1,1,70,0,0.313167," ","integrate(x^5*(a+b*arctanh(c*x)),x, algorithm=""maxima"")","\frac{1}{6} \, a x^{6} + \frac{1}{180} \, {\left(30 \, x^{6} \operatorname{artanh}\left(c x\right) + c {\left(\frac{2 \, {\left(3 \, c^{4} x^{5} + 5 \, c^{2} x^{3} + 15 \, x\right)}}{c^{6}} - \frac{15 \, \log\left(c x + 1\right)}{c^{7}} + \frac{15 \, \log\left(c x - 1\right)}{c^{7}}\right)}\right)} b"," ",0,"1/6*a*x^6 + 1/180*(30*x^6*arctanh(c*x) + c*(2*(3*c^4*x^5 + 5*c^2*x^3 + 15*x)/c^6 - 15*log(c*x + 1)/c^7 + 15*log(c*x - 1)/c^7))*b","A",0
2,1,55,0,0.306945," ","integrate(x^4*(a+b*arctanh(c*x)),x, algorithm=""maxima"")","\frac{1}{5} \, a x^{5} + \frac{1}{20} \, {\left(4 \, x^{5} \operatorname{artanh}\left(c x\right) + c {\left(\frac{c^{2} x^{4} + 2 \, x^{2}}{c^{4}} + \frac{2 \, \log\left(c^{2} x^{2} - 1\right)}{c^{6}}\right)}\right)} b"," ",0,"1/5*a*x^5 + 1/20*(4*x^5*arctanh(c*x) + c*((c^2*x^4 + 2*x^2)/c^4 + 2*log(c^2*x^2 - 1)/c^6))*b","A",0
3,1,61,0,0.307562," ","integrate(x^3*(a+b*arctanh(c*x)),x, algorithm=""maxima"")","\frac{1}{4} \, a x^{4} + \frac{1}{24} \, {\left(6 \, x^{4} \operatorname{artanh}\left(c x\right) + c {\left(\frac{2 \, {\left(c^{2} x^{3} + 3 \, x\right)}}{c^{4}} - \frac{3 \, \log\left(c x + 1\right)}{c^{5}} + \frac{3 \, \log\left(c x - 1\right)}{c^{5}}\right)}\right)} b"," ",0,"1/4*a*x^4 + 1/24*(6*x^4*arctanh(c*x) + c*(2*(c^2*x^3 + 3*x)/c^4 - 3*log(c*x + 1)/c^5 + 3*log(c*x - 1)/c^5))*b","A",0
4,1,44,0,0.309259," ","integrate(x^2*(a+b*arctanh(c*x)),x, algorithm=""maxima"")","\frac{1}{3} \, a x^{3} + \frac{1}{6} \, {\left(2 \, x^{3} \operatorname{artanh}\left(c x\right) + c {\left(\frac{x^{2}}{c^{2}} + \frac{\log\left(c^{2} x^{2} - 1\right)}{c^{4}}\right)}\right)} b"," ",0,"1/3*a*x^3 + 1/6*(2*x^3*arctanh(c*x) + c*(x^2/c^2 + log(c^2*x^2 - 1)/c^4))*b","A",0
5,1,50,0,0.302877," ","integrate(x*(a+b*arctanh(c*x)),x, algorithm=""maxima"")","\frac{1}{2} \, a x^{2} + \frac{1}{4} \, {\left(2 \, x^{2} \operatorname{artanh}\left(c x\right) + c {\left(\frac{2 \, x}{c^{2}} - \frac{\log\left(c x + 1\right)}{c^{3}} + \frac{\log\left(c x - 1\right)}{c^{3}}\right)}\right)} b"," ",0,"1/2*a*x^2 + 1/4*(2*x^2*arctanh(c*x) + c*(2*x/c^2 - log(c*x + 1)/c^3 + log(c*x - 1)/c^3))*b","A",0
6,1,30,0,0.326315," ","integrate(a+b*arctanh(c*x),x, algorithm=""maxima"")","a x + \frac{{\left(2 \, c x \operatorname{artanh}\left(c x\right) + \log\left(-c^{2} x^{2} + 1\right)\right)} b}{2 \, c}"," ",0,"a*x + 1/2*(2*c*x*arctanh(c*x) + log(-c^2*x^2 + 1))*b/c","A",0
7,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x))/x,x, algorithm=""maxima"")","\frac{1}{2} \, b \int \frac{\log\left(c x + 1\right) - \log\left(-c x + 1\right)}{x}\,{d x} + a \log\left(x\right)"," ",0,"1/2*b*integrate((log(c*x + 1) - log(-c*x + 1))/x, x) + a*log(x)","F",0
8,1,39,0,0.321303," ","integrate((a+b*arctanh(c*x))/x^2,x, algorithm=""maxima"")","-\frac{1}{2} \, {\left(c {\left(\log\left(c^{2} x^{2} - 1\right) - \log\left(x^{2}\right)\right)} + \frac{2 \, \operatorname{artanh}\left(c x\right)}{x}\right)} b - \frac{a}{x}"," ",0,"-1/2*(c*(log(c^2*x^2 - 1) - log(x^2)) + 2*arctanh(c*x)/x)*b - a/x","A",0
9,1,45,0,0.319994," ","integrate((a+b*arctanh(c*x))/x^3,x, algorithm=""maxima"")","\frac{1}{4} \, {\left({\left(c \log\left(c x + 1\right) - c \log\left(c x - 1\right) - \frac{2}{x}\right)} c - \frac{2 \, \operatorname{artanh}\left(c x\right)}{x^{2}}\right)} b - \frac{a}{2 \, x^{2}}"," ",0,"1/4*((c*log(c*x + 1) - c*log(c*x - 1) - 2/x)*c - 2*arctanh(c*x)/x^2)*b - 1/2*a/x^2","A",0
10,1,49,0,0.317283," ","integrate((a+b*arctanh(c*x))/x^4,x, algorithm=""maxima"")","-\frac{1}{6} \, {\left({\left(c^{2} \log\left(c^{2} x^{2} - 1\right) - c^{2} \log\left(x^{2}\right) + \frac{1}{x^{2}}\right)} c + \frac{2 \, \operatorname{artanh}\left(c x\right)}{x^{3}}\right)} b - \frac{a}{3 \, x^{3}}"," ",0,"-1/6*((c^2*log(c^2*x^2 - 1) - c^2*log(x^2) + 1/x^2)*c + 2*arctanh(c*x)/x^3)*b - 1/3*a/x^3","A",0
11,1,60,0,0.317075," ","integrate((a+b*arctanh(c*x))/x^5,x, algorithm=""maxima"")","\frac{1}{24} \, {\left({\left(3 \, c^{3} \log\left(c x + 1\right) - 3 \, c^{3} \log\left(c x - 1\right) - \frac{2 \, {\left(3 \, c^{2} x^{2} + 1\right)}}{x^{3}}\right)} c - \frac{6 \, \operatorname{artanh}\left(c x\right)}{x^{4}}\right)} b - \frac{a}{4 \, x^{4}}"," ",0,"1/24*((3*c^3*log(c*x + 1) - 3*c^3*log(c*x - 1) - 2*(3*c^2*x^2 + 1)/x^3)*c - 6*arctanh(c*x)/x^4)*b - 1/4*a/x^4","A",0
12,1,61,0,0.327417," ","integrate((a+b*arctanh(c*x))/x^6,x, algorithm=""maxima"")","-\frac{1}{20} \, {\left({\left(2 \, c^{4} \log\left(c^{2} x^{2} - 1\right) - 2 \, c^{4} \log\left(x^{2}\right) + \frac{2 \, c^{2} x^{2} + 1}{x^{4}}\right)} c + \frac{4 \, \operatorname{artanh}\left(c x\right)}{x^{5}}\right)} b - \frac{a}{5 \, x^{5}}"," ",0,"-1/20*((2*c^4*log(c^2*x^2 - 1) - 2*c^4*log(x^2) + (2*c^2*x^2 + 1)/x^4)*c + 4*arctanh(c*x)/x^5)*b - 1/5*a/x^5","A",0
13,1,215,0,0.367980," ","integrate(x^5*(a+b*arctanh(c*x))^2,x, algorithm=""maxima"")","\frac{1}{6} \, b^{2} x^{6} \operatorname{artanh}\left(c x\right)^{2} + \frac{1}{6} \, a^{2} x^{6} + \frac{1}{90} \, {\left(30 \, x^{6} \operatorname{artanh}\left(c x\right) + c {\left(\frac{2 \, {\left(3 \, c^{4} x^{5} + 5 \, c^{2} x^{3} + 15 \, x\right)}}{c^{6}} - \frac{15 \, \log\left(c x + 1\right)}{c^{7}} + \frac{15 \, \log\left(c x - 1\right)}{c^{7}}\right)}\right)} a b + \frac{1}{360} \, {\left(4 \, c {\left(\frac{2 \, {\left(3 \, c^{4} x^{5} + 5 \, c^{2} x^{3} + 15 \, x\right)}}{c^{6}} - \frac{15 \, \log\left(c x + 1\right)}{c^{7}} + \frac{15 \, \log\left(c x - 1\right)}{c^{7}}\right)} \operatorname{artanh}\left(c x\right) + \frac{6 \, c^{4} x^{4} + 32 \, c^{2} x^{2} - 2 \, {\left(15 \, \log\left(c x - 1\right) - 46\right)} \log\left(c x + 1\right) + 15 \, \log\left(c x + 1\right)^{2} + 15 \, \log\left(c x - 1\right)^{2} + 92 \, \log\left(c x - 1\right)}{c^{6}}\right)} b^{2}"," ",0,"1/6*b^2*x^6*arctanh(c*x)^2 + 1/6*a^2*x^6 + 1/90*(30*x^6*arctanh(c*x) + c*(2*(3*c^4*x^5 + 5*c^2*x^3 + 15*x)/c^6 - 15*log(c*x + 1)/c^7 + 15*log(c*x - 1)/c^7))*a*b + 1/360*(4*c*(2*(3*c^4*x^5 + 5*c^2*x^3 + 15*x)/c^6 - 15*log(c*x + 1)/c^7 + 15*log(c*x - 1)/c^7)*arctanh(c*x) + (6*c^4*x^4 + 32*c^2*x^2 - 2*(15*log(c*x - 1) - 46)*log(c*x + 1) + 15*log(c*x + 1)^2 + 15*log(c*x - 1)^2 + 92*log(c*x - 1))/c^6)*b^2","A",0
14,0,0,0,0.000000," ","integrate(x^4*(a+b*arctanh(c*x))^2,x, algorithm=""maxima"")","\frac{1}{5} \, a^{2} x^{5} + \frac{1}{10} \, {\left(4 \, x^{5} \operatorname{artanh}\left(c x\right) + c {\left(\frac{c^{2} x^{4} + 2 \, x^{2}}{c^{4}} + \frac{2 \, \log\left(c^{2} x^{2} - 1\right)}{c^{6}}\right)}\right)} a b - \frac{1}{36000} \, {\left(24 \, c^{6} {\left(\frac{2 \, {\left(3 \, c^{4} x^{5} + 5 \, c^{2} x^{3} + 15 \, x\right)}}{c^{10}} - \frac{15 \, \log\left(c x + 1\right)}{c^{11}} + \frac{15 \, \log\left(c x - 1\right)}{c^{11}}\right)} - 45 \, c^{5} {\left(\frac{c^{2} x^{4} + 2 \, x^{2}}{c^{8}} + \frac{2 \, \log\left(c^{2} x^{2} - 1\right)}{c^{10}}\right)} - 1080000 \, c^{5} \int \frac{x^{5} \log\left(c x + 1\right)}{150 \, {\left(c^{6} x^{2} - c^{4}\right)}}\,{d x} + 50 \, c^{4} {\left(\frac{2 \, {\left(c^{2} x^{3} + 3 \, x\right)}}{c^{8}} - \frac{3 \, \log\left(c x + 1\right)}{c^{9}} + \frac{3 \, \log\left(c x - 1\right)}{c^{9}}\right)} - 300 \, c^{3} {\left(\frac{x^{2}}{c^{6}} + \frac{\log\left(c^{2} x^{2} - 1\right)}{c^{8}}\right)} + 900 \, c^{2} {\left(\frac{2 \, x}{c^{6}} - \frac{\log\left(c x + 1\right)}{c^{7}} + \frac{\log\left(c x - 1\right)}{c^{7}}\right)} - 540000 \, c \int \frac{x \log\left(c x + 1\right)}{150 \, {\left(c^{6} x^{2} - c^{4}\right)}}\,{d x} - \frac{60 \, {\left(30 \, c^{5} x^{5} \log\left(c x + 1\right)^{2} + {\left(12 \, c^{5} x^{5} - 15 \, c^{4} x^{4} + 20 \, c^{3} x^{3} - 30 \, c^{2} x^{2} + 60 \, c x - 60 \, {\left(c^{5} x^{5} + 1\right)} \log\left(c x + 1\right)\right)} \log\left(-c x + 1\right)\right)}}{c^{5}} - \frac{72 \, {\left(c x - 1\right)}^{5} {\left(25 \, \log\left(-c x + 1\right)^{2} - 10 \, \log\left(-c x + 1\right) + 2\right)} + 1125 \, {\left(c x - 1\right)}^{4} {\left(8 \, \log\left(-c x + 1\right)^{2} - 4 \, \log\left(-c x + 1\right) + 1\right)} + 2000 \, {\left(c x - 1\right)}^{3} {\left(9 \, \log\left(-c x + 1\right)^{2} - 6 \, \log\left(-c x + 1\right) + 2\right)} + 9000 \, {\left(c x - 1\right)}^{2} {\left(2 \, \log\left(-c x + 1\right)^{2} - 2 \, \log\left(-c x + 1\right) + 1\right)} + 9000 \, {\left(c x - 1\right)} {\left(\log\left(-c x + 1\right)^{2} - 2 \, \log\left(-c x + 1\right) + 2\right)}}{c^{5}} + \frac{1800 \, \log\left(150 \, c^{6} x^{2} - 150 \, c^{4}\right)}{c^{5}} - 540000 \, \int \frac{\log\left(c x + 1\right)}{150 \, {\left(c^{6} x^{2} - c^{4}\right)}}\,{d x}\right)} b^{2}"," ",0,"1/5*a^2*x^5 + 1/10*(4*x^5*arctanh(c*x) + c*((c^2*x^4 + 2*x^2)/c^4 + 2*log(c^2*x^2 - 1)/c^6))*a*b - 1/36000*(24*c^6*(2*(3*c^4*x^5 + 5*c^2*x^3 + 15*x)/c^10 - 15*log(c*x + 1)/c^11 + 15*log(c*x - 1)/c^11) - 45*c^5*((c^2*x^4 + 2*x^2)/c^8 + 2*log(c^2*x^2 - 1)/c^10) - 1080000*c^5*integrate(1/150*x^5*log(c*x + 1)/(c^6*x^2 - c^4), x) + 50*c^4*(2*(c^2*x^3 + 3*x)/c^8 - 3*log(c*x + 1)/c^9 + 3*log(c*x - 1)/c^9) - 300*c^3*(x^2/c^6 + log(c^2*x^2 - 1)/c^8) + 900*c^2*(2*x/c^6 - log(c*x + 1)/c^7 + log(c*x - 1)/c^7) - 540000*c*integrate(1/150*x*log(c*x + 1)/(c^6*x^2 - c^4), x) - 60*(30*c^5*x^5*log(c*x + 1)^2 + (12*c^5*x^5 - 15*c^4*x^4 + 20*c^3*x^3 - 30*c^2*x^2 + 60*c*x - 60*(c^5*x^5 + 1)*log(c*x + 1))*log(-c*x + 1))/c^5 - (72*(c*x - 1)^5*(25*log(-c*x + 1)^2 - 10*log(-c*x + 1) + 2) + 1125*(c*x - 1)^4*(8*log(-c*x + 1)^2 - 4*log(-c*x + 1) + 1) + 2000*(c*x - 1)^3*(9*log(-c*x + 1)^2 - 6*log(-c*x + 1) + 2) + 9000*(c*x - 1)^2*(2*log(-c*x + 1)^2 - 2*log(-c*x + 1) + 1) + 9000*(c*x - 1)*(log(-c*x + 1)^2 - 2*log(-c*x + 1) + 2))/c^5 + 1800*log(150*c^6*x^2 - 150*c^4)/c^5 - 540000*integrate(1/150*log(c*x + 1)/(c^6*x^2 - c^4), x))*b^2","F",0
15,1,189,0,0.331465," ","integrate(x^3*(a+b*arctanh(c*x))^2,x, algorithm=""maxima"")","\frac{1}{4} \, b^{2} x^{4} \operatorname{artanh}\left(c x\right)^{2} + \frac{1}{4} \, a^{2} x^{4} + \frac{1}{12} \, {\left(6 \, x^{4} \operatorname{artanh}\left(c x\right) + c {\left(\frac{2 \, {\left(c^{2} x^{3} + 3 \, x\right)}}{c^{4}} - \frac{3 \, \log\left(c x + 1\right)}{c^{5}} + \frac{3 \, \log\left(c x - 1\right)}{c^{5}}\right)}\right)} a b + \frac{1}{48} \, {\left(4 \, c {\left(\frac{2 \, {\left(c^{2} x^{3} + 3 \, x\right)}}{c^{4}} - \frac{3 \, \log\left(c x + 1\right)}{c^{5}} + \frac{3 \, \log\left(c x - 1\right)}{c^{5}}\right)} \operatorname{artanh}\left(c x\right) + \frac{4 \, c^{2} x^{2} - 2 \, {\left(3 \, \log\left(c x - 1\right) - 8\right)} \log\left(c x + 1\right) + 3 \, \log\left(c x + 1\right)^{2} + 3 \, \log\left(c x - 1\right)^{2} + 16 \, \log\left(c x - 1\right)}{c^{4}}\right)} b^{2}"," ",0,"1/4*b^2*x^4*arctanh(c*x)^2 + 1/4*a^2*x^4 + 1/12*(6*x^4*arctanh(c*x) + c*(2*(c^2*x^3 + 3*x)/c^4 - 3*log(c*x + 1)/c^5 + 3*log(c*x - 1)/c^5))*a*b + 1/48*(4*c*(2*(c^2*x^3 + 3*x)/c^4 - 3*log(c*x + 1)/c^5 + 3*log(c*x - 1)/c^5)*arctanh(c*x) + (4*c^2*x^2 - 2*(3*log(c*x - 1) - 8)*log(c*x + 1) + 3*log(c*x + 1)^2 + 3*log(c*x - 1)^2 + 16*log(c*x - 1))/c^4)*b^2","A",0
16,0,0,0,0.000000," ","integrate(x^2*(a+b*arctanh(c*x))^2,x, algorithm=""maxima"")","\frac{1}{3} \, a^{2} x^{3} + \frac{1}{3} \, {\left(2 \, x^{3} \operatorname{artanh}\left(c x\right) + c {\left(\frac{x^{2}}{c^{2}} + \frac{\log\left(c^{2} x^{2} - 1\right)}{c^{4}}\right)}\right)} a b - \frac{1}{216} \, {\left(2 \, c^{4} {\left(\frac{2 \, {\left(c^{2} x^{3} + 3 \, x\right)}}{c^{6}} - \frac{3 \, \log\left(c x + 1\right)}{c^{7}} + \frac{3 \, \log\left(c x - 1\right)}{c^{7}}\right)} - 3 \, c^{3} {\left(\frac{x^{2}}{c^{4}} + \frac{\log\left(c^{2} x^{2} - 1\right)}{c^{6}}\right)} - 648 \, c^{3} \int \frac{x^{3} \log\left(c x + 1\right)}{9 \, {\left(c^{4} x^{2} - c^{2}\right)}}\,{d x} + 9 \, c^{2} {\left(\frac{2 \, x}{c^{4}} - \frac{\log\left(c x + 1\right)}{c^{5}} + \frac{\log\left(c x - 1\right)}{c^{5}}\right)} - 324 \, c \int \frac{x \log\left(c x + 1\right)}{9 \, {\left(c^{4} x^{2} - c^{2}\right)}}\,{d x} - \frac{6 \, {\left(3 \, c^{3} x^{3} \log\left(c x + 1\right)^{2} + {\left(2 \, c^{3} x^{3} - 3 \, c^{2} x^{2} + 6 \, c x - 6 \, {\left(c^{3} x^{3} + 1\right)} \log\left(c x + 1\right)\right)} \log\left(-c x + 1\right)\right)}}{c^{3}} - \frac{2 \, {\left(c x - 1\right)}^{3} {\left(9 \, \log\left(-c x + 1\right)^{2} - 6 \, \log\left(-c x + 1\right) + 2\right)} + 27 \, {\left(c x - 1\right)}^{2} {\left(2 \, \log\left(-c x + 1\right)^{2} - 2 \, \log\left(-c x + 1\right) + 1\right)} + 54 \, {\left(c x - 1\right)} {\left(\log\left(-c x + 1\right)^{2} - 2 \, \log\left(-c x + 1\right) + 2\right)}}{c^{3}} + \frac{18 \, \log\left(9 \, c^{4} x^{2} - 9 \, c^{2}\right)}{c^{3}} - 324 \, \int \frac{\log\left(c x + 1\right)}{9 \, {\left(c^{4} x^{2} - c^{2}\right)}}\,{d x}\right)} b^{2}"," ",0,"1/3*a^2*x^3 + 1/3*(2*x^3*arctanh(c*x) + c*(x^2/c^2 + log(c^2*x^2 - 1)/c^4))*a*b - 1/216*(2*c^4*(2*(c^2*x^3 + 3*x)/c^6 - 3*log(c*x + 1)/c^7 + 3*log(c*x - 1)/c^7) - 3*c^3*(x^2/c^4 + log(c^2*x^2 - 1)/c^6) - 648*c^3*integrate(1/9*x^3*log(c*x + 1)/(c^4*x^2 - c^2), x) + 9*c^2*(2*x/c^4 - log(c*x + 1)/c^5 + log(c*x - 1)/c^5) - 324*c*integrate(1/9*x*log(c*x + 1)/(c^4*x^2 - c^2), x) - 6*(3*c^3*x^3*log(c*x + 1)^2 + (2*c^3*x^3 - 3*c^2*x^2 + 6*c*x - 6*(c^3*x^3 + 1)*log(c*x + 1))*log(-c*x + 1))/c^3 - (2*(c*x - 1)^3*(9*log(-c*x + 1)^2 - 6*log(-c*x + 1) + 2) + 27*(c*x - 1)^2*(2*log(-c*x + 1)^2 - 2*log(-c*x + 1) + 1) + 54*(c*x - 1)*(log(-c*x + 1)^2 - 2*log(-c*x + 1) + 2))/c^3 + 18*log(9*c^4*x^2 - 9*c^2)/c^3 - 324*integrate(1/9*log(c*x + 1)/(c^4*x^2 - c^2), x))*b^2","F",0
17,1,158,0,0.325003," ","integrate(x*(a+b*arctanh(c*x))^2,x, algorithm=""maxima"")","\frac{1}{2} \, b^{2} x^{2} \operatorname{artanh}\left(c x\right)^{2} + \frac{1}{2} \, a^{2} x^{2} + \frac{1}{2} \, {\left(2 \, x^{2} \operatorname{artanh}\left(c x\right) + c {\left(\frac{2 \, x}{c^{2}} - \frac{\log\left(c x + 1\right)}{c^{3}} + \frac{\log\left(c x - 1\right)}{c^{3}}\right)}\right)} a b + \frac{1}{8} \, {\left(4 \, c {\left(\frac{2 \, x}{c^{2}} - \frac{\log\left(c x + 1\right)}{c^{3}} + \frac{\log\left(c x - 1\right)}{c^{3}}\right)} \operatorname{artanh}\left(c x\right) - \frac{2 \, {\left(\log\left(c x - 1\right) - 2\right)} \log\left(c x + 1\right) - \log\left(c x + 1\right)^{2} - \log\left(c x - 1\right)^{2} - 4 \, \log\left(c x - 1\right)}{c^{2}}\right)} b^{2}"," ",0,"1/2*b^2*x^2*arctanh(c*x)^2 + 1/2*a^2*x^2 + 1/2*(2*x^2*arctanh(c*x) + c*(2*x/c^2 - log(c*x + 1)/c^3 + log(c*x - 1)/c^3))*a*b + 1/8*(4*c*(2*x/c^2 - log(c*x + 1)/c^3 + log(c*x - 1)/c^3)*arctanh(c*x) - (2*(log(c*x - 1) - 2)*log(c*x + 1) - log(c*x + 1)^2 - log(c*x - 1)^2 - 4*log(c*x - 1))/c^2)*b^2","B",0
18,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x))^2,x, algorithm=""maxima"")","-\frac{1}{4} \, {\left(c^{2} {\left(\frac{2 \, x}{c^{2}} - \frac{\log\left(c x + 1\right)}{c^{3}} + \frac{\log\left(c x - 1\right)}{c^{3}}\right)} - 6 \, c \int \frac{x \log\left(c x + 1\right)}{c^{2} x^{2} - 1}\,{d x} - \frac{{\left(c x - 1\right)} {\left(\log\left(-c x + 1\right)^{2} - 2 \, \log\left(-c x + 1\right) + 2\right)}}{c} - \frac{c x \log\left(c x + 1\right)^{2} + 2 \, {\left(c x - {\left(c x + 1\right)} \log\left(c x + 1\right)\right)} \log\left(-c x + 1\right)}{c} + \frac{\log\left(c^{2} x^{2} - 1\right)}{c} - 2 \, \int \frac{\log\left(c x + 1\right)}{c^{2} x^{2} - 1}\,{d x}\right)} b^{2} + a^{2} x + \frac{{\left(2 \, c x \operatorname{artanh}\left(c x\right) + \log\left(-c^{2} x^{2} + 1\right)\right)} a b}{c}"," ",0,"-1/4*(c^2*(2*x/c^2 - log(c*x + 1)/c^3 + log(c*x - 1)/c^3) - 6*c*integrate(x*log(c*x + 1)/(c^2*x^2 - 1), x) - (c*x - 1)*(log(-c*x + 1)^2 - 2*log(-c*x + 1) + 2)/c - (c*x*log(c*x + 1)^2 + 2*(c*x - (c*x + 1)*log(c*x + 1))*log(-c*x + 1))/c + log(c^2*x^2 - 1)/c - 2*integrate(log(c*x + 1)/(c^2*x^2 - 1), x))*b^2 + a^2*x + (2*c*x*arctanh(c*x) + log(-c^2*x^2 + 1))*a*b/c","F",0
19,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x))^2/x,x, algorithm=""maxima"")","a^{2} \log\left(x\right) + \int \frac{b^{2} {\left(\log\left(c x + 1\right) - \log\left(-c x + 1\right)\right)}^{2}}{4 \, x} + \frac{a b {\left(\log\left(c x + 1\right) - \log\left(-c x + 1\right)\right)}}{x}\,{d x}"," ",0,"a^2*log(x) + integrate(1/4*b^2*(log(c*x + 1) - log(-c*x + 1))^2/x + a*b*(log(c*x + 1) - log(-c*x + 1))/x, x)","F",0
20,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x))^2/x^2,x, algorithm=""maxima"")","-{\left(c {\left(\log\left(c^{2} x^{2} - 1\right) - \log\left(x^{2}\right)\right)} + \frac{2 \, \operatorname{artanh}\left(c x\right)}{x}\right)} a b - \frac{1}{4} \, b^{2} {\left(\frac{\log\left(-c x + 1\right)^{2}}{x} + \int -\frac{{\left(c x - 1\right)} \log\left(c x + 1\right)^{2} + 2 \, {\left(c x - {\left(c x - 1\right)} \log\left(c x + 1\right)\right)} \log\left(-c x + 1\right)}{c x^{3} - x^{2}}\,{d x}\right)} - \frac{a^{2}}{x}"," ",0,"-(c*(log(c^2*x^2 - 1) - log(x^2)) + 2*arctanh(c*x)/x)*a*b - 1/4*b^2*(log(-c*x + 1)^2/x + integrate(-((c*x - 1)*log(c*x + 1)^2 + 2*(c*x - (c*x - 1)*log(c*x + 1))*log(-c*x + 1))/(c*x^3 - x^2), x)) - a^2/x","F",0
21,1,151,0,0.323360," ","integrate((a+b*arctanh(c*x))^2/x^3,x, algorithm=""maxima"")","\frac{1}{2} \, {\left({\left(c \log\left(c x + 1\right) - c \log\left(c x - 1\right) - \frac{2}{x}\right)} c - \frac{2 \, \operatorname{artanh}\left(c x\right)}{x^{2}}\right)} a b + \frac{1}{8} \, {\left({\left(2 \, {\left(\log\left(c x - 1\right) - 2\right)} \log\left(c x + 1\right) - \log\left(c x + 1\right)^{2} - \log\left(c x - 1\right)^{2} - 4 \, \log\left(c x - 1\right) + 8 \, \log\left(x\right)\right)} c^{2} + 4 \, {\left(c \log\left(c x + 1\right) - c \log\left(c x - 1\right) - \frac{2}{x}\right)} c \operatorname{artanh}\left(c x\right)\right)} b^{2} - \frac{b^{2} \operatorname{artanh}\left(c x\right)^{2}}{2 \, x^{2}} - \frac{a^{2}}{2 \, x^{2}}"," ",0,"1/2*((c*log(c*x + 1) - c*log(c*x - 1) - 2/x)*c - 2*arctanh(c*x)/x^2)*a*b + 1/8*((2*(log(c*x - 1) - 2)*log(c*x + 1) - log(c*x + 1)^2 - log(c*x - 1)^2 - 4*log(c*x - 1) + 8*log(x))*c^2 + 4*(c*log(c*x + 1) - c*log(c*x - 1) - 2/x)*c*arctanh(c*x))*b^2 - 1/2*b^2*arctanh(c*x)^2/x^2 - 1/2*a^2/x^2","B",0
22,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x))^2/x^4,x, algorithm=""maxima"")","-\frac{1}{3} \, {\left({\left(c^{2} \log\left(c^{2} x^{2} - 1\right) - c^{2} \log\left(x^{2}\right) + \frac{1}{x^{2}}\right)} c + \frac{2 \, \operatorname{artanh}\left(c x\right)}{x^{3}}\right)} a b - \frac{1}{12} \, b^{2} {\left(\frac{\log\left(-c x + 1\right)^{2}}{x^{3}} + 3 \, \int -\frac{3 \, {\left(c x - 1\right)} \log\left(c x + 1\right)^{2} + 2 \, {\left(c x - 3 \, {\left(c x - 1\right)} \log\left(c x + 1\right)\right)} \log\left(-c x + 1\right)}{3 \, {\left(c x^{5} - x^{4}\right)}}\,{d x}\right)} - \frac{a^{2}}{3 \, x^{3}}"," ",0,"-1/3*((c^2*log(c^2*x^2 - 1) - c^2*log(x^2) + 1/x^2)*c + 2*arctanh(c*x)/x^3)*a*b - 1/12*b^2*(log(-c*x + 1)^2/x^3 + 3*integrate(-1/3*(3*(c*x - 1)*log(c*x + 1)^2 + 2*(c*x - 3*(c*x - 1)*log(c*x + 1))*log(-c*x + 1))/(c*x^5 - x^4), x)) - 1/3*a^2/x^3","F",0
23,1,224,0,0.336848," ","integrate((a+b*arctanh(c*x))^2/x^5,x, algorithm=""maxima"")","\frac{1}{12} \, {\left({\left(3 \, c^{3} \log\left(c x + 1\right) - 3 \, c^{3} \log\left(c x - 1\right) - \frac{2 \, {\left(3 \, c^{2} x^{2} + 1\right)}}{x^{3}}\right)} c - \frac{6 \, \operatorname{artanh}\left(c x\right)}{x^{4}}\right)} a b + \frac{1}{48} \, {\left({\left(32 \, c^{2} \log\left(x\right) - \frac{3 \, c^{2} x^{2} \log\left(c x + 1\right)^{2} + 3 \, c^{2} x^{2} \log\left(c x - 1\right)^{2} + 16 \, c^{2} x^{2} \log\left(c x - 1\right) - 2 \, {\left(3 \, c^{2} x^{2} \log\left(c x - 1\right) - 8 \, c^{2} x^{2}\right)} \log\left(c x + 1\right) + 4}{x^{2}}\right)} c^{2} + 4 \, {\left(3 \, c^{3} \log\left(c x + 1\right) - 3 \, c^{3} \log\left(c x - 1\right) - \frac{2 \, {\left(3 \, c^{2} x^{2} + 1\right)}}{x^{3}}\right)} c \operatorname{artanh}\left(c x\right)\right)} b^{2} - \frac{b^{2} \operatorname{artanh}\left(c x\right)^{2}}{4 \, x^{4}} - \frac{a^{2}}{4 \, x^{4}}"," ",0,"1/12*((3*c^3*log(c*x + 1) - 3*c^3*log(c*x - 1) - 2*(3*c^2*x^2 + 1)/x^3)*c - 6*arctanh(c*x)/x^4)*a*b + 1/48*((32*c^2*log(x) - (3*c^2*x^2*log(c*x + 1)^2 + 3*c^2*x^2*log(c*x - 1)^2 + 16*c^2*x^2*log(c*x - 1) - 2*(3*c^2*x^2*log(c*x - 1) - 8*c^2*x^2)*log(c*x + 1) + 4)/x^2)*c^2 + 4*(3*c^3*log(c*x + 1) - 3*c^3*log(c*x - 1) - 2*(3*c^2*x^2 + 1)/x^3)*c*arctanh(c*x))*b^2 - 1/4*b^2*arctanh(c*x)^2/x^4 - 1/4*a^2/x^4","B",0
24,0,0,0,0.000000," ","integrate(x^5*(a+b*arctanh(c*x))^3,x, algorithm=""maxima"")","\frac{1}{2} \, a b^{2} x^{6} \operatorname{artanh}\left(c x\right)^{2} + \frac{1}{6} \, a^{3} x^{6} + \frac{1}{60} \, {\left(30 \, x^{6} \operatorname{artanh}\left(c x\right) + c {\left(\frac{2 \, {\left(3 \, c^{4} x^{5} + 5 \, c^{2} x^{3} + 15 \, x\right)}}{c^{6}} - \frac{15 \, \log\left(c x + 1\right)}{c^{7}} + \frac{15 \, \log\left(c x - 1\right)}{c^{7}}\right)}\right)} a^{2} b + \frac{1}{120} \, {\left(4 \, c {\left(\frac{2 \, {\left(3 \, c^{4} x^{5} + 5 \, c^{2} x^{3} + 15 \, x\right)}}{c^{6}} - \frac{15 \, \log\left(c x + 1\right)}{c^{7}} + \frac{15 \, \log\left(c x - 1\right)}{c^{7}}\right)} \operatorname{artanh}\left(c x\right) + \frac{6 \, c^{4} x^{4} + 32 \, c^{2} x^{2} - 2 \, {\left(15 \, \log\left(c x - 1\right) - 46\right)} \log\left(c x + 1\right) + 15 \, \log\left(c x + 1\right)^{2} + 15 \, \log\left(c x - 1\right)^{2} + 92 \, \log\left(c x - 1\right)}{c^{6}}\right)} a b^{2} - \frac{1}{1728000} \, {\left(500 \, c^{7} {\left(\frac{2 \, c^{4} x^{6} + 3 \, c^{2} x^{4} + 6 \, x^{2}}{c^{11}} + \frac{6 \, \log\left(c^{2} x^{2} - 1\right)}{c^{13}}\right)} + 728 \, c^{6} {\left(\frac{2 \, {\left(3 \, c^{4} x^{5} + 5 \, c^{2} x^{3} + 15 \, x\right)}}{c^{11}} - \frac{15 \, \log\left(c x + 1\right)}{c^{12}} + \frac{15 \, \log\left(c x - 1\right)}{c^{12}}\right)} + 1485 \, c^{5} {\left(\frac{c^{2} x^{4} + 2 \, x^{2}}{c^{9}} + \frac{2 \, \log\left(c^{2} x^{2} - 1\right)}{c^{11}}\right)} - 622080000 \, c^{5} \int \frac{x^{5} \log\left(c x + 1\right)}{3600 \, {\left(c^{7} x^{2} - c^{5}\right)}}\,{d x} + 9750 \, c^{4} {\left(\frac{2 \, {\left(c^{2} x^{3} + 3 \, x\right)}}{c^{9}} - \frac{3 \, \log\left(c x + 1\right)}{c^{10}} + \frac{3 \, \log\left(c x - 1\right)}{c^{10}}\right)} - 2700 \, c^{3} {\left(\frac{x^{2}}{c^{7}} + \frac{\log\left(c^{2} x^{2} - 1\right)}{c^{9}}\right)} - 1036800000 \, c^{3} \int \frac{x^{3} \log\left(c x + 1\right)}{3600 \, {\left(c^{7} x^{2} - c^{5}\right)}}\,{d x} + 227700 \, c^{2} {\left(\frac{2 \, x}{c^{7}} - \frac{\log\left(c x + 1\right)}{c^{8}} + \frac{\log\left(c x - 1\right)}{c^{8}}\right)} - 5495040000 \, c \int \frac{x \log\left(c x + 1\right)}{3600 \, {\left(c^{7} x^{2} - c^{5}\right)}}\,{d x} + \frac{1000 \, {\left(36 \, \log\left(-c x + 1\right)^{3} - 18 \, \log\left(-c x + 1\right)^{2} + 6 \, \log\left(-c x + 1\right) - 1\right)} {\left(c x - 1\right)}^{6} + 1728 \, {\left(125 \, \log\left(-c x + 1\right)^{3} - 75 \, \log\left(-c x + 1\right)^{2} + 30 \, \log\left(-c x + 1\right) - 6\right)} {\left(c x - 1\right)}^{5} + 16875 \, {\left(32 \, \log\left(-c x + 1\right)^{3} - 24 \, \log\left(-c x + 1\right)^{2} + 12 \, \log\left(-c x + 1\right) - 3\right)} {\left(c x - 1\right)}^{4} + 80000 \, {\left(9 \, \log\left(-c x + 1\right)^{3} - 9 \, \log\left(-c x + 1\right)^{2} + 6 \, \log\left(-c x + 1\right) - 2\right)} {\left(c x - 1\right)}^{3} + 135000 \, {\left(4 \, \log\left(-c x + 1\right)^{3} - 6 \, \log\left(-c x + 1\right)^{2} + 6 \, \log\left(-c x + 1\right) - 3\right)} {\left(c x - 1\right)}^{2} + 216000 \, {\left(\log\left(-c x + 1\right)^{3} - 3 \, \log\left(-c x + 1\right)^{2} + 6 \, \log\left(-c x + 1\right) - 6\right)} {\left(c x - 1\right)}}{c^{6}} - \frac{60 \, {\left(600 \, {\left(c^{6} x^{6} - 1\right)} \log\left(c x + 1\right)^{3} + 240 \, {\left(3 \, c^{5} x^{5} + 5 \, c^{3} x^{3} + 15 \, c x\right)} \log\left(c x + 1\right)^{2} - 30 \, {\left(10 \, c^{6} x^{6} - 12 \, c^{5} x^{5} + 15 \, c^{4} x^{4} - 20 \, c^{3} x^{3} + 30 \, c^{2} x^{2} - 60 \, c x - 60 \, {\left(c^{6} x^{6} - 1\right)} \log\left(c x + 1\right) + 37\right)} \log\left(-c x + 1\right)^{2} + {\left(100 \, c^{6} x^{6} + 264 \, c^{5} x^{5} - 165 \, c^{4} x^{4} + 1140 \, c^{3} x^{3} - 1230 \, c^{2} x^{2} - 1800 \, {\left(c^{6} x^{6} - 1\right)} \log\left(c x + 1\right)^{2} + 8820 \, c x - 480 \, {\left(3 \, c^{5} x^{5} + 5 \, c^{3} x^{3} + 15 \, c x + 23\right)} \log\left(c x + 1\right)\right)} \log\left(-c x + 1\right)\right)}}{c^{6}} + \frac{264600 \, \log\left(3600 \, c^{7} x^{2} - 3600 \, c^{5}\right)}{c^{6}} - 2384640000 \, \int \frac{\log\left(c x + 1\right)}{3600 \, {\left(c^{7} x^{2} - c^{5}\right)}}\,{d x}\right)} b^{3}"," ",0,"1/2*a*b^2*x^6*arctanh(c*x)^2 + 1/6*a^3*x^6 + 1/60*(30*x^6*arctanh(c*x) + c*(2*(3*c^4*x^5 + 5*c^2*x^3 + 15*x)/c^6 - 15*log(c*x + 1)/c^7 + 15*log(c*x - 1)/c^7))*a^2*b + 1/120*(4*c*(2*(3*c^4*x^5 + 5*c^2*x^3 + 15*x)/c^6 - 15*log(c*x + 1)/c^7 + 15*log(c*x - 1)/c^7)*arctanh(c*x) + (6*c^4*x^4 + 32*c^2*x^2 - 2*(15*log(c*x - 1) - 46)*log(c*x + 1) + 15*log(c*x + 1)^2 + 15*log(c*x - 1)^2 + 92*log(c*x - 1))/c^6)*a*b^2 - 1/1728000*(500*c^7*((2*c^4*x^6 + 3*c^2*x^4 + 6*x^2)/c^11 + 6*log(c^2*x^2 - 1)/c^13) + 728*c^6*(2*(3*c^4*x^5 + 5*c^2*x^3 + 15*x)/c^11 - 15*log(c*x + 1)/c^12 + 15*log(c*x - 1)/c^12) + 1485*c^5*((c^2*x^4 + 2*x^2)/c^9 + 2*log(c^2*x^2 - 1)/c^11) - 622080000*c^5*integrate(1/3600*x^5*log(c*x + 1)/(c^7*x^2 - c^5), x) + 9750*c^4*(2*(c^2*x^3 + 3*x)/c^9 - 3*log(c*x + 1)/c^10 + 3*log(c*x - 1)/c^10) - 2700*c^3*(x^2/c^7 + log(c^2*x^2 - 1)/c^9) - 1036800000*c^3*integrate(1/3600*x^3*log(c*x + 1)/(c^7*x^2 - c^5), x) + 227700*c^2*(2*x/c^7 - log(c*x + 1)/c^8 + log(c*x - 1)/c^8) - 5495040000*c*integrate(1/3600*x*log(c*x + 1)/(c^7*x^2 - c^5), x) + (1000*(36*log(-c*x + 1)^3 - 18*log(-c*x + 1)^2 + 6*log(-c*x + 1) - 1)*(c*x - 1)^6 + 1728*(125*log(-c*x + 1)^3 - 75*log(-c*x + 1)^2 + 30*log(-c*x + 1) - 6)*(c*x - 1)^5 + 16875*(32*log(-c*x + 1)^3 - 24*log(-c*x + 1)^2 + 12*log(-c*x + 1) - 3)*(c*x - 1)^4 + 80000*(9*log(-c*x + 1)^3 - 9*log(-c*x + 1)^2 + 6*log(-c*x + 1) - 2)*(c*x - 1)^3 + 135000*(4*log(-c*x + 1)^3 - 6*log(-c*x + 1)^2 + 6*log(-c*x + 1) - 3)*(c*x - 1)^2 + 216000*(log(-c*x + 1)^3 - 3*log(-c*x + 1)^2 + 6*log(-c*x + 1) - 6)*(c*x - 1))/c^6 - 60*(600*(c^6*x^6 - 1)*log(c*x + 1)^3 + 240*(3*c^5*x^5 + 5*c^3*x^3 + 15*c*x)*log(c*x + 1)^2 - 30*(10*c^6*x^6 - 12*c^5*x^5 + 15*c^4*x^4 - 20*c^3*x^3 + 30*c^2*x^2 - 60*c*x - 60*(c^6*x^6 - 1)*log(c*x + 1) + 37)*log(-c*x + 1)^2 + (100*c^6*x^6 + 264*c^5*x^5 - 165*c^4*x^4 + 1140*c^3*x^3 - 1230*c^2*x^2 - 1800*(c^6*x^6 - 1)*log(c*x + 1)^2 + 8820*c*x - 480*(3*c^5*x^5 + 5*c^3*x^3 + 15*c*x + 23)*log(c*x + 1))*log(-c*x + 1))/c^6 + 264600*log(3600*c^7*x^2 - 3600*c^5)/c^6 - 2384640000*integrate(1/3600*log(c*x + 1)/(c^7*x^2 - c^5), x))*b^3","F",0
25,0,0,0,0.000000," ","integrate(x^4*(a+b*arctanh(c*x))^3,x, algorithm=""maxima"")","\frac{1}{5} \, a^{3} x^{5} + \frac{3}{20} \, {\left(4 \, x^{5} \operatorname{artanh}\left(c x\right) + c {\left(\frac{c^{2} x^{4} + 2 \, x^{2}}{c^{4}} + \frac{2 \, \log\left(c^{2} x^{2} - 1\right)}{c^{6}}\right)}\right)} a^{2} b - \frac{2 \, {\left(b^{3} c^{5} x^{5} - b^{3}\right)} \log\left(-c x + 1\right)^{3} - 3 \, {\left(4 \, a b^{2} c^{5} x^{5} + b^{3} c^{4} x^{4} + 2 \, b^{3} c^{2} x^{2} + 2 \, {\left(b^{3} c^{5} x^{5} + b^{3}\right)} \log\left(c x + 1\right)\right)} \log\left(-c x + 1\right)^{2}}{80 \, c^{5}} - \int -\frac{5 \, {\left(b^{3} c^{5} x^{5} - b^{3} c^{4} x^{4}\right)} \log\left(c x + 1\right)^{3} + 30 \, {\left(a b^{2} c^{5} x^{5} - a b^{2} c^{4} x^{4}\right)} \log\left(c x + 1\right)^{2} - 3 \, {\left(4 \, a b^{2} c^{5} x^{5} + b^{3} c^{4} x^{4} + 2 \, b^{3} c^{2} x^{2} + 5 \, {\left(b^{3} c^{5} x^{5} - b^{3} c^{4} x^{4}\right)} \log\left(c x + 1\right)^{2} - 2 \, {\left(10 \, a b^{2} c^{4} x^{4} - {\left(10 \, a b^{2} c^{5} + b^{3} c^{5}\right)} x^{5} - b^{3}\right)} \log\left(c x + 1\right)\right)} \log\left(-c x + 1\right)}{40 \, {\left(c^{5} x - c^{4}\right)}}\,{d x}"," ",0,"1/5*a^3*x^5 + 3/20*(4*x^5*arctanh(c*x) + c*((c^2*x^4 + 2*x^2)/c^4 + 2*log(c^2*x^2 - 1)/c^6))*a^2*b - 1/80*(2*(b^3*c^5*x^5 - b^3)*log(-c*x + 1)^3 - 3*(4*a*b^2*c^5*x^5 + b^3*c^4*x^4 + 2*b^3*c^2*x^2 + 2*(b^3*c^5*x^5 + b^3)*log(c*x + 1))*log(-c*x + 1)^2)/c^5 - integrate(-1/40*(5*(b^3*c^5*x^5 - b^3*c^4*x^4)*log(c*x + 1)^3 + 30*(a*b^2*c^5*x^5 - a*b^2*c^4*x^4)*log(c*x + 1)^2 - 3*(4*a*b^2*c^5*x^5 + b^3*c^4*x^4 + 2*b^3*c^2*x^2 + 5*(b^3*c^5*x^5 - b^3*c^4*x^4)*log(c*x + 1)^2 - 2*(10*a*b^2*c^4*x^4 - (10*a*b^2*c^5 + b^3*c^5)*x^5 - b^3)*log(c*x + 1))*log(-c*x + 1))/(c^5*x - c^4), x)","F",0
26,0,0,0,0.000000," ","integrate(x^3*(a+b*arctanh(c*x))^3,x, algorithm=""maxima"")","\frac{3}{4} \, a b^{2} x^{4} \operatorname{artanh}\left(c x\right)^{2} + \frac{1}{4} \, a^{3} x^{4} + \frac{1}{8} \, {\left(6 \, x^{4} \operatorname{artanh}\left(c x\right) + c {\left(\frac{2 \, {\left(c^{2} x^{3} + 3 \, x\right)}}{c^{4}} - \frac{3 \, \log\left(c x + 1\right)}{c^{5}} + \frac{3 \, \log\left(c x - 1\right)}{c^{5}}\right)}\right)} a^{2} b + \frac{1}{16} \, {\left(4 \, c {\left(\frac{2 \, {\left(c^{2} x^{3} + 3 \, x\right)}}{c^{4}} - \frac{3 \, \log\left(c x + 1\right)}{c^{5}} + \frac{3 \, \log\left(c x - 1\right)}{c^{5}}\right)} \operatorname{artanh}\left(c x\right) + \frac{4 \, c^{2} x^{2} - 2 \, {\left(3 \, \log\left(c x - 1\right) - 8\right)} \log\left(c x + 1\right) + 3 \, \log\left(c x + 1\right)^{2} + 3 \, \log\left(c x - 1\right)^{2} + 16 \, \log\left(c x - 1\right)}{c^{4}}\right)} a b^{2} - \frac{1}{9216} \, {\left(27 \, c^{5} {\left(\frac{c^{2} x^{4} + 2 \, x^{2}}{c^{7}} + \frac{2 \, \log\left(c^{2} x^{2} - 1\right)}{c^{9}}\right)} + 74 \, c^{4} {\left(\frac{2 \, {\left(c^{2} x^{3} + 3 \, x\right)}}{c^{7}} - \frac{3 \, \log\left(c x + 1\right)}{c^{8}} + \frac{3 \, \log\left(c x - 1\right)}{c^{8}}\right)} + 60 \, c^{3} {\left(\frac{x^{2}}{c^{5}} + \frac{\log\left(c^{2} x^{2} - 1\right)}{c^{7}}\right)} - 221184 \, c^{3} \int \frac{x^{3} \log\left(c x + 1\right)}{96 \, {\left(c^{5} x^{2} - c^{3}\right)}}\,{d x} + 1692 \, c^{2} {\left(\frac{2 \, x}{c^{5}} - \frac{\log\left(c x + 1\right)}{c^{6}} + \frac{\log\left(c x - 1\right)}{c^{6}}\right)} - 1105920 \, c \int \frac{x \log\left(c x + 1\right)}{96 \, {\left(c^{5} x^{2} - c^{3}\right)}}\,{d x} + \frac{9 \, {\left(32 \, \log\left(-c x + 1\right)^{3} - 24 \, \log\left(-c x + 1\right)^{2} + 12 \, \log\left(-c x + 1\right) - 3\right)} {\left(c x - 1\right)}^{4} + 128 \, {\left(9 \, \log\left(-c x + 1\right)^{3} - 9 \, \log\left(-c x + 1\right)^{2} + 6 \, \log\left(-c x + 1\right) - 2\right)} {\left(c x - 1\right)}^{3} + 432 \, {\left(4 \, \log\left(-c x + 1\right)^{3} - 6 \, \log\left(-c x + 1\right)^{2} + 6 \, \log\left(-c x + 1\right) - 3\right)} {\left(c x - 1\right)}^{2} + 1152 \, {\left(\log\left(-c x + 1\right)^{3} - 3 \, \log\left(-c x + 1\right)^{2} + 6 \, \log\left(-c x + 1\right) - 6\right)} {\left(c x - 1\right)}}{c^{4}} - \frac{12 \, {\left(24 \, {\left(c^{4} x^{4} - 1\right)} \log\left(c x + 1\right)^{3} + 48 \, {\left(c^{3} x^{3} + 3 \, c x\right)} \log\left(c x + 1\right)^{2} - 6 \, {\left(3 \, c^{4} x^{4} - 4 \, c^{3} x^{3} + 6 \, c^{2} x^{2} - 12 \, c x - 12 \, {\left(c^{4} x^{4} - 1\right)} \log\left(c x + 1\right) + 7\right)} \log\left(-c x + 1\right)^{2} + {\left(9 \, c^{4} x^{4} + 28 \, c^{3} x^{3} - 18 \, c^{2} x^{2} - 72 \, {\left(c^{4} x^{4} - 1\right)} \log\left(c x + 1\right)^{2} + 300 \, c x - 96 \, {\left(c^{3} x^{3} + 3 \, c x + 4\right)} \log\left(c x + 1\right)\right)} \log\left(-c x + 1\right)\right)}}{c^{4}} + \frac{1800 \, \log\left(96 \, c^{5} x^{2} - 96 \, c^{3}\right)}{c^{4}} - 442368 \, \int \frac{\log\left(c x + 1\right)}{96 \, {\left(c^{5} x^{2} - c^{3}\right)}}\,{d x}\right)} b^{3}"," ",0,"3/4*a*b^2*x^4*arctanh(c*x)^2 + 1/4*a^3*x^4 + 1/8*(6*x^4*arctanh(c*x) + c*(2*(c^2*x^3 + 3*x)/c^4 - 3*log(c*x + 1)/c^5 + 3*log(c*x - 1)/c^5))*a^2*b + 1/16*(4*c*(2*(c^2*x^3 + 3*x)/c^4 - 3*log(c*x + 1)/c^5 + 3*log(c*x - 1)/c^5)*arctanh(c*x) + (4*c^2*x^2 - 2*(3*log(c*x - 1) - 8)*log(c*x + 1) + 3*log(c*x + 1)^2 + 3*log(c*x - 1)^2 + 16*log(c*x - 1))/c^4)*a*b^2 - 1/9216*(27*c^5*((c^2*x^4 + 2*x^2)/c^7 + 2*log(c^2*x^2 - 1)/c^9) + 74*c^4*(2*(c^2*x^3 + 3*x)/c^7 - 3*log(c*x + 1)/c^8 + 3*log(c*x - 1)/c^8) + 60*c^3*(x^2/c^5 + log(c^2*x^2 - 1)/c^7) - 221184*c^3*integrate(1/96*x^3*log(c*x + 1)/(c^5*x^2 - c^3), x) + 1692*c^2*(2*x/c^5 - log(c*x + 1)/c^6 + log(c*x - 1)/c^6) - 1105920*c*integrate(1/96*x*log(c*x + 1)/(c^5*x^2 - c^3), x) + (9*(32*log(-c*x + 1)^3 - 24*log(-c*x + 1)^2 + 12*log(-c*x + 1) - 3)*(c*x - 1)^4 + 128*(9*log(-c*x + 1)^3 - 9*log(-c*x + 1)^2 + 6*log(-c*x + 1) - 2)*(c*x - 1)^3 + 432*(4*log(-c*x + 1)^3 - 6*log(-c*x + 1)^2 + 6*log(-c*x + 1) - 3)*(c*x - 1)^2 + 1152*(log(-c*x + 1)^3 - 3*log(-c*x + 1)^2 + 6*log(-c*x + 1) - 6)*(c*x - 1))/c^4 - 12*(24*(c^4*x^4 - 1)*log(c*x + 1)^3 + 48*(c^3*x^3 + 3*c*x)*log(c*x + 1)^2 - 6*(3*c^4*x^4 - 4*c^3*x^3 + 6*c^2*x^2 - 12*c*x - 12*(c^4*x^4 - 1)*log(c*x + 1) + 7)*log(-c*x + 1)^2 + (9*c^4*x^4 + 28*c^3*x^3 - 18*c^2*x^2 - 72*(c^4*x^4 - 1)*log(c*x + 1)^2 + 300*c*x - 96*(c^3*x^3 + 3*c*x + 4)*log(c*x + 1))*log(-c*x + 1))/c^4 + 1800*log(96*c^5*x^2 - 96*c^3)/c^4 - 442368*integrate(1/96*log(c*x + 1)/(c^5*x^2 - c^3), x))*b^3","F",0
27,0,0,0,0.000000," ","integrate(x^2*(a+b*arctanh(c*x))^3,x, algorithm=""maxima"")","\frac{1}{3} \, a^{3} x^{3} + \frac{1}{2} \, {\left(2 \, x^{3} \operatorname{artanh}\left(c x\right) + c {\left(\frac{x^{2}}{c^{2}} + \frac{\log\left(c^{2} x^{2} - 1\right)}{c^{4}}\right)}\right)} a^{2} b - \frac{{\left(b^{3} c^{3} x^{3} - b^{3}\right)} \log\left(-c x + 1\right)^{3} - 3 \, {\left(2 \, a b^{2} c^{3} x^{3} + b^{3} c^{2} x^{2} + {\left(b^{3} c^{3} x^{3} + b^{3}\right)} \log\left(c x + 1\right)\right)} \log\left(-c x + 1\right)^{2}}{24 \, c^{3}} - \int -\frac{{\left(b^{3} c^{3} x^{3} - b^{3} c^{2} x^{2}\right)} \log\left(c x + 1\right)^{3} + 6 \, {\left(a b^{2} c^{3} x^{3} - a b^{2} c^{2} x^{2}\right)} \log\left(c x + 1\right)^{2} - {\left(4 \, a b^{2} c^{3} x^{3} + 2 \, b^{3} c^{2} x^{2} + 3 \, {\left(b^{3} c^{3} x^{3} - b^{3} c^{2} x^{2}\right)} \log\left(c x + 1\right)^{2} - 2 \, {\left(6 \, a b^{2} c^{2} x^{2} - {\left(6 \, a b^{2} c^{3} + b^{3} c^{3}\right)} x^{3} - b^{3}\right)} \log\left(c x + 1\right)\right)} \log\left(-c x + 1\right)}{8 \, {\left(c^{3} x - c^{2}\right)}}\,{d x}"," ",0,"1/3*a^3*x^3 + 1/2*(2*x^3*arctanh(c*x) + c*(x^2/c^2 + log(c^2*x^2 - 1)/c^4))*a^2*b - 1/24*((b^3*c^3*x^3 - b^3)*log(-c*x + 1)^3 - 3*(2*a*b^2*c^3*x^3 + b^3*c^2*x^2 + (b^3*c^3*x^3 + b^3)*log(c*x + 1))*log(-c*x + 1)^2)/c^3 - integrate(-1/8*((b^3*c^3*x^3 - b^3*c^2*x^2)*log(c*x + 1)^3 + 6*(a*b^2*c^3*x^3 - a*b^2*c^2*x^2)*log(c*x + 1)^2 - (4*a*b^2*c^3*x^3 + 2*b^3*c^2*x^2 + 3*(b^3*c^3*x^3 - b^3*c^2*x^2)*log(c*x + 1)^2 - 2*(6*a*b^2*c^2*x^2 - (6*a*b^2*c^3 + b^3*c^3)*x^3 - b^3)*log(c*x + 1))*log(-c*x + 1))/(c^3*x - c^2), x)","F",0
28,0,0,0,0.000000," ","integrate(x*(a+b*arctanh(c*x))^3,x, algorithm=""maxima"")","\frac{3}{2} \, a b^{2} x^{2} \operatorname{artanh}\left(c x\right)^{2} + \frac{1}{2} \, a^{3} x^{2} + \frac{3}{4} \, {\left(2 \, x^{2} \operatorname{artanh}\left(c x\right) + c {\left(\frac{2 \, x}{c^{2}} - \frac{\log\left(c x + 1\right)}{c^{3}} + \frac{\log\left(c x - 1\right)}{c^{3}}\right)}\right)} a^{2} b + \frac{3}{8} \, {\left(4 \, c {\left(\frac{2 \, x}{c^{2}} - \frac{\log\left(c x + 1\right)}{c^{3}} + \frac{\log\left(c x - 1\right)}{c^{3}}\right)} \operatorname{artanh}\left(c x\right) - \frac{2 \, {\left(\log\left(c x - 1\right) - 2\right)} \log\left(c x + 1\right) - \log\left(c x + 1\right)^{2} - \log\left(c x - 1\right)^{2} - 4 \, \log\left(c x - 1\right)}{c^{2}}\right)} a b^{2} - \frac{1}{64} \, {\left(3 \, c^{3} {\left(\frac{x^{2}}{c^{3}} + \frac{\log\left(c^{2} x^{2} - 1\right)}{c^{5}}\right)} + 21 \, c^{2} {\left(\frac{2 \, x}{c^{3}} - \frac{\log\left(c x + 1\right)}{c^{4}} + \frac{\log\left(c x - 1\right)}{c^{4}}\right)} - 576 \, c \int \frac{x \log\left(c x + 1\right)}{4 \, {\left(c^{3} x^{2} - c\right)}}\,{d x} - \frac{2 \, {\left(12 \, c x \log\left(c x + 1\right)^{2} + 2 \, {\left(c^{2} x^{2} - 1\right)} \log\left(c x + 1\right)^{3} - 3 \, {\left(c^{2} x^{2} - 2 \, c x - 2 \, {\left(c^{2} x^{2} - 1\right)} \log\left(c x + 1\right) + 1\right)} \log\left(-c x + 1\right)^{2} + 3 \, {\left(c^{2} x^{2} - 2 \, {\left(c^{2} x^{2} - 1\right)} \log\left(c x + 1\right)^{2} + 6 \, c x - 8 \, {\left(c x + 1\right)} \log\left(c x + 1\right)\right)} \log\left(-c x + 1\right)\right)}}{c^{2}} + \frac{{\left(4 \, \log\left(-c x + 1\right)^{3} - 6 \, \log\left(-c x + 1\right)^{2} + 6 \, \log\left(-c x + 1\right) - 3\right)} {\left(c x - 1\right)}^{2} + 8 \, {\left(\log\left(-c x + 1\right)^{3} - 3 \, \log\left(-c x + 1\right)^{2} + 6 \, \log\left(-c x + 1\right) - 6\right)} {\left(c x - 1\right)}}{c^{2}} + \frac{18 \, \log\left(4 \, c^{3} x^{2} - 4 \, c\right)}{c^{2}} - 192 \, \int \frac{\log\left(c x + 1\right)}{4 \, {\left(c^{3} x^{2} - c\right)}}\,{d x}\right)} b^{3}"," ",0,"3/2*a*b^2*x^2*arctanh(c*x)^2 + 1/2*a^3*x^2 + 3/4*(2*x^2*arctanh(c*x) + c*(2*x/c^2 - log(c*x + 1)/c^3 + log(c*x - 1)/c^3))*a^2*b + 3/8*(4*c*(2*x/c^2 - log(c*x + 1)/c^3 + log(c*x - 1)/c^3)*arctanh(c*x) - (2*(log(c*x - 1) - 2)*log(c*x + 1) - log(c*x + 1)^2 - log(c*x - 1)^2 - 4*log(c*x - 1))/c^2)*a*b^2 - 1/64*(3*c^3*(x^2/c^3 + log(c^2*x^2 - 1)/c^5) + 21*c^2*(2*x/c^3 - log(c*x + 1)/c^4 + log(c*x - 1)/c^4) - 576*c*integrate(1/4*x*log(c*x + 1)/(c^3*x^2 - c), x) - 2*(12*c*x*log(c*x + 1)^2 + 2*(c^2*x^2 - 1)*log(c*x + 1)^3 - 3*(c^2*x^2 - 2*c*x - 2*(c^2*x^2 - 1)*log(c*x + 1) + 1)*log(-c*x + 1)^2 + 3*(c^2*x^2 - 2*(c^2*x^2 - 1)*log(c*x + 1)^2 + 6*c*x - 8*(c*x + 1)*log(c*x + 1))*log(-c*x + 1))/c^2 + ((4*log(-c*x + 1)^3 - 6*log(-c*x + 1)^2 + 6*log(-c*x + 1) - 3)*(c*x - 1)^2 + 8*(log(-c*x + 1)^3 - 3*log(-c*x + 1)^2 + 6*log(-c*x + 1) - 6)*(c*x - 1))/c^2 + 18*log(4*c^3*x^2 - 4*c)/c^2 - 192*integrate(1/4*log(c*x + 1)/(c^3*x^2 - c), x))*b^3","F",0
