1,1,114,0,0.481846," ","integrate(x^3*(c*d*x+d)*(a+b*arctanh(c*x)),x, algorithm=""fricas"")","\frac{24 \, a c^{5} d x^{5} + 6 \, {\left(5 \, a + b\right)} c^{4} d x^{4} + 10 \, b c^{3} d x^{3} + 12 \, b c^{2} d x^{2} + 30 \, b c d x - 3 \, b d \log\left(c x + 1\right) + 27 \, b d \log\left(c x - 1\right) + 3 \, {\left(4 \, b c^{5} d x^{5} + 5 \, b c^{4} d x^{4}\right)} \log\left(-\frac{c x + 1}{c x - 1}\right)}{120 \, c^{4}}"," ",0,"1/120*(24*a*c^5*d*x^5 + 6*(5*a + b)*c^4*d*x^4 + 10*b*c^3*d*x^3 + 12*b*c^2*d*x^2 + 30*b*c*d*x - 3*b*d*log(c*x + 1) + 27*b*d*log(c*x - 1) + 3*(4*b*c^5*d*x^5 + 5*b*c^4*d*x^4)*log(-(c*x + 1)/(c*x - 1)))/c^4","A",0
2,1,102,0,0.656310," ","integrate(x^2*(c*d*x+d)*(a+b*arctanh(c*x)),x, algorithm=""fricas"")","\frac{6 \, a c^{4} d x^{4} + 2 \, {\left(4 \, a + b\right)} c^{3} d x^{3} + 4 \, b c^{2} d x^{2} + 6 \, b c d x + b d \log\left(c x + 1\right) + 7 \, b d \log\left(c x - 1\right) + {\left(3 \, b c^{4} d x^{4} + 4 \, b c^{3} d x^{3}\right)} \log\left(-\frac{c x + 1}{c x - 1}\right)}{24 \, c^{3}}"," ",0,"1/24*(6*a*c^4*d*x^4 + 2*(4*a + b)*c^3*d*x^3 + 4*b*c^2*d*x^2 + 6*b*c*d*x + b*d*log(c*x + 1) + 7*b*d*log(c*x - 1) + (3*b*c^4*d*x^4 + 4*b*c^3*d*x^3)*log(-(c*x + 1)/(c*x - 1)))/c^3","A",0
3,1,93,0,0.543059," ","integrate(x*(c*d*x+d)*(a+b*arctanh(c*x)),x, algorithm=""fricas"")","\frac{4 \, a c^{3} d x^{3} + 2 \, {\left(3 \, a + b\right)} c^{2} d x^{2} + 6 \, b c d x - b d \log\left(c x + 1\right) + 5 \, b d \log\left(c x - 1\right) + {\left(2 \, b c^{3} d x^{3} + 3 \, b c^{2} d x^{2}\right)} \log\left(-\frac{c x + 1}{c x - 1}\right)}{12 \, c^{2}}"," ",0,"1/12*(4*a*c^3*d*x^3 + 2*(3*a + b)*c^2*d*x^2 + 6*b*c*d*x - b*d*log(c*x + 1) + 5*b*d*log(c*x - 1) + (2*b*c^3*d*x^3 + 3*b*c^2*d*x^2)*log(-(c*x + 1)/(c*x - 1)))/c^2","A",0
4,1,77,0,0.588066," ","integrate((c*d*x+d)*(a+b*arctanh(c*x)),x, algorithm=""fricas"")","\frac{2 \, a c^{2} d x^{2} + 2 \, {\left(2 \, a + b\right)} c d x + b d \log\left(c x + 1\right) + 3 \, b d \log\left(c x - 1\right) + {\left(b c^{2} d x^{2} + 2 \, b c d x\right)} \log\left(-\frac{c x + 1}{c x - 1}\right)}{4 \, c}"," ",0,"1/4*(2*a*c^2*d*x^2 + 2*(2*a + b)*c*d*x + b*d*log(c*x + 1) + 3*b*d*log(c*x - 1) + (b*c^2*d*x^2 + 2*b*c*d*x)*log(-(c*x + 1)/(c*x - 1)))/c","A",0
5,0,0,0,0.419019," ","integrate((c*d*x+d)*(a+b*arctanh(c*x))/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{a c d x + a d + {\left(b c d x + b d\right)} \operatorname{artanh}\left(c x\right)}{x}, x\right)"," ",0,"integral((a*c*d*x + a*d + (b*c*d*x + b*d)*arctanh(c*x))/x, x)","F",0
6,0,0,0,0.420887," ","integrate((c*d*x+d)*(a+b*arctanh(c*x))/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{a c d x + a d + {\left(b c d x + b d\right)} \operatorname{artanh}\left(c x\right)}{x^{2}}, x\right)"," ",0,"integral((a*c*d*x + a*d + (b*c*d*x + b*d)*arctanh(c*x))/x^2, x)","F",0
7,1,89,0,0.480780," ","integrate((c*d*x+d)*(a+b*arctanh(c*x))/x^3,x, algorithm=""fricas"")","-\frac{b c^{2} d x^{2} \log\left(c x + 1\right) + 3 \, b c^{2} d x^{2} \log\left(c x - 1\right) - 4 \, b c^{2} d x^{2} \log\left(x\right) + 2 \, {\left(2 \, a + b\right)} c d x + 2 \, a d + {\left(2 \, b c d x + b d\right)} \log\left(-\frac{c x + 1}{c x - 1}\right)}{4 \, x^{2}}"," ",0,"-1/4*(b*c^2*d*x^2*log(c*x + 1) + 3*b*c^2*d*x^2*log(c*x - 1) - 4*b*c^2*d*x^2*log(x) + 2*(2*a + b)*c*d*x + 2*a*d + (2*b*c*d*x + b*d)*log(-(c*x + 1)/(c*x - 1)))/x^2","A",0
8,1,101,0,0.451242," ","integrate((c*d*x+d)*(a+b*arctanh(c*x))/x^4,x, algorithm=""fricas"")","\frac{b c^{3} d x^{3} \log\left(c x + 1\right) - 5 \, b c^{3} d x^{3} \log\left(c x - 1\right) + 4 \, b c^{3} d x^{3} \log\left(x\right) - 6 \, b c^{2} d x^{2} - 2 \, {\left(3 \, a + b\right)} c d x - 4 \, a d - {\left(3 \, b c d x + 2 \, b d\right)} \log\left(-\frac{c x + 1}{c x - 1}\right)}{12 \, x^{3}}"," ",0,"1/12*(b*c^3*d*x^3*log(c*x + 1) - 5*b*c^3*d*x^3*log(c*x - 1) + 4*b*c^3*d*x^3*log(x) - 6*b*c^2*d*x^2 - 2*(3*a + b)*c*d*x - 4*a*d - (3*b*c*d*x + 2*b*d)*log(-(c*x + 1)/(c*x - 1)))/x^3","A",0
9,1,110,0,0.457186," ","integrate((c*d*x+d)*(a+b*arctanh(c*x))/x^5,x, algorithm=""fricas"")","-\frac{b c^{4} d x^{4} \log\left(c x + 1\right) + 7 \, b c^{4} d x^{4} \log\left(c x - 1\right) - 8 \, b c^{4} d x^{4} \log\left(x\right) + 6 \, b c^{3} d x^{3} + 4 \, b c^{2} d x^{2} + 2 \, {\left(4 \, a + b\right)} c d x + 6 \, a d + {\left(4 \, b c d x + 3 \, b d\right)} \log\left(-\frac{c x + 1}{c x - 1}\right)}{24 \, x^{4}}"," ",0,"-1/24*(b*c^4*d*x^4*log(c*x + 1) + 7*b*c^4*d*x^4*log(c*x - 1) - 8*b*c^4*d*x^4*log(x) + 6*b*c^3*d*x^3 + 4*b*c^2*d*x^2 + 2*(4*a + b)*c*d*x + 6*a*d + (4*b*c*d*x + 3*b*d)*log(-(c*x + 1)/(c*x - 1)))/x^4","A",0
10,1,162,0,0.451798," ","integrate(x^3*(c*d*x+d)^2*(a+b*arctanh(c*x)),x, algorithm=""fricas"")","\frac{60 \, a c^{6} d^{2} x^{6} + 12 \, {\left(12 \, a + b\right)} c^{5} d^{2} x^{5} + 18 \, {\left(5 \, a + 2 \, b\right)} c^{4} d^{2} x^{4} + 50 \, b c^{3} d^{2} x^{3} + 72 \, b c^{2} d^{2} x^{2} + 150 \, b c d^{2} x - 3 \, b d^{2} \log\left(c x + 1\right) + 147 \, b d^{2} \log\left(c x - 1\right) + 3 \, {\left(10 \, b c^{6} d^{2} x^{6} + 24 \, b c^{5} d^{2} x^{5} + 15 \, b c^{4} d^{2} x^{4}\right)} \log\left(-\frac{c x + 1}{c x - 1}\right)}{360 \, c^{4}}"," ",0,"1/360*(60*a*c^6*d^2*x^6 + 12*(12*a + b)*c^5*d^2*x^5 + 18*(5*a + 2*b)*c^4*d^2*x^4 + 50*b*c^3*d^2*x^3 + 72*b*c^2*d^2*x^2 + 150*b*c*d^2*x - 3*b*d^2*log(c*x + 1) + 147*b*d^2*log(c*x - 1) + 3*(10*b*c^6*d^2*x^6 + 24*b*c^5*d^2*x^5 + 15*b*c^4*d^2*x^4)*log(-(c*x + 1)/(c*x - 1)))/c^4","A",0
11,1,146,0,0.503745," ","integrate(x^2*(c*d*x+d)^2*(a+b*arctanh(c*x)),x, algorithm=""fricas"")","\frac{12 \, a c^{5} d^{2} x^{5} + 3 \, {\left(10 \, a + b\right)} c^{4} d^{2} x^{4} + 10 \, {\left(2 \, a + b\right)} c^{3} d^{2} x^{3} + 16 \, b c^{2} d^{2} x^{2} + 30 \, b c d^{2} x + b d^{2} \log\left(c x + 1\right) + 31 \, b d^{2} \log\left(c x - 1\right) + {\left(6 \, b c^{5} d^{2} x^{5} + 15 \, b c^{4} d^{2} x^{4} + 10 \, b c^{3} d^{2} x^{3}\right)} \log\left(-\frac{c x + 1}{c x - 1}\right)}{60 \, c^{3}}"," ",0,"1/60*(12*a*c^5*d^2*x^5 + 3*(10*a + b)*c^4*d^2*x^4 + 10*(2*a + b)*c^3*d^2*x^3 + 16*b*c^2*d^2*x^2 + 30*b*c*d^2*x + b*d^2*log(c*x + 1) + 31*b*d^2*log(c*x - 1) + (6*b*c^5*d^2*x^5 + 15*b*c^4*d^2*x^4 + 10*b*c^3*d^2*x^3)*log(-(c*x + 1)/(c*x - 1)))/c^3","A",0
12,1,137,0,0.691494," ","integrate(x*(c*d*x+d)^2*(a+b*arctanh(c*x)),x, algorithm=""fricas"")","\frac{6 \, a c^{4} d^{2} x^{4} + 2 \, {\left(8 \, a + b\right)} c^{3} d^{2} x^{3} + 4 \, {\left(3 \, a + 2 \, b\right)} c^{2} d^{2} x^{2} + 18 \, b c d^{2} x - b d^{2} \log\left(c x + 1\right) + 17 \, b d^{2} \log\left(c x - 1\right) + {\left(3 \, b c^{4} d^{2} x^{4} + 8 \, b c^{3} d^{2} x^{3} + 6 \, b c^{2} d^{2} x^{2}\right)} \log\left(-\frac{c x + 1}{c x - 1}\right)}{24 \, c^{2}}"," ",0,"1/24*(6*a*c^4*d^2*x^4 + 2*(8*a + b)*c^3*d^2*x^3 + 4*(3*a + 2*b)*c^2*d^2*x^2 + 18*b*c*d^2*x - b*d^2*log(c*x + 1) + 17*b*d^2*log(c*x - 1) + (3*b*c^4*d^2*x^4 + 8*b*c^3*d^2*x^3 + 6*b*c^2*d^2*x^2)*log(-(c*x + 1)/(c*x - 1)))/c^2","A",0
13,1,114,0,0.453388," ","integrate((c*d*x+d)^2*(a+b*arctanh(c*x)),x, algorithm=""fricas"")","\frac{2 \, a c^{3} d^{2} x^{3} + {\left(6 \, a + b\right)} c^{2} d^{2} x^{2} + 6 \, {\left(a + b\right)} c d^{2} x + b d^{2} \log\left(c x + 1\right) + 7 \, b d^{2} \log\left(c x - 1\right) + {\left(b c^{3} d^{2} x^{3} + 3 \, b c^{2} d^{2} x^{2} + 3 \, b c d^{2} x\right)} \log\left(-\frac{c x + 1}{c x - 1}\right)}{6 \, c}"," ",0,"1/6*(2*a*c^3*d^2*x^3 + (6*a + b)*c^2*d^2*x^2 + 6*(a + b)*c*d^2*x + b*d^2*log(c*x + 1) + 7*b*d^2*log(c*x - 1) + (b*c^3*d^2*x^3 + 3*b*c^2*d^2*x^2 + 3*b*c*d^2*x)*log(-(c*x + 1)/(c*x - 1)))/c","A",0
14,0,0,0,0.411138," ","integrate((c*d*x+d)^2*(a+b*arctanh(c*x))/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{a c^{2} d^{2} x^{2} + 2 \, a c d^{2} x + a d^{2} + {\left(b c^{2} d^{2} x^{2} + 2 \, b c d^{2} x + b d^{2}\right)} \operatorname{artanh}\left(c x\right)}{x}, x\right)"," ",0,"integral((a*c^2*d^2*x^2 + 2*a*c*d^2*x + a*d^2 + (b*c^2*d^2*x^2 + 2*b*c*d^2*x + b*d^2)*arctanh(c*x))/x, x)","F",0
15,0,0,0,0.462255," ","integrate((c*d*x+d)^2*(a+b*arctanh(c*x))/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{a c^{2} d^{2} x^{2} + 2 \, a c d^{2} x + a d^{2} + {\left(b c^{2} d^{2} x^{2} + 2 \, b c d^{2} x + b d^{2}\right)} \operatorname{artanh}\left(c x\right)}{x^{2}}, x\right)"," ",0,"integral((a*c^2*d^2*x^2 + 2*a*c*d^2*x + a*d^2 + (b*c^2*d^2*x^2 + 2*b*c*d^2*x + b*d^2)*arctanh(c*x))/x^2, x)","F",0
16,0,0,0,0.614750," ","integrate((c*d*x+d)^2*(a+b*arctanh(c*x))/x^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{a c^{2} d^{2} x^{2} + 2 \, a c d^{2} x + a d^{2} + {\left(b c^{2} d^{2} x^{2} + 2 \, b c d^{2} x + b d^{2}\right)} \operatorname{artanh}\left(c x\right)}{x^{3}}, x\right)"," ",0,"integral((a*c^2*d^2*x^2 + 2*a*c*d^2*x + a*d^2 + (b*c^2*d^2*x^2 + 2*b*c*d^2*x + b*d^2)*arctanh(c*x))/x^3, x)","F",0
17,1,128,0,0.632759," ","integrate((c*d*x+d)^2*(a+b*arctanh(c*x))/x^4,x, algorithm=""fricas"")","-\frac{b c^{3} d^{2} x^{3} \log\left(c x + 1\right) + 7 \, b c^{3} d^{2} x^{3} \log\left(c x - 1\right) - 8 \, b c^{3} d^{2} x^{3} \log\left(x\right) + 6 \, {\left(a + b\right)} c^{2} d^{2} x^{2} + {\left(6 \, a + b\right)} c d^{2} x + 2 \, a d^{2} + {\left(3 \, b c^{2} d^{2} x^{2} + 3 \, b c d^{2} x + b d^{2}\right)} \log\left(-\frac{c x + 1}{c x - 1}\right)}{6 \, x^{3}}"," ",0,"-1/6*(b*c^3*d^2*x^3*log(c*x + 1) + 7*b*c^3*d^2*x^3*log(c*x - 1) - 8*b*c^3*d^2*x^3*log(x) + 6*(a + b)*c^2*d^2*x^2 + (6*a + b)*c*d^2*x + 2*a*d^2 + (3*b*c^2*d^2*x^2 + 3*b*c*d^2*x + b*d^2)*log(-(c*x + 1)/(c*x - 1)))/x^3","A",0
18,1,147,0,0.695750," ","integrate((c*d*x+d)^2*(a+b*arctanh(c*x))/x^5,x, algorithm=""fricas"")","\frac{b c^{4} d^{2} x^{4} \log\left(c x + 1\right) - 17 \, b c^{4} d^{2} x^{4} \log\left(c x - 1\right) + 16 \, b c^{4} d^{2} x^{4} \log\left(x\right) - 18 \, b c^{3} d^{2} x^{3} - 4 \, {\left(3 \, a + 2 \, b\right)} c^{2} d^{2} x^{2} - 2 \, {\left(8 \, a + b\right)} c d^{2} x - 6 \, a d^{2} - {\left(6 \, b c^{2} d^{2} x^{2} + 8 \, b c d^{2} x + 3 \, b d^{2}\right)} \log\left(-\frac{c x + 1}{c x - 1}\right)}{24 \, x^{4}}"," ",0,"1/24*(b*c^4*d^2*x^4*log(c*x + 1) - 17*b*c^4*d^2*x^4*log(c*x - 1) + 16*b*c^4*d^2*x^4*log(x) - 18*b*c^3*d^2*x^3 - 4*(3*a + 2*b)*c^2*d^2*x^2 - 2*(8*a + b)*c*d^2*x - 6*a*d^2 - (6*b*c^2*d^2*x^2 + 8*b*c*d^2*x + 3*b*d^2)*log(-(c*x + 1)/(c*x - 1)))/x^4","A",0
19,1,156,0,0.535401," ","integrate((c*d*x+d)^2*(a+b*arctanh(c*x))/x^6,x, algorithm=""fricas"")","-\frac{b c^{5} d^{2} x^{5} \log\left(c x + 1\right) + 31 \, b c^{5} d^{2} x^{5} \log\left(c x - 1\right) - 32 \, b c^{5} d^{2} x^{5} \log\left(x\right) + 30 \, b c^{4} d^{2} x^{4} + 16 \, b c^{3} d^{2} x^{3} + 10 \, {\left(2 \, a + b\right)} c^{2} d^{2} x^{2} + 3 \, {\left(10 \, a + b\right)} c d^{2} x + 12 \, a d^{2} + {\left(10 \, b c^{2} d^{2} x^{2} + 15 \, b c d^{2} x + 6 \, b d^{2}\right)} \log\left(-\frac{c x + 1}{c x - 1}\right)}{60 \, x^{5}}"," ",0,"-1/60*(b*c^5*d^2*x^5*log(c*x + 1) + 31*b*c^5*d^2*x^5*log(c*x - 1) - 32*b*c^5*d^2*x^5*log(x) + 30*b*c^4*d^2*x^4 + 16*b*c^3*d^2*x^3 + 10*(2*a + b)*c^2*d^2*x^2 + 3*(10*a + b)*c*d^2*x + 12*a*d^2 + (10*b*c^2*d^2*x^2 + 15*b*c*d^2*x + 6*b*d^2)*log(-(c*x + 1)/(c*x - 1)))/x^5","A",0
20,1,190,0,0.440634," ","integrate(x^3*(c*d*x+d)^3*(a+b*arctanh(c*x)),x, algorithm=""fricas"")","\frac{120 \, a c^{7} d^{3} x^{7} + 20 \, {\left(21 \, a + b\right)} c^{6} d^{3} x^{6} + 84 \, {\left(6 \, a + b\right)} c^{5} d^{3} x^{5} + 6 \, {\left(35 \, a + 26 \, b\right)} c^{4} d^{3} x^{4} + 210 \, b c^{3} d^{3} x^{3} + 312 \, b c^{2} d^{3} x^{2} + 630 \, b c d^{3} x - 3 \, b d^{3} \log\left(c x + 1\right) + 627 \, b d^{3} \log\left(c x - 1\right) + 3 \, {\left(20 \, b c^{7} d^{3} x^{7} + 70 \, b c^{6} d^{3} x^{6} + 84 \, b c^{5} d^{3} x^{5} + 35 \, b c^{4} d^{3} x^{4}\right)} \log\left(-\frac{c x + 1}{c x - 1}\right)}{840 \, c^{4}}"," ",0,"1/840*(120*a*c^7*d^3*x^7 + 20*(21*a + b)*c^6*d^3*x^6 + 84*(6*a + b)*c^5*d^3*x^5 + 6*(35*a + 26*b)*c^4*d^3*x^4 + 210*b*c^3*d^3*x^3 + 312*b*c^2*d^3*x^2 + 630*b*c*d^3*x - 3*b*d^3*log(c*x + 1) + 627*b*d^3*log(c*x - 1) + 3*(20*b*c^7*d^3*x^7 + 70*b*c^6*d^3*x^6 + 84*b*c^5*d^3*x^5 + 35*b*c^4*d^3*x^4)*log(-(c*x + 1)/(c*x - 1)))/c^4","A",0
21,1,178,0,0.439422," ","integrate(x^2*(c*d*x+d)^3*(a+b*arctanh(c*x)),x, algorithm=""fricas"")","\frac{60 \, a c^{6} d^{3} x^{6} + 12 \, {\left(18 \, a + b\right)} c^{5} d^{3} x^{5} + 54 \, {\left(5 \, a + b\right)} c^{4} d^{3} x^{4} + 10 \, {\left(12 \, a + 11 \, b\right)} c^{3} d^{3} x^{3} + 168 \, b c^{2} d^{3} x^{2} + 330 \, b c d^{3} x + 3 \, b d^{3} \log\left(c x + 1\right) + 333 \, b d^{3} \log\left(c x - 1\right) + 3 \, {\left(10 \, b c^{6} d^{3} x^{6} + 36 \, b c^{5} d^{3} x^{5} + 45 \, b c^{4} d^{3} x^{4} + 20 \, b c^{3} d^{3} x^{3}\right)} \log\left(-\frac{c x + 1}{c x - 1}\right)}{360 \, c^{3}}"," ",0,"1/360*(60*a*c^6*d^3*x^6 + 12*(18*a + b)*c^5*d^3*x^5 + 54*(5*a + b)*c^4*d^3*x^4 + 10*(12*a + 11*b)*c^3*d^3*x^3 + 168*b*c^2*d^3*x^2 + 330*b*c*d^3*x + 3*b*d^3*log(c*x + 1) + 333*b*d^3*log(c*x - 1) + 3*(10*b*c^6*d^3*x^6 + 36*b*c^5*d^3*x^5 + 45*b*c^4*d^3*x^4 + 20*b*c^3*d^3*x^3)*log(-(c*x + 1)/(c*x - 1)))/c^3","A",0
22,1,165,0,0.489405," ","integrate(x*(c*d*x+d)^3*(a+b*arctanh(c*x)),x, algorithm=""fricas"")","\frac{8 \, a c^{5} d^{3} x^{5} + 2 \, {\left(15 \, a + b\right)} c^{4} d^{3} x^{4} + 10 \, {\left(4 \, a + b\right)} c^{3} d^{3} x^{3} + 4 \, {\left(5 \, a + 6 \, b\right)} c^{2} d^{3} x^{2} + 50 \, b c d^{3} x - b d^{3} \log\left(c x + 1\right) + 49 \, b d^{3} \log\left(c x - 1\right) + {\left(4 \, b c^{5} d^{3} x^{5} + 15 \, b c^{4} d^{3} x^{4} + 20 \, b c^{3} d^{3} x^{3} + 10 \, b c^{2} d^{3} x^{2}\right)} \log\left(-\frac{c x + 1}{c x - 1}\right)}{40 \, c^{2}}"," ",0,"1/40*(8*a*c^5*d^3*x^5 + 2*(15*a + b)*c^4*d^3*x^4 + 10*(4*a + b)*c^3*d^3*x^3 + 4*(5*a + 6*b)*c^2*d^3*x^2 + 50*b*c*d^3*x - b*d^3*log(c*x + 1) + 49*b*d^3*log(c*x - 1) + (4*b*c^5*d^3*x^5 + 15*b*c^4*d^3*x^4 + 20*b*c^3*d^3*x^3 + 10*b*c^2*d^3*x^2)*log(-(c*x + 1)/(c*x - 1)))/c^2","A",0
23,1,149,0,0.485973," ","integrate((c*d*x+d)^3*(a+b*arctanh(c*x)),x, algorithm=""fricas"")","\frac{6 \, a c^{4} d^{3} x^{4} + 2 \, {\left(12 \, a + b\right)} c^{3} d^{3} x^{3} + 12 \, {\left(3 \, a + b\right)} c^{2} d^{3} x^{2} + 6 \, {\left(4 \, a + 7 \, b\right)} c d^{3} x + 3 \, b d^{3} \log\left(c x + 1\right) + 45 \, b d^{3} \log\left(c x - 1\right) + 3 \, {\left(b c^{4} d^{3} x^{4} + 4 \, b c^{3} d^{3} x^{3} + 6 \, b c^{2} d^{3} x^{2} + 4 \, b c d^{3} x\right)} \log\left(-\frac{c x + 1}{c x - 1}\right)}{24 \, c}"," ",0,"1/24*(6*a*c^4*d^3*x^4 + 2*(12*a + b)*c^3*d^3*x^3 + 12*(3*a + b)*c^2*d^3*x^2 + 6*(4*a + 7*b)*c*d^3*x + 3*b*d^3*log(c*x + 1) + 45*b*d^3*log(c*x - 1) + 3*(b*c^4*d^3*x^4 + 4*b*c^3*d^3*x^3 + 6*b*c^2*d^3*x^2 + 4*b*c*d^3*x)*log(-(c*x + 1)/(c*x - 1)))/c","A",0
24,0,0,0,0.406830," ","integrate((c*d*x+d)^3*(a+b*arctanh(c*x))/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{a c^{3} d^{3} x^{3} + 3 \, a c^{2} d^{3} x^{2} + 3 \, a c d^{3} x + a d^{3} + {\left(b c^{3} d^{3} x^{3} + 3 \, b c^{2} d^{3} x^{2} + 3 \, b c d^{3} x + b d^{3}\right)} \operatorname{artanh}\left(c x\right)}{x}, x\right)"," ",0,"integral((a*c^3*d^3*x^3 + 3*a*c^2*d^3*x^2 + 3*a*c*d^3*x + a*d^3 + (b*c^3*d^3*x^3 + 3*b*c^2*d^3*x^2 + 3*b*c*d^3*x + b*d^3)*arctanh(c*x))/x, x)","F",0
25,0,0,0,0.459227," ","integrate((c*d*x+d)^3*(a+b*arctanh(c*x))/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{a c^{3} d^{3} x^{3} + 3 \, a c^{2} d^{3} x^{2} + 3 \, a c d^{3} x + a d^{3} + {\left(b c^{3} d^{3} x^{3} + 3 \, b c^{2} d^{3} x^{2} + 3 \, b c d^{3} x + b d^{3}\right)} \operatorname{artanh}\left(c x\right)}{x^{2}}, x\right)"," ",0,"integral((a*c^3*d^3*x^3 + 3*a*c^2*d^3*x^2 + 3*a*c*d^3*x + a*d^3 + (b*c^3*d^3*x^3 + 3*b*c^2*d^3*x^2 + 3*b*c*d^3*x + b*d^3)*arctanh(c*x))/x^2, x)","F",0
26,0,0,0,0.577124," ","integrate((c*d*x+d)^3*(a+b*arctanh(c*x))/x^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{a c^{3} d^{3} x^{3} + 3 \, a c^{2} d^{3} x^{2} + 3 \, a c d^{3} x + a d^{3} + {\left(b c^{3} d^{3} x^{3} + 3 \, b c^{2} d^{3} x^{2} + 3 \, b c d^{3} x + b d^{3}\right)} \operatorname{artanh}\left(c x\right)}{x^{3}}, x\right)"," ",0,"integral((a*c^3*d^3*x^3 + 3*a*c^2*d^3*x^2 + 3*a*c*d^3*x + a*d^3 + (b*c^3*d^3*x^3 + 3*b*c^2*d^3*x^2 + 3*b*c*d^3*x + b*d^3)*arctanh(c*x))/x^3, x)","F",0
27,0,0,0,0.444677," ","integrate((c*d*x+d)^3*(a+b*arctanh(c*x))/x^4,x, algorithm=""fricas"")","{\rm integral}\left(\frac{a c^{3} d^{3} x^{3} + 3 \, a c^{2} d^{3} x^{2} + 3 \, a c d^{3} x + a d^{3} + {\left(b c^{3} d^{3} x^{3} + 3 \, b c^{2} d^{3} x^{2} + 3 \, b c d^{3} x + b d^{3}\right)} \operatorname{artanh}\left(c x\right)}{x^{4}}, x\right)"," ",0,"integral((a*c^3*d^3*x^3 + 3*a*c^2*d^3*x^2 + 3*a*c*d^3*x + a*d^3 + (b*c^3*d^3*x^3 + 3*b*c^2*d^3*x^2 + 3*b*c*d^3*x + b*d^3)*arctanh(c*x))/x^4, x)","F",0
28,1,163,0,0.423293," ","integrate((c*d*x+d)^3*(a+b*arctanh(c*x))/x^5,x, algorithm=""fricas"")","-\frac{3 \, b c^{4} d^{3} x^{4} \log\left(c x + 1\right) + 45 \, b c^{4} d^{3} x^{4} \log\left(c x - 1\right) - 48 \, b c^{4} d^{3} x^{4} \log\left(x\right) + 6 \, {\left(4 \, a + 7 \, b\right)} c^{3} d^{3} x^{3} + 12 \, {\left(3 \, a + b\right)} c^{2} d^{3} x^{2} + 2 \, {\left(12 \, a + b\right)} c d^{3} x + 6 \, a d^{3} + 3 \, {\left(4 \, b c^{3} d^{3} x^{3} + 6 \, b c^{2} d^{3} x^{2} + 4 \, b c d^{3} x + b d^{3}\right)} \log\left(-\frac{c x + 1}{c x - 1}\right)}{24 \, x^{4}}"," ",0,"-1/24*(3*b*c^4*d^3*x^4*log(c*x + 1) + 45*b*c^4*d^3*x^4*log(c*x - 1) - 48*b*c^4*d^3*x^4*log(x) + 6*(4*a + 7*b)*c^3*d^3*x^3 + 12*(3*a + b)*c^2*d^3*x^2 + 2*(12*a + b)*c*d^3*x + 6*a*d^3 + 3*(4*b*c^3*d^3*x^3 + 6*b*c^2*d^3*x^2 + 4*b*c*d^3*x + b*d^3)*log(-(c*x + 1)/(c*x - 1)))/x^4","A",0
29,1,175,0,0.452249," ","integrate((c*d*x+d)^3*(a+b*arctanh(c*x))/x^6,x, algorithm=""fricas"")","\frac{b c^{5} d^{3} x^{5} \log\left(c x + 1\right) - 49 \, b c^{5} d^{3} x^{5} \log\left(c x - 1\right) + 48 \, b c^{5} d^{3} x^{5} \log\left(x\right) - 50 \, b c^{4} d^{3} x^{4} - 4 \, {\left(5 \, a + 6 \, b\right)} c^{3} d^{3} x^{3} - 10 \, {\left(4 \, a + b\right)} c^{2} d^{3} x^{2} - 2 \, {\left(15 \, a + b\right)} c d^{3} x - 8 \, a d^{3} - {\left(10 \, b c^{3} d^{3} x^{3} + 20 \, b c^{2} d^{3} x^{2} + 15 \, b c d^{3} x + 4 \, b d^{3}\right)} \log\left(-\frac{c x + 1}{c x - 1}\right)}{40 \, x^{5}}"," ",0,"1/40*(b*c^5*d^3*x^5*log(c*x + 1) - 49*b*c^5*d^3*x^5*log(c*x - 1) + 48*b*c^5*d^3*x^5*log(x) - 50*b*c^4*d^3*x^4 - 4*(5*a + 6*b)*c^3*d^3*x^3 - 10*(4*a + b)*c^2*d^3*x^2 - 2*(15*a + b)*c*d^3*x - 8*a*d^3 - (10*b*c^3*d^3*x^3 + 20*b*c^2*d^3*x^2 + 15*b*c*d^3*x + 4*b*d^3)*log(-(c*x + 1)/(c*x - 1)))/x^5","A",0
30,1,188,0,0.480276," ","integrate((c*d*x+d)^3*(a+b*arctanh(c*x))/x^7,x, algorithm=""fricas"")","-\frac{3 \, b c^{6} d^{3} x^{6} \log\left(c x + 1\right) + 333 \, b c^{6} d^{3} x^{6} \log\left(c x - 1\right) - 336 \, b c^{6} d^{3} x^{6} \log\left(x\right) + 330 \, b c^{5} d^{3} x^{5} + 168 \, b c^{4} d^{3} x^{4} + 10 \, {\left(12 \, a + 11 \, b\right)} c^{3} d^{3} x^{3} + 54 \, {\left(5 \, a + b\right)} c^{2} d^{3} x^{2} + 12 \, {\left(18 \, a + b\right)} c d^{3} x + 60 \, a d^{3} + 3 \, {\left(20 \, b c^{3} d^{3} x^{3} + 45 \, b c^{2} d^{3} x^{2} + 36 \, b c d^{3} x + 10 \, b d^{3}\right)} \log\left(-\frac{c x + 1}{c x - 1}\right)}{360 \, x^{6}}"," ",0,"-1/360*(3*b*c^6*d^3*x^6*log(c*x + 1) + 333*b*c^6*d^3*x^6*log(c*x - 1) - 336*b*c^6*d^3*x^6*log(x) + 330*b*c^5*d^3*x^5 + 168*b*c^4*d^3*x^4 + 10*(12*a + 11*b)*c^3*d^3*x^3 + 54*(5*a + b)*c^2*d^3*x^2 + 12*(18*a + b)*c*d^3*x + 60*a*d^3 + 3*(20*b*c^3*d^3*x^3 + 45*b*c^2*d^3*x^2 + 36*b*c*d^3*x + 10*b*d^3)*log(-(c*x + 1)/(c*x - 1)))/x^6","A",0
31,1,222,0,0.548255," ","integrate(x^3*(c*d*x+d)^4*(a+b*arctanh(c*x)),x, algorithm=""fricas"")","\frac{210 \, a c^{8} d^{4} x^{8} + 30 \, {\left(32 \, a + b\right)} c^{7} d^{4} x^{7} + 80 \, {\left(21 \, a + 2 \, b\right)} c^{6} d^{4} x^{6} + 42 \, {\left(32 \, a + 9 \, b\right)} c^{5} d^{4} x^{5} + 12 \, {\left(35 \, a + 48 \, b\right)} c^{4} d^{4} x^{4} + 770 \, b c^{3} d^{4} x^{3} + 1152 \, b c^{2} d^{4} x^{2} + 2310 \, b c d^{4} x - 3 \, b d^{4} \log\left(c x + 1\right) + 2307 \, b d^{4} \log\left(c x - 1\right) + 3 \, {\left(35 \, b c^{8} d^{4} x^{8} + 160 \, b c^{7} d^{4} x^{7} + 280 \, b c^{6} d^{4} x^{6} + 224 \, b c^{5} d^{4} x^{5} + 70 \, b c^{4} d^{4} x^{4}\right)} \log\left(-\frac{c x + 1}{c x - 1}\right)}{1680 \, c^{4}}"," ",0,"1/1680*(210*a*c^8*d^4*x^8 + 30*(32*a + b)*c^7*d^4*x^7 + 80*(21*a + 2*b)*c^6*d^4*x^6 + 42*(32*a + 9*b)*c^5*d^4*x^5 + 12*(35*a + 48*b)*c^4*d^4*x^4 + 770*b*c^3*d^4*x^3 + 1152*b*c^2*d^4*x^2 + 2310*b*c*d^4*x - 3*b*d^4*log(c*x + 1) + 2307*b*d^4*log(c*x - 1) + 3*(35*b*c^8*d^4*x^8 + 160*b*c^7*d^4*x^7 + 280*b*c^6*d^4*x^6 + 224*b*c^5*d^4*x^5 + 70*b*c^4*d^4*x^4)*log(-(c*x + 1)/(c*x - 1)))/c^4","A",0
32,1,208,0,0.519762," ","integrate(x^2*(c*d*x+d)^4*(a+b*arctanh(c*x)),x, algorithm=""fricas"")","\frac{180 \, a c^{7} d^{4} x^{7} + 30 \, {\left(28 \, a + b\right)} c^{6} d^{4} x^{6} + 168 \, {\left(9 \, a + b\right)} c^{5} d^{4} x^{5} + 9 \, {\left(140 \, a + 47 \, b\right)} c^{4} d^{4} x^{4} + 140 \, {\left(3 \, a + 5 \, b\right)} c^{3} d^{4} x^{3} + 1056 \, b c^{2} d^{4} x^{2} + 2100 \, b c d^{4} x + 6 \, b d^{4} \log\left(c x + 1\right) + 2106 \, b d^{4} \log\left(c x - 1\right) + 6 \, {\left(15 \, b c^{7} d^{4} x^{7} + 70 \, b c^{6} d^{4} x^{6} + 126 \, b c^{5} d^{4} x^{5} + 105 \, b c^{4} d^{4} x^{4} + 35 \, b c^{3} d^{4} x^{3}\right)} \log\left(-\frac{c x + 1}{c x - 1}\right)}{1260 \, c^{3}}"," ",0,"1/1260*(180*a*c^7*d^4*x^7 + 30*(28*a + b)*c^6*d^4*x^6 + 168*(9*a + b)*c^5*d^4*x^5 + 9*(140*a + 47*b)*c^4*d^4*x^4 + 140*(3*a + 5*b)*c^3*d^4*x^3 + 1056*b*c^2*d^4*x^2 + 2100*b*c*d^4*x + 6*b*d^4*log(c*x + 1) + 2106*b*d^4*log(c*x - 1) + 6*(15*b*c^7*d^4*x^7 + 70*b*c^6*d^4*x^6 + 126*b*c^5*d^4*x^5 + 105*b*c^4*d^4*x^4 + 35*b*c^3*d^4*x^3)*log(-(c*x + 1)/(c*x - 1)))/c^3","A",0
33,1,198,0,0.504584," ","integrate(x*(c*d*x+d)^4*(a+b*arctanh(c*x)),x, algorithm=""fricas"")","\frac{30 \, a c^{6} d^{4} x^{6} + 6 \, {\left(24 \, a + b\right)} c^{5} d^{4} x^{5} + 18 \, {\left(15 \, a + 2 \, b\right)} c^{4} d^{4} x^{4} + 20 \, {\left(12 \, a + 5 \, b\right)} c^{3} d^{4} x^{3} + 6 \, {\left(15 \, a + 32 \, b\right)} c^{2} d^{4} x^{2} + 390 \, b c d^{4} x - 3 \, b d^{4} \log\left(c x + 1\right) + 387 \, b d^{4} \log\left(c x - 1\right) + 3 \, {\left(5 \, b c^{6} d^{4} x^{6} + 24 \, b c^{5} d^{4} x^{5} + 45 \, b c^{4} d^{4} x^{4} + 40 \, b c^{3} d^{4} x^{3} + 15 \, b c^{2} d^{4} x^{2}\right)} \log\left(-\frac{c x + 1}{c x - 1}\right)}{180 \, c^{2}}"," ",0,"1/180*(30*a*c^6*d^4*x^6 + 6*(24*a + b)*c^5*d^4*x^5 + 18*(15*a + 2*b)*c^4*d^4*x^4 + 20*(12*a + 5*b)*c^3*d^4*x^3 + 6*(15*a + 32*b)*c^2*d^4*x^2 + 390*b*c*d^4*x - 3*b*d^4*log(c*x + 1) + 387*b*d^4*log(c*x - 1) + 3*(5*b*c^6*d^4*x^6 + 24*b*c^5*d^4*x^5 + 45*b*c^4*d^4*x^4 + 40*b*c^3*d^4*x^3 + 15*b*c^2*d^4*x^2)*log(-(c*x + 1)/(c*x - 1)))/c^2","A",0
34,1,177,0,0.427504," ","integrate((c*d*x+d)^4*(a+b*arctanh(c*x)),x, algorithm=""fricas"")","\frac{12 \, a c^{5} d^{4} x^{5} + 3 \, {\left(20 \, a + b\right)} c^{4} d^{4} x^{4} + 20 \, {\left(6 \, a + b\right)} c^{3} d^{4} x^{3} + 6 \, {\left(20 \, a + 11 \, b\right)} c^{2} d^{4} x^{2} + 60 \, {\left(a + 3 \, b\right)} c d^{4} x + 6 \, b d^{4} \log\left(c x + 1\right) + 186 \, b d^{4} \log\left(c x - 1\right) + 6 \, {\left(b c^{5} d^{4} x^{5} + 5 \, b c^{4} d^{4} x^{4} + 10 \, b c^{3} d^{4} x^{3} + 10 \, b c^{2} d^{4} x^{2} + 5 \, b c d^{4} x\right)} \log\left(-\frac{c x + 1}{c x - 1}\right)}{60 \, c}"," ",0,"1/60*(12*a*c^5*d^4*x^5 + 3*(20*a + b)*c^4*d^4*x^4 + 20*(6*a + b)*c^3*d^4*x^3 + 6*(20*a + 11*b)*c^2*d^4*x^2 + 60*(a + 3*b)*c*d^4*x + 6*b*d^4*log(c*x + 1) + 186*b*d^4*log(c*x - 1) + 6*(b*c^5*d^4*x^5 + 5*b*c^4*d^4*x^4 + 10*b*c^3*d^4*x^3 + 10*b*c^2*d^4*x^2 + 5*b*c*d^4*x)*log(-(c*x + 1)/(c*x - 1)))/c","A",0
35,0,0,0,0.486086," ","integrate((c*d*x+d)^4*(a+b*arctanh(c*x))/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{a c^{4} d^{4} x^{4} + 4 \, a c^{3} d^{4} x^{3} + 6 \, a c^{2} d^{4} x^{2} + 4 \, a c d^{4} x + a d^{4} + {\left(b c^{4} d^{4} x^{4} + 4 \, b c^{3} d^{4} x^{3} + 6 \, b c^{2} d^{4} x^{2} + 4 \, b c d^{4} x + b d^{4}\right)} \operatorname{artanh}\left(c x\right)}{x}, x\right)"," ",0,"integral((a*c^4*d^4*x^4 + 4*a*c^3*d^4*x^3 + 6*a*c^2*d^4*x^2 + 4*a*c*d^4*x + a*d^4 + (b*c^4*d^4*x^4 + 4*b*c^3*d^4*x^3 + 6*b*c^2*d^4*x^2 + 4*b*c*d^4*x + b*d^4)*arctanh(c*x))/x, x)","F",0
36,0,0,0,0.487556," ","integrate((c*d*x+d)^4*(a+b*arctanh(c*x))/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{a c^{4} d^{4} x^{4} + 4 \, a c^{3} d^{4} x^{3} + 6 \, a c^{2} d^{4} x^{2} + 4 \, a c d^{4} x + a d^{4} + {\left(b c^{4} d^{4} x^{4} + 4 \, b c^{3} d^{4} x^{3} + 6 \, b c^{2} d^{4} x^{2} + 4 \, b c d^{4} x + b d^{4}\right)} \operatorname{artanh}\left(c x\right)}{x^{2}}, x\right)"," ",0,"integral((a*c^4*d^4*x^4 + 4*a*c^3*d^4*x^3 + 6*a*c^2*d^4*x^2 + 4*a*c*d^4*x + a*d^4 + (b*c^4*d^4*x^4 + 4*b*c^3*d^4*x^3 + 6*b*c^2*d^4*x^2 + 4*b*c*d^4*x + b*d^4)*arctanh(c*x))/x^2, x)","F",0
37,0,0,0,0.421212," ","integrate((c*d*x+d)^4*(a+b*arctanh(c*x))/x^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{a c^{4} d^{4} x^{4} + 4 \, a c^{3} d^{4} x^{3} + 6 \, a c^{2} d^{4} x^{2} + 4 \, a c d^{4} x + a d^{4} + {\left(b c^{4} d^{4} x^{4} + 4 \, b c^{3} d^{4} x^{3} + 6 \, b c^{2} d^{4} x^{2} + 4 \, b c d^{4} x + b d^{4}\right)} \operatorname{artanh}\left(c x\right)}{x^{3}}, x\right)"," ",0,"integral((a*c^4*d^4*x^4 + 4*a*c^3*d^4*x^3 + 6*a*c^2*d^4*x^2 + 4*a*c*d^4*x + a*d^4 + (b*c^4*d^4*x^4 + 4*b*c^3*d^4*x^3 + 6*b*c^2*d^4*x^2 + 4*b*c*d^4*x + b*d^4)*arctanh(c*x))/x^3, x)","F",0
38,0,0,0,0.833724," ","integrate((c*d*x+d)^4*(a+b*arctanh(c*x))/x^4,x, algorithm=""fricas"")","{\rm integral}\left(\frac{a c^{4} d^{4} x^{4} + 4 \, a c^{3} d^{4} x^{3} + 6 \, a c^{2} d^{4} x^{2} + 4 \, a c d^{4} x + a d^{4} + {\left(b c^{4} d^{4} x^{4} + 4 \, b c^{3} d^{4} x^{3} + 6 \, b c^{2} d^{4} x^{2} + 4 \, b c d^{4} x + b d^{4}\right)} \operatorname{artanh}\left(c x\right)}{x^{4}}, x\right)"," ",0,"integral((a*c^4*d^4*x^4 + 4*a*c^3*d^4*x^3 + 6*a*c^2*d^4*x^2 + 4*a*c*d^4*x + a*d^4 + (b*c^4*d^4*x^4 + 4*b*c^3*d^4*x^3 + 6*b*c^2*d^4*x^2 + 4*b*c*d^4*x + b*d^4)*arctanh(c*x))/x^4, x)","F",0
39,0,0,0,0.412696," ","integrate((c*d*x+d)^4*(a+b*arctanh(c*x))/x^5,x, algorithm=""fricas"")","{\rm integral}\left(\frac{a c^{4} d^{4} x^{4} + 4 \, a c^{3} d^{4} x^{3} + 6 \, a c^{2} d^{4} x^{2} + 4 \, a c d^{4} x + a d^{4} + {\left(b c^{4} d^{4} x^{4} + 4 \, b c^{3} d^{4} x^{3} + 6 \, b c^{2} d^{4} x^{2} + 4 \, b c d^{4} x + b d^{4}\right)} \operatorname{artanh}\left(c x\right)}{x^{5}}, x\right)"," ",0,"integral((a*c^4*d^4*x^4 + 4*a*c^3*d^4*x^3 + 6*a*c^2*d^4*x^2 + 4*a*c*d^4*x + a*d^4 + (b*c^4*d^4*x^4 + 4*b*c^3*d^4*x^3 + 6*b*c^2*d^4*x^2 + 4*b*c*d^4*x + b*d^4)*arctanh(c*x))/x^5, x)","F",0
40,1,191,0,0.477556," ","integrate((c*d*x+d)^4*(a+b*arctanh(c*x))/x^6,x, algorithm=""fricas"")","-\frac{6 \, b c^{5} d^{4} x^{5} \log\left(c x + 1\right) + 186 \, b c^{5} d^{4} x^{5} \log\left(c x - 1\right) - 192 \, b c^{5} d^{4} x^{5} \log\left(x\right) + 60 \, {\left(a + 3 \, b\right)} c^{4} d^{4} x^{4} + 6 \, {\left(20 \, a + 11 \, b\right)} c^{3} d^{4} x^{3} + 20 \, {\left(6 \, a + b\right)} c^{2} d^{4} x^{2} + 3 \, {\left(20 \, a + b\right)} c d^{4} x + 12 \, a d^{4} + 6 \, {\left(5 \, b c^{4} d^{4} x^{4} + 10 \, b c^{3} d^{4} x^{3} + 10 \, b c^{2} d^{4} x^{2} + 5 \, b c d^{4} x + b d^{4}\right)} \log\left(-\frac{c x + 1}{c x - 1}\right)}{60 \, x^{5}}"," ",0,"-1/60*(6*b*c^5*d^4*x^5*log(c*x + 1) + 186*b*c^5*d^4*x^5*log(c*x - 1) - 192*b*c^5*d^4*x^5*log(x) + 60*(a + 3*b)*c^4*d^4*x^4 + 6*(20*a + 11*b)*c^3*d^4*x^3 + 20*(6*a + b)*c^2*d^4*x^2 + 3*(20*a + b)*c*d^4*x + 12*a*d^4 + 6*(5*b*c^4*d^4*x^4 + 10*b*c^3*d^4*x^3 + 10*b*c^2*d^4*x^2 + 5*b*c*d^4*x + b*d^4)*log(-(c*x + 1)/(c*x - 1)))/x^5","A",0
41,1,208,0,0.470491," ","integrate((c*d*x+d)^4*(a+b*arctanh(c*x))/x^7,x, algorithm=""fricas"")","\frac{3 \, b c^{6} d^{4} x^{6} \log\left(c x + 1\right) - 387 \, b c^{6} d^{4} x^{6} \log\left(c x - 1\right) + 384 \, b c^{6} d^{4} x^{6} \log\left(x\right) - 390 \, b c^{5} d^{4} x^{5} - 6 \, {\left(15 \, a + 32 \, b\right)} c^{4} d^{4} x^{4} - 20 \, {\left(12 \, a + 5 \, b\right)} c^{3} d^{4} x^{3} - 18 \, {\left(15 \, a + 2 \, b\right)} c^{2} d^{4} x^{2} - 6 \, {\left(24 \, a + b\right)} c d^{4} x - 30 \, a d^{4} - 3 \, {\left(15 \, b c^{4} d^{4} x^{4} + 40 \, b c^{3} d^{4} x^{3} + 45 \, b c^{2} d^{4} x^{2} + 24 \, b c d^{4} x + 5 \, b d^{4}\right)} \log\left(-\frac{c x + 1}{c x - 1}\right)}{180 \, x^{6}}"," ",0,"1/180*(3*b*c^6*d^4*x^6*log(c*x + 1) - 387*b*c^6*d^4*x^6*log(c*x - 1) + 384*b*c^6*d^4*x^6*log(x) - 390*b*c^5*d^4*x^5 - 6*(15*a + 32*b)*c^4*d^4*x^4 - 20*(12*a + 5*b)*c^3*d^4*x^3 - 18*(15*a + 2*b)*c^2*d^4*x^2 - 6*(24*a + b)*c*d^4*x - 30*a*d^4 - 3*(15*b*c^4*d^4*x^4 + 40*b*c^3*d^4*x^3 + 45*b*c^2*d^4*x^2 + 24*b*c*d^4*x + 5*b*d^4)*log(-(c*x + 1)/(c*x - 1)))/x^6","A",0
42,1,218,0,0.604805," ","integrate((c*d*x+d)^4*(a+b*arctanh(c*x))/x^8,x, algorithm=""fricas"")","-\frac{6 \, b c^{7} d^{4} x^{7} \log\left(c x + 1\right) + 2106 \, b c^{7} d^{4} x^{7} \log\left(c x - 1\right) - 2112 \, b c^{7} d^{4} x^{7} \log\left(x\right) + 2100 \, b c^{6} d^{4} x^{6} + 1056 \, b c^{5} d^{4} x^{5} + 140 \, {\left(3 \, a + 5 \, b\right)} c^{4} d^{4} x^{4} + 9 \, {\left(140 \, a + 47 \, b\right)} c^{3} d^{4} x^{3} + 168 \, {\left(9 \, a + b\right)} c^{2} d^{4} x^{2} + 30 \, {\left(28 \, a + b\right)} c d^{4} x + 180 \, a d^{4} + 6 \, {\left(35 \, b c^{4} d^{4} x^{4} + 105 \, b c^{3} d^{4} x^{3} + 126 \, b c^{2} d^{4} x^{2} + 70 \, b c d^{4} x + 15 \, b d^{4}\right)} \log\left(-\frac{c x + 1}{c x - 1}\right)}{1260 \, x^{7}}"," ",0,"-1/1260*(6*b*c^7*d^4*x^7*log(c*x + 1) + 2106*b*c^7*d^4*x^7*log(c*x - 1) - 2112*b*c^7*d^4*x^7*log(x) + 2100*b*c^6*d^4*x^6 + 1056*b*c^5*d^4*x^5 + 140*(3*a + 5*b)*c^4*d^4*x^4 + 9*(140*a + 47*b)*c^3*d^4*x^3 + 168*(9*a + b)*c^2*d^4*x^2 + 30*(28*a + b)*c*d^4*x + 180*a*d^4 + 6*(35*b*c^4*d^4*x^4 + 105*b*c^3*d^4*x^3 + 126*b*c^2*d^4*x^2 + 70*b*c*d^4*x + 15*b*d^4)*log(-(c*x + 1)/(c*x - 1)))/x^7","A",0
43,0,0,0,0.595537," ","integrate(x^3*(a+b*arctanh(c*x))/(c*d*x+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b x^{3} \operatorname{artanh}\left(c x\right) + a x^{3}}{c d x + d}, x\right)"," ",0,"integral((b*x^3*arctanh(c*x) + a*x^3)/(c*d*x + d), x)","F",0
44,0,0,0,0.434129," ","integrate(x^2*(a+b*arctanh(c*x))/(c*d*x+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b x^{2} \operatorname{artanh}\left(c x\right) + a x^{2}}{c d x + d}, x\right)"," ",0,"integral((b*x^2*arctanh(c*x) + a*x^2)/(c*d*x + d), x)","F",0
45,0,0,0,0.449593," ","integrate(x*(a+b*arctanh(c*x))/(c*d*x+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b x \operatorname{artanh}\left(c x\right) + a x}{c d x + d}, x\right)"," ",0,"integral((b*x*arctanh(c*x) + a*x)/(c*d*x + d), x)","F",0
46,0,0,0,0.419403," ","integrate((a+b*arctanh(c*x))/(c*d*x+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \operatorname{artanh}\left(c x\right) + a}{c d x + d}, x\right)"," ",0,"integral((b*arctanh(c*x) + a)/(c*d*x + d), x)","F",0
47,0,0,0,0.520970," ","integrate((a+b*arctanh(c*x))/x/(c*d*x+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \operatorname{artanh}\left(c x\right) + a}{c d x^{2} + d x}, x\right)"," ",0,"integral((b*arctanh(c*x) + a)/(c*d*x^2 + d*x), x)","F",0
48,0,0,0,0.604914," ","integrate((a+b*arctanh(c*x))/x^2/(c*d*x+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \operatorname{artanh}\left(c x\right) + a}{c d x^{3} + d x^{2}}, x\right)"," ",0,"integral((b*arctanh(c*x) + a)/(c*d*x^3 + d*x^2), x)","F",0
49,0,0,0,0.633923," ","integrate((a+b*arctanh(c*x))/x^3/(c*d*x+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \operatorname{artanh}\left(c x\right) + a}{c d x^{4} + d x^{3}}, x\right)"," ",0,"integral((b*arctanh(c*x) + a)/(c*d*x^4 + d*x^3), x)","F",0
50,0,0,0,0.610357," ","integrate((a+b*arctanh(c*x))/x^4/(c*d*x+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \operatorname{artanh}\left(c x\right) + a}{c d x^{5} + d x^{4}}, x\right)"," ",0,"integral((b*arctanh(c*x) + a)/(c*d*x^5 + d*x^4), x)","F",0
51,0,0,0,0.522299," ","integrate(x^3*(a+b*arctanh(c*x))/(c*d*x+d)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b x^{3} \operatorname{artanh}\left(c x\right) + a x^{3}}{c^{2} d^{2} x^{2} + 2 \, c d^{2} x + d^{2}}, x\right)"," ",0,"integral((b*x^3*arctanh(c*x) + a*x^3)/(c^2*d^2*x^2 + 2*c*d^2*x + d^2), x)","F",0
52,0,0,0,0.630489," ","integrate(x^2*(a+b*arctanh(c*x))/(c*d*x+d)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b x^{2} \operatorname{artanh}\left(c x\right) + a x^{2}}{c^{2} d^{2} x^{2} + 2 \, c d^{2} x + d^{2}}, x\right)"," ",0,"integral((b*x^2*arctanh(c*x) + a*x^2)/(c^2*d^2*x^2 + 2*c*d^2*x + d^2), x)","F",0
53,0,0,0,0.645573," ","integrate(x*(a+b*arctanh(c*x))/(c*d*x+d)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b x \operatorname{artanh}\left(c x\right) + a x}{c^{2} d^{2} x^{2} + 2 \, c d^{2} x + d^{2}}, x\right)"," ",0,"integral((b*x*arctanh(c*x) + a*x)/(c^2*d^2*x^2 + 2*c*d^2*x + d^2), x)","F",0
54,1,49,0,1.292181," ","integrate((a+b*arctanh(c*x))/(c*d*x+d)^2,x, algorithm=""fricas"")","\frac{{\left(b c x - b\right)} \log\left(-\frac{c x + 1}{c x - 1}\right) - 4 \, a - 2 \, b}{4 \, {\left(c^{2} d^{2} x + c d^{2}\right)}}"," ",0,"1/4*((b*c*x - b)*log(-(c*x + 1)/(c*x - 1)) - 4*a - 2*b)/(c^2*d^2*x + c*d^2)","A",0
55,0,0,0,0.404864," ","integrate((a+b*arctanh(c*x))/x/(c*d*x+d)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \operatorname{artanh}\left(c x\right) + a}{c^{2} d^{2} x^{3} + 2 \, c d^{2} x^{2} + d^{2} x}, x\right)"," ",0,"integral((b*arctanh(c*x) + a)/(c^2*d^2*x^3 + 2*c*d^2*x^2 + d^2*x), x)","F",0
56,0,0,0,0.649343," ","integrate((a+b*arctanh(c*x))/x^2/(c*d*x+d)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \operatorname{artanh}\left(c x\right) + a}{c^{2} d^{2} x^{4} + 2 \, c d^{2} x^{3} + d^{2} x^{2}}, x\right)"," ",0,"integral((b*arctanh(c*x) + a)/(c^2*d^2*x^4 + 2*c*d^2*x^3 + d^2*x^2), x)","F",0
57,0,0,0,1.532172," ","integrate((a+b*arctanh(c*x))/x^3/(c*d*x+d)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \operatorname{artanh}\left(c x\right) + a}{c^{2} d^{2} x^{5} + 2 \, c d^{2} x^{4} + d^{2} x^{3}}, x\right)"," ",0,"integral((b*arctanh(c*x) + a)/(c^2*d^2*x^5 + 2*c*d^2*x^4 + d^2*x^3), x)","F",0
