1,1,67,0,1.332798," ","integrate(x^5*(a+b*arctanh(c*x)),x, algorithm=""fricas"")","\frac{30 \, a c^{6} x^{6} + 6 \, b c^{5} x^{5} + 10 \, b c^{3} x^{3} + 30 \, b c x + 15 \, {\left(b c^{6} x^{6} - b\right)} \log\left(-\frac{c x + 1}{c x - 1}\right)}{180 \, c^{6}}"," ",0,"1/180*(30*a*c^6*x^6 + 6*b*c^5*x^5 + 10*b*c^3*x^3 + 30*b*c*x + 15*(b*c^6*x^6 - b)*log(-(c*x + 1)/(c*x - 1)))/c^6","A",0
2,1,69,0,1.346529," ","integrate(x^4*(a+b*arctanh(c*x)),x, algorithm=""fricas"")","\frac{2 \, b c^{5} x^{5} \log\left(-\frac{c x + 1}{c x - 1}\right) + 4 \, a c^{5} x^{5} + b c^{4} x^{4} + 2 \, b c^{2} x^{2} + 2 \, b \log\left(c^{2} x^{2} - 1\right)}{20 \, c^{5}}"," ",0,"1/20*(2*b*c^5*x^5*log(-(c*x + 1)/(c*x - 1)) + 4*a*c^5*x^5 + b*c^4*x^4 + 2*b*c^2*x^2 + 2*b*log(c^2*x^2 - 1))/c^5","A",0
3,1,58,0,0.802388," ","integrate(x^3*(a+b*arctanh(c*x)),x, algorithm=""fricas"")","\frac{6 \, a c^{4} x^{4} + 2 \, b c^{3} x^{3} + 6 \, b c x + 3 \, {\left(b c^{4} x^{4} - b\right)} \log\left(-\frac{c x + 1}{c x - 1}\right)}{24 \, c^{4}}"," ",0,"1/24*(6*a*c^4*x^4 + 2*b*c^3*x^3 + 6*b*c*x + 3*(b*c^4*x^4 - b)*log(-(c*x + 1)/(c*x - 1)))/c^4","A",0
4,1,58,0,0.579975," ","integrate(x^2*(a+b*arctanh(c*x)),x, algorithm=""fricas"")","\frac{b c^{3} x^{3} \log\left(-\frac{c x + 1}{c x - 1}\right) + 2 \, a c^{3} x^{3} + b c^{2} x^{2} + b \log\left(c^{2} x^{2} - 1\right)}{6 \, c^{3}}"," ",0,"1/6*(b*c^3*x^3*log(-(c*x + 1)/(c*x - 1)) + 2*a*c^3*x^3 + b*c^2*x^2 + b*log(c^2*x^2 - 1))/c^3","A",0
5,1,48,0,0.579949," ","integrate(x*(a+b*arctanh(c*x)),x, algorithm=""fricas"")","\frac{2 \, a c^{2} x^{2} + 2 \, b c x + {\left(b c^{2} x^{2} - b\right)} \log\left(-\frac{c x + 1}{c x - 1}\right)}{4 \, c^{2}}"," ",0,"1/4*(2*a*c^2*x^2 + 2*b*c*x + (b*c^2*x^2 - b)*log(-(c*x + 1)/(c*x - 1)))/c^2","A",0
6,1,42,0,0.562436," ","integrate(a+b*arctanh(c*x),x, algorithm=""fricas"")","\frac{b c x \log\left(-\frac{c x + 1}{c x - 1}\right) + 2 \, a c x + b \log\left(c^{2} x^{2} - 1\right)}{2 \, c}"," ",0,"1/2*(b*c*x*log(-(c*x + 1)/(c*x - 1)) + 2*a*c*x + b*log(c^2*x^2 - 1))/c","A",0
7,0,0,0,0.562036," ","integrate((a+b*arctanh(c*x))/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \operatorname{artanh}\left(c x\right) + a}{x}, x\right)"," ",0,"integral((b*arctanh(c*x) + a)/x, x)","F",0
8,1,47,0,0.695996," ","integrate((a+b*arctanh(c*x))/x^2,x, algorithm=""fricas"")","-\frac{b c x \log\left(c^{2} x^{2} - 1\right) - 2 \, b c x \log\left(x\right) + b \log\left(-\frac{c x + 1}{c x - 1}\right) + 2 \, a}{2 \, x}"," ",0,"-1/2*(b*c*x*log(c^2*x^2 - 1) - 2*b*c*x*log(x) + b*log(-(c*x + 1)/(c*x - 1)) + 2*a)/x","A",0
9,1,43,0,1.301079," ","integrate((a+b*arctanh(c*x))/x^3,x, algorithm=""fricas"")","-\frac{2 \, b c x - {\left(b c^{2} x^{2} - b\right)} \log\left(-\frac{c x + 1}{c x - 1}\right) + 2 \, a}{4 \, x^{2}}"," ",0,"-1/4*(2*b*c*x - (b*c^2*x^2 - b)*log(-(c*x + 1)/(c*x - 1)) + 2*a)/x^2","A",0
10,1,59,0,0.592173," ","integrate((a+b*arctanh(c*x))/x^4,x, algorithm=""fricas"")","-\frac{b c^{3} x^{3} \log\left(c^{2} x^{2} - 1\right) - 2 \, b c^{3} x^{3} \log\left(x\right) + b c x + b \log\left(-\frac{c x + 1}{c x - 1}\right) + 2 \, a}{6 \, x^{3}}"," ",0,"-1/6*(b*c^3*x^3*log(c^2*x^2 - 1) - 2*b*c^3*x^3*log(x) + b*c*x + b*log(-(c*x + 1)/(c*x - 1)) + 2*a)/x^3","A",0
11,1,52,0,1.212480," ","integrate((a+b*arctanh(c*x))/x^5,x, algorithm=""fricas"")","-\frac{6 \, b c^{3} x^{3} + 2 \, b c x - 3 \, {\left(b c^{4} x^{4} - b\right)} \log\left(-\frac{c x + 1}{c x - 1}\right) + 6 \, a}{24 \, x^{4}}"," ",0,"-1/24*(6*b*c^3*x^3 + 2*b*c*x - 3*(b*c^4*x^4 - b)*log(-(c*x + 1)/(c*x - 1)) + 6*a)/x^4","A",0
12,1,70,0,0.628069," ","integrate((a+b*arctanh(c*x))/x^6,x, algorithm=""fricas"")","-\frac{2 \, b c^{5} x^{5} \log\left(c^{2} x^{2} - 1\right) - 4 \, b c^{5} x^{5} \log\left(x\right) + 2 \, b c^{3} x^{3} + b c x + 2 \, b \log\left(-\frac{c x + 1}{c x - 1}\right) + 4 \, a}{20 \, x^{5}}"," ",0,"-1/20*(2*b*c^5*x^5*log(c^2*x^2 - 1) - 4*b*c^5*x^5*log(x) + 2*b*c^3*x^3 + b*c*x + 2*b*log(-(c*x + 1)/(c*x - 1)) + 4*a)/x^5","A",0
13,1,193,0,1.181193," ","integrate(x^5*(a+b*arctanh(c*x))^2,x, algorithm=""fricas"")","\frac{60 \, a^{2} c^{6} x^{6} + 24 \, a b c^{5} x^{5} + 6 \, b^{2} c^{4} x^{4} + 40 \, a b c^{3} x^{3} + 32 \, b^{2} c^{2} x^{2} + 120 \, a b c x + 15 \, {\left(b^{2} c^{6} x^{6} - b^{2}\right)} \log\left(-\frac{c x + 1}{c x - 1}\right)^{2} - 4 \, {\left(15 \, a b - 23 \, b^{2}\right)} \log\left(c x + 1\right) + 4 \, {\left(15 \, a b + 23 \, b^{2}\right)} \log\left(c x - 1\right) + 4 \, {\left(15 \, a b c^{6} x^{6} + 3 \, b^{2} c^{5} x^{5} + 5 \, b^{2} c^{3} x^{3} + 15 \, b^{2} c x\right)} \log\left(-\frac{c x + 1}{c x - 1}\right)}{360 \, c^{6}}"," ",0,"1/360*(60*a^2*c^6*x^6 + 24*a*b*c^5*x^5 + 6*b^2*c^4*x^4 + 40*a*b*c^3*x^3 + 32*b^2*c^2*x^2 + 120*a*b*c*x + 15*(b^2*c^6*x^6 - b^2)*log(-(c*x + 1)/(c*x - 1))^2 - 4*(15*a*b - 23*b^2)*log(c*x + 1) + 4*(15*a*b + 23*b^2)*log(c*x - 1) + 4*(15*a*b*c^6*x^6 + 3*b^2*c^5*x^5 + 5*b^2*c^3*x^3 + 15*b^2*c*x)*log(-(c*x + 1)/(c*x - 1)))/c^6","A",0
14,0,0,0,0.599982," ","integrate(x^4*(a+b*arctanh(c*x))^2,x, algorithm=""fricas"")","{\rm integral}\left(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}, x\right)"," ",0,"integral(b^2*x^4*arctanh(c*x)^2 + 2*a*b*x^4*arctanh(c*x) + a^2*x^4, x)","F",0
15,1,160,0,0.574240," ","integrate(x^3*(a+b*arctanh(c*x))^2,x, algorithm=""fricas"")","\frac{12 \, a^{2} c^{4} x^{4} + 8 \, a b c^{3} x^{3} + 4 \, b^{2} c^{2} x^{2} + 24 \, a b c x + 3 \, {\left(b^{2} c^{4} x^{4} - b^{2}\right)} \log\left(-\frac{c x + 1}{c x - 1}\right)^{2} - 4 \, {\left(3 \, a b - 4 \, b^{2}\right)} \log\left(c x + 1\right) + 4 \, {\left(3 \, a b + 4 \, b^{2}\right)} \log\left(c x - 1\right) + 4 \, {\left(3 \, a b c^{4} x^{4} + b^{2} c^{3} x^{3} + 3 \, b^{2} c x\right)} \log\left(-\frac{c x + 1}{c x - 1}\right)}{48 \, c^{4}}"," ",0,"1/48*(12*a^2*c^4*x^4 + 8*a*b*c^3*x^3 + 4*b^2*c^2*x^2 + 24*a*b*c*x + 3*(b^2*c^4*x^4 - b^2)*log(-(c*x + 1)/(c*x - 1))^2 - 4*(3*a*b - 4*b^2)*log(c*x + 1) + 4*(3*a*b + 4*b^2)*log(c*x - 1) + 4*(3*a*b*c^4*x^4 + b^2*c^3*x^3 + 3*b^2*c*x)*log(-(c*x + 1)/(c*x - 1)))/c^4","A",0
16,0,0,0,0.443925," ","integrate(x^2*(a+b*arctanh(c*x))^2,x, algorithm=""fricas"")","{\rm integral}\left(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}, x\right)"," ",0,"integral(b^2*x^2*arctanh(c*x)^2 + 2*a*b*x^2*arctanh(c*x) + a^2*x^2, x)","F",0
17,1,122,0,0.613395," ","integrate(x*(a+b*arctanh(c*x))^2,x, algorithm=""fricas"")","\frac{4 \, a^{2} c^{2} x^{2} + 8 \, a b c x + {\left(b^{2} c^{2} x^{2} - b^{2}\right)} \log\left(-\frac{c x + 1}{c x - 1}\right)^{2} - 4 \, {\left(a b - b^{2}\right)} \log\left(c x + 1\right) + 4 \, {\left(a b + b^{2}\right)} \log\left(c x - 1\right) + 4 \, {\left(a b c^{2} x^{2} + b^{2} c x\right)} \log\left(-\frac{c x + 1}{c x - 1}\right)}{8 \, c^{2}}"," ",0,"1/8*(4*a^2*c^2*x^2 + 8*a*b*c*x + (b^2*c^2*x^2 - b^2)*log(-(c*x + 1)/(c*x - 1))^2 - 4*(a*b - b^2)*log(c*x + 1) + 4*(a*b + b^2)*log(c*x - 1) + 4*(a*b*c^2*x^2 + b^2*c*x)*log(-(c*x + 1)/(c*x - 1)))/c^2","A",0
18,0,0,0,0.528422," ","integrate((a+b*arctanh(c*x))^2,x, algorithm=""fricas"")","{\rm integral}\left(b^{2} \operatorname{artanh}\left(c x\right)^{2} + 2 \, a b \operatorname{artanh}\left(c x\right) + a^{2}, x\right)"," ",0,"integral(b^2*arctanh(c*x)^2 + 2*a*b*arctanh(c*x) + a^2, x)","F",0
19,0,0,0,0.618414," ","integrate((a+b*arctanh(c*x))^2/x,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}}{x}, x\right)"," ",0,"integral((b^2*arctanh(c*x)^2 + 2*a*b*arctanh(c*x) + a^2)/x, x)","F",0
20,0,0,0,0.652140," ","integrate((a+b*arctanh(c*x))^2/x^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}}{x^{2}}, x\right)"," ",0,"integral((b^2*arctanh(c*x)^2 + 2*a*b*arctanh(c*x) + a^2)/x^2, x)","F",0
21,1,135,0,0.707393," ","integrate((a+b*arctanh(c*x))^2/x^3,x, algorithm=""fricas"")","\frac{8 \, b^{2} c^{2} x^{2} \log\left(x\right) + 4 \, {\left(a b - b^{2}\right)} c^{2} x^{2} \log\left(c x + 1\right) - 4 \, {\left(a b + b^{2}\right)} c^{2} x^{2} \log\left(c x - 1\right) - 8 \, a b c x + {\left(b^{2} c^{2} x^{2} - b^{2}\right)} \log\left(-\frac{c x + 1}{c x - 1}\right)^{2} - 4 \, a^{2} - 4 \, {\left(b^{2} c x + a b\right)} \log\left(-\frac{c x + 1}{c x - 1}\right)}{8 \, x^{2}}"," ",0,"1/8*(8*b^2*c^2*x^2*log(x) + 4*(a*b - b^2)*c^2*x^2*log(c*x + 1) - 4*(a*b + b^2)*c^2*x^2*log(c*x - 1) - 8*a*b*c*x + (b^2*c^2*x^2 - b^2)*log(-(c*x + 1)/(c*x - 1))^2 - 4*a^2 - 4*(b^2*c*x + a*b)*log(-(c*x + 1)/(c*x - 1)))/x^2","A",0
22,0,0,0,0.460345," ","integrate((a+b*arctanh(c*x))^2/x^4,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}}{x^{4}}, x\right)"," ",0,"integral((b^2*arctanh(c*x)^2 + 2*a*b*arctanh(c*x) + a^2)/x^4, x)","F",0
23,1,173,0,0.900041," ","integrate((a+b*arctanh(c*x))^2/x^5,x, algorithm=""fricas"")","\frac{32 \, b^{2} c^{4} x^{4} \log\left(x\right) + 4 \, {\left(3 \, a b - 4 \, b^{2}\right)} c^{4} x^{4} \log\left(c x + 1\right) - 4 \, {\left(3 \, a b + 4 \, b^{2}\right)} c^{4} x^{4} \log\left(c x - 1\right) - 24 \, a b c^{3} x^{3} - 4 \, b^{2} c^{2} x^{2} - 8 \, a b c x + 3 \, {\left(b^{2} c^{4} x^{4} - b^{2}\right)} \log\left(-\frac{c x + 1}{c x - 1}\right)^{2} - 12 \, a^{2} - 4 \, {\left(3 \, b^{2} c^{3} x^{3} + b^{2} c x + 3 \, a b\right)} \log\left(-\frac{c x + 1}{c x - 1}\right)}{48 \, x^{4}}"," ",0,"1/48*(32*b^2*c^4*x^4*log(x) + 4*(3*a*b - 4*b^2)*c^4*x^4*log(c*x + 1) - 4*(3*a*b + 4*b^2)*c^4*x^4*log(c*x - 1) - 24*a*b*c^3*x^3 - 4*b^2*c^2*x^2 - 8*a*b*c*x + 3*(b^2*c^4*x^4 - b^2)*log(-(c*x + 1)/(c*x - 1))^2 - 12*a^2 - 4*(3*b^2*c^3*x^3 + b^2*c*x + 3*a*b)*log(-(c*x + 1)/(c*x - 1)))/x^4","A",0
24,0,0,0,0.513942," ","integrate(x^5*(a+b*arctanh(c*x))^3,x, algorithm=""fricas"")","{\rm integral}\left(b^{3} x^{5} \operatorname{artanh}\left(c x\right)^{3} + 3 \, a b^{2} x^{5} \operatorname{artanh}\left(c x\right)^{2} + 3 \, a^{2} b x^{5} \operatorname{artanh}\left(c x\right) + a^{3} x^{5}, x\right)"," ",0,"integral(b^3*x^5*arctanh(c*x)^3 + 3*a*b^2*x^5*arctanh(c*x)^2 + 3*a^2*b*x^5*arctanh(c*x) + a^3*x^5, x)","F",0
25,0,0,0,0.692461," ","integrate(x^4*(a+b*arctanh(c*x))^3,x, algorithm=""fricas"")","{\rm integral}\left(b^{3} x^{4} \operatorname{artanh}\left(c x\right)^{3} + 3 \, a b^{2} x^{4} \operatorname{artanh}\left(c x\right)^{2} + 3 \, a^{2} b x^{4} \operatorname{artanh}\left(c x\right) + a^{3} x^{4}, x\right)"," ",0,"integral(b^3*x^4*arctanh(c*x)^3 + 3*a*b^2*x^4*arctanh(c*x)^2 + 3*a^2*b*x^4*arctanh(c*x) + a^3*x^4, x)","F",0
26,0,0,0,1.142887," ","integrate(x^3*(a+b*arctanh(c*x))^3,x, algorithm=""fricas"")","{\rm integral}\left(b^{3} x^{3} \operatorname{artanh}\left(c x\right)^{3} + 3 \, a b^{2} x^{3} \operatorname{artanh}\left(c x\right)^{2} + 3 \, a^{2} b x^{3} \operatorname{artanh}\left(c x\right) + a^{3} x^{3}, x\right)"," ",0,"integral(b^3*x^3*arctanh(c*x)^3 + 3*a*b^2*x^3*arctanh(c*x)^2 + 3*a^2*b*x^3*arctanh(c*x) + a^3*x^3, x)","F",0
27,0,0,0,0.649404," ","integrate(x^2*(a+b*arctanh(c*x))^3,x, algorithm=""fricas"")","{\rm integral}\left(b^{3} x^{2} \operatorname{artanh}\left(c x\right)^{3} + 3 \, a b^{2} x^{2} \operatorname{artanh}\left(c x\right)^{2} + 3 \, a^{2} b x^{2} \operatorname{artanh}\left(c x\right) + a^{3} x^{2}, x\right)"," ",0,"integral(b^3*x^2*arctanh(c*x)^3 + 3*a*b^2*x^2*arctanh(c*x)^2 + 3*a^2*b*x^2*arctanh(c*x) + a^3*x^2, x)","F",0
28,0,0,0,0.518584," ","integrate(x*(a+b*arctanh(c*x))^3,x, algorithm=""fricas"")","{\rm integral}\left(b^{3} x \operatorname{artanh}\left(c x\right)^{3} + 3 \, a b^{2} x \operatorname{artanh}\left(c x\right)^{2} + 3 \, a^{2} b x \operatorname{artanh}\left(c x\right) + a^{3} x, x\right)"," ",0,"integral(b^3*x*arctanh(c*x)^3 + 3*a*b^2*x*arctanh(c*x)^2 + 3*a^2*b*x*arctanh(c*x) + a^3*x, x)","F",0
29,0,0,0,0.641937," ","integrate((a+b*arctanh(c*x))^3,x, algorithm=""fricas"")","{\rm integral}\left(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}, 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, x)","F",0
30,0,0,0,0.822255," ","integrate((a+b*arctanh(c*x))^3/x,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}}{x}, 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)/x, x)","F",0
31,0,0,0,1.594704," ","integrate((a+b*arctanh(c*x))^3/x^2,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}}{x^{2}}, 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)/x^2, x)","F",0
32,0,0,0,0.549582," ","integrate((a+b*arctanh(c*x))^3/x^3,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}}{x^{3}}, 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)/x^3, x)","F",0
33,0,0,0,0.626746," ","integrate((a+b*arctanh(c*x))^3/x^4,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}}{x^{4}}, 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)/x^4, x)","F",0
34,0,0,0,1.050510," ","integrate((a+b*arctanh(c*x))^3/x^5,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}}{x^{5}}, 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)/x^5, x)","F",0
35,1,296,0,0.578599," ","integrate((d*x)^(5/2)*(a+b*arctanh(c*x)),x, algorithm=""fricas"")","\left[-\frac{10 \, b d^{2} \sqrt{\frac{d}{c}} \arctan\left(\frac{\sqrt{d x} c \sqrt{\frac{d}{c}}}{d}\right) - 5 \, b d^{2} \sqrt{\frac{d}{c}} \log\left(\frac{c d x - 2 \, \sqrt{d x} c \sqrt{\frac{d}{c}} + d}{c x - 1}\right) - {\left(5 \, b c^{3} d^{2} x^{3} \log\left(-\frac{c x + 1}{c x - 1}\right) + 10 \, a c^{3} d^{2} x^{3} + 4 \, b c^{2} d^{2} x^{2} + 20 \, b d^{2}\right)} \sqrt{d x}}{35 \, c^{3}}, \frac{10 \, b d^{2} \sqrt{-\frac{d}{c}} \arctan\left(\frac{\sqrt{d x} c \sqrt{-\frac{d}{c}}}{d}\right) + 5 \, b d^{2} \sqrt{-\frac{d}{c}} \log\left(\frac{c d x - 2 \, \sqrt{d x} c \sqrt{-\frac{d}{c}} - d}{c x + 1}\right) + {\left(5 \, b c^{3} d^{2} x^{3} \log\left(-\frac{c x + 1}{c x - 1}\right) + 10 \, a c^{3} d^{2} x^{3} + 4 \, b c^{2} d^{2} x^{2} + 20 \, b d^{2}\right)} \sqrt{d x}}{35 \, c^{3}}\right]"," ",0,"[-1/35*(10*b*d^2*sqrt(d/c)*arctan(sqrt(d*x)*c*sqrt(d/c)/d) - 5*b*d^2*sqrt(d/c)*log((c*d*x - 2*sqrt(d*x)*c*sqrt(d/c) + d)/(c*x - 1)) - (5*b*c^3*d^2*x^3*log(-(c*x + 1)/(c*x - 1)) + 10*a*c^3*d^2*x^3 + 4*b*c^2*d^2*x^2 + 20*b*d^2)*sqrt(d*x))/c^3, 1/35*(10*b*d^2*sqrt(-d/c)*arctan(sqrt(d*x)*c*sqrt(-d/c)/d) + 5*b*d^2*sqrt(-d/c)*log((c*d*x - 2*sqrt(d*x)*c*sqrt(-d/c) - d)/(c*x + 1)) + (5*b*c^3*d^2*x^3*log(-(c*x + 1)/(c*x - 1)) + 10*a*c^3*d^2*x^3 + 4*b*c^2*d^2*x^2 + 20*b*d^2)*sqrt(d*x))/c^3]","A",0
36,1,255,0,0.663677," ","integrate((d*x)^(3/2)*(a+b*arctanh(c*x)),x, algorithm=""fricas"")","\left[\frac{6 \, b d \sqrt{\frac{d}{c}} \arctan\left(\frac{\sqrt{d x} c \sqrt{\frac{d}{c}}}{d}\right) + 3 \, b d \sqrt{\frac{d}{c}} \log\left(\frac{c d x - 2 \, \sqrt{d x} c \sqrt{\frac{d}{c}} + d}{c x - 1}\right) + {\left(3 \, b c^{2} d x^{2} \log\left(-\frac{c x + 1}{c x - 1}\right) + 6 \, a c^{2} d x^{2} + 4 \, b c d x\right)} \sqrt{d x}}{15 \, c^{2}}, \frac{6 \, b d \sqrt{-\frac{d}{c}} \arctan\left(\frac{\sqrt{d x} c \sqrt{-\frac{d}{c}}}{d}\right) + 3 \, b d \sqrt{-\frac{d}{c}} \log\left(\frac{c d x + 2 \, \sqrt{d x} c \sqrt{-\frac{d}{c}} - d}{c x + 1}\right) + {\left(3 \, b c^{2} d x^{2} \log\left(-\frac{c x + 1}{c x - 1}\right) + 6 \, a c^{2} d x^{2} + 4 \, b c d x\right)} \sqrt{d x}}{15 \, c^{2}}\right]"," ",0,"[1/15*(6*b*d*sqrt(d/c)*arctan(sqrt(d*x)*c*sqrt(d/c)/d) + 3*b*d*sqrt(d/c)*log((c*d*x - 2*sqrt(d*x)*c*sqrt(d/c) + d)/(c*x - 1)) + (3*b*c^2*d*x^2*log(-(c*x + 1)/(c*x - 1)) + 6*a*c^2*d*x^2 + 4*b*c*d*x)*sqrt(d*x))/c^2, 1/15*(6*b*d*sqrt(-d/c)*arctan(sqrt(d*x)*c*sqrt(-d/c)/d) + 3*b*d*sqrt(-d/c)*log((c*d*x + 2*sqrt(d*x)*c*sqrt(-d/c) - d)/(c*x + 1)) + (3*b*c^2*d*x^2*log(-(c*x + 1)/(c*x - 1)) + 6*a*c^2*d*x^2 + 4*b*c*d*x)*sqrt(d*x))/c^2]","A",0
37,1,223,0,0.749779," ","integrate((d*x)^(1/2)*(a+b*arctanh(c*x)),x, algorithm=""fricas"")","\left[-\frac{2 \, b \sqrt{\frac{d}{c}} \arctan\left(\frac{\sqrt{d x} c \sqrt{\frac{d}{c}}}{d}\right) - b \sqrt{\frac{d}{c}} \log\left(\frac{c d x - 2 \, \sqrt{d x} c \sqrt{\frac{d}{c}} + d}{c x - 1}\right) - {\left(b c x \log\left(-\frac{c x + 1}{c x - 1}\right) + 2 \, a c x + 4 \, b\right)} \sqrt{d x}}{3 \, c}, \frac{2 \, b \sqrt{-\frac{d}{c}} \arctan\left(\frac{\sqrt{d x} c \sqrt{-\frac{d}{c}}}{d}\right) + b \sqrt{-\frac{d}{c}} \log\left(\frac{c d x - 2 \, \sqrt{d x} c \sqrt{-\frac{d}{c}} - d}{c x + 1}\right) + {\left(b c x \log\left(-\frac{c x + 1}{c x - 1}\right) + 2 \, a c x + 4 \, b\right)} \sqrt{d x}}{3 \, c}\right]"," ",0,"[-1/3*(2*b*sqrt(d/c)*arctan(sqrt(d*x)*c*sqrt(d/c)/d) - b*sqrt(d/c)*log((c*d*x - 2*sqrt(d*x)*c*sqrt(d/c) + d)/(c*x - 1)) - (b*c*x*log(-(c*x + 1)/(c*x - 1)) + 2*a*c*x + 4*b)*sqrt(d*x))/c, 1/3*(2*b*sqrt(-d/c)*arctan(sqrt(d*x)*c*sqrt(-d/c)/d) + b*sqrt(-d/c)*log((c*d*x - 2*sqrt(d*x)*c*sqrt(-d/c) - d)/(c*x + 1)) + (b*c*x*log(-(c*x + 1)/(c*x - 1)) + 2*a*c*x + 4*b)*sqrt(d*x))/c]","A",0
38,1,211,0,0.552722," ","integrate((a+b*arctanh(c*x))/(d*x)^(1/2),x, algorithm=""fricas"")","\left[-\frac{2 \, \sqrt{c d} b \arctan\left(\frac{\sqrt{c d} \sqrt{d x}}{c d x}\right) - \sqrt{c d} b \log\left(\frac{c d x - 2 \, \sqrt{c d} \sqrt{d x} + d}{c x - 1}\right) - {\left(b c \log\left(-\frac{c x + 1}{c x - 1}\right) + 2 \, a c\right)} \sqrt{d x}}{c d}, \frac{2 \, \sqrt{-c d} b \arctan\left(\frac{\sqrt{-c d} \sqrt{d x}}{c d x}\right) - \sqrt{-c d} b \log\left(\frac{c d x - 2 \, \sqrt{-c d} \sqrt{d x} - d}{c x + 1}\right) + {\left(b c \log\left(-\frac{c x + 1}{c x - 1}\right) + 2 \, a c\right)} \sqrt{d x}}{c d}\right]"," ",0,"[-(2*sqrt(c*d)*b*arctan(sqrt(c*d)*sqrt(d*x)/(c*d*x)) - sqrt(c*d)*b*log((c*d*x - 2*sqrt(c*d)*sqrt(d*x) + d)/(c*x - 1)) - (b*c*log(-(c*x + 1)/(c*x - 1)) + 2*a*c)*sqrt(d*x))/(c*d), (2*sqrt(-c*d)*b*arctan(sqrt(-c*d)*sqrt(d*x)/(c*d*x)) - sqrt(-c*d)*b*log((c*d*x - 2*sqrt(-c*d)*sqrt(d*x) - d)/(c*x + 1)) + (b*c*log(-(c*x + 1)/(c*x - 1)) + 2*a*c)*sqrt(d*x))/(c*d)]","A",0
39,1,221,0,0.653696," ","integrate((a+b*arctanh(c*x))/(d*x)^(3/2),x, algorithm=""fricas"")","\left[-\frac{2 \, b d x \sqrt{\frac{c}{d}} \arctan\left(\frac{\sqrt{d x} \sqrt{\frac{c}{d}}}{c x}\right) - b d x \sqrt{\frac{c}{d}} \log\left(\frac{c x + 2 \, \sqrt{d x} \sqrt{\frac{c}{d}} + 1}{c x - 1}\right) + \sqrt{d x} {\left(b \log\left(-\frac{c x + 1}{c x - 1}\right) + 2 \, a\right)}}{d^{2} x}, -\frac{2 \, b d x \sqrt{-\frac{c}{d}} \arctan\left(\frac{\sqrt{d x} \sqrt{-\frac{c}{d}}}{c x}\right) - b d x \sqrt{-\frac{c}{d}} \log\left(\frac{c x + 2 \, \sqrt{d x} \sqrt{-\frac{c}{d}} - 1}{c x + 1}\right) + \sqrt{d x} {\left(b \log\left(-\frac{c x + 1}{c x - 1}\right) + 2 \, a\right)}}{d^{2} x}\right]"," ",0,"[-(2*b*d*x*sqrt(c/d)*arctan(sqrt(d*x)*sqrt(c/d)/(c*x)) - b*d*x*sqrt(c/d)*log((c*x + 2*sqrt(d*x)*sqrt(c/d) + 1)/(c*x - 1)) + sqrt(d*x)*(b*log(-(c*x + 1)/(c*x - 1)) + 2*a))/(d^2*x), -(2*b*d*x*sqrt(-c/d)*arctan(sqrt(d*x)*sqrt(-c/d)/(c*x)) - b*d*x*sqrt(-c/d)*log((c*x + 2*sqrt(d*x)*sqrt(-c/d) - 1)/(c*x + 1)) + sqrt(d*x)*(b*log(-(c*x + 1)/(c*x - 1)) + 2*a))/(d^2*x)]","A",0
40,1,243,0,1.265285," ","integrate((a+b*arctanh(c*x))/(d*x)^(5/2),x, algorithm=""fricas"")","\left[\frac{2 \, b c d x^{2} \sqrt{\frac{c}{d}} \arctan\left(\frac{\sqrt{d x} \sqrt{\frac{c}{d}}}{c x}\right) + b c d x^{2} \sqrt{\frac{c}{d}} \log\left(\frac{c x + 2 \, \sqrt{d x} \sqrt{\frac{c}{d}} + 1}{c x - 1}\right) - {\left(4 \, b c x + b \log\left(-\frac{c x + 1}{c x - 1}\right) + 2 \, a\right)} \sqrt{d x}}{3 \, d^{3} x^{2}}, -\frac{2 \, b c d x^{2} \sqrt{-\frac{c}{d}} \arctan\left(\frac{\sqrt{d x} \sqrt{-\frac{c}{d}}}{c x}\right) - b c d x^{2} \sqrt{-\frac{c}{d}} \log\left(\frac{c x - 2 \, \sqrt{d x} \sqrt{-\frac{c}{d}} - 1}{c x + 1}\right) + {\left(4 \, b c x + b \log\left(-\frac{c x + 1}{c x - 1}\right) + 2 \, a\right)} \sqrt{d x}}{3 \, d^{3} x^{2}}\right]"," ",0,"[1/3*(2*b*c*d*x^2*sqrt(c/d)*arctan(sqrt(d*x)*sqrt(c/d)/(c*x)) + b*c*d*x^2*sqrt(c/d)*log((c*x + 2*sqrt(d*x)*sqrt(c/d) + 1)/(c*x - 1)) - (4*b*c*x + b*log(-(c*x + 1)/(c*x - 1)) + 2*a)*sqrt(d*x))/(d^3*x^2), -1/3*(2*b*c*d*x^2*sqrt(-c/d)*arctan(sqrt(d*x)*sqrt(-c/d)/(c*x)) - b*c*d*x^2*sqrt(-c/d)*log((c*x - 2*sqrt(d*x)*sqrt(-c/d) - 1)/(c*x + 1)) + (4*b*c*x + b*log(-(c*x + 1)/(c*x - 1)) + 2*a)*sqrt(d*x))/(d^3*x^2)]","A",0