29,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x))^3,x, algorithm=""maxima"")","a^{3} x + \frac{3 \, {\left(2 \, c x \operatorname{artanh}\left(c x\right) + \log\left(-c^{2} x^{2} + 1\right)\right)} a^{2} b}{2 \, c} - \frac{{\left(b^{3} c x - b^{3}\right)} \log\left(-c x + 1\right)^{3} - 3 \, {\left(2 \, a b^{2} c x + {\left(b^{3} c x + b^{3}\right)} \log\left(c x + 1\right)\right)} \log\left(-c x + 1\right)^{2}}{8 \, c} - \int -\frac{{\left(b^{3} c x - b^{3}\right)} \log\left(c x + 1\right)^{3} + 6 \, {\left(a b^{2} c x - a b^{2}\right)} \log\left(c x + 1\right)^{2} - 3 \, {\left(4 \, a b^{2} c x + {\left(b^{3} c x - b^{3}\right)} \log\left(c x + 1\right)^{2} - 2 \, {\left(2 \, a b^{2} - b^{3} - {\left(2 \, a b^{2} c + b^{3} c\right)} x\right)} \log\left(c x + 1\right)\right)} \log\left(-c x + 1\right)}{8 \, {\left(c x - 1\right)}}\,{d x}"," ",0,"a^3*x + 3/2*(2*c*x*arctanh(c*x) + log(-c^2*x^2 + 1))*a^2*b/c - 1/8*((b^3*c*x - b^3)*log(-c*x + 1)^3 - 3*(2*a*b^2*c*x + (b^3*c*x + b^3)*log(c*x + 1))*log(-c*x + 1)^2)/c - integrate(-1/8*((b^3*c*x - b^3)*log(c*x + 1)^3 + 6*(a*b^2*c*x - a*b^2)*log(c*x + 1)^2 - 3*(4*a*b^2*c*x + (b^3*c*x - b^3)*log(c*x + 1)^2 - 2*(2*a*b^2 - b^3 - (2*a*b^2*c + b^3*c)*x)*log(c*x + 1))*log(-c*x + 1))/(c*x - 1), x)","F",0
30,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x))^3/x,x, algorithm=""maxima"")","a^{3} \log\left(x\right) + \int \frac{b^{3} {\left(\log\left(c x + 1\right) - \log\left(-c x + 1\right)\right)}^{3}}{8 \, x} + \frac{3 \, a b^{2} {\left(\log\left(c x + 1\right) - \log\left(-c x + 1\right)\right)}^{2}}{4 \, x} + \frac{3 \, a^{2} b {\left(\log\left(c x + 1\right) - \log\left(-c x + 1\right)\right)}}{2 \, x}\,{d x}"," ",0,"a^3*log(x) + integrate(1/8*b^3*(log(c*x + 1) - log(-c*x + 1))^3/x + 3/4*a*b^2*(log(c*x + 1) - log(-c*x + 1))^2/x + 3/2*a^2*b*(log(c*x + 1) - log(-c*x + 1))/x, x)","F",0
31,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x))^3/x^2,x, algorithm=""maxima"")","-\frac{3}{2} \, {\left(c {\left(\log\left(c^{2} x^{2} - 1\right) - \log\left(x^{2}\right)\right)} + \frac{2 \, \operatorname{artanh}\left(c x\right)}{x}\right)} a^{2} b - \frac{a^{3}}{x} - \frac{{\left(b^{3} c x - b^{3}\right)} \log\left(-c x + 1\right)^{3} + 3 \, {\left(2 \, a b^{2} + {\left(b^{3} c x + b^{3}\right)} \log\left(c x + 1\right)\right)} \log\left(-c x + 1\right)^{2}}{8 \, x} - \int -\frac{{\left(b^{3} c x - b^{3}\right)} \log\left(c x + 1\right)^{3} + 6 \, {\left(a b^{2} c x - a b^{2}\right)} \log\left(c x + 1\right)^{2} + 3 \, {\left(4 \, a b^{2} c x - {\left(b^{3} c x - b^{3}\right)} \log\left(c x + 1\right)^{2} + 2 \, {\left(b^{3} c^{2} x^{2} + 2 \, a b^{2} - {\left(2 \, a b^{2} c - b^{3} c\right)} x\right)} \log\left(c x + 1\right)\right)} \log\left(-c x + 1\right)}{8 \, {\left(c x^{3} - x^{2}\right)}}\,{d x}"," ",0,"-3/2*(c*(log(c^2*x^2 - 1) - log(x^2)) + 2*arctanh(c*x)/x)*a^2*b - a^3/x - 1/8*((b^3*c*x - b^3)*log(-c*x + 1)^3 + 3*(2*a*b^2 + (b^3*c*x + b^3)*log(c*x + 1))*log(-c*x + 1)^2)/x - integrate(-1/8*((b^3*c*x - b^3)*log(c*x + 1)^3 + 6*(a*b^2*c*x - a*b^2)*log(c*x + 1)^2 + 3*(4*a*b^2*c*x - (b^3*c*x - b^3)*log(c*x + 1)^2 + 2*(b^3*c^2*x^2 + 2*a*b^2 - (2*a*b^2*c - b^3*c)*x)*log(c*x + 1))*log(-c*x + 1))/(c*x^3 - x^2), x)","F",0
32,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x))^3/x^3,x, algorithm=""maxima"")","\frac{3}{4} \, {\left({\left(c \log\left(c x + 1\right) - c \log\left(c x - 1\right) - \frac{2}{x}\right)} c - \frac{2 \, \operatorname{artanh}\left(c x\right)}{x^{2}}\right)} a^{2} b + \frac{3}{8} \, {\left({\left(2 \, {\left(\log\left(c x - 1\right) - 2\right)} \log\left(c x + 1\right) - \log\left(c x + 1\right)^{2} - \log\left(c x - 1\right)^{2} - 4 \, \log\left(c x - 1\right) + 8 \, \log\left(x\right)\right)} c^{2} + 4 \, {\left(c \log\left(c x + 1\right) - c \log\left(c x - 1\right) - \frac{2}{x}\right)} c \operatorname{artanh}\left(c x\right)\right)} a b^{2} - \frac{1}{16} \, b^{3} {\left(\frac{{\left(c^{2} x^{2} - 1\right)} \log\left(-c x + 1\right)^{3} + 3 \, {\left(2 \, c x - {\left(c^{2} x^{2} - 1\right)} \log\left(c x + 1\right)\right)} \log\left(-c x + 1\right)^{2}}{x^{2}} + 2 \, \int -\frac{{\left(c x - 1\right)} \log\left(c x + 1\right)^{3} + 3 \, {\left(2 \, c^{2} x^{2} - {\left(c x - 1\right)} \log\left(c x + 1\right)^{2} - {\left(c^{3} x^{3} - c x\right)} \log\left(c x + 1\right)\right)} \log\left(-c x + 1\right)}{c x^{4} - x^{3}}\,{d x}\right)} - \frac{3 \, a b^{2} \operatorname{artanh}\left(c x\right)^{2}}{2 \, x^{2}} - \frac{a^{3}}{2 \, x^{2}}"," ",0,"3/4*((c*log(c*x + 1) - c*log(c*x - 1) - 2/x)*c - 2*arctanh(c*x)/x^2)*a^2*b + 3/8*((2*(log(c*x - 1) - 2)*log(c*x + 1) - log(c*x + 1)^2 - log(c*x - 1)^2 - 4*log(c*x - 1) + 8*log(x))*c^2 + 4*(c*log(c*x + 1) - c*log(c*x - 1) - 2/x)*c*arctanh(c*x))*a*b^2 - 1/16*b^3*(((c^2*x^2 - 1)*log(-c*x + 1)^3 + 3*(2*c*x - (c^2*x^2 - 1)*log(c*x + 1))*log(-c*x + 1)^2)/x^2 + 2*integrate(-((c*x - 1)*log(c*x + 1)^3 + 3*(2*c^2*x^2 - (c*x - 1)*log(c*x + 1)^2 - (c^3*x^3 - c*x)*log(c*x + 1))*log(-c*x + 1))/(c*x^4 - x^3), x)) - 3/2*a*b^2*arctanh(c*x)^2/x^2 - 1/2*a^3/x^2","F",0
33,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x))^3/x^4,x, algorithm=""maxima"")","-\frac{1}{2} \, {\left({\left(c^{2} \log\left(c^{2} x^{2} - 1\right) - c^{2} \log\left(x^{2}\right) + \frac{1}{x^{2}}\right)} c + \frac{2 \, \operatorname{artanh}\left(c x\right)}{x^{3}}\right)} a^{2} b - \frac{a^{3}}{3 \, x^{3}} - \frac{{\left(b^{3} c^{3} x^{3} - b^{3}\right)} \log\left(-c x + 1\right)^{3} + 3 \, {\left(b^{3} c x + 2 \, a b^{2} + {\left(b^{3} c^{3} x^{3} + b^{3}\right)} \log\left(c x + 1\right)\right)} \log\left(-c x + 1\right)^{2}}{24 \, x^{3}} - \int -\frac{{\left(b^{3} c x - b^{3}\right)} \log\left(c x + 1\right)^{3} + 6 \, {\left(a b^{2} c x - a b^{2}\right)} \log\left(c x + 1\right)^{2} + {\left(2 \, b^{3} c^{2} x^{2} + 4 \, a b^{2} c x - 3 \, {\left(b^{3} c x - b^{3}\right)} \log\left(c x + 1\right)^{2} + 2 \, {\left(b^{3} c^{4} x^{4} + 6 \, a b^{2} - {\left(6 \, a b^{2} c - b^{3} c\right)} x\right)} \log\left(c x + 1\right)\right)} \log\left(-c x + 1\right)}{8 \, {\left(c x^{5} - x^{4}\right)}}\,{d x}"," ",0,"-1/2*((c^2*log(c^2*x^2 - 1) - c^2*log(x^2) + 1/x^2)*c + 2*arctanh(c*x)/x^3)*a^2*b - 1/3*a^3/x^3 - 1/24*((b^3*c^3*x^3 - b^3)*log(-c*x + 1)^3 + 3*(b^3*c*x + 2*a*b^2 + (b^3*c^3*x^3 + b^3)*log(c*x + 1))*log(-c*x + 1)^2)/x^3 - integrate(-1/8*((b^3*c*x - b^3)*log(c*x + 1)^3 + 6*(a*b^2*c*x - a*b^2)*log(c*x + 1)^2 + (2*b^3*c^2*x^2 + 4*a*b^2*c*x - 3*(b^3*c*x - b^3)*log(c*x + 1)^2 + 2*(b^3*c^4*x^4 + 6*a*b^2 - (6*a*b^2*c - b^3*c)*x)*log(c*x + 1))*log(-c*x + 1))/(c*x^5 - x^4), x)","F",0
34,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x))^3/x^5,x, algorithm=""maxima"")","\frac{1}{8} \, {\left({\left(3 \, c^{3} \log\left(c x + 1\right) - 3 \, c^{3} \log\left(c x - 1\right) - \frac{2 \, {\left(3 \, c^{2} x^{2} + 1\right)}}{x^{3}}\right)} c - \frac{6 \, \operatorname{artanh}\left(c x\right)}{x^{4}}\right)} a^{2} b + \frac{1}{16} \, {\left({\left(32 \, c^{2} \log\left(x\right) - \frac{3 \, c^{2} x^{2} \log\left(c x + 1\right)^{2} + 3 \, c^{2} x^{2} \log\left(c x - 1\right)^{2} + 16 \, c^{2} x^{2} \log\left(c x - 1\right) - 2 \, {\left(3 \, c^{2} x^{2} \log\left(c x - 1\right) - 8 \, c^{2} x^{2}\right)} \log\left(c x + 1\right) + 4}{x^{2}}\right)} c^{2} + 4 \, {\left(3 \, c^{3} \log\left(c x + 1\right) - 3 \, c^{3} \log\left(c x - 1\right) - \frac{2 \, {\left(3 \, c^{2} x^{2} + 1\right)}}{x^{3}}\right)} c \operatorname{artanh}\left(c x\right)\right)} a b^{2} - \frac{1}{32} \, b^{3} {\left(\frac{{\left(c^{4} x^{4} - 1\right)} \log\left(-c x + 1\right)^{3} + {\left(6 \, c^{3} x^{3} + 2 \, c x - 3 \, {\left(c^{4} x^{4} - 1\right)} \log\left(c x + 1\right)\right)} \log\left(-c x + 1\right)^{2}}{x^{4}} + 4 \, \int -\frac{2 \, {\left(c x - 1\right)} \log\left(c x + 1\right)^{3} + {\left(6 \, c^{4} x^{4} + 2 \, c^{2} x^{2} - 6 \, {\left(c x - 1\right)} \log\left(c x + 1\right)^{2} - 3 \, {\left(c^{5} x^{5} - c x\right)} \log\left(c x + 1\right)\right)} \log\left(-c x + 1\right)}{2 \, {\left(c x^{6} - x^{5}\right)}}\,{d x}\right)} - \frac{3 \, a b^{2} \operatorname{artanh}\left(c x\right)^{2}}{4 \, x^{4}} - \frac{a^{3}}{4 \, x^{4}}"," ",0,"1/8*((3*c^3*log(c*x + 1) - 3*c^3*log(c*x - 1) - 2*(3*c^2*x^2 + 1)/x^3)*c - 6*arctanh(c*x)/x^4)*a^2*b + 1/16*((32*c^2*log(x) - (3*c^2*x^2*log(c*x + 1)^2 + 3*c^2*x^2*log(c*x - 1)^2 + 16*c^2*x^2*log(c*x - 1) - 2*(3*c^2*x^2*log(c*x - 1) - 8*c^2*x^2)*log(c*x + 1) + 4)/x^2)*c^2 + 4*(3*c^3*log(c*x + 1) - 3*c^3*log(c*x - 1) - 2*(3*c^2*x^2 + 1)/x^3)*c*arctanh(c*x))*a*b^2 - 1/32*b^3*(((c^4*x^4 - 1)*log(-c*x + 1)^3 + (6*c^3*x^3 + 2*c*x - 3*(c^4*x^4 - 1)*log(c*x + 1))*log(-c*x + 1)^2)/x^4 + 4*integrate(-1/2*(2*(c*x - 1)*log(c*x + 1)^3 + (6*c^4*x^4 + 2*c^2*x^2 - 6*(c*x - 1)*log(c*x + 1)^2 - 3*(c^5*x^5 - c*x)*log(c*x + 1))*log(-c*x + 1))/(c*x^6 - x^5), x)) - 3/4*a*b^2*arctanh(c*x)^2/x^4 - 1/4*a^3/x^4","F",0
35,1,134,0,0.424386," ","integrate((d*x)^(5/2)*(a+b*arctanh(c*x)),x, algorithm=""maxima"")","\frac{10 \, \left(d x\right)^{\frac{7}{2}} a + {\left(10 \, \left(d x\right)^{\frac{7}{2}} \operatorname{artanh}\left(c x\right) - \frac{{\left(\frac{10 \, d^{5} \arctan\left(\frac{\sqrt{d x} c}{\sqrt{c d}}\right)}{\sqrt{c d} c^{4}} - \frac{5 \, d^{5} \log\left(\frac{\sqrt{d x} c - \sqrt{c d}}{\sqrt{d x} c + \sqrt{c d}}\right)}{\sqrt{c d} c^{4}} - \frac{4 \, {\left(\left(d x\right)^{\frac{5}{2}} c^{2} d^{2} + 5 \, \sqrt{d x} d^{4}\right)}}{c^{4}}\right)} c}{d}\right)} b}{35 \, d}"," ",0,"1/35*(10*(d*x)^(7/2)*a + (10*(d*x)^(7/2)*arctanh(c*x) - (10*d^5*arctan(sqrt(d*x)*c/sqrt(c*d))/(sqrt(c*d)*c^4) - 5*d^5*log((sqrt(d*x)*c - sqrt(c*d))/(sqrt(d*x)*c + sqrt(c*d)))/(sqrt(c*d)*c^4) - 4*((d*x)^(5/2)*c^2*d^2 + 5*sqrt(d*x)*d^4)/c^4)*c/d)*b)/d","A",0
36,1,118,0,0.429711," ","integrate((d*x)^(3/2)*(a+b*arctanh(c*x)),x, algorithm=""maxima"")","\frac{6 \, \left(d x\right)^{\frac{5}{2}} a + {\left(6 \, \left(d x\right)^{\frac{5}{2}} \operatorname{artanh}\left(c x\right) + \frac{{\left(\frac{4 \, \left(d x\right)^{\frac{3}{2}} d^{2}}{c^{2}} + \frac{6 \, d^{4} \arctan\left(\frac{\sqrt{d x} c}{\sqrt{c d}}\right)}{\sqrt{c d} c^{3}} + \frac{3 \, d^{4} \log\left(\frac{\sqrt{d x} c - \sqrt{c d}}{\sqrt{d x} c + \sqrt{c d}}\right)}{\sqrt{c d} c^{3}}\right)} c}{d}\right)} b}{15 \, d}"," ",0,"1/15*(6*(d*x)^(5/2)*a + (6*(d*x)^(5/2)*arctanh(c*x) + (4*(d*x)^(3/2)*d^2/c^2 + 6*d^4*arctan(sqrt(d*x)*c/sqrt(c*d))/(sqrt(c*d)*c^3) + 3*d^4*log((sqrt(d*x)*c - sqrt(c*d))/(sqrt(d*x)*c + sqrt(c*d)))/(sqrt(c*d)*c^3))*c/d)*b)/d","A",0
37,1,119,0,0.429784," ","integrate((d*x)^(1/2)*(a+b*arctanh(c*x)),x, algorithm=""maxima"")","\frac{2 \, \left(d x\right)^{\frac{3}{2}} a + {\left(2 \, \left(d x\right)^{\frac{3}{2}} \operatorname{artanh}\left(c x\right) - \frac{{\left(\frac{2 \, d^{3} \arctan\left(\frac{\sqrt{d x} c}{\sqrt{c d}}\right)}{\sqrt{c d} c^{2}} - \frac{d^{3} \log\left(\frac{\sqrt{d x} c - \sqrt{c d}}{\sqrt{d x} c + \sqrt{c d}}\right)}{\sqrt{c d} c^{2}} - \frac{4 \, \sqrt{d x} d^{2}}{c^{2}}\right)} c}{d}\right)} b}{3 \, d}"," ",0,"1/3*(2*(d*x)^(3/2)*a + (2*(d*x)^(3/2)*arctanh(c*x) - (2*d^3*arctan(sqrt(d*x)*c/sqrt(c*d))/(sqrt(c*d)*c^2) - d^3*log((sqrt(d*x)*c - sqrt(c*d))/(sqrt(d*x)*c + sqrt(c*d)))/(sqrt(c*d)*c^2) - 4*sqrt(d*x)*d^2/c^2)*c/d)*b)/d","A",0
38,1,103,0,0.428477," ","integrate((a+b*arctanh(c*x))/(d*x)^(1/2),x, algorithm=""maxima"")","\frac{{\left(2 \, \sqrt{d x} \operatorname{artanh}\left(c x\right) + \frac{{\left(\frac{2 \, d^{2} \arctan\left(\frac{\sqrt{d x} c}{\sqrt{c d}}\right)}{\sqrt{c d} c} + \frac{d^{2} \log\left(\frac{\sqrt{d x} c - \sqrt{c d}}{\sqrt{d x} c + \sqrt{c d}}\right)}{\sqrt{c d} c}\right)} c}{d}\right)} b + 2 \, \sqrt{d x} a}{d}"," ",0,"((2*sqrt(d*x)*arctanh(c*x) + (2*d^2*arctan(sqrt(d*x)*c/sqrt(c*d))/(sqrt(c*d)*c) + d^2*log((sqrt(d*x)*c - sqrt(c*d))/(sqrt(d*x)*c + sqrt(c*d)))/(sqrt(c*d)*c))*c/d)*b + 2*sqrt(d*x)*a)/d","A",0
39,1,94,0,0.433680," ","integrate((a+b*arctanh(c*x))/(d*x)^(3/2),x, algorithm=""maxima"")","\frac{b {\left(\frac{{\left(\frac{2 \, d \arctan\left(\frac{\sqrt{d x} c}{\sqrt{c d}}\right)}{\sqrt{c d}} - \frac{d \log\left(\frac{\sqrt{d x} c - \sqrt{c d}}{\sqrt{d x} c + \sqrt{c d}}\right)}{\sqrt{c d}}\right)} c}{d} - \frac{2 \, \operatorname{artanh}\left(c x\right)}{\sqrt{d x}}\right)} - \frac{2 \, a}{\sqrt{d x}}}{d}"," ",0,"(b*((2*d*arctan(sqrt(d*x)*c/sqrt(c*d))/sqrt(c*d) - d*log((sqrt(d*x)*c - sqrt(c*d))/(sqrt(d*x)*c + sqrt(c*d)))/sqrt(c*d))*c/d - 2*arctanh(c*x)/sqrt(d*x)) - 2*a/sqrt(d*x))/d","A",0
40,1,101,0,0.426932," ","integrate((a+b*arctanh(c*x))/(d*x)^(5/2),x, algorithm=""maxima"")","-\frac{b {\left(\frac{{\left(\frac{2 \, c \arctan\left(\frac{\sqrt{d x} c}{\sqrt{c d}}\right)}{\sqrt{c d}} + \frac{c \log\left(\frac{\sqrt{d x} c - \sqrt{c d}}{\sqrt{d x} c + \sqrt{c d}}\right)}{\sqrt{c d}} + \frac{4}{\sqrt{d x}}\right)} c}{d} + \frac{2 \, \operatorname{artanh}\left(c x\right)}{\left(d x\right)^{\frac{3}{2}}}\right)} + \frac{2 \, a}{\left(d x\right)^{\frac{3}{2}}}}{3 \, d}"," ",0,"-1/3*(b*((2*c*arctan(sqrt(d*x)*c/sqrt(c*d))/sqrt(c*d) + c*log((sqrt(d*x)*c - sqrt(c*d))/(sqrt(d*x)*c + sqrt(c*d)))/sqrt(c*d) + 4/sqrt(d*x))*c/d + 2*arctanh(c*x)/(d*x)^(3/2)) + 2*a/(d*x)^(3/2))/d","A",0
41,1,112,0,0.433748," ","integrate((a+b*arctanh(c*x))/(d*x)^(7/2),x, algorithm=""maxima"")","\frac{b {\left(\frac{{\left(\frac{6 \, c^{2} \arctan\left(\frac{\sqrt{d x} c}{\sqrt{c d}}\right)}{\sqrt{c d} d} - \frac{3 \, c^{2} \log\left(\frac{\sqrt{d x} c - \sqrt{c d}}{\sqrt{d x} c + \sqrt{c d}}\right)}{\sqrt{c d} d} - \frac{4}{\left(d x\right)^{\frac{3}{2}}}\right)} c}{d} - \frac{6 \, \operatorname{artanh}\left(c x\right)}{\left(d x\right)^{\frac{5}{2}}}\right)} - \frac{6 \, a}{\left(d x\right)^{\frac{5}{2}}}}{15 \, d}"," ",0,"1/15*(b*((6*c^2*arctan(sqrt(d*x)*c/sqrt(c*d))/(sqrt(c*d)*d) - 3*c^2*log((sqrt(d*x)*c - sqrt(c*d))/(sqrt(d*x)*c + sqrt(c*d)))/(sqrt(c*d)*d) - 4/(d*x)^(3/2))*c/d - 6*arctanh(c*x)/(d*x)^(5/2)) - 6*a/(d*x)^(5/2))/d","A",0
42,1,130,0,0.415173," ","integrate((a+b*arctanh(c*x))/(d*x)^(9/2),x, algorithm=""maxima"")","-\frac{b {\left(\frac{{\left(\frac{10 \, c^{3} \arctan\left(\frac{\sqrt{d x} c}{\sqrt{c d}}\right)}{\sqrt{c d} d^{2}} + \frac{5 \, c^{3} \log\left(\frac{\sqrt{d x} c - \sqrt{c d}}{\sqrt{d x} c + \sqrt{c d}}\right)}{\sqrt{c d} d^{2}} + \frac{4 \, {\left(5 \, c^{2} d^{2} x^{2} + d^{2}\right)}}{\left(d x\right)^{\frac{5}{2}} d^{2}}\right)} c}{d} + \frac{10 \, \operatorname{artanh}\left(c x\right)}{\left(d x\right)^{\frac{7}{2}}}\right)} + \frac{10 \, a}{\left(d x\right)^{\frac{7}{2}}}}{35 \, d}"," ",0,"-1/35*(b*((10*c^3*arctan(sqrt(d*x)*c/sqrt(c*d))/(sqrt(c*d)*d^2) + 5*c^3*log((sqrt(d*x)*c - sqrt(c*d))/(sqrt(d*x)*c + sqrt(c*d)))/(sqrt(c*d)*d^2) + 4*(5*c^2*d^2*x^2 + d^2)/((d*x)^(5/2)*d^2))*c/d + 10*arctanh(c*x)/(d*x)^(7/2)) + 10*a/(d*x)^(7/2))/d","A",0
43,0,0,0,0.000000," ","integrate((d*x)^m*(a+b*arctanh(c*x))^3,x, algorithm=""maxima"")","-\frac{b^{3} d^{m} x x^{m} \log\left(-c x + 1\right)^{3}}{8 \, {\left(m + 1\right)}} + \frac{\left(d x\right)^{m + 1} a^{3}}{d {\left(m + 1\right)}} + \int \frac{{\left(b^{3} c d^{m} {\left(m + 1\right)} x - b^{3} d^{m} {\left(m + 1\right)}\right)} x^{m} \log\left(c x + 1\right)^{3} + 6 \, {\left(a b^{2} c d^{m} {\left(m + 1\right)} x - a b^{2} d^{m} {\left(m + 1\right)}\right)} x^{m} \log\left(c x + 1\right)^{2} + 12 \, {\left(a^{2} b c d^{m} {\left(m + 1\right)} x - a^{2} b d^{m} {\left(m + 1\right)}\right)} x^{m} \log\left(c x + 1\right) + 3 \, {\left({\left(b^{3} c d^{m} {\left(m + 1\right)} x - b^{3} d^{m} {\left(m + 1\right)}\right)} x^{m} \log\left(c x + 1\right) - {\left(2 \, a b^{2} d^{m} {\left(m + 1\right)} - {\left(2 \, a b^{2} c d^{m} {\left(m + 1\right)} + b^{3} c d^{m}\right)} x\right)} x^{m}\right)} \log\left(-c x + 1\right)^{2} - 3 \, {\left({\left(b^{3} c d^{m} {\left(m + 1\right)} x - b^{3} d^{m} {\left(m + 1\right)}\right)} x^{m} \log\left(c x + 1\right)^{2} + 4 \, {\left(a b^{2} c d^{m} {\left(m + 1\right)} x - a b^{2} d^{m} {\left(m + 1\right)}\right)} x^{m} \log\left(c x + 1\right) + 4 \, {\left(a^{2} b c d^{m} {\left(m + 1\right)} x - a^{2} b d^{m} {\left(m + 1\right)}\right)} x^{m}\right)} \log\left(-c x + 1\right)}{8 \, {\left(c {\left(m + 1\right)} x - m - 1\right)}}\,{d x}"," ",0,"-1/8*b^3*d^m*x*x^m*log(-c*x + 1)^3/(m + 1) + (d*x)^(m + 1)*a^3/(d*(m + 1)) + integrate(1/8*((b^3*c*d^m*(m + 1)*x - b^3*d^m*(m + 1))*x^m*log(c*x + 1)^3 + 6*(a*b^2*c*d^m*(m + 1)*x - a*b^2*d^m*(m + 1))*x^m*log(c*x + 1)^2 + 12*(a^2*b*c*d^m*(m + 1)*x - a^2*b*d^m*(m + 1))*x^m*log(c*x + 1) + 3*((b^3*c*d^m*(m + 1)*x - b^3*d^m*(m + 1))*x^m*log(c*x + 1) - (2*a*b^2*d^m*(m + 1) - (2*a*b^2*c*d^m*(m + 1) + b^3*c*d^m)*x)*x^m)*log(-c*x + 1)^2 - 3*((b^3*c*d^m*(m + 1)*x - b^3*d^m*(m + 1))*x^m*log(c*x + 1)^2 + 4*(a*b^2*c*d^m*(m + 1)*x - a*b^2*d^m*(m + 1))*x^m*log(c*x + 1) + 4*(a^2*b*c*d^m*(m + 1)*x - a^2*b*d^m*(m + 1))*x^m)*log(-c*x + 1))/(c*(m + 1)*x - m - 1), x)","F",0
44,0,0,0,0.000000," ","integrate((d*x)^m*(a+b*arctanh(c*x))^2,x, algorithm=""maxima"")","\frac{b^{2} d^{m} x x^{m} \log\left(-c x + 1\right)^{2}}{4 \, {\left(m + 1\right)}} + \frac{\left(d x\right)^{m + 1} a^{2}}{d {\left(m + 1\right)}} - \int -\frac{{\left(b^{2} c d^{m} {\left(m + 1\right)} x - b^{2} d^{m} {\left(m + 1\right)}\right)} x^{m} \log\left(c x + 1\right)^{2} + 4 \, {\left(a b c d^{m} {\left(m + 1\right)} x - a b d^{m} {\left(m + 1\right)}\right)} x^{m} \log\left(c x + 1\right) - 2 \, {\left({\left(b^{2} c d^{m} {\left(m + 1\right)} x - b^{2} d^{m} {\left(m + 1\right)}\right)} x^{m} \log\left(c x + 1\right) - {\left(2 \, a b d^{m} {\left(m + 1\right)} - {\left(2 \, a b c d^{m} {\left(m + 1\right)} + b^{2} c d^{m}\right)} x\right)} x^{m}\right)} \log\left(-c x + 1\right)}{4 \, {\left(c {\left(m + 1\right)} x - m - 1\right)}}\,{d x}"," ",0,"1/4*b^2*d^m*x*x^m*log(-c*x + 1)^2/(m + 1) + (d*x)^(m + 1)*a^2/(d*(m + 1)) - integrate(-1/4*((b^2*c*d^m*(m + 1)*x - b^2*d^m*(m + 1))*x^m*log(c*x + 1)^2 + 4*(a*b*c*d^m*(m + 1)*x - a*b*d^m*(m + 1))*x^m*log(c*x + 1) - 2*((b^2*c*d^m*(m + 1)*x - b^2*d^m*(m + 1))*x^m*log(c*x + 1) - (2*a*b*d^m*(m + 1) - (2*a*b*c*d^m*(m + 1) + b^2*c*d^m)*x)*x^m)*log(-c*x + 1))/(c*(m + 1)*x - m - 1), x)","F",0
45,0,0,0,0.000000," ","integrate((d*x)^m*(a+b*arctanh(c*x)),x, algorithm=""maxima"")","\frac{1}{2} \, {\left(2 \, c d^{m} \int \frac{x x^{m}}{c^{2} {\left(m + 1\right)} x^{2} - m - 1}\,{d x} + \frac{d^{m} x x^{m} \log\left(c x + 1\right) - d^{m} x x^{m} \log\left(-c x + 1\right)}{m + 1}\right)} b + \frac{\left(d x\right)^{m + 1} a}{d {\left(m + 1\right)}}"," ",0,"1/2*(2*c*d^m*integrate(x*x^m/(c^2*(m + 1)*x^2 - m - 1), x) + (d^m*x*x^m*log(c*x + 1) - d^m*x*x^m*log(-c*x + 1))/(m + 1))*b + (d*x)^(m + 1)*a/(d*(m + 1))","F",0
46,0,0,0,0.000000," ","integrate((d*x)^m/(a+b*arctanh(c*x)),x, algorithm=""maxima"")","\int \frac{\left(d x\right)^{m}}{b \operatorname{artanh}\left(c x\right) + a}\,{d x}"," ",0,"integrate((d*x)^m/(b*arctanh(c*x) + a), x)","F",0
47,0,0,0,0.000000," ","integrate((d*x)^m/(a+b*arctanh(c*x))^2,x, algorithm=""maxima"")","\frac{2 \, {\left(c^{2} d^{m} x^{2} - d^{m}\right)} x^{m}}{b^{2} c \log\left(c x + 1\right) - b^{2} c \log\left(-c x + 1\right) + 2 \, a b c} + \int -\frac{2 \, {\left(c^{2} d^{m} {\left(m + 2\right)} x^{2} - d^{m} m\right)} x^{m}}{b^{2} c x \log\left(c x + 1\right) - b^{2} c x \log\left(-c x + 1\right) + 2 \, a b c x}\,{d x}"," ",0,"2*(c^2*d^m*x^2 - d^m)*x^m/(b^2*c*log(c*x + 1) - b^2*c*log(-c*x + 1) + 2*a*b*c) + integrate(-2*(c^2*d^m*(m + 2)*x^2 - d^m*m)*x^m/(b^2*c*x*log(c*x + 1) - b^2*c*x*log(-c*x + 1) + 2*a*b*c*x), x)","F",0
48,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x))^p,x, algorithm=""maxima"")","\int {\left(b \operatorname{artanh}\left(c x\right) + a\right)}^{p}\,{d x}"," ",0,"integrate((b*arctanh(c*x) + a)^p, x)","F",0
49,0,0,0,0.000000," ","integrate((d*x)^m*(a+b*arctanh(c*x))^p,x, algorithm=""maxima"")","\int \left(d x\right)^{m} {\left(b \operatorname{artanh}\left(c x\right) + a\right)}^{p}\,{d x}"," ",0,"integrate((d*x)^m*(b*arctanh(c*x) + a)^p, x)","F",0
50,1,69,0,0.314934," ","integrate(x^7*(a+b*arctanh(c*x^2)),x, algorithm=""maxima"")","\frac{1}{8} \, a x^{8} + \frac{1}{48} \, {\left(6 \, x^{8} \operatorname{artanh}\left(c x^{2}\right) + c {\left(\frac{2 \, {\left(c^{2} x^{6} + 3 \, x^{2}\right)}}{c^{4}} - \frac{3 \, \log\left(c x^{2} + 1\right)}{c^{5}} + \frac{3 \, \log\left(c x^{2} - 1\right)}{c^{5}}\right)}\right)} b"," ",0,"1/8*a*x^8 + 1/48*(6*x^8*arctanh(c*x^2) + c*(2*(c^2*x^6 + 3*x^2)/c^4 - 3*log(c*x^2 + 1)/c^5 + 3*log(c*x^2 - 1)/c^5))*b","A",0
51,1,46,0,0.317692," ","integrate(x^5*(a+b*arctanh(c*x^2)),x, algorithm=""maxima"")","\frac{1}{6} \, a x^{6} + \frac{1}{12} \, {\left(2 \, x^{6} \operatorname{artanh}\left(c x^{2}\right) + {\left(\frac{x^{4}}{c^{2}} + \frac{\log\left(c^{2} x^{4} - 1\right)}{c^{4}}\right)} c\right)} b"," ",0,"1/6*a*x^6 + 1/12*(2*x^6*arctanh(c*x^2) + (x^4/c^2 + log(c^2*x^4 - 1)/c^4)*c)*b","A",0
52,1,58,0,0.336697," ","integrate(x^3*(a+b*arctanh(c*x^2)),x, algorithm=""maxima"")","\frac{1}{4} \, a x^{4} + \frac{1}{8} \, {\left(2 \, x^{4} \operatorname{artanh}\left(c x^{2}\right) + c {\left(\frac{2 \, x^{2}}{c^{2}} - \frac{\log\left(c x^{2} + 1\right)}{c^{3}} + \frac{\log\left(c x^{2} - 1\right)}{c^{3}}\right)}\right)} b"," ",0,"1/4*a*x^4 + 1/8*(2*x^4*arctanh(c*x^2) + c*(2*x^2/c^2 - log(c*x^2 + 1)/c^3 + log(c*x^2 - 1)/c^3))*b","A",0
53,1,37,0,0.314982," ","integrate(x*(a+b*arctanh(c*x^2)),x, algorithm=""maxima"")","\frac{1}{2} \, a x^{2} + \frac{{\left(2 \, c x^{2} \operatorname{artanh}\left(c x^{2}\right) + \log\left(-c^{2} x^{4} + 1\right)\right)} b}{4 \, c}"," ",0,"1/2*a*x^2 + 1/4*(2*c*x^2*arctanh(c*x^2) + log(-c^2*x^4 + 1))*b/c","A",0
54,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x^2))/x,x, algorithm=""maxima"")","\frac{1}{2} \, b \int \frac{\log\left(c x^{2} + 1\right) - \log\left(-c x^{2} + 1\right)}{x}\,{d x} + a \log\left(x\right)"," ",0,"1/2*b*integrate((log(c*x^2 + 1) - log(-c*x^2 + 1))/x, x) + a*log(x)","F",0
55,1,41,0,0.312187," ","integrate((a+b*arctanh(c*x^2))/x^3,x, algorithm=""maxima"")","-\frac{1}{4} \, {\left(c {\left(\log\left(c^{2} x^{4} - 1\right) - \log\left(x^{4}\right)\right)} + \frac{2 \, \operatorname{artanh}\left(c x^{2}\right)}{x^{2}}\right)} b - \frac{a}{2 \, x^{2}}"," ",0,"-1/4*(c*(log(c^2*x^4 - 1) - log(x^4)) + 2*arctanh(c*x^2)/x^2)*b - 1/2*a/x^2","A",0
56,1,51,0,0.322091," ","integrate((a+b*arctanh(c*x^2))/x^5,x, algorithm=""maxima"")","\frac{1}{8} \, {\left({\left(c \log\left(c x^{2} + 1\right) - c \log\left(c x^{2} - 1\right) - \frac{2}{x^{2}}\right)} c - \frac{2 \, \operatorname{artanh}\left(c x^{2}\right)}{x^{4}}\right)} b - \frac{a}{4 \, x^{4}}"," ",0,"1/8*((c*log(c*x^2 + 1) - c*log(c*x^2 - 1) - 2/x^2)*c - 2*arctanh(c*x^2)/x^4)*b - 1/4*a/x^4","A",0
57,1,51,0,0.310163," ","integrate((a+b*arctanh(c*x^2))/x^7,x, algorithm=""maxima"")","-\frac{1}{12} \, {\left({\left(c^{2} \log\left(c^{2} x^{4} - 1\right) - c^{2} \log\left(x^{4}\right) + \frac{1}{x^{4}}\right)} c + \frac{2 \, \operatorname{artanh}\left(c x^{2}\right)}{x^{6}}\right)} b - \frac{a}{6 \, x^{6}}"," ",0,"-1/12*((c^2*log(c^2*x^4 - 1) - c^2*log(x^4) + 1/x^4)*c + 2*arctanh(c*x^2)/x^6)*b - 1/6*a/x^6","A",0
58,1,69,0,0.411484," ","integrate(x^4*(a+b*arctanh(c*x^2)),x, algorithm=""maxima"")","\frac{1}{5} \, a x^{5} + \frac{1}{30} \, {\left(6 \, x^{5} \operatorname{artanh}\left(c x^{2}\right) + c {\left(\frac{4 \, x^{3}}{c^{2}} + \frac{6 \, \arctan\left(\sqrt{c} x\right)}{c^{\frac{7}{2}}} + \frac{3 \, \log\left(\frac{c x - \sqrt{c}}{c x + \sqrt{c}}\right)}{c^{\frac{7}{2}}}\right)}\right)} b"," ",0,"1/5*a*x^5 + 1/30*(6*x^5*arctanh(c*x^2) + c*(4*x^3/c^2 + 6*arctan(sqrt(c)*x)/c^(7/2) + 3*log((c*x - sqrt(c))/(c*x + sqrt(c)))/c^(7/2)))*b","A",0
59,1,66,0,0.407500," ","integrate(x^2*(a+b*arctanh(c*x^2)),x, algorithm=""maxima"")","\frac{1}{3} \, a x^{3} + \frac{1}{6} \, {\left(2 \, x^{3} \operatorname{artanh}\left(c x^{2}\right) + c {\left(\frac{4 \, x}{c^{2}} - \frac{2 \, \arctan\left(\sqrt{c} x\right)}{c^{\frac{5}{2}}} + \frac{\log\left(\frac{c x - \sqrt{c}}{c x + \sqrt{c}}\right)}{c^{\frac{5}{2}}}\right)}\right)} b"," ",0,"1/3*a*x^3 + 1/6*(2*x^3*arctanh(c*x^2) + c*(4*x/c^2 - 2*arctan(sqrt(c)*x)/c^(5/2) + log((c*x - sqrt(c))/(c*x + sqrt(c)))/c^(5/2)))*b","A",0
60,1,55,0,0.401820," ","integrate(a+b*arctanh(c*x^2),x, algorithm=""maxima"")","\frac{1}{2} \, {\left(c {\left(\frac{2 \, \arctan\left(\sqrt{c} x\right)}{c^{\frac{3}{2}}} + \frac{\log\left(\frac{c x - \sqrt{c}}{c x + \sqrt{c}}\right)}{c^{\frac{3}{2}}}\right)} + 2 \, x \operatorname{artanh}\left(c x^{2}\right)\right)} b + a x"," ",0,"1/2*(c*(2*arctan(sqrt(c)*x)/c^(3/2) + log((c*x - sqrt(c))/(c*x + sqrt(c)))/c^(3/2)) + 2*x*arctanh(c*x^2))*b + a*x","A",0
61,1,61,0,0.412589," ","integrate((a+b*arctanh(c*x^2))/x^2,x, algorithm=""maxima"")","\frac{1}{2} \, {\left(c {\left(\frac{2 \, \arctan\left(\sqrt{c} x\right)}{\sqrt{c}} - \frac{\log\left(\frac{c x - \sqrt{c}}{c x + \sqrt{c}}\right)}{\sqrt{c}}\right)} - \frac{2 \, \operatorname{artanh}\left(c x^{2}\right)}{x}\right)} b - \frac{a}{x}"," ",0,"1/2*(c*(2*arctan(sqrt(c)*x)/sqrt(c) - log((c*x - sqrt(c))/(c*x + sqrt(c)))/sqrt(c)) - 2*arctanh(c*x^2)/x)*b - a/x","A",0
62,1,65,0,0.408762," ","integrate((a+b*arctanh(c*x^2))/x^4,x, algorithm=""maxima"")","-\frac{1}{6} \, {\left({\left(2 \, \sqrt{c} \arctan\left(\sqrt{c} x\right) + \sqrt{c} \log\left(\frac{c x - \sqrt{c}}{c x + \sqrt{c}}\right) + \frac{4}{x}\right)} c + \frac{2 \, \operatorname{artanh}\left(c x^{2}\right)}{x^{3}}\right)} b - \frac{a}{3 \, x^{3}}"," ",0,"-1/6*((2*sqrt(c)*arctan(sqrt(c)*x) + sqrt(c)*log((c*x - sqrt(c))/(c*x + sqrt(c))) + 4/x)*c + 2*arctanh(c*x^2)/x^3)*b - 1/3*a/x^3","A",0
63,1,66,0,0.404655," ","integrate((a+b*arctanh(c*x^2))/x^6,x, algorithm=""maxima"")","\frac{1}{30} \, {\left({\left(6 \, c^{\frac{3}{2}} \arctan\left(\sqrt{c} x\right) - 3 \, c^{\frac{3}{2}} \log\left(\frac{c x - \sqrt{c}}{c x + \sqrt{c}}\right) - \frac{4}{x^{3}}\right)} c - \frac{6 \, \operatorname{artanh}\left(c x^{2}\right)}{x^{5}}\right)} b - \frac{a}{5 \, x^{5}}"," ",0,"1/30*((6*c^(3/2)*arctan(sqrt(c)*x) - 3*c^(3/2)*log((c*x - sqrt(c))/(c*x + sqrt(c))) - 4/x^3)*c - 6*arctanh(c*x^2)/x^5)*b - 1/5*a/x^5","A",0
64,1,217,0,0.331634," ","integrate(x^7*(a+b*arctanh(c*x^2))^2,x, algorithm=""maxima"")","\frac{1}{8} \, b^{2} x^{8} \operatorname{artanh}\left(c x^{2}\right)^{2} + \frac{1}{8} \, a^{2} x^{8} + \frac{1}{24} \, {\left(6 \, x^{8} \operatorname{artanh}\left(c x^{2}\right) + c {\left(\frac{2 \, {\left(c^{2} x^{6} + 3 \, x^{2}\right)}}{c^{4}} - \frac{3 \, \log\left(c x^{2} + 1\right)}{c^{5}} + \frac{3 \, \log\left(c x^{2} - 1\right)}{c^{5}}\right)}\right)} a b + \frac{1}{96} \, {\left(4 \, c {\left(\frac{2 \, {\left(c^{2} x^{6} + 3 \, x^{2}\right)}}{c^{4}} - \frac{3 \, \log\left(c x^{2} + 1\right)}{c^{5}} + \frac{3 \, \log\left(c x^{2} - 1\right)}{c^{5}}\right)} \operatorname{artanh}\left(c x^{2}\right) + \frac{4 \, c^{2} x^{4} - 2 \, {\left(3 \, \log\left(c x^{2} - 1\right) - 8\right)} \log\left(c x^{2} + 1\right) + 3 \, \log\left(c x^{2} + 1\right)^{2} + 3 \, \log\left(c x^{2} - 1\right)^{2} + 16 \, \log\left(c x^{2} - 1\right)}{c^{4}}\right)} b^{2}"," ",0,"1/8*b^2*x^8*arctanh(c*x^2)^2 + 1/8*a^2*x^8 + 1/24*(6*x^8*arctanh(c*x^2) + c*(2*(c^2*x^6 + 3*x^2)/c^4 - 3*log(c*x^2 + 1)/c^5 + 3*log(c*x^2 - 1)/c^5))*a*b + 1/96*(4*c*(2*(c^2*x^6 + 3*x^2)/c^4 - 3*log(c*x^2 + 1)/c^5 + 3*log(c*x^2 - 1)/c^5)*arctanh(c*x^2) + (4*c^2*x^4 - 2*(3*log(c*x^2 - 1) - 8)*log(c*x^2 + 1) + 3*log(c*x^2 + 1)^2 + 3*log(c*x^2 - 1)^2 + 16*log(c*x^2 - 1))/c^4)*b^2","A",0
65,0,0,0,0.000000," ","integrate(x^5*(a+b*arctanh(c*x^2))^2,x, algorithm=""maxima"")","\frac{1}{6} \, a^{2} x^{6} + \frac{1}{6} \, {\left(2 \, x^{6} \operatorname{artanh}\left(c x^{2}\right) + {\left(\frac{x^{4}}{c^{2}} + \frac{\log\left(c^{2} x^{4} - 1\right)}{c^{4}}\right)} c\right)} a b + \frac{1}{432} \, {\left(18 \, x^{6} \log\left(-c x^{2} + 1\right)^{2} - 2 \, c^{4} {\left(\frac{2 \, {\left(c^{2} x^{6} + 3 \, x^{2}\right)}}{c^{6}} - \frac{3 \, \log\left(c x^{2} + 1\right)}{c^{7}} + \frac{3 \, \log\left(c x^{2} - 1\right)}{c^{7}}\right)} + 3 \, c^{3} {\left(\frac{x^{4}}{c^{4}} + \frac{\log\left(c^{2} x^{4} - 1\right)}{c^{6}}\right)} + 1296 \, c^{3} \int \frac{x^{7} \log\left(c x^{2} + 1\right)}{9 \, {\left(c^{4} x^{4} - c^{2}\right)}}\,{d x} - 9 \, c^{2} {\left(\frac{2 \, x^{2}}{c^{4}} - \frac{\log\left(c x^{2} + 1\right)}{c^{5}} + \frac{\log\left(c x^{2} - 1\right)}{c^{5}}\right)} - 6 \, c {\left(\frac{2 \, c^{2} x^{6} + 3 \, c x^{4} + 6 \, x^{2}}{c^{3}} + \frac{6 \, \log\left(c x^{2} - 1\right)}{c^{4}}\right)} \log\left(-c x^{2} + 1\right) + 648 \, c \int \frac{x^{3} \log\left(c x^{2} + 1\right)}{9 \, {\left(c^{4} x^{4} - c^{2}\right)}}\,{d x} + \frac{6 \, {\left(3 \, c^{3} x^{6} \log\left(c x^{2} + 1\right)^{2} + {\left(2 \, c^{3} x^{6} - 3 \, c^{2} x^{4} + 6 \, c x^{2} - 6 \, {\left(c^{3} x^{6} + 1\right)} \log\left(c x^{2} + 1\right)\right)} \log\left(-c x^{2} + 1\right)\right)}}{c^{3}} + \frac{4 \, c^{3} x^{6} + 15 \, c^{2} x^{4} + 66 \, c x^{2} + 18 \, \log\left(c x^{2} - 1\right)^{2} + 66 \, \log\left(c x^{2} - 1\right)}{c^{3}} - \frac{18 \, \log\left(9 \, c^{4} x^{4} - 9 \, c^{2}\right)}{c^{3}} + 648 \, \int \frac{x \log\left(c x^{2} + 1\right)}{9 \, {\left(c^{4} x^{4} - c^{2}\right)}}\,{d x}\right)} b^{2}"," ",0,"1/6*a^2*x^6 + 1/6*(2*x^6*arctanh(c*x^2) + (x^4/c^2 + log(c^2*x^4 - 1)/c^4)*c)*a*b + 1/432*(18*x^6*log(-c*x^2 + 1)^2 - 2*c^4*(2*(c^2*x^6 + 3*x^2)/c^6 - 3*log(c*x^2 + 1)/c^7 + 3*log(c*x^2 - 1)/c^7) + 3*c^3*(x^4/c^4 + log(c^2*x^4 - 1)/c^6) + 1296*c^3*integrate(1/9*x^7*log(c*x^2 + 1)/(c^4*x^4 - c^2), x) - 9*c^2*(2*x^2/c^4 - log(c*x^2 + 1)/c^5 + log(c*x^2 - 1)/c^5) - 6*c*((2*c^2*x^6 + 3*c*x^4 + 6*x^2)/c^3 + 6*log(c*x^2 - 1)/c^4)*log(-c*x^2 + 1) + 648*c*integrate(1/9*x^3*log(c*x^2 + 1)/(c^4*x^4 - c^2), x) + 6*(3*c^3*x^6*log(c*x^2 + 1)^2 + (2*c^3*x^6 - 3*c^2*x^4 + 6*c*x^2 - 6*(c^3*x^6 + 1)*log(c*x^2 + 1))*log(-c*x^2 + 1))/c^3 + (4*c^3*x^6 + 15*c^2*x^4 + 66*c*x^2 + 18*log(c*x^2 - 1)^2 + 66*log(c*x^2 - 1))/c^3 - 18*log(9*c^4*x^4 - 9*c^2)/c^3 + 648*integrate(1/9*x*log(c*x^2 + 1)/(c^4*x^4 - c^2), x))*b^2","F",0
66,1,186,0,0.325310," ","integrate(x^3*(a+b*arctanh(c*x^2))^2,x, algorithm=""maxima"")","\frac{1}{4} \, b^{2} x^{4} \operatorname{artanh}\left(c x^{2}\right)^{2} + \frac{1}{4} \, a^{2} x^{4} + \frac{1}{4} \, {\left(2 \, x^{4} \operatorname{artanh}\left(c x^{2}\right) + c {\left(\frac{2 \, x^{2}}{c^{2}} - \frac{\log\left(c x^{2} + 1\right)}{c^{3}} + \frac{\log\left(c x^{2} - 1\right)}{c^{3}}\right)}\right)} a b + \frac{1}{16} \, {\left(4 \, c {\left(\frac{2 \, x^{2}}{c^{2}} - \frac{\log\left(c x^{2} + 1\right)}{c^{3}} + \frac{\log\left(c x^{2} - 1\right)}{c^{3}}\right)} \operatorname{artanh}\left(c x^{2}\right) - \frac{2 \, {\left(\log\left(c x^{2} - 1\right) - 2\right)} \log\left(c x^{2} + 1\right) - \log\left(c x^{2} + 1\right)^{2} - \log\left(c x^{2} - 1\right)^{2} - 4 \, \log\left(c x^{2} - 1\right)}{c^{2}}\right)} b^{2}"," ",0,"1/4*b^2*x^4*arctanh(c*x^2)^2 + 1/4*a^2*x^4 + 1/4*(2*x^4*arctanh(c*x^2) + c*(2*x^2/c^2 - log(c*x^2 + 1)/c^3 + log(c*x^2 - 1)/c^3))*a*b + 1/16*(4*c*(2*x^2/c^2 - log(c*x^2 + 1)/c^3 + log(c*x^2 - 1)/c^3)*arctanh(c*x^2) - (2*(log(c*x^2 - 1) - 2)*log(c*x^2 + 1) - log(c*x^2 + 1)^2 - log(c*x^2 - 1)^2 - 4*log(c*x^2 - 1))/c^2)*b^2","B",0
67,0,0,0,0.000000," ","integrate(x*(a+b*arctanh(c*x^2))^2,x, algorithm=""maxima"")","\frac{1}{2} \, a^{2} x^{2} + \frac{1}{8} \, {\left(x^{2} \log\left(-c x^{2} + 1\right)^{2} - c^{2} {\left(\frac{2 \, x^{2}}{c^{2}} - \frac{\log\left(c x^{2} + 1\right)}{c^{3}} + \frac{\log\left(c x^{2} - 1\right)}{c^{3}}\right)} - 2 \, c {\left(\frac{x^{2}}{c} + \frac{\log\left(c x^{2} - 1\right)}{c^{2}}\right)} \log\left(-c x^{2} + 1\right) + 12 \, c \int \frac{x^{3} \log\left(c x^{2} + 1\right)}{c^{2} x^{4} - 1}\,{d x} + \frac{c x^{2} \log\left(c x^{2} + 1\right)^{2} + 2 \, {\left(c x^{2} - {\left(c x^{2} + 1\right)} \log\left(c x^{2} + 1\right)\right)} \log\left(-c x^{2} + 1\right)}{c} + \frac{2 \, c x^{2} + \log\left(c x^{2} - 1\right)^{2} + 2 \, \log\left(c x^{2} - 1\right)}{c} - \frac{\log\left(c^{2} x^{4} - 1\right)}{c} + 4 \, \int \frac{x \log\left(c x^{2} + 1\right)}{c^{2} x^{4} - 1}\,{d x}\right)} b^{2} + \frac{{\left(2 \, c x^{2} \operatorname{artanh}\left(c x^{2}\right) + \log\left(-c^{2} x^{4} + 1\right)\right)} a b}{2 \, c}"," ",0,"1/2*a^2*x^2 + 1/8*(x^2*log(-c*x^2 + 1)^2 - c^2*(2*x^2/c^2 - log(c*x^2 + 1)/c^3 + log(c*x^2 - 1)/c^3) - 2*c*(x^2/c + log(c*x^2 - 1)/c^2)*log(-c*x^2 + 1) + 12*c*integrate(x^3*log(c*x^2 + 1)/(c^2*x^4 - 1), x) + (c*x^2*log(c*x^2 + 1)^2 + 2*(c*x^2 - (c*x^2 + 1)*log(c*x^2 + 1))*log(-c*x^2 + 1))/c + (2*c*x^2 + log(c*x^2 - 1)^2 + 2*log(c*x^2 - 1))/c - log(c^2*x^4 - 1)/c + 4*integrate(x*log(c*x^2 + 1)/(c^2*x^4 - 1), x))*b^2 + 1/2*(2*c*x^2*arctanh(c*x^2) + log(-c^2*x^4 + 1))*a*b/c","F",0
68,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x^2))^2/x,x, algorithm=""maxima"")","a^{2} \log\left(x\right) + \int \frac{b^{2} {\left(\log\left(c x^{2} + 1\right) - \log\left(-c x^{2} + 1\right)\right)}^{2}}{4 \, x} + \frac{a b {\left(\log\left(c x^{2} + 1\right) - \log\left(-c x^{2} + 1\right)\right)}}{x}\,{d x}"," ",0,"a^2*log(x) + integrate(1/4*b^2*(log(c*x^2 + 1) - log(-c*x^2 + 1))^2/x + a*b*(log(c*x^2 + 1) - log(-c*x^2 + 1))/x, x)","F",0
69,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x^2))^2/x^3,x, algorithm=""maxima"")","-\frac{1}{2} \, {\left(c {\left(\log\left(c^{2} x^{4} - 1\right) - \log\left(x^{4}\right)\right)} + \frac{2 \, \operatorname{artanh}\left(c x^{2}\right)}{x^{2}}\right)} a b - \frac{1}{8} \, b^{2} {\left(\frac{\log\left(-c x^{2} + 1\right)^{2}}{x^{2}} + 2 \, \int -\frac{{\left(c x^{2} - 1\right)} \log\left(c x^{2} + 1\right)^{2} + 2 \, {\left(c x^{2} - {\left(c x^{2} - 1\right)} \log\left(c x^{2} + 1\right)\right)} \log\left(-c x^{2} + 1\right)}{c x^{5} - x^{3}}\,{d x}\right)} - \frac{a^{2}}{2 \, x^{2}}"," ",0,"-1/2*(c*(log(c^2*x^4 - 1) - log(x^4)) + 2*arctanh(c*x^2)/x^2)*a*b - 1/8*b^2*(log(-c*x^2 + 1)^2/x^2 + 2*integrate(-((c*x^2 - 1)*log(c*x^2 + 1)^2 + 2*(c*x^2 - (c*x^2 - 1)*log(c*x^2 + 1))*log(-c*x^2 + 1))/(c*x^5 - x^3), x)) - 1/2*a^2/x^2","F",0
70,1,175,0,0.327736," ","integrate((a+b*arctanh(c*x^2))^2/x^5,x, algorithm=""maxima"")","\frac{1}{4} \, {\left({\left(c \log\left(c x^{2} + 1\right) - c \log\left(c x^{2} - 1\right) - \frac{2}{x^{2}}\right)} c - \frac{2 \, \operatorname{artanh}\left(c x^{2}\right)}{x^{4}}\right)} a b + \frac{1}{16} \, {\left({\left(2 \, {\left(\log\left(c x^{2} - 1\right) - 2\right)} \log\left(c x^{2} + 1\right) - \log\left(c x^{2} + 1\right)^{2} - \log\left(c x^{2} - 1\right)^{2} - 4 \, \log\left(c x^{2} - 1\right) + 16 \, \log\left(x\right)\right)} c^{2} + 4 \, {\left(c \log\left(c x^{2} + 1\right) - c \log\left(c x^{2} - 1\right) - \frac{2}{x^{2}}\right)} c \operatorname{artanh}\left(c x^{2}\right)\right)} b^{2} - \frac{b^{2} \operatorname{artanh}\left(c x^{2}\right)^{2}}{4 \, x^{4}} - \frac{a^{2}}{4 \, x^{4}}"," ",0,"1/4*((c*log(c*x^2 + 1) - c*log(c*x^2 - 1) - 2/x^2)*c - 2*arctanh(c*x^2)/x^4)*a*b + 1/16*((2*(log(c*x^2 - 1) - 2)*log(c*x^2 + 1) - log(c*x^2 + 1)^2 - log(c*x^2 - 1)^2 - 4*log(c*x^2 - 1) + 16*log(x))*c^2 + 4*(c*log(c*x^2 + 1) - c*log(c*x^2 - 1) - 2/x^2)*c*arctanh(c*x^2))*b^2 - 1/4*b^2*arctanh(c*x^2)^2/x^4 - 1/4*a^2/x^4","B",0