58,0,0,0,0.760255," ","integrate(x^4*(a+b*arctanh(c*x))/(c*d*x+d)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b x^{4} \operatorname{artanh}\left(c x\right) + a x^{4}}{c^{3} d^{3} x^{3} + 3 \, c^{2} d^{3} x^{2} + 3 \, c d^{3} x + d^{3}}, x\right)"," ",0,"integral((b*x^4*arctanh(c*x) + a*x^4)/(c^3*d^3*x^3 + 3*c^2*d^3*x^2 + 3*c*d^3*x + d^3), x)","F",0
59,0,0,0,0.517470," ","integrate(x^3*(a+b*arctanh(c*x))/(c*d*x+d)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b x^{3} \operatorname{artanh}\left(c x\right) + a x^{3}}{c^{3} d^{3} x^{3} + 3 \, c^{2} d^{3} x^{2} + 3 \, c d^{3} x + d^{3}}, x\right)"," ",0,"integral((b*x^3*arctanh(c*x) + a*x^3)/(c^3*d^3*x^3 + 3*c^2*d^3*x^2 + 3*c*d^3*x + d^3), x)","F",0
60,0,0,0,0.562371," ","integrate(x^2*(a+b*arctanh(c*x))/(c*d*x+d)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b x^{2} \operatorname{artanh}\left(c x\right) + a x^{2}}{c^{3} d^{3} x^{3} + 3 \, c^{2} d^{3} x^{2} + 3 \, c d^{3} x + d^{3}}, x\right)"," ",0,"integral((b*x^2*arctanh(c*x) + a*x^2)/(c^3*d^3*x^3 + 3*c^2*d^3*x^2 + 3*c*d^3*x + d^3), x)","F",0
61,1,84,0,0.416519," ","integrate(x*(a+b*arctanh(c*x))/(c*d*x+d)^3,x, algorithm=""fricas"")","-\frac{2 \, {\left(8 \, a + 3 \, b\right)} c x - {\left(3 \, b c^{2} x^{2} - 2 \, b c x - b\right)} \log\left(-\frac{c x + 1}{c x - 1}\right) + 8 \, a + 4 \, b}{16 \, {\left(c^{4} d^{3} x^{2} + 2 \, c^{3} d^{3} x + c^{2} d^{3}\right)}}"," ",0,"-1/16*(2*(8*a + 3*b)*c*x - (3*b*c^2*x^2 - 2*b*c*x - b)*log(-(c*x + 1)/(c*x - 1)) + 8*a + 4*b)/(c^4*d^3*x^2 + 2*c^3*d^3*x + c^2*d^3)","A",0
62,1,75,0,0.413174," ","integrate((a+b*arctanh(c*x))/(c*d*x+d)^3,x, algorithm=""fricas"")","-\frac{2 \, b c x - {\left(b c^{2} x^{2} + 2 \, b c x - 3 \, b\right)} \log\left(-\frac{c x + 1}{c x - 1}\right) + 8 \, a + 4 \, b}{16 \, {\left(c^{3} d^{3} x^{2} + 2 \, c^{2} d^{3} x + c d^{3}\right)}}"," ",0,"-1/16*(2*b*c*x - (b*c^2*x^2 + 2*b*c*x - 3*b)*log(-(c*x + 1)/(c*x - 1)) + 8*a + 4*b)/(c^3*d^3*x^2 + 2*c^2*d^3*x + c*d^3)","A",0
63,0,0,0,0.541531," ","integrate((a+b*arctanh(c*x))/x/(c*d*x+d)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \operatorname{artanh}\left(c x\right) + a}{c^{3} d^{3} x^{4} + 3 \, c^{2} d^{3} x^{3} + 3 \, c d^{3} x^{2} + d^{3} x}, x\right)"," ",0,"integral((b*arctanh(c*x) + a)/(c^3*d^3*x^4 + 3*c^2*d^3*x^3 + 3*c*d^3*x^2 + d^3*x), x)","F",0
64,0,0,0,0.446498," ","integrate((a+b*arctanh(c*x))/x^2/(c*d*x+d)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \operatorname{artanh}\left(c x\right) + a}{c^{3} d^{3} x^{5} + 3 \, c^{2} d^{3} x^{4} + 3 \, c d^{3} x^{3} + d^{3} x^{2}}, x\right)"," ",0,"integral((b*arctanh(c*x) + a)/(c^3*d^3*x^5 + 3*c^2*d^3*x^4 + 3*c*d^3*x^3 + d^3*x^2), x)","F",0
65,0,0,0,0.433152," ","integrate((a+b*arctanh(c*x))/x^3/(c*d*x+d)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \operatorname{artanh}\left(c x\right) + a}{c^{3} d^{3} x^{6} + 3 \, c^{2} d^{3} x^{5} + 3 \, c d^{3} x^{4} + d^{3} x^{3}}, x\right)"," ",0,"integral((b*arctanh(c*x) + a)/(c^3*d^3*x^6 + 3*c^2*d^3*x^5 + 3*c*d^3*x^4 + d^3*x^3), x)","F",0
66,1,91,0,0.432298," ","integrate((a+b*arctanh(c*x))/(c*x+1)^4,x, algorithm=""fricas"")","-\frac{6 \, b c^{2} x^{2} + 18 \, b c x - 3 \, {\left(b c^{3} x^{3} + 3 \, b c^{2} x^{2} + 3 \, b c x - 7 \, b\right)} \log\left(-\frac{c x + 1}{c x - 1}\right) + 48 \, a + 20 \, b}{144 \, {\left(c^{4} x^{3} + 3 \, c^{3} x^{2} + 3 \, c^{2} x + c\right)}}"," ",0,"-1/144*(6*b*c^2*x^2 + 18*b*c*x - 3*(b*c^3*x^3 + 3*b*c^2*x^2 + 3*b*c*x - 7*b)*log(-(c*x + 1)/(c*x - 1)) + 48*a + 20*b)/(c^4*x^3 + 3*c^3*x^2 + 3*c^2*x + c)","A",0
67,0,0,0,0.402323," ","integrate(arctanh(a*x)/(a*c*x^2+c*x),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{artanh}\left(a x\right)}{a c x^{2} + c x}, x\right)"," ",0,"integral(arctanh(a*x)/(a*c*x^2 + c*x), x)","F",0
68,0,0,0,0.436891," ","integrate(x^3*(c*d*x+d)*(a+b*arctanh(c*x))^2,x, algorithm=""fricas"")","{\rm integral}\left(a^{2} c d x^{4} + a^{2} d x^{3} + {\left(b^{2} c d x^{4} + b^{2} d x^{3}\right)} \operatorname{artanh}\left(c x\right)^{2} + 2 \, {\left(a b c d x^{4} + a b d x^{3}\right)} \operatorname{artanh}\left(c x\right), x\right)"," ",0,"integral(a^2*c*d*x^4 + a^2*d*x^3 + (b^2*c*d*x^4 + b^2*d*x^3)*arctanh(c*x)^2 + 2*(a*b*c*d*x^4 + a*b*d*x^3)*arctanh(c*x), x)","F",0
69,0,0,0,0.505814," ","integrate(x^2*(c*d*x+d)*(a+b*arctanh(c*x))^2,x, algorithm=""fricas"")","{\rm integral}\left(a^{2} c d x^{3} + a^{2} d x^{2} + {\left(b^{2} c d x^{3} + b^{2} d x^{2}\right)} \operatorname{artanh}\left(c x\right)^{2} + 2 \, {\left(a b c d x^{3} + a b d x^{2}\right)} \operatorname{artanh}\left(c x\right), x\right)"," ",0,"integral(a^2*c*d*x^3 + a^2*d*x^2 + (b^2*c*d*x^3 + b^2*d*x^2)*arctanh(c*x)^2 + 2*(a*b*c*d*x^3 + a*b*d*x^2)*arctanh(c*x), x)","F",0
70,0,0,0,0.605973," ","integrate(x*(c*d*x+d)*(a+b*arctanh(c*x))^2,x, algorithm=""fricas"")","{\rm integral}\left(a^{2} c d x^{2} + a^{2} d x + {\left(b^{2} c d x^{2} + b^{2} d x\right)} \operatorname{artanh}\left(c x\right)^{2} + 2 \, {\left(a b c d x^{2} + a b d x\right)} \operatorname{artanh}\left(c x\right), x\right)"," ",0,"integral(a^2*c*d*x^2 + a^2*d*x + (b^2*c*d*x^2 + b^2*d*x)*arctanh(c*x)^2 + 2*(a*b*c*d*x^2 + a*b*d*x)*arctanh(c*x), x)","F",0
71,0,0,0,0.454122," ","integrate((c*d*x+d)*(a+b*arctanh(c*x))^2,x, algorithm=""fricas"")","{\rm integral}\left(a^{2} c d x + a^{2} d + {\left(b^{2} c d x + b^{2} d\right)} \operatorname{artanh}\left(c x\right)^{2} + 2 \, {\left(a b c d x + a b d\right)} \operatorname{artanh}\left(c x\right), x\right)"," ",0,"integral(a^2*c*d*x + a^2*d + (b^2*c*d*x + b^2*d)*arctanh(c*x)^2 + 2*(a*b*c*d*x + a*b*d)*arctanh(c*x), x)","F",0
72,0,0,0,0.471522," ","integrate((c*d*x+d)*(a+b*arctanh(c*x))^2/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{a^{2} c d x + a^{2} d + {\left(b^{2} c d x + b^{2} d\right)} \operatorname{artanh}\left(c x\right)^{2} + 2 \, {\left(a b c d x + a b d\right)} \operatorname{artanh}\left(c x\right)}{x}, x\right)"," ",0,"integral((a^2*c*d*x + a^2*d + (b^2*c*d*x + b^2*d)*arctanh(c*x)^2 + 2*(a*b*c*d*x + a*b*d)*arctanh(c*x))/x, x)","F",0
73,0,0,0,0.471560," ","integrate((c*d*x+d)*(a+b*arctanh(c*x))^2/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{a^{2} c d x + a^{2} d + {\left(b^{2} c d x + b^{2} d\right)} \operatorname{artanh}\left(c x\right)^{2} + 2 \, {\left(a b c d x + a b d\right)} \operatorname{artanh}\left(c x\right)}{x^{2}}, x\right)"," ",0,"integral((a^2*c*d*x + a^2*d + (b^2*c*d*x + b^2*d)*arctanh(c*x)^2 + 2*(a*b*c*d*x + a*b*d)*arctanh(c*x))/x^2, x)","F",0
74,0,0,0,0.509157," ","integrate((c*d*x+d)*(a+b*arctanh(c*x))^2/x^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{a^{2} c d x + a^{2} d + {\left(b^{2} c d x + b^{2} d\right)} \operatorname{artanh}\left(c x\right)^{2} + 2 \, {\left(a b c d x + a b d\right)} \operatorname{artanh}\left(c x\right)}{x^{3}}, x\right)"," ",0,"integral((a^2*c*d*x + a^2*d + (b^2*c*d*x + b^2*d)*arctanh(c*x)^2 + 2*(a*b*c*d*x + a*b*d)*arctanh(c*x))/x^3, x)","F",0
75,0,0,0,0.459306," ","integrate((c*d*x+d)*(a+b*arctanh(c*x))^2/x^4,x, algorithm=""fricas"")","{\rm integral}\left(\frac{a^{2} c d x + a^{2} d + {\left(b^{2} c d x + b^{2} d\right)} \operatorname{artanh}\left(c x\right)^{2} + 2 \, {\left(a b c d x + a b d\right)} \operatorname{artanh}\left(c x\right)}{x^{4}}, x\right)"," ",0,"integral((a^2*c*d*x + a^2*d + (b^2*c*d*x + b^2*d)*arctanh(c*x)^2 + 2*(a*b*c*d*x + a*b*d)*arctanh(c*x))/x^4, x)","F",0
76,0,0,0,0.745353," ","integrate(x^3*(c*d*x+d)^2*(a+b*arctanh(c*x))^2,x, algorithm=""fricas"")","{\rm integral}\left(a^{2} c^{2} d^{2} x^{5} + 2 \, a^{2} c d^{2} x^{4} + a^{2} d^{2} x^{3} + {\left(b^{2} c^{2} d^{2} x^{5} + 2 \, b^{2} c d^{2} x^{4} + b^{2} d^{2} x^{3}\right)} \operatorname{artanh}\left(c x\right)^{2} + 2 \, {\left(a b c^{2} d^{2} x^{5} + 2 \, a b c d^{2} x^{4} + a b d^{2} x^{3}\right)} \operatorname{artanh}\left(c x\right), x\right)"," ",0,"integral(a^2*c^2*d^2*x^5 + 2*a^2*c*d^2*x^4 + a^2*d^2*x^3 + (b^2*c^2*d^2*x^5 + 2*b^2*c*d^2*x^4 + b^2*d^2*x^3)*arctanh(c*x)^2 + 2*(a*b*c^2*d^2*x^5 + 2*a*b*c*d^2*x^4 + a*b*d^2*x^3)*arctanh(c*x), x)","F",0
77,0,0,0,0.454641," ","integrate(x^2*(c*d*x+d)^2*(a+b*arctanh(c*x))^2,x, algorithm=""fricas"")","{\rm integral}\left(a^{2} c^{2} d^{2} x^{4} + 2 \, a^{2} c d^{2} x^{3} + a^{2} d^{2} x^{2} + {\left(b^{2} c^{2} d^{2} x^{4} + 2 \, b^{2} c d^{2} x^{3} + b^{2} d^{2} x^{2}\right)} \operatorname{artanh}\left(c x\right)^{2} + 2 \, {\left(a b c^{2} d^{2} x^{4} + 2 \, a b c d^{2} x^{3} + a b d^{2} x^{2}\right)} \operatorname{artanh}\left(c x\right), x\right)"," ",0,"integral(a^2*c^2*d^2*x^4 + 2*a^2*c*d^2*x^3 + a^2*d^2*x^2 + (b^2*c^2*d^2*x^4 + 2*b^2*c*d^2*x^3 + b^2*d^2*x^2)*arctanh(c*x)^2 + 2*(a*b*c^2*d^2*x^4 + 2*a*b*c*d^2*x^3 + a*b*d^2*x^2)*arctanh(c*x), x)","F",0
78,0,0,0,0.640832," ","integrate(x*(c*d*x+d)^2*(a+b*arctanh(c*x))^2,x, algorithm=""fricas"")","{\rm integral}\left(a^{2} c^{2} d^{2} x^{3} + 2 \, a^{2} c d^{2} x^{2} + a^{2} d^{2} x + {\left(b^{2} c^{2} d^{2} x^{3} + 2 \, b^{2} c d^{2} x^{2} + b^{2} d^{2} x\right)} \operatorname{artanh}\left(c x\right)^{2} + 2 \, {\left(a b c^{2} d^{2} x^{3} + 2 \, a b c d^{2} x^{2} + a b d^{2} x\right)} \operatorname{artanh}\left(c x\right), x\right)"," ",0,"integral(a^2*c^2*d^2*x^3 + 2*a^2*c*d^2*x^2 + a^2*d^2*x + (b^2*c^2*d^2*x^3 + 2*b^2*c*d^2*x^2 + b^2*d^2*x)*arctanh(c*x)^2 + 2*(a*b*c^2*d^2*x^3 + 2*a*b*c*d^2*x^2 + a*b*d^2*x)*arctanh(c*x), x)","F",0
79,0,0,0,0.766335," ","integrate((c*d*x+d)^2*(a+b*arctanh(c*x))^2,x, algorithm=""fricas"")","{\rm integral}\left(a^{2} c^{2} d^{2} x^{2} + 2 \, a^{2} c d^{2} x + a^{2} d^{2} + {\left(b^{2} c^{2} d^{2} x^{2} + 2 \, b^{2} c d^{2} x + b^{2} d^{2}\right)} \operatorname{artanh}\left(c x\right)^{2} + 2 \, {\left(a b c^{2} d^{2} x^{2} + 2 \, a b c d^{2} x + a b d^{2}\right)} \operatorname{artanh}\left(c x\right), x\right)"," ",0,"integral(a^2*c^2*d^2*x^2 + 2*a^2*c*d^2*x + a^2*d^2 + (b^2*c^2*d^2*x^2 + 2*b^2*c*d^2*x + b^2*d^2)*arctanh(c*x)^2 + 2*(a*b*c^2*d^2*x^2 + 2*a*b*c*d^2*x + a*b*d^2)*arctanh(c*x), x)","F",0
80,0,0,0,0.709775," ","integrate((c*d*x+d)^2*(a+b*arctanh(c*x))^2/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{a^{2} c^{2} d^{2} x^{2} + 2 \, a^{2} c d^{2} x + a^{2} d^{2} + {\left(b^{2} c^{2} d^{2} x^{2} + 2 \, b^{2} c d^{2} x + b^{2} d^{2}\right)} \operatorname{artanh}\left(c x\right)^{2} + 2 \, {\left(a b c^{2} d^{2} x^{2} + 2 \, a b c d^{2} x + a b d^{2}\right)} \operatorname{artanh}\left(c x\right)}{x}, x\right)"," ",0,"integral((a^2*c^2*d^2*x^2 + 2*a^2*c*d^2*x + a^2*d^2 + (b^2*c^2*d^2*x^2 + 2*b^2*c*d^2*x + b^2*d^2)*arctanh(c*x)^2 + 2*(a*b*c^2*d^2*x^2 + 2*a*b*c*d^2*x + a*b*d^2)*arctanh(c*x))/x, x)","F",0
81,0,0,0,0.651000," ","integrate((c*d*x+d)^2*(a+b*arctanh(c*x))^2/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{a^{2} c^{2} d^{2} x^{2} + 2 \, a^{2} c d^{2} x + a^{2} d^{2} + {\left(b^{2} c^{2} d^{2} x^{2} + 2 \, b^{2} c d^{2} x + b^{2} d^{2}\right)} \operatorname{artanh}\left(c x\right)^{2} + 2 \, {\left(a b c^{2} d^{2} x^{2} + 2 \, a b c d^{2} x + a b d^{2}\right)} \operatorname{artanh}\left(c x\right)}{x^{2}}, x\right)"," ",0,"integral((a^2*c^2*d^2*x^2 + 2*a^2*c*d^2*x + a^2*d^2 + (b^2*c^2*d^2*x^2 + 2*b^2*c*d^2*x + b^2*d^2)*arctanh(c*x)^2 + 2*(a*b*c^2*d^2*x^2 + 2*a*b*c*d^2*x + a*b*d^2)*arctanh(c*x))/x^2, x)","F",0
82,0,0,0,0.463232," ","integrate((c*d*x+d)^2*(a+b*arctanh(c*x))^2/x^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{a^{2} c^{2} d^{2} x^{2} + 2 \, a^{2} c d^{2} x + a^{2} d^{2} + {\left(b^{2} c^{2} d^{2} x^{2} + 2 \, b^{2} c d^{2} x + b^{2} d^{2}\right)} \operatorname{artanh}\left(c x\right)^{2} + 2 \, {\left(a b c^{2} d^{2} x^{2} + 2 \, a b c d^{2} x + a b d^{2}\right)} \operatorname{artanh}\left(c x\right)}{x^{3}}, x\right)"," ",0,"integral((a^2*c^2*d^2*x^2 + 2*a^2*c*d^2*x + a^2*d^2 + (b^2*c^2*d^2*x^2 + 2*b^2*c*d^2*x + b^2*d^2)*arctanh(c*x)^2 + 2*(a*b*c^2*d^2*x^2 + 2*a*b*c*d^2*x + a*b*d^2)*arctanh(c*x))/x^3, x)","F",0
83,0,0,0,0.645675," ","integrate((c*d*x+d)^2*(a+b*arctanh(c*x))^2/x^4,x, algorithm=""fricas"")","{\rm integral}\left(\frac{a^{2} c^{2} d^{2} x^{2} + 2 \, a^{2} c d^{2} x + a^{2} d^{2} + {\left(b^{2} c^{2} d^{2} x^{2} + 2 \, b^{2} c d^{2} x + b^{2} d^{2}\right)} \operatorname{artanh}\left(c x\right)^{2} + 2 \, {\left(a b c^{2} d^{2} x^{2} + 2 \, a b c d^{2} x + a b d^{2}\right)} \operatorname{artanh}\left(c x\right)}{x^{4}}, x\right)"," ",0,"integral((a^2*c^2*d^2*x^2 + 2*a^2*c*d^2*x + a^2*d^2 + (b^2*c^2*d^2*x^2 + 2*b^2*c*d^2*x + b^2*d^2)*arctanh(c*x)^2 + 2*(a*b*c^2*d^2*x^2 + 2*a*b*c*d^2*x + a*b*d^2)*arctanh(c*x))/x^4, x)","F",0
84,0,0,0,0.540864," ","integrate(x^3*(c*d*x+d)^3*(a+b*arctanh(c*x))^2,x, algorithm=""fricas"")","{\rm integral}\left(a^{2} c^{3} d^{3} x^{6} + 3 \, a^{2} c^{2} d^{3} x^{5} + 3 \, a^{2} c d^{3} x^{4} + a^{2} d^{3} x^{3} + {\left(b^{2} c^{3} d^{3} x^{6} + 3 \, b^{2} c^{2} d^{3} x^{5} + 3 \, b^{2} c d^{3} x^{4} + b^{2} d^{3} x^{3}\right)} \operatorname{artanh}\left(c x\right)^{2} + 2 \, {\left(a b c^{3} d^{3} x^{6} + 3 \, a b c^{2} d^{3} x^{5} + 3 \, a b c d^{3} x^{4} + a b d^{3} x^{3}\right)} \operatorname{artanh}\left(c x\right), x\right)"," ",0,"integral(a^2*c^3*d^3*x^6 + 3*a^2*c^2*d^3*x^5 + 3*a^2*c*d^3*x^4 + a^2*d^3*x^3 + (b^2*c^3*d^3*x^6 + 3*b^2*c^2*d^3*x^5 + 3*b^2*c*d^3*x^4 + b^2*d^3*x^3)*arctanh(c*x)^2 + 2*(a*b*c^3*d^3*x^6 + 3*a*b*c^2*d^3*x^5 + 3*a*b*c*d^3*x^4 + a*b*d^3*x^3)*arctanh(c*x), x)","F",0
85,0,0,0,0.692048," ","integrate(x^2*(c*d*x+d)^3*(a+b*arctanh(c*x))^2,x, algorithm=""fricas"")","{\rm integral}\left(a^{2} c^{3} d^{3} x^{5} + 3 \, a^{2} c^{2} d^{3} x^{4} + 3 \, a^{2} c d^{3} x^{3} + a^{2} d^{3} x^{2} + {\left(b^{2} c^{3} d^{3} x^{5} + 3 \, b^{2} c^{2} d^{3} x^{4} + 3 \, b^{2} c d^{3} x^{3} + b^{2} d^{3} x^{2}\right)} \operatorname{artanh}\left(c x\right)^{2} + 2 \, {\left(a b c^{3} d^{3} x^{5} + 3 \, a b c^{2} d^{3} x^{4} + 3 \, a b c d^{3} x^{3} + a b d^{3} x^{2}\right)} \operatorname{artanh}\left(c x\right), x\right)"," ",0,"integral(a^2*c^3*d^3*x^5 + 3*a^2*c^2*d^3*x^4 + 3*a^2*c*d^3*x^3 + a^2*d^3*x^2 + (b^2*c^3*d^3*x^5 + 3*b^2*c^2*d^3*x^4 + 3*b^2*c*d^3*x^3 + b^2*d^3*x^2)*arctanh(c*x)^2 + 2*(a*b*c^3*d^3*x^5 + 3*a*b*c^2*d^3*x^4 + 3*a*b*c*d^3*x^3 + a*b*d^3*x^2)*arctanh(c*x), x)","F",0
86,0,0,0,0.488776," ","integrate(x*(c*d*x+d)^3*(a+b*arctanh(c*x))^2,x, algorithm=""fricas"")","{\rm integral}\left(a^{2} c^{3} d^{3} x^{4} + 3 \, a^{2} c^{2} d^{3} x^{3} + 3 \, a^{2} c d^{3} x^{2} + a^{2} d^{3} x + {\left(b^{2} c^{3} d^{3} x^{4} + 3 \, b^{2} c^{2} d^{3} x^{3} + 3 \, b^{2} c d^{3} x^{2} + b^{2} d^{3} x\right)} \operatorname{artanh}\left(c x\right)^{2} + 2 \, {\left(a b c^{3} d^{3} x^{4} + 3 \, a b c^{2} d^{3} x^{3} + 3 \, a b c d^{3} x^{2} + a b d^{3} x\right)} \operatorname{artanh}\left(c x\right), x\right)"," ",0,"integral(a^2*c^3*d^3*x^4 + 3*a^2*c^2*d^3*x^3 + 3*a^2*c*d^3*x^2 + a^2*d^3*x + (b^2*c^3*d^3*x^4 + 3*b^2*c^2*d^3*x^3 + 3*b^2*c*d^3*x^2 + b^2*d^3*x)*arctanh(c*x)^2 + 2*(a*b*c^3*d^3*x^4 + 3*a*b*c^2*d^3*x^3 + 3*a*b*c*d^3*x^2 + a*b*d^3*x)*arctanh(c*x), x)","F",0
87,0,0,0,0.577073," ","integrate((c*d*x+d)^3*(a+b*arctanh(c*x))^2,x, algorithm=""fricas"")","{\rm integral}\left(a^{2} c^{3} d^{3} x^{3} + 3 \, a^{2} c^{2} d^{3} x^{2} + 3 \, a^{2} c d^{3} x + a^{2} d^{3} + {\left(b^{2} c^{3} d^{3} x^{3} + 3 \, b^{2} c^{2} d^{3} x^{2} + 3 \, b^{2} c d^{3} x + b^{2} d^{3}\right)} \operatorname{artanh}\left(c x\right)^{2} + 2 \, {\left(a b c^{3} d^{3} x^{3} + 3 \, a b c^{2} d^{3} x^{2} + 3 \, a b c d^{3} x + a b d^{3}\right)} \operatorname{artanh}\left(c x\right), x\right)"," ",0,"integral(a^2*c^3*d^3*x^3 + 3*a^2*c^2*d^3*x^2 + 3*a^2*c*d^3*x + a^2*d^3 + (b^2*c^3*d^3*x^3 + 3*b^2*c^2*d^3*x^2 + 3*b^2*c*d^3*x + b^2*d^3)*arctanh(c*x)^2 + 2*(a*b*c^3*d^3*x^3 + 3*a*b*c^2*d^3*x^2 + 3*a*b*c*d^3*x + a*b*d^3)*arctanh(c*x), x)","F",0
88,0,0,0,0.625316," ","integrate((c*d*x+d)^3*(a+b*arctanh(c*x))^2/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{a^{2} c^{3} d^{3} x^{3} + 3 \, a^{2} c^{2} d^{3} x^{2} + 3 \, a^{2} c d^{3} x + a^{2} d^{3} + {\left(b^{2} c^{3} d^{3} x^{3} + 3 \, b^{2} c^{2} d^{3} x^{2} + 3 \, b^{2} c d^{3} x + b^{2} d^{3}\right)} \operatorname{artanh}\left(c x\right)^{2} + 2 \, {\left(a b c^{3} d^{3} x^{3} + 3 \, a b c^{2} d^{3} x^{2} + 3 \, a b c d^{3} x + a b d^{3}\right)} \operatorname{artanh}\left(c x\right)}{x}, x\right)"," ",0,"integral((a^2*c^3*d^3*x^3 + 3*a^2*c^2*d^3*x^2 + 3*a^2*c*d^3*x + a^2*d^3 + (b^2*c^3*d^3*x^3 + 3*b^2*c^2*d^3*x^2 + 3*b^2*c*d^3*x + b^2*d^3)*arctanh(c*x)^2 + 2*(a*b*c^3*d^3*x^3 + 3*a*b*c^2*d^3*x^2 + 3*a*b*c*d^3*x + a*b*d^3)*arctanh(c*x))/x, x)","F",0
89,0,0,0,0.858891," ","integrate((c*d*x+d)^3*(a+b*arctanh(c*x))^2/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{a^{2} c^{3} d^{3} x^{3} + 3 \, a^{2} c^{2} d^{3} x^{2} + 3 \, a^{2} c d^{3} x + a^{2} d^{3} + {\left(b^{2} c^{3} d^{3} x^{3} + 3 \, b^{2} c^{2} d^{3} x^{2} + 3 \, b^{2} c d^{3} x + b^{2} d^{3}\right)} \operatorname{artanh}\left(c x\right)^{2} + 2 \, {\left(a b c^{3} d^{3} x^{3} + 3 \, a b c^{2} d^{3} x^{2} + 3 \, a b c d^{3} x + a b d^{3}\right)} \operatorname{artanh}\left(c x\right)}{x^{2}}, x\right)"," ",0,"integral((a^2*c^3*d^3*x^3 + 3*a^2*c^2*d^3*x^2 + 3*a^2*c*d^3*x + a^2*d^3 + (b^2*c^3*d^3*x^3 + 3*b^2*c^2*d^3*x^2 + 3*b^2*c*d^3*x + b^2*d^3)*arctanh(c*x)^2 + 2*(a*b*c^3*d^3*x^3 + 3*a*b*c^2*d^3*x^2 + 3*a*b*c*d^3*x + a*b*d^3)*arctanh(c*x))/x^2, x)","F",0
90,0,0,0,0.576000," ","integrate((c*d*x+d)^3*(a+b*arctanh(c*x))^2/x^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{a^{2} c^{3} d^{3} x^{3} + 3 \, a^{2} c^{2} d^{3} x^{2} + 3 \, a^{2} c d^{3} x + a^{2} d^{3} + {\left(b^{2} c^{3} d^{3} x^{3} + 3 \, b^{2} c^{2} d^{3} x^{2} + 3 \, b^{2} c d^{3} x + b^{2} d^{3}\right)} \operatorname{artanh}\left(c x\right)^{2} + 2 \, {\left(a b c^{3} d^{3} x^{3} + 3 \, a b c^{2} d^{3} x^{2} + 3 \, a b c d^{3} x + a b d^{3}\right)} \operatorname{artanh}\left(c x\right)}{x^{3}}, x\right)"," ",0,"integral((a^2*c^3*d^3*x^3 + 3*a^2*c^2*d^3*x^2 + 3*a^2*c*d^3*x + a^2*d^3 + (b^2*c^3*d^3*x^3 + 3*b^2*c^2*d^3*x^2 + 3*b^2*c*d^3*x + b^2*d^3)*arctanh(c*x)^2 + 2*(a*b*c^3*d^3*x^3 + 3*a*b*c^2*d^3*x^2 + 3*a*b*c*d^3*x + a*b*d^3)*arctanh(c*x))/x^3, x)","F",0
91,0,0,0,0.510779," ","integrate((c*d*x+d)^3*(a+b*arctanh(c*x))^2/x^4,x, algorithm=""fricas"")","{\rm integral}\left(\frac{a^{2} c^{3} d^{3} x^{3} + 3 \, a^{2} c^{2} d^{3} x^{2} + 3 \, a^{2} c d^{3} x + a^{2} d^{3} + {\left(b^{2} c^{3} d^{3} x^{3} + 3 \, b^{2} c^{2} d^{3} x^{2} + 3 \, b^{2} c d^{3} x + b^{2} d^{3}\right)} \operatorname{artanh}\left(c x\right)^{2} + 2 \, {\left(a b c^{3} d^{3} x^{3} + 3 \, a b c^{2} d^{3} x^{2} + 3 \, a b c d^{3} x + a b d^{3}\right)} \operatorname{artanh}\left(c x\right)}{x^{4}}, x\right)"," ",0,"integral((a^2*c^3*d^3*x^3 + 3*a^2*c^2*d^3*x^2 + 3*a^2*c*d^3*x + a^2*d^3 + (b^2*c^3*d^3*x^3 + 3*b^2*c^2*d^3*x^2 + 3*b^2*c*d^3*x + b^2*d^3)*arctanh(c*x)^2 + 2*(a*b*c^3*d^3*x^3 + 3*a*b*c^2*d^3*x^2 + 3*a*b*c*d^3*x + a*b*d^3)*arctanh(c*x))/x^4, x)","F",0
92,0,0,0,0.632267," ","integrate((c*d*x+d)^3*(a+b*arctanh(c*x))^2/x^5,x, algorithm=""fricas"")","{\rm integral}\left(\frac{a^{2} c^{3} d^{3} x^{3} + 3 \, a^{2} c^{2} d^{3} x^{2} + 3 \, a^{2} c d^{3} x + a^{2} d^{3} + {\left(b^{2} c^{3} d^{3} x^{3} + 3 \, b^{2} c^{2} d^{3} x^{2} + 3 \, b^{2} c d^{3} x + b^{2} d^{3}\right)} \operatorname{artanh}\left(c x\right)^{2} + 2 \, {\left(a b c^{3} d^{3} x^{3} + 3 \, a b c^{2} d^{3} x^{2} + 3 \, a b c d^{3} x + a b d^{3}\right)} \operatorname{artanh}\left(c x\right)}{x^{5}}, x\right)"," ",0,"integral((a^2*c^3*d^3*x^3 + 3*a^2*c^2*d^3*x^2 + 3*a^2*c*d^3*x + a^2*d^3 + (b^2*c^3*d^3*x^3 + 3*b^2*c^2*d^3*x^2 + 3*b^2*c*d^3*x + b^2*d^3)*arctanh(c*x)^2 + 2*(a*b*c^3*d^3*x^3 + 3*a*b*c^2*d^3*x^2 + 3*a*b*c*d^3*x + a*b*d^3)*arctanh(c*x))/x^5, x)","F",0
93,0,0,0,0.605027," ","integrate((c*d*x+d)^3*(a+b*arctanh(c*x))^2/x^6,x, algorithm=""fricas"")","{\rm integral}\left(\frac{a^{2} c^{3} d^{3} x^{3} + 3 \, a^{2} c^{2} d^{3} x^{2} + 3 \, a^{2} c d^{3} x + a^{2} d^{3} + {\left(b^{2} c^{3} d^{3} x^{3} + 3 \, b^{2} c^{2} d^{3} x^{2} + 3 \, b^{2} c d^{3} x + b^{2} d^{3}\right)} \operatorname{artanh}\left(c x\right)^{2} + 2 \, {\left(a b c^{3} d^{3} x^{3} + 3 \, a b c^{2} d^{3} x^{2} + 3 \, a b c d^{3} x + a b d^{3}\right)} \operatorname{artanh}\left(c x\right)}{x^{6}}, x\right)"," ",0,"integral((a^2*c^3*d^3*x^3 + 3*a^2*c^2*d^3*x^2 + 3*a^2*c*d^3*x + a^2*d^3 + (b^2*c^3*d^3*x^3 + 3*b^2*c^2*d^3*x^2 + 3*b^2*c*d^3*x + b^2*d^3)*arctanh(c*x)^2 + 2*(a*b*c^3*d^3*x^3 + 3*a*b*c^2*d^3*x^2 + 3*a*b*c*d^3*x + a*b*d^3)*arctanh(c*x))/x^6, x)","F",0
94,0,0,0,0.691474," ","integrate((c*d*x+d)^3*(a+b*arctanh(c*x))^2/x^7,x, algorithm=""fricas"")","{\rm integral}\left(\frac{a^{2} c^{3} d^{3} x^{3} + 3 \, a^{2} c^{2} d^{3} x^{2} + 3 \, a^{2} c d^{3} x + a^{2} d^{3} + {\left(b^{2} c^{3} d^{3} x^{3} + 3 \, b^{2} c^{2} d^{3} x^{2} + 3 \, b^{2} c d^{3} x + b^{2} d^{3}\right)} \operatorname{artanh}\left(c x\right)^{2} + 2 \, {\left(a b c^{3} d^{3} x^{3} + 3 \, a b c^{2} d^{3} x^{2} + 3 \, a b c d^{3} x + a b d^{3}\right)} \operatorname{artanh}\left(c x\right)}{x^{7}}, x\right)"," ",0,"integral((a^2*c^3*d^3*x^3 + 3*a^2*c^2*d^3*x^2 + 3*a^2*c*d^3*x + a^2*d^3 + (b^2*c^3*d^3*x^3 + 3*b^2*c^2*d^3*x^2 + 3*b^2*c*d^3*x + b^2*d^3)*arctanh(c*x)^2 + 2*(a*b*c^3*d^3*x^3 + 3*a*b*c^2*d^3*x^2 + 3*a*b*c*d^3*x + a*b*d^3)*arctanh(c*x))/x^7, x)","F",0
95,0,0,0,0.415602," ","integrate(x^3*(a+b*arctanh(c*x))^2/(c*d*x+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} x^{3} \operatorname{artanh}\left(c x\right)^{2} + 2 \, a b x^{3} \operatorname{artanh}\left(c x\right) + a^{2} x^{3}}{c d x + d}, x\right)"," ",0,"integral((b^2*x^3*arctanh(c*x)^2 + 2*a*b*x^3*arctanh(c*x) + a^2*x^3)/(c*d*x + d), x)","F",0
96,0,0,0,0.529607," ","integrate(x^2*(a+b*arctanh(c*x))^2/(c*d*x+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} x^{2} \operatorname{artanh}\left(c x\right)^{2} + 2 \, a b x^{2} \operatorname{artanh}\left(c x\right) + a^{2} x^{2}}{c d x + d}, x\right)"," ",0,"integral((b^2*x^2*arctanh(c*x)^2 + 2*a*b*x^2*arctanh(c*x) + a^2*x^2)/(c*d*x + d), x)","F",0
97,0,0,0,0.431980," ","integrate(x*(a+b*arctanh(c*x))^2/(c*d*x+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} x \operatorname{artanh}\left(c x\right)^{2} + 2 \, a b x \operatorname{artanh}\left(c x\right) + a^{2} x}{c d x + d}, x\right)"," ",0,"integral((b^2*x*arctanh(c*x)^2 + 2*a*b*x*arctanh(c*x) + a^2*x)/(c*d*x + d), x)","F",0
98,0,0,0,0.534117," ","integrate((a+b*arctanh(c*x))^2/(c*d*x+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} \operatorname{artanh}\left(c x\right)^{2} + 2 \, a b \operatorname{artanh}\left(c x\right) + a^{2}}{c d x + d}, x\right)"," ",0,"integral((b^2*arctanh(c*x)^2 + 2*a*b*arctanh(c*x) + a^2)/(c*d*x + d), x)","F",0
99,0,0,0,0.409054," ","integrate((a+b*arctanh(c*x))^2/x/(c*d*x+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} \operatorname{artanh}\left(c x\right)^{2} + 2 \, a b \operatorname{artanh}\left(c x\right) + a^{2}}{c d x^{2} + d x}, x\right)"," ",0,"integral((b^2*arctanh(c*x)^2 + 2*a*b*arctanh(c*x) + a^2)/(c*d*x^2 + d*x), x)","F",0
100,0,0,0,0.620086," ","integrate((a+b*arctanh(c*x))^2/x^2/(c*d*x+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} \operatorname{artanh}\left(c x\right)^{2} + 2 \, a b \operatorname{artanh}\left(c x\right) + a^{2}}{c d x^{3} + d x^{2}}, x\right)"," ",0,"integral((b^2*arctanh(c*x)^2 + 2*a*b*arctanh(c*x) + a^2)/(c*d*x^3 + d*x^2), x)","F",0
101,0,0,0,0.489894," ","integrate((a+b*arctanh(c*x))^2/x^3/(c*d*x+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} \operatorname{artanh}\left(c x\right)^{2} + 2 \, a b \operatorname{artanh}\left(c x\right) + a^{2}}{c d x^{4} + d x^{3}}, x\right)"," ",0,"integral((b^2*arctanh(c*x)^2 + 2*a*b*arctanh(c*x) + a^2)/(c*d*x^4 + d*x^3), x)","F",0
102,0,0,0,0.515084," ","integrate((a+b*arctanh(c*x))^2/x^4/(c*d*x+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} \operatorname{artanh}\left(c x\right)^{2} + 2 \, a b \operatorname{artanh}\left(c x\right) + a^{2}}{c d x^{5} + d x^{4}}, x\right)"," ",0,"integral((b^2*arctanh(c*x)^2 + 2*a*b*arctanh(c*x) + a^2)/(c*d*x^5 + d*x^4), x)","F",0
103,0,0,0,0.797024," ","integrate(x^4*(a+b*arctanh(c*x))^2/(c*d*x+d)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} x^{4} \operatorname{artanh}\left(c x\right)^{2} + 2 \, a b x^{4} \operatorname{artanh}\left(c x\right) + a^{2} x^{4}}{c^{2} d^{2} x^{2} + 2 \, c d^{2} x + d^{2}}, x\right)"," ",0,"integral((b^2*x^4*arctanh(c*x)^2 + 2*a*b*x^4*arctanh(c*x) + a^2*x^4)/(c^2*d^2*x^2 + 2*c*d^2*x + d^2), x)","F",0
104,0,0,0,0.705746," ","integrate(x^3*(a+b*arctanh(c*x))^2/(c*d*x+d)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} x^{3} \operatorname{artanh}\left(c x\right)^{2} + 2 \, a b x^{3} \operatorname{artanh}\left(c x\right) + a^{2} x^{3}}{c^{2} d^{2} x^{2} + 2 \, c d^{2} x + d^{2}}, x\right)"," ",0,"integral((b^2*x^3*arctanh(c*x)^2 + 2*a*b*x^3*arctanh(c*x) + a^2*x^3)/(c^2*d^2*x^2 + 2*c*d^2*x + d^2), x)","F",0
105,0,0,0,0.504776," ","integrate(x^2*(a+b*arctanh(c*x))^2/(c*d*x+d)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} x^{2} \operatorname{artanh}\left(c x\right)^{2} + 2 \, a b x^{2} \operatorname{artanh}\left(c x\right) + a^{2} x^{2}}{c^{2} d^{2} x^{2} + 2 \, c d^{2} x + d^{2}}, x\right)"," ",0,"integral((b^2*x^2*arctanh(c*x)^2 + 2*a*b*x^2*arctanh(c*x) + a^2*x^2)/(c^2*d^2*x^2 + 2*c*d^2*x + d^2), x)","F",0
106,0,0,0,0.489698," ","integrate(x*(a+b*arctanh(c*x))^2/(c*d*x+d)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} x \operatorname{artanh}\left(c x\right)^{2} + 2 \, a b x \operatorname{artanh}\left(c x\right) + a^{2} x}{c^{2} d^{2} x^{2} + 2 \, c d^{2} x + d^{2}}, x\right)"," ",0,"integral((b^2*x*arctanh(c*x)^2 + 2*a*b*x*arctanh(c*x) + a^2*x)/(c^2*d^2*x^2 + 2*c*d^2*x + d^2), x)","F",0
107,1,101,0,0.457970," ","integrate((a+b*arctanh(c*x))^2/(c*d*x+d)^2,x, algorithm=""fricas"")","\frac{{\left(b^{2} c x - b^{2}\right)} \log\left(-\frac{c x + 1}{c x - 1}\right)^{2} - 8 \, a^{2} - 8 \, a b - 4 \, b^{2} + 2 \, {\left({\left(2 \, a b + b^{2}\right)} c x - 2 \, a b - b^{2}\right)} \log\left(-\frac{c x + 1}{c x - 1}\right)}{8 \, {\left(c^{2} d^{2} x + c d^{2}\right)}}"," ",0,"1/8*((b^2*c*x - b^2)*log(-(c*x + 1)/(c*x - 1))^2 - 8*a^2 - 8*a*b - 4*b^2 + 2*((2*a*b + b^2)*c*x - 2*a*b - b^2)*log(-(c*x + 1)/(c*x - 1)))/(c^2*d^2*x + c*d^2)","A",0
108,0,0,0,0.563336," ","integrate((a+b*arctanh(c*x))^2/x/(c*d*x+d)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} \operatorname{artanh}\left(c x\right)^{2} + 2 \, a b \operatorname{artanh}\left(c x\right) + a^{2}}{c^{2} d^{2} x^{3} + 2 \, c d^{2} x^{2} + d^{2} x}, x\right)"," ",0,"integral((b^2*arctanh(c*x)^2 + 2*a*b*arctanh(c*x) + a^2)/(c^2*d^2*x^3 + 2*c*d^2*x^2 + d^2*x), x)","F",0
109,0,0,0,0.520163," ","integrate((a+b*arctanh(c*x))^2/x^2/(c*d*x+d)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} \operatorname{artanh}\left(c x\right)^{2} + 2 \, a b \operatorname{artanh}\left(c x\right) + a^{2}}{c^{2} d^{2} x^{4} + 2 \, c d^{2} x^{3} + d^{2} x^{2}}, x\right)"," ",0,"integral((b^2*arctanh(c*x)^2 + 2*a*b*arctanh(c*x) + a^2)/(c^2*d^2*x^4 + 2*c*d^2*x^3 + d^2*x^2), x)","F",0
110,0,0,0,0.675898," ","integrate((a+b*arctanh(c*x))^2/x^3/(c*d*x+d)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} \operatorname{artanh}\left(c x\right)^{2} + 2 \, a b \operatorname{artanh}\left(c x\right) + a^{2}}{c^{2} d^{2} x^{5} + 2 \, c d^{2} x^{4} + d^{2} x^{3}}, x\right)"," ",0,"integral((b^2*arctanh(c*x)^2 + 2*a*b*arctanh(c*x) + a^2)/(c^2*d^2*x^5 + 2*c*d^2*x^4 + d^2*x^3), x)","F",0
111,0,0,0,1.061386," ","integrate(x^4*(a+b*arctanh(c*x))^2/(c*d*x+d)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} x^{4} \operatorname{artanh}\left(c x\right)^{2} + 2 \, a b x^{4} \operatorname{artanh}\left(c x\right) + a^{2} x^{4}}{c^{3} d^{3} x^{3} + 3 \, c^{2} d^{3} x^{2} + 3 \, c d^{3} x + d^{3}}, x\right)"," ",0,"integral((b^2*x^4*arctanh(c*x)^2 + 2*a*b*x^4*arctanh(c*x) + a^2*x^4)/(c^3*d^3*x^3 + 3*c^2*d^3*x^2 + 3*c*d^3*x + d^3), x)","F",0
112,0,0,0,0.755926," ","integrate(x^3*(a+b*arctanh(c*x))^2/(c*d*x+d)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} x^{3} \operatorname{artanh}\left(c x\right)^{2} + 2 \, a b x^{3} \operatorname{artanh}\left(c x\right) + a^{2} x^{3}}{c^{3} d^{3} x^{3} + 3 \, c^{2} d^{3} x^{2} + 3 \, c d^{3} x + d^{3}}, x\right)"," ",0,"integral((b^2*x^3*arctanh(c*x)^2 + 2*a*b*x^3*arctanh(c*x) + a^2*x^3)/(c^3*d^3*x^3 + 3*c^2*d^3*x^2 + 3*c*d^3*x + d^3), x)","F",0
113,0,0,0,0.436739," ","integrate(x^2*(a+b*arctanh(c*x))^2/(c*d*x+d)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} x^{2} \operatorname{artanh}\left(c x\right)^{2} + 2 \, a b x^{2} \operatorname{artanh}\left(c x\right) + a^{2} x^{2}}{c^{3} d^{3} x^{3} + 3 \, c^{2} d^{3} x^{2} + 3 \, c d^{3} x + d^{3}}, x\right)"," ",0,"integral((b^2*x^2*arctanh(c*x)^2 + 2*a*b*x^2*arctanh(c*x) + a^2*x^2)/(c^3*d^3*x^3 + 3*c^2*d^3*x^2 + 3*c*d^3*x + d^3), x)","F",0
114,1,164,0,0.625363," ","integrate(x*(a+b*arctanh(c*x))^2/(c*d*x+d)^3,x, algorithm=""fricas"")","-\frac{2 \, {\left(16 \, a^{2} + 12 \, a b + 5 \, b^{2}\right)} c x - {\left(3 \, b^{2} c^{2} x^{2} - 2 \, b^{2} c x - b^{2}\right)} \log\left(-\frac{c x + 1}{c x - 1}\right)^{2} + 16 \, a^{2} + 16 \, a b + 8 \, b^{2} - {\left({\left(12 \, a b + 5 \, b^{2}\right)} c^{2} x^{2} - 2 \, {\left(4 \, a b + b^{2}\right)} c x - 4 \, a b - 3 \, b^{2}\right)} \log\left(-\frac{c x + 1}{c x - 1}\right)}{32 \, {\left(c^{4} d^{3} x^{2} + 2 \, c^{3} d^{3} x + c^{2} d^{3}\right)}}"," ",0,"-1/32*(2*(16*a^2 + 12*a*b + 5*b^2)*c*x - (3*b^2*c^2*x^2 - 2*b^2*c*x - b^2)*log(-(c*x + 1)/(c*x - 1))^2 + 16*a^2 + 16*a*b + 8*b^2 - ((12*a*b + 5*b^2)*c^2*x^2 - 2*(4*a*b + b^2)*c*x - 4*a*b - 3*b^2)*log(-(c*x + 1)/(c*x - 1)))/(c^4*d^3*x^2 + 2*c^3*d^3*x + c^2*d^3)","A",0
115,1,156,0,1.133502," ","integrate((a+b*arctanh(c*x))^2/(c*d*x+d)^3,x, algorithm=""fricas"")","-\frac{2 \, {\left(4 \, a b + 3 \, b^{2}\right)} c x - {\left(b^{2} c^{2} x^{2} + 2 \, b^{2} c x - 3 \, b^{2}\right)} \log\left(-\frac{c x + 1}{c x - 1}\right)^{2} + 16 \, a^{2} + 16 \, a b + 8 \, b^{2} - {\left({\left(4 \, a b + 3 \, b^{2}\right)} c^{2} x^{2} + 2 \, {\left(4 \, a b + b^{2}\right)} c x - 12 \, a b - 5 \, b^{2}\right)} \log\left(-\frac{c x + 1}{c x - 1}\right)}{32 \, {\left(c^{3} d^{3} x^{2} + 2 \, c^{2} d^{3} x + c d^{3}\right)}}"," ",0,"-1/32*(2*(4*a*b + 3*b^2)*c*x - (b^2*c^2*x^2 + 2*b^2*c*x - 3*b^2)*log(-(c*x + 1)/(c*x - 1))^2 + 16*a^2 + 16*a*b + 8*b^2 - ((4*a*b + 3*b^2)*c^2*x^2 + 2*(4*a*b + b^2)*c*x - 12*a*b - 5*b^2)*log(-(c*x + 1)/(c*x - 1)))/(c^3*d^3*x^2 + 2*c^2*d^3*x + c*d^3)","A",0
116,0,0,0,0.659329," ","integrate((a+b*arctanh(c*x))^2/x/(c*d*x+d)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} \operatorname{artanh}\left(c x\right)^{2} + 2 \, a b \operatorname{artanh}\left(c x\right) + a^{2}}{c^{3} d^{3} x^{4} + 3 \, c^{2} d^{3} x^{3} + 3 \, c d^{3} x^{2} + d^{3} x}, x\right)"," ",0,"integral((b^2*arctanh(c*x)^2 + 2*a*b*arctanh(c*x) + a^2)/(c^3*d^3*x^4 + 3*c^2*d^3*x^3 + 3*c*d^3*x^2 + d^3*x), x)","F",0
117,0,0,0,1.627017," ","integrate((a+b*arctanh(c*x))^2/x^2/(c*d*x+d)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} \operatorname{artanh}\left(c x\right)^{2} + 2 \, a b \operatorname{artanh}\left(c x\right) + a^{2}}{c^{3} d^{3} x^{5} + 3 \, c^{2} d^{3} x^{4} + 3 \, c d^{3} x^{3} + d^{3} x^{2}}, x\right)"," ",0,"integral((b^2*arctanh(c*x)^2 + 2*a*b*arctanh(c*x) + a^2)/(c^3*d^3*x^5 + 3*c^2*d^3*x^4 + 3*c*d^3*x^3 + d^3*x^2), x)","F",0
118,1,203,0,0.623473," ","integrate((a+b*arctanh(c*x))^2/(c*x+1)^4,x, algorithm=""fricas"")","-\frac{6 \, {\left(12 \, a b + 11 \, b^{2}\right)} c^{2} x^{2} + 54 \, {\left(4 \, a b + 3 \, b^{2}\right)} c x - 9 \, {\left(b^{2} c^{3} x^{3} + 3 \, b^{2} c^{2} x^{2} + 3 \, b^{2} c x - 7 \, b^{2}\right)} \log\left(-\frac{c x + 1}{c x - 1}\right)^{2} + 288 \, a^{2} + 240 \, a b + 112 \, b^{2} - 3 \, {\left({\left(12 \, a b + 11 \, b^{2}\right)} c^{3} x^{3} + 3 \, {\left(12 \, a b + 7 \, b^{2}\right)} c^{2} x^{2} + 3 \, {\left(12 \, a b - b^{2}\right)} c x - 84 \, a b - 29 \, b^{2}\right)} \log\left(-\frac{c x + 1}{c x - 1}\right)}{864 \, {\left(c^{4} x^{3} + 3 \, c^{3} x^{2} + 3 \, c^{2} x + c\right)}}"," ",0,"-1/864*(6*(12*a*b + 11*b^2)*c^2*x^2 + 54*(4*a*b + 3*b^2)*c*x - 9*(b^2*c^3*x^3 + 3*b^2*c^2*x^2 + 3*b^2*c*x - 7*b^2)*log(-(c*x + 1)/(c*x - 1))^2 + 288*a^2 + 240*a*b + 112*b^2 - 3*((12*a*b + 11*b^2)*c^3*x^3 + 3*(12*a*b + 7*b^2)*c^2*x^2 + 3*(12*a*b - b^2)*c*x - 84*a*b - 29*b^2)*log(-(c*x + 1)/(c*x - 1)))/(c^4*x^3 + 3*c^3*x^2 + 3*c^2*x + c)","A",0
119,0,0,0,1.954312," ","integrate(arctanh(a*x)^2/(-a*c*x^2+c*x),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\operatorname{artanh}\left(a x\right)^{2}}{a c x^{2} - c x}, x\right)"," ",0,"integral(-arctanh(a*x)^2/(a*c*x^2 - c*x), x)","F",0
120,0,0,0,0.563212," ","integrate((c*x+1)^3*(a+b*arctanh(c*x))^3,x, algorithm=""fricas"")","{\rm integral}\left(a^{3} c^{3} x^{3} + 3 \, a^{3} c^{2} x^{2} + 3 \, a^{3} c x + {\left(b^{3} c^{3} x^{3} + 3 \, b^{3} c^{2} x^{2} + 3 \, b^{3} c x + b^{3}\right)} \operatorname{artanh}\left(c x\right)^{3} + a^{3} + 3 \, {\left(a b^{2} c^{3} x^{3} + 3 \, a b^{2} c^{2} x^{2} + 3 \, a b^{2} c x + a b^{2}\right)} \operatorname{artanh}\left(c x\right)^{2} + 3 \, {\left(a^{2} b c^{3} x^{3} + 3 \, a^{2} b c^{2} x^{2} + 3 \, a^{2} b c x + a^{2} b\right)} \operatorname{artanh}\left(c x\right), x\right)"," ",0,"integral(a^3*c^3*x^3 + 3*a^3*c^2*x^2 + 3*a^3*c*x + (b^3*c^3*x^3 + 3*b^3*c^2*x^2 + 3*b^3*c*x + b^3)*arctanh(c*x)^3 + a^3 + 3*(a*b^2*c^3*x^3 + 3*a*b^2*c^2*x^2 + 3*a*b^2*c*x + a*b^2)*arctanh(c*x)^2 + 3*(a^2*b*c^3*x^3 + 3*a^2*b*c^2*x^2 + 3*a^2*b*c*x + a^2*b)*arctanh(c*x), x)","F",0
121,0,0,0,0.665995," ","integrate((c*x+1)^2*(a+b*arctanh(c*x))^3,x, algorithm=""fricas"")","{\rm integral}\left(a^{3} c^{2} x^{2} + 2 \, a^{3} c x + {\left(b^{3} c^{2} x^{2} + 2 \, b^{3} c x + b^{3}\right)} \operatorname{artanh}\left(c x\right)^{3} + a^{3} + 3 \, {\left(a b^{2} c^{2} x^{2} + 2 \, a b^{2} c x + a b^{2}\right)} \operatorname{artanh}\left(c x\right)^{2} + 3 \, {\left(a^{2} b c^{2} x^{2} + 2 \, a^{2} b c x + a^{2} b\right)} \operatorname{artanh}\left(c x\right), x\right)"," ",0,"integral(a^3*c^2*x^2 + 2*a^3*c*x + (b^3*c^2*x^2 + 2*b^3*c*x + b^3)*arctanh(c*x)^3 + a^3 + 3*(a*b^2*c^2*x^2 + 2*a*b^2*c*x + a*b^2)*arctanh(c*x)^2 + 3*(a^2*b*c^2*x^2 + 2*a^2*b*c*x + a^2*b)*arctanh(c*x), x)","F",0