41,1,253,0,0.647118," ","integrate((a+b*arctanh(c*x))/(d*x)^(7/2),x, algorithm=""fricas"")","\left[-\frac{6 \, b c^{2} d x^{3} \sqrt{\frac{c}{d}} \arctan\left(\frac{\sqrt{d x} \sqrt{\frac{c}{d}}}{c x}\right) - 3 \, b c^{2} d x^{3} \sqrt{\frac{c}{d}} \log\left(\frac{c x + 2 \, \sqrt{d x} \sqrt{\frac{c}{d}} + 1}{c x - 1}\right) + {\left(4 \, b c x + 3 \, b \log\left(-\frac{c x + 1}{c x - 1}\right) + 6 \, a\right)} \sqrt{d x}}{15 \, d^{4} x^{3}}, -\frac{6 \, b c^{2} d x^{3} \sqrt{-\frac{c}{d}} \arctan\left(\frac{\sqrt{d x} \sqrt{-\frac{c}{d}}}{c x}\right) - 3 \, b c^{2} d x^{3} \sqrt{-\frac{c}{d}} \log\left(\frac{c x + 2 \, \sqrt{d x} \sqrt{-\frac{c}{d}} - 1}{c x + 1}\right) + {\left(4 \, b c x + 3 \, b \log\left(-\frac{c x + 1}{c x - 1}\right) + 6 \, a\right)} \sqrt{d x}}{15 \, d^{4} x^{3}}\right]"," ",0,"[-1/15*(6*b*c^2*d*x^3*sqrt(c/d)*arctan(sqrt(d*x)*sqrt(c/d)/(c*x)) - 3*b*c^2*d*x^3*sqrt(c/d)*log((c*x + 2*sqrt(d*x)*sqrt(c/d) + 1)/(c*x - 1)) + (4*b*c*x + 3*b*log(-(c*x + 1)/(c*x - 1)) + 6*a)*sqrt(d*x))/(d^4*x^3), -1/15*(6*b*c^2*d*x^3*sqrt(-c/d)*arctan(sqrt(d*x)*sqrt(-c/d)/(c*x)) - 3*b*c^2*d*x^3*sqrt(-c/d)*log((c*x + 2*sqrt(d*x)*sqrt(-c/d) - 1)/(c*x + 1)) + (4*b*c*x + 3*b*log(-(c*x + 1)/(c*x - 1)) + 6*a)*sqrt(d*x))/(d^4*x^3)]","A",0
42,1,272,0,1.481874," ","integrate((a+b*arctanh(c*x))/(d*x)^(9/2),x, algorithm=""fricas"")","\left[\frac{10 \, b c^{3} d x^{4} \sqrt{\frac{c}{d}} \arctan\left(\frac{\sqrt{d x} \sqrt{\frac{c}{d}}}{c x}\right) + 5 \, b c^{3} d x^{4} \sqrt{\frac{c}{d}} \log\left(\frac{c x + 2 \, \sqrt{d x} \sqrt{\frac{c}{d}} + 1}{c x - 1}\right) - {\left(20 \, b c^{3} x^{3} + 4 \, b c x + 5 \, b \log\left(-\frac{c x + 1}{c x - 1}\right) + 10 \, a\right)} \sqrt{d x}}{35 \, d^{5} x^{4}}, -\frac{10 \, b c^{3} d x^{4} \sqrt{-\frac{c}{d}} \arctan\left(\frac{\sqrt{d x} \sqrt{-\frac{c}{d}}}{c x}\right) - 5 \, b c^{3} d x^{4} \sqrt{-\frac{c}{d}} \log\left(\frac{c x - 2 \, \sqrt{d x} \sqrt{-\frac{c}{d}} - 1}{c x + 1}\right) + {\left(20 \, b c^{3} x^{3} + 4 \, b c x + 5 \, b \log\left(-\frac{c x + 1}{c x - 1}\right) + 10 \, a\right)} \sqrt{d x}}{35 \, d^{5} x^{4}}\right]"," ",0,"[1/35*(10*b*c^3*d*x^4*sqrt(c/d)*arctan(sqrt(d*x)*sqrt(c/d)/(c*x)) + 5*b*c^3*d*x^4*sqrt(c/d)*log((c*x + 2*sqrt(d*x)*sqrt(c/d) + 1)/(c*x - 1)) - (20*b*c^3*x^3 + 4*b*c*x + 5*b*log(-(c*x + 1)/(c*x - 1)) + 10*a)*sqrt(d*x))/(d^5*x^4), -1/35*(10*b*c^3*d*x^4*sqrt(-c/d)*arctan(sqrt(d*x)*sqrt(-c/d)/(c*x)) - 5*b*c^3*d*x^4*sqrt(-c/d)*log((c*x - 2*sqrt(d*x)*sqrt(-c/d) - 1)/(c*x + 1)) + (20*b*c^3*x^3 + 4*b*c*x + 5*b*log(-(c*x + 1)/(c*x - 1)) + 10*a)*sqrt(d*x))/(d^5*x^4)]","A",0
43,0,0,0,1.078548," ","integrate((d*x)^m*(a+b*arctanh(c*x))^3,x, algorithm=""fricas"")","{\rm integral}\left({\left(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}\right)} \left(d x\right)^{m}, 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)*(d*x)^m, x)","F",0
44,0,0,0,0.563785," ","integrate((d*x)^m*(a+b*arctanh(c*x))^2,x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{2} \operatorname{artanh}\left(c x\right)^{2} + 2 \, a b \operatorname{artanh}\left(c x\right) + a^{2}\right)} \left(d x\right)^{m}, x\right)"," ",0,"integral((b^2*arctanh(c*x)^2 + 2*a*b*arctanh(c*x) + a^2)*(d*x)^m, x)","F",0
45,0,0,0,0.739217," ","integrate((d*x)^m*(a+b*arctanh(c*x)),x, algorithm=""fricas"")","{\rm integral}\left({\left(b \operatorname{artanh}\left(c x\right) + a\right)} \left(d x\right)^{m}, x\right)"," ",0,"integral((b*arctanh(c*x) + a)*(d*x)^m, x)","F",0
46,0,0,0,1.538090," ","integrate((d*x)^m/(a+b*arctanh(c*x)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(d x\right)^{m}}{b \operatorname{artanh}\left(c x\right) + a}, x\right)"," ",0,"integral((d*x)^m/(b*arctanh(c*x) + a), x)","F",0
47,0,0,0,1.367615," ","integrate((d*x)^m/(a+b*arctanh(c*x))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(d x\right)^{m}}{b^{2} \operatorname{artanh}\left(c x\right)^{2} + 2 \, a b \operatorname{artanh}\left(c x\right) + a^{2}}, x\right)"," ",0,"integral((d*x)^m/(b^2*arctanh(c*x)^2 + 2*a*b*arctanh(c*x) + a^2), x)","F",0
48,0,0,0,2.140225," ","integrate((a+b*arctanh(c*x))^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(b \operatorname{artanh}\left(c x\right) + a\right)}^{p}, x\right)"," ",0,"integral((b*arctanh(c*x) + a)^p, x)","F",0
49,0,0,0,1.055711," ","integrate((d*x)^m*(a+b*arctanh(c*x))^p,x, algorithm=""fricas"")","{\rm integral}\left(\left(d x\right)^{m} {\left(b \operatorname{artanh}\left(c x\right) + a\right)}^{p}, x\right)"," ",0,"integral((d*x)^m*(b*arctanh(c*x) + a)^p, x)","F",0
50,1,64,0,0.713167," ","integrate(x^7*(a+b*arctanh(c*x^2)),x, algorithm=""fricas"")","\frac{6 \, a c^{4} x^{8} + 2 \, b c^{3} x^{6} + 6 \, b c x^{2} + 3 \, {\left(b c^{4} x^{8} - b\right)} \log\left(-\frac{c x^{2} + 1}{c x^{2} - 1}\right)}{48 \, c^{4}}"," ",0,"1/48*(6*a*c^4*x^8 + 2*b*c^3*x^6 + 6*b*c*x^2 + 3*(b*c^4*x^8 - b)*log(-(c*x^2 + 1)/(c*x^2 - 1)))/c^4","A",0
51,1,62,0,1.071465," ","integrate(x^5*(a+b*arctanh(c*x^2)),x, algorithm=""fricas"")","\frac{b c^{3} x^{6} \log\left(-\frac{c x^{2} + 1}{c x^{2} - 1}\right) + 2 \, a c^{3} x^{6} + b c^{2} x^{4} + b \log\left(c^{2} x^{4} - 1\right)}{12 \, c^{3}}"," ",0,"1/12*(b*c^3*x^6*log(-(c*x^2 + 1)/(c*x^2 - 1)) + 2*a*c^3*x^6 + b*c^2*x^4 + b*log(c^2*x^4 - 1))/c^3","A",0
52,1,54,0,1.465683," ","integrate(x^3*(a+b*arctanh(c*x^2)),x, algorithm=""fricas"")","\frac{2 \, a c^{2} x^{4} + 2 \, b c x^{2} + {\left(b c^{2} x^{4} - b\right)} \log\left(-\frac{c x^{2} + 1}{c x^{2} - 1}\right)}{8 \, c^{2}}"," ",0,"1/8*(2*a*c^2*x^4 + 2*b*c*x^2 + (b*c^2*x^4 - b)*log(-(c*x^2 + 1)/(c*x^2 - 1)))/c^2","A",0
53,1,50,0,0.842844," ","integrate(x*(a+b*arctanh(c*x^2)),x, algorithm=""fricas"")","\frac{b c x^{2} \log\left(-\frac{c x^{2} + 1}{c x^{2} - 1}\right) + 2 \, a c x^{2} + b \log\left(c^{2} x^{4} - 1\right)}{4 \, c}"," ",0,"1/4*(b*c*x^2*log(-(c*x^2 + 1)/(c*x^2 - 1)) + 2*a*c*x^2 + b*log(c^2*x^4 - 1))/c","A",0
54,0,0,0,0.412339," ","integrate((a+b*arctanh(c*x^2))/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \operatorname{artanh}\left(c x^{2}\right) + a}{x}, x\right)"," ",0,"integral((b*arctanh(c*x^2) + a)/x, x)","F",0
55,1,55,0,0.698429," ","integrate((a+b*arctanh(c*x^2))/x^3,x, algorithm=""fricas"")","-\frac{b c x^{2} \log\left(c^{2} x^{4} - 1\right) - 4 \, b c x^{2} \log\left(x\right) + b \log\left(-\frac{c x^{2} + 1}{c x^{2} - 1}\right) + 2 \, a}{4 \, x^{2}}"," ",0,"-1/4*(b*c*x^2*log(c^2*x^4 - 1) - 4*b*c*x^2*log(x) + b*log(-(c*x^2 + 1)/(c*x^2 - 1)) + 2*a)/x^2","A",0
56,1,49,0,1.103768," ","integrate((a+b*arctanh(c*x^2))/x^5,x, algorithm=""fricas"")","-\frac{2 \, b c x^{2} - {\left(b c^{2} x^{4} - b\right)} \log\left(-\frac{c x^{2} + 1}{c x^{2} - 1}\right) + 2 \, a}{8 \, x^{4}}"," ",0,"-1/8*(2*b*c*x^2 - (b*c^2*x^4 - b)*log(-(c*x^2 + 1)/(c*x^2 - 1)) + 2*a)/x^4","A",0
57,1,65,0,0.892190," ","integrate((a+b*arctanh(c*x^2))/x^7,x, algorithm=""fricas"")","-\frac{b c^{3} x^{6} \log\left(c^{2} x^{4} - 1\right) - 4 \, b c^{3} x^{6} \log\left(x\right) + b c x^{2} + b \log\left(-\frac{c x^{2} + 1}{c x^{2} - 1}\right) + 2 \, a}{12 \, x^{6}}"," ",0,"-1/12*(b*c^3*x^6*log(c^2*x^4 - 1) - 4*b*c^3*x^6*log(x) + b*c*x^2 + b*log(-(c*x^2 + 1)/(c*x^2 - 1)) + 2*a)/x^6","A",0
58,1,197,0,0.878566," ","integrate(x^4*(a+b*arctanh(c*x^2)),x, algorithm=""fricas"")","\left[\frac{3 \, b c^{3} x^{5} \log\left(-\frac{c x^{2} + 1}{c x^{2} - 1}\right) + 6 \, a c^{3} x^{5} + 4 \, b c^{2} x^{3} + 6 \, b \sqrt{c} \arctan\left(\sqrt{c} x\right) + 3 \, b \sqrt{c} \log\left(\frac{c x^{2} - 2 \, \sqrt{c} x + 1}{c x^{2} - 1}\right)}{30 \, c^{3}}, \frac{3 \, b c^{3} x^{5} \log\left(-\frac{c x^{2} + 1}{c x^{2} - 1}\right) + 6 \, a c^{3} x^{5} + 4 \, b c^{2} x^{3} + 6 \, b \sqrt{-c} \arctan\left(\sqrt{-c} x\right) - 3 \, b \sqrt{-c} \log\left(\frac{c x^{2} - 2 \, \sqrt{-c} x - 1}{c x^{2} + 1}\right)}{30 \, c^{3}}\right]"," ",0,"[1/30*(3*b*c^3*x^5*log(-(c*x^2 + 1)/(c*x^2 - 1)) + 6*a*c^3*x^5 + 4*b*c^2*x^3 + 6*b*sqrt(c)*arctan(sqrt(c)*x) + 3*b*sqrt(c)*log((c*x^2 - 2*sqrt(c)*x + 1)/(c*x^2 - 1)))/c^3, 1/30*(3*b*c^3*x^5*log(-(c*x^2 + 1)/(c*x^2 - 1)) + 6*a*c^3*x^5 + 4*b*c^2*x^3 + 6*b*sqrt(-c)*arctan(sqrt(-c)*x) - 3*b*sqrt(-c)*log((c*x^2 - 2*sqrt(-c)*x - 1)/(c*x^2 + 1)))/c^3]","A",0
59,1,186,0,0.921044," ","integrate(x^2*(a+b*arctanh(c*x^2)),x, algorithm=""fricas"")","\left[\frac{b c^{2} x^{3} \log\left(-\frac{c x^{2} + 1}{c x^{2} - 1}\right) + 2 \, a c^{2} x^{3} + 4 \, b c x - 2 \, b \sqrt{c} \arctan\left(\sqrt{c} x\right) + b \sqrt{c} \log\left(\frac{c x^{2} - 2 \, \sqrt{c} x + 1}{c x^{2} - 1}\right)}{6 \, c^{2}}, \frac{b c^{2} x^{3} \log\left(-\frac{c x^{2} + 1}{c x^{2} - 1}\right) + 2 \, a c^{2} x^{3} + 4 \, b c x + 2 \, b \sqrt{-c} \arctan\left(\sqrt{-c} x\right) - b \sqrt{-c} \log\left(\frac{c x^{2} + 2 \, \sqrt{-c} x - 1}{c x^{2} + 1}\right)}{6 \, c^{2}}\right]"," ",0,"[1/6*(b*c^2*x^3*log(-(c*x^2 + 1)/(c*x^2 - 1)) + 2*a*c^2*x^3 + 4*b*c*x - 2*b*sqrt(c)*arctan(sqrt(c)*x) + b*sqrt(c)*log((c*x^2 - 2*sqrt(c)*x + 1)/(c*x^2 - 1)))/c^2, 1/6*(b*c^2*x^3*log(-(c*x^2 + 1)/(c*x^2 - 1)) + 2*a*c^2*x^3 + 4*b*c*x + 2*b*sqrt(-c)*arctan(sqrt(-c)*x) - b*sqrt(-c)*log((c*x^2 + 2*sqrt(-c)*x - 1)/(c*x^2 + 1)))/c^2]","A",0
60,1,160,0,0.876934," ","integrate(a+b*arctanh(c*x^2),x, algorithm=""fricas"")","\left[\frac{b c x \log\left(-\frac{c x^{2} + 1}{c x^{2} - 1}\right) + 2 \, a c x + 2 \, b \sqrt{c} \arctan\left(\sqrt{c} x\right) + b \sqrt{c} \log\left(\frac{c x^{2} - 2 \, \sqrt{c} x + 1}{c x^{2} - 1}\right)}{2 \, c}, \frac{b c x \log\left(-\frac{c x^{2} + 1}{c x^{2} - 1}\right) + 2 \, a c x + 2 \, b \sqrt{-c} \arctan\left(\sqrt{-c} x\right) - b \sqrt{-c} \log\left(\frac{c x^{2} - 2 \, \sqrt{-c} x - 1}{c x^{2} + 1}\right)}{2 \, c}\right]"," ",0,"[1/2*(b*c*x*log(-(c*x^2 + 1)/(c*x^2 - 1)) + 2*a*c*x + 2*b*sqrt(c)*arctan(sqrt(c)*x) + b*sqrt(c)*log((c*x^2 - 2*sqrt(c)*x + 1)/(c*x^2 - 1)))/c, 1/2*(b*c*x*log(-(c*x^2 + 1)/(c*x^2 - 1)) + 2*a*c*x + 2*b*sqrt(-c)*arctan(sqrt(-c)*x) - b*sqrt(-c)*log((c*x^2 - 2*sqrt(-c)*x - 1)/(c*x^2 + 1)))/c]","B",0
61,1,157,0,1.161675," ","integrate((a+b*arctanh(c*x^2))/x^2,x, algorithm=""fricas"")","\left[\frac{2 \, b \sqrt{c} x \arctan\left(\sqrt{c} x\right) + b \sqrt{c} x \log\left(\frac{c x^{2} + 2 \, \sqrt{c} x + 1}{c x^{2} - 1}\right) - b \log\left(-\frac{c x^{2} + 1}{c x^{2} - 1}\right) - 2 \, a}{2 \, x}, -\frac{2 \, b \sqrt{-c} x \arctan\left(\sqrt{-c} x\right) - b \sqrt{-c} x \log\left(\frac{c x^{2} + 2 \, \sqrt{-c} x - 1}{c x^{2} + 1}\right) + b \log\left(-\frac{c x^{2} + 1}{c x^{2} - 1}\right) + 2 \, a}{2 \, x}\right]"," ",0,"[1/2*(2*b*sqrt(c)*x*arctan(sqrt(c)*x) + b*sqrt(c)*x*log((c*x^2 + 2*sqrt(c)*x + 1)/(c*x^2 - 1)) - b*log(-(c*x^2 + 1)/(c*x^2 - 1)) - 2*a)/x, -1/2*(2*b*sqrt(-c)*x*arctan(sqrt(-c)*x) - b*sqrt(-c)*x*log((c*x^2 + 2*sqrt(-c)*x - 1)/(c*x^2 + 1)) + b*log(-(c*x^2 + 1)/(c*x^2 - 1)) + 2*a)/x]","A",0
62,1,181,0,0.976044," ","integrate((a+b*arctanh(c*x^2))/x^4,x, algorithm=""fricas"")","\left[-\frac{2 \, b c^{\frac{3}{2}} x^{3} \arctan\left(\sqrt{c} x\right) - b c^{\frac{3}{2}} x^{3} \log\left(\frac{c x^{2} + 2 \, \sqrt{c} x + 1}{c x^{2} - 1}\right) + 4 \, b c x^{2} + b \log\left(-\frac{c x^{2} + 1}{c x^{2} - 1}\right) + 2 \, a}{6 \, x^{3}}, -\frac{2 \, b \sqrt{-c} c x^{3} \arctan\left(\sqrt{-c} x\right) - b \sqrt{-c} c x^{3} \log\left(\frac{c x^{2} - 2 \, \sqrt{-c} x - 1}{c x^{2} + 1}\right) + 4 \, b c x^{2} + b \log\left(-\frac{c x^{2} + 1}{c x^{2} - 1}\right) + 2 \, a}{6 \, x^{3}}\right]"," ",0,"[-1/6*(2*b*c^(3/2)*x^3*arctan(sqrt(c)*x) - b*c^(3/2)*x^3*log((c*x^2 + 2*sqrt(c)*x + 1)/(c*x^2 - 1)) + 4*b*c*x^2 + b*log(-(c*x^2 + 1)/(c*x^2 - 1)) + 2*a)/x^3, -1/6*(2*b*sqrt(-c)*c*x^3*arctan(sqrt(-c)*x) - b*sqrt(-c)*c*x^3*log((c*x^2 - 2*sqrt(-c)*x - 1)/(c*x^2 + 1)) + 4*b*c*x^2 + b*log(-(c*x^2 + 1)/(c*x^2 - 1)) + 2*a)/x^3]","A",0
63,1,187,0,1.017081," ","integrate((a+b*arctanh(c*x^2))/x^6,x, algorithm=""fricas"")","\left[\frac{6 \, b c^{\frac{5}{2}} x^{5} \arctan\left(\sqrt{c} x\right) + 3 \, b c^{\frac{5}{2}} x^{5} \log\left(\frac{c x^{2} + 2 \, \sqrt{c} x + 1}{c x^{2} - 1}\right) - 4 \, b c x^{2} - 3 \, b \log\left(-\frac{c x^{2} + 1}{c x^{2} - 1}\right) - 6 \, a}{30 \, x^{5}}, -\frac{6 \, b \sqrt{-c} c^{2} x^{5} \arctan\left(\sqrt{-c} x\right) - 3 \, b \sqrt{-c} c^{2} x^{5} \log\left(\frac{c x^{2} + 2 \, \sqrt{-c} x - 1}{c x^{2} + 1}\right) + 4 \, b c x^{2} + 3 \, b \log\left(-\frac{c x^{2} + 1}{c x^{2} - 1}\right) + 6 \, a}{30 \, x^{5}}\right]"," ",0,"[1/30*(6*b*c^(5/2)*x^5*arctan(sqrt(c)*x) + 3*b*c^(5/2)*x^5*log((c*x^2 + 2*sqrt(c)*x + 1)/(c*x^2 - 1)) - 4*b*c*x^2 - 3*b*log(-(c*x^2 + 1)/(c*x^2 - 1)) - 6*a)/x^5, -1/30*(6*b*sqrt(-c)*c^2*x^5*arctan(sqrt(-c)*x) - 3*b*sqrt(-c)*c^2*x^5*log((c*x^2 + 2*sqrt(-c)*x - 1)/(c*x^2 + 1)) + 4*b*c*x^2 + 3*b*log(-(c*x^2 + 1)/(c*x^2 - 1)) + 6*a)/x^5]","A",0
64,1,176,0,0.861342," ","integrate(x^7*(a+b*arctanh(c*x^2))^2,x, algorithm=""fricas"")","\frac{12 \, a^{2} c^{4} x^{8} + 8 \, a b c^{3} x^{6} + 4 \, b^{2} c^{2} x^{4} + 24 \, a b c x^{2} + 3 \, {\left(b^{2} c^{4} x^{8} - b^{2}\right)} \log\left(-\frac{c x^{2} + 1}{c x^{2} - 1}\right)^{2} - 4 \, {\left(3 \, a b - 4 \, b^{2}\right)} \log\left(c x^{2} + 1\right) + 4 \, {\left(3 \, a b + 4 \, b^{2}\right)} \log\left(c x^{2} - 1\right) + 4 \, {\left(3 \, a b c^{4} x^{8} + b^{2} c^{3} x^{6} + 3 \, b^{2} c x^{2}\right)} \log\left(-\frac{c x^{2} + 1}{c x^{2} - 1}\right)}{96 \, c^{4}}"," ",0,"1/96*(12*a^2*c^4*x^8 + 8*a*b*c^3*x^6 + 4*b^2*c^2*x^4 + 24*a*b*c*x^2 + 3*(b^2*c^4*x^8 - b^2)*log(-(c*x^2 + 1)/(c*x^2 - 1))^2 - 4*(3*a*b - 4*b^2)*log(c*x^2 + 1) + 4*(3*a*b + 4*b^2)*log(c*x^2 - 1) + 4*(3*a*b*c^4*x^8 + b^2*c^3*x^6 + 3*b^2*c*x^2)*log(-(c*x^2 + 1)/(c*x^2 - 1)))/c^4","A",0
65,0,0,0,0.882300," ","integrate(x^5*(a+b*arctanh(c*x^2))^2,x, algorithm=""fricas"")","{\rm integral}\left(b^{2} x^{5} \operatorname{artanh}\left(c x^{2}\right)^{2} + 2 \, a b x^{5} \operatorname{artanh}\left(c x^{2}\right) + a^{2} x^{5}, x\right)"," ",0,"integral(b^2*x^5*arctanh(c*x^2)^2 + 2*a*b*x^5*arctanh(c*x^2) + a^2*x^5, x)","F",0
66,1,138,0,0.796152," ","integrate(x^3*(a+b*arctanh(c*x^2))^2,x, algorithm=""fricas"")","\frac{4 \, a^{2} c^{2} x^{4} + 8 \, a b c x^{2} + {\left(b^{2} c^{2} x^{4} - b^{2}\right)} \log\left(-\frac{c x^{2} + 1}{c x^{2} - 1}\right)^{2} - 4 \, {\left(a b - b^{2}\right)} \log\left(c x^{2} + 1\right) + 4 \, {\left(a b + b^{2}\right)} \log\left(c x^{2} - 1\right) + 4 \, {\left(a b c^{2} x^{4} + b^{2} c x^{2}\right)} \log\left(-\frac{c x^{2} + 1}{c x^{2} - 1}\right)}{16 \, c^{2}}"," ",0,"1/16*(4*a^2*c^2*x^4 + 8*a*b*c*x^2 + (b^2*c^2*x^4 - b^2)*log(-(c*x^2 + 1)/(c*x^2 - 1))^2 - 4*(a*b - b^2)*log(c*x^2 + 1) + 4*(a*b + b^2)*log(c*x^2 - 1) + 4*(a*b*c^2*x^4 + b^2*c*x^2)*log(-(c*x^2 + 1)/(c*x^2 - 1)))/c^2","A",0
67,0,0,0,0.957473," ","integrate(x*(a+b*arctanh(c*x^2))^2,x, algorithm=""fricas"")","{\rm integral}\left(b^{2} x \operatorname{artanh}\left(c x^{2}\right)^{2} + 2 \, a b x \operatorname{artanh}\left(c x^{2}\right) + a^{2} x, x\right)"," ",0,"integral(b^2*x*arctanh(c*x^2)^2 + 2*a*b*x*arctanh(c*x^2) + a^2*x, x)","F",0
68,0,0,0,0.843050," ","integrate((a+b*arctanh(c*x^2))^2/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} \operatorname{artanh}\left(c x^{2}\right)^{2} + 2 \, a b \operatorname{artanh}\left(c x^{2}\right) + a^{2}}{x}, x\right)"," ",0,"integral((b^2*arctanh(c*x^2)^2 + 2*a*b*arctanh(c*x^2) + a^2)/x, x)","F",0
69,0,0,0,0.733103," ","integrate((a+b*arctanh(c*x^2))^2/x^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} \operatorname{artanh}\left(c x^{2}\right)^{2} + 2 \, a b \operatorname{artanh}\left(c x^{2}\right) + a^{2}}{x^{3}}, x\right)"," ",0,"integral((b^2*arctanh(c*x^2)^2 + 2*a*b*arctanh(c*x^2) + a^2)/x^3, x)","F",0
70,1,151,0,0.843578," ","integrate((a+b*arctanh(c*x^2))^2/x^5,x, algorithm=""fricas"")","\frac{16 \, b^{2} c^{2} x^{4} \log\left(x\right) + 4 \, {\left(a b - b^{2}\right)} c^{2} x^{4} \log\left(c x^{2} + 1\right) - 4 \, {\left(a b + b^{2}\right)} c^{2} x^{4} \log\left(c x^{2} - 1\right) - 8 \, a b c x^{2} + {\left(b^{2} c^{2} x^{4} - b^{2}\right)} \log\left(-\frac{c x^{2} + 1}{c x^{2} - 1}\right)^{2} - 4 \, a^{2} - 4 \, {\left(b^{2} c x^{2} + a b\right)} \log\left(-\frac{c x^{2} + 1}{c x^{2} - 1}\right)}{16 \, x^{4}}"," ",0,"1/16*(16*b^2*c^2*x^4*log(x) + 4*(a*b - b^2)*c^2*x^4*log(c*x^2 + 1) - 4*(a*b + b^2)*c^2*x^4*log(c*x^2 - 1) - 8*a*b*c*x^2 + (b^2*c^2*x^4 - b^2)*log(-(c*x^2 + 1)/(c*x^2 - 1))^2 - 4*a^2 - 4*(b^2*c*x^2 + a*b)*log(-(c*x^2 + 1)/(c*x^2 - 1)))/x^4","A",0
71,-1,0,0,0.000000," ","integrate(x^4*(a+b*arctanh(c*x^2))^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
72,0,0,0,0.881956," ","integrate(x^2*(a+b*arctanh(c*x^2))^2,x, algorithm=""fricas"")","{\rm integral}\left(b^{2} x^{2} \operatorname{artanh}\left(c x^{2}\right)^{2} + 2 \, a b x^{2} \operatorname{artanh}\left(c x^{2}\right) + a^{2} x^{2}, x\right)"," ",0,"integral(b^2*x^2*arctanh(c*x^2)^2 + 2*a*b*x^2*arctanh(c*x^2) + a^2*x^2, x)","F",0
73,0,0,0,0.989676," ","integrate((a+b*arctanh(c*x^2))^2,x, algorithm=""fricas"")","{\rm integral}\left(b^{2} \operatorname{artanh}\left(c x^{2}\right)^{2} + 2 \, a b \operatorname{artanh}\left(c x^{2}\right) + a^{2}, x\right)"," ",0,"integral(b^2*arctanh(c*x^2)^2 + 2*a*b*arctanh(c*x^2) + a^2, x)","F",0
74,0,0,0,0.464810," ","integrate((a+b*arctanh(c*x^2))^2/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} \operatorname{artanh}\left(c x^{2}\right)^{2} + 2 \, a b \operatorname{artanh}\left(c x^{2}\right) + a^{2}}{x^{2}}, x\right)"," ",0,"integral((b^2*arctanh(c*x^2)^2 + 2*a*b*arctanh(c*x^2) + a^2)/x^2, x)","F",0
75,0,0,0,2.144635," ","integrate((a+b*arctanh(c*x^2))^2/x^4,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} \operatorname{artanh}\left(c x^{2}\right)^{2} + 2 \, a b \operatorname{artanh}\left(c x^{2}\right) + a^{2}}{x^{4}}, x\right)"," ",0,"integral((b^2*arctanh(c*x^2)^2 + 2*a*b*arctanh(c*x^2) + a^2)/x^4, x)","F",0
76,0,0,0,0.677002," ","integrate((a+b*arctanh(c*x^2))^2/x^6,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} \operatorname{artanh}\left(c x^{2}\right)^{2} + 2 \, a b \operatorname{artanh}\left(c x^{2}\right) + a^{2}}{x^{6}}, x\right)"," ",0,"integral((b^2*arctanh(c*x^2)^2 + 2*a*b*arctanh(c*x^2) + a^2)/x^6, x)","F",0
77,0,0,0,0.659882," ","integrate(x^3*(a+b*arctanh(c*x^2))^3,x, algorithm=""fricas"")","{\rm integral}\left(b^{3} x^{3} \operatorname{artanh}\left(c x^{2}\right)^{3} + 3 \, a b^{2} x^{3} \operatorname{artanh}\left(c x^{2}\right)^{2} + 3 \, a^{2} b x^{3} \operatorname{artanh}\left(c x^{2}\right) + a^{3} x^{3}, x\right)"," ",0,"integral(b^3*x^3*arctanh(c*x^2)^3 + 3*a*b^2*x^3*arctanh(c*x^2)^2 + 3*a^2*b*x^3*arctanh(c*x^2) + a^3*x^3, x)","F",0
78,0,0,0,0.904228," ","integrate(x*(a+b*arctanh(c*x^2))^3,x, algorithm=""fricas"")","{\rm integral}\left(b^{3} x \operatorname{artanh}\left(c x^{2}\right)^{3} + 3 \, a b^{2} x \operatorname{artanh}\left(c x^{2}\right)^{2} + 3 \, a^{2} b x \operatorname{artanh}\left(c x^{2}\right) + a^{3} x, x\right)"," ",0,"integral(b^3*x*arctanh(c*x^2)^3 + 3*a*b^2*x*arctanh(c*x^2)^2 + 3*a^2*b*x*arctanh(c*x^2) + a^3*x, x)","F",0
79,0,0,0,1.120777," ","integrate((a+b*arctanh(c*x^2))^3/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{3} \operatorname{artanh}\left(c x^{2}\right)^{3} + 3 \, a b^{2} \operatorname{artanh}\left(c x^{2}\right)^{2} + 3 \, a^{2} b \operatorname{artanh}\left(c x^{2}\right) + a^{3}}{x}, x\right)"," ",0,"integral((b^3*arctanh(c*x^2)^3 + 3*a*b^2*arctanh(c*x^2)^2 + 3*a^2*b*arctanh(c*x^2) + a^3)/x, x)","F",0
