1,1,51,0,0.702642," ","integrate(x^5*arccoth(a*x),x, algorithm=""fricas"")","\frac{6 \, a^{5} x^{5} + 10 \, a^{3} x^{3} + 30 \, a x + 15 \, {\left(a^{6} x^{6} - 1\right)} \log\left(\frac{a x + 1}{a x - 1}\right)}{180 \, a^{6}}"," ",0,"1/180*(6*a^5*x^5 + 10*a^3*x^3 + 30*a*x + 15*(a^6*x^6 - 1)*log((a*x + 1)/(a*x - 1)))/a^6","A",0
2,1,55,0,0.583538," ","integrate(x^4*arccoth(a*x),x, algorithm=""fricas"")","\frac{2 \, a^{5} x^{5} \log\left(\frac{a x + 1}{a x - 1}\right) + a^{4} x^{4} + 2 \, a^{2} x^{2} + 2 \, \log\left(a^{2} x^{2} - 1\right)}{20 \, a^{5}}"," ",0,"1/20*(2*a^5*x^5*log((a*x + 1)/(a*x - 1)) + a^4*x^4 + 2*a^2*x^2 + 2*log(a^2*x^2 - 1))/a^5","A",0
3,1,43,0,0.421831," ","integrate(x^3*arccoth(a*x),x, algorithm=""fricas"")","\frac{2 \, a^{3} x^{3} + 6 \, a x + 3 \, {\left(a^{4} x^{4} - 1\right)} \log\left(\frac{a x + 1}{a x - 1}\right)}{24 \, a^{4}}"," ",0,"1/24*(2*a^3*x^3 + 6*a*x + 3*(a^4*x^4 - 1)*log((a*x + 1)/(a*x - 1)))/a^4","A",0
4,1,44,0,0.519159," ","integrate(x^2*arccoth(a*x),x, algorithm=""fricas"")","\frac{a^{3} x^{3} \log\left(\frac{a x + 1}{a x - 1}\right) + a^{2} x^{2} + \log\left(a^{2} x^{2} - 1\right)}{6 \, a^{3}}"," ",0,"1/6*(a^3*x^3*log((a*x + 1)/(a*x - 1)) + a^2*x^2 + log(a^2*x^2 - 1))/a^3","A",0
5,1,34,0,0.580730," ","integrate(x*arccoth(a*x),x, algorithm=""fricas"")","\frac{2 \, a x + {\left(a^{2} x^{2} - 1\right)} \log\left(\frac{a x + 1}{a x - 1}\right)}{4 \, a^{2}}"," ",0,"1/4*(2*a*x + (a^2*x^2 - 1)*log((a*x + 1)/(a*x - 1)))/a^2","A",0
6,1,33,0,0.610596," ","integrate(arccoth(a*x),x, algorithm=""fricas"")","\frac{a x \log\left(\frac{a x + 1}{a x - 1}\right) + \log\left(a^{2} x^{2} - 1\right)}{2 \, a}"," ",0,"1/2*(a*x*log((a*x + 1)/(a*x - 1)) + log(a^2*x^2 - 1))/a","A",0
7,0,0,0,0.444273," ","integrate(arccoth(a*x)/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{arcoth}\left(a x\right)}{x}, x\right)"," ",0,"integral(arccoth(a*x)/x, x)","F",0
8,1,39,0,0.449251," ","integrate(arccoth(a*x)/x^2,x, algorithm=""fricas"")","-\frac{a x \log\left(a^{2} x^{2} - 1\right) - 2 \, a x \log\left(x\right) + \log\left(\frac{a x + 1}{a x - 1}\right)}{2 \, x}"," ",0,"-1/2*(a*x*log(a^2*x^2 - 1) - 2*a*x*log(x) + log((a*x + 1)/(a*x - 1)))/x","A",0
9,1,35,0,0.524786," ","integrate(arccoth(a*x)/x^3,x, algorithm=""fricas"")","-\frac{2 \, a x - {\left(a^{2} x^{2} - 1\right)} \log\left(\frac{a x + 1}{a x - 1}\right)}{4 \, x^{2}}"," ",0,"-1/4*(2*a*x - (a^2*x^2 - 1)*log((a*x + 1)/(a*x - 1)))/x^2","A",0
10,1,50,0,1.044062," ","integrate(arccoth(a*x)/x^4,x, algorithm=""fricas"")","-\frac{a^{3} x^{3} \log\left(a^{2} x^{2} - 1\right) - 2 \, a^{3} x^{3} \log\left(x\right) + a x + \log\left(\frac{a x + 1}{a x - 1}\right)}{6 \, x^{3}}"," ",0,"-1/6*(a^3*x^3*log(a^2*x^2 - 1) - 2*a^3*x^3*log(x) + a*x + log((a*x + 1)/(a*x - 1)))/x^3","A",0
11,1,43,0,0.515293," ","integrate(arccoth(a*x)/x^5,x, algorithm=""fricas"")","-\frac{6 \, a^{3} x^{3} + 2 \, a x - 3 \, {\left(a^{4} x^{4} - 1\right)} \log\left(\frac{a x + 1}{a x - 1}\right)}{24 \, x^{4}}"," ",0,"-1/24*(6*a^3*x^3 + 2*a*x - 3*(a^4*x^4 - 1)*log((a*x + 1)/(a*x - 1)))/x^4","A",0
12,1,98,0,0.531131," ","integrate(x^5*arccoth(a*x)^2,x, algorithm=""fricas"")","\frac{6 \, a^{4} x^{4} + 32 \, a^{2} x^{2} + 15 \, {\left(a^{6} x^{6} - 1\right)} \log\left(\frac{a x + 1}{a x - 1}\right)^{2} + 4 \, {\left(3 \, a^{5} x^{5} + 5 \, a^{3} x^{3} + 15 \, a x\right)} \log\left(\frac{a x + 1}{a x - 1}\right) + 92 \, \log\left(a^{2} x^{2} - 1\right)}{360 \, a^{6}}"," ",0,"1/360*(6*a^4*x^4 + 32*a^2*x^2 + 15*(a^6*x^6 - 1)*log((a*x + 1)/(a*x - 1))^2 + 4*(3*a^5*x^5 + 5*a^3*x^3 + 15*a*x)*log((a*x + 1)/(a*x - 1)) + 92*log(a^2*x^2 - 1))/a^6","A",0
13,0,0,0,0.741235," ","integrate(x^4*arccoth(a*x)^2,x, algorithm=""fricas"")","{\rm integral}\left(x^{4} \operatorname{arcoth}\left(a x\right)^{2}, x\right)"," ",0,"integral(x^4*arccoth(a*x)^2, x)","F",0
14,1,81,0,0.531738," ","integrate(x^3*arccoth(a*x)^2,x, algorithm=""fricas"")","\frac{4 \, a^{2} x^{2} + 3 \, {\left(a^{4} x^{4} - 1\right)} \log\left(\frac{a x + 1}{a x - 1}\right)^{2} + 4 \, {\left(a^{3} x^{3} + 3 \, a x\right)} \log\left(\frac{a x + 1}{a x - 1}\right) + 16 \, \log\left(a^{2} x^{2} - 1\right)}{48 \, a^{4}}"," ",0,"1/48*(4*a^2*x^2 + 3*(a^4*x^4 - 1)*log((a*x + 1)/(a*x - 1))^2 + 4*(a^3*x^3 + 3*a*x)*log((a*x + 1)/(a*x - 1)) + 16*log(a^2*x^2 - 1))/a^4","A",0
15,0,0,0,0.429171," ","integrate(x^2*arccoth(a*x)^2,x, algorithm=""fricas"")","{\rm integral}\left(x^{2} \operatorname{arcoth}\left(a x\right)^{2}, x\right)"," ",0,"integral(x^2*arccoth(a*x)^2, x)","F",0
16,1,62,0,0.531311," ","integrate(x*arccoth(a*x)^2,x, algorithm=""fricas"")","\frac{4 \, a x \log\left(\frac{a x + 1}{a x - 1}\right) + {\left(a^{2} x^{2} - 1\right)} \log\left(\frac{a x + 1}{a x - 1}\right)^{2} + 4 \, \log\left(a^{2} x^{2} - 1\right)}{8 \, a^{2}}"," ",0,"1/8*(4*a*x*log((a*x + 1)/(a*x - 1)) + (a^2*x^2 - 1)*log((a*x + 1)/(a*x - 1))^2 + 4*log(a^2*x^2 - 1))/a^2","A",0
17,0,0,0,0.425805," ","integrate(arccoth(a*x)^2,x, algorithm=""fricas"")","{\rm integral}\left(\operatorname{arcoth}\left(a x\right)^{2}, x\right)"," ",0,"integral(arccoth(a*x)^2, x)","F",0
18,0,0,0,0.379774," ","integrate(arccoth(a*x)^2/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{arcoth}\left(a x\right)^{2}}{x}, x\right)"," ",0,"integral(arccoth(a*x)^2/x, x)","F",0
19,0,0,0,0.518351," ","integrate(arccoth(a*x)^2/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{arcoth}\left(a x\right)^{2}}{x^{2}}, x\right)"," ",0,"integral(arccoth(a*x)^2/x^2, x)","F",0
20,1,79,0,0.547881," ","integrate(arccoth(a*x)^2/x^3,x, algorithm=""fricas"")","-\frac{4 \, a^{2} x^{2} \log\left(a^{2} x^{2} - 1\right) - 8 \, a^{2} x^{2} \log\left(x\right) + 4 \, a x \log\left(\frac{a x + 1}{a x - 1}\right) - {\left(a^{2} x^{2} - 1\right)} \log\left(\frac{a x + 1}{a x - 1}\right)^{2}}{8 \, x^{2}}"," ",0,"-1/8*(4*a^2*x^2*log(a^2*x^2 - 1) - 8*a^2*x^2*log(x) + 4*a*x*log((a*x + 1)/(a*x - 1)) - (a^2*x^2 - 1)*log((a*x + 1)/(a*x - 1))^2)/x^2","A",0
21,0,0,0,0.456961," ","integrate(arccoth(a*x)^2/x^4,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{arcoth}\left(a x\right)^{2}}{x^{4}}, x\right)"," ",0,"integral(arccoth(a*x)^2/x^4, x)","F",0
22,1,97,0,0.657402," ","integrate(arccoth(a*x)^2/x^5,x, algorithm=""fricas"")","-\frac{16 \, a^{4} x^{4} \log\left(a^{2} x^{2} - 1\right) - 32 \, a^{4} x^{4} \log\left(x\right) + 4 \, a^{2} x^{2} - 3 \, {\left(a^{4} x^{4} - 1\right)} \log\left(\frac{a x + 1}{a x - 1}\right)^{2} + 4 \, {\left(3 \, a^{3} x^{3} + a x\right)} \log\left(\frac{a x + 1}{a x - 1}\right)}{48 \, x^{4}}"," ",0,"-1/48*(16*a^4*x^4*log(a^2*x^2 - 1) - 32*a^4*x^4*log(x) + 4*a^2*x^2 - 3*(a^4*x^4 - 1)*log((a*x + 1)/(a*x - 1))^2 + 4*(3*a^3*x^3 + a*x)*log((a*x + 1)/(a*x - 1)))/x^4","A",0
23,0,0,0,1.266284," ","integrate(x^5*arccoth(a*x)^3,x, algorithm=""fricas"")","{\rm integral}\left(x^{5} \operatorname{arcoth}\left(a x\right)^{3}, x\right)"," ",0,"integral(x^5*arccoth(a*x)^3, x)","F",0
24,0,0,0,1.954216," ","integrate(x^4*arccoth(a*x)^3,x, algorithm=""fricas"")","{\rm integral}\left(x^{4} \operatorname{arcoth}\left(a x\right)^{3}, x\right)"," ",0,"integral(x^4*arccoth(a*x)^3, x)","F",0
25,0,0,0,0.481450," ","integrate(x^3*arccoth(a*x)^3,x, algorithm=""fricas"")","{\rm integral}\left(x^{3} \operatorname{arcoth}\left(a x\right)^{3}, x\right)"," ",0,"integral(x^3*arccoth(a*x)^3, x)","F",0
26,0,0,0,0.677006," ","integrate(x^2*arccoth(a*x)^3,x, algorithm=""fricas"")","{\rm integral}\left(x^{2} \operatorname{arcoth}\left(a x\right)^{3}, x\right)"," ",0,"integral(x^2*arccoth(a*x)^3, x)","F",0
27,0,0,0,0.548434," ","integrate(x*arccoth(a*x)^3,x, algorithm=""fricas"")","{\rm integral}\left(x \operatorname{arcoth}\left(a x\right)^{3}, x\right)"," ",0,"integral(x*arccoth(a*x)^3, x)","F",0
28,0,0,0,0.385721," ","integrate(arccoth(a*x)^3,x, algorithm=""fricas"")","{\rm integral}\left(\operatorname{arcoth}\left(a x\right)^{3}, x\right)"," ",0,"integral(arccoth(a*x)^3, x)","F",0
29,0,0,0,0.474452," ","integrate(arccoth(a*x)^3/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{arcoth}\left(a x\right)^{3}}{x}, x\right)"," ",0,"integral(arccoth(a*x)^3/x, x)","F",0
30,0,0,0,0.809628," ","integrate(arccoth(a*x)^3/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{arcoth}\left(a x\right)^{3}}{x^{2}}, x\right)"," ",0,"integral(arccoth(a*x)^3/x^2, x)","F",0
31,0,0,0,0.556598," ","integrate(arccoth(a*x)^3/x^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{arcoth}\left(a x\right)^{3}}{x^{3}}, x\right)"," ",0,"integral(arccoth(a*x)^3/x^3, x)","F",0
32,0,0,0,0.635966," ","integrate(arccoth(a*x)^3/x^4,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{arcoth}\left(a x\right)^{3}}{x^{4}}, x\right)"," ",0,"integral(arccoth(a*x)^3/x^4, x)","F",0
33,0,0,0,0.509815," ","integrate(arccoth(a*x)^3/x^5,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{arcoth}\left(a x\right)^{3}}{x^{5}}, x\right)"," ",0,"integral(arccoth(a*x)^3/x^5, x)","F",0
34,0,0,0,0.545890," ","integrate(arccoth(c*x)^2/(e*x+d),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{arcoth}\left(c x\right)^{2}}{e x + d}, x\right)"," ",0,"integral(arccoth(c*x)^2/(e*x + d), x)","F",0
35,1,247,0,0.563030," ","integrate((d*x^2+c)^4*arccoth(a*x),x, algorithm=""fricas"")","\frac{105 \, a^{8} d^{4} x^{8} + 20 \, {\left(36 \, a^{8} c d^{3} + 7 \, a^{6} d^{4}\right)} x^{6} + 6 \, {\left(378 \, a^{8} c^{2} d^{2} + 180 \, a^{6} c d^{3} + 35 \, a^{4} d^{4}\right)} x^{4} + 12 \, {\left(420 \, a^{8} c^{3} d + 378 \, a^{6} c^{2} d^{2} + 180 \, a^{4} c d^{3} + 35 \, a^{2} d^{4}\right)} x^{2} + 12 \, {\left(315 \, a^{8} c^{4} + 420 \, a^{6} c^{3} d + 378 \, a^{4} c^{2} d^{2} + 180 \, a^{2} c d^{3} + 35 \, d^{4}\right)} \log\left(a^{2} x^{2} - 1\right) + 12 \, {\left(35 \, a^{9} d^{4} x^{9} + 180 \, a^{9} c d^{3} x^{7} + 378 \, a^{9} c^{2} d^{2} x^{5} + 420 \, a^{9} c^{3} d x^{3} + 315 \, a^{9} c^{4} x\right)} \log\left(\frac{a x + 1}{a x - 1}\right)}{7560 \, a^{9}}"," ",0,"1/7560*(105*a^8*d^4*x^8 + 20*(36*a^8*c*d^3 + 7*a^6*d^4)*x^6 + 6*(378*a^8*c^2*d^2 + 180*a^6*c*d^3 + 35*a^4*d^4)*x^4 + 12*(420*a^8*c^3*d + 378*a^6*c^2*d^2 + 180*a^4*c*d^3 + 35*a^2*d^4)*x^2 + 12*(315*a^8*c^4 + 420*a^6*c^3*d + 378*a^4*c^2*d^2 + 180*a^2*c*d^3 + 35*d^4)*log(a^2*x^2 - 1) + 12*(35*a^9*d^4*x^9 + 180*a^9*c*d^3*x^7 + 378*a^9*c^2*d^2*x^5 + 420*a^9*c^3*d*x^3 + 315*a^9*c^4*x)*log((a*x + 1)/(a*x - 1)))/a^9","A",0
36,1,177,0,0.599437," ","integrate((d*x^2+c)^3*arccoth(a*x),x, algorithm=""fricas"")","\frac{10 \, a^{6} d^{3} x^{6} + 3 \, {\left(21 \, a^{6} c d^{2} + 5 \, a^{4} d^{3}\right)} x^{4} + 6 \, {\left(35 \, a^{6} c^{2} d + 21 \, a^{4} c d^{2} + 5 \, a^{2} d^{3}\right)} x^{2} + 6 \, {\left(35 \, a^{6} c^{3} + 35 \, a^{4} c^{2} d + 21 \, a^{2} c d^{2} + 5 \, d^{3}\right)} \log\left(a^{2} x^{2} - 1\right) + 6 \, {\left(5 \, a^{7} d^{3} x^{7} + 21 \, a^{7} c d^{2} x^{5} + 35 \, a^{7} c^{2} d x^{3} + 35 \, a^{7} c^{3} x\right)} \log\left(\frac{a x + 1}{a x - 1}\right)}{420 \, a^{7}}"," ",0,"1/420*(10*a^6*d^3*x^6 + 3*(21*a^6*c*d^2 + 5*a^4*d^3)*x^4 + 6*(35*a^6*c^2*d + 21*a^4*c*d^2 + 5*a^2*d^3)*x^2 + 6*(35*a^6*c^3 + 35*a^4*c^2*d + 21*a^2*c*d^2 + 5*d^3)*log(a^2*x^2 - 1) + 6*(5*a^7*d^3*x^7 + 21*a^7*c*d^2*x^5 + 35*a^7*c^2*d*x^3 + 35*a^7*c^3*x)*log((a*x + 1)/(a*x - 1)))/a^7","A",0
37,1,118,0,0.455172," ","integrate((d*x^2+c)^2*arccoth(a*x),x, algorithm=""fricas"")","\frac{3 \, a^{4} d^{2} x^{4} + 2 \, {\left(10 \, a^{4} c d + 3 \, a^{2} d^{2}\right)} x^{2} + 2 \, {\left(15 \, a^{4} c^{2} + 10 \, a^{2} c d + 3 \, d^{2}\right)} \log\left(a^{2} x^{2} - 1\right) + 2 \, {\left(3 \, a^{5} d^{2} x^{5} + 10 \, a^{5} c d x^{3} + 15 \, a^{5} c^{2} x\right)} \log\left(\frac{a x + 1}{a x - 1}\right)}{60 \, a^{5}}"," ",0,"1/60*(3*a^4*d^2*x^4 + 2*(10*a^4*c*d + 3*a^2*d^2)*x^2 + 2*(15*a^4*c^2 + 10*a^2*c*d + 3*d^2)*log(a^2*x^2 - 1) + 2*(3*a^5*d^2*x^5 + 10*a^5*c*d*x^3 + 15*a^5*c^2*x)*log((a*x + 1)/(a*x - 1)))/a^5","A",0
38,1,64,0,0.494483," ","integrate((d*x^2+c)*arccoth(a*x),x, algorithm=""fricas"")","\frac{a^{2} d x^{2} + {\left(3 \, a^{2} c + d\right)} \log\left(a^{2} x^{2} - 1\right) + {\left(a^{3} d x^{3} + 3 \, a^{3} c x\right)} \log\left(\frac{a x + 1}{a x - 1}\right)}{6 \, a^{3}}"," ",0,"1/6*(a^2*d*x^2 + (3*a^2*c + d)*log(a^2*x^2 - 1) + (a^3*d*x^3 + 3*a^3*c*x)*log((a*x + 1)/(a*x - 1)))/a^3","A",0
39,0,0,0,0.521124," ","integrate(arccoth(a*x)/(d*x^2+c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{arcoth}\left(a x\right)}{d x^{2} + c}, x\right)"," ",0,"integral(arccoth(a*x)/(d*x^2 + c), x)","F",0
40,0,0,0,0.598067," ","integrate(arccoth(a*x)/(d*x^2+c)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{arcoth}\left(a x\right)}{d^{2} x^{4} + 2 \, c d x^{2} + c^{2}}, x\right)"," ",0,"integral(arccoth(a*x)/(d^2*x^4 + 2*c*d*x^2 + c^2), x)","F",0
41,0,0,0,0.799767," ","integrate(arccoth(a*x)/(d*x^2+c)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{arcoth}\left(a x\right)}{d^{3} x^{6} + 3 \, c d^{2} x^{4} + 3 \, c^{2} d x^{2} + c^{3}}, x\right)"," ",0,"integral(arccoth(a*x)/(d^3*x^6 + 3*c*d^2*x^4 + 3*c^2*d*x^2 + c^3), x)","F",0
42,0,0,0,0.502587," ","integrate((d*x^2+c)^(1/2)*arccoth(a*x),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{d x^{2} + c} \operatorname{arcoth}\left(a x\right), x\right)"," ",0,"integral(sqrt(d*x^2 + c)*arccoth(a*x), x)","F",0
43,0,0,0,0.424634," ","integrate(arccoth(a*x)/(d*x^2+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{arcoth}\left(a x\right)}{\sqrt{d x^{2} + c}}, x\right)"," ",0,"integral(arccoth(a*x)/sqrt(d*x^2 + c), x)","F",0
44,1,354,0,0.503827," ","integrate(arccoth(a*x)/(d*x^2+c)^(3/2),x, algorithm=""fricas"")","\left[\frac{2 \, {\left(a^{2} c + d\right)} \sqrt{d x^{2} + c} x \log\left(\frac{a x + 1}{a x - 1}\right) + \sqrt{a^{2} c + d} {\left(d x^{2} + c\right)} \log\left(\frac{a^{4} d^{2} x^{4} + 8 \, a^{4} c^{2} + 8 \, a^{2} c d + 2 \, {\left(4 \, a^{4} c d + 3 \, a^{2} d^{2}\right)} x^{2} - 4 \, {\left(a^{3} d x^{2} + 2 \, a^{3} c + a d\right)} \sqrt{a^{2} c + d} \sqrt{d x^{2} + c} + d^{2}}{a^{4} x^{4} - 2 \, a^{2} x^{2} + 1}\right)}{4 \, {\left(a^{2} c^{3} + c^{2} d + {\left(a^{2} c^{2} d + c d^{2}\right)} x^{2}\right)}}, \frac{{\left(a^{2} c + d\right)} \sqrt{d x^{2} + c} x \log\left(\frac{a x + 1}{a x - 1}\right) + \sqrt{-a^{2} c - d} {\left(d x^{2} + c\right)} \arctan\left(\frac{{\left(a^{2} d x^{2} + 2 \, a^{2} c + d\right)} \sqrt{-a^{2} c - d} \sqrt{d x^{2} + c}}{2 \, {\left(a^{3} c^{2} + a c d + {\left(a^{3} c d + a d^{2}\right)} x^{2}\right)}}\right)}{2 \, {\left(a^{2} c^{3} + c^{2} d + {\left(a^{2} c^{2} d + c d^{2}\right)} x^{2}\right)}}\right]"," ",0,"[1/4*(2*(a^2*c + d)*sqrt(d*x^2 + c)*x*log((a*x + 1)/(a*x - 1)) + sqrt(a^2*c + d)*(d*x^2 + c)*log((a^4*d^2*x^4 + 8*a^4*c^2 + 8*a^2*c*d + 2*(4*a^4*c*d + 3*a^2*d^2)*x^2 - 4*(a^3*d*x^2 + 2*a^3*c + a*d)*sqrt(a^2*c + d)*sqrt(d*x^2 + c) + d^2)/(a^4*x^4 - 2*a^2*x^2 + 1)))/(a^2*c^3 + c^2*d + (a^2*c^2*d + c*d^2)*x^2), 1/2*((a^2*c + d)*sqrt(d*x^2 + c)*x*log((a*x + 1)/(a*x - 1)) + sqrt(-a^2*c - d)*(d*x^2 + c)*arctan(1/2*(a^2*d*x^2 + 2*a^2*c + d)*sqrt(-a^2*c - d)*sqrt(d*x^2 + c)/(a^3*c^2 + a*c*d + (a^3*c*d + a*d^2)*x^2)))/(a^2*c^3 + c^2*d + (a^2*c^2*d + c*d^2)*x^2)]","B",0
45,1,728,0,0.692219," ","integrate(arccoth(a*x)/(d*x^2+c)^(5/2),x, algorithm=""fricas"")","\left[\frac{{\left(3 \, a^{2} c^{3} + {\left(3 \, a^{2} c d^{2} + 2 \, d^{3}\right)} x^{4} + 2 \, c^{2} d + 2 \, {\left(3 \, a^{2} c^{2} d + 2 \, c d^{2}\right)} x^{2}\right)} \sqrt{a^{2} c + d} \log\left(\frac{a^{4} d^{2} x^{4} + 8 \, a^{4} c^{2} + 8 \, a^{2} c d + 2 \, {\left(4 \, a^{4} c d + 3 \, a^{2} d^{2}\right)} x^{2} - 4 \, {\left(a^{3} d x^{2} + 2 \, a^{3} c + a d\right)} \sqrt{a^{2} c + d} \sqrt{d x^{2} + c} + d^{2}}{a^{4} x^{4} - 2 \, a^{2} x^{2} + 1}\right) + 2 \, {\left(2 \, a^{3} c^{3} + 2 \, a c^{2} d + 2 \, {\left(a^{3} c^{2} d + a c d^{2}\right)} x^{2} + {\left(2 \, {\left(a^{4} c^{2} d + 2 \, a^{2} c d^{2} + d^{3}\right)} x^{3} + 3 \, {\left(a^{4} c^{3} + 2 \, a^{2} c^{2} d + c d^{2}\right)} x\right)} \log\left(\frac{a x + 1}{a x - 1}\right)\right)} \sqrt{d x^{2} + c}}{12 \, {\left(a^{4} c^{6} + 2 \, a^{2} c^{5} d + c^{4} d^{2} + {\left(a^{4} c^{4} d^{2} + 2 \, a^{2} c^{3} d^{3} + c^{2} d^{4}\right)} x^{4} + 2 \, {\left(a^{4} c^{5} d + 2 \, a^{2} c^{4} d^{2} + c^{3} d^{3}\right)} x^{2}\right)}}, \frac{{\left(3 \, a^{2} c^{3} + {\left(3 \, a^{2} c d^{2} + 2 \, d^{3}\right)} x^{4} + 2 \, c^{2} d + 2 \, {\left(3 \, a^{2} c^{2} d + 2 \, c d^{2}\right)} x^{2}\right)} \sqrt{-a^{2} c - d} \arctan\left(\frac{{\left(a^{2} d x^{2} + 2 \, a^{2} c + d\right)} \sqrt{-a^{2} c - d} \sqrt{d x^{2} + c}}{2 \, {\left(a^{3} c^{2} + a c d + {\left(a^{3} c d + a d^{2}\right)} x^{2}\right)}}\right) + {\left(2 \, a^{3} c^{3} + 2 \, a c^{2} d + 2 \, {\left(a^{3} c^{2} d + a c d^{2}\right)} x^{2} + {\left(2 \, {\left(a^{4} c^{2} d + 2 \, a^{2} c d^{2} + d^{3}\right)} x^{3} + 3 \, {\left(a^{4} c^{3} + 2 \, a^{2} c^{2} d + c d^{2}\right)} x\right)} \log\left(\frac{a x + 1}{a x - 1}\right)\right)} \sqrt{d x^{2} + c}}{6 \, {\left(a^{4} c^{6} + 2 \, a^{2} c^{5} d + c^{4} d^{2} + {\left(a^{4} c^{4} d^{2} + 2 \, a^{2} c^{3} d^{3} + c^{2} d^{4}\right)} x^{4} + 2 \, {\left(a^{4} c^{5} d + 2 \, a^{2} c^{4} d^{2} + c^{3} d^{3}\right)} x^{2}\right)}}\right]"," ",0,"[1/12*((3*a^2*c^3 + (3*a^2*c*d^2 + 2*d^3)*x^4 + 2*c^2*d + 2*(3*a^2*c^2*d + 2*c*d^2)*x^2)*sqrt(a^2*c + d)*log((a^4*d^2*x^4 + 8*a^4*c^2 + 8*a^2*c*d + 2*(4*a^4*c*d + 3*a^2*d^2)*x^2 - 4*(a^3*d*x^2 + 2*a^3*c + a*d)*sqrt(a^2*c + d)*sqrt(d*x^2 + c) + d^2)/(a^4*x^4 - 2*a^2*x^2 + 1)) + 2*(2*a^3*c^3 + 2*a*c^2*d + 2*(a^3*c^2*d + a*c*d^2)*x^2 + (2*(a^4*c^2*d + 2*a^2*c*d^2 + d^3)*x^3 + 3*(a^4*c^3 + 2*a^2*c^2*d + c*d^2)*x)*log((a*x + 1)/(a*x - 1)))*sqrt(d*x^2 + c))/(a^4*c^6 + 2*a^2*c^5*d + c^4*d^2 + (a^4*c^4*d^2 + 2*a^2*c^3*d^3 + c^2*d^4)*x^4 + 2*(a^4*c^5*d + 2*a^2*c^4*d^2 + c^3*d^3)*x^2), 1/6*((3*a^2*c^3 + (3*a^2*c*d^2 + 2*d^3)*x^4 + 2*c^2*d + 2*(3*a^2*c^2*d + 2*c*d^2)*x^2)*sqrt(-a^2*c - d)*arctan(1/2*(a^2*d*x^2 + 2*a^2*c + d)*sqrt(-a^2*c - d)*sqrt(d*x^2 + c)/(a^3*c^2 + a*c*d + (a^3*c*d + a*d^2)*x^2)) + (2*a^3*c^3 + 2*a*c^2*d + 2*(a^3*c^2*d + a*c*d^2)*x^2 + (2*(a^4*c^2*d + 2*a^2*c*d^2 + d^3)*x^3 + 3*(a^4*c^3 + 2*a^2*c^2*d + c*d^2)*x)*log((a*x + 1)/(a*x - 1)))*sqrt(d*x^2 + c))/(a^4*c^6 + 2*a^2*c^5*d + c^4*d^2 + (a^4*c^4*d^2 + 2*a^2*c^3*d^3 + c^2*d^4)*x^4 + 2*(a^4*c^5*d + 2*a^2*c^4*d^2 + c^3*d^3)*x^2)]","B",0
46,1,1278,0,0.748952," ","integrate(arccoth(a*x)/(d*x^2+c)^(7/2),x, algorithm=""fricas"")","\left[\frac{{\left(15 \, a^{4} c^{5} + 20 \, a^{2} c^{4} d + {\left(15 \, a^{4} c^{2} d^{3} + 20 \, a^{2} c d^{4} + 8 \, d^{5}\right)} x^{6} + 8 \, c^{3} d^{2} + 3 \, {\left(15 \, a^{4} c^{3} d^{2} + 20 \, a^{2} c^{2} d^{3} + 8 \, c d^{4}\right)} x^{4} + 3 \, {\left(15 \, a^{4} c^{4} d + 20 \, a^{2} c^{3} d^{2} + 8 \, c^{2} d^{3}\right)} x^{2}\right)} \sqrt{a^{2} c + d} \log\left(\frac{a^{4} d^{2} x^{4} + 8 \, a^{4} c^{2} + 8 \, a^{2} c d + 2 \, {\left(4 \, a^{4} c d + 3 \, a^{2} d^{2}\right)} x^{2} - 4 \, {\left(a^{3} d x^{2} + 2 \, a^{3} c + a d\right)} \sqrt{a^{2} c + d} \sqrt{d x^{2} + c} + d^{2}}{a^{4} x^{4} - 2 \, a^{2} x^{2} + 1}\right) + 2 \, {\left(16 \, a^{5} c^{5} + 26 \, a^{3} c^{4} d + 10 \, a c^{3} d^{2} + 2 \, {\left(7 \, a^{5} c^{3} d^{2} + 11 \, a^{3} c^{2} d^{3} + 4 \, a c d^{4}\right)} x^{4} + 6 \, {\left(5 \, a^{5} c^{4} d + 8 \, a^{3} c^{3} d^{2} + 3 \, a c^{2} d^{3}\right)} x^{2} + {\left(8 \, {\left(a^{6} c^{3} d^{2} + 3 \, a^{4} c^{2} d^{3} + 3 \, a^{2} c d^{4} + d^{5}\right)} x^{5} + 20 \, {\left(a^{6} c^{4} d + 3 \, a^{4} c^{3} d^{2} + 3 \, a^{2} c^{2} d^{3} + c d^{4}\right)} x^{3} + 15 \, {\left(a^{6} c^{5} + 3 \, a^{4} c^{4} d + 3 \, a^{2} c^{3} d^{2} + c^{2} d^{3}\right)} x\right)} \log\left(\frac{a x + 1}{a x - 1}\right)\right)} \sqrt{d x^{2} + c}}{60 \, {\left(a^{6} c^{9} + 3 \, a^{4} c^{8} d + 3 \, a^{2} c^{7} d^{2} + c^{6} d^{3} + {\left(a^{6} c^{6} d^{3} + 3 \, a^{4} c^{5} d^{4} + 3 \, a^{2} c^{4} d^{5} + c^{3} d^{6}\right)} x^{6} + 3 \, {\left(a^{6} c^{7} d^{2} + 3 \, a^{4} c^{6} d^{3} + 3 \, a^{2} c^{5} d^{4} + c^{4} d^{5}\right)} x^{4} + 3 \, {\left(a^{6} c^{8} d + 3 \, a^{4} c^{7} d^{2} + 3 \, a^{2} c^{6} d^{3} + c^{5} d^{4}\right)} x^{2}\right)}}, \frac{{\left(15 \, a^{4} c^{5} + 20 \, a^{2} c^{4} d + {\left(15 \, a^{4} c^{2} d^{3} + 20 \, a^{2} c d^{4} + 8 \, d^{5}\right)} x^{6} + 8 \, c^{3} d^{2} + 3 \, {\left(15 \, a^{4} c^{3} d^{2} + 20 \, a^{2} c^{2} d^{3} + 8 \, c d^{4}\right)} x^{4} + 3 \, {\left(15 \, a^{4} c^{4} d + 20 \, a^{2} c^{3} d^{2} + 8 \, c^{2} d^{3}\right)} x^{2}\right)} \sqrt{-a^{2} c - d} \arctan\left(\frac{{\left(a^{2} d x^{2} + 2 \, a^{2} c + d\right)} \sqrt{-a^{2} c - d} \sqrt{d x^{2} + c}}{2 \, {\left(a^{3} c^{2} + a c d + {\left(a^{3} c d + a d^{2}\right)} x^{2}\right)}}\right) + {\left(16 \, a^{5} c^{5} + 26 \, a^{3} c^{4} d + 10 \, a c^{3} d^{2} + 2 \, {\left(7 \, a^{5} c^{3} d^{2} + 11 \, a^{3} c^{2} d^{3} + 4 \, a c d^{4}\right)} x^{4} + 6 \, {\left(5 \, a^{5} c^{4} d + 8 \, a^{3} c^{3} d^{2} + 3 \, a c^{2} d^{3}\right)} x^{2} + {\left(8 \, {\left(a^{6} c^{3} d^{2} + 3 \, a^{4} c^{2} d^{3} + 3 \, a^{2} c d^{4} + d^{5}\right)} x^{5} + 20 \, {\left(a^{6} c^{4} d + 3 \, a^{4} c^{3} d^{2} + 3 \, a^{2} c^{2} d^{3} + c d^{4}\right)} x^{3} + 15 \, {\left(a^{6} c^{5} + 3 \, a^{4} c^{4} d + 3 \, a^{2} c^{3} d^{2} + c^{2} d^{3}\right)} x\right)} \log\left(\frac{a x + 1}{a x - 1}\right)\right)} \sqrt{d x^{2} + c}}{30 \, {\left(a^{6} c^{9} + 3 \, a^{4} c^{8} d + 3 \, a^{2} c^{7} d^{2} + c^{6} d^{3} + {\left(a^{6} c^{6} d^{3} + 3 \, a^{4} c^{5} d^{4} + 3 \, a^{2} c^{4} d^{5} + c^{3} d^{6}\right)} x^{6} + 3 \, {\left(a^{6} c^{7} d^{2} + 3 \, a^{4} c^{6} d^{3} + 3 \, a^{2} c^{5} d^{4} + c^{4} d^{5}\right)} x^{4} + 3 \, {\left(a^{6} c^{8} d + 3 \, a^{4} c^{7} d^{2} + 3 \, a^{2} c^{6} d^{3} + c^{5} d^{4}\right)} x^{2}\right)}}\right]"," ",0,"[1/60*((15*a^4*c^5 + 20*a^2*c^4*d + (15*a^4*c^2*d^3 + 20*a^2*c*d^4 + 8*d^5)*x^6 + 8*c^3*d^2 + 3*(15*a^4*c^3*d^2 + 20*a^2*c^2*d^3 + 8*c*d^4)*x^4 + 3*(15*a^4*c^4*d + 20*a^2*c^3*d^2 + 8*c^2*d^3)*x^2)*sqrt(a^2*c + d)*log((a^4*d^2*x^4 + 8*a^4*c^2 + 8*a^2*c*d + 2*(4*a^4*c*d + 3*a^2*d^2)*x^2 - 4*(a^3*d*x^2 + 2*a^3*c + a*d)*sqrt(a^2*c + d)*sqrt(d*x^2 + c) + d^2)/(a^4*x^4 - 2*a^2*x^2 + 1)) + 2*(16*a^5*c^5 + 26*a^3*c^4*d + 10*a*c^3*d^2 + 2*(7*a^5*c^3*d^2 + 11*a^3*c^2*d^3 + 4*a*c*d^4)*x^4 + 6*(5*a^5*c^4*d + 8*a^3*c^3*d^2 + 3*a*c^2*d^3)*x^2 + (8*(a^6*c^3*d^2 + 3*a^4*c^2*d^3 + 3*a^2*c*d^4 + d^5)*x^5 + 20*(a^6*c^4*d + 3*a^4*c^3*d^2 + 3*a^2*c^2*d^3 + c*d^4)*x^3 + 15*(a^6*c^5 + 3*a^4*c^4*d + 3*a^2*c^3*d^2 + c^2*d^3)*x)*log((a*x + 1)/(a*x - 1)))*sqrt(d*x^2 + c))/(a^6*c^9 + 3*a^4*c^8*d + 3*a^2*c^7*d^2 + c^6*d^3 + (a^6*c^6*d^3 + 3*a^4*c^5*d^4 + 3*a^2*c^4*d^5 + c^3*d^6)*x^6 + 3*(a^6*c^7*d^2 + 3*a^4*c^6*d^3 + 3*a^2*c^5*d^4 + c^4*d^5)*x^4 + 3*(a^6*c^8*d + 3*a^4*c^7*d^2 + 3*a^2*c^6*d^3 + c^5*d^4)*x^2), 1/30*((15*a^4*c^5 + 20*a^2*c^4*d + (15*a^4*c^2*d^3 + 20*a^2*c*d^4 + 8*d^5)*x^6 + 8*c^3*d^2 + 3*(15*a^4*c^3*d^2 + 20*a^2*c^2*d^3 + 8*c*d^4)*x^4 + 3*(15*a^4*c^4*d + 20*a^2*c^3*d^2 + 8*c^2*d^3)*x^2)*sqrt(-a^2*c - d)*arctan(1/2*(a^2*d*x^2 + 2*a^2*c + d)*sqrt(-a^2*c - d)*sqrt(d*x^2 + c)/(a^3*c^2 + a*c*d + (a^3*c*d + a*d^2)*x^2)) + (16*a^5*c^5 + 26*a^3*c^4*d + 10*a*c^3*d^2 + 2*(7*a^5*c^3*d^2 + 11*a^3*c^2*d^3 + 4*a*c*d^4)*x^4 + 6*(5*a^5*c^4*d + 8*a^3*c^3*d^2 + 3*a*c^2*d^3)*x^2 + (8*(a^6*c^3*d^2 + 3*a^4*c^2*d^3 + 3*a^2*c*d^4 + d^5)*x^5 + 20*(a^6*c^4*d + 3*a^4*c^3*d^2 + 3*a^2*c^2*d^3 + c*d^4)*x^3 + 15*(a^6*c^5 + 3*a^4*c^4*d + 3*a^2*c^3*d^2 + c^2*d^3)*x)*log((a*x + 1)/(a*x - 1)))*sqrt(d*x^2 + c))/(a^6*c^9 + 3*a^4*c^8*d + 3*a^2*c^7*d^2 + c^6*d^3 + (a^6*c^6*d^3 + 3*a^4*c^5*d^4 + 3*a^2*c^4*d^5 + c^3*d^6)*x^6 + 3*(a^6*c^7*d^2 + 3*a^4*c^6*d^3 + 3*a^2*c^5*d^4 + c^4*d^5)*x^4 + 3*(a^6*c^8*d + 3*a^4*c^7*d^2 + 3*a^2*c^6*d^3 + c^5*d^4)*x^2)]","B",0
47,1,2004,0,0.932119," ","integrate(arccoth(a*x)/(d*x^2+c)^(9/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(35 \, a^{6} c^{7} + 70 \, a^{4} c^{6} d + 56 \, a^{2} c^{5} d^{2} + {\left(35 \, a^{6} c^{3} d^{4} + 70 \, a^{4} c^{2} d^{5} + 56 \, a^{2} c d^{6} + 16 \, d^{7}\right)} x^{8} + 16 \, c^{4} d^{3} + 4 \, {\left(35 \, a^{6} c^{4} d^{3} + 70 \, a^{4} c^{3} d^{4} + 56 \, a^{2} c^{2} d^{5} + 16 \, c d^{6}\right)} x^{6} + 6 \, {\left(35 \, a^{6} c^{5} d^{2} + 70 \, a^{4} c^{4} d^{3} + 56 \, a^{2} c^{3} d^{4} + 16 \, c^{2} d^{5}\right)} x^{4} + 4 \, {\left(35 \, a^{6} c^{6} d + 70 \, a^{4} c^{5} d^{2} + 56 \, a^{2} c^{4} d^{3} + 16 \, c^{3} d^{4}\right)} x^{2}\right)} \sqrt{a^{2} c + d} \log\left(\frac{a^{4} d^{2} x^{4} + 8 \, a^{4} c^{2} + 8 \, a^{2} c d + 2 \, {\left(4 \, a^{4} c d + 3 \, a^{2} d^{2}\right)} x^{2} - 4 \, {\left(a^{3} d x^{2} + 2 \, a^{3} c + a d\right)} \sqrt{a^{2} c + d} \sqrt{d x^{2} + c} + d^{2}}{a^{4} x^{4} - 2 \, a^{2} x^{2} + 1}\right) + 2 \, {\left(142 \, a^{7} c^{7} + 320 \, a^{5} c^{6} d + 244 \, a^{3} c^{5} d^{2} + 66 \, a c^{4} d^{3} + 6 \, {\left(19 \, a^{7} c^{4} d^{3} + 41 \, a^{5} c^{3} d^{4} + 30 \, a^{3} c^{2} d^{5} + 8 \, a c d^{6}\right)} x^{6} + 2 \, {\left(182 \, a^{7} c^{5} d^{2} + 397 \, a^{5} c^{4} d^{3} + 293 \, a^{3} c^{3} d^{4} + 78 \, a c^{2} d^{5}\right)} x^{4} + 2 \, {\left(196 \, a^{7} c^{6} d + 434 \, a^{5} c^{5} d^{2} + 325 \, a^{3} c^{4} d^{3} + 87 \, a c^{3} d^{4}\right)} x^{2} + 3 \, {\left(16 \, {\left(a^{8} c^{4} d^{3} + 4 \, a^{6} c^{3} d^{4} + 6 \, a^{4} c^{2} d^{5} + 4 \, a^{2} c d^{6} + d^{7}\right)} x^{7} + 56 \, {\left(a^{8} c^{5} d^{2} + 4 \, a^{6} c^{4} d^{3} + 6 \, a^{4} c^{3} d^{4} + 4 \, a^{2} c^{2} d^{5} + c d^{6}\right)} x^{5} + 70 \, {\left(a^{8} c^{6} d + 4 \, a^{6} c^{5} d^{2} + 6 \, a^{4} c^{4} d^{3} + 4 \, a^{2} c^{3} d^{4} + c^{2} d^{5}\right)} x^{3} + 35 \, {\left(a^{8} c^{7} + 4 \, a^{6} c^{6} d + 6 \, a^{4} c^{5} d^{2} + 4 \, a^{2} c^{4} d^{3} + c^{3} d^{4}\right)} x\right)} \log\left(\frac{a x + 1}{a x - 1}\right)\right)} \sqrt{d x^{2} + c}}{420 \, {\left(a^{8} c^{12} + 4 \, a^{6} c^{11} d + 6 \, a^{4} c^{10} d^{2} + 4 \, a^{2} c^{9} d^{3} + c^{8} d^{4} + {\left(a^{8} c^{8} d^{4} + 4 \, a^{6} c^{7} d^{5} + 6 \, a^{4} c^{6} d^{6} + 4 \, a^{2} c^{5} d^{7} + c^{4} d^{8}\right)} x^{8} + 4 \, {\left(a^{8} c^{9} d^{3} + 4 \, a^{6} c^{8} d^{4} + 6 \, a^{4} c^{7} d^{5} + 4 \, a^{2} c^{6} d^{6} + c^{5} d^{7}\right)} x^{6} + 6 \, {\left(a^{8} c^{10} d^{2} + 4 \, a^{6} c^{9} d^{3} + 6 \, a^{4} c^{8} d^{4} + 4 \, a^{2} c^{7} d^{5} + c^{6} d^{6}\right)} x^{4} + 4 \, {\left(a^{8} c^{11} d + 4 \, a^{6} c^{10} d^{2} + 6 \, a^{4} c^{9} d^{3} + 4 \, a^{2} c^{8} d^{4} + c^{7} d^{5}\right)} x^{2}\right)}}, \frac{3 \, {\left(35 \, a^{6} c^{7} + 70 \, a^{4} c^{6} d + 56 \, a^{2} c^{5} d^{2} + {\left(35 \, a^{6} c^{3} d^{4} + 70 \, a^{4} c^{2} d^{5} + 56 \, a^{2} c d^{6} + 16 \, d^{7}\right)} x^{8} + 16 \, c^{4} d^{3} + 4 \, {\left(35 \, a^{6} c^{4} d^{3} + 70 \, a^{4} c^{3} d^{4} + 56 \, a^{2} c^{2} d^{5} + 16 \, c d^{6}\right)} x^{6} + 6 \, {\left(35 \, a^{6} c^{5} d^{2} + 70 \, a^{4} c^{4} d^{3} + 56 \, a^{2} c^{3} d^{4} + 16 \, c^{2} d^{5}\right)} x^{4} + 4 \, {\left(35 \, a^{6} c^{6} d + 70 \, a^{4} c^{5} d^{2} + 56 \, a^{2} c^{4} d^{3} + 16 \, c^{3} d^{4}\right)} x^{2}\right)} \sqrt{-a^{2} c - d} \arctan\left(\frac{{\left(a^{2} d x^{2} + 2 \, a^{2} c + d\right)} \sqrt{-a^{2} c - d} \sqrt{d x^{2} + c}}{2 \, {\left(a^{3} c^{2} + a c d + {\left(a^{3} c d + a d^{2}\right)} x^{2}\right)}}\right) + {\left(142 \, a^{7} c^{7} + 320 \, a^{5} c^{6} d + 244 \, a^{3} c^{5} d^{2} + 66 \, a c^{4} d^{3} + 6 \, {\left(19 \, a^{7} c^{4} d^{3} + 41 \, a^{5} c^{3} d^{4} + 30 \, a^{3} c^{2} d^{5} + 8 \, a c d^{6}\right)} x^{6} + 2 \, {\left(182 \, a^{7} c^{5} d^{2} + 397 \, a^{5} c^{4} d^{3} + 293 \, a^{3} c^{3} d^{4} + 78 \, a c^{2} d^{5}\right)} x^{4} + 2 \, {\left(196 \, a^{7} c^{6} d + 434 \, a^{5} c^{5} d^{2} + 325 \, a^{3} c^{4} d^{3} + 87 \, a c^{3} d^{4}\right)} x^{2} + 3 \, {\left(16 \, {\left(a^{8} c^{4} d^{3} + 4 \, a^{6} c^{3} d^{4} + 6 \, a^{4} c^{2} d^{5} + 4 \, a^{2} c d^{6} + d^{7}\right)} x^{7} + 56 \, {\left(a^{8} c^{5} d^{2} + 4 \, a^{6} c^{4} d^{3} + 6 \, a^{4} c^{3} d^{4} + 4 \, a^{2} c^{2} d^{5} + c d^{6}\right)} x^{5} + 70 \, {\left(a^{8} c^{6} d + 4 \, a^{6} c^{5} d^{2} + 6 \, a^{4} c^{4} d^{3} + 4 \, a^{2} c^{3} d^{4} + c^{2} d^{5}\right)} x^{3} + 35 \, {\left(a^{8} c^{7} + 4 \, a^{6} c^{6} d + 6 \, a^{4} c^{5} d^{2} + 4 \, a^{2} c^{4} d^{3} + c^{3} d^{4}\right)} x\right)} \log\left(\frac{a x + 1}{a x - 1}\right)\right)} \sqrt{d x^{2} + c}}{210 \, {\left(a^{8} c^{12} + 4 \, a^{6} c^{11} d + 6 \, a^{4} c^{10} d^{2} + 4 \, a^{2} c^{9} d^{3} + c^{8} d^{4} + {\left(a^{8} c^{8} d^{4} + 4 \, a^{6} c^{7} d^{5} + 6 \, a^{4} c^{6} d^{6} + 4 \, a^{2} c^{5} d^{7} + c^{4} d^{8}\right)} x^{8} + 4 \, {\left(a^{8} c^{9} d^{3} + 4 \, a^{6} c^{8} d^{4} + 6 \, a^{4} c^{7} d^{5} + 4 \, a^{2} c^{6} d^{6} + c^{5} d^{7}\right)} x^{6} + 6 \, {\left(a^{8} c^{10} d^{2} + 4 \, a^{6} c^{9} d^{3} + 6 \, a^{4} c^{8} d^{4} + 4 \, a^{2} c^{7} d^{5} + c^{6} d^{6}\right)} x^{4} + 4 \, {\left(a^{8} c^{11} d + 4 \, a^{6} c^{10} d^{2} + 6 \, a^{4} c^{9} d^{3} + 4 \, a^{2} c^{8} d^{4} + c^{7} d^{5}\right)} x^{2}\right)}}\right]"," ",0,"[1/420*(3*(35*a^6*c^7 + 70*a^4*c^6*d + 56*a^2*c^5*d^2 + (35*a^6*c^3*d^4 + 70*a^4*c^2*d^5 + 56*a^2*c*d^6 + 16*d^7)*x^8 + 16*c^4*d^3 + 4*(35*a^6*c^4*d^3 + 70*a^4*c^3*d^4 + 56*a^2*c^2*d^5 + 16*c*d^6)*x^6 + 6*(35*a^6*c^5*d^2 + 70*a^4*c^4*d^3 + 56*a^2*c^3*d^4 + 16*c^2*d^5)*x^4 + 4*(35*a^6*c^6*d + 70*a^4*c^5*d^2 + 56*a^2*c^4*d^3 + 16*c^3*d^4)*x^2)*sqrt(a^2*c + d)*log((a^4*d^2*x^4 + 8*a^4*c^2 + 8*a^2*c*d + 2*(4*a^4*c*d + 3*a^2*d^2)*x^2 - 4*(a^3*d*x^2 + 2*a^3*c + a*d)*sqrt(a^2*c + d)*sqrt(d*x^2 + c) + d^2)/(a^4*x^4 - 2*a^2*x^2 + 1)) + 2*(142*a^7*c^7 + 320*a^5*c^6*d + 244*a^3*c^5*d^2 + 66*a*c^4*d^3 + 6*(19*a^7*c^4*d^3 + 41*a^5*c^3*d^4 + 30*a^3*c^2*d^5 + 8*a*c*d^6)*x^6 + 2*(182*a^7*c^5*d^2 + 397*a^5*c^4*d^3 + 293*a^3*c^3*d^4 + 78*a*c^2*d^5)*x^4 + 2*(196*a^7*c^6*d + 434*a^5*c^5*d^2 + 325*a^3*c^4*d^3 + 87*a*c^3*d^4)*x^2 + 3*(16*(a^8*c^4*d^3 + 4*a^6*c^3*d^4 + 6*a^4*c^2*d^5 + 4*a^2*c*d^6 + d^7)*x^7 + 56*(a^8*c^5*d^2 + 4*a^6*c^4*d^3 + 6*a^4*c^3*d^4 + 4*a^2*c^2*d^5 + c*d^6)*x^5 + 70*(a^8*c^6*d + 4*a^6*c^5*d^2 + 6*a^4*c^4*d^3 + 4*a^2*c^3*d^4 + c^2*d^5)*x^3 + 35*(a^8*c^7 + 4*a^6*c^6*d + 6*a^4*c^5*d^2 + 4*a^2*c^4*d^3 + c^3*d^4)*x)*log((a*x + 1)/(a*x - 1)))*sqrt(d*x^2 + c))/(a^8*c^12 + 4*a^6*c^11*d + 6*a^4*c^10*d^2 + 4*a^2*c^9*d^3 + c^8*d^4 + (a^8*c^8*d^4 + 4*a^6*c^7*d^5 + 6*a^4*c^6*d^6 + 4*a^2*c^5*d^7 + c^4*d^8)*x^8 + 4*(a^8*c^9*d^3 + 4*a^6*c^8*d^4 + 6*a^4*c^7*d^5 + 4*a^2*c^6*d^6 + c^5*d^7)*x^6 + 6*(a^8*c^10*d^2 + 4*a^6*c^9*d^3 + 6*a^4*c^8*d^4 + 4*a^2*c^7*d^5 + c^6*d^6)*x^4 + 4*(a^8*c^11*d + 4*a^6*c^10*d^2 + 6*a^4*c^9*d^3 + 4*a^2*c^8*d^4 + c^7*d^5)*x^2), 1/210*(3*(35*a^6*c^7 + 70*a^4*c^6*d + 56*a^2*c^5*d^2 + (35*a^6*c^3*d^4 + 70*a^4*c^2*d^5 + 56*a^2*c*d^6 + 16*d^7)*x^8 + 16*c^4*d^3 + 4*(35*a^6*c^4*d^3 + 70*a^4*c^3*d^4 + 56*a^2*c^2*d^5 + 16*c*d^6)*x^6 + 6*(35*a^6*c^5*d^2 + 70*a^4*c^4*d^3 + 56*a^2*c^3*d^4 + 16*c^2*d^5)*x^4 + 4*(35*a^6*c^6*d + 70*a^4*c^5*d^2 + 56*a^2*c^4*d^3 + 16*c^3*d^4)*x^2)*sqrt(-a^2*c - d)*arctan(1/2*(a^2*d*x^2 + 2*a^2*c + d)*sqrt(-a^2*c - d)*sqrt(d*x^2 + c)/(a^3*c^2 + a*c*d + (a^3*c*d + a*d^2)*x^2)) + (142*a^7*c^7 + 320*a^5*c^6*d + 244*a^3*c^5*d^2 + 66*a*c^4*d^3 + 6*(19*a^7*c^4*d^3 + 41*a^5*c^3*d^4 + 30*a^3*c^2*d^5 + 8*a*c*d^6)*x^6 + 2*(182*a^7*c^5*d^2 + 397*a^5*c^4*d^3 + 293*a^3*c^3*d^4 + 78*a*c^2*d^5)*x^4 + 2*(196*a^7*c^6*d + 434*a^5*c^5*d^2 + 325*a^3*c^4*d^3 + 87*a*c^3*d^4)*x^2 + 3*(16*(a^8*c^4*d^3 + 4*a^6*c^3*d^4 + 6*a^4*c^2*d^5 + 4*a^2*c*d^6 + d^7)*x^7 + 56*(a^8*c^5*d^2 + 4*a^6*c^4*d^3 + 6*a^4*c^3*d^4 + 4*a^2*c^2*d^5 + c*d^6)*x^5 + 70*(a^8*c^6*d + 4*a^6*c^5*d^2 + 6*a^4*c^4*d^3 + 4*a^2*c^3*d^4 + c^2*d^5)*x^3 + 35*(a^8*c^7 + 4*a^6*c^6*d + 6*a^4*c^5*d^2 + 4*a^2*c^4*d^3 + c^3*d^4)*x)*log((a*x + 1)/(a*x - 1)))*sqrt(d*x^2 + c))/(a^8*c^12 + 4*a^6*c^11*d + 6*a^4*c^10*d^2 + 4*a^2*c^9*d^3 + c^8*d^4 + (a^8*c^8*d^4 + 4*a^6*c^7*d^5 + 6*a^4*c^6*d^6 + 4*a^2*c^5*d^7 + c^4*d^8)*x^8 + 4*(a^8*c^9*d^3 + 4*a^6*c^8*d^4 + 6*a^4*c^7*d^5 + 4*a^2*c^6*d^6 + c^5*d^7)*x^6 + 6*(a^8*c^10*d^2 + 4*a^6*c^9*d^3 + 6*a^4*c^8*d^4 + 4*a^2*c^7*d^5 + c^6*d^6)*x^4 + 4*(a^8*c^11*d + 4*a^6*c^10*d^2 + 6*a^4*c^9*d^3 + 4*a^2*c^8*d^4 + c^7*d^5)*x^2)]","B",0
48,0,0,0,0.807136," ","integrate((-a*x^2+a)^(1/2)*arccoth(x),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{-a x^{2} + a} \operatorname{arcoth}\left(x\right), x\right)"," ",0,"integral(sqrt(-a*x^2 + a)*arccoth(x), x)","F",0
49,0,0,0,0.510865," ","integrate(arccoth(x)/(-a*x^2+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-a x^{2} + a} \operatorname{arcoth}\left(x\right)}{a x^{2} - a}, x\right)"," ",0,"integral(-sqrt(-a*x^2 + a)*arccoth(x)/(a*x^2 - a), x)","F",0
50,1,41,0,0.469323," ","integrate(arccoth(x)/(-a*x^2+a)^(3/2),x, algorithm=""fricas"")","-\frac{\sqrt{-a x^{2} + a} {\left(x \log\left(\frac{x + 1}{x - 1}\right) - 2\right)}}{2 \, {\left(a^{2} x^{2} - a^{2}\right)}}"," ",0,"-1/2*sqrt(-a*x^2 + a)*(x*log((x + 1)/(x - 1)) - 2)/(a^2*x^2 - a^2)","A",0
51,1,61,0,0.470562," ","integrate(arccoth(x)/(-a*x^2+a)^(5/2),x, algorithm=""fricas"")","\frac{\sqrt{-a x^{2} + a} {\left(12 \, x^{2} - 3 \, {\left(2 \, x^{3} - 3 \, x\right)} \log\left(\frac{x + 1}{x - 1}\right) - 14\right)}}{18 \, {\left(a^{3} x^{4} - 2 \, a^{3} x^{2} + a^{3}\right)}}"," ",0,"1/18*sqrt(-a*x^2 + a)*(12*x^2 - 3*(2*x^3 - 3*x)*log((x + 1)/(x - 1)) - 14)/(a^3*x^4 - 2*a^3*x^2 + a^3)","A",0
52,1,81,0,0.553852," ","integrate(arccoth(x)/(-a*x^2+a)^(7/2),x, algorithm=""fricas"")","\frac{{\left(240 \, x^{4} - 520 \, x^{2} - 15 \, {\left(8 \, x^{5} - 20 \, x^{3} + 15 \, x\right)} \log\left(\frac{x + 1}{x - 1}\right) + 298\right)} \sqrt{-a x^{2} + a}}{450 \, {\left(a^{4} x^{6} - 3 \, a^{4} x^{4} + 3 \, a^{4} x^{2} - a^{4}\right)}}"," ",0,"1/450*(240*x^4 - 520*x^2 - 15*(8*x^5 - 20*x^3 + 15*x)*log((x + 1)/(x - 1)) + 298)*sqrt(-a*x^2 + a)/(a^4*x^6 - 3*a^4*x^4 + 3*a^4*x^2 - a^4)","A",0
53,1,11,0,0.466291," ","integrate(1/(-x^2+1)/arccoth(x),x, algorithm=""fricas"")","\log\left(\log\left(\frac{x + 1}{x - 1}\right)\right)"," ",0,"log(log((x + 1)/(x - 1)))","B",0
54,1,62,0,0.599507," ","integrate(arccoth(x)^n/(-x^2+1),x, algorithm=""fricas"")","\frac{\cosh\left(n \log\left(\frac{1}{2} \, \log\left(\frac{x + 1}{x - 1}\right)\right)\right) \log\left(\frac{x + 1}{x - 1}\right) + \log\left(\frac{x + 1}{x - 1}\right) \sinh\left(n \log\left(\frac{1}{2} \, \log\left(\frac{x + 1}{x - 1}\right)\right)\right)}{2 \, {\left(n + 1\right)}}"," ",0,"1/2*(cosh(n*log(1/2*log((x + 1)/(x - 1))))*log((x + 1)/(x - 1)) + log((x + 1)/(x - 1))*sinh(n*log(1/2*log((x + 1)/(x - 1)))))/(n + 1)","B",0
55,1,63,0,0.529509," ","integrate(arccoth(x)^2/(-x^2+1)^2,x, algorithm=""fricas"")","\frac{{\left(x^{2} - 1\right)} \log\left(\frac{x + 1}{x - 1}\right)^{3} - 6 \, x \log\left(\frac{x + 1}{x - 1}\right)^{2} + 6 \, {\left(x^{2} + 1\right)} \log\left(\frac{x + 1}{x - 1}\right) - 12 \, x}{48 \, {\left(x^{2} - 1\right)}}"," ",0,"1/48*((x^2 - 1)*log((x + 1)/(x - 1))^3 - 6*x*log((x + 1)/(x - 1))^2 + 6*(x^2 + 1)*log((x + 1)/(x - 1)) - 12*x)/(x^2 - 1)","A",0
56,0,0,0,0.435256," ","integrate(x*arccoth(x)/(-x^2+1),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{x \operatorname{arcoth}\left(x\right)}{x^{2} - 1}, x\right)"," ",0,"integral(-x*arccoth(x)/(x^2 - 1), x)","F",0
57,1,14,0,0.412572," ","integrate(arccoth(x)/(-x^2+1),x, algorithm=""fricas"")","\frac{1}{8} \, \log\left(\frac{x + 1}{x - 1}\right)^{2}"," ",0,"1/8*log((x + 1)/(x - 1))^2","B",0
58,1,29,0,0.388114," ","integrate(x*arccoth(x)/(-x^2+1)^2,x, algorithm=""fricas"")","-\frac{{\left(x^{2} + 1\right)} \log\left(\frac{x + 1}{x - 1}\right) - 2 \, x}{8 \, {\left(x^{2} - 1\right)}}"," ",0,"-1/8*((x^2 + 1)*log((x + 1)/(x - 1)) - 2*x)/(x^2 - 1)","A",0
59,1,42,0,0.521555," ","integrate(arccoth(x)/(-x^2+1)^2,x, algorithm=""fricas"")","\frac{{\left(x^{2} - 1\right)} \log\left(\frac{x + 1}{x - 1}\right)^{2} - 4 \, x \log\left(\frac{x + 1}{x - 1}\right) + 4}{16 \, {\left(x^{2} - 1\right)}}"," ",0,"1/16*((x^2 - 1)*log((x + 1)/(x - 1))^2 - 4*x*log((x + 1)/(x - 1)) + 4)/(x^2 - 1)","A",0
60,1,47,0,0.610204," ","integrate(x*arccoth(x)/(-x^2+1)^3,x, algorithm=""fricas"")","\frac{6 \, x^{3} - {\left(3 \, x^{4} - 6 \, x^{2} - 5\right)} \log\left(\frac{x + 1}{x - 1}\right) - 10 \, x}{64 \, {\left(x^{4} - 2 \, x^{2} + 1\right)}}"," ",0,"1/64*(6*x^3 - (3*x^4 - 6*x^2 - 5)*log((x + 1)/(x - 1)) - 10*x)/(x^4 - 2*x^2 + 1)","A",0
61,1,66,0,0.398612," ","integrate(arccoth(x)/(-x^2+1)^3,x, algorithm=""fricas"")","\frac{3 \, {\left(x^{4} - 2 \, x^{2} + 1\right)} \log\left(\frac{x + 1}{x - 1}\right)^{2} + 12 \, x^{2} - 4 \, {\left(3 \, x^{3} - 5 \, x\right)} \log\left(\frac{x + 1}{x - 1}\right) - 16}{64 \, {\left(x^{4} - 2 \, x^{2} + 1\right)}}"," ",0,"1/64*(3*(x^4 - 2*x^2 + 1)*log((x + 1)/(x - 1))^2 + 12*x^2 - 4*(3*x^3 - 5*x)*log((x + 1)/(x - 1)) - 16)/(x^4 - 2*x^2 + 1)","A",0
62,1,112,0,0.501356," ","integrate(x^3*arccoth(b*x+a),x, algorithm=""fricas"")","\frac{3 \, b^{4} x^{4} \log\left(\frac{b x + a + 1}{b x + a - 1}\right) + 2 \, b^{3} x^{3} - 6 \, a b^{2} x^{2} + 6 \, {\left(3 \, a^{2} + 1\right)} b x - 3 \, {\left(a^{4} + 4 \, a^{3} + 6 \, a^{2} + 4 \, 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)}{24 \, b^{4}}"," ",0,"1/24*(3*b^4*x^4*log((b*x + a + 1)/(b*x + a - 1)) + 2*b^3*x^3 - 6*a*b^2*x^2 + 6*(3*a^2 + 1)*b*x - 3*(a^4 + 4*a^3 + 6*a^2 + 4*a + 1)*log(b*x + a + 1) + 3*(a^4 - 4*a^3 + 6*a^2 - 4*a + 1)*log(b*x + a - 1))/b^4","A",0
63,1,84,0,0.555721," ","integrate(x^2*arccoth(b*x+a),x, algorithm=""fricas"")","\frac{b^{3} x^{3} \log\left(\frac{b x + a + 1}{b x + a - 1}\right) + b^{2} x^{2} - 4 \, a b x + {\left(a^{3} + 3 \, a^{2} + 3 \, 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)}{6 \, b^{3}}"," ",0,"1/6*(b^3*x^3*log((b*x + a + 1)/(b*x + a - 1)) + b^2*x^2 - 4*a*b*x + (a^3 + 3*a^2 + 3*a + 1)*log(b*x + a + 1) - (a^3 - 3*a^2 + 3*a - 1)*log(b*x + a - 1))/b^3","A",0
64,1,66,0,0.841645," ","integrate(x*arccoth(b*x+a),x, algorithm=""fricas"")","\frac{b^{2} x^{2} \log\left(\frac{b x + a + 1}{b x + a - 1}\right) + 2 \, b x - {\left(a^{2} + 2 \, a + 1\right)} \log\left(b x + a + 1\right) + {\left(a^{2} - 2 \, a + 1\right)} \log\left(b x + a - 1\right)}{4 \, b^{2}}"," ",0,"1/4*(b^2*x^2*log((b*x + a + 1)/(b*x + a - 1)) + 2*b*x - (a^2 + 2*a + 1)*log(b*x + a + 1) + (a^2 - 2*a + 1)*log(b*x + a - 1))/b^2","A",0
65,1,48,0,0.668555," ","integrate(arccoth(b*x+a),x, algorithm=""fricas"")","\frac{b x \log\left(\frac{b x + a + 1}{b x + a - 1}\right) + {\left(a + 1\right)} \log\left(b x + a + 1\right) - {\left(a - 1\right)} \log\left(b x + a - 1\right)}{2 \, b}"," ",0,"1/2*(b*x*log((b*x + a + 1)/(b*x + a - 1)) + (a + 1)*log(b*x + a + 1) - (a - 1)*log(b*x + a - 1))/b","A",0
66,0,0,0,0.698889," ","integrate(arccoth(b*x+a)/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{arcoth}\left(b x + a\right)}{x}, x\right)"," ",0,"integral(arccoth(b*x + a)/x, x)","F",0
67,1,68,0,0.678686," ","integrate(arccoth(b*x+a)/x^2,x, algorithm=""fricas"")","-\frac{{\left(a - 1\right)} b x \log\left(b x + a + 1\right) - {\left(a + 1\right)} b x \log\left(b x + a - 1\right) + 2 \, b x \log\left(x\right) + {\left(a^{2} - 1\right)} \log\left(\frac{b x + a + 1}{b x + a - 1}\right)}{2 \, {\left(a^{2} - 1\right)} x}"," ",0,"-1/2*((a - 1)*b*x*log(b*x + a + 1) - (a + 1)*b*x*log(b*x + a - 1) + 2*b*x*log(x) + (a^2 - 1)*log((b*x + a + 1)/(b*x + a - 1)))/((a^2 - 1)*x)","A",0
68,1,111,0,0.722339," ","integrate(arccoth(b*x+a)/x^3,x, algorithm=""fricas"")","\frac{{\left(a^{2} - 2 \, a + 1\right)} b^{2} x^{2} \log\left(b x + a + 1\right) - {\left(a^{2} + 2 \, a + 1\right)} b^{2} x^{2} \log\left(b x + a - 1\right) + 4 \, a b^{2} x^{2} \log\left(x\right) + 2 \, {\left(a^{2} - 1\right)} b x - {\left(a^{4} - 2 \, a^{2} + 1\right)} \log\left(\frac{b x + a + 1}{b x + a - 1}\right)}{4 \, {\left(a^{4} - 2 \, a^{2} + 1\right)} x^{2}}"," ",0,"1/4*((a^2 - 2*a + 1)*b^2*x^2*log(b*x + a + 1) - (a^2 + 2*a + 1)*b^2*x^2*log(b*x + a - 1) + 4*a*b^2*x^2*log(x) + 2*(a^2 - 1)*b*x - (a^4 - 2*a^2 + 1)*log((b*x + a + 1)/(b*x + a - 1)))/((a^4 - 2*a^2 + 1)*x^2)","A",0
69,0,0,0,0.772017," ","integrate(x^3*arccoth(b*x+a)^2,x, algorithm=""fricas"")","{\rm integral}\left(x^{3} \operatorname{arcoth}\left(b x + a\right)^{2}, x\right)"," ",0,"integral(x^3*arccoth(b*x + a)^2, x)","F",0
70,0,0,0,0.481105," ","integrate(x^2*arccoth(b*x+a)^2,x, algorithm=""fricas"")","{\rm integral}\left(x^{2} \operatorname{arcoth}\left(b x + a\right)^{2}, x\right)"," ",0,"integral(x^2*arccoth(b*x + a)^2, x)","F",0
71,0,0,0,0.681644," ","integrate(x*arccoth(b*x+a)^2,x, algorithm=""fricas"")","{\rm integral}\left(x \operatorname{arcoth}\left(b x + a\right)^{2}, x\right)"," ",0,"integral(x*arccoth(b*x + a)^2, x)","F",0
