1,1,61,0,0.301934," ","integrate(x^5*arccoth(a*x),x, algorithm=""maxima"")","\frac{1}{6} \, x^{6} \operatorname{arcoth}\left(a x\right) + \frac{1}{180} \, a {\left(\frac{2 \, {\left(3 \, a^{4} x^{5} + 5 \, a^{2} x^{3} + 15 \, x\right)}}{a^{6}} - \frac{15 \, \log\left(a x + 1\right)}{a^{7}} + \frac{15 \, \log\left(a x - 1\right)}{a^{7}}\right)}"," ",0,"1/6*x^6*arccoth(a*x) + 1/180*a*(2*(3*a^4*x^5 + 5*a^2*x^3 + 15*x)/a^6 - 15*log(a*x + 1)/a^7 + 15*log(a*x - 1)/a^7)","A",0
2,1,46,0,0.299992," ","integrate(x^4*arccoth(a*x),x, algorithm=""maxima"")","\frac{1}{5} \, x^{5} \operatorname{arcoth}\left(a x\right) + \frac{1}{20} \, a {\left(\frac{a^{2} x^{4} + 2 \, x^{2}}{a^{4}} + \frac{2 \, \log\left(a^{2} x^{2} - 1\right)}{a^{6}}\right)}"," ",0,"1/5*x^5*arccoth(a*x) + 1/20*a*((a^2*x^4 + 2*x^2)/a^4 + 2*log(a^2*x^2 - 1)/a^6)","A",0
3,1,52,0,0.297353," ","integrate(x^3*arccoth(a*x),x, algorithm=""maxima"")","\frac{1}{4} \, x^{4} \operatorname{arcoth}\left(a x\right) + \frac{1}{24} \, a {\left(\frac{2 \, {\left(a^{2} x^{3} + 3 \, x\right)}}{a^{4}} - \frac{3 \, \log\left(a x + 1\right)}{a^{5}} + \frac{3 \, \log\left(a x - 1\right)}{a^{5}}\right)}"," ",0,"1/4*x^4*arccoth(a*x) + 1/24*a*(2*(a^2*x^3 + 3*x)/a^4 - 3*log(a*x + 1)/a^5 + 3*log(a*x - 1)/a^5)","A",0
4,1,35,0,0.305117," ","integrate(x^2*arccoth(a*x),x, algorithm=""maxima"")","\frac{1}{3} \, x^{3} \operatorname{arcoth}\left(a x\right) + \frac{1}{6} \, a {\left(\frac{x^{2}}{a^{2}} + \frac{\log\left(a^{2} x^{2} - 1\right)}{a^{4}}\right)}"," ",0,"1/3*x^3*arccoth(a*x) + 1/6*a*(x^2/a^2 + log(a^2*x^2 - 1)/a^4)","A",0
5,1,41,0,0.302428," ","integrate(x*arccoth(a*x),x, algorithm=""maxima"")","\frac{1}{2} \, x^{2} \operatorname{arcoth}\left(a x\right) + \frac{1}{4} \, a {\left(\frac{2 \, x}{a^{2}} - \frac{\log\left(a x + 1\right)}{a^{3}} + \frac{\log\left(a x - 1\right)}{a^{3}}\right)}"," ",0,"1/2*x^2*arccoth(a*x) + 1/4*a*(2*x/a^2 - log(a*x + 1)/a^3 + log(a*x - 1)/a^3)","A",0
6,1,25,0,0.301042," ","integrate(arccoth(a*x),x, algorithm=""maxima"")","\frac{2 \, a x \operatorname{arcoth}\left(a x\right) + \log\left(-a^{2} x^{2} + 1\right)}{2 \, a}"," ",0,"1/2*(2*a*x*arccoth(a*x) + log(-a^2*x^2 + 1))/a","A",0
7,1,86,0,0.304987," ","integrate(arccoth(a*x)/x,x, algorithm=""maxima"")","-\frac{1}{2} \, a {\left(\frac{\log\left(a x + 1\right)}{a} - \frac{\log\left(a x - 1\right)}{a}\right)} \log\left(x\right) - \frac{1}{2} \, a {\left(\frac{\log\left(a x - 1\right) \log\left(a x\right) + {\rm Li}_2\left(-a x + 1\right)}{a} - \frac{\log\left(a x + 1\right) \log\left(-a x\right) + {\rm Li}_2\left(a x + 1\right)}{a}\right)} + \operatorname{arcoth}\left(a x\right) \log\left(x\right)"," ",0,"-1/2*a*(log(a*x + 1)/a - log(a*x - 1)/a)*log(x) - 1/2*a*((log(a*x - 1)*log(a*x) + dilog(-a*x + 1))/a - (log(a*x + 1)*log(-a*x) + dilog(a*x + 1))/a) + arccoth(a*x)*log(x)","B",0
8,1,30,0,0.305262," ","integrate(arccoth(a*x)/x^2,x, algorithm=""maxima"")","-\frac{1}{2} \, a {\left(\log\left(a^{2} x^{2} - 1\right) - \log\left(x^{2}\right)\right)} - \frac{\operatorname{arcoth}\left(a x\right)}{x}"," ",0,"-1/2*a*(log(a^2*x^2 - 1) - log(x^2)) - arccoth(a*x)/x","A",0
9,1,36,0,0.306593," ","integrate(arccoth(a*x)/x^3,x, algorithm=""maxima"")","\frac{1}{4} \, {\left(a \log\left(a x + 1\right) - a \log\left(a x - 1\right) - \frac{2}{x}\right)} a - \frac{\operatorname{arcoth}\left(a x\right)}{2 \, x^{2}}"," ",0,"1/4*(a*log(a*x + 1) - a*log(a*x - 1) - 2/x)*a - 1/2*arccoth(a*x)/x^2","A",0
10,1,40,0,0.310048," ","integrate(arccoth(a*x)/x^4,x, algorithm=""maxima"")","-\frac{1}{6} \, {\left(a^{2} \log\left(a^{2} x^{2} - 1\right) - a^{2} \log\left(x^{2}\right) + \frac{1}{x^{2}}\right)} a - \frac{\operatorname{arcoth}\left(a x\right)}{3 \, x^{3}}"," ",0,"-1/6*(a^2*log(a^2*x^2 - 1) - a^2*log(x^2) + 1/x^2)*a - 1/3*arccoth(a*x)/x^3","A",0
11,1,51,0,0.305664," ","integrate(arccoth(a*x)/x^5,x, algorithm=""maxima"")","\frac{1}{24} \, {\left(3 \, a^{3} \log\left(a x + 1\right) - 3 \, a^{3} \log\left(a x - 1\right) - \frac{2 \, {\left(3 \, a^{2} x^{2} + 1\right)}}{x^{3}}\right)} a - \frac{\operatorname{arcoth}\left(a x\right)}{4 \, x^{4}}"," ",0,"1/24*(3*a^3*log(a*x + 1) - 3*a^3*log(a*x - 1) - 2*(3*a^2*x^2 + 1)/x^3)*a - 1/4*arccoth(a*x)/x^4","A",0
12,1,135,0,0.305220," ","integrate(x^5*arccoth(a*x)^2,x, algorithm=""maxima"")","\frac{1}{6} \, x^{6} \operatorname{arcoth}\left(a x\right)^{2} + \frac{1}{90} \, a {\left(\frac{2 \, {\left(3 \, a^{4} x^{5} + 5 \, a^{2} x^{3} + 15 \, x\right)}}{a^{6}} - \frac{15 \, \log\left(a x + 1\right)}{a^{7}} + \frac{15 \, \log\left(a x - 1\right)}{a^{7}}\right)} \operatorname{arcoth}\left(a x\right) + \frac{6 \, a^{4} x^{4} + 32 \, a^{2} x^{2} - 2 \, {\left(15 \, \log\left(a x - 1\right) - 46\right)} \log\left(a x + 1\right) + 15 \, \log\left(a x + 1\right)^{2} + 15 \, \log\left(a x - 1\right)^{2} + 92 \, \log\left(a x - 1\right)}{360 \, a^{6}}"," ",0,"1/6*x^6*arccoth(a*x)^2 + 1/90*a*(2*(3*a^4*x^5 + 5*a^2*x^3 + 15*x)/a^6 - 15*log(a*x + 1)/a^7 + 15*log(a*x - 1)/a^7)*arccoth(a*x) + 1/360*(6*a^4*x^4 + 32*a^2*x^2 - 2*(15*log(a*x - 1) - 46)*log(a*x + 1) + 15*log(a*x + 1)^2 + 15*log(a*x - 1)^2 + 92*log(a*x - 1))/a^6","A",0
13,1,155,0,0.319433," ","integrate(x^4*arccoth(a*x)^2,x, algorithm=""maxima"")","\frac{1}{5} \, x^{5} \operatorname{arcoth}\left(a x\right)^{2} + \frac{1}{60} \, a^{2} {\left(\frac{2 \, a^{3} x^{3} + 18 \, a x - 3 \, \log\left(a x + 1\right)^{2} + 6 \, \log\left(a x + 1\right) \log\left(a x - 1\right) + 3 \, \log\left(a x - 1\right)^{2} + 9 \, \log\left(a x - 1\right)}{a^{7}} - \frac{12 \, {\left(\log\left(a x - 1\right) \log\left(\frac{1}{2} \, a x + \frac{1}{2}\right) + {\rm Li}_2\left(-\frac{1}{2} \, a x + \frac{1}{2}\right)\right)}}{a^{7}} - \frac{9 \, \log\left(a x + 1\right)}{a^{7}}\right)} + \frac{1}{10} \, a {\left(\frac{a^{2} x^{4} + 2 \, x^{2}}{a^{4}} + \frac{2 \, \log\left(a^{2} x^{2} - 1\right)}{a^{6}}\right)} \operatorname{arcoth}\left(a x\right)"," ",0,"1/5*x^5*arccoth(a*x)^2 + 1/60*a^2*((2*a^3*x^3 + 18*a*x - 3*log(a*x + 1)^2 + 6*log(a*x + 1)*log(a*x - 1) + 3*log(a*x - 1)^2 + 9*log(a*x - 1))/a^7 - 12*(log(a*x - 1)*log(1/2*a*x + 1/2) + dilog(-1/2*a*x + 1/2))/a^7 - 9*log(a*x + 1)/a^7) + 1/10*a*((a^2*x^4 + 2*x^2)/a^4 + 2*log(a^2*x^2 - 1)/a^6)*arccoth(a*x)","A",0
14,1,118,0,0.319743," ","integrate(x^3*arccoth(a*x)^2,x, algorithm=""maxima"")","\frac{1}{4} \, x^{4} \operatorname{arcoth}\left(a x\right)^{2} + \frac{1}{12} \, a {\left(\frac{2 \, {\left(a^{2} x^{3} + 3 \, x\right)}}{a^{4}} - \frac{3 \, \log\left(a x + 1\right)}{a^{5}} + \frac{3 \, \log\left(a x - 1\right)}{a^{5}}\right)} \operatorname{arcoth}\left(a x\right) + \frac{4 \, a^{2} x^{2} - 2 \, {\left(3 \, \log\left(a x - 1\right) - 8\right)} \log\left(a x + 1\right) + 3 \, \log\left(a x + 1\right)^{2} + 3 \, \log\left(a x - 1\right)^{2} + 16 \, \log\left(a x - 1\right)}{48 \, a^{4}}"," ",0,"1/4*x^4*arccoth(a*x)^2 + 1/12*a*(2*(a^2*x^3 + 3*x)/a^4 - 3*log(a*x + 1)/a^5 + 3*log(a*x - 1)/a^5)*arccoth(a*x) + 1/48*(4*a^2*x^2 - 2*(3*log(a*x - 1) - 8)*log(a*x + 1) + 3*log(a*x + 1)^2 + 3*log(a*x - 1)^2 + 16*log(a*x - 1))/a^4","A",0
15,1,134,0,0.310974," ","integrate(x^2*arccoth(a*x)^2,x, algorithm=""maxima"")","\frac{1}{3} \, x^{3} \operatorname{arcoth}\left(a x\right)^{2} + \frac{1}{12} \, a^{2} {\left(\frac{4 \, a x - \log\left(a x + 1\right)^{2} + 2 \, \log\left(a x + 1\right) \log\left(a x - 1\right) + \log\left(a x - 1\right)^{2} + 2 \, \log\left(a x - 1\right)}{a^{5}} - \frac{4 \, {\left(\log\left(a x - 1\right) \log\left(\frac{1}{2} \, a x + \frac{1}{2}\right) + {\rm Li}_2\left(-\frac{1}{2} \, a x + \frac{1}{2}\right)\right)}}{a^{5}} - \frac{2 \, \log\left(a x + 1\right)}{a^{5}}\right)} + \frac{1}{3} \, a {\left(\frac{x^{2}}{a^{2}} + \frac{\log\left(a^{2} x^{2} - 1\right)}{a^{4}}\right)} \operatorname{arcoth}\left(a x\right)"," ",0,"1/3*x^3*arccoth(a*x)^2 + 1/12*a^2*((4*a*x - log(a*x + 1)^2 + 2*log(a*x + 1)*log(a*x - 1) + log(a*x - 1)^2 + 2*log(a*x - 1))/a^5 - 4*(log(a*x - 1)*log(1/2*a*x + 1/2) + dilog(-1/2*a*x + 1/2))/a^5 - 2*log(a*x + 1)/a^5) + 1/3*a*(x^2/a^2 + log(a^2*x^2 - 1)/a^4)*arccoth(a*x)","A",0
16,1,97,0,0.315710," ","integrate(x*arccoth(a*x)^2,x, algorithm=""maxima"")","\frac{1}{2} \, x^{2} \operatorname{arcoth}\left(a x\right)^{2} + \frac{1}{2} \, a {\left(\frac{2 \, x}{a^{2}} - \frac{\log\left(a x + 1\right)}{a^{3}} + \frac{\log\left(a x - 1\right)}{a^{3}}\right)} \operatorname{arcoth}\left(a x\right) - \frac{2 \, {\left(\log\left(a x - 1\right) - 2\right)} \log\left(a x + 1\right) - \log\left(a x + 1\right)^{2} - \log\left(a x - 1\right)^{2} - 4 \, \log\left(a x - 1\right)}{8 \, a^{2}}"," ",0,"1/2*x^2*arccoth(a*x)^2 + 1/2*a*(2*x/a^2 - log(a*x + 1)/a^3 + log(a*x - 1)/a^3)*arccoth(a*x) - 1/8*(2*(log(a*x - 1) - 2)*log(a*x + 1) - log(a*x + 1)^2 - log(a*x - 1)^2 - 4*log(a*x - 1))/a^2","B",0
17,1,135,0,0.322743," ","integrate(arccoth(a*x)^2,x, algorithm=""maxima"")","x \operatorname{arcoth}\left(a x\right)^{2} + \frac{1}{4} \, {\left(a {\left(\frac{\log\left(a x + 1\right)^{2} + 2 \, \log\left(a x + 1\right) \log\left(a x - 1\right) - \log\left(a x - 1\right)^{2}}{a^{3}} - \frac{4 \, {\left(\log\left(a x - 1\right) \log\left(\frac{1}{2} \, a x + \frac{1}{2}\right) + {\rm Li}_2\left(-\frac{1}{2} \, a x + \frac{1}{2}\right)\right)}}{a^{3}}\right)} - \frac{2 \, {\left(\frac{\log\left(a x + 1\right)}{a} - \frac{\log\left(a x - 1\right)}{a}\right)} \log\left(a^{2} x^{2} - 1\right)}{a}\right)} a + \frac{\operatorname{arcoth}\left(a x\right) \log\left(a^{2} x^{2} - 1\right)}{a}"," ",0,"x*arccoth(a*x)^2 + 1/4*(a*((log(a*x + 1)^2 + 2*log(a*x + 1)*log(a*x - 1) - log(a*x - 1)^2)/a^3 - 4*(log(a*x - 1)*log(1/2*a*x + 1/2) + dilog(-1/2*a*x + 1/2))/a^3) - 2*(log(a*x + 1)/a - log(a*x - 1)/a)*log(a^2*x^2 - 1)/a)*a + arccoth(a*x)*log(a^2*x^2 - 1)/a","B",0
18,0,0,0,0.000000," ","integrate(arccoth(a*x)^2/x,x, algorithm=""maxima"")","\int \frac{\operatorname{arcoth}\left(a x\right)^{2}}{x}\,{d x}"," ",0,"integrate(arccoth(a*x)^2/x, x)","F",0
19,1,146,0,0.318580," ","integrate(arccoth(a*x)^2/x^2,x, algorithm=""maxima"")","\frac{1}{4} \, a^{2} {\left(\frac{\log\left(a x + 1\right)^{2} - 2 \, \log\left(a x + 1\right) \log\left(a x - 1\right) - \log\left(a x - 1\right)^{2}}{a} + \frac{4 \, {\left(\log\left(a x - 1\right) \log\left(\frac{1}{2} \, a x + \frac{1}{2}\right) + {\rm Li}_2\left(-\frac{1}{2} \, a x + \frac{1}{2}\right)\right)}}{a} - \frac{4 \, {\left(\log\left(a x + 1\right) \log\left(x\right) + {\rm Li}_2\left(-a x\right)\right)}}{a} + \frac{4 \, {\left(\log\left(-a x + 1\right) \log\left(x\right) + {\rm Li}_2\left(a x\right)\right)}}{a}\right)} - a {\left(\log\left(a^{2} x^{2} - 1\right) - \log\left(x^{2}\right)\right)} \operatorname{arcoth}\left(a x\right) - \frac{\operatorname{arcoth}\left(a x\right)^{2}}{x}"," ",0,"1/4*a^2*((log(a*x + 1)^2 - 2*log(a*x + 1)*log(a*x - 1) - log(a*x - 1)^2)/a + 4*(log(a*x - 1)*log(1/2*a*x + 1/2) + dilog(-1/2*a*x + 1/2))/a - 4*(log(a*x + 1)*log(x) + dilog(-a*x))/a + 4*(log(-a*x + 1)*log(x) + dilog(a*x))/a) - a*(log(a^2*x^2 - 1) - log(x^2))*arccoth(a*x) - arccoth(a*x)^2/x","B",0
20,1,96,0,0.311098," ","integrate(arccoth(a*x)^2/x^3,x, algorithm=""maxima"")","\frac{1}{8} \, {\left(2 \, {\left(\log\left(a x - 1\right) - 2\right)} \log\left(a x + 1\right) - \log\left(a x + 1\right)^{2} - \log\left(a x - 1\right)^{2} - 4 \, \log\left(a x - 1\right) + 8 \, \log\left(x\right)\right)} a^{2} + \frac{1}{2} \, {\left(a \log\left(a x + 1\right) - a \log\left(a x - 1\right) - \frac{2}{x}\right)} a \operatorname{arcoth}\left(a x\right) - \frac{\operatorname{arcoth}\left(a x\right)^{2}}{2 \, x^{2}}"," ",0,"1/8*(2*(log(a*x - 1) - 2)*log(a*x + 1) - log(a*x + 1)^2 - log(a*x - 1)^2 - 4*log(a*x - 1) + 8*log(x))*a^2 + 1/2*(a*log(a*x + 1) - a*log(a*x - 1) - 2/x)*a*arccoth(a*x) - 1/2*arccoth(a*x)^2/x^2","A",0
21,1,176,0,0.321658," ","integrate(arccoth(a*x)^2/x^4,x, algorithm=""maxima"")","\frac{1}{12} \, {\left(4 \, {\left(\log\left(a x - 1\right) \log\left(\frac{1}{2} \, a x + \frac{1}{2}\right) + {\rm Li}_2\left(-\frac{1}{2} \, a x + \frac{1}{2}\right)\right)} a - 4 \, {\left(\log\left(a x + 1\right) \log\left(x\right) + {\rm Li}_2\left(-a x\right)\right)} a + 4 \, {\left(\log\left(-a x + 1\right) \log\left(x\right) + {\rm Li}_2\left(a x\right)\right)} a + 2 \, a \log\left(a x + 1\right) - 2 \, a \log\left(a x - 1\right) + \frac{a x \log\left(a x + 1\right)^{2} - 2 \, a x \log\left(a x + 1\right) \log\left(a x - 1\right) - a x \log\left(a x - 1\right)^{2} - 4}{x}\right)} a^{2} - \frac{1}{3} \, {\left(a^{2} \log\left(a^{2} x^{2} - 1\right) - a^{2} \log\left(x^{2}\right) + \frac{1}{x^{2}}\right)} a \operatorname{arcoth}\left(a x\right) - \frac{\operatorname{arcoth}\left(a x\right)^{2}}{3 \, x^{3}}"," ",0,"1/12*(4*(log(a*x - 1)*log(1/2*a*x + 1/2) + dilog(-1/2*a*x + 1/2))*a - 4*(log(a*x + 1)*log(x) + dilog(-a*x))*a + 4*(log(-a*x + 1)*log(x) + dilog(a*x))*a + 2*a*log(a*x + 1) - 2*a*log(a*x - 1) + (a*x*log(a*x + 1)^2 - 2*a*x*log(a*x + 1)*log(a*x - 1) - a*x*log(a*x - 1)^2 - 4)/x)*a^2 - 1/3*(a^2*log(a^2*x^2 - 1) - a^2*log(x^2) + 1/x^2)*a*arccoth(a*x) - 1/3*arccoth(a*x)^2/x^3","A",0
22,1,154,0,0.322000," ","integrate(arccoth(a*x)^2/x^5,x, algorithm=""maxima"")","\frac{1}{48} \, {\left(32 \, a^{2} \log\left(x\right) - \frac{3 \, a^{2} x^{2} \log\left(a x + 1\right)^{2} + 3 \, a^{2} x^{2} \log\left(a x - 1\right)^{2} + 16 \, a^{2} x^{2} \log\left(a x - 1\right) - 2 \, {\left(3 \, a^{2} x^{2} \log\left(a x - 1\right) - 8 \, a^{2} x^{2}\right)} \log\left(a x + 1\right) + 4}{x^{2}}\right)} a^{2} + \frac{1}{12} \, {\left(3 \, a^{3} \log\left(a x + 1\right) - 3 \, a^{3} \log\left(a x - 1\right) - \frac{2 \, {\left(3 \, a^{2} x^{2} + 1\right)}}{x^{3}}\right)} a \operatorname{arcoth}\left(a x\right) - \frac{\operatorname{arcoth}\left(a x\right)^{2}}{4 \, x^{4}}"," ",0,"1/48*(32*a^2*log(x) - (3*a^2*x^2*log(a*x + 1)^2 + 3*a^2*x^2*log(a*x - 1)^2 + 16*a^2*x^2*log(a*x - 1) - 2*(3*a^2*x^2*log(a*x - 1) - 8*a^2*x^2)*log(a*x + 1) + 4)/x^2)*a^2 + 1/12*(3*a^3*log(a*x + 1) - 3*a^3*log(a*x - 1) - 2*(3*a^2*x^2 + 1)/x^3)*a*arccoth(a*x) - 1/4*arccoth(a*x)^2/x^4","B",0
23,1,289,0,0.327070," ","integrate(x^5*arccoth(a*x)^3,x, algorithm=""maxima"")","\frac{1}{6} \, x^{6} \operatorname{arcoth}\left(a x\right)^{3} + \frac{1}{60} \, a {\left(\frac{2 \, {\left(3 \, a^{4} x^{5} + 5 \, a^{2} x^{3} + 15 \, x\right)}}{a^{6}} - \frac{15 \, \log\left(a x + 1\right)}{a^{7}} + \frac{15 \, \log\left(a x - 1\right)}{a^{7}}\right)} \operatorname{arcoth}\left(a x\right)^{2} + \frac{1}{240} \, a {\left(\frac{\frac{4 \, a^{3} x^{3} + {\left(15 \, \log\left(a x - 1\right) - 46\right)} \log\left(a x + 1\right)^{2} - 5 \, \log\left(a x + 1\right)^{3} + 5 \, \log\left(a x - 1\right)^{3} + 76 \, a x - {\left(15 \, \log\left(a x - 1\right)^{2} - 92 \, \log\left(a x - 1\right)\right)} \log\left(a x + 1\right) + 46 \, \log\left(a x - 1\right)^{2} + 38 \, \log\left(a x - 1\right)}{a} - \frac{184 \, {\left(\log\left(a x - 1\right) \log\left(\frac{1}{2} \, a x + \frac{1}{2}\right) + {\rm Li}_2\left(-\frac{1}{2} \, a x + \frac{1}{2}\right)\right)}}{a} - \frac{38 \, \log\left(a x + 1\right)}{a}}{a^{6}} + \frac{2 \, {\left(6 \, a^{4} x^{4} + 32 \, a^{2} x^{2} - 2 \, {\left(15 \, \log\left(a x - 1\right) - 46\right)} \log\left(a x + 1\right) + 15 \, \log\left(a x + 1\right)^{2} + 15 \, \log\left(a x - 1\right)^{2} + 92 \, \log\left(a x - 1\right)\right)} \operatorname{arcoth}\left(a x\right)}{a^{7}}\right)}"," ",0,"1/6*x^6*arccoth(a*x)^3 + 1/60*a*(2*(3*a^4*x^5 + 5*a^2*x^3 + 15*x)/a^6 - 15*log(a*x + 1)/a^7 + 15*log(a*x - 1)/a^7)*arccoth(a*x)^2 + 1/240*a*(((4*a^3*x^3 + (15*log(a*x - 1) - 46)*log(a*x + 1)^2 - 5*log(a*x + 1)^3 + 5*log(a*x - 1)^3 + 76*a*x - (15*log(a*x - 1)^2 - 92*log(a*x - 1))*log(a*x + 1) + 46*log(a*x - 1)^2 + 38*log(a*x - 1))/a - 184*(log(a*x - 1)*log(1/2*a*x + 1/2) + dilog(-1/2*a*x + 1/2))/a - 38*log(a*x + 1)/a)/a^6 + 2*(6*a^4*x^4 + 32*a^2*x^2 - 2*(15*log(a*x - 1) - 46)*log(a*x + 1) + 15*log(a*x + 1)^2 + 15*log(a*x - 1)^2 + 92*log(a*x - 1))*arccoth(a*x)/a^7)","A",0
24,0,0,0,0.000000," ","integrate(x^4*arccoth(a*x)^3,x, algorithm=""maxima"")","\frac{2 \, {\left(a^{5} x^{5} + 1\right)} \log\left(a x + 1\right)^{3} + 3 \, {\left(a^{4} x^{4} + 2 \, a^{2} x^{2} - 2 \, {\left(a^{5} x^{5} - 1\right)} \log\left(a x - 1\right)\right)} \log\left(a x + 1\right)^{2}}{80 \, a^{5}} + \frac{1}{8} \, \int -\frac{5 \, {\left(a^{5} x^{5} + a^{4} x^{4}\right)} \log\left(a x - 1\right)^{3} + 3 \, {\left(a^{4} x^{4} + 2 \, a^{2} x^{2} - 5 \, {\left(a^{5} x^{5} + a^{4} x^{4}\right)} \log\left(a x - 1\right)^{2} - 2 \, {\left(a^{5} x^{5} - 1\right)} \log\left(a x - 1\right)\right)} \log\left(a x + 1\right)}{5 \, {\left(a^{5} x + a^{4}\right)}}\,{d x}"," ",0,"1/80*(2*(a^5*x^5 + 1)*log(a*x + 1)^3 + 3*(a^4*x^4 + 2*a^2*x^2 - 2*(a^5*x^5 - 1)*log(a*x - 1))*log(a*x + 1)^2)/a^5 + 1/8*integrate(-1/5*(5*(a^5*x^5 + a^4*x^4)*log(a*x - 1)^3 + 3*(a^4*x^4 + 2*a^2*x^2 - 5*(a^5*x^5 + a^4*x^4)*log(a*x - 1)^2 - 2*(a^5*x^5 - 1)*log(a*x - 1))*log(a*x + 1))/(a^5*x + a^4), x)","F",0
25,1,262,0,0.329581," ","integrate(x^3*arccoth(a*x)^3,x, algorithm=""maxima"")","\frac{1}{4} \, x^{4} \operatorname{arcoth}\left(a x\right)^{3} + \frac{1}{8} \, a {\left(\frac{2 \, {\left(a^{2} x^{3} + 3 \, x\right)}}{a^{4}} - \frac{3 \, \log\left(a x + 1\right)}{a^{5}} + \frac{3 \, \log\left(a x - 1\right)}{a^{5}}\right)} \operatorname{arcoth}\left(a x\right)^{2} + \frac{1}{32} \, a {\left(\frac{\frac{{\left(3 \, \log\left(a x - 1\right) - 8\right)} \log\left(a x + 1\right)^{2} - \log\left(a x + 1\right)^{3} + \log\left(a x - 1\right)^{3} + 8 \, a x - {\left(3 \, \log\left(a x - 1\right)^{2} - 16 \, \log\left(a x - 1\right)\right)} \log\left(a x + 1\right) + 8 \, \log\left(a x - 1\right)^{2} + 4 \, \log\left(a x - 1\right)}{a} - \frac{32 \, {\left(\log\left(a x - 1\right) \log\left(\frac{1}{2} \, a x + \frac{1}{2}\right) + {\rm Li}_2\left(-\frac{1}{2} \, a x + \frac{1}{2}\right)\right)}}{a} - \frac{4 \, \log\left(a x + 1\right)}{a}}{a^{4}} + \frac{2 \, {\left(4 \, a^{2} x^{2} - 2 \, {\left(3 \, \log\left(a x - 1\right) - 8\right)} \log\left(a x + 1\right) + 3 \, \log\left(a x + 1\right)^{2} + 3 \, \log\left(a x - 1\right)^{2} + 16 \, \log\left(a x - 1\right)\right)} \operatorname{arcoth}\left(a x\right)}{a^{5}}\right)}"," ",0,"1/4*x^4*arccoth(a*x)^3 + 1/8*a*(2*(a^2*x^3 + 3*x)/a^4 - 3*log(a*x + 1)/a^5 + 3*log(a*x - 1)/a^5)*arccoth(a*x)^2 + 1/32*a*((((3*log(a*x - 1) - 8)*log(a*x + 1)^2 - log(a*x + 1)^3 + log(a*x - 1)^3 + 8*a*x - (3*log(a*x - 1)^2 - 16*log(a*x - 1))*log(a*x + 1) + 8*log(a*x - 1)^2 + 4*log(a*x - 1))/a - 32*(log(a*x - 1)*log(1/2*a*x + 1/2) + dilog(-1/2*a*x + 1/2))/a - 4*log(a*x + 1)/a)/a^4 + 2*(4*a^2*x^2 - 2*(3*log(a*x - 1) - 8)*log(a*x + 1) + 3*log(a*x + 1)^2 + 3*log(a*x - 1)^2 + 16*log(a*x - 1))*arccoth(a*x)/a^5)","B",0
26,0,0,0,0.000000," ","integrate(x^2*arccoth(a*x)^3,x, algorithm=""maxima"")","\frac{{\left(a^{3} x^{3} + 1\right)} \log\left(a x + 1\right)^{3} + 3 \, {\left(a^{2} x^{2} - {\left(a^{3} x^{3} - 1\right)} \log\left(a x - 1\right)\right)} \log\left(a x + 1\right)^{2}}{24 \, a^{3}} + \frac{1}{8} \, \int -\frac{{\left(a^{3} x^{3} + a^{2} x^{2}\right)} \log\left(a x - 1\right)^{3} + {\left(2 \, a^{2} x^{2} - 3 \, {\left(a^{3} x^{3} + a^{2} x^{2}\right)} \log\left(a x - 1\right)^{2} - 2 \, {\left(a^{3} x^{3} - 1\right)} \log\left(a x - 1\right)\right)} \log\left(a x + 1\right)}{a^{3} x + a^{2}}\,{d x}"," ",0,"1/24*((a^3*x^3 + 1)*log(a*x + 1)^3 + 3*(a^2*x^2 - (a^3*x^3 - 1)*log(a*x - 1))*log(a*x + 1)^2)/a^3 + 1/8*integrate(-((a^3*x^3 + a^2*x^2)*log(a*x - 1)^3 + (2*a^2*x^2 - 3*(a^3*x^3 + a^2*x^2)*log(a*x - 1)^2 - 2*(a^3*x^3 - 1)*log(a*x - 1))*log(a*x + 1))/(a^3*x + a^2), x)","F",0
27,1,215,0,0.326247," ","integrate(x*arccoth(a*x)^3,x, algorithm=""maxima"")","\frac{1}{2} \, x^{2} \operatorname{arcoth}\left(a x\right)^{3} + \frac{3}{4} \, a {\left(\frac{2 \, x}{a^{2}} - \frac{\log\left(a x + 1\right)}{a^{3}} + \frac{\log\left(a x - 1\right)}{a^{3}}\right)} \operatorname{arcoth}\left(a x\right)^{2} + \frac{1}{16} \, a {\left(\frac{\frac{3 \, {\left(\log\left(a x - 1\right) - 2\right)} \log\left(a x + 1\right)^{2} - \log\left(a x + 1\right)^{3} + \log\left(a x - 1\right)^{3} - 3 \, {\left(\log\left(a x - 1\right)^{2} - 4 \, \log\left(a x - 1\right)\right)} \log\left(a x + 1\right) + 6 \, \log\left(a x - 1\right)^{2}}{a} - \frac{24 \, {\left(\log\left(a x - 1\right) \log\left(\frac{1}{2} \, a x + \frac{1}{2}\right) + {\rm Li}_2\left(-\frac{1}{2} \, a x + \frac{1}{2}\right)\right)}}{a}}{a^{2}} - \frac{6 \, {\left(2 \, {\left(\log\left(a x - 1\right) - 2\right)} \log\left(a x + 1\right) - \log\left(a x + 1\right)^{2} - \log\left(a x - 1\right)^{2} - 4 \, \log\left(a x - 1\right)\right)} \operatorname{arcoth}\left(a x\right)}{a^{3}}\right)}"," ",0,"1/2*x^2*arccoth(a*x)^3 + 3/4*a*(2*x/a^2 - log(a*x + 1)/a^3 + log(a*x - 1)/a^3)*arccoth(a*x)^2 + 1/16*a*(((3*(log(a*x - 1) - 2)*log(a*x + 1)^2 - log(a*x + 1)^3 + log(a*x - 1)^3 - 3*(log(a*x - 1)^2 - 4*log(a*x - 1))*log(a*x + 1) + 6*log(a*x - 1)^2)/a - 24*(log(a*x - 1)*log(1/2*a*x + 1/2) + dilog(-1/2*a*x + 1/2))/a)/a^2 - 6*(2*(log(a*x - 1) - 2)*log(a*x + 1) - log(a*x + 1)^2 - log(a*x - 1)^2 - 4*log(a*x - 1))*arccoth(a*x)/a^3)","B",0
28,0,0,0,0.000000," ","integrate(arccoth(a*x)^3,x, algorithm=""maxima"")","\frac{{\left(a x + 1\right)} \log\left(a x + 1\right)^{3} - 3 \, {\left(a x - 1\right)} \log\left(a x + 1\right)^{2} \log\left(a x - 1\right)}{8 \, a} + \frac{1}{8} \, \int -\frac{{\left(a x + 1\right)} \log\left(a x - 1\right)^{3} - 3 \, {\left({\left(a x + 1\right)} \log\left(a x - 1\right)^{2} + 2 \, {\left(a x - 1\right)} \log\left(a x - 1\right)\right)} \log\left(a x + 1\right)}{a x + 1}\,{d x}"," ",0,"1/8*((a*x + 1)*log(a*x + 1)^3 - 3*(a*x - 1)*log(a*x + 1)^2*log(a*x - 1))/a + 1/8*integrate(-((a*x + 1)*log(a*x - 1)^3 - 3*((a*x + 1)*log(a*x - 1)^2 + 2*(a*x - 1)*log(a*x - 1))*log(a*x + 1))/(a*x + 1), x)","F",0
29,0,0,0,0.000000," ","integrate(arccoth(a*x)^3/x,x, algorithm=""maxima"")","\int \frac{\operatorname{arcoth}\left(a x\right)^{3}}{x}\,{d x}"," ",0,"integrate(arccoth(a*x)^3/x, x)","F",0
30,0,0,0,0.000000," ","integrate(arccoth(a*x)^3/x^2,x, algorithm=""maxima"")","\frac{1}{8} \, a {\left(\log\left(a x + 1\right) - \log\left(x\right)\right)} \log\left(a\right)^{3} + \frac{3}{8} \, a \int \frac{x \log\left(a x - 1\right)}{a x^{3} + x^{2}}\,{d x} \log\left(a\right)^{2} - \frac{3}{8} \, a \int \frac{x \log\left(x\right)}{a x^{3} + x^{2}}\,{d x} \log\left(a\right)^{2} - \frac{1}{8} \, {\left(a \log\left(a x + 1\right) - a \log\left(x\right) - \frac{1}{x}\right)} \log\left(a\right)^{3} + \frac{3}{4} \, a^{2} \int \frac{x^{2} \log\left(a x + 1\right) \log\left(a x - 1\right)}{a x^{3} + x^{2}}\,{d x} - \frac{3}{2} \, a^{2} \int \frac{x^{2} \log\left(a x + 1\right) \log\left(x\right)}{a x^{3} + x^{2}}\,{d x} + \frac{3}{4} \, a \int \frac{x \log\left(a x - 1\right) \log\left(x\right)}{a x^{3} + x^{2}}\,{d x} \log\left(a\right) - \frac{3}{8} \, a \int \frac{x \log\left(x\right)^{2}}{a x^{3} + x^{2}}\,{d x} \log\left(a\right) + \frac{3}{8} \, \int \frac{\log\left(a x - 1\right)}{a x^{3} + x^{2}}\,{d x} \log\left(a\right)^{2} - \frac{3}{8} \, \int \frac{\log\left(x\right)}{a x^{3} + x^{2}}\,{d x} \log\left(a\right)^{2} + \frac{3}{8} \, a \int \frac{x \log\left(a x + 1\right) \log\left(a x - 1\right)^{2}}{a x^{3} + x^{2}}\,{d x} - \frac{3}{8} \, a \int \frac{x \log\left(a x - 1\right)^{2} \log\left(x\right)}{a x^{3} + x^{2}}\,{d x} + \frac{3}{8} \, a \int \frac{x \log\left(a x - 1\right) \log\left(x\right)^{2}}{a x^{3} + x^{2}}\,{d x} - \frac{1}{8} \, a \int \frac{x \log\left(x\right)^{3}}{a x^{3} + x^{2}}\,{d x} - \frac{3}{4} \, a \int \frac{x \log\left(a x + 1\right) \log\left(a x - 1\right)}{a x^{3} + x^{2}}\,{d x} - \frac{3}{8} \, \int \frac{a x \log\left(a x - 1\right)^{2}}{a x^{3} + x^{2}}\,{d x} \log\left(a\right) - \frac{3}{8} \, \int \frac{\log\left(a x - 1\right)^{2}}{a x^{3} + x^{2}}\,{d x} \log\left(a\right) + \frac{3}{4} \, \int \frac{\log\left(a x - 1\right) \log\left(x\right)}{a x^{3} + x^{2}}\,{d x} \log\left(a\right) - \frac{3}{8} \, \int \frac{\log\left(x\right)^{2}}{a x^{3} + x^{2}}\,{d x} \log\left(a\right) - \frac{3 \, {\left(a^{2} \log\left(a x - 1\right) - a^{2} \log\left(x\right) + \frac{a}{x}\right)} \log\left(-\frac{1}{a x} + 1\right)^{2}}{8 \, a} + \frac{\log\left(-\frac{1}{a x} + 1\right)^{3}}{8 \, x} - \frac{{\left(a x + 1\right)} \log\left(a x + 1\right)^{3} - 3 \, {\left(2 \, a x \log\left(x\right) - {\left(a x - 1\right)} \log\left(a x - 1\right)\right)} \log\left(a x + 1\right)^{2}}{8 \, x} + \frac{\frac{3 \, {\left(a^{3} x \log\left(a x - 1\right)^{2} + a^{3} x \log\left(x\right)^{2} - 2 \, a^{3} x \log\left(x\right) + 2 \, a^{2} - 2 \, {\left(a^{3} x \log\left(x\right) - a^{3} x\right)} \log\left(a x - 1\right)\right)} \log\left(-\frac{1}{a x} + 1\right)}{a x} - \frac{a^{4} x \log\left(a x - 1\right)^{3} - a^{4} x \log\left(x\right)^{3} + 3 \, a^{4} x \log\left(x\right)^{2} - 6 \, a^{4} x \log\left(x\right) + 6 \, a^{3} - 3 \, {\left(a^{4} x \log\left(x\right) - a^{4} x\right)} \log\left(a x - 1\right)^{2} + 3 \, {\left(a^{4} x \log\left(x\right)^{2} - 2 \, a^{4} x \log\left(x\right) + 2 \, a^{4} x\right)} \log\left(a x - 1\right)}{a^{2} x}}{8 \, a} + \frac{3}{8} \, \int \frac{\log\left(a x + 1\right) \log\left(a x - 1\right)^{2}}{a x^{3} + x^{2}}\,{d x} - \frac{3}{8} \, \int \frac{\log\left(a x - 1\right)^{2} \log\left(x\right)}{a x^{3} + x^{2}}\,{d x} + \frac{3}{8} \, \int \frac{\log\left(a x - 1\right) \log\left(x\right)^{2}}{a x^{3} + x^{2}}\,{d x} - \frac{1}{8} \, \int \frac{\log\left(x\right)^{3}}{a x^{3} + x^{2}}\,{d x}"," ",0,"1/8*a*(log(a*x + 1) - log(x))*log(a)^3 + 3/8*a*integrate(x*log(a*x - 1)/(a*x^3 + x^2), x)*log(a)^2 - 3/8*a*integrate(x*log(x)/(a*x^3 + x^2), x)*log(a)^2 - 1/8*(a*log(a*x + 1) - a*log(x) - 1/x)*log(a)^3 + 3/4*a^2*integrate(x^2*log(a*x + 1)*log(a*x - 1)/(a*x^3 + x^2), x) - 3/2*a^2*integrate(x^2*log(a*x + 1)*log(x)/(a*x^3 + x^2), x) + 3/4*a*integrate(x*log(a*x - 1)*log(x)/(a*x^3 + x^2), x)*log(a) - 3/8*a*integrate(x*log(x)^2/(a*x^3 + x^2), x)*log(a) + 3/8*integrate(log(a*x - 1)/(a*x^3 + x^2), x)*log(a)^2 - 3/8*integrate(log(x)/(a*x^3 + x^2), x)*log(a)^2 + 3/8*a*integrate(x*log(a*x + 1)*log(a*x - 1)^2/(a*x^3 + x^2), x) - 3/8*a*integrate(x*log(a*x - 1)^2*log(x)/(a*x^3 + x^2), x) + 3/8*a*integrate(x*log(a*x - 1)*log(x)^2/(a*x^3 + x^2), x) - 1/8*a*integrate(x*log(x)^3/(a*x^3 + x^2), x) - 3/4*a*integrate(x*log(a*x + 1)*log(a*x - 1)/(a*x^3 + x^2), x) - 3/8*integrate(a*x*log(a*x - 1)^2/(a*x^3 + x^2), x)*log(a) - 3/8*integrate(log(a*x - 1)^2/(a*x^3 + x^2), x)*log(a) + 3/4*integrate(log(a*x - 1)*log(x)/(a*x^3 + x^2), x)*log(a) - 3/8*integrate(log(x)^2/(a*x^3 + x^2), x)*log(a) - 3/8*(a^2*log(a*x - 1) - a^2*log(x) + a/x)*log(-1/(a*x) + 1)^2/a + 1/8*log(-1/(a*x) + 1)^3/x - 1/8*((a*x + 1)*log(a*x + 1)^3 - 3*(2*a*x*log(x) - (a*x - 1)*log(a*x - 1))*log(a*x + 1)^2)/x + 1/8*(3*(a^3*x*log(a*x - 1)^2 + a^3*x*log(x)^2 - 2*a^3*x*log(x) + 2*a^2 - 2*(a^3*x*log(x) - a^3*x)*log(a*x - 1))*log(-1/(a*x) + 1)/(a*x) - (a^4*x*log(a*x - 1)^3 - a^4*x*log(x)^3 + 3*a^4*x*log(x)^2 - 6*a^4*x*log(x) + 6*a^3 - 3*(a^4*x*log(x) - a^4*x)*log(a*x - 1)^2 + 3*(a^4*x*log(x)^2 - 2*a^4*x*log(x) + 2*a^4*x)*log(a*x - 1))/(a^2*x))/a + 3/8*integrate(log(a*x + 1)*log(a*x - 1)^2/(a*x^3 + x^2), x) - 3/8*integrate(log(a*x - 1)^2*log(x)/(a*x^3 + x^2), x) + 3/8*integrate(log(a*x - 1)*log(x)^2/(a*x^3 + x^2), x) - 1/8*integrate(log(x)^3/(a*x^3 + x^2), x)","F",0
31,1,252,0,0.334943," ","integrate(arccoth(a*x)^3/x^3,x, algorithm=""maxima"")","\frac{3}{4} \, {\left(a \log\left(a x + 1\right) - a \log\left(a x - 1\right) - \frac{2}{x}\right)} a \operatorname{arcoth}\left(a x\right)^{2} - \frac{1}{16} \, {\left(a^{2} {\left(\frac{3 \, {\left(\log\left(a x - 1\right) - 2\right)} \log\left(a x + 1\right)^{2} - \log\left(a x + 1\right)^{3} + \log\left(a x - 1\right)^{3} - 3 \, {\left(\log\left(a x - 1\right)^{2} - 4 \, \log\left(a x - 1\right)\right)} \log\left(a x + 1\right) + 6 \, \log\left(a x - 1\right)^{2}}{a} - \frac{24 \, {\left(\log\left(a x - 1\right) \log\left(\frac{1}{2} \, a x + \frac{1}{2}\right) + {\rm Li}_2\left(-\frac{1}{2} \, a x + \frac{1}{2}\right)\right)}}{a} + \frac{24 \, {\left(\log\left(a x + 1\right) \log\left(x\right) + {\rm Li}_2\left(-a x\right)\right)}}{a} - \frac{24 \, {\left(\log\left(-a x + 1\right) \log\left(x\right) + {\rm Li}_2\left(a x\right)\right)}}{a}\right)} - 6 \, {\left(2 \, {\left(\log\left(a x - 1\right) - 2\right)} \log\left(a x + 1\right) - \log\left(a x + 1\right)^{2} - \log\left(a x - 1\right)^{2} - 4 \, \log\left(a x - 1\right) + 8 \, \log\left(x\right)\right)} a \operatorname{arcoth}\left(a x\right)\right)} a - \frac{\operatorname{arcoth}\left(a x\right)^{3}}{2 \, x^{2}}"," ",0,"3/4*(a*log(a*x + 1) - a*log(a*x - 1) - 2/x)*a*arccoth(a*x)^2 - 1/16*(a^2*((3*(log(a*x - 1) - 2)*log(a*x + 1)^2 - log(a*x + 1)^3 + log(a*x - 1)^3 - 3*(log(a*x - 1)^2 - 4*log(a*x - 1))*log(a*x + 1) + 6*log(a*x - 1)^2)/a - 24*(log(a*x - 1)*log(1/2*a*x + 1/2) + dilog(-1/2*a*x + 1/2))/a + 24*(log(a*x + 1)*log(x) + dilog(-a*x))/a - 24*(log(-a*x + 1)*log(x) + dilog(a*x))/a) - 6*(2*(log(a*x - 1) - 2)*log(a*x + 1) - log(a*x + 1)^2 - log(a*x - 1)^2 - 4*log(a*x - 1) + 8*log(x))*a*arccoth(a*x))*a - 1/2*arccoth(a*x)^3/x^2","B",0
32,0,0,0,0.000000," ","integrate(arccoth(a*x)^3/x^4,x, algorithm=""maxima"")","\frac{1}{4} \, a^{4} \int \frac{x^{4} \log\left(a x + 1\right) \log\left(a x - 1\right)}{a x^{5} + x^{4}}\,{d x} - \frac{1}{2} \, a^{4} \int \frac{x^{4} \log\left(a x + 1\right) \log\left(x\right)}{a x^{5} + x^{4}}\,{d x} + \frac{1}{16} \, {\left(2 \, a^{2} \log\left(a x + 1\right) - 2 \, a^{2} \log\left(x\right) - \frac{2 \, a x - 1}{x^{2}}\right)} a \log\left(a\right)^{3} + \frac{3}{8} \, a \int \frac{x \log\left(a x - 1\right)}{a x^{5} + x^{4}}\,{d x} \log\left(a\right)^{2} - \frac{3}{8} \, a \int \frac{x \log\left(x\right)}{a x^{5} + x^{4}}\,{d x} \log\left(a\right)^{2} - \frac{1}{48} \, {\left(6 \, a^{3} \log\left(a x + 1\right) - 6 \, a^{3} \log\left(x\right) - \frac{6 \, a^{2} x^{2} - 3 \, a x + 2}{x^{3}}\right)} \log\left(a\right)^{3} + \frac{1}{4} \, a^{2} \int \frac{x^{2} \log\left(a x + 1\right)}{a x^{5} + x^{4}}\,{d x} + \frac{3}{4} \, a \int \frac{x \log\left(a x - 1\right) \log\left(x\right)}{a x^{5} + x^{4}}\,{d x} \log\left(a\right) - \frac{3}{8} \, a \int \frac{x \log\left(x\right)^{2}}{a x^{5} + x^{4}}\,{d x} \log\left(a\right) + \frac{3}{8} \, \int \frac{\log\left(a x - 1\right)}{a x^{5} + x^{4}}\,{d x} \log\left(a\right)^{2} - \frac{3}{8} \, \int \frac{\log\left(x\right)}{a x^{5} + x^{4}}\,{d x} \log\left(a\right)^{2} + \frac{3}{8} \, a \int \frac{x \log\left(a x + 1\right) \log\left(a x - 1\right)^{2}}{a x^{5} + x^{4}}\,{d x} - \frac{3}{8} \, a \int \frac{x \log\left(a x - 1\right)^{2} \log\left(x\right)}{a x^{5} + x^{4}}\,{d x} + \frac{3}{8} \, a \int \frac{x \log\left(a x - 1\right) \log\left(x\right)^{2}}{a x^{5} + x^{4}}\,{d x} - \frac{1}{8} \, a \int \frac{x \log\left(x\right)^{3}}{a x^{5} + x^{4}}\,{d x} - \frac{1}{4} \, a \int \frac{x \log\left(a x + 1\right) \log\left(a x - 1\right)}{a x^{5} + x^{4}}\,{d x} - \frac{3}{8} \, \int \frac{a x \log\left(a x - 1\right)^{2}}{a x^{5} + x^{4}}\,{d x} \log\left(a\right) - \frac{3}{8} \, \int \frac{\log\left(a x - 1\right)^{2}}{a x^{5} + x^{4}}\,{d x} \log\left(a\right) + \frac{3}{4} \, \int \frac{\log\left(a x - 1\right) \log\left(x\right)}{a x^{5} + x^{4}}\,{d x} \log\left(a\right) - \frac{3}{8} \, \int \frac{\log\left(x\right)^{2}}{a x^{5} + x^{4}}\,{d x} \log\left(a\right) - \frac{{\left(6 \, a^{4} \log\left(a x - 1\right) - 6 \, a^{4} \log\left(x\right) + \frac{6 \, a^{3} x^{2} + 3 \, a^{2} x + 2 \, a}{x^{3}}\right)} \log\left(-\frac{1}{a x} + 1\right)^{2}}{48 \, a} + \frac{\frac{6 \, {\left(18 \, a^{5} x^{3} \log\left(a x - 1\right)^{2} + 18 \, a^{5} x^{3} \log\left(x\right)^{2} - 66 \, a^{5} x^{3} \log\left(x\right) + 66 \, a^{4} x^{2} + 15 \, a^{3} x + 4 \, a^{2} - 6 \, {\left(6 \, a^{5} x^{3} \log\left(x\right) - 11 \, a^{5} x^{3}\right)} \log\left(a x - 1\right)\right)} \log\left(-\frac{1}{a x} + 1\right)}{a x^{3}} - \frac{36 \, a^{6} x^{3} \log\left(a x - 1\right)^{3} - 36 \, a^{6} x^{3} \log\left(x\right)^{3} + 198 \, a^{6} x^{3} \log\left(x\right)^{2} - 510 \, a^{6} x^{3} \log\left(x\right) + 510 \, a^{5} x^{2} + 57 \, a^{4} x + 8 \, a^{3} - 18 \, {\left(6 \, a^{6} x^{3} \log\left(x\right) - 11 \, a^{6} x^{3}\right)} \log\left(a x - 1\right)^{2} + 6 \, {\left(18 \, a^{6} x^{3} \log\left(x\right)^{2} - 66 \, a^{6} x^{3} \log\left(x\right) + 85 \, a^{6} x^{3}\right)} \log\left(a x - 1\right)}{a^{2} x^{3}}}{864 \, a} + \frac{\log\left(-\frac{1}{a x} + 1\right)^{3}}{24 \, x^{3}} - \frac{{\left(a^{3} x^{3} + 1\right)} \log\left(a x + 1\right)^{3} - 3 \, {\left(2 \, a^{3} x^{3} \log\left(x\right) - a x - {\left(a^{3} x^{3} - 1\right)} \log\left(a x - 1\right)\right)} \log\left(a x + 1\right)^{2}}{24 \, x^{3}} + \frac{3}{8} \, \int \frac{\log\left(a x + 1\right) \log\left(a x - 1\right)^{2}}{a x^{5} + x^{4}}\,{d x} - \frac{3}{8} \, \int \frac{\log\left(a x - 1\right)^{2} \log\left(x\right)}{a x^{5} + x^{4}}\,{d x} + \frac{3}{8} \, \int \frac{\log\left(a x - 1\right) \log\left(x\right)^{2}}{a x^{5} + x^{4}}\,{d x} - \frac{1}{8} \, \int \frac{\log\left(x\right)^{3}}{a x^{5} + x^{4}}\,{d x}"," ",0,"1/4*a^4*integrate(x^4*log(a*x + 1)*log(a*x - 1)/(a*x^5 + x^4), x) - 1/2*a^4*integrate(x^4*log(a*x + 1)*log(x)/(a*x^5 + x^4), x) + 1/16*(2*a^2*log(a*x + 1) - 2*a^2*log(x) - (2*a*x - 1)/x^2)*a*log(a)^3 + 3/8*a*integrate(x*log(a*x - 1)/(a*x^5 + x^4), x)*log(a)^2 - 3/8*a*integrate(x*log(x)/(a*x^5 + x^4), x)*log(a)^2 - 1/48*(6*a^3*log(a*x + 1) - 6*a^3*log(x) - (6*a^2*x^2 - 3*a*x + 2)/x^3)*log(a)^3 + 1/4*a^2*integrate(x^2*log(a*x + 1)/(a*x^5 + x^4), x) + 3/4*a*integrate(x*log(a*x - 1)*log(x)/(a*x^5 + x^4), x)*log(a) - 3/8*a*integrate(x*log(x)^2/(a*x^5 + x^4), x)*log(a) + 3/8*integrate(log(a*x - 1)/(a*x^5 + x^4), x)*log(a)^2 - 3/8*integrate(log(x)/(a*x^5 + x^4), x)*log(a)^2 + 3/8*a*integrate(x*log(a*x + 1)*log(a*x - 1)^2/(a*x^5 + x^4), x) - 3/8*a*integrate(x*log(a*x - 1)^2*log(x)/(a*x^5 + x^4), x) + 3/8*a*integrate(x*log(a*x - 1)*log(x)^2/(a*x^5 + x^4), x) - 1/8*a*integrate(x*log(x)^3/(a*x^5 + x^4), x) - 1/4*a*integrate(x*log(a*x + 1)*log(a*x - 1)/(a*x^5 + x^4), x) - 3/8*integrate(a*x*log(a*x - 1)^2/(a*x^5 + x^4), x)*log(a) - 3/8*integrate(log(a*x - 1)^2/(a*x^5 + x^4), x)*log(a) + 3/4*integrate(log(a*x - 1)*log(x)/(a*x^5 + x^4), x)*log(a) - 3/8*integrate(log(x)^2/(a*x^5 + x^4), x)*log(a) - 1/48*(6*a^4*log(a*x - 1) - 6*a^4*log(x) + (6*a^3*x^2 + 3*a^2*x + 2*a)/x^3)*log(-1/(a*x) + 1)^2/a + 1/864*(6*(18*a^5*x^3*log(a*x - 1)^2 + 18*a^5*x^3*log(x)^2 - 66*a^5*x^3*log(x) + 66*a^4*x^2 + 15*a^3*x + 4*a^2 - 6*(6*a^5*x^3*log(x) - 11*a^5*x^3)*log(a*x - 1))*log(-1/(a*x) + 1)/(a*x^3) - (36*a^6*x^3*log(a*x - 1)^3 - 36*a^6*x^3*log(x)^3 + 198*a^6*x^3*log(x)^2 - 510*a^6*x^3*log(x) + 510*a^5*x^2 + 57*a^4*x + 8*a^3 - 18*(6*a^6*x^3*log(x) - 11*a^6*x^3)*log(a*x - 1)^2 + 6*(18*a^6*x^3*log(x)^2 - 66*a^6*x^3*log(x) + 85*a^6*x^3)*log(a*x - 1))/(a^2*x^3))/a + 1/24*log(-1/(a*x) + 1)^3/x^3 - 1/24*((a^3*x^3 + 1)*log(a*x + 1)^3 - 3*(2*a^3*x^3*log(x) - a*x - (a^3*x^3 - 1)*log(a*x - 1))*log(a*x + 1)^2)/x^3 + 3/8*integrate(log(a*x + 1)*log(a*x - 1)^2/(a*x^5 + x^4), x) - 3/8*integrate(log(a*x - 1)^2*log(x)/(a*x^5 + x^4), x) + 3/8*integrate(log(a*x - 1)*log(x)^2/(a*x^5 + x^4), x) - 1/8*integrate(log(x)^3/(a*x^5 + x^4), x)","F",0
33,1,342,0,0.340414," ","integrate(arccoth(a*x)^3/x^5,x, algorithm=""maxima"")","\frac{1}{8} \, {\left(3 \, a^{3} \log\left(a x + 1\right) - 3 \, a^{3} \log\left(a x - 1\right) - \frac{2 \, {\left(3 \, a^{2} x^{2} + 1\right)}}{x^{3}}\right)} a \operatorname{arcoth}\left(a x\right)^{2} + \frac{1}{32} \, {\left({\left(32 \, {\left(\log\left(a x - 1\right) \log\left(\frac{1}{2} \, a x + \frac{1}{2}\right) + {\rm Li}_2\left(-\frac{1}{2} \, a x + \frac{1}{2}\right)\right)} a - 32 \, {\left(\log\left(a x + 1\right) \log\left(x\right) + {\rm Li}_2\left(-a x\right)\right)} a + 32 \, {\left(\log\left(-a x + 1\right) \log\left(x\right) + {\rm Li}_2\left(a x\right)\right)} a + 4 \, a \log\left(a x + 1\right) - 4 \, a \log\left(a x - 1\right) + \frac{a x \log\left(a x + 1\right)^{3} - a x \log\left(a x - 1\right)^{3} - 8 \, a x \log\left(a x - 1\right)^{2} - {\left(3 \, a x \log\left(a x - 1\right) - 8 \, a x\right)} \log\left(a x + 1\right)^{2} + {\left(3 \, a x \log\left(a x - 1\right)^{2} - 16 \, a x \log\left(a x - 1\right)\right)} \log\left(a x + 1\right) - 8}{x}\right)} a^{2} + 2 \, {\left(32 \, a^{2} \log\left(x\right) - \frac{3 \, a^{2} x^{2} \log\left(a x + 1\right)^{2} + 3 \, a^{2} x^{2} \log\left(a x - 1\right)^{2} + 16 \, a^{2} x^{2} \log\left(a x - 1\right) - 2 \, {\left(3 \, a^{2} x^{2} \log\left(a x - 1\right) - 8 \, a^{2} x^{2}\right)} \log\left(a x + 1\right) + 4}{x^{2}}\right)} a \operatorname{arcoth}\left(a x\right)\right)} a - \frac{\operatorname{arcoth}\left(a x\right)^{3}}{4 \, x^{4}}"," ",0,"1/8*(3*a^3*log(a*x + 1) - 3*a^3*log(a*x - 1) - 2*(3*a^2*x^2 + 1)/x^3)*a*arccoth(a*x)^2 + 1/32*((32*(log(a*x - 1)*log(1/2*a*x + 1/2) + dilog(-1/2*a*x + 1/2))*a - 32*(log(a*x + 1)*log(x) + dilog(-a*x))*a + 32*(log(-a*x + 1)*log(x) + dilog(a*x))*a + 4*a*log(a*x + 1) - 4*a*log(a*x - 1) + (a*x*log(a*x + 1)^3 - a*x*log(a*x - 1)^3 - 8*a*x*log(a*x - 1)^2 - (3*a*x*log(a*x - 1) - 8*a*x)*log(a*x + 1)^2 + (3*a*x*log(a*x - 1)^2 - 16*a*x*log(a*x - 1))*log(a*x + 1) - 8)/x)*a^2 + 2*(32*a^2*log(x) - (3*a^2*x^2*log(a*x + 1)^2 + 3*a^2*x^2*log(a*x - 1)^2 + 16*a^2*x^2*log(a*x - 1) - 2*(3*a^2*x^2*log(a*x - 1) - 8*a^2*x^2)*log(a*x + 1) + 4)/x^2)*a*arccoth(a*x))*a - 1/4*arccoth(a*x)^3/x^4","B",0
34,0,0,0,0.000000," ","integrate(arccoth(c*x)^2/(e*x+d),x, algorithm=""maxima"")","\int \frac{\operatorname{arcoth}\left(c x\right)^{2}}{e x + d}\,{d x}"," ",0,"integrate(arccoth(c*x)^2/(e*x + d), x)","F",0
