1,1,442,0,0.312304," ","integrate(x^5*(a+b*arctanh(c*x)),x, algorithm=""giac"")","\frac{1}{45} \, c {\left(\frac{15 \, {\left(\frac{3 \, {\left(c x + 1\right)}^{5} b}{{\left(c x - 1\right)}^{5}} + \frac{10 \, {\left(c x + 1\right)}^{3} b}{{\left(c x - 1\right)}^{3}} + \frac{3 \, {\left(c x + 1\right)} b}{c x - 1}\right)} \log\left(-\frac{c x + 1}{c x - 1}\right)}{\frac{{\left(c x + 1\right)}^{6} c^{7}}{{\left(c x - 1\right)}^{6}} - \frac{6 \, {\left(c x + 1\right)}^{5} c^{7}}{{\left(c x - 1\right)}^{5}} + \frac{15 \, {\left(c x + 1\right)}^{4} c^{7}}{{\left(c x - 1\right)}^{4}} - \frac{20 \, {\left(c x + 1\right)}^{3} c^{7}}{{\left(c x - 1\right)}^{3}} + \frac{15 \, {\left(c x + 1\right)}^{2} c^{7}}{{\left(c x - 1\right)}^{2}} - \frac{6 \, {\left(c x + 1\right)} c^{7}}{c x - 1} + c^{7}} + \frac{\frac{90 \, {\left(c x + 1\right)}^{5} a}{{\left(c x - 1\right)}^{5}} + \frac{300 \, {\left(c x + 1\right)}^{3} a}{{\left(c x - 1\right)}^{3}} + \frac{90 \, {\left(c x + 1\right)} a}{c x - 1} + \frac{45 \, {\left(c x + 1\right)}^{5} b}{{\left(c x - 1\right)}^{5}} - \frac{135 \, {\left(c x + 1\right)}^{4} b}{{\left(c x - 1\right)}^{4}} + \frac{230 \, {\left(c x + 1\right)}^{3} b}{{\left(c x - 1\right)}^{3}} - \frac{210 \, {\left(c x + 1\right)}^{2} b}{{\left(c x - 1\right)}^{2}} + \frac{93 \, {\left(c x + 1\right)} b}{c x - 1} - 23 \, b}{\frac{{\left(c x + 1\right)}^{6} c^{7}}{{\left(c x - 1\right)}^{6}} - \frac{6 \, {\left(c x + 1\right)}^{5} c^{7}}{{\left(c x - 1\right)}^{5}} + \frac{15 \, {\left(c x + 1\right)}^{4} c^{7}}{{\left(c x - 1\right)}^{4}} - \frac{20 \, {\left(c x + 1\right)}^{3} c^{7}}{{\left(c x - 1\right)}^{3}} + \frac{15 \, {\left(c x + 1\right)}^{2} c^{7}}{{\left(c x - 1\right)}^{2}} - \frac{6 \, {\left(c x + 1\right)} c^{7}}{c x - 1} + c^{7}}\right)}"," ",0,"1/45*c*(15*(3*(c*x + 1)^5*b/(c*x - 1)^5 + 10*(c*x + 1)^3*b/(c*x - 1)^3 + 3*(c*x + 1)*b/(c*x - 1))*log(-(c*x + 1)/(c*x - 1))/((c*x + 1)^6*c^7/(c*x - 1)^6 - 6*(c*x + 1)^5*c^7/(c*x - 1)^5 + 15*(c*x + 1)^4*c^7/(c*x - 1)^4 - 20*(c*x + 1)^3*c^7/(c*x - 1)^3 + 15*(c*x + 1)^2*c^7/(c*x - 1)^2 - 6*(c*x + 1)*c^7/(c*x - 1) + c^7) + (90*(c*x + 1)^5*a/(c*x - 1)^5 + 300*(c*x + 1)^3*a/(c*x - 1)^3 + 90*(c*x + 1)*a/(c*x - 1) + 45*(c*x + 1)^5*b/(c*x - 1)^5 - 135*(c*x + 1)^4*b/(c*x - 1)^4 + 230*(c*x + 1)^3*b/(c*x - 1)^3 - 210*(c*x + 1)^2*b/(c*x - 1)^2 + 93*(c*x + 1)*b/(c*x - 1) - 23*b)/((c*x + 1)^6*c^7/(c*x - 1)^6 - 6*(c*x + 1)^5*c^7/(c*x - 1)^5 + 15*(c*x + 1)^4*c^7/(c*x - 1)^4 - 20*(c*x + 1)^3*c^7/(c*x - 1)^3 + 15*(c*x + 1)^2*c^7/(c*x - 1)^2 - 6*(c*x + 1)*c^7/(c*x - 1) + c^7))","B",0
2,1,403,0,0.251352," ","integrate(x^4*(a+b*arctanh(c*x)),x, algorithm=""giac"")","\frac{1}{5} \, c {\left(\frac{{\left(\frac{5 \, {\left(c x + 1\right)}^{4} b}{{\left(c x - 1\right)}^{4}} + \frac{10 \, {\left(c x + 1\right)}^{2} b}{{\left(c x - 1\right)}^{2}} + b\right)} \log\left(-\frac{c x + 1}{c x - 1}\right)}{\frac{{\left(c x + 1\right)}^{5} c^{6}}{{\left(c x - 1\right)}^{5}} - \frac{5 \, {\left(c x + 1\right)}^{4} c^{6}}{{\left(c x - 1\right)}^{4}} + \frac{10 \, {\left(c x + 1\right)}^{3} c^{6}}{{\left(c x - 1\right)}^{3}} - \frac{10 \, {\left(c x + 1\right)}^{2} c^{6}}{{\left(c x - 1\right)}^{2}} + \frac{5 \, {\left(c x + 1\right)} c^{6}}{c x - 1} - c^{6}} + \frac{2 \, {\left(\frac{5 \, {\left(c x + 1\right)}^{4} a}{{\left(c x - 1\right)}^{4}} + \frac{10 \, {\left(c x + 1\right)}^{2} a}{{\left(c x - 1\right)}^{2}} + a + \frac{2 \, {\left(c x + 1\right)}^{4} b}{{\left(c x - 1\right)}^{4}} - \frac{4 \, {\left(c x + 1\right)}^{3} b}{{\left(c x - 1\right)}^{3}} + \frac{4 \, {\left(c x + 1\right)}^{2} b}{{\left(c x - 1\right)}^{2}} - \frac{2 \, {\left(c x + 1\right)} b}{c x - 1}\right)}}{\frac{{\left(c x + 1\right)}^{5} c^{6}}{{\left(c x - 1\right)}^{5}} - \frac{5 \, {\left(c x + 1\right)}^{4} c^{6}}{{\left(c x - 1\right)}^{4}} + \frac{10 \, {\left(c x + 1\right)}^{3} c^{6}}{{\left(c x - 1\right)}^{3}} - \frac{10 \, {\left(c x + 1\right)}^{2} c^{6}}{{\left(c x - 1\right)}^{2}} + \frac{5 \, {\left(c x + 1\right)} c^{6}}{c x - 1} - c^{6}} - \frac{b \log\left(-\frac{c x + 1}{c x - 1} + 1\right)}{c^{6}} + \frac{b \log\left(-\frac{c x + 1}{c x - 1}\right)}{c^{6}}\right)}"," ",0,"1/5*c*((5*(c*x + 1)^4*b/(c*x - 1)^4 + 10*(c*x + 1)^2*b/(c*x - 1)^2 + b)*log(-(c*x + 1)/(c*x - 1))/((c*x + 1)^5*c^6/(c*x - 1)^5 - 5*(c*x + 1)^4*c^6/(c*x - 1)^4 + 10*(c*x + 1)^3*c^6/(c*x - 1)^3 - 10*(c*x + 1)^2*c^6/(c*x - 1)^2 + 5*(c*x + 1)*c^6/(c*x - 1) - c^6) + 2*(5*(c*x + 1)^4*a/(c*x - 1)^4 + 10*(c*x + 1)^2*a/(c*x - 1)^2 + a + 2*(c*x + 1)^4*b/(c*x - 1)^4 - 4*(c*x + 1)^3*b/(c*x - 1)^3 + 4*(c*x + 1)^2*b/(c*x - 1)^2 - 2*(c*x + 1)*b/(c*x - 1))/((c*x + 1)^5*c^6/(c*x - 1)^5 - 5*(c*x + 1)^4*c^6/(c*x - 1)^4 + 10*(c*x + 1)^3*c^6/(c*x - 1)^3 - 10*(c*x + 1)^2*c^6/(c*x - 1)^2 + 5*(c*x + 1)*c^6/(c*x - 1) - c^6) - b*log(-(c*x + 1)/(c*x - 1) + 1)/c^6 + b*log(-(c*x + 1)/(c*x - 1))/c^6)","B",0
3,1,296,0,0.164541," ","integrate(x^3*(a+b*arctanh(c*x)),x, algorithm=""giac"")","\frac{1}{3} \, c {\left(\frac{3 \, {\left(\frac{{\left(c x + 1\right)}^{3} b}{{\left(c x - 1\right)}^{3}} + \frac{{\left(c x + 1\right)} b}{c x - 1}\right)} \log\left(-\frac{c x + 1}{c x - 1}\right)}{\frac{{\left(c x + 1\right)}^{4} c^{5}}{{\left(c x - 1\right)}^{4}} - \frac{4 \, {\left(c x + 1\right)}^{3} c^{5}}{{\left(c x - 1\right)}^{3}} + \frac{6 \, {\left(c x + 1\right)}^{2} c^{5}}{{\left(c x - 1\right)}^{2}} - \frac{4 \, {\left(c x + 1\right)} c^{5}}{c x - 1} + c^{5}} + \frac{\frac{6 \, {\left(c x + 1\right)}^{3} a}{{\left(c x - 1\right)}^{3}} + \frac{6 \, {\left(c x + 1\right)} a}{c x - 1} + \frac{3 \, {\left(c x + 1\right)}^{3} b}{{\left(c x - 1\right)}^{3}} - \frac{6 \, {\left(c x + 1\right)}^{2} b}{{\left(c x - 1\right)}^{2}} + \frac{5 \, {\left(c x + 1\right)} b}{c x - 1} - 2 \, b}{\frac{{\left(c x + 1\right)}^{4} c^{5}}{{\left(c x - 1\right)}^{4}} - \frac{4 \, {\left(c x + 1\right)}^{3} c^{5}}{{\left(c x - 1\right)}^{3}} + \frac{6 \, {\left(c x + 1\right)}^{2} c^{5}}{{\left(c x - 1\right)}^{2}} - \frac{4 \, {\left(c x + 1\right)} c^{5}}{c x - 1} + c^{5}}\right)}"," ",0,"1/3*c*(3*((c*x + 1)^3*b/(c*x - 1)^3 + (c*x + 1)*b/(c*x - 1))*log(-(c*x + 1)/(c*x - 1))/((c*x + 1)^4*c^5/(c*x - 1)^4 - 4*(c*x + 1)^3*c^5/(c*x - 1)^3 + 6*(c*x + 1)^2*c^5/(c*x - 1)^2 - 4*(c*x + 1)*c^5/(c*x - 1) + c^5) + (6*(c*x + 1)^3*a/(c*x - 1)^3 + 6*(c*x + 1)*a/(c*x - 1) + 3*(c*x + 1)^3*b/(c*x - 1)^3 - 6*(c*x + 1)^2*b/(c*x - 1)^2 + 5*(c*x + 1)*b/(c*x - 1) - 2*b)/((c*x + 1)^4*c^5/(c*x - 1)^4 - 4*(c*x + 1)^3*c^5/(c*x - 1)^3 + 6*(c*x + 1)^2*c^5/(c*x - 1)^2 - 4*(c*x + 1)*c^5/(c*x - 1) + c^5))","B",0
4,1,258,0,0.228564," ","integrate(x^2*(a+b*arctanh(c*x)),x, algorithm=""giac"")","\frac{1}{3} \, c {\left(\frac{{\left(\frac{3 \, {\left(c x + 1\right)}^{2} b}{{\left(c x - 1\right)}^{2}} + b\right)} \log\left(-\frac{c x + 1}{c x - 1}\right)}{\frac{{\left(c x + 1\right)}^{3} c^{4}}{{\left(c x - 1\right)}^{3}} - \frac{3 \, {\left(c x + 1\right)}^{2} c^{4}}{{\left(c x - 1\right)}^{2}} + \frac{3 \, {\left(c x + 1\right)} c^{4}}{c x - 1} - c^{4}} + \frac{2 \, {\left(\frac{3 \, {\left(c x + 1\right)}^{2} a}{{\left(c x - 1\right)}^{2}} + a + \frac{{\left(c x + 1\right)}^{2} b}{{\left(c x - 1\right)}^{2}} - \frac{{\left(c x + 1\right)} b}{c x - 1}\right)}}{\frac{{\left(c x + 1\right)}^{3} c^{4}}{{\left(c x - 1\right)}^{3}} - \frac{3 \, {\left(c x + 1\right)}^{2} c^{4}}{{\left(c x - 1\right)}^{2}} + \frac{3 \, {\left(c x + 1\right)} c^{4}}{c x - 1} - c^{4}} - \frac{b \log\left(-\frac{c x + 1}{c x - 1} + 1\right)}{c^{4}} + \frac{b \log\left(-\frac{c x + 1}{c x - 1}\right)}{c^{4}}\right)}"," ",0,"1/3*c*((3*(c*x + 1)^2*b/(c*x - 1)^2 + b)*log(-(c*x + 1)/(c*x - 1))/((c*x + 1)^3*c^4/(c*x - 1)^3 - 3*(c*x + 1)^2*c^4/(c*x - 1)^2 + 3*(c*x + 1)*c^4/(c*x - 1) - c^4) + 2*(3*(c*x + 1)^2*a/(c*x - 1)^2 + a + (c*x + 1)^2*b/(c*x - 1)^2 - (c*x + 1)*b/(c*x - 1))/((c*x + 1)^3*c^4/(c*x - 1)^3 - 3*(c*x + 1)^2*c^4/(c*x - 1)^2 + 3*(c*x + 1)*c^4/(c*x - 1) - c^4) - b*log(-(c*x + 1)/(c*x - 1) + 1)/c^4 + b*log(-(c*x + 1)/(c*x - 1))/c^4)","B",0
5,1,148,0,0.290813," ","integrate(x*(a+b*arctanh(c*x)),x, algorithm=""giac"")","c {\left(\frac{{\left(c x + 1\right)} b \log\left(-\frac{c x + 1}{c x - 1}\right)}{{\left(\frac{{\left(c x + 1\right)}^{2} c^{3}}{{\left(c x - 1\right)}^{2}} - \frac{2 \, {\left(c x + 1\right)} c^{3}}{c x - 1} + c^{3}\right)} {\left(c x - 1\right)}} + \frac{\frac{2 \, {\left(c x + 1\right)} a}{c x - 1} + \frac{{\left(c x + 1\right)} b}{c x - 1} - b}{\frac{{\left(c x + 1\right)}^{2} c^{3}}{{\left(c x - 1\right)}^{2}} - \frac{2 \, {\left(c x + 1\right)} c^{3}}{c x - 1} + c^{3}}\right)}"," ",0,"c*((c*x + 1)*b*log(-(c*x + 1)/(c*x - 1))/(((c*x + 1)^2*c^3/(c*x - 1)^2 - 2*(c*x + 1)*c^3/(c*x - 1) + c^3)*(c*x - 1)) + (2*(c*x + 1)*a/(c*x - 1) + (c*x + 1)*b/(c*x - 1) - b)/((c*x + 1)^2*c^3/(c*x - 1)^2 - 2*(c*x + 1)*c^3/(c*x - 1) + c^3))","B",0
6,1,156,0,0.185294," ","integrate(a+b*arctanh(c*x),x, algorithm=""giac"")","b c {\left(\frac{\log\left(\frac{{\left| -c x - 1 \right|}}{{\left| c x - 1 \right|}}\right)}{c^{2}} - \frac{\log\left({\left| -\frac{c x + 1}{c x - 1} + 1 \right|}\right)}{c^{2}} + \frac{\log\left(-\frac{\frac{c {\left(\frac{c x + 1}{c x - 1} + 1\right)}}{\frac{{\left(c x + 1\right)} c}{c x - 1} - c} + 1}{\frac{c {\left(\frac{c x + 1}{c x - 1} + 1\right)}}{\frac{{\left(c x + 1\right)} c}{c x - 1} - c} - 1}\right)}{c^{2} {\left(\frac{c x + 1}{c x - 1} - 1\right)}}\right)} + a x"," ",0,"b*c*(log(abs(-c*x - 1)/abs(c*x - 1))/c^2 - log(abs(-(c*x + 1)/(c*x - 1) + 1))/c^2 + log(-(c*((c*x + 1)/(c*x - 1) + 1)/((c*x + 1)*c/(c*x - 1) - c) + 1)/(c*((c*x + 1)/(c*x - 1) + 1)/((c*x + 1)*c/(c*x - 1) - c) - 1))/(c^2*((c*x + 1)/(c*x - 1) - 1))) + a*x","B",0
7,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x))/x,x, algorithm=""giac"")","\int \frac{b \operatorname{artanh}\left(c x\right) + a}{x}\,{d x}"," ",0,"integrate((b*arctanh(c*x) + a)/x, x)","F",0
8,1,94,0,0.132775," ","integrate((a+b*arctanh(c*x))/x^2,x, algorithm=""giac"")","{\left(b \log\left(-\frac{c x + 1}{c x - 1} - 1\right) - b \log\left(-\frac{c x + 1}{c x - 1}\right) + \frac{b \log\left(-\frac{c x + 1}{c x - 1}\right)}{\frac{c x + 1}{c x - 1} + 1} + \frac{2 \, a}{\frac{c x + 1}{c x - 1} + 1}\right)} c"," ",0,"(b*log(-(c*x + 1)/(c*x - 1) - 1) - b*log(-(c*x + 1)/(c*x - 1)) + b*log(-(c*x + 1)/(c*x - 1))/((c*x + 1)/(c*x - 1) + 1) + 2*a/((c*x + 1)/(c*x - 1) + 1))*c","B",0
9,1,135,0,0.147641," ","integrate((a+b*arctanh(c*x))/x^3,x, algorithm=""giac"")","{\left(\frac{{\left(c x + 1\right)} b c \log\left(-\frac{c x + 1}{c x - 1}\right)}{{\left(c x - 1\right)} {\left(\frac{{\left(c x + 1\right)}^{2}}{{\left(c x - 1\right)}^{2}} + \frac{2 \, {\left(c x + 1\right)}}{c x - 1} + 1\right)}} + \frac{\frac{2 \, {\left(c x + 1\right)} a c}{c x - 1} + \frac{{\left(c x + 1\right)} b c}{c x - 1} + b c}{\frac{{\left(c x + 1\right)}^{2}}{{\left(c x - 1\right)}^{2}} + \frac{2 \, {\left(c x + 1\right)}}{c x - 1} + 1}\right)} c"," ",0,"((c*x + 1)*b*c*log(-(c*x + 1)/(c*x - 1))/((c*x - 1)*((c*x + 1)^2/(c*x - 1)^2 + 2*(c*x + 1)/(c*x - 1) + 1)) + (2*(c*x + 1)*a*c/(c*x - 1) + (c*x + 1)*b*c/(c*x - 1) + b*c)/((c*x + 1)^2/(c*x - 1)^2 + 2*(c*x + 1)/(c*x - 1) + 1))*c","B",0
10,1,251,0,0.144311," ","integrate((a+b*arctanh(c*x))/x^4,x, algorithm=""giac"")","\frac{1}{3} \, {\left(b c^{2} \log\left(-\frac{c x + 1}{c x - 1} - 1\right) - b c^{2} \log\left(-\frac{c x + 1}{c x - 1}\right) + \frac{{\left(\frac{3 \, {\left(c x + 1\right)}^{2} b c^{2}}{{\left(c x - 1\right)}^{2}} + b c^{2}\right)} \log\left(-\frac{c x + 1}{c x - 1}\right)}{\frac{{\left(c x + 1\right)}^{3}}{{\left(c x - 1\right)}^{3}} + \frac{3 \, {\left(c x + 1\right)}^{2}}{{\left(c x - 1\right)}^{2}} + \frac{3 \, {\left(c x + 1\right)}}{c x - 1} + 1} + \frac{2 \, {\left(\frac{3 \, {\left(c x + 1\right)}^{2} a c^{2}}{{\left(c x - 1\right)}^{2}} + a c^{2} + \frac{{\left(c x + 1\right)}^{2} b c^{2}}{{\left(c x - 1\right)}^{2}} + \frac{{\left(c x + 1\right)} b c^{2}}{c x - 1}\right)}}{\frac{{\left(c x + 1\right)}^{3}}{{\left(c x - 1\right)}^{3}} + \frac{3 \, {\left(c x + 1\right)}^{2}}{{\left(c x - 1\right)}^{2}} + \frac{3 \, {\left(c x + 1\right)}}{c x - 1} + 1}\right)} c"," ",0,"1/3*(b*c^2*log(-(c*x + 1)/(c*x - 1) - 1) - b*c^2*log(-(c*x + 1)/(c*x - 1)) + (3*(c*x + 1)^2*b*c^2/(c*x - 1)^2 + b*c^2)*log(-(c*x + 1)/(c*x - 1))/((c*x + 1)^3/(c*x - 1)^3 + 3*(c*x + 1)^2/(c*x - 1)^2 + 3*(c*x + 1)/(c*x - 1) + 1) + 2*(3*(c*x + 1)^2*a*c^2/(c*x - 1)^2 + a*c^2 + (c*x + 1)^2*b*c^2/(c*x - 1)^2 + (c*x + 1)*b*c^2/(c*x - 1))/((c*x + 1)^3/(c*x - 1)^3 + 3*(c*x + 1)^2/(c*x - 1)^2 + 3*(c*x + 1)/(c*x - 1) + 1))*c","B",0
11,1,292,0,0.130241," ","integrate((a+b*arctanh(c*x))/x^5,x, algorithm=""giac"")","\frac{1}{3} \, c {\left(\frac{3 \, {\left(\frac{{\left(c x + 1\right)}^{3} b c^{3}}{{\left(c x - 1\right)}^{3}} + \frac{{\left(c x + 1\right)} b c^{3}}{c x - 1}\right)} \log\left(-\frac{c x + 1}{c x - 1}\right)}{\frac{{\left(c x + 1\right)}^{4}}{{\left(c x - 1\right)}^{4}} + \frac{4 \, {\left(c x + 1\right)}^{3}}{{\left(c x - 1\right)}^{3}} + \frac{6 \, {\left(c x + 1\right)}^{2}}{{\left(c x - 1\right)}^{2}} + \frac{4 \, {\left(c x + 1\right)}}{c x - 1} + 1} + \frac{\frac{6 \, {\left(c x + 1\right)}^{3} a c^{3}}{{\left(c x - 1\right)}^{3}} + \frac{6 \, {\left(c x + 1\right)} a c^{3}}{c x - 1} + \frac{3 \, {\left(c x + 1\right)}^{3} b c^{3}}{{\left(c x - 1\right)}^{3}} + \frac{6 \, {\left(c x + 1\right)}^{2} b c^{3}}{{\left(c x - 1\right)}^{2}} + \frac{5 \, {\left(c x + 1\right)} b c^{3}}{c x - 1} + 2 \, b c^{3}}{\frac{{\left(c x + 1\right)}^{4}}{{\left(c x - 1\right)}^{4}} + \frac{4 \, {\left(c x + 1\right)}^{3}}{{\left(c x - 1\right)}^{3}} + \frac{6 \, {\left(c x + 1\right)}^{2}}{{\left(c x - 1\right)}^{2}} + \frac{4 \, {\left(c x + 1\right)}}{c x - 1} + 1}\right)}"," ",0,"1/3*c*(3*((c*x + 1)^3*b*c^3/(c*x - 1)^3 + (c*x + 1)*b*c^3/(c*x - 1))*log(-(c*x + 1)/(c*x - 1))/((c*x + 1)^4/(c*x - 1)^4 + 4*(c*x + 1)^3/(c*x - 1)^3 + 6*(c*x + 1)^2/(c*x - 1)^2 + 4*(c*x + 1)/(c*x - 1) + 1) + (6*(c*x + 1)^3*a*c^3/(c*x - 1)^3 + 6*(c*x + 1)*a*c^3/(c*x - 1) + 3*(c*x + 1)^3*b*c^3/(c*x - 1)^3 + 6*(c*x + 1)^2*b*c^3/(c*x - 1)^2 + 5*(c*x + 1)*b*c^3/(c*x - 1) + 2*b*c^3)/((c*x + 1)^4/(c*x - 1)^4 + 4*(c*x + 1)^3/(c*x - 1)^3 + 6*(c*x + 1)^2/(c*x - 1)^2 + 4*(c*x + 1)/(c*x - 1) + 1))","B",0
12,1,397,0,0.158407," ","integrate((a+b*arctanh(c*x))/x^6,x, algorithm=""giac"")","\frac{1}{5} \, {\left(b c^{4} \log\left(-\frac{c x + 1}{c x - 1} - 1\right) - b c^{4} \log\left(-\frac{c x + 1}{c x - 1}\right) + \frac{{\left(\frac{5 \, {\left(c x + 1\right)}^{4} b c^{4}}{{\left(c x - 1\right)}^{4}} + \frac{10 \, {\left(c x + 1\right)}^{2} b c^{4}}{{\left(c x - 1\right)}^{2}} + b c^{4}\right)} \log\left(-\frac{c x + 1}{c x - 1}\right)}{\frac{{\left(c x + 1\right)}^{5}}{{\left(c x - 1\right)}^{5}} + \frac{5 \, {\left(c x + 1\right)}^{4}}{{\left(c x - 1\right)}^{4}} + \frac{10 \, {\left(c x + 1\right)}^{3}}{{\left(c x - 1\right)}^{3}} + \frac{10 \, {\left(c x + 1\right)}^{2}}{{\left(c x - 1\right)}^{2}} + \frac{5 \, {\left(c x + 1\right)}}{c x - 1} + 1} + \frac{2 \, {\left(\frac{5 \, {\left(c x + 1\right)}^{4} a c^{4}}{{\left(c x - 1\right)}^{4}} + \frac{10 \, {\left(c x + 1\right)}^{2} a c^{4}}{{\left(c x - 1\right)}^{2}} + a c^{4} + \frac{2 \, {\left(c x + 1\right)}^{4} b c^{4}}{{\left(c x - 1\right)}^{4}} + \frac{4 \, {\left(c x + 1\right)}^{3} b c^{4}}{{\left(c x - 1\right)}^{3}} + \frac{4 \, {\left(c x + 1\right)}^{2} b c^{4}}{{\left(c x - 1\right)}^{2}} + \frac{2 \, {\left(c x + 1\right)} b c^{4}}{c x - 1}\right)}}{\frac{{\left(c x + 1\right)}^{5}}{{\left(c x - 1\right)}^{5}} + \frac{5 \, {\left(c x + 1\right)}^{4}}{{\left(c x - 1\right)}^{4}} + \frac{10 \, {\left(c x + 1\right)}^{3}}{{\left(c x - 1\right)}^{3}} + \frac{10 \, {\left(c x + 1\right)}^{2}}{{\left(c x - 1\right)}^{2}} + \frac{5 \, {\left(c x + 1\right)}}{c x - 1} + 1}\right)} c"," ",0,"1/5*(b*c^4*log(-(c*x + 1)/(c*x - 1) - 1) - b*c^4*log(-(c*x + 1)/(c*x - 1)) + (5*(c*x + 1)^4*b*c^4/(c*x - 1)^4 + 10*(c*x + 1)^2*b*c^4/(c*x - 1)^2 + b*c^4)*log(-(c*x + 1)/(c*x - 1))/((c*x + 1)^5/(c*x - 1)^5 + 5*(c*x + 1)^4/(c*x - 1)^4 + 10*(c*x + 1)^3/(c*x - 1)^3 + 10*(c*x + 1)^2/(c*x - 1)^2 + 5*(c*x + 1)/(c*x - 1) + 1) + 2*(5*(c*x + 1)^4*a*c^4/(c*x - 1)^4 + 10*(c*x + 1)^2*a*c^4/(c*x - 1)^2 + a*c^4 + 2*(c*x + 1)^4*b*c^4/(c*x - 1)^4 + 4*(c*x + 1)^3*b*c^4/(c*x - 1)^3 + 4*(c*x + 1)^2*b*c^4/(c*x - 1)^2 + 2*(c*x + 1)*b*c^4/(c*x - 1))/((c*x + 1)^5/(c*x - 1)^5 + 5*(c*x + 1)^4/(c*x - 1)^4 + 10*(c*x + 1)^3/(c*x - 1)^3 + 10*(c*x + 1)^2/(c*x - 1)^2 + 5*(c*x + 1)/(c*x - 1) + 1))*c","B",0
13,1,889,0,0.176803," ","integrate(x^5*(a+b*arctanh(c*x))^2,x, algorithm=""giac"")","\frac{1}{90} \, {\left(\frac{15 \, {\left(\frac{3 \, {\left(c x + 1\right)}^{5} b^{2}}{{\left(c x - 1\right)}^{5}} + \frac{10 \, {\left(c x + 1\right)}^{3} b^{2}}{{\left(c x - 1\right)}^{3}} + \frac{3 \, {\left(c x + 1\right)} b^{2}}{c x - 1}\right)} \log\left(-\frac{c x + 1}{c x - 1}\right)^{2}}{\frac{{\left(c x + 1\right)}^{6} c^{7}}{{\left(c x - 1\right)}^{6}} - \frac{6 \, {\left(c x + 1\right)}^{5} c^{7}}{{\left(c x - 1\right)}^{5}} + \frac{15 \, {\left(c x + 1\right)}^{4} c^{7}}{{\left(c x - 1\right)}^{4}} - \frac{20 \, {\left(c x + 1\right)}^{3} c^{7}}{{\left(c x - 1\right)}^{3}} + \frac{15 \, {\left(c x + 1\right)}^{2} c^{7}}{{\left(c x - 1\right)}^{2}} - \frac{6 \, {\left(c x + 1\right)} c^{7}}{c x - 1} + c^{7}} + \frac{2 \, {\left(\frac{90 \, {\left(c x + 1\right)}^{5} a b}{{\left(c x - 1\right)}^{5}} + \frac{300 \, {\left(c x + 1\right)}^{3} a b}{{\left(c x - 1\right)}^{3}} + \frac{90 \, {\left(c x + 1\right)} a b}{c x - 1} + \frac{45 \, {\left(c x + 1\right)}^{5} b^{2}}{{\left(c x - 1\right)}^{5}} - \frac{135 \, {\left(c x + 1\right)}^{4} b^{2}}{{\left(c x - 1\right)}^{4}} + \frac{230 \, {\left(c x + 1\right)}^{3} b^{2}}{{\left(c x - 1\right)}^{3}} - \frac{210 \, {\left(c x + 1\right)}^{2} b^{2}}{{\left(c x - 1\right)}^{2}} + \frac{93 \, {\left(c x + 1\right)} b^{2}}{c x - 1} - 23 \, b^{2}\right)} \log\left(-\frac{c x + 1}{c x - 1}\right)}{\frac{{\left(c x + 1\right)}^{6} c^{7}}{{\left(c x - 1\right)}^{6}} - \frac{6 \, {\left(c x + 1\right)}^{5} c^{7}}{{\left(c x - 1\right)}^{5}} + \frac{15 \, {\left(c x + 1\right)}^{4} c^{7}}{{\left(c x - 1\right)}^{4}} - \frac{20 \, {\left(c x + 1\right)}^{3} c^{7}}{{\left(c x - 1\right)}^{3}} + \frac{15 \, {\left(c x + 1\right)}^{2} c^{7}}{{\left(c x - 1\right)}^{2}} - \frac{6 \, {\left(c x + 1\right)} c^{7}}{c x - 1} + c^{7}} + \frac{4 \, {\left(\frac{45 \, {\left(c x + 1\right)}^{5} a^{2}}{{\left(c x - 1\right)}^{5}} + \frac{150 \, {\left(c x + 1\right)}^{3} a^{2}}{{\left(c x - 1\right)}^{3}} + \frac{45 \, {\left(c x + 1\right)} a^{2}}{c x - 1} + \frac{45 \, {\left(c x + 1\right)}^{5} a b}{{\left(c x - 1\right)}^{5}} - \frac{135 \, {\left(c x + 1\right)}^{4} a b}{{\left(c x - 1\right)}^{4}} + \frac{230 \, {\left(c x + 1\right)}^{3} a b}{{\left(c x - 1\right)}^{3}} - \frac{210 \, {\left(c x + 1\right)}^{2} a b}{{\left(c x - 1\right)}^{2}} + \frac{93 \, {\left(c x + 1\right)} a b}{c x - 1} - 23 \, a b + \frac{11 \, {\left(c x + 1\right)}^{5} b^{2}}{{\left(c x - 1\right)}^{5}} - \frac{38 \, {\left(c x + 1\right)}^{4} b^{2}}{{\left(c x - 1\right)}^{4}} + \frac{54 \, {\left(c x + 1\right)}^{3} b^{2}}{{\left(c x - 1\right)}^{3}} - \frac{38 \, {\left(c x + 1\right)}^{2} b^{2}}{{\left(c x - 1\right)}^{2}} + \frac{11 \, {\left(c x + 1\right)} b^{2}}{c x - 1}\right)}}{\frac{{\left(c x + 1\right)}^{6} c^{7}}{{\left(c x - 1\right)}^{6}} - \frac{6 \, {\left(c x + 1\right)}^{5} c^{7}}{{\left(c x - 1\right)}^{5}} + \frac{15 \, {\left(c x + 1\right)}^{4} c^{7}}{{\left(c x - 1\right)}^{4}} - \frac{20 \, {\left(c x + 1\right)}^{3} c^{7}}{{\left(c x - 1\right)}^{3}} + \frac{15 \, {\left(c x + 1\right)}^{2} c^{7}}{{\left(c x - 1\right)}^{2}} - \frac{6 \, {\left(c x + 1\right)} c^{7}}{c x - 1} + c^{7}} - \frac{46 \, b^{2} \log\left(-\frac{c x + 1}{c x - 1} + 1\right)}{c^{7}} + \frac{46 \, b^{2} \log\left(-\frac{c x + 1}{c x - 1}\right)}{c^{7}}\right)} c"," ",0,"1/90*(15*(3*(c*x + 1)^5*b^2/(c*x - 1)^5 + 10*(c*x + 1)^3*b^2/(c*x - 1)^3 + 3*(c*x + 1)*b^2/(c*x - 1))*log(-(c*x + 1)/(c*x - 1))^2/((c*x + 1)^6*c^7/(c*x - 1)^6 - 6*(c*x + 1)^5*c^7/(c*x - 1)^5 + 15*(c*x + 1)^4*c^7/(c*x - 1)^4 - 20*(c*x + 1)^3*c^7/(c*x - 1)^3 + 15*(c*x + 1)^2*c^7/(c*x - 1)^2 - 6*(c*x + 1)*c^7/(c*x - 1) + c^7) + 2*(90*(c*x + 1)^5*a*b/(c*x - 1)^5 + 300*(c*x + 1)^3*a*b/(c*x - 1)^3 + 90*(c*x + 1)*a*b/(c*x - 1) + 45*(c*x + 1)^5*b^2/(c*x - 1)^5 - 135*(c*x + 1)^4*b^2/(c*x - 1)^4 + 230*(c*x + 1)^3*b^2/(c*x - 1)^3 - 210*(c*x + 1)^2*b^2/(c*x - 1)^2 + 93*(c*x + 1)*b^2/(c*x - 1) - 23*b^2)*log(-(c*x + 1)/(c*x - 1))/((c*x + 1)^6*c^7/(c*x - 1)^6 - 6*(c*x + 1)^5*c^7/(c*x - 1)^5 + 15*(c*x + 1)^4*c^7/(c*x - 1)^4 - 20*(c*x + 1)^3*c^7/(c*x - 1)^3 + 15*(c*x + 1)^2*c^7/(c*x - 1)^2 - 6*(c*x + 1)*c^7/(c*x - 1) + c^7) + 4*(45*(c*x + 1)^5*a^2/(c*x - 1)^5 + 150*(c*x + 1)^3*a^2/(c*x - 1)^3 + 45*(c*x + 1)*a^2/(c*x - 1) + 45*(c*x + 1)^5*a*b/(c*x - 1)^5 - 135*(c*x + 1)^4*a*b/(c*x - 1)^4 + 230*(c*x + 1)^3*a*b/(c*x - 1)^3 - 210*(c*x + 1)^2*a*b/(c*x - 1)^2 + 93*(c*x + 1)*a*b/(c*x - 1) - 23*a*b + 11*(c*x + 1)^5*b^2/(c*x - 1)^5 - 38*(c*x + 1)^4*b^2/(c*x - 1)^4 + 54*(c*x + 1)^3*b^2/(c*x - 1)^3 - 38*(c*x + 1)^2*b^2/(c*x - 1)^2 + 11*(c*x + 1)*b^2/(c*x - 1))/((c*x + 1)^6*c^7/(c*x - 1)^6 - 6*(c*x + 1)^5*c^7/(c*x - 1)^5 + 15*(c*x + 1)^4*c^7/(c*x - 1)^4 - 20*(c*x + 1)^3*c^7/(c*x - 1)^3 + 15*(c*x + 1)^2*c^7/(c*x - 1)^2 - 6*(c*x + 1)*c^7/(c*x - 1) + c^7) - 46*b^2*log(-(c*x + 1)/(c*x - 1) + 1)/c^7 + 46*b^2*log(-(c*x + 1)/(c*x - 1))/c^7)*c","B",0
