh(a*x))+1/2*Chi(4*arctanh(a*x))-1/4*sinh(2*arctanh(a*x))/arctanh(a*x)+1/2*Chi(2*arctanh(a*x)))","A"
334,1,60,47,0.232000," ","int(1/(-a^2*x^2+1)^3/arctanh(a*x)^2,x)","\frac{-\frac{3}{8 \arctanh \left(a x \right)}-\frac{\cosh \left(2 \arctanh \left(a x \right)\right)}{2 \arctanh \left(a x \right)}+\Shi \left(2 \arctanh \left(a x \right)\right)-\frac{\cosh \left(4 \arctanh \left(a x \right)\right)}{8 \arctanh \left(a x \right)}+\frac{\Shi \left(4 \arctanh \left(a x \right)\right)}{2}}{a}"," ",0,"1/a*(-3/8/arctanh(a*x)-1/2/arctanh(a*x)*cosh(2*arctanh(a*x))+Shi(2*arctanh(a*x))-1/8/arctanh(a*x)*cosh(4*arctanh(a*x))+1/2*Shi(4*arctanh(a*x)))","A"
335,0,0,94,0.638000," ","int(1/x/(-a^2*x^2+1)^3/arctanh(a*x)^2,x)","\int \frac{1}{x \left(-a^{2} x^{2}+1\right)^{3} \arctanh \left(a x \right)^{2}}\, dx"," ",0,"int(1/x/(-a^2*x^2+1)^3/arctanh(a*x)^2,x)","F"
336,1,90,98,0.254000," ","int(x^4/(-a^2*x^2+1)^3/arctanh(a*x)^3,x)","\frac{-\frac{3}{16 \arctanh \left(a x \right)^{2}}+\frac{\cosh \left(2 \arctanh \left(a x \right)\right)}{4 \arctanh \left(a x \right)^{2}}+\frac{\sinh \left(2 \arctanh \left(a x \right)\right)}{2 \arctanh \left(a x \right)}-\Chi \left(2 \arctanh \left(a x \right)\right)-\frac{\cosh \left(4 \arctanh \left(a x \right)\right)}{16 \arctanh \left(a x \right)^{2}}-\frac{\sinh \left(4 \arctanh \left(a x \right)\right)}{4 \arctanh \left(a x \right)}+\Chi \left(4 \arctanh \left(a x \right)\right)}{a^{5}}"," ",0,"1/a^5*(-3/16/arctanh(a*x)^2+1/4/arctanh(a*x)^2*cosh(2*arctanh(a*x))+1/2*sinh(2*arctanh(a*x))/arctanh(a*x)-Chi(2*arctanh(a*x))-1/16/arctanh(a*x)^2*cosh(4*arctanh(a*x))-1/4/arctanh(a*x)*sinh(4*arctanh(a*x))+Chi(4*arctanh(a*x)))","A"
337,1,82,99,0.183000," ","int(x^3/(-a^2*x^2+1)^3/arctanh(a*x)^3,x)","\frac{\frac{\sinh \left(2 \arctanh \left(a x \right)\right)}{8 \arctanh \left(a x \right)^{2}}+\frac{\cosh \left(2 \arctanh \left(a x \right)\right)}{4 \arctanh \left(a x \right)}-\frac{\Shi \left(2 \arctanh \left(a x \right)\right)}{2}-\frac{\sinh \left(4 \arctanh \left(a x \right)\right)}{16 \arctanh \left(a x \right)^{2}}-\frac{\cosh \left(4 \arctanh \left(a x \right)\right)}{4 \arctanh \left(a x \right)}+\Shi \left(4 \arctanh \left(a x \right)\right)}{a^{4}}"," ",0,"1/a^4*(1/8*sinh(2*arctanh(a*x))/arctanh(a*x)^2+1/4/arctanh(a*x)*cosh(2*arctanh(a*x))-1/2*Shi(2*arctanh(a*x))-1/16/arctanh(a*x)^2*sinh(4*arctanh(a*x))-1/4/arctanh(a*x)*cosh(4*arctanh(a*x))+Shi(4*arctanh(a*x)))","A"
338,1,51,84,0.164000," ","int(x^2/(-a^2*x^2+1)^3/arctanh(a*x)^3,x)","\frac{\frac{1}{16 \arctanh \left(a x \right)^{2}}-\frac{\cosh \left(4 \arctanh \left(a x \right)\right)}{16 \arctanh \left(a x \right)^{2}}-\frac{\sinh \left(4 \arctanh \left(a x \right)\right)}{4 \arctanh \left(a x \right)}+\Chi \left(4 \arctanh \left(a x \right)\right)}{a^{3}}"," ",0,"1/a^3*(1/16/arctanh(a*x)^2-1/16/arctanh(a*x)^2*cosh(4*arctanh(a*x))-1/4/arctanh(a*x)*sinh(4*arctanh(a*x))+Chi(4*arctanh(a*x)))","A"
339,1,82,94,0.184000," ","int(x/(-a^2*x^2+1)^3/arctanh(a*x)^3,x)","\frac{-\frac{\sinh \left(2 \arctanh \left(a x \right)\right)}{8 \arctanh \left(a x \right)^{2}}-\frac{\cosh \left(2 \arctanh \left(a x \right)\right)}{4 \arctanh \left(a x \right)}+\frac{\Shi \left(2 \arctanh \left(a x \right)\right)}{2}-\frac{\sinh \left(4 \arctanh \left(a x \right)\right)}{16 \arctanh \left(a x \right)^{2}}-\frac{\cosh \left(4 \arctanh \left(a x \right)\right)}{4 \arctanh \left(a x \right)}+\Shi \left(4 \arctanh \left(a x \right)\right)}{a^{2}}"," ",0,"1/a^2*(-1/8*sinh(2*arctanh(a*x))/arctanh(a*x)^2-1/4/arctanh(a*x)*cosh(2*arctanh(a*x))+1/2*Shi(2*arctanh(a*x))-1/16/arctanh(a*x)^2*sinh(4*arctanh(a*x))-1/4/arctanh(a*x)*cosh(4*arctanh(a*x))+Shi(4*arctanh(a*x)))","A"
340,1,88,67,0.237000," ","int(1/(-a^2*x^2+1)^3/arctanh(a*x)^3,x)","\frac{-\frac{3}{16 \arctanh \left(a x \right)^{2}}-\frac{\cosh \left(2 \arctanh \left(a x \right)\right)}{4 \arctanh \left(a x \right)^{2}}-\frac{\sinh \left(2 \arctanh \left(a x \right)\right)}{2 \arctanh \left(a x \right)}+\Chi \left(2 \arctanh \left(a x \right)\right)-\frac{\cosh \left(4 \arctanh \left(a x \right)\right)}{16 \arctanh \left(a x \right)^{2}}-\frac{\sinh \left(4 \arctanh \left(a x \right)\right)}{4 \arctanh \left(a x \right)}+\Chi \left(4 \arctanh \left(a x \right)\right)}{a}"," ",0,"1/a*(-3/16/arctanh(a*x)^2-1/4/arctanh(a*x)^2*cosh(2*arctanh(a*x))-1/2*sinh(2*arctanh(a*x))/arctanh(a*x)+Chi(2*arctanh(a*x))-1/16/arctanh(a*x)^2*cosh(4*arctanh(a*x))-1/4/arctanh(a*x)*sinh(4*arctanh(a*x))+Chi(4*arctanh(a*x)))","A"
341,0,0,162,0.650000," ","int(1/x/(-a^2*x^2+1)^3/arctanh(a*x)^3,x)","\int \frac{1}{x \left(-a^{2} x^{2}+1\right)^{3} \arctanh \left(a x \right)^{3}}\, dx"," ",0,"int(1/x/(-a^2*x^2+1)^3/arctanh(a*x)^3,x)","F"
342,1,122,115,0.230000," ","int(1/(-a^2*x^2+1)^3/arctanh(a*x)^4,x)","\frac{-\frac{1}{8 \arctanh \left(a x \right)^{3}}-\frac{\cosh \left(2 \arctanh \left(a x \right)\right)}{6 \arctanh \left(a x \right)^{3}}-\frac{\sinh \left(2 \arctanh \left(a x \right)\right)}{6 \arctanh \left(a x \right)^{2}}-\frac{\cosh \left(2 \arctanh \left(a x \right)\right)}{3 \arctanh \left(a x \right)}+\frac{2 \Shi \left(2 \arctanh \left(a x \right)\right)}{3}-\frac{\cosh \left(4 \arctanh \left(a x \right)\right)}{24 \arctanh \left(a x \right)^{3}}-\frac{\sinh \left(4 \arctanh \left(a x \right)\right)}{12 \arctanh \left(a x \right)^{2}}-\frac{\cosh \left(4 \arctanh \left(a x \right)\right)}{3 \arctanh \left(a x \right)}+\frac{4 \Shi \left(4 \arctanh \left(a x \right)\right)}{3}}{a}"," ",0,"1/a*(-1/8/arctanh(a*x)^3-1/6/arctanh(a*x)^3*cosh(2*arctanh(a*x))-1/6*sinh(2*arctanh(a*x))/arctanh(a*x)^2-1/3/arctanh(a*x)*cosh(2*arctanh(a*x))+2/3*Shi(2*arctanh(a*x))-1/24/arctanh(a*x)^3*cosh(4*arctanh(a*x))-1/12/arctanh(a*x)^2*sinh(4*arctanh(a*x))-1/3/arctanh(a*x)*cosh(4*arctanh(a*x))+4/3*Shi(4*arctanh(a*x)))","A"
343,1,152,156,0.232000," ","int(1/(-a^2*x^2+1)^3/arctanh(a*x)^5,x)","\frac{-\frac{3}{32 \arctanh \left(a x \right)^{4}}-\frac{\cosh \left(2 \arctanh \left(a x \right)\right)}{8 \arctanh \left(a x \right)^{4}}-\frac{\sinh \left(2 \arctanh \left(a x \right)\right)}{12 \arctanh \left(a x \right)^{3}}-\frac{\cosh \left(2 \arctanh \left(a x \right)\right)}{12 \arctanh \left(a x \right)^{2}}-\frac{\sinh \left(2 \arctanh \left(a x \right)\right)}{6 \arctanh \left(a x \right)}+\frac{\Chi \left(2 \arctanh \left(a x \right)\right)}{3}-\frac{\cosh \left(4 \arctanh \left(a x \right)\right)}{32 \arctanh \left(a x \right)^{4}}-\frac{\sinh \left(4 \arctanh \left(a x \right)\right)}{24 \arctanh \left(a x \right)^{3}}-\frac{\cosh \left(4 \arctanh \left(a x \right)\right)}{12 \arctanh \left(a x \right)^{2}}-\frac{\sinh \left(4 \arctanh \left(a x \right)\right)}{3 \arctanh \left(a x \right)}+\frac{4 \Chi \left(4 \arctanh \left(a x \right)\right)}{3}}{a}"," ",0,"1/a*(-3/32/arctanh(a*x)^4-1/8/arctanh(a*x)^4*cosh(2*arctanh(a*x))-1/12/arctanh(a*x)^3*sinh(2*arctanh(a*x))-1/12/arctanh(a*x)^2*cosh(2*arctanh(a*x))-1/6*sinh(2*arctanh(a*x))/arctanh(a*x)+1/3*Chi(2*arctanh(a*x))-1/32/arctanh(a*x)^4*cosh(4*arctanh(a*x))-1/24/arctanh(a*x)^3*sinh(4*arctanh(a*x))-1/12/arctanh(a*x)^2*cosh(4*arctanh(a*x))-1/3/arctanh(a*x)*sinh(4*arctanh(a*x))+4/3*Chi(4*arctanh(a*x)))","A"
344,1,182,235,0.232000," ","int(1/(-a^2*x^2+1)^3/arctanh(a*x)^6,x)","\frac{-\frac{3}{40 \arctanh \left(a x \right)^{5}}-\frac{\cosh \left(2 \arctanh \left(a x \right)\right)}{10 \arctanh \left(a x \right)^{5}}-\frac{\sinh \left(2 \arctanh \left(a x \right)\right)}{20 \arctanh \left(a x \right)^{4}}-\frac{\cosh \left(2 \arctanh \left(a x \right)\right)}{30 \arctanh \left(a x \right)^{3}}-\frac{\sinh \left(2 \arctanh \left(a x \right)\right)}{30 \arctanh \left(a x \right)^{2}}-\frac{\cosh \left(2 \arctanh \left(a x \right)\right)}{15 \arctanh \left(a x \right)}+\frac{2 \Shi \left(2 \arctanh \left(a x \right)\right)}{15}-\frac{\cosh \left(4 \arctanh \left(a x \right)\right)}{40 \arctanh \left(a x \right)^{5}}-\frac{\sinh \left(4 \arctanh \left(a x \right)\right)}{40 \arctanh \left(a x \right)^{4}}-\frac{\cosh \left(4 \arctanh \left(a x \right)\right)}{30 \arctanh \left(a x \right)^{3}}-\frac{\sinh \left(4 \arctanh \left(a x \right)\right)}{15 \arctanh \left(a x \right)^{2}}-\frac{4 \cosh \left(4 \arctanh \left(a x \right)\right)}{15 \arctanh \left(a x \right)}+\frac{16 \Shi \left(4 \arctanh \left(a x \right)\right)}{15}}{a}"," ",0,"1/a*(-3/40/arctanh(a*x)^5-1/10/arctanh(a*x)^5*cosh(2*arctanh(a*x))-1/20/arctanh(a*x)^4*sinh(2*arctanh(a*x))-1/30/arctanh(a*x)^3*cosh(2*arctanh(a*x))-1/30*sinh(2*arctanh(a*x))/arctanh(a*x)^2-1/15/arctanh(a*x)*cosh(2*arctanh(a*x))+2/15*Shi(2*arctanh(a*x))-1/40/arctanh(a*x)^5*cosh(4*arctanh(a*x))-1/40/arctanh(a*x)^4*sinh(4*arctanh(a*x))-1/30/arctanh(a*x)^3*cosh(4*arctanh(a*x))-1/15/arctanh(a*x)^2*sinh(4*arctanh(a*x))-4/15/arctanh(a*x)*cosh(4*arctanh(a*x))+16/15*Shi(4*arctanh(a*x)))","A"
345,1,281,120,0.067000," ","int(arctanh(a*x)/(-a^2*x^2+1)^4,x)","-\frac{\arctanh \left(a x \right)}{48 a \left(a x -1\right)^{3}}+\frac{\arctanh \left(a x \right)}{16 a \left(a x -1\right)^{2}}-\frac{5 \arctanh \left(a x \right)}{32 a \left(a x -1\right)}-\frac{5 \arctanh \left(a x \right) \ln \left(a x -1\right)}{32 a}-\frac{\arctanh \left(a x \right)}{48 a \left(a x +1\right)^{3}}-\frac{\arctanh \left(a x \right)}{16 a \left(a x +1\right)^{2}}-\frac{5 \arctanh \left(a x \right)}{32 a \left(a x +1\right)}+\frac{5 \arctanh \left(a x \right) \ln \left(a x +1\right)}{32 a}-\frac{5 \ln \left(a x -1\right)^{2}}{128 a}+\frac{5 \ln \left(a x -1\right) \ln \left(\frac{1}{2}+\frac{a x}{2}\right)}{64 a}-\frac{5 \ln \left(a x +1\right)^{2}}{128 a}-\frac{5 \ln \left(-\frac{a x}{2}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{a x}{2}\right)}{64 a}+\frac{5 \ln \left(-\frac{a x}{2}+\frac{1}{2}\right) \ln \left(a x +1\right)}{64 a}+\frac{1}{288 a \left(a x -1\right)^{3}}-\frac{7}{384 a \left(a x -1\right)^{2}}+\frac{37}{384 a \left(a x -1\right)}-\frac{1}{288 a \left(a x +1\right)^{3}}-\frac{7}{384 a \left(a x +1\right)^{2}}-\frac{37}{384 a \left(a x +1\right)}"," ",0,"-1/48/a*arctanh(a*x)/(a*x-1)^3+1/16/a*arctanh(a*x)/(a*x-1)^2-5/32/a*arctanh(a*x)/(a*x-1)-5/32/a*arctanh(a*x)*ln(a*x-1)-1/48/a*arctanh(a*x)/(a*x+1)^3-1/16/a*arctanh(a*x)/(a*x+1)^2-5/32/a*arctanh(a*x)/(a*x+1)+5/32/a*arctanh(a*x)*ln(a*x+1)-5/128/a*ln(a*x-1)^2+5/64/a*ln(a*x-1)*ln(1/2+1/2*a*x)-5/128/a*ln(a*x+1)^2-5/64/a*ln(-1/2*a*x+1/2)*ln(1/2+1/2*a*x)+5/64/a*ln(-1/2*a*x+1/2)*ln(a*x+1)+1/288/a/(a*x-1)^3-7/384/a/(a*x-1)^2+37/384/a/(a*x-1)-1/288/a/(a*x+1)^3-7/384/a/(a*x+1)^2-37/384/a/(a*x+1)","B"
346,1,3447,192,0.857000," ","int(arctanh(a*x)^2/(-a^2*x^2+1)^4,x)","\text{output too large to display}"," 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3*arctanh(a*x)^3*x^2-35/384*a/(a*x-1)^3/(a*x+1)^3*arctanh(a*x)*x^2+5/48*a^5/(a*x-1)^3/(a*x+1)^3*arctanh(a*x)^3*x^6+245/1152*a^5/(a*x-1)^3/(a*x+1)^3*arctanh(a*x)*x^6-5/16*a^3/(a*x-1)^3/(a*x+1)^3*arctanh(a*x)^3*x^4-125/384*a^3/(a*x-1)^3/(a*x+1)^3*arctanh(a*x)*x^4","C"
347,1,3550,263,0.973000," ","int(arctanh(a*x)^3/(-a^2*x^2+1)^4,x)","\text{output too large to display}"," ",0,"5/32*I*a^5/(a*x-1)^3/(a*x+1)^3*arctanh(a*x)^3*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))^3*x^6-5/64*I*a^5/(a*x-1)^3/(a*x+1)^3*arctanh(a*x)^3*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^3*x^6-5/32*I*a^5/(a*x-1)^3/(a*x+1)^3*arctanh(a*x)^3*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*x^6+15/64*I*a^3/(a*x-1)^3/(a*x+1)^3*arctanh(a*x)^3*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1))^3*x^4-15/32*I*a^3/(a*x-1)^3/(a*x+1)^3*arctanh(a*x)^3*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))^3*x^4+15/64*I*a^3/(a*x-1)^3/(a*x+1)^3*arctanh(a*x)^3*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^3*x^4+15/32*I*a^3/(a*x-1)^3/(a*x+1)^3*arctanh(a*x)^3*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*x^4-15/64*I*a/(a*x-1)^3/(a*x+1)^3*arctanh(a*x)^3*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1))^3*x^2+15/32*I*a/(a*x-1)^3/(a*x+1)^3*arctanh(a*x)^3*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))^3*x^2-15/64*I*a/(a*x-1)^3/(a*x+1)^3*arctanh(a*x)^3*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^3*x^2+5/64*I/a/(a*x-1)^3/(a*x+1)^3*Pi*arctanh(a*x)^3*csgn(I*(a*x+1)/(-a^2*x^2+1)^(1/2))^2*csgn(I*(a*x+1)^2/(a^2*x^2-1))+5/64*I/a/(a*x-1)^3/(a*x+1)^3*Pi*arctanh(a*x)^3*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2+5/32*I/a/(a*x-1)^3/(a*x+1)^3*Pi*arctanh(a*x)^3*csgn(I*(a*x+1)/(-a^2*x^2+1)^(1/2))*csgn(I*(a*x+1)^2/(a^2*x^2-1))^2-5/64*I/a/(a*x-1)^3/(a*x+1)^3*Pi*arctanh(a*x)^3*csgn(I*(a*x+1)^2/(a^2*x^2-1))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2-15/32*I*a/(a*x-1)^3/(a*x+1)^3*arctanh(a*x)^3*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*x^2-5/64*I*a^5/(a*x-1)^3/(a*x+1)^3*arctanh(a*x)^3*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1))^3*x^6+5/64*I*a^5/(a*x-1)^3/(a*x+1)^3*arctanh(a*x)^3*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*(a*x+1)^2/(a^2*x^2-1))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))*x^6+15/64*I*a/(a*x-1)^3/(a*x+1)^3*arctanh(a*x)^3*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*(a*x+1)^2/(a^2*x^2-1))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))*x^2-15/64*I*a^3/(a*x-1)^3/(a*x+1)^3*arctanh(a*x)^3*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*(a*x+1)^2/(a^2*x^2-1))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))*x^4+9485/55296*a^5/(a*x-1)^3/(a*x+1)^3*x^6-3605/18432*a^3/(a*x-1)^3/(a*x+1)^3*x^4-2795/18432*a/(a*x-1)^3/(a*x+1)^3*x^2-299/384/(a*x-1)^3/(a*x+1)^3*arctanh(a*x)*x-5/64/a/(a*x-1)^3/(a*x+1)^3*arctanh(a*x)^4+299/768/a/(a*x-1)^3/(a*x+1)^3*arctanh(a*x)^2+15/32*I*a^3/(a*x-1)^3/(a*x+1)^3*arctanh(a*x)^3*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1))^2*csgn(I*(a*x+1)/(-a^2*x^2+1)^(1/2))*x^4-5/64*I/a/(a*x-1)^3/(a*x+1)^3*Pi*arctanh(a*x)^3*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*(a*x+1)^2/(a^2*x^2-1))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))-15/64*I*a/(a*x-1)^3/(a*x+1)^3*arctanh(a*x)^3*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*x^2-15/64*I*a^3/(a*x-1)^3/(a*x+1)^3*arctanh(a*x)^3*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*x^4+15/64*I*a^3/(a*x-1)^3/(a*x+1)^3*arctanh(a*x)^3*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1))*csgn(I*(a*x+1)/(-a^2*x^2+1)^(1/2))^2*x^4+15/64*I*a^3/(a*x-1)^3/(a*x+1)^3*arctanh(a*x)^3*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*x^4-15/32*I*a/(a*x-1)^3/(a*x+1)^3*arctanh(a*x)^3*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1))^2*csgn(I*(a*x+1)/(-a^2*x^2+1)^(1/2))*x^2+15/64*I*a/(a*x-1)^3/(a*x+1)^3*arctanh(a*x)^3*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*x^2-15/64*I*a/(a*x-1)^3/(a*x+1)^3*arctanh(a*x)^3*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1))*csgn(I*(a*x+1)/(-a^2*x^2+1)^(1/2))^2*x^2-5/32*I*a^5/(a*x-1)^3/(a*x+1)^3*arctanh(a*x)^3*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1))^2*csgn(I*(a*x+1)/(-a^2*x^2+1)^(1/2))*x^6+5/64*I*a^5/(a*x-1)^3/(a*x+1)^3*arctanh(a*x)^3*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*x^6-5/64*I*a^5/(a*x-1)^3/(a*x+1)^3*arctanh(a*x)^3*Pi*csgn(I*(a*x+1)^2/(a^2*x^2-1))*csgn(I*(a*x+1)/(-a^2*x^2+1)^(1/2))^2*x^6-5/64*I*a^5/(a*x-1)^3/(a*x+1)^3*arctanh(a*x)^3*Pi*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^2*x^6-5/32*I/a/(a*x-1)^3/(a*x+1)^3*Pi*arctanh(a*x)^3+5/32/a*arctanh(a*x)^3*ln(a*x+1)-5/16/a*arctanh(a*x)^3*ln((a*x+1)/(-a^2*x^2+1)^(1/2))+15/64*a/(a*x-1)^3/(a*x+1)^3*arctanh(a*x)^4*x^2+25/18*a^2/(a*x-1)^3/(a*x+1)^3*arctanh(a*x)*x^3+9971/55296/a/(a*x-1)^3/(a*x+1)^3-1/48/a*arctanh(a*x)^3/(a*x-1)^3+1/16/a*arctanh(a*x)^3/(a*x-1)^2-5/32/a*arctanh(a*x)^3/(a*x-1)-5/32/a*arctanh(a*x)^3*ln(a*x-1)-1/48/a*arctanh(a*x)^3/(a*x+1)^3-1/16/a*arctanh(a*x)^3/(a*x+1)^2-35/256*a/(a*x-1)^3/(a*x+1)^3*arctanh(a*x)^2*x^2+5/64*a^5/(a*x-1)^3/(a*x+1)^3*arctanh(a*x)^4*x^6+245/768*a^5/(a*x-1)^3/(a*x+1)^3*arctanh(a*x)^2*x^6-15/64*a^3/(a*x-1)^3/(a*x+1)^3*arctanh(a*x)^4*x^4-245/384*a^4/(a*x-1)^3/(a*x+1)^3*arctanh(a*x)*x^5-125/256*a^3/(a*x-1)^3/(a*x+1)^3*arctanh(a*x)^2*x^4-5/32/a*arctanh(a*x)^3/(a*x+1)-15/32*I*a^3/(a*x-1)^3/(a*x+1)^3*arctanh(a*x)^3*Pi*x^4+15/32*I*a/(a*x-1)^3/(a*x+1)^3*arctanh(a*x)^3*Pi*x^2+5/64*I/a/(a*x-1)^3/(a*x+1)^3*Pi*arctanh(a*x)^3*csgn(I*(a*x+1)^2/(a^2*x^2-1))^3-5/32*I/a/(a*x-1)^3/(a*x+1)^3*Pi*arctanh(a*x)^3*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))^3+5/64*I/a/(a*x-1)^3/(a*x+1)^3*Pi*arctanh(a*x)^3*csgn(I*(a*x+1)^2/(a^2*x^2-1)/(1+(a*x+1)^2/(-a^2*x^2+1)))^3+5/32*I/a/(a*x-1)^3/(a*x+1)^3*Pi*arctanh(a*x)^3*csgn(I/(1+(a*x+1)^2/(-a^2*x^2+1)))^2+5/32*I*a^5/(a*x-1)^3/(a*x+1)^3*arctanh(a*x)^3*Pi*x^6","C"
348,-2,0,188,180.000000," ","int(arctanh(a*x)^(1/2)/(-a^2*x^2+1)^4,x)","\int \frac{\sqrt{\arctanh \left(a x \right)}}{\left(-a^{2} x^{2}+1\right)^{4}}\, dx"," ",0,"int(arctanh(a*x)^(1/2)/(-a^2*x^2+1)^4,x)","F"
349,0,0,24,0.832000," ","int(x^8/(-a^2*x^2+1)^4/arctanh(a*x),x)","\int \frac{x^{8}}{\left(-a^{2} x^{2}+1\right)^{4} \arctanh \left(a x \right)}\, dx"," ",0,"int(x^8/(-a^2*x^2+1)^4/arctanh(a*x),x)","F"
350,0,0,24,0.740000," ","int(x^7/(-a^2*x^2+1)^4/arctanh(a*x),x)","\int \frac{x^{7}}{\left(-a^{2} x^{2}+1\right)^{4} \arctanh \left(a x \right)}\, dx"," ",0,"int(x^7/(-a^2*x^2+1)^4/arctanh(a*x),x)","F"
351,1,48,47,0.305000," ","int(x^6/(-a^2*x^2+1)^4/arctanh(a*x),x)","\frac{15 \Chi \left(2 \arctanh \left(a x \right)\right)}{32 a^{7}}-\frac{3 \Chi \left(4 \arctanh \left(a x \right)\right)}{16 a^{7}}+\frac{\Chi \left(6 \arctanh \left(a x \right)\right)}{32 a^{7}}-\frac{5 \ln \left(\arctanh \left(a x \right)\right)}{16 a^{7}}"," ",0,"15/32*Chi(2*arctanh(a*x))/a^7-3/16*Chi(4*arctanh(a*x))/a^7+1/32*Chi(6*arctanh(a*x))/a^7-5/16*ln(arctanh(a*x))/a^7","A"
352,1,33,37,0.231000," ","int(x^5/(-a^2*x^2+1)^4/arctanh(a*x),x)","\frac{-\frac{\Shi \left(4 \arctanh \left(a x \right)\right)}{8}+\frac{\Shi \left(6 \arctanh \left(a x \right)\right)}{32}+\frac{5 \Shi \left(2 \arctanh \left(a x \right)\right)}{32}}{a^{6}}"," ",0,"1/a^6*(-1/8*Shi(4*arctanh(a*x))+1/32*Shi(6*arctanh(a*x))+5/32*Shi(2*arctanh(a*x)))","A"
353,1,48,47,0.265000," ","int(x^4/(-a^2*x^2+1)^4/arctanh(a*x),x)","-\frac{\Chi \left(2 \arctanh \left(a x \right)\right)}{32 a^{5}}-\frac{\Chi \left(4 \arctanh \left(a x \right)\right)}{16 a^{5}}+\frac{\Chi \left(6 \arctanh \left(a x \right)\right)}{32 a^{5}}+\frac{\ln \left(\arctanh \left(a x \right)\right)}{16 a^{5}}"," ",0,"-1/32*Chi(2*arctanh(a*x))/a^5-1/16*Chi(4*arctanh(a*x))/a^5+1/32*Chi(6*arctanh(a*x))/a^5+1/16*ln(arctanh(a*x))/a^5","A"
354,1,24,25,0.186000," ","int(x^3/(-a^2*x^2+1)^4/arctanh(a*x),x)","\frac{\frac{\Shi \left(6 \arctanh \left(a x \right)\right)}{32}-\frac{3 \Shi \left(2 \arctanh \left(a x \right)\right)}{32}}{a^{4}}"," ",0,"1/a^4*(1/32*Shi(6*arctanh(a*x))-3/32*Shi(2*arctanh(a*x)))","A"
355,1,48,47,0.256000," ","int(x^2/(-a^2*x^2+1)^4/arctanh(a*x),x)","-\frac{\Chi \left(2 \arctanh \left(a x \right)\right)}{32 a^{3}}+\frac{\Chi \left(4 \arctanh \left(a x \right)\right)}{16 a^{3}}+\frac{\Chi \left(6 \arctanh \left(a x \right)\right)}{32 a^{3}}-\frac{\ln \left(\arctanh \left(a x \right)\right)}{16 a^{3}}"," ",0,"-1/32*Chi(2*arctanh(a*x))/a^3+1/16*Chi(4*arctanh(a*x))/a^3+1/32*Chi(6*arctanh(a*x))/a^3-1/16*ln(arctanh(a*x))/a^3","A"
356,1,33,37,0.227000," ","int(x/(-a^2*x^2+1)^4/arctanh(a*x),x)","\frac{\frac{\Shi \left(4 \arctanh \left(a x \right)\right)}{8}+\frac{\Shi \left(6 \arctanh \left(a x \right)\right)}{32}+\frac{5 \Shi \left(2 \arctanh \left(a x \right)\right)}{32}}{a^{2}}"," ",0,"1/a^2*(1/8*Shi(4*arctanh(a*x))+1/32*Shi(6*arctanh(a*x))+5/32*Shi(2*arctanh(a*x)))","A"
357,1,48,47,0.280000," ","int(1/(-a^2*x^2+1)^4/arctanh(a*x),x)","\frac{15 \Chi \left(2 \arctanh \left(a x \right)\right)}{32 a}+\frac{3 \Chi \left(4 \arctanh \left(a x \right)\right)}{16 a}+\frac{\Chi \left(6 \arctanh \left(a x \right)\right)}{32 a}+\frac{5 \ln \left(\arctanh \left(a x \right)\right)}{16 a}"," ",0,"15/32*Chi(2*arctanh(a*x))/a+3/16*Chi(4*arctanh(a*x))/a+1/32*Chi(6*arctanh(a*x))/a+5/16*ln(arctanh(a*x))/a","A"
358,0,0,24,0.712000," ","int(1/x/(-a^2*x^2+1)^4/arctanh(a*x),x)","\int \frac{1}{x \left(-a^{2} x^{2}+1\right)^{4} \arctanh \left(a x \right)}\, dx"," ",0,"int(1/x/(-a^2*x^2+1)^4/arctanh(a*x),x)","F"
359,0,0,24,0.878000," ","int(1/x^2/(-a^2*x^2+1)^4/arctanh(a*x),x)","\int \frac{1}{x^{2} \left(-a^{2} x^{2}+1\right)^{4} \arctanh \left(a x \right)}\, dx"," ",0,"int(1/x^2/(-a^2*x^2+1)^4/arctanh(a*x),x)","F"
360,1,78,61,0.230000," ","int(x/(-a^2*x^2+1)^4/arctanh(a*x)^2,x)","\frac{-\frac{\sinh \left(4 \arctanh \left(a x \right)\right)}{8 \arctanh \left(a x \right)}+\frac{\Chi \left(4 \arctanh \left(a x \right)\right)}{2}-\frac{\sinh \left(6 \arctanh \left(a x \right)\right)}{32 \arctanh \left(a x \right)}+\frac{3 \Chi \left(6 \arctanh \left(a x \right)\right)}{16}-\frac{5 \sinh \left(2 \arctanh \left(a x \right)\right)}{32 \arctanh \left(a x \right)}+\frac{5 \Chi \left(2 \arctanh \left(a x \right)\right)}{16}}{a^{2}}"," ",0,"1/a^2*(-1/8/arctanh(a*x)*sinh(4*arctanh(a*x))+1/2*Chi(4*arctanh(a*x))-1/32/arctanh(a*x)*sinh(6*arctanh(a*x))+3/16*Chi(6*arctanh(a*x))-5/32*sinh(2*arctanh(a*x))/arctanh(a*x)+5/16*Chi(2*arctanh(a*x)))","A"
361,1,86,60,0.275000," ","int(1/(-a^2*x^2+1)^4/arctanh(a*x)^2,x)","\frac{-\frac{5}{16 \arctanh \left(a x \right)}-\frac{15 \cosh \left(2 \arctanh \left(a x \right)\right)}{32 \arctanh \left(a x \right)}+\frac{15 \Shi \left(2 \arctanh \left(a x \right)\right)}{16}-\frac{3 \cosh \left(4 \arctanh \left(a x \right)\right)}{16 \arctanh \left(a x \right)}+\frac{3 \Shi \left(4 \arctanh \left(a x \right)\right)}{4}-\frac{\cosh \left(6 \arctanh \left(a x \right)\right)}{32 \arctanh \left(a x \right)}+\frac{3 \Shi \left(6 \arctanh \left(a x \right)\right)}{16}}{a}"," ",0,"1/a*(-5/16/arctanh(a*x)-15/32/arctanh(a*x)*cosh(2*arctanh(a*x))+15/16*Shi(2*arctanh(a*x))-3/16/arctanh(a*x)*cosh(4*arctanh(a*x))+3/4*Shi(4*arctanh(a*x))-1/32/arctanh(a*x)*cosh(6*arctanh(a*x))+3/16*Shi(6*arctanh(a*x)))","A"
362,1,121,106,0.236000," ","int(x/(-a^2*x^2+1)^4/arctanh(a*x)^3,x)","\frac{-\frac{5 \sinh \left(2 \arctanh \left(a x \right)\right)}{64 \arctanh \left(a x \right)^{2}}-\frac{5 \cosh \left(2 \arctanh \left(a x \right)\right)}{32 \arctanh \left(a x \right)}+\frac{5 \Shi \left(2 \arctanh \left(a x \right)\right)}{16}-\frac{\sinh \left(4 \arctanh \left(a x \right)\right)}{16 \arctanh \left(a x \right)^{2}}-\frac{\cosh \left(4 \arctanh \left(a x \right)\right)}{4 \arctanh \left(a x \right)}+\Shi \left(4 \arctanh \left(a x \right)\right)-\frac{\sinh \left(6 \arctanh \left(a x \right)\right)}{64 \arctanh \left(a x \right)^{2}}-\frac{3 \cosh \left(6 \arctanh \left(a x \right)\right)}{32 \arctanh \left(a x \right)}+\frac{9 \Shi \left(6 \arctanh \left(a x \right)\right)}{16}}{a^{2}}"," ",0,"1/a^2*(-5/64*sinh(2*arctanh(a*x))/arctanh(a*x)^2-5/32/arctanh(a*x)*cosh(2*arctanh(a*x))+5/16*Shi(2*arctanh(a*x))-1/16/arctanh(a*x)^2*sinh(4*arctanh(a*x))-1/4/arctanh(a*x)*cosh(4*arctanh(a*x))+Shi(4*arctanh(a*x))-1/64/arctanh(a*x)^2*sinh(6*arctanh(a*x))-3/32/arctanh(a*x)*cosh(6*arctanh(a*x))+9/16*Shi(6*arctanh(a*x)))","A"
363,1,131,81,0.282000," ","int(1/(-a^2*x^2+1)^4/arctanh(a*x)^3,x)","\frac{-\frac{5}{32 \arctanh \left(a x \right)^{2}}-\frac{15 \cosh \left(2 \arctanh \left(a x \right)\right)}{64 \arctanh \left(a x \right)^{2}}-\frac{15 \sinh \left(2 \arctanh \left(a x \right)\right)}{32 \arctanh \left(a x \right)}+\frac{15 \Chi \left(2 \arctanh \left(a x \right)\right)}{16}-\frac{3 \cosh \left(4 \arctanh \left(a x \right)\right)}{32 \arctanh \left(a x \right)^{2}}-\frac{3 \sinh \left(4 \arctanh \left(a x \right)\right)}{8 \arctanh \left(a x \right)}+\frac{3 \Chi \left(4 \arctanh \left(a x \right)\right)}{2}-\frac{\cosh \left(6 \arctanh \left(a x \right)\right)}{64 \arctanh \left(a x \right)^{2}}-\frac{3 \sinh \left(6 \arctanh \left(a x \right)\right)}{32 \arctanh \left(a x \right)}+\frac{9 \Chi \left(6 \arctanh \left(a x \right)\right)}{16}}{a}"," ",0,"1/a*(-5/32/arctanh(a*x)^2-15/64/arctanh(a*x)^2*cosh(2*arctanh(a*x))-15/32*sinh(2*arctanh(a*x))/arctanh(a*x)+15/16*Chi(2*arctanh(a*x))-3/32/arctanh(a*x)^2*cosh(4*arctanh(a*x))-3/8/arctanh(a*x)*sinh(4*arctanh(a*x))+3/2*Chi(4*arctanh(a*x))-1/64/arctanh(a*x)^2*cosh(6*arctanh(a*x))-3/32/arctanh(a*x)*sinh(6*arctanh(a*x))+9/16*Chi(6*arctanh(a*x)))","A"
364,1,120,117,0.445000," ","int(x^5*arctanh(a*x)/(-a^2*x^2+1)^(1/2),x)","-\frac{\sqrt{-\left(a x -1\right) \left(a x +1\right)}\, \left(24 a^{4} x^{4} \arctanh \left(a x \right)+6 x^{3} a^{3}+32 a^{2} x^{2} \arctanh \left(a x \right)+25 a x +64 \arctanh \left(a x \right)\right)}{120 a^{6}}+\frac{89 i \ln \left(\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}+i\right)}{120 a^{6}}-\frac{89 i \ln \left(\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}-i\right)}{120 a^{6}}"," ",0,"-1/120/a^6*(-(a*x-1)*(a*x+1))^(1/2)*(24*a^4*x^4*arctanh(a*x)+6*x^3*a^3+32*a^2*x^2*arctanh(a*x)+25*a*x+64*arctanh(a*x))+89/120*I*ln((a*x+1)/(-a^2*x^2+1)^(1/2)+I)/a^6-89/120*I*ln((a*x+1)/(-a^2*x^2+1)^(1/2)-I)/a^6","C"
365,1,175,159,0.470000," ","int(x^4*arctanh(a*x)/(-a^2*x^2+1)^(1/2),x)","-\frac{\sqrt{-\left(a x -1\right) \left(a x +1\right)}\, \left(6 a^{3} x^{3} \arctanh \left(a x \right)+2 a^{2} x^{2}+9 a x \arctanh \left(a x \right)+13\right)}{24 a^{5}}-\frac{3 i \ln \left(1+\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right) \arctanh \left(a x \right)}{8 a^{5}}+\frac{3 i \ln \left(1-\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right) \arctanh \left(a x \right)}{8 a^{5}}-\frac{3 i \dilog \left(1+\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right)}{8 a^{5}}+\frac{3 i \dilog \left(1-\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right)}{8 a^{5}}"," ",0,"-1/24/a^5*(-(a*x-1)*(a*x+1))^(1/2)*(6*a^3*x^3*arctanh(a*x)+2*a^2*x^2+9*a*x*arctanh(a*x)+13)-3/8*I*ln(1+I*(a*x+1)/(-a^2*x^2+1)^(1/2))*arctanh(a*x)/a^5+3/8*I*ln(1-I*(a*x+1)/(-a^2*x^2+1)^(1/2))*arctanh(a*x)/a^5-3/8*I*dilog(1+I*(a*x+1)/(-a^2*x^2+1)^(1/2))/a^5+3/8*I*dilog(1-I*(a*x+1)/(-a^2*x^2+1)^(1/2))/a^5","A"
366,1,99,73,0.376000," ","int(x^3*arctanh(a*x)/(-a^2*x^2+1)^(1/2),x)","-\frac{\sqrt{-\left(a x -1\right) \left(a x +1\right)}\, \left(2 a^{2} x^{2} \arctanh \left(a x \right)+a x +4 \arctanh \left(a x \right)\right)}{6 a^{4}}+\frac{5 i \ln \left(\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}+i\right)}{6 a^{4}}-\frac{5 i \ln \left(\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}-i\right)}{6 a^{4}}"," ",0,"-1/6/a^4*(-(a*x-1)*(a*x+1))^(1/2)*(2*a^2*x^2*arctanh(a*x)+a*x+4*arctanh(a*x))+5/6*I*ln((a*x+1)/(-a^2*x^2+1)^(1/2)+I)/a^4-5/6*I*ln((a*x+1)/(-a^2*x^2+1)^(1/2)-I)/a^4","C"
367,1,154,118,0.407000," ","int(x^2*arctanh(a*x)/(-a^2*x^2+1)^(1/2),x)","-\frac{\left(a x \arctanh \left(a x \right)+1\right) \sqrt{-\left(a x -1\right) \left(a x +1\right)}}{2 a^{3}}-\frac{i \ln \left(1+\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right) \arctanh \left(a x \right)}{2 a^{3}}+\frac{i \ln \left(1-\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right) \arctanh \left(a x \right)}{2 a^{3}}-\frac{i \dilog \left(1+\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right)}{2 a^{3}}+\frac{i \dilog \left(1-\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right)}{2 a^{3}}"," ",0,"-1/2*(a*x*arctanh(a*x)+1)*(-(a*x-1)*(a*x+1))^(1/2)/a^3-1/2*I*ln(1+I*(a*x+1)/(-a^2*x^2+1)^(1/2))*arctanh(a*x)/a^3+1/2*I*ln(1-I*(a*x+1)/(-a^2*x^2+1)^(1/2))*arctanh(a*x)/a^3-1/2*I*dilog(1+I*(a*x+1)/(-a^2*x^2+1)^(1/2))/a^3+1/2*I*dilog(1-I*(a*x+1)/(-a^2*x^2+1)^(1/2))/a^3","A"
368,1,81,30,0.308000," ","int(x*arctanh(a*x)/(-a^2*x^2+1)^(1/2),x)","-\frac{\sqrt{-\left(a x -1\right) \left(a x +1\right)}\, \arctanh \left(a x \right)}{a^{2}}+\frac{i \ln \left(\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}+i\right)}{a^{2}}-\frac{i \ln \left(\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}-i\right)}{a^{2}}"," ",0,"-1/a^2*(-(a*x-1)*(a*x+1))^(1/2)*arctanh(a*x)+I*ln((a*x+1)/(-a^2*x^2+1)^(1/2)+I)/a^2-I*ln((a*x+1)/(-a^2*x^2+1)^(1/2)-I)/a^2","C"