122,0,0,0,0.708513," ","integrate((c*x+1)*(a+b*arctanh(c*x))^3,x, algorithm=""fricas"")","{\rm integral}\left(a^{3} c x + {\left(b^{3} c x + b^{3}\right)} \operatorname{artanh}\left(c x\right)^{3} + a^{3} + 3 \, {\left(a b^{2} c x + a b^{2}\right)} \operatorname{artanh}\left(c x\right)^{2} + 3 \, {\left(a^{2} b c x + a^{2} b\right)} \operatorname{artanh}\left(c x\right), x\right)"," ",0,"integral(a^3*c*x + (b^3*c*x + b^3)*arctanh(c*x)^3 + a^3 + 3*(a*b^2*c*x + a*b^2)*arctanh(c*x)^2 + 3*(a^2*b*c*x + a^2*b)*arctanh(c*x), x)","F",0
123,0,0,0,0.696871," ","integrate((a+b*arctanh(c*x))^3/(c*x+1),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{3} \operatorname{artanh}\left(c x\right)^{3} + 3 \, a b^{2} \operatorname{artanh}\left(c x\right)^{2} + 3 \, a^{2} b \operatorname{artanh}\left(c x\right) + a^{3}}{c x + 1}, x\right)"," ",0,"integral((b^3*arctanh(c*x)^3 + 3*a*b^2*arctanh(c*x)^2 + 3*a^2*b*arctanh(c*x) + a^3)/(c*x + 1), x)","F",0
124,1,160,0,0.873746," ","integrate((a+b*arctanh(c*x))^3/(c*x+1)^2,x, algorithm=""fricas"")","\frac{{\left(b^{3} c x - b^{3}\right)} \log\left(-\frac{c x + 1}{c x - 1}\right)^{3} - 16 \, a^{3} - 24 \, a^{2} b - 24 \, a b^{2} - 12 \, b^{3} - 3 \, {\left(2 \, a b^{2} + b^{3} - {\left(2 \, a b^{2} + b^{3}\right)} c x\right)} \log\left(-\frac{c x + 1}{c x - 1}\right)^{2} - 6 \, {\left(2 \, a^{2} b + 2 \, a b^{2} + b^{3} - {\left(2 \, a^{2} b + 2 \, a b^{2} + b^{3}\right)} c x\right)} \log\left(-\frac{c x + 1}{c x - 1}\right)}{16 \, {\left(c^{2} x + c\right)}}"," ",0,"1/16*((b^3*c*x - b^3)*log(-(c*x + 1)/(c*x - 1))^3 - 16*a^3 - 24*a^2*b - 24*a*b^2 - 12*b^3 - 3*(2*a*b^2 + b^3 - (2*a*b^2 + b^3)*c*x)*log(-(c*x + 1)/(c*x - 1))^2 - 6*(2*a^2*b + 2*a*b^2 + b^3 - (2*a^2*b + 2*a*b^2 + b^3)*c*x)*log(-(c*x + 1)/(c*x - 1)))/(c^2*x + c)","A",0
125,1,250,0,0.655471," ","integrate((a+b*arctanh(c*x))^3/(c*x+1)^3,x, algorithm=""fricas"")","\frac{2 \, {\left(b^{3} c^{2} x^{2} + 2 \, b^{3} c x - 3 \, b^{3}\right)} \log\left(-\frac{c x + 1}{c x - 1}\right)^{3} - 64 \, a^{3} - 96 \, a^{2} b - 96 \, a b^{2} - 48 \, b^{3} - 6 \, {\left(8 \, a^{2} b + 12 \, a b^{2} + 7 \, b^{3}\right)} c x + 3 \, {\left({\left(4 \, a b^{2} + 3 \, b^{3}\right)} c^{2} x^{2} - 12 \, a b^{2} - 5 \, b^{3} + 2 \, {\left(4 \, a b^{2} + b^{3}\right)} c x\right)} \log\left(-\frac{c x + 1}{c x - 1}\right)^{2} + 3 \, {\left({\left(8 \, a^{2} b + 12 \, a b^{2} + 7 \, b^{3}\right)} c^{2} x^{2} - 24 \, a^{2} b - 20 \, a b^{2} - 9 \, b^{3} + 2 \, {\left(8 \, a^{2} b + 4 \, a b^{2} + b^{3}\right)} c x\right)} \log\left(-\frac{c x + 1}{c x - 1}\right)}{128 \, {\left(c^{3} x^{2} + 2 \, c^{2} x + c\right)}}"," ",0,"1/128*(2*(b^3*c^2*x^2 + 2*b^3*c*x - 3*b^3)*log(-(c*x + 1)/(c*x - 1))^3 - 64*a^3 - 96*a^2*b - 96*a*b^2 - 48*b^3 - 6*(8*a^2*b + 12*a*b^2 + 7*b^3)*c*x + 3*((4*a*b^2 + 3*b^3)*c^2*x^2 - 12*a*b^2 - 5*b^3 + 2*(4*a*b^2 + b^3)*c*x)*log(-(c*x + 1)/(c*x - 1))^2 + 3*((8*a^2*b + 12*a*b^2 + 7*b^3)*c^2*x^2 - 24*a^2*b - 20*a*b^2 - 9*b^3 + 2*(8*a^2*b + 4*a*b^2 + b^3)*c*x)*log(-(c*x + 1)/(c*x - 1)))/(c^3*x^2 + 2*c^2*x + c)","A",0
126,1,345,0,0.763215," ","integrate((a+b*arctanh(c*x))^3/(c*x+1)^4,x, algorithm=""fricas"")","-\frac{6 \, {\left(72 \, a^{2} b + 132 \, a b^{2} + 85 \, b^{3}\right)} c^{2} x^{2} - 18 \, {\left(b^{3} c^{3} x^{3} + 3 \, b^{3} c^{2} x^{2} + 3 \, b^{3} c x - 7 \, b^{3}\right)} \log\left(-\frac{c x + 1}{c x - 1}\right)^{3} + 1152 \, a^{3} + 1440 \, a^{2} b + 1344 \, a b^{2} + 656 \, b^{3} + 162 \, {\left(8 \, a^{2} b + 12 \, a b^{2} + 7 \, b^{3}\right)} c x - 9 \, {\left({\left(12 \, a b^{2} + 11 \, b^{3}\right)} c^{3} x^{3} + 3 \, {\left(12 \, a b^{2} + 7 \, b^{3}\right)} c^{2} x^{2} - 84 \, a b^{2} - 29 \, b^{3} + 3 \, {\left(12 \, a b^{2} - b^{3}\right)} c x\right)} \log\left(-\frac{c x + 1}{c x - 1}\right)^{2} - 3 \, {\left({\left(72 \, a^{2} b + 132 \, a b^{2} + 85 \, b^{3}\right)} c^{3} x^{3} + 3 \, {\left(72 \, a^{2} b + 84 \, a b^{2} + 41 \, b^{3}\right)} c^{2} x^{2} - 504 \, a^{2} b - 348 \, a b^{2} - 139 \, b^{3} + 3 \, {\left(72 \, a^{2} b - 12 \, a b^{2} - 23 \, b^{3}\right)} c x\right)} \log\left(-\frac{c x + 1}{c x - 1}\right)}{3456 \, {\left(c^{4} x^{3} + 3 \, c^{3} x^{2} + 3 \, c^{2} x + c\right)}}"," ",0,"-1/3456*(6*(72*a^2*b + 132*a*b^2 + 85*b^3)*c^2*x^2 - 18*(b^3*c^3*x^3 + 3*b^3*c^2*x^2 + 3*b^3*c*x - 7*b^3)*log(-(c*x + 1)/(c*x - 1))^3 + 1152*a^3 + 1440*a^2*b + 1344*a*b^2 + 656*b^3 + 162*(8*a^2*b + 12*a*b^2 + 7*b^3)*c*x - 9*((12*a*b^2 + 11*b^3)*c^3*x^3 + 3*(12*a*b^2 + 7*b^3)*c^2*x^2 - 84*a*b^2 - 29*b^3 + 3*(12*a*b^2 - b^3)*c*x)*log(-(c*x + 1)/(c*x - 1))^2 - 3*((72*a^2*b + 132*a*b^2 + 85*b^3)*c^3*x^3 + 3*(72*a^2*b + 84*a*b^2 + 41*b^3)*c^2*x^2 - 504*a^2*b - 348*a*b^2 - 139*b^3 + 3*(72*a^2*b - 12*a*b^2 - 23*b^3)*c*x)*log(-(c*x + 1)/(c*x - 1)))/(c^4*x^3 + 3*c^3*x^2 + 3*c^2*x + c)","A",0
127,0,0,0,0.745731," ","integrate(x^2*arctanh(a*x)^3/(a*c*x+c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{2} \operatorname{artanh}\left(a x\right)^{3}}{a c x + c}, x\right)"," ",0,"integral(x^2*arctanh(a*x)^3/(a*c*x + c), x)","F",0
128,0,0,0,0.661868," ","integrate(x*arctanh(a*x)^3/(a*c*x+c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x \operatorname{artanh}\left(a x\right)^{3}}{a c x + c}, x\right)"," ",0,"integral(x*arctanh(a*x)^3/(a*c*x + c), x)","F",0
129,0,0,0,0.569567," ","integrate(arctanh(a*x)^3/(a*c*x+c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{artanh}\left(a x\right)^{3}}{a c x + c}, x\right)"," ",0,"integral(arctanh(a*x)^3/(a*c*x + c), x)","F",0
130,0,0,0,0.589583," ","integrate(arctanh(a*x)^3/x/(a*c*x+c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{artanh}\left(a x\right)^{3}}{a c x^{2} + c x}, x\right)"," ",0,"integral(arctanh(a*x)^3/(a*c*x^2 + c*x), x)","F",0
131,0,0,0,0.581316," ","integrate(arctanh(a*x)^3/(a*c*x^2+c*x),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{artanh}\left(a x\right)^{3}}{a c x^{2} + c x}, x\right)"," ",0,"integral(arctanh(a*x)^3/(a*c*x^2 + c*x), x)","F",0
132,0,0,0,0.588719," ","integrate(arctanh(a*x)^3/x^2/(a*c*x+c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{artanh}\left(a x\right)^{3}}{a c x^{3} + c x^{2}}, x\right)"," ",0,"integral(arctanh(a*x)^3/(a*c*x^3 + c*x^2), x)","F",0
133,0,0,0,0.531157," ","integrate(arctanh(a*x)^3/x^3/(a*c*x+c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{artanh}\left(a x\right)^{3}}{a c x^{4} + c x^{3}}, x\right)"," ",0,"integral(arctanh(a*x)^3/(a*c*x^4 + c*x^3), x)","F",0
134,0,0,0,0.585902," ","integrate(x^2*arctanh(a*x)^4/(-a*c*x+c),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{x^{2} \operatorname{artanh}\left(a x\right)^{4}}{a c x - c}, x\right)"," ",0,"integral(-x^2*arctanh(a*x)^4/(a*c*x - c), x)","F",0
135,0,0,0,0.573537," ","integrate(x*arctanh(a*x)^4/(-a*c*x+c),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{x \operatorname{artanh}\left(a x\right)^{4}}{a c x - c}, x\right)"," ",0,"integral(-x*arctanh(a*x)^4/(a*c*x - c), x)","F",0
136,0,0,0,0.578366," ","integrate(arctanh(a*x)^4/(-a*c*x+c),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\operatorname{artanh}\left(a x\right)^{4}}{a c x - c}, x\right)"," ",0,"integral(-arctanh(a*x)^4/(a*c*x - c), x)","F",0
137,0,0,0,0.535898," ","integrate(arctanh(a*x)^4/x/(-a*c*x+c),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\operatorname{artanh}\left(a x\right)^{4}}{a c x^{2} - c x}, x\right)"," ",0,"integral(-arctanh(a*x)^4/(a*c*x^2 - c*x), x)","F",0
138,0,0,0,0.650779," ","integrate(arctanh(a*x)^4/(-a*c*x^2+c*x),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\operatorname{artanh}\left(a x\right)^{4}}{a c x^{2} - c x}, x\right)"," ",0,"integral(-arctanh(a*x)^4/(a*c*x^2 - c*x), x)","F",0
139,0,0,0,0.475123," ","integrate(arctanh(a*x)^4/x^2/(-a*c*x+c),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\operatorname{artanh}\left(a x\right)^{4}}{a c x^{3} - c x^{2}}, x\right)"," ",0,"integral(-arctanh(a*x)^4/(a*c*x^3 - c*x^2), x)","F",0
140,0,0,0,0.476880," ","integrate(arctanh(a*x)^4/x^3/(-a*c*x+c),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\operatorname{artanh}\left(a x\right)^{4}}{a c x^{4} - c x^{3}}, x\right)"," ",0,"integral(-arctanh(a*x)^4/(a*c*x^4 - c*x^3), x)","F",0
141,0,0,0,0.500972," ","integrate(x/(a*c*x+c)/arctanh(a*x),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x}{{\left(a c x + c\right)} \operatorname{artanh}\left(a x\right)}, x\right)"," ",0,"integral(x/((a*c*x + c)*arctanh(a*x)), x)","F",0
142,0,0,0,0.671777," ","integrate(1/(a*c*x+c)/arctanh(a*x),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{{\left(a c x + c\right)} \operatorname{artanh}\left(a x\right)}, x\right)"," ",0,"integral(1/((a*c*x + c)*arctanh(a*x)), x)","F",0
143,0,0,0,0.624207," ","integrate(1/x/(a*c*x+c)/arctanh(a*x),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{{\left(a c x^{2} + c x\right)} \operatorname{artanh}\left(a x\right)}, x\right)"," ",0,"integral(1/((a*c*x^2 + c*x)*arctanh(a*x)), x)","F",0
144,0,0,0,0.546647," ","integrate(x/(a*c*x+c)/arctanh(a*x)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{x}{{\left(a c x + c\right)} \operatorname{artanh}\left(a x\right)^{2}}, x\right)"," ",0,"integral(x/((a*c*x + c)*arctanh(a*x)^2), x)","F",0
145,0,0,0,0.482315," ","integrate(1/(a*c*x+c)/arctanh(a*x)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{{\left(a c x + c\right)} \operatorname{artanh}\left(a x\right)^{2}}, x\right)"," ",0,"integral(1/((a*c*x + c)*arctanh(a*x)^2), x)","F",0
146,0,0,0,0.558999," ","integrate(1/x/(a*c*x+c)/arctanh(a*x)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{{\left(a c x^{2} + c x\right)} \operatorname{artanh}\left(a x\right)^{2}}, x\right)"," ",0,"integral(1/((a*c*x^2 + c*x)*arctanh(a*x)^2), x)","F",0
147,0,0,0,0.566283," ","integrate(x^3*(a+b*arctanh(c*x))/(e*x+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b x^{3} \operatorname{artanh}\left(c x\right) + a x^{3}}{e x + d}, x\right)"," ",0,"integral((b*x^3*arctanh(c*x) + a*x^3)/(e*x + d), x)","F",0
148,0,0,0,0.580055," ","integrate(x^2*(a+b*arctanh(c*x))/(e*x+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b x^{2} \operatorname{artanh}\left(c x\right) + a x^{2}}{e x + d}, x\right)"," ",0,"integral((b*x^2*arctanh(c*x) + a*x^2)/(e*x + d), x)","F",0
149,0,0,0,0.634931," ","integrate(x*(a+b*arctanh(c*x))/(e*x+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b x \operatorname{artanh}\left(c x\right) + a x}{e x + d}, x\right)"," ",0,"integral((b*x*arctanh(c*x) + a*x)/(e*x + d), x)","F",0
150,0,0,0,0.694634," ","integrate((a+b*arctanh(c*x))/(e*x+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \operatorname{artanh}\left(c x\right) + a}{e x + d}, x\right)"," ",0,"integral((b*arctanh(c*x) + a)/(e*x + d), x)","F",0
151,0,0,0,0.617663," ","integrate((a+b*arctanh(c*x))/x/(e*x+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \operatorname{artanh}\left(c x\right) + a}{e x^{2} + d x}, x\right)"," ",0,"integral((b*arctanh(c*x) + a)/(e*x^2 + d*x), x)","F",0
152,0,0,0,0.568476," ","integrate((a+b*arctanh(c*x))/x^2/(e*x+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \operatorname{artanh}\left(c x\right) + a}{e x^{3} + d x^{2}}, x\right)"," ",0,"integral((b*arctanh(c*x) + a)/(e*x^3 + d*x^2), x)","F",0
153,0,0,0,0.589454," ","integrate((a+b*arctanh(c*x))/x^3/(e*x+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \operatorname{artanh}\left(c x\right) + a}{e x^{4} + d x^{3}}, x\right)"," ",0,"integral((b*arctanh(c*x) + a)/(e*x^4 + d*x^3), x)","F",0
154,0,0,0,0.680643," ","integrate(x^2*(a+b*arctanh(c*x))^2/(e*x+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} x^{2} \operatorname{artanh}\left(c x\right)^{2} + 2 \, a b x^{2} \operatorname{artanh}\left(c x\right) + a^{2} x^{2}}{e x + d}, x\right)"," ",0,"integral((b^2*x^2*arctanh(c*x)^2 + 2*a*b*x^2*arctanh(c*x) + a^2*x^2)/(e*x + d), x)","F",0
155,0,0,0,0.452577," ","integrate(x*(a+b*arctanh(c*x))^2/(e*x+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} x \operatorname{artanh}\left(c x\right)^{2} + 2 \, a b x \operatorname{artanh}\left(c x\right) + a^{2} x}{e x + d}, x\right)"," ",0,"integral((b^2*x*arctanh(c*x)^2 + 2*a*b*x*arctanh(c*x) + a^2*x)/(e*x + d), x)","F",0
156,0,0,0,0.567495," ","integrate((a+b*arctanh(c*x))^2/(e*x+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} \operatorname{artanh}\left(c x\right)^{2} + 2 \, a b \operatorname{artanh}\left(c x\right) + a^{2}}{e x + d}, x\right)"," ",0,"integral((b^2*arctanh(c*x)^2 + 2*a*b*arctanh(c*x) + a^2)/(e*x + d), x)","F",0
157,0,0,0,0.665435," ","integrate((a+b*arctanh(c*x))^2/x/(e*x+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} \operatorname{artanh}\left(c x\right)^{2} + 2 \, a b \operatorname{artanh}\left(c x\right) + a^{2}}{e x^{2} + d x}, x\right)"," ",0,"integral((b^2*arctanh(c*x)^2 + 2*a*b*arctanh(c*x) + a^2)/(e*x^2 + d*x), x)","F",0
158,0,0,0,0.611613," ","integrate((a+b*arctanh(c*x))^2/x^2/(e*x+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} \operatorname{artanh}\left(c x\right)^{2} + 2 \, a b \operatorname{artanh}\left(c x\right) + a^{2}}{e x^{3} + d x^{2}}, x\right)"," ",0,"integral((b^2*arctanh(c*x)^2 + 2*a*b*arctanh(c*x) + a^2)/(e*x^3 + d*x^2), x)","F",0
159,0,0,0,0.709998," ","integrate(arctanh(c*x)^2/x/(e*x+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{artanh}\left(c x\right)^{2}}{e x^{2} + d x}, x\right)"," ",0,"integral(arctanh(c*x)^2/(e*x^2 + d*x), x)","F",0
160,0,0,0,0.541953," ","integrate(1/(e*x+d)/(a+b*arctan(c*x)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{a e x + a d + {\left(b e x + b d\right)} \arctan\left(c x\right)}, x\right)"," ",0,"integral(1/(a*e*x + a*d + (b*e*x + b*d)*arctan(c*x)), x)","F",0
161,1,76,0,0.563826," ","integrate(x^4*(-a^2*x^2+1)*arctanh(a*x),x, algorithm=""fricas"")","-\frac{5 \, a^{6} x^{6} - 3 \, a^{4} x^{4} - 6 \, a^{2} x^{2} + 3 \, {\left(5 \, a^{7} x^{7} - 7 \, a^{5} x^{5}\right)} \log\left(-\frac{a x + 1}{a x - 1}\right) - 6 \, \log\left(a^{2} x^{2} - 1\right)}{210 \, a^{5}}"," ",0,"-1/210*(5*a^6*x^6 - 3*a^4*x^4 - 6*a^2*x^2 + 3*(5*a^7*x^7 - 7*a^5*x^5)*log(-(a*x + 1)/(a*x - 1)) - 6*log(a^2*x^2 - 1))/a^5","A",0
162,1,61,0,0.666538," ","integrate(x^3*(-a^2*x^2+1)*arctanh(a*x),x, algorithm=""fricas"")","-\frac{12 \, a^{5} x^{5} - 10 \, a^{3} x^{3} - 30 \, a x + 15 \, {\left(2 \, a^{6} x^{6} - 3 \, a^{4} x^{4} + 1\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)}{360 \, a^{4}}"," ",0,"-1/360*(12*a^5*x^5 - 10*a^3*x^3 - 30*a*x + 15*(2*a^6*x^6 - 3*a^4*x^4 + 1)*log(-(a*x + 1)/(a*x - 1)))/a^4","A",0
163,1,68,0,0.541609," ","integrate(x^2*(-a^2*x^2+1)*arctanh(a*x),x, algorithm=""fricas"")","-\frac{3 \, a^{4} x^{4} - 4 \, a^{2} x^{2} + 2 \, {\left(3 \, a^{5} x^{5} - 5 \, a^{3} x^{3}\right)} \log\left(-\frac{a x + 1}{a x - 1}\right) - 4 \, \log\left(a^{2} x^{2} - 1\right)}{60 \, a^{3}}"," ",0,"-1/60*(3*a^4*x^4 - 4*a^2*x^2 + 2*(3*a^5*x^5 - 5*a^3*x^3)*log(-(a*x + 1)/(a*x - 1)) - 4*log(a^2*x^2 - 1))/a^3","A",0
164,1,52,0,0.582923," ","integrate(x*(-a^2*x^2+1)*arctanh(a*x),x, algorithm=""fricas"")","-\frac{2 \, a^{3} x^{3} - 6 \, a x + 3 \, {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)}{24 \, a^{2}}"," ",0,"-1/24*(2*a^3*x^3 - 6*a*x + 3*(a^4*x^4 - 2*a^2*x^2 + 1)*log(-(a*x + 1)/(a*x - 1)))/a^2","A",0
165,1,53,0,0.476733," ","integrate((-a^2*x^2+1)*arctanh(a*x),x, algorithm=""fricas"")","-\frac{a^{2} x^{2} + {\left(a^{3} x^{3} - 3 \, a x\right)} \log\left(-\frac{a x + 1}{a x - 1}\right) - 2 \, \log\left(a^{2} x^{2} - 1\right)}{6 \, a}"," ",0,"-1/6*(a^2*x^2 + (a^3*x^3 - 3*a*x)*log(-(a*x + 1)/(a*x - 1)) - 2*log(a^2*x^2 - 1))/a","A",0
166,0,0,0,1.431266," ","integrate((-a^2*x^2+1)*arctanh(a*x)/x,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(a^{2} x^{2} - 1\right)} \operatorname{artanh}\left(a x\right)}{x}, x\right)"," ",0,"integral(-(a^2*x^2 - 1)*arctanh(a*x)/x, x)","F",0
167,1,51,0,0.590998," ","integrate((-a^2*x^2+1)*arctanh(a*x)/x^2,x, algorithm=""fricas"")","-\frac{2 \, a x \log\left(a^{2} x^{2} - 1\right) - 2 \, a x \log\left(x\right) + {\left(a^{2} x^{2} + 1\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)}{2 \, x}"," ",0,"-1/2*(2*a*x*log(a^2*x^2 - 1) - 2*a*x*log(x) + (a^2*x^2 + 1)*log(-(a*x + 1)/(a*x - 1)))/x","A",0
168,0,0,0,0.529287," ","integrate((-a^2*x^2+1)*arctanh(a*x)/x^3,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(a^{2} x^{2} - 1\right)} \operatorname{artanh}\left(a x\right)}{x^{3}}, x\right)"," ",0,"integral(-(a^2*x^2 - 1)*arctanh(a*x)/x^3, x)","F",0
169,1,64,0,0.591845," ","integrate((-a^2*x^2+1)*arctanh(a*x)/x^4,x, algorithm=""fricas"")","\frac{2 \, a^{3} x^{3} \log\left(a^{2} x^{2} - 1\right) - 4 \, a^{3} x^{3} \log\left(x\right) - a x + {\left(3 \, a^{2} x^{2} - 1\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)}{6 \, x^{3}}"," ",0,"1/6*(2*a^3*x^3*log(a^2*x^2 - 1) - 4*a^3*x^3*log(x) - a*x + (3*a^2*x^2 - 1)*log(-(a*x + 1)/(a*x - 1)))/x^3","A",0
170,1,52,0,1.409873," ","integrate((-a^2*x^2+1)*arctanh(a*x)/x^5,x, algorithm=""fricas"")","\frac{6 \, a^{3} x^{3} - 2 \, a x - 3 \, {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)}{24 \, x^{4}}"," ",0,"1/24*(6*a^3*x^3 - 2*a*x - 3*(a^4*x^4 - 2*a^2*x^2 + 1)*log(-(a*x + 1)/(a*x - 1)))/x^4","A",0
171,1,73,0,0.524082," ","integrate((-a^2*x^2+1)*arctanh(a*x)/x^6,x, algorithm=""fricas"")","\frac{4 \, a^{5} x^{5} \log\left(a^{2} x^{2} - 1\right) - 8 \, a^{5} x^{5} \log\left(x\right) + 4 \, a^{3} x^{3} - 3 \, a x + 2 \, {\left(5 \, a^{2} x^{2} - 3\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)}{60 \, x^{5}}"," ",0,"1/60*(4*a^5*x^5*log(a^2*x^2 - 1) - 8*a^5*x^5*log(x) + 4*a^3*x^3 - 3*a*x + 2*(5*a^2*x^2 - 3)*log(-(a*x + 1)/(a*x - 1)))/x^5","A",0
172,0,0,0,0.588590," ","integrate(x^4*(-a^2*x^2+1)*arctanh(a*x)^2,x, algorithm=""fricas"")","{\rm integral}\left(-{\left(a^{2} x^{6} - x^{4}\right)} \operatorname{artanh}\left(a x\right)^{2}, x\right)"," ",0,"integral(-(a^2*x^6 - x^4)*arctanh(a*x)^2, x)","F",0
173,1,109,0,0.616118," ","integrate(x^3*(-a^2*x^2+1)*arctanh(a*x)^2,x, algorithm=""fricas"")","-\frac{12 \, a^{4} x^{4} + 4 \, a^{2} x^{2} + 15 \, {\left(2 \, a^{6} x^{6} - 3 \, a^{4} x^{4} + 1\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)^{2} + 4 \, {\left(6 \, a^{5} x^{5} - 5 \, a^{3} x^{3} - 15 \, a x\right)} \log\left(-\frac{a x + 1}{a x - 1}\right) - 56 \, \log\left(a^{2} x^{2} - 1\right)}{720 \, a^{4}}"," ",0,"-1/720*(12*a^4*x^4 + 4*a^2*x^2 + 15*(2*a^6*x^6 - 3*a^4*x^4 + 1)*log(-(a*x + 1)/(a*x - 1))^2 + 4*(6*a^5*x^5 - 5*a^3*x^3 - 15*a*x)*log(-(a*x + 1)/(a*x - 1)) - 56*log(a^2*x^2 - 1))/a^4","A",0
174,0,0,0,0.781239," ","integrate(x^2*(-a^2*x^2+1)*arctanh(a*x)^2,x, algorithm=""fricas"")","{\rm integral}\left(-{\left(a^{2} x^{4} - x^{2}\right)} \operatorname{artanh}\left(a x\right)^{2}, x\right)"," ",0,"integral(-(a^2*x^4 - x^2)*arctanh(a*x)^2, x)","F",0
175,1,91,0,0.531023," ","integrate(x*(-a^2*x^2+1)*arctanh(a*x)^2,x, algorithm=""fricas"")","-\frac{4 \, a^{2} x^{2} + 3 \, {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)^{2} + 4 \, {\left(a^{3} x^{3} - 3 \, a x\right)} \log\left(-\frac{a x + 1}{a x - 1}\right) - 8 \, \log\left(a^{2} x^{2} - 1\right)}{48 \, a^{2}}"," ",0,"-1/48*(4*a^2*x^2 + 3*(a^4*x^4 - 2*a^2*x^2 + 1)*log(-(a*x + 1)/(a*x - 1))^2 + 4*(a^3*x^3 - 3*a*x)*log(-(a*x + 1)/(a*x - 1)) - 8*log(a^2*x^2 - 1))/a^2","A",0
176,0,0,0,0.719116," ","integrate((-a^2*x^2+1)*arctanh(a*x)^2,x, algorithm=""fricas"")","{\rm integral}\left(-{\left(a^{2} x^{2} - 1\right)} \operatorname{artanh}\left(a x\right)^{2}, x\right)"," ",0,"integral(-(a^2*x^2 - 1)*arctanh(a*x)^2, x)","F",0
177,0,0,0,1.025912," ","integrate((-a^2*x^2+1)*arctanh(a*x)^2/x,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(a^{2} x^{2} - 1\right)} \operatorname{artanh}\left(a x\right)^{2}}{x}, x\right)"," ",0,"integral(-(a^2*x^2 - 1)*arctanh(a*x)^2/x, x)","F",0
178,0,0,0,1.515715," ","integrate((-a^2*x^2+1)*arctanh(a*x)^2/x^2,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(a^{2} x^{2} - 1\right)} \operatorname{artanh}\left(a x\right)^{2}}{x^{2}}, x\right)"," ",0,"integral(-(a^2*x^2 - 1)*arctanh(a*x)^2/x^2, x)","F",0
179,0,0,0,0.729604," ","integrate((-a^2*x^2+1)*arctanh(a*x)^2/x^3,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(a^{2} x^{2} - 1\right)} \operatorname{artanh}\left(a x\right)^{2}}{x^{3}}, x\right)"," ",0,"integral(-(a^2*x^2 - 1)*arctanh(a*x)^2/x^3, x)","F",0
180,0,0,0,0.467048," ","integrate((-a^2*x^2+1)*arctanh(a*x)^2/x^4,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(a^{2} x^{2} - 1\right)} \operatorname{artanh}\left(a x\right)^{2}}{x^{4}}, x\right)"," ",0,"integral(-(a^2*x^2 - 1)*arctanh(a*x)^2/x^4, x)","F",0
181,1,108,0,0.871133," ","integrate((-a^2*x^2+1)*arctanh(a*x)^2/x^5,x, algorithm=""fricas"")","\frac{8 \, a^{4} x^{4} \log\left(a^{2} x^{2} - 1\right) - 16 \, a^{4} x^{4} \log\left(x\right) - 4 \, a^{2} x^{2} - 3 \, {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)^{2} + 4 \, {\left(3 \, a^{3} x^{3} - a x\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)}{48 \, x^{4}}"," ",0,"1/48*(8*a^4*x^4*log(a^2*x^2 - 1) - 16*a^4*x^4*log(x) - 4*a^2*x^2 - 3*(a^4*x^4 - 2*a^2*x^2 + 1)*log(-(a*x + 1)/(a*x - 1))^2 + 4*(3*a^3*x^3 - a*x)*log(-(a*x + 1)/(a*x - 1)))/x^4","A",0
182,0,0,0,0.589840," ","integrate((-a^2*x^2+1)*arctanh(a*x)^2/x^6,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(a^{2} x^{2} - 1\right)} \operatorname{artanh}\left(a x\right)^{2}}{x^{6}}, x\right)"," ",0,"integral(-(a^2*x^2 - 1)*arctanh(a*x)^2/x^6, x)","F",0
183,0,0,0,1.333066," ","integrate((-a^2*x^2+1)*arctanh(a*x)^3,x, algorithm=""fricas"")","{\rm integral}\left(-{\left(a^{2} x^{2} - 1\right)} \operatorname{artanh}\left(a x\right)^{3}, x\right)"," ",0,"integral(-(a^2*x^2 - 1)*arctanh(a*x)^3, x)","F",0
184,0,0,0,0.536469," ","integrate(x*arctanh(1/2*x*2^(1/2))/(-x^2+1),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{x \operatorname{artanh}\left(\frac{1}{2} \, \sqrt{2} x\right)}{x^{2} - 1}, x\right)"," ",0,"integral(-x*arctanh(1/2*sqrt(2)*x)/(x^2 - 1), x)","F",0
185,0,0,0,0.595525," ","integrate(x*(-a^2*x^2+1)/arctanh(a*x),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{a^{2} x^{3} - x}{\operatorname{artanh}\left(a x\right)}, x\right)"," ",0,"integral(-(a^2*x^3 - x)/arctanh(a*x), x)","F",0
186,0,0,0,0.699004," ","integrate((-a^2*x^2+1)/arctanh(a*x),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{a^{2} x^{2} - 1}{\operatorname{artanh}\left(a x\right)}, x\right)"," ",0,"integral(-(a^2*x^2 - 1)/arctanh(a*x), x)","F",0
187,0,0,0,1.383318," ","integrate((-a^2*x^2+1)/x/arctanh(a*x),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{a^{2} x^{2} - 1}{x \operatorname{artanh}\left(a x\right)}, x\right)"," ",0,"integral(-(a^2*x^2 - 1)/(x*arctanh(a*x)), x)","F",0
188,0,0,0,0.595877," ","integrate(x*(-a^2*x^2+1)/arctanh(a*x)^2,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{a^{2} x^{3} - x}{\operatorname{artanh}\left(a x\right)^{2}}, x\right)"," ",0,"integral(-(a^2*x^3 - x)/arctanh(a*x)^2, x)","F",0
189,0,0,0,0.591431," ","integrate((-a^2*x^2+1)/arctanh(a*x)^2,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{a^{2} x^{2} - 1}{\operatorname{artanh}\left(a x\right)^{2}}, x\right)"," ",0,"integral(-(a^2*x^2 - 1)/arctanh(a*x)^2, x)","F",0
190,0,0,0,0.664927," ","integrate((-a^2*x^2+1)/x/arctanh(a*x)^2,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{a^{2} x^{2} - 1}{x \operatorname{artanh}\left(a x\right)^{2}}, x\right)"," ",0,"integral(-(a^2*x^2 - 1)/(x*arctanh(a*x)^2), x)","F",0
191,0,0,0,0.753468," ","integrate((-a^2*x^2+1)/arctanh(a*x)^3,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{a^{2} x^{2} - 1}{\operatorname{artanh}\left(a x\right)^{3}}, x\right)"," ",0,"integral(-(a^2*x^2 - 1)/arctanh(a*x)^3, x)","F",0
192,1,92,0,0.563769," ","integrate(x^4*(-a^2*x^2+1)^2*arctanh(a*x),x, algorithm=""fricas"")","\frac{105 \, a^{8} x^{8} - 220 \, a^{6} x^{6} + 48 \, a^{4} x^{4} + 96 \, a^{2} x^{2} + 12 \, {\left(35 \, a^{9} x^{9} - 90 \, a^{7} x^{7} + 63 \, a^{5} x^{5}\right)} \log\left(-\frac{a x + 1}{a x - 1}\right) + 96 \, \log\left(a^{2} x^{2} - 1\right)}{7560 \, a^{5}}"," ",0,"1/7560*(105*a^8*x^8 - 220*a^6*x^6 + 48*a^4*x^4 + 96*a^2*x^2 + 12*(35*a^9*x^9 - 90*a^7*x^7 + 63*a^5*x^5)*log(-(a*x + 1)/(a*x - 1)) + 96*log(a^2*x^2 - 1))/a^5","A",0
193,1,77,0,0.505642," ","integrate(x^3*(-a^2*x^2+1)^2*arctanh(a*x),x, algorithm=""fricas"")","\frac{18 \, a^{7} x^{7} - 42 \, a^{5} x^{5} + 14 \, a^{3} x^{3} + 42 \, a x + 21 \, {\left(3 \, a^{8} x^{8} - 8 \, a^{6} x^{6} + 6 \, a^{4} x^{4} - 1\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)}{1008 \, a^{4}}"," ",0,"1/1008*(18*a^7*x^7 - 42*a^5*x^5 + 14*a^3*x^3 + 42*a*x + 21*(3*a^8*x^8 - 8*a^6*x^6 + 6*a^4*x^4 - 1)*log(-(a*x + 1)/(a*x - 1)))/a^4","A",0
194,1,84,0,0.776271," ","integrate(x^2*(-a^2*x^2+1)^2*arctanh(a*x),x, algorithm=""fricas"")","\frac{10 \, a^{6} x^{6} - 27 \, a^{4} x^{4} + 16 \, a^{2} x^{2} + 2 \, {\left(15 \, a^{7} x^{7} - 42 \, a^{5} x^{5} + 35 \, a^{3} x^{3}\right)} \log\left(-\frac{a x + 1}{a x - 1}\right) + 16 \, \log\left(a^{2} x^{2} - 1\right)}{420 \, a^{3}}"," ",0,"1/420*(10*a^6*x^6 - 27*a^4*x^4 + 16*a^2*x^2 + 2*(15*a^7*x^7 - 42*a^5*x^5 + 35*a^3*x^3)*log(-(a*x + 1)/(a*x - 1)) + 16*log(a^2*x^2 - 1))/a^3","A",0
195,1,68,0,0.603616," ","integrate(x*(-a^2*x^2+1)^2*arctanh(a*x),x, algorithm=""fricas"")","\frac{6 \, a^{5} x^{5} - 20 \, a^{3} x^{3} + 30 \, a x + 15 \, {\left(a^{6} x^{6} - 3 \, a^{4} x^{4} + 3 \, a^{2} x^{2} - 1\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)}{180 \, a^{2}}"," ",0,"1/180*(6*a^5*x^5 - 20*a^3*x^3 + 30*a*x + 15*(a^6*x^6 - 3*a^4*x^4 + 3*a^2*x^2 - 1)*log(-(a*x + 1)/(a*x - 1)))/a^2","A",0
196,1,72,0,0.594227," ","integrate((-a^2*x^2+1)^2*arctanh(a*x),x, algorithm=""fricas"")","\frac{3 \, a^{4} x^{4} - 14 \, a^{2} x^{2} + 2 \, {\left(3 \, a^{5} x^{5} - 10 \, a^{3} x^{3} + 15 \, a x\right)} \log\left(-\frac{a x + 1}{a x - 1}\right) + 16 \, \log\left(a^{2} x^{2} - 1\right)}{60 \, a}"," ",0,"1/60*(3*a^4*x^4 - 14*a^2*x^2 + 2*(3*a^5*x^5 - 10*a^3*x^3 + 15*a*x)*log(-(a*x + 1)/(a*x - 1)) + 16*log(a^2*x^2 - 1))/a","A",0
197,0,0,0,0.612754," ","integrate((-a^2*x^2+1)^2*arctanh(a*x)/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \operatorname{artanh}\left(a x\right)}{x}, x\right)"," ",0,"integral((a^4*x^4 - 2*a^2*x^2 + 1)*arctanh(a*x)/x, x)","F",0
198,1,66,0,0.533353," ","integrate((-a^2*x^2+1)^2*arctanh(a*x)/x^2,x, algorithm=""fricas"")","\frac{a^{3} x^{3} - 8 \, a x \log\left(a^{2} x^{2} - 1\right) + 6 \, a x \log\left(x\right) + {\left(a^{4} x^{4} - 6 \, a^{2} x^{2} - 3\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)}{6 \, x}"," ",0,"1/6*(a^3*x^3 - 8*a*x*log(a^2*x^2 - 1) + 6*a*x*log(x) + (a^4*x^4 - 6*a^2*x^2 - 3)*log(-(a*x + 1)/(a*x - 1)))/x","A",0
199,0,0,0,0.633218," ","integrate((-a^2*x^2+1)^2*arctanh(a*x)/x^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \operatorname{artanh}\left(a x\right)}{x^{3}}, x\right)"," ",0,"integral((a^4*x^4 - 2*a^2*x^2 + 1)*arctanh(a*x)/x^3, x)","F",0
200,1,72,0,0.714021," ","integrate((-a^2*x^2+1)^2*arctanh(a*x)/x^4,x, algorithm=""fricas"")","\frac{8 \, a^{3} x^{3} \log\left(a^{2} x^{2} - 1\right) - 10 \, a^{3} x^{3} \log\left(x\right) - a x + {\left(3 \, a^{4} x^{4} + 6 \, a^{2} x^{2} - 1\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)}{6 \, x^{3}}"," ",0,"1/6*(8*a^3*x^3*log(a^2*x^2 - 1) - 10*a^3*x^3*log(x) - a*x + (3*a^4*x^4 + 6*a^2*x^2 - 1)*log(-(a*x + 1)/(a*x - 1)))/x^3","A",0
201,0,0,0,0.709913," ","integrate((-a^2*x^2+1)^2*arctanh(a*x)/x^5,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \operatorname{artanh}\left(a x\right)}{x^{5}}, x\right)"," ",0,"integral((a^4*x^4 - 2*a^2*x^2 + 1)*arctanh(a*x)/x^5, x)","F",0
202,1,81,0,0.553395," ","integrate((-a^2*x^2+1)^2*arctanh(a*x)/x^6,x, algorithm=""fricas"")","-\frac{16 \, a^{5} x^{5} \log\left(a^{2} x^{2} - 1\right) - 32 \, a^{5} x^{5} \log\left(x\right) - 14 \, a^{3} x^{3} + 3 \, a x + 2 \, {\left(15 \, a^{4} x^{4} - 10 \, a^{2} x^{2} + 3\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)}{60 \, x^{5}}"," ",0,"-1/60*(16*a^5*x^5*log(a^2*x^2 - 1) - 32*a^5*x^5*log(x) - 14*a^3*x^3 + 3*a*x + 2*(15*a^4*x^4 - 10*a^2*x^2 + 3)*log(-(a*x + 1)/(a*x - 1)))/x^5","A",0
203,0,0,0,0.616877," ","integrate(x^4*(-a^2*x^2+1)^2*arctanh(a*x)^2,x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{4} x^{8} - 2 \, a^{2} x^{6} + x^{4}\right)} \operatorname{artanh}\left(a x\right)^{2}, x\right)"," ",0,"integral((a^4*x^8 - 2*a^2*x^6 + x^4)*arctanh(a*x)^2, x)","F",0
204,1,133,0,0.572553," ","integrate(x^3*(-a^2*x^2+1)^2*arctanh(a*x)^2,x, algorithm=""fricas"")","\frac{12 \, a^{6} x^{6} - 24 \, a^{4} x^{4} - 20 \, a^{2} x^{2} + 21 \, {\left(3 \, a^{8} x^{8} - 8 \, a^{6} x^{6} + 6 \, a^{4} x^{4} - 1\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)^{2} + 4 \, {\left(9 \, a^{7} x^{7} - 21 \, a^{5} x^{5} + 7 \, a^{3} x^{3} + 21 \, a x\right)} \log\left(-\frac{a x + 1}{a x - 1}\right) + 64 \, \log\left(a^{2} x^{2} - 1\right)}{2016 \, a^{4}}"," ",0,"1/2016*(12*a^6*x^6 - 24*a^4*x^4 - 20*a^2*x^2 + 21*(3*a^8*x^8 - 8*a^6*x^6 + 6*a^4*x^4 - 1)*log(-(a*x + 1)/(a*x - 1))^2 + 4*(9*a^7*x^7 - 21*a^5*x^5 + 7*a^3*x^3 + 21*a*x)*log(-(a*x + 1)/(a*x - 1)) + 64*log(a^2*x^2 - 1))/a^4","A",0
205,0,0,0,0.590346," ","integrate(x^2*(-a^2*x^2+1)^2*arctanh(a*x)^2,x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{4} x^{6} - 2 \, a^{2} x^{4} + x^{2}\right)} \operatorname{artanh}\left(a x\right)^{2}, x\right)"," ",0,"integral((a^4*x^6 - 2*a^2*x^4 + x^2)*arctanh(a*x)^2, x)","F",0
206,1,116,0,0.678282," ","integrate(x*(-a^2*x^2+1)^2*arctanh(a*x)^2,x, algorithm=""fricas"")","\frac{6 \, a^{4} x^{4} - 28 \, a^{2} x^{2} + 15 \, {\left(a^{6} x^{6} - 3 \, a^{4} x^{4} + 3 \, a^{2} x^{2} - 1\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)^{2} + 4 \, {\left(3 \, a^{5} x^{5} - 10 \, a^{3} x^{3} + 15 \, a x\right)} \log\left(-\frac{a x + 1}{a x - 1}\right) + 32 \, \log\left(a^{2} x^{2} - 1\right)}{360 \, a^{2}}"," ",0,"1/360*(6*a^4*x^4 - 28*a^2*x^2 + 15*(a^6*x^6 - 3*a^4*x^4 + 3*a^2*x^2 - 1)*log(-(a*x + 1)/(a*x - 1))^2 + 4*(3*a^5*x^5 - 10*a^3*x^3 + 15*a*x)*log(-(a*x + 1)/(a*x - 1)) + 32*log(a^2*x^2 - 1))/a^2","A",0
207,0,0,0,0.763132," ","integrate((-a^2*x^2+1)^2*arctanh(a*x)^2,x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \operatorname{artanh}\left(a x\right)^{2}, x\right)"," ",0,"integral((a^4*x^4 - 2*a^2*x^2 + 1)*arctanh(a*x)^2, x)","F",0
208,0,0,0,0.605693," ","integrate((-a^2*x^2+1)^2*arctanh(a*x)^2/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \operatorname{artanh}\left(a x\right)^{2}}{x}, x\right)"," ",0,"integral((a^4*x^4 - 2*a^2*x^2 + 1)*arctanh(a*x)^2/x, x)","F",0
209,0,0,0,0.627656," ","integrate((-a^2*x^2+1)^2*arctanh(a*x)^2/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \operatorname{artanh}\left(a x\right)^{2}}{x^{2}}, x\right)"," ",0,"integral((a^4*x^4 - 2*a^2*x^2 + 1)*arctanh(a*x)^2/x^2, x)","F",0
210,0,0,0,0.602302," ","integrate((-a^2*x^2+1)^2*arctanh(a*x)^2/x^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \operatorname{artanh}\left(a x\right)^{2}}{x^{3}}, x\right)"," ",0,"integral((a^4*x^4 - 2*a^2*x^2 + 1)*arctanh(a*x)^2/x^3, x)","F",0
211,0,0,0,2.102646," ","integrate((-a^2*x^2+1)^2*arctanh(a*x)^2/x^4,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \operatorname{artanh}\left(a x\right)^{2}}{x^{4}}, x\right)"," ",0,"integral((a^4*x^4 - 2*a^2*x^2 + 1)*arctanh(a*x)^2/x^4, x)","F",0
212,0,0,0,0.693904," ","integrate((-a^2*x^2+1)^2*arctanh(a*x)^2/x^5,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \operatorname{artanh}\left(a x\right)^{2}}{x^{5}}, x\right)"," ",0,"integral((a^4*x^4 - 2*a^2*x^2 + 1)*arctanh(a*x)^2/x^5, x)","F",0
213,0,0,0,0.682508," ","integrate((-a^2*x^2+1)^2*arctanh(a*x)^2/x^6,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \operatorname{artanh}\left(a x\right)^{2}}{x^{6}}, x\right)"," ",0,"integral((a^4*x^4 - 2*a^2*x^2 + 1)*arctanh(a*x)^2/x^6, x)","F",0
214,1,132,0,0.587250," ","integrate((-a^2*x^2+1)^2*arctanh(a*x)^2/x^7,x, algorithm=""fricas"")","-\frac{32 \, a^{6} x^{6} \log\left(a^{2} x^{2} - 1\right) - 64 \, a^{6} x^{6} \log\left(x\right) - 28 \, a^{4} x^{4} + 6 \, a^{2} x^{2} - 15 \, {\left(a^{6} x^{6} - 3 \, a^{4} x^{4} + 3 \, a^{2} x^{2} - 1\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)^{2} + 4 \, {\left(15 \, a^{5} x^{5} - 10 \, a^{3} x^{3} + 3 \, a x\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)}{360 \, x^{6}}"," ",0,"-1/360*(32*a^6*x^6*log(a^2*x^2 - 1) - 64*a^6*x^6*log(x) - 28*a^4*x^4 + 6*a^2*x^2 - 15*(a^6*x^6 - 3*a^4*x^4 + 3*a^2*x^2 - 1)*log(-(a*x + 1)/(a*x - 1))^2 + 4*(15*a^5*x^5 - 10*a^3*x^3 + 3*a*x)*log(-(a*x + 1)/(a*x - 1)))/x^6","A",0
215,0,0,0,0.648283," ","integrate((-a^2*x^2+1)^2*arctanh(a*x)^2/x^8,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \operatorname{artanh}\left(a x\right)^{2}}{x^{8}}, x\right)"," ",0,"integral((a^4*x^4 - 2*a^2*x^2 + 1)*arctanh(a*x)^2/x^8, x)","F",0
216,1,148,0,0.607508," ","integrate((-a^2*x^2+1)^2*arctanh(a*x)^2/x^9,x, algorithm=""fricas"")","-\frac{64 \, a^{8} x^{8} \log\left(a^{2} x^{2} - 1\right) - 128 \, a^{8} x^{8} \log\left(x\right) - 20 \, a^{6} x^{6} - 24 \, a^{4} x^{4} + 12 \, a^{2} x^{2} - 21 \, {\left(a^{8} x^{8} - 6 \, a^{4} x^{4} + 8 \, a^{2} x^{2} - 3\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)^{2} + 4 \, {\left(21 \, a^{7} x^{7} + 7 \, a^{5} x^{5} - 21 \, a^{3} x^{3} + 9 \, a x\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)}{2016 \, x^{8}}"," ",0,"-1/2016*(64*a^8*x^8*log(a^2*x^2 - 1) - 128*a^8*x^8*log(x) - 20*a^6*x^6 - 24*a^4*x^4 + 12*a^2*x^2 - 21*(a^8*x^8 - 6*a^4*x^4 + 8*a^2*x^2 - 3)*log(-(a*x + 1)/(a*x - 1))^2 + 4*(21*a^7*x^7 + 7*a^5*x^5 - 21*a^3*x^3 + 9*a*x)*log(-(a*x + 1)/(a*x - 1)))/x^8","A",0
217,0,0,0,0.552828," ","integrate((-a^2*x^2+1)^2*arctanh(a*x)^3,x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \operatorname{artanh}\left(a x\right)^{3}, x\right)"," ",0,"integral((a^4*x^4 - 2*a^2*x^2 + 1)*arctanh(a*x)^3, x)","F",0
218,0,0,0,0.404942," ","integrate(x*(-a^2*x^2+1)^2/arctanh(a*x),x, algorithm=""fricas"")","{\rm integral}\left(\frac{a^{4} x^{5} - 2 \, a^{2} x^{3} + x}{\operatorname{artanh}\left(a x\right)}, x\right)"," ",0,"integral((a^4*x^5 - 2*a^2*x^3 + x)/arctanh(a*x), x)","F",0
219,0,0,0,1.329305," ","integrate((-a^2*x^2+1)^2/arctanh(a*x),x, algorithm=""fricas"")","{\rm integral}\left(\frac{a^{4} x^{4} - 2 \, a^{2} x^{2} + 1}{\operatorname{artanh}\left(a x\right)}, x\right)"," ",0,"integral((a^4*x^4 - 2*a^2*x^2 + 1)/arctanh(a*x), x)","F",0