71,0,0,0,0.000000," ","integrate(x^4*(a+b*arctanh(c*x^2))^2,x, algorithm=""maxima"")","\frac{1}{5} \, a^{2} x^{5} + \frac{1}{15} \, {\left(6 \, x^{5} \operatorname{artanh}\left(c x^{2}\right) + c {\left(\frac{4 \, x^{3}}{c^{2}} + \frac{6 \, \arctan\left(\sqrt{c} x\right)}{c^{\frac{7}{2}}} + \frac{3 \, \log\left(\frac{c x - \sqrt{c}}{c x + \sqrt{c}}\right)}{c^{\frac{7}{2}}}\right)}\right)} a b + \frac{1}{20} \, {\left(x^{5} \log\left(-c x^{2} + 1\right)^{2} - 5 \, \int -\frac{5 \, {\left(c x^{6} - x^{4}\right)} \log\left(c x^{2} + 1\right)^{2} - 2 \, {\left(2 \, c x^{6} + 5 \, {\left(c x^{6} - x^{4}\right)} \log\left(c x^{2} + 1\right)\right)} \log\left(-c x^{2} + 1\right)}{5 \, {\left(c x^{2} - 1\right)}}\,{d x}\right)} b^{2}"," ",0,"1/5*a^2*x^5 + 1/15*(6*x^5*arctanh(c*x^2) + c*(4*x^3/c^2 + 6*arctan(sqrt(c)*x)/c^(7/2) + 3*log((c*x - sqrt(c))/(c*x + sqrt(c)))/c^(7/2)))*a*b + 1/20*(x^5*log(-c*x^2 + 1)^2 - 5*integrate(-1/5*(5*(c*x^6 - x^4)*log(c*x^2 + 1)^2 - 2*(2*c*x^6 + 5*(c*x^6 - x^4)*log(c*x^2 + 1))*log(-c*x^2 + 1))/(c*x^2 - 1), x))*b^2","F",0
72,0,0,0,0.000000," ","integrate(x^2*(a+b*arctanh(c*x^2))^2,x, algorithm=""maxima"")","\frac{1}{3} \, a^{2} x^{3} + \frac{1}{3} \, {\left(2 \, x^{3} \operatorname{artanh}\left(c x^{2}\right) + c {\left(\frac{4 \, x}{c^{2}} - \frac{2 \, \arctan\left(\sqrt{c} x\right)}{c^{\frac{5}{2}}} + \frac{\log\left(\frac{c x - \sqrt{c}}{c x + \sqrt{c}}\right)}{c^{\frac{5}{2}}}\right)}\right)} a b + \frac{1}{12} \, {\left(x^{3} \log\left(-c x^{2} + 1\right)^{2} - 3 \, \int -\frac{3 \, {\left(c x^{4} - x^{2}\right)} \log\left(c x^{2} + 1\right)^{2} - 2 \, {\left(2 \, c x^{4} + 3 \, {\left(c x^{4} - x^{2}\right)} \log\left(c x^{2} + 1\right)\right)} \log\left(-c x^{2} + 1\right)}{3 \, {\left(c x^{2} - 1\right)}}\,{d x}\right)} b^{2}"," ",0,"1/3*a^2*x^3 + 1/3*(2*x^3*arctanh(c*x^2) + c*(4*x/c^2 - 2*arctan(sqrt(c)*x)/c^(5/2) + log((c*x - sqrt(c))/(c*x + sqrt(c)))/c^(5/2)))*a*b + 1/12*(x^3*log(-c*x^2 + 1)^2 - 3*integrate(-1/3*(3*(c*x^4 - x^2)*log(c*x^2 + 1)^2 - 2*(2*c*x^4 + 3*(c*x^4 - x^2)*log(c*x^2 + 1))*log(-c*x^2 + 1))/(c*x^2 - 1), x))*b^2","F",0
73,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x^2))^2,x, algorithm=""maxima"")","{\left(c {\left(\frac{2 \, \arctan\left(\sqrt{c} x\right)}{c^{\frac{3}{2}}} + \frac{\log\left(\frac{c x - \sqrt{c}}{c x + \sqrt{c}}\right)}{c^{\frac{3}{2}}}\right)} + 2 \, x \operatorname{artanh}\left(c x^{2}\right)\right)} a b + \frac{1}{4} \, {\left(x \log\left(-c x^{2} + 1\right)^{2} - \int -\frac{{\left(c x^{2} - 1\right)} \log\left(c x^{2} + 1\right)^{2} - 2 \, {\left(2 \, c x^{2} + {\left(c x^{2} - 1\right)} \log\left(c x^{2} + 1\right)\right)} \log\left(-c x^{2} + 1\right)}{c x^{2} - 1}\,{d x}\right)} b^{2} + a^{2} x"," ",0,"(c*(2*arctan(sqrt(c)*x)/c^(3/2) + log((c*x - sqrt(c))/(c*x + sqrt(c)))/c^(3/2)) + 2*x*arctanh(c*x^2))*a*b + 1/4*(x*log(-c*x^2 + 1)^2 - integrate(-((c*x^2 - 1)*log(c*x^2 + 1)^2 - 2*(2*c*x^2 + (c*x^2 - 1)*log(c*x^2 + 1))*log(-c*x^2 + 1))/(c*x^2 - 1), x))*b^2 + a^2*x","F",0
74,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x^2))^2/x^2,x, algorithm=""maxima"")","{\left(c {\left(\frac{2 \, \arctan\left(\sqrt{c} x\right)}{\sqrt{c}} - \frac{\log\left(\frac{c x - \sqrt{c}}{c x + \sqrt{c}}\right)}{\sqrt{c}}\right)} - \frac{2 \, \operatorname{artanh}\left(c x^{2}\right)}{x}\right)} a b - \frac{1}{4} \, b^{2} {\left(\frac{\log\left(-c x^{2} + 1\right)^{2}}{x} + \int -\frac{{\left(c x^{2} - 1\right)} \log\left(c x^{2} + 1\right)^{2} + 2 \, {\left(2 \, c x^{2} - {\left(c x^{2} - 1\right)} \log\left(c x^{2} + 1\right)\right)} \log\left(-c x^{2} + 1\right)}{c x^{4} - x^{2}}\,{d x}\right)} - \frac{a^{2}}{x}"," ",0,"(c*(2*arctan(sqrt(c)*x)/sqrt(c) - log((c*x - sqrt(c))/(c*x + sqrt(c)))/sqrt(c)) - 2*arctanh(c*x^2)/x)*a*b - 1/4*b^2*(log(-c*x^2 + 1)^2/x + integrate(-((c*x^2 - 1)*log(c*x^2 + 1)^2 + 2*(2*c*x^2 - (c*x^2 - 1)*log(c*x^2 + 1))*log(-c*x^2 + 1))/(c*x^4 - x^2), x)) - a^2/x","F",0
75,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x^2))^2/x^4,x, algorithm=""maxima"")","-\frac{1}{3} \, {\left({\left(2 \, \sqrt{c} \arctan\left(\sqrt{c} x\right) + \sqrt{c} \log\left(\frac{c x - \sqrt{c}}{c x + \sqrt{c}}\right) + \frac{4}{x}\right)} c + \frac{2 \, \operatorname{artanh}\left(c x^{2}\right)}{x^{3}}\right)} a b - \frac{1}{12} \, b^{2} {\left(\frac{\log\left(-c x^{2} + 1\right)^{2}}{x^{3}} + 3 \, \int -\frac{3 \, {\left(c x^{2} - 1\right)} \log\left(c x^{2} + 1\right)^{2} + 2 \, {\left(2 \, c x^{2} - 3 \, {\left(c x^{2} - 1\right)} \log\left(c x^{2} + 1\right)\right)} \log\left(-c x^{2} + 1\right)}{3 \, {\left(c x^{6} - x^{4}\right)}}\,{d x}\right)} - \frac{a^{2}}{3 \, x^{3}}"," ",0,"-1/3*((2*sqrt(c)*arctan(sqrt(c)*x) + sqrt(c)*log((c*x - sqrt(c))/(c*x + sqrt(c))) + 4/x)*c + 2*arctanh(c*x^2)/x^3)*a*b - 1/12*b^2*(log(-c*x^2 + 1)^2/x^3 + 3*integrate(-1/3*(3*(c*x^2 - 1)*log(c*x^2 + 1)^2 + 2*(2*c*x^2 - 3*(c*x^2 - 1)*log(c*x^2 + 1))*log(-c*x^2 + 1))/(c*x^6 - x^4), x)) - 1/3*a^2/x^3","F",0
76,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x^2))^2/x^6,x, algorithm=""maxima"")","\frac{1}{15} \, {\left({\left(6 \, c^{\frac{3}{2}} \arctan\left(\sqrt{c} x\right) - 3 \, c^{\frac{3}{2}} \log\left(\frac{c x - \sqrt{c}}{c x + \sqrt{c}}\right) - \frac{4}{x^{3}}\right)} c - \frac{6 \, \operatorname{artanh}\left(c x^{2}\right)}{x^{5}}\right)} a b - \frac{1}{20} \, b^{2} {\left(\frac{\log\left(-c x^{2} + 1\right)^{2}}{x^{5}} + 5 \, \int -\frac{5 \, {\left(c x^{2} - 1\right)} \log\left(c x^{2} + 1\right)^{2} + 2 \, {\left(2 \, c x^{2} - 5 \, {\left(c x^{2} - 1\right)} \log\left(c x^{2} + 1\right)\right)} \log\left(-c x^{2} + 1\right)}{5 \, {\left(c x^{8} - x^{6}\right)}}\,{d x}\right)} - \frac{a^{2}}{5 \, x^{5}}"," ",0,"1/15*((6*c^(3/2)*arctan(sqrt(c)*x) - 3*c^(3/2)*log((c*x - sqrt(c))/(c*x + sqrt(c))) - 4/x^3)*c - 6*arctanh(c*x^2)/x^5)*a*b - 1/20*b^2*(log(-c*x^2 + 1)^2/x^5 + 5*integrate(-1/5*(5*(c*x^2 - 1)*log(c*x^2 + 1)^2 + 2*(2*c*x^2 - 5*(c*x^2 - 1)*log(c*x^2 + 1))*log(-c*x^2 + 1))/(c*x^8 - x^6), x)) - 1/5*a^2/x^5","F",0
77,0,0,0,0.000000," ","integrate(x^3*(a+b*arctanh(c*x^2))^3,x, algorithm=""maxima"")","\frac{3}{4} \, a b^{2} x^{4} \operatorname{artanh}\left(c x^{2}\right)^{2} + \frac{1}{4} \, a^{3} x^{4} + \frac{3}{8} \, {\left(2 \, x^{4} \operatorname{artanh}\left(c x^{2}\right) + c {\left(\frac{2 \, x^{2}}{c^{2}} - \frac{\log\left(c x^{2} + 1\right)}{c^{3}} + \frac{\log\left(c x^{2} - 1\right)}{c^{3}}\right)}\right)} a^{2} b + \frac{3}{16} \, {\left(4 \, c {\left(\frac{2 \, x^{2}}{c^{2}} - \frac{\log\left(c x^{2} + 1\right)}{c^{3}} + \frac{\log\left(c x^{2} - 1\right)}{c^{3}}\right)} \operatorname{artanh}\left(c x^{2}\right) - \frac{2 \, {\left(\log\left(c x^{2} - 1\right) - 2\right)} \log\left(c x^{2} + 1\right) - \log\left(c x^{2} + 1\right)^{2} - \log\left(c x^{2} - 1\right)^{2} - 4 \, \log\left(c x^{2} - 1\right)}{c^{2}}\right)} a b^{2} - \frac{1}{128} \, {\left(4 \, x^{4} \log\left(-c x^{2} + 1\right)^{3} + 3 \, c^{3} {\left(\frac{x^{4}}{c^{3}} + \frac{\log\left(c^{2} x^{4} - 1\right)}{c^{5}}\right)} - 6 \, c {\left(\frac{c x^{4} + 2 \, x^{2}}{c^{2}} + \frac{2 \, \log\left(c x^{2} - 1\right)}{c^{3}}\right)} \log\left(-c x^{2} + 1\right)^{2} + 21 \, c^{2} {\left(\frac{2 \, x^{2}}{c^{3}} - \frac{\log\left(c x^{2} + 1\right)}{c^{4}} + \frac{\log\left(c x^{2} - 1\right)}{c^{4}}\right)} + c {\left(\frac{6 \, {\left(c^{2} x^{4} + 6 \, c x^{2} + 2 \, \log\left(c x^{2} - 1\right)^{2} + 6 \, \log\left(c x^{2} - 1\right)\right)} \log\left(-c x^{2} + 1\right)}{c^{3}} - \frac{3 \, c^{2} x^{4} + 42 \, c x^{2} + 4 \, \log\left(c x^{2} - 1\right)^{3} + 18 \, \log\left(c x^{2} - 1\right)^{2} + 42 \, \log\left(c x^{2} - 1\right)}{c^{3}}\right)} - 1152 \, c \int \frac{x^{3} \log\left(c x^{2} + 1\right)}{4 \, {\left(c^{3} x^{4} - c\right)}}\,{d x} - \frac{2 \, {\left(12 \, c x^{2} \log\left(c x^{2} + 1\right)^{2} + 2 \, {\left(c^{2} x^{4} - 1\right)} \log\left(c x^{2} + 1\right)^{3} - 3 \, {\left(c^{2} x^{4} - 2 \, c x^{2} - 2 \, {\left(c^{2} x^{4} - 1\right)} \log\left(c x^{2} + 1\right) + 1\right)} \log\left(-c x^{2} + 1\right)^{2} + 3 \, {\left(c^{2} x^{4} + 6 \, c x^{2} - 2 \, {\left(c^{2} x^{4} - 1\right)} \log\left(c x^{2} + 1\right)^{2} - 8 \, {\left(c x^{2} + 1\right)} \log\left(c x^{2} + 1\right)\right)} \log\left(-c x^{2} + 1\right)\right)}}{c^{2}} + \frac{18 \, \log\left(4 \, c^{3} x^{4} - 4 \, c\right)}{c^{2}} - 384 \, \int \frac{x \log\left(c x^{2} + 1\right)}{4 \, {\left(c^{3} x^{4} - c\right)}}\,{d x}\right)} b^{3}"," ",0,"3/4*a*b^2*x^4*arctanh(c*x^2)^2 + 1/4*a^3*x^4 + 3/8*(2*x^4*arctanh(c*x^2) + c*(2*x^2/c^2 - log(c*x^2 + 1)/c^3 + log(c*x^2 - 1)/c^3))*a^2*b + 3/16*(4*c*(2*x^2/c^2 - log(c*x^2 + 1)/c^3 + log(c*x^2 - 1)/c^3)*arctanh(c*x^2) - (2*(log(c*x^2 - 1) - 2)*log(c*x^2 + 1) - log(c*x^2 + 1)^2 - log(c*x^2 - 1)^2 - 4*log(c*x^2 - 1))/c^2)*a*b^2 - 1/128*(4*x^4*log(-c*x^2 + 1)^3 + 3*c^3*(x^4/c^3 + log(c^2*x^4 - 1)/c^5) - 6*c*((c*x^4 + 2*x^2)/c^2 + 2*log(c*x^2 - 1)/c^3)*log(-c*x^2 + 1)^2 + 21*c^2*(2*x^2/c^3 - log(c*x^2 + 1)/c^4 + log(c*x^2 - 1)/c^4) + c*(6*(c^2*x^4 + 6*c*x^2 + 2*log(c*x^2 - 1)^2 + 6*log(c*x^2 - 1))*log(-c*x^2 + 1)/c^3 - (3*c^2*x^4 + 42*c*x^2 + 4*log(c*x^2 - 1)^3 + 18*log(c*x^2 - 1)^2 + 42*log(c*x^2 - 1))/c^3) - 1152*c*integrate(1/4*x^3*log(c*x^2 + 1)/(c^3*x^4 - c), x) - 2*(12*c*x^2*log(c*x^2 + 1)^2 + 2*(c^2*x^4 - 1)*log(c*x^2 + 1)^3 - 3*(c^2*x^4 - 2*c*x^2 - 2*(c^2*x^4 - 1)*log(c*x^2 + 1) + 1)*log(-c*x^2 + 1)^2 + 3*(c^2*x^4 + 6*c*x^2 - 2*(c^2*x^4 - 1)*log(c*x^2 + 1)^2 - 8*(c*x^2 + 1)*log(c*x^2 + 1))*log(-c*x^2 + 1))/c^2 + 18*log(4*c^3*x^4 - 4*c)/c^2 - 384*integrate(1/4*x*log(c*x^2 + 1)/(c^3*x^4 - c), x))*b^3","F",0
78,0,0,0,0.000000," ","integrate(x*(a+b*arctanh(c*x^2))^3,x, algorithm=""maxima"")","\frac{1}{2} \, a^{3} x^{2} + \frac{3 \, {\left(2 \, c x^{2} \operatorname{artanh}\left(c x^{2}\right) + \log\left(-c^{2} x^{4} + 1\right)\right)} a^{2} b}{4 \, c} - \frac{{\left(b^{3} c x^{2} - b^{3}\right)} \log\left(-c x^{2} + 1\right)^{3} - 3 \, {\left(2 \, a b^{2} c x^{2} + {\left(b^{3} c x^{2} + b^{3}\right)} \log\left(c x^{2} + 1\right)\right)} \log\left(-c x^{2} + 1\right)^{2}}{16 \, c} - \int -\frac{{\left(b^{3} c x^{3} - b^{3} x\right)} \log\left(c x^{2} + 1\right)^{3} + 6 \, {\left(a b^{2} c x^{3} - a b^{2} x\right)} \log\left(c x^{2} + 1\right)^{2} - 3 \, {\left(4 \, a b^{2} c x^{3} + {\left(b^{3} c x^{3} - b^{3} x\right)} \log\left(c x^{2} + 1\right)^{2} + 2 \, {\left({\left(2 \, a b^{2} c + b^{3} c\right)} x^{3} - {\left(2 \, a b^{2} - b^{3}\right)} x\right)} \log\left(c x^{2} + 1\right)\right)} \log\left(-c x^{2} + 1\right)}{8 \, {\left(c x^{2} - 1\right)}}\,{d x}"," ",0,"1/2*a^3*x^2 + 3/4*(2*c*x^2*arctanh(c*x^2) + log(-c^2*x^4 + 1))*a^2*b/c - 1/16*((b^3*c*x^2 - b^3)*log(-c*x^2 + 1)^3 - 3*(2*a*b^2*c*x^2 + (b^3*c*x^2 + b^3)*log(c*x^2 + 1))*log(-c*x^2 + 1)^2)/c - integrate(-1/8*((b^3*c*x^3 - b^3*x)*log(c*x^2 + 1)^3 + 6*(a*b^2*c*x^3 - a*b^2*x)*log(c*x^2 + 1)^2 - 3*(4*a*b^2*c*x^3 + (b^3*c*x^3 - b^3*x)*log(c*x^2 + 1)^2 + 2*((2*a*b^2*c + b^3*c)*x^3 - (2*a*b^2 - b^3)*x)*log(c*x^2 + 1))*log(-c*x^2 + 1))/(c*x^2 - 1), x)","F",0
79,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x^2))^3/x,x, algorithm=""maxima"")","a^{3} \log\left(x\right) + \int \frac{b^{3} {\left(\log\left(c x^{2} + 1\right) - \log\left(-c x^{2} + 1\right)\right)}^{3}}{8 \, x} + \frac{3 \, a b^{2} {\left(\log\left(c x^{2} + 1\right) - \log\left(-c x^{2} + 1\right)\right)}^{2}}{4 \, x} + \frac{3 \, a^{2} b {\left(\log\left(c x^{2} + 1\right) - \log\left(-c x^{2} + 1\right)\right)}}{2 \, x}\,{d x}"," ",0,"a^3*log(x) + integrate(1/8*b^3*(log(c*x^2 + 1) - log(-c*x^2 + 1))^3/x + 3/4*a*b^2*(log(c*x^2 + 1) - log(-c*x^2 + 1))^2/x + 3/2*a^2*b*(log(c*x^2 + 1) - log(-c*x^2 + 1))/x, x)","F",0
80,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x^2))^3/x^3,x, algorithm=""maxima"")","-\frac{3}{4} \, {\left(c {\left(\log\left(c^{2} x^{4} - 1\right) - \log\left(x^{4}\right)\right)} + \frac{2 \, \operatorname{artanh}\left(c x^{2}\right)}{x^{2}}\right)} a^{2} b - \frac{a^{3}}{2 \, x^{2}} - \frac{{\left(b^{3} c x^{2} - b^{3}\right)} \log\left(-c x^{2} + 1\right)^{3} + 3 \, {\left(2 \, a b^{2} + {\left(b^{3} c x^{2} + b^{3}\right)} \log\left(c x^{2} + 1\right)\right)} \log\left(-c x^{2} + 1\right)^{2}}{16 \, x^{2}} - \int -\frac{{\left(b^{3} c x^{2} - b^{3}\right)} \log\left(c x^{2} + 1\right)^{3} + 6 \, {\left(a b^{2} c x^{2} - a b^{2}\right)} \log\left(c x^{2} + 1\right)^{2} + 3 \, {\left(4 \, a b^{2} c x^{2} - {\left(b^{3} c x^{2} - b^{3}\right)} \log\left(c x^{2} + 1\right)^{2} + 2 \, {\left(b^{3} c^{2} x^{4} + 2 \, a b^{2} - {\left(2 \, a b^{2} c - b^{3} c\right)} x^{2}\right)} \log\left(c x^{2} + 1\right)\right)} \log\left(-c x^{2} + 1\right)}{8 \, {\left(c x^{5} - x^{3}\right)}}\,{d x}"," ",0,"-3/4*(c*(log(c^2*x^4 - 1) - log(x^4)) + 2*arctanh(c*x^2)/x^2)*a^2*b - 1/2*a^3/x^2 - 1/16*((b^3*c*x^2 - b^3)*log(-c*x^2 + 1)^3 + 3*(2*a*b^2 + (b^3*c*x^2 + b^3)*log(c*x^2 + 1))*log(-c*x^2 + 1)^2)/x^2 - integrate(-1/8*((b^3*c*x^2 - b^3)*log(c*x^2 + 1)^3 + 6*(a*b^2*c*x^2 - a*b^2)*log(c*x^2 + 1)^2 + 3*(4*a*b^2*c*x^2 - (b^3*c*x^2 - b^3)*log(c*x^2 + 1)^2 + 2*(b^3*c^2*x^4 + 2*a*b^2 - (2*a*b^2*c - b^3*c)*x^2)*log(c*x^2 + 1))*log(-c*x^2 + 1))/(c*x^5 - x^3), x)","F",0
81,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x^2))^3/x^5,x, algorithm=""maxima"")","\frac{3}{8} \, {\left({\left(c \log\left(c x^{2} + 1\right) - c \log\left(c x^{2} - 1\right) - \frac{2}{x^{2}}\right)} c - \frac{2 \, \operatorname{artanh}\left(c x^{2}\right)}{x^{4}}\right)} a^{2} b + \frac{3}{16} \, {\left({\left(2 \, {\left(\log\left(c x^{2} - 1\right) - 2\right)} \log\left(c x^{2} + 1\right) - \log\left(c x^{2} + 1\right)^{2} - \log\left(c x^{2} - 1\right)^{2} - 4 \, \log\left(c x^{2} - 1\right) + 16 \, \log\left(x\right)\right)} c^{2} + 4 \, {\left(c \log\left(c x^{2} + 1\right) - c \log\left(c x^{2} - 1\right) - \frac{2}{x^{2}}\right)} c \operatorname{artanh}\left(c x^{2}\right)\right)} a b^{2} - \frac{1}{32} \, b^{3} {\left(\frac{{\left(c^{2} x^{4} - 1\right)} \log\left(-c x^{2} + 1\right)^{3} + 3 \, {\left(2 \, c x^{2} - {\left(c^{2} x^{4} - 1\right)} \log\left(c x^{2} + 1\right)\right)} \log\left(-c x^{2} + 1\right)^{2}}{x^{4}} + 4 \, \int -\frac{{\left(c x^{2} - 1\right)} \log\left(c x^{2} + 1\right)^{3} + 3 \, {\left(2 \, c^{2} x^{4} - {\left(c x^{2} - 1\right)} \log\left(c x^{2} + 1\right)^{2} - {\left(c^{3} x^{6} - c x^{2}\right)} \log\left(c x^{2} + 1\right)\right)} \log\left(-c x^{2} + 1\right)}{c x^{7} - x^{5}}\,{d x}\right)} - \frac{3 \, a b^{2} \operatorname{artanh}\left(c x^{2}\right)^{2}}{4 \, x^{4}} - \frac{a^{3}}{4 \, x^{4}}"," ",0,"3/8*((c*log(c*x^2 + 1) - c*log(c*x^2 - 1) - 2/x^2)*c - 2*arctanh(c*x^2)/x^4)*a^2*b + 3/16*((2*(log(c*x^2 - 1) - 2)*log(c*x^2 + 1) - log(c*x^2 + 1)^2 - log(c*x^2 - 1)^2 - 4*log(c*x^2 - 1) + 16*log(x))*c^2 + 4*(c*log(c*x^2 + 1) - c*log(c*x^2 - 1) - 2/x^2)*c*arctanh(c*x^2))*a*b^2 - 1/32*b^3*(((c^2*x^4 - 1)*log(-c*x^2 + 1)^3 + 3*(2*c*x^2 - (c^2*x^4 - 1)*log(c*x^2 + 1))*log(-c*x^2 + 1)^2)/x^4 + 4*integrate(-((c*x^2 - 1)*log(c*x^2 + 1)^3 + 3*(2*c^2*x^4 - (c*x^2 - 1)*log(c*x^2 + 1)^2 - (c^3*x^6 - c*x^2)*log(c*x^2 + 1))*log(-c*x^2 + 1))/(c*x^7 - x^5), x)) - 3/4*a*b^2*arctanh(c*x^2)^2/x^4 - 1/4*a^3/x^4","F",0
82,1,316,0,0.421913," ","integrate((d*x)^(5/2)*(a+b*arctanh(c*x^2)),x, algorithm=""maxima"")","\frac{12 \, \left(d x\right)^{\frac{7}{2}} a + {\left(12 \, \left(d x\right)^{\frac{7}{2}} \operatorname{artanh}\left(c x^{2}\right) - \frac{{\left(\frac{3 \, d^{6} {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} c^{\frac{1}{4}} \sqrt{d} + 2 \, \sqrt{d x} \sqrt{c}\right)}}{2 \, \sqrt{\sqrt{c} d}}\right)}{\sqrt{\sqrt{c} d} \sqrt{c}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} c^{\frac{1}{4}} \sqrt{d} - 2 \, \sqrt{d x} \sqrt{c}\right)}}{2 \, \sqrt{\sqrt{c} d}}\right)}{\sqrt{\sqrt{c} d} \sqrt{c}} - \frac{\sqrt{2} \log\left(\sqrt{c} d x + \sqrt{2} \sqrt{d x} c^{\frac{1}{4}} \sqrt{d} + d\right)}{c^{\frac{3}{4}} \sqrt{d}} + \frac{\sqrt{2} \log\left(\sqrt{c} d x - \sqrt{2} \sqrt{d x} c^{\frac{1}{4}} \sqrt{d} + d\right)}{c^{\frac{3}{4}} \sqrt{d}}\right)}}{c^{2}} - \frac{6 \, d^{6} {\left(\frac{2 \, \arctan\left(\frac{\sqrt{d x} \sqrt{c}}{\sqrt{\sqrt{c} d}}\right)}{\sqrt{\sqrt{c} d} \sqrt{c}} + \frac{\log\left(\frac{\sqrt{d x} \sqrt{c} - \sqrt{\sqrt{c} d}}{\sqrt{d x} \sqrt{c} + \sqrt{\sqrt{c} d}}\right)}{\sqrt{\sqrt{c} d} \sqrt{c}}\right)}}{c^{2}} - \frac{16 \, \left(d x\right)^{\frac{3}{2}} d^{4}}{c^{2}}\right)} c}{d^{2}}\right)} b}{42 \, d}"," ",0,"1/42*(12*(d*x)^(7/2)*a + (12*(d*x)^(7/2)*arctanh(c*x^2) - (3*d^6*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*c^(1/4)*sqrt(d) + 2*sqrt(d*x)*sqrt(c))/sqrt(sqrt(c)*d))/(sqrt(sqrt(c)*d)*sqrt(c)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*c^(1/4)*sqrt(d) - 2*sqrt(d*x)*sqrt(c))/sqrt(sqrt(c)*d))/(sqrt(sqrt(c)*d)*sqrt(c)) - sqrt(2)*log(sqrt(c)*d*x + sqrt(2)*sqrt(d*x)*c^(1/4)*sqrt(d) + d)/(c^(3/4)*sqrt(d)) + sqrt(2)*log(sqrt(c)*d*x - sqrt(2)*sqrt(d*x)*c^(1/4)*sqrt(d) + d)/(c^(3/4)*sqrt(d)))/c^2 - 6*d^6*(2*arctan(sqrt(d*x)*sqrt(c)/sqrt(sqrt(c)*d))/(sqrt(sqrt(c)*d)*sqrt(c)) + log((sqrt(d*x)*sqrt(c) - sqrt(sqrt(c)*d))/(sqrt(d*x)*sqrt(c) + sqrt(sqrt(c)*d)))/(sqrt(sqrt(c)*d)*sqrt(c)))/c^2 - 16*(d*x)^(3/2)*d^4/c^2)*c/d^2)*b)/d","A",0
83,1,310,0,0.427135," ","integrate((d*x)^(3/2)*(a+b*arctanh(c*x^2)),x, algorithm=""maxima"")","\frac{4 \, \left(d x\right)^{\frac{5}{2}} a + {\left(4 \, \left(d x\right)^{\frac{5}{2}} \operatorname{artanh}\left(c x^{2}\right) + \frac{{\left(\frac{16 \, \sqrt{d x} d^{4}}{c^{2}} - \frac{\frac{2 \, \sqrt{2} d^{5} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} c^{\frac{1}{4}} \sqrt{d} + 2 \, \sqrt{d x} \sqrt{c}\right)}}{2 \, \sqrt{\sqrt{c} d}}\right)}{\sqrt{\sqrt{c} d}} + \frac{2 \, \sqrt{2} d^{5} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} c^{\frac{1}{4}} \sqrt{d} - 2 \, \sqrt{d x} \sqrt{c}\right)}}{2 \, \sqrt{\sqrt{c} d}}\right)}{\sqrt{\sqrt{c} d}} + \frac{\sqrt{2} d^{\frac{9}{2}} \log\left(\sqrt{c} d x + \sqrt{2} \sqrt{d x} c^{\frac{1}{4}} \sqrt{d} + d\right)}{c^{\frac{1}{4}}} - \frac{\sqrt{2} d^{\frac{9}{2}} \log\left(\sqrt{c} d x - \sqrt{2} \sqrt{d x} c^{\frac{1}{4}} \sqrt{d} + d\right)}{c^{\frac{1}{4}}}}{c^{2}} - \frac{2 \, {\left(\frac{2 \, d^{5} \arctan\left(\frac{\sqrt{d x} \sqrt{c}}{\sqrt{\sqrt{c} d}}\right)}{\sqrt{\sqrt{c} d}} - \frac{d^{5} \log\left(\frac{\sqrt{d x} \sqrt{c} - \sqrt{\sqrt{c} d}}{\sqrt{d x} \sqrt{c} + \sqrt{\sqrt{c} d}}\right)}{\sqrt{\sqrt{c} d}}\right)}}{c^{2}}\right)} c}{d^{2}}\right)} b}{10 \, d}"," ",0,"1/10*(4*(d*x)^(5/2)*a + (4*(d*x)^(5/2)*arctanh(c*x^2) + (16*sqrt(d*x)*d^4/c^2 - (2*sqrt(2)*d^5*arctan(1/2*sqrt(2)*(sqrt(2)*c^(1/4)*sqrt(d) + 2*sqrt(d*x)*sqrt(c))/sqrt(sqrt(c)*d))/sqrt(sqrt(c)*d) + 2*sqrt(2)*d^5*arctan(-1/2*sqrt(2)*(sqrt(2)*c^(1/4)*sqrt(d) - 2*sqrt(d*x)*sqrt(c))/sqrt(sqrt(c)*d))/sqrt(sqrt(c)*d) + sqrt(2)*d^(9/2)*log(sqrt(c)*d*x + sqrt(2)*sqrt(d*x)*c^(1/4)*sqrt(d) + d)/c^(1/4) - sqrt(2)*d^(9/2)*log(sqrt(c)*d*x - sqrt(2)*sqrt(d*x)*c^(1/4)*sqrt(d) + d)/c^(1/4))/c^2 - 2*(2*d^5*arctan(sqrt(d*x)*sqrt(c)/sqrt(sqrt(c)*d))/sqrt(sqrt(c)*d) - d^5*log((sqrt(d*x)*sqrt(c) - sqrt(sqrt(c)*d))/(sqrt(d*x)*sqrt(c) + sqrt(sqrt(c)*d)))/sqrt(sqrt(c)*d))/c^2)*c/d^2)*b)/d","A",0
84,1,301,0,0.421812," ","integrate((d*x)^(1/2)*(a+b*arctanh(c*x^2)),x, algorithm=""maxima"")","\frac{4 \, \left(d x\right)^{\frac{3}{2}} a + {\left(4 \, \left(d x\right)^{\frac{3}{2}} \operatorname{artanh}\left(c x^{2}\right) + \frac{{\left(\frac{d^{4} {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} c^{\frac{1}{4}} \sqrt{d} + 2 \, \sqrt{d x} \sqrt{c}\right)}}{2 \, \sqrt{\sqrt{c} d}}\right)}{\sqrt{\sqrt{c} d} \sqrt{c}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} c^{\frac{1}{4}} \sqrt{d} - 2 \, \sqrt{d x} \sqrt{c}\right)}}{2 \, \sqrt{\sqrt{c} d}}\right)}{\sqrt{\sqrt{c} d} \sqrt{c}} - \frac{\sqrt{2} \log\left(\sqrt{c} d x + \sqrt{2} \sqrt{d x} c^{\frac{1}{4}} \sqrt{d} + d\right)}{c^{\frac{3}{4}} \sqrt{d}} + \frac{\sqrt{2} \log\left(\sqrt{c} d x - \sqrt{2} \sqrt{d x} c^{\frac{1}{4}} \sqrt{d} + d\right)}{c^{\frac{3}{4}} \sqrt{d}}\right)}}{c} + \frac{2 \, d^{4} {\left(\frac{2 \, \arctan\left(\frac{\sqrt{d x} \sqrt{c}}{\sqrt{\sqrt{c} d}}\right)}{\sqrt{\sqrt{c} d} \sqrt{c}} + \frac{\log\left(\frac{\sqrt{d x} \sqrt{c} - \sqrt{\sqrt{c} d}}{\sqrt{d x} \sqrt{c} + \sqrt{\sqrt{c} d}}\right)}{\sqrt{\sqrt{c} d} \sqrt{c}}\right)}}{c}\right)} c}{d^{2}}\right)} b}{6 \, d}"," ",0,"1/6*(4*(d*x)^(3/2)*a + (4*(d*x)^(3/2)*arctanh(c*x^2) + (d^4*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*c^(1/4)*sqrt(d) + 2*sqrt(d*x)*sqrt(c))/sqrt(sqrt(c)*d))/(sqrt(sqrt(c)*d)*sqrt(c)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*c^(1/4)*sqrt(d) - 2*sqrt(d*x)*sqrt(c))/sqrt(sqrt(c)*d))/(sqrt(sqrt(c)*d)*sqrt(c)) - sqrt(2)*log(sqrt(c)*d*x + sqrt(2)*sqrt(d*x)*c^(1/4)*sqrt(d) + d)/(c^(3/4)*sqrt(d)) + sqrt(2)*log(sqrt(c)*d*x - sqrt(2)*sqrt(d*x)*c^(1/4)*sqrt(d) + d)/(c^(3/4)*sqrt(d)))/c + 2*d^4*(2*arctan(sqrt(d*x)*sqrt(c)/sqrt(sqrt(c)*d))/(sqrt(sqrt(c)*d)*sqrt(c)) + log((sqrt(d*x)*sqrt(c) - sqrt(sqrt(c)*d))/(sqrt(d*x)*sqrt(c) + sqrt(sqrt(c)*d)))/(sqrt(sqrt(c)*d)*sqrt(c)))/c)*c/d^2)*b)/d","A",0
85,1,296,0,0.418837," ","integrate((a+b*arctanh(c*x^2))/(d*x)^(1/2),x, algorithm=""maxima"")","\frac{{\left(4 \, \sqrt{d x} \operatorname{artanh}\left(c x^{2}\right) + \frac{c {\left(\frac{\frac{2 \, \sqrt{2} d^{3} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} c^{\frac{1}{4}} \sqrt{d} + 2 \, \sqrt{d x} \sqrt{c}\right)}}{2 \, \sqrt{\sqrt{c} d}}\right)}{\sqrt{\sqrt{c} d}} + \frac{2 \, \sqrt{2} d^{3} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} c^{\frac{1}{4}} \sqrt{d} - 2 \, \sqrt{d x} \sqrt{c}\right)}}{2 \, \sqrt{\sqrt{c} d}}\right)}{\sqrt{\sqrt{c} d}} + \frac{\sqrt{2} d^{\frac{5}{2}} \log\left(\sqrt{c} d x + \sqrt{2} \sqrt{d x} c^{\frac{1}{4}} \sqrt{d} + d\right)}{c^{\frac{1}{4}}} - \frac{\sqrt{2} d^{\frac{5}{2}} \log\left(\sqrt{c} d x - \sqrt{2} \sqrt{d x} c^{\frac{1}{4}} \sqrt{d} + d\right)}{c^{\frac{1}{4}}}}{c} - \frac{2 \, {\left(\frac{2 \, d^{3} \arctan\left(\frac{\sqrt{d x} \sqrt{c}}{\sqrt{\sqrt{c} d}}\right)}{\sqrt{\sqrt{c} d}} - \frac{d^{3} \log\left(\frac{\sqrt{d x} \sqrt{c} - \sqrt{\sqrt{c} d}}{\sqrt{d x} \sqrt{c} + \sqrt{\sqrt{c} d}}\right)}{\sqrt{\sqrt{c} d}}\right)}}{c}\right)}}{d^{2}}\right)} b + 4 \, \sqrt{d x} a}{2 \, d}"," ",0,"1/2*((4*sqrt(d*x)*arctanh(c*x^2) + c*((2*sqrt(2)*d^3*arctan(1/2*sqrt(2)*(sqrt(2)*c^(1/4)*sqrt(d) + 2*sqrt(d*x)*sqrt(c))/sqrt(sqrt(c)*d))/sqrt(sqrt(c)*d) + 2*sqrt(2)*d^3*arctan(-1/2*sqrt(2)*(sqrt(2)*c^(1/4)*sqrt(d) - 2*sqrt(d*x)*sqrt(c))/sqrt(sqrt(c)*d))/sqrt(sqrt(c)*d) + sqrt(2)*d^(5/2)*log(sqrt(c)*d*x + sqrt(2)*sqrt(d*x)*c^(1/4)*sqrt(d) + d)/c^(1/4) - sqrt(2)*d^(5/2)*log(sqrt(c)*d*x - sqrt(2)*sqrt(d*x)*c^(1/4)*sqrt(d) + d)/c^(1/4))/c - 2*(2*d^3*arctan(sqrt(d*x)*sqrt(c)/sqrt(sqrt(c)*d))/sqrt(sqrt(c)*d) - d^3*log((sqrt(d*x)*sqrt(c) - sqrt(sqrt(c)*d))/(sqrt(d*x)*sqrt(c) + sqrt(sqrt(c)*d)))/sqrt(sqrt(c)*d))/c)/d^2)*b + 4*sqrt(d*x)*a)/d","A",0
86,1,296,0,0.411028," ","integrate((a+b*arctanh(c*x^2))/(d*x)^(3/2),x, algorithm=""maxima"")","-\frac{b {\left(\frac{4 \, \operatorname{artanh}\left(c x^{2}\right)}{\sqrt{d x}} - \frac{{\left(d^{2} {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} c^{\frac{1}{4}} \sqrt{d} + 2 \, \sqrt{d x} \sqrt{c}\right)}}{2 \, \sqrt{\sqrt{c} d}}\right)}{\sqrt{\sqrt{c} d} \sqrt{c}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} c^{\frac{1}{4}} \sqrt{d} - 2 \, \sqrt{d x} \sqrt{c}\right)}}{2 \, \sqrt{\sqrt{c} d}}\right)}{\sqrt{\sqrt{c} d} \sqrt{c}} - \frac{\sqrt{2} \log\left(\sqrt{c} d x + \sqrt{2} \sqrt{d x} c^{\frac{1}{4}} \sqrt{d} + d\right)}{c^{\frac{3}{4}} \sqrt{d}} + \frac{\sqrt{2} \log\left(\sqrt{c} d x - \sqrt{2} \sqrt{d x} c^{\frac{1}{4}} \sqrt{d} + d\right)}{c^{\frac{3}{4}} \sqrt{d}}\right)} - 2 \, d^{2} {\left(\frac{2 \, \arctan\left(\frac{\sqrt{d x} \sqrt{c}}{\sqrt{\sqrt{c} d}}\right)}{\sqrt{\sqrt{c} d} \sqrt{c}} + \frac{\log\left(\frac{\sqrt{d x} \sqrt{c} - \sqrt{\sqrt{c} d}}{\sqrt{d x} \sqrt{c} + \sqrt{\sqrt{c} d}}\right)}{\sqrt{\sqrt{c} d} \sqrt{c}}\right)}\right)} c}{d^{2}}\right)} + \frac{4 \, a}{\sqrt{d x}}}{2 \, d}"," ",0,"-1/2*(b*(4*arctanh(c*x^2)/sqrt(d*x) - (d^2*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*c^(1/4)*sqrt(d) + 2*sqrt(d*x)*sqrt(c))/sqrt(sqrt(c)*d))/(sqrt(sqrt(c)*d)*sqrt(c)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*c^(1/4)*sqrt(d) - 2*sqrt(d*x)*sqrt(c))/sqrt(sqrt(c)*d))/(sqrt(sqrt(c)*d)*sqrt(c)) - sqrt(2)*log(sqrt(c)*d*x + sqrt(2)*sqrt(d*x)*c^(1/4)*sqrt(d) + d)/(c^(3/4)*sqrt(d)) + sqrt(2)*log(sqrt(c)*d*x - sqrt(2)*sqrt(d*x)*c^(1/4)*sqrt(d) + d)/(c^(3/4)*sqrt(d))) - 2*d^2*(2*arctan(sqrt(d*x)*sqrt(c)/sqrt(sqrt(c)*d))/(sqrt(sqrt(c)*d)*sqrt(c)) + log((sqrt(d*x)*sqrt(c) - sqrt(sqrt(c)*d))/(sqrt(d*x)*sqrt(c) + sqrt(sqrt(c)*d)))/(sqrt(sqrt(c)*d)*sqrt(c))))*c/d^2) + 4*a/sqrt(d*x))/d","A",0
87,1,277,0,0.436915," ","integrate((a+b*arctanh(c*x^2))/(d*x)^(5/2),x, algorithm=""maxima"")","\frac{b {\left(\frac{{\left(\frac{2 \, \sqrt{2} d \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} c^{\frac{1}{4}} \sqrt{d} + 2 \, \sqrt{d x} \sqrt{c}\right)}}{2 \, \sqrt{\sqrt{c} d}}\right)}{\sqrt{\sqrt{c} d}} + \frac{2 \, \sqrt{2} d \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} c^{\frac{1}{4}} \sqrt{d} - 2 \, \sqrt{d x} \sqrt{c}\right)}}{2 \, \sqrt{\sqrt{c} d}}\right)}{\sqrt{\sqrt{c} d}} + \frac{\sqrt{2} \sqrt{d} \log\left(\sqrt{c} d x + \sqrt{2} \sqrt{d x} c^{\frac{1}{4}} \sqrt{d} + d\right)}{c^{\frac{1}{4}}} - \frac{\sqrt{2} \sqrt{d} \log\left(\sqrt{c} d x - \sqrt{2} \sqrt{d x} c^{\frac{1}{4}} \sqrt{d} + d\right)}{c^{\frac{1}{4}}} + \frac{4 \, d \arctan\left(\frac{\sqrt{d x} \sqrt{c}}{\sqrt{\sqrt{c} d}}\right)}{\sqrt{\sqrt{c} d}} - \frac{2 \, d \log\left(\frac{\sqrt{d x} \sqrt{c} - \sqrt{\sqrt{c} d}}{\sqrt{d x} \sqrt{c} + \sqrt{\sqrt{c} d}}\right)}{\sqrt{\sqrt{c} d}}\right)} c}{d^{2}} - \frac{4 \, \operatorname{artanh}\left(c x^{2}\right)}{\left(d x\right)^{\frac{3}{2}}}\right)} - \frac{4 \, a}{\left(d x\right)^{\frac{3}{2}}}}{6 \, d}"," ",0,"1/6*(b*((2*sqrt(2)*d*arctan(1/2*sqrt(2)*(sqrt(2)*c^(1/4)*sqrt(d) + 2*sqrt(d*x)*sqrt(c))/sqrt(sqrt(c)*d))/sqrt(sqrt(c)*d) + 2*sqrt(2)*d*arctan(-1/2*sqrt(2)*(sqrt(2)*c^(1/4)*sqrt(d) - 2*sqrt(d*x)*sqrt(c))/sqrt(sqrt(c)*d))/sqrt(sqrt(c)*d) + sqrt(2)*sqrt(d)*log(sqrt(c)*d*x + sqrt(2)*sqrt(d*x)*c^(1/4)*sqrt(d) + d)/c^(1/4) - sqrt(2)*sqrt(d)*log(sqrt(c)*d*x - sqrt(2)*sqrt(d*x)*c^(1/4)*sqrt(d) + d)/c^(1/4) + 4*d*arctan(sqrt(d*x)*sqrt(c)/sqrt(sqrt(c)*d))/sqrt(sqrt(c)*d) - 2*d*log((sqrt(d*x)*sqrt(c) - sqrt(sqrt(c)*d))/(sqrt(d*x)*sqrt(c) + sqrt(sqrt(c)*d)))/sqrt(sqrt(c)*d))*c/d^2 - 4*arctanh(c*x^2)/(d*x)^(3/2)) - 4*a/(d*x)^(3/2))/d","A",0
88,1,298,0,0.424907," ","integrate((a+b*arctanh(c*x^2))/(d*x)^(7/2),x, algorithm=""maxima"")","-\frac{b {\left(\frac{{\left(c {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} c^{\frac{1}{4}} \sqrt{d} + 2 \, \sqrt{d x} \sqrt{c}\right)}}{2 \, \sqrt{\sqrt{c} d}}\right)}{\sqrt{\sqrt{c} d} \sqrt{c}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} c^{\frac{1}{4}} \sqrt{d} - 2 \, \sqrt{d x} \sqrt{c}\right)}}{2 \, \sqrt{\sqrt{c} d}}\right)}{\sqrt{\sqrt{c} d} \sqrt{c}} - \frac{\sqrt{2} \log\left(\sqrt{c} d x + \sqrt{2} \sqrt{d x} c^{\frac{1}{4}} \sqrt{d} + d\right)}{c^{\frac{3}{4}} \sqrt{d}} + \frac{\sqrt{2} \log\left(\sqrt{c} d x - \sqrt{2} \sqrt{d x} c^{\frac{1}{4}} \sqrt{d} + d\right)}{c^{\frac{3}{4}} \sqrt{d}}\right)} + 2 \, c {\left(\frac{2 \, \arctan\left(\frac{\sqrt{d x} \sqrt{c}}{\sqrt{\sqrt{c} d}}\right)}{\sqrt{\sqrt{c} d} \sqrt{c}} + \frac{\log\left(\frac{\sqrt{d x} \sqrt{c} - \sqrt{\sqrt{c} d}}{\sqrt{d x} \sqrt{c} + \sqrt{\sqrt{c} d}}\right)}{\sqrt{\sqrt{c} d} \sqrt{c}}\right)} + \frac{16}{\sqrt{d x}}\right)} c}{d^{2}} + \frac{4 \, \operatorname{artanh}\left(c x^{2}\right)}{\left(d x\right)^{\frac{5}{2}}}\right)} + \frac{4 \, a}{\left(d x\right)^{\frac{5}{2}}}}{10 \, d}"," ",0,"-1/10*(b*((c*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*c^(1/4)*sqrt(d) + 2*sqrt(d*x)*sqrt(c))/sqrt(sqrt(c)*d))/(sqrt(sqrt(c)*d)*sqrt(c)) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*c^(1/4)*sqrt(d) - 2*sqrt(d*x)*sqrt(c))/sqrt(sqrt(c)*d))/(sqrt(sqrt(c)*d)*sqrt(c)) - sqrt(2)*log(sqrt(c)*d*x + sqrt(2)*sqrt(d*x)*c^(1/4)*sqrt(d) + d)/(c^(3/4)*sqrt(d)) + sqrt(2)*log(sqrt(c)*d*x - sqrt(2)*sqrt(d*x)*c^(1/4)*sqrt(d) + d)/(c^(3/4)*sqrt(d))) + 2*c*(2*arctan(sqrt(d*x)*sqrt(c)/sqrt(sqrt(c)*d))/(sqrt(sqrt(c)*d)*sqrt(c)) + log((sqrt(d*x)*sqrt(c) - sqrt(sqrt(c)*d))/(sqrt(d*x)*sqrt(c) + sqrt(sqrt(c)*d)))/(sqrt(sqrt(c)*d)*sqrt(c))) + 16/sqrt(d*x))*c/d^2 + 4*arctanh(c*x^2)/(d*x)^(5/2)) + 4*a/(d*x)^(5/2))/d","A",0
89,1,297,0,0.412988," ","integrate((a+b*arctanh(c*x^2))/(d*x)^(9/2),x, algorithm=""maxima"")","-\frac{b {\left(\frac{c {\left(\frac{6 \, \sqrt{2} c \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} c^{\frac{1}{4}} \sqrt{d} + 2 \, \sqrt{d x} \sqrt{c}\right)}}{2 \, \sqrt{\sqrt{c} d}}\right)}{\sqrt{\sqrt{c} d} d} + \frac{6 \, \sqrt{2} c \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} c^{\frac{1}{4}} \sqrt{d} - 2 \, \sqrt{d x} \sqrt{c}\right)}}{2 \, \sqrt{\sqrt{c} d}}\right)}{\sqrt{\sqrt{c} d} d} + \frac{3 \, \sqrt{2} c^{\frac{3}{4}} \log\left(\sqrt{c} d x + \sqrt{2} \sqrt{d x} c^{\frac{1}{4}} \sqrt{d} + d\right)}{d^{\frac{3}{2}}} - \frac{3 \, \sqrt{2} c^{\frac{3}{4}} \log\left(\sqrt{c} d x - \sqrt{2} \sqrt{d x} c^{\frac{1}{4}} \sqrt{d} + d\right)}{d^{\frac{3}{2}}} - \frac{12 \, c \arctan\left(\frac{\sqrt{d x} \sqrt{c}}{\sqrt{\sqrt{c} d}}\right)}{\sqrt{\sqrt{c} d} d} + \frac{6 \, c \log\left(\frac{\sqrt{d x} \sqrt{c} - \sqrt{\sqrt{c} d}}{\sqrt{d x} \sqrt{c} + \sqrt{\sqrt{c} d}}\right)}{\sqrt{\sqrt{c} d} d} + \frac{16}{\left(d x\right)^{\frac{3}{2}}}\right)}}{d^{2}} + \frac{12 \, \operatorname{artanh}\left(c x^{2}\right)}{\left(d x\right)^{\frac{7}{2}}}\right)} + \frac{12 \, a}{\left(d x\right)^{\frac{7}{2}}}}{42 \, d}"," ",0,"-1/42*(b*(c*(6*sqrt(2)*c*arctan(1/2*sqrt(2)*(sqrt(2)*c^(1/4)*sqrt(d) + 2*sqrt(d*x)*sqrt(c))/sqrt(sqrt(c)*d))/(sqrt(sqrt(c)*d)*d) + 6*sqrt(2)*c*arctan(-1/2*sqrt(2)*(sqrt(2)*c^(1/4)*sqrt(d) - 2*sqrt(d*x)*sqrt(c))/sqrt(sqrt(c)*d))/(sqrt(sqrt(c)*d)*d) + 3*sqrt(2)*c^(3/4)*log(sqrt(c)*d*x + sqrt(2)*sqrt(d*x)*c^(1/4)*sqrt(d) + d)/d^(3/2) - 3*sqrt(2)*c^(3/4)*log(sqrt(c)*d*x - sqrt(2)*sqrt(d*x)*c^(1/4)*sqrt(d) + d)/d^(3/2) - 12*c*arctan(sqrt(d*x)*sqrt(c)/sqrt(sqrt(c)*d))/(sqrt(sqrt(c)*d)*d) + 6*c*log((sqrt(d*x)*sqrt(c) - sqrt(sqrt(c)*d))/(sqrt(d*x)*sqrt(c) + sqrt(sqrt(c)*d)))/(sqrt(sqrt(c)*d)*d) + 16/(d*x)^(3/2))/d^2 + 12*arctanh(c*x^2)/(d*x)^(7/2)) + 12*a/(d*x)^(7/2))/d","A",0
90,0,0,0,0.000000," ","integrate((d*x)^(1/2)*(a+b*arctanh(c*x^2))^2,x, algorithm=""maxima"")","\frac{1}{6} \, b^{2} \sqrt{d} x^{\frac{3}{2}} \log\left(-c x^{2} + 1\right)^{2} + \frac{1}{6} \, a^{2} c \sqrt{d} {\left(\frac{4 \, x^{\frac{3}{2}}}{c} - \frac{3 \, {\left(\frac{i \, {\left(\log\left(i \, c^{\frac{1}{4}} \sqrt{x} + 1\right) - \log\left(-i \, c^{\frac{1}{4}} \sqrt{x} + 1\right)\right)}}{c^{\frac{3}{4}}} - \frac{\log\left(\frac{\sqrt{c} \sqrt{x} - c^{\frac{1}{4}}}{\sqrt{c} \sqrt{x} + c^{\frac{1}{4}}}\right)}{c^{\frac{3}{4}}}\right)}}{c}\right)} + 3 \, b^{2} c \sqrt{d} \int \frac{x^{\frac{5}{2}} \log\left(c x^{2} + 1\right)^{2}}{12 \, {\left(c x^{2} - 1\right)}}\,{d x} - 6 \, b^{2} c \sqrt{d} \int \frac{x^{\frac{5}{2}} \log\left(c x^{2} + 1\right) \log\left(-c x^{2} + 1\right)}{12 \, {\left(c x^{2} - 1\right)}}\,{d x} + 12 \, a b c \sqrt{d} \int \frac{x^{\frac{5}{2}} \log\left(c x^{2} + 1\right)}{12 \, {\left(c x^{2} - 1\right)}}\,{d x} - 12 \, a b c \sqrt{d} \int \frac{x^{\frac{5}{2}} \log\left(-c x^{2} + 1\right)}{12 \, {\left(c x^{2} - 1\right)}}\,{d x} - 8 \, b^{2} c \sqrt{d} \int \frac{x^{\frac{5}{2}} \log\left(-c x^{2} + 1\right)}{12 \, {\left(c x^{2} - 1\right)}}\,{d x} + \frac{1}{2} \, a^{2} \sqrt{d} {\left(\frac{i \, {\left(\log\left(i \, c^{\frac{1}{4}} \sqrt{x} + 1\right) - \log\left(-i \, c^{\frac{1}{4}} \sqrt{x} + 1\right)\right)}}{c^{\frac{3}{4}}} - \frac{\log\left(\frac{\sqrt{c} \sqrt{x} - c^{\frac{1}{4}}}{\sqrt{c} \sqrt{x} + c^{\frac{1}{4}}}\right)}{c^{\frac{3}{4}}}\right)} - 3 \, b^{2} \sqrt{d} \int \frac{\sqrt{x} \log\left(c x^{2} + 1\right)^{2}}{12 \, {\left(c x^{2} - 1\right)}}\,{d x} + 6 \, b^{2} \sqrt{d} \int \frac{\sqrt{x} \log\left(c x^{2} + 1\right) \log\left(-c x^{2} + 1\right)}{12 \, {\left(c x^{2} - 1\right)}}\,{d x} - 12 \, a b \sqrt{d} \int \frac{\sqrt{x} \log\left(c x^{2} + 1\right)}{12 \, {\left(c x^{2} - 1\right)}}\,{d x} + 12 \, a b \sqrt{d} \int \frac{\sqrt{x} \log\left(-c x^{2} + 1\right)}{12 \, {\left(c x^{2} - 1\right)}}\,{d x}"," ",0,"1/6*b^2*sqrt(d)*x^(3/2)*log(-c*x^2 + 1)^2 + 1/6*a^2*c*sqrt(d)*(4*x^(3/2)/c - 3*(I*(log(I*c^(1/4)*sqrt(x) + 1) - log(-I*c^(1/4)*sqrt(x) + 1))/c^(3/4) - log((sqrt(c)*sqrt(x) - c^(1/4))/(sqrt(c)*sqrt(x) + c^(1/4)))/c^(3/4))/c) + 3*b^2*c*sqrt(d)*integrate(1/12*x^(5/2)*log(c*x^2 + 1)^2/(c*x^2 - 1), x) - 6*b^2*c*sqrt(d)*integrate(1/12*x^(5/2)*log(c*x^2 + 1)*log(-c*x^2 + 1)/(c*x^2 - 1), x) + 12*a*b*c*sqrt(d)*integrate(1/12*x^(5/2)*log(c*x^2 + 1)/(c*x^2 - 1), x) - 12*a*b*c*sqrt(d)*integrate(1/12*x^(5/2)*log(-c*x^2 + 1)/(c*x^2 - 1), x) - 8*b^2*c*sqrt(d)*integrate(1/12*x^(5/2)*log(-c*x^2 + 1)/(c*x^2 - 1), x) + 1/2*a^2*sqrt(d)*(I*(log(I*c^(1/4)*sqrt(x) + 1) - log(-I*c^(1/4)*sqrt(x) + 1))/c^(3/4) - log((sqrt(c)*sqrt(x) - c^(1/4))/(sqrt(c)*sqrt(x) + c^(1/4)))/c^(3/4)) - 3*b^2*sqrt(d)*integrate(1/12*sqrt(x)*log(c*x^2 + 1)^2/(c*x^2 - 1), x) + 6*b^2*sqrt(d)*integrate(1/12*sqrt(x)*log(c*x^2 + 1)*log(-c*x^2 + 1)/(c*x^2 - 1), x) - 12*a*b*sqrt(d)*integrate(1/12*sqrt(x)*log(c*x^2 + 1)/(c*x^2 - 1), x) + 12*a*b*sqrt(d)*integrate(1/12*sqrt(x)*log(-c*x^2 + 1)/(c*x^2 - 1), x)","F",0
91,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x^2))^2/(d*x)^(1/2),x, algorithm=""maxima"")","-\frac{1}{2} \, a^{2} c {\left(\frac{-\frac{i \, {\left(\log\left(i \, c^{\frac{1}{4}} \sqrt{x} + 1\right) - \log\left(-i \, c^{\frac{1}{4}} \sqrt{x} + 1\right)\right)}}{c^{\frac{1}{4}}} - \frac{\log\left(\frac{\sqrt{c} \sqrt{x} - c^{\frac{1}{4}}}{\sqrt{c} \sqrt{x} + c^{\frac{1}{4}}}\right)}{c^{\frac{1}{4}}}}{c \sqrt{d}} - \frac{4 \, \sqrt{x}}{c \sqrt{d}}\right)} + b^{2} c \int \frac{x^{\frac{3}{2}} \log\left(c x^{2} + 1\right)^{2}}{4 \, {\left(c \sqrt{d} x^{2} - \sqrt{d}\right)}}\,{d x} - 2 \, b^{2} c \int \frac{x^{\frac{3}{2}} \log\left(c x^{2} + 1\right) \log\left(-c x^{2} + 1\right)}{4 \, {\left(c \sqrt{d} x^{2} - \sqrt{d}\right)}}\,{d x} + 4 \, a b c \int \frac{x^{\frac{3}{2}} \log\left(c x^{2} + 1\right)}{4 \, {\left(c \sqrt{d} x^{2} - \sqrt{d}\right)}}\,{d x} - 4 \, a b c \int \frac{x^{\frac{3}{2}} \log\left(-c x^{2} + 1\right)}{4 \, {\left(c \sqrt{d} x^{2} - \sqrt{d}\right)}}\,{d x} - 8 \, b^{2} c \int \frac{x^{\frac{3}{2}} \log\left(-c x^{2} + 1\right)}{4 \, {\left(c \sqrt{d} x^{2} - \sqrt{d}\right)}}\,{d x} + \frac{b^{2} \sqrt{x} \log\left(-c x^{2} + 1\right)^{2}}{2 \, \sqrt{d}} - b^{2} \int \frac{\log\left(c x^{2} + 1\right)^{2}}{4 \, {\left(c \sqrt{d} x^{2} - \sqrt{d}\right)} \sqrt{x}}\,{d x} + 2 \, b^{2} \int \frac{\log\left(c x^{2} + 1\right) \log\left(-c x^{2} + 1\right)}{4 \, {\left(c \sqrt{d} x^{2} - \sqrt{d}\right)} \sqrt{x}}\,{d x} - 4 \, a b \int \frac{\log\left(c x^{2} + 1\right)}{4 \, {\left(c \sqrt{d} x^{2} - \sqrt{d}\right)} \sqrt{x}}\,{d x} + 4 \, a b \int \frac{\log\left(-c x^{2} + 1\right)}{4 \, {\left(c \sqrt{d} x^{2} - \sqrt{d}\right)} \sqrt{x}}\,{d x} + \frac{a^{2} {\left(-\frac{i \, {\left(\log\left(i \, c^{\frac{1}{4}} \sqrt{x} + 1\right) - \log\left(-i \, c^{\frac{1}{4}} \sqrt{x} + 1\right)\right)}}{c^{\frac{1}{4}}} - \frac{\log\left(\frac{\sqrt{c} \sqrt{x} - c^{\frac{1}{4}}}{\sqrt{c} \sqrt{x} + c^{\frac{1}{4}}}\right)}{c^{\frac{1}{4}}}\right)}}{2 \, \sqrt{d}}"," ",0,"-1/2*a^2*c*((-I*(log(I*c^(1/4)*sqrt(x) + 1) - log(-I*c^(1/4)*sqrt(x) + 1))/c^(1/4) - log((sqrt(c)*sqrt(x) - c^(1/4))/(sqrt(c)*sqrt(x) + c^(1/4)))/c^(1/4))/(c*sqrt(d)) - 4*sqrt(x)/(c*sqrt(d))) + b^2*c*integrate(1/4*x^(3/2)*log(c*x^2 + 1)^2/(c*sqrt(d)*x^2 - sqrt(d)), x) - 2*b^2*c*integrate(1/4*x^(3/2)*log(c*x^2 + 1)*log(-c*x^2 + 1)/(c*sqrt(d)*x^2 - sqrt(d)), x) + 4*a*b*c*integrate(1/4*x^(3/2)*log(c*x^2 + 1)/(c*sqrt(d)*x^2 - sqrt(d)), x) - 4*a*b*c*integrate(1/4*x^(3/2)*log(-c*x^2 + 1)/(c*sqrt(d)*x^2 - sqrt(d)), x) - 8*b^2*c*integrate(1/4*x^(3/2)*log(-c*x^2 + 1)/(c*sqrt(d)*x^2 - sqrt(d)), x) + 1/2*b^2*sqrt(x)*log(-c*x^2 + 1)^2/sqrt(d) - b^2*integrate(1/4*log(c*x^2 + 1)^2/((c*sqrt(d)*x^2 - sqrt(d))*sqrt(x)), x) + 2*b^2*integrate(1/4*log(c*x^2 + 1)*log(-c*x^2 + 1)/((c*sqrt(d)*x^2 - sqrt(d))*sqrt(x)), x) - 4*a*b*integrate(1/4*log(c*x^2 + 1)/((c*sqrt(d)*x^2 - sqrt(d))*sqrt(x)), x) + 4*a*b*integrate(1/4*log(-c*x^2 + 1)/((c*sqrt(d)*x^2 - sqrt(d))*sqrt(x)), x) + 1/2*a^2*(-I*(log(I*c^(1/4)*sqrt(x) + 1) - log(-I*c^(1/4)*sqrt(x) + 1))/c^(1/4) - log((sqrt(c)*sqrt(x) - c^(1/4))/(sqrt(c)*sqrt(x) + c^(1/4)))/c^(1/4))/sqrt(d)","F",0