14,0,0,0,0.000000," ","integrate(x^4*(a+b*arctanh(c*x))^2,x, algorithm=""giac"")","\int {\left(b \operatorname{artanh}\left(c x\right) + a\right)}^{2} x^{4}\,{d x}"," ",0,"integrate((b*arctanh(c*x) + a)^2*x^4, x)","F",0
15,1,603,0,0.167606," ","integrate(x^3*(a+b*arctanh(c*x))^2,x, algorithm=""giac"")","\frac{1}{6} \, {\left(\frac{3 \, {\left(\frac{{\left(c x + 1\right)}^{3} b^{2}}{{\left(c x - 1\right)}^{3}} + \frac{{\left(c x + 1\right)} b^{2}}{c x - 1}\right)} \log\left(-\frac{c x + 1}{c x - 1}\right)^{2}}{\frac{{\left(c x + 1\right)}^{4} c^{5}}{{\left(c x - 1\right)}^{4}} - \frac{4 \, {\left(c x + 1\right)}^{3} c^{5}}{{\left(c x - 1\right)}^{3}} + \frac{6 \, {\left(c x + 1\right)}^{2} c^{5}}{{\left(c x - 1\right)}^{2}} - \frac{4 \, {\left(c x + 1\right)} c^{5}}{c x - 1} + c^{5}} + \frac{2 \, {\left(\frac{6 \, {\left(c x + 1\right)}^{3} a b}{{\left(c x - 1\right)}^{3}} + \frac{6 \, {\left(c x + 1\right)} a b}{c x - 1} + \frac{3 \, {\left(c x + 1\right)}^{3} b^{2}}{{\left(c x - 1\right)}^{3}} - \frac{6 \, {\left(c x + 1\right)}^{2} b^{2}}{{\left(c x - 1\right)}^{2}} + \frac{5 \, {\left(c x + 1\right)} b^{2}}{c x - 1} - 2 \, b^{2}\right)} \log\left(-\frac{c x + 1}{c x - 1}\right)}{\frac{{\left(c x + 1\right)}^{4} c^{5}}{{\left(c x - 1\right)}^{4}} - \frac{4 \, {\left(c x + 1\right)}^{3} c^{5}}{{\left(c x - 1\right)}^{3}} + \frac{6 \, {\left(c x + 1\right)}^{2} c^{5}}{{\left(c x - 1\right)}^{2}} - \frac{4 \, {\left(c x + 1\right)} c^{5}}{c x - 1} + c^{5}} + \frac{2 \, {\left(\frac{6 \, {\left(c x + 1\right)}^{3} a^{2}}{{\left(c x - 1\right)}^{3}} + \frac{6 \, {\left(c x + 1\right)} a^{2}}{c x - 1} + \frac{6 \, {\left(c x + 1\right)}^{3} a b}{{\left(c x - 1\right)}^{3}} - \frac{12 \, {\left(c x + 1\right)}^{2} a b}{{\left(c x - 1\right)}^{2}} + \frac{10 \, {\left(c x + 1\right)} a b}{c x - 1} - 4 \, a b + \frac{{\left(c x + 1\right)}^{3} b^{2}}{{\left(c x - 1\right)}^{3}} - \frac{2 \, {\left(c x + 1\right)}^{2} b^{2}}{{\left(c x - 1\right)}^{2}} + \frac{{\left(c x + 1\right)} b^{2}}{c x - 1}\right)}}{\frac{{\left(c x + 1\right)}^{4} c^{5}}{{\left(c x - 1\right)}^{4}} - \frac{4 \, {\left(c x + 1\right)}^{3} c^{5}}{{\left(c x - 1\right)}^{3}} + \frac{6 \, {\left(c x + 1\right)}^{2} c^{5}}{{\left(c x - 1\right)}^{2}} - \frac{4 \, {\left(c x + 1\right)} c^{5}}{c x - 1} + c^{5}} - \frac{4 \, b^{2} \log\left(-\frac{c x + 1}{c x - 1} + 1\right)}{c^{5}} + \frac{4 \, b^{2} \log\left(-\frac{c x + 1}{c x - 1}\right)}{c^{5}}\right)} c"," ",0,"1/6*(3*((c*x + 1)^3*b^2/(c*x - 1)^3 + (c*x + 1)*b^2/(c*x - 1))*log(-(c*x + 1)/(c*x - 1))^2/((c*x + 1)^4*c^5/(c*x - 1)^4 - 4*(c*x + 1)^3*c^5/(c*x - 1)^3 + 6*(c*x + 1)^2*c^5/(c*x - 1)^2 - 4*(c*x + 1)*c^5/(c*x - 1) + c^5) + 2*(6*(c*x + 1)^3*a*b/(c*x - 1)^3 + 6*(c*x + 1)*a*b/(c*x - 1) + 3*(c*x + 1)^3*b^2/(c*x - 1)^3 - 6*(c*x + 1)^2*b^2/(c*x - 1)^2 + 5*(c*x + 1)*b^2/(c*x - 1) - 2*b^2)*log(-(c*x + 1)/(c*x - 1))/((c*x + 1)^4*c^5/(c*x - 1)^4 - 4*(c*x + 1)^3*c^5/(c*x - 1)^3 + 6*(c*x + 1)^2*c^5/(c*x - 1)^2 - 4*(c*x + 1)*c^5/(c*x - 1) + c^5) + 2*(6*(c*x + 1)^3*a^2/(c*x - 1)^3 + 6*(c*x + 1)*a^2/(c*x - 1) + 6*(c*x + 1)^3*a*b/(c*x - 1)^3 - 12*(c*x + 1)^2*a*b/(c*x - 1)^2 + 10*(c*x + 1)*a*b/(c*x - 1) - 4*a*b + (c*x + 1)^3*b^2/(c*x - 1)^3 - 2*(c*x + 1)^2*b^2/(c*x - 1)^2 + (c*x + 1)*b^2/(c*x - 1))/((c*x + 1)^4*c^5/(c*x - 1)^4 - 4*(c*x + 1)^3*c^5/(c*x - 1)^3 + 6*(c*x + 1)^2*c^5/(c*x - 1)^2 - 4*(c*x + 1)*c^5/(c*x - 1) + c^5) - 4*b^2*log(-(c*x + 1)/(c*x - 1) + 1)/c^5 + 4*b^2*log(-(c*x + 1)/(c*x - 1))/c^5)*c","B",0
16,0,0,0,0.000000," ","integrate(x^2*(a+b*arctanh(c*x))^2,x, algorithm=""giac"")","\int {\left(b \operatorname{artanh}\left(c x\right) + a\right)}^{2} x^{2}\,{d x}"," ",0,"integrate((b*arctanh(c*x) + a)^2*x^2, x)","F",0
17,1,301,0,0.161406," ","integrate(x*(a+b*arctanh(c*x))^2,x, algorithm=""giac"")","\frac{1}{2} \, {\left(\frac{{\left(c x + 1\right)} b^{2} \log\left(-\frac{c x + 1}{c x - 1}\right)^{2}}{{\left(\frac{{\left(c x + 1\right)}^{2} c^{3}}{{\left(c x - 1\right)}^{2}} - \frac{2 \, {\left(c x + 1\right)} c^{3}}{c x - 1} + c^{3}\right)} {\left(c x - 1\right)}} + \frac{2 \, {\left(\frac{2 \, {\left(c x + 1\right)} a b}{c x - 1} + \frac{{\left(c x + 1\right)} b^{2}}{c x - 1} - b^{2}\right)} \log\left(-\frac{c x + 1}{c x - 1}\right)}{\frac{{\left(c x + 1\right)}^{2} c^{3}}{{\left(c x - 1\right)}^{2}} - \frac{2 \, {\left(c x + 1\right)} c^{3}}{c x - 1} + c^{3}} + \frac{4 \, {\left(\frac{{\left(c x + 1\right)} a^{2}}{c x - 1} + \frac{{\left(c x + 1\right)} a b}{c x - 1} - a b\right)}}{\frac{{\left(c x + 1\right)}^{2} c^{3}}{{\left(c x - 1\right)}^{2}} - \frac{2 \, {\left(c x + 1\right)} c^{3}}{c x - 1} + c^{3}} - \frac{2 \, b^{2} \log\left(-\frac{c x + 1}{c x - 1} + 1\right)}{c^{3}} + \frac{2 \, b^{2} \log\left(-\frac{c x + 1}{c x - 1}\right)}{c^{3}}\right)} c"," ",0,"1/2*((c*x + 1)*b^2*log(-(c*x + 1)/(c*x - 1))^2/(((c*x + 1)^2*c^3/(c*x - 1)^2 - 2*(c*x + 1)*c^3/(c*x - 1) + c^3)*(c*x - 1)) + 2*(2*(c*x + 1)*a*b/(c*x - 1) + (c*x + 1)*b^2/(c*x - 1) - b^2)*log(-(c*x + 1)/(c*x - 1))/((c*x + 1)^2*c^3/(c*x - 1)^2 - 2*(c*x + 1)*c^3/(c*x - 1) + c^3) + 4*((c*x + 1)*a^2/(c*x - 1) + (c*x + 1)*a*b/(c*x - 1) - a*b)/((c*x + 1)^2*c^3/(c*x - 1)^2 - 2*(c*x + 1)*c^3/(c*x - 1) + c^3) - 2*b^2*log(-(c*x + 1)/(c*x - 1) + 1)/c^3 + 2*b^2*log(-(c*x + 1)/(c*x - 1))/c^3)*c","B",0
18,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x))^2,x, algorithm=""giac"")","\int {\left(b \operatorname{artanh}\left(c x\right) + a\right)}^{2}\,{d x}"," ",0,"integrate((b*arctanh(c*x) + a)^2, x)","F",0
19,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x))^2/x,x, algorithm=""giac"")","\int \frac{{\left(b \operatorname{artanh}\left(c x\right) + a\right)}^{2}}{x}\,{d x}"," ",0,"integrate((b*arctanh(c*x) + a)^2/x, x)","F",0
20,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x))^2/x^2,x, algorithm=""giac"")","\int \frac{{\left(b \operatorname{artanh}\left(c x\right) + a\right)}^{2}}{x^{2}}\,{d x}"," ",0,"integrate((b*arctanh(c*x) + a)^2/x^2, x)","F",0
21,1,278,0,0.158236," ","integrate((a+b*arctanh(c*x))^2/x^3,x, algorithm=""giac"")","\frac{1}{2} \, {\left(2 \, b^{2} c \log\left(-\frac{c x + 1}{c x - 1} - 1\right) - 2 \, b^{2} c \log\left(-\frac{c x + 1}{c x - 1}\right) + \frac{{\left(c x + 1\right)} b^{2} c \log\left(-\frac{c x + 1}{c x - 1}\right)^{2}}{{\left(c x - 1\right)} {\left(\frac{{\left(c x + 1\right)}^{2}}{{\left(c x - 1\right)}^{2}} + \frac{2 \, {\left(c x + 1\right)}}{c x - 1} + 1\right)}} + \frac{2 \, {\left(\frac{2 \, {\left(c x + 1\right)} a b c}{c x - 1} + \frac{{\left(c x + 1\right)} b^{2} c}{c x - 1} + b^{2} c\right)} \log\left(-\frac{c x + 1}{c x - 1}\right)}{\frac{{\left(c x + 1\right)}^{2}}{{\left(c x - 1\right)}^{2}} + \frac{2 \, {\left(c x + 1\right)}}{c x - 1} + 1} + \frac{4 \, {\left(\frac{{\left(c x + 1\right)} a^{2} c}{c x - 1} + \frac{{\left(c x + 1\right)} a b c}{c x - 1} + a b c\right)}}{\frac{{\left(c x + 1\right)}^{2}}{{\left(c x - 1\right)}^{2}} + \frac{2 \, {\left(c x + 1\right)}}{c x - 1} + 1}\right)} c"," ",0,"1/2*(2*b^2*c*log(-(c*x + 1)/(c*x - 1) - 1) - 2*b^2*c*log(-(c*x + 1)/(c*x - 1)) + (c*x + 1)*b^2*c*log(-(c*x + 1)/(c*x - 1))^2/((c*x - 1)*((c*x + 1)^2/(c*x - 1)^2 + 2*(c*x + 1)/(c*x - 1) + 1)) + 2*(2*(c*x + 1)*a*b*c/(c*x - 1) + (c*x + 1)*b^2*c/(c*x - 1) + b^2*c)*log(-(c*x + 1)/(c*x - 1))/((c*x + 1)^2/(c*x - 1)^2 + 2*(c*x + 1)/(c*x - 1) + 1) + 4*((c*x + 1)*a^2*c/(c*x - 1) + (c*x + 1)*a*b*c/(c*x - 1) + a*b*c)/((c*x + 1)^2/(c*x - 1)^2 + 2*(c*x + 1)/(c*x - 1) + 1))*c","B",0
22,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x))^2/x^4,x, algorithm=""giac"")","\int \frac{{\left(b \operatorname{artanh}\left(c x\right) + a\right)}^{2}}{x^{4}}\,{d x}"," ",0,"integrate((b*arctanh(c*x) + a)^2/x^4, x)","F",0
23,1,612,0,0.152930," ","integrate((a+b*arctanh(c*x))^2/x^5,x, algorithm=""giac"")","\frac{1}{6} \, {\left(4 \, b^{2} c^{3} \log\left(-\frac{c x + 1}{c x - 1} - 1\right) - 4 \, b^{2} c^{3} \log\left(-\frac{c x + 1}{c x - 1}\right) + \frac{3 \, {\left(\frac{{\left(c x + 1\right)}^{3} b^{2} c^{3}}{{\left(c x - 1\right)}^{3}} + \frac{{\left(c x + 1\right)} b^{2} c^{3}}{c x - 1}\right)} \log\left(-\frac{c x + 1}{c x - 1}\right)^{2}}{\frac{{\left(c x + 1\right)}^{4}}{{\left(c x - 1\right)}^{4}} + \frac{4 \, {\left(c x + 1\right)}^{3}}{{\left(c x - 1\right)}^{3}} + \frac{6 \, {\left(c x + 1\right)}^{2}}{{\left(c x - 1\right)}^{2}} + \frac{4 \, {\left(c x + 1\right)}}{c x - 1} + 1} + \frac{2 \, {\left(\frac{6 \, {\left(c x + 1\right)}^{3} a b c^{3}}{{\left(c x - 1\right)}^{3}} + \frac{6 \, {\left(c x + 1\right)} a b c^{3}}{c x - 1} + \frac{3 \, {\left(c x + 1\right)}^{3} b^{2} c^{3}}{{\left(c x - 1\right)}^{3}} + \frac{6 \, {\left(c x + 1\right)}^{2} b^{2} c^{3}}{{\left(c x - 1\right)}^{2}} + \frac{5 \, {\left(c x + 1\right)} b^{2} c^{3}}{c x - 1} + 2 \, b^{2} c^{3}\right)} \log\left(-\frac{c x + 1}{c x - 1}\right)}{\frac{{\left(c x + 1\right)}^{4}}{{\left(c x - 1\right)}^{4}} + \frac{4 \, {\left(c x + 1\right)}^{3}}{{\left(c x - 1\right)}^{3}} + \frac{6 \, {\left(c x + 1\right)}^{2}}{{\left(c x - 1\right)}^{2}} + \frac{4 \, {\left(c x + 1\right)}}{c x - 1} + 1} + \frac{2 \, {\left(\frac{6 \, {\left(c x + 1\right)}^{3} a^{2} c^{3}}{{\left(c x - 1\right)}^{3}} + \frac{6 \, {\left(c x + 1\right)} a^{2} c^{3}}{c x - 1} + \frac{6 \, {\left(c x + 1\right)}^{3} a b c^{3}}{{\left(c x - 1\right)}^{3}} + \frac{12 \, {\left(c x + 1\right)}^{2} a b c^{3}}{{\left(c x - 1\right)}^{2}} + \frac{10 \, {\left(c x + 1\right)} a b c^{3}}{c x - 1} + 4 \, a b c^{3} + \frac{{\left(c x + 1\right)}^{3} b^{2} c^{3}}{{\left(c x - 1\right)}^{3}} + \frac{2 \, {\left(c x + 1\right)}^{2} b^{2} c^{3}}{{\left(c x - 1\right)}^{2}} + \frac{{\left(c x + 1\right)} b^{2} c^{3}}{c x - 1}\right)}}{\frac{{\left(c x + 1\right)}^{4}}{{\left(c x - 1\right)}^{4}} + \frac{4 \, {\left(c x + 1\right)}^{3}}{{\left(c x - 1\right)}^{3}} + \frac{6 \, {\left(c x + 1\right)}^{2}}{{\left(c x - 1\right)}^{2}} + \frac{4 \, {\left(c x + 1\right)}}{c x - 1} + 1}\right)} c"," ",0,"1/6*(4*b^2*c^3*log(-(c*x + 1)/(c*x - 1) - 1) - 4*b^2*c^3*log(-(c*x + 1)/(c*x - 1)) + 3*((c*x + 1)^3*b^2*c^3/(c*x - 1)^3 + (c*x + 1)*b^2*c^3/(c*x - 1))*log(-(c*x + 1)/(c*x - 1))^2/((c*x + 1)^4/(c*x - 1)^4 + 4*(c*x + 1)^3/(c*x - 1)^3 + 6*(c*x + 1)^2/(c*x - 1)^2 + 4*(c*x + 1)/(c*x - 1) + 1) + 2*(6*(c*x + 1)^3*a*b*c^3/(c*x - 1)^3 + 6*(c*x + 1)*a*b*c^3/(c*x - 1) + 3*(c*x + 1)^3*b^2*c^3/(c*x - 1)^3 + 6*(c*x + 1)^2*b^2*c^3/(c*x - 1)^2 + 5*(c*x + 1)*b^2*c^3/(c*x - 1) + 2*b^2*c^3)*log(-(c*x + 1)/(c*x - 1))/((c*x + 1)^4/(c*x - 1)^4 + 4*(c*x + 1)^3/(c*x - 1)^3 + 6*(c*x + 1)^2/(c*x - 1)^2 + 4*(c*x + 1)/(c*x - 1) + 1) + 2*(6*(c*x + 1)^3*a^2*c^3/(c*x - 1)^3 + 6*(c*x + 1)*a^2*c^3/(c*x - 1) + 6*(c*x + 1)^3*a*b*c^3/(c*x - 1)^3 + 12*(c*x + 1)^2*a*b*c^3/(c*x - 1)^2 + 10*(c*x + 1)*a*b*c^3/(c*x - 1) + 4*a*b*c^3 + (c*x + 1)^3*b^2*c^3/(c*x - 1)^3 + 2*(c*x + 1)^2*b^2*c^3/(c*x - 1)^2 + (c*x + 1)*b^2*c^3/(c*x - 1))/((c*x + 1)^4/(c*x - 1)^4 + 4*(c*x + 1)^3/(c*x - 1)^3 + 6*(c*x + 1)^2/(c*x - 1)^2 + 4*(c*x + 1)/(c*x - 1) + 1))*c","B",0
24,0,0,0,0.000000," ","integrate(x^5*(a+b*arctanh(c*x))^3,x, algorithm=""giac"")","\int {\left(b \operatorname{artanh}\left(c x\right) + a\right)}^{3} x^{5}\,{d x}"," ",0,"integrate((b*arctanh(c*x) + a)^3*x^5, x)","F",0
25,0,0,0,0.000000," ","integrate(x^4*(a+b*arctanh(c*x))^3,x, algorithm=""giac"")","\int {\left(b \operatorname{artanh}\left(c x\right) + a\right)}^{3} x^{4}\,{d x}"," ",0,"integrate((b*arctanh(c*x) + a)^3*x^4, x)","F",0
26,0,0,0,0.000000," ","integrate(x^3*(a+b*arctanh(c*x))^3,x, algorithm=""giac"")","\int {\left(b \operatorname{artanh}\left(c x\right) + a\right)}^{3} x^{3}\,{d x}"," ",0,"integrate((b*arctanh(c*x) + a)^3*x^3, x)","F",0
27,0,0,0,0.000000," ","integrate(x^2*(a+b*arctanh(c*x))^3,x, algorithm=""giac"")","\int {\left(b \operatorname{artanh}\left(c x\right) + a\right)}^{3} x^{2}\,{d x}"," ",0,"integrate((b*arctanh(c*x) + a)^3*x^2, x)","F",0
28,0,0,0,0.000000," ","integrate(x*(a+b*arctanh(c*x))^3,x, algorithm=""giac"")","\int {\left(b \operatorname{artanh}\left(c x\right) + a\right)}^{3} x\,{d x}"," ",0,"integrate((b*arctanh(c*x) + a)^3*x, x)","F",0
29,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x))^3,x, algorithm=""giac"")","\int {\left(b \operatorname{artanh}\left(c x\right) + a\right)}^{3}\,{d x}"," ",0,"integrate((b*arctanh(c*x) + a)^3, x)","F",0
30,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x))^3/x,x, algorithm=""giac"")","\int \frac{{\left(b \operatorname{artanh}\left(c x\right) + a\right)}^{3}}{x}\,{d x}"," ",0,"integrate((b*arctanh(c*x) + a)^3/x, x)","F",0
31,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x))^3/x^2,x, algorithm=""giac"")","\int \frac{{\left(b \operatorname{artanh}\left(c x\right) + a\right)}^{3}}{x^{2}}\,{d x}"," ",0,"integrate((b*arctanh(c*x) + a)^3/x^2, x)","F",0
32,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x))^3/x^3,x, algorithm=""giac"")","\int \frac{{\left(b \operatorname{artanh}\left(c x\right) + a\right)}^{3}}{x^{3}}\,{d x}"," ",0,"integrate((b*arctanh(c*x) + a)^3/x^3, x)","F",0
33,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x))^3/x^4,x, algorithm=""giac"")","\int \frac{{\left(b \operatorname{artanh}\left(c x\right) + a\right)}^{3}}{x^{4}}\,{d x}"," ",0,"integrate((b*arctanh(c*x) + a)^3/x^4, x)","F",0
34,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x))^3/x^5,x, algorithm=""giac"")","\int \frac{{\left(b \operatorname{artanh}\left(c x\right) + a\right)}^{3}}{x^{5}}\,{d x}"," ",0,"integrate((b*arctanh(c*x) + a)^3/x^5, x)","F",0
35,0,0,0,0.000000," ","integrate((d*x)^(5/2)*(a+b*arctanh(c*x)),x, algorithm=""giac"")","\int \left(d x\right)^{\frac{5}{2}} {\left(b \operatorname{artanh}\left(c x\right) + a\right)}\,{d x}"," ",0,"integrate((d*x)^(5/2)*(b*arctanh(c*x) + a), x)","F",0
36,0,0,0,0.000000," ","integrate((d*x)^(3/2)*(a+b*arctanh(c*x)),x, algorithm=""giac"")","\int \left(d x\right)^{\frac{3}{2}} {\left(b \operatorname{artanh}\left(c x\right) + a\right)}\,{d x}"," ",0,"integrate((d*x)^(3/2)*(b*arctanh(c*x) + a), x)","F",0
37,0,0,0,0.000000," ","integrate((d*x)^(1/2)*(a+b*arctanh(c*x)),x, algorithm=""giac"")","\int \sqrt{d x} {\left(b \operatorname{artanh}\left(c x\right) + a\right)}\,{d x}"," ",0,"integrate(sqrt(d*x)*(b*arctanh(c*x) + a), x)","F",0
38,1,88,0,0.151982," ","integrate((a+b*arctanh(c*x))/(d*x)^(1/2),x, algorithm=""giac"")","\frac{{\left(2 \, c d {\left(\frac{\arctan\left(\frac{\sqrt{d x} c}{\sqrt{c d}}\right)}{\sqrt{c d} c} + \frac{\arctan\left(\frac{\sqrt{d x} c}{\sqrt{-c d}}\right)}{\sqrt{-c d} c}\right)} + \sqrt{d x} \log\left(-\frac{c x + 1}{c x - 1}\right)\right)} b + 2 \, \sqrt{d x} a}{d}"," ",0,"((2*c*d*(arctan(sqrt(d*x)*c/sqrt(c*d))/(sqrt(c*d)*c) + arctan(sqrt(d*x)*c/sqrt(-c*d))/(sqrt(-c*d)*c)) + sqrt(d*x)*log(-(c*x + 1)/(c*x - 1)))*b + 2*sqrt(d*x)*a)/d","A",0
39,1,93,0,0.172198," ","integrate((a+b*arctanh(c*x))/(d*x)^(3/2),x, algorithm=""giac"")","\frac{2 \, b c d {\left(\frac{\arctan\left(\frac{\sqrt{d x} c}{\sqrt{c d}}\right)}{\sqrt{c d} d} - \frac{\arctan\left(\frac{\sqrt{d x} c}{\sqrt{-c d}}\right)}{\sqrt{-c d} d}\right)} - \frac{b \log\left(-\frac{c d x + d}{c d x - d}\right)}{\sqrt{d x}} - \frac{2 \, a}{\sqrt{d x}}}{d}"," ",0,"(2*b*c*d*(arctan(sqrt(d*x)*c/sqrt(c*d))/(sqrt(c*d)*d) - arctan(sqrt(d*x)*c/sqrt(-c*d))/(sqrt(-c*d)*d)) - b*log(-(c*d*x + d)/(c*d*x - d))/sqrt(d*x) - 2*a/sqrt(d*x))/d","A",0
40,1,117,0,0.186131," ","integrate((a+b*arctanh(c*x))/(d*x)^(5/2),x, algorithm=""giac"")","-\frac{\frac{2 \, b c^{2} \arctan\left(\frac{\sqrt{d x} c}{\sqrt{c d}}\right)}{\sqrt{c d} d} + \frac{2 \, b c^{2} \arctan\left(\frac{\sqrt{d x} c}{\sqrt{-c d}}\right)}{\sqrt{-c d} d} + \frac{b \log\left(-\frac{c d x + d}{c d x - d}\right)}{\sqrt{d x} d x} + \frac{2 \, {\left(2 \, b c d x + a d\right)}}{\sqrt{d x} d^{2} x}}{3 \, d}"," ",0,"-1/3*(2*b*c^2*arctan(sqrt(d*x)*c/sqrt(c*d))/(sqrt(c*d)*d) + 2*b*c^2*arctan(sqrt(d*x)*c/sqrt(-c*d))/(sqrt(-c*d)*d) + b*log(-(c*d*x + d)/(c*d*x - d))/(sqrt(d*x)*d*x) + 2*(2*b*c*d*x + a*d)/(sqrt(d*x)*d^2*x))/d","A",0
41,1,117,0,0.202350," ","integrate((a+b*arctanh(c*x))/(d*x)^(7/2),x, algorithm=""giac"")","\frac{6 \, b c^{3} {\left(\frac{\arctan\left(\frac{\sqrt{d x} c}{\sqrt{c d}}\right)}{\sqrt{c d} d^{2}} - \frac{\arctan\left(\frac{\sqrt{d x} c}{\sqrt{-c d}}\right)}{\sqrt{-c d} d^{2}}\right)} - \frac{3 \, b \log\left(-\frac{c d x + d}{c d x - d}\right)}{\sqrt{d x} d^{2} x^{2}} - \frac{2 \, {\left(2 \, b c d x + 3 \, a d\right)}}{\sqrt{d x} d^{3} x^{2}}}{15 \, d}"," ",0,"1/15*(6*b*c^3*(arctan(sqrt(d*x)*c/sqrt(c*d))/(sqrt(c*d)*d^2) - arctan(sqrt(d*x)*c/sqrt(-c*d))/(sqrt(-c*d)*d^2)) - 3*b*log(-(c*d*x + d)/(c*d*x - d))/(sqrt(d*x)*d^2*x^2) - 2*(2*b*c*d*x + 3*a*d)/(sqrt(d*x)*d^3*x^2))/d","A",0
42,1,135,0,0.204031," ","integrate((a+b*arctanh(c*x))/(d*x)^(9/2),x, algorithm=""giac"")","-\frac{\frac{10 \, b c^{4} \arctan\left(\frac{\sqrt{d x} c}{\sqrt{c d}}\right)}{\sqrt{c d} d^{3}} + \frac{10 \, b c^{4} \arctan\left(\frac{\sqrt{d x} c}{\sqrt{-c d}}\right)}{\sqrt{-c d} d^{3}} + \frac{5 \, b \log\left(-\frac{c d x + d}{c d x - d}\right)}{\sqrt{d x} d^{3} x^{3}} + \frac{2 \, {\left(10 \, b c^{3} d^{3} x^{3} + 2 \, b c d^{3} x + 5 \, a d^{3}\right)}}{\sqrt{d x} d^{6} x^{3}}}{35 \, d}"," ",0,"-1/35*(10*b*c^4*arctan(sqrt(d*x)*c/sqrt(c*d))/(sqrt(c*d)*d^3) + 10*b*c^4*arctan(sqrt(d*x)*c/sqrt(-c*d))/(sqrt(-c*d)*d^3) + 5*b*log(-(c*d*x + d)/(c*d*x - d))/(sqrt(d*x)*d^3*x^3) + 2*(10*b*c^3*d^3*x^3 + 2*b*c*d^3*x + 5*a*d^3)/(sqrt(d*x)*d^6*x^3))/d","A",0
43,0,0,0,0.000000," ","integrate((d*x)^m*(a+b*arctanh(c*x))^3,x, algorithm=""giac"")","\int {\left(b \operatorname{artanh}\left(c x\right) + a\right)}^{3} \left(d x\right)^{m}\,{d x}"," ",0,"integrate((b*arctanh(c*x) + a)^3*(d*x)^m, x)","F",0