220,0,0,0,0.635725," ","integrate((-a^2*x^2+1)^2/x/arctanh(a*x),x, algorithm=""fricas"")","{\rm integral}\left(\frac{a^{4} x^{4} - 2 \, a^{2} x^{2} + 1}{x \operatorname{artanh}\left(a x\right)}, x\right)"," ",0,"integral((a^4*x^4 - 2*a^2*x^2 + 1)/(x*arctanh(a*x)), x)","F",0
221,0,0,0,0.560098," ","integrate(x*(-a^2*x^2+1)^2/arctanh(a*x)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{a^{4} x^{5} - 2 \, a^{2} x^{3} + x}{\operatorname{artanh}\left(a x\right)^{2}}, x\right)"," ",0,"integral((a^4*x^5 - 2*a^2*x^3 + x)/arctanh(a*x)^2, x)","F",0
222,0,0,0,0.556967," ","integrate((-a^2*x^2+1)^2/arctanh(a*x)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{a^{4} x^{4} - 2 \, a^{2} x^{2} + 1}{\operatorname{artanh}\left(a x\right)^{2}}, x\right)"," ",0,"integral((a^4*x^4 - 2*a^2*x^2 + 1)/arctanh(a*x)^2, x)","F",0
223,0,0,0,0.512730," ","integrate((-a^2*x^2+1)^2/x/arctanh(a*x)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{a^{4} x^{4} - 2 \, a^{2} x^{2} + 1}{x \operatorname{artanh}\left(a x\right)^{2}}, x\right)"," ",0,"integral((a^4*x^4 - 2*a^2*x^2 + 1)/(x*arctanh(a*x)^2), x)","F",0
224,1,88,0,0.518591," ","integrate((-a^2*x^2+1)^3*arctanh(a*x),x, algorithm=""fricas"")","-\frac{5 \, a^{6} x^{6} - 24 \, a^{4} x^{4} + 57 \, a^{2} x^{2} + 3 \, {\left(5 \, a^{7} x^{7} - 21 \, a^{5} x^{5} + 35 \, a^{3} x^{3} - 35 \, a x\right)} \log\left(-\frac{a x + 1}{a x - 1}\right) - 48 \, \log\left(a^{2} x^{2} - 1\right)}{210 \, a}"," ",0,"-1/210*(5*a^6*x^6 - 24*a^4*x^4 + 57*a^2*x^2 + 3*(5*a^7*x^7 - 21*a^5*x^5 + 35*a^3*x^3 - 35*a*x)*log(-(a*x + 1)/(a*x - 1)) - 48*log(a^2*x^2 - 1))/a","A",0
225,0,0,0,0.499621," ","integrate((-a^2*x^2+1)^3*arctanh(a*x)^2,x, algorithm=""fricas"")","{\rm integral}\left(-{\left(a^{6} x^{6} - 3 \, a^{4} x^{4} + 3 \, a^{2} x^{2} - 1\right)} \operatorname{artanh}\left(a x\right)^{2}, x\right)"," ",0,"integral(-(a^6*x^6 - 3*a^4*x^4 + 3*a^2*x^2 - 1)*arctanh(a*x)^2, x)","F",0
226,0,0,0,0.457291," ","integrate((-a^2*x^2+1)^3*arctanh(a*x)^3,x, algorithm=""fricas"")","{\rm integral}\left(-{\left(a^{6} x^{6} - 3 \, a^{4} x^{4} + 3 \, a^{2} x^{2} - 1\right)} \operatorname{artanh}\left(a x\right)^{3}, x\right)"," ",0,"integral(-(a^6*x^6 - 3*a^4*x^4 + 3*a^2*x^2 - 1)*arctanh(a*x)^3, x)","F",0
227,0,0,0,0.550437," ","integrate(x^3*arctanh(a*x)/(-a^2*x^2+1),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{x^{3} \operatorname{artanh}\left(a x\right)}{a^{2} x^{2} - 1}, x\right)"," ",0,"integral(-x^3*arctanh(a*x)/(a^2*x^2 - 1), x)","F",0
228,1,56,0,0.548027," ","integrate(x^2*arctanh(a*x)/(-a^2*x^2+1),x, algorithm=""fricas"")","-\frac{4 \, a x \log\left(-\frac{a x + 1}{a x - 1}\right) - \log\left(-\frac{a x + 1}{a x - 1}\right)^{2} + 4 \, \log\left(a^{2} x^{2} - 1\right)}{8 \, a^{3}}"," ",0,"-1/8*(4*a*x*log(-(a*x + 1)/(a*x - 1)) - log(-(a*x + 1)/(a*x - 1))^2 + 4*log(a^2*x^2 - 1))/a^3","A",0
229,0,0,0,0.533568," ","integrate(x*arctanh(a*x)/(-a^2*x^2+1),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{x \operatorname{artanh}\left(a x\right)}{a^{2} x^{2} - 1}, x\right)"," ",0,"integral(-x*arctanh(a*x)/(a^2*x^2 - 1), x)","F",0
230,1,22,0,0.628790," ","integrate(arctanh(a*x)/(-a^2*x^2+1),x, algorithm=""fricas"")","\frac{\log\left(-\frac{a x + 1}{a x - 1}\right)^{2}}{8 \, a}"," ",0,"1/8*log(-(a*x + 1)/(a*x - 1))^2/a","A",0
231,0,0,0,1.506079," ","integrate(arctanh(a*x)/x/(-a^2*x^2+1),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\operatorname{artanh}\left(a x\right)}{a^{2} x^{3} - x}, x\right)"," ",0,"integral(-arctanh(a*x)/(a^2*x^3 - x), x)","F",0
232,1,63,0,0.809725," ","integrate(arctanh(a*x)/x^2/(-a^2*x^2+1),x, algorithm=""fricas"")","\frac{a x \log\left(-\frac{a x + 1}{a x - 1}\right)^{2} - 4 \, a x \log\left(a^{2} x^{2} - 1\right) + 8 \, a x \log\left(x\right) - 4 \, \log\left(-\frac{a x + 1}{a x - 1}\right)}{8 \, x}"," ",0,"1/8*(a*x*log(-(a*x + 1)/(a*x - 1))^2 - 4*a*x*log(a^2*x^2 - 1) + 8*a*x*log(x) - 4*log(-(a*x + 1)/(a*x - 1)))/x","A",0
233,0,0,0,0.681692," ","integrate(arctanh(a*x)/x^3/(-a^2*x^2+1),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\operatorname{artanh}\left(a x\right)}{a^{2} x^{5} - x^{3}}, x\right)"," ",0,"integral(-arctanh(a*x)/(a^2*x^5 - x^3), x)","F",0
234,0,0,0,0.516564," ","integrate(x^3*arctanh(a*x)^2/(-a^2*x^2+1),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{x^{3} \operatorname{artanh}\left(a x\right)^{2}}{a^{2} x^{2} - 1}, x\right)"," ",0,"integral(-x^3*arctanh(a*x)^2/(a^2*x^2 - 1), x)","F",0
235,0,0,0,0.396393," ","integrate(x^2*arctanh(a*x)^2/(-a^2*x^2+1),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{x^{2} \operatorname{artanh}\left(a x\right)^{2}}{a^{2} x^{2} - 1}, x\right)"," ",0,"integral(-x^2*arctanh(a*x)^2/(a^2*x^2 - 1), x)","F",0
236,0,0,0,0.522527," ","integrate(x*arctanh(a*x)^2/(-a^2*x^2+1),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{x \operatorname{artanh}\left(a x\right)^{2}}{a^{2} x^{2} - 1}, x\right)"," ",0,"integral(-x*arctanh(a*x)^2/(a^2*x^2 - 1), x)","F",0
237,1,22,0,0.540295," ","integrate(arctanh(a*x)^2/(-a^2*x^2+1),x, algorithm=""fricas"")","\frac{\log\left(-\frac{a x + 1}{a x - 1}\right)^{3}}{24 \, a}"," ",0,"1/24*log(-(a*x + 1)/(a*x - 1))^3/a","A",0
238,0,0,0,0.401274," ","integrate(arctanh(a*x)^2/x/(-a^2*x^2+1),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\operatorname{artanh}\left(a x\right)^{2}}{a^{2} x^{3} - x}, x\right)"," ",0,"integral(-arctanh(a*x)^2/(a^2*x^3 - x), x)","F",0
239,0,0,0,0.471195," ","integrate(arctanh(a*x)^2/x^2/(-a^2*x^2+1),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\operatorname{artanh}\left(a x\right)^{2}}{a^{2} x^{4} - x^{2}}, x\right)"," ",0,"integral(-arctanh(a*x)^2/(a^2*x^4 - x^2), x)","F",0
240,0,0,0,0.613158," ","integrate(arctanh(a*x)^2/x^3/(-a^2*x^2+1),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\operatorname{artanh}\left(a x\right)^{2}}{a^{2} x^{5} - x^{3}}, x\right)"," ",0,"integral(-arctanh(a*x)^2/(a^2*x^5 - x^3), x)","F",0
241,0,0,0,0.508536," ","integrate(x^3*arctanh(a*x)^3/(-a^2*x^2+1),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{x^{3} \operatorname{artanh}\left(a x\right)^{3}}{a^{2} x^{2} - 1}, x\right)"," ",0,"integral(-x^3*arctanh(a*x)^3/(a^2*x^2 - 1), x)","F",0
242,0,0,0,0.481769," ","integrate(x^2*arctanh(a*x)^3/(-a^2*x^2+1),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{x^{2} \operatorname{artanh}\left(a x\right)^{3}}{a^{2} x^{2} - 1}, x\right)"," ",0,"integral(-x^2*arctanh(a*x)^3/(a^2*x^2 - 1), x)","F",0
243,0,0,0,1.024053," ","integrate(x*arctanh(a*x)^3/(-a^2*x^2+1),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{x \operatorname{artanh}\left(a x\right)^{3}}{a^{2} x^{2} - 1}, x\right)"," ",0,"integral(-x*arctanh(a*x)^3/(a^2*x^2 - 1), x)","F",0
244,1,22,0,0.753779," ","integrate(arctanh(a*x)^3/(-a^2*x^2+1),x, algorithm=""fricas"")","\frac{\log\left(-\frac{a x + 1}{a x - 1}\right)^{4}}{64 \, a}"," ",0,"1/64*log(-(a*x + 1)/(a*x - 1))^4/a","A",0
245,0,0,0,1.461216," ","integrate(arctanh(a*x)^3/x/(-a^2*x^2+1),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\operatorname{artanh}\left(a x\right)^{3}}{a^{2} x^{3} - x}, x\right)"," ",0,"integral(-arctanh(a*x)^3/(a^2*x^3 - x), x)","F",0
246,0,0,0,0.495291," ","integrate(arctanh(a*x)^3/x^2/(-a^2*x^2+1),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\operatorname{artanh}\left(a x\right)^{3}}{a^{2} x^{4} - x^{2}}, x\right)"," ",0,"integral(-arctanh(a*x)^3/(a^2*x^4 - x^2), x)","F",0
247,0,0,0,0.585459," ","integrate(arctanh(a*x)^3/x^3/(-a^2*x^2+1),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\operatorname{artanh}\left(a x\right)^{3}}{a^{2} x^{5} - x^{3}}, x\right)"," ",0,"integral(-arctanh(a*x)^3/(a^2*x^5 - x^3), x)","F",0
248,1,25,0,0.650735," ","integrate(arctanh(a*x)^(1/2)/(-a^2*x^2+1),x, algorithm=""fricas"")","\frac{\sqrt{2} \log\left(-\frac{a x + 1}{a x - 1}\right)^{\frac{3}{2}}}{6 \, a}"," ",0,"1/6*sqrt(2)*log(-(a*x + 1)/(a*x - 1))^(3/2)/a","B",0
249,0,0,0,0.739368," ","integrate(x/(-a^2*x^2+1)/arctanh(a*x),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{x}{{\left(a^{2} x^{2} - 1\right)} \operatorname{artanh}\left(a x\right)}, x\right)"," ",0,"integral(-x/((a^2*x^2 - 1)*arctanh(a*x)), x)","F",0
250,1,20,0,0.972887," ","integrate(1/(-a^2*x^2+1)/arctanh(a*x),x, algorithm=""fricas"")","\frac{\log\left(\log\left(-\frac{a x + 1}{a x - 1}\right)\right)}{a}"," ",0,"log(log(-(a*x + 1)/(a*x - 1)))/a","B",0
251,0,0,0,1.091443," ","integrate(1/x/(-a^2*x^2+1)/arctanh(a*x),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{1}{{\left(a^{2} x^{3} - x\right)} \operatorname{artanh}\left(a x\right)}, x\right)"," ",0,"integral(-1/((a^2*x^3 - x)*arctanh(a*x)), x)","F",0
252,0,0,0,0.749329," ","integrate(x/(-a^2*x^2+1)/arctanh(a*x)^2,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{x}{{\left(a^{2} x^{2} - 1\right)} \operatorname{artanh}\left(a x\right)^{2}}, x\right)"," ",0,"integral(-x/((a^2*x^2 - 1)*arctanh(a*x)^2), x)","F",0
253,1,22,0,0.496030," ","integrate(1/(-a^2*x^2+1)/arctanh(a*x)^2,x, algorithm=""fricas"")","-\frac{2}{a \log\left(-\frac{a x + 1}{a x - 1}\right)}"," ",0,"-2/(a*log(-(a*x + 1)/(a*x - 1)))","A",0
254,0,0,0,0.598674," ","integrate(1/x/(-a^2*x^2+1)/arctanh(a*x)^2,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{1}{{\left(a^{2} x^{3} - x\right)} \operatorname{artanh}\left(a x\right)^{2}}, x\right)"," ",0,"integral(-1/((a^2*x^3 - x)*arctanh(a*x)^2), x)","F",0
255,0,0,0,0.531623," ","integrate(x/(-a^2*x^2+1)/arctanh(a*x)^3,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{x}{{\left(a^{2} x^{2} - 1\right)} \operatorname{artanh}\left(a x\right)^{3}}, x\right)"," ",0,"integral(-x/((a^2*x^2 - 1)*arctanh(a*x)^3), x)","F",0
256,1,22,0,0.419735," ","integrate(1/(-a^2*x^2+1)/arctanh(a*x)^3,x, algorithm=""fricas"")","-\frac{2}{a \log\left(-\frac{a x + 1}{a x - 1}\right)^{2}}"," ",0,"-2/(a*log(-(a*x + 1)/(a*x - 1))^2)","A",0
257,0,0,0,0.389615," ","integrate(1/x/(-a^2*x^2+1)/arctanh(a*x)^3,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{1}{{\left(a^{2} x^{3} - x\right)} \operatorname{artanh}\left(a x\right)^{3}}, x\right)"," ",0,"integral(-1/((a^2*x^3 - x)*arctanh(a*x)^3), x)","F",0
258,1,84,0,0.511233," ","integrate(arctanh(a*x)^p/(-a^2*x^2+1),x, algorithm=""fricas"")","\frac{\cosh\left(p \log\left(\frac{1}{2} \, \log\left(-\frac{a x + 1}{a x - 1}\right)\right)\right) \log\left(-\frac{a x + 1}{a x - 1}\right) + \log\left(-\frac{a x + 1}{a x - 1}\right) \sinh\left(p \log\left(\frac{1}{2} \, \log\left(-\frac{a x + 1}{a x - 1}\right)\right)\right)}{2 \, {\left(a p + a\right)}}"," ",0,"1/2*(cosh(p*log(1/2*log(-(a*x + 1)/(a*x - 1))))*log(-(a*x + 1)/(a*x - 1)) + log(-(a*x + 1)/(a*x - 1))*sinh(p*log(1/2*log(-(a*x + 1)/(a*x - 1)))))/(a*p + a)","B",0
259,0,0,0,0.631293," ","integrate(x^3*arctanh(a*x)/(-a^2*x^2+1)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{3} \operatorname{artanh}\left(a x\right)}{a^{4} x^{4} - 2 \, a^{2} x^{2} + 1}, x\right)"," ",0,"integral(x^3*arctanh(a*x)/(a^4*x^4 - 2*a^2*x^2 + 1), x)","F",0
260,1,65,0,0.716490," ","integrate(x^2*arctanh(a*x)/(-a^2*x^2+1)^2,x, algorithm=""fricas"")","-\frac{4 \, a x \log\left(-\frac{a x + 1}{a x - 1}\right) + {\left(a^{2} x^{2} - 1\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)^{2} - 4}{16 \, {\left(a^{5} x^{2} - a^{3}\right)}}"," ",0,"-1/16*(4*a*x*log(-(a*x + 1)/(a*x - 1)) + (a^2*x^2 - 1)*log(-(a*x + 1)/(a*x - 1))^2 - 4)/(a^5*x^2 - a^3)","A",0
261,1,48,0,0.402239," ","integrate(x*arctanh(a*x)/(-a^2*x^2+1)^2,x, algorithm=""fricas"")","\frac{2 \, a x - {\left(a^{2} x^{2} + 1\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)}{8 \, {\left(a^{4} x^{2} - a^{2}\right)}}"," ",0,"1/8*(2*a*x - (a^2*x^2 + 1)*log(-(a*x + 1)/(a*x - 1)))/(a^4*x^2 - a^2)","A",0
262,1,64,0,0.555870," ","integrate(arctanh(a*x)/(-a^2*x^2+1)^2,x, algorithm=""fricas"")","-\frac{4 \, a x \log\left(-\frac{a x + 1}{a x - 1}\right) - {\left(a^{2} x^{2} - 1\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)^{2} - 4}{16 \, {\left(a^{3} x^{2} - a\right)}}"," ",0,"-1/16*(4*a*x*log(-(a*x + 1)/(a*x - 1)) - (a^2*x^2 - 1)*log(-(a*x + 1)/(a*x - 1))^2 - 4)/(a^3*x^2 - a)","A",0
263,0,0,0,1.011803," ","integrate(arctanh(a*x)/x/(-a^2*x^2+1)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{artanh}\left(a x\right)}{a^{4} x^{5} - 2 \, a^{2} x^{3} + x}, x\right)"," ",0,"integral(arctanh(a*x)/(a^4*x^5 - 2*a^2*x^3 + x), x)","F",0
264,1,118,0,0.902957," ","integrate(arctanh(a*x)/x^2/(-a^2*x^2+1)^2,x, algorithm=""fricas"")","\frac{3 \, {\left(a^{3} x^{3} - a x\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)^{2} + 4 \, a x - 8 \, {\left(a^{3} x^{3} - a x\right)} \log\left(a^{2} x^{2} - 1\right) + 16 \, {\left(a^{3} x^{3} - a x\right)} \log\left(x\right) - 4 \, {\left(3 \, a^{2} x^{2} - 2\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)}{16 \, {\left(a^{2} x^{3} - x\right)}}"," ",0,"1/16*(3*(a^3*x^3 - a*x)*log(-(a*x + 1)/(a*x - 1))^2 + 4*a*x - 8*(a^3*x^3 - a*x)*log(a^2*x^2 - 1) + 16*(a^3*x^3 - a*x)*log(x) - 4*(3*a^2*x^2 - 2)*log(-(a*x + 1)/(a*x - 1)))/(a^2*x^3 - x)","A",0
265,0,0,0,0.605612," ","integrate(arctanh(a*x)/x^3/(-a^2*x^2+1)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{artanh}\left(a x\right)}{a^{4} x^{7} - 2 \, a^{2} x^{5} + x^{3}}, x\right)"," ",0,"integral(arctanh(a*x)/(a^4*x^7 - 2*a^2*x^5 + x^3), x)","F",0
266,0,0,0,1.074174," ","integrate(x^3*arctanh(a*x)^2/(-a^2*x^2+1)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{3} \operatorname{artanh}\left(a x\right)^{2}}{a^{4} x^{4} - 2 \, a^{2} x^{2} + 1}, x\right)"," ",0,"integral(x^3*arctanh(a*x)^2/(a^4*x^4 - 2*a^2*x^2 + 1), x)","F",0
267,1,96,0,0.571028," ","integrate(x^2*arctanh(a*x)^2/(-a^2*x^2+1)^2,x, algorithm=""fricas"")","-\frac{6 \, a x \log\left(-\frac{a x + 1}{a x - 1}\right)^{2} + {\left(a^{2} x^{2} - 1\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)^{3} + 12 \, a x - 6 \, {\left(a^{2} x^{2} + 1\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)}{48 \, {\left(a^{5} x^{2} - a^{3}\right)}}"," ",0,"-1/48*(6*a*x*log(-(a*x + 1)/(a*x - 1))^2 + (a^2*x^2 - 1)*log(-(a*x + 1)/(a*x - 1))^3 + 12*a*x - 6*(a^2*x^2 + 1)*log(-(a*x + 1)/(a*x - 1)))/(a^5*x^2 - a^3)","A",0
268,1,66,0,0.620891," ","integrate(x*arctanh(a*x)^2/(-a^2*x^2+1)^2,x, algorithm=""fricas"")","\frac{4 \, a x \log\left(-\frac{a x + 1}{a x - 1}\right) - {\left(a^{2} x^{2} + 1\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)^{2} - 4}{16 \, {\left(a^{4} x^{2} - a^{2}\right)}}"," ",0,"1/16*(4*a*x*log(-(a*x + 1)/(a*x - 1)) - (a^2*x^2 + 1)*log(-(a*x + 1)/(a*x - 1))^2 - 4)/(a^4*x^2 - a^2)","A",0
269,1,95,0,0.539764," ","integrate(arctanh(a*x)^2/(-a^2*x^2+1)^2,x, algorithm=""fricas"")","-\frac{6 \, a x \log\left(-\frac{a x + 1}{a x - 1}\right)^{2} - {\left(a^{2} x^{2} - 1\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)^{3} + 12 \, a x - 6 \, {\left(a^{2} x^{2} + 1\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)}{48 \, {\left(a^{3} x^{2} - a\right)}}"," ",0,"-1/48*(6*a*x*log(-(a*x + 1)/(a*x - 1))^2 - (a^2*x^2 - 1)*log(-(a*x + 1)/(a*x - 1))^3 + 12*a*x - 6*(a^2*x^2 + 1)*log(-(a*x + 1)/(a*x - 1)))/(a^3*x^2 - a)","A",0
270,0,0,0,0.550877," ","integrate(arctanh(a*x)^2/x/(-a^2*x^2+1)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{artanh}\left(a x\right)^{2}}{a^{4} x^{5} - 2 \, a^{2} x^{3} + x}, x\right)"," ",0,"integral(arctanh(a*x)^2/(a^4*x^5 - 2*a^2*x^3 + x), x)","F",0
271,0,0,0,0.714643," ","integrate(arctanh(a*x)^2/x^2/(-a^2*x^2+1)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{artanh}\left(a x\right)^{2}}{a^{4} x^{6} - 2 \, a^{2} x^{4} + x^{2}}, x\right)"," ",0,"integral(arctanh(a*x)^2/(a^4*x^6 - 2*a^2*x^4 + x^2), x)","F",0
272,0,0,0,0.535335," ","integrate(arctanh(a*x)^2/x^3/(-a^2*x^2+1)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{artanh}\left(a x\right)^{2}}{a^{4} x^{7} - 2 \, a^{2} x^{5} + x^{3}}, x\right)"," ",0,"integral(arctanh(a*x)^2/(a^4*x^7 - 2*a^2*x^5 + x^3), x)","F",0
273,0,0,0,1.521856," ","integrate(x^3*arctanh(a*x)^3/(-a^2*x^2+1)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{3} \operatorname{artanh}\left(a x\right)^{3}}{a^{4} x^{4} - 2 \, a^{2} x^{2} + 1}, x\right)"," ",0,"integral(x^3*arctanh(a*x)^3/(a^4*x^4 - 2*a^2*x^2 + 1), x)","F",0
274,1,114,0,1.031835," ","integrate(x^2*arctanh(a*x)^3/(-a^2*x^2+1)^2,x, algorithm=""fricas"")","-\frac{8 \, a x \log\left(-\frac{a x + 1}{a x - 1}\right)^{3} + {\left(a^{2} x^{2} - 1\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)^{4} + 48 \, a x \log\left(-\frac{a x + 1}{a x - 1}\right) - 12 \, {\left(a^{2} x^{2} + 1\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)^{2} - 48}{128 \, {\left(a^{5} x^{2} - a^{3}\right)}}"," ",0,"-1/128*(8*a*x*log(-(a*x + 1)/(a*x - 1))^3 + (a^2*x^2 - 1)*log(-(a*x + 1)/(a*x - 1))^4 + 48*a*x*log(-(a*x + 1)/(a*x - 1)) - 12*(a^2*x^2 + 1)*log(-(a*x + 1)/(a*x - 1))^2 - 48)/(a^5*x^2 - a^3)","A",0
275,1,97,0,0.457460," ","integrate(x*arctanh(a*x)^3/(-a^2*x^2+1)^2,x, algorithm=""fricas"")","\frac{6 \, a x \log\left(-\frac{a x + 1}{a x - 1}\right)^{2} - {\left(a^{2} x^{2} + 1\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)^{3} + 12 \, a x - 6 \, {\left(a^{2} x^{2} + 1\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)}{32 \, {\left(a^{4} x^{2} - a^{2}\right)}}"," ",0,"1/32*(6*a*x*log(-(a*x + 1)/(a*x - 1))^2 - (a^2*x^2 + 1)*log(-(a*x + 1)/(a*x - 1))^3 + 12*a*x - 6*(a^2*x^2 + 1)*log(-(a*x + 1)/(a*x - 1)))/(a^4*x^2 - a^2)","A",0
276,1,113,0,1.146250," ","integrate(arctanh(a*x)^3/(-a^2*x^2+1)^2,x, algorithm=""fricas"")","-\frac{8 \, a x \log\left(-\frac{a x + 1}{a x - 1}\right)^{3} - {\left(a^{2} x^{2} - 1\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)^{4} + 48 \, a x \log\left(-\frac{a x + 1}{a x - 1}\right) - 12 \, {\left(a^{2} x^{2} + 1\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)^{2} - 48}{128 \, {\left(a^{3} x^{2} - a\right)}}"," ",0,"-1/128*(8*a*x*log(-(a*x + 1)/(a*x - 1))^3 - (a^2*x^2 - 1)*log(-(a*x + 1)/(a*x - 1))^4 + 48*a*x*log(-(a*x + 1)/(a*x - 1)) - 12*(a^2*x^2 + 1)*log(-(a*x + 1)/(a*x - 1))^2 - 48)/(a^3*x^2 - a)","A",0
277,0,0,0,0.590581," ","integrate(arctanh(a*x)^3/x/(-a^2*x^2+1)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{artanh}\left(a x\right)^{3}}{a^{4} x^{5} - 2 \, a^{2} x^{3} + x}, x\right)"," ",0,"integral(arctanh(a*x)^3/(a^4*x^5 - 2*a^2*x^3 + x), x)","F",0
278,0,0,0,0.647701," ","integrate(arctanh(a*x)^3/x^2/(-a^2*x^2+1)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{artanh}\left(a x\right)^{3}}{a^{4} x^{6} - 2 \, a^{2} x^{4} + x^{2}}, x\right)"," ",0,"integral(arctanh(a*x)^3/(a^4*x^6 - 2*a^2*x^4 + x^2), x)","F",0
279,0,0,0,0.629852," ","integrate(arctanh(a*x)^3/x^3/(-a^2*x^2+1)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{artanh}\left(a x\right)^{3}}{a^{4} x^{7} - 2 \, a^{2} x^{5} + x^{3}}, x\right)"," ",0,"integral(arctanh(a*x)^3/(a^4*x^7 - 2*a^2*x^5 + x^3), x)","F",0
280,-2,0,0,0.000000," ","integrate(arctanh(a*x)^(1/2)/(-a^2*x^2+1)^2,x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
281,0,0,0,0.524978," ","integrate(x^4/(-a^2*x^2+1)^2/arctanh(a*x),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{4}}{{\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \operatorname{artanh}\left(a x\right)}, x\right)"," ",0,"integral(x^4/((a^4*x^4 - 2*a^2*x^2 + 1)*arctanh(a*x)), x)","F",0
282,0,0,0,0.621449," ","integrate(x^3/(-a^2*x^2+1)^2/arctanh(a*x),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{3}}{{\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \operatorname{artanh}\left(a x\right)}, x\right)"," ",0,"integral(x^3/((a^4*x^4 - 2*a^2*x^2 + 1)*arctanh(a*x)), x)","F",0
283,1,58,0,0.523867," ","integrate(x^2/(-a^2*x^2+1)^2/arctanh(a*x),x, algorithm=""fricas"")","-\frac{2 \, \log\left(\log\left(-\frac{a x + 1}{a x - 1}\right)\right) - \operatorname{log\_integral}\left(-\frac{a x + 1}{a x - 1}\right) - \operatorname{log\_integral}\left(-\frac{a x - 1}{a x + 1}\right)}{4 \, a^{3}}"," ",0,"-1/4*(2*log(log(-(a*x + 1)/(a*x - 1))) - log_integral(-(a*x + 1)/(a*x - 1)) - log_integral(-(a*x - 1)/(a*x + 1)))/a^3","B",0
284,1,38,0,0.461358," ","integrate(x/(-a^2*x^2+1)^2/arctanh(a*x),x, algorithm=""fricas"")","\frac{\operatorname{log\_integral}\left(-\frac{a x + 1}{a x - 1}\right) - \operatorname{log\_integral}\left(-\frac{a x - 1}{a x + 1}\right)}{4 \, a^{2}}"," ",0,"1/4*(log_integral(-(a*x + 1)/(a*x - 1)) - log_integral(-(a*x - 1)/(a*x + 1)))/a^2","B",0
285,1,54,0,1.017173," ","integrate(1/(-a^2*x^2+1)^2/arctanh(a*x),x, algorithm=""fricas"")","\frac{2 \, \log\left(\log\left(-\frac{a x + 1}{a x - 1}\right)\right) + \operatorname{log\_integral}\left(-\frac{a x + 1}{a x - 1}\right) + \operatorname{log\_integral}\left(-\frac{a x - 1}{a x + 1}\right)}{4 \, a}"," ",0,"1/4*(2*log(log(-(a*x + 1)/(a*x - 1))) + log_integral(-(a*x + 1)/(a*x - 1)) + log_integral(-(a*x - 1)/(a*x + 1)))/a","B",0
286,0,0,0,1.275574," ","integrate(1/x/(-a^2*x^2+1)^2/arctanh(a*x),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{{\left(a^{4} x^{5} - 2 \, a^{2} x^{3} + x\right)} \operatorname{artanh}\left(a x\right)}, x\right)"," ",0,"integral(1/((a^4*x^5 - 2*a^2*x^3 + x)*arctanh(a*x)), x)","F",0
287,0,0,0,0.425861," ","integrate(x^3/(-a^2*x^2+1)^2/arctanh(a*x)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{3}}{{\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \operatorname{artanh}\left(a x\right)^{2}}, x\right)"," ",0,"integral(x^3/((a^4*x^4 - 2*a^2*x^2 + 1)*arctanh(a*x)^2), x)","F",0
288,1,111,0,1.367331," ","integrate(x^2/(-a^2*x^2+1)^2/arctanh(a*x)^2,x, algorithm=""fricas"")","\frac{4 \, a^{2} x^{2} + {\left({\left(a^{2} x^{2} - 1\right)} \operatorname{log\_integral}\left(-\frac{a x + 1}{a x - 1}\right) - {\left(a^{2} x^{2} - 1\right)} \operatorname{log\_integral}\left(-\frac{a x - 1}{a x + 1}\right)\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)}{2 \, {\left(a^{5} x^{2} - a^{3}\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)}"," ",0,"1/2*(4*a^2*x^2 + ((a^2*x^2 - 1)*log_integral(-(a*x + 1)/(a*x - 1)) - (a^2*x^2 - 1)*log_integral(-(a*x - 1)/(a*x + 1)))*log(-(a*x + 1)/(a*x - 1)))/((a^5*x^2 - a^3)*log(-(a*x + 1)/(a*x - 1)))","B",0
289,1,106,0,0.589208," ","integrate(x/(-a^2*x^2+1)^2/arctanh(a*x)^2,x, algorithm=""fricas"")","\frac{4 \, a x + {\left({\left(a^{2} x^{2} - 1\right)} \operatorname{log\_integral}\left(-\frac{a x + 1}{a x - 1}\right) + {\left(a^{2} x^{2} - 1\right)} \operatorname{log\_integral}\left(-\frac{a x - 1}{a x + 1}\right)\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)}{2 \, {\left(a^{4} x^{2} - a^{2}\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)}"," ",0,"1/2*(4*a*x + ((a^2*x^2 - 1)*log_integral(-(a*x + 1)/(a*x - 1)) + (a^2*x^2 - 1)*log_integral(-(a*x - 1)/(a*x + 1)))*log(-(a*x + 1)/(a*x - 1)))/((a^4*x^2 - a^2)*log(-(a*x + 1)/(a*x - 1)))","B",0
290,1,102,0,0.591143," ","integrate(1/(-a^2*x^2+1)^2/arctanh(a*x)^2,x, algorithm=""fricas"")","\frac{{\left({\left(a^{2} x^{2} - 1\right)} \operatorname{log\_integral}\left(-\frac{a x + 1}{a x - 1}\right) - {\left(a^{2} x^{2} - 1\right)} \operatorname{log\_integral}\left(-\frac{a x - 1}{a x + 1}\right)\right)} \log\left(-\frac{a x + 1}{a x - 1}\right) + 4}{2 \, {\left(a^{3} x^{2} - a\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)}"," ",0,"1/2*(((a^2*x^2 - 1)*log_integral(-(a*x + 1)/(a*x - 1)) - (a^2*x^2 - 1)*log_integral(-(a*x - 1)/(a*x + 1)))*log(-(a*x + 1)/(a*x - 1)) + 4)/((a^3*x^2 - a)*log(-(a*x + 1)/(a*x - 1)))","B",0
291,0,0,0,0.599679," ","integrate(1/x/(-a^2*x^2+1)^2/arctanh(a*x)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{{\left(a^{4} x^{5} - 2 \, a^{2} x^{3} + x\right)} \operatorname{artanh}\left(a x\right)^{2}}, x\right)"," ",0,"integral(1/((a^4*x^5 - 2*a^2*x^3 + x)*arctanh(a*x)^2), x)","F",0
292,0,0,0,0.585807," ","integrate(x^3/(-a^2*x^2+1)^2/arctanh(a*x)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{3}}{{\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \operatorname{artanh}\left(a x\right)^{3}}, x\right)"," ",0,"integral(x^3/((a^4*x^4 - 2*a^2*x^2 + 1)*arctanh(a*x)^3), x)","F",0
293,1,131,0,0.448572," ","integrate(x^2/(-a^2*x^2+1)^2/arctanh(a*x)^3,x, algorithm=""fricas"")","\frac{4 \, a^{2} x^{2} + 4 \, a x \log\left(-\frac{a x + 1}{a x - 1}\right) + {\left({\left(a^{2} x^{2} - 1\right)} \operatorname{log\_integral}\left(-\frac{a x + 1}{a x - 1}\right) + {\left(a^{2} x^{2} - 1\right)} \operatorname{log\_integral}\left(-\frac{a x - 1}{a x + 1}\right)\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)^{2}}{2 \, {\left(a^{5} x^{2} - a^{3}\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)^{2}}"," ",0,"1/2*(4*a^2*x^2 + 4*a*x*log(-(a*x + 1)/(a*x - 1)) + ((a^2*x^2 - 1)*log_integral(-(a*x + 1)/(a*x - 1)) + (a^2*x^2 - 1)*log_integral(-(a*x - 1)/(a*x + 1)))*log(-(a*x + 1)/(a*x - 1))^2)/((a^5*x^2 - a^3)*log(-(a*x + 1)/(a*x - 1))^2)","B",0
294,1,135,0,0.537771," ","integrate(x/(-a^2*x^2+1)^2/arctanh(a*x)^3,x, algorithm=""fricas"")","\frac{{\left({\left(a^{2} x^{2} - 1\right)} \operatorname{log\_integral}\left(-\frac{a x + 1}{a x - 1}\right) - {\left(a^{2} x^{2} - 1\right)} \operatorname{log\_integral}\left(-\frac{a x - 1}{a x + 1}\right)\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)^{2} + 4 \, a x + 2 \, {\left(a^{2} x^{2} + 1\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)}{2 \, {\left(a^{4} x^{2} - a^{2}\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)^{2}}"," ",0,"1/2*(((a^2*x^2 - 1)*log_integral(-(a*x + 1)/(a*x - 1)) - (a^2*x^2 - 1)*log_integral(-(a*x - 1)/(a*x + 1)))*log(-(a*x + 1)/(a*x - 1))^2 + 4*a*x + 2*(a^2*x^2 + 1)*log(-(a*x + 1)/(a*x - 1)))/((a^4*x^2 - a^2)*log(-(a*x + 1)/(a*x - 1))^2)","B",0
295,1,122,0,0.519552," ","integrate(1/(-a^2*x^2+1)^2/arctanh(a*x)^3,x, algorithm=""fricas"")","\frac{4 \, a x \log\left(-\frac{a x + 1}{a x - 1}\right) + {\left({\left(a^{2} x^{2} - 1\right)} \operatorname{log\_integral}\left(-\frac{a x + 1}{a x - 1}\right) + {\left(a^{2} x^{2} - 1\right)} \operatorname{log\_integral}\left(-\frac{a x - 1}{a x + 1}\right)\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)^{2} + 4}{2 \, {\left(a^{3} x^{2} - a\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)^{2}}"," ",0,"1/2*(4*a*x*log(-(a*x + 1)/(a*x - 1)) + ((a^2*x^2 - 1)*log_integral(-(a*x + 1)/(a*x - 1)) + (a^2*x^2 - 1)*log_integral(-(a*x - 1)/(a*x + 1)))*log(-(a*x + 1)/(a*x - 1))^2 + 4)/((a^3*x^2 - a)*log(-(a*x + 1)/(a*x - 1))^2)","B",0
296,0,0,0,0.617095," ","integrate(1/x/(-a^2*x^2+1)^2/arctanh(a*x)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{{\left(a^{4} x^{5} - 2 \, a^{2} x^{3} + x\right)} \operatorname{artanh}\left(a x\right)^{3}}, x\right)"," ",0,"integral(1/((a^4*x^5 - 2*a^2*x^3 + x)*arctanh(a*x)^3), x)","F",0
297,1,151,0,0.915062," ","integrate(1/(-a^2*x^2+1)^2/arctanh(a*x)^4,x, algorithm=""fricas"")","\frac{{\left({\left(a^{2} x^{2} - 1\right)} \operatorname{log\_integral}\left(-\frac{a x + 1}{a x - 1}\right) - {\left(a^{2} x^{2} - 1\right)} \operatorname{log\_integral}\left(-\frac{a x - 1}{a x + 1}\right)\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)^{3} + 4 \, a x \log\left(-\frac{a x + 1}{a x - 1}\right) + 2 \, {\left(a^{2} x^{2} + 1\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)^{2} + 8}{3 \, {\left(a^{3} x^{2} - a\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)^{3}}"," ",0,"1/3*(((a^2*x^2 - 1)*log_integral(-(a*x + 1)/(a*x - 1)) - (a^2*x^2 - 1)*log_integral(-(a*x - 1)/(a*x + 1)))*log(-(a*x + 1)/(a*x - 1))^3 + 4*a*x*log(-(a*x + 1)/(a*x - 1)) + 2*(a^2*x^2 + 1)*log(-(a*x + 1)/(a*x - 1))^2 + 8)/((a^3*x^2 - a)*log(-(a*x + 1)/(a*x - 1))^3)","A",0
298,1,171,0,0.698654," ","integrate(1/(-a^2*x^2+1)^2/arctanh(a*x)^5,x, algorithm=""fricas"")","\frac{4 \, a x \log\left(-\frac{a x + 1}{a x - 1}\right)^{3} + {\left({\left(a^{2} x^{2} - 1\right)} \operatorname{log\_integral}\left(-\frac{a x + 1}{a x - 1}\right) + {\left(a^{2} x^{2} - 1\right)} \operatorname{log\_integral}\left(-\frac{a x - 1}{a x + 1}\right)\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)^{4} + 8 \, a x \log\left(-\frac{a x + 1}{a x - 1}\right) + 2 \, {\left(a^{2} x^{2} + 1\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)^{2} + 24}{6 \, {\left(a^{3} x^{2} - a\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)^{4}}"," ",0,"1/6*(4*a*x*log(-(a*x + 1)/(a*x - 1))^3 + ((a^2*x^2 - 1)*log_integral(-(a*x + 1)/(a*x - 1)) + (a^2*x^2 - 1)*log_integral(-(a*x - 1)/(a*x + 1)))*log(-(a*x + 1)/(a*x - 1))^4 + 8*a*x*log(-(a*x + 1)/(a*x - 1)) + 2*(a^2*x^2 + 1)*log(-(a*x + 1)/(a*x - 1))^2 + 24)/((a^3*x^2 - a)*log(-(a*x + 1)/(a*x - 1))^4)","A",0
299,1,200,0,0.788233," ","integrate(1/(-a^2*x^2+1)^2/arctanh(a*x)^6,x, algorithm=""fricas"")","\frac{{\left({\left(a^{2} x^{2} - 1\right)} \operatorname{log\_integral}\left(-\frac{a x + 1}{a x - 1}\right) - {\left(a^{2} x^{2} - 1\right)} \operatorname{log\_integral}\left(-\frac{a x - 1}{a x + 1}\right)\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)^{5} + 4 \, a x \log\left(-\frac{a x + 1}{a x - 1}\right)^{3} + 2 \, {\left(a^{2} x^{2} + 1\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)^{4} + 24 \, a x \log\left(-\frac{a x + 1}{a x - 1}\right) + 4 \, {\left(a^{2} x^{2} + 1\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)^{2} + 96}{15 \, {\left(a^{3} x^{2} - a\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)^{5}}"," ",0,"1/15*(((a^2*x^2 - 1)*log_integral(-(a*x + 1)/(a*x - 1)) - (a^2*x^2 - 1)*log_integral(-(a*x - 1)/(a*x + 1)))*log(-(a*x + 1)/(a*x - 1))^5 + 4*a*x*log(-(a*x + 1)/(a*x - 1))^3 + 2*(a^2*x^2 + 1)*log(-(a*x + 1)/(a*x - 1))^4 + 24*a*x*log(-(a*x + 1)/(a*x - 1)) + 4*(a^2*x^2 + 1)*log(-(a*x + 1)/(a*x - 1))^2 + 96)/((a^3*x^2 - a)*log(-(a*x + 1)/(a*x - 1))^5)","A",0
300,1,220,0,0.584438," ","integrate(1/(-a^2*x^2+1)^2/arctanh(a*x)^7,x, algorithm=""fricas"")","\frac{4 \, a x \log\left(-\frac{a x + 1}{a x - 1}\right)^{5} + {\left({\left(a^{2} x^{2} - 1\right)} \operatorname{log\_integral}\left(-\frac{a x + 1}{a x - 1}\right) + {\left(a^{2} x^{2} - 1\right)} \operatorname{log\_integral}\left(-\frac{a x - 1}{a x + 1}\right)\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)^{6} + 8 \, a x \log\left(-\frac{a x + 1}{a x - 1}\right)^{3} + 2 \, {\left(a^{2} x^{2} + 1\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)^{4} + 96 \, a x \log\left(-\frac{a x + 1}{a x - 1}\right) + 12 \, {\left(a^{2} x^{2} + 1\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)^{2} + 480}{45 \, {\left(a^{3} x^{2} - a\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)^{6}}"," ",0,"1/45*(4*a*x*log(-(a*x + 1)/(a*x - 1))^5 + ((a^2*x^2 - 1)*log_integral(-(a*x + 1)/(a*x - 1)) + (a^2*x^2 - 1)*log_integral(-(a*x - 1)/(a*x + 1)))*log(-(a*x + 1)/(a*x - 1))^6 + 8*a*x*log(-(a*x + 1)/(a*x - 1))^3 + 2*(a^2*x^2 + 1)*log(-(a*x + 1)/(a*x - 1))^4 + 96*a*x*log(-(a*x + 1)/(a*x - 1)) + 12*(a^2*x^2 + 1)*log(-(a*x + 1)/(a*x - 1))^2 + 480)/((a^3*x^2 - a)*log(-(a*x + 1)/(a*x - 1))^6)","A",0
301,1,249,0,1.078960," ","integrate(1/(-a^2*x^2+1)^2/arctanh(a*x)^8,x, algorithm=""fricas"")","\frac{2 \, {\left({\left({\left(a^{2} x^{2} - 1\right)} \operatorname{log\_integral}\left(-\frac{a x + 1}{a x - 1}\right) - {\left(a^{2} x^{2} - 1\right)} \operatorname{log\_integral}\left(-\frac{a x - 1}{a x + 1}\right)\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)^{7} + 4 \, a x \log\left(-\frac{a x + 1}{a x - 1}\right)^{5} + 2 \, {\left(a^{2} x^{2} + 1\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)^{6} + 24 \, a x \log\left(-\frac{a x + 1}{a x - 1}\right)^{3} + 4 \, {\left(a^{2} x^{2} + 1\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)^{4} + 480 \, a x \log\left(-\frac{a x + 1}{a x - 1}\right) + 48 \, {\left(a^{2} x^{2} + 1\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)^{2} + 2880\right)}}{315 \, {\left(a^{3} x^{2} - a\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)^{7}}"," ",0,"2/315*(((a^2*x^2 - 1)*log_integral(-(a*x + 1)/(a*x - 1)) - (a^2*x^2 - 1)*log_integral(-(a*x - 1)/(a*x + 1)))*log(-(a*x + 1)/(a*x - 1))^7 + 4*a*x*log(-(a*x + 1)/(a*x - 1))^5 + 2*(a^2*x^2 + 1)*log(-(a*x + 1)/(a*x - 1))^6 + 24*a*x*log(-(a*x + 1)/(a*x - 1))^3 + 4*(a^2*x^2 + 1)*log(-(a*x + 1)/(a*x - 1))^4 + 480*a*x*log(-(a*x + 1)/(a*x - 1)) + 48*(a^2*x^2 + 1)*log(-(a*x + 1)/(a*x - 1))^2 + 2880)/((a^3*x^2 - a)*log(-(a*x + 1)/(a*x - 1))^7)","A",0
302,1,71,0,0.799248," ","integrate(x^3*arctanh(a*x)/(-a^2*x^2+1)^3,x, algorithm=""fricas"")","-\frac{10 \, a^{3} x^{3} - 6 \, a x - {\left(5 \, a^{4} x^{4} + 6 \, a^{2} x^{2} - 3\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)}{64 \, {\left(a^{8} x^{4} - 2 \, a^{6} x^{2} + a^{4}\right)}}"," ",0,"-1/64*(10*a^3*x^3 - 6*a*x - (5*a^4*x^4 + 6*a^2*x^2 - 3)*log(-(a*x + 1)/(a*x - 1)))/(a^8*x^4 - 2*a^6*x^2 + a^4)","A",0
303,1,95,0,0.511398," ","integrate(x^2*arctanh(a*x)/(-a^2*x^2+1)^3,x, algorithm=""fricas"")","-\frac{4 \, a^{2} x^{2} + {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)^{2} - 4 \, {\left(a^{3} x^{3} + a x\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)}{64 \, {\left(a^{7} x^{4} - 2 \, a^{5} x^{2} + a^{3}\right)}}"," ",0,"-1/64*(4*a^2*x^2 + (a^4*x^4 - 2*a^2*x^2 + 1)*log(-(a*x + 1)/(a*x - 1))^2 - 4*(a^3*x^3 + a*x)*log(-(a*x + 1)/(a*x - 1)))/(a^7*x^4 - 2*a^5*x^2 + a^3)","A",0
304,1,71,0,0.564125," ","integrate(x*arctanh(a*x)/(-a^2*x^2+1)^3,x, algorithm=""fricas"")","\frac{6 \, a^{3} x^{3} - 10 \, a x - {\left(3 \, a^{4} x^{4} - 6 \, a^{2} x^{2} - 5\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)}{64 \, {\left(a^{6} x^{4} - 2 \, a^{4} x^{2} + a^{2}\right)}}"," ",0,"1/64*(6*a^3*x^3 - 10*a*x - (3*a^4*x^4 - 6*a^2*x^2 - 5)*log(-(a*x + 1)/(a*x - 1)))/(a^6*x^4 - 2*a^4*x^2 + a^2)","A",0
305,1,97,0,0.809810," ","integrate(arctanh(a*x)/(-a^2*x^2+1)^3,x, algorithm=""fricas"")","\frac{12 \, a^{2} x^{2} + 3 \, {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)^{2} - 4 \, {\left(3 \, a^{3} x^{3} - 5 \, a x\right)} \log\left(-\frac{a x + 1}{a x - 1}\right) - 16}{64 \, {\left(a^{5} x^{4} - 2 \, a^{3} x^{2} + a\right)}}"," ",0,"1/64*(12*a^2*x^2 + 3*(a^4*x^4 - 2*a^2*x^2 + 1)*log(-(a*x + 1)/(a*x - 1))^2 - 4*(3*a^3*x^3 - 5*a*x)*log(-(a*x + 1)/(a*x - 1)) - 16)/(a^5*x^4 - 2*a^3*x^2 + a)","A",0
306,0,0,0,0.622733," ","integrate(arctanh(a*x)/x/(-a^2*x^2+1)^3,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\operatorname{artanh}\left(a x\right)}{a^{6} x^{7} - 3 \, a^{4} x^{5} + 3 \, a^{2} x^{3} - x}, x\right)"," ",0,"integral(-arctanh(a*x)/(a^6*x^7 - 3*a^4*x^5 + 3*a^2*x^3 - x), x)","F",0