92,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x^2))^2/(d*x)^(3/2),x, algorithm=""maxima"")","b^{2} c \int \frac{x^{\frac{3}{2}} \log\left(c x^{2} + 1\right)^{2}}{4 \, {\left(c d^{\frac{3}{2}} x^{3} - d^{\frac{3}{2}} x\right)}}\,{d x} - 2 \, b^{2} c \int \frac{x^{\frac{3}{2}} \log\left(c x^{2} + 1\right) \log\left(-c x^{2} + 1\right)}{4 \, {\left(c d^{\frac{3}{2}} x^{3} - d^{\frac{3}{2}} x\right)}}\,{d x} + 4 \, a b c \int \frac{x^{\frac{3}{2}} \log\left(c x^{2} + 1\right)}{4 \, {\left(c d^{\frac{3}{2}} x^{3} - d^{\frac{3}{2}} x\right)}}\,{d x} - 4 \, a b c \int \frac{x^{\frac{3}{2}} \log\left(-c x^{2} + 1\right)}{4 \, {\left(c d^{\frac{3}{2}} x^{3} - d^{\frac{3}{2}} x\right)}}\,{d x} + 8 \, b^{2} c \int \frac{x^{\frac{3}{2}} \log\left(-c x^{2} + 1\right)}{4 \, {\left(c d^{\frac{3}{2}} x^{3} - d^{\frac{3}{2}} x\right)}}\,{d x} + \frac{1}{2} \, a^{2} {\left(\frac{c {\left(\frac{i \, {\left(\log\left(i \, c^{\frac{1}{4}} \sqrt{x} + 1\right) - \log\left(-i \, c^{\frac{1}{4}} \sqrt{x} + 1\right)\right)}}{c^{\frac{3}{4}}} - \frac{\log\left(\frac{\sqrt{c} \sqrt{x} - c^{\frac{1}{4}}}{\sqrt{c} \sqrt{x} + c^{\frac{1}{4}}}\right)}{c^{\frac{3}{4}}}\right)}}{d^{\frac{3}{2}}} - \frac{4}{d^{\frac{3}{2}} \sqrt{x}}\right)} - b^{2} \int \frac{\log\left(c x^{2} + 1\right)^{2}}{4 \, {\left(c d^{\frac{3}{2}} x^{3} - d^{\frac{3}{2}} x\right)} \sqrt{x}}\,{d x} + 2 \, b^{2} \int \frac{\log\left(c x^{2} + 1\right) \log\left(-c x^{2} + 1\right)}{4 \, {\left(c d^{\frac{3}{2}} x^{3} - d^{\frac{3}{2}} x\right)} \sqrt{x}}\,{d x} - 4 \, a b \int \frac{\log\left(c x^{2} + 1\right)}{4 \, {\left(c d^{\frac{3}{2}} x^{3} - d^{\frac{3}{2}} x\right)} \sqrt{x}}\,{d x} + 4 \, a b \int \frac{\log\left(-c x^{2} + 1\right)}{4 \, {\left(c d^{\frac{3}{2}} x^{3} - d^{\frac{3}{2}} x\right)} \sqrt{x}}\,{d x} - \frac{a^{2} c {\left(\frac{i \, {\left(\log\left(i \, c^{\frac{1}{4}} \sqrt{x} + 1\right) - \log\left(-i \, c^{\frac{1}{4}} \sqrt{x} + 1\right)\right)}}{c^{\frac{3}{4}}} - \frac{\log\left(\frac{\sqrt{c} \sqrt{x} - c^{\frac{1}{4}}}{\sqrt{c} \sqrt{x} + c^{\frac{1}{4}}}\right)}{c^{\frac{3}{4}}}\right)}}{2 \, d^{\frac{3}{2}}} - \frac{b^{2} \log\left(-c x^{2} + 1\right)^{2}}{2 \, d^{\frac{3}{2}} \sqrt{x}}"," ",0,"b^2*c*integrate(1/4*x^(3/2)*log(c*x^2 + 1)^2/(c*d^(3/2)*x^3 - d^(3/2)*x), x) - 2*b^2*c*integrate(1/4*x^(3/2)*log(c*x^2 + 1)*log(-c*x^2 + 1)/(c*d^(3/2)*x^3 - d^(3/2)*x), x) + 4*a*b*c*integrate(1/4*x^(3/2)*log(c*x^2 + 1)/(c*d^(3/2)*x^3 - d^(3/2)*x), x) - 4*a*b*c*integrate(1/4*x^(3/2)*log(-c*x^2 + 1)/(c*d^(3/2)*x^3 - d^(3/2)*x), x) + 8*b^2*c*integrate(1/4*x^(3/2)*log(-c*x^2 + 1)/(c*d^(3/2)*x^3 - d^(3/2)*x), x) + 1/2*a^2*(c*(I*(log(I*c^(1/4)*sqrt(x) + 1) - log(-I*c^(1/4)*sqrt(x) + 1))/c^(3/4) - log((sqrt(c)*sqrt(x) - c^(1/4))/(sqrt(c)*sqrt(x) + c^(1/4)))/c^(3/4))/d^(3/2) - 4/(d^(3/2)*sqrt(x))) - b^2*integrate(1/4*log(c*x^2 + 1)^2/((c*d^(3/2)*x^3 - d^(3/2)*x)*sqrt(x)), x) + 2*b^2*integrate(1/4*log(c*x^2 + 1)*log(-c*x^2 + 1)/((c*d^(3/2)*x^3 - d^(3/2)*x)*sqrt(x)), x) - 4*a*b*integrate(1/4*log(c*x^2 + 1)/((c*d^(3/2)*x^3 - d^(3/2)*x)*sqrt(x)), x) + 4*a*b*integrate(1/4*log(-c*x^2 + 1)/((c*d^(3/2)*x^3 - d^(3/2)*x)*sqrt(x)), x) - 1/2*a^2*c*(I*(log(I*c^(1/4)*sqrt(x) + 1) - log(-I*c^(1/4)*sqrt(x) + 1))/c^(3/4) - log((sqrt(c)*sqrt(x) - c^(1/4))/(sqrt(c)*sqrt(x) + c^(1/4)))/c^(3/4))/d^(3/2) - 1/2*b^2*log(-c*x^2 + 1)^2/(d^(3/2)*sqrt(x))","F",0
93,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x^2))^2/(d*x)^(5/2),x, algorithm=""maxima"")","3 \, b^{2} c \int \frac{x^{\frac{3}{2}} \log\left(c x^{2} + 1\right)^{2}}{12 \, {\left(c d^{\frac{5}{2}} x^{4} - d^{\frac{5}{2}} x^{2}\right)}}\,{d x} - 6 \, b^{2} c \int \frac{x^{\frac{3}{2}} \log\left(c x^{2} + 1\right) \log\left(-c x^{2} + 1\right)}{12 \, {\left(c d^{\frac{5}{2}} x^{4} - d^{\frac{5}{2}} x^{2}\right)}}\,{d x} + 12 \, a b c \int \frac{x^{\frac{3}{2}} \log\left(c x^{2} + 1\right)}{12 \, {\left(c d^{\frac{5}{2}} x^{4} - d^{\frac{5}{2}} x^{2}\right)}}\,{d x} - 12 \, a b c \int \frac{x^{\frac{3}{2}} \log\left(-c x^{2} + 1\right)}{12 \, {\left(c d^{\frac{5}{2}} x^{4} - d^{\frac{5}{2}} x^{2}\right)}}\,{d x} + 8 \, b^{2} c \int \frac{x^{\frac{3}{2}} \log\left(-c x^{2} + 1\right)}{12 \, {\left(c d^{\frac{5}{2}} x^{4} - d^{\frac{5}{2}} x^{2}\right)}}\,{d x} + \frac{1}{6} \, a^{2} {\left(\frac{3 \, {\left(-i \, c^{\frac{3}{4}} {\left(\log\left(i \, c^{\frac{1}{4}} \sqrt{x} + 1\right) - \log\left(-i \, c^{\frac{1}{4}} \sqrt{x} + 1\right)\right)} - c^{\frac{3}{4}} \log\left(\frac{\sqrt{c} \sqrt{x} - c^{\frac{1}{4}}}{\sqrt{c} \sqrt{x} + c^{\frac{1}{4}}}\right)\right)}}{d^{\frac{5}{2}}} - \frac{4}{d^{\frac{5}{2}} x^{\frac{3}{2}}}\right)} - 3 \, b^{2} \int \frac{\log\left(c x^{2} + 1\right)^{2}}{12 \, {\left(c d^{\frac{5}{2}} x^{4} - d^{\frac{5}{2}} x^{2}\right)} \sqrt{x}}\,{d x} + 6 \, b^{2} \int \frac{\log\left(c x^{2} + 1\right) \log\left(-c x^{2} + 1\right)}{12 \, {\left(c d^{\frac{5}{2}} x^{4} - d^{\frac{5}{2}} x^{2}\right)} \sqrt{x}}\,{d x} - 12 \, a b \int \frac{\log\left(c x^{2} + 1\right)}{12 \, {\left(c d^{\frac{5}{2}} x^{4} - d^{\frac{5}{2}} x^{2}\right)} \sqrt{x}}\,{d x} + 12 \, a b \int \frac{\log\left(-c x^{2} + 1\right)}{12 \, {\left(c d^{\frac{5}{2}} x^{4} - d^{\frac{5}{2}} x^{2}\right)} \sqrt{x}}\,{d x} - \frac{a^{2} c {\left(-\frac{i \, {\left(\log\left(i \, c^{\frac{1}{4}} \sqrt{x} + 1\right) - \log\left(-i \, c^{\frac{1}{4}} \sqrt{x} + 1\right)\right)}}{c^{\frac{1}{4}}} - \frac{\log\left(\frac{\sqrt{c} \sqrt{x} - c^{\frac{1}{4}}}{\sqrt{c} \sqrt{x} + c^{\frac{1}{4}}}\right)}{c^{\frac{1}{4}}}\right)}}{2 \, d^{\frac{5}{2}}} - \frac{b^{2} \log\left(-c x^{2} + 1\right)^{2}}{6 \, d^{\frac{5}{2}} x^{\frac{3}{2}}}"," ",0,"3*b^2*c*integrate(1/12*x^(3/2)*log(c*x^2 + 1)^2/(c*d^(5/2)*x^4 - d^(5/2)*x^2), x) - 6*b^2*c*integrate(1/12*x^(3/2)*log(c*x^2 + 1)*log(-c*x^2 + 1)/(c*d^(5/2)*x^4 - d^(5/2)*x^2), x) + 12*a*b*c*integrate(1/12*x^(3/2)*log(c*x^2 + 1)/(c*d^(5/2)*x^4 - d^(5/2)*x^2), x) - 12*a*b*c*integrate(1/12*x^(3/2)*log(-c*x^2 + 1)/(c*d^(5/2)*x^4 - d^(5/2)*x^2), x) + 8*b^2*c*integrate(1/12*x^(3/2)*log(-c*x^2 + 1)/(c*d^(5/2)*x^4 - d^(5/2)*x^2), x) + 1/6*a^2*(3*(-I*c^(3/4)*(log(I*c^(1/4)*sqrt(x) + 1) - log(-I*c^(1/4)*sqrt(x) + 1)) - c^(3/4)*log((sqrt(c)*sqrt(x) - c^(1/4))/(sqrt(c)*sqrt(x) + c^(1/4))))/d^(5/2) - 4/(d^(5/2)*x^(3/2))) - 3*b^2*integrate(1/12*log(c*x^2 + 1)^2/((c*d^(5/2)*x^4 - d^(5/2)*x^2)*sqrt(x)), x) + 6*b^2*integrate(1/12*log(c*x^2 + 1)*log(-c*x^2 + 1)/((c*d^(5/2)*x^4 - d^(5/2)*x^2)*sqrt(x)), x) - 12*a*b*integrate(1/12*log(c*x^2 + 1)/((c*d^(5/2)*x^4 - d^(5/2)*x^2)*sqrt(x)), x) + 12*a*b*integrate(1/12*log(-c*x^2 + 1)/((c*d^(5/2)*x^4 - d^(5/2)*x^2)*sqrt(x)), x) - 1/2*a^2*c*(-I*(log(I*c^(1/4)*sqrt(x) + 1) - log(-I*c^(1/4)*sqrt(x) + 1))/c^(1/4) - log((sqrt(c)*sqrt(x) - c^(1/4))/(sqrt(c)*sqrt(x) + c^(1/4)))/c^(1/4))/d^(5/2) - 1/6*b^2*log(-c*x^2 + 1)^2/(d^(5/2)*x^(3/2))","F",0
94,0,0,0,0.000000," ","integrate((d*x)^m*(a+b*arctanh(c*x^2))^3,x, algorithm=""maxima"")","-\frac{b^{3} d^{m} x x^{m} \log\left(-c x^{2} + 1\right)^{3}}{8 \, {\left(m + 1\right)}} + \frac{\left(d x\right)^{m + 1} a^{3}}{d {\left(m + 1\right)}} + \int \frac{{\left(b^{3} c d^{m} {\left(m + 1\right)} x^{2} - b^{3} d^{m} {\left(m + 1\right)}\right)} x^{m} \log\left(c x^{2} + 1\right)^{3} + 6 \, {\left(a b^{2} c d^{m} {\left(m + 1\right)} x^{2} - a b^{2} d^{m} {\left(m + 1\right)}\right)} x^{m} \log\left(c x^{2} + 1\right)^{2} + 12 \, {\left(a^{2} b c d^{m} {\left(m + 1\right)} x^{2} - a^{2} b d^{m} {\left(m + 1\right)}\right)} x^{m} \log\left(c x^{2} + 1\right) + 3 \, {\left({\left(b^{3} c d^{m} {\left(m + 1\right)} x^{2} - b^{3} d^{m} {\left(m + 1\right)}\right)} x^{m} \log\left(c x^{2} + 1\right) - 2 \, {\left(a b^{2} d^{m} {\left(m + 1\right)} - {\left(a b^{2} c d^{m} {\left(m + 1\right)} + b^{3} c d^{m}\right)} x^{2}\right)} x^{m}\right)} \log\left(-c x^{2} + 1\right)^{2} - 3 \, {\left({\left(b^{3} c d^{m} {\left(m + 1\right)} x^{2} - b^{3} d^{m} {\left(m + 1\right)}\right)} x^{m} \log\left(c x^{2} + 1\right)^{2} + 4 \, {\left(a b^{2} c d^{m} {\left(m + 1\right)} x^{2} - a b^{2} d^{m} {\left(m + 1\right)}\right)} x^{m} \log\left(c x^{2} + 1\right) + 4 \, {\left(a^{2} b c d^{m} {\left(m + 1\right)} x^{2} - a^{2} b d^{m} {\left(m + 1\right)}\right)} x^{m}\right)} \log\left(-c x^{2} + 1\right)}{8 \, {\left(c {\left(m + 1\right)} x^{2} - m - 1\right)}}\,{d x}"," ",0,"-1/8*b^3*d^m*x*x^m*log(-c*x^2 + 1)^3/(m + 1) + (d*x)^(m + 1)*a^3/(d*(m + 1)) + integrate(1/8*((b^3*c*d^m*(m + 1)*x^2 - b^3*d^m*(m + 1))*x^m*log(c*x^2 + 1)^3 + 6*(a*b^2*c*d^m*(m + 1)*x^2 - a*b^2*d^m*(m + 1))*x^m*log(c*x^2 + 1)^2 + 12*(a^2*b*c*d^m*(m + 1)*x^2 - a^2*b*d^m*(m + 1))*x^m*log(c*x^2 + 1) + 3*((b^3*c*d^m*(m + 1)*x^2 - b^3*d^m*(m + 1))*x^m*log(c*x^2 + 1) - 2*(a*b^2*d^m*(m + 1) - (a*b^2*c*d^m*(m + 1) + b^3*c*d^m)*x^2)*x^m)*log(-c*x^2 + 1)^2 - 3*((b^3*c*d^m*(m + 1)*x^2 - b^3*d^m*(m + 1))*x^m*log(c*x^2 + 1)^2 + 4*(a*b^2*c*d^m*(m + 1)*x^2 - a*b^2*d^m*(m + 1))*x^m*log(c*x^2 + 1) + 4*(a^2*b*c*d^m*(m + 1)*x^2 - a^2*b*d^m*(m + 1))*x^m)*log(-c*x^2 + 1))/(c*(m + 1)*x^2 - m - 1), x)","F",0
95,0,0,0,0.000000," ","integrate((d*x)^m*(a+b*arctanh(c*x^2))^2,x, algorithm=""maxima"")","\frac{b^{2} d^{m} x x^{m} \log\left(-c x^{2} + 1\right)^{2}}{4 \, {\left(m + 1\right)}} + \frac{\left(d x\right)^{m + 1} a^{2}}{d {\left(m + 1\right)}} - \int -\frac{{\left(b^{2} c d^{m} {\left(m + 1\right)} x^{2} - b^{2} d^{m} {\left(m + 1\right)}\right)} x^{m} \log\left(c x^{2} + 1\right)^{2} + 4 \, {\left(a b c d^{m} {\left(m + 1\right)} x^{2} - a b d^{m} {\left(m + 1\right)}\right)} x^{m} \log\left(c x^{2} + 1\right) - 2 \, {\left({\left(b^{2} c d^{m} {\left(m + 1\right)} x^{2} - b^{2} d^{m} {\left(m + 1\right)}\right)} x^{m} \log\left(c x^{2} + 1\right) - 2 \, {\left(a b d^{m} {\left(m + 1\right)} - {\left(a b c d^{m} {\left(m + 1\right)} + b^{2} c d^{m}\right)} x^{2}\right)} x^{m}\right)} \log\left(-c x^{2} + 1\right)}{4 \, {\left(c {\left(m + 1\right)} x^{2} - m - 1\right)}}\,{d x}"," ",0,"1/4*b^2*d^m*x*x^m*log(-c*x^2 + 1)^2/(m + 1) + (d*x)^(m + 1)*a^2/(d*(m + 1)) - integrate(-1/4*((b^2*c*d^m*(m + 1)*x^2 - b^2*d^m*(m + 1))*x^m*log(c*x^2 + 1)^2 + 4*(a*b*c*d^m*(m + 1)*x^2 - a*b*d^m*(m + 1))*x^m*log(c*x^2 + 1) - 2*((b^2*c*d^m*(m + 1)*x^2 - b^2*d^m*(m + 1))*x^m*log(c*x^2 + 1) - 2*(a*b*d^m*(m + 1) - (a*b*c*d^m*(m + 1) + b^2*c*d^m)*x^2)*x^m)*log(-c*x^2 + 1))/(c*(m + 1)*x^2 - m - 1), x)","F",0
96,0,0,0,0.000000," ","integrate((d*x)^m*(a+b*arctanh(c*x^2)),x, algorithm=""maxima"")","\frac{1}{2} \, {\left(4 \, c d^{m} \int \frac{x^{2} x^{m}}{c^{2} {\left(m + 1\right)} x^{4} - m - 1}\,{d x} + \frac{d^{m} x x^{m} \log\left(c x^{2} + 1\right) - d^{m} x x^{m} \log\left(-c x^{2} + 1\right)}{m + 1}\right)} b + \frac{\left(d x\right)^{m + 1} a}{d {\left(m + 1\right)}}"," ",0,"1/2*(4*c*d^m*integrate(x^2*x^m/(c^2*(m + 1)*x^4 - m - 1), x) + (d^m*x*x^m*log(c*x^2 + 1) - d^m*x*x^m*log(-c*x^2 + 1))/(m + 1))*b + (d*x)^(m + 1)*a/(d*(m + 1))","F",0
97,0,0,0,0.000000," ","integrate((d*x)^m/(a+b*arctanh(c*x^2)),x, algorithm=""maxima"")","\int \frac{\left(d x\right)^{m}}{b \operatorname{artanh}\left(c x^{2}\right) + a}\,{d x}"," ",0,"integrate((d*x)^m/(b*arctanh(c*x^2) + a), x)","F",0
98,0,0,0,0.000000," ","integrate((d*x)^m/(a+b*arctanh(c*x^2))^2,x, algorithm=""maxima"")","\frac{{\left(c^{2} d^{m} x^{4} - d^{m}\right)} x^{m}}{b^{2} c x \log\left(c x^{2} + 1\right) - b^{2} c x \log\left(-c x^{2} + 1\right) + 2 \, a b c x} + \int -\frac{{\left(c^{2} d^{m} {\left(m + 3\right)} x^{4} - d^{m} {\left(m - 1\right)}\right)} x^{m}}{b^{2} c x^{2} \log\left(c x^{2} + 1\right) - b^{2} c x^{2} \log\left(-c x^{2} + 1\right) + 2 \, a b c x^{2}}\,{d x}"," ",0,"(c^2*d^m*x^4 - d^m)*x^m/(b^2*c*x*log(c*x^2 + 1) - b^2*c*x*log(-c*x^2 + 1) + 2*a*b*c*x) + integrate(-(c^2*d^m*(m + 3)*x^4 - d^m*(m - 1))*x^m/(b^2*c*x^2*log(c*x^2 + 1) - b^2*c*x^2*log(-c*x^2 + 1) + 2*a*b*c*x^2), x)","F",0
99,1,69,0,0.303506," ","integrate(x^11*(a+b*arctanh(c*x^3)),x, algorithm=""maxima"")","\frac{1}{12} \, a x^{12} + \frac{1}{72} \, {\left(6 \, x^{12} \operatorname{artanh}\left(c x^{3}\right) + c {\left(\frac{2 \, {\left(c^{2} x^{9} + 3 \, x^{3}\right)}}{c^{4}} - \frac{3 \, \log\left(c x^{3} + 1\right)}{c^{5}} + \frac{3 \, \log\left(c x^{3} - 1\right)}{c^{5}}\right)}\right)} b"," ",0,"1/12*a*x^12 + 1/72*(6*x^12*arctanh(c*x^3) + c*(2*(c^2*x^9 + 3*x^3)/c^4 - 3*log(c*x^3 + 1)/c^5 + 3*log(c*x^3 - 1)/c^5))*b","A",0
100,1,46,0,0.306152," ","integrate(x^8*(a+b*arctanh(c*x^3)),x, algorithm=""maxima"")","\frac{1}{9} \, a x^{9} + \frac{1}{18} \, {\left(2 \, x^{9} \operatorname{artanh}\left(c x^{3}\right) + {\left(\frac{x^{6}}{c^{2}} + \frac{\log\left(c^{2} x^{6} - 1\right)}{c^{4}}\right)} c\right)} b"," ",0,"1/9*a*x^9 + 1/18*(2*x^9*arctanh(c*x^3) + (x^6/c^2 + log(c^2*x^6 - 1)/c^4)*c)*b","A",0
101,1,58,0,0.304509," ","integrate(x^5*(a+b*arctanh(c*x^3)),x, algorithm=""maxima"")","\frac{1}{6} \, a x^{6} + \frac{1}{12} \, {\left(2 \, x^{6} \operatorname{artanh}\left(c x^{3}\right) + c {\left(\frac{2 \, x^{3}}{c^{2}} - \frac{\log\left(c x^{3} + 1\right)}{c^{3}} + \frac{\log\left(c x^{3} - 1\right)}{c^{3}}\right)}\right)} b"," ",0,"1/6*a*x^6 + 1/12*(2*x^6*arctanh(c*x^3) + c*(2*x^3/c^2 - log(c*x^3 + 1)/c^3 + log(c*x^3 - 1)/c^3))*b","A",0
102,1,37,0,0.299589," ","integrate(x^2*(a+b*arctanh(c*x^3)),x, algorithm=""maxima"")","\frac{1}{3} \, a x^{3} + \frac{{\left(2 \, c x^{3} \operatorname{artanh}\left(c x^{3}\right) + \log\left(-c^{2} x^{6} + 1\right)\right)} b}{6 \, c}"," ",0,"1/3*a*x^3 + 1/6*(2*c*x^3*arctanh(c*x^3) + log(-c^2*x^6 + 1))*b/c","A",0
103,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x^3))/x,x, algorithm=""maxima"")","\frac{1}{2} \, b \int \frac{\log\left(c x^{3} + 1\right) - \log\left(-c x^{3} + 1\right)}{x}\,{d x} + a \log\left(x\right)"," ",0,"1/2*b*integrate((log(c*x^3 + 1) - log(-c*x^3 + 1))/x, x) + a*log(x)","F",0
104,1,41,0,0.306942," ","integrate((a+b*arctanh(c*x^3))/x^4,x, algorithm=""maxima"")","-\frac{1}{6} \, {\left(c {\left(\log\left(c^{2} x^{6} - 1\right) - \log\left(x^{6}\right)\right)} + \frac{2 \, \operatorname{artanh}\left(c x^{3}\right)}{x^{3}}\right)} b - \frac{a}{3 \, x^{3}}"," ",0,"-1/6*(c*(log(c^2*x^6 - 1) - log(x^6)) + 2*arctanh(c*x^3)/x^3)*b - 1/3*a/x^3","A",0
105,1,51,0,0.306418," ","integrate((a+b*arctanh(c*x^3))/x^7,x, algorithm=""maxima"")","\frac{1}{12} \, {\left({\left(c \log\left(c x^{3} + 1\right) - c \log\left(c x^{3} - 1\right) - \frac{2}{x^{3}}\right)} c - \frac{2 \, \operatorname{artanh}\left(c x^{3}\right)}{x^{6}}\right)} b - \frac{a}{6 \, x^{6}}"," ",0,"1/12*((c*log(c*x^3 + 1) - c*log(c*x^3 - 1) - 2/x^3)*c - 2*arctanh(c*x^3)/x^6)*b - 1/6*a/x^6","A",0
106,1,51,0,0.300338," ","integrate((a+b*arctanh(c*x^3))/x^10,x, algorithm=""maxima"")","-\frac{1}{18} \, {\left({\left(c^{2} \log\left(c^{2} x^{6} - 1\right) - c^{2} \log\left(x^{6}\right) + \frac{1}{x^{6}}\right)} c + \frac{2 \, \operatorname{artanh}\left(c x^{3}\right)}{x^{9}}\right)} b - \frac{a}{9 \, x^{9}}"," ",0,"-1/18*((c^2*log(c^2*x^6 - 1) - c^2*log(x^6) + 1/x^6)*c + 2*arctanh(c*x^3)/x^9)*b - 1/9*a/x^9","A",0
107,1,162,0,0.402471," ","integrate(x^3*(a+b*arctanh(c*x^3)),x, algorithm=""maxima"")","\frac{1}{4} \, a x^{4} + \frac{1}{16} \, {\left(4 \, x^{4} \operatorname{artanh}\left(c x^{3}\right) - c {\left(\frac{2 \, \sqrt{3} \arctan\left(\frac{\sqrt{3} {\left(2 \, c^{\frac{2}{3}} x + c^{\frac{1}{3}}\right)}}{3 \, c^{\frac{1}{3}}}\right)}{c^{\frac{7}{3}}} + \frac{2 \, \sqrt{3} \arctan\left(\frac{\sqrt{3} {\left(2 \, c^{\frac{2}{3}} x - c^{\frac{1}{3}}\right)}}{3 \, c^{\frac{1}{3}}}\right)}{c^{\frac{7}{3}}} - \frac{12 \, x}{c^{2}} + \frac{\log\left(c^{\frac{2}{3}} x^{2} + c^{\frac{1}{3}} x + 1\right)}{c^{\frac{7}{3}}} - \frac{\log\left(c^{\frac{2}{3}} x^{2} - c^{\frac{1}{3}} x + 1\right)}{c^{\frac{7}{3}}} + \frac{2 \, \log\left(\frac{c^{\frac{1}{3}} x + 1}{c^{\frac{1}{3}}}\right)}{c^{\frac{7}{3}}} - \frac{2 \, \log\left(\frac{c^{\frac{1}{3}} x - 1}{c^{\frac{1}{3}}}\right)}{c^{\frac{7}{3}}}\right)}\right)} b"," ",0,"1/4*a*x^4 + 1/16*(4*x^4*arctanh(c*x^3) - c*(2*sqrt(3)*arctan(1/3*sqrt(3)*(2*c^(2/3)*x + c^(1/3))/c^(1/3))/c^(7/3) + 2*sqrt(3)*arctan(1/3*sqrt(3)*(2*c^(2/3)*x - c^(1/3))/c^(1/3))/c^(7/3) - 12*x/c^2 + log(c^(2/3)*x^2 + c^(1/3)*x + 1)/c^(7/3) - log(c^(2/3)*x^2 - c^(1/3)*x + 1)/c^(7/3) + 2*log((c^(1/3)*x + 1)/c^(1/3))/c^(7/3) - 2*log((c^(1/3)*x - 1)/c^(1/3))/c^(7/3)))*b","A",0
108,1,90,0,0.402580," ","integrate(a+b*arctanh(c*x^3),x, algorithm=""maxima"")","\frac{1}{4} \, {\left(c {\left(\frac{2 \, \sqrt{3} \arctan\left(\frac{\sqrt{3} {\left(2 \, c^{\frac{4}{3}} x^{2} + c^{\frac{2}{3}}\right)}}{3 \, c^{\frac{2}{3}}}\right)}{c^{\frac{4}{3}}} - \frac{\log\left(c^{\frac{4}{3}} x^{4} + c^{\frac{2}{3}} x^{2} + 1\right)}{c^{\frac{4}{3}}} + \frac{2 \, \log\left(\frac{c^{\frac{2}{3}} x^{2} - 1}{c^{\frac{2}{3}}}\right)}{c^{\frac{4}{3}}}\right)} + 4 \, x \operatorname{artanh}\left(c x^{3}\right)\right)} b + a x"," ",0,"1/4*(c*(2*sqrt(3)*arctan(1/3*sqrt(3)*(2*c^(4/3)*x^2 + c^(2/3))/c^(2/3))/c^(4/3) - log(c^(4/3)*x^4 + c^(2/3)*x^2 + 1)/c^(4/3) + 2*log((c^(2/3)*x^2 - 1)/c^(2/3))/c^(4/3)) + 4*x*arctanh(c*x^3))*b + a*x","A",0
109,1,155,0,0.404864," ","integrate((a+b*arctanh(c*x^3))/x^3,x, algorithm=""maxima"")","\frac{1}{8} \, {\left({\left(\frac{2 \, \sqrt{3} \arctan\left(\frac{\sqrt{3} {\left(2 \, c^{\frac{2}{3}} x + c^{\frac{1}{3}}\right)}}{3 \, c^{\frac{1}{3}}}\right)}{c^{\frac{1}{3}}} + \frac{2 \, \sqrt{3} \arctan\left(\frac{\sqrt{3} {\left(2 \, c^{\frac{2}{3}} x - c^{\frac{1}{3}}\right)}}{3 \, c^{\frac{1}{3}}}\right)}{c^{\frac{1}{3}}} + \frac{\log\left(c^{\frac{2}{3}} x^{2} + c^{\frac{1}{3}} x + 1\right)}{c^{\frac{1}{3}}} - \frac{\log\left(c^{\frac{2}{3}} x^{2} - c^{\frac{1}{3}} x + 1\right)}{c^{\frac{1}{3}}} + \frac{2 \, \log\left(\frac{c^{\frac{1}{3}} x + 1}{c^{\frac{1}{3}}}\right)}{c^{\frac{1}{3}}} - \frac{2 \, \log\left(\frac{c^{\frac{1}{3}} x - 1}{c^{\frac{1}{3}}}\right)}{c^{\frac{1}{3}}}\right)} c - \frac{4 \, \operatorname{artanh}\left(c x^{3}\right)}{x^{2}}\right)} b - \frac{a}{2 \, x^{2}}"," ",0,"1/8*((2*sqrt(3)*arctan(1/3*sqrt(3)*(2*c^(2/3)*x + c^(1/3))/c^(1/3))/c^(1/3) + 2*sqrt(3)*arctan(1/3*sqrt(3)*(2*c^(2/3)*x - c^(1/3))/c^(1/3))/c^(1/3) + log(c^(2/3)*x^2 + c^(1/3)*x + 1)/c^(1/3) - log(c^(2/3)*x^2 - c^(1/3)*x + 1)/c^(1/3) + 2*log((c^(1/3)*x + 1)/c^(1/3))/c^(1/3) - 2*log((c^(1/3)*x - 1)/c^(1/3))/c^(1/3))*c - 4*arctanh(c*x^3)/x^2)*b - 1/2*a/x^2","A",0
110,1,100,0,0.423998," ","integrate((a+b*arctanh(c*x^3))/x^6,x, algorithm=""maxima"")","-\frac{1}{20} \, {\left({\left(2 \, \sqrt{3} c^{\frac{2}{3}} \arctan\left(\frac{\sqrt{3} {\left(2 \, c^{\frac{4}{3}} x^{2} + c^{\frac{2}{3}}\right)}}{3 \, c^{\frac{2}{3}}}\right) - c^{\frac{2}{3}} \log\left(c^{\frac{4}{3}} x^{4} + c^{\frac{2}{3}} x^{2} + 1\right) + 2 \, c^{\frac{2}{3}} \log\left(\frac{c^{\frac{2}{3}} x^{2} - 1}{c^{\frac{2}{3}}}\right) + \frac{6}{x^{2}}\right)} c + \frac{4 \, \operatorname{artanh}\left(c x^{3}\right)}{x^{5}}\right)} b - \frac{a}{5 \, x^{5}}"," ",0,"-1/20*((2*sqrt(3)*c^(2/3)*arctan(1/3*sqrt(3)*(2*c^(4/3)*x^2 + c^(2/3))/c^(2/3)) - c^(2/3)*log(c^(4/3)*x^4 + c^(2/3)*x^2 + 1) + 2*c^(2/3)*log((c^(2/3)*x^2 - 1)/c^(2/3)) + 6/x^2)*c + 4*arctanh(c*x^3)/x^5)*b - 1/5*a/x^5","A",0
111,1,164,0,0.414479," ","integrate(x^7*(a+b*arctanh(c*x^3)),x, algorithm=""maxima"")","\frac{1}{8} \, a x^{8} + \frac{1}{160} \, {\left(20 \, x^{8} \operatorname{artanh}\left(c x^{3}\right) + {\left(\frac{12 \, x^{5}}{c^{2}} + \frac{10 \, \sqrt{3} \arctan\left(\frac{\sqrt{3} {\left(2 \, c^{\frac{2}{3}} x + c^{\frac{1}{3}}\right)}}{3 \, c^{\frac{1}{3}}}\right)}{c^{\frac{11}{3}}} + \frac{10 \, \sqrt{3} \arctan\left(\frac{\sqrt{3} {\left(2 \, c^{\frac{2}{3}} x - c^{\frac{1}{3}}\right)}}{3 \, c^{\frac{1}{3}}}\right)}{c^{\frac{11}{3}}} - \frac{5 \, \log\left(c^{\frac{2}{3}} x^{2} + c^{\frac{1}{3}} x + 1\right)}{c^{\frac{11}{3}}} + \frac{5 \, \log\left(c^{\frac{2}{3}} x^{2} - c^{\frac{1}{3}} x + 1\right)}{c^{\frac{11}{3}}} - \frac{10 \, \log\left(\frac{c^{\frac{1}{3}} x + 1}{c^{\frac{1}{3}}}\right)}{c^{\frac{11}{3}}} + \frac{10 \, \log\left(\frac{c^{\frac{1}{3}} x - 1}{c^{\frac{1}{3}}}\right)}{c^{\frac{11}{3}}}\right)} c\right)} b"," ",0,"1/8*a*x^8 + 1/160*(20*x^8*arctanh(c*x^3) + (12*x^5/c^2 + 10*sqrt(3)*arctan(1/3*sqrt(3)*(2*c^(2/3)*x + c^(1/3))/c^(1/3))/c^(11/3) + 10*sqrt(3)*arctan(1/3*sqrt(3)*(2*c^(2/3)*x - c^(1/3))/c^(1/3))/c^(11/3) - 5*log(c^(2/3)*x^2 + c^(1/3)*x + 1)/c^(11/3) + 5*log(c^(2/3)*x^2 - c^(1/3)*x + 1)/c^(11/3) - 10*log((c^(1/3)*x + 1)/c^(1/3))/c^(11/3) + 10*log((c^(1/3)*x - 1)/c^(1/3))/c^(11/3))*c)*b","A",0
112,1,103,0,0.414454," ","integrate(x^4*(a+b*arctanh(c*x^3)),x, algorithm=""maxima"")","\frac{1}{5} \, a x^{5} + \frac{1}{20} \, {\left(4 \, x^{5} \operatorname{artanh}\left(c x^{3}\right) + c {\left(\frac{6 \, x^{2}}{c^{2}} - \frac{2 \, \sqrt{3} \arctan\left(\frac{\sqrt{3} {\left(2 \, c^{\frac{4}{3}} x^{2} + c^{\frac{2}{3}}\right)}}{3 \, c^{\frac{2}{3}}}\right)}{c^{\frac{8}{3}}} - \frac{\log\left(c^{\frac{4}{3}} x^{4} + c^{\frac{2}{3}} x^{2} + 1\right)}{c^{\frac{8}{3}}} + \frac{2 \, \log\left(\frac{c^{\frac{2}{3}} x^{2} - 1}{c^{\frac{2}{3}}}\right)}{c^{\frac{8}{3}}}\right)}\right)} b"," ",0,"1/5*a*x^5 + 1/20*(4*x^5*arctanh(c*x^3) + c*(6*x^2/c^2 - 2*sqrt(3)*arctan(1/3*sqrt(3)*(2*c^(4/3)*x^2 + c^(2/3))/c^(2/3))/c^(8/3) - log(c^(4/3)*x^4 + c^(2/3)*x^2 + 1)/c^(8/3) + 2*log((c^(2/3)*x^2 - 1)/c^(2/3))/c^(8/3)))*b","A",0
113,1,155,0,0.412245," ","integrate(x*(a+b*arctanh(c*x^3)),x, algorithm=""maxima"")","\frac{1}{2} \, a x^{2} + \frac{1}{8} \, {\left(4 \, x^{2} \operatorname{artanh}\left(c x^{3}\right) + c {\left(\frac{2 \, \sqrt{3} \arctan\left(\frac{\sqrt{3} {\left(2 \, c^{\frac{2}{3}} x + c^{\frac{1}{3}}\right)}}{3 \, c^{\frac{1}{3}}}\right)}{c^{\frac{5}{3}}} + \frac{2 \, \sqrt{3} \arctan\left(\frac{\sqrt{3} {\left(2 \, c^{\frac{2}{3}} x - c^{\frac{1}{3}}\right)}}{3 \, c^{\frac{1}{3}}}\right)}{c^{\frac{5}{3}}} - \frac{\log\left(c^{\frac{2}{3}} x^{2} + c^{\frac{1}{3}} x + 1\right)}{c^{\frac{5}{3}}} + \frac{\log\left(c^{\frac{2}{3}} x^{2} - c^{\frac{1}{3}} x + 1\right)}{c^{\frac{5}{3}}} - \frac{2 \, \log\left(\frac{c^{\frac{1}{3}} x + 1}{c^{\frac{1}{3}}}\right)}{c^{\frac{5}{3}}} + \frac{2 \, \log\left(\frac{c^{\frac{1}{3}} x - 1}{c^{\frac{1}{3}}}\right)}{c^{\frac{5}{3}}}\right)}\right)} b"," ",0,"1/2*a*x^2 + 1/8*(4*x^2*arctanh(c*x^3) + c*(2*sqrt(3)*arctan(1/3*sqrt(3)*(2*c^(2/3)*x + c^(1/3))/c^(1/3))/c^(5/3) + 2*sqrt(3)*arctan(1/3*sqrt(3)*(2*c^(2/3)*x - c^(1/3))/c^(1/3))/c^(5/3) - log(c^(2/3)*x^2 + c^(1/3)*x + 1)/c^(5/3) + log(c^(2/3)*x^2 - c^(1/3)*x + 1)/c^(5/3) - 2*log((c^(1/3)*x + 1)/c^(1/3))/c^(5/3) + 2*log((c^(1/3)*x - 1)/c^(1/3))/c^(5/3)))*b","A",0
114,1,94,0,0.411861," ","integrate((a+b*arctanh(c*x^3))/x^2,x, algorithm=""maxima"")","\frac{1}{4} \, {\left(c {\left(\frac{2 \, \sqrt{3} \arctan\left(\frac{\sqrt{3} {\left(2 \, c^{\frac{4}{3}} x^{2} + c^{\frac{2}{3}}\right)}}{3 \, c^{\frac{2}{3}}}\right)}{c^{\frac{2}{3}}} + \frac{\log\left(c^{\frac{4}{3}} x^{4} + c^{\frac{2}{3}} x^{2} + 1\right)}{c^{\frac{2}{3}}} - \frac{2 \, \log\left(\frac{c^{\frac{2}{3}} x^{2} - 1}{c^{\frac{2}{3}}}\right)}{c^{\frac{2}{3}}}\right)} - \frac{4 \, \operatorname{artanh}\left(c x^{3}\right)}{x}\right)} b - \frac{a}{x}"," ",0,"1/4*(c*(2*sqrt(3)*arctan(1/3*sqrt(3)*(2*c^(4/3)*x^2 + c^(2/3))/c^(2/3))/c^(2/3) + log(c^(4/3)*x^4 + c^(2/3)*x^2 + 1)/c^(2/3) - 2*log((c^(2/3)*x^2 - 1)/c^(2/3))/c^(2/3)) - 4*arctanh(c*x^3)/x)*b - a/x","A",0
115,1,160,0,0.417651," ","integrate((a+b*arctanh(c*x^3))/x^5,x, algorithm=""maxima"")","-\frac{1}{16} \, {\left({\left(2 \, \sqrt{3} c^{\frac{1}{3}} \arctan\left(\frac{\sqrt{3} {\left(2 \, c^{\frac{2}{3}} x + c^{\frac{1}{3}}\right)}}{3 \, c^{\frac{1}{3}}}\right) + 2 \, \sqrt{3} c^{\frac{1}{3}} \arctan\left(\frac{\sqrt{3} {\left(2 \, c^{\frac{2}{3}} x - c^{\frac{1}{3}}\right)}}{3 \, c^{\frac{1}{3}}}\right) - c^{\frac{1}{3}} \log\left(c^{\frac{2}{3}} x^{2} + c^{\frac{1}{3}} x + 1\right) + c^{\frac{1}{3}} \log\left(c^{\frac{2}{3}} x^{2} - c^{\frac{1}{3}} x + 1\right) - 2 \, c^{\frac{1}{3}} \log\left(\frac{c^{\frac{1}{3}} x + 1}{c^{\frac{1}{3}}}\right) + 2 \, c^{\frac{1}{3}} \log\left(\frac{c^{\frac{1}{3}} x - 1}{c^{\frac{1}{3}}}\right) + \frac{12}{x}\right)} c + \frac{4 \, \operatorname{artanh}\left(c x^{3}\right)}{x^{4}}\right)} b - \frac{a}{4 \, x^{4}}"," ",0,"-1/16*((2*sqrt(3)*c^(1/3)*arctan(1/3*sqrt(3)*(2*c^(2/3)*x + c^(1/3))/c^(1/3)) + 2*sqrt(3)*c^(1/3)*arctan(1/3*sqrt(3)*(2*c^(2/3)*x - c^(1/3))/c^(1/3)) - c^(1/3)*log(c^(2/3)*x^2 + c^(1/3)*x + 1) + c^(1/3)*log(c^(2/3)*x^2 - c^(1/3)*x + 1) - 2*c^(1/3)*log((c^(1/3)*x + 1)/c^(1/3)) + 2*c^(1/3)*log((c^(1/3)*x - 1)/c^(1/3)) + 12/x)*c + 4*arctanh(c*x^3)/x^4)*b - 1/4*a/x^4","A",0
116,1,217,0,0.324119," ","integrate(x^11*(a+b*arctanh(c*x^3))^2,x, algorithm=""maxima"")","\frac{1}{12} \, b^{2} x^{12} \operatorname{artanh}\left(c x^{3}\right)^{2} + \frac{1}{12} \, a^{2} x^{12} + \frac{1}{36} \, {\left(6 \, x^{12} \operatorname{artanh}\left(c x^{3}\right) + c {\left(\frac{2 \, {\left(c^{2} x^{9} + 3 \, x^{3}\right)}}{c^{4}} - \frac{3 \, \log\left(c x^{3} + 1\right)}{c^{5}} + \frac{3 \, \log\left(c x^{3} - 1\right)}{c^{5}}\right)}\right)} a b + \frac{1}{144} \, {\left(4 \, c {\left(\frac{2 \, {\left(c^{2} x^{9} + 3 \, x^{3}\right)}}{c^{4}} - \frac{3 \, \log\left(c x^{3} + 1\right)}{c^{5}} + \frac{3 \, \log\left(c x^{3} - 1\right)}{c^{5}}\right)} \operatorname{artanh}\left(c x^{3}\right) + \frac{4 \, c^{2} x^{6} - 2 \, {\left(3 \, \log\left(c x^{3} - 1\right) - 8\right)} \log\left(c x^{3} + 1\right) + 3 \, \log\left(c x^{3} + 1\right)^{2} + 3 \, \log\left(c x^{3} - 1\right)^{2} + 16 \, \log\left(c x^{3} - 1\right)}{c^{4}}\right)} b^{2}"," ",0,"1/12*b^2*x^12*arctanh(c*x^3)^2 + 1/12*a^2*x^12 + 1/36*(6*x^12*arctanh(c*x^3) + c*(2*(c^2*x^9 + 3*x^3)/c^4 - 3*log(c*x^3 + 1)/c^5 + 3*log(c*x^3 - 1)/c^5))*a*b + 1/144*(4*c*(2*(c^2*x^9 + 3*x^3)/c^4 - 3*log(c*x^3 + 1)/c^5 + 3*log(c*x^3 - 1)/c^5)*arctanh(c*x^3) + (4*c^2*x^6 - 2*(3*log(c*x^3 - 1) - 8)*log(c*x^3 + 1) + 3*log(c*x^3 + 1)^2 + 3*log(c*x^3 - 1)^2 + 16*log(c*x^3 - 1))/c^4)*b^2","A",0
117,0,0,0,0.000000," ","integrate(x^8*(a+b*arctanh(c*x^3))^2,x, algorithm=""maxima"")","\frac{1}{9} \, a^{2} x^{9} + \frac{1}{9} \, {\left(2 \, x^{9} \operatorname{artanh}\left(c x^{3}\right) + {\left(\frac{x^{6}}{c^{2}} + \frac{\log\left(c^{2} x^{6} - 1\right)}{c^{4}}\right)} c\right)} a b + \frac{1}{648} \, {\left(18 \, x^{9} \log\left(-c x^{3} + 1\right)^{2} - 2 \, c^{4} {\left(\frac{2 \, {\left(c^{2} x^{9} + 3 \, x^{3}\right)}}{c^{6}} - \frac{3 \, \log\left(c x^{3} + 1\right)}{c^{7}} + \frac{3 \, \log\left(c x^{3} - 1\right)}{c^{7}}\right)} + 3 \, {\left(\frac{x^{6}}{c^{4}} + \frac{\log\left(c^{2} x^{6} - 1\right)}{c^{6}}\right)} c^{3} + 1944 \, c^{3} \int \frac{x^{11} \log\left(c x^{3} + 1\right)}{9 \, {\left(c^{4} x^{6} - c^{2}\right)}}\,{d x} - 9 \, c^{2} {\left(\frac{2 \, x^{3}}{c^{4}} - \frac{\log\left(c x^{3} + 1\right)}{c^{5}} + \frac{\log\left(c x^{3} - 1\right)}{c^{5}}\right)} - 6 \, c {\left(\frac{2 \, c^{2} x^{9} + 3 \, c x^{6} + 6 \, x^{3}}{c^{3}} + \frac{6 \, \log\left(c x^{3} - 1\right)}{c^{4}}\right)} \log\left(-c x^{3} + 1\right) + 972 \, c \int \frac{x^{5} \log\left(c x^{3} + 1\right)}{9 \, {\left(c^{4} x^{6} - c^{2}\right)}}\,{d x} + \frac{6 \, {\left(3 \, c^{3} x^{9} \log\left(c x^{3} + 1\right)^{2} + {\left(2 \, c^{3} x^{9} - 3 \, c^{2} x^{6} + 6 \, c x^{3} - 6 \, {\left(c^{3} x^{9} + 1\right)} \log\left(c x^{3} + 1\right)\right)} \log\left(-c x^{3} + 1\right)\right)}}{c^{3}} + \frac{4 \, c^{3} x^{9} + 15 \, c^{2} x^{6} + 66 \, c x^{3} + 18 \, \log\left(c x^{3} - 1\right)^{2} + 66 \, \log\left(c x^{3} - 1\right)}{c^{3}} - \frac{18 \, \log\left(9 \, c^{4} x^{6} - 9 \, c^{2}\right)}{c^{3}} + 972 \, \int \frac{x^{2} \log\left(c x^{3} + 1\right)}{9 \, {\left(c^{4} x^{6} - c^{2}\right)}}\,{d x}\right)} b^{2}"," ",0,"1/9*a^2*x^9 + 1/9*(2*x^9*arctanh(c*x^3) + (x^6/c^2 + log(c^2*x^6 - 1)/c^4)*c)*a*b + 1/648*(18*x^9*log(-c*x^3 + 1)^2 - 2*c^4*(2*(c^2*x^9 + 3*x^3)/c^6 - 3*log(c*x^3 + 1)/c^7 + 3*log(c*x^3 - 1)/c^7) + 3*(x^6/c^4 + log(c^2*x^6 - 1)/c^6)*c^3 + 1944*c^3*integrate(1/9*x^11*log(c*x^3 + 1)/(c^4*x^6 - c^2), x) - 9*c^2*(2*x^3/c^4 - log(c*x^3 + 1)/c^5 + log(c*x^3 - 1)/c^5) - 6*c*((2*c^2*x^9 + 3*c*x^6 + 6*x^3)/c^3 + 6*log(c*x^3 - 1)/c^4)*log(-c*x^3 + 1) + 972*c*integrate(1/9*x^5*log(c*x^3 + 1)/(c^4*x^6 - c^2), x) + 6*(3*c^3*x^9*log(c*x^3 + 1)^2 + (2*c^3*x^9 - 3*c^2*x^6 + 6*c*x^3 - 6*(c^3*x^9 + 1)*log(c*x^3 + 1))*log(-c*x^3 + 1))/c^3 + (4*c^3*x^9 + 15*c^2*x^6 + 66*c*x^3 + 18*log(c*x^3 - 1)^2 + 66*log(c*x^3 - 1))/c^3 - 18*log(9*c^4*x^6 - 9*c^2)/c^3 + 972*integrate(1/9*x^2*log(c*x^3 + 1)/(c^4*x^6 - c^2), x))*b^2","F",0
118,1,186,0,0.321769," ","integrate(x^5*(a+b*arctanh(c*x^3))^2,x, algorithm=""maxima"")","\frac{1}{6} \, b^{2} x^{6} \operatorname{artanh}\left(c x^{3}\right)^{2} + \frac{1}{6} \, a^{2} x^{6} + \frac{1}{6} \, {\left(2 \, x^{6} \operatorname{artanh}\left(c x^{3}\right) + c {\left(\frac{2 \, x^{3}}{c^{2}} - \frac{\log\left(c x^{3} + 1\right)}{c^{3}} + \frac{\log\left(c x^{3} - 1\right)}{c^{3}}\right)}\right)} a b + \frac{1}{24} \, {\left(4 \, c {\left(\frac{2 \, x^{3}}{c^{2}} - \frac{\log\left(c x^{3} + 1\right)}{c^{3}} + \frac{\log\left(c x^{3} - 1\right)}{c^{3}}\right)} \operatorname{artanh}\left(c x^{3}\right) - \frac{2 \, {\left(\log\left(c x^{3} - 1\right) - 2\right)} \log\left(c x^{3} + 1\right) - \log\left(c x^{3} + 1\right)^{2} - \log\left(c x^{3} - 1\right)^{2} - 4 \, \log\left(c x^{3} - 1\right)}{c^{2}}\right)} b^{2}"," ",0,"1/6*b^2*x^6*arctanh(c*x^3)^2 + 1/6*a^2*x^6 + 1/6*(2*x^6*arctanh(c*x^3) + c*(2*x^3/c^2 - log(c*x^3 + 1)/c^3 + log(c*x^3 - 1)/c^3))*a*b + 1/24*(4*c*(2*x^3/c^2 - log(c*x^3 + 1)/c^3 + log(c*x^3 - 1)/c^3)*arctanh(c*x^3) - (2*(log(c*x^3 - 1) - 2)*log(c*x^3 + 1) - log(c*x^3 + 1)^2 - log(c*x^3 - 1)^2 - 4*log(c*x^3 - 1))/c^2)*b^2","B",0
119,0,0,0,0.000000," ","integrate(x^2*(a+b*arctanh(c*x^3))^2,x, algorithm=""maxima"")","\frac{1}{3} \, a^{2} x^{3} + \frac{1}{12} \, {\left(x^{3} \log\left(-c x^{3} + 1\right)^{2} - c^{2} {\left(\frac{2 \, x^{3}}{c^{2}} - \frac{\log\left(c x^{3} + 1\right)}{c^{3}} + \frac{\log\left(c x^{3} - 1\right)}{c^{3}}\right)} - 2 \, {\left(\frac{x^{3}}{c} + \frac{\log\left(c x^{3} - 1\right)}{c^{2}}\right)} c \log\left(-c x^{3} + 1\right) + 18 \, c \int \frac{x^{5} \log\left(c x^{3} + 1\right)}{c^{2} x^{6} - 1}\,{d x} + \frac{c x^{3} \log\left(c x^{3} + 1\right)^{2} + 2 \, {\left(c x^{3} - {\left(c x^{3} + 1\right)} \log\left(c x^{3} + 1\right)\right)} \log\left(-c x^{3} + 1\right)}{c} + \frac{2 \, c x^{3} + \log\left(c x^{3} - 1\right)^{2} + 2 \, \log\left(c x^{3} - 1\right)}{c} - \frac{\log\left(c^{2} x^{6} - 1\right)}{c} + 6 \, \int \frac{x^{2} \log\left(c x^{3} + 1\right)}{c^{2} x^{6} - 1}\,{d x}\right)} b^{2} + \frac{{\left(2 \, c x^{3} \operatorname{artanh}\left(c x^{3}\right) + \log\left(-c^{2} x^{6} + 1\right)\right)} a b}{3 \, c}"," ",0,"1/3*a^2*x^3 + 1/12*(x^3*log(-c*x^3 + 1)^2 - c^2*(2*x^3/c^2 - log(c*x^3 + 1)/c^3 + log(c*x^3 - 1)/c^3) - 2*(x^3/c + log(c*x^3 - 1)/c^2)*c*log(-c*x^3 + 1) + 18*c*integrate(x^5*log(c*x^3 + 1)/(c^2*x^6 - 1), x) + (c*x^3*log(c*x^3 + 1)^2 + 2*(c*x^3 - (c*x^3 + 1)*log(c*x^3 + 1))*log(-c*x^3 + 1))/c + (2*c*x^3 + log(c*x^3 - 1)^2 + 2*log(c*x^3 - 1))/c - log(c^2*x^6 - 1)/c + 6*integrate(x^2*log(c*x^3 + 1)/(c^2*x^6 - 1), x))*b^2 + 1/3*(2*c*x^3*arctanh(c*x^3) + log(-c^2*x^6 + 1))*a*b/c","F",0
120,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x^3))^2/x,x, algorithm=""maxima"")","a^{2} \log\left(x\right) + \int \frac{b^{2} {\left(\log\left(c x^{3} + 1\right) - \log\left(-c x^{3} + 1\right)\right)}^{2}}{4 \, x} + \frac{a b {\left(\log\left(c x^{3} + 1\right) - \log\left(-c x^{3} + 1\right)\right)}}{x}\,{d x}"," ",0,"a^2*log(x) + integrate(1/4*b^2*(log(c*x^3 + 1) - log(-c*x^3 + 1))^2/x + a*b*(log(c*x^3 + 1) - log(-c*x^3 + 1))/x, x)","F",0
121,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x^3))^2/x^4,x, algorithm=""maxima"")","-\frac{1}{3} \, {\left(c {\left(\log\left(c^{2} x^{6} - 1\right) - \log\left(x^{6}\right)\right)} + \frac{2 \, \operatorname{artanh}\left(c x^{3}\right)}{x^{3}}\right)} a b - \frac{1}{12} \, b^{2} {\left(\frac{\log\left(-c x^{3} + 1\right)^{2}}{x^{3}} + 3 \, \int -\frac{{\left(c x^{3} - 1\right)} \log\left(c x^{3} + 1\right)^{2} + 2 \, {\left(c x^{3} - {\left(c x^{3} - 1\right)} \log\left(c x^{3} + 1\right)\right)} \log\left(-c x^{3} + 1\right)}{c x^{7} - x^{4}}\,{d x}\right)} - \frac{a^{2}}{3 \, x^{3}}"," ",0,"-1/3*(c*(log(c^2*x^6 - 1) - log(x^6)) + 2*arctanh(c*x^3)/x^3)*a*b - 1/12*b^2*(log(-c*x^3 + 1)^2/x^3 + 3*integrate(-((c*x^3 - 1)*log(c*x^3 + 1)^2 + 2*(c*x^3 - (c*x^3 - 1)*log(c*x^3 + 1))*log(-c*x^3 + 1))/(c*x^7 - x^4), x)) - 1/3*a^2/x^3","F",0
122,1,175,0,0.329357," ","integrate((a+b*arctanh(c*x^3))^2/x^7,x, algorithm=""maxima"")","\frac{1}{6} \, {\left({\left(c \log\left(c x^{3} + 1\right) - c \log\left(c x^{3} - 1\right) - \frac{2}{x^{3}}\right)} c - \frac{2 \, \operatorname{artanh}\left(c x^{3}\right)}{x^{6}}\right)} a b + \frac{1}{24} \, {\left({\left(2 \, {\left(\log\left(c x^{3} - 1\right) - 2\right)} \log\left(c x^{3} + 1\right) - \log\left(c x^{3} + 1\right)^{2} - \log\left(c x^{3} - 1\right)^{2} - 4 \, \log\left(c x^{3} - 1\right) + 24 \, \log\left(x\right)\right)} c^{2} + 4 \, {\left(c \log\left(c x^{3} + 1\right) - c \log\left(c x^{3} - 1\right) - \frac{2}{x^{3}}\right)} c \operatorname{artanh}\left(c x^{3}\right)\right)} b^{2} - \frac{b^{2} \operatorname{artanh}\left(c x^{3}\right)^{2}}{6 \, x^{6}} - \frac{a^{2}}{6 \, x^{6}}"," ",0,"1/6*((c*log(c*x^3 + 1) - c*log(c*x^3 - 1) - 2/x^3)*c - 2*arctanh(c*x^3)/x^6)*a*b + 1/24*((2*(log(c*x^3 - 1) - 2)*log(c*x^3 + 1) - log(c*x^3 + 1)^2 - log(c*x^3 - 1)^2 - 4*log(c*x^3 - 1) + 24*log(x))*c^2 + 4*(c*log(c*x^3 + 1) - c*log(c*x^3 - 1) - 2/x^3)*c*arctanh(c*x^3))*b^2 - 1/6*b^2*arctanh(c*x^3)^2/x^6 - 1/6*a^2/x^6","B",0
123,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x^3))^2/x^10,x, algorithm=""maxima"")","-\frac{1}{9} \, {\left({\left(c^{2} \log\left(c^{2} x^{6} - 1\right) - c^{2} \log\left(x^{6}\right) + \frac{1}{x^{6}}\right)} c + \frac{2 \, \operatorname{artanh}\left(c x^{3}\right)}{x^{9}}\right)} a b - \frac{1}{36} \, b^{2} {\left(\frac{\log\left(-c x^{3} + 1\right)^{2}}{x^{9}} + 9 \, \int -\frac{3 \, {\left(c x^{3} - 1\right)} \log\left(c x^{3} + 1\right)^{2} + 2 \, {\left(c x^{3} - 3 \, {\left(c x^{3} - 1\right)} \log\left(c x^{3} + 1\right)\right)} \log\left(-c x^{3} + 1\right)}{3 \, {\left(c x^{13} - x^{10}\right)}}\,{d x}\right)} - \frac{a^{2}}{9 \, x^{9}}"," ",0,"-1/9*((c^2*log(c^2*x^6 - 1) - c^2*log(x^6) + 1/x^6)*c + 2*arctanh(c*x^3)/x^9)*a*b - 1/36*b^2*(log(-c*x^3 + 1)^2/x^9 + 9*integrate(-1/3*(3*(c*x^3 - 1)*log(c*x^3 + 1)^2 + 2*(c*x^3 - 3*(c*x^3 - 1)*log(c*x^3 + 1))*log(-c*x^3 + 1))/(c*x^13 - x^10), x)) - 1/9*a^2/x^9","F",0
124,0,0,0,0.000000," ","integrate(x^8*(a+b*arctanh(c*x^3))^3,x, algorithm=""maxima"")","\frac{1}{9} \, a^{3} x^{9} + \frac{1}{6} \, {\left(2 \, x^{9} \operatorname{artanh}\left(c x^{3}\right) + {\left(\frac{x^{6}}{c^{2}} + \frac{\log\left(c^{2} x^{6} - 1\right)}{c^{4}}\right)} c\right)} a^{2} b - \frac{{\left(b^{3} c^{3} x^{9} - b^{3}\right)} \log\left(-c x^{3} + 1\right)^{3} - 3 \, {\left(2 \, a b^{2} c^{3} x^{9} + b^{3} c^{2} x^{6} + {\left(b^{3} c^{3} x^{9} + b^{3}\right)} \log\left(c x^{3} + 1\right)\right)} \log\left(-c x^{3} + 1\right)^{2}}{72 \, c^{3}} - \int -\frac{{\left(b^{3} c^{3} x^{11} - b^{3} c^{2} x^{8}\right)} \log\left(c x^{3} + 1\right)^{3} + 6 \, {\left(a b^{2} c^{3} x^{11} - a b^{2} c^{2} x^{8}\right)} \log\left(c x^{3} + 1\right)^{2} - {\left(4 \, a b^{2} c^{3} x^{11} + 2 \, b^{3} c^{2} x^{8} + 3 \, {\left(b^{3} c^{3} x^{11} - b^{3} c^{2} x^{8}\right)} \log\left(c x^{3} + 1\right)^{2} - 2 \, {\left(6 \, a b^{2} c^{2} x^{8} - {\left(6 \, a b^{2} c^{3} + b^{3} c^{3}\right)} x^{11} - b^{3} x^{2}\right)} \log\left(c x^{3} + 1\right)\right)} \log\left(-c x^{3} + 1\right)}{8 \, {\left(c^{3} x^{3} - c^{2}\right)}}\,{d x}"," ",0,"1/9*a^3*x^9 + 1/6*(2*x^9*arctanh(c*x^3) + (x^6/c^2 + log(c^2*x^6 - 1)/c^4)*c)*a^2*b - 1/72*((b^3*c^3*x^9 - b^3)*log(-c*x^3 + 1)^3 - 3*(2*a*b^2*c^3*x^9 + b^3*c^2*x^6 + (b^3*c^3*x^9 + b^3)*log(c*x^3 + 1))*log(-c*x^3 + 1)^2)/c^3 - integrate(-1/8*((b^3*c^3*x^11 - b^3*c^2*x^8)*log(c*x^3 + 1)^3 + 6*(a*b^2*c^3*x^11 - a*b^2*c^2*x^8)*log(c*x^3 + 1)^2 - (4*a*b^2*c^3*x^11 + 2*b^3*c^2*x^8 + 3*(b^3*c^3*x^11 - b^3*c^2*x^8)*log(c*x^3 + 1)^2 - 2*(6*a*b^2*c^2*x^8 - (6*a*b^2*c^3 + b^3*c^3)*x^11 - b^3*x^2)*log(c*x^3 + 1))*log(-c*x^3 + 1))/(c^3*x^3 - c^2), x)","F",0