44,0,0,0,0.000000," ","integrate((d*x)^m*(a+b*arctanh(c*x))^2,x, algorithm=""giac"")","\int {\left(b \operatorname{artanh}\left(c x\right) + a\right)}^{2} \left(d x\right)^{m}\,{d x}"," ",0,"integrate((b*arctanh(c*x) + a)^2*(d*x)^m, x)","F",0
45,0,0,0,0.000000," ","integrate((d*x)^m*(a+b*arctanh(c*x)),x, algorithm=""giac"")","\int {\left(b \operatorname{artanh}\left(c x\right) + a\right)} \left(d x\right)^{m}\,{d x}"," ",0,"integrate((b*arctanh(c*x) + a)*(d*x)^m, x)","F",0
46,0,0,0,0.000000," ","integrate((d*x)^m/(a+b*arctanh(c*x)),x, algorithm=""giac"")","\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=""giac"")","\int \frac{\left(d x\right)^{m}}{{\left(b \operatorname{artanh}\left(c x\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((d*x)^m/(b*arctanh(c*x) + a)^2, x)","F",0
48,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x))^p,x, algorithm=""giac"")","\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=""giac"")","\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
50,1,78,0,0.160573," ","integrate(x^7*(a+b*arctanh(c*x^2)),x, algorithm=""giac"")","\frac{1}{16} \, b x^{8} \log\left(-\frac{c x^{2} + 1}{c x^{2} - 1}\right) + \frac{1}{8} \, a x^{8} + \frac{b x^{6}}{24 \, c} + \frac{b x^{2}}{8 \, c^{3}} - \frac{b \log\left(c x^{2} + 1\right)}{16 \, c^{4}} + \frac{b \log\left(c x^{2} - 1\right)}{16 \, c^{4}}"," ",0,"1/16*b*x^8*log(-(c*x^2 + 1)/(c*x^2 - 1)) + 1/8*a*x^8 + 1/24*b*x^6/c + 1/8*b*x^2/c^3 - 1/16*b*log(c*x^2 + 1)/c^4 + 1/16*b*log(c*x^2 - 1)/c^4","A",0
51,1,57,0,0.132311," ","integrate(x^5*(a+b*arctanh(c*x^2)),x, algorithm=""giac"")","\frac{1}{12} \, b x^{6} \log\left(-\frac{c x^{2} + 1}{c x^{2} - 1}\right) + \frac{1}{6} \, a x^{6} + \frac{b x^{4}}{12 \, c} + \frac{b \log\left(c^{2} x^{4} - 1\right)}{12 \, c^{3}}"," ",0,"1/12*b*x^6*log(-(c*x^2 + 1)/(c*x^2 - 1)) + 1/6*a*x^6 + 1/12*b*x^4/c + 1/12*b*log(c^2*x^4 - 1)/c^3","A",0
52,1,181,0,0.162453," ","integrate(x^3*(a+b*arctanh(c*x^2)),x, algorithm=""giac"")","\frac{1}{2} \, c {\left(\frac{{\left(c x^{2} + 1\right)} b \log\left(-\frac{c x^{2} + 1}{c x^{2} - 1}\right)}{{\left(\frac{{\left(c x^{2} + 1\right)}^{2} c^{3}}{{\left(c x^{2} - 1\right)}^{2}} - \frac{2 \, {\left(c x^{2} + 1\right)} c^{3}}{c x^{2} - 1} + c^{3}\right)} {\left(c x^{2} - 1\right)}} + \frac{\frac{2 \, {\left(c x^{2} + 1\right)} a}{c x^{2} - 1} + \frac{{\left(c x^{2} + 1\right)} b}{c x^{2} - 1} - b}{\frac{{\left(c x^{2} + 1\right)}^{2} c^{3}}{{\left(c x^{2} - 1\right)}^{2}} - \frac{2 \, {\left(c x^{2} + 1\right)} c^{3}}{c x^{2} - 1} + c^{3}}\right)}"," ",0,"1/2*c*((c*x^2 + 1)*b*log(-(c*x^2 + 1)/(c*x^2 - 1))/(((c*x^2 + 1)^2*c^3/(c*x^2 - 1)^2 - 2*(c*x^2 + 1)*c^3/(c*x^2 - 1) + c^3)*(c*x^2 - 1)) + (2*(c*x^2 + 1)*a/(c*x^2 - 1) + (c*x^2 + 1)*b/(c*x^2 - 1) - b)/((c*x^2 + 1)^2*c^3/(c*x^2 - 1)^2 - 2*(c*x^2 + 1)*c^3/(c*x^2 - 1) + c^3))","B",0
53,1,188,0,0.150506," ","integrate(x*(a+b*arctanh(c*x^2)),x, algorithm=""giac"")","\frac{1}{2} \, a x^{2} + \frac{1}{2} \, b c {\left(\frac{\log\left(\frac{{\left| -c x^{2} - 1 \right|}}{{\left| c x^{2} - 1 \right|}}\right)}{c^{2}} - \frac{\log\left({\left| -\frac{c x^{2} + 1}{c x^{2} - 1} + 1 \right|}\right)}{c^{2}} + \frac{\log\left(-\frac{\frac{c {\left(\frac{c x^{2} + 1}{c x^{2} - 1} + 1\right)}}{\frac{{\left(c x^{2} + 1\right)} c}{c x^{2} - 1} - c} + 1}{\frac{c {\left(\frac{c x^{2} + 1}{c x^{2} - 1} + 1\right)}}{\frac{{\left(c x^{2} + 1\right)} c}{c x^{2} - 1} - c} - 1}\right)}{c^{2} {\left(\frac{c x^{2} + 1}{c x^{2} - 1} - 1\right)}}\right)}"," ",0,"1/2*a*x^2 + 1/2*b*c*(log(abs(-c*x^2 - 1)/abs(c*x^2 - 1))/c^2 - log(abs(-(c*x^2 + 1)/(c*x^2 - 1) + 1))/c^2 + log(-(c*((c*x^2 + 1)/(c*x^2 - 1) + 1)/((c*x^2 + 1)*c/(c*x^2 - 1) - c) + 1)/(c*((c*x^2 + 1)/(c*x^2 - 1) + 1)/((c*x^2 + 1)*c/(c*x^2 - 1) - c) - 1))/(c^2*((c*x^2 + 1)/(c*x^2 - 1) - 1)))","B",0
54,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x^2))/x,x, algorithm=""giac"")","\int \frac{b \operatorname{artanh}\left(c x^{2}\right) + a}{x}\,{d x}"," ",0,"integrate((b*arctanh(c*x^2) + a)/x, x)","F",0
55,1,51,0,0.147887," ","integrate((a+b*arctanh(c*x^2))/x^3,x, algorithm=""giac"")","-\frac{1}{4} \, b c \log\left(c^{2} x^{4} - 1\right) + b c \log\left(x\right) - \frac{b \log\left(-\frac{c x^{2} + 1}{c x^{2} - 1}\right)}{4 \, x^{2}} - \frac{a}{2 \, x^{2}}"," ",0,"-1/4*b*c*log(c^2*x^4 - 1) + b*c*log(x) - 1/4*b*log(-(c*x^2 + 1)/(c*x^2 - 1))/x^2 - 1/2*a/x^2","A",0
56,1,67,0,0.137659," ","integrate((a+b*arctanh(c*x^2))/x^5,x, algorithm=""giac"")","\frac{1}{8} \, b c^{2} \log\left(c x^{2} + 1\right) - \frac{1}{8} \, b c^{2} \log\left(c x^{2} - 1\right) - \frac{b \log\left(-\frac{c x^{2} + 1}{c x^{2} - 1}\right)}{8 \, x^{4}} - \frac{b c x^{2} + a}{4 \, x^{4}}"," ",0,"1/8*b*c^2*log(c*x^2 + 1) - 1/8*b*c^2*log(c*x^2 - 1) - 1/8*b*log(-(c*x^2 + 1)/(c*x^2 - 1))/x^4 - 1/4*(b*c*x^2 + a)/x^4","A",0
57,1,65,0,0.150396," ","integrate((a+b*arctanh(c*x^2))/x^7,x, algorithm=""giac"")","-\frac{1}{12} \, b c^{3} \log\left(c^{2} x^{4} - 1\right) + \frac{1}{3} \, b c^{3} \log\left(x\right) - \frac{b \log\left(-\frac{c x^{2} + 1}{c x^{2} - 1}\right)}{12 \, x^{6}} - \frac{b c x^{2} + 2 \, a}{12 \, x^{6}}"," ",0,"-1/12*b*c^3*log(c^2*x^4 - 1) + 1/3*b*c^3*log(x) - 1/12*b*log(-(c*x^2 + 1)/(c*x^2 - 1))/x^6 - 1/12*(b*c*x^2 + 2*a)/x^6","A",0
58,1,73,0,0.394163," ","integrate(x^4*(a+b*arctanh(c*x^2)),x, algorithm=""giac"")","\frac{1}{10} \, b x^{5} \log\left(-\frac{c x^{2} + 1}{c x^{2} - 1}\right) + \frac{1}{5} \, a x^{5} + \frac{2 \, b x^{3}}{15 \, c} + \frac{b \arctan\left(\sqrt{c} x\right)}{5 \, c^{\frac{5}{2}}} + \frac{b \arctan\left(\frac{c x}{\sqrt{-c}}\right)}{5 \, \sqrt{-c} c^{2}}"," ",0,"1/10*b*x^5*log(-(c*x^2 + 1)/(c*x^2 - 1)) + 1/5*a*x^5 + 2/15*b*x^3/c + 1/5*b*arctan(sqrt(c)*x)/c^(5/2) + 1/5*b*arctan(c*x/sqrt(-c))/(sqrt(-c)*c^2)","A",0
59,1,75,0,0.295791," ","integrate(x^2*(a+b*arctanh(c*x^2)),x, algorithm=""giac"")","-\frac{1}{3} \, b c^{5} {\left(\frac{\arctan\left(\sqrt{c} x\right)}{c^{\frac{13}{2}}} - \frac{\arctan\left(\frac{c x}{\sqrt{-c}}\right)}{\sqrt{-c} c^{6}}\right)} + \frac{1}{6} \, b x^{3} \log\left(-\frac{c x^{2} + 1}{c x^{2} - 1}\right) + \frac{1}{3} \, a x^{3} + \frac{2 \, b x}{3 \, c}"," ",0,"-1/3*b*c^5*(arctan(sqrt(c)*x)/c^(13/2) - arctan(c*x/sqrt(-c))/(sqrt(-c)*c^6)) + 1/6*b*x^3*log(-(c*x^2 + 1)/(c*x^2 - 1)) + 1/3*a*x^3 + 2/3*b*x/c","A",0
60,1,83,0,0.128972," ","integrate(a+b*arctanh(c*x^2),x, algorithm=""giac"")","\frac{1}{2} \, {\left(c {\left(\frac{2 \, \sqrt{{\left| c \right|}} \arctan\left(x \sqrt{{\left| c \right|}}\right)}{c^{2}} - \frac{\sqrt{{\left| c \right|}} \log\left({\left| x + \frac{1}{\sqrt{{\left| c \right|}}} \right|}\right)}{c^{2}} + \frac{\sqrt{{\left| c \right|}} \log\left({\left| x - \frac{1}{\sqrt{{\left| c \right|}}} \right|}\right)}{c^{2}}\right)} + x \log\left(-\frac{c x^{2} + 1}{c x^{2} - 1}\right)\right)} b + a x"," ",0,"1/2*(c*(2*sqrt(abs(c))*arctan(x*sqrt(abs(c)))/c^2 - sqrt(abs(c))*log(abs(x + 1/sqrt(abs(c))))/c^2 + sqrt(abs(c))*log(abs(x - 1/sqrt(abs(c))))/c^2) + x*log(-(c*x^2 + 1)/(c*x^2 - 1)))*b + a*x","B",0
61,1,79,0,0.169914," ","integrate((a+b*arctanh(c*x^2))/x^2,x, algorithm=""giac"")","\frac{1}{2} \, b c {\left(\frac{2 \, \arctan\left(x \sqrt{{\left| c \right|}}\right)}{\sqrt{{\left| c \right|}}} + \frac{\log\left({\left| x + \frac{1}{\sqrt{{\left| c \right|}}} \right|}\right)}{\sqrt{{\left| c \right|}}} - \frac{\log\left({\left| x - \frac{1}{\sqrt{{\left| c \right|}}} \right|}\right)}{\sqrt{{\left| c \right|}}}\right)} - \frac{b \log\left(-\frac{c x^{2} + 1}{c x^{2} - 1}\right)}{2 \, x} - \frac{a}{x}"," ",0,"1/2*b*c*(2*arctan(x*sqrt(abs(c)))/sqrt(abs(c)) + log(abs(x + 1/sqrt(abs(c))))/sqrt(abs(c)) - log(abs(x - 1/sqrt(abs(c))))/sqrt(abs(c))) - 1/2*b*log(-(c*x^2 + 1)/(c*x^2 - 1))/x - a/x","B",0
62,1,93,0,0.181676," ","integrate((a+b*arctanh(c*x^2))/x^4,x, algorithm=""giac"")","-\frac{b c^{3} \arctan\left(x \sqrt{{\left| c \right|}}\right)}{3 \, {\left| c \right|}^{\frac{3}{2}}} + \frac{1}{6} \, b c \sqrt{{\left| c \right|}} \log\left({\left| x + \frac{1}{\sqrt{{\left| c \right|}}} \right|}\right) - \frac{b c^{3} \log\left({\left| x - \frac{1}{\sqrt{{\left| c \right|}}} \right|}\right)}{6 \, {\left| c \right|}^{\frac{3}{2}}} - \frac{b \log\left(-\frac{c x^{2} + 1}{c x^{2} - 1}\right)}{6 \, x^{3}} - \frac{2 \, b c x^{2} + a}{3 \, x^{3}}"," ",0,"-1/3*b*c^3*arctan(x*sqrt(abs(c)))/abs(c)^(3/2) + 1/6*b*c*sqrt(abs(c))*log(abs(x + 1/sqrt(abs(c)))) - 1/6*b*c^3*log(abs(x - 1/sqrt(abs(c))))/abs(c)^(3/2) - 1/6*b*log(-(c*x^2 + 1)/(c*x^2 - 1))/x^3 - 1/3*(2*b*c*x^2 + a)/x^3","A",0
63,1,91,0,0.218588," ","integrate((a+b*arctanh(c*x^2))/x^6,x, algorithm=""giac"")","\frac{1}{10} \, b c^{3} {\left(\frac{2 \, \arctan\left(x \sqrt{{\left| c \right|}}\right)}{\sqrt{{\left| c \right|}}} + \frac{\log\left({\left| x + \frac{1}{\sqrt{{\left| c \right|}}} \right|}\right)}{\sqrt{{\left| c \right|}}} - \frac{\log\left({\left| x - \frac{1}{\sqrt{{\left| c \right|}}} \right|}\right)}{\sqrt{{\left| c \right|}}}\right)} - \frac{b \log\left(-\frac{c x^{2} + 1}{c x^{2} - 1}\right)}{10 \, x^{5}} - \frac{2 \, b c x^{2} + 3 \, a}{15 \, x^{5}}"," ",0,"1/10*b*c^3*(2*arctan(x*sqrt(abs(c)))/sqrt(abs(c)) + log(abs(x + 1/sqrt(abs(c))))/sqrt(abs(c)) - log(abs(x - 1/sqrt(abs(c))))/sqrt(abs(c))) - 1/10*b*log(-(c*x^2 + 1)/(c*x^2 - 1))/x^5 - 1/15*(2*b*c*x^2 + 3*a)/x^5","A",0
64,1,175,0,0.279579," ","integrate(x^7*(a+b*arctanh(c*x^2))^2,x, algorithm=""giac"")","\frac{1}{8} \, a^{2} x^{8} + \frac{a b x^{6}}{12 \, c} + \frac{b^{2} x^{4}}{24 \, c^{2}} + \frac{1}{32} \, {\left(b^{2} x^{8} - \frac{b^{2}}{c^{4}}\right)} \log\left(-\frac{c x^{2} + 1}{c x^{2} - 1}\right)^{2} + \frac{1}{24} \, {\left(3 \, a b x^{8} + \frac{b^{2} x^{6}}{c} + \frac{3 \, b^{2} x^{2}}{c^{3}}\right)} \log\left(-\frac{c x^{2} + 1}{c x^{2} - 1}\right) + \frac{a b x^{2}}{4 \, c^{3}} - \frac{{\left(3 \, a b - 4 \, b^{2}\right)} \log\left(c x^{2} + 1\right)}{24 \, c^{4}} + \frac{{\left(3 \, a b + 4 \, b^{2}\right)} \log\left(c x^{2} - 1\right)}{24 \, c^{4}}"," ",0,"1/8*a^2*x^8 + 1/12*a*b*x^6/c + 1/24*b^2*x^4/c^2 + 1/32*(b^2*x^8 - b^2/c^4)*log(-(c*x^2 + 1)/(c*x^2 - 1))^2 + 1/24*(3*a*b*x^8 + b^2*x^6/c + 3*b^2*x^2/c^3)*log(-(c*x^2 + 1)/(c*x^2 - 1)) + 1/4*a*b*x^2/c^3 - 1/24*(3*a*b - 4*b^2)*log(c*x^2 + 1)/c^4 + 1/24*(3*a*b + 4*b^2)*log(c*x^2 - 1)/c^4","A",0
65,0,0,0,0.000000," ","integrate(x^5*(a+b*arctanh(c*x^2))^2,x, algorithm=""giac"")","\int {\left(b \operatorname{artanh}\left(c x^{2}\right) + a\right)}^{2} x^{5}\,{d x}"," ",0,"integrate((b*arctanh(c*x^2) + a)^2*x^5, x)","F",0
66,1,361,0,0.190713," ","integrate(x^3*(a+b*arctanh(c*x^2))^2,x, algorithm=""giac"")","\frac{1}{4} \, {\left(\frac{{\left(c x^{2} + 1\right)} b^{2} \log\left(-\frac{c x^{2} + 1}{c x^{2} - 1}\right)^{2}}{{\left(\frac{{\left(c x^{2} + 1\right)}^{2} c^{3}}{{\left(c x^{2} - 1\right)}^{2}} - \frac{2 \, {\left(c x^{2} + 1\right)} c^{3}}{c x^{2} - 1} + c^{3}\right)} {\left(c x^{2} - 1\right)}} + \frac{2 \, {\left(\frac{2 \, {\left(c x^{2} + 1\right)} a b}{c x^{2} - 1} + \frac{{\left(c x^{2} + 1\right)} b^{2}}{c x^{2} - 1} - b^{2}\right)} \log\left(-\frac{c x^{2} + 1}{c x^{2} - 1}\right)}{\frac{{\left(c x^{2} + 1\right)}^{2} c^{3}}{{\left(c x^{2} - 1\right)}^{2}} - \frac{2 \, {\left(c x^{2} + 1\right)} c^{3}}{c x^{2} - 1} + c^{3}} + \frac{4 \, {\left(\frac{{\left(c x^{2} + 1\right)} a^{2}}{c x^{2} - 1} + \frac{{\left(c x^{2} + 1\right)} a b}{c x^{2} - 1} - a b\right)}}{\frac{{\left(c x^{2} + 1\right)}^{2} c^{3}}{{\left(c x^{2} - 1\right)}^{2}} - \frac{2 \, {\left(c x^{2} + 1\right)} c^{3}}{c x^{2} - 1} + c^{3}} - \frac{2 \, b^{2} \log\left(-\frac{c x^{2} + 1}{c x^{2} - 1} + 1\right)}{c^{3}} + \frac{2 \, b^{2} \log\left(-\frac{c x^{2} + 1}{c x^{2} - 1}\right)}{c^{3}}\right)} c"," ",0,"1/4*((c*x^2 + 1)*b^2*log(-(c*x^2 + 1)/(c*x^2 - 1))^2/(((c*x^2 + 1)^2*c^3/(c*x^2 - 1)^2 - 2*(c*x^2 + 1)*c^3/(c*x^2 - 1) + c^3)*(c*x^2 - 1)) + 2*(2*(c*x^2 + 1)*a*b/(c*x^2 - 1) + (c*x^2 + 1)*b^2/(c*x^2 - 1) - b^2)*log(-(c*x^2 + 1)/(c*x^2 - 1))/((c*x^2 + 1)^2*c^3/(c*x^2 - 1)^2 - 2*(c*x^2 + 1)*c^3/(c*x^2 - 1) + c^3) + 4*((c*x^2 + 1)*a^2/(c*x^2 - 1) + (c*x^2 + 1)*a*b/(c*x^2 - 1) - a*b)/((c*x^2 + 1)^2*c^3/(c*x^2 - 1)^2 - 2*(c*x^2 + 1)*c^3/(c*x^2 - 1) + c^3) - 2*b^2*log(-(c*x^2 + 1)/(c*x^2 - 1) + 1)/c^3 + 2*b^2*log(-(c*x^2 + 1)/(c*x^2 - 1))/c^3)*c","B",0
67,0,0,0,0.000000," ","integrate(x*(a+b*arctanh(c*x^2))^2,x, algorithm=""giac"")","\int {\left(b \operatorname{artanh}\left(c x^{2}\right) + a\right)}^{2} x\,{d x}"," ",0,"integrate((b*arctanh(c*x^2) + a)^2*x, x)","F",0
68,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x^2))^2/x,x, algorithm=""giac"")","\int \frac{{\left(b \operatorname{artanh}\left(c x^{2}\right) + a\right)}^{2}}{x}\,{d x}"," ",0,"integrate((b*arctanh(c*x^2) + a)^2/x, x)","F",0
69,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x^2))^2/x^3,x, algorithm=""giac"")","\int \frac{{\left(b \operatorname{artanh}\left(c x^{2}\right) + a\right)}^{2}}{x^{3}}\,{d x}"," ",0,"integrate((b*arctanh(c*x^2) + a)^2/x^3, x)","F",0
70,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x^2))^2/x^5,x, algorithm=""giac"")","\int \frac{{\left(b \operatorname{artanh}\left(c x^{2}\right) + a\right)}^{2}}{x^{5}}\,{d x}"," ",0,"integrate((b*arctanh(c*x^2) + a)^2/x^5, x)","F",0
71,0,0,0,0.000000," ","integrate(x^4*(a+b*arctanh(c*x^2))^2,x, algorithm=""giac"")","\int {\left(b \operatorname{artanh}\left(c x^{2}\right) + a\right)}^{2} x^{4}\,{d x}"," ",0,"integrate((b*arctanh(c*x^2) + a)^2*x^4, x)","F",0
72,0,0,0,0.000000," ","integrate(x^2*(a+b*arctanh(c*x^2))^2,x, algorithm=""giac"")","\int {\left(b \operatorname{artanh}\left(c x^{2}\right) + a\right)}^{2} x^{2}\,{d x}"," ",0,"integrate((b*arctanh(c*x^2) + a)^2*x^2, x)","F",0
73,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x^2))^2,x, algorithm=""giac"")","\int {\left(b \operatorname{artanh}\left(c x^{2}\right) + a\right)}^{2}\,{d x}"," ",0,"integrate((b*arctanh(c*x^2) + a)^2, x)","F",0
74,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x^2))^2/x^2,x, algorithm=""giac"")","\int \frac{{\left(b \operatorname{artanh}\left(c x^{2}\right) + a\right)}^{2}}{x^{2}}\,{d x}"," ",0,"integrate((b*arctanh(c*x^2) + a)^2/x^2, x)","F",0
75,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x^2))^2/x^4,x, algorithm=""giac"")","\int \frac{{\left(b \operatorname{artanh}\left(c x^{2}\right) + a\right)}^{2}}{x^{4}}\,{d x}"," ",0,"integrate((b*arctanh(c*x^2) + a)^2/x^4, x)","F",0
76,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x^2))^2/x^6,x, algorithm=""giac"")","\int \frac{{\left(b \operatorname{artanh}\left(c x^{2}\right) + a\right)}^{2}}{x^{6}}\,{d x}"," ",0,"integrate((b*arctanh(c*x^2) + a)^2/x^6, x)","F",0
77,0,0,0,0.000000," ","integrate(x^3*(a+b*arctanh(c*x^2))^3,x, algorithm=""giac"")","\int {\left(b \operatorname{artanh}\left(c x^{2}\right) + a\right)}^{3} x^{3}\,{d x}"," ",0,"integrate((b*arctanh(c*x^2) + a)^3*x^3, x)","F",0
78,0,0,0,0.000000," ","integrate(x*(a+b*arctanh(c*x^2))^3,x, algorithm=""giac"")","\int {\left(b \operatorname{artanh}\left(c x^{2}\right) + a\right)}^{3} x\,{d x}"," ",0,"integrate((b*arctanh(c*x^2) + a)^3*x, x)","F",0
79,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x^2))^3/x,x, algorithm=""giac"")","\int \frac{{\left(b \operatorname{artanh}\left(c x^{2}\right) + a\right)}^{3}}{x}\,{d x}"," ",0,"integrate((b*arctanh(c*x^2) + a)^3/x, x)","F",0
80,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x^2))^3/x^3,x, algorithm=""giac"")","\int \frac{{\left(b \operatorname{artanh}\left(c x^{2}\right) + a\right)}^{3}}{x^{3}}\,{d x}"," ",0,"integrate((b*arctanh(c*x^2) + a)^3/x^3, x)","F",0
81,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x^2))^3/x^5,x, algorithm=""giac"")","\int \frac{{\left(b \operatorname{artanh}\left(c x^{2}\right) + a\right)}^{3}}{x^{5}}\,{d x}"," ",0,"integrate((b*arctanh(c*x^2) + a)^3/x^5, x)","F",0
82,0,0,0,0.000000," ","integrate((d*x)^(5/2)*(a+b*arctanh(c*x^2)),x, algorithm=""giac"")","\int \left(d x\right)^{\frac{5}{2}} {\left(b \operatorname{artanh}\left(c x^{2}\right) + a\right)}\,{d x}"," ",0,"integrate((d*x)^(5/2)*(b*arctanh(c*x^2) + a), x)","F",0
83,0,0,0,0.000000," ","integrate((d*x)^(3/2)*(a+b*arctanh(c*x^2)),x, algorithm=""giac"")","\int \left(d x\right)^{\frac{3}{2}} {\left(b \operatorname{artanh}\left(c x^{2}\right) + a\right)}\,{d x}"," ",0,"integrate((d*x)^(3/2)*(b*arctanh(c*x^2) + a), x)","F",0
84,0,0,0,0.000000," ","integrate((d*x)^(1/2)*(a+b*arctanh(c*x^2)),x, algorithm=""giac"")","\int \sqrt{d x} {\left(b \operatorname{artanh}\left(c x^{2}\right) + a\right)}\,{d x}"," ",0,"integrate(sqrt(d*x)*(b*arctanh(c*x^2) + a), x)","F",0
85,1,493,0,0.164178," ","integrate((a+b*arctanh(c*x^2))/(d*x)^(1/2),x, algorithm=""giac"")","\frac{{\left(c d^{2} {\left(\frac{2 \, \sqrt{2} \left(c^{3} d^{2}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{d^{2}}{c}\right)^{\frac{1}{4}} + 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{d^{2}}{c}\right)^{\frac{1}{4}}}\right)}{c^{2} d^{2}} + \frac{2 \, \sqrt{2} \left(c^{3} d^{2}\right)^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{d^{2}}{c}\right)^{\frac{1}{4}} - 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{d^{2}}{c}\right)^{\frac{1}{4}}}\right)}{c^{2} d^{2}} - \frac{2 \, \sqrt{2} \left(-c^{3} d^{2}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(-\frac{d^{2}}{c}\right)^{\frac{1}{4}} + 2 \, \sqrt{d x}\right)}}{2 \, \left(-\frac{d^{2}}{c}\right)^{\frac{1}{4}}}\right)}{c^{2} d^{2}} - \frac{2 \, \sqrt{2} \left(-c^{3} d^{2}\right)^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(-\frac{d^{2}}{c}\right)^{\frac{1}{4}} - 2 \, \sqrt{d x}\right)}}{2 \, \left(-\frac{d^{2}}{c}\right)^{\frac{1}{4}}}\right)}{c^{2} d^{2}} + \frac{\sqrt{2} \left(c^{3} d^{2}\right)^{\frac{1}{4}} \log\left(d x + \sqrt{2} \sqrt{d x} \left(\frac{d^{2}}{c}\right)^{\frac{1}{4}} + \sqrt{\frac{d^{2}}{c}}\right)}{c^{2} d^{2}} - \frac{\sqrt{2} \left(c^{3} d^{2}\right)^{\frac{1}{4}} \log\left(d x - \sqrt{2} \sqrt{d x} \left(\frac{d^{2}}{c}\right)^{\frac{1}{4}} + \sqrt{\frac{d^{2}}{c}}\right)}{c^{2} d^{2}} - \frac{\sqrt{2} \left(-c^{3} d^{2}\right)^{\frac{1}{4}} \log\left(d x + \sqrt{2} \sqrt{d x} \left(-\frac{d^{2}}{c}\right)^{\frac{1}{4}} + \sqrt{-\frac{d^{2}}{c}}\right)}{c^{2} d^{2}} + \frac{\sqrt{2} \left(-c^{3} d^{2}\right)^{\frac{1}{4}} \log\left(d x - \sqrt{2} \sqrt{d x} \left(-\frac{d^{2}}{c}\right)^{\frac{1}{4}} + \sqrt{-\frac{d^{2}}{c}}\right)}{c^{2} d^{2}}\right)} + 2 \, \sqrt{d x} \log\left(-\frac{c x^{2} + 1}{c x^{2} - 1}\right)\right)} b + 4 \, \sqrt{d x} a}{2 \, d}"," ",0,"1/2*((c*d^2*(2*sqrt(2)*(c^3*d^2)^(1/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(d^2/c)^(1/4) + 2*sqrt(d*x))/(d^2/c)^(1/4))/(c^2*d^2) + 2*sqrt(2)*(c^3*d^2)^(1/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(d^2/c)^(1/4) - 2*sqrt(d*x))/(d^2/c)^(1/4))/(c^2*d^2) - 2*sqrt(2)*(-c^3*d^2)^(1/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(-d^2/c)^(1/4) + 2*sqrt(d*x))/(-d^2/c)^(1/4))/(c^2*d^2) - 2*sqrt(2)*(-c^3*d^2)^(1/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(-d^2/c)^(1/4) - 2*sqrt(d*x))/(-d^2/c)^(1/4))/(c^2*d^2) + sqrt(2)*(c^3*d^2)^(1/4)*log(d*x + sqrt(2)*sqrt(d*x)*(d^2/c)^(1/4) + sqrt(d^2/c))/(c^2*d^2) - sqrt(2)*(c^3*d^2)^(1/4)*log(d*x - sqrt(2)*sqrt(d*x)*(d^2/c)^(1/4) + sqrt(d^2/c))/(c^2*d^2) - sqrt(2)*(-c^3*d^2)^(1/4)*log(d*x + sqrt(2)*sqrt(d*x)*(-d^2/c)^(1/4) + sqrt(-d^2/c))/(c^2*d^2) + sqrt(2)*(-c^3*d^2)^(1/4)*log(d*x - sqrt(2)*sqrt(d*x)*(-d^2/c)^(1/4) + sqrt(-d^2/c))/(c^2*d^2)) + 2*sqrt(d*x)*log(-(c*x^2 + 1)/(c*x^2 - 1)))*b + 4*sqrt(d*x)*a)/d","B",0