369,1,126,79,0.450000," ","int(arctanh(a*x)/(-a^2*x^2+1)^(1/2),x)","\frac{i \arctanh \left(a x \right) \ln \left(1-\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right)}{a}-\frac{i \arctanh \left(a x \right) \ln \left(1+\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right)}{a}-\frac{i \dilog \left(1+\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right)}{a}+\frac{i \dilog \left(1-\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right)}{a}"," ",0,"I/a*arctanh(a*x)*ln(1-I*(a*x+1)/(-a^2*x^2+1)^(1/2))-I/a*arctanh(a*x)*ln(1+I*(a*x+1)/(-a^2*x^2+1)^(1/2))-I/a*dilog(1+I*(a*x+1)/(-a^2*x^2+1)^(1/2))+I/a*dilog(1-I*(a*x+1)/(-a^2*x^2+1)^(1/2))","A"
370,1,99,63,0.423000," ","int(arctanh(a*x)/x/(-a^2*x^2+1)^(1/2),x)","-\arctanh \left(a x \right) \ln \left(1+\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)-\polylog \left(2, -\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)+\arctanh \left(a x \right) \ln \left(1-\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)+\polylog \left(2, \frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)"," ",0,"-arctanh(a*x)*ln(1+(a*x+1)/(-a^2*x^2+1)^(1/2))-polylog(2,-(a*x+1)/(-a^2*x^2+1)^(1/2))+arctanh(a*x)*ln(1-(a*x+1)/(-a^2*x^2+1)^(1/2))+polylog(2,(a*x+1)/(-a^2*x^2+1)^(1/2))","A"
371,1,72,38,0.405000," ","int(arctanh(a*x)/x^2/(-a^2*x^2+1)^(1/2),x)","-\frac{\sqrt{-\left(a x -1\right) \left(a x +1\right)}\, \arctanh \left(a x \right)}{x}-a \ln \left(1+\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)+a \ln \left(\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}-1\right)"," ",0,"-(-(a*x-1)*(a*x+1))^(1/2)*arctanh(a*x)/x-a*ln(1+(a*x+1)/(-a^2*x^2+1)^(1/2))+a*ln((a*x+1)/(-a^2*x^2+1)^(1/2)-1)","A"
372,1,141,113,0.448000," ","int(arctanh(a*x)/x^3/(-a^2*x^2+1)^(1/2),x)","-\frac{\sqrt{-\left(a x -1\right) \left(a x +1\right)}\, \left(a x +\arctanh \left(a x \right)\right)}{2 x^{2}}-\frac{a^{2} \arctanh \left(a x \right) \ln \left(1+\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{2}-\frac{a^{2} \polylog \left(2, -\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{2}+\frac{a^{2} \arctanh \left(a x \right) \ln \left(1-\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{2}+\frac{a^{2} \polylog \left(2, \frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{2}"," ",0,"-1/2*(-(a*x-1)*(a*x+1))^(1/2)*(a*x+arctanh(a*x))/x^2-1/2*a^2*arctanh(a*x)*ln(1+(a*x+1)/(-a^2*x^2+1)^(1/2))-1/2*a^2*polylog(2,-(a*x+1)/(-a^2*x^2+1)^(1/2))+1/2*a^2*arctanh(a*x)*ln(1-(a*x+1)/(-a^2*x^2+1)^(1/2))+1/2*a^2*polylog(2,(a*x+1)/(-a^2*x^2+1)^(1/2))","A"
373,1,175,167,0.393000," ","int(x^3*arctanh(a*x)^2/(-a^2*x^2+1)^(1/2),x)","-\frac{\sqrt{-\left(a x -1\right) \left(a x +1\right)}\, \left(a^{2} x^{2} \arctanh \left(a x \right)^{2}+a x \arctanh \left(a x \right)+2 \arctanh \left(a x \right)^{2}+1\right)}{3 a^{4}}-\frac{5 i \ln \left(1+\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right) \arctanh \left(a x \right)}{3 a^{4}}+\frac{5 i \ln \left(1-\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right) \arctanh \left(a x \right)}{3 a^{4}}-\frac{5 i \dilog \left(1+\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right)}{3 a^{4}}+\frac{5 i \dilog \left(1-\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right)}{3 a^{4}}"," ",0,"-1/3/a^4*(-(a*x-1)*(a*x+1))^(1/2)*(a^2*x^2*arctanh(a*x)^2+a*x*arctanh(a*x)+2*arctanh(a*x)^2+1)-5/3*I*ln(1+I*(a*x+1)/(-a^2*x^2+1)^(1/2))*arctanh(a*x)/a^4+5/3*I*ln(1-I*(a*x+1)/(-a^2*x^2+1)^(1/2))*arctanh(a*x)/a^4-5/3*I*dilog(1+I*(a*x+1)/(-a^2*x^2+1)^(1/2))/a^4+5/3*I*dilog(1-I*(a*x+1)/(-a^2*x^2+1)^(1/2))/a^4","A"
374,0,0,203,0.389000," ","int(x^2*arctanh(a*x)^2/(-a^2*x^2+1)^(1/2),x)","\int \frac{x^{2} \arctanh \left(a x \right)^{2}}{\sqrt{-a^{2} x^{2}+1}}\, dx"," ",0,"int(x^2*arctanh(a*x)^2/(-a^2*x^2+1)^(1/2),x)","F"
375,1,151,102,0.329000," ","int(x*arctanh(a*x)^2/(-a^2*x^2+1)^(1/2),x)","-\frac{\sqrt{-\left(a x -1\right) \left(a x +1\right)}\, \arctanh \left(a x \right)^{2}}{a^{2}}-\frac{2 i \ln \left(1+\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right) \arctanh \left(a x \right)}{a^{2}}+\frac{2 i \ln \left(1-\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right) \arctanh \left(a x \right)}{a^{2}}-\frac{2 i \dilog \left(1+\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right)}{a^{2}}+\frac{2 i \dilog \left(1-\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right)}{a^{2}}"," ",0,"-1/a^2*(-(a*x-1)*(a*x+1))^(1/2)*arctanh(a*x)^2-2*I*ln(1+I*(a*x+1)/(-a^2*x^2+1)^(1/2))*arctanh(a*x)/a^2+2*I*ln(1-I*(a*x+1)/(-a^2*x^2+1)^(1/2))*arctanh(a*x)/a^2-2*I*dilog(1+I*(a*x+1)/(-a^2*x^2+1)^(1/2))/a^2+2*I*dilog(1-I*(a*x+1)/(-a^2*x^2+1)^(1/2))/a^2","A"
376,0,0,151,0.389000," ","int(arctanh(a*x)^2/(-a^2*x^2+1)^(1/2),x)","\int \frac{\arctanh \left(a x \right)^{2}}{\sqrt{-a^{2} x^{2}+1}}\, dx"," ",0,"int(arctanh(a*x)^2/(-a^2*x^2+1)^(1/2),x)","F"
377,1,158,126,0.437000," ","int(arctanh(a*x)^2/x/(-a^2*x^2+1)^(1/2),x)","-\arctanh \left(a x \right)^{2} \ln \left(1+\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)-2 \arctanh \left(a x \right) \polylog \left(2, -\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)+2 \polylog \left(3, -\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)+\arctanh \left(a x \right)^{2} \ln \left(1-\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)+2 \arctanh \left(a x \right) \polylog \left(2, \frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)-2 \polylog \left(3, \frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)"," ",0,"-arctanh(a*x)^2*ln(1+(a*x+1)/(-a^2*x^2+1)^(1/2))-2*arctanh(a*x)*polylog(2,-(a*x+1)/(-a^2*x^2+1)^(1/2))+2*polylog(3,-(a*x+1)/(-a^2*x^2+1)^(1/2))+arctanh(a*x)^2*ln(1-(a*x+1)/(-a^2*x^2+1)^(1/2))+2*arctanh(a*x)*polylog(2,(a*x+1)/(-a^2*x^2+1)^(1/2))-2*polylog(3,(a*x+1)/(-a^2*x^2+1)^(1/2))","A"
378,1,131,91,0.413000," ","int(arctanh(a*x)^2/x^2/(-a^2*x^2+1)^(1/2),x)","-\frac{\sqrt{-\left(a x -1\right) \left(a x +1\right)}\, \arctanh \left(a x \right)^{2}}{x}-2 a \arctanh \left(a x \right) \ln \left(1+\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)-2 a \polylog \left(2, -\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)+2 a \arctanh \left(a x \right) \ln \left(1-\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)+2 a \polylog \left(2, \frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)"," ",0,"-(-(a*x-1)*(a*x+1))^(1/2)*arctanh(a*x)^2/x-2*a*arctanh(a*x)*ln(1+(a*x+1)/(-a^2*x^2+1)^(1/2))-2*a*polylog(2,-(a*x+1)/(-a^2*x^2+1)^(1/2))+2*a*arctanh(a*x)*ln(1-(a*x+1)/(-a^2*x^2+1)^(1/2))+2*a*polylog(2,(a*x+1)/(-a^2*x^2+1)^(1/2))","A"
379,1,231,202,0.456000," ","int(arctanh(a*x)^2/x^3/(-a^2*x^2+1)^(1/2),x)","-\frac{\sqrt{-\left(a x -1\right) \left(a x +1\right)}\, \arctanh \left(a x \right) \left(2 a x +\arctanh \left(a x \right)\right)}{2 x^{2}}-\frac{a^{2} \arctanh \left(a x \right)^{2} \ln \left(1+\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{2}-a^{2} \arctanh \left(a x \right) \polylog \left(2, -\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)+a^{2} \polylog \left(3, -\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)+\frac{a^{2} \arctanh \left(a x \right)^{2} \ln \left(1-\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{2}+a^{2} \arctanh \left(a x \right) \polylog \left(2, \frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)-a^{2} \polylog \left(3, \frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)-2 a^{2} \arctanh \left(\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)"," ",0,"-1/2*(-(a*x-1)*(a*x+1))^(1/2)*arctanh(a*x)*(2*a*x+arctanh(a*x))/x^2-1/2*a^2*arctanh(a*x)^2*ln(1+(a*x+1)/(-a^2*x^2+1)^(1/2))-a^2*arctanh(a*x)*polylog(2,-(a*x+1)/(-a^2*x^2+1)^(1/2))+a^2*polylog(3,-(a*x+1)/(-a^2*x^2+1)^(1/2))+1/2*a^2*arctanh(a*x)^2*ln(1-(a*x+1)/(-a^2*x^2+1)^(1/2))+a^2*arctanh(a*x)*polylog(2,(a*x+1)/(-a^2*x^2+1)^(1/2))-a^2*polylog(3,(a*x+1)/(-a^2*x^2+1)^(1/2))-2*a^2*arctanh((a*x+1)/(-a^2*x^2+1)^(1/2))","A"
380,0,0,253,0.505000," ","int(x^3*arctanh(a*x)^3/(-a^2*x^2+1)^(1/2),x)","\int \frac{x^{3} \arctanh \left(a x \right)^{3}}{\sqrt{-a^{2} x^{2}+1}}\, dx"," ",0,"int(x^3*arctanh(a*x)^3/(-a^2*x^2+1)^(1/2),x)","F"
381,0,0,343,0.495000," ","int(x^2*arctanh(a*x)^3/(-a^2*x^2+1)^(1/2),x)","\int \frac{x^{2} \arctanh \left(a x \right)^{3}}{\sqrt{-a^{2} x^{2}+1}}\, dx"," ",0,"int(x^2*arctanh(a*x)^3/(-a^2*x^2+1)^(1/2),x)","F"
382,0,0,174,0.423000," ","int(x*arctanh(a*x)^3/(-a^2*x^2+1)^(1/2),x)","\int \frac{x \arctanh \left(a x \right)^{3}}{\sqrt{-a^{2} x^{2}+1}}\, dx"," ",0,"int(x*arctanh(a*x)^3/(-a^2*x^2+1)^(1/2),x)","F"
383,0,0,219,0.414000," ","int(arctanh(a*x)^3/(-a^2*x^2+1)^(1/2),x)","\int \frac{\arctanh \left(a x \right)^{3}}{\sqrt{-a^{2} x^{2}+1}}\, dx"," ",0,"int(arctanh(a*x)^3/(-a^2*x^2+1)^(1/2),x)","F"
384,1,215,183,0.464000," ","int(arctanh(a*x)^3/x/(-a^2*x^2+1)^(1/2),x)","-\arctanh \left(a x \right)^{3} \ln \left(1+\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)-3 \arctanh \left(a x \right)^{2} \polylog \left(2, -\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)+6 \arctanh \left(a x \right) \polylog \left(3, -\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)-6 \polylog \left(4, -\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)+\arctanh \left(a x \right)^{3} \ln \left(1-\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)+3 \arctanh \left(a x \right)^{2} \polylog \left(2, \frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)-6 \arctanh \left(a x \right) \polylog \left(3, \frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)+6 \polylog \left(4, \frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)"," ",0,"-arctanh(a*x)^3*ln(1+(a*x+1)/(-a^2*x^2+1)^(1/2))-3*arctanh(a*x)^2*polylog(2,-(a*x+1)/(-a^2*x^2+1)^(1/2))+6*arctanh(a*x)*polylog(3,-(a*x+1)/(-a^2*x^2+1)^(1/2))-6*polylog(4,-(a*x+1)/(-a^2*x^2+1)^(1/2))+arctanh(a*x)^3*ln(1-(a*x+1)/(-a^2*x^2+1)^(1/2))+3*arctanh(a*x)^2*polylog(2,(a*x+1)/(-a^2*x^2+1)^(1/2))-6*arctanh(a*x)*polylog(3,(a*x+1)/(-a^2*x^2+1)^(1/2))+6*polylog(4,(a*x+1)/(-a^2*x^2+1)^(1/2))","A"
385,1,190,154,0.433000," ","int(arctanh(a*x)^3/x^2/(-a^2*x^2+1)^(1/2),x)","-\frac{\sqrt{-\left(a x -1\right) \left(a x +1\right)}\, \arctanh \left(a x \right)^{3}}{x}-3 a \arctanh \left(a x \right)^{2} \ln \left(1+\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)-6 a \arctanh \left(a x \right) \polylog \left(2, -\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)+6 a \polylog \left(3, -\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)+3 a \arctanh \left(a x \right)^{2} \ln \left(1-\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)+6 a \arctanh \left(a x \right) \polylog \left(2, \frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)-6 a \polylog \left(3, \frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)"," ",0,"-(-(a*x-1)*(a*x+1))^(1/2)*arctanh(a*x)^3/x-3*a*arctanh(a*x)^2*ln(1+(a*x+1)/(-a^2*x^2+1)^(1/2))-6*a*arctanh(a*x)*polylog(2,-(a*x+1)/(-a^2*x^2+1)^(1/2))+6*a*polylog(3,-(a*x+1)/(-a^2*x^2+1)^(1/2))+3*a*arctanh(a*x)^2*ln(1-(a*x+1)/(-a^2*x^2+1)^(1/2))+6*a*arctanh(a*x)*polylog(2,(a*x+1)/(-a^2*x^2+1)^(1/2))-6*a*polylog(3,(a*x+1)/(-a^2*x^2+1)^(1/2))","A"
386,1,386,324,0.500000," ","int(arctanh(a*x)^3/x^3/(-a^2*x^2+1)^(1/2),x)","-\frac{\sqrt{-\left(a x -1\right) \left(a x +1\right)}\, \arctanh \left(a x \right)^{2} \left(3 a x +\arctanh \left(a x \right)\right)}{2 x^{2}}-\frac{a^{2} \arctanh \left(a x \right)^{3} \ln \left(1+\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{2}-\frac{3 a^{2} \arctanh \left(a x \right)^{2} \polylog \left(2, -\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{2}+3 a^{2} \arctanh \left(a x \right) \polylog \left(3, -\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)-3 a^{2} \polylog \left(4, -\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)+\frac{a^{2} \arctanh \left(a x \right)^{3} \ln \left(1-\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{2}+\frac{3 a^{2} \arctanh \left(a x \right)^{2} \polylog \left(2, \frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{2}-3 a^{2} \arctanh \left(a x \right) \polylog \left(3, \frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)+3 a^{2} \polylog \left(4, \frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)-3 a^{2} \arctanh \left(a x \right) \ln \left(1+\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)-3 a^{2} \polylog \left(2, -\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)+3 a^{2} \arctanh \left(a x \right) \ln \left(1-\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)+3 a^{2} \polylog \left(2, \frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)"," ",0,"-1/2*(-(a*x-1)*(a*x+1))^(1/2)*arctanh(a*x)^2*(3*a*x+arctanh(a*x))/x^2-1/2*a^2*arctanh(a*x)^3*ln(1+(a*x+1)/(-a^2*x^2+1)^(1/2))-3/2*a^2*arctanh(a*x)^2*polylog(2,-(a*x+1)/(-a^2*x^2+1)^(1/2))+3*a^2*arctanh(a*x)*polylog(3,-(a*x+1)/(-a^2*x^2+1)^(1/2))-3*a^2*polylog(4,-(a*x+1)/(-a^2*x^2+1)^(1/2))+1/2*a^2*arctanh(a*x)^3*ln(1-(a*x+1)/(-a^2*x^2+1)^(1/2))+3/2*a^2*arctanh(a*x)^2*polylog(2,(a*x+1)/(-a^2*x^2+1)^(1/2))-3*a^2*arctanh(a*x)*polylog(3,(a*x+1)/(-a^2*x^2+1)^(1/2))+3*a^2*polylog(4,(a*x+1)/(-a^2*x^2+1)^(1/2))-3*a^2*arctanh(a*x)*ln(1+(a*x+1)/(-a^2*x^2+1)^(1/2))-3*a^2*polylog(2,-(a*x+1)/(-a^2*x^2+1)^(1/2))+3*a^2*arctanh(a*x)*ln(1-(a*x+1)/(-a^2*x^2+1)^(1/2))+3*a^2*polylog(2,(a*x+1)/(-a^2*x^2+1)^(1/2))","A"
387,0,0,22,1.171000," ","int(x^m*arctanh(a*x)/(-a^2*x^2+1)^(3/2),x)","\int \frac{x^{m} \arctanh \left(a x \right)}{\left(-a^{2} x^{2}+1\right)^{\frac{3}{2}}}\, dx"," ",0,"int(x^m*arctanh(a*x)/(-a^2*x^2+1)^(3/2),x)","F"
388,1,144,68,0.415000," ","int(x^3*arctanh(a*x)/(-a^2*x^2+1)^(3/2),x)","-\frac{\left(\arctanh \left(a x \right)-1\right) \sqrt{-\left(a x -1\right) \left(a x +1\right)}}{2 a^{4} \left(a x -1\right)}+\frac{\left(\arctanh \left(a x \right)+1\right) \sqrt{-\left(a x -1\right) \left(a x +1\right)}}{2 a^{4} \left(a x +1\right)}+\frac{\arctanh \left(a x \right) \sqrt{-\left(a x -1\right) \left(a x +1\right)}}{a^{4}}+\frac{i \ln \left(\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}-i\right)}{a^{4}}-\frac{i \ln \left(\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}+i\right)}{a^{4}}"," ",0,"-1/2*(arctanh(a*x)-1)*(-(a*x-1)*(a*x+1))^(1/2)/a^4/(a*x-1)+1/2*(arctanh(a*x)+1)*(-(a*x-1)*(a*x+1))^(1/2)/a^4/(a*x+1)+arctanh(a*x)*(-(a*x-1)*(a*x+1))^(1/2)/a^4+I*ln((a*x+1)/(-a^2*x^2+1)^(1/2)-I)/a^4-I*ln((a*x+1)/(-a^2*x^2+1)^(1/2)+I)/a^4","C"
389,1,190,117,0.392000," ","int(x^2*arctanh(a*x)/(-a^2*x^2+1)^(3/2),x)","-\frac{\left(\arctanh \left(a x \right)-1\right) \sqrt{-\left(a x -1\right) \left(a x +1\right)}}{2 a^{3} \left(a x -1\right)}-\frac{\left(\arctanh \left(a x \right)+1\right) \sqrt{-\left(a x -1\right) \left(a x +1\right)}}{2 a^{3} \left(a x +1\right)}+\frac{i \ln \left(1+\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right) \arctanh \left(a x \right)}{a^{3}}-\frac{i \ln \left(1-\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right) \arctanh \left(a x \right)}{a^{3}}+\frac{i \dilog \left(1+\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right)}{a^{3}}-\frac{i \dilog \left(1-\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right)}{a^{3}}"," ",0,"-1/2*(arctanh(a*x)-1)*(-(a*x-1)*(a*x+1))^(1/2)/a^3/(a*x-1)-1/2*(arctanh(a*x)+1)*(-(a*x-1)*(a*x+1))^(1/2)/a^3/(a*x+1)+I*ln(1+I*(a*x+1)/(-a^2*x^2+1)^(1/2))*arctanh(a*x)/a^3-I*ln(1-I*(a*x+1)/(-a^2*x^2+1)^(1/2))*arctanh(a*x)/a^3+I*dilog(1+I*(a*x+1)/(-a^2*x^2+1)^(1/2))/a^3-I*dilog(1-I*(a*x+1)/(-a^2*x^2+1)^(1/2))/a^3","A"
390,1,66,39,0.322000," ","int(x*arctanh(a*x)/(-a^2*x^2+1)^(3/2),x)","-\frac{\left(\arctanh \left(a x \right)-1\right) \sqrt{-\left(a x -1\right) \left(a x +1\right)}}{2 a^{2} \left(a x -1\right)}+\frac{\left(\arctanh \left(a x \right)+1\right) \sqrt{-\left(a x -1\right) \left(a x +1\right)}}{2 a^{2} \left(a x +1\right)}"," ",0,"-1/2*(arctanh(a*x)-1)*(-(a*x-1)*(a*x+1))^(1/2)/a^2/(a*x-1)+1/2*(arctanh(a*x)+1)*(-(a*x-1)*(a*x+1))^(1/2)/a^2/(a*x+1)","A"
391,1,38,36,0.266000," ","int(arctanh(a*x)/(-a^2*x^2+1)^(3/2),x)","-\frac{\sqrt{-a^{2} x^{2}+1}\, \left(a x \arctanh \left(a x \right)-1\right)}{a \left(a^{2} x^{2}-1\right)}"," ",0,"-1/a*(-a^2*x^2+1)^(1/2)*(a*x*arctanh(a*x)-1)/(a^2*x^2-1)","A"
392,1,157,96,0.428000," ","int(arctanh(a*x)/x/(-a^2*x^2+1)^(3/2),x)","-\frac{\left(\arctanh \left(a x \right)-1\right) \sqrt{-\left(a x -1\right) \left(a x +1\right)}}{2 \left(a x -1\right)}+\frac{\left(\arctanh \left(a x \right)+1\right) \sqrt{-\left(a x -1\right) \left(a x +1\right)}}{2 a x +2}-\arctanh \left(a x \right) \ln \left(1+\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)-\polylog \left(2, -\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)+\arctanh \left(a x \right) \ln \left(1-\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)+\polylog \left(2, \frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)"," ",0,"-1/2*(arctanh(a*x)-1)*(-(a*x-1)*(a*x+1))^(1/2)/(a*x-1)+1/2*(arctanh(a*x)+1)*(-(a*x-1)*(a*x+1))^(1/2)/(a*x+1)-arctanh(a*x)*ln(1+(a*x+1)/(-a^2*x^2+1)^(1/2))-polylog(2,-(a*x+1)/(-a^2*x^2+1)^(1/2))+arctanh(a*x)*ln(1-(a*x+1)/(-a^2*x^2+1)^(1/2))+polylog(2,(a*x+1)/(-a^2*x^2+1)^(1/2))","A"
393,1,132,74,0.436000," ","int(arctanh(a*x)/x^2/(-a^2*x^2+1)^(3/2),x)","-\frac{a \left(\arctanh \left(a x \right)-1\right) \sqrt{-\left(a x -1\right) \left(a x +1\right)}}{2 \left(a x -1\right)}-\frac{\left(\arctanh \left(a x \right)+1\right) a \sqrt{-\left(a x -1\right) \left(a x +1\right)}}{2 \left(a x +1\right)}-\frac{\sqrt{-\left(a x -1\right) \left(a x +1\right)}\, \arctanh \left(a x \right)}{x}+a \ln \left(\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}-1\right)-a \ln \left(1+\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)"," ",0,"-1/2*a*(arctanh(a*x)-1)*(-(a*x-1)*(a*x+1))^(1/2)/(a*x-1)-1/2*(arctanh(a*x)+1)*a*(-(a*x-1)*(a*x+1))^(1/2)/(a*x+1)-(-(a*x-1)*(a*x+1))^(1/2)*arctanh(a*x)/x+a*ln((a*x+1)/(-a^2*x^2+1)^(1/2)-1)-a*ln(1+(a*x+1)/(-a^2*x^2+1)^(1/2))","A"
394,1,205,151,0.454000," ","int(arctanh(a*x)/x^3/(-a^2*x^2+1)^(3/2),x)","-\frac{a^{2} \left(\arctanh \left(a x \right)-1\right) \sqrt{-\left(a x -1\right) \left(a x +1\right)}}{2 \left(a x -1\right)}+\frac{\left(\arctanh \left(a x \right)+1\right) a^{2} \sqrt{-\left(a x -1\right) \left(a x +1\right)}}{2 a x +2}-\frac{\sqrt{-\left(a x -1\right) \left(a x +1\right)}\, \left(a x +\arctanh \left(a x \right)\right)}{2 x^{2}}-\frac{3 a^{2} \arctanh \left(a x \right) \ln \left(1+\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{2}-\frac{3 a^{2} \polylog \left(2, -\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{2}+\frac{3 a^{2} \arctanh \left(a x \right) \ln \left(1-\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{2}+\frac{3 a^{2} \polylog \left(2, \frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{2}"," ",0,"-1/2*a^2*(arctanh(a*x)-1)*(-(a*x-1)*(a*x+1))^(1/2)/(a*x-1)+1/2*(arctanh(a*x)+1)*a^2*(-(a*x-1)*(a*x+1))^(1/2)/(a*x+1)-1/2*(-(a*x-1)*(a*x+1))^(1/2)*(a*x+arctanh(a*x))/x^2-3/2*a^2*arctanh(a*x)*ln(1+(a*x+1)/(-a^2*x^2+1)^(1/2))-3/2*a^2*polylog(2,-(a*x+1)/(-a^2*x^2+1)^(1/2))+3/2*a^2*arctanh(a*x)*ln(1-(a*x+1)/(-a^2*x^2+1)^(1/2))+3/2*a^2*polylog(2,(a*x+1)/(-a^2*x^2+1)^(1/2))","A"
395,0,0,24,1.073000," ","int(x^m*arctanh(a*x)^2/(-a^2*x^2+1)^(3/2),x)","\int \frac{x^{m} \arctanh \left(a x \right)^{2}}{\left(-a^{2} x^{2}+1\right)^{\frac{3}{2}}}\, dx"," ",0,"int(x^m*arctanh(a*x)^2/(-a^2*x^2+1)^(3/2),x)","F"
396,1,230,162,0.428000," ","int(x^3*arctanh(a*x)^2/(-a^2*x^2+1)^(3/2),x)","-\frac{\left(\arctanh \left(a x \right)^{2}-2 \arctanh \left(a x \right)+2\right) \sqrt{-\left(a x -1\right) \left(a x +1\right)}}{2 a^{4} \left(a x -1\right)}+\frac{\left(\arctanh \left(a x \right)^{2}+2 \arctanh \left(a x \right)+2\right) \sqrt{-\left(a x -1\right) \left(a x +1\right)}}{2 a^{4} \left(a x +1\right)}+\frac{\arctanh \left(a x \right)^{2} \sqrt{-\left(a x -1\right) \left(a x +1\right)}}{a^{4}}+\frac{2 i \ln \left(1+\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right) \arctanh \left(a x \right)}{a^{4}}-\frac{2 i \ln \left(1-\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right) \arctanh \left(a x \right)}{a^{4}}+\frac{2 i \dilog \left(1+\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right)}{a^{4}}-\frac{2 i \dilog \left(1-\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right)}{a^{4}}"," ",0,"-1/2*(arctanh(a*x)^2-2*arctanh(a*x)+2)*(-(a*x-1)*(a*x+1))^(1/2)/a^4/(a*x-1)+1/2*(arctanh(a*x)^2+2*arctanh(a*x)+2)*(-(a*x-1)*(a*x+1))^(1/2)/a^4/(a*x+1)+arctanh(a*x)^2*(-(a*x-1)*(a*x+1))^(1/2)/a^4+2*I*ln(1+I*(a*x+1)/(-a^2*x^2+1)^(1/2))*arctanh(a*x)/a^4-2*I*ln(1-I*(a*x+1)/(-a^2*x^2+1)^(1/2))*arctanh(a*x)/a^4+2*I*dilog(1+I*(a*x+1)/(-a^2*x^2+1)^(1/2))/a^4-2*I*dilog(1-I*(a*x+1)/(-a^2*x^2+1)^(1/2))/a^4","A"
397,0,0,213,0.395000," ","int(x^2*arctanh(a*x)^2/(-a^2*x^2+1)^(3/2),x)","\int \frac{x^{2} \arctanh \left(a x \right)^{2}}{\left(-a^{2} x^{2}+1\right)^{\frac{3}{2}}}\, dx"," ",0,"int(x^2*arctanh(a*x)^2/(-a^2*x^2+1)^(3/2),x)","F"
398,1,82,62,0.323000," ","int(x*arctanh(a*x)^2/(-a^2*x^2+1)^(3/2),x)","-\frac{\left(\arctanh \left(a x \right)^{2}-2 \arctanh \left(a x \right)+2\right) \sqrt{-\left(a x -1\right) \left(a x +1\right)}}{2 a^{2} \left(a x -1\right)}+\frac{\left(\arctanh \left(a x \right)^{2}+2 \arctanh \left(a x \right)+2\right) \sqrt{-\left(a x -1\right) \left(a x +1\right)}}{2 a^{2} \left(a x +1\right)}"," ",0,"-1/2*(arctanh(a*x)^2-2*arctanh(a*x)+2)*(-(a*x-1)*(a*x+1))^(1/2)/a^2/(a*x-1)+1/2*(arctanh(a*x)^2+2*arctanh(a*x)+2)*(-(a*x-1)*(a*x+1))^(1/2)/a^2/(a*x+1)","A"
399,1,49,57,0.266000," ","int(arctanh(a*x)^2/(-a^2*x^2+1)^(3/2),x)","-\frac{\sqrt{-a^{2} x^{2}+1}\, \left(\arctanh \left(a x \right)^{2} a x +2 a x -2 \arctanh \left(a x \right)\right)}{a \left(a^{2} x^{2}-1\right)}"," ",0,"-1/a*(-a^2*x^2+1)^(1/2)*(arctanh(a*x)^2*a*x+2*a*x-2*arctanh(a*x))/(a^2*x^2-1)","A"
400,1,232,179,0.450000," ","int(arctanh(a*x)^2/x/(-a^2*x^2+1)^(3/2),x)","-\frac{\left(\arctanh \left(a x \right)^{2}-2 \arctanh \left(a x \right)+2\right) \sqrt{-\left(a x -1\right) \left(a x +1\right)}}{2 \left(a x -1\right)}+\frac{\left(\arctanh \left(a x \right)^{2}+2 \arctanh \left(a x \right)+2\right) \sqrt{-\left(a x -1\right) \left(a x +1\right)}}{2 a x +2}-\arctanh \left(a x \right)^{2} \ln \left(1+\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)-2 \arctanh \left(a x \right) \polylog \left(2, -\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)+2 \polylog \left(3, -\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)+\arctanh \left(a x \right)^{2} \ln \left(1-\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)+2 \arctanh \left(a x \right) \polylog \left(2, \frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)-2 \polylog \left(3, \frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)"," ",0,"-1/2*(arctanh(a*x)^2-2*arctanh(a*x)+2)*(-(a*x-1)*(a*x+1))^(1/2)/(a*x-1)+1/2*(arctanh(a*x)^2+2*arctanh(a*x)+2)*(-(a*x-1)*(a*x+1))^(1/2)/(a*x+1)-arctanh(a*x)^2*ln(1+(a*x+1)/(-a^2*x^2+1)^(1/2))-2*arctanh(a*x)*polylog(2,-(a*x+1)/(-a^2*x^2+1)^(1/2))+2*polylog(3,-(a*x+1)/(-a^2*x^2+1)^(1/2))+arctanh(a*x)^2*ln(1-(a*x+1)/(-a^2*x^2+1)^(1/2))+2*arctanh(a*x)*polylog(2,(a*x+1)/(-a^2*x^2+1)^(1/2))-2*polylog(3,(a*x+1)/(-a^2*x^2+1)^(1/2))","A"
401,1,207,151,0.456000," ","int(arctanh(a*x)^2/x^2/(-a^2*x^2+1)^(3/2),x)","-\frac{a \left(\arctanh \left(a x \right)^{2}-2 \arctanh \left(a x \right)+2\right) \sqrt{-\left(a x -1\right) \left(a x +1\right)}}{2 \left(a x -1\right)}-\frac{\left(\arctanh \left(a x \right)^{2}+2 \arctanh \left(a x \right)+2\right) a \sqrt{-\left(a x -1\right) \left(a x +1\right)}}{2 \left(a x +1\right)}-\frac{\sqrt{-\left(a x -1\right) \left(a x +1\right)}\, \arctanh \left(a x \right)^{2}}{x}-2 a \arctanh \left(a x \right) \ln \left(1+\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)-2 a \polylog \left(2, -\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)+2 a \arctanh \left(a x \right) \ln \left(1-\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)+2 a \polylog \left(2, \frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)"," ",0,"-1/2*a*(arctanh(a*x)^2-2*arctanh(a*x)+2)*(-(a*x-1)*(a*x+1))^(1/2)/(a*x-1)-1/2*(arctanh(a*x)^2+2*arctanh(a*x)+2)*a*(-(a*x-1)*(a*x+1))^(1/2)/(a*x+1)-(-(a*x-1)*(a*x+1))^(1/2)*arctanh(a*x)^2/x-2*a*arctanh(a*x)*ln(1+(a*x+1)/(-a^2*x^2+1)^(1/2))-2*a*polylog(2,-(a*x+1)/(-a^2*x^2+1)^(1/2))+2*a*arctanh(a*x)*ln(1-(a*x+1)/(-a^2*x^2+1)^(1/2))+2*a*polylog(2,(a*x+1)/(-a^2*x^2+1)^(1/2))","A"
402,1,313,265,0.479000," ","int(arctanh(a*x)^2/x^3/(-a^2*x^2+1)^(3/2),x)","-\frac{a^{2} \left(\arctanh \left(a x \right)^{2}-2 \arctanh \left(a x \right)+2\right) \sqrt{-\left(a x -1\right) \left(a x +1\right)}}{2 \left(a x -1\right)}+\frac{\left(\arctanh \left(a x \right)^{2}+2 \arctanh \left(a x \right)+2\right) a^{2} \sqrt{-\left(a x -1\right) \left(a x +1\right)}}{2 a x +2}-\frac{\sqrt{-\left(a x -1\right) \left(a x +1\right)}\, \arctanh \left(a x \right) \left(2 a x +\arctanh \left(a x \right)\right)}{2 x^{2}}-2 a^{2} \arctanh \left(\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)-\frac{3 a^{2} \arctanh \left(a x \right)^{2} \ln \left(1+\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{2}-3 a^{2} \arctanh \left(a x \right) \polylog \left(2, -\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)+3 a^{2} \polylog \left(3, -\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)+\frac{3 a^{2} \arctanh \left(a x \right)^{2} \ln \left(1-\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{2}+3 a^{2} \arctanh \left(a x \right) \polylog \left(2, \frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)-3 a^{2} \polylog \left(3, \frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)"," ",0,"-1/2*a^2*(arctanh(a*x)^2-2*arctanh(a*x)+2)*(-(a*x-1)*(a*x+1))^(1/2)/(a*x-1)+1/2*(arctanh(a*x)^2+2*arctanh(a*x)+2)*a^2*(-(a*x-1)*(a*x+1))^(1/2)/(a*x+1)-1/2*(-(a*x-1)*(a*x+1))^(1/2)*arctanh(a*x)*(2*a*x+arctanh(a*x))/x^2-2*a^2*arctanh((a*x+1)/(-a^2*x^2+1)^(1/2))-3/2*a^2*arctanh(a*x)^2*ln(1+(a*x+1)/(-a^2*x^2+1)^(1/2))-3*a^2*arctanh(a*x)*polylog(2,-(a*x+1)/(-a^2*x^2+1)^(1/2))+3*a^2*polylog(3,-(a*x+1)/(-a^2*x^2+1)^(1/2))+3/2*a^2*arctanh(a*x)^2*ln(1-(a*x+1)/(-a^2*x^2+1)^(1/2))+3*a^2*arctanh(a*x)*polylog(2,(a*x+1)/(-a^2*x^2+1)^(1/2))-3*a^2*polylog(3,(a*x+1)/(-a^2*x^2+1)^(1/2))","A"
403,0,0,24,1.087000," ","int(x^m*arctanh(a*x)^3/(-a^2*x^2+1)^(3/2),x)","\int \frac{x^{m} \arctanh \left(a x \right)^{3}}{\left(-a^{2} x^{2}+1\right)^{\frac{3}{2}}}\, dx"," ",0,"int(x^m*arctanh(a*x)^3/(-a^2*x^2+1)^(3/2),x)","F"
404,0,0,258,0.508000," ","int(x^3*arctanh(a*x)^3/(-a^2*x^2+1)^(3/2),x)","\int \frac{x^{3} \arctanh \left(a x \right)^{3}}{\left(-a^{2} x^{2}+1\right)^{\frac{3}{2}}}\, dx"," ",0,"int(x^3*arctanh(a*x)^3/(-a^2*x^2+1)^(3/2),x)","F"
405,0,0,304,0.467000," ","int(x^2*arctanh(a*x)^3/(-a^2*x^2+1)^(3/2),x)","\int \frac{x^{2} \arctanh \left(a x \right)^{3}}{\left(-a^{2} x^{2}+1\right)^{\frac{3}{2}}}\, dx"," ",0,"int(x^2*arctanh(a*x)^3/(-a^2*x^2+1)^(3/2),x)","F"
406,1,98,86,0.326000," ","int(x*arctanh(a*x)^3/(-a^2*x^2+1)^(3/2),x)","-\frac{\left(\arctanh \left(a x \right)^{3}-3 \arctanh \left(a x \right)^{2}+6 \arctanh \left(a x \right)-6\right) \sqrt{-\left(a x -1\right) \left(a x +1\right)}}{2 a^{2} \left(a x -1\right)}+\frac{\left(\arctanh \left(a x \right)^{3}+3 \arctanh \left(a x \right)^{2}+6 \arctanh \left(a x \right)+6\right) \sqrt{-\left(a x -1\right) \left(a x +1\right)}}{2 a^{2} \left(a x +1\right)}"," ",0,"-1/2*(arctanh(a*x)^3-3*arctanh(a*x)^2+6*arctanh(a*x)-6)*(-(a*x-1)*(a*x+1))^(1/2)/a^2/(a*x-1)+1/2*(arctanh(a*x)^3+3*arctanh(a*x)^2+6*arctanh(a*x)+6)*(-(a*x-1)*(a*x+1))^(1/2)/a^2/(a*x+1)","A"
407,1,56,80,0.269000," ","int(arctanh(a*x)^3/(-a^2*x^2+1)^(3/2),x)","-\frac{\sqrt{-a^{2} x^{2}+1}\, \left(\arctanh \left(a x \right)^{3} a x +6 a x \arctanh \left(a x \right)-3 \arctanh \left(a x \right)^{2}-6\right)}{a \left(a^{2} x^{2}-1\right)}"," ",0,"-1/a*(-a^2*x^2+1)^(1/2)*(arctanh(a*x)^3*a*x+6*a*x*arctanh(a*x)-3*arctanh(a*x)^2-6)/(a^2*x^2-1)","A"