307,1,161,0,0.865934," ","integrate(arctanh(a*x)/x^2/(-a^2*x^2+1)^3,x, algorithm=""fricas"")","\frac{28 \, a^{3} x^{3} + 15 \, {\left(a^{5} x^{5} - 2 \, a^{3} x^{3} + a x\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)^{2} - 32 \, a x - 32 \, {\left(a^{5} x^{5} - 2 \, a^{3} x^{3} + a x\right)} \log\left(a^{2} x^{2} - 1\right) + 64 \, {\left(a^{5} x^{5} - 2 \, a^{3} x^{3} + a x\right)} \log\left(x\right) - 4 \, {\left(15 \, a^{4} x^{4} - 25 \, a^{2} x^{2} + 8\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)}{64 \, {\left(a^{4} x^{5} - 2 \, a^{2} x^{3} + x\right)}}"," ",0,"1/64*(28*a^3*x^3 + 15*(a^5*x^5 - 2*a^3*x^3 + a*x)*log(-(a*x + 1)/(a*x - 1))^2 - 32*a*x - 32*(a^5*x^5 - 2*a^3*x^3 + a*x)*log(a^2*x^2 - 1) + 64*(a^5*x^5 - 2*a^3*x^3 + a*x)*log(x) - 4*(15*a^4*x^4 - 25*a^2*x^2 + 8)*log(-(a*x + 1)/(a*x - 1)))/(a^4*x^5 - 2*a^2*x^3 + x)","A",0
308,1,99,0,0.702470," ","integrate(x^3*arctanh(a*x)^2/(-a^2*x^2+1)^3,x, algorithm=""fricas"")","\frac{20 \, a^{2} x^{2} + {\left(5 \, a^{4} x^{4} + 6 \, a^{2} x^{2} - 3\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)^{2} - 4 \, {\left(5 \, a^{3} x^{3} - 3 \, a x\right)} \log\left(-\frac{a x + 1}{a x - 1}\right) - 16}{128 \, {\left(a^{8} x^{4} - 2 \, a^{6} x^{2} + a^{4}\right)}}"," ",0,"1/128*(20*a^2*x^2 + (5*a^4*x^4 + 6*a^2*x^2 - 3)*log(-(a*x + 1)/(a*x - 1))^2 - 4*(5*a^3*x^3 - 3*a*x)*log(-(a*x + 1)/(a*x - 1)) - 16)/(a^8*x^4 - 2*a^6*x^2 + a^4)","A",0
309,1,136,0,0.619641," ","integrate(x^2*arctanh(a*x)^2/(-a^2*x^2+1)^3,x, algorithm=""fricas"")","\frac{6 \, a^{3} x^{3} - 2 \, {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)^{3} + 12 \, {\left(a^{3} x^{3} + a x\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)^{2} + 6 \, a x - 3 \, {\left(a^{4} x^{4} + 6 \, a^{2} x^{2} + 1\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)}{384 \, {\left(a^{7} x^{4} - 2 \, a^{5} x^{2} + a^{3}\right)}}"," ",0,"1/384*(6*a^3*x^3 - 2*(a^4*x^4 - 2*a^2*x^2 + 1)*log(-(a*x + 1)/(a*x - 1))^3 + 12*(a^3*x^3 + a*x)*log(-(a*x + 1)/(a*x - 1))^2 + 6*a*x - 3*(a^4*x^4 + 6*a^2*x^2 + 1)*log(-(a*x + 1)/(a*x - 1)))/(a^7*x^4 - 2*a^5*x^2 + a^3)","A",0
310,1,99,0,0.492729," ","integrate(x*arctanh(a*x)^2/(-a^2*x^2+1)^3,x, algorithm=""fricas"")","-\frac{12 \, a^{2} x^{2} + {\left(3 \, a^{4} x^{4} - 6 \, a^{2} x^{2} - 5\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)^{2} - 4 \, {\left(3 \, a^{3} x^{3} - 5 \, a x\right)} \log\left(-\frac{a x + 1}{a x - 1}\right) - 16}{128 \, {\left(a^{6} x^{4} - 2 \, a^{4} x^{2} + a^{2}\right)}}"," ",0,"-1/128*(12*a^2*x^2 + (3*a^4*x^4 - 6*a^2*x^2 - 5)*log(-(a*x + 1)/(a*x - 1))^2 - 4*(3*a^3*x^3 - 5*a*x)*log(-(a*x + 1)/(a*x - 1)) - 16)/(a^6*x^4 - 2*a^4*x^2 + a^2)","A",0
311,1,137,0,0.538480," ","integrate(arctanh(a*x)^2/(-a^2*x^2+1)^3,x, algorithm=""fricas"")","-\frac{30 \, a^{3} x^{3} - 2 \, {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)^{3} + 4 \, {\left(3 \, a^{3} x^{3} - 5 \, a x\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)^{2} - 34 \, a x - {\left(15 \, a^{4} x^{4} - 6 \, a^{2} x^{2} - 17\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)}{128 \, {\left(a^{5} x^{4} - 2 \, a^{3} x^{2} + a\right)}}"," ",0,"-1/128*(30*a^3*x^3 - 2*(a^4*x^4 - 2*a^2*x^2 + 1)*log(-(a*x + 1)/(a*x - 1))^3 + 4*(3*a^3*x^3 - 5*a*x)*log(-(a*x + 1)/(a*x - 1))^2 - 34*a*x - (15*a^4*x^4 - 6*a^2*x^2 - 17)*log(-(a*x + 1)/(a*x - 1)))/(a^5*x^4 - 2*a^3*x^2 + a)","A",0
312,0,0,0,0.665829," ","integrate(arctanh(a*x)^2/x/(-a^2*x^2+1)^3,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\operatorname{artanh}\left(a x\right)^{2}}{a^{6} x^{7} - 3 \, a^{4} x^{5} + 3 \, a^{2} x^{3} - x}, x\right)"," ",0,"integral(-arctanh(a*x)^2/(a^6*x^7 - 3*a^4*x^5 + 3*a^2*x^3 - x), x)","F",0
313,0,0,0,0.656514," ","integrate(arctanh(a*x)^2/x^2/(-a^2*x^2+1)^3,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\operatorname{artanh}\left(a x\right)^{2}}{a^{6} x^{8} - 3 \, a^{4} x^{6} + 3 \, a^{2} x^{4} - x^{2}}, x\right)"," ",0,"integral(-arctanh(a*x)^2/(a^6*x^8 - 3*a^4*x^6 + 3*a^2*x^4 - x^2), x)","F",0
314,1,140,0,1.517563," ","integrate(x^3*arctanh(a*x)^3/(-a^2*x^2+1)^3,x, algorithm=""fricas"")","-\frac{102 \, a^{3} x^{3} - 2 \, {\left(5 \, a^{4} x^{4} + 6 \, a^{2} x^{2} - 3\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)^{3} + 12 \, {\left(5 \, a^{3} x^{3} - 3 \, a x\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)^{2} - 90 \, a x - 3 \, {\left(17 \, a^{4} x^{4} + 6 \, a^{2} x^{2} - 15\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)}{512 \, {\left(a^{8} x^{4} - 2 \, a^{6} x^{2} + a^{4}\right)}}"," ",0,"-1/512*(102*a^3*x^3 - 2*(5*a^4*x^4 + 6*a^2*x^2 - 3)*log(-(a*x + 1)/(a*x - 1))^3 + 12*(5*a^3*x^3 - 3*a*x)*log(-(a*x + 1)/(a*x - 1))^2 - 90*a*x - 3*(17*a^4*x^4 + 6*a^2*x^2 - 15)*log(-(a*x + 1)/(a*x - 1)))/(a^8*x^4 - 2*a^6*x^2 + a^4)","A",0
315,1,161,0,0.516744," ","integrate(x^2*arctanh(a*x)^3/(-a^2*x^2+1)^3,x, algorithm=""fricas"")","-\frac{{\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)^{4} + 12 \, a^{2} x^{2} - 8 \, {\left(a^{3} x^{3} + a x\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)^{3} + 3 \, {\left(a^{4} x^{4} + 6 \, a^{2} x^{2} + 1\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)^{2} - 12 \, {\left(a^{3} x^{3} + a x\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)}{512 \, {\left(a^{7} x^{4} - 2 \, a^{5} x^{2} + a^{3}\right)}}"," ",0,"-1/512*((a^4*x^4 - 2*a^2*x^2 + 1)*log(-(a*x + 1)/(a*x - 1))^4 + 12*a^2*x^2 - 8*(a^3*x^3 + a*x)*log(-(a*x + 1)/(a*x - 1))^3 + 3*(a^4*x^4 + 6*a^2*x^2 + 1)*log(-(a*x + 1)/(a*x - 1))^2 - 12*(a^3*x^3 + a*x)*log(-(a*x + 1)/(a*x - 1)))/(a^7*x^4 - 2*a^5*x^2 + a^3)","A",0
316,1,140,0,0.456857," ","integrate(x*arctanh(a*x)^3/(-a^2*x^2+1)^3,x, algorithm=""fricas"")","\frac{90 \, a^{3} x^{3} - 2 \, {\left(3 \, a^{4} x^{4} - 6 \, a^{2} x^{2} - 5\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)^{3} + 12 \, {\left(3 \, a^{3} x^{3} - 5 \, a x\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)^{2} - 102 \, a x - 3 \, {\left(15 \, a^{4} x^{4} - 6 \, a^{2} x^{2} - 17\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)}{512 \, {\left(a^{6} x^{4} - 2 \, a^{4} x^{2} + a^{2}\right)}}"," ",0,"1/512*(90*a^3*x^3 - 2*(3*a^4*x^4 - 6*a^2*x^2 - 5)*log(-(a*x + 1)/(a*x - 1))^3 + 12*(3*a^3*x^3 - 5*a*x)*log(-(a*x + 1)/(a*x - 1))^2 - 102*a*x - 3*(15*a^4*x^4 - 6*a^2*x^2 - 17)*log(-(a*x + 1)/(a*x - 1)))/(a^6*x^4 - 2*a^4*x^2 + a^2)","A",0
317,1,166,0,0.569513," ","integrate(arctanh(a*x)^3/(-a^2*x^2+1)^3,x, algorithm=""fricas"")","\frac{3 \, {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)^{4} + 180 \, a^{2} x^{2} - 8 \, {\left(3 \, a^{3} x^{3} - 5 \, a x\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)^{3} + 3 \, {\left(15 \, a^{4} x^{4} - 6 \, a^{2} x^{2} - 17\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)^{2} - 12 \, {\left(15 \, a^{3} x^{3} - 17 \, a x\right)} \log\left(-\frac{a x + 1}{a x - 1}\right) - 192}{512 \, {\left(a^{5} x^{4} - 2 \, a^{3} x^{2} + a\right)}}"," ",0,"1/512*(3*(a^4*x^4 - 2*a^2*x^2 + 1)*log(-(a*x + 1)/(a*x - 1))^4 + 180*a^2*x^2 - 8*(3*a^3*x^3 - 5*a*x)*log(-(a*x + 1)/(a*x - 1))^3 + 3*(15*a^4*x^4 - 6*a^2*x^2 - 17)*log(-(a*x + 1)/(a*x - 1))^2 - 12*(15*a^3*x^3 - 17*a*x)*log(-(a*x + 1)/(a*x - 1)) - 192)/(a^5*x^4 - 2*a^3*x^2 + a)","A",0
318,0,0,0,0.603961," ","integrate(arctanh(a*x)^3/x/(-a^2*x^2+1)^3,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\operatorname{artanh}\left(a x\right)^{3}}{a^{6} x^{7} - 3 \, a^{4} x^{5} + 3 \, a^{2} x^{3} - x}, x\right)"," ",0,"integral(-arctanh(a*x)^3/(a^6*x^7 - 3*a^4*x^5 + 3*a^2*x^3 - x), x)","F",0
319,0,0,0,0.559483," ","integrate(arctanh(a*x)^3/x^2/(-a^2*x^2+1)^3,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\operatorname{artanh}\left(a x\right)^{3}}{a^{6} x^{8} - 3 \, a^{4} x^{6} + 3 \, a^{2} x^{4} - x^{2}}, x\right)"," ",0,"integral(-arctanh(a*x)^3/(a^6*x^8 - 3*a^4*x^6 + 3*a^2*x^4 - x^2), x)","F",0
320,-2,0,0,0.000000," ","integrate(arctanh(a*x)^(1/2)/(-a^2*x^2+1)^3,x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
321,0,0,0,0.555852," ","integrate(x^6/(-a^2*x^2+1)^3/arctanh(a*x),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{x^{6}}{{\left(a^{6} x^{6} - 3 \, a^{4} x^{4} + 3 \, a^{2} x^{2} - 1\right)} \operatorname{artanh}\left(a x\right)}, x\right)"," ",0,"integral(-x^6/((a^6*x^6 - 3*a^4*x^4 + 3*a^2*x^2 - 1)*arctanh(a*x)), x)","F",0
322,0,0,0,0.640931," ","integrate(x^5/(-a^2*x^2+1)^3/arctanh(a*x),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{x^{5}}{{\left(a^{6} x^{6} - 3 \, a^{4} x^{4} + 3 \, a^{2} x^{2} - 1\right)} \operatorname{artanh}\left(a x\right)}, x\right)"," ",0,"integral(-x^5/((a^6*x^6 - 3*a^4*x^4 + 3*a^2*x^2 - 1)*arctanh(a*x)), x)","F",0
323,1,118,0,0.593516," ","integrate(x^4/(-a^2*x^2+1)^3/arctanh(a*x),x, algorithm=""fricas"")","\frac{6 \, \log\left(\log\left(-\frac{a x + 1}{a x - 1}\right)\right) + \operatorname{log\_integral}\left(\frac{a^{2} x^{2} + 2 \, a x + 1}{a^{2} x^{2} - 2 \, a x + 1}\right) + \operatorname{log\_integral}\left(\frac{a^{2} x^{2} - 2 \, a x + 1}{a^{2} x^{2} + 2 \, a x + 1}\right) - 4 \, \operatorname{log\_integral}\left(-\frac{a x + 1}{a x - 1}\right) - 4 \, \operatorname{log\_integral}\left(-\frac{a x - 1}{a x + 1}\right)}{16 \, a^{5}}"," ",0,"1/16*(6*log(log(-(a*x + 1)/(a*x - 1))) + log_integral((a^2*x^2 + 2*a*x + 1)/(a^2*x^2 - 2*a*x + 1)) + log_integral((a^2*x^2 - 2*a*x + 1)/(a^2*x^2 + 2*a*x + 1)) - 4*log_integral(-(a*x + 1)/(a*x - 1)) - 4*log_integral(-(a*x - 1)/(a*x + 1)))/a^5","B",0
324,1,102,0,0.498225," ","integrate(x^3/(-a^2*x^2+1)^3/arctanh(a*x),x, algorithm=""fricas"")","\frac{\operatorname{log\_integral}\left(\frac{a^{2} x^{2} + 2 \, a x + 1}{a^{2} x^{2} - 2 \, a x + 1}\right) - \operatorname{log\_integral}\left(\frac{a^{2} x^{2} - 2 \, a x + 1}{a^{2} x^{2} + 2 \, a x + 1}\right) - 2 \, \operatorname{log\_integral}\left(-\frac{a x + 1}{a x - 1}\right) + 2 \, \operatorname{log\_integral}\left(-\frac{a x - 1}{a x + 1}\right)}{16 \, a^{4}}"," ",0,"1/16*(log_integral((a^2*x^2 + 2*a*x + 1)/(a^2*x^2 - 2*a*x + 1)) - log_integral((a^2*x^2 - 2*a*x + 1)/(a^2*x^2 + 2*a*x + 1)) - 2*log_integral(-(a*x + 1)/(a*x - 1)) + 2*log_integral(-(a*x - 1)/(a*x + 1)))/a^4","B",0
325,1,88,0,0.606673," ","integrate(x^2/(-a^2*x^2+1)^3/arctanh(a*x),x, algorithm=""fricas"")","-\frac{2 \, \log\left(\log\left(-\frac{a x + 1}{a x - 1}\right)\right) - \operatorname{log\_integral}\left(\frac{a^{2} x^{2} + 2 \, a x + 1}{a^{2} x^{2} - 2 \, a x + 1}\right) - \operatorname{log\_integral}\left(\frac{a^{2} x^{2} - 2 \, a x + 1}{a^{2} x^{2} + 2 \, a x + 1}\right)}{16 \, a^{3}}"," ",0,"-1/16*(2*log(log(-(a*x + 1)/(a*x - 1))) - log_integral((a^2*x^2 + 2*a*x + 1)/(a^2*x^2 - 2*a*x + 1)) - log_integral((a^2*x^2 - 2*a*x + 1)/(a^2*x^2 + 2*a*x + 1)))/a^3","B",0
326,1,102,0,0.621130," ","integrate(x/(-a^2*x^2+1)^3/arctanh(a*x),x, algorithm=""fricas"")","\frac{\operatorname{log\_integral}\left(\frac{a^{2} x^{2} + 2 \, a x + 1}{a^{2} x^{2} - 2 \, a x + 1}\right) - \operatorname{log\_integral}\left(\frac{a^{2} x^{2} - 2 \, a x + 1}{a^{2} x^{2} + 2 \, a x + 1}\right) + 2 \, \operatorname{log\_integral}\left(-\frac{a x + 1}{a x - 1}\right) - 2 \, \operatorname{log\_integral}\left(-\frac{a x - 1}{a x + 1}\right)}{16 \, a^{2}}"," ",0,"1/16*(log_integral((a^2*x^2 + 2*a*x + 1)/(a^2*x^2 - 2*a*x + 1)) - log_integral((a^2*x^2 - 2*a*x + 1)/(a^2*x^2 + 2*a*x + 1)) + 2*log_integral(-(a*x + 1)/(a*x - 1)) - 2*log_integral(-(a*x - 1)/(a*x + 1)))/a^2","B",0
327,1,118,0,0.513205," ","integrate(1/(-a^2*x^2+1)^3/arctanh(a*x),x, algorithm=""fricas"")","\frac{6 \, \log\left(\log\left(-\frac{a x + 1}{a x - 1}\right)\right) + \operatorname{log\_integral}\left(\frac{a^{2} x^{2} + 2 \, a x + 1}{a^{2} x^{2} - 2 \, a x + 1}\right) + \operatorname{log\_integral}\left(\frac{a^{2} x^{2} - 2 \, a x + 1}{a^{2} x^{2} + 2 \, a x + 1}\right) + 4 \, \operatorname{log\_integral}\left(-\frac{a x + 1}{a x - 1}\right) + 4 \, \operatorname{log\_integral}\left(-\frac{a x - 1}{a x + 1}\right)}{16 \, a}"," ",0,"1/16*(6*log(log(-(a*x + 1)/(a*x - 1))) + log_integral((a^2*x^2 + 2*a*x + 1)/(a^2*x^2 - 2*a*x + 1)) + log_integral((a^2*x^2 - 2*a*x + 1)/(a^2*x^2 + 2*a*x + 1)) + 4*log_integral(-(a*x + 1)/(a*x - 1)) + 4*log_integral(-(a*x - 1)/(a*x + 1)))/a","B",0
328,0,0,0,0.535354," ","integrate(1/x/(-a^2*x^2+1)^3/arctanh(a*x),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{1}{{\left(a^{6} x^{7} - 3 \, a^{4} x^{5} + 3 \, a^{2} x^{3} - x\right)} \operatorname{artanh}\left(a x\right)}, x\right)"," ",0,"integral(-1/((a^6*x^7 - 3*a^4*x^5 + 3*a^2*x^3 - x)*arctanh(a*x)), x)","F",0
329,0,0,0,1.355454," ","integrate(x^5/(-a^2*x^2+1)^3/arctanh(a*x)^2,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{x^{5}}{{\left(a^{6} x^{6} - 3 \, a^{4} x^{4} + 3 \, a^{2} x^{2} - 1\right)} \operatorname{artanh}\left(a x\right)^{2}}, x\right)"," ",0,"integral(-x^5/((a^6*x^6 - 3*a^4*x^4 + 3*a^2*x^2 - 1)*arctanh(a*x)^2), x)","F",0
330,1,232,0,0.694175," ","integrate(x^4/(-a^2*x^2+1)^3/arctanh(a*x)^2,x, algorithm=""fricas"")","-\frac{8 \, a^{4} x^{4} - {\left({\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \operatorname{log\_integral}\left(\frac{a^{2} x^{2} + 2 \, a x + 1}{a^{2} x^{2} - 2 \, a x + 1}\right) - {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \operatorname{log\_integral}\left(\frac{a^{2} x^{2} - 2 \, a x + 1}{a^{2} x^{2} + 2 \, a x + 1}\right) - 2 \, {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \operatorname{log\_integral}\left(-\frac{a x + 1}{a x - 1}\right) + 2 \, {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \operatorname{log\_integral}\left(-\frac{a x - 1}{a x + 1}\right)\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)}{4 \, {\left(a^{9} x^{4} - 2 \, a^{7} x^{2} + a^{5}\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)}"," ",0,"-1/4*(8*a^4*x^4 - ((a^4*x^4 - 2*a^2*x^2 + 1)*log_integral((a^2*x^2 + 2*a*x + 1)/(a^2*x^2 - 2*a*x + 1)) - (a^4*x^4 - 2*a^2*x^2 + 1)*log_integral((a^2*x^2 - 2*a*x + 1)/(a^2*x^2 + 2*a*x + 1)) - 2*(a^4*x^4 - 2*a^2*x^2 + 1)*log_integral(-(a*x + 1)/(a*x - 1)) + 2*(a^4*x^4 - 2*a^2*x^2 + 1)*log_integral(-(a*x - 1)/(a*x + 1)))*log(-(a*x + 1)/(a*x - 1)))/((a^9*x^4 - 2*a^7*x^2 + a^5)*log(-(a*x + 1)/(a*x - 1)))","B",0
331,1,231,0,0.709130," ","integrate(x^3/(-a^2*x^2+1)^3/arctanh(a*x)^2,x, algorithm=""fricas"")","-\frac{8 \, a^{3} x^{3} - {\left({\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \operatorname{log\_integral}\left(\frac{a^{2} x^{2} + 2 \, a x + 1}{a^{2} x^{2} - 2 \, a x + 1}\right) + {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \operatorname{log\_integral}\left(\frac{a^{2} x^{2} - 2 \, a x + 1}{a^{2} x^{2} + 2 \, a x + 1}\right) - {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \operatorname{log\_integral}\left(-\frac{a x + 1}{a x - 1}\right) - {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \operatorname{log\_integral}\left(-\frac{a x - 1}{a x + 1}\right)\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)}{4 \, {\left(a^{8} x^{4} - 2 \, a^{6} x^{2} + a^{4}\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)}"," ",0,"-1/4*(8*a^3*x^3 - ((a^4*x^4 - 2*a^2*x^2 + 1)*log_integral((a^2*x^2 + 2*a*x + 1)/(a^2*x^2 - 2*a*x + 1)) + (a^4*x^4 - 2*a^2*x^2 + 1)*log_integral((a^2*x^2 - 2*a*x + 1)/(a^2*x^2 + 2*a*x + 1)) - (a^4*x^4 - 2*a^2*x^2 + 1)*log_integral(-(a*x + 1)/(a*x - 1)) - (a^4*x^4 - 2*a^2*x^2 + 1)*log_integral(-(a*x - 1)/(a*x + 1)))*log(-(a*x + 1)/(a*x - 1)))/((a^8*x^4 - 2*a^6*x^2 + a^4)*log(-(a*x + 1)/(a*x - 1)))","B",0
332,1,164,0,0.616346," ","integrate(x^2/(-a^2*x^2+1)^3/arctanh(a*x)^2,x, algorithm=""fricas"")","-\frac{8 \, a^{2} x^{2} - {\left({\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \operatorname{log\_integral}\left(\frac{a^{2} x^{2} + 2 \, a x + 1}{a^{2} x^{2} - 2 \, a x + 1}\right) - {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \operatorname{log\_integral}\left(\frac{a^{2} x^{2} - 2 \, a x + 1}{a^{2} x^{2} + 2 \, a x + 1}\right)\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)}{4 \, {\left(a^{7} x^{4} - 2 \, a^{5} x^{2} + a^{3}\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)}"," ",0,"-1/4*(8*a^2*x^2 - ((a^4*x^4 - 2*a^2*x^2 + 1)*log_integral((a^2*x^2 + 2*a*x + 1)/(a^2*x^2 - 2*a*x + 1)) - (a^4*x^4 - 2*a^2*x^2 + 1)*log_integral((a^2*x^2 - 2*a*x + 1)/(a^2*x^2 + 2*a*x + 1)))*log(-(a*x + 1)/(a*x - 1)))/((a^7*x^4 - 2*a^5*x^2 + a^3)*log(-(a*x + 1)/(a*x - 1)))","B",0
333,1,225,0,0.537687," ","integrate(x/(-a^2*x^2+1)^3/arctanh(a*x)^2,x, algorithm=""fricas"")","-\frac{8 \, a x - {\left({\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \operatorname{log\_integral}\left(\frac{a^{2} x^{2} + 2 \, a x + 1}{a^{2} x^{2} - 2 \, a x + 1}\right) + {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \operatorname{log\_integral}\left(\frac{a^{2} x^{2} - 2 \, a x + 1}{a^{2} x^{2} + 2 \, a x + 1}\right) + {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \operatorname{log\_integral}\left(-\frac{a x + 1}{a x - 1}\right) + {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \operatorname{log\_integral}\left(-\frac{a x - 1}{a x + 1}\right)\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)}{4 \, {\left(a^{6} x^{4} - 2 \, a^{4} x^{2} + a^{2}\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)}"," ",0,"-1/4*(8*a*x - ((a^4*x^4 - 2*a^2*x^2 + 1)*log_integral((a^2*x^2 + 2*a*x + 1)/(a^2*x^2 - 2*a*x + 1)) + (a^4*x^4 - 2*a^2*x^2 + 1)*log_integral((a^2*x^2 - 2*a*x + 1)/(a^2*x^2 + 2*a*x + 1)) + (a^4*x^4 - 2*a^2*x^2 + 1)*log_integral(-(a*x + 1)/(a*x - 1)) + (a^4*x^4 - 2*a^2*x^2 + 1)*log_integral(-(a*x - 1)/(a*x + 1)))*log(-(a*x + 1)/(a*x - 1)))/((a^6*x^4 - 2*a^4*x^2 + a^2)*log(-(a*x + 1)/(a*x - 1)))","B",0
334,1,222,0,0.547582," ","integrate(1/(-a^2*x^2+1)^3/arctanh(a*x)^2,x, algorithm=""fricas"")","\frac{{\left({\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \operatorname{log\_integral}\left(\frac{a^{2} x^{2} + 2 \, a x + 1}{a^{2} x^{2} - 2 \, a x + 1}\right) - {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \operatorname{log\_integral}\left(\frac{a^{2} x^{2} - 2 \, a x + 1}{a^{2} x^{2} + 2 \, a x + 1}\right) + 2 \, {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \operatorname{log\_integral}\left(-\frac{a x + 1}{a x - 1}\right) - 2 \, {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \operatorname{log\_integral}\left(-\frac{a x - 1}{a x + 1}\right)\right)} \log\left(-\frac{a x + 1}{a x - 1}\right) - 8}{4 \, {\left(a^{5} x^{4} - 2 \, a^{3} x^{2} + a\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)}"," ",0,"1/4*(((a^4*x^4 - 2*a^2*x^2 + 1)*log_integral((a^2*x^2 + 2*a*x + 1)/(a^2*x^2 - 2*a*x + 1)) - (a^4*x^4 - 2*a^2*x^2 + 1)*log_integral((a^2*x^2 - 2*a*x + 1)/(a^2*x^2 + 2*a*x + 1)) + 2*(a^4*x^4 - 2*a^2*x^2 + 1)*log_integral(-(a*x + 1)/(a*x - 1)) - 2*(a^4*x^4 - 2*a^2*x^2 + 1)*log_integral(-(a*x - 1)/(a*x + 1)))*log(-(a*x + 1)/(a*x - 1)) - 8)/((a^5*x^4 - 2*a^3*x^2 + a)*log(-(a*x + 1)/(a*x - 1)))","B",0
335,0,0,0,0.613913," ","integrate(1/x/(-a^2*x^2+1)^3/arctanh(a*x)^2,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{1}{{\left(a^{6} x^{7} - 3 \, a^{4} x^{5} + 3 \, a^{2} x^{3} - x\right)} \operatorname{artanh}\left(a x\right)^{2}}, x\right)"," ",0,"integral(-1/((a^6*x^7 - 3*a^4*x^5 + 3*a^2*x^3 - x)*arctanh(a*x)^2), x)","F",0
336,1,256,0,0.665860," ","integrate(x^4/(-a^2*x^2+1)^3/arctanh(a*x)^3,x, algorithm=""fricas"")","-\frac{4 \, a^{4} x^{4} + 8 \, a^{3} x^{3} \log\left(-\frac{a x + 1}{a x - 1}\right) - {\left({\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \operatorname{log\_integral}\left(\frac{a^{2} x^{2} + 2 \, a x + 1}{a^{2} x^{2} - 2 \, a x + 1}\right) + {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \operatorname{log\_integral}\left(\frac{a^{2} x^{2} - 2 \, a x + 1}{a^{2} x^{2} + 2 \, a x + 1}\right) - {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \operatorname{log\_integral}\left(-\frac{a x + 1}{a x - 1}\right) - {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \operatorname{log\_integral}\left(-\frac{a x - 1}{a x + 1}\right)\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)^{2}}{2 \, {\left(a^{9} x^{4} - 2 \, a^{7} x^{2} + a^{5}\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)^{2}}"," ",0,"-1/2*(4*a^4*x^4 + 8*a^3*x^3*log(-(a*x + 1)/(a*x - 1)) - ((a^4*x^4 - 2*a^2*x^2 + 1)*log_integral((a^2*x^2 + 2*a*x + 1)/(a^2*x^2 - 2*a*x + 1)) + (a^4*x^4 - 2*a^2*x^2 + 1)*log_integral((a^2*x^2 - 2*a*x + 1)/(a^2*x^2 + 2*a*x + 1)) - (a^4*x^4 - 2*a^2*x^2 + 1)*log_integral(-(a*x + 1)/(a*x - 1)) - (a^4*x^4 - 2*a^2*x^2 + 1)*log_integral(-(a*x - 1)/(a*x + 1)))*log(-(a*x + 1)/(a*x - 1))^2)/((a^9*x^4 - 2*a^7*x^2 + a^5)*log(-(a*x + 1)/(a*x - 1))^2)","B",0
337,1,267,0,0.595774," ","integrate(x^3/(-a^2*x^2+1)^3/arctanh(a*x)^3,x, algorithm=""fricas"")","-\frac{8 \, a^{3} x^{3} - {\left(2 \, {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \operatorname{log\_integral}\left(\frac{a^{2} x^{2} + 2 \, a x + 1}{a^{2} x^{2} - 2 \, a x + 1}\right) - 2 \, {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \operatorname{log\_integral}\left(\frac{a^{2} x^{2} - 2 \, a x + 1}{a^{2} x^{2} + 2 \, a x + 1}\right) - {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \operatorname{log\_integral}\left(-\frac{a x + 1}{a x - 1}\right) + {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \operatorname{log\_integral}\left(-\frac{a x - 1}{a x + 1}\right)\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)^{2} + 4 \, {\left(a^{4} x^{4} + 3 \, a^{2} x^{2}\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)}{4 \, {\left(a^{8} x^{4} - 2 \, a^{6} x^{2} + a^{4}\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)^{2}}"," ",0,"-1/4*(8*a^3*x^3 - (2*(a^4*x^4 - 2*a^2*x^2 + 1)*log_integral((a^2*x^2 + 2*a*x + 1)/(a^2*x^2 - 2*a*x + 1)) - 2*(a^4*x^4 - 2*a^2*x^2 + 1)*log_integral((a^2*x^2 - 2*a*x + 1)/(a^2*x^2 + 2*a*x + 1)) - (a^4*x^4 - 2*a^2*x^2 + 1)*log_integral(-(a*x + 1)/(a*x - 1)) + (a^4*x^4 - 2*a^2*x^2 + 1)*log_integral(-(a*x - 1)/(a*x + 1)))*log(-(a*x + 1)/(a*x - 1))^2 + 4*(a^4*x^4 + 3*a^2*x^2)*log(-(a*x + 1)/(a*x - 1)))/((a^8*x^4 - 2*a^6*x^2 + a^4)*log(-(a*x + 1)/(a*x - 1))^2)","B",0
338,1,193,0,0.530030," ","integrate(x^2/(-a^2*x^2+1)^3/arctanh(a*x)^3,x, algorithm=""fricas"")","-\frac{4 \, a^{2} x^{2} - {\left({\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \operatorname{log\_integral}\left(\frac{a^{2} x^{2} + 2 \, a x + 1}{a^{2} x^{2} - 2 \, a x + 1}\right) + {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \operatorname{log\_integral}\left(\frac{a^{2} x^{2} - 2 \, a x + 1}{a^{2} x^{2} + 2 \, a x + 1}\right)\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)^{2} + 4 \, {\left(a^{3} x^{3} + a x\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)}{2 \, {\left(a^{7} x^{4} - 2 \, a^{5} x^{2} + a^{3}\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)^{2}}"," ",0,"-1/2*(4*a^2*x^2 - ((a^4*x^4 - 2*a^2*x^2 + 1)*log_integral((a^2*x^2 + 2*a*x + 1)/(a^2*x^2 - 2*a*x + 1)) + (a^4*x^4 - 2*a^2*x^2 + 1)*log_integral((a^2*x^2 - 2*a*x + 1)/(a^2*x^2 + 2*a*x + 1)))*log(-(a*x + 1)/(a*x - 1))^2 + 4*(a^3*x^3 + a*x)*log(-(a*x + 1)/(a*x - 1)))/((a^7*x^4 - 2*a^5*x^2 + a^3)*log(-(a*x + 1)/(a*x - 1))^2)","B",0
339,1,256,0,0.564753," ","integrate(x/(-a^2*x^2+1)^3/arctanh(a*x)^3,x, algorithm=""fricas"")","\frac{{\left(2 \, {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \operatorname{log\_integral}\left(\frac{a^{2} x^{2} + 2 \, a x + 1}{a^{2} x^{2} - 2 \, a x + 1}\right) - 2 \, {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \operatorname{log\_integral}\left(\frac{a^{2} x^{2} - 2 \, a x + 1}{a^{2} x^{2} + 2 \, a x + 1}\right) + {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \operatorname{log\_integral}\left(-\frac{a x + 1}{a x - 1}\right) - {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \operatorname{log\_integral}\left(-\frac{a x - 1}{a x + 1}\right)\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)^{2} - 8 \, a x - 4 \, {\left(3 \, a^{2} x^{2} + 1\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)}{4 \, {\left(a^{6} x^{4} - 2 \, a^{4} x^{2} + a^{2}\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)^{2}}"," ",0,"1/4*((2*(a^4*x^4 - 2*a^2*x^2 + 1)*log_integral((a^2*x^2 + 2*a*x + 1)/(a^2*x^2 - 2*a*x + 1)) - 2*(a^4*x^4 - 2*a^2*x^2 + 1)*log_integral((a^2*x^2 - 2*a*x + 1)/(a^2*x^2 + 2*a*x + 1)) + (a^4*x^4 - 2*a^2*x^2 + 1)*log_integral(-(a*x + 1)/(a*x - 1)) - (a^4*x^4 - 2*a^2*x^2 + 1)*log_integral(-(a*x - 1)/(a*x + 1)))*log(-(a*x + 1)/(a*x - 1))^2 - 8*a*x - 4*(3*a^2*x^2 + 1)*log(-(a*x + 1)/(a*x - 1)))/((a^6*x^4 - 2*a^4*x^2 + a^2)*log(-(a*x + 1)/(a*x - 1))^2)","B",0
340,1,241,0,0.975312," ","integrate(1/(-a^2*x^2+1)^3/arctanh(a*x)^3,x, algorithm=""fricas"")","-\frac{8 \, a x \log\left(-\frac{a x + 1}{a x - 1}\right) - {\left({\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \operatorname{log\_integral}\left(\frac{a^{2} x^{2} + 2 \, a x + 1}{a^{2} x^{2} - 2 \, a x + 1}\right) + {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \operatorname{log\_integral}\left(\frac{a^{2} x^{2} - 2 \, a x + 1}{a^{2} x^{2} + 2 \, a x + 1}\right) + {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \operatorname{log\_integral}\left(-\frac{a x + 1}{a x - 1}\right) + {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \operatorname{log\_integral}\left(-\frac{a x - 1}{a x + 1}\right)\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)^{2} + 4}{2 \, {\left(a^{5} x^{4} - 2 \, a^{3} x^{2} + a\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)^{2}}"," ",0,"-1/2*(8*a*x*log(-(a*x + 1)/(a*x - 1)) - ((a^4*x^4 - 2*a^2*x^2 + 1)*log_integral((a^2*x^2 + 2*a*x + 1)/(a^2*x^2 - 2*a*x + 1)) + (a^4*x^4 - 2*a^2*x^2 + 1)*log_integral((a^2*x^2 - 2*a*x + 1)/(a^2*x^2 + 2*a*x + 1)) + (a^4*x^4 - 2*a^2*x^2 + 1)*log_integral(-(a*x + 1)/(a*x - 1)) + (a^4*x^4 - 2*a^2*x^2 + 1)*log_integral(-(a*x - 1)/(a*x + 1)))*log(-(a*x + 1)/(a*x - 1))^2 + 4)/((a^5*x^4 - 2*a^3*x^2 + a)*log(-(a*x + 1)/(a*x - 1))^2)","B",0
341,0,0,0,0.555928," ","integrate(1/x/(-a^2*x^2+1)^3/arctanh(a*x)^3,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{1}{{\left(a^{6} x^{7} - 3 \, a^{4} x^{5} + 3 \, a^{2} x^{3} - x\right)} \operatorname{artanh}\left(a x\right)^{3}}, x\right)"," ",0,"integral(-1/((a^6*x^7 - 3*a^4*x^5 + 3*a^2*x^3 - x)*arctanh(a*x)^3), x)","F",0
342,1,272,0,0.514530," ","integrate(1/(-a^2*x^2+1)^3/arctanh(a*x)^4,x, algorithm=""fricas"")","\frac{{\left(2 \, {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \operatorname{log\_integral}\left(\frac{a^{2} x^{2} + 2 \, a x + 1}{a^{2} x^{2} - 2 \, a x + 1}\right) - 2 \, {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \operatorname{log\_integral}\left(\frac{a^{2} x^{2} - 2 \, a x + 1}{a^{2} x^{2} + 2 \, a x + 1}\right) + {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \operatorname{log\_integral}\left(-\frac{a x + 1}{a x - 1}\right) - {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \operatorname{log\_integral}\left(-\frac{a x - 1}{a x + 1}\right)\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)^{3} - 8 \, a x \log\left(-\frac{a x + 1}{a x - 1}\right) - 4 \, {\left(3 \, a^{2} x^{2} + 1\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)^{2} - 8}{3 \, {\left(a^{5} x^{4} - 2 \, a^{3} x^{2} + a\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)^{3}}"," ",0,"1/3*((2*(a^4*x^4 - 2*a^2*x^2 + 1)*log_integral((a^2*x^2 + 2*a*x + 1)/(a^2*x^2 - 2*a*x + 1)) - 2*(a^4*x^4 - 2*a^2*x^2 + 1)*log_integral((a^2*x^2 - 2*a*x + 1)/(a^2*x^2 + 2*a*x + 1)) + (a^4*x^4 - 2*a^2*x^2 + 1)*log_integral(-(a*x + 1)/(a*x - 1)) - (a^4*x^4 - 2*a^2*x^2 + 1)*log_integral(-(a*x - 1)/(a*x + 1)))*log(-(a*x + 1)/(a*x - 1))^3 - 8*a*x*log(-(a*x + 1)/(a*x - 1)) - 4*(3*a^2*x^2 + 1)*log(-(a*x + 1)/(a*x - 1))^2 - 8)/((a^5*x^4 - 2*a^3*x^2 + a)*log(-(a*x + 1)/(a*x - 1))^3)","B",0
343,1,303,0,0.592658," ","integrate(1/(-a^2*x^2+1)^3/arctanh(a*x)^5,x, algorithm=""fricas"")","\frac{{\left(4 \, {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \operatorname{log\_integral}\left(\frac{a^{2} x^{2} + 2 \, a x + 1}{a^{2} x^{2} - 2 \, a x + 1}\right) + 4 \, {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \operatorname{log\_integral}\left(\frac{a^{2} x^{2} - 2 \, a x + 1}{a^{2} x^{2} + 2 \, a x + 1}\right) + {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \operatorname{log\_integral}\left(-\frac{a x + 1}{a x - 1}\right) + {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \operatorname{log\_integral}\left(-\frac{a x - 1}{a x + 1}\right)\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)^{4} - 4 \, {\left(3 \, a^{3} x^{3} + 5 \, a x\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)^{3} - 16 \, a x \log\left(-\frac{a x + 1}{a x - 1}\right) - 4 \, {\left(3 \, a^{2} x^{2} + 1\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)^{2} - 24}{6 \, {\left(a^{5} x^{4} - 2 \, a^{3} x^{2} + a\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)^{4}}"," ",0,"1/6*((4*(a^4*x^4 - 2*a^2*x^2 + 1)*log_integral((a^2*x^2 + 2*a*x + 1)/(a^2*x^2 - 2*a*x + 1)) + 4*(a^4*x^4 - 2*a^2*x^2 + 1)*log_integral((a^2*x^2 - 2*a*x + 1)/(a^2*x^2 + 2*a*x + 1)) + (a^4*x^4 - 2*a^2*x^2 + 1)*log_integral(-(a*x + 1)/(a*x - 1)) + (a^4*x^4 - 2*a^2*x^2 + 1)*log_integral(-(a*x - 1)/(a*x + 1)))*log(-(a*x + 1)/(a*x - 1))^4 - 4*(3*a^3*x^3 + 5*a*x)*log(-(a*x + 1)/(a*x - 1))^3 - 16*a*x*log(-(a*x + 1)/(a*x - 1)) - 4*(3*a^2*x^2 + 1)*log(-(a*x + 1)/(a*x - 1))^2 - 24)/((a^5*x^4 - 2*a^3*x^2 + a)*log(-(a*x + 1)/(a*x - 1))^4)","B",0
344,1,341,0,0.517303," ","integrate(1/(-a^2*x^2+1)^3/arctanh(a*x)^6,x, algorithm=""fricas"")","\frac{{\left(8 \, {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \operatorname{log\_integral}\left(\frac{a^{2} x^{2} + 2 \, a x + 1}{a^{2} x^{2} - 2 \, a x + 1}\right) - 8 \, {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \operatorname{log\_integral}\left(\frac{a^{2} x^{2} - 2 \, a x + 1}{a^{2} x^{2} + 2 \, a x + 1}\right) + {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \operatorname{log\_integral}\left(-\frac{a x + 1}{a x - 1}\right) - {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \operatorname{log\_integral}\left(-\frac{a x - 1}{a x + 1}\right)\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)^{5} - 2 \, {\left(3 \, a^{4} x^{4} + 24 \, a^{2} x^{2} + 5\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)^{4} - 4 \, {\left(3 \, a^{3} x^{3} + 5 \, a x\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)^{3} - 48 \, a x \log\left(-\frac{a x + 1}{a x - 1}\right) - 8 \, {\left(3 \, a^{2} x^{2} + 1\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)^{2} - 96}{15 \, {\left(a^{5} x^{4} - 2 \, a^{3} x^{2} + a\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)^{5}}"," ",0,"1/15*((8*(a^4*x^4 - 2*a^2*x^2 + 1)*log_integral((a^2*x^2 + 2*a*x + 1)/(a^2*x^2 - 2*a*x + 1)) - 8*(a^4*x^4 - 2*a^2*x^2 + 1)*log_integral((a^2*x^2 - 2*a*x + 1)/(a^2*x^2 + 2*a*x + 1)) + (a^4*x^4 - 2*a^2*x^2 + 1)*log_integral(-(a*x + 1)/(a*x - 1)) - (a^4*x^4 - 2*a^2*x^2 + 1)*log_integral(-(a*x - 1)/(a*x + 1)))*log(-(a*x + 1)/(a*x - 1))^5 - 2*(3*a^4*x^4 + 24*a^2*x^2 + 5)*log(-(a*x + 1)/(a*x - 1))^4 - 4*(3*a^3*x^3 + 5*a*x)*log(-(a*x + 1)/(a*x - 1))^3 - 48*a*x*log(-(a*x + 1)/(a*x - 1)) - 8*(3*a^2*x^2 + 1)*log(-(a*x + 1)/(a*x - 1))^2 - 96)/((a^5*x^4 - 2*a^3*x^2 + a)*log(-(a*x + 1)/(a*x - 1))^5)","A",0
345,1,131,0,0.472422," ","integrate(arctanh(a*x)/(-a^2*x^2+1)^4,x, algorithm=""fricas"")","\frac{180 \, a^{4} x^{4} - 420 \, a^{2} x^{2} + 45 \, {\left(a^{6} x^{6} - 3 \, a^{4} x^{4} + 3 \, a^{2} x^{2} - 1\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)^{2} - 12 \, {\left(15 \, a^{5} x^{5} - 40 \, a^{3} x^{3} + 33 \, a x\right)} \log\left(-\frac{a x + 1}{a x - 1}\right) + 272}{1152 \, {\left(a^{7} x^{6} - 3 \, a^{5} x^{4} + 3 \, a^{3} x^{2} - a\right)}}"," ",0,"1/1152*(180*a^4*x^4 - 420*a^2*x^2 + 45*(a^6*x^6 - 3*a^4*x^4 + 3*a^2*x^2 - 1)*log(-(a*x + 1)/(a*x - 1))^2 - 12*(15*a^5*x^5 - 40*a^3*x^3 + 33*a*x)*log(-(a*x + 1)/(a*x - 1)) + 272)/(a^7*x^6 - 3*a^5*x^4 + 3*a^3*x^2 - a)","A",0
346,1,179,0,0.529496," ","integrate(arctanh(a*x)^2/(-a^2*x^2+1)^4,x, algorithm=""fricas"")","-\frac{1470 \, a^{5} x^{5} - 3200 \, a^{3} x^{3} - 90 \, {\left(a^{6} x^{6} - 3 \, a^{4} x^{4} + 3 \, a^{2} x^{2} - 1\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)^{3} + 36 \, {\left(15 \, a^{5} x^{5} - 40 \, a^{3} x^{3} + 33 \, a x\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)^{2} + 1794 \, a x - 3 \, {\left(245 \, a^{6} x^{6} - 375 \, a^{4} x^{4} - 105 \, a^{2} x^{2} + 299\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)}{6912 \, {\left(a^{7} x^{6} - 3 \, a^{5} x^{4} + 3 \, a^{3} x^{2} - a\right)}}"," ",0,"-1/6912*(1470*a^5*x^5 - 3200*a^3*x^3 - 90*(a^6*x^6 - 3*a^4*x^4 + 3*a^2*x^2 - 1)*log(-(a*x + 1)/(a*x - 1))^3 + 36*(15*a^5*x^5 - 40*a^3*x^3 + 33*a*x)*log(-(a*x + 1)/(a*x - 1))^2 + 1794*a*x - 3*(245*a^6*x^6 - 375*a^4*x^4 - 105*a^2*x^2 + 299)*log(-(a*x + 1)/(a*x - 1)))/(a^7*x^6 - 3*a^5*x^4 + 3*a^3*x^2 - a)","A",0
347,1,216,0,0.711480," ","integrate(arctanh(a*x)^3/(-a^2*x^2+1)^4,x, algorithm=""fricas"")","\frac{8820 \, a^{4} x^{4} + 135 \, {\left(a^{6} x^{6} - 3 \, a^{4} x^{4} + 3 \, a^{2} x^{2} - 1\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)^{4} - 18420 \, a^{2} x^{2} - 72 \, {\left(15 \, a^{5} x^{5} - 40 \, a^{3} x^{3} + 33 \, a x\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)^{3} + 9 \, {\left(245 \, a^{6} x^{6} - 375 \, a^{4} x^{4} - 105 \, a^{2} x^{2} + 299\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)^{2} - 12 \, {\left(735 \, a^{5} x^{5} - 1600 \, a^{3} x^{3} + 897 \, a x\right)} \log\left(-\frac{a x + 1}{a x - 1}\right) + 9728}{27648 \, {\left(a^{7} x^{6} - 3 \, a^{5} x^{4} + 3 \, a^{3} x^{2} - a\right)}}"," ",0,"1/27648*(8820*a^4*x^4 + 135*(a^6*x^6 - 3*a^4*x^4 + 3*a^2*x^2 - 1)*log(-(a*x + 1)/(a*x - 1))^4 - 18420*a^2*x^2 - 72*(15*a^5*x^5 - 40*a^3*x^3 + 33*a*x)*log(-(a*x + 1)/(a*x - 1))^3 + 9*(245*a^6*x^6 - 375*a^4*x^4 - 105*a^2*x^2 + 299)*log(-(a*x + 1)/(a*x - 1))^2 - 12*(735*a^5*x^5 - 1600*a^3*x^3 + 897*a*x)*log(-(a*x + 1)/(a*x - 1)) + 9728)/(a^7*x^6 - 3*a^5*x^4 + 3*a^3*x^2 - a)","A",0
348,-2,0,0,0.000000," ","integrate(arctanh(a*x)^(1/2)/(-a^2*x^2+1)^4,x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
349,0,0,0,0.858529," ","integrate(x^8/(-a^2*x^2+1)^4/arctanh(a*x),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{8}}{{\left(a^{8} x^{8} - 4 \, a^{6} x^{6} + 6 \, a^{4} x^{4} - 4 \, a^{2} x^{2} + 1\right)} \operatorname{artanh}\left(a x\right)}, x\right)"," ",0,"integral(x^8/((a^8*x^8 - 4*a^6*x^6 + 6*a^4*x^4 - 4*a^2*x^2 + 1)*arctanh(a*x)), x)","F",0