72,0,0,0,0.436365," ","integrate(arccoth(b*x+a)^2,x, algorithm=""fricas"")","{\rm integral}\left(\operatorname{arcoth}\left(b x + a\right)^{2}, x\right)"," ",0,"integral(arccoth(b*x + a)^2, x)","F",0
73,0,0,0,0.466963," ","integrate(arccoth(b*x+a)^2/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{arcoth}\left(b x + a\right)^{2}}{x}, x\right)"," ",0,"integral(arccoth(b*x + a)^2/x, x)","F",0
74,0,0,0,0.471885," ","integrate(arccoth(b*x+a)^2/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{arcoth}\left(b x + a\right)^{2}}{x^{2}}, x\right)"," ",0,"integral(arccoth(b*x + a)^2/x^2, x)","F",0
75,0,0,0,0.407131," ","integrate(arccoth(b*x+a)^2/x^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{arcoth}\left(b x + a\right)^{2}}{x^{3}}, x\right)"," ",0,"integral(arccoth(b*x + a)^2/x^3, x)","F",0
76,0,0,0,0.411922," ","integrate(arccoth(b*x+a)/(d*x^2+c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{arcoth}\left(b x + a\right)}{d x^{2} + c}, x\right)"," ",0,"integral(arccoth(b*x + a)/(d*x^2 + c), x)","F",0
77,0,0,0,0.713770," ","integrate(arccoth(b*x+a)/(d*x+c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{arcoth}\left(b x + a\right)}{d x + c}, x\right)"," ",0,"integral(arccoth(b*x + a)/(d*x + c), x)","F",0
78,0,0,0,0.583219," ","integrate(arccoth(b*x+a)/(c+d/x),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x \operatorname{arcoth}\left(b x + a\right)}{c x + d}, x\right)"," ",0,"integral(x*arccoth(b*x + a)/(c*x + d), x)","F",0
79,0,0,0,0.495497," ","integrate(arccoth(b*x+a)/(c+d/x^2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{2} \operatorname{arcoth}\left(b x + a\right)}{c x^{2} + d}, x\right)"," ",0,"integral(x^2*arccoth(b*x + a)/(c*x^2 + d), x)","F",0
80,0,0,0,0.469746," ","integrate(arccoth(b*x+a)/(c+d*x^(1/2)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{d \sqrt{x} \operatorname{arcoth}\left(b x + a\right) - c \operatorname{arcoth}\left(b x + a\right)}{d^{2} x - c^{2}}, x\right)"," ",0,"integral((d*sqrt(x)*arccoth(b*x + a) - c*arccoth(b*x + a))/(d^2*x - c^2), x)","F",0
81,0,0,0,0.652953," ","integrate(arccoth(b*x+a)/(c+d/x^(1/2)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{c x \operatorname{arcoth}\left(b x + a\right) - d \sqrt{x} \operatorname{arcoth}\left(b x + a\right)}{c^{2} x - d^{2}}, x\right)"," ",0,"integral((c*x*arccoth(b*x + a) - d*sqrt(x)*arccoth(b*x + a))/(c^2*x - d^2), x)","F",0
82,0,0,0,0.650183," ","integrate(arccoth(e*x+d)/(c*x^2+b*x+a),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{arcoth}\left(e x + d\right)}{c x^{2} + b x + a}, x\right)"," ",0,"integral(arccoth(e*x + d)/(c*x^2 + b*x + a), x)","F",0
83,1,38,0,0.465946," ","integrate(x^2*arccoth(x^(1/2)),x, algorithm=""fricas"")","\frac{1}{6} \, {\left(x^{3} - 1\right)} \log\left(\frac{x + 2 \, \sqrt{x} + 1}{x - 1}\right) + \frac{1}{45} \, {\left(3 \, x^{2} + 5 \, x + 15\right)} \sqrt{x}"," ",0,"1/6*(x^3 - 1)*log((x + 2*sqrt(x) + 1)/(x - 1)) + 1/45*(3*x^2 + 5*x + 15)*sqrt(x)","A",0
84,1,31,0,0.568815," ","integrate(x*arccoth(x^(1/2)),x, algorithm=""fricas"")","\frac{1}{4} \, {\left(x^{2} - 1\right)} \log\left(\frac{x + 2 \, \sqrt{x} + 1}{x - 1}\right) + \frac{1}{6} \, {\left(x + 3\right)} \sqrt{x}"," ",0,"1/4*(x^2 - 1)*log((x + 2*sqrt(x) + 1)/(x - 1)) + 1/6*(x + 3)*sqrt(x)","A",0
85,1,24,0,0.621727," ","integrate(arccoth(x^(1/2)),x, algorithm=""fricas"")","\frac{1}{2} \, {\left(x - 1\right)} \log\left(\frac{x + 2 \, \sqrt{x} + 1}{x - 1}\right) + \sqrt{x}"," ",0,"1/2*(x - 1)*log((x + 2*sqrt(x) + 1)/(x - 1)) + sqrt(x)","A",0
86,0,0,0,0.655976," ","integrate(arccoth(x^(1/2))/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{arcoth}\left(\sqrt{x}\right)}{x}, x\right)"," ",0,"integral(arccoth(sqrt(x))/x, x)","F",0
87,1,30,0,0.492893," ","integrate(arccoth(x^(1/2))/x^2,x, algorithm=""fricas"")","\frac{{\left(x - 1\right)} \log\left(\frac{x + 2 \, \sqrt{x} + 1}{x - 1}\right) - 2 \, \sqrt{x}}{2 \, x}"," ",0,"1/2*((x - 1)*log((x + 2*sqrt(x) + 1)/(x - 1)) - 2*sqrt(x))/x","A",0
88,1,38,0,0.507007," ","integrate(arccoth(x^(1/2))/x^3,x, algorithm=""fricas"")","\frac{3 \, {\left(x^{2} - 1\right)} \log\left(\frac{x + 2 \, \sqrt{x} + 1}{x - 1}\right) - 2 \, {\left(3 \, x + 1\right)} \sqrt{x}}{12 \, x^{2}}"," ",0,"1/12*(3*(x^2 - 1)*log((x + 2*sqrt(x) + 1)/(x - 1)) - 2*(3*x + 1)*sqrt(x))/x^2","A",0
89,1,35,0,1.267912," ","integrate(x^(3/2)*arccoth(x^(1/2)),x, algorithm=""fricas"")","\frac{1}{5} \, x^{\frac{5}{2}} \log\left(\frac{x + 2 \, \sqrt{x} + 1}{x - 1}\right) + \frac{1}{10} \, x^{2} + \frac{1}{5} \, x + \frac{1}{5} \, \log\left(x - 1\right)"," ",0,"1/5*x^(5/2)*log((x + 2*sqrt(x) + 1)/(x - 1)) + 1/10*x^2 + 1/5*x + 1/5*log(x - 1)","A",0
90,1,30,0,0.645459," ","integrate(arccoth(x^(1/2))*x^(1/2),x, algorithm=""fricas"")","\frac{1}{3} \, x^{\frac{3}{2}} \log\left(\frac{x + 2 \, \sqrt{x} + 1}{x - 1}\right) + \frac{1}{3} \, x + \frac{1}{3} \, \log\left(x - 1\right)"," ",0,"1/3*x^(3/2)*log((x + 2*sqrt(x) + 1)/(x - 1)) + 1/3*x + 1/3*log(x - 1)","A",0
91,1,24,0,0.649194," ","integrate(arccoth(x^(1/2))/x^(1/2),x, algorithm=""fricas"")","\sqrt{x} \log\left(\frac{x + 2 \, \sqrt{x} + 1}{x - 1}\right) + \log\left(x - 1\right)"," ",0,"sqrt(x)*log((x + 2*sqrt(x) + 1)/(x - 1)) + log(x - 1)","A",0
92,1,36,0,0.489044," ","integrate(arccoth(x^(1/2))/x^(3/2),x, algorithm=""fricas"")","-\frac{x \log\left(x - 1\right) - x \log\left(x\right) + \sqrt{x} \log\left(\frac{x + 2 \, \sqrt{x} + 1}{x - 1}\right)}{x}"," ",0,"-(x*log(x - 1) - x*log(x) + sqrt(x)*log((x + 2*sqrt(x) + 1)/(x - 1)))/x","A",0
93,0,0,0,0.508496," ","integrate(arccoth(a*x^5)/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{arcoth}\left(a x^{5}\right)}{x}, x\right)"," ",0,"integral(arccoth(a*x^5)/x, x)","F",0
94,1,23,0,0.992208," ","integrate(arccoth(1/x),x, algorithm=""fricas"")","\frac{1}{2} \, x \log\left(-\frac{x + 1}{x - 1}\right) + \frac{1}{2} \, \log\left(x^{2} - 1\right)"," ",0,"1/2*x*log(-(x + 1)/(x - 1)) + 1/2*log(x^2 - 1)","A",0
95,1,128,0,0.581040," ","integrate(arccoth(a*x^n)/x,x, algorithm=""fricas"")","-\frac{n \log\left(a \cosh\left(n \log\left(x\right)\right) + a \sinh\left(n \log\left(x\right)\right) + 1\right) \log\left(x\right) - n \log\left(-a \cosh\left(n \log\left(x\right)\right) - a \sinh\left(n \log\left(x\right)\right) + 1\right) \log\left(x\right) - n \log\left(x\right) \log\left(\frac{a \cosh\left(n \log\left(x\right)\right) + a \sinh\left(n \log\left(x\right)\right) + 1}{a \cosh\left(n \log\left(x\right)\right) + a \sinh\left(n \log\left(x\right)\right) - 1}\right) - {\rm Li}_2\left(a \cosh\left(n \log\left(x\right)\right) + a \sinh\left(n \log\left(x\right)\right)\right) + {\rm Li}_2\left(-a \cosh\left(n \log\left(x\right)\right) - a \sinh\left(n \log\left(x\right)\right)\right)}{2 \, n}"," ",0,"-1/2*(n*log(a*cosh(n*log(x)) + a*sinh(n*log(x)) + 1)*log(x) - n*log(-a*cosh(n*log(x)) - a*sinh(n*log(x)) + 1)*log(x) - n*log(x)*log((a*cosh(n*log(x)) + a*sinh(n*log(x)) + 1)/(a*cosh(n*log(x)) + a*sinh(n*log(x)) - 1)) - dilog(a*cosh(n*log(x)) + a*sinh(n*log(x))) + dilog(-a*cosh(n*log(x)) - a*sinh(n*log(x))))/n","B",0
96,1,44,0,0.568003," ","integrate((b*x+a)*arccoth(b*x+a),x, algorithm=""fricas"")","\frac{2 \, b x + {\left(b^{2} x^{2} + 2 \, a b x + a^{2} - 1\right)} \log\left(\frac{b x + a + 1}{b x + a - 1}\right)}{4 \, b}"," ",0,"1/4*(2*b*x + (b^2*x^2 + 2*a*b*x + a^2 - 1)*log((b*x + a + 1)/(b*x + a - 1)))/b","A",0
97,1,86,0,0.575231," ","integrate((b*x+a)^2*arccoth(b*x+a),x, algorithm=""fricas"")","\frac{b^{2} x^{2} + 2 \, a b x + {\left(a^{3} + 1\right)} \log\left(b x + a + 1\right) - {\left(a^{3} - 1\right)} \log\left(b x + a - 1\right) + {\left(b^{3} x^{3} + 3 \, a b^{2} x^{2} + 3 \, a^{2} b x\right)} \log\left(\frac{b x + a + 1}{b x + a - 1}\right)}{6 \, b}"," ",0,"1/6*(b^2*x^2 + 2*a*b*x + (a^3 + 1)*log(b*x + a + 1) - (a^3 - 1)*log(b*x + a - 1) + (b^3*x^3 + 3*a*b^2*x^2 + 3*a^2*b*x)*log((b*x + a + 1)/(b*x + a - 1)))/b","A",0
98,0,0,0,0.831194," ","integrate(arccoth(b*x+a)/(b*x+a),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{arcoth}\left(b x + a\right)}{b x + a}, x\right)"," ",0,"integral(arccoth(b*x + a)/(b*x + a), x)","F",0
99,1,67,0,0.543056," ","integrate(arccoth(b*x+a)/(b*x+a)^2,x, algorithm=""fricas"")","-\frac{{\left(b x + a\right)} \log\left(b^{2} x^{2} + 2 \, a b x + a^{2} - 1\right) - 2 \, {\left(b x + a\right)} \log\left(b x + a\right) + \log\left(\frac{b x + a + 1}{b x + a - 1}\right)}{2 \, {\left(b^{2} x + a b\right)}}"," ",0,"-1/2*((b*x + a)*log(b^2*x^2 + 2*a*b*x + a^2 - 1) - 2*(b*x + a)*log(b*x + a) + log((b*x + a + 1)/(b*x + a - 1)))/(b^2*x + a*b)","A",0
100,0,0,0,0.551230," ","integrate(arccoth(1+x)/(2+2*x),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{arcoth}\left(x + 1\right)}{2 \, {\left(x + 1\right)}}, x\right)"," ",0,"integral(1/2*arccoth(x + 1)/(x + 1), x)","F",0
101,0,0,0,1.089990," ","integrate(arccoth(b*x+a)/(a*d/b+d*x),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \operatorname{arcoth}\left(b x + a\right)}{b d x + a d}, x\right)"," ",0,"integral(b*arccoth(b*x + a)/(b*d*x + a*d), x)","F",0
102,1,385,0,0.550625," ","integrate((f*x+e)^3*(a+b*arccoth(d*x+c)),x, algorithm=""fricas"")","\frac{6 \, a d^{4} f^{3} x^{4} + 2 \, {\left(12 \, a d^{4} e f^{2} + b d^{3} f^{3}\right)} x^{3} + 6 \, {\left(6 \, a d^{4} e^{2} f + 2 \, b d^{3} e f^{2} - b c d^{2} f^{3}\right)} x^{2} + 6 \, {\left(4 \, a d^{4} e^{3} + 6 \, b d^{3} e^{2} f - 8 \, b c d^{2} e f^{2} + {\left(3 \, b c^{2} + b\right)} d f^{3}\right)} x + 3 \, {\left(4 \, {\left(b c + b\right)} d^{3} e^{3} - 6 \, {\left(b c^{2} + 2 \, b c + b\right)} d^{2} e^{2} f + 4 \, {\left(b c^{3} + 3 \, b c^{2} + 3 \, b c + b\right)} d e f^{2} - {\left(b c^{4} + 4 \, b c^{3} + 6 \, b c^{2} + 4 \, b c + b\right)} f^{3}\right)} \log\left(d x + c + 1\right) - 3 \, {\left(4 \, {\left(b c - b\right)} d^{3} e^{3} - 6 \, {\left(b c^{2} - 2 \, b c + b\right)} d^{2} e^{2} f + 4 \, {\left(b c^{3} - 3 \, b c^{2} + 3 \, b c - b\right)} d e f^{2} - {\left(b c^{4} - 4 \, b c^{3} + 6 \, b c^{2} - 4 \, b c + b\right)} f^{3}\right)} \log\left(d x + c - 1\right) + 3 \, {\left(b d^{4} f^{3} x^{4} + 4 \, b d^{4} e f^{2} x^{3} + 6 \, b d^{4} e^{2} f x^{2} + 4 \, b d^{4} e^{3} x\right)} \log\left(\frac{d x + c + 1}{d x + c - 1}\right)}{24 \, d^{4}}"," ",0,"1/24*(6*a*d^4*f^3*x^4 + 2*(12*a*d^4*e*f^2 + b*d^3*f^3)*x^3 + 6*(6*a*d^4*e^2*f + 2*b*d^3*e*f^2 - b*c*d^2*f^3)*x^2 + 6*(4*a*d^4*e^3 + 6*b*d^3*e^2*f - 8*b*c*d^2*e*f^2 + (3*b*c^2 + b)*d*f^3)*x + 3*(4*(b*c + b)*d^3*e^3 - 6*(b*c^2 + 2*b*c + b)*d^2*e^2*f + 4*(b*c^3 + 3*b*c^2 + 3*b*c + b)*d*e*f^2 - (b*c^4 + 4*b*c^3 + 6*b*c^2 + 4*b*c + b)*f^3)*log(d*x + c + 1) - 3*(4*(b*c - b)*d^3*e^3 - 6*(b*c^2 - 2*b*c + b)*d^2*e^2*f + 4*(b*c^3 - 3*b*c^2 + 3*b*c - b)*d*e*f^2 - (b*c^4 - 4*b*c^3 + 6*b*c^2 - 4*b*c + b)*f^3)*log(d*x + c - 1) + 3*(b*d^4*f^3*x^4 + 4*b*d^4*e*f^2*x^3 + 6*b*d^4*e^2*f*x^2 + 4*b*d^4*e^3*x)*log((d*x + c + 1)/(d*x + c - 1)))/d^4","B",0
103,1,241,0,0.430094," ","integrate((f*x+e)^2*(a+b*arccoth(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, a d^{3} f^{2} x^{3} + {\left(6 \, a d^{3} e f + b d^{2} f^{2}\right)} x^{2} + 2 \, {\left(3 \, a d^{3} e^{2} + 3 \, b d^{2} e f - 2 \, b c d f^{2}\right)} x + {\left(3 \, {\left(b c + b\right)} d^{2} e^{2} - 3 \, {\left(b c^{2} + 2 \, b c + b\right)} d e f + {\left(b c^{3} + 3 \, b c^{2} + 3 \, b c + b\right)} f^{2}\right)} \log\left(d x + c + 1\right) - {\left(3 \, {\left(b c - b\right)} d^{2} e^{2} - 3 \, {\left(b c^{2} - 2 \, b c + b\right)} d e f + {\left(b c^{3} - 3 \, b c^{2} + 3 \, b c - b\right)} f^{2}\right)} \log\left(d x + c - 1\right) + {\left(b d^{3} f^{2} x^{3} + 3 \, b d^{3} e f x^{2} + 3 \, b d^{3} e^{2} x\right)} \log\left(\frac{d x + c + 1}{d x + c - 1}\right)}{6 \, d^{3}}"," ",0,"1/6*(2*a*d^3*f^2*x^3 + (6*a*d^3*e*f + b*d^2*f^2)*x^2 + 2*(3*a*d^3*e^2 + 3*b*d^2*e*f - 2*b*c*d*f^2)*x + (3*(b*c + b)*d^2*e^2 - 3*(b*c^2 + 2*b*c + b)*d*e*f + (b*c^3 + 3*b*c^2 + 3*b*c + b)*f^2)*log(d*x + c + 1) - (3*(b*c - b)*d^2*e^2 - 3*(b*c^2 - 2*b*c + b)*d*e*f + (b*c^3 - 3*b*c^2 + 3*b*c - b)*f^2)*log(d*x + c - 1) + (b*d^3*f^2*x^3 + 3*b*d^3*e*f*x^2 + 3*b*d^3*e^2*x)*log((d*x + c + 1)/(d*x + c - 1)))/d^3","B",0
104,1,133,0,0.453829," ","integrate((f*x+e)*(a+b*arccoth(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, a d^{2} f x^{2} + 2 \, {\left(2 \, a d^{2} e + b d f\right)} x + {\left(2 \, {\left(b c + b\right)} d e - {\left(b c^{2} + 2 \, b c + b\right)} f\right)} \log\left(d x + c + 1\right) - {\left(2 \, {\left(b c - b\right)} d e - {\left(b c^{2} - 2 \, b c + b\right)} f\right)} \log\left(d x + c - 1\right) + {\left(b d^{2} f x^{2} + 2 \, b d^{2} e x\right)} \log\left(\frac{d x + c + 1}{d x + c - 1}\right)}{4 \, d^{2}}"," ",0,"1/4*(2*a*d^2*f*x^2 + 2*(2*a*d^2*e + b*d*f)*x + (2*(b*c + b)*d*e - (b*c^2 + 2*b*c + b)*f)*log(d*x + c + 1) - (2*(b*c - b)*d*e - (b*c^2 - 2*b*c + b)*f)*log(d*x + c - 1) + (b*d^2*f*x^2 + 2*b*d^2*e*x)*log((d*x + c + 1)/(d*x + c - 1)))/d^2","A",0
105,1,60,0,0.876474," ","integrate(a+b*arccoth(d*x+c),x, algorithm=""fricas"")","\frac{b d x \log\left(\frac{d x + c + 1}{d x + c - 1}\right) + 2 \, a d x + {\left(b c + b\right)} \log\left(d x + c + 1\right) - {\left(b c - b\right)} \log\left(d x + c - 1\right)}{2 \, d}"," ",0,"1/2*(b*d*x*log((d*x + c + 1)/(d*x + c - 1)) + 2*a*d*x + (b*c + b)*log(d*x + c + 1) - (b*c - b)*log(d*x + c - 1))/d","A",0
106,0,0,0,0.643935," ","integrate((a+b*arccoth(d*x+c))/(f*x+e),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \operatorname{arcoth}\left(d x + c\right) + a}{f x + e}, x\right)"," ",0,"integral((b*arccoth(d*x + c) + a)/(f*x + e), x)","F",0
107,1,262,0,0.796599," ","integrate((a+b*arccoth(d*x+c))/(f*x+e)^2,x, algorithm=""fricas"")","-\frac{2 \, a d^{2} e^{2} - 4 \, a c d e f + 2 \, {\left(a c^{2} - a\right)} f^{2} - {\left(b d^{2} e^{2} - {\left(b c - b\right)} d e f + {\left(b d^{2} e f - {\left(b c - b\right)} d f^{2}\right)} x\right)} \log\left(d x + c + 1\right) + {\left(b d^{2} e^{2} - {\left(b c + b\right)} d e f + {\left(b d^{2} e f - {\left(b c + b\right)} d f^{2}\right)} x\right)} \log\left(d x + c - 1\right) + 2 \, {\left(b d f^{2} x + b d e f\right)} \log\left(f x + e\right) + {\left(b d^{2} e^{2} - 2 \, b c d e f + {\left(b c^{2} - b\right)} f^{2}\right)} \log\left(\frac{d x + c + 1}{d x + c - 1}\right)}{2 \, {\left(d^{2} e^{3} f - 2 \, c d e^{2} f^{2} + {\left(c^{2} - 1\right)} e f^{3} + {\left(d^{2} e^{2} f^{2} - 2 \, c d e f^{3} + {\left(c^{2} - 1\right)} f^{4}\right)} x\right)}}"," ",0,"-1/2*(2*a*d^2*e^2 - 4*a*c*d*e*f + 2*(a*c^2 - a)*f^2 - (b*d^2*e^2 - (b*c - b)*d*e*f + (b*d^2*e*f - (b*c - b)*d*f^2)*x)*log(d*x + c + 1) + (b*d^2*e^2 - (b*c + b)*d*e*f + (b*d^2*e*f - (b*c + b)*d*f^2)*x)*log(d*x + c - 1) + 2*(b*d*f^2*x + b*d*e*f)*log(f*x + e) + (b*d^2*e^2 - 2*b*c*d*e*f + (b*c^2 - b)*f^2)*log((d*x + c + 1)/(d*x + c - 1)))/(d^2*e^3*f - 2*c*d*e^2*f^2 + (c^2 - 1)*e*f^3 + (d^2*e^2*f^2 - 2*c*d*e*f^3 + (c^2 - 1)*f^4)*x)","B",0
108,1,833,0,1.699806," ","integrate((a+b*arccoth(d*x+c))/(f*x+e)^3,x, algorithm=""fricas"")","-\frac{2 \, a d^{4} e^{4} - 2 \, {\left(4 \, a c + b\right)} d^{3} e^{3} f + 4 \, {\left(3 \, a c^{2} + b c - a\right)} d^{2} e^{2} f^{2} - 2 \, {\left(4 \, a c^{3} + b c^{2} - 4 \, a c - b\right)} d e f^{3} + 2 \, {\left(a c^{4} - 2 \, a c^{2} + a\right)} f^{4} - 2 \, {\left(b d^{3} e^{2} f^{2} - 2 \, b c d^{2} e f^{3} + {\left(b c^{2} - b\right)} d f^{4}\right)} x - {\left(b d^{4} e^{4} - 2 \, {\left(b c - b\right)} d^{3} e^{3} f + {\left(b c^{2} - 2 \, b c + b\right)} d^{2} e^{2} f^{2} + {\left(b d^{4} e^{2} f^{2} - 2 \, {\left(b c - b\right)} d^{3} e f^{3} + {\left(b c^{2} - 2 \, b c + b\right)} d^{2} f^{4}\right)} x^{2} + 2 \, {\left(b d^{4} e^{3} f - 2 \, {\left(b c - b\right)} d^{3} e^{2} f^{2} + {\left(b c^{2} - 2 \, b c + b\right)} d^{2} e f^{3}\right)} x\right)} \log\left(d x + c + 1\right) + {\left(b d^{4} e^{4} - 2 \, {\left(b c + b\right)} d^{3} e^{3} f + {\left(b c^{2} + 2 \, b c + b\right)} d^{2} e^{2} f^{2} + {\left(b d^{4} e^{2} f^{2} - 2 \, {\left(b c + b\right)} d^{3} e f^{3} + {\left(b c^{2} + 2 \, b c + b\right)} d^{2} f^{4}\right)} x^{2} + 2 \, {\left(b d^{4} e^{3} f - 2 \, {\left(b c + b\right)} d^{3} e^{2} f^{2} + {\left(b c^{2} + 2 \, b c + b\right)} d^{2} e f^{3}\right)} x\right)} \log\left(d x + c - 1\right) + 4 \, {\left(b d^{3} e^{3} f - b c d^{2} e^{2} f^{2} + {\left(b d^{3} e f^{3} - b c d^{2} f^{4}\right)} x^{2} + 2 \, {\left(b d^{3} e^{2} f^{2} - b c d^{2} e f^{3}\right)} x\right)} \log\left(f x + e\right) + {\left(b d^{4} e^{4} - 4 \, b c d^{3} e^{3} f + 2 \, {\left(3 \, b c^{2} - b\right)} d^{2} e^{2} f^{2} - 4 \, {\left(b c^{3} - b c\right)} d e f^{3} + {\left(b c^{4} - 2 \, b c^{2} + b\right)} f^{4}\right)} \log\left(\frac{d x + c + 1}{d x + c - 1}\right)}{4 \, {\left(d^{4} e^{6} f - 4 \, c d^{3} e^{5} f^{2} + 2 \, {\left(3 \, c^{2} - 1\right)} d^{2} e^{4} f^{3} - 4 \, {\left(c^{3} - c\right)} d e^{3} f^{4} + {\left(c^{4} - 2 \, c^{2} + 1\right)} e^{2} f^{5} + {\left(d^{4} e^{4} f^{3} - 4 \, c d^{3} e^{3} f^{4} + 2 \, {\left(3 \, c^{2} - 1\right)} d^{2} e^{2} f^{5} - 4 \, {\left(c^{3} - c\right)} d e f^{6} + {\left(c^{4} - 2 \, c^{2} + 1\right)} f^{7}\right)} x^{2} + 2 \, {\left(d^{4} e^{5} f^{2} - 4 \, c d^{3} e^{4} f^{3} + 2 \, {\left(3 \, c^{2} - 1\right)} d^{2} e^{3} f^{4} - 4 \, {\left(c^{3} - c\right)} d e^{2} f^{5} + {\left(c^{4} - 2 \, c^{2} + 1\right)} e f^{6}\right)} x\right)}}"," ",0,"-1/4*(2*a*d^4*e^4 - 2*(4*a*c + b)*d^3*e^3*f + 4*(3*a*c^2 + b*c - a)*d^2*e^2*f^2 - 2*(4*a*c^3 + b*c^2 - 4*a*c - b)*d*e*f^3 + 2*(a*c^4 - 2*a*c^2 + a)*f^4 - 2*(b*d^3*e^2*f^2 - 2*b*c*d^2*e*f^3 + (b*c^2 - b)*d*f^4)*x - (b*d^4*e^4 - 2*(b*c - b)*d^3*e^3*f + (b*c^2 - 2*b*c + b)*d^2*e^2*f^2 + (b*d^4*e^2*f^2 - 2*(b*c - b)*d^3*e*f^3 + (b*c^2 - 2*b*c + b)*d^2*f^4)*x^2 + 2*(b*d^4*e^3*f - 2*(b*c - b)*d^3*e^2*f^2 + (b*c^2 - 2*b*c + b)*d^2*e*f^3)*x)*log(d*x + c + 1) + (b*d^4*e^4 - 2*(b*c + b)*d^3*e^3*f + (b*c^2 + 2*b*c + b)*d^2*e^2*f^2 + (b*d^4*e^2*f^2 - 2*(b*c + b)*d^3*e*f^3 + (b*c^2 + 2*b*c + b)*d^2*f^4)*x^2 + 2*(b*d^4*e^3*f - 2*(b*c + b)*d^3*e^2*f^2 + (b*c^2 + 2*b*c + b)*d^2*e*f^3)*x)*log(d*x + c - 1) + 4*(b*d^3*e^3*f - b*c*d^2*e^2*f^2 + (b*d^3*e*f^3 - b*c*d^2*f^4)*x^2 + 2*(b*d^3*e^2*f^2 - b*c*d^2*e*f^3)*x)*log(f*x + e) + (b*d^4*e^4 - 4*b*c*d^3*e^3*f + 2*(3*b*c^2 - b)*d^2*e^2*f^2 - 4*(b*c^3 - b*c)*d*e*f^3 + (b*c^4 - 2*b*c^2 + b)*f^4)*log((d*x + c + 1)/(d*x + c - 1)))/(d^4*e^6*f - 4*c*d^3*e^5*f^2 + 2*(3*c^2 - 1)*d^2*e^4*f^3 - 4*(c^3 - c)*d*e^3*f^4 + (c^4 - 2*c^2 + 1)*e^2*f^5 + (d^4*e^4*f^3 - 4*c*d^3*e^3*f^4 + 2*(3*c^2 - 1)*d^2*e^2*f^5 - 4*(c^3 - c)*d*e*f^6 + (c^4 - 2*c^2 + 1)*f^7)*x^2 + 2*(d^4*e^5*f^2 - 4*c*d^3*e^4*f^3 + 2*(3*c^2 - 1)*d^2*e^3*f^4 - 4*(c^3 - c)*d*e^2*f^5 + (c^4 - 2*c^2 + 1)*e*f^6)*x)","B",0
109,0,0,0,0.582610," ","integrate((f*x+e)^2*(a+b*arccoth(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(a^{2} f^{2} x^{2} + 2 \, a^{2} e f x + a^{2} e^{2} + {\left(b^{2} f^{2} x^{2} + 2 \, b^{2} e f x + b^{2} e^{2}\right)} \operatorname{arcoth}\left(d x + c\right)^{2} + 2 \, {\left(a b f^{2} x^{2} + 2 \, a b e f x + a b e^{2}\right)} \operatorname{arcoth}\left(d x + c\right), x\right)"," ",0,"integral(a^2*f^2*x^2 + 2*a^2*e*f*x + a^2*e^2 + (b^2*f^2*x^2 + 2*b^2*e*f*x + b^2*e^2)*arccoth(d*x + c)^2 + 2*(a*b*f^2*x^2 + 2*a*b*e*f*x + a*b*e^2)*arccoth(d*x + c), x)","F",0
110,0,0,0,0.395783," ","integrate((f*x+e)*(a+b*arccoth(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(a^{2} f x + a^{2} e + {\left(b^{2} f x + b^{2} e\right)} \operatorname{arcoth}\left(d x + c\right)^{2} + 2 \, {\left(a b f x + a b e\right)} \operatorname{arcoth}\left(d x + c\right), x\right)"," ",0,"integral(a^2*f*x + a^2*e + (b^2*f*x + b^2*e)*arccoth(d*x + c)^2 + 2*(a*b*f*x + a*b*e)*arccoth(d*x + c), x)","F",0
111,0,0,0,0.452870," ","integrate((a+b*arccoth(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(b^{2} \operatorname{arcoth}\left(d x + c\right)^{2} + 2 \, a b \operatorname{arcoth}\left(d x + c\right) + a^{2}, x\right)"," ",0,"integral(b^2*arccoth(d*x + c)^2 + 2*a*b*arccoth(d*x + c) + a^2, x)","F",0
112,0,0,0,0.486463," ","integrate((a+b*arccoth(d*x+c))^2/(f*x+e),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} \operatorname{arcoth}\left(d x + c\right)^{2} + 2 \, a b \operatorname{arcoth}\left(d x + c\right) + a^{2}}{f x + e}, x\right)"," ",0,"integral((b^2*arccoth(d*x + c)^2 + 2*a*b*arccoth(d*x + c) + a^2)/(f*x + e), x)","F",0
113,0,0,0,0.527347," ","integrate((a+b*arccoth(d*x+c))^2/(f*x+e)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} \operatorname{arcoth}\left(d x + c\right)^{2} + 2 \, a b \operatorname{arcoth}\left(d x + c\right) + a^{2}}{f^{2} x^{2} + 2 \, e f x + e^{2}}, x\right)"," ",0,"integral((b^2*arccoth(d*x + c)^2 + 2*a*b*arccoth(d*x + c) + a^2)/(f^2*x^2 + 2*e*f*x + e^2), x)","F",0
114,0,0,0,0.440284," ","integrate((f*x+e)^2*(a+b*arccoth(d*x+c))^3,x, algorithm=""fricas"")","{\rm integral}\left(a^{3} f^{2} x^{2} + 2 \, a^{3} e f x + a^{3} e^{2} + {\left(b^{3} f^{2} x^{2} + 2 \, b^{3} e f x + b^{3} e^{2}\right)} \operatorname{arcoth}\left(d x + c\right)^{3} + 3 \, {\left(a b^{2} f^{2} x^{2} + 2 \, a b^{2} e f x + a b^{2} e^{2}\right)} \operatorname{arcoth}\left(d x + c\right)^{2} + 3 \, {\left(a^{2} b f^{2} x^{2} + 2 \, a^{2} b e f x + a^{2} b e^{2}\right)} \operatorname{arcoth}\left(d x + c\right), x\right)"," ",0,"integral(a^3*f^2*x^2 + 2*a^3*e*f*x + a^3*e^2 + (b^3*f^2*x^2 + 2*b^3*e*f*x + b^3*e^2)*arccoth(d*x + c)^3 + 3*(a*b^2*f^2*x^2 + 2*a*b^2*e*f*x + a*b^2*e^2)*arccoth(d*x + c)^2 + 3*(a^2*b*f^2*x^2 + 2*a^2*b*e*f*x + a^2*b*e^2)*arccoth(d*x + c), x)","F",0
115,0,0,0,0.648724," ","integrate((f*x+e)*(a+b*arccoth(d*x+c))^3,x, algorithm=""fricas"")","{\rm integral}\left(a^{3} f x + a^{3} e + {\left(b^{3} f x + b^{3} e\right)} \operatorname{arcoth}\left(d x + c\right)^{3} + 3 \, {\left(a b^{2} f x + a b^{2} e\right)} \operatorname{arcoth}\left(d x + c\right)^{2} + 3 \, {\left(a^{2} b f x + a^{2} b e\right)} \operatorname{arcoth}\left(d x + c\right), x\right)"," ",0,"integral(a^3*f*x + a^3*e + (b^3*f*x + b^3*e)*arccoth(d*x + c)^3 + 3*(a*b^2*f*x + a*b^2*e)*arccoth(d*x + c)^2 + 3*(a^2*b*f*x + a^2*b*e)*arccoth(d*x + c), x)","F",0
116,0,0,0,0.594971," ","integrate((a+b*arccoth(d*x+c))^3,x, algorithm=""fricas"")","{\rm integral}\left(b^{3} \operatorname{arcoth}\left(d x + c\right)^{3} + 3 \, a b^{2} \operatorname{arcoth}\left(d x + c\right)^{2} + 3 \, a^{2} b \operatorname{arcoth}\left(d x + c\right) + a^{3}, x\right)"," ",0,"integral(b^3*arccoth(d*x + c)^3 + 3*a*b^2*arccoth(d*x + c)^2 + 3*a^2*b*arccoth(d*x + c) + a^3, x)","F",0
117,0,0,0,0.671602," ","integrate((a+b*arccoth(d*x+c))^3/(f*x+e),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{3} \operatorname{arcoth}\left(d x + c\right)^{3} + 3 \, a b^{2} \operatorname{arcoth}\left(d x + c\right)^{2} + 3 \, a^{2} b \operatorname{arcoth}\left(d x + c\right) + a^{3}}{f x + e}, x\right)"," ",0,"integral((b^3*arccoth(d*x + c)^3 + 3*a*b^2*arccoth(d*x + c)^2 + 3*a^2*b*arccoth(d*x + c) + a^3)/(f*x + e), x)","F",0
118,0,0,0,0.555992," ","integrate((a+b*arccoth(d*x+c))^3/(f*x+e)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{3} \operatorname{arcoth}\left(d x + c\right)^{3} + 3 \, a b^{2} \operatorname{arcoth}\left(d x + c\right)^{2} + 3 \, a^{2} b \operatorname{arcoth}\left(d x + c\right) + a^{3}}{f^{2} x^{2} + 2 \, e f x + e^{2}}, x\right)"," ",0,"integral((b^3*arccoth(d*x + c)^3 + 3*a*b^2*arccoth(d*x + c)^2 + 3*a^2*b*arccoth(d*x + c) + a^3)/(f^2*x^2 + 2*e*f*x + e^2), x)","F",0
119,0,0,0,0.393939," ","integrate((f*x+e)^m*(a+b*arccoth(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(b \operatorname{arcoth}\left(d x + c\right) + a\right)} {\left(f x + e\right)}^{m}, x\right)"," ",0,"integral((b*arccoth(d*x + c) + a)*(f*x + e)^m, x)","F",0
120,0,0,0,0.481117," ","integrate((f*x+e)^m*(a+b*arccoth(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{2} \operatorname{arcoth}\left(d x + c\right)^{2} + 2 \, a b \operatorname{arcoth}\left(d x + c\right) + a^{2}\right)} {\left(f x + e\right)}^{m}, x\right)"," ",0,"integral((b^2*arccoth(d*x + c)^2 + 2*a*b*arccoth(d*x + c) + a^2)*(f*x + e)^m, x)","F",0
121,0,0,0,0.621035," ","integrate((f*x+e)^m*(a+b*arccoth(d*x+c))^3,x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{3} \operatorname{arcoth}\left(d x + c\right)^{3} + 3 \, a b^{2} \operatorname{arcoth}\left(d x + c\right)^{2} + 3 \, a^{2} b \operatorname{arcoth}\left(d x + c\right) + a^{3}\right)} {\left(f x + e\right)}^{m}, x\right)"," ",0,"integral((b^3*arccoth(d*x + c)^3 + 3*a*b^2*arccoth(d*x + c)^2 + 3*a^2*b*arccoth(d*x + c) + a^3)*(f*x + e)^m, x)","F",0
122,0,0,0,0.842203," ","integrate((a+b*arccoth((-c*x+1)^(1/2)/(c*x+1)^(1/2)))^n/(-c^2*x^2+1),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(b \operatorname{arcoth}\left(\frac{\sqrt{-c x + 1}}{\sqrt{c x + 1}}\right) + a\right)}^{n}}{c^{2} x^{2} - 1}, x\right)"," ",0,"integral(-(b*arccoth(sqrt(-c*x + 1)/sqrt(c*x + 1)) + a)^n/(c^2*x^2 - 1), x)","F",0
123,0,0,0,0.435762," ","integrate((a+b*arccoth((-c*x+1)^(1/2)/(c*x+1)^(1/2)))^3/(-c^2*x^2+1),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{b^{3} \operatorname{arcoth}\left(\frac{\sqrt{-c x + 1}}{\sqrt{c x + 1}}\right)^{3} + 3 \, a b^{2} \operatorname{arcoth}\left(\frac{\sqrt{-c x + 1}}{\sqrt{c x + 1}}\right)^{2} + 3 \, a^{2} b \operatorname{arcoth}\left(\frac{\sqrt{-c x + 1}}{\sqrt{c x + 1}}\right) + a^{3}}{c^{2} x^{2} - 1}, x\right)"," ",0,"integral(-(b^3*arccoth(sqrt(-c*x + 1)/sqrt(c*x + 1))^3 + 3*a*b^2*arccoth(sqrt(-c*x + 1)/sqrt(c*x + 1))^2 + 3*a^2*b*arccoth(sqrt(-c*x + 1)/sqrt(c*x + 1)) + a^3)/(c^2*x^2 - 1), x)","F",0
124,0,0,0,0.617313," ","integrate((a+b*arccoth((-c*x+1)^(1/2)/(c*x+1)^(1/2)))^2/(-c^2*x^2+1),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{b^{2} \operatorname{arcoth}\left(\frac{\sqrt{-c x + 1}}{\sqrt{c x + 1}}\right)^{2} + 2 \, a b \operatorname{arcoth}\left(\frac{\sqrt{-c x + 1}}{\sqrt{c x + 1}}\right) + a^{2}}{c^{2} x^{2} - 1}, x\right)"," ",0,"integral(-(b^2*arccoth(sqrt(-c*x + 1)/sqrt(c*x + 1))^2 + 2*a*b*arccoth(sqrt(-c*x + 1)/sqrt(c*x + 1)) + a^2)/(c^2*x^2 - 1), x)","F",0
125,0,0,0,0.712399," ","integrate((a+b*arccoth((-c*x+1)^(1/2)/(c*x+1)^(1/2)))/(-c^2*x^2+1),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{b \operatorname{arcoth}\left(\frac{\sqrt{-c x + 1}}{\sqrt{c x + 1}}\right) + a}{c^{2} x^{2} - 1}, x\right)"," ",0,"integral(-(b*arccoth(sqrt(-c*x + 1)/sqrt(c*x + 1)) + a)/(c^2*x^2 - 1), x)","F",0
126,0,0,0,0.557664," ","integrate(1/(-c^2*x^2+1)/(a+b*arccoth((-c*x+1)^(1/2)/(c*x+1)^(1/2))),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{1}{a c^{2} x^{2} + {\left(b c^{2} x^{2} - b\right)} \operatorname{arcoth}\left(\frac{\sqrt{-c x + 1}}{\sqrt{c x + 1}}\right) - a}, x\right)"," ",0,"integral(-1/(a*c^2*x^2 + (b*c^2*x^2 - b)*arccoth(sqrt(-c*x + 1)/sqrt(c*x + 1)) - a), x)","F",0
127,0,0,0,0.480555," ","integrate(1/(-c^2*x^2+1)/(a+b*arccoth((-c*x+1)^(1/2)/(c*x+1)^(1/2)))^2,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{1}{a^{2} c^{2} x^{2} + {\left(b^{2} c^{2} x^{2} - b^{2}\right)} \operatorname{arcoth}\left(\frac{\sqrt{-c x + 1}}{\sqrt{c x + 1}}\right)^{2} - a^{2} + 2 \, {\left(a b c^{2} x^{2} - a b\right)} \operatorname{arcoth}\left(\frac{\sqrt{-c x + 1}}{\sqrt{c x + 1}}\right)}, x\right)"," ",0,"integral(-1/(a^2*c^2*x^2 + (b^2*c^2*x^2 - b^2)*arccoth(sqrt(-c*x + 1)/sqrt(c*x + 1))^2 - a^2 + 2*(a*b*c^2*x^2 - a*b)*arccoth(sqrt(-c*x + 1)/sqrt(c*x + 1))), x)","F",0
128,1,33,0,0.538353," ","integrate(x^m*arccoth(tanh(b*x+a)),x, algorithm=""fricas"")","\frac{{\left({\left(b m + b\right)} x^{2} + {\left(a m + 2 \, a\right)} x\right)} x^{m}}{m^{2} + 3 \, m + 2}"," ",0,"((b*m + b)*x^2 + (a*m + 2*a)*x)*x^m/(m^2 + 3*m + 2)","A",0
129,1,13,0,0.636660," ","integrate(x^2*arccoth(tanh(b*x+a)),x, algorithm=""fricas"")","\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
130,1,13,0,0.446440," ","integrate(x*arccoth(tanh(b*x+a)),x, algorithm=""fricas"")","\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
131,1,10,0,0.427912," ","integrate(arccoth(tanh(b*x+a)),x, algorithm=""fricas"")","\frac{1}{2} \, b x^{2} + a x"," ",0,"1/2*b*x^2 + a*x","A",0
132,1,8,0,0.475444," ","integrate(arccoth(tanh(b*x+a))/x,x, algorithm=""fricas"")","b x + a \log\left(x\right)"," ",0,"b*x + a*log(x)","A",0
133,1,13,0,0.938939," ","integrate(arccoth(tanh(b*x+a))/x^2,x, algorithm=""fricas"")","\frac{b x \log\left(x\right) - a}{x}"," ",0,"(b*x*log(x) - a)/x","A",0
134,1,11,0,1.206513," ","integrate(arccoth(tanh(b*x+a))/x^3,x, algorithm=""fricas"")","-\frac{2 \, b x + a}{2 \, x^{2}}"," ",0,"-1/2*(2*b*x + a)/x^2","A",0
135,1,13,0,0.570920," ","integrate(arccoth(tanh(b*x+a))/x^4,x, algorithm=""fricas"")","-\frac{3 \, b x + 2 \, a}{6 \, x^{3}}"," ",0,"-1/6*(3*b*x + 2*a)/x^3","A",0
136,1,101,0,0.500943," ","integrate(x^m*arccoth(tanh(b*x+a))^2,x, algorithm=""fricas"")","\frac{{\left(4 \, {\left(b^{2} m^{2} + 3 \, b^{2} m + 2 \, b^{2}\right)} x^{3} + 8 \, {\left(a b m^{2} + 4 \, a b m + 3 \, a b\right)} x^{2} + {\left(4 \, a^{2} m^{2} - \pi^{2} {\left(m^{2} + 5 \, m + 6\right)} + 20 \, a^{2} m + 24 \, a^{2}\right)} x\right)} x^{m}}{4 \, {\left(m^{3} + 6 \, m^{2} + 11 \, m + 6\right)}}"," ",0,"1/4*(4*(b^2*m^2 + 3*b^2*m + 2*b^2)*x^3 + 8*(a*b*m^2 + 4*a*b*m + 3*a*b)*x^2 + (4*a^2*m^2 - pi^2*(m^2 + 5*m + 6) + 20*a^2*m + 24*a^2)*x)*x^m/(m^3 + 6*m^2 + 11*m + 6)","A",0
137,1,30,0,0.575428," ","integrate(x^3*arccoth(tanh(b*x+a))^2,x, algorithm=""fricas"")","\frac{1}{6} \, b^{2} x^{6} + \frac{2}{5} \, a b x^{5} - \frac{1}{16} \, {\left(\pi^{2} - 4 \, a^{2}\right)} x^{4}"," ",0,"1/6*b^2*x^6 + 2/5*a*b*x^5 - 1/16*(pi^2 - 4*a^2)*x^4","A",0
138,1,30,0,0.527239," ","integrate(x^2*arccoth(tanh(b*x+a))^2,x, algorithm=""fricas"")","\frac{1}{5} \, b^{2} x^{5} + \frac{1}{2} \, a b x^{4} - \frac{1}{12} \, {\left(\pi^{2} - 4 \, a^{2}\right)} x^{3}"," ",0,"1/5*b^2*x^5 + 1/2*a*b*x^4 - 1/12*(pi^2 - 4*a^2)*x^3","A",0
139,1,30,0,0.666604," ","integrate(x*arccoth(tanh(b*x+a))^2,x, algorithm=""fricas"")","\frac{1}{4} \, b^{2} x^{4} + \frac{2}{3} \, a b x^{3} - \frac{1}{8} \, {\left(\pi^{2} - 4 \, a^{2}\right)} x^{2}"," ",0,"1/4*b^2*x^4 + 2/3*a*b*x^3 - 1/8*(pi^2 - 4*a^2)*x^2","A",0
140,1,27,0,0.630510," ","integrate(arccoth(tanh(b*x+a))^2,x, algorithm=""fricas"")","\frac{1}{3} \, b^{2} x^{3} + a b x^{2} - \frac{1}{4} \, {\left(\pi^{2} - 4 \, a^{2}\right)} x"," ",0,"1/3*b^2*x^3 + a*b*x^2 - 1/4*(pi^2 - 4*a^2)*x","A",0
141,1,27,0,0.616641," ","integrate(arccoth(tanh(b*x+a))^2/x,x, algorithm=""fricas"")","\frac{1}{2} \, b^{2} x^{2} + 2 \, a b x - \frac{1}{4} \, {\left(\pi^{2} - 4 \, a^{2}\right)} \log\left(x\right)"," ",0,"1/2*b^2*x^2 + 2*a*b*x - 1/4*(pi^2 - 4*a^2)*log(x)","A",0
142,1,29,0,0.581441," ","integrate(arccoth(tanh(b*x+a))^2/x^2,x, algorithm=""fricas"")","\frac{4 \, b^{2} x^{2} + 8 \, a b x \log\left(x\right) + \pi^{2} - 4 \, a^{2}}{4 \, x}"," ",0,"1/4*(4*b^2*x^2 + 8*a*b*x*log(x) + pi^2 - 4*a^2)/x","A",0
143,1,29,0,0.420689," ","integrate(arccoth(tanh(b*x+a))^2/x^3,x, algorithm=""fricas"")","\frac{8 \, b^{2} x^{2} \log\left(x\right) - 16 \, a b x + \pi^{2} - 4 \, a^{2}}{8 \, x^{2}}"," ",0,"1/8*(8*b^2*x^2*log(x) - 16*a*b*x + pi^2 - 4*a^2)/x^2","A",0
144,1,29,0,1.438517," ","integrate(arccoth(tanh(b*x+a))^2/x^4,x, algorithm=""fricas"")","-\frac{12 \, b^{2} x^{2} + 12 \, a b x - \pi^{2} + 4 \, a^{2}}{12 \, x^{3}}"," ",0,"-1/12*(12*b^2*x^2 + 12*a*b*x - pi^2 + 4*a^2)/x^3","A",0
145,1,29,0,0.614856," ","integrate(arccoth(tanh(b*x+a))^2/x^5,x, algorithm=""fricas"")","-\frac{24 \, b^{2} x^{2} + 32 \, a b x - 3 \, \pi^{2} + 12 \, a^{2}}{48 \, x^{4}}"," ",0,"-1/48*(24*b^2*x^2 + 32*a*b*x - 3*pi^2 + 12*a^2)/x^4","A",0
146,1,209,0,0.615972," ","integrate(x^m*arccoth(tanh(b*x+a))^3,x, algorithm=""fricas"")","\frac{{\left(4 \, {\left(b^{3} m^{3} + 6 \, b^{3} m^{2} + 11 \, b^{3} m + 6 \, b^{3}\right)} x^{4} + 12 \, {\left(a b^{2} m^{3} + 7 \, a b^{2} m^{2} + 14 \, a b^{2} m + 8 \, a b^{2}\right)} x^{3} + 3 \, {\left(4 \, a^{2} b m^{3} + 32 \, a^{2} b m^{2} + 76 \, a^{2} b m - \pi^{2} {\left(b m^{3} + 8 \, b m^{2} + 19 \, b m + 12 \, b\right)} + 48 \, a^{2} b\right)} x^{2} + {\left(4 \, a^{3} m^{3} + 36 \, a^{3} m^{2} + 104 \, a^{3} m - 3 \, \pi^{2} {\left(a m^{3} + 9 \, a m^{2} + 26 \, a m + 24 \, a\right)} + 96 \, a^{3}\right)} x\right)} x^{m}}{4 \, {\left(m^{4} + 10 \, m^{3} + 35 \, m^{2} + 50 \, m + 24\right)}}"," ",0,"1/4*(4*(b^3*m^3 + 6*b^3*m^2 + 11*b^3*m + 6*b^3)*x^4 + 12*(a*b^2*m^3 + 7*a*b^2*m^2 + 14*a*b^2*m + 8*a*b^2)*x^3 + 3*(4*a^2*b*m^3 + 32*a^2*b*m^2 + 76*a^2*b*m - pi^2*(b*m^3 + 8*b*m^2 + 19*b*m + 12*b) + 48*a^2*b)*x^2 + (4*a^3*m^3 + 36*a^3*m^2 + 104*a^3*m - 3*pi^2*(a*m^3 + 9*a*m^2 + 26*a*m + 24*a) + 96*a^3)*x)*x^m/(m^4 + 10*m^3 + 35*m^2 + 50*m + 24)","A",0
147,1,52,0,0.624479," ","integrate(x^4*arccoth(tanh(b*x+a))^3,x, algorithm=""fricas"")","\frac{1}{8} \, b^{3} x^{8} + \frac{3}{7} \, a b^{2} x^{7} - \frac{1}{8} \, {\left(\pi^{2} b - 4 \, a^{2} b\right)} x^{6} - \frac{1}{20} \, {\left(3 \, \pi^{2} a - 4 \, a^{3}\right)} x^{5}"," ",0,"1/8*b^3*x^8 + 3/7*a*b^2*x^7 - 1/8*(pi^2*b - 4*a^2*b)*x^6 - 1/20*(3*pi^2*a - 4*a^3)*x^5","A",0
148,1,52,0,0.461456," ","integrate(x^3*arccoth(tanh(b*x+a))^3,x, algorithm=""fricas"")","\frac{1}{7} \, b^{3} x^{7} + \frac{1}{2} \, a b^{2} x^{6} - \frac{3}{20} \, {\left(\pi^{2} b - 4 \, a^{2} b\right)} x^{5} - \frac{1}{16} \, {\left(3 \, \pi^{2} a - 4 \, a^{3}\right)} x^{4}"," ",0,"1/7*b^3*x^7 + 1/2*a*b^2*x^6 - 3/20*(pi^2*b - 4*a^2*b)*x^5 - 1/16*(3*pi^2*a - 4*a^3)*x^4","A",0
149,1,52,0,0.714249," ","integrate(x^2*arccoth(tanh(b*x+a))^3,x, algorithm=""fricas"")","\frac{1}{6} \, b^{3} x^{6} + \frac{3}{5} \, a b^{2} x^{5} - \frac{3}{16} \, {\left(\pi^{2} b - 4 \, a^{2} b\right)} x^{4} - \frac{1}{12} \, {\left(3 \, \pi^{2} a - 4 \, a^{3}\right)} x^{3}"," ",0,"1/6*b^3*x^6 + 3/5*a*b^2*x^5 - 3/16*(pi^2*b - 4*a^2*b)*x^4 - 1/12*(3*pi^2*a - 4*a^3)*x^3","A",0
150,1,52,0,0.550473," ","integrate(x*arccoth(tanh(b*x+a))^3,x, algorithm=""fricas"")","\frac{1}{5} \, b^{3} x^{5} + \frac{3}{4} \, a b^{2} x^{4} - \frac{1}{4} \, {\left(\pi^{2} b - 4 \, a^{2} b\right)} x^{3} - \frac{1}{8} \, {\left(3 \, \pi^{2} a - 4 \, a^{3}\right)} x^{2}"," ",0,"1/5*b^3*x^5 + 3/4*a*b^2*x^4 - 1/4*(pi^2*b - 4*a^2*b)*x^3 - 1/8*(3*pi^2*a - 4*a^3)*x^2","A",0
151,1,49,0,0.927890," ","integrate(arccoth(tanh(b*x+a))^3,x, algorithm=""fricas"")","\frac{1}{4} \, b^{3} x^{4} + a b^{2} x^{3} - \frac{3}{8} \, {\left(\pi^{2} b - 4 \, a^{2} b\right)} x^{2} - \frac{1}{4} \, {\left(3 \, \pi^{2} a - 4 \, a^{3}\right)} x"," ",0,"1/4*b^3*x^4 + a*b^2*x^3 - 3/8*(pi^2*b - 4*a^2*b)*x^2 - 1/4*(3*pi^2*a - 4*a^3)*x","B",0
152,1,49,0,0.672671," ","integrate(arccoth(tanh(b*x+a))^3/x,x, algorithm=""fricas"")","\frac{1}{3} \, b^{3} x^{3} + \frac{3}{2} \, a b^{2} x^{2} - \frac{3}{4} \, {\left(\pi^{2} b - 4 \, a^{2} b\right)} x - \frac{1}{4} \, {\left(3 \, \pi^{2} a - 4 \, a^{3}\right)} \log\left(x\right)"," ",0,"1/3*b^3*x^3 + 3/2*a*b^2*x^2 - 3/4*(pi^2*b - 4*a^2*b)*x - 1/4*(3*pi^2*a - 4*a^3)*log(x)","A",0
153,1,51,0,0.460810," ","integrate(arccoth(tanh(b*x+a))^3/x^2,x, algorithm=""fricas"")","\frac{2 \, b^{3} x^{3} + 12 \, a b^{2} x^{2} + 3 \, \pi^{2} a - 4 \, a^{3} - 3 \, {\left(\pi^{2} b - 4 \, a^{2} b\right)} x \log\left(x\right)}{4 \, x}"," ",0,"1/4*(2*b^3*x^3 + 12*a*b^2*x^2 + 3*pi^2*a - 4*a^3 - 3*(pi^2*b - 4*a^2*b)*x*log(x))/x","A",0
154,1,51,0,0.513840," ","integrate(arccoth(tanh(b*x+a))^3/x^3,x, algorithm=""fricas"")","\frac{8 \, b^{3} x^{3} + 24 \, a b^{2} x^{2} \log\left(x\right) + 3 \, \pi^{2} a - 4 \, a^{3} + 6 \, {\left(\pi^{2} b - 4 \, a^{2} b\right)} x}{8 \, x^{2}}"," ",0,"1/8*(8*b^3*x^3 + 24*a*b^2*x^2*log(x) + 3*pi^2*a - 4*a^3 + 6*(pi^2*b - 4*a^2*b)*x)/x^2","A",0
155,1,51,0,0.924982," ","integrate(arccoth(tanh(b*x+a))^3/x^4,x, algorithm=""fricas"")","\frac{24 \, b^{3} x^{3} \log\left(x\right) - 72 \, a b^{2} x^{2} + 6 \, \pi^{2} a - 8 \, a^{3} + 9 \, {\left(\pi^{2} b - 4 \, a^{2} b\right)} x}{24 \, x^{3}}"," ",0,"1/24*(24*b^3*x^3*log(x) - 72*a*b^2*x^2 + 6*pi^2*a - 8*a^3 + 9*(pi^2*b - 4*a^2*b)*x)/x^3","A",0
156,1,49,0,0.468190," ","integrate(arccoth(tanh(b*x+a))^3/x^5,x, algorithm=""fricas"")","-\frac{16 \, b^{3} x^{3} + 24 \, a b^{2} x^{2} - 3 \, \pi^{2} a + 4 \, a^{3} - 4 \, {\left(\pi^{2} b - 4 \, a^{2} b\right)} x}{16 \, x^{4}}"," ",0,"-1/16*(16*b^3*x^3 + 24*a*b^2*x^2 - 3*pi^2*a + 4*a^3 - 4*(pi^2*b - 4*a^2*b)*x)/x^4","A",0
157,1,49,0,0.507392," ","integrate(arccoth(tanh(b*x+a))^3/x^6,x, algorithm=""fricas"")","-\frac{40 \, b^{3} x^{3} + 80 \, a b^{2} x^{2} - 12 \, \pi^{2} a + 16 \, a^{3} - 15 \, {\left(\pi^{2} b - 4 \, a^{2} b\right)} x}{80 \, x^{5}}"," ",0,"-1/80*(40*b^3*x^3 + 80*a*b^2*x^2 - 12*pi^2*a + 16*a^3 - 15*(pi^2*b - 4*a^2*b)*x)/x^5","A",0
158,0,0,0,0.549411," ","integrate(x^m/arccoth(tanh(b*x+a)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{m}}{\operatorname{arcoth}\left(\tanh\left(b x + a\right)\right)}, x\right)"," ",0,"integral(x^m/arccoth(tanh(b*x + a)), x)","F",0
159,1,127,0,0.592304," ","integrate(x^3/arccoth(tanh(b*x+a)),x, algorithm=""fricas"")","\frac{8 \, b^{3} x^{3} - 12 \, a b^{2} x^{2} - 6 \, {\left(\pi^{2} b - 4 \, a^{2} b\right)} x - 6 \, {\left(\pi^{3} - 12 \, \pi a^{2}\right)} \arctan\left(-\frac{2 \, b x + 2 \, a - \sqrt{4 \, b^{2} x^{2} + 8 \, a b x + \pi^{2} + 4 \, a^{2}}}{\pi}\right) + 3 \, {\left(3 \, \pi^{2} a - 4 \, a^{3}\right)} \log\left(4 \, b^{2} x^{2} + 8 \, a b x + \pi^{2} + 4 \, a^{2}\right)}{24 \, b^{4}}"," ",0,"1/24*(8*b^3*x^3 - 12*a*b^2*x^2 - 6*(pi^2*b - 4*a^2*b)*x - 6*(pi^3 - 12*pi*a^2)*arctan(-(2*b*x + 2*a - sqrt(4*b^2*x^2 + 8*a*b*x + pi^2 + 4*a^2))/pi) + 3*(3*pi^2*a - 4*a^3)*log(4*b^2*x^2 + 8*a*b*x + pi^2 + 4*a^2))/b^4","A",0
160,1,97,0,0.475777," ","integrate(x^2/arccoth(tanh(b*x+a)),x, algorithm=""fricas"")","\frac{4 \, b^{2} x^{2} - 8 \, a b x - 16 \, \pi a \arctan\left(-\frac{2 \, b x + 2 \, a - \sqrt{4 \, b^{2} x^{2} + 8 \, a b x + \pi^{2} + 4 \, a^{2}}}{\pi}\right) - {\left(\pi^{2} - 4 \, a^{2}\right)} \log\left(4 \, b^{2} x^{2} + 8 \, a b x + \pi^{2} + 4 \, a^{2}\right)}{8 \, b^{3}}"," ",0,"1/8*(4*b^2*x^2 - 8*a*b*x - 16*pi*a*arctan(-(2*b*x + 2*a - sqrt(4*b^2*x^2 + 8*a*b*x + pi^2 + 4*a^2))/pi) - (pi^2 - 4*a^2)*log(4*b^2*x^2 + 8*a*b*x + pi^2 + 4*a^2))/b^3","A",0
161,1,79,0,0.595841," ","integrate(x/arccoth(tanh(b*x+a)),x, algorithm=""fricas"")","\frac{2 \, b x + 2 \, \pi \arctan\left(-\frac{2 \, b x + 2 \, a - \sqrt{4 \, b^{2} x^{2} + 8 \, a b x + \pi^{2} + 4 \, a^{2}}}{\pi}\right) - a \log\left(4 \, b^{2} x^{2} + 8 \, a b x + \pi^{2} + 4 \, a^{2}\right)}{2 \, b^{2}}"," ",0,"1/2*(2*b*x + 2*pi*arctan(-(2*b*x + 2*a - sqrt(4*b^2*x^2 + 8*a*b*x + pi^2 + 4*a^2))/pi) - a*log(4*b^2*x^2 + 8*a*b*x + pi^2 + 4*a^2))/b^2","B",0
162,1,28,0,0.683881," ","integrate(1/arccoth(tanh(b*x+a)),x, algorithm=""fricas"")","\frac{\log\left(4 \, b^{2} x^{2} + 8 \, a b x + \pi^{2} + 4 \, a^{2}\right)}{2 \, b}"," ",0,"1/2*log(4*b^2*x^2 + 8*a*b*x + pi^2 + 4*a^2)/b","B",0
163,1,87,0,0.520736," ","integrate(1/x/arccoth(tanh(b*x+a)),x, algorithm=""fricas"")","-\frac{2 \, {\left(2 \, \pi \arctan\left(-\frac{2 \, b x + 2 \, a - \sqrt{4 \, b^{2} x^{2} + 8 \, a b x + \pi^{2} + 4 \, a^{2}}}{\pi}\right) + a \log\left(4 \, b^{2} x^{2} + 8 \, a b x + \pi^{2} + 4 \, a^{2}\right) - 2 \, a \log\left(x\right)\right)}}{\pi^{2} + 4 \, a^{2}}"," ",0,"-2*(2*pi*arctan(-(2*b*x + 2*a - sqrt(4*b^2*x^2 + 8*a*b*x + pi^2 + 4*a^2))/pi) + a*log(4*b^2*x^2 + 8*a*b*x + pi^2 + 4*a^2) - 2*a*log(x))/(pi^2 + 4*a^2)","A",0
164,1,137,0,0.587787," ","integrate(1/x^2/arccoth(tanh(b*x+a)),x, algorithm=""fricas"")","\frac{2 \, {\left(16 \, \pi a b x \arctan\left(-\frac{2 \, b x + 2 \, a - \sqrt{4 \, b^{2} x^{2} + 8 \, a b x + \pi^{2} + 4 \, a^{2}}}{\pi}\right) - 2 \, \pi^{2} a - 8 \, a^{3} - {\left(\pi^{2} b - 4 \, a^{2} b\right)} x \log\left(4 \, b^{2} x^{2} + 8 \, a b x + \pi^{2} + 4 \, a^{2}\right) + 2 \, {\left(\pi^{2} b - 4 \, a^{2} b\right)} x \log\left(x\right)\right)}}{{\left(\pi^{4} + 8 \, \pi^{2} a^{2} + 16 \, a^{4}\right)} x}"," ",0,"2*(16*pi*a*b*x*arctan(-(2*b*x + 2*a - sqrt(4*b^2*x^2 + 8*a*b*x + pi^2 + 4*a^2))/pi) - 2*pi^2*a - 8*a^3 - (pi^2*b - 4*a^2*b)*x*log(4*b^2*x^2 + 8*a*b*x + pi^2 + 4*a^2) + 2*(pi^2*b - 4*a^2*b)*x*log(x))/((pi^4 + 8*pi^2*a^2 + 16*a^4)*x)","B",0
165,1,199,0,0.676252," ","integrate(1/x^3/arccoth(tanh(b*x+a)),x, algorithm=""fricas"")","-\frac{2 \, {\left(\pi^{4} a + 8 \, \pi^{2} a^{3} + 16 \, a^{5} - 8 \, {\left(\pi^{3} b^{2} - 12 \, \pi a^{2} b^{2}\right)} x^{2} \arctan\left(-\frac{2 \, b x + 2 \, a - \sqrt{4 \, b^{2} x^{2} + 8 \, a b x + \pi^{2} + 4 \, a^{2}}}{\pi}\right) - 4 \, {\left(3 \, \pi^{2} a b^{2} - 4 \, a^{3} b^{2}\right)} x^{2} \log\left(4 \, b^{2} x^{2} + 8 \, a b x + \pi^{2} + 4 \, a^{2}\right) + 8 \, {\left(3 \, \pi^{2} a b^{2} - 4 \, a^{3} b^{2}\right)} x^{2} \log\left(x\right) + 2 \, {\left(\pi^{4} b - 16 \, a^{4} b\right)} x\right)}}{{\left(\pi^{6} + 12 \, \pi^{4} a^{2} + 48 \, \pi^{2} a^{4} + 64 \, a^{6}\right)} x^{2}}"," ",0,"-2*(pi^4*a + 8*pi^2*a^3 + 16*a^5 - 8*(pi^3*b^2 - 12*pi*a^2*b^2)*x^2*arctan(-(2*b*x + 2*a - sqrt(4*b^2*x^2 + 8*a*b*x + pi^2 + 4*a^2))/pi) - 4*(3*pi^2*a*b^2 - 4*a^3*b^2)*x^2*log(4*b^2*x^2 + 8*a*b*x + pi^2 + 4*a^2) + 8*(3*pi^2*a*b^2 - 4*a^3*b^2)*x^2*log(x) + 2*(pi^4*b - 16*a^4*b)*x)/((pi^6 + 12*pi^4*a^2 + 48*pi^2*a^4 + 64*a^6)*x^2)","B",0