80,0,0,0,1.286036," ","integrate((a+b*arctanh(c*x^2))^3/x^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{3} \operatorname{artanh}\left(c x^{2}\right)^{3} + 3 \, a b^{2} \operatorname{artanh}\left(c x^{2}\right)^{2} + 3 \, a^{2} b \operatorname{artanh}\left(c x^{2}\right) + a^{3}}{x^{3}}, x\right)"," ",0,"integral((b^3*arctanh(c*x^2)^3 + 3*a*b^2*arctanh(c*x^2)^2 + 3*a^2*b*arctanh(c*x^2) + a^3)/x^3, x)","F",0
81,0,0,0,1.156553," ","integrate((a+b*arctanh(c*x^2))^3/x^5,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{3} \operatorname{artanh}\left(c x^{2}\right)^{3} + 3 \, a b^{2} \operatorname{artanh}\left(c x^{2}\right)^{2} + 3 \, a^{2} b \operatorname{artanh}\left(c x^{2}\right) + a^{3}}{x^{5}}, x\right)"," ",0,"integral((b^3*arctanh(c*x^2)^3 + 3*a*b^2*arctanh(c*x^2)^2 + 3*a^2*b*arctanh(c*x^2) + a^3)/x^5, x)","F",0
82,1,57,0,1.309149," ","integrate((d*x)^(5/2)*(a+b*arctanh(c*x^2)),x, algorithm=""fricas"")","\frac{{\left(3 \, b c d^{2} x^{3} \log\left(-\frac{c x^{2} + 1}{c x^{2} - 1}\right) + 6 \, a c d^{2} x^{3} + 8 \, b d^{2} x\right)} \sqrt{d x}}{21 \, c}"," ",0,"1/21*(3*b*c*d^2*x^3*log(-(c*x^2 + 1)/(c*x^2 - 1)) + 6*a*c*d^2*x^3 + 8*b*d^2*x)*sqrt(d*x)/c","A",0
83,1,49,0,2.031244," ","integrate((d*x)^(3/2)*(a+b*arctanh(c*x^2)),x, algorithm=""fricas"")","\frac{{\left(b c d x^{2} \log\left(-\frac{c x^{2} + 1}{c x^{2} - 1}\right) + 2 \, a c d x^{2} + 8 \, b d\right)} \sqrt{d x}}{5 \, c}"," ",0,"1/5*(b*c*d*x^2*log(-(c*x^2 + 1)/(c*x^2 - 1)) + 2*a*c*d*x^2 + 8*b*d)*sqrt(d*x)/c","A",0
84,1,34,0,1.291986," ","integrate((d*x)^(1/2)*(a+b*arctanh(c*x^2)),x, algorithm=""fricas"")","\frac{1}{3} \, {\left(b x \log\left(-\frac{c x^{2} + 1}{c x^{2} - 1}\right) + 2 \, a x\right)} \sqrt{d x}"," ",0,"1/3*(b*x*log(-(c*x^2 + 1)/(c*x^2 - 1)) + 2*a*x)*sqrt(d*x)","A",0
85,1,34,0,1.961311," ","integrate((a+b*arctanh(c*x^2))/(d*x)^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{d x} {\left(b \log\left(-\frac{c x^{2} + 1}{c x^{2} - 1}\right) + 2 \, a\right)}}{d}"," ",0,"sqrt(d*x)*(b*log(-(c*x^2 + 1)/(c*x^2 - 1)) + 2*a)/d","A",0
86,1,38,0,1.829441," ","integrate((a+b*arctanh(c*x^2))/(d*x)^(3/2),x, algorithm=""fricas"")","-\frac{\sqrt{d x} {\left(b \log\left(-\frac{c x^{2} + 1}{c x^{2} - 1}\right) + 2 \, a\right)}}{d^{2} x}"," ",0,"-sqrt(d*x)*(b*log(-(c*x^2 + 1)/(c*x^2 - 1)) + 2*a)/(d^2*x)","A",0
87,1,38,0,0.891027," ","integrate((a+b*arctanh(c*x^2))/(d*x)^(5/2),x, algorithm=""fricas"")","-\frac{\sqrt{d x} {\left(b \log\left(-\frac{c x^{2} + 1}{c x^{2} - 1}\right) + 2 \, a\right)}}{3 \, d^{3} x^{2}}"," ",0,"-1/3*sqrt(d*x)*(b*log(-(c*x^2 + 1)/(c*x^2 - 1)) + 2*a)/(d^3*x^2)","A",0
88,1,45,0,1.121827," ","integrate((a+b*arctanh(c*x^2))/(d*x)^(7/2),x, algorithm=""fricas"")","-\frac{{\left(8 \, b c x^{2} + b \log\left(-\frac{c x^{2} + 1}{c x^{2} - 1}\right) + 2 \, a\right)} \sqrt{d x}}{5 \, d^{4} x^{3}}"," ",0,"-1/5*(8*b*c*x^2 + b*log(-(c*x^2 + 1)/(c*x^2 - 1)) + 2*a)*sqrt(d*x)/(d^4*x^3)","A",0
89,1,46,0,0.701736," ","integrate((a+b*arctanh(c*x^2))/(d*x)^(9/2),x, algorithm=""fricas"")","-\frac{{\left(8 \, b c x^{2} + 3 \, b \log\left(-\frac{c x^{2} + 1}{c x^{2} - 1}\right) + 6 \, a\right)} \sqrt{d x}}{21 \, d^{5} x^{4}}"," ",0,"-1/21*(8*b*c*x^2 + 3*b*log(-(c*x^2 + 1)/(c*x^2 - 1)) + 6*a)*sqrt(d*x)/(d^5*x^4)","A",0
90,0,0,0,1.080740," ","integrate((d*x)^(1/2)*(a+b*arctanh(c*x^2))^2,x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{2} \operatorname{artanh}\left(c x^{2}\right)^{2} + 2 \, a b \operatorname{artanh}\left(c x^{2}\right) + a^{2}\right)} \sqrt{d x}, x\right)"," ",0,"integral((b^2*arctanh(c*x^2)^2 + 2*a*b*arctanh(c*x^2) + a^2)*sqrt(d*x), x)","F",0
91,0,0,0,0.644555," ","integrate((a+b*arctanh(c*x^2))^2/(d*x)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b^{2} \operatorname{artanh}\left(c x^{2}\right)^{2} + 2 \, a b \operatorname{artanh}\left(c x^{2}\right) + a^{2}\right)} \sqrt{d x}}{d x}, x\right)"," ",0,"integral((b^2*arctanh(c*x^2)^2 + 2*a*b*arctanh(c*x^2) + a^2)*sqrt(d*x)/(d*x), x)","F",0
92,0,0,0,0.433468," ","integrate((a+b*arctanh(c*x^2))^2/(d*x)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b^{2} \operatorname{artanh}\left(c x^{2}\right)^{2} + 2 \, a b \operatorname{artanh}\left(c x^{2}\right) + a^{2}\right)} \sqrt{d x}}{d^{2} x^{2}}, x\right)"," ",0,"integral((b^2*arctanh(c*x^2)^2 + 2*a*b*arctanh(c*x^2) + a^2)*sqrt(d*x)/(d^2*x^2), x)","F",0
93,0,0,0,0.582674," ","integrate((a+b*arctanh(c*x^2))^2/(d*x)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b^{2} \operatorname{artanh}\left(c x^{2}\right)^{2} + 2 \, a b \operatorname{artanh}\left(c x^{2}\right) + a^{2}\right)} \sqrt{d x}}{d^{3} x^{3}}, x\right)"," ",0,"integral((b^2*arctanh(c*x^2)^2 + 2*a*b*arctanh(c*x^2) + a^2)*sqrt(d*x)/(d^3*x^3), x)","F",0
94,0,0,0,0.544910," ","integrate((d*x)^m*(a+b*arctanh(c*x^2))^3,x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{3} \operatorname{artanh}\left(c x^{2}\right)^{3} + 3 \, a b^{2} \operatorname{artanh}\left(c x^{2}\right)^{2} + 3 \, a^{2} b \operatorname{artanh}\left(c x^{2}\right) + a^{3}\right)} \left(d x\right)^{m}, x\right)"," ",0,"integral((b^3*arctanh(c*x^2)^3 + 3*a*b^2*arctanh(c*x^2)^2 + 3*a^2*b*arctanh(c*x^2) + a^3)*(d*x)^m, x)","F",0
95,0,0,0,0.495488," ","integrate((d*x)^m*(a+b*arctanh(c*x^2))^2,x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{2} \operatorname{artanh}\left(c x^{2}\right)^{2} + 2 \, a b \operatorname{artanh}\left(c x^{2}\right) + a^{2}\right)} \left(d x\right)^{m}, x\right)"," ",0,"integral((b^2*arctanh(c*x^2)^2 + 2*a*b*arctanh(c*x^2) + a^2)*(d*x)^m, x)","F",0
96,0,0,0,0.563259," ","integrate((d*x)^m*(a+b*arctanh(c*x^2)),x, algorithm=""fricas"")","{\rm integral}\left({\left(b \operatorname{artanh}\left(c x^{2}\right) + a\right)} \left(d x\right)^{m}, x\right)"," ",0,"integral((b*arctanh(c*x^2) + a)*(d*x)^m, x)","F",0
97,0,0,0,1.024037," ","integrate((d*x)^m/(a+b*arctanh(c*x^2)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(d x\right)^{m}}{b \operatorname{artanh}\left(c x^{2}\right) + a}, x\right)"," ",0,"integral((d*x)^m/(b*arctanh(c*x^2) + a), x)","F",0
98,0,0,0,0.927611," ","integrate((d*x)^m/(a+b*arctanh(c*x^2))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(d x\right)^{m}}{b^{2} \operatorname{artanh}\left(c x^{2}\right)^{2} + 2 \, a b \operatorname{artanh}\left(c x^{2}\right) + a^{2}}, x\right)"," ",0,"integral((d*x)^m/(b^2*arctanh(c*x^2)^2 + 2*a*b*arctanh(c*x^2) + a^2), x)","F",0
99,1,64,0,0.595036," ","integrate(x^11*(a+b*arctanh(c*x^3)),x, algorithm=""fricas"")","\frac{6 \, a c^{4} x^{12} + 2 \, b c^{3} x^{9} + 6 \, b c x^{3} + 3 \, {\left(b c^{4} x^{12} - b\right)} \log\left(-\frac{c x^{3} + 1}{c x^{3} - 1}\right)}{72 \, c^{4}}"," ",0,"1/72*(6*a*c^4*x^12 + 2*b*c^3*x^9 + 6*b*c*x^3 + 3*(b*c^4*x^12 - b)*log(-(c*x^3 + 1)/(c*x^3 - 1)))/c^4","A",0
100,1,62,0,0.568421," ","integrate(x^8*(a+b*arctanh(c*x^3)),x, algorithm=""fricas"")","\frac{b c^{3} x^{9} \log\left(-\frac{c x^{3} + 1}{c x^{3} - 1}\right) + 2 \, a c^{3} x^{9} + b c^{2} x^{6} + b \log\left(c^{2} x^{6} - 1\right)}{18 \, c^{3}}"," ",0,"1/18*(b*c^3*x^9*log(-(c*x^3 + 1)/(c*x^3 - 1)) + 2*a*c^3*x^9 + b*c^2*x^6 + b*log(c^2*x^6 - 1))/c^3","A",0
101,1,54,0,0.710268," ","integrate(x^5*(a+b*arctanh(c*x^3)),x, algorithm=""fricas"")","\frac{2 \, a c^{2} x^{6} + 2 \, b c x^{3} + {\left(b c^{2} x^{6} - b\right)} \log\left(-\frac{c x^{3} + 1}{c x^{3} - 1}\right)}{12 \, c^{2}}"," ",0,"1/12*(2*a*c^2*x^6 + 2*b*c*x^3 + (b*c^2*x^6 - b)*log(-(c*x^3 + 1)/(c*x^3 - 1)))/c^2","A",0
102,1,50,0,0.659209," ","integrate(x^2*(a+b*arctanh(c*x^3)),x, algorithm=""fricas"")","\frac{b c x^{3} \log\left(-\frac{c x^{3} + 1}{c x^{3} - 1}\right) + 2 \, a c x^{3} + b \log\left(c^{2} x^{6} - 1\right)}{6 \, c}"," ",0,"1/6*(b*c*x^3*log(-(c*x^3 + 1)/(c*x^3 - 1)) + 2*a*c*x^3 + b*log(c^2*x^6 - 1))/c","A",0
103,0,0,0,0.732902," ","integrate((a+b*arctanh(c*x^3))/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \operatorname{artanh}\left(c x^{3}\right) + a}{x}, x\right)"," ",0,"integral((b*arctanh(c*x^3) + a)/x, x)","F",0
104,1,55,0,0.636952," ","integrate((a+b*arctanh(c*x^3))/x^4,x, algorithm=""fricas"")","-\frac{b c x^{3} \log\left(c^{2} x^{6} - 1\right) - 6 \, b c x^{3} \log\left(x\right) + b \log\left(-\frac{c x^{3} + 1}{c x^{3} - 1}\right) + 2 \, a}{6 \, x^{3}}"," ",0,"-1/6*(b*c*x^3*log(c^2*x^6 - 1) - 6*b*c*x^3*log(x) + b*log(-(c*x^3 + 1)/(c*x^3 - 1)) + 2*a)/x^3","A",0
105,1,49,0,0.561800," ","integrate((a+b*arctanh(c*x^3))/x^7,x, algorithm=""fricas"")","-\frac{2 \, b c x^{3} - {\left(b c^{2} x^{6} - b\right)} \log\left(-\frac{c x^{3} + 1}{c x^{3} - 1}\right) + 2 \, a}{12 \, x^{6}}"," ",0,"-1/12*(2*b*c*x^3 - (b*c^2*x^6 - b)*log(-(c*x^3 + 1)/(c*x^3 - 1)) + 2*a)/x^6","A",0
106,1,65,0,0.683532," ","integrate((a+b*arctanh(c*x^3))/x^10,x, algorithm=""fricas"")","-\frac{b c^{3} x^{9} \log\left(c^{2} x^{6} - 1\right) - 6 \, b c^{3} x^{9} \log\left(x\right) + b c x^{3} + b \log\left(-\frac{c x^{3} + 1}{c x^{3} - 1}\right) + 2 \, a}{18 \, x^{9}}"," ",0,"-1/18*(b*c^3*x^9*log(c^2*x^6 - 1) - 6*b*c^3*x^9*log(x) + b*c*x^3 + b*log(-(c*x^3 + 1)/(c*x^3 - 1)) + 2*a)/x^9","A",0
107,1,981,0,0.752937," ","integrate(x^3*(a+b*arctanh(c*x^3)),x, algorithm=""fricas"")","\left[\frac{2 \, b c^{2} x^{4} \log\left(-\frac{c x^{3} + 1}{c x^{3} - 1}\right) + 4 \, a c^{2} x^{4} + \sqrt{3} b c \sqrt{\frac{\left(-c\right)^{\frac{1}{3}}}{c}} \log\left(\frac{2 \, c x^{3} - \sqrt{3} {\left(2 \, c x^{2} + \left(-c\right)^{\frac{2}{3}} x + \left(-c\right)^{\frac{1}{3}}\right)} \sqrt{\frac{\left(-c\right)^{\frac{1}{3}}}{c}} + 3 \, \left(-c\right)^{\frac{1}{3}} x - 1}{c x^{3} + 1}\right) + \sqrt{3} b c \sqrt{-\frac{1}{c^{\frac{2}{3}}}} \log\left(\frac{2 \, c x^{3} - \sqrt{3} {\left(2 \, c x^{2} - c^{\frac{2}{3}} x - c^{\frac{1}{3}}\right)} \sqrt{-\frac{1}{c^{\frac{2}{3}}}} - 3 \, c^{\frac{1}{3}} x + 1}{c x^{3} - 1}\right) + 12 \, b c x + b \left(-c\right)^{\frac{2}{3}} \log\left(c x^{2} - \left(-c\right)^{\frac{2}{3}} x - \left(-c\right)^{\frac{1}{3}}\right) - b c^{\frac{2}{3}} \log\left(c x^{2} + c^{\frac{2}{3}} x + c^{\frac{1}{3}}\right) - 2 \, b \left(-c\right)^{\frac{2}{3}} \log\left(c x + \left(-c\right)^{\frac{2}{3}}\right) + 2 \, b c^{\frac{2}{3}} \log\left(c x - c^{\frac{2}{3}}\right)}{16 \, c^{2}}, \frac{2 \, b c^{2} x^{4} \log\left(-\frac{c x^{3} + 1}{c x^{3} - 1}\right) + 4 \, a c^{2} x^{4} - 2 \, \sqrt{3} b c \sqrt{-\frac{\left(-c\right)^{\frac{1}{3}}}{c}} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, \left(-c\right)^{\frac{2}{3}} x + \left(-c\right)^{\frac{1}{3}}\right)} \sqrt{-\frac{\left(-c\right)^{\frac{1}{3}}}{c}}\right) + \sqrt{3} b c \sqrt{-\frac{1}{c^{\frac{2}{3}}}} \log\left(\frac{2 \, c x^{3} - \sqrt{3} {\left(2 \, c x^{2} - c^{\frac{2}{3}} x - c^{\frac{1}{3}}\right)} \sqrt{-\frac{1}{c^{\frac{2}{3}}}} - 3 \, c^{\frac{1}{3}} x + 1}{c x^{3} - 1}\right) + 12 \, b c x + b \left(-c\right)^{\frac{2}{3}} \log\left(c x^{2} - \left(-c\right)^{\frac{2}{3}} x - \left(-c\right)^{\frac{1}{3}}\right) - b c^{\frac{2}{3}} \log\left(c x^{2} + c^{\frac{2}{3}} x + c^{\frac{1}{3}}\right) - 2 \, b \left(-c\right)^{\frac{2}{3}} \log\left(c x + \left(-c\right)^{\frac{2}{3}}\right) + 2 \, b c^{\frac{2}{3}} \log\left(c x - c^{\frac{2}{3}}\right)}{16 \, c^{2}}, \frac{2 \, b c^{2} x^{4} \log\left(-\frac{c x^{3} + 1}{c x^{3} - 1}\right) + 4 \, a c^{2} x^{4} + \sqrt{3} b c \sqrt{\frac{\left(-c\right)^{\frac{1}{3}}}{c}} \log\left(\frac{2 \, c x^{3} - \sqrt{3} {\left(2 \, c x^{2} + \left(-c\right)^{\frac{2}{3}} x + \left(-c\right)^{\frac{1}{3}}\right)} \sqrt{\frac{\left(-c\right)^{\frac{1}{3}}}{c}} + 3 \, \left(-c\right)^{\frac{1}{3}} x - 1}{c x^{3} + 1}\right) - 2 \, \sqrt{3} b c^{\frac{2}{3}} \arctan\left(\frac{\sqrt{3} {\left(2 \, c^{\frac{2}{3}} x + c^{\frac{1}{3}}\right)}}{3 \, c^{\frac{1}{3}}}\right) + 12 \, b c x + b \left(-c\right)^{\frac{2}{3}} \log\left(c x^{2} - \left(-c\right)^{\frac{2}{3}} x - \left(-c\right)^{\frac{1}{3}}\right) - b c^{\frac{2}{3}} \log\left(c x^{2} + c^{\frac{2}{3}} x + c^{\frac{1}{3}}\right) - 2 \, b \left(-c\right)^{\frac{2}{3}} \log\left(c x + \left(-c\right)^{\frac{2}{3}}\right) + 2 \, b c^{\frac{2}{3}} \log\left(c x - c^{\frac{2}{3}}\right)}{16 \, c^{2}}, \frac{2 \, b c^{2} x^{4} \log\left(-\frac{c x^{3} + 1}{c x^{3} - 1}\right) + 4 \, a c^{2} x^{4} - 2 \, \sqrt{3} b c \sqrt{-\frac{\left(-c\right)^{\frac{1}{3}}}{c}} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, \left(-c\right)^{\frac{2}{3}} x + \left(-c\right)^{\frac{1}{3}}\right)} \sqrt{-\frac{\left(-c\right)^{\frac{1}{3}}}{c}}\right) - 2 \, \sqrt{3} b c^{\frac{2}{3}} \arctan\left(\frac{\sqrt{3} {\left(2 \, c^{\frac{2}{3}} x + c^{\frac{1}{3}}\right)}}{3 \, c^{\frac{1}{3}}}\right) + 12 \, b c x + b \left(-c\right)^{\frac{2}{3}} \log\left(c x^{2} - \left(-c\right)^{\frac{2}{3}} x - \left(-c\right)^{\frac{1}{3}}\right) - b c^{\frac{2}{3}} \log\left(c x^{2} + c^{\frac{2}{3}} x + c^{\frac{1}{3}}\right) - 2 \, b \left(-c\right)^{\frac{2}{3}} \log\left(c x + \left(-c\right)^{\frac{2}{3}}\right) + 2 \, b c^{\frac{2}{3}} \log\left(c x - c^{\frac{2}{3}}\right)}{16 \, c^{2}}\right]"," ",0,"[1/16*(2*b*c^2*x^4*log(-(c*x^3 + 1)/(c*x^3 - 1)) + 4*a*c^2*x^4 + sqrt(3)*b*c*sqrt((-c)^(1/3)/c)*log((2*c*x^3 - sqrt(3)*(2*c*x^2 + (-c)^(2/3)*x + (-c)^(1/3))*sqrt((-c)^(1/3)/c) + 3*(-c)^(1/3)*x - 1)/(c*x^3 + 1)) + sqrt(3)*b*c*sqrt(-1/c^(2/3))*log((2*c*x^3 - sqrt(3)*(2*c*x^2 - c^(2/3)*x - c^(1/3))*sqrt(-1/c^(2/3)) - 3*c^(1/3)*x + 1)/(c*x^3 - 1)) + 12*b*c*x + b*(-c)^(2/3)*log(c*x^2 - (-c)^(2/3)*x - (-c)^(1/3)) - b*c^(2/3)*log(c*x^2 + c^(2/3)*x + c^(1/3)) - 2*b*(-c)^(2/3)*log(c*x + (-c)^(2/3)) + 2*b*c^(2/3)*log(c*x - c^(2/3)))/c^2, 1/16*(2*b*c^2*x^4*log(-(c*x^3 + 1)/(c*x^3 - 1)) + 4*a*c^2*x^4 - 2*sqrt(3)*b*c*sqrt(-(-c)^(1/3)/c)*arctan(1/3*sqrt(3)*(2*(-c)^(2/3)*x + (-c)^(1/3))*sqrt(-(-c)^(1/3)/c)) + sqrt(3)*b*c*sqrt(-1/c^(2/3))*log((2*c*x^3 - sqrt(3)*(2*c*x^2 - c^(2/3)*x - c^(1/3))*sqrt(-1/c^(2/3)) - 3*c^(1/3)*x + 1)/(c*x^3 - 1)) + 12*b*c*x + b*(-c)^(2/3)*log(c*x^2 - (-c)^(2/3)*x - (-c)^(1/3)) - b*c^(2/3)*log(c*x^2 + c^(2/3)*x + c^(1/3)) - 2*b*(-c)^(2/3)*log(c*x + (-c)^(2/3)) + 2*b*c^(2/3)*log(c*x - c^(2/3)))/c^2, 1/16*(2*b*c^2*x^4*log(-(c*x^3 + 1)/(c*x^3 - 1)) + 4*a*c^2*x^4 + sqrt(3)*b*c*sqrt((-c)^(1/3)/c)*log((2*c*x^3 - sqrt(3)*(2*c*x^2 + (-c)^(2/3)*x + (-c)^(1/3))*sqrt((-c)^(1/3)/c) + 3*(-c)^(1/3)*x - 1)/(c*x^3 + 1)) - 2*sqrt(3)*b*c^(2/3)*arctan(1/3*sqrt(3)*(2*c^(2/3)*x + c^(1/3))/c^(1/3)) + 12*b*c*x + b*(-c)^(2/3)*log(c*x^2 - (-c)^(2/3)*x - (-c)^(1/3)) - b*c^(2/3)*log(c*x^2 + c^(2/3)*x + c^(1/3)) - 2*b*(-c)^(2/3)*log(c*x + (-c)^(2/3)) + 2*b*c^(2/3)*log(c*x - c^(2/3)))/c^2, 1/16*(2*b*c^2*x^4*log(-(c*x^3 + 1)/(c*x^3 - 1)) + 4*a*c^2*x^4 - 2*sqrt(3)*b*c*sqrt(-(-c)^(1/3)/c)*arctan(1/3*sqrt(3)*(2*(-c)^(2/3)*x + (-c)^(1/3))*sqrt(-(-c)^(1/3)/c)) - 2*sqrt(3)*b*c^(2/3)*arctan(1/3*sqrt(3)*(2*c^(2/3)*x + c^(1/3))/c^(1/3)) + 12*b*c*x + b*(-c)^(2/3)*log(c*x^2 - (-c)^(2/3)*x - (-c)^(1/3)) - b*c^(2/3)*log(c*x^2 + c^(2/3)*x + c^(1/3)) - 2*b*(-c)^(2/3)*log(c*x + (-c)^(2/3)) + 2*b*c^(2/3)*log(c*x - c^(2/3)))/c^2]","A",0
108,1,260,0,1.003981," ","integrate(a+b*arctanh(c*x^3),x, algorithm=""fricas"")","\left[\frac{\sqrt{3} b c \sqrt{-\frac{1}{c^{\frac{2}{3}}}} \log\left(\frac{2 \, c^{2} x^{6} - 3 \, c^{\frac{2}{3}} x^{2} + \sqrt{3} {\left(2 \, c^{\frac{5}{3}} x^{4} - c x^{2} - c^{\frac{1}{3}}\right)} \sqrt{-\frac{1}{c^{\frac{2}{3}}}} + 1}{c^{2} x^{6} - 1}\right) + 2 \, b c x \log\left(-\frac{c x^{3} + 1}{c x^{3} - 1}\right) + 4 \, a c x - b c^{\frac{2}{3}} \log\left(c^{2} x^{4} + c^{\frac{4}{3}} x^{2} + c^{\frac{2}{3}}\right) + 2 \, b c^{\frac{2}{3}} \log\left(c x^{2} - c^{\frac{1}{3}}\right)}{4 \, c}, \frac{2 \, b c x \log\left(-\frac{c x^{3} + 1}{c x^{3} - 1}\right) + 2 \, \sqrt{3} b c^{\frac{2}{3}} \arctan\left(\frac{\sqrt{3} {\left(2 \, c x^{2} + c^{\frac{1}{3}}\right)}}{3 \, c^{\frac{1}{3}}}\right) + 4 \, a c x - b c^{\frac{2}{3}} \log\left(c^{2} x^{4} + c^{\frac{4}{3}} x^{2} + c^{\frac{2}{3}}\right) + 2 \, b c^{\frac{2}{3}} \log\left(c x^{2} - c^{\frac{1}{3}}\right)}{4 \, c}\right]"," ",0,"[1/4*(sqrt(3)*b*c*sqrt(-1/c^(2/3))*log((2*c^2*x^6 - 3*c^(2/3)*x^2 + sqrt(3)*(2*c^(5/3)*x^4 - c*x^2 - c^(1/3))*sqrt(-1/c^(2/3)) + 1)/(c^2*x^6 - 1)) + 2*b*c*x*log(-(c*x^3 + 1)/(c*x^3 - 1)) + 4*a*c*x - b*c^(2/3)*log(c^2*x^4 + c^(4/3)*x^2 + c^(2/3)) + 2*b*c^(2/3)*log(c*x^2 - c^(1/3)))/c, 1/4*(2*b*c*x*log(-(c*x^3 + 1)/(c*x^3 - 1)) + 2*sqrt(3)*b*c^(2/3)*arctan(1/3*sqrt(3)*(2*c*x^2 + c^(1/3))/c^(1/3)) + 4*a*c*x - b*c^(2/3)*log(c^2*x^4 + c^(4/3)*x^2 + c^(2/3)) + 2*b*c^(2/3)*log(c*x^2 - c^(1/3)))/c]","A",0
109,1,228,0,0.652367," ","integrate((a+b*arctanh(c*x^3))/x^3,x, algorithm=""fricas"")","-\frac{2 \, \sqrt{3} \left(-c^{2}\right)^{\frac{1}{3}} b x^{2} \arctan\left(\frac{2 \, \sqrt{3} \left(-c^{2}\right)^{\frac{2}{3}} x + \sqrt{3} c}{3 \, c}\right) - 2 \, \sqrt{3} b {\left(c^{2}\right)}^{\frac{1}{3}} x^{2} \arctan\left(\frac{2 \, \sqrt{3} {\left(c^{2}\right)}^{\frac{2}{3}} x - \sqrt{3} c}{3 \, c}\right) + \left(-c^{2}\right)^{\frac{1}{3}} b x^{2} \log\left(c^{2} x^{2} - \left(-c^{2}\right)^{\frac{1}{3}} c x + \left(-c^{2}\right)^{\frac{2}{3}}\right) + b {\left(c^{2}\right)}^{\frac{1}{3}} x^{2} \log\left(c^{2} x^{2} - {\left(c^{2}\right)}^{\frac{1}{3}} c x + {\left(c^{2}\right)}^{\frac{2}{3}}\right) - 2 \, \left(-c^{2}\right)^{\frac{1}{3}} b x^{2} \log\left(c x + \left(-c^{2}\right)^{\frac{1}{3}}\right) - 2 \, b {\left(c^{2}\right)}^{\frac{1}{3}} x^{2} \log\left(c x + {\left(c^{2}\right)}^{\frac{1}{3}}\right) + 2 \, b \log\left(-\frac{c x^{3} + 1}{c x^{3} - 1}\right) + 4 \, a}{8 \, x^{2}}"," ",0,"-1/8*(2*sqrt(3)*(-c^2)^(1/3)*b*x^2*arctan(1/3*(2*sqrt(3)*(-c^2)^(2/3)*x + sqrt(3)*c)/c) - 2*sqrt(3)*b*(c^2)^(1/3)*x^2*arctan(1/3*(2*sqrt(3)*(c^2)^(2/3)*x - sqrt(3)*c)/c) + (-c^2)^(1/3)*b*x^2*log(c^2*x^2 - (-c^2)^(1/3)*c*x + (-c^2)^(2/3)) + b*(c^2)^(1/3)*x^2*log(c^2*x^2 - (c^2)^(1/3)*c*x + (c^2)^(2/3)) - 2*(-c^2)^(1/3)*b*x^2*log(c*x + (-c^2)^(1/3)) - 2*b*(c^2)^(1/3)*x^2*log(c*x + (c^2)^(1/3)) + 2*b*log(-(c*x^3 + 1)/(c*x^3 - 1)) + 4*a)/x^2","A",0
110,1,151,0,0.966647," ","integrate((a+b*arctanh(c*x^3))/x^6,x, algorithm=""fricas"")","-\frac{2 \, \sqrt{3} \left(-c^{2}\right)^{\frac{1}{3}} b c x^{5} \arctan\left(\frac{2}{3} \, \sqrt{3} \left(-c^{2}\right)^{\frac{1}{3}} x^{2} - \frac{1}{3} \, \sqrt{3}\right) + \left(-c^{2}\right)^{\frac{1}{3}} b c x^{5} \log\left(c^{2} x^{4} + \left(-c^{2}\right)^{\frac{2}{3}} x^{2} - \left(-c^{2}\right)^{\frac{1}{3}}\right) - 2 \, \left(-c^{2}\right)^{\frac{1}{3}} b c x^{5} \log\left(c^{2} x^{2} - \left(-c^{2}\right)^{\frac{2}{3}}\right) + 6 \, b c x^{3} + 2 \, b \log\left(-\frac{c x^{3} + 1}{c x^{3} - 1}\right) + 4 \, a}{20 \, x^{5}}"," ",0,"-1/20*(2*sqrt(3)*(-c^2)^(1/3)*b*c*x^5*arctan(2/3*sqrt(3)*(-c^2)^(1/3)*x^2 - 1/3*sqrt(3)) + (-c^2)^(1/3)*b*c*x^5*log(c^2*x^4 + (-c^2)^(2/3)*x^2 - (-c^2)^(1/3)) - 2*(-c^2)^(1/3)*b*c*x^5*log(c^2*x^2 - (-c^2)^(2/3)) + 6*b*c*x^3 + 2*b*log(-(c*x^3 + 1)/(c*x^3 - 1)) + 4*a)/x^5","A",0
111,1,248,0,0.643710," ","integrate(x^7*(a+b*arctanh(c*x^3)),x, algorithm=""fricas"")","\frac{10 \, b c^{4} x^{8} \log\left(-\frac{c x^{3} + 1}{c x^{3} - 1}\right) + 20 \, a c^{4} x^{8} + 12 \, b c^{3} x^{5} + 10 \, \sqrt{3} b c \sqrt{-\left(-c^{2}\right)^{\frac{1}{3}}} \arctan\left(\frac{\sqrt{3} {\left(2 \, c x + \left(-c^{2}\right)^{\frac{1}{3}}\right)} \sqrt{-\left(-c^{2}\right)^{\frac{1}{3}}}}{3 \, c}\right) + 10 \, \sqrt{3} b {\left(c^{2}\right)}^{\frac{1}{6}} c \arctan\left(\frac{\sqrt{3} {\left(c^{2}\right)}^{\frac{1}{6}} {\left(2 \, c x + {\left(c^{2}\right)}^{\frac{1}{3}}\right)}}{3 \, c}\right) + 5 \, \left(-c^{2}\right)^{\frac{2}{3}} b \log\left(c^{2} x^{2} + \left(-c^{2}\right)^{\frac{1}{3}} c x + \left(-c^{2}\right)^{\frac{2}{3}}\right) - 5 \, b {\left(c^{2}\right)}^{\frac{2}{3}} \log\left(c^{2} x^{2} + {\left(c^{2}\right)}^{\frac{1}{3}} c x + {\left(c^{2}\right)}^{\frac{2}{3}}\right) - 10 \, \left(-c^{2}\right)^{\frac{2}{3}} b \log\left(c x - \left(-c^{2}\right)^{\frac{1}{3}}\right) + 10 \, b {\left(c^{2}\right)}^{\frac{2}{3}} \log\left(c x - {\left(c^{2}\right)}^{\frac{1}{3}}\right)}{160 \, c^{4}}"," ",0,"1/160*(10*b*c^4*x^8*log(-(c*x^3 + 1)/(c*x^3 - 1)) + 20*a*c^4*x^8 + 12*b*c^3*x^5 + 10*sqrt(3)*b*c*sqrt(-(-c^2)^(1/3))*arctan(1/3*sqrt(3)*(2*c*x + (-c^2)^(1/3))*sqrt(-(-c^2)^(1/3))/c) + 10*sqrt(3)*b*(c^2)^(1/6)*c*arctan(1/3*sqrt(3)*(c^2)^(1/6)*(2*c*x + (c^2)^(1/3))/c) + 5*(-c^2)^(2/3)*b*log(c^2*x^2 + (-c^2)^(1/3)*c*x + (-c^2)^(2/3)) - 5*b*(c^2)^(2/3)*log(c^2*x^2 + (c^2)^(1/3)*c*x + (c^2)^(2/3)) - 10*(-c^2)^(2/3)*b*log(c*x - (-c^2)^(1/3)) + 10*b*(c^2)^(2/3)*log(c*x - (c^2)^(1/3)))/c^4","A",0