35,1,276,0,0.306757," ","integrate((d*x^2+c)^4*arccoth(a*x),x, algorithm=""maxima"")","\frac{1}{7560} \, a {\left(\frac{105 \, a^{6} d^{4} x^{8} + 20 \, {\left(36 \, a^{6} c d^{3} + 7 \, a^{4} d^{4}\right)} x^{6} + 6 \, {\left(378 \, a^{6} c^{2} d^{2} + 180 \, a^{4} c d^{3} + 35 \, a^{2} d^{4}\right)} x^{4} + 12 \, {\left(420 \, a^{6} c^{3} d + 378 \, a^{4} c^{2} d^{2} + 180 \, a^{2} c d^{3} + 35 \, d^{4}\right)} x^{2}}{a^{8}} + \frac{12 \, {\left(315 \, a^{8} c^{4} + 420 \, a^{6} c^{3} d + 378 \, a^{4} c^{2} d^{2} + 180 \, a^{2} c d^{3} + 35 \, d^{4}\right)} \log\left(a x + 1\right)}{a^{10}} + \frac{12 \, {\left(315 \, a^{8} c^{4} + 420 \, a^{6} c^{3} d + 378 \, a^{4} c^{2} d^{2} + 180 \, a^{2} c d^{3} + 35 \, d^{4}\right)} \log\left(a x - 1\right)}{a^{10}}\right)} + \frac{1}{315} \, {\left(35 \, d^{4} x^{9} + 180 \, c d^{3} x^{7} + 378 \, c^{2} d^{2} x^{5} + 420 \, c^{3} d x^{3} + 315 \, c^{4} x\right)} \operatorname{arcoth}\left(a x\right)"," ",0,"1/7560*a*((105*a^6*d^4*x^8 + 20*(36*a^6*c*d^3 + 7*a^4*d^4)*x^6 + 6*(378*a^6*c^2*d^2 + 180*a^4*c*d^3 + 35*a^2*d^4)*x^4 + 12*(420*a^6*c^3*d + 378*a^4*c^2*d^2 + 180*a^2*c*d^3 + 35*d^4)*x^2)/a^8 + 12*(315*a^8*c^4 + 420*a^6*c^3*d + 378*a^4*c^2*d^2 + 180*a^2*c*d^3 + 35*d^4)*log(a*x + 1)/a^10 + 12*(315*a^8*c^4 + 420*a^6*c^3*d + 378*a^4*c^2*d^2 + 180*a^2*c*d^3 + 35*d^4)*log(a*x - 1)/a^10) + 1/315*(35*d^4*x^9 + 180*c*d^3*x^7 + 378*c^2*d^2*x^5 + 420*c^3*d*x^3 + 315*c^4*x)*arccoth(a*x)","A",0
36,1,198,0,0.306378," ","integrate((d*x^2+c)^3*arccoth(a*x),x, algorithm=""maxima"")","\frac{1}{420} \, a {\left(\frac{10 \, a^{4} d^{3} x^{6} + 3 \, {\left(21 \, a^{4} c d^{2} + 5 \, a^{2} d^{3}\right)} x^{4} + 6 \, {\left(35 \, a^{4} c^{2} d + 21 \, a^{2} c d^{2} + 5 \, d^{3}\right)} x^{2}}{a^{6}} + \frac{6 \, {\left(35 \, a^{6} c^{3} + 35 \, a^{4} c^{2} d + 21 \, a^{2} c d^{2} + 5 \, d^{3}\right)} \log\left(a x + 1\right)}{a^{8}} + \frac{6 \, {\left(35 \, a^{6} c^{3} + 35 \, a^{4} c^{2} d + 21 \, a^{2} c d^{2} + 5 \, d^{3}\right)} \log\left(a x - 1\right)}{a^{8}}\right)} + \frac{1}{35} \, {\left(5 \, d^{3} x^{7} + 21 \, c d^{2} x^{5} + 35 \, c^{2} d x^{3} + 35 \, c^{3} x\right)} \operatorname{arcoth}\left(a x\right)"," ",0,"1/420*a*((10*a^4*d^3*x^6 + 3*(21*a^4*c*d^2 + 5*a^2*d^3)*x^4 + 6*(35*a^4*c^2*d + 21*a^2*c*d^2 + 5*d^3)*x^2)/a^6 + 6*(35*a^6*c^3 + 35*a^4*c^2*d + 21*a^2*c*d^2 + 5*d^3)*log(a*x + 1)/a^8 + 6*(35*a^6*c^3 + 35*a^4*c^2*d + 21*a^2*c*d^2 + 5*d^3)*log(a*x - 1)/a^8) + 1/35*(5*d^3*x^7 + 21*c*d^2*x^5 + 35*c^2*d*x^3 + 35*c^3*x)*arccoth(a*x)","A",0
37,1,131,0,0.303644," ","integrate((d*x^2+c)^2*arccoth(a*x),x, algorithm=""maxima"")","\frac{1}{60} \, a {\left(\frac{3 \, a^{2} d^{2} x^{4} + 2 \, {\left(10 \, a^{2} c d + 3 \, d^{2}\right)} x^{2}}{a^{4}} + \frac{2 \, {\left(15 \, a^{4} c^{2} + 10 \, a^{2} c d + 3 \, d^{2}\right)} \log\left(a x + 1\right)}{a^{6}} + \frac{2 \, {\left(15 \, a^{4} c^{2} + 10 \, a^{2} c d + 3 \, d^{2}\right)} \log\left(a x - 1\right)}{a^{6}}\right)} + \frac{1}{15} \, {\left(3 \, d^{2} x^{5} + 10 \, c d x^{3} + 15 \, c^{2} x\right)} \operatorname{arcoth}\left(a x\right)"," ",0,"1/60*a*((3*a^2*d^2*x^4 + 2*(10*a^2*c*d + 3*d^2)*x^2)/a^4 + 2*(15*a^4*c^2 + 10*a^2*c*d + 3*d^2)*log(a*x + 1)/a^6 + 2*(15*a^4*c^2 + 10*a^2*c*d + 3*d^2)*log(a*x - 1)/a^6) + 1/15*(3*d^2*x^5 + 10*c*d*x^3 + 15*c^2*x)*arccoth(a*x)","A",0
38,1,65,0,0.303214," ","integrate((d*x^2+c)*arccoth(a*x),x, algorithm=""maxima"")","\frac{1}{6} \, a {\left(\frac{d x^{2}}{a^{2}} + \frac{{\left(3 \, a^{2} c + d\right)} \log\left(a x + 1\right)}{a^{4}} + \frac{{\left(3 \, a^{2} c + d\right)} \log\left(a x - 1\right)}{a^{4}}\right)} + \frac{1}{3} \, {\left(d x^{3} + 3 \, c x\right)} \operatorname{arcoth}\left(a x\right)"," ",0,"1/6*a*(d*x^2/a^2 + (3*a^2*c + d)*log(a*x + 1)/a^4 + (3*a^2*c + d)*log(a*x - 1)/a^4) + 1/3*(d*x^3 + 3*c*x)*arccoth(a*x)","A",0
39,1,406,0,0.537309," ","integrate(arccoth(a*x)/(d*x^2+c),x, algorithm=""maxima"")","\frac{\operatorname{arcoth}\left(a x\right) \arctan\left(\frac{d x}{\sqrt{c d}}\right)}{\sqrt{c d}} + \frac{{\left(\arctan\left(\frac{{\left(a^{2} x + a\right)} \sqrt{c} \sqrt{d}}{a^{2} c + d}, \frac{a d x + d}{a^{2} c + d}\right) - \arctan\left(\frac{{\left(a^{2} x - a\right)} \sqrt{c} \sqrt{d}}{a^{2} c + d}, -\frac{a d x - d}{a^{2} c + d}\right)\right)} \log\left(d x^{2} + c\right) - \arctan\left(\frac{\sqrt{d} x}{\sqrt{c}}\right) \log\left(\frac{a^{2} d x^{2} + 2 \, a d x + d}{a^{2} c + d}\right) + \arctan\left(\frac{\sqrt{d} x}{\sqrt{c}}\right) \log\left(\frac{a^{2} d x^{2} - 2 \, a d x + d}{a^{2} c + d}\right) - i \, {\rm Li}_2\left(\frac{a^{2} c + a d x - {\left(i \, a^{2} x - i \, a\right)} \sqrt{c} \sqrt{d}}{a^{2} c + 2 i \, a \sqrt{c} \sqrt{d} - d}\right) - i \, {\rm Li}_2\left(\frac{a^{2} c - a d x + {\left(i \, a^{2} x + i \, a\right)} \sqrt{c} \sqrt{d}}{a^{2} c + 2 i \, a \sqrt{c} \sqrt{d} - d}\right) + i \, {\rm Li}_2\left(\frac{a^{2} c + a d x + {\left(i \, a^{2} x - i \, a\right)} \sqrt{c} \sqrt{d}}{a^{2} c - 2 i \, a \sqrt{c} \sqrt{d} - d}\right) + i \, {\rm Li}_2\left(\frac{a^{2} c - a d x - {\left(i \, a^{2} x + i \, a\right)} \sqrt{c} \sqrt{d}}{a^{2} c - 2 i \, a \sqrt{c} \sqrt{d} - d}\right)}{4 \, \sqrt{c d}}"," ",0,"arccoth(a*x)*arctan(d*x/sqrt(c*d))/sqrt(c*d) + 1/4*((arctan2((a^2*x + a)*sqrt(c)*sqrt(d)/(a^2*c + d), (a*d*x + d)/(a^2*c + d)) - arctan2((a^2*x - a)*sqrt(c)*sqrt(d)/(a^2*c + d), -(a*d*x - d)/(a^2*c + d)))*log(d*x^2 + c) - arctan(sqrt(d)*x/sqrt(c))*log((a^2*d*x^2 + 2*a*d*x + d)/(a^2*c + d)) + arctan(sqrt(d)*x/sqrt(c))*log((a^2*d*x^2 - 2*a*d*x + d)/(a^2*c + d)) - I*dilog((a^2*c + a*d*x - (I*a^2*x - I*a)*sqrt(c)*sqrt(d))/(a^2*c + 2*I*a*sqrt(c)*sqrt(d) - d)) - I*dilog((a^2*c - a*d*x + (I*a^2*x + I*a)*sqrt(c)*sqrt(d))/(a^2*c + 2*I*a*sqrt(c)*sqrt(d) - d)) + I*dilog((a^2*c + a*d*x + (I*a^2*x - I*a)*sqrt(c)*sqrt(d))/(a^2*c - 2*I*a*sqrt(c)*sqrt(d) - d)) + I*dilog((a^2*c - a*d*x - (I*a^2*x + I*a)*sqrt(c)*sqrt(d))/(a^2*c - 2*I*a*sqrt(c)*sqrt(d) - d)))/sqrt(c*d)","A",0
40,1,550,0,0.514204," ","integrate(arccoth(a*x)/(d*x^2+c)^2,x, algorithm=""maxima"")","\frac{1}{2} \, {\left(\frac{x}{c d x^{2} + c^{2}} + \frac{\arctan\left(\frac{d x}{\sqrt{c d}}\right)}{\sqrt{c d} c}\right)} \operatorname{arcoth}\left(a x\right) - \frac{{\left(2 \, a c d \log\left(d x^{2} + c\right) - 2 \, a c d \log\left(a x + 1\right) - 2 \, a c d \log\left(a x - 1\right) + {\left({\left(a^{2} c + d\right)} \arctan\left(\frac{\sqrt{d} x}{\sqrt{c}}\right) \log\left(\frac{a^{2} d x^{2} + 2 \, a d x + d}{a^{2} c + d}\right) - {\left(a^{2} c + d\right)} \arctan\left(\frac{\sqrt{d} x}{\sqrt{c}}\right) \log\left(\frac{a^{2} d x^{2} - 2 \, a d x + d}{a^{2} c + d}\right) + {\left(i \, a^{2} c + i \, d\right)} {\rm Li}_2\left(\frac{a^{2} c + a d x - {\left(i \, a^{2} x - i \, a\right)} \sqrt{c} \sqrt{d}}{a^{2} c + 2 i \, a \sqrt{c} \sqrt{d} - d}\right) + {\left(i \, a^{2} c + i \, d\right)} {\rm Li}_2\left(\frac{a^{2} c - a d x + {\left(i \, a^{2} x + i \, a\right)} \sqrt{c} \sqrt{d}}{a^{2} c + 2 i \, a \sqrt{c} \sqrt{d} - d}\right) + {\left(-i \, a^{2} c - i \, d\right)} {\rm Li}_2\left(\frac{a^{2} c + a d x + {\left(i \, a^{2} x - i \, a\right)} \sqrt{c} \sqrt{d}}{a^{2} c - 2 i \, a \sqrt{c} \sqrt{d} - d}\right) + {\left(-i \, a^{2} c - i \, d\right)} {\rm Li}_2\left(\frac{a^{2} c - a d x - {\left(i \, a^{2} x + i \, a\right)} \sqrt{c} \sqrt{d}}{a^{2} c - 2 i \, a \sqrt{c} \sqrt{d} - d}\right) - {\left({\left(a^{2} c + d\right)} \arctan\left(\frac{{\left(a^{2} x + a\right)} \sqrt{c} \sqrt{d}}{a^{2} c + d}, \frac{a d x + d}{a^{2} c + d}\right) - {\left(a^{2} c + d\right)} \arctan\left(\frac{{\left(a^{2} x - a\right)} \sqrt{c} \sqrt{d}}{a^{2} c + d}, -\frac{a d x - d}{a^{2} c + d}\right)\right)} \log\left(d x^{2} + c\right)\right)} \sqrt{c} \sqrt{d}\right)} a}{8 \, {\left(a^{3} c^{3} d + a c^{2} d^{2}\right)}}"," ",0,"1/2*(x/(c*d*x^2 + c^2) + arctan(d*x/sqrt(c*d))/(sqrt(c*d)*c))*arccoth(a*x) - 1/8*(2*a*c*d*log(d*x^2 + c) - 2*a*c*d*log(a*x + 1) - 2*a*c*d*log(a*x - 1) + ((a^2*c + d)*arctan(sqrt(d)*x/sqrt(c))*log((a^2*d*x^2 + 2*a*d*x + d)/(a^2*c + d)) - (a^2*c + d)*arctan(sqrt(d)*x/sqrt(c))*log((a^2*d*x^2 - 2*a*d*x + d)/(a^2*c + d)) + (I*a^2*c + I*d)*dilog((a^2*c + a*d*x - (I*a^2*x - I*a)*sqrt(c)*sqrt(d))/(a^2*c + 2*I*a*sqrt(c)*sqrt(d) - d)) + (I*a^2*c + I*d)*dilog((a^2*c - a*d*x + (I*a^2*x + I*a)*sqrt(c)*sqrt(d))/(a^2*c + 2*I*a*sqrt(c)*sqrt(d) - d)) + (-I*a^2*c - I*d)*dilog((a^2*c + a*d*x + (I*a^2*x - I*a)*sqrt(c)*sqrt(d))/(a^2*c - 2*I*a*sqrt(c)*sqrt(d) - d)) + (-I*a^2*c - I*d)*dilog((a^2*c - a*d*x - (I*a^2*x + I*a)*sqrt(c)*sqrt(d))/(a^2*c - 2*I*a*sqrt(c)*sqrt(d) - d)) - ((a^2*c + d)*arctan2((a^2*x + a)*sqrt(c)*sqrt(d)/(a^2*c + d), (a*d*x + d)/(a^2*c + d)) - (a^2*c + d)*arctan2((a^2*x - a)*sqrt(c)*sqrt(d)/(a^2*c + d), -(a*d*x - d)/(a^2*c + d)))*log(d*x^2 + c))*sqrt(c)*sqrt(d))*a/(a^3*c^3*d + a*c^2*d^2)","A",0
41,1,1084,0,0.583792," ","integrate(arccoth(a*x)/(d*x^2+c)^3,x, algorithm=""maxima"")","\frac{1}{8} \, {\left(\frac{3 \, d x^{3} + 5 \, c x}{c^{2} d^{2} x^{4} + 2 \, c^{3} d x^{2} + c^{4}} + \frac{3 \, \arctan\left(\frac{d x}{\sqrt{c d}}\right)}{\sqrt{c d} c^{2}}\right)} \operatorname{arcoth}\left(a x\right) + \frac{{\left(4 \, a^{3} c^{3} d + 4 \, a c^{2} d^{2} - {\left(3 \, {\left(a^{4} c^{3} + 2 \, a^{2} c^{2} d + c d^{2} + {\left(a^{4} c^{2} d + 2 \, a^{2} c d^{2} + d^{3}\right)} x^{2}\right)} \arctan\left(\frac{\sqrt{d} x}{\sqrt{c}}\right) \log\left(\frac{a^{2} d x^{2} + 2 \, a d x + d}{a^{2} c + d}\right) - 3 \, {\left(a^{4} c^{3} + 2 \, a^{2} c^{2} d + c d^{2} + {\left(a^{4} c^{2} d + 2 \, a^{2} c d^{2} + d^{3}\right)} x^{2}\right)} \arctan\left(\frac{\sqrt{d} x}{\sqrt{c}}\right) \log\left(\frac{a^{2} d x^{2} - 2 \, a d x + d}{a^{2} c + d}\right) + {\left(3 i \, a^{4} c^{3} + 6 i \, a^{2} c^{2} d + 3 i \, c d^{2} + {\left(3 i \, a^{4} c^{2} d + 6 i \, a^{2} c d^{2} + 3 i \, d^{3}\right)} x^{2}\right)} {\rm Li}_2\left(\frac{a^{2} c + a d x - {\left(i \, a^{2} x - i \, a\right)} \sqrt{c} \sqrt{d}}{a^{2} c + 2 i \, a \sqrt{c} \sqrt{d} - d}\right) + {\left(3 i \, a^{4} c^{3} + 6 i \, a^{2} c^{2} d + 3 i \, c d^{2} + {\left(3 i \, a^{4} c^{2} d + 6 i \, a^{2} c d^{2} + 3 i \, d^{3}\right)} x^{2}\right)} {\rm Li}_2\left(\frac{a^{2} c - a d x + {\left(i \, a^{2} x + i \, a\right)} \sqrt{c} \sqrt{d}}{a^{2} c + 2 i \, a \sqrt{c} \sqrt{d} - d}\right) + {\left(-3 i \, a^{4} c^{3} - 6 i \, a^{2} c^{2} d - 3 i \, c d^{2} + {\left(-3 i \, a^{4} c^{2} d - 6 i \, a^{2} c d^{2} - 3 i \, d^{3}\right)} x^{2}\right)} {\rm Li}_2\left(\frac{a^{2} c + a d x + {\left(i \, a^{2} x - i \, a\right)} \sqrt{c} \sqrt{d}}{a^{2} c - 2 i \, a \sqrt{c} \sqrt{d} - d}\right) + {\left(-3 i \, a^{4} c^{3} - 6 i \, a^{2} c^{2} d - 3 i \, c d^{2} + {\left(-3 i \, a^{4} c^{2} d - 6 i \, a^{2} c d^{2} - 3 i \, d^{3}\right)} x^{2}\right)} {\rm Li}_2\left(\frac{a^{2} c - a d x - {\left(i \, a^{2} x + i \, a\right)} \sqrt{c} \sqrt{d}}{a^{2} c - 2 i \, a \sqrt{c} \sqrt{d} - d}\right) - 3 \, {\left({\left(a^{4} c^{3} + 2 \, a^{2} c^{2} d + c d^{2} + {\left(a^{4} c^{2} d + 2 \, a^{2} c d^{2} + d^{3}\right)} x^{2}\right)} \arctan\left(\frac{{\left(a^{2} x + a\right)} \sqrt{c} \sqrt{d}}{a^{2} c + d}, \frac{a d x + d}{a^{2} c + d}\right) - {\left(a^{4} c^{3} + 2 \, a^{2} c^{2} d + c d^{2} + {\left(a^{4} c^{2} d + 2 \, a^{2} c d^{2} + d^{3}\right)} x^{2}\right)} \arctan\left(\frac{{\left(a^{2} x - a\right)} \sqrt{c} \sqrt{d}}{a^{2} c + d}, -\frac{a d x - d}{a^{2} c + d}\right)\right)} \log\left(d x^{2} + c\right)\right)} \sqrt{c} \sqrt{d} - 2 \, {\left(5 \, a^{3} c^{3} d + 3 \, a c^{2} d^{2} + {\left(5 \, a^{3} c^{2} d^{2} + 3 \, a c d^{3}\right)} x^{2}\right)} \log\left(d x^{2} + c\right) + 2 \, {\left(5 \, a^{3} c^{3} d + 3 \, a c^{2} d^{2} + {\left(5 \, a^{3} c^{2} d^{2} + 3 \, a c d^{3}\right)} x^{2}\right)} \log\left(a x + 1\right) + 2 \, {\left(5 \, a^{3} c^{3} d + 3 \, a c^{2} d^{2} + {\left(5 \, a^{3} c^{2} d^{2} + 3 \, a c d^{3}\right)} x^{2}\right)} \log\left(a x - 1\right)\right)} a}{32 \, {\left(a^{5} c^{6} d + 2 \, a^{3} c^{5} d^{2} + a c^{4} d^{3} + {\left(a^{5} c^{5} d^{2} + 2 \, a^{3} c^{4} d^{3} + a c^{3} d^{4}\right)} x^{2}\right)}}"," ",0,"1/8*((3*d*x^3 + 5*c*x)/(c^2*d^2*x^4 + 2*c^3*d*x^2 + c^4) + 3*arctan(d*x/sqrt(c*d))/(sqrt(c*d)*c^2))*arccoth(a*x) + 1/32*(4*a^3*c^3*d + 4*a*c^2*d^2 - (3*(a^4*c^3 + 2*a^2*c^2*d + c*d^2 + (a^4*c^2*d + 2*a^2*c*d^2 + d^3)*x^2)*arctan(sqrt(d)*x/sqrt(c))*log((a^2*d*x^2 + 2*a*d*x + d)/(a^2*c + d)) - 3*(a^4*c^3 + 2*a^2*c^2*d + c*d^2 + (a^4*c^2*d + 2*a^2*c*d^2 + d^3)*x^2)*arctan(sqrt(d)*x/sqrt(c))*log((a^2*d*x^2 - 2*a*d*x + d)/(a^2*c + d)) + (3*I*a^4*c^3 + 6*I*a^2*c^2*d + 3*I*c*d^2 + (3*I*a^4*c^2*d + 6*I*a^2*c*d^2 + 3*I*d^3)*x^2)*dilog((a^2*c + a*d*x - (I*a^2*x - I*a)*sqrt(c)*sqrt(d))/(a^2*c + 2*I*a*sqrt(c)*sqrt(d) - d)) + (3*I*a^4*c^3 + 6*I*a^2*c^2*d + 3*I*c*d^2 + (3*I*a^4*c^2*d + 6*I*a^2*c*d^2 + 3*I*d^3)*x^2)*dilog((a^2*c - a*d*x + (I*a^2*x + I*a)*sqrt(c)*sqrt(d))/(a^2*c + 2*I*a*sqrt(c)*sqrt(d) - d)) + (-3*I*a^4*c^3 - 6*I*a^2*c^2*d - 3*I*c*d^2 + (-3*I*a^4*c^2*d - 6*I*a^2*c*d^2 - 3*I*d^3)*x^2)*dilog((a^2*c + a*d*x + (I*a^2*x - I*a)*sqrt(c)*sqrt(d))/(a^2*c - 2*I*a*sqrt(c)*sqrt(d) - d)) + (-3*I*a^4*c^3 - 6*I*a^2*c^2*d - 3*I*c*d^2 + (-3*I*a^4*c^2*d - 6*I*a^2*c*d^2 - 3*I*d^3)*x^2)*dilog((a^2*c - a*d*x - (I*a^2*x + I*a)*sqrt(c)*sqrt(d))/(a^2*c - 2*I*a*sqrt(c)*sqrt(d) - d)) - 3*((a^4*c^3 + 2*a^2*c^2*d + c*d^2 + (a^4*c^2*d + 2*a^2*c*d^2 + d^3)*x^2)*arctan2((a^2*x + a)*sqrt(c)*sqrt(d)/(a^2*c + d), (a*d*x + d)/(a^2*c + d)) - (a^4*c^3 + 2*a^2*c^2*d + c*d^2 + (a^4*c^2*d + 2*a^2*c*d^2 + d^3)*x^2)*arctan2((a^2*x - a)*sqrt(c)*sqrt(d)/(a^2*c + d), -(a*d*x - d)/(a^2*c + d)))*log(d*x^2 + c))*sqrt(c)*sqrt(d) - 2*(5*a^3*c^3*d + 3*a*c^2*d^2 + (5*a^3*c^2*d^2 + 3*a*c*d^3)*x^2)*log(d*x^2 + c) + 2*(5*a^3*c^3*d + 3*a*c^2*d^2 + (5*a^3*c^2*d^2 + 3*a*c*d^3)*x^2)*log(a*x + 1) + 2*(5*a^3*c^3*d + 3*a*c^2*d^2 + (5*a^3*c^2*d^2 + 3*a*c*d^3)*x^2)*log(a*x - 1))*a/(a^5*c^6*d + 2*a^3*c^5*d^2 + a*c^4*d^3 + (a^5*c^5*d^2 + 2*a^3*c^4*d^3 + a*c^3*d^4)*x^2)","B",0
42,0,0,0,0.000000," ","integrate((d*x^2+c)^(1/2)*arccoth(a*x),x, algorithm=""maxima"")","\int \sqrt{d x^{2} + c} \operatorname{arcoth}\left(a x\right)\,{d x}"," ",0,"integrate(sqrt(d*x^2 + c)*arccoth(a*x), x)","F",0
43,0,0,0,0.000000," ","integrate(arccoth(a*x)/(d*x^2+c)^(1/2),x, algorithm=""maxima"")","\int \frac{\operatorname{arcoth}\left(a x\right)}{\sqrt{d x^{2} + c}}\,{d x}"," ",0,"integrate(arccoth(a*x)/sqrt(d*x^2 + c), x)","F",0
44,1,153,0,0.340334," ","integrate(arccoth(a*x)/(d*x^2+c)^(3/2),x, algorithm=""maxima"")","\frac{a^{2} {\left(\frac{\operatorname{arsinh}\left(-\frac{2 \, a^{2} c}{\sqrt{c d} {\left| 2 \, a^{2} x + 2 \, a \right|}} + \frac{2 \, a d x}{\sqrt{c d} {\left| 2 \, a^{2} x + 2 \, a \right|}}\right)}{a^{3} \sqrt{c + \frac{d}{a^{2}}}} - \frac{\operatorname{arsinh}\left(\frac{2 \, a^{2} c}{\sqrt{c d} {\left| 2 \, a^{2} x - 2 \, a \right|}} + \frac{2 \, a d x}{\sqrt{c d} {\left| 2 \, a^{2} x - 2 \, a \right|}}\right)}{a^{3} \sqrt{c + \frac{d}{a^{2}}}}\right)}}{2 \, c} + \frac{x \operatorname{arcoth}\left(a x\right)}{\sqrt{d x^{2} + c} c}"," ",0,"1/2*a^2*(arcsinh(-2*a^2*c/(sqrt(c*d)*abs(2*a^2*x + 2*a)) + 2*a*d*x/(sqrt(c*d)*abs(2*a^2*x + 2*a)))/(a^3*sqrt(c + d/a^2)) - arcsinh(2*a^2*c/(sqrt(c*d)*abs(2*a^2*x - 2*a)) + 2*a*d*x/(sqrt(c*d)*abs(2*a^2*x - 2*a)))/(a^3*sqrt(c + d/a^2)))/c + x*arccoth(a*x)/(sqrt(d*x^2 + c)*c)","B",0
45,1,223,0,0.414762," ","integrate(arccoth(a*x)/(d*x^2+c)^(5/2),x, algorithm=""maxima"")","\frac{1}{6} \, a {\left(\frac{\frac{a d \log\left(\frac{\sqrt{d x^{2} + c} a^{2} - \sqrt{a^{2} c + d} a}{\sqrt{d x^{2} + c} a^{2} + \sqrt{a^{2} c + d} a}\right)}{{\left(a^{2} c^{2} + c d\right)} \sqrt{a^{2} c + d}} + \frac{2 \, d}{{\left(a^{2} c^{2} + c d\right)} \sqrt{d x^{2} + c}}}{d} + \frac{2 \, \log\left(\frac{\sqrt{d x^{2} + c} a^{2} - \sqrt{a^{2} c + d} a}{\sqrt{d x^{2} + c} a^{2} + \sqrt{a^{2} c + d} a}\right)}{\sqrt{a^{2} c + d} a c^{2}}\right)} + \frac{1}{3} \, {\left(\frac{2 \, x}{\sqrt{d x^{2} + c} c^{2}} + \frac{x}{{\left(d x^{2} + c\right)}^{\frac{3}{2}} c}\right)} \operatorname{arcoth}\left(a x\right)"," ",0,"1/6*a*((a*d*log((sqrt(d*x^2 + c)*a^2 - sqrt(a^2*c + d)*a)/(sqrt(d*x^2 + c)*a^2 + sqrt(a^2*c + d)*a))/((a^2*c^2 + c*d)*sqrt(a^2*c + d)) + 2*d/((a^2*c^2 + c*d)*sqrt(d*x^2 + c)))/d + 2*log((sqrt(d*x^2 + c)*a^2 - sqrt(a^2*c + d)*a)/(sqrt(d*x^2 + c)*a^2 + sqrt(a^2*c + d)*a))/(sqrt(a^2*c + d)*a*c^2)) + 1/3*(2*x/(sqrt(d*x^2 + c)*c^2) + x/((d*x^2 + c)^(3/2)*c))*arccoth(a*x)","B",0
46,1,401,0,0.422737," ","integrate(arccoth(a*x)/(d*x^2+c)^(7/2),x, algorithm=""maxima"")","\frac{1}{30} \, a {\left(\frac{\frac{3 \, a^{3} d \log\left(\frac{\sqrt{d x^{2} + c} a^{2} - \sqrt{a^{2} c + d} a}{\sqrt{d x^{2} + c} a^{2} + \sqrt{a^{2} c + d} a}\right)}{{\left(a^{4} c^{3} + 2 \, a^{2} c^{2} d + c d^{2}\right)} \sqrt{a^{2} c + d}} + \frac{2 \, {\left(3 \, {\left(d x^{2} + c\right)} a^{2} d + a^{2} c d + d^{2}\right)}}{{\left(a^{4} c^{3} + 2 \, a^{2} c^{2} d + c d^{2}\right)} {\left(d x^{2} + c\right)}^{\frac{3}{2}}}}{d} + \frac{4 \, {\left(\frac{a d \log\left(\frac{\sqrt{d x^{2} + c} a^{2} - \sqrt{a^{2} c + d} a}{\sqrt{d x^{2} + c} a^{2} + \sqrt{a^{2} c + d} a}\right)}{{\left(a^{2} c^{3} + c^{2} d\right)} \sqrt{a^{2} c + d}} + \frac{2 \, d}{{\left(a^{2} c^{3} + c^{2} d\right)} \sqrt{d x^{2} + c}}\right)}}{d} + \frac{8 \, \log\left(\frac{\sqrt{d x^{2} + c} a^{2} - \sqrt{a^{2} c + d} a}{\sqrt{d x^{2} + c} a^{2} + \sqrt{a^{2} c + d} a}\right)}{\sqrt{a^{2} c + d} a c^{3}}\right)} + \frac{1}{15} \, {\left(\frac{8 \, x}{\sqrt{d x^{2} + c} c^{3}} + \frac{4 \, x}{{\left(d x^{2} + c\right)}^{\frac{3}{2}} c^{2}} + \frac{3 \, x}{{\left(d x^{2} + c\right)}^{\frac{5}{2}} c}\right)} \operatorname{arcoth}\left(a x\right)"," ",0,"1/30*a*((3*a^3*d*log((sqrt(d*x^2 + c)*a^2 - sqrt(a^2*c + d)*a)/(sqrt(d*x^2 + c)*a^2 + sqrt(a^2*c + d)*a))/((a^4*c^3 + 2*a^2*c^2*d + c*d^2)*sqrt(a^2*c + d)) + 2*(3*(d*x^2 + c)*a^2*d + a^2*c*d + d^2)/((a^4*c^3 + 2*a^2*c^2*d + c*d^2)*(d*x^2 + c)^(3/2)))/d + 4*(a*d*log((sqrt(d*x^2 + c)*a^2 - sqrt(a^2*c + d)*a)/(sqrt(d*x^2 + c)*a^2 + sqrt(a^2*c + d)*a))/((a^2*c^3 + c^2*d)*sqrt(a^2*c + d)) + 2*d/((a^2*c^3 + c^2*d)*sqrt(d*x^2 + c)))/d + 8*log((sqrt(d*x^2 + c)*a^2 - sqrt(a^2*c + d)*a)/(sqrt(d*x^2 + c)*a^2 + sqrt(a^2*c + d)*a))/(sqrt(a^2*c + d)*a*c^3)) + 1/15*(8*x/(sqrt(d*x^2 + c)*c^3) + 4*x/((d*x^2 + c)^(3/2)*c^2) + 3*x/((d*x^2 + c)^(5/2)*c))*arccoth(a*x)","B",0
47,1,639,0,0.430620," ","integrate(arccoth(a*x)/(d*x^2+c)^(9/2),x, algorithm=""maxima"")","\frac{1}{210} \, a {\left(\frac{\frac{15 \, a^{5} d \log\left(\frac{\sqrt{d x^{2} + c} a^{2} - \sqrt{a^{2} c + d} a}{\sqrt{d x^{2} + c} a^{2} + \sqrt{a^{2} c + d} a}\right)}{{\left(a^{6} c^{4} + 3 \, a^{4} c^{3} d + 3 \, a^{2} c^{2} d^{2} + c d^{3}\right)} \sqrt{a^{2} c + d}} + \frac{2 \, {\left(15 \, {\left(d x^{2} + c\right)}^{2} a^{4} d + 3 \, a^{4} c^{2} d + 6 \, a^{2} c d^{2} + 3 \, d^{3} + 5 \, {\left(a^{4} c d + a^{2} d^{2}\right)} {\left(d x^{2} + c\right)}\right)}}{{\left(a^{6} c^{4} + 3 \, a^{4} c^{3} d + 3 \, a^{2} c^{2} d^{2} + c d^{3}\right)} {\left(d x^{2} + c\right)}^{\frac{5}{2}}}}{d} + \frac{6 \, {\left(\frac{3 \, a^{3} d \log\left(\frac{\sqrt{d x^{2} + c} a^{2} - \sqrt{a^{2} c + d} a}{\sqrt{d x^{2} + c} a^{2} + \sqrt{a^{2} c + d} a}\right)}{{\left(a^{4} c^{4} + 2 \, a^{2} c^{3} d + c^{2} d^{2}\right)} \sqrt{a^{2} c + d}} + \frac{2 \, {\left(3 \, {\left(d x^{2} + c\right)} a^{2} d + a^{2} c d + d^{2}\right)}}{{\left(a^{4} c^{4} + 2 \, a^{2} c^{3} d + c^{2} d^{2}\right)} {\left(d x^{2} + c\right)}^{\frac{3}{2}}}\right)}}{d} + \frac{24 \, {\left(\frac{a d \log\left(\frac{\sqrt{d x^{2} + c} a^{2} - \sqrt{a^{2} c + d} a}{\sqrt{d x^{2} + c} a^{2} + \sqrt{a^{2} c + d} a}\right)}{{\left(a^{2} c^{4} + c^{3} d\right)} \sqrt{a^{2} c + d}} + \frac{2 \, d}{{\left(a^{2} c^{4} + c^{3} d\right)} \sqrt{d x^{2} + c}}\right)}}{d} + \frac{48 \, \log\left(\frac{\sqrt{d x^{2} + c} a^{2} - \sqrt{a^{2} c + d} a}{\sqrt{d x^{2} + c} a^{2} + \sqrt{a^{2} c + d} a}\right)}{\sqrt{a^{2} c + d} a c^{4}}\right)} + \frac{1}{35} \, {\left(\frac{16 \, x}{\sqrt{d x^{2} + c} c^{4}} + \frac{8 \, x}{{\left(d x^{2} + c\right)}^{\frac{3}{2}} c^{3}} + \frac{6 \, x}{{\left(d x^{2} + c\right)}^{\frac{5}{2}} c^{2}} + \frac{5 \, x}{{\left(d x^{2} + c\right)}^{\frac{7}{2}} c}\right)} \operatorname{arcoth}\left(a x\right)"," ",0,"1/210*a*((15*a^5*d*log((sqrt(d*x^2 + c)*a^2 - sqrt(a^2*c + d)*a)/(sqrt(d*x^2 + c)*a^2 + sqrt(a^2*c + d)*a))/((a^6*c^4 + 3*a^4*c^3*d + 3*a^2*c^2*d^2 + c*d^3)*sqrt(a^2*c + d)) + 2*(15*(d*x^2 + c)^2*a^4*d + 3*a^4*c^2*d + 6*a^2*c*d^2 + 3*d^3 + 5*(a^4*c*d + a^2*d^2)*(d*x^2 + c))/((a^6*c^4 + 3*a^4*c^3*d + 3*a^2*c^2*d^2 + c*d^3)*(d*x^2 + c)^(5/2)))/d + 6*(3*a^3*d*log((sqrt(d*x^2 + c)*a^2 - sqrt(a^2*c + d)*a)/(sqrt(d*x^2 + c)*a^2 + sqrt(a^2*c + d)*a))/((a^4*c^4 + 2*a^2*c^3*d + c^2*d^2)*sqrt(a^2*c + d)) + 2*(3*(d*x^2 + c)*a^2*d + a^2*c*d + d^2)/((a^4*c^4 + 2*a^2*c^3*d + c^2*d^2)*(d*x^2 + c)^(3/2)))/d + 24*(a*d*log((sqrt(d*x^2 + c)*a^2 - sqrt(a^2*c + d)*a)/(sqrt(d*x^2 + c)*a^2 + sqrt(a^2*c + d)*a))/((a^2*c^4 + c^3*d)*sqrt(a^2*c + d)) + 2*d/((a^2*c^4 + c^3*d)*sqrt(d*x^2 + c)))/d + 48*log((sqrt(d*x^2 + c)*a^2 - sqrt(a^2*c + d)*a)/(sqrt(d*x^2 + c)*a^2 + sqrt(a^2*c + d)*a))/(sqrt(a^2*c + d)*a*c^4)) + 1/35*(16*x/(sqrt(d*x^2 + c)*c^4) + 8*x/((d*x^2 + c)^(3/2)*c^3) + 6*x/((d*x^2 + c)^(5/2)*c^2) + 5*x/((d*x^2 + c)^(7/2)*c))*arccoth(a*x)","B",0
48,0,0,0,0.000000," ","integrate((-a*x^2+a)^(1/2)*arccoth(x),x, algorithm=""maxima"")","\int \sqrt{-a x^{2} + a} \operatorname{arcoth}\left(x\right)\,{d x}"," ",0,"integrate(sqrt(-a*x^2 + a)*arccoth(x), x)","F",0
49,0,0,0,0.000000," ","integrate(arccoth(x)/(-a*x^2+a)^(1/2),x, algorithm=""maxima"")","\int \frac{\operatorname{arcoth}\left(x\right)}{\sqrt{-a x^{2} + a}}\,{d x}"," ",0,"integrate(arccoth(x)/sqrt(-a*x^2 + a), x)","F",0
50,1,63,0,0.407570," ","integrate(arccoth(x)/(-a*x^2+a)^(3/2),x, algorithm=""maxima"")","\frac{x \operatorname{arcoth}\left(x\right)}{\sqrt{-a x^{2} + a} a} - \frac{\frac{\sqrt{-a x^{2} + a}}{a x + a} - \frac{\sqrt{-a x^{2} + a}}{a x - a}}{2 \, a}"," ",0,"x*arccoth(x)/(sqrt(-a*x^2 + a)*a) - 1/2*(sqrt(-a*x^2 + a)/(a*x + a) - sqrt(-a*x^2 + a)/(a*x - a))/a","A",0
51,1,67,0,0.318806," ","integrate(arccoth(x)/(-a*x^2+a)^(5/2),x, algorithm=""maxima"")","\frac{1}{3} \, {\left(\frac{2 \, x}{\sqrt{-a x^{2} + a} a^{2}} + \frac{x}{{\left(-a x^{2} + a\right)}^{\frac{3}{2}} a}\right)} \operatorname{arcoth}\left(x\right) - \frac{2}{3 \, \sqrt{-a x^{2} + a} a^{2}} - \frac{1}{9 \, {\left(-a x^{2} + a\right)}^{\frac{3}{2}} a}"," ",0,"1/3*(2*x/(sqrt(-a*x^2 + a)*a^2) + x/((-a*x^2 + a)^(3/2)*a))*arccoth(x) - 2/3/(sqrt(-a*x^2 + a)*a^2) - 1/9/((-a*x^2 + a)^(3/2)*a)","A",0
52,1,99,0,0.323021," ","integrate(arccoth(x)/(-a*x^2+a)^(7/2),x, algorithm=""maxima"")","\frac{1}{15} \, {\left(\frac{8 \, x}{\sqrt{-a x^{2} + a} a^{3}} + \frac{4 \, x}{{\left(-a x^{2} + a\right)}^{\frac{3}{2}} a^{2}} + \frac{3 \, x}{{\left(-a x^{2} + a\right)}^{\frac{5}{2}} a}\right)} \operatorname{arcoth}\left(x\right) - \frac{8}{15 \, \sqrt{-a x^{2} + a} a^{3}} - \frac{4}{45 \, {\left(-a x^{2} + a\right)}^{\frac{3}{2}} a^{2}} - \frac{1}{25 \, {\left(-a x^{2} + a\right)}^{\frac{5}{2}} a}"," ",0,"1/15*(8*x/(sqrt(-a*x^2 + a)*a^3) + 4*x/((-a*x^2 + a)^(3/2)*a^2) + 3*x/((-a*x^2 + a)^(5/2)*a))*arccoth(x) - 8/15/(sqrt(-a*x^2 + a)*a^3) - 4/45/((-a*x^2 + a)^(3/2)*a^2) - 1/25/((-a*x^2 + a)^(5/2)*a)","A",0
53,1,3,0,0.303519," ","integrate(1/(-x^2+1)/arccoth(x),x, algorithm=""maxima"")","\log\left(\operatorname{arcoth}\left(x\right)\right)"," ",0,"log(arccoth(x))","A",0
54,1,12,0,0.303282," ","integrate(arccoth(x)^n/(-x^2+1),x, algorithm=""maxima"")","\frac{\operatorname{arcoth}\left(x\right)^{n + 1}}{n + 1}"," ",0,"arccoth(x)^(n + 1)/(n + 1)","A",0
55,1,171,0,0.308832," ","integrate(arccoth(x)^2/(-x^2+1)^2,x, algorithm=""maxima"")","-\frac{1}{4} \, {\left(\frac{2 \, x}{x^{2} - 1} - \log\left(x + 1\right) + \log\left(x - 1\right)\right)} \operatorname{arcoth}\left(x\right)^{2} - \frac{{\left({\left(x^{2} - 1\right)} \log\left(x + 1\right)^{2} - 2 \, {\left(x^{2} - 1\right)} \log\left(x + 1\right) \log\left(x - 1\right) + {\left(x^{2} - 1\right)} \log\left(x - 1\right)^{2} - 4\right)} \operatorname{arcoth}\left(x\right)}{8 \, {\left(x^{2} - 1\right)}} + \frac{{\left(x^{2} - 1\right)} \log\left(x + 1\right)^{3} - 3 \, {\left(x^{2} - 1\right)} \log\left(x + 1\right)^{2} \log\left(x - 1\right) - {\left(x^{2} - 1\right)} \log\left(x - 1\right)^{3} + 3 \, {\left({\left(x^{2} - 1\right)} \log\left(x - 1\right)^{2} + 2 \, x^{2} - 2\right)} \log\left(x + 1\right) - 6 \, {\left(x^{2} - 1\right)} \log\left(x - 1\right) - 12 \, x}{48 \, {\left(x^{2} - 1\right)}}"," ",0,"-1/4*(2*x/(x^2 - 1) - log(x + 1) + log(x - 1))*arccoth(x)^2 - 1/8*((x^2 - 1)*log(x + 1)^2 - 2*(x^2 - 1)*log(x + 1)*log(x - 1) + (x^2 - 1)*log(x - 1)^2 - 4)*arccoth(x)/(x^2 - 1) + 1/48*((x^2 - 1)*log(x + 1)^3 - 3*(x^2 - 1)*log(x + 1)^2*log(x - 1) - (x^2 - 1)*log(x - 1)^3 + 3*((x^2 - 1)*log(x - 1)^2 + 2*x^2 - 2)*log(x + 1) - 6*(x^2 - 1)*log(x - 1) - 12*x)/(x^2 - 1)","B",0
56,1,76,0,0.303730," ","integrate(x*arccoth(x)/(-x^2+1),x, algorithm=""maxima"")","\frac{1}{4} \, {\left(\log\left(x + 1\right) - \log\left(x - 1\right)\right)} \log\left(x^{2} - 1\right) - \frac{1}{2} \, \operatorname{arcoth}\left(x\right) \log\left(x^{2} - 1\right) - \frac{1}{8} \, \log\left(x + 1\right)^{2} - \frac{1}{4} \, \log\left(x + 1\right) \log\left(x - 1\right) + \frac{1}{8} \, \log\left(x - 1\right)^{2} + \frac{1}{2} \, \log\left(x - 1\right) \log\left(\frac{1}{2} \, x + \frac{1}{2}\right) + \frac{1}{2} \, {\rm Li}_2\left(-\frac{1}{2} \, x + \frac{1}{2}\right)"," ",0,"1/4*(log(x + 1) - log(x - 1))*log(x^2 - 1) - 1/2*arccoth(x)*log(x^2 - 1) - 1/8*log(x + 1)^2 - 1/4*log(x + 1)*log(x - 1) + 1/8*log(x - 1)^2 + 1/2*log(x - 1)*log(1/2*x + 1/2) + 1/2*dilog(-1/2*x + 1/2)","B",0
57,1,6,0,0.298123," ","integrate(arccoth(x)/(-x^2+1),x, algorithm=""maxima"")","\frac{1}{2} \, \operatorname{arcoth}\left(x\right)^{2}"," ",0,"1/2*arccoth(x)^2","A",0
58,1,34,0,0.297581," ","integrate(x*arccoth(x)/(-x^2+1)^2,x, algorithm=""maxima"")","\frac{x}{4 \, {\left(x^{2} - 1\right)}} - \frac{\operatorname{arcoth}\left(x\right)}{2 \, {\left(x^{2} - 1\right)}} - \frac{1}{8} \, \log\left(x + 1\right) + \frac{1}{8} \, \log\left(x - 1\right)"," ",0,"1/4*x/(x^2 - 1) - 1/2*arccoth(x)/(x^2 - 1) - 1/8*log(x + 1) + 1/8*log(x - 1)","A",0
59,1,76,0,0.302942," ","integrate(arccoth(x)/(-x^2+1)^2,x, algorithm=""maxima"")","-\frac{1}{4} \, {\left(\frac{2 \, x}{x^{2} - 1} - \log\left(x + 1\right) + \log\left(x - 1\right)\right)} \operatorname{arcoth}\left(x\right) - \frac{{\left(x^{2} - 1\right)} \log\left(x + 1\right)^{2} - 2 \, {\left(x^{2} - 1\right)} \log\left(x + 1\right) \log\left(x - 1\right) + {\left(x^{2} - 1\right)} \log\left(x - 1\right)^{2} - 4}{16 \, {\left(x^{2} - 1\right)}}"," ",0,"-1/4*(2*x/(x^2 - 1) - log(x + 1) + log(x - 1))*arccoth(x) - 1/16*((x^2 - 1)*log(x + 1)^2 - 2*(x^2 - 1)*log(x + 1)*log(x - 1) + (x^2 - 1)*log(x - 1)^2 - 4)/(x^2 - 1)","B",0
60,1,47,0,0.302423," ","integrate(x*arccoth(x)/(-x^2+1)^3,x, algorithm=""maxima"")","\frac{3 \, x^{3} - 5 \, x}{32 \, {\left(x^{4} - 2 \, x^{2} + 1\right)}} + \frac{\operatorname{arcoth}\left(x\right)}{4 \, {\left(x^{2} - 1\right)}^{2}} - \frac{3}{64} \, \log\left(x + 1\right) + \frac{3}{64} \, \log\left(x - 1\right)"," ",0,"1/32*(3*x^3 - 5*x)/(x^4 - 2*x^2 + 1) + 1/4*arccoth(x)/(x^2 - 1)^2 - 3/64*log(x + 1) + 3/64*log(x - 1)","A",0
61,1,118,0,0.306659," ","integrate(arccoth(x)/(-x^2+1)^3,x, algorithm=""maxima"")","-\frac{1}{16} \, {\left(\frac{2 \, {\left(3 \, x^{3} - 5 \, x\right)}}{x^{4} - 2 \, x^{2} + 1} - 3 \, \log\left(x + 1\right) + 3 \, \log\left(x - 1\right)\right)} \operatorname{arcoth}\left(x\right) - \frac{3 \, {\left(x^{4} - 2 \, x^{2} + 1\right)} \log\left(x + 1\right)^{2} - 6 \, {\left(x^{4} - 2 \, x^{2} + 1\right)} \log\left(x + 1\right) \log\left(x - 1\right) + 3 \, {\left(x^{4} - 2 \, x^{2} + 1\right)} \log\left(x - 1\right)^{2} - 12 \, x^{2} + 16}{64 \, {\left(x^{4} - 2 \, x^{2} + 1\right)}}"," ",0,"-1/16*(2*(3*x^3 - 5*x)/(x^4 - 2*x^2 + 1) - 3*log(x + 1) + 3*log(x - 1))*arccoth(x) - 1/64*(3*(x^4 - 2*x^2 + 1)*log(x + 1)^2 - 6*(x^4 - 2*x^2 + 1)*log(x + 1)*log(x - 1) + 3*(x^4 - 2*x^2 + 1)*log(x - 1)^2 - 12*x^2 + 16)/(x^4 - 2*x^2 + 1)","B",0
62,1,106,0,0.306082," ","integrate(x^3*arccoth(b*x+a),x, algorithm=""maxima"")","\frac{1}{4} \, x^{4} \operatorname{arcoth}\left(b x + a\right) + \frac{1}{24} \, b {\left(\frac{2 \, {\left(b^{2} x^{3} - 3 \, a b x^{2} + 3 \, {\left(3 \, a^{2} + 1\right)} x\right)}}{b^{4}} - \frac{3 \, {\left(a^{4} + 4 \, a^{3} + 6 \, a^{2} + 4 \, a + 1\right)} \log\left(b x + a + 1\right)}{b^{5}} + \frac{3 \, {\left(a^{4} - 4 \, a^{3} + 6 \, a^{2} - 4 \, a + 1\right)} \log\left(b x + a - 1\right)}{b^{5}}\right)}"," ",0,"1/4*x^4*arccoth(b*x + a) + 1/24*b*(2*(b^2*x^3 - 3*a*b*x^2 + 3*(3*a^2 + 1)*x)/b^4 - 3*(a^4 + 4*a^3 + 6*a^2 + 4*a + 1)*log(b*x + a + 1)/b^5 + 3*(a^4 - 4*a^3 + 6*a^2 - 4*a + 1)*log(b*x + a - 1)/b^5)","A",0
63,1,79,0,0.306615," ","integrate(x^2*arccoth(b*x+a),x, algorithm=""maxima"")","\frac{1}{3} \, x^{3} \operatorname{arcoth}\left(b x + a\right) + \frac{1}{6} \, b {\left(\frac{b x^{2} - 4 \, a x}{b^{3}} + \frac{{\left(a^{3} + 3 \, a^{2} + 3 \, a + 1\right)} \log\left(b x + a + 1\right)}{b^{4}} - \frac{{\left(a^{3} - 3 \, a^{2} + 3 \, a - 1\right)} \log\left(b x + a - 1\right)}{b^{4}}\right)}"," ",0,"1/3*x^3*arccoth(b*x + a) + 1/6*b*((b*x^2 - 4*a*x)/b^3 + (a^3 + 3*a^2 + 3*a + 1)*log(b*x + a + 1)/b^4 - (a^3 - 3*a^2 + 3*a - 1)*log(b*x + a - 1)/b^4)","A",0
64,1,61,0,0.302920," ","integrate(x*arccoth(b*x+a),x, algorithm=""maxima"")","\frac{1}{2} \, x^{2} \operatorname{arcoth}\left(b x + a\right) + \frac{1}{4} \, b {\left(\frac{2 \, x}{b^{2}} - \frac{{\left(a^{2} + 2 \, a + 1\right)} \log\left(b x + a + 1\right)}{b^{3}} + \frac{{\left(a^{2} - 2 \, a + 1\right)} \log\left(b x + a - 1\right)}{b^{3}}\right)}"," ",0,"1/2*x^2*arccoth(b*x + a) + 1/4*b*(2*x/b^2 - (a^2 + 2*a + 1)*log(b*x + a + 1)/b^3 + (a^2 - 2*a + 1)*log(b*x + a - 1)/b^3)","A",0
65,1,31,0,0.310011," ","integrate(arccoth(b*x+a),x, algorithm=""maxima"")","\frac{2 \, {\left(b x + a\right)} \operatorname{arcoth}\left(b x + a\right) + \log\left(-{\left(b x + a\right)}^{2} + 1\right)}{2 \, b}"," ",0,"1/2*(2*(b*x + a)*arccoth(b*x + a) + log(-(b*x + a)^2 + 1))/b","A",0
66,1,128,0,0.309359," ","integrate(arccoth(b*x+a)/x,x, algorithm=""maxima"")","-\frac{1}{2} \, b {\left(\frac{\log\left(b x + a + 1\right)}{b} - \frac{\log\left(b x + a - 1\right)}{b}\right)} \log\left(x\right) + \frac{1}{2} \, b {\left(\frac{\log\left(b x + a + 1\right) \log\left(-\frac{b x + a + 1}{a + 1} + 1\right) + {\rm Li}_2\left(\frac{b x + a + 1}{a + 1}\right)}{b} - \frac{\log\left(b x + a - 1\right) \log\left(-\frac{b x + a - 1}{a - 1} + 1\right) + {\rm Li}_2\left(\frac{b x + a - 1}{a - 1}\right)}{b}\right)} + \operatorname{arcoth}\left(b x + a\right) \log\left(x\right)"," ",0,"-1/2*b*(log(b*x + a + 1)/b - log(b*x + a - 1)/b)*log(x) + 1/2*b*((log(b*x + a + 1)*log(-(b*x + a + 1)/(a + 1) + 1) + dilog((b*x + a + 1)/(a + 1)))/b - (log(b*x + a - 1)*log(-(b*x + a - 1)/(a - 1) + 1) + dilog((b*x + a - 1)/(a - 1)))/b) + arccoth(b*x + a)*log(x)","A",0
67,1,54,0,0.313843," ","integrate(arccoth(b*x+a)/x^2,x, algorithm=""maxima"")","-\frac{1}{2} \, b {\left(\frac{\log\left(b x + a + 1\right)}{a + 1} - \frac{\log\left(b x + a - 1\right)}{a - 1} + \frac{2 \, \log\left(x\right)}{a^{2} - 1}\right)} - \frac{\operatorname{arcoth}\left(b x + a\right)}{x}"," ",0,"-1/2*b*(log(b*x + a + 1)/(a + 1) - log(b*x + a - 1)/(a - 1) + 2*log(x)/(a^2 - 1)) - arccoth(b*x + a)/x","A",0
68,1,85,0,0.304652," ","integrate(arccoth(b*x+a)/x^3,x, algorithm=""maxima"")","\frac{1}{4} \, {\left(\frac{4 \, a b \log\left(x\right)}{a^{4} - 2 \, a^{2} + 1} + \frac{b \log\left(b x + a + 1\right)}{a^{2} + 2 \, a + 1} - \frac{b \log\left(b x + a - 1\right)}{a^{2} - 2 \, a + 1} + \frac{2}{{\left(a^{2} - 1\right)} x}\right)} b - \frac{\operatorname{arcoth}\left(b x + a\right)}{2 \, x^{2}}"," ",0,"1/4*(4*a*b*log(x)/(a^4 - 2*a^2 + 1) + b*log(b*x + a + 1)/(a^2 + 2*a + 1) - b*log(b*x + a - 1)/(a^2 - 2*a + 1) + 2/((a^2 - 1)*x))*b - 1/2*arccoth(b*x + a)/x^2","A",0
69,1,320,0,0.341252," ","integrate(x^3*arccoth(b*x+a)^2,x, algorithm=""maxima"")","\frac{1}{4} \, x^{4} \operatorname{arcoth}\left(b x + a\right)^{2} + \frac{1}{48} \, b^{2} {\left(\frac{48 \, {\left(a^{3} + a\right)} {\left(\log\left(b x + a - 1\right) \log\left(\frac{1}{2} \, b x + \frac{1}{2} \, a + \frac{1}{2}\right) + {\rm Li}_2\left(-\frac{1}{2} \, b x - \frac{1}{2} \, a + \frac{1}{2}\right)\right)}}{b^{6}} + \frac{4 \, {\left(13 \, a^{3} + 18 \, a^{2} + 9 \, a + 4\right)} \log\left(b x + a + 1\right)}{b^{6}} + \frac{4 \, b^{2} x^{2} - 40 \, a b x + 3 \, {\left(a^{4} + 4 \, a^{3} + 6 \, a^{2} + 4 \, a + 1\right)} \log\left(b x + a + 1\right)^{2} - 6 \, {\left(a^{4} + 4 \, a^{3} + 6 \, a^{2} + 4 \, a + 1\right)} \log\left(b x + a + 1\right) \log\left(b x + a - 1\right) + 3 \, {\left(a^{4} - 4 \, a^{3} + 6 \, a^{2} - 4 \, a + 1\right)} \log\left(b x + a - 1\right)^{2} - 4 \, {\left(13 \, a^{3} - 18 \, a^{2} + 9 \, a - 4\right)} \log\left(b x + a - 1\right)}{b^{6}}\right)} + \frac{1}{12} \, b {\left(\frac{2 \, {\left(b^{2} x^{3} - 3 \, a b x^{2} + 3 \, {\left(3 \, a^{2} + 1\right)} x\right)}}{b^{4}} - \frac{3 \, {\left(a^{4} + 4 \, a^{3} + 6 \, a^{2} + 4 \, a + 1\right)} \log\left(b x + a + 1\right)}{b^{5}} + \frac{3 \, {\left(a^{4} - 4 \, a^{3} + 6 \, a^{2} - 4 \, a + 1\right)} \log\left(b x + a - 1\right)}{b^{5}}\right)} \operatorname{arcoth}\left(b x + a\right)"," ",0,"1/4*x^4*arccoth(b*x + a)^2 + 1/48*b^2*(48*(a^3 + a)*(log(b*x + a - 1)*log(1/2*b*x + 1/2*a + 1/2) + dilog(-1/2*b*x - 1/2*a + 1/2))/b^6 + 4*(13*a^3 + 18*a^2 + 9*a + 4)*log(b*x + a + 1)/b^6 + (4*b^2*x^2 - 40*a*b*x + 3*(a^4 + 4*a^3 + 6*a^2 + 4*a + 1)*log(b*x + a + 1)^2 - 6*(a^4 + 4*a^3 + 6*a^2 + 4*a + 1)*log(b*x + a + 1)*log(b*x + a - 1) + 3*(a^4 - 4*a^3 + 6*a^2 - 4*a + 1)*log(b*x + a - 1)^2 - 4*(13*a^3 - 18*a^2 + 9*a - 4)*log(b*x + a - 1))/b^6) + 1/12*b*(2*(b^2*x^3 - 3*a*b*x^2 + 3*(3*a^2 + 1)*x)/b^4 - 3*(a^4 + 4*a^3 + 6*a^2 + 4*a + 1)*log(b*x + a + 1)/b^5 + 3*(a^4 - 4*a^3 + 6*a^2 - 4*a + 1)*log(b*x + a - 1)/b^5)*arccoth(b*x + a)","A",0
70,1,259,0,0.333225," ","integrate(x^2*arccoth(b*x+a)^2,x, algorithm=""maxima"")","\frac{1}{3} \, x^{3} \operatorname{arcoth}\left(b x + a\right)^{2} - \frac{1}{12} \, b^{2} {\left(\frac{4 \, {\left(3 \, a^{2} + 1\right)} {\left(\log\left(b x + a - 1\right) \log\left(\frac{1}{2} \, b x + \frac{1}{2} \, a + \frac{1}{2}\right) + {\rm Li}_2\left(-\frac{1}{2} \, b x - \frac{1}{2} \, a + \frac{1}{2}\right)\right)}}{b^{5}} + \frac{2 \, {\left(5 \, a^{2} + 6 \, a + 1\right)} \log\left(b x + a + 1\right)}{b^{5}} + \frac{{\left(a^{3} + 3 \, a^{2} + 3 \, a + 1\right)} \log\left(b x + a + 1\right)^{2} - 2 \, {\left(a^{3} + 3 \, a^{2} + 3 \, a + 1\right)} \log\left(b x + a + 1\right) \log\left(b x + a - 1\right) + {\left(a^{3} - 3 \, a^{2} + 3 \, a - 1\right)} \log\left(b x + a - 1\right)^{2} - 4 \, b x - 2 \, {\left(5 \, a^{2} - 6 \, a + 1\right)} \log\left(b x + a - 1\right)}{b^{5}}\right)} + \frac{1}{3} \, b {\left(\frac{b x^{2} - 4 \, a x}{b^{3}} + \frac{{\left(a^{3} + 3 \, a^{2} + 3 \, a + 1\right)} \log\left(b x + a + 1\right)}{b^{4}} - \frac{{\left(a^{3} - 3 \, a^{2} + 3 \, a - 1\right)} \log\left(b x + a - 1\right)}{b^{4}}\right)} \operatorname{arcoth}\left(b x + a\right)"," ",0,"1/3*x^3*arccoth(b*x + a)^2 - 1/12*b^2*(4*(3*a^2 + 1)*(log(b*x + a - 1)*log(1/2*b*x + 1/2*a + 1/2) + dilog(-1/2*b*x - 1/2*a + 1/2))/b^5 + 2*(5*a^2 + 6*a + 1)*log(b*x + a + 1)/b^5 + ((a^3 + 3*a^2 + 3*a + 1)*log(b*x + a + 1)^2 - 2*(a^3 + 3*a^2 + 3*a + 1)*log(b*x + a + 1)*log(b*x + a - 1) + (a^3 - 3*a^2 + 3*a - 1)*log(b*x + a - 1)^2 - 4*b*x - 2*(5*a^2 - 6*a + 1)*log(b*x + a - 1))/b^5) + 1/3*b*((b*x^2 - 4*a*x)/b^3 + (a^3 + 3*a^2 + 3*a + 1)*log(b*x + a + 1)/b^4 - (a^3 - 3*a^2 + 3*a - 1)*log(b*x + a - 1)/b^4)*arccoth(b*x + a)","A",0
71,1,202,0,0.335729," ","integrate(x*arccoth(b*x+a)^2,x, algorithm=""maxima"")","\frac{1}{2} \, x^{2} \operatorname{arcoth}\left(b x + a\right)^{2} + \frac{1}{8} \, b^{2} {\left(\frac{8 \, {\left(\log\left(b x + a - 1\right) \log\left(\frac{1}{2} \, b x + \frac{1}{2} \, a + \frac{1}{2}\right) + {\rm Li}_2\left(-\frac{1}{2} \, b x - \frac{1}{2} \, a + \frac{1}{2}\right)\right)} a}{b^{4}} + \frac{4 \, {\left(a + 1\right)} \log\left(b x + a + 1\right)}{b^{4}} + \frac{{\left(a^{2} + 2 \, a + 1\right)} \log\left(b x + a + 1\right)^{2} - 2 \, {\left(a^{2} + 2 \, a + 1\right)} \log\left(b x + a + 1\right) \log\left(b x + a - 1\right) + {\left(a^{2} - 2 \, a + 1\right)} \log\left(b x + a - 1\right)^{2} - 4 \, {\left(a - 1\right)} \log\left(b x + a - 1\right)}{b^{4}}\right)} + \frac{1}{2} \, b {\left(\frac{2 \, x}{b^{2}} - \frac{{\left(a^{2} + 2 \, a + 1\right)} \log\left(b x + a + 1\right)}{b^{3}} + \frac{{\left(a^{2} - 2 \, a + 1\right)} \log\left(b x + a - 1\right)}{b^{3}}\right)} \operatorname{arcoth}\left(b x + a\right)"," ",0,"1/2*x^2*arccoth(b*x + a)^2 + 1/8*b^2*(8*(log(b*x + a - 1)*log(1/2*b*x + 1/2*a + 1/2) + dilog(-1/2*b*x - 1/2*a + 1/2))*a/b^4 + 4*(a + 1)*log(b*x + a + 1)/b^4 + ((a^2 + 2*a + 1)*log(b*x + a + 1)^2 - 2*(a^2 + 2*a + 1)*log(b*x + a + 1)*log(b*x + a - 1) + (a^2 - 2*a + 1)*log(b*x + a - 1)^2 - 4*(a - 1)*log(b*x + a - 1))/b^4) + 1/2*b*(2*x/b^2 - (a^2 + 2*a + 1)*log(b*x + a + 1)/b^3 + (a^2 - 2*a + 1)*log(b*x + a - 1)/b^3)*arccoth(b*x + a)","A",0
72,1,139,0,0.329602," ","integrate(arccoth(b*x+a)^2,x, algorithm=""maxima"")","-\frac{1}{4} \, b^{2} {\left(\frac{{\left(a + 1\right)} \log\left(b x + a + 1\right)^{2} - 2 \, {\left(a + 1\right)} \log\left(b x + a + 1\right) \log\left(b x + a - 1\right) + {\left(a - 1\right)} \log\left(b x + a - 1\right)^{2}}{b^{3}} + \frac{4 \, {\left(\log\left(b x + a - 1\right) \log\left(\frac{1}{2} \, b x + \frac{1}{2} \, a + \frac{1}{2}\right) + {\rm Li}_2\left(-\frac{1}{2} \, b x - \frac{1}{2} \, a + \frac{1}{2}\right)\right)}}{b^{3}}\right)} + b {\left(\frac{{\left(a + 1\right)} \log\left(b x + a + 1\right)}{b^{2}} - \frac{{\left(a - 1\right)} \log\left(b x + a - 1\right)}{b^{2}}\right)} \operatorname{arcoth}\left(b x + a\right) + x \operatorname{arcoth}\left(b x + a\right)^{2}"," ",0,"-1/4*b^2*(((a + 1)*log(b*x + a + 1)^2 - 2*(a + 1)*log(b*x + a + 1)*log(b*x + a - 1) + (a - 1)*log(b*x + a - 1)^2)/b^3 + 4*(log(b*x + a - 1)*log(1/2*b*x + 1/2*a + 1/2) + dilog(-1/2*b*x - 1/2*a + 1/2))/b^3) + b*((a + 1)*log(b*x + a + 1)/b^2 - (a - 1)*log(b*x + a - 1)/b^2)*arccoth(b*x + a) + x*arccoth(b*x + a)^2","A",0
73,0,0,0,0.000000," ","integrate(arccoth(b*x+a)^2/x,x, algorithm=""maxima"")","\int \frac{\operatorname{arcoth}\left(b x + a\right)^{2}}{x}\,{d x}"," ",0,"integrate(arccoth(b*x + a)^2/x, x)","F",0