166,0,0,0,0.846218," ","integrate(x^m/arccoth(tanh(b*x+a))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{m}}{\operatorname{arcoth}\left(\tanh\left(b x + a\right)\right)^{2}}, x\right)"," ",0,"integral(x^m/arccoth(tanh(b*x + a))^2, x)","F",0
167,1,326,0,0.518259," ","integrate(x^4/arccoth(tanh(b*x+a))^2,x, algorithm=""fricas"")","\frac{16 \, b^{5} x^{5} - 16 \, a b^{4} x^{4} + 9 \, \pi^{4} a + 24 \, \pi^{2} a^{3} - 48 \, a^{5} - 32 \, {\left(\pi^{2} b^{3} - 2 \, a^{2} b^{3}\right)} x^{3} - 12 \, {\left(7 \, \pi^{2} a b^{2} - 20 \, a^{3} b^{2}\right)} x^{2} - 12 \, {\left(\pi^{4} b - 6 \, \pi^{2} a^{2} b - 8 \, a^{4} b\right)} x - 12 \, {\left(\pi^{5} - 8 \, \pi^{3} a^{2} - 48 \, \pi a^{4} + 4 \, {\left(\pi^{3} b^{2} - 12 \, \pi a^{2} b^{2}\right)} x^{2} + 8 \, {\left(\pi^{3} a b - 12 \, \pi a^{3} b\right)} x\right)} \arctan\left(-\frac{2 \, b x + 2 \, a - \sqrt{4 \, b^{2} x^{2} + 8 \, a b x + \pi^{2} + 4 \, a^{2}}}{\pi}\right) + 6 \, {\left(3 \, \pi^{4} a + 8 \, \pi^{2} a^{3} - 16 \, a^{5} + 4 \, {\left(3 \, \pi^{2} a b^{2} - 4 \, a^{3} b^{2}\right)} x^{2} + 8 \, {\left(3 \, \pi^{2} a^{2} b - 4 \, a^{4} b\right)} x\right)} \log\left(4 \, b^{2} x^{2} + 8 \, a b x + \pi^{2} + 4 \, a^{2}\right)}{12 \, {\left(4 \, b^{7} x^{2} + 8 \, a b^{6} x + \pi^{2} b^{5} + 4 \, a^{2} b^{5}\right)}}"," ",0,"1/12*(16*b^5*x^5 - 16*a*b^4*x^4 + 9*pi^4*a + 24*pi^2*a^3 - 48*a^5 - 32*(pi^2*b^3 - 2*a^2*b^3)*x^3 - 12*(7*pi^2*a*b^2 - 20*a^3*b^2)*x^2 - 12*(pi^4*b - 6*pi^2*a^2*b - 8*a^4*b)*x - 12*(pi^5 - 8*pi^3*a^2 - 48*pi*a^4 + 4*(pi^3*b^2 - 12*pi*a^2*b^2)*x^2 + 8*(pi^3*a*b - 12*pi*a^3*b)*x)*arctan(-(2*b*x + 2*a - sqrt(4*b^2*x^2 + 8*a*b*x + pi^2 + 4*a^2))/pi) + 6*(3*pi^4*a + 8*pi^2*a^3 - 16*a^5 + 4*(3*pi^2*a*b^2 - 4*a^3*b^2)*x^2 + 8*(3*pi^2*a^2*b - 4*a^4*b)*x)*log(4*b^2*x^2 + 8*a*b*x + pi^2 + 4*a^2))/(4*b^7*x^2 + 8*a*b^6*x + pi^2*b^5 + 4*a^2*b^5)","B",0
168,1,244,0,0.503248," ","integrate(x^3/arccoth(tanh(b*x+a))^2,x, algorithm=""fricas"")","\frac{16 \, b^{4} x^{4} - 32 \, a b^{3} x^{3} - 2 \, \pi^{4} + 32 \, a^{4} + 4 \, {\left(\pi^{2} b^{2} - 28 \, a^{2} b^{2}\right)} x^{2} - 8 \, {\left(5 \, \pi^{2} a b + 4 \, a^{3} b\right)} x - 48 \, {\left(4 \, \pi a b^{2} x^{2} + 8 \, \pi a^{2} b x + \pi^{3} a + 4 \, \pi a^{3}\right)} \arctan\left(-\frac{2 \, b x + 2 \, a - \sqrt{4 \, b^{2} x^{2} + 8 \, a b x + \pi^{2} + 4 \, a^{2}}}{\pi}\right) - 3 \, {\left(\pi^{4} - 16 \, a^{4} + 4 \, {\left(\pi^{2} b^{2} - 4 \, a^{2} b^{2}\right)} x^{2} + 8 \, {\left(\pi^{2} a b - 4 \, a^{3} b\right)} x\right)} \log\left(4 \, b^{2} x^{2} + 8 \, a b x + \pi^{2} + 4 \, a^{2}\right)}{8 \, {\left(4 \, b^{6} x^{2} + 8 \, a b^{5} x + \pi^{2} b^{4} + 4 \, a^{2} b^{4}\right)}}"," ",0,"1/8*(16*b^4*x^4 - 32*a*b^3*x^3 - 2*pi^4 + 32*a^4 + 4*(pi^2*b^2 - 28*a^2*b^2)*x^2 - 8*(5*pi^2*a*b + 4*a^3*b)*x - 48*(4*pi*a*b^2*x^2 + 8*pi*a^2*b*x + pi^3*a + 4*pi*a^3)*arctan(-(2*b*x + 2*a - sqrt(4*b^2*x^2 + 8*a*b*x + pi^2 + 4*a^2))/pi) - 3*(pi^4 - 16*a^4 + 4*(pi^2*b^2 - 4*a^2*b^2)*x^2 + 8*(pi^2*a*b - 4*a^3*b)*x)*log(4*b^2*x^2 + 8*a*b*x + pi^2 + 4*a^2))/(4*b^6*x^2 + 8*a*b^5*x + pi^2*b^4 + 4*a^2*b^4)","B",0
169,1,189,0,0.455527," ","integrate(x^2/arccoth(tanh(b*x+a))^2,x, algorithm=""fricas"")","\frac{4 \, b^{3} x^{3} + 8 \, a b^{2} x^{2} + 2 \, \pi^{2} b x - \pi^{2} a - 4 \, a^{3} + 2 \, {\left(4 \, \pi b^{2} x^{2} + 8 \, \pi a b x + \pi^{3} + 4 \, \pi a^{2}\right)} \arctan\left(-\frac{2 \, b x + 2 \, a - \sqrt{4 \, b^{2} x^{2} + 8 \, a b x + \pi^{2} + 4 \, a^{2}}}{\pi}\right) - {\left(4 \, a b^{2} x^{2} + 8 \, a^{2} b x + \pi^{2} a + 4 \, a^{3}\right)} \log\left(4 \, b^{2} x^{2} + 8 \, a b x + \pi^{2} + 4 \, a^{2}\right)}{4 \, b^{5} x^{2} + 8 \, a b^{4} x + \pi^{2} b^{3} + 4 \, a^{2} b^{3}}"," ",0,"(4*b^3*x^3 + 8*a*b^2*x^2 + 2*pi^2*b*x - pi^2*a - 4*a^3 + 2*(4*pi*b^2*x^2 + 8*pi*a*b*x + pi^3 + 4*pi*a^2)*arctan(-(2*b*x + 2*a - sqrt(4*b^2*x^2 + 8*a*b*x + pi^2 + 4*a^2))/pi) - (4*a*b^2*x^2 + 8*a^2*b*x + pi^2*a + 4*a^3)*log(4*b^2*x^2 + 8*a*b*x + pi^2 + 4*a^2))/(4*b^5*x^2 + 8*a*b^4*x + pi^2*b^3 + 4*a^2*b^3)","B",0
170,1,97,0,0.746110," ","integrate(x/arccoth(tanh(b*x+a))^2,x, algorithm=""fricas"")","\frac{8 \, a b x + 2 \, \pi^{2} + 8 \, a^{2} + {\left(4 \, b^{2} x^{2} + 8 \, a b x + \pi^{2} + 4 \, a^{2}\right)} \log\left(4 \, b^{2} x^{2} + 8 \, a b x + \pi^{2} + 4 \, a^{2}\right)}{2 \, {\left(4 \, b^{4} x^{2} + 8 \, a b^{3} x + \pi^{2} b^{2} + 4 \, a^{2} b^{2}\right)}}"," ",0,"1/2*(8*a*b*x + 2*pi^2 + 8*a^2 + (4*b^2*x^2 + 8*a*b*x + pi^2 + 4*a^2)*log(4*b^2*x^2 + 8*a*b*x + pi^2 + 4*a^2))/(4*b^4*x^2 + 8*a*b^3*x + pi^2*b^2 + 4*a^2*b^2)","B",0
171,1,36,0,0.645967," ","integrate(1/arccoth(tanh(b*x+a))^2,x, algorithm=""fricas"")","-\frac{4 \, {\left(b x + a\right)}}{4 \, b^{3} x^{2} + 8 \, a b^{2} x + \pi^{2} b + 4 \, a^{2} b}"," ",0,"-4*(b*x + a)/(4*b^3*x^2 + 8*a*b^2*x + pi^2*b + 4*a^2*b)","B",0
172,1,306,0,0.458191," ","integrate(1/x/arccoth(tanh(b*x+a))^2,x, algorithm=""fricas"")","-\frac{2 \, {\left(2 \, \pi^{4} - 32 \, a^{4} - 8 \, {\left(\pi^{2} a b + 4 \, a^{3} b\right)} x + 16 \, {\left(4 \, \pi a b^{2} x^{2} + 8 \, \pi a^{2} b x + \pi^{3} a + 4 \, \pi a^{3}\right)} \arctan\left(-\frac{2 \, b x + 2 \, a - \sqrt{4 \, b^{2} x^{2} + 8 \, a b x + \pi^{2} + 4 \, a^{2}}}{\pi}\right) - {\left(\pi^{4} - 16 \, a^{4} + 4 \, {\left(\pi^{2} b^{2} - 4 \, a^{2} b^{2}\right)} x^{2} + 8 \, {\left(\pi^{2} a b - 4 \, a^{3} b\right)} x\right)} \log\left(4 \, b^{2} x^{2} + 8 \, a b x + \pi^{2} + 4 \, a^{2}\right) + 2 \, {\left(\pi^{4} - 16 \, a^{4} + 4 \, {\left(\pi^{2} b^{2} - 4 \, a^{2} b^{2}\right)} x^{2} + 8 \, {\left(\pi^{2} a b - 4 \, a^{3} b\right)} x\right)} \log\left(x\right)\right)}}{\pi^{6} + 12 \, \pi^{4} a^{2} + 48 \, \pi^{2} a^{4} + 64 \, a^{6} + 4 \, {\left(\pi^{4} b^{2} + 8 \, \pi^{2} a^{2} b^{2} + 16 \, a^{4} b^{2}\right)} x^{2} + 8 \, {\left(\pi^{4} a b + 8 \, \pi^{2} a^{3} b + 16 \, a^{5} b\right)} x}"," ",0,"-2*(2*pi^4 - 32*a^4 - 8*(pi^2*a*b + 4*a^3*b)*x + 16*(4*pi*a*b^2*x^2 + 8*pi*a^2*b*x + pi^3*a + 4*pi*a^3)*arctan(-(2*b*x + 2*a - sqrt(4*b^2*x^2 + 8*a*b*x + pi^2 + 4*a^2))/pi) - (pi^4 - 16*a^4 + 4*(pi^2*b^2 - 4*a^2*b^2)*x^2 + 8*(pi^2*a*b - 4*a^3*b)*x)*log(4*b^2*x^2 + 8*a*b*x + pi^2 + 4*a^2) + 2*(pi^4 - 16*a^4 + 4*(pi^2*b^2 - 4*a^2*b^2)*x^2 + 8*(pi^2*a*b - 4*a^3*b)*x)*log(x))/(pi^6 + 12*pi^4*a^2 + 48*pi^2*a^4 + 64*a^6 + 4*(pi^4*b^2 + 8*pi^2*a^2*b^2 + 16*a^4*b^2)*x^2 + 8*(pi^4*a*b + 8*pi^2*a^3*b + 16*a^5*b)*x)","B",0
173,1,480,0,0.684742," ","integrate(1/x^2/arccoth(tanh(b*x+a))^2,x, algorithm=""fricas"")","\frac{4 \, {\left(\pi^{6} + 4 \, \pi^{4} a^{2} - 16 \, \pi^{2} a^{4} - 64 \, a^{6} + 8 \, {\left(\pi^{4} b^{2} - 16 \, a^{4} b^{2}\right)} x^{2} + 4 \, {\left(5 \, \pi^{4} a b + 8 \, \pi^{2} a^{3} b - 48 \, a^{5} b\right)} x - 8 \, {\left(4 \, {\left(\pi^{3} b^{3} - 12 \, \pi a^{2} b^{3}\right)} x^{3} + 8 \, {\left(\pi^{3} a b^{2} - 12 \, \pi a^{3} b^{2}\right)} x^{2} + {\left(\pi^{5} b - 8 \, \pi^{3} a^{2} b - 48 \, \pi a^{4} b\right)} x\right)} \arctan\left(-\frac{2 \, b x + 2 \, a - \sqrt{4 \, b^{2} x^{2} + 8 \, a b x + \pi^{2} + 4 \, a^{2}}}{\pi}\right) - 4 \, {\left(4 \, {\left(3 \, \pi^{2} a b^{3} - 4 \, a^{3} b^{3}\right)} x^{3} + 8 \, {\left(3 \, \pi^{2} a^{2} b^{2} - 4 \, a^{4} b^{2}\right)} x^{2} + {\left(3 \, \pi^{4} a b + 8 \, \pi^{2} a^{3} b - 16 \, a^{5} b\right)} x\right)} \log\left(4 \, b^{2} x^{2} + 8 \, a b x + \pi^{2} + 4 \, a^{2}\right) + 8 \, {\left(4 \, {\left(3 \, \pi^{2} a b^{3} - 4 \, a^{3} b^{3}\right)} x^{3} + 8 \, {\left(3 \, \pi^{2} a^{2} b^{2} - 4 \, a^{4} b^{2}\right)} x^{2} + {\left(3 \, \pi^{4} a b + 8 \, \pi^{2} a^{3} b - 16 \, a^{5} b\right)} x\right)} \log\left(x\right)\right)}}{4 \, {\left(\pi^{6} b^{2} + 12 \, \pi^{4} a^{2} b^{2} + 48 \, \pi^{2} a^{4} b^{2} + 64 \, a^{6} b^{2}\right)} x^{3} + 8 \, {\left(\pi^{6} a b + 12 \, \pi^{4} a^{3} b + 48 \, \pi^{2} a^{5} b + 64 \, a^{7} b\right)} x^{2} + {\left(\pi^{8} + 16 \, \pi^{6} a^{2} + 96 \, \pi^{4} a^{4} + 256 \, \pi^{2} a^{6} + 256 \, a^{8}\right)} x}"," ",0,"4*(pi^6 + 4*pi^4*a^2 - 16*pi^2*a^4 - 64*a^6 + 8*(pi^4*b^2 - 16*a^4*b^2)*x^2 + 4*(5*pi^4*a*b + 8*pi^2*a^3*b - 48*a^5*b)*x - 8*(4*(pi^3*b^3 - 12*pi*a^2*b^3)*x^3 + 8*(pi^3*a*b^2 - 12*pi*a^3*b^2)*x^2 + (pi^5*b - 8*pi^3*a^2*b - 48*pi*a^4*b)*x)*arctan(-(2*b*x + 2*a - sqrt(4*b^2*x^2 + 8*a*b*x + pi^2 + 4*a^2))/pi) - 4*(4*(3*pi^2*a*b^3 - 4*a^3*b^3)*x^3 + 8*(3*pi^2*a^2*b^2 - 4*a^4*b^2)*x^2 + (3*pi^4*a*b + 8*pi^2*a^3*b - 16*a^5*b)*x)*log(4*b^2*x^2 + 8*a*b*x + pi^2 + 4*a^2) + 8*(4*(3*pi^2*a*b^3 - 4*a^3*b^3)*x^3 + 8*(3*pi^2*a^2*b^2 - 4*a^4*b^2)*x^2 + (3*pi^4*a*b + 8*pi^2*a^3*b - 16*a^5*b)*x)*log(x))/(4*(pi^6*b^2 + 12*pi^4*a^2*b^2 + 48*pi^2*a^4*b^2 + 64*a^6*b^2)*x^3 + 8*(pi^6*a*b + 12*pi^4*a^3*b + 48*pi^2*a^5*b + 64*a^7*b)*x^2 + (pi^8 + 16*pi^6*a^2 + 96*pi^4*a^4 + 256*pi^2*a^6 + 256*a^8)*x)","B",0
174,1,644,0,0.548455," ","integrate(1/x^3/arccoth(tanh(b*x+a))^2,x, algorithm=""fricas"")","\frac{2 \, {\left(\pi^{8} + 8 \, \pi^{6} a^{2} - 128 \, \pi^{2} a^{6} - 256 \, a^{8} - 96 \, {\left(3 \, \pi^{4} a b^{3} + 8 \, \pi^{2} a^{3} b^{3} - 16 \, a^{5} b^{3}\right)} x^{3} + 12 \, {\left(\pi^{6} b^{2} - 44 \, \pi^{4} a^{2} b^{2} - 144 \, \pi^{2} a^{4} b^{2} + 192 \, a^{6} b^{2}\right)} x^{2} - 8 \, {\left(5 \, \pi^{6} a b + 36 \, \pi^{4} a^{3} b + 48 \, \pi^{2} a^{5} b - 64 \, a^{7} b\right)} x + 384 \, {\left(4 \, {\left(\pi^{3} a b^{4} - 4 \, \pi a^{3} b^{4}\right)} x^{4} + 8 \, {\left(\pi^{3} a^{2} b^{3} - 4 \, \pi a^{4} b^{3}\right)} x^{3} + {\left(\pi^{5} a b^{2} - 16 \, \pi a^{5} b^{2}\right)} x^{2}\right)} \arctan\left(-\frac{2 \, b x + 2 \, a - \sqrt{4 \, b^{2} x^{2} + 8 \, a b x + \pi^{2} + 4 \, a^{2}}}{\pi}\right) - 12 \, {\left(4 \, {\left(\pi^{4} b^{4} - 24 \, \pi^{2} a^{2} b^{4} + 16 \, a^{4} b^{4}\right)} x^{4} + 8 \, {\left(\pi^{4} a b^{3} - 24 \, \pi^{2} a^{3} b^{3} + 16 \, a^{5} b^{3}\right)} x^{3} + {\left(\pi^{6} b^{2} - 20 \, \pi^{4} a^{2} b^{2} - 80 \, \pi^{2} a^{4} b^{2} + 64 \, a^{6} b^{2}\right)} x^{2}\right)} \log\left(4 \, b^{2} x^{2} + 8 \, a b x + \pi^{2} + 4 \, a^{2}\right) + 24 \, {\left(4 \, {\left(\pi^{4} b^{4} - 24 \, \pi^{2} a^{2} b^{4} + 16 \, a^{4} b^{4}\right)} x^{4} + 8 \, {\left(\pi^{4} a b^{3} - 24 \, \pi^{2} a^{3} b^{3} + 16 \, a^{5} b^{3}\right)} x^{3} + {\left(\pi^{6} b^{2} - 20 \, \pi^{4} a^{2} b^{2} - 80 \, \pi^{2} a^{4} b^{2} + 64 \, a^{6} b^{2}\right)} x^{2}\right)} \log\left(x\right)\right)}}{4 \, {\left(\pi^{8} b^{2} + 16 \, \pi^{6} a^{2} b^{2} + 96 \, \pi^{4} a^{4} b^{2} + 256 \, \pi^{2} a^{6} b^{2} + 256 \, a^{8} b^{2}\right)} x^{4} + 8 \, {\left(\pi^{8} a b + 16 \, \pi^{6} a^{3} b + 96 \, \pi^{4} a^{5} b + 256 \, \pi^{2} a^{7} b + 256 \, a^{9} b\right)} x^{3} + {\left(\pi^{10} + 20 \, \pi^{8} a^{2} + 160 \, \pi^{6} a^{4} + 640 \, \pi^{4} a^{6} + 1280 \, \pi^{2} a^{8} + 1024 \, a^{10}\right)} x^{2}}"," ",0,"2*(pi^8 + 8*pi^6*a^2 - 128*pi^2*a^6 - 256*a^8 - 96*(3*pi^4*a*b^3 + 8*pi^2*a^3*b^3 - 16*a^5*b^3)*x^3 + 12*(pi^6*b^2 - 44*pi^4*a^2*b^2 - 144*pi^2*a^4*b^2 + 192*a^6*b^2)*x^2 - 8*(5*pi^6*a*b + 36*pi^4*a^3*b + 48*pi^2*a^5*b - 64*a^7*b)*x + 384*(4*(pi^3*a*b^4 - 4*pi*a^3*b^4)*x^4 + 8*(pi^3*a^2*b^3 - 4*pi*a^4*b^3)*x^3 + (pi^5*a*b^2 - 16*pi*a^5*b^2)*x^2)*arctan(-(2*b*x + 2*a - sqrt(4*b^2*x^2 + 8*a*b*x + pi^2 + 4*a^2))/pi) - 12*(4*(pi^4*b^4 - 24*pi^2*a^2*b^4 + 16*a^4*b^4)*x^4 + 8*(pi^4*a*b^3 - 24*pi^2*a^3*b^3 + 16*a^5*b^3)*x^3 + (pi^6*b^2 - 20*pi^4*a^2*b^2 - 80*pi^2*a^4*b^2 + 64*a^6*b^2)*x^2)*log(4*b^2*x^2 + 8*a*b*x + pi^2 + 4*a^2) + 24*(4*(pi^4*b^4 - 24*pi^2*a^2*b^4 + 16*a^4*b^4)*x^4 + 8*(pi^4*a*b^3 - 24*pi^2*a^3*b^3 + 16*a^5*b^3)*x^3 + (pi^6*b^2 - 20*pi^4*a^2*b^2 - 80*pi^2*a^4*b^2 + 64*a^6*b^2)*x^2)*log(x))/(4*(pi^8*b^2 + 16*pi^6*a^2*b^2 + 96*pi^4*a^4*b^2 + 256*pi^2*a^6*b^2 + 256*a^8*b^2)*x^4 + 8*(pi^8*a*b + 16*pi^6*a^3*b + 96*pi^4*a^5*b + 256*pi^2*a^7*b + 256*a^9*b)*x^3 + (pi^10 + 20*pi^8*a^2 + 160*pi^6*a^4 + 640*pi^4*a^6 + 1280*pi^2*a^8 + 1024*a^10)*x^2)","B",0
175,0,0,0,0.508267," ","integrate(x^m/arccoth(tanh(b*x+a))^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{m}}{\operatorname{arcoth}\left(\tanh\left(b x + a\right)\right)^{3}}, x\right)"," ",0,"integral(x^m/arccoth(tanh(b*x + a))^3, x)","F",0
176,1,493,0,1.143734," ","integrate(x^4/arccoth(tanh(b*x+a))^3,x, algorithm=""fricas"")","\frac{64 \, b^{6} x^{6} - 128 \, a b^{5} x^{5} - 7 \, \pi^{6} - 28 \, \pi^{4} a^{2} + 112 \, \pi^{2} a^{4} + 448 \, a^{6} + 32 \, {\left(\pi^{2} b^{4} - 36 \, a^{2} b^{4}\right)} x^{4} - 512 \, {\left(\pi^{2} a b^{3} + 3 \, a^{3} b^{3}\right)} x^{3} - 32 \, {\left(\pi^{4} b^{2} + 32 \, \pi^{2} a^{2} b^{2}\right)} x^{2} - 32 \, {\left(5 \, \pi^{4} a b + 12 \, \pi^{2} a^{3} b - 32 \, a^{5} b\right)} x - 96 \, {\left(16 \, \pi a b^{4} x^{4} + 64 \, \pi a^{2} b^{3} x^{3} + \pi^{5} a + 8 \, \pi^{3} a^{3} + 16 \, \pi a^{5} + 8 \, {\left(\pi^{3} a b^{2} + 12 \, \pi a^{3} b^{2}\right)} x^{2} + 16 \, {\left(\pi^{3} a^{2} b + 4 \, \pi a^{4} b\right)} x\right)} \arctan\left(-\frac{2 \, b x + 2 \, a - \sqrt{4 \, b^{2} x^{2} + 8 \, a b x + \pi^{2} + 4 \, a^{2}}}{\pi}\right) - 6 \, {\left(\pi^{6} + 4 \, \pi^{4} a^{2} - 16 \, \pi^{2} a^{4} - 64 \, a^{6} + 16 \, {\left(\pi^{2} b^{4} - 4 \, a^{2} b^{4}\right)} x^{4} + 64 \, {\left(\pi^{2} a b^{3} - 4 \, a^{3} b^{3}\right)} x^{3} + 8 \, {\left(\pi^{4} b^{2} + 8 \, \pi^{2} a^{2} b^{2} - 48 \, a^{4} b^{2}\right)} x^{2} + 16 \, {\left(\pi^{4} a b - 16 \, a^{5} b\right)} x\right)} \log\left(4 \, b^{2} x^{2} + 8 \, a b x + \pi^{2} + 4 \, a^{2}\right)}{8 \, {\left(16 \, b^{9} x^{4} + 64 \, a b^{8} x^{3} + \pi^{4} b^{5} + 8 \, \pi^{2} a^{2} b^{5} + 16 \, a^{4} b^{5} + 8 \, {\left(\pi^{2} b^{7} + 12 \, a^{2} b^{7}\right)} x^{2} + 16 \, {\left(\pi^{2} a b^{6} + 4 \, a^{3} b^{6}\right)} x\right)}}"," ",0,"1/8*(64*b^6*x^6 - 128*a*b^5*x^5 - 7*pi^6 - 28*pi^4*a^2 + 112*pi^2*a^4 + 448*a^6 + 32*(pi^2*b^4 - 36*a^2*b^4)*x^4 - 512*(pi^2*a*b^3 + 3*a^3*b^3)*x^3 - 32*(pi^4*b^2 + 32*pi^2*a^2*b^2)*x^2 - 32*(5*pi^4*a*b + 12*pi^2*a^3*b - 32*a^5*b)*x - 96*(16*pi*a*b^4*x^4 + 64*pi*a^2*b^3*x^3 + pi^5*a + 8*pi^3*a^3 + 16*pi*a^5 + 8*(pi^3*a*b^2 + 12*pi*a^3*b^2)*x^2 + 16*(pi^3*a^2*b + 4*pi*a^4*b)*x)*arctan(-(2*b*x + 2*a - sqrt(4*b^2*x^2 + 8*a*b*x + pi^2 + 4*a^2))/pi) - 6*(pi^6 + 4*pi^4*a^2 - 16*pi^2*a^4 - 64*a^6 + 16*(pi^2*b^4 - 4*a^2*b^4)*x^4 + 64*(pi^2*a*b^3 - 4*a^3*b^3)*x^3 + 8*(pi^4*b^2 + 8*pi^2*a^2*b^2 - 48*a^4*b^2)*x^2 + 16*(pi^4*a*b - 16*a^5*b)*x)*log(4*b^2*x^2 + 8*a*b*x + pi^2 + 4*a^2))/(16*b^9*x^4 + 64*a*b^8*x^3 + pi^4*b^5 + 8*pi^2*a^2*b^5 + 16*a^4*b^5 + 8*(pi^2*b^7 + 12*a^2*b^7)*x^2 + 16*(pi^2*a*b^6 + 4*a^3*b^6)*x)","B",0
177,1,418,0,0.646163," ","integrate(x^3/arccoth(tanh(b*x+a))^3,x, algorithm=""fricas"")","\frac{32 \, b^{5} x^{5} + 128 \, a b^{4} x^{4} - 5 \, \pi^{4} a - 40 \, \pi^{2} a^{3} - 80 \, a^{5} + 8 \, {\left(5 \, \pi^{2} b^{3} + 12 \, a^{2} b^{3}\right)} x^{3} + 4 \, {\left(11 \, \pi^{2} a b^{2} - 36 \, a^{3} b^{2}\right)} x^{2} + 2 \, {\left(3 \, \pi^{4} b - 16 \, \pi^{2} a^{2} b - 112 \, a^{4} b\right)} x + 6 \, {\left(16 \, \pi b^{4} x^{4} + 64 \, \pi a b^{3} x^{3} + \pi^{5} + 8 \, \pi^{3} a^{2} + 16 \, \pi a^{4} + 8 \, {\left(\pi^{3} b^{2} + 12 \, \pi a^{2} b^{2}\right)} x^{2} + 16 \, {\left(\pi^{3} a b + 4 \, \pi a^{3} b\right)} x\right)} \arctan\left(-\frac{2 \, b x + 2 \, a - \sqrt{4 \, b^{2} x^{2} + 8 \, a b x + \pi^{2} + 4 \, a^{2}}}{\pi}\right) - 3 \, {\left(16 \, a b^{4} x^{4} + 64 \, a^{2} b^{3} x^{3} + \pi^{4} a + 8 \, \pi^{2} a^{3} + 16 \, a^{5} + 8 \, {\left(\pi^{2} a b^{2} + 12 \, a^{3} b^{2}\right)} x^{2} + 16 \, {\left(\pi^{2} a^{2} b + 4 \, a^{4} b\right)} x\right)} \log\left(4 \, b^{2} x^{2} + 8 \, a b x + \pi^{2} + 4 \, a^{2}\right)}{2 \, {\left(16 \, b^{8} x^{4} + 64 \, a b^{7} x^{3} + \pi^{4} b^{4} + 8 \, \pi^{2} a^{2} b^{4} + 16 \, a^{4} b^{4} + 8 \, {\left(\pi^{2} b^{6} + 12 \, a^{2} b^{6}\right)} x^{2} + 16 \, {\left(\pi^{2} a b^{5} + 4 \, a^{3} b^{5}\right)} x\right)}}"," ",0,"1/2*(32*b^5*x^5 + 128*a*b^4*x^4 - 5*pi^4*a - 40*pi^2*a^3 - 80*a^5 + 8*(5*pi^2*b^3 + 12*a^2*b^3)*x^3 + 4*(11*pi^2*a*b^2 - 36*a^3*b^2)*x^2 + 2*(3*pi^4*b - 16*pi^2*a^2*b - 112*a^4*b)*x + 6*(16*pi*b^4*x^4 + 64*pi*a*b^3*x^3 + pi^5 + 8*pi^3*a^2 + 16*pi*a^4 + 8*(pi^3*b^2 + 12*pi*a^2*b^2)*x^2 + 16*(pi^3*a*b + 4*pi*a^3*b)*x)*arctan(-(2*b*x + 2*a - sqrt(4*b^2*x^2 + 8*a*b*x + pi^2 + 4*a^2))/pi) - 3*(16*a*b^4*x^4 + 64*a^2*b^3*x^3 + pi^4*a + 8*pi^2*a^3 + 16*a^5 + 8*(pi^2*a*b^2 + 12*a^3*b^2)*x^2 + 16*(pi^2*a^2*b + 4*a^4*b)*x)*log(4*b^2*x^2 + 8*a*b*x + pi^2 + 4*a^2))/(16*b^8*x^4 + 64*a*b^7*x^3 + pi^4*b^4 + 8*pi^2*a^2*b^4 + 16*a^4*b^4 + 8*(pi^2*b^6 + 12*a^2*b^6)*x^2 + 16*(pi^2*a*b^5 + 4*a^3*b^5)*x)","B",0
178,1,250,0,0.508579," ","integrate(x^2/arccoth(tanh(b*x+a))^3,x, algorithm=""fricas"")","\frac{64 \, a b^{3} x^{3} + 3 \, \pi^{4} + 24 \, \pi^{2} a^{2} + 48 \, a^{4} + 4 \, {\left(5 \, \pi^{2} b^{2} + 44 \, a^{2} b^{2}\right)} x^{2} + 40 \, {\left(\pi^{2} a b + 4 \, a^{3} b\right)} x + {\left(16 \, b^{4} x^{4} + 64 \, a b^{3} x^{3} + \pi^{4} + 8 \, \pi^{2} a^{2} + 16 \, a^{4} + 8 \, {\left(\pi^{2} b^{2} + 12 \, a^{2} b^{2}\right)} x^{2} + 16 \, {\left(\pi^{2} a b + 4 \, a^{3} b\right)} x\right)} \log\left(4 \, b^{2} x^{2} + 8 \, a b x + \pi^{2} + 4 \, a^{2}\right)}{2 \, {\left(16 \, b^{7} x^{4} + 64 \, a b^{6} x^{3} + \pi^{4} b^{3} + 8 \, \pi^{2} a^{2} b^{3} + 16 \, a^{4} b^{3} + 8 \, {\left(\pi^{2} b^{5} + 12 \, a^{2} b^{5}\right)} x^{2} + 16 \, {\left(\pi^{2} a b^{4} + 4 \, a^{3} b^{4}\right)} x\right)}}"," ",0,"1/2*(64*a*b^3*x^3 + 3*pi^4 + 24*pi^2*a^2 + 48*a^4 + 4*(5*pi^2*b^2 + 44*a^2*b^2)*x^2 + 40*(pi^2*a*b + 4*a^3*b)*x + (16*b^4*x^4 + 64*a*b^3*x^3 + pi^4 + 8*pi^2*a^2 + 16*a^4 + 8*(pi^2*b^2 + 12*a^2*b^2)*x^2 + 16*(pi^2*a*b + 4*a^3*b)*x)*log(4*b^2*x^2 + 8*a*b*x + pi^2 + 4*a^2))/(16*b^7*x^4 + 64*a*b^6*x^3 + pi^4*b^3 + 8*pi^2*a^2*b^3 + 16*a^4*b^3 + 8*(pi^2*b^5 + 12*a^2*b^5)*x^2 + 16*(pi^2*a*b^4 + 4*a^3*b^4)*x)","B",0
179,1,124,0,0.844118," ","integrate(x/arccoth(tanh(b*x+a))^3,x, algorithm=""fricas"")","-\frac{2 \, {\left(8 \, b^{3} x^{3} + 20 \, a b^{2} x^{2} + 16 \, a^{2} b x + \pi^{2} a + 4 \, a^{3}\right)}}{16 \, b^{6} x^{4} + 64 \, a b^{5} x^{3} + \pi^{4} b^{2} + 8 \, \pi^{2} a^{2} b^{2} + 16 \, a^{4} b^{2} + 8 \, {\left(\pi^{2} b^{4} + 12 \, a^{2} b^{4}\right)} x^{2} + 16 \, {\left(\pi^{2} a b^{3} + 4 \, a^{3} b^{3}\right)} x}"," ",0,"-2*(8*b^3*x^3 + 20*a*b^2*x^2 + 16*a^2*b*x + pi^2*a + 4*a^3)/(16*b^6*x^4 + 64*a*b^5*x^3 + pi^4*b^2 + 8*pi^2*a^2*b^2 + 16*a^4*b^2 + 8*(pi^2*b^4 + 12*a^2*b^4)*x^2 + 16*(pi^2*a*b^3 + 4*a^3*b^3)*x)","B",0
180,1,107,0,0.567400," ","integrate(1/arccoth(tanh(b*x+a))^3,x, algorithm=""fricas"")","-\frac{2 \, {\left(4 \, b^{2} x^{2} + 8 \, a b x - \pi^{2} + 4 \, a^{2}\right)}}{16 \, b^{5} x^{4} + 64 \, a b^{4} x^{3} + \pi^{4} b + 8 \, \pi^{2} a^{2} b + 16 \, a^{4} b + 8 \, {\left(\pi^{2} b^{3} + 12 \, a^{2} b^{3}\right)} x^{2} + 16 \, {\left(\pi^{2} a b^{2} + 4 \, a^{3} b^{2}\right)} x}"," ",0,"-2*(4*b^2*x^2 + 8*a*b*x - pi^2 + 4*a^2)/(16*b^5*x^4 + 64*a*b^4*x^3 + pi^4*b + 8*pi^2*a^2*b + 16*a^4*b + 8*(pi^2*b^3 + 12*a^2*b^3)*x^2 + 16*(pi^2*a*b^2 + 4*a^3*b^2)*x)","B",0
181,1,811,0,0.614784," ","integrate(1/x/arccoth(tanh(b*x+a))^3,x, algorithm=""fricas"")","-\frac{8 \, {\left(9 \, \pi^{6} a + 60 \, \pi^{4} a^{3} + 48 \, \pi^{2} a^{5} - 192 \, a^{7} + 8 \, {\left(\pi^{4} b^{3} - 16 \, a^{4} b^{3}\right)} x^{3} + 4 \, {\left(9 \, \pi^{4} a b^{2} + 8 \, \pi^{2} a^{3} b^{2} - 112 \, a^{5} b^{2}\right)} x^{2} + 4 \, {\left(\pi^{6} b + 16 \, \pi^{4} a^{2} b + 16 \, \pi^{2} a^{4} b - 128 \, a^{6} b\right)} x - 2 \, {\left(\pi^{7} - 4 \, \pi^{5} a^{2} - 80 \, \pi^{3} a^{4} - 192 \, \pi a^{6} + 16 \, {\left(\pi^{3} b^{4} - 12 \, \pi a^{2} b^{4}\right)} x^{4} + 64 \, {\left(\pi^{3} a b^{3} - 12 \, \pi a^{3} b^{3}\right)} x^{3} + 8 \, {\left(\pi^{5} b^{2} - 144 \, \pi a^{4} b^{2}\right)} x^{2} + 16 \, {\left(\pi^{5} a b - 8 \, \pi^{3} a^{3} b - 48 \, \pi a^{5} b\right)} x\right)} \arctan\left(-\frac{2 \, b x + 2 \, a - \sqrt{4 \, b^{2} x^{2} + 8 \, a b x + \pi^{2} + 4 \, a^{2}}}{\pi}\right) - {\left(3 \, \pi^{6} a + 20 \, \pi^{4} a^{3} + 16 \, \pi^{2} a^{5} - 64 \, a^{7} + 16 \, {\left(3 \, \pi^{2} a b^{4} - 4 \, a^{3} b^{4}\right)} x^{4} + 64 \, {\left(3 \, \pi^{2} a^{2} b^{3} - 4 \, a^{4} b^{3}\right)} x^{3} + 8 \, {\left(3 \, \pi^{4} a b^{2} + 32 \, \pi^{2} a^{3} b^{2} - 48 \, a^{5} b^{2}\right)} x^{2} + 16 \, {\left(3 \, \pi^{4} a^{2} b + 8 \, \pi^{2} a^{4} b - 16 \, a^{6} b\right)} x\right)} \log\left(4 \, b^{2} x^{2} + 8 \, a b x + \pi^{2} + 4 \, a^{2}\right) + 2 \, {\left(3 \, \pi^{6} a + 20 \, \pi^{4} a^{3} + 16 \, \pi^{2} a^{5} - 64 \, a^{7} + 16 \, {\left(3 \, \pi^{2} a b^{4} - 4 \, a^{3} b^{4}\right)} x^{4} + 64 \, {\left(3 \, \pi^{2} a^{2} b^{3} - 4 \, a^{4} b^{3}\right)} x^{3} + 8 \, {\left(3 \, \pi^{4} a b^{2} + 32 \, \pi^{2} a^{3} b^{2} - 48 \, a^{5} b^{2}\right)} x^{2} + 16 \, {\left(3 \, \pi^{4} a^{2} b + 8 \, \pi^{2} a^{4} b - 16 \, a^{6} b\right)} x\right)} \log\left(x\right)\right)}}{\pi^{10} + 20 \, \pi^{8} a^{2} + 160 \, \pi^{6} a^{4} + 640 \, \pi^{4} a^{6} + 1280 \, \pi^{2} a^{8} + 1024 \, a^{10} + 16 \, {\left(\pi^{6} b^{4} + 12 \, \pi^{4} a^{2} b^{4} + 48 \, \pi^{2} a^{4} b^{4} + 64 \, a^{6} b^{4}\right)} x^{4} + 64 \, {\left(\pi^{6} a b^{3} + 12 \, \pi^{4} a^{3} b^{3} + 48 \, \pi^{2} a^{5} b^{3} + 64 \, a^{7} b^{3}\right)} x^{3} + 8 \, {\left(\pi^{8} b^{2} + 24 \, \pi^{6} a^{2} b^{2} + 192 \, \pi^{4} a^{4} b^{2} + 640 \, \pi^{2} a^{6} b^{2} + 768 \, a^{8} b^{2}\right)} x^{2} + 16 \, {\left(\pi^{8} a b + 16 \, \pi^{6} a^{3} b + 96 \, \pi^{4} a^{5} b + 256 \, \pi^{2} a^{7} b + 256 \, a^{9} b\right)} x}"," ",0,"-8*(9*pi^6*a + 60*pi^4*a^3 + 48*pi^2*a^5 - 192*a^7 + 8*(pi^4*b^3 - 16*a^4*b^3)*x^3 + 4*(9*pi^4*a*b^2 + 8*pi^2*a^3*b^2 - 112*a^5*b^2)*x^2 + 4*(pi^6*b + 16*pi^4*a^2*b + 16*pi^2*a^4*b - 128*a^6*b)*x - 2*(pi^7 - 4*pi^5*a^2 - 80*pi^3*a^4 - 192*pi*a^6 + 16*(pi^3*b^4 - 12*pi*a^2*b^4)*x^4 + 64*(pi^3*a*b^3 - 12*pi*a^3*b^3)*x^3 + 8*(pi^5*b^2 - 144*pi*a^4*b^2)*x^2 + 16*(pi^5*a*b - 8*pi^3*a^3*b - 48*pi*a^5*b)*x)*arctan(-(2*b*x + 2*a - sqrt(4*b^2*x^2 + 8*a*b*x + pi^2 + 4*a^2))/pi) - (3*pi^6*a + 20*pi^4*a^3 + 16*pi^2*a^5 - 64*a^7 + 16*(3*pi^2*a*b^4 - 4*a^3*b^4)*x^4 + 64*(3*pi^2*a^2*b^3 - 4*a^4*b^3)*x^3 + 8*(3*pi^4*a*b^2 + 32*pi^2*a^3*b^2 - 48*a^5*b^2)*x^2 + 16*(3*pi^4*a^2*b + 8*pi^2*a^4*b - 16*a^6*b)*x)*log(4*b^2*x^2 + 8*a*b*x + pi^2 + 4*a^2) + 2*(3*pi^6*a + 20*pi^4*a^3 + 16*pi^2*a^5 - 64*a^7 + 16*(3*pi^2*a*b^4 - 4*a^3*b^4)*x^4 + 64*(3*pi^2*a^2*b^3 - 4*a^4*b^3)*x^3 + 8*(3*pi^4*a*b^2 + 32*pi^2*a^3*b^2 - 48*a^5*b^2)*x^2 + 16*(3*pi^4*a^2*b + 8*pi^2*a^4*b - 16*a^6*b)*x)*log(x))/(pi^10 + 20*pi^8*a^2 + 160*pi^6*a^4 + 640*pi^4*a^6 + 1280*pi^2*a^8 + 1024*a^10 + 16*(pi^6*b^4 + 12*pi^4*a^2*b^4 + 48*pi^2*a^4*b^4 + 64*a^6*b^4)*x^4 + 64*(pi^6*a*b^3 + 12*pi^4*a^3*b^3 + 48*pi^2*a^5*b^3 + 64*a^7*b^3)*x^3 + 8*(pi^8*b^2 + 24*pi^6*a^2*b^2 + 192*pi^4*a^4*b^2 + 640*pi^2*a^6*b^2 + 768*a^8*b^2)*x^2 + 16*(pi^8*a*b + 16*pi^6*a^3*b + 96*pi^4*a^5*b + 256*pi^2*a^7*b + 256*a^9*b)*x)","B",0
182,1,1078,0,0.536193," ","integrate(1/x^2/arccoth(tanh(b*x+a))^3,x, algorithm=""fricas"")","\frac{8 \, {\left(6 \, \pi^{8} a + 64 \, \pi^{6} a^{3} + 192 \, \pi^{4} a^{5} - 512 \, a^{9} + 96 \, {\left(3 \, \pi^{4} a b^{4} + 8 \, \pi^{2} a^{3} b^{4} - 16 \, a^{5} b^{4}\right)} x^{4} - 12 \, {\left(\pi^{6} b^{3} - 92 \, \pi^{4} a^{2} b^{3} - 272 \, \pi^{2} a^{4} b^{3} + 448 \, a^{6} b^{3}\right)} x^{3} + 8 \, {\left(11 \, \pi^{6} a b^{2} + 228 \, \pi^{4} a^{3} b^{2} + 528 \, \pi^{2} a^{5} b^{2} - 832 \, a^{7} b^{2}\right)} x^{2} - {\left(5 \, \pi^{8} b - 176 \, \pi^{6} a^{2} b - 1440 \, \pi^{4} a^{4} b - 1792 \, \pi^{2} a^{6} b + 3328 \, a^{8} b\right)} x - 96 \, {\left(16 \, {\left(\pi^{3} a b^{5} - 4 \, \pi a^{3} b^{5}\right)} x^{5} + 64 \, {\left(\pi^{3} a^{2} b^{4} - 4 \, \pi a^{4} b^{4}\right)} x^{4} + 8 \, {\left(\pi^{5} a b^{3} + 8 \, \pi^{3} a^{3} b^{3} - 48 \, \pi a^{5} b^{3}\right)} x^{3} + 16 \, {\left(\pi^{5} a^{2} b^{2} - 16 \, \pi a^{6} b^{2}\right)} x^{2} + {\left(\pi^{7} a b + 4 \, \pi^{5} a^{3} b - 16 \, \pi^{3} a^{5} b - 64 \, \pi a^{7} b\right)} x\right)} \arctan\left(-\frac{2 \, b x + 2 \, a - \sqrt{4 \, b^{2} x^{2} + 8 \, a b x + \pi^{2} + 4 \, a^{2}}}{\pi}\right) + 3 \, {\left(16 \, {\left(\pi^{4} b^{5} - 24 \, \pi^{2} a^{2} b^{5} + 16 \, a^{4} b^{5}\right)} x^{5} + 64 \, {\left(\pi^{4} a b^{4} - 24 \, \pi^{2} a^{3} b^{4} + 16 \, a^{5} b^{4}\right)} x^{4} + 8 \, {\left(\pi^{6} b^{3} - 12 \, \pi^{4} a^{2} b^{3} - 272 \, \pi^{2} a^{4} b^{3} + 192 \, a^{6} b^{3}\right)} x^{3} + 16 \, {\left(\pi^{6} a b^{2} - 20 \, \pi^{4} a^{3} b^{2} - 80 \, \pi^{2} a^{5} b^{2} + 64 \, a^{7} b^{2}\right)} x^{2} + {\left(\pi^{8} b - 16 \, \pi^{6} a^{2} b - 160 \, \pi^{4} a^{4} b - 256 \, \pi^{2} a^{6} b + 256 \, a^{8} b\right)} x\right)} \log\left(4 \, b^{2} x^{2} + 8 \, a b x + \pi^{2} + 4 \, a^{2}\right) - 6 \, {\left(16 \, {\left(\pi^{4} b^{5} - 24 \, \pi^{2} a^{2} b^{5} + 16 \, a^{4} b^{5}\right)} x^{5} + 64 \, {\left(\pi^{4} a b^{4} - 24 \, \pi^{2} a^{3} b^{4} + 16 \, a^{5} b^{4}\right)} x^{4} + 8 \, {\left(\pi^{6} b^{3} - 12 \, \pi^{4} a^{2} b^{3} - 272 \, \pi^{2} a^{4} b^{3} + 192 \, a^{6} b^{3}\right)} x^{3} + 16 \, {\left(\pi^{6} a b^{2} - 20 \, \pi^{4} a^{3} b^{2} - 80 \, \pi^{2} a^{5} b^{2} + 64 \, a^{7} b^{2}\right)} x^{2} + {\left(\pi^{8} b - 16 \, \pi^{6} a^{2} b - 160 \, \pi^{4} a^{4} b - 256 \, \pi^{2} a^{6} b + 256 \, a^{8} b\right)} x\right)} \log\left(x\right)\right)}}{16 \, {\left(\pi^{8} b^{4} + 16 \, \pi^{6} a^{2} b^{4} + 96 \, \pi^{4} a^{4} b^{4} + 256 \, \pi^{2} a^{6} b^{4} + 256 \, a^{8} b^{4}\right)} x^{5} + 64 \, {\left(\pi^{8} a b^{3} + 16 \, \pi^{6} a^{3} b^{3} + 96 \, \pi^{4} a^{5} b^{3} + 256 \, \pi^{2} a^{7} b^{3} + 256 \, a^{9} b^{3}\right)} x^{4} + 8 \, {\left(\pi^{10} b^{2} + 28 \, \pi^{8} a^{2} b^{2} + 288 \, \pi^{6} a^{4} b^{2} + 1408 \, \pi^{4} a^{6} b^{2} + 3328 \, \pi^{2} a^{8} b^{2} + 3072 \, a^{10} b^{2}\right)} x^{3} + 16 \, {\left(\pi^{10} a b + 20 \, \pi^{8} a^{3} b + 160 \, \pi^{6} a^{5} b + 640 \, \pi^{4} a^{7} b + 1280 \, \pi^{2} a^{9} b + 1024 \, a^{11} b\right)} x^{2} + {\left(\pi^{12} + 24 \, \pi^{10} a^{2} + 240 \, \pi^{8} a^{4} + 1280 \, \pi^{6} a^{6} + 3840 \, \pi^{4} a^{8} + 6144 \, \pi^{2} a^{10} + 4096 \, a^{12}\right)} x}"," ",0,"8*(6*pi^8*a + 64*pi^6*a^3 + 192*pi^4*a^5 - 512*a^9 + 96*(3*pi^4*a*b^4 + 8*pi^2*a^3*b^4 - 16*a^5*b^4)*x^4 - 12*(pi^6*b^3 - 92*pi^4*a^2*b^3 - 272*pi^2*a^4*b^3 + 448*a^6*b^3)*x^3 + 8*(11*pi^6*a*b^2 + 228*pi^4*a^3*b^2 + 528*pi^2*a^5*b^2 - 832*a^7*b^2)*x^2 - (5*pi^8*b - 176*pi^6*a^2*b - 1440*pi^4*a^4*b - 1792*pi^2*a^6*b + 3328*a^8*b)*x - 96*(16*(pi^3*a*b^5 - 4*pi*a^3*b^5)*x^5 + 64*(pi^3*a^2*b^4 - 4*pi*a^4*b^4)*x^4 + 8*(pi^5*a*b^3 + 8*pi^3*a^3*b^3 - 48*pi*a^5*b^3)*x^3 + 16*(pi^5*a^2*b^2 - 16*pi*a^6*b^2)*x^2 + (pi^7*a*b + 4*pi^5*a^3*b - 16*pi^3*a^5*b - 64*pi*a^7*b)*x)*arctan(-(2*b*x + 2*a - sqrt(4*b^2*x^2 + 8*a*b*x + pi^2 + 4*a^2))/pi) + 3*(16*(pi^4*b^5 - 24*pi^2*a^2*b^5 + 16*a^4*b^5)*x^5 + 64*(pi^4*a*b^4 - 24*pi^2*a^3*b^4 + 16*a^5*b^4)*x^4 + 8*(pi^6*b^3 - 12*pi^4*a^2*b^3 - 272*pi^2*a^4*b^3 + 192*a^6*b^3)*x^3 + 16*(pi^6*a*b^2 - 20*pi^4*a^3*b^2 - 80*pi^2*a^5*b^2 + 64*a^7*b^2)*x^2 + (pi^8*b - 16*pi^6*a^2*b - 160*pi^4*a^4*b - 256*pi^2*a^6*b + 256*a^8*b)*x)*log(4*b^2*x^2 + 8*a*b*x + pi^2 + 4*a^2) - 6*(16*(pi^4*b^5 - 24*pi^2*a^2*b^5 + 16*a^4*b^5)*x^5 + 64*(pi^4*a*b^4 - 24*pi^2*a^3*b^4 + 16*a^5*b^4)*x^4 + 8*(pi^6*b^3 - 12*pi^4*a^2*b^3 - 272*pi^2*a^4*b^3 + 192*a^6*b^3)*x^3 + 16*(pi^6*a*b^2 - 20*pi^4*a^3*b^2 - 80*pi^2*a^5*b^2 + 64*a^7*b^2)*x^2 + (pi^8*b - 16*pi^6*a^2*b - 160*pi^4*a^4*b - 256*pi^2*a^6*b + 256*a^8*b)*x)*log(x))/(16*(pi^8*b^4 + 16*pi^6*a^2*b^4 + 96*pi^4*a^4*b^4 + 256*pi^2*a^6*b^4 + 256*a^8*b^4)*x^5 + 64*(pi^8*a*b^3 + 16*pi^6*a^3*b^3 + 96*pi^4*a^5*b^3 + 256*pi^2*a^7*b^3 + 256*a^9*b^3)*x^4 + 8*(pi^10*b^2 + 28*pi^8*a^2*b^2 + 288*pi^6*a^4*b^2 + 1408*pi^4*a^6*b^2 + 3328*pi^2*a^8*b^2 + 3072*a^10*b^2)*x^3 + 16*(pi^10*a*b + 20*pi^8*a^3*b + 160*pi^6*a^5*b + 640*pi^4*a^7*b + 1280*pi^2*a^9*b + 1024*a^11*b)*x^2 + (pi^12 + 24*pi^10*a^2 + 240*pi^8*a^4 + 1280*pi^6*a^6 + 3840*pi^4*a^8 + 6144*pi^2*a^10 + 4096*a^12)*x)","B",0
183,1,1316,0,0.622923," ","integrate(1/x^3/arccoth(tanh(b*x+a))^3,x, algorithm=""fricas"")","\frac{8 \, {\left(3 \, \pi^{10} a + 44 \, \pi^{8} a^{3} + 224 \, \pi^{6} a^{5} + 384 \, \pi^{4} a^{7} - 256 \, \pi^{2} a^{9} - 1024 \, a^{11} + 192 \, {\left(\pi^{6} b^{5} - 20 \, \pi^{4} a^{2} b^{5} - 80 \, \pi^{2} a^{4} b^{5} + 64 \, a^{6} b^{5}\right)} x^{5} + 96 \, {\left(11 \, \pi^{6} a b^{4} - 140 \, \pi^{4} a^{3} b^{4} - 624 \, \pi^{2} a^{5} b^{4} + 448 \, a^{7} b^{4}\right)} x^{4} + 16 \, {\left(5 \, \pi^{8} b^{3} + 16 \, \pi^{6} a^{2} b^{3} - 1440 \, \pi^{4} a^{4} b^{3} - 4864 \, \pi^{2} a^{6} b^{3} + 3328 \, a^{8} b^{3}\right)} x^{3} + 4 \, {\left(65 \, \pi^{8} a b^{2} - 272 \, \pi^{6} a^{3} b^{2} - 4896 \, \pi^{4} a^{5} b^{2} - 9472 \, \pi^{2} a^{7} b^{2} + 6400 \, a^{9} b^{2}\right)} x^{2} + 2 \, {\left(3 \, \pi^{10} b - 12 \, \pi^{8} a^{2} b - 416 \, \pi^{6} a^{4} b - 1920 \, \pi^{4} a^{6} b - 2304 \, \pi^{2} a^{8} b + 1024 \, a^{10} b\right)} x - 48 \, {\left(16 \, {\left(\pi^{5} b^{6} - 40 \, \pi^{3} a^{2} b^{6} + 80 \, \pi a^{4} b^{6}\right)} x^{6} + 64 \, {\left(\pi^{5} a b^{5} - 40 \, \pi^{3} a^{3} b^{5} + 80 \, \pi a^{5} b^{5}\right)} x^{5} + 8 \, {\left(\pi^{7} b^{4} - 28 \, \pi^{5} a^{2} b^{4} - 400 \, \pi^{3} a^{4} b^{4} + 960 \, \pi a^{6} b^{4}\right)} x^{4} + 16 \, {\left(\pi^{7} a b^{3} - 36 \, \pi^{5} a^{3} b^{3} - 80 \, \pi^{3} a^{5} b^{3} + 320 \, \pi a^{7} b^{3}\right)} x^{3} + {\left(\pi^{9} b^{2} - 32 \, \pi^{7} a^{2} b^{2} - 224 \, \pi^{5} a^{4} b^{2} + 1280 \, \pi a^{8} b^{2}\right)} x^{2}\right)} \arctan\left(-\frac{2 \, b x + 2 \, a - \sqrt{4 \, b^{2} x^{2} + 8 \, a b x + \pi^{2} + 4 \, a^{2}}}{\pi}\right) - 24 \, {\left(16 \, {\left(5 \, \pi^{4} a b^{6} - 40 \, \pi^{2} a^{3} b^{6} + 16 \, a^{5} b^{6}\right)} x^{6} + 64 \, {\left(5 \, \pi^{4} a^{2} b^{5} - 40 \, \pi^{2} a^{4} b^{5} + 16 \, a^{6} b^{5}\right)} x^{5} + 8 \, {\left(5 \, \pi^{6} a b^{4} + 20 \, \pi^{4} a^{3} b^{4} - 464 \, \pi^{2} a^{5} b^{4} + 192 \, a^{7} b^{4}\right)} x^{4} + 16 \, {\left(5 \, \pi^{6} a^{2} b^{3} - 20 \, \pi^{4} a^{4} b^{3} - 144 \, \pi^{2} a^{6} b^{3} + 64 \, a^{8} b^{3}\right)} x^{3} + {\left(5 \, \pi^{8} a b^{2} - 224 \, \pi^{4} a^{5} b^{2} - 512 \, \pi^{2} a^{7} b^{2} + 256 \, a^{9} b^{2}\right)} x^{2}\right)} \log\left(4 \, b^{2} x^{2} + 8 \, a b x + \pi^{2} + 4 \, a^{2}\right) + 48 \, {\left(16 \, {\left(5 \, \pi^{4} a b^{6} - 40 \, \pi^{2} a^{3} b^{6} + 16 \, a^{5} b^{6}\right)} x^{6} + 64 \, {\left(5 \, \pi^{4} a^{2} b^{5} - 40 \, \pi^{2} a^{4} b^{5} + 16 \, a^{6} b^{5}\right)} x^{5} + 8 \, {\left(5 \, \pi^{6} a b^{4} + 20 \, \pi^{4} a^{3} b^{4} - 464 \, \pi^{2} a^{5} b^{4} + 192 \, a^{7} b^{4}\right)} x^{4} + 16 \, {\left(5 \, \pi^{6} a^{2} b^{3} - 20 \, \pi^{4} a^{4} b^{3} - 144 \, \pi^{2} a^{6} b^{3} + 64 \, a^{8} b^{3}\right)} x^{3} + {\left(5 \, \pi^{8} a b^{2} - 224 \, \pi^{4} a^{5} b^{2} - 512 \, \pi^{2} a^{7} b^{2} + 256 \, a^{9} b^{2}\right)} x^{2}\right)} \log\left(x\right)\right)}}{16 \, {\left(\pi^{10} b^{4} + 20 \, \pi^{8} a^{2} b^{4} + 160 \, \pi^{6} a^{4} b^{4} + 640 \, \pi^{4} a^{6} b^{4} + 1280 \, \pi^{2} a^{8} b^{4} + 1024 \, a^{10} b^{4}\right)} x^{6} + 64 \, {\left(\pi^{10} a b^{3} + 20 \, \pi^{8} a^{3} b^{3} + 160 \, \pi^{6} a^{5} b^{3} + 640 \, \pi^{4} a^{7} b^{3} + 1280 \, \pi^{2} a^{9} b^{3} + 1024 \, a^{11} b^{3}\right)} x^{5} + 8 \, {\left(\pi^{12} b^{2} + 32 \, \pi^{10} a^{2} b^{2} + 400 \, \pi^{8} a^{4} b^{2} + 2560 \, \pi^{6} a^{6} b^{2} + 8960 \, \pi^{4} a^{8} b^{2} + 16384 \, \pi^{2} a^{10} b^{2} + 12288 \, a^{12} b^{2}\right)} x^{4} + 16 \, {\left(\pi^{12} a b + 24 \, \pi^{10} a^{3} b + 240 \, \pi^{8} a^{5} b + 1280 \, \pi^{6} a^{7} b + 3840 \, \pi^{4} a^{9} b + 6144 \, \pi^{2} a^{11} b + 4096 \, a^{13} b\right)} x^{3} + {\left(\pi^{14} + 28 \, \pi^{12} a^{2} + 336 \, \pi^{10} a^{4} + 2240 \, \pi^{8} a^{6} + 8960 \, \pi^{6} a^{8} + 21504 \, \pi^{4} a^{10} + 28672 \, \pi^{2} a^{12} + 16384 \, a^{14}\right)} x^{2}}"," ",0,"8*(3*pi^10*a + 44*pi^8*a^3 + 224*pi^6*a^5 + 384*pi^4*a^7 - 256*pi^2*a^9 - 1024*a^11 + 192*(pi^6*b^5 - 20*pi^4*a^2*b^5 - 80*pi^2*a^4*b^5 + 64*a^6*b^5)*x^5 + 96*(11*pi^6*a*b^4 - 140*pi^4*a^3*b^4 - 624*pi^2*a^5*b^4 + 448*a^7*b^4)*x^4 + 16*(5*pi^8*b^3 + 16*pi^6*a^2*b^3 - 1440*pi^4*a^4*b^3 - 4864*pi^2*a^6*b^3 + 3328*a^8*b^3)*x^3 + 4*(65*pi^8*a*b^2 - 272*pi^6*a^3*b^2 - 4896*pi^4*a^5*b^2 - 9472*pi^2*a^7*b^2 + 6400*a^9*b^2)*x^2 + 2*(3*pi^10*b - 12*pi^8*a^2*b - 416*pi^6*a^4*b - 1920*pi^4*a^6*b - 2304*pi^2*a^8*b + 1024*a^10*b)*x - 48*(16*(pi^5*b^6 - 40*pi^3*a^2*b^6 + 80*pi*a^4*b^6)*x^6 + 64*(pi^5*a*b^5 - 40*pi^3*a^3*b^5 + 80*pi*a^5*b^5)*x^5 + 8*(pi^7*b^4 - 28*pi^5*a^2*b^4 - 400*pi^3*a^4*b^4 + 960*pi*a^6*b^4)*x^4 + 16*(pi^7*a*b^3 - 36*pi^5*a^3*b^3 - 80*pi^3*a^5*b^3 + 320*pi*a^7*b^3)*x^3 + (pi^9*b^2 - 32*pi^7*a^2*b^2 - 224*pi^5*a^4*b^2 + 1280*pi*a^8*b^2)*x^2)*arctan(-(2*b*x + 2*a - sqrt(4*b^2*x^2 + 8*a*b*x + pi^2 + 4*a^2))/pi) - 24*(16*(5*pi^4*a*b^6 - 40*pi^2*a^3*b^6 + 16*a^5*b^6)*x^6 + 64*(5*pi^4*a^2*b^5 - 40*pi^2*a^4*b^5 + 16*a^6*b^5)*x^5 + 8*(5*pi^6*a*b^4 + 20*pi^4*a^3*b^4 - 464*pi^2*a^5*b^4 + 192*a^7*b^4)*x^4 + 16*(5*pi^6*a^2*b^3 - 20*pi^4*a^4*b^3 - 144*pi^2*a^6*b^3 + 64*a^8*b^3)*x^3 + (5*pi^8*a*b^2 - 224*pi^4*a^5*b^2 - 512*pi^2*a^7*b^2 + 256*a^9*b^2)*x^2)*log(4*b^2*x^2 + 8*a*b*x + pi^2 + 4*a^2) + 48*(16*(5*pi^4*a*b^6 - 40*pi^2*a^3*b^6 + 16*a^5*b^6)*x^6 + 64*(5*pi^4*a^2*b^5 - 40*pi^2*a^4*b^5 + 16*a^6*b^5)*x^5 + 8*(5*pi^6*a*b^4 + 20*pi^4*a^3*b^4 - 464*pi^2*a^5*b^4 + 192*a^7*b^4)*x^4 + 16*(5*pi^6*a^2*b^3 - 20*pi^4*a^4*b^3 - 144*pi^2*a^6*b^3 + 64*a^8*b^3)*x^3 + (5*pi^8*a*b^2 - 224*pi^4*a^5*b^2 - 512*pi^2*a^7*b^2 + 256*a^9*b^2)*x^2)*log(x))/(16*(pi^10*b^4 + 20*pi^8*a^2*b^4 + 160*pi^6*a^4*b^4 + 640*pi^4*a^6*b^4 + 1280*pi^2*a^8*b^4 + 1024*a^10*b^4)*x^6 + 64*(pi^10*a*b^3 + 20*pi^8*a^3*b^3 + 160*pi^6*a^5*b^3 + 640*pi^4*a^7*b^3 + 1280*pi^2*a^9*b^3 + 1024*a^11*b^3)*x^5 + 8*(pi^12*b^2 + 32*pi^10*a^2*b^2 + 400*pi^8*a^4*b^2 + 2560*pi^6*a^6*b^2 + 8960*pi^4*a^8*b^2 + 16384*pi^2*a^10*b^2 + 12288*a^12*b^2)*x^4 + 16*(pi^12*a*b + 24*pi^10*a^3*b + 240*pi^8*a^5*b + 1280*pi^6*a^7*b + 3840*pi^4*a^9*b + 6144*pi^2*a^11*b + 4096*a^13*b)*x^3 + (pi^14 + 28*pi^12*a^2 + 336*pi^10*a^4 + 2240*pi^8*a^6 + 8960*pi^6*a^8 + 21504*pi^4*a^10 + 28672*pi^2*a^12 + 16384*a^14)*x^2)","B",0
184,0,0,0,0.423437," ","integrate(x^m*arccoth(tanh(b*x+a))^n,x, algorithm=""fricas"")","{\rm integral}\left(x^{m} \operatorname{arcoth}\left(\tanh\left(b x + a\right)\right)^{n}, x\right)"," ",0,"integral(x^m*arccoth(tanh(b*x + a))^n, x)","F",0
185,1,583,0,0.720892," ","integrate(x^4*arccoth(tanh(b*x+a))^n,x, algorithm=""fricas"")","\frac{2 \, {\left(2 \, {\left(b^{5} n^{4} + 10 \, b^{5} n^{3} + 35 \, b^{5} n^{2} + 50 \, b^{5} n + 24 \, b^{5}\right)} x^{5} + 15 \, \pi^{4} a - 120 \, \pi^{2} a^{3} + 48 \, a^{5} + 2 \, {\left(a b^{4} n^{4} + 6 \, a b^{4} n^{3} + 11 \, a b^{4} n^{2} + 6 \, a b^{4} n\right)} x^{4} - 2 \, {\left(4 \, a^{2} b^{3} n^{3} + 12 \, a^{2} b^{3} n^{2} + 8 \, a^{2} b^{3} n - \pi^{2} {\left(b^{3} n^{3} + 3 \, b^{3} n^{2} + 2 \, b^{3} n\right)}\right)} x^{3} + 6 \, {\left(4 \, a^{3} b^{2} n^{2} + 4 \, a^{3} b^{2} n - 3 \, \pi^{2} {\left(a b^{2} n^{2} + a b^{2} n\right)}\right)} x^{2} - 3 \, {\left(\pi^{4} b n - 24 \, \pi^{2} a^{2} b n + 16 \, a^{4} b n\right)} x\right)} {\left(b^{2} x^{2} + 2 \, a b x + \frac{1}{4} \, \pi^{2} + a^{2}\right)}^{\frac{1}{2} \, n} \cos\left(2 \, n \arctan\left(-\frac{2 \, b x}{\pi} - \frac{2 \, a}{\pi} + \frac{\sqrt{4 \, b^{2} x^{2} + 8 \, a b x + \pi^{2} + 4 \, a^{2}}}{\pi}\right)\right) - {\left(2 \, \pi {\left(b^{4} n^{4} + 6 \, b^{4} n^{3} + 11 \, b^{4} n^{2} + 6 \, b^{4} n\right)} x^{4} + 3 \, \pi^{5} - 120 \, \pi^{3} a^{2} + 240 \, \pi a^{4} - 16 \, \pi {\left(a b^{3} n^{3} + 3 \, a b^{3} n^{2} + 2 \, a b^{3} n\right)} x^{3} - 6 \, {\left(\pi^{3} {\left(b^{2} n^{2} + b^{2} n\right)} - 12 \, \pi {\left(a^{2} b^{2} n^{2} + a^{2} b^{2} n\right)}\right)} x^{2} + 48 \, {\left(\pi^{3} a b n - 4 \, \pi a^{3} b n\right)} x\right)} {\left(b^{2} x^{2} + 2 \, a b x + \frac{1}{4} \, \pi^{2} + a^{2}\right)}^{\frac{1}{2} \, n} \sin\left(2 \, n \arctan\left(-\frac{2 \, b x}{\pi} - \frac{2 \, a}{\pi} + \frac{\sqrt{4 \, b^{2} x^{2} + 8 \, a b x + \pi^{2} + 4 \, a^{2}}}{\pi}\right)\right)}{4 \, {\left(b^{5} n^{5} + 15 \, b^{5} n^{4} + 85 \, b^{5} n^{3} + 225 \, b^{5} n^{2} + 274 \, b^{5} n + 120 \, b^{5}\right)}}"," ",0,"1/4*(2*(2*(b^5*n^4 + 10*b^5*n^3 + 35*b^5*n^2 + 50*b^5*n + 24*b^5)*x^5 + 15*pi^4*a - 120*pi^2*a^3 + 48*a^5 + 2*(a*b^4*n^4 + 6*a*b^4*n^3 + 11*a*b^4*n^2 + 6*a*b^4*n)*x^4 - 2*(4*a^2*b^3*n^3 + 12*a^2*b^3*n^2 + 8*a^2*b^3*n - pi^2*(b^3*n^3 + 3*b^3*n^2 + 2*b^3*n))*x^3 + 6*(4*a^3*b^2*n^2 + 4*a^3*b^2*n - 3*pi^2*(a*b^2*n^2 + a*b^2*n))*x^2 - 3*(pi^4*b*n - 24*pi^2*a^2*b*n + 16*a^4*b*n)*x)*(b^2*x^2 + 2*a*b*x + 1/4*pi^2 + a^2)^(1/2*n)*cos(2*n*arctan(-2*b*x/pi - 2*a/pi + sqrt(4*b^2*x^2 + 8*a*b*x + pi^2 + 4*a^2)/pi)) - (2*pi*(b^4*n^4 + 6*b^4*n^3 + 11*b^4*n^2 + 6*b^4*n)*x^4 + 3*pi^5 - 120*pi^3*a^2 + 240*pi*a^4 - 16*pi*(a*b^3*n^3 + 3*a*b^3*n^2 + 2*a*b^3*n)*x^3 - 6*(pi^3*(b^2*n^2 + b^2*n) - 12*pi*(a^2*b^2*n^2 + a^2*b^2*n))*x^2 + 48*(pi^3*a*b*n - 4*pi*a^3*b*n)*x)*(b^2*x^2 + 2*a*b*x + 1/4*pi^2 + a^2)^(1/2*n)*sin(2*n*arctan(-2*b*x/pi - 2*a/pi + sqrt(4*b^2*x^2 + 8*a*b*x + pi^2 + 4*a^2)/pi)))/(b^5*n^5 + 15*b^5*n^4 + 85*b^5*n^3 + 225*b^5*n^2 + 274*b^5*n + 120*b^5)","B",0
186,1,411,0,1.475722," ","integrate(x^3*arccoth(tanh(b*x+a))^n,x, algorithm=""fricas"")","\frac{{\left(8 \, {\left(b^{4} n^{3} + 6 \, b^{4} n^{2} + 11 \, b^{4} n + 6 \, b^{4}\right)} x^{4} - 3 \, \pi^{4} + 72 \, \pi^{2} a^{2} - 48 \, a^{4} + 8 \, {\left(a b^{3} n^{3} + 3 \, a b^{3} n^{2} + 2 \, a b^{3} n\right)} x^{3} - 6 \, {\left(4 \, a^{2} b^{2} n^{2} + 4 \, a^{2} b^{2} n - \pi^{2} {\left(b^{2} n^{2} + b^{2} n\right)}\right)} x^{2} - 12 \, {\left(3 \, \pi^{2} a b n - 4 \, a^{3} b n\right)} x\right)} {\left(b^{2} x^{2} + 2 \, a b x + \frac{1}{4} \, \pi^{2} + a^{2}\right)}^{\frac{1}{2} \, n} \cos\left(2 \, n \arctan\left(-\frac{2 \, b x}{\pi} - \frac{2 \, a}{\pi} + \frac{\sqrt{4 \, b^{2} x^{2} + 8 \, a b x + \pi^{2} + 4 \, a^{2}}}{\pi}\right)\right) - 2 \, {\left(2 \, \pi {\left(b^{3} n^{3} + 3 \, b^{3} n^{2} + 2 \, b^{3} n\right)} x^{3} + 12 \, \pi^{3} a - 48 \, \pi a^{3} - 12 \, \pi {\left(a b^{2} n^{2} + a b^{2} n\right)} x^{2} - 3 \, {\left(\pi^{3} b n - 12 \, \pi a^{2} b n\right)} x\right)} {\left(b^{2} x^{2} + 2 \, a b x + \frac{1}{4} \, \pi^{2} + a^{2}\right)}^{\frac{1}{2} \, n} \sin\left(2 \, n \arctan\left(-\frac{2 \, b x}{\pi} - \frac{2 \, a}{\pi} + \frac{\sqrt{4 \, b^{2} x^{2} + 8 \, a b x + \pi^{2} + 4 \, a^{2}}}{\pi}\right)\right)}{8 \, {\left(b^{4} n^{4} + 10 \, b^{4} n^{3} + 35 \, b^{4} n^{2} + 50 \, b^{4} n + 24 \, b^{4}\right)}}"," ",0,"1/8*((8*(b^4*n^3 + 6*b^4*n^2 + 11*b^4*n + 6*b^4)*x^4 - 3*pi^4 + 72*pi^2*a^2 - 48*a^4 + 8*(a*b^3*n^3 + 3*a*b^3*n^2 + 2*a*b^3*n)*x^3 - 6*(4*a^2*b^2*n^2 + 4*a^2*b^2*n - pi^2*(b^2*n^2 + b^2*n))*x^2 - 12*(3*pi^2*a*b*n - 4*a^3*b*n)*x)*(b^2*x^2 + 2*a*b*x + 1/4*pi^2 + a^2)^(1/2*n)*cos(2*n*arctan(-2*b*x/pi - 2*a/pi + sqrt(4*b^2*x^2 + 8*a*b*x + pi^2 + 4*a^2)/pi)) - 2*(2*pi*(b^3*n^3 + 3*b^3*n^2 + 2*b^3*n)*x^3 + 12*pi^3*a - 48*pi*a^3 - 12*pi*(a*b^2*n^2 + a*b^2*n)*x^2 - 3*(pi^3*b*n - 12*pi*a^2*b*n)*x)*(b^2*x^2 + 2*a*b*x + 1/4*pi^2 + a^2)^(1/2*n)*sin(2*n*arctan(-2*b*x/pi - 2*a/pi + sqrt(4*b^2*x^2 + 8*a*b*x + pi^2 + 4*a^2)/pi)))/(b^4*n^4 + 10*b^4*n^3 + 35*b^4*n^2 + 50*b^4*n + 24*b^4)","B",0
187,1,287,0,0.464396," ","integrate(x^2*arccoth(tanh(b*x+a))^n,x, algorithm=""fricas"")","\frac{2 \, {\left(2 \, {\left(b^{3} n^{2} + 3 \, b^{3} n + 2 \, b^{3}\right)} x^{3} - 3 \, \pi^{2} a + 4 \, a^{3} + 2 \, {\left(a b^{2} n^{2} + a b^{2} n\right)} x^{2} + {\left(\pi^{2} b n - 4 \, a^{2} b n\right)} x\right)} {\left(b^{2} x^{2} + 2 \, a b x + \frac{1}{4} \, \pi^{2} + a^{2}\right)}^{\frac{1}{2} \, n} \cos\left(2 \, n \arctan\left(-\frac{2 \, b x}{\pi} - \frac{2 \, a}{\pi} + \frac{\sqrt{4 \, b^{2} x^{2} + 8 \, a b x + \pi^{2} + 4 \, a^{2}}}{\pi}\right)\right) + {\left(8 \, \pi a b n x - 2 \, \pi {\left(b^{2} n^{2} + b^{2} n\right)} x^{2} + \pi^{3} - 12 \, \pi a^{2}\right)} {\left(b^{2} x^{2} + 2 \, a b x + \frac{1}{4} \, \pi^{2} + a^{2}\right)}^{\frac{1}{2} \, n} \sin\left(2 \, n \arctan\left(-\frac{2 \, b x}{\pi} - \frac{2 \, a}{\pi} + \frac{\sqrt{4 \, b^{2} x^{2} + 8 \, a b x + \pi^{2} + 4 \, a^{2}}}{\pi}\right)\right)}{4 \, {\left(b^{3} n^{3} + 6 \, b^{3} n^{2} + 11 \, b^{3} n + 6 \, b^{3}\right)}}"," ",0,"1/4*(2*(2*(b^3*n^2 + 3*b^3*n + 2*b^3)*x^3 - 3*pi^2*a + 4*a^3 + 2*(a*b^2*n^2 + a*b^2*n)*x^2 + (pi^2*b*n - 4*a^2*b*n)*x)*(b^2*x^2 + 2*a*b*x + 1/4*pi^2 + a^2)^(1/2*n)*cos(2*n*arctan(-2*b*x/pi - 2*a/pi + sqrt(4*b^2*x^2 + 8*a*b*x + pi^2 + 4*a^2)/pi)) + (8*pi*a*b*n*x - 2*pi*(b^2*n^2 + b^2*n)*x^2 + pi^3 - 12*pi*a^2)*(b^2*x^2 + 2*a*b*x + 1/4*pi^2 + a^2)^(1/2*n)*sin(2*n*arctan(-2*b*x/pi - 2*a/pi + sqrt(4*b^2*x^2 + 8*a*b*x + pi^2 + 4*a^2)/pi)))/(b^3*n^3 + 6*b^3*n^2 + 11*b^3*n + 6*b^3)","B",0