112,1,166,0,0.771549," ","integrate(x^4*(a+b*arctanh(c*x^3)),x, algorithm=""fricas"")","\frac{2 \, b c^{3} x^{5} \log\left(-\frac{c x^{3} + 1}{c x^{3} - 1}\right) + 4 \, a c^{3} x^{5} + 6 \, b c^{2} x^{2} - 2 \, \sqrt{3} b {\left(c^{2}\right)}^{\frac{1}{6}} c \arctan\left(-\frac{\sqrt{3} {\left(4 \, c^{2} x^{4} - 2 \, {\left(c^{2}\right)}^{\frac{2}{3}} x^{2} + {\left(c^{2}\right)}^{\frac{1}{3}}\right)} {\left(c^{2}\right)}^{\frac{1}{6}}}{8 \, c^{3} x^{6} + c}\right) - b {\left(c^{2}\right)}^{\frac{2}{3}} \log\left(c^{2} x^{4} + {\left(c^{2}\right)}^{\frac{2}{3}} x^{2} + {\left(c^{2}\right)}^{\frac{1}{3}}\right) + 2 \, b {\left(c^{2}\right)}^{\frac{2}{3}} \log\left(c^{2} x^{2} - {\left(c^{2}\right)}^{\frac{2}{3}}\right)}{20 \, c^{3}}"," ",0,"1/20*(2*b*c^3*x^5*log(-(c*x^3 + 1)/(c*x^3 - 1)) + 4*a*c^3*x^5 + 6*b*c^2*x^2 - 2*sqrt(3)*b*(c^2)^(1/6)*c*arctan(-sqrt(3)*(4*c^2*x^4 - 2*(c^2)^(2/3)*x^2 + (c^2)^(1/3))*(c^2)^(1/6)/(8*c^3*x^6 + c)) - b*(c^2)^(2/3)*log(c^2*x^4 + (c^2)^(2/3)*x^2 + (c^2)^(1/3)) + 2*b*(c^2)^(2/3)*log(c^2*x^2 - (c^2)^(2/3)))/c^3","A",0
113,1,238,0,0.613960," ","integrate(x*(a+b*arctanh(c*x^3)),x, algorithm=""fricas"")","\frac{2 \, b c^{2} x^{2} \log\left(-\frac{c x^{3} + 1}{c x^{3} - 1}\right) + 4 \, a c^{2} x^{2} + 2 \, \sqrt{3} b c \sqrt{-\left(-c^{2}\right)^{\frac{1}{3}}} \arctan\left(\frac{\sqrt{3} {\left(2 \, c x + \left(-c^{2}\right)^{\frac{1}{3}}\right)} \sqrt{-\left(-c^{2}\right)^{\frac{1}{3}}}}{3 \, c}\right) + 2 \, \sqrt{3} b {\left(c^{2}\right)}^{\frac{1}{6}} c \arctan\left(\frac{\sqrt{3} {\left(c^{2}\right)}^{\frac{1}{6}} {\left(2 \, c x + {\left(c^{2}\right)}^{\frac{1}{3}}\right)}}{3 \, c}\right) + \left(-c^{2}\right)^{\frac{2}{3}} b \log\left(c^{2} x^{2} + \left(-c^{2}\right)^{\frac{1}{3}} c x + \left(-c^{2}\right)^{\frac{2}{3}}\right) - b {\left(c^{2}\right)}^{\frac{2}{3}} \log\left(c^{2} x^{2} + {\left(c^{2}\right)}^{\frac{1}{3}} c x + {\left(c^{2}\right)}^{\frac{2}{3}}\right) - 2 \, \left(-c^{2}\right)^{\frac{2}{3}} b \log\left(c x - \left(-c^{2}\right)^{\frac{1}{3}}\right) + 2 \, b {\left(c^{2}\right)}^{\frac{2}{3}} \log\left(c x - {\left(c^{2}\right)}^{\frac{1}{3}}\right)}{8 \, c^{2}}"," ",0,"1/8*(2*b*c^2*x^2*log(-(c*x^3 + 1)/(c*x^3 - 1)) + 4*a*c^2*x^2 + 2*sqrt(3)*b*c*sqrt(-(-c^2)^(1/3))*arctan(1/3*sqrt(3)*(2*c*x + (-c^2)^(1/3))*sqrt(-(-c^2)^(1/3))/c) + 2*sqrt(3)*b*(c^2)^(1/6)*c*arctan(1/3*sqrt(3)*(c^2)^(1/6)*(2*c*x + (c^2)^(1/3))/c) + (-c^2)^(2/3)*b*log(c^2*x^2 + (-c^2)^(1/3)*c*x + (-c^2)^(2/3)) - b*(c^2)^(2/3)*log(c^2*x^2 + (c^2)^(1/3)*c*x + (c^2)^(2/3)) - 2*(-c^2)^(2/3)*b*log(c*x - (-c^2)^(1/3)) + 2*b*(c^2)^(2/3)*log(c*x - (c^2)^(1/3)))/c^2","A",0
114,1,117,0,0.728046," ","integrate((a+b*arctanh(c*x^3))/x^2,x, algorithm=""fricas"")","-\frac{2 \, \sqrt{3} b \left(-c\right)^{\frac{1}{3}} x \arctan\left(\frac{2}{3} \, \sqrt{3} \left(-c\right)^{\frac{2}{3}} x^{2} + \frac{1}{3} \, \sqrt{3}\right) + b \left(-c\right)^{\frac{1}{3}} x \log\left(c^{2} x^{4} - \left(-c\right)^{\frac{1}{3}} c x^{2} + \left(-c\right)^{\frac{2}{3}}\right) - 2 \, b \left(-c\right)^{\frac{1}{3}} x \log\left(c x^{2} + \left(-c\right)^{\frac{1}{3}}\right) + 2 \, b \log\left(-\frac{c x^{3} + 1}{c x^{3} - 1}\right) + 4 \, a}{4 \, x}"," ",0,"-1/4*(2*sqrt(3)*b*(-c)^(1/3)*x*arctan(2/3*sqrt(3)*(-c)^(2/3)*x^2 + 1/3*sqrt(3)) + b*(-c)^(1/3)*x*log(c^2*x^4 - (-c)^(1/3)*c*x^2 + (-c)^(2/3)) - 2*b*(-c)^(1/3)*x*log(c*x^2 + (-c)^(1/3)) + 2*b*log(-(c*x^3 + 1)/(c*x^3 - 1)) + 4*a)/x","A",0
115,1,196,0,0.578243," ","integrate((a+b*arctanh(c*x^3))/x^5,x, algorithm=""fricas"")","-\frac{2 \, \sqrt{3} b \left(-c\right)^{\frac{1}{3}} c x^{4} \arctan\left(\frac{2}{3} \, \sqrt{3} \left(-c\right)^{\frac{1}{3}} x - \frac{1}{3} \, \sqrt{3}\right) + 2 \, \sqrt{3} b c^{\frac{4}{3}} x^{4} \arctan\left(\frac{2}{3} \, \sqrt{3} c^{\frac{1}{3}} x - \frac{1}{3} \, \sqrt{3}\right) + b \left(-c\right)^{\frac{1}{3}} c x^{4} \log\left(c x^{2} + \left(-c\right)^{\frac{2}{3}} x - \left(-c\right)^{\frac{1}{3}}\right) + b c^{\frac{4}{3}} x^{4} \log\left(c x^{2} - c^{\frac{2}{3}} x + c^{\frac{1}{3}}\right) - 2 \, b \left(-c\right)^{\frac{1}{3}} c x^{4} \log\left(c x - \left(-c\right)^{\frac{2}{3}}\right) - 2 \, b c^{\frac{4}{3}} x^{4} \log\left(c x + c^{\frac{2}{3}}\right) + 12 \, b c x^{3} + 2 \, b \log\left(-\frac{c x^{3} + 1}{c x^{3} - 1}\right) + 4 \, a}{16 \, x^{4}}"," ",0,"-1/16*(2*sqrt(3)*b*(-c)^(1/3)*c*x^4*arctan(2/3*sqrt(3)*(-c)^(1/3)*x - 1/3*sqrt(3)) + 2*sqrt(3)*b*c^(4/3)*x^4*arctan(2/3*sqrt(3)*c^(1/3)*x - 1/3*sqrt(3)) + b*(-c)^(1/3)*c*x^4*log(c*x^2 + (-c)^(2/3)*x - (-c)^(1/3)) + b*c^(4/3)*x^4*log(c*x^2 - c^(2/3)*x + c^(1/3)) - 2*b*(-c)^(1/3)*c*x^4*log(c*x - (-c)^(2/3)) - 2*b*c^(4/3)*x^4*log(c*x + c^(2/3)) + 12*b*c*x^3 + 2*b*log(-(c*x^3 + 1)/(c*x^3 - 1)) + 4*a)/x^4","A",0
116,1,176,0,0.572285," ","integrate(x^11*(a+b*arctanh(c*x^3))^2,x, algorithm=""fricas"")","\frac{12 \, a^{2} c^{4} x^{12} + 8 \, a b c^{3} x^{9} + 4 \, b^{2} c^{2} x^{6} + 24 \, a b c x^{3} + 3 \, {\left(b^{2} c^{4} x^{12} - b^{2}\right)} \log\left(-\frac{c x^{3} + 1}{c x^{3} - 1}\right)^{2} - 4 \, {\left(3 \, a b - 4 \, b^{2}\right)} \log\left(c x^{3} + 1\right) + 4 \, {\left(3 \, a b + 4 \, b^{2}\right)} \log\left(c x^{3} - 1\right) + 4 \, {\left(3 \, a b c^{4} x^{12} + b^{2} c^{3} x^{9} + 3 \, b^{2} c x^{3}\right)} \log\left(-\frac{c x^{3} + 1}{c x^{3} - 1}\right)}{144 \, c^{4}}"," ",0,"1/144*(12*a^2*c^4*x^12 + 8*a*b*c^3*x^9 + 4*b^2*c^2*x^6 + 24*a*b*c*x^3 + 3*(b^2*c^4*x^12 - b^2)*log(-(c*x^3 + 1)/(c*x^3 - 1))^2 - 4*(3*a*b - 4*b^2)*log(c*x^3 + 1) + 4*(3*a*b + 4*b^2)*log(c*x^3 - 1) + 4*(3*a*b*c^4*x^12 + b^2*c^3*x^9 + 3*b^2*c*x^3)*log(-(c*x^3 + 1)/(c*x^3 - 1)))/c^4","A",0
117,0,0,0,0.660279," ","integrate(x^8*(a+b*arctanh(c*x^3))^2,x, algorithm=""fricas"")","{\rm integral}\left(b^{2} x^{8} \operatorname{artanh}\left(c x^{3}\right)^{2} + 2 \, a b x^{8} \operatorname{artanh}\left(c x^{3}\right) + a^{2} x^{8}, x\right)"," ",0,"integral(b^2*x^8*arctanh(c*x^3)^2 + 2*a*b*x^8*arctanh(c*x^3) + a^2*x^8, x)","F",0
118,1,138,0,0.553937," ","integrate(x^5*(a+b*arctanh(c*x^3))^2,x, algorithm=""fricas"")","\frac{4 \, a^{2} c^{2} x^{6} + 8 \, a b c x^{3} + {\left(b^{2} c^{2} x^{6} - b^{2}\right)} \log\left(-\frac{c x^{3} + 1}{c x^{3} - 1}\right)^{2} - 4 \, {\left(a b - b^{2}\right)} \log\left(c x^{3} + 1\right) + 4 \, {\left(a b + b^{2}\right)} \log\left(c x^{3} - 1\right) + 4 \, {\left(a b c^{2} x^{6} + b^{2} c x^{3}\right)} \log\left(-\frac{c x^{3} + 1}{c x^{3} - 1}\right)}{24 \, c^{2}}"," ",0,"1/24*(4*a^2*c^2*x^6 + 8*a*b*c*x^3 + (b^2*c^2*x^6 - b^2)*log(-(c*x^3 + 1)/(c*x^3 - 1))^2 - 4*(a*b - b^2)*log(c*x^3 + 1) + 4*(a*b + b^2)*log(c*x^3 - 1) + 4*(a*b*c^2*x^6 + b^2*c*x^3)*log(-(c*x^3 + 1)/(c*x^3 - 1)))/c^2","A",0
119,0,0,0,0.620257," ","integrate(x^2*(a+b*arctanh(c*x^3))^2,x, algorithm=""fricas"")","{\rm integral}\left(b^{2} x^{2} \operatorname{artanh}\left(c x^{3}\right)^{2} + 2 \, a b x^{2} \operatorname{artanh}\left(c x^{3}\right) + a^{2} x^{2}, x\right)"," ",0,"integral(b^2*x^2*arctanh(c*x^3)^2 + 2*a*b*x^2*arctanh(c*x^3) + a^2*x^2, x)","F",0
120,0,0,0,0.756079," ","integrate((a+b*arctanh(c*x^3))^2/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} \operatorname{artanh}\left(c x^{3}\right)^{2} + 2 \, a b \operatorname{artanh}\left(c x^{3}\right) + a^{2}}{x}, x\right)"," ",0,"integral((b^2*arctanh(c*x^3)^2 + 2*a*b*arctanh(c*x^3) + a^2)/x, x)","F",0
121,0,0,0,1.247496," ","integrate((a+b*arctanh(c*x^3))^2/x^4,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} \operatorname{artanh}\left(c x^{3}\right)^{2} + 2 \, a b \operatorname{artanh}\left(c x^{3}\right) + a^{2}}{x^{4}}, x\right)"," ",0,"integral((b^2*arctanh(c*x^3)^2 + 2*a*b*arctanh(c*x^3) + a^2)/x^4, x)","F",0
122,1,151,0,1.362614," ","integrate((a+b*arctanh(c*x^3))^2/x^7,x, algorithm=""fricas"")","\frac{24 \, b^{2} c^{2} x^{6} \log\left(x\right) + 4 \, {\left(a b - b^{2}\right)} c^{2} x^{6} \log\left(c x^{3} + 1\right) - 4 \, {\left(a b + b^{2}\right)} c^{2} x^{6} \log\left(c x^{3} - 1\right) - 8 \, a b c x^{3} + {\left(b^{2} c^{2} x^{6} - b^{2}\right)} \log\left(-\frac{c x^{3} + 1}{c x^{3} - 1}\right)^{2} - 4 \, a^{2} - 4 \, {\left(b^{2} c x^{3} + a b\right)} \log\left(-\frac{c x^{3} + 1}{c x^{3} - 1}\right)}{24 \, x^{6}}"," ",0,"1/24*(24*b^2*c^2*x^6*log(x) + 4*(a*b - b^2)*c^2*x^6*log(c*x^3 + 1) - 4*(a*b + b^2)*c^2*x^6*log(c*x^3 - 1) - 8*a*b*c*x^3 + (b^2*c^2*x^6 - b^2)*log(-(c*x^3 + 1)/(c*x^3 - 1))^2 - 4*a^2 - 4*(b^2*c*x^3 + a*b)*log(-(c*x^3 + 1)/(c*x^3 - 1)))/x^6","A",0
123,0,0,0,0.625734," ","integrate((a+b*arctanh(c*x^3))^2/x^10,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} \operatorname{artanh}\left(c x^{3}\right)^{2} + 2 \, a b \operatorname{artanh}\left(c x^{3}\right) + a^{2}}{x^{10}}, x\right)"," ",0,"integral((b^2*arctanh(c*x^3)^2 + 2*a*b*arctanh(c*x^3) + a^2)/x^10, x)","F",0
124,0,0,0,0.578294," ","integrate(x^8*(a+b*arctanh(c*x^3))^3,x, algorithm=""fricas"")","{\rm integral}\left(b^{3} x^{8} \operatorname{artanh}\left(c x^{3}\right)^{3} + 3 \, a b^{2} x^{8} \operatorname{artanh}\left(c x^{3}\right)^{2} + 3 \, a^{2} b x^{8} \operatorname{artanh}\left(c x^{3}\right) + a^{3} x^{8}, x\right)"," ",0,"integral(b^3*x^8*arctanh(c*x^3)^3 + 3*a*b^2*x^8*arctanh(c*x^3)^2 + 3*a^2*b*x^8*arctanh(c*x^3) + a^3*x^8, x)","F",0
125,0,0,0,0.951328," ","integrate(x^5*(a+b*arctanh(c*x^3))^3,x, algorithm=""fricas"")","{\rm integral}\left(b^{3} x^{5} \operatorname{artanh}\left(c x^{3}\right)^{3} + 3 \, a b^{2} x^{5} \operatorname{artanh}\left(c x^{3}\right)^{2} + 3 \, a^{2} b x^{5} \operatorname{artanh}\left(c x^{3}\right) + a^{3} x^{5}, x\right)"," ",0,"integral(b^3*x^5*arctanh(c*x^3)^3 + 3*a*b^2*x^5*arctanh(c*x^3)^2 + 3*a^2*b*x^5*arctanh(c*x^3) + a^3*x^5, x)","F",0
126,0,0,0,0.763575," ","integrate(x^2*(a+b*arctanh(c*x^3))^3,x, algorithm=""fricas"")","{\rm integral}\left(b^{3} x^{2} \operatorname{artanh}\left(c x^{3}\right)^{3} + 3 \, a b^{2} x^{2} \operatorname{artanh}\left(c x^{3}\right)^{2} + 3 \, a^{2} b x^{2} \operatorname{artanh}\left(c x^{3}\right) + a^{3} x^{2}, x\right)"," ",0,"integral(b^3*x^2*arctanh(c*x^3)^3 + 3*a*b^2*x^2*arctanh(c*x^3)^2 + 3*a^2*b*x^2*arctanh(c*x^3) + a^3*x^2, x)","F",0
127,0,0,0,0.692033," ","integrate((a+b*arctanh(c*x^3))^3/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{3} \operatorname{artanh}\left(c x^{3}\right)^{3} + 3 \, a b^{2} \operatorname{artanh}\left(c x^{3}\right)^{2} + 3 \, a^{2} b \operatorname{artanh}\left(c x^{3}\right) + a^{3}}{x}, x\right)"," ",0,"integral((b^3*arctanh(c*x^3)^3 + 3*a*b^2*arctanh(c*x^3)^2 + 3*a^2*b*arctanh(c*x^3) + a^3)/x, x)","F",0
128,0,0,0,0.525521," ","integrate((a+b*arctanh(c*x^3))^3/x^4,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{3} \operatorname{artanh}\left(c x^{3}\right)^{3} + 3 \, a b^{2} \operatorname{artanh}\left(c x^{3}\right)^{2} + 3 \, a^{2} b \operatorname{artanh}\left(c x^{3}\right) + a^{3}}{x^{4}}, x\right)"," ",0,"integral((b^3*arctanh(c*x^3)^3 + 3*a*b^2*arctanh(c*x^3)^2 + 3*a^2*b*arctanh(c*x^3) + a^3)/x^4, x)","F",0
129,0,0,0,0.555920," ","integrate((a+b*arctanh(c*x^3))^3/x^7,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{3} \operatorname{artanh}\left(c x^{3}\right)^{3} + 3 \, a b^{2} \operatorname{artanh}\left(c x^{3}\right)^{2} + 3 \, a^{2} b \operatorname{artanh}\left(c x^{3}\right) + a^{3}}{x^{7}}, x\right)"," ",0,"integral((b^3*arctanh(c*x^3)^3 + 3*a*b^2*arctanh(c*x^3)^2 + 3*a^2*b*arctanh(c*x^3) + a^3)/x^7, x)","F",0
130,0,0,0,0.635230," ","integrate((d*x)^m*(a+b*arctanh(c*x^3))^3,x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{3} \operatorname{artanh}\left(c x^{3}\right)^{3} + 3 \, a b^{2} \operatorname{artanh}\left(c x^{3}\right)^{2} + 3 \, a^{2} b \operatorname{artanh}\left(c x^{3}\right) + a^{3}\right)} \left(d x\right)^{m}, x\right)"," ",0,"integral((b^3*arctanh(c*x^3)^3 + 3*a*b^2*arctanh(c*x^3)^2 + 3*a^2*b*arctanh(c*x^3) + a^3)*(d*x)^m, x)","F",0
131,0,0,0,1.055924," ","integrate((d*x)^m*(a+b*arctanh(c*x^3))^2,x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{2} \operatorname{artanh}\left(c x^{3}\right)^{2} + 2 \, a b \operatorname{artanh}\left(c x^{3}\right) + a^{2}\right)} \left(d x\right)^{m}, x\right)"," ",0,"integral((b^2*arctanh(c*x^3)^2 + 2*a*b*arctanh(c*x^3) + a^2)*(d*x)^m, x)","F",0
132,0,0,0,0.545405," ","integrate((d*x)^m*(a+b*arctanh(c*x^3)),x, algorithm=""fricas"")","{\rm integral}\left({\left(b \operatorname{artanh}\left(c x^{3}\right) + a\right)} \left(d x\right)^{m}, x\right)"," ",0,"integral((b*arctanh(c*x^3) + a)*(d*x)^m, x)","F",0
133,0,0,0,0.669375," ","integrate((d*x)^m/(a+b*arctanh(c*x^3)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(d x\right)^{m}}{b \operatorname{artanh}\left(c x^{3}\right) + a}, x\right)"," ",0,"integral((d*x)^m/(b*arctanh(c*x^3) + a), x)","F",0
134,0,0,0,1.068516," ","integrate((d*x)^m/(a+b*arctanh(c*x^3))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(d x\right)^{m}}{b^{2} \operatorname{artanh}\left(c x^{3}\right)^{2} + 2 \, a b \operatorname{artanh}\left(c x^{3}\right) + a^{2}}, x\right)"," ",0,"integral((d*x)^m/(b^2*arctanh(c*x^3)^2 + 2*a*b*arctanh(c*x^3) + a^2), x)","F",0
135,1,48,0,0.666826," ","integrate(x^3*(a+b*arctanh(c/x)),x, algorithm=""fricas"")","\frac{1}{4} \, b c^{3} x + \frac{1}{12} \, b c x^{3} + \frac{1}{4} \, a x^{4} - \frac{1}{8} \, {\left(b c^{4} - b x^{4}\right)} \log\left(-\frac{c + x}{c - x}\right)"," ",0,"1/4*b*c^3*x + 1/12*b*c*x^3 + 1/4*a*x^4 - 1/8*(b*c^4 - b*x^4)*log(-(c + x)/(c - x))","A",0
136,1,49,0,0.678581," ","integrate(x^2*(a+b*arctanh(c/x)),x, algorithm=""fricas"")","\frac{1}{6} \, b c^{3} \log\left(-c^{2} + x^{2}\right) + \frac{1}{6} \, b x^{3} \log\left(-\frac{c + x}{c - x}\right) + \frac{1}{6} \, b c x^{2} + \frac{1}{3} \, a x^{3}"," ",0,"1/6*b*c^3*log(-c^2 + x^2) + 1/6*b*x^3*log(-(c + x)/(c - x)) + 1/6*b*c*x^2 + 1/3*a*x^3","A",0
137,1,39,0,0.616906," ","integrate(x*(a+b*arctanh(c/x)),x, algorithm=""fricas"")","\frac{1}{2} \, b c x + \frac{1}{2} \, a x^{2} - \frac{1}{4} \, {\left(b c^{2} - b x^{2}\right)} \log\left(-\frac{c + x}{c - x}\right)"," ",0,"1/2*b*c*x + 1/2*a*x^2 - 1/4*(b*c^2 - b*x^2)*log(-(c + x)/(c - x))","A",0
138,1,35,0,0.555741," ","integrate(a+b*arctanh(c/x),x, algorithm=""fricas"")","\frac{1}{2} \, b c \log\left(-c^{2} + x^{2}\right) + \frac{1}{2} \, b x \log\left(-\frac{c + x}{c - x}\right) + a x"," ",0,"1/2*b*c*log(-c^2 + x^2) + 1/2*b*x*log(-(c + x)/(c - x)) + a*x","A",0
139,0,0,0,0.651305," ","integrate((a+b*arctanh(c/x))/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \operatorname{artanh}\left(\frac{c}{x}\right) + a}{x}, x\right)"," ",0,"integral((b*arctanh(c/x) + a)/x, x)","F",0
140,1,48,0,0.656875," ","integrate((a+b*arctanh(c/x))/x^2,x, algorithm=""fricas"")","-\frac{b x \log\left(-c^{2} + x^{2}\right) - 2 \, b x \log\left(x\right) + b c \log\left(-\frac{c + x}{c - x}\right) + 2 \, a c}{2 \, c x}"," ",0,"-1/2*(b*x*log(-c^2 + x^2) - 2*b*x*log(x) + b*c*log(-(c + x)/(c - x)) + 2*a*c)/(c*x)","A",0
141,1,46,0,0.509165," ","integrate((a+b*arctanh(c/x))/x^3,x, algorithm=""fricas"")","-\frac{2 \, a c^{2} + 2 \, b c x + {\left(b c^{2} - b x^{2}\right)} \log\left(-\frac{c + x}{c - x}\right)}{4 \, c^{2} x^{2}}"," ",0,"-1/4*(2*a*c^2 + 2*b*c*x + (b*c^2 - b*x^2)*log(-(c + x)/(c - x)))/(c^2*x^2)","A",0
142,1,62,0,1.118331," ","integrate((a+b*arctanh(c/x))/x^4,x, algorithm=""fricas"")","-\frac{b x^{3} \log\left(-c^{2} + x^{2}\right) - 2 \, b x^{3} \log\left(x\right) + b c^{3} \log\left(-\frac{c + x}{c - x}\right) + 2 \, a c^{3} + b c^{2} x}{6 \, c^{3} x^{3}}"," ",0,"-1/6*(b*x^3*log(-c^2 + x^2) - 2*b*x^3*log(x) + b*c^3*log(-(c + x)/(c - x)) + 2*a*c^3 + b*c^2*x)/(c^3*x^3)","A",0
143,1,149,0,0.593714," ","integrate(x^3*(a+b*arctanh(c/x))^2,x, algorithm=""fricas"")","\frac{1}{2} \, a b c^{3} x + \frac{1}{12} \, b^{2} c^{2} x^{2} + \frac{1}{6} \, a b c x^{3} + \frac{1}{4} \, a^{2} x^{4} - \frac{1}{12} \, {\left(3 \, a b - 4 \, b^{2}\right)} c^{4} \log\left(c + x\right) + \frac{1}{12} \, {\left(3 \, a b + 4 \, b^{2}\right)} c^{4} \log\left(-c + x\right) - \frac{1}{16} \, {\left(b^{2} c^{4} - b^{2} x^{4}\right)} \log\left(-\frac{c + x}{c - x}\right)^{2} + \frac{1}{12} \, {\left(3 \, b^{2} c^{3} x + b^{2} c x^{3} + 3 \, a b x^{4}\right)} \log\left(-\frac{c + x}{c - x}\right)"," ",0,"1/2*a*b*c^3*x + 1/12*b^2*c^2*x^2 + 1/6*a*b*c*x^3 + 1/4*a^2*x^4 - 1/12*(3*a*b - 4*b^2)*c^4*log(c + x) + 1/12*(3*a*b + 4*b^2)*c^4*log(-c + x) - 1/16*(b^2*c^4 - b^2*x^4)*log(-(c + x)/(c - x))^2 + 1/12*(3*b^2*c^3*x + b^2*c*x^3 + 3*a*b*x^4)*log(-(c + x)/(c - x))","A",0
144,0,0,0,0.557637," ","integrate(x^2*(a+b*arctanh(c/x))^2,x, algorithm=""fricas"")","{\rm integral}\left(b^{2} x^{2} \operatorname{artanh}\left(\frac{c}{x}\right)^{2} + 2 \, a b x^{2} \operatorname{artanh}\left(\frac{c}{x}\right) + a^{2} x^{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, x)","F",0
145,1,111,0,0.640732," ","integrate(x*(a+b*arctanh(c/x))^2,x, algorithm=""fricas"")","a b c x + \frac{1}{2} \, a^{2} x^{2} - \frac{1}{2} \, {\left(a b - b^{2}\right)} c^{2} \log\left(c + x\right) + \frac{1}{2} \, {\left(a b + b^{2}\right)} c^{2} \log\left(-c + x\right) - \frac{1}{8} \, {\left(b^{2} c^{2} - b^{2} x^{2}\right)} \log\left(-\frac{c + x}{c - x}\right)^{2} + \frac{1}{2} \, {\left(b^{2} c x + a b x^{2}\right)} \log\left(-\frac{c + x}{c - x}\right)"," ",0,"a*b*c*x + 1/2*a^2*x^2 - 1/2*(a*b - b^2)*c^2*log(c + x) + 1/2*(a*b + b^2)*c^2*log(-c + x) - 1/8*(b^2*c^2 - b^2*x^2)*log(-(c + x)/(c - x))^2 + 1/2*(b^2*c*x + a*b*x^2)*log(-(c + x)/(c - x))","A",0
146,0,0,0,1.694628," ","integrate((a+b*arctanh(c/x))^2,x, algorithm=""fricas"")","{\rm integral}\left(b^{2} \operatorname{artanh}\left(\frac{c}{x}\right)^{2} + 2 \, a b \operatorname{artanh}\left(\frac{c}{x}\right) + a^{2}, x\right)"," ",0,"integral(b^2*arctanh(c/x)^2 + 2*a*b*arctanh(c/x) + a^2, x)","F",0
147,0,0,0,0.665005," ","integrate((a+b*arctanh(c/x))^2/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} \operatorname{artanh}\left(\frac{c}{x}\right)^{2} + 2 \, a b \operatorname{artanh}\left(\frac{c}{x}\right) + a^{2}}{x}, x\right)"," ",0,"integral((b^2*arctanh(c/x)^2 + 2*a*b*arctanh(c/x) + a^2)/x, x)","F",0
148,0,0,0,0.964617," ","integrate((a+b*arctanh(c/x))^2/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} \operatorname{artanh}\left(\frac{c}{x}\right)^{2} + 2 \, a b \operatorname{artanh}\left(\frac{c}{x}\right) + a^{2}}{x^{2}}, x\right)"," ",0,"integral((b^2*arctanh(c/x)^2 + 2*a*b*arctanh(c/x) + a^2)/x^2, x)","F",0
149,1,130,0,0.699538," ","integrate((a+b*arctanh(c/x))^2/x^3,x, algorithm=""fricas"")","\frac{8 \, b^{2} x^{2} \log\left(x\right) - 4 \, a^{2} c^{2} - 8 \, a b c x + 4 \, {\left(a b - b^{2}\right)} x^{2} \log\left(c + x\right) - 4 \, {\left(a b + b^{2}\right)} x^{2} \log\left(-c + x\right) - {\left(b^{2} c^{2} - b^{2} x^{2}\right)} \log\left(-\frac{c + x}{c - x}\right)^{2} - 4 \, {\left(a b c^{2} + b^{2} c x\right)} \log\left(-\frac{c + x}{c - x}\right)}{8 \, c^{2} x^{2}}"," ",0,"1/8*(8*b^2*x^2*log(x) - 4*a^2*c^2 - 8*a*b*c*x + 4*(a*b - b^2)*x^2*log(c + x) - 4*(a*b + b^2)*x^2*log(-c + x) - (b^2*c^2 - b^2*x^2)*log(-(c + x)/(c - x))^2 - 4*(a*b*c^2 + b^2*c*x)*log(-(c + x)/(c - x)))/(c^2*x^2)","A",0