74,1,244,0,0.322064," ","integrate(arccoth(b*x+a)^2/x^2,x, algorithm=""maxima"")","\frac{1}{4} \, b^{2} {\left(\frac{{\left(a - 1\right)} \log\left(b x + a + 1\right)^{2} - 2 \, {\left(a - 1\right)} \log\left(b x + a + 1\right) \log\left(b x + a - 1\right) + {\left(a + 1\right)} \log\left(b x + a - 1\right)^{2}}{a^{2} b - b} - \frac{4 \, {\left(\log\left(b x + a - 1\right) \log\left(\frac{1}{2} \, b x + \frac{1}{2} \, a + \frac{1}{2}\right) + {\rm Li}_2\left(-\frac{1}{2} \, b x - \frac{1}{2} \, a + \frac{1}{2}\right)\right)}}{a^{2} b - b} + \frac{4 \, {\left(\log\left(\frac{b x}{a + 1} + 1\right) \log\left(x\right) + {\rm Li}_2\left(-\frac{b x}{a + 1}\right)\right)}}{a^{2} b - b} - \frac{4 \, {\left(\log\left(\frac{b x}{a - 1} + 1\right) \log\left(x\right) + {\rm Li}_2\left(-\frac{b x}{a - 1}\right)\right)}}{a^{2} b - b}\right)} - b {\left(\frac{\log\left(b x + a + 1\right)}{a + 1} - \frac{\log\left(b x + a - 1\right)}{a - 1} + \frac{2 \, \log\left(x\right)}{a^{2} - 1}\right)} \operatorname{arcoth}\left(b x + a\right) - \frac{\operatorname{arcoth}\left(b x + a\right)^{2}}{x}"," ",0,"1/4*b^2*(((a - 1)*log(b*x + a + 1)^2 - 2*(a - 1)*log(b*x + a + 1)*log(b*x + a - 1) + (a + 1)*log(b*x + a - 1)^2)/(a^2*b - b) - 4*(log(b*x + a - 1)*log(1/2*b*x + 1/2*a + 1/2) + dilog(-1/2*b*x - 1/2*a + 1/2))/(a^2*b - b) + 4*(log(b*x/(a + 1) + 1)*log(x) + dilog(-b*x/(a + 1)))/(a^2*b - b) - 4*(log(b*x/(a - 1) + 1)*log(x) + dilog(-b*x/(a - 1)))/(a^2*b - b)) - b*(log(b*x + a + 1)/(a + 1) - log(b*x + a - 1)/(a - 1) + 2*log(x)/(a^2 - 1))*arccoth(b*x + a) - arccoth(b*x + a)^2/x","A",0
75,1,360,0,0.336779," ","integrate(arccoth(b*x+a)^2/x^3,x, algorithm=""maxima"")","\frac{1}{8} \, {\left(\frac{8 \, {\left(\log\left(b x + a - 1\right) \log\left(\frac{1}{2} \, b x + \frac{1}{2} \, a + \frac{1}{2}\right) + {\rm Li}_2\left(-\frac{1}{2} \, b x - \frac{1}{2} \, a + \frac{1}{2}\right)\right)} a}{a^{4} - 2 \, a^{2} + 1} - \frac{8 \, {\left(\log\left(\frac{b x}{a + 1} + 1\right) \log\left(x\right) + {\rm Li}_2\left(-\frac{b x}{a + 1}\right)\right)} a}{a^{4} - 2 \, a^{2} + 1} + \frac{8 \, {\left(\log\left(\frac{b x}{a - 1} + 1\right) \log\left(x\right) + {\rm Li}_2\left(-\frac{b x}{a - 1}\right)\right)} a}{a^{4} - 2 \, a^{2} + 1} - \frac{{\left(a^{2} - 2 \, a + 1\right)} \log\left(b x + a + 1\right)^{2} - 2 \, {\left(a^{2} - 2 \, a + 1\right)} \log\left(b x + a + 1\right) \log\left(b x + a - 1\right) + {\left(a^{2} + 2 \, a + 1\right)} \log\left(b x + a - 1\right)^{2}}{a^{4} - 2 \, a^{2} + 1} + \frac{4 \, \log\left(b x + a + 1\right)}{a^{3} + a^{2} - a - 1} - \frac{4 \, \log\left(b x + a - 1\right)}{a^{3} - a^{2} - a + 1} + \frac{8 \, \log\left(x\right)}{a^{4} - 2 \, a^{2} + 1}\right)} b^{2} + \frac{1}{2} \, {\left(\frac{4 \, a b \log\left(x\right)}{a^{4} - 2 \, a^{2} + 1} + \frac{b \log\left(b x + a + 1\right)}{a^{2} + 2 \, a + 1} - \frac{b \log\left(b x + a - 1\right)}{a^{2} - 2 \, a + 1} + \frac{2}{{\left(a^{2} - 1\right)} x}\right)} b \operatorname{arcoth}\left(b x + a\right) - \frac{\operatorname{arcoth}\left(b x + a\right)^{2}}{2 \, x^{2}}"," ",0,"1/8*(8*(log(b*x + a - 1)*log(1/2*b*x + 1/2*a + 1/2) + dilog(-1/2*b*x - 1/2*a + 1/2))*a/(a^4 - 2*a^2 + 1) - 8*(log(b*x/(a + 1) + 1)*log(x) + dilog(-b*x/(a + 1)))*a/(a^4 - 2*a^2 + 1) + 8*(log(b*x/(a - 1) + 1)*log(x) + dilog(-b*x/(a - 1)))*a/(a^4 - 2*a^2 + 1) - ((a^2 - 2*a + 1)*log(b*x + a + 1)^2 - 2*(a^2 - 2*a + 1)*log(b*x + a + 1)*log(b*x + a - 1) + (a^2 + 2*a + 1)*log(b*x + a - 1)^2)/(a^4 - 2*a^2 + 1) + 4*log(b*x + a + 1)/(a^3 + a^2 - a - 1) - 4*log(b*x + a - 1)/(a^3 - a^2 - a + 1) + 8*log(x)/(a^4 - 2*a^2 + 1))*b^2 + 1/2*(4*a*b*log(x)/(a^4 - 2*a^2 + 1) + b*log(b*x + a + 1)/(a^2 + 2*a + 1) - b*log(b*x + a - 1)/(a^2 - 2*a + 1) + 2/((a^2 - 1)*x))*b*arccoth(b*x + a) - 1/2*arccoth(b*x + a)^2/x^2","A",0
76,1,589,0,0.594972," ","integrate(arccoth(b*x+a)/(d*x^2+c),x, algorithm=""maxima"")","\frac{\operatorname{arcoth}\left(b x + a\right) \arctan\left(\frac{d x}{\sqrt{c d}}\right)}{\sqrt{c d}} + \frac{{\left(\arctan\left(\frac{{\left(b^{2} x + {\left(a + 1\right)} b\right)} \sqrt{c} \sqrt{d}}{b^{2} c + {\left(a^{2} + 2 \, a + 1\right)} d}, \frac{{\left(a + 1\right)} b d x + {\left(a^{2} + 2 \, a + 1\right)} d}{b^{2} c + {\left(a^{2} + 2 \, a + 1\right)} d}\right) - \arctan\left(\frac{{\left(b^{2} x + {\left(a - 1\right)} b\right)} \sqrt{c} \sqrt{d}}{b^{2} c + {\left(a^{2} - 2 \, a + 1\right)} d}, \frac{{\left(a - 1\right)} b d x + {\left(a^{2} - 2 \, a + 1\right)} d}{b^{2} c + {\left(a^{2} - 2 \, a + 1\right)} d}\right)\right)} \log\left(d x^{2} + c\right) - \arctan\left(\frac{\sqrt{d} x}{\sqrt{c}}\right) \log\left(\frac{b^{2} d x^{2} + 2 \, {\left(a + 1\right)} b d x + {\left(a^{2} + 2 \, a + 1\right)} d}{b^{2} c + {\left(a^{2} + 2 \, a + 1\right)} d}\right) + \arctan\left(\frac{\sqrt{d} x}{\sqrt{c}}\right) \log\left(\frac{b^{2} d x^{2} + 2 \, {\left(a - 1\right)} b d x + {\left(a^{2} - 2 \, a + 1\right)} d}{b^{2} c + {\left(a^{2} - 2 \, a + 1\right)} d}\right) - i \, {\rm Li}_2\left(\frac{{\left(a + 1\right)} b d x + b^{2} c - {\left(i \, b^{2} x + {\left(-i \, a - i\right)} b\right)} \sqrt{c} \sqrt{d}}{b^{2} c + {\left(2 i \, a + 2 i\right)} b \sqrt{c} \sqrt{d} - {\left(a^{2} + 2 \, a + 1\right)} d}\right) + i \, {\rm Li}_2\left(\frac{{\left(a + 1\right)} b d x + b^{2} c + {\left(i \, b^{2} x + {\left(-i \, a - i\right)} b\right)} \sqrt{c} \sqrt{d}}{b^{2} c - {\left(2 i \, a + 2 i\right)} b \sqrt{c} \sqrt{d} - {\left(a^{2} + 2 \, a + 1\right)} d}\right) + i \, {\rm Li}_2\left(\frac{{\left(a - 1\right)} b d x + b^{2} c - {\left(i \, b^{2} x + {\left(-i \, a + i\right)} b\right)} \sqrt{c} \sqrt{d}}{b^{2} c + {\left(2 i \, a - 2 i\right)} b \sqrt{c} \sqrt{d} - {\left(a^{2} - 2 \, a + 1\right)} d}\right) - i \, {\rm Li}_2\left(\frac{{\left(a - 1\right)} b d x + b^{2} c + {\left(i \, b^{2} x + {\left(-i \, a + i\right)} b\right)} \sqrt{c} \sqrt{d}}{b^{2} c - {\left(2 i \, a - 2 i\right)} b \sqrt{c} \sqrt{d} - {\left(a^{2} - 2 \, a + 1\right)} d}\right)}{4 \, \sqrt{c d}}"," ",0,"arccoth(b*x + a)*arctan(d*x/sqrt(c*d))/sqrt(c*d) + 1/4*((arctan2((b^2*x + (a + 1)*b)*sqrt(c)*sqrt(d)/(b^2*c + (a^2 + 2*a + 1)*d), ((a + 1)*b*d*x + (a^2 + 2*a + 1)*d)/(b^2*c + (a^2 + 2*a + 1)*d)) - arctan2((b^2*x + (a - 1)*b)*sqrt(c)*sqrt(d)/(b^2*c + (a^2 - 2*a + 1)*d), ((a - 1)*b*d*x + (a^2 - 2*a + 1)*d)/(b^2*c + (a^2 - 2*a + 1)*d)))*log(d*x^2 + c) - arctan(sqrt(d)*x/sqrt(c))*log((b^2*d*x^2 + 2*(a + 1)*b*d*x + (a^2 + 2*a + 1)*d)/(b^2*c + (a^2 + 2*a + 1)*d)) + arctan(sqrt(d)*x/sqrt(c))*log((b^2*d*x^2 + 2*(a - 1)*b*d*x + (a^2 - 2*a + 1)*d)/(b^2*c + (a^2 - 2*a + 1)*d)) - I*dilog(((a + 1)*b*d*x + b^2*c - (I*b^2*x + (-I*a - I)*b)*sqrt(c)*sqrt(d))/(b^2*c + (2*I*a + 2*I)*b*sqrt(c)*sqrt(d) - (a^2 + 2*a + 1)*d)) + I*dilog(((a + 1)*b*d*x + b^2*c + (I*b^2*x + (-I*a - I)*b)*sqrt(c)*sqrt(d))/(b^2*c - (2*I*a + 2*I)*b*sqrt(c)*sqrt(d) - (a^2 + 2*a + 1)*d)) + I*dilog(((a - 1)*b*d*x + b^2*c - (I*b^2*x + (-I*a + I)*b)*sqrt(c)*sqrt(d))/(b^2*c + (2*I*a - 2*I)*b*sqrt(c)*sqrt(d) - (a^2 - 2*a + 1)*d)) - I*dilog(((a - 1)*b*d*x + b^2*c + (I*b^2*x + (-I*a + I)*b)*sqrt(c)*sqrt(d))/(b^2*c - (2*I*a - 2*I)*b*sqrt(c)*sqrt(d) - (a^2 - 2*a + 1)*d)))/sqrt(c*d)","C",0
77,1,192,0,0.332324," ","integrate(arccoth(b*x+a)/(d*x+c),x, algorithm=""maxima"")","-\frac{1}{2} \, b {\left(\frac{\log\left(b x + a - 1\right) \log\left(\frac{b d x + a d - d}{b c - a d + d} + 1\right) + {\rm Li}_2\left(-\frac{b d x + a d - d}{b c - a d + d}\right)}{b d} - \frac{\log\left(b x + a + 1\right) \log\left(\frac{b d x + a d + d}{b c - a d - d} + 1\right) + {\rm Li}_2\left(-\frac{b d x + a d + d}{b c - a d - d}\right)}{b d}\right)} - \frac{b {\left(\frac{\log\left(b x + a + 1\right)}{b} - \frac{\log\left(b x + a - 1\right)}{b}\right)} \log\left(d x + c\right)}{2 \, d} + \frac{\operatorname{arcoth}\left(b x + a\right) \log\left(d x + c\right)}{d}"," ",0,"-1/2*b*((log(b*x + a - 1)*log((b*d*x + a*d - d)/(b*c - a*d + d) + 1) + dilog(-(b*d*x + a*d - d)/(b*c - a*d + d)))/(b*d) - (log(b*x + a + 1)*log((b*d*x + a*d + d)/(b*c - a*d - d) + 1) + dilog(-(b*d*x + a*d + d)/(b*c - a*d - d)))/(b*d)) - 1/2*b*(log(b*x + a + 1)/b - log(b*x + a - 1)/b)*log(d*x + c)/d + arccoth(b*x + a)*log(d*x + c)/d","A",0
78,1,192,0,0.340102," ","integrate(arccoth(b*x+a)/(c+d/x),x, algorithm=""maxima"")","\frac{1}{2} \, b {\left(\frac{{\left(\log\left(c x + d\right) \log\left(\frac{b c x + b d}{a c - b d + c} + 1\right) + {\rm Li}_2\left(-\frac{b c x + b d}{a c - b d + c}\right)\right)} d}{b c^{2}} - \frac{{\left(\log\left(c x + d\right) \log\left(\frac{b c x + b d}{a c - b d - c} + 1\right) + {\rm Li}_2\left(-\frac{b c x + b d}{a c - b d - c}\right)\right)} d}{b c^{2}} + \frac{{\left(a + 1\right)} \log\left(b x + a + 1\right)}{b^{2} c} - \frac{{\left(a - 1\right)} \log\left(b x + a - 1\right)}{b^{2} c}\right)} + {\left(\frac{x}{c} - \frac{d \log\left(c x + d\right)}{c^{2}}\right)} \operatorname{arcoth}\left(b x + a\right)"," ",0,"1/2*b*((log(c*x + d)*log((b*c*x + b*d)/(a*c - b*d + c) + 1) + dilog(-(b*c*x + b*d)/(a*c - b*d + c)))*d/(b*c^2) - (log(c*x + d)*log((b*c*x + b*d)/(a*c - b*d - c) + 1) + dilog(-(b*c*x + b*d)/(a*c - b*d - c)))*d/(b*c^2) + (a + 1)*log(b*x + a + 1)/(b^2*c) - (a - 1)*log(b*x + a - 1)/(b^2*c)) + (x/c - d*log(c*x + d)/c^2)*arccoth(b*x + a)","A",0
79,1,647,0,0.550014," ","integrate(arccoth(b*x+a)/(c+d/x^2),x, algorithm=""maxima"")","-{\left(\frac{d \arctan\left(\frac{c x}{\sqrt{c d}}\right)}{\sqrt{c d} c} - \frac{x}{c}\right)} \operatorname{arcoth}\left(b x + a\right) + \frac{2 \, {\left(a + 1\right)} c \log\left(b x + a + 1\right) - 2 \, {\left(a - 1\right)} c \log\left(b x + a - 1\right) + {\left(b \arctan\left(\frac{\sqrt{c} x}{\sqrt{d}}\right) \log\left(\frac{b^{2} c x^{2} + 2 \, {\left(a + 1\right)} b c x + {\left(a^{2} + 2 \, a + 1\right)} c}{b^{2} d + {\left(a^{2} + 2 \, a + 1\right)} c}\right) - b \arctan\left(\frac{\sqrt{c} x}{\sqrt{d}}\right) \log\left(\frac{b^{2} c x^{2} + 2 \, {\left(a - 1\right)} b c x + {\left(a^{2} - 2 \, a + 1\right)} c}{b^{2} d + {\left(a^{2} - 2 \, a + 1\right)} c}\right) + i \, b {\rm Li}_2\left(\frac{{\left(a + 1\right)} b c x + b^{2} d - {\left(i \, b^{2} x + {\left(-i \, a - i\right)} b\right)} \sqrt{c} \sqrt{d}}{{\left(2 i \, a + 2 i\right)} b \sqrt{c} \sqrt{d} + b^{2} d - {\left(a^{2} + 2 \, a + 1\right)} c}\right) - i \, b {\rm Li}_2\left(-\frac{{\left(a + 1\right)} b c x + b^{2} d + {\left(i \, b^{2} x + {\left(-i \, a - i\right)} b\right)} \sqrt{c} \sqrt{d}}{{\left(2 i \, a + 2 i\right)} b \sqrt{c} \sqrt{d} - b^{2} d + {\left(a^{2} + 2 \, a + 1\right)} c}\right) - i \, b {\rm Li}_2\left(\frac{{\left(a - 1\right)} b c x + b^{2} d - {\left(i \, b^{2} x + {\left(-i \, a + i\right)} b\right)} \sqrt{c} \sqrt{d}}{{\left(2 i \, a - 2 i\right)} b \sqrt{c} \sqrt{d} + b^{2} d - {\left(a^{2} - 2 \, a + 1\right)} c}\right) + i \, b {\rm Li}_2\left(-\frac{{\left(a - 1\right)} b c x + b^{2} d + {\left(i \, b^{2} x + {\left(-i \, a + i\right)} b\right)} \sqrt{c} \sqrt{d}}{{\left(2 i \, a - 2 i\right)} b \sqrt{c} \sqrt{d} - b^{2} d + {\left(a^{2} - 2 \, a + 1\right)} c}\right) - {\left(b \arctan\left(\frac{{\left(b^{2} x + {\left(a + 1\right)} b\right)} \sqrt{c} \sqrt{d}}{b^{2} d + {\left(a^{2} + 2 \, a + 1\right)} c}, \frac{{\left(a + 1\right)} b c x + {\left(a^{2} + 2 \, a + 1\right)} c}{b^{2} d + {\left(a^{2} + 2 \, a + 1\right)} c}\right) - b \arctan\left(\frac{{\left(b^{2} x + {\left(a - 1\right)} b\right)} \sqrt{c} \sqrt{d}}{b^{2} d + {\left(a^{2} - 2 \, a + 1\right)} c}, \frac{{\left(a - 1\right)} b c x + {\left(a^{2} - 2 \, a + 1\right)} c}{b^{2} d + {\left(a^{2} - 2 \, a + 1\right)} c}\right)\right)} \log\left(c x^{2} + d\right)\right)} \sqrt{c} \sqrt{d}}{4 \, b c^{2}}"," ",0,"-(d*arctan(c*x/sqrt(c*d))/(sqrt(c*d)*c) - x/c)*arccoth(b*x + a) + 1/4*(2*(a + 1)*c*log(b*x + a + 1) - 2*(a - 1)*c*log(b*x + a - 1) + (b*arctan(sqrt(c)*x/sqrt(d))*log((b^2*c*x^2 + 2*(a + 1)*b*c*x + (a^2 + 2*a + 1)*c)/(b^2*d + (a^2 + 2*a + 1)*c)) - b*arctan(sqrt(c)*x/sqrt(d))*log((b^2*c*x^2 + 2*(a - 1)*b*c*x + (a^2 - 2*a + 1)*c)/(b^2*d + (a^2 - 2*a + 1)*c)) + I*b*dilog(((a + 1)*b*c*x + b^2*d - (I*b^2*x + (-I*a - I)*b)*sqrt(c)*sqrt(d))/((2*I*a + 2*I)*b*sqrt(c)*sqrt(d) + b^2*d - (a^2 + 2*a + 1)*c)) - I*b*dilog(-((a + 1)*b*c*x + b^2*d + (I*b^2*x + (-I*a - I)*b)*sqrt(c)*sqrt(d))/((2*I*a + 2*I)*b*sqrt(c)*sqrt(d) - b^2*d + (a^2 + 2*a + 1)*c)) - I*b*dilog(((a - 1)*b*c*x + b^2*d - (I*b^2*x + (-I*a + I)*b)*sqrt(c)*sqrt(d))/((2*I*a - 2*I)*b*sqrt(c)*sqrt(d) + b^2*d - (a^2 - 2*a + 1)*c)) + I*b*dilog(-((a - 1)*b*c*x + b^2*d + (I*b^2*x + (-I*a + I)*b)*sqrt(c)*sqrt(d))/((2*I*a - 2*I)*b*sqrt(c)*sqrt(d) - b^2*d + (a^2 - 2*a + 1)*c)) - (b*arctan2((b^2*x + (a + 1)*b)*sqrt(c)*sqrt(d)/(b^2*d + (a^2 + 2*a + 1)*c), ((a + 1)*b*c*x + (a^2 + 2*a + 1)*c)/(b^2*d + (a^2 + 2*a + 1)*c)) - b*arctan2((b^2*x + (a - 1)*b)*sqrt(c)*sqrt(d)/(b^2*d + (a^2 - 2*a + 1)*c), ((a - 1)*b*c*x + (a^2 - 2*a + 1)*c)/(b^2*d + (a^2 - 2*a + 1)*c)))*log(c*x^2 + d))*sqrt(c)*sqrt(d))/(b*c^2)","C",0
80,0,0,0,0.000000," ","integrate(arccoth(b*x+a)/(c+d*x^(1/2)),x, algorithm=""maxima"")","\int \frac{\operatorname{arcoth}\left(b x + a\right)}{d \sqrt{x} + c}\,{d x}"," ",0,"integrate(arccoth(b*x + a)/(d*sqrt(x) + c), x)","F",0
81,0,0,0,0.000000," ","integrate(arccoth(b*x+a)/(c+d/x^(1/2)),x, algorithm=""maxima"")","\frac{{\left(b x + a + 1\right)} \log\left(b x + a + 1\right) - {\left(b x + a - 1\right)} \log\left(b x + a - 1\right)}{2 \, b c} - \frac{1}{2} \, \int \frac{d \log\left(b x + a + 1\right) - d \log\left(b x + a - 1\right)}{c^{2} \sqrt{x} + c d}\,{d x}"," ",0,"1/2*((b*x + a + 1)*log(b*x + a + 1) - (b*x + a - 1)*log(b*x + a - 1))/(b*c) - 1/2*integrate((d*log(b*x + a + 1) - d*log(b*x + a - 1))/(c^2*sqrt(x) + c*d), x)","F",0
82,-2,0,0,0.000000," ","integrate(arccoth(e*x+d)/(c*x^2+b*x+a),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a*c-b^2>0)', see `assume?` for more details)Is 4*a*c-b^2 positive or negative?","F(-2)",0
83,1,41,0,0.301097," ","integrate(x^2*arccoth(x^(1/2)),x, algorithm=""maxima"")","\frac{1}{3} \, x^{3} \operatorname{arcoth}\left(\sqrt{x}\right) + \frac{1}{15} \, x^{\frac{5}{2}} + \frac{1}{9} \, x^{\frac{3}{2}} + \frac{1}{3} \, \sqrt{x} - \frac{1}{6} \, \log\left(\sqrt{x} + 1\right) + \frac{1}{6} \, \log\left(\sqrt{x} - 1\right)"," ",0,"1/3*x^3*arccoth(sqrt(x)) + 1/15*x^(5/2) + 1/9*x^(3/2) + 1/3*sqrt(x) - 1/6*log(sqrt(x) + 1) + 1/6*log(sqrt(x) - 1)","A",0
84,1,36,0,0.307884," ","integrate(x*arccoth(x^(1/2)),x, algorithm=""maxima"")","\frac{1}{2} \, x^{2} \operatorname{arcoth}\left(\sqrt{x}\right) + \frac{1}{6} \, x^{\frac{3}{2}} + \frac{1}{2} \, \sqrt{x} - \frac{1}{4} \, \log\left(\sqrt{x} + 1\right) + \frac{1}{4} \, \log\left(\sqrt{x} - 1\right)"," ",0,"1/2*x^2*arccoth(sqrt(x)) + 1/6*x^(3/2) + 1/2*sqrt(x) - 1/4*log(sqrt(x) + 1) + 1/4*log(sqrt(x) - 1)","A",0
85,1,26,0,0.301319," ","integrate(arccoth(x^(1/2)),x, algorithm=""maxima"")","x \operatorname{arcoth}\left(\sqrt{x}\right) + \sqrt{x} - \frac{1}{2} \, \log\left(\sqrt{x} + 1\right) + \frac{1}{2} \, \log\left(\sqrt{x} - 1\right)"," ",0,"x*arccoth(sqrt(x)) + sqrt(x) - 1/2*log(sqrt(x) + 1) + 1/2*log(sqrt(x) - 1)","A",0
86,1,66,0,0.309925," ","integrate(arccoth(x^(1/2))/x,x, algorithm=""maxima"")","-\frac{1}{2} \, {\left(\log\left(\sqrt{x} + 1\right) - \log\left(\sqrt{x} - 1\right)\right)} \log\left(x\right) + \operatorname{arcoth}\left(\sqrt{x}\right) \log\left(x\right) + \log\left(-\sqrt{x}\right) \log\left(\sqrt{x} + 1\right) - \frac{1}{2} \, \log\left(x\right) \log\left(\sqrt{x} - 1\right) + {\rm Li}_2\left(\sqrt{x} + 1\right) - {\rm Li}_2\left(-\sqrt{x} + 1\right)"," ",0,"-1/2*(log(sqrt(x) + 1) - log(sqrt(x) - 1))*log(x) + arccoth(sqrt(x))*log(x) + log(-sqrt(x))*log(sqrt(x) + 1) - 1/2*log(x)*log(sqrt(x) - 1) + dilog(sqrt(x) + 1) - dilog(-sqrt(x) + 1)","B",0
87,1,31,0,0.304997," ","integrate(arccoth(x^(1/2))/x^2,x, algorithm=""maxima"")","-\frac{\operatorname{arcoth}\left(\sqrt{x}\right)}{x} - \frac{1}{\sqrt{x}} + \frac{1}{2} \, \log\left(\sqrt{x} + 1\right) - \frac{1}{2} \, \log\left(\sqrt{x} - 1\right)"," ",0,"-arccoth(sqrt(x))/x - 1/sqrt(x) + 1/2*log(sqrt(x) + 1) - 1/2*log(sqrt(x) - 1)","A",0
88,1,36,0,0.310918," ","integrate(arccoth(x^(1/2))/x^3,x, algorithm=""maxima"")","-\frac{3 \, x + 1}{6 \, x^{\frac{3}{2}}} - \frac{\operatorname{arcoth}\left(\sqrt{x}\right)}{2 \, x^{2}} + \frac{1}{4} \, \log\left(\sqrt{x} + 1\right) - \frac{1}{4} \, \log\left(\sqrt{x} - 1\right)"," ",0,"-1/6*(3*x + 1)/x^(3/2) - 1/2*arccoth(sqrt(x))/x^2 + 1/4*log(sqrt(x) + 1) - 1/4*log(sqrt(x) - 1)","A",0
89,1,24,0,0.309147," ","integrate(x^(3/2)*arccoth(x^(1/2)),x, algorithm=""maxima"")","\frac{2}{5} \, x^{\frac{5}{2}} \operatorname{arcoth}\left(\sqrt{x}\right) + \frac{1}{10} \, x^{2} + \frac{1}{5} \, x + \frac{1}{5} \, \log\left(x - 1\right)"," ",0,"2/5*x^(5/2)*arccoth(sqrt(x)) + 1/10*x^2 + 1/5*x + 1/5*log(x - 1)","A",0
90,1,19,0,0.307273," ","integrate(arccoth(x^(1/2))*x^(1/2),x, algorithm=""maxima"")","\frac{2}{3} \, x^{\frac{3}{2}} \operatorname{arcoth}\left(\sqrt{x}\right) + \frac{1}{3} \, x + \frac{1}{3} \, \log\left(x - 1\right)"," ",0,"2/3*x^(3/2)*arccoth(sqrt(x)) + 1/3*x + 1/3*log(x - 1)","A",0
91,1,16,0,0.303890," ","integrate(arccoth(x^(1/2))/x^(1/2),x, algorithm=""maxima"")","2 \, \sqrt{x} \operatorname{arcoth}\left(\sqrt{x}\right) + \log\left(-x + 1\right)"," ",0,"2*sqrt(x)*arccoth(sqrt(x)) + log(-x + 1)","A",0
92,1,18,0,0.312746," ","integrate(arccoth(x^(1/2))/x^(3/2),x, algorithm=""maxima"")","-\frac{2 \, \operatorname{arcoth}\left(\sqrt{x}\right)}{\sqrt{x}} - \log\left(x - 1\right) + \log\left(x\right)"," ",0,"-2*arccoth(sqrt(x))/sqrt(x) - log(x - 1) + log(x)","A",0
93,1,104,0,0.306408," ","integrate(arccoth(a*x^5)/x,x, algorithm=""maxima"")","-\frac{1}{2} \, a {\left(\frac{\log\left(a x^{5} + 1\right)}{a} - \frac{\log\left(a x^{5} - 1\right)}{a}\right)} \log\left(x\right) - \frac{1}{10} \, a {\left(\frac{\log\left(a x^{5} - 1\right) \log\left(a x^{5}\right) + {\rm Li}_2\left(-a x^{5} + 1\right)}{a} - \frac{\log\left(a x^{5} + 1\right) \log\left(-a x^{5}\right) + {\rm Li}_2\left(a x^{5} + 1\right)}{a}\right)} + \operatorname{arcoth}\left(a x^{5}\right) \log\left(x\right)"," ",0,"-1/2*a*(log(a*x^5 + 1)/a - log(a*x^5 - 1)/a)*log(x) - 1/10*a*((log(a*x^5 - 1)*log(a*x^5) + dilog(-a*x^5 + 1))/a - (log(a*x^5 + 1)*log(-a*x^5) + dilog(a*x^5 + 1))/a) + arccoth(a*x^5)*log(x)","B",0
94,1,15,0,0.303461," ","integrate(arccoth(1/x),x, algorithm=""maxima"")","x \operatorname{arcoth}\left(\frac{1}{x}\right) + \frac{1}{2} \, \log\left(x^{2} - 1\right)"," ",0,"x*arccoth(1/x) + 1/2*log(x^2 - 1)","A",0
95,1,147,0,0.417125," ","integrate(arccoth(a*x^n)/x,x, algorithm=""maxima"")","-\frac{1}{2} \, a n {\left(\frac{\log\left(\frac{a x^{n} + 1}{a}\right)}{a n} - \frac{\log\left(\frac{a x^{n} - 1}{a}\right)}{a n}\right)} \log\left(x\right) + \frac{1}{2} \, a n {\left(\frac{\log\left(a x^{n} + 1\right) \log\left(x\right) - \log\left(a x^{n} - 1\right) \log\left(x\right)}{a n} - \frac{n \log\left(a x^{n} + 1\right) \log\left(x\right) + {\rm Li}_2\left(-a x^{n}\right)}{a n^{2}} + \frac{n \log\left(-a x^{n} + 1\right) \log\left(x\right) + {\rm Li}_2\left(a x^{n}\right)}{a n^{2}}\right)} + \operatorname{arcoth}\left(a x^{n}\right) \log\left(x\right)"," ",0,"-1/2*a*n*(log((a*x^n + 1)/a)/(a*n) - log((a*x^n - 1)/a)/(a*n))*log(x) + 1/2*a*n*((log(a*x^n + 1)*log(x) - log(a*x^n - 1)*log(x))/(a*n) - (n*log(a*x^n + 1)*log(x) + dilog(-a*x^n))/(a*n^2) + (n*log(-a*x^n + 1)*log(x) + dilog(a*x^n))/(a*n^2)) + arccoth(a*x^n)*log(x)","B",0
96,1,62,0,0.305875," ","integrate((b*x+a)*arccoth(b*x+a),x, algorithm=""maxima"")","\frac{1}{4} \, b {\left(\frac{2 \, x}{b} + \frac{{\left(a^{2} - 1\right)} \log\left(b x + a + 1\right)}{b^{2}} - \frac{{\left(a^{2} - 1\right)} \log\left(b x + a - 1\right)}{b^{2}}\right)} + \frac{1}{2} \, {\left(b x^{2} + 2 \, a x\right)} \operatorname{arcoth}\left(b x + a\right)"," ",0,"1/4*b*(2*x/b + (a^2 - 1)*log(b*x + a + 1)/b^2 - (a^2 - 1)*log(b*x + a - 1)/b^2) + 1/2*(b*x^2 + 2*a*x)*arccoth(b*x + a)","A",0
97,1,81,0,0.306071," ","integrate((b*x+a)^2*arccoth(b*x+a),x, algorithm=""maxima"")","\frac{1}{6} \, b {\left(\frac{b x^{2} + 2 \, a x}{b} + \frac{{\left(a^{3} + 1\right)} \log\left(b x + a + 1\right)}{b^{2}} - \frac{{\left(a^{3} - 1\right)} \log\left(b x + a - 1\right)}{b^{2}}\right)} + \frac{1}{3} \, {\left(b^{2} x^{3} + 3 \, a b x^{2} + 3 \, a^{2} x\right)} \operatorname{arcoth}\left(b x + a\right)"," ",0,"1/6*b*((b*x^2 + 2*a*x)/b + (a^3 + 1)*log(b*x + a + 1)/b^2 - (a^3 - 1)*log(b*x + a - 1)/b^2) + 1/3*(b^2*x^3 + 3*a*b*x^2 + 3*a^2*x)*arccoth(b*x + a)","A",0
98,1,112,0,0.319788," ","integrate(arccoth(b*x+a)/(b*x+a),x, algorithm=""maxima"")","-\frac{1}{2} \, b {\left(\frac{\log\left(b x + a\right) \log\left(b x + a - 1\right) + {\rm Li}_2\left(-b x - a + 1\right)}{b^{2}} - \frac{\log\left(b x + a + 1\right) \log\left(-b x - a\right) + {\rm Li}_2\left(b x + a + 1\right)}{b^{2}}\right)} - \frac{1}{2} \, {\left(\frac{\log\left(b x + a + 1\right)}{b} - \frac{\log\left(b x + a - 1\right)}{b}\right)} \log\left(b x + a\right) + \frac{\operatorname{arcoth}\left(b x + a\right) \log\left(b x + a\right)}{b}"," ",0,"-1/2*b*((log(b*x + a)*log(b*x + a - 1) + dilog(-b*x - a + 1))/b^2 - (log(b*x + a + 1)*log(-b*x - a) + dilog(b*x + a + 1))/b^2) - 1/2*(log(b*x + a + 1)/b - log(b*x + a - 1)/b)*log(b*x + a) + arccoth(b*x + a)*log(b*x + a)/b","B",0
99,1,53,0,0.310670," ","integrate(arccoth(b*x+a)/(b*x+a)^2,x, algorithm=""maxima"")","-\frac{\log\left(b x + a + 1\right)}{2 \, b} + \frac{\log\left(b x + a\right)}{b} - \frac{\log\left(b x + a - 1\right)}{2 \, b} - \frac{\operatorname{arcoth}\left(b x + a\right)}{{\left(b x + a\right)} b}"," ",0,"-1/2*log(b*x + a + 1)/b + log(b*x + a)/b - 1/2*log(b*x + a - 1)/b - arccoth(b*x + a)/((b*x + a)*b)","A",0
100,1,58,0,0.306400," ","integrate(arccoth(1+x)/(2+2*x),x, algorithm=""maxima"")","-\frac{1}{4} \, {\left(\log\left(x + 2\right) - \log\left(x\right)\right)} \log\left(x + 1\right) + \frac{1}{2} \, \operatorname{arcoth}\left(x + 1\right) \log\left(x + 1\right) - \frac{1}{4} \, \log\left(x + 1\right) \log\left(x\right) + \frac{1}{4} \, \log\left(x + 2\right) \log\left(-x - 1\right) - \frac{1}{4} \, {\rm Li}_2\left(-x\right) + \frac{1}{4} \, {\rm Li}_2\left(x + 2\right)"," ",0,"-1/4*(log(x + 2) - log(x))*log(x + 1) + 1/2*arccoth(x + 1)*log(x + 1) - 1/4*log(x + 1)*log(x) + 1/4*log(x + 2)*log(-x - 1) - 1/4*dilog(-x) + 1/4*dilog(x + 2)","B",0
101,1,132,0,0.325899," ","integrate(arccoth(b*x+a)/(a*d/b+d*x),x, algorithm=""maxima"")","-\frac{1}{2} \, b {\left(\frac{\log\left(b x + a\right) \log\left(b x + a - 1\right) + {\rm Li}_2\left(-b x - a + 1\right)}{b d} - \frac{\log\left(b x + a + 1\right) \log\left(-b x - a\right) + {\rm Li}_2\left(b x + a + 1\right)}{b d}\right)} - \frac{b {\left(\frac{\log\left(b x + a + 1\right)}{b} - \frac{\log\left(b x + a - 1\right)}{b}\right)} \log\left(d x + \frac{a d}{b}\right)}{2 \, d} + \frac{\operatorname{arcoth}\left(b x + a\right) \log\left(d x + \frac{a d}{b}\right)}{d}"," ",0,"-1/2*b*((log(b*x + a)*log(b*x + a - 1) + dilog(-b*x - a + 1))/(b*d) - (log(b*x + a + 1)*log(-b*x - a) + dilog(b*x + a + 1))/(b*d)) - 1/2*b*(log(b*x + a + 1)/b - log(b*x + a - 1)/b)*log(d*x + a*d/b)/d + arccoth(b*x + a)*log(d*x + a*d/b)/d","B",0
102,1,333,0,0.310611," ","integrate((f*x+e)^3*(a+b*arccoth(d*x+c)),x, algorithm=""maxima"")","\frac{1}{4} \, a f^{3} x^{4} + a e f^{2} x^{3} + \frac{3}{2} \, a e^{2} f x^{2} + \frac{3}{4} \, {\left(2 \, x^{2} \operatorname{arcoth}\left(d x + c\right) + d {\left(\frac{2 \, x}{d^{2}} - \frac{{\left(c^{2} + 2 \, c + 1\right)} \log\left(d x + c + 1\right)}{d^{3}} + \frac{{\left(c^{2} - 2 \, c + 1\right)} \log\left(d x + c - 1\right)}{d^{3}}\right)}\right)} b e^{2} f + \frac{1}{2} \, {\left(2 \, x^{3} \operatorname{arcoth}\left(d x + c\right) + d {\left(\frac{d x^{2} - 4 \, c x}{d^{3}} + \frac{{\left(c^{3} + 3 \, c^{2} + 3 \, c + 1\right)} \log\left(d x + c + 1\right)}{d^{4}} - \frac{{\left(c^{3} - 3 \, c^{2} + 3 \, c - 1\right)} \log\left(d x + c - 1\right)}{d^{4}}\right)}\right)} b e f^{2} + \frac{1}{24} \, {\left(6 \, x^{4} \operatorname{arcoth}\left(d x + c\right) + d {\left(\frac{2 \, {\left(d^{2} x^{3} - 3 \, c d x^{2} + 3 \, {\left(3 \, c^{2} + 1\right)} x\right)}}{d^{4}} - \frac{3 \, {\left(c^{4} + 4 \, c^{3} + 6 \, c^{2} + 4 \, c + 1\right)} \log\left(d x + c + 1\right)}{d^{5}} + \frac{3 \, {\left(c^{4} - 4 \, c^{3} + 6 \, c^{2} - 4 \, c + 1\right)} \log\left(d x + c - 1\right)}{d^{5}}\right)}\right)} b f^{3} + a e^{3} x + \frac{{\left(2 \, {\left(d x + c\right)} \operatorname{arcoth}\left(d x + c\right) + \log\left(-{\left(d x + c\right)}^{2} + 1\right)\right)} b e^{3}}{2 \, d}"," ",0,"1/4*a*f^3*x^4 + a*e*f^2*x^3 + 3/2*a*e^2*f*x^2 + 3/4*(2*x^2*arccoth(d*x + c) + d*(2*x/d^2 - (c^2 + 2*c + 1)*log(d*x + c + 1)/d^3 + (c^2 - 2*c + 1)*log(d*x + c - 1)/d^3))*b*e^2*f + 1/2*(2*x^3*arccoth(d*x + c) + d*((d*x^2 - 4*c*x)/d^3 + (c^3 + 3*c^2 + 3*c + 1)*log(d*x + c + 1)/d^4 - (c^3 - 3*c^2 + 3*c - 1)*log(d*x + c - 1)/d^4))*b*e*f^2 + 1/24*(6*x^4*arccoth(d*x + c) + d*(2*(d^2*x^3 - 3*c*d*x^2 + 3*(3*c^2 + 1)*x)/d^4 - 3*(c^4 + 4*c^3 + 6*c^2 + 4*c + 1)*log(d*x + c + 1)/d^5 + 3*(c^4 - 4*c^3 + 6*c^2 - 4*c + 1)*log(d*x + c - 1)/d^5))*b*f^3 + a*e^3*x + 1/2*(2*(d*x + c)*arccoth(d*x + c) + log(-(d*x + c)^2 + 1))*b*e^3/d","B",0
103,1,207,0,0.299010," ","integrate((f*x+e)^2*(a+b*arccoth(d*x+c)),x, algorithm=""maxima"")","\frac{1}{3} \, a f^{2} x^{3} + a e f x^{2} + \frac{1}{2} \, {\left(2 \, x^{2} \operatorname{arcoth}\left(d x + c\right) + d {\left(\frac{2 \, x}{d^{2}} - \frac{{\left(c^{2} + 2 \, c + 1\right)} \log\left(d x + c + 1\right)}{d^{3}} + \frac{{\left(c^{2} - 2 \, c + 1\right)} \log\left(d x + c - 1\right)}{d^{3}}\right)}\right)} b e f + \frac{1}{6} \, {\left(2 \, x^{3} \operatorname{arcoth}\left(d x + c\right) + d {\left(\frac{d x^{2} - 4 \, c x}{d^{3}} + \frac{{\left(c^{3} + 3 \, c^{2} + 3 \, c + 1\right)} \log\left(d x + c + 1\right)}{d^{4}} - \frac{{\left(c^{3} - 3 \, c^{2} + 3 \, c - 1\right)} \log\left(d x + c - 1\right)}{d^{4}}\right)}\right)} b f^{2} + a e^{2} x + \frac{{\left(2 \, {\left(d x + c\right)} \operatorname{arcoth}\left(d x + c\right) + \log\left(-{\left(d x + c\right)}^{2} + 1\right)\right)} b e^{2}}{2 \, d}"," ",0,"1/3*a*f^2*x^3 + a*e*f*x^2 + 1/2*(2*x^2*arccoth(d*x + c) + d*(2*x/d^2 - (c^2 + 2*c + 1)*log(d*x + c + 1)/d^3 + (c^2 - 2*c + 1)*log(d*x + c - 1)/d^3))*b*e*f + 1/6*(2*x^3*arccoth(d*x + c) + d*((d*x^2 - 4*c*x)/d^3 + (c^3 + 3*c^2 + 3*c + 1)*log(d*x + c + 1)/d^4 - (c^3 - 3*c^2 + 3*c - 1)*log(d*x + c - 1)/d^4))*b*f^2 + a*e^2*x + 1/2*(2*(d*x + c)*arccoth(d*x + c) + log(-(d*x + c)^2 + 1))*b*e^2/d","A",0
104,1,109,0,0.301274," ","integrate((f*x+e)*(a+b*arccoth(d*x+c)),x, algorithm=""maxima"")","\frac{1}{2} \, a f x^{2} + \frac{1}{4} \, {\left(2 \, x^{2} \operatorname{arcoth}\left(d x + c\right) + d {\left(\frac{2 \, x}{d^{2}} - \frac{{\left(c^{2} + 2 \, c + 1\right)} \log\left(d x + c + 1\right)}{d^{3}} + \frac{{\left(c^{2} - 2 \, c + 1\right)} \log\left(d x + c - 1\right)}{d^{3}}\right)}\right)} b f + a e x + \frac{{\left(2 \, {\left(d x + c\right)} \operatorname{arcoth}\left(d x + c\right) + \log\left(-{\left(d x + c\right)}^{2} + 1\right)\right)} b e}{2 \, d}"," ",0,"1/2*a*f*x^2 + 1/4*(2*x^2*arccoth(d*x + c) + d*(2*x/d^2 - (c^2 + 2*c + 1)*log(d*x + c + 1)/d^3 + (c^2 - 2*c + 1)*log(d*x + c - 1)/d^3))*b*f + a*e*x + 1/2*(2*(d*x + c)*arccoth(d*x + c) + log(-(d*x + c)^2 + 1))*b*e/d","A",0
105,1,36,0,0.296900," ","integrate(a+b*arccoth(d*x+c),x, algorithm=""maxima"")","a x + \frac{{\left(2 \, {\left(d x + c\right)} \operatorname{arcoth}\left(d x + c\right) + \log\left(-{\left(d x + c\right)}^{2} + 1\right)\right)} b}{2 \, d}"," ",0,"a*x + 1/2*(2*(d*x + c)*arccoth(d*x + c) + log(-(d*x + c)^2 + 1))*b/d","A",0
106,0,0,0,0.000000," ","integrate((a+b*arccoth(d*x+c))/(f*x+e),x, algorithm=""maxima"")","\frac{1}{2} \, b \int \frac{\log\left(\frac{1}{d x + c} + 1\right) - \log\left(-\frac{1}{d x + c} + 1\right)}{f x + e}\,{d x} + \frac{a \log\left(f x + e\right)}{f}"," ",0,"1/2*b*integrate((log(1/(d*x + c) + 1) - log(-1/(d*x + c) + 1))/(f*x + e), x) + a*log(f*x + e)/f","F",0
107,1,121,0,0.311259," ","integrate((a+b*arccoth(d*x+c))/(f*x+e)^2,x, algorithm=""maxima"")","\frac{1}{2} \, {\left(d {\left(\frac{\log\left(d x + c + 1\right)}{d e f - {\left(c + 1\right)} f^{2}} - \frac{\log\left(d x + c - 1\right)}{d e f - {\left(c - 1\right)} f^{2}} - \frac{2 \, \log\left(f x + e\right)}{d^{2} e^{2} - 2 \, c d e f + {\left(c^{2} - 1\right)} f^{2}}\right)} - \frac{2 \, \operatorname{arcoth}\left(d x + c\right)}{f^{2} x + e f}\right)} b - \frac{a}{f^{2} x + e f}"," ",0,"1/2*(d*(log(d*x + c + 1)/(d*e*f - (c + 1)*f^2) - log(d*x + c - 1)/(d*e*f - (c - 1)*f^2) - 2*log(f*x + e)/(d^2*e^2 - 2*c*d*e*f + (c^2 - 1)*f^2)) - 2*arccoth(d*x + c)/(f^2*x + e*f))*b - a/(f^2*x + e*f)","A",0
108,1,291,0,0.332671," ","integrate((a+b*arccoth(d*x+c))/(f*x+e)^3,x, algorithm=""maxima"")","\frac{1}{4} \, {\left(d {\left(\frac{d \log\left(d x + c + 1\right)}{d^{2} e^{2} f - 2 \, {\left(c + 1\right)} d e f^{2} + {\left(c^{2} + 2 \, c + 1\right)} f^{3}} - \frac{d \log\left(d x + c - 1\right)}{d^{2} e^{2} f - 2 \, {\left(c - 1\right)} d e f^{2} + {\left(c^{2} - 2 \, c + 1\right)} f^{3}} - \frac{4 \, {\left(d^{2} e - c d f\right)} \log\left(f x + e\right)}{d^{4} e^{4} - 4 \, c d^{3} e^{3} f + 2 \, {\left(3 \, c^{2} - 1\right)} d^{2} e^{2} f^{2} - 4 \, {\left(c^{3} - c\right)} d e f^{3} + {\left(c^{4} - 2 \, c^{2} + 1\right)} f^{4}} + \frac{2}{d^{2} e^{3} - 2 \, c d e^{2} f + {\left(c^{2} - 1\right)} e f^{2} + {\left(d^{2} e^{2} f - 2 \, c d e f^{2} + {\left(c^{2} - 1\right)} f^{3}\right)} x}\right)} - \frac{2 \, \operatorname{arcoth}\left(d x + c\right)}{f^{3} x^{2} + 2 \, e f^{2} x + e^{2} f}\right)} b - \frac{a}{2 \, {\left(f^{3} x^{2} + 2 \, e f^{2} x + e^{2} f\right)}}"," ",0,"1/4*(d*(d*log(d*x + c + 1)/(d^2*e^2*f - 2*(c + 1)*d*e*f^2 + (c^2 + 2*c + 1)*f^3) - d*log(d*x + c - 1)/(d^2*e^2*f - 2*(c - 1)*d*e*f^2 + (c^2 - 2*c + 1)*f^3) - 4*(d^2*e - c*d*f)*log(f*x + e)/(d^4*e^4 - 4*c*d^3*e^3*f + 2*(3*c^2 - 1)*d^2*e^2*f^2 - 4*(c^3 - c)*d*e*f^3 + (c^4 - 2*c^2 + 1)*f^4) + 2/(d^2*e^3 - 2*c*d*e^2*f + (c^2 - 1)*e*f^2 + (d^2*e^2*f - 2*c*d*e*f^2 + (c^2 - 1)*f^3)*x)) - 2*arccoth(d*x + c)/(f^3*x^2 + 2*e*f^2*x + e^2*f))*b - 1/2*a/(f^3*x^2 + 2*e*f^2*x + e^2*f)","A",0
109,1,791,0,0.617503," ","integrate((f*x+e)^2*(a+b*arccoth(d*x+c))^2,x, algorithm=""maxima"")","\frac{1}{3} \, a^{2} f^{2} x^{3} + a^{2} e f x^{2} + {\left(2 \, x^{2} \operatorname{arcoth}\left(d x + c\right) + d {\left(\frac{2 \, x}{d^{2}} - \frac{{\left(c^{2} + 2 \, c + 1\right)} \log\left(d x + c + 1\right)}{d^{3}} + \frac{{\left(c^{2} - 2 \, c + 1\right)} \log\left(d x + c - 1\right)}{d^{3}}\right)}\right)} a b e f + \frac{1}{3} \, {\left(2 \, x^{3} \operatorname{arcoth}\left(d x + c\right) + d {\left(\frac{d x^{2} - 4 \, c x}{d^{3}} + \frac{{\left(c^{3} + 3 \, c^{2} + 3 \, c + 1\right)} \log\left(d x + c + 1\right)}{d^{4}} - \frac{{\left(c^{3} - 3 \, c^{2} + 3 \, c - 1\right)} \log\left(d x + c - 1\right)}{d^{4}}\right)}\right)} a b f^{2} + a^{2} e^{2} x + \frac{{\left(2 \, {\left(d x + c\right)} \operatorname{arcoth}\left(d x + c\right) + \log\left(-{\left(d x + c\right)}^{2} + 1\right)\right)} a b e^{2}}{d} - \frac{{\left(3 \, d^{2} e^{2} - 6 \, c d e f + 3 \, c^{2} f^{2} + f^{2}\right)} {\left(\log\left(d x + c - 1\right) \log\left(\frac{1}{2} \, d x + \frac{1}{2} \, c + \frac{1}{2}\right) + {\rm Li}_2\left(-\frac{1}{2} \, d x - \frac{1}{2} \, c + \frac{1}{2}\right)\right)} b^{2}}{3 \, d^{3}} - \frac{{\left(5 \, c^{2} f^{2} - 6 \, d e f - 6 \, {\left(d e f - f^{2}\right)} c + f^{2}\right)} b^{2} \log\left(d x + c + 1\right)}{6 \, d^{3}} + \frac{4 \, b^{2} d f^{2} x + {\left(b^{2} d^{3} f^{2} x^{3} + 3 \, b^{2} d^{3} e f x^{2} + 3 \, b^{2} d^{3} e^{2} x + {\left(c^{3} f^{2} + 3 \, d^{2} e^{2} - 3 \, {\left(d e f - f^{2}\right)} c^{2} - 3 \, d e f + 3 \, {\left(d^{2} e^{2} - 2 \, d e f + f^{2}\right)} c + f^{2}\right)} b^{2}\right)} \log\left(d x + c + 1\right)^{2} + {\left(b^{2} d^{3} f^{2} x^{3} + 3 \, b^{2} d^{3} e f x^{2} + 3 \, b^{2} d^{3} e^{2} x + {\left(c^{3} f^{2} - 3 \, d^{2} e^{2} - 3 \, {\left(d e f + f^{2}\right)} c^{2} - 3 \, d e f + 3 \, {\left(d^{2} e^{2} + 2 \, d e f + f^{2}\right)} c - f^{2}\right)} b^{2}\right)} \log\left(d x + c - 1\right)^{2} + 2 \, {\left(b^{2} d^{2} f^{2} x^{2} + 2 \, {\left(3 \, d^{2} e f - 2 \, c d f^{2}\right)} b^{2} x - {\left(b^{2} d^{3} f^{2} x^{3} + 3 \, b^{2} d^{3} e f x^{2} + 3 \, b^{2} d^{3} e^{2} x + {\left(c^{3} f^{2} - 3 \, d^{2} e^{2} - 3 \, {\left(d e f + f^{2}\right)} c^{2} - 3 \, d e f + 3 \, {\left(d^{2} e^{2} + 2 \, d e f + f^{2}\right)} c - f^{2}\right)} b^{2}\right)} \log\left(d x + c - 1\right)\right)} \log\left(d x + c + 1\right) - 2 \, {\left(b^{2} d^{2} f^{2} x^{2} + 2 \, {\left(3 \, d^{2} e f - 2 \, c d f^{2}\right)} b^{2} x - {\left(5 \, c^{2} f^{2} + 6 \, d e f - 6 \, {\left(d e f + f^{2}\right)} c + f^{2}\right)} b^{2}\right)} \log\left(d x + c - 1\right)}{12 \, d^{3}}"," ",0,"1/3*a^2*f^2*x^3 + a^2*e*f*x^2 + (2*x^2*arccoth(d*x + c) + d*(2*x/d^2 - (c^2 + 2*c + 1)*log(d*x + c + 1)/d^3 + (c^2 - 2*c + 1)*log(d*x + c - 1)/d^3))*a*b*e*f + 1/3*(2*x^3*arccoth(d*x + c) + d*((d*x^2 - 4*c*x)/d^3 + (c^3 + 3*c^2 + 3*c + 1)*log(d*x + c + 1)/d^4 - (c^3 - 3*c^2 + 3*c - 1)*log(d*x + c - 1)/d^4))*a*b*f^2 + a^2*e^2*x + (2*(d*x + c)*arccoth(d*x + c) + log(-(d*x + c)^2 + 1))*a*b*e^2/d - 1/3*(3*d^2*e^2 - 6*c*d*e*f + 3*c^2*f^2 + f^2)*(log(d*x + c - 1)*log(1/2*d*x + 1/2*c + 1/2) + dilog(-1/2*d*x - 1/2*c + 1/2))*b^2/d^3 - 1/6*(5*c^2*f^2 - 6*d*e*f - 6*(d*e*f - f^2)*c + f^2)*b^2*log(d*x + c + 1)/d^3 + 1/12*(4*b^2*d*f^2*x + (b^2*d^3*f^2*x^3 + 3*b^2*d^3*e*f*x^2 + 3*b^2*d^3*e^2*x + (c^3*f^2 + 3*d^2*e^2 - 3*(d*e*f - f^2)*c^2 - 3*d*e*f + 3*(d^2*e^2 - 2*d*e*f + f^2)*c + f^2)*b^2)*log(d*x + c + 1)^2 + (b^2*d^3*f^2*x^3 + 3*b^2*d^3*e*f*x^2 + 3*b^2*d^3*e^2*x + (c^3*f^2 - 3*d^2*e^2 - 3*(d*e*f + f^2)*c^2 - 3*d*e*f + 3*(d^2*e^2 + 2*d*e*f + f^2)*c - f^2)*b^2)*log(d*x + c - 1)^2 + 2*(b^2*d^2*f^2*x^2 + 2*(3*d^2*e*f - 2*c*d*f^2)*b^2*x - (b^2*d^3*f^2*x^3 + 3*b^2*d^3*e*f*x^2 + 3*b^2*d^3*e^2*x + (c^3*f^2 - 3*d^2*e^2 - 3*(d*e*f + f^2)*c^2 - 3*d*e*f + 3*(d^2*e^2 + 2*d*e*f + f^2)*c - f^2)*b^2)*log(d*x + c - 1))*log(d*x + c + 1) - 2*(b^2*d^2*f^2*x^2 + 2*(3*d^2*e*f - 2*c*d*f^2)*b^2*x - (5*c^2*f^2 + 6*d*e*f - 6*(d*e*f + f^2)*c + f^2)*b^2)*log(d*x + c - 1))/d^3","B",0
110,1,400,0,0.612311," ","integrate((f*x+e)*(a+b*arccoth(d*x+c))^2,x, algorithm=""maxima"")","\frac{1}{2} \, a^{2} f x^{2} + \frac{1}{2} \, {\left(2 \, x^{2} \operatorname{arcoth}\left(d x + c\right) + d {\left(\frac{2 \, x}{d^{2}} - \frac{{\left(c^{2} + 2 \, c + 1\right)} \log\left(d x + c + 1\right)}{d^{3}} + \frac{{\left(c^{2} - 2 \, c + 1\right)} \log\left(d x + c - 1\right)}{d^{3}}\right)}\right)} a b f + a^{2} e x + \frac{{\left(2 \, {\left(d x + c\right)} \operatorname{arcoth}\left(d x + c\right) + \log\left(-{\left(d x + c\right)}^{2} + 1\right)\right)} a b e}{d} - \frac{{\left(d e - c f\right)} {\left(\log\left(d x + c - 1\right) \log\left(\frac{1}{2} \, d x + \frac{1}{2} \, c + \frac{1}{2}\right) + {\rm Li}_2\left(-\frac{1}{2} \, d x - \frac{1}{2} \, c + \frac{1}{2}\right)\right)} b^{2}}{d^{2}} + \frac{{\left(c f + f\right)} b^{2} \log\left(d x + c + 1\right)}{2 \, d^{2}} + \frac{{\left(b^{2} d^{2} f x^{2} + 2 \, b^{2} d^{2} e x - {\left(c^{2} f - 2 \, {\left(d e - f\right)} c - 2 \, d e + f\right)} b^{2}\right)} \log\left(d x + c + 1\right)^{2} + {\left(b^{2} d^{2} f x^{2} + 2 \, b^{2} d^{2} e x - {\left(c^{2} f - 2 \, {\left(d e + f\right)} c + 2 \, d e + f\right)} b^{2}\right)} \log\left(d x + c - 1\right)^{2} + 2 \, {\left(2 \, b^{2} d f x - {\left(b^{2} d^{2} f x^{2} + 2 \, b^{2} d^{2} e x - {\left(c^{2} f - 2 \, {\left(d e + f\right)} c + 2 \, d e + f\right)} b^{2}\right)} \log\left(d x + c - 1\right)\right)} \log\left(d x + c + 1\right) - 4 \, {\left(b^{2} d f x + {\left(c f - f\right)} b^{2}\right)} \log\left(d x + c - 1\right)}{8 \, d^{2}}"," ",0,"1/2*a^2*f*x^2 + 1/2*(2*x^2*arccoth(d*x + c) + d*(2*x/d^2 - (c^2 + 2*c + 1)*log(d*x + c + 1)/d^3 + (c^2 - 2*c + 1)*log(d*x + c - 1)/d^3))*a*b*f + a^2*e*x + (2*(d*x + c)*arccoth(d*x + c) + log(-(d*x + c)^2 + 1))*a*b*e/d - (d*e - c*f)*(log(d*x + c - 1)*log(1/2*d*x + 1/2*c + 1/2) + dilog(-1/2*d*x - 1/2*c + 1/2))*b^2/d^2 + 1/2*(c*f + f)*b^2*log(d*x + c + 1)/d^2 + 1/8*((b^2*d^2*f*x^2 + 2*b^2*d^2*e*x - (c^2*f - 2*(d*e - f)*c - 2*d*e + f)*b^2)*log(d*x + c + 1)^2 + (b^2*d^2*f*x^2 + 2*b^2*d^2*e*x - (c^2*f - 2*(d*e + f)*c + 2*d*e + f)*b^2)*log(d*x + c - 1)^2 + 2*(2*b^2*d*f*x - (b^2*d^2*f*x^2 + 2*b^2*d^2*e*x - (c^2*f - 2*(d*e + f)*c + 2*d*e + f)*b^2)*log(d*x + c - 1))*log(d*x + c + 1) - 4*(b^2*d*f*x + (c*f - f)*b^2)*log(d*x + c - 1))/d^2","A",0
111,0,0,0,0.000000," ","integrate((a+b*arccoth(d*x+c))^2,x, algorithm=""maxima"")","a^{2} x + \frac{1}{4} \, b^{2} {\left(\frac{d x \log\left(d x + c - 1\right)^{2} + {\left(d x + c + 1\right)} \log\left(d x + c + 1\right)^{2} - 2 \, {\left(d x + c - 1\right)} \log\left(d x + c + 1\right) \log\left(d x + c - 1\right)}{d} + \int \frac{2 \, {\left(c^{2} + {\left(c d - 3 \, d\right)} x - 2 \, c + 1\right)} \log\left(d x + c - 1\right)}{d^{2} x^{2} + 2 \, c d x + c^{2} - 1}\,{d x}\right)} + \frac{{\left(2 \, {\left(d x + c\right)} \operatorname{arcoth}\left(d x + c\right) + \log\left(-{\left(d x + c\right)}^{2} + 1\right)\right)} a b}{d}"," ",0,"a^2*x + 1/4*b^2*((d*x*log(d*x + c - 1)^2 + (d*x + c + 1)*log(d*x + c + 1)^2 - 2*(d*x + c - 1)*log(d*x + c + 1)*log(d*x + c - 1))/d + integrate(2*(c^2 + (c*d - 3*d)*x - 2*c + 1)*log(d*x + c - 1)/(d^2*x^2 + 2*c*d*x + c^2 - 1), x)) + (2*(d*x + c)*arccoth(d*x + c) + log(-(d*x + c)^2 + 1))*a*b/d","F",0
112,0,0,0,0.000000," ","integrate((a+b*arccoth(d*x+c))^2/(f*x+e),x, algorithm=""maxima"")","\frac{a^{2} \log\left(f x + e\right)}{f} + \int \frac{b^{2} {\left(\log\left(\frac{1}{d x + c} + 1\right) - \log\left(-\frac{1}{d x + c} + 1\right)\right)}^{2}}{4 \, {\left(f x + e\right)}} + \frac{a b {\left(\log\left(\frac{1}{d x + c} + 1\right) - \log\left(-\frac{1}{d x + c} + 1\right)\right)}}{f x + e}\,{d x}"," ",0,"a^2*log(f*x + e)/f + integrate(1/4*b^2*(log(1/(d*x + c) + 1) - log(-1/(d*x + c) + 1))^2/(f*x + e) + a*b*(log(1/(d*x + c) + 1) - log(-1/(d*x + c) + 1))/(f*x + e), x)","F",0