188,1,210,0,0.573963," ","integrate(x*arccoth(tanh(b*x+a))^n,x, algorithm=""fricas"")","\frac{{\left(4 \, a b n x + 4 \, {\left(b^{2} n + b^{2}\right)} x^{2} + \pi^{2} - 4 \, a^{2}\right)} {\left(b^{2} x^{2} + 2 \, a b x + \frac{1}{4} \, \pi^{2} + a^{2}\right)}^{\frac{1}{2} \, n} \cos\left(2 \, n \arctan\left(-\frac{2 \, b x}{\pi} - \frac{2 \, a}{\pi} + \frac{\sqrt{4 \, b^{2} x^{2} + 8 \, a b x + \pi^{2} + 4 \, a^{2}}}{\pi}\right)\right) - 2 \, {\left(\pi b n x - 2 \, \pi a\right)} {\left(b^{2} x^{2} + 2 \, a b x + \frac{1}{4} \, \pi^{2} + a^{2}\right)}^{\frac{1}{2} \, n} \sin\left(2 \, n \arctan\left(-\frac{2 \, b x}{\pi} - \frac{2 \, a}{\pi} + \frac{\sqrt{4 \, b^{2} x^{2} + 8 \, a b x + \pi^{2} + 4 \, a^{2}}}{\pi}\right)\right)}{4 \, {\left(b^{2} n^{2} + 3 \, b^{2} n + 2 \, b^{2}\right)}}"," ",0,"1/4*((4*a*b*n*x + 4*(b^2*n + b^2)*x^2 + pi^2 - 4*a^2)*(b^2*x^2 + 2*a*b*x + 1/4*pi^2 + a^2)^(1/2*n)*cos(2*n*arctan(-2*b*x/pi - 2*a/pi + sqrt(4*b^2*x^2 + 8*a*b*x + pi^2 + 4*a^2)/pi)) - 2*(pi*b*n*x - 2*pi*a)*(b^2*x^2 + 2*a*b*x + 1/4*pi^2 + a^2)^(1/2*n)*sin(2*n*arctan(-2*b*x/pi - 2*a/pi + sqrt(4*b^2*x^2 + 8*a*b*x + pi^2 + 4*a^2)/pi)))/(b^2*n^2 + 3*b^2*n + 2*b^2)","B",0
189,1,164,0,0.573337," ","integrate(arccoth(tanh(b*x+a))^n,x, algorithm=""fricas"")","\frac{2 \, {\left(b x + a\right)} {\left(b^{2} x^{2} + 2 \, a b x + \frac{1}{4} \, \pi^{2} + a^{2}\right)}^{\frac{1}{2} \, n} \cos\left(2 \, n \arctan\left(-\frac{2 \, b x}{\pi} - \frac{2 \, a}{\pi} + \frac{\sqrt{4 \, b^{2} x^{2} + 8 \, a b x + \pi^{2} + 4 \, a^{2}}}{\pi}\right)\right) - \pi {\left(b^{2} x^{2} + 2 \, a b x + \frac{1}{4} \, \pi^{2} + a^{2}\right)}^{\frac{1}{2} \, n} \sin\left(2 \, n \arctan\left(-\frac{2 \, b x}{\pi} - \frac{2 \, a}{\pi} + \frac{\sqrt{4 \, b^{2} x^{2} + 8 \, a b x + \pi^{2} + 4 \, a^{2}}}{\pi}\right)\right)}{2 \, {\left(b n + b\right)}}"," ",0,"1/2*(2*(b*x + a)*(b^2*x^2 + 2*a*b*x + 1/4*pi^2 + a^2)^(1/2*n)*cos(2*n*arctan(-2*b*x/pi - 2*a/pi + sqrt(4*b^2*x^2 + 8*a*b*x + pi^2 + 4*a^2)/pi)) - pi*(b^2*x^2 + 2*a*b*x + 1/4*pi^2 + a^2)^(1/2*n)*sin(2*n*arctan(-2*b*x/pi - 2*a/pi + sqrt(4*b^2*x^2 + 8*a*b*x + pi^2 + 4*a^2)/pi)))/(b*n + b)","B",0
190,0,0,0,0.918404," ","integrate(arccoth(tanh(b*x+a))^n/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{arcoth}\left(\tanh\left(b x + a\right)\right)^{n}}{x}, x\right)"," ",0,"integral(arccoth(tanh(b*x + a))^n/x, x)","F",0
191,0,0,0,0.539939," ","integrate(arccoth(tanh(b*x+a))^n/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{arcoth}\left(\tanh\left(b x + a\right)\right)^{n}}{x^{2}}, x\right)"," ",0,"integral(arccoth(tanh(b*x + a))^n/x^2, x)","F",0
192,0,0,0,0.590226," ","integrate(arccoth(tanh(b*x+a))^n/x^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{arcoth}\left(\tanh\left(b x + a\right)\right)^{n}}{x^{3}}, x\right)"," ",0,"integral(arccoth(tanh(b*x + a))^n/x^3, x)","F",0
193,1,33,0,0.473563," ","integrate(x^m*arccoth(tanh(b*x+a)),x, algorithm=""fricas"")","\frac{{\left({\left(b m + b\right)} x^{2} + {\left(a m + 2 \, a\right)} x\right)} x^{m}}{m^{2} + 3 \, m + 2}"," ",0,"((b*m + b)*x^2 + (a*m + 2*a)*x)*x^m/(m^2 + 3*m + 2)","A",0
194,1,13,0,0.392170," ","integrate(x^2*arccoth(coth(b*x+a)),x, algorithm=""fricas"")","\frac{1}{4} x^{4} b + \frac{1}{3} x^{3} a"," ",0,"1/4*x^4*b + 1/3*x^3*a","A",0
195,1,13,0,0.358275," ","integrate(x*arccoth(coth(b*x+a)),x, algorithm=""fricas"")","\frac{1}{3} x^{3} b + \frac{1}{2} x^{2} a"," ",0,"1/3*x^3*b + 1/2*x^2*a","A",0
196,1,10,0,0.507132," ","integrate(arccoth(coth(b*x+a)),x, algorithm=""fricas"")","\frac{1}{2} x^{2} b + x a"," ",0,"1/2*x^2*b + x*a","A",0
197,1,8,0,0.498755," ","integrate(arccoth(coth(b*x+a))/x,x, algorithm=""fricas"")","b x + a \log\left(x\right)"," ",0,"b*x + a*log(x)","A",0
198,1,13,0,0.506253," ","integrate(arccoth(coth(b*x+a))/x^2,x, algorithm=""fricas"")","\frac{b x \log\left(x\right) - a}{x}"," ",0,"(b*x*log(x) - a)/x","A",0
199,1,11,0,0.536138," ","integrate(arccoth(coth(b*x+a))/x^3,x, algorithm=""fricas"")","-\frac{2 \, b x + a}{2 \, x^{2}}"," ",0,"-1/2*(2*b*x + a)/x^2","A",0
200,1,57,0,1.387544," ","integrate(arccoth(cosh(x)),x, algorithm=""fricas"")","\frac{1}{2} \, x \log\left(\frac{\cosh\left(x\right) + 1}{\cosh\left(x\right) - 1}\right) - x \log\left(\cosh\left(x\right) + \sinh\left(x\right) + 1\right) + x \log\left(-\cosh\left(x\right) - \sinh\left(x\right) + 1\right) + {\rm Li}_2\left(\cosh\left(x\right) + \sinh\left(x\right)\right) - {\rm Li}_2\left(-\cosh\left(x\right) - \sinh\left(x\right)\right)"," ",0,"1/2*x*log((cosh(x) + 1)/(cosh(x) - 1)) - x*log(cosh(x) + sinh(x) + 1) + x*log(-cosh(x) - sinh(x) + 1) + dilog(cosh(x) + sinh(x)) - dilog(-cosh(x) - sinh(x))","B",0
201,1,87,0,2.014379," ","integrate(x*arccoth(cosh(x)),x, algorithm=""fricas"")","\frac{1}{4} \, x^{2} \log\left(\frac{\cosh\left(x\right) + 1}{\cosh\left(x\right) - 1}\right) - \frac{1}{2} \, x^{2} \log\left(\cosh\left(x\right) + \sinh\left(x\right) + 1\right) + \frac{1}{2} \, x^{2} \log\left(-\cosh\left(x\right) - \sinh\left(x\right) + 1\right) + x {\rm Li}_2\left(\cosh\left(x\right) + \sinh\left(x\right)\right) - x {\rm Li}_2\left(-\cosh\left(x\right) - \sinh\left(x\right)\right) - {\rm polylog}\left(3, \cosh\left(x\right) + \sinh\left(x\right)\right) + {\rm polylog}\left(3, -\cosh\left(x\right) - \sinh\left(x\right)\right)"," ",0,"1/4*x^2*log((cosh(x) + 1)/(cosh(x) - 1)) - 1/2*x^2*log(cosh(x) + sinh(x) + 1) + 1/2*x^2*log(-cosh(x) - sinh(x) + 1) + x*dilog(cosh(x) + sinh(x)) - x*dilog(-cosh(x) - sinh(x)) - polylog(3, cosh(x) + sinh(x)) + polylog(3, -cosh(x) - sinh(x))","C",0
202,1,117,0,1.561314," ","integrate(x^2*arccoth(cosh(x)),x, algorithm=""fricas"")","\frac{1}{6} \, x^{3} \log\left(\frac{\cosh\left(x\right) + 1}{\cosh\left(x\right) - 1}\right) - \frac{1}{3} \, x^{3} \log\left(\cosh\left(x\right) + \sinh\left(x\right) + 1\right) + \frac{1}{3} \, x^{3} \log\left(-\cosh\left(x\right) - \sinh\left(x\right) + 1\right) + x^{2} {\rm Li}_2\left(\cosh\left(x\right) + \sinh\left(x\right)\right) - x^{2} {\rm Li}_2\left(-\cosh\left(x\right) - \sinh\left(x\right)\right) - 2 \, x {\rm polylog}\left(3, \cosh\left(x\right) + \sinh\left(x\right)\right) + 2 \, x {\rm polylog}\left(3, -\cosh\left(x\right) - \sinh\left(x\right)\right) + 2 \, {\rm polylog}\left(4, \cosh\left(x\right) + \sinh\left(x\right)\right) - 2 \, {\rm polylog}\left(4, -\cosh\left(x\right) - \sinh\left(x\right)\right)"," ",0,"1/6*x^3*log((cosh(x) + 1)/(cosh(x) - 1)) - 1/3*x^3*log(cosh(x) + sinh(x) + 1) + 1/3*x^3*log(-cosh(x) - sinh(x) + 1) + x^2*dilog(cosh(x) + sinh(x)) - x^2*dilog(-cosh(x) - sinh(x)) - 2*x*polylog(3, cosh(x) + sinh(x)) + 2*x*polylog(3, -cosh(x) - sinh(x)) + 2*polylog(4, cosh(x) + sinh(x)) - 2*polylog(4, -cosh(x) - sinh(x))","C",0
203,1,899,0,0.796415," ","integrate(x^2*arccoth(c+d*tanh(b*x+a)),x, algorithm=""fricas"")","\frac{b^{3} x^{3} \log\left(\frac{{\left(c + 1\right)} \cosh\left(b x + a\right) + d \sinh\left(b x + a\right)}{{\left(c - 1\right)} \cosh\left(b x + a\right) + d \sinh\left(b x + a\right)}\right) - 3 \, b^{2} x^{2} {\rm Li}_2\left(\sqrt{-\frac{c + d + 1}{c - d + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - 3 \, b^{2} x^{2} {\rm Li}_2\left(-\sqrt{-\frac{c + d + 1}{c - d + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + 3 \, b^{2} x^{2} {\rm Li}_2\left(\sqrt{-\frac{c + d - 1}{c - d - 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + 3 \, b^{2} x^{2} {\rm Li}_2\left(-\sqrt{-\frac{c + d - 1}{c - d - 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + a^{3} \log\left(2 \, {\left(c + d + 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(c + d + 1\right)} \sinh\left(b x + a\right) + 2 \, {\left(c - d + 1\right)} \sqrt{-\frac{c + d + 1}{c - d + 1}}\right) + a^{3} \log\left(2 \, {\left(c + d + 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(c + d + 1\right)} \sinh\left(b x + a\right) - 2 \, {\left(c - d + 1\right)} \sqrt{-\frac{c + d + 1}{c - d + 1}}\right) - a^{3} \log\left(2 \, {\left(c + d - 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(c + d - 1\right)} \sinh\left(b x + a\right) + 2 \, {\left(c - d - 1\right)} \sqrt{-\frac{c + d - 1}{c - d - 1}}\right) - a^{3} \log\left(2 \, {\left(c + d - 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(c + d - 1\right)} \sinh\left(b x + a\right) - 2 \, {\left(c - d - 1\right)} \sqrt{-\frac{c + d - 1}{c - d - 1}}\right) + 6 \, b x {\rm polylog}\left(3, \sqrt{-\frac{c + d + 1}{c - d + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + 6 \, b x {\rm polylog}\left(3, -\sqrt{-\frac{c + d + 1}{c - d + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - 6 \, b x {\rm polylog}\left(3, \sqrt{-\frac{c + d - 1}{c - d - 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - 6 \, b x {\rm polylog}\left(3, -\sqrt{-\frac{c + d - 1}{c - d - 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - {\left(b^{3} x^{3} + a^{3}\right)} \log\left(\sqrt{-\frac{c + d + 1}{c - d + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) - {\left(b^{3} x^{3} + a^{3}\right)} \log\left(-\sqrt{-\frac{c + d + 1}{c - d + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) + {\left(b^{3} x^{3} + a^{3}\right)} \log\left(\sqrt{-\frac{c + d - 1}{c - d - 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) + {\left(b^{3} x^{3} + a^{3}\right)} \log\left(-\sqrt{-\frac{c + d - 1}{c - d - 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) - 6 \, {\rm polylog}\left(4, \sqrt{-\frac{c + d + 1}{c - d + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - 6 \, {\rm polylog}\left(4, -\sqrt{-\frac{c + d + 1}{c - d + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + 6 \, {\rm polylog}\left(4, \sqrt{-\frac{c + d - 1}{c - d - 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + 6 \, {\rm polylog}\left(4, -\sqrt{-\frac{c + d - 1}{c - d - 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right)}{6 \, b^{3}}"," ",0,"1/6*(b^3*x^3*log(((c + 1)*cosh(b*x + a) + d*sinh(b*x + a))/((c - 1)*cosh(b*x + a) + d*sinh(b*x + a))) - 3*b^2*x^2*dilog(sqrt(-(c + d + 1)/(c - d + 1))*(cosh(b*x + a) + sinh(b*x + a))) - 3*b^2*x^2*dilog(-sqrt(-(c + d + 1)/(c - d + 1))*(cosh(b*x + a) + sinh(b*x + a))) + 3*b^2*x^2*dilog(sqrt(-(c + d - 1)/(c - d - 1))*(cosh(b*x + a) + sinh(b*x + a))) + 3*b^2*x^2*dilog(-sqrt(-(c + d - 1)/(c - d - 1))*(cosh(b*x + a) + sinh(b*x + a))) + a^3*log(2*(c + d + 1)*cosh(b*x + a) + 2*(c + d + 1)*sinh(b*x + a) + 2*(c - d + 1)*sqrt(-(c + d + 1)/(c - d + 1))) + a^3*log(2*(c + d + 1)*cosh(b*x + a) + 2*(c + d + 1)*sinh(b*x + a) - 2*(c - d + 1)*sqrt(-(c + d + 1)/(c - d + 1))) - a^3*log(2*(c + d - 1)*cosh(b*x + a) + 2*(c + d - 1)*sinh(b*x + a) + 2*(c - d - 1)*sqrt(-(c + d - 1)/(c - d - 1))) - a^3*log(2*(c + d - 1)*cosh(b*x + a) + 2*(c + d - 1)*sinh(b*x + a) - 2*(c - d - 1)*sqrt(-(c + d - 1)/(c - d - 1))) + 6*b*x*polylog(3, sqrt(-(c + d + 1)/(c - d + 1))*(cosh(b*x + a) + sinh(b*x + a))) + 6*b*x*polylog(3, -sqrt(-(c + d + 1)/(c - d + 1))*(cosh(b*x + a) + sinh(b*x + a))) - 6*b*x*polylog(3, sqrt(-(c + d - 1)/(c - d - 1))*(cosh(b*x + a) + sinh(b*x + a))) - 6*b*x*polylog(3, -sqrt(-(c + d - 1)/(c - d - 1))*(cosh(b*x + a) + sinh(b*x + a))) - (b^3*x^3 + a^3)*log(sqrt(-(c + d + 1)/(c - d + 1))*(cosh(b*x + a) + sinh(b*x + a)) + 1) - (b^3*x^3 + a^3)*log(-sqrt(-(c + d + 1)/(c - d + 1))*(cosh(b*x + a) + sinh(b*x + a)) + 1) + (b^3*x^3 + a^3)*log(sqrt(-(c + d - 1)/(c - d - 1))*(cosh(b*x + a) + sinh(b*x + a)) + 1) + (b^3*x^3 + a^3)*log(-sqrt(-(c + d - 1)/(c - d - 1))*(cosh(b*x + a) + sinh(b*x + a)) + 1) - 6*polylog(4, sqrt(-(c + d + 1)/(c - d + 1))*(cosh(b*x + a) + sinh(b*x + a))) - 6*polylog(4, -sqrt(-(c + d + 1)/(c - d + 1))*(cosh(b*x + a) + sinh(b*x + a))) + 6*polylog(4, sqrt(-(c + d - 1)/(c - d - 1))*(cosh(b*x + a) + sinh(b*x + a))) + 6*polylog(4, -sqrt(-(c + d - 1)/(c - d - 1))*(cosh(b*x + a) + sinh(b*x + a))))/b^3","C",0
204,1,745,0,0.748651," ","integrate(x*arccoth(c+d*tanh(b*x+a)),x, algorithm=""fricas"")","\frac{b^{2} x^{2} \log\left(\frac{{\left(c + 1\right)} \cosh\left(b x + a\right) + d \sinh\left(b x + a\right)}{{\left(c - 1\right)} \cosh\left(b x + a\right) + d \sinh\left(b x + a\right)}\right) - 2 \, b x {\rm Li}_2\left(\sqrt{-\frac{c + d + 1}{c - d + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - 2 \, b x {\rm Li}_2\left(-\sqrt{-\frac{c + d + 1}{c - d + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + 2 \, b x {\rm Li}_2\left(\sqrt{-\frac{c + d - 1}{c - d - 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + 2 \, b x {\rm Li}_2\left(-\sqrt{-\frac{c + d - 1}{c - d - 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - a^{2} \log\left(2 \, {\left(c + d + 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(c + d + 1\right)} \sinh\left(b x + a\right) + 2 \, {\left(c - d + 1\right)} \sqrt{-\frac{c + d + 1}{c - d + 1}}\right) - a^{2} \log\left(2 \, {\left(c + d + 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(c + d + 1\right)} \sinh\left(b x + a\right) - 2 \, {\left(c - d + 1\right)} \sqrt{-\frac{c + d + 1}{c - d + 1}}\right) + a^{2} \log\left(2 \, {\left(c + d - 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(c + d - 1\right)} \sinh\left(b x + a\right) + 2 \, {\left(c - d - 1\right)} \sqrt{-\frac{c + d - 1}{c - d - 1}}\right) + a^{2} \log\left(2 \, {\left(c + d - 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(c + d - 1\right)} \sinh\left(b x + a\right) - 2 \, {\left(c - d - 1\right)} \sqrt{-\frac{c + d - 1}{c - d - 1}}\right) - {\left(b^{2} x^{2} - a^{2}\right)} \log\left(\sqrt{-\frac{c + d + 1}{c - d + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) - {\left(b^{2} x^{2} - a^{2}\right)} \log\left(-\sqrt{-\frac{c + d + 1}{c - d + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) + {\left(b^{2} x^{2} - a^{2}\right)} \log\left(\sqrt{-\frac{c + d - 1}{c - d - 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) + {\left(b^{2} x^{2} - a^{2}\right)} \log\left(-\sqrt{-\frac{c + d - 1}{c - d - 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) + 2 \, {\rm polylog}\left(3, \sqrt{-\frac{c + d + 1}{c - d + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + 2 \, {\rm polylog}\left(3, -\sqrt{-\frac{c + d + 1}{c - d + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - 2 \, {\rm polylog}\left(3, \sqrt{-\frac{c + d - 1}{c - d - 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - 2 \, {\rm polylog}\left(3, -\sqrt{-\frac{c + d - 1}{c - d - 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right)}{4 \, b^{2}}"," ",0,"1/4*(b^2*x^2*log(((c + 1)*cosh(b*x + a) + d*sinh(b*x + a))/((c - 1)*cosh(b*x + a) + d*sinh(b*x + a))) - 2*b*x*dilog(sqrt(-(c + d + 1)/(c - d + 1))*(cosh(b*x + a) + sinh(b*x + a))) - 2*b*x*dilog(-sqrt(-(c + d + 1)/(c - d + 1))*(cosh(b*x + a) + sinh(b*x + a))) + 2*b*x*dilog(sqrt(-(c + d - 1)/(c - d - 1))*(cosh(b*x + a) + sinh(b*x + a))) + 2*b*x*dilog(-sqrt(-(c + d - 1)/(c - d - 1))*(cosh(b*x + a) + sinh(b*x + a))) - a^2*log(2*(c + d + 1)*cosh(b*x + a) + 2*(c + d + 1)*sinh(b*x + a) + 2*(c - d + 1)*sqrt(-(c + d + 1)/(c - d + 1))) - a^2*log(2*(c + d + 1)*cosh(b*x + a) + 2*(c + d + 1)*sinh(b*x + a) - 2*(c - d + 1)*sqrt(-(c + d + 1)/(c - d + 1))) + a^2*log(2*(c + d - 1)*cosh(b*x + a) + 2*(c + d - 1)*sinh(b*x + a) + 2*(c - d - 1)*sqrt(-(c + d - 1)/(c - d - 1))) + a^2*log(2*(c + d - 1)*cosh(b*x + a) + 2*(c + d - 1)*sinh(b*x + a) - 2*(c - d - 1)*sqrt(-(c + d - 1)/(c - d - 1))) - (b^2*x^2 - a^2)*log(sqrt(-(c + d + 1)/(c - d + 1))*(cosh(b*x + a) + sinh(b*x + a)) + 1) - (b^2*x^2 - a^2)*log(-sqrt(-(c + d + 1)/(c - d + 1))*(cosh(b*x + a) + sinh(b*x + a)) + 1) + (b^2*x^2 - a^2)*log(sqrt(-(c + d - 1)/(c - d - 1))*(cosh(b*x + a) + sinh(b*x + a)) + 1) + (b^2*x^2 - a^2)*log(-sqrt(-(c + d - 1)/(c - d - 1))*(cosh(b*x + a) + sinh(b*x + a)) + 1) + 2*polylog(3, sqrt(-(c + d + 1)/(c - d + 1))*(cosh(b*x + a) + sinh(b*x + a))) + 2*polylog(3, -sqrt(-(c + d + 1)/(c - d + 1))*(cosh(b*x + a) + sinh(b*x + a))) - 2*polylog(3, sqrt(-(c + d - 1)/(c - d - 1))*(cosh(b*x + a) + sinh(b*x + a))) - 2*polylog(3, -sqrt(-(c + d - 1)/(c - d - 1))*(cosh(b*x + a) + sinh(b*x + a))))/b^2","C",0
205,1,551,0,0.853842," ","integrate(arccoth(c+d*tanh(b*x+a)),x, algorithm=""fricas"")","\frac{b x \log\left(\frac{{\left(c + 1\right)} \cosh\left(b x + a\right) + d \sinh\left(b x + a\right)}{{\left(c - 1\right)} \cosh\left(b x + a\right) + d \sinh\left(b x + a\right)}\right) + a \log\left(2 \, {\left(c + d + 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(c + d + 1\right)} \sinh\left(b x + a\right) + 2 \, {\left(c - d + 1\right)} \sqrt{-\frac{c + d + 1}{c - d + 1}}\right) + a \log\left(2 \, {\left(c + d + 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(c + d + 1\right)} \sinh\left(b x + a\right) - 2 \, {\left(c - d + 1\right)} \sqrt{-\frac{c + d + 1}{c - d + 1}}\right) - a \log\left(2 \, {\left(c + d - 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(c + d - 1\right)} \sinh\left(b x + a\right) + 2 \, {\left(c - d - 1\right)} \sqrt{-\frac{c + d - 1}{c - d - 1}}\right) - a \log\left(2 \, {\left(c + d - 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(c + d - 1\right)} \sinh\left(b x + a\right) - 2 \, {\left(c - d - 1\right)} \sqrt{-\frac{c + d - 1}{c - d - 1}}\right) - {\left(b x + a\right)} \log\left(\sqrt{-\frac{c + d + 1}{c - d + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) - {\left(b x + a\right)} \log\left(-\sqrt{-\frac{c + d + 1}{c - d + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) + {\left(b x + a\right)} \log\left(\sqrt{-\frac{c + d - 1}{c - d - 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) + {\left(b x + a\right)} \log\left(-\sqrt{-\frac{c + d - 1}{c - d - 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) - {\rm Li}_2\left(\sqrt{-\frac{c + d + 1}{c - d + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - {\rm Li}_2\left(-\sqrt{-\frac{c + d + 1}{c - d + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + {\rm Li}_2\left(\sqrt{-\frac{c + d - 1}{c - d - 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + {\rm Li}_2\left(-\sqrt{-\frac{c + d - 1}{c - d - 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right)}{2 \, b}"," ",0,"1/2*(b*x*log(((c + 1)*cosh(b*x + a) + d*sinh(b*x + a))/((c - 1)*cosh(b*x + a) + d*sinh(b*x + a))) + a*log(2*(c + d + 1)*cosh(b*x + a) + 2*(c + d + 1)*sinh(b*x + a) + 2*(c - d + 1)*sqrt(-(c + d + 1)/(c - d + 1))) + a*log(2*(c + d + 1)*cosh(b*x + a) + 2*(c + d + 1)*sinh(b*x + a) - 2*(c - d + 1)*sqrt(-(c + d + 1)/(c - d + 1))) - a*log(2*(c + d - 1)*cosh(b*x + a) + 2*(c + d - 1)*sinh(b*x + a) + 2*(c - d - 1)*sqrt(-(c + d - 1)/(c - d - 1))) - a*log(2*(c + d - 1)*cosh(b*x + a) + 2*(c + d - 1)*sinh(b*x + a) - 2*(c - d - 1)*sqrt(-(c + d - 1)/(c - d - 1))) - (b*x + a)*log(sqrt(-(c + d + 1)/(c - d + 1))*(cosh(b*x + a) + sinh(b*x + a)) + 1) - (b*x + a)*log(-sqrt(-(c + d + 1)/(c - d + 1))*(cosh(b*x + a) + sinh(b*x + a)) + 1) + (b*x + a)*log(sqrt(-(c + d - 1)/(c - d - 1))*(cosh(b*x + a) + sinh(b*x + a)) + 1) + (b*x + a)*log(-sqrt(-(c + d - 1)/(c - d - 1))*(cosh(b*x + a) + sinh(b*x + a)) + 1) - dilog(sqrt(-(c + d + 1)/(c - d + 1))*(cosh(b*x + a) + sinh(b*x + a))) - dilog(-sqrt(-(c + d + 1)/(c - d + 1))*(cosh(b*x + a) + sinh(b*x + a))) + dilog(sqrt(-(c + d - 1)/(c - d - 1))*(cosh(b*x + a) + sinh(b*x + a))) + dilog(-sqrt(-(c + d - 1)/(c - d - 1))*(cosh(b*x + a) + sinh(b*x + a))))/b","B",0
206,0,0,0,0.773943," ","integrate(arccoth(c+d*tanh(b*x+a))/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{arcoth}\left(d \tanh\left(b x + a\right) + c\right)}{x}, x\right)"," ",0,"integral(arccoth(d*tanh(b*x + a) + c)/x, x)","F",0
207,1,450,0,1.751466," ","integrate(x^3*arccoth(1+d+d*tanh(b*x+a)),x, algorithm=""fricas"")","\frac{2 \, b^{5} x^{5} + 5 \, b^{4} x^{4} \log\left(\frac{{\left(d + 2\right)} \cosh\left(b x + a\right) + d \sinh\left(b x + a\right)}{d \cosh\left(b x + a\right) + d \sinh\left(b x + a\right)}\right) - 20 \, b^{3} x^{3} {\rm Li}_2\left(\frac{1}{2} \, \sqrt{-4 \, d - 4} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - 20 \, b^{3} x^{3} {\rm Li}_2\left(-\frac{1}{2} \, \sqrt{-4 \, d - 4} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - 5 \, a^{4} \log\left(2 \, {\left(d + 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(d + 1\right)} \sinh\left(b x + a\right) + \sqrt{-4 \, d - 4}\right) - 5 \, a^{4} \log\left(2 \, {\left(d + 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(d + 1\right)} \sinh\left(b x + a\right) - \sqrt{-4 \, d - 4}\right) + 60 \, b^{2} x^{2} {\rm polylog}\left(3, \frac{1}{2} \, \sqrt{-4 \, d - 4} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + 60 \, b^{2} x^{2} {\rm polylog}\left(3, -\frac{1}{2} \, \sqrt{-4 \, d - 4} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - 120 \, b x {\rm polylog}\left(4, \frac{1}{2} \, \sqrt{-4 \, d - 4} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - 120 \, b x {\rm polylog}\left(4, -\frac{1}{2} \, \sqrt{-4 \, d - 4} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - 5 \, {\left(b^{4} x^{4} - a^{4}\right)} \log\left(\frac{1}{2} \, \sqrt{-4 \, d - 4} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) - 5 \, {\left(b^{4} x^{4} - a^{4}\right)} \log\left(-\frac{1}{2} \, \sqrt{-4 \, d - 4} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) + 120 \, {\rm polylog}\left(5, \frac{1}{2} \, \sqrt{-4 \, d - 4} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + 120 \, {\rm polylog}\left(5, -\frac{1}{2} \, \sqrt{-4 \, d - 4} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right)}{40 \, b^{4}}"," ",0,"1/40*(2*b^5*x^5 + 5*b^4*x^4*log(((d + 2)*cosh(b*x + a) + d*sinh(b*x + a))/(d*cosh(b*x + a) + d*sinh(b*x + a))) - 20*b^3*x^3*dilog(1/2*sqrt(-4*d - 4)*(cosh(b*x + a) + sinh(b*x + a))) - 20*b^3*x^3*dilog(-1/2*sqrt(-4*d - 4)*(cosh(b*x + a) + sinh(b*x + a))) - 5*a^4*log(2*(d + 1)*cosh(b*x + a) + 2*(d + 1)*sinh(b*x + a) + sqrt(-4*d - 4)) - 5*a^4*log(2*(d + 1)*cosh(b*x + a) + 2*(d + 1)*sinh(b*x + a) - sqrt(-4*d - 4)) + 60*b^2*x^2*polylog(3, 1/2*sqrt(-4*d - 4)*(cosh(b*x + a) + sinh(b*x + a))) + 60*b^2*x^2*polylog(3, -1/2*sqrt(-4*d - 4)*(cosh(b*x + a) + sinh(b*x + a))) - 120*b*x*polylog(4, 1/2*sqrt(-4*d - 4)*(cosh(b*x + a) + sinh(b*x + a))) - 120*b*x*polylog(4, -1/2*sqrt(-4*d - 4)*(cosh(b*x + a) + sinh(b*x + a))) - 5*(b^4*x^4 - a^4)*log(1/2*sqrt(-4*d - 4)*(cosh(b*x + a) + sinh(b*x + a)) + 1) - 5*(b^4*x^4 - a^4)*log(-1/2*sqrt(-4*d - 4)*(cosh(b*x + a) + sinh(b*x + a)) + 1) + 120*polylog(5, 1/2*sqrt(-4*d - 4)*(cosh(b*x + a) + sinh(b*x + a))) + 120*polylog(5, -1/2*sqrt(-4*d - 4)*(cosh(b*x + a) + sinh(b*x + a))))/b^4","C",0
208,1,381,0,3.990203," ","integrate(x^2*arccoth(1+d+d*tanh(b*x+a)),x, algorithm=""fricas"")","\frac{b^{4} x^{4} + 2 \, b^{3} x^{3} \log\left(\frac{{\left(d + 2\right)} \cosh\left(b x + a\right) + d \sinh\left(b x + a\right)}{d \cosh\left(b x + a\right) + d \sinh\left(b x + a\right)}\right) - 6 \, b^{2} x^{2} {\rm Li}_2\left(\frac{1}{2} \, \sqrt{-4 \, d - 4} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - 6 \, b^{2} x^{2} {\rm Li}_2\left(-\frac{1}{2} \, \sqrt{-4 \, d - 4} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + 2 \, a^{3} \log\left(2 \, {\left(d + 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(d + 1\right)} \sinh\left(b x + a\right) + \sqrt{-4 \, d - 4}\right) + 2 \, a^{3} \log\left(2 \, {\left(d + 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(d + 1\right)} \sinh\left(b x + a\right) - \sqrt{-4 \, d - 4}\right) + 12 \, b x {\rm polylog}\left(3, \frac{1}{2} \, \sqrt{-4 \, d - 4} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + 12 \, b x {\rm polylog}\left(3, -\frac{1}{2} \, \sqrt{-4 \, d - 4} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - 2 \, {\left(b^{3} x^{3} + a^{3}\right)} \log\left(\frac{1}{2} \, \sqrt{-4 \, d - 4} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) - 2 \, {\left(b^{3} x^{3} + a^{3}\right)} \log\left(-\frac{1}{2} \, \sqrt{-4 \, d - 4} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) - 12 \, {\rm polylog}\left(4, \frac{1}{2} \, \sqrt{-4 \, d - 4} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - 12 \, {\rm polylog}\left(4, -\frac{1}{2} \, \sqrt{-4 \, d - 4} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right)}{12 \, b^{3}}"," ",0,"1/12*(b^4*x^4 + 2*b^3*x^3*log(((d + 2)*cosh(b*x + a) + d*sinh(b*x + a))/(d*cosh(b*x + a) + d*sinh(b*x + a))) - 6*b^2*x^2*dilog(1/2*sqrt(-4*d - 4)*(cosh(b*x + a) + sinh(b*x + a))) - 6*b^2*x^2*dilog(-1/2*sqrt(-4*d - 4)*(cosh(b*x + a) + sinh(b*x + a))) + 2*a^3*log(2*(d + 1)*cosh(b*x + a) + 2*(d + 1)*sinh(b*x + a) + sqrt(-4*d - 4)) + 2*a^3*log(2*(d + 1)*cosh(b*x + a) + 2*(d + 1)*sinh(b*x + a) - sqrt(-4*d - 4)) + 12*b*x*polylog(3, 1/2*sqrt(-4*d - 4)*(cosh(b*x + a) + sinh(b*x + a))) + 12*b*x*polylog(3, -1/2*sqrt(-4*d - 4)*(cosh(b*x + a) + sinh(b*x + a))) - 2*(b^3*x^3 + a^3)*log(1/2*sqrt(-4*d - 4)*(cosh(b*x + a) + sinh(b*x + a)) + 1) - 2*(b^3*x^3 + a^3)*log(-1/2*sqrt(-4*d - 4)*(cosh(b*x + a) + sinh(b*x + a)) + 1) - 12*polylog(4, 1/2*sqrt(-4*d - 4)*(cosh(b*x + a) + sinh(b*x + a))) - 12*polylog(4, -1/2*sqrt(-4*d - 4)*(cosh(b*x + a) + sinh(b*x + a))))/b^3","C",0
209,1,322,0,0.752792," ","integrate(x*arccoth(1+d+d*tanh(b*x+a)),x, algorithm=""fricas"")","\frac{2 \, b^{3} x^{3} + 3 \, b^{2} x^{2} \log\left(\frac{{\left(d + 2\right)} \cosh\left(b x + a\right) + d \sinh\left(b x + a\right)}{d \cosh\left(b x + a\right) + d \sinh\left(b x + a\right)}\right) - 6 \, b x {\rm Li}_2\left(\frac{1}{2} \, \sqrt{-4 \, d - 4} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - 6 \, b x {\rm Li}_2\left(-\frac{1}{2} \, \sqrt{-4 \, d - 4} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - 3 \, a^{2} \log\left(2 \, {\left(d + 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(d + 1\right)} \sinh\left(b x + a\right) + \sqrt{-4 \, d - 4}\right) - 3 \, a^{2} \log\left(2 \, {\left(d + 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(d + 1\right)} \sinh\left(b x + a\right) - \sqrt{-4 \, d - 4}\right) - 3 \, {\left(b^{2} x^{2} - a^{2}\right)} \log\left(\frac{1}{2} \, \sqrt{-4 \, d - 4} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) - 3 \, {\left(b^{2} x^{2} - a^{2}\right)} \log\left(-\frac{1}{2} \, \sqrt{-4 \, d - 4} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) + 6 \, {\rm polylog}\left(3, \frac{1}{2} \, \sqrt{-4 \, d - 4} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + 6 \, {\rm polylog}\left(3, -\frac{1}{2} \, \sqrt{-4 \, d - 4} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right)}{12 \, b^{2}}"," ",0,"1/12*(2*b^3*x^3 + 3*b^2*x^2*log(((d + 2)*cosh(b*x + a) + d*sinh(b*x + a))/(d*cosh(b*x + a) + d*sinh(b*x + a))) - 6*b*x*dilog(1/2*sqrt(-4*d - 4)*(cosh(b*x + a) + sinh(b*x + a))) - 6*b*x*dilog(-1/2*sqrt(-4*d - 4)*(cosh(b*x + a) + sinh(b*x + a))) - 3*a^2*log(2*(d + 1)*cosh(b*x + a) + 2*(d + 1)*sinh(b*x + a) + sqrt(-4*d - 4)) - 3*a^2*log(2*(d + 1)*cosh(b*x + a) + 2*(d + 1)*sinh(b*x + a) - sqrt(-4*d - 4)) - 3*(b^2*x^2 - a^2)*log(1/2*sqrt(-4*d - 4)*(cosh(b*x + a) + sinh(b*x + a)) + 1) - 3*(b^2*x^2 - a^2)*log(-1/2*sqrt(-4*d - 4)*(cosh(b*x + a) + sinh(b*x + a)) + 1) + 6*polylog(3, 1/2*sqrt(-4*d - 4)*(cosh(b*x + a) + sinh(b*x + a))) + 6*polylog(3, -1/2*sqrt(-4*d - 4)*(cosh(b*x + a) + sinh(b*x + a))))/b^2","C",0
210,1,238,0,0.969172," ","integrate(arccoth(1+d+d*tanh(b*x+a)),x, algorithm=""fricas"")","\frac{b^{2} x^{2} + b x \log\left(\frac{{\left(d + 2\right)} \cosh\left(b x + a\right) + d \sinh\left(b x + a\right)}{d \cosh\left(b x + a\right) + d \sinh\left(b x + a\right)}\right) + a \log\left(2 \, {\left(d + 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(d + 1\right)} \sinh\left(b x + a\right) + \sqrt{-4 \, d - 4}\right) + a \log\left(2 \, {\left(d + 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(d + 1\right)} \sinh\left(b x + a\right) - \sqrt{-4 \, d - 4}\right) - {\left(b x + a\right)} \log\left(\frac{1}{2} \, \sqrt{-4 \, d - 4} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) - {\left(b x + a\right)} \log\left(-\frac{1}{2} \, \sqrt{-4 \, d - 4} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) - {\rm Li}_2\left(\frac{1}{2} \, \sqrt{-4 \, d - 4} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - {\rm Li}_2\left(-\frac{1}{2} \, \sqrt{-4 \, d - 4} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right)}{2 \, b}"," ",0,"1/2*(b^2*x^2 + b*x*log(((d + 2)*cosh(b*x + a) + d*sinh(b*x + a))/(d*cosh(b*x + a) + d*sinh(b*x + a))) + a*log(2*(d + 1)*cosh(b*x + a) + 2*(d + 1)*sinh(b*x + a) + sqrt(-4*d - 4)) + a*log(2*(d + 1)*cosh(b*x + a) + 2*(d + 1)*sinh(b*x + a) - sqrt(-4*d - 4)) - (b*x + a)*log(1/2*sqrt(-4*d - 4)*(cosh(b*x + a) + sinh(b*x + a)) + 1) - (b*x + a)*log(-1/2*sqrt(-4*d - 4)*(cosh(b*x + a) + sinh(b*x + a)) + 1) - dilog(1/2*sqrt(-4*d - 4)*(cosh(b*x + a) + sinh(b*x + a))) - dilog(-1/2*sqrt(-4*d - 4)*(cosh(b*x + a) + sinh(b*x + a))))/b","B",0
211,0,0,0,0.685831," ","integrate(arccoth(1+d+d*tanh(b*x+a))/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{arcoth}\left(d \tanh\left(b x + a\right) + d + 1\right)}{x}, x\right)"," ",0,"integral(arccoth(d*tanh(b*x + a) + d + 1)/x, x)","F",0
212,1,423,0,0.692631," ","integrate(x^3*arccoth(1-d-d*tanh(b*x+a)),x, algorithm=""fricas"")","\frac{2 \, b^{5} x^{5} - 5 \, b^{4} x^{4} \log\left(\frac{d \cosh\left(b x + a\right) + d \sinh\left(b x + a\right)}{{\left(d - 2\right)} \cosh\left(b x + a\right) + d \sinh\left(b x + a\right)}\right) - 20 \, b^{3} x^{3} {\rm Li}_2\left(\sqrt{d - 1} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - 20 \, b^{3} x^{3} {\rm Li}_2\left(-\sqrt{d - 1} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - 5 \, a^{4} \log\left(2 \, {\left(d - 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(d - 1\right)} \sinh\left(b x + a\right) + 2 \, \sqrt{d - 1}\right) - 5 \, a^{4} \log\left(2 \, {\left(d - 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(d - 1\right)} \sinh\left(b x + a\right) - 2 \, \sqrt{d - 1}\right) + 60 \, b^{2} x^{2} {\rm polylog}\left(3, \sqrt{d - 1} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + 60 \, b^{2} x^{2} {\rm polylog}\left(3, -\sqrt{d - 1} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - 120 \, b x {\rm polylog}\left(4, \sqrt{d - 1} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - 120 \, b x {\rm polylog}\left(4, -\sqrt{d - 1} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - 5 \, {\left(b^{4} x^{4} - a^{4}\right)} \log\left(\sqrt{d - 1} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) - 5 \, {\left(b^{4} x^{4} - a^{4}\right)} \log\left(-\sqrt{d - 1} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) + 120 \, {\rm polylog}\left(5, \sqrt{d - 1} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + 120 \, {\rm polylog}\left(5, -\sqrt{d - 1} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right)}{40 \, b^{4}}"," ",0,"1/40*(2*b^5*x^5 - 5*b^4*x^4*log((d*cosh(b*x + a) + d*sinh(b*x + a))/((d - 2)*cosh(b*x + a) + d*sinh(b*x + a))) - 20*b^3*x^3*dilog(sqrt(d - 1)*(cosh(b*x + a) + sinh(b*x + a))) - 20*b^3*x^3*dilog(-sqrt(d - 1)*(cosh(b*x + a) + sinh(b*x + a))) - 5*a^4*log(2*(d - 1)*cosh(b*x + a) + 2*(d - 1)*sinh(b*x + a) + 2*sqrt(d - 1)) - 5*a^4*log(2*(d - 1)*cosh(b*x + a) + 2*(d - 1)*sinh(b*x + a) - 2*sqrt(d - 1)) + 60*b^2*x^2*polylog(3, sqrt(d - 1)*(cosh(b*x + a) + sinh(b*x + a))) + 60*b^2*x^2*polylog(3, -sqrt(d - 1)*(cosh(b*x + a) + sinh(b*x + a))) - 120*b*x*polylog(4, sqrt(d - 1)*(cosh(b*x + a) + sinh(b*x + a))) - 120*b*x*polylog(4, -sqrt(d - 1)*(cosh(b*x + a) + sinh(b*x + a))) - 5*(b^4*x^4 - a^4)*log(sqrt(d - 1)*(cosh(b*x + a) + sinh(b*x + a)) + 1) - 5*(b^4*x^4 - a^4)*log(-sqrt(d - 1)*(cosh(b*x + a) + sinh(b*x + a)) + 1) + 120*polylog(5, sqrt(d - 1)*(cosh(b*x + a) + sinh(b*x + a))) + 120*polylog(5, -sqrt(d - 1)*(cosh(b*x + a) + sinh(b*x + a))))/b^4","C",0
213,1,359,0,1.861063," ","integrate(x^2*arccoth(1-d-d*tanh(b*x+a)),x, algorithm=""fricas"")","\frac{b^{4} x^{4} - 2 \, b^{3} x^{3} \log\left(\frac{d \cosh\left(b x + a\right) + d \sinh\left(b x + a\right)}{{\left(d - 2\right)} \cosh\left(b x + a\right) + d \sinh\left(b x + a\right)}\right) - 6 \, b^{2} x^{2} {\rm Li}_2\left(\sqrt{d - 1} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - 6 \, b^{2} x^{2} {\rm Li}_2\left(-\sqrt{d - 1} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + 2 \, a^{3} \log\left(2 \, {\left(d - 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(d - 1\right)} \sinh\left(b x + a\right) + 2 \, \sqrt{d - 1}\right) + 2 \, a^{3} \log\left(2 \, {\left(d - 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(d - 1\right)} \sinh\left(b x + a\right) - 2 \, \sqrt{d - 1}\right) + 12 \, b x {\rm polylog}\left(3, \sqrt{d - 1} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + 12 \, b x {\rm polylog}\left(3, -\sqrt{d - 1} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - 2 \, {\left(b^{3} x^{3} + a^{3}\right)} \log\left(\sqrt{d - 1} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) - 2 \, {\left(b^{3} x^{3} + a^{3}\right)} \log\left(-\sqrt{d - 1} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) - 12 \, {\rm polylog}\left(4, \sqrt{d - 1} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - 12 \, {\rm polylog}\left(4, -\sqrt{d - 1} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right)}{12 \, b^{3}}"," ",0,"1/12*(b^4*x^4 - 2*b^3*x^3*log((d*cosh(b*x + a) + d*sinh(b*x + a))/((d - 2)*cosh(b*x + a) + d*sinh(b*x + a))) - 6*b^2*x^2*dilog(sqrt(d - 1)*(cosh(b*x + a) + sinh(b*x + a))) - 6*b^2*x^2*dilog(-sqrt(d - 1)*(cosh(b*x + a) + sinh(b*x + a))) + 2*a^3*log(2*(d - 1)*cosh(b*x + a) + 2*(d - 1)*sinh(b*x + a) + 2*sqrt(d - 1)) + 2*a^3*log(2*(d - 1)*cosh(b*x + a) + 2*(d - 1)*sinh(b*x + a) - 2*sqrt(d - 1)) + 12*b*x*polylog(3, sqrt(d - 1)*(cosh(b*x + a) + sinh(b*x + a))) + 12*b*x*polylog(3, -sqrt(d - 1)*(cosh(b*x + a) + sinh(b*x + a))) - 2*(b^3*x^3 + a^3)*log(sqrt(d - 1)*(cosh(b*x + a) + sinh(b*x + a)) + 1) - 2*(b^3*x^3 + a^3)*log(-sqrt(d - 1)*(cosh(b*x + a) + sinh(b*x + a)) + 1) - 12*polylog(4, sqrt(d - 1)*(cosh(b*x + a) + sinh(b*x + a))) - 12*polylog(4, -sqrt(d - 1)*(cosh(b*x + a) + sinh(b*x + a))))/b^3","C",0
214,1,305,0,1.012727," ","integrate(x*arccoth(1-d-d*tanh(b*x+a)),x, algorithm=""fricas"")","\frac{2 \, b^{3} x^{3} - 3 \, b^{2} x^{2} \log\left(\frac{d \cosh\left(b x + a\right) + d \sinh\left(b x + a\right)}{{\left(d - 2\right)} \cosh\left(b x + a\right) + d \sinh\left(b x + a\right)}\right) - 6 \, b x {\rm Li}_2\left(\sqrt{d - 1} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - 6 \, b x {\rm Li}_2\left(-\sqrt{d - 1} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - 3 \, a^{2} \log\left(2 \, {\left(d - 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(d - 1\right)} \sinh\left(b x + a\right) + 2 \, \sqrt{d - 1}\right) - 3 \, a^{2} \log\left(2 \, {\left(d - 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(d - 1\right)} \sinh\left(b x + a\right) - 2 \, \sqrt{d - 1}\right) - 3 \, {\left(b^{2} x^{2} - a^{2}\right)} \log\left(\sqrt{d - 1} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) - 3 \, {\left(b^{2} x^{2} - a^{2}\right)} \log\left(-\sqrt{d - 1} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) + 6 \, {\rm polylog}\left(3, \sqrt{d - 1} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + 6 \, {\rm polylog}\left(3, -\sqrt{d - 1} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right)}{12 \, b^{2}}"," ",0,"1/12*(2*b^3*x^3 - 3*b^2*x^2*log((d*cosh(b*x + a) + d*sinh(b*x + a))/((d - 2)*cosh(b*x + a) + d*sinh(b*x + a))) - 6*b*x*dilog(sqrt(d - 1)*(cosh(b*x + a) + sinh(b*x + a))) - 6*b*x*dilog(-sqrt(d - 1)*(cosh(b*x + a) + sinh(b*x + a))) - 3*a^2*log(2*(d - 1)*cosh(b*x + a) + 2*(d - 1)*sinh(b*x + a) + 2*sqrt(d - 1)) - 3*a^2*log(2*(d - 1)*cosh(b*x + a) + 2*(d - 1)*sinh(b*x + a) - 2*sqrt(d - 1)) - 3*(b^2*x^2 - a^2)*log(sqrt(d - 1)*(cosh(b*x + a) + sinh(b*x + a)) + 1) - 3*(b^2*x^2 - a^2)*log(-sqrt(d - 1)*(cosh(b*x + a) + sinh(b*x + a)) + 1) + 6*polylog(3, sqrt(d - 1)*(cosh(b*x + a) + sinh(b*x + a))) + 6*polylog(3, -sqrt(d - 1)*(cosh(b*x + a) + sinh(b*x + a))))/b^2","C",0
215,1,227,0,0.800308," ","integrate(arccoth(1-d-d*tanh(b*x+a)),x, algorithm=""fricas"")","\frac{b^{2} x^{2} - b x \log\left(\frac{d \cosh\left(b x + a\right) + d \sinh\left(b x + a\right)}{{\left(d - 2\right)} \cosh\left(b x + a\right) + d \sinh\left(b x + a\right)}\right) + a \log\left(2 \, {\left(d - 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(d - 1\right)} \sinh\left(b x + a\right) + 2 \, \sqrt{d - 1}\right) + a \log\left(2 \, {\left(d - 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(d - 1\right)} \sinh\left(b x + a\right) - 2 \, \sqrt{d - 1}\right) - {\left(b x + a\right)} \log\left(\sqrt{d - 1} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) - {\left(b x + a\right)} \log\left(-\sqrt{d - 1} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) - {\rm Li}_2\left(\sqrt{d - 1} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - {\rm Li}_2\left(-\sqrt{d - 1} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right)}{2 \, b}"," ",0,"1/2*(b^2*x^2 - b*x*log((d*cosh(b*x + a) + d*sinh(b*x + a))/((d - 2)*cosh(b*x + a) + d*sinh(b*x + a))) + a*log(2*(d - 1)*cosh(b*x + a) + 2*(d - 1)*sinh(b*x + a) + 2*sqrt(d - 1)) + a*log(2*(d - 1)*cosh(b*x + a) + 2*(d - 1)*sinh(b*x + a) - 2*sqrt(d - 1)) - (b*x + a)*log(sqrt(d - 1)*(cosh(b*x + a) + sinh(b*x + a)) + 1) - (b*x + a)*log(-sqrt(d - 1)*(cosh(b*x + a) + sinh(b*x + a)) + 1) - dilog(sqrt(d - 1)*(cosh(b*x + a) + sinh(b*x + a))) - dilog(-sqrt(d - 1)*(cosh(b*x + a) + sinh(b*x + a))))/b","B",0
216,0,0,0,0.523786," ","integrate(arccoth(1-d-d*tanh(b*x+a))/x,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\operatorname{arcoth}\left(d \tanh\left(b x + a\right) + d - 1\right)}{x}, x\right)"," ",0,"integral(-arccoth(d*tanh(b*x + a) + d - 1)/x, x)","F",0