150,0,0,0,0.615056," ","integrate(x^3*(a+b*arctanh(c/x))^3,x, algorithm=""fricas"")","{\rm integral}\left(b^{3} x^{3} \operatorname{artanh}\left(\frac{c}{x}\right)^{3} + 3 \, a b^{2} x^{3} \operatorname{artanh}\left(\frac{c}{x}\right)^{2} + 3 \, a^{2} b x^{3} \operatorname{artanh}\left(\frac{c}{x}\right) + a^{3} x^{3}, x\right)"," ",0,"integral(b^3*x^3*arctanh(c/x)^3 + 3*a*b^2*x^3*arctanh(c/x)^2 + 3*a^2*b*x^3*arctanh(c/x) + a^3*x^3, x)","F",0
151,0,0,0,0.522191," ","integrate(x^2*(a+b*arctanh(c/x))^3,x, algorithm=""fricas"")","{\rm integral}\left(b^{3} x^{2} \operatorname{artanh}\left(\frac{c}{x}\right)^{3} + 3 \, a b^{2} x^{2} \operatorname{artanh}\left(\frac{c}{x}\right)^{2} + 3 \, a^{2} b x^{2} \operatorname{artanh}\left(\frac{c}{x}\right) + a^{3} x^{2}, x\right)"," ",0,"integral(b^3*x^2*arctanh(c/x)^3 + 3*a*b^2*x^2*arctanh(c/x)^2 + 3*a^2*b*x^2*arctanh(c/x) + a^3*x^2, x)","F",0
152,0,0,0,0.486928," ","integrate(x*(a+b*arctanh(c/x))^3,x, algorithm=""fricas"")","{\rm integral}\left(b^{3} x \operatorname{artanh}\left(\frac{c}{x}\right)^{3} + 3 \, a b^{2} x \operatorname{artanh}\left(\frac{c}{x}\right)^{2} + 3 \, a^{2} b x \operatorname{artanh}\left(\frac{c}{x}\right) + a^{3} x, x\right)"," ",0,"integral(b^3*x*arctanh(c/x)^3 + 3*a*b^2*x*arctanh(c/x)^2 + 3*a^2*b*x*arctanh(c/x) + a^3*x, x)","F",0
153,0,0,0,0.889260," ","integrate((a+b*arctanh(c/x))^3,x, algorithm=""fricas"")","{\rm integral}\left(b^{3} \operatorname{artanh}\left(\frac{c}{x}\right)^{3} + 3 \, a b^{2} \operatorname{artanh}\left(\frac{c}{x}\right)^{2} + 3 \, a^{2} b \operatorname{artanh}\left(\frac{c}{x}\right) + a^{3}, 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, x)","F",0
154,0,0,0,0.718779," ","integrate((a+b*arctanh(c/x))^3/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{3} \operatorname{artanh}\left(\frac{c}{x}\right)^{3} + 3 \, a b^{2} \operatorname{artanh}\left(\frac{c}{x}\right)^{2} + 3 \, a^{2} b \operatorname{artanh}\left(\frac{c}{x}\right) + a^{3}}{x}, 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)/x, x)","F",0
155,0,0,0,0.541718," ","integrate((a+b*arctanh(c/x))^3/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{3} \operatorname{artanh}\left(\frac{c}{x}\right)^{3} + 3 \, a b^{2} \operatorname{artanh}\left(\frac{c}{x}\right)^{2} + 3 \, a^{2} b \operatorname{artanh}\left(\frac{c}{x}\right) + a^{3}}{x^{2}}, 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)/x^2, x)","F",0
156,0,0,0,0.625482," ","integrate((a+b*arctanh(c/x))^3/x^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{3} \operatorname{artanh}\left(\frac{c}{x}\right)^{3} + 3 \, a b^{2} \operatorname{artanh}\left(\frac{c}{x}\right)^{2} + 3 \, a^{2} b \operatorname{artanh}\left(\frac{c}{x}\right) + a^{3}}{x^{3}}, 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)/x^3, x)","F",0
157,1,53,0,0.531574," ","integrate(x^7*(a+b*arctanh(c/x^2)),x, algorithm=""fricas"")","\frac{1}{8} \, a x^{8} + \frac{1}{24} \, b c x^{6} + \frac{1}{8} \, b c^{3} x^{2} + \frac{1}{16} \, {\left(b x^{8} - b c^{4}\right)} \log\left(\frac{x^{2} + c}{x^{2} - c}\right)"," ",0,"1/8*a*x^8 + 1/24*b*c*x^6 + 1/8*b*c^3*x^2 + 1/16*(b*x^8 - b*c^4)*log((x^2 + c)/(x^2 - c))","A",0
158,1,52,0,0.574221," ","integrate(x^5*(a+b*arctanh(c/x^2)),x, algorithm=""fricas"")","\frac{1}{12} \, b x^{6} \log\left(\frac{x^{2} + c}{x^{2} - c}\right) + \frac{1}{6} \, a x^{6} + \frac{1}{12} \, b c x^{4} + \frac{1}{12} \, b c^{3} \log\left(x^{4} - c^{2}\right)"," ",0,"1/12*b*x^6*log((x^2 + c)/(x^2 - c)) + 1/6*a*x^6 + 1/12*b*c*x^4 + 1/12*b*c^3*log(x^4 - c^2)","A",0
159,1,44,0,0.549186," ","integrate(x^3*(a+b*arctanh(c/x^2)),x, algorithm=""fricas"")","\frac{1}{4} \, a x^{4} + \frac{1}{4} \, b c x^{2} + \frac{1}{8} \, {\left(b x^{4} - b c^{2}\right)} \log\left(\frac{x^{2} + c}{x^{2} - c}\right)"," ",0,"1/4*a*x^4 + 1/4*b*c*x^2 + 1/8*(b*x^4 - b*c^2)*log((x^2 + c)/(x^2 - c))","A",0
160,1,43,0,0.682884," ","integrate(x*(a+b*arctanh(c/x^2)),x, algorithm=""fricas"")","\frac{1}{4} \, b x^{2} \log\left(\frac{x^{2} + c}{x^{2} - c}\right) + \frac{1}{2} \, a x^{2} + \frac{1}{4} \, b c \log\left(x^{4} - c^{2}\right)"," ",0,"1/4*b*x^2*log((x^2 + c)/(x^2 - c)) + 1/2*a*x^2 + 1/4*b*c*log(x^4 - c^2)","A",0
161,0,0,0,0.514981," ","integrate((a+b*arctanh(c/x^2))/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \operatorname{artanh}\left(\frac{c}{x^{2}}\right) + a}{x}, x\right)"," ",0,"integral((b*arctanh(c/x^2) + a)/x, x)","F",0
162,1,55,0,0.553978," ","integrate((a+b*arctanh(c/x^2))/x^3,x, algorithm=""fricas"")","-\frac{b x^{2} \log\left(x^{4} - c^{2}\right) - 4 \, b x^{2} \log\left(x\right) + b c \log\left(\frac{x^{2} + c}{x^{2} - c}\right) + 2 \, a c}{4 \, c x^{2}}"," ",0,"-1/4*(b*x^2*log(x^4 - c^2) - 4*b*x^2*log(x) + b*c*log((x^2 + c)/(x^2 - c)) + 2*a*c)/(c*x^2)","A",0
163,1,52,0,0.691494," ","integrate((a+b*arctanh(c/x^2))/x^5,x, algorithm=""fricas"")","-\frac{2 \, b c x^{2} + 2 \, a c^{2} - {\left(b x^{4} - b c^{2}\right)} \log\left(\frac{x^{2} + c}{x^{2} - c}\right)}{8 \, c^{2} x^{4}}"," ",0,"-1/8*(2*b*c*x^2 + 2*a*c^2 - (b*x^4 - b*c^2)*log((x^2 + c)/(x^2 - c)))/(c^2*x^4)","A",0
164,1,67,0,0.637345," ","integrate((a+b*arctanh(c/x^2))/x^7,x, algorithm=""fricas"")","-\frac{b x^{6} \log\left(x^{4} - c^{2}\right) - 4 \, b x^{6} \log\left(x\right) + b c^{2} x^{2} + b c^{3} \log\left(\frac{x^{2} + c}{x^{2} - c}\right) + 2 \, a c^{3}}{12 \, c^{3} x^{6}}"," ",0,"-1/12*(b*x^6*log(x^4 - c^2) - 4*b*x^6*log(x) + b*c^2*x^2 + b*c^3*log((x^2 + c)/(x^2 - c)) + 2*a*c^3)/(c^3*x^6)","A",0
165,1,170,0,0.625283," ","integrate(x^4*(a+b*arctanh(c/x^2)),x, algorithm=""fricas"")","\left[\frac{1}{10} \, b x^{5} \log\left(\frac{x^{2} + c}{x^{2} - c}\right) + \frac{1}{5} \, a x^{5} + \frac{2}{15} \, b c x^{3} + \frac{1}{5} \, b c^{\frac{5}{2}} \arctan\left(\frac{x}{\sqrt{c}}\right) + \frac{1}{10} \, b c^{\frac{5}{2}} \log\left(\frac{x^{2} - 2 \, \sqrt{c} x + c}{x^{2} - c}\right), \frac{1}{10} \, b x^{5} \log\left(\frac{x^{2} + c}{x^{2} - c}\right) + \frac{1}{5} \, a x^{5} + \frac{2}{15} \, b c x^{3} + \frac{1}{5} \, b \sqrt{-c} c^{2} \arctan\left(\frac{\sqrt{-c} x}{c}\right) + \frac{1}{10} \, b \sqrt{-c} c^{2} \log\left(\frac{x^{2} + 2 \, \sqrt{-c} x - c}{x^{2} + c}\right)\right]"," ",0,"[1/10*b*x^5*log((x^2 + c)/(x^2 - c)) + 1/5*a*x^5 + 2/15*b*c*x^3 + 1/5*b*c^(5/2)*arctan(x/sqrt(c)) + 1/10*b*c^(5/2)*log((x^2 - 2*sqrt(c)*x + c)/(x^2 - c)), 1/10*b*x^5*log((x^2 + c)/(x^2 - c)) + 1/5*a*x^5 + 2/15*b*c*x^3 + 1/5*b*sqrt(-c)*c^2*arctan(sqrt(-c)*x/c) + 1/10*b*sqrt(-c)*c^2*log((x^2 + 2*sqrt(-c)*x - c)/(x^2 + c))]","A",0
166,1,162,0,0.646024," ","integrate(x^2*(a+b*arctanh(c/x^2)),x, algorithm=""fricas"")","\left[\frac{1}{6} \, b x^{3} \log\left(\frac{x^{2} + c}{x^{2} - c}\right) + \frac{1}{3} \, a x^{3} - \frac{1}{3} \, b c^{\frac{3}{2}} \arctan\left(\frac{x}{\sqrt{c}}\right) + \frac{1}{6} \, b c^{\frac{3}{2}} \log\left(\frac{x^{2} - 2 \, \sqrt{c} x + c}{x^{2} - c}\right) + \frac{2}{3} \, b c x, \frac{1}{6} \, b x^{3} \log\left(\frac{x^{2} + c}{x^{2} - c}\right) + \frac{1}{3} \, a x^{3} + \frac{1}{3} \, b \sqrt{-c} c \arctan\left(\frac{\sqrt{-c} x}{c}\right) + \frac{1}{6} \, b \sqrt{-c} c \log\left(\frac{x^{2} - 2 \, \sqrt{-c} x - c}{x^{2} + c}\right) + \frac{2}{3} \, b c x\right]"," ",0,"[1/6*b*x^3*log((x^2 + c)/(x^2 - c)) + 1/3*a*x^3 - 1/3*b*c^(3/2)*arctan(x/sqrt(c)) + 1/6*b*c^(3/2)*log((x^2 - 2*sqrt(c)*x + c)/(x^2 - c)) + 2/3*b*c*x, 1/6*b*x^3*log((x^2 + c)/(x^2 - c)) + 1/3*a*x^3 + 1/3*b*sqrt(-c)*c*arctan(sqrt(-c)*x/c) + 1/6*b*sqrt(-c)*c*log((x^2 - 2*sqrt(-c)*x - c)/(x^2 + c)) + 2/3*b*c*x]","A",0
167,1,138,0,0.584807," ","integrate(a+b*arctanh(c/x^2),x, algorithm=""fricas"")","\left[\frac{1}{2} \, b x \log\left(\frac{x^{2} + c}{x^{2} - c}\right) + b \sqrt{c} \arctan\left(\frac{x}{\sqrt{c}}\right) + \frac{1}{2} \, b \sqrt{c} \log\left(\frac{x^{2} - 2 \, \sqrt{c} x + c}{x^{2} - c}\right) + a x, \frac{1}{2} \, b x \log\left(\frac{x^{2} + c}{x^{2} - c}\right) + b \sqrt{-c} \arctan\left(\frac{\sqrt{-c} x}{c}\right) + \frac{1}{2} \, b \sqrt{-c} \log\left(\frac{x^{2} + 2 \, \sqrt{-c} x - c}{x^{2} + c}\right) + a x\right]"," ",0,"[1/2*b*x*log((x^2 + c)/(x^2 - c)) + b*sqrt(c)*arctan(x/sqrt(c)) + 1/2*b*sqrt(c)*log((x^2 - 2*sqrt(c)*x + c)/(x^2 - c)) + a*x, 1/2*b*x*log((x^2 + c)/(x^2 - c)) + b*sqrt(-c)*arctan(sqrt(-c)*x/c) + 1/2*b*sqrt(-c)*log((x^2 + 2*sqrt(-c)*x - c)/(x^2 + c)) + a*x]","A",0
168,1,159,0,0.533789," ","integrate((a+b*arctanh(c/x^2))/x^2,x, algorithm=""fricas"")","\left[\frac{2 \, b \sqrt{c} x \arctan\left(\frac{x}{\sqrt{c}}\right) + b \sqrt{c} x \log\left(\frac{x^{2} + 2 \, \sqrt{c} x + c}{x^{2} - c}\right) - b c \log\left(\frac{x^{2} + c}{x^{2} - c}\right) - 2 \, a c}{2 \, c x}, -\frac{2 \, b \sqrt{-c} x \arctan\left(\frac{\sqrt{-c} x}{c}\right) + b \sqrt{-c} x \log\left(\frac{x^{2} - 2 \, \sqrt{-c} x - c}{x^{2} + c}\right) + b c \log\left(\frac{x^{2} + c}{x^{2} - c}\right) + 2 \, a c}{2 \, c x}\right]"," ",0,"[1/2*(2*b*sqrt(c)*x*arctan(x/sqrt(c)) + b*sqrt(c)*x*log((x^2 + 2*sqrt(c)*x + c)/(x^2 - c)) - b*c*log((x^2 + c)/(x^2 - c)) - 2*a*c)/(c*x), -1/2*(2*b*sqrt(-c)*x*arctan(sqrt(-c)*x/c) + b*sqrt(-c)*x*log((x^2 - 2*sqrt(-c)*x - c)/(x^2 + c)) + b*c*log((x^2 + c)/(x^2 - c)) + 2*a*c)/(c*x)]","A",0
169,1,189,0,0.648606," ","integrate((a+b*arctanh(c/x^2))/x^4,x, algorithm=""fricas"")","\left[-\frac{2 \, b \sqrt{c} x^{3} \arctan\left(\frac{x}{\sqrt{c}}\right) - b \sqrt{c} x^{3} \log\left(\frac{x^{2} + 2 \, \sqrt{c} x + c}{x^{2} - c}\right) + 4 \, b c x^{2} + b c^{2} \log\left(\frac{x^{2} + c}{x^{2} - c}\right) + 2 \, a c^{2}}{6 \, c^{2} x^{3}}, -\frac{2 \, b \sqrt{-c} x^{3} \arctan\left(\frac{\sqrt{-c} x}{c}\right) + b \sqrt{-c} x^{3} \log\left(\frac{x^{2} + 2 \, \sqrt{-c} x - c}{x^{2} + c}\right) + 4 \, b c x^{2} + b c^{2} \log\left(\frac{x^{2} + c}{x^{2} - c}\right) + 2 \, a c^{2}}{6 \, c^{2} x^{3}}\right]"," ",0,"[-1/6*(2*b*sqrt(c)*x^3*arctan(x/sqrt(c)) - b*sqrt(c)*x^3*log((x^2 + 2*sqrt(c)*x + c)/(x^2 - c)) + 4*b*c*x^2 + b*c^2*log((x^2 + c)/(x^2 - c)) + 2*a*c^2)/(c^2*x^3), -1/6*(2*b*sqrt(-c)*x^3*arctan(sqrt(-c)*x/c) + b*sqrt(-c)*x^3*log((x^2 + 2*sqrt(-c)*x - c)/(x^2 + c)) + 4*b*c*x^2 + b*c^2*log((x^2 + c)/(x^2 - c)) + 2*a*c^2)/(c^2*x^3)]","A",0
170,1,196,0,0.529836," ","integrate((a+b*arctanh(c/x^2))/x^6,x, algorithm=""fricas"")","\left[\frac{6 \, b \sqrt{c} x^{5} \arctan\left(\frac{x}{\sqrt{c}}\right) + 3 \, b \sqrt{c} x^{5} \log\left(\frac{x^{2} + 2 \, \sqrt{c} x + c}{x^{2} - c}\right) - 4 \, b c^{2} x^{2} - 3 \, b c^{3} \log\left(\frac{x^{2} + c}{x^{2} - c}\right) - 6 \, a c^{3}}{30 \, c^{3} x^{5}}, -\frac{6 \, b \sqrt{-c} x^{5} \arctan\left(\frac{\sqrt{-c} x}{c}\right) + 3 \, b \sqrt{-c} x^{5} \log\left(\frac{x^{2} - 2 \, \sqrt{-c} x - c}{x^{2} + c}\right) + 4 \, b c^{2} x^{2} + 3 \, b c^{3} \log\left(\frac{x^{2} + c}{x^{2} - c}\right) + 6 \, a c^{3}}{30 \, c^{3} x^{5}}\right]"," ",0,"[1/30*(6*b*sqrt(c)*x^5*arctan(x/sqrt(c)) + 3*b*sqrt(c)*x^5*log((x^2 + 2*sqrt(c)*x + c)/(x^2 - c)) - 4*b*c^2*x^2 - 3*b*c^3*log((x^2 + c)/(x^2 - c)) - 6*a*c^3)/(c^3*x^5), -1/30*(6*b*sqrt(-c)*x^5*arctan(sqrt(-c)*x/c) + 3*b*sqrt(-c)*x^5*log((x^2 - 2*sqrt(-c)*x - c)/(x^2 + c)) + 4*b*c^2*x^2 + 3*b*c^3*log((x^2 + c)/(x^2 - c)) + 6*a*c^3)/(c^3*x^5)]","A",0
171,1,126,0,0.423622," ","integrate(x^3*(a+b*arctanh(c/x^2))^2,x, algorithm=""fricas"")","\frac{1}{4} \, a^{2} x^{4} + \frac{1}{2} \, a b c x^{2} - \frac{1}{4} \, {\left(a b - b^{2}\right)} c^{2} \log\left(x^{2} + c\right) + \frac{1}{4} \, {\left(a b + b^{2}\right)} c^{2} \log\left(x^{2} - c\right) + \frac{1}{16} \, {\left(b^{2} x^{4} - b^{2} c^{2}\right)} \log\left(\frac{x^{2} + c}{x^{2} - c}\right)^{2} + \frac{1}{4} \, {\left(a b x^{4} + b^{2} c x^{2}\right)} \log\left(\frac{x^{2} + c}{x^{2} - c}\right)"," ",0,"1/4*a^2*x^4 + 1/2*a*b*c*x^2 - 1/4*(a*b - b^2)*c^2*log(x^2 + c) + 1/4*(a*b + b^2)*c^2*log(x^2 - c) + 1/16*(b^2*x^4 - b^2*c^2)*log((x^2 + c)/(x^2 - c))^2 + 1/4*(a*b*x^4 + b^2*c*x^2)*log((x^2 + c)/(x^2 - c))","A",0
172,0,0,0,0.729215," ","integrate(x*(a+b*arctanh(c/x^2))^2,x, algorithm=""fricas"")","{\rm integral}\left(b^{2} x \operatorname{artanh}\left(\frac{c}{x^{2}}\right)^{2} + 2 \, a b x \operatorname{artanh}\left(\frac{c}{x^{2}}\right) + a^{2} x, x\right)"," ",0,"integral(b^2*x*arctanh(c/x^2)^2 + 2*a*b*x*arctanh(c/x^2) + a^2*x, x)","F",0
173,0,0,0,0.484634," ","integrate((a+b*arctanh(c/x^2))^2/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} \operatorname{artanh}\left(\frac{c}{x^{2}}\right)^{2} + 2 \, a b \operatorname{artanh}\left(\frac{c}{x^{2}}\right) + a^{2}}{x}, x\right)"," ",0,"integral((b^2*arctanh(c/x^2)^2 + 2*a*b*arctanh(c/x^2) + a^2)/x, x)","F",0
174,0,0,0,0.555898," ","integrate((a+b*arctanh(c/x^2))^2/x^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} \operatorname{artanh}\left(\frac{c}{x^{2}}\right)^{2} + 2 \, a b \operatorname{artanh}\left(\frac{c}{x^{2}}\right) + a^{2}}{x^{3}}, x\right)"," ",0,"integral((b^2*arctanh(c/x^2)^2 + 2*a*b*arctanh(c/x^2) + a^2)/x^3, x)","F",0
175,1,143,0,0.500343," ","integrate((a+b*arctanh(c/x^2))^2/x^5,x, algorithm=""fricas"")","\frac{16 \, b^{2} x^{4} \log\left(x\right) + 4 \, {\left(a b - b^{2}\right)} x^{4} \log\left(x^{2} + c\right) - 4 \, {\left(a b + b^{2}\right)} x^{4} \log\left(x^{2} - c\right) - 8 \, a b c x^{2} - 4 \, a^{2} c^{2} + {\left(b^{2} x^{4} - b^{2} c^{2}\right)} \log\left(\frac{x^{2} + c}{x^{2} - c}\right)^{2} - 4 \, {\left(b^{2} c x^{2} + a b c^{2}\right)} \log\left(\frac{x^{2} + c}{x^{2} - c}\right)}{16 \, c^{2} x^{4}}"," ",0,"1/16*(16*b^2*x^4*log(x) + 4*(a*b - b^2)*x^4*log(x^2 + c) - 4*(a*b + b^2)*x^4*log(x^2 - c) - 8*a*b*c*x^2 - 4*a^2*c^2 + (b^2*x^4 - b^2*c^2)*log((x^2 + c)/(x^2 - c))^2 - 4*(b^2*c*x^2 + a*b*c^2)*log((x^2 + c)/(x^2 - c)))/(c^2*x^4)","A",0
176,0,0,0,0.571305," ","integrate(x^4*(a+b*arctanh(c/x^2))^2,x, algorithm=""fricas"")","{\rm integral}\left(b^{2} x^{4} \operatorname{artanh}\left(\frac{c}{x^{2}}\right)^{2} + 2 \, a b x^{4} \operatorname{artanh}\left(\frac{c}{x^{2}}\right) + a^{2} x^{4}, x\right)"," ",0,"integral(b^2*x^4*arctanh(c/x^2)^2 + 2*a*b*x^4*arctanh(c/x^2) + a^2*x^4, x)","F",0
177,0,0,0,0.642328," ","integrate(x^2*(a+b*arctanh(c/x^2))^2,x, algorithm=""fricas"")","{\rm integral}\left(b^{2} x^{2} \operatorname{artanh}\left(\frac{c}{x^{2}}\right)^{2} + 2 \, a b x^{2} \operatorname{artanh}\left(\frac{c}{x^{2}}\right) + a^{2} x^{2}, x\right)"," ",0,"integral(b^2*x^2*arctanh(c/x^2)^2 + 2*a*b*x^2*arctanh(c/x^2) + a^2*x^2, x)","F",0
178,0,0,0,0.601758," ","integrate((a+b*arctanh(c/x^2))^2,x, algorithm=""fricas"")","{\rm integral}\left(b^{2} \operatorname{artanh}\left(\frac{c}{x^{2}}\right)^{2} + 2 \, a b \operatorname{artanh}\left(\frac{c}{x^{2}}\right) + a^{2}, x\right)"," ",0,"integral(b^2*arctanh(c/x^2)^2 + 2*a*b*arctanh(c/x^2) + a^2, x)","F",0
179,0,0,0,0.896801," ","integrate((a+b*arctanh(c/x^2))^2/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} \operatorname{artanh}\left(\frac{c}{x^{2}}\right)^{2} + 2 \, a b \operatorname{artanh}\left(\frac{c}{x^{2}}\right) + a^{2}}{x^{2}}, x\right)"," ",0,"integral((b^2*arctanh(c/x^2)^2 + 2*a*b*arctanh(c/x^2) + a^2)/x^2, x)","F",0
180,0,0,0,0.616259," ","integrate((a+b*arctanh(c/x^2))^2/x^4,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} \operatorname{artanh}\left(\frac{c}{x^{2}}\right)^{2} + 2 \, a b \operatorname{artanh}\left(\frac{c}{x^{2}}\right) + a^{2}}{x^{4}}, x\right)"," ",0,"integral((b^2*arctanh(c/x^2)^2 + 2*a*b*arctanh(c/x^2) + a^2)/x^4, x)","F",0
181,0,0,0,0.655725," ","integrate((a+b*arctanh(c/x^2))^2/x^6,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} \operatorname{artanh}\left(\frac{c}{x^{2}}\right)^{2} + 2 \, a b \operatorname{artanh}\left(\frac{c}{x^{2}}\right) + a^{2}}{x^{6}}, x\right)"," ",0,"integral((b^2*arctanh(c/x^2)^2 + 2*a*b*arctanh(c/x^2) + a^2)/x^6, x)","F",0
182,0,0,0,0.965761," ","integrate((d*x)^m*(a+b*arctanh(c/x^2))^3,x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{3} \operatorname{artanh}\left(\frac{c}{x^{2}}\right)^{3} + 3 \, a b^{2} \operatorname{artanh}\left(\frac{c}{x^{2}}\right)^{2} + 3 \, a^{2} b \operatorname{artanh}\left(\frac{c}{x^{2}}\right) + a^{3}\right)} \left(d x\right)^{m}, x\right)"," ",0,"integral((b^3*arctanh(c/x^2)^3 + 3*a*b^2*arctanh(c/x^2)^2 + 3*a^2*b*arctanh(c/x^2) + a^3)*(d*x)^m, x)","F",0
183,0,0,0,0.514844," ","integrate((d*x)^m*(a+b*arctanh(c/x^2))^2,x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{2} \operatorname{artanh}\left(\frac{c}{x^{2}}\right)^{2} + 2 \, a b \operatorname{artanh}\left(\frac{c}{x^{2}}\right) + a^{2}\right)} \left(d x\right)^{m}, x\right)"," ",0,"integral((b^2*arctanh(c/x^2)^2 + 2*a*b*arctanh(c/x^2) + a^2)*(d*x)^m, x)","F",0
184,0,0,0,0.540740," ","integrate((d*x)^m*(a+b*arctanh(c/x^2)),x, algorithm=""fricas"")","{\rm integral}\left({\left(b \operatorname{artanh}\left(\frac{c}{x^{2}}\right) + a\right)} \left(d x\right)^{m}, x\right)"," ",0,"integral((b*arctanh(c/x^2) + a)*(d*x)^m, x)","F",0
185,0,0,0,0.856751," ","integrate((d*x)^m/(a+b*arctanh(c/x^2)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(d x\right)^{m}}{b \operatorname{artanh}\left(\frac{c}{x^{2}}\right) + a}, x\right)"," ",0,"integral((d*x)^m/(b*arctanh(c/x^2) + a), x)","F",0
186,0,0,0,0.720402," ","integrate((d*x)^m/(a+b*arctanh(c/x^2))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(d x\right)^{m}}{b^{2} \operatorname{artanh}\left(\frac{c}{x^{2}}\right)^{2} + 2 \, a b \operatorname{artanh}\left(\frac{c}{x^{2}}\right) + a^{2}}, x\right)"," ",0,"integral((d*x)^m/(b^2*arctanh(c/x^2)^2 + 2*a*b*arctanh(c/x^2) + a^2), x)","F",0
187,1,89,0,0.639327," ","integrate(x^3*(a+b*arctanh(c*x^(1/2))),x, algorithm=""fricas"")","\frac{210 \, a c^{8} x^{4} + 105 \, {\left(b c^{8} x^{4} - b\right)} \log\left(-\frac{c^{2} x + 2 \, c \sqrt{x} + 1}{c^{2} x - 1}\right) + 2 \, {\left(15 \, b c^{7} x^{3} + 21 \, b c^{5} x^{2} + 35 \, b c^{3} x + 105 \, b c\right)} \sqrt{x}}{840 \, c^{8}}"," ",0,"1/840*(210*a*c^8*x^4 + 105*(b*c^8*x^4 - b)*log(-(c^2*x + 2*c*sqrt(x) + 1)/(c^2*x - 1)) + 2*(15*b*c^7*x^3 + 21*b*c^5*x^2 + 35*b*c^3*x + 105*b*c)*sqrt(x))/c^8","A",0
188,1,80,0,0.678031," ","integrate(x^2*(a+b*arctanh(c*x^(1/2))),x, algorithm=""fricas"")","\frac{30 \, a c^{6} x^{3} + 15 \, {\left(b c^{6} x^{3} - b\right)} \log\left(-\frac{c^{2} x + 2 \, c \sqrt{x} + 1}{c^{2} x - 1}\right) + 2 \, {\left(3 \, b c^{5} x^{2} + 5 \, b c^{3} x + 15 \, b c\right)} \sqrt{x}}{90 \, c^{6}}"," ",0,"1/90*(30*a*c^6*x^3 + 15*(b*c^6*x^3 - b)*log(-(c^2*x + 2*c*sqrt(x) + 1)/(c^2*x - 1)) + 2*(3*b*c^5*x^2 + 5*b*c^3*x + 15*b*c)*sqrt(x))/c^6","A",0
189,1,70,0,0.610608," ","integrate(x*(a+b*arctanh(c*x^(1/2))),x, algorithm=""fricas"")","\frac{6 \, a c^{4} x^{2} + 3 \, {\left(b c^{4} x^{2} - b\right)} \log\left(-\frac{c^{2} x + 2 \, c \sqrt{x} + 1}{c^{2} x - 1}\right) + 2 \, {\left(b c^{3} x + 3 \, b c\right)} \sqrt{x}}{12 \, c^{4}}"," ",0,"1/12*(6*a*c^4*x^2 + 3*(b*c^4*x^2 - b)*log(-(c^2*x + 2*c*sqrt(x) + 1)/(c^2*x - 1)) + 2*(b*c^3*x + 3*b*c)*sqrt(x))/c^4","A",0
190,1,56,0,1.213210," ","integrate(a+b*arctanh(c*x^(1/2)),x, algorithm=""fricas"")","\frac{2 \, a c^{2} x + 2 \, b c \sqrt{x} + {\left(b c^{2} x - b\right)} \log\left(-\frac{c^{2} x + 2 \, c \sqrt{x} + 1}{c^{2} x - 1}\right)}{2 \, c^{2}}"," ",0,"1/2*(2*a*c^2*x + 2*b*c*sqrt(x) + (b*c^2*x - b)*log(-(c^2*x + 2*c*sqrt(x) + 1)/(c^2*x - 1)))/c^2","A",0
191,0,0,0,0.527981," ","integrate((a+b*arctanh(c*x^(1/2)))/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \operatorname{artanh}\left(c \sqrt{x}\right) + a}{x}, x\right)"," ",0,"integral((b*arctanh(c*sqrt(x)) + a)/x, x)","F",0
192,1,53,0,0.798499," ","integrate((a+b*arctanh(c*x^(1/2)))/x^2,x, algorithm=""fricas"")","-\frac{2 \, b c \sqrt{x} - {\left(b c^{2} x - b\right)} \log\left(-\frac{c^{2} x + 2 \, c \sqrt{x} + 1}{c^{2} x - 1}\right) + 2 \, a}{2 \, x}"," ",0,"-1/2*(2*b*c*sqrt(x) - (b*c^2*x - b)*log(-(c^2*x + 2*c*sqrt(x) + 1)/(c^2*x - 1)) + 2*a)/x","A",0