113,0,0,0,0.000000," ","integrate((a+b*arccoth(d*x+c))^2/(f*x+e)^2,x, algorithm=""maxima"")","{\left(d {\left(\frac{\log\left(d x + c + 1\right)}{d e f - {\left(c + 1\right)} f^{2}} - \frac{\log\left(d x + c - 1\right)}{d e f - {\left(c - 1\right)} f^{2}} - \frac{2 \, \log\left(f x + e\right)}{d^{2} e^{2} - 2 \, c d e f + {\left(c^{2} - 1\right)} f^{2}}\right)} - \frac{2 \, \operatorname{arcoth}\left(d x + c\right)}{f^{2} x + e f}\right)} a b - \frac{1}{4} \, b^{2} {\left(\frac{\log\left(d x + c + 1\right)^{2}}{f^{2} x + e f} + \int -\frac{{\left(d f x + c f + f\right)} \log\left(d x + c - 1\right)^{2} + 2 \, {\left(d f x + d e - {\left(d f x + c f + f\right)} \log\left(d x + c - 1\right)\right)} \log\left(d x + c + 1\right)}{d f^{3} x^{3} + c e^{2} f + e^{2} f + {\left(2 \, d e f^{2} + c f^{3} + f^{3}\right)} x^{2} + {\left(d e^{2} f + 2 \, c e f^{2} + 2 \, e f^{2}\right)} x}\,{d x}\right)} - \frac{a^{2}}{f^{2} x + e f}"," ",0,"(d*(log(d*x + c + 1)/(d*e*f - (c + 1)*f^2) - log(d*x + c - 1)/(d*e*f - (c - 1)*f^2) - 2*log(f*x + e)/(d^2*e^2 - 2*c*d*e*f + (c^2 - 1)*f^2)) - 2*arccoth(d*x + c)/(f^2*x + e*f))*a*b - 1/4*b^2*(log(d*x + c + 1)^2/(f^2*x + e*f) + integrate(-((d*f*x + c*f + f)*log(d*x + c - 1)^2 + 2*(d*f*x + d*e - (d*f*x + c*f + f)*log(d*x + c - 1))*log(d*x + c + 1))/(d*f^3*x^3 + c*e^2*f + e^2*f + (2*d*e*f^2 + c*f^3 + f^3)*x^2 + (d*e^2*f + 2*c*e*f^2 + 2*e*f^2)*x), x)) - a^2/(f^2*x + e*f)","F",0
114,0,0,0,0.000000," ","integrate((f*x+e)^2*(a+b*arccoth(d*x+c))^3,x, algorithm=""maxima"")","\frac{1}{3} \, a^{3} f^{2} x^{3} + a^{3} e f x^{2} + \frac{3}{2} \, {\left(2 \, x^{2} \operatorname{arcoth}\left(d x + c\right) + d {\left(\frac{2 \, x}{d^{2}} - \frac{{\left(c^{2} + 2 \, c + 1\right)} \log\left(d x + c + 1\right)}{d^{3}} + \frac{{\left(c^{2} - 2 \, c + 1\right)} \log\left(d x + c - 1\right)}{d^{3}}\right)}\right)} a^{2} b e f + \frac{1}{2} \, {\left(2 \, x^{3} \operatorname{arcoth}\left(d x + c\right) + d {\left(\frac{d x^{2} - 4 \, c x}{d^{3}} + \frac{{\left(c^{3} + 3 \, c^{2} + 3 \, c + 1\right)} \log\left(d x + c + 1\right)}{d^{4}} - \frac{{\left(c^{3} - 3 \, c^{2} + 3 \, c - 1\right)} \log\left(d x + c - 1\right)}{d^{4}}\right)}\right)} a^{2} b f^{2} + a^{3} e^{2} x + \frac{3 \, {\left(2 \, {\left(d x + c\right)} \operatorname{arcoth}\left(d x + c\right) + \log\left(-{\left(d x + c\right)}^{2} + 1\right)\right)} a^{2} b e^{2}}{2 \, d} + \frac{{\left(b^{3} d^{3} f^{2} x^{3} + 3 \, b^{3} d^{3} e f x^{2} + 3 \, b^{3} d^{3} e^{2} x + {\left(c^{3} f^{2} + 3 \, d^{2} e^{2} - 3 \, {\left(d e f - f^{2}\right)} c^{2} - 3 \, d e f + 3 \, {\left(d^{2} e^{2} - 2 \, d e f + f^{2}\right)} c + f^{2}\right)} b^{3}\right)} \log\left(d x + c + 1\right)^{3} + 3 \, {\left(2 \, a b^{2} d^{3} f^{2} x^{3} + {\left(6 \, a b^{2} d^{3} e f + b^{3} d^{2} f^{2}\right)} x^{2} + 2 \, {\left(3 \, a b^{2} d^{3} e^{2} + {\left(3 \, d^{2} e f - 2 \, c d f^{2}\right)} b^{3}\right)} x - {\left(b^{3} d^{3} f^{2} x^{3} + 3 \, b^{3} d^{3} e f x^{2} + 3 \, b^{3} d^{3} e^{2} x + {\left(c^{3} f^{2} - 3 \, d^{2} e^{2} - 3 \, {\left(d e f + f^{2}\right)} c^{2} - 3 \, d e f + 3 \, {\left(d^{2} e^{2} + 2 \, d e f + f^{2}\right)} c - f^{2}\right)} b^{3}\right)} \log\left(d x + c - 1\right)\right)} \log\left(d x + c + 1\right)^{2}}{24 \, d^{3}} + \int -\frac{{\left(b^{3} d^{3} f^{2} x^{3} + {\left(2 \, d^{3} e f + c d^{2} f^{2} + d^{2} f^{2}\right)} b^{3} x^{2} + {\left(d^{3} e^{2} + 2 \, c d^{2} e f + 2 \, d^{2} e f\right)} b^{3} x + {\left(c d^{2} e^{2} + d^{2} e^{2}\right)} b^{3}\right)} \log\left(d x + c - 1\right)^{3} - 6 \, {\left(a b^{2} d^{3} f^{2} x^{3} + {\left(2 \, d^{3} e f + c d^{2} f^{2} + d^{2} f^{2}\right)} a b^{2} x^{2} + {\left(d^{3} e^{2} + 2 \, c d^{2} e f + 2 \, d^{2} e f\right)} a b^{2} x + {\left(c d^{2} e^{2} + d^{2} e^{2}\right)} a b^{2}\right)} \log\left(d x + c - 1\right)^{2} + {\left(4 \, a b^{2} d^{3} f^{2} x^{3} + 2 \, {\left(6 \, a b^{2} d^{3} e f + b^{3} d^{2} f^{2}\right)} x^{2} - 3 \, {\left(b^{3} d^{3} f^{2} x^{3} + {\left(2 \, d^{3} e f + c d^{2} f^{2} + d^{2} f^{2}\right)} b^{3} x^{2} + {\left(d^{3} e^{2} + 2 \, c d^{2} e f + 2 \, d^{2} e f\right)} b^{3} x + {\left(c d^{2} e^{2} + d^{2} e^{2}\right)} b^{3}\right)} \log\left(d x + c - 1\right)^{2} + 4 \, {\left(3 \, a b^{2} d^{3} e^{2} + {\left(3 \, d^{2} e f - 2 \, c d f^{2}\right)} b^{3}\right)} x + 2 \, {\left(6 \, {\left(c d^{2} e^{2} + d^{2} e^{2}\right)} a b^{2} - {\left(c^{3} f^{2} - 3 \, d^{2} e^{2} - 3 \, {\left(d e f + f^{2}\right)} c^{2} - 3 \, d e f + 3 \, {\left(d^{2} e^{2} + 2 \, d e f + f^{2}\right)} c - f^{2}\right)} b^{3} + {\left(6 \, a b^{2} d^{3} f^{2} - b^{3} d^{3} f^{2}\right)} x^{3} - 3 \, {\left(b^{3} d^{3} e f - 2 \, {\left(2 \, d^{3} e f + c d^{2} f^{2} + d^{2} f^{2}\right)} a b^{2}\right)} x^{2} - 3 \, {\left(b^{3} d^{3} e^{2} - 2 \, {\left(d^{3} e^{2} + 2 \, c d^{2} e f + 2 \, d^{2} e f\right)} a b^{2}\right)} x\right)} \log\left(d x + c - 1\right)\right)} \log\left(d x + c + 1\right)}{8 \, {\left(d^{3} x + c d^{2} + d^{2}\right)}}\,{d x}"," ",0,"1/3*a^3*f^2*x^3 + a^3*e*f*x^2 + 3/2*(2*x^2*arccoth(d*x + c) + d*(2*x/d^2 - (c^2 + 2*c + 1)*log(d*x + c + 1)/d^3 + (c^2 - 2*c + 1)*log(d*x + c - 1)/d^3))*a^2*b*e*f + 1/2*(2*x^3*arccoth(d*x + c) + d*((d*x^2 - 4*c*x)/d^3 + (c^3 + 3*c^2 + 3*c + 1)*log(d*x + c + 1)/d^4 - (c^3 - 3*c^2 + 3*c - 1)*log(d*x + c - 1)/d^4))*a^2*b*f^2 + a^3*e^2*x + 3/2*(2*(d*x + c)*arccoth(d*x + c) + log(-(d*x + c)^2 + 1))*a^2*b*e^2/d + 1/24*((b^3*d^3*f^2*x^3 + 3*b^3*d^3*e*f*x^2 + 3*b^3*d^3*e^2*x + (c^3*f^2 + 3*d^2*e^2 - 3*(d*e*f - f^2)*c^2 - 3*d*e*f + 3*(d^2*e^2 - 2*d*e*f + f^2)*c + f^2)*b^3)*log(d*x + c + 1)^3 + 3*(2*a*b^2*d^3*f^2*x^3 + (6*a*b^2*d^3*e*f + b^3*d^2*f^2)*x^2 + 2*(3*a*b^2*d^3*e^2 + (3*d^2*e*f - 2*c*d*f^2)*b^3)*x - (b^3*d^3*f^2*x^3 + 3*b^3*d^3*e*f*x^2 + 3*b^3*d^3*e^2*x + (c^3*f^2 - 3*d^2*e^2 - 3*(d*e*f + f^2)*c^2 - 3*d*e*f + 3*(d^2*e^2 + 2*d*e*f + f^2)*c - f^2)*b^3)*log(d*x + c - 1))*log(d*x + c + 1)^2)/d^3 + integrate(-1/8*((b^3*d^3*f^2*x^3 + (2*d^3*e*f + c*d^2*f^2 + d^2*f^2)*b^3*x^2 + (d^3*e^2 + 2*c*d^2*e*f + 2*d^2*e*f)*b^3*x + (c*d^2*e^2 + d^2*e^2)*b^3)*log(d*x + c - 1)^3 - 6*(a*b^2*d^3*f^2*x^3 + (2*d^3*e*f + c*d^2*f^2 + d^2*f^2)*a*b^2*x^2 + (d^3*e^2 + 2*c*d^2*e*f + 2*d^2*e*f)*a*b^2*x + (c*d^2*e^2 + d^2*e^2)*a*b^2)*log(d*x + c - 1)^2 + (4*a*b^2*d^3*f^2*x^3 + 2*(6*a*b^2*d^3*e*f + b^3*d^2*f^2)*x^2 - 3*(b^3*d^3*f^2*x^3 + (2*d^3*e*f + c*d^2*f^2 + d^2*f^2)*b^3*x^2 + (d^3*e^2 + 2*c*d^2*e*f + 2*d^2*e*f)*b^3*x + (c*d^2*e^2 + d^2*e^2)*b^3)*log(d*x + c - 1)^2 + 4*(3*a*b^2*d^3*e^2 + (3*d^2*e*f - 2*c*d*f^2)*b^3)*x + 2*(6*(c*d^2*e^2 + d^2*e^2)*a*b^2 - (c^3*f^2 - 3*d^2*e^2 - 3*(d*e*f + f^2)*c^2 - 3*d*e*f + 3*(d^2*e^2 + 2*d*e*f + f^2)*c - f^2)*b^3 + (6*a*b^2*d^3*f^2 - b^3*d^3*f^2)*x^3 - 3*(b^3*d^3*e*f - 2*(2*d^3*e*f + c*d^2*f^2 + d^2*f^2)*a*b^2)*x^2 - 3*(b^3*d^3*e^2 - 2*(d^3*e^2 + 2*c*d^2*e*f + 2*d^2*e*f)*a*b^2)*x)*log(d*x + c - 1))*log(d*x + c + 1))/(d^3*x + c*d^2 + d^2), x)","F",0
115,0,0,0,0.000000," ","integrate((f*x+e)*(a+b*arccoth(d*x+c))^3,x, algorithm=""maxima"")","\frac{1}{2} \, a^{3} f x^{2} + \frac{3}{4} \, {\left(2 \, x^{2} \operatorname{arcoth}\left(d x + c\right) + d {\left(\frac{2 \, x}{d^{2}} - \frac{{\left(c^{2} + 2 \, c + 1\right)} \log\left(d x + c + 1\right)}{d^{3}} + \frac{{\left(c^{2} - 2 \, c + 1\right)} \log\left(d x + c - 1\right)}{d^{3}}\right)}\right)} a^{2} b f + a^{3} e x + \frac{3 \, {\left(2 \, {\left(d x + c\right)} \operatorname{arcoth}\left(d x + c\right) + \log\left(-{\left(d x + c\right)}^{2} + 1\right)\right)} a^{2} b e}{2 \, d} + \frac{{\left(b^{3} d^{2} f x^{2} + 2 \, b^{3} d^{2} e x - {\left(c^{2} f - 2 \, {\left(d e - f\right)} c - 2 \, d e + f\right)} b^{3}\right)} \log\left(d x + c + 1\right)^{3} + 3 \, {\left(2 \, a b^{2} d^{2} f x^{2} + 2 \, {\left(2 \, a b^{2} d^{2} e + b^{3} d f\right)} x - {\left(b^{3} d^{2} f x^{2} + 2 \, b^{3} d^{2} e x - {\left(c^{2} f - 2 \, {\left(d e + f\right)} c + 2 \, d e + f\right)} b^{3}\right)} \log\left(d x + c - 1\right)\right)} \log\left(d x + c + 1\right)^{2}}{16 \, d^{2}} + \int -\frac{{\left(b^{3} d^{2} f x^{2} + {\left(d^{2} e + c d f + d f\right)} b^{3} x + {\left(c d e + d e\right)} b^{3}\right)} \log\left(d x + c - 1\right)^{3} - 6 \, {\left(a b^{2} d^{2} f x^{2} + {\left(d^{2} e + c d f + d f\right)} a b^{2} x + {\left(c d e + d e\right)} a b^{2}\right)} \log\left(d x + c - 1\right)^{2} + 3 \, {\left(2 \, a b^{2} d^{2} f x^{2} - {\left(b^{3} d^{2} f x^{2} + {\left(d^{2} e + c d f + d f\right)} b^{3} x + {\left(c d e + d e\right)} b^{3}\right)} \log\left(d x + c - 1\right)^{2} + 2 \, {\left(2 \, a b^{2} d^{2} e + b^{3} d f\right)} x + {\left(4 \, {\left(c d e + d e\right)} a b^{2} + {\left(c^{2} f - 2 \, {\left(d e + f\right)} c + 2 \, d e + f\right)} b^{3} + {\left(4 \, a b^{2} d^{2} f - b^{3} d^{2} f\right)} x^{2} - 2 \, {\left(b^{3} d^{2} e - 2 \, {\left(d^{2} e + c d f + d f\right)} a b^{2}\right)} x\right)} \log\left(d x + c - 1\right)\right)} \log\left(d x + c + 1\right)}{8 \, {\left(d^{2} x + c d + d\right)}}\,{d x}"," ",0,"1/2*a^3*f*x^2 + 3/4*(2*x^2*arccoth(d*x + c) + d*(2*x/d^2 - (c^2 + 2*c + 1)*log(d*x + c + 1)/d^3 + (c^2 - 2*c + 1)*log(d*x + c - 1)/d^3))*a^2*b*f + a^3*e*x + 3/2*(2*(d*x + c)*arccoth(d*x + c) + log(-(d*x + c)^2 + 1))*a^2*b*e/d + 1/16*((b^3*d^2*f*x^2 + 2*b^3*d^2*e*x - (c^2*f - 2*(d*e - f)*c - 2*d*e + f)*b^3)*log(d*x + c + 1)^3 + 3*(2*a*b^2*d^2*f*x^2 + 2*(2*a*b^2*d^2*e + b^3*d*f)*x - (b^3*d^2*f*x^2 + 2*b^3*d^2*e*x - (c^2*f - 2*(d*e + f)*c + 2*d*e + f)*b^3)*log(d*x + c - 1))*log(d*x + c + 1)^2)/d^2 + integrate(-1/8*((b^3*d^2*f*x^2 + (d^2*e + c*d*f + d*f)*b^3*x + (c*d*e + d*e)*b^3)*log(d*x + c - 1)^3 - 6*(a*b^2*d^2*f*x^2 + (d^2*e + c*d*f + d*f)*a*b^2*x + (c*d*e + d*e)*a*b^2)*log(d*x + c - 1)^2 + 3*(2*a*b^2*d^2*f*x^2 - (b^3*d^2*f*x^2 + (d^2*e + c*d*f + d*f)*b^3*x + (c*d*e + d*e)*b^3)*log(d*x + c - 1)^2 + 2*(2*a*b^2*d^2*e + b^3*d*f)*x + (4*(c*d*e + d*e)*a*b^2 + (c^2*f - 2*(d*e + f)*c + 2*d*e + f)*b^3 + (4*a*b^2*d^2*f - b^3*d^2*f)*x^2 - 2*(b^3*d^2*e - 2*(d^2*e + c*d*f + d*f)*a*b^2)*x)*log(d*x + c - 1))*log(d*x + c + 1))/(d^2*x + c*d + d), x)","F",0
116,0,0,0,0.000000," ","integrate((a+b*arccoth(d*x+c))^3,x, algorithm=""maxima"")","a^{3} x + \frac{3 \, {\left(2 \, {\left(d x + c\right)} \operatorname{arcoth}\left(d x + c\right) + \log\left(-{\left(d x + c\right)}^{2} + 1\right)\right)} a^{2} b}{2 \, d} + \frac{{\left(b^{3} d x + b^{3} {\left(c + 1\right)}\right)} \log\left(d x + c + 1\right)^{3} + 3 \, {\left(2 \, a b^{2} d x - {\left(b^{3} d x + b^{3} {\left(c - 1\right)}\right)} \log\left(d x + c - 1\right)\right)} \log\left(d x + c + 1\right)^{2}}{8 \, d} + \int -\frac{{\left(b^{3} d x + b^{3} {\left(c + 1\right)}\right)} \log\left(d x + c - 1\right)^{3} - 6 \, {\left(a b^{2} d x + a b^{2} {\left(c + 1\right)}\right)} \log\left(d x + c - 1\right)^{2} + 3 \, {\left(4 \, a b^{2} d x - {\left(b^{3} d x + b^{3} {\left(c + 1\right)}\right)} \log\left(d x + c - 1\right)^{2} + 2 \, {\left(2 \, a b^{2} {\left(c + 1\right)} - b^{3} {\left(c - 1\right)} + {\left(2 \, a b^{2} d - b^{3} d\right)} x\right)} \log\left(d x + c - 1\right)\right)} \log\left(d x + c + 1\right)}{8 \, {\left(d x + c + 1\right)}}\,{d x}"," ",0,"a^3*x + 3/2*(2*(d*x + c)*arccoth(d*x + c) + log(-(d*x + c)^2 + 1))*a^2*b/d + 1/8*((b^3*d*x + b^3*(c + 1))*log(d*x + c + 1)^3 + 3*(2*a*b^2*d*x - (b^3*d*x + b^3*(c - 1))*log(d*x + c - 1))*log(d*x + c + 1)^2)/d + integrate(-1/8*((b^3*d*x + b^3*(c + 1))*log(d*x + c - 1)^3 - 6*(a*b^2*d*x + a*b^2*(c + 1))*log(d*x + c - 1)^2 + 3*(4*a*b^2*d*x - (b^3*d*x + b^3*(c + 1))*log(d*x + c - 1)^2 + 2*(2*a*b^2*(c + 1) - b^3*(c - 1) + (2*a*b^2*d - b^3*d)*x)*log(d*x + c - 1))*log(d*x + c + 1))/(d*x + c + 1), x)","F",0
117,0,0,0,0.000000," ","integrate((a+b*arccoth(d*x+c))^3/(f*x+e),x, algorithm=""maxima"")","\frac{a^{3} \log\left(f x + e\right)}{f} + \int \frac{b^{3} {\left(\log\left(\frac{1}{d x + c} + 1\right) - \log\left(-\frac{1}{d x + c} + 1\right)\right)}^{3}}{8 \, {\left(f x + e\right)}} + \frac{3 \, a b^{2} {\left(\log\left(\frac{1}{d x + c} + 1\right) - \log\left(-\frac{1}{d x + c} + 1\right)\right)}^{2}}{4 \, {\left(f x + e\right)}} + \frac{3 \, a^{2} b {\left(\log\left(\frac{1}{d x + c} + 1\right) - \log\left(-\frac{1}{d x + c} + 1\right)\right)}}{2 \, {\left(f x + e\right)}}\,{d x}"," ",0,"a^3*log(f*x + e)/f + integrate(1/8*b^3*(log(1/(d*x + c) + 1) - log(-1/(d*x + c) + 1))^3/(f*x + e) + 3/4*a*b^2*(log(1/(d*x + c) + 1) - log(-1/(d*x + c) + 1))^2/(f*x + e) + 3/2*a^2*b*(log(1/(d*x + c) + 1) - log(-1/(d*x + c) + 1))/(f*x + e), x)","F",0
118,0,0,0,0.000000," ","integrate((a+b*arccoth(d*x+c))^3/(f*x+e)^2,x, algorithm=""maxima"")","\frac{3}{2} \, {\left(d {\left(\frac{\log\left(d x + c + 1\right)}{d e f - {\left(c + 1\right)} f^{2}} - \frac{\log\left(d x + c - 1\right)}{d e f - {\left(c - 1\right)} f^{2}} - \frac{2 \, \log\left(f x + e\right)}{d^{2} e^{2} - 2 \, c d e f + {\left(c^{2} - 1\right)} f^{2}}\right)} - \frac{2 \, \operatorname{arcoth}\left(d x + c\right)}{f^{2} x + e f}\right)} a^{2} b - \frac{a^{3}}{f^{2} x + e f} + \frac{{\left({\left(d^{2} e f - c d f^{2} + d f^{2}\right)} b^{3} x + {\left(c d e f - c^{2} f^{2} + d e f + f^{2}\right)} b^{3}\right)} \log\left(d x + c + 1\right)^{3} - 3 \, {\left(2 \, {\left(d^{2} e^{2} - 2 \, c d e f + c^{2} f^{2} - f^{2}\right)} a b^{2} + {\left({\left(d^{2} e f - c d f^{2} - d f^{2}\right)} b^{3} x + {\left(c d e f - c^{2} f^{2} - d e f + f^{2}\right)} b^{3}\right)} \log\left(d x + c - 1\right)\right)} \log\left(d x + c + 1\right)^{2}}{8 \, {\left(d^{2} e^{3} f - 2 \, c d e^{2} f^{2} + c^{2} e f^{3} - e f^{3} + {\left(d^{2} e^{2} f^{2} - 2 \, c d e f^{3} + c^{2} f^{4} - f^{4}\right)} x\right)}} + \int -\frac{{\left({\left(d^{2} e f - c d f^{2} + d f^{2}\right)} b^{3} x + {\left(c d e f - c^{2} f^{2} + d e f + f^{2}\right)} b^{3}\right)} \log\left(d x + c - 1\right)^{3} - 6 \, {\left({\left(d^{2} e f - c d f^{2} + d f^{2}\right)} a b^{2} x + {\left(c d e f - c^{2} f^{2} + d e f + f^{2}\right)} a b^{2}\right)} \log\left(d x + c - 1\right)^{2} - 3 \, {\left(4 \, {\left(d^{2} e f - c d f^{2} + d f^{2}\right)} a b^{2} x + 4 \, {\left(d^{2} e^{2} - c d e f + d e f\right)} a b^{2} + {\left({\left(d^{2} e f - c d f^{2} + d f^{2}\right)} b^{3} x + {\left(c d e f - c^{2} f^{2} + d e f + f^{2}\right)} b^{3}\right)} \log\left(d x + c - 1\right)^{2} + 2 \, {\left(b^{3} d^{2} f^{2} x^{2} - 2 \, {\left(c d e f - c^{2} f^{2} + d e f + f^{2}\right)} a b^{2} + {\left(c d e f - d e f\right)} b^{3} - {\left(2 \, {\left(d^{2} e f - c d f^{2} + d f^{2}\right)} a b^{2} - {\left(d^{2} e f + c d f^{2} - d f^{2}\right)} b^{3}\right)} x\right)} \log\left(d x + c - 1\right)\right)} \log\left(d x + c + 1\right)}{8 \, {\left(c d e^{3} f - c^{2} e^{2} f^{2} + d e^{3} f + e^{2} f^{2} + {\left(d^{2} e f^{3} - c d f^{4} + d f^{4}\right)} x^{3} + {\left(2 \, d^{2} e^{2} f^{2} - c d e f^{3} - c^{2} f^{4} + 3 \, d e f^{3} + f^{4}\right)} x^{2} + {\left(d^{2} e^{3} f + c d e^{2} f^{2} - 2 \, c^{2} e f^{3} + 3 \, d e^{2} f^{2} + 2 \, e f^{3}\right)} x\right)}}\,{d x}"," ",0,"3/2*(d*(log(d*x + c + 1)/(d*e*f - (c + 1)*f^2) - log(d*x + c - 1)/(d*e*f - (c - 1)*f^2) - 2*log(f*x + e)/(d^2*e^2 - 2*c*d*e*f + (c^2 - 1)*f^2)) - 2*arccoth(d*x + c)/(f^2*x + e*f))*a^2*b - a^3/(f^2*x + e*f) + 1/8*(((d^2*e*f - c*d*f^2 + d*f^2)*b^3*x + (c*d*e*f - c^2*f^2 + d*e*f + f^2)*b^3)*log(d*x + c + 1)^3 - 3*(2*(d^2*e^2 - 2*c*d*e*f + c^2*f^2 - f^2)*a*b^2 + ((d^2*e*f - c*d*f^2 - d*f^2)*b^3*x + (c*d*e*f - c^2*f^2 - d*e*f + f^2)*b^3)*log(d*x + c - 1))*log(d*x + c + 1)^2)/(d^2*e^3*f - 2*c*d*e^2*f^2 + c^2*e*f^3 - e*f^3 + (d^2*e^2*f^2 - 2*c*d*e*f^3 + c^2*f^4 - f^4)*x) + integrate(-1/8*(((d^2*e*f - c*d*f^2 + d*f^2)*b^3*x + (c*d*e*f - c^2*f^2 + d*e*f + f^2)*b^3)*log(d*x + c - 1)^3 - 6*((d^2*e*f - c*d*f^2 + d*f^2)*a*b^2*x + (c*d*e*f - c^2*f^2 + d*e*f + f^2)*a*b^2)*log(d*x + c - 1)^2 - 3*(4*(d^2*e*f - c*d*f^2 + d*f^2)*a*b^2*x + 4*(d^2*e^2 - c*d*e*f + d*e*f)*a*b^2 + ((d^2*e*f - c*d*f^2 + d*f^2)*b^3*x + (c*d*e*f - c^2*f^2 + d*e*f + f^2)*b^3)*log(d*x + c - 1)^2 + 2*(b^3*d^2*f^2*x^2 - 2*(c*d*e*f - c^2*f^2 + d*e*f + f^2)*a*b^2 + (c*d*e*f - d*e*f)*b^3 - (2*(d^2*e*f - c*d*f^2 + d*f^2)*a*b^2 - (d^2*e*f + c*d*f^2 - d*f^2)*b^3)*x)*log(d*x + c - 1))*log(d*x + c + 1))/(c*d*e^3*f - c^2*e^2*f^2 + d*e^3*f + e^2*f^2 + (d^2*e*f^3 - c*d*f^4 + d*f^4)*x^3 + (2*d^2*e^2*f^2 - c*d*e*f^3 - c^2*f^4 + 3*d*e*f^3 + f^4)*x^2 + (d^2*e^3*f + c*d*e^2*f^2 - 2*c^2*e*f^3 + 3*d*e^2*f^2 + 2*e*f^3)*x), x)","F",0
119,0,0,0,0.000000," ","integrate((f*x+e)^m*(a+b*arccoth(d*x+c)),x, algorithm=""maxima"")","\frac{1}{2} \, b {\left(\frac{{\left(f x + e\right)} {\left(f x + e\right)}^{m} \log\left(d x + c + 1\right)}{f {\left(m + 1\right)}} - \int \frac{{\left(d f x + d e + {\left(d f {\left(m + 1\right)} x + c f {\left(m + 1\right)} + f {\left(m + 1\right)}\right)} \log\left(d x + c - 1\right)\right)} {\left(f x + e\right)}^{m}}{d f {\left(m + 1\right)} x + c f {\left(m + 1\right)} + f {\left(m + 1\right)}}\,{d x}\right)} + \frac{{\left(f x + e\right)}^{m + 1} a}{f {\left(m + 1\right)}}"," ",0,"1/2*b*((f*x + e)*(f*x + e)^m*log(d*x + c + 1)/(f*(m + 1)) - integrate((d*f*x + d*e + (d*f*(m + 1)*x + c*f*(m + 1) + f*(m + 1))*log(d*x + c - 1))*(f*x + e)^m/(d*f*(m + 1)*x + c*f*(m + 1) + f*(m + 1)), x)) + (f*x + e)^(m + 1)*a/(f*(m + 1))","F",0
120,0,0,0,0.000000," ","integrate((f*x+e)^m*(a+b*arccoth(d*x+c))^2,x, algorithm=""maxima"")","\frac{{\left(b^{2} f x + b^{2} e\right)} {\left(f x + e\right)}^{m} \log\left(d x + c + 1\right)^{2}}{4 \, f {\left(m + 1\right)}} + \frac{{\left(f x + e\right)}^{m + 1} a^{2}}{f {\left(m + 1\right)}} - \int -\frac{{\left({\left(b^{2} d f {\left(m + 1\right)} x + {\left(c f {\left(m + 1\right)} + f {\left(m + 1\right)}\right)} b^{2}\right)} \log\left(d x + c - 1\right)^{2} - 2 \, {\left(b^{2} d e - 2 \, {\left(c f {\left(m + 1\right)} + f {\left(m + 1\right)}\right)} a b - {\left(2 \, a b d f {\left(m + 1\right)} - b^{2} d f\right)} x + {\left(b^{2} d f {\left(m + 1\right)} x + {\left(c f {\left(m + 1\right)} + f {\left(m + 1\right)}\right)} b^{2}\right)} \log\left(d x + c - 1\right)\right)} \log\left(d x + c + 1\right) - 4 \, {\left(a b d f {\left(m + 1\right)} x + {\left(c f {\left(m + 1\right)} + f {\left(m + 1\right)}\right)} a b\right)} \log\left(d x + c - 1\right)\right)} {\left(f x + e\right)}^{m}}{4 \, {\left(d f {\left(m + 1\right)} x + c f {\left(m + 1\right)} + f {\left(m + 1\right)}\right)}}\,{d x}"," ",0,"1/4*(b^2*f*x + b^2*e)*(f*x + e)^m*log(d*x + c + 1)^2/(f*(m + 1)) + (f*x + e)^(m + 1)*a^2/(f*(m + 1)) - integrate(-1/4*((b^2*d*f*(m + 1)*x + (c*f*(m + 1) + f*(m + 1))*b^2)*log(d*x + c - 1)^2 - 2*(b^2*d*e - 2*(c*f*(m + 1) + f*(m + 1))*a*b - (2*a*b*d*f*(m + 1) - b^2*d*f)*x + (b^2*d*f*(m + 1)*x + (c*f*(m + 1) + f*(m + 1))*b^2)*log(d*x + c - 1))*log(d*x + c + 1) - 4*(a*b*d*f*(m + 1)*x + (c*f*(m + 1) + f*(m + 1))*a*b)*log(d*x + c - 1))*(f*x + e)^m/(d*f*(m + 1)*x + c*f*(m + 1) + f*(m + 1)), x)","F",0
121,0,0,0,0.000000," ","integrate((f*x+e)^m*(a+b*arccoth(d*x+c))^3,x, algorithm=""maxima"")","\frac{{\left(b^{3} f x + b^{3} e\right)} {\left(f x + e\right)}^{m} \log\left(d x + c + 1\right)^{3}}{8 \, f {\left(m + 1\right)}} + \frac{{\left(f x + e\right)}^{m + 1} a^{3}}{f {\left(m + 1\right)}} - \int \frac{{\left({\left(b^{3} d f {\left(m + 1\right)} x + {\left(c f {\left(m + 1\right)} + f {\left(m + 1\right)}\right)} b^{3}\right)} \log\left(d x + c - 1\right)^{3} + 3 \, {\left(b^{3} d e - 2 \, {\left(c f {\left(m + 1\right)} + f {\left(m + 1\right)}\right)} a b^{2} - {\left(2 \, a b^{2} d f {\left(m + 1\right)} - b^{3} d f\right)} x + {\left(b^{3} d f {\left(m + 1\right)} x + {\left(c f {\left(m + 1\right)} + f {\left(m + 1\right)}\right)} b^{3}\right)} \log\left(d x + c - 1\right)\right)} \log\left(d x + c + 1\right)^{2} - 6 \, {\left(a b^{2} d f {\left(m + 1\right)} x + {\left(c f {\left(m + 1\right)} + f {\left(m + 1\right)}\right)} a b^{2}\right)} \log\left(d x + c - 1\right)^{2} - 3 \, {\left(4 \, a^{2} b d f {\left(m + 1\right)} x + 4 \, {\left(c f {\left(m + 1\right)} + f {\left(m + 1\right)}\right)} a^{2} b + {\left(b^{3} d f {\left(m + 1\right)} x + {\left(c f {\left(m + 1\right)} + f {\left(m + 1\right)}\right)} b^{3}\right)} \log\left(d x + c - 1\right)^{2} - 4 \, {\left(a b^{2} d f {\left(m + 1\right)} x + {\left(c f {\left(m + 1\right)} + f {\left(m + 1\right)}\right)} a b^{2}\right)} \log\left(d x + c - 1\right)\right)} \log\left(d x + c + 1\right) + 12 \, {\left(a^{2} b d f {\left(m + 1\right)} x + {\left(c f {\left(m + 1\right)} + f {\left(m + 1\right)}\right)} a^{2} b\right)} \log\left(d x + c - 1\right)\right)} {\left(f x + e\right)}^{m}}{8 \, {\left(d f {\left(m + 1\right)} x + c f {\left(m + 1\right)} + f {\left(m + 1\right)}\right)}}\,{d x}"," ",0,"1/8*(b^3*f*x + b^3*e)*(f*x + e)^m*log(d*x + c + 1)^3/(f*(m + 1)) + (f*x + e)^(m + 1)*a^3/(f*(m + 1)) - integrate(1/8*((b^3*d*f*(m + 1)*x + (c*f*(m + 1) + f*(m + 1))*b^3)*log(d*x + c - 1)^3 + 3*(b^3*d*e - 2*(c*f*(m + 1) + f*(m + 1))*a*b^2 - (2*a*b^2*d*f*(m + 1) - b^3*d*f)*x + (b^3*d*f*(m + 1)*x + (c*f*(m + 1) + f*(m + 1))*b^3)*log(d*x + c - 1))*log(d*x + c + 1)^2 - 6*(a*b^2*d*f*(m + 1)*x + (c*f*(m + 1) + f*(m + 1))*a*b^2)*log(d*x + c - 1)^2 - 3*(4*a^2*b*d*f*(m + 1)*x + 4*(c*f*(m + 1) + f*(m + 1))*a^2*b + (b^3*d*f*(m + 1)*x + (c*f*(m + 1) + f*(m + 1))*b^3)*log(d*x + c - 1)^2 - 4*(a*b^2*d*f*(m + 1)*x + (c*f*(m + 1) + f*(m + 1))*a*b^2)*log(d*x + c - 1))*log(d*x + c + 1) + 12*(a^2*b*d*f*(m + 1)*x + (c*f*(m + 1) + f*(m + 1))*a^2*b)*log(d*x + c - 1))*(f*x + e)^m/(d*f*(m + 1)*x + c*f*(m + 1) + f*(m + 1)), x)","F",0
122,0,0,0,0.000000," ","integrate((a+b*arccoth((-c*x+1)^(1/2)/(c*x+1)^(1/2)))^n/(-c^2*x^2+1),x, algorithm=""maxima"")","-\int \frac{{\left(b \operatorname{arcoth}\left(\frac{\sqrt{-c x + 1}}{\sqrt{c x + 1}}\right) + a\right)}^{n}}{c^{2} x^{2} - 1}\,{d x}"," ",0,"-integrate((b*arccoth(sqrt(-c*x + 1)/sqrt(c*x + 1)) + a)^n/(c^2*x^2 - 1), x)","F",0
123,0,0,0,0.000000," ","integrate((a+b*arccoth((-c*x+1)^(1/2)/(c*x+1)^(1/2)))^3/(-c^2*x^2+1),x, algorithm=""maxima"")","\frac{1}{2} \, a^{3} {\left(\frac{\log\left(c x + 1\right)}{c} - \frac{\log\left(c x - 1\right)}{c}\right)} - \frac{{\left(b^{3} \log\left(c x + 1\right) - b^{3} \log\left(-c x + 1\right)\right)} \log\left(-\sqrt{c x + 1} + \sqrt{-c x + 1}\right)^{3}}{16 \, c} - \int \frac{4 \, {\left(\sqrt{c x + 1} b^{3} - \sqrt{-c x + 1} b^{3}\right)} \log\left(\sqrt{c x + 1} + \sqrt{-c x + 1}\right)^{3} + 24 \, {\left(\sqrt{c x + 1} a b^{2} - \sqrt{-c x + 1} a b^{2}\right)} \log\left(\sqrt{c x + 1} + \sqrt{-c x + 1}\right)^{2} + 3 \, {\left(4 \, {\left(\sqrt{c x + 1} b^{3} - \sqrt{-c x + 1} b^{3}\right)} \log\left(\sqrt{c x + 1} + \sqrt{-c x + 1}\right) + {\left(8 \, a b^{2} - {\left(b^{3} c x - b^{3}\right)} \log\left(c x + 1\right) + {\left(b^{3} c x - b^{3}\right)} \log\left(-c x + 1\right)\right)} \sqrt{c x + 1} - {\left(8 \, a b^{2} - {\left(b^{3} c x + b^{3}\right)} \log\left(c x + 1\right) + {\left(b^{3} c x + b^{3}\right)} \log\left(-c x + 1\right)\right)} \sqrt{-c x + 1}\right)} \log\left(-\sqrt{c x + 1} + \sqrt{-c x + 1}\right)^{2} + 48 \, {\left(\sqrt{c x + 1} a^{2} b - \sqrt{-c x + 1} a^{2} b\right)} \log\left(\sqrt{c x + 1} + \sqrt{-c x + 1}\right) - 12 \, {\left(4 \, \sqrt{c x + 1} a^{2} b - 4 \, \sqrt{-c x + 1} a^{2} b + {\left(\sqrt{c x + 1} b^{3} - \sqrt{-c x + 1} b^{3}\right)} \log\left(\sqrt{c x + 1} + \sqrt{-c x + 1}\right)^{2} + 4 \, {\left(\sqrt{c x + 1} a b^{2} - \sqrt{-c x + 1} a b^{2}\right)} \log\left(\sqrt{c x + 1} + \sqrt{-c x + 1}\right)\right)} \log\left(-\sqrt{c x + 1} + \sqrt{-c x + 1}\right)}{32 \, {\left({\left(c^{2} x^{2} - 1\right)} \sqrt{c x + 1} - {\left(c^{2} x^{2} - 1\right)} \sqrt{-c x + 1}\right)}}\,{d x}"," ",0,"1/2*a^3*(log(c*x + 1)/c - log(c*x - 1)/c) - 1/16*(b^3*log(c*x + 1) - b^3*log(-c*x + 1))*log(-sqrt(c*x + 1) + sqrt(-c*x + 1))^3/c - integrate(1/32*(4*(sqrt(c*x + 1)*b^3 - sqrt(-c*x + 1)*b^3)*log(sqrt(c*x + 1) + sqrt(-c*x + 1))^3 + 24*(sqrt(c*x + 1)*a*b^2 - sqrt(-c*x + 1)*a*b^2)*log(sqrt(c*x + 1) + sqrt(-c*x + 1))^2 + 3*(4*(sqrt(c*x + 1)*b^3 - sqrt(-c*x + 1)*b^3)*log(sqrt(c*x + 1) + sqrt(-c*x + 1)) + (8*a*b^2 - (b^3*c*x - b^3)*log(c*x + 1) + (b^3*c*x - b^3)*log(-c*x + 1))*sqrt(c*x + 1) - (8*a*b^2 - (b^3*c*x + b^3)*log(c*x + 1) + (b^3*c*x + b^3)*log(-c*x + 1))*sqrt(-c*x + 1))*log(-sqrt(c*x + 1) + sqrt(-c*x + 1))^2 + 48*(sqrt(c*x + 1)*a^2*b - sqrt(-c*x + 1)*a^2*b)*log(sqrt(c*x + 1) + sqrt(-c*x + 1)) - 12*(4*sqrt(c*x + 1)*a^2*b - 4*sqrt(-c*x + 1)*a^2*b + (sqrt(c*x + 1)*b^3 - sqrt(-c*x + 1)*b^3)*log(sqrt(c*x + 1) + sqrt(-c*x + 1))^2 + 4*(sqrt(c*x + 1)*a*b^2 - sqrt(-c*x + 1)*a*b^2)*log(sqrt(c*x + 1) + sqrt(-c*x + 1)))*log(-sqrt(c*x + 1) + sqrt(-c*x + 1)))/((c^2*x^2 - 1)*sqrt(c*x + 1) - (c^2*x^2 - 1)*sqrt(-c*x + 1)), x)","F",0
124,0,0,0,0.000000," ","integrate((a+b*arccoth((-c*x+1)^(1/2)/(c*x+1)^(1/2)))^2/(-c^2*x^2+1),x, algorithm=""maxima"")","\frac{1}{2} \, a^{2} {\left(\frac{\log\left(c x + 1\right)}{c} - \frac{\log\left(c x - 1\right)}{c}\right)} + \frac{{\left(b^{2} \log\left(c x + 1\right) - b^{2} \log\left(-c x + 1\right)\right)} \log\left(-\sqrt{c x + 1} + \sqrt{-c x + 1}\right)^{2}}{8 \, c} + \int -\frac{2 \, {\left(\sqrt{c x + 1} b^{2} - \sqrt{-c x + 1} b^{2}\right)} \log\left(\sqrt{c x + 1} + \sqrt{-c x + 1}\right)^{2} + 8 \, {\left(\sqrt{c x + 1} a b - \sqrt{-c x + 1} a b\right)} \log\left(\sqrt{c x + 1} + \sqrt{-c x + 1}\right) - {\left(4 \, {\left(\sqrt{c x + 1} b^{2} - \sqrt{-c x + 1} b^{2}\right)} \log\left(\sqrt{c x + 1} + \sqrt{-c x + 1}\right) + {\left(8 \, a b - {\left(b^{2} c x - b^{2}\right)} \log\left(c x + 1\right) + {\left(b^{2} c x - b^{2}\right)} \log\left(-c x + 1\right)\right)} \sqrt{c x + 1} - {\left(8 \, a b - {\left(b^{2} c x + b^{2}\right)} \log\left(c x + 1\right) + {\left(b^{2} c x + b^{2}\right)} \log\left(-c x + 1\right)\right)} \sqrt{-c x + 1}\right)} \log\left(-\sqrt{c x + 1} + \sqrt{-c x + 1}\right)}{8 \, {\left({\left(c^{2} x^{2} - 1\right)} \sqrt{c x + 1} - {\left(c^{2} x^{2} - 1\right)} \sqrt{-c x + 1}\right)}}\,{d x}"," ",0,"1/2*a^2*(log(c*x + 1)/c - log(c*x - 1)/c) + 1/8*(b^2*log(c*x + 1) - b^2*log(-c*x + 1))*log(-sqrt(c*x + 1) + sqrt(-c*x + 1))^2/c + integrate(-1/8*(2*(sqrt(c*x + 1)*b^2 - sqrt(-c*x + 1)*b^2)*log(sqrt(c*x + 1) + sqrt(-c*x + 1))^2 + 8*(sqrt(c*x + 1)*a*b - sqrt(-c*x + 1)*a*b)*log(sqrt(c*x + 1) + sqrt(-c*x + 1)) - (4*(sqrt(c*x + 1)*b^2 - sqrt(-c*x + 1)*b^2)*log(sqrt(c*x + 1) + sqrt(-c*x + 1)) + (8*a*b - (b^2*c*x - b^2)*log(c*x + 1) + (b^2*c*x - b^2)*log(-c*x + 1))*sqrt(c*x + 1) - (8*a*b - (b^2*c*x + b^2)*log(c*x + 1) + (b^2*c*x + b^2)*log(-c*x + 1))*sqrt(-c*x + 1))*log(-sqrt(c*x + 1) + sqrt(-c*x + 1)))/((c^2*x^2 - 1)*sqrt(c*x + 1) - (c^2*x^2 - 1)*sqrt(-c*x + 1)), x)","F",0
125,0,0,0,0.000000," ","integrate((a+b*arccoth((-c*x+1)^(1/2)/(c*x+1)^(1/2)))/(-c^2*x^2+1),x, algorithm=""maxima"")","\frac{1}{4} \, b {\left(\frac{{\left(\log\left(c x + 1\right) - \log\left(-c x + 1\right)\right)} \log\left(\sqrt{c x + 1} + \sqrt{-c x + 1}\right) - {\left(\log\left(c x + 1\right) - \log\left(-c x + 1\right)\right)} \log\left(-\sqrt{c x + 1} + \sqrt{-c x + 1}\right)}{c} - 2 \, \int -\frac{\sqrt{c x + 1} {\left(\log\left(c x + 1\right) - \log\left(-c x + 1\right)\right)}}{2 \, {\left({\left(c^{2} x^{2} - 1\right)} \sqrt{c x + 1} + {\left(c^{2} x^{2} - 1\right)} \sqrt{-c x + 1}\right)}}\,{d x} - 2 \, \int \frac{\sqrt{c x + 1} {\left(\log\left(c x + 1\right) - \log\left(-c x + 1\right)\right)}}{2 \, {\left({\left(c^{2} x^{2} - 1\right)} \sqrt{c x + 1} - {\left(c^{2} x^{2} - 1\right)} \sqrt{-c x + 1}\right)}}\,{d x}\right)} + \frac{1}{2} \, a {\left(\frac{\log\left(c x + 1\right)}{c} - \frac{\log\left(c x - 1\right)}{c}\right)}"," ",0,"1/4*b*(((log(c*x + 1) - log(-c*x + 1))*log(sqrt(c*x + 1) + sqrt(-c*x + 1)) - (log(c*x + 1) - log(-c*x + 1))*log(-sqrt(c*x + 1) + sqrt(-c*x + 1)))/c - 2*integrate(-1/2*sqrt(c*x + 1)*(log(c*x + 1) - log(-c*x + 1))/((c^2*x^2 - 1)*sqrt(c*x + 1) + (c^2*x^2 - 1)*sqrt(-c*x + 1)), x) - 2*integrate(1/2*sqrt(c*x + 1)*(log(c*x + 1) - log(-c*x + 1))/((c^2*x^2 - 1)*sqrt(c*x + 1) - (c^2*x^2 - 1)*sqrt(-c*x + 1)), x)) + 1/2*a*(log(c*x + 1)/c - log(c*x - 1)/c)","F",0
126,0,0,0,0.000000," ","integrate(1/(-c^2*x^2+1)/(a+b*arccoth((-c*x+1)^(1/2)/(c*x+1)^(1/2))),x, algorithm=""maxima"")","-\int \frac{1}{{\left(c^{2} x^{2} - 1\right)} {\left(b \operatorname{arcoth}\left(\frac{\sqrt{-c x + 1}}{\sqrt{c x + 1}}\right) + a\right)}}\,{d x}"," ",0,"-integrate(1/((c^2*x^2 - 1)*(b*arccoth(sqrt(-c*x + 1)/sqrt(c*x + 1)) + a)), x)","F",0
127,0,0,0,0.000000," ","integrate(1/(-c^2*x^2+1)/(a+b*arccoth((-c*x+1)^(1/2)/(c*x+1)^(1/2)))^2,x, algorithm=""maxima"")","\frac{4 \, c x}{\sqrt{c x + 1} \sqrt{-c x + 1} b^{2} c \log\left(\sqrt{c x + 1} + \sqrt{-c x + 1}\right) - \sqrt{c x + 1} \sqrt{-c x + 1} b^{2} c \log\left(-\sqrt{c x + 1} + \sqrt{-c x + 1}\right) + 2 \, \sqrt{c x + 1} \sqrt{-c x + 1} a b c} - \int -\frac{4}{{\left(b^{2} c^{2} x^{2} - b^{2}\right)} \sqrt{c x + 1} \sqrt{-c x + 1} \log\left(\sqrt{c x + 1} + \sqrt{-c x + 1}\right) - {\left(b^{2} c^{2} x^{2} - b^{2}\right)} \sqrt{c x + 1} \sqrt{-c x + 1} \log\left(-\sqrt{c x + 1} + \sqrt{-c x + 1}\right) + 2 \, {\left(a b c^{2} x^{2} - a b\right)} \sqrt{c x + 1} \sqrt{-c x + 1}}\,{d x}"," ",0,"4*c*x/(sqrt(c*x + 1)*sqrt(-c*x + 1)*b^2*c*log(sqrt(c*x + 1) + sqrt(-c*x + 1)) - sqrt(c*x + 1)*sqrt(-c*x + 1)*b^2*c*log(-sqrt(c*x + 1) + sqrt(-c*x + 1)) + 2*sqrt(c*x + 1)*sqrt(-c*x + 1)*a*b*c) - integrate(-4/((b^2*c^2*x^2 - b^2)*sqrt(c*x + 1)*sqrt(-c*x + 1)*log(sqrt(c*x + 1) + sqrt(-c*x + 1)) - (b^2*c^2*x^2 - b^2)*sqrt(c*x + 1)*sqrt(-c*x + 1)*log(-sqrt(c*x + 1) + sqrt(-c*x + 1)) + 2*(a*b*c^2*x^2 - a*b)*sqrt(c*x + 1)*sqrt(-c*x + 1)), x)","F",0
128,1,38,0,0.339000," ","integrate(x^m*arccoth(tanh(b*x+a)),x, algorithm=""maxima"")","-\frac{b x^{2} x^{m}}{{\left(m + 2\right)} {\left(m + 1\right)}} + \frac{x^{m + 1} \operatorname{arcoth}\left(\tanh\left(b x + a\right)\right)}{m + 1}"," ",0,"-b*x^2*x^m/((m + 2)*(m + 1)) + x^(m + 1)*arccoth(tanh(b*x + a))/(m + 1)","A",0
129,1,19,0,0.378406," ","integrate(x^2*arccoth(tanh(b*x+a)),x, algorithm=""maxima"")","-\frac{1}{12} \, b x^{4} + \frac{1}{3} \, x^{3} \operatorname{arcoth}\left(\tanh\left(b x + a\right)\right)"," ",0,"-1/12*b*x^4 + 1/3*x^3*arccoth(tanh(b*x + a))","A",0
130,1,19,0,0.377824," ","integrate(x*arccoth(tanh(b*x+a)),x, algorithm=""maxima"")","-\frac{1}{6} \, b x^{3} + \frac{1}{2} \, x^{2} \operatorname{arcoth}\left(\tanh\left(b x + a\right)\right)"," ",0,"-1/6*b*x^3 + 1/2*x^2*arccoth(tanh(b*x + a))","A",0
131,1,16,0,0.381299," ","integrate(arccoth(tanh(b*x+a)),x, algorithm=""maxima"")","-\frac{1}{2} \, b x^{2} + x \operatorname{arcoth}\left(\tanh\left(b x + a\right)\right)"," ",0,"-1/2*b*x^2 + x*arccoth(tanh(b*x + a))","A",0
132,1,34,0,0.325507," ","integrate(arccoth(tanh(b*x+a))/x,x, algorithm=""maxima"")","-b {\left(x + \frac{a}{b}\right)} \log\left(x\right) + b {\left(x + \frac{a \log\left(x\right)}{b}\right)} + \operatorname{arcoth}\left(\tanh\left(b x + a\right)\right) \log\left(x\right)"," ",0,"-b*(x + a/b)*log(x) + b*(x + a*log(x)/b) + arccoth(tanh(b*x + a))*log(x)","A",0
133,1,17,0,0.385606," ","integrate(arccoth(tanh(b*x+a))/x^2,x, algorithm=""maxima"")","b \log\left(x\right) - \frac{\operatorname{arcoth}\left(\tanh\left(b x + a\right)\right)}{x}"," ",0,"b*log(x) - arccoth(tanh(b*x + a))/x","A",0
134,1,19,0,0.377915," ","integrate(arccoth(tanh(b*x+a))/x^3,x, algorithm=""maxima"")","-\frac{b}{2 \, x} - \frac{\operatorname{arcoth}\left(\tanh\left(b x + a\right)\right)}{2 \, x^{2}}"," ",0,"-1/2*b/x - 1/2*arccoth(tanh(b*x + a))/x^2","A",0
135,1,19,0,0.376716," ","integrate(arccoth(tanh(b*x+a))/x^4,x, algorithm=""maxima"")","-\frac{b}{6 \, x^{2}} - \frac{\operatorname{arcoth}\left(\tanh\left(b x + a\right)\right)}{3 \, x^{3}}"," ",0,"-1/6*b/x^2 - 1/3*arccoth(tanh(b*x + a))/x^3","A",0
136,1,73,0,0.388626," ","integrate(x^m*arccoth(tanh(b*x+a))^2,x, algorithm=""maxima"")","\frac{2 \, b^{2} x^{3} x^{m}}{{\left(m + 3\right)} {\left(m + 2\right)} {\left(m + 1\right)}} - \frac{2 \, b x^{2} x^{m} \operatorname{arcoth}\left(\tanh\left(b x + a\right)\right)}{{\left(m + 2\right)} {\left(m + 1\right)}} + \frac{x^{m + 1} \operatorname{arcoth}\left(\tanh\left(b x + a\right)\right)^{2}}{m + 1}"," ",0,"2*b^2*x^3*x^m/((m + 3)*(m + 2)*(m + 1)) - 2*b*x^2*x^m*arccoth(tanh(b*x + a))/((m + 2)*(m + 1)) + x^(m + 1)*arccoth(tanh(b*x + a))^2/(m + 1)","A",0
137,1,36,0,0.445018," ","integrate(x^3*arccoth(tanh(b*x+a))^2,x, algorithm=""maxima"")","\frac{1}{60} \, b^{2} x^{6} - \frac{1}{10} \, b x^{5} \operatorname{arcoth}\left(\tanh\left(b x + a\right)\right) + \frac{1}{4} \, x^{4} \operatorname{arcoth}\left(\tanh\left(b x + a\right)\right)^{2}"," ",0,"1/60*b^2*x^6 - 1/10*b*x^5*arccoth(tanh(b*x + a)) + 1/4*x^4*arccoth(tanh(b*x + a))^2","A",0
138,1,36,0,0.445390," ","integrate(x^2*arccoth(tanh(b*x+a))^2,x, algorithm=""maxima"")","\frac{1}{30} \, b^{2} x^{5} - \frac{1}{6} \, b x^{4} \operatorname{arcoth}\left(\tanh\left(b x + a\right)\right) + \frac{1}{3} \, x^{3} \operatorname{arcoth}\left(\tanh\left(b x + a\right)\right)^{2}"," ",0,"1/30*b^2*x^5 - 1/6*b*x^4*arccoth(tanh(b*x + a)) + 1/3*x^3*arccoth(tanh(b*x + a))^2","A",0
139,1,36,0,0.448095," ","integrate(x*arccoth(tanh(b*x+a))^2,x, algorithm=""maxima"")","\frac{1}{12} \, b^{2} x^{4} - \frac{1}{3} \, b x^{3} \operatorname{arcoth}\left(\tanh\left(b x + a\right)\right) + \frac{1}{2} \, x^{2} \operatorname{arcoth}\left(\tanh\left(b x + a\right)\right)^{2}"," ",0,"1/12*b^2*x^4 - 1/3*b*x^3*arccoth(tanh(b*x + a)) + 1/2*x^2*arccoth(tanh(b*x + a))^2","A",0
140,1,33,0,0.443375," ","integrate(arccoth(tanh(b*x+a))^2,x, algorithm=""maxima"")","\frac{1}{3} \, b^{2} x^{3} - b x^{2} \operatorname{arcoth}\left(\tanh\left(b x + a\right)\right) + x \operatorname{arcoth}\left(\tanh\left(b x + a\right)\right)^{2}"," ",0,"1/3*b^2*x^3 - b*x^2*arccoth(tanh(b*x + a)) + x*arccoth(tanh(b*x + a))^2","B",0
141,1,38,0,0.727203," ","integrate(arccoth(tanh(b*x+a))^2/x,x, algorithm=""maxima"")","\frac{1}{2} \, b^{2} x^{2} + \frac{1}{8} \, {\left(-8 i \, \pi b + 16 \, a b\right)} x - \frac{1}{4} \, {\left(\pi^{2} + 4 i \, \pi a - 4 \, a^{2}\right)} \log\left(x\right)"," ",0,"1/2*b^2*x^2 + 1/8*(-8*I*pi*b + 16*a*b)*x - 1/4*(pi^2 + 4*I*pi*a - 4*a^2)*log(x)","C",0
142,1,54,0,0.384709," ","integrate(arccoth(tanh(b*x+a))^2/x^2,x, algorithm=""maxima"")","2 \, b \operatorname{arcoth}\left(\tanh\left(b x + a\right)\right) \log\left(x\right) - 2 \, {\left(b {\left(x + \frac{a}{b}\right)} \log\left(x\right) - b {\left(x + \frac{a \log\left(x\right)}{b}\right)}\right)} b - \frac{\operatorname{arcoth}\left(\tanh\left(b x + a\right)\right)^{2}}{x}"," ",0,"2*b*arccoth(tanh(b*x + a))*log(x) - 2*(b*(x + a/b)*log(x) - b*(x + a*log(x)/b))*b - arccoth(tanh(b*x + a))^2/x","A",0
143,1,34,0,0.457619," ","integrate(arccoth(tanh(b*x+a))^2/x^3,x, algorithm=""maxima"")","b^{2} \log\left(x\right) - \frac{b \operatorname{arcoth}\left(\tanh\left(b x + a\right)\right)}{x} - \frac{\operatorname{arcoth}\left(\tanh\left(b x + a\right)\right)^{2}}{2 \, x^{2}}"," ",0,"b^2*log(x) - b*arccoth(tanh(b*x + a))/x - 1/2*arccoth(tanh(b*x + a))^2/x^2","A",0
144,1,36,0,0.451393," ","integrate(arccoth(tanh(b*x+a))^2/x^4,x, algorithm=""maxima"")","-\frac{b^{2}}{3 \, x} - \frac{b \operatorname{arcoth}\left(\tanh\left(b x + a\right)\right)}{3 \, x^{2}} - \frac{\operatorname{arcoth}\left(\tanh\left(b x + a\right)\right)^{2}}{3 \, x^{3}}"," ",0,"-1/3*b^2/x - 1/3*b*arccoth(tanh(b*x + a))/x^2 - 1/3*arccoth(tanh(b*x + a))^2/x^3","A",0
145,1,36,0,0.453816," ","integrate(arccoth(tanh(b*x+a))^2/x^5,x, algorithm=""maxima"")","-\frac{b^{2}}{12 \, x^{2}} - \frac{b \operatorname{arcoth}\left(\tanh\left(b x + a\right)\right)}{6 \, x^{3}} - \frac{\operatorname{arcoth}\left(\tanh\left(b x + a\right)\right)^{2}}{4 \, x^{4}}"," ",0,"-1/12*b^2/x^2 - 1/6*b*arccoth(tanh(b*x + a))/x^3 - 1/4*arccoth(tanh(b*x + a))^2/x^4","A",0
146,1,109,0,0.463239," ","integrate(x^m*arccoth(tanh(b*x+a))^3,x, algorithm=""maxima"")","-\frac{3 \, b x^{2} x^{m} \operatorname{arcoth}\left(\tanh\left(b x + a\right)\right)^{2}}{{\left(m + 2\right)} {\left(m + 1\right)}} + \frac{x^{m + 1} \operatorname{arcoth}\left(\tanh\left(b x + a\right)\right)^{3}}{m + 1} - \frac{6 \, {\left(\frac{b^{2} x^{4} x^{m}}{{\left(m + 4\right)} {\left(m + 3\right)} {\left(m + 2\right)}} - \frac{b x^{3} x^{m} \operatorname{arcoth}\left(\tanh\left(b x + a\right)\right)}{{\left(m + 3\right)} {\left(m + 2\right)}}\right)} b}{m + 1}"," ",0,"-3*b*x^2*x^m*arccoth(tanh(b*x + a))^2/((m + 2)*(m + 1)) + x^(m + 1)*arccoth(tanh(b*x + a))^3/(m + 1) - 6*(b^2*x^4*x^m/((m + 4)*(m + 3)*(m + 2)) - b*x^3*x^m*arccoth(tanh(b*x + a))/((m + 3)*(m + 2)))*b/(m + 1)","A",0
147,1,54,0,0.519445," ","integrate(x^4*arccoth(tanh(b*x+a))^3,x, algorithm=""maxima"")","-\frac{1}{10} \, b x^{6} \operatorname{arcoth}\left(\tanh\left(b x + a\right)\right)^{2} + \frac{1}{5} \, x^{5} \operatorname{arcoth}\left(\tanh\left(b x + a\right)\right)^{3} - \frac{1}{280} \, {\left(b^{2} x^{8} - 8 \, b x^{7} \operatorname{arcoth}\left(\tanh\left(b x + a\right)\right)\right)} b"," ",0,"-1/10*b*x^6*arccoth(tanh(b*x + a))^2 + 1/5*x^5*arccoth(tanh(b*x + a))^3 - 1/280*(b^2*x^8 - 8*b*x^7*arccoth(tanh(b*x + a)))*b","A",0
148,1,54,0,0.516237," ","integrate(x^3*arccoth(tanh(b*x+a))^3,x, algorithm=""maxima"")","-\frac{3}{20} \, b x^{5} \operatorname{arcoth}\left(\tanh\left(b x + a\right)\right)^{2} + \frac{1}{4} \, x^{4} \operatorname{arcoth}\left(\tanh\left(b x + a\right)\right)^{3} - \frac{1}{140} \, {\left(b^{2} x^{7} - 7 \, b x^{6} \operatorname{arcoth}\left(\tanh\left(b x + a\right)\right)\right)} b"," ",0,"-3/20*b*x^5*arccoth(tanh(b*x + a))^2 + 1/4*x^4*arccoth(tanh(b*x + a))^3 - 1/140*(b^2*x^7 - 7*b*x^6*arccoth(tanh(b*x + a)))*b","A",0
149,1,54,0,0.515835," ","integrate(x^2*arccoth(tanh(b*x+a))^3,x, algorithm=""maxima"")","-\frac{1}{4} \, b x^{4} \operatorname{arcoth}\left(\tanh\left(b x + a\right)\right)^{2} + \frac{1}{3} \, x^{3} \operatorname{arcoth}\left(\tanh\left(b x + a\right)\right)^{3} - \frac{1}{60} \, {\left(b^{2} x^{6} - 6 \, b x^{5} \operatorname{arcoth}\left(\tanh\left(b x + a\right)\right)\right)} b"," ",0,"-1/4*b*x^4*arccoth(tanh(b*x + a))^2 + 1/3*x^3*arccoth(tanh(b*x + a))^3 - 1/60*(b^2*x^6 - 6*b*x^5*arccoth(tanh(b*x + a)))*b","A",0