125,0,0,0,0.000000," ","integrate(x^5*(a+b*arctanh(c*x^3))^3,x, algorithm=""maxima"")","\frac{1}{2} \, a b^{2} x^{6} \operatorname{artanh}\left(c x^{3}\right)^{2} + \frac{1}{6} \, a^{3} x^{6} + \frac{1}{4} \, {\left(2 \, x^{6} \operatorname{artanh}\left(c x^{3}\right) + c {\left(\frac{2 \, x^{3}}{c^{2}} - \frac{\log\left(c x^{3} + 1\right)}{c^{3}} + \frac{\log\left(c x^{3} - 1\right)}{c^{3}}\right)}\right)} a^{2} b + \frac{1}{8} \, {\left(4 \, c {\left(\frac{2 \, x^{3}}{c^{2}} - \frac{\log\left(c x^{3} + 1\right)}{c^{3}} + \frac{\log\left(c x^{3} - 1\right)}{c^{3}}\right)} \operatorname{artanh}\left(c x^{3}\right) - \frac{2 \, {\left(\log\left(c x^{3} - 1\right) - 2\right)} \log\left(c x^{3} + 1\right) - \log\left(c x^{3} + 1\right)^{2} - \log\left(c x^{3} - 1\right)^{2} - 4 \, \log\left(c x^{3} - 1\right)}{c^{2}}\right)} a b^{2} - \frac{1}{192} \, {\left(4 \, x^{6} \log\left(-c x^{3} + 1\right)^{3} + 3 \, {\left(\frac{x^{6}}{c^{3}} + \frac{\log\left(c^{2} x^{6} - 1\right)}{c^{5}}\right)} c^{3} - 6 \, c {\left(\frac{c x^{6} + 2 \, x^{3}}{c^{2}} + \frac{2 \, \log\left(c x^{3} - 1\right)}{c^{3}}\right)} \log\left(-c x^{3} + 1\right)^{2} + 21 \, c^{2} {\left(\frac{2 \, x^{3}}{c^{3}} - \frac{\log\left(c x^{3} + 1\right)}{c^{4}} + \frac{\log\left(c x^{3} - 1\right)}{c^{4}}\right)} + c {\left(\frac{6 \, {\left(c^{2} x^{6} + 6 \, c x^{3} + 2 \, \log\left(c x^{3} - 1\right)^{2} + 6 \, \log\left(c x^{3} - 1\right)\right)} \log\left(-c x^{3} + 1\right)}{c^{3}} - \frac{3 \, c^{2} x^{6} + 42 \, c x^{3} + 4 \, \log\left(c x^{3} - 1\right)^{3} + 18 \, \log\left(c x^{3} - 1\right)^{2} + 42 \, \log\left(c x^{3} - 1\right)}{c^{3}}\right)} - 1728 \, c \int \frac{x^{5} \log\left(c x^{3} + 1\right)}{4 \, {\left(c^{3} x^{6} - c\right)}}\,{d x} - \frac{2 \, {\left(12 \, c x^{3} \log\left(c x^{3} + 1\right)^{2} + 2 \, {\left(c^{2} x^{6} - 1\right)} \log\left(c x^{3} + 1\right)^{3} - 3 \, {\left(c^{2} x^{6} - 2 \, c x^{3} - 2 \, {\left(c^{2} x^{6} - 1\right)} \log\left(c x^{3} + 1\right) + 1\right)} \log\left(-c x^{3} + 1\right)^{2} + 3 \, {\left(c^{2} x^{6} + 6 \, c x^{3} - 2 \, {\left(c^{2} x^{6} - 1\right)} \log\left(c x^{3} + 1\right)^{2} - 8 \, {\left(c x^{3} + 1\right)} \log\left(c x^{3} + 1\right)\right)} \log\left(-c x^{3} + 1\right)\right)}}{c^{2}} + \frac{18 \, \log\left(4 \, c^{3} x^{6} - 4 \, c\right)}{c^{2}} - 576 \, \int \frac{x^{2} \log\left(c x^{3} + 1\right)}{4 \, {\left(c^{3} x^{6} - c\right)}}\,{d x}\right)} b^{3}"," ",0,"1/2*a*b^2*x^6*arctanh(c*x^3)^2 + 1/6*a^3*x^6 + 1/4*(2*x^6*arctanh(c*x^3) + c*(2*x^3/c^2 - log(c*x^3 + 1)/c^3 + log(c*x^3 - 1)/c^3))*a^2*b + 1/8*(4*c*(2*x^3/c^2 - log(c*x^3 + 1)/c^3 + log(c*x^3 - 1)/c^3)*arctanh(c*x^3) - (2*(log(c*x^3 - 1) - 2)*log(c*x^3 + 1) - log(c*x^3 + 1)^2 - log(c*x^3 - 1)^2 - 4*log(c*x^3 - 1))/c^2)*a*b^2 - 1/192*(4*x^6*log(-c*x^3 + 1)^3 + 3*(x^6/c^3 + log(c^2*x^6 - 1)/c^5)*c^3 - 6*c*((c*x^6 + 2*x^3)/c^2 + 2*log(c*x^3 - 1)/c^3)*log(-c*x^3 + 1)^2 + 21*c^2*(2*x^3/c^3 - log(c*x^3 + 1)/c^4 + log(c*x^3 - 1)/c^4) + c*(6*(c^2*x^6 + 6*c*x^3 + 2*log(c*x^3 - 1)^2 + 6*log(c*x^3 - 1))*log(-c*x^3 + 1)/c^3 - (3*c^2*x^6 + 42*c*x^3 + 4*log(c*x^3 - 1)^3 + 18*log(c*x^3 - 1)^2 + 42*log(c*x^3 - 1))/c^3) - 1728*c*integrate(1/4*x^5*log(c*x^3 + 1)/(c^3*x^6 - c), x) - 2*(12*c*x^3*log(c*x^3 + 1)^2 + 2*(c^2*x^6 - 1)*log(c*x^3 + 1)^3 - 3*(c^2*x^6 - 2*c*x^3 - 2*(c^2*x^6 - 1)*log(c*x^3 + 1) + 1)*log(-c*x^3 + 1)^2 + 3*(c^2*x^6 + 6*c*x^3 - 2*(c^2*x^6 - 1)*log(c*x^3 + 1)^2 - 8*(c*x^3 + 1)*log(c*x^3 + 1))*log(-c*x^3 + 1))/c^2 + 18*log(4*c^3*x^6 - 4*c)/c^2 - 576*integrate(1/4*x^2*log(c*x^3 + 1)/(c^3*x^6 - c), x))*b^3","F",0
126,0,0,0,0.000000," ","integrate(x^2*(a+b*arctanh(c*x^3))^3,x, algorithm=""maxima"")","\frac{1}{3} \, a^{3} x^{3} + \frac{{\left(2 \, c x^{3} \operatorname{artanh}\left(c x^{3}\right) + \log\left(-c^{2} x^{6} + 1\right)\right)} a^{2} b}{2 \, c} - \frac{{\left(b^{3} c x^{3} - b^{3}\right)} \log\left(-c x^{3} + 1\right)^{3} - 3 \, {\left(2 \, a b^{2} c x^{3} + {\left(b^{3} c x^{3} + b^{3}\right)} \log\left(c x^{3} + 1\right)\right)} \log\left(-c x^{3} + 1\right)^{2}}{24 \, c} - \int -\frac{{\left(b^{3} c x^{5} - b^{3} x^{2}\right)} \log\left(c x^{3} + 1\right)^{3} + 6 \, {\left(a b^{2} c x^{5} - a b^{2} x^{2}\right)} \log\left(c x^{3} + 1\right)^{2} - 3 \, {\left(4 \, a b^{2} c x^{5} + {\left(b^{3} c x^{5} - b^{3} x^{2}\right)} \log\left(c x^{3} + 1\right)^{2} + 2 \, {\left({\left(2 \, a b^{2} c + b^{3} c\right)} x^{5} - {\left(2 \, a b^{2} - b^{3}\right)} x^{2}\right)} \log\left(c x^{3} + 1\right)\right)} \log\left(-c x^{3} + 1\right)}{8 \, {\left(c x^{3} - 1\right)}}\,{d x}"," ",0,"1/3*a^3*x^3 + 1/2*(2*c*x^3*arctanh(c*x^3) + log(-c^2*x^6 + 1))*a^2*b/c - 1/24*((b^3*c*x^3 - b^3)*log(-c*x^3 + 1)^3 - 3*(2*a*b^2*c*x^3 + (b^3*c*x^3 + b^3)*log(c*x^3 + 1))*log(-c*x^3 + 1)^2)/c - integrate(-1/8*((b^3*c*x^5 - b^3*x^2)*log(c*x^3 + 1)^3 + 6*(a*b^2*c*x^5 - a*b^2*x^2)*log(c*x^3 + 1)^2 - 3*(4*a*b^2*c*x^5 + (b^3*c*x^5 - b^3*x^2)*log(c*x^3 + 1)^2 + 2*((2*a*b^2*c + b^3*c)*x^5 - (2*a*b^2 - b^3)*x^2)*log(c*x^3 + 1))*log(-c*x^3 + 1))/(c*x^3 - 1), x)","F",0
127,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x^3))^3/x,x, algorithm=""maxima"")","a^{3} \log\left(x\right) + \int \frac{b^{3} {\left(\log\left(c x^{3} + 1\right) - \log\left(-c x^{3} + 1\right)\right)}^{3}}{8 \, x} + \frac{3 \, a b^{2} {\left(\log\left(c x^{3} + 1\right) - \log\left(-c x^{3} + 1\right)\right)}^{2}}{4 \, x} + \frac{3 \, a^{2} b {\left(\log\left(c x^{3} + 1\right) - \log\left(-c x^{3} + 1\right)\right)}}{2 \, x}\,{d x}"," ",0,"a^3*log(x) + integrate(1/8*b^3*(log(c*x^3 + 1) - log(-c*x^3 + 1))^3/x + 3/4*a*b^2*(log(c*x^3 + 1) - log(-c*x^3 + 1))^2/x + 3/2*a^2*b*(log(c*x^3 + 1) - log(-c*x^3 + 1))/x, x)","F",0
128,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x^3))^3/x^4,x, algorithm=""maxima"")","-\frac{1}{2} \, {\left(c {\left(\log\left(c^{2} x^{6} - 1\right) - \log\left(x^{6}\right)\right)} + \frac{2 \, \operatorname{artanh}\left(c x^{3}\right)}{x^{3}}\right)} a^{2} b - \frac{a^{3}}{3 \, x^{3}} - \frac{{\left(b^{3} c x^{3} - b^{3}\right)} \log\left(-c x^{3} + 1\right)^{3} + 3 \, {\left(2 \, a b^{2} + {\left(b^{3} c x^{3} + b^{3}\right)} \log\left(c x^{3} + 1\right)\right)} \log\left(-c x^{3} + 1\right)^{2}}{24 \, x^{3}} - \int -\frac{{\left(b^{3} c x^{3} - b^{3}\right)} \log\left(c x^{3} + 1\right)^{3} + 6 \, {\left(a b^{2} c x^{3} - a b^{2}\right)} \log\left(c x^{3} + 1\right)^{2} + 3 \, {\left(4 \, a b^{2} c x^{3} - {\left(b^{3} c x^{3} - b^{3}\right)} \log\left(c x^{3} + 1\right)^{2} + 2 \, {\left(b^{3} c^{2} x^{6} - {\left(2 \, a b^{2} c - b^{3} c\right)} x^{3} + 2 \, a b^{2}\right)} \log\left(c x^{3} + 1\right)\right)} \log\left(-c x^{3} + 1\right)}{8 \, {\left(c x^{7} - x^{4}\right)}}\,{d x}"," ",0,"-1/2*(c*(log(c^2*x^6 - 1) - log(x^6)) + 2*arctanh(c*x^3)/x^3)*a^2*b - 1/3*a^3/x^3 - 1/24*((b^3*c*x^3 - b^3)*log(-c*x^3 + 1)^3 + 3*(2*a*b^2 + (b^3*c*x^3 + b^3)*log(c*x^3 + 1))*log(-c*x^3 + 1)^2)/x^3 - integrate(-1/8*((b^3*c*x^3 - b^3)*log(c*x^3 + 1)^3 + 6*(a*b^2*c*x^3 - a*b^2)*log(c*x^3 + 1)^2 + 3*(4*a*b^2*c*x^3 - (b^3*c*x^3 - b^3)*log(c*x^3 + 1)^2 + 2*(b^3*c^2*x^6 - (2*a*b^2*c - b^3*c)*x^3 + 2*a*b^2)*log(c*x^3 + 1))*log(-c*x^3 + 1))/(c*x^7 - x^4), x)","F",0
129,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x^3))^3/x^7,x, algorithm=""maxima"")","\frac{1}{4} \, {\left({\left(c \log\left(c x^{3} + 1\right) - c \log\left(c x^{3} - 1\right) - \frac{2}{x^{3}}\right)} c - \frac{2 \, \operatorname{artanh}\left(c x^{3}\right)}{x^{6}}\right)} a^{2} b + \frac{1}{8} \, {\left({\left(2 \, {\left(\log\left(c x^{3} - 1\right) - 2\right)} \log\left(c x^{3} + 1\right) - \log\left(c x^{3} + 1\right)^{2} - \log\left(c x^{3} - 1\right)^{2} - 4 \, \log\left(c x^{3} - 1\right) + 24 \, \log\left(x\right)\right)} c^{2} + 4 \, {\left(c \log\left(c x^{3} + 1\right) - c \log\left(c x^{3} - 1\right) - \frac{2}{x^{3}}\right)} c \operatorname{artanh}\left(c x^{3}\right)\right)} a b^{2} - \frac{1}{48} \, b^{3} {\left(\frac{{\left(c^{2} x^{6} - 1\right)} \log\left(-c x^{3} + 1\right)^{3} + 3 \, {\left(2 \, c x^{3} - {\left(c^{2} x^{6} - 1\right)} \log\left(c x^{3} + 1\right)\right)} \log\left(-c x^{3} + 1\right)^{2}}{x^{6}} + 6 \, \int -\frac{{\left(c x^{3} - 1\right)} \log\left(c x^{3} + 1\right)^{3} + 3 \, {\left(2 \, c^{2} x^{6} - {\left(c x^{3} - 1\right)} \log\left(c x^{3} + 1\right)^{2} - {\left(c^{3} x^{9} - c x^{3}\right)} \log\left(c x^{3} + 1\right)\right)} \log\left(-c x^{3} + 1\right)}{c x^{10} - x^{7}}\,{d x}\right)} - \frac{a b^{2} \operatorname{artanh}\left(c x^{3}\right)^{2}}{2 \, x^{6}} - \frac{a^{3}}{6 \, x^{6}}"," ",0,"1/4*((c*log(c*x^3 + 1) - c*log(c*x^3 - 1) - 2/x^3)*c - 2*arctanh(c*x^3)/x^6)*a^2*b + 1/8*((2*(log(c*x^3 - 1) - 2)*log(c*x^3 + 1) - log(c*x^3 + 1)^2 - log(c*x^3 - 1)^2 - 4*log(c*x^3 - 1) + 24*log(x))*c^2 + 4*(c*log(c*x^3 + 1) - c*log(c*x^3 - 1) - 2/x^3)*c*arctanh(c*x^3))*a*b^2 - 1/48*b^3*(((c^2*x^6 - 1)*log(-c*x^3 + 1)^3 + 3*(2*c*x^3 - (c^2*x^6 - 1)*log(c*x^3 + 1))*log(-c*x^3 + 1)^2)/x^6 + 6*integrate(-((c*x^3 - 1)*log(c*x^3 + 1)^3 + 3*(2*c^2*x^6 - (c*x^3 - 1)*log(c*x^3 + 1)^2 - (c^3*x^9 - c*x^3)*log(c*x^3 + 1))*log(-c*x^3 + 1))/(c*x^10 - x^7), x)) - 1/2*a*b^2*arctanh(c*x^3)^2/x^6 - 1/6*a^3/x^6","F",0
130,0,0,0,0.000000," ","integrate((d*x)^m*(a+b*arctanh(c*x^3))^3,x, algorithm=""maxima"")","-\frac{b^{3} d^{m} x x^{m} \log\left(-c x^{3} + 1\right)^{3}}{8 \, {\left(m + 1\right)}} + \frac{\left(d x\right)^{m + 1} a^{3}}{d {\left(m + 1\right)}} + \int \frac{{\left(b^{3} c d^{m} {\left(m + 1\right)} x^{3} - b^{3} d^{m} {\left(m + 1\right)}\right)} x^{m} \log\left(c x^{3} + 1\right)^{3} + 6 \, {\left(a b^{2} c d^{m} {\left(m + 1\right)} x^{3} - a b^{2} d^{m} {\left(m + 1\right)}\right)} x^{m} \log\left(c x^{3} + 1\right)^{2} + 12 \, {\left(a^{2} b c d^{m} {\left(m + 1\right)} x^{3} - a^{2} b d^{m} {\left(m + 1\right)}\right)} x^{m} \log\left(c x^{3} + 1\right) + 3 \, {\left({\left(b^{3} c d^{m} {\left(m + 1\right)} x^{3} - b^{3} d^{m} {\left(m + 1\right)}\right)} x^{m} \log\left(c x^{3} + 1\right) - {\left(2 \, a b^{2} d^{m} {\left(m + 1\right)} - {\left(2 \, a b^{2} c d^{m} {\left(m + 1\right)} + 3 \, b^{3} c d^{m}\right)} x^{3}\right)} x^{m}\right)} \log\left(-c x^{3} + 1\right)^{2} - 3 \, {\left({\left(b^{3} c d^{m} {\left(m + 1\right)} x^{3} - b^{3} d^{m} {\left(m + 1\right)}\right)} x^{m} \log\left(c x^{3} + 1\right)^{2} + 4 \, {\left(a b^{2} c d^{m} {\left(m + 1\right)} x^{3} - a b^{2} d^{m} {\left(m + 1\right)}\right)} x^{m} \log\left(c x^{3} + 1\right) + 4 \, {\left(a^{2} b c d^{m} {\left(m + 1\right)} x^{3} - a^{2} b d^{m} {\left(m + 1\right)}\right)} x^{m}\right)} \log\left(-c x^{3} + 1\right)}{8 \, {\left(c {\left(m + 1\right)} x^{3} - m - 1\right)}}\,{d x}"," ",0,"-1/8*b^3*d^m*x*x^m*log(-c*x^3 + 1)^3/(m + 1) + (d*x)^(m + 1)*a^3/(d*(m + 1)) + integrate(1/8*((b^3*c*d^m*(m + 1)*x^3 - b^3*d^m*(m + 1))*x^m*log(c*x^3 + 1)^3 + 6*(a*b^2*c*d^m*(m + 1)*x^3 - a*b^2*d^m*(m + 1))*x^m*log(c*x^3 + 1)^2 + 12*(a^2*b*c*d^m*(m + 1)*x^3 - a^2*b*d^m*(m + 1))*x^m*log(c*x^3 + 1) + 3*((b^3*c*d^m*(m + 1)*x^3 - b^3*d^m*(m + 1))*x^m*log(c*x^3 + 1) - (2*a*b^2*d^m*(m + 1) - (2*a*b^2*c*d^m*(m + 1) + 3*b^3*c*d^m)*x^3)*x^m)*log(-c*x^3 + 1)^2 - 3*((b^3*c*d^m*(m + 1)*x^3 - b^3*d^m*(m + 1))*x^m*log(c*x^3 + 1)^2 + 4*(a*b^2*c*d^m*(m + 1)*x^3 - a*b^2*d^m*(m + 1))*x^m*log(c*x^3 + 1) + 4*(a^2*b*c*d^m*(m + 1)*x^3 - a^2*b*d^m*(m + 1))*x^m)*log(-c*x^3 + 1))/(c*(m + 1)*x^3 - m - 1), x)","F",0
131,0,0,0,0.000000," ","integrate((d*x)^m*(a+b*arctanh(c*x^3))^2,x, algorithm=""maxima"")","\frac{b^{2} d^{m} x x^{m} \log\left(-c x^{3} + 1\right)^{2}}{4 \, {\left(m + 1\right)}} + \frac{\left(d x\right)^{m + 1} a^{2}}{d {\left(m + 1\right)}} - \int -\frac{{\left(b^{2} c d^{m} {\left(m + 1\right)} x^{3} - b^{2} d^{m} {\left(m + 1\right)}\right)} x^{m} \log\left(c x^{3} + 1\right)^{2} + 4 \, {\left(a b c d^{m} {\left(m + 1\right)} x^{3} - a b d^{m} {\left(m + 1\right)}\right)} x^{m} \log\left(c x^{3} + 1\right) - 2 \, {\left({\left(b^{2} c d^{m} {\left(m + 1\right)} x^{3} - b^{2} d^{m} {\left(m + 1\right)}\right)} x^{m} \log\left(c x^{3} + 1\right) - {\left(2 \, a b d^{m} {\left(m + 1\right)} - {\left(2 \, a b c d^{m} {\left(m + 1\right)} + 3 \, b^{2} c d^{m}\right)} x^{3}\right)} x^{m}\right)} \log\left(-c x^{3} + 1\right)}{4 \, {\left(c {\left(m + 1\right)} x^{3} - m - 1\right)}}\,{d x}"," ",0,"1/4*b^2*d^m*x*x^m*log(-c*x^3 + 1)^2/(m + 1) + (d*x)^(m + 1)*a^2/(d*(m + 1)) - integrate(-1/4*((b^2*c*d^m*(m + 1)*x^3 - b^2*d^m*(m + 1))*x^m*log(c*x^3 + 1)^2 + 4*(a*b*c*d^m*(m + 1)*x^3 - a*b*d^m*(m + 1))*x^m*log(c*x^3 + 1) - 2*((b^2*c*d^m*(m + 1)*x^3 - b^2*d^m*(m + 1))*x^m*log(c*x^3 + 1) - (2*a*b*d^m*(m + 1) - (2*a*b*c*d^m*(m + 1) + 3*b^2*c*d^m)*x^3)*x^m)*log(-c*x^3 + 1))/(c*(m + 1)*x^3 - m - 1), x)","F",0
132,0,0,0,0.000000," ","integrate((d*x)^m*(a+b*arctanh(c*x^3)),x, algorithm=""maxima"")","\frac{1}{2} \, {\left(6 \, c d^{m} \int \frac{x^{3} x^{m}}{c^{2} {\left(m + 1\right)} x^{6} - m - 1}\,{d x} + \frac{d^{m} x x^{m} \log\left(c x^{3} + 1\right) - d^{m} x x^{m} \log\left(-c x^{3} + 1\right)}{m + 1}\right)} b + \frac{\left(d x\right)^{m + 1} a}{d {\left(m + 1\right)}}"," ",0,"1/2*(6*c*d^m*integrate(x^3*x^m/(c^2*(m + 1)*x^6 - m - 1), x) + (d^m*x*x^m*log(c*x^3 + 1) - d^m*x*x^m*log(-c*x^3 + 1))/(m + 1))*b + (d*x)^(m + 1)*a/(d*(m + 1))","F",0
133,0,0,0,0.000000," ","integrate((d*x)^m/(a+b*arctanh(c*x^3)),x, algorithm=""maxima"")","\int \frac{\left(d x\right)^{m}}{b \operatorname{artanh}\left(c x^{3}\right) + a}\,{d x}"," ",0,"integrate((d*x)^m/(b*arctanh(c*x^3) + a), x)","F",0
134,0,0,0,0.000000," ","integrate((d*x)^m/(a+b*arctanh(c*x^3))^2,x, algorithm=""maxima"")","\frac{2 \, {\left(c^{2} d^{m} x^{6} - d^{m}\right)} x^{m}}{3 \, {\left(b^{2} c x^{2} \log\left(c x^{3} + 1\right) - b^{2} c x^{2} \log\left(-c x^{3} + 1\right) + 2 \, a b c x^{2}\right)}} + \int -\frac{2 \, {\left(c^{2} d^{m} {\left(m + 4\right)} x^{6} - d^{m} {\left(m - 2\right)}\right)} x^{m}}{3 \, {\left(b^{2} c x^{3} \log\left(c x^{3} + 1\right) - b^{2} c x^{3} \log\left(-c x^{3} + 1\right) + 2 \, a b c x^{3}\right)}}\,{d x}"," ",0,"2/3*(c^2*d^m*x^6 - d^m)*x^m/(b^2*c*x^2*log(c*x^3 + 1) - b^2*c*x^2*log(-c*x^3 + 1) + 2*a*b*c*x^2) + integrate(-2/3*(c^2*d^m*(m + 4)*x^6 - d^m*(m - 2))*x^m/(b^2*c*x^3*log(c*x^3 + 1) - b^2*c*x^3*log(-c*x^3 + 1) + 2*a*b*c*x^3), x)","F",0
135,1,57,0,0.312393," ","integrate(x^3*(a+b*arctanh(c/x)),x, algorithm=""maxima"")","\frac{1}{4} \, a x^{4} + \frac{1}{24} \, {\left(6 \, x^{4} \operatorname{artanh}\left(\frac{c}{x}\right) - {\left(3 \, c^{3} \log\left(c + x\right) - 3 \, c^{3} \log\left(-c + x\right) - 6 \, c^{2} x - 2 \, x^{3}\right)} c\right)} b"," ",0,"1/4*a*x^4 + 1/24*(6*x^4*arctanh(c/x) - (3*c^3*log(c + x) - 3*c^3*log(-c + x) - 6*c^2*x - 2*x^3)*c)*b","A",0
136,1,42,0,0.317536," ","integrate(x^2*(a+b*arctanh(c/x)),x, algorithm=""maxima"")","\frac{1}{3} \, a x^{3} + \frac{1}{6} \, {\left(2 \, x^{3} \operatorname{artanh}\left(\frac{c}{x}\right) + {\left(c^{2} \log\left(-c^{2} + x^{2}\right) + x^{2}\right)} c\right)} b"," ",0,"1/3*a*x^3 + 1/6*(2*x^3*arctanh(c/x) + (c^2*log(-c^2 + x^2) + x^2)*c)*b","A",0
137,1,44,0,0.319249," ","integrate(x*(a+b*arctanh(c/x)),x, algorithm=""maxima"")","\frac{1}{2} \, a x^{2} + \frac{1}{4} \, {\left(2 \, x^{2} \operatorname{artanh}\left(\frac{c}{x}\right) - {\left(c \log\left(c + x\right) - c \log\left(-c + x\right) - 2 \, x\right)} c\right)} b"," ",0,"1/2*a*x^2 + 1/4*(2*x^2*arctanh(c/x) - (c*log(c + x) - c*log(-c + x) - 2*x)*c)*b","A",0
138,1,29,0,0.313892," ","integrate(a+b*arctanh(c/x),x, algorithm=""maxima"")","\frac{1}{2} \, {\left(2 \, x \operatorname{artanh}\left(\frac{c}{x}\right) + c \log\left(-c^{2} + x^{2}\right)\right)} b + a x"," ",0,"1/2*(2*x*arctanh(c/x) + c*log(-c^2 + x^2))*b + a*x","A",0
139,0,0,0,0.000000," ","integrate((a+b*arctanh(c/x))/x,x, algorithm=""maxima"")","\frac{1}{2} \, b \int \frac{\log\left(\frac{c}{x} + 1\right) - \log\left(-\frac{c}{x} + 1\right)}{x}\,{d x} + a \log\left(x\right)"," ",0,"1/2*b*integrate((log(c/x + 1) - log(-c/x + 1))/x, x) + a*log(x)","F",0
140,1,37,0,0.314015," ","integrate((a+b*arctanh(c/x))/x^2,x, algorithm=""maxima"")","-\frac{b {\left(\frac{2 \, c \operatorname{artanh}\left(\frac{c}{x}\right)}{x} + \log\left(-\frac{c^{2}}{x^{2}} + 1\right)\right)}}{2 \, c} - \frac{a}{x}"," ",0,"-1/2*b*(2*c*arctanh(c/x)/x + log(-c^2/x^2 + 1))/c - a/x","A",0
141,1,52,0,0.320382," ","integrate((a+b*arctanh(c/x))/x^3,x, algorithm=""maxima"")","\frac{1}{4} \, {\left(c {\left(\frac{\log\left(c + x\right)}{c^{3}} - \frac{\log\left(-c + x\right)}{c^{3}} - \frac{2}{c^{2} x}\right)} - \frac{2 \, \operatorname{artanh}\left(\frac{c}{x}\right)}{x^{2}}\right)} b - \frac{a}{2 \, x^{2}}"," ",0,"1/4*(c*(log(c + x)/c^3 - log(-c + x)/c^3 - 2/(c^2*x)) - 2*arctanh(c/x)/x^2)*b - 1/2*a/x^2","A",0
142,1,55,0,0.317163," ","integrate((a+b*arctanh(c/x))/x^4,x, algorithm=""maxima"")","-\frac{1}{6} \, {\left(c {\left(\frac{\log\left(-c^{2} + x^{2}\right)}{c^{4}} - \frac{\log\left(x^{2}\right)}{c^{4}} + \frac{1}{c^{2} x^{2}}\right)} + \frac{2 \, \operatorname{artanh}\left(\frac{c}{x}\right)}{x^{3}}\right)} b - \frac{a}{3 \, x^{3}}"," ",0,"-1/6*(c*(log(-c^2 + x^2)/c^4 - log(x^2)/c^4 + 1/(c^2*x^2)) + 2*arctanh(c/x)/x^3)*b - 1/3*a/x^3","A",0
143,1,189,0,0.335700," ","integrate(x^3*(a+b*arctanh(c/x))^2,x, algorithm=""maxima"")","\frac{1}{4} \, b^{2} x^{4} \operatorname{artanh}\left(\frac{c}{x}\right)^{2} + \frac{1}{4} \, a^{2} x^{4} + \frac{1}{12} \, {\left(6 \, x^{4} \operatorname{artanh}\left(\frac{c}{x}\right) - {\left(3 \, c^{3} \log\left(c + x\right) - 3 \, c^{3} \log\left(-c + x\right) - 6 \, c^{2} x - 2 \, x^{3}\right)} c\right)} a b + \frac{1}{48} \, {\left({\left(3 \, c^{2} \log\left(c + x\right)^{2} + 3 \, c^{2} \log\left(-c + x\right)^{2} + 16 \, c^{2} \log\left(c + x\right) + 4 \, x^{2} - 2 \, {\left(3 \, c^{2} \log\left(c + x\right) - 8 \, c^{2}\right)} \log\left(-c + x\right)\right)} c^{2} - 4 \, {\left(3 \, c^{3} \log\left(c + x\right) - 3 \, c^{3} \log\left(-c + x\right) - 6 \, c^{2} x - 2 \, x^{3}\right)} c \operatorname{artanh}\left(\frac{c}{x}\right)\right)} b^{2}"," ",0,"1/4*b^2*x^4*arctanh(c/x)^2 + 1/4*a^2*x^4 + 1/12*(6*x^4*arctanh(c/x) - (3*c^3*log(c + x) - 3*c^3*log(-c + x) - 6*c^2*x - 2*x^3)*c)*a*b + 1/48*((3*c^2*log(c + x)^2 + 3*c^2*log(-c + x)^2 + 16*c^2*log(c + x) + 4*x^2 - 2*(3*c^2*log(c + x) - 8*c^2)*log(-c + x))*c^2 - 4*(3*c^3*log(c + x) - 3*c^3*log(-c + x) - 6*c^2*x - 2*x^3)*c*arctanh(c/x))*b^2","A",0
144,0,0,0,0.000000," ","integrate(x^2*(a+b*arctanh(c/x))^2,x, algorithm=""maxima"")","\frac{1}{3} \, a^{2} x^{3} + \frac{1}{3} \, {\left(2 \, x^{3} \operatorname{artanh}\left(\frac{c}{x}\right) + {\left(c^{2} \log\left(-c^{2} + x^{2}\right) + x^{2}\right)} c\right)} a b + \frac{1}{12} \, {\left(6 \, c^{4} \int -\frac{\log\left(c + x\right)}{3 \, {\left(c^{2} - x^{2}\right)}}\,{d x} + x^{3} \log\left(c + x\right)^{2} + 6 \, c^{3} \int -\frac{x \log\left(c + x\right)}{3 \, {\left(c^{2} - x^{2}\right)}}\,{d x} - {\left(c \log\left(c + x\right) - c \log\left(-c + x\right) - 2 \, x\right)} c^{2} - {\left(c^{3} - x^{3}\right)} \log\left(-c + x\right)^{2} + {\left(c^{2} \log\left(-c^{2} + x^{2}\right) + x^{2}\right)} c + 12 \, c \int -\frac{x^{3} \log\left(c + x\right)}{3 \, {\left(c^{2} - x^{2}\right)}}\,{d x} - 2 \, {\left(c x^{2} + {\left(c^{3} + x^{3}\right)} \log\left(c + x\right)\right)} \log\left(-c + x\right)\right)} b^{2}"," ",0,"1/3*a^2*x^3 + 1/3*(2*x^3*arctanh(c/x) + (c^2*log(-c^2 + x^2) + x^2)*c)*a*b + 1/12*(6*c^4*integrate(-1/3*log(c + x)/(c^2 - x^2), x) + x^3*log(c + x)^2 + 6*c^3*integrate(-1/3*x*log(c + x)/(c^2 - x^2), x) - (c*log(c + x) - c*log(-c + x) - 2*x)*c^2 - (c^3 - x^3)*log(-c + x)^2 + (c^2*log(-c^2 + x^2) + x^2)*c + 12*c*integrate(-1/3*x^3*log(c + x)/(c^2 - x^2), x) - 2*(c*x^2 + (c^3 + x^3)*log(c + x))*log(-c + x))*b^2","F",0
145,1,136,0,0.330850," ","integrate(x*(a+b*arctanh(c/x))^2,x, algorithm=""maxima"")","\frac{1}{2} \, b^{2} x^{2} \operatorname{artanh}\left(\frac{c}{x}\right)^{2} + \frac{1}{2} \, a^{2} x^{2} + \frac{1}{2} \, {\left(2 \, x^{2} \operatorname{artanh}\left(\frac{c}{x}\right) - {\left(c \log\left(c + x\right) - c \log\left(-c + x\right) - 2 \, x\right)} c\right)} a b + \frac{1}{8} \, {\left({\left(\log\left(c + x\right)^{2} - 2 \, {\left(\log\left(c + x\right) - 2\right)} \log\left(-c + x\right) + \log\left(-c + x\right)^{2} + 4 \, \log\left(c + x\right)\right)} c^{2} - 4 \, {\left(c \log\left(c + x\right) - c \log\left(-c + x\right) - 2 \, x\right)} c \operatorname{artanh}\left(\frac{c}{x}\right)\right)} b^{2}"," ",0,"1/2*b^2*x^2*arctanh(c/x)^2 + 1/2*a^2*x^2 + 1/2*(2*x^2*arctanh(c/x) - (c*log(c + x) - c*log(-c + x) - 2*x)*c)*a*b + 1/8*((log(c + x)^2 - 2*(log(c + x) - 2)*log(-c + x) + log(-c + x)^2 + 4*log(c + x))*c^2 - 4*(c*log(c + x) - c*log(-c + x) - 2*x)*c*arctanh(c/x))*b^2","A",0
146,0,0,0,0.000000," ","integrate((a+b*arctanh(c/x))^2,x, algorithm=""maxima"")","{\left(2 \, x \operatorname{artanh}\left(\frac{c}{x}\right) + c \log\left(-c^{2} + x^{2}\right)\right)} a b + \frac{1}{4} \, {\left(x \log\left(c + x\right)^{2} - 2 \, {\left(c + x\right)} \log\left(c + x\right) \log\left(-c + x\right) - {\left(c - x\right)} \log\left(-c + x\right)^{2} + \int -\frac{2 \, {\left(c^{2} + 3 \, c x\right)} \log\left(c + x\right)}{c^{2} - x^{2}}\,{d x}\right)} b^{2} + a^{2} x"," ",0,"(2*x*arctanh(c/x) + c*log(-c^2 + x^2))*a*b + 1/4*(x*log(c + x)^2 - 2*(c + x)*log(c + x)*log(-c + x) - (c - x)*log(-c + x)^2 + integrate(-2*(c^2 + 3*c*x)*log(c + x)/(c^2 - x^2), x))*b^2 + a^2*x","F",0
147,0,0,0,0.000000," ","integrate((a+b*arctanh(c/x))^2/x,x, algorithm=""maxima"")","a^{2} \log\left(x\right) + \int \frac{b^{2} {\left(\log\left(\frac{c}{x} + 1\right) - \log\left(-\frac{c}{x} + 1\right)\right)}^{2}}{4 \, x} + \frac{a b {\left(\log\left(\frac{c}{x} + 1\right) - \log\left(-\frac{c}{x} + 1\right)\right)}}{x}\,{d x}"," ",0,"a^2*log(x) + integrate(1/4*b^2*(log(c/x + 1) - log(-c/x + 1))^2/x + a*b*(log(c/x + 1) - log(-c/x + 1))/x, x)","F",0
148,0,0,0,0.000000," ","integrate((a+b*arctanh(c/x))^2/x^2,x, algorithm=""maxima"")","\frac{1}{4} \, {\left(c^{3} \int -\frac{\log\left(x\right)^{2}}{c^{3} x^{2} - c x^{4}}\,{d x} + c^{2} {\left(\frac{\log\left(-c^{2} + x^{2}\right)}{c^{3}} - \frac{\log\left(x^{2}\right)}{c^{3}}\right)} - 4 \, c^{2} \int -\frac{x \log\left(c + x\right)}{c^{3} x^{2} - c x^{4}}\,{d x} + 2 \, c^{2} \int -\frac{x \log\left(x\right)}{c^{3} x^{2} - c x^{4}}\,{d x} + 2 \, c {\left(\frac{\log\left(-c + x\right)}{c^{2}} - \frac{\log\left(x\right)}{c^{2}} + \frac{1}{c x}\right)} \log\left(-\frac{c}{x} + 1\right) - c {\left(\frac{\log\left(c + x\right)}{c^{2}} - \frac{\log\left(-c + x\right)}{c^{2}}\right)} - c \int -\frac{x^{2} \log\left(x\right)^{2}}{c^{3} x^{2} - c x^{4}}\,{d x} - 2 \, c \int -\frac{x^{2} \log\left(c + x\right)}{c^{3} x^{2} - c x^{4}}\,{d x} + 4 \, c \int -\frac{x^{2} \log\left(x\right)}{c^{3} x^{2} - c x^{4}}\,{d x} - \frac{\log\left(-\frac{c}{x} + 1\right)^{2}}{x} - \frac{c \log\left(c + x\right)^{2} - 2 \, {\left({\left(c + x\right)} \log\left(c + x\right) - {\left(c + x\right)} \log\left(x\right) - c\right)} \log\left(-c + x\right)}{c x} - \frac{x \log\left(-c + x\right)^{2} + x \log\left(x\right)^{2} - 2 \, {\left(x \log\left(x\right) - x\right)} \log\left(-c + x\right) - 2 \, x \log\left(x\right) + 2 \, c}{c x} - 2 \, \int -\frac{x^{3} \log\left(c + x\right)}{c^{3} x^{2} - c x^{4}}\,{d x} + 2 \, \int -\frac{x^{3} \log\left(x\right)}{c^{3} x^{2} - c x^{4}}\,{d x}\right)} b^{2} - \frac{a b {\left(\frac{2 \, c \operatorname{artanh}\left(\frac{c}{x}\right)}{x} + \log\left(-\frac{c^{2}}{x^{2}} + 1\right)\right)}}{c} - \frac{a^{2}}{x}"," ",0,"1/4*(c^3*integrate(-log(x)^2/(c^3*x^2 - c*x^4), x) + c^2*(log(-c^2 + x^2)/c^3 - log(x^2)/c^3) - 4*c^2*integrate(-x*log(c + x)/(c^3*x^2 - c*x^4), x) + 2*c^2*integrate(-x*log(x)/(c^3*x^2 - c*x^4), x) + 2*c*(log(-c + x)/c^2 - log(x)/c^2 + 1/(c*x))*log(-c/x + 1) - c*(log(c + x)/c^2 - log(-c + x)/c^2) - c*integrate(-x^2*log(x)^2/(c^3*x^2 - c*x^4), x) - 2*c*integrate(-x^2*log(c + x)/(c^3*x^2 - c*x^4), x) + 4*c*integrate(-x^2*log(x)/(c^3*x^2 - c*x^4), x) - log(-c/x + 1)^2/x - (c*log(c + x)^2 - 2*((c + x)*log(c + x) - (c + x)*log(x) - c)*log(-c + x))/(c*x) - (x*log(-c + x)^2 + x*log(x)^2 - 2*(x*log(x) - x)*log(-c + x) - 2*x*log(x) + 2*c)/(c*x) - 2*integrate(-x^3*log(c + x)/(c^3*x^2 - c*x^4), x) + 2*integrate(-x^3*log(x)/(c^3*x^2 - c*x^4), x))*b^2 - a*b*(2*c*arctanh(c/x)/x + log(-c^2/x^2 + 1))/c - a^2/x","F",0
149,1,165,0,0.329368," ","integrate((a+b*arctanh(c/x))^2/x^3,x, algorithm=""maxima"")","\frac{1}{2} \, {\left(c {\left(\frac{\log\left(c + x\right)}{c^{3}} - \frac{\log\left(-c + x\right)}{c^{3}} - \frac{2}{c^{2} x}\right)} - \frac{2 \, \operatorname{artanh}\left(\frac{c}{x}\right)}{x^{2}}\right)} a b - \frac{1}{8} \, {\left(c^{2} {\left(\frac{\log\left(c + x\right)^{2} - 2 \, {\left(\log\left(c + x\right) - 2\right)} \log\left(-c + x\right) + \log\left(-c + x\right)^{2} + 4 \, \log\left(c + x\right)}{c^{4}} - \frac{8 \, \log\left(x\right)}{c^{4}}\right)} - 4 \, c {\left(\frac{\log\left(c + x\right)}{c^{3}} - \frac{\log\left(-c + x\right)}{c^{3}} - \frac{2}{c^{2} x}\right)} \operatorname{artanh}\left(\frac{c}{x}\right)\right)} b^{2} - \frac{b^{2} \operatorname{artanh}\left(\frac{c}{x}\right)^{2}}{2 \, x^{2}} - \frac{a^{2}}{2 \, x^{2}}"," ",0,"1/2*(c*(log(c + x)/c^3 - log(-c + x)/c^3 - 2/(c^2*x)) - 2*arctanh(c/x)/x^2)*a*b - 1/8*(c^2*((log(c + x)^2 - 2*(log(c + x) - 2)*log(-c + x) + log(-c + x)^2 + 4*log(c + x))/c^4 - 8*log(x)/c^4) - 4*c*(log(c + x)/c^3 - log(-c + x)/c^3 - 2/(c^2*x))*arctanh(c/x))*b^2 - 1/2*b^2*arctanh(c/x)^2/x^2 - 1/2*a^2/x^2","B",0
150,0,0,0,0.000000," ","integrate(x^3*(a+b*arctanh(c/x))^3,x, algorithm=""maxima"")","\frac{3}{4} \, a b^{2} x^{4} \operatorname{artanh}\left(\frac{c}{x}\right)^{2} + \frac{1}{4} \, a^{3} x^{4} + \frac{1}{8} \, {\left(6 \, x^{4} \operatorname{artanh}\left(\frac{c}{x}\right) - {\left(3 \, c^{3} \log\left(c + x\right) - 3 \, c^{3} \log\left(-c + x\right) - 6 \, c^{2} x - 2 \, x^{3}\right)} c\right)} a^{2} b + \frac{1}{16} \, {\left({\left(3 \, c^{2} \log\left(c + x\right)^{2} + 3 \, c^{2} \log\left(-c + x\right)^{2} + 16 \, c^{2} \log\left(c + x\right) + 4 \, x^{2} - 2 \, {\left(3 \, c^{2} \log\left(c + x\right) - 8 \, c^{2}\right)} \log\left(-c + x\right)\right)} c^{2} - 4 \, {\left(3 \, c^{3} \log\left(c + x\right) - 3 \, c^{3} \log\left(-c + x\right) - 6 \, c^{2} x - 2 \, x^{3}\right)} c \operatorname{artanh}\left(\frac{c}{x}\right)\right)} a b^{2} + \frac{1}{32} \, {\left(16 \, c^{5} \int -\frac{\log\left(c + x\right)}{c^{2} - x^{2}}\,{d x} + 40 \, c^{4} \int -\frac{x \log\left(c + x\right)}{c^{2} - x^{2}}\,{d x} - 2 \, {\left(c \log\left(c + x\right) - c \log\left(-c + x\right) - 2 \, x\right)} c^{3} - {\left(c^{4} - x^{4}\right)} \log\left(c + x\right)^{3} + {\left(c^{4} - x^{4}\right)} \log\left(-c + x\right)^{3} + 2 \, {\left(c^{2} \log\left(-c^{2} + x^{2}\right) + x^{2}\right)} c^{2} + 8 \, c^{2} \int -\frac{x^{3} \log\left(c + x\right)}{c^{2} - x^{2}}\,{d x} + 2 \, {\left(3 \, c^{3} x + c x^{3}\right)} \log\left(c + x\right)^{2} - {\left(8 \, c^{4} - 6 \, c^{3} x - 2 \, c x^{3} + 3 \, {\left(c^{4} - x^{4}\right)} \log\left(c + x\right)\right)} \log\left(-c + x\right)^{2} - {\left(4 \, c^{2} x^{2} - 3 \, {\left(c^{4} - x^{4}\right)} \log\left(c + x\right)^{2} + 4 \, {\left(4 \, c^{4} + 3 \, c^{3} x + c x^{3}\right)} \log\left(c + x\right)\right)} \log\left(-c + x\right)\right)} b^{3}"," ",0,"3/4*a*b^2*x^4*arctanh(c/x)^2 + 1/4*a^3*x^4 + 1/8*(6*x^4*arctanh(c/x) - (3*c^3*log(c + x) - 3*c^3*log(-c + x) - 6*c^2*x - 2*x^3)*c)*a^2*b + 1/16*((3*c^2*log(c + x)^2 + 3*c^2*log(-c + x)^2 + 16*c^2*log(c + x) + 4*x^2 - 2*(3*c^2*log(c + x) - 8*c^2)*log(-c + x))*c^2 - 4*(3*c^3*log(c + x) - 3*c^3*log(-c + x) - 6*c^2*x - 2*x^3)*c*arctanh(c/x))*a*b^2 + 1/32*(16*c^5*integrate(-log(c + x)/(c^2 - x^2), x) + 40*c^4*integrate(-x*log(c + x)/(c^2 - x^2), x) - 2*(c*log(c + x) - c*log(-c + x) - 2*x)*c^3 - (c^4 - x^4)*log(c + x)^3 + (c^4 - x^4)*log(-c + x)^3 + 2*(c^2*log(-c^2 + x^2) + x^2)*c^2 + 8*c^2*integrate(-x^3*log(c + x)/(c^2 - x^2), x) + 2*(3*c^3*x + c*x^3)*log(c + x)^2 - (8*c^4 - 6*c^3*x - 2*c*x^3 + 3*(c^4 - x^4)*log(c + x))*log(-c + x)^2 - (4*c^2*x^2 - 3*(c^4 - x^4)*log(c + x)^2 + 4*(4*c^4 + 3*c^3*x + c*x^3)*log(c + x))*log(-c + x))*b^3","F",0
151,0,0,0,0.000000," ","integrate(x^2*(a+b*arctanh(c/x))^3,x, algorithm=""maxima"")","\frac{1}{3} \, a^{3} x^{3} + \frac{1}{2} \, {\left(2 \, x^{3} \operatorname{artanh}\left(\frac{c}{x}\right) + {\left(c^{2} \log\left(-c^{2} + x^{2}\right) + x^{2}\right)} c\right)} a^{2} b + \frac{1}{24} \, {\left(b^{3} c^{3} - b^{3} x^{3}\right)} \log\left(-c + x\right)^{3} + \frac{1}{8} \, {\left(b^{3} c x^{2} + 2 \, a b^{2} x^{3} + {\left(b^{3} c^{3} + b^{3} x^{3}\right)} \log\left(c + x\right)\right)} \log\left(-c + x\right)^{2} - \int -\frac{{\left(b^{3} c x^{2} - b^{3} x^{3}\right)} \log\left(c + x\right)^{3} + 6 \, {\left(a b^{2} c x^{2} - a b^{2} x^{3}\right)} \log\left(c + x\right)^{2} + {\left(2 \, b^{3} c x^{2} + 4 \, a b^{2} x^{3} - 3 \, {\left(b^{3} c x^{2} - b^{3} x^{3}\right)} \log\left(c + x\right)^{2} + 2 \, {\left(b^{3} c^{3} - 6 \, a b^{2} c x^{2} + {\left(6 \, a b^{2} + b^{3}\right)} x^{3}\right)} \log\left(c + x\right)\right)} \log\left(-c + x\right)}{8 \, {\left(c - x\right)}}\,{d x}"," ",0,"1/3*a^3*x^3 + 1/2*(2*x^3*arctanh(c/x) + (c^2*log(-c^2 + x^2) + x^2)*c)*a^2*b + 1/24*(b^3*c^3 - b^3*x^3)*log(-c + x)^3 + 1/8*(b^3*c*x^2 + 2*a*b^2*x^3 + (b^3*c^3 + b^3*x^3)*log(c + x))*log(-c + x)^2 - integrate(-1/8*((b^3*c*x^2 - b^3*x^3)*log(c + x)^3 + 6*(a*b^2*c*x^2 - a*b^2*x^3)*log(c + x)^2 + (2*b^3*c*x^2 + 4*a*b^2*x^3 - 3*(b^3*c*x^2 - b^3*x^3)*log(c + x)^2 + 2*(b^3*c^3 - 6*a*b^2*c*x^2 + (6*a*b^2 + b^3)*x^3)*log(c + x))*log(-c + x))/(c - x), x)","F",0
152,0,0,0,0.000000," ","integrate(x*(a+b*arctanh(c/x))^3,x, algorithm=""maxima"")","\frac{3}{2} \, a b^{2} x^{2} \operatorname{artanh}\left(\frac{c}{x}\right)^{2} + \frac{1}{2} \, a^{3} x^{2} + \frac{3}{4} \, {\left(2 \, x^{2} \operatorname{artanh}\left(\frac{c}{x}\right) - {\left(c \log\left(c + x\right) - c \log\left(-c + x\right) - 2 \, x\right)} c\right)} a^{2} b + \frac{3}{8} \, {\left({\left(\log\left(c + x\right)^{2} - 2 \, {\left(\log\left(c + x\right) - 2\right)} \log\left(-c + x\right) + \log\left(-c + x\right)^{2} + 4 \, \log\left(c + x\right)\right)} c^{2} - 4 \, {\left(c \log\left(c + x\right) - c \log\left(-c + x\right) - 2 \, x\right)} c \operatorname{artanh}\left(\frac{c}{x}\right)\right)} a b^{2} + \frac{1}{16} \, {\left(6 \, c x \log\left(c + x\right)^{2} - {\left(c^{2} - x^{2}\right)} \log\left(c + x\right)^{3} + {\left(c^{2} - x^{2}\right)} \log\left(-c + x\right)^{3} - 3 \, {\left(2 \, c^{2} - 2 \, c x + {\left(c^{2} - x^{2}\right)} \log\left(c + x\right)\right)} \log\left(-c + x\right)^{2} + 3 \, {\left({\left(c^{2} - x^{2}\right)} \log\left(c + x\right)^{2} - 4 \, {\left(c^{2} + c x\right)} \log\left(c + x\right)\right)} \log\left(-c + x\right) + 2 \, \int -\frac{6 \, {\left(c^{3} + 3 \, c^{2} x\right)} \log\left(c + x\right)}{c^{2} - x^{2}}\,{d x}\right)} b^{3}"," ",0,"3/2*a*b^2*x^2*arctanh(c/x)^2 + 1/2*a^3*x^2 + 3/4*(2*x^2*arctanh(c/x) - (c*log(c + x) - c*log(-c + x) - 2*x)*c)*a^2*b + 3/8*((log(c + x)^2 - 2*(log(c + x) - 2)*log(-c + x) + log(-c + x)^2 + 4*log(c + x))*c^2 - 4*(c*log(c + x) - c*log(-c + x) - 2*x)*c*arctanh(c/x))*a*b^2 + 1/16*(6*c*x*log(c + x)^2 - (c^2 - x^2)*log(c + x)^3 + (c^2 - x^2)*log(-c + x)^3 - 3*(2*c^2 - 2*c*x + (c^2 - x^2)*log(c + x))*log(-c + x)^2 + 3*((c^2 - x^2)*log(c + x)^2 - 4*(c^2 + c*x)*log(c + x))*log(-c + x) + 2*integrate(-6*(c^3 + 3*c^2*x)*log(c + x)/(c^2 - x^2), x))*b^3","F",0
153,0,0,0,0.000000," ","integrate((a+b*arctanh(c/x))^3,x, algorithm=""maxima"")","\frac{3}{2} \, {\left(2 \, x \operatorname{artanh}\left(\frac{c}{x}\right) + c \log\left(-c^{2} + x^{2}\right)\right)} a^{2} b + a^{3} x + \frac{1}{8} \, {\left(b^{3} c - b^{3} x\right)} \log\left(-c + x\right)^{3} + \frac{3}{8} \, {\left(2 \, a b^{2} x + {\left(b^{3} c + b^{3} x\right)} \log\left(c + x\right)\right)} \log\left(-c + x\right)^{2} - \int -\frac{{\left(b^{3} c - b^{3} x\right)} \log\left(c + x\right)^{3} + 6 \, {\left(a b^{2} c - a b^{2} x\right)} \log\left(c + x\right)^{2} + 3 \, {\left(4 \, a b^{2} x - {\left(b^{3} c - b^{3} x\right)} \log\left(c + x\right)^{2} - 2 \, {\left(2 \, a b^{2} c - b^{3} c - {\left(2 \, a b^{2} + b^{3}\right)} x\right)} \log\left(c + x\right)\right)} \log\left(-c + x\right)}{8 \, {\left(c - x\right)}}\,{d x}"," ",0,"3/2*(2*x*arctanh(c/x) + c*log(-c^2 + x^2))*a^2*b + a^3*x + 1/8*(b^3*c - b^3*x)*log(-c + x)^3 + 3/8*(2*a*b^2*x + (b^3*c + b^3*x)*log(c + x))*log(-c + x)^2 - integrate(-1/8*((b^3*c - b^3*x)*log(c + x)^3 + 6*(a*b^2*c - a*b^2*x)*log(c + x)^2 + 3*(4*a*b^2*x - (b^3*c - b^3*x)*log(c + x)^2 - 2*(2*a*b^2*c - b^3*c - (2*a*b^2 + b^3)*x)*log(c + x))*log(-c + x))/(c - x), x)","F",0
154,0,0,0,0.000000," ","integrate((a+b*arctanh(c/x))^3/x,x, algorithm=""maxima"")","a^{3} \log\left(x\right) + \int \frac{b^{3} {\left(\log\left(\frac{c}{x} + 1\right) - \log\left(-\frac{c}{x} + 1\right)\right)}^{3}}{8 \, x} + \frac{3 \, a b^{2} {\left(\log\left(\frac{c}{x} + 1\right) - \log\left(-\frac{c}{x} + 1\right)\right)}^{2}}{4 \, x} + \frac{3 \, a^{2} b {\left(\log\left(\frac{c}{x} + 1\right) - \log\left(-\frac{c}{x} + 1\right)\right)}}{2 \, x}\,{d x}"," ",0,"a^3*log(x) + integrate(1/8*b^3*(log(c/x + 1) - log(-c/x + 1))^3/x + 3/4*a*b^2*(log(c/x + 1) - log(-c/x + 1))^2/x + 3/2*a^2*b*(log(c/x + 1) - log(-c/x + 1))/x, x)","F",0
155,0,0,0,0.000000," ","integrate((a+b*arctanh(c/x))^3/x^2,x, algorithm=""maxima"")","-\frac{3 \, a^{2} b {\left(\frac{2 \, c \operatorname{artanh}\left(\frac{c}{x}\right)}{x} + \log\left(-\frac{c^{2}}{x^{2}} + 1\right)\right)}}{2 \, c} - \frac{a^{3}}{x} + \frac{{\left(b^{3} c - b^{3} x\right)} \log\left(-c + x\right)^{3} - 3 \, {\left(2 \, a b^{2} c + {\left(b^{3} c + b^{3} x\right)} \log\left(c + x\right)\right)} \log\left(-c + x\right)^{2}}{8 \, c x} - \int -\frac{{\left(b^{3} c^{2} - b^{3} c x\right)} \log\left(c + x\right)^{3} + 6 \, {\left(a b^{2} c^{2} - a b^{2} c x\right)} \log\left(c + x\right)^{2} - 3 \, {\left(4 \, a b^{2} c x + {\left(b^{3} c^{2} - b^{3} c x\right)} \log\left(c + x\right)^{2} + 2 \, {\left(2 \, a b^{2} c^{2} + b^{3} x^{2} - {\left(2 \, a b^{2} c - b^{3} c\right)} x\right)} \log\left(c + x\right)\right)} \log\left(-c + x\right)}{8 \, {\left(c^{2} x^{2} - c x^{3}\right)}}\,{d x}"," ",0,"-3/2*a^2*b*(2*c*arctanh(c/x)/x + log(-c^2/x^2 + 1))/c - a^3/x + 1/8*((b^3*c - b^3*x)*log(-c + x)^3 - 3*(2*a*b^2*c + (b^3*c + b^3*x)*log(c + x))*log(-c + x)^2)/(c*x) - integrate(-1/8*((b^3*c^2 - b^3*c*x)*log(c + x)^3 + 6*(a*b^2*c^2 - a*b^2*c*x)*log(c + x)^2 - 3*(4*a*b^2*c*x + (b^3*c^2 - b^3*c*x)*log(c + x)^2 + 2*(2*a*b^2*c^2 + b^3*x^2 - (2*a*b^2*c - b^3*c)*x)*log(c + x))*log(-c + x))/(c^2*x^2 - c*x^3), x)","F",0