350,0,0,0,0.546701," ","integrate(x^7/(-a^2*x^2+1)^4/arctanh(a*x),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{7}}{{\left(a^{8} x^{8} - 4 \, a^{6} x^{6} + 6 \, a^{4} x^{4} - 4 \, a^{2} x^{2} + 1\right)} \operatorname{artanh}\left(a x\right)}, x\right)"," ",0,"integral(x^7/((a^8*x^8 - 4*a^6*x^6 + 6*a^4*x^4 - 4*a^2*x^2 + 1)*arctanh(a*x)), x)","F",0
351,1,220,0,0.940226," ","integrate(x^6/(-a^2*x^2+1)^4/arctanh(a*x),x, algorithm=""fricas"")","-\frac{20 \, \log\left(\log\left(-\frac{a x + 1}{a x - 1}\right)\right) - \operatorname{log\_integral}\left(-\frac{a^{3} x^{3} + 3 \, a^{2} x^{2} + 3 \, a x + 1}{a^{3} x^{3} - 3 \, a^{2} x^{2} + 3 \, a x - 1}\right) - \operatorname{log\_integral}\left(-\frac{a^{3} x^{3} - 3 \, a^{2} x^{2} + 3 \, a x - 1}{a^{3} x^{3} + 3 \, a^{2} x^{2} + 3 \, a x + 1}\right) + 6 \, \operatorname{log\_integral}\left(\frac{a^{2} x^{2} + 2 \, a x + 1}{a^{2} x^{2} - 2 \, a x + 1}\right) + 6 \, \operatorname{log\_integral}\left(\frac{a^{2} x^{2} - 2 \, a x + 1}{a^{2} x^{2} + 2 \, a x + 1}\right) - 15 \, \operatorname{log\_integral}\left(-\frac{a x + 1}{a x - 1}\right) - 15 \, \operatorname{log\_integral}\left(-\frac{a x - 1}{a x + 1}\right)}{64 \, a^{7}}"," ",0,"-1/64*(20*log(log(-(a*x + 1)/(a*x - 1))) - log_integral(-(a^3*x^3 + 3*a^2*x^2 + 3*a*x + 1)/(a^3*x^3 - 3*a^2*x^2 + 3*a*x - 1)) - log_integral(-(a^3*x^3 - 3*a^2*x^2 + 3*a*x - 1)/(a^3*x^3 + 3*a^2*x^2 + 3*a*x + 1)) + 6*log_integral((a^2*x^2 + 2*a*x + 1)/(a^2*x^2 - 2*a*x + 1)) + 6*log_integral((a^2*x^2 - 2*a*x + 1)/(a^2*x^2 + 2*a*x + 1)) - 15*log_integral(-(a*x + 1)/(a*x - 1)) - 15*log_integral(-(a*x - 1)/(a*x + 1)))/a^7","B",0
352,1,200,0,0.514838," ","integrate(x^5/(-a^2*x^2+1)^4/arctanh(a*x),x, algorithm=""fricas"")","\frac{\operatorname{log\_integral}\left(-\frac{a^{3} x^{3} + 3 \, a^{2} x^{2} + 3 \, a x + 1}{a^{3} x^{3} - 3 \, a^{2} x^{2} + 3 \, a x - 1}\right) - \operatorname{log\_integral}\left(-\frac{a^{3} x^{3} - 3 \, a^{2} x^{2} + 3 \, a x - 1}{a^{3} x^{3} + 3 \, a^{2} x^{2} + 3 \, a x + 1}\right) - 4 \, \operatorname{log\_integral}\left(\frac{a^{2} x^{2} + 2 \, a x + 1}{a^{2} x^{2} - 2 \, a x + 1}\right) + 4 \, \operatorname{log\_integral}\left(\frac{a^{2} x^{2} - 2 \, a x + 1}{a^{2} x^{2} + 2 \, a x + 1}\right) + 5 \, \operatorname{log\_integral}\left(-\frac{a x + 1}{a x - 1}\right) - 5 \, \operatorname{log\_integral}\left(-\frac{a x - 1}{a x + 1}\right)}{64 \, a^{6}}"," ",0,"1/64*(log_integral(-(a^3*x^3 + 3*a^2*x^2 + 3*a*x + 1)/(a^3*x^3 - 3*a^2*x^2 + 3*a*x - 1)) - log_integral(-(a^3*x^3 - 3*a^2*x^2 + 3*a*x - 1)/(a^3*x^3 + 3*a^2*x^2 + 3*a*x + 1)) - 4*log_integral((a^2*x^2 + 2*a*x + 1)/(a^2*x^2 - 2*a*x + 1)) + 4*log_integral((a^2*x^2 - 2*a*x + 1)/(a^2*x^2 + 2*a*x + 1)) + 5*log_integral(-(a*x + 1)/(a*x - 1)) - 5*log_integral(-(a*x - 1)/(a*x + 1)))/a^6","B",0
353,1,216,0,0.455279," ","integrate(x^4/(-a^2*x^2+1)^4/arctanh(a*x),x, algorithm=""fricas"")","\frac{4 \, \log\left(\log\left(-\frac{a x + 1}{a x - 1}\right)\right) + \operatorname{log\_integral}\left(-\frac{a^{3} x^{3} + 3 \, a^{2} x^{2} + 3 \, a x + 1}{a^{3} x^{3} - 3 \, a^{2} x^{2} + 3 \, a x - 1}\right) + \operatorname{log\_integral}\left(-\frac{a^{3} x^{3} - 3 \, a^{2} x^{2} + 3 \, a x - 1}{a^{3} x^{3} + 3 \, a^{2} x^{2} + 3 \, a x + 1}\right) - 2 \, \operatorname{log\_integral}\left(\frac{a^{2} x^{2} + 2 \, a x + 1}{a^{2} x^{2} - 2 \, a x + 1}\right) - 2 \, \operatorname{log\_integral}\left(\frac{a^{2} x^{2} - 2 \, a x + 1}{a^{2} x^{2} + 2 \, a x + 1}\right) - \operatorname{log\_integral}\left(-\frac{a x + 1}{a x - 1}\right) - \operatorname{log\_integral}\left(-\frac{a x - 1}{a x + 1}\right)}{64 \, a^{5}}"," ",0,"1/64*(4*log(log(-(a*x + 1)/(a*x - 1))) + log_integral(-(a^3*x^3 + 3*a^2*x^2 + 3*a*x + 1)/(a^3*x^3 - 3*a^2*x^2 + 3*a*x - 1)) + log_integral(-(a^3*x^3 - 3*a^2*x^2 + 3*a*x - 1)/(a^3*x^3 + 3*a^2*x^2 + 3*a*x + 1)) - 2*log_integral((a^2*x^2 + 2*a*x + 1)/(a^2*x^2 - 2*a*x + 1)) - 2*log_integral((a^2*x^2 - 2*a*x + 1)/(a^2*x^2 + 2*a*x + 1)) - log_integral(-(a*x + 1)/(a*x - 1)) - log_integral(-(a*x - 1)/(a*x + 1)))/a^5","B",0
354,1,136,0,0.465554," ","integrate(x^3/(-a^2*x^2+1)^4/arctanh(a*x),x, algorithm=""fricas"")","\frac{\operatorname{log\_integral}\left(-\frac{a^{3} x^{3} + 3 \, a^{2} x^{2} + 3 \, a x + 1}{a^{3} x^{3} - 3 \, a^{2} x^{2} + 3 \, a x - 1}\right) - \operatorname{log\_integral}\left(-\frac{a^{3} x^{3} - 3 \, a^{2} x^{2} + 3 \, a x - 1}{a^{3} x^{3} + 3 \, a^{2} x^{2} + 3 \, a x + 1}\right) - 3 \, \operatorname{log\_integral}\left(-\frac{a x + 1}{a x - 1}\right) + 3 \, \operatorname{log\_integral}\left(-\frac{a x - 1}{a x + 1}\right)}{64 \, a^{4}}"," ",0,"1/64*(log_integral(-(a^3*x^3 + 3*a^2*x^2 + 3*a*x + 1)/(a^3*x^3 - 3*a^2*x^2 + 3*a*x - 1)) - log_integral(-(a^3*x^3 - 3*a^2*x^2 + 3*a*x - 1)/(a^3*x^3 + 3*a^2*x^2 + 3*a*x + 1)) - 3*log_integral(-(a*x + 1)/(a*x - 1)) + 3*log_integral(-(a*x - 1)/(a*x + 1)))/a^4","B",0
355,1,216,0,0.443428," ","integrate(x^2/(-a^2*x^2+1)^4/arctanh(a*x),x, algorithm=""fricas"")","-\frac{4 \, \log\left(\log\left(-\frac{a x + 1}{a x - 1}\right)\right) - \operatorname{log\_integral}\left(-\frac{a^{3} x^{3} + 3 \, a^{2} x^{2} + 3 \, a x + 1}{a^{3} x^{3} - 3 \, a^{2} x^{2} + 3 \, a x - 1}\right) - \operatorname{log\_integral}\left(-\frac{a^{3} x^{3} - 3 \, a^{2} x^{2} + 3 \, a x - 1}{a^{3} x^{3} + 3 \, a^{2} x^{2} + 3 \, a x + 1}\right) - 2 \, \operatorname{log\_integral}\left(\frac{a^{2} x^{2} + 2 \, a x + 1}{a^{2} x^{2} - 2 \, a x + 1}\right) - 2 \, \operatorname{log\_integral}\left(\frac{a^{2} x^{2} - 2 \, a x + 1}{a^{2} x^{2} + 2 \, a x + 1}\right) + \operatorname{log\_integral}\left(-\frac{a x + 1}{a x - 1}\right) + \operatorname{log\_integral}\left(-\frac{a x - 1}{a x + 1}\right)}{64 \, a^{3}}"," ",0,"-1/64*(4*log(log(-(a*x + 1)/(a*x - 1))) - log_integral(-(a^3*x^3 + 3*a^2*x^2 + 3*a*x + 1)/(a^3*x^3 - 3*a^2*x^2 + 3*a*x - 1)) - log_integral(-(a^3*x^3 - 3*a^2*x^2 + 3*a*x - 1)/(a^3*x^3 + 3*a^2*x^2 + 3*a*x + 1)) - 2*log_integral((a^2*x^2 + 2*a*x + 1)/(a^2*x^2 - 2*a*x + 1)) - 2*log_integral((a^2*x^2 - 2*a*x + 1)/(a^2*x^2 + 2*a*x + 1)) + log_integral(-(a*x + 1)/(a*x - 1)) + log_integral(-(a*x - 1)/(a*x + 1)))/a^3","B",0
356,1,200,0,0.569880," ","integrate(x/(-a^2*x^2+1)^4/arctanh(a*x),x, algorithm=""fricas"")","\frac{\operatorname{log\_integral}\left(-\frac{a^{3} x^{3} + 3 \, a^{2} x^{2} + 3 \, a x + 1}{a^{3} x^{3} - 3 \, a^{2} x^{2} + 3 \, a x - 1}\right) - \operatorname{log\_integral}\left(-\frac{a^{3} x^{3} - 3 \, a^{2} x^{2} + 3 \, a x - 1}{a^{3} x^{3} + 3 \, a^{2} x^{2} + 3 \, a x + 1}\right) + 4 \, \operatorname{log\_integral}\left(\frac{a^{2} x^{2} + 2 \, a x + 1}{a^{2} x^{2} - 2 \, a x + 1}\right) - 4 \, \operatorname{log\_integral}\left(\frac{a^{2} x^{2} - 2 \, a x + 1}{a^{2} x^{2} + 2 \, a x + 1}\right) + 5 \, \operatorname{log\_integral}\left(-\frac{a x + 1}{a x - 1}\right) - 5 \, \operatorname{log\_integral}\left(-\frac{a x - 1}{a x + 1}\right)}{64 \, a^{2}}"," ",0,"1/64*(log_integral(-(a^3*x^3 + 3*a^2*x^2 + 3*a*x + 1)/(a^3*x^3 - 3*a^2*x^2 + 3*a*x - 1)) - log_integral(-(a^3*x^3 - 3*a^2*x^2 + 3*a*x - 1)/(a^3*x^3 + 3*a^2*x^2 + 3*a*x + 1)) + 4*log_integral((a^2*x^2 + 2*a*x + 1)/(a^2*x^2 - 2*a*x + 1)) - 4*log_integral((a^2*x^2 - 2*a*x + 1)/(a^2*x^2 + 2*a*x + 1)) + 5*log_integral(-(a*x + 1)/(a*x - 1)) - 5*log_integral(-(a*x - 1)/(a*x + 1)))/a^2","B",0
357,1,216,0,0.668081," ","integrate(1/(-a^2*x^2+1)^4/arctanh(a*x),x, algorithm=""fricas"")","\frac{20 \, \log\left(\log\left(-\frac{a x + 1}{a x - 1}\right)\right) + \operatorname{log\_integral}\left(-\frac{a^{3} x^{3} + 3 \, a^{2} x^{2} + 3 \, a x + 1}{a^{3} x^{3} - 3 \, a^{2} x^{2} + 3 \, a x - 1}\right) + \operatorname{log\_integral}\left(-\frac{a^{3} x^{3} - 3 \, a^{2} x^{2} + 3 \, a x - 1}{a^{3} x^{3} + 3 \, a^{2} x^{2} + 3 \, a x + 1}\right) + 6 \, \operatorname{log\_integral}\left(\frac{a^{2} x^{2} + 2 \, a x + 1}{a^{2} x^{2} - 2 \, a x + 1}\right) + 6 \, \operatorname{log\_integral}\left(\frac{a^{2} x^{2} - 2 \, a x + 1}{a^{2} x^{2} + 2 \, a x + 1}\right) + 15 \, \operatorname{log\_integral}\left(-\frac{a x + 1}{a x - 1}\right) + 15 \, \operatorname{log\_integral}\left(-\frac{a x - 1}{a x + 1}\right)}{64 \, a}"," ",0,"1/64*(20*log(log(-(a*x + 1)/(a*x - 1))) + log_integral(-(a^3*x^3 + 3*a^2*x^2 + 3*a*x + 1)/(a^3*x^3 - 3*a^2*x^2 + 3*a*x - 1)) + log_integral(-(a^3*x^3 - 3*a^2*x^2 + 3*a*x - 1)/(a^3*x^3 + 3*a^2*x^2 + 3*a*x + 1)) + 6*log_integral((a^2*x^2 + 2*a*x + 1)/(a^2*x^2 - 2*a*x + 1)) + 6*log_integral((a^2*x^2 - 2*a*x + 1)/(a^2*x^2 + 2*a*x + 1)) + 15*log_integral(-(a*x + 1)/(a*x - 1)) + 15*log_integral(-(a*x - 1)/(a*x + 1)))/a","B",0
358,0,0,0,0.558006," ","integrate(1/x/(-a^2*x^2+1)^4/arctanh(a*x),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{{\left(a^{8} x^{9} - 4 \, a^{6} x^{7} + 6 \, a^{4} x^{5} - 4 \, a^{2} x^{3} + x\right)} \operatorname{artanh}\left(a x\right)}, x\right)"," ",0,"integral(1/((a^8*x^9 - 4*a^6*x^7 + 6*a^4*x^5 - 4*a^2*x^3 + x)*arctanh(a*x)), x)","F",0
359,0,0,0,0.532777," ","integrate(1/x^2/(-a^2*x^2+1)^4/arctanh(a*x),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{{\left(a^{8} x^{10} - 4 \, a^{6} x^{8} + 6 \, a^{4} x^{6} - 4 \, a^{2} x^{4} + x^{2}\right)} \operatorname{artanh}\left(a x\right)}, x\right)"," ",0,"integral(1/((a^8*x^10 - 4*a^6*x^8 + 6*a^4*x^6 - 4*a^2*x^4 + x^2)*arctanh(a*x)), x)","F",0
360,1,418,0,0.589310," ","integrate(x/(-a^2*x^2+1)^4/arctanh(a*x)^2,x, algorithm=""fricas"")","\frac{64 \, a x + {\left(3 \, {\left(a^{6} x^{6} - 3 \, a^{4} x^{4} + 3 \, a^{2} x^{2} - 1\right)} \operatorname{log\_integral}\left(-\frac{a^{3} x^{3} + 3 \, a^{2} x^{2} + 3 \, a x + 1}{a^{3} x^{3} - 3 \, a^{2} x^{2} + 3 \, a x - 1}\right) + 3 \, {\left(a^{6} x^{6} - 3 \, a^{4} x^{4} + 3 \, a^{2} x^{2} - 1\right)} \operatorname{log\_integral}\left(-\frac{a^{3} x^{3} - 3 \, a^{2} x^{2} + 3 \, a x - 1}{a^{3} x^{3} + 3 \, a^{2} x^{2} + 3 \, a x + 1}\right) + 8 \, {\left(a^{6} x^{6} - 3 \, a^{4} x^{4} + 3 \, a^{2} x^{2} - 1\right)} \operatorname{log\_integral}\left(\frac{a^{2} x^{2} + 2 \, a x + 1}{a^{2} x^{2} - 2 \, a x + 1}\right) + 8 \, {\left(a^{6} x^{6} - 3 \, a^{4} x^{4} + 3 \, a^{2} x^{2} - 1\right)} \operatorname{log\_integral}\left(\frac{a^{2} x^{2} - 2 \, a x + 1}{a^{2} x^{2} + 2 \, a x + 1}\right) + 5 \, {\left(a^{6} x^{6} - 3 \, a^{4} x^{4} + 3 \, a^{2} x^{2} - 1\right)} \operatorname{log\_integral}\left(-\frac{a x + 1}{a x - 1}\right) + 5 \, {\left(a^{6} x^{6} - 3 \, a^{4} x^{4} + 3 \, a^{2} x^{2} - 1\right)} \operatorname{log\_integral}\left(-\frac{a x - 1}{a x + 1}\right)\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)}{32 \, {\left(a^{8} x^{6} - 3 \, a^{6} x^{4} + 3 \, a^{4} x^{2} - a^{2}\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)}"," ",0,"1/32*(64*a*x + (3*(a^6*x^6 - 3*a^4*x^4 + 3*a^2*x^2 - 1)*log_integral(-(a^3*x^3 + 3*a^2*x^2 + 3*a*x + 1)/(a^3*x^3 - 3*a^2*x^2 + 3*a*x - 1)) + 3*(a^6*x^6 - 3*a^4*x^4 + 3*a^2*x^2 - 1)*log_integral(-(a^3*x^3 - 3*a^2*x^2 + 3*a*x - 1)/(a^3*x^3 + 3*a^2*x^2 + 3*a*x + 1)) + 8*(a^6*x^6 - 3*a^4*x^4 + 3*a^2*x^2 - 1)*log_integral((a^2*x^2 + 2*a*x + 1)/(a^2*x^2 - 2*a*x + 1)) + 8*(a^6*x^6 - 3*a^4*x^4 + 3*a^2*x^2 - 1)*log_integral((a^2*x^2 - 2*a*x + 1)/(a^2*x^2 + 2*a*x + 1)) + 5*(a^6*x^6 - 3*a^4*x^4 + 3*a^2*x^2 - 1)*log_integral(-(a*x + 1)/(a*x - 1)) + 5*(a^6*x^6 - 3*a^4*x^4 + 3*a^2*x^2 - 1)*log_integral(-(a*x - 1)/(a*x + 1)))*log(-(a*x + 1)/(a*x - 1)))/((a^8*x^6 - 3*a^6*x^4 + 3*a^4*x^2 - a^2)*log(-(a*x + 1)/(a*x - 1)))","B",0
361,1,413,0,0.490750," ","integrate(1/(-a^2*x^2+1)^4/arctanh(a*x)^2,x, algorithm=""fricas"")","\frac{3 \, {\left({\left(a^{6} x^{6} - 3 \, a^{4} x^{4} + 3 \, a^{2} x^{2} - 1\right)} \operatorname{log\_integral}\left(-\frac{a^{3} x^{3} + 3 \, a^{2} x^{2} + 3 \, a x + 1}{a^{3} x^{3} - 3 \, a^{2} x^{2} + 3 \, a x - 1}\right) - {\left(a^{6} x^{6} - 3 \, a^{4} x^{4} + 3 \, a^{2} x^{2} - 1\right)} \operatorname{log\_integral}\left(-\frac{a^{3} x^{3} - 3 \, a^{2} x^{2} + 3 \, a x - 1}{a^{3} x^{3} + 3 \, a^{2} x^{2} + 3 \, a x + 1}\right) + 4 \, {\left(a^{6} x^{6} - 3 \, a^{4} x^{4} + 3 \, a^{2} x^{2} - 1\right)} \operatorname{log\_integral}\left(\frac{a^{2} x^{2} + 2 \, a x + 1}{a^{2} x^{2} - 2 \, a x + 1}\right) - 4 \, {\left(a^{6} x^{6} - 3 \, a^{4} x^{4} + 3 \, a^{2} x^{2} - 1\right)} \operatorname{log\_integral}\left(\frac{a^{2} x^{2} - 2 \, a x + 1}{a^{2} x^{2} + 2 \, a x + 1}\right) + 5 \, {\left(a^{6} x^{6} - 3 \, a^{4} x^{4} + 3 \, a^{2} x^{2} - 1\right)} \operatorname{log\_integral}\left(-\frac{a x + 1}{a x - 1}\right) - 5 \, {\left(a^{6} x^{6} - 3 \, a^{4} x^{4} + 3 \, a^{2} x^{2} - 1\right)} \operatorname{log\_integral}\left(-\frac{a x - 1}{a x + 1}\right)\right)} \log\left(-\frac{a x + 1}{a x - 1}\right) + 64}{32 \, {\left(a^{7} x^{6} - 3 \, a^{5} x^{4} + 3 \, a^{3} x^{2} - a\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)}"," ",0,"1/32*(3*((a^6*x^6 - 3*a^4*x^4 + 3*a^2*x^2 - 1)*log_integral(-(a^3*x^3 + 3*a^2*x^2 + 3*a*x + 1)/(a^3*x^3 - 3*a^2*x^2 + 3*a*x - 1)) - (a^6*x^6 - 3*a^4*x^4 + 3*a^2*x^2 - 1)*log_integral(-(a^3*x^3 - 3*a^2*x^2 + 3*a*x - 1)/(a^3*x^3 + 3*a^2*x^2 + 3*a*x + 1)) + 4*(a^6*x^6 - 3*a^4*x^4 + 3*a^2*x^2 - 1)*log_integral((a^2*x^2 + 2*a*x + 1)/(a^2*x^2 - 2*a*x + 1)) - 4*(a^6*x^6 - 3*a^4*x^4 + 3*a^2*x^2 - 1)*log_integral((a^2*x^2 - 2*a*x + 1)/(a^2*x^2 + 2*a*x + 1)) + 5*(a^6*x^6 - 3*a^4*x^4 + 3*a^2*x^2 - 1)*log_integral(-(a*x + 1)/(a*x - 1)) - 5*(a^6*x^6 - 3*a^4*x^4 + 3*a^2*x^2 - 1)*log_integral(-(a*x - 1)/(a*x + 1)))*log(-(a*x + 1)/(a*x - 1)) + 64)/((a^7*x^6 - 3*a^5*x^4 + 3*a^3*x^2 - a)*log(-(a*x + 1)/(a*x - 1)))","B",0
362,1,447,0,0.509622," ","integrate(x/(-a^2*x^2+1)^4/arctanh(a*x)^3,x, algorithm=""fricas"")","\frac{{\left(9 \, {\left(a^{6} x^{6} - 3 \, a^{4} x^{4} + 3 \, a^{2} x^{2} - 1\right)} \operatorname{log\_integral}\left(-\frac{a^{3} x^{3} + 3 \, a^{2} x^{2} + 3 \, a x + 1}{a^{3} x^{3} - 3 \, a^{2} x^{2} + 3 \, a x - 1}\right) - 9 \, {\left(a^{6} x^{6} - 3 \, a^{4} x^{4} + 3 \, a^{2} x^{2} - 1\right)} \operatorname{log\_integral}\left(-\frac{a^{3} x^{3} - 3 \, a^{2} x^{2} + 3 \, a x - 1}{a^{3} x^{3} + 3 \, a^{2} x^{2} + 3 \, a x + 1}\right) + 16 \, {\left(a^{6} x^{6} - 3 \, a^{4} x^{4} + 3 \, a^{2} x^{2} - 1\right)} \operatorname{log\_integral}\left(\frac{a^{2} x^{2} + 2 \, a x + 1}{a^{2} x^{2} - 2 \, a x + 1}\right) - 16 \, {\left(a^{6} x^{6} - 3 \, a^{4} x^{4} + 3 \, a^{2} x^{2} - 1\right)} \operatorname{log\_integral}\left(\frac{a^{2} x^{2} - 2 \, a x + 1}{a^{2} x^{2} + 2 \, a x + 1}\right) + 5 \, {\left(a^{6} x^{6} - 3 \, a^{4} x^{4} + 3 \, a^{2} x^{2} - 1\right)} \operatorname{log\_integral}\left(-\frac{a x + 1}{a x - 1}\right) - 5 \, {\left(a^{6} x^{6} - 3 \, a^{4} x^{4} + 3 \, a^{2} x^{2} - 1\right)} \operatorname{log\_integral}\left(-\frac{a x - 1}{a x + 1}\right)\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)^{2} + 64 \, a x + 32 \, {\left(5 \, a^{2} x^{2} + 1\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)}{32 \, {\left(a^{8} x^{6} - 3 \, a^{6} x^{4} + 3 \, a^{4} x^{2} - a^{2}\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)^{2}}"," ",0,"1/32*((9*(a^6*x^6 - 3*a^4*x^4 + 3*a^2*x^2 - 1)*log_integral(-(a^3*x^3 + 3*a^2*x^2 + 3*a*x + 1)/(a^3*x^3 - 3*a^2*x^2 + 3*a*x - 1)) - 9*(a^6*x^6 - 3*a^4*x^4 + 3*a^2*x^2 - 1)*log_integral(-(a^3*x^3 - 3*a^2*x^2 + 3*a*x - 1)/(a^3*x^3 + 3*a^2*x^2 + 3*a*x + 1)) + 16*(a^6*x^6 - 3*a^4*x^4 + 3*a^2*x^2 - 1)*log_integral((a^2*x^2 + 2*a*x + 1)/(a^2*x^2 - 2*a*x + 1)) - 16*(a^6*x^6 - 3*a^4*x^4 + 3*a^2*x^2 - 1)*log_integral((a^2*x^2 - 2*a*x + 1)/(a^2*x^2 + 2*a*x + 1)) + 5*(a^6*x^6 - 3*a^4*x^4 + 3*a^2*x^2 - 1)*log_integral(-(a*x + 1)/(a*x - 1)) - 5*(a^6*x^6 - 3*a^4*x^4 + 3*a^2*x^2 - 1)*log_integral(-(a*x - 1)/(a*x + 1)))*log(-(a*x + 1)/(a*x - 1))^2 + 64*a*x + 32*(5*a^2*x^2 + 1)*log(-(a*x + 1)/(a*x - 1)))/((a^8*x^6 - 3*a^6*x^4 + 3*a^4*x^2 - a^2)*log(-(a*x + 1)/(a*x - 1))^2)","B",0
363,1,435,0,0.712806," ","integrate(1/(-a^2*x^2+1)^4/arctanh(a*x)^3,x, algorithm=""fricas"")","\frac{192 \, a x \log\left(-\frac{a x + 1}{a x - 1}\right) + 3 \, {\left(3 \, {\left(a^{6} x^{6} - 3 \, a^{4} x^{4} + 3 \, a^{2} x^{2} - 1\right)} \operatorname{log\_integral}\left(-\frac{a^{3} x^{3} + 3 \, a^{2} x^{2} + 3 \, a x + 1}{a^{3} x^{3} - 3 \, a^{2} x^{2} + 3 \, a x - 1}\right) + 3 \, {\left(a^{6} x^{6} - 3 \, a^{4} x^{4} + 3 \, a^{2} x^{2} - 1\right)} \operatorname{log\_integral}\left(-\frac{a^{3} x^{3} - 3 \, a^{2} x^{2} + 3 \, a x - 1}{a^{3} x^{3} + 3 \, a^{2} x^{2} + 3 \, a x + 1}\right) + 8 \, {\left(a^{6} x^{6} - 3 \, a^{4} x^{4} + 3 \, a^{2} x^{2} - 1\right)} \operatorname{log\_integral}\left(\frac{a^{2} x^{2} + 2 \, a x + 1}{a^{2} x^{2} - 2 \, a x + 1}\right) + 8 \, {\left(a^{6} x^{6} - 3 \, a^{4} x^{4} + 3 \, a^{2} x^{2} - 1\right)} \operatorname{log\_integral}\left(\frac{a^{2} x^{2} - 2 \, a x + 1}{a^{2} x^{2} + 2 \, a x + 1}\right) + 5 \, {\left(a^{6} x^{6} - 3 \, a^{4} x^{4} + 3 \, a^{2} x^{2} - 1\right)} \operatorname{log\_integral}\left(-\frac{a x + 1}{a x - 1}\right) + 5 \, {\left(a^{6} x^{6} - 3 \, a^{4} x^{4} + 3 \, a^{2} x^{2} - 1\right)} \operatorname{log\_integral}\left(-\frac{a x - 1}{a x + 1}\right)\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)^{2} + 64}{32 \, {\left(a^{7} x^{6} - 3 \, a^{5} x^{4} + 3 \, a^{3} x^{2} - a\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)^{2}}"," ",0,"1/32*(192*a*x*log(-(a*x + 1)/(a*x - 1)) + 3*(3*(a^6*x^6 - 3*a^4*x^4 + 3*a^2*x^2 - 1)*log_integral(-(a^3*x^3 + 3*a^2*x^2 + 3*a*x + 1)/(a^3*x^3 - 3*a^2*x^2 + 3*a*x - 1)) + 3*(a^6*x^6 - 3*a^4*x^4 + 3*a^2*x^2 - 1)*log_integral(-(a^3*x^3 - 3*a^2*x^2 + 3*a*x - 1)/(a^3*x^3 + 3*a^2*x^2 + 3*a*x + 1)) + 8*(a^6*x^6 - 3*a^4*x^4 + 3*a^2*x^2 - 1)*log_integral((a^2*x^2 + 2*a*x + 1)/(a^2*x^2 - 2*a*x + 1)) + 8*(a^6*x^6 - 3*a^4*x^4 + 3*a^2*x^2 - 1)*log_integral((a^2*x^2 - 2*a*x + 1)/(a^2*x^2 + 2*a*x + 1)) + 5*(a^6*x^6 - 3*a^4*x^4 + 3*a^2*x^2 - 1)*log_integral(-(a*x + 1)/(a*x - 1)) + 5*(a^6*x^6 - 3*a^4*x^4 + 3*a^2*x^2 - 1)*log_integral(-(a*x - 1)/(a*x + 1)))*log(-(a*x + 1)/(a*x - 1))^2 + 64)/((a^7*x^6 - 3*a^5*x^4 + 3*a^3*x^2 - a)*log(-(a*x + 1)/(a*x - 1))^2)","B",0
364,1,91,0,0.598612," ","integrate(x^5*arctanh(a*x)/(-a^2*x^2+1)^(1/2),x, algorithm=""fricas"")","-\frac{{\left(6 \, a^{3} x^{3} + 25 \, a x + 4 \, {\left(3 \, a^{4} x^{4} + 4 \, a^{2} x^{2} + 8\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)\right)} \sqrt{-a^{2} x^{2} + 1} + 178 \, \arctan\left(\frac{\sqrt{-a^{2} x^{2} + 1} - 1}{a x}\right)}{120 \, a^{6}}"," ",0,"-1/120*((6*a^3*x^3 + 25*a*x + 4*(3*a^4*x^4 + 4*a^2*x^2 + 8)*log(-(a*x + 1)/(a*x - 1)))*sqrt(-a^2*x^2 + 1) + 178*arctan((sqrt(-a^2*x^2 + 1) - 1)/(a*x)))/a^6","A",0
365,0,0,0,0.637923," ","integrate(x^4*arctanh(a*x)/(-a^2*x^2+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-a^{2} x^{2} + 1} x^{4} \operatorname{artanh}\left(a x\right)}{a^{2} x^{2} - 1}, x\right)"," ",0,"integral(-sqrt(-a^2*x^2 + 1)*x^4*arctanh(a*x)/(a^2*x^2 - 1), x)","F",0
366,1,72,0,0.491269," ","integrate(x^3*arctanh(a*x)/(-a^2*x^2+1)^(1/2),x, algorithm=""fricas"")","-\frac{\sqrt{-a^{2} x^{2} + 1} {\left(a x + {\left(a^{2} x^{2} + 2\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)\right)} + 10 \, \arctan\left(\frac{\sqrt{-a^{2} x^{2} + 1} - 1}{a x}\right)}{6 \, a^{4}}"," ",0,"-1/6*(sqrt(-a^2*x^2 + 1)*(a*x + (a^2*x^2 + 2)*log(-(a*x + 1)/(a*x - 1))) + 10*arctan((sqrt(-a^2*x^2 + 1) - 1)/(a*x)))/a^4","A",0
367,0,0,0,0.513810," ","integrate(x^2*arctanh(a*x)/(-a^2*x^2+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-a^{2} x^{2} + 1} x^{2} \operatorname{artanh}\left(a x\right)}{a^{2} x^{2} - 1}, x\right)"," ",0,"integral(-sqrt(-a^2*x^2 + 1)*x^2*arctanh(a*x)/(a^2*x^2 - 1), x)","F",0
368,1,58,0,0.468504," ","integrate(x*arctanh(a*x)/(-a^2*x^2+1)^(1/2),x, algorithm=""fricas"")","-\frac{\sqrt{-a^{2} x^{2} + 1} \log\left(-\frac{a x + 1}{a x - 1}\right) + 4 \, \arctan\left(\frac{\sqrt{-a^{2} x^{2} + 1} - 1}{a x}\right)}{2 \, a^{2}}"," ",0,"-1/2*(sqrt(-a^2*x^2 + 1)*log(-(a*x + 1)/(a*x - 1)) + 4*arctan((sqrt(-a^2*x^2 + 1) - 1)/(a*x)))/a^2","A",0
369,0,0,0,0.866468," ","integrate(arctanh(a*x)/(-a^2*x^2+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-a^{2} x^{2} + 1} \operatorname{artanh}\left(a x\right)}{a^{2} x^{2} - 1}, x\right)"," ",0,"integral(-sqrt(-a^2*x^2 + 1)*arctanh(a*x)/(a^2*x^2 - 1), x)","F",0
370,0,0,0,0.569343," ","integrate(arctanh(a*x)/x/(-a^2*x^2+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-a^{2} x^{2} + 1} \operatorname{artanh}\left(a x\right)}{a^{2} x^{3} - x}, x\right)"," ",0,"integral(-sqrt(-a^2*x^2 + 1)*arctanh(a*x)/(a^2*x^3 - x), x)","F",0
371,1,58,0,0.529730," ","integrate(arctanh(a*x)/x^2/(-a^2*x^2+1)^(1/2),x, algorithm=""fricas"")","\frac{2 \, a x \log\left(\frac{\sqrt{-a^{2} x^{2} + 1} - 1}{x}\right) - \sqrt{-a^{2} x^{2} + 1} \log\left(-\frac{a x + 1}{a x - 1}\right)}{2 \, x}"," ",0,"1/2*(2*a*x*log((sqrt(-a^2*x^2 + 1) - 1)/x) - sqrt(-a^2*x^2 + 1)*log(-(a*x + 1)/(a*x - 1)))/x","A",0
372,0,0,0,0.871473," ","integrate(arctanh(a*x)/x^3/(-a^2*x^2+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-a^{2} x^{2} + 1} \operatorname{artanh}\left(a x\right)}{a^{2} x^{5} - x^{3}}, x\right)"," ",0,"integral(-sqrt(-a^2*x^2 + 1)*arctanh(a*x)/(a^2*x^5 - x^3), x)","F",0
373,0,0,0,0.664209," ","integrate(x^3*arctanh(a*x)^2/(-a^2*x^2+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-a^{2} x^{2} + 1} x^{3} \operatorname{artanh}\left(a x\right)^{2}}{a^{2} x^{2} - 1}, x\right)"," ",0,"integral(-sqrt(-a^2*x^2 + 1)*x^3*arctanh(a*x)^2/(a^2*x^2 - 1), x)","F",0
374,0,0,0,0.923809," ","integrate(x^2*arctanh(a*x)^2/(-a^2*x^2+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-a^{2} x^{2} + 1} x^{2} \operatorname{artanh}\left(a x\right)^{2}}{a^{2} x^{2} - 1}, x\right)"," ",0,"integral(-sqrt(-a^2*x^2 + 1)*x^2*arctanh(a*x)^2/(a^2*x^2 - 1), x)","F",0
375,0,0,0,0.906664," ","integrate(x*arctanh(a*x)^2/(-a^2*x^2+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-a^{2} x^{2} + 1} x \operatorname{artanh}\left(a x\right)^{2}}{a^{2} x^{2} - 1}, x\right)"," ",0,"integral(-sqrt(-a^2*x^2 + 1)*x*arctanh(a*x)^2/(a^2*x^2 - 1), x)","F",0
376,0,0,0,0.684562," ","integrate(arctanh(a*x)^2/(-a^2*x^2+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-a^{2} x^{2} + 1} \operatorname{artanh}\left(a x\right)^{2}}{a^{2} x^{2} - 1}, x\right)"," ",0,"integral(-sqrt(-a^2*x^2 + 1)*arctanh(a*x)^2/(a^2*x^2 - 1), x)","F",0
377,0,0,0,0.501885," ","integrate(arctanh(a*x)^2/x/(-a^2*x^2+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-a^{2} x^{2} + 1} \operatorname{artanh}\left(a x\right)^{2}}{a^{2} x^{3} - x}, x\right)"," ",0,"integral(-sqrt(-a^2*x^2 + 1)*arctanh(a*x)^2/(a^2*x^3 - x), x)","F",0
378,0,0,0,0.847595," ","integrate(arctanh(a*x)^2/x^2/(-a^2*x^2+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-a^{2} x^{2} + 1} \operatorname{artanh}\left(a x\right)^{2}}{a^{2} x^{4} - x^{2}}, x\right)"," ",0,"integral(-sqrt(-a^2*x^2 + 1)*arctanh(a*x)^2/(a^2*x^4 - x^2), x)","F",0
379,0,0,0,0.633416," ","integrate(arctanh(a*x)^2/x^3/(-a^2*x^2+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-a^{2} x^{2} + 1} \operatorname{artanh}\left(a x\right)^{2}}{a^{2} x^{5} - x^{3}}, x\right)"," ",0,"integral(-sqrt(-a^2*x^2 + 1)*arctanh(a*x)^2/(a^2*x^5 - x^3), x)","F",0
380,0,0,0,0.534035," ","integrate(x^3*arctanh(a*x)^3/(-a^2*x^2+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-a^{2} x^{2} + 1} x^{3} \operatorname{artanh}\left(a x\right)^{3}}{a^{2} x^{2} - 1}, x\right)"," ",0,"integral(-sqrt(-a^2*x^2 + 1)*x^3*arctanh(a*x)^3/(a^2*x^2 - 1), x)","F",0
381,0,0,0,0.582497," ","integrate(x^2*arctanh(a*x)^3/(-a^2*x^2+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-a^{2} x^{2} + 1} x^{2} \operatorname{artanh}\left(a x\right)^{3}}{a^{2} x^{2} - 1}, x\right)"," ",0,"integral(-sqrt(-a^2*x^2 + 1)*x^2*arctanh(a*x)^3/(a^2*x^2 - 1), x)","F",0
382,0,0,0,0.592136," ","integrate(x*arctanh(a*x)^3/(-a^2*x^2+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-a^{2} x^{2} + 1} x \operatorname{artanh}\left(a x\right)^{3}}{a^{2} x^{2} - 1}, x\right)"," ",0,"integral(-sqrt(-a^2*x^2 + 1)*x*arctanh(a*x)^3/(a^2*x^2 - 1), x)","F",0
383,0,0,0,0.602753," ","integrate(arctanh(a*x)^3/(-a^2*x^2+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-a^{2} x^{2} + 1} \operatorname{artanh}\left(a x\right)^{3}}{a^{2} x^{2} - 1}, x\right)"," ",0,"integral(-sqrt(-a^2*x^2 + 1)*arctanh(a*x)^3/(a^2*x^2 - 1), x)","F",0
384,0,0,0,0.710782," ","integrate(arctanh(a*x)^3/x/(-a^2*x^2+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-a^{2} x^{2} + 1} \operatorname{artanh}\left(a x\right)^{3}}{a^{2} x^{3} - x}, x\right)"," ",0,"integral(-sqrt(-a^2*x^2 + 1)*arctanh(a*x)^3/(a^2*x^3 - x), x)","F",0
385,0,0,0,0.499580," ","integrate(arctanh(a*x)^3/x^2/(-a^2*x^2+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-a^{2} x^{2} + 1} \operatorname{artanh}\left(a x\right)^{3}}{a^{2} x^{4} - x^{2}}, x\right)"," ",0,"integral(-sqrt(-a^2*x^2 + 1)*arctanh(a*x)^3/(a^2*x^4 - x^2), x)","F",0
386,0,0,0,0.504326," ","integrate(arctanh(a*x)^3/x^3/(-a^2*x^2+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-a^{2} x^{2} + 1} \operatorname{artanh}\left(a x\right)^{3}}{a^{2} x^{5} - x^{3}}, x\right)"," ",0,"integral(-sqrt(-a^2*x^2 + 1)*arctanh(a*x)^3/(a^2*x^5 - x^3), x)","F",0
387,0,0,0,0.825985," ","integrate(x^m*arctanh(a*x)/(-a^2*x^2+1)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-a^{2} x^{2} + 1} x^{m} \operatorname{artanh}\left(a x\right)}{a^{4} x^{4} - 2 \, a^{2} x^{2} + 1}, x\right)"," ",0,"integral(sqrt(-a^2*x^2 + 1)*x^m*arctanh(a*x)/(a^4*x^4 - 2*a^2*x^2 + 1), x)","F",0
388,1,94,0,0.624378," ","integrate(x^3*arctanh(a*x)/(-a^2*x^2+1)^(3/2),x, algorithm=""fricas"")","\frac{4 \, {\left(a^{2} x^{2} - 1\right)} \arctan\left(\frac{\sqrt{-a^{2} x^{2} + 1} - 1}{a x}\right) + \sqrt{-a^{2} x^{2} + 1} {\left(2 \, a x + {\left(a^{2} x^{2} - 2\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)\right)}}{2 \, {\left(a^{6} x^{2} - a^{4}\right)}}"," ",0,"1/2*(4*(a^2*x^2 - 1)*arctan((sqrt(-a^2*x^2 + 1) - 1)/(a*x)) + sqrt(-a^2*x^2 + 1)*(2*a*x + (a^2*x^2 - 2)*log(-(a*x + 1)/(a*x - 1))))/(a^6*x^2 - a^4)","A",0
389,0,0,0,0.541497," ","integrate(x^2*arctanh(a*x)/(-a^2*x^2+1)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-a^{2} x^{2} + 1} x^{2} \operatorname{artanh}\left(a x\right)}{a^{4} x^{4} - 2 \, a^{2} x^{2} + 1}, x\right)"," ",0,"integral(sqrt(-a^2*x^2 + 1)*x^2*arctanh(a*x)/(a^4*x^4 - 2*a^2*x^2 + 1), x)","F",0
390,1,51,0,0.534173," ","integrate(x*arctanh(a*x)/(-a^2*x^2+1)^(3/2),x, algorithm=""fricas"")","\frac{\sqrt{-a^{2} x^{2} + 1} {\left(2 \, a x - \log\left(-\frac{a x + 1}{a x - 1}\right)\right)}}{2 \, {\left(a^{4} x^{2} - a^{2}\right)}}"," ",0,"1/2*sqrt(-a^2*x^2 + 1)*(2*a*x - log(-(a*x + 1)/(a*x - 1)))/(a^4*x^2 - a^2)","A",0
391,1,47,0,0.508320," ","integrate(arctanh(a*x)/(-a^2*x^2+1)^(3/2),x, algorithm=""fricas"")","-\frac{\sqrt{-a^{2} x^{2} + 1} {\left(a x \log\left(-\frac{a x + 1}{a x - 1}\right) - 2\right)}}{2 \, {\left(a^{3} x^{2} - a\right)}}"," ",0,"-1/2*sqrt(-a^2*x^2 + 1)*(a*x*log(-(a*x + 1)/(a*x - 1)) - 2)/(a^3*x^2 - a)","A",0
392,0,0,0,0.809319," ","integrate(arctanh(a*x)/x/(-a^2*x^2+1)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-a^{2} x^{2} + 1} \operatorname{artanh}\left(a x\right)}{a^{4} x^{5} - 2 \, a^{2} x^{3} + x}, x\right)"," ",0,"integral(sqrt(-a^2*x^2 + 1)*arctanh(a*x)/(a^4*x^5 - 2*a^2*x^3 + x), x)","F",0
393,1,107,0,0.430859," ","integrate(arctanh(a*x)/x^2/(-a^2*x^2+1)^(3/2),x, algorithm=""fricas"")","-\frac{2 \, a^{3} x^{3} - 2 \, a x - 2 \, {\left(a^{3} x^{3} - a x\right)} \log\left(\frac{\sqrt{-a^{2} x^{2} + 1} - 1}{x}\right) - \sqrt{-a^{2} x^{2} + 1} {\left(2 \, a x - {\left(2 \, a^{2} x^{2} - 1\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)\right)}}{2 \, {\left(a^{2} x^{3} - x\right)}}"," ",0,"-1/2*(2*a^3*x^3 - 2*a*x - 2*(a^3*x^3 - a*x)*log((sqrt(-a^2*x^2 + 1) - 1)/x) - sqrt(-a^2*x^2 + 1)*(2*a*x - (2*a^2*x^2 - 1)*log(-(a*x + 1)/(a*x - 1))))/(a^2*x^3 - x)","A",0
394,0,0,0,0.569873," ","integrate(arctanh(a*x)/x^3/(-a^2*x^2+1)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-a^{2} x^{2} + 1} \operatorname{artanh}\left(a x\right)}{a^{4} x^{7} - 2 \, a^{2} x^{5} + x^{3}}, x\right)"," ",0,"integral(sqrt(-a^2*x^2 + 1)*arctanh(a*x)/(a^4*x^7 - 2*a^2*x^5 + x^3), x)","F",0
395,0,0,0,0.530763," ","integrate(x^m*arctanh(a*x)^2/(-a^2*x^2+1)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-a^{2} x^{2} + 1} x^{m} \operatorname{artanh}\left(a x\right)^{2}}{a^{4} x^{4} - 2 \, a^{2} x^{2} + 1}, x\right)"," ",0,"integral(sqrt(-a^2*x^2 + 1)*x^m*arctanh(a*x)^2/(a^4*x^4 - 2*a^2*x^2 + 1), x)","F",0
396,0,0,0,0.578604," ","integrate(x^3*arctanh(a*x)^2/(-a^2*x^2+1)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-a^{2} x^{2} + 1} x^{3} \operatorname{artanh}\left(a x\right)^{2}}{a^{4} x^{4} - 2 \, a^{2} x^{2} + 1}, x\right)"," ",0,"integral(sqrt(-a^2*x^2 + 1)*x^3*arctanh(a*x)^2/(a^4*x^4 - 2*a^2*x^2 + 1), x)","F",0
397,0,0,0,0.399599," ","integrate(x^2*arctanh(a*x)^2/(-a^2*x^2+1)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-a^{2} x^{2} + 1} x^{2} \operatorname{artanh}\left(a x\right)^{2}}{a^{4} x^{4} - 2 \, a^{2} x^{2} + 1}, x\right)"," ",0,"integral(sqrt(-a^2*x^2 + 1)*x^2*arctanh(a*x)^2/(a^4*x^4 - 2*a^2*x^2 + 1), x)","F",0
398,1,69,0,0.506590," ","integrate(x*arctanh(a*x)^2/(-a^2*x^2+1)^(3/2),x, algorithm=""fricas"")","\frac{\sqrt{-a^{2} x^{2} + 1} {\left(4 \, a x \log\left(-\frac{a x + 1}{a x - 1}\right) - \log\left(-\frac{a x + 1}{a x - 1}\right)^{2} - 8\right)}}{4 \, {\left(a^{4} x^{2} - a^{2}\right)}}"," ",0,"1/4*sqrt(-a^2*x^2 + 1)*(4*a*x*log(-(a*x + 1)/(a*x - 1)) - log(-(a*x + 1)/(a*x - 1))^2 - 8)/(a^4*x^2 - a^2)","A",0
399,1,69,0,0.505269," ","integrate(arctanh(a*x)^2/(-a^2*x^2+1)^(3/2),x, algorithm=""fricas"")","-\frac{\sqrt{-a^{2} x^{2} + 1} {\left(a x \log\left(-\frac{a x + 1}{a x - 1}\right)^{2} + 8 \, a x - 4 \, \log\left(-\frac{a x + 1}{a x - 1}\right)\right)}}{4 \, {\left(a^{3} x^{2} - a\right)}}"," ",0,"-1/4*sqrt(-a^2*x^2 + 1)*(a*x*log(-(a*x + 1)/(a*x - 1))^2 + 8*a*x - 4*log(-(a*x + 1)/(a*x - 1)))/(a^3*x^2 - a)","A",0
400,0,0,0,0.450136," ","integrate(arctanh(a*x)^2/x/(-a^2*x^2+1)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-a^{2} x^{2} + 1} \operatorname{artanh}\left(a x\right)^{2}}{a^{4} x^{5} - 2 \, a^{2} x^{3} + x}, x\right)"," ",0,"integral(sqrt(-a^2*x^2 + 1)*arctanh(a*x)^2/(a^4*x^5 - 2*a^2*x^3 + x), x)","F",0
401,0,0,0,0.495653," ","integrate(arctanh(a*x)^2/x^2/(-a^2*x^2+1)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-a^{2} x^{2} + 1} \operatorname{artanh}\left(a x\right)^{2}}{a^{4} x^{6} - 2 \, a^{2} x^{4} + x^{2}}, x\right)"," ",0,"integral(sqrt(-a^2*x^2 + 1)*arctanh(a*x)^2/(a^4*x^6 - 2*a^2*x^4 + x^2), x)","F",0
402,0,0,0,0.460705," ","integrate(arctanh(a*x)^2/x^3/(-a^2*x^2+1)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-a^{2} x^{2} + 1} \operatorname{artanh}\left(a x\right)^{2}}{a^{4} x^{7} - 2 \, a^{2} x^{5} + x^{3}}, x\right)"," ",0,"integral(sqrt(-a^2*x^2 + 1)*arctanh(a*x)^2/(a^4*x^7 - 2*a^2*x^5 + x^3), x)","F",0
403,0,0,0,0.555891," ","integrate(x^m*arctanh(a*x)^3/(-a^2*x^2+1)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-a^{2} x^{2} + 1} x^{m} \operatorname{artanh}\left(a x\right)^{3}}{a^{4} x^{4} - 2 \, a^{2} x^{2} + 1}, x\right)"," ",0,"integral(sqrt(-a^2*x^2 + 1)*x^m*arctanh(a*x)^3/(a^4*x^4 - 2*a^2*x^2 + 1), x)","F",0
404,0,0,0,0.765732," ","integrate(x^3*arctanh(a*x)^3/(-a^2*x^2+1)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-a^{2} x^{2} + 1} x^{3} \operatorname{artanh}\left(a x\right)^{3}}{a^{4} x^{4} - 2 \, a^{2} x^{2} + 1}, x\right)"," ",0,"integral(sqrt(-a^2*x^2 + 1)*x^3*arctanh(a*x)^3/(a^4*x^4 - 2*a^2*x^2 + 1), x)","F",0
405,0,0,0,0.652996," ","integrate(x^2*arctanh(a*x)^3/(-a^2*x^2+1)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-a^{2} x^{2} + 1} x^{2} \operatorname{artanh}\left(a x\right)^{3}}{a^{4} x^{4} - 2 \, a^{2} x^{2} + 1}, x\right)"," ",0,"integral(sqrt(-a^2*x^2 + 1)*x^2*arctanh(a*x)^3/(a^4*x^4 - 2*a^2*x^2 + 1), x)","F",0
406,1,91,0,0.418290," ","integrate(x*arctanh(a*x)^3/(-a^2*x^2+1)^(3/2),x, algorithm=""fricas"")","\frac{\sqrt{-a^{2} x^{2} + 1} {\left(6 \, a x \log\left(-\frac{a x + 1}{a x - 1}\right)^{2} - \log\left(-\frac{a x + 1}{a x - 1}\right)^{3} + 48 \, a x - 24 \, \log\left(-\frac{a x + 1}{a x - 1}\right)\right)}}{8 \, {\left(a^{4} x^{2} - a^{2}\right)}}"," ",0,"1/8*sqrt(-a^2*x^2 + 1)*(6*a*x*log(-(a*x + 1)/(a*x - 1))^2 - log(-(a*x + 1)/(a*x - 1))^3 + 48*a*x - 24*log(-(a*x + 1)/(a*x - 1)))/(a^4*x^2 - a^2)","A",0
407,1,87,0,0.472687," ","integrate(arctanh(a*x)^3/(-a^2*x^2+1)^(3/2),x, algorithm=""fricas"")","-\frac{{\left(a x \log\left(-\frac{a x + 1}{a x - 1}\right)^{3} + 24 \, a x \log\left(-\frac{a x + 1}{a x - 1}\right) - 6 \, \log\left(-\frac{a x + 1}{a x - 1}\right)^{2} - 48\right)} \sqrt{-a^{2} x^{2} + 1}}{8 \, {\left(a^{3} x^{2} - a\right)}}"," ",0,"-1/8*(a*x*log(-(a*x + 1)/(a*x - 1))^3 + 24*a*x*log(-(a*x + 1)/(a*x - 1)) - 6*log(-(a*x + 1)/(a*x - 1))^2 - 48)*sqrt(-a^2*x^2 + 1)/(a^3*x^2 - a)","A",0
408,0,0,0,0.535137," ","integrate(arctanh(a*x)^3/x/(-a^2*x^2+1)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-a^{2} x^{2} + 1} \operatorname{artanh}\left(a x\right)^{3}}{a^{4} x^{5} - 2 \, a^{2} x^{3} + x}, x\right)"," ",0,"integral(sqrt(-a^2*x^2 + 1)*arctanh(a*x)^3/(a^4*x^5 - 2*a^2*x^3 + x), x)","F",0
409,0,0,0,0.499282," ","integrate(arctanh(a*x)^3/x^2/(-a^2*x^2+1)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-a^{2} x^{2} + 1} \operatorname{artanh}\left(a x\right)^{3}}{a^{4} x^{6} - 2 \, a^{2} x^{4} + x^{2}}, x\right)"," ",0,"integral(sqrt(-a^2*x^2 + 1)*arctanh(a*x)^3/(a^4*x^6 - 2*a^2*x^4 + x^2), x)","F",0
410,0,0,0,0.546677," ","integrate(arctanh(a*x)^3/x^3/(-a^2*x^2+1)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-a^{2} x^{2} + 1} \operatorname{artanh}\left(a x\right)^{3}}{a^{4} x^{7} - 2 \, a^{2} x^{5} + x^{3}}, x\right)"," ",0,"integral(sqrt(-a^2*x^2 + 1)*arctanh(a*x)^3/(a^4*x^7 - 2*a^2*x^5 + x^3), x)","F",0
411,0,0,0,1.191005," ","integrate(x^m/(-a^2*x^2+1)^(3/2)/arctanh(a*x),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-a^{2} x^{2} + 1} x^{m}}{{\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \operatorname{artanh}\left(a x\right)}, x\right)"," ",0,"integral(sqrt(-a^2*x^2 + 1)*x^m/((a^4*x^4 - 2*a^2*x^2 + 1)*arctanh(a*x)), x)","F",0