217,1,879,0,0.564762," ","integrate(x^2*arccoth(c+d*coth(b*x+a)),x, algorithm=""fricas"")","\frac{b^{3} x^{3} \log\left(\frac{d \cosh\left(b x + a\right) + {\left(c + 1\right)} \sinh\left(b x + a\right)}{d \cosh\left(b x + a\right) + {\left(c - 1\right)} \sinh\left(b x + a\right)}\right) - 3 \, b^{2} x^{2} {\rm Li}_2\left(\sqrt{\frac{c + d + 1}{c - d + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - 3 \, b^{2} x^{2} {\rm Li}_2\left(-\sqrt{\frac{c + d + 1}{c - d + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + 3 \, b^{2} x^{2} {\rm Li}_2\left(\sqrt{\frac{c + d - 1}{c - d - 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + 3 \, b^{2} x^{2} {\rm Li}_2\left(-\sqrt{\frac{c + d - 1}{c - d - 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + a^{3} \log\left(2 \, {\left(c + d + 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(c + d + 1\right)} \sinh\left(b x + a\right) + 2 \, {\left(c - d + 1\right)} \sqrt{\frac{c + d + 1}{c - d + 1}}\right) + a^{3} \log\left(2 \, {\left(c + d + 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(c + d + 1\right)} \sinh\left(b x + a\right) - 2 \, {\left(c - d + 1\right)} \sqrt{\frac{c + d + 1}{c - d + 1}}\right) - a^{3} \log\left(2 \, {\left(c + d - 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(c + d - 1\right)} \sinh\left(b x + a\right) + 2 \, {\left(c - d - 1\right)} \sqrt{\frac{c + d - 1}{c - d - 1}}\right) - a^{3} \log\left(2 \, {\left(c + d - 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(c + d - 1\right)} \sinh\left(b x + a\right) - 2 \, {\left(c - d - 1\right)} \sqrt{\frac{c + d - 1}{c - d - 1}}\right) + 6 \, b x {\rm polylog}\left(3, \sqrt{\frac{c + d + 1}{c - d + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + 6 \, b x {\rm polylog}\left(3, -\sqrt{\frac{c + d + 1}{c - d + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - 6 \, b x {\rm polylog}\left(3, \sqrt{\frac{c + d - 1}{c - d - 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - 6 \, b x {\rm polylog}\left(3, -\sqrt{\frac{c + d - 1}{c - d - 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - {\left(b^{3} x^{3} + a^{3}\right)} \log\left(\sqrt{\frac{c + d + 1}{c - d + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) - {\left(b^{3} x^{3} + a^{3}\right)} \log\left(-\sqrt{\frac{c + d + 1}{c - d + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) + {\left(b^{3} x^{3} + a^{3}\right)} \log\left(\sqrt{\frac{c + d - 1}{c - d - 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) + {\left(b^{3} x^{3} + a^{3}\right)} \log\left(-\sqrt{\frac{c + d - 1}{c - d - 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) - 6 \, {\rm polylog}\left(4, \sqrt{\frac{c + d + 1}{c - d + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - 6 \, {\rm polylog}\left(4, -\sqrt{\frac{c + d + 1}{c - d + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + 6 \, {\rm polylog}\left(4, \sqrt{\frac{c + d - 1}{c - d - 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + 6 \, {\rm polylog}\left(4, -\sqrt{\frac{c + d - 1}{c - d - 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right)}{6 \, b^{3}}"," ",0,"1/6*(b^3*x^3*log((d*cosh(b*x + a) + (c + 1)*sinh(b*x + a))/(d*cosh(b*x + a) + (c - 1)*sinh(b*x + a))) - 3*b^2*x^2*dilog(sqrt((c + d + 1)/(c - d + 1))*(cosh(b*x + a) + sinh(b*x + a))) - 3*b^2*x^2*dilog(-sqrt((c + d + 1)/(c - d + 1))*(cosh(b*x + a) + sinh(b*x + a))) + 3*b^2*x^2*dilog(sqrt((c + d - 1)/(c - d - 1))*(cosh(b*x + a) + sinh(b*x + a))) + 3*b^2*x^2*dilog(-sqrt((c + d - 1)/(c - d - 1))*(cosh(b*x + a) + sinh(b*x + a))) + a^3*log(2*(c + d + 1)*cosh(b*x + a) + 2*(c + d + 1)*sinh(b*x + a) + 2*(c - d + 1)*sqrt((c + d + 1)/(c - d + 1))) + a^3*log(2*(c + d + 1)*cosh(b*x + a) + 2*(c + d + 1)*sinh(b*x + a) - 2*(c - d + 1)*sqrt((c + d + 1)/(c - d + 1))) - a^3*log(2*(c + d - 1)*cosh(b*x + a) + 2*(c + d - 1)*sinh(b*x + a) + 2*(c - d - 1)*sqrt((c + d - 1)/(c - d - 1))) - a^3*log(2*(c + d - 1)*cosh(b*x + a) + 2*(c + d - 1)*sinh(b*x + a) - 2*(c - d - 1)*sqrt((c + d - 1)/(c - d - 1))) + 6*b*x*polylog(3, sqrt((c + d + 1)/(c - d + 1))*(cosh(b*x + a) + sinh(b*x + a))) + 6*b*x*polylog(3, -sqrt((c + d + 1)/(c - d + 1))*(cosh(b*x + a) + sinh(b*x + a))) - 6*b*x*polylog(3, sqrt((c + d - 1)/(c - d - 1))*(cosh(b*x + a) + sinh(b*x + a))) - 6*b*x*polylog(3, -sqrt((c + d - 1)/(c - d - 1))*(cosh(b*x + a) + sinh(b*x + a))) - (b^3*x^3 + a^3)*log(sqrt((c + d + 1)/(c - d + 1))*(cosh(b*x + a) + sinh(b*x + a)) + 1) - (b^3*x^3 + a^3)*log(-sqrt((c + d + 1)/(c - d + 1))*(cosh(b*x + a) + sinh(b*x + a)) + 1) + (b^3*x^3 + a^3)*log(sqrt((c + d - 1)/(c - d - 1))*(cosh(b*x + a) + sinh(b*x + a)) + 1) + (b^3*x^3 + a^3)*log(-sqrt((c + d - 1)/(c - d - 1))*(cosh(b*x + a) + sinh(b*x + a)) + 1) - 6*polylog(4, sqrt((c + d + 1)/(c - d + 1))*(cosh(b*x + a) + sinh(b*x + a))) - 6*polylog(4, -sqrt((c + d + 1)/(c - d + 1))*(cosh(b*x + a) + sinh(b*x + a))) + 6*polylog(4, sqrt((c + d - 1)/(c - d - 1))*(cosh(b*x + a) + sinh(b*x + a))) + 6*polylog(4, -sqrt((c + d - 1)/(c - d - 1))*(cosh(b*x + a) + sinh(b*x + a))))/b^3","C",0
218,1,729,0,0.622034," ","integrate(x*arccoth(c+d*coth(b*x+a)),x, algorithm=""fricas"")","\frac{b^{2} x^{2} \log\left(\frac{d \cosh\left(b x + a\right) + {\left(c + 1\right)} \sinh\left(b x + a\right)}{d \cosh\left(b x + a\right) + {\left(c - 1\right)} \sinh\left(b x + a\right)}\right) - 2 \, b x {\rm Li}_2\left(\sqrt{\frac{c + d + 1}{c - d + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - 2 \, b x {\rm Li}_2\left(-\sqrt{\frac{c + d + 1}{c - d + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + 2 \, b x {\rm Li}_2\left(\sqrt{\frac{c + d - 1}{c - d - 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + 2 \, b x {\rm Li}_2\left(-\sqrt{\frac{c + d - 1}{c - d - 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - a^{2} \log\left(2 \, {\left(c + d + 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(c + d + 1\right)} \sinh\left(b x + a\right) + 2 \, {\left(c - d + 1\right)} \sqrt{\frac{c + d + 1}{c - d + 1}}\right) - a^{2} \log\left(2 \, {\left(c + d + 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(c + d + 1\right)} \sinh\left(b x + a\right) - 2 \, {\left(c - d + 1\right)} \sqrt{\frac{c + d + 1}{c - d + 1}}\right) + a^{2} \log\left(2 \, {\left(c + d - 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(c + d - 1\right)} \sinh\left(b x + a\right) + 2 \, {\left(c - d - 1\right)} \sqrt{\frac{c + d - 1}{c - d - 1}}\right) + a^{2} \log\left(2 \, {\left(c + d - 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(c + d - 1\right)} \sinh\left(b x + a\right) - 2 \, {\left(c - d - 1\right)} \sqrt{\frac{c + d - 1}{c - d - 1}}\right) - {\left(b^{2} x^{2} - a^{2}\right)} \log\left(\sqrt{\frac{c + d + 1}{c - d + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) - {\left(b^{2} x^{2} - a^{2}\right)} \log\left(-\sqrt{\frac{c + d + 1}{c - d + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) + {\left(b^{2} x^{2} - a^{2}\right)} \log\left(\sqrt{\frac{c + d - 1}{c - d - 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) + {\left(b^{2} x^{2} - a^{2}\right)} \log\left(-\sqrt{\frac{c + d - 1}{c - d - 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) + 2 \, {\rm polylog}\left(3, \sqrt{\frac{c + d + 1}{c - d + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + 2 \, {\rm polylog}\left(3, -\sqrt{\frac{c + d + 1}{c - d + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - 2 \, {\rm polylog}\left(3, \sqrt{\frac{c + d - 1}{c - d - 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - 2 \, {\rm polylog}\left(3, -\sqrt{\frac{c + d - 1}{c - d - 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right)}{4 \, b^{2}}"," ",0,"1/4*(b^2*x^2*log((d*cosh(b*x + a) + (c + 1)*sinh(b*x + a))/(d*cosh(b*x + a) + (c - 1)*sinh(b*x + a))) - 2*b*x*dilog(sqrt((c + d + 1)/(c - d + 1))*(cosh(b*x + a) + sinh(b*x + a))) - 2*b*x*dilog(-sqrt((c + d + 1)/(c - d + 1))*(cosh(b*x + a) + sinh(b*x + a))) + 2*b*x*dilog(sqrt((c + d - 1)/(c - d - 1))*(cosh(b*x + a) + sinh(b*x + a))) + 2*b*x*dilog(-sqrt((c + d - 1)/(c - d - 1))*(cosh(b*x + a) + sinh(b*x + a))) - a^2*log(2*(c + d + 1)*cosh(b*x + a) + 2*(c + d + 1)*sinh(b*x + a) + 2*(c - d + 1)*sqrt((c + d + 1)/(c - d + 1))) - a^2*log(2*(c + d + 1)*cosh(b*x + a) + 2*(c + d + 1)*sinh(b*x + a) - 2*(c - d + 1)*sqrt((c + d + 1)/(c - d + 1))) + a^2*log(2*(c + d - 1)*cosh(b*x + a) + 2*(c + d - 1)*sinh(b*x + a) + 2*(c - d - 1)*sqrt((c + d - 1)/(c - d - 1))) + a^2*log(2*(c + d - 1)*cosh(b*x + a) + 2*(c + d - 1)*sinh(b*x + a) - 2*(c - d - 1)*sqrt((c + d - 1)/(c - d - 1))) - (b^2*x^2 - a^2)*log(sqrt((c + d + 1)/(c - d + 1))*(cosh(b*x + a) + sinh(b*x + a)) + 1) - (b^2*x^2 - a^2)*log(-sqrt((c + d + 1)/(c - d + 1))*(cosh(b*x + a) + sinh(b*x + a)) + 1) + (b^2*x^2 - a^2)*log(sqrt((c + d - 1)/(c - d - 1))*(cosh(b*x + a) + sinh(b*x + a)) + 1) + (b^2*x^2 - a^2)*log(-sqrt((c + d - 1)/(c - d - 1))*(cosh(b*x + a) + sinh(b*x + a)) + 1) + 2*polylog(3, sqrt((c + d + 1)/(c - d + 1))*(cosh(b*x + a) + sinh(b*x + a))) + 2*polylog(3, -sqrt((c + d + 1)/(c - d + 1))*(cosh(b*x + a) + sinh(b*x + a))) - 2*polylog(3, sqrt((c + d - 1)/(c - d - 1))*(cosh(b*x + a) + sinh(b*x + a))) - 2*polylog(3, -sqrt((c + d - 1)/(c - d - 1))*(cosh(b*x + a) + sinh(b*x + a))))/b^2","C",0
219,1,539,0,0.483145," ","integrate(arccoth(c+d*coth(b*x+a)),x, algorithm=""fricas"")","\frac{b x \log\left(\frac{d \cosh\left(b x + a\right) + {\left(c + 1\right)} \sinh\left(b x + a\right)}{d \cosh\left(b x + a\right) + {\left(c - 1\right)} \sinh\left(b x + a\right)}\right) + a \log\left(2 \, {\left(c + d + 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(c + d + 1\right)} \sinh\left(b x + a\right) + 2 \, {\left(c - d + 1\right)} \sqrt{\frac{c + d + 1}{c - d + 1}}\right) + a \log\left(2 \, {\left(c + d + 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(c + d + 1\right)} \sinh\left(b x + a\right) - 2 \, {\left(c - d + 1\right)} \sqrt{\frac{c + d + 1}{c - d + 1}}\right) - a \log\left(2 \, {\left(c + d - 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(c + d - 1\right)} \sinh\left(b x + a\right) + 2 \, {\left(c - d - 1\right)} \sqrt{\frac{c + d - 1}{c - d - 1}}\right) - a \log\left(2 \, {\left(c + d - 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(c + d - 1\right)} \sinh\left(b x + a\right) - 2 \, {\left(c - d - 1\right)} \sqrt{\frac{c + d - 1}{c - d - 1}}\right) - {\left(b x + a\right)} \log\left(\sqrt{\frac{c + d + 1}{c - d + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) - {\left(b x + a\right)} \log\left(-\sqrt{\frac{c + d + 1}{c - d + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) + {\left(b x + a\right)} \log\left(\sqrt{\frac{c + d - 1}{c - d - 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) + {\left(b x + a\right)} \log\left(-\sqrt{\frac{c + d - 1}{c - d - 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) - {\rm Li}_2\left(\sqrt{\frac{c + d + 1}{c - d + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - {\rm Li}_2\left(-\sqrt{\frac{c + d + 1}{c - d + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + {\rm Li}_2\left(\sqrt{\frac{c + d - 1}{c - d - 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + {\rm Li}_2\left(-\sqrt{\frac{c + d - 1}{c - d - 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right)}{2 \, b}"," ",0,"1/2*(b*x*log((d*cosh(b*x + a) + (c + 1)*sinh(b*x + a))/(d*cosh(b*x + a) + (c - 1)*sinh(b*x + a))) + a*log(2*(c + d + 1)*cosh(b*x + a) + 2*(c + d + 1)*sinh(b*x + a) + 2*(c - d + 1)*sqrt((c + d + 1)/(c - d + 1))) + a*log(2*(c + d + 1)*cosh(b*x + a) + 2*(c + d + 1)*sinh(b*x + a) - 2*(c - d + 1)*sqrt((c + d + 1)/(c - d + 1))) - a*log(2*(c + d - 1)*cosh(b*x + a) + 2*(c + d - 1)*sinh(b*x + a) + 2*(c - d - 1)*sqrt((c + d - 1)/(c - d - 1))) - a*log(2*(c + d - 1)*cosh(b*x + a) + 2*(c + d - 1)*sinh(b*x + a) - 2*(c - d - 1)*sqrt((c + d - 1)/(c - d - 1))) - (b*x + a)*log(sqrt((c + d + 1)/(c - d + 1))*(cosh(b*x + a) + sinh(b*x + a)) + 1) - (b*x + a)*log(-sqrt((c + d + 1)/(c - d + 1))*(cosh(b*x + a) + sinh(b*x + a)) + 1) + (b*x + a)*log(sqrt((c + d - 1)/(c - d - 1))*(cosh(b*x + a) + sinh(b*x + a)) + 1) + (b*x + a)*log(-sqrt((c + d - 1)/(c - d - 1))*(cosh(b*x + a) + sinh(b*x + a)) + 1) - dilog(sqrt((c + d + 1)/(c - d + 1))*(cosh(b*x + a) + sinh(b*x + a))) - dilog(-sqrt((c + d + 1)/(c - d + 1))*(cosh(b*x + a) + sinh(b*x + a))) + dilog(sqrt((c + d - 1)/(c - d - 1))*(cosh(b*x + a) + sinh(b*x + a))) + dilog(-sqrt((c + d - 1)/(c - d - 1))*(cosh(b*x + a) + sinh(b*x + a))))/b","B",0
220,0,0,0,1.065719," ","integrate(arccoth(c+d*coth(b*x+a))/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{arcoth}\left(d \coth\left(b x + a\right) + c\right)}{x}, x\right)"," ",0,"integral(arccoth(d*coth(b*x + a) + c)/x, x)","F",0
221,1,423,0,0.528364," ","integrate(x^3*arccoth(1+d+d*coth(b*x+a)),x, algorithm=""fricas"")","\frac{2 \, b^{5} x^{5} + 5 \, b^{4} x^{4} \log\left(\frac{d \cosh\left(b x + a\right) + {\left(d + 2\right)} \sinh\left(b x + a\right)}{d \cosh\left(b x + a\right) + d \sinh\left(b x + a\right)}\right) - 20 \, b^{3} x^{3} {\rm Li}_2\left(\sqrt{d + 1} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - 20 \, b^{3} x^{3} {\rm Li}_2\left(-\sqrt{d + 1} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - 5 \, a^{4} \log\left(2 \, {\left(d + 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(d + 1\right)} \sinh\left(b x + a\right) + 2 \, \sqrt{d + 1}\right) - 5 \, a^{4} \log\left(2 \, {\left(d + 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(d + 1\right)} \sinh\left(b x + a\right) - 2 \, \sqrt{d + 1}\right) + 60 \, b^{2} x^{2} {\rm polylog}\left(3, \sqrt{d + 1} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + 60 \, b^{2} x^{2} {\rm polylog}\left(3, -\sqrt{d + 1} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - 120 \, b x {\rm polylog}\left(4, \sqrt{d + 1} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - 120 \, b x {\rm polylog}\left(4, -\sqrt{d + 1} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - 5 \, {\left(b^{4} x^{4} - a^{4}\right)} \log\left(\sqrt{d + 1} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) - 5 \, {\left(b^{4} x^{4} - a^{4}\right)} \log\left(-\sqrt{d + 1} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) + 120 \, {\rm polylog}\left(5, \sqrt{d + 1} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + 120 \, {\rm polylog}\left(5, -\sqrt{d + 1} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right)}{40 \, b^{4}}"," ",0,"1/40*(2*b^5*x^5 + 5*b^4*x^4*log((d*cosh(b*x + a) + (d + 2)*sinh(b*x + a))/(d*cosh(b*x + a) + d*sinh(b*x + a))) - 20*b^3*x^3*dilog(sqrt(d + 1)*(cosh(b*x + a) + sinh(b*x + a))) - 20*b^3*x^3*dilog(-sqrt(d + 1)*(cosh(b*x + a) + sinh(b*x + a))) - 5*a^4*log(2*(d + 1)*cosh(b*x + a) + 2*(d + 1)*sinh(b*x + a) + 2*sqrt(d + 1)) - 5*a^4*log(2*(d + 1)*cosh(b*x + a) + 2*(d + 1)*sinh(b*x + a) - 2*sqrt(d + 1)) + 60*b^2*x^2*polylog(3, sqrt(d + 1)*(cosh(b*x + a) + sinh(b*x + a))) + 60*b^2*x^2*polylog(3, -sqrt(d + 1)*(cosh(b*x + a) + sinh(b*x + a))) - 120*b*x*polylog(4, sqrt(d + 1)*(cosh(b*x + a) + sinh(b*x + a))) - 120*b*x*polylog(4, -sqrt(d + 1)*(cosh(b*x + a) + sinh(b*x + a))) - 5*(b^4*x^4 - a^4)*log(sqrt(d + 1)*(cosh(b*x + a) + sinh(b*x + a)) + 1) - 5*(b^4*x^4 - a^4)*log(-sqrt(d + 1)*(cosh(b*x + a) + sinh(b*x + a)) + 1) + 120*polylog(5, sqrt(d + 1)*(cosh(b*x + a) + sinh(b*x + a))) + 120*polylog(5, -sqrt(d + 1)*(cosh(b*x + a) + sinh(b*x + a))))/b^4","C",0
222,1,359,0,0.872299," ","integrate(x^2*arccoth(1+d+d*coth(b*x+a)),x, algorithm=""fricas"")","\frac{b^{4} x^{4} + 2 \, b^{3} x^{3} \log\left(\frac{d \cosh\left(b x + a\right) + {\left(d + 2\right)} \sinh\left(b x + a\right)}{d \cosh\left(b x + a\right) + d \sinh\left(b x + a\right)}\right) - 6 \, b^{2} x^{2} {\rm Li}_2\left(\sqrt{d + 1} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - 6 \, b^{2} x^{2} {\rm Li}_2\left(-\sqrt{d + 1} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + 2 \, a^{3} \log\left(2 \, {\left(d + 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(d + 1\right)} \sinh\left(b x + a\right) + 2 \, \sqrt{d + 1}\right) + 2 \, a^{3} \log\left(2 \, {\left(d + 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(d + 1\right)} \sinh\left(b x + a\right) - 2 \, \sqrt{d + 1}\right) + 12 \, b x {\rm polylog}\left(3, \sqrt{d + 1} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + 12 \, b x {\rm polylog}\left(3, -\sqrt{d + 1} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - 2 \, {\left(b^{3} x^{3} + a^{3}\right)} \log\left(\sqrt{d + 1} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) - 2 \, {\left(b^{3} x^{3} + a^{3}\right)} \log\left(-\sqrt{d + 1} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) - 12 \, {\rm polylog}\left(4, \sqrt{d + 1} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - 12 \, {\rm polylog}\left(4, -\sqrt{d + 1} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right)}{12 \, b^{3}}"," ",0,"1/12*(b^4*x^4 + 2*b^3*x^3*log((d*cosh(b*x + a) + (d + 2)*sinh(b*x + a))/(d*cosh(b*x + a) + d*sinh(b*x + a))) - 6*b^2*x^2*dilog(sqrt(d + 1)*(cosh(b*x + a) + sinh(b*x + a))) - 6*b^2*x^2*dilog(-sqrt(d + 1)*(cosh(b*x + a) + sinh(b*x + a))) + 2*a^3*log(2*(d + 1)*cosh(b*x + a) + 2*(d + 1)*sinh(b*x + a) + 2*sqrt(d + 1)) + 2*a^3*log(2*(d + 1)*cosh(b*x + a) + 2*(d + 1)*sinh(b*x + a) - 2*sqrt(d + 1)) + 12*b*x*polylog(3, sqrt(d + 1)*(cosh(b*x + a) + sinh(b*x + a))) + 12*b*x*polylog(3, -sqrt(d + 1)*(cosh(b*x + a) + sinh(b*x + a))) - 2*(b^3*x^3 + a^3)*log(sqrt(d + 1)*(cosh(b*x + a) + sinh(b*x + a)) + 1) - 2*(b^3*x^3 + a^3)*log(-sqrt(d + 1)*(cosh(b*x + a) + sinh(b*x + a)) + 1) - 12*polylog(4, sqrt(d + 1)*(cosh(b*x + a) + sinh(b*x + a))) - 12*polylog(4, -sqrt(d + 1)*(cosh(b*x + a) + sinh(b*x + a))))/b^3","C",0
223,1,305,0,0.639478," ","integrate(x*arccoth(1+d+d*coth(b*x+a)),x, algorithm=""fricas"")","\frac{2 \, b^{3} x^{3} + 3 \, b^{2} x^{2} \log\left(\frac{d \cosh\left(b x + a\right) + {\left(d + 2\right)} \sinh\left(b x + a\right)}{d \cosh\left(b x + a\right) + d \sinh\left(b x + a\right)}\right) - 6 \, b x {\rm Li}_2\left(\sqrt{d + 1} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - 6 \, b x {\rm Li}_2\left(-\sqrt{d + 1} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - 3 \, a^{2} \log\left(2 \, {\left(d + 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(d + 1\right)} \sinh\left(b x + a\right) + 2 \, \sqrt{d + 1}\right) - 3 \, a^{2} \log\left(2 \, {\left(d + 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(d + 1\right)} \sinh\left(b x + a\right) - 2 \, \sqrt{d + 1}\right) - 3 \, {\left(b^{2} x^{2} - a^{2}\right)} \log\left(\sqrt{d + 1} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) - 3 \, {\left(b^{2} x^{2} - a^{2}\right)} \log\left(-\sqrt{d + 1} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) + 6 \, {\rm polylog}\left(3, \sqrt{d + 1} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + 6 \, {\rm polylog}\left(3, -\sqrt{d + 1} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right)}{12 \, b^{2}}"," ",0,"1/12*(2*b^3*x^3 + 3*b^2*x^2*log((d*cosh(b*x + a) + (d + 2)*sinh(b*x + a))/(d*cosh(b*x + a) + d*sinh(b*x + a))) - 6*b*x*dilog(sqrt(d + 1)*(cosh(b*x + a) + sinh(b*x + a))) - 6*b*x*dilog(-sqrt(d + 1)*(cosh(b*x + a) + sinh(b*x + a))) - 3*a^2*log(2*(d + 1)*cosh(b*x + a) + 2*(d + 1)*sinh(b*x + a) + 2*sqrt(d + 1)) - 3*a^2*log(2*(d + 1)*cosh(b*x + a) + 2*(d + 1)*sinh(b*x + a) - 2*sqrt(d + 1)) - 3*(b^2*x^2 - a^2)*log(sqrt(d + 1)*(cosh(b*x + a) + sinh(b*x + a)) + 1) - 3*(b^2*x^2 - a^2)*log(-sqrt(d + 1)*(cosh(b*x + a) + sinh(b*x + a)) + 1) + 6*polylog(3, sqrt(d + 1)*(cosh(b*x + a) + sinh(b*x + a))) + 6*polylog(3, -sqrt(d + 1)*(cosh(b*x + a) + sinh(b*x + a))))/b^2","C",0
224,1,226,0,0.485067," ","integrate(arccoth(1+d+d*coth(b*x+a)),x, algorithm=""fricas"")","\frac{b^{2} x^{2} + b x \log\left(\frac{d \cosh\left(b x + a\right) + {\left(d + 2\right)} \sinh\left(b x + a\right)}{d \cosh\left(b x + a\right) + d \sinh\left(b x + a\right)}\right) + a \log\left(2 \, {\left(d + 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(d + 1\right)} \sinh\left(b x + a\right) + 2 \, \sqrt{d + 1}\right) + a \log\left(2 \, {\left(d + 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(d + 1\right)} \sinh\left(b x + a\right) - 2 \, \sqrt{d + 1}\right) - {\left(b x + a\right)} \log\left(\sqrt{d + 1} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) - {\left(b x + a\right)} \log\left(-\sqrt{d + 1} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) - {\rm Li}_2\left(\sqrt{d + 1} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - {\rm Li}_2\left(-\sqrt{d + 1} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right)}{2 \, b}"," ",0,"1/2*(b^2*x^2 + b*x*log((d*cosh(b*x + a) + (d + 2)*sinh(b*x + a))/(d*cosh(b*x + a) + d*sinh(b*x + a))) + a*log(2*(d + 1)*cosh(b*x + a) + 2*(d + 1)*sinh(b*x + a) + 2*sqrt(d + 1)) + a*log(2*(d + 1)*cosh(b*x + a) + 2*(d + 1)*sinh(b*x + a) - 2*sqrt(d + 1)) - (b*x + a)*log(sqrt(d + 1)*(cosh(b*x + a) + sinh(b*x + a)) + 1) - (b*x + a)*log(-sqrt(d + 1)*(cosh(b*x + a) + sinh(b*x + a)) + 1) - dilog(sqrt(d + 1)*(cosh(b*x + a) + sinh(b*x + a))) - dilog(-sqrt(d + 1)*(cosh(b*x + a) + sinh(b*x + a))))/b","B",0
225,0,0,0,0.695718," ","integrate(arccoth(1+d+d*coth(b*x+a))/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{arcoth}\left(d \coth\left(b x + a\right) + d + 1\right)}{x}, x\right)"," ",0,"integral(arccoth(d*coth(b*x + a) + d + 1)/x, x)","F",0
226,1,450,0,0.569812," ","integrate(x^3*arccoth(1-d-d*coth(b*x+a)),x, algorithm=""fricas"")","\frac{2 \, b^{5} x^{5} - 5 \, b^{4} x^{4} \log\left(\frac{d \cosh\left(b x + a\right) + d \sinh\left(b x + a\right)}{d \cosh\left(b x + a\right) + {\left(d - 2\right)} \sinh\left(b x + a\right)}\right) - 20 \, b^{3} x^{3} {\rm Li}_2\left(\frac{1}{2} \, \sqrt{-4 \, d + 4} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - 20 \, b^{3} x^{3} {\rm Li}_2\left(-\frac{1}{2} \, \sqrt{-4 \, d + 4} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - 5 \, a^{4} \log\left(2 \, {\left(d - 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(d - 1\right)} \sinh\left(b x + a\right) + \sqrt{-4 \, d + 4}\right) - 5 \, a^{4} \log\left(2 \, {\left(d - 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(d - 1\right)} \sinh\left(b x + a\right) - \sqrt{-4 \, d + 4}\right) + 60 \, b^{2} x^{2} {\rm polylog}\left(3, \frac{1}{2} \, \sqrt{-4 \, d + 4} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + 60 \, b^{2} x^{2} {\rm polylog}\left(3, -\frac{1}{2} \, \sqrt{-4 \, d + 4} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - 120 \, b x {\rm polylog}\left(4, \frac{1}{2} \, \sqrt{-4 \, d + 4} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - 120 \, b x {\rm polylog}\left(4, -\frac{1}{2} \, \sqrt{-4 \, d + 4} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - 5 \, {\left(b^{4} x^{4} - a^{4}\right)} \log\left(\frac{1}{2} \, \sqrt{-4 \, d + 4} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) - 5 \, {\left(b^{4} x^{4} - a^{4}\right)} \log\left(-\frac{1}{2} \, \sqrt{-4 \, d + 4} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) + 120 \, {\rm polylog}\left(5, \frac{1}{2} \, \sqrt{-4 \, d + 4} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + 120 \, {\rm polylog}\left(5, -\frac{1}{2} \, \sqrt{-4 \, d + 4} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right)}{40 \, b^{4}}"," ",0,"1/40*(2*b^5*x^5 - 5*b^4*x^4*log((d*cosh(b*x + a) + d*sinh(b*x + a))/(d*cosh(b*x + a) + (d - 2)*sinh(b*x + a))) - 20*b^3*x^3*dilog(1/2*sqrt(-4*d + 4)*(cosh(b*x + a) + sinh(b*x + a))) - 20*b^3*x^3*dilog(-1/2*sqrt(-4*d + 4)*(cosh(b*x + a) + sinh(b*x + a))) - 5*a^4*log(2*(d - 1)*cosh(b*x + a) + 2*(d - 1)*sinh(b*x + a) + sqrt(-4*d + 4)) - 5*a^4*log(2*(d - 1)*cosh(b*x + a) + 2*(d - 1)*sinh(b*x + a) - sqrt(-4*d + 4)) + 60*b^2*x^2*polylog(3, 1/2*sqrt(-4*d + 4)*(cosh(b*x + a) + sinh(b*x + a))) + 60*b^2*x^2*polylog(3, -1/2*sqrt(-4*d + 4)*(cosh(b*x + a) + sinh(b*x + a))) - 120*b*x*polylog(4, 1/2*sqrt(-4*d + 4)*(cosh(b*x + a) + sinh(b*x + a))) - 120*b*x*polylog(4, -1/2*sqrt(-4*d + 4)*(cosh(b*x + a) + sinh(b*x + a))) - 5*(b^4*x^4 - a^4)*log(1/2*sqrt(-4*d + 4)*(cosh(b*x + a) + sinh(b*x + a)) + 1) - 5*(b^4*x^4 - a^4)*log(-1/2*sqrt(-4*d + 4)*(cosh(b*x + a) + sinh(b*x + a)) + 1) + 120*polylog(5, 1/2*sqrt(-4*d + 4)*(cosh(b*x + a) + sinh(b*x + a))) + 120*polylog(5, -1/2*sqrt(-4*d + 4)*(cosh(b*x + a) + sinh(b*x + a))))/b^4","C",0
227,1,381,0,0.532290," ","integrate(x^2*arccoth(1-d-d*coth(b*x+a)),x, algorithm=""fricas"")","\frac{b^{4} x^{4} - 2 \, b^{3} x^{3} \log\left(\frac{d \cosh\left(b x + a\right) + d \sinh\left(b x + a\right)}{d \cosh\left(b x + a\right) + {\left(d - 2\right)} \sinh\left(b x + a\right)}\right) - 6 \, b^{2} x^{2} {\rm Li}_2\left(\frac{1}{2} \, \sqrt{-4 \, d + 4} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - 6 \, b^{2} x^{2} {\rm Li}_2\left(-\frac{1}{2} \, \sqrt{-4 \, d + 4} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + 2 \, a^{3} \log\left(2 \, {\left(d - 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(d - 1\right)} \sinh\left(b x + a\right) + \sqrt{-4 \, d + 4}\right) + 2 \, a^{3} \log\left(2 \, {\left(d - 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(d - 1\right)} \sinh\left(b x + a\right) - \sqrt{-4 \, d + 4}\right) + 12 \, b x {\rm polylog}\left(3, \frac{1}{2} \, \sqrt{-4 \, d + 4} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + 12 \, b x {\rm polylog}\left(3, -\frac{1}{2} \, \sqrt{-4 \, d + 4} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - 2 \, {\left(b^{3} x^{3} + a^{3}\right)} \log\left(\frac{1}{2} \, \sqrt{-4 \, d + 4} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) - 2 \, {\left(b^{3} x^{3} + a^{3}\right)} \log\left(-\frac{1}{2} \, \sqrt{-4 \, d + 4} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) - 12 \, {\rm polylog}\left(4, \frac{1}{2} \, \sqrt{-4 \, d + 4} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - 12 \, {\rm polylog}\left(4, -\frac{1}{2} \, \sqrt{-4 \, d + 4} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right)}{12 \, b^{3}}"," ",0,"1/12*(b^4*x^4 - 2*b^3*x^3*log((d*cosh(b*x + a) + d*sinh(b*x + a))/(d*cosh(b*x + a) + (d - 2)*sinh(b*x + a))) - 6*b^2*x^2*dilog(1/2*sqrt(-4*d + 4)*(cosh(b*x + a) + sinh(b*x + a))) - 6*b^2*x^2*dilog(-1/2*sqrt(-4*d + 4)*(cosh(b*x + a) + sinh(b*x + a))) + 2*a^3*log(2*(d - 1)*cosh(b*x + a) + 2*(d - 1)*sinh(b*x + a) + sqrt(-4*d + 4)) + 2*a^3*log(2*(d - 1)*cosh(b*x + a) + 2*(d - 1)*sinh(b*x + a) - sqrt(-4*d + 4)) + 12*b*x*polylog(3, 1/2*sqrt(-4*d + 4)*(cosh(b*x + a) + sinh(b*x + a))) + 12*b*x*polylog(3, -1/2*sqrt(-4*d + 4)*(cosh(b*x + a) + sinh(b*x + a))) - 2*(b^3*x^3 + a^3)*log(1/2*sqrt(-4*d + 4)*(cosh(b*x + a) + sinh(b*x + a)) + 1) - 2*(b^3*x^3 + a^3)*log(-1/2*sqrt(-4*d + 4)*(cosh(b*x + a) + sinh(b*x + a)) + 1) - 12*polylog(4, 1/2*sqrt(-4*d + 4)*(cosh(b*x + a) + sinh(b*x + a))) - 12*polylog(4, -1/2*sqrt(-4*d + 4)*(cosh(b*x + a) + sinh(b*x + a))))/b^3","C",0
228,1,322,0,0.527295," ","integrate(x*arccoth(1-d-d*coth(b*x+a)),x, algorithm=""fricas"")","\frac{2 \, b^{3} x^{3} - 3 \, b^{2} x^{2} \log\left(\frac{d \cosh\left(b x + a\right) + d \sinh\left(b x + a\right)}{d \cosh\left(b x + a\right) + {\left(d - 2\right)} \sinh\left(b x + a\right)}\right) - 6 \, b x {\rm Li}_2\left(\frac{1}{2} \, \sqrt{-4 \, d + 4} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - 6 \, b x {\rm Li}_2\left(-\frac{1}{2} \, \sqrt{-4 \, d + 4} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - 3 \, a^{2} \log\left(2 \, {\left(d - 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(d - 1\right)} \sinh\left(b x + a\right) + \sqrt{-4 \, d + 4}\right) - 3 \, a^{2} \log\left(2 \, {\left(d - 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(d - 1\right)} \sinh\left(b x + a\right) - \sqrt{-4 \, d + 4}\right) - 3 \, {\left(b^{2} x^{2} - a^{2}\right)} \log\left(\frac{1}{2} \, \sqrt{-4 \, d + 4} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) - 3 \, {\left(b^{2} x^{2} - a^{2}\right)} \log\left(-\frac{1}{2} \, \sqrt{-4 \, d + 4} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) + 6 \, {\rm polylog}\left(3, \frac{1}{2} \, \sqrt{-4 \, d + 4} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + 6 \, {\rm polylog}\left(3, -\frac{1}{2} \, \sqrt{-4 \, d + 4} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right)}{12 \, b^{2}}"," ",0,"1/12*(2*b^3*x^3 - 3*b^2*x^2*log((d*cosh(b*x + a) + d*sinh(b*x + a))/(d*cosh(b*x + a) + (d - 2)*sinh(b*x + a))) - 6*b*x*dilog(1/2*sqrt(-4*d + 4)*(cosh(b*x + a) + sinh(b*x + a))) - 6*b*x*dilog(-1/2*sqrt(-4*d + 4)*(cosh(b*x + a) + sinh(b*x + a))) - 3*a^2*log(2*(d - 1)*cosh(b*x + a) + 2*(d - 1)*sinh(b*x + a) + sqrt(-4*d + 4)) - 3*a^2*log(2*(d - 1)*cosh(b*x + a) + 2*(d - 1)*sinh(b*x + a) - sqrt(-4*d + 4)) - 3*(b^2*x^2 - a^2)*log(1/2*sqrt(-4*d + 4)*(cosh(b*x + a) + sinh(b*x + a)) + 1) - 3*(b^2*x^2 - a^2)*log(-1/2*sqrt(-4*d + 4)*(cosh(b*x + a) + sinh(b*x + a)) + 1) + 6*polylog(3, 1/2*sqrt(-4*d + 4)*(cosh(b*x + a) + sinh(b*x + a))) + 6*polylog(3, -1/2*sqrt(-4*d + 4)*(cosh(b*x + a) + sinh(b*x + a))))/b^2","C",0
229,1,239,0,0.835651," ","integrate(arccoth(1-d-d*coth(b*x+a)),x, algorithm=""fricas"")","\frac{b^{2} x^{2} - b x \log\left(\frac{d \cosh\left(b x + a\right) + d \sinh\left(b x + a\right)}{d \cosh\left(b x + a\right) + {\left(d - 2\right)} \sinh\left(b x + a\right)}\right) + a \log\left(2 \, {\left(d - 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(d - 1\right)} \sinh\left(b x + a\right) + \sqrt{-4 \, d + 4}\right) + a \log\left(2 \, {\left(d - 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(d - 1\right)} \sinh\left(b x + a\right) - \sqrt{-4 \, d + 4}\right) - {\left(b x + a\right)} \log\left(\frac{1}{2} \, \sqrt{-4 \, d + 4} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) - {\left(b x + a\right)} \log\left(-\frac{1}{2} \, \sqrt{-4 \, d + 4} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) - {\rm Li}_2\left(\frac{1}{2} \, \sqrt{-4 \, d + 4} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - {\rm Li}_2\left(-\frac{1}{2} \, \sqrt{-4 \, d + 4} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right)}{2 \, b}"," ",0,"1/2*(b^2*x^2 - b*x*log((d*cosh(b*x + a) + d*sinh(b*x + a))/(d*cosh(b*x + a) + (d - 2)*sinh(b*x + a))) + a*log(2*(d - 1)*cosh(b*x + a) + 2*(d - 1)*sinh(b*x + a) + sqrt(-4*d + 4)) + a*log(2*(d - 1)*cosh(b*x + a) + 2*(d - 1)*sinh(b*x + a) - sqrt(-4*d + 4)) - (b*x + a)*log(1/2*sqrt(-4*d + 4)*(cosh(b*x + a) + sinh(b*x + a)) + 1) - (b*x + a)*log(-1/2*sqrt(-4*d + 4)*(cosh(b*x + a) + sinh(b*x + a)) + 1) - dilog(1/2*sqrt(-4*d + 4)*(cosh(b*x + a) + sinh(b*x + a))) - dilog(-1/2*sqrt(-4*d + 4)*(cosh(b*x + a) + sinh(b*x + a))))/b","B",0
230,0,0,0,0.420830," ","integrate(arccoth(1-d-d*coth(b*x+a))/x,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\operatorname{arcoth}\left(d \coth\left(b x + a\right) + d - 1\right)}{x}, x\right)"," ",0,"integral(-arccoth(d*coth(b*x + a) + d - 1)/x, x)","F",0
231,1,1808,0,0.771768," ","integrate((f*x+e)^3*arccoth(tan(b*x+a)),x, algorithm=""fricas"")","-\frac{3 \, f^{3} {\rm polylog}\left(5, \frac{i \, \tan\left(b x + a\right)^{2} + 2 \, \tan\left(b x + a\right) - i}{\tan\left(b x + a\right)^{2} + 1}\right) - 3 \, f^{3} {\rm polylog}\left(5, \frac{i \, \tan\left(b x + a\right)^{2} - 2 \, \tan\left(b x + a\right) - i}{\tan\left(b x + a\right)^{2} + 1}\right) + 3 \, f^{3} {\rm polylog}\left(5, \frac{-i \, \tan\left(b x + a\right)^{2} + 2 \, \tan\left(b x + a\right) + i}{\tan\left(b x + a\right)^{2} + 1}\right) - 3 \, f^{3} {\rm polylog}\left(5, \frac{-i \, \tan\left(b x + a\right)^{2} - 2 \, \tan\left(b x + a\right) + i}{\tan\left(b x + a\right)^{2} + 1}\right) - {\left(4 i \, b^{3} f^{3} x^{3} + 12 i \, b^{3} e f^{2} x^{2} + 12 i \, b^{3} e^{2} f x + 4 i \, b^{3} e^{3}\right)} {\rm Li}_2\left(-\frac{\left(i + 1\right) \, \tan\left(b x + a\right)^{2} + 2 \, \tan\left(b x + a\right) - i + 1}{\tan\left(b x + a\right)^{2} + 1} + 1\right) - {\left(4 i \, b^{3} f^{3} x^{3} + 12 i \, b^{3} e f^{2} x^{2} + 12 i \, b^{3} e^{2} f x + 4 i \, b^{3} e^{3}\right)} {\rm Li}_2\left(-\frac{\left(i + 1\right) \, \tan\left(b x + a\right)^{2} - 2 \, \tan\left(b x + a\right) - i + 1}{\tan\left(b x + a\right)^{2} + 1} + 1\right) - {\left(-4 i \, b^{3} f^{3} x^{3} - 12 i \, b^{3} e f^{2} x^{2} - 12 i \, b^{3} e^{2} f x - 4 i \, b^{3} e^{3}\right)} {\rm Li}_2\left(-\frac{-\left(i - 1\right) \, \tan\left(b x + a\right)^{2} + 2 \, \tan\left(b x + a\right) + i + 1}{\tan\left(b x + a\right)^{2} + 1} + 1\right) - {\left(-4 i \, b^{3} f^{3} x^{3} - 12 i \, b^{3} e f^{2} x^{2} - 12 i \, b^{3} e^{2} f x - 4 i \, b^{3} e^{3}\right)} {\rm Li}_2\left(-\frac{-\left(i - 1\right) \, \tan\left(b x + a\right)^{2} - 2 \, \tan\left(b x + a\right) + i + 1}{\tan\left(b x + a\right)^{2} + 1} + 1\right) + 2 \, {\left(b^{4} f^{3} x^{4} + 4 \, b^{4} e f^{2} x^{3} + 6 \, b^{4} e^{2} f x^{2} + 4 \, b^{4} e^{3} x + 4 \, a b^{3} e^{3} - 6 \, a^{2} b^{2} e^{2} f + 4 \, a^{3} b e f^{2} - a^{4} f^{3}\right)} \log\left(\frac{\left(i + 1\right) \, \tan\left(b x + a\right)^{2} + 2 \, \tan\left(b x + a\right) - i + 1}{\tan\left(b x + a\right)^{2} + 1}\right) - 2 \, {\left(4 \, a b^{3} e^{3} - 6 \, a^{2} b^{2} e^{2} f + 4 \, a^{3} b e f^{2} - a^{4} f^{3}\right)} \log\left(\frac{\left(i + 1\right) \, \tan\left(b x + a\right)^{2} + 2 i \, \tan\left(b x + a\right) + i - 1}{\tan\left(b x + a\right)^{2} + 1}\right) + 2 \, {\left(4 \, a b^{3} e^{3} - 6 \, a^{2} b^{2} e^{2} f + 4 \, a^{3} b e f^{2} - a^{4} f^{3}\right)} \log\left(\frac{\left(i + 1\right) \, \tan\left(b x + a\right)^{2} - 2 i \, \tan\left(b x + a\right) + i - 1}{\tan\left(b x + a\right)^{2} + 1}\right) - 2 \, {\left(b^{4} f^{3} x^{4} + 4 \, b^{4} e f^{2} x^{3} + 6 \, b^{4} e^{2} f x^{2} + 4 \, b^{4} e^{3} x + 4 \, a b^{3} e^{3} - 6 \, a^{2} b^{2} e^{2} f + 4 \, a^{3} b e f^{2} - a^{4} f^{3}\right)} \log\left(\frac{\left(i + 1\right) \, \tan\left(b x + a\right)^{2} - 2 \, \tan\left(b x + a\right) - i + 1}{\tan\left(b x + a\right)^{2} + 1}\right) + 2 \, {\left(b^{4} f^{3} x^{4} + 4 \, b^{4} e f^{2} x^{3} + 6 \, b^{4} e^{2} f x^{2} + 4 \, b^{4} e^{3} x + 4 \, a b^{3} e^{3} - 6 \, a^{2} b^{2} e^{2} f + 4 \, a^{3} b e f^{2} - a^{4} f^{3}\right)} \log\left(\frac{-\left(i - 1\right) \, \tan\left(b x + a\right)^{2} + 2 \, \tan\left(b x + a\right) + i + 1}{\tan\left(b x + a\right)^{2} + 1}\right) - 2 \, {\left(b^{4} f^{3} x^{4} + 4 \, b^{4} e f^{2} x^{3} + 6 \, b^{4} e^{2} f x^{2} + 4 \, b^{4} e^{3} x + 4 \, a b^{3} e^{3} - 6 \, a^{2} b^{2} e^{2} f + 4 \, a^{3} b e f^{2} - a^{4} f^{3}\right)} \log\left(\frac{-\left(i - 1\right) \, \tan\left(b x + a\right)^{2} - 2 \, \tan\left(b x + a\right) + i + 1}{\tan\left(b x + a\right)^{2} + 1}\right) - 2 \, {\left(4 \, a b^{3} e^{3} - 6 \, a^{2} b^{2} e^{2} f + 4 \, a^{3} b e f^{2} - a^{4} f^{3}\right)} \log\left(\frac{\left(i - 1\right) \, \tan\left(b x + a\right)^{2} + 2 i \, \tan\left(b x + a\right) + i + 1}{\tan\left(b x + a\right)^{2} + 1}\right) + 2 \, {\left(4 \, a b^{3} e^{3} - 6 \, a^{2} b^{2} e^{2} f + 4 \, a^{3} b e f^{2} - a^{4} f^{3}\right)} \log\left(\frac{\left(i - 1\right) \, \tan\left(b x + a\right)^{2} - 2 i \, \tan\left(b x + a\right) + i + 1}{\tan\left(b x + a\right)^{2} + 1}\right) - 4 \, {\left(b^{4} f^{3} x^{4} + 4 \, b^{4} e f^{2} x^{3} + 6 \, b^{4} e^{2} f x^{2} + 4 \, b^{4} e^{3} x\right)} \log\left(\frac{\tan\left(b x + a\right) + 1}{\tan\left(b x + a\right) - 1}\right) - {\left(6 i \, b f^{3} x + 6 i \, b e f^{2}\right)} {\rm polylog}\left(4, \frac{i \, \tan\left(b x + a\right)^{2} + 2 \, \tan\left(b x + a\right) - i}{\tan\left(b x + a\right)^{2} + 1}\right) - {\left(6 i \, b f^{3} x + 6 i \, b e f^{2}\right)} {\rm polylog}\left(4, \frac{i \, \tan\left(b x + a\right)^{2} - 2 \, \tan\left(b x + a\right) - i}{\tan\left(b x + a\right)^{2} + 1}\right) - {\left(-6 i \, b f^{3} x - 6 i \, b e f^{2}\right)} {\rm polylog}\left(4, \frac{-i \, \tan\left(b x + a\right)^{2} + 2 \, \tan\left(b x + a\right) + i}{\tan\left(b x + a\right)^{2} + 1}\right) - {\left(-6 i \, b f^{3} x - 6 i \, b e f^{2}\right)} {\rm polylog}\left(4, \frac{-i \, \tan\left(b x + a\right)^{2} - 2 \, \tan\left(b x + a\right) + i}{\tan\left(b x + a\right)^{2} + 1}\right) - 6 \, {\left(b^{2} f^{3} x^{2} + 2 \, b^{2} e f^{2} x + b^{2} e^{2} f\right)} {\rm polylog}\left(3, \frac{i \, \tan\left(b x + a\right)^{2} + 2 \, \tan\left(b x + a\right) - i}{\tan\left(b x + a\right)^{2} + 1}\right) + 6 \, {\left(b^{2} f^{3} x^{2} + 2 \, b^{2} e f^{2} x + b^{2} e^{2} f\right)} {\rm polylog}\left(3, \frac{i \, \tan\left(b x + a\right)^{2} - 2 \, \tan\left(b x + a\right) - i}{\tan\left(b x + a\right)^{2} + 1}\right) - 6 \, {\left(b^{2} f^{3} x^{2} + 2 \, b^{2} e f^{2} x + b^{2} e^{2} f\right)} {\rm polylog}\left(3, \frac{-i \, \tan\left(b x + a\right)^{2} + 2 \, \tan\left(b x + a\right) + i}{\tan\left(b x + a\right)^{2} + 1}\right) + 6 \, {\left(b^{2} f^{3} x^{2} + 2 \, b^{2} e f^{2} x + b^{2} e^{2} f\right)} {\rm polylog}\left(3, \frac{-i \, \tan\left(b x + a\right)^{2} - 2 \, \tan\left(b x + a\right) + i}{\tan\left(b x + a\right)^{2} + 1}\right)}{32 \, b^{4}}"," ",0,"-1/32*(3*f^3*polylog(5, (I*tan(b*x + a)^2 + 2*tan(b*x + a) - I)/(tan(b*x + a)^2 + 1)) - 3*f^3*polylog(5, (I*tan(b*x + a)^2 - 2*tan(b*x + a) - I)/(tan(b*x + a)^2 + 1)) + 3*f^3*polylog(5, (-I*tan(b*x + a)^2 + 2*tan(b*x + a) + I)/(tan(b*x + a)^2 + 1)) - 3*f^3*polylog(5, (-I*tan(b*x + a)^2 - 2*tan(b*x + a) + I)/(tan(b*x + a)^2 + 1)) - (4*I*b^3*f^3*x^3 + 12*I*b^3*e*f^2*x^2 + 12*I*b^3*e^2*f*x + 4*I*b^3*e^3)*dilog(-((I + 1)*tan(b*x + a)^2 + 2*tan(b*x + a) - I + 1)/(tan(b*x + a)^2 + 1) + 1) - (4*I*b^3*f^3*x^3 + 12*I*b^3*e*f^2*x^2 + 12*I*b^3*e^2*f*x + 4*I*b^3*e^3)*dilog(-((I + 1)*tan(b*x + a)^2 - 2*tan(b*x + a) - I + 1)/(tan(b*x + a)^2 + 1) + 1) - (-4*I*b^3*f^3*x^3 - 12*I*b^3*e*f^2*x^2 - 12*I*b^3*e^2*f*x - 4*I*b^3*e^3)*dilog(-(-(I - 1)*tan(b*x + a)^2 + 2*tan(b*x + a) + I + 1)/(tan(b*x + a)^2 + 1) + 1) - (-4*I*b^3*f^3*x^3 - 12*I*b^3*e*f^2*x^2 - 12*I*b^3*e^2*f*x - 4*I*b^3*e^3)*dilog(-(-(I - 1)*tan(b*x + a)^2 - 2*tan(b*x + a) + I + 1)/(tan(b*x + a)^2 + 1) + 1) + 2*(b^4*f^3*x^4 + 4*b^4*e*f^2*x^3 + 6*b^4*e^2*f*x^2 + 4*b^4*e^3*x + 4*a*b^3*e^3 - 6*a^2*b^2*e^2*f + 4*a^3*b*e*f^2 - a^4*f^3)*log(((I + 1)*tan(b*x + a)^2 + 2*tan(b*x + a) - I + 1)/(tan(b*x + a)^2 + 1)) - 2*(4*a*b^3*e^3 - 6*a^2*b^2*e^2*f + 4*a^3*b*e*f^2 - a^4*f^3)*log(((I + 1)*tan(b*x + a)^2 + 2*I*tan(b*x + a) + I - 1)/(tan(b*x + a)^2 + 1)) + 2*(4*a*b^3*e^3 - 6*a^2*b^2*e^2*f + 4*a^3*b*e*f^2 - a^4*f^3)*log(((I + 1)*tan(b*x + a)^2 - 2*I*tan(b*x + a) + I - 1)/(tan(b*x + a)^2 + 1)) - 2*(b^4*f^3*x^4 + 4*b^4*e*f^2*x^3 + 6*b^4*e^2*f*x^2 + 4*b^4*e^3*x + 4*a*b^3*e^3 - 6*a^2*b^2*e^2*f + 4*a^3*b*e*f^2 - a^4*f^3)*log(((I + 1)*tan(b*x + a)^2 - 2*tan(b*x + a) - I + 1)/(tan(b*x + a)^2 + 1)) + 2*(b^4*f^3*x^4 + 4*b^4*e*f^2*x^3 + 6*b^4*e^2*f*x^2 + 4*b^4*e^3*x + 4*a*b^3*e^3 - 6*a^2*b^2*e^2*f + 4*a^3*b*e*f^2 - a^4*f^3)*log((-(I - 1)*tan(b*x + a)^2 + 2*tan(b*x + a) + I + 1)/(tan(b*x + a)^2 + 1)) - 2*(b^4*f^3*x^4 + 4*b^4*e*f^2*x^3 + 6*b^4*e^2*f*x^2 + 4*b^4*e^3*x + 4*a*b^3*e^3 - 6*a^2*b^2*e^2*f + 4*a^3*b*e*f^2 - a^4*f^3)*log((-(I - 1)*tan(b*x + a)^2 - 2*tan(b*x + a) + I + 1)/(tan(b*x + a)^2 + 1)) - 2*(4*a*b^3*e^3 - 6*a^2*b^2*e^2*f + 4*a^3*b*e*f^2 - a^4*f^3)*log(((I - 1)*tan(b*x + a)^2 + 2*I*tan(b*x + a) + I + 1)/(tan(b*x + a)^2 + 1)) + 2*(4*a*b^3*e^3 - 6*a^2*b^2*e^2*f + 4*a^3*b*e*f^2 - a^4*f^3)*log(((I - 1)*tan(b*x + a)^2 - 2*I*tan(b*x + a) + I + 1)/(tan(b*x + a)^2 + 1)) - 4*(b^4*f^3*x^4 + 4*b^4*e*f^2*x^3 + 6*b^4*e^2*f*x^2 + 4*b^4*e^3*x)*log((tan(b*x + a) + 1)/(tan(b*x + a) - 1)) - (6*I*b*f^3*x + 6*I*b*e*f^2)*polylog(4, (I*tan(b*x + a)^2 + 2*tan(b*x + a) - I)/(tan(b*x + a)^2 + 1)) - (6*I*b*f^3*x + 6*I*b*e*f^2)*polylog(4, (I*tan(b*x + a)^2 - 2*tan(b*x + a) - I)/(tan(b*x + a)^2 + 1)) - (-6*I*b*f^3*x - 6*I*b*e*f^2)*polylog(4, (-I*tan(b*x + a)^2 + 2*tan(b*x + a) + I)/(tan(b*x + a)^2 + 1)) - (-6*I*b*f^3*x - 6*I*b*e*f^2)*polylog(4, (-I*tan(b*x + a)^2 - 2*tan(b*x + a) + I)/(tan(b*x + a)^2 + 1)) - 6*(b^2*f^3*x^2 + 2*b^2*e*f^2*x + b^2*e^2*f)*polylog(3, (I*tan(b*x + a)^2 + 2*tan(b*x + a) - I)/(tan(b*x + a)^2 + 1)) + 6*(b^2*f^3*x^2 + 2*b^2*e*f^2*x + b^2*e^2*f)*polylog(3, (I*tan(b*x + a)^2 - 2*tan(b*x + a) - I)/(tan(b*x + a)^2 + 1)) - 6*(b^2*f^3*x^2 + 2*b^2*e*f^2*x + b^2*e^2*f)*polylog(3, (-I*tan(b*x + a)^2 + 2*tan(b*x + a) + I)/(tan(b*x + a)^2 + 1)) + 6*(b^2*f^3*x^2 + 2*b^2*e*f^2*x + b^2*e^2*f)*polylog(3, (-I*tan(b*x + a)^2 - 2*tan(b*x + a) + I)/(tan(b*x + a)^2 + 1)))/b^4","C",0