86,1,505,0,0.850612," ","integrate((a+b*arctanh(c*x^2))/(d*x)^(3/2),x, algorithm=""giac"")","-\frac{\frac{2 \, b \log\left(-\frac{c d^{2} x^{2} + d^{2}}{c d^{2} x^{2} - d^{2}}\right)}{\sqrt{d x}} + \frac{4 \, a}{\sqrt{d x}} - \frac{2 \, \sqrt{2} \left(c^{3} d^{2}\right)^{\frac{3}{4}} b \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{d^{2}}{c}\right)^{\frac{1}{4}} + 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{d^{2}}{c}\right)^{\frac{1}{4}}}\right)}{c^{2} d^{2}} - \frac{2 \, \sqrt{2} \left(c^{3} d^{2}\right)^{\frac{3}{4}} b \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{d^{2}}{c}\right)^{\frac{1}{4}} - 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{d^{2}}{c}\right)^{\frac{1}{4}}}\right)}{c^{2} d^{2}} - \frac{2 \, \sqrt{2} \left(-c^{3} d^{2}\right)^{\frac{3}{4}} b \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(-\frac{d^{2}}{c}\right)^{\frac{1}{4}} + 2 \, \sqrt{d x}\right)}}{2 \, \left(-\frac{d^{2}}{c}\right)^{\frac{1}{4}}}\right)}{c^{2} d^{2}} - \frac{2 \, \sqrt{2} \left(-c^{3} d^{2}\right)^{\frac{3}{4}} b \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(-\frac{d^{2}}{c}\right)^{\frac{1}{4}} - 2 \, \sqrt{d x}\right)}}{2 \, \left(-\frac{d^{2}}{c}\right)^{\frac{1}{4}}}\right)}{c^{2} d^{2}} + \frac{\sqrt{2} \left(c^{3} d^{2}\right)^{\frac{3}{4}} b \log\left(d x + \sqrt{2} \sqrt{d x} \left(\frac{d^{2}}{c}\right)^{\frac{1}{4}} + \sqrt{\frac{d^{2}}{c}}\right)}{c^{2} d^{2}} - \frac{\sqrt{2} \left(c^{3} d^{2}\right)^{\frac{3}{4}} b \log\left(d x - \sqrt{2} \sqrt{d x} \left(\frac{d^{2}}{c}\right)^{\frac{1}{4}} + \sqrt{\frac{d^{2}}{c}}\right)}{c^{2} d^{2}} + \frac{\sqrt{2} \left(-c^{3} d^{2}\right)^{\frac{3}{4}} b \log\left(d x + \sqrt{2} \sqrt{d x} \left(-\frac{d^{2}}{c}\right)^{\frac{1}{4}} + \sqrt{-\frac{d^{2}}{c}}\right)}{c^{2} d^{2}} - \frac{\sqrt{2} \left(-c^{3} d^{2}\right)^{\frac{3}{4}} b \log\left(d x - \sqrt{2} \sqrt{d x} \left(-\frac{d^{2}}{c}\right)^{\frac{1}{4}} + \sqrt{-\frac{d^{2}}{c}}\right)}{c^{2} d^{2}}}{2 \, d}"," ",0,"-1/2*(2*b*log(-(c*d^2*x^2 + d^2)/(c*d^2*x^2 - d^2))/sqrt(d*x) + 4*a/sqrt(d*x) - 2*sqrt(2)*(c^3*d^2)^(3/4)*b*arctan(1/2*sqrt(2)*(sqrt(2)*(d^2/c)^(1/4) + 2*sqrt(d*x))/(d^2/c)^(1/4))/(c^2*d^2) - 2*sqrt(2)*(c^3*d^2)^(3/4)*b*arctan(-1/2*sqrt(2)*(sqrt(2)*(d^2/c)^(1/4) - 2*sqrt(d*x))/(d^2/c)^(1/4))/(c^2*d^2) - 2*sqrt(2)*(-c^3*d^2)^(3/4)*b*arctan(1/2*sqrt(2)*(sqrt(2)*(-d^2/c)^(1/4) + 2*sqrt(d*x))/(-d^2/c)^(1/4))/(c^2*d^2) - 2*sqrt(2)*(-c^3*d^2)^(3/4)*b*arctan(-1/2*sqrt(2)*(sqrt(2)*(-d^2/c)^(1/4) - 2*sqrt(d*x))/(-d^2/c)^(1/4))/(c^2*d^2) + sqrt(2)*(c^3*d^2)^(3/4)*b*log(d*x + sqrt(2)*sqrt(d*x)*(d^2/c)^(1/4) + sqrt(d^2/c))/(c^2*d^2) - sqrt(2)*(c^3*d^2)^(3/4)*b*log(d*x - sqrt(2)*sqrt(d*x)*(d^2/c)^(1/4) + sqrt(d^2/c))/(c^2*d^2) + sqrt(2)*(-c^3*d^2)^(3/4)*b*log(d*x + sqrt(2)*sqrt(d*x)*(-d^2/c)^(1/4) + sqrt(-d^2/c))/(c^2*d^2) - sqrt(2)*(-c^3*d^2)^(3/4)*b*log(d*x - sqrt(2)*sqrt(d*x)*(-d^2/c)^(1/4) + sqrt(-d^2/c))/(c^2*d^2))/d","B",0
87,1,516,0,0.732441," ","integrate((a+b*arctanh(c*x^2))/(d*x)^(5/2),x, algorithm=""giac"")","\frac{b c d^{2} {\left(\frac{2 \, \sqrt{2} \left(c^{3} d^{2}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{d^{2}}{c}\right)^{\frac{1}{4}} + 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{d^{2}}{c}\right)^{\frac{1}{4}}}\right)}{c d^{4}} + \frac{2 \, \sqrt{2} \left(c^{3} d^{2}\right)^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{d^{2}}{c}\right)^{\frac{1}{4}} - 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{d^{2}}{c}\right)^{\frac{1}{4}}}\right)}{c d^{4}} + \frac{2 \, \sqrt{2} \left(-c^{3} d^{2}\right)^{\frac{1}{4}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(-\frac{d^{2}}{c}\right)^{\frac{1}{4}} + 2 \, \sqrt{d x}\right)}}{2 \, \left(-\frac{d^{2}}{c}\right)^{\frac{1}{4}}}\right)}{c d^{4}} + \frac{2 \, \sqrt{2} \left(-c^{3} d^{2}\right)^{\frac{1}{4}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(-\frac{d^{2}}{c}\right)^{\frac{1}{4}} - 2 \, \sqrt{d x}\right)}}{2 \, \left(-\frac{d^{2}}{c}\right)^{\frac{1}{4}}}\right)}{c d^{4}} + \frac{\sqrt{2} \left(c^{3} d^{2}\right)^{\frac{1}{4}} \log\left(d x + \sqrt{2} \sqrt{d x} \left(\frac{d^{2}}{c}\right)^{\frac{1}{4}} + \sqrt{\frac{d^{2}}{c}}\right)}{c d^{4}} - \frac{\sqrt{2} \left(c^{3} d^{2}\right)^{\frac{1}{4}} \log\left(d x - \sqrt{2} \sqrt{d x} \left(\frac{d^{2}}{c}\right)^{\frac{1}{4}} + \sqrt{\frac{d^{2}}{c}}\right)}{c d^{4}} + \frac{\sqrt{2} \left(-c^{3} d^{2}\right)^{\frac{1}{4}} \log\left(d x + \sqrt{2} \sqrt{d x} \left(-\frac{d^{2}}{c}\right)^{\frac{1}{4}} + \sqrt{-\frac{d^{2}}{c}}\right)}{c d^{4}} - \frac{\sqrt{2} \left(-c^{3} d^{2}\right)^{\frac{1}{4}} \log\left(d x - \sqrt{2} \sqrt{d x} \left(-\frac{d^{2}}{c}\right)^{\frac{1}{4}} + \sqrt{-\frac{d^{2}}{c}}\right)}{c d^{4}}\right)} - \frac{2 \, b \log\left(-\frac{c d^{2} x^{2} + d^{2}}{c d^{2} x^{2} - d^{2}}\right)}{\sqrt{d x} d x} - \frac{4 \, a}{\sqrt{d x} d x}}{6 \, d}"," ",0,"1/6*(b*c*d^2*(2*sqrt(2)*(c^3*d^2)^(1/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(d^2/c)^(1/4) + 2*sqrt(d*x))/(d^2/c)^(1/4))/(c*d^4) + 2*sqrt(2)*(c^3*d^2)^(1/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(d^2/c)^(1/4) - 2*sqrt(d*x))/(d^2/c)^(1/4))/(c*d^4) + 2*sqrt(2)*(-c^3*d^2)^(1/4)*arctan(1/2*sqrt(2)*(sqrt(2)*(-d^2/c)^(1/4) + 2*sqrt(d*x))/(-d^2/c)^(1/4))/(c*d^4) + 2*sqrt(2)*(-c^3*d^2)^(1/4)*arctan(-1/2*sqrt(2)*(sqrt(2)*(-d^2/c)^(1/4) - 2*sqrt(d*x))/(-d^2/c)^(1/4))/(c*d^4) + sqrt(2)*(c^3*d^2)^(1/4)*log(d*x + sqrt(2)*sqrt(d*x)*(d^2/c)^(1/4) + sqrt(d^2/c))/(c*d^4) - sqrt(2)*(c^3*d^2)^(1/4)*log(d*x - sqrt(2)*sqrt(d*x)*(d^2/c)^(1/4) + sqrt(d^2/c))/(c*d^4) + sqrt(2)*(-c^3*d^2)^(1/4)*log(d*x + sqrt(2)*sqrt(d*x)*(-d^2/c)^(1/4) + sqrt(-d^2/c))/(c*d^4) - sqrt(2)*(-c^3*d^2)^(1/4)*log(d*x - sqrt(2)*sqrt(d*x)*(-d^2/c)^(1/4) + sqrt(-d^2/c))/(c*d^4)) - 2*b*log(-(c*d^2*x^2 + d^2)/(c*d^2*x^2 - d^2))/(sqrt(d*x)*d*x) - 4*a/(sqrt(d*x)*d*x))/d","B",0
88,1,532,0,2.612924," ","integrate((a+b*arctanh(c*x^2))/(d*x)^(7/2),x, algorithm=""giac"")","-\frac{\frac{2 \, \sqrt{2} \left(c^{3} d^{2}\right)^{\frac{3}{4}} b \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{d^{2}}{c}\right)^{\frac{1}{4}} + 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{d^{2}}{c}\right)^{\frac{1}{4}}}\right)}{c d^{4}} + \frac{2 \, \sqrt{2} \left(c^{3} d^{2}\right)^{\frac{3}{4}} b \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{d^{2}}{c}\right)^{\frac{1}{4}} - 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{d^{2}}{c}\right)^{\frac{1}{4}}}\right)}{c d^{4}} - \frac{2 \, \sqrt{2} \left(-c^{3} d^{2}\right)^{\frac{3}{4}} b \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(-\frac{d^{2}}{c}\right)^{\frac{1}{4}} + 2 \, \sqrt{d x}\right)}}{2 \, \left(-\frac{d^{2}}{c}\right)^{\frac{1}{4}}}\right)}{c d^{4}} - \frac{2 \, \sqrt{2} \left(-c^{3} d^{2}\right)^{\frac{3}{4}} b \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(-\frac{d^{2}}{c}\right)^{\frac{1}{4}} - 2 \, \sqrt{d x}\right)}}{2 \, \left(-\frac{d^{2}}{c}\right)^{\frac{1}{4}}}\right)}{c d^{4}} - \frac{\sqrt{2} \left(c^{3} d^{2}\right)^{\frac{3}{4}} b \log\left(d x + \sqrt{2} \sqrt{d x} \left(\frac{d^{2}}{c}\right)^{\frac{1}{4}} + \sqrt{\frac{d^{2}}{c}}\right)}{c d^{4}} + \frac{\sqrt{2} \left(c^{3} d^{2}\right)^{\frac{3}{4}} b \log\left(d x - \sqrt{2} \sqrt{d x} \left(\frac{d^{2}}{c}\right)^{\frac{1}{4}} + \sqrt{\frac{d^{2}}{c}}\right)}{c d^{4}} + \frac{\sqrt{2} \left(-c^{3} d^{2}\right)^{\frac{3}{4}} b \log\left(d x + \sqrt{2} \sqrt{d x} \left(-\frac{d^{2}}{c}\right)^{\frac{1}{4}} + \sqrt{-\frac{d^{2}}{c}}\right)}{c d^{4}} - \frac{\sqrt{2} \left(-c^{3} d^{2}\right)^{\frac{3}{4}} b \log\left(d x - \sqrt{2} \sqrt{d x} \left(-\frac{d^{2}}{c}\right)^{\frac{1}{4}} + \sqrt{-\frac{d^{2}}{c}}\right)}{c d^{4}} + \frac{2 \, b \log\left(-\frac{c d^{2} x^{2} + d^{2}}{c d^{2} x^{2} - d^{2}}\right)}{\sqrt{d x} d^{2} x^{2}} + \frac{4 \, {\left(4 \, b c d^{2} x^{2} + a d^{2}\right)}}{\sqrt{d x} d^{4} x^{2}}}{10 \, d}"," ",0,"-1/10*(2*sqrt(2)*(c^3*d^2)^(3/4)*b*arctan(1/2*sqrt(2)*(sqrt(2)*(d^2/c)^(1/4) + 2*sqrt(d*x))/(d^2/c)^(1/4))/(c*d^4) + 2*sqrt(2)*(c^3*d^2)^(3/4)*b*arctan(-1/2*sqrt(2)*(sqrt(2)*(d^2/c)^(1/4) - 2*sqrt(d*x))/(d^2/c)^(1/4))/(c*d^4) - 2*sqrt(2)*(-c^3*d^2)^(3/4)*b*arctan(1/2*sqrt(2)*(sqrt(2)*(-d^2/c)^(1/4) + 2*sqrt(d*x))/(-d^2/c)^(1/4))/(c*d^4) - 2*sqrt(2)*(-c^3*d^2)^(3/4)*b*arctan(-1/2*sqrt(2)*(sqrt(2)*(-d^2/c)^(1/4) - 2*sqrt(d*x))/(-d^2/c)^(1/4))/(c*d^4) - sqrt(2)*(c^3*d^2)^(3/4)*b*log(d*x + sqrt(2)*sqrt(d*x)*(d^2/c)^(1/4) + sqrt(d^2/c))/(c*d^4) + sqrt(2)*(c^3*d^2)^(3/4)*b*log(d*x - sqrt(2)*sqrt(d*x)*(d^2/c)^(1/4) + sqrt(d^2/c))/(c*d^4) + sqrt(2)*(-c^3*d^2)^(3/4)*b*log(d*x + sqrt(2)*sqrt(d*x)*(-d^2/c)^(1/4) + sqrt(-d^2/c))/(c*d^4) - sqrt(2)*(-c^3*d^2)^(3/4)*b*log(d*x - sqrt(2)*sqrt(d*x)*(-d^2/c)^(1/4) + sqrt(-d^2/c))/(c*d^4) + 2*b*log(-(c*d^2*x^2 + d^2)/(c*d^2*x^2 - d^2))/(sqrt(d*x)*d^2*x^2) + 4*(4*b*c*d^2*x^2 + a*d^2)/(sqrt(d*x)*d^4*x^2))/d","B",0
89,1,519,0,7.782936," ","integrate((a+b*arctanh(c*x^2))/(d*x)^(9/2),x, algorithm=""giac"")","-\frac{\frac{6 \, \sqrt{2} \left(c^{3} d^{2}\right)^{\frac{1}{4}} b c \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{d^{2}}{c}\right)^{\frac{1}{4}} + 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{d^{2}}{c}\right)^{\frac{1}{4}}}\right)}{d^{4}} + \frac{6 \, \sqrt{2} \left(c^{3} d^{2}\right)^{\frac{1}{4}} b c \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(\frac{d^{2}}{c}\right)^{\frac{1}{4}} - 2 \, \sqrt{d x}\right)}}{2 \, \left(\frac{d^{2}}{c}\right)^{\frac{1}{4}}}\right)}{d^{4}} - \frac{6 \, \sqrt{2} \left(-c^{3} d^{2}\right)^{\frac{1}{4}} b c \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \left(-\frac{d^{2}}{c}\right)^{\frac{1}{4}} + 2 \, \sqrt{d x}\right)}}{2 \, \left(-\frac{d^{2}}{c}\right)^{\frac{1}{4}}}\right)}{d^{4}} - \frac{6 \, \sqrt{2} \left(-c^{3} d^{2}\right)^{\frac{1}{4}} b c \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \left(-\frac{d^{2}}{c}\right)^{\frac{1}{4}} - 2 \, \sqrt{d x}\right)}}{2 \, \left(-\frac{d^{2}}{c}\right)^{\frac{1}{4}}}\right)}{d^{4}} + \frac{3 \, \sqrt{2} \left(c^{3} d^{2}\right)^{\frac{1}{4}} b c \log\left(d x + \sqrt{2} \sqrt{d x} \left(\frac{d^{2}}{c}\right)^{\frac{1}{4}} + \sqrt{\frac{d^{2}}{c}}\right)}{d^{4}} - \frac{3 \, \sqrt{2} \left(c^{3} d^{2}\right)^{\frac{1}{4}} b c \log\left(d x - \sqrt{2} \sqrt{d x} \left(\frac{d^{2}}{c}\right)^{\frac{1}{4}} + \sqrt{\frac{d^{2}}{c}}\right)}{d^{4}} - \frac{3 \, \sqrt{2} \left(-c^{3} d^{2}\right)^{\frac{1}{4}} b c \log\left(d x + \sqrt{2} \sqrt{d x} \left(-\frac{d^{2}}{c}\right)^{\frac{1}{4}} + \sqrt{-\frac{d^{2}}{c}}\right)}{d^{4}} + \frac{3 \, \sqrt{2} \left(-c^{3} d^{2}\right)^{\frac{1}{4}} b c \log\left(d x - \sqrt{2} \sqrt{d x} \left(-\frac{d^{2}}{c}\right)^{\frac{1}{4}} + \sqrt{-\frac{d^{2}}{c}}\right)}{d^{4}} + \frac{6 \, b \log\left(-\frac{c d^{2} x^{2} + d^{2}}{c d^{2} x^{2} - d^{2}}\right)}{\sqrt{d x} d^{3} x^{3}} + \frac{4 \, {\left(4 \, b c d^{2} x^{2} + 3 \, a d^{2}\right)}}{\sqrt{d x} d^{5} x^{3}}}{42 \, d}"," ",0,"-1/42*(6*sqrt(2)*(c^3*d^2)^(1/4)*b*c*arctan(1/2*sqrt(2)*(sqrt(2)*(d^2/c)^(1/4) + 2*sqrt(d*x))/(d^2/c)^(1/4))/d^4 + 6*sqrt(2)*(c^3*d^2)^(1/4)*b*c*arctan(-1/2*sqrt(2)*(sqrt(2)*(d^2/c)^(1/4) - 2*sqrt(d*x))/(d^2/c)^(1/4))/d^4 - 6*sqrt(2)*(-c^3*d^2)^(1/4)*b*c*arctan(1/2*sqrt(2)*(sqrt(2)*(-d^2/c)^(1/4) + 2*sqrt(d*x))/(-d^2/c)^(1/4))/d^4 - 6*sqrt(2)*(-c^3*d^2)^(1/4)*b*c*arctan(-1/2*sqrt(2)*(sqrt(2)*(-d^2/c)^(1/4) - 2*sqrt(d*x))/(-d^2/c)^(1/4))/d^4 + 3*sqrt(2)*(c^3*d^2)^(1/4)*b*c*log(d*x + sqrt(2)*sqrt(d*x)*(d^2/c)^(1/4) + sqrt(d^2/c))/d^4 - 3*sqrt(2)*(c^3*d^2)^(1/4)*b*c*log(d*x - sqrt(2)*sqrt(d*x)*(d^2/c)^(1/4) + sqrt(d^2/c))/d^4 - 3*sqrt(2)*(-c^3*d^2)^(1/4)*b*c*log(d*x + sqrt(2)*sqrt(d*x)*(-d^2/c)^(1/4) + sqrt(-d^2/c))/d^4 + 3*sqrt(2)*(-c^3*d^2)^(1/4)*b*c*log(d*x - sqrt(2)*sqrt(d*x)*(-d^2/c)^(1/4) + sqrt(-d^2/c))/d^4 + 6*b*log(-(c*d^2*x^2 + d^2)/(c*d^2*x^2 - d^2))/(sqrt(d*x)*d^3*x^3) + 4*(4*b*c*d^2*x^2 + 3*a*d^2)/(sqrt(d*x)*d^5*x^3))/d","B",0
90,0,0,0,0.000000," ","integrate((d*x)^(1/2)*(a+b*arctanh(c*x^2))^2,x, algorithm=""giac"")","\int \sqrt{d x} {\left(b \operatorname{artanh}\left(c x^{2}\right) + a\right)}^{2}\,{d x}"," ",0,"integrate(sqrt(d*x)*(b*arctanh(c*x^2) + a)^2, x)","F",0
91,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x^2))^2/(d*x)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(b \operatorname{artanh}\left(c x^{2}\right) + a\right)}^{2}}{\sqrt{d x}}\,{d x}"," ",0,"integrate((b*arctanh(c*x^2) + a)^2/sqrt(d*x), x)","F",0
92,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x^2))^2/(d*x)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(b \operatorname{artanh}\left(c x^{2}\right) + a\right)}^{2}}{\left(d x\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*arctanh(c*x^2) + a)^2/(d*x)^(3/2), x)","F",0
93,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x^2))^2/(d*x)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(b \operatorname{artanh}\left(c x^{2}\right) + a\right)}^{2}}{\left(d x\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((b*arctanh(c*x^2) + a)^2/(d*x)^(5/2), x)","F",0
94,0,0,0,0.000000," ","integrate((d*x)^m*(a+b*arctanh(c*x^2))^3,x, algorithm=""giac"")","\int {\left(b \operatorname{artanh}\left(c x^{2}\right) + a\right)}^{3} \left(d x\right)^{m}\,{d x}"," ",0,"integrate((b*arctanh(c*x^2) + a)^3*(d*x)^m, x)","F",0
95,0,0,0,0.000000," ","integrate((d*x)^m*(a+b*arctanh(c*x^2))^2,x, algorithm=""giac"")","\int {\left(b \operatorname{artanh}\left(c x^{2}\right) + a\right)}^{2} \left(d x\right)^{m}\,{d x}"," ",0,"integrate((b*arctanh(c*x^2) + a)^2*(d*x)^m, x)","F",0
96,0,0,0,0.000000," ","integrate((d*x)^m*(a+b*arctanh(c*x^2)),x, algorithm=""giac"")","\int {\left(b \operatorname{artanh}\left(c x^{2}\right) + a\right)} \left(d x\right)^{m}\,{d x}"," ",0,"integrate((b*arctanh(c*x^2) + a)*(d*x)^m, x)","F",0
97,0,0,0,0.000000," ","integrate((d*x)^m/(a+b*arctanh(c*x^2)),x, algorithm=""giac"")","\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=""giac"")","\int \frac{\left(d x\right)^{m}}{{\left(b \operatorname{artanh}\left(c x^{2}\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((d*x)^m/(b*arctanh(c*x^2) + a)^2, x)","F",0
99,1,78,0,0.143212," ","integrate(x^11*(a+b*arctanh(c*x^3)),x, algorithm=""giac"")","\frac{1}{24} \, b x^{12} \log\left(-\frac{c x^{3} + 1}{c x^{3} - 1}\right) + \frac{1}{12} \, a x^{12} + \frac{b x^{9}}{36 \, c} + \frac{b x^{3}}{12 \, c^{3}} - \frac{b \log\left(c x^{3} + 1\right)}{24 \, c^{4}} + \frac{b \log\left(c x^{3} - 1\right)}{24 \, c^{4}}"," ",0,"1/24*b*x^12*log(-(c*x^3 + 1)/(c*x^3 - 1)) + 1/12*a*x^12 + 1/36*b*x^9/c + 1/12*b*x^3/c^3 - 1/24*b*log(c*x^3 + 1)/c^4 + 1/24*b*log(c*x^3 - 1)/c^4","A",0
100,1,57,0,0.158402," ","integrate(x^8*(a+b*arctanh(c*x^3)),x, algorithm=""giac"")","\frac{1}{18} \, b x^{9} \log\left(-\frac{c x^{3} + 1}{c x^{3} - 1}\right) + \frac{1}{9} \, a x^{9} + \frac{b x^{6}}{18 \, c} + \frac{b \log\left(c^{2} x^{6} - 1\right)}{18 \, c^{3}}"," ",0,"1/18*b*x^9*log(-(c*x^3 + 1)/(c*x^3 - 1)) + 1/9*a*x^9 + 1/18*b*x^6/c + 1/18*b*log(c^2*x^6 - 1)/c^3","A",0
101,1,181,0,0.144927," ","integrate(x^5*(a+b*arctanh(c*x^3)),x, algorithm=""giac"")","\frac{1}{3} \, c {\left(\frac{{\left(c x^{3} + 1\right)} b \log\left(-\frac{c x^{3} + 1}{c x^{3} - 1}\right)}{{\left(c x^{3} - 1\right)} {\left(\frac{{\left(c x^{3} + 1\right)}^{2} c^{3}}{{\left(c x^{3} - 1\right)}^{2}} - \frac{2 \, {\left(c x^{3} + 1\right)} c^{3}}{c x^{3} - 1} + c^{3}\right)}} + \frac{\frac{2 \, {\left(c x^{3} + 1\right)} a}{c x^{3} - 1} + \frac{{\left(c x^{3} + 1\right)} b}{c x^{3} - 1} - b}{\frac{{\left(c x^{3} + 1\right)}^{2} c^{3}}{{\left(c x^{3} - 1\right)}^{2}} - \frac{2 \, {\left(c x^{3} + 1\right)} c^{3}}{c x^{3} - 1} + c^{3}}\right)}"," ",0,"1/3*c*((c*x^3 + 1)*b*log(-(c*x^3 + 1)/(c*x^3 - 1))/((c*x^3 - 1)*((c*x^3 + 1)^2*c^3/(c*x^3 - 1)^2 - 2*(c*x^3 + 1)*c^3/(c*x^3 - 1) + c^3)) + (2*(c*x^3 + 1)*a/(c*x^3 - 1) + (c*x^3 + 1)*b/(c*x^3 - 1) - b)/((c*x^3 + 1)^2*c^3/(c*x^3 - 1)^2 - 2*(c*x^3 + 1)*c^3/(c*x^3 - 1) + c^3))","B",0
102,1,188,0,0.159682," ","integrate(x^2*(a+b*arctanh(c*x^3)),x, algorithm=""giac"")","\frac{1}{3} \, a x^{3} + \frac{1}{3} \, b c {\left(\frac{\log\left(\frac{{\left| -c x^{3} - 1 \right|}}{{\left| c x^{3} - 1 \right|}}\right)}{c^{2}} - \frac{\log\left({\left| -\frac{c x^{3} + 1}{c x^{3} - 1} + 1 \right|}\right)}{c^{2}} + \frac{\log\left(-\frac{\frac{c {\left(\frac{c x^{3} + 1}{c x^{3} - 1} + 1\right)}}{\frac{{\left(c x^{3} + 1\right)} c}{c x^{3} - 1} - c} + 1}{\frac{c {\left(\frac{c x^{3} + 1}{c x^{3} - 1} + 1\right)}}{\frac{{\left(c x^{3} + 1\right)} c}{c x^{3} - 1} - c} - 1}\right)}{c^{2} {\left(\frac{c x^{3} + 1}{c x^{3} - 1} - 1\right)}}\right)}"," ",0,"1/3*a*x^3 + 1/3*b*c*(log(abs(-c*x^3 - 1)/abs(c*x^3 - 1))/c^2 - log(abs(-(c*x^3 + 1)/(c*x^3 - 1) + 1))/c^2 + log(-(c*((c*x^3 + 1)/(c*x^3 - 1) + 1)/((c*x^3 + 1)*c/(c*x^3 - 1) - c) + 1)/(c*((c*x^3 + 1)/(c*x^3 - 1) + 1)/((c*x^3 + 1)*c/(c*x^3 - 1) - c) - 1))/(c^2*((c*x^3 + 1)/(c*x^3 - 1) - 1)))","B",0
103,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x^3))/x,x, algorithm=""giac"")","\int \frac{b \operatorname{artanh}\left(c x^{3}\right) + a}{x}\,{d x}"," ",0,"integrate((b*arctanh(c*x^3) + a)/x, x)","F",0
104,1,51,0,0.153821," ","integrate((a+b*arctanh(c*x^3))/x^4,x, algorithm=""giac"")","-\frac{1}{6} \, b c \log\left(c^{2} x^{6} - 1\right) + b c \log\left(x\right) - \frac{b \log\left(-\frac{c x^{3} + 1}{c x^{3} - 1}\right)}{6 \, x^{3}} - \frac{a}{3 \, x^{3}}"," ",0,"-1/6*b*c*log(c^2*x^6 - 1) + b*c*log(x) - 1/6*b*log(-(c*x^3 + 1)/(c*x^3 - 1))/x^3 - 1/3*a/x^3","A",0
105,1,67,0,0.148500," ","integrate((a+b*arctanh(c*x^3))/x^7,x, algorithm=""giac"")","\frac{1}{12} \, b c^{2} \log\left(c x^{3} + 1\right) - \frac{1}{12} \, b c^{2} \log\left(c x^{3} - 1\right) - \frac{b \log\left(-\frac{c x^{3} + 1}{c x^{3} - 1}\right)}{12 \, x^{6}} - \frac{b c x^{3} + a}{6 \, x^{6}}"," ",0,"1/12*b*c^2*log(c*x^3 + 1) - 1/12*b*c^2*log(c*x^3 - 1) - 1/12*b*log(-(c*x^3 + 1)/(c*x^3 - 1))/x^6 - 1/6*(b*c*x^3 + a)/x^6","A",0
106,1,65,0,0.134593," ","integrate((a+b*arctanh(c*x^3))/x^10,x, algorithm=""giac"")","-\frac{1}{18} \, b c^{3} \log\left(c^{2} x^{6} - 1\right) + \frac{1}{3} \, b c^{3} \log\left(x\right) - \frac{b \log\left(-\frac{c x^{3} + 1}{c x^{3} - 1}\right)}{18 \, x^{9}} - \frac{b c x^{3} + 2 \, a}{18 \, x^{9}}"," ",0,"-1/18*b*c^3*log(c^2*x^6 - 1) + 1/3*b*c^3*log(x) - 1/18*b*log(-(c*x^3 + 1)/(c*x^3 - 1))/x^9 - 1/18*(b*c*x^3 + 2*a)/x^9","A",0
107,1,207,0,0.199198," ","integrate(x^3*(a+b*arctanh(c*x^3)),x, algorithm=""giac"")","\frac{1}{16} \, b c^{7} {\left(\frac{2 \, \left(-\frac{1}{c}\right)^{\frac{1}{3}} \log\left({\left| x - \left(-\frac{1}{c}\right)^{\frac{1}{3}} \right|}\right)}{c^{8}} - \frac{2 \, \sqrt{3} {\left| c \right|}^{\frac{2}{3}} \arctan\left(\frac{1}{3} \, \sqrt{3} c^{\frac{1}{3}} {\left(2 \, x + \frac{1}{c^{\frac{1}{3}}}\right)}\right)}{c^{9}} - \frac{2 \, \sqrt{3} \left(-c^{2}\right)^{\frac{1}{3}} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{1}{c}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{1}{c}\right)^{\frac{1}{3}}}\right)}{c^{9}} - \frac{{\left| c \right|}^{\frac{2}{3}} \log\left(x^{2} + \frac{x}{c^{\frac{1}{3}}} + \frac{1}{c^{\frac{2}{3}}}\right)}{c^{9}} + \frac{2 \, \log\left({\left| x - \frac{1}{c^{\frac{1}{3}}} \right|}\right)}{c^{\frac{25}{3}}} - \frac{\left(-c^{2}\right)^{\frac{1}{3}} \log\left(x^{2} + x \left(-\frac{1}{c}\right)^{\frac{1}{3}} + \left(-\frac{1}{c}\right)^{\frac{2}{3}}\right)}{c^{9}}\right)} + \frac{1}{8} \, b x^{4} \log\left(-\frac{c x^{3} + 1}{c x^{3} - 1}\right) + \frac{1}{4} \, a x^{4} + \frac{3 \, b x}{4 \, c}"," ",0,"1/16*b*c^7*(2*(-1/c)^(1/3)*log(abs(x - (-1/c)^(1/3)))/c^8 - 2*sqrt(3)*abs(c)^(2/3)*arctan(1/3*sqrt(3)*c^(1/3)*(2*x + 1/c^(1/3)))/c^9 - 2*sqrt(3)*(-c^2)^(1/3)*arctan(1/3*sqrt(3)*(2*x + (-1/c)^(1/3))/(-1/c)^(1/3))/c^9 - abs(c)^(2/3)*log(x^2 + x/c^(1/3) + 1/c^(2/3))/c^9 + 2*log(abs(x - 1/c^(1/3)))/c^(25/3) - (-c^2)^(1/3)*log(x^2 + x*(-1/c)^(1/3) + (-1/c)^(2/3))/c^9) + 1/8*b*x^4*log(-(c*x^3 + 1)/(c*x^3 - 1)) + 1/4*a*x^4 + 3/4*b*x/c","A",0