412,0,0,0,0.558610," ","integrate(x^2/(-a^2*x^2+1)^(3/2)/arctanh(a*x),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-a^{2} x^{2} + 1} x^{2}}{{\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \operatorname{artanh}\left(a x\right)}, x\right)"," ",0,"integral(sqrt(-a^2*x^2 + 1)*x^2/((a^4*x^4 - 2*a^2*x^2 + 1)*arctanh(a*x)), x)","F",0
413,0,0,0,0.451866," ","integrate(x/(-a^2*x^2+1)^(3/2)/arctanh(a*x),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-a^{2} x^{2} + 1} x}{{\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \operatorname{artanh}\left(a x\right)}, x\right)"," ",0,"integral(sqrt(-a^2*x^2 + 1)*x/((a^4*x^4 - 2*a^2*x^2 + 1)*arctanh(a*x)), x)","F",0
414,0,0,0,0.439175," ","integrate(1/(-a^2*x^2+1)^(3/2)/arctanh(a*x),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-a^{2} x^{2} + 1}}{{\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \operatorname{artanh}\left(a x\right)}, x\right)"," ",0,"integral(sqrt(-a^2*x^2 + 1)/((a^4*x^4 - 2*a^2*x^2 + 1)*arctanh(a*x)), x)","F",0
415,0,0,0,0.528756," ","integrate(1/x/(-a^2*x^2+1)^(3/2)/arctanh(a*x),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-a^{2} x^{2} + 1}}{{\left(a^{4} x^{5} - 2 \, a^{2} x^{3} + x\right)} \operatorname{artanh}\left(a x\right)}, x\right)"," ",0,"integral(sqrt(-a^2*x^2 + 1)/((a^4*x^5 - 2*a^2*x^3 + x)*arctanh(a*x)), x)","F",0
416,0,0,0,0.441633," ","integrate(x^m/(-a^2*x^2+1)^(3/2)/arctanh(a*x)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-a^{2} x^{2} + 1} x^{m}}{{\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \operatorname{artanh}\left(a x\right)^{2}}, x\right)"," ",0,"integral(sqrt(-a^2*x^2 + 1)*x^m/((a^4*x^4 - 2*a^2*x^2 + 1)*arctanh(a*x)^2), x)","F",0
417,0,0,0,0.435761," ","integrate(x^2/(-a^2*x^2+1)^(3/2)/arctanh(a*x)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-a^{2} x^{2} + 1} x^{2}}{{\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \operatorname{artanh}\left(a x\right)^{2}}, x\right)"," ",0,"integral(sqrt(-a^2*x^2 + 1)*x^2/((a^4*x^4 - 2*a^2*x^2 + 1)*arctanh(a*x)^2), x)","F",0
418,0,0,0,0.673762," ","integrate(x/(-a^2*x^2+1)^(3/2)/arctanh(a*x)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-a^{2} x^{2} + 1} x}{{\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \operatorname{artanh}\left(a x\right)^{2}}, x\right)"," ",0,"integral(sqrt(-a^2*x^2 + 1)*x/((a^4*x^4 - 2*a^2*x^2 + 1)*arctanh(a*x)^2), x)","F",0
419,0,0,0,0.613407," ","integrate(1/(-a^2*x^2+1)^(3/2)/arctanh(a*x)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-a^{2} x^{2} + 1}}{{\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \operatorname{artanh}\left(a x\right)^{2}}, x\right)"," ",0,"integral(sqrt(-a^2*x^2 + 1)/((a^4*x^4 - 2*a^2*x^2 + 1)*arctanh(a*x)^2), x)","F",0
420,0,0,0,0.463589," ","integrate(1/x/(-a^2*x^2+1)^(3/2)/arctanh(a*x)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-a^{2} x^{2} + 1}}{{\left(a^{4} x^{5} - 2 \, a^{2} x^{3} + x\right)} \operatorname{artanh}\left(a x\right)^{2}}, x\right)"," ",0,"integral(sqrt(-a^2*x^2 + 1)/((a^4*x^5 - 2*a^2*x^3 + x)*arctanh(a*x)^2), x)","F",0
421,0,0,0,0.646973," ","integrate(x^m/(-a^2*x^2+1)^(3/2)/arctanh(a*x)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-a^{2} x^{2} + 1} x^{m}}{{\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \operatorname{artanh}\left(a x\right)^{3}}, x\right)"," ",0,"integral(sqrt(-a^2*x^2 + 1)*x^m/((a^4*x^4 - 2*a^2*x^2 + 1)*arctanh(a*x)^3), x)","F",0
422,0,0,0,0.561342," ","integrate(x^2/(-a^2*x^2+1)^(3/2)/arctanh(a*x)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-a^{2} x^{2} + 1} x^{2}}{{\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \operatorname{artanh}\left(a x\right)^{3}}, x\right)"," ",0,"integral(sqrt(-a^2*x^2 + 1)*x^2/((a^4*x^4 - 2*a^2*x^2 + 1)*arctanh(a*x)^3), x)","F",0
423,0,0,0,0.557518," ","integrate(x/(-a^2*x^2+1)^(3/2)/arctanh(a*x)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-a^{2} x^{2} + 1} x}{{\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \operatorname{artanh}\left(a x\right)^{3}}, x\right)"," ",0,"integral(sqrt(-a^2*x^2 + 1)*x/((a^4*x^4 - 2*a^2*x^2 + 1)*arctanh(a*x)^3), x)","F",0
424,0,0,0,0.669090," ","integrate(1/(-a^2*x^2+1)^(3/2)/arctanh(a*x)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-a^{2} x^{2} + 1}}{{\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \operatorname{artanh}\left(a x\right)^{3}}, x\right)"," ",0,"integral(sqrt(-a^2*x^2 + 1)/((a^4*x^4 - 2*a^2*x^2 + 1)*arctanh(a*x)^3), x)","F",0
425,0,0,0,0.611241," ","integrate(1/x/(-a^2*x^2+1)^(3/2)/arctanh(a*x)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-a^{2} x^{2} + 1}}{{\left(a^{4} x^{5} - 2 \, a^{2} x^{3} + x\right)} \operatorname{artanh}\left(a x\right)^{3}}, x\right)"," ",0,"integral(sqrt(-a^2*x^2 + 1)/((a^4*x^5 - 2*a^2*x^3 + x)*arctanh(a*x)^3), x)","F",0
426,0,0,0,0.537412," ","integrate(x^4*arctanh(a*x)*(-a^2*x^2+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{-a^{2} x^{2} + 1} x^{4} \operatorname{artanh}\left(a x\right), x\right)"," ",0,"integral(sqrt(-a^2*x^2 + 1)*x^4*arctanh(a*x), x)","F",0
427,1,91,0,0.514570," ","integrate(x^3*arctanh(a*x)*(-a^2*x^2+1)^(1/2),x, algorithm=""fricas"")","\frac{{\left(6 \, a^{3} x^{3} + 5 \, a x + 4 \, {\left(3 \, a^{4} x^{4} - a^{2} x^{2} - 2\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)\right)} \sqrt{-a^{2} x^{2} + 1} - 22 \, \arctan\left(\frac{\sqrt{-a^{2} x^{2} + 1} - 1}{a x}\right)}{120 \, a^{4}}"," ",0,"1/120*((6*a^3*x^3 + 5*a*x + 4*(3*a^4*x^4 - a^2*x^2 - 2)*log(-(a*x + 1)/(a*x - 1)))*sqrt(-a^2*x^2 + 1) - 22*arctan((sqrt(-a^2*x^2 + 1) - 1)/(a*x)))/a^4","A",0
428,0,0,0,0.427045," ","integrate(x^2*arctanh(a*x)*(-a^2*x^2+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{-a^{2} x^{2} + 1} x^{2} \operatorname{artanh}\left(a x\right), x\right)"," ",0,"integral(sqrt(-a^2*x^2 + 1)*x^2*arctanh(a*x), x)","F",0
429,1,72,0,0.558599," ","integrate(x*arctanh(a*x)*(-a^2*x^2+1)^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{-a^{2} x^{2} + 1} {\left(a x + {\left(a^{2} x^{2} - 1\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)\right)} - 2 \, \arctan\left(\frac{\sqrt{-a^{2} x^{2} + 1} - 1}{a x}\right)}{6 \, a^{2}}"," ",0,"1/6*(sqrt(-a^2*x^2 + 1)*(a*x + (a^2*x^2 - 1)*log(-(a*x + 1)/(a*x - 1))) - 2*arctan((sqrt(-a^2*x^2 + 1) - 1)/(a*x)))/a^2","A",0
430,0,0,0,0.543963," ","integrate((-a^2*x^2+1)^(1/2)*arctanh(a*x),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{-a^{2} x^{2} + 1} \operatorname{artanh}\left(a x\right), x\right)"," ",0,"integral(sqrt(-a^2*x^2 + 1)*arctanh(a*x), x)","F",0
431,0,0,0,0.548458," ","integrate(arctanh(a*x)*(-a^2*x^2+1)^(1/2)/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-a^{2} x^{2} + 1} \operatorname{artanh}\left(a x\right)}{x}, x\right)"," ",0,"integral(sqrt(-a^2*x^2 + 1)*arctanh(a*x)/x, x)","F",0
432,0,0,0,0.564892," ","integrate(arctanh(a*x)*(-a^2*x^2+1)^(1/2)/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-a^{2} x^{2} + 1} \operatorname{artanh}\left(a x\right)}{x^{2}}, x\right)"," ",0,"integral(sqrt(-a^2*x^2 + 1)*arctanh(a*x)/x^2, x)","F",0
433,0,0,0,0.481928," ","integrate(arctanh(a*x)*(-a^2*x^2+1)^(1/2)/x^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-a^{2} x^{2} + 1} \operatorname{artanh}\left(a x\right)}{x^{3}}, x\right)"," ",0,"integral(sqrt(-a^2*x^2 + 1)*arctanh(a*x)/x^3, x)","F",0
434,1,75,0,0.438516," ","integrate(arctanh(a*x)*(-a^2*x^2+1)^(1/2)/x^4,x, algorithm=""fricas"")","-\frac{a^{3} x^{3} \log\left(\frac{\sqrt{-a^{2} x^{2} + 1} - 1}{x}\right) + \sqrt{-a^{2} x^{2} + 1} {\left(a x - {\left(a^{2} x^{2} - 1\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)\right)}}{6 \, x^{3}}"," ",0,"-1/6*(a^3*x^3*log((sqrt(-a^2*x^2 + 1) - 1)/x) + sqrt(-a^2*x^2 + 1)*(a*x - (a^2*x^2 - 1)*log(-(a*x + 1)/(a*x - 1))))/x^3","A",0
435,0,0,0,0.497641," ","integrate(arctanh(a*x)*(-a^2*x^2+1)^(1/2)/x^5,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-a^{2} x^{2} + 1} \operatorname{artanh}\left(a x\right)}{x^{5}}, x\right)"," ",0,"integral(sqrt(-a^2*x^2 + 1)*arctanh(a*x)/x^5, x)","F",0
436,1,93,0,0.667218," ","integrate(arctanh(a*x)*(-a^2*x^2+1)^(1/2)/x^6,x, algorithm=""fricas"")","-\frac{11 \, a^{5} x^{5} \log\left(\frac{\sqrt{-a^{2} x^{2} + 1} - 1}{x}\right) + {\left(5 \, a^{3} x^{3} + 6 \, a x - 4 \, {\left(2 \, a^{4} x^{4} + a^{2} x^{2} - 3\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)\right)} \sqrt{-a^{2} x^{2} + 1}}{120 \, x^{5}}"," ",0,"-1/120*(11*a^5*x^5*log((sqrt(-a^2*x^2 + 1) - 1)/x) + (5*a^3*x^3 + 6*a*x - 4*(2*a^4*x^4 + a^2*x^2 - 3)*log(-(a*x + 1)/(a*x - 1)))*sqrt(-a^2*x^2 + 1))/x^5","A",0
437,0,0,0,0.563329," ","integrate(arctanh(a*x)*(-a^2*x^2+1)^(1/2)/x^7,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-a^{2} x^{2} + 1} \operatorname{artanh}\left(a x\right)}{x^{7}}, x\right)"," ",0,"integral(sqrt(-a^2*x^2 + 1)*arctanh(a*x)/x^7, x)","F",0
438,0,0,0,0.602955," ","integrate(x^4*arctanh(a*x)^2*(-a^2*x^2+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{-a^{2} x^{2} + 1} x^{4} \operatorname{artanh}\left(a x\right)^{2}, x\right)"," ",0,"integral(sqrt(-a^2*x^2 + 1)*x^4*arctanh(a*x)^2, x)","F",0
439,0,0,0,0.494938," ","integrate(x^3*arctanh(a*x)^2*(-a^2*x^2+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{-a^{2} x^{2} + 1} x^{3} \operatorname{artanh}\left(a x\right)^{2}, x\right)"," ",0,"integral(sqrt(-a^2*x^2 + 1)*x^3*arctanh(a*x)^2, x)","F",0
440,0,0,0,0.491254," ","integrate(x^2*arctanh(a*x)^2*(-a^2*x^2+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{-a^{2} x^{2} + 1} x^{2} \operatorname{artanh}\left(a x\right)^{2}, x\right)"," ",0,"integral(sqrt(-a^2*x^2 + 1)*x^2*arctanh(a*x)^2, x)","F",0
441,0,0,0,0.546834," ","integrate(x*arctanh(a*x)^2*(-a^2*x^2+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{-a^{2} x^{2} + 1} x \operatorname{artanh}\left(a x\right)^{2}, x\right)"," ",0,"integral(sqrt(-a^2*x^2 + 1)*x*arctanh(a*x)^2, x)","F",0
442,0,0,0,0.439523," ","integrate((-a^2*x^2+1)^(1/2)*arctanh(a*x)^2,x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{-a^{2} x^{2} + 1} \operatorname{artanh}\left(a x\right)^{2}, x\right)"," ",0,"integral(sqrt(-a^2*x^2 + 1)*arctanh(a*x)^2, x)","F",0
443,0,0,0,0.622742," ","integrate(arctanh(a*x)^2*(-a^2*x^2+1)^(1/2)/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-a^{2} x^{2} + 1} \operatorname{artanh}\left(a x\right)^{2}}{x}, x\right)"," ",0,"integral(sqrt(-a^2*x^2 + 1)*arctanh(a*x)^2/x, x)","F",0
444,0,0,0,0.524124," ","integrate(arctanh(a*x)^2*(-a^2*x^2+1)^(1/2)/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-a^{2} x^{2} + 1} \operatorname{artanh}\left(a x\right)^{2}}{x^{2}}, x\right)"," ",0,"integral(sqrt(-a^2*x^2 + 1)*arctanh(a*x)^2/x^2, x)","F",0
445,0,0,0,0.662137," ","integrate(arctanh(a*x)^2*(-a^2*x^2+1)^(1/2)/x^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-a^{2} x^{2} + 1} \operatorname{artanh}\left(a x\right)^{2}}{x^{3}}, x\right)"," ",0,"integral(sqrt(-a^2*x^2 + 1)*arctanh(a*x)^2/x^3, x)","F",0
446,0,0,0,0.441365," ","integrate(arctanh(a*x)^2*(-a^2*x^2+1)^(1/2)/x^4,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-a^{2} x^{2} + 1} \operatorname{artanh}\left(a x\right)^{2}}{x^{4}}, x\right)"," ",0,"integral(sqrt(-a^2*x^2 + 1)*arctanh(a*x)^2/x^4, x)","F",0
447,0,0,0,0.439666," ","integrate(x^4*(-a^2*x^2+1)^(3/2)*arctanh(a*x),x, algorithm=""fricas"")","{\rm integral}\left(-{\left(a^{2} x^{6} - x^{4}\right)} \sqrt{-a^{2} x^{2} + 1} \operatorname{artanh}\left(a x\right), x\right)"," ",0,"integral(-(a^2*x^6 - x^4)*sqrt(-a^2*x^2 + 1)*arctanh(a*x), x)","F",0
448,1,106,0,0.484155," ","integrate(x^3*(-a^2*x^2+1)^(3/2)*arctanh(a*x),x, algorithm=""fricas"")","-\frac{{\left(40 \, a^{5} x^{5} - 46 \, a^{3} x^{3} - 45 \, a x + 24 \, {\left(5 \, a^{6} x^{6} - 8 \, a^{4} x^{4} + a^{2} x^{2} + 2\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)\right)} \sqrt{-a^{2} x^{2} + 1} + 102 \, \arctan\left(\frac{\sqrt{-a^{2} x^{2} + 1} - 1}{a x}\right)}{1680 \, a^{4}}"," ",0,"-1/1680*((40*a^5*x^5 - 46*a^3*x^3 - 45*a*x + 24*(5*a^6*x^6 - 8*a^4*x^4 + a^2*x^2 + 2)*log(-(a*x + 1)/(a*x - 1)))*sqrt(-a^2*x^2 + 1) + 102*arctan((sqrt(-a^2*x^2 + 1) - 1)/(a*x)))/a^4","A",0
449,0,0,0,0.566483," ","integrate(x^2*(-a^2*x^2+1)^(3/2)*arctanh(a*x),x, algorithm=""fricas"")","{\rm integral}\left(-{\left(a^{2} x^{4} - x^{2}\right)} \sqrt{-a^{2} x^{2} + 1} \operatorname{artanh}\left(a x\right), x\right)"," ",0,"integral(-(a^2*x^4 - x^2)*sqrt(-a^2*x^2 + 1)*arctanh(a*x), x)","F",0
450,1,90,0,0.593901," ","integrate(x*(-a^2*x^2+1)^(3/2)*arctanh(a*x),x, algorithm=""fricas"")","-\frac{{\left(2 \, a^{3} x^{3} - 5 \, a x + 4 \, {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)\right)} \sqrt{-a^{2} x^{2} + 1} + 6 \, \arctan\left(\frac{\sqrt{-a^{2} x^{2} + 1} - 1}{a x}\right)}{40 \, a^{2}}"," ",0,"-1/40*((2*a^3*x^3 - 5*a*x + 4*(a^4*x^4 - 2*a^2*x^2 + 1)*log(-(a*x + 1)/(a*x - 1)))*sqrt(-a^2*x^2 + 1) + 6*arctan((sqrt(-a^2*x^2 + 1) - 1)/(a*x)))/a^2","A",0
451,0,0,0,0.489533," ","integrate((-a^2*x^2+1)^(3/2)*arctanh(a*x),x, algorithm=""fricas"")","{\rm integral}\left(-{\left(a^{2} x^{2} - 1\right)} \sqrt{-a^{2} x^{2} + 1} \operatorname{artanh}\left(a x\right), x\right)"," ",0,"integral(-(a^2*x^2 - 1)*sqrt(-a^2*x^2 + 1)*arctanh(a*x), x)","F",0
452,0,0,0,0.488218," ","integrate((-a^2*x^2+1)^(3/2)*arctanh(a*x)/x,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(a^{2} x^{2} - 1\right)} \sqrt{-a^{2} x^{2} + 1} \operatorname{artanh}\left(a x\right)}{x}, x\right)"," ",0,"integral(-(a^2*x^2 - 1)*sqrt(-a^2*x^2 + 1)*arctanh(a*x)/x, x)","F",0
453,0,0,0,0.473347," ","integrate((-a^2*x^2+1)^(3/2)*arctanh(a*x)/x^2,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(a^{2} x^{2} - 1\right)} \sqrt{-a^{2} x^{2} + 1} \operatorname{artanh}\left(a x\right)}{x^{2}}, x\right)"," ",0,"integral(-(a^2*x^2 - 1)*sqrt(-a^2*x^2 + 1)*arctanh(a*x)/x^2, x)","F",0
454,0,0,0,0.490195," ","integrate((-a^2*x^2+1)^(3/2)*arctanh(a*x)/x^3,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(a^{2} x^{2} - 1\right)} \sqrt{-a^{2} x^{2} + 1} \operatorname{artanh}\left(a x\right)}{x^{3}}, x\right)"," ",0,"integral(-(a^2*x^2 - 1)*sqrt(-a^2*x^2 + 1)*arctanh(a*x)/x^3, x)","F",0
455,0,0,0,0.549238," ","integrate((-a^2*x^2+1)^(3/2)*arctanh(a*x)/x^4,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(a^{2} x^{2} - 1\right)} \sqrt{-a^{2} x^{2} + 1} \operatorname{artanh}\left(a x\right)}{x^{4}}, x\right)"," ",0,"integral(-(a^2*x^2 - 1)*sqrt(-a^2*x^2 + 1)*arctanh(a*x)/x^4, x)","F",0
456,0,0,0,0.503411," ","integrate((-a^2*x^2+1)^(3/2)*arctanh(a*x)/x^5,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(a^{2} x^{2} - 1\right)} \sqrt{-a^{2} x^{2} + 1} \operatorname{artanh}\left(a x\right)}{x^{5}}, x\right)"," ",0,"integral(-(a^2*x^2 - 1)*sqrt(-a^2*x^2 + 1)*arctanh(a*x)/x^5, x)","F",0
457,1,93,0,0.489224," ","integrate((-a^2*x^2+1)^(3/2)*arctanh(a*x)/x^6,x, algorithm=""fricas"")","\frac{3 \, a^{5} x^{5} \log\left(\frac{\sqrt{-a^{2} x^{2} + 1} - 1}{x}\right) + {\left(5 \, a^{3} x^{3} - 2 \, a x - 4 \, {\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)\right)} \sqrt{-a^{2} x^{2} + 1}}{40 \, x^{5}}"," ",0,"1/40*(3*a^5*x^5*log((sqrt(-a^2*x^2 + 1) - 1)/x) + (5*a^3*x^3 - 2*a*x - 4*(a^4*x^4 - 2*a^2*x^2 + 1)*log(-(a*x + 1)/(a*x - 1)))*sqrt(-a^2*x^2 + 1))/x^5","A",0
458,0,0,0,0.491736," ","integrate((-a^2*x^2+1)^(3/2)*arctanh(a*x)/x^7,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(a^{2} x^{2} - 1\right)} \sqrt{-a^{2} x^{2} + 1} \operatorname{artanh}\left(a x\right)}{x^{7}}, x\right)"," ",0,"integral(-(a^2*x^2 - 1)*sqrt(-a^2*x^2 + 1)*arctanh(a*x)/x^7, x)","F",0
459,0,0,0,0.464321," ","integrate((-a^2*x^2+1)^(5/2)*arctanh(a*x),x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \sqrt{-a^{2} x^{2} + 1} \operatorname{artanh}\left(a x\right), x\right)"," ",0,"integral((a^4*x^4 - 2*a^2*x^2 + 1)*sqrt(-a^2*x^2 + 1)*arctanh(a*x), x)","F",0
460,0,0,0,0.410234," ","integrate((-a^2*x^2+1)^(3/2)*arctanh(a*x),x, algorithm=""fricas"")","{\rm integral}\left(-{\left(a^{2} x^{2} - 1\right)} \sqrt{-a^{2} x^{2} + 1} \operatorname{artanh}\left(a x\right), x\right)"," ",0,"integral(-(a^2*x^2 - 1)*sqrt(-a^2*x^2 + 1)*arctanh(a*x), x)","F",0
461,0,0,0,0.457664," ","integrate((-a^2*x^2+1)^(1/2)*arctanh(a*x),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{-a^{2} x^{2} + 1} \operatorname{artanh}\left(a x\right), x\right)"," ",0,"integral(sqrt(-a^2*x^2 + 1)*arctanh(a*x), x)","F",0
462,1,73,0,0.489060," ","integrate(arctanh(a*x)/(-a^2*x^2+1)^(5/2),x, algorithm=""fricas"")","\frac{{\left(12 \, a^{2} x^{2} - 3 \, {\left(2 \, a^{3} x^{3} - 3 \, a x\right)} \log\left(-\frac{a x + 1}{a x - 1}\right) - 14\right)} \sqrt{-a^{2} x^{2} + 1}}{18 \, {\left(a^{5} x^{4} - 2 \, a^{3} x^{2} + a\right)}}"," ",0,"1/18*(12*a^2*x^2 - 3*(2*a^3*x^3 - 3*a*x)*log(-(a*x + 1)/(a*x - 1)) - 14)*sqrt(-a^2*x^2 + 1)/(a^5*x^4 - 2*a^3*x^2 + a)","A",0
463,1,99,0,0.444487," ","integrate(arctanh(a*x)/(-a^2*x^2+1)^(7/2),x, algorithm=""fricas"")","\frac{{\left(240 \, a^{4} x^{4} - 520 \, a^{2} x^{2} - 15 \, {\left(8 \, a^{5} x^{5} - 20 \, a^{3} x^{3} + 15 \, a x\right)} \log\left(-\frac{a x + 1}{a x - 1}\right) + 298\right)} \sqrt{-a^{2} x^{2} + 1}}{450 \, {\left(a^{7} x^{6} - 3 \, a^{5} x^{4} + 3 \, a^{3} x^{2} - a\right)}}"," ",0,"1/450*(240*a^4*x^4 - 520*a^2*x^2 - 15*(8*a^5*x^5 - 20*a^3*x^3 + 15*a*x)*log(-(a*x + 1)/(a*x - 1)) + 298)*sqrt(-a^2*x^2 + 1)/(a^7*x^6 - 3*a^5*x^4 + 3*a^3*x^2 - a)","A",0
464,1,121,0,0.461097," ","integrate(arctanh(a*x)/(-a^2*x^2+1)^(9/2),x, algorithm=""fricas"")","\frac{{\left(3360 \, a^{6} x^{6} - 10640 \, a^{4} x^{4} + 11452 \, a^{2} x^{2} - 105 \, {\left(16 \, a^{7} x^{7} - 56 \, a^{5} x^{5} + 70 \, a^{3} x^{3} - 35 \, a x\right)} \log\left(-\frac{a x + 1}{a x - 1}\right) - 4322\right)} \sqrt{-a^{2} x^{2} + 1}}{7350 \, {\left(a^{9} x^{8} - 4 \, a^{7} x^{6} + 6 \, a^{5} x^{4} - 4 \, a^{3} x^{2} + a\right)}}"," ",0,"1/7350*(3360*a^6*x^6 - 10640*a^4*x^4 + 11452*a^2*x^2 - 105*(16*a^7*x^7 - 56*a^5*x^5 + 70*a^3*x^3 - 35*a*x)*log(-(a*x + 1)/(a*x - 1)) - 4322)*sqrt(-a^2*x^2 + 1)/(a^9*x^8 - 4*a^7*x^6 + 6*a^5*x^4 - 4*a^3*x^2 + a)","A",0
465,0,0,0,0.419230," ","integrate((-a^2*c*x^2+c)^(3/2)*arctanh(a*x),x, algorithm=""fricas"")","{\rm integral}\left(-{\left(a^{2} c x^{2} - c\right)} \sqrt{-a^{2} c x^{2} + c} \operatorname{artanh}\left(a x\right), x\right)"," ",0,"integral(-(a^2*c*x^2 - c)*sqrt(-a^2*c*x^2 + c)*arctanh(a*x), x)","F",0
466,0,0,0,0.432468," ","integrate((-a^2*c*x^2+c)^(1/2)*arctanh(a*x),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{-a^{2} c x^{2} + c} \operatorname{artanh}\left(a x\right), x\right)"," ",0,"integral(sqrt(-a^2*c*x^2 + c)*arctanh(a*x), x)","F",0
467,0,0,0,0.511751," ","integrate(arctanh(a*x)/(-a^2*c*x^2+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-a^{2} c x^{2} + c} \operatorname{artanh}\left(a x\right)}{a^{2} c x^{2} - c}, x\right)"," ",0,"integral(-sqrt(-a^2*c*x^2 + c)*arctanh(a*x)/(a^2*c*x^2 - c), x)","F",0
468,1,54,0,0.515036," ","integrate(arctanh(a*x)/(-a^2*c*x^2+c)^(3/2),x, algorithm=""fricas"")","-\frac{\sqrt{-a^{2} c x^{2} + c} {\left(a x \log\left(-\frac{a x + 1}{a x - 1}\right) - 2\right)}}{2 \, {\left(a^{3} c^{2} x^{2} - a c^{2}\right)}}"," ",0,"-1/2*sqrt(-a^2*c*x^2 + c)*(a*x*log(-(a*x + 1)/(a*x - 1)) - 2)/(a^3*c^2*x^2 - a*c^2)","A",0
469,1,84,0,0.451581," ","integrate(arctanh(a*x)/(-a^2*c*x^2+c)^(5/2),x, algorithm=""fricas"")","\frac{\sqrt{-a^{2} c x^{2} + c} {\left(12 \, a^{2} x^{2} - 3 \, {\left(2 \, a^{3} x^{3} - 3 \, a x\right)} \log\left(-\frac{a x + 1}{a x - 1}\right) - 14\right)}}{18 \, {\left(a^{5} c^{3} x^{4} - 2 \, a^{3} c^{3} x^{2} + a c^{3}\right)}}"," ",0,"1/18*sqrt(-a^2*c*x^2 + c)*(12*a^2*x^2 - 3*(2*a^3*x^3 - 3*a*x)*log(-(a*x + 1)/(a*x - 1)) - 14)/(a^5*c^3*x^4 - 2*a^3*c^3*x^2 + a*c^3)","A",0
470,1,112,0,0.497875," ","integrate(arctanh(a*x)/(-a^2*c*x^2+c)^(7/2),x, algorithm=""fricas"")","\frac{{\left(240 \, a^{4} x^{4} - 520 \, a^{2} x^{2} - 15 \, {\left(8 \, a^{5} x^{5} - 20 \, a^{3} x^{3} + 15 \, a x\right)} \log\left(-\frac{a x + 1}{a x - 1}\right) + 298\right)} \sqrt{-a^{2} c x^{2} + c}}{450 \, {\left(a^{7} c^{4} x^{6} - 3 \, a^{5} c^{4} x^{4} + 3 \, a^{3} c^{4} x^{2} - a c^{4}\right)}}"," ",0,"1/450*(240*a^4*x^4 - 520*a^2*x^2 - 15*(8*a^5*x^5 - 20*a^3*x^3 + 15*a*x)*log(-(a*x + 1)/(a*x - 1)) + 298)*sqrt(-a^2*c*x^2 + c)/(a^7*c^4*x^6 - 3*a^5*c^4*x^4 + 3*a^3*c^4*x^2 - a*c^4)","A",0
471,0,0,0,0.429055," ","integrate((-a^2*x^2+1)^(1/2)*arctanh(a*x)^2,x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{-a^{2} x^{2} + 1} \operatorname{artanh}\left(a x\right)^{2}, x\right)"," ",0,"integral(sqrt(-a^2*x^2 + 1)*arctanh(a*x)^2, x)","F",0
472,1,105,0,0.514781," ","integrate(arctanh(a*x)^2/(-a^2*x^2+1)^(5/2),x, algorithm=""fricas"")","-\frac{{\left(160 \, a^{3} x^{3} + 9 \, {\left(2 \, a^{3} x^{3} - 3 \, a x\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)^{2} - 168 \, a x - 12 \, {\left(6 \, a^{2} x^{2} - 7\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)\right)} \sqrt{-a^{2} x^{2} + 1}}{108 \, {\left(a^{5} x^{4} - 2 \, a^{3} x^{2} + a\right)}}"," ",0,"-1/108*(160*a^3*x^3 + 9*(2*a^3*x^3 - 3*a*x)*log(-(a*x + 1)/(a*x - 1))^2 - 168*a*x - 12*(6*a^2*x^2 - 7)*log(-(a*x + 1)/(a*x - 1)))*sqrt(-a^2*x^2 + 1)/(a^5*x^4 - 2*a^3*x^2 + a)","A",0
473,1,139,0,0.495893," ","integrate(arctanh(a*x)^2/(-a^2*x^2+1)^(7/2),x, algorithm=""fricas"")","-\frac{{\left(16576 \, a^{5} x^{5} - 34240 \, a^{3} x^{3} + 225 \, {\left(8 \, a^{5} x^{5} - 20 \, a^{3} x^{3} + 15 \, a x\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)^{2} + 17880 \, a x - 60 \, {\left(120 \, a^{4} x^{4} - 260 \, a^{2} x^{2} + 149\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)\right)} \sqrt{-a^{2} x^{2} + 1}}{13500 \, {\left(a^{7} x^{6} - 3 \, a^{5} x^{4} + 3 \, a^{3} x^{2} - a\right)}}"," ",0,"-1/13500*(16576*a^5*x^5 - 34240*a^3*x^3 + 225*(8*a^5*x^5 - 20*a^3*x^3 + 15*a*x)*log(-(a*x + 1)/(a*x - 1))^2 + 17880*a*x - 60*(120*a^4*x^4 - 260*a^2*x^2 + 149)*log(-(a*x + 1)/(a*x - 1)))*sqrt(-a^2*x^2 + 1)/(a^7*x^6 - 3*a^5*x^4 + 3*a^3*x^2 - a)","A",0
474,1,169,0,0.589634," ","integrate(arctanh(a*x)^2/(-a^2*x^2+1)^(9/2),x, algorithm=""fricas"")","-\frac{{\left(1653248 \, a^{7} x^{7} - 5080768 \, a^{5} x^{5} + 5233760 \, a^{3} x^{3} + 11025 \, {\left(16 \, a^{7} x^{7} - 56 \, a^{5} x^{5} + 70 \, a^{3} x^{3} - 35 \, a x\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)^{2} - 1815240 \, a x - 420 \, {\left(1680 \, a^{6} x^{6} - 5320 \, a^{4} x^{4} + 5726 \, a^{2} x^{2} - 2161\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)\right)} \sqrt{-a^{2} x^{2} + 1}}{1543500 \, {\left(a^{9} x^{8} - 4 \, a^{7} x^{6} + 6 \, a^{5} x^{4} - 4 \, a^{3} x^{2} + a\right)}}"," ",0,"-1/1543500*(1653248*a^7*x^7 - 5080768*a^5*x^5 + 5233760*a^3*x^3 + 11025*(16*a^7*x^7 - 56*a^5*x^5 + 70*a^3*x^3 - 35*a*x)*log(-(a*x + 1)/(a*x - 1))^2 - 1815240*a*x - 420*(1680*a^6*x^6 - 5320*a^4*x^4 + 5726*a^2*x^2 - 2161)*log(-(a*x + 1)/(a*x - 1)))*sqrt(-a^2*x^2 + 1)/(a^9*x^8 - 4*a^7*x^6 + 6*a^5*x^4 - 4*a^3*x^2 + a)","A",0
475,0,0,0,0.589625," ","integrate((-a^2*x^2+1)^(1/2)*arctanh(a*x)^3,x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{-a^{2} x^{2} + 1} \operatorname{artanh}\left(a x\right)^{3}, x\right)"," ",0,"integral(sqrt(-a^2*x^2 + 1)*arctanh(a*x)^3, x)","F",0
476,1,134,0,0.463170," ","integrate(arctanh(a*x)^3/(-a^2*x^2+1)^(5/2),x, algorithm=""fricas"")","\frac{{\left(960 \, a^{2} x^{2} - 9 \, {\left(2 \, a^{3} x^{3} - 3 \, a x\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)^{3} + 18 \, {\left(6 \, a^{2} x^{2} - 7\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)^{2} - 24 \, {\left(20 \, a^{3} x^{3} - 21 \, a x\right)} \log\left(-\frac{a x + 1}{a x - 1}\right) - 976\right)} \sqrt{-a^{2} x^{2} + 1}}{216 \, {\left(a^{5} x^{4} - 2 \, a^{3} x^{2} + a\right)}}"," ",0,"1/216*(960*a^2*x^2 - 9*(2*a^3*x^3 - 3*a*x)*log(-(a*x + 1)/(a*x - 1))^3 + 18*(6*a^2*x^2 - 7)*log(-(a*x + 1)/(a*x - 1))^2 - 24*(20*a^3*x^3 - 21*a*x)*log(-(a*x + 1)/(a*x - 1)) - 976)*sqrt(-a^2*x^2 + 1)/(a^5*x^4 - 2*a^3*x^2 + a)","A",0
477,1,176,0,0.473022," ","integrate(arctanh(a*x)^3/(-a^2*x^2+1)^(7/2),x, algorithm=""fricas"")","\frac{{\left(497280 \, a^{4} x^{4} - 1005440 \, a^{2} x^{2} - 1125 \, {\left(8 \, a^{5} x^{5} - 20 \, a^{3} x^{3} + 15 \, a x\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)^{3} + 450 \, {\left(120 \, a^{4} x^{4} - 260 \, a^{2} x^{2} + 149\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)^{2} - 120 \, {\left(2072 \, a^{5} x^{5} - 4280 \, a^{3} x^{3} + 2235 \, a x\right)} \log\left(-\frac{a x + 1}{a x - 1}\right) + 509456\right)} \sqrt{-a^{2} x^{2} + 1}}{135000 \, {\left(a^{7} x^{6} - 3 \, a^{5} x^{4} + 3 \, a^{3} x^{2} - a\right)}}"," ",0,"1/135000*(497280*a^4*x^4 - 1005440*a^2*x^2 - 1125*(8*a^5*x^5 - 20*a^3*x^3 + 15*a*x)*log(-(a*x + 1)/(a*x - 1))^3 + 450*(120*a^4*x^4 - 260*a^2*x^2 + 149)*log(-(a*x + 1)/(a*x - 1))^2 - 120*(2072*a^5*x^5 - 4280*a^3*x^3 + 2235*a*x)*log(-(a*x + 1)/(a*x - 1)) + 509456)*sqrt(-a^2*x^2 + 1)/(a^7*x^6 - 3*a^5*x^4 + 3*a^3*x^2 - a)","A",0
478,1,214,0,0.520333," ","integrate(arctanh(a*x)^3/(-a^2*x^2+1)^(9/2),x, algorithm=""fricas"")","\frac{{\left(347182080 \, a^{6} x^{6} - 1050017920 \, a^{4} x^{4} + 1059832256 \, a^{2} x^{2} - 385875 \, {\left(16 \, a^{7} x^{7} - 56 \, a^{5} x^{5} + 70 \, a^{3} x^{3} - 35 \, a x\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)^{3} + 22050 \, {\left(1680 \, a^{6} x^{6} - 5320 \, a^{4} x^{4} + 5726 \, a^{2} x^{2} - 2161\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)^{2} - 840 \, {\left(206656 \, a^{7} x^{7} - 635096 \, a^{5} x^{5} + 654220 \, a^{3} x^{3} - 226905 \, a x\right)} \log\left(-\frac{a x + 1}{a x - 1}\right) - 357266416\right)} \sqrt{-a^{2} x^{2} + 1}}{108045000 \, {\left(a^{9} x^{8} - 4 \, a^{7} x^{6} + 6 \, a^{5} x^{4} - 4 \, a^{3} x^{2} + a\right)}}"," ",0,"1/108045000*(347182080*a^6*x^6 - 1050017920*a^4*x^4 + 1059832256*a^2*x^2 - 385875*(16*a^7*x^7 - 56*a^5*x^5 + 70*a^3*x^3 - 35*a*x)*log(-(a*x + 1)/(a*x - 1))^3 + 22050*(1680*a^6*x^6 - 5320*a^4*x^4 + 5726*a^2*x^2 - 2161)*log(-(a*x + 1)/(a*x - 1))^2 - 840*(206656*a^7*x^7 - 635096*a^5*x^5 + 654220*a^3*x^3 - 226905*a*x)*log(-(a*x + 1)/(a*x - 1)) - 357266416)*sqrt(-a^2*x^2 + 1)/(a^9*x^8 - 4*a^7*x^6 + 6*a^5*x^4 - 4*a^3*x^2 + a)","A",0
479,0,0,0,0.453195," ","integrate((-a^2*x^2+1)^(1/2)/arctanh(a*x),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-a^{2} x^{2} + 1}}{\operatorname{artanh}\left(a x\right)}, x\right)"," ",0,"integral(sqrt(-a^2*x^2 + 1)/arctanh(a*x), x)","F",0
480,0,0,0,0.581792," ","integrate(1/(-a^2*x^2+1)^(1/2)/arctanh(a*x),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-a^{2} x^{2} + 1}}{{\left(a^{2} x^{2} - 1\right)} \operatorname{artanh}\left(a x\right)}, x\right)"," ",0,"integral(-sqrt(-a^2*x^2 + 1)/((a^2*x^2 - 1)*arctanh(a*x)), x)","F",0
481,0,0,0,0.629808," ","integrate(1/(-a^2*x^2+1)^(3/2)/arctanh(a*x),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-a^{2} x^{2} + 1}}{{\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \operatorname{artanh}\left(a x\right)}, x\right)"," ",0,"integral(sqrt(-a^2*x^2 + 1)/((a^4*x^4 - 2*a^2*x^2 + 1)*arctanh(a*x)), x)","F",0
482,0,0,0,0.559128," ","integrate(1/(-a^2*x^2+1)^(5/2)/arctanh(a*x),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-a^{2} x^{2} + 1}}{{\left(a^{6} x^{6} - 3 \, a^{4} x^{4} + 3 \, a^{2} x^{2} - 1\right)} \operatorname{artanh}\left(a x\right)}, x\right)"," ",0,"integral(-sqrt(-a^2*x^2 + 1)/((a^6*x^6 - 3*a^4*x^4 + 3*a^2*x^2 - 1)*arctanh(a*x)), x)","F",0
483,0,0,0,0.440953," ","integrate(1/(-a^2*x^2+1)^(7/2)/arctanh(a*x),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-a^{2} x^{2} + 1}}{{\left(a^{8} x^{8} - 4 \, a^{6} x^{6} + 6 \, a^{4} x^{4} - 4 \, a^{2} x^{2} + 1\right)} \operatorname{artanh}\left(a x\right)}, x\right)"," ",0,"integral(sqrt(-a^2*x^2 + 1)/((a^8*x^8 - 4*a^6*x^6 + 6*a^4*x^4 - 4*a^2*x^2 + 1)*arctanh(a*x)), x)","F",0
484,0,0,0,0.485902," ","integrate(1/(-a^2*x^2+1)^(9/2)/arctanh(a*x),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-a^{2} x^{2} + 1}}{{\left(a^{10} x^{10} - 5 \, a^{8} x^{8} + 10 \, a^{6} x^{6} - 10 \, a^{4} x^{4} + 5 \, a^{2} x^{2} - 1\right)} \operatorname{artanh}\left(a x\right)}, x\right)"," ",0,"integral(-sqrt(-a^2*x^2 + 1)/((a^10*x^10 - 5*a^8*x^8 + 10*a^6*x^6 - 10*a^4*x^4 + 5*a^2*x^2 - 1)*arctanh(a*x)), x)","F",0
485,0,0,0,0.580558," ","integrate((-a^2*x^2+1)^(1/2)/arctanh(a*x)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-a^{2} x^{2} + 1}}{\operatorname{artanh}\left(a x\right)^{2}}, x\right)"," ",0,"integral(sqrt(-a^2*x^2 + 1)/arctanh(a*x)^2, x)","F",0
486,0,0,0,0.682841," ","integrate(1/(-a^2*x^2+1)^(1/2)/arctanh(a*x)^2,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-a^{2} x^{2} + 1}}{{\left(a^{2} x^{2} - 1\right)} \operatorname{artanh}\left(a x\right)^{2}}, x\right)"," ",0,"integral(-sqrt(-a^2*x^2 + 1)/((a^2*x^2 - 1)*arctanh(a*x)^2), x)","F",0
487,0,0,0,0.590770," ","integrate(1/(-a^2*x^2+1)^(3/2)/arctanh(a*x)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-a^{2} x^{2} + 1}}{{\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \operatorname{artanh}\left(a x\right)^{2}}, x\right)"," ",0,"integral(sqrt(-a^2*x^2 + 1)/((a^4*x^4 - 2*a^2*x^2 + 1)*arctanh(a*x)^2), x)","F",0
488,0,0,0,0.540669," ","integrate(1/(-a^2*x^2+1)^(5/2)/arctanh(a*x)^2,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-a^{2} x^{2} + 1}}{{\left(a^{6} x^{6} - 3 \, a^{4} x^{4} + 3 \, a^{2} x^{2} - 1\right)} \operatorname{artanh}\left(a x\right)^{2}}, x\right)"," ",0,"integral(-sqrt(-a^2*x^2 + 1)/((a^6*x^6 - 3*a^4*x^4 + 3*a^2*x^2 - 1)*arctanh(a*x)^2), x)","F",0
489,0,0,0,0.433782," ","integrate(1/(-a^2*x^2+1)^(7/2)/arctanh(a*x)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-a^{2} x^{2} + 1}}{{\left(a^{8} x^{8} - 4 \, a^{6} x^{6} + 6 \, a^{4} x^{4} - 4 \, a^{2} x^{2} + 1\right)} \operatorname{artanh}\left(a x\right)^{2}}, x\right)"," ",0,"integral(sqrt(-a^2*x^2 + 1)/((a^8*x^8 - 4*a^6*x^6 + 6*a^4*x^4 - 4*a^2*x^2 + 1)*arctanh(a*x)^2), x)","F",0
490,0,0,0,0.710716," ","integrate(1/(-a^2*x^2+1)^(9/2)/arctanh(a*x)^2,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-a^{2} x^{2} + 1}}{{\left(a^{10} x^{10} - 5 \, a^{8} x^{8} + 10 \, a^{6} x^{6} - 10 \, a^{4} x^{4} + 5 \, a^{2} x^{2} - 1\right)} \operatorname{artanh}\left(a x\right)^{2}}, x\right)"," ",0,"integral(-sqrt(-a^2*x^2 + 1)/((a^10*x^10 - 5*a^8*x^8 + 10*a^6*x^6 - 10*a^4*x^4 + 5*a^2*x^2 - 1)*arctanh(a*x)^2), x)","F",0
491,0,0,0,0.569807," ","integrate((-a^2*x^2+1)^(1/2)/arctanh(a*x)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-a^{2} x^{2} + 1}}{\operatorname{artanh}\left(a x\right)^{3}}, x\right)"," ",0,"integral(sqrt(-a^2*x^2 + 1)/arctanh(a*x)^3, x)","F",0
492,0,0,0,0.427521," ","integrate(1/(-a^2*x^2+1)^(1/2)/arctanh(a*x)^3,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-a^{2} x^{2} + 1}}{{\left(a^{2} x^{2} - 1\right)} \operatorname{artanh}\left(a x\right)^{3}}, x\right)"," ",0,"integral(-sqrt(-a^2*x^2 + 1)/((a^2*x^2 - 1)*arctanh(a*x)^3), x)","F",0
493,0,0,0,0.533064," ","integrate(1/(-a^2*x^2+1)^(3/2)/arctanh(a*x)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-a^{2} x^{2} + 1}}{{\left(a^{4} x^{4} - 2 \, a^{2} x^{2} + 1\right)} \operatorname{artanh}\left(a x\right)^{3}}, x\right)"," ",0,"integral(sqrt(-a^2*x^2 + 1)/((a^4*x^4 - 2*a^2*x^2 + 1)*arctanh(a*x)^3), x)","F",0
494,0,0,0,0.477421," ","integrate(1/(-a^2*x^2+1)^(5/2)/arctanh(a*x)^3,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-a^{2} x^{2} + 1}}{{\left(a^{6} x^{6} - 3 \, a^{4} x^{4} + 3 \, a^{2} x^{2} - 1\right)} \operatorname{artanh}\left(a x\right)^{3}}, x\right)"," ",0,"integral(-sqrt(-a^2*x^2 + 1)/((a^6*x^6 - 3*a^4*x^4 + 3*a^2*x^2 - 1)*arctanh(a*x)^3), x)","F",0
495,0,0,0,0.588045," ","integrate(1/(-a^2*x^2+1)^(7/2)/arctanh(a*x)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-a^{2} x^{2} + 1}}{{\left(a^{8} x^{8} - 4 \, a^{6} x^{6} + 6 \, a^{4} x^{4} - 4 \, a^{2} x^{2} + 1\right)} \operatorname{artanh}\left(a x\right)^{3}}, x\right)"," ",0,"integral(sqrt(-a^2*x^2 + 1)/((a^8*x^8 - 4*a^6*x^6 + 6*a^4*x^4 - 4*a^2*x^2 + 1)*arctanh(a*x)^3), x)","F",0
496,0,0,0,0.605856," ","integrate(1/(-a^2*x^2+1)^(9/2)/arctanh(a*x)^3,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-a^{2} x^{2} + 1}}{{\left(a^{10} x^{10} - 5 \, a^{8} x^{8} + 10 \, a^{6} x^{6} - 10 \, a^{4} x^{4} + 5 \, a^{2} x^{2} - 1\right)} \operatorname{artanh}\left(a x\right)^{3}}, x\right)"," ",0,"integral(-sqrt(-a^2*x^2 + 1)/((a^10*x^10 - 5*a^8*x^8 + 10*a^6*x^6 - 10*a^4*x^4 + 5*a^2*x^2 - 1)*arctanh(a*x)^3), x)","F",0
497,0,0,0,0.695647," ","integrate((e*x+d)*(a+b*arctanh(c*x))^2/(-c^2*x^2+1),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{a^{2} e x + a^{2} d + {\left(b^{2} e x + b^{2} d\right)} \operatorname{artanh}\left(c x\right)^{2} + 2 \, {\left(a b e x + a b d\right)} \operatorname{artanh}\left(c x\right)}{c^{2} x^{2} - 1}, x\right)"," ",0,"integral(-(a^2*e*x + a^2*d + (b^2*e*x + b^2*d)*arctanh(c*x)^2 + 2*(a*b*e*x + a*b*d)*arctanh(c*x))/(c^2*x^2 - 1), x)","F",0
498,1,248,0,0.491604," ","integrate((d*x^2+c)^4*arctanh(a*x),x, algorithm=""fricas"")","\frac{105 \, a^{8} d^{4} x^{8} + 20 \, {\left(36 \, a^{8} c d^{3} + 7 \, a^{6} d^{4}\right)} x^{6} + 6 \, {\left(378 \, a^{8} c^{2} d^{2} + 180 \, a^{6} c d^{3} + 35 \, a^{4} d^{4}\right)} x^{4} + 12 \, {\left(420 \, a^{8} c^{3} d + 378 \, a^{6} c^{2} d^{2} + 180 \, a^{4} c d^{3} + 35 \, a^{2} d^{4}\right)} x^{2} + 12 \, {\left(315 \, a^{8} c^{4} + 420 \, a^{6} c^{3} d + 378 \, a^{4} c^{2} d^{2} + 180 \, a^{2} c d^{3} + 35 \, d^{4}\right)} \log\left(a^{2} x^{2} - 1\right) + 12 \, {\left(35 \, a^{9} d^{4} x^{9} + 180 \, a^{9} c d^{3} x^{7} + 378 \, a^{9} c^{2} d^{2} x^{5} + 420 \, a^{9} c^{3} d x^{3} + 315 \, a^{9} c^{4} x\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)}{7560 \, a^{9}}"," ",0,"1/7560*(105*a^8*d^4*x^8 + 20*(36*a^8*c*d^3 + 7*a^6*d^4)*x^6 + 6*(378*a^8*c^2*d^2 + 180*a^6*c*d^3 + 35*a^4*d^4)*x^4 + 12*(420*a^8*c^3*d + 378*a^6*c^2*d^2 + 180*a^4*c*d^3 + 35*a^2*d^4)*x^2 + 12*(315*a^8*c^4 + 420*a^6*c^3*d + 378*a^4*c^2*d^2 + 180*a^2*c*d^3 + 35*d^4)*log(a^2*x^2 - 1) + 12*(35*a^9*d^4*x^9 + 180*a^9*c*d^3*x^7 + 378*a^9*c^2*d^2*x^5 + 420*a^9*c^3*d*x^3 + 315*a^9*c^4*x)*log(-(a*x + 1)/(a*x - 1)))/a^9","A",0