232,1,1278,0,0.914361," ","integrate((f*x+e)^2*arccoth(tan(b*x+a)),x, algorithm=""fricas"")","\frac{3 i \, f^{2} {\rm polylog}\left(4, \frac{i \, \tan\left(b x + a\right)^{2} + 2 \, \tan\left(b x + a\right) - i}{\tan\left(b x + a\right)^{2} + 1}\right) + 3 i \, f^{2} {\rm polylog}\left(4, \frac{i \, \tan\left(b x + a\right)^{2} - 2 \, \tan\left(b x + a\right) - i}{\tan\left(b x + a\right)^{2} + 1}\right) - 3 i \, f^{2} {\rm polylog}\left(4, \frac{-i \, \tan\left(b x + a\right)^{2} + 2 \, \tan\left(b x + a\right) + i}{\tan\left(b x + a\right)^{2} + 1}\right) - 3 i \, f^{2} {\rm polylog}\left(4, \frac{-i \, \tan\left(b x + a\right)^{2} - 2 \, \tan\left(b x + a\right) + i}{\tan\left(b x + a\right)^{2} + 1}\right) + {\left(6 i \, b^{2} f^{2} x^{2} + 12 i \, b^{2} e f x + 6 i \, b^{2} e^{2}\right)} {\rm Li}_2\left(-\frac{\left(i + 1\right) \, \tan\left(b x + a\right)^{2} + 2 \, \tan\left(b x + a\right) - i + 1}{\tan\left(b x + a\right)^{2} + 1} + 1\right) + {\left(6 i \, b^{2} f^{2} x^{2} + 12 i \, b^{2} e f x + 6 i \, b^{2} e^{2}\right)} {\rm Li}_2\left(-\frac{\left(i + 1\right) \, \tan\left(b x + a\right)^{2} - 2 \, \tan\left(b x + a\right) - i + 1}{\tan\left(b x + a\right)^{2} + 1} + 1\right) + {\left(-6 i \, b^{2} f^{2} x^{2} - 12 i \, b^{2} e f x - 6 i \, b^{2} e^{2}\right)} {\rm Li}_2\left(-\frac{-\left(i - 1\right) \, \tan\left(b x + a\right)^{2} + 2 \, \tan\left(b x + a\right) + i + 1}{\tan\left(b x + a\right)^{2} + 1} + 1\right) + {\left(-6 i \, b^{2} f^{2} x^{2} - 12 i \, b^{2} e f x - 6 i \, b^{2} e^{2}\right)} {\rm Li}_2\left(-\frac{-\left(i - 1\right) \, \tan\left(b x + a\right)^{2} - 2 \, \tan\left(b x + a\right) + i + 1}{\tan\left(b x + a\right)^{2} + 1} + 1\right) - 4 \, {\left(b^{3} f^{2} x^{3} + 3 \, b^{3} e f x^{2} + 3 \, b^{3} e^{2} x + 3 \, a b^{2} e^{2} - 3 \, a^{2} b e f + a^{3} f^{2}\right)} \log\left(\frac{\left(i + 1\right) \, \tan\left(b x + a\right)^{2} + 2 \, \tan\left(b x + a\right) - i + 1}{\tan\left(b x + a\right)^{2} + 1}\right) + 4 \, {\left(3 \, a b^{2} e^{2} - 3 \, a^{2} b e f + a^{3} f^{2}\right)} \log\left(\frac{\left(i + 1\right) \, \tan\left(b x + a\right)^{2} + 2 i \, \tan\left(b x + a\right) + i - 1}{\tan\left(b x + a\right)^{2} + 1}\right) - 4 \, {\left(3 \, a b^{2} e^{2} - 3 \, a^{2} b e f + a^{3} f^{2}\right)} \log\left(\frac{\left(i + 1\right) \, \tan\left(b x + a\right)^{2} - 2 i \, \tan\left(b x + a\right) + i - 1}{\tan\left(b x + a\right)^{2} + 1}\right) + 4 \, {\left(b^{3} f^{2} x^{3} + 3 \, b^{3} e f x^{2} + 3 \, b^{3} e^{2} x + 3 \, a b^{2} e^{2} - 3 \, a^{2} b e f + a^{3} f^{2}\right)} \log\left(\frac{\left(i + 1\right) \, \tan\left(b x + a\right)^{2} - 2 \, \tan\left(b x + a\right) - i + 1}{\tan\left(b x + a\right)^{2} + 1}\right) - 4 \, {\left(b^{3} f^{2} x^{3} + 3 \, b^{3} e f x^{2} + 3 \, b^{3} e^{2} x + 3 \, a b^{2} e^{2} - 3 \, a^{2} b e f + a^{3} f^{2}\right)} \log\left(\frac{-\left(i - 1\right) \, \tan\left(b x + a\right)^{2} + 2 \, \tan\left(b x + a\right) + i + 1}{\tan\left(b x + a\right)^{2} + 1}\right) + 4 \, {\left(b^{3} f^{2} x^{3} + 3 \, b^{3} e f x^{2} + 3 \, b^{3} e^{2} x + 3 \, a b^{2} e^{2} - 3 \, a^{2} b e f + a^{3} f^{2}\right)} \log\left(\frac{-\left(i - 1\right) \, \tan\left(b x + a\right)^{2} - 2 \, \tan\left(b x + a\right) + i + 1}{\tan\left(b x + a\right)^{2} + 1}\right) + 4 \, {\left(3 \, a b^{2} e^{2} - 3 \, a^{2} b e f + a^{3} f^{2}\right)} \log\left(\frac{\left(i - 1\right) \, \tan\left(b x + a\right)^{2} + 2 i \, \tan\left(b x + a\right) + i + 1}{\tan\left(b x + a\right)^{2} + 1}\right) - 4 \, {\left(3 \, a b^{2} e^{2} - 3 \, a^{2} b e f + a^{3} f^{2}\right)} \log\left(\frac{\left(i - 1\right) \, \tan\left(b x + a\right)^{2} - 2 i \, \tan\left(b x + a\right) + i + 1}{\tan\left(b x + a\right)^{2} + 1}\right) + 8 \, {\left(b^{3} f^{2} x^{3} + 3 \, b^{3} e f x^{2} + 3 \, b^{3} e^{2} x\right)} \log\left(\frac{\tan\left(b x + a\right) + 1}{\tan\left(b x + a\right) - 1}\right) + 6 \, {\left(b f^{2} x + b e f\right)} {\rm polylog}\left(3, \frac{i \, \tan\left(b x + a\right)^{2} + 2 \, \tan\left(b x + a\right) - i}{\tan\left(b x + a\right)^{2} + 1}\right) - 6 \, {\left(b f^{2} x + b e f\right)} {\rm polylog}\left(3, \frac{i \, \tan\left(b x + a\right)^{2} - 2 \, \tan\left(b x + a\right) - i}{\tan\left(b x + a\right)^{2} + 1}\right) + 6 \, {\left(b f^{2} x + b e f\right)} {\rm polylog}\left(3, \frac{-i \, \tan\left(b x + a\right)^{2} + 2 \, \tan\left(b x + a\right) + i}{\tan\left(b x + a\right)^{2} + 1}\right) - 6 \, {\left(b f^{2} x + b e f\right)} {\rm polylog}\left(3, \frac{-i \, \tan\left(b x + a\right)^{2} - 2 \, \tan\left(b x + a\right) + i}{\tan\left(b x + a\right)^{2} + 1}\right)}{48 \, b^{3}}"," ",0,"1/48*(3*I*f^2*polylog(4, (I*tan(b*x + a)^2 + 2*tan(b*x + a) - I)/(tan(b*x + a)^2 + 1)) + 3*I*f^2*polylog(4, (I*tan(b*x + a)^2 - 2*tan(b*x + a) - I)/(tan(b*x + a)^2 + 1)) - 3*I*f^2*polylog(4, (-I*tan(b*x + a)^2 + 2*tan(b*x + a) + I)/(tan(b*x + a)^2 + 1)) - 3*I*f^2*polylog(4, (-I*tan(b*x + a)^2 - 2*tan(b*x + a) + I)/(tan(b*x + a)^2 + 1)) + (6*I*b^2*f^2*x^2 + 12*I*b^2*e*f*x + 6*I*b^2*e^2)*dilog(-((I + 1)*tan(b*x + a)^2 + 2*tan(b*x + a) - I + 1)/(tan(b*x + a)^2 + 1) + 1) + (6*I*b^2*f^2*x^2 + 12*I*b^2*e*f*x + 6*I*b^2*e^2)*dilog(-((I + 1)*tan(b*x + a)^2 - 2*tan(b*x + a) - I + 1)/(tan(b*x + a)^2 + 1) + 1) + (-6*I*b^2*f^2*x^2 - 12*I*b^2*e*f*x - 6*I*b^2*e^2)*dilog(-(-(I - 1)*tan(b*x + a)^2 + 2*tan(b*x + a) + I + 1)/(tan(b*x + a)^2 + 1) + 1) + (-6*I*b^2*f^2*x^2 - 12*I*b^2*e*f*x - 6*I*b^2*e^2)*dilog(-(-(I - 1)*tan(b*x + a)^2 - 2*tan(b*x + a) + I + 1)/(tan(b*x + a)^2 + 1) + 1) - 4*(b^3*f^2*x^3 + 3*b^3*e*f*x^2 + 3*b^3*e^2*x + 3*a*b^2*e^2 - 3*a^2*b*e*f + a^3*f^2)*log(((I + 1)*tan(b*x + a)^2 + 2*tan(b*x + a) - I + 1)/(tan(b*x + a)^2 + 1)) + 4*(3*a*b^2*e^2 - 3*a^2*b*e*f + a^3*f^2)*log(((I + 1)*tan(b*x + a)^2 + 2*I*tan(b*x + a) + I - 1)/(tan(b*x + a)^2 + 1)) - 4*(3*a*b^2*e^2 - 3*a^2*b*e*f + a^3*f^2)*log(((I + 1)*tan(b*x + a)^2 - 2*I*tan(b*x + a) + I - 1)/(tan(b*x + a)^2 + 1)) + 4*(b^3*f^2*x^3 + 3*b^3*e*f*x^2 + 3*b^3*e^2*x + 3*a*b^2*e^2 - 3*a^2*b*e*f + a^3*f^2)*log(((I + 1)*tan(b*x + a)^2 - 2*tan(b*x + a) - I + 1)/(tan(b*x + a)^2 + 1)) - 4*(b^3*f^2*x^3 + 3*b^3*e*f*x^2 + 3*b^3*e^2*x + 3*a*b^2*e^2 - 3*a^2*b*e*f + a^3*f^2)*log((-(I - 1)*tan(b*x + a)^2 + 2*tan(b*x + a) + I + 1)/(tan(b*x + a)^2 + 1)) + 4*(b^3*f^2*x^3 + 3*b^3*e*f*x^2 + 3*b^3*e^2*x + 3*a*b^2*e^2 - 3*a^2*b*e*f + a^3*f^2)*log((-(I - 1)*tan(b*x + a)^2 - 2*tan(b*x + a) + I + 1)/(tan(b*x + a)^2 + 1)) + 4*(3*a*b^2*e^2 - 3*a^2*b*e*f + a^3*f^2)*log(((I - 1)*tan(b*x + a)^2 + 2*I*tan(b*x + a) + I + 1)/(tan(b*x + a)^2 + 1)) - 4*(3*a*b^2*e^2 - 3*a^2*b*e*f + a^3*f^2)*log(((I - 1)*tan(b*x + a)^2 - 2*I*tan(b*x + a) + I + 1)/(tan(b*x + a)^2 + 1)) + 8*(b^3*f^2*x^3 + 3*b^3*e*f*x^2 + 3*b^3*e^2*x)*log((tan(b*x + a) + 1)/(tan(b*x + a) - 1)) + 6*(b*f^2*x + b*e*f)*polylog(3, (I*tan(b*x + a)^2 + 2*tan(b*x + a) - I)/(tan(b*x + a)^2 + 1)) - 6*(b*f^2*x + b*e*f)*polylog(3, (I*tan(b*x + a)^2 - 2*tan(b*x + a) - I)/(tan(b*x + a)^2 + 1)) + 6*(b*f^2*x + b*e*f)*polylog(3, (-I*tan(b*x + a)^2 + 2*tan(b*x + a) + I)/(tan(b*x + a)^2 + 1)) - 6*(b*f^2*x + b*e*f)*polylog(3, (-I*tan(b*x + a)^2 - 2*tan(b*x + a) + I)/(tan(b*x + a)^2 + 1)))/b^3","C",0
233,1,830,0,0.656444," ","integrate((f*x+e)*arccoth(tan(b*x+a)),x, algorithm=""fricas"")","\frac{{\left(2 i \, b f x + 2 i \, b e\right)} {\rm Li}_2\left(-\frac{\left(i + 1\right) \, \tan\left(b x + a\right)^{2} + 2 \, \tan\left(b x + a\right) - i + 1}{\tan\left(b x + a\right)^{2} + 1} + 1\right) + {\left(2 i \, b f x + 2 i \, b e\right)} {\rm Li}_2\left(-\frac{\left(i + 1\right) \, \tan\left(b x + a\right)^{2} - 2 \, \tan\left(b x + a\right) - i + 1}{\tan\left(b x + a\right)^{2} + 1} + 1\right) + {\left(-2 i \, b f x - 2 i \, b e\right)} {\rm Li}_2\left(-\frac{-\left(i - 1\right) \, \tan\left(b x + a\right)^{2} + 2 \, \tan\left(b x + a\right) + i + 1}{\tan\left(b x + a\right)^{2} + 1} + 1\right) + {\left(-2 i \, b f x - 2 i \, b e\right)} {\rm Li}_2\left(-\frac{-\left(i - 1\right) \, \tan\left(b x + a\right)^{2} - 2 \, \tan\left(b x + a\right) + i + 1}{\tan\left(b x + a\right)^{2} + 1} + 1\right) - 2 \, {\left(b^{2} f x^{2} + 2 \, b^{2} e x + 2 \, a b e - a^{2} f\right)} \log\left(\frac{\left(i + 1\right) \, \tan\left(b x + a\right)^{2} + 2 \, \tan\left(b x + a\right) - i + 1}{\tan\left(b x + a\right)^{2} + 1}\right) + 2 \, {\left(2 \, a b e - a^{2} f\right)} \log\left(\frac{\left(i + 1\right) \, \tan\left(b x + a\right)^{2} + 2 i \, \tan\left(b x + a\right) + i - 1}{\tan\left(b x + a\right)^{2} + 1}\right) - 2 \, {\left(2 \, a b e - a^{2} f\right)} \log\left(\frac{\left(i + 1\right) \, \tan\left(b x + a\right)^{2} - 2 i \, \tan\left(b x + a\right) + i - 1}{\tan\left(b x + a\right)^{2} + 1}\right) + 2 \, {\left(b^{2} f x^{2} + 2 \, b^{2} e x + 2 \, a b e - a^{2} f\right)} \log\left(\frac{\left(i + 1\right) \, \tan\left(b x + a\right)^{2} - 2 \, \tan\left(b x + a\right) - i + 1}{\tan\left(b x + a\right)^{2} + 1}\right) - 2 \, {\left(b^{2} f x^{2} + 2 \, b^{2} e x + 2 \, a b e - a^{2} f\right)} \log\left(\frac{-\left(i - 1\right) \, \tan\left(b x + a\right)^{2} + 2 \, \tan\left(b x + a\right) + i + 1}{\tan\left(b x + a\right)^{2} + 1}\right) + 2 \, {\left(b^{2} f x^{2} + 2 \, b^{2} e x + 2 \, a b e - a^{2} f\right)} \log\left(\frac{-\left(i - 1\right) \, \tan\left(b x + a\right)^{2} - 2 \, \tan\left(b x + a\right) + i + 1}{\tan\left(b x + a\right)^{2} + 1}\right) + 2 \, {\left(2 \, a b e - a^{2} f\right)} \log\left(\frac{\left(i - 1\right) \, \tan\left(b x + a\right)^{2} + 2 i \, \tan\left(b x + a\right) + i + 1}{\tan\left(b x + a\right)^{2} + 1}\right) - 2 \, {\left(2 \, a b e - a^{2} f\right)} \log\left(\frac{\left(i - 1\right) \, \tan\left(b x + a\right)^{2} - 2 i \, \tan\left(b x + a\right) + i + 1}{\tan\left(b x + a\right)^{2} + 1}\right) + 4 \, {\left(b^{2} f x^{2} + 2 \, b^{2} e x\right)} \log\left(\frac{\tan\left(b x + a\right) + 1}{\tan\left(b x + a\right) - 1}\right) + f {\rm polylog}\left(3, \frac{i \, \tan\left(b x + a\right)^{2} + 2 \, \tan\left(b x + a\right) - i}{\tan\left(b x + a\right)^{2} + 1}\right) - f {\rm polylog}\left(3, \frac{i \, \tan\left(b x + a\right)^{2} - 2 \, \tan\left(b x + a\right) - i}{\tan\left(b x + a\right)^{2} + 1}\right) + f {\rm polylog}\left(3, \frac{-i \, \tan\left(b x + a\right)^{2} + 2 \, \tan\left(b x + a\right) + i}{\tan\left(b x + a\right)^{2} + 1}\right) - f {\rm polylog}\left(3, \frac{-i \, \tan\left(b x + a\right)^{2} - 2 \, \tan\left(b x + a\right) + i}{\tan\left(b x + a\right)^{2} + 1}\right)}{16 \, b^{2}}"," ",0,"1/16*((2*I*b*f*x + 2*I*b*e)*dilog(-((I + 1)*tan(b*x + a)^2 + 2*tan(b*x + a) - I + 1)/(tan(b*x + a)^2 + 1) + 1) + (2*I*b*f*x + 2*I*b*e)*dilog(-((I + 1)*tan(b*x + a)^2 - 2*tan(b*x + a) - I + 1)/(tan(b*x + a)^2 + 1) + 1) + (-2*I*b*f*x - 2*I*b*e)*dilog(-(-(I - 1)*tan(b*x + a)^2 + 2*tan(b*x + a) + I + 1)/(tan(b*x + a)^2 + 1) + 1) + (-2*I*b*f*x - 2*I*b*e)*dilog(-(-(I - 1)*tan(b*x + a)^2 - 2*tan(b*x + a) + I + 1)/(tan(b*x + a)^2 + 1) + 1) - 2*(b^2*f*x^2 + 2*b^2*e*x + 2*a*b*e - a^2*f)*log(((I + 1)*tan(b*x + a)^2 + 2*tan(b*x + a) - I + 1)/(tan(b*x + a)^2 + 1)) + 2*(2*a*b*e - a^2*f)*log(((I + 1)*tan(b*x + a)^2 + 2*I*tan(b*x + a) + I - 1)/(tan(b*x + a)^2 + 1)) - 2*(2*a*b*e - a^2*f)*log(((I + 1)*tan(b*x + a)^2 - 2*I*tan(b*x + a) + I - 1)/(tan(b*x + a)^2 + 1)) + 2*(b^2*f*x^2 + 2*b^2*e*x + 2*a*b*e - a^2*f)*log(((I + 1)*tan(b*x + a)^2 - 2*tan(b*x + a) - I + 1)/(tan(b*x + a)^2 + 1)) - 2*(b^2*f*x^2 + 2*b^2*e*x + 2*a*b*e - a^2*f)*log((-(I - 1)*tan(b*x + a)^2 + 2*tan(b*x + a) + I + 1)/(tan(b*x + a)^2 + 1)) + 2*(b^2*f*x^2 + 2*b^2*e*x + 2*a*b*e - a^2*f)*log((-(I - 1)*tan(b*x + a)^2 - 2*tan(b*x + a) + I + 1)/(tan(b*x + a)^2 + 1)) + 2*(2*a*b*e - a^2*f)*log(((I - 1)*tan(b*x + a)^2 + 2*I*tan(b*x + a) + I + 1)/(tan(b*x + a)^2 + 1)) - 2*(2*a*b*e - a^2*f)*log(((I - 1)*tan(b*x + a)^2 - 2*I*tan(b*x + a) + I + 1)/(tan(b*x + a)^2 + 1)) + 4*(b^2*f*x^2 + 2*b^2*e*x)*log((tan(b*x + a) + 1)/(tan(b*x + a) - 1)) + f*polylog(3, (I*tan(b*x + a)^2 + 2*tan(b*x + a) - I)/(tan(b*x + a)^2 + 1)) - f*polylog(3, (I*tan(b*x + a)^2 - 2*tan(b*x + a) - I)/(tan(b*x + a)^2 + 1)) + f*polylog(3, (-I*tan(b*x + a)^2 + 2*tan(b*x + a) + I)/(tan(b*x + a)^2 + 1)) - f*polylog(3, (-I*tan(b*x + a)^2 - 2*tan(b*x + a) + I)/(tan(b*x + a)^2 + 1)))/b^2","C",0
234,1,498,0,1.009881," ","integrate(arccoth(tan(b*x+a)),x, algorithm=""fricas"")","\frac{4 \, b x \log\left(\frac{\tan\left(b x + a\right) + 1}{\tan\left(b x + a\right) - 1}\right) - 2 \, {\left(b x + a\right)} \log\left(\frac{\left(i + 1\right) \, \tan\left(b x + a\right)^{2} + 2 \, \tan\left(b x + a\right) - i + 1}{\tan\left(b x + a\right)^{2} + 1}\right) + 2 \, a \log\left(\frac{\left(i + 1\right) \, \tan\left(b x + a\right)^{2} + 2 i \, \tan\left(b x + a\right) + i - 1}{\tan\left(b x + a\right)^{2} + 1}\right) - 2 \, a \log\left(\frac{\left(i + 1\right) \, \tan\left(b x + a\right)^{2} - 2 i \, \tan\left(b x + a\right) + i - 1}{\tan\left(b x + a\right)^{2} + 1}\right) + 2 \, {\left(b x + a\right)} \log\left(\frac{\left(i + 1\right) \, \tan\left(b x + a\right)^{2} - 2 \, \tan\left(b x + a\right) - i + 1}{\tan\left(b x + a\right)^{2} + 1}\right) - 2 \, {\left(b x + a\right)} \log\left(\frac{-\left(i - 1\right) \, \tan\left(b x + a\right)^{2} + 2 \, \tan\left(b x + a\right) + i + 1}{\tan\left(b x + a\right)^{2} + 1}\right) + 2 \, {\left(b x + a\right)} \log\left(\frac{-\left(i - 1\right) \, \tan\left(b x + a\right)^{2} - 2 \, \tan\left(b x + a\right) + i + 1}{\tan\left(b x + a\right)^{2} + 1}\right) + 2 \, a \log\left(\frac{\left(i - 1\right) \, \tan\left(b x + a\right)^{2} + 2 i \, \tan\left(b x + a\right) + i + 1}{\tan\left(b x + a\right)^{2} + 1}\right) - 2 \, a \log\left(\frac{\left(i - 1\right) \, \tan\left(b x + a\right)^{2} - 2 i \, \tan\left(b x + a\right) + i + 1}{\tan\left(b x + a\right)^{2} + 1}\right) + i \, {\rm Li}_2\left(-\frac{\left(i + 1\right) \, \tan\left(b x + a\right)^{2} + 2 \, \tan\left(b x + a\right) - i + 1}{\tan\left(b x + a\right)^{2} + 1} + 1\right) + i \, {\rm Li}_2\left(-\frac{\left(i + 1\right) \, \tan\left(b x + a\right)^{2} - 2 \, \tan\left(b x + a\right) - i + 1}{\tan\left(b x + a\right)^{2} + 1} + 1\right) - i \, {\rm Li}_2\left(-\frac{-\left(i - 1\right) \, \tan\left(b x + a\right)^{2} + 2 \, \tan\left(b x + a\right) + i + 1}{\tan\left(b x + a\right)^{2} + 1} + 1\right) - i \, {\rm Li}_2\left(-\frac{-\left(i - 1\right) \, \tan\left(b x + a\right)^{2} - 2 \, \tan\left(b x + a\right) + i + 1}{\tan\left(b x + a\right)^{2} + 1} + 1\right)}{8 \, b}"," ",0,"1/8*(4*b*x*log((tan(b*x + a) + 1)/(tan(b*x + a) - 1)) - 2*(b*x + a)*log(((I + 1)*tan(b*x + a)^2 + 2*tan(b*x + a) - I + 1)/(tan(b*x + a)^2 + 1)) + 2*a*log(((I + 1)*tan(b*x + a)^2 + 2*I*tan(b*x + a) + I - 1)/(tan(b*x + a)^2 + 1)) - 2*a*log(((I + 1)*tan(b*x + a)^2 - 2*I*tan(b*x + a) + I - 1)/(tan(b*x + a)^2 + 1)) + 2*(b*x + a)*log(((I + 1)*tan(b*x + a)^2 - 2*tan(b*x + a) - I + 1)/(tan(b*x + a)^2 + 1)) - 2*(b*x + a)*log((-(I - 1)*tan(b*x + a)^2 + 2*tan(b*x + a) + I + 1)/(tan(b*x + a)^2 + 1)) + 2*(b*x + a)*log((-(I - 1)*tan(b*x + a)^2 - 2*tan(b*x + a) + I + 1)/(tan(b*x + a)^2 + 1)) + 2*a*log(((I - 1)*tan(b*x + a)^2 + 2*I*tan(b*x + a) + I + 1)/(tan(b*x + a)^2 + 1)) - 2*a*log(((I - 1)*tan(b*x + a)^2 - 2*I*tan(b*x + a) + I + 1)/(tan(b*x + a)^2 + 1)) + I*dilog(-((I + 1)*tan(b*x + a)^2 + 2*tan(b*x + a) - I + 1)/(tan(b*x + a)^2 + 1) + 1) + I*dilog(-((I + 1)*tan(b*x + a)^2 - 2*tan(b*x + a) - I + 1)/(tan(b*x + a)^2 + 1) + 1) - I*dilog(-(-(I - 1)*tan(b*x + a)^2 + 2*tan(b*x + a) + I + 1)/(tan(b*x + a)^2 + 1) + 1) - I*dilog(-(-(I - 1)*tan(b*x + a)^2 - 2*tan(b*x + a) + I + 1)/(tan(b*x + a)^2 + 1) + 1))/b","B",0
235,0,0,0,0.559115," ","integrate(arccoth(tan(b*x+a))/(f*x+e),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{arcoth}\left(\tan\left(b x + a\right)\right)}{f x + e}, x\right)"," ",0,"integral(arccoth(tan(b*x + a))/(f*x + e), x)","F",0
236,1,2160,0,0.962185," ","integrate(x^2*arccoth(c+d*tan(b*x+a)),x, algorithm=""fricas"")","\frac{8 \, b^{3} x^{3} \log\left(\frac{d \tan\left(b x + a\right) + c + 1}{d \tan\left(b x + a\right) + c - 1}\right) + 6 i \, b^{2} x^{2} {\rm Li}_2\left(-\frac{{\left(2 i \, {\left(c + 1\right)} d + 2 \, d^{2}\right)} \tan\left(b x + a\right)^{2} + 2 \, c^{2} - 2 i \, {\left(c + 1\right)} d + {\left(2 i \, c^{2} + 4 \, {\left(c + 1\right)} d - 2 i \, d^{2} + 4 i \, c + 2 i\right)} \tan\left(b x + a\right) + 4 \, c + 2}{{\left(c^{2} + d^{2} + 2 \, c + 1\right)} \tan\left(b x + a\right)^{2} + c^{2} + d^{2} + 2 \, c + 1} + 1\right) - 6 i \, b^{2} x^{2} {\rm Li}_2\left(-\frac{{\left(-2 i \, {\left(c + 1\right)} d + 2 \, d^{2}\right)} \tan\left(b x + a\right)^{2} + 2 \, c^{2} + 2 i \, {\left(c + 1\right)} d + {\left(-2 i \, c^{2} + 4 \, {\left(c + 1\right)} d + 2 i \, d^{2} - 4 i \, c - 2 i\right)} \tan\left(b x + a\right) + 4 \, c + 2}{{\left(c^{2} + d^{2} + 2 \, c + 1\right)} \tan\left(b x + a\right)^{2} + c^{2} + d^{2} + 2 \, c + 1} + 1\right) + 6 i \, b^{2} x^{2} {\rm Li}_2\left(\frac{2 \, {\left(i \, {\left(c - 1\right)} d - d^{2}\right)} \tan\left(b x + a\right)^{2} - 2 \, c^{2} - 2 i \, {\left(c - 1\right)} d - {\left(-2 i \, c^{2} + 4 \, {\left(c - 1\right)} d + 2 i \, d^{2} + 4 i \, c - 2 i\right)} \tan\left(b x + a\right) + 4 \, c - 2}{{\left(c^{2} + d^{2} - 2 \, c + 1\right)} \tan\left(b x + a\right)^{2} + c^{2} + d^{2} - 2 \, c + 1} + 1\right) - 6 i \, b^{2} x^{2} {\rm Li}_2\left(\frac{2 \, {\left(-i \, {\left(c - 1\right)} d - d^{2}\right)} \tan\left(b x + a\right)^{2} - 2 \, c^{2} + 2 i \, {\left(c - 1\right)} d - {\left(2 i \, c^{2} + 4 \, {\left(c - 1\right)} d - 2 i \, d^{2} - 4 i \, c + 2 i\right)} \tan\left(b x + a\right) + 4 \, c - 2}{{\left(c^{2} + d^{2} - 2 \, c + 1\right)} \tan\left(b x + a\right)^{2} + c^{2} + d^{2} - 2 \, c + 1} + 1\right) + 4 \, a^{3} \log\left(\frac{{\left(i \, {\left(c + 1\right)} d + d^{2}\right)} \tan\left(b x + a\right)^{2} - c^{2} + i \, {\left(c + 1\right)} d + {\left(i \, c^{2} + i \, d^{2} + 2 i \, c + i\right)} \tan\left(b x + a\right) - 2 \, c - 1}{\tan\left(b x + a\right)^{2} + 1}\right) + 4 \, a^{3} \log\left(\frac{{\left(i \, {\left(c + 1\right)} d - d^{2}\right)} \tan\left(b x + a\right)^{2} + c^{2} + i \, {\left(c + 1\right)} d + {\left(i \, c^{2} + i \, d^{2} + 2 i \, c + i\right)} \tan\left(b x + a\right) + 2 \, c + 1}{\tan\left(b x + a\right)^{2} + 1}\right) - 4 \, a^{3} \log\left(\frac{{\left(i \, {\left(c - 1\right)} d + d^{2}\right)} \tan\left(b x + a\right)^{2} - c^{2} + i \, {\left(c - 1\right)} d + {\left(i \, c^{2} + i \, d^{2} - 2 i \, c + i\right)} \tan\left(b x + a\right) + 2 \, c - 1}{\tan\left(b x + a\right)^{2} + 1}\right) - 4 \, a^{3} \log\left(\frac{{\left(i \, {\left(c - 1\right)} d - d^{2}\right)} \tan\left(b x + a\right)^{2} + c^{2} + i \, {\left(c - 1\right)} d + {\left(i \, c^{2} + i \, d^{2} - 2 i \, c + i\right)} \tan\left(b x + a\right) - 2 \, c + 1}{\tan\left(b x + a\right)^{2} + 1}\right) - 6 \, b x {\rm polylog}\left(3, \frac{{\left(c^{2} + 2 i \, {\left(c + 1\right)} d - d^{2} + 2 \, c + 1\right)} \tan\left(b x + a\right)^{2} - c^{2} - 2 i \, {\left(c + 1\right)} d + d^{2} + {\left(2 i \, c^{2} - 4 \, {\left(c + 1\right)} d - 2 i \, d^{2} + 4 i \, c + 2 i\right)} \tan\left(b x + a\right) - 2 \, c - 1}{{\left(c^{2} + d^{2} + 2 \, c + 1\right)} \tan\left(b x + a\right)^{2} + c^{2} + d^{2} + 2 \, c + 1}\right) - 6 \, b x {\rm polylog}\left(3, \frac{{\left(c^{2} - 2 i \, {\left(c + 1\right)} d - d^{2} + 2 \, c + 1\right)} \tan\left(b x + a\right)^{2} - c^{2} + 2 i \, {\left(c + 1\right)} d + d^{2} + {\left(-2 i \, c^{2} - 4 \, {\left(c + 1\right)} d + 2 i \, d^{2} - 4 i \, c - 2 i\right)} \tan\left(b x + a\right) - 2 \, c - 1}{{\left(c^{2} + d^{2} + 2 \, c + 1\right)} \tan\left(b x + a\right)^{2} + c^{2} + d^{2} + 2 \, c + 1}\right) + 6 \, b x {\rm polylog}\left(3, \frac{{\left(c^{2} + 2 i \, {\left(c - 1\right)} d - d^{2} - 2 \, c + 1\right)} \tan\left(b x + a\right)^{2} - c^{2} - 2 i \, {\left(c - 1\right)} d + d^{2} + {\left(2 i \, c^{2} - 4 \, {\left(c - 1\right)} d - 2 i \, d^{2} - 4 i \, c + 2 i\right)} \tan\left(b x + a\right) + 2 \, c - 1}{{\left(c^{2} + d^{2} - 2 \, c + 1\right)} \tan\left(b x + a\right)^{2} + c^{2} + d^{2} - 2 \, c + 1}\right) + 6 \, b x {\rm polylog}\left(3, \frac{{\left(c^{2} - 2 i \, {\left(c - 1\right)} d - d^{2} - 2 \, c + 1\right)} \tan\left(b x + a\right)^{2} - c^{2} + 2 i \, {\left(c - 1\right)} d + d^{2} + {\left(-2 i \, c^{2} - 4 \, {\left(c - 1\right)} d + 2 i \, d^{2} + 4 i \, c - 2 i\right)} \tan\left(b x + a\right) + 2 \, c - 1}{{\left(c^{2} + d^{2} - 2 \, c + 1\right)} \tan\left(b x + a\right)^{2} + c^{2} + d^{2} - 2 \, c + 1}\right) - 4 \, {\left(b^{3} x^{3} + a^{3}\right)} \log\left(\frac{{\left(2 i \, {\left(c + 1\right)} d + 2 \, d^{2}\right)} \tan\left(b x + a\right)^{2} + 2 \, c^{2} - 2 i \, {\left(c + 1\right)} d + {\left(2 i \, c^{2} + 4 \, {\left(c + 1\right)} d - 2 i \, d^{2} + 4 i \, c + 2 i\right)} \tan\left(b x + a\right) + 4 \, c + 2}{{\left(c^{2} + d^{2} + 2 \, c + 1\right)} \tan\left(b x + a\right)^{2} + c^{2} + d^{2} + 2 \, c + 1}\right) - 4 \, {\left(b^{3} x^{3} + a^{3}\right)} \log\left(\frac{{\left(-2 i \, {\left(c + 1\right)} d + 2 \, d^{2}\right)} \tan\left(b x + a\right)^{2} + 2 \, c^{2} + 2 i \, {\left(c + 1\right)} d + {\left(-2 i \, c^{2} + 4 \, {\left(c + 1\right)} d + 2 i \, d^{2} - 4 i \, c - 2 i\right)} \tan\left(b x + a\right) + 4 \, c + 2}{{\left(c^{2} + d^{2} + 2 \, c + 1\right)} \tan\left(b x + a\right)^{2} + c^{2} + d^{2} + 2 \, c + 1}\right) + 4 \, {\left(b^{3} x^{3} + a^{3}\right)} \log\left(-\frac{2 \, {\left(i \, {\left(c - 1\right)} d - d^{2}\right)} \tan\left(b x + a\right)^{2} - 2 \, c^{2} - 2 i \, {\left(c - 1\right)} d - {\left(-2 i \, c^{2} + 4 \, {\left(c - 1\right)} d + 2 i \, d^{2} + 4 i \, c - 2 i\right)} \tan\left(b x + a\right) + 4 \, c - 2}{{\left(c^{2} + d^{2} - 2 \, c + 1\right)} \tan\left(b x + a\right)^{2} + c^{2} + d^{2} - 2 \, c + 1}\right) + 4 \, {\left(b^{3} x^{3} + a^{3}\right)} \log\left(-\frac{2 \, {\left(-i \, {\left(c - 1\right)} d - d^{2}\right)} \tan\left(b x + a\right)^{2} - 2 \, c^{2} + 2 i \, {\left(c - 1\right)} d - {\left(2 i \, c^{2} + 4 \, {\left(c - 1\right)} d - 2 i \, d^{2} - 4 i \, c + 2 i\right)} \tan\left(b x + a\right) + 4 \, c - 2}{{\left(c^{2} + d^{2} - 2 \, c + 1\right)} \tan\left(b x + a\right)^{2} + c^{2} + d^{2} - 2 \, c + 1}\right) + 3 i \, {\rm polylog}\left(4, \frac{{\left(c^{2} + 2 i \, {\left(c + 1\right)} d - d^{2} + 2 \, c + 1\right)} \tan\left(b x + a\right)^{2} - c^{2} - 2 i \, {\left(c + 1\right)} d + d^{2} + {\left(2 i \, c^{2} - 4 \, {\left(c + 1\right)} d - 2 i \, d^{2} + 4 i \, c + 2 i\right)} \tan\left(b x + a\right) - 2 \, c - 1}{{\left(c^{2} + d^{2} + 2 \, c + 1\right)} \tan\left(b x + a\right)^{2} + c^{2} + d^{2} + 2 \, c + 1}\right) - 3 i \, {\rm polylog}\left(4, \frac{{\left(c^{2} - 2 i \, {\left(c + 1\right)} d - d^{2} + 2 \, c + 1\right)} \tan\left(b x + a\right)^{2} - c^{2} + 2 i \, {\left(c + 1\right)} d + d^{2} + {\left(-2 i \, c^{2} - 4 \, {\left(c + 1\right)} d + 2 i \, d^{2} - 4 i \, c - 2 i\right)} \tan\left(b x + a\right) - 2 \, c - 1}{{\left(c^{2} + d^{2} + 2 \, c + 1\right)} \tan\left(b x + a\right)^{2} + c^{2} + d^{2} + 2 \, c + 1}\right) - 3 i \, {\rm polylog}\left(4, \frac{{\left(c^{2} + 2 i \, {\left(c - 1\right)} d - d^{2} - 2 \, c + 1\right)} \tan\left(b x + a\right)^{2} - c^{2} - 2 i \, {\left(c - 1\right)} d + d^{2} + {\left(2 i \, c^{2} - 4 \, {\left(c - 1\right)} d - 2 i \, d^{2} - 4 i \, c + 2 i\right)} \tan\left(b x + a\right) + 2 \, c - 1}{{\left(c^{2} + d^{2} - 2 \, c + 1\right)} \tan\left(b x + a\right)^{2} + c^{2} + d^{2} - 2 \, c + 1}\right) + 3 i \, {\rm polylog}\left(4, \frac{{\left(c^{2} - 2 i \, {\left(c - 1\right)} d - d^{2} - 2 \, c + 1\right)} \tan\left(b x + a\right)^{2} - c^{2} + 2 i \, {\left(c - 1\right)} d + d^{2} + {\left(-2 i \, c^{2} - 4 \, {\left(c - 1\right)} d + 2 i \, d^{2} + 4 i \, c - 2 i\right)} \tan\left(b x + a\right) + 2 \, c - 1}{{\left(c^{2} + d^{2} - 2 \, c + 1\right)} \tan\left(b x + a\right)^{2} + c^{2} + d^{2} - 2 \, c + 1}\right)}{48 \, b^{3}}"," ",0,"1/48*(8*b^3*x^3*log((d*tan(b*x + a) + c + 1)/(d*tan(b*x + a) + c - 1)) + 6*I*b^2*x^2*dilog(-((2*I*(c + 1)*d + 2*d^2)*tan(b*x + a)^2 + 2*c^2 - 2*I*(c + 1)*d + (2*I*c^2 + 4*(c + 1)*d - 2*I*d^2 + 4*I*c + 2*I)*tan(b*x + a) + 4*c + 2)/((c^2 + d^2 + 2*c + 1)*tan(b*x + a)^2 + c^2 + d^2 + 2*c + 1) + 1) - 6*I*b^2*x^2*dilog(-((-2*I*(c + 1)*d + 2*d^2)*tan(b*x + a)^2 + 2*c^2 + 2*I*(c + 1)*d + (-2*I*c^2 + 4*(c + 1)*d + 2*I*d^2 - 4*I*c - 2*I)*tan(b*x + a) + 4*c + 2)/((c^2 + d^2 + 2*c + 1)*tan(b*x + a)^2 + c^2 + d^2 + 2*c + 1) + 1) + 6*I*b^2*x^2*dilog((2*(I*(c - 1)*d - d^2)*tan(b*x + a)^2 - 2*c^2 - 2*I*(c - 1)*d - (-2*I*c^2 + 4*(c - 1)*d + 2*I*d^2 + 4*I*c - 2*I)*tan(b*x + a) + 4*c - 2)/((c^2 + d^2 - 2*c + 1)*tan(b*x + a)^2 + c^2 + d^2 - 2*c + 1) + 1) - 6*I*b^2*x^2*dilog((2*(-I*(c - 1)*d - d^2)*tan(b*x + a)^2 - 2*c^2 + 2*I*(c - 1)*d - (2*I*c^2 + 4*(c - 1)*d - 2*I*d^2 - 4*I*c + 2*I)*tan(b*x + a) + 4*c - 2)/((c^2 + d^2 - 2*c + 1)*tan(b*x + a)^2 + c^2 + d^2 - 2*c + 1) + 1) + 4*a^3*log(((I*(c + 1)*d + d^2)*tan(b*x + a)^2 - c^2 + I*(c + 1)*d + (I*c^2 + I*d^2 + 2*I*c + I)*tan(b*x + a) - 2*c - 1)/(tan(b*x + a)^2 + 1)) + 4*a^3*log(((I*(c + 1)*d - d^2)*tan(b*x + a)^2 + c^2 + I*(c + 1)*d + (I*c^2 + I*d^2 + 2*I*c + I)*tan(b*x + a) + 2*c + 1)/(tan(b*x + a)^2 + 1)) - 4*a^3*log(((I*(c - 1)*d + d^2)*tan(b*x + a)^2 - c^2 + I*(c - 1)*d + (I*c^2 + I*d^2 - 2*I*c + I)*tan(b*x + a) + 2*c - 1)/(tan(b*x + a)^2 + 1)) - 4*a^3*log(((I*(c - 1)*d - d^2)*tan(b*x + a)^2 + c^2 + I*(c - 1)*d + (I*c^2 + I*d^2 - 2*I*c + I)*tan(b*x + a) - 2*c + 1)/(tan(b*x + a)^2 + 1)) - 6*b*x*polylog(3, ((c^2 + 2*I*(c + 1)*d - d^2 + 2*c + 1)*tan(b*x + a)^2 - c^2 - 2*I*(c + 1)*d + d^2 + (2*I*c^2 - 4*(c + 1)*d - 2*I*d^2 + 4*I*c + 2*I)*tan(b*x + a) - 2*c - 1)/((c^2 + d^2 + 2*c + 1)*tan(b*x + a)^2 + c^2 + d^2 + 2*c + 1)) - 6*b*x*polylog(3, ((c^2 - 2*I*(c + 1)*d - d^2 + 2*c + 1)*tan(b*x + a)^2 - c^2 + 2*I*(c + 1)*d + d^2 + (-2*I*c^2 - 4*(c + 1)*d + 2*I*d^2 - 4*I*c - 2*I)*tan(b*x + a) - 2*c - 1)/((c^2 + d^2 + 2*c + 1)*tan(b*x + a)^2 + c^2 + d^2 + 2*c + 1)) + 6*b*x*polylog(3, ((c^2 + 2*I*(c - 1)*d - d^2 - 2*c + 1)*tan(b*x + a)^2 - c^2 - 2*I*(c - 1)*d + d^2 + (2*I*c^2 - 4*(c - 1)*d - 2*I*d^2 - 4*I*c + 2*I)*tan(b*x + a) + 2*c - 1)/((c^2 + d^2 - 2*c + 1)*tan(b*x + a)^2 + c^2 + d^2 - 2*c + 1)) + 6*b*x*polylog(3, ((c^2 - 2*I*(c - 1)*d - d^2 - 2*c + 1)*tan(b*x + a)^2 - c^2 + 2*I*(c - 1)*d + d^2 + (-2*I*c^2 - 4*(c - 1)*d + 2*I*d^2 + 4*I*c - 2*I)*tan(b*x + a) + 2*c - 1)/((c^2 + d^2 - 2*c + 1)*tan(b*x + a)^2 + c^2 + d^2 - 2*c + 1)) - 4*(b^3*x^3 + a^3)*log(((2*I*(c + 1)*d + 2*d^2)*tan(b*x + a)^2 + 2*c^2 - 2*I*(c + 1)*d + (2*I*c^2 + 4*(c + 1)*d - 2*I*d^2 + 4*I*c + 2*I)*tan(b*x + a) + 4*c + 2)/((c^2 + d^2 + 2*c + 1)*tan(b*x + a)^2 + c^2 + d^2 + 2*c + 1)) - 4*(b^3*x^3 + a^3)*log(((-2*I*(c + 1)*d + 2*d^2)*tan(b*x + a)^2 + 2*c^2 + 2*I*(c + 1)*d + (-2*I*c^2 + 4*(c + 1)*d + 2*I*d^2 - 4*I*c - 2*I)*tan(b*x + a) + 4*c + 2)/((c^2 + d^2 + 2*c + 1)*tan(b*x + a)^2 + c^2 + d^2 + 2*c + 1)) + 4*(b^3*x^3 + a^3)*log(-(2*(I*(c - 1)*d - d^2)*tan(b*x + a)^2 - 2*c^2 - 2*I*(c - 1)*d - (-2*I*c^2 + 4*(c - 1)*d + 2*I*d^2 + 4*I*c - 2*I)*tan(b*x + a) + 4*c - 2)/((c^2 + d^2 - 2*c + 1)*tan(b*x + a)^2 + c^2 + d^2 - 2*c + 1)) + 4*(b^3*x^3 + a^3)*log(-(2*(-I*(c - 1)*d - d^2)*tan(b*x + a)^2 - 2*c^2 + 2*I*(c - 1)*d - (2*I*c^2 + 4*(c - 1)*d - 2*I*d^2 - 4*I*c + 2*I)*tan(b*x + a) + 4*c - 2)/((c^2 + d^2 - 2*c + 1)*tan(b*x + a)^2 + c^2 + d^2 - 2*c + 1)) + 3*I*polylog(4, ((c^2 + 2*I*(c + 1)*d - d^2 + 2*c + 1)*tan(b*x + a)^2 - c^2 - 2*I*(c + 1)*d + d^2 + (2*I*c^2 - 4*(c + 1)*d - 2*I*d^2 + 4*I*c + 2*I)*tan(b*x + a) - 2*c - 1)/((c^2 + d^2 + 2*c + 1)*tan(b*x + a)^2 + c^2 + d^2 + 2*c + 1)) - 3*I*polylog(4, ((c^2 - 2*I*(c + 1)*d - d^2 + 2*c + 1)*tan(b*x + a)^2 - c^2 + 2*I*(c + 1)*d + d^2 + (-2*I*c^2 - 4*(c + 1)*d + 2*I*d^2 - 4*I*c - 2*I)*tan(b*x + a) - 2*c - 1)/((c^2 + d^2 + 2*c + 1)*tan(b*x + a)^2 + c^2 + d^2 + 2*c + 1)) - 3*I*polylog(4, ((c^2 + 2*I*(c - 1)*d - d^2 - 2*c + 1)*tan(b*x + a)^2 - c^2 - 2*I*(c - 1)*d + d^2 + (2*I*c^2 - 4*(c - 1)*d - 2*I*d^2 - 4*I*c + 2*I)*tan(b*x + a) + 2*c - 1)/((c^2 + d^2 - 2*c + 1)*tan(b*x + a)^2 + c^2 + d^2 - 2*c + 1)) + 3*I*polylog(4, ((c^2 - 2*I*(c - 1)*d - d^2 - 2*c + 1)*tan(b*x + a)^2 - c^2 + 2*I*(c - 1)*d + d^2 + (-2*I*c^2 - 4*(c - 1)*d + 2*I*d^2 + 4*I*c - 2*I)*tan(b*x + a) + 2*c - 1)/((c^2 + d^2 - 2*c + 1)*tan(b*x + a)^2 + c^2 + d^2 - 2*c + 1)))/b^3","C",0
237,1,1688,0,0.828152," ","integrate(x*arccoth(c+d*tan(b*x+a)),x, algorithm=""fricas"")","\frac{4 \, b^{2} x^{2} \log\left(\frac{d \tan\left(b x + a\right) + c + 1}{d \tan\left(b x + a\right) + c - 1}\right) + 2 i \, b x {\rm Li}_2\left(-\frac{{\left(2 i \, {\left(c + 1\right)} d + 2 \, d^{2}\right)} \tan\left(b x + a\right)^{2} + 2 \, c^{2} - 2 i \, {\left(c + 1\right)} d + {\left(2 i \, c^{2} + 4 \, {\left(c + 1\right)} d - 2 i \, d^{2} + 4 i \, c + 2 i\right)} \tan\left(b x + a\right) + 4 \, c + 2}{{\left(c^{2} + d^{2} + 2 \, c + 1\right)} \tan\left(b x + a\right)^{2} + c^{2} + d^{2} + 2 \, c + 1} + 1\right) - 2 i \, b x {\rm Li}_2\left(-\frac{{\left(-2 i \, {\left(c + 1\right)} d + 2 \, d^{2}\right)} \tan\left(b x + a\right)^{2} + 2 \, c^{2} + 2 i \, {\left(c + 1\right)} d + {\left(-2 i \, c^{2} + 4 \, {\left(c + 1\right)} d + 2 i \, d^{2} - 4 i \, c - 2 i\right)} \tan\left(b x + a\right) + 4 \, c + 2}{{\left(c^{2} + d^{2} + 2 \, c + 1\right)} \tan\left(b x + a\right)^{2} + c^{2} + d^{2} + 2 \, c + 1} + 1\right) + 2 i \, b x {\rm Li}_2\left(\frac{2 \, {\left(i \, {\left(c - 1\right)} d - d^{2}\right)} \tan\left(b x + a\right)^{2} - 2 \, c^{2} - 2 i \, {\left(c - 1\right)} d - {\left(-2 i \, c^{2} + 4 \, {\left(c - 1\right)} d + 2 i \, d^{2} + 4 i \, c - 2 i\right)} \tan\left(b x + a\right) + 4 \, c - 2}{{\left(c^{2} + d^{2} - 2 \, c + 1\right)} \tan\left(b x + a\right)^{2} + c^{2} + d^{2} - 2 \, c + 1} + 1\right) - 2 i \, b x {\rm Li}_2\left(\frac{2 \, {\left(-i \, {\left(c - 1\right)} d - d^{2}\right)} \tan\left(b x + a\right)^{2} - 2 \, c^{2} + 2 i \, {\left(c - 1\right)} d - {\left(2 i \, c^{2} + 4 \, {\left(c - 1\right)} d - 2 i \, d^{2} - 4 i \, c + 2 i\right)} \tan\left(b x + a\right) + 4 \, c - 2}{{\left(c^{2} + d^{2} - 2 \, c + 1\right)} \tan\left(b x + a\right)^{2} + c^{2} + d^{2} - 2 \, c + 1} + 1\right) - 2 \, a^{2} \log\left(\frac{{\left(i \, {\left(c + 1\right)} d + d^{2}\right)} \tan\left(b x + a\right)^{2} - c^{2} + i \, {\left(c + 1\right)} d + {\left(i \, c^{2} + i \, d^{2} + 2 i \, c + i\right)} \tan\left(b x + a\right) - 2 \, c - 1}{\tan\left(b x + a\right)^{2} + 1}\right) - 2 \, a^{2} \log\left(\frac{{\left(i \, {\left(c + 1\right)} d - d^{2}\right)} \tan\left(b x + a\right)^{2} + c^{2} + i \, {\left(c + 1\right)} d + {\left(i \, c^{2} + i \, d^{2} + 2 i \, c + i\right)} \tan\left(b x + a\right) + 2 \, c + 1}{\tan\left(b x + a\right)^{2} + 1}\right) + 2 \, a^{2} \log\left(\frac{{\left(i \, {\left(c - 1\right)} d + d^{2}\right)} \tan\left(b x + a\right)^{2} - c^{2} + i \, {\left(c - 1\right)} d + {\left(i \, c^{2} + i \, d^{2} - 2 i \, c + i\right)} \tan\left(b x + a\right) + 2 \, c - 1}{\tan\left(b x + a\right)^{2} + 1}\right) + 2 \, a^{2} \log\left(\frac{{\left(i \, {\left(c - 1\right)} d - d^{2}\right)} \tan\left(b x + a\right)^{2} + c^{2} + i \, {\left(c - 1\right)} d + {\left(i \, c^{2} + i \, d^{2} - 2 i \, c + i\right)} \tan\left(b x + a\right) - 2 \, c + 1}{\tan\left(b x + a\right)^{2} + 1}\right) - 2 \, {\left(b^{2} x^{2} - a^{2}\right)} \log\left(\frac{{\left(2 i \, {\left(c + 1\right)} d + 2 \, d^{2}\right)} \tan\left(b x + a\right)^{2} + 2 \, c^{2} - 2 i \, {\left(c + 1\right)} d + {\left(2 i \, c^{2} + 4 \, {\left(c + 1\right)} d - 2 i \, d^{2} + 4 i \, c + 2 i\right)} \tan\left(b x + a\right) + 4 \, c + 2}{{\left(c^{2} + d^{2} + 2 \, c + 1\right)} \tan\left(b x + a\right)^{2} + c^{2} + d^{2} + 2 \, c + 1}\right) - 2 \, {\left(b^{2} x^{2} - a^{2}\right)} \log\left(\frac{{\left(-2 i \, {\left(c + 1\right)} d + 2 \, d^{2}\right)} \tan\left(b x + a\right)^{2} + 2 \, c^{2} + 2 i \, {\left(c + 1\right)} d + {\left(-2 i \, c^{2} + 4 \, {\left(c + 1\right)} d + 2 i \, d^{2} - 4 i \, c - 2 i\right)} \tan\left(b x + a\right) + 4 \, c + 2}{{\left(c^{2} + d^{2} + 2 \, c + 1\right)} \tan\left(b x + a\right)^{2} + c^{2} + d^{2} + 2 \, c + 1}\right) + 2 \, {\left(b^{2} x^{2} - a^{2}\right)} \log\left(-\frac{2 \, {\left(i \, {\left(c - 1\right)} d - d^{2}\right)} \tan\left(b x + a\right)^{2} - 2 \, c^{2} - 2 i \, {\left(c - 1\right)} d - {\left(-2 i \, c^{2} + 4 \, {\left(c - 1\right)} d + 2 i \, d^{2} + 4 i \, c - 2 i\right)} \tan\left(b x + a\right) + 4 \, c - 2}{{\left(c^{2} + d^{2} - 2 \, c + 1\right)} \tan\left(b x + a\right)^{2} + c^{2} + d^{2} - 2 \, c + 1}\right) + 2 \, {\left(b^{2} x^{2} - a^{2}\right)} \log\left(-\frac{2 \, {\left(-i \, {\left(c - 1\right)} d - d^{2}\right)} \tan\left(b x + a\right)^{2} - 2 \, c^{2} + 2 i \, {\left(c - 1\right)} d - {\left(2 i \, c^{2} + 4 \, {\left(c - 1\right)} d - 2 i \, d^{2} - 4 i \, c + 2 i\right)} \tan\left(b x + a\right) + 4 \, c - 2}{{\left(c^{2} + d^{2} - 2 \, c + 1\right)} \tan\left(b x + a\right)^{2} + c^{2} + d^{2} - 2 \, c + 1}\right) - {\rm polylog}\left(3, \frac{{\left(c^{2} + 2 i \, {\left(c + 1\right)} d - d^{2} + 2 \, c + 1\right)} \tan\left(b x + a\right)^{2} - c^{2} - 2 i \, {\left(c + 1\right)} d + d^{2} + {\left(2 i \, c^{2} - 4 \, {\left(c + 1\right)} d - 2 i \, d^{2} + 4 i \, c + 2 i\right)} \tan\left(b x + a\right) - 2 \, c - 1}{{\left(c^{2} + d^{2} + 2 \, c + 1\right)} \tan\left(b x + a\right)^{2} + c^{2} + d^{2} + 2 \, c + 1}\right) - {\rm polylog}\left(3, \frac{{\left(c^{2} - 2 i \, {\left(c + 1\right)} d - d^{2} + 2 \, c + 1\right)} \tan\left(b x + a\right)^{2} - c^{2} + 2 i \, {\left(c + 1\right)} d + d^{2} + {\left(-2 i \, c^{2} - 4 \, {\left(c + 1\right)} d + 2 i \, d^{2} - 4 i \, c - 2 i\right)} \tan\left(b x + a\right) - 2 \, c - 1}{{\left(c^{2} + d^{2} + 2 \, c + 1\right)} \tan\left(b x + a\right)^{2} + c^{2} + d^{2} + 2 \, c + 1}\right) + {\rm polylog}\left(3, \frac{{\left(c^{2} + 2 i \, {\left(c - 1\right)} d - d^{2} - 2 \, c + 1\right)} \tan\left(b x + a\right)^{2} - c^{2} - 2 i \, {\left(c - 1\right)} d + d^{2} + {\left(2 i \, c^{2} - 4 \, {\left(c - 1\right)} d - 2 i \, d^{2} - 4 i \, c + 2 i\right)} \tan\left(b x + a\right) + 2 \, c - 1}{{\left(c^{2} + d^{2} - 2 \, c + 1\right)} \tan\left(b x + a\right)^{2} + c^{2} + d^{2} - 2 \, c + 1}\right) + {\rm polylog}\left(3, \frac{{\left(c^{2} - 2 i \, {\left(c - 1\right)} d - d^{2} - 2 \, c + 1\right)} \tan\left(b x + a\right)^{2} - c^{2} + 2 i \, {\left(c - 1\right)} d + d^{2} + {\left(-2 i \, c^{2} - 4 \, {\left(c - 1\right)} d + 2 i \, d^{2} + 4 i \, c - 2 i\right)} \tan\left(b x + a\right) + 2 \, c - 1}{{\left(c^{2} + d^{2} - 2 \, c + 1\right)} \tan\left(b x + a\right)^{2} + c^{2} + d^{2} - 2 \, c + 1}\right)}{16 \, b^{2}}"," ",0,"1/16*(4*b^2*x^2*log((d*tan(b*x + a) + c + 1)/(d*tan(b*x + a) + c - 1)) + 2*I*b*x*dilog(-((2*I*(c + 1)*d + 2*d^2)*tan(b*x + a)^2 + 2*c^2 - 2*I*(c + 1)*d + (2*I*c^2 + 4*(c + 1)*d - 2*I*d^2 + 4*I*c + 2*I)*tan(b*x + a) + 4*c + 2)/((c^2 + d^2 + 2*c + 1)*tan(b*x + a)^2 + c^2 + d^2 + 2*c + 1) + 1) - 2*I*b*x*dilog(-((-2*I*(c + 1)*d + 2*d^2)*tan(b*x + a)^2 + 2*c^2 + 2*I*(c + 1)*d + (-2*I*c^2 + 4*(c + 1)*d + 2*I*d^2 - 4*I*c - 2*I)*tan(b*x + a) + 4*c + 2)/((c^2 + d^2 + 2*c + 1)*tan(b*x + a)^2 + c^2 + d^2 + 2*c + 1) + 1) + 2*I*b*x*dilog((2*(I*(c - 1)*d - d^2)*tan(b*x + a)^2 - 2*c^2 - 2*I*(c - 1)*d - (-2*I*c^2 + 4*(c - 1)*d + 2*I*d^2 + 4*I*c - 2*I)*tan(b*x + a) + 4*c - 2)/((c^2 + d^2 - 2*c + 1)*tan(b*x + a)^2 + c^2 + d^2 - 2*c + 1) + 1) - 2*I*b*x*dilog((2*(-I*(c - 1)*d - d^2)*tan(b*x + a)^2 - 2*c^2 + 2*I*(c - 1)*d - (2*I*c^2 + 4*(c - 1)*d - 2*I*d^2 - 4*I*c + 2*I)*tan(b*x + a) + 4*c - 2)/((c^2 + d^2 - 2*c + 1)*tan(b*x + a)^2 + c^2 + d^2 - 2*c + 1) + 1) - 2*a^2*log(((I*(c + 1)*d + d^2)*tan(b*x + a)^2 - c^2 + I*(c + 1)*d + (I*c^2 + I*d^2 + 2*I*c + I)*tan(b*x + a) - 2*c - 1)/(tan(b*x + a)^2 + 1)) - 2*a^2*log(((I*(c + 1)*d - d^2)*tan(b*x + a)^2 + c^2 + I*(c + 1)*d + (I*c^2 + I*d^2 + 2*I*c + I)*tan(b*x + a) + 2*c + 1)/(tan(b*x + a)^2 + 1)) + 2*a^2*log(((I*(c - 1)*d + d^2)*tan(b*x + a)^2 - c^2 + I*(c - 1)*d + (I*c^2 + I*d^2 - 2*I*c + I)*tan(b*x + a) + 2*c - 1)/(tan(b*x + a)^2 + 1)) + 2*a^2*log(((I*(c - 1)*d - d^2)*tan(b*x + a)^2 + c^2 + I*(c - 1)*d + (I*c^2 + I*d^2 - 2*I*c + I)*tan(b*x + a) - 2*c + 1)/(tan(b*x + a)^2 + 1)) - 2*(b^2*x^2 - a^2)*log(((2*I*(c + 1)*d + 2*d^2)*tan(b*x + a)^2 + 2*c^2 - 2*I*(c + 1)*d + (2*I*c^2 + 4*(c + 1)*d - 2*I*d^2 + 4*I*c + 2*I)*tan(b*x + a) + 4*c + 2)/((c^2 + d^2 + 2*c + 1)*tan(b*x + a)^2 + c^2 + d^2 + 2*c + 1)) - 2*(b^2*x^2 - a^2)*log(((-2*I*(c + 1)*d + 2*d^2)*tan(b*x + a)^2 + 2*c^2 + 2*I*(c + 1)*d + (-2*I*c^2 + 4*(c + 1)*d + 2*I*d^2 - 4*I*c - 2*I)*tan(b*x + a) + 4*c + 2)/((c^2 + d^2 + 2*c + 1)*tan(b*x + a)^2 + c^2 + d^2 + 2*c + 1)) + 2*(b^2*x^2 - a^2)*log(-(2*(I*(c - 1)*d - d^2)*tan(b*x + a)^2 - 2*c^2 - 2*I*(c - 1)*d - (-2*I*c^2 + 4*(c - 1)*d + 2*I*d^2 + 4*I*c - 2*I)*tan(b*x + a) + 4*c - 2)/((c^2 + d^2 - 2*c + 1)*tan(b*x + a)^2 + c^2 + d^2 - 2*c + 1)) + 2*(b^2*x^2 - a^2)*log(-(2*(-I*(c - 1)*d - d^2)*tan(b*x + a)^2 - 2*c^2 + 2*I*(c - 1)*d - (2*I*c^2 + 4*(c - 1)*d - 2*I*d^2 - 4*I*c + 2*I)*tan(b*x + a) + 4*c - 2)/((c^2 + d^2 - 2*c + 1)*tan(b*x + a)^2 + c^2 + d^2 - 2*c + 1)) - polylog(3, ((c^2 + 2*I*(c + 1)*d - d^2 + 2*c + 1)*tan(b*x + a)^2 - c^2 - 2*I*(c + 1)*d + d^2 + (2*I*c^2 - 4*(c + 1)*d - 2*I*d^2 + 4*I*c + 2*I)*tan(b*x + a) - 2*c - 1)/((c^2 + d^2 + 2*c + 1)*tan(b*x + a)^2 + c^2 + d^2 + 2*c + 1)) - polylog(3, ((c^2 - 2*I*(c + 1)*d - d^2 + 2*c + 1)*tan(b*x + a)^2 - c^2 + 2*I*(c + 1)*d + d^2 + (-2*I*c^2 - 4*(c + 1)*d + 2*I*d^2 - 4*I*c - 2*I)*tan(b*x + a) - 2*c - 1)/((c^2 + d^2 + 2*c + 1)*tan(b*x + a)^2 + c^2 + d^2 + 2*c + 1)) + polylog(3, ((c^2 + 2*I*(c - 1)*d - d^2 - 2*c + 1)*tan(b*x + a)^2 - c^2 - 2*I*(c - 1)*d + d^2 + (2*I*c^2 - 4*(c - 1)*d - 2*I*d^2 - 4*I*c + 2*I)*tan(b*x + a) + 2*c - 1)/((c^2 + d^2 - 2*c + 1)*tan(b*x + a)^2 + c^2 + d^2 - 2*c + 1)) + polylog(3, ((c^2 - 2*I*(c - 1)*d - d^2 - 2*c + 1)*tan(b*x + a)^2 - c^2 + 2*I*(c - 1)*d + d^2 + (-2*I*c^2 - 4*(c - 1)*d + 2*I*d^2 + 4*I*c - 2*I)*tan(b*x + a) + 2*c - 1)/((c^2 + d^2 - 2*c + 1)*tan(b*x + a)^2 + c^2 + d^2 - 2*c + 1)))/b^2","C",0
238,1,1188,0,0.826626," ","integrate(arccoth(c+d*tan(b*x+a)),x, algorithm=""fricas"")","\frac{4 \, b x \log\left(\frac{d \tan\left(b x + a\right) + c + 1}{d \tan\left(b x + a\right) + c - 1}\right) - 2 \, {\left(b x + a\right)} \log\left(\frac{{\left(2 i \, {\left(c + 1\right)} d + 2 \, d^{2}\right)} \tan\left(b x + a\right)^{2} + 2 \, c^{2} - 2 i \, {\left(c + 1\right)} d + {\left(2 i \, c^{2} + 4 \, {\left(c + 1\right)} d - 2 i \, d^{2} + 4 i \, c + 2 i\right)} \tan\left(b x + a\right) + 4 \, c + 2}{{\left(c^{2} + d^{2} + 2 \, c + 1\right)} \tan\left(b x + a\right)^{2} + c^{2} + d^{2} + 2 \, c + 1}\right) - 2 \, {\left(b x + a\right)} \log\left(\frac{{\left(-2 i \, {\left(c + 1\right)} d + 2 \, d^{2}\right)} \tan\left(b x + a\right)^{2} + 2 \, c^{2} + 2 i \, {\left(c + 1\right)} d + {\left(-2 i \, c^{2} + 4 \, {\left(c + 1\right)} d + 2 i \, d^{2} - 4 i \, c - 2 i\right)} \tan\left(b x + a\right) + 4 \, c + 2}{{\left(c^{2} + d^{2} + 2 \, c + 1\right)} \tan\left(b x + a\right)^{2} + c^{2} + d^{2} + 2 \, c + 1}\right) + 2 \, {\left(b x + a\right)} \log\left(-\frac{2 \, {\left(i \, {\left(c - 1\right)} d - d^{2}\right)} \tan\left(b x + a\right)^{2} - 2 \, c^{2} - 2 i \, {\left(c - 1\right)} d - {\left(-2 i \, c^{2} + 4 \, {\left(c - 1\right)} d + 2 i \, d^{2} + 4 i \, c - 2 i\right)} \tan\left(b x + a\right) + 4 \, c - 2}{{\left(c^{2} + d^{2} - 2 \, c + 1\right)} \tan\left(b x + a\right)^{2} + c^{2} + d^{2} - 2 \, c + 1}\right) + 2 \, {\left(b x + a\right)} \log\left(-\frac{2 \, {\left(-i \, {\left(c - 1\right)} d - d^{2}\right)} \tan\left(b x + a\right)^{2} - 2 \, c^{2} + 2 i \, {\left(c - 1\right)} d - {\left(2 i \, c^{2} + 4 \, {\left(c - 1\right)} d - 2 i \, d^{2} - 4 i \, c + 2 i\right)} \tan\left(b x + a\right) + 4 \, c - 2}{{\left(c^{2} + d^{2} - 2 \, c + 1\right)} \tan\left(b x + a\right)^{2} + c^{2} + d^{2} - 2 \, c + 1}\right) + 2 \, a \log\left(\frac{{\left(i \, {\left(c + 1\right)} d + d^{2}\right)} \tan\left(b x + a\right)^{2} - c^{2} + i \, {\left(c + 1\right)} d + {\left(i \, c^{2} + i \, d^{2} + 2 i \, c + i\right)} \tan\left(b x + a\right) - 2 \, c - 1}{\tan\left(b x + a\right)^{2} + 1}\right) + 2 \, a \log\left(\frac{{\left(i \, {\left(c + 1\right)} d - d^{2}\right)} \tan\left(b x + a\right)^{2} + c^{2} + i \, {\left(c + 1\right)} d + {\left(i \, c^{2} + i \, d^{2} + 2 i \, c + i\right)} \tan\left(b x + a\right) + 2 \, c + 1}{\tan\left(b x + a\right)^{2} + 1}\right) - 2 \, a \log\left(\frac{{\left(i \, {\left(c - 1\right)} d + d^{2}\right)} \tan\left(b x + a\right)^{2} - c^{2} + i \, {\left(c - 1\right)} d + {\left(i \, c^{2} + i \, d^{2} - 2 i \, c + i\right)} \tan\left(b x + a\right) + 2 \, c - 1}{\tan\left(b x + a\right)^{2} + 1}\right) - 2 \, a \log\left(\frac{{\left(i \, {\left(c - 1\right)} d - d^{2}\right)} \tan\left(b x + a\right)^{2} + c^{2} + i \, {\left(c - 1\right)} d + {\left(i \, c^{2} + i \, d^{2} - 2 i \, c + i\right)} \tan\left(b x + a\right) - 2 \, c + 1}{\tan\left(b x + a\right)^{2} + 1}\right) + i \, {\rm Li}_2\left(-\frac{{\left(2 i \, {\left(c + 1\right)} d + 2 \, d^{2}\right)} \tan\left(b x + a\right)^{2} + 2 \, c^{2} - 2 i \, {\left(c + 1\right)} d + {\left(2 i \, c^{2} + 4 \, {\left(c + 1\right)} d - 2 i \, d^{2} + 4 i \, c + 2 i\right)} \tan\left(b x + a\right) + 4 \, c + 2}{{\left(c^{2} + d^{2} + 2 \, c + 1\right)} \tan\left(b x + a\right)^{2} + c^{2} + d^{2} + 2 \, c + 1} + 1\right) - i \, {\rm Li}_2\left(-\frac{{\left(-2 i \, {\left(c + 1\right)} d + 2 \, d^{2}\right)} \tan\left(b x + a\right)^{2} + 2 \, c^{2} + 2 i \, {\left(c + 1\right)} d + {\left(-2 i \, c^{2} + 4 \, {\left(c + 1\right)} d + 2 i \, d^{2} - 4 i \, c - 2 i\right)} \tan\left(b x + a\right) + 4 \, c + 2}{{\left(c^{2} + d^{2} + 2 \, c + 1\right)} \tan\left(b x + a\right)^{2} + c^{2} + d^{2} + 2 \, c + 1} + 1\right) + i \, {\rm Li}_2\left(\frac{2 \, {\left(i \, {\left(c - 1\right)} d - d^{2}\right)} \tan\left(b x + a\right)^{2} - 2 \, c^{2} - 2 i \, {\left(c - 1\right)} d - {\left(-2 i \, c^{2} + 4 \, {\left(c - 1\right)} d + 2 i \, d^{2} + 4 i \, c - 2 i\right)} \tan\left(b x + a\right) + 4 \, c - 2}{{\left(c^{2} + d^{2} - 2 \, c + 1\right)} \tan\left(b x + a\right)^{2} + c^{2} + d^{2} - 2 \, c + 1} + 1\right) - i \, {\rm Li}_2\left(\frac{2 \, {\left(-i \, {\left(c - 1\right)} d - d^{2}\right)} \tan\left(b x + a\right)^{2} - 2 \, c^{2} + 2 i \, {\left(c - 1\right)} d - {\left(2 i \, c^{2} + 4 \, {\left(c - 1\right)} d - 2 i \, d^{2} - 4 i \, c + 2 i\right)} \tan\left(b x + a\right) + 4 \, c - 2}{{\left(c^{2} + d^{2} - 2 \, c + 1\right)} \tan\left(b x + a\right)^{2} + c^{2} + d^{2} - 2 \, c + 1} + 1\right)}{8 \, b}"," ",0,"1/8*(4*b*x*log((d*tan(b*x + a) + c + 1)/(d*tan(b*x + a) + c - 1)) - 2*(b*x + a)*log(((2*I*(c + 1)*d + 2*d^2)*tan(b*x + a)^2 + 2*c^2 - 2*I*(c + 1)*d + (2*I*c^2 + 4*(c + 1)*d - 2*I*d^2 + 4*I*c + 2*I)*tan(b*x + a) + 4*c + 2)/((c^2 + d^2 + 2*c + 1)*tan(b*x + a)^2 + c^2 + d^2 + 2*c + 1)) - 2*(b*x + a)*log(((-2*I*(c + 1)*d + 2*d^2)*tan(b*x + a)^2 + 2*c^2 + 2*I*(c + 1)*d + (-2*I*c^2 + 4*(c + 1)*d + 2*I*d^2 - 4*I*c - 2*I)*tan(b*x + a) + 4*c + 2)/((c^2 + d^2 + 2*c + 1)*tan(b*x + a)^2 + c^2 + d^2 + 2*c + 1)) + 2*(b*x + a)*log(-(2*(I*(c - 1)*d - d^2)*tan(b*x + a)^2 - 2*c^2 - 2*I*(c - 1)*d - (-2*I*c^2 + 4*(c - 1)*d + 2*I*d^2 + 4*I*c - 2*I)*tan(b*x + a) + 4*c - 2)/((c^2 + d^2 - 2*c + 1)*tan(b*x + a)^2 + c^2 + d^2 - 2*c + 1)) + 2*(b*x + a)*log(-(2*(-I*(c - 1)*d - d^2)*tan(b*x + a)^2 - 2*c^2 + 2*I*(c - 1)*d - (2*I*c^2 + 4*(c - 1)*d - 2*I*d^2 - 4*I*c + 2*I)*tan(b*x + a) + 4*c - 2)/((c^2 + d^2 - 2*c + 1)*tan(b*x + a)^2 + c^2 + d^2 - 2*c + 1)) + 2*a*log(((I*(c + 1)*d + d^2)*tan(b*x + a)^2 - c^2 + I*(c + 1)*d + (I*c^2 + I*d^2 + 2*I*c + I)*tan(b*x + a) - 2*c - 1)/(tan(b*x + a)^2 + 1)) + 2*a*log(((I*(c + 1)*d - d^2)*tan(b*x + a)^2 + c^2 + I*(c + 1)*d + (I*c^2 + I*d^2 + 2*I*c + I)*tan(b*x + a) + 2*c + 1)/(tan(b*x + a)^2 + 1)) - 2*a*log(((I*(c - 1)*d + d^2)*tan(b*x + a)^2 - c^2 + I*(c - 1)*d + (I*c^2 + I*d^2 - 2*I*c + I)*tan(b*x + a) + 2*c - 1)/(tan(b*x + a)^2 + 1)) - 2*a*log(((I*(c - 1)*d - d^2)*tan(b*x + a)^2 + c^2 + I*(c - 1)*d + (I*c^2 + I*d^2 - 2*I*c + I)*tan(b*x + a) - 2*c + 1)/(tan(b*x + a)^2 + 1)) + I*dilog(-((2*I*(c + 1)*d + 2*d^2)*tan(b*x + a)^2 + 2*c^2 - 2*I*(c + 1)*d + (2*I*c^2 + 4*(c + 1)*d - 2*I*d^2 + 4*I*c + 2*I)*tan(b*x + a) + 4*c + 2)/((c^2 + d^2 + 2*c + 1)*tan(b*x + a)^2 + c^2 + d^2 + 2*c + 1) + 1) - I*dilog(-((-2*I*(c + 1)*d + 2*d^2)*tan(b*x + a)^2 + 2*c^2 + 2*I*(c + 1)*d + (-2*I*c^2 + 4*(c + 1)*d + 2*I*d^2 - 4*I*c - 2*I)*tan(b*x + a) + 4*c + 2)/((c^2 + d^2 + 2*c + 1)*tan(b*x + a)^2 + c^2 + d^2 + 2*c + 1) + 1) + I*dilog((2*(I*(c - 1)*d - d^2)*tan(b*x + a)^2 - 2*c^2 - 2*I*(c - 1)*d - (-2*I*c^2 + 4*(c - 1)*d + 2*I*d^2 + 4*I*c - 2*I)*tan(b*x + a) + 4*c - 2)/((c^2 + d^2 - 2*c + 1)*tan(b*x + a)^2 + c^2 + d^2 - 2*c + 1) + 1) - I*dilog((2*(-I*(c - 1)*d - d^2)*tan(b*x + a)^2 - 2*c^2 + 2*I*(c - 1)*d - (2*I*c^2 + 4*(c - 1)*d - 2*I*d^2 - 4*I*c + 2*I)*tan(b*x + a) + 4*c - 2)/((c^2 + d^2 - 2*c + 1)*tan(b*x + a)^2 + c^2 + d^2 - 2*c + 1) + 1))/b","B",0