193,1,64,0,0.562574," ","integrate((a+b*arctanh(c*x^(1/2)))/x^3,x, algorithm=""fricas"")","\frac{3 \, {\left(b c^{4} x^{2} - b\right)} \log\left(-\frac{c^{2} x + 2 \, c \sqrt{x} + 1}{c^{2} x - 1}\right) - 2 \, {\left(3 \, b c^{3} x + b c\right)} \sqrt{x} - 6 \, a}{12 \, x^{2}}"," ",0,"1/12*(3*(b*c^4*x^2 - b)*log(-(c^2*x + 2*c*sqrt(x) + 1)/(c^2*x - 1)) - 2*(3*b*c^3*x + b*c)*sqrt(x) - 6*a)/x^2","A",0
194,1,74,0,0.774373," ","integrate((a+b*arctanh(c*x^(1/2)))/x^4,x, algorithm=""fricas"")","\frac{15 \, {\left(b c^{6} x^{3} - b\right)} \log\left(-\frac{c^{2} x + 2 \, c \sqrt{x} + 1}{c^{2} x - 1}\right) - 2 \, {\left(15 \, b c^{5} x^{2} + 5 \, b c^{3} x + 3 \, b c\right)} \sqrt{x} - 30 \, a}{90 \, x^{3}}"," ",0,"1/90*(15*(b*c^6*x^3 - b)*log(-(c^2*x + 2*c*sqrt(x) + 1)/(c^2*x - 1)) - 2*(15*b*c^5*x^2 + 5*b*c^3*x + 3*b*c)*sqrt(x) - 30*a)/x^3","A",0
195,1,273,0,1.521037," ","integrate(x^3*(a+b*arctanh(c*x^(1/2)))^2,x, algorithm=""fricas"")","\frac{420 \, a^{2} c^{8} x^{4} + 20 \, b^{2} c^{6} x^{3} + 72 \, b^{2} c^{4} x^{2} + 284 \, b^{2} c^{2} x + 105 \, {\left(b^{2} c^{8} x^{4} - b^{2}\right)} \log\left(-\frac{c^{2} x + 2 \, c \sqrt{x} + 1}{c^{2} x - 1}\right)^{2} + 4 \, {\left(105 \, a b c^{8} - 105 \, a b + 176 \, b^{2}\right)} \log\left(c \sqrt{x} + 1\right) - 4 \, {\left(105 \, a b c^{8} - 105 \, a b - 176 \, b^{2}\right)} \log\left(c \sqrt{x} - 1\right) + 4 \, {\left(105 \, a b c^{8} x^{4} - 105 \, a b c^{8} + {\left(15 \, b^{2} c^{7} x^{3} + 21 \, b^{2} c^{5} x^{2} + 35 \, b^{2} c^{3} x + 105 \, b^{2} c\right)} \sqrt{x}\right)} \log\left(-\frac{c^{2} x + 2 \, c \sqrt{x} + 1}{c^{2} x - 1}\right) + 8 \, {\left(15 \, a b c^{7} x^{3} + 21 \, a b c^{5} x^{2} + 35 \, a b c^{3} x + 105 \, a b c\right)} \sqrt{x}}{1680 \, c^{8}}"," ",0,"1/1680*(420*a^2*c^8*x^4 + 20*b^2*c^6*x^3 + 72*b^2*c^4*x^2 + 284*b^2*c^2*x + 105*(b^2*c^8*x^4 - b^2)*log(-(c^2*x + 2*c*sqrt(x) + 1)/(c^2*x - 1))^2 + 4*(105*a*b*c^8 - 105*a*b + 176*b^2)*log(c*sqrt(x) + 1) - 4*(105*a*b*c^8 - 105*a*b - 176*b^2)*log(c*sqrt(x) - 1) + 4*(105*a*b*c^8*x^4 - 105*a*b*c^8 + (15*b^2*c^7*x^3 + 21*b^2*c^5*x^2 + 35*b^2*c^3*x + 105*b^2*c)*sqrt(x))*log(-(c^2*x + 2*c*sqrt(x) + 1)/(c^2*x - 1)) + 8*(15*a*b*c^7*x^3 + 21*a*b*c^5*x^2 + 35*a*b*c^3*x + 105*a*b*c)*sqrt(x))/c^8","A",0
196,1,241,0,1.213573," ","integrate(x^2*(a+b*arctanh(c*x^(1/2)))^2,x, algorithm=""fricas"")","\frac{60 \, a^{2} c^{6} x^{3} + 6 \, b^{2} c^{4} x^{2} + 32 \, b^{2} c^{2} x + 15 \, {\left(b^{2} c^{6} x^{3} - b^{2}\right)} \log\left(-\frac{c^{2} x + 2 \, c \sqrt{x} + 1}{c^{2} x - 1}\right)^{2} + 4 \, {\left(15 \, a b c^{6} - 15 \, a b + 23 \, b^{2}\right)} \log\left(c \sqrt{x} + 1\right) - 4 \, {\left(15 \, a b c^{6} - 15 \, a b - 23 \, b^{2}\right)} \log\left(c \sqrt{x} - 1\right) + 4 \, {\left(15 \, a b c^{6} x^{3} - 15 \, a b c^{6} + {\left(3 \, b^{2} c^{5} x^{2} + 5 \, b^{2} c^{3} x + 15 \, b^{2} c\right)} \sqrt{x}\right)} \log\left(-\frac{c^{2} x + 2 \, c \sqrt{x} + 1}{c^{2} x - 1}\right) + 8 \, {\left(3 \, a b c^{5} x^{2} + 5 \, a b c^{3} x + 15 \, a b c\right)} \sqrt{x}}{180 \, c^{6}}"," ",0,"1/180*(60*a^2*c^6*x^3 + 6*b^2*c^4*x^2 + 32*b^2*c^2*x + 15*(b^2*c^6*x^3 - b^2)*log(-(c^2*x + 2*c*sqrt(x) + 1)/(c^2*x - 1))^2 + 4*(15*a*b*c^6 - 15*a*b + 23*b^2)*log(c*sqrt(x) + 1) - 4*(15*a*b*c^6 - 15*a*b - 23*b^2)*log(c*sqrt(x) - 1) + 4*(15*a*b*c^6*x^3 - 15*a*b*c^6 + (3*b^2*c^5*x^2 + 5*b^2*c^3*x + 15*b^2*c)*sqrt(x))*log(-(c^2*x + 2*c*sqrt(x) + 1)/(c^2*x - 1)) + 8*(3*a*b*c^5*x^2 + 5*a*b*c^3*x + 15*a*b*c)*sqrt(x))/c^6","A",0
197,1,207,0,0.918694," ","integrate(x*(a+b*arctanh(c*x^(1/2)))^2,x, algorithm=""fricas"")","\frac{12 \, a^{2} c^{4} x^{2} + 4 \, b^{2} c^{2} x + 3 \, {\left(b^{2} c^{4} x^{2} - b^{2}\right)} \log\left(-\frac{c^{2} x + 2 \, c \sqrt{x} + 1}{c^{2} x - 1}\right)^{2} + 4 \, {\left(3 \, a b c^{4} - 3 \, a b + 4 \, b^{2}\right)} \log\left(c \sqrt{x} + 1\right) - 4 \, {\left(3 \, a b c^{4} - 3 \, a b - 4 \, b^{2}\right)} \log\left(c \sqrt{x} - 1\right) + 4 \, {\left(3 \, a b c^{4} x^{2} - 3 \, a b c^{4} + {\left(b^{2} c^{3} x + 3 \, b^{2} c\right)} \sqrt{x}\right)} \log\left(-\frac{c^{2} x + 2 \, c \sqrt{x} + 1}{c^{2} x - 1}\right) + 8 \, {\left(a b c^{3} x + 3 \, a b c\right)} \sqrt{x}}{24 \, c^{4}}"," ",0,"1/24*(12*a^2*c^4*x^2 + 4*b^2*c^2*x + 3*(b^2*c^4*x^2 - b^2)*log(-(c^2*x + 2*c*sqrt(x) + 1)/(c^2*x - 1))^2 + 4*(3*a*b*c^4 - 3*a*b + 4*b^2)*log(c*sqrt(x) + 1) - 4*(3*a*b*c^4 - 3*a*b - 4*b^2)*log(c*sqrt(x) - 1) + 4*(3*a*b*c^4*x^2 - 3*a*b*c^4 + (b^2*c^3*x + 3*b^2*c)*sqrt(x))*log(-(c^2*x + 2*c*sqrt(x) + 1)/(c^2*x - 1)) + 8*(a*b*c^3*x + 3*a*b*c)*sqrt(x))/c^4","A",0
198,1,165,0,1.132118," ","integrate((a+b*arctanh(c*x^(1/2)))^2,x, algorithm=""fricas"")","\frac{4 \, a^{2} c^{2} x + 8 \, a b c \sqrt{x} + {\left(b^{2} c^{2} x - b^{2}\right)} \log\left(-\frac{c^{2} x + 2 \, c \sqrt{x} + 1}{c^{2} x - 1}\right)^{2} + 4 \, {\left(a b c^{2} - a b + b^{2}\right)} \log\left(c \sqrt{x} + 1\right) - 4 \, {\left(a b c^{2} - a b - b^{2}\right)} \log\left(c \sqrt{x} - 1\right) + 4 \, {\left(a b c^{2} x - a b c^{2} + b^{2} c \sqrt{x}\right)} \log\left(-\frac{c^{2} x + 2 \, c \sqrt{x} + 1}{c^{2} x - 1}\right)}{4 \, c^{2}}"," ",0,"1/4*(4*a^2*c^2*x + 8*a*b*c*sqrt(x) + (b^2*c^2*x - b^2)*log(-(c^2*x + 2*c*sqrt(x) + 1)/(c^2*x - 1))^2 + 4*(a*b*c^2 - a*b + b^2)*log(c*sqrt(x) + 1) - 4*(a*b*c^2 - a*b - b^2)*log(c*sqrt(x) - 1) + 4*(a*b*c^2*x - a*b*c^2 + b^2*c*sqrt(x))*log(-(c^2*x + 2*c*sqrt(x) + 1)/(c^2*x - 1)))/c^2","B",0
199,0,0,0,1.156776," ","integrate((a+b*arctanh(c*x^(1/2)))^2/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} \operatorname{artanh}\left(c \sqrt{x}\right)^{2} + 2 \, a b \operatorname{artanh}\left(c \sqrt{x}\right) + a^{2}}{x}, x\right)"," ",0,"integral((b^2*arctanh(c*sqrt(x))^2 + 2*a*b*arctanh(c*sqrt(x)) + a^2)/x, x)","F",0
200,1,157,0,0.715622," ","integrate((a+b*arctanh(c*x^(1/2)))^2/x^2,x, algorithm=""fricas"")","\frac{8 \, b^{2} c^{2} x \log\left(\sqrt{x}\right) + 4 \, {\left(a b - b^{2}\right)} c^{2} x \log\left(c \sqrt{x} + 1\right) - 4 \, {\left(a b + b^{2}\right)} c^{2} x \log\left(c \sqrt{x} - 1\right) - 8 \, a b c \sqrt{x} + {\left(b^{2} c^{2} x - b^{2}\right)} \log\left(-\frac{c^{2} x + 2 \, c \sqrt{x} + 1}{c^{2} x - 1}\right)^{2} - 4 \, a^{2} - 4 \, {\left(b^{2} c \sqrt{x} + a b\right)} \log\left(-\frac{c^{2} x + 2 \, c \sqrt{x} + 1}{c^{2} x - 1}\right)}{4 \, x}"," ",0,"1/4*(8*b^2*c^2*x*log(sqrt(x)) + 4*(a*b - b^2)*c^2*x*log(c*sqrt(x) + 1) - 4*(a*b + b^2)*c^2*x*log(c*sqrt(x) - 1) - 8*a*b*c*sqrt(x) + (b^2*c^2*x - b^2)*log(-(c^2*x + 2*c*sqrt(x) + 1)/(c^2*x - 1))^2 - 4*a^2 - 4*(b^2*c*sqrt(x) + a*b)*log(-(c^2*x + 2*c*sqrt(x) + 1)/(c^2*x - 1)))/x","B",0
201,1,201,0,0.736336," ","integrate((a+b*arctanh(c*x^(1/2)))^2/x^3,x, algorithm=""fricas"")","\frac{32 \, b^{2} c^{4} x^{2} \log\left(\sqrt{x}\right) + 4 \, {\left(3 \, a b - 4 \, b^{2}\right)} c^{4} x^{2} \log\left(c \sqrt{x} + 1\right) - 4 \, {\left(3 \, a b + 4 \, b^{2}\right)} c^{4} x^{2} \log\left(c \sqrt{x} - 1\right) - 4 \, b^{2} c^{2} x + 3 \, {\left(b^{2} c^{4} x^{2} - b^{2}\right)} \log\left(-\frac{c^{2} x + 2 \, c \sqrt{x} + 1}{c^{2} x - 1}\right)^{2} - 12 \, a^{2} - 4 \, {\left(3 \, a b + {\left(3 \, b^{2} c^{3} x + b^{2} c\right)} \sqrt{x}\right)} \log\left(-\frac{c^{2} x + 2 \, c \sqrt{x} + 1}{c^{2} x - 1}\right) - 8 \, {\left(3 \, a b c^{3} x + a b c\right)} \sqrt{x}}{24 \, x^{2}}"," ",0,"1/24*(32*b^2*c^4*x^2*log(sqrt(x)) + 4*(3*a*b - 4*b^2)*c^4*x^2*log(c*sqrt(x) + 1) - 4*(3*a*b + 4*b^2)*c^4*x^2*log(c*sqrt(x) - 1) - 4*b^2*c^2*x + 3*(b^2*c^4*x^2 - b^2)*log(-(c^2*x + 2*c*sqrt(x) + 1)/(c^2*x - 1))^2 - 12*a^2 - 4*(3*a*b + (3*b^2*c^3*x + b^2*c)*sqrt(x))*log(-(c^2*x + 2*c*sqrt(x) + 1)/(c^2*x - 1)) - 8*(3*a*b*c^3*x + a*b*c)*sqrt(x))/x^2","A",0
202,0,0,0,0.608524," ","integrate(x^3*(a+b*arctanh(c*x^(1/2)))^3,x, algorithm=""fricas"")","{\rm integral}\left(b^{3} x^{3} \operatorname{artanh}\left(c \sqrt{x}\right)^{3} + 3 \, a b^{2} x^{3} \operatorname{artanh}\left(c \sqrt{x}\right)^{2} + 3 \, a^{2} b x^{3} \operatorname{artanh}\left(c \sqrt{x}\right) + a^{3} x^{3}, x\right)"," ",0,"integral(b^3*x^3*arctanh(c*sqrt(x))^3 + 3*a*b^2*x^3*arctanh(c*sqrt(x))^2 + 3*a^2*b*x^3*arctanh(c*sqrt(x)) + a^3*x^3, x)","F",0
203,0,0,0,1.715581," ","integrate(x^2*(a+b*arctanh(c*x^(1/2)))^3,x, algorithm=""fricas"")","{\rm integral}\left(b^{3} x^{2} \operatorname{artanh}\left(c \sqrt{x}\right)^{3} + 3 \, a b^{2} x^{2} \operatorname{artanh}\left(c \sqrt{x}\right)^{2} + 3 \, a^{2} b x^{2} \operatorname{artanh}\left(c \sqrt{x}\right) + a^{3} x^{2}, x\right)"," ",0,"integral(b^3*x^2*arctanh(c*sqrt(x))^3 + 3*a*b^2*x^2*arctanh(c*sqrt(x))^2 + 3*a^2*b*x^2*arctanh(c*sqrt(x)) + a^3*x^2, x)","F",0
204,0,0,0,0.709965," ","integrate(x*(a+b*arctanh(c*x^(1/2)))^3,x, algorithm=""fricas"")","{\rm integral}\left(b^{3} x \operatorname{artanh}\left(c \sqrt{x}\right)^{3} + 3 \, a b^{2} x \operatorname{artanh}\left(c \sqrt{x}\right)^{2} + 3 \, a^{2} b x \operatorname{artanh}\left(c \sqrt{x}\right) + a^{3} x, x\right)"," ",0,"integral(b^3*x*arctanh(c*sqrt(x))^3 + 3*a*b^2*x*arctanh(c*sqrt(x))^2 + 3*a^2*b*x*arctanh(c*sqrt(x)) + a^3*x, x)","F",0
205,0,0,0,1.347193," ","integrate((a+b*arctanh(c*x^(1/2)))^3,x, algorithm=""fricas"")","{\rm integral}\left(b^{3} \operatorname{artanh}\left(c \sqrt{x}\right)^{3} + 3 \, a b^{2} \operatorname{artanh}\left(c \sqrt{x}\right)^{2} + 3 \, a^{2} b \operatorname{artanh}\left(c \sqrt{x}\right) + a^{3}, x\right)"," ",0,"integral(b^3*arctanh(c*sqrt(x))^3 + 3*a*b^2*arctanh(c*sqrt(x))^2 + 3*a^2*b*arctanh(c*sqrt(x)) + a^3, x)","F",0
206,0,0,0,1.224426," ","integrate((a+b*arctanh(c*x^(1/2)))^3/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{3} \operatorname{artanh}\left(c \sqrt{x}\right)^{3} + 3 \, a b^{2} \operatorname{artanh}\left(c \sqrt{x}\right)^{2} + 3 \, a^{2} b \operatorname{artanh}\left(c \sqrt{x}\right) + a^{3}}{x}, x\right)"," ",0,"integral((b^3*arctanh(c*sqrt(x))^3 + 3*a*b^2*arctanh(c*sqrt(x))^2 + 3*a^2*b*arctanh(c*sqrt(x)) + a^3)/x, x)","F",0
207,0,0,0,0.628130," ","integrate((a+b*arctanh(c*x^(1/2)))^3/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{3} \operatorname{artanh}\left(c \sqrt{x}\right)^{3} + 3 \, a b^{2} \operatorname{artanh}\left(c \sqrt{x}\right)^{2} + 3 \, a^{2} b \operatorname{artanh}\left(c \sqrt{x}\right) + a^{3}}{x^{2}}, x\right)"," ",0,"integral((b^3*arctanh(c*sqrt(x))^3 + 3*a*b^2*arctanh(c*sqrt(x))^2 + 3*a^2*b*arctanh(c*sqrt(x)) + a^3)/x^2, x)","F",0
208,0,0,0,0.728260," ","integrate((a+b*arctanh(c*x^(1/2)))^3/x^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{3} \operatorname{artanh}\left(c \sqrt{x}\right)^{3} + 3 \, a b^{2} \operatorname{artanh}\left(c \sqrt{x}\right)^{2} + 3 \, a^{2} b \operatorname{artanh}\left(c \sqrt{x}\right) + a^{3}}{x^{3}}, x\right)"," ",0,"integral((b^3*arctanh(c*sqrt(x))^3 + 3*a*b^2*arctanh(c*sqrt(x))^2 + 3*a^2*b*arctanh(c*sqrt(x)) + a^3)/x^3, x)","F",0
209,1,36,0,0.784819," ","integrate(x^(3/2)*arctanh(x^(1/2)),x, algorithm=""fricas"")","\frac{1}{5} \, x^{\frac{5}{2}} \log\left(-\frac{x + 2 \, \sqrt{x} + 1}{x - 1}\right) + \frac{1}{10} \, x^{2} + \frac{1}{5} \, x + \frac{1}{5} \, \log\left(x - 1\right)"," ",0,"1/5*x^(5/2)*log(-(x + 2*sqrt(x) + 1)/(x - 1)) + 1/10*x^2 + 1/5*x + 1/5*log(x - 1)","A",0
210,1,31,0,1.004993," ","integrate(arctanh(x^(1/2))*x^(1/2),x, algorithm=""fricas"")","\frac{1}{3} \, x^{\frac{3}{2}} \log\left(-\frac{x + 2 \, \sqrt{x} + 1}{x - 1}\right) + \frac{1}{3} \, x + \frac{1}{3} \, \log\left(x - 1\right)"," ",0,"1/3*x^(3/2)*log(-(x + 2*sqrt(x) + 1)/(x - 1)) + 1/3*x + 1/3*log(x - 1)","A",0
211,1,25,0,0.579403," ","integrate(arctanh(x^(1/2))/x^(1/2),x, algorithm=""fricas"")","\sqrt{x} \log\left(-\frac{x + 2 \, \sqrt{x} + 1}{x - 1}\right) + \log\left(x - 1\right)"," ",0,"sqrt(x)*log(-(x + 2*sqrt(x) + 1)/(x - 1)) + log(x - 1)","A",0
212,1,37,0,0.959738," ","integrate(arctanh(x^(1/2))/x^(3/2),x, algorithm=""fricas"")","-\frac{x \log\left(x - 1\right) - x \log\left(x\right) + \sqrt{x} \log\left(-\frac{x + 2 \, \sqrt{x} + 1}{x - 1}\right)}{x}"," ",0,"-(x*log(x - 1) - x*log(x) + sqrt(x)*log(-(x + 2*sqrt(x) + 1)/(x - 1)))/x","A",0
213,1,1803,0,3.706382," ","integrate(x^3*(a+b*arctanh(c*x^(3/2))),x, algorithm=""fricas"")","\frac{40 \, a c x^{4} + 24 \, b x^{\frac{5}{2}} - 20 \, \sqrt{3} \sqrt{{\left(\left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(b^{3} - \frac{{\left(c^{8} - 1\right)} b^{3}}{c^{8}} + \frac{b^{3}}{c^{8}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} + 2 \, b\right)}^{2} - 4 \, {\left(\left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(b^{3} - \frac{{\left(c^{8} - 1\right)} b^{3}}{c^{8}} + \frac{b^{3}}{c^{8}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} + 2 \, b\right)} b + 4 \, b^{2}} c \arctan\left(\frac{4 \, \sqrt{3} \sqrt{{\left(\left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(b^{3} - \frac{{\left(c^{8} - 1\right)} b^{3}}{c^{8}} + \frac{b^{3}}{c^{8}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} + 2 \, b\right)}^{2} b^{2} c^{5} \sqrt{x} + 4 \, b^{4} c^{5} \sqrt{x} + 4 \, b^{4} c^{2} + 4 \, b^{4} x - 2 \, {\left(2 \, b^{3} c^{5} \sqrt{x} + b^{3} c^{2}\right)} {\left(\left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(b^{3} - \frac{{\left(c^{8} - 1\right)} b^{3}}{c^{8}} + \frac{b^{3}}{c^{8}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} + 2 \, b\right)}} \sqrt{{\left(\left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(b^{3} - \frac{{\left(c^{8} - 1\right)} b^{3}}{c^{8}} + \frac{b^{3}}{c^{8}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} + 2 \, b\right)}^{2} - 4 \, {\left(\left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(b^{3} - \frac{{\left(c^{8} - 1\right)} b^{3}}{c^{8}} + \frac{b^{3}}{c^{8}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} + 2 \, b\right)} b + 4 \, b^{2}} c^{3} - \sqrt{3} {\left({\left(\left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(b^{3} - \frac{{\left(c^{8} - 1\right)} b^{3}}{c^{8}} + \frac{b^{3}}{c^{8}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} + 2 \, b\right)}^{2} c^{8} - 4 \, {\left(\left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(b^{3} - \frac{{\left(c^{8} - 1\right)} b^{3}}{c^{8}} + \frac{b^{3}}{c^{8}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} + 2 \, b\right)} b c^{8} + 4 \, b^{2} c^{8} + 8 \, b^{2} c^{3} \sqrt{x}\right)} \sqrt{{\left(\left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(b^{3} - \frac{{\left(c^{8} - 1\right)} b^{3}}{c^{8}} + \frac{b^{3}}{c^{8}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} + 2 \, b\right)}^{2} - 4 \, {\left(\left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(b^{3} - \frac{{\left(c^{8} - 1\right)} b^{3}}{c^{8}} + \frac{b^{3}}{c^{8}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} + 2 \, b\right)} b + 4 \, b^{2}}}{24 \, b^{3}}\right) - 10 \, {\left(\left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(b^{3} - \frac{{\left(c^{8} - 1\right)} b^{3}}{c^{8}} + \frac{b^{3}}{c^{8}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} + 2 \, b\right)} c \log\left(-\frac{1}{4} \, {\left(\left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(b^{3} - \frac{{\left(c^{8} - 1\right)} b^{3}}{c^{8}} + \frac{b^{3}}{c^{8}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} + 2 \, b\right)}^{2} c^{5} + {\left(\left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(b^{3} - \frac{{\left(c^{8} - 1\right)} b^{3}}{c^{8}} + \frac{b^{3}}{c^{8}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} + 2 \, b\right)} b c^{5} - b^{2} c^{5} + b^{2} \sqrt{x}\right) - 20 \, {\left(4 \, {\left(-\frac{1}{1024} \, b^{3} + \frac{{\left(c^{8} - 1\right)} b^{3}}{1024 \, c^{8}} + \frac{b^{3}}{1024 \, c^{8}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} - b\right)} c \log\left({\left(4 \, {\left(-\frac{1}{1024} \, b^{3} + \frac{{\left(c^{8} - 1\right)} b^{3}}{1024 \, c^{8}} + \frac{b^{3}}{1024 \, c^{8}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} - b\right)}^{2} c^{5} + 2 \, {\left(4 \, {\left(-\frac{1}{1024} \, b^{3} + \frac{{\left(c^{8} - 1\right)} b^{3}}{1024 \, c^{8}} + \frac{b^{3}}{1024 \, c^{8}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} - b\right)} b c^{5} + b^{2} c^{5} + b^{2} \sqrt{x}\right) - 40 \, \sqrt{3 \, {\left(4 \, {\left(-\frac{1}{1024} \, b^{3} + \frac{{\left(c^{8} - 1\right)} b^{3}}{1024 \, c^{8}} + \frac{b^{3}}{1024 \, c^{8}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} - b\right)}^{2} + 6 \, {\left(4 \, {\left(-\frac{1}{1024} \, b^{3} + \frac{{\left(c^{8} - 1\right)} b^{3}}{1024 \, c^{8}} + \frac{b^{3}}{1024 \, c^{8}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} - b\right)} b + 3 \, b^{2}} c \arctan\left(\frac{{\left({\left(4 \, {\left(-\frac{1}{1024} \, b^{3} + \frac{{\left(c^{8} - 1\right)} b^{3}}{1024 \, c^{8}} + \frac{b^{3}}{1024 \, c^{8}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} - b\right)}^{2} c^{8} + 2 \, {\left(4 \, {\left(-\frac{1}{1024} \, b^{3} + \frac{{\left(c^{8} - 1\right)} b^{3}}{1024 \, c^{8}} + \frac{b^{3}}{1024 \, c^{8}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} - b\right)} b c^{8} + b^{2} c^{8} - 2 \, b^{2} c^{3} \sqrt{x} + \sqrt{-4 \, {\left(4 \, {\left(-\frac{1}{1024} \, b^{3} + \frac{{\left(c^{8} - 1\right)} b^{3}}{1024 \, c^{8}} + \frac{b^{3}}{1024 \, c^{8}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} - b\right)}^{2} b^{2} c^{5} \sqrt{x} - 4 \, b^{4} c^{5} \sqrt{x} + 4 \, b^{4} c^{2} + 4 \, b^{4} x - 4 \, {\left(2 \, b^{3} c^{5} \sqrt{x} - b^{3} c^{2}\right)} {\left(4 \, {\left(-\frac{1}{1024} \, b^{3} + \frac{{\left(c^{8} - 1\right)} b^{3}}{1024 \, c^{8}} + \frac{b^{3}}{1024 \, c^{8}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} - b\right)}} c^{3}\right)} \sqrt{3 \, {\left(4 \, {\left(-\frac{1}{1024} \, b^{3} + \frac{{\left(c^{8} - 1\right)} b^{3}}{1024 \, c^{8}} + \frac{b^{3}}{1024 \, c^{8}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} - b\right)}^{2} + 6 \, {\left(4 \, {\left(-\frac{1}{1024} \, b^{3} + \frac{{\left(c^{8} - 1\right)} b^{3}}{1024 \, c^{8}} + \frac{b^{3}}{1024 \, c^{8}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} - b\right)} b + 3 \, b^{2}}}{3 \, b^{3}}\right) + 5 \, {\left({\left(\left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(b^{3} - \frac{{\left(c^{8} - 1\right)} b^{3}}{c^{8}} + \frac{b^{3}}{c^{8}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} + 2 \, b\right)} c - 6 \, b c\right)} \log\left({\left(\left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(b^{3} - \frac{{\left(c^{8} - 1\right)} b^{3}}{c^{8}} + \frac{b^{3}}{c^{8}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} + 2 \, b\right)}^{2} b^{2} c^{5} \sqrt{x} + 4 \, b^{4} c^{5} \sqrt{x} + 4 \, b^{4} c^{2} + 4 \, b^{4} x - 2 \, {\left(2 \, b^{3} c^{5} \sqrt{x} + b^{3} c^{2}\right)} {\left(\left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(b^{3} - \frac{{\left(c^{8} - 1\right)} b^{3}}{c^{8}} + \frac{b^{3}}{c^{8}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} + 2 \, b\right)}\right) + 10 \, {\left({\left(4 \, {\left(-\frac{1}{1024} \, b^{3} + \frac{{\left(c^{8} - 1\right)} b^{3}}{1024 \, c^{8}} + \frac{b^{3}}{1024 \, c^{8}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} - b\right)} c + 3 \, b c\right)} \log\left(-4 \, {\left(4 \, {\left(-\frac{1}{1024} \, b^{3} + \frac{{\left(c^{8} - 1\right)} b^{3}}{1024 \, c^{8}} + \frac{b^{3}}{1024 \, c^{8}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} - b\right)}^{2} b^{2} c^{5} \sqrt{x} - 4 \, b^{4} c^{5} \sqrt{x} + 4 \, b^{4} c^{2} + 4 \, b^{4} x - 4 \, {\left(2 \, b^{3} c^{5} \sqrt{x} - b^{3} c^{2}\right)} {\left(4 \, {\left(-\frac{1}{1024} \, b^{3} + \frac{{\left(c^{8} - 1\right)} b^{3}}{1024 \, c^{8}} + \frac{b^{3}}{1024 \, c^{8}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} - b\right)}\right) + 20 \, {\left(b c x^{4} - b c\right)} \log\left(-\frac{c^{2} x^{3} + 2 \, c