150,1,54,0,0.523968," ","integrate(x*arccoth(tanh(b*x+a))^3,x, algorithm=""maxima"")","-\frac{1}{2} \, b x^{3} \operatorname{arcoth}\left(\tanh\left(b x + a\right)\right)^{2} + \frac{1}{2} \, x^{2} \operatorname{arcoth}\left(\tanh\left(b x + a\right)\right)^{3} - \frac{1}{20} \, {\left(b^{2} x^{5} - 5 \, b x^{4} \operatorname{arcoth}\left(\tanh\left(b x + a\right)\right)\right)} b"," ",0,"-1/2*b*x^3*arccoth(tanh(b*x + a))^2 + 1/2*x^2*arccoth(tanh(b*x + a))^3 - 1/20*(b^2*x^5 - 5*b*x^4*arccoth(tanh(b*x + a)))*b","A",0
151,1,51,0,0.523567," ","integrate(arccoth(tanh(b*x+a))^3,x, algorithm=""maxima"")","-\frac{3}{2} \, b x^{2} \operatorname{arcoth}\left(\tanh\left(b x + a\right)\right)^{2} + x \operatorname{arcoth}\left(\tanh\left(b x + a\right)\right)^{3} - \frac{1}{4} \, {\left(b^{2} x^{4} - 4 \, b x^{3} \operatorname{arcoth}\left(\tanh\left(b x + a\right)\right)\right)} b"," ",0,"-3/2*b*x^2*arccoth(tanh(b*x + a))^2 + x*arccoth(tanh(b*x + a))^3 - 1/4*(b^2*x^4 - 4*b*x^3*arccoth(tanh(b*x + a)))*b","B",0
152,1,75,0,0.756248," ","integrate(arccoth(tanh(b*x+a))^3/x,x, algorithm=""maxima"")","\frac{1}{3} \, b^{3} x^{3} + \frac{1}{24} \, {\left(-18 i \, \pi b^{2} + 36 \, a b^{2}\right)} x^{2} - \frac{1}{24} \, {\left(18 \, \pi^{2} b + 72 i \, \pi a b - 72 \, a^{2} b\right)} x + \frac{1}{8} \, {\left(i \, \pi^{3} - 6 \, \pi^{2} a - 12 i \, \pi a^{2} + 8 \, a^{3}\right)} \log\left(x\right)"," ",0,"1/3*b^3*x^3 + 1/24*(-18*I*pi*b^2 + 36*a*b^2)*x^2 - 1/24*(18*pi^2*b + 72*I*pi*a*b - 72*a^2*b)*x + 1/8*(I*pi^3 - 6*pi^2*a - 12*I*pi*a^2 + 8*a^3)*log(x)","C",0
153,1,124,0,0.612579," ","integrate(arccoth(tanh(b*x+a))^3/x^2,x, algorithm=""maxima"")","3 \, b \operatorname{arcoth}\left(\tanh\left(b x + a\right)\right)^{2} \log\left(x\right) - \frac{3}{2} \, {\left(2 \, \operatorname{arcoth}\left(\tanh\left(b x + a\right)\right)^{2} \log\left(x\right) - {\left(b x^{2} - 2 \, {\left(-i \, \pi - 2 \, a\right)} x + 2 \, {\left(-\frac{i \, \pi {\left(b x + a\right)}}{b} - \frac{{\left(b x + a\right)}^{2}}{b}\right)} \log\left(x\right) + \frac{2 \, \operatorname{arcoth}\left(\tanh\left(b x + a\right)\right)^{2} \log\left(x\right)}{b} + \frac{2 \, {\left(i \, \pi a + a^{2}\right)} \log\left(x\right)}{b}\right)} b\right)} b - \frac{\operatorname{arcoth}\left(\tanh\left(b x + a\right)\right)^{3}}{x}"," ",0,"3*b*arccoth(tanh(b*x + a))^2*log(x) - 3/2*(2*arccoth(tanh(b*x + a))^2*log(x) - (b*x^2 - 2*(-I*pi - 2*a)*x + 2*(-I*pi*(b*x + a)/b - (b*x + a)^2/b)*log(x) + 2*arccoth(tanh(b*x + a))^2*log(x)/b + 2*(I*pi*a + a^2)*log(x)/b)*b)*b - arccoth(tanh(b*x + a))^3/x","C",0
154,1,72,0,0.461920," ","integrate(arccoth(tanh(b*x+a))^3/x^3,x, algorithm=""maxima"")","3 \, {\left(b \operatorname{arcoth}\left(\tanh\left(b x + a\right)\right) \log\left(x\right) - {\left(b {\left(x + \frac{a}{b}\right)} \log\left(x\right) - b {\left(x + \frac{a \log\left(x\right)}{b}\right)}\right)} b\right)} b - \frac{3 \, b \operatorname{arcoth}\left(\tanh\left(b x + a\right)\right)^{2}}{2 \, x} - \frac{\operatorname{arcoth}\left(\tanh\left(b x + a\right)\right)^{3}}{2 \, x^{2}}"," ",0,"3*(b*arccoth(tanh(b*x + a))*log(x) - (b*(x + a/b)*log(x) - b*(x + a*log(x)/b))*b)*b - 3/2*b*arccoth(tanh(b*x + a))^2/x - 1/2*arccoth(tanh(b*x + a))^3/x^2","A",0
155,1,52,0,0.586869," ","integrate(arccoth(tanh(b*x+a))^3/x^4,x, algorithm=""maxima"")","{\left(b^{2} \log\left(x\right) - \frac{b \operatorname{arcoth}\left(\tanh\left(b x + a\right)\right)}{x}\right)} b - \frac{b \operatorname{arcoth}\left(\tanh\left(b x + a\right)\right)^{2}}{2 \, x^{2}} - \frac{\operatorname{arcoth}\left(\tanh\left(b x + a\right)\right)^{3}}{3 \, x^{3}}"," ",0,"(b^2*log(x) - b*arccoth(tanh(b*x + a))/x)*b - 1/2*b*arccoth(tanh(b*x + a))^2/x^2 - 1/3*arccoth(tanh(b*x + a))^3/x^3","A",0
156,1,53,0,0.524482," ","integrate(arccoth(tanh(b*x+a))^3/x^5,x, algorithm=""maxima"")","-\frac{1}{4} \, b {\left(\frac{b^{2}}{x} + \frac{b \operatorname{arcoth}\left(\tanh\left(b x + a\right)\right)}{x^{2}}\right)} - \frac{b \operatorname{arcoth}\left(\tanh\left(b x + a\right)\right)^{2}}{4 \, x^{3}} - \frac{\operatorname{arcoth}\left(\tanh\left(b x + a\right)\right)^{3}}{4 \, x^{4}}"," ",0,"-1/4*b*(b^2/x + b*arccoth(tanh(b*x + a))/x^2) - 1/4*b*arccoth(tanh(b*x + a))^2/x^3 - 1/4*arccoth(tanh(b*x + a))^3/x^4","A",0
157,1,54,0,0.536647," ","integrate(arccoth(tanh(b*x+a))^3/x^6,x, algorithm=""maxima"")","-\frac{1}{20} \, b {\left(\frac{b^{2}}{x^{2}} + \frac{2 \, b \operatorname{arcoth}\left(\tanh\left(b x + a\right)\right)}{x^{3}}\right)} - \frac{3 \, b \operatorname{arcoth}\left(\tanh\left(b x + a\right)\right)^{2}}{20 \, x^{4}} - \frac{\operatorname{arcoth}\left(\tanh\left(b x + a\right)\right)^{3}}{5 \, x^{5}}"," ",0,"-1/20*b*(b^2/x^2 + 2*b*arccoth(tanh(b*x + a))/x^3) - 3/20*b*arccoth(tanh(b*x + a))^2/x^4 - 1/5*arccoth(tanh(b*x + a))^3/x^5","A",0
158,0,0,0,0.000000," ","integrate(x^m/arccoth(tanh(b*x+a)),x, algorithm=""maxima"")","\int \frac{x^{m}}{\operatorname{arcoth}\left(\tanh\left(b x + a\right)\right)}\,{d x}"," ",0,"integrate(x^m/arccoth(tanh(b*x + a)), x)","F",0
159,1,86,0,0.530854," ","integrate(x^3/arccoth(tanh(b*x+a)),x, algorithm=""maxima"")","\frac{4 \, b^{2} x^{3} + {\left(3 i \, \pi b - 6 \, a b\right)} x^{2} - {\left(3 \, \pi^{2} + 12 i \, \pi a - 12 \, a^{2}\right)} x}{12 \, b^{3}} - \frac{{\left(i \, \pi^{3} - 6 \, \pi^{2} a - 12 i \, \pi a^{2} + 8 \, a^{3}\right)} \log\left(-i \, \pi + 2 \, b x + 2 \, a\right)}{8 \, b^{4}}"," ",0,"1/12*(4*b^2*x^3 + (3*I*pi*b - 6*a*b)*x^2 - (3*pi^2 + 12*I*pi*a - 12*a^2)*x)/b^3 - 1/8*(I*pi^3 - 6*pi^2*a - 12*I*pi*a^2 + 8*a^3)*log(-I*pi + 2*b*x + 2*a)/b^4","C",0
160,1,51,0,0.529109," ","integrate(x^2/arccoth(tanh(b*x+a)),x, algorithm=""maxima"")","\frac{b x^{2} + {\left(i \, \pi - 2 \, a\right)} x}{2 \, b^{2}} - \frac{{\left(\pi^{2} + 4 i \, \pi a - 4 \, a^{2}\right)} \log\left(-i \, \pi + 2 \, b x + 2 \, a\right)}{4 \, b^{3}}"," ",0,"1/2*(b*x^2 + (I*pi - 2*a)*x)/b^2 - 1/4*(pi^2 + 4*I*pi*a - 4*a^2)*log(-I*pi + 2*b*x + 2*a)/b^3","C",0
161,1,30,0,0.524562," ","integrate(x/arccoth(tanh(b*x+a)),x, algorithm=""maxima"")","\frac{x}{b} - \frac{{\left(-i \, \pi + 2 \, a\right)} \log\left(-i \, \pi + 2 \, b x + 2 \, a\right)}{2 \, b^{2}}"," ",0,"x/b - 1/2*(-I*pi + 2*a)*log(-I*pi + 2*b*x + 2*a)/b^2","C",0
162,1,16,0,0.411343," ","integrate(1/arccoth(tanh(b*x+a)),x, algorithm=""maxima"")","\frac{\log\left(-\frac{1}{2} i \, \pi - b x - a\right)}{b}"," ",0,"log(-1/2*I*pi - b*x - a)/b","C",0
163,1,37,0,0.523022," ","integrate(1/x/arccoth(tanh(b*x+a)),x, algorithm=""maxima"")","\frac{2 \, \log\left(-i \, \pi + 2 \, b x + 2 \, a\right)}{i \, \pi - 2 \, a} - \frac{2 \, \log\left(x\right)}{i \, \pi - 2 \, a}"," ",0,"2*log(-I*pi + 2*b*x + 2*a)/(I*pi - 2*a) - 2*log(x)/(I*pi - 2*a)","C",0
164,1,65,0,0.523447," ","integrate(1/x^2/arccoth(tanh(b*x+a)),x, algorithm=""maxima"")","-\frac{4 \, b \log\left(-i \, \pi + 2 \, b x + 2 \, a\right)}{\pi^{2} + 4 i \, \pi a - 4 \, a^{2}} + \frac{4 \, b \log\left(x\right)}{\pi^{2} + 4 i \, \pi a - 4 \, a^{2}} + \frac{2}{{\left(i \, \pi - 2 \, a\right)} x}"," ",0,"-4*b*log(-I*pi + 2*b*x + 2*a)/(pi^2 + 4*I*pi*a - 4*a^2) + 4*b*log(x)/(pi^2 + 4*I*pi*a - 4*a^2) + 2/((I*pi - 2*a)*x)","C",0
165,1,108,0,0.545934," ","integrate(1/x^3/arccoth(tanh(b*x+a)),x, algorithm=""maxima"")","\frac{8 \, b^{2} \log\left(-i \, \pi + 2 \, b x + 2 \, a\right)}{-i \, \pi^{3} + 6 \, \pi^{2} a + 12 i \, \pi a^{2} - 8 \, a^{3}} - \frac{8 \, b^{2} \log\left(x\right)}{-i \, \pi^{3} + 6 \, \pi^{2} a + 12 i \, \pi a^{2} - 8 \, a^{3}} - \frac{2 \, {\left(i \, \pi + 4 \, b x - 2 \, a\right)}}{{\left(2 \, \pi^{2} + 8 i \, \pi a - 8 \, a^{2}\right)} x^{2}}"," ",0,"8*b^2*log(-I*pi + 2*b*x + 2*a)/(-I*pi^3 + 6*pi^2*a + 12*I*pi*a^2 - 8*a^3) - 8*b^2*log(x)/(-I*pi^3 + 6*pi^2*a + 12*I*pi*a^2 - 8*a^3) - 2*(I*pi + 4*b*x - 2*a)/((2*pi^2 + 8*I*pi*a - 8*a^2)*x^2)","C",0
166,0,0,0,0.000000," ","integrate(x^m/arccoth(tanh(b*x+a))^2,x, algorithm=""maxima"")","\int \frac{x^{m}}{\operatorname{arcoth}\left(\tanh\left(b x + a\right)\right)^{2}}\,{d x}"," ",0,"integrate(x^m/arccoth(tanh(b*x + a))^2, x)","F",0
167,1,178,0,0.769016," ","integrate(x^4/arccoth(tanh(b*x+a))^2,x, algorithm=""maxima"")","\frac{4 \, {\left(16 \, b^{4} x^{4} - 3 \, \pi^{4} - 24 i \, \pi^{3} a + 72 \, \pi^{2} a^{2} + 96 i \, \pi a^{3} - 48 \, a^{4} + {\left(16 i \, \pi b^{3} - 32 \, a b^{3}\right)} x^{3} - {\left(24 \, \pi^{2} b^{2} + 96 i \, \pi a b^{2} - 96 \, a^{2} b^{2}\right)} x^{2} + {\left(18 i \, \pi^{3} b - 108 \, \pi^{2} a b - 216 i \, \pi a^{2} b + 144 \, a^{3} b\right)} x\right)}}{192 \, b^{6} x - 96 i \, \pi b^{5} + 192 \, a b^{5}} - \frac{{\left(i \, \pi^{3} - 6 \, \pi^{2} a - 12 i \, \pi a^{2} + 8 \, a^{3}\right)} \log\left(-i \, \pi + 2 \, b x + 2 \, a\right)}{2 \, b^{5}}"," ",0,"4*(16*b^4*x^4 - 3*pi^4 - 24*I*pi^3*a + 72*pi^2*a^2 + 96*I*pi*a^3 - 48*a^4 + (16*I*pi*b^3 - 32*a*b^3)*x^3 - (24*pi^2*b^2 + 96*I*pi*a*b^2 - 96*a^2*b^2)*x^2 + (18*I*pi^3*b - 108*pi^2*a*b - 216*I*pi*a^2*b + 144*a^3*b)*x)/(192*b^6*x - 96*I*pi*b^5 + 192*a*b^5) - 1/2*(I*pi^3 - 6*pi^2*a - 12*I*pi*a^2 + 8*a^3)*log(-I*pi + 2*b*x + 2*a)/b^5","C",0
168,1,124,0,0.762724," ","integrate(x^3/arccoth(tanh(b*x+a))^2,x, algorithm=""maxima"")","\frac{4 \, {\left(4 \, b^{3} x^{3} + i \, \pi^{3} - 6 \, \pi^{2} a - 12 i \, \pi a^{2} + 8 \, a^{3} + {\left(6 i \, \pi b^{2} - 12 \, a b^{2}\right)} x^{2} + {\left(4 \, \pi^{2} b + 16 i \, \pi a b - 16 \, a^{2} b\right)} x\right)}}{32 \, b^{5} x - 16 i \, \pi b^{4} + 32 \, a b^{4}} - \frac{{\left(3 \, \pi^{2} + 12 i \, \pi a - 12 \, a^{2}\right)} \log\left(-i \, \pi + 2 \, b x + 2 \, a\right)}{4 \, b^{4}}"," ",0,"4*(4*b^3*x^3 + I*pi^3 - 6*pi^2*a - 12*I*pi*a^2 + 8*a^3 + (6*I*pi*b^2 - 12*a*b^2)*x^2 + (4*pi^2*b + 16*I*pi*a*b - 16*a^2*b)*x)/(32*b^5*x - 16*I*pi*b^4 + 32*a*b^4) - 1/4*(3*pi^2 + 12*I*pi*a - 12*a^2)*log(-I*pi + 2*b*x + 2*a)/b^4","C",0
169,1,80,0,0.748411," ","integrate(x^2/arccoth(tanh(b*x+a))^2,x, algorithm=""maxima"")","\frac{4 \, {\left(4 \, b^{2} x^{2} + \pi^{2} + 4 i \, \pi a - 4 \, a^{2} + {\left(-2 i \, \pi b + 4 \, a b\right)} x\right)}}{16 \, b^{4} x - 8 i \, \pi b^{3} + 16 \, a b^{3}} - \frac{{\left(-i \, \pi + 2 \, a\right)} \log\left(-i \, \pi + 2 \, b x + 2 \, a\right)}{b^{3}}"," ",0,"4*(4*b^2*x^2 + pi^2 + 4*I*pi*a - 4*a^2 + (-2*I*pi*b + 4*a*b)*x)/(16*b^4*x - 8*I*pi*b^3 + 16*a*b^3) - (-I*pi + 2*a)*log(-I*pi + 2*b*x + 2*a)/b^3","C",0
170,1,47,0,0.755134," ","integrate(x/arccoth(tanh(b*x+a))^2,x, algorithm=""maxima"")","\frac{4 \, {\left(-i \, \pi + 2 \, a\right)}}{8 \, b^{3} x - 4 i \, \pi b^{2} + 8 \, a b^{2}} + \frac{\log\left(-i \, \pi + 2 \, b x + 2 \, a\right)}{b^{2}}"," ",0,"4*(-I*pi + 2*a)/(8*b^3*x - 4*I*pi*b^2 + 8*a*b^2) + log(-I*pi + 2*b*x + 2*a)/b^2","C",0
171,1,18,0,0.411928," ","integrate(1/arccoth(tanh(b*x+a))^2,x, algorithm=""maxima"")","\frac{4}{-2 \, {\left(i \, \pi + 2 \, b x + 2 \, a\right)} b}"," ",0,"4/((-2*I*pi - 4*b*x - 4*a)*b)","C",0
172,1,77,0,0.767629," ","integrate(1/x/arccoth(tanh(b*x+a))^2,x, algorithm=""maxima"")","\frac{4 \, \log\left(-i \, \pi + 2 \, b x + 2 \, a\right)}{\pi^{2} + 4 i \, \pi a - 4 \, a^{2}} - \frac{4 \, \log\left(x\right)}{\pi^{2} + 4 i \, \pi a - 4 \, a^{2}} - \frac{4}{\pi^{2} + 4 i \, \pi a - 4 \, a^{2} + {\left(2 i \, \pi b - 4 \, a b\right)} x}"," ",0,"4*log(-I*pi + 2*b*x + 2*a)/(pi^2 + 4*I*pi*a - 4*a^2) - 4*log(x)/(pi^2 + 4*I*pi*a - 4*a^2) - 4/(pi^2 + 4*I*pi*a - 4*a^2 + (2*I*pi*b - 4*a*b)*x)","C",0
173,1,135,0,0.775808," ","integrate(1/x^2/arccoth(tanh(b*x+a))^2,x, algorithm=""maxima"")","-\frac{16 \, b \log\left(-i \, \pi + 2 \, b x + 2 \, a\right)}{-i \, \pi^{3} + 6 \, \pi^{2} a + 12 i \, \pi a^{2} - 8 \, a^{3}} + \frac{16 \, b \log\left(x\right)}{-i \, \pi^{3} + 6 \, \pi^{2} a + 12 i \, \pi a^{2} - 8 \, a^{3}} - \frac{4 \, {\left(i \, \pi - 4 \, b x - 2 \, a\right)}}{{\left(2 \, \pi^{2} b + 8 i \, \pi a b - 8 \, a^{2} b\right)} x^{2} - {\left(i \, \pi^{3} - 6 \, \pi^{2} a - 12 i \, \pi a^{2} + 8 \, a^{3}\right)} x}"," ",0,"-16*b*log(-I*pi + 2*b*x + 2*a)/(-I*pi^3 + 6*pi^2*a + 12*I*pi*a^2 - 8*a^3) + 16*b*log(x)/(-I*pi^3 + 6*pi^2*a + 12*I*pi*a^2 - 8*a^3) - 4*(I*pi - 4*b*x - 2*a)/((2*pi^2*b + 8*I*pi*a*b - 8*a^2*b)*x^2 - (I*pi^3 - 6*pi^2*a - 12*I*pi*a^2 + 8*a^3)*x)","C",0
174,1,191,0,0.756629," ","integrate(1/x^3/arccoth(tanh(b*x+a))^2,x, algorithm=""maxima"")","-\frac{48 \, b^{2} \log\left(-i \, \pi + 2 \, b x + 2 \, a\right)}{\pi^{4} + 8 i \, \pi^{3} a - 24 \, \pi^{2} a^{2} - 32 i \, \pi a^{3} + 16 \, a^{4}} + \frac{48 \, b^{2} \log\left(x\right)}{\pi^{4} + 8 i \, \pi^{3} a - 24 \, \pi^{2} a^{2} - 32 i \, \pi a^{3} + 16 \, a^{4}} - \frac{4 \, {\left(24 \, b^{2} x^{2} + \pi^{2} + 4 i \, \pi a - 4 \, a^{2} + {\left(-6 i \, \pi b + 12 \, a b\right)} x\right)}}{{\left(-4 i \, \pi^{3} b + 24 \, \pi^{2} a b + 48 i \, \pi a^{2} b - 32 \, a^{3} b\right)} x^{3} - {\left(2 \, \pi^{4} + 16 i \, \pi^{3} a - 48 \, \pi^{2} a^{2} - 64 i \, \pi a^{3} + 32 \, a^{4}\right)} x^{2}}"," ",0,"-48*b^2*log(-I*pi + 2*b*x + 2*a)/(pi^4 + 8*I*pi^3*a - 24*pi^2*a^2 - 32*I*pi*a^3 + 16*a^4) + 48*b^2*log(x)/(pi^4 + 8*I*pi^3*a - 24*pi^2*a^2 - 32*I*pi*a^3 + 16*a^4) - 4*(24*b^2*x^2 + pi^2 + 4*I*pi*a - 4*a^2 + (-6*I*pi*b + 12*a*b)*x)/((-4*I*pi^3*b + 24*pi^2*a*b + 48*I*pi*a^2*b - 32*a^3*b)*x^3 - (2*pi^4 + 16*I*pi^3*a - 48*pi^2*a^2 - 64*I*pi*a^3 + 32*a^4)*x^2)","C",0
175,0,0,0,0.000000," ","integrate(x^m/arccoth(tanh(b*x+a))^3,x, algorithm=""maxima"")","\int \frac{x^{m}}{\operatorname{arcoth}\left(\tanh\left(b x + a\right)\right)^{3}}\,{d x}"," ",0,"integrate(x^m/arccoth(tanh(b*x + a))^3, x)","F",0
176,1,197,0,1.149698," ","integrate(x^4/arccoth(tanh(b*x+a))^3,x, algorithm=""maxima"")","\frac{8 \, {\left(16 \, b^{4} x^{4} + 7 \, \pi^{4} + 56 i \, \pi^{3} a - 168 \, \pi^{2} a^{2} - 224 i \, \pi a^{3} + 112 \, a^{4} + {\left(32 i \, \pi b^{3} - 64 \, a b^{3}\right)} x^{3} + {\left(44 \, \pi^{2} b^{2} + 176 i \, \pi a b^{2} - 176 \, a^{2} b^{2}\right)} x^{2} + {\left(4 i \, \pi^{3} b - 24 \, \pi^{2} a b - 48 i \, \pi a^{2} b + 32 \, a^{3} b\right)} x\right)}}{256 \, b^{7} x^{2} - 64 \, \pi^{2} b^{5} - 256 i \, \pi a b^{5} + 256 \, a^{2} b^{5} + {\left(-256 i \, \pi b^{6} + 512 \, a b^{6}\right)} x} - \frac{{\left(3 \, \pi^{2} + 12 i \, \pi a - 12 \, a^{2}\right)} \log\left(-i \, \pi + 2 \, b x + 2 \, a\right)}{2 \, b^{5}}"," ",0,"8*(16*b^4*x^4 + 7*pi^4 + 56*I*pi^3*a - 168*pi^2*a^2 - 224*I*pi*a^3 + 112*a^4 + (32*I*pi*b^3 - 64*a*b^3)*x^3 + (44*pi^2*b^2 + 176*I*pi*a*b^2 - 176*a^2*b^2)*x^2 + (4*I*pi^3*b - 24*pi^2*a*b - 48*I*pi*a^2*b + 32*a^3*b)*x)/(256*b^7*x^2 - 64*pi^2*b^5 - 256*I*pi*a*b^5 + 256*a^2*b^5 + (-256*I*pi*b^6 + 512*a*b^6)*x) - 1/2*(3*pi^2 + 12*I*pi*a - 12*a^2)*log(-I*pi + 2*b*x + 2*a)/b^5","C",0
177,1,144,0,1.145532," ","integrate(x^3/arccoth(tanh(b*x+a))^3,x, algorithm=""maxima"")","\frac{8 \, {\left(16 \, b^{3} x^{3} - 5 i \, \pi^{3} + 30 \, \pi^{2} a + 60 i \, \pi a^{2} - 40 \, a^{3} + {\left(-16 i \, \pi b^{2} + 32 \, a b^{2}\right)} x^{2} + {\left(8 \, \pi^{2} b + 32 i \, \pi a b - 32 \, a^{2} b\right)} x\right)}}{128 \, b^{6} x^{2} - 32 \, \pi^{2} b^{4} - 128 i \, \pi a b^{4} + 128 \, a^{2} b^{4} + {\left(-128 i \, \pi b^{5} + 256 \, a b^{5}\right)} x} - \frac{3 \, {\left(-i \, \pi + 2 \, a\right)} \log\left(-i \, \pi + 2 \, b x + 2 \, a\right)}{2 \, b^{4}}"," ",0,"8*(16*b^3*x^3 - 5*I*pi^3 + 30*pi^2*a + 60*I*pi*a^2 - 40*a^3 + (-16*I*pi*b^2 + 32*a*b^2)*x^2 + (8*pi^2*b + 32*I*pi*a*b - 32*a^2*b)*x)/(128*b^6*x^2 - 32*pi^2*b^4 - 128*I*pi*a*b^4 + 128*a^2*b^4 + (-128*I*pi*b^5 + 256*a*b^5)*x) - 3/2*(-I*pi + 2*a)*log(-I*pi + 2*b*x + 2*a)/b^4","C",0
178,1,94,0,1.122623," ","integrate(x^2/arccoth(tanh(b*x+a))^3,x, algorithm=""maxima"")","-\frac{8 \, {\left(3 \, \pi^{2} + 12 i \, \pi a - 12 \, a^{2} + {\left(8 i \, \pi b - 16 \, a b\right)} x\right)}}{64 \, b^{5} x^{2} - 16 \, \pi^{2} b^{3} - 64 i \, \pi a b^{3} + 64 \, a^{2} b^{3} + {\left(-64 i \, \pi b^{4} + 128 \, a b^{4}\right)} x} + \frac{\log\left(-i \, \pi + 2 \, b x + 2 \, a\right)}{b^{3}}"," ",0,"-8*(3*pi^2 + 12*I*pi*a - 12*a^2 + (8*I*pi*b - 16*a*b)*x)/(64*b^5*x^2 - 16*pi^2*b^3 - 64*I*pi*a*b^3 + 64*a^2*b^3 + (-64*I*pi*b^4 + 128*a*b^4)*x) + log(-I*pi + 2*b*x + 2*a)/b^3","C",0
179,1,62,0,1.111836," ","integrate(x/arccoth(tanh(b*x+a))^3,x, algorithm=""maxima"")","-\frac{8 \, {\left(-i \, \pi + 4 \, b x + 2 \, a\right)}}{32 \, b^{4} x^{2} - 8 \, \pi^{2} b^{2} - 32 i \, \pi a b^{2} + 32 \, a^{2} b^{2} + {\left(-32 i \, \pi b^{3} + 64 \, a b^{3}\right)} x}"," ",0,"-8*(-I*pi + 4*b*x + 2*a)/(32*b^4*x^2 - 8*pi^2*b^2 - 32*I*pi*a*b^2 + 32*a^2*b^2 + (-32*I*pi*b^3 + 64*a*b^3)*x)","C",0
180,1,30,0,0.430068," ","integrate(1/arccoth(tanh(b*x+a))^3,x, algorithm=""maxima"")","\frac{8}{{\left(4 \, \pi^{2} - 16 i \, \pi {\left(b x + a\right)} - 16 \, {\left(b x + a\right)}^{2}\right)} b}"," ",0,"8/((4*pi^2 - 16*I*pi*(b*x + a) - 16*(b*x + a)^2)*b)","C",0
181,1,173,0,1.132489," ","integrate(1/x/arccoth(tanh(b*x+a))^3,x, algorithm=""maxima"")","\frac{8 \, {\left(-3 i \, \pi + 4 \, b x + 6 \, a\right)}}{2 \, \pi^{4} + 16 i \, \pi^{3} a - 48 \, \pi^{2} a^{2} - 64 i \, \pi a^{3} + 32 \, a^{4} - {\left(8 \, \pi^{2} b^{2} + 32 i \, \pi a b^{2} - 32 \, a^{2} b^{2}\right)} x^{2} + {\left(8 i \, \pi^{3} b - 48 \, \pi^{2} a b - 96 i \, \pi a^{2} b + 64 \, a^{3} b\right)} x} + \frac{8 \, \log\left(-i \, \pi + 2 \, b x + 2 \, a\right)}{-i \, \pi^{3} + 6 \, \pi^{2} a + 12 i \, \pi a^{2} - 8 \, a^{3}} - \frac{8 \, \log\left(x\right)}{-i \, \pi^{3} + 6 \, \pi^{2} a + 12 i \, \pi a^{2} - 8 \, a^{3}}"," ",0,"8*(-3*I*pi + 4*b*x + 6*a)/(2*pi^4 + 16*I*pi^3*a - 48*pi^2*a^2 - 64*I*pi*a^3 + 32*a^4 - (8*pi^2*b^2 + 32*I*pi*a*b^2 - 32*a^2*b^2)*x^2 + (8*I*pi^3*b - 48*pi^2*a*b - 96*I*pi*a^2*b + 64*a^3*b)*x) + 8*log(-I*pi + 2*b*x + 2*a)/(-I*pi^3 + 6*pi^2*a + 12*I*pi*a^2 - 8*a^3) - 8*log(x)/(-I*pi^3 + 6*pi^2*a + 12*I*pi*a^2 - 8*a^3)","C",0
182,1,243,0,1.151799," ","integrate(1/x^2/arccoth(tanh(b*x+a))^3,x, algorithm=""maxima"")","\frac{48 \, b \log\left(-i \, \pi + 2 \, b x + 2 \, a\right)}{\pi^{4} + 8 i \, \pi^{3} a - 24 \, \pi^{2} a^{2} - 32 i \, \pi a^{3} + 16 \, a^{4}} - \frac{48 \, b \log\left(x\right)}{\pi^{4} + 8 i \, \pi^{3} a - 24 \, \pi^{2} a^{2} - 32 i \, \pi a^{3} + 16 \, a^{4}} + \frac{8 \, {\left(12 \, b^{2} x^{2} - \pi^{2} - 4 i \, \pi a + 4 \, a^{2} + {\left(-9 i \, \pi b + 18 \, a b\right)} x\right)}}{{\left(-4 i \, \pi^{3} b^{2} + 24 \, \pi^{2} a b^{2} + 48 i \, \pi a^{2} b^{2} - 32 \, a^{3} b^{2}\right)} x^{3} - {\left(4 \, \pi^{4} b + 32 i \, \pi^{3} a b - 96 \, \pi^{2} a^{2} b - 128 i \, \pi a^{3} b + 64 \, a^{4} b\right)} x^{2} + {\left(i \, \pi^{5} - 10 \, \pi^{4} a - 40 i \, \pi^{3} a^{2} + 80 \, \pi^{2} a^{3} + 80 i \, \pi a^{4} - 32 \, a^{5}\right)} x}"," ",0,"48*b*log(-I*pi + 2*b*x + 2*a)/(pi^4 + 8*I*pi^3*a - 24*pi^2*a^2 - 32*I*pi*a^3 + 16*a^4) - 48*b*log(x)/(pi^4 + 8*I*pi^3*a - 24*pi^2*a^2 - 32*I*pi*a^3 + 16*a^4) + 8*(12*b^2*x^2 - pi^2 - 4*I*pi*a + 4*a^2 + (-9*I*pi*b + 18*a*b)*x)/((-4*I*pi^3*b^2 + 24*pi^2*a*b^2 + 48*I*pi*a^2*b^2 - 32*a^3*b^2)*x^3 - (4*pi^4*b + 32*I*pi^3*a*b - 96*pi^2*a^2*b - 128*I*pi*a^3*b + 64*a^4*b)*x^2 + (I*pi^5 - 10*pi^4*a - 40*I*pi^3*a^2 + 80*pi^2*a^3 + 80*I*pi*a^4 - 32*a^5)*x)","C",0
183,1,332,0,1.153575," ","integrate(1/x^3/arccoth(tanh(b*x+a))^3,x, algorithm=""maxima"")","\frac{192 \, b^{2} \log\left(-i \, \pi + 2 \, b x + 2 \, a\right)}{i \, \pi^{5} - 10 \, \pi^{4} a - 40 i \, \pi^{3} a^{2} + 80 \, \pi^{2} a^{3} + 80 i \, \pi a^{4} - 32 \, a^{5}} - \frac{192 \, b^{2} \log\left(x\right)}{i \, \pi^{5} - 10 \, \pi^{4} a - 40 i \, \pi^{3} a^{2} + 80 \, \pi^{2} a^{3} + 80 i \, \pi a^{4} - 32 \, a^{5}} + \frac{8 \, {\left(96 \, b^{3} x^{3} - i \, \pi^{3} + 6 \, \pi^{2} a + 12 i \, \pi a^{2} - 8 \, a^{3} + {\left(-72 i \, \pi b^{2} + 144 \, a b^{2}\right)} x^{2} - {\left(8 \, \pi^{2} b + 32 i \, \pi a b - 32 \, a^{2} b\right)} x\right)}}{{\left(8 \, \pi^{4} b^{2} + 64 i \, \pi^{3} a b^{2} - 192 \, \pi^{2} a^{2} b^{2} - 256 i \, \pi a^{3} b^{2} + 128 \, a^{4} b^{2}\right)} x^{4} + {\left(-8 i \, \pi^{5} b + 80 \, \pi^{4} a b + 320 i \, \pi^{3} a^{2} b - 640 \, \pi^{2} a^{3} b - 640 i \, \pi a^{4} b + 256 \, a^{5} b\right)} x^{3} - {\left(2 \, \pi^{6} + 24 i \, \pi^{5} a - 120 \, \pi^{4} a^{2} - 320 i \, \pi^{3} a^{3} + 480 \, \pi^{2} a^{4} + 384 i \, \pi a^{5} - 128 \, a^{6}\right)} x^{2}}"," ",0,"192*b^2*log(-I*pi + 2*b*x + 2*a)/(I*pi^5 - 10*pi^4*a - 40*I*pi^3*a^2 + 80*pi^2*a^3 + 80*I*pi*a^4 - 32*a^5) - 192*b^2*log(x)/(I*pi^5 - 10*pi^4*a - 40*I*pi^3*a^2 + 80*pi^2*a^3 + 80*I*pi*a^4 - 32*a^5) + 8*(96*b^3*x^3 - I*pi^3 + 6*pi^2*a + 12*I*pi*a^2 - 8*a^3 + (-72*I*pi*b^2 + 144*a*b^2)*x^2 - (8*pi^2*b + 32*I*pi*a*b - 32*a^2*b)*x)/((8*pi^4*b^2 + 64*I*pi^3*a*b^2 - 192*pi^2*a^2*b^2 - 256*I*pi*a^3*b^2 + 128*a^4*b^2)*x^4 + (-8*I*pi^5*b + 80*pi^4*a*b + 320*I*pi^3*a^2*b - 640*pi^2*a^3*b - 640*I*pi*a^4*b + 256*a^5*b)*x^3 - (2*pi^6 + 24*I*pi^5*a - 120*pi^4*a^2 - 320*I*pi^3*a^3 + 480*pi^2*a^4 + 384*I*pi*a^5 - 128*a^6)*x^2)","C",0
184,0,0,0,0.000000," ","integrate(x^m*arccoth(tanh(b*x+a))^n,x, algorithm=""maxima"")","\int x^{m} \operatorname{arcoth}\left(\tanh\left(b x + a\right)\right)^{n}\,{d x}"," ",0,"integrate(x^m*arccoth(tanh(b*x + a))^n, x)","F",0
185,1,380,0,0.535908," ","integrate(x^4*arccoth(tanh(b*x+a))^n,x, algorithm=""maxima"")","\frac{{\left(4 \, {\left(n^{4} + 10 \, n^{3} + 35 \, n^{2} + 50 \, n + 24\right)} b^{5} x^{5} - 3 i \, \pi^{5} + 30 \, \pi^{4} a + 120 i \, \pi^{3} a^{2} - 240 \, \pi^{2} a^{3} - 240 i \, \pi a^{4} + 96 \, a^{5} - 2 \, {\left(i \, \pi {\left(n^{4} + 6 \, n^{3} + 11 \, n^{2} + 6 \, n\right)} b^{4} - 2 \, {\left(n^{4} + 6 \, n^{3} + 11 \, n^{2} + 6 \, n\right)} a b^{4}\right)} x^{4} + {\left(4 \, \pi^{2} {\left(n^{3} + 3 \, n^{2} + 2 \, n\right)} b^{3} + 16 i \, \pi {\left(n^{3} + 3 \, n^{2} + 2 \, n\right)} a b^{3} - 16 \, {\left(n^{3} + 3 \, n^{2} + 2 \, n\right)} a^{2} b^{3}\right)} x^{3} + {\left(6 i \, \pi^{3} {\left(n^{2} + n\right)} b^{2} - 36 \, \pi^{2} {\left(n^{2} + n\right)} a b^{2} - 72 i \, \pi {\left(n^{2} + n\right)} a^{2} b^{2} + 48 \, {\left(n^{2} + n\right)} a^{3} b^{2}\right)} x^{2} - {\left(6 \, \pi^{4} b n + 48 i \, \pi^{3} a b n - 144 \, \pi^{2} a^{2} b n - 192 i \, \pi a^{3} b n + 96 \, a^{4} b n\right)} x\right)} {\left(\cosh\left(-n \log\left(-i \, \pi + 2 \, b x + 2 \, a\right)\right) - \sinh\left(-n \log\left(-i \, \pi + 2 \, b x + 2 \, a\right)\right)\right)}}{{\left(2^{n + 2} n^{5} + 15 \cdot 2^{n + 2} n^{4} + 85 \cdot 2^{n + 2} n^{3} + 225 \cdot 2^{n + 2} n^{2} + 137 \cdot 2^{n + 3} n + 15 \cdot 2^{n + 5}\right)} b^{5}}"," ",0,"(4*(n^4 + 10*n^3 + 35*n^2 + 50*n + 24)*b^5*x^5 - 3*I*pi^5 + 30*pi^4*a + 120*I*pi^3*a^2 - 240*pi^2*a^3 - 240*I*pi*a^4 + 96*a^5 - 2*(I*pi*(n^4 + 6*n^3 + 11*n^2 + 6*n)*b^4 - 2*(n^4 + 6*n^3 + 11*n^2 + 6*n)*a*b^4)*x^4 + (4*pi^2*(n^3 + 3*n^2 + 2*n)*b^3 + 16*I*pi*(n^3 + 3*n^2 + 2*n)*a*b^3 - 16*(n^3 + 3*n^2 + 2*n)*a^2*b^3)*x^3 + (6*I*pi^3*(n^2 + n)*b^2 - 36*pi^2*(n^2 + n)*a*b^2 - 72*I*pi*(n^2 + n)*a^2*b^2 + 48*(n^2 + n)*a^3*b^2)*x^2 - (6*pi^4*b*n + 48*I*pi^3*a*b*n - 144*pi^2*a^2*b*n - 192*I*pi*a^3*b*n + 96*a^4*b*n)*x)*(cosh(-n*log(-I*pi + 2*b*x + 2*a)) - sinh(-n*log(-I*pi + 2*b*x + 2*a)))/((2^(n + 2)*n^5 + 15*2^(n + 2)*n^4 + 85*2^(n + 2)*n^3 + 225*2^(n + 2)*n^2 + 137*2^(n + 3)*n + 15*2^(n + 5))*b^5)","C",0
186,1,255,0,0.533507," ","integrate(x^3*arccoth(tanh(b*x+a))^n,x, algorithm=""maxima"")","\frac{{\left(8 \, {\left(n^{3} + 6 \, n^{2} + 11 \, n + 6\right)} b^{4} x^{4} - 3 \, \pi^{4} - 24 i \, \pi^{3} a + 72 \, \pi^{2} a^{2} + 96 i \, \pi a^{3} - 48 \, a^{4} + {\left(-4 i \, \pi {\left(n^{3} + 3 \, n^{2} + 2 \, n\right)} b^{3} + 8 \, {\left(n^{3} + 3 \, n^{2} + 2 \, n\right)} a b^{3}\right)} x^{3} + {\left(6 \, \pi^{2} {\left(n^{2} + n\right)} b^{2} + 24 i \, \pi {\left(n^{2} + n\right)} a b^{2} - 24 \, {\left(n^{2} + n\right)} a^{2} b^{2}\right)} x^{2} + {\left(6 i \, \pi^{3} b n - 36 \, \pi^{2} a b n - 72 i \, \pi a^{2} b n + 48 \, a^{3} b n\right)} x\right)} {\left(\cosh\left(-n \log\left(-i \, \pi + 2 \, b x + 2 \, a\right)\right) - \sinh\left(-n \log\left(-i \, \pi + 2 \, b x + 2 \, a\right)\right)\right)}}{{\left(2^{n + 3} n^{4} + 5 \cdot 2^{n + 4} n^{3} + 35 \cdot 2^{n + 3} n^{2} + 25 \cdot 2^{n + 4} n + 3 \cdot 2^{n + 6}\right)} b^{4}}"," ",0,"(8*(n^3 + 6*n^2 + 11*n + 6)*b^4*x^4 - 3*pi^4 - 24*I*pi^3*a + 72*pi^2*a^2 + 96*I*pi*a^3 - 48*a^4 + (-4*I*pi*(n^3 + 3*n^2 + 2*n)*b^3 + 8*(n^3 + 3*n^2 + 2*n)*a*b^3)*x^3 + (6*pi^2*(n^2 + n)*b^2 + 24*I*pi*(n^2 + n)*a*b^2 - 24*(n^2 + n)*a^2*b^2)*x^2 + (6*I*pi^3*b*n - 36*pi^2*a*b*n - 72*I*pi*a^2*b*n + 48*a^3*b*n)*x)*(cosh(-n*log(-I*pi + 2*b*x + 2*a)) - sinh(-n*log(-I*pi + 2*b*x + 2*a)))/((2^(n + 3)*n^4 + 5*2^(n + 4)*n^3 + 35*2^(n + 3)*n^2 + 25*2^(n + 4)*n + 3*2^(n + 6))*b^4)","C",0
187,1,166,0,0.543184," ","integrate(x^2*arccoth(tanh(b*x+a))^n,x, algorithm=""maxima"")","\frac{{\left(4 \, {\left(n^{2} + 3 \, n + 2\right)} b^{3} x^{3} + i \, \pi^{3} - 6 \, \pi^{2} a - 12 i \, \pi a^{2} + 8 \, a^{3} - 2 \, {\left(i \, \pi {\left(n^{2} + n\right)} b^{2} - 2 \, {\left(n^{2} + n\right)} a b^{2}\right)} x^{2} + {\left(2 \, \pi^{2} b n + 8 i \, \pi a b n - 8 \, a^{2} b n\right)} x\right)} {\left(\cosh\left(-n \log\left(-i \, \pi + 2 \, b x + 2 \, a\right)\right) - \sinh\left(-n \log\left(-i \, \pi + 2 \, b x + 2 \, a\right)\right)\right)}}{{\left(2^{n + 2} n^{3} + 3 \cdot 2^{n + 3} n^{2} + 11 \cdot 2^{n + 2} n + 3 \cdot 2^{n + 3}\right)} b^{3}}"," ",0,"(4*(n^2 + 3*n + 2)*b^3*x^3 + I*pi^3 - 6*pi^2*a - 12*I*pi*a^2 + 8*a^3 - 2*(I*pi*(n^2 + n)*b^2 - 2*(n^2 + n)*a*b^2)*x^2 + (2*pi^2*b*n + 8*I*pi*a*b*n - 8*a^2*b*n)*x)*(cosh(-n*log(-I*pi + 2*b*x + 2*a)) - sinh(-n*log(-I*pi + 2*b*x + 2*a)))/((2^(n + 2)*n^3 + 3*2^(n + 3)*n^2 + 11*2^(n + 2)*n + 3*2^(n + 3))*b^3)","C",0
188,1,101,0,0.536513," ","integrate(x*arccoth(tanh(b*x+a))^n,x, algorithm=""maxima"")","\frac{{\left(4 \, b^{2} {\left(n + 1\right)} x^{2} + \pi^{2} + 4 i \, \pi a - 4 \, a^{2} + {\left(-2 i \, \pi b n + 4 \, a b n\right)} x\right)} {\left(\cosh\left(-n \log\left(-i \, \pi + 2 \, b x + 2 \, a\right)\right) - \sinh\left(-n \log\left(-i \, \pi + 2 \, b x + 2 \, a\right)\right)\right)}}{{\left(2^{n + 2} n^{2} + 3 \cdot 2^{n + 2} n + 2^{n + 3}\right)} b^{2}}"," ",0,"(4*b^2*(n + 1)*x^2 + pi^2 + 4*I*pi*a - 4*a^2 + (-2*I*pi*b*n + 4*a*b*n)*x)*(cosh(-n*log(-I*pi + 2*b*x + 2*a)) - sinh(-n*log(-I*pi + 2*b*x + 2*a)))/((2^(n + 2)*n^2 + 3*2^(n + 2)*n + 2^(n + 3))*b^2)","C",0
189,1,65,0,0.525256," ","integrate(arccoth(tanh(b*x+a))^n,x, algorithm=""maxima"")","\frac{{\left(-i \, \pi + 2 \, b x + 2 \, a\right)} {\left(\cosh\left(-n \log\left(-i \, \pi + 2 \, b x + 2 \, a\right)\right) - \sinh\left(-n \log\left(-i \, \pi + 2 \, b x + 2 \, a\right)\right)\right)}}{{\left(2^{n + 1} n + 2^{n + 1}\right)} b}"," ",0,"(-I*pi + 2*b*x + 2*a)*(cosh(-n*log(-I*pi + 2*b*x + 2*a)) - sinh(-n*log(-I*pi + 2*b*x + 2*a)))/((2^(n + 1)*n + 2^(n + 1))*b)","C",0
190,0,0,0,0.000000," ","integrate(arccoth(tanh(b*x+a))^n/x,x, algorithm=""maxima"")","\int \frac{\operatorname{arcoth}\left(\tanh\left(b x + a\right)\right)^{n}}{x}\,{d x}"," ",0,"integrate(arccoth(tanh(b*x + a))^n/x, x)","F",0
191,0,0,0,0.000000," ","integrate(arccoth(tanh(b*x+a))^n/x^2,x, algorithm=""maxima"")","\int \frac{\operatorname{arcoth}\left(\tanh\left(b x + a\right)\right)^{n}}{x^{2}}\,{d x}"," ",0,"integrate(arccoth(tanh(b*x + a))^n/x^2, x)","F",0
192,0,0,0,0.000000," ","integrate(arccoth(tanh(b*x+a))^n/x^3,x, algorithm=""maxima"")","\int \frac{\operatorname{arcoth}\left(\tanh\left(b x + a\right)\right)^{n}}{x^{3}}\,{d x}"," ",0,"integrate(arccoth(tanh(b*x + a))^n/x^3, x)","F",0
193,1,38,0,0.321734," ","integrate(x^m*arccoth(tanh(b*x+a)),x, algorithm=""maxima"")","-\frac{b x^{2} x^{m}}{{\left(m + 2\right)} {\left(m + 1\right)}} + \frac{x^{m + 1} \operatorname{arcoth}\left(\tanh\left(b x + a\right)\right)}{m + 1}"," ",0,"-b*x^2*x^m/((m + 2)*(m + 1)) + x^(m + 1)*arccoth(tanh(b*x + a))/(m + 1)","A",0
194,1,13,0,0.308583," ","integrate(x^2*arccoth(coth(b*x+a)),x, algorithm=""maxima"")","\frac{1}{4} \, b x^{4} + \frac{1}{3} \, a x^{3}"," ",0,"1/4*b*x^4 + 1/3*a*x^3","A",0
195,1,13,0,0.314460," ","integrate(x*arccoth(coth(b*x+a)),x, algorithm=""maxima"")","\frac{1}{3} \, b x^{3} + \frac{1}{2} \, a x^{2}"," ",0,"1/3*b*x^3 + 1/2*a*x^2","A",0
196,1,10,0,0.305662," ","integrate(arccoth(coth(b*x+a)),x, algorithm=""maxima"")","\frac{1}{2} \, b x^{2} + a x"," ",0,"1/2*b*x^2 + a*x","A",0
197,1,8,0,0.307107," ","integrate(arccoth(coth(b*x+a))/x,x, algorithm=""maxima"")","b x + a \log\left(x\right)"," ",0,"b*x + a*log(x)","A",0
198,1,11,0,0.310634," ","integrate(arccoth(coth(b*x+a))/x^2,x, algorithm=""maxima"")","b \log\left(x\right) - \frac{a}{x}"," ",0,"b*log(x) - a/x","A",0
199,1,11,0,0.309346," ","integrate(arccoth(coth(b*x+a))/x^3,x, algorithm=""maxima"")","-\frac{2 \, b x + a}{2 \, x^{2}}"," ",0,"-1/2*(2*b*x + a)/x^2","A",0
200,1,33,0,0.365526," ","integrate(arccoth(cosh(x)),x, algorithm=""maxima"")","x \operatorname{arcoth}\left(\cosh\left(x\right)\right) - x \log\left(e^{x} + 1\right) + x \log\left(-e^{x} + 1\right) - {\rm Li}_2\left(-e^{x}\right) + {\rm Li}_2\left(e^{x}\right)"," ",0,"x*arccoth(cosh(x)) - x*log(e^x + 1) + x*log(-e^x + 1) - dilog(-e^x) + dilog(e^x)","A",0
201,1,56,0,0.375232," ","integrate(x*arccoth(cosh(x)),x, algorithm=""maxima"")","\frac{1}{2} \, x^{2} \operatorname{arcoth}\left(\cosh\left(x\right)\right) - \frac{1}{2} \, x^{2} \log\left(e^{x} + 1\right) + \frac{1}{2} \, x^{2} \log\left(-e^{x} + 1\right) - x {\rm Li}_2\left(-e^{x}\right) + x {\rm Li}_2\left(e^{x}\right) + {\rm Li}_{3}(-e^{x}) - {\rm Li}_{3}(e^{x})"," ",0,"1/2*x^2*arccoth(cosh(x)) - 1/2*x^2*log(e^x + 1) + 1/2*x^2*log(-e^x + 1) - x*dilog(-e^x) + x*dilog(e^x) + polylog(3, -e^x) - polylog(3, e^x)","A",0
202,1,78,0,0.372925," ","integrate(x^2*arccoth(cosh(x)),x, algorithm=""maxima"")","\frac{1}{3} \, x^{3} \operatorname{arcoth}\left(\cosh\left(x\right)\right) - \frac{1}{3} \, x^{3} \log\left(e^{x} + 1\right) + \frac{1}{3} \, x^{3} \log\left(-e^{x} + 1\right) - x^{2} {\rm Li}_2\left(-e^{x}\right) + x^{2} {\rm Li}_2\left(e^{x}\right) + 2 \, x {\rm Li}_{3}(-e^{x}) - 2 \, x {\rm Li}_{3}(e^{x}) - 2 \, {\rm Li}_{4}(-e^{x}) + 2 \, {\rm Li}_{4}(e^{x})"," ",0,"1/3*x^3*arccoth(cosh(x)) - 1/3*x^3*log(e^x + 1) + 1/3*x^3*log(-e^x + 1) - x^2*dilog(-e^x) + x^2*dilog(e^x) + 2*x*polylog(3, -e^x) - 2*x*polylog(3, e^x) - 2*polylog(4, -e^x) + 2*polylog(4, e^x)","A",0
203,1,281,0,0.709064," ","integrate(x^2*arccoth(c+d*tanh(b*x+a)),x, algorithm=""maxima"")","\frac{1}{3} \, x^{3} \operatorname{arcoth}\left(d \tanh\left(b x + a\right) + c\right) - \frac{1}{18} \, b d {\left(\frac{4 \, b^{3} x^{3} \log\left(\frac{{\left(c + d + 1\right)} e^{\left(2 \, b x + 2 \, a\right)}}{c - d + 1} + 1\right) + 6 \, b^{2} x^{2} {\rm Li}_2\left(-\frac{{\left(c + d + 1\right)} e^{\left(2 \, b x + 2 \, a\right)}}{c - d + 1}\right) - 6 \, b x {\rm Li}_{3}(-\frac{{\left(c + d + 1\right)} e^{\left(2 \, b x + 2 \, a\right)}}{c - d + 1}) + 3 \, {\rm Li}_{4}(-\frac{{\left(c + d + 1\right)} e^{\left(2 \, b x + 2 \, a\right)}}{c - d + 1})}{b^{4} d} - \frac{4 \, b^{3} x^{3} \log\left(\frac{{\left(c + d - 1\right)} e^{\left(2 \, b x + 2 \, a\right)}}{c - d - 1} + 1\right) + 6 \, b^{2} x^{2} {\rm Li}_2\left(-\frac{{\left(c + d - 1\right)} e^{\left(2 \, b x + 2 \, a\right)}}{c - d - 1}\right) - 6 \, b x {\rm Li}_{3}(-\frac{{\left(c + d - 1\right)} e^{\left(2 \, b x + 2 \, a\right)}}{c - d - 1}) + 3 \, {\rm Li}_{4}(-\frac{{\left(c + d - 1\right)} e^{\left(2 \, b x + 2 \, a\right)}}{c - d - 1})}{b^{4} d}\right)}"," ",0,"1/3*x^3*arccoth(d*tanh(b*x + a) + c) - 1/18*b*d*((4*b^3*x^3*log((c + d + 1)*e^(2*b*x + 2*a)/(c - d + 1) + 1) + 6*b^2*x^2*dilog(-(c + d + 1)*e^(2*b*x + 2*a)/(c - d + 1)) - 6*b*x*polylog(3, -(c + d + 1)*e^(2*b*x + 2*a)/(c - d + 1)) + 3*polylog(4, -(c + d + 1)*e^(2*b*x + 2*a)/(c - d + 1)))/(b^4*d) - (4*b^3*x^3*log((c + d - 1)*e^(2*b*x + 2*a)/(c - d - 1) + 1) + 6*b^2*x^2*dilog(-(c + d - 1)*e^(2*b*x + 2*a)/(c - d - 1)) - 6*b*x*polylog(3, -(c + d - 1)*e^(2*b*x + 2*a)/(c - d - 1)) + 3*polylog(4, -(c + d - 1)*e^(2*b*x + 2*a)/(c - d - 1)))/(b^4*d))","A",0
204,1,215,0,0.714424," ","integrate(x*arccoth(c+d*tanh(b*x+a)),x, algorithm=""maxima"")","-\frac{1}{8} \, b d {\left(\frac{2 \, b^{2} x^{2} \log\left(\frac{{\left(c + d + 1\right)} e^{\left(2 \, b x + 2 \, a\right)}}{c - d + 1} + 1\right) + 2 \, b x {\rm Li}_2\left(-\frac{{\left(c + d + 1\right)} e^{\left(2 \, b x + 2 \, a\right)}}{c - d + 1}\right) - {\rm Li}_{3}(-\frac{{\left(c + d + 1\right)} e^{\left(2 \, b x + 2 \, a\right)}}{c - d + 1})}{b^{3} d} - \frac{2 \, b^{2} x^{2} \log\left(\frac{{\left(c + d - 1\right)} e^{\left(2 \, b x + 2 \, a\right)}}{c - d - 1} + 1\right) + 2 \, b x {\rm Li}_2\left(-\frac{{\left(c + d - 1\right)} e^{\left(2 \, b x + 2 \, a\right)}}{c - d - 1}\right) - {\rm Li}_{3}(-\frac{{\left(c + d - 1\right)} e^{\left(2 \, b x + 2 \, a\right)}}{c - d - 1})}{b^{3} d}\right)} + \frac{1}{2} \, x^{2} \operatorname{arcoth}\left(d \tanh\left(b x + a\right) + c\right)"," ",0,"-1/8*b*d*((2*b^2*x^2*log((c + d + 1)*e^(2*b*x + 2*a)/(c - d + 1) + 1) + 2*b*x*dilog(-(c + d + 1)*e^(2*b*x + 2*a)/(c - d + 1)) - polylog(3, -(c + d + 1)*e^(2*b*x + 2*a)/(c - d + 1)))/(b^3*d) - (2*b^2*x^2*log((c + d - 1)*e^(2*b*x + 2*a)/(c - d - 1) + 1) + 2*b*x*dilog(-(c + d - 1)*e^(2*b*x + 2*a)/(c - d - 1)) - polylog(3, -(c + d - 1)*e^(2*b*x + 2*a)/(c - d - 1)))/(b^3*d)) + 1/2*x^2*arccoth(d*tanh(b*x + a) + c)","A",0
205,1,142,0,0.688039," ","integrate(arccoth(c+d*tanh(b*x+a)),x, algorithm=""maxima"")","-\frac{1}{4} \, b d {\left(\frac{2 \, b x \log\left(\frac{{\left(c + d + 1\right)} e^{\left(2 \, b x + 2 \, a\right)}}{c - d + 1} + 1\right) + {\rm Li}_2\left(-\frac{{\left(c + d + 1\right)} e^{\left(2 \, b x + 2 \, a\right)}}{c - d + 1}\right)}{b^{2} d} - \frac{2 \, b x \log\left(\frac{{\left(c + d - 1\right)} e^{\left(2 \, b x + 2 \, a\right)}}{c - d - 1} + 1\right) + {\rm Li}_2\left(-\frac{{\left(c + d - 1\right)} e^{\left(2 \, b x + 2 \, a\right)}}{c - d - 1}\right)}{b^{2} d}\right)} + x \operatorname{arcoth}\left(d \tanh\left(b x + a\right) + c\right)"," ",0,"-1/4*b*d*((2*b*x*log((c + d + 1)*e^(2*b*x + 2*a)/(c - d + 1) + 1) + dilog(-(c + d + 1)*e^(2*b*x + 2*a)/(c - d + 1)))/(b^2*d) - (2*b*x*log((c + d - 1)*e^(2*b*x + 2*a)/(c - d - 1) + 1) + dilog(-(c + d - 1)*e^(2*b*x + 2*a)/(c - d - 1)))/(b^2*d)) + x*arccoth(d*tanh(b*x + a) + c)","A",0
206,0,0,0,0.000000," ","integrate(arccoth(c+d*tanh(b*x+a))/x,x, algorithm=""maxima"")","\int \frac{\operatorname{arcoth}\left(d \tanh\left(b x + a\right) + c\right)}{x}\,{d x}"," ",0,"integrate(arccoth(d*tanh(b*x + a) + c)/x, x)","F",0
207,1,149,0,1.123541," ","integrate(x^3*arccoth(1+d+d*tanh(b*x+a)),x, algorithm=""maxima"")","\frac{1}{4} \, x^{4} \operatorname{arcoth}\left(d \tanh\left(b x + a\right) + d + 1\right) + \frac{1}{40} \, {\left(\frac{2 \, x^{5}}{d} - \frac{5 \, {\left(2 \, b^{4} x^{4} \log\left({\left(d + 1\right)} e^{\left(2 \, b x + 2 \, a\right)} + 1\right) + 4 \, b^{3} x^{3} {\rm Li}_2\left(-{\left(d + 1\right)} e^{\left(2 \, b x + 2 \, a\right)}\right) - 6 \, b^{2} x^{2} {\rm Li}_{3}(-{\left(d + 1\right)} e^{\left(2 \, b x + 2 \, a\right)}) + 6 \, b x {\rm Li}_{4}(-{\left(d + 1\right)} e^{\left(2 \, b x + 2 \, a\right)}) - 3 \, {\rm Li}_{5}(-{\left(d + 1\right)} e^{\left(2 \, b x + 2 \, a\right)})\right)}}{b^{5} d}\right)} b d"," ",0,"1/4*x^4*arccoth(d*tanh(b*x + a) + d + 1) + 1/40*(2*x^5/d - 5*(2*b^4*x^4*log((d + 1)*e^(2*b*x + 2*a) + 1) + 4*b^3*x^3*dilog(-(d + 1)*e^(2*b*x + 2*a)) - 6*b^2*x^2*polylog(3, -(d + 1)*e^(2*b*x + 2*a)) + 6*b*x*polylog(4, -(d + 1)*e^(2*b*x + 2*a)) - 3*polylog(5, -(d + 1)*e^(2*b*x + 2*a)))/(b^5*d))*b*d","A",0
208,1,125,0,1.093822," ","integrate(x^2*arccoth(1+d+d*tanh(b*x+a)),x, algorithm=""maxima"")","\frac{1}{3} \, x^{3} \operatorname{arcoth}\left(d \tanh\left(b x + a\right) + d + 1\right) + \frac{1}{36} \, {\left(\frac{3 \, x^{4}}{d} - \frac{2 \, {\left(4 \, b^{3} x^{3} \log\left({\left(d + 1\right)} e^{\left(2 \, b x + 2 \, a\right)} + 1\right) + 6 \, b^{2} x^{2} {\rm Li}_2\left(-{\left(d + 1\right)} e^{\left(2 \, b x + 2 \, a\right)}\right) - 6 \, b x {\rm Li}_{3}(-{\left(d + 1\right)} e^{\left(2 \, b x + 2 \, a\right)}) + 3 \, {\rm Li}_{4}(-{\left(d + 1\right)} e^{\left(2 \, b x + 2 \, a\right)})\right)}}{b^{4} d}\right)} b d"," ",0,"1/3*x^3*arccoth(d*tanh(b*x + a) + d + 1) + 1/36*(3*x^4/d - 2*(4*b^3*x^3*log((d + 1)*e^(2*b*x + 2*a) + 1) + 6*b^2*x^2*dilog(-(d + 1)*e^(2*b*x + 2*a)) - 6*b*x*polylog(3, -(d + 1)*e^(2*b*x + 2*a)) + 3*polylog(4, -(d + 1)*e^(2*b*x + 2*a)))/(b^4*d))*b*d","A",0
209,1,101,0,1.098954," ","integrate(x*arccoth(1+d+d*tanh(b*x+a)),x, algorithm=""maxima"")","\frac{1}{24} \, {\left(\frac{4 \, x^{3}}{d} - \frac{3 \, {\left(2 \, b^{2} x^{2} \log\left({\left(d + 1\right)} e^{\left(2 \, b x + 2 \, a\right)} + 1\right) + 2 \, b x {\rm Li}_2\left(-{\left(d + 1\right)} e^{\left(2 \, b x + 2 \, a\right)}\right) - {\rm Li}_{3}(-{\left(d + 1\right)} e^{\left(2 \, b x + 2 \, a\right)})\right)}}{b^{3} d}\right)} b d + \frac{1}{2} \, x^{2} \operatorname{arcoth}\left(d \tanh\left(b x + a\right) + d + 1\right)"," ",0,"1/24*(4*x^3/d - 3*(2*b^2*x^2*log((d + 1)*e^(2*b*x + 2*a) + 1) + 2*b*x*dilog(-(d + 1)*e^(2*b*x + 2*a)) - polylog(3, -(d + 1)*e^(2*b*x + 2*a)))/(b^3*d))*b*d + 1/2*x^2*arccoth(d*tanh(b*x + a) + d + 1)","A",0
210,1,72,0,1.098748," ","integrate(arccoth(1+d+d*tanh(b*x+a)),x, algorithm=""maxima"")","\frac{1}{4} \, b d {\left(\frac{2 \, x^{2}}{d} - \frac{2 \, b x \log\left({\left(d + 1\right)} e^{\left(2 \, b x + 2 \, a\right)} + 1\right) + {\rm Li}_2\left(-{\left(d + 1\right)} e^{\left(2 \, b x + 2 \, a\right)}\right)}{b^{2} d}\right)} + x \operatorname{arcoth}\left(d \tanh\left(b x + a\right) + d + 1\right)"," ",0,"1/4*b*d*(2*x^2/d - (2*b*x*log((d + 1)*e^(2*b*x + 2*a) + 1) + dilog(-(d + 1)*e^(2*b*x + 2*a)))/(b^2*d)) + x*arccoth(d*tanh(b*x + a) + d + 1)","A",0
211,0,0,0,0.000000," ","integrate(arccoth(1+d+d*tanh(b*x+a))/x,x, algorithm=""maxima"")","\int \frac{\operatorname{arcoth}\left(d \tanh\left(b x + a\right) + d + 1\right)}{x}\,{d x}"," ",0,"integrate(arccoth(d*tanh(b*x + a) + d + 1)/x, x)","F",0
212,1,146,0,1.099722," ","integrate(x^3*arccoth(1-d-d*tanh(b*x+a)),x, algorithm=""maxima"")","-\frac{1}{4} \, x^{4} \operatorname{arcoth}\left(d \tanh\left(b x + a\right) + d - 1\right) + \frac{1}{40} \, {\left(\frac{2 \, x^{5}}{d} - \frac{5 \, {\left(2 \, b^{4} x^{4} \log\left(-{\left(d - 1\right)} e^{\left(2 \, b x + 2 \, a\right)} + 1\right) + 4 \, b^{3} x^{3} {\rm Li}_2\left({\left(d - 1\right)} e^{\left(2 \, b x + 2 \, a\right)}\right) - 6 \, b^{2} x^{2} {\rm Li}_{3}({\left(d - 1\right)} e^{\left(2 \, b x + 2 \, a\right)}) + 6 \, b x {\rm Li}_{4}({\left(d - 1\right)} e^{\left(2 \, b x + 2 \, a\right)}) - 3 \, {\rm Li}_{5}({\left(d - 1\right)} e^{\left(2 \, b x + 2 \, a\right)})\right)}}{b^{5} d}\right)} b d"," ",0,"-1/4*x^4*arccoth(d*tanh(b*x + a) + d - 1) + 1/40*(2*x^5/d - 5*(2*b^4*x^4*log(-(d - 1)*e^(2*b*x + 2*a) + 1) + 4*b^3*x^3*dilog((d - 1)*e^(2*b*x + 2*a)) - 6*b^2*x^2*polylog(3, (d - 1)*e^(2*b*x + 2*a)) + 6*b*x*polylog(4, (d - 1)*e^(2*b*x + 2*a)) - 3*polylog(5, (d - 1)*e^(2*b*x + 2*a)))/(b^5*d))*b*d","A",0