108,1,109,0,0.129118," ","integrate(a+b*arctanh(c*x^3),x, algorithm=""giac"")","\frac{1}{4} \, {\left(c {\left(\frac{2 \, \sqrt{3} {\left| c \right|}^{\frac{2}{3}} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x^{2} + \frac{1}{{\left| c \right|}^{\frac{2}{3}}}\right)} {\left| c \right|}^{\frac{2}{3}}\right)}{c^{2}} - \frac{{\left| c \right|}^{\frac{2}{3}} \log\left(x^{4} + \frac{x^{2}}{{\left| c \right|}^{\frac{2}{3}}} + \frac{1}{{\left| c \right|}^{\frac{4}{3}}}\right)}{c^{2}} + \frac{2 \, \log\left({\left| x^{2} - \frac{1}{{\left| c \right|}^{\frac{2}{3}}} \right|}\right)}{{\left| c \right|}^{\frac{4}{3}}}\right)} + 2 \, x \log\left(-\frac{c x^{3} + 1}{c x^{3} - 1}\right)\right)} b + a x"," ",0,"1/4*(c*(2*sqrt(3)*abs(c)^(2/3)*arctan(1/3*sqrt(3)*(2*x^2 + 1/abs(c)^(2/3))*abs(c)^(2/3))/c^2 - abs(c)^(2/3)*log(x^4 + x^2/abs(c)^(2/3) + 1/abs(c)^(4/3))/c^2 + 2*log(abs(x^2 - 1/abs(c)^(2/3)))/abs(c)^(4/3)) + 2*x*log(-(c*x^3 + 1)/(c*x^3 - 1)))*b + a*x","A",0
109,1,165,0,0.211421," ","integrate((a+b*arctanh(c*x^3))/x^3,x, algorithm=""giac"")","\frac{1}{8} \, {\left(\frac{2 \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x + \frac{1}{{\left| c \right|}^{\frac{1}{3}}}\right)} {\left| c \right|}^{\frac{1}{3}}\right)}{{\left| c \right|}^{\frac{1}{3}}} + \frac{2 \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x - \frac{1}{{\left| c \right|}^{\frac{1}{3}}}\right)} {\left| c \right|}^{\frac{1}{3}}\right)}{{\left| c \right|}^{\frac{1}{3}}} + \frac{\log\left(x^{2} + \frac{x}{{\left| c \right|}^{\frac{1}{3}}} + \frac{1}{{\left| c \right|}^{\frac{2}{3}}}\right)}{{\left| c \right|}^{\frac{1}{3}}} - \frac{\log\left(x^{2} - \frac{x}{{\left| c \right|}^{\frac{1}{3}}} + \frac{1}{{\left| c \right|}^{\frac{2}{3}}}\right)}{{\left| c \right|}^{\frac{1}{3}}} + \frac{2 \, \log\left({\left| x + \frac{1}{{\left| c \right|}^{\frac{1}{3}}} \right|}\right)}{{\left| c \right|}^{\frac{1}{3}}} - \frac{2 \, \log\left({\left| x - \frac{1}{{\left| c \right|}^{\frac{1}{3}}} \right|}\right)}{{\left| c \right|}^{\frac{1}{3}}}\right)} b c - \frac{b \log\left(-\frac{c x^{3} + 1}{c x^{3} - 1}\right)}{4 \, x^{2}} - \frac{a}{2 \, x^{2}}"," ",0,"1/8*(2*sqrt(3)*arctan(1/3*sqrt(3)*(2*x + 1/abs(c)^(1/3))*abs(c)^(1/3))/abs(c)^(1/3) + 2*sqrt(3)*arctan(1/3*sqrt(3)*(2*x - 1/abs(c)^(1/3))*abs(c)^(1/3))/abs(c)^(1/3) + log(x^2 + x/abs(c)^(1/3) + 1/abs(c)^(2/3))/abs(c)^(1/3) - log(x^2 - x/abs(c)^(1/3) + 1/abs(c)^(2/3))/abs(c)^(1/3) + 2*log(abs(x + 1/abs(c)^(1/3)))/abs(c)^(1/3) - 2*log(abs(x - 1/abs(c)^(1/3)))/abs(c)^(1/3))*b*c - 1/4*b*log(-(c*x^3 + 1)/(c*x^3 - 1))/x^2 - 1/2*a/x^2","A",0
110,1,125,0,0.165274," ","integrate((a+b*arctanh(c*x^3))/x^6,x, algorithm=""giac"")","-\frac{1}{20} \, b c^{3} {\left(\frac{2 \, \sqrt{3} {\left| c \right|}^{\frac{2}{3}} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x^{2} + \frac{1}{{\left| c \right|}^{\frac{2}{3}}}\right)} {\left| c \right|}^{\frac{2}{3}}\right)}{c^{2}} - \frac{{\left| c \right|}^{\frac{2}{3}} \log\left(x^{4} + \frac{x^{2}}{{\left| c \right|}^{\frac{2}{3}}} + \frac{1}{{\left| c \right|}^{\frac{4}{3}}}\right)}{c^{2}} + \frac{2 \, \log\left({\left| x^{2} - \frac{1}{{\left| c \right|}^{\frac{2}{3}}} \right|}\right)}{{\left| c \right|}^{\frac{4}{3}}}\right)} - \frac{b \log\left(-\frac{c x^{3} + 1}{c x^{3} - 1}\right)}{10 \, x^{5}} - \frac{3 \, b c x^{3} + 2 \, a}{10 \, x^{5}}"," ",0,"-1/20*b*c^3*(2*sqrt(3)*abs(c)^(2/3)*arctan(1/3*sqrt(3)*(2*x^2 + 1/abs(c)^(2/3))*abs(c)^(2/3))/c^2 - abs(c)^(2/3)*log(x^4 + x^2/abs(c)^(2/3) + 1/abs(c)^(4/3))/c^2 + 2*log(abs(x^2 - 1/abs(c)^(2/3)))/abs(c)^(4/3)) - 1/10*b*log(-(c*x^3 + 1)/(c*x^3 - 1))/x^5 - 1/10*(3*b*c*x^3 + 2*a)/x^5","A",0
111,1,208,0,0.288113," ","integrate(x^7*(a+b*arctanh(c*x^3)),x, algorithm=""giac"")","\frac{1}{16} \, b x^{8} \log\left(-\frac{c x^{3} + 1}{c x^{3} - 1}\right) + \frac{1}{8} \, a x^{8} + \frac{3 \, b x^{5}}{40 \, c} - \frac{b \left(-\frac{1}{c}\right)^{\frac{2}{3}} \log\left({\left| x - \left(-\frac{1}{c}\right)^{\frac{1}{3}} \right|}\right)}{16 \, c^{2}} + \frac{\sqrt{3} b \arctan\left(\frac{\sqrt{3} {\left(2 \, x + \left(-\frac{1}{c}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{1}{c}\right)^{\frac{1}{3}}}\right)}{16 \, \left(-c^{2}\right)^{\frac{1}{3}} c^{2}} + \frac{\sqrt{3} b {\left| c \right|}^{\frac{4}{3}} \arctan\left(\frac{1}{3} \, \sqrt{3} c^{\frac{1}{3}} {\left(2 \, x + \frac{1}{c^{\frac{1}{3}}}\right)}\right)}{16 \, c^{4}} - \frac{b \log\left(x^{2} + x \left(-\frac{1}{c}\right)^{\frac{1}{3}} + \left(-\frac{1}{c}\right)^{\frac{2}{3}}\right)}{32 \, \left(-c^{2}\right)^{\frac{1}{3}} c^{2}} - \frac{b \log\left(x^{2} + \frac{x}{c^{\frac{1}{3}}} + \frac{1}{c^{\frac{2}{3}}}\right)}{32 \, c^{2} {\left| c \right|}^{\frac{2}{3}}} + \frac{b \log\left({\left| x - \frac{1}{c^{\frac{1}{3}}} \right|}\right)}{16 \, c^{\frac{8}{3}}}"," ",0,"1/16*b*x^8*log(-(c*x^3 + 1)/(c*x^3 - 1)) + 1/8*a*x^8 + 3/40*b*x^5/c - 1/16*b*(-1/c)^(2/3)*log(abs(x - (-1/c)^(1/3)))/c^2 + 1/16*sqrt(3)*b*arctan(1/3*sqrt(3)*(2*x + (-1/c)^(1/3))/(-1/c)^(1/3))/((-c^2)^(1/3)*c^2) + 1/16*sqrt(3)*b*abs(c)^(4/3)*arctan(1/3*sqrt(3)*c^(1/3)*(2*x + 1/c^(1/3)))/c^4 - 1/32*b*log(x^2 + x*(-1/c)^(1/3) + (-1/c)^(2/3))/((-c^2)^(1/3)*c^2) - 1/32*b*log(x^2 + x/c^(1/3) + 1/c^(2/3))/(c^2*abs(c)^(2/3)) + 1/16*b*log(abs(x - 1/c^(1/3)))/c^(8/3)","A",0
112,1,126,0,0.154795," ","integrate(x^4*(a+b*arctanh(c*x^3)),x, algorithm=""giac"")","-\frac{1}{20} \, b c^{9} {\left(\frac{2 \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x^{2} + \frac{1}{{\left| c \right|}^{\frac{2}{3}}}\right)} {\left| c \right|}^{\frac{2}{3}}\right)}{c^{10} {\left| c \right|}^{\frac{2}{3}}} + \frac{\log\left(x^{4} + \frac{x^{2}}{{\left| c \right|}^{\frac{2}{3}}} + \frac{1}{{\left| c \right|}^{\frac{4}{3}}}\right)}{c^{10} {\left| c \right|}^{\frac{2}{3}}} - \frac{2 \, \log\left({\left| x^{2} - \frac{1}{{\left| c \right|}^{\frac{2}{3}}} \right|}\right)}{c^{10} {\left| c \right|}^{\frac{2}{3}}}\right)} + \frac{1}{10} \, b x^{5} \log\left(-\frac{c x^{3} + 1}{c x^{3} - 1}\right) + \frac{1}{5} \, a x^{5} + \frac{3 \, b x^{2}}{10 \, c}"," ",0,"-1/20*b*c^9*(2*sqrt(3)*arctan(1/3*sqrt(3)*(2*x^2 + 1/abs(c)^(2/3))*abs(c)^(2/3))/(c^10*abs(c)^(2/3)) + log(x^4 + x^2/abs(c)^(2/3) + 1/abs(c)^(4/3))/(c^10*abs(c)^(2/3)) - 2*log(abs(x^2 - 1/abs(c)^(2/3)))/(c^10*abs(c)^(2/3))) + 1/10*b*x^5*log(-(c*x^3 + 1)/(c*x^3 - 1)) + 1/5*a*x^5 + 3/10*b*x^2/c","A",0
113,1,179,0,0.440243," ","integrate(x*(a+b*arctanh(c*x^3)),x, algorithm=""giac"")","\frac{1}{4} \, b x^{2} \log\left(-\frac{c x^{3} + 1}{c x^{3} - 1}\right) + \frac{1}{2} \, a x^{2} + \frac{\sqrt{3} b {\left| c \right|}^{\frac{1}{3}} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x + \frac{1}{{\left| c \right|}^{\frac{1}{3}}}\right)} {\left| c \right|}^{\frac{1}{3}}\right)}{4 \, c} + \frac{\sqrt{3} b {\left| c \right|}^{\frac{1}{3}} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x - \frac{1}{{\left| c \right|}^{\frac{1}{3}}}\right)} {\left| c \right|}^{\frac{1}{3}}\right)}{4 \, c} - \frac{b c \log\left(x^{2} + \frac{x}{{\left| c \right|}^{\frac{1}{3}}} + \frac{1}{{\left| c \right|}^{\frac{2}{3}}}\right)}{8 \, {\left| c \right|}^{\frac{5}{3}}} + \frac{b c \log\left(x^{2} - \frac{x}{{\left| c \right|}^{\frac{1}{3}}} + \frac{1}{{\left| c \right|}^{\frac{2}{3}}}\right)}{8 \, {\left| c \right|}^{\frac{5}{3}}} - \frac{b c \log\left({\left| x + \frac{1}{{\left| c \right|}^{\frac{1}{3}}} \right|}\right)}{4 \, {\left| c \right|}^{\frac{5}{3}}} + \frac{b {\left| c \right|}^{\frac{1}{3}} \log\left({\left| x - \frac{1}{{\left| c \right|}^{\frac{1}{3}}} \right|}\right)}{4 \, c}"," ",0,"1/4*b*x^2*log(-(c*x^3 + 1)/(c*x^3 - 1)) + 1/2*a*x^2 + 1/4*sqrt(3)*b*abs(c)^(1/3)*arctan(1/3*sqrt(3)*(2*x + 1/abs(c)^(1/3))*abs(c)^(1/3))/c + 1/4*sqrt(3)*b*abs(c)^(1/3)*arctan(1/3*sqrt(3)*(2*x - 1/abs(c)^(1/3))*abs(c)^(1/3))/c - 1/8*b*c*log(x^2 + x/abs(c)^(1/3) + 1/abs(c)^(2/3))/abs(c)^(5/3) + 1/8*b*c*log(x^2 - x/abs(c)^(1/3) + 1/abs(c)^(2/3))/abs(c)^(5/3) - 1/4*b*c*log(abs(x + 1/abs(c)^(1/3)))/abs(c)^(5/3) + 1/4*b*abs(c)^(1/3)*log(abs(x - 1/abs(c)^(1/3)))/c","A",0
114,1,106,0,0.148828," ","integrate((a+b*arctanh(c*x^3))/x^2,x, algorithm=""giac"")","\frac{1}{4} \, b c {\left(\frac{2 \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x^{2} + \frac{1}{{\left| c \right|}^{\frac{2}{3}}}\right)} {\left| c \right|}^{\frac{2}{3}}\right)}{{\left| c \right|}^{\frac{2}{3}}} + \frac{\log\left(x^{4} + \frac{x^{2}}{{\left| c \right|}^{\frac{2}{3}}} + \frac{1}{{\left| c \right|}^{\frac{4}{3}}}\right)}{{\left| c \right|}^{\frac{2}{3}}} - \frac{2 \, \log\left({\left| x^{2} - \frac{1}{{\left| c \right|}^{\frac{2}{3}}} \right|}\right)}{{\left| c \right|}^{\frac{2}{3}}}\right)} - \frac{b \log\left(-\frac{c x^{3} + 1}{c x^{3} - 1}\right)}{2 \, x} - \frac{a}{x}"," ",0,"1/4*b*c*(2*sqrt(3)*arctan(1/3*sqrt(3)*(2*x^2 + 1/abs(c)^(2/3))*abs(c)^(2/3))/abs(c)^(2/3) + log(x^4 + x^2/abs(c)^(2/3) + 1/abs(c)^(4/3))/abs(c)^(2/3) - 2*log(abs(x^2 - 1/abs(c)^(2/3)))/abs(c)^(2/3)) - 1/2*b*log(-(c*x^3 + 1)/(c*x^3 - 1))/x - a/x","A",0
115,1,187,0,0.435980," ","integrate((a+b*arctanh(c*x^3))/x^5,x, algorithm=""giac"")","-\frac{1}{8} \, \sqrt{3} b c {\left| c \right|}^{\frac{1}{3}} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x + \frac{1}{{\left| c \right|}^{\frac{1}{3}}}\right)} {\left| c \right|}^{\frac{1}{3}}\right) - \frac{1}{8} \, \sqrt{3} b c {\left| c \right|}^{\frac{1}{3}} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x - \frac{1}{{\left| c \right|}^{\frac{1}{3}}}\right)} {\left| c \right|}^{\frac{1}{3}}\right) + \frac{b c^{3} \log\left(x^{2} + \frac{x}{{\left| c \right|}^{\frac{1}{3}}} + \frac{1}{{\left| c \right|}^{\frac{2}{3}}}\right)}{16 \, {\left| c \right|}^{\frac{5}{3}}} - \frac{b c^{3} \log\left(x^{2} - \frac{x}{{\left| c \right|}^{\frac{1}{3}}} + \frac{1}{{\left| c \right|}^{\frac{2}{3}}}\right)}{16 \, {\left| c \right|}^{\frac{5}{3}}} + \frac{1}{8} \, b c {\left| c \right|}^{\frac{1}{3}} \log\left({\left| x + \frac{1}{{\left| c \right|}^{\frac{1}{3}}} \right|}\right) - \frac{b c^{3} \log\left({\left| x - \frac{1}{{\left| c \right|}^{\frac{1}{3}}} \right|}\right)}{8 \, {\left| c \right|}^{\frac{5}{3}}} - \frac{b \log\left(-\frac{c x^{3} + 1}{c x^{3} - 1}\right)}{8 \, x^{4}} - \frac{3 \, b c x^{3} + a}{4 \, x^{4}}"," ",0,"-1/8*sqrt(3)*b*c*abs(c)^(1/3)*arctan(1/3*sqrt(3)*(2*x + 1/abs(c)^(1/3))*abs(c)^(1/3)) - 1/8*sqrt(3)*b*c*abs(c)^(1/3)*arctan(1/3*sqrt(3)*(2*x - 1/abs(c)^(1/3))*abs(c)^(1/3)) + 1/16*b*c^3*log(x^2 + x/abs(c)^(1/3) + 1/abs(c)^(2/3))/abs(c)^(5/3) - 1/16*b*c^3*log(x^2 - x/abs(c)^(1/3) + 1/abs(c)^(2/3))/abs(c)^(5/3) + 1/8*b*c*abs(c)^(1/3)*log(abs(x + 1/abs(c)^(1/3))) - 1/8*b*c^3*log(abs(x - 1/abs(c)^(1/3)))/abs(c)^(5/3) - 1/8*b*log(-(c*x^3 + 1)/(c*x^3 - 1))/x^4 - 1/4*(3*b*c*x^3 + a)/x^4","A",0
116,1,175,0,0.297897," ","integrate(x^11*(a+b*arctanh(c*x^3))^2,x, algorithm=""giac"")","\frac{1}{12} \, a^{2} x^{12} + \frac{a b x^{9}}{18 \, c} + \frac{b^{2} x^{6}}{36 \, c^{2}} + \frac{1}{48} \, {\left(b^{2} x^{12} - \frac{b^{2}}{c^{4}}\right)} \log\left(-\frac{c x^{3} + 1}{c x^{3} - 1}\right)^{2} + \frac{a b x^{3}}{6 \, c^{3}} + \frac{1}{36} \, {\left(3 \, a b x^{12} + \frac{b^{2} x^{9}}{c} + \frac{3 \, b^{2} x^{3}}{c^{3}}\right)} \log\left(-\frac{c x^{3} + 1}{c x^{3} - 1}\right) - \frac{{\left(3 \, a b - 4 \, b^{2}\right)} \log\left(c x^{3} + 1\right)}{36 \, c^{4}} + \frac{{\left(3 \, a b + 4 \, b^{2}\right)} \log\left(c x^{3} - 1\right)}{36 \, c^{4}}"," ",0,"1/12*a^2*x^12 + 1/18*a*b*x^9/c + 1/36*b^2*x^6/c^2 + 1/48*(b^2*x^12 - b^2/c^4)*log(-(c*x^3 + 1)/(c*x^3 - 1))^2 + 1/6*a*b*x^3/c^3 + 1/36*(3*a*b*x^12 + b^2*x^9/c + 3*b^2*x^3/c^3)*log(-(c*x^3 + 1)/(c*x^3 - 1)) - 1/36*(3*a*b - 4*b^2)*log(c*x^3 + 1)/c^4 + 1/36*(3*a*b + 4*b^2)*log(c*x^3 - 1)/c^4","A",0
117,0,0,0,0.000000," ","integrate(x^8*(a+b*arctanh(c*x^3))^2,x, algorithm=""giac"")","\int {\left(b \operatorname{artanh}\left(c x^{3}\right) + a\right)}^{2} x^{8}\,{d x}"," ",0,"integrate((b*arctanh(c*x^3) + a)^2*x^8, x)","F",0
118,1,361,0,0.245216," ","integrate(x^5*(a+b*arctanh(c*x^3))^2,x, algorithm=""giac"")","\frac{1}{6} \, {\left(\frac{{\left(c x^{3} + 1\right)} b^{2} \log\left(-\frac{c x^{3} + 1}{c x^{3} - 1}\right)^{2}}{{\left(c x^{3} - 1\right)} {\left(\frac{{\left(c x^{3} + 1\right)}^{2} c^{3}}{{\left(c x^{3} - 1\right)}^{2}} - \frac{2 \, {\left(c x^{3} + 1\right)} c^{3}}{c x^{3} - 1} + c^{3}\right)}} + \frac{2 \, {\left(\frac{2 \, {\left(c x^{3} + 1\right)} a b}{c x^{3} - 1} + \frac{{\left(c x^{3} + 1\right)} b^{2}}{c x^{3} - 1} - b^{2}\right)} \log\left(-\frac{c x^{3} + 1}{c x^{3} - 1}\right)}{\frac{{\left(c x^{3} + 1\right)}^{2} c^{3}}{{\left(c x^{3} - 1\right)}^{2}} - \frac{2 \, {\left(c x^{3} + 1\right)} c^{3}}{c x^{3} - 1} + c^{3}} + \frac{4 \, {\left(\frac{{\left(c x^{3} + 1\right)} a^{2}}{c x^{3} - 1} + \frac{{\left(c x^{3} + 1\right)} a b}{c x^{3} - 1} - a b\right)}}{\frac{{\left(c x^{3} + 1\right)}^{2} c^{3}}{{\left(c x^{3} - 1\right)}^{2}} - \frac{2 \, {\left(c x^{3} + 1\right)} c^{3}}{c x^{3} - 1} + c^{3}} - \frac{2 \, b^{2} \log\left(-\frac{c x^{3} + 1}{c x^{3} - 1} + 1\right)}{c^{3}} + \frac{2 \, b^{2} \log\left(-\frac{c x^{3} + 1}{c x^{3} - 1}\right)}{c^{3}}\right)} c"," ",0,"1/6*((c*x^3 + 1)*b^2*log(-(c*x^3 + 1)/(c*x^3 - 1))^2/((c*x^3 - 1)*((c*x^3 + 1)^2*c^3/(c*x^3 - 1)^2 - 2*(c*x^3 + 1)*c^3/(c*x^3 - 1) + c^3)) + 2*(2*(c*x^3 + 1)*a*b/(c*x^3 - 1) + (c*x^3 + 1)*b^2/(c*x^3 - 1) - b^2)*log(-(c*x^3 + 1)/(c*x^3 - 1))/((c*x^3 + 1)^2*c^3/(c*x^3 - 1)^2 - 2*(c*x^3 + 1)*c^3/(c*x^3 - 1) + c^3) + 4*((c*x^3 + 1)*a^2/(c*x^3 - 1) + (c*x^3 + 1)*a*b/(c*x^3 - 1) - a*b)/((c*x^3 + 1)^2*c^3/(c*x^3 - 1)^2 - 2*(c*x^3 + 1)*c^3/(c*x^3 - 1) + c^3) - 2*b^2*log(-(c*x^3 + 1)/(c*x^3 - 1) + 1)/c^3 + 2*b^2*log(-(c*x^3 + 1)/(c*x^3 - 1))/c^3)*c","B",0
119,0,0,0,0.000000," ","integrate(x^2*(a+b*arctanh(c*x^3))^2,x, algorithm=""giac"")","\int {\left(b \operatorname{artanh}\left(c x^{3}\right) + a\right)}^{2} x^{2}\,{d x}"," ",0,"integrate((b*arctanh(c*x^3) + a)^2*x^2, x)","F",0
120,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x^3))^2/x,x, algorithm=""giac"")","\int \frac{{\left(b \operatorname{artanh}\left(c x^{3}\right) + a\right)}^{2}}{x}\,{d x}"," ",0,"integrate((b*arctanh(c*x^3) + a)^2/x, x)","F",0
121,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x^3))^2/x^4,x, algorithm=""giac"")","\int \frac{{\left(b \operatorname{artanh}\left(c x^{3}\right) + a\right)}^{2}}{x^{4}}\,{d x}"," ",0,"integrate((b*arctanh(c*x^3) + a)^2/x^4, x)","F",0
122,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x^3))^2/x^7,x, algorithm=""giac"")","\int \frac{{\left(b \operatorname{artanh}\left(c x^{3}\right) + a\right)}^{2}}{x^{7}}\,{d x}"," ",0,"integrate((b*arctanh(c*x^3) + a)^2/x^7, x)","F",0
123,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x^3))^2/x^10,x, algorithm=""giac"")","\int \frac{{\left(b \operatorname{artanh}\left(c x^{3}\right) + a\right)}^{2}}{x^{10}}\,{d x}"," ",0,"integrate((b*arctanh(c*x^3) + a)^2/x^10, x)","F",0
124,0,0,0,0.000000," ","integrate(x^8*(a+b*arctanh(c*x^3))^3,x, algorithm=""giac"")","\int {\left(b \operatorname{artanh}\left(c x^{3}\right) + a\right)}^{3} x^{8}\,{d x}"," ",0,"integrate((b*arctanh(c*x^3) + a)^3*x^8, x)","F",0
125,0,0,0,0.000000," ","integrate(x^5*(a+b*arctanh(c*x^3))^3,x, algorithm=""giac"")","\int {\left(b \operatorname{artanh}\left(c x^{3}\right) + a\right)}^{3} x^{5}\,{d x}"," ",0,"integrate((b*arctanh(c*x^3) + a)^3*x^5, x)","F",0
126,0,0,0,0.000000," ","integrate(x^2*(a+b*arctanh(c*x^3))^3,x, algorithm=""giac"")","\int {\left(b \operatorname{artanh}\left(c x^{3}\right) + a\right)}^{3} x^{2}\,{d x}"," ",0,"integrate((b*arctanh(c*x^3) + a)^3*x^2, x)","F",0
127,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x^3))^3/x,x, algorithm=""giac"")","\int \frac{{\left(b \operatorname{artanh}\left(c x^{3}\right) + a\right)}^{3}}{x}\,{d x}"," ",0,"integrate((b*arctanh(c*x^3) + a)^3/x, x)","F",0
128,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x^3))^3/x^4,x, algorithm=""giac"")","\int \frac{{\left(b \operatorname{artanh}\left(c x^{3}\right) + a\right)}^{3}}{x^{4}}\,{d x}"," ",0,"integrate((b*arctanh(c*x^3) + a)^3/x^4, x)","F",0
129,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x^3))^3/x^7,x, algorithm=""giac"")","\int \frac{{\left(b \operatorname{artanh}\left(c x^{3}\right) + a\right)}^{3}}{x^{7}}\,{d x}"," ",0,"integrate((b*arctanh(c*x^3) + a)^3/x^7, x)","F",0
130,0,0,0,0.000000," ","integrate((d*x)^m*(a+b*arctanh(c*x^3))^3,x, algorithm=""giac"")","\int {\left(b \operatorname{artanh}\left(c x^{3}\right) + a\right)}^{3} \left(d x\right)^{m}\,{d x}"," ",0,"integrate((b*arctanh(c*x^3) + a)^3*(d*x)^m, x)","F",0
131,0,0,0,0.000000," ","integrate((d*x)^m*(a+b*arctanh(c*x^3))^2,x, algorithm=""giac"")","\int {\left(b \operatorname{artanh}\left(c x^{3}\right) + a\right)}^{2} \left(d x\right)^{m}\,{d x}"," ",0,"integrate((b*arctanh(c*x^3) + a)^2*(d*x)^m, x)","F",0
132,0,0,0,0.000000," ","integrate((d*x)^m*(a+b*arctanh(c*x^3)),x, algorithm=""giac"")","\int {\left(b \operatorname{artanh}\left(c x^{3}\right) + a\right)} \left(d x\right)^{m}\,{d x}"," ",0,"integrate((b*arctanh(c*x^3) + a)*(d*x)^m, x)","F",0
133,0,0,0,0.000000," ","integrate((d*x)^m/(a+b*arctanh(c*x^3)),x, algorithm=""giac"")","\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=""giac"")","\int \frac{\left(d x\right)^{m}}{{\left(b \operatorname{artanh}\left(c x^{3}\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((d*x)^m/(b*arctanh(c*x^3) + a)^2, x)","F",0
135,1,262,0,0.173618," ","integrate(x^3*(a+b*arctanh(c/x)),x, algorithm=""giac"")","-\frac{\frac{3 \, {\left(\frac{b {\left(c + x\right)}^{3} c^{5}}{{\left(c - x\right)}^{3}} + \frac{b {\left(c + x\right)} c^{5}}{c - x}\right)} \log\left(-\frac{c + x}{c - x}\right)}{\frac{{\left(c + x\right)}^{4}}{{\left(c - x\right)}^{4}} + \frac{4 \, {\left(c + x\right)}^{3}}{{\left(c - x\right)}^{3}} + \frac{6 \, {\left(c + x\right)}^{2}}{{\left(c - x\right)}^{2}} + \frac{4 \, {\left(c + x\right)}}{c - x} + 1} + \frac{2 \, b c^{5} + \frac{6 \, a {\left(c + x\right)}^{3} c^{5}}{{\left(c - x\right)}^{3}} + \frac{3 \, b {\left(c + x\right)}^{3} c^{5}}{{\left(c - x\right)}^{3}} + \frac{6 \, b {\left(c + x\right)}^{2} c^{5}}{{\left(c - x\right)}^{2}} + \frac{6 \, a {\left(c + x\right)} c^{5}}{c - x} + \frac{5 \, b {\left(c + x\right)} c^{5}}{c - x}}{\frac{{\left(c + x\right)}^{4}}{{\left(c - x\right)}^{4}} + \frac{4 \, {\left(c + x\right)}^{3}}{{\left(c - x\right)}^{3}} + \frac{6 \, {\left(c + x\right)}^{2}}{{\left(c - x\right)}^{2}} + \frac{4 \, {\left(c + x\right)}}{c - x} + 1}}{3 \, c}"," ",0,"-1/3*(3*(b*(c + x)^3*c^5/(c - x)^3 + b*(c + x)*c^5/(c - x))*log(-(c + x)/(c - x))/((c + x)^4/(c - x)^4 + 4*(c + x)^3/(c - x)^3 + 6*(c + x)^2/(c - x)^2 + 4*(c + x)/(c - x) + 1) + (2*b*c^5 + 6*a*(c + x)^3*c^5/(c - x)^3 + 3*b*(c + x)^3*c^5/(c - x)^3 + 6*b*(c + x)^2*c^5/(c - x)^2 + 6*a*(c + x)*c^5/(c - x) + 5*b*(c + x)*c^5/(c - x))/((c + x)^4/(c - x)^4 + 4*(c + x)^3/(c - x)^3 + 6*(c + x)^2/(c - x)^2 + 4*(c + x)/(c - x) + 1))/c","B",0