x^{\frac{3}{2}} + 1}{c^{2} x^{3} - 1}\right)}{160 \, c}"," ",0,"1/160*(40*a*c*x^4 + 24*b*x^(5/2) - 20*sqrt(3)*sqrt(((1/2)^(1/3)*(b^3 - (c^8 - 1)*b^3/c^8 + b^3/c^8)^(1/3)*(I*sqrt(3) + 1) + 2*b)^2 - 4*((1/2)^(1/3)*(b^3 - (c^8 - 1)*b^3/c^8 + b^3/c^8)^(1/3)*(I*sqrt(3) + 1) + 2*b)*b + 4*b^2)*c*arctan(1/24*(4*sqrt(3)*sqrt(((1/2)^(1/3)*(b^3 - (c^8 - 1)*b^3/c^8 + b^3/c^8)^(1/3)*(I*sqrt(3) + 1) + 2*b)^2*b^2*c^5*sqrt(x) + 4*b^4*c^5*sqrt(x) + 4*b^4*c^2 + 4*b^4*x - 2*(2*b^3*c^5*sqrt(x) + b^3*c^2)*((1/2)^(1/3)*(b^3 - (c^8 - 1)*b^3/c^8 + b^3/c^8)^(1/3)*(I*sqrt(3) + 1) + 2*b))*sqrt(((1/2)^(1/3)*(b^3 - (c^8 - 1)*b^3/c^8 + b^3/c^8)^(1/3)*(I*sqrt(3) + 1) + 2*b)^2 - 4*((1/2)^(1/3)*(b^3 - (c^8 - 1)*b^3/c^8 + b^3/c^8)^(1/3)*(I*sqrt(3) + 1) + 2*b)*b + 4*b^2)*c^3 - sqrt(3)*(((1/2)^(1/3)*(b^3 - (c^8 - 1)*b^3/c^8 + b^3/c^8)^(1/3)*(I*sqrt(3) + 1) + 2*b)^2*c^8 - 4*((1/2)^(1/3)*(b^3 - (c^8 - 1)*b^3/c^8 + b^3/c^8)^(1/3)*(I*sqrt(3) + 1) + 2*b)*b*c^8 + 4*b^2*c^8 + 8*b^2*c^3*sqrt(x))*sqrt(((1/2)^(1/3)*(b^3 - (c^8 - 1)*b^3/c^8 + b^3/c^8)^(1/3)*(I*sqrt(3) + 1) + 2*b)^2 - 4*((1/2)^(1/3)*(b^3 - (c^8 - 1)*b^3/c^8 + b^3/c^8)^(1/3)*(I*sqrt(3) + 1) + 2*b)*b + 4*b^2))/b^3) - 10*((1/2)^(1/3)*(b^3 - (c^8 - 1)*b^3/c^8 + b^3/c^8)^(1/3)*(I*sqrt(3) + 1) + 2*b)*c*log(-1/4*((1/2)^(1/3)*(b^3 - (c^8 - 1)*b^3/c^8 + b^3/c^8)^(1/3)*(I*sqrt(3) + 1) + 2*b)^2*c^5 + ((1/2)^(1/3)*(b^3 - (c^8 - 1)*b^3/c^8 + b^3/c^8)^(1/3)*(I*sqrt(3) + 1) + 2*b)*b*c^5 - b^2*c^5 + b^2*sqrt(x)) - 20*(4*(-1/1024*b^3 + 1/1024*(c^8 - 1)*b^3/c^8 + 1/1024*b^3/c^8)^(1/3)*(I*sqrt(3) + 1) - b)*c*log((4*(-1/1024*b^3 + 1/1024*(c^8 - 1)*b^3/c^8 + 1/1024*b^3/c^8)^(1/3)*(I*sqrt(3) + 1) - b)^2*c^5 + 2*(4*(-1/1024*b^3 + 1/1024*(c^8 - 1)*b^3/c^8 + 1/1024*b^3/c^8)^(1/3)*(I*sqrt(3) + 1) - b)*b*c^5 + b^2*c^5 + b^2*sqrt(x)) - 40*sqrt(3*(4*(-1/1024*b^3 + 1/1024*(c^8 - 1)*b^3/c^8 + 1/1024*b^3/c^8)^(1/3)*(I*sqrt(3) + 1) - b)^2 + 6*(4*(-1/1024*b^3 + 1/1024*(c^8 - 1)*b^3/c^8 + 1/1024*b^3/c^8)^(1/3)*(I*sqrt(3) + 1) - b)*b + 3*b^2)*c*arctan(1/3*((4*(-1/1024*b^3 + 1/1024*(c^8 - 1)*b^3/c^8 + 1/1024*b^3/c^8)^(1/3)*(I*sqrt(3) + 1) - b)^2*c^8 + 2*(4*(-1/1024*b^3 + 1/1024*(c^8 - 1)*b^3/c^8 + 1/1024*b^3/c^8)^(1/3)*(I*sqrt(3) + 1) - b)*b*c^8 + b^2*c^8 - 2*b^2*c^3*sqrt(x) + sqrt(-4*(4*(-1/1024*b^3 + 1/1024*(c^8 - 1)*b^3/c^8 + 1/1024*b^3/c^8)^(1/3)*(I*sqrt(3) + 1) - b)^2*b^2*c^5*sqrt(x) - 4*b^4*c^5*sqrt(x) + 4*b^4*c^2 + 4*b^4*x - 4*(2*b^3*c^5*sqrt(x) - b^3*c^2)*(4*(-1/1024*b^3 + 1/1024*(c^8 - 1)*b^3/c^8 + 1/1024*b^3/c^8)^(1/3)*(I*sqrt(3) + 1) - b))*c^3)*sqrt(3*(4*(-1/1024*b^3 + 1/1024*(c^8 - 1)*b^3/c^8 + 1/1024*b^3/c^8)^(1/3)*(I*sqrt(3) + 1) - b)^2 + 6*(4*(-1/1024*b^3 + 1/1024*(c^8 - 1)*b^3/c^8 + 1/1024*b^3/c^8)^(1/3)*(I*sqrt(3) + 1) - b)*b + 3*b^2)/b^3) + 5*(((1/2)^(1/3)*(b^3 - (c^8 - 1)*b^3/c^8 + b^3/c^8)^(1/3)*(I*sqrt(3) + 1) + 2*b)*c - 6*b*c)*log(((1/2)^(1/3)*(b^3 - (c^8 - 1)*b^3/c^8 + b^3/c^8)^(1/3)*(I*sqrt(3) + 1) + 2*b)^2*b^2*c^5*sqrt(x) + 4*b^4*c^5*sqrt(x) + 4*b^4*c^2 + 4*b^4*x - 2*(2*b^3*c^5*sqrt(x) + b^3*c^2)*((1/2)^(1/3)*(b^3 - (c^8 - 1)*b^3/c^8 + b^3/c^8)^(1/3)*(I*sqrt(3) + 1) + 2*b)) + 10*((4*(-1/1024*b^3 + 1/1024*(c^8 - 1)*b^3/c^8 + 1/1024*b^3/c^8)^(1/3)*(I*sqrt(3) + 1) - b)*c + 3*b*c)*log(-4*(4*(-1/1024*b^3 + 1/1024*(c^8 - 1)*b^3/c^8 + 1/1024*b^3/c^8)^(1/3)*(I*sqrt(3) + 1) - b)^2*b^2*c^5*sqrt(x) - 4*b^4*c^5*sqrt(x) + 4*b^4*c^2 + 4*b^4*x - 4*(2*b^3*c^5*sqrt(x) - b^3*c^2)*(4*(-1/1024*b^3 + 1/1024*(c^8 - 1)*b^3/c^8 + 1/1024*b^3/c^8)^(1/3)*(I*sqrt(3) + 1) - b)) + 20*(b*c*x^4 - b*c)*log(-(c^2*x^3 + 2*c*x^(3/2) + 1)/(c^2*x^3 - 1)))/c","C",0
214,1,64,0,0.673876," ","integrate(x^2*(a+b*arctanh(c*x^(3/2))),x, algorithm=""fricas"")","\frac{2 \, a c^{2} x^{3} + 2 \, b c x^{\frac{3}{2}} + {\left(b c^{2} x^{3} - b\right)} \log\left(-\frac{c^{2} x^{3} + 2 \, c x^{\frac{3}{2}} + 1}{c^{2} x^{3} - 1}\right)}{6 \, c^{2}}"," ",0,"1/6*(2*a*c^2*x^3 + 2*b*c*x^(3/2) + (b*c^2*x^3 - b)*log(-(c^2*x^3 + 2*c*x^(3/2) + 1)/(c^2*x^3 - 1)))/c^2","A",0
215,1,1848,0,3.946778," ","integrate(x*(a+b*arctanh(c*x^(3/2))),x, algorithm=""fricas"")","\frac{8 \, a c x^{2} + 4 \, \sqrt{3} \sqrt{{\left(\left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(b^{3} - \frac{{\left(c^{4} - 1\right)} b^{3}}{c^{4}} + \frac{b^{3}}{c^{4}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} + 2 \, b\right)}^{2} - 4 \, {\left(\left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(b^{3} - \frac{{\left(c^{4} - 1\right)} b^{3}}{c^{4}} + \frac{b^{3}}{c^{4}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} + 2 \, b\right)} b + 4 \, b^{2}} c \arctan\left(-\frac{2 \, \sqrt{3} \sqrt{{\left(\left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(b^{3} - \frac{{\left(c^{4} - 1\right)} b^{3}}{c^{4}} + \frac{b^{3}}{c^{4}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} + 2 \, b\right)}^{2} c^{2} + 4 \, b^{2} c^{2} + 4 \, b^{2} c \sqrt{x} + 4 \, b^{2} x - 2 \, {\left(2 \, b c^{2} + b c \sqrt{x}\right)} {\left(\left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(b^{3} - \frac{{\left(c^{4} - 1\right)} b^{3}}{c^{4}} + \frac{b^{3}}{c^{4}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} + 2 \, b\right)}} {\left({\left(\left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(b^{3} - \frac{{\left(c^{4} - 1\right)} b^{3}}{c^{4}} + \frac{b^{3}}{c^{4}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} + 2 \, b\right)} c^{3} - 2 \, b c^{3}\right)} \sqrt{{\left(\left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(b^{3} - \frac{{\left(c^{4} - 1\right)} b^{3}}{c^{4}} + \frac{b^{3}}{c^{4}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} + 2 \, b\right)}^{2} - 4 \, {\left(\left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(b^{3} - \frac{{\left(c^{4} - 1\right)} b^{3}}{c^{4}} + \frac{b^{3}}{c^{4}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} + 2 \, b\right)} b + 4 \, b^{2}} + \sqrt{3} {\left({\left(\left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(b^{3} - \frac{{\left(c^{4} - 1\right)} b^{3}}{c^{4}} + \frac{b^{3}}{c^{4}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} + 2 \, b\right)}^{2} c^{4} + 4 \, b^{2} c^{4} + 8 \, b^{2} c^{3} \sqrt{x} - 4 \, {\left(b c^{4} + b c^{3} \sqrt{x}\right)} {\left(\left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(b^{3} - \frac{{\left(c^{4} - 1\right)} b^{3}}{c^{4}} + \frac{b^{3}}{c^{4}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} + 2 \, b\right)}\right)} \sqrt{{\left(\left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(b^{3} - \frac{{\left(c^{4} - 1\right)} b^{3}}{c^{4}} + \frac{b^{3}}{c^{4}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} + 2 \, b\right)}^{2} - 4 \, {\left(\left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(b^{3} - \frac{{\left(c^{4} - 1\right)} b^{3}}{c^{4}} + \frac{b^{3}}{c^{4}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} + 2 \, b\right)} b + 4 \, b^{2}}}{24 \, b^{3}}\right) - 2 \, {\left(\left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(b^{3} - \frac{{\left(c^{4} - 1\right)} b^{3}}{c^{4}} + \frac{b^{3}}{c^{4}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} + 2 \, b\right)} c \log\left(\frac{1}{2} \, {\left(\left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(b^{3} - \frac{{\left(c^{4} - 1\right)} b^{3}}{c^{4}} + \frac{b^{3}}{c^{4}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} + 2 \, b\right)} c - b c + b \sqrt{x}\right) - 4 \, {\left(2 \, {\left(-\frac{1}{128} \, b^{3} + \frac{{\left(c^{4} - 1\right)} b^{3}}{128 \, c^{4}} + \frac{b^{3}}{128 \, c^{4}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} - b\right)} c \log\left({\left(2 \, {\left(-\frac{1}{128} \, b^{3} + \frac{{\left(c^{4} - 1\right)} b^{3}}{128 \, c^{4}} + \frac{b^{3}}{128 \, c^{4}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} - b\right)} c + b c + b \sqrt{x}\right) - 8 \, \sqrt{3 \, {\left(2 \, {\left(-\frac{1}{128} \, b^{3} + \frac{{\left(c^{4} - 1\right)} b^{3}}{128 \, c^{4}} + \frac{b^{3}}{128 \, c^{4}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} - b\right)}^{2} + 6 \, {\left(2 \, {\left(-\frac{1}{128} \, b^{3} + \frac{{\left(c^{4} - 1\right)} b^{3}}{128 \, c^{4}} + \frac{b^{3}}{128 \, c^{4}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} - b\right)} b + 3 \, b^{2}} c \arctan\left(-\frac{2 \, \sqrt{{\left(2 \, {\left(-\frac{1}{128} \, b^{3} + \frac{{\left(c^{4} - 1\right)} b^{3}}{128 \, c^{4}} + \frac{b^{3}}{128 \, c^{4}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} - b\right)}^{2} c^{2} + b^{2} c^{2} - b^{2} c \sqrt{x} + b^{2} x + {\left(2 \, b c^{2} - b c \sqrt{x}\right)} {\left(2 \, {\left(-\frac{1}{128} \, b^{3} + \frac{{\left(c^{4} - 1\right)} b^{3}}{128 \, c^{4}} + \frac{b^{3}}{128 \, c^{4}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} - b\right)}} {\left({\left(2 \, {\left(-\frac{1}{128} \, b^{3} + \frac{{\left(c^{4} - 1\right)} b^{3}}{128 \, c^{4}} + \frac{b^{3}}{128 \, c^{4}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} - b\right)} c^{3} + b c^{3}\right)} \sqrt{3 \, {\left(2 \, {\left(-\frac{1}{128} \, b^{3} + \frac{{\left(c^{4} - 1\right)} b^{3}}{128 \, c^{4}} + \frac{b^{3}}{128 \, c^{4}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} - b\right)}^{2} + 6 \, {\left(2 \, {\left(-\frac{1}{128} \, b^{3} + \frac{{\left(c^{4} - 1\right)} b^{3}}{128 \, c^{4}} + \frac{b^{3}}{128 \, c^{4}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} - b\right)} b + 3 \, b^{2}} + {\left({\left(2 \, {\left(-\frac{1}{128} \, b^{3} + \frac{{\left(c^{4} - 1\right)} b^{3}}{128 \, c^{4}} + \frac{b^{3}}{128 \, c^{4}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} - b\right)}^{2} c^{4} + b^{2} c^{4} - 2 \, b^{2} c^{3} \sqrt{x} + 2 \, {\left(b c^{4} - b c^{3} \sqrt{x}\right)} {\left(2 \, {\left(-\frac{1}{128} \, b^{3} + \frac{{\left(c^{4} - 1\right)} b^{3}}{128 \, c^{4}} + \frac{b^{3}}{128 \, c^{4}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} - b\right)}\right)} \sqrt{3 \, {\left(2 \, {\left(-\frac{1}{128} \, b^{3} + \frac{{\left(c^{4} - 1\right)} b^{3}}{128 \, c^{4}} + \frac{b^{3}}{128 \, c^{4}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} - b\right)}^{2} + 6 \, {\left(2 \, {\left(-\frac{1}{128} \, b^{3} + \frac{{\left(c^{4} - 1\right)} b^{3}}{128 \, c^{4}} + \frac{b^{3}}{128 \, c^{4}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} - b\right)} b + 3 \, b^{2}}}{3 \, b^{3}}\right) + {\left({\left(\left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(b^{3} - \frac{{\left(c^{4} - 1\right)} b^{3}}{c^{4}} + \frac{b^{3}}{c^{4}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} + 2 \, b\right)} c - 6 \, b c\right)} \log\left({\left(\left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(b^{3} - \frac{{\left(c^{4} - 1\right)} b^{3}}{c^{4}} + \frac{b^{3}}{c^{4}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} + 2 \, b\right)}^{2} c^{2} + 4 \, b^{2} c^{2} + 4 \, b^{2} c \sqrt{x} + 4 \, b^{2} x - 2 \, {\left(2 \, b c^{2} + b c \sqrt{x}\right)} {\left(\left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(b^{3} - \frac{{\left(c^{4} - 1\right)} b^{3}}{c^{4}} + \frac{b^{3}}{c^{4}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} + 2 \, b\right)}\right) + 2 \, {\left({\left(2 \, {\left(-\frac{1}{128} \, b^{3} + \frac{{\left(c^{4} - 1\right)} b^{3}}{128 \, c^{4}} + \frac{b^{3}}{128 \, c^{4}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} - b\right)} c + 3 \, b c\right)} \log\left(4 \, {\left(2 \, {\left(-\frac{1}{128} \, b^{3} + \frac{{\left(c^{4} - 1\right)} b^{3}}{128 \, c^{4}} + \frac{b^{3}}{128 \, c^{4}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} - b\right)}^{2} c^{2} + 4 \, b^{2} c^{2} - 4 \, b^{2} c \sqrt{x} + 4 \, b^{2} x + 4 \, {\left(2 \, b c^{2} - b c \sqrt{x}\right)} {\left(2 \, {\left(-\frac{1}{128} \, b^{3} + \frac{{\left(c^{4} - 1\right)} b^{3}}{128 \, c^{4}} + \frac{b^{3}}{128 \, c^{4}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} - b\right)}\right) + 4 \, {\left(b c x^{2} - b c\right)} \log\left(-\frac{c^{2} x^{3} + 2 \, c x^{\frac{3}{2}} + 1}{c^{2} x^{3} - 1}\right) + 24 \, b \sqrt{x}}{16 \, c}"," ",0,"1/16*(8*a*c*x^2 + 4*sqrt(3)*sqrt(((1/2)^(1/3)*(b^3 - (c^4 - 1)*b^3/c^4 + b^3/c^4)^(1/3)*(I*sqrt(3) + 1) + 2*b)^2 - 4*((1/2)^(1/3)*(b^3 - (c^4 - 1)*b^3/c^4 + b^3/c^4)^(1/3)*(I*sqrt(3) + 1) + 2*b)*b + 4*b^2)*c*arctan(-1/24*(2*sqrt(3)*sqrt(((1/2)^(1/3)*(b^3 - (c^4 - 1)*b^3/c^4 + b^3/c^4)^(1/3)*(I*sqrt(3) + 1) + 2*b)^2*c^2 + 4*b^2*c^2 + 4*b^2*c*sqrt(x) + 4*b^2*x - 2*(2*b*c^2 + b*c*sqrt(x))*((1/2)^(1/3)*(b^3 - (c^4 - 1)*b^3/c^4 + b^3/c^4)^(1/3)*(I*sqrt(3) + 1) + 2*b))*(((1/2)^(1/3)*(b^3 - (c^4 - 1)*b^3/c^4 + b^3/c^4)^(1/3)*(I*sqrt(3) + 1) + 2*b)*c^3 - 2*b*c^3)*sqrt(((1/2)^(1/3)*(b^3 - (c^4 - 1)*b^3/c^4 + b^3/c^4)^(1/3)*(I*sqrt(3) + 1) + 2*b)^2 - 4*((1/2)^(1/3)*(b^3 - (c^4 - 1)*b^3/c^4 + b^3/c^4)^(1/3)*(I*sqrt(3) + 1) + 2*b)*b + 4*b^2) + sqrt(3)*(((1/2)^(1/3)*(b^3 - (c^4 - 1)*b^3/c^4 + b^3/c^4)^(1/3)*(I*sqrt(3) + 1) + 2*b)^2*c^4 + 4*b^2*c^4 + 8*b^2*c^3*sqrt(x) - 4*(b*c^4 + b*c^3*sqrt(x))*((1/2)^(1/3)*(b^3 - (c^4 - 1)*b^3/c^4 + b^3/c^4)^(1/3)*(I*sqrt(3) + 1) + 2*b))*sqrt(((1/2)^(1/3)*(b^3 - (c^4 - 1)*b^3/c^4 + b^3/c^4)^(1/3)*(I*sqrt(3) + 1) + 2*b)^2 - 4*((1/2)^(1/3)*(b^3 - (c^4 - 1)*b^3/c^4 + b^3/c^4)^(1/3)*(I*sqrt(3) + 1) + 2*b)*b + 4*b^2))/b^3) - 2*((1/2)^(1/3)*(b^3 - (c^4 - 1)*b^3/c^4 + b^3/c^4)^(1/3)*(I*sqrt(3) + 1) + 2*b)*c*log(1/2*((1/2)^(1/3)*(b^3 - (c^4 - 1)*b^3/c^4 + b^3/c^4)^(1/3)*(I*sqrt(3) + 1) + 2*b)*c - b*c + b*sqrt(x)) - 4*(2*(-1/128*b^3 + 1/128*(c^4 - 1)*b^3/c^4 + 1/128*b^3/c^4)^(1/3)*(I*sqrt(3) + 1) - b)*c*log((2*(-1/128*b^3 + 1/128*(c^4 - 1)*b^3/c^4 + 1/128*b^3/c^4)^(1/3)*(I*sqrt(3) + 1) - b)*c + b*c + b*sqrt(x)) - 8*sqrt(3*(2*(-1/128*b^3 + 1/128*(c^4 - 1)*b^3/c^4 + 1/128*b^3/c^4)^(1/3)*(I*sqrt(3) + 1) - b)^2 + 6*(2*(-1/128*b^3 + 1/128*(c^4 - 1)*b^3/c^4 + 1/128*b^3/c^4)^(1/3)*(I*sqrt(3) + 1) - b)*b + 3*b^2)*c*arctan(-1/3*(2*sqrt((2*(-1/128*b^3 + 1/128*(c^4 - 1)*b^3/c^4 + 1/128*b^3/c^4)^(1/3)*(I*sqrt(3) + 1) - b)^2*c^2 + b^2*c^2 - b^2*c*sqrt(x) + b^2*x + (2*b*c^2 - b*c*sqrt(x))*(2*(-1/128*b^3 + 1/128*(c^4 - 1)*b^3/c^4 + 1/128*b^3/c^4)^(1/3)*(I*sqrt(3) + 1) - b))*((2*(-1/128*b^3 + 1/128*(c^4 - 1)*b^3/c^4 + 1/128*b^3/c^4)^(1/3)*(I*sqrt(3) + 1) - b)*c^3 + b*c^3)*sqrt(3*(2*(-1/128*b^3 + 1/128*(c^4 - 1)*b^3/c^4 + 1/128*b^3/c^4)^(1/3)*(I*sqrt(3) + 1) - b)^2 + 6*(2*(-1/128*b^3 + 1/128*(c^4 - 1)*b^3/c^4 + 1/128*b^3/c^4)^(1/3)*(I*sqrt(3) + 1) - b)*b + 3*b^2) + ((2*(-1/128*b^3 + 1/128*(c^4 - 1)*b^3/c^4 + 1/128*b^3/c^4)^(1/3)*(I*sqrt(3) + 1) - b)^2*c^4 + b^2*c^4 - 2*b^2*c^3*sqrt(x) + 2*(b*c^4 - b*c^3*sqrt(x))*(2*(-1/128*b^3 + 1/128*(c^4 - 1)*b^3/c^4 + 1/128*b^3/c^4)^(1/3)*(I*sqrt(3) + 1) - b))*sqrt(3*(2*(-1/128*b^3 + 1/128*(c^4 - 1)*b^3/c^4 + 1/128*b^3/c^4)^(1/3)*(I*sqrt(3) + 1) - b)^2 + 6*(2*(-1/128*b^3 + 1/128*(c^4 - 1)*b^3/c^4 + 1/128*b^3/c^4)^(1/3)*(I*sqrt(3) + 1) - b)*b + 3*b^2))/b^3) + (((1/2)^(1/3)*(b^3 - (c^4 - 1)*b^3/c^4 + b^3/c^4)^(1/3)*(I*sqrt(3) + 1) + 2*b)*c - 6*b*c)*log(((1/2)^(1/3)*(b^3 - (c^4 - 1)*b^3/c^4 + b^3/c^4)^(1/3)*(I*sqrt(3) + 1) + 2*b)^2*c^2 + 4*b^2*c^2 + 4*b^2*c*sqrt(x) + 4*b^2*x - 2*(2*b*c^2 + b*c*sqrt(x))*((1/2)^(1/3)*(b^3 - (c^4 - 1)*b^3/c^4 + b^3/c^4)^(1/3)*(I*sqrt(3) + 1) + 2*b)) + 2*((2*(-1/128*b^3 + 1/128*(c^4 - 1)*b^3/c^4 + 1/128*b^3/c^4)^(1/3)*(I*sqrt(3) + 1) - b)*c + 3*b*c)*log(4*(2*(-1/128*b^3 + 1/128*(c^4 - 1)*b^3/c^4 + 1/128*b^3/c^4)^(1/3)*(I*sqrt(3) + 1) - b)^2*c^2 + 4*b^2*c^2 - 4*b^2*c*sqrt(x) + 4*b^2*x + 4*(2*b*c^2 - b*c*sqrt(x))*(2*(-1/128*b^3 + 1/128*(c^4 - 1)*b^3/c^4 + 1/128*b^3/c^4)^(1/3)*(I*sqrt(3) + 1) - b)) + 4*(b*c*x^2 - b*c)*log(-(c^2*x^3 + 2*c*x^(3/2) + 1)/(c^2*x^3 - 1)) + 24*b*sqrt(x))/c","C",0
216,1,1682,0,3.595533," ","integrate(a+b*arctanh(c*x^(3/2)),x, algorithm=""fricas"")","a x - \frac{1}{2} \, \sqrt{3} \sqrt{{\left(\left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(b^{3} - \frac{{\left(c^{2} - 1\right)} b^{3}}{c^{2}} + \frac{b^{3}}{c^{2}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} + 2 \, b\right)}^{2} - 4 \, {\left(\left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(b^{3} - \frac{{\left(c^{2} - 1\right)} b^{3}}{c^{2}} + \frac{b^{3}}{c^{2}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} + 2 \, b\right)} b + 4 \, b^{2}} \arctan\left(\frac{4 \, \sqrt{3} \sqrt{{\left(\left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(b^{3} - \frac{{\left(c^{2} - 1\right)} b^{3}}{c^{2}} + \frac{b^{3}}{c^{2}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} + 2 \, b\right)}^{2} b^{2} c \sqrt{x} + 4 \, b^{4} c \sqrt{x} + 4 \, b^{4} x + 4 \, b^{4} - 2 \, {\left(2 \, b^{3} c \sqrt{x} + b^{3}\right)} {\left(\left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(b^{3} - \frac{{\left(c^{2} - 1\right)} b^{3}}{c^{2}} + \frac{b^{3}}{c^{2}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} + 2 \, b\right)}} \sqrt{{\left(\left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(b^{3} - \frac{{\left(c^{2} - 1\right)} b^{3}}{c^{2}} + \frac{b^{3}}{c^{2}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} + 2 \, b\right)}^{2} - 4 \, {\left(\left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(b^{3} - \frac{{\left(c^{2} - 1\right)} b^{3}}{c^{2}} + \frac{b^{3}}{c^{2}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} + 2 \, b\right)} b + 4 \, b^{2}} c - \sqrt{3} {\left({\left(\left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(b^{3} - \frac{{\left(c^{2} - 1\right)} b^{3}}{c^{2}} + \frac{b^{3}}{c^{2}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} + 2 \, b\right)}^{2} c^{2} - 4 \, {\left(\left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(b^{3} - \frac{{\left(c^{2} - 1\right)} b^{3}}{c^{2}} + \frac{b^{3}}{c^{2}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} + 2 \, b\right)} b c^{2} + 4 \, b^{2} c^{2} + 8 \, b^{2} c \sqrt{x}\right)} \sqrt{{\left(\left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(b^{3} - \frac{{\left(c^{2} - 1\right)} b^{3}}{c^{2}} + \frac{b^{3}}{c^{2}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} + 2 \, b\right)}^{2} - 4 \, {\left(\left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(b^{3} - \frac{{\left(c^{2} - 1\right)} b^{3}}{c^{2}} + \frac{b^{3}}{c^{2}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} + 2 \, b\right)} b + 4 \, b^{2}}}{24 \, b^{3}}\right) + \frac{1}{8} \, {\left(\left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(b^{3} - \frac{{\left(c^{2} - 1\right)} b^{3}}{c^{2}} + \frac{b^{3}}{c^{2}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} - 4 \, b\right)} \log\left({\left(\left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(b^{3} - \frac{{\left(c^{2} - 1\right)} b^{3}}{c^{2}} + \frac{b^{3}}{c^{2}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} + 2 \, b\right)}^{2} b^{2} c \sqrt{x} + 4 \, b^{4} c \sqrt{x} + 4 \, b^{4} x + 4 \, b^{4} - 2 \, {\left(2 \, b^{3} c \sqrt{x} + b^{3}\right)} {\left(\left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(b^{3} - \frac{{\left(c^{2} - 1\right)} b^{3}}{c^{2}} + \frac{b^{3}}{c^{2}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} + 2 \, b\right)}\right) + \frac{1}{4} \, {\left({\left(-\frac{1}{16} \, b^{3} + \frac{{\left(c^{2} - 1\right)} b^{3}}{16 \, c^{2}} + \frac{b^{3}}{16 \, c^{2}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} + 2 \, b\right)} \log\left(-4 \, {\left({\left(-\frac{1}{16} \, b^{3} + \frac{{\left(c^{2} - 1\right)} b^{3}}{16 \, c^{2}} + \frac{b^{3}}{16 \, c^{2}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} - b\right)}^{2} b^{2} c \sqrt{x} - 4 \, b^{4} c \sqrt{x} + 4 \, b^{4} x + 4 \, b^{4} - 4 \, {\left(2 \, b^{3} c \sqrt{x} - b^{3}\right)} {\left({\left(-\frac{1}{16} \, b^{3} + \frac{{\left(c^{2} - 1\right)} b^{3}}{16 \, c^{2}} + \frac{b^{3}}{16 \, c^{2}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} - b\right)}\right) - \frac{1}{4} \, {\left(\left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(b^{3} - \frac{{\left(c^{2} - 