156,0,0,0,0.000000," ","integrate((a+b*arctanh(c/x))^3/x^3,x, algorithm=""maxima"")","\frac{3}{4} \, {\left(c {\left(\frac{\log\left(c + x\right)}{c^{3}} - \frac{\log\left(-c + x\right)}{c^{3}} - \frac{2}{c^{2} x}\right)} - \frac{2 \, \operatorname{artanh}\left(\frac{c}{x}\right)}{x^{2}}\right)} a^{2} b - \frac{3}{8} \, {\left(c^{2} {\left(\frac{\log\left(c + x\right)^{2} - 2 \, {\left(\log\left(c + x\right) - 2\right)} \log\left(-c + x\right) + \log\left(-c + x\right)^{2} + 4 \, \log\left(c + x\right)}{c^{4}} - \frac{8 \, \log\left(x\right)}{c^{4}}\right)} - 4 \, c {\left(\frac{\log\left(c + x\right)}{c^{3}} - \frac{\log\left(-c + x\right)}{c^{3}} - \frac{2}{c^{2} x}\right)} \operatorname{artanh}\left(\frac{c}{x}\right)\right)} a b^{2} + \frac{1}{64} \, {\left(32 \, c^{4} \int -\frac{\log\left(x\right)^{3}}{4 \, {\left(c^{4} x^{3} - c^{2} x^{5}\right)}}\,{d x} - 3 \, c^{3} {\left(\frac{\log\left(c + x\right)}{c^{5}} - \frac{\log\left(-c + x\right)}{c^{5}} - \frac{2}{c^{4} x}\right)} + 48 \, c^{3} \int -\frac{x \log\left(x\right)^{2}}{4 \, {\left(c^{4} x^{3} - c^{2} x^{5}\right)}}\,{d x} + 48 \, c^{3} \int -\frac{x \log\left(x\right)}{4 \, {\left(c^{4} x^{3} - c^{2} x^{5}\right)}}\,{d x} - 6 \, c {\left(\frac{2 \, \log\left(-c + x\right)}{c^{3}} - \frac{2 \, \log\left(x\right)}{c^{3}} + \frac{c + 2 \, x}{c^{2} x^{2}}\right)} \log\left(-\frac{c}{x} + 1\right)^{2} + 21 \, c^{2} {\left(\frac{\log\left(c + x\right)}{c^{4}} + \frac{\log\left(-c + x\right)}{c^{4}} - \frac{2 \, \log\left(x\right)}{c^{4}}\right)} - 32 \, c^{2} \int -\frac{x^{2} \log\left(x\right)^{3}}{4 \, {\left(c^{4} x^{3} - c^{2} x^{5}\right)}}\,{d x} + 48 \, c^{2} \int -\frac{x^{2} \log\left(x\right)^{2}}{4 \, {\left(c^{4} x^{3} - c^{2} x^{5}\right)}}\,{d x} - 384 \, c^{2} \int -\frac{x^{2} \log\left(c + x\right)}{4 \, {\left(c^{4} x^{3} - c^{2} x^{5}\right)}}\,{d x} + 144 \, c^{2} \int -\frac{x^{2} \log\left(x\right)}{4 \, {\left(c^{4} x^{3} - c^{2} x^{5}\right)}}\,{d x} - 18 \, c {\left(\frac{\log\left(c + x\right)}{c^{3}} - \frac{\log\left(-c + x\right)}{c^{3}}\right)} + c {\left(\frac{6 \, {\left(2 \, x^{2} \log\left(-c + x\right)^{2} + 2 \, x^{2} \log\left(x\right)^{2} - 6 \, x^{2} \log\left(x\right) + c^{2} + 6 \, c x - 2 \, {\left(2 \, x^{2} \log\left(x\right) - 3 \, x^{2}\right)} \log\left(-c + x\right)\right)} \log\left(-\frac{c}{x} + 1\right)}{c^{3} x^{2}} - \frac{4 \, x^{2} \log\left(-c + x\right)^{3} - 4 \, x^{2} \log\left(x\right)^{3} + 18 \, x^{2} \log\left(x\right)^{2} - 6 \, {\left(2 \, x^{2} \log\left(x\right) - 3 \, x^{2}\right)} \log\left(-c + x\right)^{2} - 42 \, x^{2} \log\left(x\right) + 3 \, c^{2} + 42 \, c x + 6 \, {\left(2 \, x^{2} \log\left(x\right)^{2} - 6 \, x^{2} \log\left(x\right) + 7 \, x^{2}\right)} \log\left(-c + x\right)}{c^{3} x^{2}}\right)} - 48 \, c \int -\frac{x^{3} \log\left(x\right)^{2}}{4 \, {\left(c^{4} x^{3} - c^{2} x^{5}\right)}}\,{d x} - 192 \, c \int -\frac{x^{3} \log\left(c + x\right)}{4 \, {\left(c^{4} x^{3} - c^{2} x^{5}\right)}}\,{d x} + 336 \, c \int -\frac{x^{3} \log\left(x\right)}{4 \, {\left(c^{4} x^{3} - c^{2} x^{5}\right)}}\,{d x} + \frac{4 \, \log\left(-\frac{c}{x} + 1\right)^{3}}{x^{2}} - \frac{2 \, {\left(12 \, c x \log\left(c + x\right)^{2} + 2 \, {\left(c^{2} - x^{2}\right)} \log\left(c + x\right)^{3} - 3 \, {\left(c^{2} - 2 \, c x + x^{2} - 2 \, {\left(c^{2} - x^{2}\right)} \log\left(c + x\right) + 2 \, {\left(c^{2} - x^{2}\right)} \log\left(x\right)\right)} \log\left(-c + x\right)^{2} - 3 \, {\left(2 \, {\left(c^{2} - x^{2}\right)} \log\left(c + x\right)^{2} - 2 \, {\left(c^{2} - x^{2}\right)} \log\left(x\right)^{2} - c^{2} - 6 \, c x + 8 \, {\left(c x + x^{2}\right)} \log\left(c + x\right) - 2 \, {\left(c^{2} + 2 \, c x + 5 \, x^{2}\right)} \log\left(x\right)\right)} \log\left(-c + x\right)\right)}}{c^{2} x^{2}} - 48 \, \int -\frac{x^{4} \log\left(x\right)^{2}}{4 \, {\left(c^{4} x^{3} - c^{2} x^{5}\right)}}\,{d x} - 192 \, \int -\frac{x^{4} \log\left(c + x\right)}{4 \, {\left(c^{4} x^{3} - c^{2} x^{5}\right)}}\,{d x} + 240 \, \int -\frac{x^{4} \log\left(x\right)}{4 \, {\left(c^{4} x^{3} - c^{2} x^{5}\right)}}\,{d x}\right)} b^{3} - \frac{3 \, a b^{2} \operatorname{artanh}\left(\frac{c}{x}\right)^{2}}{2 \, x^{2}} - \frac{a^{3}}{2 \, x^{2}}"," ",0,"3/4*(c*(log(c + x)/c^3 - log(-c + x)/c^3 - 2/(c^2*x)) - 2*arctanh(c/x)/x^2)*a^2*b - 3/8*(c^2*((log(c + x)^2 - 2*(log(c + x) - 2)*log(-c + x) + log(-c + x)^2 + 4*log(c + x))/c^4 - 8*log(x)/c^4) - 4*c*(log(c + x)/c^3 - log(-c + x)/c^3 - 2/(c^2*x))*arctanh(c/x))*a*b^2 + 1/64*(32*c^4*integrate(-1/4*log(x)^3/(c^4*x^3 - c^2*x^5), x) - 3*c^3*(log(c + x)/c^5 - log(-c + x)/c^5 - 2/(c^4*x)) + 48*c^3*integrate(-1/4*x*log(x)^2/(c^4*x^3 - c^2*x^5), x) + 48*c^3*integrate(-1/4*x*log(x)/(c^4*x^3 - c^2*x^5), x) - 6*c*(2*log(-c + x)/c^3 - 2*log(x)/c^3 + (c + 2*x)/(c^2*x^2))*log(-c/x + 1)^2 + 21*c^2*(log(c + x)/c^4 + log(-c + x)/c^4 - 2*log(x)/c^4) - 32*c^2*integrate(-1/4*x^2*log(x)^3/(c^4*x^3 - c^2*x^5), x) + 48*c^2*integrate(-1/4*x^2*log(x)^2/(c^4*x^3 - c^2*x^5), x) - 384*c^2*integrate(-1/4*x^2*log(c + x)/(c^4*x^3 - c^2*x^5), x) + 144*c^2*integrate(-1/4*x^2*log(x)/(c^4*x^3 - c^2*x^5), x) - 18*c*(log(c + x)/c^3 - log(-c + x)/c^3) + c*(6*(2*x^2*log(-c + x)^2 + 2*x^2*log(x)^2 - 6*x^2*log(x) + c^2 + 6*c*x - 2*(2*x^2*log(x) - 3*x^2)*log(-c + x))*log(-c/x + 1)/(c^3*x^2) - (4*x^2*log(-c + x)^3 - 4*x^2*log(x)^3 + 18*x^2*log(x)^2 - 6*(2*x^2*log(x) - 3*x^2)*log(-c + x)^2 - 42*x^2*log(x) + 3*c^2 + 42*c*x + 6*(2*x^2*log(x)^2 - 6*x^2*log(x) + 7*x^2)*log(-c + x))/(c^3*x^2)) - 48*c*integrate(-1/4*x^3*log(x)^2/(c^4*x^3 - c^2*x^5), x) - 192*c*integrate(-1/4*x^3*log(c + x)/(c^4*x^3 - c^2*x^5), x) + 336*c*integrate(-1/4*x^3*log(x)/(c^4*x^3 - c^2*x^5), x) + 4*log(-c/x + 1)^3/x^2 - 2*(12*c*x*log(c + x)^2 + 2*(c^2 - x^2)*log(c + x)^3 - 3*(c^2 - 2*c*x + x^2 - 2*(c^2 - x^2)*log(c + x) + 2*(c^2 - x^2)*log(x))*log(-c + x)^2 - 3*(2*(c^2 - x^2)*log(c + x)^2 - 2*(c^2 - x^2)*log(x)^2 - c^2 - 6*c*x + 8*(c*x + x^2)*log(c + x) - 2*(c^2 + 2*c*x + 5*x^2)*log(x))*log(-c + x))/(c^2*x^2) - 48*integrate(-1/4*x^4*log(x)^2/(c^4*x^3 - c^2*x^5), x) - 192*integrate(-1/4*x^4*log(c + x)/(c^4*x^3 - c^2*x^5), x) + 240*integrate(-1/4*x^4*log(x)/(c^4*x^3 - c^2*x^5), x))*b^3 - 3/2*a*b^2*arctanh(c/x)^2/x^2 - 1/2*a^3/x^2","F",0
157,1,62,0,0.319240," ","integrate(x^7*(a+b*arctanh(c/x^2)),x, algorithm=""maxima"")","\frac{1}{8} \, a x^{8} + \frac{1}{48} \, {\left(6 \, x^{8} \operatorname{artanh}\left(\frac{c}{x^{2}}\right) + {\left(2 \, x^{6} + 6 \, c^{2} x^{2} - 3 \, c^{3} \log\left(x^{2} + c\right) + 3 \, c^{3} \log\left(x^{2} - c\right)\right)} c\right)} b"," ",0,"1/8*a*x^8 + 1/48*(6*x^8*arctanh(c/x^2) + (2*x^6 + 6*c^2*x^2 - 3*c^3*log(x^2 + c) + 3*c^3*log(x^2 - c))*c)*b","A",0
158,1,42,0,0.318125," ","integrate(x^5*(a+b*arctanh(c/x^2)),x, algorithm=""maxima"")","\frac{1}{6} \, a x^{6} + \frac{1}{12} \, {\left(2 \, x^{6} \operatorname{artanh}\left(\frac{c}{x^{2}}\right) + {\left(x^{4} + c^{2} \log\left(x^{4} - c^{2}\right)\right)} c\right)} b"," ",0,"1/6*a*x^6 + 1/12*(2*x^6*arctanh(c/x^2) + (x^4 + c^2*log(x^4 - c^2))*c)*b","A",0
159,1,49,0,0.314970," ","integrate(x^3*(a+b*arctanh(c/x^2)),x, algorithm=""maxima"")","\frac{1}{4} \, a x^{4} + \frac{1}{8} \, {\left(2 \, x^{4} \operatorname{artanh}\left(\frac{c}{x^{2}}\right) + {\left(2 \, x^{2} - c \log\left(x^{2} + c\right) + c \log\left(x^{2} - c\right)\right)} c\right)} b"," ",0,"1/4*a*x^4 + 1/8*(2*x^4*arctanh(c/x^2) + (2*x^2 - c*log(x^2 + c) + c*log(x^2 - c))*c)*b","A",0
160,1,34,0,0.324415," ","integrate(x*(a+b*arctanh(c/x^2)),x, algorithm=""maxima"")","\frac{1}{2} \, a x^{2} + \frac{1}{4} \, {\left(2 \, x^{2} \operatorname{artanh}\left(\frac{c}{x^{2}}\right) + c \log\left(x^{4} - c^{2}\right)\right)} b"," ",0,"1/2*a*x^2 + 1/4*(2*x^2*arctanh(c/x^2) + c*log(x^4 - c^2))*b","A",0
161,0,0,0,0.000000," ","integrate((a+b*arctanh(c/x^2))/x,x, algorithm=""maxima"")","\frac{1}{2} \, b \int \frac{\log\left(\frac{c}{x^{2}} + 1\right) - \log\left(-\frac{c}{x^{2}} + 1\right)}{x}\,{d x} + a \log\left(x\right)"," ",0,"1/2*b*integrate((log(c/x^2 + 1) - log(-c/x^2 + 1))/x, x) + a*log(x)","F",0
162,1,37,0,0.318401," ","integrate((a+b*arctanh(c/x^2))/x^3,x, algorithm=""maxima"")","-\frac{b {\left(\frac{2 \, c \operatorname{artanh}\left(\frac{c}{x^{2}}\right)}{x^{2}} + \log\left(-\frac{c^{2}}{x^{4}} + 1\right)\right)}}{4 \, c} - \frac{a}{2 \, x^{2}}"," ",0,"-1/4*b*(2*c*arctanh(c/x^2)/x^2 + log(-c^2/x^4 + 1))/c - 1/2*a/x^2","A",0
163,1,56,0,0.304754," ","integrate((a+b*arctanh(c/x^2))/x^5,x, algorithm=""maxima"")","\frac{1}{8} \, {\left(c {\left(\frac{\log\left(x^{2} + c\right)}{c^{3}} - \frac{\log\left(x^{2} - c\right)}{c^{3}} - \frac{2}{c^{2} x^{2}}\right)} - \frac{2 \, \operatorname{artanh}\left(\frac{c}{x^{2}}\right)}{x^{4}}\right)} b - \frac{a}{4 \, x^{4}}"," ",0,"1/8*(c*(log(x^2 + c)/c^3 - log(x^2 - c)/c^3 - 2/(c^2*x^2)) - 2*arctanh(c/x^2)/x^4)*b - 1/4*a/x^4","A",0
164,1,55,0,0.321532," ","integrate((a+b*arctanh(c/x^2))/x^7,x, algorithm=""maxima"")","-\frac{1}{12} \, {\left(c {\left(\frac{\log\left(x^{4} - c^{2}\right)}{c^{4}} - \frac{\log\left(x^{4}\right)}{c^{4}} + \frac{1}{c^{2} x^{4}}\right)} + \frac{2 \, \operatorname{artanh}\left(\frac{c}{x^{2}}\right)}{x^{6}}\right)} b - \frac{a}{6 \, x^{6}}"," ",0,"-1/12*(c*(log(x^4 - c^2)/c^4 - log(x^4)/c^4 + 1/(c^2*x^4)) + 2*arctanh(c/x^2)/x^6)*b - 1/6*a/x^6","A",0
165,1,62,0,0.413022," ","integrate(x^4*(a+b*arctanh(c/x^2)),x, algorithm=""maxima"")","\frac{1}{5} \, a x^{5} + \frac{1}{30} \, {\left(6 \, x^{5} \operatorname{artanh}\left(\frac{c}{x^{2}}\right) + {\left(4 \, x^{3} + 6 \, c^{\frac{3}{2}} \arctan\left(\frac{x}{\sqrt{c}}\right) + 3 \, c^{\frac{3}{2}} \log\left(\frac{x - \sqrt{c}}{x + \sqrt{c}}\right)\right)} c\right)} b"," ",0,"1/5*a*x^5 + 1/30*(6*x^5*arctanh(c/x^2) + (4*x^3 + 6*c^(3/2)*arctan(x/sqrt(c)) + 3*c^(3/2)*log((x - sqrt(c))/(x + sqrt(c))))*c)*b","A",0
166,1,61,0,0.420269," ","integrate(x^2*(a+b*arctanh(c/x^2)),x, algorithm=""maxima"")","\frac{1}{3} \, a x^{3} + \frac{1}{6} \, {\left(2 \, x^{3} \operatorname{artanh}\left(\frac{c}{x^{2}}\right) - {\left(2 \, \sqrt{c} \arctan\left(\frac{x}{\sqrt{c}}\right) - \sqrt{c} \log\left(\frac{x - \sqrt{c}}{x + \sqrt{c}}\right) - 4 \, x\right)} c\right)} b"," ",0,"1/3*a*x^3 + 1/6*(2*x^3*arctanh(c/x^2) - (2*sqrt(c)*arctan(x/sqrt(c)) - sqrt(c)*log((x - sqrt(c))/(x + sqrt(c))) - 4*x)*c)*b","A",0
167,1,51,0,0.422096," ","integrate(a+b*arctanh(c/x^2),x, algorithm=""maxima"")","\frac{1}{2} \, {\left(c {\left(\frac{2 \, \arctan\left(\frac{x}{\sqrt{c}}\right)}{\sqrt{c}} + \frac{\log\left(\frac{x - \sqrt{c}}{x + \sqrt{c}}\right)}{\sqrt{c}}\right)} + 2 \, x \operatorname{artanh}\left(\frac{c}{x^{2}}\right)\right)} b + a x"," ",0,"1/2*(c*(2*arctan(x/sqrt(c))/sqrt(c) + log((x - sqrt(c))/(x + sqrt(c)))/sqrt(c)) + 2*x*arctanh(c/x^2))*b + a*x","A",0
168,1,57,0,0.423126," ","integrate((a+b*arctanh(c/x^2))/x^2,x, algorithm=""maxima"")","\frac{1}{2} \, {\left(c {\left(\frac{2 \, \arctan\left(\frac{x}{\sqrt{c}}\right)}{c^{\frac{3}{2}}} - \frac{\log\left(\frac{x - \sqrt{c}}{x + \sqrt{c}}\right)}{c^{\frac{3}{2}}}\right)} - \frac{2 \, \operatorname{artanh}\left(\frac{c}{x^{2}}\right)}{x}\right)} b - \frac{a}{x}"," ",0,"1/2*(c*(2*arctan(x/sqrt(c))/c^(3/2) - log((x - sqrt(c))/(x + sqrt(c)))/c^(3/2)) - 2*arctanh(c/x^2)/x)*b - a/x","A",0
169,1,64,0,0.414302," ","integrate((a+b*arctanh(c/x^2))/x^4,x, algorithm=""maxima"")","-\frac{1}{6} \, {\left(c {\left(\frac{2 \, \arctan\left(\frac{x}{\sqrt{c}}\right)}{c^{\frac{5}{2}}} + \frac{\log\left(\frac{x - \sqrt{c}}{x + \sqrt{c}}\right)}{c^{\frac{5}{2}}} + \frac{4}{c^{2} x}\right)} + \frac{2 \, \operatorname{artanh}\left(\frac{c}{x^{2}}\right)}{x^{3}}\right)} b - \frac{a}{3 \, x^{3}}"," ",0,"-1/6*(c*(2*arctan(x/sqrt(c))/c^(5/2) + log((x - sqrt(c))/(x + sqrt(c)))/c^(5/2) + 4/(c^2*x)) + 2*arctanh(c/x^2)/x^3)*b - 1/3*a/x^3","A",0
170,1,65,0,0.415986," ","integrate((a+b*arctanh(c/x^2))/x^6,x, algorithm=""maxima"")","\frac{1}{30} \, {\left(c {\left(\frac{6 \, \arctan\left(\frac{x}{\sqrt{c}}\right)}{c^{\frac{7}{2}}} - \frac{3 \, \log\left(\frac{x - \sqrt{c}}{x + \sqrt{c}}\right)}{c^{\frac{7}{2}}} - \frac{4}{c^{2} x^{3}}\right)} - \frac{6 \, \operatorname{artanh}\left(\frac{c}{x^{2}}\right)}{x^{5}}\right)} b - \frac{a}{5 \, x^{5}}"," ",0,"1/30*(c*(6*arctan(x/sqrt(c))/c^(7/2) - 3*log((x - sqrt(c))/(x + sqrt(c)))/c^(7/2) - 4/(c^2*x^3)) - 6*arctanh(c/x^2)/x^5)*b - 1/5*a/x^5","A",0
171,1,157,0,0.333879," ","integrate(x^3*(a+b*arctanh(c/x^2))^2,x, algorithm=""maxima"")","\frac{1}{4} \, b^{2} x^{4} \operatorname{artanh}\left(\frac{c}{x^{2}}\right)^{2} + \frac{1}{4} \, a^{2} x^{4} + \frac{1}{4} \, {\left(2 \, x^{4} \operatorname{artanh}\left(\frac{c}{x^{2}}\right) + {\left(2 \, x^{2} - c \log\left(x^{2} + c\right) + c \log\left(x^{2} - c\right)\right)} c\right)} a b + \frac{1}{16} \, {\left({\left(\log\left(x^{2} + c\right)^{2} - 2 \, {\left(\log\left(x^{2} + c\right) - 2\right)} \log\left(x^{2} - c\right) + \log\left(x^{2} - c\right)^{2} + 4 \, \log\left(x^{2} + c\right)\right)} c^{2} + 4 \, {\left(2 \, x^{2} - c \log\left(x^{2} + c\right) + c \log\left(x^{2} - c\right)\right)} c \operatorname{artanh}\left(\frac{c}{x^{2}}\right)\right)} b^{2}"," ",0,"1/4*b^2*x^4*arctanh(c/x^2)^2 + 1/4*a^2*x^4 + 1/4*(2*x^4*arctanh(c/x^2) + (2*x^2 - c*log(x^2 + c) + c*log(x^2 - c))*c)*a*b + 1/16*((log(x^2 + c)^2 - 2*(log(x^2 + c) - 2)*log(x^2 - c) + log(x^2 - c)^2 + 4*log(x^2 + c))*c^2 + 4*(2*x^2 - c*log(x^2 + c) + c*log(x^2 - c))*c*arctanh(c/x^2))*b^2","A",0
172,0,0,0,0.000000," ","integrate(x*(a+b*arctanh(c/x^2))^2,x, algorithm=""maxima"")","\frac{1}{2} \, a^{2} x^{2} + \frac{1}{2} \, {\left(2 \, x^{2} \operatorname{artanh}\left(\frac{c}{x^{2}}\right) + c \log\left(x^{4} - c^{2}\right)\right)} a b + \frac{1}{8} \, {\left(x^{2} \log\left(x^{2} + c\right)^{2} - 2 \, {\left(x^{2} + c\right)} \log\left(x^{2} + c\right) \log\left(x^{2} - c\right) + {\left(x^{2} - c\right)} \log\left(x^{2} - c\right)^{2} + 2 \, \int \frac{2 \, {\left(3 \, c x^{3} + c^{2} x\right)} \log\left(x^{2} + c\right)}{x^{4} - c^{2}}\,{d x}\right)} b^{2}"," ",0,"1/2*a^2*x^2 + 1/2*(2*x^2*arctanh(c/x^2) + c*log(x^4 - c^2))*a*b + 1/8*(x^2*log(x^2 + c)^2 - 2*(x^2 + c)*log(x^2 + c)*log(x^2 - c) + (x^2 - c)*log(x^2 - c)^2 + 2*integrate(2*(3*c*x^3 + c^2*x)*log(x^2 + c)/(x^4 - c^2), x))*b^2","F",0
173,0,0,0,0.000000," ","integrate((a+b*arctanh(c/x^2))^2/x,x, algorithm=""maxima"")","a^{2} \log\left(x\right) + \int \frac{b^{2} {\left(\log\left(\frac{c}{x^{2}} + 1\right) - \log\left(-\frac{c}{x^{2}} + 1\right)\right)}^{2}}{4 \, x} + \frac{a b {\left(\log\left(\frac{c}{x^{2}} + 1\right) - \log\left(-\frac{c}{x^{2}} + 1\right)\right)}}{x}\,{d x}"," ",0,"a^2*log(x) + integrate(1/4*b^2*(log(c/x^2 + 1) - log(-c/x^2 + 1))^2/x + a*b*(log(c/x^2 + 1) - log(-c/x^2 + 1))/x, x)","F",0
174,0,0,0,0.000000," ","integrate((a+b*arctanh(c/x^2))^2/x^3,x, algorithm=""maxima"")","\frac{1}{8} \, {\left(8 \, c^{3} \int \frac{\log\left(x\right)^{2}}{c x^{7} - c^{3} x^{3}}\,{d x} + c^{2} {\left(\frac{\log\left(x^{2} + c\right)}{c^{3}} + \frac{\log\left(x^{2} - c\right)}{c^{3}} - \frac{4 \, \log\left(x\right)}{c^{3}}\right)} - 8 \, c^{2} \int \frac{x^{2} \log\left(x^{2} + c\right)}{c x^{7} - c^{3} x^{3}}\,{d x} + 8 \, c^{2} \int \frac{x^{2} \log\left(x\right)}{c x^{7} - c^{3} x^{3}}\,{d x} + 2 \, c {\left(\frac{\log\left(x^{2} - c\right)}{c^{2}} - \frac{\log\left(x^{2}\right)}{c^{2}} + \frac{1}{c x^{2}}\right)} \log\left(-\frac{c}{x^{2}} + 1\right) - c {\left(\frac{\log\left(x^{2} + c\right)}{c^{2}} - \frac{\log\left(x^{2} - c\right)}{c^{2}}\right)} - 8 \, c \int \frac{x^{4} \log\left(x\right)^{2}}{c x^{7} - c^{3} x^{3}}\,{d x} - 4 \, c \int \frac{x^{4} \log\left(x^{2} + c\right)}{c x^{7} - c^{3} x^{3}}\,{d x} + 16 \, c \int \frac{x^{4} \log\left(x\right)}{c x^{7} - c^{3} x^{3}}\,{d x} - \frac{\log\left(-\frac{c}{x^{2}} + 1\right)^{2}}{x^{2}} - \frac{x^{2} \log\left(x^{2} - c\right)^{2} + 4 \, x^{2} \log\left(x\right)^{2} - 4 \, x^{2} \log\left(x\right) - 2 \, {\left(2 \, x^{2} \log\left(x\right) - x^{2}\right)} \log\left(x^{2} - c\right) + 2 \, c}{c x^{2}} - \frac{c \log\left(x^{2} + c\right)^{2} - 2 \, {\left({\left(x^{2} + c\right)} \log\left(x^{2} + c\right) - 2 \, {\left(x^{2} + c\right)} \log\left(x\right) - c\right)} \log\left(x^{2} - c\right)}{c x^{2}} - 4 \, \int \frac{x^{6} \log\left(x^{2} + c\right)}{c x^{7} - c^{3} x^{3}}\,{d x} + 8 \, \int \frac{x^{6} \log\left(x\right)}{c x^{7} - c^{3} x^{3}}\,{d x}\right)} b^{2} - \frac{a b {\left(\frac{2 \, c \operatorname{artanh}\left(\frac{c}{x^{2}}\right)}{x^{2}} + \log\left(-\frac{c^{2}}{x^{4}} + 1\right)\right)}}{2 \, c} - \frac{a^{2}}{2 \, x^{2}}"," ",0,"1/8*(8*c^3*integrate(log(x)^2/(c*x^7 - c^3*x^3), x) + c^2*(log(x^2 + c)/c^3 + log(x^2 - c)/c^3 - 4*log(x)/c^3) - 8*c^2*integrate(x^2*log(x^2 + c)/(c*x^7 - c^3*x^3), x) + 8*c^2*integrate(x^2*log(x)/(c*x^7 - c^3*x^3), x) + 2*c*(log(x^2 - c)/c^2 - log(x^2)/c^2 + 1/(c*x^2))*log(-c/x^2 + 1) - c*(log(x^2 + c)/c^2 - log(x^2 - c)/c^2) - 8*c*integrate(x^4*log(x)^2/(c*x^7 - c^3*x^3), x) - 4*c*integrate(x^4*log(x^2 + c)/(c*x^7 - c^3*x^3), x) + 16*c*integrate(x^4*log(x)/(c*x^7 - c^3*x^3), x) - log(-c/x^2 + 1)^2/x^2 - (x^2*log(x^2 - c)^2 + 4*x^2*log(x)^2 - 4*x^2*log(x) - 2*(2*x^2*log(x) - x^2)*log(x^2 - c) + 2*c)/(c*x^2) - (c*log(x^2 + c)^2 - 2*((x^2 + c)*log(x^2 + c) - 2*(x^2 + c)*log(x) - c)*log(x^2 - c))/(c*x^2) - 4*integrate(x^6*log(x^2 + c)/(c*x^7 - c^3*x^3), x) + 8*integrate(x^6*log(x)/(c*x^7 - c^3*x^3), x))*b^2 - 1/2*a*b*(2*c*arctanh(c/x^2)/x^2 + log(-c^2/x^4 + 1))/c - 1/2*a^2/x^2","F",0
175,1,183,0,0.327890," ","integrate((a+b*arctanh(c/x^2))^2/x^5,x, algorithm=""maxima"")","\frac{1}{4} \, {\left(c {\left(\frac{\log\left(x^{2} + c\right)}{c^{3}} - \frac{\log\left(x^{2} - c\right)}{c^{3}} - \frac{2}{c^{2} x^{2}}\right)} - \frac{2 \, \operatorname{artanh}\left(\frac{c}{x^{2}}\right)}{x^{4}}\right)} a b - \frac{1}{16} \, {\left(c^{2} {\left(\frac{\log\left(x^{2} + c\right)^{2} - 2 \, {\left(\log\left(x^{2} + c\right) - 2\right)} \log\left(x^{2} - c\right) + \log\left(x^{2} - c\right)^{2} + 4 \, \log\left(x^{2} + c\right)}{c^{4}} - \frac{16 \, \log\left(x\right)}{c^{4}}\right)} - 4 \, c {\left(\frac{\log\left(x^{2} + c\right)}{c^{3}} - \frac{\log\left(x^{2} - c\right)}{c^{3}} - \frac{2}{c^{2} x^{2}}\right)} \operatorname{artanh}\left(\frac{c}{x^{2}}\right)\right)} b^{2} - \frac{b^{2} \operatorname{artanh}\left(\frac{c}{x^{2}}\right)^{2}}{4 \, x^{4}} - \frac{a^{2}}{4 \, x^{4}}"," ",0,"1/4*(c*(log(x^2 + c)/c^3 - log(x^2 - c)/c^3 - 2/(c^2*x^2)) - 2*arctanh(c/x^2)/x^4)*a*b - 1/16*(c^2*((log(x^2 + c)^2 - 2*(log(x^2 + c) - 2)*log(x^2 - c) + log(x^2 - c)^2 + 4*log(x^2 + c))/c^4 - 16*log(x)/c^4) - 4*c*(log(x^2 + c)/c^3 - log(x^2 - c)/c^3 - 2/(c^2*x^2))*arctanh(c/x^2))*b^2 - 1/4*b^2*arctanh(c/x^2)^2/x^4 - 1/4*a^2/x^4","B",0
176,0,0,0,0.000000," ","integrate(x^4*(a+b*arctanh(c/x^2))^2,x, algorithm=""maxima"")","\frac{1}{5} \, a^{2} x^{5} + \frac{1}{15} \, {\left(6 \, x^{5} \operatorname{artanh}\left(\frac{c}{x^{2}}\right) + {\left(4 \, x^{3} + 6 \, c^{\frac{3}{2}} \arctan\left(\frac{x}{\sqrt{c}}\right) + 3 \, c^{\frac{3}{2}} \log\left(\frac{x - \sqrt{c}}{x + \sqrt{c}}\right)\right)} c\right)} a b + \frac{1}{20} \, {\left(x^{5} \log\left(x^{2} - c\right)^{2} - 5 \, \int -\frac{5 \, {\left(x^{6} - c x^{4}\right)} \log\left(x^{2} + c\right)^{2} - 2 \, {\left(2 \, x^{6} + 5 \, {\left(x^{6} - c x^{4}\right)} \log\left(x^{2} + c\right)\right)} \log\left(x^{2} - c\right)}{5 \, {\left(x^{2} - c\right)}}\,{d x}\right)} b^{2}"," ",0,"1/5*a^2*x^5 + 1/15*(6*x^5*arctanh(c/x^2) + (4*x^3 + 6*c^(3/2)*arctan(x/sqrt(c)) + 3*c^(3/2)*log((x - sqrt(c))/(x + sqrt(c))))*c)*a*b + 1/20*(x^5*log(x^2 - c)^2 - 5*integrate(-1/5*(5*(x^6 - c*x^4)*log(x^2 + c)^2 - 2*(2*x^6 + 5*(x^6 - c*x^4)*log(x^2 + c))*log(x^2 - c))/(x^2 - c), x))*b^2","F",0
177,0,0,0,0.000000," ","integrate(x^2*(a+b*arctanh(c/x^2))^2,x, algorithm=""maxima"")","\frac{1}{3} \, a^{2} x^{3} + \frac{1}{3} \, {\left(2 \, x^{3} \operatorname{artanh}\left(\frac{c}{x^{2}}\right) - {\left(2 \, \sqrt{c} \arctan\left(\frac{x}{\sqrt{c}}\right) - \sqrt{c} \log\left(\frac{x - \sqrt{c}}{x + \sqrt{c}}\right) - 4 \, x\right)} c\right)} a b + \frac{1}{12} \, {\left(x^{3} \log\left(x^{2} - c\right)^{2} - 3 \, \int -\frac{3 \, {\left(x^{4} - c x^{2}\right)} \log\left(x^{2} + c\right)^{2} - 2 \, {\left(2 \, x^{4} + 3 \, {\left(x^{4} - c x^{2}\right)} \log\left(x^{2} + c\right)\right)} \log\left(x^{2} - c\right)}{3 \, {\left(x^{2} - c\right)}}\,{d x}\right)} b^{2}"," ",0,"1/3*a^2*x^3 + 1/3*(2*x^3*arctanh(c/x^2) - (2*sqrt(c)*arctan(x/sqrt(c)) - sqrt(c)*log((x - sqrt(c))/(x + sqrt(c))) - 4*x)*c)*a*b + 1/12*(x^3*log(x^2 - c)^2 - 3*integrate(-1/3*(3*(x^4 - c*x^2)*log(x^2 + c)^2 - 2*(2*x^4 + 3*(x^4 - c*x^2)*log(x^2 + c))*log(x^2 - c))/(x^2 - c), x))*b^2","F",0
178,0,0,0,0.000000," ","integrate((a+b*arctanh(c/x^2))^2,x, algorithm=""maxima"")","{\left(c {\left(\frac{2 \, \arctan\left(\frac{x}{\sqrt{c}}\right)}{\sqrt{c}} + \frac{\log\left(\frac{x - \sqrt{c}}{x + \sqrt{c}}\right)}{\sqrt{c}}\right)} + 2 \, x \operatorname{artanh}\left(\frac{c}{x^{2}}\right)\right)} a b + \frac{1}{4} \, {\left(x \log\left(x^{2} - c\right)^{2} - \int -\frac{{\left(x^{2} - c\right)} \log\left(x^{2} + c\right)^{2} - 2 \, {\left(2 \, x^{2} + {\left(x^{2} - c\right)} \log\left(x^{2} + c\right)\right)} \log\left(x^{2} - c\right)}{x^{2} - c}\,{d x}\right)} b^{2} + a^{2} x"," ",0,"(c*(2*arctan(x/sqrt(c))/sqrt(c) + log((x - sqrt(c))/(x + sqrt(c)))/sqrt(c)) + 2*x*arctanh(c/x^2))*a*b + 1/4*(x*log(x^2 - c)^2 - integrate(-((x^2 - c)*log(x^2 + c)^2 - 2*(2*x^2 + (x^2 - c)*log(x^2 + c))*log(x^2 - c))/(x^2 - c), x))*b^2 + a^2*x","F",0
179,0,0,0,0.000000," ","integrate((a+b*arctanh(c/x^2))^2/x^2,x, algorithm=""maxima"")","{\left(c {\left(\frac{2 \, \arctan\left(\frac{x}{\sqrt{c}}\right)}{c^{\frac{3}{2}}} - \frac{\log\left(\frac{x - \sqrt{c}}{x + \sqrt{c}}\right)}{c^{\frac{3}{2}}}\right)} - \frac{2 \, \operatorname{artanh}\left(\frac{c}{x^{2}}\right)}{x}\right)} a b - \frac{1}{4} \, b^{2} {\left(\frac{\log\left(x^{2} - c\right)^{2}}{x} + \int -\frac{{\left(x^{2} - c\right)} \log\left(x^{2} + c\right)^{2} + 2 \, {\left(2 \, x^{2} - {\left(x^{2} - c\right)} \log\left(x^{2} + c\right)\right)} \log\left(x^{2} - c\right)}{x^{4} - c x^{2}}\,{d x}\right)} - \frac{a^{2}}{x}"," ",0,"(c*(2*arctan(x/sqrt(c))/c^(3/2) - log((x - sqrt(c))/(x + sqrt(c)))/c^(3/2)) - 2*arctanh(c/x^2)/x)*a*b - 1/4*b^2*(log(x^2 - c)^2/x + integrate(-((x^2 - c)*log(x^2 + c)^2 + 2*(2*x^2 - (x^2 - c)*log(x^2 + c))*log(x^2 - c))/(x^4 - c*x^2), x)) - a^2/x","F",0
180,0,0,0,0.000000," ","integrate((a+b*arctanh(c/x^2))^2/x^4,x, algorithm=""maxima"")","-\frac{1}{3} \, {\left(c {\left(\frac{2 \, \arctan\left(\frac{x}{\sqrt{c}}\right)}{c^{\frac{5}{2}}} + \frac{\log\left(\frac{x - \sqrt{c}}{x + \sqrt{c}}\right)}{c^{\frac{5}{2}}} + \frac{4}{c^{2} x}\right)} + \frac{2 \, \operatorname{artanh}\left(\frac{c}{x^{2}}\right)}{x^{3}}\right)} a b - \frac{1}{12} \, b^{2} {\left(\frac{\log\left(x^{2} - c\right)^{2}}{x^{3}} + 3 \, \int -\frac{3 \, {\left(x^{2} - c\right)} \log\left(x^{2} + c\right)^{2} + 2 \, {\left(2 \, x^{2} - 3 \, {\left(x^{2} - c\right)} \log\left(x^{2} + c\right)\right)} \log\left(x^{2} - c\right)}{3 \, {\left(x^{6} - c x^{4}\right)}}\,{d x}\right)} - \frac{a^{2}}{3 \, x^{3}}"," ",0,"-1/3*(c*(2*arctan(x/sqrt(c))/c^(5/2) + log((x - sqrt(c))/(x + sqrt(c)))/c^(5/2) + 4/(c^2*x)) + 2*arctanh(c/x^2)/x^3)*a*b - 1/12*b^2*(log(x^2 - c)^2/x^3 + 3*integrate(-1/3*(3*(x^2 - c)*log(x^2 + c)^2 + 2*(2*x^2 - 3*(x^2 - c)*log(x^2 + c))*log(x^2 - c))/(x^6 - c*x^4), x)) - 1/3*a^2/x^3","F",0
181,0,0,0,0.000000," ","integrate((a+b*arctanh(c/x^2))^2/x^6,x, algorithm=""maxima"")","\frac{1}{15} \, {\left(c {\left(\frac{6 \, \arctan\left(\frac{x}{\sqrt{c}}\right)}{c^{\frac{7}{2}}} - \frac{3 \, \log\left(\frac{x - \sqrt{c}}{x + \sqrt{c}}\right)}{c^{\frac{7}{2}}} - \frac{4}{c^{2} x^{3}}\right)} - \frac{6 \, \operatorname{artanh}\left(\frac{c}{x^{2}}\right)}{x^{5}}\right)} a b - \frac{1}{20} \, b^{2} {\left(\frac{\log\left(x^{2} - c\right)^{2}}{x^{5}} + 5 \, \int -\frac{5 \, {\left(x^{2} - c\right)} \log\left(x^{2} + c\right)^{2} + 2 \, {\left(2 \, x^{2} - 5 \, {\left(x^{2} - c\right)} \log\left(x^{2} + c\right)\right)} \log\left(x^{2} - c\right)}{5 \, {\left(x^{8} - c x^{6}\right)}}\,{d x}\right)} - \frac{a^{2}}{5 \, x^{5}}"," ",0,"1/15*(c*(6*arctan(x/sqrt(c))/c^(7/2) - 3*log((x - sqrt(c))/(x + sqrt(c)))/c^(7/2) - 4/(c^2*x^3)) - 6*arctanh(c/x^2)/x^5)*a*b - 1/20*b^2*(log(x^2 - c)^2/x^5 + 5*integrate(-1/5*(5*(x^2 - c)*log(x^2 + c)^2 + 2*(2*x^2 - 5*(x^2 - c)*log(x^2 + c))*log(x^2 - c))/(x^8 - c*x^6), x)) - 1/5*a^2/x^5","F",0
182,0,0,0,0.000000," ","integrate((d*x)^m*(a+b*arctanh(c/x^2))^3,x, algorithm=""maxima"")","-\frac{b^{3} d^{m} x x^{m} \log\left(x^{2} - c\right)^{3}}{8 \, {\left(m + 1\right)}} + \frac{\left(d x\right)^{m + 1} a^{3}}{d {\left(m + 1\right)}} + \int \frac{{\left(b^{3} d^{m} {\left(m + 1\right)} x^{2} - b^{3} c d^{m} {\left(m + 1\right)}\right)} x^{m} \log\left(x^{2} + c\right)^{3} + 6 \, {\left(a b^{2} d^{m} {\left(m + 1\right)} x^{2} - a b^{2} c d^{m} {\left(m + 1\right)}\right)} x^{m} \log\left(x^{2} + c\right)^{2} + 12 \, {\left(a^{2} b d^{m} {\left(m + 1\right)} x^{2} - a^{2} b c d^{m} {\left(m + 1\right)}\right)} x^{m} \log\left(x^{2} + c\right) + 3 \, {\left({\left(b^{3} d^{m} {\left(m + 1\right)} x^{2} - b^{3} c d^{m} {\left(m + 1\right)}\right)} x^{m} \log\left(x^{2} + c\right) - 2 \, {\left(a b^{2} c d^{m} {\left(m + 1\right)} - {\left(a b^{2} d^{m} {\left(m + 1\right)} + b^{3} d^{m}\right)} x^{2}\right)} x^{m}\right)} \log\left(x^{2} - c\right)^{2} - 3 \, {\left({\left(b^{3} d^{m} {\left(m + 1\right)} x^{2} - b^{3} c d^{m} {\left(m + 1\right)}\right)} x^{m} \log\left(x^{2} + c\right)^{2} + 4 \, {\left(a b^{2} d^{m} {\left(m + 1\right)} x^{2} - a b^{2} c d^{m} {\left(m + 1\right)}\right)} x^{m} \log\left(x^{2} + c\right) + 4 \, {\left(a^{2} b d^{m} {\left(m + 1\right)} x^{2} - a^{2} b c d^{m} {\left(m + 1\right)}\right)} x^{m}\right)} \log\left(x^{2} - c\right)}{8 \, {\left({\left(m + 1\right)} x^{2} - c {\left(m + 1\right)}\right)}}\,{d x}"," ",0,"-1/8*b^3*d^m*x*x^m*log(x^2 - c)^3/(m + 1) + (d*x)^(m + 1)*a^3/(d*(m + 1)) + integrate(1/8*((b^3*d^m*(m + 1)*x^2 - b^3*c*d^m*(m + 1))*x^m*log(x^2 + c)^3 + 6*(a*b^2*d^m*(m + 1)*x^2 - a*b^2*c*d^m*(m + 1))*x^m*log(x^2 + c)^2 + 12*(a^2*b*d^m*(m + 1)*x^2 - a^2*b*c*d^m*(m + 1))*x^m*log(x^2 + c) + 3*((b^3*d^m*(m + 1)*x^2 - b^3*c*d^m*(m + 1))*x^m*log(x^2 + c) - 2*(a*b^2*c*d^m*(m + 1) - (a*b^2*d^m*(m + 1) + b^3*d^m)*x^2)*x^m)*log(x^2 - c)^2 - 3*((b^3*d^m*(m + 1)*x^2 - b^3*c*d^m*(m + 1))*x^m*log(x^2 + c)^2 + 4*(a*b^2*d^m*(m + 1)*x^2 - a*b^2*c*d^m*(m + 1))*x^m*log(x^2 + c) + 4*(a^2*b*d^m*(m + 1)*x^2 - a^2*b*c*d^m*(m + 1))*x^m)*log(x^2 - c))/((m + 1)*x^2 - c*(m + 1)), x)","F",0
183,0,0,0,0.000000," ","integrate((d*x)^m*(a+b*arctanh(c/x^2))^2,x, algorithm=""maxima"")","\frac{b^{2} d^{m} x x^{m} \log\left(x^{2} - c\right)^{2}}{4 \, {\left(m + 1\right)}} + \frac{\left(d x\right)^{m + 1} a^{2}}{d {\left(m + 1\right)}} - \int -\frac{{\left(b^{2} d^{m} {\left(m + 1\right)} x^{2} - b^{2} c d^{m} {\left(m + 1\right)}\right)} x^{m} \log\left(x^{2} + c\right)^{2} + 4 \, {\left(a b d^{m} {\left(m + 1\right)} x^{2} - a b c d^{m} {\left(m + 1\right)}\right)} x^{m} \log\left(x^{2} + c\right) - 2 \, {\left({\left(b^{2} d^{m} {\left(m + 1\right)} x^{2} - b^{2} c d^{m} {\left(m + 1\right)}\right)} x^{m} \log\left(x^{2} + c\right) - 2 \, {\left(a b c d^{m} {\left(m + 1\right)} - {\left(a b d^{m} {\left(m + 1\right)} + b^{2} d^{m}\right)} x^{2}\right)} x^{m}\right)} \log\left(x^{2} - c\right)}{4 \, {\left({\left(m + 1\right)} x^{2} - c {\left(m + 1\right)}\right)}}\,{d x}"," ",0,"1/4*b^2*d^m*x*x^m*log(x^2 - c)^2/(m + 1) + (d*x)^(m + 1)*a^2/(d*(m + 1)) - integrate(-1/4*((b^2*d^m*(m + 1)*x^2 - b^2*c*d^m*(m + 1))*x^m*log(x^2 + c)^2 + 4*(a*b*d^m*(m + 1)*x^2 - a*b*c*d^m*(m + 1))*x^m*log(x^2 + c) - 2*((b^2*d^m*(m + 1)*x^2 - b^2*c*d^m*(m + 1))*x^m*log(x^2 + c) - 2*(a*b*c*d^m*(m + 1) - (a*b*d^m*(m + 1) + b^2*d^m)*x^2)*x^m)*log(x^2 - c))/((m + 1)*x^2 - c*(m + 1)), x)","F",0
184,0,0,0,0.000000," ","integrate((d*x)^m*(a+b*arctanh(c/x^2)),x, algorithm=""maxima"")","\frac{1}{2} \, {\left(4 \, c d^{m} \int \frac{x^{2} x^{m}}{{\left(m + 1\right)} x^{4} - c^{2} {\left(m + 1\right)}}\,{d x} + \frac{d^{m} x x^{m} \log\left(x^{2} + c\right) - d^{m} x x^{m} \log\left(x^{2} - c\right)}{m + 1}\right)} b + \frac{\left(d x\right)^{m + 1} a}{d {\left(m + 1\right)}}"," ",0,"1/2*(4*c*d^m*integrate(x^2*x^m/((m + 1)*x^4 - c^2*(m + 1)), x) + (d^m*x*x^m*log(x^2 + c) - d^m*x*x^m*log(x^2 - c))/(m + 1))*b + (d*x)^(m + 1)*a/(d*(m + 1))","F",0
185,0,0,0,0.000000," ","integrate((d*x)^m/(a+b*arctanh(c/x^2)),x, algorithm=""maxima"")","\int \frac{\left(d x\right)^{m}}{b \operatorname{artanh}\left(\frac{c}{x^{2}}\right) + a}\,{d x}"," ",0,"integrate((d*x)^m/(b*arctanh(c/x^2) + a), x)","F",0
186,0,0,0,0.000000," ","integrate((d*x)^m/(a+b*arctanh(c/x^2))^2,x, algorithm=""maxima"")","\frac{{\left(d^{m} x^{4} - c^{2} d^{m}\right)} x^{m}}{b^{2} c x \log\left(x^{2} + c\right) - b^{2} c x \log\left(x^{2} - c\right) + 2 \, a b c x} + \int -\frac{{\left(d^{m} {\left(m + 3\right)} x^{4} - c^{2} d^{m} {\left(m - 1\right)}\right)} x^{m}}{b^{2} c x^{2} \log\left(x^{2} + c\right) - b^{2} c x^{2} \log\left(x^{2} - c\right) + 2 \, a b c x^{2}}\,{d x}"," ",0,"(d^m*x^4 - c^2*d^m)*x^m/(b^2*c*x*log(x^2 + c) - b^2*c*x*log(x^2 - c) + 2*a*b*c*x) + integrate(-(d^m*(m + 3)*x^4 - c^2*d^m*(m - 1))*x^m/(b^2*c*x^2*log(x^2 + c) - b^2*c*x^2*log(x^2 - c) + 2*a*b*c*x^2), x)","F",0
187,1,86,0,0.318230," ","integrate(x^3*(a+b*arctanh(c*x^(1/2))),x, algorithm=""maxima"")","\frac{1}{4} \, a x^{4} + \frac{1}{840} \, {\left(210 \, x^{4} \operatorname{artanh}\left(c \sqrt{x}\right) + c {\left(\frac{2 \, {\left(15 \, c^{6} x^{\frac{7}{2}} + 21 \, c^{4} x^{\frac{5}{2}} + 35 \, c^{2} x^{\frac{3}{2}} + 105 \, \sqrt{x}\right)}}{c^{8}} - \frac{105 \, \log\left(c \sqrt{x} + 1\right)}{c^{9}} + \frac{105 \, \log\left(c \sqrt{x} - 1\right)}{c^{9}}\right)}\right)} b"," ",0,"1/4*a*x^4 + 1/840*(210*x^4*arctanh(c*sqrt(x)) + c*(2*(15*c^6*x^(7/2) + 21*c^4*x^(5/2) + 35*c^2*x^(3/2) + 105*sqrt(x))/c^8 - 105*log(c*sqrt(x) + 1)/c^9 + 105*log(c*sqrt(x) - 1)/c^9))*b","A",0
188,1,78,0,0.318170," ","integrate(x^2*(a+b*arctanh(c*x^(1/2))),x, algorithm=""maxima"")","\frac{1}{3} \, a x^{3} + \frac{1}{90} \, {\left(30 \, x^{3} \operatorname{artanh}\left(c \sqrt{x}\right) + c {\left(\frac{2 \, {\left(3 \, c^{4} x^{\frac{5}{2}} + 5 \, c^{2} x^{\frac{3}{2}} + 15 \, \sqrt{x}\right)}}{c^{6}} - \frac{15 \, \log\left(c \sqrt{x} + 1\right)}{c^{7}} + \frac{15 \, \log\left(c \sqrt{x} - 1\right)}{c^{7}}\right)}\right)} b"," ",0,"1/3*a*x^3 + 1/90*(30*x^3*arctanh(c*sqrt(x)) + c*(2*(3*c^4*x^(5/2) + 5*c^2*x^(3/2) + 15*sqrt(x))/c^6 - 15*log(c*sqrt(x) + 1)/c^7 + 15*log(c*sqrt(x) - 1)/c^7))*b","A",0
189,1,69,0,0.313515," ","integrate(x*(a+b*arctanh(c*x^(1/2))),x, algorithm=""maxima"")","\frac{1}{2} \, a x^{2} + \frac{1}{12} \, {\left(6 \, x^{2} \operatorname{artanh}\left(c \sqrt{x}\right) + c {\left(\frac{2 \, {\left(c^{2} x^{\frac{3}{2}} + 3 \, \sqrt{x}\right)}}{c^{4}} - \frac{3 \, \log\left(c \sqrt{x} + 1\right)}{c^{5}} + \frac{3 \, \log\left(c \sqrt{x} - 1\right)}{c^{5}}\right)}\right)} b"," ",0,"1/2*a*x^2 + 1/12*(6*x^2*arctanh(c*sqrt(x)) + c*(2*(c^2*x^(3/2) + 3*sqrt(x))/c^4 - 3*log(c*sqrt(x) + 1)/c^5 + 3*log(c*sqrt(x) - 1)/c^5))*b","A",0
190,1,53,0,0.316587," ","integrate(a+b*arctanh(c*x^(1/2)),x, algorithm=""maxima"")","\frac{1}{2} \, {\left(c {\left(\frac{2 \, \sqrt{x}}{c^{2}} - \frac{\log\left(c \sqrt{x} + 1\right)}{c^{3}} + \frac{\log\left(c \sqrt{x} - 1\right)}{c^{3}}\right)} + 2 \, x \operatorname{artanh}\left(c \sqrt{x}\right)\right)} b + a x"," ",0,"1/2*(c*(2*sqrt(x)/c^2 - log(c*sqrt(x) + 1)/c^3 + log(c*sqrt(x) - 1)/c^3) + 2*x*arctanh(c*sqrt(x)))*b + a*x","A",0
191,1,61,0,0.463921," ","integrate((a+b*arctanh(c*x^(1/2)))/x,x, algorithm=""maxima"")","-{\left(\log\left(c \sqrt{x}\right) \log\left(-c \sqrt{x} + 1\right) + {\rm Li}_2\left(-c \sqrt{x} + 1\right)\right)} b + {\left(\log\left(c \sqrt{x} + 1\right) \log\left(-c \sqrt{x}\right) + {\rm Li}_2\left(c \sqrt{x} + 1\right)\right)} b + a \log\left(x\right)"," ",0,"-(log(c*sqrt(x))*log(-c*sqrt(x) + 1) + dilog(-c*sqrt(x) + 1))*b + (log(c*sqrt(x) + 1)*log(-c*sqrt(x)) + dilog(c*sqrt(x) + 1))*b + a*log(x)","B",0
192,1,51,0,0.318094," ","integrate((a+b*arctanh(c*x^(1/2)))/x^2,x, algorithm=""maxima"")","\frac{1}{2} \, {\left({\left(c \log\left(c \sqrt{x} + 1\right) - c \log\left(c \sqrt{x} - 1\right) - \frac{2}{\sqrt{x}}\right)} c - \frac{2 \, \operatorname{artanh}\left(c \sqrt{x}\right)}{x}\right)} b - \frac{a}{x}"," ",0,"1/2*((c*log(c*sqrt(x) + 1) - c*log(c*sqrt(x) - 1) - 2/sqrt(x))*c - 2*arctanh(c*sqrt(x))/x)*b - a/x","A",0
193,1,64,0,0.309914," ","integrate((a+b*arctanh(c*x^(1/2)))/x^3,x, algorithm=""maxima"")","\frac{1}{12} \, {\left({\left(3 \, c^{3} \log\left(c \sqrt{x} + 1\right) - 3 \, c^{3} \log\left(c \sqrt{x} - 1\right) - \frac{2 \, {\left(3 \, c^{2} x + 1\right)}}{x^{\frac{3}{2}}}\right)} c - \frac{6 \, \operatorname{artanh}\left(c \sqrt{x}\right)}{x^{2}}\right)} b - \frac{a}{2 \, x^{2}}"," ",0,"1/12*((3*c^3*log(c*sqrt(x) + 1) - 3*c^3*log(c*sqrt(x) - 1) - 2*(3*c^2*x + 1)/x^(3/2))*c - 6*arctanh(c*sqrt(x))/x^2)*b - 1/2*a/x^2","A",0
194,1,72,0,0.315180," ","integrate((a+b*arctanh(c*x^(1/2)))/x^4,x, algorithm=""maxima"")","\frac{1}{90} \, {\left({\left(15 \, c^{5} \log\left(c \sqrt{x} + 1\right) - 15 \, c^{5} \log\left(c \sqrt{x} - 1\right) - \frac{2 \, {\left(15 \, c^{4} x^{2} + 5 \, c^{2} x + 3\right)}}{x^{\frac{5}{2}}}\right)} c - \frac{30 \, \operatorname{artanh}\left(c \sqrt{x}\right)}{x^{3}}\right)} b - \frac{a}{3 \, x^{3}}"," ",0,"1/90*((15*c^5*log(c*sqrt(x) + 1) - 15*c^5*log(c*sqrt(x) - 1) - 2*(15*c^4*x^2 + 5*c^2*x + 3)/x^(5/2))*c - 30*arctanh(c*sqrt(x))/x^3)*b - 1/3*a/x^3","A",0
195,1,265,0,0.335946," ","integrate(x^3*(a+b*arctanh(c*x^(1/2)))^2,x, algorithm=""maxima"")","\frac{1}{4} \, b^{2} x^{4} \operatorname{artanh}\left(c \sqrt{x}\right)^{2} + \frac{1}{4} \, a^{2} x^{4} + \frac{1}{420} \, {\left(210 \, x^{4} \operatorname{artanh}\left(c \sqrt{x}\right) + c {\left(\frac{2 \, {\left(15 \, c^{6} x^{\frac{7}{2}} + 21 \, c^{4} x^{\frac{5}{2}} + 35 \, c^{2} x^{\frac{3}{2}} + 105 \, \sqrt{x}\right)}}{c^{8}} - \frac{105 \, \log\left(c \sqrt{x} + 1\right)}{c^{9}} + \frac{105 \, \log\left(c \sqrt{x} - 1\right)}{c^{9}}\right)}\right)} a b + \frac{1}{1680} \, {\left(4 \, c {\left(\frac{2 \, {\left(15 \, c^{6} x^{\frac{7}{2}} + 21 \, c^{4} x^{\frac{5}{2}} + 35 \, c^{2} x^{\frac{3}{2}} + 105 \, \sqrt{x}\right)}}{c^{8}} - \frac{105 \, \log\left(c \sqrt{x} + 1\right)}{c^{9}} + \frac{105 \, \log\left(c \sqrt{x} - 1\right)}{c^{9}}\right)} \operatorname{artanh}\left(c \sqrt{x}\right) + \frac{20 \, c^{6} x^{3} + 72 \, c^{4} x^{2} + 284 \, c^{2} x - 2 \, {\left(105 \, \log\left(c \sqrt{x} - 1\right) - 352\right)} \log\left(c \sqrt{x} + 1\right) + 105 \, \log\left(c \sqrt{x} + 1\right)^{2} + 105 \, \log\left(c \sqrt{x} - 1\right)^{2} + 704 \, \log\left(c \sqrt{x} - 1\right)}{c^{8}}\right)} b^{2}"," ",0,"1/4*b^2*x^4*arctanh(c*sqrt(x))^2 + 1/4*a^2*x^4 + 1/420*(210*x^4*arctanh(c*sqrt(x)) + c*(2*(15*c^6*x^(7/2) + 21*c^4*x^(5/2) + 35*c^2*x^(3/2) + 105*sqrt(x))/c^8 - 105*log(c*sqrt(x) + 1)/c^9 + 105*log(c*sqrt(x) - 1)/c^9))*a*b + 1/1680*(4*c*(2*(15*c^6*x^(7/2) + 21*c^4*x^(5/2) + 35*c^2*x^(3/2) + 105*sqrt(x))/c^8 - 105*log(c*sqrt(x) + 1)/c^9 + 105*log(c*sqrt(x) - 1)/c^9)*arctanh(c*sqrt(x)) + (20*c^6*x^3 + 72*c^4*x^2 + 284*c^2*x - 2*(105*log(c*sqrt(x) - 1) - 352)*log(c*sqrt(x) + 1) + 105*log(c*sqrt(x) + 1)^2 + 105*log(c*sqrt(x) - 1)^2 + 704*log(c*sqrt(x) - 1))/c^8)*b^2","A",0
196,1,241,0,0.335640," ","integrate(x^2*(a+b*arctanh(c*x^(1/2)))^2,x, algorithm=""maxima"")","\frac{1}{3} \, b^{2} x^{3} \operatorname{artanh}\left(c \sqrt{x}\right)^{2} + \frac{1}{3} \, a^{2} x^{3} + \frac{1}{45} \, {\left(30 \, x^{3} \operatorname{artanh}\left(c \sqrt{x}\right) + c {\left(\frac{2 \, {\left(3 \, c^{4} x^{\frac{5}{2}} + 5 \, c^{2} x^{\frac{3}{2}} + 15 \, \sqrt{x}\right)}}{c^{6}} - \frac{15 \, \log\left(c \sqrt{x} + 1\right)}{c^{7}} + \frac{15 \, \log\left(c \sqrt{x} - 1\right)}{c^{7}}\right)}\right)} a b + \frac{1}{180} \, {\left(4 \, c {\left(\frac{2 \, {\left(3 \, c^{4} x^{\frac{5}{2}} + 5 \, c^{2} x^{\frac{3}{2}} + 15 \, \sqrt{x}\right)}}{c^{6}} - \frac{15 \, \log\left(c \sqrt{x} + 1\right)}{c^{7}} + \frac{15 \, \log\left(c \sqrt{x} - 1\right)}{c^{7}}\right)} \operatorname{artanh}\left(c \sqrt{x}\right) + \frac{6 \, c^{4} x^{2} + 32 \, c^{2} x - 2 \, {\left(15 \, \log\left(c \sqrt{x} - 1\right) - 46\right)} \log\left(c \sqrt{x} + 1\right) + 15 \, \log\left(c \sqrt{x} + 1\right)^{2} + 15 \, \log\left(c \sqrt{x} - 1\right)^{2} + 92 \, \log\left(c \sqrt{x} - 1\right)}{c^{6}}\right)} b^{2}"," ",0,"1/3*b^2*x^3*arctanh(c*sqrt(x))^2 + 1/3*a^2*x^3 + 1/45*(30*x^3*arctanh(c*sqrt(x)) + c*(2*(3*c^4*x^(5/2) + 5*c^2*x^(3/2) + 15*sqrt(x))/c^6 - 15*log(c*sqrt(x) + 1)/c^7 + 15*log(c*sqrt(x) - 1)/c^7))*a*b + 1/180*(4*c*(2*(3*c^4*x^(5/2) + 5*c^2*x^(3/2) + 15*sqrt(x))/c^6 - 15*log(c*sqrt(x) + 1)/c^7 + 15*log(c*sqrt(x) - 1)/c^7)*arctanh(c*sqrt(x)) + (6*c^4*x^2 + 32*c^2*x - 2*(15*log(c*sqrt(x) - 1) - 46)*log(c*sqrt(x) + 1) + 15*log(c*sqrt(x) + 1)^2 + 15*log(c*sqrt(x) - 1)^2 + 92*log(c*sqrt(x) - 1))/c^6)*b^2","A",0