136,1,227,0,0.199200," ","integrate(x^2*(a+b*arctanh(c/x)),x, algorithm=""giac"")","-\frac{b c^{4} \log\left(-\frac{c + x}{c - x} - 1\right) - b c^{4} \log\left(-\frac{c + x}{c - x}\right) + \frac{{\left(b c^{4} + \frac{3 \, b {\left(c + x\right)}^{2} c^{4}}{{\left(c - x\right)}^{2}}\right)} \log\left(-\frac{c + x}{c - x}\right)}{\frac{{\left(c + x\right)}^{3}}{{\left(c - x\right)}^{3}} + \frac{3 \, {\left(c + x\right)}^{2}}{{\left(c - x\right)}^{2}} + \frac{3 \, {\left(c + x\right)}}{c - x} + 1} + \frac{2 \, {\left(a c^{4} + \frac{3 \, a {\left(c + x\right)}^{2} c^{4}}{{\left(c - x\right)}^{2}} + \frac{b {\left(c + x\right)}^{2} c^{4}}{{\left(c - x\right)}^{2}} + \frac{b {\left(c + x\right)} c^{4}}{c - x}\right)}}{\frac{{\left(c + x\right)}^{3}}{{\left(c - x\right)}^{3}} + \frac{3 \, {\left(c + x\right)}^{2}}{{\left(c - x\right)}^{2}} + \frac{3 \, {\left(c + x\right)}}{c - x} + 1}}{3 \, c}"," ",0,"-1/3*(b*c^4*log(-(c + x)/(c - x) - 1) - b*c^4*log(-(c + x)/(c - x)) + (b*c^4 + 3*b*(c + x)^2*c^4/(c - x)^2)*log(-(c + x)/(c - x))/((c + x)^3/(c - x)^3 + 3*(c + x)^2/(c - x)^2 + 3*(c + x)/(c - x) + 1) + 2*(a*c^4 + 3*a*(c + x)^2*c^4/(c - x)^2 + b*(c + x)^2*c^4/(c - x)^2 + b*(c + x)*c^4/(c - x))/((c + x)^3/(c - x)^3 + 3*(c + x)^2/(c - x)^2 + 3*(c + x)/(c - x) + 1))/c","B",0
137,1,130,0,0.377273," ","integrate(x*(a+b*arctanh(c/x)),x, algorithm=""giac"")","-\frac{\frac{b {\left(c + x\right)} c^{3} \log\left(-\frac{c + x}{c - x}\right)}{{\left(c - x\right)} {\left(\frac{{\left(c + x\right)}^{2}}{{\left(c - x\right)}^{2}} + \frac{2 \, {\left(c + x\right)}}{c - x} + 1\right)}} + \frac{b c^{3} + \frac{2 \, a {\left(c + x\right)} c^{3}}{c - x} + \frac{b {\left(c + x\right)} c^{3}}{c - x}}{\frac{{\left(c + x\right)}^{2}}{{\left(c - x\right)}^{2}} + \frac{2 \, {\left(c + x\right)}}{c - x} + 1}}{c}"," ",0,"-(b*(c + x)*c^3*log(-(c + x)/(c - x))/((c - x)*((c + x)^2/(c - x)^2 + 2*(c + x)/(c - x) + 1)) + (b*c^3 + 2*a*(c + x)*c^3/(c - x) + b*(c + x)*c^3/(c - x))/((c + x)^2/(c - x)^2 + 2*(c + x)/(c - x) + 1))/c","B",0
138,1,150,0,0.214004," ","integrate(a+b*arctanh(c/x),x, algorithm=""giac"")","a x + \frac{{\left(c^{2} {\left(\log\left(\frac{{\left| -c - x \right|}}{{\left| c - x \right|}}\right) - \log\left({\left| -\frac{c + x}{c - x} - 1 \right|}\right)\right)} - \frac{c^{2} \log\left(-\frac{\frac{c {\left(\frac{c + x}{{\left(c - x\right)} c} + \frac{1}{c}\right)}}{\frac{c + x}{c - x} - 1} + 1}{\frac{c {\left(\frac{c + x}{{\left(c - x\right)} c} + \frac{1}{c}\right)}}{\frac{c + x}{c - x} - 1} - 1}\right)}{\frac{c + x}{c - x} + 1}\right)} b}{c}"," ",0,"a*x + (c^2*(log(abs(-c - x)/abs(c - x)) - log(abs(-(c + x)/(c - x) - 1))) - c^2*log(-(c*((c + x)/((c - x)*c) + 1/c)/((c + x)/(c - x) - 1) + 1)/(c*((c + x)/((c - x)*c) + 1/c)/((c + x)/(c - x) - 1) - 1))/((c + x)/(c - x) + 1))*b/c","B",0
139,0,0,0,0.000000," ","integrate((a+b*arctanh(c/x))/x,x, algorithm=""giac"")","\int \frac{b \operatorname{artanh}\left(\frac{c}{x}\right) + a}{x}\,{d x}"," ",0,"integrate((b*arctanh(c/x) + a)/x, x)","F",0
140,1,87,0,0.197819," ","integrate((a+b*arctanh(c/x))/x^2,x, algorithm=""giac"")","\frac{b \log\left(-\frac{c + x}{c - x} + 1\right) - b \log\left(-\frac{c + x}{c - x}\right) - \frac{b \log\left(-\frac{c + x}{c - x}\right)}{\frac{c + x}{c - x} - 1} - \frac{2 \, a}{\frac{c + x}{c - x} - 1}}{c}"," ",0,"(b*log(-(c + x)/(c - x) + 1) - b*log(-(c + x)/(c - x)) - b*log(-(c + x)/(c - x))/((c + x)/(c - x) - 1) - 2*a/((c + x)/(c - x) - 1))/c","B",0
141,1,123,0,0.169450," ","integrate((a+b*arctanh(c/x))/x^3,x, algorithm=""giac"")","-\frac{\frac{b {\left(c + x\right)} \log\left(-\frac{c + x}{c - x}\right)}{{\left(\frac{{\left(c + x\right)}^{2} c}{{\left(c - x\right)}^{2}} - \frac{2 \, {\left(c + x\right)} c}{c - x} + c\right)} {\left(c - x\right)}} - \frac{b - \frac{2 \, a {\left(c + x\right)}}{c - x} - \frac{b {\left(c + x\right)}}{c - x}}{\frac{{\left(c + x\right)}^{2} c}{{\left(c - x\right)}^{2}} - \frac{2 \, {\left(c + x\right)} c}{c - x} + c}}{c}"," ",0,"-(b*(c + x)*log(-(c + x)/(c - x))/(((c + x)^2*c/(c - x)^2 - 2*(c + x)*c/(c - x) + c)*(c - x)) - (b - 2*a*(c + x)/(c - x) - b*(c + x)/(c - x))/((c + x)^2*c/(c - x)^2 - 2*(c + x)*c/(c - x) + c))/c","B",0
142,1,234,0,0.310326," ","integrate((a+b*arctanh(c/x))/x^4,x, algorithm=""giac"")","-\frac{\frac{{\left(b + \frac{3 \, b {\left(c + x\right)}^{2}}{{\left(c - x\right)}^{2}}\right)} \log\left(-\frac{c + x}{c - x}\right)}{\frac{{\left(c + x\right)}^{3} c^{2}}{{\left(c - x\right)}^{3}} - \frac{3 \, {\left(c + x\right)}^{2} c^{2}}{{\left(c - x\right)}^{2}} + \frac{3 \, {\left(c + x\right)} c^{2}}{c - x} - c^{2}} + \frac{2 \, {\left(a + \frac{3 \, a {\left(c + x\right)}^{2}}{{\left(c - x\right)}^{2}} + \frac{b {\left(c + x\right)}^{2}}{{\left(c - x\right)}^{2}} - \frac{b {\left(c + x\right)}}{c - x}\right)}}{\frac{{\left(c + x\right)}^{3} c^{2}}{{\left(c - x\right)}^{3}} - \frac{3 \, {\left(c + x\right)}^{2} c^{2}}{{\left(c - x\right)}^{2}} + \frac{3 \, {\left(c + x\right)} c^{2}}{c - x} - c^{2}} - \frac{b \log\left(-\frac{c + x}{c - x} + 1\right)}{c^{2}} + \frac{b \log\left(-\frac{c + x}{c - x}\right)}{c^{2}}}{3 \, c}"," ",0,"-1/3*((b + 3*b*(c + x)^2/(c - x)^2)*log(-(c + x)/(c - x))/((c + x)^3*c^2/(c - x)^3 - 3*(c + x)^2*c^2/(c - x)^2 + 3*(c + x)*c^2/(c - x) - c^2) + 2*(a + 3*a*(c + x)^2/(c - x)^2 + b*(c + x)^2/(c - x)^2 - b*(c + x)/(c - x))/((c + x)^3*c^2/(c - x)^3 - 3*(c + x)^2*c^2/(c - x)^2 + 3*(c + x)*c^2/(c - x) - c^2) - b*log(-(c + x)/(c - x) + 1)/c^2 + b*log(-(c + x)/(c - x))/c^2)/c","B",0
143,1,552,0,0.174992," ","integrate(x^3*(a+b*arctanh(c/x))^2,x, algorithm=""giac"")","-\frac{4 \, b^{2} c^{5} \log\left(-\frac{c + x}{c - x} - 1\right) - 4 \, b^{2} c^{5} \log\left(-\frac{c + x}{c - x}\right) + \frac{3 \, {\left(\frac{b^{2} {\left(c + x\right)}^{3} c^{5}}{{\left(c - x\right)}^{3}} + \frac{b^{2} {\left(c + x\right)} c^{5}}{c - x}\right)} \log\left(-\frac{c + x}{c - x}\right)^{2}}{\frac{{\left(c + x\right)}^{4}}{{\left(c - x\right)}^{4}} + \frac{4 \, {\left(c + x\right)}^{3}}{{\left(c - x\right)}^{3}} + \frac{6 \, {\left(c + x\right)}^{2}}{{\left(c - x\right)}^{2}} + \frac{4 \, {\left(c + x\right)}}{c - x} + 1} + \frac{2 \, {\left(2 \, b^{2} c^{5} + \frac{6 \, a b {\left(c + x\right)}^{3} c^{5}}{{\left(c - x\right)}^{3}} + \frac{3 \, b^{2} {\left(c + x\right)}^{3} c^{5}}{{\left(c - x\right)}^{3}} + \frac{6 \, b^{2} {\left(c + x\right)}^{2} c^{5}}{{\left(c - x\right)}^{2}} + \frac{6 \, a b {\left(c + x\right)} c^{5}}{c - x} + \frac{5 \, b^{2} {\left(c + x\right)} c^{5}}{c - x}\right)} \log\left(-\frac{c + x}{c - x}\right)}{\frac{{\left(c + x\right)}^{4}}{{\left(c - x\right)}^{4}} + \frac{4 \, {\left(c + x\right)}^{3}}{{\left(c - x\right)}^{3}} + \frac{6 \, {\left(c + x\right)}^{2}}{{\left(c - x\right)}^{2}} + \frac{4 \, {\left(c + x\right)}}{c - x} + 1} + \frac{2 \, {\left(4 \, a b c^{5} + \frac{6 \, a^{2} {\left(c + x\right)}^{3} c^{5}}{{\left(c - x\right)}^{3}} + \frac{6 \, a b {\left(c + x\right)}^{3} c^{5}}{{\left(c - x\right)}^{3}} + \frac{b^{2} {\left(c + x\right)}^{3} c^{5}}{{\left(c - x\right)}^{3}} + \frac{12 \, a b {\left(c + x\right)}^{2} c^{5}}{{\left(c - x\right)}^{2}} + \frac{2 \, b^{2} {\left(c + x\right)}^{2} c^{5}}{{\left(c - x\right)}^{2}} + \frac{6 \, a^{2} {\left(c + x\right)} c^{5}}{c - x} + \frac{10 \, a b {\left(c + x\right)} c^{5}}{c - x} + \frac{b^{2} {\left(c + x\right)} c^{5}}{c - x}\right)}}{\frac{{\left(c + x\right)}^{4}}{{\left(c - x\right)}^{4}} + \frac{4 \, {\left(c + x\right)}^{3}}{{\left(c - x\right)}^{3}} + \frac{6 \, {\left(c + x\right)}^{2}}{{\left(c - x\right)}^{2}} + \frac{4 \, {\left(c + x\right)}}{c - x} + 1}}{6 \, c}"," ",0,"-1/6*(4*b^2*c^5*log(-(c + x)/(c - x) - 1) - 4*b^2*c^5*log(-(c + x)/(c - x)) + 3*(b^2*(c + x)^3*c^5/(c - x)^3 + b^2*(c + x)*c^5/(c - x))*log(-(c + x)/(c - x))^2/((c + x)^4/(c - x)^4 + 4*(c + x)^3/(c - x)^3 + 6*(c + x)^2/(c - x)^2 + 4*(c + x)/(c - x) + 1) + 2*(2*b^2*c^5 + 6*a*b*(c + x)^3*c^5/(c - x)^3 + 3*b^2*(c + x)^3*c^5/(c - x)^3 + 6*b^2*(c + x)^2*c^5/(c - x)^2 + 6*a*b*(c + x)*c^5/(c - x) + 5*b^2*(c + x)*c^5/(c - x))*log(-(c + x)/(c - x))/((c + x)^4/(c - x)^4 + 4*(c + x)^3/(c - x)^3 + 6*(c + x)^2/(c - x)^2 + 4*(c + x)/(c - x) + 1) + 2*(4*a*b*c^5 + 6*a^2*(c + x)^3*c^5/(c - x)^3 + 6*a*b*(c + x)^3*c^5/(c - x)^3 + b^2*(c + x)^3*c^5/(c - x)^3 + 12*a*b*(c + x)^2*c^5/(c - x)^2 + 2*b^2*(c + x)^2*c^5/(c - x)^2 + 6*a^2*(c + x)*c^5/(c - x) + 10*a*b*(c + x)*c^5/(c - x) + b^2*(c + x)*c^5/(c - x))/((c + x)^4/(c - x)^4 + 4*(c + x)^3/(c - x)^3 + 6*(c + x)^2/(c - x)^2 + 4*(c + x)/(c - x) + 1))/c","B",0
144,0,0,0,0.000000," ","integrate(x^2*(a+b*arctanh(c/x))^2,x, algorithm=""giac"")","\int {\left(b \operatorname{artanh}\left(\frac{c}{x}\right) + a\right)}^{2} x^{2}\,{d x}"," ",0,"integrate((b*arctanh(c/x) + a)^2*x^2, x)","F",0
145,1,268,0,0.580868," ","integrate(x*(a+b*arctanh(c/x))^2,x, algorithm=""giac"")","-\frac{2 \, b^{2} c^{3} \log\left(-\frac{c + x}{c - x} - 1\right) - 2 \, b^{2} c^{3} \log\left(-\frac{c + x}{c - x}\right) + \frac{b^{2} {\left(c + x\right)} c^{3} \log\left(-\frac{c + x}{c - x}\right)^{2}}{{\left(c - x\right)} {\left(\frac{{\left(c + x\right)}^{2}}{{\left(c - x\right)}^{2}} + \frac{2 \, {\left(c + x\right)}}{c - x} + 1\right)}} + \frac{2 \, {\left(b^{2} c^{3} + \frac{2 \, a b {\left(c + x\right)} c^{3}}{c - x} + \frac{b^{2} {\left(c + x\right)} c^{3}}{c - x}\right)} \log\left(-\frac{c + x}{c - x}\right)}{\frac{{\left(c + x\right)}^{2}}{{\left(c - x\right)}^{2}} + \frac{2 \, {\left(c + x\right)}}{c - x} + 1} + \frac{4 \, {\left(a b c^{3} + \frac{a^{2} {\left(c + x\right)} c^{3}}{c - x} + \frac{a b {\left(c + x\right)} c^{3}}{c - x}\right)}}{\frac{{\left(c + x\right)}^{2}}{{\left(c - x\right)}^{2}} + \frac{2 \, {\left(c + x\right)}}{c - x} + 1}}{2 \, c}"," ",0,"-1/2*(2*b^2*c^3*log(-(c + x)/(c - x) - 1) - 2*b^2*c^3*log(-(c + x)/(c - x)) + b^2*(c + x)*c^3*log(-(c + x)/(c - x))^2/((c - x)*((c + x)^2/(c - x)^2 + 2*(c + x)/(c - x) + 1)) + 2*(b^2*c^3 + 2*a*b*(c + x)*c^3/(c - x) + b^2*(c + x)*c^3/(c - x))*log(-(c + x)/(c - x))/((c + x)^2/(c - x)^2 + 2*(c + x)/(c - x) + 1) + 4*(a*b*c^3 + a^2*(c + x)*c^3/(c - x) + a*b*(c + x)*c^3/(c - x))/((c + x)^2/(c - x)^2 + 2*(c + x)/(c - x) + 1))/c","B",0
146,0,0,0,0.000000," ","integrate((a+b*arctanh(c/x))^2,x, algorithm=""giac"")","\int {\left(b \operatorname{artanh}\left(\frac{c}{x}\right) + a\right)}^{2}\,{d x}"," ",0,"integrate((b*arctanh(c/x) + a)^2, x)","F",0
147,0,0,0,0.000000," ","integrate((a+b*arctanh(c/x))^2/x,x, algorithm=""giac"")","\int \frac{{\left(b \operatorname{artanh}\left(\frac{c}{x}\right) + a\right)}^{2}}{x}\,{d x}"," ",0,"integrate((b*arctanh(c/x) + a)^2/x, x)","F",0
148,0,0,0,0.000000," ","integrate((a+b*arctanh(c/x))^2/x^2,x, algorithm=""giac"")","\int \frac{{\left(b \operatorname{artanh}\left(\frac{c}{x}\right) + a\right)}^{2}}{x^{2}}\,{d x}"," ",0,"integrate((b*arctanh(c/x) + a)^2/x^2, x)","F",0
149,1,255,0,0.176876," ","integrate((a+b*arctanh(c/x))^2/x^3,x, algorithm=""giac"")","-\frac{\frac{b^{2} {\left(c + x\right)} \log\left(-\frac{c + x}{c - x}\right)^{2}}{{\left(\frac{{\left(c + x\right)}^{2} c}{{\left(c - x\right)}^{2}} - \frac{2 \, {\left(c + x\right)} c}{c - x} + c\right)} {\left(c - x\right)}} - \frac{2 \, b^{2} \log\left(-\frac{c + x}{c - x} + 1\right)}{c} + \frac{2 \, b^{2} \log\left(-\frac{c + x}{c - x}\right)}{c} - \frac{2 \, {\left(b^{2} - \frac{2 \, a b {\left(c + x\right)}}{c - x} - \frac{b^{2} {\left(c + x\right)}}{c - x}\right)} \log\left(-\frac{c + x}{c - x}\right)}{\frac{{\left(c + x\right)}^{2} c}{{\left(c - x\right)}^{2}} - \frac{2 \, {\left(c + x\right)} c}{c - x} + c} - \frac{4 \, {\left(a b - \frac{a^{2} {\left(c + x\right)}}{c - x} - \frac{a b {\left(c + x\right)}}{c - x}\right)}}{\frac{{\left(c + x\right)}^{2} c}{{\left(c - x\right)}^{2}} - \frac{2 \, {\left(c + x\right)} c}{c - x} + c}}{2 \, c}"," ",0,"-1/2*(b^2*(c + x)*log(-(c + x)/(c - x))^2/(((c + x)^2*c/(c - x)^2 - 2*(c + x)*c/(c - x) + c)*(c - x)) - 2*b^2*log(-(c + x)/(c - x) + 1)/c + 2*b^2*log(-(c + x)/(c - x))/c - 2*(b^2 - 2*a*b*(c + x)/(c - x) - b^2*(c + x)/(c - x))*log(-(c + x)/(c - x))/((c + x)^2*c/(c - x)^2 - 2*(c + x)*c/(c - x) + c) - 4*(a*b - a^2*(c + x)/(c - x) - a*b*(c + x)/(c - x))/((c + x)^2*c/(c - x)^2 - 2*(c + x)*c/(c - x) + c))/c","B",0
150,0,0,0,0.000000," ","integrate(x^3*(a+b*arctanh(c/x))^3,x, algorithm=""giac"")","\int {\left(b \operatorname{artanh}\left(\frac{c}{x}\right) + a\right)}^{3} x^{3}\,{d x}"," ",0,"integrate((b*arctanh(c/x) + a)^3*x^3, x)","F",0
151,0,0,0,0.000000," ","integrate(x^2*(a+b*arctanh(c/x))^3,x, algorithm=""giac"")","\int {\left(b \operatorname{artanh}\left(\frac{c}{x}\right) + a\right)}^{3} x^{2}\,{d x}"," ",0,"integrate((b*arctanh(c/x) + a)^3*x^2, x)","F",0
152,0,0,0,0.000000," ","integrate(x*(a+b*arctanh(c/x))^3,x, algorithm=""giac"")","\int {\left(b \operatorname{artanh}\left(\frac{c}{x}\right) + a\right)}^{3} x\,{d x}"," ",0,"integrate((b*arctanh(c/x) + a)^3*x, x)","F",0
153,0,0,0,0.000000," ","integrate((a+b*arctanh(c/x))^3,x, algorithm=""giac"")","\int {\left(b \operatorname{artanh}\left(\frac{c}{x}\right) + a\right)}^{3}\,{d x}"," ",0,"integrate((b*arctanh(c/x) + a)^3, x)","F",0
154,0,0,0,0.000000," ","integrate((a+b*arctanh(c/x))^3/x,x, algorithm=""giac"")","\int \frac{{\left(b \operatorname{artanh}\left(\frac{c}{x}\right) + a\right)}^{3}}{x}\,{d x}"," ",0,"integrate((b*arctanh(c/x) + a)^3/x, x)","F",0
155,0,0,0,0.000000," ","integrate((a+b*arctanh(c/x))^3/x^2,x, algorithm=""giac"")","\int \frac{{\left(b \operatorname{artanh}\left(\frac{c}{x}\right) + a\right)}^{3}}{x^{2}}\,{d x}"," ",0,"integrate((b*arctanh(c/x) + a)^3/x^2, x)","F",0
156,0,0,0,0.000000," ","integrate((a+b*arctanh(c/x))^3/x^3,x, algorithm=""giac"")","\int \frac{{\left(b \operatorname{artanh}\left(\frac{c}{x}\right) + a\right)}^{3}}{x^{3}}\,{d x}"," ",0,"integrate((b*arctanh(c/x) + a)^3/x^3, x)","F",0
157,1,71,0,0.152460," ","integrate(x^7*(a+b*arctanh(c/x^2)),x, algorithm=""giac"")","\frac{1}{16} \, b x^{8} \log\left(\frac{x^{2} + c}{x^{2} - c}\right) + \frac{1}{8} \, a x^{8} + \frac{1}{24} \, b c x^{6} + \frac{1}{8} \, b c^{3} x^{2} - \frac{1}{16} \, b c^{4} \log\left(x^{2} + c\right) + \frac{1}{16} \, b c^{4} \log\left(-x^{2} + c\right)"," ",0,"1/16*b*x^8*log((x^2 + c)/(x^2 - c)) + 1/8*a*x^8 + 1/24*b*c*x^6 + 1/8*b*c^3*x^2 - 1/16*b*c^4*log(x^2 + c) + 1/16*b*c^4*log(-x^2 + c)","A",0
158,1,52,0,0.153561," ","integrate(x^5*(a+b*arctanh(c/x^2)),x, algorithm=""giac"")","\frac{1}{12} \, b x^{6} \log\left(\frac{x^{2} + c}{x^{2} - c}\right) + \frac{1}{6} \, a x^{6} + \frac{1}{12} \, b c x^{4} + \frac{1}{12} \, b c^{3} \log\left(x^{4} - c^{2}\right)"," ",0,"1/12*b*x^6*log((x^2 + c)/(x^2 - c)) + 1/6*a*x^6 + 1/12*b*c*x^4 + 1/12*b*c^3*log(x^4 - c^2)","A",0
159,1,162,0,0.179724," ","integrate(x^3*(a+b*arctanh(c/x^2)),x, algorithm=""giac"")","\frac{\frac{{\left(x^{2} + c\right)} b c^{3} \log\left(\frac{x^{2} + c}{x^{2} - c}\right)}{{\left(x^{2} - c\right)} {\left(\frac{{\left(x^{2} + c\right)}^{2}}{{\left(x^{2} - c\right)}^{2}} - \frac{2 \, {\left(x^{2} + c\right)}}{x^{2} - c} + 1\right)}} + \frac{\frac{2 \, {\left(x^{2} + c\right)} a c^{3}}{x^{2} - c} + \frac{{\left(x^{2} + c\right)} b c^{3}}{x^{2} - c} - b c^{3}}{\frac{{\left(x^{2} + c\right)}^{2}}{{\left(x^{2} - c\right)}^{2}} - \frac{2 \, {\left(x^{2} + c\right)}}{x^{2} - c} + 1}}{2 \, c}"," ",0,"1/2*((x^2 + c)*b*c^3*log((x^2 + c)/(x^2 - c))/((x^2 - c)*((x^2 + c)^2/(x^2 - c)^2 - 2*(x^2 + c)/(x^2 - c) + 1)) + (2*(x^2 + c)*a*c^3/(x^2 - c) + (x^2 + c)*b*c^3/(x^2 - c) - b*c^3)/((x^2 + c)^2/(x^2 - c)^2 - 2*(x^2 + c)/(x^2 - c) + 1))/c","B",0
160,1,184,0,0.168779," ","integrate(x*(a+b*arctanh(c/x^2)),x, algorithm=""giac"")","\frac{1}{2} \, a x^{2} + \frac{{\left(c^{2} {\left(\log\left(\frac{{\left| -x^{2} - c \right|}}{{\left| -x^{2} + c \right|}}\right) - \log\left({\left| \frac{x^{2} + c}{x^{2} - c} - 1 \right|}\right)\right)} + \frac{c^{2} \log\left(-\frac{\frac{c {\left(\frac{x^{2} + c}{{\left(x^{2} - c\right)} c} - \frac{1}{c}\right)}}{\frac{x^{2} + c}{x^{2} - c} + 1} + 1}{\frac{c {\left(\frac{x^{2} + c}{{\left(x^{2} - c\right)} c} - \frac{1}{c}\right)}}{\frac{x^{2} + c}{x^{2} - c} + 1} - 1}\right)}{\frac{x^{2} + c}{x^{2} - c} - 1}\right)} b}{2 \, c}"," ",0,"1/2*a*x^2 + 1/2*(c^2*(log(abs(-x^2 - c)/abs(-x^2 + c)) - log(abs((x^2 + c)/(x^2 - c) - 1))) + c^2*log(-(c*((x^2 + c)/((x^2 - c)*c) - 1/c)/((x^2 + c)/(x^2 - c) + 1) + 1)/(c*((x^2 + c)/((x^2 - c)*c) - 1/c)/((x^2 + c)/(x^2 - c) + 1) - 1))/((x^2 + c)/(x^2 - c) - 1))*b/c","B",0
161,0,0,0,0.000000," ","integrate((a+b*arctanh(c/x^2))/x,x, algorithm=""giac"")","\int \frac{b \operatorname{artanh}\left(\frac{c}{x^{2}}\right) + a}{x}\,{d x}"," ",0,"integrate((b*arctanh(c/x^2) + a)/x, x)","F",0
162,1,52,0,0.188704," ","integrate((a+b*arctanh(c/x^2))/x^3,x, algorithm=""giac"")","-\frac{b \log\left(x^{4} - c^{2}\right)}{4 \, c} + \frac{b \log\left(x\right)}{c} - \frac{b \log\left(\frac{x^{2} + c}{x^{2} - c}\right)}{4 \, x^{2}} - \frac{a}{2 \, x^{2}}"," ",0,"-1/4*b*log(x^4 - c^2)/c + b*log(x)/c - 1/4*b*log((x^2 + c)/(x^2 - c))/x^2 - 1/2*a/x^2","A",0
163,1,66,0,0.698544," ","integrate((a+b*arctanh(c/x^2))/x^5,x, algorithm=""giac"")","\frac{b \log\left(x^{2} + c\right)}{8 \, c^{2}} - \frac{b \log\left(-x^{2} + c\right)}{8 \, c^{2}} - \frac{b \log\left(\frac{x^{2} + c}{x^{2} - c}\right)}{8 \, x^{4}} - \frac{b x^{2} + a c}{4 \, c x^{4}}"," ",0,"1/8*b*log(x^2 + c)/c^2 - 1/8*b*log(-x^2 + c)/c^2 - 1/8*b*log((x^2 + c)/(x^2 - c))/x^4 - 1/4*(b*x^2 + a*c)/(c*x^4)","A",0
164,1,65,0,0.238564," ","integrate((a+b*arctanh(c/x^2))/x^7,x, algorithm=""giac"")","-\frac{b \log\left(x^{4} - c^{2}\right)}{12 \, c^{3}} + \frac{b \log\left(x\right)}{3 \, c^{3}} - \frac{b \log\left(\frac{x^{2} + c}{x^{2} - c}\right)}{12 \, x^{6}} - \frac{b x^{2} + 2 \, a c}{12 \, c x^{6}}"," ",0,"-1/12*b*log(x^4 - c^2)/c^3 + 1/3*b*log(x)/c^3 - 1/12*b*log((x^2 + c)/(x^2 - c))/x^6 - 1/12*(b*x^2 + 2*a*c)/(c*x^6)","A",0
165,1,67,0,0.303184," ","integrate(x^4*(a+b*arctanh(c/x^2)),x, algorithm=""giac"")","\frac{1}{10} \, b x^{5} \log\left(\frac{x^{2} + c}{x^{2} - c}\right) + \frac{1}{5} \, a x^{5} + \frac{2}{15} \, b c x^{3} + \frac{b c^{3} \arctan\left(\frac{x}{\sqrt{-c}}\right)}{5 \, \sqrt{-c}} + \frac{1}{5} \, b c^{\frac{5}{2}} \arctan\left(\frac{x}{\sqrt{c}}\right)"," ",0,"1/10*b*x^5*log((x^2 + c)/(x^2 - c)) + 1/5*a*x^5 + 2/15*b*c*x^3 + 1/5*b*c^3*arctan(x/sqrt(-c))/sqrt(-c) + 1/5*b*c^(5/2)*arctan(x/sqrt(c))","A",0
166,1,69,0,0.207262," ","integrate(x^2*(a+b*arctanh(c/x^2)),x, algorithm=""giac"")","\frac{1}{3} \, b c^{3} {\left(\frac{\arctan\left(\frac{x}{\sqrt{-c}}\right)}{\sqrt{-c} c} - \frac{\arctan\left(\frac{x}{\sqrt{c}}\right)}{c^{\frac{3}{2}}}\right)} + \frac{1}{6} \, b x^{3} \log\left(\frac{x^{2} + c}{x^{2} - c}\right) + \frac{1}{3} \, a x^{3} + \frac{2}{3} \, b c x"," ",0,"1/3*b*c^3*(arctan(x/sqrt(-c))/(sqrt(-c)*c) - arctan(x/sqrt(c))/c^(3/2)) + 1/6*b*x^3*log((x^2 + c)/(x^2 - c)) + 1/3*a*x^3 + 2/3*b*c*x","A",0
167,1,57,0,0.361307," ","integrate(a+b*arctanh(c/x^2),x, algorithm=""giac"")","\frac{1}{2} \, {\left(2 \, c {\left(\frac{\arctan\left(\frac{x}{\sqrt{-c}}\right)}{\sqrt{-c}} + \frac{\arctan\left(\frac{x}{\sqrt{c}}\right)}{\sqrt{c}}\right)} + x \log\left(-\frac{\frac{c}{x^{2}} + 1}{\frac{c}{x^{2}} - 1}\right)\right)} b + a x"," ",0,"1/2*(2*c*(arctan(x/sqrt(-c))/sqrt(-c) + arctan(x/sqrt(c))/sqrt(c)) + x*log(-(c/x^2 + 1)/(c/x^2 - 1)))*b + a*x","A",0
168,1,62,0,0.223772," ","integrate((a+b*arctanh(c/x^2))/x^2,x, algorithm=""giac"")","-b c {\left(\frac{\arctan\left(\frac{x}{\sqrt{-c}}\right)}{\sqrt{-c} c} - \frac{\arctan\left(\frac{x}{\sqrt{c}}\right)}{c^{\frac{3}{2}}}\right)} - \frac{b \log\left(\frac{x^{2} + c}{x^{2} - c}\right)}{2 \, x} - \frac{a}{x}"," ",0,"-b*c*(arctan(x/sqrt(-c))/(sqrt(-c)*c) - arctan(x/sqrt(c))/c^(3/2)) - 1/2*b*log((x^2 + c)/(x^2 - c))/x - a/x","A",0
169,1,72,0,0.251888," ","integrate((a+b*arctanh(c/x^2))/x^4,x, algorithm=""giac"")","-\frac{b \arctan\left(\frac{x}{\sqrt{-c}}\right)}{3 \, \sqrt{-c} c} - \frac{b \arctan\left(\frac{x}{\sqrt{c}}\right)}{3 \, c^{\frac{3}{2}}} - \frac{b \log\left(\frac{x^{2} + c}{x^{2} - c}\right)}{6 \, x^{3}} - \frac{2 \, b x^{2} + a c}{3 \, c x^{3}}"," ",0,"-1/3*b*arctan(x/sqrt(-c))/(sqrt(-c)*c) - 1/3*b*arctan(x/sqrt(c))/c^(3/2) - 1/6*b*log((x^2 + c)/(x^2 - c))/x^3 - 1/3*(2*b*x^2 + a*c)/(c*x^3)","A",0