239,0,0,0,0.593147," ","integrate(arccoth(c+d*tan(b*x+a))/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{arcoth}\left(d \tan\left(b x + a\right) + c\right)}{x}, x\right)"," ",0,"integral(arccoth(d*tan(b*x + a) + c)/x, x)","F",0
240,1,348,0,0.506365," ","integrate(x^2*arccoth(1-I*d+d*tan(b*x+a)),x, algorithm=""fricas"")","\frac{i \, b^{4} x^{4} + 2 \, b^{3} x^{3} \log\left(\frac{{\left({\left(d + i\right)} e^{\left(2 i \, b x + 2 i \, a\right)} + i\right)} e^{\left(-2 i \, b x - 2 i \, a\right)}}{d}\right) + 6 i \, b^{2} x^{2} {\rm Li}_2\left(\frac{1}{2} \, \sqrt{4 i \, d - 4} e^{\left(i \, b x + i \, a\right)}\right) + 6 i \, b^{2} x^{2} {\rm Li}_2\left(-\frac{1}{2} \, \sqrt{4 i \, d - 4} e^{\left(i \, b x + i \, a\right)}\right) - i \, a^{4} + 2 \, a^{3} \log\left(\frac{{\left(2 \, d + 2 i\right)} e^{\left(i \, b x + i \, a\right)} + i \, \sqrt{4 i \, d - 4}}{2 \, d + 2 i}\right) + 2 \, a^{3} \log\left(\frac{{\left(2 \, d + 2 i\right)} e^{\left(i \, b x + i \, a\right)} - i \, \sqrt{4 i \, d - 4}}{2 \, d + 2 i}\right) - 12 \, b x {\rm polylog}\left(3, \frac{1}{2} \, \sqrt{4 i \, d - 4} e^{\left(i \, b x + i \, a\right)}\right) - 12 \, b x {\rm polylog}\left(3, -\frac{1}{2} \, \sqrt{4 i \, d - 4} e^{\left(i \, b x + i \, a\right)}\right) - 2 \, {\left(b^{3} x^{3} + a^{3}\right)} \log\left(\frac{1}{2} \, \sqrt{4 i \, d - 4} e^{\left(i \, b x + i \, a\right)} + 1\right) - 2 \, {\left(b^{3} x^{3} + a^{3}\right)} \log\left(-\frac{1}{2} \, \sqrt{4 i \, d - 4} e^{\left(i \, b x + i \, a\right)} + 1\right) - 12 i \, {\rm polylog}\left(4, \frac{1}{2} \, \sqrt{4 i \, d - 4} e^{\left(i \, b x + i \, a\right)}\right) - 12 i \, {\rm polylog}\left(4, -\frac{1}{2} \, \sqrt{4 i \, d - 4} e^{\left(i \, b x + i \, a\right)}\right)}{12 \, b^{3}}"," ",0,"1/12*(I*b^4*x^4 + 2*b^3*x^3*log(((d + I)*e^(2*I*b*x + 2*I*a) + I)*e^(-2*I*b*x - 2*I*a)/d) + 6*I*b^2*x^2*dilog(1/2*sqrt(4*I*d - 4)*e^(I*b*x + I*a)) + 6*I*b^2*x^2*dilog(-1/2*sqrt(4*I*d - 4)*e^(I*b*x + I*a)) - I*a^4 + 2*a^3*log(((2*d + 2*I)*e^(I*b*x + I*a) + I*sqrt(4*I*d - 4))/(2*d + 2*I)) + 2*a^3*log(((2*d + 2*I)*e^(I*b*x + I*a) - I*sqrt(4*I*d - 4))/(2*d + 2*I)) - 12*b*x*polylog(3, 1/2*sqrt(4*I*d - 4)*e^(I*b*x + I*a)) - 12*b*x*polylog(3, -1/2*sqrt(4*I*d - 4)*e^(I*b*x + I*a)) - 2*(b^3*x^3 + a^3)*log(1/2*sqrt(4*I*d - 4)*e^(I*b*x + I*a) + 1) - 2*(b^3*x^3 + a^3)*log(-1/2*sqrt(4*I*d - 4)*e^(I*b*x + I*a) + 1) - 12*I*polylog(4, 1/2*sqrt(4*I*d - 4)*e^(I*b*x + I*a)) - 12*I*polylog(4, -1/2*sqrt(4*I*d - 4)*e^(I*b*x + I*a)))/b^3","C",0
241,1,296,0,0.577924," ","integrate(x*arccoth(1-I*d+d*tan(b*x+a)),x, algorithm=""fricas"")","\frac{2 i \, b^{3} x^{3} + 3 \, b^{2} x^{2} \log\left(\frac{{\left({\left(d + i\right)} e^{\left(2 i \, b x + 2 i \, a\right)} + i\right)} e^{\left(-2 i \, b x - 2 i \, a\right)}}{d}\right) + 2 i \, a^{3} + 6 i \, b x {\rm Li}_2\left(\frac{1}{2} \, \sqrt{4 i \, d - 4} e^{\left(i \, b x + i \, a\right)}\right) + 6 i \, b x {\rm Li}_2\left(-\frac{1}{2} \, \sqrt{4 i \, d - 4} e^{\left(i \, b x + i \, a\right)}\right) - 3 \, a^{2} \log\left(\frac{{\left(2 \, d + 2 i\right)} e^{\left(i \, b x + i \, a\right)} + i \, \sqrt{4 i \, d - 4}}{2 \, d + 2 i}\right) - 3 \, a^{2} \log\left(\frac{{\left(2 \, d + 2 i\right)} e^{\left(i \, b x + i \, a\right)} - i \, \sqrt{4 i \, d - 4}}{2 \, d + 2 i}\right) - 3 \, {\left(b^{2} x^{2} - a^{2}\right)} \log\left(\frac{1}{2} \, \sqrt{4 i \, d - 4} e^{\left(i \, b x + i \, a\right)} + 1\right) - 3 \, {\left(b^{2} x^{2} - a^{2}\right)} \log\left(-\frac{1}{2} \, \sqrt{4 i \, d - 4} e^{\left(i \, b x + i \, a\right)} + 1\right) - 6 \, {\rm polylog}\left(3, \frac{1}{2} \, \sqrt{4 i \, d - 4} e^{\left(i \, b x + i \, a\right)}\right) - 6 \, {\rm polylog}\left(3, -\frac{1}{2} \, \sqrt{4 i \, d - 4} e^{\left(i \, b x + i \, a\right)}\right)}{12 \, b^{2}}"," ",0,"1/12*(2*I*b^3*x^3 + 3*b^2*x^2*log(((d + I)*e^(2*I*b*x + 2*I*a) + I)*e^(-2*I*b*x - 2*I*a)/d) + 2*I*a^3 + 6*I*b*x*dilog(1/2*sqrt(4*I*d - 4)*e^(I*b*x + I*a)) + 6*I*b*x*dilog(-1/2*sqrt(4*I*d - 4)*e^(I*b*x + I*a)) - 3*a^2*log(((2*d + 2*I)*e^(I*b*x + I*a) + I*sqrt(4*I*d - 4))/(2*d + 2*I)) - 3*a^2*log(((2*d + 2*I)*e^(I*b*x + I*a) - I*sqrt(4*I*d - 4))/(2*d + 2*I)) - 3*(b^2*x^2 - a^2)*log(1/2*sqrt(4*I*d - 4)*e^(I*b*x + I*a) + 1) - 3*(b^2*x^2 - a^2)*log(-1/2*sqrt(4*I*d - 4)*e^(I*b*x + I*a) + 1) - 6*polylog(3, 1/2*sqrt(4*I*d - 4)*e^(I*b*x + I*a)) - 6*polylog(3, -1/2*sqrt(4*I*d - 4)*e^(I*b*x + I*a)))/b^2","C",0
242,1,221,0,0.633449," ","integrate(arccoth(1-I*d+d*tan(b*x+a)),x, algorithm=""fricas"")","\frac{i \, b^{2} x^{2} + b x \log\left(\frac{{\left({\left(d + i\right)} e^{\left(2 i \, b x + 2 i \, a\right)} + i\right)} e^{\left(-2 i \, b x - 2 i \, a\right)}}{d}\right) - i \, a^{2} - {\left(b x + a\right)} \log\left(\frac{1}{2} \, \sqrt{4 i \, d - 4} e^{\left(i \, b x + i \, a\right)} + 1\right) - {\left(b x + a\right)} \log\left(-\frac{1}{2} \, \sqrt{4 i \, d - 4} e^{\left(i \, b x + i \, a\right)} + 1\right) + a \log\left(\frac{{\left(2 \, d + 2 i\right)} e^{\left(i \, b x + i \, a\right)} + i \, \sqrt{4 i \, d - 4}}{2 \, d + 2 i}\right) + a \log\left(\frac{{\left(2 \, d + 2 i\right)} e^{\left(i \, b x + i \, a\right)} - i \, \sqrt{4 i \, d - 4}}{2 \, d + 2 i}\right) + i \, {\rm Li}_2\left(\frac{1}{2} \, \sqrt{4 i \, d - 4} e^{\left(i \, b x + i \, a\right)}\right) + i \, {\rm Li}_2\left(-\frac{1}{2} \, \sqrt{4 i \, d - 4} e^{\left(i \, b x + i \, a\right)}\right)}{2 \, b}"," ",0,"1/2*(I*b^2*x^2 + b*x*log(((d + I)*e^(2*I*b*x + 2*I*a) + I)*e^(-2*I*b*x - 2*I*a)/d) - I*a^2 - (b*x + a)*log(1/2*sqrt(4*I*d - 4)*e^(I*b*x + I*a) + 1) - (b*x + a)*log(-1/2*sqrt(4*I*d - 4)*e^(I*b*x + I*a) + 1) + a*log(((2*d + 2*I)*e^(I*b*x + I*a) + I*sqrt(4*I*d - 4))/(2*d + 2*I)) + a*log(((2*d + 2*I)*e^(I*b*x + I*a) - I*sqrt(4*I*d - 4))/(2*d + 2*I)) + I*dilog(1/2*sqrt(4*I*d - 4)*e^(I*b*x + I*a)) + I*dilog(-1/2*sqrt(4*I*d - 4)*e^(I*b*x + I*a)))/b","B",0
243,0,0,0,0.712120," ","integrate(arccoth(1-I*d+d*tan(b*x+a))/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\log\left(\frac{{\left({\left(d + i\right)} e^{\left(2 i \, b x + 2 i \, a\right)} + i\right)} e^{\left(-2 i \, b x - 2 i \, a\right)}}{d}\right)}{2 \, x}, x\right)"," ",0,"integral(1/2*log(((d + I)*e^(2*I*b*x + 2*I*a) + I)*e^(-2*I*b*x - 2*I*a)/d)/x, x)","F",0
244,1,348,0,0.672965," ","integrate(x^2*arccoth(1+I*d-d*tan(b*x+a)),x, algorithm=""fricas"")","\frac{i \, b^{4} x^{4} - 2 \, b^{3} x^{3} \log\left(\frac{d e^{\left(2 i \, b x + 2 i \, a\right)}}{{\left(d - i\right)} e^{\left(2 i \, b x + 2 i \, a\right)} - i}\right) + 6 i \, b^{2} x^{2} {\rm Li}_2\left(\frac{1}{2} \, \sqrt{-4 i \, d - 4} e^{\left(i \, b x + i \, a\right)}\right) + 6 i \, b^{2} x^{2} {\rm Li}_2\left(-\frac{1}{2} \, \sqrt{-4 i \, d - 4} e^{\left(i \, b x + i \, a\right)}\right) - i \, a^{4} + 2 \, a^{3} \log\left(\frac{{\left(2 \, d - 2 i\right)} e^{\left(i \, b x + i \, a\right)} + i \, \sqrt{-4 i \, d - 4}}{2 \, d - 2 i}\right) + 2 \, a^{3} \log\left(\frac{{\left(2 \, d - 2 i\right)} e^{\left(i \, b x + i \, a\right)} - i \, \sqrt{-4 i \, d - 4}}{2 \, d - 2 i}\right) - 12 \, b x {\rm polylog}\left(3, \frac{1}{2} \, \sqrt{-4 i \, d - 4} e^{\left(i \, b x + i \, a\right)}\right) - 12 \, b x {\rm polylog}\left(3, -\frac{1}{2} \, \sqrt{-4 i \, d - 4} e^{\left(i \, b x + i \, a\right)}\right) - 2 \, {\left(b^{3} x^{3} + a^{3}\right)} \log\left(\frac{1}{2} \, \sqrt{-4 i \, d - 4} e^{\left(i \, b x + i \, a\right)} + 1\right) - 2 \, {\left(b^{3} x^{3} + a^{3}\right)} \log\left(-\frac{1}{2} \, \sqrt{-4 i \, d - 4} e^{\left(i \, b x + i \, a\right)} + 1\right) - 12 i \, {\rm polylog}\left(4, \frac{1}{2} \, \sqrt{-4 i \, d - 4} e^{\left(i \, b x + i \, a\right)}\right) - 12 i \, {\rm polylog}\left(4, -\frac{1}{2} \, \sqrt{-4 i \, d - 4} e^{\left(i \, b x + i \, a\right)}\right)}{12 \, b^{3}}"," ",0,"1/12*(I*b^4*x^4 - 2*b^3*x^3*log(d*e^(2*I*b*x + 2*I*a)/((d - I)*e^(2*I*b*x + 2*I*a) - I)) + 6*I*b^2*x^2*dilog(1/2*sqrt(-4*I*d - 4)*e^(I*b*x + I*a)) + 6*I*b^2*x^2*dilog(-1/2*sqrt(-4*I*d - 4)*e^(I*b*x + I*a)) - I*a^4 + 2*a^3*log(((2*d - 2*I)*e^(I*b*x + I*a) + I*sqrt(-4*I*d - 4))/(2*d - 2*I)) + 2*a^3*log(((2*d - 2*I)*e^(I*b*x + I*a) - I*sqrt(-4*I*d - 4))/(2*d - 2*I)) - 12*b*x*polylog(3, 1/2*sqrt(-4*I*d - 4)*e^(I*b*x + I*a)) - 12*b*x*polylog(3, -1/2*sqrt(-4*I*d - 4)*e^(I*b*x + I*a)) - 2*(b^3*x^3 + a^3)*log(1/2*sqrt(-4*I*d - 4)*e^(I*b*x + I*a) + 1) - 2*(b^3*x^3 + a^3)*log(-1/2*sqrt(-4*I*d - 4)*e^(I*b*x + I*a) + 1) - 12*I*polylog(4, 1/2*sqrt(-4*I*d - 4)*e^(I*b*x + I*a)) - 12*I*polylog(4, -1/2*sqrt(-4*I*d - 4)*e^(I*b*x + I*a)))/b^3","C",0
245,1,296,0,0.740856," ","integrate(x*arccoth(1+I*d-d*tan(b*x+a)),x, algorithm=""fricas"")","\frac{2 i \, b^{3} x^{3} - 3 \, b^{2} x^{2} \log\left(\frac{d e^{\left(2 i \, b x + 2 i \, a\right)}}{{\left(d - i\right)} e^{\left(2 i \, b x + 2 i \, a\right)} - i}\right) + 2 i \, a^{3} + 6 i \, b x {\rm Li}_2\left(\frac{1}{2} \, \sqrt{-4 i \, d - 4} e^{\left(i \, b x + i \, a\right)}\right) + 6 i \, b x {\rm Li}_2\left(-\frac{1}{2} \, \sqrt{-4 i \, d - 4} e^{\left(i \, b x + i \, a\right)}\right) - 3 \, a^{2} \log\left(\frac{{\left(2 \, d - 2 i\right)} e^{\left(i \, b x + i \, a\right)} + i \, \sqrt{-4 i \, d - 4}}{2 \, d - 2 i}\right) - 3 \, a^{2} \log\left(\frac{{\left(2 \, d - 2 i\right)} e^{\left(i \, b x + i \, a\right)} - i \, \sqrt{-4 i \, d - 4}}{2 \, d - 2 i}\right) - 3 \, {\left(b^{2} x^{2} - a^{2}\right)} \log\left(\frac{1}{2} \, \sqrt{-4 i \, d - 4} e^{\left(i \, b x + i \, a\right)} + 1\right) - 3 \, {\left(b^{2} x^{2} - a^{2}\right)} \log\left(-\frac{1}{2} \, \sqrt{-4 i \, d - 4} e^{\left(i \, b x + i \, a\right)} + 1\right) - 6 \, {\rm polylog}\left(3, \frac{1}{2} \, \sqrt{-4 i \, d - 4} e^{\left(i \, b x + i \, a\right)}\right) - 6 \, {\rm polylog}\left(3, -\frac{1}{2} \, \sqrt{-4 i \, d - 4} e^{\left(i \, b x + i \, a\right)}\right)}{12 \, b^{2}}"," ",0,"1/12*(2*I*b^3*x^3 - 3*b^2*x^2*log(d*e^(2*I*b*x + 2*I*a)/((d - I)*e^(2*I*b*x + 2*I*a) - I)) + 2*I*a^3 + 6*I*b*x*dilog(1/2*sqrt(-4*I*d - 4)*e^(I*b*x + I*a)) + 6*I*b*x*dilog(-1/2*sqrt(-4*I*d - 4)*e^(I*b*x + I*a)) - 3*a^2*log(((2*d - 2*I)*e^(I*b*x + I*a) + I*sqrt(-4*I*d - 4))/(2*d - 2*I)) - 3*a^2*log(((2*d - 2*I)*e^(I*b*x + I*a) - I*sqrt(-4*I*d - 4))/(2*d - 2*I)) - 3*(b^2*x^2 - a^2)*log(1/2*sqrt(-4*I*d - 4)*e^(I*b*x + I*a) + 1) - 3*(b^2*x^2 - a^2)*log(-1/2*sqrt(-4*I*d - 4)*e^(I*b*x + I*a) + 1) - 6*polylog(3, 1/2*sqrt(-4*I*d - 4)*e^(I*b*x + I*a)) - 6*polylog(3, -1/2*sqrt(-4*I*d - 4)*e^(I*b*x + I*a)))/b^2","C",0
246,1,222,0,0.480526," ","integrate(arccoth(1+I*d-d*tan(b*x+a)),x, algorithm=""fricas"")","\frac{i \, b^{2} x^{2} - b x \log\left(\frac{d e^{\left(2 i \, b x + 2 i \, a\right)}}{{\left(d - i\right)} e^{\left(2 i \, b x + 2 i \, a\right)} - i}\right) - i \, a^{2} - {\left(b x + a\right)} \log\left(\frac{1}{2} \, \sqrt{-4 i \, d - 4} e^{\left(i \, b x + i \, a\right)} + 1\right) - {\left(b x + a\right)} \log\left(-\frac{1}{2} \, \sqrt{-4 i \, d - 4} e^{\left(i \, b x + i \, a\right)} + 1\right) + a \log\left(\frac{{\left(2 \, d - 2 i\right)} e^{\left(i \, b x + i \, a\right)} + i \, \sqrt{-4 i \, d - 4}}{2 \, d - 2 i}\right) + a \log\left(\frac{{\left(2 \, d - 2 i\right)} e^{\left(i \, b x + i \, a\right)} - i \, \sqrt{-4 i \, d - 4}}{2 \, d - 2 i}\right) + i \, {\rm Li}_2\left(\frac{1}{2} \, \sqrt{-4 i \, d - 4} e^{\left(i \, b x + i \, a\right)}\right) + i \, {\rm Li}_2\left(-\frac{1}{2} \, \sqrt{-4 i \, d - 4} e^{\left(i \, b x + i \, a\right)}\right)}{2 \, b}"," ",0,"1/2*(I*b^2*x^2 - b*x*log(d*e^(2*I*b*x + 2*I*a)/((d - I)*e^(2*I*b*x + 2*I*a) - I)) - I*a^2 - (b*x + a)*log(1/2*sqrt(-4*I*d - 4)*e^(I*b*x + I*a) + 1) - (b*x + a)*log(-1/2*sqrt(-4*I*d - 4)*e^(I*b*x + I*a) + 1) + a*log(((2*d - 2*I)*e^(I*b*x + I*a) + I*sqrt(-4*I*d - 4))/(2*d - 2*I)) + a*log(((2*d - 2*I)*e^(I*b*x + I*a) - I*sqrt(-4*I*d - 4))/(2*d - 2*I)) + I*dilog(1/2*sqrt(-4*I*d - 4)*e^(I*b*x + I*a)) + I*dilog(-1/2*sqrt(-4*I*d - 4)*e^(I*b*x + I*a)))/b","B",0
247,0,0,0,0.632650," ","integrate(arccoth(1+I*d-d*tan(b*x+a))/x,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\log\left(\frac{d e^{\left(2 i \, b x + 2 i \, a\right)}}{{\left(d - i\right)} e^{\left(2 i \, b x + 2 i \, a\right)} - i}\right)}{2 \, x}, x\right)"," ",0,"integral(-1/2*log(d*e^(2*I*b*x + 2*I*a)/((d - I)*e^(2*I*b*x + 2*I*a) - I))/x, x)","F",0
248,1,1566,0,0.799605," ","integrate((f*x+e)^3*arccoth(cot(b*x+a)),x, algorithm=""fricas"")","-\frac{3 \, f^{3} {\rm polylog}\left(5, i \, \cos\left(2 \, b x + 2 \, a\right) + \sin\left(2 \, b x + 2 \, a\right)\right) - 3 \, f^{3} {\rm polylog}\left(5, i \, \cos\left(2 \, b x + 2 \, a\right) - \sin\left(2 \, b x + 2 \, a\right)\right) + 3 \, f^{3} {\rm polylog}\left(5, -i \, \cos\left(2 \, b x + 2 \, a\right) + \sin\left(2 \, b x + 2 \, a\right)\right) - 3 \, f^{3} {\rm polylog}\left(5, -i \, \cos\left(2 \, b x + 2 \, a\right) - \sin\left(2 \, b x + 2 \, a\right)\right) - {\left(4 i \, b^{3} f^{3} x^{3} + 12 i \, b^{3} e f^{2} x^{2} + 12 i \, b^{3} e^{2} f x + 4 i \, b^{3} e^{3}\right)} {\rm Li}_2\left(i \, \cos\left(2 \, b x + 2 \, a\right) + \sin\left(2 \, b x + 2 \, a\right)\right) - {\left(4 i \, b^{3} f^{3} x^{3} + 12 i \, b^{3} e f^{2} x^{2} + 12 i \, b^{3} e^{2} f x + 4 i \, b^{3} e^{3}\right)} {\rm Li}_2\left(i \, \cos\left(2 \, b x + 2 \, a\right) - \sin\left(2 \, b x + 2 \, a\right)\right) - {\left(-4 i \, b^{3} f^{3} x^{3} - 12 i \, b^{3} e f^{2} x^{2} - 12 i \, b^{3} e^{2} f x - 4 i \, b^{3} e^{3}\right)} {\rm Li}_2\left(-i \, \cos\left(2 \, b x + 2 \, a\right) + \sin\left(2 \, b x + 2 \, a\right)\right) - {\left(-4 i \, b^{3} f^{3} x^{3} - 12 i \, b^{3} e f^{2} x^{2} - 12 i \, b^{3} e^{2} f x - 4 i \, b^{3} e^{3}\right)} {\rm Li}_2\left(-i \, \cos\left(2 \, b x + 2 \, a\right) - \sin\left(2 \, b x + 2 \, a\right)\right) - 4 \, {\left(b^{4} f^{3} x^{4} + 4 \, b^{4} e f^{2} x^{3} + 6 \, b^{4} e^{2} f x^{2} + 4 \, b^{4} e^{3} x\right)} \log\left(\frac{\cos\left(2 \, b x + 2 \, a\right) + \sin\left(2 \, b x + 2 \, a\right) + 1}{\cos\left(2 \, b x + 2 \, a\right) - \sin\left(2 \, b x + 2 \, a\right) + 1}\right) - 2 \, {\left(4 \, a b^{3} e^{3} - 6 \, a^{2} b^{2} e^{2} f + 4 \, a^{3} b e f^{2} - a^{4} f^{3}\right)} \log\left(\cos\left(2 \, b x + 2 \, a\right) + i \, \sin\left(2 \, b x + 2 \, a\right) + i\right) + 2 \, {\left(4 \, a b^{3} e^{3} - 6 \, a^{2} b^{2} e^{2} f + 4 \, a^{3} b e f^{2} - a^{4} f^{3}\right)} \log\left(\cos\left(2 \, b x + 2 \, a\right) - i \, \sin\left(2 \, b x + 2 \, a\right) + i\right) + 2 \, {\left(b^{4} f^{3} x^{4} + 4 \, b^{4} e f^{2} x^{3} + 6 \, b^{4} e^{2} f x^{2} + 4 \, b^{4} e^{3} x + 4 \, a b^{3} e^{3} - 6 \, a^{2} b^{2} e^{2} f + 4 \, a^{3} b e f^{2} - a^{4} f^{3}\right)} \log\left(i \, \cos\left(2 \, b x + 2 \, a\right) + \sin\left(2 \, b x + 2 \, a\right) + 1\right) - 2 \, {\left(b^{4} f^{3} x^{4} + 4 \, b^{4} e f^{2} x^{3} + 6 \, b^{4} e^{2} f x^{2} + 4 \, b^{4} e^{3} x + 4 \, a b^{3} e^{3} - 6 \, a^{2} b^{2} e^{2} f + 4 \, a^{3} b e f^{2} - a^{4} f^{3}\right)} \log\left(i \, \cos\left(2 \, b x + 2 \, a\right) - \sin\left(2 \, b x + 2 \, a\right) + 1\right) + 2 \, {\left(b^{4} f^{3} x^{4} + 4 \, b^{4} e f^{2} x^{3} + 6 \, b^{4} e^{2} f x^{2} + 4 \, b^{4} e^{3} x + 4 \, a b^{3} e^{3} - 6 \, a^{2} b^{2} e^{2} f + 4 \, a^{3} b e f^{2} - a^{4} f^{3}\right)} \log\left(-i \, \cos\left(2 \, b x + 2 \, a\right) + \sin\left(2 \, b x + 2 \, a\right) + 1\right) - 2 \, {\left(b^{4} f^{3} x^{4} + 4 \, b^{4} e f^{2} x^{3} + 6 \, b^{4} e^{2} f x^{2} + 4 \, b^{4} e^{3} x + 4 \, a b^{3} e^{3} - 6 \, a^{2} b^{2} e^{2} f + 4 \, a^{3} b e f^{2} - a^{4} f^{3}\right)} \log\left(-i \, \cos\left(2 \, b x + 2 \, a\right) - \sin\left(2 \, b x + 2 \, a\right) + 1\right) - 2 \, {\left(4 \, a b^{3} e^{3} - 6 \, a^{2} b^{2} e^{2} f + 4 \, a^{3} b e f^{2} - a^{4} f^{3}\right)} \log\left(-\cos\left(2 \, b x + 2 \, a\right) + i \, \sin\left(2 \, b x + 2 \, a\right) + i\right) + 2 \, {\left(4 \, a b^{3} e^{3} - 6 \, a^{2} b^{2} e^{2} f + 4 \, a^{3} b e f^{2} - a^{4} f^{3}\right)} \log\left(-\cos\left(2 \, b x + 2 \, a\right) - i \, \sin\left(2 \, b x + 2 \, a\right) + i\right) - {\left(-6 i \, b f^{3} x - 6 i \, b e f^{2}\right)} {\rm polylog}\left(4, i \, \cos\left(2 \, b x + 2 \, a\right) + \sin\left(2 \, b x + 2 \, a\right)\right) - {\left(-6 i \, b f^{3} x - 6 i \, b e f^{2}\right)} {\rm polylog}\left(4, i \, \cos\left(2 \, b x + 2 \, a\right) - \sin\left(2 \, b x + 2 \, a\right)\right) - {\left(6 i \, b f^{3} x + 6 i \, b e f^{2}\right)} {\rm polylog}\left(4, -i \, \cos\left(2 \, b x + 2 \, a\right) + \sin\left(2 \, b x + 2 \, a\right)\right) - {\left(6 i \, b f^{3} x + 6 i \, b e f^{2}\right)} {\rm polylog}\left(4, -i \, \cos\left(2 \, b x + 2 \, a\right) - \sin\left(2 \, b x + 2 \, a\right)\right) - 6 \, {\left(b^{2} f^{3} x^{2} + 2 \, b^{2} e f^{2} x + b^{2} e^{2} f\right)} {\rm polylog}\left(3, i \, \cos\left(2 \, b x + 2 \, a\right) + \sin\left(2 \, b x + 2 \, a\right)\right) + 6 \, {\left(b^{2} f^{3} x^{2} + 2 \, b^{2} e f^{2} x + b^{2} e^{2} f\right)} {\rm polylog}\left(3, i \, \cos\left(2 \, b x + 2 \, a\right) - \sin\left(2 \, b x + 2 \, a\right)\right) - 6 \, {\left(b^{2} f^{3} x^{2} + 2 \, b^{2} e f^{2} x + b^{2} e^{2} f\right)} {\rm polylog}\left(3, -i \, \cos\left(2 \, b x + 2 \, a\right) + \sin\left(2 \, b x + 2 \, a\right)\right) + 6 \, {\left(b^{2} f^{3} x^{2} + 2 \, b^{2} e f^{2} x + b^{2} e^{2} f\right)} {\rm polylog}\left(3, -i \, \cos\left(2 \, b x + 2 \, a\right) - \sin\left(2 \, b x + 2 \, a\right)\right)}{32 \, b^{4}}"," ",0,"-1/32*(3*f^3*polylog(5, I*cos(2*b*x + 2*a) + sin(2*b*x + 2*a)) - 3*f^3*polylog(5, I*cos(2*b*x + 2*a) - sin(2*b*x + 2*a)) + 3*f^3*polylog(5, -I*cos(2*b*x + 2*a) + sin(2*b*x + 2*a)) - 3*f^3*polylog(5, -I*cos(2*b*x + 2*a) - sin(2*b*x + 2*a)) - (4*I*b^3*f^3*x^3 + 12*I*b^3*e*f^2*x^2 + 12*I*b^3*e^2*f*x + 4*I*b^3*e^3)*dilog(I*cos(2*b*x + 2*a) + sin(2*b*x + 2*a)) - (4*I*b^3*f^3*x^3 + 12*I*b^3*e*f^2*x^2 + 12*I*b^3*e^2*f*x + 4*I*b^3*e^3)*dilog(I*cos(2*b*x + 2*a) - sin(2*b*x + 2*a)) - (-4*I*b^3*f^3*x^3 - 12*I*b^3*e*f^2*x^2 - 12*I*b^3*e^2*f*x - 4*I*b^3*e^3)*dilog(-I*cos(2*b*x + 2*a) + sin(2*b*x + 2*a)) - (-4*I*b^3*f^3*x^3 - 12*I*b^3*e*f^2*x^2 - 12*I*b^3*e^2*f*x - 4*I*b^3*e^3)*dilog(-I*cos(2*b*x + 2*a) - sin(2*b*x + 2*a)) - 4*(b^4*f^3*x^4 + 4*b^4*e*f^2*x^3 + 6*b^4*e^2*f*x^2 + 4*b^4*e^3*x)*log((cos(2*b*x + 2*a) + sin(2*b*x + 2*a) + 1)/(cos(2*b*x + 2*a) - sin(2*b*x + 2*a) + 1)) - 2*(4*a*b^3*e^3 - 6*a^2*b^2*e^2*f + 4*a^3*b*e*f^2 - a^4*f^3)*log(cos(2*b*x + 2*a) + I*sin(2*b*x + 2*a) + I) + 2*(4*a*b^3*e^3 - 6*a^2*b^2*e^2*f + 4*a^3*b*e*f^2 - a^4*f^3)*log(cos(2*b*x + 2*a) - I*sin(2*b*x + 2*a) + I) + 2*(b^4*f^3*x^4 + 4*b^4*e*f^2*x^3 + 6*b^4*e^2*f*x^2 + 4*b^4*e^3*x + 4*a*b^3*e^3 - 6*a^2*b^2*e^2*f + 4*a^3*b*e*f^2 - a^4*f^3)*log(I*cos(2*b*x + 2*a) + sin(2*b*x + 2*a) + 1) - 2*(b^4*f^3*x^4 + 4*b^4*e*f^2*x^3 + 6*b^4*e^2*f*x^2 + 4*b^4*e^3*x + 4*a*b^3*e^3 - 6*a^2*b^2*e^2*f + 4*a^3*b*e*f^2 - a^4*f^3)*log(I*cos(2*b*x + 2*a) - sin(2*b*x + 2*a) + 1) + 2*(b^4*f^3*x^4 + 4*b^4*e*f^2*x^3 + 6*b^4*e^2*f*x^2 + 4*b^4*e^3*x + 4*a*b^3*e^3 - 6*a^2*b^2*e^2*f + 4*a^3*b*e*f^2 - a^4*f^3)*log(-I*cos(2*b*x + 2*a) + sin(2*b*x + 2*a) + 1) - 2*(b^4*f^3*x^4 + 4*b^4*e*f^2*x^3 + 6*b^4*e^2*f*x^2 + 4*b^4*e^3*x + 4*a*b^3*e^3 - 6*a^2*b^2*e^2*f + 4*a^3*b*e*f^2 - a^4*f^3)*log(-I*cos(2*b*x + 2*a) - sin(2*b*x + 2*a) + 1) - 2*(4*a*b^3*e^3 - 6*a^2*b^2*e^2*f + 4*a^3*b*e*f^2 - a^4*f^3)*log(-cos(2*b*x + 2*a) + I*sin(2*b*x + 2*a) + I) + 2*(4*a*b^3*e^3 - 6*a^2*b^2*e^2*f + 4*a^3*b*e*f^2 - a^4*f^3)*log(-cos(2*b*x + 2*a) - I*sin(2*b*x + 2*a) + I) - (-6*I*b*f^3*x - 6*I*b*e*f^2)*polylog(4, I*cos(2*b*x + 2*a) + sin(2*b*x + 2*a)) - (-6*I*b*f^3*x - 6*I*b*e*f^2)*polylog(4, I*cos(2*b*x + 2*a) - sin(2*b*x + 2*a)) - (6*I*b*f^3*x + 6*I*b*e*f^2)*polylog(4, -I*cos(2*b*x + 2*a) + sin(2*b*x + 2*a)) - (6*I*b*f^3*x + 6*I*b*e*f^2)*polylog(4, -I*cos(2*b*x + 2*a) - sin(2*b*x + 2*a)) - 6*(b^2*f^3*x^2 + 2*b^2*e*f^2*x + b^2*e^2*f)*polylog(3, I*cos(2*b*x + 2*a) + sin(2*b*x + 2*a)) + 6*(b^2*f^3*x^2 + 2*b^2*e*f^2*x + b^2*e^2*f)*polylog(3, I*cos(2*b*x + 2*a) - sin(2*b*x + 2*a)) - 6*(b^2*f^3*x^2 + 2*b^2*e*f^2*x + b^2*e^2*f)*polylog(3, -I*cos(2*b*x + 2*a) + sin(2*b*x + 2*a)) + 6*(b^2*f^3*x^2 + 2*b^2*e*f^2*x + b^2*e^2*f)*polylog(3, -I*cos(2*b*x + 2*a) - sin(2*b*x + 2*a)))/b^4","C",0
249,1,1080,0,0.721979," ","integrate((f*x+e)^2*arccoth(cot(b*x+a)),x, algorithm=""fricas"")","\frac{-3 i \, f^{2} {\rm polylog}\left(4, i \, \cos\left(2 \, b x + 2 \, a\right) + \sin\left(2 \, b x + 2 \, a\right)\right) - 3 i \, f^{2} {\rm polylog}\left(4, i \, \cos\left(2 \, b x + 2 \, a\right) - \sin\left(2 \, b x + 2 \, a\right)\right) + 3 i \, f^{2} {\rm polylog}\left(4, -i \, \cos\left(2 \, b x + 2 \, a\right) + \sin\left(2 \, b x + 2 \, a\right)\right) + 3 i \, f^{2} {\rm polylog}\left(4, -i \, \cos\left(2 \, b x + 2 \, a\right) - \sin\left(2 \, b x + 2 \, a\right)\right) + {\left(6 i \, b^{2} f^{2} x^{2} + 12 i \, b^{2} e f x + 6 i \, b^{2} e^{2}\right)} {\rm Li}_2\left(i \, \cos\left(2 \, b x + 2 \, a\right) + \sin\left(2 \, b x + 2 \, a\right)\right) + {\left(6 i \, b^{2} f^{2} x^{2} + 12 i \, b^{2} e f x + 6 i \, b^{2} e^{2}\right)} {\rm Li}_2\left(i \, \cos\left(2 \, b x + 2 \, a\right) - \sin\left(2 \, b x + 2 \, a\right)\right) + {\left(-6 i \, b^{2} f^{2} x^{2} - 12 i \, b^{2} e f x - 6 i \, b^{2} e^{2}\right)} {\rm Li}_2\left(-i \, \cos\left(2 \, b x + 2 \, a\right) + \sin\left(2 \, b x + 2 \, a\right)\right) + {\left(-6 i \, b^{2} f^{2} x^{2} - 12 i \, b^{2} e f x - 6 i \, b^{2} e^{2}\right)} {\rm Li}_2\left(-i \, \cos\left(2 \, b x + 2 \, a\right) - \sin\left(2 \, b x + 2 \, a\right)\right) + 8 \, {\left(b^{3} f^{2} x^{3} + 3 \, b^{3} e f x^{2} + 3 \, b^{3} e^{2} x\right)} \log\left(\frac{\cos\left(2 \, b x + 2 \, a\right) + \sin\left(2 \, b x + 2 \, a\right) + 1}{\cos\left(2 \, b x + 2 \, a\right) - \sin\left(2 \, b x + 2 \, a\right) + 1}\right) + 4 \, {\left(3 \, a b^{2} e^{2} - 3 \, a^{2} b e f + a^{3} f^{2}\right)} \log\left(\cos\left(2 \, b x + 2 \, a\right) + i \, \sin\left(2 \, b x + 2 \, a\right) + i\right) - 4 \, {\left(3 \, a b^{2} e^{2} - 3 \, a^{2} b e f + a^{3} f^{2}\right)} \log\left(\cos\left(2 \, b x + 2 \, a\right) - i \, \sin\left(2 \, b x + 2 \, a\right) + i\right) - 4 \, {\left(b^{3} f^{2} x^{3} + 3 \, b^{3} e f x^{2} + 3 \, b^{3} e^{2} x + 3 \, a b^{2} e^{2} - 3 \, a^{2} b e f + a^{3} f^{2}\right)} \log\left(i \, \cos\left(2 \, b x + 2 \, a\right) + \sin\left(2 \, b x + 2 \, a\right) + 1\right) + 4 \, {\left(b^{3} f^{2} x^{3} + 3 \, b^{3} e f x^{2} + 3 \, b^{3} e^{2} x + 3 \, a b^{2} e^{2} - 3 \, a^{2} b e f + a^{3} f^{2}\right)} \log\left(i \, \cos\left(2 \, b x + 2 \, a\right) - \sin\left(2 \, b x + 2 \, a\right) + 1\right) - 4 \, {\left(b^{3} f^{2} x^{3} + 3 \, b^{3} e f x^{2} + 3 \, b^{3} e^{2} x + 3 \, a b^{2} e^{2} - 3 \, a^{2} b e f + a^{3} f^{2}\right)} \log\left(-i \, \cos\left(2 \, b x + 2 \, a\right) + \sin\left(2 \, b x + 2 \, a\right) + 1\right) + 4 \, {\left(b^{3} f^{2} x^{3} + 3 \, b^{3} e f x^{2} + 3 \, b^{3} e^{2} x + 3 \, a b^{2} e^{2} - 3 \, a^{2} b e f + a^{3} f^{2}\right)} \log\left(-i \, \cos\left(2 \, b x + 2 \, a\right) - \sin\left(2 \, b x + 2 \, a\right) + 1\right) + 4 \, {\left(3 \, a b^{2} e^{2} - 3 \, a^{2} b e f + a^{3} f^{2}\right)} \log\left(-\cos\left(2 \, b x + 2 \, a\right) + i \, \sin\left(2 \, b x + 2 \, a\right) + i\right) - 4 \, {\left(3 \, a b^{2} e^{2} - 3 \, a^{2} b e f + a^{3} f^{2}\right)} \log\left(-\cos\left(2 \, b x + 2 \, a\right) - i \, \sin\left(2 \, b x + 2 \, a\right) + i\right) + 6 \, {\left(b f^{2} x + b e f\right)} {\rm polylog}\left(3, i \, \cos\left(2 \, b x + 2 \, a\right) + \sin\left(2 \, b x + 2 \, a\right)\right) - 6 \, {\left(b f^{2} x + b e f\right)} {\rm polylog}\left(3, i \, \cos\left(2 \, b x + 2 \, a\right) - \sin\left(2 \, b x + 2 \, a\right)\right) + 6 \, {\left(b f^{2} x + b e f\right)} {\rm polylog}\left(3, -i \, \cos\left(2 \, b x + 2 \, a\right) + \sin\left(2 \, b x + 2 \, a\right)\right) - 6 \, {\left(b f^{2} x + b e f\right)} {\rm polylog}\left(3, -i \, \cos\left(2 \, b x + 2 \, a\right) - \sin\left(2 \, b x + 2 \, a\right)\right)}{48 \, b^{3}}"," ",0,"1/48*(-3*I*f^2*polylog(4, I*cos(2*b*x + 2*a) + sin(2*b*x + 2*a)) - 3*I*f^2*polylog(4, I*cos(2*b*x + 2*a) - sin(2*b*x + 2*a)) + 3*I*f^2*polylog(4, -I*cos(2*b*x + 2*a) + sin(2*b*x + 2*a)) + 3*I*f^2*polylog(4, -I*cos(2*b*x + 2*a) - sin(2*b*x + 2*a)) + (6*I*b^2*f^2*x^2 + 12*I*b^2*e*f*x + 6*I*b^2*e^2)*dilog(I*cos(2*b*x + 2*a) + sin(2*b*x + 2*a)) + (6*I*b^2*f^2*x^2 + 12*I*b^2*e*f*x + 6*I*b^2*e^2)*dilog(I*cos(2*b*x + 2*a) - sin(2*b*x + 2*a)) + (-6*I*b^2*f^2*x^2 - 12*I*b^2*e*f*x - 6*I*b^2*e^2)*dilog(-I*cos(2*b*x + 2*a) + sin(2*b*x + 2*a)) + (-6*I*b^2*f^2*x^2 - 12*I*b^2*e*f*x - 6*I*b^2*e^2)*dilog(-I*cos(2*b*x + 2*a) - sin(2*b*x + 2*a)) + 8*(b^3*f^2*x^3 + 3*b^3*e*f*x^2 + 3*b^3*e^2*x)*log((cos(2*b*x + 2*a) + sin(2*b*x + 2*a) + 1)/(cos(2*b*x + 2*a) - sin(2*b*x + 2*a) + 1)) + 4*(3*a*b^2*e^2 - 3*a^2*b*e*f + a^3*f^2)*log(cos(2*b*x + 2*a) + I*sin(2*b*x + 2*a) + I) - 4*(3*a*b^2*e^2 - 3*a^2*b*e*f + a^3*f^2)*log(cos(2*b*x + 2*a) - I*sin(2*b*x + 2*a) + I) - 4*(b^3*f^2*x^3 + 3*b^3*e*f*x^2 + 3*b^3*e^2*x + 3*a*b^2*e^2 - 3*a^2*b*e*f + a^3*f^2)*log(I*cos(2*b*x + 2*a) + sin(2*b*x + 2*a) + 1) + 4*(b^3*f^2*x^3 + 3*b^3*e*f*x^2 + 3*b^3*e^2*x + 3*a*b^2*e^2 - 3*a^2*b*e*f + a^3*f^2)*log(I*cos(2*b*x + 2*a) - sin(2*b*x + 2*a) + 1) - 4*(b^3*f^2*x^3 + 3*b^3*e*f*x^2 + 3*b^3*e^2*x + 3*a*b^2*e^2 - 3*a^2*b*e*f + a^3*f^2)*log(-I*cos(2*b*x + 2*a) + sin(2*b*x + 2*a) + 1) + 4*(b^3*f^2*x^3 + 3*b^3*e*f*x^2 + 3*b^3*e^2*x + 3*a*b^2*e^2 - 3*a^2*b*e*f + a^3*f^2)*log(-I*cos(2*b*x + 2*a) - sin(2*b*x + 2*a) + 1) + 4*(3*a*b^2*e^2 - 3*a^2*b*e*f + a^3*f^2)*log(-cos(2*b*x + 2*a) + I*sin(2*b*x + 2*a) + I) - 4*(3*a*b^2*e^2 - 3*a^2*b*e*f + a^3*f^2)*log(-cos(2*b*x + 2*a) - I*sin(2*b*x + 2*a) + I) + 6*(b*f^2*x + b*e*f)*polylog(3, I*cos(2*b*x + 2*a) + sin(2*b*x + 2*a)) - 6*(b*f^2*x + b*e*f)*polylog(3, I*cos(2*b*x + 2*a) - sin(2*b*x + 2*a)) + 6*(b*f^2*x + b*e*f)*polylog(3, -I*cos(2*b*x + 2*a) + sin(2*b*x + 2*a)) - 6*(b*f^2*x + b*e*f)*polylog(3, -I*cos(2*b*x + 2*a) - sin(2*b*x + 2*a)))/b^3","C",0
250,1,676,0,0.560356," ","integrate((f*x+e)*arccoth(cot(b*x+a)),x, algorithm=""fricas"")","\frac{{\left(2 i \, b f x + 2 i \, b e\right)} {\rm Li}_2\left(i \, \cos\left(2 \, b x + 2 \, a\right) + \sin\left(2 \, b x + 2 \, a\right)\right) + {\left(2 i \, b f x + 2 i \, b e\right)} {\rm Li}_2\left(i \, \cos\left(2 \, b x + 2 \, a\right) - \sin\left(2 \, b x + 2 \, a\right)\right) + {\left(-2 i \, b f x - 2 i \, b e\right)} {\rm Li}_2\left(-i \, \cos\left(2 \, b x + 2 \, a\right) + \sin\left(2 \, b x + 2 \, a\right)\right) + {\left(-2 i \, b f x - 2 i \, b e\right)} {\rm Li}_2\left(-i \, \cos\left(2 \, b x + 2 \, a\right) - \sin\left(2 \, b x + 2 \, a\right)\right) + 4 \, {\left(b^{2} f x^{2} + 2 \, b^{2} e x\right)} \log\left(\frac{\cos\left(2 \, b x + 2 \, a\right) + \sin\left(2 \, b x + 2 \, a\right) + 1}{\cos\left(2 \, b x + 2 \, a\right) - \sin\left(2 \, b x + 2 \, a\right) + 1}\right) + 2 \, {\left(2 \, a b e - a^{2} f\right)} \log\left(\cos\left(2 \, b x + 2 \, a\right) + i \, \sin\left(2 \, b x + 2 \, a\right) + i\right) - 2 \, {\left(2 \, a b e - a^{2} f\right)} \log\left(\cos\left(2 \, b x + 2 \, a\right) - i \, \sin\left(2 \, b x + 2 \, a\right) + i\right) - 2 \, {\left(b^{2} f x^{2} + 2 \, b^{2} e x + 2 \, a b e - a^{2} f\right)} \log\left(i \, \cos\left(2 \, b x + 2 \, a\right) + \sin\left(2 \, b x + 2 \, a\right) + 1\right) + 2 \, {\left(b^{2} f x^{2} + 2 \, b^{2} e x + 2 \, a b e - a^{2} f\right)} \log\left(i \, \cos\left(2 \, b x + 2 \, a\right) - \sin\left(2 \, b x + 2 \, a\right) + 1\right) - 2 \, {\left(b^{2} f x^{2} + 2 \, b^{2} e x + 2 \, a b e - a^{2} f\right)} \log\left(-i \, \cos\left(2 \, b x + 2 \, a\right) + \sin\left(2 \, b x + 2 \, a\right) + 1\right) + 2 \, {\left(b^{2} f x^{2} + 2 \, b^{2} e x + 2 \, a b e - a^{2} f\right)} \log\left(-i \, \cos\left(2 \, b x + 2 \, a\right) - \sin\left(2 \, b x + 2 \, a\right) + 1\right) + 2 \, {\left(2 \, a b e - a^{2} f\right)} \log\left(-\cos\left(2 \, b x + 2 \, a\right) + i \, \sin\left(2 \, b x + 2 \, a\right) + i\right) - 2 \, {\left(2 \, a b e - a^{2} f\right)} \log\left(-\cos\left(2 \, b x + 2 \, a\right) - i \, \sin\left(2 \, b x + 2 \, a\right) + i\right) + f {\rm polylog}\left(3, i \, \cos\left(2 \, b x + 2 \, a\right) + \sin\left(2 \, b x + 2 \, a\right)\right) - f {\rm polylog}\left(3, i \, \cos\left(2 \, b x + 2 \, a\right) - \sin\left(2 \, b x + 2 \, a\right)\right) + f {\rm polylog}\left(3, -i \, \cos\left(2 \, b x + 2 \, a\right) + \sin\left(2 \, b x + 2 \, a\right)\right) - f {\rm polylog}\left(3, -i \, \cos\left(2 \, b x + 2 \, a\right) - \sin\left(2 \, b x + 2 \, a\right)\right)}{16 \, b^{2}}"," ",0,"1/16*((2*I*b*f*x + 2*I*b*e)*dilog(I*cos(2*b*x + 2*a) + sin(2*b*x + 2*a)) + (2*I*b*f*x + 2*I*b*e)*dilog(I*cos(2*b*x + 2*a) - sin(2*b*x + 2*a)) + (-2*I*b*f*x - 2*I*b*e)*dilog(-I*cos(2*b*x + 2*a) + sin(2*b*x + 2*a)) + (-2*I*b*f*x - 2*I*b*e)*dilog(-I*cos(2*b*x + 2*a) - sin(2*b*x + 2*a)) + 4*(b^2*f*x^2 + 2*b^2*e*x)*log((cos(2*b*x + 2*a) + sin(2*b*x + 2*a) + 1)/(cos(2*b*x + 2*a) - sin(2*b*x + 2*a) + 1)) + 2*(2*a*b*e - a^2*f)*log(cos(2*b*x + 2*a) + I*sin(2*b*x + 2*a) + I) - 2*(2*a*b*e - a^2*f)*log(cos(2*b*x + 2*a) - I*sin(2*b*x + 2*a) + I) - 2*(b^2*f*x^2 + 2*b^2*e*x + 2*a*b*e - a^2*f)*log(I*cos(2*b*x + 2*a) + sin(2*b*x + 2*a) + 1) + 2*(b^2*f*x^2 + 2*b^2*e*x + 2*a*b*e - a^2*f)*log(I*cos(2*b*x + 2*a) - sin(2*b*x + 2*a) + 1) - 2*(b^2*f*x^2 + 2*b^2*e*x + 2*a*b*e - a^2*f)*log(-I*cos(2*b*x + 2*a) + sin(2*b*x + 2*a) + 1) + 2*(b^2*f*x^2 + 2*b^2*e*x + 2*a*b*e - a^2*f)*log(-I*cos(2*b*x + 2*a) - sin(2*b*x + 2*a) + 1) + 2*(2*a*b*e - a^2*f)*log(-cos(2*b*x + 2*a) + I*sin(2*b*x + 2*a) + I) - 2*(2*a*b*e - a^2*f)*log(-cos(2*b*x + 2*a) - I*sin(2*b*x + 2*a) + I) + f*polylog(3, I*cos(2*b*x + 2*a) + sin(2*b*x + 2*a)) - f*polylog(3, I*cos(2*b*x + 2*a) - sin(2*b*x + 2*a)) + f*polylog(3, -I*cos(2*b*x + 2*a) + sin(2*b*x + 2*a)) - f*polylog(3, -I*cos(2*b*x + 2*a) - sin(2*b*x + 2*a)))/b^2","C",0
251,1,388,0,0.694410," ","integrate(arccoth(cot(b*x+a)),x, algorithm=""fricas"")","\frac{4 \, b x \log\left(\frac{\cos\left(2 \, b x + 2 \, a\right) + \sin\left(2 \, b x + 2 \, a\right) + 1}{\cos\left(2 \, b x + 2 \, a\right) - \sin\left(2 \, b x + 2 \, a\right) + 1}\right) + 2 \, a \log\left(\cos\left(2 \, b x + 2 \, a\right) + i \, \sin\left(2 \, b x + 2 \, a\right) + i\right) - 2 \, a \log\left(\cos\left(2 \, b x + 2 \, a\right) - i \, \sin\left(2 \, b x + 2 \, a\right) + i\right) - 2 \, {\left(b x + a\right)} \log\left(i \, \cos\left(2 \, b x + 2 \, a\right) + \sin\left(2 \, b x + 2 \, a\right) + 1\right) + 2 \, {\left(b x + a\right)} \log\left(i \, \cos\left(2 \, b x + 2 \, a\right) - \sin\left(2 \, b x + 2 \, a\right) + 1\right) - 2 \, {\left(b x + a\right)} \log\left(-i \, \cos\left(2 \, b x + 2 \, a\right) + \sin\left(2 \, b x + 2 \, a\right) + 1\right) + 2 \, {\left(b x + a\right)} \log\left(-i \, \cos\left(2 \, b x + 2 \, a\right) - \sin\left(2 \, b x + 2 \, a\right) + 1\right) + 2 \, a \log\left(-\cos\left(2 \, b x + 2 \, a\right) + i \, \sin\left(2 \, b x + 2 \, a\right) + i\right) - 2 \, a \log\left(-\cos\left(2 \, b x + 2 \, a\right) - i \, \sin\left(2 \, b x + 2 \, a\right) + i\right) + i \, {\rm Li}_2\left(i \, \cos\left(2 \, b x + 2 \, a\right) + \sin\left(2 \, b x + 2 \, a\right)\right) + i \, {\rm Li}_2\left(i \, \cos\left(2 \, b x + 2 \, a\right) - \sin\left(2 \, b x + 2 \, a\right)\right) - i \, {\rm Li}_2\left(-i \, \cos\left(2 \, b x + 2 \, a\right) + \sin\left(2 \, b x + 2 \, a\right)\right) - i \, {\rm Li}_2\left(-i \, \cos\left(2 \, b x + 2 \, a\right) - \sin\left(2 \, b x + 2 \, a\right)\right)}{8 \, b}"," ",0,"1/8*(4*b*x*log((cos(2*b*x + 2*a) + sin(2*b*x + 2*a) + 1)/(cos(2*b*x + 2*a) - sin(2*b*x + 2*a) + 1)) + 2*a*log(cos(2*b*x + 2*a) + I*sin(2*b*x + 2*a) + I) - 2*a*log(cos(2*b*x + 2*a) - I*sin(2*b*x + 2*a) + I) - 2*(b*x + a)*log(I*cos(2*b*x + 2*a) + sin(2*b*x + 2*a) + 1) + 2*(b*x + a)*log(I*cos(2*b*x + 2*a) - sin(2*b*x + 2*a) + 1) - 2*(b*x + a)*log(-I*cos(2*b*x + 2*a) + sin(2*b*x + 2*a) + 1) + 2*(b*x + a)*log(-I*cos(2*b*x + 2*a) - sin(2*b*x + 2*a) + 1) + 2*a*log(-cos(2*b*x + 2*a) + I*sin(2*b*x + 2*a) + I) - 2*a*log(-cos(2*b*x + 2*a) - I*sin(2*b*x + 2*a) + I) + I*dilog(I*cos(2*b*x + 2*a) + sin(2*b*x + 2*a)) + I*dilog(I*cos(2*b*x + 2*a) - sin(2*b*x + 2*a)) - I*dilog(-I*cos(2*b*x + 2*a) + sin(2*b*x + 2*a)) - I*dilog(-I*cos(2*b*x + 2*a) - sin(2*b*x + 2*a)))/b","B",0
252,0,0,0,0.593064," ","integrate(arccoth(cot(b*x+a))/(f*x+e),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{arcoth}\left(\cot\left(b x + a\right)\right)}{f x + e}, x\right)"," ",0,"integral(arccoth(cot(b*x + a))/(f*x + e), x)","F",0
253,1,1798,0,0.832522," ","integrate(x^2*arccoth(c+d*cot(b*x+a)),x, algorithm=""fricas"")","\frac{8 \, b^{3} x^{3} \log\left(\frac{d \cos\left(2 \, b x + 2 \, a\right) + {\left(c + 1\right)} \sin\left(2 \, b x + 2 \, a\right) + d}{d \cos\left(2 \, b x + 2 \, a\right) + {\left(c - 1\right)} \sin\left(2 \, b x + 2 \, a\right) + d}\right) + 6 i \, b^{2} x^{2} {\rm Li}_2\left(-\frac{c^{2} + d^{2} - {\left(c^{2} + 2 i \, {\left(c + 1\right)} d - d^{2} + 2 \, c + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(-i \, c^{2} + 2 \, {\left(c + 1\right)} d + i \, d^{2} - 2 i \, c - i\right)} \sin\left(2 \, b x + 2 \, a\right) + 2 \, c + 1}{c^{2} + d^{2} + 2 \, c + 1} + 1\right) - 6 i \, b^{2} x^{2} {\rm Li}_2\left(-\frac{c^{2} + d^{2} - {\left(c^{2} - 2 i \, {\left(c + 1\right)} d - d^{2} + 2 \, c + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(i \, c^{2} + 2 \, {\left(c + 1\right)} d - i \, d^{2} + 2 i \, c + i\right)} \sin\left(2 \, b x + 2 \, a\right) + 2 \, c + 1}{c^{2} + d^{2} + 2 \, c + 1} + 1\right) - 6 i \, b^{2} x^{2} {\rm Li}_2\left(-\frac{c^{2} + d^{2} - {\left(c^{2} + 2 i \, {\left(c - 1\right)} d - d^{2} - 2 \, c + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(-i \, c^{2} + 2 \, {\left(c - 1\right)} d + i \, d^{2} + 2 i \, c - i\right)} \sin\left(2 \, b x + 2 \, a\right) - 2 \, c + 1}{c^{2} + d^{2} - 2 \, c + 1} + 1\right) + 6 i \, b^{2} x^{2} {\rm Li}_2\left(-\frac{c^{2} + d^{2} - {\left(c^{2} - 2 i \, {\left(c - 1\right)} d - d^{2} - 2 \, c + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(i \, c^{2} + 2 \, {\left(c - 1\right)} d - i \, d^{2} - 2 i \, c + i\right)} \sin\left(2 \, b x + 2 \, a\right) - 2 \, c + 1}{c^{2} + d^{2} - 2 \, c + 1} + 1\right) + 4 \, a^{3} \log\left(\frac{1}{2} \, c^{2} + i \, {\left(c + 1\right)} d - \frac{1}{2} \, d^{2} - \frac{1}{2} \, {\left(c^{2} + d^{2} + 2 \, c + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + \frac{1}{2} \, {\left(i \, c^{2} + i \, d^{2} + 2 i \, c + i\right)} \sin\left(2 \, b x + 2 \, a\right) + c + \frac{1}{2}\right) - 4 \, a^{3} \log\left(\frac{1}{2} \, c^{2} + i \, {\left(c - 1\right)} d - \frac{1}{2} \, d^{2} - \frac{1}{2} \, {\left(c^{2} + d^{2} - 2 \, c + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + \frac{1}{2} \, {\left(i \, c^{2} + i \, d^{2} - 2 i \, c + i\right)} \sin\left(2 \, b x + 2 \, a\right) - c + \frac{1}{2}\right) + 4 \, a^{3} \log\left(-\frac{1}{2} \, c^{2} + i \, {\left(c + 1\right)} d + \frac{1}{2} \, d^{2} + \frac{1}{2} \, {\left(c^{2} + d^{2} + 2 \, c + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + \frac{1}{2} \, {\left(i \, c^{2} + i \, d^{2} + 2 i \, c + i\right)} \sin\left(2 \, b x + 2 \, a\right) - c - \frac{1}{2}\right) - 4 \, a^{3} \log\left(-\frac{1}{2} \, c^{2} + i \, {\left(c - 1\right)} d + \frac{1}{2} \, d^{2} + \frac{1}{2} \, {\left(c^{2} + d^{2} - 2 \, c + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + \frac{1}{2} \, {\left(i \, c^{2} + i \, d^{2} - 2 i \, c + i\right)} \sin\left(2 \, b x + 2 \, a\right) + c - \frac{1}{2}\right) - 6 \, b x {\rm polylog}\left(3, \frac{{\left(c^{2} + 2 i \, {\left(c + 1\right)} d - d^{2} + 2 \, c + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(i \, c^{2} - 2 \, {\left(c + 1\right)} d - i \, d^{2} + 2 i \, c + i\right)} \sin\left(2 \, b x + 2 \, a\right)}{c^{2} + d^{2} + 2 \, c + 1}\right) - 6 \, b x {\rm polylog}\left(3, \frac{{\left(c^{2} - 2 i \, {\left(c + 1\right)} d - d^{2} + 2 \, c + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(-i \, c^{2} - 2 \, {\left(c + 1\right)} d + i \, d^{2} - 2 i \, c - i\right)} \sin\left(2 \, b x + 2 \, a\right)}{c^{2} + d^{2} + 2 \, c + 1}\right) + 6 \, b x {\rm polylog}\left(3, \frac{{\left(c^{2} + 2 i \, {\left(c - 1\right)} d - d^{2} - 2 \, c + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(i \, c^{2} - 2 \, {\left(c - 1\right)} d - i \, d^{2} - 2 i \, c + i\right)} \sin\left(2 \, b x + 2 \, a\right)}{c^{2} + d^{2} - 2 \, c + 1}\right) + 6 \, b x {\rm polylog}\left(3, \frac{{\left(c^{2} - 2 i \, {\left(c - 1\right)} d - d^{2} - 2 \, c + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(-i \, c^{2} - 2 \, {\left(c - 1\right)} d + i \, d^{2} + 2 i \, c - i\right)} \sin\left(2 \, b x + 2 \, a\right)}{c^{2} + d^{2} - 2 \, c + 1}\right) - 4 \, {\left(b^{3} x^{3} + a^{3}\right)} \log\left(\frac{c^{2} + d^{2} - {\left(c^{2} + 2 i \, {\left(c + 1\right)} d - d^{2} + 2 \, c + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(-i \, c^{2} + 2 \, {\left(c + 1\right)} d + i \, d^{2} - 2 i \, c - i\right)} \sin\left(2 \, b x + 2 \, a\right) + 2 \, c + 1}{c^{2} + d^{2} + 2 \, c + 1}\right) - 4 \, {\left(b^{3} x^{3} + a^{3}\right)} \log\left(\frac{c^{2} + d^{2} - {\left(c^{2} - 2 i \, {\left(c + 1\right)} d - d^{2} + 2 \, c + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(i \, c^{2} + 2 \, {\left(c + 1\right)} d - i \, d^{2} + 2 i \, c + i\right)} \sin\left(2 \, b x + 2 \, a\right) + 2 \, c + 1}{c^{2} + d^{2} + 2 \, c + 1}\right) + 4 \, {\left(b^{3} x^{3} + a^{3}\right)} \log\left(\frac{c^{2} + d^{2} - {\left(c^{2} + 2 i \, {\left(c - 1\right)} d - d^{2} - 2 \, c + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(-i \, c^{2} + 2 \, {\left(c - 1\right)} d + i \, d^{2} + 2 i \, c - i\right)} \sin\left(2 \, b x + 2 \, a\right) - 2 \, c + 1}{c^{2} + d^{2} - 2 \, c + 1}\right) + 4 \, {\left(b^{3} x^{3} + a^{3}\right)} \log\left(\frac{c^{2} + d^{2} - {\left(c^{2} - 2 i \, {\left(c - 1\right)} d - d^{2} - 2 \, c + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(i \, c^{2} + 2 \, {\left(c - 1\right)} d - i \, d^{2} - 2 i \, c + i\right)} \sin\left(2 \, b x + 2 \, a\right) - 2 \, c + 1}{c^{2} + d^{2} - 2 \, c + 1}\right) - 3 i \, {\rm polylog}\left(4, \frac{{\left(c^{2} + 2 i \, {\left(c + 1\right)} d - d^{2} + 2 \, c + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(i \, c^{2} - 2 \, {\left(c + 1\right)} d - i \, d^{2} + 2 i \, c + i\right)} \sin\left(2 \, b x + 2 \, a\right)}{c^{2} + d^{2} + 2 \, c + 1}\right) + 3 i \, {\rm polylog}\left(4, \frac{{\left(c^{2} - 2 i \, {\left(c + 1\right)} d - d^{2} + 2 \, c + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(-i \, c^{2} - 2 \, {\left(c + 1\right)} d + i \, d^{2} - 2 i \, c - i\right)} \sin\left(2 \, b x + 2 \, a\right)}{c^{2} + d^{2} + 2 \, c + 1}\right) + 3 i \, {\rm polylog}\left(4, \frac{{\left(c^{2} + 2 i \, {\left(c - 1\right)} d - d^{2} - 2 \, c + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(i \, c^{2} - 2 \, {\left(c - 1\right)} d - i \, d^{2} - 2 i \, c + i\right)} \sin\left(2 \, b x + 2 \, a\right)}{c^{2} + d^{2} - 2 \, c + 1}\right) - 3 i \, {\rm polylog}\left(4, \frac{{\left(c^{2} - 2 i \, {\left(c - 1\right)} d - d^{2} - 2 \, c + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(-i \, c^{2} - 2 \, {\left(c - 1\right)} d + i \, d^{2} + 2 i \, c - i\right)} \sin\left(2 \, b x + 2 \, a\right)}{c^{2} + d^{2} - 2 \, c + 1}\right)}{48 \, b^{3}}"," ",0,"1/48*(8*b^3*x^3*log((d*cos(2*b*x + 2*a) + (c + 1)*sin(2*b*x + 2*a) + d)/(d*cos(2*b*x + 2*a) + (c - 1)*sin(2*b*x + 2*a) + d)) + 6*I*b^2*x^2*dilog(-(c^2 + d^2 - (c^2 + 2*I*(c + 1)*d - d^2 + 2*c + 1)*cos(2*b*x + 2*a) + (-I*c^2 + 2*(c + 1)*d + I*d^2 - 2*I*c - I)*sin(2*b*x + 2*a) + 2*c + 1)/(c^2 + d^2 + 2*c + 1) + 1) - 6*I*b^2*x^2*dilog(-(c^2 + d^2 - (c^2 - 2*I*(c + 1)*d - d^2 + 2*c + 1)*cos(2*b*x + 2*a) + (I*c^2 + 2*(c + 1)*d - I*d^2 + 2*I*c + I)*sin(2*b*x + 2*a) + 2*c + 1)/(c^2 + d^2 + 2*c + 1) + 1) - 6*I*b^2*x^2*dilog(-(c^2 + d^2 - (c^2 + 2*I*(c - 1)*d - d^2 - 2*c + 1)*cos(2*b*x + 2*a) + (-I*c^2 + 2*(c - 1)*d + I*d^2 + 2*I*c - I)*sin(2*b*x + 2*a) - 2*c + 1)/(c^2 + d^2 - 2*c + 1) + 1) + 6*I*b^2*x^2*dilog(-(c^2 + d^2 - (c^2 - 2*I*(c - 1)*d - d^2 - 2*c + 1)*cos(2*b*x + 2*a) + (I*c^2 + 2*(c - 1)*d - I*d^2 - 2*I*c + I)*sin(2*b*x + 2*a) - 2*c + 1)/(c^2 + d^2 - 2*c + 1) + 1) + 4*a^3*log(1/2*c^2 + I*(c + 1)*d - 1/2*d^2 - 1/2*(c^2 + d^2 + 2*c + 1)*cos(2*b*x + 2*a) + 1/2*(I*c^2 + I*d^2 + 2*I*c + I)*sin(2*b*x + 2*a) + c + 1/2) - 4*a^3*log(1/2*c^2 + I*(c - 1)*d - 1/2*d^2 - 1/2*(c^2 + d^2 - 2*c + 1)*cos(2*b*x + 2*a) + 1/2*(I*c^2 + I*d^2 - 2*I*c + I)*sin(2*b*x + 2*a) - c + 1/2) + 4*a^3*log(-1/2*c^2 + I*(c + 1)*d + 1/2*d^2 + 1/2*(c^2 + d^2 + 2*c + 1)*cos(2*b*x + 2*a) + 1/2*(I*c^2 + I*d^2 + 2*I*c + I)*sin(2*b*x + 2*a) - c - 1/2) - 4*a^3*log(-1/2*c^2 + I*(c - 1)*d + 1/2*d^2 + 1/2*(c^2 + d^2 - 2*c + 1)*cos(2*b*x + 2*a) + 1/2*(I*c^2 + I*d^2 - 2*I*c + I)*sin(2*b*x + 2*a) + c - 1/2) - 6*b*x*polylog(3, ((c^2 + 2*I*(c + 1)*d - d^2 + 2*c + 1)*cos(2*b*x + 2*a) + (I*c^2 - 2*(c + 1)*d - I*d^2 + 2*I*c + I)*sin(2*b*x + 2*a))/(c^2 + d^2 + 2*c + 1)) - 6*b*x*polylog(3, ((c^2 - 2*I*(c + 1)*d - d^2 + 2*c + 1)*cos(2*b*x + 2*a) + (-I*c^2 - 2*(c + 1)*d + I*d^2 - 2*I*c - I)*sin(2*b*x + 2*a))/(c^2 + d^2 + 2*c + 1)) + 6*b*x*polylog(3, ((c^2 + 2*I*(c - 1)*d - d^2 - 2*c + 1)*cos(2*b*x + 2*a) + (I*c^2 - 2*(c - 1)*d - I*d^2 - 2*I*c + I)*sin(2*b*x + 2*a))/(c^2 + d^2 - 2*c + 1)) + 6*b*x*polylog(3, ((c^2 - 2*I*(c - 1)*d - d^2 - 2*c + 1)*cos(2*b*x + 2*a) + (-I*c^2 - 2*(c - 1)*d + I*d^2 + 2*I*c - I)*sin(2*b*x + 2*a))/(c^2 + d^2 - 2*c + 1)) - 4*(b^3*x^3 + a^3)*log((c^2 + d^2 - (c^2 + 2*I*(c + 1)*d - d^2 + 2*c + 1)*cos(2*b*x + 2*a) + (-I*c^2 + 2*(c + 1)*d + I*d^2 - 2*I*c - I)*sin(2*b*x + 2*a) + 2*c + 1)/(c^2 + d^2 + 2*c + 1)) - 4*(b^3*x^3 + a^3)*log((c^2 + d^2 - (c^2 - 2*I*(c + 1)*d - d^2 + 2*c + 1)*cos(2*b*x + 2*a) + (I*c^2 + 2*(c + 1)*d - I*d^2 + 2*I*c + I)*sin(2*b*x + 2*a) + 2*c + 1)/(c^2 + d^2 + 2*c + 1)) + 4*(b^3*x^3 + a^3)*log((c^2 + d^2 - (c^2 + 2*I*(c - 1)*d - d^2 - 2*c + 1)*cos(2*b*x + 2*a) + (-I*c^2 + 2*(c - 1)*d + I*d^2 + 2*I*c - I)*sin(2*b*x + 2*a) - 2*c + 1)/(c^2 + d^2 - 2*c + 1)) + 4*(b^3*x^3 + a^3)*log((c^2 + d^2 - (c^2 - 2*I*(c - 1)*d - d^2 - 2*c + 1)*cos(2*b*x + 2*a) + (I*c^2 + 2*(c - 1)*d - I*d^2 - 2*I*c + I)*sin(2*b*x + 2*a) - 2*c + 1)/(c^2 + d^2 - 2*c + 1)) - 3*I*polylog(4, ((c^2 + 2*I*(c + 1)*d - d^2 + 2*c + 1)*cos(2*b*x + 2*a) + (I*c^2 - 2*(c + 1)*d - I*d^2 + 2*I*c + I)*sin(2*b*x + 2*a))/(c^2 + d^2 + 2*c + 1)) + 3*I*polylog(4, ((c^2 - 2*I*(c + 1)*d - d^2 + 2*c + 1)*cos(2*b*x + 2*a) + (-I*c^2 - 2*(c + 1)*d + I*d^2 - 2*I*c - I)*sin(2*b*x + 2*a))/(c^2 + d^2 + 2*c + 1)) + 3*I*polylog(4, ((c^2 + 2*I*(c - 1)*d - d^2 - 2*c + 1)*cos(2*b*x + 2*a) + (I*c^2 - 2*(c - 1)*d - I*d^2 - 2*I*c + I)*sin(2*b*x + 2*a))/(c^2 + d^2 - 2*c + 1)) - 3*I*polylog(4, ((c^2 - 2*I*(c - 1)*d - d^2 - 2*c + 1)*cos(2*b*x + 2*a) + (-I*c^2 - 2*(c - 1)*d + I*d^2 + 2*I*c - I)*sin(2*b*x + 2*a))/(c^2 + d^2 - 2*c + 1)))/b^3","C",0