197,1,215,0,0.329563," ","integrate(x*(a+b*arctanh(c*x^(1/2)))^2,x, algorithm=""maxima"")","\frac{1}{2} \, b^{2} x^{2} \operatorname{artanh}\left(c \sqrt{x}\right)^{2} + \frac{1}{2} \, a^{2} x^{2} + \frac{1}{6} \, {\left(6 \, x^{2} \operatorname{artanh}\left(c \sqrt{x}\right) + c {\left(\frac{2 \, {\left(c^{2} x^{\frac{3}{2}} + 3 \, \sqrt{x}\right)}}{c^{4}} - \frac{3 \, \log\left(c \sqrt{x} + 1\right)}{c^{5}} + \frac{3 \, \log\left(c \sqrt{x} - 1\right)}{c^{5}}\right)}\right)} a b + \frac{1}{24} \, {\left(4 \, c {\left(\frac{2 \, {\left(c^{2} x^{\frac{3}{2}} + 3 \, \sqrt{x}\right)}}{c^{4}} - \frac{3 \, \log\left(c \sqrt{x} + 1\right)}{c^{5}} + \frac{3 \, \log\left(c \sqrt{x} - 1\right)}{c^{5}}\right)} \operatorname{artanh}\left(c \sqrt{x}\right) + \frac{4 \, c^{2} x - 2 \, {\left(3 \, \log\left(c \sqrt{x} - 1\right) - 8\right)} \log\left(c \sqrt{x} + 1\right) + 3 \, \log\left(c \sqrt{x} + 1\right)^{2} + 3 \, \log\left(c \sqrt{x} - 1\right)^{2} + 16 \, \log\left(c \sqrt{x} - 1\right)}{c^{4}}\right)} b^{2}"," ",0,"1/2*b^2*x^2*arctanh(c*sqrt(x))^2 + 1/2*a^2*x^2 + 1/6*(6*x^2*arctanh(c*sqrt(x)) + c*(2*(c^2*x^(3/2) + 3*sqrt(x))/c^4 - 3*log(c*sqrt(x) + 1)/c^5 + 3*log(c*sqrt(x) - 1)/c^5))*a*b + 1/24*(4*c*(2*(c^2*x^(3/2) + 3*sqrt(x))/c^4 - 3*log(c*sqrt(x) + 1)/c^5 + 3*log(c*sqrt(x) - 1)/c^5)*arctanh(c*sqrt(x)) + (4*c^2*x - 2*(3*log(c*sqrt(x) - 1) - 8)*log(c*sqrt(x) + 1) + 3*log(c*sqrt(x) + 1)^2 + 3*log(c*sqrt(x) - 1)^2 + 16*log(c*sqrt(x) - 1))/c^4)*b^2","B",0
198,1,175,0,0.339055," ","integrate((a+b*arctanh(c*x^(1/2)))^2,x, algorithm=""maxima"")","{\left(c {\left(\frac{2 \, \sqrt{x}}{c^{2}} - \frac{\log\left(c \sqrt{x} + 1\right)}{c^{3}} + \frac{\log\left(c \sqrt{x} - 1\right)}{c^{3}}\right)} + 2 \, x \operatorname{artanh}\left(c \sqrt{x}\right)\right)} a b + \frac{1}{4} \, {\left(4 \, c {\left(\frac{2 \, \sqrt{x}}{c^{2}} - \frac{\log\left(c \sqrt{x} + 1\right)}{c^{3}} + \frac{\log\left(c \sqrt{x} - 1\right)}{c^{3}}\right)} \operatorname{artanh}\left(c \sqrt{x}\right) + 4 \, x \operatorname{artanh}\left(c \sqrt{x}\right)^{2} - \frac{2 \, {\left(\log\left(c \sqrt{x} - 1\right) - 2\right)} \log\left(c \sqrt{x} + 1\right) - \log\left(c \sqrt{x} + 1\right)^{2} - \log\left(c \sqrt{x} - 1\right)^{2} - 4 \, \log\left(c \sqrt{x} - 1\right)}{c^{2}}\right)} b^{2} + a^{2} x"," ",0,"(c*(2*sqrt(x)/c^2 - log(c*sqrt(x) + 1)/c^3 + log(c*sqrt(x) - 1)/c^3) + 2*x*arctanh(c*sqrt(x)))*a*b + 1/4*(4*c*(2*sqrt(x)/c^2 - log(c*sqrt(x) + 1)/c^3 + log(c*sqrt(x) - 1)/c^3)*arctanh(c*sqrt(x)) + 4*x*arctanh(c*sqrt(x))^2 - (2*(log(c*sqrt(x) - 1) - 2)*log(c*sqrt(x) + 1) - log(c*sqrt(x) + 1)^2 - log(c*sqrt(x) - 1)^2 - 4*log(c*sqrt(x) - 1))/c^2)*b^2 + a^2*x","B",0
199,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x^(1/2)))^2/x,x, algorithm=""maxima"")","\frac{1}{4} \, b^{2} \int \frac{\log\left(c \sqrt{x} + 1\right)^{2}}{x}\,{d x} - \frac{1}{2} \, b^{2} \int \frac{\log\left(c \sqrt{x} + 1\right) \log\left(-c \sqrt{x} + 1\right)}{x}\,{d x} + \frac{1}{4} \, b^{2} \int \frac{\log\left(-c \sqrt{x} + 1\right)^{2}}{x}\,{d x} + a b \int \frac{\log\left(c \sqrt{x} + 1\right)}{x}\,{d x} - a b \int \frac{\log\left(-c \sqrt{x} + 1\right)}{x}\,{d x} + a^{2} \log\left(x\right)"," ",0,"1/4*b^2*integrate(log(c*sqrt(x) + 1)^2/x, x) - 1/2*b^2*integrate(log(c*sqrt(x) + 1)*log(-c*sqrt(x) + 1)/x, x) + 1/4*b^2*integrate(log(-c*sqrt(x) + 1)^2/x, x) + a*b*integrate(log(c*sqrt(x) + 1)/x, x) - a*b*integrate(log(-c*sqrt(x) + 1)/x, x) + a^2*log(x)","F",0
200,1,174,0,0.334866," ","integrate((a+b*arctanh(c*x^(1/2)))^2/x^2,x, algorithm=""maxima"")","{\left({\left(c \log\left(c \sqrt{x} + 1\right) - c \log\left(c \sqrt{x} - 1\right) - \frac{2}{\sqrt{x}}\right)} c - \frac{2 \, \operatorname{artanh}\left(c \sqrt{x}\right)}{x}\right)} a b + \frac{1}{4} \, {\left({\left(2 \, {\left(\log\left(c \sqrt{x} - 1\right) - 2\right)} \log\left(c \sqrt{x} + 1\right) - \log\left(c \sqrt{x} + 1\right)^{2} - \log\left(c \sqrt{x} - 1\right)^{2} - 4 \, \log\left(c \sqrt{x} - 1\right) + 4 \, \log\left(x\right)\right)} c^{2} + 4 \, {\left(c \log\left(c \sqrt{x} + 1\right) - c \log\left(c \sqrt{x} - 1\right) - \frac{2}{\sqrt{x}}\right)} c \operatorname{artanh}\left(c \sqrt{x}\right)\right)} b^{2} - \frac{b^{2} \operatorname{artanh}\left(c \sqrt{x}\right)^{2}}{x} - \frac{a^{2}}{x}"," ",0,"((c*log(c*sqrt(x) + 1) - c*log(c*sqrt(x) - 1) - 2/sqrt(x))*c - 2*arctanh(c*sqrt(x))/x)*a*b + 1/4*((2*(log(c*sqrt(x) - 1) - 2)*log(c*sqrt(x) + 1) - log(c*sqrt(x) + 1)^2 - log(c*sqrt(x) - 1)^2 - 4*log(c*sqrt(x) - 1) + 4*log(x))*c^2 + 4*(c*log(c*sqrt(x) + 1) - c*log(c*sqrt(x) - 1) - 2/sqrt(x))*c*arctanh(c*sqrt(x)))*b^2 - b^2*arctanh(c*sqrt(x))^2/x - a^2/x","B",0
201,1,234,0,0.334603," ","integrate((a+b*arctanh(c*x^(1/2)))^2/x^3,x, algorithm=""maxima"")","\frac{1}{6} \, {\left({\left(3 \, c^{3} \log\left(c \sqrt{x} + 1\right) - 3 \, c^{3} \log\left(c \sqrt{x} - 1\right) - \frac{2 \, {\left(3 \, c^{2} x + 1\right)}}{x^{\frac{3}{2}}}\right)} c - \frac{6 \, \operatorname{artanh}\left(c \sqrt{x}\right)}{x^{2}}\right)} a b + \frac{1}{24} \, {\left({\left(16 \, c^{2} \log\left(x\right) - \frac{3 \, c^{2} x \log\left(c \sqrt{x} + 1\right)^{2} + 3 \, c^{2} x \log\left(c \sqrt{x} - 1\right)^{2} + 16 \, c^{2} x \log\left(c \sqrt{x} - 1\right) - 2 \, {\left(3 \, c^{2} x \log\left(c \sqrt{x} - 1\right) - 8 \, c^{2} x\right)} \log\left(c \sqrt{x} + 1\right) + 4}{x}\right)} c^{2} + 4 \, {\left(3 \, c^{3} \log\left(c \sqrt{x} + 1\right) - 3 \, c^{3} \log\left(c \sqrt{x} - 1\right) - \frac{2 \, {\left(3 \, c^{2} x + 1\right)}}{x^{\frac{3}{2}}}\right)} c \operatorname{artanh}\left(c \sqrt{x}\right)\right)} b^{2} - \frac{b^{2} \operatorname{artanh}\left(c \sqrt{x}\right)^{2}}{2 \, x^{2}} - \frac{a^{2}}{2 \, x^{2}}"," ",0,"1/6*((3*c^3*log(c*sqrt(x) + 1) - 3*c^3*log(c*sqrt(x) - 1) - 2*(3*c^2*x + 1)/x^(3/2))*c - 6*arctanh(c*sqrt(x))/x^2)*a*b + 1/24*((16*c^2*log(x) - (3*c^2*x*log(c*sqrt(x) + 1)^2 + 3*c^2*x*log(c*sqrt(x) - 1)^2 + 16*c^2*x*log(c*sqrt(x) - 1) - 2*(3*c^2*x*log(c*sqrt(x) - 1) - 8*c^2*x)*log(c*sqrt(x) + 1) + 4)/x)*c^2 + 4*(3*c^3*log(c*sqrt(x) + 1) - 3*c^3*log(c*sqrt(x) - 1) - 2*(3*c^2*x + 1)/x^(3/2))*c*arctanh(c*sqrt(x)))*b^2 - 1/2*b^2*arctanh(c*sqrt(x))^2/x^2 - 1/2*a^2/x^2","B",0
202,1,1972,0,1.280858," ","integrate(x^3*(a+b*arctanh(c*x^(1/2)))^3,x, algorithm=""maxima"")","\frac{1}{4} \, a^{3} x^{4} - \frac{1}{26880} \, a b^{2} c {\left(\frac{315 \, c^{7} x^{4} + 500 \, c^{5} x^{3} + 1002 \, c^{3} x^{2} + 3684 \, c x - 12 \, {\left(105 \, c^{7} x^{4} + 120 \, c^{6} x^{\frac{7}{2}} + 140 \, c^{5} x^{3} + 168 \, c^{4} x^{\frac{5}{2}} + 210 \, c^{3} x^{2} + 280 \, c^{2} x^{\frac{3}{2}} + 420 \, c x + 840 \, \sqrt{x}\right)} \log\left(c \sqrt{x} + 1\right)}{c^{8}} - \frac{6396 \, \log\left(c \sqrt{x} + 1\right)}{c^{9}} - \frac{6396 \, \log\left(c \sqrt{x} - 1\right)}{c^{9}}\right)} - \frac{1}{2240} \, {\left(840 \, x^{4} \log\left(c \sqrt{x} + 1\right) - c {\left(\frac{105 \, c^{7} x^{4} - 120 \, c^{6} x^{\frac{7}{2}} + 140 \, c^{5} x^{3} - 168 \, c^{4} x^{\frac{5}{2}} + 210 \, c^{3} x^{2} - 280 \, c^{2} x^{\frac{3}{2}} + 420 \, c x - 840 \, \sqrt{x}}{c^{8}} + \frac{840 \, \log\left(c \sqrt{x} + 1\right)}{c^{9}}\right)}\right)} a b^{2} \log\left(-c \sqrt{x} + 1\right) + \frac{1}{2240} \, {\left(840 \, x^{4} \log\left(c \sqrt{x} + 1\right) - c {\left(\frac{105 \, c^{7} x^{4} - 120 \, c^{6} x^{\frac{7}{2}} + 140 \, c^{5} x^{3} - 168 \, c^{4} x^{\frac{5}{2}} + 210 \, c^{3} x^{2} - 280 \, c^{2} x^{\frac{3}{2}} + 420 \, c x - 840 \, \sqrt{x}}{c^{8}} + \frac{840 \, \log\left(c \sqrt{x} + 1\right)}{c^{9}}\right)}\right)} a^{2} b - \frac{1}{2240} \, {\left(840 \, x^{4} \log\left(-c \sqrt{x} + 1\right) - c {\left(\frac{105 \, c^{7} x^{4} + 120 \, c^{6} x^{\frac{7}{2}} + 140 \, c^{5} x^{3} + 168 \, c^{4} x^{\frac{5}{2}} + 210 \, c^{3} x^{2} + 280 \, c^{2} x^{\frac{3}{2}} + 420 \, c x + 840 \, \sqrt{x}}{c^{8}} + \frac{840 \, \log\left(c \sqrt{x} - 1\right)}{c^{9}}\right)}\right)} a^{2} b + \frac{{\left(11025 \, {\left(32 \, \log\left(-c \sqrt{x} + 1\right)^{2} - 8 \, \log\left(-c \sqrt{x} + 1\right) + 1\right)} {\left(c \sqrt{x} - 1\right)}^{8} + 57600 \, {\left(49 \, \log\left(-c \sqrt{x} + 1\right)^{2} - 14 \, \log\left(-c \sqrt{x} + 1\right) + 2\right)} {\left(c \sqrt{x} - 1\right)}^{7} + 548800 \, {\left(18 \, \log\left(-c \sqrt{x} + 1\right)^{2} - 6 \, \log\left(-c \sqrt{x} + 1\right) + 1\right)} {\left(c \sqrt{x} - 1\right)}^{6} + 790272 \, {\left(25 \, \log\left(-c \sqrt{x} + 1\right)^{2} - 10 \, \log\left(-c \sqrt{x} + 1\right) + 2\right)} {\left(c \sqrt{x} - 1\right)}^{5} + 3087000 \, {\left(8 \, \log\left(-c \sqrt{x} + 1\right)^{2} - 4 \, \log\left(-c \sqrt{x} + 1\right) + 1\right)} {\left(c \sqrt{x} - 1\right)}^{4} + 2195200 \, {\left(9 \, \log\left(-c \sqrt{x} + 1\right)^{2} - 6 \, \log\left(-c \sqrt{x} + 1\right) + 2\right)} {\left(c \sqrt{x} - 1\right)}^{3} + 4939200 \, {\left(2 \, \log\left(-c \sqrt{x} + 1\right)^{2} - 2 \, \log\left(-c \sqrt{x} + 1\right) + 1\right)} {\left(c \sqrt{x} - 1\right)}^{2} + 2822400 \, {\left(\log\left(-c \sqrt{x} + 1\right)^{2} - 2 \, \log\left(-c \sqrt{x} + 1\right) + 2\right)} {\left(c \sqrt{x} - 1\right)}\right)} a b^{2}}{1881600 \, c^{8}} - \frac{{\left(385875 \, {\left(256 \, \log\left(-c \sqrt{x} + 1\right)^{3} - 96 \, \log\left(-c \sqrt{x} + 1\right)^{2} + 24 \, \log\left(-c \sqrt{x} + 1\right) - 3\right)} {\left(c \sqrt{x} - 1\right)}^{8} + 2304000 \, {\left(343 \, \log\left(-c \sqrt{x} + 1\right)^{3} - 147 \, \log\left(-c \sqrt{x} + 1\right)^{2} + 42 \, \log\left(-c \sqrt{x} + 1\right) - 6\right)} {\left(c \sqrt{x} - 1\right)}^{7} + 76832000 \, {\left(36 \, \log\left(-c \sqrt{x} + 1\right)^{3} - 18 \, \log\left(-c \sqrt{x} + 1\right)^{2} + 6 \, \log\left(-c \sqrt{x} + 1\right) - 1\right)} {\left(c \sqrt{x} - 1\right)}^{6} + 44255232 \, {\left(125 \, \log\left(-c \sqrt{x} + 1\right)^{3} - 75 \, \log\left(-c \sqrt{x} + 1\right)^{2} + 30 \, \log\left(-c \sqrt{x} + 1\right) - 6\right)} {\left(c \sqrt{x} - 1\right)}^{5} + 216090000 \, {\left(32 \, \log\left(-c \sqrt{x} + 1\right)^{3} - 24 \, \log\left(-c \sqrt{x} + 1\right)^{2} + 12 \, \log\left(-c \sqrt{x} + 1\right) - 3\right)} {\left(c \sqrt{x} - 1\right)}^{4} + 614656000 \, {\left(9 \, \log\left(-c \sqrt{x} + 1\right)^{3} - 9 \, \log\left(-c \sqrt{x} + 1\right)^{2} + 6 \, \log\left(-c \sqrt{x} + 1\right) - 2\right)} {\left(c \sqrt{x} - 1\right)}^{3} + 691488000 \, {\left(4 \, \log\left(-c \sqrt{x} + 1\right)^{3} - 6 \, \log\left(-c \sqrt{x} + 1\right)^{2} + 6 \, \log\left(-c \sqrt{x} + 1\right) - 3\right)} {\left(c \sqrt{x} - 1\right)}^{2} + 790272000 \, {\left(\log\left(-c \sqrt{x} + 1\right)^{3} - 3 \, \log\left(-c \sqrt{x} + 1\right)^{2} + 6 \, \log\left(-c \sqrt{x} + 1\right) - 6\right)} {\left(c \sqrt{x} - 1\right)}\right)} b^{3}}{3161088000 \, c^{8}} + \frac{44 \, {\left(\log\left(c \sqrt{x} + 1\right) \log\left(-\frac{1}{2} \, c \sqrt{x} + \frac{1}{2}\right) + {\rm Li}_2\left(\frac{1}{2} \, c \sqrt{x} + \frac{1}{2}\right)\right)} b^{3}}{35 \, c^{8}} - \frac{1881559 \, b^{3} \log\left(c \sqrt{x} - 1\right)}{3763200 \, c^{8}} + \frac{{\left(2283 \, a b^{2} - 752 \, b^{3}\right)} \log\left(c \sqrt{x} + 1\right)}{2240 \, c^{8}} + \frac{1157625 \, {\left(16 \, a b^{2} c^{8} - b^{3} c^{8}\right)} x^{4} - 27000 \, {\left(1680 \, a b^{2} c^{7} + 169 \, b^{3} c^{7}\right)} x^{\frac{7}{2}} + 3500 \, {\left(24528 \, a b^{2} c^{6} - 3565 \, b^{3} c^{6}\right)} x^{3} + 98784000 \, {\left(b^{3} c^{8} x^{4} - b^{3}\right)} \log\left(c \sqrt{x} + 1\right)^{3} - 168 \, {\left(895440 \, a b^{2} c^{5} + 44269 \, b^{3} c^{5}\right)} x^{\frac{5}{2}} + 210 \, {\left(1248240 \, a b^{2} c^{4} - 334699 \, b^{3} c^{4}\right)} x^{2} + 5644800 \, {\left(105 \, a b^{2} c^{8} x^{4} + 15 \, b^{3} c^{7} x^{\frac{7}{2}} + 21 \, b^{3} c^{5} x^{\frac{5}{2}} + 35 \, b^{3} c^{3} x^{\frac{3}{2}} + 105 \, b^{3} c \sqrt{x} - 105 \, a b^{2} + 176 \, b^{3}\right)} \log\left(c \sqrt{x} + 1\right)^{2} - 352800 \, {\left(105 \, b^{3} c^{8} x^{4} - 120 \, b^{3} c^{7} x^{\frac{7}{2}} + 140 \, b^{3} c^{6} x^{3} - 168 \, b^{3} c^{5} x^{\frac{5}{2}} + 210 \, b^{3} c^{4} x^{2} - 280 \, b^{3} c^{3} x^{\frac{3}{2}} + 420 \, b^{3} c^{2} x - 840 \, b^{3} c \sqrt{x} + 533 \, b^{3} - 840 \, {\left(b^{3} c^{8} x^{4} - b^{3}\right)} \log\left(c \sqrt{x} + 1\right)\right)} \log\left(-c \sqrt{x} + 1\right)^{2} - 280 \, {\left(1718640 \, a b^{2} c^{3} + 2899 \, b^{3} c^{3}\right)} x^{\frac{3}{2}} + 420 \, {\left(2424240 \, a b^{2} c^{2} - 1227199 \, b^{3} c^{2}\right)} x - 1411200 \, {\left(105 \, a b^{2} c^{8} x^{4} - 120 \, a b^{2} c^{7} x^{\frac{7}{2}} - 168 \, a b^{2} c^{5} x^{\frac{5}{2}} - 280 \, a b^{2} c^{3} x^{\frac{3}{2}} - 840 \, a b^{2} c \sqrt{x} + 20 \, {\left(7 \, a b^{2} c^{6} - 2 \, b^{3} c^{6}\right)} x^{3} + 6 \, {\left(35 \, a b^{2} c^{4} - 24 \, b^{3} c^{4}\right)} x^{2} + 4 \, {\left(105 \, a b^{2} c^{2} - 142 \, b^{3} c^{2}\right)} x\right)} \log\left(c \sqrt{x} + 1\right) + 840 \, {\left(11025 \, b^{3} c^{8} x^{4} + 27000 \, b^{3} c^{7} x^{\frac{7}{2}} - 16100 \, b^{3} c^{6} x^{3} + 89544 \, b^{3} c^{5} x^{\frac{5}{2}} - 85890 \, b^{3} c^{4} x^{2} + 286440 \, b^{3} c^{3} x^{\frac{3}{2}} - 348180 \, b^{3} c^{2} x + 1917720 \, b^{3} c \sqrt{x} - 352800 \, {\left(b^{3} c^{8} x^{4} - b^{3}\right)} \log\left(c \sqrt{x} + 1\right)^{2} - 13440 \, {\left(15 \, b^{3} c^{7} x^{\frac{7}{2}} + 21 \, b^{3} c^{5} x^{\frac{5}{2}} + 35 \, b^{3} c^{3} x^{\frac{3}{2}} + 105 \, b^{3} c \sqrt{x} + 176 \, b^{3}\right)} \log\left(c \sqrt{x} + 1\right)\right)} \log\left(-c \sqrt{x} + 1\right) - 840 \, {\left(3835440 \, a b^{2} c + 618199 \, b^{3} c\right)} \sqrt{x}}{3161088000 \, c^{8}}"," ",0,"1/4*a^3*x^4 - 1/26880*a*b^2*c*((315*c^7*x^4 + 500*c^5*x^3 + 1002*c^3*x^2 + 3684*c*x - 12*(105*c^7*x^4 + 120*c^6*x^(7/2) + 140*c^5*x^3 + 168*c^4*x^(5/2) + 210*c^3*x^2 + 280*c^2*x^(3/2) + 420*c*x + 840*sqrt(x))*log(c*sqrt(x) + 1))/c^8 - 6396*log(c*sqrt(x) + 1)/c^9 - 6396*log(c*sqrt(x) - 1)/c^9) - 1/2240*(840*x^4*log(c*sqrt(x) + 1) - c*((105*c^7*x^4 - 120*c^6*x^(7/2) + 140*c^5*x^3 - 168*c^4*x^(5/2) + 210*c^3*x^2 - 280*c^2*x^(3/2) + 420*c*x - 840*sqrt(x))/c^8 + 840*log(c*sqrt(x) + 1)/c^9))*a*b^2*log(-c*sqrt(x) + 1) + 1/2240*(840*x^4*log(c*sqrt(x) + 1) - c*((105*c^7*x^4 - 120*c^6*x^(7/2) + 140*c^5*x^3 - 168*c^4*x^(5/2) + 210*c^3*x^2 - 280*c^2*x^(3/2) + 420*c*x - 840*sqrt(x))/c^8 + 840*log(c*sqrt(x) + 1)/c^9))*a^2*b - 1/2240*(840*x^4*log(-c*sqrt(x) + 1) - c*((105*c^7*x^4 + 120*c^6*x^(7/2) + 140*c^5*x^3 + 168*c^4*x^(5/2) + 210*c^3*x^2 + 280*c^2*x^(3/2) + 420*c*x + 840*sqrt(x))/c^8 + 840*log(c*sqrt(x) - 1)/c^9))*a^2*b + 1/1881600*(11025*(32*log(-c*sqrt(x) + 1)^2 - 8*log(-c*sqrt(x) + 1) + 1)*(c*sqrt(x) - 1)^8 + 57600*(49*log(-c*sqrt(x) + 1)^2 - 14*log(-c*sqrt(x) + 1) + 2)*(c*sqrt(x) - 1)^7 + 548800*(18*log(-c*sqrt(x) + 1)^2 - 6*log(-c*sqrt(x) + 1) + 1)*(c*sqrt(x) - 1)^6 + 790272*(25*log(-c*sqrt(x) + 1)^2 - 10*log(-c*sqrt(x) + 1) + 2)*(c*sqrt(x) - 1)^5 + 3087000*(8*log(-c*sqrt(x) + 1)^2 - 4*log(-c*sqrt(x) + 1) + 1)*(c*sqrt(x) - 1)^4 + 2195200*(9*log(-c*sqrt(x) + 1)^2 - 6*log(-c*sqrt(x) + 1) + 2)*(c*sqrt(x) - 1)^3 + 4939200*(2*log(-c*sqrt(x) + 1)^2 - 2*log(-c*sqrt(x) + 1) + 1)*(c*sqrt(x) - 1)^2 + 2822400*(log(-c*sqrt(x) + 1)^2 - 2*log(-c*sqrt(x) + 1) + 2)*(c*sqrt(x) - 1))*a*b^2/c^8 - 1/3161088000*(385875*(256*log(-c*sqrt(x) + 1)^3 - 96*log(-c*sqrt(x) + 1)^2 + 24*log(-c*sqrt(x) + 1) - 3)*(c*sqrt(x) - 1)^8 + 2304000*(343*log(-c*sqrt(x) + 1)^3 - 147*log(-c*sqrt(x) + 1)^2 + 42*log(-c*sqrt(x) + 1) - 6)*(c*sqrt(x) - 1)^7 + 76832000*(36*log(-c*sqrt(x) + 1)^3 - 18*log(-c*sqrt(x) + 1)^2 + 6*log(-c*sqrt(x) + 1) - 1)*(c*sqrt(x) - 1)^6 + 44255232*(125*log(-c*sqrt(x) + 1)^3 - 75*log(-c*sqrt(x) + 1)^2 + 30*log(-c*sqrt(x) + 1) - 6)*(c*sqrt(x) - 1)^5 + 216090000*(32*log(-c*sqrt(x) + 1)^3 - 24*log(-c*sqrt(x) + 1)^2 + 12*log(-c*sqrt(x) + 1) - 3)*(c*sqrt(x) - 1)^4 + 614656000*(9*log(-c*sqrt(x) + 1)^3 - 9*log(-c*sqrt(x) + 1)^2 + 6*log(-c*sqrt(x) + 1) - 2)*(c*sqrt(x) - 1)^3 + 691488000*(4*log(-c*sqrt(x) + 1)^3 - 6*log(-c*sqrt(x) + 1)^2 + 6*log(-c*sqrt(x) + 1) - 3)*(c*sqrt(x) - 1)^2 + 790272000*(log(-c*sqrt(x) + 1)^3 - 3*log(-c*sqrt(x) + 1)^2 + 6*log(-c*sqrt(x) + 1) - 6)*(c*sqrt(x) - 1))*b^3/c^8 + 44/35*(log(c*sqrt(x) + 1)*log(-1/2*c*sqrt(x) + 1/2) + dilog(1/2*c*sqrt(x) + 1/2))*b^3/c^8 - 1881559/3763200*b^3*log(c*sqrt(x) - 1)/c^8 + 1/2240*(2283*a*b^2 - 752*b^3)*log(c*sqrt(x) + 1)/c^8 + 1/3161088000*(1157625*(16*a*b^2*c^8 - b^3*c^8)*x^4 - 27000*(1680*a*b^2*c^7 + 169*b^3*c^7)*x^(7/2) + 3500*(24528*a*b^2*c^6 - 3565*b^3*c^6)*x^3 + 98784000*(b^3*c^8*x^4 - b^3)*log(c*sqrt(x) + 1)^3 - 168*(895440*a*b^2*c^5 + 44269*b^3*c^5)*x^(5/2) + 210*(1248240*a*b^2*c^4 - 334699*b^3*c^4)*x^2 + 5644800*(105*a*b^2*c^8*x^4 + 15*b^3*c^7*x^(7/2) + 21*b^3*c^5*x^(5/2) + 35*b^3*c^3*x^(3/2) + 105*b^3*c*sqrt(x) - 105*a*b^2 + 176*b^3)*log(c*sqrt(x) + 1)^2 - 352800*(105*b^3*c^8*x^4 - 120*b^3*c^7*x^(7/2) + 140*b^3*c^6*x^3 - 168*b^3*c^5*x^(5/2) + 210*b^3*c^4*x^2 - 280*b^3*c^3*x^(3/2) + 420*b^3*c^2*x - 840*b^3*c*sqrt(x) + 533*b^3 - 840*(b^3*c^8*x^4 - b^3)*log(c*sqrt(x) + 1))*log(-c*sqrt(x) + 1)^2 - 280*(1718640*a*b^2*c^3 + 2899*b^3*c^3)*x^(3/2) + 420*(2424240*a*b^2*c^2 - 1227199*b^3*c^2)*x - 1411200*(105*a*b^2*c^8*x^4 - 120*a*b^2*c^7*x^(7/2) - 168*a*b^2*c^5*x^(5/2) - 280*a*b^2*c^3*x^(3/2) - 840*a*b^2*c*sqrt(x) + 20*(7*a*b^2*c^6 - 2*b^3*c^6)*x^3 + 6*(35*a*b^2*c^4 - 24*b^3*c^4)*x^2 + 4*(105*a*b^2*c^2 - 142*b^3*c^2)*x)*log(c*sqrt(x) + 1) + 840*(11025*b^3*c^8*x^4 + 27000*b^3*c^7*x^(7/2) - 16100*b^3*c^6*x^3 + 89544*b^3*c^5*x^(5/2) - 85890*b^3*c^4*x^2 + 286440*b^3*c^3*x^(3/2) - 348180*b^3*c^2*x + 1917720*b^3*c*sqrt(x) - 352800*(b^3*c^8*x^4 - b^3)*log(c*sqrt(x) + 1)^2 - 13440*(15*b^3*c^7*x^(7/2) + 21*b^3*c^5*x^(5/2) + 35*b^3*c^3*x^(3/2) + 105*b^3*c*sqrt(x) + 176*b^3)*log(c*sqrt(x) + 1))*log(-c*sqrt(x) + 1) - 840*(3835440*a*b^2*c + 618199*b^3*c)*sqrt(x))/c^8","B",0
203,1,1579,0,1.143200," ","integrate(x^2*(a+b*arctanh(c*x^(1/2)))^3,x, algorithm=""maxima"")","\frac{1}{3} \, a^{3} x^{3} - \frac{1}{720} \, a b^{2} c {\left(\frac{20 \, c^{5} x^{3} + 39 \, c^{3} x^{2} + 138 \, c x - 6 \, {\left(10 \, c^{5} x^{3} + 12 \, c^{4} x^{\frac{5}{2}} + 15 \, c^{3} x^{2} + 20 \, c^{2} x^{\frac{3}{2}} + 30 \, c x + 60 \, \sqrt{x}\right)} \log\left(c \sqrt{x} + 1\right)}{c^{6}} - \frac{222 \, \log\left(c \sqrt{x} + 1\right)}{c^{7}} - \frac{222 \, \log\left(c \sqrt{x} - 1\right)}{c^{7}}\right)} - \frac{1}{120} \, {\left(60 \, x^{3} \log\left(c \sqrt{x} + 1\right) - c {\left(\frac{10 \, c^{5} x^{3} - 12 \, c^{4} x^{\frac{5}{2}} + 15 \, c^{3} x^{2} - 20 \, c^{2} x^{\frac{3}{2}} + 30 \, c x - 60 \, \sqrt{x}}{c^{6}} + \frac{60 \, \log\left(c \sqrt{x} + 1\right)}{c^{7}}\right)}\right)} a b^{2} \log\left(-c \sqrt{x} + 1\right) + \frac{1}{120} \, {\left(60 \, x^{3} \log\left(c \sqrt{x} + 1\right) - c {\left(\frac{10 \, c^{5} x^{3} - 12 \, c^{4} x^{\frac{5}{2}} + 15 \, c^{3} x^{2} - 20 \, c^{2} x^{\frac{3}{2}} + 30 \, c x - 60 \, \sqrt{x}}{c^{6}} + \frac{60 \, \log\left(c \sqrt{x} + 1\right)}{c^{7}}\right)}\right)} a^{2} b - \frac{1}{120} \, {\left(60 \, x^{3} \log\left(-c \sqrt{x} + 1\right) - c {\left(\frac{10 \, c^{5} x^{3} + 12 \, c^{4} x^{\frac{5}{2}} + 15 \, c^{3} x^{2} + 20 \, c^{2} x^{\frac{3}{2}} + 30 \, c x + 60 \, \sqrt{x}}{c^{6}} + \frac{60 \, \log\left(c \sqrt{x} - 1\right)}{c^{7}}\right)}\right)} a^{2} b + \frac{{\left(100 \, {\left(18 \, \log\left(-c \sqrt{x} + 1\right)^{2} - 6 \, \log\left(-c \sqrt{x} + 1\right) + 1\right)} {\left(c \sqrt{x} - 1\right)}^{6} + 432 \, {\left(25 \, \log\left(-c \sqrt{x} + 1\right)^{2} - 10 \, \log\left(-c \sqrt{x} + 1\right) + 2\right)} {\left(c \sqrt{x} - 1\right)}^{5} + 3375 \, {\left(8 \, \log\left(-c \sqrt{x} + 1\right)^{2} - 4 \, \log\left(-c \sqrt{x} + 1\right) + 1\right)} {\left(c \sqrt{x} - 1\right)}^{4} + 4000 \, {\left(9 \, \log\left(-c \sqrt{x} + 1\right)^{2} - 6 \, \log\left(-c \sqrt{x} + 1\right) + 2\right)} {\left(c \sqrt{x} - 1\right)}^{3} + 13500 \, {\left(2 \, \log\left(-c \sqrt{x} + 1\right)^{2} - 2 \, \log\left(-c \sqrt{x} + 1\right) + 1\right)} {\left(c \sqrt{x} - 1\right)}^{2} + 10800 \, {\left(\log\left(-c \sqrt{x} + 1\right)^{2} - 2 \, \log\left(-c \sqrt{x} + 1\right) + 2\right)} {\left(c \sqrt{x} - 1\right)}\right)} a b^{2}}{7200 \, c^{6}} - \frac{{\left(1000 \, {\left(36 \, \log\left(-c \sqrt{x} + 1\right)^{3} - 18 \, \log\left(-c \sqrt{x} + 1\right)^{2} + 6 \, \log\left(-c \sqrt{x} + 1\right) - 1\right)} {\left(c \sqrt{x} - 1\right)}^{6} + 1728 \, {\left(125 \, \log\left(-c \sqrt{x} + 1\right)^{3} - 75 \, \log\left(-c \sqrt{x} + 1\right)^{2} + 30 \, \log\left(-c \sqrt{x} + 1\right) - 6\right)} {\left(c \sqrt{x} - 1\right)}^{5} + 16875 \, {\left(32 \, \log\left(-c \sqrt{x} + 1\right)^{3} - 24 \, \log\left(-c \sqrt{x} + 1\right)^{2} + 12 \, \log\left(-c \sqrt{x} + 1\right) - 3\right)} {\left(c \sqrt{x} - 1\right)}^{4} + 80000 \, {\left(9 \, \log\left(-c \sqrt{x} + 1\right)^{3} - 9 \, \log\left(-c \sqrt{x} + 1\right)^{2} + 6 \, \log\left(-c \sqrt{x} + 1\right) - 2\right)} {\left(c \sqrt{x} - 1\right)}^{3} + 135000 \, {\left(4 \, \log\left(-c \sqrt{x} + 1\right)^{3} - 6 \, \log\left(-c \sqrt{x} + 1\right)^{2} + 6 \, \log\left(-c \sqrt{x} + 1\right) - 3\right)} {\left(c \sqrt{x} - 1\right)}^{2} + 216000 \, {\left(\log\left(-c \sqrt{x} + 1\right)^{3} - 3 \, \log\left(-c \sqrt{x} + 1\right)^{2} + 6 \, \log\left(-c \sqrt{x} + 1\right) - 6\right)} {\left(c \sqrt{x} - 1\right)}\right)} b^{3}}{864000 \, c^{6}} + \frac{23 \, {\left(\log\left(c \sqrt{x} + 1\right) \log\left(-\frac{1}{2} \, c \sqrt{x} + \frac{1}{2}\right) + {\rm Li}_2\left(\frac{1}{2} \, c \sqrt{x} + \frac{1}{2}\right)\right)} b^{3}}{15 \, c^{6}} - \frac{8929 \, b^{3} \log\left(c \sqrt{x} - 1\right)}{14400 \, c^{6}} + \frac{{\left(147 \, a b^{2} - 38 \, b^{3}\right)} \log\left(c \sqrt{x} + 1\right)}{120 \, c^{6}} + \frac{1000 \, {\left(12 \, a b^{2} c^{6} - b^{3} c^{6}\right)} x^{3} + 36000 \, {\left(b^{3} c^{6} x^{3} - b^{3}\right)} \log\left(c \sqrt{x} + 1\right)^{3} - 48 \, {\left(660 \, a b^{2} c^{5} + 91 \, b^{3} c^{5}\right)} x^{\frac{5}{2}} + 15 \, {\left(4440 \, a b^{2} c^{4} - 919 \, b^{3} c^{4}\right)} x^{2} + 14400 \, {\left(15 \, a b^{2} c^{6} x^{3} + 3 \, b^{3} c^{5} x^{\frac{5}{2}} + 5 \, b^{3} c^{3} x^{\frac{3}{2}} + 15 \, b^{3} c \sqrt{x} - 15 \, a b^{2} + 23 \, b^{3}\right)} \log\left(c \sqrt{x} + 1\right)^{2} - 1800 \, {\left(10 \, b^{3} c^{6} x^{3} - 12 \, b^{3} c^{5} x^{\frac{5}{2}} + 15 \, b^{3} c^{4} x^{2} - 20 \, b^{3} c^{3} x^{\frac{3}{2}} + 30 \, b^{3} c^{2} x - 60 \, b^{3} c \sqrt{x} + 37 \, b^{3} - 60 \, {\left(b^{3} c^{6} x^{3} - b^{3}\right)} \log\left(c \sqrt{x} + 1\right)\right)} \log\left(-c \sqrt{x} + 1\right)^{2} - 20 \, {\left(6840 \, a b^{2} c^{3} + 619 \, b^{3} c^{3}\right)} x^{\frac{3}{2}} + 870 \, {\left(360 \, a b^{2} c^{2} - 161 \, b^{3} c^{2}\right)} x - 7200 \, {\left(10 \, a b^{2} c^{6} x^{3} - 12 \, a b^{2} c^{5} x^{\frac{5}{2}} - 20 \, a b^{2} c^{3} x^{\frac{3}{2}} - 60 \, a b^{2} c \sqrt{x} + 3 \, {\left(5 \, a b^{2} c^{4} - 2 \, b^{3} c^{4}\right)} x^{2} + 2 \, {\left(15 \, a b^{2} c^{2} - 16 \, b^{3} c^{2}\right)} x\right)} \log\left(c \sqrt{x} + 1\right) + 60 \, {\left(100 \, b^{3} c^{6} x^{3} + 264 \, b^{3} c^{5} x^{\frac{5}{2}} - 165 \, b^{3} c^{4} x^{2} + 1140 \, b^{3} c^{3} x^{\frac{3}{2}} - 1230 \, b^{3} c^{2} x + 8820 \, b^{3} c \sqrt{x} - 1800 \, {\left(b^{3} c^{6} x^{3} - b^{3}\right)} \log\left(c \sqrt{x} + 1\right)^{2} - 480 \, {\left(3 \, b^{3} c^{5} x^{\frac{5}{2}} + 5 \, b^{3} c^{3} x^{\frac{3}{2}} + 15 \, b^{3} c \sqrt{x} + 23 \, b^{3}\right)} \log\left(c \sqrt{x} + 1\right)\right)} \log\left(-c \sqrt{x} + 1\right) - 60 \, {\left(17640 \, a b^{2} c + 4369 \, b^{3} c\right)} \sqrt{x}}{864000 \, c^{6}}"," ",0,"1/3*a^3*x^3 - 1/720*a*b^2*c*((20*c^5*x^3 + 39*c^3*x^2 + 138*c*x - 6*(10*c^5*x^3 + 12*c^4*x^(5/2) + 15*c^3*x^2 + 20*c^2*x^(3/2) + 30*c*x + 60*sqrt(x))*log(c*sqrt(x) + 1))/c^6 - 222*log(c*sqrt(x) + 1)/c^7 - 222*log(c*sqrt(x) - 1)/c^7) - 1/120*(60*x^3*log(c*sqrt(x) + 1) - c*((10*c^5*x^3 - 12*c^4*x^(5/2) + 15*c^3*x^2 - 20*c^2*x^(3/2) + 30*c*x - 60*sqrt(x))/c^6 + 60*log(c*sqrt(x) + 1)/c^7))*a*b^2*log(-c*sqrt(x) + 1) + 1/120*(60*x^3*log(c*sqrt(x) + 1) - c*((10*c^5*x^3 - 12*c^4*x^(5/2) + 15*c^3*x^2 - 20*c^2*x^(3/2) + 30*c*x - 60*sqrt(x))/c^6 + 60*log(c*sqrt(x) + 1)/c^7))*a^2*b - 1/120*(60*x^3*log(-c*sqrt(x) + 1) - c*((10*c^5*x^3 + 12*c^4*x^(5/2) + 15*c^3*x^2 + 20*c^2*x^(3/2) + 30*c*x + 60*sqrt(x))/c^6 + 60*log(c*sqrt(x) - 1)/c^7))*a^2*b + 1/7200*(100*(18*log(-c*sqrt(x) + 1)^2 - 6*log(-c*sqrt(x) + 1) + 1)*(c*sqrt(x) - 1)^6 + 432*(25*log(-c*sqrt(x) + 1)^2 - 10*log(-c*sqrt(x) + 1) + 2)*(c*sqrt(x) - 1)^5 + 3375*(8*log(-c*sqrt(x) + 1)^2 - 4*log(-c*sqrt(x) + 1) + 1)*(c*sqrt(x) - 1)^4 + 4000*(9*log(-c*sqrt(x) + 1)^2 - 6*log(-c*sqrt(x) + 1) + 2)*(c*sqrt(x) - 1)^3 + 13500*(2*log(-c*sqrt(x) + 1)^2 - 2*log(-c*sqrt(x) + 1) + 1)*(c*sqrt(x) - 1)^2 + 10800*(log(-c*sqrt(x) + 1)^2 - 2*log(-c*sqrt(x) + 1) + 2)*(c*sqrt(x) - 1))*a*b^2/c^6 - 1/864000*(1000*(36*log(-c*sqrt(x) + 1)^3 - 18*log(-c*sqrt(x) + 1)^2 + 6*log(-c*sqrt(x) + 1) - 1)*(c*sqrt(x) - 1)^6 + 1728*(125*log(-c*sqrt(x) + 1)^3 - 75*log(-c*sqrt(x) + 1)^2 + 30*log(-c*sqrt(x) + 1) - 6)*(c*sqrt(x) - 1)^5 + 16875*(32*log(-c*sqrt(x) + 1)^3 - 24*log(-c*sqrt(x) + 1)^2 + 12*log(-c*sqrt(x) + 1) - 3)*(c*sqrt(x) - 1)^4 + 80000*(9*log(-c*sqrt(x) + 1)^3 - 9*log(-c*sqrt(x) + 1)^2 + 6*log(-c*sqrt(x) + 1) - 2)*(c*sqrt(x) - 1)^3 + 135000*(4*log(-c*sqrt(x) + 1)^3 - 6*log(-c*sqrt(x) + 1)^2 + 6*log(-c*sqrt(x) + 1) - 3)*(c*sqrt(x) - 1)^2 + 216000*(log(-c*sqrt(x) + 1)^3 - 3*log(-c*sqrt(x) + 1)^2 + 6*log(-c*sqrt(x) + 1) - 6)*(c*sqrt(x) - 1))*b^3/c^6 + 23/15*(log(c*sqrt(x) + 1)*log(-1/2*c*sqrt(x) + 1/2) + dilog(1/2*c*sqrt(x) + 1/2))*b^3/c^6 - 8929/14400*b^3*log(c*sqrt(x) - 1)/c^6 + 1/120*(147*a*b^2 - 38*b^3)*log(c*sqrt(x) + 1)/c^6 + 1/864000*(1000*(12*a*b^2*c^6 - b^3*c^6)*x^3 + 36000*(b^3*c^6*x^3 - b^3)*log(c*sqrt(x) + 1)^3 - 48*(660*a*b^2*c^5 + 91*b^3*c^5)*x^(5/2) + 15*(4440*a*b^2*c^4 - 919*b^3*c^4)*x^2 + 14400*(15*a*b^2*c^6*x^3 + 3*b^3*c^5*x^(5/2) + 5*b^3*c^3*x^(3/2) + 15*b^3*c*sqrt(x) - 15*a*b^2 + 23*b^3)*log(c*sqrt(x) + 1)^2 - 1800*(10*b^3*c^6*x^3 - 12*b^3*c^5*x^(5/2) + 15*b^3*c^4*x^2 - 20*b^3*c^3*x^(3/2) + 30*b^3*c^2*x - 60*b^3*c*sqrt(x) + 37*b^3 - 60*(b^3*c^6*x^3 - b^3)*log(c*sqrt(x) + 1))*log(-c*sqrt(x) + 1)^2 - 20*(6840*a*b^2*c^3 + 619*b^3*c^3)*x^(3/2) + 870*(360*a*b^2*c^2 - 161*b^3*c^2)*x - 7200*(10*a*b^2*c^6*x^3 - 12*a*b^2*c^5*x^(5/2) - 20*a*b^2*c^3*x^(3/2) - 60*a*b^2*c*sqrt(x) + 3*(5*a*b^2*c^4 - 2*b^3*c^4)*x^2 + 2*(15*a*b^2*c^2 - 16*b^3*c^2)*x)*log(c*sqrt(x) + 1) + 60*(100*b^3*c^6*x^3 + 264*b^3*c^5*x^(5/2) - 165*b^3*c^4*x^2 + 1140*b^3*c^3*x^(3/2) - 1230*b^3*c^2*x + 8820*b^3*c*sqrt(x) - 1800*(b^3*c^6*x^3 - b^3)*log(c*sqrt(x) + 1)^2 - 480*(3*b^3*c^5*x^(5/2) + 5*b^3*c^3*x^(3/2) + 15*b^3*c*sqrt(x) + 23*b^3)*log(c*sqrt(x) + 1))*log(-c*sqrt(x) + 1) - 60*(17640*a*b^2*c + 4369*b^3*c)*sqrt(x))/c^6","B",0
204,1,1184,0,1.039534," ","integrate(x*(a+b*arctanh(c*x^(1/2)))^3,x, algorithm=""maxima"")","\frac{1}{2} \, a^{3} x^{2} - \frac{1}{32} \, a b^{2} c {\left(\frac{3 \, c^{3} x^{2} + 10 \, c x - 2 \, {\left(3 \, c^{3} x^{2} + 4 \, c^{2} x^{\frac{3}{2}} + 6 \, c x + 12 \, \sqrt{x}\right)} \log\left(c \sqrt{x} + 1\right)}{c^{4}} - \frac{14 \, \log\left(c \sqrt{x} + 1\right)}{c^{5}} - \frac{14 \, \log\left(c \sqrt{x} - 1\right)}{c^{5}}\right)} - \frac{1}{16} \, {\left(12 \, x^{2} \log\left(c \sqrt{x} + 1\right) - c {\left(\frac{3 \, c^{3} x^{2} - 4 \, c^{2} x^{\frac{3}{2}} + 6 \, c x - 12 \, \sqrt{x}}{c^{4}} + \frac{12 \, \log\left(c \sqrt{x} + 1\right)}{c^{5}}\right)}\right)} a b^{2} \log\left(-c \sqrt{x} + 1\right) + \frac{1}{16} \, {\left(12 \, x^{2} \log\left(c \sqrt{x} + 1\right) - c {\left(\frac{3 \, c^{3} x^{2} - 4 \, c^{2} x^{\frac{3}{2}} + 6 \, c x - 12 \, \sqrt{x}}{c^{4}} + \frac{12 \, \log\left(c \sqrt{x} + 1\right)}{c^{5}}\right)}\right)} a^{2} b - \frac{1}{16} \, {\left(12 \, x^{2} \log\left(-c \sqrt{x} + 1\right) - c {\left(\frac{3 \, c^{3} x^{2} + 4 \, c^{2} x^{\frac{3}{2}} + 6 \, c x + 12 \, \sqrt{x}}{c^{4}} + \frac{12 \, \log\left(c \sqrt{x} - 1\right)}{c^{5}}\right)}\right)} a^{2} b + \frac{{\left(9 \, {\left(8 \, \log\left(-c \sqrt{x} + 1\right)^{2} - 4 \, \log\left(-c \sqrt{x} + 1\right) + 1\right)} {\left(c \sqrt{x} - 1\right)}^{4} + 32 \, {\left(9 \, \log\left(-c \sqrt{x} + 1\right)^{2} - 6 \, \log\left(-c \sqrt{x} + 1\right) + 2\right)} {\left(c \sqrt{x} - 1\right)}^{3} + 216 \, {\left(2 \, \log\left(-c \sqrt{x} + 1\right)^{2} - 2 \, \log\left(-c \sqrt{x} + 1\right) + 1\right)} {\left(c \sqrt{x} - 1\right)}^{2} + 288 \, {\left(\log\left(-c \sqrt{x} + 1\right)^{2} - 2 \, \log\left(-c \sqrt{x} + 1\right) + 2\right)} {\left(c \sqrt{x} - 1\right)}\right)} a b^{2}}{192 \, c^{4}} - \frac{{\left(9 \, {\left(32 \, \log\left(-c \sqrt{x} + 1\right)^{3} - 24 \, \log\left(-c \sqrt{x} + 1\right)^{2} + 12 \, \log\left(-c \sqrt{x} + 1\right) - 3\right)} {\left(c \sqrt{x} - 1\right)}^{4} + 128 \, {\left(9 \, \log\left(-c \sqrt{x} + 1\right)^{3} - 9 \, \log\left(-c \sqrt{x} + 1\right)^{2} + 6 \, \log\left(-c \sqrt{x} + 1\right) - 2\right)} {\left(c \sqrt{x} - 1\right)}^{3} + 432 \, {\left(4 \, \log\left(-c \sqrt{x} + 1\right)^{3} - 6 \, \log\left(-c \sqrt{x} + 1\right)^{2} + 6 \, \log\left(-c \sqrt{x} + 1\right) - 3\right)} {\left(c \sqrt{x} - 1\right)}^{2} + 1152 \, {\left(\log\left(-c \sqrt{x} + 1\right)^{3} - 3 \, \log\left(-c \sqrt{x} + 1\right)^{2} + 6 \, \log\left(-c \sqrt{x} + 1\right) - 6\right)} {\left(c \sqrt{x} - 1\right)}\right)} b^{3}}{4608 \, c^{4}} + \frac{2 \, {\left(\log\left(c \sqrt{x} + 1\right) \log\left(-\frac{1}{2} \, c \sqrt{x} + \frac{1}{2}\right) + {\rm Li}_2\left(\frac{1}{2} \, c \sqrt{x} + \frac{1}{2}\right)\right)} b^{3}}{c^{4}} - \frac{319 \, b^{3} \log\left(c \sqrt{x} - 1\right)}{384 \, c^{4}} + \frac{{\left(25 \, a b^{2} - 4 \, b^{3}\right)} \log\left(c \sqrt{x} + 1\right)}{16 \, c^{4}} + \frac{288 \, {\left(b^{3} c^{4} x^{2} - b^{3}\right)} \log\left(c \sqrt{x} + 1\right)^{3} + 27 \, {\left(8 \, a b^{2} c^{4} - b^{3} c^{4}\right)} x^{2} + 576 \, {\left(3 \, a b^{2} c^{4} x^{2} + b^{3} c^{3} x^{\frac{3}{2}} + 3 \, b^{3} c \sqrt{x} - 3 \, a b^{2} + 4 \, b^{3}\right)} \log\left(c \sqrt{x} + 1\right)^{2} - 72 \, {\left(3 \, b^{3} c^{4} x^{2} - 4 \, b^{3} c^{3} x^{\frac{3}{2}} + 6 \, b^{3} c^{2} x - 12 \, b^{3} c \sqrt{x} + 7 \, b^{3} - 12 \, {\left(b^{3} c^{4} x^{2} - b^{3}\right)} \log\left(c \sqrt{x} + 1\right)\right)} \log\left(-c \sqrt{x} + 1\right)^{2} - 4 \, {\left(168 \, a b^{2} c^{3} + 37 \, b^{3} c^{3}\right)} x^{\frac{3}{2}} + 6 \, {\left(312 \, a b^{2} c^{2} - 115 \, b^{3} c^{2}\right)} x - 288 \, {\left(3 \, a b^{2} c^{4} x^{2} - 4 \, a b^{2} c^{3} x^{\frac{3}{2}} - 12 \, a b^{2} c \sqrt{x} + 2 \, {\left(3 \, a b^{2} c^{2} - 2 \, b^{3} c^{2}\right)} x\right)} \log\left(c \sqrt{x} + 1\right) + 12 \, {\left(9 \, b^{3} c^{4} x^{2} + 28 \, b^{3} c^{3} x^{\frac{3}{2}} - 18 \, b^{3} c^{2} x + 300 \, b^{3} c \sqrt{x} - 72 \, {\left(b^{3} c^{4} x^{2} - b^{3}\right)} \log\left(c \sqrt{x} + 1\right)^{2} - 96 \, {\left(b^{3} c^{3} x^{\frac{3}{2}} + 3 \, b^{3} c \sqrt{x} + 4 \, b^{3}\right)} \log\left(c \sqrt{x} + 1\right)\right)} \log\left(-c \sqrt{x} + 1\right) - 12 \, {\left(600 \, a b^{2} c + 223 \, b^{3} c\right)} \sqrt{x}}{4608 \, c^{4}}"," ",0,"1/2*a^3*x^2 - 1/32*a*b^2*c*((3*c^3*x^2 + 10*c*x - 2*(3*c^3*x^2 + 4*c^2*x^(3/2) + 6*c*x + 12*sqrt(x))*log(c*sqrt(x) + 1))/c^4 - 14*log(c*sqrt(x) + 1)/c^5 - 14*log(c*sqrt(x) - 1)/c^5) - 1/16*(12*x^2*log(c*sqrt(x) + 1) - c*((3*c^3*x^2 - 4*c^2*x^(3/2) + 6*c*x - 12*sqrt(x))/c^4 + 12*log(c*sqrt(x) + 1)/c^5))*a*b^2*log(-c*sqrt(x) + 1) + 1/16*(12*x^2*log(c*sqrt(x) + 1) - c*((3*c^3*x^2 - 4*c^2*x^(3/2) + 6*c*x - 12*sqrt(x))/c^4 + 12*log(c*sqrt(x) + 1)/c^5))*a^2*b - 1/16*(12*x^2*log(-c*sqrt(x) + 1) - c*((3*c^3*x^2 + 4*c^2*x^(3/2) + 6*c*x + 12*sqrt(x))/c^4 + 12*log(c*sqrt(x) - 1)/c^5))*a^2*b + 1/192*(9*(8*log(-c*sqrt(x) + 1)^2 - 4*log(-c*sqrt(x) + 1) + 1)*(c*sqrt(x) - 1)^4 + 32*(9*log(-c*sqrt(x) + 1)^2 - 6*log(-c*sqrt(x) + 1) + 2)*(c*sqrt(x) - 1)^3 + 216*(2*log(-c*sqrt(x) + 1)^2 - 2*log(-c*sqrt(x) + 1) + 1)*(c*sqrt(x) - 1)^2 + 288*(log(-c*sqrt(x) + 1)^2 - 2*log(-c*sqrt(x) + 1) + 2)*(c*sqrt(x) - 1))*a*b^2/c^4 - 1/4608*(9*(32*log(-c*sqrt(x) + 1)^3 - 24*log(-c*sqrt(x) + 1)^2 + 12*log(-c*sqrt(x) + 1) - 3)*(c*sqrt(x) - 1)^4 + 128*(9*log(-c*sqrt(x) + 1)^3 - 9*log(-c*sqrt(x) + 1)^2 + 6*log(-c*sqrt(x) + 1) - 2)*(c*sqrt(x) - 1)^3 + 432*(4*log(-c*sqrt(x) + 1)^3 - 6*log(-c*sqrt(x) + 1)^2 + 6*log(-c*sqrt(x) + 1) - 3)*(c*sqrt(x) - 1)^2 + 1152*(log(-c*sqrt(x) + 1)^3 - 3*log(-c*sqrt(x) + 1)^2 + 6*log(-c*sqrt(x) + 1) - 6)*(c*sqrt(x) - 1))*b^3/c^4 + 2*(log(c*sqrt(x) + 1)*log(-1/2*c*sqrt(x) + 1/2) + dilog(1/2*c*sqrt(x) + 1/2))*b^3/c^4 - 319/384*b^3*log(c*sqrt(x) - 1)/c^4 + 1/16*(25*a*b^2 - 4*b^3)*log(c*sqrt(x) + 1)/c^4 + 1/4608*(288*(b^3*c^4*x^2 - b^3)*log(c*sqrt(x) + 1)^3 + 27*(8*a*b^2*c^4 - b^3*c^4)*x^2 + 576*(3*a*b^2*c^4*x^2 + b^3*c^3*x^(3/2) + 3*b^3*c*sqrt(x) - 3*a*b^2 + 4*b^3)*log(c*sqrt(x) + 1)^2 - 72*(3*b^3*c^4*x^2 - 4*b^3*c^3*x^(3/2) + 6*b^3*c^2*x - 12*b^3*c*sqrt(x) + 7*b^3 - 12*(b^3*c^4*x^2 - b^3)*log(c*sqrt(x) + 1))*log(-c*sqrt(x) + 1)^2 - 4*(168*a*b^2*c^3 + 37*b^3*c^3)*x^(3/2) + 6*(312*a*b^2*c^2 - 115*b^3*c^2)*x - 288*(3*a*b^2*c^4*x^2 - 4*a*b^2*c^3*x^(3/2) - 12*a*b^2*c*sqrt(x) + 2*(3*a*b^2*c^2 - 2*b^3*c^2)*x)*log(c*sqrt(x) + 1) + 12*(9*b^3*c^4*x^2 + 28*b^3*c^3*x^(3/2) - 18*b^3*c^2*x + 300*b^3*c*sqrt(x) - 72*(b^3*c^4*x^2 - b^3)*log(c*sqrt(x) + 1)^2 - 96*(b^3*c^3*x^(3/2) + 3*b^3*c*sqrt(x) + 4*b^3)*log(c*sqrt(x) + 1))*log(-c*sqrt(x) + 1) - 12*(600*a*b^2*c + 223*b^3*c)*sqrt(x))/c^4","B",0
205,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x^(1/2)))^3,x, algorithm=""maxima"")","\frac{3}{2} \, {\left(c {\left(\frac{2 \, \sqrt{x}}{c^{2}} - \frac{\log\left(c \sqrt{x} + 1\right)}{c^{3}} + \frac{\log\left(c \sqrt{x} - 1\right)}{c^{3}}\right)} + 2 \, x \operatorname{artanh}\left(c \sqrt{x}\right)\right)} a^{2} b + \frac{3}{4} \, {\left(4 \, c {\left(\frac{2 \, \sqrt{x}}{c^{2}} - \frac{\log\left(c \sqrt{x} + 1\right)}{c^{3}} + \frac{\log\left(c \sqrt{x} - 1\right)}{c^{3}}\right)} \operatorname{artanh}\left(c \sqrt{x}\right) + 4 \, x \operatorname{artanh}\left(c \sqrt{x}\right)^{2} - \frac{2 \, {\left(\log\left(c \sqrt{x} - 1\right) - 2\right)} \log\left(c \sqrt{x} + 1\right) - \log\left(c \sqrt{x} + 1\right)^{2} - \log\left(c \sqrt{x} - 1\right)^{2} - 4 \, \log\left(c \sqrt{x} - 1\right)}{c^{2}}\right)} a b^{2} + a^{3} x - \frac{1}{32} \, b^{3} {\left(\frac{{\left(4 \, \log\left(-c \sqrt{x} + 1\right)^{3} - 6 \, \log\left(-c \sqrt{x} + 1\right)^{2} + 6 \, \log\left(-c \sqrt{x} + 1\right) - 3\right)} {\left(c \sqrt{x} - 1\right)}^{2} + 8 \, {\left(\log\left(-c \sqrt{x} + 1\right)^{3} - 3 \, \log\left(-c \sqrt{x} + 1\right)^{2} + 6 \, \log\left(-c \sqrt{x} + 1\right) - 6\right)} {\left(c \sqrt{x} - 1\right)}}{c^{2}} - 4 \, \int \log\left(c \sqrt{x} + 1\right)^{3} - 3 \, \log\left(c \sqrt{x} + 1\right)^{2} \log\left(-c \sqrt{x} + 1\right) + 3 \, \log\left(c \sqrt{x} + 1\right) \log\left(-c \sqrt{x} + 1\right)^{2}\,{d x}\right)}"," ",0,"3/2*(c*(2*sqrt(x)/c^2 - log(c*sqrt(x) + 1)/c^3 + log(c*sqrt(x) - 1)/c^3) + 2*x*arctanh(c*sqrt(x)))*a^2*b + 3/4*(4*c*(2*sqrt(x)/c^2 - log(c*sqrt(x) + 1)/c^3 + log(c*sqrt(x) - 1)/c^3)*arctanh(c*sqrt(x)) + 4*x*arctanh(c*sqrt(x))^2 - (2*(log(c*sqrt(x) - 1) - 2)*log(c*sqrt(x) + 1) - log(c*sqrt(x) + 1)^2 - log(c*sqrt(x) - 1)^2 - 4*log(c*sqrt(x) - 1))/c^2)*a*b^2 + a^3*x - 1/32*b^3*(((4*log(-c*sqrt(x) + 1)^3 - 6*log(-c*sqrt(x) + 1)^2 + 6*log(-c*sqrt(x) + 1) - 3)*(c*sqrt(x) - 1)^2 + 8*(log(-c*sqrt(x) + 1)^3 - 3*log(-c*sqrt(x) + 1)^2 + 6*log(-c*sqrt(x) + 1) - 6)*(c*sqrt(x) - 1))/c^2 - 4*integrate(log(c*sqrt(x) + 1)^3 - 3*log(c*sqrt(x) + 1)^2*log(-c*sqrt(x) + 1) + 3*log(c*sqrt(x) + 1)*log(-c*sqrt(x) + 1)^2, x))","F",0