170,1,74,0,0.182664," ","integrate((a+b*arctanh(c/x^2))/x^6,x, algorithm=""giac"")","-\frac{1}{5} \, b {\left(\frac{\arctan\left(\frac{x}{\sqrt{-c}}\right)}{\sqrt{-c} c^{2}} - \frac{\arctan\left(\frac{x}{\sqrt{c}}\right)}{c^{\frac{5}{2}}}\right)} - \frac{b \log\left(\frac{x^{2} + c}{x^{2} - c}\right)}{10 \, x^{5}} - \frac{2 \, b x^{2} + 3 \, a c}{15 \, c x^{5}}"," ",0,"-1/5*b*(arctan(x/sqrt(-c))/(sqrt(-c)*c^2) - arctan(x/sqrt(c))/c^(5/2)) - 1/10*b*log((x^2 + c)/(x^2 - c))/x^5 - 1/15*(2*b*x^2 + 3*a*c)/(c*x^5)","A",0
171,1,327,0,0.290232," ","integrate(x^3*(a+b*arctanh(c/x^2))^2,x, algorithm=""giac"")","-\frac{2 \, b^{2} c^{3} \log\left(\frac{x^{2} + c}{x^{2} - c} - 1\right) - 2 \, b^{2} c^{3} \log\left(\frac{x^{2} + c}{x^{2} - c}\right) - \frac{{\left(x^{2} + c\right)} b^{2} c^{3} \log\left(\frac{x^{2} + c}{x^{2} - c}\right)^{2}}{{\left(x^{2} - c\right)} {\left(\frac{{\left(x^{2} + c\right)}^{2}}{{\left(x^{2} - c\right)}^{2}} - \frac{2 \, {\left(x^{2} + c\right)}}{x^{2} - c} + 1\right)}} - \frac{2 \, {\left(\frac{2 \, {\left(x^{2} + c\right)} a b c^{3}}{x^{2} - c} + \frac{{\left(x^{2} + c\right)} b^{2} c^{3}}{x^{2} - c} - b^{2} c^{3}\right)} \log\left(\frac{x^{2} + c}{x^{2} - c}\right)}{\frac{{\left(x^{2} + c\right)}^{2}}{{\left(x^{2} - c\right)}^{2}} - \frac{2 \, {\left(x^{2} + c\right)}}{x^{2} - c} + 1} - \frac{4 \, {\left(\frac{{\left(x^{2} + c\right)} a^{2} c^{3}}{x^{2} - c} + \frac{{\left(x^{2} + c\right)} a b c^{3}}{x^{2} - c} - a b c^{3}\right)}}{\frac{{\left(x^{2} + c\right)}^{2}}{{\left(x^{2} - c\right)}^{2}} - \frac{2 \, {\left(x^{2} + c\right)}}{x^{2} - c} + 1}}{4 \, c}"," ",0,"-1/4*(2*b^2*c^3*log((x^2 + c)/(x^2 - c) - 1) - 2*b^2*c^3*log((x^2 + c)/(x^2 - c)) - (x^2 + c)*b^2*c^3*log((x^2 + c)/(x^2 - c))^2/((x^2 - c)*((x^2 + c)^2/(x^2 - c)^2 - 2*(x^2 + c)/(x^2 - c) + 1)) - 2*(2*(x^2 + c)*a*b*c^3/(x^2 - c) + (x^2 + c)*b^2*c^3/(x^2 - c) - b^2*c^3)*log((x^2 + c)/(x^2 - c))/((x^2 + c)^2/(x^2 - c)^2 - 2*(x^2 + c)/(x^2 - c) + 1) - 4*((x^2 + c)*a^2*c^3/(x^2 - c) + (x^2 + c)*a*b*c^3/(x^2 - c) - a*b*c^3)/((x^2 + c)^2/(x^2 - c)^2 - 2*(x^2 + c)/(x^2 - c) + 1))/c","B",0
172,0,0,0,0.000000," ","integrate(x*(a+b*arctanh(c/x^2))^2,x, algorithm=""giac"")","\int {\left(b \operatorname{artanh}\left(\frac{c}{x^{2}}\right) + a\right)}^{2} x\,{d x}"," ",0,"integrate((b*arctanh(c/x^2) + a)^2*x, x)","F",0
173,0,0,0,0.000000," ","integrate((a+b*arctanh(c/x^2))^2/x,x, algorithm=""giac"")","\int \frac{{\left(b \operatorname{artanh}\left(\frac{c}{x^{2}}\right) + a\right)}^{2}}{x}\,{d x}"," ",0,"integrate((b*arctanh(c/x^2) + a)^2/x, x)","F",0
174,0,0,0,0.000000," ","integrate((a+b*arctanh(c/x^2))^2/x^3,x, algorithm=""giac"")","\int \frac{{\left(b \operatorname{artanh}\left(\frac{c}{x^{2}}\right) + a\right)}^{2}}{x^{3}}\,{d x}"," ",0,"integrate((b*arctanh(c/x^2) + a)^2/x^3, x)","F",0
175,0,0,0,0.000000," ","integrate((a+b*arctanh(c/x^2))^2/x^5,x, algorithm=""giac"")","\int \frac{{\left(b \operatorname{artanh}\left(\frac{c}{x^{2}}\right) + a\right)}^{2}}{x^{5}}\,{d x}"," ",0,"integrate((b*arctanh(c/x^2) + a)^2/x^5, x)","F",0
176,0,0,0,0.000000," ","integrate(x^4*(a+b*arctanh(c/x^2))^2,x, algorithm=""giac"")","\int {\left(b \operatorname{artanh}\left(\frac{c}{x^{2}}\right) + a\right)}^{2} x^{4}\,{d x}"," ",0,"integrate((b*arctanh(c/x^2) + a)^2*x^4, x)","F",0
177,0,0,0,0.000000," ","integrate(x^2*(a+b*arctanh(c/x^2))^2,x, algorithm=""giac"")","\int {\left(b \operatorname{artanh}\left(\frac{c}{x^{2}}\right) + a\right)}^{2} x^{2}\,{d x}"," ",0,"integrate((b*arctanh(c/x^2) + a)^2*x^2, x)","F",0
178,0,0,0,0.000000," ","integrate((a+b*arctanh(c/x^2))^2,x, algorithm=""giac"")","\int {\left(b \operatorname{artanh}\left(\frac{c}{x^{2}}\right) + a\right)}^{2}\,{d x}"," ",0,"integrate((b*arctanh(c/x^2) + a)^2, x)","F",0
179,0,0,0,0.000000," ","integrate((a+b*arctanh(c/x^2))^2/x^2,x, algorithm=""giac"")","\int \frac{{\left(b \operatorname{artanh}\left(\frac{c}{x^{2}}\right) + a\right)}^{2}}{x^{2}}\,{d x}"," ",0,"integrate((b*arctanh(c/x^2) + a)^2/x^2, x)","F",0
180,0,0,0,0.000000," ","integrate((a+b*arctanh(c/x^2))^2/x^4,x, algorithm=""giac"")","\int \frac{{\left(b \operatorname{artanh}\left(\frac{c}{x^{2}}\right) + a\right)}^{2}}{x^{4}}\,{d x}"," ",0,"integrate((b*arctanh(c/x^2) + a)^2/x^4, x)","F",0
181,0,0,0,0.000000," ","integrate((a+b*arctanh(c/x^2))^2/x^6,x, algorithm=""giac"")","\int \frac{{\left(b \operatorname{artanh}\left(\frac{c}{x^{2}}\right) + a\right)}^{2}}{x^{6}}\,{d x}"," ",0,"integrate((b*arctanh(c/x^2) + a)^2/x^6, x)","F",0
182,0,0,0,0.000000," ","integrate((d*x)^m*(a+b*arctanh(c/x^2))^3,x, algorithm=""giac"")","\int {\left(b \operatorname{artanh}\left(\frac{c}{x^{2}}\right) + a\right)}^{3} \left(d x\right)^{m}\,{d x}"," ",0,"integrate((b*arctanh(c/x^2) + a)^3*(d*x)^m, x)","F",0
183,0,0,0,0.000000," ","integrate((d*x)^m*(a+b*arctanh(c/x^2))^2,x, algorithm=""giac"")","\int {\left(b \operatorname{artanh}\left(\frac{c}{x^{2}}\right) + a\right)}^{2} \left(d x\right)^{m}\,{d x}"," ",0,"integrate((b*arctanh(c/x^2) + a)^2*(d*x)^m, x)","F",0
184,0,0,0,0.000000," ","integrate((d*x)^m*(a+b*arctanh(c/x^2)),x, algorithm=""giac"")","\int {\left(b \operatorname{artanh}\left(\frac{c}{x^{2}}\right) + a\right)} \left(d x\right)^{m}\,{d x}"," ",0,"integrate((b*arctanh(c/x^2) + a)*(d*x)^m, x)","F",0
185,0,0,0,0.000000," ","integrate((d*x)^m/(a+b*arctanh(c/x^2)),x, algorithm=""giac"")","\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=""giac"")","\int \frac{\left(d x\right)^{m}}{{\left(b \operatorname{artanh}\left(\frac{c}{x^{2}}\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((d*x)^m/(b*arctanh(c/x^2) + a)^2, x)","F",0
187,1,359,0,0.205043," ","integrate(x^3*(a+b*arctanh(c*x^(1/2))),x, algorithm=""giac"")","\frac{1}{4} \, a x^{4} + \frac{2}{105} \, b c {\left(\frac{\frac{105 \, {\left(c \sqrt{x} + 1\right)}^{6}}{{\left(c \sqrt{x} - 1\right)}^{6}} - \frac{315 \, {\left(c \sqrt{x} + 1\right)}^{5}}{{\left(c \sqrt{x} - 1\right)}^{5}} + \frac{770 \, {\left(c \sqrt{x} + 1\right)}^{4}}{{\left(c \sqrt{x} - 1\right)}^{4}} - \frac{770 \, {\left(c \sqrt{x} + 1\right)}^{3}}{{\left(c \sqrt{x} - 1\right)}^{3}} + \frac{609 \, {\left(c \sqrt{x} + 1\right)}^{2}}{{\left(c \sqrt{x} - 1\right)}^{2}} - \frac{203 \, {\left(c \sqrt{x} + 1\right)}}{c \sqrt{x} - 1} + 44}{c^{9} {\left(\frac{c \sqrt{x} + 1}{c \sqrt{x} - 1} - 1\right)}^{7}} + \frac{105 \, {\left(\frac{{\left(c \sqrt{x} + 1\right)}^{7}}{{\left(c \sqrt{x} - 1\right)}^{7}} + \frac{7 \, {\left(c \sqrt{x} + 1\right)}^{5}}{{\left(c \sqrt{x} - 1\right)}^{5}} + \frac{7 \, {\left(c \sqrt{x} + 1\right)}^{3}}{{\left(c \sqrt{x} - 1\right)}^{3}} + \frac{c \sqrt{x} + 1}{c \sqrt{x} - 1}\right)} \log\left(-\frac{\frac{c {\left(\frac{c \sqrt{x} + 1}{c \sqrt{x} - 1} + 1\right)}}{\frac{{\left(c \sqrt{x} + 1\right)} c}{c \sqrt{x} - 1} - c} + 1}{\frac{c {\left(\frac{c \sqrt{x} + 1}{c \sqrt{x} - 1} + 1\right)}}{\frac{{\left(c \sqrt{x} + 1\right)} c}{c \sqrt{x} - 1} - c} - 1}\right)}{c^{9} {\left(\frac{c \sqrt{x} + 1}{c \sqrt{x} - 1} - 1\right)}^{8}}\right)}"," ",0,"1/4*a*x^4 + 2/105*b*c*((105*(c*sqrt(x) + 1)^6/(c*sqrt(x) - 1)^6 - 315*(c*sqrt(x) + 1)^5/(c*sqrt(x) - 1)^5 + 770*(c*sqrt(x) + 1)^4/(c*sqrt(x) - 1)^4 - 770*(c*sqrt(x) + 1)^3/(c*sqrt(x) - 1)^3 + 609*(c*sqrt(x) + 1)^2/(c*sqrt(x) - 1)^2 - 203*(c*sqrt(x) + 1)/(c*sqrt(x) - 1) + 44)/(c^9*((c*sqrt(x) + 1)/(c*sqrt(x) - 1) - 1)^7) + 105*((c*sqrt(x) + 1)^7/(c*sqrt(x) - 1)^7 + 7*(c*sqrt(x) + 1)^5/(c*sqrt(x) - 1)^5 + 7*(c*sqrt(x) + 1)^3/(c*sqrt(x) - 1)^3 + (c*sqrt(x) + 1)/(c*sqrt(x) - 1))*log(-(c*((c*sqrt(x) + 1)/(c*sqrt(x) - 1) + 1)/((c*sqrt(x) + 1)*c/(c*sqrt(x) - 1) - c) + 1)/(c*((c*sqrt(x) + 1)/(c*sqrt(x) - 1) + 1)/((c*sqrt(x) + 1)*c/(c*sqrt(x) - 1) - c) - 1))/(c^9*((c*sqrt(x) + 1)/(c*sqrt(x) - 1) - 1)^8))","B",0
188,1,301,0,0.197194," ","integrate(x^2*(a+b*arctanh(c*x^(1/2))),x, algorithm=""giac"")","\frac{1}{3} \, a x^{3} + \frac{2}{45} \, b c {\left(\frac{\frac{45 \, {\left(c \sqrt{x} + 1\right)}^{4}}{{\left(c \sqrt{x} - 1\right)}^{4}} - \frac{90 \, {\left(c \sqrt{x} + 1\right)}^{3}}{{\left(c \sqrt{x} - 1\right)}^{3}} + \frac{140 \, {\left(c \sqrt{x} + 1\right)}^{2}}{{\left(c \sqrt{x} - 1\right)}^{2}} - \frac{70 \, {\left(c \sqrt{x} + 1\right)}}{c \sqrt{x} - 1} + 23}{c^{7} {\left(\frac{c \sqrt{x} + 1}{c \sqrt{x} - 1} - 1\right)}^{5}} + \frac{15 \, {\left(\frac{3 \, {\left(c \sqrt{x} + 1\right)}^{5}}{{\left(c \sqrt{x} - 1\right)}^{5}} + \frac{10 \, {\left(c \sqrt{x} + 1\right)}^{3}}{{\left(c \sqrt{x} - 1\right)}^{3}} + \frac{3 \, {\left(c \sqrt{x} + 1\right)}}{c \sqrt{x} - 1}\right)} \log\left(-\frac{\frac{c {\left(\frac{c \sqrt{x} + 1}{c \sqrt{x} - 1} + 1\right)}}{\frac{{\left(c \sqrt{x} + 1\right)} c}{c \sqrt{x} - 1} - c} + 1}{\frac{c {\left(\frac{c \sqrt{x} + 1}{c \sqrt{x} - 1} + 1\right)}}{\frac{{\left(c \sqrt{x} + 1\right)} c}{c \sqrt{x} - 1} - c} - 1}\right)}{c^{7} {\left(\frac{c \sqrt{x} + 1}{c \sqrt{x} - 1} - 1\right)}^{6}}\right)}"," ",0,"1/3*a*x^3 + 2/45*b*c*((45*(c*sqrt(x) + 1)^4/(c*sqrt(x) - 1)^4 - 90*(c*sqrt(x) + 1)^3/(c*sqrt(x) - 1)^3 + 140*(c*sqrt(x) + 1)^2/(c*sqrt(x) - 1)^2 - 70*(c*sqrt(x) + 1)/(c*sqrt(x) - 1) + 23)/(c^7*((c*sqrt(x) + 1)/(c*sqrt(x) - 1) - 1)^5) + 15*(3*(c*sqrt(x) + 1)^5/(c*sqrt(x) - 1)^5 + 10*(c*sqrt(x) + 1)^3/(c*sqrt(x) - 1)^3 + 3*(c*sqrt(x) + 1)/(c*sqrt(x) - 1))*log(-(c*((c*sqrt(x) + 1)/(c*sqrt(x) - 1) + 1)/((c*sqrt(x) + 1)*c/(c*sqrt(x) - 1) - c) + 1)/(c*((c*sqrt(x) + 1)/(c*sqrt(x) - 1) + 1)/((c*sqrt(x) + 1)*c/(c*sqrt(x) - 1) - c) - 1))/(c^7*((c*sqrt(x) + 1)/(c*sqrt(x) - 1) - 1)^6))","B",0
189,1,239,0,0.212225," ","integrate(x*(a+b*arctanh(c*x^(1/2))),x, algorithm=""giac"")","\frac{1}{2} \, a x^{2} + \frac{2}{3} \, b c {\left(\frac{\frac{3 \, {\left(c \sqrt{x} + 1\right)}^{2}}{{\left(c \sqrt{x} - 1\right)}^{2}} - \frac{3 \, {\left(c \sqrt{x} + 1\right)}}{c \sqrt{x} - 1} + 2}{c^{5} {\left(\frac{c \sqrt{x} + 1}{c \sqrt{x} - 1} - 1\right)}^{3}} + \frac{3 \, {\left(\frac{{\left(c \sqrt{x} + 1\right)}^{3}}{{\left(c \sqrt{x} - 1\right)}^{3}} + \frac{c \sqrt{x} + 1}{c \sqrt{x} - 1}\right)} \log\left(-\frac{\frac{c {\left(\frac{c \sqrt{x} + 1}{c \sqrt{x} - 1} + 1\right)}}{\frac{{\left(c \sqrt{x} + 1\right)} c}{c \sqrt{x} - 1} - c} + 1}{\frac{c {\left(\frac{c \sqrt{x} + 1}{c \sqrt{x} - 1} + 1\right)}}{\frac{{\left(c \sqrt{x} + 1\right)} c}{c \sqrt{x} - 1} - c} - 1}\right)}{c^{5} {\left(\frac{c \sqrt{x} + 1}{c \sqrt{x} - 1} - 1\right)}^{4}}\right)}"," ",0,"1/2*a*x^2 + 2/3*b*c*((3*(c*sqrt(x) + 1)^2/(c*sqrt(x) - 1)^2 - 3*(c*sqrt(x) + 1)/(c*sqrt(x) - 1) + 2)/(c^5*((c*sqrt(x) + 1)/(c*sqrt(x) - 1) - 1)^3) + 3*((c*sqrt(x) + 1)^3/(c*sqrt(x) - 1)^3 + (c*sqrt(x) + 1)/(c*sqrt(x) - 1))*log(-(c*((c*sqrt(x) + 1)/(c*sqrt(x) - 1) + 1)/((c*sqrt(x) + 1)*c/(c*sqrt(x) - 1) - c) + 1)/(c*((c*sqrt(x) + 1)/(c*sqrt(x) - 1) + 1)/((c*sqrt(x) + 1)*c/(c*sqrt(x) - 1) - c) - 1))/(c^5*((c*sqrt(x) + 1)/(c*sqrt(x) - 1) - 1)^4))","B",0
190,1,174,0,0.196705," ","integrate(a+b*arctanh(c*x^(1/2)),x, algorithm=""giac"")","2 \, b c {\left(\frac{1}{c^{3} {\left(\frac{c \sqrt{x} + 1}{c \sqrt{x} - 1} - 1\right)}} + \frac{{\left(c \sqrt{x} + 1\right)} \log\left(-\frac{\frac{c {\left(\frac{c \sqrt{x} + 1}{c \sqrt{x} - 1} + 1\right)}}{\frac{{\left(c \sqrt{x} + 1\right)} c}{c \sqrt{x} - 1} - c} + 1}{\frac{c {\left(\frac{c \sqrt{x} + 1}{c \sqrt{x} - 1} + 1\right)}}{\frac{{\left(c \sqrt{x} + 1\right)} c}{c \sqrt{x} - 1} - c} - 1}\right)}{{\left(c \sqrt{x} - 1\right)} c^{3} {\left(\frac{c \sqrt{x} + 1}{c \sqrt{x} - 1} - 1\right)}^{2}}\right)} + a x"," ",0,"2*b*c*(1/(c^3*((c*sqrt(x) + 1)/(c*sqrt(x) - 1) - 1)) + (c*sqrt(x) + 1)*log(-(c*((c*sqrt(x) + 1)/(c*sqrt(x) - 1) + 1)/((c*sqrt(x) + 1)*c/(c*sqrt(x) - 1) - c) + 1)/(c*((c*sqrt(x) + 1)/(c*sqrt(x) - 1) + 1)/((c*sqrt(x) + 1)*c/(c*sqrt(x) - 1) - c) - 1))/((c*sqrt(x) - 1)*c^3*((c*sqrt(x) + 1)/(c*sqrt(x) - 1) - 1)^2)) + a*x","B",0
191,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x^(1/2)))/x,x, algorithm=""giac"")","\int \frac{b \operatorname{artanh}\left(c \sqrt{x}\right) + a}{x}\,{d x}"," ",0,"integrate((b*arctanh(c*sqrt(x)) + a)/x, x)","F",0
192,1,168,0,0.431003," ","integrate((a+b*arctanh(c*x^(1/2)))/x^2,x, algorithm=""giac"")","2 \, {\left(\frac{{\left(c \sqrt{x} + 1\right)} b c \log\left(-\frac{c \sqrt{x} + 1}{c \sqrt{x} - 1}\right)}{{\left(c \sqrt{x} - 1\right)} {\left(\frac{{\left(c \sqrt{x} + 1\right)}^{2}}{{\left(c \sqrt{x} - 1\right)}^{2}} + \frac{2 \, {\left(c \sqrt{x} + 1\right)}}{c \sqrt{x} - 1} + 1\right)}} + \frac{\frac{2 \, {\left(c \sqrt{x} + 1\right)} a c}{c \sqrt{x} - 1} + \frac{{\left(c \sqrt{x} + 1\right)} b c}{c \sqrt{x} - 1} + b c}{\frac{{\left(c \sqrt{x} + 1\right)}^{2}}{{\left(c \sqrt{x} - 1\right)}^{2}} + \frac{2 \, {\left(c \sqrt{x} + 1\right)}}{c \sqrt{x} - 1} + 1}\right)} c"," ",0,"2*((c*sqrt(x) + 1)*b*c*log(-(c*sqrt(x) + 1)/(c*sqrt(x) - 1))/((c*sqrt(x) - 1)*((c*sqrt(x) + 1)^2/(c*sqrt(x) - 1)^2 + 2*(c*sqrt(x) + 1)/(c*sqrt(x) - 1) + 1)) + (2*(c*sqrt(x) + 1)*a*c/(c*sqrt(x) - 1) + (c*sqrt(x) + 1)*b*c/(c*sqrt(x) - 1) + b*c)/((c*sqrt(x) + 1)^2/(c*sqrt(x) - 1)^2 + 2*(c*sqrt(x) + 1)/(c*sqrt(x) - 1) + 1))*c","B",0
193,1,356,0,0.195311," ","integrate((a+b*arctanh(c*x^(1/2)))/x^3,x, algorithm=""giac"")","\frac{2}{3} \, c {\left(\frac{3 \, {\left(\frac{{\left(c \sqrt{x} + 1\right)}^{3} b c^{3}}{{\left(c \sqrt{x} - 1\right)}^{3}} + \frac{{\left(c \sqrt{x} + 1\right)} b c^{3}}{c \sqrt{x} - 1}\right)} \log\left(-\frac{c \sqrt{x} + 1}{c \sqrt{x} - 1}\right)}{\frac{{\left(c \sqrt{x} + 1\right)}^{4}}{{\left(c \sqrt{x} - 1\right)}^{4}} + \frac{4 \, {\left(c \sqrt{x} + 1\right)}^{3}}{{\left(c \sqrt{x} - 1\right)}^{3}} + \frac{6 \, {\left(c \sqrt{x} + 1\right)}^{2}}{{\left(c \sqrt{x} - 1\right)}^{2}} + \frac{4 \, {\left(c \sqrt{x} + 1\right)}}{c \sqrt{x} - 1} + 1} + \frac{\frac{6 \, {\left(c \sqrt{x} + 1\right)}^{3} a c^{3}}{{\left(c \sqrt{x} - 1\right)}^{3}} + \frac{6 \, {\left(c \sqrt{x} + 1\right)} a c^{3}}{c \sqrt{x} - 1} + \frac{3 \, {\left(c \sqrt{x} + 1\right)}^{3} b c^{3}}{{\left(c \sqrt{x} - 1\right)}^{3}} + \frac{6 \, {\left(c \sqrt{x} + 1\right)}^{2} b c^{3}}{{\left(c \sqrt{x} - 1\right)}^{2}} + \frac{5 \, {\left(c \sqrt{x} + 1\right)} b c^{3}}{c \sqrt{x} - 1} + 2 \, b c^{3}}{\frac{{\left(c \sqrt{x} + 1\right)}^{4}}{{\left(c \sqrt{x} - 1\right)}^{4}} + \frac{4 \, {\left(c \sqrt{x} + 1\right)}^{3}}{{\left(c \sqrt{x} - 1\right)}^{3}} + \frac{6 \, {\left(c \sqrt{x} + 1\right)}^{2}}{{\left(c \sqrt{x} - 1\right)}^{2}} + \frac{4 \, {\left(c \sqrt{x} + 1\right)}}{c \sqrt{x} - 1} + 1}\right)}"," ",0,"2/3*c*(3*((c*sqrt(x) + 1)^3*b*c^3/(c*sqrt(x) - 1)^3 + (c*sqrt(x) + 1)*b*c^3/(c*sqrt(x) - 1))*log(-(c*sqrt(x) + 1)/(c*sqrt(x) - 1))/((c*sqrt(x) + 1)^4/(c*sqrt(x) - 1)^4 + 4*(c*sqrt(x) + 1)^3/(c*sqrt(x) - 1)^3 + 6*(c*sqrt(x) + 1)^2/(c*sqrt(x) - 1)^2 + 4*(c*sqrt(x) + 1)/(c*sqrt(x) - 1) + 1) + (6*(c*sqrt(x) + 1)^3*a*c^3/(c*sqrt(x) - 1)^3 + 6*(c*sqrt(x) + 1)*a*c^3/(c*sqrt(x) - 1) + 3*(c*sqrt(x) + 1)^3*b*c^3/(c*sqrt(x) - 1)^3 + 6*(c*sqrt(x) + 1)^2*b*c^3/(c*sqrt(x) - 1)^2 + 5*(c*sqrt(x) + 1)*b*c^3/(c*sqrt(x) - 1) + 2*b*c^3)/((c*sqrt(x) + 1)^4/(c*sqrt(x) - 1)^4 + 4*(c*sqrt(x) + 1)^3/(c*sqrt(x) - 1)^3 + 6*(c*sqrt(x) + 1)^2/(c*sqrt(x) - 1)^2 + 4*(c*sqrt(x) + 1)/(c*sqrt(x) - 1) + 1))","B",0
194,1,534,0,0.218815," ","integrate((a+b*arctanh(c*x^(1/2)))/x^4,x, algorithm=""giac"")","\frac{2}{45} \, c {\left(\frac{15 \, {\left(\frac{3 \, {\left(c \sqrt{x} + 1\right)}^{5} b c^{5}}{{\left(c \sqrt{x} - 1\right)}^{5}} + \frac{10 \, {\left(c \sqrt{x} + 1\right)}^{3} b c^{5}}{{\left(c \sqrt{x} - 1\right)}^{3}} + \frac{3 \, {\left(c \sqrt{x} + 1\right)} b c^{5}}{c \sqrt{x} - 1}\right)} \log\left(-\frac{c \sqrt{x} + 1}{c \sqrt{x} - 1}\right)}{\frac{{\left(c \sqrt{x} + 1\right)}^{6}}{{\left(c \sqrt{x} - 1\right)}^{6}} + \frac{6 \, {\left(c \sqrt{x} + 1\right)}^{5}}{{\left(c \sqrt{x} - 1\right)}^{5}} + \frac{15 \, {\left(c \sqrt{x} + 1\right)}^{4}}{{\left(c \sqrt{x} - 1\right)}^{4}} + \frac{20 \, {\left(c \sqrt{x} + 1\right)}^{3}}{{\left(c \sqrt{x} - 1\right)}^{3}} + \frac{15 \, {\left(c \sqrt{x} + 1\right)}^{2}}{{\left(c \sqrt{x} - 1\right)}^{2}} + \frac{6 \, {\left(c \sqrt{x} + 1\right)}}{c \sqrt{x} - 1} + 1} + \frac{\frac{90 \, {\left(c \sqrt{x} + 1\right)}^{5} a c^{5}}{{\left(c \sqrt{x} - 1\right)}^{5}} + \frac{300 \, {\left(c \sqrt{x} + 1\right)}^{3} a c^{5}}{{\left(c \sqrt{x} - 1\right)}^{3}} + \frac{90 \, {\left(c \sqrt{x} + 1\right)} a c^{5}}{c \sqrt{x} - 1} + \frac{45 \, {\left(c \sqrt{x} + 1\right)}^{5} b c^{5}}{{\left(c \sqrt{x} - 1\right)}^{5}} + \frac{135 \, {\left(c \sqrt{x} + 1\right)}^{4} b c^{5}}{{\left(c \sqrt{x} - 1\right)}^{4}} + \frac{230 \, {\left(c \sqrt{x} + 1\right)}^{3} b c^{5}}{{\left(c \sqrt{x} - 1\right)}^{3}} + \frac{210 \, {\left(c \sqrt{x} + 1\right)}^{2} b c^{5}}{{\left(c \sqrt{x} - 1\right)}^{2}} + \frac{93 \, {\left(c \sqrt{x} + 1\right)} b c^{5}}{c \sqrt{x} - 1} + 23 \, b c^{5}}{\frac{{\left(c \sqrt{x} + 1\right)}^{6}}{{\left(c \sqrt{x} - 1\right)}^{6}} + \frac{6 \, {\left(c \sqrt{x} + 1\right)}^{5}}{{\left(c \sqrt{x} - 1\right)}^{5}} + \frac{15 \, {\left(c \sqrt{x} + 1\right)}^{4}}{{\left(c \sqrt{x} - 1\right)}^{4}} + \frac{20 \, {\left(c \sqrt{x} + 1\right)}^{3}}{{\left(c \sqrt{x} - 1\right)}^{3}} + \frac{15 \, {\left(c \sqrt{x} + 1\right)}^{2}}{{\left(c \sqrt{x} - 1\right)}^{2}} + \frac{6 \, {\left(c \sqrt{x} + 1\right)}}{c \sqrt{x} - 1} + 1}\right)}"," ",0,"2/45*c*(15*(3*(c*sqrt(x) + 1)^5*b*c^5/(c*sqrt(x) - 1)^5 + 10*(c*sqrt(x) + 1)^3*b*c^5/(c*sqrt(x) - 1)^3 + 3*(c*sqrt(x) + 1)*b*c^5/(c*sqrt(x) - 1))*log(-(c*sqrt(x) + 1)/(c*sqrt(x) - 1))/((c*sqrt(x) + 1)^6/(c*sqrt(x) - 1)^6 + 6*(c*sqrt(x) + 1)^5/(c*sqrt(x) - 1)^5 + 15*(c*sqrt(x) + 1)^4/(c*sqrt(x) - 1)^4 + 20*(c*sqrt(x) + 1)^3/(c*sqrt(x) - 1)^3 + 15*(c*sqrt(x) + 1)^2/(c*sqrt(x) - 1)^2 + 6*(c*sqrt(x) + 1)/(c*sqrt(x) - 1) + 1) + (90*(c*sqrt(x) + 1)^5*a*c^5/(c*sqrt(x) - 1)^5 + 300*(c*sqrt(x) + 1)^3*a*c^5/(c*sqrt(x) - 1)^3 + 90*(c*sqrt(x) + 1)*a*c^5/(c*sqrt(x) - 1) + 45*(c*sqrt(x) + 1)^5*b*c^5/(c*sqrt(x) - 1)^5 + 135*(c*sqrt(x) + 1)^4*b*c^5/(c*sqrt(x) - 1)^4 + 230*(c*sqrt(x) + 1)^3*b*c^5/(c*sqrt(x) - 1)^3 + 210*(c*sqrt(x) + 1)^2*b*c^5/(c*sqrt(x) - 1)^2 + 93*(c*sqrt(x) + 1)*b*c^5/(c*sqrt(x) - 1) + 23*b*c^5)/((c*sqrt(x) + 1)^6/(c*sqrt(x) - 1)^6 + 6*(c*sqrt(x) + 1)^5/(c*sqrt(x) - 1)^5 + 15*(c*sqrt(x) + 1)^4/(c*sqrt(x) - 1)^4 + 20*(c*sqrt(x) + 1)^3/(c*sqrt(x) - 1)^3 + 15*(c*sqrt(x) + 1)^2/(c*sqrt(x) - 1)^2 + 6*(c*sqrt(x) + 1)/(c*sqrt(x) - 1) + 1))","B",0
195,0,0,0,0.000000," ","integrate(x^3*(a+b*arctanh(c*x^(1/2)))^2,x, algorithm=""giac"")","\int {\left(b \operatorname{artanh}\left(c \sqrt{x}\right) + a\right)}^{2} x^{3}\,{d x}"," ",0,"integrate((b*arctanh(c*sqrt(x)) + a)^2*x^3, x)","F",0
196,0,0,0,0.000000," ","integrate(x^2*(a+b*arctanh(c*x^(1/2)))^2,x, algorithm=""giac"")","\int {\left(b \operatorname{artanh}\left(c \sqrt{x}\right) + a\right)}^{2} x^{2}\,{d x}"," ",0,"integrate((b*arctanh(c*sqrt(x)) + a)^2*x^2, x)","F",0
197,0,0,0,0.000000," ","integrate(x*(a+b*arctanh(c*x^(1/2)))^2,x, algorithm=""giac"")","\int {\left(b \operatorname{artanh}\left(c \sqrt{x}\right) + a\right)}^{2} x\,{d x}"," ",0,"integrate((b*arctanh(c*sqrt(x)) + a)^2*x, x)","F",0
198,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x^(1/2)))^2,x, algorithm=""giac"")","\int {\left(b \operatorname{artanh}\left(c \sqrt{x}\right) + a\right)}^{2}\,{d x}"," ",0,"integrate((b*arctanh(c*sqrt(x)) + a)^2, x)","F",0
199,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x^(1/2)))^2/x,x, algorithm=""giac"")","\int \frac{{\left(b \operatorname{artanh}\left(c \sqrt{x}\right) + a\right)}^{2}}{x}\,{d x}"," ",0,"integrate((b*arctanh(c*sqrt(x)) + a)^2/x, x)","F",0