408,1,305,258,0.474000," ","int(arctanh(a*x)^3/x/(-a^2*x^2+1)^(3/2),x)","-\frac{\left(\arctanh \left(a x \right)^{3}-3 \arctanh \left(a x \right)^{2}+6 \arctanh \left(a x \right)-6\right) \sqrt{-\left(a x -1\right) \left(a x +1\right)}}{2 \left(a x -1\right)}+\frac{\left(\arctanh \left(a x \right)^{3}+3 \arctanh \left(a x \right)^{2}+6 \arctanh \left(a x \right)+6\right) \sqrt{-\left(a x -1\right) \left(a x +1\right)}}{2 a x +2}-\arctanh \left(a x \right)^{3} \ln \left(1+\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)-3 \arctanh \left(a x \right)^{2} \polylog \left(2, -\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)+6 \arctanh \left(a x \right) \polylog \left(3, -\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)-6 \polylog \left(4, -\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)+\arctanh \left(a x \right)^{3} \ln \left(1-\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)+3 \arctanh \left(a x \right)^{2} \polylog \left(2, \frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)-6 \arctanh \left(a x \right) \polylog \left(3, \frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)+6 \polylog \left(4, \frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)"," ",0,"-1/2*(arctanh(a*x)^3-3*arctanh(a*x)^2+6*arctanh(a*x)-6)*(-(a*x-1)*(a*x+1))^(1/2)/(a*x-1)+1/2*(arctanh(a*x)^3+3*arctanh(a*x)^2+6*arctanh(a*x)+6)*(-(a*x-1)*(a*x+1))^(1/2)/(a*x+1)-arctanh(a*x)^3*ln(1+(a*x+1)/(-a^2*x^2+1)^(1/2))-3*arctanh(a*x)^2*polylog(2,-(a*x+1)/(-a^2*x^2+1)^(1/2))+6*arctanh(a*x)*polylog(3,-(a*x+1)/(-a^2*x^2+1)^(1/2))-6*polylog(4,-(a*x+1)/(-a^2*x^2+1)^(1/2))+arctanh(a*x)^3*ln(1-(a*x+1)/(-a^2*x^2+1)^(1/2))+3*arctanh(a*x)^2*polylog(2,(a*x+1)/(-a^2*x^2+1)^(1/2))-6*arctanh(a*x)*polylog(3,(a*x+1)/(-a^2*x^2+1)^(1/2))+6*polylog(4,(a*x+1)/(-a^2*x^2+1)^(1/2))","A"
409,1,282,235,0.477000," ","int(arctanh(a*x)^3/x^2/(-a^2*x^2+1)^(3/2),x)","-\frac{a \left(\arctanh \left(a x \right)^{3}-3 \arctanh \left(a x \right)^{2}+6 \arctanh \left(a x \right)-6\right) \sqrt{-\left(a x -1\right) \left(a x +1\right)}}{2 \left(a x -1\right)}-\frac{\left(\arctanh \left(a x \right)^{3}+3 \arctanh \left(a x \right)^{2}+6 \arctanh \left(a x \right)+6\right) a \sqrt{-\left(a x -1\right) \left(a x +1\right)}}{2 \left(a x +1\right)}-\frac{\sqrt{-\left(a x -1\right) \left(a x +1\right)}\, \arctanh \left(a x \right)^{3}}{x}-3 a \arctanh \left(a x \right)^{2} \ln \left(1+\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)-6 a \arctanh \left(a x \right) \polylog \left(2, -\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)+6 a \polylog \left(3, -\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)+3 a \arctanh \left(a x \right)^{2} \ln \left(1-\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)+6 a \arctanh \left(a x \right) \polylog \left(2, \frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)-6 a \polylog \left(3, \frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)"," ",0,"-1/2*a*(arctanh(a*x)^3-3*arctanh(a*x)^2+6*arctanh(a*x)-6)*(-(a*x-1)*(a*x+1))^(1/2)/(a*x-1)-1/2*(arctanh(a*x)^3+3*arctanh(a*x)^2+6*arctanh(a*x)+6)*a*(-(a*x-1)*(a*x+1))^(1/2)/(a*x+1)-(-(a*x-1)*(a*x+1))^(1/2)*arctanh(a*x)^3/x-3*a*arctanh(a*x)^2*ln(1+(a*x+1)/(-a^2*x^2+1)^(1/2))-6*a*arctanh(a*x)*polylog(2,-(a*x+1)/(-a^2*x^2+1)^(1/2))+6*a*polylog(3,-(a*x+1)/(-a^2*x^2+1)^(1/2))+3*a*arctanh(a*x)^2*ln(1-(a*x+1)/(-a^2*x^2+1)^(1/2))+6*a*arctanh(a*x)*polylog(2,(a*x+1)/(-a^2*x^2+1)^(1/2))-6*a*polylog(3,(a*x+1)/(-a^2*x^2+1)^(1/2))","A"
410,1,482,409,0.544000," ","int(arctanh(a*x)^3/x^3/(-a^2*x^2+1)^(3/2),x)","-\frac{a^{2} \left(\arctanh \left(a x \right)^{3}-3 \arctanh \left(a x \right)^{2}+6 \arctanh \left(a x \right)-6\right) \sqrt{-\left(a x -1\right) \left(a x +1\right)}}{2 \left(a x -1\right)}+\frac{\left(\arctanh \left(a x \right)^{3}+3 \arctanh \left(a x \right)^{2}+6 \arctanh \left(a x \right)+6\right) a^{2} \sqrt{-\left(a x -1\right) \left(a x +1\right)}}{2 a x +2}-\frac{\sqrt{-\left(a x -1\right) \left(a x +1\right)}\, \arctanh \left(a x \right)^{2} \left(3 a x +\arctanh \left(a x \right)\right)}{2 x^{2}}-\frac{3 a^{2} \arctanh \left(a x \right)^{3} \ln \left(1+\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{2}-\frac{9 a^{2} \arctanh \left(a x \right)^{2} \polylog \left(2, -\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{2}+9 a^{2} \arctanh \left(a x \right) \polylog \left(3, -\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)-9 a^{2} \polylog \left(4, -\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)+\frac{3 a^{2} \arctanh \left(a x \right)^{3} \ln \left(1-\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{2}+\frac{9 a^{2} \arctanh \left(a x \right)^{2} \polylog \left(2, \frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{2}-9 a^{2} \arctanh \left(a x \right) \polylog \left(3, \frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)+9 a^{2} \polylog \left(4, \frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)-3 a^{2} \arctanh \left(a x \right) \ln \left(1+\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)-3 a^{2} \polylog \left(2, -\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)+3 a^{2} \arctanh \left(a x \right) \ln \left(1-\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)+3 a^{2} \polylog \left(2, \frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)"," ",0,"-1/2*a^2*(arctanh(a*x)^3-3*arctanh(a*x)^2+6*arctanh(a*x)-6)*(-(a*x-1)*(a*x+1))^(1/2)/(a*x-1)+1/2*(arctanh(a*x)^3+3*arctanh(a*x)^2+6*arctanh(a*x)+6)*a^2*(-(a*x-1)*(a*x+1))^(1/2)/(a*x+1)-1/2*(-(a*x-1)*(a*x+1))^(1/2)*arctanh(a*x)^2*(3*a*x+arctanh(a*x))/x^2-3/2*a^2*arctanh(a*x)^3*ln(1+(a*x+1)/(-a^2*x^2+1)^(1/2))-9/2*a^2*arctanh(a*x)^2*polylog(2,-(a*x+1)/(-a^2*x^2+1)^(1/2))+9*a^2*arctanh(a*x)*polylog(3,-(a*x+1)/(-a^2*x^2+1)^(1/2))-9*a^2*polylog(4,-(a*x+1)/(-a^2*x^2+1)^(1/2))+3/2*a^2*arctanh(a*x)^3*ln(1-(a*x+1)/(-a^2*x^2+1)^(1/2))+9/2*a^2*arctanh(a*x)^2*polylog(2,(a*x+1)/(-a^2*x^2+1)^(1/2))-9*a^2*arctanh(a*x)*polylog(3,(a*x+1)/(-a^2*x^2+1)^(1/2))+9*a^2*polylog(4,(a*x+1)/(-a^2*x^2+1)^(1/2))-3*a^2*arctanh(a*x)*ln(1+(a*x+1)/(-a^2*x^2+1)^(1/2))-3*a^2*polylog(2,-(a*x+1)/(-a^2*x^2+1)^(1/2))+3*a^2*arctanh(a*x)*ln(1-(a*x+1)/(-a^2*x^2+1)^(1/2))+3*a^2*polylog(2,(a*x+1)/(-a^2*x^2+1)^(1/2))","A"
411,0,0,24,1.099000," ","int(x^m/(-a^2*x^2+1)^(3/2)/arctanh(a*x),x)","\int \frac{x^{m}}{\left(-a^{2} x^{2}+1\right)^{\frac{3}{2}} \arctanh \left(a x \right)}\, dx"," ",0,"int(x^m/(-a^2*x^2+1)^(3/2)/arctanh(a*x),x)","F"
412,0,0,24,0.463000," ","int(x^2/(-a^2*x^2+1)^(3/2)/arctanh(a*x),x)","\int \frac{x^{2}}{\left(-a^{2} x^{2}+1\right)^{\frac{3}{2}} \arctanh \left(a x \right)}\, dx"," ",0,"int(x^2/(-a^2*x^2+1)^(3/2)/arctanh(a*x),x)","F"
413,1,26,9,0.323000," ","int(x/(-a^2*x^2+1)^(3/2)/arctanh(a*x),x)","-\frac{\Ei \left(1, -\arctanh \left(a x \right)\right)}{2 a^{2}}+\frac{\Ei \left(1, \arctanh \left(a x \right)\right)}{2 a^{2}}"," ",0,"-1/2*Ei(1,-arctanh(a*x))/a^2+1/2*Ei(1,arctanh(a*x))/a^2","B"
414,1,10,9,0.276000," ","int(1/(-a^2*x^2+1)^(3/2)/arctanh(a*x),x)","\frac{\Chi \left(\arctanh \left(a x \right)\right)}{a}"," ",0,"Chi(arctanh(a*x))/a","A"
415,0,0,24,0.514000," ","int(1/x/(-a^2*x^2+1)^(3/2)/arctanh(a*x),x)","\int \frac{1}{x \left(-a^{2} x^{2}+1\right)^{\frac{3}{2}} \arctanh \left(a x \right)}\, dx"," ",0,"int(1/x/(-a^2*x^2+1)^(3/2)/arctanh(a*x),x)","F"
416,0,0,24,1.067000," ","int(x^m/(-a^2*x^2+1)^(3/2)/arctanh(a*x)^2,x)","\int \frac{x^{m}}{\left(-a^{2} x^{2}+1\right)^{\frac{3}{2}} \arctanh \left(a x \right)^{2}}\, dx"," ",0,"int(x^m/(-a^2*x^2+1)^(3/2)/arctanh(a*x)^2,x)","F"
417,0,0,59,0.489000," ","int(x^2/(-a^2*x^2+1)^(3/2)/arctanh(a*x)^2,x)","\int \frac{x^{2}}{\left(-a^{2} x^{2}+1\right)^{\frac{3}{2}} \arctanh \left(a x \right)^{2}}\, dx"," ",0,"int(x^2/(-a^2*x^2+1)^(3/2)/arctanh(a*x)^2,x)","F"
418,1,90,34,0.346000," ","int(x/(-a^2*x^2+1)^(3/2)/arctanh(a*x)^2,x)","\frac{\sqrt{-\left(a x -1\right) \left(a x +1\right)}}{2 a^{2} \left(a x -1\right) \arctanh \left(a x \right)}-\frac{\Ei \left(1, -\arctanh \left(a x \right)\right)}{2 a^{2}}+\frac{\sqrt{-\left(a x -1\right) \left(a x +1\right)}}{2 a^{2} \left(a x +1\right) \arctanh \left(a x \right)}-\frac{\Ei \left(1, \arctanh \left(a x \right)\right)}{2 a^{2}}"," ",0,"1/2*(-(a*x-1)*(a*x+1))^(1/2)/a^2/(a*x-1)/arctanh(a*x)-1/2*Ei(1,-arctanh(a*x))/a^2+1/2*(-(a*x-1)*(a*x+1))^(1/2)/a^2/(a*x+1)/arctanh(a*x)-1/2*Ei(1,arctanh(a*x))/a^2","B"
419,1,62,33,0.326000," ","int(1/(-a^2*x^2+1)^(3/2)/arctanh(a*x)^2,x)","\frac{\arctanh \left(a x \right) \Shi \left(\arctanh \left(a x \right)\right) x^{2} a^{2}-\Shi \left(\arctanh \left(a x \right)\right) \arctanh \left(a x \right)+\sqrt{-a^{2} x^{2}+1}}{a \arctanh \left(a x \right) \left(a^{2} x^{2}-1\right)}"," ",0,"1/a*(arctanh(a*x)*Shi(arctanh(a*x))*x^2*a^2-Shi(arctanh(a*x))*arctanh(a*x)+(-a^2*x^2+1)^(1/2))/arctanh(a*x)/(a^2*x^2-1)","A"
420,0,0,83,0.551000," ","int(1/x/(-a^2*x^2+1)^(3/2)/arctanh(a*x)^2,x)","\int \frac{1}{x \left(-a^{2} x^{2}+1\right)^{\frac{3}{2}} \arctanh \left(a x \right)^{2}}\, dx"," ",0,"int(1/x/(-a^2*x^2+1)^(3/2)/arctanh(a*x)^2,x)","F"
421,0,0,24,1.073000," ","int(x^m/(-a^2*x^2+1)^(3/2)/arctanh(a*x)^3,x)","\int \frac{x^{m}}{\left(-a^{2} x^{2}+1\right)^{\frac{3}{2}} \arctanh \left(a x \right)^{3}}\, dx"," ",0,"int(x^m/(-a^2*x^2+1)^(3/2)/arctanh(a*x)^3,x)","F"
422,0,0,84,0.419000," ","int(x^2/(-a^2*x^2+1)^(3/2)/arctanh(a*x)^3,x)","\int \frac{x^{2}}{\left(-a^{2} x^{2}+1\right)^{\frac{3}{2}} \arctanh \left(a x \right)^{3}}\, dx"," ",0,"int(x^2/(-a^2*x^2+1)^(3/2)/arctanh(a*x)^3,x)","F"
423,1,154,58,0.362000," ","int(x/(-a^2*x^2+1)^(3/2)/arctanh(a*x)^3,x)","\frac{\sqrt{-\left(a x -1\right) \left(a x +1\right)}}{4 a^{2} \left(a x -1\right) \arctanh \left(a x \right)^{2}}+\frac{\sqrt{-\left(a x -1\right) \left(a x +1\right)}}{4 a^{2} \left(a x -1\right) \arctanh \left(a x \right)}-\frac{\Ei \left(1, -\arctanh \left(a x \right)\right)}{4 a^{2}}+\frac{\sqrt{-\left(a x -1\right) \left(a x +1\right)}}{4 a^{2} \left(a x +1\right) \arctanh \left(a x \right)^{2}}-\frac{\sqrt{-\left(a x -1\right) \left(a x +1\right)}}{4 a^{2} \left(a x +1\right) \arctanh \left(a x \right)}+\frac{\Ei \left(1, \arctanh \left(a x \right)\right)}{4 a^{2}}"," ",0,"1/4*(-(a*x-1)*(a*x+1))^(1/2)/a^2/(a*x-1)/arctanh(a*x)^2+1/4*(-(a*x-1)*(a*x+1))^(1/2)/a^2/(a*x-1)/arctanh(a*x)-1/4*Ei(1,-arctanh(a*x))/a^2+1/4*(-(a*x-1)*(a*x+1))^(1/2)/a^2/(a*x+1)/arctanh(a*x)^2-1/4*(-(a*x-1)*(a*x+1))^(1/2)/a^2/(a*x+1)/arctanh(a*x)+1/4*Ei(1,arctanh(a*x))/a^2","B"
424,1,86,55,0.340000," ","int(1/(-a^2*x^2+1)^(3/2)/arctanh(a*x)^3,x)","\frac{\arctanh \left(a x \right)^{2} \Chi \left(\arctanh \left(a x \right)\right) x^{2} a^{2}+\sqrt{-a^{2} x^{2}+1}\, a x \arctanh \left(a x \right)-\Chi \left(\arctanh \left(a x \right)\right) \arctanh \left(a x \right)^{2}+\sqrt{-a^{2} x^{2}+1}}{2 a \arctanh \left(a x \right)^{2} \left(a^{2} x^{2}-1\right)}"," ",0,"1/2/a*(arctanh(a*x)^2*Chi(arctanh(a*x))*x^2*a^2+(-a^2*x^2+1)^(1/2)*a*x*arctanh(a*x)-Chi(arctanh(a*x))*arctanh(a*x)^2+(-a^2*x^2+1)^(1/2))/arctanh(a*x)^2/(a^2*x^2-1)","A"
425,0,0,105,0.552000," ","int(1/x/(-a^2*x^2+1)^(3/2)/arctanh(a*x)^3,x)","\int \frac{1}{x \left(-a^{2} x^{2}+1\right)^{\frac{3}{2}} \arctanh \left(a x \right)^{3}}\, dx"," ",0,"int(1/x/(-a^2*x^2+1)^(3/2)/arctanh(a*x)^3,x)","F"
426,1,195,197,0.455000," ","int(x^4*arctanh(a*x)*(-a^2*x^2+1)^(1/2),x)","\frac{\sqrt{-\left(a x -1\right) \left(a x +1\right)}\, \left(120 \arctanh \left(a x \right) x^{5} a^{5}+24 x^{4} a^{4}-30 a^{3} x^{3} \arctanh \left(a x \right)+22 a^{2} x^{2}-45 a x \arctanh \left(a x \right)-1\right)}{720 a^{5}}-\frac{i \ln \left(1+\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right) \arctanh \left(a x \right)}{16 a^{5}}+\frac{i \ln \left(1-\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right) \arctanh \left(a x \right)}{16 a^{5}}-\frac{i \dilog \left(1+\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right)}{16 a^{5}}+\frac{i \dilog \left(1-\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right)}{16 a^{5}}"," ",0,"1/720/a^5*(-(a*x-1)*(a*x+1))^(1/2)*(120*arctanh(a*x)*x^5*a^5+24*x^4*a^4-30*a^3*x^3*arctanh(a*x)+22*a^2*x^2-45*a*x*arctanh(a*x)-1)-1/16*I*ln(1+I*(a*x+1)/(-a^2*x^2+1)^(1/2))*arctanh(a*x)/a^5+1/16*I*ln(1-I*(a*x+1)/(-a^2*x^2+1)^(1/2))*arctanh(a*x)/a^5-1/16*I*dilog(1+I*(a*x+1)/(-a^2*x^2+1)^(1/2))/a^5+1/16*I*dilog(1-I*(a*x+1)/(-a^2*x^2+1)^(1/2))/a^5","A"
427,1,120,114,0.393000," ","int(x^3*arctanh(a*x)*(-a^2*x^2+1)^(1/2),x)","\frac{\sqrt{-\left(a x -1\right) \left(a x +1\right)}\, \left(24 a^{4} x^{4} \arctanh \left(a x \right)+6 x^{3} a^{3}-8 a^{2} x^{2} \arctanh \left(a x \right)+5 a x -16 \arctanh \left(a x \right)\right)}{120 a^{4}}+\frac{11 i \ln \left(\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}+i\right)}{120 a^{4}}-\frac{11 i \ln \left(\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}-i\right)}{120 a^{4}}"," ",0,"1/120/a^4*(-(a*x-1)*(a*x+1))^(1/2)*(24*a^4*x^4*arctanh(a*x)+6*x^3*a^3-8*a^2*x^2*arctanh(a*x)+5*a*x-16*arctanh(a*x))+11/120*I*ln((a*x+1)/(-a^2*x^2+1)^(1/2)+I)/a^4-11/120*I*ln((a*x+1)/(-a^2*x^2+1)^(1/2)-I)/a^4","C"
428,1,175,156,0.396000," ","int(x^2*arctanh(a*x)*(-a^2*x^2+1)^(1/2),x)","\frac{\sqrt{-\left(a x -1\right) \left(a x +1\right)}\, \left(6 a^{3} x^{3} \arctanh \left(a x \right)+2 a^{2} x^{2}-3 a x \arctanh \left(a x \right)+1\right)}{24 a^{3}}-\frac{i \ln \left(1+\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right) \arctanh \left(a x \right)}{8 a^{3}}+\frac{i \ln \left(1-\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right) \arctanh \left(a x \right)}{8 a^{3}}-\frac{i \dilog \left(1+\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right)}{8 a^{3}}+\frac{i \dilog \left(1-\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right)}{8 a^{3}}"," ",0,"1/24/a^3*(-(a*x-1)*(a*x+1))^(1/2)*(6*a^3*x^3*arctanh(a*x)+2*a^2*x^2-3*a*x*arctanh(a*x)+1)-1/8*I*ln(1+I*(a*x+1)/(-a^2*x^2+1)^(1/2))*arctanh(a*x)/a^3+1/8*I*ln(1-I*(a*x+1)/(-a^2*x^2+1)^(1/2))*arctanh(a*x)/a^3-1/8*I*dilog(1+I*(a*x+1)/(-a^2*x^2+1)^(1/2))/a^3+1/8*I*dilog(1-I*(a*x+1)/(-a^2*x^2+1)^(1/2))/a^3","A"
429,1,99,49,0.322000," ","int(x*arctanh(a*x)*(-a^2*x^2+1)^(1/2),x)","\frac{\sqrt{-\left(a x -1\right) \left(a x +1\right)}\, \left(2 a^{2} x^{2} \arctanh \left(a x \right)+a x -2 \arctanh \left(a x \right)\right)}{6 a^{2}}+\frac{i \ln \left(\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}+i\right)}{6 a^{2}}-\frac{i \ln \left(\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}-i\right)}{6 a^{2}}"," ",0,"1/6/a^2*(-(a*x-1)*(a*x+1))^(1/2)*(2*a^2*x^2*arctanh(a*x)+a*x-2*arctanh(a*x))+1/6*I*ln((a*x+1)/(-a^2*x^2+1)^(1/2)+I)/a^2-1/6*I*ln((a*x+1)/(-a^2*x^2+1)^(1/2)-I)/a^2","C"
430,1,152,115,0.755000," ","int((-a^2*x^2+1)^(1/2)*arctanh(a*x),x)","\frac{\left(a x \arctanh \left(a x \right)+1\right) \sqrt{-a^{2} x^{2}+1}}{2 a}-\frac{i \arctanh \left(a x \right) \ln \left(1+\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right)}{2 a}+\frac{i \arctanh \left(a x \right) \ln \left(1-\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right)}{2 a}-\frac{i \dilog \left(1+\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right)}{2 a}+\frac{i \dilog \left(1-\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right)}{2 a}"," ",0,"1/2*(a*x*arctanh(a*x)+1)*(-a^2*x^2+1)^(1/2)/a-1/2*I/a*arctanh(a*x)*ln(1+I*(a*x+1)/(-a^2*x^2+1)^(1/2))+1/2*I/a*arctanh(a*x)*ln(1-I*(a*x+1)/(-a^2*x^2+1)^(1/2))-1/2*I/a*dilog(1+I*(a*x+1)/(-a^2*x^2+1)^(1/2))+1/2*I/a*dilog(1-I*(a*x+1)/(-a^2*x^2+1)^(1/2))","A"
431,1,113,86,0.419000," ","int(arctanh(a*x)*(-a^2*x^2+1)^(1/2)/x,x)","\sqrt{-\left(a x -1\right) \left(a x +1\right)}\, \arctanh \left(a x \right)-2 \arctan \left(\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)-\dilog \left(\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)-\dilog \left(1+\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)-\arctanh \left(a x \right) \ln \left(1+\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)"," ",0,"(-(a*x-1)*(a*x+1))^(1/2)*arctanh(a*x)-2*arctan((a*x+1)/(-a^2*x^2+1)^(1/2))-dilog((a*x+1)/(-a^2*x^2+1)^(1/2))-dilog(1+(a*x+1)/(-a^2*x^2+1)^(1/2))-arctanh(a*x)*ln(1+(a*x+1)/(-a^2*x^2+1)^(1/2))","A"
432,1,188,110,0.446000," ","int(arctanh(a*x)*(-a^2*x^2+1)^(1/2)/x^2,x)","-\frac{\sqrt{-\left(a x -1\right) \left(a x +1\right)}\, \arctanh \left(a x \right)}{x}-i a \ln \left(1-\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right) \arctanh \left(a x \right)-i a \dilog \left(1-\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right)+i a \ln \left(1+\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right) \arctanh \left(a x \right)+i a \dilog \left(1+\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right)+a \ln \left(\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}-1\right)-a \ln \left(1+\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)"," ",0,"-(-(a*x-1)*(a*x+1))^(1/2)*arctanh(a*x)/x-I*a*ln(1-I*(a*x+1)/(-a^2*x^2+1)^(1/2))*arctanh(a*x)-I*a*dilog(1-I*(a*x+1)/(-a^2*x^2+1)^(1/2))+I*a*ln(1+I*(a*x+1)/(-a^2*x^2+1)^(1/2))*arctanh(a*x)+I*a*dilog(1+I*(a*x+1)/(-a^2*x^2+1)^(1/2))+a*ln((a*x+1)/(-a^2*x^2+1)^(1/2)-1)-a*ln(1+(a*x+1)/(-a^2*x^2+1)^(1/2))","A"
433,1,141,112,0.429000," ","int(arctanh(a*x)*(-a^2*x^2+1)^(1/2)/x^3,x)","-\frac{\sqrt{-\left(a x -1\right) \left(a x +1\right)}\, \left(a x +\arctanh \left(a x \right)\right)}{2 x^{2}}+\frac{a^{2} \arctanh \left(a x \right) \ln \left(1+\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{2}+\frac{a^{2} \polylog \left(2, -\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{2}-\frac{a^{2} \arctanh \left(a x \right) \ln \left(1-\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{2}-\frac{a^{2} \polylog \left(2, \frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{2}"," ",0,"-1/2*(-(a*x-1)*(a*x+1))^(1/2)*(a*x+arctanh(a*x))/x^2+1/2*a^2*arctanh(a*x)*ln(1+(a*x+1)/(-a^2*x^2+1)^(1/2))+1/2*a^2*polylog(2,-(a*x+1)/(-a^2*x^2+1)^(1/2))-1/2*a^2*arctanh(a*x)*ln(1-(a*x+1)/(-a^2*x^2+1)^(1/2))-1/2*a^2*polylog(2,(a*x+1)/(-a^2*x^2+1)^(1/2))","A"
434,1,96,58,0.416000," ","int(arctanh(a*x)*(-a^2*x^2+1)^(1/2)/x^4,x)","\frac{\sqrt{-\left(a x -1\right) \left(a x +1\right)}\, \left(2 a^{2} x^{2} \arctanh \left(a x \right)-a x -2 \arctanh \left(a x \right)\right)}{6 x^{3}}-\frac{a^{3} \ln \left(\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}-1\right)}{6}+\frac{a^{3} \ln \left(1+\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{6}"," ",0,"1/6*(-(a*x-1)*(a*x+1))^(1/2)*(2*a^2*x^2*arctanh(a*x)-a*x-2*arctanh(a*x))/x^3-1/6*a^3*ln((a*x+1)/(-a^2*x^2+1)^(1/2)-1)+1/6*a^3*ln(1+(a*x+1)/(-a^2*x^2+1)^(1/2))","A"
435,1,164,157,0.449000," ","int(arctanh(a*x)*(-a^2*x^2+1)^(1/2)/x^5,x)","\frac{\sqrt{-\left(a x -1\right) \left(a x +1\right)}\, \left(-x^{3} a^{3}+3 a^{2} x^{2} \arctanh \left(a x \right)-2 a x -6 \arctanh \left(a x \right)\right)}{24 x^{4}}+\frac{a^{4} \arctanh \left(a x \right) \ln \left(1+\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{8}+\frac{a^{4} \polylog \left(2, -\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{8}-\frac{a^{4} \arctanh \left(a x \right) \ln \left(1-\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{8}-\frac{a^{4} \polylog \left(2, \frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{8}"," ",0,"1/24*(-(a*x-1)*(a*x+1))^(1/2)*(-x^3*a^3+3*a^2*x^2*arctanh(a*x)-2*a*x-6*arctanh(a*x))/x^4+1/8*a^4*arctanh(a*x)*ln(1+(a*x+1)/(-a^2*x^2+1)^(1/2))+1/8*a^4*polylog(2,-(a*x+1)/(-a^2*x^2+1)^(1/2))-1/8*a^4*arctanh(a*x)*ln(1-(a*x+1)/(-a^2*x^2+1)^(1/2))-1/8*a^4*polylog(2,(a*x+1)/(-a^2*x^2+1)^(1/2))","A"
436,1,116,126,0.435000," ","int(arctanh(a*x)*(-a^2*x^2+1)^(1/2)/x^6,x)","\frac{\sqrt{-\left(a x -1\right) \left(a x +1\right)}\, \left(16 a^{4} x^{4} \arctanh \left(a x \right)-5 x^{3} a^{3}+8 a^{2} x^{2} \arctanh \left(a x \right)-6 a x -24 \arctanh \left(a x \right)\right)}{120 x^{5}}+\frac{11 a^{5} \ln \left(1+\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{120}-\frac{11 a^{5} \ln \left(\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}-1\right)}{120}"," ",0,"1/120*(-(a*x-1)*(a*x+1))^(1/2)*(16*a^4*x^4*arctanh(a*x)-5*x^3*a^3+8*a^2*x^2*arctanh(a*x)-6*a*x-24*arctanh(a*x))/x^5+11/120*a^5*ln(1+(a*x+1)/(-a^2*x^2+1)^(1/2))-11/120*a^5*ln((a*x+1)/(-a^2*x^2+1)^(1/2)-1)","A"
437,1,183,201,0.472000," ","int(arctanh(a*x)*(-a^2*x^2+1)^(1/2)/x^7,x)","\frac{\sqrt{-\left(a x -1\right) \left(a x +1\right)}\, \left(x^{5} a^{5}+45 a^{4} x^{4} \arctanh \left(a x \right)-22 x^{3} a^{3}+30 a^{2} x^{2} \arctanh \left(a x \right)-24 a x -120 \arctanh \left(a x \right)\right)}{720 x^{6}}+\frac{a^{6} \arctanh \left(a x \right) \ln \left(1+\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{16}+\frac{a^{6} \polylog \left(2, -\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{16}-\frac{a^{6} \arctanh \left(a x \right) \ln \left(1-\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{16}-\frac{a^{6} \polylog \left(2, \frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{16}"," ",0,"1/720*(-(a*x-1)*(a*x+1))^(1/2)*(x^5*a^5+45*a^4*x^4*arctanh(a*x)-22*x^3*a^3+30*a^2*x^2*arctanh(a*x)-24*a*x-120*arctanh(a*x))/x^6+1/16*a^6*arctanh(a*x)*ln(1+(a*x+1)/(-a^2*x^2+1)^(1/2))+1/16*a^6*polylog(2,-(a*x+1)/(-a^2*x^2+1)^(1/2))-1/16*a^6*arctanh(a*x)*ln(1-(a*x+1)/(-a^2*x^2+1)^(1/2))-1/16*a^6*polylog(2,(a*x+1)/(-a^2*x^2+1)^(1/2))","A"
438,0,0,340,0.605000," ","int(x^4*arctanh(a*x)^2*(-a^2*x^2+1)^(1/2),x)","\int x^{4} \arctanh \left(a x \right)^{2} \sqrt{-a^{2} x^{2}+1}\, dx"," ",0,"int(x^4*arctanh(a*x)^2*(-a^2*x^2+1)^(1/2),x)","F"
439,1,211,231,0.424000," ","int(x^3*arctanh(a*x)^2*(-a^2*x^2+1)^(1/2),x)","\frac{\sqrt{-\left(a x -1\right) \left(a x +1\right)}\, \left(12 a^{4} x^{4} \arctanh \left(a x \right)^{2}+6 a^{3} x^{3} \arctanh \left(a x \right)-4 a^{2} x^{2} \arctanh \left(a x \right)^{2}+2 a^{2} x^{2}+5 a x \arctanh \left(a x \right)-8 \arctanh \left(a x \right)^{2}+9\right)}{60 a^{4}}-\frac{11 i \ln \left(1+\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right) \arctanh \left(a x \right)}{60 a^{4}}+\frac{11 i \ln \left(1-\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right) \arctanh \left(a x \right)}{60 a^{4}}-\frac{11 i \dilog \left(1+\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right)}{60 a^{4}}+\frac{11 i \dilog \left(1-\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right)}{60 a^{4}}"," ",0,"1/60/a^4*(-(a*x-1)*(a*x+1))^(1/2)*(12*a^4*x^4*arctanh(a*x)^2+6*a^3*x^3*arctanh(a*x)-4*a^2*x^2*arctanh(a*x)^2+2*a^2*x^2+5*a*x*arctanh(a*x)-8*arctanh(a*x)^2+9)-11/60*I*ln(1+I*(a*x+1)/(-a^2*x^2+1)^(1/2))*arctanh(a*x)/a^4+11/60*I*ln(1-I*(a*x+1)/(-a^2*x^2+1)^(1/2))*arctanh(a*x)/a^4-11/60*I*dilog(1+I*(a*x+1)/(-a^2*x^2+1)^(1/2))/a^4+11/60*I*dilog(1-I*(a*x+1)/(-a^2*x^2+1)^(1/2))/a^4","A"
440,0,0,270,0.498000," ","int(x^2*arctanh(a*x)^2*(-a^2*x^2+1)^(1/2),x)","\int x^{2} \arctanh \left(a x \right)^{2} \sqrt{-a^{2} x^{2}+1}\, dx"," ",0,"int(x^2*arctanh(a*x)^2*(-a^2*x^2+1)^(1/2),x)","F"
441,1,175,141,0.350000," ","int(x*arctanh(a*x)^2*(-a^2*x^2+1)^(1/2),x)","\frac{\sqrt{-\left(a x -1\right) \left(a x +1\right)}\, \left(a^{2} x^{2} \arctanh \left(a x \right)^{2}+a x \arctanh \left(a x \right)-\arctanh \left(a x \right)^{2}+1\right)}{3 a^{2}}-\frac{i \ln \left(1+\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right) \arctanh \left(a x \right)}{3 a^{2}}+\frac{i \ln \left(1-\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right) \arctanh \left(a x \right)}{3 a^{2}}-\frac{i \dilog \left(1+\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right)}{3 a^{2}}+\frac{i \dilog \left(1-\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right)}{3 a^{2}}"," ",0,"1/3/a^2*(-(a*x-1)*(a*x+1))^(1/2)*(a^2*x^2*arctanh(a*x)^2+a*x*arctanh(a*x)-arctanh(a*x)^2+1)-1/3*I*ln(1+I*(a*x+1)/(-a^2*x^2+1)^(1/2))*arctanh(a*x)/a^2+1/3*I*ln(1-I*(a*x+1)/(-a^2*x^2+1)^(1/2))*arctanh(a*x)/a^2-1/3*I*dilog(1+I*(a*x+1)/(-a^2*x^2+1)^(1/2))/a^2+1/3*I*dilog(1-I*(a*x+1)/(-a^2*x^2+1)^(1/2))/a^2","A"
442,0,0,200,0.799000," ","int((-a^2*x^2+1)^(1/2)*arctanh(a*x)^2,x)","\int \sqrt{-a^{2} x^{2}+1}\, \arctanh \left(a x \right)^{2}\, dx"," ",0,"int((-a^2*x^2+1)^(1/2)*arctanh(a*x)^2,x)","F"
443,0,0,214,0.450000," ","int(arctanh(a*x)^2*(-a^2*x^2+1)^(1/2)/x,x)","\int \frac{\arctanh \left(a x \right)^{2} \sqrt{-a^{2} x^{2}+1}}{x}\, dx"," ",0,"int(arctanh(a*x)^2*(-a^2*x^2+1)^(1/2)/x,x)","F"
444,0,0,231,0.479000," ","int(arctanh(a*x)^2*(-a^2*x^2+1)^(1/2)/x^2,x)","\int \frac{\arctanh \left(a x \right)^{2} \sqrt{-a^{2} x^{2}+1}}{x^{2}}\, dx"," ",0,"int(arctanh(a*x)^2*(-a^2*x^2+1)^(1/2)/x^2,x)","F"
445,1,231,201,0.456000," ","int(arctanh(a*x)^2*(-a^2*x^2+1)^(1/2)/x^3,x)","-\frac{\sqrt{-\left(a x -1\right) \left(a x +1\right)}\, \arctanh \left(a x \right) \left(2 a x +\arctanh \left(a x \right)\right)}{2 x^{2}}+\frac{a^{2} \arctanh \left(a x \right)^{2} \ln \left(1+\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{2}+a^{2} \arctanh \left(a x \right) \polylog \left(2, -\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)-a^{2} \polylog \left(3, -\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)-\frac{a^{2} \arctanh \left(a x \right)^{2} \ln \left(1-\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{2}-a^{2} \arctanh \left(a x \right) \polylog \left(2, \frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)+a^{2} \polylog \left(3, \frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)-2 a^{2} \arctanh \left(\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)"," ",0,"-1/2*(-(a*x-1)*(a*x+1))^(1/2)*arctanh(a*x)*(2*a*x+arctanh(a*x))/x^2+1/2*a^2*arctanh(a*x)^2*ln(1+(a*x+1)/(-a^2*x^2+1)^(1/2))+a^2*arctanh(a*x)*polylog(2,-(a*x+1)/(-a^2*x^2+1)^(1/2))-a^2*polylog(3,-(a*x+1)/(-a^2*x^2+1)^(1/2))-1/2*a^2*arctanh(a*x)^2*ln(1-(a*x+1)/(-a^2*x^2+1)^(1/2))-a^2*arctanh(a*x)*polylog(2,(a*x+1)/(-a^2*x^2+1)^(1/2))+a^2*polylog(3,(a*x+1)/(-a^2*x^2+1)^(1/2))-2*a^2*arctanh((a*x+1)/(-a^2*x^2+1)^(1/2))","A"
446,1,171,139,0.442000," ","int(arctanh(a*x)^2*(-a^2*x^2+1)^(1/2)/x^4,x)","\frac{\sqrt{-\left(a x -1\right) \left(a x +1\right)}\, \left(a^{2} x^{2} \arctanh \left(a x \right)^{2}-a^{2} x^{2}-a x \arctanh \left(a x \right)-\arctanh \left(a x \right)^{2}\right)}{3 x^{3}}+\frac{a^{3} \arctanh \left(a x \right) \ln \left(1+\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{3}+\frac{a^{3} \polylog \left(2, -\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{3}-\frac{a^{3} \arctanh \left(a x \right) \ln \left(1-\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{3}-\frac{a^{3} \polylog \left(2, \frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{3}"," ",0,"1/3*(-(a*x-1)*(a*x+1))^(1/2)*(a^2*x^2*arctanh(a*x)^2-a^2*x^2-a*x*arctanh(a*x)-arctanh(a*x)^2)/x^3+1/3*a^3*arctanh(a*x)*ln(1+(a*x+1)/(-a^2*x^2+1)^(1/2))+1/3*a^3*polylog(2,-(a*x+1)/(-a^2*x^2+1)^(1/2))-1/3*a^3*arctanh(a*x)*ln(1-(a*x+1)/(-a^2*x^2+1)^(1/2))-1/3*a^3*polylog(2,(a*x+1)/(-a^2*x^2+1)^(1/2))","A"
447,1,215,238,0.458000," ","int(x^4*(-a^2*x^2+1)^(3/2)*arctanh(a*x),x)","-\frac{\sqrt{-\left(a x -1\right) \left(a x +1\right)}\, \left(1680 \arctanh \left(a x \right) x^{7} a^{7}+240 x^{6} a^{6}-2520 \arctanh \left(a x \right) x^{5} a^{5}-216 x^{4} a^{4}+210 a^{3} x^{3} \arctanh \left(a x \right)-218 a^{2} x^{2}+315 a x \arctanh \left(a x \right)-121\right)}{13440 a^{5}}-\frac{3 i \ln \left(1+\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right) \arctanh \left(a x \right)}{128 a^{5}}+\frac{3 i \ln \left(1-\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right) \arctanh \left(a x \right)}{128 a^{5}}-\frac{3 i \dilog \left(1+\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right)}{128 a^{5}}+\frac{3 i \dilog \left(1-\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right)}{128 a^{5}}"," ",0,"-1/13440/a^5*(-(a*x-1)*(a*x+1))^(1/2)*(1680*arctanh(a*x)*x^7*a^7+240*x^6*a^6-2520*arctanh(a*x)*x^5*a^5-216*x^4*a^4+210*a^3*x^3*arctanh(a*x)-218*a^2*x^2+315*a*x*arctanh(a*x)-121)-3/128*I*ln(1+I*(a*x+1)/(-a^2*x^2+1)^(1/2))*arctanh(a*x)/a^5+3/128*I*ln(1-I*(a*x+1)/(-a^2*x^2+1)^(1/2))*arctanh(a*x)/a^5-3/128*I*dilog(1+I*(a*x+1)/(-a^2*x^2+1)^(1/2))/a^5+3/128*I*dilog(1-I*(a*x+1)/(-a^2*x^2+1)^(1/2))/a^5","A"