213,1,123,0,1.107361," ","integrate(x^2*arccoth(1-d-d*tanh(b*x+a)),x, algorithm=""maxima"")","-\frac{1}{3} \, x^{3} \operatorname{arcoth}\left(d \tanh\left(b x + a\right) + d - 1\right) + \frac{1}{36} \, {\left(\frac{3 \, x^{4}}{d} - \frac{2 \, {\left(4 \, b^{3} x^{3} \log\left(-{\left(d - 1\right)} e^{\left(2 \, b x + 2 \, a\right)} + 1\right) + 6 \, b^{2} x^{2} {\rm Li}_2\left({\left(d - 1\right)} e^{\left(2 \, b x + 2 \, a\right)}\right) - 6 \, b x {\rm Li}_{3}({\left(d - 1\right)} e^{\left(2 \, b x + 2 \, a\right)}) + 3 \, {\rm Li}_{4}({\left(d - 1\right)} e^{\left(2 \, b x + 2 \, a\right)})\right)}}{b^{4} d}\right)} b d"," ",0,"-1/3*x^3*arccoth(d*tanh(b*x + a) + d - 1) + 1/36*(3*x^4/d - 2*(4*b^3*x^3*log(-(d - 1)*e^(2*b*x + 2*a) + 1) + 6*b^2*x^2*dilog((d - 1)*e^(2*b*x + 2*a)) - 6*b*x*polylog(3, (d - 1)*e^(2*b*x + 2*a)) + 3*polylog(4, (d - 1)*e^(2*b*x + 2*a)))/(b^4*d))*b*d","A",0
214,1,100,0,1.097547," ","integrate(x*arccoth(1-d-d*tanh(b*x+a)),x, algorithm=""maxima"")","\frac{1}{24} \, {\left(\frac{4 \, x^{3}}{d} - \frac{3 \, {\left(2 \, b^{2} x^{2} \log\left(-{\left(d - 1\right)} e^{\left(2 \, b x + 2 \, a\right)} + 1\right) + 2 \, b x {\rm Li}_2\left({\left(d - 1\right)} e^{\left(2 \, b x + 2 \, a\right)}\right) - {\rm Li}_{3}({\left(d - 1\right)} e^{\left(2 \, b x + 2 \, a\right)})\right)}}{b^{3} d}\right)} b d - \frac{1}{2} \, x^{2} \operatorname{arcoth}\left(d \tanh\left(b x + a\right) + d - 1\right)"," ",0,"1/24*(4*x^3/d - 3*(2*b^2*x^2*log(-(d - 1)*e^(2*b*x + 2*a) + 1) + 2*b*x*dilog((d - 1)*e^(2*b*x + 2*a)) - polylog(3, (d - 1)*e^(2*b*x + 2*a)))/(b^3*d))*b*d - 1/2*x^2*arccoth(d*tanh(b*x + a) + d - 1)","A",0
215,1,73,0,1.102364," ","integrate(arccoth(1-d-d*tanh(b*x+a)),x, algorithm=""maxima"")","\frac{1}{4} \, b d {\left(\frac{2 \, x^{2}}{d} - \frac{2 \, b x \log\left(-{\left(d - 1\right)} e^{\left(2 \, b x + 2 \, a\right)} + 1\right) + {\rm Li}_2\left({\left(d - 1\right)} e^{\left(2 \, b x + 2 \, a\right)}\right)}{b^{2} d}\right)} - x \operatorname{arcoth}\left(d \tanh\left(b x + a\right) + d - 1\right)"," ",0,"1/4*b*d*(2*x^2/d - (2*b*x*log(-(d - 1)*e^(2*b*x + 2*a) + 1) + dilog((d - 1)*e^(2*b*x + 2*a)))/(b^2*d)) - x*arccoth(d*tanh(b*x + a) + d - 1)","A",0
216,0,0,0,0.000000," ","integrate(arccoth(1-d-d*tanh(b*x+a))/x,x, algorithm=""maxima"")","-\int \frac{\operatorname{arcoth}\left(d \tanh\left(b x + a\right) + d - 1\right)}{x}\,{d x}"," ",0,"-integrate(arccoth(d*tanh(b*x + a) + d - 1)/x, x)","F",0
217,1,277,0,0.701079," ","integrate(x^2*arccoth(c+d*coth(b*x+a)),x, algorithm=""maxima"")","\frac{1}{3} \, x^{3} \operatorname{arcoth}\left(d \coth\left(b x + a\right) + c\right) - \frac{1}{18} \, b d {\left(\frac{4 \, b^{3} x^{3} \log\left(-\frac{{\left(c + d + 1\right)} e^{\left(2 \, b x + 2 \, a\right)}}{c - d + 1} + 1\right) + 6 \, b^{2} x^{2} {\rm Li}_2\left(\frac{{\left(c + d + 1\right)} e^{\left(2 \, b x + 2 \, a\right)}}{c - d + 1}\right) - 6 \, b x {\rm Li}_{3}(\frac{{\left(c + d + 1\right)} e^{\left(2 \, b x + 2 \, a\right)}}{c - d + 1}) + 3 \, {\rm Li}_{4}(\frac{{\left(c + d + 1\right)} e^{\left(2 \, b x + 2 \, a\right)}}{c - d + 1})}{b^{4} d} - \frac{4 \, b^{3} x^{3} \log\left(-\frac{{\left(c + d - 1\right)} e^{\left(2 \, b x + 2 \, a\right)}}{c - d - 1} + 1\right) + 6 \, b^{2} x^{2} {\rm Li}_2\left(\frac{{\left(c + d - 1\right)} e^{\left(2 \, b x + 2 \, a\right)}}{c - d - 1}\right) - 6 \, b x {\rm Li}_{3}(\frac{{\left(c + d - 1\right)} e^{\left(2 \, b x + 2 \, a\right)}}{c - d - 1}) + 3 \, {\rm Li}_{4}(\frac{{\left(c + d - 1\right)} e^{\left(2 \, b x + 2 \, a\right)}}{c - d - 1})}{b^{4} d}\right)}"," ",0,"1/3*x^3*arccoth(d*coth(b*x + a) + c) - 1/18*b*d*((4*b^3*x^3*log(-(c + d + 1)*e^(2*b*x + 2*a)/(c - d + 1) + 1) + 6*b^2*x^2*dilog((c + d + 1)*e^(2*b*x + 2*a)/(c - d + 1)) - 6*b*x*polylog(3, (c + d + 1)*e^(2*b*x + 2*a)/(c - d + 1)) + 3*polylog(4, (c + d + 1)*e^(2*b*x + 2*a)/(c - d + 1)))/(b^4*d) - (4*b^3*x^3*log(-(c + d - 1)*e^(2*b*x + 2*a)/(c - d - 1) + 1) + 6*b^2*x^2*dilog((c + d - 1)*e^(2*b*x + 2*a)/(c - d - 1)) - 6*b*x*polylog(3, (c + d - 1)*e^(2*b*x + 2*a)/(c - d - 1)) + 3*polylog(4, (c + d - 1)*e^(2*b*x + 2*a)/(c - d - 1)))/(b^4*d))","A",0
218,1,213,0,0.738307," ","integrate(x*arccoth(c+d*coth(b*x+a)),x, algorithm=""maxima"")","-\frac{1}{8} \, b d {\left(\frac{2 \, b^{2} x^{2} \log\left(-\frac{{\left(c + d + 1\right)} e^{\left(2 \, b x + 2 \, a\right)}}{c - d + 1} + 1\right) + 2 \, b x {\rm Li}_2\left(\frac{{\left(c + d + 1\right)} e^{\left(2 \, b x + 2 \, a\right)}}{c - d + 1}\right) - {\rm Li}_{3}(\frac{{\left(c + d + 1\right)} e^{\left(2 \, b x + 2 \, a\right)}}{c - d + 1})}{b^{3} d} - \frac{2 \, b^{2} x^{2} \log\left(-\frac{{\left(c + d - 1\right)} e^{\left(2 \, b x + 2 \, a\right)}}{c - d - 1} + 1\right) + 2 \, b x {\rm Li}_2\left(\frac{{\left(c + d - 1\right)} e^{\left(2 \, b x + 2 \, a\right)}}{c - d - 1}\right) - {\rm Li}_{3}(\frac{{\left(c + d - 1\right)} e^{\left(2 \, b x + 2 \, a\right)}}{c - d - 1})}{b^{3} d}\right)} + \frac{1}{2} \, x^{2} \operatorname{arcoth}\left(d \coth\left(b x + a\right) + c\right)"," ",0,"-1/8*b*d*((2*b^2*x^2*log(-(c + d + 1)*e^(2*b*x + 2*a)/(c - d + 1) + 1) + 2*b*x*dilog((c + d + 1)*e^(2*b*x + 2*a)/(c - d + 1)) - polylog(3, (c + d + 1)*e^(2*b*x + 2*a)/(c - d + 1)))/(b^3*d) - (2*b^2*x^2*log(-(c + d - 1)*e^(2*b*x + 2*a)/(c - d - 1) + 1) + 2*b*x*dilog((c + d - 1)*e^(2*b*x + 2*a)/(c - d - 1)) - polylog(3, (c + d - 1)*e^(2*b*x + 2*a)/(c - d - 1)))/(b^3*d)) + 1/2*x^2*arccoth(d*coth(b*x + a) + c)","A",0
219,1,142,0,0.712935," ","integrate(arccoth(c+d*coth(b*x+a)),x, algorithm=""maxima"")","-\frac{1}{4} \, b d {\left(\frac{2 \, b x \log\left(-\frac{{\left(c + d + 1\right)} e^{\left(2 \, b x + 2 \, a\right)}}{c - d + 1} + 1\right) + {\rm Li}_2\left(\frac{{\left(c + d + 1\right)} e^{\left(2 \, b x + 2 \, a\right)}}{c - d + 1}\right)}{b^{2} d} - \frac{2 \, b x \log\left(-\frac{{\left(c + d - 1\right)} e^{\left(2 \, b x + 2 \, a\right)}}{c - d - 1} + 1\right) + {\rm Li}_2\left(\frac{{\left(c + d - 1\right)} e^{\left(2 \, b x + 2 \, a\right)}}{c - d - 1}\right)}{b^{2} d}\right)} + x \operatorname{arcoth}\left(d \coth\left(b x + a\right) + c\right)"," ",0,"-1/4*b*d*((2*b*x*log(-(c + d + 1)*e^(2*b*x + 2*a)/(c - d + 1) + 1) + dilog((c + d + 1)*e^(2*b*x + 2*a)/(c - d + 1)))/(b^2*d) - (2*b*x*log(-(c + d - 1)*e^(2*b*x + 2*a)/(c - d - 1) + 1) + dilog((c + d - 1)*e^(2*b*x + 2*a)/(c - d - 1)))/(b^2*d)) + x*arccoth(d*coth(b*x + a) + c)","A",0
220,0,0,0,0.000000," ","integrate(arccoth(c+d*coth(b*x+a))/x,x, algorithm=""maxima"")","\int \frac{\operatorname{arcoth}\left(d \coth\left(b x + a\right) + c\right)}{x}\,{d x}"," ",0,"integrate(arccoth(d*coth(b*x + a) + c)/x, x)","F",0
221,1,146,0,1.092041," ","integrate(x^3*arccoth(1+d+d*coth(b*x+a)),x, algorithm=""maxima"")","\frac{1}{4} \, x^{4} \operatorname{arcoth}\left(d \coth\left(b x + a\right) + d + 1\right) + \frac{1}{40} \, {\left(\frac{2 \, x^{5}}{d} - \frac{5 \, {\left(2 \, b^{4} x^{4} \log\left(-{\left(d + 1\right)} e^{\left(2 \, b x + 2 \, a\right)} + 1\right) + 4 \, b^{3} x^{3} {\rm Li}_2\left({\left(d + 1\right)} e^{\left(2 \, b x + 2 \, a\right)}\right) - 6 \, b^{2} x^{2} {\rm Li}_{3}({\left(d + 1\right)} e^{\left(2 \, b x + 2 \, a\right)}) + 6 \, b x {\rm Li}_{4}({\left(d + 1\right)} e^{\left(2 \, b x + 2 \, a\right)}) - 3 \, {\rm Li}_{5}({\left(d + 1\right)} e^{\left(2 \, b x + 2 \, a\right)})\right)}}{b^{5} d}\right)} b d"," ",0,"1/4*x^4*arccoth(d*coth(b*x + a) + d + 1) + 1/40*(2*x^5/d - 5*(2*b^4*x^4*log(-(d + 1)*e^(2*b*x + 2*a) + 1) + 4*b^3*x^3*dilog((d + 1)*e^(2*b*x + 2*a)) - 6*b^2*x^2*polylog(3, (d + 1)*e^(2*b*x + 2*a)) + 6*b*x*polylog(4, (d + 1)*e^(2*b*x + 2*a)) - 3*polylog(5, (d + 1)*e^(2*b*x + 2*a)))/(b^5*d))*b*d","A",0
222,1,123,0,1.107478," ","integrate(x^2*arccoth(1+d+d*coth(b*x+a)),x, algorithm=""maxima"")","\frac{1}{3} \, x^{3} \operatorname{arcoth}\left(d \coth\left(b x + a\right) + d + 1\right) + \frac{1}{36} \, {\left(\frac{3 \, x^{4}}{d} - \frac{2 \, {\left(4 \, b^{3} x^{3} \log\left(-{\left(d + 1\right)} e^{\left(2 \, b x + 2 \, a\right)} + 1\right) + 6 \, b^{2} x^{2} {\rm Li}_2\left({\left(d + 1\right)} e^{\left(2 \, b x + 2 \, a\right)}\right) - 6 \, b x {\rm Li}_{3}({\left(d + 1\right)} e^{\left(2 \, b x + 2 \, a\right)}) + 3 \, {\rm Li}_{4}({\left(d + 1\right)} e^{\left(2 \, b x + 2 \, a\right)})\right)}}{b^{4} d}\right)} b d"," ",0,"1/3*x^3*arccoth(d*coth(b*x + a) + d + 1) + 1/36*(3*x^4/d - 2*(4*b^3*x^3*log(-(d + 1)*e^(2*b*x + 2*a) + 1) + 6*b^2*x^2*dilog((d + 1)*e^(2*b*x + 2*a)) - 6*b*x*polylog(3, (d + 1)*e^(2*b*x + 2*a)) + 3*polylog(4, (d + 1)*e^(2*b*x + 2*a)))/(b^4*d))*b*d","A",0
223,1,100,0,1.099761," ","integrate(x*arccoth(1+d+d*coth(b*x+a)),x, algorithm=""maxima"")","\frac{1}{24} \, {\left(\frac{4 \, x^{3}}{d} - \frac{3 \, {\left(2 \, b^{2} x^{2} \log\left(-{\left(d + 1\right)} e^{\left(2 \, b x + 2 \, a\right)} + 1\right) + 2 \, b x {\rm Li}_2\left({\left(d + 1\right)} e^{\left(2 \, b x + 2 \, a\right)}\right) - {\rm Li}_{3}({\left(d + 1\right)} e^{\left(2 \, b x + 2 \, a\right)})\right)}}{b^{3} d}\right)} b d + \frac{1}{2} \, x^{2} \operatorname{arcoth}\left(d \coth\left(b x + a\right) + d + 1\right)"," ",0,"1/24*(4*x^3/d - 3*(2*b^2*x^2*log(-(d + 1)*e^(2*b*x + 2*a) + 1) + 2*b*x*dilog((d + 1)*e^(2*b*x + 2*a)) - polylog(3, (d + 1)*e^(2*b*x + 2*a)))/(b^3*d))*b*d + 1/2*x^2*arccoth(d*coth(b*x + a) + d + 1)","A",0
224,1,72,0,1.098432," ","integrate(arccoth(1+d+d*coth(b*x+a)),x, algorithm=""maxima"")","\frac{1}{4} \, b d {\left(\frac{2 \, x^{2}}{d} - \frac{2 \, b x \log\left(-{\left(d + 1\right)} e^{\left(2 \, b x + 2 \, a\right)} + 1\right) + {\rm Li}_2\left({\left(d + 1\right)} e^{\left(2 \, b x + 2 \, a\right)}\right)}{b^{2} d}\right)} + x \operatorname{arcoth}\left(d \coth\left(b x + a\right) + d + 1\right)"," ",0,"1/4*b*d*(2*x^2/d - (2*b*x*log(-(d + 1)*e^(2*b*x + 2*a) + 1) + dilog((d + 1)*e^(2*b*x + 2*a)))/(b^2*d)) + x*arccoth(d*coth(b*x + a) + d + 1)","A",0
225,0,0,0,0.000000," ","integrate(arccoth(1+d+d*coth(b*x+a))/x,x, algorithm=""maxima"")","\int \frac{\operatorname{arcoth}\left(d \coth\left(b x + a\right) + d + 1\right)}{x}\,{d x}"," ",0,"integrate(arccoth(d*coth(b*x + a) + d + 1)/x, x)","F",0
226,1,149,0,1.099456," ","integrate(x^3*arccoth(1-d-d*coth(b*x+a)),x, algorithm=""maxima"")","-\frac{1}{4} \, x^{4} \operatorname{arcoth}\left(d \coth\left(b x + a\right) + d - 1\right) + \frac{1}{40} \, {\left(\frac{2 \, x^{5}}{d} - \frac{5 \, {\left(2 \, b^{4} x^{4} \log\left({\left(d - 1\right)} e^{\left(2 \, b x + 2 \, a\right)} + 1\right) + 4 \, b^{3} x^{3} {\rm Li}_2\left(-{\left(d - 1\right)} e^{\left(2 \, b x + 2 \, a\right)}\right) - 6 \, b^{2} x^{2} {\rm Li}_{3}(-{\left(d - 1\right)} e^{\left(2 \, b x + 2 \, a\right)}) + 6 \, b x {\rm Li}_{4}(-{\left(d - 1\right)} e^{\left(2 \, b x + 2 \, a\right)}) - 3 \, {\rm Li}_{5}(-{\left(d - 1\right)} e^{\left(2 \, b x + 2 \, a\right)})\right)}}{b^{5} d}\right)} b d"," ",0,"-1/4*x^4*arccoth(d*coth(b*x + a) + d - 1) + 1/40*(2*x^5/d - 5*(2*b^4*x^4*log((d - 1)*e^(2*b*x + 2*a) + 1) + 4*b^3*x^3*dilog(-(d - 1)*e^(2*b*x + 2*a)) - 6*b^2*x^2*polylog(3, -(d - 1)*e^(2*b*x + 2*a)) + 6*b*x*polylog(4, -(d - 1)*e^(2*b*x + 2*a)) - 3*polylog(5, -(d - 1)*e^(2*b*x + 2*a)))/(b^5*d))*b*d","A",0
227,1,125,0,1.104254," ","integrate(x^2*arccoth(1-d-d*coth(b*x+a)),x, algorithm=""maxima"")","-\frac{1}{3} \, x^{3} \operatorname{arcoth}\left(d \coth\left(b x + a\right) + d - 1\right) + \frac{1}{36} \, {\left(\frac{3 \, x^{4}}{d} - \frac{2 \, {\left(4 \, b^{3} x^{3} \log\left({\left(d - 1\right)} e^{\left(2 \, b x + 2 \, a\right)} + 1\right) + 6 \, b^{2} x^{2} {\rm Li}_2\left(-{\left(d - 1\right)} e^{\left(2 \, b x + 2 \, a\right)}\right) - 6 \, b x {\rm Li}_{3}(-{\left(d - 1\right)} e^{\left(2 \, b x + 2 \, a\right)}) + 3 \, {\rm Li}_{4}(-{\left(d - 1\right)} e^{\left(2 \, b x + 2 \, a\right)})\right)}}{b^{4} d}\right)} b d"," ",0,"-1/3*x^3*arccoth(d*coth(b*x + a) + d - 1) + 1/36*(3*x^4/d - 2*(4*b^3*x^3*log((d - 1)*e^(2*b*x + 2*a) + 1) + 6*b^2*x^2*dilog(-(d - 1)*e^(2*b*x + 2*a)) - 6*b*x*polylog(3, -(d - 1)*e^(2*b*x + 2*a)) + 3*polylog(4, -(d - 1)*e^(2*b*x + 2*a)))/(b^4*d))*b*d","A",0
228,1,101,0,1.115029," ","integrate(x*arccoth(1-d-d*coth(b*x+a)),x, algorithm=""maxima"")","\frac{1}{24} \, {\left(\frac{4 \, x^{3}}{d} - \frac{3 \, {\left(2 \, b^{2} x^{2} \log\left({\left(d - 1\right)} e^{\left(2 \, b x + 2 \, a\right)} + 1\right) + 2 \, b x {\rm Li}_2\left(-{\left(d - 1\right)} e^{\left(2 \, b x + 2 \, a\right)}\right) - {\rm Li}_{3}(-{\left(d - 1\right)} e^{\left(2 \, b x + 2 \, a\right)})\right)}}{b^{3} d}\right)} b d - \frac{1}{2} \, x^{2} \operatorname{arcoth}\left(d \coth\left(b x + a\right) + d - 1\right)"," ",0,"1/24*(4*x^3/d - 3*(2*b^2*x^2*log((d - 1)*e^(2*b*x + 2*a) + 1) + 2*b*x*dilog(-(d - 1)*e^(2*b*x + 2*a)) - polylog(3, -(d - 1)*e^(2*b*x + 2*a)))/(b^3*d))*b*d - 1/2*x^2*arccoth(d*coth(b*x + a) + d - 1)","A",0
229,1,73,0,1.111355," ","integrate(arccoth(1-d-d*coth(b*x+a)),x, algorithm=""maxima"")","\frac{1}{4} \, b d {\left(\frac{2 \, x^{2}}{d} - \frac{2 \, b x \log\left({\left(d - 1\right)} e^{\left(2 \, b x + 2 \, a\right)} + 1\right) + {\rm Li}_2\left(-{\left(d - 1\right)} e^{\left(2 \, b x + 2 \, a\right)}\right)}{b^{2} d}\right)} - x \operatorname{arcoth}\left(d \coth\left(b x + a\right) + d - 1\right)"," ",0,"1/4*b*d*(2*x^2/d - (2*b*x*log((d - 1)*e^(2*b*x + 2*a) + 1) + dilog(-(d - 1)*e^(2*b*x + 2*a)))/(b^2*d)) - x*arccoth(d*coth(b*x + a) + d - 1)","A",0
230,0,0,0,0.000000," ","integrate(arccoth(1-d-d*coth(b*x+a))/x,x, algorithm=""maxima"")","-\int \frac{\operatorname{arcoth}\left(d \coth\left(b x + a\right) + d - 1\right)}{x}\,{d x}"," ",0,"-integrate(arccoth(d*coth(b*x + a) + d - 1)/x, x)","F",0
231,0,0,0,0.000000," ","integrate((f*x+e)^3*arccoth(tan(b*x+a)),x, algorithm=""maxima"")","\frac{1}{16} \, {\left(f^{3} x^{4} + 4 \, e f^{2} x^{3} + 6 \, e^{2} f x^{2} + 4 \, e^{3} x\right)} \log\left(2 \, \cos\left(2 \, b x + 2 \, a\right)^{2} + 2 \, \sin\left(2 \, b x + 2 \, a\right)^{2} + 4 \, \sin\left(2 \, b x + 2 \, a\right) + 2\right) - \frac{1}{16} \, {\left(f^{3} x^{4} + 4 \, e f^{2} x^{3} + 6 \, e^{2} f x^{2} + 4 \, e^{3} x\right)} \log\left(2 \, \cos\left(2 \, b x + 2 \, a\right)^{2} + 2 \, \sin\left(2 \, b x + 2 \, a\right)^{2} - 4 \, \sin\left(2 \, b x + 2 \, a\right) + 2\right) - \int \frac{{\left(b f^{3} x^{4} + 4 \, b e f^{2} x^{3} + 6 \, b e^{2} f x^{2} + 4 \, b e^{3} x\right)} \cos\left(4 \, b x + 4 \, a\right) \cos\left(2 \, b x + 2 \, a\right) + {\left(b f^{3} x^{4} + 4 \, b e f^{2} x^{3} + 6 \, b e^{2} f x^{2} + 4 \, b e^{3} x\right)} \sin\left(4 \, b x + 4 \, a\right) \sin\left(2 \, b x + 2 \, a\right) + {\left(b f^{3} x^{4} + 4 \, b e f^{2} x^{3} + 6 \, b e^{2} f x^{2} + 4 \, b e^{3} x\right)} \cos\left(2 \, b x + 2 \, a\right)}{2 \, {\left(\cos\left(4 \, b x + 4 \, a\right)^{2} + \sin\left(4 \, b x + 4 \, a\right)^{2} + 2 \, \cos\left(4 \, b x + 4 \, a\right) + 1\right)}}\,{d x}"," ",0,"1/16*(f^3*x^4 + 4*e*f^2*x^3 + 6*e^2*f*x^2 + 4*e^3*x)*log(2*cos(2*b*x + 2*a)^2 + 2*sin(2*b*x + 2*a)^2 + 4*sin(2*b*x + 2*a) + 2) - 1/16*(f^3*x^4 + 4*e*f^2*x^3 + 6*e^2*f*x^2 + 4*e^3*x)*log(2*cos(2*b*x + 2*a)^2 + 2*sin(2*b*x + 2*a)^2 - 4*sin(2*b*x + 2*a) + 2) - integrate(1/2*((b*f^3*x^4 + 4*b*e*f^2*x^3 + 6*b*e^2*f*x^2 + 4*b*e^3*x)*cos(4*b*x + 4*a)*cos(2*b*x + 2*a) + (b*f^3*x^4 + 4*b*e*f^2*x^3 + 6*b*e^2*f*x^2 + 4*b*e^3*x)*sin(4*b*x + 4*a)*sin(2*b*x + 2*a) + (b*f^3*x^4 + 4*b*e*f^2*x^3 + 6*b*e^2*f*x^2 + 4*b*e^3*x)*cos(2*b*x + 2*a))/(cos(4*b*x + 4*a)^2 + sin(4*b*x + 4*a)^2 + 2*cos(4*b*x + 4*a) + 1), x)","F",0
232,0,0,0,0.000000," ","integrate((f*x+e)^2*arccoth(tan(b*x+a)),x, algorithm=""maxima"")","\frac{1}{12} \, {\left(f^{2} x^{3} + 3 \, e f x^{2} + 3 \, e^{2} x\right)} \log\left(2 \, \cos\left(2 \, b x + 2 \, a\right)^{2} + 2 \, \sin\left(2 \, b x + 2 \, a\right)^{2} + 4 \, \sin\left(2 \, b x + 2 \, a\right) + 2\right) - \frac{1}{12} \, {\left(f^{2} x^{3} + 3 \, e f x^{2} + 3 \, e^{2} x\right)} \log\left(2 \, \cos\left(2 \, b x + 2 \, a\right)^{2} + 2 \, \sin\left(2 \, b x + 2 \, a\right)^{2} - 4 \, \sin\left(2 \, b x + 2 \, a\right) + 2\right) - \int \frac{2 \, {\left({\left(b f^{2} x^{3} + 3 \, b e f x^{2} + 3 \, b e^{2} x\right)} \cos\left(4 \, b x + 4 \, a\right) \cos\left(2 \, b x + 2 \, a\right) + {\left(b f^{2} x^{3} + 3 \, b e f x^{2} + 3 \, b e^{2} x\right)} \sin\left(4 \, b x + 4 \, a\right) \sin\left(2 \, b x + 2 \, a\right) + {\left(b f^{2} x^{3} + 3 \, b e f x^{2} + 3 \, b e^{2} x\right)} \cos\left(2 \, b x + 2 \, a\right)\right)}}{3 \, {\left(\cos\left(4 \, b x + 4 \, a\right)^{2} + \sin\left(4 \, b x + 4 \, a\right)^{2} + 2 \, \cos\left(4 \, b x + 4 \, a\right) + 1\right)}}\,{d x}"," ",0,"1/12*(f^2*x^3 + 3*e*f*x^2 + 3*e^2*x)*log(2*cos(2*b*x + 2*a)^2 + 2*sin(2*b*x + 2*a)^2 + 4*sin(2*b*x + 2*a) + 2) - 1/12*(f^2*x^3 + 3*e*f*x^2 + 3*e^2*x)*log(2*cos(2*b*x + 2*a)^2 + 2*sin(2*b*x + 2*a)^2 - 4*sin(2*b*x + 2*a) + 2) - integrate(2/3*((b*f^2*x^3 + 3*b*e*f*x^2 + 3*b*e^2*x)*cos(4*b*x + 4*a)*cos(2*b*x + 2*a) + (b*f^2*x^3 + 3*b*e*f*x^2 + 3*b*e^2*x)*sin(4*b*x + 4*a)*sin(2*b*x + 2*a) + (b*f^2*x^3 + 3*b*e*f*x^2 + 3*b*e^2*x)*cos(2*b*x + 2*a))/(cos(4*b*x + 4*a)^2 + sin(4*b*x + 4*a)^2 + 2*cos(4*b*x + 4*a) + 1), x)","F",0
233,0,0,0,0.000000," ","integrate((f*x+e)*arccoth(tan(b*x+a)),x, algorithm=""maxima"")","\frac{1}{8} \, {\left(f x^{2} + 2 \, e x\right)} \log\left(2 \, \cos\left(2 \, b x + 2 \, a\right)^{2} + 2 \, \sin\left(2 \, b x + 2 \, a\right)^{2} + 4 \, \sin\left(2 \, b x + 2 \, a\right) + 2\right) - \frac{1}{8} \, {\left(f x^{2} + 2 \, e x\right)} \log\left(2 \, \cos\left(2 \, b x + 2 \, a\right)^{2} + 2 \, \sin\left(2 \, b x + 2 \, a\right)^{2} - 4 \, \sin\left(2 \, b x + 2 \, a\right) + 2\right) - \int \frac{{\left(b f x^{2} + 2 \, b e x\right)} \cos\left(4 \, b x + 4 \, a\right) \cos\left(2 \, b x + 2 \, a\right) + {\left(b f x^{2} + 2 \, b e x\right)} \sin\left(4 \, b x + 4 \, a\right) \sin\left(2 \, b x + 2 \, a\right) + {\left(b f x^{2} + 2 \, b e x\right)} \cos\left(2 \, b x + 2 \, a\right)}{\cos\left(4 \, b x + 4 \, a\right)^{2} + \sin\left(4 \, b x + 4 \, a\right)^{2} + 2 \, \cos\left(4 \, b x + 4 \, a\right) + 1}\,{d x}"," ",0,"1/8*(f*x^2 + 2*e*x)*log(2*cos(2*b*x + 2*a)^2 + 2*sin(2*b*x + 2*a)^2 + 4*sin(2*b*x + 2*a) + 2) - 1/8*(f*x^2 + 2*e*x)*log(2*cos(2*b*x + 2*a)^2 + 2*sin(2*b*x + 2*a)^2 - 4*sin(2*b*x + 2*a) + 2) - integrate(((b*f*x^2 + 2*b*e*x)*cos(4*b*x + 4*a)*cos(2*b*x + 2*a) + (b*f*x^2 + 2*b*e*x)*sin(4*b*x + 4*a)*sin(2*b*x + 2*a) + (b*f*x^2 + 2*b*e*x)*cos(2*b*x + 2*a))/(cos(4*b*x + 4*a)^2 + sin(4*b*x + 4*a)^2 + 2*cos(4*b*x + 4*a) + 1), x)","F",0
234,1,182,0,0.463360," ","integrate(arccoth(tan(b*x+a)),x, algorithm=""maxima"")","\frac{4 \, {\left(b x + a\right)} \operatorname{arcoth}\left(\tan\left(b x + a\right)\right) + {\left(\arctan\left(\frac{1}{2} \, \tan\left(b x + a\right) + \frac{1}{2}, \frac{1}{2} \, \tan\left(b x + a\right) + \frac{1}{2}\right) - \arctan\left(\frac{1}{2} \, \tan\left(b x + a\right) - \frac{1}{2}, -\frac{1}{2} \, \tan\left(b x + a\right) + \frac{1}{2}\right)\right)} \log\left(\tan\left(b x + a\right)^{2} + 1\right) - {\left(b x + a\right)} \log\left(\frac{1}{2} \, \tan\left(b x + a\right)^{2} + \tan\left(b x + a\right) + \frac{1}{2}\right) + {\left(b x + a\right)} \log\left(\frac{1}{2} \, \tan\left(b x + a\right)^{2} - \tan\left(b x + a\right) + \frac{1}{2}\right) - i \, {\rm Li}_2\left(\left(\frac{1}{2} i + \frac{1}{2}\right) \, \tan\left(b x + a\right) - \frac{1}{2} i + \frac{1}{2}\right) + i \, {\rm Li}_2\left(-\left(\frac{1}{2} i - \frac{1}{2}\right) \, \tan\left(b x + a\right) + \frac{1}{2} i + \frac{1}{2}\right) + i \, {\rm Li}_2\left(\left(\frac{1}{2} i - \frac{1}{2}\right) \, \tan\left(b x + a\right) + \frac{1}{2} i + \frac{1}{2}\right) - i \, {\rm Li}_2\left(-\left(\frac{1}{2} i + \frac{1}{2}\right) \, \tan\left(b x + a\right) - \frac{1}{2} i + \frac{1}{2}\right)}{4 \, b}"," ",0,"1/4*(4*(b*x + a)*arccoth(tan(b*x + a)) + (arctan2(1/2*tan(b*x + a) + 1/2, 1/2*tan(b*x + a) + 1/2) - arctan2(1/2*tan(b*x + a) - 1/2, -1/2*tan(b*x + a) + 1/2))*log(tan(b*x + a)^2 + 1) - (b*x + a)*log(1/2*tan(b*x + a)^2 + tan(b*x + a) + 1/2) + (b*x + a)*log(1/2*tan(b*x + a)^2 - tan(b*x + a) + 1/2) - I*dilog((1/2*I + 1/2)*tan(b*x + a) - 1/2*I + 1/2) + I*dilog(-(1/2*I - 1/2)*tan(b*x + a) + 1/2*I + 1/2) + I*dilog((1/2*I - 1/2)*tan(b*x + a) + 1/2*I + 1/2) - I*dilog(-(1/2*I + 1/2)*tan(b*x + a) - 1/2*I + 1/2))/b","B",0
235,0,0,0,0.000000," ","integrate(arccoth(tan(b*x+a))/(f*x+e),x, algorithm=""maxima"")","\int \frac{\operatorname{arcoth}\left(\tan\left(b x + a\right)\right)}{f x + e}\,{d x}"," ",0,"integrate(arccoth(tan(b*x + a))/(f*x + e), x)","F",0
236,0,0,0,0.000000," ","integrate(x^2*arccoth(c+d*tan(b*x+a)),x, algorithm=""maxima"")","\frac{1}{12} \, x^{3} \log\left({\left(c^{2} + d^{2} + 2 \, c + 1\right)} \cos\left(2 \, b x + 2 \, a\right)^{2} + 4 \, {\left(c + 1\right)} d \sin\left(2 \, b x + 2 \, a\right) + {\left(c^{2} + d^{2} + 2 \, c + 1\right)} \sin\left(2 \, b x + 2 \, a\right)^{2} + c^{2} + d^{2} + 2 \, {\left(c^{2} - d^{2} + 2 \, c + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + 2 \, c + 1\right) - \frac{1}{12} \, x^{3} \log\left({\left(c^{2} + d^{2} - 2 \, c + 1\right)} \cos\left(2 \, b x + 2 \, a\right)^{2} + 4 \, {\left(c - 1\right)} d \sin\left(2 \, b x + 2 \, a\right) + {\left(c^{2} + d^{2} - 2 \, c + 1\right)} \sin\left(2 \, b x + 2 \, a\right)^{2} + c^{2} + d^{2} + 2 \, {\left(c^{2} - d^{2} - 2 \, c + 1\right)} \cos\left(2 \, b x + 2 \, a\right) - 2 \, c + 1\right) - 4 \, b d \int -\frac{2 \, {\left(c^{2} + d^{2} - 1\right)} x^{3} \cos\left(2 \, b x + 2 \, a\right)^{2} + 2 \, c d x^{3} \sin\left(2 \, b x + 2 \, a\right) + 2 \, {\left(c^{2} + d^{2} - 1\right)} x^{3} \sin\left(2 \, b x + 2 \, a\right)^{2} + {\left(c^{2} - d^{2} - 1\right)} x^{3} \cos\left(2 \, b x + 2 \, a\right) - {\left(2 \, c d x^{3} \sin\left(2 \, b x + 2 \, a\right) - {\left(c^{2} - d^{2} - 1\right)} x^{3} \cos\left(2 \, b x + 2 \, a\right)\right)} \cos\left(4 \, b x + 4 \, a\right) + {\left(2 \, c d x^{3} \cos\left(2 \, b x + 2 \, a\right) + {\left(c^{2} - d^{2} - 1\right)} x^{3} \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(4 \, b x + 4 \, a\right)}{3 \, {\left(c^{4} + d^{4} + 2 \, {\left(c^{2} + 1\right)} d^{2} + {\left(c^{4} + d^{4} + 2 \, {\left(c^{2} + 1\right)} d^{2} - 2 \, c^{2} + 1\right)} \cos\left(4 \, b x + 4 \, a\right)^{2} + 4 \, {\left(c^{4} + d^{4} + 2 \, {\left(c^{2} - 1\right)} d^{2} - 2 \, c^{2} + 1\right)} \cos\left(2 \, b x + 2 \, a\right)^{2} + {\left(c^{4} + d^{4} + 2 \, {\left(c^{2} + 1\right)} d^{2} - 2 \, c^{2} + 1\right)} \sin\left(4 \, b x + 4 \, a\right)^{2} + 4 \, {\left(c^{4} + d^{4} + 2 \, {\left(c^{2} - 1\right)} d^{2} - 2 \, c^{2} + 1\right)} \sin\left(2 \, b x + 2 \, a\right)^{2} - 2 \, c^{2} + 2 \, {\left(c^{4} + d^{4} - 2 \, {\left(3 \, c^{2} - 1\right)} d^{2} - 2 \, c^{2} + 2 \, {\left(c^{4} - d^{4} - 2 \, c^{2} + 1\right)} \cos\left(2 \, b x + 2 \, a\right) - 4 \, {\left(c d^{3} + {\left(c^{3} - c\right)} d\right)} \sin\left(2 \, b x + 2 \, a\right) + 1\right)} \cos\left(4 \, b x + 4 \, a\right) + 4 \, {\left(c^{4} - d^{4} - 2 \, c^{2} + 1\right)} \cos\left(2 \, b x + 2 \, a\right) - 4 \, {\left(2 \, c d^{3} - 2 \, {\left(c^{3} - c\right)} d - 2 \, {\left(c d^{3} + {\left(c^{3} - c\right)} d\right)} \cos\left(2 \, b x + 2 \, a\right) - {\left(c^{4} - d^{4} - 2 \, c^{2} + 1\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(4 \, b x + 4 \, a\right) + 8 \, {\left(c d^{3} + {\left(c^{3} - c\right)} d\right)} \sin\left(2 \, b x + 2 \, a\right) + 1\right)}}\,{d x}"," ",0,"1/12*x^3*log((c^2 + d^2 + 2*c + 1)*cos(2*b*x + 2*a)^2 + 4*(c + 1)*d*sin(2*b*x + 2*a) + (c^2 + d^2 + 2*c + 1)*sin(2*b*x + 2*a)^2 + c^2 + d^2 + 2*(c^2 - d^2 + 2*c + 1)*cos(2*b*x + 2*a) + 2*c + 1) - 1/12*x^3*log((c^2 + d^2 - 2*c + 1)*cos(2*b*x + 2*a)^2 + 4*(c - 1)*d*sin(2*b*x + 2*a) + (c^2 + d^2 - 2*c + 1)*sin(2*b*x + 2*a)^2 + c^2 + d^2 + 2*(c^2 - d^2 - 2*c + 1)*cos(2*b*x + 2*a) - 2*c + 1) - 4*b*d*integrate(-1/3*(2*(c^2 + d^2 - 1)*x^3*cos(2*b*x + 2*a)^2 + 2*c*d*x^3*sin(2*b*x + 2*a) + 2*(c^2 + d^2 - 1)*x^3*sin(2*b*x + 2*a)^2 + (c^2 - d^2 - 1)*x^3*cos(2*b*x + 2*a) - (2*c*d*x^3*sin(2*b*x + 2*a) - (c^2 - d^2 - 1)*x^3*cos(2*b*x + 2*a))*cos(4*b*x + 4*a) + (2*c*d*x^3*cos(2*b*x + 2*a) + (c^2 - d^2 - 1)*x^3*sin(2*b*x + 2*a))*sin(4*b*x + 4*a))/(c^4 + d^4 + 2*(c^2 + 1)*d^2 + (c^4 + d^4 + 2*(c^2 + 1)*d^2 - 2*c^2 + 1)*cos(4*b*x + 4*a)^2 + 4*(c^4 + d^4 + 2*(c^2 - 1)*d^2 - 2*c^2 + 1)*cos(2*b*x + 2*a)^2 + (c^4 + d^4 + 2*(c^2 + 1)*d^2 - 2*c^2 + 1)*sin(4*b*x + 4*a)^2 + 4*(c^4 + d^4 + 2*(c^2 - 1)*d^2 - 2*c^2 + 1)*sin(2*b*x + 2*a)^2 - 2*c^2 + 2*(c^4 + d^4 - 2*(3*c^2 - 1)*d^2 - 2*c^2 + 2*(c^4 - d^4 - 2*c^2 + 1)*cos(2*b*x + 2*a) - 4*(c*d^3 + (c^3 - c)*d)*sin(2*b*x + 2*a) + 1)*cos(4*b*x + 4*a) + 4*(c^4 - d^4 - 2*c^2 + 1)*cos(2*b*x + 2*a) - 4*(2*c*d^3 - 2*(c^3 - c)*d - 2*(c*d^3 + (c^3 - c)*d)*cos(2*b*x + 2*a) - (c^4 - d^4 - 2*c^2 + 1)*sin(2*b*x + 2*a))*sin(4*b*x + 4*a) + 8*(c*d^3 + (c^3 - c)*d)*sin(2*b*x + 2*a) + 1), x)","F",0
237,0,0,0,0.000000," ","integrate(x*arccoth(c+d*tan(b*x+a)),x, algorithm=""maxima"")","-2 \, b d \int -\frac{2 \, {\left(c^{2} + d^{2} - 1\right)} x^{2} \cos\left(2 \, b x + 2 \, a\right)^{2} + 2 \, c d x^{2} \sin\left(2 \, b x + 2 \, a\right) + 2 \, {\left(c^{2} + d^{2} - 1\right)} x^{2} \sin\left(2 \, b x + 2 \, a\right)^{2} + {\left(c^{2} - d^{2} - 1\right)} x^{2} \cos\left(2 \, b x + 2 \, a\right) - {\left(2 \, c d x^{2} \sin\left(2 \, b x + 2 \, a\right) - {\left(c^{2} - d^{2} - 1\right)} x^{2} \cos\left(2 \, b x + 2 \, a\right)\right)} \cos\left(4 \, b x + 4 \, a\right) + {\left(2 \, c d x^{2} \cos\left(2 \, b x + 2 \, a\right) + {\left(c^{2} - d^{2} - 1\right)} x^{2} \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(4 \, b x + 4 \, a\right)}{c^{4} + d^{4} + 2 \, {\left(c^{2} + 1\right)} d^{2} + {\left(c^{4} + d^{4} + 2 \, {\left(c^{2} + 1\right)} d^{2} - 2 \, c^{2} + 1\right)} \cos\left(4 \, b x + 4 \, a\right)^{2} + 4 \, {\left(c^{4} + d^{4} + 2 \, {\left(c^{2} - 1\right)} d^{2} - 2 \, c^{2} + 1\right)} \cos\left(2 \, b x + 2 \, a\right)^{2} + {\left(c^{4} + d^{4} + 2 \, {\left(c^{2} + 1\right)} d^{2} - 2 \, c^{2} + 1\right)} \sin\left(4 \, b x + 4 \, a\right)^{2} + 4 \, {\left(c^{4} + d^{4} + 2 \, {\left(c^{2} - 1\right)} d^{2} - 2 \, c^{2} + 1\right)} \sin\left(2 \, b x + 2 \, a\right)^{2} - 2 \, c^{2} + 2 \, {\left(c^{4} + d^{4} - 2 \, {\left(3 \, c^{2} - 1\right)} d^{2} - 2 \, c^{2} + 2 \, {\left(c^{4} - d^{4} - 2 \, c^{2} + 1\right)} \cos\left(2 \, b x + 2 \, a\right) - 4 \, {\left(c d^{3} + {\left(c^{3} - c\right)} d\right)} \sin\left(2 \, b x + 2 \, a\right) + 1\right)} \cos\left(4 \, b x + 4 \, a\right) + 4 \, {\left(c^{4} - d^{4} - 2 \, c^{2} + 1\right)} \cos\left(2 \, b x + 2 \, a\right) - 4 \, {\left(2 \, c d^{3} - 2 \, {\left(c^{3} - c\right)} d - 2 \, {\left(c d^{3} + {\left(c^{3} - c\right)} d\right)} \cos\left(2 \, b x + 2 \, a\right) - {\left(c^{4} - d^{4} - 2 \, c^{2} + 1\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(4 \, b x + 4 \, a\right) + 8 \, {\left(c d^{3} + {\left(c^{3} - c\right)} d\right)} \sin\left(2 \, b x + 2 \, a\right) + 1}\,{d x} + \frac{1}{8} \, x^{2} \log\left({\left(c^{2} + d^{2} + 2 \, c + 1\right)} \cos\left(2 \, b x + 2 \, a\right)^{2} + 4 \, {\left(c + 1\right)} d \sin\left(2 \, b x + 2 \, a\right) + {\left(c^{2} + d^{2} + 2 \, c + 1\right)} \sin\left(2 \, b x + 2 \, a\right)^{2} + c^{2} + d^{2} + 2 \, {\left(c^{2} - d^{2} + 2 \, c + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + 2 \, c + 1\right) - \frac{1}{8} \, x^{2} \log\left({\left(c^{2} + d^{2} - 2 \, c + 1\right)} \cos\left(2 \, b x + 2 \, a\right)^{2} + 4 \, {\left(c - 1\right)} d \sin\left(2 \, b x + 2 \, a\right) + {\left(c^{2} + d^{2} - 2 \, c + 1\right)} \sin\left(2 \, b x + 2 \, a\right)^{2} + c^{2} + d^{2} + 2 \, {\left(c^{2} - d^{2} - 2 \, c + 1\right)} \cos\left(2 \, b x + 2 \, a\right) - 2 \, c + 1\right)"," ",0,"-2*b*d*integrate(-(2*(c^2 + d^2 - 1)*x^2*cos(2*b*x + 2*a)^2 + 2*c*d*x^2*sin(2*b*x + 2*a) + 2*(c^2 + d^2 - 1)*x^2*sin(2*b*x + 2*a)^2 + (c^2 - d^2 - 1)*x^2*cos(2*b*x + 2*a) - (2*c*d*x^2*sin(2*b*x + 2*a) - (c^2 - d^2 - 1)*x^2*cos(2*b*x + 2*a))*cos(4*b*x + 4*a) + (2*c*d*x^2*cos(2*b*x + 2*a) + (c^2 - d^2 - 1)*x^2*sin(2*b*x + 2*a))*sin(4*b*x + 4*a))/(c^4 + d^4 + 2*(c^2 + 1)*d^2 + (c^4 + d^4 + 2*(c^2 + 1)*d^2 - 2*c^2 + 1)*cos(4*b*x + 4*a)^2 + 4*(c^4 + d^4 + 2*(c^2 - 1)*d^2 - 2*c^2 + 1)*cos(2*b*x + 2*a)^2 + (c^4 + d^4 + 2*(c^2 + 1)*d^2 - 2*c^2 + 1)*sin(4*b*x + 4*a)^2 + 4*(c^4 + d^4 + 2*(c^2 - 1)*d^2 - 2*c^2 + 1)*sin(2*b*x + 2*a)^2 - 2*c^2 + 2*(c^4 + d^4 - 2*(3*c^2 - 1)*d^2 - 2*c^2 + 2*(c^4 - d^4 - 2*c^2 + 1)*cos(2*b*x + 2*a) - 4*(c*d^3 + (c^3 - c)*d)*sin(2*b*x + 2*a) + 1)*cos(4*b*x + 4*a) + 4*(c^4 - d^4 - 2*c^2 + 1)*cos(2*b*x + 2*a) - 4*(2*c*d^3 - 2*(c^3 - c)*d - 2*(c*d^3 + (c^3 - c)*d)*cos(2*b*x + 2*a) - (c^4 - d^4 - 2*c^2 + 1)*sin(2*b*x + 2*a))*sin(4*b*x + 4*a) + 8*(c*d^3 + (c^3 - c)*d)*sin(2*b*x + 2*a) + 1), x) + 1/8*x^2*log((c^2 + d^2 + 2*c + 1)*cos(2*b*x + 2*a)^2 + 4*(c + 1)*d*sin(2*b*x + 2*a) + (c^2 + d^2 + 2*c + 1)*sin(2*b*x + 2*a)^2 + c^2 + d^2 + 2*(c^2 - d^2 + 2*c + 1)*cos(2*b*x + 2*a) + 2*c + 1) - 1/8*x^2*log((c^2 + d^2 - 2*c + 1)*cos(2*b*x + 2*a)^2 + 4*(c - 1)*d*sin(2*b*x + 2*a) + (c^2 + d^2 - 2*c + 1)*sin(2*b*x + 2*a)^2 + c^2 + d^2 + 2*(c^2 - d^2 - 2*c + 1)*cos(2*b*x + 2*a) - 2*c + 1)","F",0
238,1,372,0,0.514834," ","integrate(arccoth(c+d*tan(b*x+a)),x, algorithm=""maxima"")","\frac{4 \, {\left(b x + a\right)} \operatorname{arcoth}\left(d \tan\left(b x + a\right) + c\right) + {\left(\arctan\left(\frac{d^{2} \tan\left(b x + a\right) + {\left(c + 1\right)} d}{c^{2} + d^{2} + 2 \, c + 1}, \frac{{\left(c + 1\right)} d \tan\left(b x + a\right) + c^{2} + 2 \, c + 1}{c^{2} + d^{2} + 2 \, c + 1}\right) - \arctan\left(\frac{d^{2} \tan\left(b x + a\right) + {\left(c - 1\right)} d}{c^{2} + d^{2} - 2 \, c + 1}, \frac{{\left(c - 1\right)} d \tan\left(b x + a\right) + c^{2} - 2 \, c + 1}{c^{2} + d^{2} - 2 \, c + 1}\right)\right)} \log\left(\tan\left(b x + a\right)^{2} + 1\right) - {\left(b x + a\right)} \log\left(\frac{d^{2} \tan\left(b x + a\right)^{2} + 2 \, {\left(c + 1\right)} d \tan\left(b x + a\right) + c^{2} + 2 \, c + 1}{c^{2} + d^{2} + 2 \, c + 1}\right) + {\left(b x + a\right)} \log\left(\frac{d^{2} \tan\left(b x + a\right)^{2} + 2 \, {\left(c - 1\right)} d \tan\left(b x + a\right) + c^{2} - 2 \, c + 1}{c^{2} + d^{2} - 2 \, c + 1}\right) - i \, {\rm Li}_2\left(-\frac{i \, d \tan\left(b x + a\right) - d}{i \, c + d + i}\right) + i \, {\rm Li}_2\left(-\frac{i \, d \tan\left(b x + a\right) - d}{i \, c + d - i}\right) - i \, {\rm Li}_2\left(\frac{i \, d \tan\left(b x + a\right) + d}{-i \, c + d + i}\right) + i \, {\rm Li}_2\left(\frac{i \, d \tan\left(b x + a\right) + d}{-i \, c + d - i}\right)}{4 \, b}"," ",0,"1/4*(4*(b*x + a)*arccoth(d*tan(b*x + a) + c) + (arctan2((d^2*tan(b*x + a) + (c + 1)*d)/(c^2 + d^2 + 2*c + 1), ((c + 1)*d*tan(b*x + a) + c^2 + 2*c + 1)/(c^2 + d^2 + 2*c + 1)) - arctan2((d^2*tan(b*x + a) + (c - 1)*d)/(c^2 + d^2 - 2*c + 1), ((c - 1)*d*tan(b*x + a) + c^2 - 2*c + 1)/(c^2 + d^2 - 2*c + 1)))*log(tan(b*x + a)^2 + 1) - (b*x + a)*log((d^2*tan(b*x + a)^2 + 2*(c + 1)*d*tan(b*x + a) + c^2 + 2*c + 1)/(c^2 + d^2 + 2*c + 1)) + (b*x + a)*log((d^2*tan(b*x + a)^2 + 2*(c - 1)*d*tan(b*x + a) + c^2 - 2*c + 1)/(c^2 + d^2 - 2*c + 1)) - I*dilog(-(I*d*tan(b*x + a) - d)/(I*c + d + I)) + I*dilog(-(I*d*tan(b*x + a) - d)/(I*c + d - I)) - I*dilog((I*d*tan(b*x + a) + d)/(-I*c + d + I)) + I*dilog((I*d*tan(b*x + a) + d)/(-I*c + d - I)))/b","B",0
239,0,0,0,0.000000," ","integrate(arccoth(c+d*tan(b*x+a))/x,x, algorithm=""maxima"")","\int \frac{\operatorname{arcoth}\left(d \tan\left(b x + a\right) + c\right)}{x}\,{d x}"," ",0,"integrate(arccoth(d*tan(b*x + a) + c)/x, x)","F",0
240,1,341,0,0.351456," ","integrate(x^2*arccoth(1-I*d+d*tan(b*x+a)),x, algorithm=""maxima"")","\frac{\frac{12 \, {\left({\left(b x + a\right)}^{3} - 3 \, {\left(b x + a\right)}^{2} a + 3 \, {\left(b x + a\right)} a^{2}\right)} \operatorname{arcoth}\left(d \tan\left(b x + a\right) - i \, d + 1\right)}{b^{2}} - \frac{-3 i \, {\left(b x + a\right)}^{4} + 12 i \, {\left(b x + a\right)}^{3} a - 18 i \, {\left(b x + a\right)}^{2} a^{2} + {\left(8 i \, {\left(b x + a\right)}^{3} - 18 i \, {\left(b x + a\right)}^{2} a + 18 i \, {\left(b x + a\right)} a^{2}\right)} \arctan\left(-d \cos\left(2 \, b x + 2 \, a\right) + \sin\left(2 \, b x + 2 \, a\right), d \sin\left(2 \, b x + 2 \, a\right) + \cos\left(2 \, b x + 2 \, a\right) + 1\right) + {\left(-12 i \, {\left(b x + a\right)}^{2} + 18 i \, {\left(b x + a\right)} a - 9 i \, a^{2}\right)} {\rm Li}_2\left({\left(i \, d - 1\right)} e^{\left(2 i \, b x + 2 i \, a\right)}\right) + {\left(4 \, {\left(b x + a\right)}^{3} - 9 \, {\left(b x + a\right)}^{2} a + 9 \, {\left(b x + a\right)} a^{2}\right)} \log\left({\left(d^{2} + 1\right)} \cos\left(2 \, b x + 2 \, a\right)^{2} + {\left(d^{2} + 1\right)} \sin\left(2 \, b x + 2 \, a\right)^{2} + 2 \, d \sin\left(2 \, b x + 2 \, a\right) + 2 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right) + 3 \, {\left(4 \, b x + a\right)} {\rm Li}_{3}({\left(i \, d - 1\right)} e^{\left(2 i \, b x + 2 i \, a\right)}) + 6 i \, {\rm Li}_{4}({\left(i \, d - 1\right)} e^{\left(2 i \, b x + 2 i \, a\right)})}{b^{2}}}{36 \, b}"," ",0,"1/36*(12*((b*x + a)^3 - 3*(b*x + a)^2*a + 3*(b*x + a)*a^2)*arccoth(d*tan(b*x + a) - I*d + 1)/b^2 - (-3*I*(b*x + a)^4 + 12*I*(b*x + a)^3*a - 18*I*(b*x + a)^2*a^2 + (8*I*(b*x + a)^3 - 18*I*(b*x + a)^2*a + 18*I*(b*x + a)*a^2)*arctan2(-d*cos(2*b*x + 2*a) + sin(2*b*x + 2*a), d*sin(2*b*x + 2*a) + cos(2*b*x + 2*a) + 1) + (-12*I*(b*x + a)^2 + 18*I*(b*x + a)*a - 9*I*a^2)*dilog((I*d - 1)*e^(2*I*b*x + 2*I*a)) + (4*(b*x + a)^3 - 9*(b*x + a)^2*a + 9*(b*x + a)*a^2)*log((d^2 + 1)*cos(2*b*x + 2*a)^2 + (d^2 + 1)*sin(2*b*x + 2*a)^2 + 2*d*sin(2*b*x + 2*a) + 2*cos(2*b*x + 2*a) + 1) + 3*(4*b*x + a)*polylog(3, (I*d - 1)*e^(2*I*b*x + 2*I*a)) + 6*I*polylog(4, (I*d - 1)*e^(2*I*b*x + 2*I*a)))/b^2)/b","B",0
241,1,247,0,0.342761," ","integrate(x*arccoth(1-I*d+d*tan(b*x+a)),x, algorithm=""maxima"")","\frac{\frac{12 \, {\left({\left(b x + a\right)}^{2} - 2 \, {\left(b x + a\right)} a\right)} \operatorname{arcoth}\left(d \tan\left(b x + a\right) - i \, d + 1\right)}{b} - \frac{-4 i \, {\left(b x + a\right)}^{3} + 12 i \, {\left(b x + a\right)}^{2} a - 6 i \, b x {\rm Li}_2\left({\left(i \, d - 1\right)} e^{\left(2 i \, b x + 2 i \, a\right)}\right) + {\left(6 i \, {\left(b x + a\right)}^{2} - 12 i \, {\left(b x + a\right)} a\right)} \arctan\left(-d \cos\left(2 \, b x + 2 \, a\right) + \sin\left(2 \, b x + 2 \, a\right), d \sin\left(2 \, b x + 2 \, a\right) + \cos\left(2 \, b x + 2 \, a\right) + 1\right) + 3 \, {\left({\left(b x + a\right)}^{2} - 2 \, {\left(b x + a\right)} a\right)} \log\left({\left(d^{2} + 1\right)} \cos\left(2 \, b x + 2 \, a\right)^{2} + {\left(d^{2} + 1\right)} \sin\left(2 \, b x + 2 \, a\right)^{2} + 2 \, d \sin\left(2 \, b x + 2 \, a\right) + 2 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right) + 3 \, {\rm Li}_{3}({\left(i \, d - 1\right)} e^{\left(2 i \, b x + 2 i \, a\right)})}{b}}{24 \, b}"," ",0,"1/24*(12*((b*x + a)^2 - 2*(b*x + a)*a)*arccoth(d*tan(b*x + a) - I*d + 1)/b - (-4*I*(b*x + a)^3 + 12*I*(b*x + a)^2*a - 6*I*b*x*dilog((I*d - 1)*e^(2*I*b*x + 2*I*a)) + (6*I*(b*x + a)^2 - 12*I*(b*x + a)*a)*arctan2(-d*cos(2*b*x + 2*a) + sin(2*b*x + 2*a), d*sin(2*b*x + 2*a) + cos(2*b*x + 2*a) + 1) + 3*((b*x + a)^2 - 2*(b*x + a)*a)*log((d^2 + 1)*cos(2*b*x + 2*a)^2 + (d^2 + 1)*sin(2*b*x + 2*a)^2 + 2*d*sin(2*b*x + 2*a) + 2*cos(2*b*x + 2*a) + 1) + 3*polylog(3, (I*d - 1)*e^(2*I*b*x + 2*I*a)))/b)/b","B",0
242,1,265,0,0.429893," ","integrate(arccoth(1-I*d+d*tan(b*x+a)),x, algorithm=""maxima"")","-\frac{4 \, {\left(b x + a\right)} d {\left(\frac{\log\left(d \tan\left(b x + a\right) - i \, d + 2\right)}{d} - \frac{\log\left(\tan\left(b x + a\right) - i\right)}{d}\right)} - d {\left(\frac{2 i \, {\left(\log\left(d \tan\left(b x + a\right) - i \, d + 2\right) \log\left(-\frac{i \, d \tan\left(b x + a\right) + d + 2 i}{2 \, d + 2 i} + 1\right) + {\rm Li}_2\left(\frac{i \, d \tan\left(b x + a\right) + d + 2 i}{2 \, d + 2 i}\right)\right)}}{d} - \frac{2 i \, \log\left(d \tan\left(b x + a\right) - i \, d + 2\right) \log\left(\tan\left(b x + a\right) - i\right) - i \, \log\left(\tan\left(b x + a\right) - i\right)^{2}}{d} + \frac{2 i \, {\left(\log\left(\frac{1}{2} \, d \tan\left(b x + a\right) - \frac{1}{2} i \, d + 1\right) \log\left(\tan\left(b x + a\right) - i\right) + {\rm Li}_2\left(-\frac{1}{2} \, d \tan\left(b x + a\right) + \frac{1}{2} i \, d\right)\right)}}{d} - \frac{2 i \, {\left(\log\left(\tan\left(b x + a\right) - i\right) \log\left(-\frac{1}{2} i \, \tan\left(b x + a\right) + \frac{1}{2}\right) + {\rm Li}_2\left(\frac{1}{2} i \, \tan\left(b x + a\right) + \frac{1}{2}\right)\right)}}{d}\right)} - 8 \, {\left(b x + a\right)} \operatorname{arcoth}\left(d \tan\left(b x + a\right) - i \, d + 1\right)}{8 \, b}"," ",0,"-1/8*(4*(b*x + a)*d*(log(d*tan(b*x + a) - I*d + 2)/d - log(tan(b*x + a) - I)/d) - d*(2*I*(log(d*tan(b*x + a) - I*d + 2)*log(-(I*d*tan(b*x + a) + d + 2*I)/(2*d + 2*I) + 1) + dilog((I*d*tan(b*x + a) + d + 2*I)/(2*d + 2*I)))/d - (2*I*log(d*tan(b*x + a) - I*d + 2)*log(tan(b*x + a) - I) - I*log(tan(b*x + a) - I)^2)/d + 2*I*(log(1/2*d*tan(b*x + a) - 1/2*I*d + 1)*log(tan(b*x + a) - I) + dilog(-1/2*d*tan(b*x + a) + 1/2*I*d))/d - 2*I*(log(tan(b*x + a) - I)*log(-1/2*I*tan(b*x + a) + 1/2) + dilog(1/2*I*tan(b*x + a) + 1/2))/d) - 8*(b*x + a)*arccoth(d*tan(b*x + a) - I*d + 1))/b","B",0