206,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x^(1/2)))^3/x,x, algorithm=""maxima"")","\frac{1}{8} \, b^{3} \int \frac{\log\left(c \sqrt{x} + 1\right)^{3}}{x}\,{d x} - \frac{3}{8} \, b^{3} \int \frac{\log\left(c \sqrt{x} + 1\right)^{2} \log\left(-c \sqrt{x} + 1\right)}{x}\,{d x} + \frac{3}{8} \, b^{3} \int \frac{\log\left(c \sqrt{x} + 1\right) \log\left(-c \sqrt{x} + 1\right)^{2}}{x}\,{d x} - \frac{1}{8} \, b^{3} \int \frac{\log\left(-c \sqrt{x} + 1\right)^{3}}{x}\,{d x} + \frac{3}{4} \, a b^{2} \int \frac{\log\left(c \sqrt{x} + 1\right)^{2}}{x}\,{d x} - \frac{3}{2} \, a b^{2} \int \frac{\log\left(c \sqrt{x} + 1\right) \log\left(-c \sqrt{x} + 1\right)}{x}\,{d x} + \frac{3}{4} \, a b^{2} \int \frac{\log\left(-c \sqrt{x} + 1\right)^{2}}{x}\,{d x} + \frac{3}{2} \, a^{2} b \int \frac{\log\left(c \sqrt{x} + 1\right)}{x}\,{d x} - \frac{3}{2} \, a^{2} b \int \frac{\log\left(-c \sqrt{x} + 1\right)}{x}\,{d x} + a^{3} \log\left(x\right)"," ",0,"1/8*b^3*integrate(log(c*sqrt(x) + 1)^3/x, x) - 3/8*b^3*integrate(log(c*sqrt(x) + 1)^2*log(-c*sqrt(x) + 1)/x, x) + 3/8*b^3*integrate(log(c*sqrt(x) + 1)*log(-c*sqrt(x) + 1)^2/x, x) - 1/8*b^3*integrate(log(-c*sqrt(x) + 1)^3/x, x) + 3/4*a*b^2*integrate(log(c*sqrt(x) + 1)^2/x, x) - 3/2*a*b^2*integrate(log(c*sqrt(x) + 1)*log(-c*sqrt(x) + 1)/x, x) + 3/4*a*b^2*integrate(log(-c*sqrt(x) + 1)^2/x, x) + 3/2*a^2*b*integrate(log(c*sqrt(x) + 1)/x, x) - 3/2*a^2*b*integrate(log(-c*sqrt(x) + 1)/x, x) + a^3*log(x)","F",0
207,1,528,0,1.729878," ","integrate((a+b*arctanh(c*x^(1/2)))^3/x^2,x, algorithm=""maxima"")","-3 \, {\left(\log\left(c \sqrt{x} + 1\right) \log\left(-\frac{1}{2} \, c \sqrt{x} + \frac{1}{2}\right) + {\rm Li}_2\left(\frac{1}{2} \, c \sqrt{x} + \frac{1}{2}\right)\right)} b^{3} c^{2} - 3 \, {\left(\log\left(c \sqrt{x}\right) \log\left(-c \sqrt{x} + 1\right) + {\rm Li}_2\left(-c \sqrt{x} + 1\right)\right)} b^{3} c^{2} + 3 \, {\left(\log\left(c \sqrt{x} + 1\right) \log\left(-c \sqrt{x}\right) + {\rm Li}_2\left(c \sqrt{x} + 1\right)\right)} b^{3} c^{2} - 3 \, a b^{2} c^{2} \log\left(c \sqrt{x} - 1\right) - \frac{3}{4} \, {\left({\left(2 \, c \log\left(c \sqrt{x} - 1\right) - c \log\left(x\right) + \frac{2}{\sqrt{x}}\right)} c - \frac{2 \, \log\left(-c \sqrt{x} + 1\right)}{x}\right)} a^{2} b - \frac{a^{3}}{x} + \frac{3}{2} \, {\left(a^{2} b c^{2} - 2 \, a b^{2} c^{2}\right)} \log\left(c \sqrt{x} + 1\right) - \frac{3}{4} \, {\left(a^{2} b c^{2} - 4 \, a b^{2} c^{2}\right)} \log\left(x\right) - \frac{12 \, a^{2} b c \sqrt{x} - {\left(b^{3} c^{2} x - b^{3}\right)} \log\left(c \sqrt{x} + 1\right)^{3} + {\left(b^{3} c^{2} x - b^{3}\right)} \log\left(-c \sqrt{x} + 1\right)^{3} + 6 \, {\left(b^{3} c \sqrt{x} + a b^{2} - {\left(a b^{2} c^{2} - b^{3} c^{2}\right)} x\right)} \log\left(c \sqrt{x} + 1\right)^{2} + 3 \, {\left(2 \, b^{3} c \sqrt{x} + 2 \, a b^{2} - 2 \, {\left(a b^{2} c^{2} + b^{3} c^{2}\right)} x - {\left(b^{3} c^{2} x - b^{3}\right)} \log\left(c \sqrt{x} + 1\right)\right)} \log\left(-c \sqrt{x} + 1\right)^{2} + 12 \, {\left(2 \, a b^{2} c \sqrt{x} + a^{2} b\right)} \log\left(c \sqrt{x} + 1\right) - 3 \, {\left(8 \, a b^{2} c \sqrt{x} - {\left(b^{3} c^{2} x - b^{3}\right)} \log\left(c \sqrt{x} + 1\right)^{2} + 4 \, {\left(b^{3} c \sqrt{x} + a b^{2} - {\left(a b^{2} c^{2} - b^{3} c^{2}\right)} x\right)} \log\left(c \sqrt{x} + 1\right)\right)} \log\left(-c \sqrt{x} + 1\right)}{8 \, x}"," ",0,"-3*(log(c*sqrt(x) + 1)*log(-1/2*c*sqrt(x) + 1/2) + dilog(1/2*c*sqrt(x) + 1/2))*b^3*c^2 - 3*(log(c*sqrt(x))*log(-c*sqrt(x) + 1) + dilog(-c*sqrt(x) + 1))*b^3*c^2 + 3*(log(c*sqrt(x) + 1)*log(-c*sqrt(x)) + dilog(c*sqrt(x) + 1))*b^3*c^2 - 3*a*b^2*c^2*log(c*sqrt(x) - 1) - 3/4*((2*c*log(c*sqrt(x) - 1) - c*log(x) + 2/sqrt(x))*c - 2*log(-c*sqrt(x) + 1)/x)*a^2*b - a^3/x + 3/2*(a^2*b*c^2 - 2*a*b^2*c^2)*log(c*sqrt(x) + 1) - 3/4*(a^2*b*c^2 - 4*a*b^2*c^2)*log(x) - 1/8*(12*a^2*b*c*sqrt(x) - (b^3*c^2*x - b^3)*log(c*sqrt(x) + 1)^3 + (b^3*c^2*x - b^3)*log(-c*sqrt(x) + 1)^3 + 6*(b^3*c*sqrt(x) + a*b^2 - (a*b^2*c^2 - b^3*c^2)*x)*log(c*sqrt(x) + 1)^2 + 3*(2*b^3*c*sqrt(x) + 2*a*b^2 - 2*(a*b^2*c^2 + b^3*c^2)*x - (b^3*c^2*x - b^3)*log(c*sqrt(x) + 1))*log(-c*sqrt(x) + 1)^2 + 12*(2*a*b^2*c*sqrt(x) + a^2*b)*log(c*sqrt(x) + 1) - 3*(8*a*b^2*c*sqrt(x) - (b^3*c^2*x - b^3)*log(c*sqrt(x) + 1)^2 + 4*(b^3*c*sqrt(x) + a*b^2 - (a*b^2*c^2 - b^3*c^2)*x)*log(c*sqrt(x) + 1))*log(-c*sqrt(x) + 1))/x","B",0
208,1,703,0,1.958996," ","integrate((a+b*arctanh(c*x^(1/2)))^3/x^3,x, algorithm=""maxima"")","-2 \, {\left(\log\left(c \sqrt{x} + 1\right) \log\left(-\frac{1}{2} \, c \sqrt{x} + \frac{1}{2}\right) + {\rm Li}_2\left(\frac{1}{2} \, c \sqrt{x} + \frac{1}{2}\right)\right)} b^{3} c^{4} - 2 \, {\left(\log\left(c \sqrt{x}\right) \log\left(-c \sqrt{x} + 1\right) + {\rm Li}_2\left(-c \sqrt{x} + 1\right)\right)} b^{3} c^{4} + 2 \, {\left(\log\left(c \sqrt{x} + 1\right) \log\left(-c \sqrt{x}\right) + {\rm Li}_2\left(c \sqrt{x} + 1\right)\right)} b^{3} c^{4} - \frac{1}{8} \, {\left({\left(6 \, c^{3} \log\left(c \sqrt{x} - 1\right) - 3 \, c^{3} \log\left(x\right) + \frac{6 \, c^{2} x + 3 \, c \sqrt{x} + 2}{x^{\frac{3}{2}}}\right)} c - \frac{6 \, \log\left(-c \sqrt{x} + 1\right)}{x^{2}}\right)} a^{2} b + \frac{1}{4} \, {\left(3 \, a^{2} b c^{4} - 8 \, a b^{2} c^{4} + b^{3} c^{4}\right)} \log\left(c \sqrt{x} + 1\right) - \frac{1}{4} \, {\left(8 \, a b^{2} c^{4} + b^{3} c^{4}\right)} \log\left(c \sqrt{x} - 1\right) - \frac{1}{8} \, {\left(3 \, a^{2} b c^{4} - 16 \, a b^{2} c^{4}\right)} \log\left(x\right) - \frac{a^{3}}{2 \, x^{2}} - \frac{4 \, a^{2} b c \sqrt{x} - {\left(b^{3} c^{4} x^{2} - b^{3}\right)} \log\left(c \sqrt{x} + 1\right)^{3} + {\left(b^{3} c^{4} x^{2} - b^{3}\right)} \log\left(-c \sqrt{x} + 1\right)^{3} + 2 \, {\left(3 \, b^{3} c^{3} x^{\frac{3}{2}} + b^{3} c \sqrt{x} + 3 \, a b^{2} - {\left(3 \, a b^{2} c^{4} - 4 \, b^{3} c^{4}\right)} x^{2}\right)} \log\left(c \sqrt{x} + 1\right)^{2} + {\left(6 \, b^{3} c^{3} x^{\frac{3}{2}} + 2 \, b^{3} c \sqrt{x} + 6 \, a b^{2} - 2 \, {\left(3 \, a b^{2} c^{4} + 4 \, b^{3} c^{4}\right)} x^{2} - 3 \, {\left(b^{3} c^{4} x^{2} - b^{3}\right)} \log\left(c \sqrt{x} + 1\right)\right)} \log\left(-c \sqrt{x} + 1\right)^{2} + 4 \, {\left(3 \, a^{2} b c^{3} + 2 \, b^{3} c^{3}\right)} x^{\frac{3}{2}} - 2 \, {\left(3 \, a^{2} b c^{2} - 4 \, a b^{2} c^{2}\right)} x + 4 \, {\left(6 \, a b^{2} c^{3} x^{\frac{3}{2}} + b^{3} c^{2} x + 2 \, a b^{2} c \sqrt{x} + 3 \, a^{2} b\right)} \log\left(c \sqrt{x} + 1\right) - {\left(24 \, a b^{2} c^{3} x^{\frac{3}{2}} + 4 \, b^{3} c^{2} x + 8 \, a b^{2} c \sqrt{x} - 3 \, {\left(b^{3} c^{4} x^{2} - b^{3}\right)} \log\left(c \sqrt{x} + 1\right)^{2} + 4 \, {\left(3 \, b^{3} c^{3} x^{\frac{3}{2}} + b^{3} c \sqrt{x} + 3 \, a b^{2} - {\left(3 \, a b^{2} c^{4} - 4 \, b^{3} c^{4}\right)} x^{2}\right)} \log\left(c \sqrt{x} + 1\right)\right)} \log\left(-c \sqrt{x} + 1\right)}{16 \, x^{2}}"," ",0,"-2*(log(c*sqrt(x) + 1)*log(-1/2*c*sqrt(x) + 1/2) + dilog(1/2*c*sqrt(x) + 1/2))*b^3*c^4 - 2*(log(c*sqrt(x))*log(-c*sqrt(x) + 1) + dilog(-c*sqrt(x) + 1))*b^3*c^4 + 2*(log(c*sqrt(x) + 1)*log(-c*sqrt(x)) + dilog(c*sqrt(x) + 1))*b^3*c^4 - 1/8*((6*c^3*log(c*sqrt(x) - 1) - 3*c^3*log(x) + (6*c^2*x + 3*c*sqrt(x) + 2)/x^(3/2))*c - 6*log(-c*sqrt(x) + 1)/x^2)*a^2*b + 1/4*(3*a^2*b*c^4 - 8*a*b^2*c^4 + b^3*c^4)*log(c*sqrt(x) + 1) - 1/4*(8*a*b^2*c^4 + b^3*c^4)*log(c*sqrt(x) - 1) - 1/8*(3*a^2*b*c^4 - 16*a*b^2*c^4)*log(x) - 1/2*a^3/x^2 - 1/16*(4*a^2*b*c*sqrt(x) - (b^3*c^4*x^2 - b^3)*log(c*sqrt(x) + 1)^3 + (b^3*c^4*x^2 - b^3)*log(-c*sqrt(x) + 1)^3 + 2*(3*b^3*c^3*x^(3/2) + b^3*c*sqrt(x) + 3*a*b^2 - (3*a*b^2*c^4 - 4*b^3*c^4)*x^2)*log(c*sqrt(x) + 1)^2 + (6*b^3*c^3*x^(3/2) + 2*b^3*c*sqrt(x) + 6*a*b^2 - 2*(3*a*b^2*c^4 + 4*b^3*c^4)*x^2 - 3*(b^3*c^4*x^2 - b^3)*log(c*sqrt(x) + 1))*log(-c*sqrt(x) + 1)^2 + 4*(3*a^2*b*c^3 + 2*b^3*c^3)*x^(3/2) - 2*(3*a^2*b*c^2 - 4*a*b^2*c^2)*x + 4*(6*a*b^2*c^3*x^(3/2) + b^3*c^2*x + 2*a*b^2*c*sqrt(x) + 3*a^2*b)*log(c*sqrt(x) + 1) - (24*a*b^2*c^3*x^(3/2) + 4*b^3*c^2*x + 8*a*b^2*c*sqrt(x) - 3*(b^3*c^4*x^2 - b^3)*log(c*sqrt(x) + 1)^2 + 4*(3*b^3*c^3*x^(3/2) + b^3*c*sqrt(x) + 3*a*b^2 - (3*a*b^2*c^4 - 4*b^3*c^4)*x^2)*log(c*sqrt(x) + 1))*log(-c*sqrt(x) + 1))/x^2","B",0
209,1,24,0,0.306709," ","integrate(x^(3/2)*arctanh(x^(1/2)),x, algorithm=""maxima"")","\frac{2}{5} \, x^{\frac{5}{2}} \operatorname{artanh}\left(\sqrt{x}\right) + \frac{1}{10} \, x^{2} + \frac{1}{5} \, x + \frac{1}{5} \, \log\left(x - 1\right)"," ",0,"2/5*x^(5/2)*arctanh(sqrt(x)) + 1/10*x^2 + 1/5*x + 1/5*log(x - 1)","A",0
210,1,19,0,0.316251," ","integrate(arctanh(x^(1/2))*x^(1/2),x, algorithm=""maxima"")","\frac{2}{3} \, x^{\frac{3}{2}} \operatorname{artanh}\left(\sqrt{x}\right) + \frac{1}{3} \, x + \frac{1}{3} \, \log\left(x - 1\right)"," ",0,"2/3*x^(3/2)*arctanh(sqrt(x)) + 1/3*x + 1/3*log(x - 1)","A",0
211,1,16,0,0.309270," ","integrate(arctanh(x^(1/2))/x^(1/2),x, algorithm=""maxima"")","2 \, \sqrt{x} \operatorname{artanh}\left(\sqrt{x}\right) + \log\left(-x + 1\right)"," ",0,"2*sqrt(x)*arctanh(sqrt(x)) + log(-x + 1)","A",0
212,1,18,0,0.308396," ","integrate(arctanh(x^(1/2))/x^(3/2),x, algorithm=""maxima"")","-\frac{2 \, \operatorname{artanh}\left(\sqrt{x}\right)}{\sqrt{x}} - \log\left(x - 1\right) + \log\left(x\right)"," ",0,"-2*arctanh(sqrt(x))/sqrt(x) - log(x - 1) + log(x)","A",0
213,1,172,0,0.425118," ","integrate(x^3*(a+b*arctanh(c*x^(3/2))),x, algorithm=""maxima"")","\frac{1}{4} \, a x^{4} + \frac{1}{80} \, {\left(20 \, x^{4} \operatorname{artanh}\left(c x^{\frac{3}{2}}\right) + c {\left(\frac{12 \, x^{\frac{5}{2}}}{c^{2}} + \frac{10 \, \sqrt{3} \arctan\left(\frac{\sqrt{3} {\left(2 \, c^{\frac{2}{3}} \sqrt{x} + c^{\frac{1}{3}}\right)}}{3 \, c^{\frac{1}{3}}}\right)}{c^{\frac{11}{3}}} + \frac{10 \, \sqrt{3} \arctan\left(\frac{\sqrt{3} {\left(2 \, c^{\frac{2}{3}} \sqrt{x} - c^{\frac{1}{3}}\right)}}{3 \, c^{\frac{1}{3}}}\right)}{c^{\frac{11}{3}}} - \frac{5 \, \log\left(c^{\frac{2}{3}} x + c^{\frac{1}{3}} \sqrt{x} + 1\right)}{c^{\frac{11}{3}}} + \frac{5 \, \log\left(c^{\frac{2}{3}} x - c^{\frac{1}{3}} \sqrt{x} + 1\right)}{c^{\frac{11}{3}}} - \frac{10 \, \log\left(\frac{c^{\frac{1}{3}} \sqrt{x} + 1}{c^{\frac{1}{3}}}\right)}{c^{\frac{11}{3}}} + \frac{10 \, \log\left(\frac{c^{\frac{1}{3}} \sqrt{x} - 1}{c^{\frac{1}{3}}}\right)}{c^{\frac{11}{3}}}\right)}\right)} b"," ",0,"1/4*a*x^4 + 1/80*(20*x^4*arctanh(c*x^(3/2)) + c*(12*x^(5/2)/c^2 + 10*sqrt(3)*arctan(1/3*sqrt(3)*(2*c^(2/3)*sqrt(x) + c^(1/3))/c^(1/3))/c^(11/3) + 10*sqrt(3)*arctan(1/3*sqrt(3)*(2*c^(2/3)*sqrt(x) - c^(1/3))/c^(1/3))/c^(11/3) - 5*log(c^(2/3)*x + c^(1/3)*sqrt(x) + 1)/c^(11/3) + 5*log(c^(2/3)*x - c^(1/3)*sqrt(x) + 1)/c^(11/3) - 10*log((c^(1/3)*sqrt(x) + 1)/c^(1/3))/c^(11/3) + 10*log((c^(1/3)*sqrt(x) - 1)/c^(1/3))/c^(11/3)))*b","A",0
214,1,58,0,0.315971," ","integrate(x^2*(a+b*arctanh(c*x^(3/2))),x, algorithm=""maxima"")","\frac{1}{3} \, a x^{3} + \frac{1}{6} \, {\left(2 \, x^{3} \operatorname{artanh}\left(c x^{\frac{3}{2}}\right) + c {\left(\frac{2 \, x^{\frac{3}{2}}}{c^{2}} - \frac{\log\left(c x^{\frac{3}{2}} + 1\right)}{c^{3}} + \frac{\log\left(c x^{\frac{3}{2}} - 1\right)}{c^{3}}\right)}\right)} b"," ",0,"1/3*a*x^3 + 1/6*(2*x^3*arctanh(c*x^(3/2)) + c*(2*x^(3/2)/c^2 - log(c*x^(3/2) + 1)/c^3 + log(c*x^(3/2) - 1)/c^3))*b","A",0
215,1,172,0,0.420773," ","integrate(x*(a+b*arctanh(c*x^(3/2))),x, algorithm=""maxima"")","\frac{1}{2} \, a x^{2} + \frac{1}{8} \, {\left(4 \, x^{2} \operatorname{artanh}\left(c x^{\frac{3}{2}}\right) - c {\left(\frac{2 \, \sqrt{3} \arctan\left(\frac{\sqrt{3} {\left(2 \, c^{\frac{2}{3}} \sqrt{x} + c^{\frac{1}{3}}\right)}}{3 \, c^{\frac{1}{3}}}\right)}{c^{\frac{7}{3}}} + \frac{2 \, \sqrt{3} \arctan\left(\frac{\sqrt{3} {\left(2 \, c^{\frac{2}{3}} \sqrt{x} - c^{\frac{1}{3}}\right)}}{3 \, c^{\frac{1}{3}}}\right)}{c^{\frac{7}{3}}} + \frac{\log\left(c^{\frac{2}{3}} x + c^{\frac{1}{3}} \sqrt{x} + 1\right)}{c^{\frac{7}{3}}} - \frac{\log\left(c^{\frac{2}{3}} x - c^{\frac{1}{3}} \sqrt{x} + 1\right)}{c^{\frac{7}{3}}} + \frac{2 \, \log\left(\frac{c^{\frac{1}{3}} \sqrt{x} + 1}{c^{\frac{1}{3}}}\right)}{c^{\frac{7}{3}}} - \frac{2 \, \log\left(\frac{c^{\frac{1}{3}} \sqrt{x} - 1}{c^{\frac{1}{3}}}\right)}{c^{\frac{7}{3}}} - \frac{12 \, \sqrt{x}}{c^{2}}\right)}\right)} b"," ",0,"1/2*a*x^2 + 1/8*(4*x^2*arctanh(c*x^(3/2)) - c*(2*sqrt(3)*arctan(1/3*sqrt(3)*(2*c^(2/3)*sqrt(x) + c^(1/3))/c^(1/3))/c^(7/3) + 2*sqrt(3)*arctan(1/3*sqrt(3)*(2*c^(2/3)*sqrt(x) - c^(1/3))/c^(1/3))/c^(7/3) + log(c^(2/3)*x + c^(1/3)*sqrt(x) + 1)/c^(7/3) - log(c^(2/3)*x - c^(1/3)*sqrt(x) + 1)/c^(7/3) + 2*log((c^(1/3)*sqrt(x) + 1)/c^(1/3))/c^(7/3) - 2*log((c^(1/3)*sqrt(x) - 1)/c^(1/3))/c^(7/3) - 12*sqrt(x)/c^2))*b","A",0
216,1,158,0,0.420854," ","integrate(a+b*arctanh(c*x^(3/2)),x, algorithm=""maxima"")","\frac{1}{4} \, {\left(c {\left(\frac{2 \, \sqrt{3} \arctan\left(\frac{\sqrt{3} {\left(2 \, c^{\frac{2}{3}} \sqrt{x} + c^{\frac{1}{3}}\right)}}{3 \, c^{\frac{1}{3}}}\right)}{c^{\frac{5}{3}}} + \frac{2 \, \sqrt{3} \arctan\left(\frac{\sqrt{3} {\left(2 \, c^{\frac{2}{3}} \sqrt{x} - c^{\frac{1}{3}}\right)}}{3 \, c^{\frac{1}{3}}}\right)}{c^{\frac{5}{3}}} - \frac{\log\left(c^{\frac{2}{3}} x + c^{\frac{1}{3}} \sqrt{x} + 1\right)}{c^{\frac{5}{3}}} + \frac{\log\left(c^{\frac{2}{3}} x - c^{\frac{1}{3}} \sqrt{x} + 1\right)}{c^{\frac{5}{3}}} - \frac{2 \, \log\left(\frac{c^{\frac{1}{3}} \sqrt{x} + 1}{c^{\frac{1}{3}}}\right)}{c^{\frac{5}{3}}} + \frac{2 \, \log\left(\frac{c^{\frac{1}{3}} \sqrt{x} - 1}{c^{\frac{1}{3}}}\right)}{c^{\frac{5}{3}}}\right)} + 4 \, x \operatorname{artanh}\left(c x^{\frac{3}{2}}\right)\right)} b + a x"," ",0,"1/4*(c*(2*sqrt(3)*arctan(1/3*sqrt(3)*(2*c^(2/3)*sqrt(x) + c^(1/3))/c^(1/3))/c^(5/3) + 2*sqrt(3)*arctan(1/3*sqrt(3)*(2*c^(2/3)*sqrt(x) - c^(1/3))/c^(1/3))/c^(5/3) - log(c^(2/3)*x + c^(1/3)*sqrt(x) + 1)/c^(5/3) + log(c^(2/3)*x - c^(1/3)*sqrt(x) + 1)/c^(5/3) - 2*log((c^(1/3)*sqrt(x) + 1)/c^(1/3))/c^(5/3) + 2*log((c^(1/3)*sqrt(x) - 1)/c^(1/3))/c^(5/3)) + 4*x*arctanh(c*x^(3/2)))*b + a*x","A",0
217,1,62,0,0.509020," ","integrate((a+b*arctanh(c*x^(3/2)))/x,x, algorithm=""maxima"")","-\frac{1}{3} \, {\left(\log\left(c x^{\frac{3}{2}}\right) \log\left(-c x^{\frac{3}{2}} + 1\right) + {\rm Li}_2\left(-c x^{\frac{3}{2}} + 1\right)\right)} b + \frac{1}{3} \, {\left(\log\left(c x^{\frac{3}{2}} + 1\right) \log\left(-c x^{\frac{3}{2}}\right) + {\rm Li}_2\left(c x^{\frac{3}{2}} + 1\right)\right)} b + a \log\left(x\right)"," ",0,"-1/3*(log(c*x^(3/2))*log(-c*x^(3/2) + 1) + dilog(-c*x^(3/2) + 1))*b + 1/3*(log(c*x^(3/2) + 1)*log(-c*x^(3/2)) + dilog(c*x^(3/2) + 1))*b + a*log(x)","B",0
218,1,163,0,0.420937," ","integrate((a+b*arctanh(c*x^(3/2)))/x^2,x, algorithm=""maxima"")","\frac{1}{4} \, {\left({\left(\frac{2 \, \sqrt{3} \arctan\left(\frac{\sqrt{3} {\left(2 \, c^{\frac{2}{3}} \sqrt{x} + c^{\frac{1}{3}}\right)}}{3 \, c^{\frac{1}{3}}}\right)}{c^{\frac{1}{3}}} + \frac{2 \, \sqrt{3} \arctan\left(\frac{\sqrt{3} {\left(2 \, c^{\frac{2}{3}} \sqrt{x} - c^{\frac{1}{3}}\right)}}{3 \, c^{\frac{1}{3}}}\right)}{c^{\frac{1}{3}}} + \frac{\log\left(c^{\frac{2}{3}} x + c^{\frac{1}{3}} \sqrt{x} + 1\right)}{c^{\frac{1}{3}}} - \frac{\log\left(c^{\frac{2}{3}} x - c^{\frac{1}{3}} \sqrt{x} + 1\right)}{c^{\frac{1}{3}}} + \frac{2 \, \log\left(\frac{c^{\frac{1}{3}} \sqrt{x} + 1}{c^{\frac{1}{3}}}\right)}{c^{\frac{1}{3}}} - \frac{2 \, \log\left(\frac{c^{\frac{1}{3}} \sqrt{x} - 1}{c^{\frac{1}{3}}}\right)}{c^{\frac{1}{3}}}\right)} c - \frac{4 \, \operatorname{artanh}\left(c x^{\frac{3}{2}}\right)}{x}\right)} b - \frac{a}{x}"," ",0,"1/4*((2*sqrt(3)*arctan(1/3*sqrt(3)*(2*c^(2/3)*sqrt(x) + c^(1/3))/c^(1/3))/c^(1/3) + 2*sqrt(3)*arctan(1/3*sqrt(3)*(2*c^(2/3)*sqrt(x) - c^(1/3))/c^(1/3))/c^(1/3) + log(c^(2/3)*x + c^(1/3)*sqrt(x) + 1)/c^(1/3) - log(c^(2/3)*x - c^(1/3)*sqrt(x) + 1)/c^(1/3) + 2*log((c^(1/3)*sqrt(x) + 1)/c^(1/3))/c^(1/3) - 2*log((c^(1/3)*sqrt(x) - 1)/c^(1/3))/c^(1/3))*c - 4*arctanh(c*x^(3/2))/x)*b - a/x","A",0
219,1,168,0,0.420803," ","integrate((a+b*arctanh(c*x^(3/2)))/x^3,x, algorithm=""maxima"")","-\frac{1}{8} \, {\left({\left(2 \, \sqrt{3} c^{\frac{1}{3}} \arctan\left(\frac{\sqrt{3} {\left(2 \, c^{\frac{2}{3}} \sqrt{x} + c^{\frac{1}{3}}\right)}}{3 \, c^{\frac{1}{3}}}\right) + 2 \, \sqrt{3} c^{\frac{1}{3}} \arctan\left(\frac{\sqrt{3} {\left(2 \, c^{\frac{2}{3}} \sqrt{x} - c^{\frac{1}{3}}\right)}}{3 \, c^{\frac{1}{3}}}\right) - c^{\frac{1}{3}} \log\left(c^{\frac{2}{3}} x + c^{\frac{1}{3}} \sqrt{x} + 1\right) + c^{\frac{1}{3}} \log\left(c^{\frac{2}{3}} x - c^{\frac{1}{3}} \sqrt{x} + 1\right) - 2 \, c^{\frac{1}{3}} \log\left(\frac{c^{\frac{1}{3}} \sqrt{x} + 1}{c^{\frac{1}{3}}}\right) + 2 \, c^{\frac{1}{3}} \log\left(\frac{c^{\frac{1}{3}} \sqrt{x} - 1}{c^{\frac{1}{3}}}\right) + \frac{12}{\sqrt{x}}\right)} c + \frac{4 \, \operatorname{artanh}\left(c x^{\frac{3}{2}}\right)}{x^{2}}\right)} b - \frac{a}{2 \, x^{2}}"," ",0,"-1/8*((2*sqrt(3)*c^(1/3)*arctan(1/3*sqrt(3)*(2*c^(2/3)*sqrt(x) + c^(1/3))/c^(1/3)) + 2*sqrt(3)*c^(1/3)*arctan(1/3*sqrt(3)*(2*c^(2/3)*sqrt(x) - c^(1/3))/c^(1/3)) - c^(1/3)*log(c^(2/3)*x + c^(1/3)*sqrt(x) + 1) + c^(1/3)*log(c^(2/3)*x - c^(1/3)*sqrt(x) + 1) - 2*c^(1/3)*log((c^(1/3)*sqrt(x) + 1)/c^(1/3)) + 2*c^(1/3)*log((c^(1/3)*sqrt(x) - 1)/c^(1/3)) + 12/sqrt(x))*c + 4*arctanh(c*x^(3/2))/x^2)*b - 1/2*a/x^2","A",0
220,1,51,0,0.307335," ","integrate((a+b*arctanh(c*x^(3/2)))/x^4,x, algorithm=""maxima"")","\frac{1}{6} \, {\left({\left(c \log\left(c x^{\frac{3}{2}} + 1\right) - c \log\left(c x^{\frac{3}{2}} - 1\right) - \frac{2}{x^{\frac{3}{2}}}\right)} c - \frac{2 \, \operatorname{artanh}\left(c x^{\frac{3}{2}}\right)}{x^{3}}\right)} b - \frac{a}{3 \, x^{3}}"," ",0,"1/6*((c*log(c*x^(3/2) + 1) - c*log(c*x^(3/2) - 1) - 2/x^(3/2))*c - 2*arctanh(c*x^(3/2))/x^3)*b - 1/3*a/x^3","A",0
221,1,186,0,0.334746," ","integrate(x^2*(a+b*arctanh(c*x^(3/2)))^2,x, algorithm=""maxima"")","\frac{1}{3} \, b^{2} x^{3} \operatorname{artanh}\left(c x^{\frac{3}{2}}\right)^{2} + \frac{1}{3} \, a^{2} x^{3} + \frac{1}{3} \, {\left(2 \, x^{3} \operatorname{artanh}\left(c x^{\frac{3}{2}}\right) + c {\left(\frac{2 \, x^{\frac{3}{2}}}{c^{2}} - \frac{\log\left(c x^{\frac{3}{2}} + 1\right)}{c^{3}} + \frac{\log\left(c x^{\frac{3}{2}} - 1\right)}{c^{3}}\right)}\right)} a b + \frac{1}{12} \, {\left(4 \, c {\left(\frac{2 \, x^{\frac{3}{2}}}{c^{2}} - \frac{\log\left(c x^{\frac{3}{2}} + 1\right)}{c^{3}} + \frac{\log\left(c x^{\frac{3}{2}} - 1\right)}{c^{3}}\right)} \operatorname{artanh}\left(c x^{\frac{3}{2}}\right) - \frac{2 \, {\left(\log\left(c x^{\frac{3}{2}} - 1\right) - 2\right)} \log\left(c x^{\frac{3}{2}} + 1\right) - \log\left(c x^{\frac{3}{2}} + 1\right)^{2} - \log\left(c x^{\frac{3}{2}} - 1\right)^{2} - 4 \, \log\left(c x^{\frac{3}{2}} - 1\right)}{c^{2}}\right)} b^{2}"," ",0,"1/3*b^2*x^3*arctanh(c*x^(3/2))^2 + 1/3*a^2*x^3 + 1/3*(2*x^3*arctanh(c*x^(3/2)) + c*(2*x^(3/2)/c^2 - log(c*x^(3/2) + 1)/c^3 + log(c*x^(3/2) - 1)/c^3))*a*b + 1/12*(4*c*(2*x^(3/2)/c^2 - log(c*x^(3/2) + 1)/c^3 + log(c*x^(3/2) - 1)/c^3)*arctanh(c*x^(3/2)) - (2*(log(c*x^(3/2) - 1) - 2)*log(c*x^(3/2) + 1) - log(c*x^(3/2) + 1)^2 - log(c*x^(3/2) - 1)^2 - 4*log(c*x^(3/2) - 1))/c^2)*b^2","B",0
222,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x^(3/2)))^2/x,x, algorithm=""maxima"")","\frac{1}{4} \, b^{2} \int \frac{\log\left(c x^{\frac{3}{2}} + 1\right)^{2}}{x}\,{d x} - \frac{1}{2} \, b^{2} \int \frac{\log\left(c x^{\frac{3}{2}} + 1\right) \log\left(-c x^{\frac{3}{2}} + 1\right)}{x}\,{d x} + \frac{1}{4} \, b^{2} \int \frac{\log\left(-c x^{\frac{3}{2}} + 1\right)^{2}}{x}\,{d x} + a b \int \frac{\log\left(c x^{\frac{3}{2}} + 1\right)}{x}\,{d x} - a b \int \frac{\log\left(-c x^{\frac{3}{2}} + 1\right)}{x}\,{d x} + a^{2} \log\left(x\right)"," ",0,"1/4*b^2*integrate(log(c*x^(3/2) + 1)^2/x, x) - 1/2*b^2*integrate(log(c*x^(3/2) + 1)*log(-c*x^(3/2) + 1)/x, x) + 1/4*b^2*integrate(log(-c*x^(3/2) + 1)^2/x, x) + a*b*integrate(log(c*x^(3/2) + 1)/x, x) - a*b*integrate(log(-c*x^(3/2) + 1)/x, x) + a^2*log(x)","F",0
223,1,175,0,0.332500," ","integrate((a+b*arctanh(c*x^(3/2)))^2/x^4,x, algorithm=""maxima"")","\frac{1}{3} \, {\left({\left(c \log\left(c x^{\frac{3}{2}} + 1\right) - c \log\left(c x^{\frac{3}{2}} - 1\right) - \frac{2}{x^{\frac{3}{2}}}\right)} c - \frac{2 \, \operatorname{artanh}\left(c x^{\frac{3}{2}}\right)}{x^{3}}\right)} a b + \frac{1}{12} \, {\left({\left(2 \, {\left(\log\left(c x^{\frac{3}{2}} - 1\right) - 2\right)} \log\left(c x^{\frac{3}{2}} + 1\right) - \log\left(c x^{\frac{3}{2}} + 1\right)^{2} - \log\left(c x^{\frac{3}{2}} - 1\right)^{2} - 4 \, \log\left(c x^{\frac{3}{2}} - 1\right) + 12 \, \log\left(x\right)\right)} c^{2} + 4 \, {\left(c \log\left(c x^{\frac{3}{2}} + 1\right) - c \log\left(c x^{\frac{3}{2}} - 1\right) - \frac{2}{x^{\frac{3}{2}}}\right)} c \operatorname{artanh}\left(c x^{\frac{3}{2}}\right)\right)} b^{2} - \frac{b^{2} \operatorname{artanh}\left(c x^{\frac{3}{2}}\right)^{2}}{3 \, x^{3}} - \frac{a^{2}}{3 \, x^{3}}"," ",0,"1/3*((c*log(c*x^(3/2) + 1) - c*log(c*x^(3/2) - 1) - 2/x^(3/2))*c - 2*arctanh(c*x^(3/2))/x^3)*a*b + 1/12*((2*(log(c*x^(3/2) - 1) - 2)*log(c*x^(3/2) + 1) - log(c*x^(3/2) + 1)^2 - log(c*x^(3/2) - 1)^2 - 4*log(c*x^(3/2) - 1) + 12*log(x))*c^2 + 4*(c*log(c*x^(3/2) + 1) - c*log(c*x^(3/2) - 1) - 2/x^(3/2))*c*arctanh(c*x^(3/2)))*b^2 - 1/3*b^2*arctanh(c*x^(3/2))^2/x^3 - 1/3*a^2/x^3","B",0
224,0,0,0,0.000000," ","integrate(x^2*(a+b*arctanh(c*x^n)),x, algorithm=""maxima"")","\frac{1}{3} \, a x^{3} + \frac{1}{6} \, {\left(x^{3} \log\left(c x^{n} + 1\right) - x^{3} \log\left(-c x^{n} + 1\right) + 3 \, n \int \frac{x^{2}}{3 \, {\left(c x^{n} + 1\right)}}\,{d x} + 3 \, n \int \frac{x^{2}}{3 \, {\left(c x^{n} - 1\right)}}\,{d x}\right)} b"," ",0,"1/3*a*x^3 + 1/6*(x^3*log(c*x^n + 1) - x^3*log(-c*x^n + 1) + 3*n*integrate(1/3*x^2/(c*x^n + 1), x) + 3*n*integrate(1/3*x^2/(c*x^n - 1), x))*b","F",0
225,0,0,0,0.000000," ","integrate(x*(a+b*arctanh(c*x^n)),x, algorithm=""maxima"")","\frac{1}{2} \, a x^{2} + \frac{1}{4} \, {\left(x^{2} \log\left(c x^{n} + 1\right) - x^{2} \log\left(-c x^{n} + 1\right) + 2 \, n \int \frac{x}{2 \, {\left(c x^{n} + 1\right)}}\,{d x} + 2 \, n \int \frac{x}{2 \, {\left(c x^{n} - 1\right)}}\,{d x}\right)} b"," ",0,"1/2*a*x^2 + 1/4*(x^2*log(c*x^n + 1) - x^2*log(-c*x^n + 1) + 2*n*integrate(1/2*x/(c*x^n + 1), x) + 2*n*integrate(1/2*x/(c*x^n - 1), x))*b","F",0
226,0,0,0,0.000000," ","integrate(a+b*arctanh(c*x^n),x, algorithm=""maxima"")","\frac{1}{2} \, {\left(n \int \frac{1}{c x^{n} + 1}\,{d x} + n \int \frac{1}{c x^{n} - 1}\,{d x} + x \log\left(c x^{n} + 1\right) - x \log\left(-c x^{n} + 1\right)\right)} b + a x"," ",0,"1/2*(n*integrate(1/(c*x^n + 1), x) + n*integrate(1/(c*x^n - 1), x) + x*log(c*x^n + 1) - x*log(-c*x^n + 1))*b + a*x","F",0
227,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x^n))/x,x, algorithm=""maxima"")","\frac{1}{2} \, {\left(n \int \frac{\log\left(x\right)}{c x x^{n} + x}\,{d x} + n \int \frac{\log\left(x\right)}{c x x^{n} - x}\,{d x} + \log\left(c x^{n} + 1\right) \log\left(x\right) - \log\left(-c x^{n} + 1\right) \log\left(x\right)\right)} b + a \log\left(x\right)"," ",0,"1/2*(n*integrate(log(x)/(c*x*x^n + x), x) + n*integrate(log(x)/(c*x*x^n - x), x) + log(c*x^n + 1)*log(x) - log(-c*x^n + 1)*log(x))*b + a*log(x)","F",0
228,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x^n))/x^2,x, algorithm=""maxima"")","-\frac{1}{2} \, {\left(n \int \frac{1}{c x^{2} x^{n} + x^{2}}\,{d x} + n \int \frac{1}{c x^{2} x^{n} - x^{2}}\,{d x} + \frac{\log\left(c x^{n} + 1\right) - \log\left(-c x^{n} + 1\right)}{x}\right)} b - \frac{a}{x}"," ",0,"-1/2*(n*integrate(1/(c*x^2*x^n + x^2), x) + n*integrate(1/(c*x^2*x^n - x^2), x) + (log(c*x^n + 1) - log(-c*x^n + 1))/x)*b - a/x","F",0
229,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x^n))/x^3,x, algorithm=""maxima"")","-\frac{1}{4} \, {\left(2 \, n \int \frac{1}{2 \, {\left(c x^{3} x^{n} + x^{3}\right)}}\,{d x} + 2 \, n \int \frac{1}{2 \, {\left(c x^{3} x^{n} - x^{3}\right)}}\,{d x} + \frac{\log\left(c x^{n} + 1\right) - \log\left(-c x^{n} + 1\right)}{x^{2}}\right)} b - \frac{a}{2 \, x^{2}}"," ",0,"-1/4*(2*n*integrate(1/2/(c*x^3*x^n + x^3), x) + 2*n*integrate(1/2/(c*x^3*x^n - x^3), x) + (log(c*x^n + 1) - log(-c*x^n + 1))/x^2)*b - 1/2*a/x^2","F",0
230,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x^n))/x^4,x, algorithm=""maxima"")","-\frac{1}{6} \, {\left(3 \, n \int \frac{1}{3 \, {\left(c x^{4} x^{n} + x^{4}\right)}}\,{d x} + 3 \, n \int \frac{1}{3 \, {\left(c x^{4} x^{n} - x^{4}\right)}}\,{d x} + \frac{\log\left(c x^{n} + 1\right) - \log\left(-c x^{n} + 1\right)}{x^{3}}\right)} b - \frac{a}{3 \, x^{3}}"," ",0,"-1/6*(3*n*integrate(1/3/(c*x^4*x^n + x^4), x) + 3*n*integrate(1/3/(c*x^4*x^n - x^4), x) + (log(c*x^n + 1) - log(-c*x^n + 1))/x^3)*b - 1/3*a/x^3","F",0
231,0,0,0,0.000000," ","integrate(x*(a+b*arctanh(c*x^n))^2,x, algorithm=""maxima"")","\frac{1}{8} \, b^{2} x^{2} \log\left(-c x^{n} + 1\right)^{2} + \frac{1}{2} \, a^{2} x^{2} - \int -\frac{{\left(b^{2} c x x^{n} - b^{2} x\right)} \log\left(c x^{n} + 1\right)^{2} + 4 \, {\left(a b c x x^{n} - a b x\right)} \log\left(c x^{n} + 1\right) + {\left(4 \, a b x - {\left(b^{2} c n + 4 \, a b c\right)} x x^{n} - 2 \, {\left(b^{2} c x x^{n} - b^{2} x\right)} \log\left(c x^{n} + 1\right)\right)} \log\left(-c x^{n} + 1\right)}{4 \, {\left(c x^{n} - 1\right)}}\,{d x}"," ",0,"1/8*b^2*x^2*log(-c*x^n + 1)^2 + 1/2*a^2*x^2 - integrate(-1/4*((b^2*c*x*x^n - b^2*x)*log(c*x^n + 1)^2 + 4*(a*b*c*x*x^n - a*b*x)*log(c*x^n + 1) + (4*a*b*x - (b^2*c*n + 4*a*b*c)*x*x^n - 2*(b^2*c*x*x^n - b^2*x)*log(c*x^n + 1))*log(-c*x^n + 1))/(c*x^n - 1), x)","F",0
232,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x^n))^2,x, algorithm=""maxima"")","\frac{1}{4} \, b^{2} x \log\left(-c x^{n} + 1\right)^{2} + a^{2} x - \int -\frac{{\left(b^{2} c x^{n} - b^{2}\right)} \log\left(c x^{n} + 1\right)^{2} + 4 \, {\left(a b c x^{n} - a b\right)} \log\left(c x^{n} + 1\right) + 2 \, {\left(2 \, a b - {\left(b^{2} c n + 2 \, a b c\right)} x^{n} - {\left(b^{2} c x^{n} - b^{2}\right)} \log\left(c x^{n} + 1\right)\right)} \log\left(-c x^{n} + 1\right)}{4 \, {\left(c x^{n} - 1\right)}}\,{d x}"," ",0,"1/4*b^2*x*log(-c*x^n + 1)^2 + a^2*x - integrate(-1/4*((b^2*c*x^n - b^2)*log(c*x^n + 1)^2 + 4*(a*b*c*x^n - a*b)*log(c*x^n + 1) + 2*(2*a*b - (b^2*c*n + 2*a*b*c)*x^n - (b^2*c*x^n - b^2)*log(c*x^n + 1))*log(-c*x^n + 1))/(c*x^n - 1), x)","F",0
233,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x^n))^2/x,x, algorithm=""maxima"")","\frac{1}{4} \, b^{2} \log\left(-c x^{n} + 1\right)^{2} \log\left(x\right) + a^{2} \log\left(x\right) - \int -\frac{{\left(b^{2} c x^{n} - b^{2}\right)} \log\left(c x^{n} + 1\right)^{2} + 4 \, {\left(a b c x^{n} - a b\right)} \log\left(c x^{n} + 1\right) + 2 \, {\left(2 \, a b - {\left(b^{2} c n \log\left(x\right) + 2 \, a b c\right)} x^{n} - {\left(b^{2} c x^{n} - b^{2}\right)} \log\left(c x^{n} + 1\right)\right)} \log\left(-c x^{n} + 1\right)}{4 \, {\left(c x x^{n} - x\right)}}\,{d x}"," ",0,"1/4*b^2*log(-c*x^n + 1)^2*log(x) + a^2*log(x) - integrate(-1/4*((b^2*c*x^n - b^2)*log(c*x^n + 1)^2 + 4*(a*b*c*x^n - a*b)*log(c*x^n + 1) + 2*(2*a*b - (b^2*c*n*log(x) + 2*a*b*c)*x^n - (b^2*c*x^n - b^2)*log(c*x^n + 1))*log(-c*x^n + 1))/(c*x*x^n - x), x)","F",0
234,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x^n))^2/x^2,x, algorithm=""maxima"")","-\frac{b^{2} \log\left(-c x^{n} + 1\right)^{2}}{4 \, x} - \frac{a^{2}}{x} - \int -\frac{{\left(b^{2} c x^{n} - b^{2}\right)} \log\left(c x^{n} + 1\right)^{2} + 4 \, {\left(a b c x^{n} - a b\right)} \log\left(c x^{n} + 1\right) + 2 \, {\left(2 \, a b + {\left(b^{2} c n - 2 \, a b c\right)} x^{n} - {\left(b^{2} c x^{n} - b^{2}\right)} \log\left(c x^{n} + 1\right)\right)} \log\left(-c x^{n} + 1\right)}{4 \, {\left(c x^{2} x^{n} - x^{2}\right)}}\,{d x}"," ",0,"-1/4*b^2*log(-c*x^n + 1)^2/x - a^2/x - integrate(-1/4*((b^2*c*x^n - b^2)*log(c*x^n + 1)^2 + 4*(a*b*c*x^n - a*b)*log(c*x^n + 1) + 2*(2*a*b + (b^2*c*n - 2*a*b*c)*x^n - (b^2*c*x^n - b^2)*log(c*x^n + 1))*log(-c*x^n + 1))/(c*x^2*x^n - x^2), x)","F",0
235,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x^n))^2/x^3,x, algorithm=""maxima"")","-\frac{b^{2} \log\left(-c x^{n} + 1\right)^{2}}{8 \, x^{2}} - \frac{a^{2}}{2 \, x^{2}} - \int -\frac{{\left(b^{2} c x^{n} - b^{2}\right)} \log\left(c x^{n} + 1\right)^{2} + 4 \, {\left(a b c x^{n} - a b\right)} \log\left(c x^{n} + 1\right) + {\left(4 \, a b + {\left(b^{2} c n - 4 \, a b c\right)} x^{n} - 2 \, {\left(b^{2} c x^{n} - b^{2}\right)} \log\left(c x^{n} + 1\right)\right)} \log\left(-c x^{n} + 1\right)}{4 \, {\left(c x^{3} x^{n} - x^{3}\right)}}\,{d x}"," ",0,"-1/8*b^2*log(-c*x^n + 1)^2/x^2 - 1/2*a^2/x^2 - integrate(-1/4*((b^2*c*x^n - b^2)*log(c*x^n + 1)^2 + 4*(a*b*c*x^n - a*b)*log(c*x^n + 1) + (4*a*b + (b^2*c*n - 4*a*b*c)*x^n - 2*(b^2*c*x^n - b^2)*log(c*x^n + 1))*log(-c*x^n + 1))/(c*x^3*x^n - x^3), x)","F",0
236,1,147,0,0.416063," ","integrate(arctanh(a*x^n)/x,x, algorithm=""maxima"")","-\frac{1}{2} \, a n {\left(\frac{\log\left(\frac{a x^{n} + 1}{a}\right)}{a n} - \frac{\log\left(\frac{a x^{n} - 1}{a}\right)}{a n}\right)} \log\left(x\right) + \frac{1}{2} \, a n {\left(\frac{\log\left(a x^{n} + 1\right) \log\left(x\right) - \log\left(a x^{n} - 1\right) \log\left(x\right)}{a n} - \frac{n \log\left(a x^{n} + 1\right) \log\left(x\right) + {\rm Li}_2\left(-a x^{n}\right)}{a n^{2}} + \frac{n \log\left(-a x^{n} + 1\right) \log\left(x\right) + {\rm Li}_2\left(a x^{n}\right)}{a n^{2}}\right)} + \operatorname{artanh}\left(a x^{n}\right) \log\left(x\right)"," ",0,"-1/2*a*n*(log((a*x^n + 1)/a)/(a*n) - log((a*x^n - 1)/a)/(a*n))*log(x) + 1/2*a*n*((log(a*x^n + 1)*log(x) - log(a*x^n - 1)*log(x))/(a*n) - (n*log(a*x^n + 1)*log(x) + dilog(-a*x^n))/(a*n^2) + (n*log(-a*x^n + 1)*log(x) + dilog(a*x^n))/(a*n^2)) + arctanh(a*x^n)*log(x)","B",0
237,1,104,0,0.310957," ","integrate(arctanh(a*x^5)/x,x, algorithm=""maxima"")","-\frac{1}{2} \, a {\left(\frac{\log\left(a x^{5} + 1\right)}{a} - \frac{\log\left(a x^{5} - 1\right)}{a}\right)} \log\left(x\right) - \frac{1}{10} \, a {\left(\frac{\log\left(a x^{5} - 1\right) \log\left(a x^{5}\right) + {\rm Li}_2\left(-a x^{5} + 1\right)}{a} - \frac{\log\left(a x^{5} + 1\right) \log\left(-a x^{5}\right) + {\rm Li}_2\left(a x^{5} + 1\right)}{a}\right)} + \operatorname{artanh}\left(a x^{5}\right) \log\left(x\right)"," ",0,"-1/2*a*(log(a*x^5 + 1)/a - log(a*x^5 - 1)/a)*log(x) - 1/10*a*((log(a*x^5 - 1)*log(a*x^5) + dilog(-a*x^5 + 1))/a - (log(a*x^5 + 1)*log(-a*x^5) + dilog(a*x^5 + 1))/a) + arctanh(a*x^5)*log(x)","B",0
238,1,15,0,0.309407," ","integrate(arctanh(1/x),x, algorithm=""maxima"")","x \operatorname{artanh}\left(\frac{1}{x}\right) + \frac{1}{2} \, \log\left(x^{2} - 1\right)"," ",0,"x*arctanh(1/x) + 1/2*log(x^2 - 1)","A",0
239,0,0,0,0.000000," ","integrate((d*x)^m*(a+b*arctanh(c*x^n))^3,x, algorithm=""maxima"")","-\frac{b^{3} d^{m} x x^{m} \log\left(-c x^{n} + 1\right)^{3}}{8 \, {\left(m + 1\right)}} + \frac{\left(d x\right)^{m + 1} a^{3}}{d {\left(m + 1\right)}} + \int \frac{{\left(b^{3} c d^{m} {\left(m + 1\right)} e^{\left(m \log\left(x\right) + n \log\left(x\right)\right)} - b^{3} d^{m} {\left(m + 1\right)} x^{m}\right)} \log\left(c x^{n} + 1\right)^{3} + 6 \, {\left(a b^{2} c d^{m} {\left(m + 1\right)} e^{\left(m \log\left(x\right) + n \log\left(x\right)\right)} - a b^{2} d^{m} {\left(m + 1\right)} x^{m}\right)} \log\left(c x^{n} + 1\right)^{2} - 3 \, {\left(2 \, a b^{2} d^{m} {\left(m + 1\right)} x^{m} - {\left(2 \, a b^{2} c d^{m} {\left(m + 1\right)} + b^{3} c d^{m} n\right)} e^{\left(m \log\left(x\right) + n \log\left(x\right)\right)} - {\left(b^{3} c d^{m} {\left(m + 1\right)} e^{\left(m \log\left(x\right) + n \log\left(x\right)\right)} - b^{3} d^{m} {\left(m + 1\right)} x^{m}\right)} \log\left(c x^{n} + 1\right)\right)} \log\left(-c x^{n} + 1\right)^{2} + 12 \, {\left(a^{2} b c d^{m} {\left(m + 1\right)} e^{\left(m \log\left(x\right) + n \log\left(x\right)\right)} - a^{2} b d^{m} {\left(m + 1\right)} x^{m}\right)} \log\left(c x^{n} + 1\right) - 3 \, {\left(4 \, a^{2} b c d^{m} {\left(m + 1\right)} e^{\left(m \log\left(x\right) + n \log\left(x\right)\right)} - 4 \, a^{2} b d^{m} {\left(m + 1\right)} x^{m} + {\left(b^{3} c d^{m} {\left(m + 1\right)} e^{\left(m \log\left(x\right) + n \log\left(x\right)\right)} - b^{3} d^{m} {\left(m + 1\right)} x^{m}\right)} \log\left(c x^{n} + 1\right)^{2} + 4 \, {\left(a b^{2} c d^{m} {\left(m + 1\right)} e^{\left(m \log\left(x\right) + n \log\left(x\right)\right)} - a b^{2} d^{m} {\left(m + 1\right)} x^{m}\right)} \log\left(c x^{n} + 1\right)\right)} \log\left(-c x^{n} + 1\right)}{8 \, {\left(c {\left(m + 1\right)} x^{n} - m - 1\right)}}\,{d x}"," ",0,"-1/8*b^3*d^m*x*x^m*log(-c*x^n + 1)^3/(m + 1) + (d*x)^(m + 1)*a^3/(d*(m + 1)) + integrate(1/8*((b^3*c*d^m*(m + 1)*e^(m*log(x) + n*log(x)) - b^3*d^m*(m + 1)*x^m)*log(c*x^n + 1)^3 + 6*(a*b^2*c*d^m*(m + 1)*e^(m*log(x) + n*log(x)) - a*b^2*d^m*(m + 1)*x^m)*log(c*x^n + 1)^2 - 3*(2*a*b^2*d^m*(m + 1)*x^m - (2*a*b^2*c*d^m*(m + 1) + b^3*c*d^m*n)*e^(m*log(x) + n*log(x)) - (b^3*c*d^m*(m + 1)*e^(m*log(x) + n*log(x)) - b^3*d^m*(m + 1)*x^m)*log(c*x^n + 1))*log(-c*x^n + 1)^2 + 12*(a^2*b*c*d^m*(m + 1)*e^(m*log(x) + n*log(x)) - a^2*b*d^m*(m + 1)*x^m)*log(c*x^n + 1) - 3*(4*a^2*b*c*d^m*(m + 1)*e^(m*log(x) + n*log(x)) - 4*a^2*b*d^m*(m + 1)*x^m + (b^3*c*d^m*(m + 1)*e^(m*log(x) + n*log(x)) - b^3*d^m*(m + 1)*x^m)*log(c*x^n + 1)^2 + 4*(a*b^2*c*d^m*(m + 1)*e^(m*log(x) + n*log(x)) - a*b^2*d^m*(m + 1)*x^m)*log(c*x^n + 1))*log(-c*x^n + 1))/(c*(m + 1)*x^n - m - 1), x)","F",0
240,0,0,0,0.000000," ","integrate((d*x)^m*(a+b*arctanh(c*x^n))^2,x, algorithm=""maxima"")","\frac{b^{2} d^{m} x x^{m} \log\left(-c x^{n} + 1\right)^{2}}{4 \, {\left(m + 1\right)}} + \frac{\left(d x\right)^{m + 1} a^{2}}{d {\left(m + 1\right)}} - \int -\frac{{\left(b^{2} c d^{m} {\left(m + 1\right)} e^{\left(m \log\left(x\right) + n \log\left(x\right)\right)} - b^{2} d^{m} {\left(m + 1\right)} x^{m}\right)} \log\left(c x^{n} + 1\right)^{2} + 4 \, {\left(a b c d^{m} {\left(m + 1\right)} e^{\left(m \log\left(x\right) + n \log\left(x\right)\right)} - a b d^{m} {\left(m + 1\right)} x^{m}\right)} \log\left(c x^{n} + 1\right) + 2 \, {\left(2 \, a b d^{m} {\left(m + 1\right)} x^{m} - {\left(2 \, a b c d^{m} {\left(m + 1\right)} + b^{2} c d^{m} n\right)} e^{\left(m \log\left(x\right) + n \log\left(x\right)\right)} - {\left(b^{2} c d^{m} {\left(m + 1\right)} e^{\left(m \log\left(x\right) + n \log\left(x\right)\right)} - b^{2} d^{m} {\left(m + 1\right)} x^{m}\right)} \log\left(c x^{n} + 1\right)\right)} \log\left(-c x^{n} + 1\right)}{4 \, {\left(c {\left(m + 1\right)} x^{n} - m - 1\right)}}\,{d x}"," ",0,"1/4*b^2*d^m*x*x^m*log(-c*x^n + 1)^2/(m + 1) + (d*x)^(m + 1)*a^2/(d*(m + 1)) - integrate(-1/4*((b^2*c*d^m*(m + 1)*e^(m*log(x) + n*log(x)) - b^2*d^m*(m + 1)*x^m)*log(c*x^n + 1)^2 + 4*(a*b*c*d^m*(m + 1)*e^(m*log(x) + n*log(x)) - a*b*d^m*(m + 1)*x^m)*log(c*x^n + 1) + 2*(2*a*b*d^m*(m + 1)*x^m - (2*a*b*c*d^m*(m + 1) + b^2*c*d^m*n)*e^(m*log(x) + n*log(x)) - (b^2*c*d^m*(m + 1)*e^(m*log(x) + n*log(x)) - b^2*d^m*(m + 1)*x^m)*log(c*x^n + 1))*log(-c*x^n + 1))/(c*(m + 1)*x^n - m - 1), x)","F",0
241,0,0,0,0.000000," ","integrate((d*x)^m*(a+b*arctanh(c*x^n)),x, algorithm=""maxima"")","\frac{1}{2} \, {\left(d^{m} n \int \frac{x^{m}}{c {\left(m + 1\right)} x^{n} + m + 1}\,{d x} + d^{m} n \int \frac{x^{m}}{c {\left(m + 1\right)} x^{n} - m - 1}\,{d x} + \frac{d^{m} x x^{m} \log\left(c x^{n} + 1\right) - d^{m} x x^{m} \log\left(-c x^{n} + 1\right)}{m + 1}\right)} b + \frac{\left(d x\right)^{m + 1} a}{d {\left(m + 1\right)}}"," ",0,"1/2*(d^m*n*integrate(x^m/(c*(m + 1)*x^n + m + 1), x) + d^m*n*integrate(x^m/(c*(m + 1)*x^n - m - 1), x) + (d^m*x*x^m*log(c*x^n + 1) - d^m*x*x^m*log(-c*x^n + 1))/(m + 1))*b + (d*x)^(m + 1)*a/(d*(m + 1))","F",0
242,0,0,0,0.000000," ","integrate((d*x)^m/(a+b*arctanh(c*x^n)),x, algorithm=""maxima"")","\int \frac{\left(d x\right)^{m}}{b \operatorname{artanh}\left(c x^{n}\right) + a}\,{d x}"," ",0,"integrate((d*x)^m/(b*arctanh(c*x^n) + a), x)","F",0
243,0,0,0,0.000000," ","integrate((d*x)^m/(a+b*arctanh(c*x^n))^2,x, algorithm=""maxima"")","\frac{2 \, {\left(c^{2} d^{m} x e^{\left(m \log\left(x\right) + 2 \, n \log\left(x\right)\right)} - d^{m} x x^{m}\right)}}{b^{2} c n x^{n} \log\left(c x^{n} + 1\right) - b^{2} c n x^{n} \log\left(-c x^{n} + 1\right) + 2 \, a b c n x^{n}} + \int -\frac{2 \, {\left(c^{2} d^{m} {\left(m + n + 1\right)} e^{\left(m \log\left(x\right) + 2 \, n \log\left(x\right)\right)} - d^{m} {\left(m - n + 1\right)} x^{m}\right)}}{b^{2} c n x^{n} \log\left(c x^{n} + 1\right) - b^{2} c n x^{n} \log\left(-c x^{n} + 1\right) + 2 \, a b c n x^{n}}\,{d x}"," ",0,"2*(c^2*d^m*x*e^(m*log(x) + 2*n*log(x)) - d^m*x*x^m)/(b^2*c*n*x^n*log(c*x^n + 1) - b^2*c*n*x^n*log(-c*x^n + 1) + 2*a*b*c*n*x^n) + integrate(-2*(c^2*d^m*(m + n + 1)*e^(m*log(x) + 2*n*log(x)) - d^m*(m - n + 1)*x^m)/(b^2*c*n*x^n*log(c*x^n + 1) - b^2*c*n*x^n*log(-c*x^n + 1) + 2*a*b*c*n*x^n), x)","F",0