448,1,140,156,0.380000," ","int(x^3*(-a^2*x^2+1)^(3/2)*arctanh(a*x),x)","-\frac{\sqrt{-\left(a x -1\right) \left(a x +1\right)}\, \left(240 \arctanh \left(a x \right) x^{6} a^{6}+40 x^{5} a^{5}-384 a^{4} x^{4} \arctanh \left(a x \right)-46 x^{3} a^{3}+48 a^{2} x^{2} \arctanh \left(a x \right)-45 a x +96 \arctanh \left(a x \right)\right)}{1680 a^{4}}+\frac{17 i \ln \left(\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}+i\right)}{560 a^{4}}-\frac{17 i \ln \left(\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}-i\right)}{560 a^{4}}"," ",0,"-1/1680/a^4*(-(a*x-1)*(a*x+1))^(1/2)*(240*arctanh(a*x)*x^6*a^6+40*x^5*a^5-384*a^4*x^4*arctanh(a*x)-46*x^3*a^3+48*a^2*x^2*arctanh(a*x)-45*a*x+96*arctanh(a*x))+17/560*I*ln((a*x+1)/(-a^2*x^2+1)^(1/2)+I)/a^4-17/560*I*ln((a*x+1)/(-a^2*x^2+1)^(1/2)-I)/a^4","C"
449,1,195,197,0.362000," ","int(x^2*(-a^2*x^2+1)^(3/2)*arctanh(a*x),x)","-\frac{\sqrt{-\left(a x -1\right) \left(a x +1\right)}\, \left(120 \arctanh \left(a x \right) x^{5} a^{5}+24 x^{4} a^{4}-210 a^{3} x^{3} \arctanh \left(a x \right)-38 a^{2} x^{2}+45 a x \arctanh \left(a x \right)-31\right)}{720 a^{3}}-\frac{i \ln \left(1+\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right) \arctanh \left(a x \right)}{16 a^{3}}+\frac{i \ln \left(1-\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right) \arctanh \left(a x \right)}{16 a^{3}}-\frac{i \dilog \left(1+\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right)}{16 a^{3}}+\frac{i \dilog \left(1-\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right)}{16 a^{3}}"," ",0,"-1/720/a^3*(-(a*x-1)*(a*x+1))^(1/2)*(120*arctanh(a*x)*x^5*a^5+24*x^4*a^4-210*a^3*x^3*arctanh(a*x)-38*a^2*x^2+45*a*x*arctanh(a*x)-31)-1/16*I*ln(1+I*(a*x+1)/(-a^2*x^2+1)^(1/2))*arctanh(a*x)/a^3+1/16*I*ln(1-I*(a*x+1)/(-a^2*x^2+1)^(1/2))*arctanh(a*x)/a^3-1/16*I*dilog(1+I*(a*x+1)/(-a^2*x^2+1)^(1/2))/a^3+1/16*I*dilog(1-I*(a*x+1)/(-a^2*x^2+1)^(1/2))/a^3","A"
450,1,120,67,0.306000," ","int(x*(-a^2*x^2+1)^(3/2)*arctanh(a*x),x)","-\frac{\sqrt{-\left(a x -1\right) \left(a x +1\right)}\, \left(8 a^{4} x^{4} \arctanh \left(a x \right)+2 x^{3} a^{3}-16 a^{2} x^{2} \arctanh \left(a x \right)-5 a x +8 \arctanh \left(a x \right)\right)}{40 a^{2}}+\frac{3 i \ln \left(\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}+i\right)}{40 a^{2}}-\frac{3 i \ln \left(\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}-i\right)}{40 a^{2}}"," ",0,"-1/40/a^2*(-(a*x-1)*(a*x+1))^(1/2)*(8*a^4*x^4*arctanh(a*x)+2*x^3*a^3-16*a^2*x^2*arctanh(a*x)-5*a*x+8*arctanh(a*x))+3/40*I*ln((a*x+1)/(-a^2*x^2+1)^(1/2)+I)/a^2-3/40*I*ln((a*x+1)/(-a^2*x^2+1)^(1/2)-I)/a^2","C"
451,1,173,151,0.960000," ","int((-a^2*x^2+1)^(3/2)*arctanh(a*x),x)","-\frac{\left(6 a^{3} x^{3} \arctanh \left(a x \right)+2 a^{2} x^{2}-15 a x \arctanh \left(a x \right)-11\right) \sqrt{-a^{2} x^{2}+1}}{24 a}-\frac{3 i \arctanh \left(a x \right) \ln \left(1+\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right)}{8 a}+\frac{3 i \arctanh \left(a x \right) \ln \left(1-\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right)}{8 a}-\frac{3 i \dilog \left(1+\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right)}{8 a}+\frac{3 i \dilog \left(1-\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right)}{8 a}"," ",0,"-1/24*(6*a^3*x^3*arctanh(a*x)+2*a^2*x^2-15*a*x*arctanh(a*x)-11)*(-a^2*x^2+1)^(1/2)/a-3/8*I/a*arctanh(a*x)*ln(1+I*(a*x+1)/(-a^2*x^2+1)^(1/2))+3/8*I/a*arctanh(a*x)*ln(1-I*(a*x+1)/(-a^2*x^2+1)^(1/2))-3/8*I/a*dilog(1+I*(a*x+1)/(-a^2*x^2+1)^(1/2))+3/8*I/a*dilog(1-I*(a*x+1)/(-a^2*x^2+1)^(1/2))","A"
452,1,132,120,0.411000," ","int((-a^2*x^2+1)^(3/2)*arctanh(a*x)/x,x)","-\frac{\sqrt{-\left(a x -1\right) \left(a x +1\right)}\, \left(2 a^{2} x^{2} \arctanh \left(a x \right)+a x -8 \arctanh \left(a x \right)\right)}{6}-\frac{7 \arctan \left(\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{3}-\dilog \left(\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)-\dilog \left(1+\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)-\arctanh \left(a x \right) \ln \left(1+\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)"," ",0,"-1/6*(-(a*x-1)*(a*x+1))^(1/2)*(2*a^2*x^2*arctanh(a*x)+a*x-8*arctanh(a*x))-7/3*arctan((a*x+1)/(-a^2*x^2+1)^(1/2))-dilog((a*x+1)/(-a^2*x^2+1)^(1/2))-dilog(1+(a*x+1)/(-a^2*x^2+1)^(1/2))-arctanh(a*x)*ln(1+(a*x+1)/(-a^2*x^2+1)^(1/2))","A"
453,1,205,147,0.442000," ","int((-a^2*x^2+1)^(3/2)*arctanh(a*x)/x^2,x)","-\frac{\left(a^{2} x^{2} \arctanh \left(a x \right)+a x +2 \arctanh \left(a x \right)\right) \sqrt{-\left(a x -1\right) \left(a x +1\right)}}{2 x}+a \ln \left(\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}-1\right)-a \ln \left(1+\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)-\frac{3 i a \ln \left(1-\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right) \arctanh \left(a x \right)}{2}-\frac{3 i a \dilog \left(1-\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right)}{2}+\frac{3 i a \ln \left(1+\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right) \arctanh \left(a x \right)}{2}+\frac{3 i a \dilog \left(1+\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right)}{2}"," ",0,"-1/2*(a^2*x^2*arctanh(a*x)+a*x+2*arctanh(a*x))*(-(a*x-1)*(a*x+1))^(1/2)/x+a*ln((a*x+1)/(-a^2*x^2+1)^(1/2)-1)-a*ln(1+(a*x+1)/(-a^2*x^2+1)^(1/2))-3/2*I*a*ln(1-I*(a*x+1)/(-a^2*x^2+1)^(1/2))*arctanh(a*x)-3/2*I*a*dilog(1-I*(a*x+1)/(-a^2*x^2+1)^(1/2))+3/2*I*a*ln(1+I*(a*x+1)/(-a^2*x^2+1)^(1/2))*arctanh(a*x)+3/2*I*a*dilog(1+I*(a*x+1)/(-a^2*x^2+1)^(1/2))","A"
454,1,145,142,0.487000," ","int((-a^2*x^2+1)^(3/2)*arctanh(a*x)/x^3,x)","-\frac{\sqrt{-\left(a x -1\right) \left(a x +1\right)}\, \left(2 a^{2} x^{2} \arctanh \left(a x \right)+a x +\arctanh \left(a x \right)\right)}{2 x^{2}}+2 a^{2} \arctan \left(\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)+\frac{3 a^{2} \dilog \left(\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{2}+\frac{3 a^{2} \dilog \left(1+\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{2}+\frac{3 a^{2} \arctanh \left(a x \right) \ln \left(1+\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{2}"," ",0,"-1/2*(-(a*x-1)*(a*x+1))^(1/2)*(2*a^2*x^2*arctanh(a*x)+a*x+arctanh(a*x))/x^2+2*a^2*arctan((a*x+1)/(-a^2*x^2+1)^(1/2))+3/2*a^2*dilog((a*x+1)/(-a^2*x^2+1)^(1/2))+3/2*a^2*dilog(1+(a*x+1)/(-a^2*x^2+1)^(1/2))+3/2*a^2*arctanh(a*x)*ln(1+(a*x+1)/(-a^2*x^2+1)^(1/2))","A"
455,1,220,159,0.470000," ","int((-a^2*x^2+1)^(3/2)*arctanh(a*x)/x^4,x)","\frac{\sqrt{-\left(a x -1\right) \left(a x +1\right)}\, \left(8 a^{2} x^{2} \arctanh \left(a x \right)-a x -2 \arctanh \left(a x \right)\right)}{6 x^{3}}-\frac{7 a^{3} \ln \left(\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}-1\right)}{6}+\frac{7 a^{3} \ln \left(1+\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{6}+i a^{3} \ln \left(1-\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right) \arctanh \left(a x \right)+i a^{3} \dilog \left(1-\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right)-i a^{3} \ln \left(1+\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right) \arctanh \left(a x \right)-i a^{3} \dilog \left(1+\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right)"," ",0,"1/6*(-(a*x-1)*(a*x+1))^(1/2)*(8*a^2*x^2*arctanh(a*x)-a*x-2*arctanh(a*x))/x^3-7/6*a^3*ln((a*x+1)/(-a^2*x^2+1)^(1/2)-1)+7/6*a^3*ln(1+(a*x+1)/(-a^2*x^2+1)^(1/2))+I*a^3*ln(1-I*(a*x+1)/(-a^2*x^2+1)^(1/2))*arctanh(a*x)+I*a^3*dilog(1-I*(a*x+1)/(-a^2*x^2+1)^(1/2))-I*a^3*ln(1+I*(a*x+1)/(-a^2*x^2+1)^(1/2))*arctanh(a*x)-I*a^3*dilog(1+I*(a*x+1)/(-a^2*x^2+1)^(1/2))","A"
456,1,164,157,0.435000," ","int((-a^2*x^2+1)^(3/2)*arctanh(a*x)/x^5,x)","\frac{\sqrt{-\left(a x -1\right) \left(a x +1\right)}\, \left(11 x^{3} a^{3}+15 a^{2} x^{2} \arctanh \left(a x \right)-2 a x -6 \arctanh \left(a x \right)\right)}{24 x^{4}}-\frac{3 a^{4} \arctanh \left(a x \right) \ln \left(1+\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{8}-\frac{3 a^{4} \polylog \left(2, -\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{8}+\frac{3 a^{4} \arctanh \left(a x \right) \ln \left(1-\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{8}+\frac{3 a^{4} \polylog \left(2, \frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{8}"," ",0,"1/24*(-(a*x-1)*(a*x+1))^(1/2)*(11*x^3*a^3+15*a^2*x^2*arctanh(a*x)-2*a*x-6*arctanh(a*x))/x^4-3/8*a^4*arctanh(a*x)*ln(1+(a*x+1)/(-a^2*x^2+1)^(1/2))-3/8*a^4*polylog(2,-(a*x+1)/(-a^2*x^2+1)^(1/2))+3/8*a^4*arctanh(a*x)*ln(1-(a*x+1)/(-a^2*x^2+1)^(1/2))+3/8*a^4*polylog(2,(a*x+1)/(-a^2*x^2+1)^(1/2))","A"
457,1,116,78,0.413000," ","int((-a^2*x^2+1)^(3/2)*arctanh(a*x)/x^6,x)","-\frac{\sqrt{-\left(a x -1\right) \left(a x +1\right)}\, \left(8 a^{4} x^{4} \arctanh \left(a x \right)-5 x^{3} a^{3}-16 a^{2} x^{2} \arctanh \left(a x \right)+2 a x +8 \arctanh \left(a x \right)\right)}{40 x^{5}}-\frac{3 a^{5} \ln \left(1+\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{40}+\frac{3 a^{5} \ln \left(\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}-1\right)}{40}"," ",0,"-1/40*(-(a*x-1)*(a*x+1))^(1/2)*(8*a^4*x^4*arctanh(a*x)-5*x^3*a^3-16*a^2*x^2*arctanh(a*x)+2*a*x+8*arctanh(a*x))/x^5-3/40*a^5*ln(1+(a*x+1)/(-a^2*x^2+1)^(1/2))+3/40*a^5*ln((a*x+1)/(-a^2*x^2+1)^(1/2)-1)","A"
458,1,184,201,0.445000," ","int((-a^2*x^2+1)^(3/2)*arctanh(a*x)/x^7,x)","-\frac{\sqrt{-\left(a x -1\right) \left(a x +1\right)}\, \left(-31 x^{5} a^{5}+45 a^{4} x^{4} \arctanh \left(a x \right)-38 x^{3} a^{3}-210 a^{2} x^{2} \arctanh \left(a x \right)+24 a x +120 \arctanh \left(a x \right)\right)}{720 x^{6}}-\frac{a^{6} \arctanh \left(a x \right) \ln \left(1+\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{16}-\frac{a^{6} \polylog \left(2, -\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{16}+\frac{a^{6} \arctanh \left(a x \right) \ln \left(1-\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{16}+\frac{a^{6} \polylog \left(2, \frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{16}"," ",0,"-1/720*(-(a*x-1)*(a*x+1))^(1/2)*(-31*x^5*a^5+45*a^4*x^4*arctanh(a*x)-38*x^3*a^3-210*a^2*x^2*arctanh(a*x)+24*a*x+120*arctanh(a*x))/x^6-1/16*a^6*arctanh(a*x)*ln(1+(a*x+1)/(-a^2*x^2+1)^(1/2))-1/16*a^6*polylog(2,-(a*x+1)/(-a^2*x^2+1)^(1/2))+1/16*a^6*arctanh(a*x)*ln(1-(a*x+1)/(-a^2*x^2+1)^(1/2))+1/16*a^6*polylog(2,(a*x+1)/(-a^2*x^2+1)^(1/2))","A"
459,1,193,187,1.135000," ","int((-a^2*x^2+1)^(5/2)*arctanh(a*x),x)","\frac{\left(120 \arctanh \left(a x \right) x^{5} a^{5}+24 x^{4} a^{4}-390 a^{3} x^{3} \arctanh \left(a x \right)-98 a^{2} x^{2}+495 a x \arctanh \left(a x \right)+299\right) \sqrt{-a^{2} x^{2}+1}}{720 a}-\frac{5 i \arctanh \left(a x \right) \ln \left(1+\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right)}{16 a}+\frac{5 i \arctanh \left(a x \right) \ln \left(1-\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right)}{16 a}-\frac{5 i \dilog \left(1+\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right)}{16 a}+\frac{5 i \dilog \left(1-\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right)}{16 a}"," ",0,"1/720*(120*arctanh(a*x)*x^5*a^5+24*x^4*a^4-390*a^3*x^3*arctanh(a*x)-98*a^2*x^2+495*a*x*arctanh(a*x)+299)*(-a^2*x^2+1)^(1/2)/a-5/16*I/a*arctanh(a*x)*ln(1+I*(a*x+1)/(-a^2*x^2+1)^(1/2))+5/16*I/a*arctanh(a*x)*ln(1-I*(a*x+1)/(-a^2*x^2+1)^(1/2))-5/16*I/a*dilog(1+I*(a*x+1)/(-a^2*x^2+1)^(1/2))+5/16*I/a*dilog(1-I*(a*x+1)/(-a^2*x^2+1)^(1/2))","A"
460,1,173,151,0.913000," ","int((-a^2*x^2+1)^(3/2)*arctanh(a*x),x)","-\frac{\left(6 a^{3} x^{3} \arctanh \left(a x \right)+2 a^{2} x^{2}-15 a x \arctanh \left(a x \right)-11\right) \sqrt{-a^{2} x^{2}+1}}{24 a}-\frac{3 i \arctanh \left(a x \right) \ln \left(1+\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right)}{8 a}+\frac{3 i \arctanh \left(a x \right) \ln \left(1-\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right)}{8 a}-\frac{3 i \dilog \left(1+\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right)}{8 a}+\frac{3 i \dilog \left(1-\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right)}{8 a}"," ",0,"-1/24*(6*a^3*x^3*arctanh(a*x)+2*a^2*x^2-15*a*x*arctanh(a*x)-11)*(-a^2*x^2+1)^(1/2)/a-3/8*I/a*arctanh(a*x)*ln(1+I*(a*x+1)/(-a^2*x^2+1)^(1/2))+3/8*I/a*arctanh(a*x)*ln(1-I*(a*x+1)/(-a^2*x^2+1)^(1/2))-3/8*I/a*dilog(1+I*(a*x+1)/(-a^2*x^2+1)^(1/2))+3/8*I/a*dilog(1-I*(a*x+1)/(-a^2*x^2+1)^(1/2))","A"
461,1,152,115,0.750000," ","int((-a^2*x^2+1)^(1/2)*arctanh(a*x),x)","\frac{\left(a x \arctanh \left(a x \right)+1\right) \sqrt{-a^{2} x^{2}+1}}{2 a}-\frac{i \arctanh \left(a x \right) \ln \left(1+\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right)}{2 a}+\frac{i \arctanh \left(a x \right) \ln \left(1-\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right)}{2 a}-\frac{i \dilog \left(1+\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right)}{2 a}+\frac{i \dilog \left(1-\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right)}{2 a}"," ",0,"1/2*(a*x*arctanh(a*x)+1)*(-a^2*x^2+1)^(1/2)/a-1/2*I/a*arctanh(a*x)*ln(1+I*(a*x+1)/(-a^2*x^2+1)^(1/2))+1/2*I/a*arctanh(a*x)*ln(1-I*(a*x+1)/(-a^2*x^2+1)^(1/2))-1/2*I/a*dilog(1+I*(a*x+1)/(-a^2*x^2+1)^(1/2))+1/2*I/a*dilog(1-I*(a*x+1)/(-a^2*x^2+1)^(1/2))","A"
462,1,59,73,0.400000," ","int(arctanh(a*x)/(-a^2*x^2+1)^(5/2),x)","-\frac{\sqrt{-a^{2} x^{2}+1}\, \left(6 a^{3} x^{3} \arctanh \left(a x \right)-6 a^{2} x^{2}-9 a x \arctanh \left(a x \right)+7\right)}{9 a \left(a^{2} x^{2}-1\right)^{2}}"," ",0,"-1/9/a*(-a^2*x^2+1)^(1/2)*(6*a^3*x^3*arctanh(a*x)-6*a^2*x^2-9*a*x*arctanh(a*x)+7)/(a^2*x^2-1)^2","A"
463,1,79,109,0.420000," ","int(arctanh(a*x)/(-a^2*x^2+1)^(7/2),x)","-\frac{\sqrt{-a^{2} x^{2}+1}\, \left(120 \arctanh \left(a x \right) x^{5} a^{5}-120 x^{4} a^{4}-300 a^{3} x^{3} \arctanh \left(a x \right)+260 a^{2} x^{2}+225 a x \arctanh \left(a x \right)-149\right)}{225 a \left(a^{2} x^{2}-1\right)^{3}}"," ",0,"-1/225/a*(-a^2*x^2+1)^(1/2)*(120*arctanh(a*x)*x^5*a^5-120*x^4*a^4-300*a^3*x^3*arctanh(a*x)+260*a^2*x^2+225*a*x*arctanh(a*x)-149)/(a^2*x^2-1)^3","A"
464,1,99,145,0.439000," ","int(arctanh(a*x)/(-a^2*x^2+1)^(9/2),x)","-\frac{\sqrt{-a^{2} x^{2}+1}\, \left(1680 \arctanh \left(a x \right) x^{7} a^{7}-1680 x^{6} a^{6}-5880 \arctanh \left(a x \right) x^{5} a^{5}+5320 x^{4} a^{4}+7350 a^{3} x^{3} \arctanh \left(a x \right)-5726 a^{2} x^{2}-3675 a x \arctanh \left(a x \right)+2161\right)}{3675 a \left(a^{2} x^{2}-1\right)^{4}}"," ",0,"-1/3675/a*(-a^2*x^2+1)^(1/2)*(1680*arctanh(a*x)*x^7*a^7-1680*x^6*a^6-5880*arctanh(a*x)*x^5*a^5+5320*x^4*a^4+7350*a^3*x^3*arctanh(a*x)-5726*a^2*x^2-3675*a*x*arctanh(a*x)+2161)/(a^2*x^2-1)^4","A"
465,1,345,241,0.560000," ","int((-a^2*c*x^2+c)^(3/2)*arctanh(a*x),x)","-\frac{c \sqrt{-\left(a x -1\right) \left(a x +1\right) c}\, \left(6 a^{3} x^{3} \arctanh \left(a x \right)+2 a^{2} x^{2}-15 a x \arctanh \left(a x \right)-11\right)}{24 a}+\frac{3 i c \sqrt{-a^{2} x^{2}+1}\, \sqrt{-\left(a x -1\right) \left(a x +1\right) c}\, \arctanh \left(a x \right) \ln \left(1+\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right)}{8 a \left(a x +1\right) \left(a x -1\right)}-\frac{3 i c \sqrt{-a^{2} x^{2}+1}\, \sqrt{-\left(a x -1\right) \left(a x +1\right) c}\, \arctanh \left(a x \right) \ln \left(1-\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right)}{8 a \left(a x +1\right) \left(a x -1\right)}+\frac{3 i c \sqrt{-a^{2} x^{2}+1}\, \sqrt{-\left(a x -1\right) \left(a x +1\right) c}\, \dilog \left(1+\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right)}{8 a \left(a x +1\right) \left(a x -1\right)}-\frac{3 i c \sqrt{-a^{2} x^{2}+1}\, \sqrt{-\left(a x -1\right) \left(a x +1\right) c}\, \dilog \left(1-\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right)}{8 a \left(a x +1\right) \left(a x -1\right)}"," ",0,"-1/24*c/a*(-(a*x-1)*(a*x+1)*c)^(1/2)*(6*a^3*x^3*arctanh(a*x)+2*a^2*x^2-15*a*x*arctanh(a*x)-11)+3/8*I*c/a/(a*x+1)*(-a^2*x^2+1)^(1/2)/(a*x-1)*(-(a*x-1)*(a*x+1)*c)^(1/2)*arctanh(a*x)*ln(1+I*(a*x+1)/(-a^2*x^2+1)^(1/2))-3/8*I*c/a/(a*x+1)*(-a^2*x^2+1)^(1/2)/(a*x-1)*(-(a*x-1)*(a*x+1)*c)^(1/2)*arctanh(a*x)*ln(1-I*(a*x+1)/(-a^2*x^2+1)^(1/2))+3/8*I*c/a/(a*x+1)*(-a^2*x^2+1)^(1/2)/(a*x-1)*(-(a*x-1)*(a*x+1)*c)^(1/2)*dilog(1+I*(a*x+1)/(-a^2*x^2+1)^(1/2))-3/8*I*c/a/(a*x+1)*(-a^2*x^2+1)^(1/2)/(a*x-1)*(-(a*x-1)*(a*x+1)*c)^(1/2)*dilog(1-I*(a*x+1)/(-a^2*x^2+1)^(1/2))","A"
466,1,319,195,0.548000," ","int((-a^2*c*x^2+c)^(1/2)*arctanh(a*x),x)","\frac{\left(a x \arctanh \left(a x \right)+1\right) \sqrt{-\left(a x -1\right) \left(a x +1\right) c}}{2 a}+\frac{i \sqrt{-\left(a x -1\right) \left(a x +1\right) c}\, \sqrt{-a^{2} x^{2}+1}\, \arctanh \left(a x \right) \ln \left(1+\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right)}{2 a \left(a x +1\right) \left(a x -1\right)}-\frac{i \sqrt{-\left(a x -1\right) \left(a x +1\right) c}\, \sqrt{-a^{2} x^{2}+1}\, \arctanh \left(a x \right) \ln \left(1-\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right)}{2 a \left(a x +1\right) \left(a x -1\right)}+\frac{i \sqrt{-\left(a x -1\right) \left(a x +1\right) c}\, \sqrt{-a^{2} x^{2}+1}\, \dilog \left(1+\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right)}{2 a \left(a x +1\right) \left(a x -1\right)}-\frac{i \sqrt{-\left(a x -1\right) \left(a x +1\right) c}\, \sqrt{-a^{2} x^{2}+1}\, \dilog \left(1-\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right)}{2 a \left(a x +1\right) \left(a x -1\right)}"," ",0,"1/2*(a*x*arctanh(a*x)+1)*(-(a*x-1)*(a*x+1)*c)^(1/2)/a+1/2*I/a*(-(a*x-1)*(a*x+1)*c)^(1/2)/(a*x+1)*(-a^2*x^2+1)^(1/2)/(a*x-1)*arctanh(a*x)*ln(1+I*(a*x+1)/(-a^2*x^2+1)^(1/2))-1/2*I/a*(-(a*x-1)*(a*x+1)*c)^(1/2)/(a*x+1)*(-a^2*x^2+1)^(1/2)/(a*x-1)*arctanh(a*x)*ln(1-I*(a*x+1)/(-a^2*x^2+1)^(1/2))+1/2*I/a*(-(a*x-1)*(a*x+1)*c)^(1/2)/(a*x+1)*(-a^2*x^2+1)^(1/2)/(a*x-1)*dilog(1+I*(a*x+1)/(-a^2*x^2+1)^(1/2))-1/2*I/a*(-(a*x-1)*(a*x+1)*c)^(1/2)/(a*x+1)*(-a^2*x^2+1)^(1/2)/(a*x-1)*dilog(1-I*(a*x+1)/(-a^2*x^2+1)^(1/2))","A"
467,1,290,154,0.517000," ","int(arctanh(a*x)/(-a^2*c*x^2+c)^(1/2),x)","\frac{i \ln \left(1+\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right) \arctanh \left(a x \right) \sqrt{-a^{2} x^{2}+1}\, \sqrt{-\left(a x -1\right) \left(a x +1\right) c}}{\left(a^{2} x^{2}-1\right) a c}-\frac{i \ln \left(1-\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right) \arctanh \left(a x \right) \sqrt{-a^{2} x^{2}+1}\, \sqrt{-\left(a x -1\right) \left(a x +1\right) c}}{\left(a^{2} x^{2}-1\right) a c}+\frac{i \dilog \left(1+\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right) \sqrt{-a^{2} x^{2}+1}\, \sqrt{-\left(a x -1\right) \left(a x +1\right) c}}{\left(a^{2} x^{2}-1\right) a c}-\frac{i \dilog \left(1-\frac{i \left(a x +1\right)}{\sqrt{-a^{2} x^{2}+1}}\right) \sqrt{-a^{2} x^{2}+1}\, \sqrt{-\left(a x -1\right) \left(a x +1\right) c}}{\left(a^{2} x^{2}-1\right) a c}"," ",0,"I*ln(1+I*(a*x+1)/(-a^2*x^2+1)^(1/2))*arctanh(a*x)*(-a^2*x^2+1)^(1/2)*(-(a*x-1)*(a*x+1)*c)^(1/2)/(a^2*x^2-1)/a/c-I*ln(1-I*(a*x+1)/(-a^2*x^2+1)^(1/2))*arctanh(a*x)*(-a^2*x^2+1)^(1/2)*(-(a*x-1)*(a*x+1)*c)^(1/2)/(a^2*x^2-1)/a/c+I*dilog(1+I*(a*x+1)/(-a^2*x^2+1)^(1/2))*(-a^2*x^2+1)^(1/2)*(-(a*x-1)*(a*x+1)*c)^(1/2)/(a^2*x^2-1)/a/c-I*dilog(1-I*(a*x+1)/(-a^2*x^2+1)^(1/2))*(-a^2*x^2+1)^(1/2)*(-(a*x-1)*(a*x+1)*c)^(1/2)/(a^2*x^2-1)/a/c","A"
468,1,74,44,0.471000," ","int(arctanh(a*x)/(-a^2*c*x^2+c)^(3/2),x)","-\frac{\left(\arctanh \left(a x \right)-1\right) \sqrt{-\left(a x -1\right) \left(a x +1\right) c}}{2 a \left(a x -1\right) c^{2}}-\frac{\left(\arctanh \left(a x \right)+1\right) \sqrt{-\left(a x -1\right) \left(a x +1\right) c}}{2 a \left(a x +1\right) c^{2}}"," ",0,"-1/2*(arctanh(a*x)-1)*(-(a*x-1)*(a*x+1)*c)^(1/2)/a/(a*x-1)/c^2-1/2*(arctanh(a*x)+1)*(-(a*x-1)*(a*x+1)*c)^(1/2)/a/(a*x+1)/c^2","A"
469,1,160,89,0.479000," ","int(arctanh(a*x)/(-a^2*c*x^2+c)^(5/2),x)","\frac{\left(a x +1\right) \left(-1+3 \arctanh \left(a x \right)\right) \sqrt{-\left(a x -1\right) \left(a x +1\right) c}}{72 a \left(a x -1\right)^{2} c^{3}}-\frac{3 \left(\arctanh \left(a x \right)-1\right) \sqrt{-\left(a x -1\right) \left(a x +1\right) c}}{8 a \left(a x -1\right) c^{3}}-\frac{3 \left(\arctanh \left(a x \right)+1\right) \sqrt{-\left(a x -1\right) \left(a x +1\right) c}}{8 a \left(a x +1\right) c^{3}}+\frac{\left(a x -1\right) \left(1+3 \arctanh \left(a x \right)\right) \sqrt{-\left(a x -1\right) \left(a x +1\right) c}}{72 a \left(a x +1\right)^{2} c^{3}}"," ",0,"1/72*(a*x+1)*(-1+3*arctanh(a*x))*(-(a*x-1)*(a*x+1)*c)^(1/2)/a/(a*x-1)^2/c^3-3/8*(arctanh(a*x)-1)*(-(a*x-1)*(a*x+1)*c)^(1/2)/a/(a*x-1)/c^3-3/8*(arctanh(a*x)+1)*(-(a*x-1)*(a*x+1)*c)^(1/2)/a/(a*x+1)/c^3+1/72*(a*x-1)*(1+3*arctanh(a*x))*(-(a*x-1)*(a*x+1)*c)^(1/2)/a/(a*x+1)^2/c^3","A"
470,1,250,133,0.494000," ","int(arctanh(a*x)/(-a^2*c*x^2+c)^(7/2),x)","-\frac{\left(a x +1\right)^{2} \left(-1+5 \arctanh \left(a x \right)\right) \sqrt{-\left(a x -1\right) \left(a x +1\right) c}}{800 a \left(a x -1\right)^{3} c^{4}}+\frac{5 \left(a x +1\right) \left(-1+3 \arctanh \left(a x \right)\right) \sqrt{-\left(a x -1\right) \left(a x +1\right) c}}{288 a \left(a x -1\right)^{2} c^{4}}-\frac{5 \left(\arctanh \left(a x \right)-1\right) \sqrt{-\left(a x -1\right) \left(a x +1\right) c}}{16 a \left(a x -1\right) c^{4}}-\frac{5 \left(\arctanh \left(a x \right)+1\right) \sqrt{-\left(a x -1\right) \left(a x +1\right) c}}{16 a \left(a x +1\right) c^{4}}+\frac{5 \left(a x -1\right) \left(1+3 \arctanh \left(a x \right)\right) \sqrt{-\left(a x -1\right) \left(a x +1\right) c}}{288 a \left(a x +1\right)^{2} c^{4}}-\frac{\left(a x -1\right)^{2} \left(1+5 \arctanh \left(a x \right)\right) \sqrt{-\left(a x -1\right) \left(a x +1\right) c}}{800 \left(a x +1\right)^{3} a \,c^{4}}"," ",0,"-1/800*(a*x+1)^2*(-1+5*arctanh(a*x))*(-(a*x-1)*(a*x+1)*c)^(1/2)/a/(a*x-1)^3/c^4+5/288*(a*x+1)*(-1+3*arctanh(a*x))*(-(a*x-1)*(a*x+1)*c)^(1/2)/a/(a*x-1)^2/c^4-5/16*(arctanh(a*x)-1)*(-(a*x-1)*(a*x+1)*c)^(1/2)/a/(a*x-1)/c^4-5/16*(arctanh(a*x)+1)*(-(a*x-1)*(a*x+1)*c)^(1/2)/a/(a*x+1)/c^4+5/288*(a*x-1)*(1+3*arctanh(a*x))*(-(a*x-1)*(a*x+1)*c)^(1/2)/a/(a*x+1)^2/c^4-1/800*(a*x-1)^2*(1+5*arctanh(a*x))*(-(a*x-1)*(a*x+1)*c)^(1/2)/(a*x+1)^3/a/c^4","A"
471,0,0,200,0.025000," ","int((-a^2*x^2+1)^(1/2)*arctanh(a*x)^2,x)","\int \sqrt{-a^{2} x^{2}+1}\, \arctanh \left(a x \right)^{2}\, dx"," ",0,"int((-a^2*x^2+1)^(1/2)*arctanh(a*x)^2,x)","F"
472,1,84,115,0.430000," ","int(arctanh(a*x)^2/(-a^2*x^2+1)^(5/2),x)","-\frac{\sqrt{-a^{2} x^{2}+1}\, \left(18 \arctanh \left(a x \right)^{2} x^{3} a^{3}+40 x^{3} a^{3}-36 a^{2} x^{2} \arctanh \left(a x \right)-27 \arctanh \left(a x \right)^{2} a x -42 a x +42 \arctanh \left(a x \right)\right)}{27 a \left(a^{2} x^{2}-1\right)^{2}}"," ",0,"-1/27/a*(-a^2*x^2+1)^(1/2)*(18*arctanh(a*x)^2*x^3*a^3+40*x^3*a^3-36*a^2*x^2*arctanh(a*x)-27*arctanh(a*x)^2*a*x-42*a*x+42*arctanh(a*x))/(a^2*x^2-1)^2","A"
473,1,118,172,0.564000," ","int(arctanh(a*x)^2/(-a^2*x^2+1)^(7/2),x)","-\frac{\sqrt{-a^{2} x^{2}+1}\, \left(1800 \arctanh \left(a x \right)^{2} x^{5} a^{5}+4144 x^{5} a^{5}-3600 a^{4} x^{4} \arctanh \left(a x \right)-4500 \arctanh \left(a x \right)^{2} x^{3} a^{3}-8560 x^{3} a^{3}+7800 a^{2} x^{2} \arctanh \left(a x \right)+3375 \arctanh \left(a x \right)^{2} a x +4470 a x -4470 \arctanh \left(a x \right)\right)}{3375 a \left(a^{2} x^{2}-1\right)^{3}}"," ",0,"-1/3375/a*(-a^2*x^2+1)^(1/2)*(1800*arctanh(a*x)^2*x^5*a^5+4144*x^5*a^5-3600*a^4*x^4*arctanh(a*x)-4500*arctanh(a*x)^2*x^3*a^3-8560*x^3*a^3+7800*a^2*x^2*arctanh(a*x)+3375*arctanh(a*x)^2*a*x+4470*a*x-4470*arctanh(a*x))/(a^2*x^2-1)^3","A"
474,1,152,229,0.694000," ","int(arctanh(a*x)^2/(-a^2*x^2+1)^(9/2),x)","-\frac{\sqrt{-a^{2} x^{2}+1}\, \left(176400 \arctanh \left(a x \right)^{2} x^{7} a^{7}+413312 x^{7} a^{7}-352800 \arctanh \left(a x \right) x^{6} a^{6}-617400 \arctanh \left(a x \right)^{2} x^{5} a^{5}-1270192 x^{5} a^{5}+1117200 a^{4} x^{4} \arctanh \left(a x \right)+771750 \arctanh \left(a x \right)^{2} x^{3} a^{3}+1308440 x^{3} a^{3}-1202460 a^{2} x^{2} \arctanh \left(a x \right)-385875 \arctanh \left(a x \right)^{2} a x -453810 a x +453810 \arctanh \left(a x \right)\right)}{385875 a \left(a^{2} x^{2}-1\right)^{4}}"," ",0,"-1/385875/a*(-a^2*x^2+1)^(1/2)*(176400*arctanh(a*x)^2*x^7*a^7+413312*x^7*a^7-352800*arctanh(a*x)*x^6*a^6-617400*arctanh(a*x)^2*x^5*a^5-1270192*x^5*a^5+1117200*a^4*x^4*arctanh(a*x)+771750*arctanh(a*x)^2*x^3*a^3+1308440*x^3*a^3-1202460*a^2*x^2*arctanh(a*x)-385875*arctanh(a*x)^2*a*x-453810*a*x+453810*arctanh(a*x))/(a^2*x^2-1)^4","A"
475,0,0,340,0.820000," ","int((-a^2*x^2+1)^(1/2)*arctanh(a*x)^3,x)","\int \sqrt{-a^{2} x^{2}+1}\, \arctanh \left(a x \right)^{3}\, dx"," ",0,"int((-a^2*x^2+1)^(1/2)*arctanh(a*x)^3,x)","F"
476,1,105,161,0.438000," ","int(arctanh(a*x)^3/(-a^2*x^2+1)^(5/2),x)","-\frac{\sqrt{-a^{2} x^{2}+1}\, \left(18 \arctanh \left(a x \right)^{3} x^{3} a^{3}+120 a^{3} x^{3} \arctanh \left(a x \right)-54 a^{2} x^{2} \arctanh \left(a x \right)^{2}-27 \arctanh \left(a x \right)^{3} a x -120 a^{2} x^{2}-126 a x \arctanh \left(a x \right)+63 \arctanh \left(a x \right)^{2}+122\right)}{27 a \left(a^{2} x^{2}-1\right)^{2}}"," ",0,"-1/27/a*(-a^2*x^2+1)^(1/2)*(18*arctanh(a*x)^3*x^3*a^3+120*a^3*x^3*arctanh(a*x)-54*a^2*x^2*arctanh(a*x)^2-27*arctanh(a*x)^3*a*x-120*a^2*x^2-126*a*x*arctanh(a*x)+63*arctanh(a*x)^2+122)/(a^2*x^2-1)^2","A"
477,1,153,241,0.456000," ","int(arctanh(a*x)^3/(-a^2*x^2+1)^(7/2),x)","-\frac{\sqrt{-a^{2} x^{2}+1}\, \left(9000 \arctanh \left(a x \right)^{3} x^{5} a^{5}+62160 \arctanh \left(a x \right) x^{5} a^{5}-27000 a^{4} x^{4} \arctanh \left(a x \right)^{2}-22500 \arctanh \left(a x \right)^{3} x^{3} a^{3}-62160 x^{4} a^{4}-128400 a^{3} x^{3} \arctanh \left(a x \right)+58500 a^{2} x^{2} \arctanh \left(a x \right)^{2}+16875 \arctanh \left(a x \right)^{3} a x +125680 a^{2} x^{2}+67050 a x \arctanh \left(a x \right)-33525 \arctanh \left(a x \right)^{2}-63682\right)}{16875 a \left(a^{2} x^{2}-1\right)^{3}}"," ",0,"-1/16875/a*(-a^2*x^2+1)^(1/2)*(9000*arctanh(a*x)^3*x^5*a^5+62160*arctanh(a*x)*x^5*a^5-27000*a^4*x^4*arctanh(a*x)^2-22500*arctanh(a*x)^3*x^3*a^3-62160*x^4*a^4-128400*a^3*x^3*arctanh(a*x)+58500*a^2*x^2*arctanh(a*x)^2+16875*arctanh(a*x)^3*a*x+125680*a^2*x^2+67050*a*x*arctanh(a*x)-33525*arctanh(a*x)^2-63682)/(a^2*x^2-1)^3","A"
478,1,201,321,0.574000," ","int(arctanh(a*x)^3/(-a^2*x^2+1)^(9/2),x)","-\frac{\sqrt{-a^{2} x^{2}+1}\, \left(6174000 \arctanh \left(a x \right)^{3} x^{7} a^{7}+43397760 \arctanh \left(a x \right) x^{7} a^{7}-18522000 \arctanh \left(a x \right)^{2} x^{6} a^{6}-21609000 \arctanh \left(a x \right)^{3} x^{5} a^{5}-43397760 x^{6} a^{6}-133370160 \arctanh \left(a x \right) x^{5} a^{5}+58653000 a^{4} x^{4} \arctanh \left(a x \right)^{2}+27011250 \arctanh \left(a x \right)^{3} x^{3} a^{3}+131252240 x^{4} a^{4}+137386200 a^{3} x^{3} \arctanh \left(a x \right)-63129150 a^{2} x^{2} \arctanh \left(a x \right)^{2}-13505625 \arctanh \left(a x \right)^{3} a x -132479032 a^{2} x^{2}-47650050 a x \arctanh \left(a x \right)+23825025 \arctanh \left(a x \right)^{2}+44658302\right)}{13505625 a \left(a^{2} x^{2}-1\right)^{4}}"," ",0,"-1/13505625/a*(-a^2*x^2+1)^(1/2)*(6174000*arctanh(a*x)^3*x^7*a^7+43397760*arctanh(a*x)*x^7*a^7-18522000*arctanh(a*x)^2*x^6*a^6-21609000*arctanh(a*x)^3*x^5*a^5-43397760*x^6*a^6-133370160*arctanh(a*x)*x^5*a^5+58653000*a^4*x^4*arctanh(a*x)^2+27011250*arctanh(a*x)^3*x^3*a^3+131252240*x^4*a^4+137386200*a^3*x^3*arctanh(a*x)-63129150*a^2*x^2*arctanh(a*x)^2-13505625*arctanh(a*x)^3*a*x-132479032*a^2*x^2-47650050*a*x*arctanh(a*x)+23825025*arctanh(a*x)^2+44658302)/(a^2*x^2-1)^4","A"
479,0,0,21,0.797000," ","int((-a^2*x^2+1)^(1/2)/arctanh(a*x),x)","\int \frac{\sqrt{-a^{2} x^{2}+1}}{\arctanh \left(a x \right)}\, dx"," ",0,"int((-a^2*x^2+1)^(1/2)/arctanh(a*x),x)","F"
480,0,0,21,0.386000," ","int(1/(-a^2*x^2+1)^(1/2)/arctanh(a*x),x)","\int \frac{1}{\sqrt{-a^{2} x^{2}+1}\, \arctanh \left(a x \right)}\, dx"," ",0,"int(1/(-a^2*x^2+1)^(1/2)/arctanh(a*x),x)","F"
481,1,10,9,0.280000," ","int(1/(-a^2*x^2+1)^(3/2)/arctanh(a*x),x)","\frac{\Chi \left(\arctanh \left(a x \right)\right)}{a}"," ",0,"Chi(arctanh(a*x))/a","A"
482,1,21,23,0.331000," ","int(1/(-a^2*x^2+1)^(5/2)/arctanh(a*x),x)","\frac{3 \Chi \left(\arctanh \left(a x \right)\right)+\Chi \left(3 \arctanh \left(a x \right)\right)}{4 a}"," ",0,"1/4*(3*Chi(arctanh(a*x))+Chi(3*arctanh(a*x)))/a","A"