243,0,0,0,0.000000," ","integrate(arccoth(1-I*d+d*tan(b*x+a))/x,x, algorithm=""maxima"")","-i \, b x + \frac{1}{4} \, {\left(-i \, \pi - 4 i \, a - 2 \, \log\left(d\right)\right)} \log\left(x\right) - \frac{1}{2} i \, \int \frac{\arctan\left(-d \cos\left(2 \, b x + 2 \, a\right) + \sin\left(2 \, b x + 2 \, a\right), -d \sin\left(2 \, b x + 2 \, a\right) - \cos\left(2 \, b x + 2 \, a\right) - 1\right)}{x}\,{d x} + \frac{1}{4} \, \int \frac{\log\left({\left(d^{2} + 1\right)} \cos\left(2 \, b x + 2 \, a\right)^{2} + {\left(d^{2} + 1\right)} \sin\left(2 \, b x + 2 \, a\right)^{2} + 2 \, d \sin\left(2 \, b x + 2 \, a\right) + 2 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right)}{x}\,{d x}"," ",0,"-I*b*x + 1/4*(-I*pi - 4*I*a - 2*log(d))*log(x) - 1/2*I*integrate(arctan2(-d*cos(2*b*x + 2*a) + sin(2*b*x + 2*a), -d*sin(2*b*x + 2*a) - cos(2*b*x + 2*a) - 1)/x, x) + 1/4*integrate(log((d^2 + 1)*cos(2*b*x + 2*a)^2 + (d^2 + 1)*sin(2*b*x + 2*a)^2 + 2*d*sin(2*b*x + 2*a) + 2*cos(2*b*x + 2*a) + 1)/x, x)","F",0
244,1,340,0,0.349629," ","integrate(x^2*arccoth(1+I*d-d*tan(b*x+a)),x, algorithm=""maxima"")","-\frac{\frac{12 \, {\left({\left(b x + a\right)}^{3} - 3 \, {\left(b x + a\right)}^{2} a + 3 \, {\left(b x + a\right)} a^{2}\right)} \operatorname{arcoth}\left(d \tan\left(b x + a\right) - i \, d - 1\right)}{b^{2}} + \frac{-3 i \, {\left(b x + a\right)}^{4} + 12 i \, {\left(b x + a\right)}^{3} a - 18 i \, {\left(b x + a\right)}^{2} a^{2} + {\left(8 i \, {\left(b x + a\right)}^{3} - 18 i \, {\left(b x + a\right)}^{2} a + 18 i \, {\left(b x + a\right)} a^{2}\right)} \arctan\left(d \cos\left(2 \, b x + 2 \, a\right) + \sin\left(2 \, b x + 2 \, a\right), -d \sin\left(2 \, b x + 2 \, a\right) + \cos\left(2 \, b x + 2 \, a\right) + 1\right) + {\left(-12 i \, {\left(b x + a\right)}^{2} + 18 i \, {\left(b x + a\right)} a - 9 i \, a^{2}\right)} {\rm Li}_2\left({\left(-i \, d - 1\right)} e^{\left(2 i \, b x + 2 i \, a\right)}\right) + {\left(4 \, {\left(b x + a\right)}^{3} - 9 \, {\left(b x + a\right)}^{2} a + 9 \, {\left(b x + a\right)} a^{2}\right)} \log\left({\left(d^{2} + 1\right)} \cos\left(2 \, b x + 2 \, a\right)^{2} + {\left(d^{2} + 1\right)} \sin\left(2 \, b x + 2 \, a\right)^{2} - 2 \, d \sin\left(2 \, b x + 2 \, a\right) + 2 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right) + 3 \, {\left(4 \, b x + a\right)} {\rm Li}_{3}({\left(-i \, d - 1\right)} e^{\left(2 i \, b x + 2 i \, a\right)}) + 6 i \, {\rm Li}_{4}({\left(-i \, d - 1\right)} e^{\left(2 i \, b x + 2 i \, a\right)})}{b^{2}}}{36 \, b}"," ",0,"-1/36*(12*((b*x + a)^3 - 3*(b*x + a)^2*a + 3*(b*x + a)*a^2)*arccoth(d*tan(b*x + a) - I*d - 1)/b^2 + (-3*I*(b*x + a)^4 + 12*I*(b*x + a)^3*a - 18*I*(b*x + a)^2*a^2 + (8*I*(b*x + a)^3 - 18*I*(b*x + a)^2*a + 18*I*(b*x + a)*a^2)*arctan2(d*cos(2*b*x + 2*a) + sin(2*b*x + 2*a), -d*sin(2*b*x + 2*a) + cos(2*b*x + 2*a) + 1) + (-12*I*(b*x + a)^2 + 18*I*(b*x + a)*a - 9*I*a^2)*dilog((-I*d - 1)*e^(2*I*b*x + 2*I*a)) + (4*(b*x + a)^3 - 9*(b*x + a)^2*a + 9*(b*x + a)*a^2)*log((d^2 + 1)*cos(2*b*x + 2*a)^2 + (d^2 + 1)*sin(2*b*x + 2*a)^2 - 2*d*sin(2*b*x + 2*a) + 2*cos(2*b*x + 2*a) + 1) + 3*(4*b*x + a)*polylog(3, (-I*d - 1)*e^(2*I*b*x + 2*I*a)) + 6*I*polylog(4, (-I*d - 1)*e^(2*I*b*x + 2*I*a)))/b^2)/b","B",0
245,1,246,0,0.341789," ","integrate(x*arccoth(1+I*d-d*tan(b*x+a)),x, algorithm=""maxima"")","-\frac{\frac{12 \, {\left({\left(b x + a\right)}^{2} - 2 \, {\left(b x + a\right)} a\right)} \operatorname{arcoth}\left(d \tan\left(b x + a\right) - i \, d - 1\right)}{b} + \frac{-4 i \, {\left(b x + a\right)}^{3} + 12 i \, {\left(b x + a\right)}^{2} a - 6 i \, b x {\rm Li}_2\left({\left(-i \, d - 1\right)} e^{\left(2 i \, b x + 2 i \, a\right)}\right) + {\left(6 i \, {\left(b x + a\right)}^{2} - 12 i \, {\left(b x + a\right)} a\right)} \arctan\left(d \cos\left(2 \, b x + 2 \, a\right) + \sin\left(2 \, b x + 2 \, a\right), -d \sin\left(2 \, b x + 2 \, a\right) + \cos\left(2 \, b x + 2 \, a\right) + 1\right) + 3 \, {\left({\left(b x + a\right)}^{2} - 2 \, {\left(b x + a\right)} a\right)} \log\left({\left(d^{2} + 1\right)} \cos\left(2 \, b x + 2 \, a\right)^{2} + {\left(d^{2} + 1\right)} \sin\left(2 \, b x + 2 \, a\right)^{2} - 2 \, d \sin\left(2 \, b x + 2 \, a\right) + 2 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right) + 3 \, {\rm Li}_{3}({\left(-i \, d - 1\right)} e^{\left(2 i \, b x + 2 i \, a\right)})}{b}}{24 \, b}"," ",0,"-1/24*(12*((b*x + a)^2 - 2*(b*x + a)*a)*arccoth(d*tan(b*x + a) - I*d - 1)/b + (-4*I*(b*x + a)^3 + 12*I*(b*x + a)^2*a - 6*I*b*x*dilog((-I*d - 1)*e^(2*I*b*x + 2*I*a)) + (6*I*(b*x + a)^2 - 12*I*(b*x + a)*a)*arctan2(d*cos(2*b*x + 2*a) + sin(2*b*x + 2*a), -d*sin(2*b*x + 2*a) + cos(2*b*x + 2*a) + 1) + 3*((b*x + a)^2 - 2*(b*x + a)*a)*log((d^2 + 1)*cos(2*b*x + 2*a)^2 + (d^2 + 1)*sin(2*b*x + 2*a)^2 - 2*d*sin(2*b*x + 2*a) + 2*cos(2*b*x + 2*a) + 1) + 3*polylog(3, (-I*d - 1)*e^(2*I*b*x + 2*I*a)))/b)/b","B",0
246,1,263,0,0.424159," ","integrate(arccoth(1+I*d-d*tan(b*x+a)),x, algorithm=""maxima"")","-\frac{4 \, {\left(b x + a\right)} d {\left(\frac{\log\left(d \tan\left(b x + a\right) - i \, d - 2\right)}{d} - \frac{\log\left(\tan\left(b x + a\right) - i\right)}{d}\right)} + d {\left(-\frac{2 i \, {\left(\log\left(d \tan\left(b x + a\right) - i \, d - 2\right) \log\left(-\frac{i \, d \tan\left(b x + a\right) + d - 2 i}{2 \, d - 2 i} + 1\right) + {\rm Li}_2\left(\frac{i \, d \tan\left(b x + a\right) + d - 2 i}{2 \, d - 2 i}\right)\right)}}{d} + \frac{2 i \, \log\left(d \tan\left(b x + a\right) - i \, d - 2\right) \log\left(\tan\left(b x + a\right) - i\right) - i \, \log\left(\tan\left(b x + a\right) - i\right)^{2}}{d} - \frac{2 i \, {\left(\log\left(-\frac{1}{2} \, d \tan\left(b x + a\right) + \frac{1}{2} i \, d + 1\right) \log\left(\tan\left(b x + a\right) - i\right) + {\rm Li}_2\left(\frac{1}{2} \, d \tan\left(b x + a\right) - \frac{1}{2} i \, d\right)\right)}}{d} + \frac{2 i \, {\left(\log\left(\tan\left(b x + a\right) - i\right) \log\left(-\frac{1}{2} i \, \tan\left(b x + a\right) + \frac{1}{2}\right) + {\rm Li}_2\left(\frac{1}{2} i \, \tan\left(b x + a\right) + \frac{1}{2}\right)\right)}}{d}\right)} + 8 \, {\left(b x + a\right)} \operatorname{arcoth}\left(d \tan\left(b x + a\right) - i \, d - 1\right)}{8 \, b}"," ",0,"-1/8*(4*(b*x + a)*d*(log(d*tan(b*x + a) - I*d - 2)/d - log(tan(b*x + a) - I)/d) + d*(-2*I*(log(d*tan(b*x + a) - I*d - 2)*log(-(I*d*tan(b*x + a) + d - 2*I)/(2*d - 2*I) + 1) + dilog((I*d*tan(b*x + a) + d - 2*I)/(2*d - 2*I)))/d + (2*I*log(d*tan(b*x + a) - I*d - 2)*log(tan(b*x + a) - I) - I*log(tan(b*x + a) - I)^2)/d - 2*I*(log(-1/2*d*tan(b*x + a) + 1/2*I*d + 1)*log(tan(b*x + a) - I) + dilog(1/2*d*tan(b*x + a) - 1/2*I*d))/d + 2*I*(log(tan(b*x + a) - I)*log(-1/2*I*tan(b*x + a) + 1/2) + dilog(1/2*I*tan(b*x + a) + 1/2))/d) + 8*(b*x + a)*arccoth(d*tan(b*x + a) - I*d - 1))/b","B",0
247,0,0,0,0.000000," ","integrate(arccoth(1+I*d-d*tan(b*x+a))/x,x, algorithm=""maxima"")","-i \, b x + \frac{1}{4} \, {\left(-i \, \pi - 4 i \, a - 2 \, \log\left(d\right)\right)} \log\left(x\right) + \frac{1}{2} i \, \int \frac{\arctan\left(d \cos\left(2 \, b x + 2 \, a\right) + \sin\left(2 \, b x + 2 \, a\right), -d \sin\left(2 \, b x + 2 \, a\right) + \cos\left(2 \, b x + 2 \, a\right) + 1\right)}{x}\,{d x} + \frac{1}{4} \, \int \frac{\log\left({\left(d^{2} + 1\right)} \cos\left(2 \, b x + 2 \, a\right)^{2} + {\left(d^{2} + 1\right)} \sin\left(2 \, b x + 2 \, a\right)^{2} - 2 \, d \sin\left(2 \, b x + 2 \, a\right) + 2 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right)}{x}\,{d x}"," ",0,"-I*b*x + 1/4*(-I*pi - 4*I*a - 2*log(d))*log(x) + 1/2*I*integrate(arctan2(d*cos(2*b*x + 2*a) + sin(2*b*x + 2*a), -d*sin(2*b*x + 2*a) + cos(2*b*x + 2*a) + 1)/x, x) + 1/4*integrate(log((d^2 + 1)*cos(2*b*x + 2*a)^2 + (d^2 + 1)*sin(2*b*x + 2*a)^2 - 2*d*sin(2*b*x + 2*a) + 2*cos(2*b*x + 2*a) + 1)/x, x)","F",0
248,0,0,0,0.000000," ","integrate((f*x+e)^3*arccoth(cot(b*x+a)),x, algorithm=""maxima"")","\frac{1}{16} \, {\left(f^{3} x^{4} + 4 \, e f^{2} x^{3} + 6 \, e^{2} f x^{2} + 4 \, e^{3} x\right)} \log\left(2 \, \cos\left(2 \, b x + 2 \, a\right)^{2} + 2 \, \sin\left(2 \, b x + 2 \, a\right)^{2} + 4 \, \sin\left(2 \, b x + 2 \, a\right) + 2\right) - \frac{1}{16} \, {\left(f^{3} x^{4} + 4 \, e f^{2} x^{3} + 6 \, e^{2} f x^{2} + 4 \, e^{3} x\right)} \log\left(2 \, \cos\left(2 \, b x + 2 \, a\right)^{2} + 2 \, \sin\left(2 \, b x + 2 \, a\right)^{2} - 4 \, \sin\left(2 \, b x + 2 \, a\right) + 2\right) - \int \frac{{\left(b f^{3} x^{4} + 4 \, b e f^{2} x^{3} + 6 \, b e^{2} f x^{2} + 4 \, b e^{3} x\right)} \cos\left(4 \, b x + 4 \, a\right) \cos\left(2 \, b x + 2 \, a\right) + {\left(b f^{3} x^{4} + 4 \, b e f^{2} x^{3} + 6 \, b e^{2} f x^{2} + 4 \, b e^{3} x\right)} \sin\left(4 \, b x + 4 \, a\right) \sin\left(2 \, b x + 2 \, a\right) + {\left(b f^{3} x^{4} + 4 \, b e f^{2} x^{3} + 6 \, b e^{2} f x^{2} + 4 \, b e^{3} x\right)} \cos\left(2 \, b x + 2 \, a\right)}{2 \, {\left(\cos\left(4 \, b x + 4 \, a\right)^{2} + \sin\left(4 \, b x + 4 \, a\right)^{2} + 2 \, \cos\left(4 \, b x + 4 \, a\right) + 1\right)}}\,{d x}"," ",0,"1/16*(f^3*x^4 + 4*e*f^2*x^3 + 6*e^2*f*x^2 + 4*e^3*x)*log(2*cos(2*b*x + 2*a)^2 + 2*sin(2*b*x + 2*a)^2 + 4*sin(2*b*x + 2*a) + 2) - 1/16*(f^3*x^4 + 4*e*f^2*x^3 + 6*e^2*f*x^2 + 4*e^3*x)*log(2*cos(2*b*x + 2*a)^2 + 2*sin(2*b*x + 2*a)^2 - 4*sin(2*b*x + 2*a) + 2) - integrate(1/2*((b*f^3*x^4 + 4*b*e*f^2*x^3 + 6*b*e^2*f*x^2 + 4*b*e^3*x)*cos(4*b*x + 4*a)*cos(2*b*x + 2*a) + (b*f^3*x^4 + 4*b*e*f^2*x^3 + 6*b*e^2*f*x^2 + 4*b*e^3*x)*sin(4*b*x + 4*a)*sin(2*b*x + 2*a) + (b*f^3*x^4 + 4*b*e*f^2*x^3 + 6*b*e^2*f*x^2 + 4*b*e^3*x)*cos(2*b*x + 2*a))/(cos(4*b*x + 4*a)^2 + sin(4*b*x + 4*a)^2 + 2*cos(4*b*x + 4*a) + 1), x)","F",0
249,0,0,0,0.000000," ","integrate((f*x+e)^2*arccoth(cot(b*x+a)),x, algorithm=""maxima"")","\frac{1}{12} \, {\left(f^{2} x^{3} + 3 \, e f x^{2} + 3 \, e^{2} x\right)} \log\left(2 \, \cos\left(2 \, b x + 2 \, a\right)^{2} + 2 \, \sin\left(2 \, b x + 2 \, a\right)^{2} + 4 \, \sin\left(2 \, b x + 2 \, a\right) + 2\right) - \frac{1}{12} \, {\left(f^{2} x^{3} + 3 \, e f x^{2} + 3 \, e^{2} x\right)} \log\left(2 \, \cos\left(2 \, b x + 2 \, a\right)^{2} + 2 \, \sin\left(2 \, b x + 2 \, a\right)^{2} - 4 \, \sin\left(2 \, b x + 2 \, a\right) + 2\right) - \int \frac{2 \, {\left({\left(b f^{2} x^{3} + 3 \, b e f x^{2} + 3 \, b e^{2} x\right)} \cos\left(4 \, b x + 4 \, a\right) \cos\left(2 \, b x + 2 \, a\right) + {\left(b f^{2} x^{3} + 3 \, b e f x^{2} + 3 \, b e^{2} x\right)} \sin\left(4 \, b x + 4 \, a\right) \sin\left(2 \, b x + 2 \, a\right) + {\left(b f^{2} x^{3} + 3 \, b e f x^{2} + 3 \, b e^{2} x\right)} \cos\left(2 \, b x + 2 \, a\right)\right)}}{3 \, {\left(\cos\left(4 \, b x + 4 \, a\right)^{2} + \sin\left(4 \, b x + 4 \, a\right)^{2} + 2 \, \cos\left(4 \, b x + 4 \, a\right) + 1\right)}}\,{d x}"," ",0,"1/12*(f^2*x^3 + 3*e*f*x^2 + 3*e^2*x)*log(2*cos(2*b*x + 2*a)^2 + 2*sin(2*b*x + 2*a)^2 + 4*sin(2*b*x + 2*a) + 2) - 1/12*(f^2*x^3 + 3*e*f*x^2 + 3*e^2*x)*log(2*cos(2*b*x + 2*a)^2 + 2*sin(2*b*x + 2*a)^2 - 4*sin(2*b*x + 2*a) + 2) - integrate(2/3*((b*f^2*x^3 + 3*b*e*f*x^2 + 3*b*e^2*x)*cos(4*b*x + 4*a)*cos(2*b*x + 2*a) + (b*f^2*x^3 + 3*b*e*f*x^2 + 3*b*e^2*x)*sin(4*b*x + 4*a)*sin(2*b*x + 2*a) + (b*f^2*x^3 + 3*b*e*f*x^2 + 3*b*e^2*x)*cos(2*b*x + 2*a))/(cos(4*b*x + 4*a)^2 + sin(4*b*x + 4*a)^2 + 2*cos(4*b*x + 4*a) + 1), x)","F",0
250,0,0,0,0.000000," ","integrate((f*x+e)*arccoth(cot(b*x+a)),x, algorithm=""maxima"")","\frac{1}{8} \, {\left(f x^{2} + 2 \, e x\right)} \log\left(2 \, \cos\left(2 \, b x + 2 \, a\right)^{2} + 2 \, \sin\left(2 \, b x + 2 \, a\right)^{2} + 4 \, \sin\left(2 \, b x + 2 \, a\right) + 2\right) - \frac{1}{8} \, {\left(f x^{2} + 2 \, e x\right)} \log\left(2 \, \cos\left(2 \, b x + 2 \, a\right)^{2} + 2 \, \sin\left(2 \, b x + 2 \, a\right)^{2} - 4 \, \sin\left(2 \, b x + 2 \, a\right) + 2\right) - \int \frac{{\left(b f x^{2} + 2 \, b e x\right)} \cos\left(4 \, b x + 4 \, a\right) \cos\left(2 \, b x + 2 \, a\right) + {\left(b f x^{2} + 2 \, b e x\right)} \sin\left(4 \, b x + 4 \, a\right) \sin\left(2 \, b x + 2 \, a\right) + {\left(b f x^{2} + 2 \, b e x\right)} \cos\left(2 \, b x + 2 \, a\right)}{\cos\left(4 \, b x + 4 \, a\right)^{2} + \sin\left(4 \, b x + 4 \, a\right)^{2} + 2 \, \cos\left(4 \, b x + 4 \, a\right) + 1}\,{d x}"," ",0,"1/8*(f*x^2 + 2*e*x)*log(2*cos(2*b*x + 2*a)^2 + 2*sin(2*b*x + 2*a)^2 + 4*sin(2*b*x + 2*a) + 2) - 1/8*(f*x^2 + 2*e*x)*log(2*cos(2*b*x + 2*a)^2 + 2*sin(2*b*x + 2*a)^2 - 4*sin(2*b*x + 2*a) + 2) - integrate(((b*f*x^2 + 2*b*e*x)*cos(4*b*x + 4*a)*cos(2*b*x + 2*a) + (b*f*x^2 + 2*b*e*x)*sin(4*b*x + 4*a)*sin(2*b*x + 2*a) + (b*f*x^2 + 2*b*e*x)*cos(2*b*x + 2*a))/(cos(4*b*x + 4*a)^2 + sin(4*b*x + 4*a)^2 + 2*cos(4*b*x + 4*a) + 1), x)","F",0
251,1,184,0,0.468597," ","integrate(arccoth(cot(b*x+a)),x, algorithm=""maxima"")","\frac{4 \, {\left(b x + a\right)} \operatorname{arcoth}\left(\frac{1}{\tan\left(b x + a\right)}\right) + {\left(\arctan\left(\frac{1}{2} \, \tan\left(b x + a\right) + \frac{1}{2}, \frac{1}{2} \, \tan\left(b x + a\right) + \frac{1}{2}\right) - \arctan\left(\frac{1}{2} \, \tan\left(b x + a\right) - \frac{1}{2}, -\frac{1}{2} \, \tan\left(b x + a\right) + \frac{1}{2}\right)\right)} \log\left(\tan\left(b x + a\right)^{2} + 1\right) - {\left(b x + a\right)} \log\left(\frac{1}{2} \, \tan\left(b x + a\right)^{2} + \tan\left(b x + a\right) + \frac{1}{2}\right) + {\left(b x + a\right)} \log\left(\frac{1}{2} \, \tan\left(b x + a\right)^{2} - \tan\left(b x + a\right) + \frac{1}{2}\right) - i \, {\rm Li}_2\left(\left(\frac{1}{2} i + \frac{1}{2}\right) \, \tan\left(b x + a\right) - \frac{1}{2} i + \frac{1}{2}\right) + i \, {\rm Li}_2\left(-\left(\frac{1}{2} i - \frac{1}{2}\right) \, \tan\left(b x + a\right) + \frac{1}{2} i + \frac{1}{2}\right) + i \, {\rm Li}_2\left(\left(\frac{1}{2} i - \frac{1}{2}\right) \, \tan\left(b x + a\right) + \frac{1}{2} i + \frac{1}{2}\right) - i \, {\rm Li}_2\left(-\left(\frac{1}{2} i + \frac{1}{2}\right) \, \tan\left(b x + a\right) - \frac{1}{2} i + \frac{1}{2}\right)}{4 \, b}"," ",0,"1/4*(4*(b*x + a)*arccoth(1/tan(b*x + a)) + (arctan2(1/2*tan(b*x + a) + 1/2, 1/2*tan(b*x + a) + 1/2) - arctan2(1/2*tan(b*x + a) - 1/2, -1/2*tan(b*x + a) + 1/2))*log(tan(b*x + a)^2 + 1) - (b*x + a)*log(1/2*tan(b*x + a)^2 + tan(b*x + a) + 1/2) + (b*x + a)*log(1/2*tan(b*x + a)^2 - tan(b*x + a) + 1/2) - I*dilog((1/2*I + 1/2)*tan(b*x + a) - 1/2*I + 1/2) + I*dilog(-(1/2*I - 1/2)*tan(b*x + a) + 1/2*I + 1/2) + I*dilog((1/2*I - 1/2)*tan(b*x + a) + 1/2*I + 1/2) - I*dilog(-(1/2*I + 1/2)*tan(b*x + a) - 1/2*I + 1/2))/b","B",0
252,0,0,0,0.000000," ","integrate(arccoth(cot(b*x+a))/(f*x+e),x, algorithm=""maxima"")","\int \frac{\operatorname{arcoth}\left(\cot\left(b x + a\right)\right)}{f x + e}\,{d x}"," ",0,"integrate(arccoth(cot(b*x + a))/(f*x + e), x)","F",0
253,0,0,0,0.000000," ","integrate(x^2*arccoth(c+d*cot(b*x+a)),x, algorithm=""maxima"")","\frac{1}{12} \, x^{3} \log\left({\left(c^{2} + d^{2} + 2 \, c + 1\right)} \cos\left(2 \, b x + 2 \, a\right)^{2} + 4 \, {\left(c + 1\right)} d \sin\left(2 \, b x + 2 \, a\right) + {\left(c^{2} + d^{2} + 2 \, c + 1\right)} \sin\left(2 \, b x + 2 \, a\right)^{2} + c^{2} + d^{2} - 2 \, {\left(c^{2} - d^{2} + 2 \, c + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + 2 \, c + 1\right) - \frac{1}{12} \, x^{3} \log\left({\left(c^{2} + d^{2} - 2 \, c + 1\right)} \cos\left(2 \, b x + 2 \, a\right)^{2} + 4 \, {\left(c - 1\right)} d \sin\left(2 \, b x + 2 \, a\right) + {\left(c^{2} + d^{2} - 2 \, c + 1\right)} \sin\left(2 \, b x + 2 \, a\right)^{2} + c^{2} + d^{2} - 2 \, {\left(c^{2} - d^{2} - 2 \, c + 1\right)} \cos\left(2 \, b x + 2 \, a\right) - 2 \, c + 1\right) - 4 \, b d \int \frac{2 \, {\left(c^{2} + d^{2} - 1\right)} x^{3} \cos\left(2 \, b x + 2 \, a\right)^{2} + 2 \, c d x^{3} \sin\left(2 \, b x + 2 \, a\right) + 2 \, {\left(c^{2} + d^{2} - 1\right)} x^{3} \sin\left(2 \, b x + 2 \, a\right)^{2} - {\left(c^{2} - d^{2} - 1\right)} x^{3} \cos\left(2 \, b x + 2 \, a\right) - {\left(2 \, c d x^{3} \sin\left(2 \, b x + 2 \, a\right) + {\left(c^{2} - d^{2} - 1\right)} x^{3} \cos\left(2 \, b x + 2 \, a\right)\right)} \cos\left(4 \, b x + 4 \, a\right) + {\left(2 \, c d x^{3} \cos\left(2 \, b x + 2 \, a\right) - {\left(c^{2} - d^{2} - 1\right)} x^{3} \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(4 \, b x + 4 \, a\right)}{3 \, {\left(c^{4} + d^{4} + 2 \, {\left(c^{2} + 1\right)} d^{2} + {\left(c^{4} + d^{4} + 2 \, {\left(c^{2} + 1\right)} d^{2} - 2 \, c^{2} + 1\right)} \cos\left(4 \, b x + 4 \, a\right)^{2} + 4 \, {\left(c^{4} + d^{4} + 2 \, {\left(c^{2} - 1\right)} d^{2} - 2 \, c^{2} + 1\right)} \cos\left(2 \, b x + 2 \, a\right)^{2} + {\left(c^{4} + d^{4} + 2 \, {\left(c^{2} + 1\right)} d^{2} - 2 \, c^{2} + 1\right)} \sin\left(4 \, b x + 4 \, a\right)^{2} + 4 \, {\left(c^{4} + d^{4} + 2 \, {\left(c^{2} - 1\right)} d^{2} - 2 \, c^{2} + 1\right)} \sin\left(2 \, b x + 2 \, a\right)^{2} - 2 \, c^{2} + 2 \, {\left(c^{4} + d^{4} - 2 \, {\left(3 \, c^{2} - 1\right)} d^{2} - 2 \, c^{2} - 2 \, {\left(c^{4} - d^{4} - 2 \, c^{2} + 1\right)} \cos\left(2 \, b x + 2 \, a\right) - 4 \, {\left(c d^{3} + {\left(c^{3} - c\right)} d\right)} \sin\left(2 \, b x + 2 \, a\right) + 1\right)} \cos\left(4 \, b x + 4 \, a\right) - 4 \, {\left(c^{4} - d^{4} - 2 \, c^{2} + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + 4 \, {\left(2 \, c d^{3} - 2 \, {\left(c^{3} - c\right)} d + 2 \, {\left(c d^{3} + {\left(c^{3} - c\right)} d\right)} \cos\left(2 \, b x + 2 \, a\right) - {\left(c^{4} - d^{4} - 2 \, c^{2} + 1\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(4 \, b x + 4 \, a\right) + 8 \, {\left(c d^{3} + {\left(c^{3} - c\right)} d\right)} \sin\left(2 \, b x + 2 \, a\right) + 1\right)}}\,{d x}"," ",0,"1/12*x^3*log((c^2 + d^2 + 2*c + 1)*cos(2*b*x + 2*a)^2 + 4*(c + 1)*d*sin(2*b*x + 2*a) + (c^2 + d^2 + 2*c + 1)*sin(2*b*x + 2*a)^2 + c^2 + d^2 - 2*(c^2 - d^2 + 2*c + 1)*cos(2*b*x + 2*a) + 2*c + 1) - 1/12*x^3*log((c^2 + d^2 - 2*c + 1)*cos(2*b*x + 2*a)^2 + 4*(c - 1)*d*sin(2*b*x + 2*a) + (c^2 + d^2 - 2*c + 1)*sin(2*b*x + 2*a)^2 + c^2 + d^2 - 2*(c^2 - d^2 - 2*c + 1)*cos(2*b*x + 2*a) - 2*c + 1) - 4*b*d*integrate(1/3*(2*(c^2 + d^2 - 1)*x^3*cos(2*b*x + 2*a)^2 + 2*c*d*x^3*sin(2*b*x + 2*a) + 2*(c^2 + d^2 - 1)*x^3*sin(2*b*x + 2*a)^2 - (c^2 - d^2 - 1)*x^3*cos(2*b*x + 2*a) - (2*c*d*x^3*sin(2*b*x + 2*a) + (c^2 - d^2 - 1)*x^3*cos(2*b*x + 2*a))*cos(4*b*x + 4*a) + (2*c*d*x^3*cos(2*b*x + 2*a) - (c^2 - d^2 - 1)*x^3*sin(2*b*x + 2*a))*sin(4*b*x + 4*a))/(c^4 + d^4 + 2*(c^2 + 1)*d^2 + (c^4 + d^4 + 2*(c^2 + 1)*d^2 - 2*c^2 + 1)*cos(4*b*x + 4*a)^2 + 4*(c^4 + d^4 + 2*(c^2 - 1)*d^2 - 2*c^2 + 1)*cos(2*b*x + 2*a)^2 + (c^4 + d^4 + 2*(c^2 + 1)*d^2 - 2*c^2 + 1)*sin(4*b*x + 4*a)^2 + 4*(c^4 + d^4 + 2*(c^2 - 1)*d^2 - 2*c^2 + 1)*sin(2*b*x + 2*a)^2 - 2*c^2 + 2*(c^4 + d^4 - 2*(3*c^2 - 1)*d^2 - 2*c^2 - 2*(c^4 - d^4 - 2*c^2 + 1)*cos(2*b*x + 2*a) - 4*(c*d^3 + (c^3 - c)*d)*sin(2*b*x + 2*a) + 1)*cos(4*b*x + 4*a) - 4*(c^4 - d^4 - 2*c^2 + 1)*cos(2*b*x + 2*a) + 4*(2*c*d^3 - 2*(c^3 - c)*d + 2*(c*d^3 + (c^3 - c)*d)*cos(2*b*x + 2*a) - (c^4 - d^4 - 2*c^2 + 1)*sin(2*b*x + 2*a))*sin(4*b*x + 4*a) + 8*(c*d^3 + (c^3 - c)*d)*sin(2*b*x + 2*a) + 1), x)","F",0
254,0,0,0,0.000000," ","integrate(x*arccoth(c+d*cot(b*x+a)),x, algorithm=""maxima"")","-2 \, b d \int \frac{2 \, {\left(c^{2} + d^{2} - 1\right)} x^{2} \cos\left(2 \, b x + 2 \, a\right)^{2} + 2 \, c d x^{2} \sin\left(2 \, b x + 2 \, a\right) + 2 \, {\left(c^{2} + d^{2} - 1\right)} x^{2} \sin\left(2 \, b x + 2 \, a\right)^{2} - {\left(c^{2} - d^{2} - 1\right)} x^{2} \cos\left(2 \, b x + 2 \, a\right) - {\left(2 \, c d x^{2} \sin\left(2 \, b x + 2 \, a\right) + {\left(c^{2} - d^{2} - 1\right)} x^{2} \cos\left(2 \, b x + 2 \, a\right)\right)} \cos\left(4 \, b x + 4 \, a\right) + {\left(2 \, c d x^{2} \cos\left(2 \, b x + 2 \, a\right) - {\left(c^{2} - d^{2} - 1\right)} x^{2} \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(4 \, b x + 4 \, a\right)}{c^{4} + d^{4} + 2 \, {\left(c^{2} + 1\right)} d^{2} + {\left(c^{4} + d^{4} + 2 \, {\left(c^{2} + 1\right)} d^{2} - 2 \, c^{2} + 1\right)} \cos\left(4 \, b x + 4 \, a\right)^{2} + 4 \, {\left(c^{4} + d^{4} + 2 \, {\left(c^{2} - 1\right)} d^{2} - 2 \, c^{2} + 1\right)} \cos\left(2 \, b x + 2 \, a\right)^{2} + {\left(c^{4} + d^{4} + 2 \, {\left(c^{2} + 1\right)} d^{2} - 2 \, c^{2} + 1\right)} \sin\left(4 \, b x + 4 \, a\right)^{2} + 4 \, {\left(c^{4} + d^{4} + 2 \, {\left(c^{2} - 1\right)} d^{2} - 2 \, c^{2} + 1\right)} \sin\left(2 \, b x + 2 \, a\right)^{2} - 2 \, c^{2} + 2 \, {\left(c^{4} + d^{4} - 2 \, {\left(3 \, c^{2} - 1\right)} d^{2} - 2 \, c^{2} - 2 \, {\left(c^{4} - d^{4} - 2 \, c^{2} + 1\right)} \cos\left(2 \, b x + 2 \, a\right) - 4 \, {\left(c d^{3} + {\left(c^{3} - c\right)} d\right)} \sin\left(2 \, b x + 2 \, a\right) + 1\right)} \cos\left(4 \, b x + 4 \, a\right) - 4 \, {\left(c^{4} - d^{4} - 2 \, c^{2} + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + 4 \, {\left(2 \, c d^{3} - 2 \, {\left(c^{3} - c\right)} d + 2 \, {\left(c d^{3} + {\left(c^{3} - c\right)} d\right)} \cos\left(2 \, b x + 2 \, a\right) - {\left(c^{4} - d^{4} - 2 \, c^{2} + 1\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(4 \, b x + 4 \, a\right) + 8 \, {\left(c d^{3} + {\left(c^{3} - c\right)} d\right)} \sin\left(2 \, b x + 2 \, a\right) + 1}\,{d x} + \frac{1}{8} \, x^{2} \log\left({\left(c^{2} + d^{2} + 2 \, c + 1\right)} \cos\left(2 \, b x + 2 \, a\right)^{2} + 4 \, {\left(c + 1\right)} d \sin\left(2 \, b x + 2 \, a\right) + {\left(c^{2} + d^{2} + 2 \, c + 1\right)} \sin\left(2 \, b x + 2 \, a\right)^{2} + c^{2} + d^{2} - 2 \, {\left(c^{2} - d^{2} + 2 \, c + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + 2 \, c + 1\right) - \frac{1}{8} \, x^{2} \log\left({\left(c^{2} + d^{2} - 2 \, c + 1\right)} \cos\left(2 \, b x + 2 \, a\right)^{2} + 4 \, {\left(c - 1\right)} d \sin\left(2 \, b x + 2 \, a\right) + {\left(c^{2} + d^{2} - 2 \, c + 1\right)} \sin\left(2 \, b x + 2 \, a\right)^{2} + c^{2} + d^{2} - 2 \, {\left(c^{2} - d^{2} - 2 \, c + 1\right)} \cos\left(2 \, b x + 2 \, a\right) - 2 \, c + 1\right)"," ",0,"-2*b*d*integrate((2*(c^2 + d^2 - 1)*x^2*cos(2*b*x + 2*a)^2 + 2*c*d*x^2*sin(2*b*x + 2*a) + 2*(c^2 + d^2 - 1)*x^2*sin(2*b*x + 2*a)^2 - (c^2 - d^2 - 1)*x^2*cos(2*b*x + 2*a) - (2*c*d*x^2*sin(2*b*x + 2*a) + (c^2 - d^2 - 1)*x^2*cos(2*b*x + 2*a))*cos(4*b*x + 4*a) + (2*c*d*x^2*cos(2*b*x + 2*a) - (c^2 - d^2 - 1)*x^2*sin(2*b*x + 2*a))*sin(4*b*x + 4*a))/(c^4 + d^4 + 2*(c^2 + 1)*d^2 + (c^4 + d^4 + 2*(c^2 + 1)*d^2 - 2*c^2 + 1)*cos(4*b*x + 4*a)^2 + 4*(c^4 + d^4 + 2*(c^2 - 1)*d^2 - 2*c^2 + 1)*cos(2*b*x + 2*a)^2 + (c^4 + d^4 + 2*(c^2 + 1)*d^2 - 2*c^2 + 1)*sin(4*b*x + 4*a)^2 + 4*(c^4 + d^4 + 2*(c^2 - 1)*d^2 - 2*c^2 + 1)*sin(2*b*x + 2*a)^2 - 2*c^2 + 2*(c^4 + d^4 - 2*(3*c^2 - 1)*d^2 - 2*c^2 - 2*(c^4 - d^4 - 2*c^2 + 1)*cos(2*b*x + 2*a) - 4*(c*d^3 + (c^3 - c)*d)*sin(2*b*x + 2*a) + 1)*cos(4*b*x + 4*a) - 4*(c^4 - d^4 - 2*c^2 + 1)*cos(2*b*x + 2*a) + 4*(2*c*d^3 - 2*(c^3 - c)*d + 2*(c*d^3 + (c^3 - c)*d)*cos(2*b*x + 2*a) - (c^4 - d^4 - 2*c^2 + 1)*sin(2*b*x + 2*a))*sin(4*b*x + 4*a) + 8*(c*d^3 + (c^3 - c)*d)*sin(2*b*x + 2*a) + 1), x) + 1/8*x^2*log((c^2 + d^2 + 2*c + 1)*cos(2*b*x + 2*a)^2 + 4*(c + 1)*d*sin(2*b*x + 2*a) + (c^2 + d^2 + 2*c + 1)*sin(2*b*x + 2*a)^2 + c^2 + d^2 - 2*(c^2 - d^2 + 2*c + 1)*cos(2*b*x + 2*a) + 2*c + 1) - 1/8*x^2*log((c^2 + d^2 - 2*c + 1)*cos(2*b*x + 2*a)^2 + 4*(c - 1)*d*sin(2*b*x + 2*a) + (c^2 + d^2 - 2*c + 1)*sin(2*b*x + 2*a)^2 + c^2 + d^2 - 2*(c^2 - d^2 - 2*c + 1)*cos(2*b*x + 2*a) - 2*c + 1)","F",0
255,1,392,0,0.541645," ","integrate(arccoth(c+d*cot(b*x+a)),x, algorithm=""maxima"")","\frac{4 \, {\left(b x + a\right)} \operatorname{arcoth}\left(c + \frac{d}{\tan\left(b x + a\right)}\right) + {\left(\arctan\left(\frac{{\left(c + 1\right)} d + {\left(c^{2} + 2 \, c + 1\right)} \tan\left(b x + a\right)}{c^{2} + d^{2} + 2 \, c + 1}, \frac{{\left(c + 1\right)} d \tan\left(b x + a\right) + d^{2}}{c^{2} + d^{2} + 2 \, c + 1}\right) - \arctan\left(\frac{{\left(c - 1\right)} d + {\left(c^{2} - 2 \, c + 1\right)} \tan\left(b x + a\right)}{c^{2} + d^{2} - 2 \, c + 1}, \frac{{\left(c - 1\right)} d \tan\left(b x + a\right) + d^{2}}{c^{2} + d^{2} - 2 \, c + 1}\right)\right)} \log\left(\tan\left(b x + a\right)^{2} + 1\right) - {\left(b x + a\right)} \log\left(\frac{2 \, {\left(c + 1\right)} d \tan\left(b x + a\right) + {\left(c^{2} + 2 \, c + 1\right)} \tan\left(b x + a\right)^{2} + d^{2}}{c^{2} + d^{2} + 2 \, c + 1}\right) + {\left(b x + a\right)} \log\left(\frac{2 \, {\left(c - 1\right)} d \tan\left(b x + a\right) + {\left(c^{2} - 2 \, c + 1\right)} \tan\left(b x + a\right)^{2} + d^{2}}{c^{2} + d^{2} - 2 \, c + 1}\right) + i \, {\rm Li}_2\left(-\frac{{\left(c + 1\right)} \tan\left(b x + a\right) - i \, c - i}{i \, c + d + i}\right) - i \, {\rm Li}_2\left(-\frac{{\left(c - 1\right)} \tan\left(b x + a\right) - i \, c + i}{i \, c + d - i}\right) + i \, {\rm Li}_2\left(-\frac{{\left(c - 1\right)} \tan\left(b x + a\right) + i \, c - i}{-i \, c + d + i}\right) - i \, {\rm Li}_2\left(-\frac{{\left(c + 1\right)} \tan\left(b x + a\right) + i \, c + i}{-i \, c + d - i}\right)}{4 \, b}"," ",0,"1/4*(4*(b*x + a)*arccoth(c + d/tan(b*x + a)) + (arctan2(((c + 1)*d + (c^2 + 2*c + 1)*tan(b*x + a))/(c^2 + d^2 + 2*c + 1), ((c + 1)*d*tan(b*x + a) + d^2)/(c^2 + d^2 + 2*c + 1)) - arctan2(((c - 1)*d + (c^2 - 2*c + 1)*tan(b*x + a))/(c^2 + d^2 - 2*c + 1), ((c - 1)*d*tan(b*x + a) + d^2)/(c^2 + d^2 - 2*c + 1)))*log(tan(b*x + a)^2 + 1) - (b*x + a)*log((2*(c + 1)*d*tan(b*x + a) + (c^2 + 2*c + 1)*tan(b*x + a)^2 + d^2)/(c^2 + d^2 + 2*c + 1)) + (b*x + a)*log((2*(c - 1)*d*tan(b*x + a) + (c^2 - 2*c + 1)*tan(b*x + a)^2 + d^2)/(c^2 + d^2 - 2*c + 1)) + I*dilog(-((c + 1)*tan(b*x + a) - I*c - I)/(I*c + d + I)) - I*dilog(-((c - 1)*tan(b*x + a) - I*c + I)/(I*c + d - I)) + I*dilog(-((c - 1)*tan(b*x + a) + I*c - I)/(-I*c + d + I)) - I*dilog(-((c + 1)*tan(b*x + a) + I*c + I)/(-I*c + d - I)))/b","B",0
256,0,0,0,0.000000," ","integrate(arccoth(c+d*cot(b*x+a))/x,x, algorithm=""maxima"")","\int \frac{\operatorname{arcoth}\left(d \cot\left(b x + a\right) + c\right)}{x}\,{d x}"," ",0,"integrate(arccoth(d*cot(b*x + a) + c)/x, x)","F",0
257,1,342,0,0.377808," ","integrate(x^2*arccoth(1+I*d+d*cot(b*x+a)),x, algorithm=""maxima"")","\frac{\frac{12 \, {\left({\left(b x + a\right)}^{3} - 3 \, {\left(b x + a\right)}^{2} a + 3 \, {\left(b x + a\right)} a^{2}\right)} \operatorname{arcoth}\left(d \cot\left(b x + a\right) + i \, d + 1\right)}{b^{2}} - \frac{-3 i \, {\left(b x + a\right)}^{4} + 12 i \, {\left(b x + a\right)}^{3} a - 18 i \, {\left(b x + a\right)}^{2} a^{2} + {\left(-8 i \, {\left(b x + a\right)}^{3} + 18 i \, {\left(b x + a\right)}^{2} a - 18 i \, {\left(b x + a\right)} a^{2}\right)} \arctan\left(d \cos\left(2 \, b x + 2 \, a\right) + \sin\left(2 \, b x + 2 \, a\right), d \sin\left(2 \, b x + 2 \, a\right) - \cos\left(2 \, b x + 2 \, a\right) + 1\right) + {\left(-12 i \, {\left(b x + a\right)}^{2} + 18 i \, {\left(b x + a\right)} a - 9 i \, a^{2}\right)} {\rm Li}_2\left({\left(i \, d + 1\right)} e^{\left(2 i \, b x + 2 i \, a\right)}\right) + {\left(4 \, {\left(b x + a\right)}^{3} - 9 \, {\left(b x + a\right)}^{2} a + 9 \, {\left(b x + a\right)} a^{2}\right)} \log\left({\left(d^{2} + 1\right)} \cos\left(2 \, b x + 2 \, a\right)^{2} + {\left(d^{2} + 1\right)} \sin\left(2 \, b x + 2 \, a\right)^{2} + 2 \, d \sin\left(2 \, b x + 2 \, a\right) - 2 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right) + 3 \, {\left(4 \, b x + a\right)} {\rm Li}_{3}({\left(i \, d + 1\right)} e^{\left(2 i \, b x + 2 i \, a\right)}) + 6 i \, {\rm Li}_{4}({\left(i \, d + 1\right)} e^{\left(2 i \, b x + 2 i \, a\right)})}{b^{2}}}{36 \, b}"," ",0,"1/36*(12*((b*x + a)^3 - 3*(b*x + a)^2*a + 3*(b*x + a)*a^2)*arccoth(d*cot(b*x + a) + I*d + 1)/b^2 - (-3*I*(b*x + a)^4 + 12*I*(b*x + a)^3*a - 18*I*(b*x + a)^2*a^2 + (-8*I*(b*x + a)^3 + 18*I*(b*x + a)^2*a - 18*I*(b*x + a)*a^2)*arctan2(d*cos(2*b*x + 2*a) + sin(2*b*x + 2*a), d*sin(2*b*x + 2*a) - cos(2*b*x + 2*a) + 1) + (-12*I*(b*x + a)^2 + 18*I*(b*x + a)*a - 9*I*a^2)*dilog((I*d + 1)*e^(2*I*b*x + 2*I*a)) + (4*(b*x + a)^3 - 9*(b*x + a)^2*a + 9*(b*x + a)*a^2)*log((d^2 + 1)*cos(2*b*x + 2*a)^2 + (d^2 + 1)*sin(2*b*x + 2*a)^2 + 2*d*sin(2*b*x + 2*a) - 2*cos(2*b*x + 2*a) + 1) + 3*(4*b*x + a)*polylog(3, (I*d + 1)*e^(2*I*b*x + 2*I*a)) + 6*I*polylog(4, (I*d + 1)*e^(2*I*b*x + 2*I*a)))/b^2)/b","B",0
258,1,248,0,0.365598," ","integrate(x*arccoth(1+I*d+d*cot(b*x+a)),x, algorithm=""maxima"")","\frac{\frac{12 \, {\left({\left(b x + a\right)}^{2} - 2 \, {\left(b x + a\right)} a\right)} \operatorname{arcoth}\left(d \cot\left(b x + a\right) + i \, d + 1\right)}{b} - \frac{-4 i \, {\left(b x + a\right)}^{3} + 12 i \, {\left(b x + a\right)}^{2} a - 6 i \, b x {\rm Li}_2\left({\left(i \, d + 1\right)} e^{\left(2 i \, b x + 2 i \, a\right)}\right) + {\left(-6 i \, {\left(b x + a\right)}^{2} + 12 i \, {\left(b x + a\right)} a\right)} \arctan\left(d \cos\left(2 \, b x + 2 \, a\right) + \sin\left(2 \, b x + 2 \, a\right), d \sin\left(2 \, b x + 2 \, a\right) - \cos\left(2 \, b x + 2 \, a\right) + 1\right) + 3 \, {\left({\left(b x + a\right)}^{2} - 2 \, {\left(b x + a\right)} a\right)} \log\left({\left(d^{2} + 1\right)} \cos\left(2 \, b x + 2 \, a\right)^{2} + {\left(d^{2} + 1\right)} \sin\left(2 \, b x + 2 \, a\right)^{2} + 2 \, d \sin\left(2 \, b x + 2 \, a\right) - 2 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right) + 3 \, {\rm Li}_{3}({\left(i \, d + 1\right)} e^{\left(2 i \, b x + 2 i \, a\right)})}{b}}{24 \, b}"," ",0,"1/24*(12*((b*x + a)^2 - 2*(b*x + a)*a)*arccoth(d*cot(b*x + a) + I*d + 1)/b - (-4*I*(b*x + a)^3 + 12*I*(b*x + a)^2*a - 6*I*b*x*dilog((I*d + 1)*e^(2*I*b*x + 2*I*a)) + (-6*I*(b*x + a)^2 + 12*I*(b*x + a)*a)*arctan2(d*cos(2*b*x + 2*a) + sin(2*b*x + 2*a), d*sin(2*b*x + 2*a) - cos(2*b*x + 2*a) + 1) + 3*((b*x + a)^2 - 2*(b*x + a)*a)*log((d^2 + 1)*cos(2*b*x + 2*a)^2 + (d^2 + 1)*sin(2*b*x + 2*a)^2 + 2*d*sin(2*b*x + 2*a) - 2*cos(2*b*x + 2*a) + 1) + 3*polylog(3, (I*d + 1)*e^(2*I*b*x + 2*I*a)))/b)/b","B",0
259,1,286,0,0.451290," ","integrate(arccoth(1+I*d+d*cot(b*x+a)),x, algorithm=""maxima"")","-\frac{4 \, {\left(b x + a\right)} d {\left(\frac{\log\left({\left(i \, d + 2\right)} \tan\left(b x + a\right) + d\right)}{d} - \frac{\log\left(i \, \tan\left(b x + a\right) + 1\right)}{d}\right)} + d {\left(-\frac{2 i \, {\left(\log\left({\left(i \, d + 2\right)} \tan\left(b x + a\right) + d\right) \log\left(\frac{{\left(d - 2 i\right)} \tan\left(b x + a\right) - i \, d}{2 i \, d + 2} + 1\right) + {\rm Li}_2\left(-\frac{{\left(d - 2 i\right)} \tan\left(b x + a\right) - i \, d}{2 i \, d + 2}\right)\right)}}{d} - \frac{2 i \, {\left(\log\left(\frac{1}{2} \, {\left(d - 2 i\right)} \tan\left(b x + a\right) - \frac{1}{2} i \, d\right) \log\left(i \, \tan\left(b x + a\right) + 1\right) + {\rm Li}_2\left(-\frac{1}{2} \, {\left(d - 2 i\right)} \tan\left(b x + a\right) + \frac{1}{2} i \, d + 1\right)\right)}}{d} + \frac{2 i \, \log\left({\left(i \, d + 2\right)} \tan\left(b x + a\right) + d\right) \log\left(i \, \tan\left(b x + a\right) + 1\right) - i \, \log\left(i \, \tan\left(b x + a\right) + 1\right)^{2}}{d} + \frac{2 i \, {\left(\log\left(i \, \tan\left(b x + a\right) + 1\right) \log\left(-\frac{1}{2} i \, \tan\left(b x + a\right) + \frac{1}{2}\right) + {\rm Li}_2\left(\frac{1}{2} i \, \tan\left(b x + a\right) + \frac{1}{2}\right)\right)}}{d}\right)} - 8 \, {\left(b x + a\right)} \operatorname{arcoth}\left(i \, d + \frac{d}{\tan\left(b x + a\right)} + 1\right)}{8 \, b}"," ",0,"-1/8*(4*(b*x + a)*d*(log((I*d + 2)*tan(b*x + a) + d)/d - log(I*tan(b*x + a) + 1)/d) + d*(-2*I*(log((I*d + 2)*tan(b*x + a) + d)*log(((d - 2*I)*tan(b*x + a) - I*d)/(2*I*d + 2) + 1) + dilog(-((d - 2*I)*tan(b*x + a) - I*d)/(2*I*d + 2)))/d - 2*I*(log(1/2*(d - 2*I)*tan(b*x + a) - 1/2*I*d)*log(I*tan(b*x + a) + 1) + dilog(-1/2*(d - 2*I)*tan(b*x + a) + 1/2*I*d + 1))/d + (2*I*log((I*d + 2)*tan(b*x + a) + d)*log(I*tan(b*x + a) + 1) - I*log(I*tan(b*x + a) + 1)^2)/d + 2*I*(log(I*tan(b*x + a) + 1)*log(-1/2*I*tan(b*x + a) + 1/2) + dilog(1/2*I*tan(b*x + a) + 1/2))/d) - 8*(b*x + a)*arccoth(I*d + d/tan(b*x + a) + 1))/b","B",0
260,0,0,0,0.000000," ","integrate(arccoth(1+I*d+d*cot(b*x+a))/x,x, algorithm=""maxima"")","-i \, b x + \frac{1}{4} \, {\left(-i \, \pi - 4 i \, a - 2 \, \log\left(d\right)\right)} \log\left(x\right) + \frac{1}{2} i \, \int \frac{\arctan\left(d \cos\left(2 \, b x + 2 \, a\right) + \sin\left(2 \, b x + 2 \, a\right), -d \sin\left(2 \, b x + 2 \, a\right) + \cos\left(2 \, b x + 2 \, a\right) - 1\right)}{x}\,{d x} + \frac{1}{4} \, \int \frac{\log\left({\left(d^{2} + 1\right)} \cos\left(2 \, b x + 2 \, a\right)^{2} + {\left(d^{2} + 1\right)} \sin\left(2 \, b x + 2 \, a\right)^{2} + 2 \, d \sin\left(2 \, b x + 2 \, a\right) - 2 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right)}{x}\,{d x}"," ",0,"-I*b*x + 1/4*(-I*pi - 4*I*a - 2*log(d))*log(x) + 1/2*I*integrate(arctan2(d*cos(2*b*x + 2*a) + sin(2*b*x + 2*a), -d*sin(2*b*x + 2*a) + cos(2*b*x + 2*a) - 1)/x, x) + 1/4*integrate(log((d^2 + 1)*cos(2*b*x + 2*a)^2 + (d^2 + 1)*sin(2*b*x + 2*a)^2 + 2*d*sin(2*b*x + 2*a) - 2*cos(2*b*x + 2*a) + 1)/x, x)","F",0
261,1,343,0,0.405521," ","integrate(x^2*arccoth(1-I*d-d*cot(b*x+a)),x, algorithm=""maxima"")","-\frac{\frac{12 \, {\left({\left(b x + a\right)}^{3} - 3 \, {\left(b x + a\right)}^{2} a + 3 \, {\left(b x + a\right)} a^{2}\right)} \operatorname{arcoth}\left(d \cot\left(b x + a\right) + i \, d - 1\right)}{b^{2}} + \frac{-3 i \, {\left(b x + a\right)}^{4} + 12 i \, {\left(b x + a\right)}^{3} a - 18 i \, {\left(b x + a\right)}^{2} a^{2} + {\left(-8 i \, {\left(b x + a\right)}^{3} + 18 i \, {\left(b x + a\right)}^{2} a - 18 i \, {\left(b x + a\right)} a^{2}\right)} \arctan\left(-d \cos\left(2 \, b x + 2 \, a\right) + \sin\left(2 \, b x + 2 \, a\right), -d \sin\left(2 \, b x + 2 \, a\right) - \cos\left(2 \, b x + 2 \, a\right) + 1\right) + {\left(-12 i \, {\left(b x + a\right)}^{2} + 18 i \, {\left(b x + a\right)} a - 9 i \, a^{2}\right)} {\rm Li}_2\left({\left(-i \, d + 1\right)} e^{\left(2 i \, b x + 2 i \, a\right)}\right) + {\left(4 \, {\left(b x + a\right)}^{3} - 9 \, {\left(b x + a\right)}^{2} a + 9 \, {\left(b x + a\right)} a^{2}\right)} \log\left({\left(d^{2} + 1\right)} \cos\left(2 \, b x + 2 \, a\right)^{2} + {\left(d^{2} + 1\right)} \sin\left(2 \, b x + 2 \, a\right)^{2} - 2 \, d \sin\left(2 \, b x + 2 \, a\right) - 2 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right) + 3 \, {\left(4 \, b x + a\right)} {\rm Li}_{3}({\left(-i \, d + 1\right)} e^{\left(2 i \, b x + 2 i \, a\right)}) + 6 i \, {\rm Li}_{4}({\left(-i \, d + 1\right)} e^{\left(2 i \, b x + 2 i \, a\right)})}{b^{2}}}{36 \, b}"," ",0,"-1/36*(12*((b*x + a)^3 - 3*(b*x + a)^2*a + 3*(b*x + a)*a^2)*arccoth(d*cot(b*x + a) + I*d - 1)/b^2 + (-3*I*(b*x + a)^4 + 12*I*(b*x + a)^3*a - 18*I*(b*x + a)^2*a^2 + (-8*I*(b*x + a)^3 + 18*I*(b*x + a)^2*a - 18*I*(b*x + a)*a^2)*arctan2(-d*cos(2*b*x + 2*a) + sin(2*b*x + 2*a), -d*sin(2*b*x + 2*a) - cos(2*b*x + 2*a) + 1) + (-12*I*(b*x + a)^2 + 18*I*(b*x + a)*a - 9*I*a^2)*dilog((-I*d + 1)*e^(2*I*b*x + 2*I*a)) + (4*(b*x + a)^3 - 9*(b*x + a)^2*a + 9*(b*x + a)*a^2)*log((d^2 + 1)*cos(2*b*x + 2*a)^2 + (d^2 + 1)*sin(2*b*x + 2*a)^2 - 2*d*sin(2*b*x + 2*a) - 2*cos(2*b*x + 2*a) + 1) + 3*(4*b*x + a)*polylog(3, (-I*d + 1)*e^(2*I*b*x + 2*I*a)) + 6*I*polylog(4, (-I*d + 1)*e^(2*I*b*x + 2*I*a)))/b^2)/b","B",0
262,1,249,0,0.377179," ","integrate(x*arccoth(1-I*d-d*cot(b*x+a)),x, algorithm=""maxima"")","-\frac{\frac{12 \, {\left({\left(b x + a\right)}^{2} - 2 \, {\left(b x + a\right)} a\right)} \operatorname{arcoth}\left(d \cot\left(b x + a\right) + i \, d - 1\right)}{b} + \frac{-4 i \, {\left(b x + a\right)}^{3} + 12 i \, {\left(b x + a\right)}^{2} a - 6 i \, b x {\rm Li}_2\left({\left(-i \, d + 1\right)} e^{\left(2 i \, b x + 2 i \, a\right)}\right) + {\left(-6 i \, {\left(b x + a\right)}^{2} + 12 i \, {\left(b x + a\right)} a\right)} \arctan\left(-d \cos\left(2 \, b x + 2 \, a\right) + \sin\left(2 \, b x + 2 \, a\right), -d \sin\left(2 \, b x + 2 \, a\right) - \cos\left(2 \, b x + 2 \, a\right) + 1\right) + 3 \, {\left({\left(b x + a\right)}^{2} - 2 \, {\left(b x + a\right)} a\right)} \log\left({\left(d^{2} + 1\right)} \cos\left(2 \, b x + 2 \, a\right)^{2} + {\left(d^{2} + 1\right)} \sin\left(2 \, b x + 2 \, a\right)^{2} - 2 \, d \sin\left(2 \, b x + 2 \, a\right) - 2 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right) + 3 \, {\rm Li}_{3}({\left(-i \, d + 1\right)} e^{\left(2 i \, b x + 2 i \, a\right)})}{b}}{24 \, b}"," ",0,"-1/24*(12*((b*x + a)^2 - 2*(b*x + a)*a)*arccoth(d*cot(b*x + a) + I*d - 1)/b + (-4*I*(b*x + a)^3 + 12*I*(b*x + a)^2*a - 6*I*b*x*dilog((-I*d + 1)*e^(2*I*b*x + 2*I*a)) + (-6*I*(b*x + a)^2 + 12*I*(b*x + a)*a)*arctan2(-d*cos(2*b*x + 2*a) + sin(2*b*x + 2*a), -d*sin(2*b*x + 2*a) - cos(2*b*x + 2*a) + 1) + 3*((b*x + a)^2 - 2*(b*x + a)*a)*log((d^2 + 1)*cos(2*b*x + 2*a)^2 + (d^2 + 1)*sin(2*b*x + 2*a)^2 - 2*d*sin(2*b*x + 2*a) - 2*cos(2*b*x + 2*a) + 1) + 3*polylog(3, (-I*d + 1)*e^(2*I*b*x + 2*I*a)))/b)/b","B",0
263,1,288,0,0.454453," ","integrate(arccoth(1-I*d-d*cot(b*x+a)),x, algorithm=""maxima"")","-\frac{4 \, {\left(b x + a\right)} d {\left(\frac{\log\left({\left(i \, d - 2\right)} \tan\left(b x + a\right) + d\right)}{d} - \frac{\log\left(i \, \tan\left(b x + a\right) + 1\right)}{d}\right)} - d {\left(\frac{2 i \, {\left(\log\left({\left(i \, d - 2\right)} \tan\left(b x + a\right) + d\right) \log\left(\frac{{\left(d + 2 i\right)} \tan\left(b x + a\right) - i \, d}{2 i \, d - 2} + 1\right) + {\rm Li}_2\left(-\frac{{\left(d + 2 i\right)} \tan\left(b x + a\right) - i \, d}{2 i \, d - 2}\right)\right)}}{d} + \frac{2 i \, {\left(\log\left(-\frac{1}{2} \, {\left(d + 2 i\right)} \tan\left(b x + a\right) + \frac{1}{2} i \, d\right) \log\left(i \, \tan\left(b x + a\right) + 1\right) + {\rm Li}_2\left(\frac{1}{2} \, {\left(d + 2 i\right)} \tan\left(b x + a\right) - \frac{1}{2} i \, d + 1\right)\right)}}{d} - \frac{2 i \, \log\left({\left(i \, d - 2\right)} \tan\left(b x + a\right) + d\right) \log\left(i \, \tan\left(b x + a\right) + 1\right) - i \, \log\left(i \, \tan\left(b x + a\right) + 1\right)^{2}}{d} - \frac{2 i \, {\left(\log\left(i \, \tan\left(b x + a\right) + 1\right) \log\left(-\frac{1}{2} i \, \tan\left(b x + a\right) + \frac{1}{2}\right) + {\rm Li}_2\left(\frac{1}{2} i \, \tan\left(b x + a\right) + \frac{1}{2}\right)\right)}}{d}\right)} + 8 \, {\left(b x + a\right)} \operatorname{arcoth}\left(i \, d + \frac{d}{\tan\left(b x + a\right)} - 1\right)}{8 \, b}"," ",0,"-1/8*(4*(b*x + a)*d*(log((I*d - 2)*tan(b*x + a) + d)/d - log(I*tan(b*x + a) + 1)/d) - d*(2*I*(log((I*d - 2)*tan(b*x + a) + d)*log(((d + 2*I)*tan(b*x + a) - I*d)/(2*I*d - 2) + 1) + dilog(-((d + 2*I)*tan(b*x + a) - I*d)/(2*I*d - 2)))/d + 2*I*(log(-1/2*(d + 2*I)*tan(b*x + a) + 1/2*I*d)*log(I*tan(b*x + a) + 1) + dilog(1/2*(d + 2*I)*tan(b*x + a) - 1/2*I*d + 1))/d - (2*I*log((I*d - 2)*tan(b*x + a) + d)*log(I*tan(b*x + a) + 1) - I*log(I*tan(b*x + a) + 1)^2)/d - 2*I*(log(I*tan(b*x + a) + 1)*log(-1/2*I*tan(b*x + a) + 1/2) + dilog(1/2*I*tan(b*x + a) + 1/2))/d) + 8*(b*x + a)*arccoth(I*d + d/tan(b*x + a) - 1))/b","B",0