1\right)} b^{3}}{c^{2}} + \frac{b^{3}}{c^{2}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} + 2 \, b\right)} \log\left(-\frac{1}{4} \, {\left(\left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(b^{3} - \frac{{\left(c^{2} - 1\right)} b^{3}}{c^{2}} + \frac{b^{3}}{c^{2}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} + 2 \, b\right)}^{2} c + {\left(\left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(b^{3} - \frac{{\left(c^{2} - 1\right)} b^{3}}{c^{2}} + \frac{b^{3}}{c^{2}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} + 2 \, b\right)} b c - b^{2} c + b^{2} \sqrt{x}\right) - \frac{1}{2} \, {\left({\left(-\frac{1}{16} \, b^{3} + \frac{{\left(c^{2} - 1\right)} b^{3}}{16 \, c^{2}} + \frac{b^{3}}{16 \, c^{2}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} - b\right)} \log\left({\left({\left(-\frac{1}{16} \, b^{3} + \frac{{\left(c^{2} - 1\right)} b^{3}}{16 \, c^{2}} + \frac{b^{3}}{16 \, c^{2}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} - b\right)}^{2} c + 2 \, {\left({\left(-\frac{1}{16} \, b^{3} + \frac{{\left(c^{2} - 1\right)} b^{3}}{16 \, c^{2}} + \frac{b^{3}}{16 \, c^{2}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} - b\right)} b c + b^{2} c + b^{2} \sqrt{x}\right) + \frac{1}{2} \, {\left(b x - b\right)} \log\left(-\frac{c^{2} x^{3} + 2 \, c x^{\frac{3}{2}} + 1}{c^{2} x^{3} - 1}\right) - \sqrt{3 \, {\left({\left(-\frac{1}{16} \, b^{3} + \frac{{\left(c^{2} - 1\right)} b^{3}}{16 \, c^{2}} + \frac{b^{3}}{16 \, c^{2}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} - b\right)}^{2} + 6 \, {\left({\left(-\frac{1}{16} \, b^{3} + \frac{{\left(c^{2} - 1\right)} b^{3}}{16 \, c^{2}} + \frac{b^{3}}{16 \, c^{2}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} - b\right)} b + 3 \, b^{2}} \arctan\left(\frac{{\left({\left({\left(-\frac{1}{16} \, b^{3} + \frac{{\left(c^{2} - 1\right)} b^{3}}{16 \, c^{2}} + \frac{b^{3}}{16 \, c^{2}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} - b\right)}^{2} c^{2} + 2 \, {\left({\left(-\frac{1}{16} \, b^{3} + \frac{{\left(c^{2} - 1\right)} b^{3}}{16 \, c^{2}} + \frac{b^{3}}{16 \, c^{2}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} - b\right)} b c^{2} + b^{2} c^{2} - 2 \, b^{2} c \sqrt{x} + \sqrt{-4 \, {\left({\left(-\frac{1}{16} \, b^{3} + \frac{{\left(c^{2} - 1\right)} b^{3}}{16 \, c^{2}} + \frac{b^{3}}{16 \, c^{2}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} - b\right)}^{2} b^{2} c \sqrt{x} - 4 \, b^{4} c \sqrt{x} + 4 \, b^{4} x + 4 \, b^{4} - 4 \, {\left(2 \, b^{3} c \sqrt{x} - b^{3}\right)} {\left({\left(-\frac{1}{16} \, b^{3} + \frac{{\left(c^{2} - 1\right)} b^{3}}{16 \, c^{2}} + \frac{b^{3}}{16 \, c^{2}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} - b\right)}} c\right)} \sqrt{3 \, {\left({\left(-\frac{1}{16} \, b^{3} + \frac{{\left(c^{2} - 1\right)} b^{3}}{16 \, c^{2}} + \frac{b^{3}}{16 \, c^{2}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} - b\right)}^{2} + 6 \, {\left({\left(-\frac{1}{16} \, b^{3} + \frac{{\left(c^{2} - 1\right)} b^{3}}{16 \, c^{2}} + \frac{b^{3}}{16 \, c^{2}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} - b\right)} b + 3 \, b^{2}}}{3 \, b^{3}}\right)"," ",0,"a*x - 1/2*sqrt(3)*sqrt(((1/2)^(1/3)*(b^3 - (c^2 - 1)*b^3/c^2 + b^3/c^2)^(1/3)*(I*sqrt(3) + 1) + 2*b)^2 - 4*((1/2)^(1/3)*(b^3 - (c^2 - 1)*b^3/c^2 + b^3/c^2)^(1/3)*(I*sqrt(3) + 1) + 2*b)*b + 4*b^2)*arctan(1/24*(4*sqrt(3)*sqrt(((1/2)^(1/3)*(b^3 - (c^2 - 1)*b^3/c^2 + b^3/c^2)^(1/3)*(I*sqrt(3) + 1) + 2*b)^2*b^2*c*sqrt(x) + 4*b^4*c*sqrt(x) + 4*b^4*x + 4*b^4 - 2*(2*b^3*c*sqrt(x) + b^3)*((1/2)^(1/3)*(b^3 - (c^2 - 1)*b^3/c^2 + b^3/c^2)^(1/3)*(I*sqrt(3) + 1) + 2*b))*sqrt(((1/2)^(1/3)*(b^3 - (c^2 - 1)*b^3/c^2 + b^3/c^2)^(1/3)*(I*sqrt(3) + 1) + 2*b)^2 - 4*((1/2)^(1/3)*(b^3 - (c^2 - 1)*b^3/c^2 + b^3/c^2)^(1/3)*(I*sqrt(3) + 1) + 2*b)*b + 4*b^2)*c - sqrt(3)*(((1/2)^(1/3)*(b^3 - (c^2 - 1)*b^3/c^2 + b^3/c^2)^(1/3)*(I*sqrt(3) + 1) + 2*b)^2*c^2 - 4*((1/2)^(1/3)*(b^3 - (c^2 - 1)*b^3/c^2 + b^3/c^2)^(1/3)*(I*sqrt(3) + 1) + 2*b)*b*c^2 + 4*b^2*c^2 + 8*b^2*c*sqrt(x))*sqrt(((1/2)^(1/3)*(b^3 - (c^2 - 1)*b^3/c^2 + b^3/c^2)^(1/3)*(I*sqrt(3) + 1) + 2*b)^2 - 4*((1/2)^(1/3)*(b^3 - (c^2 - 1)*b^3/c^2 + b^3/c^2)^(1/3)*(I*sqrt(3) + 1) + 2*b)*b + 4*b^2))/b^3) + 1/8*((1/2)^(1/3)*(b^3 - (c^2 - 1)*b^3/c^2 + b^3/c^2)^(1/3)*(I*sqrt(3) + 1) - 4*b)*log(((1/2)^(1/3)*(b^3 - (c^2 - 1)*b^3/c^2 + b^3/c^2)^(1/3)*(I*sqrt(3) + 1) + 2*b)^2*b^2*c*sqrt(x) + 4*b^4*c*sqrt(x) + 4*b^4*x + 4*b^4 - 2*(2*b^3*c*sqrt(x) + b^3)*((1/2)^(1/3)*(b^3 - (c^2 - 1)*b^3/c^2 + b^3/c^2)^(1/3)*(I*sqrt(3) + 1) + 2*b)) + 1/4*((-1/16*b^3 + 1/16*(c^2 - 1)*b^3/c^2 + 1/16*b^3/c^2)^(1/3)*(I*sqrt(3) + 1) + 2*b)*log(-4*((-1/16*b^3 + 1/16*(c^2 - 1)*b^3/c^2 + 1/16*b^3/c^2)^(1/3)*(I*sqrt(3) + 1) - b)^2*b^2*c*sqrt(x) - 4*b^4*c*sqrt(x) + 4*b^4*x + 4*b^4 - 4*(2*b^3*c*sqrt(x) - b^3)*((-1/16*b^3 + 1/16*(c^2 - 1)*b^3/c^2 + 1/16*b^3/c^2)^(1/3)*(I*sqrt(3) + 1) - b)) - 1/4*((1/2)^(1/3)*(b^3 - (c^2 - 1)*b^3/c^2 + b^3/c^2)^(1/3)*(I*sqrt(3) + 1) + 2*b)*log(-1/4*((1/2)^(1/3)*(b^3 - (c^2 - 1)*b^3/c^2 + b^3/c^2)^(1/3)*(I*sqrt(3) + 1) + 2*b)^2*c + ((1/2)^(1/3)*(b^3 - (c^2 - 1)*b^3/c^2 + b^3/c^2)^(1/3)*(I*sqrt(3) + 1) + 2*b)*b*c - b^2*c + b^2*sqrt(x)) - 1/2*((-1/16*b^3 + 1/16*(c^2 - 1)*b^3/c^2 + 1/16*b^3/c^2)^(1/3)*(I*sqrt(3) + 1) - b)*log(((-1/16*b^3 + 1/16*(c^2 - 1)*b^3/c^2 + 1/16*b^3/c^2)^(1/3)*(I*sqrt(3) + 1) - b)^2*c + 2*((-1/16*b^3 + 1/16*(c^2 - 1)*b^3/c^2 + 1/16*b^3/c^2)^(1/3)*(I*sqrt(3) + 1) - b)*b*c + b^2*c + b^2*sqrt(x)) + 1/2*(b*x - b)*log(-(c^2*x^3 + 2*c*x^(3/2) + 1)/(c^2*x^3 - 1)) - sqrt(3*((-1/16*b^3 + 1/16*(c^2 - 1)*b^3/c^2 + 1/16*b^3/c^2)^(1/3)*(I*sqrt(3) + 1) - b)^2 + 6*((-1/16*b^3 + 1/16*(c^2 - 1)*b^3/c^2 + 1/16*b^3/c^2)^(1/3)*(I*sqrt(3) + 1) - b)*b + 3*b^2)*arctan(1/3*(((-1/16*b^3 + 1/16*(c^2 - 1)*b^3/c^2 + 1/16*b^3/c^2)^(1/3)*(I*sqrt(3) + 1) - b)^2*c^2 + 2*((-1/16*b^3 + 1/16*(c^2 - 1)*b^3/c^2 + 1/16*b^3/c^2)^(1/3)*(I*sqrt(3) + 1) - b)*b*c^2 + b^2*c^2 - 2*b^2*c*sqrt(x) + sqrt(-4*((-1/16*b^3 + 1/16*(c^2 - 1)*b^3/c^2 + 1/16*b^3/c^2)^(1/3)*(I*sqrt(3) + 1) - b)^2*b^2*c*sqrt(x) - 4*b^4*c*sqrt(x) + 4*b^4*x + 4*b^4 - 4*(2*b^3*c*sqrt(x) - b^3)*((-1/16*b^3 + 1/16*(c^2 - 1)*b^3/c^2 + 1/16*b^3/c^2)^(1/3)*(I*sqrt(3) + 1) - b))*c)*sqrt(3*((-1/16*b^3 + 1/16*(c^2 - 1)*b^3/c^2 + 1/16*b^3/c^2)^(1/3)*(I*sqrt(3) + 1) - b)^2 + 6*((-1/16*b^3 + 1/16*(c^2 - 1)*b^3/c^2 + 1/16*b^3/c^2)^(1/3)*(I*sqrt(3) + 1) - b)*b + 3*b^2)/b^3)","C",0
217,0,0,0,0.930428," ","integrate((a+b*arctanh(c*x^(3/2)))/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \operatorname{artanh}\left(c x^{\frac{3}{2}}\right) + a}{x}, x\right)"," ",0,"integral((b*arctanh(c*x^(3/2)) + a)/x, x)","F",0
218,1,234,0,0.744613," ","integrate((a+b*arctanh(c*x^(3/2)))/x^2,x, algorithm=""fricas"")","-\frac{2 \, \sqrt{3} \left(-c^{2}\right)^{\frac{1}{3}} b x \arctan\left(\frac{2 \, \sqrt{3} \left(-c^{2}\right)^{\frac{2}{3}} \sqrt{x} + \sqrt{3} c}{3 \, c}\right) - 2 \, \sqrt{3} b {\left(c^{2}\right)}^{\frac{1}{3}} x \arctan\left(\frac{2 \, \sqrt{3} {\left(c^{2}\right)}^{\frac{2}{3}} \sqrt{x} - \sqrt{3} c}{3 \, c}\right) + \left(-c^{2}\right)^{\frac{1}{3}} b x \log\left(c^{2} x - \left(-c^{2}\right)^{\frac{1}{3}} c \sqrt{x} + \left(-c^{2}\right)^{\frac{2}{3}}\right) + b {\left(c^{2}\right)}^{\frac{1}{3}} x \log\left(c^{2} x - {\left(c^{2}\right)}^{\frac{1}{3}} c \sqrt{x} + {\left(c^{2}\right)}^{\frac{2}{3}}\right) - 2 \, \left(-c^{2}\right)^{\frac{1}{3}} b x \log\left(c \sqrt{x} + \left(-c^{2}\right)^{\frac{1}{3}}\right) - 2 \, b {\left(c^{2}\right)}^{\frac{1}{3}} x \log\left(c \sqrt{x} + {\left(c^{2}\right)}^{\frac{1}{3}}\right) + 2 \, b \log\left(-\frac{c^{2} x^{3} + 2 \, c x^{\frac{3}{2}} + 1}{c^{2} x^{3} - 1}\right) + 4 \, a}{4 \, x}"," ",0,"-1/4*(2*sqrt(3)*(-c^2)^(1/3)*b*x*arctan(1/3*(2*sqrt(3)*(-c^2)^(2/3)*sqrt(x) + sqrt(3)*c)/c) - 2*sqrt(3)*b*(c^2)^(1/3)*x*arctan(1/3*(2*sqrt(3)*(c^2)^(2/3)*sqrt(x) - sqrt(3)*c)/c) + (-c^2)^(1/3)*b*x*log(c^2*x - (-c^2)^(1/3)*c*sqrt(x) + (-c^2)^(2/3)) + b*(c^2)^(1/3)*x*log(c^2*x - (c^2)^(1/3)*c*sqrt(x) + (c^2)^(2/3)) - 2*(-c^2)^(1/3)*b*x*log(c*sqrt(x) + (-c^2)^(1/3)) - 2*b*(c^2)^(1/3)*x*log(c*sqrt(x) + (c^2)^(1/3)) + 2*b*log(-(c^2*x^3 + 2*c*x^(3/2) + 1)/(c^2*x^3 - 1)) + 4*a)/x","A",0
219,1,214,0,0.633586," ","integrate((a+b*arctanh(c*x^(3/2)))/x^3,x, algorithm=""fricas"")","-\frac{2 \, \sqrt{3} b \left(-c\right)^{\frac{1}{3}} c x^{2} \arctan\left(\frac{2}{3} \, \sqrt{3} \left(-c\right)^{\frac{1}{3}} \sqrt{x} - \frac{1}{3} \, \sqrt{3}\right) + 2 \, \sqrt{3} b c^{\frac{4}{3}} x^{2} \arctan\left(\frac{2}{3} \, \sqrt{3} c^{\frac{1}{3}} \sqrt{x} - \frac{1}{3} \, \sqrt{3}\right) + b \left(-c\right)^{\frac{1}{3}} c x^{2} \log\left(c x + \left(-c\right)^{\frac{2}{3}} \sqrt{x} - \left(-c\right)^{\frac{1}{3}}\right) + b c^{\frac{4}{3}} x^{2} \log\left(c x - c^{\frac{2}{3}} \sqrt{x} + c^{\frac{1}{3}}\right) - 2 \, b \left(-c\right)^{\frac{1}{3}} c x^{2} \log\left(c \sqrt{x} - \left(-c\right)^{\frac{2}{3}}\right) - 2 \, b c^{\frac{4}{3}} x^{2} \log\left(c \sqrt{x} + c^{\frac{2}{3}}\right) + 12 \, b c x^{\frac{3}{2}} + 2 \, b \log\left(-\frac{c^{2} x^{3} + 2 \, c x^{\frac{3}{2}} + 1}{c^{2} x^{3} - 1}\right) + 4 \, a}{8 \, x^{2}}"," ",0,"-1/8*(2*sqrt(3)*b*(-c)^(1/3)*c*x^2*arctan(2/3*sqrt(3)*(-c)^(1/3)*sqrt(x) - 1/3*sqrt(3)) + 2*sqrt(3)*b*c^(4/3)*x^2*arctan(2/3*sqrt(3)*c^(1/3)*sqrt(x) - 1/3*sqrt(3)) + b*(-c)^(1/3)*c*x^2*log(c*x + (-c)^(2/3)*sqrt(x) - (-c)^(1/3)) + b*c^(4/3)*x^2*log(c*x - c^(2/3)*sqrt(x) + c^(1/3)) - 2*b*(-c)^(1/3)*c*x^2*log(c*sqrt(x) - (-c)^(2/3)) - 2*b*c^(4/3)*x^2*log(c*sqrt(x) + c^(2/3)) + 12*b*c*x^(3/2) + 2*b*log(-(c^2*x^3 + 2*c*x^(3/2) + 1)/(c^2*x^3 - 1)) + 4*a)/x^2","A",0
220,1,59,0,0.705312," ","integrate((a+b*arctanh(c*x^(3/2)))/x^4,x, algorithm=""fricas"")","-\frac{2 \, b c x^{\frac{3}{2}} - {\left(b c^{2} x^{3} - b\right)} \log\left(-\frac{c^{2} x^{3} + 2 \, c x^{\frac{3}{2}} + 1}{c^{2} x^{3} - 1}\right) + 2 \, a}{6 \, x^{3}}"," ",0,"-1/6*(2*b*c*x^(3/2) - (b*c^2*x^3 - b)*log(-(c^2*x^3 + 2*c*x^(3/2) + 1)/(c^2*x^3 - 1)) + 2*a)/x^3","A",0
221,1,179,0,0.836541," ","integrate(x^2*(a+b*arctanh(c*x^(3/2)))^2,x, algorithm=""fricas"")","\frac{4 \, a^{2} c^{2} x^{3} + 8 \, a b c x^{\frac{3}{2}} + {\left(b^{2} c^{2} x^{3} - b^{2}\right)} \log\left(-\frac{c^{2} x^{3} + 2 \, c x^{\frac{3}{2}} + 1}{c^{2} x^{3} - 1}\right)^{2} + 4 \, {\left(a b c^{2} - a b + b^{2}\right)} \log\left(c x^{\frac{3}{2}} + 1\right) - 4 \, {\left(a b c^{2} - a b - b^{2}\right)} \log\left(c x^{\frac{3}{2}} - 1\right) + 4 \, {\left(a b c^{2} x^{3} + b^{2} c x^{\frac{3}{2}} - a b c^{2}\right)} \log\left(-\frac{c^{2} x^{3} + 2 \, c x^{\frac{3}{2}} + 1}{c^{2} x^{3} - 1}\right)}{12 \, c^{2}}"," ",0,"1/12*(4*a^2*c^2*x^3 + 8*a*b*c*x^(3/2) + (b^2*c^2*x^3 - b^2)*log(-(c^2*x^3 + 2*c*x^(3/2) + 1)/(c^2*x^3 - 1))^2 + 4*(a*b*c^2 - a*b + b^2)*log(c*x^(3/2) + 1) - 4*(a*b*c^2 - a*b - b^2)*log(c*x^(3/2) - 1) + 4*(a*b*c^2*x^3 + b^2*c*x^(3/2) - a*b*c^2)*log(-(c^2*x^3 + 2*c*x^(3/2) + 1)/(c^2*x^3 - 1)))/c^2","B",0
222,0,0,0,0.697809," ","integrate((a+b*arctanh(c*x^(3/2)))^2/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} \operatorname{artanh}\left(c x^{\frac{3}{2}}\right)^{2} + 2 \, a b \operatorname{artanh}\left(c x^{\frac{3}{2}}\right) + a^{2}}{x}, x\right)"," ",0,"integral((b^2*arctanh(c*x^(3/2))^2 + 2*a*b*arctanh(c*x^(3/2)) + a^2)/x, x)","F",0
223,1,173,0,1.458656," ","integrate((a+b*arctanh(c*x^(3/2)))^2/x^4,x, algorithm=""fricas"")","\frac{24 \, b^{2} c^{2} x^{3} \log\left(\sqrt{x}\right) + 4 \, {\left(a b - b^{2}\right)} c^{2} x^{3} \log\left(c x^{\frac{3}{2}} + 1\right) - 4 \, {\left(a b + b^{2}\right)} c^{2} x^{3} \log\left(c x^{\frac{3}{2}} - 1\right) - 8 \, a b c x^{\frac{3}{2}} + {\left(b^{2} c^{2} x^{3} - b^{2}\right)} \log\left(-\frac{c^{2} x^{3} + 2 \, c x^{\frac{3}{2}} + 1}{c^{2} x^{3} - 1}\right)^{2} - 4 \, a^{2} - 4 \, {\left(b^{2} c x^{\frac{3}{2}} + a b\right)} \log\left(-\frac{c^{2} x^{3} + 2 \, c x^{\frac{3}{2}} + 1}{c^{2} x^{3} - 1}\right)}{12 \, x^{3}}"," ",0,"1/12*(24*b^2*c^2*x^3*log(sqrt(x)) + 4*(a*b - b^2)*c^2*x^3*log(c*x^(3/2) + 1) - 4*(a*b + b^2)*c^2*x^3*log(c*x^(3/2) - 1) - 8*a*b*c*x^(3/2) + (b^2*c^2*x^3 - b^2)*log(-(c^2*x^3 + 2*c*x^(3/2) + 1)/(c^2*x^3 - 1))^2 - 4*a^2 - 4*(b^2*c*x^(3/2) + a*b)*log(-(c^2*x^3 + 2*c*x^(3/2) + 1)/(c^2*x^3 - 1)))/x^3","B",0
224,0,0,0,0.973131," ","integrate(x^2*(a+b*arctanh(c*x^n)),x, algorithm=""fricas"")","{\rm integral}\left(b x^{2} \operatorname{artanh}\left(c x^{n}\right) + a x^{2}, x\right)"," ",0,"integral(b*x^2*arctanh(c*x^n) + a*x^2, x)","F",0
225,0,0,0,0.664042," ","integrate(x*(a+b*arctanh(c*x^n)),x, algorithm=""fricas"")","{\rm integral}\left(b x \operatorname{artanh}\left(c x^{n}\right) + a x, x\right)"," ",0,"integral(b*x*arctanh(c*x^n) + a*x, x)","F",0
226,0,0,0,0.502929," ","integrate(a+b*arctanh(c*x^n),x, algorithm=""fricas"")","{\rm integral}\left(b \operatorname{artanh}\left(c x^{n}\right) + a, x\right)"," ",0,"integral(b*arctanh(c*x^n) + a, x)","F",0
227,1,141,0,0.669444," ","integrate((a+b*arctanh(c*x^n))/x,x, algorithm=""fricas"")","-\frac{b n \log\left(c \cosh\left(n \log\left(x\right)\right) + c \sinh\left(n \log\left(x\right)\right) + 1\right) \log\left(x\right) - b n \log\left(-c \cosh\left(n \log\left(x\right)\right) - c \sinh\left(n \log\left(x\right)\right) + 1\right) \log\left(x\right) - b n \log\left(x\right) \log\left(-\frac{c \cosh\left(n \log\left(x\right)\right) + c \sinh\left(n \log\left(x\right)\right) + 1}{c \cosh\left(n \log\left(x\right)\right) + c \sinh\left(n \log\left(x\right)\right) - 1}\right) - 2 \, a n \log\left(x\right) - b {\rm Li}_2\left(c \cosh\left(n \log\left(x\right)\right) + c \sinh\left(n \log\left(x\right)\right)\right) + b {\rm Li}_2\left(-c \cosh\left(n \log\left(x\right)\right) - c \sinh\left(n \log\left(x\right)\right)\right)}{2 \, n}"," ",0,"-1/2*(b*n*log(c*cosh(n*log(x)) + c*sinh(n*log(x)) + 1)*log(x) - b*n*log(-c*cosh(n*log(x)) - c*sinh(n*log(x)) + 1)*log(x) - b*n*log(x)*log(-(c*cosh(n*log(x)) + c*sinh(n*log(x)) + 1)/(c*cosh(n*log(x)) + c*sinh(n*log(x)) - 1)) - 2*a*n*log(x) - b*dilog(c*cosh(n*log(x)) + c*sinh(n*log(x))) + b*dilog(-c*cosh(n*log(x)) - c*sinh(n*log(x))))/n","B",0
228,0,0,0,0.765545," ","integrate((a+b*arctanh(c*x^n))/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \operatorname{artanh}\left(c x^{n}\right) + a}{x^{2}}, x\right)"," ",0,"integral((b*arctanh(c*x^n) + a)/x^2, x)","F",0
229,0,0,0,0.733232," ","integrate((a+b*arctanh(c*x^n))/x^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \operatorname{artanh}\left(c x^{n}\right) + a}{x^{3}}, x\right)"," ",0,"integral((b*arctanh(c*x^n) + a)/x^3, x)","F",0
230,0,0,0,0.698732," ","integrate((a+b*arctanh(c*x^n))/x^4,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \operatorname{artanh}\left(c x^{n}\right) + a}{x^{4}}, x\right)"," ",0,"integral((b*arctanh(c*x^n) + a)/x^4, x)","F",0
231,0,0,0,0.636948," ","integrate(x*(a+b*arctanh(c*x^n))^2,x, algorithm=""fricas"")","{\rm integral}\left(b^{2} x \operatorname{artanh}\left(c x^{n}\right)^{2} + 2 \, a b x \operatorname{artanh}\left(c x^{n}\right) + a^{2} x, x\right)"," ",0,"integral(b^2*x*arctanh(c*x^n)^2 + 2*a*b*x*arctanh(c*x^n) + a^2*x, x)","F",0
232,0,0,0,0.979561," ","integrate((a+b*arctanh(c*x^n))^2,x, algorithm=""fricas"")","{\rm integral}\left(b^{2} \operatorname{artanh}\left(c x^{n}\right)^{2} + 2 \, a b \operatorname{artanh}\left(c x^{n}\right) + a^{2}, x\right)"," ",0,"integral(b^2*arctanh(c*x^n)^2 + 2*a*b*arctanh(c*x^n) + a^2, x)","F",0
233,0,0,0,1.252023," ","integrate((a+b*arctanh(c*x^n))^2/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} \operatorname{artanh}\left(c x^{n}\right)^{2} + 2 \, a b \operatorname{artanh}\left(c x^{n}\right) + a^{2}}{x}, x\right)"," ",0,"integral((b^2*arctanh(c*x^n)^2 + 2*a*b*arctanh(c*x^n) + a^2)/x, x)","F",0
234,0,0,0,1.135603," ","integrate((a+b*arctanh(c*x^n))^2/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} \operatorname{artanh}\left(c x^{n}\right)^{2} + 2 \, a b \operatorname{artanh}\left(c x^{n}\right) + a^{2}}{x^{2}}, x\right)"," ",0,"integral((b^2*arctanh(c*x^n)^2 + 2*a*b*arctanh(c*x^n) + a^2)/x^2, x)","F",0
235,0,0,0,1.180062," ","integrate((a+b*arctanh(c*x^n))^2/x^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} \operatorname{artanh}\left(c x^{n}\right)^{2} + 2 \, a b \operatorname{artanh}\left(c x^{n}\right) + a^{2}}{x^{3}}, x\right)"," ",0,"integral((b^2*arctanh(c*x^n)^2 + 2*a*b*arctanh(c*x^n) + a^2)/x^3, x)","F",0
236,1,129,0,1.315883," ","integrate(arctanh(a*x^n)/x,x, algorithm=""fricas"")","-\frac{n \log\left(a \cosh\left(n \log\left(x\right)\right) + a \sinh\left(n \log\left(x\right)\right) + 1\right) \log\left(x\right) - n \log\left(-a \cosh\left(n \log\left(x\right)\right) - a \sinh\left(n \log\left(x\right)\right) + 1\right) \log\left(x\right) - n \log\left(x\right) \log\left(-\frac{a \cosh\left(n \log\left(x\right)\right) + a \sinh\left(n \log\left(x\right)\right) + 1}{a \cosh\left(n \log\left(x\right)\right) + a \sinh\left(n \log\left(x\right)\right) - 1}\right) - {\rm Li}_2\left(a \cosh\left(n \log\left(x\right)\right) + a \sinh\left(n \log\left(x\right)\right)\right) + {\rm Li}_2\left(-a \cosh\left(n \log\left(x\right)\right) - a \sinh\left(n \log\left(x\right)\right)\right)}{2 \, n}"," ",0,"-1/2*(n*log(a*cosh(n*log(x)) + a*sinh(n*log(x)) + 1)*log(x) - n*log(-a*cosh(n*log(x)) - a*sinh(n*log(x)) + 1)*log(x) - n*log(x)*log(-(a*cosh(n*log(x)) + a*sinh(n*log(x)) + 1)/(a*cosh(n*log(x)) + a*sinh(n*log(x)) - 1)) - dilog(a*cosh(n*log(x)) + a*sinh(n*log(x))) + dilog(-a*cosh(n*log(x)) - a*sinh(n*log(x))))/n","B",0
237,0,0,0,0.511647," ","integrate(arctanh(a*x^5)/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{artanh}\left(a x^{5}\right)}{x}, x\right)"," ",0,"integral(arctanh(a*x^5)/x, x)","F",0
238,1,22,0,0.635121," ","integrate(arctanh(1/x),x, algorithm=""fricas"")","\frac{1}{2} \, x \log\left(\frac{x + 1}{x - 1}\right) + \frac{1}{2} \, \log\left(x^{2} - 1\right)"," ",0,"1/2*x*log((x + 1)/(x - 1)) + 1/2*log(x^2 - 1)","A",0
239,0,0,0,0.685062," ","integrate((d*x)^m*(a+b*arctanh(c*x^n))^3,x, algorithm=""fricas"")","{\rm integral}\left(\left(d x\right)^{m} b^{3} \operatorname{artanh}\left(c x^{n}\right)^{3} + 3 \, \left(d x\right)^{m} a b^{2} \operatorname{artanh}\left(c x^{n}\right)^{2} + 3 \, \left(d x\right)^{m} a^{2} b \operatorname{artanh}\left(c x^{n}\right) + \left(d x\right)^{m} a^{3}, x\right)"," ",0,"integral((d*x)^m*b^3*arctanh(c*x^n)^3 + 3*(d*x)^m*a*b^2*arctanh(c*x^n)^2 + 3*(d*x)^m*a^2*b*arctanh(c*x^n) + (d*x)^m*a^3, x)","F",0
240,0,0,0,0.527014," ","integrate((d*x)^m*(a+b*arctanh(c*x^n))^2,x, algorithm=""fricas"")","{\rm integral}\left(\left(d x\right)^{m} b^{2} \operatorname{artanh}\left(c x^{n}\right)^{2} + 2 \, \left(d x\right)^{m} a b \operatorname{artanh}\left(c x^{n}\right) + \left(d x\right)^{m} a^{2}, x\right)"," ",0,"integral((d*x)^m*b^2*arctanh(c*x^n)^2 + 2*(d*x)^m*a*b*arctanh(c*x^n) + (d*x)^m*a^2, x)","F",0
241,0,0,0,0.811810," ","integrate((d*x)^m*(a+b*arctanh(c*x^n)),x, algorithm=""fricas"")","{\rm integral}\left(\left(d x\right)^{m} b \operatorname{artanh}\left(c x^{n}\right) + \left(d x\right)^{m} a, x\right)"," ",0,"integral((d*x)^m*b*arctanh(c*x^n) + (d*x)^m*a, x)","F",0
242,0,0,0,1.073534," ","integrate((d*x)^m/(a+b*arctanh(c*x^n)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(d x\right)^{m}}{b \operatorname{artanh}\left(c x^{n}\right) + a}, x\right)"," ",0,"integral((d*x)^m/(b*arctanh(c*x^n) + a), x)","F",0
243,0,0,0,0.587796," ","integrate((d*x)^m/(a+b*arctanh(c*x^n))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(d x\right)^{m}}{b^{2} \operatorname{artanh}\left(c x^{n}\right)^{2} + 2 \, a b \operatorname{artanh}\left(c x^{n}\right) + a^{2}}, x\right)"," ",0,"integral((d*x)^m/(b^2*arctanh(c*x^n)^2 + 2*a*b*arctanh(c*x^n) + a^2), x)","F",0