483,1,30,35,0.377000," ","int(1/(-a^2*x^2+1)^(7/2)/arctanh(a*x),x)","\frac{10 \Chi \left(\arctanh \left(a x \right)\right)+5 \Chi \left(3 \arctanh \left(a x \right)\right)+\Chi \left(5 \arctanh \left(a x \right)\right)}{16 a}"," ",0,"1/16*(10*Chi(arctanh(a*x))+5*Chi(3*arctanh(a*x))+Chi(5*arctanh(a*x)))/a","A"
484,1,39,47,0.434000," ","int(1/(-a^2*x^2+1)^(9/2)/arctanh(a*x),x)","\frac{35 \Chi \left(\arctanh \left(a x \right)\right)+21 \Chi \left(3 \arctanh \left(a x \right)\right)+7 \Chi \left(5 \arctanh \left(a x \right)\right)+\Chi \left(7 \arctanh \left(a x \right)\right)}{64 a}"," ",0,"1/64*(35*Chi(arctanh(a*x))+21*Chi(3*arctanh(a*x))+7*Chi(5*arctanh(a*x))+Chi(7*arctanh(a*x)))/a","A"
485,0,0,21,0.807000," ","int((-a^2*x^2+1)^(1/2)/arctanh(a*x)^2,x)","\int \frac{\sqrt{-a^{2} x^{2}+1}}{\arctanh \left(a x \right)^{2}}\, dx"," ",0,"int((-a^2*x^2+1)^(1/2)/arctanh(a*x)^2,x)","F"
486,0,0,21,0.398000," ","int(1/(-a^2*x^2+1)^(1/2)/arctanh(a*x)^2,x)","\int \frac{1}{\sqrt{-a^{2} x^{2}+1}\, \arctanh \left(a x \right)^{2}}\, dx"," ",0,"int(1/(-a^2*x^2+1)^(1/2)/arctanh(a*x)^2,x)","F"
487,1,62,33,0.330000," ","int(1/(-a^2*x^2+1)^(3/2)/arctanh(a*x)^2,x)","\frac{\arctanh \left(a x \right) \Shi \left(\arctanh \left(a x \right)\right) x^{2} a^{2}-\Shi \left(\arctanh \left(a x \right)\right) \arctanh \left(a x \right)+\sqrt{-a^{2} x^{2}+1}}{a \arctanh \left(a x \right) \left(a^{2} x^{2}-1\right)}"," ",0,"1/a*(arctanh(a*x)*Shi(arctanh(a*x))*x^2*a^2-Shi(arctanh(a*x))*arctanh(a*x)+(-a^2*x^2+1)^(1/2))/arctanh(a*x)/(a^2*x^2-1)","A"
488,1,120,46,0.433000," ","int(1/(-a^2*x^2+1)^(5/2)/arctanh(a*x)^2,x)","\frac{3 \arctanh \left(a x \right) \Shi \left(\arctanh \left(a x \right)\right) x^{2} a^{2}+3 \arctanh \left(a x \right) \Shi \left(3 \arctanh \left(a x \right)\right) x^{2} a^{2}-\cosh \left(3 \arctanh \left(a x \right)\right) x^{2} a^{2}-3 \Shi \left(\arctanh \left(a x \right)\right) \arctanh \left(a x \right)-3 \Shi \left(3 \arctanh \left(a x \right)\right) \arctanh \left(a x \right)+3 \sqrt{-a^{2} x^{2}+1}+\cosh \left(3 \arctanh \left(a x \right)\right)}{4 a \arctanh \left(a x \right) \left(a^{2} x^{2}-1\right)}"," ",0,"1/4/a*(3*arctanh(a*x)*Shi(arctanh(a*x))*x^2*a^2+3*arctanh(a*x)*Shi(3*arctanh(a*x))*x^2*a^2-cosh(3*arctanh(a*x))*x^2*a^2-3*Shi(arctanh(a*x))*arctanh(a*x)-3*Shi(3*arctanh(a*x))*arctanh(a*x)+3*(-a^2*x^2+1)^(1/2)+cosh(3*arctanh(a*x)))/arctanh(a*x)/(a^2*x^2-1)","B"
489,1,176,58,0.531000," ","int(1/(-a^2*x^2+1)^(7/2)/arctanh(a*x)^2,x)","\frac{10 \arctanh \left(a x \right) \Shi \left(\arctanh \left(a x \right)\right) x^{2} a^{2}+15 \arctanh \left(a x \right) \Shi \left(3 \arctanh \left(a x \right)\right) x^{2} a^{2}+5 \arctanh \left(a x \right) \Shi \left(5 \arctanh \left(a x \right)\right) x^{2} a^{2}-5 \cosh \left(3 \arctanh \left(a x \right)\right) x^{2} a^{2}-\cosh \left(5 \arctanh \left(a x \right)\right) x^{2} a^{2}-10 \Shi \left(\arctanh \left(a x \right)\right) \arctanh \left(a x \right)-15 \Shi \left(3 \arctanh \left(a x \right)\right) \arctanh \left(a x \right)-5 \Shi \left(5 \arctanh \left(a x \right)\right) \arctanh \left(a x \right)+10 \sqrt{-a^{2} x^{2}+1}+5 \cosh \left(3 \arctanh \left(a x \right)\right)+\cosh \left(5 \arctanh \left(a x \right)\right)}{16 a \arctanh \left(a x \right) \left(a^{2} x^{2}-1\right)}"," ",0,"1/16/a*(10*arctanh(a*x)*Shi(arctanh(a*x))*x^2*a^2+15*arctanh(a*x)*Shi(3*arctanh(a*x))*x^2*a^2+5*arctanh(a*x)*Shi(5*arctanh(a*x))*x^2*a^2-5*cosh(3*arctanh(a*x))*x^2*a^2-cosh(5*arctanh(a*x))*x^2*a^2-10*Shi(arctanh(a*x))*arctanh(a*x)-15*Shi(3*arctanh(a*x))*arctanh(a*x)-5*Shi(5*arctanh(a*x))*arctanh(a*x)+10*(-a^2*x^2+1)^(1/2)+5*cosh(3*arctanh(a*x))+cosh(5*arctanh(a*x)))/arctanh(a*x)/(a^2*x^2-1)","B"
490,1,232,70,0.622000," ","int(1/(-a^2*x^2+1)^(9/2)/arctanh(a*x)^2,x)","\frac{35 \arctanh \left(a x \right) \Shi \left(\arctanh \left(a x \right)\right) x^{2} a^{2}+63 \arctanh \left(a x \right) \Shi \left(3 \arctanh \left(a x \right)\right) x^{2} a^{2}+35 \arctanh \left(a x \right) \Shi \left(5 \arctanh \left(a x \right)\right) x^{2} a^{2}+7 \arctanh \left(a x \right) \Shi \left(7 \arctanh \left(a x \right)\right) x^{2} a^{2}-21 \cosh \left(3 \arctanh \left(a x \right)\right) x^{2} a^{2}-7 \cosh \left(5 \arctanh \left(a x \right)\right) x^{2} a^{2}-\cosh \left(7 \arctanh \left(a x \right)\right) x^{2} a^{2}-35 \Shi \left(\arctanh \left(a x \right)\right) \arctanh \left(a x \right)-63 \Shi \left(3 \arctanh \left(a x \right)\right) \arctanh \left(a x \right)-35 \Shi \left(5 \arctanh \left(a x \right)\right) \arctanh \left(a x \right)-7 \Shi \left(7 \arctanh \left(a x \right)\right) \arctanh \left(a x \right)+35 \sqrt{-a^{2} x^{2}+1}+21 \cosh \left(3 \arctanh \left(a x \right)\right)+7 \cosh \left(5 \arctanh \left(a x \right)\right)+\cosh \left(7 \arctanh \left(a x \right)\right)}{64 a \arctanh \left(a x \right) \left(a^{2} x^{2}-1\right)}"," ",0,"1/64/a*(35*arctanh(a*x)*Shi(arctanh(a*x))*x^2*a^2+63*arctanh(a*x)*Shi(3*arctanh(a*x))*x^2*a^2+35*arctanh(a*x)*Shi(5*arctanh(a*x))*x^2*a^2+7*arctanh(a*x)*Shi(7*arctanh(a*x))*x^2*a^2-21*cosh(3*arctanh(a*x))*x^2*a^2-7*cosh(5*arctanh(a*x))*x^2*a^2-cosh(7*arctanh(a*x))*x^2*a^2-35*Shi(arctanh(a*x))*arctanh(a*x)-63*Shi(3*arctanh(a*x))*arctanh(a*x)-35*Shi(5*arctanh(a*x))*arctanh(a*x)-7*Shi(7*arctanh(a*x))*arctanh(a*x)+35*(-a^2*x^2+1)^(1/2)+21*cosh(3*arctanh(a*x))+7*cosh(5*arctanh(a*x))+cosh(7*arctanh(a*x)))/arctanh(a*x)/(a^2*x^2-1)","B"
491,0,0,21,0.918000," ","int((-a^2*x^2+1)^(1/2)/arctanh(a*x)^3,x)","\int \frac{\sqrt{-a^{2} x^{2}+1}}{\arctanh \left(a x \right)^{3}}\, dx"," ",0,"int((-a^2*x^2+1)^(1/2)/arctanh(a*x)^3,x)","F"
492,0,0,21,0.574000," ","int(1/(-a^2*x^2+1)^(1/2)/arctanh(a*x)^3,x)","\int \frac{1}{\sqrt{-a^{2} x^{2}+1}\, \arctanh \left(a x \right)^{3}}\, dx"," ",0,"int(1/(-a^2*x^2+1)^(1/2)/arctanh(a*x)^3,x)","F"
493,1,86,55,0.343000," ","int(1/(-a^2*x^2+1)^(3/2)/arctanh(a*x)^3,x)","\frac{\arctanh \left(a x \right)^{2} \Chi \left(\arctanh \left(a x \right)\right) x^{2} a^{2}+\sqrt{-a^{2} x^{2}+1}\, a x \arctanh \left(a x \right)-\Chi \left(\arctanh \left(a x \right)\right) \arctanh \left(a x \right)^{2}+\sqrt{-a^{2} x^{2}+1}}{2 a \arctanh \left(a x \right)^{2} \left(a^{2} x^{2}-1\right)}"," ",0,"1/2/a*(arctanh(a*x)^2*Chi(arctanh(a*x))*x^2*a^2+(-a^2*x^2+1)^(1/2)*a*x*arctanh(a*x)-Chi(arctanh(a*x))*arctanh(a*x)^2+(-a^2*x^2+1)^(1/2))/arctanh(a*x)^2/(a^2*x^2-1)","A"
494,1,180,67,0.465000," ","int(1/(-a^2*x^2+1)^(5/2)/arctanh(a*x)^3,x)","\frac{3 \arctanh \left(a x \right)^{2} \Chi \left(\arctanh \left(a x \right)\right) x^{2} a^{2}+9 \arctanh \left(a x \right)^{2} \Chi \left(3 \arctanh \left(a x \right)\right) x^{2} a^{2}-3 \arctanh \left(a x \right) \sinh \left(3 \arctanh \left(a x \right)\right) x^{2} a^{2}-\cosh \left(3 \arctanh \left(a x \right)\right) x^{2} a^{2}+3 \sqrt{-a^{2} x^{2}+1}\, a x \arctanh \left(a x \right)-3 \Chi \left(\arctanh \left(a x \right)\right) \arctanh \left(a x \right)^{2}-9 \Chi \left(3 \arctanh \left(a x \right)\right) \arctanh \left(a x \right)^{2}+3 \sinh \left(3 \arctanh \left(a x \right)\right) \arctanh \left(a x \right)+3 \sqrt{-a^{2} x^{2}+1}+\cosh \left(3 \arctanh \left(a x \right)\right)}{8 a \arctanh \left(a x \right)^{2} \left(a^{2} x^{2}-1\right)}"," ",0,"1/8/a*(3*arctanh(a*x)^2*Chi(arctanh(a*x))*x^2*a^2+9*arctanh(a*x)^2*Chi(3*arctanh(a*x))*x^2*a^2-3*arctanh(a*x)*sinh(3*arctanh(a*x))*x^2*a^2-cosh(3*arctanh(a*x))*x^2*a^2+3*(-a^2*x^2+1)^(1/2)*a*x*arctanh(a*x)-3*Chi(arctanh(a*x))*arctanh(a*x)^2-9*Chi(3*arctanh(a*x))*arctanh(a*x)^2+3*sinh(3*arctanh(a*x))*arctanh(a*x)+3*(-a^2*x^2+1)^(1/2)+cosh(3*arctanh(a*x)))/arctanh(a*x)^2/(a^2*x^2-1)","B"
495,1,272,79,0.561000," ","int(1/(-a^2*x^2+1)^(7/2)/arctanh(a*x)^3,x)","\frac{10 \arctanh \left(a x \right)^{2} \Chi \left(\arctanh \left(a x \right)\right) x^{2} a^{2}+45 \arctanh \left(a x \right)^{2} \Chi \left(3 \arctanh \left(a x \right)\right) x^{2} a^{2}+25 \arctanh \left(a x \right)^{2} \Chi \left(5 \arctanh \left(a x \right)\right) x^{2} a^{2}-15 \arctanh \left(a x \right) \sinh \left(3 \arctanh \left(a x \right)\right) x^{2} a^{2}-5 \arctanh \left(a x \right) \sinh \left(5 \arctanh \left(a x \right)\right) x^{2} a^{2}-5 \cosh \left(3 \arctanh \left(a x \right)\right) x^{2} a^{2}-\cosh \left(5 \arctanh \left(a x \right)\right) x^{2} a^{2}+10 \sqrt{-a^{2} x^{2}+1}\, a x \arctanh \left(a x \right)-10 \Chi \left(\arctanh \left(a x \right)\right) \arctanh \left(a x \right)^{2}-45 \Chi \left(3 \arctanh \left(a x \right)\right) \arctanh \left(a x \right)^{2}-25 \Chi \left(5 \arctanh \left(a x \right)\right) \arctanh \left(a x \right)^{2}+15 \sinh \left(3 \arctanh \left(a x \right)\right) \arctanh \left(a x \right)+5 \sinh \left(5 \arctanh \left(a x \right)\right) \arctanh \left(a x \right)+10 \sqrt{-a^{2} x^{2}+1}+5 \cosh \left(3 \arctanh \left(a x \right)\right)+\cosh \left(5 \arctanh \left(a x \right)\right)}{32 a \arctanh \left(a x \right)^{2} \left(a^{2} x^{2}-1\right)}"," ",0,"1/32/a*(10*arctanh(a*x)^2*Chi(arctanh(a*x))*x^2*a^2+45*arctanh(a*x)^2*Chi(3*arctanh(a*x))*x^2*a^2+25*arctanh(a*x)^2*Chi(5*arctanh(a*x))*x^2*a^2-15*arctanh(a*x)*sinh(3*arctanh(a*x))*x^2*a^2-5*arctanh(a*x)*sinh(5*arctanh(a*x))*x^2*a^2-5*cosh(3*arctanh(a*x))*x^2*a^2-cosh(5*arctanh(a*x))*x^2*a^2+10*(-a^2*x^2+1)^(1/2)*a*x*arctanh(a*x)-10*Chi(arctanh(a*x))*arctanh(a*x)^2-45*Chi(3*arctanh(a*x))*arctanh(a*x)^2-25*Chi(5*arctanh(a*x))*arctanh(a*x)^2+15*sinh(3*arctanh(a*x))*arctanh(a*x)+5*sinh(5*arctanh(a*x))*arctanh(a*x)+10*(-a^2*x^2+1)^(1/2)+5*cosh(3*arctanh(a*x))+cosh(5*arctanh(a*x)))/arctanh(a*x)^2/(a^2*x^2-1)","B"
496,1,364,91,0.683000," ","int(1/(-a^2*x^2+1)^(9/2)/arctanh(a*x)^3,x)","\frac{35 \arctanh \left(a x \right)^{2} \Chi \left(\arctanh \left(a x \right)\right) x^{2} a^{2}+189 \arctanh \left(a x \right)^{2} \Chi \left(3 \arctanh \left(a x \right)\right) x^{2} a^{2}+175 \arctanh \left(a x \right)^{2} \Chi \left(5 \arctanh \left(a x \right)\right) x^{2} a^{2}+49 \arctanh \left(a x \right)^{2} \Chi \left(7 \arctanh \left(a x \right)\right) x^{2} a^{2}-63 \arctanh \left(a x \right) \sinh \left(3 \arctanh \left(a x \right)\right) x^{2} a^{2}-35 \arctanh \left(a x \right) \sinh \left(5 \arctanh \left(a x \right)\right) x^{2} a^{2}-7 \arctanh \left(a x \right) \sinh \left(7 \arctanh \left(a x \right)\right) x^{2} a^{2}-21 \cosh \left(3 \arctanh \left(a x \right)\right) x^{2} a^{2}-7 \cosh \left(5 \arctanh \left(a x \right)\right) x^{2} a^{2}-\cosh \left(7 \arctanh \left(a x \right)\right) x^{2} a^{2}+35 \sqrt{-a^{2} x^{2}+1}\, a x \arctanh \left(a x \right)-35 \Chi \left(\arctanh \left(a x \right)\right) \arctanh \left(a x \right)^{2}-189 \Chi \left(3 \arctanh \left(a x \right)\right) \arctanh \left(a x \right)^{2}-175 \Chi \left(5 \arctanh \left(a x \right)\right) \arctanh \left(a x \right)^{2}-49 \Chi \left(7 \arctanh \left(a x \right)\right) \arctanh \left(a x \right)^{2}+63 \sinh \left(3 \arctanh \left(a x \right)\right) \arctanh \left(a x \right)+35 \sinh \left(5 \arctanh \left(a x \right)\right) \arctanh \left(a x \right)+7 \sinh \left(7 \arctanh \left(a x \right)\right) \arctanh \left(a x \right)+35 \sqrt{-a^{2} x^{2}+1}+21 \cosh \left(3 \arctanh \left(a x \right)\right)+7 \cosh \left(5 \arctanh \left(a x \right)\right)+\cosh \left(7 \arctanh \left(a x \right)\right)}{128 a \arctanh \left(a x \right)^{2} \left(a^{2} x^{2}-1\right)}"," ",0,"1/128/a*(35*arctanh(a*x)^2*Chi(arctanh(a*x))*x^2*a^2+189*arctanh(a*x)^2*Chi(3*arctanh(a*x))*x^2*a^2+175*arctanh(a*x)^2*Chi(5*arctanh(a*x))*x^2*a^2+49*arctanh(a*x)^2*Chi(7*arctanh(a*x))*x^2*a^2-63*arctanh(a*x)*sinh(3*arctanh(a*x))*x^2*a^2-35*arctanh(a*x)*sinh(5*arctanh(a*x))*x^2*a^2-7*arctanh(a*x)*sinh(7*arctanh(a*x))*x^2*a^2-21*cosh(3*arctanh(a*x))*x^2*a^2-7*cosh(5*arctanh(a*x))*x^2*a^2-cosh(7*arctanh(a*x))*x^2*a^2+35*(-a^2*x^2+1)^(1/2)*a*x*arctanh(a*x)-35*Chi(arctanh(a*x))*arctanh(a*x)^2-189*Chi(3*arctanh(a*x))*arctanh(a*x)^2-175*Chi(5*arctanh(a*x))*arctanh(a*x)^2-49*Chi(7*arctanh(a*x))*arctanh(a*x)^2+63*sinh(3*arctanh(a*x))*arctanh(a*x)+35*sinh(5*arctanh(a*x))*arctanh(a*x)+7*sinh(7*arctanh(a*x))*arctanh(a*x)+35*(-a^2*x^2+1)^(1/2)+21*cosh(3*arctanh(a*x))+7*cosh(5*arctanh(a*x))+cosh(7*arctanh(a*x)))/arctanh(a*x)^2/(a^2*x^2-1)","B"
497,1,1871,116,0.696000," ","int((e*x+d)*(a+b*arctanh(c*x))^2/(-c^2*x^2+1),x)","\frac{i b^{2} \arctanh \left(c x \right)^{2} \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{c^{2} x^{2}-1}\right) \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{\left(c^{2} x^{2}-1\right) \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}\right)^{2} \pi  d}{4 c}-\frac{i b^{2} \arctanh \left(c x \right)^{2} \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{\left(c^{2} x^{2}-1\right) \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}\right)^{2} \mathrm{csgn}\left(\frac{i}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right) \pi  d}{4 c}-\frac{i b^{2} \arctanh \left(c x \right)^{2} \mathrm{csgn}\left(\frac{i \left(c x +1\right)}{\sqrt{-c^{2} x^{2}+1}}\right)^{2} \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{c^{2} x^{2}-1}\right) \pi  d}{4 c}+\frac{i b^{2} \arctanh \left(c x \right)^{2} \mathrm{csgn}\left(\frac{i \left(c x +1\right)}{\sqrt{-c^{2} x^{2}+1}}\right)^{2} \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{c^{2} x^{2}-1}\right) \pi  e}{4 c^{2}}+\frac{i b^{2} \arctanh \left(c x \right)^{2} \mathrm{csgn}\left(\frac{i \left(c x +1\right)}{\sqrt{-c^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{c^{2} x^{2}-1}\right)^{2} \pi  e}{2 c^{2}}-\frac{i b^{2} \arctanh \left(c x \right)^{2} \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{c^{2} x^{2}-1}\right) \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{\left(c^{2} x^{2}-1\right) \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}\right)^{2} \pi  e}{4 c^{2}}+\frac{i b^{2} \arctanh \left(c x \right)^{2} \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{\left(c^{2} x^{2}-1\right) \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}\right)^{2} \mathrm{csgn}\left(\frac{i}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right) \pi  e}{4 c^{2}}-\frac{i b^{2} \arctanh \left(c x \right)^{2} \mathrm{csgn}\left(\frac{i \left(c x +1\right)}{\sqrt{-c^{2} x^{2}+1}}\right) \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{c^{2} x^{2}-1}\right)^{2} \pi  d}{2 c}-\frac{a b \ln \left(c x +1\right) \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) e}{2 c^{2}}+\frac{a b \ln \left(c x -1\right) \ln \left(\frac{1}{2}+\frac{c x}{2}\right) e}{2 c^{2}}+\frac{a b \ln \left(c x -1\right) \ln \left(\frac{1}{2}+\frac{c x}{2}\right) d}{2 c}+\frac{a b \ln \left(c x +1\right) \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) d}{2 c}-\frac{a b \ln \left(\frac{1}{2}+\frac{c x}{2}\right) \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) d}{2 c}+\frac{i b^{2} \arctanh \left(c x \right)^{2} \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{c^{2} x^{2}-1}\right) \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{\left(c^{2} x^{2}-1\right) \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}\right) \mathrm{csgn}\left(\frac{i}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right) \pi  d}{4 c}-\frac{i b^{2} \arctanh \left(c x \right)^{2} \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{c^{2} x^{2}-1}\right) \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{\left(c^{2} x^{2}-1\right) \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}\right) \mathrm{csgn}\left(\frac{i}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right) \pi  e}{4 c^{2}}-\frac{a^{2} \ln \left(c x -1\right) e}{2 c^{2}}-\frac{b^{2} \arctanh \left(c x \right)^{2} \ln \left(c x -1\right) d}{2 c}+\frac{b^{2} \arctanh \left(c x \right)^{2} \ln \left(c x +1\right) d}{2 c}-\frac{b^{2} \arctanh \left(c x \right)^{2} \ln \left(c x +1\right) e}{2 c^{2}}+\frac{b^{2} \arctanh \left(c x \right)^{2} \ln \left(\frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right) e}{c^{2}}+\frac{b^{2} e \arctanh \left(c x \right) \polylog \left(2, -\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}{c^{2}}-\frac{b^{2} \arctanh \left(c x \right)^{2} \ln \left(c x -1\right) e}{2 c^{2}}+\frac{a b \dilog \left(\frac{1}{2}+\frac{c x}{2}\right) e}{c^{2}}+\frac{b^{2} \arctanh \left(c x \right)^{2} \ln \left(2\right) e}{c^{2}}-\frac{b^{2} \arctanh \left(c x \right)^{2} \ln \left(\frac{c x +1}{\sqrt{-c^{2} x^{2}+1}}\right) d}{c}+\frac{a^{2} \ln \left(c x +1\right) d}{2 c}-\frac{a^{2} \ln \left(c x -1\right) d}{2 c}+\frac{a b \ln \left(\frac{1}{2}+\frac{c x}{2}\right) \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) e}{2 c^{2}}-\frac{a b \arctanh \left(c x \right) \ln \left(c x +1\right) e}{c^{2}}+\frac{a b \arctanh \left(c x \right) \ln \left(c x +1\right) d}{c}-\frac{a b \arctanh \left(c x \right) \ln \left(c x -1\right) d}{c}-\frac{a b \arctanh \left(c x \right) \ln \left(c x -1\right) e}{c^{2}}-\frac{a^{2} \ln \left(c x +1\right) e}{2 c^{2}}-\frac{b^{2} e \polylog \left(3, -\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}{2 c^{2}}+\frac{b^{2} d \arctanh \left(c x \right)^{3}}{3 c}-\frac{b^{2} e \arctanh \left(c x \right)^{3}}{3 c^{2}}+\frac{i b^{2} \arctanh \left(c x \right)^{2} \pi  e}{2 c^{2}}+\frac{i b^{2} \arctanh \left(c x \right)^{2} \pi  d}{2 c}-\frac{a b \ln \left(c x +1\right)^{2} d}{4 c}-\frac{a b \ln \left(c x -1\right)^{2} d}{4 c}-\frac{a b \ln \left(c x -1\right)^{2} e}{4 c^{2}}+\frac{a b \ln \left(c x +1\right)^{2} e}{4 c^{2}}-\frac{i b^{2} \arctanh \left(c x \right)^{2} \mathrm{csgn}\left(\frac{i}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right)^{2} \pi  d}{2 c}-\frac{i b^{2} \arctanh \left(c x \right)^{2} \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{c^{2} x^{2}-1}\right)^{3} \pi  d}{4 c}-\frac{i b^{2} \arctanh \left(c x \right)^{2} \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{\left(c^{2} x^{2}-1\right) \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}\right)^{3} \pi  d}{4 c}-\frac{i b^{2} \arctanh \left(c x \right)^{2} \mathrm{csgn}\left(\frac{i}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right)^{2} \pi  e}{2 c^{2}}+\frac{i b^{2} \arctanh \left(c x \right)^{2} \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{c^{2} x^{2}-1}\right)^{3} \pi  e}{4 c^{2}}+\frac{i b^{2} \arctanh \left(c x \right)^{2} \mathrm{csgn}\left(\frac{i \left(c x +1\right)^{2}}{\left(c^{2} x^{2}-1\right) \left(1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}\right)}\right)^{3} \pi  e}{4 c^{2}}+\frac{i b^{2} \arctanh \left(c x \right)^{2} \mathrm{csgn}\left(\frac{i}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right)^{3} \pi  e}{2 c^{2}}+\frac{i b^{2} \arctanh \left(c x \right)^{2} \mathrm{csgn}\left(\frac{i}{1+\frac{\left(c x +1\right)^{2}}{-c^{2} x^{2}+1}}\right)^{3} \pi  d}{2 c}"," ",0,"-1/2*I/c*b^2*arctanh(c*x)^2*csgn(I*(c*x+1)/(-c^2*x^2+1)^(1/2))*csgn(I*(c*x+1)^2/(c^2*x^2-1))^2*Pi*d+1/4*I/c*b^2*arctanh(c*x)^2*csgn(I*(c*x+1)^2/(c^2*x^2-1))*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^2*Pi*d-1/4*I/c*b^2*arctanh(c*x)^2*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^2*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))*Pi*d-1/4*I/c*b^2*arctanh(c*x)^2*csgn(I*(c*x+1)/(-c^2*x^2+1)^(1/2))^2*csgn(I*(c*x+1)^2/(c^2*x^2-1))*Pi*d+1/4*I/c^2*b^2*arctanh(c*x)^2*csgn(I*(c*x+1)/(-c^2*x^2+1)^(1/2))^2*csgn(I*(c*x+1)^2/(c^2*x^2-1))*Pi*e+1/2*I/c^2*b^2*arctanh(c*x)^2*csgn(I*(c*x+1)/(-c^2*x^2+1)^(1/2))*csgn(I*(c*x+1)^2/(c^2*x^2-1))^2*Pi*e-1/4*I/c^2*b^2*arctanh(c*x)^2*csgn(I*(c*x+1)^2/(c^2*x^2-1))*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^2*Pi*e+1/4*I/c^2*b^2*arctanh(c*x)^2*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^2*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))*Pi*e-1/c^2*a*b*arctanh(c*x)*ln(c*x+1)*e-1/2/c^2*a*b*ln(c*x+1)*ln(-1/2*c*x+1/2)*e+1/2/c^2*a*b*ln(c*x-1)*ln(1/2+1/2*c*x)*e+1/c*a*b*arctanh(c*x)*ln(c*x+1)*d+1/2/c*a*b*ln(c*x-1)*ln(1/2+1/2*c*x)*d+1/2/c*a*b*ln(c*x+1)*ln(-1/2*c*x+1/2)*d-1/2/c*a*b*ln(1/2+1/2*c*x)*ln(-1/2*c*x+1/2)*d-1/c*a*b*arctanh(c*x)*ln(c*x-1)*d+1/4*I/c*b^2*arctanh(c*x)^2*csgn(I*(c*x+1)^2/(c^2*x^2-1))*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))*Pi*d-1/4*I/c^2*b^2*arctanh(c*x)^2*csgn(I*(c*x+1)^2/(c^2*x^2-1))*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))*Pi*e-1/2/c^2*b^2*e*polylog(3,-(c*x+1)^2/(-c^2*x^2+1))-1/2/c^2*a^2*ln(c*x-1)*e+1/3/c*b^2*d*arctanh(c*x)^3+1/2/c*a^2*ln(c*x+1)*d-1/2/c*a^2*ln(c*x-1)*d+1/2*I/c^2*b^2*arctanh(c*x)^2*Pi*e+1/2*I/c*b^2*arctanh(c*x)^2*Pi*d-1/c^2*a*b*arctanh(c*x)*ln(c*x-1)*e+1/2/c^2*a*b*ln(1/2+1/2*c*x)*ln(-1/2*c*x+1/2)*e-1/3/c^2*b^2*e*arctanh(c*x)^3-1/2/c^2*a^2*ln(c*x+1)*e-1/4/c*a*b*ln(c*x+1)^2*d+1/4*I/c^2*b^2*arctanh(c*x)^2*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^3*Pi*e+1/2*I/c^2*b^2*arctanh(c*x)^2*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))^3*Pi*e+1/2*I/c*b^2*arctanh(c*x)^2*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))^3*Pi*d-1/2*I/c*b^2*arctanh(c*x)^2*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))^2*Pi*d-1/4*I/c*b^2*arctanh(c*x)^2*csgn(I*(c*x+1)^2/(c^2*x^2-1))^3*Pi*d-1/4*I/c*b^2*arctanh(c*x)^2*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1)))^3*Pi*d-1/2*I/c^2*b^2*arctanh(c*x)^2*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1)))^2*Pi*e+1/4*I/c^2*b^2*arctanh(c*x)^2*csgn(I*(c*x+1)^2/(c^2*x^2-1))^3*Pi*e-1/2/c*b^2*arctanh(c*x)^2*ln(c*x-1)*d+1/2/c*b^2*arctanh(c*x)^2*ln(c*x+1)*d-1/2/c^2*b^2*arctanh(c*x)^2*ln(c*x+1)*e-1/4/c*a*b*ln(c*x-1)^2*d-1/4/c^2*a*b*ln(c*x-1)^2*e+1/c^2*b^2*arctanh(c*x)^2*ln((c*x+1)/(-c^2*x^2+1)^(1/2))*e+1/c^2*b^2*e*arctanh(c*x)*polylog(2,-(c*x+1)^2/(-c^2*x^2+1))-1/2/c^2*b^2*arctanh(c*x)^2*ln(c*x-1)*e+1/c^2*a*b*dilog(1/2+1/2*c*x)*e+1/c^2*b^2*arctanh(c*x)^2*ln(2)*e+1/4/c^2*a*b*ln(c*x+1)^2*e-1/c*b^2*arctanh(c*x)^2*ln((c*x+1)/(-c^2*x^2+1)^(1/2))*d","C"
498,1,334,227,0.034000," ","int((d*x^2+c)^4*arctanh(a*x),x)","\frac{6 c^{2} d^{2} x^{5} \arctanh \left(a x \right)}{5}+\frac{4 c \,d^{3} x^{7} \arctanh \left(a x \right)}{7}+\frac{2 c \,d^{3} x^{6}}{21 a}+\frac{2 x^{2} c \,d^{3}}{7 a^{5}}+\frac{3 c^{2} d^{2} x^{4}}{10 a}+\frac{2 c^{3} d \,x^{2}}{3 a}+\frac{4 c^{3} d \,x^{3} \arctanh \left(a x \right)}{3}+\frac{x^{4} c \,d^{3}}{7 a^{3}}+\frac{2 \ln \left(a x -1\right) c^{3} d}{3 a^{3}}+\frac{3 c^{2} d^{2} x^{2}}{5 a^{3}}+\frac{2 \ln \left(a x -1\right) c \,d^{3}}{7 a^{7}}+\frac{2 \ln \left(a x +1\right) c^{3} d}{3 a^{3}}+\frac{3 \ln \left(a x +1\right) c^{2} d^{2}}{5 a^{5}}+\frac{2 \ln \left(a x +1\right) c \,d^{3}}{7 a^{7}}+\frac{3 \ln \left(a x -1\right) c^{2} d^{2}}{5 a^{5}}+c^{4} x \arctanh \left(a x \right)+\frac{d^{4} x^{9} \arctanh \left(a x \right)}{9}+\frac{x^{4} d^{4}}{36 a^{5}}+\frac{x^{6} d^{4}}{54 a^{3}}+\frac{\ln \left(a x +1\right) c^{4}}{2 a}+\frac{\ln \left(a x +1\right) d^{4}}{18 a^{9}}+\frac{\ln \left(a x -1\right) c^{4}}{2 a}+\frac{\ln \left(a x -1\right) d^{4}}{18 a^{9}}+\frac{x^{2} d^{4}}{18 a^{7}}+\frac{d^{4} x^{8}}{72 a}"," ",0,"2/21/a*c*d^3*x^6+2/7/a^5*x^2*c*d^3+3/10/a*c^2*d^2*x^4+2/3/a*c^3*d*x^2+1/7/a^3*x^4*c*d^3+2/3/a^3*ln(a*x-1)*c^3*d+3/5/a^3*c^2*d^2*x^2+2/7/a^7*ln(a*x-1)*c*d^3+2/3/a^3*ln(a*x+1)*c^3*d+3/5/a^5*ln(a*x+1)*c^2*d^2+2/7/a^7*ln(a*x+1)*c*d^3+3/5/a^5*ln(a*x-1)*c^2*d^2+1/36/a^5*x^4*d^4+1/54/a^3*x^6*d^4+1/2/a*ln(a*x+1)*c^4+1/18/a^9*ln(a*x+1)*d^4+1/2/a*ln(a*x-1)*c^4+1/18/a^9*ln(a*x-1)*d^4+1/18/a^7*x^2*d^4+c^4*x*arctanh(a*x)+1/72*d^4*x^8/a+1/9*d^4*x^9*arctanh(a*x)+4/3*c^3*d*x^3*arctanh(a*x)+6/5*c^2*d^2*x^5*arctanh(a*x)+4/7*c*d^3*x^7*arctanh(a*x)","A"
499,1,233,157,0.032000," ","int((d*x^2+c)^3*arctanh(a*x),x)","\frac{d^{3} x^{7} \arctanh \left(a x \right)}{7}+\frac{3 c \,d^{2} x^{5} \arctanh \left(a x \right)}{5}+c^{2} d \,x^{3} \arctanh \left(a x \right)+c^{3} x \arctanh \left(a x \right)+\frac{d^{3} x^{6}}{42 a}+\frac{3 c \,d^{2} x^{2}}{10 a^{3}}+\frac{x^{2} c^{2} d}{2 a}+\frac{3 c \,d^{2} x^{4}}{20 a}+\frac{\ln \left(a x +1\right) c^{3}}{2 a}+\frac{\ln \left(a x +1\right) c^{2} d}{2 a^{3}}+\frac{3 \ln \left(a x +1\right) c \,d^{2}}{10 a^{5}}+\frac{\ln \left(a x +1\right) d^{3}}{14 a^{7}}+\frac{d^{3} x^{2}}{14 a^{5}}+\frac{x^{4} d^{3}}{28 a^{3}}+\frac{\ln \left(a x -1\right) c^{3}}{2 a}+\frac{\ln \left(a x -1\right) c^{2} d}{2 a^{3}}+\frac{3 \ln \left(a x -1\right) c \,d^{2}}{10 a^{5}}+\frac{\ln \left(a x -1\right) d^{3}}{14 a^{7}}"," ",0,"1/7*d^3*x^7*arctanh(a*x)+3/5*c*d^2*x^5*arctanh(a*x)+c^2*d*x^3*arctanh(a*x)+c^3*x*arctanh(a*x)+1/42*d^3*x^6/a+3/10/a^3*c*d^2*x^2+1/2/a*x^2*c^2*d+3/20/a*c*d^2*x^4+1/2/a*ln(a*x+1)*c^3+1/2/a^3*ln(a*x+1)*c^2*d+3/10/a^5*ln(a*x+1)*c*d^2+1/14/a^7*ln(a*x+1)*d^3+1/14/a^5*d^3*x^2+1/28/a^3*x^4*d^3+1/2/a*ln(a*x-1)*c^3+1/2/a^3*ln(a*x-1)*c^2*d+3/10/a^5*ln(a*x-1)*c*d^2+1/14/a^7*ln(a*x-1)*d^3","A"
500,1,148,100,0.033000," ","int((d*x^2+c)^2*arctanh(a*x),x)","\frac{d^{2} x^{5} \arctanh \left(a x \right)}{5}+\frac{2 c d \,x^{3} \arctanh \left(a x \right)}{3}+c^{2} x \arctanh \left(a x \right)+\frac{d^{2} x^{4}}{20 a}+\frac{x^{2} c d}{3 a}+\frac{x^{2} d^{2}}{10 a^{3}}+\frac{\ln \left(a x -1\right) c^{2}}{2 a}+\frac{\ln \left(a x -1\right) c d}{3 a^{3}}+\frac{\ln \left(a x -1\right) d^{2}}{10 a^{5}}+\frac{\ln \left(a x +1\right) c^{2}}{2 a}+\frac{\ln \left(a x +1\right) c d}{3 a^{3}}+\frac{\ln \left(a x +1\right) d^{2}}{10 a^{5}}"," ",0,"1/5*d^2*x^5*arctanh(a*x)+2/3*c*d*x^3*arctanh(a*x)+c^2*x*arctanh(a*x)+1/20*d^2*x^4/a+1/3/a*x^2*c*d+1/10/a^3*x^2*d^2+1/2/a*ln(a*x-1)*c^2+1/3/a^3*ln(a*x-1)*c*d+1/10/a^5*ln(a*x-1)*d^2+1/2/a*ln(a*x+1)*c^2+1/3/a^3*ln(a*x+1)*c*d+1/10/a^5*ln(a*x+1)*d^2","A"
501,1,76,51,0.030000," ","int((d*x^2+c)*arctanh(a*x),x)","\frac{d \,x^{3} \arctanh \left(a x \right)}{3}+c x \arctanh \left(a x \right)+\frac{d \,x^{2}}{6 a}+\frac{\ln \left(a x -1\right) c}{2 a}+\frac{\ln \left(a x -1\right) d}{6 a^{3}}+\frac{\ln \left(a x +1\right) c}{2 a}+\frac{\ln \left(a x +1\right) d}{6 a^{3}}"," ",0,"1/3*d*x^3*arctanh(a*x)+c*x*arctanh(a*x)+1/6*d*x^2/a+1/2/a*ln(a*x-1)*c+1/6/a^3*ln(a*x-1)*d+1/2/a*ln(a*x+1)*c+1/6/a^3*ln(a*x+1)*d","A"
502,1,833,325,0.624000," ","int(arctanh(a*x)/(d*x^2+c),x)","\frac{a^{3} \ln \left(1-\frac{\left(a^{2} c +d \right) \left(a x +1\right)^{2}}{\left(-a^{2} x^{2}+1\right) \left(-a^{2} c -2 \sqrt{-a^{2} c d}+d \right)}\right) \arctanh \left(a x \right) \sqrt{-a^{2} c d}\, c}{2 d \left(a^{4} c^{2}+2 a^{2} c d +d^{2}\right)}+\frac{a \ln \left(1-\frac{\left(a^{2} c +d \right) \left(a x +1\right)^{2}}{\left(-a^{2} x^{2}+1\right) \left(-a^{2} c -2 \sqrt{-a^{2} c d}+d \right)}\right) \arctanh \left(a x \right) \sqrt{-a^{2} c d}}{a^{4} c^{2}+2 a^{2} c d +d^{2}}-\frac{a^{3} \arctanh \left(a x \right)^{2} \sqrt{-a^{2} c d}\, c}{2 d \left(a^{4} c^{2}+2 a^{2} c d +d^{2}\right)}-\frac{a \arctanh \left(a x \right)^{2} \sqrt{-a^{2} c d}}{a^{4} c^{2}+2 a^{2} c d +d^{2}}+\frac{a^{3} \polylog \left(2, \frac{\left(a^{2} c +d \right) \left(a x +1\right)^{2}}{\left(-a^{2} x^{2}+1\right) \left(-a^{2} c -2 \sqrt{-a^{2} c d}+d \right)}\right) \sqrt{-a^{2} c d}\, c}{4 d \left(a^{4} c^{2}+2 a^{2} c d +d^{2}\right)}+\frac{a \polylog \left(2, \frac{\left(a^{2} c +d \right) \left(a x +1\right)^{2}}{\left(-a^{2} x^{2}+1\right) \left(-a^{2} c -2 \sqrt{-a^{2} c d}+d \right)}\right) \sqrt{-a^{2} c d}}{2 a^{4} c^{2}+4 a^{2} c d +2 d^{2}}+\frac{\ln \left(1-\frac{\left(a^{2} c +d \right) \left(a x +1\right)^{2}}{\left(-a^{2} x^{2}+1\right) \left(-a^{2} c -2 \sqrt{-a^{2} c d}+d \right)}\right) \arctanh \left(a x \right) \sqrt{-a^{2} c d}\, d}{2 a c \left(a^{4} c^{2}+2 a^{2} c d +d^{2}\right)}-\frac{\arctanh \left(a x \right)^{2} \sqrt{-a^{2} c d}\, d}{2 a c \left(a^{4} c^{2}+2 a^{2} c d +d^{2}\right)}+\frac{\polylog \left(2, \frac{\left(a^{2} c +d \right) \left(a x +1\right)^{2}}{\left(-a^{2} x^{2}+1\right) \left(-a^{2} c -2 \sqrt{-a^{2} c d}+d \right)}\right) \sqrt{-a^{2} c d}\, d}{4 a c \left(a^{4} c^{2}+2 a^{2} c d +d^{2}\right)}-\frac{\sqrt{-a^{2} c d}\, \arctanh \left(a x \right) \ln \left(1-\frac{\left(a^{2} c +d \right) \left(a x +1\right)^{2}}{\left(-a^{2} x^{2}+1\right) \left(-a^{2} c +2 \sqrt{-a^{2} c d}+d \right)}\right)}{2 a c d}+\frac{\sqrt{-a^{2} c d}\, \arctanh \left(a x \right)^{2}}{2 a c d}-\frac{\sqrt{-a^{2} c d}\, \polylog \left(2, \frac{\left(a^{2} c +d \right) \left(a x +1\right)^{2}}{\left(-a^{2} x^{2}+1\right) \left(-a^{2} c +2 \sqrt{-a^{2} c d}+d \right)}\right)}{4 a c d}"," ",0,"1/2*a^3/d/(a^4*c^2+2*a^2*c*d+d^2)*ln(1-(a^2*c+d)*(a*x+1)^2/(-a^2*x^2+1)/(-a^2*c-2*(-a^2*c*d)^(1/2)+d))*arctanh(a*x)*(-a^2*c*d)^(1/2)*c+a/(a^4*c^2+2*a^2*c*d+d^2)*ln(1-(a^2*c+d)*(a*x+1)^2/(-a^2*x^2+1)/(-a^2*c-2*(-a^2*c*d)^(1/2)+d))*arctanh(a*x)*(-a^2*c*d)^(1/2)-1/2*a^3/d/(a^4*c^2+2*a^2*c*d+d^2)*arctanh(a*x)^2*(-a^2*c*d)^(1/2)*c-a/(a^4*c^2+2*a^2*c*d+d^2)*arctanh(a*x)^2*(-a^2*c*d)^(1/2)+1/4*a^3/d/(a^4*c^2+2*a^2*c*d+d^2)*polylog(2,(a^2*c+d)*(a*x+1)^2/(-a^2*x^2+1)/(-a^2*c-2*(-a^2*c*d)^(1/2)+d))*(-a^2*c*d)^(1/2)*c+1/2*a/(a^4*c^2+2*a^2*c*d+d^2)*polylog(2,(a^2*c+d)*(a*x+1)^2/(-a^2*x^2+1)/(-a^2*c-2*(-a^2*c*d)^(1/2)+d))*(-a^2*c*d)^(1/2)+1/2/a/c/(a^4*c^2+2*a^2*c*d+d^2)*ln(1-(a^2*c+d)*(a*x+1)^2/(-a^2*x^2+1)/(-a^2*c-2*(-a^2*c*d)^(1/2)+d))*arctanh(a*x)*(-a^2*c*d)^(1/2)*d-1/2/a/c/(a^4*c^2+2*a^2*c*d+d^2)*arctanh(a*x)^2*(-a^2*c*d)^(1/2)*d+1/4/a/c/(a^4*c^2+2*a^2*c*d+d^2)*polylog(2,(a^2*c+d)*(a*x+1)^2/(-a^2*x^2+1)/(-a^2*c-2*(-a^2*c*d)^(1/2)+d))*(-a^2*c*d)^(1/2)*d-1/2/a*(-a^2*c*d)^(1/2)/c/d*arctanh(a*x)*ln(1-(a^2*c+d)*(a*x+1)^2/(-a^2*x^2+1)/(-a^2*c+2*(-a^2*c*d)^(1/2)+d))+1/2/a*(-a^2*c*d)^(1/2)/c/d*arctanh(a*x)^2-1/4/a*(-a^2*c*d)^(1/2)/c/d*polylog(2,(a^2*c+d)*(a*x+1)^2/(-a^2*x^2+1)/(-a^2*c+2*(-a^2*c*d)^(1/2)+d))","B"