264,0,0,0,0.000000," ","integrate(arccoth(1-I*d-d*cot(b*x+a))/x,x, algorithm=""maxima"")","-i \, b x + \frac{1}{4} \, {\left(-i \, \pi - 4 i \, a - 2 \, \log\left(d\right)\right)} \log\left(x\right) - \frac{1}{2} i \, \int \frac{\arctan\left(-d \cos\left(2 \, b x + 2 \, a\right) + \sin\left(2 \, b x + 2 \, a\right), -d \sin\left(2 \, b x + 2 \, a\right) - \cos\left(2 \, b x + 2 \, a\right) + 1\right)}{x}\,{d x} + \frac{1}{4} \, \int \frac{\log\left({\left(d^{2} + 1\right)} \cos\left(2 \, b x + 2 \, a\right)^{2} + {\left(d^{2} + 1\right)} \sin\left(2 \, b x + 2 \, a\right)^{2} - 2 \, d \sin\left(2 \, b x + 2 \, a\right) - 2 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right)}{x}\,{d x}"," ",0,"-I*b*x + 1/4*(-I*pi - 4*I*a - 2*log(d))*log(x) - 1/2*I*integrate(arctan2(-d*cos(2*b*x + 2*a) + sin(2*b*x + 2*a), -d*sin(2*b*x + 2*a) - cos(2*b*x + 2*a) + 1)/x, x) + 1/4*integrate(log((d^2 + 1)*cos(2*b*x + 2*a)^2 + (d^2 + 1)*sin(2*b*x + 2*a)^2 - 2*d*sin(2*b*x + 2*a) - 2*cos(2*b*x + 2*a) + 1)/x, x)","F",0
265,0,0,0,0.000000," ","integrate((a+b*arccoth(c*x^n))*(d+e*log(f*x^m))/x,x, algorithm=""maxima"")","\frac{a e \log\left(f x^{m}\right)^{2}}{2 \, m} + a d \log\left(x\right) - \frac{1}{4} \, {\left(b e m \log\left(x\right)^{2} - 2 \, b e \log\left(x\right) \log\left(x^{m}\right) - 2 \, {\left(e \log\left(f\right) + d\right)} b \log\left(x\right)\right)} \log\left(c x^{n} + 1\right) + \frac{1}{4} \, {\left(b e m \log\left(x\right)^{2} - 2 \, b e \log\left(x\right) \log\left(x^{m}\right) - 2 \, {\left(e \log\left(f\right) + d\right)} b \log\left(x\right)\right)} \log\left(c x^{n} - 1\right) + \int \frac{2 \, b c e n x^{n} \log\left(x\right) \log\left(x^{m}\right) - {\left(b c e m n \log\left(x\right)^{2} - 2 \, {\left(e n \log\left(f\right) + d n\right)} b c \log\left(x\right)\right)} x^{n}}{2 \, {\left(c^{2} x x^{2 \, n} - x\right)}}\,{d x}"," ",0,"1/2*a*e*log(f*x^m)^2/m + a*d*log(x) - 1/4*(b*e*m*log(x)^2 - 2*b*e*log(x)*log(x^m) - 2*(e*log(f) + d)*b*log(x))*log(c*x^n + 1) + 1/4*(b*e*m*log(x)^2 - 2*b*e*log(x)*log(x^m) - 2*(e*log(f) + d)*b*log(x))*log(c*x^n - 1) + integrate(1/2*(2*b*c*e*n*x^n*log(x)*log(x^m) - (b*c*e*m*n*log(x)^2 - 2*(e*n*log(f) + d*n)*b*c*log(x))*x^n)/(c^2*x*x^(2*n) - x), x)","F",0
266,1,328,0,0.351197," ","integrate(x^5*(a+b*arccoth(c*x))*(d+e*log(-c^2*x^2+1)),x, algorithm=""maxima"")","\frac{1}{6} \, a d x^{6} + \frac{1}{36} \, {\left(6 \, x^{6} \log\left(-c^{2} x^{2} + 1\right) - c^{2} {\left(\frac{2 \, c^{4} x^{6} + 3 \, c^{2} x^{4} + 6 \, x^{2}}{c^{6}} + \frac{6 \, \log\left(c^{2} x^{2} - 1\right)}{c^{8}}\right)}\right)} b e \operatorname{arcoth}\left(c x\right) + \frac{1}{180} \, {\left(30 \, x^{6} \operatorname{arcoth}\left(c x\right) + c {\left(\frac{2 \, {\left(3 \, c^{4} x^{5} + 5 \, c^{2} x^{3} + 15 \, x\right)}}{c^{6}} - \frac{15 \, \log\left(c x + 1\right)}{c^{7}} + \frac{15 \, \log\left(c x - 1\right)}{c^{7}}\right)}\right)} b d + \frac{1}{36} \, {\left(6 \, x^{6} \log\left(-c^{2} x^{2} + 1\right) - c^{2} {\left(\frac{2 \, c^{4} x^{6} + 3 \, c^{2} x^{4} + 6 \, x^{2}}{c^{6}} + \frac{6 \, \log\left(c^{2} x^{2} - 1\right)}{c^{8}}\right)}\right)} a e + \frac{{\left({\left(60 i \, \pi c^{5} - 44 \, c^{5}\right)} x^{5} + {\left(100 i \, \pi c^{3} - 190 \, c^{3}\right)} x^{3} + {\left(300 i \, \pi c - 1470 \, c\right)} x - 5 \, {\left(30 i \, \pi - 12 \, c^{5} x^{5} - 20 \, c^{3} x^{3} - 60 \, c x - 147\right)} \log\left(c x + 1\right) - 5 \, {\left(-30 i \, \pi - 12 \, c^{5} x^{5} - 20 \, c^{3} x^{3} - 60 \, c x + 147\right)} \log\left(c x - 1\right)\right)} b e}{1800 \, c^{6}}"," ",0,"1/6*a*d*x^6 + 1/36*(6*x^6*log(-c^2*x^2 + 1) - c^2*((2*c^4*x^6 + 3*c^2*x^4 + 6*x^2)/c^6 + 6*log(c^2*x^2 - 1)/c^8))*b*e*arccoth(c*x) + 1/180*(30*x^6*arccoth(c*x) + c*(2*(3*c^4*x^5 + 5*c^2*x^3 + 15*x)/c^6 - 15*log(c*x + 1)/c^7 + 15*log(c*x - 1)/c^7))*b*d + 1/36*(6*x^6*log(-c^2*x^2 + 1) - c^2*((2*c^4*x^6 + 3*c^2*x^4 + 6*x^2)/c^6 + 6*log(c^2*x^2 - 1)/c^8))*a*e + 1/1800*((60*I*pi*c^5 - 44*c^5)*x^5 + (100*I*pi*c^3 - 190*c^3)*x^3 + (300*I*pi*c - 1470*c)*x - 5*(30*I*pi - 12*c^5*x^5 - 20*c^3*x^3 - 60*c*x - 147)*log(c*x + 1) - 5*(-30*I*pi - 12*c^5*x^5 - 20*c^3*x^3 - 60*c*x + 147)*log(c*x - 1))*b*e/c^6","C",0
267,1,269,0,0.349365," ","integrate(x^3*(a+b*arccoth(c*x))*(d+e*log(-c^2*x^2+1)),x, algorithm=""maxima"")","\frac{1}{4} \, a d x^{4} + \frac{1}{8} \, {\left(2 \, x^{4} \log\left(-c^{2} x^{2} + 1\right) - c^{2} {\left(\frac{c^{2} x^{4} + 2 \, x^{2}}{c^{4}} + \frac{2 \, \log\left(c^{2} x^{2} - 1\right)}{c^{6}}\right)}\right)} b e \operatorname{arcoth}\left(c x\right) + \frac{1}{24} \, {\left(6 \, x^{4} \operatorname{arcoth}\left(c x\right) + c {\left(\frac{2 \, {\left(c^{2} x^{3} + 3 \, x\right)}}{c^{4}} - \frac{3 \, \log\left(c x + 1\right)}{c^{5}} + \frac{3 \, \log\left(c x - 1\right)}{c^{5}}\right)}\right)} b d + \frac{1}{8} \, {\left(2 \, x^{4} \log\left(-c^{2} x^{2} + 1\right) - c^{2} {\left(\frac{c^{2} x^{4} + 2 \, x^{2}}{c^{4}} + \frac{2 \, \log\left(c^{2} x^{2} - 1\right)}{c^{6}}\right)}\right)} a e + \frac{{\left({\left(12 i \, \pi c^{3} - 14 \, c^{3}\right)} x^{3} + {\left(36 i \, \pi c - 150 \, c\right)} x - 3 \, {\left(6 i \, \pi - 4 \, c^{3} x^{3} - 12 \, c x - 25\right)} \log\left(c x + 1\right) - 3 \, {\left(-6 i \, \pi - 4 \, c^{3} x^{3} - 12 \, c x + 25\right)} \log\left(c x - 1\right)\right)} b e}{144 \, c^{4}}"," ",0,"1/4*a*d*x^4 + 1/8*(2*x^4*log(-c^2*x^2 + 1) - c^2*((c^2*x^4 + 2*x^2)/c^4 + 2*log(c^2*x^2 - 1)/c^6))*b*e*arccoth(c*x) + 1/24*(6*x^4*arccoth(c*x) + c*(2*(c^2*x^3 + 3*x)/c^4 - 3*log(c*x + 1)/c^5 + 3*log(c*x - 1)/c^5))*b*d + 1/8*(2*x^4*log(-c^2*x^2 + 1) - c^2*((c^2*x^4 + 2*x^2)/c^4 + 2*log(c^2*x^2 - 1)/c^6))*a*e + 1/144*((12*I*pi*c^3 - 14*c^3)*x^3 + (36*I*pi*c - 150*c)*x - 3*(6*I*pi - 4*c^3*x^3 - 12*c*x - 25)*log(c*x + 1) - 3*(-6*I*pi - 4*c^3*x^3 - 12*c*x + 25)*log(c*x - 1))*b*e/c^4","C",0
268,1,171,0,0.344187," ","integrate(x*(a+b*arccoth(c*x))*(d+e*log(-c^2*x^2+1)),x, algorithm=""maxima"")","\frac{1}{2} \, a d x^{2} + \frac{1}{4} \, {\left(2 \, x^{2} \operatorname{arcoth}\left(c x\right) + c {\left(\frac{2 \, x}{c^{2}} - \frac{\log\left(c x + 1\right)}{c^{3}} + \frac{\log\left(c x - 1\right)}{c^{3}}\right)}\right)} b d - \frac{{\left(c^{2} x^{2} - {\left(c^{2} x^{2} - 1\right)} \log\left(-c^{2} x^{2} + 1\right) - 1\right)} b e \operatorname{arcoth}\left(c x\right)}{2 \, c^{2}} - \frac{{\left(c^{2} x^{2} - {\left(c^{2} x^{2} - 1\right)} \log\left(-c^{2} x^{2} + 1\right) - 1\right)} a e}{2 \, c^{2}} - \frac{{\left(3 \, c x - {\left(c x + 1\right)} \log\left(c x + 1\right) - {\left(c x - 1\right)} \log\left(-c x + 1\right)\right)} b e}{2 \, c^{2}}"," ",0,"1/2*a*d*x^2 + 1/4*(2*x^2*arccoth(c*x) + c*(2*x/c^2 - log(c*x + 1)/c^3 + log(c*x - 1)/c^3))*b*d - 1/2*(c^2*x^2 - (c^2*x^2 - 1)*log(-c^2*x^2 + 1) - 1)*b*e*arccoth(c*x)/c^2 - 1/2*(c^2*x^2 - (c^2*x^2 - 1)*log(-c^2*x^2 + 1) - 1)*a*e/c^2 - 1/2*(3*c*x - (c*x + 1)*log(c*x + 1) - (c*x - 1)*log(-c*x + 1))*b*e/c^2","A",0
269,1,167,0,0.536378," ","integrate((a+b*arccoth(c*x))*(d+e*log(-c^2*x^2+1))/x,x, algorithm=""maxima"")","i \, \pi a e \log\left(x\right) - \frac{1}{2} \, {\left(\log\left(c x - 1\right)^{2} \log\left(c x\right) + 2 \, {\rm Li}_2\left(-c x + 1\right) \log\left(c x - 1\right) - 2 \, {\rm Li}_{3}(-c x + 1)\right)} b e + \frac{1}{2} \, {\left(\log\left(c x + 1\right)^{2} \log\left(-c x\right) + 2 \, {\rm Li}_2\left(c x + 1\right) \log\left(c x + 1\right) - 2 \, {\rm Li}_{3}(c x + 1)\right)} b e + a d \log\left(x\right) - \frac{1}{2} \, {\left(i \, \pi b e + b d - 2 \, a e\right)} {\left(\log\left(c x - 1\right) \log\left(c x\right) + {\rm Li}_2\left(-c x + 1\right)\right)} - \frac{1}{2} \, {\left(-i \, \pi b e - b d - 2 \, a e\right)} {\left(\log\left(c x + 1\right) \log\left(-c x\right) + {\rm Li}_2\left(c x + 1\right)\right)}"," ",0,"I*pi*a*e*log(x) - 1/2*(log(c*x - 1)^2*log(c*x) + 2*dilog(-c*x + 1)*log(c*x - 1) - 2*polylog(3, -c*x + 1))*b*e + 1/2*(log(c*x + 1)^2*log(-c*x) + 2*dilog(c*x + 1)*log(c*x + 1) - 2*polylog(3, c*x + 1))*b*e + a*d*log(x) - 1/2*(I*pi*b*e + b*d - 2*a*e)*(log(c*x - 1)*log(c*x) + dilog(-c*x + 1)) - 1/2*(-I*pi*b*e - b*d - 2*a*e)*(log(c*x + 1)*log(-c*x) + dilog(c*x + 1))","C",0
270,0,0,0,0.000000," ","integrate((a+b*arccoth(c*x))*(d+e*log(-c^2*x^2+1))/x^3,x, algorithm=""maxima"")","\frac{1}{4} \, {\left({\left(c \log\left(c x + 1\right) - c \log\left(c x - 1\right) - \frac{2}{x}\right)} c - \frac{2 \, \operatorname{arcoth}\left(c x\right)}{x^{2}}\right)} b d + \frac{1}{2} \, {\left(c^{2} {\left(\log\left(c^{2} x^{2} - 1\right) - \log\left(x^{2}\right)\right)} - \frac{\log\left(-c^{2} x^{2} + 1\right)}{x^{2}}\right)} a e - \frac{1}{4} \, b e {\left(\frac{\log\left(c x + 1\right)^{2}}{x^{2}} - 2 \, \int -\frac{{\left(c x + 1\right)} \log\left(c x - 1\right)^{2} - {\left(i \, \pi + {\left(i \, \pi c + c\right)} x\right)} \log\left(c x + 1\right) - {\left(-i \, \pi - i \, \pi c x\right)} \log\left(c x - 1\right)}{c x^{4} + x^{3}}\,{d x}\right)} - \frac{a d}{2 \, x^{2}}"," ",0,"1/4*((c*log(c*x + 1) - c*log(c*x - 1) - 2/x)*c - 2*arccoth(c*x)/x^2)*b*d + 1/2*(c^2*(log(c^2*x^2 - 1) - log(x^2)) - log(-c^2*x^2 + 1)/x^2)*a*e - 1/4*b*e*(log(c*x + 1)^2/x^2 - 2*integrate(-((c*x + 1)*log(c*x - 1)^2 - (I*pi + (I*pi*c + c)*x)*log(c*x + 1) - (-I*pi - I*pi*c*x)*log(c*x - 1))/(c*x^4 + x^3), x)) - 1/2*a*d/x^2","F",0
271,0,0,0,0.000000," ","integrate((a+b*arccoth(c*x))*(d+e*log(-c^2*x^2+1))/x^5,x, algorithm=""maxima"")","\frac{1}{24} \, {\left({\left(3 \, c^{3} \log\left(c x + 1\right) - 3 \, c^{3} \log\left(c x - 1\right) - \frac{2 \, {\left(3 \, c^{2} x^{2} + 1\right)}}{x^{3}}\right)} c - \frac{6 \, \operatorname{arcoth}\left(c x\right)}{x^{4}}\right)} b d + \frac{1}{4} \, {\left({\left(c^{2} \log\left(c^{2} x^{2} - 1\right) - c^{2} \log\left(x^{2}\right) + \frac{1}{x^{2}}\right)} c^{2} - \frac{\log\left(-c^{2} x^{2} + 1\right)}{x^{4}}\right)} a e - \frac{1}{8} \, b e {\left(\frac{\log\left(c x + 1\right)^{2}}{x^{4}} - 4 \, \int -\frac{2 \, {\left(c x + 1\right)} \log\left(c x - 1\right)^{2} - {\left(2 i \, \pi + {\left(2 i \, \pi c + c\right)} x\right)} \log\left(c x + 1\right) - {\left(-2 i \, \pi - 2 i \, \pi c x\right)} \log\left(c x - 1\right)}{2 \, {\left(c x^{6} + x^{5}\right)}}\,{d x}\right)} - \frac{a d}{4 \, x^{4}}"," ",0,"1/24*((3*c^3*log(c*x + 1) - 3*c^3*log(c*x - 1) - 2*(3*c^2*x^2 + 1)/x^3)*c - 6*arccoth(c*x)/x^4)*b*d + 1/4*((c^2*log(c^2*x^2 - 1) - c^2*log(x^2) + 1/x^2)*c^2 - log(-c^2*x^2 + 1)/x^4)*a*e - 1/8*b*e*(log(c*x + 1)^2/x^4 - 4*integrate(-1/2*(2*(c*x + 1)*log(c*x - 1)^2 - (2*I*pi + (2*I*pi*c + c)*x)*log(c*x + 1) - (-2*I*pi - 2*I*pi*c*x)*log(c*x - 1))/(c*x^6 + x^5), x)) - 1/4*a*d/x^4","F",0
272,1,314,0,0.338571," ","integrate(x^4*(a+b*arccoth(c*x))*(d+e*log(-c^2*x^2+1)),x, algorithm=""maxima"")","\frac{1}{5} \, a d x^{5} + \frac{1}{75} \, {\left(15 \, x^{5} \log\left(-c^{2} x^{2} + 1\right) - c^{2} {\left(\frac{2 \, {\left(3 \, c^{4} x^{5} + 5 \, c^{2} x^{3} + 15 \, x\right)}}{c^{6}} - \frac{15 \, \log\left(c x + 1\right)}{c^{7}} + \frac{15 \, \log\left(c x - 1\right)}{c^{7}}\right)}\right)} b e \operatorname{arcoth}\left(c x\right) + \frac{1}{20} \, {\left(4 \, x^{5} \operatorname{arcoth}\left(c x\right) + c {\left(\frac{c^{2} x^{4} + 2 \, x^{2}}{c^{4}} + \frac{2 \, \log\left(c^{2} x^{2} - 1\right)}{c^{6}}\right)}\right)} b d + \frac{1}{75} \, {\left(15 \, x^{5} \log\left(-c^{2} x^{2} + 1\right) - c^{2} {\left(\frac{2 \, {\left(3 \, c^{4} x^{5} + 5 \, c^{2} x^{3} + 15 \, x\right)}}{c^{6}} - \frac{15 \, \log\left(c x + 1\right)}{c^{7}} + \frac{15 \, \log\left(c x - 1\right)}{c^{7}}\right)}\right)} a e + \frac{{\left({\left(30 i \, \pi c^{4} - 27 \, c^{4}\right)} x^{4} + {\left(60 i \, \pi c^{2} - 154 \, c^{2}\right)} x^{2} + {\left(60 i \, \pi + 30 \, c^{4} x^{4} + 60 \, c^{2} x^{2} + 120 \, \log\left(c x - 1\right) - 274\right)} \log\left(c x + 1\right) - 2 \, {\left(-30 i \, \pi - 15 \, c^{4} x^{4} - 30 \, c^{2} x^{2} + 137\right)} \log\left(c x - 1\right)\right)} b e}{600 \, c^{5}}"," ",0,"1/5*a*d*x^5 + 1/75*(15*x^5*log(-c^2*x^2 + 1) - c^2*(2*(3*c^4*x^5 + 5*c^2*x^3 + 15*x)/c^6 - 15*log(c*x + 1)/c^7 + 15*log(c*x - 1)/c^7))*b*e*arccoth(c*x) + 1/20*(4*x^5*arccoth(c*x) + c*((c^2*x^4 + 2*x^2)/c^4 + 2*log(c^2*x^2 - 1)/c^6))*b*d + 1/75*(15*x^5*log(-c^2*x^2 + 1) - c^2*(2*(3*c^4*x^5 + 5*c^2*x^3 + 15*x)/c^6 - 15*log(c*x + 1)/c^7 + 15*log(c*x - 1)/c^7))*a*e + 1/600*((30*I*pi*c^4 - 27*c^4)*x^4 + (60*I*pi*c^2 - 154*c^2)*x^2 + (60*I*pi + 30*c^4*x^4 + 60*c^2*x^2 + 120*log(c*x - 1) - 274)*log(c*x + 1) - 2*(-30*I*pi - 15*c^4*x^4 - 30*c^2*x^2 + 137)*log(c*x - 1))*b*e/c^5","C",0
273,1,252,0,0.331178," ","integrate(x^2*(a+b*arccoth(c*x))*(d+e*log(-c^2*x^2+1)),x, algorithm=""maxima"")","\frac{1}{3} \, a d x^{3} + \frac{1}{9} \, {\left(3 \, x^{3} \log\left(-c^{2} x^{2} + 1\right) - c^{2} {\left(\frac{2 \, {\left(c^{2} x^{3} + 3 \, x\right)}}{c^{4}} - \frac{3 \, \log\left(c x + 1\right)}{c^{5}} + \frac{3 \, \log\left(c x - 1\right)}{c^{5}}\right)}\right)} b e \operatorname{arcoth}\left(c x\right) + \frac{1}{6} \, {\left(2 \, x^{3} \operatorname{arcoth}\left(c x\right) + c {\left(\frac{x^{2}}{c^{2}} + \frac{\log\left(c^{2} x^{2} - 1\right)}{c^{4}}\right)}\right)} b d + \frac{1}{9} \, {\left(3 \, x^{3} \log\left(-c^{2} x^{2} + 1\right) - c^{2} {\left(\frac{2 \, {\left(c^{2} x^{3} + 3 \, x\right)}}{c^{4}} - \frac{3 \, \log\left(c x + 1\right)}{c^{5}} + \frac{3 \, \log\left(c x - 1\right)}{c^{5}}\right)}\right)} a e + \frac{{\left({\left(3 i \, \pi c^{2} - 5 \, c^{2}\right)} x^{2} + {\left(3 i \, \pi + 3 \, c^{2} x^{2} + 6 \, \log\left(c x - 1\right) - 11\right)} \log\left(c x + 1\right) + {\left(3 i \, \pi + 3 \, c^{2} x^{2} - 11\right)} \log\left(c x - 1\right)\right)} b e}{18 \, c^{3}}"," ",0,"1/3*a*d*x^3 + 1/9*(3*x^3*log(-c^2*x^2 + 1) - c^2*(2*(c^2*x^3 + 3*x)/c^4 - 3*log(c*x + 1)/c^5 + 3*log(c*x - 1)/c^5))*b*e*arccoth(c*x) + 1/6*(2*x^3*arccoth(c*x) + c*(x^2/c^2 + log(c^2*x^2 - 1)/c^4))*b*d + 1/9*(3*x^3*log(-c^2*x^2 + 1) - c^2*(2*(c^2*x^3 + 3*x)/c^4 - 3*log(c*x + 1)/c^5 + 3*log(c*x - 1)/c^5))*a*e + 1/18*((3*I*pi*c^2 - 5*c^2)*x^2 + (3*I*pi + 3*c^2*x^2 + 6*log(c*x - 1) - 11)*log(c*x + 1) + (3*I*pi + 3*c^2*x^2 - 11)*log(c*x - 1))*b*e/c^3","C",0
274,1,178,0,0.331679," ","integrate((a+b*arccoth(c*x))*(d+e*log(-c^2*x^2+1)),x, algorithm=""maxima"")","-{\left(c^{2} {\left(\frac{2 \, x}{c^{2}} - \frac{\log\left(c x + 1\right)}{c^{3}} + \frac{\log\left(c x - 1\right)}{c^{3}}\right)} - x \log\left(-c^{2} x^{2} + 1\right)\right)} b e \operatorname{arcoth}\left(c x\right) - {\left(c^{2} {\left(\frac{2 \, x}{c^{2}} - \frac{\log\left(c x + 1\right)}{c^{3}} + \frac{\log\left(c x - 1\right)}{c^{3}}\right)} - x \log\left(-c^{2} x^{2} + 1\right)\right)} a e + a d x + \frac{{\left(2 \, c x \operatorname{arcoth}\left(c x\right) + \log\left(-c^{2} x^{2} + 1\right)\right)} b d}{2 \, c} + \frac{{\left({\left(i \, \pi + 2 \, \log\left(c x - 1\right) - 2\right)} \log\left(c x + 1\right) + {\left(i \, \pi - 2\right)} \log\left(c x - 1\right)\right)} b e}{2 \, c}"," ",0,"-(c^2*(2*x/c^2 - log(c*x + 1)/c^3 + log(c*x - 1)/c^3) - x*log(-c^2*x^2 + 1))*b*e*arccoth(c*x) - (c^2*(2*x/c^2 - log(c*x + 1)/c^3 + log(c*x - 1)/c^3) - x*log(-c^2*x^2 + 1))*a*e + a*d*x + 1/2*(2*c*x*arccoth(c*x) + log(-c^2*x^2 + 1))*b*d/c + 1/2*((I*pi + 2*log(c*x - 1) - 2)*log(c*x + 1) + (I*pi - 2)*log(c*x - 1))*b*e/c","C",0
275,0,0,0,0.000000," ","integrate((a+b*arccoth(c*x))*(d+e*log(-c^2*x^2+1))/x^2,x, algorithm=""maxima"")","-\frac{1}{2} \, {\left(c {\left(\log\left(c^{2} x^{2} - 1\right) - \log\left(x^{2}\right)\right)} + \frac{2 \, \operatorname{arcoth}\left(c x\right)}{x}\right)} b d - {\left(c^{2} {\left(\frac{\log\left(c x + 1\right)}{c} - \frac{\log\left(c x - 1\right)}{c}\right)} + \frac{\log\left(-c^{2} x^{2} + 1\right)}{x}\right)} a e - \frac{1}{2} \, b e {\left(\frac{\log\left(c x + 1\right)^{2}}{x} - \int -\frac{{\left(c x + 1\right)} \log\left(c x - 1\right)^{2} - {\left(i \, \pi + {\left(i \, \pi c + 2 \, c\right)} x\right)} \log\left(c x + 1\right) - {\left(-i \, \pi - i \, \pi c x\right)} \log\left(c x - 1\right)}{c x^{3} + x^{2}}\,{d x}\right)} - \frac{a d}{x}"," ",0,"-1/2*(c*(log(c^2*x^2 - 1) - log(x^2)) + 2*arccoth(c*x)/x)*b*d - (c^2*(log(c*x + 1)/c - log(c*x - 1)/c) + log(-c^2*x^2 + 1)/x)*a*e - 1/2*b*e*(log(c*x + 1)^2/x - integrate(-((c*x + 1)*log(c*x - 1)^2 - (I*pi + (I*pi*c + 2*c)*x)*log(c*x + 1) - (-I*pi - I*pi*c*x)*log(c*x - 1))/(c*x^3 + x^2), x)) - a*d/x","F",0
276,0,0,0,0.000000," ","integrate((a+b*arccoth(c*x))*(d+e*log(-c^2*x^2+1))/x^4,x, algorithm=""maxima"")","-\frac{1}{6} \, {\left({\left(c^{2} \log\left(c^{2} x^{2} - 1\right) - c^{2} \log\left(x^{2}\right) + \frac{1}{x^{2}}\right)} c + \frac{2 \, \operatorname{arcoth}\left(c x\right)}{x^{3}}\right)} b d - \frac{1}{3} \, {\left({\left(c \log\left(c x + 1\right) - c \log\left(c x - 1\right) - \frac{2}{x}\right)} c^{2} + \frac{\log\left(-c^{2} x^{2} + 1\right)}{x^{3}}\right)} a e - \frac{1}{6} \, b e {\left(\frac{\log\left(c x + 1\right)^{2}}{x^{3}} - 3 \, \int -\frac{3 \, {\left(c x + 1\right)} \log\left(c x - 1\right)^{2} - {\left(3 i \, \pi + {\left(3 i \, \pi c + 2 \, c\right)} x\right)} \log\left(c x + 1\right) - {\left(-3 i \, \pi - 3 i \, \pi c x\right)} \log\left(c x - 1\right)}{3 \, {\left(c x^{5} + x^{4}\right)}}\,{d x}\right)} - \frac{a d}{3 \, x^{3}}"," ",0,"-1/6*((c^2*log(c^2*x^2 - 1) - c^2*log(x^2) + 1/x^2)*c + 2*arccoth(c*x)/x^3)*b*d - 1/3*((c*log(c*x + 1) - c*log(c*x - 1) - 2/x)*c^2 + log(-c^2*x^2 + 1)/x^3)*a*e - 1/6*b*e*(log(c*x + 1)^2/x^3 - 3*integrate(-1/3*(3*(c*x + 1)*log(c*x - 1)^2 - (3*I*pi + (3*I*pi*c + 2*c)*x)*log(c*x + 1) - (-3*I*pi - 3*I*pi*c*x)*log(c*x - 1))/(c*x^5 + x^4), x)) - 1/3*a*d/x^3","F",0
277,0,0,0,0.000000," ","integrate((a+b*arccoth(c*x))*(d+e*log(-c^2*x^2+1))/x^6,x, algorithm=""maxima"")","-\frac{1}{20} \, {\left({\left(2 \, c^{4} \log\left(c^{2} x^{2} - 1\right) - 2 \, c^{4} \log\left(x^{2}\right) + \frac{2 \, c^{2} x^{2} + 1}{x^{4}}\right)} c + \frac{4 \, \operatorname{arcoth}\left(c x\right)}{x^{5}}\right)} b d - \frac{1}{15} \, {\left({\left(3 \, c^{3} \log\left(c x + 1\right) - 3 \, c^{3} \log\left(c x - 1\right) - \frac{2 \, {\left(3 \, c^{2} x^{2} + 1\right)}}{x^{3}}\right)} c^{2} + \frac{3 \, \log\left(-c^{2} x^{2} + 1\right)}{x^{5}}\right)} a e - \frac{1}{10} \, b e {\left(\frac{\log\left(c x + 1\right)^{2}}{x^{5}} - 5 \, \int -\frac{5 \, {\left(c x + 1\right)} \log\left(c x - 1\right)^{2} - {\left(5 i \, \pi + {\left(5 i \, \pi c + 2 \, c\right)} x\right)} \log\left(c x + 1\right) - {\left(-5 i \, \pi - 5 i \, \pi c x\right)} \log\left(c x - 1\right)}{5 \, {\left(c x^{7} + x^{6}\right)}}\,{d x}\right)} - \frac{a d}{5 \, x^{5}}"," ",0,"-1/20*((2*c^4*log(c^2*x^2 - 1) - 2*c^4*log(x^2) + (2*c^2*x^2 + 1)/x^4)*c + 4*arccoth(c*x)/x^5)*b*d - 1/15*((3*c^3*log(c*x + 1) - 3*c^3*log(c*x - 1) - 2*(3*c^2*x^2 + 1)/x^3)*c^2 + 3*log(-c^2*x^2 + 1)/x^5)*a*e - 1/10*b*e*(log(c*x + 1)^2/x^5 - 5*integrate(-1/5*(5*(c*x + 1)*log(c*x - 1)^2 - (5*I*pi + (5*I*pi*c + 2*c)*x)*log(c*x + 1) - (-5*I*pi - 5*I*pi*c*x)*log(c*x - 1))/(c*x^7 + x^6), x)) - 1/5*a*d/x^5","F",0
278,0,0,0,0.000000," ","integrate(x*(a+b*arccoth(c*x))*(d+e*log(g*x^2+f)),x, algorithm=""maxima"")","\frac{1}{2} \, a d x^{2} + \frac{1}{4} \, {\left(2 \, x^{2} \operatorname{arcoth}\left(c x\right) + c {\left(\frac{2 \, x}{c^{2}} - \frac{\log\left(c x + 1\right)}{c^{3}} + \frac{\log\left(c x - 1\right)}{c^{3}}\right)}\right)} b d - \frac{1}{4} \, {\left(2 \, c^{2} g \int \frac{x^{3} \log\left(c x + 1\right)}{c^{2} g x^{2} + c^{2} f}\,{d x} - 2 \, c^{2} g \int \frac{x^{3} \log\left(c x - 1\right)}{c^{2} g x^{2} + c^{2} f}\,{d x} - 2 \, c g {\left(-\frac{i \, f {\left(\log\left(\frac{i \, g x}{\sqrt{f g}} + 1\right) - \log\left(-\frac{i \, g x}{\sqrt{f g}} + 1\right)\right)}}{\sqrt{f g} c^{2} g} - \frac{2 \, x}{c^{2} g}\right)} - 2 \, g \int \frac{x \log\left(c x + 1\right)}{c^{2} g x^{2} + c^{2} f}\,{d x} + 2 \, g \int \frac{x \log\left(c x - 1\right)}{c^{2} g x^{2} + c^{2} f}\,{d x} - \frac{{\left(2 \, c x + {\left(c^{2} x^{2} - 1\right)} \log\left(c x + 1\right) - {\left(c^{2} x^{2} - 1\right)} \log\left(c x - 1\right)\right)} \log\left(g x^{2} + f\right)}{c^{2}}\right)} b e - \frac{{\left(g x^{2} - {\left(g x^{2} + f\right)} \log\left(g x^{2} + f\right) + f\right)} a e}{2 \, g}"," ",0,"1/2*a*d*x^2 + 1/4*(2*x^2*arccoth(c*x) + c*(2*x/c^2 - log(c*x + 1)/c^3 + log(c*x - 1)/c^3))*b*d - 1/4*(2*c^2*g*integrate(x^3*log(c*x + 1)/(c^2*g*x^2 + c^2*f), x) - 2*c^2*g*integrate(x^3*log(c*x - 1)/(c^2*g*x^2 + c^2*f), x) - 2*c*g*(-I*f*(log(I*g*x/sqrt(f*g) + 1) - log(-I*g*x/sqrt(f*g) + 1))/(sqrt(f*g)*c^2*g) - 2*x/(c^2*g)) - 2*g*integrate(x*log(c*x + 1)/(c^2*g*x^2 + c^2*f), x) + 2*g*integrate(x*log(c*x - 1)/(c^2*g*x^2 + c^2*f), x) - (2*c*x + (c^2*x^2 - 1)*log(c*x + 1) - (c^2*x^2 - 1)*log(c*x - 1))*log(g*x^2 + f)/c^2)*b*e - 1/2*(g*x^2 - (g*x^2 + f)*log(g*x^2 + f) + f)*a*e/g","F",0
279,0,0,0,0.000000," ","integrate((a+b*arccoth(c*x))*(d+e*log(g*x^2+f)),x, algorithm=""maxima"")","{\left(2 \, g {\left(\frac{f \arctan\left(\frac{g x}{\sqrt{f g}}\right)}{\sqrt{f g} g} - \frac{x}{g}\right)} + x \log\left(g x^{2} + f\right)\right)} a e + a d x + \frac{1}{2} \, b e {\left(\frac{{\left({\left(c x + 1\right)} \log\left(c x + 1\right) - {\left(c x - 1\right)} \log\left(c x - 1\right)\right)} \log\left(g x^{2} + f\right)}{c} - \int \frac{2 \, {\left({\left(c g x^{2} + g x\right)} \log\left(c x + 1\right) - {\left(c g x^{2} - g x\right)} \log\left(c x - 1\right)\right)}}{c g x^{2} + c f}\,{d x}\right)} + \frac{{\left(2 \, c x \operatorname{arcoth}\left(c x\right) + \log\left(-c^{2} x^{2} + 1\right)\right)} b d}{2 \, c}"," ",0,"(2*g*(f*arctan(g*x/sqrt(f*g))/(sqrt(f*g)*g) - x/g) + x*log(g*x^2 + f))*a*e + a*d*x + 1/2*b*e*(((c*x + 1)*log(c*x + 1) - (c*x - 1)*log(c*x - 1))*log(g*x^2 + f)/c - integrate(2*((c*g*x^2 + g*x)*log(c*x + 1) - (c*g*x^2 - g*x)*log(c*x - 1))/(c*g*x^2 + c*f), x)) + 1/2*(2*c*x*arccoth(c*x) + log(-c^2*x^2 + 1))*b*d/c","F",0
280,0,0,0,0.000000," ","integrate((a+b*arccoth(c*x))*(d+e*log(g*x^2+f))/x,x, algorithm=""maxima"")","a d \log\left(x\right) + \int \frac{b e {\left(\log\left(\frac{1}{c x} + 1\right) - \log\left(-\frac{1}{c x} + 1\right)\right)} \log\left(g x^{2} + f\right)}{2 \, x} + \frac{b d {\left(\log\left(\frac{1}{c x} + 1\right) - \log\left(-\frac{1}{c x} + 1\right)\right)}}{2 \, x} + \frac{a e \log\left(g x^{2} + f\right)}{x}\,{d x}"," ",0,"a*d*log(x) + integrate(1/2*b*e*(log(1/(c*x) + 1) - log(-1/(c*x) + 1))*log(g*x^2 + f)/x + 1/2*b*d*(log(1/(c*x) + 1) - log(-1/(c*x) + 1))/x + a*e*log(g*x^2 + f)/x, x)","F",0
281,0,0,0,0.000000," ","integrate((a+b*arccoth(c*x))*(d+e*log(g*x^2+f))/x^2,x, algorithm=""maxima"")","-\frac{1}{2} \, {\left(c {\left(\log\left(c^{2} x^{2} - 1\right) - \log\left(x^{2}\right)\right)} + \frac{2 \, \operatorname{arcoth}\left(c x\right)}{x}\right)} b d + {\left(\frac{2 \, g \arctan\left(\frac{g x}{\sqrt{f g}}\right)}{\sqrt{f g}} - \frac{\log\left(g x^{2} + f\right)}{x}\right)} a e + \frac{1}{2} \, b e \int \frac{{\left(\log\left(\frac{1}{c x} + 1\right) - \log\left(-\frac{1}{c x} + 1\right)\right)} \log\left(g x^{2} + f\right)}{x^{2}}\,{d x} - \frac{a d}{x}"," ",0,"-1/2*(c*(log(c^2*x^2 - 1) - log(x^2)) + 2*arccoth(c*x)/x)*b*d + (2*g*arctan(g*x/sqrt(f*g))/sqrt(f*g) - log(g*x^2 + f)/x)*a*e + 1/2*b*e*integrate((log(1/(c*x) + 1) - log(-1/(c*x) + 1))*log(g*x^2 + f)/x^2, x) - a*d/x","F",0
282,0,0,0,0.000000," ","integrate((a+b*arccoth(c*x))*(d+e*log(g*x^2+f))/x^3,x, algorithm=""maxima"")","\frac{1}{4} \, {\left({\left(c \log\left(c x + 1\right) - c \log\left(c x - 1\right) - \frac{2}{x}\right)} c - \frac{2 \, \operatorname{arcoth}\left(c x\right)}{x^{2}}\right)} b d - \frac{1}{2} \, {\left(g {\left(\frac{\log\left(g x^{2} + f\right)}{f} - \frac{\log\left(x^{2}\right)}{f}\right)} + \frac{\log\left(g x^{2} + f\right)}{x^{2}}\right)} a e - \frac{1}{4} \, {\left(2 \, c^{2} g \int \frac{x^{2} \log\left(c x + 1\right)}{g x^{3} + f x}\,{d x} - 2 \, c^{2} g \int \frac{x^{2} \log\left(c x - 1\right)}{g x^{3} + f x}\,{d x} + \frac{2 i \, c g {\left(\log\left(\frac{i \, g x}{\sqrt{f g}} + 1\right) - \log\left(-\frac{i \, g x}{\sqrt{f g}} + 1\right)\right)}}{\sqrt{f g}} - 2 \, g \int \frac{\log\left(c x + 1\right)}{g x^{3} + f x}\,{d x} + 2 \, g \int \frac{\log\left(c x - 1\right)}{g x^{3} + f x}\,{d x} + \frac{{\left(2 \, c x - {\left(c^{2} x^{2} - 1\right)} \log\left(c x + 1\right) + {\left(c^{2} x^{2} - 1\right)} \log\left(c x - 1\right)\right)} \log\left(g x^{2} + f\right)}{x^{2}}\right)} b e - \frac{a d}{2 \, x^{2}}"," ",0,"1/4*((c*log(c*x + 1) - c*log(c*x - 1) - 2/x)*c - 2*arccoth(c*x)/x^2)*b*d - 1/2*(g*(log(g*x^2 + f)/f - log(x^2)/f) + log(g*x^2 + f)/x^2)*a*e - 1/4*(2*c^2*g*integrate(x^2*log(c*x + 1)/(g*x^3 + f*x), x) - 2*c^2*g*integrate(x^2*log(c*x - 1)/(g*x^3 + f*x), x) + 2*I*c*g*(log(I*g*x/sqrt(f*g) + 1) - log(-I*g*x/sqrt(f*g) + 1))/sqrt(f*g) - 2*g*integrate(log(c*x + 1)/(g*x^3 + f*x), x) + 2*g*integrate(log(c*x - 1)/(g*x^3 + f*x), x) + (2*c*x - (c^2*x^2 - 1)*log(c*x + 1) + (c^2*x^2 - 1)*log(c*x - 1))*log(g*x^2 + f)/x^2)*b*e - 1/2*a*d/x^2","F",0
283,1,58,0,0.317553," ","integrate(arccoth(exp(x)),x, algorithm=""maxima"")","-\frac{1}{2} \, x {\left(\log\left(e^{x} + 1\right) - \log\left(e^{x} - 1\right)\right)} + x \operatorname{arcoth}\left(e^{x}\right) + \frac{1}{2} \, \log\left(-e^{x}\right) \log\left(e^{x} + 1\right) - \frac{1}{2} \, x \log\left(e^{x} - 1\right) + \frac{1}{2} \, {\rm Li}_2\left(e^{x} + 1\right) - \frac{1}{2} \, {\rm Li}_2\left(-e^{x} + 1\right)"," ",0,"-1/2*x*(log(e^x + 1) - log(e^x - 1)) + x*arccoth(e^x) + 1/2*log(-e^x)*log(e^x + 1) - 1/2*x*log(e^x - 1) + 1/2*dilog(e^x + 1) - 1/2*dilog(-e^x + 1)","B",0
284,1,59,0,0.322308," ","integrate(x*arccoth(exp(x)),x, algorithm=""maxima"")","\frac{1}{2} \, x^{2} \operatorname{arcoth}\left(e^{x}\right) - \frac{1}{4} \, x^{2} \log\left(e^{x} + 1\right) + \frac{1}{4} \, x^{2} \log\left(-e^{x} + 1\right) - \frac{1}{2} \, x {\rm Li}_2\left(-e^{x}\right) + \frac{1}{2} \, x {\rm Li}_2\left(e^{x}\right) + \frac{1}{2} \, {\rm Li}_{3}(-e^{x}) - \frac{1}{2} \, {\rm Li}_{3}(e^{x})"," ",0,"1/2*x^2*arccoth(e^x) - 1/4*x^2*log(e^x + 1) + 1/4*x^2*log(-e^x + 1) - 1/2*x*dilog(-e^x) + 1/2*x*dilog(e^x) + 1/2*polylog(3, -e^x) - 1/2*polylog(3, e^x)","A",0
285,1,76,0,0.318710," ","integrate(x^2*arccoth(exp(x)),x, algorithm=""maxima"")","\frac{1}{3} \, x^{3} \operatorname{arcoth}\left(e^{x}\right) - \frac{1}{6} \, x^{3} \log\left(e^{x} + 1\right) + \frac{1}{6} \, x^{3} \log\left(-e^{x} + 1\right) - \frac{1}{2} \, x^{2} {\rm Li}_2\left(-e^{x}\right) + \frac{1}{2} \, x^{2} {\rm Li}_2\left(e^{x}\right) + x {\rm Li}_{3}(-e^{x}) - x {\rm Li}_{3}(e^{x}) - {\rm Li}_{4}(-e^{x}) + {\rm Li}_{4}(e^{x})"," ",0,"1/3*x^3*arccoth(e^x) - 1/6*x^3*log(e^x + 1) + 1/6*x^3*log(-e^x + 1) - 1/2*x^2*dilog(-e^x) + 1/2*x^2*dilog(e^x) + x*polylog(3, -e^x) - x*polylog(3, e^x) - polylog(4, -e^x) + polylog(4, e^x)","A",0
286,1,107,0,0.329987," ","integrate(arccoth(exp(b*x+a)),x, algorithm=""maxima"")","\frac{{\left(b x + a\right)} \operatorname{arcoth}\left(e^{\left(b x + a\right)}\right)}{b} - \frac{{\left(b x + a\right)} {\left(\log\left(e^{\left(b x + a\right)} + 1\right) - \log\left(e^{\left(b x + a\right)} - 1\right)\right)} - \log\left(-e^{\left(b x + a\right)}\right) \log\left(e^{\left(b x + a\right)} + 1\right) + {\left(b x + a\right)} \log\left(e^{\left(b x + a\right)} - 1\right) - {\rm Li}_2\left(e^{\left(b x + a\right)} + 1\right) + {\rm Li}_2\left(-e^{\left(b x + a\right)} + 1\right)}{2 \, b}"," ",0,"(b*x + a)*arccoth(e^(b*x + a))/b - 1/2*((b*x + a)*(log(e^(b*x + a) + 1) - log(e^(b*x + a) - 1)) - log(-e^(b*x + a))*log(e^(b*x + a) + 1) + (b*x + a)*log(e^(b*x + a) - 1) - dilog(e^(b*x + a) + 1) + dilog(-e^(b*x + a) + 1))/b","B",0
287,1,108,0,0.343396," ","integrate(x*arccoth(exp(b*x+a)),x, algorithm=""maxima"")","\frac{1}{2} \, x^{2} \operatorname{arcoth}\left(e^{\left(b x + a\right)}\right) - \frac{1}{4} \, b {\left(\frac{b^{2} x^{2} \log\left(e^{\left(b x + a\right)} + 1\right) + 2 \, b x {\rm Li}_2\left(-e^{\left(b x + a\right)}\right) - 2 \, {\rm Li}_{3}(-e^{\left(b x + a\right)})}{b^{3}} - \frac{b^{2} x^{2} \log\left(-e^{\left(b x + a\right)} + 1\right) + 2 \, b x {\rm Li}_2\left(e^{\left(b x + a\right)}\right) - 2 \, {\rm Li}_{3}(e^{\left(b x + a\right)})}{b^{3}}\right)}"," ",0,"1/2*x^2*arccoth(e^(b*x + a)) - 1/4*b*((b^2*x^2*log(e^(b*x + a) + 1) + 2*b*x*dilog(-e^(b*x + a)) - 2*polylog(3, -e^(b*x + a)))/b^3 - (b^2*x^2*log(-e^(b*x + a) + 1) + 2*b*x*dilog(e^(b*x + a)) - 2*polylog(3, e^(b*x + a)))/b^3)","A",0
288,1,142,0,0.345616," ","integrate(x^2*arccoth(exp(b*x+a)),x, algorithm=""maxima"")","\frac{1}{3} \, x^{3} \operatorname{arcoth}\left(e^{\left(b x + a\right)}\right) - \frac{1}{6} \, b {\left(\frac{b^{3} x^{3} \log\left(e^{\left(b x + a\right)} + 1\right) + 3 \, b^{2} x^{2} {\rm Li}_2\left(-e^{\left(b x + a\right)}\right) - 6 \, b x {\rm Li}_{3}(-e^{\left(b x + a\right)}) + 6 \, {\rm Li}_{4}(-e^{\left(b x + a\right)})}{b^{4}} - \frac{b^{3} x^{3} \log\left(-e^{\left(b x + a\right)} + 1\right) + 3 \, b^{2} x^{2} {\rm Li}_2\left(e^{\left(b x + a\right)}\right) - 6 \, b x {\rm Li}_{3}(e^{\left(b x + a\right)}) + 6 \, {\rm Li}_{4}(e^{\left(b x + a\right)})}{b^{4}}\right)}"," ",0,"1/3*x^3*arccoth(e^(b*x + a)) - 1/6*b*((b^3*x^3*log(e^(b*x + a) + 1) + 3*b^2*x^2*dilog(-e^(b*x + a)) - 6*b*x*polylog(3, -e^(b*x + a)) + 6*polylog(4, -e^(b*x + a)))/b^4 - (b^3*x^3*log(-e^(b*x + a) + 1) + 3*b^2*x^2*dilog(e^(b*x + a)) - 6*b*x*polylog(3, e^(b*x + a)) + 6*polylog(4, e^(b*x + a)))/b^4)","A",0
289,1,202,0,0.332575," ","integrate(arccoth(a+b*f^(d*x+c)),x, algorithm=""maxima"")","\frac{{\left(d x + c\right)} \operatorname{arcoth}\left(b f^{d x + c} + a\right)}{d} - \frac{{\left(d x + c\right)} b {\left(\frac{\log\left(b f^{d x + c} + a + 1\right)}{b} - \frac{\log\left(b f^{d x + c} + a - 1\right)}{b}\right)} \log\left(f\right) - b {\left(\frac{\log\left(b f^{d x + c} + a + 1\right) \log\left(-\frac{b f^{d x + c} + a + 1}{a + 1} + 1\right) + {\rm Li}_2\left(\frac{b f^{d x + c} + a + 1}{a + 1}\right)}{b} - \frac{\log\left(b f^{d x + c} + a - 1\right) \log\left(-\frac{b f^{d x + c} + a - 1}{a - 1} + 1\right) + {\rm Li}_2\left(\frac{b f^{d x + c} + a - 1}{a - 1}\right)}{b}\right)}}{2 \, d \log\left(f\right)}"," ",0,"(d*x + c)*arccoth(b*f^(d*x + c) + a)/d - 1/2*((d*x + c)*b*(log(b*f^(d*x + c) + a + 1)/b - log(b*f^(d*x + c) + a - 1)/b)*log(f) - b*((log(b*f^(d*x + c) + a + 1)*log(-(b*f^(d*x + c) + a + 1)/(a + 1) + 1) + dilog((b*f^(d*x + c) + a + 1)/(a + 1)))/b - (log(b*f^(d*x + c) + a - 1)*log(-(b*f^(d*x + c) + a - 1)/(a - 1) + 1) + dilog((b*f^(d*x + c) + a - 1)/(a - 1)))/b))/(d*log(f))","A",0
290,1,194,0,0.376289," ","integrate(x*arccoth(a+b*f^(d*x+c)),x, algorithm=""maxima"")","-\frac{1}{4} \, b d {\left(\frac{d^{2} x^{2} \log\left(\frac{b f^{d x} f^{c}}{a + 1} + 1\right) \log\left(f\right)^{2} + 2 \, d x {\rm Li}_2\left(-\frac{b f^{d x} f^{c}}{a + 1}\right) \log\left(f\right) - 2 \, {\rm Li}_{3}(-\frac{b f^{d x} f^{c}}{a + 1})}{b d^{3} \log\left(f\right)^{3}} - \frac{d^{2} x^{2} \log\left(\frac{b f^{d x} f^{c}}{a - 1} + 1\right) \log\left(f\right)^{2} + 2 \, d x {\rm Li}_2\left(-\frac{b f^{d x} f^{c}}{a - 1}\right) \log\left(f\right) - 2 \, {\rm Li}_{3}(-\frac{b f^{d x} f^{c}}{a - 1})}{b d^{3} \log\left(f\right)^{3}}\right)} \log\left(f\right) + \frac{1}{2} \, x^{2} \operatorname{arcoth}\left(b f^{d x + c} + a\right)"," ",0,"-1/4*b*d*((d^2*x^2*log(b*f^(d*x)*f^c/(a + 1) + 1)*log(f)^2 + 2*d*x*dilog(-b*f^(d*x)*f^c/(a + 1))*log(f) - 2*polylog(3, -b*f^(d*x)*f^c/(a + 1)))/(b*d^3*log(f)^3) - (d^2*x^2*log(b*f^(d*x)*f^c/(a - 1) + 1)*log(f)^2 + 2*d*x*dilog(-b*f^(d*x)*f^c/(a - 1))*log(f) - 2*polylog(3, -b*f^(d*x)*f^c/(a - 1)))/(b*d^3*log(f)^3))*log(f) + 1/2*x^2*arccoth(b*f^(d*x + c) + a)","A",0
291,1,254,0,0.374527," ","integrate(x^2*arccoth(a+b*f^(d*x+c)),x, algorithm=""maxima"")","\frac{1}{3} \, x^{3} \operatorname{arcoth}\left(b f^{d x + c} + a\right) - \frac{1}{6} \, b d {\left(\frac{d^{3} x^{3} \log\left(\frac{b f^{d x} f^{c}}{a + 1} + 1\right) \log\left(f\right)^{3} + 3 \, d^{2} x^{2} {\rm Li}_2\left(-\frac{b f^{d x} f^{c}}{a + 1}\right) \log\left(f\right)^{2} - 6 \, d x \log\left(f\right) {\rm Li}_{3}(-\frac{b f^{d x} f^{c}}{a + 1}) + 6 \, {\rm Li}_{4}(-\frac{b f^{d x} f^{c}}{a + 1})}{b d^{4} \log\left(f\right)^{4}} - \frac{d^{3} x^{3} \log\left(\frac{b f^{d x} f^{c}}{a - 1} + 1\right) \log\left(f\right)^{3} + 3 \, d^{2} x^{2} {\rm Li}_2\left(-\frac{b f^{d x} f^{c}}{a - 1}\right) \log\left(f\right)^{2} - 6 \, d x \log\left(f\right) {\rm Li}_{3}(-\frac{b f^{d x} f^{c}}{a - 1}) + 6 \, {\rm Li}_{4}(-\frac{b f^{d x} f^{c}}{a - 1})}{b d^{4} \log\left(f\right)^{4}}\right)} \log\left(f\right)"," ",0,"1/3*x^3*arccoth(b*f^(d*x + c) + a) - 1/6*b*d*((d^3*x^3*log(b*f^(d*x)*f^c/(a + 1) + 1)*log(f)^3 + 3*d^2*x^2*dilog(-b*f^(d*x)*f^c/(a + 1))*log(f)^2 - 6*d*x*log(f)*polylog(3, -b*f^(d*x)*f^c/(a + 1)) + 6*polylog(4, -b*f^(d*x)*f^c/(a + 1)))/(b*d^4*log(f)^4) - (d^3*x^3*log(b*f^(d*x)*f^c/(a - 1) + 1)*log(f)^3 + 3*d^2*x^2*dilog(-b*f^(d*x)*f^c/(a - 1))*log(f)^2 - 6*d*x*log(f)*polylog(3, -b*f^(d*x)*f^c/(a - 1)) + 6*polylog(4, -b*f^(d*x)*f^c/(a - 1)))/(b*d^4*log(f)^4))*log(f)","A",0
292,1,21,0,0.331207," ","integrate(1/(-a*x^2+a)/(b-2*b*arccoth(x)),x, algorithm=""maxima"")","-\frac{\log\left(\log\left(x + 1\right) - \log\left(x - 1\right) - 1\right)}{2 \, a b}"," ",0,"-1/2*log(log(x + 1) - log(x - 1) - 1)/(a*b)","A",0
293,1,37,0,0.324911," ","integrate(x^3*arccoth(b*x^4+a),x, algorithm=""maxima"")","\frac{2 \, {\left(b x^{4} + a\right)} \operatorname{arcoth}\left(b x^{4} + a\right) + \log\left(-{\left(b x^{4} + a\right)}^{2} + 1\right)}{8 \, b}"," ",0,"1/8*(2*(b*x^4 + a)*arccoth(b*x^4 + a) + log(-(b*x^4 + a)^2 + 1))/b","A",0
294,1,40,0,0.304313," ","integrate(x^(-1+n)*arccoth(a+b*x^n),x, algorithm=""maxima"")","\frac{2 \, {\left(b x^{n} + a\right)} \operatorname{arcoth}\left(b x^{n} + a\right) + \log\left(-{\left(b x^{n} + a\right)}^{2} + 1\right)}{2 \, b n}"," ",0,"1/2*(2*(b*x^n + a)*arccoth(b*x^n + a) + log(-(b*x^n + a)^2 + 1))/(b*n)","A",0
295,1,184,0,0.414521," ","integrate(exp(c*(b*x+a))*arccoth(sinh(b*c*x+a*c)),x, algorithm=""maxima"")","\frac{\operatorname{arcoth}\left(\sinh\left(b c x + a c\right)\right) e^{\left({\left(b x + a\right)} c\right)}}{b c} + \frac{\sqrt{2} \log\left(-\frac{\sqrt{2} - e^{\left(b c x + a c\right)} + 1}{\sqrt{2} + e^{\left(b c x + a c\right)} - 1}\right)}{2 \, b c} - \frac{\sqrt{2} \log\left(-\frac{\sqrt{2} - e^{\left(b c x + a c\right)} - 1}{\sqrt{2} + e^{\left(b c x + a c\right)} + 1}\right)}{2 \, b c} + \frac{\log\left(e^{\left(2 \, b c x + 2 \, a c\right)} + 2 \, e^{\left(b c x + a c\right)} - 1\right)}{2 \, b c} + \frac{\log\left(e^{\left(2 \, b c x + 2 \, a c\right)} - 2 \, e^{\left(b c x + a c\right)} - 1\right)}{2 \, b c}"," ",0,"arccoth(sinh(b*c*x + a*c))*e^((b*x + a)*c)/(b*c) + 1/2*sqrt(2)*log(-(sqrt(2) - e^(b*c*x + a*c) + 1)/(sqrt(2) + e^(b*c*x + a*c) - 1))/(b*c) - 1/2*sqrt(2)*log(-(sqrt(2) - e^(b*c*x + a*c) - 1)/(sqrt(2) + e^(b*c*x + a*c) + 1))/(b*c) + 1/2*log(e^(2*b*c*x + 2*a*c) + 2*e^(b*c*x + a*c) - 1)/(b*c) + 1/2*log(e^(2*b*c*x + 2*a*c) - 2*e^(b*c*x + a*c) - 1)/(b*c)","B",0
296,1,64,0,0.325987," ","integrate(exp(c*(b*x+a))*arccoth(cosh(b*c*x+a*c)),x, algorithm=""maxima"")","\frac{\operatorname{arcoth}\left(\cosh\left(b c x + a c\right)\right) e^{\left({\left(b x + a\right)} c\right)}}{b c} + \frac{\log\left(e^{\left(b c x + a c\right)} + 1\right)}{b c} + \frac{\log\left(e^{\left(b c x + a c\right)} - 1\right)}{b c}"," ",0,"arccoth(cosh(b*c*x + a*c))*e^((b*x + a)*c)/(b*c) + log(e^(b*c*x + a*c) + 1)/(b*c) + log(e^(b*c*x + a*c) - 1)/(b*c)","A",0
297,1,43,0,0.334947," ","integrate(exp(c*(b*x+a))*arccoth(tanh(b*c*x+a*c)),x, algorithm=""maxima"")","\frac{\operatorname{arcoth}\left(\tanh\left(b c x + a c\right)\right) e^{\left({\left(b x + a\right)} c\right)}}{b c} - \frac{e^{\left(b c x + a c\right)}}{b c}"," ",0,"arccoth(tanh(b*c*x + a*c))*e^((b*x + a)*c)/(b*c) - e^(b*c*x + a*c)/(b*c)","A",0
298,1,42,0,0.314513," ","integrate(exp(c*(b*x+a))*arccoth(coth(b*c*x+a*c)),x, algorithm=""maxima"")","\frac{a e^{\left(b c x + a c\right)}}{b} + \frac{{\left(b c x e^{\left(a c\right)} - e^{\left(a c\right)}\right)} e^{\left(b c x\right)}}{b c}"," ",0,"a*e^(b*c*x + a*c)/b + (b*c*x*e^(a*c) - e^(a*c))*e^(b*c*x)/(b*c)","A",0
299,1,64,0,0.333832," ","integrate(exp(c*(b*x+a))*arccoth(sech(b*c*x+a*c)),x, algorithm=""maxima"")","\frac{\operatorname{arcoth}\left(\operatorname{sech}\left(b c x + a c\right)\right) e^{\left({\left(b x + a\right)} c\right)}}{b c} + \frac{\log\left(e^{\left(b c x + a c\right)} + 1\right)}{b c} + \frac{\log\left(e^{\left(b c x + a c\right)} - 1\right)}{b c}"," ",0,"arccoth(sech(b*c*x + a*c))*e^((b*x + a)*c)/(b*c) + log(e^(b*c*x + a*c) + 1)/(b*c) + log(e^(b*c*x + a*c) - 1)/(b*c)","A",0
300,1,184,0,0.420532," ","integrate(exp(c*(b*x+a))*arccoth(csch(b*c*x+a*c)),x, algorithm=""maxima"")","\frac{\operatorname{arcoth}\left(\operatorname{csch}\left(b c x + a c\right)\right) e^{\left({\left(b x + a\right)} c\right)}}{b c} + \frac{\sqrt{2} \log\left(-\frac{\sqrt{2} - e^{\left(b c x + a c\right)} + 1}{\sqrt{2} + e^{\left(b c x + a c\right)} - 1}\right)}{2 \, b c} - \frac{\sqrt{2} \log\left(-\frac{\sqrt{2} - e^{\left(b c x + a c\right)} - 1}{\sqrt{2} + e^{\left(b c x + a c\right)} + 1}\right)}{2 \, b c} + \frac{\log\left(e^{\left(2 \, b c x + 2 \, a c\right)} + 2 \, e^{\left(b c x + a c\right)} - 1\right)}{2 \, b c} + \frac{\log\left(e^{\left(2 \, b c x + 2 \, a c\right)} - 2 \, e^{\left(b c x + a c\right)} - 1\right)}{2 \, b c}"," ",0,"arccoth(csch(b*c*x + a*c))*e^((b*x + a)*c)/(b*c) + 1/2*sqrt(2)*log(-(sqrt(2) - e^(b*c*x + a*c) + 1)/(sqrt(2) + e^(b*c*x + a*c) - 1))/(b*c) - 1/2*sqrt(2)*log(-(sqrt(2) - e^(b*c*x + a*c) - 1)/(sqrt(2) + e^(b*c*x + a*c) + 1))/(b*c) + 1/2*log(e^(2*b*c*x + 2*a*c) + 2*e^(b*c*x + a*c) - 1)/(b*c) + 1/2*log(e^(2*b*c*x + 2*a*c) - 2*e^(b*c*x + a*c) - 1)/(b*c)","B",0