499,1,178,0,0.521265," ","integrate((d*x^2+c)^3*arctanh(a*x),x, algorithm=""fricas"")","\frac{10 \, a^{6} d^{3} x^{6} + 3 \, {\left(21 \, a^{6} c d^{2} + 5 \, a^{4} d^{3}\right)} x^{4} + 6 \, {\left(35 \, a^{6} c^{2} d + 21 \, a^{4} c d^{2} + 5 \, a^{2} d^{3}\right)} x^{2} + 6 \, {\left(35 \, a^{6} c^{3} + 35 \, a^{4} c^{2} d + 21 \, a^{2} c d^{2} + 5 \, d^{3}\right)} \log\left(a^{2} x^{2} - 1\right) + 6 \, {\left(5 \, a^{7} d^{3} x^{7} + 21 \, a^{7} c d^{2} x^{5} + 35 \, a^{7} c^{2} d x^{3} + 35 \, a^{7} c^{3} x\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)}{420 \, a^{7}}"," ",0,"1/420*(10*a^6*d^3*x^6 + 3*(21*a^6*c*d^2 + 5*a^4*d^3)*x^4 + 6*(35*a^6*c^2*d + 21*a^4*c*d^2 + 5*a^2*d^3)*x^2 + 6*(35*a^6*c^3 + 35*a^4*c^2*d + 21*a^2*c*d^2 + 5*d^3)*log(a^2*x^2 - 1) + 6*(5*a^7*d^3*x^7 + 21*a^7*c*d^2*x^5 + 35*a^7*c^2*d*x^3 + 35*a^7*c^3*x)*log(-(a*x + 1)/(a*x - 1)))/a^7","A",0
500,1,119,0,0.490576," ","integrate((d*x^2+c)^2*arctanh(a*x),x, algorithm=""fricas"")","\frac{3 \, a^{4} d^{2} x^{4} + 2 \, {\left(10 \, a^{4} c d + 3 \, a^{2} d^{2}\right)} x^{2} + 2 \, {\left(15 \, a^{4} c^{2} + 10 \, a^{2} c d + 3 \, d^{2}\right)} \log\left(a^{2} x^{2} - 1\right) + 2 \, {\left(3 \, a^{5} d^{2} x^{5} + 10 \, a^{5} c d x^{3} + 15 \, a^{5} c^{2} x\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)}{60 \, a^{5}}"," ",0,"1/60*(3*a^4*d^2*x^4 + 2*(10*a^4*c*d + 3*a^2*d^2)*x^2 + 2*(15*a^4*c^2 + 10*a^2*c*d + 3*d^2)*log(a^2*x^2 - 1) + 2*(3*a^5*d^2*x^5 + 10*a^5*c*d*x^3 + 15*a^5*c^2*x)*log(-(a*x + 1)/(a*x - 1)))/a^5","A",0
501,1,65,0,0.503225," ","integrate((d*x^2+c)*arctanh(a*x),x, algorithm=""fricas"")","\frac{a^{2} d x^{2} + {\left(3 \, a^{2} c + d\right)} \log\left(a^{2} x^{2} - 1\right) + {\left(a^{3} d x^{3} + 3 \, a^{3} c x\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)}{6 \, a^{3}}"," ",0,"1/6*(a^2*d*x^2 + (3*a^2*c + d)*log(a^2*x^2 - 1) + (a^3*d*x^3 + 3*a^3*c*x)*log(-(a*x + 1)/(a*x - 1)))/a^3","A",0
502,0,0,0,0.578319," ","integrate(arctanh(a*x)/(d*x^2+c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{artanh}\left(a x\right)}{d x^{2} + c}, x\right)"," ",0,"integral(arctanh(a*x)/(d*x^2 + c), x)","F",0
503,0,0,0,0.605524," ","integrate(arctanh(a*x)/(d*x^2+c)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{artanh}\left(a x\right)}{d^{2} x^{4} + 2 \, c d x^{2} + c^{2}}, x\right)"," ",0,"integral(arctanh(a*x)/(d^2*x^4 + 2*c*d*x^2 + c^2), x)","F",0
504,0,0,0,0.601916," ","integrate(arctanh(a*x)/(d*x^2+c)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{artanh}\left(a x\right)}{d^{3} x^{6} + 3 \, c d^{2} x^{4} + 3 \, c^{2} d x^{2} + c^{3}}, x\right)"," ",0,"integral(arctanh(a*x)/(d^3*x^6 + 3*c*d^2*x^4 + 3*c^2*d*x^2 + c^3), x)","F",0
505,1,22,0,0.487978," ","integrate(1/(-a*x^2+a)/(b-2*b*arctanh(x)),x, algorithm=""fricas"")","-\frac{\log\left(\log\left(-\frac{x + 1}{x - 1}\right) - 1\right)}{2 \, a b}"," ",0,"-1/2*log(log(-(x + 1)/(x - 1)) - 1)/(a*b)","A",0
506,0,0,0,0.471911," ","integrate(arctanh(b*x)/(-x^2+1),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\operatorname{artanh}\left(b x\right)}{x^{2} - 1}, x\right)"," ",0,"integral(-arctanh(b*x)/(x^2 - 1), x)","F",0
507,0,0,0,0.651891," ","integrate(arctanh(b*x+a)/(-x^2+1),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\operatorname{artanh}\left(b x + a\right)}{x^{2} - 1}, x\right)"," ",0,"integral(-arctanh(b*x + a)/(x^2 - 1), x)","F",0
508,0,0,0,0.549163," ","integrate(arctanh(x)/(b*x+a),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{artanh}\left(x\right)}{b x + a}, x\right)"," ",0,"integral(arctanh(x)/(b*x + a), x)","F",0
509,0,0,0,0.421141," ","integrate(arctanh(x)/(b*x^2+a),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{artanh}\left(x\right)}{b x^{2} + a}, x\right)"," ",0,"integral(arctanh(x)/(b*x^2 + a), x)","F",0
510,0,0,0,0.878319," ","integrate(arctanh(x)/(c*x^2+b*x+a),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{artanh}\left(x\right)}{c x^{2} + b x + a}, x\right)"," ",0,"integral(arctanh(x)/(c*x^2 + b*x + a), x)","F",0
511,0,0,0,0.455602," ","integrate((d*x^2+c)^(1/2)*arctanh(a*x),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{d x^{2} + c} \operatorname{artanh}\left(a x\right), x\right)"," ",0,"integral(sqrt(d*x^2 + c)*arctanh(a*x), x)","F",0
512,0,0,0,0.481562," ","integrate(arctanh(a*x)/(d*x^2+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{artanh}\left(a x\right)}{\sqrt{d x^{2} + c}}, x\right)"," ",0,"integral(arctanh(a*x)/sqrt(d*x^2 + c), x)","F",0
513,1,356,0,0.817931," ","integrate(arctanh(a*x)/(d*x^2+c)^(3/2),x, algorithm=""fricas"")","\left[\frac{2 \, {\left(a^{2} c + d\right)} \sqrt{d x^{2} + c} x \log\left(-\frac{a x + 1}{a x - 1}\right) + \sqrt{a^{2} c + d} {\left(d x^{2} + c\right)} \log\left(\frac{a^{4} d^{2} x^{4} + 8 \, a^{4} c^{2} + 8 \, a^{2} c d + 2 \, {\left(4 \, a^{4} c d + 3 \, a^{2} d^{2}\right)} x^{2} - 4 \, {\left(a^{3} d x^{2} + 2 \, a^{3} c + a d\right)} \sqrt{a^{2} c + d} \sqrt{d x^{2} + c} + d^{2}}{a^{4} x^{4} - 2 \, a^{2} x^{2} + 1}\right)}{4 \, {\left(a^{2} c^{3} + c^{2} d + {\left(a^{2} c^{2} d + c d^{2}\right)} x^{2}\right)}}, \frac{{\left(a^{2} c + d\right)} \sqrt{d x^{2} + c} x \log\left(-\frac{a x + 1}{a x - 1}\right) + \sqrt{-a^{2} c - d} {\left(d x^{2} + c\right)} \arctan\left(\frac{{\left(a^{2} d x^{2} + 2 \, a^{2} c + d\right)} \sqrt{-a^{2} c - d} \sqrt{d x^{2} + c}}{2 \, {\left(a^{3} c^{2} + a c d + {\left(a^{3} c d + a d^{2}\right)} x^{2}\right)}}\right)}{2 \, {\left(a^{2} c^{3} + c^{2} d + {\left(a^{2} c^{2} d + c d^{2}\right)} x^{2}\right)}}\right]"," ",0,"[1/4*(2*(a^2*c + d)*sqrt(d*x^2 + c)*x*log(-(a*x + 1)/(a*x - 1)) + sqrt(a^2*c + d)*(d*x^2 + c)*log((a^4*d^2*x^4 + 8*a^4*c^2 + 8*a^2*c*d + 2*(4*a^4*c*d + 3*a^2*d^2)*x^2 - 4*(a^3*d*x^2 + 2*a^3*c + a*d)*sqrt(a^2*c + d)*sqrt(d*x^2 + c) + d^2)/(a^4*x^4 - 2*a^2*x^2 + 1)))/(a^2*c^3 + c^2*d + (a^2*c^2*d + c*d^2)*x^2), 1/2*((a^2*c + d)*sqrt(d*x^2 + c)*x*log(-(a*x + 1)/(a*x - 1)) + sqrt(-a^2*c - d)*(d*x^2 + c)*arctan(1/2*(a^2*d*x^2 + 2*a^2*c + d)*sqrt(-a^2*c - d)*sqrt(d*x^2 + c)/(a^3*c^2 + a*c*d + (a^3*c*d + a*d^2)*x^2)))/(a^2*c^3 + c^2*d + (a^2*c^2*d + c*d^2)*x^2)]","B",0
514,1,730,0,0.602652," ","integrate(arctanh(a*x)/(d*x^2+c)^(5/2),x, algorithm=""fricas"")","\left[\frac{{\left(3 \, a^{2} c^{3} + {\left(3 \, a^{2} c d^{2} + 2 \, d^{3}\right)} x^{4} + 2 \, c^{2} d + 2 \, {\left(3 \, a^{2} c^{2} d + 2 \, c d^{2}\right)} x^{2}\right)} \sqrt{a^{2} c + d} \log\left(\frac{a^{4} d^{2} x^{4} + 8 \, a^{4} c^{2} + 8 \, a^{2} c d + 2 \, {\left(4 \, a^{4} c d + 3 \, a^{2} d^{2}\right)} x^{2} - 4 \, {\left(a^{3} d x^{2} + 2 \, a^{3} c + a d\right)} \sqrt{a^{2} c + d} \sqrt{d x^{2} + c} + d^{2}}{a^{4} x^{4} - 2 \, a^{2} x^{2} + 1}\right) + 2 \, {\left(2 \, a^{3} c^{3} + 2 \, a c^{2} d + 2 \, {\left(a^{3} c^{2} d + a c d^{2}\right)} x^{2} + {\left(2 \, {\left(a^{4} c^{2} d + 2 \, a^{2} c d^{2} + d^{3}\right)} x^{3} + 3 \, {\left(a^{4} c^{3} + 2 \, a^{2} c^{2} d + c d^{2}\right)} x\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)\right)} \sqrt{d x^{2} + c}}{12 \, {\left(a^{4} c^{6} + 2 \, a^{2} c^{5} d + c^{4} d^{2} + {\left(a^{4} c^{4} d^{2} + 2 \, a^{2} c^{3} d^{3} + c^{2} d^{4}\right)} x^{4} + 2 \, {\left(a^{4} c^{5} d + 2 \, a^{2} c^{4} d^{2} + c^{3} d^{3}\right)} x^{2}\right)}}, \frac{{\left(3 \, a^{2} c^{3} + {\left(3 \, a^{2} c d^{2} + 2 \, d^{3}\right)} x^{4} + 2 \, c^{2} d + 2 \, {\left(3 \, a^{2} c^{2} d + 2 \, c d^{2}\right)} x^{2}\right)} \sqrt{-a^{2} c - d} \arctan\left(\frac{{\left(a^{2} d x^{2} + 2 \, a^{2} c + d\right)} \sqrt{-a^{2} c - d} \sqrt{d x^{2} + c}}{2 \, {\left(a^{3} c^{2} + a c d + {\left(a^{3} c d + a d^{2}\right)} x^{2}\right)}}\right) + {\left(2 \, a^{3} c^{3} + 2 \, a c^{2} d + 2 \, {\left(a^{3} c^{2} d + a c d^{2}\right)} x^{2} + {\left(2 \, {\left(a^{4} c^{2} d + 2 \, a^{2} c d^{2} + d^{3}\right)} x^{3} + 3 \, {\left(a^{4} c^{3} + 2 \, a^{2} c^{2} d + c d^{2}\right)} x\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)\right)} \sqrt{d x^{2} + c}}{6 \, {\left(a^{4} c^{6} + 2 \, a^{2} c^{5} d + c^{4} d^{2} + {\left(a^{4} c^{4} d^{2} + 2 \, a^{2} c^{3} d^{3} + c^{2} d^{4}\right)} x^{4} + 2 \, {\left(a^{4} c^{5} d + 2 \, a^{2} c^{4} d^{2} + c^{3} d^{3}\right)} x^{2}\right)}}\right]"," ",0,"[1/12*((3*a^2*c^3 + (3*a^2*c*d^2 + 2*d^3)*x^4 + 2*c^2*d + 2*(3*a^2*c^2*d + 2*c*d^2)*x^2)*sqrt(a^2*c + d)*log((a^4*d^2*x^4 + 8*a^4*c^2 + 8*a^2*c*d + 2*(4*a^4*c*d + 3*a^2*d^2)*x^2 - 4*(a^3*d*x^2 + 2*a^3*c + a*d)*sqrt(a^2*c + d)*sqrt(d*x^2 + c) + d^2)/(a^4*x^4 - 2*a^2*x^2 + 1)) + 2*(2*a^3*c^3 + 2*a*c^2*d + 2*(a^3*c^2*d + a*c*d^2)*x^2 + (2*(a^4*c^2*d + 2*a^2*c*d^2 + d^3)*x^3 + 3*(a^4*c^3 + 2*a^2*c^2*d + c*d^2)*x)*log(-(a*x + 1)/(a*x - 1)))*sqrt(d*x^2 + c))/(a^4*c^6 + 2*a^2*c^5*d + c^4*d^2 + (a^4*c^4*d^2 + 2*a^2*c^3*d^3 + c^2*d^4)*x^4 + 2*(a^4*c^5*d + 2*a^2*c^4*d^2 + c^3*d^3)*x^2), 1/6*((3*a^2*c^3 + (3*a^2*c*d^2 + 2*d^3)*x^4 + 2*c^2*d + 2*(3*a^2*c^2*d + 2*c*d^2)*x^2)*sqrt(-a^2*c - d)*arctan(1/2*(a^2*d*x^2 + 2*a^2*c + d)*sqrt(-a^2*c - d)*sqrt(d*x^2 + c)/(a^3*c^2 + a*c*d + (a^3*c*d + a*d^2)*x^2)) + (2*a^3*c^3 + 2*a*c^2*d + 2*(a^3*c^2*d + a*c*d^2)*x^2 + (2*(a^4*c^2*d + 2*a^2*c*d^2 + d^3)*x^3 + 3*(a^4*c^3 + 2*a^2*c^2*d + c*d^2)*x)*log(-(a*x + 1)/(a*x - 1)))*sqrt(d*x^2 + c))/(a^4*c^6 + 2*a^2*c^5*d + c^4*d^2 + (a^4*c^4*d^2 + 2*a^2*c^3*d^3 + c^2*d^4)*x^4 + 2*(a^4*c^5*d + 2*a^2*c^4*d^2 + c^3*d^3)*x^2)]","B",0
515,1,1280,0,0.707215," ","integrate(arctanh(a*x)/(d*x^2+c)^(7/2),x, algorithm=""fricas"")","\left[\frac{{\left(15 \, a^{4} c^{5} + 20 \, a^{2} c^{4} d + {\left(15 \, a^{4} c^{2} d^{3} + 20 \, a^{2} c d^{4} + 8 \, d^{5}\right)} x^{6} + 8 \, c^{3} d^{2} + 3 \, {\left(15 \, a^{4} c^{3} d^{2} + 20 \, a^{2} c^{2} d^{3} + 8 \, c d^{4}\right)} x^{4} + 3 \, {\left(15 \, a^{4} c^{4} d + 20 \, a^{2} c^{3} d^{2} + 8 \, c^{2} d^{3}\right)} x^{2}\right)} \sqrt{a^{2} c + d} \log\left(\frac{a^{4} d^{2} x^{4} + 8 \, a^{4} c^{2} + 8 \, a^{2} c d + 2 \, {\left(4 \, a^{4} c d + 3 \, a^{2} d^{2}\right)} x^{2} - 4 \, {\left(a^{3} d x^{2} + 2 \, a^{3} c + a d\right)} \sqrt{a^{2} c + d} \sqrt{d x^{2} + c} + d^{2}}{a^{4} x^{4} - 2 \, a^{2} x^{2} + 1}\right) + 2 \, {\left(16 \, a^{5} c^{5} + 26 \, a^{3} c^{4} d + 10 \, a c^{3} d^{2} + 2 \, {\left(7 \, a^{5} c^{3} d^{2} + 11 \, a^{3} c^{2} d^{3} + 4 \, a c d^{4}\right)} x^{4} + 6 \, {\left(5 \, a^{5} c^{4} d + 8 \, a^{3} c^{3} d^{2} + 3 \, a c^{2} d^{3}\right)} x^{2} + {\left(8 \, {\left(a^{6} c^{3} d^{2} + 3 \, a^{4} c^{2} d^{3} + 3 \, a^{2} c d^{4} + d^{5}\right)} x^{5} + 20 \, {\left(a^{6} c^{4} d + 3 \, a^{4} c^{3} d^{2} + 3 \, a^{2} c^{2} d^{3} + c d^{4}\right)} x^{3} + 15 \, {\left(a^{6} c^{5} + 3 \, a^{4} c^{4} d + 3 \, a^{2} c^{3} d^{2} + c^{2} d^{3}\right)} x\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)\right)} \sqrt{d x^{2} + c}}{60 \, {\left(a^{6} c^{9} + 3 \, a^{4} c^{8} d + 3 \, a^{2} c^{7} d^{2} + c^{6} d^{3} + {\left(a^{6} c^{6} d^{3} + 3 \, a^{4} c^{5} d^{4} + 3 \, a^{2} c^{4} d^{5} + c^{3} d^{6}\right)} x^{6} + 3 \, {\left(a^{6} c^{7} d^{2} + 3 \, a^{4} c^{6} d^{3} + 3 \, a^{2} c^{5} d^{4} + c^{4} d^{5}\right)} x^{4} + 3 \, {\left(a^{6} c^{8} d + 3 \, a^{4} c^{7} d^{2} + 3 \, a^{2} c^{6} d^{3} + c^{5} d^{4}\right)} x^{2}\right)}}, \frac{{\left(15 \, a^{4} c^{5} + 20 \, a^{2} c^{4} d + {\left(15 \, a^{4} c^{2} d^{3} + 20 \, a^{2} c d^{4} + 8 \, d^{5}\right)} x^{6} + 8 \, c^{3} d^{2} + 3 \, {\left(15 \, a^{4} c^{3} d^{2} + 20 \, a^{2} c^{2} d^{3} + 8 \, c d^{4}\right)} x^{4} + 3 \, {\left(15 \, a^{4} c^{4} d + 20 \, a^{2} c^{3} d^{2} + 8 \, c^{2} d^{3}\right)} x^{2}\right)} \sqrt{-a^{2} c - d} \arctan\left(\frac{{\left(a^{2} d x^{2} + 2 \, a^{2} c + d\right)} \sqrt{-a^{2} c - d} \sqrt{d x^{2} + c}}{2 \, {\left(a^{3} c^{2} + a c d + {\left(a^{3} c d + a d^{2}\right)} x^{2}\right)}}\right) + {\left(16 \, a^{5} c^{5} + 26 \, a^{3} c^{4} d + 10 \, a c^{3} d^{2} + 2 \, {\left(7 \, a^{5} c^{3} d^{2} + 11 \, a^{3} c^{2} d^{3} + 4 \, a c d^{4}\right)} x^{4} + 6 \, {\left(5 \, a^{5} c^{4} d + 8 \, a^{3} c^{3} d^{2} + 3 \, a c^{2} d^{3}\right)} x^{2} + {\left(8 \, {\left(a^{6} c^{3} d^{2} + 3 \, a^{4} c^{2} d^{3} + 3 \, a^{2} c d^{4} + d^{5}\right)} x^{5} + 20 \, {\left(a^{6} c^{4} d + 3 \, a^{4} c^{3} d^{2} + 3 \, a^{2} c^{2} d^{3} + c d^{4}\right)} x^{3} + 15 \, {\left(a^{6} c^{5} + 3 \, a^{4} c^{4} d + 3 \, a^{2} c^{3} d^{2} + c^{2} d^{3}\right)} x\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)\right)} \sqrt{d x^{2} + c}}{30 \, {\left(a^{6} c^{9} + 3 \, a^{4} c^{8} d + 3 \, a^{2} c^{7} d^{2} + c^{6} d^{3} + {\left(a^{6} c^{6} d^{3} + 3 \, a^{4} c^{5} d^{4} + 3 \, a^{2} c^{4} d^{5} + c^{3} d^{6}\right)} x^{6} + 3 \, {\left(a^{6} c^{7} d^{2} + 3 \, a^{4} c^{6} d^{3} + 3 \, a^{2} c^{5} d^{4} + c^{4} d^{5}\right)} x^{4} + 3 \, {\left(a^{6} c^{8} d + 3 \, a^{4} c^{7} d^{2} + 3 \, a^{2} c^{6} d^{3} + c^{5} d^{4}\right)} x^{2}\right)}}\right]"," ",0,"[1/60*((15*a^4*c^5 + 20*a^2*c^4*d + (15*a^4*c^2*d^3 + 20*a^2*c*d^4 + 8*d^5)*x^6 + 8*c^3*d^2 + 3*(15*a^4*c^3*d^2 + 20*a^2*c^2*d^3 + 8*c*d^4)*x^4 + 3*(15*a^4*c^4*d + 20*a^2*c^3*d^2 + 8*c^2*d^3)*x^2)*sqrt(a^2*c + d)*log((a^4*d^2*x^4 + 8*a^4*c^2 + 8*a^2*c*d + 2*(4*a^4*c*d + 3*a^2*d^2)*x^2 - 4*(a^3*d*x^2 + 2*a^3*c + a*d)*sqrt(a^2*c + d)*sqrt(d*x^2 + c) + d^2)/(a^4*x^4 - 2*a^2*x^2 + 1)) + 2*(16*a^5*c^5 + 26*a^3*c^4*d + 10*a*c^3*d^2 + 2*(7*a^5*c^3*d^2 + 11*a^3*c^2*d^3 + 4*a*c*d^4)*x^4 + 6*(5*a^5*c^4*d + 8*a^3*c^3*d^2 + 3*a*c^2*d^3)*x^2 + (8*(a^6*c^3*d^2 + 3*a^4*c^2*d^3 + 3*a^2*c*d^4 + d^5)*x^5 + 20*(a^6*c^4*d + 3*a^4*c^3*d^2 + 3*a^2*c^2*d^3 + c*d^4)*x^3 + 15*(a^6*c^5 + 3*a^4*c^4*d + 3*a^2*c^3*d^2 + c^2*d^3)*x)*log(-(a*x + 1)/(a*x - 1)))*sqrt(d*x^2 + c))/(a^6*c^9 + 3*a^4*c^8*d + 3*a^2*c^7*d^2 + c^6*d^3 + (a^6*c^6*d^3 + 3*a^4*c^5*d^4 + 3*a^2*c^4*d^5 + c^3*d^6)*x^6 + 3*(a^6*c^7*d^2 + 3*a^4*c^6*d^3 + 3*a^2*c^5*d^4 + c^4*d^5)*x^4 + 3*(a^6*c^8*d + 3*a^4*c^7*d^2 + 3*a^2*c^6*d^3 + c^5*d^4)*x^2), 1/30*((15*a^4*c^5 + 20*a^2*c^4*d + (15*a^4*c^2*d^3 + 20*a^2*c*d^4 + 8*d^5)*x^6 + 8*c^3*d^2 + 3*(15*a^4*c^3*d^2 + 20*a^2*c^2*d^3 + 8*c*d^4)*x^4 + 3*(15*a^4*c^4*d + 20*a^2*c^3*d^2 + 8*c^2*d^3)*x^2)*sqrt(-a^2*c - d)*arctan(1/2*(a^2*d*x^2 + 2*a^2*c + d)*sqrt(-a^2*c - d)*sqrt(d*x^2 + c)/(a^3*c^2 + a*c*d + (a^3*c*d + a*d^2)*x^2)) + (16*a^5*c^5 + 26*a^3*c^4*d + 10*a*c^3*d^2 + 2*(7*a^5*c^3*d^2 + 11*a^3*c^2*d^3 + 4*a*c*d^4)*x^4 + 6*(5*a^5*c^4*d + 8*a^3*c^3*d^2 + 3*a*c^2*d^3)*x^2 + (8*(a^6*c^3*d^2 + 3*a^4*c^2*d^3 + 3*a^2*c*d^4 + d^5)*x^5 + 20*(a^6*c^4*d + 3*a^4*c^3*d^2 + 3*a^2*c^2*d^3 + c*d^4)*x^3 + 15*(a^6*c^5 + 3*a^4*c^4*d + 3*a^2*c^3*d^2 + c^2*d^3)*x)*log(-(a*x + 1)/(a*x - 1)))*sqrt(d*x^2 + c))/(a^6*c^9 + 3*a^4*c^8*d + 3*a^2*c^7*d^2 + c^6*d^3 + (a^6*c^6*d^3 + 3*a^4*c^5*d^4 + 3*a^2*c^4*d^5 + c^3*d^6)*x^6 + 3*(a^6*c^7*d^2 + 3*a^4*c^6*d^3 + 3*a^2*c^5*d^4 + c^4*d^5)*x^4 + 3*(a^6*c^8*d + 3*a^4*c^7*d^2 + 3*a^2*c^6*d^3 + c^5*d^4)*x^2)]","B",0
516,1,2006,0,0.922709," ","integrate(arctanh(a*x)/(d*x^2+c)^(9/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(35 \, a^{6} c^{7} + 70 \, a^{4} c^{6} d + 56 \, a^{2} c^{5} d^{2} + {\left(35 \, a^{6} c^{3} d^{4} + 70 \, a^{4} c^{2} d^{5} + 56 \, a^{2} c d^{6} + 16 \, d^{7}\right)} x^{8} + 16 \, c^{4} d^{3} + 4 \, {\left(35 \, a^{6} c^{4} d^{3} + 70 \, a^{4} c^{3} d^{4} + 56 \, a^{2} c^{2} d^{5} + 16 \, c d^{6}\right)} x^{6} + 6 \, {\left(35 \, a^{6} c^{5} d^{2} + 70 \, a^{4} c^{4} d^{3} + 56 \, a^{2} c^{3} d^{4} + 16 \, c^{2} d^{5}\right)} x^{4} + 4 \, {\left(35 \, a^{6} c^{6} d + 70 \, a^{4} c^{5} d^{2} + 56 \, a^{2} c^{4} d^{3} + 16 \, c^{3} d^{4}\right)} x^{2}\right)} \sqrt{a^{2} c + d} \log\left(\frac{a^{4} d^{2} x^{4} + 8 \, a^{4} c^{2} + 8 \, a^{2} c d + 2 \, {\left(4 \, a^{4} c d + 3 \, a^{2} d^{2}\right)} x^{2} - 4 \, {\left(a^{3} d x^{2} + 2 \, a^{3} c + a d\right)} \sqrt{a^{2} c + d} \sqrt{d x^{2} + c} + d^{2}}{a^{4} x^{4} - 2 \, a^{2} x^{2} + 1}\right) + 2 \, {\left(142 \, a^{7} c^{7} + 320 \, a^{5} c^{6} d + 244 \, a^{3} c^{5} d^{2} + 66 \, a c^{4} d^{3} + 6 \, {\left(19 \, a^{7} c^{4} d^{3} + 41 \, a^{5} c^{3} d^{4} + 30 \, a^{3} c^{2} d^{5} + 8 \, a c d^{6}\right)} x^{6} + 2 \, {\left(182 \, a^{7} c^{5} d^{2} + 397 \, a^{5} c^{4} d^{3} + 293 \, a^{3} c^{3} d^{4} + 78 \, a c^{2} d^{5}\right)} x^{4} + 2 \, {\left(196 \, a^{7} c^{6} d + 434 \, a^{5} c^{5} d^{2} + 325 \, a^{3} c^{4} d^{3} + 87 \, a c^{3} d^{4}\right)} x^{2} + 3 \, {\left(16 \, {\left(a^{8} c^{4} d^{3} + 4 \, a^{6} c^{3} d^{4} + 6 \, a^{4} c^{2} d^{5} + 4 \, a^{2} c d^{6} + d^{7}\right)} x^{7} + 56 \, {\left(a^{8} c^{5} d^{2} + 4 \, a^{6} c^{4} d^{3} + 6 \, a^{4} c^{3} d^{4} + 4 \, a^{2} c^{2} d^{5} + c d^{6}\right)} x^{5} + 70 \, {\left(a^{8} c^{6} d + 4 \, a^{6} c^{5} d^{2} + 6 \, a^{4} c^{4} d^{3} + 4 \, a^{2} c^{3} d^{4} + c^{2} d^{5}\right)} x^{3} + 35 \, {\left(a^{8} c^{7} + 4 \, a^{6} c^{6} d + 6 \, a^{4} c^{5} d^{2} + 4 \, a^{2} c^{4} d^{3} + c^{3} d^{4}\right)} x\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)\right)} \sqrt{d x^{2} + c}}{420 \, {\left(a^{8} c^{12} + 4 \, a^{6} c^{11} d + 6 \, a^{4} c^{10} d^{2} + 4 \, a^{2} c^{9} d^{3} + c^{8} d^{4} + {\left(a^{8} c^{8} d^{4} + 4 \, a^{6} c^{7} d^{5} + 6 \, a^{4} c^{6} d^{6} + 4 \, a^{2} c^{5} d^{7} + c^{4} d^{8}\right)} x^{8} + 4 \, {\left(a^{8} c^{9} d^{3} + 4 \, a^{6} c^{8} d^{4} + 6 \, a^{4} c^{7} d^{5} + 4 \, a^{2} c^{6} d^{6} + c^{5} d^{7}\right)} x^{6} + 6 \, {\left(a^{8} c^{10} d^{2} + 4 \, a^{6} c^{9} d^{3} + 6 \, a^{4} c^{8} d^{4} + 4 \, a^{2} c^{7} d^{5} + c^{6} d^{6}\right)} x^{4} + 4 \, {\left(a^{8} c^{11} d + 4 \, a^{6} c^{10} d^{2} + 6 \, a^{4} c^{9} d^{3} + 4 \, a^{2} c^{8} d^{4} + c^{7} d^{5}\right)} x^{2}\right)}}, \frac{3 \, {\left(35 \, a^{6} c^{7} + 70 \, a^{4} c^{6} d + 56 \, a^{2} c^{5} d^{2} + {\left(35 \, a^{6} c^{3} d^{4} + 70 \, a^{4} c^{2} d^{5} + 56 \, a^{2} c d^{6} + 16 \, d^{7}\right)} x^{8} + 16 \, c^{4} d^{3} + 4 \, {\left(35 \, a^{6} c^{4} d^{3} + 70 \, a^{4} c^{3} d^{4} + 56 \, a^{2} c^{2} d^{5} + 16 \, c d^{6}\right)} x^{6} + 6 \, {\left(35 \, a^{6} c^{5} d^{2} + 70 \, a^{4} c^{4} d^{3} + 56 \, a^{2} c^{3} d^{4} + 16 \, c^{2} d^{5}\right)} x^{4} + 4 \, {\left(35 \, a^{6} c^{6} d + 70 \, a^{4} c^{5} d^{2} + 56 \, a^{2} c^{4} d^{3} + 16 \, c^{3} d^{4}\right)} x^{2}\right)} \sqrt{-a^{2} c - d} \arctan\left(\frac{{\left(a^{2} d x^{2} + 2 \, a^{2} c + d\right)} \sqrt{-a^{2} c - d} \sqrt{d x^{2} + c}}{2 \, {\left(a^{3} c^{2} + a c d + {\left(a^{3} c d + a d^{2}\right)} x^{2}\right)}}\right) + {\left(142 \, a^{7} c^{7} + 320 \, a^{5} c^{6} d + 244 \, a^{3} c^{5} d^{2} + 66 \, a c^{4} d^{3} + 6 \, {\left(19 \, a^{7} c^{4} d^{3} + 41 \, a^{5} c^{3} d^{4} + 30 \, a^{3} c^{2} d^{5} + 8 \, a c d^{6}\right)} x^{6} + 2 \, {\left(182 \, a^{7} c^{5} d^{2} + 397 \, a^{5} c^{4} d^{3} + 293 \, a^{3} c^{3} d^{4} + 78 \, a c^{2} d^{5}\right)} x^{4} + 2 \, {\left(196 \, a^{7} c^{6} d + 434 \, a^{5} c^{5} d^{2} + 325 \, a^{3} c^{4} d^{3} + 87 \, a c^{3} d^{4}\right)} x^{2} + 3 \, {\left(16 \, {\left(a^{8} c^{4} d^{3} + 4 \, a^{6} c^{3} d^{4} + 6 \, a^{4} c^{2} d^{5} + 4 \, a^{2} c d^{6} + d^{7}\right)} x^{7} + 56 \, {\left(a^{8} c^{5} d^{2} + 4 \, a^{6} c^{4} d^{3} + 6 \, a^{4} c^{3} d^{4} + 4 \, a^{2} c^{2} d^{5} + c d^{6}\right)} x^{5} + 70 \, {\left(a^{8} c^{6} d + 4 \, a^{6} c^{5} d^{2} + 6 \, a^{4} c^{4} d^{3} + 4 \, a^{2} c^{3} d^{4} + c^{2} d^{5}\right)} x^{3} + 35 \, {\left(a^{8} c^{7} + 4 \, a^{6} c^{6} d + 6 \, a^{4} c^{5} d^{2} + 4 \, a^{2} c^{4} d^{3} + c^{3} d^{4}\right)} x\right)} \log\left(-\frac{a x + 1}{a x - 1}\right)\right)} \sqrt{d x^{2} + c}}{210 \, {\left(a^{8} c^{12} + 4 \, a^{6} c^{11} d + 6 \, a^{4} c^{10} d^{2} + 4 \, a^{2} c^{9} d^{3} + c^{8} d^{4} + {\left(a^{8} c^{8} d^{4} + 4 \, a^{6} c^{7} d^{5} + 6 \, a^{4} c^{6} d^{6} + 4 \, a^{2} c^{5} d^{7} + c^{4} d^{8}\right)} x^{8} + 4 \, {\left(a^{8} c^{9} d^{3} + 4 \, a^{6} c^{8} d^{4} + 6 \, a^{4} c^{7} d^{5} + 4 \, a^{2} c^{6} d^{6} + c^{5} d^{7}\right)} x^{6} + 6 \, {\left(a^{8} c^{10} d^{2} + 4 \, a^{6} c^{9} d^{3} + 6 \, a^{4} c^{8} d^{4} + 4 \, a^{2} c^{7} d^{5} + c^{6} d^{6}\right)} x^{4} + 4 \, {\left(a^{8} c^{11} d + 4 \, a^{6} c^{10} d^{2} + 6 \, a^{4} c^{9} d^{3} + 4 \, a^{2} c^{8} d^{4} + c^{7} d^{5}\right)} x^{2}\right)}}\right]"," ",0,"[1/420*(3*(35*a^6*c^7 + 70*a^4*c^6*d + 56*a^2*c^5*d^2 + (35*a^6*c^3*d^4 + 70*a^4*c^2*d^5 + 56*a^2*c*d^6 + 16*d^7)*x^8 + 16*c^4*d^3 + 4*(35*a^6*c^4*d^3 + 70*a^4*c^3*d^4 + 56*a^2*c^2*d^5 + 16*c*d^6)*x^6 + 6*(35*a^6*c^5*d^2 + 70*a^4*c^4*d^3 + 56*a^2*c^3*d^4 + 16*c^2*d^5)*x^4 + 4*(35*a^6*c^6*d + 70*a^4*c^5*d^2 + 56*a^2*c^4*d^3 + 16*c^3*d^4)*x^2)*sqrt(a^2*c + d)*log((a^4*d^2*x^4 + 8*a^4*c^2 + 8*a^2*c*d + 2*(4*a^4*c*d + 3*a^2*d^2)*x^2 - 4*(a^3*d*x^2 + 2*a^3*c + a*d)*sqrt(a^2*c + d)*sqrt(d*x^2 + c) + d^2)/(a^4*x^4 - 2*a^2*x^2 + 1)) + 2*(142*a^7*c^7 + 320*a^5*c^6*d + 244*a^3*c^5*d^2 + 66*a*c^4*d^3 + 6*(19*a^7*c^4*d^3 + 41*a^5*c^3*d^4 + 30*a^3*c^2*d^5 + 8*a*c*d^6)*x^6 + 2*(182*a^7*c^5*d^2 + 397*a^5*c^4*d^3 + 293*a^3*c^3*d^4 + 78*a*c^2*d^5)*x^4 + 2*(196*a^7*c^6*d + 434*a^5*c^5*d^2 + 325*a^3*c^4*d^3 + 87*a*c^3*d^4)*x^2 + 3*(16*(a^8*c^4*d^3 + 4*a^6*c^3*d^4 + 6*a^4*c^2*d^5 + 4*a^2*c*d^6 + d^7)*x^7 + 56*(a^8*c^5*d^2 + 4*a^6*c^4*d^3 + 6*a^4*c^3*d^4 + 4*a^2*c^2*d^5 + c*d^6)*x^5 + 70*(a^8*c^6*d + 4*a^6*c^5*d^2 + 6*a^4*c^4*d^3 + 4*a^2*c^3*d^4 + c^2*d^5)*x^3 + 35*(a^8*c^7 + 4*a^6*c^6*d + 6*a^4*c^5*d^2 + 4*a^2*c^4*d^3 + c^3*d^4)*x)*log(-(a*x + 1)/(a*x - 1)))*sqrt(d*x^2 + c))/(a^8*c^12 + 4*a^6*c^11*d + 6*a^4*c^10*d^2 + 4*a^2*c^9*d^3 + c^8*d^4 + (a^8*c^8*d^4 + 4*a^6*c^7*d^5 + 6*a^4*c^6*d^6 + 4*a^2*c^5*d^7 + c^4*d^8)*x^8 + 4*(a^8*c^9*d^3 + 4*a^6*c^8*d^4 + 6*a^4*c^7*d^5 + 4*a^2*c^6*d^6 + c^5*d^7)*x^6 + 6*(a^8*c^10*d^2 + 4*a^6*c^9*d^3 + 6*a^4*c^8*d^4 + 4*a^2*c^7*d^5 + c^6*d^6)*x^4 + 4*(a^8*c^11*d + 4*a^6*c^10*d^2 + 6*a^4*c^9*d^3 + 4*a^2*c^8*d^4 + c^7*d^5)*x^2), 1/210*(3*(35*a^6*c^7 + 70*a^4*c^6*d + 56*a^2*c^5*d^2 + (35*a^6*c^3*d^4 + 70*a^4*c^2*d^5 + 56*a^2*c*d^6 + 16*d^7)*x^8 + 16*c^4*d^3 + 4*(35*a^6*c^4*d^3 + 70*a^4*c^3*d^4 + 56*a^2*c^2*d^5 + 16*c*d^6)*x^6 + 6*(35*a^6*c^5*d^2 + 70*a^4*c^4*d^3 + 56*a^2*c^3*d^4 + 16*c^2*d^5)*x^4 + 4*(35*a^6*c^6*d + 70*a^4*c^5*d^2 + 56*a^2*c^4*d^3 + 16*c^3*d^4)*x^2)*sqrt(-a^2*c - d)*arctan(1/2*(a^2*d*x^2 + 2*a^2*c + d)*sqrt(-a^2*c - d)*sqrt(d*x^2 + c)/(a^3*c^2 + a*c*d + (a^3*c*d + a*d^2)*x^2)) + (142*a^7*c^7 + 320*a^5*c^6*d + 244*a^3*c^5*d^2 + 66*a*c^4*d^3 + 6*(19*a^7*c^4*d^3 + 41*a^5*c^3*d^4 + 30*a^3*c^2*d^5 + 8*a*c*d^6)*x^6 + 2*(182*a^7*c^5*d^2 + 397*a^5*c^4*d^3 + 293*a^3*c^3*d^4 + 78*a*c^2*d^5)*x^4 + 2*(196*a^7*c^6*d + 434*a^5*c^5*d^2 + 325*a^3*c^4*d^3 + 87*a*c^3*d^4)*x^2 + 3*(16*(a^8*c^4*d^3 + 4*a^6*c^3*d^4 + 6*a^4*c^2*d^5 + 4*a^2*c*d^6 + d^7)*x^7 + 56*(a^8*c^5*d^2 + 4*a^6*c^4*d^3 + 6*a^4*c^3*d^4 + 4*a^2*c^2*d^5 + c*d^6)*x^5 + 70*(a^8*c^6*d + 4*a^6*c^5*d^2 + 6*a^4*c^4*d^3 + 4*a^2*c^3*d^4 + c^2*d^5)*x^3 + 35*(a^8*c^7 + 4*a^6*c^6*d + 6*a^4*c^5*d^2 + 4*a^2*c^4*d^3 + c^3*d^4)*x)*log(-(a*x + 1)/(a*x - 1)))*sqrt(d*x^2 + c))/(a^8*c^12 + 4*a^6*c^11*d + 6*a^4*c^10*d^2 + 4*a^2*c^9*d^3 + c^8*d^4 + (a^8*c^8*d^4 + 4*a^6*c^7*d^5 + 6*a^4*c^6*d^6 + 4*a^2*c^5*d^7 + c^4*d^8)*x^8 + 4*(a^8*c^9*d^3 + 4*a^6*c^8*d^4 + 6*a^4*c^7*d^5 + 4*a^2*c^6*d^6 + c^5*d^7)*x^6 + 6*(a^8*c^10*d^2 + 4*a^6*c^9*d^3 + 6*a^4*c^8*d^4 + 4*a^2*c^7*d^5 + c^6*d^6)*x^4 + 4*(a^8*c^11*d + 4*a^6*c^10*d^2 + 6*a^4*c^9*d^3 + 4*a^2*c^8*d^4 + c^7*d^5)*x^2)]","B",0
517,0,0,0,0.488358," ","integrate((-a*x^2+a)^(1/2)*arctanh(x),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{-a x^{2} + a} \operatorname{artanh}\left(x\right), x\right)"," ",0,"integral(sqrt(-a*x^2 + a)*arctanh(x), x)","F",0
518,0,0,0,0.516540," ","integrate(arctanh(x)/(-a*x^2+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-a x^{2} + a} \operatorname{artanh}\left(x\right)}{a x^{2} - a}, x\right)"," ",0,"integral(-sqrt(-a*x^2 + a)*arctanh(x)/(a*x^2 - a), x)","F",0
519,1,42,0,0.466077," ","integrate(arctanh(x)/(-a*x^2+a)^(3/2),x, algorithm=""fricas"")","-\frac{\sqrt{-a x^{2} + a} {\left(x \log\left(-\frac{x + 1}{x - 1}\right) - 2\right)}}{2 \, {\left(a^{2} x^{2} - a^{2}\right)}}"," ",0,"-1/2*sqrt(-a*x^2 + a)*(x*log(-(x + 1)/(x - 1)) - 2)/(a^2*x^2 - a^2)","A",0
520,1,62,0,0.482167," ","integrate(arctanh(x)/(-a*x^2+a)^(5/2),x, algorithm=""fricas"")","\frac{\sqrt{-a x^{2} + a} {\left(12 \, x^{2} - 3 \, {\left(2 \, x^{3} - 3 \, x\right)} \log\left(-\frac{x + 1}{x - 1}\right) - 14\right)}}{18 \, {\left(a^{3} x^{4} - 2 \, a^{3} x^{2} + a^{3}\right)}}"," ",0,"1/18*sqrt(-a*x^2 + a)*(12*x^2 - 3*(2*x^3 - 3*x)*log(-(x + 1)/(x - 1)) - 14)/(a^3*x^4 - 2*a^3*x^2 + a^3)","A",0
521,1,82,0,0.559645," ","integrate(arctanh(x)/(-a*x^2+a)^(7/2),x, algorithm=""fricas"")","\frac{{\left(240 \, x^{4} - 520 \, x^{2} - 15 \, {\left(8 \, x^{5} - 20 \, x^{3} + 15 \, x\right)} \log\left(-\frac{x + 1}{x - 1}\right) + 298\right)} \sqrt{-a x^{2} + a}}{450 \, {\left(a^{4} x^{6} - 3 \, a^{4} x^{4} + 3 \, a^{4} x^{2} - a^{4}\right)}}"," ",0,"1/450*(240*x^4 - 520*x^2 - 15*(8*x^5 - 20*x^3 + 15*x)*log(-(x + 1)/(x - 1)) + 298)*sqrt(-a*x^2 + a)/(a^4*x^6 - 3*a^4*x^4 + 3*a^4*x^2 - a^4)","A",0
522,1,251,0,0.529659," ","integrate(x^4*(a+b*arctanh(c*x))*(d+e*log(-c^2*x^2+1)),x, algorithm=""fricas"")","-\frac{80 \, a c^{3} e x^{3} - 24 \, {\left(5 \, a c^{5} d - 2 \, a c^{5} e\right)} x^{5} - 3 \, {\left(10 \, b c^{4} d - 9 \, b c^{4} e\right)} x^{4} + 240 \, a c e x - 30 \, b e \log\left(-c^{2} x^{2} + 1\right)^{2} - 30 \, b e \log\left(-\frac{c x + 1}{c x - 1}\right)^{2} - 2 \, {\left(30 \, b c^{2} d - 77 \, b c^{2} e\right)} x^{2} - 2 \, {\left(60 \, a c^{5} e x^{5} + 15 \, b c^{4} e x^{4} + 30 \, b c^{2} e x^{2} + 30 \, b d - 137 \, b e\right)} \log\left(-c^{2} x^{2} + 1\right) - 4 \, {\left(15 \, b c^{5} e x^{5} \log\left(-c^{2} x^{2} + 1\right) - 10 \, b c^{3} e x^{3} + 3 \, {\left(5 \, b c^{5} d - 2 \, b c^{5} e\right)} x^{5} - 30 \, b c e x + 30 \, a e\right)} \log\left(-\frac{c x + 1}{c x - 1}\right)}{600 \, c^{5}}"," ",0,"-1/600*(80*a*c^3*e*x^3 - 24*(5*a*c^5*d - 2*a*c^5*e)*x^5 - 3*(10*b*c^4*d - 9*b*c^4*e)*x^4 + 240*a*c*e*x - 30*b*e*log(-c^2*x^2 + 1)^2 - 30*b*e*log(-(c*x + 1)/(c*x - 1))^2 - 2*(30*b*c^2*d - 77*b*c^2*e)*x^2 - 2*(60*a*c^5*e*x^5 + 15*b*c^4*e*x^4 + 30*b*c^2*e*x^2 + 30*b*d - 137*b*e)*log(-c^2*x^2 + 1) - 4*(15*b*c^5*e*x^5*log(-c^2*x^2 + 1) - 10*b*c^3*e*x^3 + 3*(5*b*c^5*d - 2*b*c^5*e)*x^5 - 30*b*c*e*x + 30*a*e)*log(-(c*x + 1)/(c*x - 1)))/c^5","A",0
523,1,196,0,0.649032," ","integrate(x^3*(a+b*arctanh(c*x))*(d+e*log(-c^2*x^2+1)),x, algorithm=""fricas"")","-\frac{36 \, a c^{2} e x^{2} - 18 \, {\left(2 \, a c^{4} d - a c^{4} e\right)} x^{4} - 2 \, {\left(6 \, b c^{3} d - 7 \, b c^{3} e\right)} x^{3} - 6 \, {\left(6 \, b c d - 25 \, b c e\right)} x - 12 \, {\left(3 \, a c^{4} e x^{4} + b c^{3} e x^{3} + 3 \, b c e x - 3 \, a e\right)} \log\left(-c^{2} x^{2} + 1\right) + 3 \, {\left(6 \, b c^{2} e x^{2} - 3 \, {\left(2 \, b c^{4} d - b c^{4} e\right)} x^{4} + 6 \, b d - 25 \, b e - 6 \, {\left(b c^{4} e x^{4} - b e\right)} \log\left(-c^{2} x^{2} + 1\right)\right)} \log\left(-\frac{c x + 1}{c x - 1}\right)}{144 \, c^{4}}"," ",0,"-1/144*(36*a*c^2*e*x^2 - 18*(2*a*c^4*d - a*c^4*e)*x^4 - 2*(6*b*c^3*d - 7*b*c^3*e)*x^3 - 6*(6*b*c*d - 25*b*c*e)*x - 12*(3*a*c^4*e*x^4 + b*c^3*e*x^3 + 3*b*c*e*x - 3*a*e)*log(-c^2*x^2 + 1) + 3*(6*b*c^2*e*x^2 - 3*(2*b*c^4*d - b*c^4*e)*x^4 + 6*b*d - 25*b*e - 6*(b*c^4*e*x^4 - b*e)*log(-c^2*x^2 + 1))*log(-(c*x + 1)/(c*x - 1)))/c^4","A",0
524,1,200,0,0.676016," ","integrate(x^2*(a+b*arctanh(c*x))*(d+e*log(-c^2*x^2+1)),x, algorithm=""fricas"")","-\frac{24 \, a c e x - 4 \, {\left(3 \, a c^{3} d - 2 \, a c^{3} e\right)} x^{3} - 3 \, b e \log\left(-c^{2} x^{2} + 1\right)^{2} - 3 \, b e \log\left(-\frac{c x + 1}{c x - 1}\right)^{2} - 2 \, {\left(3 \, b c^{2} d - 5 \, b c^{2} e\right)} x^{2} - 2 \, {\left(6 \, a c^{3} e x^{3} + 3 \, b c^{2} e x^{2} + 3 \, b d - 11 \, b e\right)} \log\left(-c^{2} x^{2} + 1\right) - 2 \, {\left(3 \, b c^{3} e x^{3} \log\left(-c^{2} x^{2} + 1\right) - 6 \, b c e x + {\left(3 \, b c^{3} d - 2 \, b c^{3} e\right)} x^{3} + 6 \, a e\right)} \log\left(-\frac{c x + 1}{c x - 1}\right)}{36 \, c^{3}}"," ",0,"-1/36*(24*a*c*e*x - 4*(3*a*c^3*d - 2*a*c^3*e)*x^3 - 3*b*e*log(-c^2*x^2 + 1)^2 - 3*b*e*log(-(c*x + 1)/(c*x - 1))^2 - 2*(3*b*c^2*d - 5*b*c^2*e)*x^2 - 2*(6*a*c^3*e*x^3 + 3*b*c^2*e*x^2 + 3*b*d - 11*b*e)*log(-c^2*x^2 + 1) - 2*(3*b*c^3*e*x^3*log(-c^2*x^2 + 1) - 6*b*c*e*x + (3*b*c^3*d - 2*b*c^3*e)*x^3 + 6*a*e)*log(-(c*x + 1)/(c*x - 1)))/c^3","A",0
525,1,139,0,0.630788," ","integrate(x*(a+b*arctanh(c*x))*(d+e*log(-c^2*x^2+1)),x, algorithm=""fricas"")","\frac{2 \, {\left(a c^{2} d - a c^{2} e\right)} x^{2} + 2 \, {\left(b c d - 3 \, b c e\right)} x + 2 \, {\left(a c^{2} e x^{2} + b c e x - a e\right)} \log\left(-c^{2} x^{2} + 1\right) + {\left({\left(b c^{2} d - b c^{2} e\right)} x^{2} - b d + 3 \, b e + {\left(b c^{2} e x^{2} - b e\right)} \log\left(-c^{2} x^{2} + 1\right)\right)} \log\left(-\frac{c x + 1}{c x - 1}\right)}{4 \, c^{2}}"," ",0,"1/4*(2*(a*c^2*d - a*c^2*e)*x^2 + 2*(b*c*d - 3*b*c*e)*x + 2*(a*c^2*e*x^2 + b*c*e*x - a*e)*log(-c^2*x^2 + 1) + ((b*c^2*d - b*c^2*e)*x^2 - b*d + 3*b*e + (b*c^2*e*x^2 - b*e)*log(-c^2*x^2 + 1))*log(-(c*x + 1)/(c*x - 1)))/c^2","A",0
526,1,132,0,0.532718," ","integrate((a+b*arctanh(c*x))*(d+e*log(-c^2*x^2+1)),x, algorithm=""fricas"")","\frac{b e \log\left(-c^{2} x^{2} + 1\right)^{2} + b e \log\left(-\frac{c x + 1}{c x - 1}\right)^{2} + 4 \, {\left(a c d - 2 \, a c e\right)} x + 2 \, {\left(2 \, a c e x + b d - 2 \, b e\right)} \log\left(-c^{2} x^{2} + 1\right) + 2 \, {\left(b c e x \log\left(-c^{2} x^{2} + 1\right) + 2 \, a e + {\left(b c d - 2 \, b c e\right)} x\right)} \log\left(-\frac{c x + 1}{c x - 1}\right)}{4 \, c}"," ",0,"1/4*(b*e*log(-c^2*x^2 + 1)^2 + b*e*log(-(c*x + 1)/(c*x - 1))^2 + 4*(a*c*d - 2*a*c*e)*x + 2*(2*a*c*e*x + b*d - 2*b*e)*log(-c^2*x^2 + 1) + 2*(b*c*e*x*log(-c^2*x^2 + 1) + 2*a*e + (b*c*d - 2*b*c*e)*x)*log(-(c*x + 1)/(c*x - 1)))/c","A",0
527,0,0,0,0.493057," ","integrate((a+b*arctanh(c*x))*(d+e*log(-c^2*x^2+1))/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b d \operatorname{artanh}\left(c x\right) + a d + {\left(b e \operatorname{artanh}\left(c x\right) + a e\right)} \log\left(-c^{2} x^{2} + 1\right)}{x}, x\right)"," ",0,"integral((b*d*arctanh(c*x) + a*d + (b*e*arctanh(c*x) + a*e)*log(-c^2*x^2 + 1))/x, x)","F",0
528,0,0,0,0.476919," ","integrate((a+b*arctanh(c*x))*(d+e*log(-c^2*x^2+1))/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b d \operatorname{artanh}\left(c x\right) + a d + {\left(b e \operatorname{artanh}\left(c x\right) + a e\right)} \log\left(-c^{2} x^{2} + 1\right)}{x^{2}}, x\right)"," ",0,"integral((b*d*arctanh(c*x) + a*d + (b*e*arctanh(c*x) + a*e)*log(-c^2*x^2 + 1))/x^2, x)","F",0
529,0,0,0,0.425268," ","integrate((a+b*arctanh(c*x))*(d+e*log(-c^2*x^2+1))/x^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b d \operatorname{artanh}\left(c x\right) + a d + {\left(b e \operatorname{artanh}\left(c x\right) + a e\right)} \log\left(-c^{2} x^{2} + 1\right)}{x^{3}}, x\right)"," ",0,"integral((b*d*arctanh(c*x) + a*d + (b*e*arctanh(c*x) + a*e)*log(-c^2*x^2 + 1))/x^3, x)","F",0
530,0,0,0,0.528778," ","integrate((a+b*arctanh(c*x))*(d+e*log(-c^2*x^2+1))/x^4,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b d \operatorname{artanh}\left(c x\right) + a d + {\left(b e \operatorname{artanh}\left(c x\right) + a e\right)} \log\left(-c^{2} x^{2} + 1\right)}{x^{4}}, x\right)"," ",0,"integral((b*d*arctanh(c*x) + a*d + (b*e*arctanh(c*x) + a*e)*log(-c^2*x^2 + 1))/x^4, x)","F",0
531,0,0,0,0.475681," ","integrate((a+b*arctanh(c*x))*(d+e*log(-c^2*x^2+1))/x^5,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b d \operatorname{artanh}\left(c x\right) + a d + {\left(b e \operatorname{artanh}\left(c x\right) + a e\right)} \log\left(-c^{2} x^{2} + 1\right)}{x^{5}}, x\right)"," ",0,"integral((b*d*arctanh(c*x) + a*d + (b*e*arctanh(c*x) + a*e)*log(-c^2*x^2 + 1))/x^5, x)","F",0
532,0,0,0,0.429986," ","integrate((a+b*arctanh(c*x))*(d+e*log(-c^2*x^2+1))/x^6,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b d \operatorname{artanh}\left(c x\right) + a d + {\left(b e \operatorname{artanh}\left(c x\right) + a e\right)} \log\left(-c^{2} x^{2} + 1\right)}{x^{6}}, x\right)"," ",0,"integral((b*d*arctanh(c*x) + a*d + (b*e*arctanh(c*x) + a*e)*log(-c^2*x^2 + 1))/x^6, x)","F",0
533,0,0,0,0.424091," ","integrate(x*(a+b*arctanh(c*x))*(d+e*log(g*x^2+f)),x, algorithm=""fricas"")","{\rm integral}\left(b d x \operatorname{artanh}\left(c x\right) + a d x + {\left(b e x \operatorname{artanh}\left(c x\right) + a e x\right)} \log\left(g x^{2} + f\right), x\right)"," ",0,"integral(b*d*x*arctanh(c*x) + a*d*x + (b*e*x*arctanh(c*x) + a*e*x)*log(g*x^2 + f), x)","F",0
534,0,0,0,0.450245," ","integrate((a+b*arctanh(c*x))*(d+e*log(g*x^2+f)),x, algorithm=""fricas"")","{\rm integral}\left(b d \operatorname{artanh}\left(c x\right) + a d + {\left(b e \operatorname{artanh}\left(c x\right) + a e\right)} \log\left(g x^{2} + f\right), x\right)"," ",0,"integral(b*d*arctanh(c*x) + a*d + (b*e*arctanh(c*x) + a*e)*log(g*x^2 + f), x)","F",0
535,0,0,0,1.087068," ","integrate((a+b*arctanh(c*x))*(d+e*log(g*x^2+f))/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b d \operatorname{artanh}\left(c x\right) + a d + {\left(b e \operatorname{artanh}\left(c x\right) + a e\right)} \log\left(g x^{2} + f\right)}{x}, x\right)"," ",0,"integral((b*d*arctanh(c*x) + a*d + (b*e*arctanh(c*x) + a*e)*log(g*x^2 + f))/x, x)","F",0
536,0,0,0,0.770470," ","integrate((a+b*arctanh(c*x))*(d+e*log(g*x^2+f))/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b d \operatorname{artanh}\left(c x\right) + a d + {\left(b e \operatorname{artanh}\left(c x\right) + a e\right)} \log\left(g x^{2} + f\right)}{x^{2}}, x\right)"," ",0,"integral((b*d*arctanh(c*x) + a*d + (b*e*arctanh(c*x) + a*e)*log(g*x^2 + f))/x^2, x)","F",0
537,0,0,0,0.706530," ","integrate((a+b*arctanh(c*x))*(d+e*log(g*x^2+f))/x^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b d \operatorname{artanh}\left(c x\right) + a d + {\left(b e \operatorname{artanh}\left(c x\right) + a e\right)} \log\left(g x^{2} + f\right)}{x^{3}}, x\right)"," ",0,"integral((b*d*arctanh(c*x) + a*d + (b*e*arctanh(c*x) + a*e)*log(g*x^2 + f))/x^3, x)","F",0
538,1,74,0,0.448971," ","integrate(arctanh(c*x)*(a+b*arctanh(c*x))/(c*x+1)^2,x, algorithm=""fricas"")","\frac{{\left(b c x - b\right)} \log\left(-\frac{c x + 1}{c x - 1}\right)^{2} + 2 \, {\left({\left(a + b\right)} c x - a - b\right)} \log\left(-\frac{c x + 1}{c x - 1}\right) - 4 \, a - 4 \, b}{8 \, {\left(c^{2} x + c\right)}}"," ",0,"1/8*((b*c*x - b)*log(-(c*x + 1)/(c*x - 1))^2 + 2*((a + b)*c*x - a - b)*log(-(c*x + 1)/(c*x - 1)) - 4*a - 4*b)/(c^2*x + c)","A",0