503,1,2346,430,1.352000," ","int(arctanh(a*x)/(d*x^2+c)^2,x)","-\frac{a^{4} \sqrt{c d}\, \arctan \left(\frac{a \sqrt{c d}}{d}\right)}{4 d \left(a^{2} c +d \right)^{2}}-\frac{a^{4} \sqrt{c d}\, \arctan \left(\frac{d^{2} x}{\left(a^{2} c +d \right) \sqrt{c d}}+\frac{d a c}{\left(a^{2} c +d \right) \sqrt{c d}}+\frac{a^{2} \sqrt{c d}\, x}{a^{2} c +d}-\frac{a \sqrt{c d}}{a^{2} c +d}\right)}{4 d \left(a^{2} c +d \right)^{2}}+\frac{a d \ln \left(\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{\left(a^{2} c +d \right)^{2} c}+\frac{\sqrt{c d}\, d \arctan \left(\frac{d^{2} x}{\left(a^{2} c +d \right) \sqrt{c d}}+\frac{d a c}{\left(a^{2} c +d \right) \sqrt{c d}}+\frac{a^{2} \sqrt{c d}\, x}{a^{2} c +d}-\frac{a \sqrt{c d}}{a^{2} c +d}\right)}{4 c^{2} \left(a^{2} c +d \right)^{2}}+\frac{3 a^{3} \ln \left(1-\frac{\left(a^{2} c +d \right) \left(a x +1\right)^{2}}{\left(-a^{2} x^{2}+1\right) \left(-a^{2} c -2 \sqrt{-a^{2} c d}+d \right)}\right) \arctanh \left(a x \right) \sqrt{-a^{2} c d}}{4 \left(a^{4} c^{2}+2 a^{2} c d +d^{2}\right) \left(a^{2} c +d \right)}+\frac{a \sqrt{-a^{2} c d}\, \arctanh \left(a x \right)^{2}}{4 c d \left(a^{2} c +d \right)}-\frac{a \sqrt{-a^{2} c d}\, \polylog \left(2, \frac{\left(a^{2} c +d \right) \left(a x +1\right)^{2}}{\left(-a^{2} x^{2}+1\right) \left(-a^{2} c +2 \sqrt{-a^{2} c d}+d \right)}\right)}{8 c d \left(a^{2} c +d \right)}-\frac{a^{3} \ln \left(\frac{a^{2} c \left(a x +1\right)^{4}}{\left(-a^{2} x^{2}+1\right)^{2}}+\frac{2 a^{2} c \left(a x +1\right)^{2}}{-a^{2} x^{2}+1}+\frac{d \left(a x +1\right)^{4}}{\left(-a^{2} x^{2}+1\right)^{2}}+a^{2} c -\frac{2 \left(a x +1\right)^{2} d}{-a^{2} x^{2}+1}+d \right)}{4 \left(a^{2} c +d \right)^{2}}+\frac{a^{2} \sqrt{c d}\, \arctan \left(\frac{a \sqrt{c d}}{d}\right)}{4 c d \left(a^{2} c +d \right)}+\frac{a^{2} \sqrt{c d}\, \arctan \left(\frac{d^{2} x}{\left(a^{2} c +d \right) \sqrt{c d}}+\frac{d a c}{\left(a^{2} c +d \right) \sqrt{c d}}+\frac{a^{2} \sqrt{c d}\, x}{a^{2} c +d}-\frac{a \sqrt{c d}}{a^{2} c +d}\right)}{4 c d \left(a^{2} c +d \right)}-\frac{\sqrt{-a^{2} c d}\, \arctanh \left(a x \right) \ln \left(1-\frac{\left(a^{2} c +d \right) \left(a x +1\right)^{2}}{\left(-a^{2} x^{2}+1\right) \left(-a^{2} c +2 \sqrt{-a^{2} c d}+d \right)}\right)}{4 a \left(a^{2} c +d \right) c^{2}}-\frac{\sqrt{c d}\, \arctan \left(\frac{a \sqrt{c d}}{d}\right)}{4 c^{2} \left(a^{2} c +d \right)}-\frac{a^{3} \arctanh \left(a x \right)}{2 \left(a^{2} c +d \right) \left(a^{2} d \,x^{2}+a^{2} c \right)}-\frac{\sqrt{c d}\, \arctan \left(\frac{d^{2} x}{\left(a^{2} c +d \right) \sqrt{c d}}+\frac{d a c}{\left(a^{2} c +d \right) \sqrt{c d}}+\frac{a^{2} \sqrt{c d}\, x}{a^{2} c +d}-\frac{a \sqrt{c d}}{a^{2} c +d}\right)}{4 c^{2} \left(a^{2} c +d \right)}+\frac{3 a d \ln \left(1-\frac{\left(a^{2} c +d \right) \left(a x +1\right)^{2}}{\left(-a^{2} x^{2}+1\right) \left(-a^{2} c -2 \sqrt{-a^{2} c d}+d \right)}\right) \arctanh \left(a x \right) \sqrt{-a^{2} c d}}{4 \left(a^{2} c +d \right) c \left(a^{4} c^{2}+2 a^{2} c d +d^{2}\right)}+\frac{a^{5} \ln \left(1-\frac{\left(a^{2} c +d \right) \left(a x +1\right)^{2}}{\left(-a^{2} x^{2}+1\right) \left(-a^{2} c -2 \sqrt{-a^{2} c d}+d \right)}\right) \arctanh \left(a x \right) \sqrt{-a^{2} c d}\, c}{4 d \left(a^{2} c +d \right) \left(a^{4} c^{2}+2 a^{2} c d +d^{2}\right)}+\frac{d^{2} \ln \left(1-\frac{\left(a^{2} c +d \right) \left(a x +1\right)^{2}}{\left(-a^{2} x^{2}+1\right) \left(-a^{2} c -2 \sqrt{-a^{2} c d}+d \right)}\right) \arctanh \left(a x \right) \sqrt{-a^{2} c d}}{4 a \left(a^{2} c +d \right) c^{2} \left(a^{4} c^{2}+2 a^{2} c d +d^{2}\right)}+\frac{a^{3} \ln \left(\frac{a x +1}{\sqrt{-a^{2} x^{2}+1}}\right)}{\left(a^{2} c +d \right)^{2}}-\frac{3 a d \arctanh \left(a x \right)^{2} \sqrt{-a^{2} c d}}{4 \left(a^{2} c +d \right) c \left(a^{4} c^{2}+2 a^{2} c d +d^{2}\right)}+\frac{a^{5} \polylog \left(2, \frac{\left(a^{2} c +d \right) \left(a x +1\right)^{2}}{\left(-a^{2} x^{2}+1\right) \left(-a^{2} c -2 \sqrt{-a^{2} c d}+d \right)}\right) \sqrt{-a^{2} c d}\, c}{8 d \left(a^{2} c +d \right) \left(a^{4} c^{2}+2 a^{2} c d +d^{2}\right)}-\frac{a d \ln \left(\frac{a^{2} c \left(a x +1\right)^{4}}{\left(-a^{2} x^{2}+1\right)^{2}}+\frac{2 a^{2} c \left(a x +1\right)^{2}}{-a^{2} x^{2}+1}+\frac{d \left(a x +1\right)^{4}}{\left(-a^{2} x^{2}+1\right)^{2}}+a^{2} c -\frac{2 \left(a x +1\right)^{2} d}{-a^{2} x^{2}+1}+d \right)}{4 \left(a^{2} c +d \right)^{2} c}+\frac{3 a d \polylog \left(2, \frac{\left(a^{2} c +d \right) \left(a x +1\right)^{2}}{\left(-a^{2} x^{2}+1\right) \left(-a^{2} c -2 \sqrt{-a^{2} c d}+d \right)}\right) \sqrt{-a^{2} c d}}{8 \left(a^{2} c +d \right) c \left(a^{4} c^{2}+2 a^{2} c d +d^{2}\right)}-\frac{a^{5} \arctanh \left(a x \right)^{2} \sqrt{-a^{2} c d}\, c}{4 d \left(a^{2} c +d \right) \left(a^{4} c^{2}+2 a^{2} c d +d^{2}\right)}-\frac{a \sqrt{-a^{2} c d}\, \arctanh \left(a x \right) \ln \left(1-\frac{\left(a^{2} c +d \right) \left(a x +1\right)^{2}}{\left(-a^{2} x^{2}+1\right) \left(-a^{2} c +2 \sqrt{-a^{2} c d}+d \right)}\right)}{4 c d \left(a^{2} c +d \right)}-\frac{a^{3} \arctanh \left(a x \right) d \,x^{2}}{2 c \left(a^{2} c +d \right) \left(a^{2} d \,x^{2}+a^{2} c \right)}+\frac{a^{2} \arctanh \left(a x \right) x d}{2 c \left(a^{2} c +d \right) \left(a^{2} d \,x^{2}+a^{2} c \right)}+\frac{d^{2} \polylog \left(2, \frac{\left(a^{2} c +d \right) \left(a x +1\right)^{2}}{\left(-a^{2} x^{2}+1\right) \left(-a^{2} c -2 \sqrt{-a^{2} c d}+d \right)}\right) \sqrt{-a^{2} c d}}{8 a \left(a^{2} c +d \right) c^{2} \left(a^{4} c^{2}+2 a^{2} c d +d^{2}\right)}-\frac{d^{2} \arctanh \left(a x \right)^{2} \sqrt{-a^{2} c d}}{4 a \left(a^{2} c +d \right) c^{2} \left(a^{4} c^{2}+2 a^{2} c d +d^{2}\right)}+\frac{\sqrt{c d}\, d \arctan \left(\frac{a \sqrt{c d}}{d}\right)}{4 c^{2} \left(a^{2} c +d \right)^{2}}+\frac{\sqrt{-a^{2} c d}\, \arctanh \left(a x \right)^{2}}{4 a \left(a^{2} c +d \right) c^{2}}-\frac{\sqrt{-a^{2} c d}\, \polylog \left(2, \frac{\left(a^{2} c +d \right) \left(a x +1\right)^{2}}{\left(-a^{2} x^{2}+1\right) \left(-a^{2} c +2 \sqrt{-a^{2} c d}+d \right)}\right)}{8 a \left(a^{2} c +d \right) c^{2}}+\frac{a^{4} \arctanh \left(a x \right) x}{2 \left(a^{2} c +d \right) \left(a^{2} d \,x^{2}+a^{2} c \right)}-\frac{3 a^{3} \arctanh \left(a x \right)^{2} \sqrt{-a^{2} c d}}{4 \left(a^{4} c^{2}+2 a^{2} c d +d^{2}\right) \left(a^{2} c +d \right)}+\frac{3 a^{3} \polylog \left(2, \frac{\left(a^{2} c +d \right) \left(a x +1\right)^{2}}{\left(-a^{2} x^{2}+1\right) \left(-a^{2} c -2 \sqrt{-a^{2} c d}+d \right)}\right) \sqrt{-a^{2} c d}}{8 \left(a^{2} c +d \right) \left(a^{4} c^{2}+2 a^{2} c d +d^{2}\right)}"," ",0,"-1/4*a^4*(c*d)^(1/2)/d/(a^2*c+d)^2*arctan(a/d*(c*d)^(1/2))-1/4*a^4*(c*d)^(1/2)/d/(a^2*c+d)^2*arctan(1/(a^2*c+d)*d^2/(c*d)^(1/2)*x+1/(a^2*c+d)*d/(c*d)^(1/2)*a*c+a^2/(a^2*c+d)*(c*d)^(1/2)*x-a/(a^2*c+d)*(c*d)^(1/2))+a/(a^2*c+d)^2/c*d*ln((a*x+1)/(-a^2*x^2+1)^(1/2))+1/4*(c*d)^(1/2)/c^2*d/(a^2*c+d)^2*arctan(1/(a^2*c+d)*d^2/(c*d)^(1/2)*x+1/(a^2*c+d)*d/(c*d)^(1/2)*a*c+a^2/(a^2*c+d)*(c*d)^(1/2)*x-a/(a^2*c+d)*(c*d)^(1/2))-1/4*a^3/(a^2*c+d)^2*ln(a^2*c*(a*x+1)^4/(-a^2*x^2+1)^2+2*a^2*c*(a*x+1)^2/(-a^2*x^2+1)+d*(a*x+1)^4/(-a^2*x^2+1)^2+a^2*c-2*(a*x+1)^2/(-a^2*x^2+1)*d+d)+1/4*a^2*(c*d)^(1/2)/c/d/(a^2*c+d)*arctan(a/d*(c*d)^(1/2))-1/4/a*(-a^2*c*d)^(1/2)/(a^2*c+d)/c^2*arctanh(a*x)*ln(1-(a^2*c+d)*(a*x+1)^2/(-a^2*x^2+1)/(-a^2*c+2*(-a^2*c*d)^(1/2)+d))+3/4*a^3/(a^4*c^2+2*a^2*c*d+d^2)/(a^2*c+d)*ln(1-(a^2*c+d)*(a*x+1)^2/(-a^2*x^2+1)/(-a^2*c-2*(-a^2*c*d)^(1/2)+d))*arctanh(a*x)*(-a^2*c*d)^(1/2)+1/4*a*(-a^2*c*d)^(1/2)/c/d/(a^2*c+d)*arctanh(a*x)^2-1/8*a*(-a^2*c*d)^(1/2)/c/d/(a^2*c+d)*polylog(2,(a^2*c+d)*(a*x+1)^2/(-a^2*x^2+1)/(-a^2*c+2*(-a^2*c*d)^(1/2)+d))+1/4*a^2*(c*d)^(1/2)/c/d/(a^2*c+d)*arctan(1/(a^2*c+d)*d^2/(c*d)^(1/2)*x+1/(a^2*c+d)*d/(c*d)^(1/2)*a*c+a^2/(a^2*c+d)*(c*d)^(1/2)*x-a/(a^2*c+d)*(c*d)^(1/2))-1/4*(c*d)^(1/2)/c^2/(a^2*c+d)*arctan(a/d*(c*d)^(1/2))-1/2*a^3*arctanh(a*x)/(a^2*c+d)/(a^2*d*x^2+a^2*c)-1/4*(c*d)^(1/2)/c^2/(a^2*c+d)*arctan(1/(a^2*c+d)*d^2/(c*d)^(1/2)*x+1/(a^2*c+d)*d/(c*d)^(1/2)*a*c+a^2/(a^2*c+d)*(c*d)^(1/2)*x-a/(a^2*c+d)*(c*d)^(1/2))+3/4*a/(a^2*c+d)/c/(a^4*c^2+2*a^2*c*d+d^2)*d*ln(1-(a^2*c+d)*(a*x+1)^2/(-a^2*x^2+1)/(-a^2*c-2*(-a^2*c*d)^(1/2)+d))*arctanh(a*x)*(-a^2*c*d)^(1/2)+1/4*a^5/d/(a^2*c+d)/(a^4*c^2+2*a^2*c*d+d^2)*ln(1-(a^2*c+d)*(a*x+1)^2/(-a^2*x^2+1)/(-a^2*c-2*(-a^2*c*d)^(1/2)+d))*arctanh(a*x)*(-a^2*c*d)^(1/2)*c+1/4/a/(a^2*c+d)/c^2*d^2/(a^4*c^2+2*a^2*c*d+d^2)*ln(1-(a^2*c+d)*(a*x+1)^2/(-a^2*x^2+1)/(-a^2*c-2*(-a^2*c*d)^(1/2)+d))*arctanh(a*x)*(-a^2*c*d)^(1/2)+a^3/(a^2*c+d)^2*ln((a*x+1)/(-a^2*x^2+1)^(1/2))-3/4*a/(a^2*c+d)/c*d/(a^4*c^2+2*a^2*c*d+d^2)*arctanh(a*x)^2*(-a^2*c*d)^(1/2)+1/8*a^5/d/(a^2*c+d)/(a^4*c^2+2*a^2*c*d+d^2)*polylog(2,(a^2*c+d)*(a*x+1)^2/(-a^2*x^2+1)/(-a^2*c-2*(-a^2*c*d)^(1/2)+d))*(-a^2*c*d)^(1/2)*c-1/4*a*(-a^2*c*d)^(1/2)/c/d/(a^2*c+d)*arctanh(a*x)*ln(1-(a^2*c+d)*(a*x+1)^2/(-a^2*x^2+1)/(-a^2*c+2*(-a^2*c*d)^(1/2)+d))-1/2*a^3*arctanh(a*x)/c/(a^2*c+d)/(a^2*d*x^2+a^2*c)*d*x^2+1/2*a^2*arctanh(a*x)/c/(a^2*c+d)/(a^2*d*x^2+a^2*c)*x*d+1/8/a/(a^2*c+d)/c^2*d^2/(a^4*c^2+2*a^2*c*d+d^2)*polylog(2,(a^2*c+d)*(a*x+1)^2/(-a^2*x^2+1)/(-a^2*c-2*(-a^2*c*d)^(1/2)+d))*(-a^2*c*d)^(1/2)-1/4/a/(a^2*c+d)/c^2*d^2/(a^4*c^2+2*a^2*c*d+d^2)*arctanh(a*x)^2*(-a^2*c*d)^(1/2)+3/8*a/(a^2*c+d)/c*d/(a^4*c^2+2*a^2*c*d+d^2)*polylog(2,(a^2*c+d)*(a*x+1)^2/(-a^2*x^2+1)/(-a^2*c-2*(-a^2*c*d)^(1/2)+d))*(-a^2*c*d)^(1/2)-1/4*a/(a^2*c+d)^2/c*d*ln(a^2*c*(a*x+1)^4/(-a^2*x^2+1)^2+2*a^2*c*(a*x+1)^2/(-a^2*x^2+1)+d*(a*x+1)^4/(-a^2*x^2+1)^2+a^2*c-2*(a*x+1)^2/(-a^2*x^2+1)*d+d)-1/4*a^5/d/(a^2*c+d)/(a^4*c^2+2*a^2*c*d+d^2)*arctanh(a*x)^2*(-a^2*c*d)^(1/2)*c+1/4*(c*d)^(1/2)/c^2*d/(a^2*c+d)^2*arctan(a/d*(c*d)^(1/2))+1/4/a*(-a^2*c*d)^(1/2)/(a^2*c+d)/c^2*arctanh(a*x)^2-1/8/a*(-a^2*c*d)^(1/2)/(a^2*c+d)/c^2*polylog(2,(a^2*c+d)*(a*x+1)^2/(-a^2*x^2+1)/(-a^2*c+2*(-a^2*c*d)^(1/2)+d))+1/2*a^4*arctanh(a*x)/(a^2*c+d)/(a^2*d*x^2+a^2*c)*x-3/4*a^3/(a^4*c^2+2*a^2*c*d+d^2)/(a^2*c+d)*arctanh(a*x)^2*(-a^2*c*d)^(1/2)+3/8*a^3/(a^2*c+d)/(a^4*c^2+2*a^2*c*d+d^2)*polylog(2,(a^2*c+d)*(a*x+1)^2/(-a^2*x^2+1)/(-a^2*c-2*(-a^2*c*d)^(1/2)+d))*(-a^2*c*d)^(1/2)","B"
504,1,4311,493,1.406000," ","int(arctanh(a*x)/(d*x^2+c)^3,x)","\text{output too large to display}"," ",0,"1/8*a^5/(a^4*c^2+2*a^2*c*d+d^2)/(a^2*d*x^2+a^2*c)^2*d+5/4*a^5/(a^4*c^2+2*a^2*c*d+d^2)/(a^2*c+d)*ln((a*x+1)/(-a^2*x^2+1)^(1/2))+3/8*a^5/(a^4*c^2+2*a^2*c*d+d^2)^2*polylog(2,(a^2*c+d)*(a*x+1)^2/(-a^2*x^2+1)/(-a^2*c-2*(-a^2*c*d)^(1/2)+d))*(-a^2*c*d)^(1/2)-3/4*a^5/(a^4*c^2+2*a^2*c*d+d^2)^2*arctanh(a*x)^2*(-a^2*c*d)^(1/2)-5/16*a^5/(a^4*c^2+2*a^2*c*d+d^2)/(a^2*c+d)*ln(a^2*c*(a*x+1)^4/(-a^2*x^2+1)^2+2*a^2*c*(a*x+1)^2/(-a^2*x^2+1)+d*(a*x+1)^4/(-a^2*x^2+1)^2+a^2*c-2*(a*x+1)^2/(-a^2*x^2+1)*d+d)+5/16*a^4*(c*d)^(1/2)/c/d/(a^4*c^2+2*a^2*c*d+d^2)*arctan(a/d*(c*d)^(1/2))-3/16*a^4*(c*d)^(1/2)/c/(a^2*c+d)/(a^4*c^2+2*a^2*c*d+d^2)*arctan(a/d*(c*d)^(1/2))-5/16*a^6*(c*d)^(1/2)/d/(a^2*c+d)/(a^4*c^2+2*a^2*c*d+d^2)*arctan(a/d*(c*d)^(1/2))+3/16*(c*d)^(1/2)/c^3*d^2/(a^2*c+d)/(a^4*c^2+2*a^2*c*d+d^2)*arctan(a/d*(c*d)^(1/2))-1/8*a^7/(a^4*c^2+2*a^2*c*d+d^2)/(a^2*d*x^2+a^2*c)^2/c*d^2*x^4+1/8*a^5/(a^4*c^2+2*a^2*c*d+d^2)/(a^2*d*x^2+a^2*c)^2/c*d^2*x^2+9/16*a^3/c/(a^4*c^2+2*a^2*c*d+d^2)^2*d*polylog(2,(a^2*c+d)*(a*x+1)^2/(-a^2*x^2+1)/(-a^2*c-2*(-a^2*c*d)^(1/2)+d))*(-a^2*c*d)^(1/2)+5/16*a^4*(c*d)^(1/2)/c/d/(a^4*c^2+2*a^2*c*d+d^2)*arctan(1/(a^2*c+d)*d^2/(c*d)^(1/2)*x+1/(a^2*c+d)*d/(c*d)^(1/2)*a*c+a^2/(a^2*c+d)*(c*d)^(1/2)*x-a/(a^2*c+d)*(c*d)^(1/2))-3/4*a/(a^4*c^2+2*a^2*c*d+d^2)^2/c^2*d^2*arctanh(a*x)^2*(-a^2*c*d)^(1/2)-3/16*a/c^2/(a^4*c^2+2*a^2*c*d+d^2)*d^2/(a^2*c+d)*ln(a^2*c*(a*x+1)^4/(-a^2*x^2+1)^2+2*a^2*c*(a*x+1)^2/(-a^2*x^2+1)+d*(a*x+1)^4/(-a^2*x^2+1)^2+a^2*c-2*(a*x+1)^2/(-a^2*x^2+1)*d+d)-1/2*a^3/c/(a^4*c^2+2*a^2*c*d+d^2)*d/(a^2*c+d)*ln(a^2*c*(a*x+1)^4/(-a^2*x^2+1)^2+2*a^2*c*(a*x+1)^2/(-a^2*x^2+1)+d*(a*x+1)^4/(-a^2*x^2+1)^2+a^2*c-2*(a*x+1)^2/(-a^2*x^2+1)*d+d)+3/4*a/c^2/(a^4*c^2+2*a^2*c*d+d^2)*d^2/(a^2*c+d)*ln((a*x+1)/(-a^2*x^2+1)^(1/2))-3/16*a^4*(c*d)^(1/2)/c/(a^2*c+d)/(a^4*c^2+2*a^2*c*d+d^2)*arctan(1/(a^2*c+d)*d^2/(c*d)^(1/2)*x+1/(a^2*c+d)*d/(c*d)^(1/2)*a*c+a^2/(a^2*c+d)*(c*d)^(1/2)*x-a/(a^2*c+d)*(c*d)^(1/2))+5/8*a^8/(a^4*c^2+2*a^2*c*d+d^2)/(a^2*d*x^2+a^2*c)^2*c*arctanh(a*x)*x-3/8*a*(-a^2*c*d)^(1/2)/c^2/(a^4*c^2+2*a^2*c*d+d^2)*arctanh(a*x)*ln(1-(a^2*c+d)*(a*x+1)^2/(-a^2*x^2+1)/(-a^2*c+2*(-a^2*c*d)^(1/2)+d))+5/4*a^6/(a^4*c^2+2*a^2*c*d+d^2)/(a^2*d*x^2+a^2*c)^2*arctanh(a*x)*x*d+3/8*a^8/(a^4*c^2+2*a^2*c*d+d^2)/(a^2*d*x^2+a^2*c)^2*arctanh(a*x)*x^3*d-5/4*a^7/(a^4*c^2+2*a^2*c*d+d^2)/(a^2*d*x^2+a^2*c)^2*arctanh(a*x)*x^2*d-3/16/a/c^3*d^3/(a^4*c^2+2*a^2*c*d+d^2)^2*arctanh(a*x)^2*(-a^2*c*d)^(1/2)-3/32/a*(-a^2*c*d)^(1/2)/c^3*d/(a^4*c^2+2*a^2*c*d+d^2)*polylog(2,(a^2*c+d)*(a*x+1)^2/(-a^2*x^2+1)/(-a^2*c+2*(-a^2*c*d)^(1/2)+d))+3/16/a*(-a^2*c*d)^(1/2)/c^3*d/(a^4*c^2+2*a^2*c*d+d^2)*arctanh(a*x)^2+3/32/a/c^3*d^3/(a^4*c^2+2*a^2*c*d+d^2)^2*polylog(2,(a^2*c+d)*(a*x+1)^2/(-a^2*x^2+1)/(-a^2*c-2*(-a^2*c*d)^(1/2)+d))*(-a^2*c*d)^(1/2)-3/16*a^7/d/(a^4*c^2+2*a^2*c*d+d^2)^2*arctanh(a*x)^2*(-a^2*c*d)^(1/2)*c-9/8*a^3/c/(a^4*c^2+2*a^2*c*d+d^2)^2*d*arctanh(a*x)^2*(-a^2*c*d)^(1/2)-3/32*a^3*(-a^2*c*d)^(1/2)/c/d/(a^4*c^2+2*a^2*c*d+d^2)*polylog(2,(a^2*c+d)*(a*x+1)^2/(-a^2*x^2+1)/(-a^2*c+2*(-a^2*c*d)^(1/2)+d))+3/16*a^3*(-a^2*c*d)^(1/2)/c/d/(a^4*c^2+2*a^2*c*d+d^2)*arctanh(a*x)^2+3/32*a^7/d/(a^4*c^2+2*a^2*c*d+d^2)^2*polylog(2,(a^2*c+d)*(a*x+1)^2/(-a^2*x^2+1)/(-a^2*c-2*(-a^2*c*d)^(1/2)+d))*(-a^2*c*d)^(1/2)*c+2*a^3/c/(a^4*c^2+2*a^2*c*d+d^2)*d/(a^2*c+d)*ln((a*x+1)/(-a^2*x^2+1)^(1/2))-5/16*a^6*(c*d)^(1/2)/d/(a^2*c+d)/(a^4*c^2+2*a^2*c*d+d^2)*arctan(1/(a^2*c+d)*d^2/(c*d)^(1/2)*x+1/(a^2*c+d)*d/(c*d)^(1/2)*a*c+a^2/(a^2*c+d)*(c*d)^(1/2)*x-a/(a^2*c+d)*(c*d)^(1/2))+3/8*a/(a^4*c^2+2*a^2*c*d+d^2)^2/c^2*d^2*polylog(2,(a^2*c+d)*(a*x+1)^2/(-a^2*x^2+1)/(-a^2*c-2*(-a^2*c*d)^(1/2)+d))*(-a^2*c*d)^(1/2)+3/16*(c*d)^(1/2)/c^3*d^2/(a^2*c+d)/(a^4*c^2+2*a^2*c*d+d^2)*arctan(1/(a^2*c+d)*d^2/(c*d)^(1/2)*x+1/(a^2*c+d)*d/(c*d)^(1/2)*a*c+a^2/(a^2*c+d)*(c*d)^(1/2)*x-a/(a^2*c+d)*(c*d)^(1/2))-5/8*a^7/(a^4*c^2+2*a^2*c*d+d^2)/(a^2*d*x^2+a^2*c)^2*c*arctanh(a*x)-1/8*a^2*(c*d)^(1/2)/c^2/(a^4*c^2+2*a^2*c*d+d^2)*arctan(1/(a^2*c+d)*d^2/(c*d)^(1/2)*x+1/(a^2*c+d)*d/(c*d)^(1/2)*a*c+a^2/(a^2*c+d)*(c*d)^(1/2)*x-a/(a^2*c+d)*(c*d)^(1/2))-1/8*a^7/(a^4*c^2+2*a^2*c*d+d^2)/(a^2*d*x^2+a^2*c)^2*d*x^2+5/16*a^2*(c*d)^(1/2)/c^2*d/(a^2*c+d)/(a^4*c^2+2*a^2*c*d+d^2)*arctan(1/(a^2*c+d)*d^2/(c*d)^(1/2)*x+1/(a^2*c+d)*d/(c*d)^(1/2)*a*c+a^2/(a^2*c+d)*(c*d)^(1/2)*x-a/(a^2*c+d)*(c*d)^(1/2))-3/4*a^5/(a^4*c^2+2*a^2*c*d+d^2)/(a^2*d*x^2+a^2*c)^2/c*arctanh(a*x)*x^2*d^2+5/8*a^4/(a^4*c^2+2*a^2*c*d+d^2)/(a^2*d*x^2+a^2*c)^2/c*arctanh(a*x)*x*d^2+3/4*a/c^2*d^2/(a^4*c^2+2*a^2*c*d+d^2)^2*ln(1-(a^2*c+d)*(a*x+1)^2/(-a^2*x^2+1)/(-a^2*c-2*(-a^2*c*d)^(1/2)+d))*arctanh(a*x)*(-a^2*c*d)^(1/2)+3/16*a^7/d/(a^4*c^2+2*a^2*c*d+d^2)^2*ln(1-(a^2*c+d)*(a*x+1)^2/(-a^2*x^2+1)/(-a^2*c-2*(-a^2*c*d)^(1/2)+d))*arctanh(a*x)*(-a^2*c*d)^(1/2)*c-3/8*a^5/(a^4*c^2+2*a^2*c*d+d^2)/(a^2*d*x^2+a^2*c)^2/c^2*arctanh(a*x)*x^4*d^3+3/4*a^6/(a^4*c^2+2*a^2*c*d+d^2)/(a^2*d*x^2+a^2*c)^2/c*arctanh(a*x)*x^3*d^2-3/16*a^3*(-a^2*c*d)^(1/2)/c/d/(a^4*c^2+2*a^2*c*d+d^2)*arctanh(a*x)*ln(1-(a^2*c+d)*(a*x+1)^2/(-a^2*x^2+1)/(-a^2*c+2*(-a^2*c*d)^(1/2)+d))+3/8*a^4/(a^4*c^2+2*a^2*c*d+d^2)/(a^2*d*x^2+a^2*c)^2/c^2*arctanh(a*x)*x^3*d^3+3/16/a/c^3*d^3/(a^4*c^2+2*a^2*c*d+d^2)^2*ln(1-(a^2*c+d)*(a*x+1)^2/(-a^2*x^2+1)/(-a^2*c-2*(-a^2*c*d)^(1/2)+d))*arctanh(a*x)*(-a^2*c*d)^(1/2)-3/16/a*(-a^2*c*d)^(1/2)/c^3*d/(a^4*c^2+2*a^2*c*d+d^2)*arctanh(a*x)*ln(1-(a^2*c+d)*(a*x+1)^2/(-a^2*x^2+1)/(-a^2*c+2*(-a^2*c*d)^(1/2)+d))+9/8*a^3/c/(a^4*c^2+2*a^2*c*d+d^2)^2*ln(1-(a^2*c+d)*(a*x+1)^2/(-a^2*x^2+1)/(-a^2*c-2*(-a^2*c*d)^(1/2)+d))*arctanh(a*x)*(-a^2*c*d)^(1/2)*d-5/8*a^7/(a^4*c^2+2*a^2*c*d+d^2)/(a^2*d*x^2+a^2*c)^2/c*arctanh(a*x)*x^4*d^2+5/16*a^2*(c*d)^(1/2)/c^2*d/(a^2*c+d)/(a^4*c^2+2*a^2*c*d+d^2)*arctan(a/d*(c*d)^(1/2))-3/16*(c*d)^(1/2)/c^3*d/(a^4*c^2+2*a^2*c*d+d^2)*arctan(a/d*(c*d)^(1/2))-1/8*a^2*(c*d)^(1/2)/c^2/(a^4*c^2+2*a^2*c*d+d^2)*arctan(a/d*(c*d)^(1/2))-3/16*(c*d)^(1/2)/c^3*d/(a^4*c^2+2*a^2*c*d+d^2)*arctan(1/(a^2*c+d)*d^2/(c*d)^(1/2)*x+1/(a^2*c+d)*d/(c*d)^(1/2)*a*c+a^2/(a^2*c+d)*(c*d)^(1/2)*x-a/(a^2*c+d)*(c*d)^(1/2))+3/8*a*(-a^2*c*d)^(1/2)/c^2/(a^4*c^2+2*a^2*c*d+d^2)*arctanh(a*x)^2-3/16*a*(-a^2*c*d)^(1/2)/c^2/(a^4*c^2+2*a^2*c*d+d^2)*polylog(2,(a^2*c+d)*(a*x+1)^2/(-a^2*x^2+1)/(-a^2*c+2*(-a^2*c*d)^(1/2)+d))+3/4*a^5/(a^4*c^2+2*a^2*c*d+d^2)^2*ln(1-(a^2*c+d)*(a*x+1)^2/(-a^2*x^2+1)/(-a^2*c-2*(-a^2*c*d)^(1/2)+d))*arctanh(a*x)*(-a^2*c*d)^(1/2)-3/8*a^5/(a^4*c^2+2*a^2*c*d+d^2)/(a^2*d*x^2+a^2*c)^2*d*arctanh(a*x)","B"
505,1,19,15,0.060000," ","int(1/(-a*x^2+a)/(b-2*b*arctanh(x)),x)","-\frac{\ln \left(2 b \arctanh \left(x \right)-b \right)}{2 a b}"," ",0,"-1/2/a*ln(2*b*arctanh(x)-b)/b","A"
506,1,176,155,0.063000," ","int(arctanh(b*x)/(-x^2+1),x)","\frac{\arctanh \left(b x \right) \ln \left(b x +b \right)}{2}-\frac{\arctanh \left(b x \right) \ln \left(b x -b \right)}{2}+\frac{\dilog \left(\frac{b x -1}{-b -1}\right)}{4}+\frac{\ln \left(b x +b \right) \ln \left(\frac{b x -1}{-b -1}\right)}{4}-\frac{\dilog \left(\frac{b x +1}{1-b}\right)}{4}-\frac{\ln \left(b x +b \right) \ln \left(\frac{b x +1}{1-b}\right)}{4}-\frac{\dilog \left(\frac{b x -1}{-1+b}\right)}{4}-\frac{\ln \left(b x -b \right) \ln \left(\frac{b x -1}{-1+b}\right)}{4}+\frac{\dilog \left(\frac{b x +1}{1+b}\right)}{4}+\frac{\ln \left(b x -b \right) \ln \left(\frac{b x +1}{1+b}\right)}{4}"," ",0,"1/2*arctanh(b*x)*ln(b*x+b)-1/2*arctanh(b*x)*ln(b*x-b)+1/4*dilog((b*x-1)/(-b-1))+1/4*ln(b*x+b)*ln((b*x-1)/(-b-1))-1/4*dilog((b*x+1)/(1-b))-1/4*ln(b*x+b)*ln((b*x+1)/(1-b))-1/4*dilog((b*x-1)/(-1+b))-1/4*ln(b*x-b)*ln((b*x-1)/(-1+b))+1/4*dilog((b*x+1)/(1+b))+1/4*ln(b*x-b)*ln((b*x+1)/(1+b))","A"
507,1,196,187,0.084000," ","int(arctanh(b*x+a)/(-x^2+1),x)","\frac{\arctanh \left(b x +a \right) \ln \left(b x +b \right)}{2}-\frac{\arctanh \left(b x +a \right) \ln \left(b x -b \right)}{2}+\frac{\dilog \left(\frac{b x +a -1}{-b -1+a}\right)}{4}+\frac{\ln \left(b x +b \right) \ln \left(\frac{b x +a -1}{-b -1+a}\right)}{4}-\frac{\dilog \left(\frac{b x +a +1}{1+a -b}\right)}{4}-\frac{\ln \left(b x +b \right) \ln \left(\frac{b x +a +1}{1+a -b}\right)}{4}+\frac{\dilog \left(\frac{b x +a +1}{1+a +b}\right)}{4}+\frac{\ln \left(b x -b \right) \ln \left(\frac{b x +a +1}{1+a +b}\right)}{4}-\frac{\dilog \left(\frac{b x +a -1}{b -1+a}\right)}{4}-\frac{\ln \left(b x -b \right) \ln \left(\frac{b x +a -1}{b -1+a}\right)}{4}"," ",0,"1/2*arctanh(b*x+a)*ln(b*x+b)-1/2*arctanh(b*x+a)*ln(b*x-b)+1/4*dilog((b*x+a-1)/(-b-1+a))+1/4*ln(b*x+b)*ln((b*x+a-1)/(-b-1+a))-1/4*dilog((b*x+a+1)/(1+a-b))-1/4*ln(b*x+b)*ln((b*x+a+1)/(1+a-b))+1/4*dilog((b*x+a+1)/(1+a+b))+1/4*ln(b*x-b)*ln((b*x+a+1)/(1+a+b))-1/4*dilog((b*x+a-1)/(b-1+a))-1/4*ln(b*x-b)*ln((b*x+a-1)/(b-1+a))","A"
508,1,110,82,0.072000," ","int(arctanh(x)/(b*x+a),x)","\frac{\ln \left(b x +a \right) \arctanh \left(x \right)}{b}-\frac{\ln \left(b x +a \right) \ln \left(\frac{b x +b}{-a +b}\right)}{2 b}-\frac{\dilog \left(\frac{b x +b}{-a +b}\right)}{2 b}+\frac{\ln \left(b x +a \right) \ln \left(\frac{b x -b}{-a -b}\right)}{2 b}+\frac{\dilog \left(\frac{b x -b}{-a -b}\right)}{2 b}"," ",0,"ln(b*x+a)/b*arctanh(x)-1/2/b*ln(b*x+a)*ln((b*x+b)/(-a+b))-1/2/b*dilog((b*x+b)/(-a+b))+1/2/b*ln(b*x+a)*ln((b*x-b)/(-a-b))+1/2/b*dilog((b*x-b)/(-a-b))","A"
509,1,606,293,0.624000," ","int(arctanh(x)/(b*x^2+a),x)","-\frac{\sqrt{-a b}\, \arctanh \left(x \right) \ln \left(1-\frac{\left(a +b \right) \left(1+x \right)^{2}}{\left(-x^{2}+1\right) \left(2 \sqrt{-a b}-a +b \right)}\right)}{2 a b}+\frac{\sqrt{-a b}\, \arctanh \left(x \right)^{2}}{2 a b}-\frac{\sqrt{-a b}\, \polylog \left(2, \frac{\left(a +b \right) \left(1+x \right)^{2}}{\left(-x^{2}+1\right) \left(2 \sqrt{-a b}-a +b \right)}\right)}{4 a b}-\frac{\left(-2 \sqrt{-a b}+a -b \right) \ln \left(1-\frac{\left(a +b \right) \left(1+x \right)^{2}}{\left(-x^{2}+1\right) \left(-2 \sqrt{-a b}-a +b \right)}\right) \arctanh \left(x \right)}{a^{2}+2 a b +b^{2}}+\frac{\left(2 a b +\sqrt{-a b}\, a -\sqrt{-a b}\, b \right) \ln \left(1-\frac{\left(a +b \right) \left(1+x \right)^{2}}{\left(-x^{2}+1\right) \left(-2 \sqrt{-a b}-a +b \right)}\right) \arctanh \left(x \right)}{2 b \left(a^{2}+2 a b +b^{2}\right)}-\frac{\left(2 a b +\sqrt{-a b}\, a -\sqrt{-a b}\, b \right) \ln \left(1-\frac{\left(a +b \right) \left(1+x \right)^{2}}{\left(-x^{2}+1\right) \left(-2 \sqrt{-a b}-a +b \right)}\right) \arctanh \left(x \right)}{2 a \left(a^{2}+2 a b +b^{2}\right)}-\frac{\arctanh \left(x \right)^{2} \sqrt{-a b}}{a^{2}+2 a b +b^{2}}-\frac{\arctanh \left(x \right)^{2} a \sqrt{-a b}}{2 b \left(a^{2}+2 a b +b^{2}\right)}-\frac{\arctanh \left(x \right)^{2} b \sqrt{-a b}}{2 a \left(a^{2}+2 a b +b^{2}\right)}+\frac{\polylog \left(2, \frac{\left(a +b \right) \left(1+x \right)^{2}}{\left(-x^{2}+1\right) \left(-2 \sqrt{-a b}-a +b \right)}\right) \sqrt{-a b}}{2 a^{2}+4 a b +2 b^{2}}+\frac{\polylog \left(2, \frac{\left(a +b \right) \left(1+x \right)^{2}}{\left(-x^{2}+1\right) \left(-2 \sqrt{-a b}-a +b \right)}\right) a \sqrt{-a b}}{4 b \left(a^{2}+2 a b +b^{2}\right)}+\frac{\polylog \left(2, \frac{\left(a +b \right) \left(1+x \right)^{2}}{\left(-x^{2}+1\right) \left(-2 \sqrt{-a b}-a +b \right)}\right) b \sqrt{-a b}}{4 a \left(a^{2}+2 a b +b^{2}\right)}"," ",0,"-1/2*(-a*b)^(1/2)/a/b*arctanh(x)*ln(1-(a+b)*(1+x)^2/(-x^2+1)/(2*(-a*b)^(1/2)-a+b))+1/2*(-a*b)^(1/2)/a/b*arctanh(x)^2-1/4*(-a*b)^(1/2)/a/b*polylog(2,(a+b)*(1+x)^2/(-x^2+1)/(2*(-a*b)^(1/2)-a+b))-(-2*(-a*b)^(1/2)+a-b)/(a^2+2*a*b+b^2)*ln(1-(a+b)*(1+x)^2/(-x^2+1)/(-2*(-a*b)^(1/2)-a+b))*arctanh(x)+1/2*(2*a*b+(-a*b)^(1/2)*a-(-a*b)^(1/2)*b)/b/(a^2+2*a*b+b^2)*ln(1-(a+b)*(1+x)^2/(-x^2+1)/(-2*(-a*b)^(1/2)-a+b))*arctanh(x)-1/2*(2*a*b+(-a*b)^(1/2)*a-(-a*b)^(1/2)*b)/a/(a^2+2*a*b+b^2)*ln(1-(a+b)*(1+x)^2/(-x^2+1)/(-2*(-a*b)^(1/2)-a+b))*arctanh(x)-1/(a^2+2*a*b+b^2)*arctanh(x)^2*(-a*b)^(1/2)-1/2/b/(a^2+2*a*b+b^2)*arctanh(x)^2*a*(-a*b)^(1/2)-1/2/a/(a^2+2*a*b+b^2)*arctanh(x)^2*b*(-a*b)^(1/2)+1/2/(a^2+2*a*b+b^2)*polylog(2,(a+b)*(1+x)^2/(-x^2+1)/(-2*(-a*b)^(1/2)-a+b))*(-a*b)^(1/2)+1/4/b/(a^2+2*a*b+b^2)*polylog(2,(a+b)*(1+x)^2/(-x^2+1)/(-2*(-a*b)^(1/2)-a+b))*a*(-a*b)^(1/2)+1/4/a/(a^2+2*a*b+b^2)*polylog(2,(a+b)*(1+x)^2/(-x^2+1)/(-2*(-a*b)^(1/2)-a+b))*b*(-a*b)^(1/2)","B"
510,1,1599,230,0.607000," ","int(arctanh(x)/(c*x^2+b*x+a),x)","-\frac{\arctanh \left(x \right)^{2} \sqrt{-4 a c +b^{2}}}{a^{2}+2 a c -b^{2}+c^{2}}+\frac{\arctanh \left(x \right)^{2} a}{a^{2}+2 a c -b^{2}+c^{2}}-\frac{\arctanh \left(x \right)^{2} c}{a^{2}+2 a c -b^{2}+c^{2}}-\frac{\polylog \left(2, \frac{\left(a +b +c \right) \left(1+x \right)^{2}}{\left(-x^{2}+1\right) \left(-\sqrt{-4 a c +b^{2}}-a +c \right)}\right) a}{2 \left(a^{2}+2 a c -b^{2}+c^{2}\right)}-\frac{\sqrt{-4 a c +b^{2}}\, \polylog \left(2, \frac{\left(a +b +c \right) \left(1+x \right)^{2}}{\left(-x^{2}+1\right) \left(\sqrt{-4 a c +b^{2}}-a +c \right)}\right)}{2 \left(4 a c -b^{2}\right)}+\frac{\sqrt{-4 a c +b^{2}}\, \arctanh \left(x \right)^{2}}{4 a c -b^{2}}+\frac{4 \arctanh \left(x \right)^{2} c^{2} a}{\left(4 a c -b^{2}\right) \left(a^{2}+2 a c -b^{2}+c^{2}\right)}-\frac{4 \arctanh \left(x \right)^{2} a^{2} c}{\left(4 a c -b^{2}\right) \left(a^{2}+2 a c -b^{2}+c^{2}\right)}+\frac{\polylog \left(2, \frac{\left(a +b +c \right) \left(1+x \right)^{2}}{\left(-x^{2}+1\right) \left(-\sqrt{-4 a c +b^{2}}-a +c \right)}\right) c \,b^{2}}{2 \left(4 a c -b^{2}\right) \left(a^{2}+2 a c -b^{2}+c^{2}\right)}+\frac{\polylog \left(2, \frac{\left(a +b +c \right) \left(1+x \right)^{2}}{\left(-x^{2}+1\right) \left(-\sqrt{-4 a c +b^{2}}-a +c \right)}\right) c^{2} \sqrt{-4 a c +b^{2}}}{2 \left(4 a c -b^{2}\right) \left(a^{2}+2 a c -b^{2}+c^{2}\right)}-\frac{2 \polylog \left(2, \frac{\left(a +b +c \right) \left(1+x \right)^{2}}{\left(-x^{2}+1\right) \left(-\sqrt{-4 a c +b^{2}}-a +c \right)}\right) c^{2} a}{\left(4 a c -b^{2}\right) \left(a^{2}+2 a c -b^{2}+c^{2}\right)}-\frac{\arctanh \left(x \right)^{2} c^{2} \sqrt{-4 a c +b^{2}}}{\left(4 a c -b^{2}\right) \left(a^{2}+2 a c -b^{2}+c^{2}\right)}+\frac{\polylog \left(2, \frac{\left(a +b +c \right) \left(1+x \right)^{2}}{\left(-x^{2}+1\right) \left(-\sqrt{-4 a c +b^{2}}-a +c \right)}\right) a^{2} \sqrt{-4 a c +b^{2}}}{2 \left(4 a c -b^{2}\right) \left(a^{2}+2 a c -b^{2}+c^{2}\right)}+\frac{2 \polylog \left(2, \frac{\left(a +b +c \right) \left(1+x \right)^{2}}{\left(-x^{2}+1\right) \left(-\sqrt{-4 a c +b^{2}}-a +c \right)}\right) a^{2} c}{\left(4 a c -b^{2}\right) \left(a^{2}+2 a c -b^{2}+c^{2}\right)}+\frac{2 \arctanh \left(x \right)^{2} a c \sqrt{-4 a c +b^{2}}}{\left(4 a c -b^{2}\right) \left(a^{2}+2 a c -b^{2}+c^{2}\right)}-\frac{\left(4 a c -b^{2}+\sqrt{-4 a c +b^{2}}\, a -\sqrt{-4 a c +b^{2}}\, c \right) \ln \left(1-\frac{\left(a +b +c \right) \left(1+x \right)^{2}}{\left(-x^{2}+1\right) \left(-\sqrt{-4 a c +b^{2}}-a +c \right)}\right) \arctanh \left(x \right) c}{\left(4 a c -b^{2}\right) \left(a^{2}+2 a c -b^{2}+c^{2}\right)}-\frac{\polylog \left(2, \frac{\left(a +b +c \right) \left(1+x \right)^{2}}{\left(-x^{2}+1\right) \left(-\sqrt{-4 a c +b^{2}}-a +c \right)}\right) a c \sqrt{-4 a c +b^{2}}}{\left(4 a c -b^{2}\right) \left(a^{2}+2 a c -b^{2}+c^{2}\right)}+\frac{\left(4 a c -b^{2}+\sqrt{-4 a c +b^{2}}\, a -\sqrt{-4 a c +b^{2}}\, c \right) \ln \left(1-\frac{\left(a +b +c \right) \left(1+x \right)^{2}}{\left(-x^{2}+1\right) \left(-\sqrt{-4 a c +b^{2}}-a +c \right)}\right) \arctanh \left(x \right) a}{\left(4 a c -b^{2}\right) \left(a^{2}+2 a c -b^{2}+c^{2}\right)}-\frac{\arctanh \left(x \right)^{2} a^{2} \sqrt{-4 a c +b^{2}}}{\left(4 a c -b^{2}\right) \left(a^{2}+2 a c -b^{2}+c^{2}\right)}-\frac{\arctanh \left(x \right)^{2} c \,b^{2}}{\left(4 a c -b^{2}\right) \left(a^{2}+2 a c -b^{2}+c^{2}\right)}+\frac{\arctanh \left(x \right)^{2} a \,b^{2}}{\left(4 a c -b^{2}\right) \left(a^{2}+2 a c -b^{2}+c^{2}\right)}-\frac{\polylog \left(2, \frac{\left(a +b +c \right) \left(1+x \right)^{2}}{\left(-x^{2}+1\right) \left(-\sqrt{-4 a c +b^{2}}-a +c \right)}\right) a \,b^{2}}{2 \left(4 a c -b^{2}\right) \left(a^{2}+2 a c -b^{2}+c^{2}\right)}-\frac{\sqrt{-4 a c +b^{2}}\, \arctanh \left(x \right) \ln \left(1-\frac{\left(a +b +c \right) \left(1+x \right)^{2}}{\left(-x^{2}+1\right) \left(\sqrt{-4 a c +b^{2}}-a +c \right)}\right)}{4 a c -b^{2}}-\frac{\left(-\sqrt{-4 a c +b^{2}}+a -c \right) \ln \left(1-\frac{\left(a +b +c \right) \left(1+x \right)^{2}}{\left(-x^{2}+1\right) \left(-\sqrt{-4 a c +b^{2}}-a +c \right)}\right) \arctanh \left(x \right)}{a^{2}+2 a c -b^{2}+c^{2}}+\frac{\polylog \left(2, \frac{\left(a +b +c \right) \left(1+x \right)^{2}}{\left(-x^{2}+1\right) \left(-\sqrt{-4 a c +b^{2}}-a +c \right)}\right) \sqrt{-4 a c +b^{2}}}{2 a^{2}+4 a c -2 b^{2}+2 c^{2}}+\frac{\polylog \left(2, \frac{\left(a +b +c \right) \left(1+x \right)^{2}}{\left(-x^{2}+1\right) \left(-\sqrt{-4 a c +b^{2}}-a +c \right)}\right) c}{2 a^{2}+4 a c -2 b^{2}+2 c^{2}}"," ",0,"-1/(4*a*c-b^2)/(a^2+2*a*c-b^2+c^2)*arctanh(x)^2*a^2*(-4*a*c+b^2)^(1/2)-1/(a^2+2*a*c-b^2+c^2)*arctanh(x)^2*(-4*a*c+b^2)^(1/2)+1/(a^2+2*a*c-b^2+c^2)*arctanh(x)^2*a-1/(a^2+2*a*c-b^2+c^2)*arctanh(x)^2*c+1/2/(a^2+2*a*c-b^2+c^2)*polylog(2,(a+b+c)*(1+x)^2/(-x^2+1)/(-(-4*a*c+b^2)^(1/2)-a+c))*(-4*a*c+b^2)^(1/2)-1/2/(a^2+2*a*c-b^2+c^2)*polylog(2,(a+b+c)*(1+x)^2/(-x^2+1)/(-(-4*a*c+b^2)^(1/2)-a+c))*a-1/(4*a*c-b^2)/(a^2+2*a*c-b^2+c^2)*arctanh(x)^2*c*b^2+1/(4*a*c-b^2)/(a^2+2*a*c-b^2+c^2)*arctanh(x)^2*a*b^2-1/(4*a*c-b^2)/(a^2+2*a*c-b^2+c^2)*arctanh(x)^2*c^2*(-4*a*c+b^2)^(1/2)+1/2/(a^2+2*a*c-b^2+c^2)*polylog(2,(a+b+c)*(1+x)^2/(-x^2+1)/(-(-4*a*c+b^2)^(1/2)-a+c))*c-1/2*(-4*a*c+b^2)^(1/2)/(4*a*c-b^2)*polylog(2,(a+b+c)*(1+x)^2/(-x^2+1)/((-4*a*c+b^2)^(1/2)-a+c))+(-4*a*c+b^2)^(1/2)/(4*a*c-b^2)*arctanh(x)^2+2/(4*a*c-b^2)/(a^2+2*a*c-b^2+c^2)*arctanh(x)^2*a*c*(-4*a*c+b^2)^(1/2)-(4*a*c-b^2+(-4*a*c+b^2)^(1/2)*a-(-4*a*c+b^2)^(1/2)*c)/(4*a*c-b^2)/(a^2+2*a*c-b^2+c^2)*ln(1-(a+b+c)*(1+x)^2/(-x^2+1)/(-(-4*a*c+b^2)^(1/2)-a+c))*arctanh(x)*c-1/(4*a*c-b^2)/(a^2+2*a*c-b^2+c^2)*polylog(2,(a+b+c)*(1+x)^2/(-x^2+1)/(-(-4*a*c+b^2)^(1/2)-a+c))*a*c*(-4*a*c+b^2)^(1/2)+(4*a*c-b^2+(-4*a*c+b^2)^(1/2)*a-(-4*a*c+b^2)^(1/2)*c)/(4*a*c-b^2)/(a^2+2*a*c-b^2+c^2)*ln(1-(a+b+c)*(1+x)^2/(-x^2+1)/(-(-4*a*c+b^2)^(1/2)-a+c))*arctanh(x)*a+1/2/(4*a*c-b^2)/(a^2+2*a*c-b^2+c^2)*polylog(2,(a+b+c)*(1+x)^2/(-x^2+1)/(-(-4*a*c+b^2)^(1/2)-a+c))*a^2*(-4*a*c+b^2)^(1/2)+2/(4*a*c-b^2)/(a^2+2*a*c-b^2+c^2)*polylog(2,(a+b+c)*(1+x)^2/(-x^2+1)/(-(-4*a*c+b^2)^(1/2)-a+c))*a^2*c-1/2/(4*a*c-b^2)/(a^2+2*a*c-b^2+c^2)*polylog(2,(a+b+c)*(1+x)^2/(-x^2+1)/(-(-4*a*c+b^2)^(1/2)-a+c))*a*b^2+1/2/(4*a*c-b^2)/(a^2+2*a*c-b^2+c^2)*polylog(2,(a+b+c)*(1+x)^2/(-x^2+1)/(-(-4*a*c+b^2)^(1/2)-a+c))*c*b^2+1/2/(4*a*c-b^2)/(a^2+2*a*c-b^2+c^2)*polylog(2,(a+b+c)*(1+x)^2/(-x^2+1)/(-(-4*a*c+b^2)^(1/2)-a+c))*c^2*(-4*a*c+b^2)^(1/2)-2/(4*a*c-b^2)/(a^2+2*a*c-b^2+c^2)*polylog(2,(a+b+c)*(1+x)^2/(-x^2+1)/(-(-4*a*c+b^2)^(1/2)-a+c))*c^2*a-(-4*a*c+b^2)^(1/2)/(4*a*c-b^2)*arctanh(x)*ln(1-(a+b+c)*(1+x)^2/(-x^2+1)/((-4*a*c+b^2)^(1/2)-a+c))-(-(-4*a*c+b^2)^(1/2)+a-c)/(a^2+2*a*c-b^2+c^2)*ln(1-(a+b+c)*(1+x)^2/(-x^2+1)/(-(-4*a*c+b^2)^(1/2)-a+c))*arctanh(x)+4/(4*a*c-b^2)/(a^2+2*a*c-b^2+c^2)*arctanh(x)^2*c^2*a-4/(4*a*c-b^2)/(a^2+2*a*c-b^2+c^2)*arctanh(x)^2*a^2*c","B"