200,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x^(1/2)))^2/x^2,x, algorithm=""giac"")","\int \frac{{\left(b \operatorname{artanh}\left(c \sqrt{x}\right) + a\right)}^{2}}{x^{2}}\,{d x}"," ",0,"integrate((b*arctanh(c*sqrt(x)) + a)^2/x^2, x)","F",0
201,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x^(1/2)))^2/x^3,x, algorithm=""giac"")","\int \frac{{\left(b \operatorname{artanh}\left(c \sqrt{x}\right) + a\right)}^{2}}{x^{3}}\,{d x}"," ",0,"integrate((b*arctanh(c*sqrt(x)) + a)^2/x^3, x)","F",0
202,0,0,0,0.000000," ","integrate(x^3*(a+b*arctanh(c*x^(1/2)))^3,x, algorithm=""giac"")","\int {\left(b \operatorname{artanh}\left(c \sqrt{x}\right) + a\right)}^{3} x^{3}\,{d x}"," ",0,"integrate((b*arctanh(c*sqrt(x)) + a)^3*x^3, x)","F",0
203,0,0,0,0.000000," ","integrate(x^2*(a+b*arctanh(c*x^(1/2)))^3,x, algorithm=""giac"")","\int {\left(b \operatorname{artanh}\left(c \sqrt{x}\right) + a\right)}^{3} x^{2}\,{d x}"," ",0,"integrate((b*arctanh(c*sqrt(x)) + a)^3*x^2, x)","F",0
204,0,0,0,0.000000," ","integrate(x*(a+b*arctanh(c*x^(1/2)))^3,x, algorithm=""giac"")","\int {\left(b \operatorname{artanh}\left(c \sqrt{x}\right) + a\right)}^{3} x\,{d x}"," ",0,"integrate((b*arctanh(c*sqrt(x)) + a)^3*x, x)","F",0
205,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x^(1/2)))^3,x, algorithm=""giac"")","\int {\left(b \operatorname{artanh}\left(c \sqrt{x}\right) + a\right)}^{3}\,{d x}"," ",0,"integrate((b*arctanh(c*sqrt(x)) + a)^3, x)","F",0
206,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x^(1/2)))^3/x,x, algorithm=""giac"")","\int \frac{{\left(b \operatorname{artanh}\left(c \sqrt{x}\right) + a\right)}^{3}}{x}\,{d x}"," ",0,"integrate((b*arctanh(c*sqrt(x)) + a)^3/x, x)","F",0
207,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x^(1/2)))^3/x^2,x, algorithm=""giac"")","\int \frac{{\left(b \operatorname{artanh}\left(c \sqrt{x}\right) + a\right)}^{3}}{x^{2}}\,{d x}"," ",0,"integrate((b*arctanh(c*sqrt(x)) + a)^3/x^2, x)","F",0
208,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x^(1/2)))^3/x^3,x, algorithm=""giac"")","\int \frac{{\left(b \operatorname{artanh}\left(c \sqrt{x}\right) + a\right)}^{3}}{x^{3}}\,{d x}"," ",0,"integrate((b*arctanh(c*sqrt(x)) + a)^3/x^3, x)","F",0
209,1,170,0,0.204234," ","integrate(x^(3/2)*arctanh(x^(1/2)),x, algorithm=""giac"")","\frac{8 \, {\left(\frac{{\left(\sqrt{x} + 1\right)}^{3}}{{\left(\sqrt{x} - 1\right)}^{3}} - \frac{{\left(\sqrt{x} + 1\right)}^{2}}{{\left(\sqrt{x} - 1\right)}^{2}} + \frac{\sqrt{x} + 1}{\sqrt{x} - 1}\right)}}{5 \, {\left(\frac{\sqrt{x} + 1}{\sqrt{x} - 1} - 1\right)}^{4}} + \frac{2 \, {\left(\frac{5 \, {\left(\sqrt{x} + 1\right)}^{4}}{{\left(\sqrt{x} - 1\right)}^{4}} + \frac{10 \, {\left(\sqrt{x} + 1\right)}^{2}}{{\left(\sqrt{x} - 1\right)}^{2}} + 1\right)} \log\left(-\frac{\sqrt{x} + 1}{\sqrt{x} - 1}\right)}{5 \, {\left(\frac{\sqrt{x} + 1}{\sqrt{x} - 1} - 1\right)}^{5}} + \frac{2}{5} \, \log\left(\frac{\sqrt{x} + 1}{{\left| \sqrt{x} - 1 \right|}}\right) - \frac{2}{5} \, \log\left({\left| -\frac{\sqrt{x} + 1}{\sqrt{x} - 1} + 1 \right|}\right)"," ",0,"8/5*((sqrt(x) + 1)^3/(sqrt(x) - 1)^3 - (sqrt(x) + 1)^2/(sqrt(x) - 1)^2 + (sqrt(x) + 1)/(sqrt(x) - 1))/((sqrt(x) + 1)/(sqrt(x) - 1) - 1)^4 + 2/5*(5*(sqrt(x) + 1)^4/(sqrt(x) - 1)^4 + 10*(sqrt(x) + 1)^2/(sqrt(x) - 1)^2 + 1)*log(-(sqrt(x) + 1)/(sqrt(x) - 1))/((sqrt(x) + 1)/(sqrt(x) - 1) - 1)^5 + 2/5*log((sqrt(x) + 1)/abs(sqrt(x) - 1)) - 2/5*log(abs(-(sqrt(x) + 1)/(sqrt(x) - 1) + 1))","B",0
210,1,121,0,0.153974," ","integrate(arctanh(x^(1/2))*x^(1/2),x, algorithm=""giac"")","\frac{2 \, {\left(\frac{3 \, {\left(\sqrt{x} + 1\right)}^{2}}{{\left(\sqrt{x} - 1\right)}^{2}} + 1\right)} \log\left(-\frac{\sqrt{x} + 1}{\sqrt{x} - 1}\right)}{3 \, {\left(\frac{\sqrt{x} + 1}{\sqrt{x} - 1} - 1\right)}^{3}} + \frac{4 \, {\left(\sqrt{x} + 1\right)}}{3 \, {\left(\sqrt{x} - 1\right)} {\left(\frac{\sqrt{x} + 1}{\sqrt{x} - 1} - 1\right)}^{2}} + \frac{2}{3} \, \log\left(\frac{\sqrt{x} + 1}{{\left| \sqrt{x} - 1 \right|}}\right) - \frac{2}{3} \, \log\left({\left| -\frac{\sqrt{x} + 1}{\sqrt{x} - 1} + 1 \right|}\right)"," ",0,"2/3*(3*(sqrt(x) + 1)^2/(sqrt(x) - 1)^2 + 1)*log(-(sqrt(x) + 1)/(sqrt(x) - 1))/((sqrt(x) + 1)/(sqrt(x) - 1) - 1)^3 + 4/3*(sqrt(x) + 1)/((sqrt(x) - 1)*((sqrt(x) + 1)/(sqrt(x) - 1) - 1)^2) + 2/3*log((sqrt(x) + 1)/abs(sqrt(x) - 1)) - 2/3*log(abs(-(sqrt(x) + 1)/(sqrt(x) - 1) + 1))","B",0
211,1,72,0,0.241631," ","integrate(arctanh(x^(1/2))/x^(1/2),x, algorithm=""giac"")","\frac{2 \, \log\left(-\frac{\sqrt{x} + 1}{\sqrt{x} - 1}\right)}{\frac{\sqrt{x} + 1}{\sqrt{x} - 1} - 1} + 2 \, \log\left(\frac{\sqrt{x} + 1}{{\left| \sqrt{x} - 1 \right|}}\right) - 2 \, \log\left({\left| -\frac{\sqrt{x} + 1}{\sqrt{x} - 1} + 1 \right|}\right)"," ",0,"2*log(-(sqrt(x) + 1)/(sqrt(x) - 1))/((sqrt(x) + 1)/(sqrt(x) - 1) - 1) + 2*log((sqrt(x) + 1)/abs(sqrt(x) - 1)) - 2*log(abs(-(sqrt(x) + 1)/(sqrt(x) - 1) + 1))","B",0
212,1,72,0,0.176829," ","integrate(arctanh(x^(1/2))/x^(3/2),x, algorithm=""giac"")","\frac{2 \, \log\left(-\frac{\sqrt{x} + 1}{\sqrt{x} - 1}\right)}{\frac{\sqrt{x} + 1}{\sqrt{x} - 1} + 1} - 2 \, \log\left(\frac{\sqrt{x} + 1}{{\left| \sqrt{x} - 1 \right|}}\right) + 2 \, \log\left({\left| -\frac{\sqrt{x} + 1}{\sqrt{x} - 1} - 1 \right|}\right)"," ",0,"2*log(-(sqrt(x) + 1)/(sqrt(x) - 1))/((sqrt(x) + 1)/(sqrt(x) - 1) + 1) - 2*log((sqrt(x) + 1)/abs(sqrt(x) - 1)) + 2*log(abs(-(sqrt(x) + 1)/(sqrt(x) - 1) - 1))","B",0
213,1,227,0,0.369250," ","integrate(x^3*(a+b*arctanh(c*x^(3/2))),x, algorithm=""giac"")","\frac{1}{4} \, a x^{4} + \frac{1}{320} \, {\left(40 \, x^{4} \log\left(-\frac{c x^{\frac{3}{2}} + 1}{c x^{\frac{3}{2}} - 1}\right) + c {\left(\frac{48 \, x^{\frac{5}{2}}}{c^{2}} - \frac{10 \, \sqrt{3} {\left(-i \, \sqrt{3} - 1\right)}^{2} {\left| c \right|}^{\frac{4}{3}} \arctan\left(\frac{\sqrt{3} {\left(2 \, \sqrt{x} + \left(-\frac{1}{c}\right)^{\frac{1}{3}}\right)}}{3 \, \left(-\frac{1}{c}\right)^{\frac{1}{3}}}\right)}{c^{5}} + \frac{5 \, {\left(-i \, \sqrt{3} - 1\right)}^{2} {\left| c \right|}^{\frac{4}{3}} \log\left(x + \sqrt{x} \left(-\frac{1}{c}\right)^{\frac{1}{3}} + \left(-\frac{1}{c}\right)^{\frac{2}{3}}\right)}{c^{5}} - \frac{40 \, \left(-\frac{1}{c}\right)^{\frac{2}{3}} \log\left({\left| \sqrt{x} - \left(-\frac{1}{c}\right)^{\frac{1}{3}} \right|}\right)}{c^{3}} + \frac{40 \, \sqrt{3} {\left| c \right|}^{\frac{4}{3}} \arctan\left(\frac{1}{3} \, \sqrt{3} c^{\frac{1}{3}} {\left(2 \, \sqrt{x} + \frac{1}{c^{\frac{1}{3}}}\right)}\right)}{c^{5}} - \frac{20 \, {\left| c \right|}^{\frac{4}{3}} \log\left(x + \frac{\sqrt{x}}{c^{\frac{1}{3}}} + \frac{1}{c^{\frac{2}{3}}}\right)}{c^{5}} + \frac{40 \, \log\left({\left| \sqrt{x} - \frac{1}{c^{\frac{1}{3}}} \right|}\right)}{c^{\frac{11}{3}}}\right)}\right)} b"," ",0,"1/4*a*x^4 + 1/320*(40*x^4*log(-(c*x^(3/2) + 1)/(c*x^(3/2) - 1)) + c*(48*x^(5/2)/c^2 - 10*sqrt(3)*(-I*sqrt(3) - 1)^2*abs(c)^(4/3)*arctan(1/3*sqrt(3)*(2*sqrt(x) + (-1/c)^(1/3))/(-1/c)^(1/3))/c^5 + 5*(-I*sqrt(3) - 1)^2*abs(c)^(4/3)*log(x + sqrt(x)*(-1/c)^(1/3) + (-1/c)^(2/3))/c^5 - 40*(-1/c)^(2/3)*log(abs(sqrt(x) - (-1/c)^(1/3)))/c^3 + 40*sqrt(3)*abs(c)^(4/3)*arctan(1/3*sqrt(3)*c^(1/3)*(2*sqrt(x) + 1/c^(1/3)))/c^5 - 20*abs(c)^(4/3)*log(x + sqrt(x)/c^(1/3) + 1/c^(2/3))/c^5 + 40*log(abs(sqrt(x) - 1/c^(1/3)))/c^(11/3)))*b","C",0
214,1,97,0,0.165421," ","integrate(x^2*(a+b*arctanh(c*x^(3/2))),x, algorithm=""giac"")","\frac{1}{3} \, a x^{3} + \frac{2}{3} \, b c {\left(\frac{1}{c^{3} {\left(\frac{c x^{\frac{3}{2}} + 1}{c x^{\frac{3}{2}} - 1} - 1\right)}} + \frac{{\left(c x^{\frac{3}{2}} + 1\right)} \log\left(-\frac{c x^{\frac{3}{2}} + 1}{c x^{\frac{3}{2}} - 1}\right)}{{\left(c x^{\frac{3}{2}} - 1\right)} c^{3} {\left(\frac{c x^{\frac{3}{2}} + 1}{c x^{\frac{3}{2}} - 1} - 1\right)}^{2}}\right)}"," ",0,"1/3*a*x^3 + 2/3*b*c*(1/(c^3*((c*x^(3/2) + 1)/(c*x^(3/2) - 1) - 1)) + (c*x^(3/2) + 1)*log(-(c*x^(3/2) + 1)/(c*x^(3/2) - 1))/((c*x^(3/2) - 1)*c^3*((c*x^(3/2) + 1)/(c*x^(3/2) - 1) - 1)^2))","B",0
215,0,0,0,0.000000," ","integrate(x*(a+b*arctanh(c*x^(3/2))),x, algorithm=""giac"")","\int {\left(b \operatorname{artanh}\left(c x^{\frac{3}{2}}\right) + a\right)} x\,{d x}"," ",0,"integrate((b*arctanh(c*x^(3/2)) + a)*x, x)","F",0
216,1,186,0,0.248834," ","integrate(a+b*arctanh(c*x^(3/2)),x, algorithm=""giac"")","\frac{1}{4} \, {\left(c {\left(\frac{2 \, \sqrt{3} {\left| c \right|}^{\frac{1}{3}} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, \sqrt{x} + \frac{1}{{\left| c \right|}^{\frac{1}{3}}}\right)} {\left| c \right|}^{\frac{1}{3}}\right)}{c^{2}} + \frac{2 \, \sqrt{3} {\left| c \right|}^{\frac{1}{3}} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, \sqrt{x} - \frac{1}{{\left| c \right|}^{\frac{1}{3}}}\right)} {\left| c \right|}^{\frac{1}{3}}\right)}{c^{2}} - \frac{{\left| c \right|}^{\frac{1}{3}} \log\left(x + \frac{\sqrt{x}}{{\left| c \right|}^{\frac{1}{3}}} + \frac{1}{{\left| c \right|}^{\frac{2}{3}}}\right)}{c^{2}} + \frac{{\left| c \right|}^{\frac{1}{3}} \log\left(x - \frac{\sqrt{x}}{{\left| c \right|}^{\frac{1}{3}}} + \frac{1}{{\left| c \right|}^{\frac{2}{3}}}\right)}{c^{2}} - \frac{2 \, {\left| c \right|}^{\frac{1}{3}} \log\left(\sqrt{x} + \frac{1}{{\left| c \right|}^{\frac{1}{3}}}\right)}{c^{2}} + \frac{2 \, {\left| c \right|}^{\frac{1}{3}} \log\left({\left| \sqrt{x} - \frac{1}{{\left| c \right|}^{\frac{1}{3}}} \right|}\right)}{c^{2}}\right)} + 2 \, x \log\left(-\frac{c x^{\frac{3}{2}} + 1}{c x^{\frac{3}{2}} - 1}\right)\right)} b + a x"," ",0,"1/4*(c*(2*sqrt(3)*abs(c)^(1/3)*arctan(1/3*sqrt(3)*(2*sqrt(x) + 1/abs(c)^(1/3))*abs(c)^(1/3))/c^2 + 2*sqrt(3)*abs(c)^(1/3)*arctan(1/3*sqrt(3)*(2*sqrt(x) - 1/abs(c)^(1/3))*abs(c)^(1/3))/c^2 - abs(c)^(1/3)*log(x + sqrt(x)/abs(c)^(1/3) + 1/abs(c)^(2/3))/c^2 + abs(c)^(1/3)*log(x - sqrt(x)/abs(c)^(1/3) + 1/abs(c)^(2/3))/c^2 - 2*abs(c)^(1/3)*log(sqrt(x) + 1/abs(c)^(1/3))/c^2 + 2*abs(c)^(1/3)*log(abs(sqrt(x) - 1/abs(c)^(1/3)))/c^2) + 2*x*log(-(c*x^(3/2) + 1)/(c*x^(3/2) - 1)))*b + a*x","A",0
217,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x^(3/2)))/x,x, algorithm=""giac"")","\int \frac{b \operatorname{artanh}\left(c x^{\frac{3}{2}}\right) + a}{x}\,{d x}"," ",0,"integrate((b*arctanh(c*x^(3/2)) + a)/x, x)","F",0
218,1,172,0,0.329355," ","integrate((a+b*arctanh(c*x^(3/2)))/x^2,x, algorithm=""giac"")","\frac{1}{4} \, {\left(\frac{2 \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, \sqrt{x} + \frac{1}{{\left| c \right|}^{\frac{1}{3}}}\right)} {\left| c \right|}^{\frac{1}{3}}\right)}{{\left| c \right|}^{\frac{1}{3}}} + \frac{2 \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, \sqrt{x} - \frac{1}{{\left| c \right|}^{\frac{1}{3}}}\right)} {\left| c \right|}^{\frac{1}{3}}\right)}{{\left| c \right|}^{\frac{1}{3}}} + \frac{\log\left(x + \frac{\sqrt{x}}{{\left| c \right|}^{\frac{1}{3}}} + \frac{1}{{\left| c \right|}^{\frac{2}{3}}}\right)}{{\left| c \right|}^{\frac{1}{3}}} - \frac{\log\left(x - \frac{\sqrt{x}}{{\left| c \right|}^{\frac{1}{3}}} + \frac{1}{{\left| c \right|}^{\frac{2}{3}}}\right)}{{\left| c \right|}^{\frac{1}{3}}} + \frac{2 \, \log\left(\sqrt{x} + \frac{1}{{\left| c \right|}^{\frac{1}{3}}}\right)}{{\left| c \right|}^{\frac{1}{3}}} - \frac{2 \, \log\left({\left| \sqrt{x} - \frac{1}{{\left| c \right|}^{\frac{1}{3}}} \right|}\right)}{{\left| c \right|}^{\frac{1}{3}}}\right)} b c - \frac{b \log\left(-\frac{c x^{\frac{3}{2}} + 1}{c x^{\frac{3}{2}} - 1}\right)}{2 \, x} - \frac{a}{x}"," ",0,"1/4*(2*sqrt(3)*arctan(1/3*sqrt(3)*(2*sqrt(x) + 1/abs(c)^(1/3))*abs(c)^(1/3))/abs(c)^(1/3) + 2*sqrt(3)*arctan(1/3*sqrt(3)*(2*sqrt(x) - 1/abs(c)^(1/3))*abs(c)^(1/3))/abs(c)^(1/3) + log(x + sqrt(x)/abs(c)^(1/3) + 1/abs(c)^(2/3))/abs(c)^(1/3) - log(x - sqrt(x)/abs(c)^(1/3) + 1/abs(c)^(2/3))/abs(c)^(1/3) + 2*log(sqrt(x) + 1/abs(c)^(1/3))/abs(c)^(1/3) - 2*log(abs(sqrt(x) - 1/abs(c)^(1/3)))/abs(c)^(1/3))*b*c - 1/2*b*log(-(c*x^(3/2) + 1)/(c*x^(3/2) - 1))/x - a/x","A",0
219,1,194,0,0.341998," ","integrate((a+b*arctanh(c*x^(3/2)))/x^3,x, algorithm=""giac"")","-\frac{1}{4} \, \sqrt{3} b c {\left| c \right|}^{\frac{1}{3}} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, \sqrt{x} + \frac{1}{{\left| c \right|}^{\frac{1}{3}}}\right)} {\left| c \right|}^{\frac{1}{3}}\right) - \frac{1}{4} \, \sqrt{3} b c {\left| c \right|}^{\frac{1}{3}} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, \sqrt{x} - \frac{1}{{\left| c \right|}^{\frac{1}{3}}}\right)} {\left| c \right|}^{\frac{1}{3}}\right) + \frac{b c^{3} \log\left(x + \frac{\sqrt{x}}{{\left| c \right|}^{\frac{1}{3}}} + \frac{1}{{\left| c \right|}^{\frac{2}{3}}}\right)}{8 \, {\left| c \right|}^{\frac{5}{3}}} - \frac{b c^{3} \log\left(x - \frac{\sqrt{x}}{{\left| c \right|}^{\frac{1}{3}}} + \frac{1}{{\left| c \right|}^{\frac{2}{3}}}\right)}{8 \, {\left| c \right|}^{\frac{5}{3}}} + \frac{1}{4} \, b c {\left| c \right|}^{\frac{1}{3}} \log\left(\sqrt{x} + \frac{1}{{\left| c \right|}^{\frac{1}{3}}}\right) - \frac{b c^{3} \log\left({\left| \sqrt{x} - \frac{1}{{\left| c \right|}^{\frac{1}{3}}} \right|}\right)}{4 \, {\left| c \right|}^{\frac{5}{3}}} - \frac{b \log\left(-\frac{c x^{\frac{3}{2}} + 1}{c x^{\frac{3}{2}} - 1}\right)}{4 \, x^{2}} - \frac{3 \, b c x^{\frac{3}{2}} + a}{2 \, x^{2}}"," ",0,"-1/4*sqrt(3)*b*c*abs(c)^(1/3)*arctan(1/3*sqrt(3)*(2*sqrt(x) + 1/abs(c)^(1/3))*abs(c)^(1/3)) - 1/4*sqrt(3)*b*c*abs(c)^(1/3)*arctan(1/3*sqrt(3)*(2*sqrt(x) - 1/abs(c)^(1/3))*abs(c)^(1/3)) + 1/8*b*c^3*log(x + sqrt(x)/abs(c)^(1/3) + 1/abs(c)^(2/3))/abs(c)^(5/3) - 1/8*b*c^3*log(x - sqrt(x)/abs(c)^(1/3) + 1/abs(c)^(2/3))/abs(c)^(5/3) + 1/4*b*c*abs(c)^(1/3)*log(sqrt(x) + 1/abs(c)^(1/3)) - 1/4*b*c^3*log(abs(sqrt(x) - 1/abs(c)^(1/3)))/abs(c)^(5/3) - 1/4*b*log(-(c*x^(3/2) + 1)/(c*x^(3/2) - 1))/x^2 - 1/2*(3*b*c*x^(3/2) + a)/x^2","A",0
220,1,67,0,0.232606," ","integrate((a+b*arctanh(c*x^(3/2)))/x^4,x, algorithm=""giac"")","\frac{1}{6} \, b c^{2} \log\left(c x^{\frac{3}{2}} + 1\right) - \frac{1}{6} \, b c^{2} \log\left(c x^{\frac{3}{2}} - 1\right) - \frac{b \log\left(-\frac{c x^{\frac{3}{2}} + 1}{c x^{\frac{3}{2}} - 1}\right)}{6 \, x^{3}} - \frac{b c x^{\frac{3}{2}} + a}{3 \, x^{3}}"," ",0,"1/6*b*c^2*log(c*x^(3/2) + 1) - 1/6*b*c^2*log(c*x^(3/2) - 1) - 1/6*b*log(-(c*x^(3/2) + 1)/(c*x^(3/2) - 1))/x^3 - 1/3*(b*c*x^(3/2) + a)/x^3","A",0
221,0,0,0,0.000000," ","integrate(x^2*(a+b*arctanh(c*x^(3/2)))^2,x, algorithm=""giac"")","\int {\left(b \operatorname{artanh}\left(c x^{\frac{3}{2}}\right) + a\right)}^{2} x^{2}\,{d x}"," ",0,"integrate((b*arctanh(c*x^(3/2)) + a)^2*x^2, x)","F",0
222,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x^(3/2)))^2/x,x, algorithm=""giac"")","\int \frac{{\left(b \operatorname{artanh}\left(c x^{\frac{3}{2}}\right) + a\right)}^{2}}{x}\,{d x}"," ",0,"integrate((b*arctanh(c*x^(3/2)) + a)^2/x, x)","F",0
223,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x^(3/2)))^2/x^4,x, algorithm=""giac"")","\int \frac{{\left(b \operatorname{artanh}\left(c x^{\frac{3}{2}}\right) + a\right)}^{2}}{x^{4}}\,{d x}"," ",0,"integrate((b*arctanh(c*x^(3/2)) + a)^2/x^4, x)","F",0
224,0,0,0,0.000000," ","integrate(x^2*(a+b*arctanh(c*x^n)),x, algorithm=""giac"")","\int {\left(b \operatorname{artanh}\left(c x^{n}\right) + a\right)} x^{2}\,{d x}"," ",0,"integrate((b*arctanh(c*x^n) + a)*x^2, x)","F",0
225,0,0,0,0.000000," ","integrate(x*(a+b*arctanh(c*x^n)),x, algorithm=""giac"")","\int {\left(b \operatorname{artanh}\left(c x^{n}\right) + a\right)} x\,{d x}"," ",0,"integrate((b*arctanh(c*x^n) + a)*x, x)","F",0
226,0,0,0,0.000000," ","integrate(a+b*arctanh(c*x^n),x, algorithm=""giac"")","\int b \operatorname{artanh}\left(c x^{n}\right) + a\,{d x}"," ",0,"integrate(b*arctanh(c*x^n) + a, x)","F",0
227,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x^n))/x,x, algorithm=""giac"")","\int \frac{b \operatorname{artanh}\left(c x^{n}\right) + a}{x}\,{d x}"," ",0,"integrate((b*arctanh(c*x^n) + a)/x, x)","F",0
228,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x^n))/x^2,x, algorithm=""giac"")","\int \frac{b \operatorname{artanh}\left(c x^{n}\right) + a}{x^{2}}\,{d x}"," ",0,"integrate((b*arctanh(c*x^n) + a)/x^2, x)","F",0
229,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x^n))/x^3,x, algorithm=""giac"")","\int \frac{b \operatorname{artanh}\left(c x^{n}\right) + a}{x^{3}}\,{d x}"," ",0,"integrate((b*arctanh(c*x^n) + a)/x^3, x)","F",0
230,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x^n))/x^4,x, algorithm=""giac"")","\int \frac{b \operatorname{artanh}\left(c x^{n}\right) + a}{x^{4}}\,{d x}"," ",0,"integrate((b*arctanh(c*x^n) + a)/x^4, x)","F",0
231,0,0,0,0.000000," ","integrate(x*(a+b*arctanh(c*x^n))^2,x, algorithm=""giac"")","\int {\left(b \operatorname{artanh}\left(c x^{n}\right) + a\right)}^{2} x\,{d x}"," ",0,"integrate((b*arctanh(c*x^n) + a)^2*x, x)","F",0
232,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x^n))^2,x, algorithm=""giac"")","\int {\left(b \operatorname{artanh}\left(c x^{n}\right) + a\right)}^{2}\,{d x}"," ",0,"integrate((b*arctanh(c*x^n) + a)^2, x)","F",0
233,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x^n))^2/x,x, algorithm=""giac"")","\int \frac{{\left(b \operatorname{artanh}\left(c x^{n}\right) + a\right)}^{2}}{x}\,{d x}"," ",0,"integrate((b*arctanh(c*x^n) + a)^2/x, x)","F",0
234,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x^n))^2/x^2,x, algorithm=""giac"")","\int \frac{{\left(b \operatorname{artanh}\left(c x^{n}\right) + a\right)}^{2}}{x^{2}}\,{d x}"," ",0,"integrate((b*arctanh(c*x^n) + a)^2/x^2, x)","F",0
235,0,0,0,0.000000," ","integrate((a+b*arctanh(c*x^n))^2/x^3,x, algorithm=""giac"")","\int \frac{{\left(b \operatorname{artanh}\left(c x^{n}\right) + a\right)}^{2}}{x^{3}}\,{d x}"," ",0,"integrate((b*arctanh(c*x^n) + a)^2/x^3, x)","F",0
236,0,0,0,0.000000," ","integrate(arctanh(a*x^n)/x,x, algorithm=""giac"")","\int \frac{\operatorname{artanh}\left(a x^{n}\right)}{x}\,{d x}"," ",0,"integrate(arctanh(a*x^n)/x, x)","F",0
237,0,0,0,0.000000," ","integrate(arctanh(a*x^5)/x,x, algorithm=""giac"")","\int \frac{\operatorname{artanh}\left(a x^{5}\right)}{x}\,{d x}"," ",0,"integrate(arctanh(a*x^5)/x, x)","F",0
238,1,101,0,0.163677," ","integrate(arctanh(1/x),x, algorithm=""giac"")","\frac{\log\left(-\frac{\frac{\frac{x + 1}{x - 1} - 1}{\frac{x + 1}{x - 1} + 1} + 1}{\frac{\frac{x + 1}{x - 1} - 1}{\frac{x + 1}{x - 1} + 1} - 1}\right)}{\frac{x + 1}{x - 1} - 1} + \log\left(\frac{{\left| x + 1 \right|}}{{\left| x - 1 \right|}}\right) - \log\left({\left| \frac{x + 1}{x - 1} - 1 \right|}\right)"," ",0,"log(-(((x + 1)/(x - 1) - 1)/((x + 1)/(x - 1) + 1) + 1)/(((x + 1)/(x - 1) - 1)/((x + 1)/(x - 1) + 1) - 1))/((x + 1)/(x - 1) - 1) + log(abs(x + 1)/abs(x - 1)) - log(abs((x + 1)/(x - 1) - 1))","B",0
239,0,0,0,0.000000," ","integrate((d*x)^m*(a+b*arctanh(c*x^n))^3,x, algorithm=""giac"")","\int {\left(b \operatorname{artanh}\left(c x^{n}\right) + a\right)}^{3} \left(d x\right)^{m}\,{d x}"," ",0,"integrate((b*arctanh(c*x^n) + a)^3*(d*x)^m, x)","F",0
240,0,0,0,0.000000," ","integrate((d*x)^m*(a+b*arctanh(c*x^n))^2,x, algorithm=""giac"")","\int {\left(b \operatorname{artanh}\left(c x^{n}\right) + a\right)}^{2} \left(d x\right)^{m}\,{d x}"," ",0,"integrate((b*arctanh(c*x^n) + a)^2*(d*x)^m, x)","F",0
241,0,0,0,0.000000," ","integrate((d*x)^m*(a+b*arctanh(c*x^n)),x, algorithm=""giac"")","\int {\left(b \operatorname{artanh}\left(c x^{n}\right) + a\right)} \left(d x\right)^{m}\,{d x}"," ",0,"integrate((b*arctanh(c*x^n) + a)*(d*x)^m, x)","F",0
242,0,0,0,0.000000," ","integrate((d*x)^m/(a+b*arctanh(c*x^n)),x, algorithm=""giac"")","\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=""giac"")","\int \frac{\left(d x\right)^{m}}{{\left(b \operatorname{artanh}\left(c x^{n}\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((d*x)^m/(b*arctanh(c*x^n) + a)^2, x)","F",0