511,0,0,16,1.399000," ","int((d*x^2+c)^(1/2)*arctanh(a*x),x)","\int \sqrt{d \,x^{2}+c}\, \arctanh \left(a x \right)\, dx"," ",0,"int((d*x^2+c)^(1/2)*arctanh(a*x),x)","F"
512,0,0,16,1.209000," ","int(arctanh(a*x)/(d*x^2+c)^(1/2),x)","\int \frac{\arctanh \left(a x \right)}{\sqrt{d \,x^{2}+c}}\, dx"," ",0,"int(arctanh(a*x)/(d*x^2+c)^(1/2),x)","F"
513,0,0,54,1.151000," ","int(arctanh(a*x)/(d*x^2+c)^(3/2),x)","\int \frac{\arctanh \left(a x \right)}{\left(d \,x^{2}+c \right)^{\frac{3}{2}}}\, dx"," ",0,"int(arctanh(a*x)/(d*x^2+c)^(3/2),x)","F"
514,0,0,108,1.168000," ","int(arctanh(a*x)/(d*x^2+c)^(5/2),x)","\int \frac{\arctanh \left(a x \right)}{\left(d \,x^{2}+c \right)^{\frac{5}{2}}}\, dx"," ",0,"int(arctanh(a*x)/(d*x^2+c)^(5/2),x)","F"
515,0,0,172,1.190000," ","int(arctanh(a*x)/(d*x^2+c)^(7/2),x)","\int \frac{\arctanh \left(a x \right)}{\left(d \,x^{2}+c \right)^{\frac{7}{2}}}\, dx"," ",0,"int(arctanh(a*x)/(d*x^2+c)^(7/2),x)","F"
516,0,0,247,1.175000," ","int(arctanh(a*x)/(d*x^2+c)^(9/2),x)","\int \frac{\arctanh \left(a x \right)}{\left(d \,x^{2}+c \right)^{\frac{9}{2}}}\, dx"," ",0,"int(arctanh(a*x)/(d*x^2+c)^(9/2),x)","F"
517,1,229,146,0.610000," ","int((-a*x^2+a)^(1/2)*arctanh(x),x)","\frac{\left(\arctanh \left(x \right) x +1\right) \sqrt{-\left(-1+x \right) \left(1+x \right) a}}{2}+\frac{i \sqrt{-\left(-1+x \right) \left(1+x \right) a}\, \sqrt{-x^{2}+1}\, \arctanh \left(x \right) \ln \left(1+\frac{i \left(1+x \right)}{\sqrt{-x^{2}+1}}\right)}{2 \left(1+x \right) \left(-1+x \right)}-\frac{i \sqrt{-\left(-1+x \right) \left(1+x \right) a}\, \sqrt{-x^{2}+1}\, \arctanh \left(x \right) \ln \left(1-\frac{i \left(1+x \right)}{\sqrt{-x^{2}+1}}\right)}{2 \left(1+x \right) \left(-1+x \right)}+\frac{i \sqrt{-\left(-1+x \right) \left(1+x \right) a}\, \sqrt{-x^{2}+1}\, \dilog \left(1+\frac{i \left(1+x \right)}{\sqrt{-x^{2}+1}}\right)}{2 \left(1+x \right) \left(-1+x \right)}-\frac{i \sqrt{-\left(-1+x \right) \left(1+x \right) a}\, \sqrt{-x^{2}+1}\, \dilog \left(1-\frac{i \left(1+x \right)}{\sqrt{-x^{2}+1}}\right)}{2 \left(1+x \right) \left(-1+x \right)}"," ",0,"1/2*(arctanh(x)*x+1)*(-(-1+x)*(1+x)*a)^(1/2)+1/2*I*(-(-1+x)*(1+x)*a)^(1/2)/(1+x)*(-x^2+1)^(1/2)/(-1+x)*arctanh(x)*ln(1+I*(1+x)/(-x^2+1)^(1/2))-1/2*I*(-(-1+x)*(1+x)*a)^(1/2)/(1+x)*(-x^2+1)^(1/2)/(-1+x)*arctanh(x)*ln(1-I*(1+x)/(-x^2+1)^(1/2))+1/2*I*(-(-1+x)*(1+x)*a)^(1/2)/(1+x)*(-x^2+1)^(1/2)/(-1+x)*dilog(1+I*(1+x)/(-x^2+1)^(1/2))-1/2*I*(-(-1+x)*(1+x)*a)^(1/2)/(1+x)*(-x^2+1)^(1/2)/(-1+x)*dilog(1-I*(1+x)/(-x^2+1)^(1/2))","A"
518,1,210,116,0.503000," ","int(arctanh(x)/(-a*x^2+a)^(1/2),x)","\frac{i \ln \left(1+\frac{i \left(1+x \right)}{\sqrt{-x^{2}+1}}\right) \arctanh \left(x \right) \sqrt{-x^{2}+1}\, \sqrt{-\left(-1+x \right) \left(1+x \right) a}}{a \left(x^{2}-1\right)}-\frac{i \ln \left(1-\frac{i \left(1+x \right)}{\sqrt{-x^{2}+1}}\right) \arctanh \left(x \right) \sqrt{-x^{2}+1}\, \sqrt{-\left(-1+x \right) \left(1+x \right) a}}{a \left(x^{2}-1\right)}+\frac{i \dilog \left(1+\frac{i \left(1+x \right)}{\sqrt{-x^{2}+1}}\right) \sqrt{-x^{2}+1}\, \sqrt{-\left(-1+x \right) \left(1+x \right) a}}{a \left(x^{2}-1\right)}-\frac{i \dilog \left(1-\frac{i \left(1+x \right)}{\sqrt{-x^{2}+1}}\right) \sqrt{-x^{2}+1}\, \sqrt{-\left(-1+x \right) \left(1+x \right) a}}{a \left(x^{2}-1\right)}"," ",0,"I*ln(1+I*(1+x)/(-x^2+1)^(1/2))*arctanh(x)*(-x^2+1)^(1/2)*(-(-1+x)*(1+x)*a)^(1/2)/a/(x^2-1)-I*ln(1-I*(1+x)/(-x^2+1)^(1/2))*arctanh(x)*(-x^2+1)^(1/2)*(-(-1+x)*(1+x)*a)^(1/2)/a/(x^2-1)+I*dilog(1+I*(1+x)/(-x^2+1)^(1/2))*(-x^2+1)^(1/2)*(-(-1+x)*(1+x)*a)^(1/2)/a/(x^2-1)-I*dilog(1-I*(1+x)/(-x^2+1)^(1/2))*(-x^2+1)^(1/2)*(-(-1+x)*(1+x)*a)^(1/2)/a/(x^2-1)","A"
519,1,52,33,0.447000," ","int(arctanh(x)/(-a*x^2+a)^(3/2),x)","-\frac{\left(\arctanh \left(x \right)-1\right) \sqrt{-\left(-1+x \right) \left(1+x \right) a}}{2 \left(-1+x \right) a^{2}}-\frac{\left(1+\arctanh \left(x \right)\right) \sqrt{-\left(-1+x \right) \left(1+x \right) a}}{2 \left(1+x \right) a^{2}}"," ",0,"-1/2*(arctanh(x)-1)*(-(-1+x)*(1+x)*a)^(1/2)/(-1+x)/a^2-1/2*(1+arctanh(x))*(-(-1+x)*(1+x)*a)^(1/2)/(1+x)/a^2","A"
520,1,112,67,0.469000," ","int(arctanh(x)/(-a*x^2+a)^(5/2),x)","\frac{\left(1+x \right) \left(-1+3 \arctanh \left(x \right)\right) \sqrt{-\left(-1+x \right) \left(1+x \right) a}}{72 \left(-1+x \right)^{2} a^{3}}-\frac{3 \left(\arctanh \left(x \right)-1\right) \sqrt{-\left(-1+x \right) \left(1+x \right) a}}{8 \left(-1+x \right) a^{3}}-\frac{3 \left(1+\arctanh \left(x \right)\right) \sqrt{-\left(-1+x \right) \left(1+x \right) a}}{8 \left(1+x \right) a^{3}}+\frac{\left(-1+x \right) \left(1+3 \arctanh \left(x \right)\right) \sqrt{-\left(-1+x \right) \left(1+x \right) a}}{72 \left(1+x \right)^{2} a^{3}}"," ",0,"1/72*(1+x)*(-1+3*arctanh(x))*(-(-1+x)*(1+x)*a)^(1/2)/(-1+x)^2/a^3-3/8*(arctanh(x)-1)*(-(-1+x)*(1+x)*a)^(1/2)/(-1+x)/a^3-3/8*(1+arctanh(x))*(-(-1+x)*(1+x)*a)^(1/2)/(1+x)/a^3+1/72*(-1+x)*(1+3*arctanh(x))*(-(-1+x)*(1+x)*a)^(1/2)/(1+x)^2/a^3","A"
521,1,176,100,0.479000," ","int(arctanh(x)/(-a*x^2+a)^(7/2),x)","-\frac{\left(1+x \right)^{2} \left(-1+5 \arctanh \left(x \right)\right) \sqrt{-\left(-1+x \right) \left(1+x \right) a}}{800 \left(-1+x \right)^{3} a^{4}}+\frac{5 \left(1+x \right) \left(-1+3 \arctanh \left(x \right)\right) \sqrt{-\left(-1+x \right) \left(1+x \right) a}}{288 \left(-1+x \right)^{2} a^{4}}-\frac{5 \left(\arctanh \left(x \right)-1\right) \sqrt{-\left(-1+x \right) \left(1+x \right) a}}{16 \left(-1+x \right) a^{4}}-\frac{5 \left(1+\arctanh \left(x \right)\right) \sqrt{-\left(-1+x \right) \left(1+x \right) a}}{16 \left(1+x \right) a^{4}}+\frac{5 \left(-1+x \right) \left(1+3 \arctanh \left(x \right)\right) \sqrt{-\left(-1+x \right) \left(1+x \right) a}}{288 \left(1+x \right)^{2} a^{4}}-\frac{\left(-1+x \right)^{2} \left(1+5 \arctanh \left(x \right)\right) \sqrt{-\left(-1+x \right) \left(1+x \right) a}}{800 \left(1+x \right)^{3} a^{4}}"," ",0,"-1/800*(1+x)^2*(-1+5*arctanh(x))*(-(-1+x)*(1+x)*a)^(1/2)/(-1+x)^3/a^4+5/288*(1+x)*(-1+3*arctanh(x))*(-(-1+x)*(1+x)*a)^(1/2)/(-1+x)^2/a^4-5/16*(arctanh(x)-1)*(-(-1+x)*(1+x)*a)^(1/2)/(-1+x)/a^4-5/16*(1+arctanh(x))*(-(-1+x)*(1+x)*a)^(1/2)/(1+x)/a^4+5/288*(-1+x)*(1+3*arctanh(x))*(-(-1+x)*(1+x)*a)^(1/2)/(1+x)^2/a^4-1/800*(-1+x)^2*(1+5*arctanh(x))*(-(-1+x)*(1+x)*a)^(1/2)/(1+x)^3/a^4","A"
522,1,4757,281,6.088000," ","int(x^4*(a+b*arctanh(c*x))*(d+e*ln(-c^2*x^2+1)),x)","\text{output too large to display}"," ",0,"-2/25*a*e*x^5+181/600*e/c^5*b-2/5*b*e*x*arctanh(c*x)/c^4-2/15*b*e*x^3*arctanh(c*x)/c^2+1/10*I/c^5*b*arctanh(c*x)*Pi*e*csgn(I*(c*x+1)^2/(c^2*x^2-1))^3+1/10*I/c^5*b*csgn(I*(1+(c*x+1)^2/(-c^2*x^2+1))^2)^3*Pi*e*arctanh(c*x)+1/40*I/c*b*Pi*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1))^2)^3*x^4*e+1/20*I/c^3*b*Pi*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1))^2)^3*x^2*e+1/40*I/c*b*Pi*csgn(I*(c*x+1)^2/(c^2*x^2-1))^3*x^4*e-3/40*I/c^5*b*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1))^2)^2*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1))^2)*e*Pi-2/5*a*e*x/c^4-77/300*b*e*x^2/c^3-2/15*a*e*x^3/c^2-9/200*b*e*x^4/c-2/25*b*e*x^5*arctanh(c*x)+1/10/c^5*b*e*(4*arctanh(c*x)*x^5*c^5+c^4*x^4+2*c^2*x^2+4*arctanh(c*x)-4*ln(1+(c*x+1)^2/(-c^2*x^2+1))-3)*ln((c*x+1)/(-c^2*x^2+1)^(1/2))-1/10*I*b*Pi*csgn(I*(c*x+1)^2/(c^2*x^2-1))*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1))^2)*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1))^2)*arctanh(c*x)*x^5*e-1/10*I/c^5*b*arctanh(c*x)*Pi*e*csgn(I*(c*x+1)^2/(c^2*x^2-1))*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1))^2)*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1))^2)-1/40*I/c*b*Pi*csgn(I*(c*x+1)^2/(c^2*x^2-1))*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1))^2)*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1))^2)*x^4*e-1/20*I/c^3*b*Pi*csgn(I*(c*x+1)^2/(c^2*x^2-1))*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1))^2)*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1))^2)*x^2*e+1/10*I/c^5*b*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1))^2)*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1))^2)*csgn(I*(c*x+1)^2/(c^2*x^2-1))*e*ln(1+(c*x+1)^2/(-c^2*x^2+1))*Pi-1/10*I/c^5*b*csgn(I*(1+(c*x+1)^2/(-c^2*x^2+1))^2)*csgn(I*(1+(c*x+1)^2/(-c^2*x^2+1)))^2*e*ln(1+(c*x+1)^2/(-c^2*x^2+1))*Pi+1/5*I/c^5*b*Pi*ln(1+(c*x+1)^2/(-c^2*x^2+1))*e*csgn(I*(1+(c*x+1)^2/(-c^2*x^2+1)))*csgn(I*(1+(c*x+1)^2/(-c^2*x^2+1))^2)^2+3/40*I/c^5*b*Pi*e*csgn(I*(c*x+1)^2/(c^2*x^2-1))*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1))^2)*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1))^2)-1/10*I/c^5*b*arctanh(c*x)*Pi*e*csgn(I*(c*x+1)^2/(c^2*x^2-1))*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1))^2)^2+1/10*I/c^5*b*arctanh(c*x)*Pi*e*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1))^2)*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1))^2)^2-1/5*I/c^5*b*csgn(I*(1+(c*x+1)^2/(-c^2*x^2+1))^2)^2*csgn(I*(1+(c*x+1)^2/(-c^2*x^2+1)))*Pi*e*arctanh(c*x)+1/5*I/c^5*b*arctanh(c*x)*Pi*e*csgn(I*(c*x+1)/(-c^2*x^2+1)^(1/2))*csgn(I*(c*x+1)^2/(c^2*x^2-1))^2-1/10*I/c^3*b*Pi*csgn(I*(1+(c*x+1)^2/(-c^2*x^2+1)))*csgn(I*(1+(c*x+1)^2/(-c^2*x^2+1))^2)^2*x^2*e+1/40*I/c*b*Pi*csgn(I*(1+(c*x+1)^2/(-c^2*x^2+1)))^2*csgn(I*(1+(c*x+1)^2/(-c^2*x^2+1))^2)*x^4*e+1/20*I/c^3*b*Pi*csgn(I*(1+(c*x+1)^2/(-c^2*x^2+1)))^2*csgn(I*(1+(c*x+1)^2/(-c^2*x^2+1))^2)*x^2*e+1/10*I/c^5*b*arctanh(c*x)*Pi*e*csgn(I*(c*x+1)/(-c^2*x^2+1)^(1/2))^2*csgn(I*(c*x+1)^2/(c^2*x^2-1))-1/40*I/c*b*Pi*csgn(I*(c*x+1)^2/(c^2*x^2-1))*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1))^2)^2*x^4*e-1/20*I/c^3*b*Pi*csgn(I*(c*x+1)^2/(c^2*x^2-1))*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1))^2)^2*x^2*e+1/10*I/c^5*b*arctanh(c*x)*Pi*e*csgn(I*(1+(c*x+1)^2/(-c^2*x^2+1)))^2*csgn(I*(1+(c*x+1)^2/(-c^2*x^2+1))^2)+1/40*I/c*b*Pi*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1))^2)*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1))^2)^2*x^4*e+1/20*I/c^3*b*Pi*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1))^2)*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1))^2)^2*x^2*e+1/20*I/c*b*Pi*csgn(I*(c*x+1)/(-c^2*x^2+1)^(1/2))*csgn(I*(c*x+1)^2/(c^2*x^2-1))^2*x^4*e+1/10*I/c^3*b*Pi*csgn(I*(c*x+1)/(-c^2*x^2+1)^(1/2))*csgn(I*(c*x+1)^2/(c^2*x^2-1))^2*x^2*e+1/40*I/c*b*Pi*csgn(I*(c*x+1)/(-c^2*x^2+1)^(1/2))^2*csgn(I*(c*x+1)^2/(c^2*x^2-1))*x^4*e+1/20*I/c^3*b*Pi*csgn(I*(c*x+1)/(-c^2*x^2+1)^(1/2))^2*csgn(I*(c*x+1)^2/(c^2*x^2-1))*x^2*e-1/20*I/c*b*Pi*csgn(I*(1+(c*x+1)^2/(-c^2*x^2+1)))*csgn(I*(1+(c*x+1)^2/(-c^2*x^2+1))^2)^2*x^4*e-1/10*I*b*Pi*csgn(I*(c*x+1)^2/(c^2*x^2-1))*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1))^2)^2*arctanh(c*x)*x^5*e+1/10*I*b*Pi*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1))^2)*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1))^2)^2*arctanh(c*x)*x^5*e+1/10*I*b*Pi*csgn(I*(1+(c*x+1)^2/(-c^2*x^2+1)))^2*csgn(I*(1+(c*x+1)^2/(-c^2*x^2+1))^2)*arctanh(c*x)*x^5*e+1/10*I*b*Pi*csgn(I*(c*x+1)/(-c^2*x^2+1)^(1/2))^2*csgn(I*(c*x+1)^2/(c^2*x^2-1))*arctanh(c*x)*x^5*e-1/5*I*b*Pi*csgn(I*(1+(c*x+1)^2/(-c^2*x^2+1)))*csgn(I*(1+(c*x+1)^2/(-c^2*x^2+1))^2)^2*arctanh(c*x)*x^5*e+1/5*I*b*Pi*csgn(I*(c*x+1)/(-c^2*x^2+1)^(1/2))*csgn(I*(c*x+1)^2/(c^2*x^2-1))^2*arctanh(c*x)*x^5*e+1/10*I/c^5*b*Pi*ln(1+(c*x+1)^2/(-c^2*x^2+1))*e*csgn(I*(c*x+1)^2/(c^2*x^2-1))*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1))^2)^2-1/10*I/c^5*b*Pi*ln(1+(c*x+1)^2/(-c^2*x^2+1))*e*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1))^2)*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1))^2)^2-1/10*I/c^5*b*Pi*ln(1+(c*x+1)^2/(-c^2*x^2+1))*e*csgn(I*(c*x+1)/(-c^2*x^2+1)^(1/2))^2*csgn(I*(c*x+1)^2/(c^2*x^2-1))-1/5*I/c^5*b*Pi*ln(1+(c*x+1)^2/(-c^2*x^2+1))*e*csgn(I*(c*x+1)/(-c^2*x^2+1)^(1/2))*csgn(I*(c*x+1)^2/(c^2*x^2-1))^2+1/5/c^5*b*d*arctanh(c*x)-46/75/c^5*b*arctanh(c*x)*e-1/5/c^5*b*d*ln(1+(c*x+1)^2/(-c^2*x^2+1))+1/5/c^5*b*ln(1+(c*x+1)^2/(-c^2*x^2+1))^2*e+137/150/c^5*b*e*ln(1+(c*x+1)^2/(-c^2*x^2+1))-1/5*a*e/c^5*ln(c*x-1)+1/5*a*e*x^5*ln(-c^2*x^2+1)+1/5*a*e/c^5*ln(c*x+1)+1/20/c*b*x^4*d+1/5*b*arctanh(c*x)*x^5*d+1/5*x^5*a*d+1/5/c^3*b*ln(2)*x^2*e-2/5/c^5*b*e*ln(1+(c*x+1)^2/(-c^2*x^2+1))*ln(2)-1/10/c*b*ln(1+(c*x+1)^2/(-c^2*x^2+1))*x^4*e+2/5*b*ln(2)*arctanh(c*x)*x^5*e-2/5*b*arctanh(c*x)*ln(1+(c*x+1)^2/(-c^2*x^2+1))*x^5*e-1/5/c^3*b*ln(1+(c*x+1)^2/(-c^2*x^2+1))*x^2*e+2/5/c^5*b*arctanh(c*x)*ln(2)*e+1/10/c*b*ln(2)*x^4*e+1/20*I/c^3*b*Pi*csgn(I*(c*x+1)^2/(c^2*x^2-1))^3*x^2*e+1/40*I/c*b*Pi*csgn(I*(1+(c*x+1)^2/(-c^2*x^2+1))^2)^3*x^4*e+1/20*I/c^3*b*Pi*csgn(I*(1+(c*x+1)^2/(-c^2*x^2+1))^2)^3*x^2*e+1/10*I*b*Pi*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1))^2)^3*arctanh(c*x)*x^5*e+1/10*I*b*Pi*csgn(I*(c*x+1)^2/(c^2*x^2-1))^3*arctanh(c*x)*x^5*e+1/10*I*b*Pi*csgn(I*(1+(c*x+1)^2/(-c^2*x^2+1))^2)^3*arctanh(c*x)*x^5*e+1/10/c^3*b*x^2*d-3/40*I/c^5*b*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1))^2)^3*e*Pi-3/40*I/c^5*b*Pi*e*csgn(I*(c*x+1)^2/(c^2*x^2-1))^3-3/40*I/c^5*b*csgn(I*(1+(c*x+1)^2/(-c^2*x^2+1))^2)^3*e*Pi-3/10/c^5*b*e*ln(2)-3/20*I/c^5*b*e*Pi*csgn(I*(c*x+1)/(-c^2*x^2+1)^(1/2))*csgn(I*(c*x+1)^2/(c^2*x^2-1))^2-3/40*I/c^5*b*Pi*e*csgn(I*(c*x+1)/(-c^2*x^2+1)^(1/2))^2*csgn(I*(c*x+1)^2/(c^2*x^2-1))-1/10*I/c^5*b*Pi*ln(1+(c*x+1)^2/(-c^2*x^2+1))*e*csgn(I*(1+(c*x+1)^2/(-c^2*x^2+1))^2)^3-1/10*I/c^5*b*Pi*ln(1+(c*x+1)^2/(-c^2*x^2+1))*e*csgn(I*(c*x+1)^2/(c^2*x^2-1))^3-1/10*I/c^5*b*Pi*ln(1+(c*x+1)^2/(-c^2*x^2+1))*e*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1))^2)^3+3/40*I/c^5*b*Pi*e*csgn(I*(c*x+1)^2/(c^2*x^2-1))*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1))^2)^2+3/20*I/c^5*b*e*Pi*csgn(I*(1+(c*x+1)^2/(-c^2*x^2+1)))*csgn(I*(1+(c*x+1)^2/(-c^2*x^2+1))^2)^2+1/10*I/c^5*b*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1))^2)^3*Pi*e*arctanh(c*x)-3/40*I/c^5*b*Pi*e*csgn(I*(1+(c*x+1)^2/(-c^2*x^2+1)))^2*csgn(I*(1+(c*x+1)^2/(-c^2*x^2+1))^2)-3/20/c^5*b*d","C"
523,1,3739,201,6.000000," ","int(x^3*(a+b*arctanh(c*x))*(d+e*ln(-c^2*x^2+1)),x)","\text{output too large to display}"," ",0,"-1/4/c^4*b*d*arctanh(c*x)+1/4*b*arctanh(c*x)*x^4*d-1/8*b*arctanh(c*x)*x^4*e-1/4*a*e/c^2*x^2-1/4*a*e/c^4*ln(c^2*x^2-1)-1/8*I/c^4*b*csgn(I*(c*x+1)^2/(c^2*x^2-1))^3*Pi*e*arctanh(c*x)-1/8*I/c^4*b*csgn(I*(1+(c*x+1)^2/(-c^2*x^2+1))^2)^3*Pi*e*arctanh(c*x)-1/6*I/c^4*b*e*Pi*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1))^2)*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1))^2)^2+1/6*I/c^4*b*e*Pi*csgn(I*(c*x+1)^2/(c^2*x^2-1))*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1))^2)^2-1/6*I/c^4*b*e*Pi*csgn(I*(c*x+1)/(-c^2*x^2+1)^(1/2))^2*csgn(I*(c*x+1)^2/(c^2*x^2-1))+1/8*I/c^3*b*csgn(I*(c*x+1)^2/(c^2*x^2-1))^3*Pi*x*e+1/24*I/c*b*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1))^2)^3*Pi*x^3*e+1/24*I/c*b*csgn(I*(c*x+1)^2/(c^2*x^2-1))^3*Pi*x^3*e+1/24*I/c*b*csgn(I*(1+(c*x+1)^2/(-c^2*x^2+1))^2)^3*Pi*x^3*e+1/8*I/c^3*b*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1))^2)^3*Pi*x*e-1/3*I/c^4*b*e*Pi*csgn(I*(c*x+1)/(-c^2*x^2+1)^(1/2))*csgn(I*(c*x+1)^2/(c^2*x^2-1))^2-1/6*I/c^4*b*e*Pi*csgn(I*(1+(c*x+1)^2/(-c^2*x^2+1)))^2*csgn(I*(1+(c*x+1)^2/(-c^2*x^2+1))^2)+1/3*I/c^4*b*e*Pi*csgn(I*(1+(c*x+1)^2/(-c^2*x^2+1)))*csgn(I*(1+(c*x+1)^2/(-c^2*x^2+1))^2)^2+1/8*I*b*arctanh(c*x)*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1))^2)^3*Pi*x^4*e+1/8*I*b*arctanh(c*x)*csgn(I*(c*x+1)^2/(c^2*x^2-1))^3*Pi*x^4*e+1/8*I*b*arctanh(c*x)*csgn(I*(1+(c*x+1)^2/(-c^2*x^2+1))^2)^3*Pi*x^4*e-25/24*b*e*x/c^3-7/72*b*e*x^3/c+41/24*b*e*arctanh(c*x)/c^4+1/4*b*d*x/c^3+1/12*b*d*x^3/c+1/8*I/c^3*b*csgn(I*(1+(c*x+1)^2/(-c^2*x^2+1))^2)^3*Pi*x*e-1/8*I/c^4*b*arctanh(c*x)*Pi*e*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1))^2)^3+1/2*b*ln(2)*arctanh(c*x)*x^4*e-1/2*b*arctanh(c*x)*ln(1+(c*x+1)^2/(-c^2*x^2+1))*x^4*e+41/36*e/c^4*b-2/3/c^4*b*e*ln(2)-1/6*I/c^4*b*e*Pi*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1))^2)^3-1/6*I/c^4*b*e*Pi*csgn(I*(c*x+1)^2/(c^2*x^2-1))^3-1/6*I/c^4*b*e*Pi*csgn(I*(1+(c*x+1)^2/(-c^2*x^2+1))^2)^3+1/4*x^4*a*e*ln(-c^2*x^2+1)+1/4*x^4*a*d-1/8*a*e*x^4+1/8*I/c^4*b*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1))^2)*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1))^2)*csgn(I*(c*x+1)^2/(c^2*x^2-1))*Pi*e*arctanh(c*x)-1/24*I/c*b*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1))^2)*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1))^2)*csgn(I*(c*x+1)^2/(c^2*x^2-1))*Pi*x^3*e-1/8*I*b*arctanh(c*x)*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1))^2)*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1))^2)*csgn(I*(c*x+1)^2/(c^2*x^2-1))*Pi*x^4*e-1/8*I/c^3*b*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1))^2)*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1))^2)*csgn(I*(c*x+1)^2/(c^2*x^2-1))*Pi*x*e+1/8*I*b*arctanh(c*x)*csgn(I*(c*x+1)/(-c^2*x^2+1)^(1/2))^2*csgn(I*(c*x+1)^2/(c^2*x^2-1))*Pi*x^4*e+1/4*I*b*arctanh(c*x)*csgn(I*(c*x+1)/(-c^2*x^2+1)^(1/2))*csgn(I*(c*x+1)^2/(c^2*x^2-1))^2*Pi*x^4*e+1/8*I*b*arctanh(c*x)*csgn(I*(1+(c*x+1)^2/(-c^2*x^2+1)))^2*csgn(I*(1+(c*x+1)^2/(-c^2*x^2+1))^2)*Pi*x^4*e-1/4*I*b*arctanh(c*x)*csgn(I*(1+(c*x+1)^2/(-c^2*x^2+1)))*csgn(I*(1+(c*x+1)^2/(-c^2*x^2+1))^2)^2*Pi*x^4*e+1/4*I/c^4*b*csgn(I*(1+(c*x+1)^2/(-c^2*x^2+1))^2)^2*csgn(I*(1+(c*x+1)^2/(-c^2*x^2+1)))*Pi*e*arctanh(c*x)+1/6*I/c^4*b*e*Pi*csgn(I*(c*x+1)^2/(c^2*x^2-1))*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1))^2)*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1))^2)+1/24*I/c*b*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1))^2)^2*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1))^2)*Pi*x^3*e-1/24*I/c*b*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1))^2)^2*csgn(I*(c*x+1)^2/(c^2*x^2-1))*Pi*x^3*e+1/24*I/c*b*csgn(I*(c*x+1)/(-c^2*x^2+1)^(1/2))^2*csgn(I*(c*x+1)^2/(c^2*x^2-1))*Pi*x^3*e+1/12*I/c*b*csgn(I*(c*x+1)/(-c^2*x^2+1)^(1/2))*csgn(I*(c*x+1)^2/(c^2*x^2-1))^2*Pi*x^3*e+1/24*I/c*b*csgn(I*(1+(c*x+1)^2/(-c^2*x^2+1)))^2*csgn(I*(1+(c*x+1)^2/(-c^2*x^2+1))^2)*Pi*x^3*e-1/12*I/c*b*csgn(I*(1+(c*x+1)^2/(-c^2*x^2+1)))*csgn(I*(1+(c*x+1)^2/(-c^2*x^2+1))^2)^2*Pi*x^3*e+1/8*I/c^3*b*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1))^2)^2*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1))^2)*Pi*x*e-1/8*I/c^3*b*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1))^2)^2*csgn(I*(c*x+1)^2/(c^2*x^2-1))*Pi*x*e+1/8*I/c^3*b*csgn(I*(c*x+1)/(-c^2*x^2+1)^(1/2))^2*csgn(I*(c*x+1)^2/(c^2*x^2-1))*Pi*x*e+1/4*I/c^3*b*csgn(I*(c*x+1)/(-c^2*x^2+1)^(1/2))*csgn(I*(c*x+1)^2/(c^2*x^2-1))^2*Pi*x*e+1/8*I/c^3*b*csgn(I*(1+(c*x+1)^2/(-c^2*x^2+1)))^2*csgn(I*(1+(c*x+1)^2/(-c^2*x^2+1))^2)*Pi*x*e-1/4*I/c^3*b*csgn(I*(1+(c*x+1)^2/(-c^2*x^2+1)))*csgn(I*(1+(c*x+1)^2/(-c^2*x^2+1))^2)^2*Pi*x*e-1/8*I/c^4*b*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1))^2)^2*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1))^2)*Pi*e*arctanh(c*x)+1/8*I/c^4*b*arctanh(c*x)*Pi*e*csgn(I*(c*x+1)^2/(c^2*x^2-1))*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1))^2)^2-1/8*I/c^4*b*csgn(I*(c*x+1)^2/(c^2*x^2-1))*csgn(I*(c*x+1)/(-c^2*x^2+1)^(1/2))^2*Pi*e*arctanh(c*x)-1/4*I/c^4*b*arctanh(c*x)*Pi*e*csgn(I*(c*x+1)/(-c^2*x^2+1)^(1/2))*csgn(I*(c*x+1)^2/(c^2*x^2-1))^2-1/8*I/c^4*b*csgn(I*(1+(c*x+1)^2/(-c^2*x^2+1))^2)*csgn(I*(1+(c*x+1)^2/(-c^2*x^2+1)))^2*Pi*e*arctanh(c*x)+1/8*I*b*arctanh(c*x)*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1))^2)^2*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1))^2)*Pi*x^4*e-1/8*I*b*arctanh(c*x)*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1))^2)^2*csgn(I*(c*x+1)^2/(c^2*x^2-1))*Pi*x^4*e-1/3/c^4*b*d+1/6/c^4*b*e*(3*arctanh(c*x)*x^3*c^3+3*arctanh(c*x)*x^2*c^2+c^2*x^2+3*arctanh(c*x)*x*c+c*x+3*arctanh(c*x)+4)*(c*x-1)*ln((c*x+1)/(-c^2*x^2+1)^(1/2))+1/6/c*b*ln(2)*x^3*e-1/6/c*b*ln(1+(c*x+1)^2/(-c^2*x^2+1))*x^3*e-1/4/c^2*b*arctanh(c*x)*x^2*e+1/2/c^3*b*ln(2)*x*e-1/2/c^3*b*ln(1+(c*x+1)^2/(-c^2*x^2+1))*x*e-1/2/c^4*b*ln(2)*arctanh(c*x)*e+1/2/c^4*b*arctanh(c*x)*e*ln(1+(c*x+1)^2/(-c^2*x^2+1))","C"
524,1,3994,221,4.133000," ","int(x^2*(a+b*arctanh(c*x))*(d+e*ln(-c^2*x^2+1)),x)","\text{output too large to display}"," ",0,"-1/6/c^3*b*d+5/18*e/c^3*b-1/3/c^3*b*e*ln(2)-2/9*a*e*x^3-2/3*b*e*x*arctanh(c*x)/c^2-2/3*a*e*x/c^2-5/18*b*e*x^2/c-2/9*b*e*x^3*arctanh(c*x)+1/6*b*d*x^2/c-1/12*I/c^3*b*e*Pi*csgn(I*(c*x+1)^2/(c^2*x^2-1))^3-1/12*I/c^3*b*e*Pi*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1))^2)^3-1/12*I/c^3*b*e*Pi*csgn(I*(1+(c*x+1)^2/(-c^2*x^2+1))^2)^3+1/3/c^3*b*ln(1+(c*x+1)^2/(-c^2*x^2+1))^2*e+1/3/c^3*b*arctanh(c*x)*d-8/9/c^3*b*arctanh(c*x)*e-1/3/c^3*b*d*ln(1+(c*x+1)^2/(-c^2*x^2+1))+11/9/c^3*b*e*ln(1+(c*x+1)^2/(-c^2*x^2+1))+1/3*b*arctanh(c*x)*x^3*d+1/3*x^3*a*d+1/3*a*e*x^3*ln(-c^2*x^2+1)+1/3*a*e/c^3*ln(c*x+1)-1/3*a*e/c^3*ln(c*x-1)+1/3/c^3*b*e*(2*arctanh(c*x)*x^3*c^3+c^2*x^2+2*arctanh(c*x)-2*ln(1+(c*x+1)^2/(-c^2*x^2+1))-1)*ln((c*x+1)/(-c^2*x^2+1)^(1/2))-1/6*I*b*arctanh(c*x)*csgn(I*(c*x+1)^2/(c^2*x^2-1))*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1))^2)*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1))^2)*Pi*x^3*e-1/6*I/c^3*b*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1))^2)*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1))^2)*csgn(I*(c*x+1)^2/(c^2*x^2-1))*Pi*e*arctanh(c*x)+1/6*I/c^3*b*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1))^2)*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1))^2)*csgn(I*(c*x+1)^2/(c^2*x^2-1))*e*ln(1+(c*x+1)^2/(-c^2*x^2+1))*Pi-1/12*I/c*b*csgn(I*(c*x+1)^2/(c^2*x^2-1))*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1))^2)*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1))^2)*Pi*x^2*e+1/6*I/c*b*csgn(I*(c*x+1)^2/(c^2*x^2-1))^2*csgn(I*(c*x+1)/(-c^2*x^2+1)^(1/2))*Pi*x^2*e-1/12*I/c*b*csgn(I*(c*x+1)^2/(c^2*x^2-1))*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1))^2)^2*Pi*x^2*e+1/12*I/c*b*csgn(I*(c*x+1)^2/(c^2*x^2-1))*csgn(I*(c*x+1)/(-c^2*x^2+1)^(1/2))^2*Pi*x^2*e+1/12*I/c*b*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1))^2)*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1))^2)^2*Pi*x^2*e-1/6*I/c*b*csgn(I*(1+(c*x+1)^2/(-c^2*x^2+1))^2)^2*csgn(I*(1+(c*x+1)^2/(-c^2*x^2+1)))*Pi*x^2*e+1/12*I/c*b*csgn(I*(1+(c*x+1)^2/(-c^2*x^2+1))^2)*csgn(I*(1+(c*x+1)^2/(-c^2*x^2+1)))^2*Pi*x^2*e+1/3*I/c^3*b*csgn(I*(c*x+1)^2/(c^2*x^2-1))^2*csgn(I*(c*x+1)/(-c^2*x^2+1)^(1/2))*Pi*e*arctanh(c*x)-1/6*I/c^3*b*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1))^2)^2*csgn(I*(c*x+1)^2/(c^2*x^2-1))*Pi*e*arctanh(c*x)-1/6*I/c^3*b*csgn(I*(1+(c*x+1)^2/(-c^2*x^2+1))^2)*csgn(I*(1+(c*x+1)^2/(-c^2*x^2+1)))^2*Pi*ln(1+(c*x+1)^2/(-c^2*x^2+1))*e+1/3*I*b*arctanh(c*x)*csgn(I*(c*x+1)^2/(c^2*x^2-1))^2*csgn(I*(c*x+1)/(-c^2*x^2+1)^(1/2))*Pi*x^3*e-1/6*I*b*arctanh(c*x)*csgn(I*(c*x+1)^2/(c^2*x^2-1))*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1))^2)^2*Pi*x^3*e+1/6*I*b*arctanh(c*x)*csgn(I*(c*x+1)^2/(c^2*x^2-1))*csgn(I*(c*x+1)/(-c^2*x^2+1)^(1/2))^2*Pi*x^3*e+1/6*I*b*arctanh(c*x)*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1))^2)*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1))^2)^2*Pi*x^3*e-1/3*I*b*arctanh(c*x)*csgn(I*(1+(c*x+1)^2/(-c^2*x^2+1))^2)^2*csgn(I*(1+(c*x+1)^2/(-c^2*x^2+1)))*Pi*x^3*e+1/6*I*b*arctanh(c*x)*csgn(I*(1+(c*x+1)^2/(-c^2*x^2+1))^2)*csgn(I*(1+(c*x+1)^2/(-c^2*x^2+1)))^2*Pi*x^3*e+1/12*I/c^3*b*e*Pi*csgn(I*(c*x+1)^2/(c^2*x^2-1))*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1))^2)*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1))^2)+1/6*I/c^3*b*Pi*arctanh(c*x)*e*csgn(I*(c*x+1)/(-c^2*x^2+1)^(1/2))^2*csgn(I*(c*x+1)^2/(c^2*x^2-1))+1/6*I/c^3*b*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1))^2)^2*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1))^2)*Pi*e*arctanh(c*x)-1/3*I/c^3*b*Pi*arctanh(c*x)*e*csgn(I*(1+(c*x+1)^2/(-c^2*x^2+1)))*csgn(I*(1+(c*x+1)^2/(-c^2*x^2+1))^2)^2+1/6*I/c^3*b*csgn(I*(1+(c*x+1)^2/(-c^2*x^2+1))^2)*csgn(I*(1+(c*x+1)^2/(-c^2*x^2+1)))^2*Pi*e*arctanh(c*x)-1/3*I/c^3*b*Pi*ln(1+(c*x+1)^2/(-c^2*x^2+1))*e*csgn(I*(c*x+1)/(-c^2*x^2+1)^(1/2))*csgn(I*(c*x+1)^2/(c^2*x^2-1))^2+1/6*I/c^3*b*Pi*ln(1+(c*x+1)^2/(-c^2*x^2+1))*e*csgn(I*(c*x+1)^2/(c^2*x^2-1))*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1))^2)^2-1/6*I/c^3*b*csgn(I*(c*x+1)^2/(c^2*x^2-1))*csgn(I*(c*x+1)/(-c^2*x^2+1)^(1/2))^2*Pi*ln(1+(c*x+1)^2/(-c^2*x^2+1))*e-1/6*I/c^3*b*Pi*ln(1+(c*x+1)^2/(-c^2*x^2+1))*e*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1))^2)*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1))^2)^2+1/3*I/c^3*b*Pi*ln(1+(c*x+1)^2/(-c^2*x^2+1))*e*csgn(I*(1+(c*x+1)^2/(-c^2*x^2+1)))*csgn(I*(1+(c*x+1)^2/(-c^2*x^2+1))^2)^2+1/6*I*b*arctanh(c*x)*csgn(I*(c*x+1)^2/(c^2*x^2-1))^3*Pi*x^3*e+1/6*I*b*arctanh(c*x)*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1))^2)^3*Pi*x^3*e+1/6*I*b*arctanh(c*x)*csgn(I*(1+(c*x+1)^2/(-c^2*x^2+1))^2)^3*Pi*x^3*e+1/12*I/c*b*csgn(I*(c*x+1)^2/(c^2*x^2-1))^3*Pi*x^2*e+1/12*I/c*b*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1))^2)^3*Pi*x^2*e-1/3/c*b*ln(1+(c*x+1)^2/(-c^2*x^2+1))*x^2*e+1/3/c*b*ln(2)*x^2*e+2/3/c^3*b*arctanh(c*x)*ln(2)*e-2/3/c^3*b*e*ln(1+(c*x+1)^2/(-c^2*x^2+1))*ln(2)-2/3*b*arctanh(c*x)*ln(1+(c*x+1)^2/(-c^2*x^2+1))*x^3*e+2/3*b*arctanh(c*x)*ln(2)*x^3*e+1/12*I/c*b*csgn(I*(1+(c*x+1)^2/(-c^2*x^2+1))^2)^3*Pi*x^2*e+1/6*I/c^3*b*csgn(I*(c*x+1)^2/(c^2*x^2-1))^3*Pi*e*arctanh(c*x)+1/6*I/c^3*b*Pi*arctanh(c*x)*e*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1))^2)^3+1/6*I/c^3*b*csgn(I*(1+(c*x+1)^2/(-c^2*x^2+1))^2)^3*Pi*e*arctanh(c*x)-1/6*I/c^3*b*Pi*ln(1+(c*x+1)^2/(-c^2*x^2+1))*e*csgn(I*(c*x+1)^2/(c^2*x^2-1))^3-1/6*I/c^3*b*Pi*ln(1+(c*x+1)^2/(-c^2*x^2+1))*e*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1))^2)^3-1/6*I/c^3*b*Pi*ln(1+(c*x+1)^2/(-c^2*x^2+1))*e*csgn(I*(1+(c*x+1)^2/(-c^2*x^2+1))^2)^3-1/6*I/c^3*b*Pi*e*csgn(I*(c*x+1)/(-c^2*x^2+1)^(1/2))*csgn(I*(c*x+1)^2/(c^2*x^2-1))^2+1/12*I/c^3*b*e*Pi*csgn(I*(c*x+1)^2/(c^2*x^2-1))*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1))^2)^2-1/12*I/c^3*b*csgn(I*(c*x+1)^2/(c^2*x^2-1))*csgn(I*(c*x+1)/(-c^2*x^2+1)^(1/2))^2*Pi*e-1/12*I/c^3*b*e*Pi*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1))^2)*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1))^2)^2+1/6*I/c^3*b*e*Pi*csgn(I*(1+(c*x+1)^2/(-c^2*x^2+1)))*csgn(I*(1+(c*x+1)^2/(-c^2*x^2+1))^2)^2-1/12*I/c^3*b*e*Pi*csgn(I*(1+(c*x+1)^2/(-c^2*x^2+1)))^2*csgn(I*(1+(c*x+1)^2/(-c^2*x^2+1))^2)","C"
525,1,2951,128,3.851000," ","int(x*(a+b*arctanh(c*x))*(d+e*ln(-c^2*x^2+1)),x)","\text{output too large to display}"," ",0,"-1/4*I*b*arctanh(c*x)*Pi*csgn(I*(c*x+1)^2/(c^2*x^2-1))*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1))^2)*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1))^2)*x^2*e-1/4*I/c*b*Pi*csgn(I*(c*x+1)^2/(c^2*x^2-1))*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1))^2)*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1))^2)*x*e+1/4*I/c^2*b*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1))^2)*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1))^2)*csgn(I*(c*x+1)^2/(c^2*x^2-1))*e*arctanh(c*x)*Pi-1/c^2*b*e*ln(2)+3/2*e/c^2*b+1/4*I/c*b*Pi*csgn(I*(c*x+1)^2/(c^2*x^2-1))*csgn(I*(c*x+1)/(-c^2*x^2+1)^(1/2))^2*x*e+1/4*I/c*b*Pi*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1))^2)^2*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1))^2)*x*e+1/2*a*e/c^2-1/2/c^2*b*d*arctanh(c*x)+1/2*b*arctanh(c*x)*x^2*d-1/2*b*arctanh(c*x)*x^2*e+1/2*a*e*ln(-c^2*x^2+1)*x^2-1/2*a*e/c^2*ln(-c^2*x^2+1)-1/2/c^2*b*d+5/2*b*e*arctanh(c*x)/c^2-1/2*I/c*b*Pi*csgn(I*(1+(c*x+1)^2/(-c^2*x^2+1))^2)^2*csgn(I*(1+(c*x+1)^2/(-c^2*x^2+1)))*x*e+1/4*I/c*b*Pi*csgn(I*(1+(c*x+1)^2/(-c^2*x^2+1))^2)*csgn(I*(1+(c*x+1)^2/(-c^2*x^2+1)))^2*x*e-1/2*I/c^2*b*csgn(I*(c*x+1)^2/(c^2*x^2-1))^2*csgn(I*(c*x+1)/(-c^2*x^2+1)^(1/2))*e*arctanh(c*x)*Pi+1/4*I/c^2*b*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1))^2)^2*csgn(I*(c*x+1)^2/(c^2*x^2-1))*Pi*e*arctanh(c*x)-1/4*I/c^2*b*csgn(I*(c*x+1)^2/(c^2*x^2-1))*csgn(I*(c*x+1)/(-c^2*x^2+1)^(1/2))^2*e*arctanh(c*x)*Pi+1/2*I*b*arctanh(c*x)*Pi*csgn(I*(c*x+1)^2/(c^2*x^2-1))^2*csgn(I*(c*x+1)/(-c^2*x^2+1)^(1/2))*x^2*e-1/4*I*b*arctanh(c*x)*Pi*csgn(I*(c*x+1)^2/(c^2*x^2-1))*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1))^2)^2*x^2*e+1/4*I*b*arctanh(c*x)*Pi*csgn(I*(c*x+1)^2/(c^2*x^2-1))*csgn(I*(c*x+1)/(-c^2*x^2+1)^(1/2))^2*x^2*e+1/4*I*b*arctanh(c*x)*Pi*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1))^2)^2*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1))^2)*x^2*e-1/2*I*b*arctanh(c*x)*Pi*csgn(I*(1+(c*x+1)^2/(-c^2*x^2+1))^2)^2*csgn(I*(1+(c*x+1)^2/(-c^2*x^2+1)))*x^2*e+1/4*I*b*arctanh(c*x)*Pi*csgn(I*(1+(c*x+1)^2/(-c^2*x^2+1))^2)*csgn(I*(1+(c*x+1)^2/(-c^2*x^2+1)))^2*x^2*e-1/4*I/c^2*b*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1))^2)^2*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1))^2)*Pi*e*arctanh(c*x)+1/2*I/c^2*b*csgn(I*(1+(c*x+1)^2/(-c^2*x^2+1))^2)^2*csgn(I*(1+(c*x+1)^2/(-c^2*x^2+1)))*e*arctanh(c*x)*Pi-1/4*I/c^2*b*csgn(I*(1+(c*x+1)^2/(-c^2*x^2+1))^2)*csgn(I*(1+(c*x+1)^2/(-c^2*x^2+1)))^2*e*arctanh(c*x)*Pi+1/4*I/c^2*b*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1))^2)*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1))^2)*csgn(I*(c*x+1)^2/(c^2*x^2-1))*e*Pi+1/2*I/c*b*Pi*csgn(I*(c*x+1)^2/(c^2*x^2-1))^2*csgn(I*(c*x+1)/(-c^2*x^2+1)^(1/2))*x*e-1/4*I/c*b*Pi*csgn(I*(c*x+1)^2/(c^2*x^2-1))*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1))^2)^2*x*e-1/2*a*e*x^2+1/2*a*x^2*d+1/2*b*d*x/c-3/2*b*e*x/c+1/c*b*ln(2)*x*e-1/c*b*ln(1+(c*x+1)^2/(-c^2*x^2+1))*x*e-1/c^2*b*ln(2)*e*arctanh(c*x)+1/c^2*b*ln(1+(c*x+1)^2/(-c^2*x^2+1))*e*arctanh(c*x)-b*arctanh(c*x)*ln(1+(c*x+1)^2/(-c^2*x^2+1))*x^2*e+b*arctanh(c*x)*ln(2)*x^2*e-1/4*I/c^2*b*e*Pi*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1))^2)^3-1/4*I/c^2*b*csgn(I*(1+(c*x+1)^2/(-c^2*x^2+1))^2)^3*e*Pi+1/c^2*b*e*(arctanh(c*x)*x*c+arctanh(c*x)+1)*(c*x-1)*ln((c*x+1)/(-c^2*x^2+1)^(1/2))-1/4*I/c^2*b*Pi*e*csgn(I*(c*x+1)^2/(c^2*x^2-1))^3-1/2*I/c^2*b*Pi*e*csgn(I*(c*x+1)/(-c^2*x^2+1)^(1/2))*csgn(I*(c*x+1)^2/(c^2*x^2-1))^2+1/4*I/c^2*b*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1))^2)^2*csgn(I*(c*x+1)^2/(c^2*x^2-1))*Pi*e-1/4*I/c^2*b*Pi*e*csgn(I*(c*x+1)/(-c^2*x^2+1)^(1/2))^2*csgn(I*(c*x+1)^2/(c^2*x^2-1))-1/4*I/c^2*b*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1))^2)^2*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1))^2)*Pi*e+1/2*I/c^2*b*csgn(I*(1+(c*x+1)^2/(-c^2*x^2+1))^2)^2*csgn(I*(1+(c*x+1)^2/(-c^2*x^2+1)))*Pi*e-1/4*I/c^2*b*csgn(I*(1+(c*x+1)^2/(-c^2*x^2+1))^2)*csgn(I*(1+(c*x+1)^2/(-c^2*x^2+1)))^2*Pi*e+1/4*I*b*arctanh(c*x)*Pi*csgn(I*(c*x+1)^2/(c^2*x^2-1))^3*x^2*e+1/4*I*b*arctanh(c*x)*Pi*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1))^2)^3*x^2*e+1/4*I*b*arctanh(c*x)*Pi*csgn(I*(1+(c*x+1)^2/(-c^2*x^2+1))^2)^3*x^2*e+1/4*I/c*b*Pi*csgn(I*(c*x+1)^2/(c^2*x^2-1))^3*x*e+1/4*I/c*b*Pi*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1))^2)^3*x*e+1/4*I/c*b*Pi*csgn(I*(1+(c*x+1)^2/(-c^2*x^2+1))^2)^3*x*e-1/4*I/c^2*b*csgn(I*(c*x+1)^2/(c^2*x^2-1))^3*Pi*e*arctanh(c*x)-1/4*I/c^2*b*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1))^2)^3*e*arctanh(c*x)*Pi-1/4*I/c^2*b*csgn(I*(1+(c*x+1)^2/(-c^2*x^2+1))^2)^3*Pi*e*arctanh(c*x)","C"
526,1,2529,102,1.481000," ","int((a+b*arctanh(c*x))*(d+e*ln(-c^2*x^2+1)),x)","\text{Expression too large to display}"," ",0,"1/2*I*b*arctanh(c*x)*Pi*csgn(I*(c*x+1)^2/(c^2*x^2-1))*csgn(I*(c*x+1)/(-c^2*x^2+1)^(1/2))^2*x*e+2*b*arctanh(c*x)*ln(2)*x*e+2/c*b*ln(2)*e*arctanh(c*x)-2/c*b*e*ln(1+(c*x+1)^2/(-c^2*x^2+1))*ln(2)-2*b*arctanh(c*x)*ln(1+(c*x+1)^2/(-c^2*x^2+1))*x*e+1/2*I*b*arctanh(c*x)*Pi*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1))^2)^3*x*e+1/2*I*b*arctanh(c*x)*Pi*csgn(I*(1+(c*x+1)^2/(-c^2*x^2+1))^2)^3*x*e+1/2*I/c*b*csgn(I*(c*x+1)^2/(c^2*x^2-1))^3*Pi*e*arctanh(c*x)+1/2*I/c*b*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1))^2)^3*e*arctanh(c*x)*Pi+1/2*I/c*b*csgn(I*(1+(c*x+1)^2/(-c^2*x^2+1))^2)^3*Pi*e*arctanh(c*x)-1/2*I/c*b*Pi*ln(1+(c*x+1)^2/(-c^2*x^2+1))*e*csgn(I*(c*x+1)^2/(c^2*x^2-1))^3-1/2*I/c*b*Pi*ln(1+(c*x+1)^2/(-c^2*x^2+1))*e*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1))^2)^3-1/2*I/c*b*Pi*ln(1+(c*x+1)^2/(-c^2*x^2+1))*e*csgn(I*(1+(c*x+1)^2/(-c^2*x^2+1))^2)^3-2*a*x*e+a*x*e*ln(-c^2*x^2+1)-1/2*I/c*b*csgn(I*(1+(c*x+1)^2/(-c^2*x^2+1))^2)*csgn(I*(1+(c*x+1)^2/(-c^2*x^2+1)))^2*e*ln(1+(c*x+1)^2/(-c^2*x^2+1))*Pi-1/2*I/c*b*csgn(I*(c*x+1)^2/(c^2*x^2-1))*csgn(I*(c*x+1)/(-c^2*x^2+1)^(1/2))^2*e*ln(1+(c*x+1)^2/(-c^2*x^2+1))*Pi+1/2*I/c*b*csgn(I*(c*x+1)^2/(c^2*x^2-1))*csgn(I*(c*x+1)/(-c^2*x^2+1)^(1/2))^2*e*arctanh(c*x)*Pi+I/c*b*csgn(I*(c*x+1)^2/(c^2*x^2-1))^2*csgn(I*(c*x+1)/(-c^2*x^2+1)^(1/2))*e*arctanh(c*x)*Pi+I/c*b*csgn(I*(1+(c*x+1)^2/(-c^2*x^2+1))^2)^2*csgn(I*(1+(c*x+1)^2/(-c^2*x^2+1)))*e*ln(1+(c*x+1)^2/(-c^2*x^2+1))*Pi+I*b*arctanh(c*x)*Pi*csgn(I*(c*x+1)^2/(c^2*x^2-1))^2*csgn(I*(c*x+1)/(-c^2*x^2+1)^(1/2))*x*e-1/2*I/c*b*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1))^2)^2*csgn(I*(c*x+1)^2/(c^2*x^2-1))*Pi*e*arctanh(c*x)-I*b*arctanh(c*x)*Pi*csgn(I*(1+(c*x+1)^2/(-c^2*x^2+1))^2)^2*csgn(I*(1+(c*x+1)^2/(-c^2*x^2+1)))*x*e+1/2*I/c*b*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1))^2)^2*csgn(I*(c*x+1)^2/(c^2*x^2-1))*e*ln(1+(c*x+1)^2/(-c^2*x^2+1))*Pi-1/2*I/c*b*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1))^2)^2*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1))^2)*e*ln(1+(c*x+1)^2/(-c^2*x^2+1))*Pi-I/c*b*csgn(I*(1+(c*x+1)^2/(-c^2*x^2+1))^2)^2*csgn(I*(1+(c*x+1)^2/(-c^2*x^2+1)))*e*arctanh(c*x)*Pi+1/2*I/c*b*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1))^2)^2*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1))^2)*Pi*e*arctanh(c*x)+1/2*I*b*arctanh(c*x)*Pi*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1))^2)*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1))^2)^2*x*e+1/2*I/c*b*csgn(I*(1+(c*x+1)^2/(-c^2*x^2+1))^2)*csgn(I*(1+(c*x+1)^2/(-c^2*x^2+1)))^2*e*arctanh(c*x)*Pi+1/2*I*b*arctanh(c*x)*Pi*csgn(I*(1+(c*x+1)^2/(-c^2*x^2+1))^2)*csgn(I*(1+(c*x+1)^2/(-c^2*x^2+1)))^2*x*e-1/2*I*b*arctanh(c*x)*Pi*csgn(I*(c*x+1)^2/(c^2*x^2-1))*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1))^2)^2*x*e-I/c*b*csgn(I*(c*x+1)^2/(c^2*x^2-1))^2*csgn(I*(c*x+1)/(-c^2*x^2+1)^(1/2))*e*ln(1+(c*x+1)^2/(-c^2*x^2+1))*Pi+a*x*d-a*e/c*ln(c*x-1)+1/c*b*ln(1+(c*x+1)^2/(-c^2*x^2+1))^2*e+1/c*b*d*arctanh(c*x)-2/c*b*e*arctanh(c*x)-1/c*b*d*ln(1+(c*x+1)^2/(-c^2*x^2+1))+2/c*b*e*ln(1+(c*x+1)^2/(-c^2*x^2+1))+b*arctanh(c*x)*x*d-2*b*e*x*arctanh(c*x)+a*e/c*ln(c*x+1)+2*ln((c*x+1)/(-c^2*x^2+1)^(1/2))*(arctanh(c*x)*x*c+arctanh(c*x)-ln(1+(c*x+1)^2/(-c^2*x^2+1)))*b*e/c-1/2*I*b*arctanh(c*x)*Pi*csgn(I*(c*x+1)^2/(c^2*x^2-1))*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1))^2)*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1))^2)*x*e-1/2*I/c*b*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1))^2)*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1))^2)*csgn(I*(c*x+1)^2/(c^2*x^2-1))*e*arctanh(c*x)*Pi+1/2*I/c*b*csgn(I*(c*x+1)^2/(c^2*x^2-1)/(1+(c*x+1)^2/(-c^2*x^2+1))^2)*csgn(I/(1+(c*x+1)^2/(-c^2*x^2+1))^2)*csgn(I*(c*x+1)^2/(c^2*x^2-1))*e*ln(1+(c*x+1)^2/(-c^2*x^2+1))*Pi+1/2*I*b*arctanh(c*x)*Pi*csgn(I*(c*x+1)^2/(c^2*x^2-1))^3*x*e","C"
527,1,1638,202,10.975000," ","int((a+b*arctanh(c*x))*(d+e*ln(-c^2*x^2+1))/x,x)","b e \polylog \left(3, -c x +1\right)-b e \polylog \left(3, c x +1\right)+\dilog \left(c x \right) a e -\frac{\dilog \left(c x \right) b d}{2}-\polylog \left(2, -c x +1\right) \ln \left(c x -1\right) b e +b e \ln \left(c x +1\right) \polylog \left(2, c x +1\right)+\ln \left(c x \right) \ln \left(c x -1\right) a e -\frac{\ln \left(c x \right) \ln \left(c x -1\right) b d}{2}-\frac{\ln \left(c x \right) \ln \left(c x -1\right)^{2} b e}{2}+\frac{b e \ln \left(-c x \right) \ln \left(c x +1\right)^{2}}{2}+\ln \left(c x \right) a d -\frac{i \ln \left(c x \right) \pi  a e \,\mathrm{csgn}\left(i \left(c x -1\right)\right) \mathrm{csgn}\left(i \left(c x +1\right)\right) \mathrm{csgn}\left(i \left(c x -1\right) \left(c x +1\right)\right)}{2}-\frac{i \ln \left(c x \right) \ln \left(c x -1\right) \pi  b e \,\mathrm{csgn}\left(i \left(c x -1\right)\right) \mathrm{csgn}\left(i \left(c x -1\right) \left(c x +1\right)\right)^{2}}{4}+\frac{i \dilog \left(c x \right) \pi  b e \,\mathrm{csgn}\left(i \left(c x -1\right)\right) \mathrm{csgn}\left(i \left(c x +1\right)\right) \mathrm{csgn}\left(i \left(c x -1\right) \left(c x +1\right)\right)}{4}-\frac{i \ln \left(c x \right) \ln \left(c x -1\right) \pi  b e \,\mathrm{csgn}\left(i \left(c x +1\right)\right) \mathrm{csgn}\left(i \left(c x -1\right) \left(c x +1\right)\right)^{2}}{4}-i \dilog \left(c x \right) \pi  b e +i \ln \left(c x \right) \pi  a e -\frac{i \ln \left(c x \right) \pi  b d}{2}+\frac{\ln \left(c x \right) \pi^{2} b e \mathrm{csgn}\left(i \left(c x -1\right)\right)^{3}}{2}+\frac{\ln \left(c x \right) \pi^{2} b e \mathrm{csgn}\left(i \left(c x -1\right) \left(c x +1\right)\right)^{3}}{4}-\frac{\ln \left(c x \right) \pi^{2} b e \mathrm{csgn}\left(i \left(c x -1\right) \left(c x +1\right)\right)^{2}}{2}+\frac{\ln \left(c x \right) \pi^{2} b e}{2}-\left(\frac{i \pi  b e \mathrm{csgn}\left(i \left(c x -1\right)\right)^{2}}{2}-\frac{i \pi  b e \mathrm{csgn}\left(i \left(c x -1\right) \left(c x +1\right)\right)^{2}}{2}-\frac{i \pi  b e \mathrm{csgn}\left(i \left(c x -1\right)\right)^{3}}{2}-\frac{i \pi  b e \,\mathrm{csgn}\left(i \left(c x -1\right)\right) \mathrm{csgn}\left(i \left(c x +1\right)\right) \mathrm{csgn}\left(i \left(c x -1\right) \left(c x +1\right)\right)}{4}+\frac{i \pi  b e \,\mathrm{csgn}\left(i \left(c x -1\right)\right) \mathrm{csgn}\left(i \left(c x -1\right) \left(c x +1\right)\right)^{2}}{4}+\frac{i \pi  b e \,\mathrm{csgn}\left(i \left(c x +1\right)\right) \mathrm{csgn}\left(i \left(c x -1\right) \left(c x +1\right)\right)^{2}}{4}+\frac{i \pi  b e \mathrm{csgn}\left(i \left(c x -1\right) \left(c x +1\right)\right)^{3}}{4}+a e +\frac{b d}{2}\right) \dilog \left(c x +1\right)+\frac{i \ln \left(c x \right) \ln \left(c x -1\right) \pi  b e \,\mathrm{csgn}\left(i \left(c x -1\right)\right) \mathrm{csgn}\left(i \left(c x +1\right)\right) \mathrm{csgn}\left(i \left(c x -1\right) \left(c x +1\right)\right)}{4}+\frac{\ln \left(c x \right) \pi^{2} b e \mathrm{csgn}\left(i \left(c x -1\right)\right)^{3} \mathrm{csgn}\left(i \left(c x +1\right)\right) \mathrm{csgn}\left(i \left(c x -1\right) \left(c x +1\right)\right)^{2}}{4}-\frac{i \ln \left(c x \right) \ln \left(c x -1\right) \pi  b e \mathrm{csgn}\left(i \left(c x -1\right) \left(c x +1\right)\right)^{3}}{4}+\frac{\ln \left(c x \right) \pi^{2} b e \mathrm{csgn}\left(i \left(c x -1\right)\right)^{3} \mathrm{csgn}\left(i \left(c x +1\right)\right) \mathrm{csgn}\left(i \left(c x -1\right) \left(c x +1\right)\right)}{4}-\frac{i \dilog \left(c x \right) \pi  b e \,\mathrm{csgn}\left(i \left(c x -1\right)\right) \mathrm{csgn}\left(i \left(c x -1\right) \left(c x +1\right)\right)^{2}}{4}-\frac{i \dilog \left(c x \right) \pi  b e \,\mathrm{csgn}\left(i \left(c x +1\right)\right) \mathrm{csgn}\left(i \left(c x -1\right) \left(c x +1\right)\right)^{2}}{4}-\frac{\ln \left(c x \right) \pi^{2} b e \,\mathrm{csgn}\left(i \left(c x -1\right)\right) \mathrm{csgn}\left(i \left(c x +1\right)\right) \mathrm{csgn}\left(i \left(c x -1\right) \left(c x +1\right)\right)}{4}+\frac{i \ln \left(c x \right) \ln \left(c x -1\right) \pi  b e \mathrm{csgn}\left(i \left(c x -1\right)\right)^{2}}{2}+\frac{i \ln \left(c x \right) \ln \left(c x -1\right) \pi  b e \mathrm{csgn}\left(i \left(c x -1\right) \left(c x +1\right)\right)^{2}}{2}+\frac{i \ln \left(c x \right) \pi  b d \mathrm{csgn}\left(i \left(c x -1\right)\right)^{2}}{2}-\frac{i \ln \left(c x \right) \pi  b d \mathrm{csgn}\left(i \left(c x -1\right)\right)^{3}}{2}+\frac{\ln \left(c x \right) \pi^{2} b e \mathrm{csgn}\left(i \left(c x -1\right)\right)^{2} \mathrm{csgn}\left(i \left(c x -1\right) \left(c x +1\right)\right)^{2}}{2}-\frac{i \dilog \left(c x \right) \pi  b e \mathrm{csgn}\left(i \left(c x -1\right) \left(c x +1\right)\right)^{3}}{4}+\frac{i \dilog \left(c x \right) \pi  b e \mathrm{csgn}\left(i \left(c x -1\right)\right)^{2}}{2}+\frac{i \dilog \left(c x \right) \pi  b e \mathrm{csgn}\left(i \left(c x -1\right) \left(c x +1\right)\right)^{2}}{2}-\frac{i \dilog \left(c x \right) \pi  b e \mathrm{csgn}\left(i \left(c x -1\right)\right)^{3}}{2}-\frac{\ln \left(c x \right) \pi^{2} b e \mathrm{csgn}\left(i \left(c x -1\right)\right)^{2}}{2}+\frac{\ln \left(c x \right) \pi^{2} b e \mathrm{csgn}\left(i \left(c x -1\right)\right)^{3} \mathrm{csgn}\left(i \left(c x -1\right) \left(c x +1\right)\right)^{3}}{4}-\frac{\ln \left(c x \right) \pi^{2} b e \mathrm{csgn}\left(i \left(c x -1\right)\right)^{2} \mathrm{csgn}\left(i \left(c x -1\right) \left(c x +1\right)\right)^{3}}{4}-\frac{3 \ln \left(c x \right) \pi^{2} b e \mathrm{csgn}\left(i \left(c x -1\right)\right)^{3} \mathrm{csgn}\left(i \left(c x -1\right) \left(c x +1\right)\right)^{2}}{4}+\frac{i \ln \left(c x \right) \pi  a e \mathrm{csgn}\left(i \left(c x -1\right) \left(c x +1\right)\right)^{3}}{2}-i \ln \left(c x \right) \ln \left(c x -1\right) \pi  b e +\frac{\ln \left(c x \right) \pi^{2} b e \,\mathrm{csgn}\left(i \left(c x -1\right)\right) \mathrm{csgn}\left(i \left(c x -1\right) \left(c x +1\right)\right)^{2}}{4}+\frac{\ln \left(c x \right) \pi^{2} b e \,\mathrm{csgn}\left(i \left(c x +1\right)\right) \mathrm{csgn}\left(i \left(c x -1\right) \left(c x +1\right)\right)^{2}}{4}+\frac{\ln \left(c x \right) \pi^{2} b e \mathrm{csgn}\left(i \left(c x -1\right)\right)^{4} \mathrm{csgn}\left(i \left(c x -1\right) \left(c x +1\right)\right)^{2}}{4}-i \ln \left(c x \right) \pi  a e \mathrm{csgn}\left(i \left(c x -1\right) \left(c x +1\right)\right)^{2}-\frac{\ln \left(c x \right) \pi^{2} b e \mathrm{csgn}\left(i \left(c x -1\right)\right)^{2} \mathrm{csgn}\left(i \left(c x +1\right)\right) \mathrm{csgn}\left(i \left(c x -1\right) \left(c x +1\right)\right)^{2}}{4}-\frac{\ln \left(c x \right) \pi^{2} b e \mathrm{csgn}\left(i \left(c x -1\right)\right)^{4} \mathrm{csgn}\left(i \left(c x +1\right)\right) \mathrm{csgn}\left(i \left(c x -1\right) \left(c x +1\right)\right)}{4}+\frac{i \ln \left(c x \right) \pi  a e \,\mathrm{csgn}\left(i \left(c x -1\right)\right) \mathrm{csgn}\left(i \left(c x -1\right) \left(c x +1\right)\right)^{2}}{2}+\frac{i \ln \left(c x \right) \pi  a e \,\mathrm{csgn}\left(i \left(c x +1\right)\right) \mathrm{csgn}\left(i \left(c x -1\right) \left(c x +1\right)\right)^{2}}{2}-\frac{i \ln \left(c x \right) \ln \left(c x -1\right) \pi  b e \mathrm{csgn}\left(i \left(c x -1\right)\right)^{3}}{2}"," ",0,"b*e*polylog(3,-c*x+1)-b*e*polylog(3,c*x+1)+ln(c*x)*ln(c*x-1)*a*e-1/2*ln(c*x)*ln(c*x-1)*b*d-1/2*ln(c*x)*ln(c*x-1)^2*b*e-polylog(2,-c*x+1)*ln(c*x-1)*b*e+1/2*b*e*ln(-c*x)*ln(c*x+1)^2+b*e*ln(c*x+1)*polylog(2,c*x+1)-1/4*I*ln(c*x)*ln(c*x-1)*Pi*b*e*csgn(I*(c*x+1))*csgn(I*(c*x-1)*(c*x+1))^2+1/4*I*dilog(c*x)*Pi*b*e*csgn(I*(c*x-1))*csgn(I*(c*x+1))*csgn(I*(c*x-1)*(c*x+1))-1/2*I*ln(c*x)*Pi*a*e*csgn(I*(c*x-1))*csgn(I*(c*x+1))*csgn(I*(c*x-1)*(c*x+1))-1/4*I*ln(c*x)*ln(c*x-1)*Pi*b*e*csgn(I*(c*x-1))*csgn(I*(c*x-1)*(c*x+1))^2+dilog(c*x)*a*e-1/2*dilog(c*x)*b*d+ln(c*x)*a*d+1/2*ln(c*x)*Pi^2*b*e-1/4*I*dilog(c*x)*Pi*b*e*csgn(I*(c*x-1)*(c*x+1))^3+1/4*I*ln(c*x)*ln(c*x-1)*Pi*b*e*csgn(I*(c*x-1))*csgn(I*(c*x+1))*csgn(I*(c*x-1)*(c*x+1))+1/4*ln(c*x)*Pi^2*b*e*csgn(I*(c*x-1))^3*csgn(I*(c*x+1))*csgn(I*(c*x-1)*(c*x+1))^2+I*ln(c*x)*Pi*a*e-1/4*I*ln(c*x)*ln(c*x-1)*Pi*b*e*csgn(I*(c*x-1)*(c*x+1))^3+1/4*ln(c*x)*Pi^2*b*e*csgn(I*(c*x-1))^3*csgn(I*(c*x-1)*(c*x+1))^3+1/4*ln(c*x)*Pi^2*b*e*csgn(I*(c*x-1))^3*csgn(I*(c*x+1))*csgn(I*(c*x-1)*(c*x+1))-(1/2*I*Pi*b*e*csgn(I*(c*x-1))^2-1/2*I*Pi*b*e*csgn(I*(c*x-1)*(c*x+1))^2-1/2*I*Pi*b*e*csgn(I*(c*x-1))^3-1/4*I*Pi*b*e*csgn(I*(c*x-1))*csgn(I*(c*x+1))*csgn(I*(c*x-1)*(c*x+1))+1/4*I*Pi*b*e*csgn(I*(c*x-1))*csgn(I*(c*x-1)*(c*x+1))^2+1/4*I*Pi*b*e*csgn(I*(c*x+1))*csgn(I*(c*x-1)*(c*x+1))^2+1/4*I*Pi*b*e*csgn(I*(c*x-1)*(c*x+1))^3+a*e+1/2*b*d)*dilog(c*x+1)-1/4*ln(c*x)*Pi^2*b*e*csgn(I*(c*x-1))*csgn(I*(c*x+1))*csgn(I*(c*x-1)*(c*x+1))+1/2*I*ln(c*x)*ln(c*x-1)*Pi*b*e*csgn(I*(c*x-1))^2+1/2*I*ln(c*x)*ln(c*x-1)*Pi*b*e*csgn(I*(c*x-1)*(c*x+1))^2-1/2*I*ln(c*x)*ln(c*x-1)*Pi*b*e*csgn(I*(c*x-1))^3-1/4*ln(c*x)*Pi^2*b*e*csgn(I*(c*x-1))^2*csgn(I*(c*x-1)*(c*x+1))^3-3/4*ln(c*x)*Pi^2*b*e*csgn(I*(c*x-1))^3*csgn(I*(c*x-1)*(c*x+1))^2-1/2*I*ln(c*x)*Pi*b*d-I*dilog(c*x)*Pi*b*e-1/4*ln(c*x)*Pi^2*b*e*csgn(I*(c*x-1))^2*csgn(I*(c*x+1))*csgn(I*(c*x-1)*(c*x+1))^2-1/4*ln(c*x)*Pi^2*b*e*csgn(I*(c*x-1))^4*csgn(I*(c*x+1))*csgn(I*(c*x-1)*(c*x+1))-1/4*I*dilog(c*x)*Pi*b*e*csgn(I*(c*x-1))*csgn(I*(c*x-1)*(c*x+1))^2-1/4*I*dilog(c*x)*Pi*b*e*csgn(I*(c*x+1))*csgn(I*(c*x-1)*(c*x+1))^2+1/2*I*ln(c*x)*Pi*a*e*csgn(I*(c*x-1))*csgn(I*(c*x-1)*(c*x+1))^2+1/2*I*ln(c*x)*Pi*a*e*csgn(I*(c*x+1))*csgn(I*(c*x-1)*(c*x+1))^2+1/2*I*ln(c*x)*Pi*a*e*csgn(I*(c*x-1)*(c*x+1))^3-I*ln(c*x)*ln(c*x-1)*Pi*b*e+1/4*ln(c*x)*Pi^2*b*e*csgn(I*(c*x-1))*csgn(I*(c*x-1)*(c*x+1))^2+1/4*ln(c*x)*Pi^2*b*e*csgn(I*(c*x+1))*csgn(I*(c*x-1)*(c*x+1))^2+1/4*ln(c*x)*Pi^2*b*e*csgn(I*(c*x-1))^4*csgn(I*(c*x-1)*(c*x+1))^2+1/2*I*dilog(c*x)*Pi*b*e*csgn(I*(c*x-1))^2+1/2*I*dilog(c*x)*Pi*b*e*csgn(I*(c*x-1)*(c*x+1))^2-I*ln(c*x)*Pi*a*e*csgn(I*(c*x-1)*(c*x+1))^2+1/2*I*ln(c*x)*Pi*b*d*csgn(I*(c*x-1))^2-1/2*I*ln(c*x)*Pi*b*d*csgn(I*(c*x-1))^3-1/2*I*dilog(c*x)*Pi*b*e*csgn(I*(c*x-1))^3+1/2*ln(c*x)*Pi^2*b*e*csgn(I*(c*x-1))^3+1/4*ln(c*x)*Pi^2*b*e*csgn(I*(c*x-1)*(c*x+1))^3+1/2*ln(c*x)*Pi^2*b*e*csgn(I*(c*x-1))^2*csgn(I*(c*x-1)*(c*x+1))^2-1/2*ln(c*x)*Pi^2*b*e*csgn(I*(c*x-1)*(c*x+1))^2-1/2*ln(c*x)*Pi^2*b*e*csgn(I*(c*x-1))^2","C"
528,0,0,101,8.293000," ","int((a+b*arctanh(c*x))*(d+e*ln(-c^2*x^2+1))/x^2,x)","\int \frac{\left(a +b \arctanh \left(c x \right)\right) \left(d +e \ln \left(-c^{2} x^{2}+1\right)\right)}{x^{2}}\, dx"," ",0,"int((a+b*arctanh(c*x))*(d+e*ln(-c^2*x^2+1))/x^2,x)","F"
529,0,0,143,26.704000," ","int((a+b*arctanh(c*x))*(d+e*ln(-c^2*x^2+1))/x^3,x)","\int \frac{\left(a +b \arctanh \left(c x \right)\right) \left(d +e \ln \left(-c^{2} x^{2}+1\right)\right)}{x^{3}}\, dx"," ",0,"int((a+b*arctanh(c*x))*(d+e*ln(-c^2*x^2+1))/x^3,x)","F"
530,-2,0,183,180.000000," ","int((a+b*arctanh(c*x))*(d+e*ln(-c^2*x^2+1))/x^4,x)","\int \frac{\left(a +b \arctanh \left(c x \right)\right) \left(d +e \ln \left(-c^{2} x^{2}+1\right)\right)}{x^{4}}\, dx"," ",0,"int((a+b*arctanh(c*x))*(d+e*ln(-c^2*x^2+1))/x^4,x)","F"
531,-2,0,218,180.000000," ","int((a+b*arctanh(c*x))*(d+e*ln(-c^2*x^2+1))/x^5,x)","\int \frac{\left(a +b \arctanh \left(c x \right)\right) \left(d +e \ln \left(-c^{2} x^{2}+1\right)\right)}{x^{5}}\, dx"," ",0,"int((a+b*arctanh(c*x))*(d+e*ln(-c^2*x^2+1))/x^5,x)","F"
532,-2,0,234,180.000000," ","int((a+b*arctanh(c*x))*(d+e*ln(-c^2*x^2+1))/x^6,x)","\int \frac{\left(a +b \arctanh \left(c x \right)\right) \left(d +e \ln \left(-c^{2} x^{2}+1\right)\right)}{x^{6}}\, dx"," ",0,"int((a+b*arctanh(c*x))*(d+e*ln(-c^2*x^2+1))/x^6,x)","F"
533,1,10161,448,2.907000," ","int(x*(a+b*arctanh(c*x))*(d+e*ln(g*x^2+f)),x)","\text{output too large to display}"," ",0,"result too large to display","C"
534,0,0,483,2.634000," ","int((a+b*arctanh(c*x))*(d+e*ln(g*x^2+f)),x)","\int \left(a +b \arctanh \left(c x \right)\right) \left(d +e \ln \left(g \,x^{2}+f \right)\right)\, dx"," ",0,"int((a+b*arctanh(c*x))*(d+e*ln(g*x^2+f)),x)","F"
535,0,0,84,1.820000," ","int((a+b*arctanh(c*x))*(d+e*ln(g*x^2+f))/x,x)","\int \frac{\left(a +b \arctanh \left(c x \right)\right) \left(d +e \ln \left(g \,x^{2}+f \right)\right)}{x}\, dx"," ",0,"int((a+b*arctanh(c*x))*(d+e*ln(g*x^2+f))/x,x)","F"
536,0,0,493,2.015000," ","int((a+b*arctanh(c*x))*(d+e*ln(g*x^2+f))/x^2,x)","\int \frac{\left(a +b \arctanh \left(c x \right)\right) \left(d +e \ln \left(g \,x^{2}+f \right)\right)}{x^{2}}\, dx"," ",0,"int((a+b*arctanh(c*x))*(d+e*ln(g*x^2+f))/x^2,x)","F"
537,1,960,408,3.589000," ","int((a+b*arctanh(c*x))*(d+e*ln(g*x^2+f))/x^3,x)","-\frac{d b \,c^{2} \ln \left(c x \right)}{4}+\frac{d b \,c^{2} \ln \left(c x +1\right)}{4}-\frac{d b \ln \left(c x +1\right)}{4 x^{2}}+\frac{d b \,c^{2} \ln \left(-c x \right)}{4}+\frac{d b \ln \left(-c x +1\right)}{4 x^{2}}+\left(-\frac{b e \ln \left(c x +1\right)}{4 x^{2}}+\frac{e \left(b \,c^{2} \ln \left(c x +1\right) x^{2}-b \,c^{2} \ln \left(-c x +1\right) x^{2}-2 x b c +b \ln \left(-c x +1\right)-2 a \right)}{4 x^{2}}\right) \ln \left(g \,x^{2}+f \right)+\frac{a e g \ln \left(x \right)}{f}-\frac{a e g \ln \left(g \,x^{2}+f \right)}{2 f}-\frac{d a}{2 x^{2}}-\frac{b \,c^{2} d \ln \left(-c x +1\right)}{4}-\frac{b c d}{2 x}+\frac{b e \ln \left(-c x +1\right) \ln \left(\frac{c \sqrt{-f g}+\left(-c x +1\right) g -g}{c \sqrt{-f g}-g}\right) c^{2}}{4}-\frac{b e \dilog \left(\frac{c \sqrt{-f g}-\left(c x +1\right) g +g}{c \sqrt{-f g}+g}\right) c^{2}}{4}-\frac{b e \dilog \left(\frac{c \sqrt{-f g}+\left(c x +1\right) g -g}{c \sqrt{-f g}-g}\right) c^{2}}{4}+\frac{b e \dilog \left(\frac{c \sqrt{-f g}-\left(-c x +1\right) g +g}{c \sqrt{-f g}+g}\right) c^{2}}{4}+\frac{b e \dilog \left(\frac{c \sqrt{-f g}+\left(-c x +1\right) g -g}{c \sqrt{-f g}-g}\right) c^{2}}{4}+\frac{b e \ln \left(-c x +1\right) \ln \left(\frac{c \sqrt{-f g}-\left(-c x +1\right) g +g}{c \sqrt{-f g}+g}\right) c^{2}}{4}+\frac{g b e \ln \left(-c x +1\right) \ln \left(\frac{c \sqrt{-f g}+\left(-c x +1\right) g -g}{c \sqrt{-f g}-g}\right)}{4 f}+\frac{g b e \dilog \left(\frac{c \sqrt{-f g}-\left(-c x +1\right) g +g}{c \sqrt{-f g}+g}\right)}{4 f}+\frac{g b e \dilog \left(\frac{c \sqrt{-f g}+\left(-c x +1\right) g -g}{c \sqrt{-f g}-g}\right)}{4 f}-\frac{g b e \dilog \left(c x +1\right)}{2 f}+\frac{g b e \dilog \left(-c x +1\right)}{2 f}-\frac{g b e \dilog \left(\frac{c \sqrt{-f g}-\left(c x +1\right) g +g}{c \sqrt{-f g}+g}\right)}{4 f}-\frac{g b e \dilog \left(\frac{c \sqrt{-f g}+\left(c x +1\right) g -g}{c \sqrt{-f g}-g}\right)}{4 f}-\frac{b e \ln \left(c x +1\right) \ln \left(\frac{c \sqrt{-f g}-\left(c x +1\right) g +g}{c \sqrt{-f g}+g}\right) c^{2}}{4}-\frac{b e \ln \left(c x +1\right) \ln \left(\frac{c \sqrt{-f g}+\left(c x +1\right) g -g}{c \sqrt{-f g}-g}\right) c^{2}}{4}-\frac{g b e \ln \left(c x +1\right) \ln \left(\frac{c \sqrt{-f g}-\left(c x +1\right) g +g}{c \sqrt{-f g}+g}\right)}{4 f}-\frac{g b e \ln \left(c x +1\right) \ln \left(\frac{c \sqrt{-f g}+\left(c x +1\right) g -g}{c \sqrt{-f g}-g}\right)}{4 f}+\frac{g e b c \arctan \left(\frac{x g}{\sqrt{f g}}\right)}{\sqrt{f g}}+\frac{g b e \ln \left(-c x +1\right) \ln \left(\frac{c \sqrt{-f g}-\left(-c x +1\right) g +g}{c \sqrt{-f g}+g}\right)}{4 f}"," ",0,"-1/4*d*b*c^2*ln(c*x)+1/4*d*b*c^2*ln(c*x+1)-1/4*d*b*ln(c*x+1)/x^2+1/4*d*b*c^2*ln(-c*x)+1/4*d*b*ln(-c*x+1)/x^2+(-1/4*b*e/x^2*ln(c*x+1)+1/4*e*(b*c^2*ln(c*x+1)*x^2-b*c^2*ln(-c*x+1)*x^2-2*x*b*c+b*ln(-c*x+1)-2*a)/x^2)*ln(g*x^2+f)+a*e*g*ln(x)/f-1/2*a*e*g*ln(g*x^2+f)/f-1/2/x^2*d*a-1/4*b*c^2*d*ln(-c*x+1)-1/2*b*c*d/x+1/4*b*e*ln(-c*x+1)*ln((c*(-f*g)^(1/2)+(-c*x+1)*g-g)/(c*(-f*g)^(1/2)-g))*c^2+1/4*g*b*e/f*dilog((c*(-f*g)^(1/2)-(-c*x+1)*g+g)/(c*(-f*g)^(1/2)+g))+1/4*g*b*e/f*dilog((c*(-f*g)^(1/2)+(-c*x+1)*g-g)/(c*(-f*g)^(1/2)-g))-1/2*g*b*e*dilog(c*x+1)/f+1/2*g*b*e*dilog(-c*x+1)/f+1/4*b*e*ln(-c*x+1)*ln((c*(-f*g)^(1/2)-(-c*x+1)*g+g)/(c*(-f*g)^(1/2)+g))*c^2-1/4*b*e*dilog((c*(-f*g)^(1/2)-(c*x+1)*g+g)/(c*(-f*g)^(1/2)+g))*c^2-1/4*b*e*dilog((c*(-f*g)^(1/2)+(c*x+1)*g-g)/(c*(-f*g)^(1/2)-g))*c^2+1/4*b*e*dilog((c*(-f*g)^(1/2)-(-c*x+1)*g+g)/(c*(-f*g)^(1/2)+g))*c^2+1/4*b*e*dilog((c*(-f*g)^(1/2)+(-c*x+1)*g-g)/(c*(-f*g)^(1/2)-g))*c^2+1/4*g*b*e/f*ln(-c*x+1)*ln((c*(-f*g)^(1/2)+(-c*x+1)*g-g)/(c*(-f*g)^(1/2)-g))-1/4*b*e*ln(c*x+1)*ln((c*(-f*g)^(1/2)-(c*x+1)*g+g)/(c*(-f*g)^(1/2)+g))*c^2-1/4*b*e*ln(c*x+1)*ln((c*(-f*g)^(1/2)+(c*x+1)*g-g)/(c*(-f*g)^(1/2)-g))*c^2-1/4*g*b*e/f*dilog((c*(-f*g)^(1/2)-(c*x+1)*g+g)/(c*(-f*g)^(1/2)+g))-1/4*g*b*e/f*dilog((c*(-f*g)^(1/2)+(c*x+1)*g-g)/(c*(-f*g)^(1/2)-g))-1/4*g*b*e/f*ln(c*x+1)*ln((c*(-f*g)^(1/2)-(c*x+1)*g+g)/(c*(-f*g)^(1/2)+g))-1/4*g*b*e/f*ln(c*x+1)*ln((c*(-f*g)^(1/2)+(c*x+1)*g-g)/(c*(-f*g)^(1/2)-g))+g*e*b*c/(f*g)^(1/2)*arctan(x*g/(f*g)^(1/2))+1/4*g*b*e/f*ln(-c*x+1)*ln((c*(-f*g)^(1/2)-(-c*x+1)*g+g)/(c*(-f*g)^(1/2)+g))","B"
538,1,247,76,0.073000," ","int(arctanh(c*x)*(a+b*arctanh(c*x))/(c*x+1)^2,x)","-\frac{a \arctanh \left(c x \right)}{c \left(c x +1\right)}-\frac{a \ln \left(c x -1\right)}{4 c}-\frac{a}{2 c \left(c x +1\right)}+\frac{a \ln \left(c x +1\right)}{4 c}-\frac{b \arctanh \left(c x \right)^{2}}{c \left(c x +1\right)}-\frac{b \arctanh \left(c x \right) \ln \left(c x -1\right)}{2 c}-\frac{b \arctanh \left(c x \right)}{c \left(c x +1\right)}+\frac{b \arctanh \left(c x \right) \ln \left(c x +1\right)}{2 c}-\frac{b \ln \left(c x -1\right)^{2}}{8 c}+\frac{b \ln \left(c x -1\right) \ln \left(\frac{1}{2}+\frac{c x}{2}\right)}{4 c}-\frac{b \ln \left(c x -1\right)}{4 c}-\frac{b}{2 c \left(c x +1\right)}+\frac{b \ln \left(c x +1\right)}{4 c}-\frac{b \ln \left(c x +1\right)^{2}}{8 c}-\frac{b \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) \ln \left(\frac{1}{2}+\frac{c x}{2}\right)}{4 c}+\frac{b \ln \left(-\frac{c x}{2}+\frac{1}{2}\right) \ln \left(c x +1\right)}{4 c}"," ",0,"-a*arctanh(c*x)/c/(c*x+1)-1/4*a/c*ln(c*x-1)-1/2*a/c/(c*x+1)+1/4*a/c*ln(c*x+1)-b*arctanh(c*x)^2/c/(c*x+1)-1/2/c*b*arctanh(c*x)*ln(c*x-1)-b*arctanh(c*x)/c/(c*x+1)+1/2/c*b*arctanh(c*x)*ln(c*x+1)-1/8/c*b*ln(c*x-1)^2+1/4/c*b*ln(c*x-1)*ln(1/2+1/2*c*x)-1/4/c*b*ln(c*x-1)-1/2*b/c/(c*x+1)+1/4/c*b*ln(c*x+1)-1/8/c*b*ln(c*x+1)^2-1/4/c*b*ln(-1/2*c*x+1/2)*ln(1/2+1/2*c*x)+1/4/c*b*ln(-1/2*c*x+1/2)*ln(c*x+1)","B"