254,1,1462,0,0.892749," ","integrate(x*arccoth(c+d*cot(b*x+a)),x, algorithm=""fricas"")","\frac{4 \, b^{2} x^{2} \log\left(\frac{d \cos\left(2 \, b x + 2 \, a\right) + {\left(c + 1\right)} \sin\left(2 \, b x + 2 \, a\right) + d}{d \cos\left(2 \, b x + 2 \, a\right) + {\left(c - 1\right)} \sin\left(2 \, b x + 2 \, a\right) + d}\right) + 2 i \, b x {\rm Li}_2\left(-\frac{c^{2} + d^{2} - {\left(c^{2} + 2 i \, {\left(c + 1\right)} d - d^{2} + 2 \, c + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(-i \, c^{2} + 2 \, {\left(c + 1\right)} d + i \, d^{2} - 2 i \, c - i\right)} \sin\left(2 \, b x + 2 \, a\right) + 2 \, c + 1}{c^{2} + d^{2} + 2 \, c + 1} + 1\right) - 2 i \, b x {\rm Li}_2\left(-\frac{c^{2} + d^{2} - {\left(c^{2} - 2 i \, {\left(c + 1\right)} d - d^{2} + 2 \, c + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(i \, c^{2} + 2 \, {\left(c + 1\right)} d - i \, d^{2} + 2 i \, c + i\right)} \sin\left(2 \, b x + 2 \, a\right) + 2 \, c + 1}{c^{2} + d^{2} + 2 \, c + 1} + 1\right) - 2 i \, b x {\rm Li}_2\left(-\frac{c^{2} + d^{2} - {\left(c^{2} + 2 i \, {\left(c - 1\right)} d - d^{2} - 2 \, c + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(-i \, c^{2} + 2 \, {\left(c - 1\right)} d + i \, d^{2} + 2 i \, c - i\right)} \sin\left(2 \, b x + 2 \, a\right) - 2 \, c + 1}{c^{2} + d^{2} - 2 \, c + 1} + 1\right) + 2 i \, b x {\rm Li}_2\left(-\frac{c^{2} + d^{2} - {\left(c^{2} - 2 i \, {\left(c - 1\right)} d - d^{2} - 2 \, c + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(i \, c^{2} + 2 \, {\left(c - 1\right)} d - i \, d^{2} - 2 i \, c + i\right)} \sin\left(2 \, b x + 2 \, a\right) - 2 \, c + 1}{c^{2} + d^{2} - 2 \, c + 1} + 1\right) - 2 \, a^{2} \log\left(\frac{1}{2} \, c^{2} + i \, {\left(c + 1\right)} d - \frac{1}{2} \, d^{2} - \frac{1}{2} \, {\left(c^{2} + d^{2} + 2 \, c + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + \frac{1}{2} \, {\left(i \, c^{2} + i \, d^{2} + 2 i \, c + i\right)} \sin\left(2 \, b x + 2 \, a\right) + c + \frac{1}{2}\right) + 2 \, a^{2} \log\left(\frac{1}{2} \, c^{2} + i \, {\left(c - 1\right)} d - \frac{1}{2} \, d^{2} - \frac{1}{2} \, {\left(c^{2} + d^{2} - 2 \, c + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + \frac{1}{2} \, {\left(i \, c^{2} + i \, d^{2} - 2 i \, c + i\right)} \sin\left(2 \, b x + 2 \, a\right) - c + \frac{1}{2}\right) - 2 \, a^{2} \log\left(-\frac{1}{2} \, c^{2} + i \, {\left(c + 1\right)} d + \frac{1}{2} \, d^{2} + \frac{1}{2} \, {\left(c^{2} + d^{2} + 2 \, c + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + \frac{1}{2} \, {\left(i \, c^{2} + i \, d^{2} + 2 i \, c + i\right)} \sin\left(2 \, b x + 2 \, a\right) - c - \frac{1}{2}\right) + 2 \, a^{2} \log\left(-\frac{1}{2} \, c^{2} + i \, {\left(c - 1\right)} d + \frac{1}{2} \, d^{2} + \frac{1}{2} \, {\left(c^{2} + d^{2} - 2 \, c + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + \frac{1}{2} \, {\left(i \, c^{2} + i \, d^{2} - 2 i \, c + i\right)} \sin\left(2 \, b x + 2 \, a\right) + c - \frac{1}{2}\right) - 2 \, {\left(b^{2} x^{2} - a^{2}\right)} \log\left(\frac{c^{2} + d^{2} - {\left(c^{2} + 2 i \, {\left(c + 1\right)} d - d^{2} + 2 \, c + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(-i \, c^{2} + 2 \, {\left(c + 1\right)} d + i \, d^{2} - 2 i \, c - i\right)} \sin\left(2 \, b x + 2 \, a\right) + 2 \, c + 1}{c^{2} + d^{2} + 2 \, c + 1}\right) - 2 \, {\left(b^{2} x^{2} - a^{2}\right)} \log\left(\frac{c^{2} + d^{2} - {\left(c^{2} - 2 i \, {\left(c + 1\right)} d - d^{2} + 2 \, c + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(i \, c^{2} + 2 \, {\left(c + 1\right)} d - i \, d^{2} + 2 i \, c + i\right)} \sin\left(2 \, b x + 2 \, a\right) + 2 \, c + 1}{c^{2} + d^{2} + 2 \, c + 1}\right) + 2 \, {\left(b^{2} x^{2} - a^{2}\right)} \log\left(\frac{c^{2} + d^{2} - {\left(c^{2} + 2 i \, {\left(c - 1\right)} d - d^{2} - 2 \, c + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(-i \, c^{2} + 2 \, {\left(c - 1\right)} d + i \, d^{2} + 2 i \, c - i\right)} \sin\left(2 \, b x + 2 \, a\right) - 2 \, c + 1}{c^{2} + d^{2} - 2 \, c + 1}\right) + 2 \, {\left(b^{2} x^{2} - a^{2}\right)} \log\left(\frac{c^{2} + d^{2} - {\left(c^{2} - 2 i \, {\left(c - 1\right)} d - d^{2} - 2 \, c + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(i \, c^{2} + 2 \, {\left(c - 1\right)} d - i \, d^{2} - 2 i \, c + i\right)} \sin\left(2 \, b x + 2 \, a\right) - 2 \, c + 1}{c^{2} + d^{2} - 2 \, c + 1}\right) - {\rm polylog}\left(3, \frac{{\left(c^{2} + 2 i \, {\left(c + 1\right)} d - d^{2} + 2 \, c + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(i \, c^{2} - 2 \, {\left(c + 1\right)} d - i \, d^{2} + 2 i \, c + i\right)} \sin\left(2 \, b x + 2 \, a\right)}{c^{2} + d^{2} + 2 \, c + 1}\right) - {\rm polylog}\left(3, \frac{{\left(c^{2} - 2 i \, {\left(c + 1\right)} d - d^{2} + 2 \, c + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(-i \, c^{2} - 2 \, {\left(c + 1\right)} d + i \, d^{2} - 2 i \, c - i\right)} \sin\left(2 \, b x + 2 \, a\right)}{c^{2} + d^{2} + 2 \, c + 1}\right) + {\rm polylog}\left(3, \frac{{\left(c^{2} + 2 i \, {\left(c - 1\right)} d - d^{2} - 2 \, c + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(i \, c^{2} - 2 \, {\left(c - 1\right)} d - i \, d^{2} - 2 i \, c + i\right)} \sin\left(2 \, b x + 2 \, a\right)}{c^{2} + d^{2} - 2 \, c + 1}\right) + {\rm polylog}\left(3, \frac{{\left(c^{2} - 2 i \, {\left(c - 1\right)} d - d^{2} - 2 \, c + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(-i \, c^{2} - 2 \, {\left(c - 1\right)} d + i \, d^{2} + 2 i \, c - i\right)} \sin\left(2 \, b x + 2 \, a\right)}{c^{2} + d^{2} - 2 \, c + 1}\right)}{16 \, b^{2}}"," ",0,"1/16*(4*b^2*x^2*log((d*cos(2*b*x + 2*a) + (c + 1)*sin(2*b*x + 2*a) + d)/(d*cos(2*b*x + 2*a) + (c - 1)*sin(2*b*x + 2*a) + d)) + 2*I*b*x*dilog(-(c^2 + d^2 - (c^2 + 2*I*(c + 1)*d - d^2 + 2*c + 1)*cos(2*b*x + 2*a) + (-I*c^2 + 2*(c + 1)*d + I*d^2 - 2*I*c - I)*sin(2*b*x + 2*a) + 2*c + 1)/(c^2 + d^2 + 2*c + 1) + 1) - 2*I*b*x*dilog(-(c^2 + d^2 - (c^2 - 2*I*(c + 1)*d - d^2 + 2*c + 1)*cos(2*b*x + 2*a) + (I*c^2 + 2*(c + 1)*d - I*d^2 + 2*I*c + I)*sin(2*b*x + 2*a) + 2*c + 1)/(c^2 + d^2 + 2*c + 1) + 1) - 2*I*b*x*dilog(-(c^2 + d^2 - (c^2 + 2*I*(c - 1)*d - d^2 - 2*c + 1)*cos(2*b*x + 2*a) + (-I*c^2 + 2*(c - 1)*d + I*d^2 + 2*I*c - I)*sin(2*b*x + 2*a) - 2*c + 1)/(c^2 + d^2 - 2*c + 1) + 1) + 2*I*b*x*dilog(-(c^2 + d^2 - (c^2 - 2*I*(c - 1)*d - d^2 - 2*c + 1)*cos(2*b*x + 2*a) + (I*c^2 + 2*(c - 1)*d - I*d^2 - 2*I*c + I)*sin(2*b*x + 2*a) - 2*c + 1)/(c^2 + d^2 - 2*c + 1) + 1) - 2*a^2*log(1/2*c^2 + I*(c + 1)*d - 1/2*d^2 - 1/2*(c^2 + d^2 + 2*c + 1)*cos(2*b*x + 2*a) + 1/2*(I*c^2 + I*d^2 + 2*I*c + I)*sin(2*b*x + 2*a) + c + 1/2) + 2*a^2*log(1/2*c^2 + I*(c - 1)*d - 1/2*d^2 - 1/2*(c^2 + d^2 - 2*c + 1)*cos(2*b*x + 2*a) + 1/2*(I*c^2 + I*d^2 - 2*I*c + I)*sin(2*b*x + 2*a) - c + 1/2) - 2*a^2*log(-1/2*c^2 + I*(c + 1)*d + 1/2*d^2 + 1/2*(c^2 + d^2 + 2*c + 1)*cos(2*b*x + 2*a) + 1/2*(I*c^2 + I*d^2 + 2*I*c + I)*sin(2*b*x + 2*a) - c - 1/2) + 2*a^2*log(-1/2*c^2 + I*(c - 1)*d + 1/2*d^2 + 1/2*(c^2 + d^2 - 2*c + 1)*cos(2*b*x + 2*a) + 1/2*(I*c^2 + I*d^2 - 2*I*c + I)*sin(2*b*x + 2*a) + c - 1/2) - 2*(b^2*x^2 - a^2)*log((c^2 + d^2 - (c^2 + 2*I*(c + 1)*d - d^2 + 2*c + 1)*cos(2*b*x + 2*a) + (-I*c^2 + 2*(c + 1)*d + I*d^2 - 2*I*c - I)*sin(2*b*x + 2*a) + 2*c + 1)/(c^2 + d^2 + 2*c + 1)) - 2*(b^2*x^2 - a^2)*log((c^2 + d^2 - (c^2 - 2*I*(c + 1)*d - d^2 + 2*c + 1)*cos(2*b*x + 2*a) + (I*c^2 + 2*(c + 1)*d - I*d^2 + 2*I*c + I)*sin(2*b*x + 2*a) + 2*c + 1)/(c^2 + d^2 + 2*c + 1)) + 2*(b^2*x^2 - a^2)*log((c^2 + d^2 - (c^2 + 2*I*(c - 1)*d - d^2 - 2*c + 1)*cos(2*b*x + 2*a) + (-I*c^2 + 2*(c - 1)*d + I*d^2 + 2*I*c - I)*sin(2*b*x + 2*a) - 2*c + 1)/(c^2 + d^2 - 2*c + 1)) + 2*(b^2*x^2 - a^2)*log((c^2 + d^2 - (c^2 - 2*I*(c - 1)*d - d^2 - 2*c + 1)*cos(2*b*x + 2*a) + (I*c^2 + 2*(c - 1)*d - I*d^2 - 2*I*c + I)*sin(2*b*x + 2*a) - 2*c + 1)/(c^2 + d^2 - 2*c + 1)) - polylog(3, ((c^2 + 2*I*(c + 1)*d - d^2 + 2*c + 1)*cos(2*b*x + 2*a) + (I*c^2 - 2*(c + 1)*d - I*d^2 + 2*I*c + I)*sin(2*b*x + 2*a))/(c^2 + d^2 + 2*c + 1)) - polylog(3, ((c^2 - 2*I*(c + 1)*d - d^2 + 2*c + 1)*cos(2*b*x + 2*a) + (-I*c^2 - 2*(c + 1)*d + I*d^2 - 2*I*c - I)*sin(2*b*x + 2*a))/(c^2 + d^2 + 2*c + 1)) + polylog(3, ((c^2 + 2*I*(c - 1)*d - d^2 - 2*c + 1)*cos(2*b*x + 2*a) + (I*c^2 - 2*(c - 1)*d - I*d^2 - 2*I*c + I)*sin(2*b*x + 2*a))/(c^2 + d^2 - 2*c + 1)) + polylog(3, ((c^2 - 2*I*(c - 1)*d - d^2 - 2*c + 1)*cos(2*b*x + 2*a) + (-I*c^2 - 2*(c - 1)*d + I*d^2 + 2*I*c - I)*sin(2*b*x + 2*a))/(c^2 + d^2 - 2*c + 1)))/b^2","C",0
255,1,1098,0,0.749914," ","integrate(arccoth(c+d*cot(b*x+a)),x, algorithm=""fricas"")","\frac{4 \, b x \log\left(\frac{d \cos\left(2 \, b x + 2 \, a\right) + {\left(c + 1\right)} \sin\left(2 \, b x + 2 \, a\right) + d}{d \cos\left(2 \, b x + 2 \, a\right) + {\left(c - 1\right)} \sin\left(2 \, b x + 2 \, a\right) + d}\right) + 2 \, a \log\left(\frac{1}{2} \, c^{2} + i \, {\left(c + 1\right)} d - \frac{1}{2} \, d^{2} - \frac{1}{2} \, {\left(c^{2} + d^{2} + 2 \, c + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + \frac{1}{2} \, {\left(i \, c^{2} + i \, d^{2} + 2 i \, c + i\right)} \sin\left(2 \, b x + 2 \, a\right) + c + \frac{1}{2}\right) - 2 \, a \log\left(\frac{1}{2} \, c^{2} + i \, {\left(c - 1\right)} d - \frac{1}{2} \, d^{2} - \frac{1}{2} \, {\left(c^{2} + d^{2} - 2 \, c + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + \frac{1}{2} \, {\left(i \, c^{2} + i \, d^{2} - 2 i \, c + i\right)} \sin\left(2 \, b x + 2 \, a\right) - c + \frac{1}{2}\right) + 2 \, a \log\left(-\frac{1}{2} \, c^{2} + i \, {\left(c + 1\right)} d + \frac{1}{2} \, d^{2} + \frac{1}{2} \, {\left(c^{2} + d^{2} + 2 \, c + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + \frac{1}{2} \, {\left(i \, c^{2} + i \, d^{2} + 2 i \, c + i\right)} \sin\left(2 \, b x + 2 \, a\right) - c - \frac{1}{2}\right) - 2 \, a \log\left(-\frac{1}{2} \, c^{2} + i \, {\left(c - 1\right)} d + \frac{1}{2} \, d^{2} + \frac{1}{2} \, {\left(c^{2} + d^{2} - 2 \, c + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + \frac{1}{2} \, {\left(i \, c^{2} + i \, d^{2} - 2 i \, c + i\right)} \sin\left(2 \, b x + 2 \, a\right) + c - \frac{1}{2}\right) - 2 \, {\left(b x + a\right)} \log\left(\frac{c^{2} + d^{2} - {\left(c^{2} + 2 i \, {\left(c + 1\right)} d - d^{2} + 2 \, c + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(-i \, c^{2} + 2 \, {\left(c + 1\right)} d + i \, d^{2} - 2 i \, c - i\right)} \sin\left(2 \, b x + 2 \, a\right) + 2 \, c + 1}{c^{2} + d^{2} + 2 \, c + 1}\right) - 2 \, {\left(b x + a\right)} \log\left(\frac{c^{2} + d^{2} - {\left(c^{2} - 2 i \, {\left(c + 1\right)} d - d^{2} + 2 \, c + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(i \, c^{2} + 2 \, {\left(c + 1\right)} d - i \, d^{2} + 2 i \, c + i\right)} \sin\left(2 \, b x + 2 \, a\right) + 2 \, c + 1}{c^{2} + d^{2} + 2 \, c + 1}\right) + 2 \, {\left(b x + a\right)} \log\left(\frac{c^{2} + d^{2} - {\left(c^{2} + 2 i \, {\left(c - 1\right)} d - d^{2} - 2 \, c + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(-i \, c^{2} + 2 \, {\left(c - 1\right)} d + i \, d^{2} + 2 i \, c - i\right)} \sin\left(2 \, b x + 2 \, a\right) - 2 \, c + 1}{c^{2} + d^{2} - 2 \, c + 1}\right) + 2 \, {\left(b x + a\right)} \log\left(\frac{c^{2} + d^{2} - {\left(c^{2} - 2 i \, {\left(c - 1\right)} d - d^{2} - 2 \, c + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(i \, c^{2} + 2 \, {\left(c - 1\right)} d - i \, d^{2} - 2 i \, c + i\right)} \sin\left(2 \, b x + 2 \, a\right) - 2 \, c + 1}{c^{2} + d^{2} - 2 \, c + 1}\right) + i \, {\rm Li}_2\left(-\frac{c^{2} + d^{2} - {\left(c^{2} + 2 i \, {\left(c + 1\right)} d - d^{2} + 2 \, c + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(-i \, c^{2} + 2 \, {\left(c + 1\right)} d + i \, d^{2} - 2 i \, c - i\right)} \sin\left(2 \, b x + 2 \, a\right) + 2 \, c + 1}{c^{2} + d^{2} + 2 \, c + 1} + 1\right) - i \, {\rm Li}_2\left(-\frac{c^{2} + d^{2} - {\left(c^{2} - 2 i \, {\left(c + 1\right)} d - d^{2} + 2 \, c + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(i \, c^{2} + 2 \, {\left(c + 1\right)} d - i \, d^{2} + 2 i \, c + i\right)} \sin\left(2 \, b x + 2 \, a\right) + 2 \, c + 1}{c^{2} + d^{2} + 2 \, c + 1} + 1\right) - i \, {\rm Li}_2\left(-\frac{c^{2} + d^{2} - {\left(c^{2} + 2 i \, {\left(c - 1\right)} d - d^{2} - 2 \, c + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(-i \, c^{2} + 2 \, {\left(c - 1\right)} d + i \, d^{2} + 2 i \, c - i\right)} \sin\left(2 \, b x + 2 \, a\right) - 2 \, c + 1}{c^{2} + d^{2} - 2 \, c + 1} + 1\right) + i \, {\rm Li}_2\left(-\frac{c^{2} + d^{2} - {\left(c^{2} - 2 i \, {\left(c - 1\right)} d - d^{2} - 2 \, c + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(i \, c^{2} + 2 \, {\left(c - 1\right)} d - i \, d^{2} - 2 i \, c + i\right)} \sin\left(2 \, b x + 2 \, a\right) - 2 \, c + 1}{c^{2} + d^{2} - 2 \, c + 1} + 1\right)}{8 \, b}"," ",0,"1/8*(4*b*x*log((d*cos(2*b*x + 2*a) + (c + 1)*sin(2*b*x + 2*a) + d)/(d*cos(2*b*x + 2*a) + (c - 1)*sin(2*b*x + 2*a) + d)) + 2*a*log(1/2*c^2 + I*(c + 1)*d - 1/2*d^2 - 1/2*(c^2 + d^2 + 2*c + 1)*cos(2*b*x + 2*a) + 1/2*(I*c^2 + I*d^2 + 2*I*c + I)*sin(2*b*x + 2*a) + c + 1/2) - 2*a*log(1/2*c^2 + I*(c - 1)*d - 1/2*d^2 - 1/2*(c^2 + d^2 - 2*c + 1)*cos(2*b*x + 2*a) + 1/2*(I*c^2 + I*d^2 - 2*I*c + I)*sin(2*b*x + 2*a) - c + 1/2) + 2*a*log(-1/2*c^2 + I*(c + 1)*d + 1/2*d^2 + 1/2*(c^2 + d^2 + 2*c + 1)*cos(2*b*x + 2*a) + 1/2*(I*c^2 + I*d^2 + 2*I*c + I)*sin(2*b*x + 2*a) - c - 1/2) - 2*a*log(-1/2*c^2 + I*(c - 1)*d + 1/2*d^2 + 1/2*(c^2 + d^2 - 2*c + 1)*cos(2*b*x + 2*a) + 1/2*(I*c^2 + I*d^2 - 2*I*c + I)*sin(2*b*x + 2*a) + c - 1/2) - 2*(b*x + a)*log((c^2 + d^2 - (c^2 + 2*I*(c + 1)*d - d^2 + 2*c + 1)*cos(2*b*x + 2*a) + (-I*c^2 + 2*(c + 1)*d + I*d^2 - 2*I*c - I)*sin(2*b*x + 2*a) + 2*c + 1)/(c^2 + d^2 + 2*c + 1)) - 2*(b*x + a)*log((c^2 + d^2 - (c^2 - 2*I*(c + 1)*d - d^2 + 2*c + 1)*cos(2*b*x + 2*a) + (I*c^2 + 2*(c + 1)*d - I*d^2 + 2*I*c + I)*sin(2*b*x + 2*a) + 2*c + 1)/(c^2 + d^2 + 2*c + 1)) + 2*(b*x + a)*log((c^2 + d^2 - (c^2 + 2*I*(c - 1)*d - d^2 - 2*c + 1)*cos(2*b*x + 2*a) + (-I*c^2 + 2*(c - 1)*d + I*d^2 + 2*I*c - I)*sin(2*b*x + 2*a) - 2*c + 1)/(c^2 + d^2 - 2*c + 1)) + 2*(b*x + a)*log((c^2 + d^2 - (c^2 - 2*I*(c - 1)*d - d^2 - 2*c + 1)*cos(2*b*x + 2*a) + (I*c^2 + 2*(c - 1)*d - I*d^2 - 2*I*c + I)*sin(2*b*x + 2*a) - 2*c + 1)/(c^2 + d^2 - 2*c + 1)) + I*dilog(-(c^2 + d^2 - (c^2 + 2*I*(c + 1)*d - d^2 + 2*c + 1)*cos(2*b*x + 2*a) + (-I*c^2 + 2*(c + 1)*d + I*d^2 - 2*I*c - I)*sin(2*b*x + 2*a) + 2*c + 1)/(c^2 + d^2 + 2*c + 1) + 1) - I*dilog(-(c^2 + d^2 - (c^2 - 2*I*(c + 1)*d - d^2 + 2*c + 1)*cos(2*b*x + 2*a) + (I*c^2 + 2*(c + 1)*d - I*d^2 + 2*I*c + I)*sin(2*b*x + 2*a) + 2*c + 1)/(c^2 + d^2 + 2*c + 1) + 1) - I*dilog(-(c^2 + d^2 - (c^2 + 2*I*(c - 1)*d - d^2 - 2*c + 1)*cos(2*b*x + 2*a) + (-I*c^2 + 2*(c - 1)*d + I*d^2 + 2*I*c - I)*sin(2*b*x + 2*a) - 2*c + 1)/(c^2 + d^2 - 2*c + 1) + 1) + I*dilog(-(c^2 + d^2 - (c^2 - 2*I*(c - 1)*d - d^2 - 2*c + 1)*cos(2*b*x + 2*a) + (I*c^2 + 2*(c - 1)*d - I*d^2 - 2*I*c + I)*sin(2*b*x + 2*a) - 2*c + 1)/(c^2 + d^2 - 2*c + 1) + 1))/b","B",0
256,0,0,0,0.577911," ","integrate(arccoth(c+d*cot(b*x+a))/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{arcoth}\left(d \cot\left(b x + a\right) + c\right)}{x}, x\right)"," ",0,"integral(arccoth(d*cot(b*x + a) + c)/x, x)","F",0
257,1,179,0,0.665223," ","integrate(x^2*arccoth(1+I*d+d*cot(b*x+a)),x, algorithm=""fricas"")","\frac{2 i \, b^{4} x^{4} + 4 \, b^{3} x^{3} \log\left(\frac{{\left({\left(d - i\right)} e^{\left(2 i \, b x + 2 i \, a\right)} + i\right)} e^{\left(-2 i \, b x - 2 i \, a\right)}}{d}\right) + 6 i \, b^{2} x^{2} {\rm Li}_2\left(-{\left(-i \, d - 1\right)} e^{\left(2 i \, b x + 2 i \, a\right)}\right) - 2 i \, a^{4} + 4 \, a^{3} \log\left(\frac{{\left(d - i\right)} e^{\left(2 i \, b x + 2 i \, a\right)} + i}{d - i}\right) - 6 \, b x {\rm polylog}\left(3, {\left(i \, d + 1\right)} e^{\left(2 i \, b x + 2 i \, a\right)}\right) - 4 \, {\left(b^{3} x^{3} + a^{3}\right)} \log\left({\left(-i \, d - 1\right)} e^{\left(2 i \, b x + 2 i \, a\right)} + 1\right) - 3 i \, {\rm polylog}\left(4, {\left(i \, d + 1\right)} e^{\left(2 i \, b x + 2 i \, a\right)}\right)}{24 \, b^{3}}"," ",0,"1/24*(2*I*b^4*x^4 + 4*b^3*x^3*log(((d - I)*e^(2*I*b*x + 2*I*a) + I)*e^(-2*I*b*x - 2*I*a)/d) + 6*I*b^2*x^2*dilog(-(-I*d - 1)*e^(2*I*b*x + 2*I*a)) - 2*I*a^4 + 4*a^3*log(((d - I)*e^(2*I*b*x + 2*I*a) + I)/(d - I)) - 6*b*x*polylog(3, (I*d + 1)*e^(2*I*b*x + 2*I*a)) - 4*(b^3*x^3 + a^3)*log((-I*d - 1)*e^(2*I*b*x + 2*I*a) + 1) - 3*I*polylog(4, (I*d + 1)*e^(2*I*b*x + 2*I*a)))/b^3","C",0
258,1,156,0,0.725207," ","integrate(x*arccoth(1+I*d+d*cot(b*x+a)),x, algorithm=""fricas"")","\frac{4 i \, b^{3} x^{3} + 6 \, b^{2} x^{2} \log\left(\frac{{\left({\left(d - i\right)} e^{\left(2 i \, b x + 2 i \, a\right)} + i\right)} e^{\left(-2 i \, b x - 2 i \, a\right)}}{d}\right) + 4 i \, a^{3} + 6 i \, b x {\rm Li}_2\left(-{\left(-i \, d - 1\right)} e^{\left(2 i \, b x + 2 i \, a\right)}\right) - 6 \, a^{2} \log\left(\frac{{\left(d - i\right)} e^{\left(2 i \, b x + 2 i \, a\right)} + i}{d - i}\right) - 6 \, {\left(b^{2} x^{2} - a^{2}\right)} \log\left({\left(-i \, d - 1\right)} e^{\left(2 i \, b x + 2 i \, a\right)} + 1\right) - 3 \, {\rm polylog}\left(3, {\left(i \, d + 1\right)} e^{\left(2 i \, b x + 2 i \, a\right)}\right)}{24 \, b^{2}}"," ",0,"1/24*(4*I*b^3*x^3 + 6*b^2*x^2*log(((d - I)*e^(2*I*b*x + 2*I*a) + I)*e^(-2*I*b*x - 2*I*a)/d) + 4*I*a^3 + 6*I*b*x*dilog(-(-I*d - 1)*e^(2*I*b*x + 2*I*a)) - 6*a^2*log(((d - I)*e^(2*I*b*x + 2*I*a) + I)/(d - I)) - 6*(b^2*x^2 - a^2)*log((-I*d - 1)*e^(2*I*b*x + 2*I*a) + 1) - 3*polylog(3, (I*d + 1)*e^(2*I*b*x + 2*I*a)))/b^2","C",0
259,1,121,0,0.521096," ","integrate(arccoth(1+I*d+d*cot(b*x+a)),x, algorithm=""fricas"")","\frac{2 i \, b^{2} x^{2} + 2 \, b x \log\left(\frac{{\left({\left(d - i\right)} e^{\left(2 i \, b x + 2 i \, a\right)} + i\right)} e^{\left(-2 i \, b x - 2 i \, a\right)}}{d}\right) - 2 i \, a^{2} - 2 \, {\left(b x + a\right)} \log\left({\left(-i \, d - 1\right)} e^{\left(2 i \, b x + 2 i \, a\right)} + 1\right) + 2 \, a \log\left(\frac{{\left(d - i\right)} e^{\left(2 i \, b x + 2 i \, a\right)} + i}{d - i}\right) + i \, {\rm Li}_2\left(-{\left(-i \, d - 1\right)} e^{\left(2 i \, b x + 2 i \, a\right)}\right)}{4 \, b}"," ",0,"1/4*(2*I*b^2*x^2 + 2*b*x*log(((d - I)*e^(2*I*b*x + 2*I*a) + I)*e^(-2*I*b*x - 2*I*a)/d) - 2*I*a^2 - 2*(b*x + a)*log((-I*d - 1)*e^(2*I*b*x + 2*I*a) + 1) + 2*a*log(((d - I)*e^(2*I*b*x + 2*I*a) + I)/(d - I)) + I*dilog(-(-I*d - 1)*e^(2*I*b*x + 2*I*a)))/b","A",0
260,0,0,0,0.640490," ","integrate(arccoth(1+I*d+d*cot(b*x+a))/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\log\left(\frac{{\left({\left(d - i\right)} e^{\left(2 i \, b x + 2 i \, a\right)} + i\right)} e^{\left(-2 i \, b x - 2 i \, a\right)}}{d}\right)}{2 \, x}, x\right)"," ",0,"integral(1/2*log(((d - I)*e^(2*I*b*x + 2*I*a) + I)*e^(-2*I*b*x - 2*I*a)/d)/x, x)","F",0
261,1,179,0,0.680864," ","integrate(x^2*arccoth(1-I*d-d*cot(b*x+a)),x, algorithm=""fricas"")","\frac{2 i \, b^{4} x^{4} - 4 \, b^{3} x^{3} \log\left(\frac{d e^{\left(2 i \, b x + 2 i \, a\right)}}{{\left(d + i\right)} e^{\left(2 i \, b x + 2 i \, a\right)} - i}\right) + 6 i \, b^{2} x^{2} {\rm Li}_2\left(-{\left(i \, d - 1\right)} e^{\left(2 i \, b x + 2 i \, a\right)}\right) - 2 i \, a^{4} + 4 \, a^{3} \log\left(\frac{{\left(d + i\right)} e^{\left(2 i \, b x + 2 i \, a\right)} - i}{d + i}\right) - 6 \, b x {\rm polylog}\left(3, {\left(-i \, d + 1\right)} e^{\left(2 i \, b x + 2 i \, a\right)}\right) - 4 \, {\left(b^{3} x^{3} + a^{3}\right)} \log\left({\left(i \, d - 1\right)} e^{\left(2 i \, b x + 2 i \, a\right)} + 1\right) - 3 i \, {\rm polylog}\left(4, {\left(-i \, d + 1\right)} e^{\left(2 i \, b x + 2 i \, a\right)}\right)}{24 \, b^{3}}"," ",0,"1/24*(2*I*b^4*x^4 - 4*b^3*x^3*log(d*e^(2*I*b*x + 2*I*a)/((d + I)*e^(2*I*b*x + 2*I*a) - I)) + 6*I*b^2*x^2*dilog(-(I*d - 1)*e^(2*I*b*x + 2*I*a)) - 2*I*a^4 + 4*a^3*log(((d + I)*e^(2*I*b*x + 2*I*a) - I)/(d + I)) - 6*b*x*polylog(3, (-I*d + 1)*e^(2*I*b*x + 2*I*a)) - 4*(b^3*x^3 + a^3)*log((I*d - 1)*e^(2*I*b*x + 2*I*a) + 1) - 3*I*polylog(4, (-I*d + 1)*e^(2*I*b*x + 2*I*a)))/b^3","C",0
262,1,156,0,0.626950," ","integrate(x*arccoth(1-I*d-d*cot(b*x+a)),x, algorithm=""fricas"")","\frac{4 i \, b^{3} x^{3} - 6 \, b^{2} x^{2} \log\left(\frac{d e^{\left(2 i \, b x + 2 i \, a\right)}}{{\left(d + i\right)} e^{\left(2 i \, b x + 2 i \, a\right)} - i}\right) + 4 i \, a^{3} + 6 i \, b x {\rm Li}_2\left(-{\left(i \, d - 1\right)} e^{\left(2 i \, b x + 2 i \, a\right)}\right) - 6 \, a^{2} \log\left(\frac{{\left(d + i\right)} e^{\left(2 i \, b x + 2 i \, a\right)} - i}{d + i}\right) - 6 \, {\left(b^{2} x^{2} - a^{2}\right)} \log\left({\left(i \, d - 1\right)} e^{\left(2 i \, b x + 2 i \, a\right)} + 1\right) - 3 \, {\rm polylog}\left(3, {\left(-i \, d + 1\right)} e^{\left(2 i \, b x + 2 i \, a\right)}\right)}{24 \, b^{2}}"," ",0,"1/24*(4*I*b^3*x^3 - 6*b^2*x^2*log(d*e^(2*I*b*x + 2*I*a)/((d + I)*e^(2*I*b*x + 2*I*a) - I)) + 4*I*a^3 + 6*I*b*x*dilog(-(I*d - 1)*e^(2*I*b*x + 2*I*a)) - 6*a^2*log(((d + I)*e^(2*I*b*x + 2*I*a) - I)/(d + I)) - 6*(b^2*x^2 - a^2)*log((I*d - 1)*e^(2*I*b*x + 2*I*a) + 1) - 3*polylog(3, (-I*d + 1)*e^(2*I*b*x + 2*I*a)))/b^2","C",0
263,1,121,0,0.711876," ","integrate(arccoth(1-I*d-d*cot(b*x+a)),x, algorithm=""fricas"")","\frac{2 i \, b^{2} x^{2} - 2 \, b x \log\left(\frac{d e^{\left(2 i \, b x + 2 i \, a\right)}}{{\left(d + i\right)} e^{\left(2 i \, b x + 2 i \, a\right)} - i}\right) - 2 i \, a^{2} - 2 \, {\left(b x + a\right)} \log\left({\left(i \, d - 1\right)} e^{\left(2 i \, b x + 2 i \, a\right)} + 1\right) + 2 \, a \log\left(\frac{{\left(d + i\right)} e^{\left(2 i \, b x + 2 i \, a\right)} - i}{d + i}\right) + i \, {\rm Li}_2\left(-{\left(i \, d - 1\right)} e^{\left(2 i \, b x + 2 i \, a\right)}\right)}{4 \, b}"," ",0,"1/4*(2*I*b^2*x^2 - 2*b*x*log(d*e^(2*I*b*x + 2*I*a)/((d + I)*e^(2*I*b*x + 2*I*a) - I)) - 2*I*a^2 - 2*(b*x + a)*log((I*d - 1)*e^(2*I*b*x + 2*I*a) + 1) + 2*a*log(((d + I)*e^(2*I*b*x + 2*I*a) - I)/(d + I)) + I*dilog(-(I*d - 1)*e^(2*I*b*x + 2*I*a)))/b","A",0
264,0,0,0,0.596267," ","integrate(arccoth(1-I*d-d*cot(b*x+a))/x,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\log\left(\frac{d e^{\left(2 i \, b x + 2 i \, a\right)}}{{\left(d + i\right)} e^{\left(2 i \, b x + 2 i \, a\right)} - i}\right)}{2 \, x}, x\right)"," ",0,"integral(-1/2*log(d*e^(2*I*b*x + 2*I*a)/((d + I)*e^(2*I*b*x + 2*I*a) - I))/x, x)","F",0
265,1,326,0,0.598475," ","integrate((a+b*arccoth(c*x^n))*(d+e*log(f*x^m))/x,x, algorithm=""fricas"")","\frac{2 \, a e m n^{2} \log\left(x\right)^{2} - 2 \, b e m {\rm polylog}\left(3, c \cosh\left(n \log\left(x\right)\right) + c \sinh\left(n \log\left(x\right)\right)\right) + 2 \, b e m {\rm polylog}\left(3, -c \cosh\left(n \log\left(x\right)\right) - c \sinh\left(n \log\left(x\right)\right)\right) + 2 \, {\left(b e m n \log\left(x\right) + b e n \log\left(f\right) + b d n\right)} {\rm Li}_2\left(c \cosh\left(n \log\left(x\right)\right) + c \sinh\left(n \log\left(x\right)\right)\right) - 2 \, {\left(b e m n \log\left(x\right) + b e n \log\left(f\right) + b d n\right)} {\rm Li}_2\left(-c \cosh\left(n \log\left(x\right)\right) - c \sinh\left(n \log\left(x\right)\right)\right) - {\left(b e m n^{2} \log\left(x\right)^{2} + 2 \, {\left(b e n^{2} \log\left(f\right) + b d n^{2}\right)} \log\left(x\right)\right)} \log\left(c \cosh\left(n \log\left(x\right)\right) + c \sinh\left(n \log\left(x\right)\right) + 1\right) + {\left(b e m n^{2} \log\left(x\right)^{2} + 2 \, {\left(b e n^{2} \log\left(f\right) + b d n^{2}\right)} \log\left(x\right)\right)} \log\left(-c \cosh\left(n \log\left(x\right)\right) - c \sinh\left(n \log\left(x\right)\right) + 1\right) + 4 \, {\left(a e n^{2} \log\left(f\right) + a d n^{2}\right)} \log\left(x\right) + {\left(b e m n^{2} \log\left(x\right)^{2} + 2 \, {\left(b e n^{2} \log\left(f\right) + b d n^{2}\right)} \log\left(x\right)\right)} \log\left(\frac{c \cosh\left(n \log\left(x\right)\right) + c \sinh\left(n \log\left(x\right)\right) + 1}{c \cosh\left(n \log\left(x\right)\right) + c \sinh\left(n \log\left(x\right)\right) - 1}\right)}{4 \, n^{2}}"," ",0,"1/4*(2*a*e*m*n^2*log(x)^2 - 2*b*e*m*polylog(3, c*cosh(n*log(x)) + c*sinh(n*log(x))) + 2*b*e*m*polylog(3, -c*cosh(n*log(x)) - c*sinh(n*log(x))) + 2*(b*e*m*n*log(x) + b*e*n*log(f) + b*d*n)*dilog(c*cosh(n*log(x)) + c*sinh(n*log(x))) - 2*(b*e*m*n*log(x) + b*e*n*log(f) + b*d*n)*dilog(-c*cosh(n*log(x)) - c*sinh(n*log(x))) - (b*e*m*n^2*log(x)^2 + 2*(b*e*n^2*log(f) + b*d*n^2)*log(x))*log(c*cosh(n*log(x)) + c*sinh(n*log(x)) + 1) + (b*e*m*n^2*log(x)^2 + 2*(b*e*n^2*log(f) + b*d*n^2)*log(x))*log(-c*cosh(n*log(x)) - c*sinh(n*log(x)) + 1) + 4*(a*e*n^2*log(f) + a*d*n^2)*log(x) + (b*e*m*n^2*log(x)^2 + 2*(b*e*n^2*log(f) + b*d*n^2)*log(x))*log((c*cosh(n*log(x)) + c*sinh(n*log(x)) + 1)/(c*cosh(n*log(x)) + c*sinh(n*log(x)) - 1)))/n^2","C",0
266,1,246,0,0.665735," ","integrate(x^5*(a+b*arccoth(c*x))*(d+e*log(-c^2*x^2+1)),x, algorithm=""fricas"")","-\frac{150 \, a c^{4} e x^{4} - 100 \, {\left(3 \, a c^{6} d - a c^{6} e\right)} x^{6} + 300 \, a c^{2} e x^{2} - 4 \, {\left(15 \, b c^{5} d - 11 \, b c^{5} e\right)} x^{5} - 10 \, {\left(10 \, b c^{3} d - 19 \, b c^{3} e\right)} x^{3} - 30 \, {\left(10 \, b c d - 49 \, b c e\right)} x - 20 \, {\left(15 \, a c^{6} e x^{6} + 3 \, b c^{5} e x^{5} + 5 \, b c^{3} e x^{3} + 15 \, b c e x - 15 \, a e\right)} \log\left(-c^{2} x^{2} + 1\right) + 5 \, {\left(15 \, b c^{4} e x^{4} - 10 \, {\left(3 \, b c^{6} d - b c^{6} e\right)} x^{6} + 30 \, b c^{2} e x^{2} + 30 \, b d - 147 \, b e - 30 \, {\left(b c^{6} e x^{6} - b e\right)} \log\left(-c^{2} x^{2} + 1\right)\right)} \log\left(\frac{c x + 1}{c x - 1}\right)}{1800 \, c^{6}}"," ",0,"-1/1800*(150*a*c^4*e*x^4 - 100*(3*a*c^6*d - a*c^6*e)*x^6 + 300*a*c^2*e*x^2 - 4*(15*b*c^5*d - 11*b*c^5*e)*x^5 - 10*(10*b*c^3*d - 19*b*c^3*e)*x^3 - 30*(10*b*c*d - 49*b*c*e)*x - 20*(15*a*c^6*e*x^6 + 3*b*c^5*e*x^5 + 5*b*c^3*e*x^3 + 15*b*c*e*x - 15*a*e)*log(-c^2*x^2 + 1) + 5*(15*b*c^4*e*x^4 - 10*(3*b*c^6*d - b*c^6*e)*x^6 + 30*b*c^2*e*x^2 + 30*b*d - 147*b*e - 30*(b*c^6*e*x^6 - b*e)*log(-c^2*x^2 + 1))*log((c*x + 1)/(c*x - 1)))/c^6","A",0
267,1,195,0,0.521712," ","integrate(x^3*(a+b*arccoth(c*x))*(d+e*log(-c^2*x^2+1)),x, algorithm=""fricas"")","-\frac{36 \, a c^{2} e x^{2} - 18 \, {\left(2 \, a c^{4} d - a c^{4} e\right)} x^{4} - 2 \, {\left(6 \, b c^{3} d - 7 \, b c^{3} e\right)} x^{3} - 6 \, {\left(6 \, b c d - 25 \, b c e\right)} x - 12 \, {\left(3 \, a c^{4} e x^{4} + b c^{3} e x^{3} + 3 \, b c e x - 3 \, a e\right)} \log\left(-c^{2} x^{2} + 1\right) + 3 \, {\left(6 \, b c^{2} e x^{2} - 3 \, {\left(2 \, b c^{4} d - b c^{4} e\right)} x^{4} + 6 \, b d - 25 \, b e - 6 \, {\left(b c^{4} e x^{4} - b e\right)} \log\left(-c^{2} x^{2} + 1\right)\right)} \log\left(\frac{c x + 1}{c x - 1}\right)}{144 \, c^{4}}"," ",0,"-1/144*(36*a*c^2*e*x^2 - 18*(2*a*c^4*d - a*c^4*e)*x^4 - 2*(6*b*c^3*d - 7*b*c^3*e)*x^3 - 6*(6*b*c*d - 25*b*c*e)*x - 12*(3*a*c^4*e*x^4 + b*c^3*e*x^3 + 3*b*c*e*x - 3*a*e)*log(-c^2*x^2 + 1) + 3*(6*b*c^2*e*x^2 - 3*(2*b*c^4*d - b*c^4*e)*x^4 + 6*b*d - 25*b*e - 6*(b*c^4*e*x^4 - b*e)*log(-c^2*x^2 + 1))*log((c*x + 1)/(c*x - 1)))/c^4","A",0
268,1,138,0,0.579497," ","integrate(x*(a+b*arccoth(c*x))*(d+e*log(-c^2*x^2+1)),x, algorithm=""fricas"")","\frac{2 \, {\left(a c^{2} d - a c^{2} e\right)} x^{2} + 2 \, {\left(b c d - 3 \, b c e\right)} x + 2 \, {\left(a c^{2} e x^{2} + b c e x - a e\right)} \log\left(-c^{2} x^{2} + 1\right) + {\left({\left(b c^{2} d - b c^{2} e\right)} x^{2} - b d + 3 \, b e + {\left(b c^{2} e x^{2} - b e\right)} \log\left(-c^{2} x^{2} + 1\right)\right)} \log\left(\frac{c x + 1}{c x - 1}\right)}{4 \, c^{2}}"," ",0,"1/4*(2*(a*c^2*d - a*c^2*e)*x^2 + 2*(b*c*d - 3*b*c*e)*x + 2*(a*c^2*e*x^2 + b*c*e*x - a*e)*log(-c^2*x^2 + 1) + ((b*c^2*d - b*c^2*e)*x^2 - b*d + 3*b*e + (b*c^2*e*x^2 - b*e)*log(-c^2*x^2 + 1))*log((c*x + 1)/(c*x - 1)))/c^2","A",0
269,0,0,0,0.502033," ","integrate((a+b*arccoth(c*x))*(d+e*log(-c^2*x^2+1))/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b d \operatorname{arcoth}\left(c x\right) + a d + {\left(b e \operatorname{arcoth}\left(c x\right) + a e\right)} \log\left(-c^{2} x^{2} + 1\right)}{x}, x\right)"," ",0,"integral((b*d*arccoth(c*x) + a*d + (b*e*arccoth(c*x) + a*e)*log(-c^2*x^2 + 1))/x, x)","F",0
270,0,0,0,0.865338," ","integrate((a+b*arccoth(c*x))*(d+e*log(-c^2*x^2+1))/x^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b d \operatorname{arcoth}\left(c x\right) + a d + {\left(b e \operatorname{arcoth}\left(c x\right) + a e\right)} \log\left(-c^{2} x^{2} + 1\right)}{x^{3}}, x\right)"," ",0,"integral((b*d*arccoth(c*x) + a*d + (b*e*arccoth(c*x) + a*e)*log(-c^2*x^2 + 1))/x^3, x)","F",0
271,0,0,0,0.509190," ","integrate((a+b*arccoth(c*x))*(d+e*log(-c^2*x^2+1))/x^5,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b d \operatorname{arcoth}\left(c x\right) + a d + {\left(b e \operatorname{arcoth}\left(c x\right) + a e\right)} \log\left(-c^{2} x^{2} + 1\right)}{x^{5}}, x\right)"," ",0,"integral((b*d*arccoth(c*x) + a*d + (b*e*arccoth(c*x) + a*e)*log(-c^2*x^2 + 1))/x^5, x)","F",0
272,1,249,0,0.607556," ","integrate(x^4*(a+b*arccoth(c*x))*(d+e*log(-c^2*x^2+1)),x, algorithm=""fricas"")","-\frac{80 \, a c^{3} e x^{3} - 24 \, {\left(5 \, a c^{5} d - 2 \, a c^{5} e\right)} x^{5} - 3 \, {\left(10 \, b c^{4} d - 9 \, b c^{4} e\right)} x^{4} + 240 \, a c e x - 30 \, b e \log\left(-c^{2} x^{2} + 1\right)^{2} - 30 \, b e \log\left(\frac{c x + 1}{c x - 1}\right)^{2} - 2 \, {\left(30 \, b c^{2} d - 77 \, b c^{2} e\right)} x^{2} - 2 \, {\left(60 \, a c^{5} e x^{5} + 15 \, b c^{4} e x^{4} + 30 \, b c^{2} e x^{2} + 30 \, b d - 137 \, b e\right)} \log\left(-c^{2} x^{2} + 1\right) - 4 \, {\left(15 \, b c^{5} e x^{5} \log\left(-c^{2} x^{2} + 1\right) - 10 \, b c^{3} e x^{3} + 3 \, {\left(5 \, b c^{5} d - 2 \, b c^{5} e\right)} x^{5} - 30 \, b c e x + 30 \, a e\right)} \log\left(\frac{c x + 1}{c x - 1}\right)}{600 \, c^{5}}"," ",0,"-1/600*(80*a*c^3*e*x^3 - 24*(5*a*c^5*d - 2*a*c^5*e)*x^5 - 3*(10*b*c^4*d - 9*b*c^4*e)*x^4 + 240*a*c*e*x - 30*b*e*log(-c^2*x^2 + 1)^2 - 30*b*e*log((c*x + 1)/(c*x - 1))^2 - 2*(30*b*c^2*d - 77*b*c^2*e)*x^2 - 2*(60*a*c^5*e*x^5 + 15*b*c^4*e*x^4 + 30*b*c^2*e*x^2 + 30*b*d - 137*b*e)*log(-c^2*x^2 + 1) - 4*(15*b*c^5*e*x^5*log(-c^2*x^2 + 1) - 10*b*c^3*e*x^3 + 3*(5*b*c^5*d - 2*b*c^5*e)*x^5 - 30*b*c*e*x + 30*a*e)*log((c*x + 1)/(c*x - 1)))/c^5","A",0
273,1,198,0,0.477112," ","integrate(x^2*(a+b*arccoth(c*x))*(d+e*log(-c^2*x^2+1)),x, algorithm=""fricas"")","-\frac{24 \, a c e x - 4 \, {\left(3 \, a c^{3} d - 2 \, a c^{3} e\right)} x^{3} - 3 \, b e \log\left(-c^{2} x^{2} + 1\right)^{2} - 3 \, b e \log\left(\frac{c x + 1}{c x - 1}\right)^{2} - 2 \, {\left(3 \, b c^{2} d - 5 \, b c^{2} e\right)} x^{2} - 2 \, {\left(6 \, a c^{3} e x^{3} + 3 \, b c^{2} e x^{2} + 3 \, b d - 11 \, b e\right)} \log\left(-c^{2} x^{2} + 1\right) - 2 \, {\left(3 \, b c^{3} e x^{3} \log\left(-c^{2} x^{2} + 1\right) - 6 \, b c e x + {\left(3 \, b c^{3} d - 2 \, b c^{3} e\right)} x^{3} + 6 \, a e\right)} \log\left(\frac{c x + 1}{c x - 1}\right)}{36 \, c^{3}}"," ",0,"-1/36*(24*a*c*e*x - 4*(3*a*c^3*d - 2*a*c^3*e)*x^3 - 3*b*e*log(-c^2*x^2 + 1)^2 - 3*b*e*log((c*x + 1)/(c*x - 1))^2 - 2*(3*b*c^2*d - 5*b*c^2*e)*x^2 - 2*(6*a*c^3*e*x^3 + 3*b*c^2*e*x^2 + 3*b*d - 11*b*e)*log(-c^2*x^2 + 1) - 2*(3*b*c^3*e*x^3*log(-c^2*x^2 + 1) - 6*b*c*e*x + (3*b*c^3*d - 2*b*c^3*e)*x^3 + 6*a*e)*log((c*x + 1)/(c*x - 1)))/c^3","A",0
274,1,130,0,0.571640," ","integrate((a+b*arccoth(c*x))*(d+e*log(-c^2*x^2+1)),x, algorithm=""fricas"")","\frac{b e \log\left(-c^{2} x^{2} + 1\right)^{2} + b e \log\left(\frac{c x + 1}{c x - 1}\right)^{2} + 4 \, {\left(a c d - 2 \, a c e\right)} x + 2 \, {\left(2 \, a c e x + b d - 2 \, b e\right)} \log\left(-c^{2} x^{2} + 1\right) + 2 \, {\left(b c e x \log\left(-c^{2} x^{2} + 1\right) + 2 \, a e + {\left(b c d - 2 \, b c e\right)} x\right)} \log\left(\frac{c x + 1}{c x - 1}\right)}{4 \, c}"," ",0,"1/4*(b*e*log(-c^2*x^2 + 1)^2 + b*e*log((c*x + 1)/(c*x - 1))^2 + 4*(a*c*d - 2*a*c*e)*x + 2*(2*a*c*e*x + b*d - 2*b*e)*log(-c^2*x^2 + 1) + 2*(b*c*e*x*log(-c^2*x^2 + 1) + 2*a*e + (b*c*d - 2*b*c*e)*x)*log((c*x + 1)/(c*x - 1)))/c","A",0
275,0,0,0,0.572332," ","integrate((a+b*arccoth(c*x))*(d+e*log(-c^2*x^2+1))/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b d \operatorname{arcoth}\left(c x\right) + a d + {\left(b e \operatorname{arcoth}\left(c x\right) + a e\right)} \log\left(-c^{2} x^{2} + 1\right)}{x^{2}}, x\right)"," ",0,"integral((b*d*arccoth(c*x) + a*d + (b*e*arccoth(c*x) + a*e)*log(-c^2*x^2 + 1))/x^2, x)","F",0
276,0,0,0,0.617755," ","integrate((a+b*arccoth(c*x))*(d+e*log(-c^2*x^2+1))/x^4,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b d \operatorname{arcoth}\left(c x\right) + a d + {\left(b e \operatorname{arcoth}\left(c x\right) + a e\right)} \log\left(-c^{2} x^{2} + 1\right)}{x^{4}}, x\right)"," ",0,"integral((b*d*arccoth(c*x) + a*d + (b*e*arccoth(c*x) + a*e)*log(-c^2*x^2 + 1))/x^4, x)","F",0
277,0,0,0,0.441522," ","integrate((a+b*arccoth(c*x))*(d+e*log(-c^2*x^2+1))/x^6,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b d \operatorname{arcoth}\left(c x\right) + a d + {\left(b e \operatorname{arcoth}\left(c x\right) + a e\right)} \log\left(-c^{2} x^{2} + 1\right)}{x^{6}}, x\right)"," ",0,"integral((b*d*arccoth(c*x) + a*d + (b*e*arccoth(c*x) + a*e)*log(-c^2*x^2 + 1))/x^6, x)","F",0
278,0,0,0,0.596586," ","integrate(x*(a+b*arccoth(c*x))*(d+e*log(g*x^2+f)),x, algorithm=""fricas"")","{\rm integral}\left(b d x \operatorname{arcoth}\left(c x\right) + a d x + {\left(b e x \operatorname{arcoth}\left(c x\right) + a e x\right)} \log\left(g x^{2} + f\right), x\right)"," ",0,"integral(b*d*x*arccoth(c*x) + a*d*x + (b*e*x*arccoth(c*x) + a*e*x)*log(g*x^2 + f), x)","F",0
279,0,0,0,0.644505," ","integrate((a+b*arccoth(c*x))*(d+e*log(g*x^2+f)),x, algorithm=""fricas"")","{\rm integral}\left(b d \operatorname{arcoth}\left(c x\right) + a d + {\left(b e \operatorname{arcoth}\left(c x\right) + a e\right)} \log\left(g x^{2} + f\right), x\right)"," ",0,"integral(b*d*arccoth(c*x) + a*d + (b*e*arccoth(c*x) + a*e)*log(g*x^2 + f), x)","F",0
280,0,0,0,0.498363," ","integrate((a+b*arccoth(c*x))*(d+e*log(g*x^2+f))/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b d \operatorname{arcoth}\left(c x\right) + a d + {\left(b e \operatorname{arcoth}\left(c x\right) + a e\right)} \log\left(g x^{2} + f\right)}{x}, x\right)"," ",0,"integral((b*d*arccoth(c*x) + a*d + (b*e*arccoth(c*x) + a*e)*log(g*x^2 + f))/x, x)","F",0
281,0,0,0,0.634864," ","integrate((a+b*arccoth(c*x))*(d+e*log(g*x^2+f))/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b d \operatorname{arcoth}\left(c x\right) + a d + {\left(b e \operatorname{arcoth}\left(c x\right) + a e\right)} \log\left(g x^{2} + f\right)}{x^{2}}, x\right)"," ",0,"integral((b*d*arccoth(c*x) + a*d + (b*e*arccoth(c*x) + a*e)*log(g*x^2 + f))/x^2, x)","F",0
282,0,0,0,0.612361," ","integrate((a+b*arccoth(c*x))*(d+e*log(g*x^2+f))/x^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b d \operatorname{arcoth}\left(c x\right) + a d + {\left(b e \operatorname{arcoth}\left(c x\right) + a e\right)} \log\left(g x^{2} + f\right)}{x^{3}}, x\right)"," ",0,"integral((b*d*arccoth(c*x) + a*d + (b*e*arccoth(c*x) + a*e)*log(g*x^2 + f))/x^3, x)","F",0
283,1,64,0,0.576910," ","integrate(arccoth(exp(x)),x, algorithm=""fricas"")","\frac{1}{2} \, x \log\left(\frac{\cosh\left(x\right) + \sinh\left(x\right) + 1}{\cosh\left(x\right) + \sinh\left(x\right) - 1}\right) - \frac{1}{2} \, x \log\left(\cosh\left(x\right) + \sinh\left(x\right) + 1\right) + \frac{1}{2} \, x \log\left(-\cosh\left(x\right) - \sinh\left(x\right) + 1\right) + \frac{1}{2} \, {\rm Li}_2\left(\cosh\left(x\right) + \sinh\left(x\right)\right) - \frac{1}{2} \, {\rm Li}_2\left(-\cosh\left(x\right) - \sinh\left(x\right)\right)"," ",0,"1/2*x*log((cosh(x) + sinh(x) + 1)/(cosh(x) + sinh(x) - 1)) - 1/2*x*log(cosh(x) + sinh(x) + 1) + 1/2*x*log(-cosh(x) - sinh(x) + 1) + 1/2*dilog(cosh(x) + sinh(x)) - 1/2*dilog(-cosh(x) - sinh(x))","B",0
284,1,94,0,0.581721," ","integrate(x*arccoth(exp(x)),x, algorithm=""fricas"")","\frac{1}{4} \, x^{2} \log\left(\frac{\cosh\left(x\right) + \sinh\left(x\right) + 1}{\cosh\left(x\right) + \sinh\left(x\right) - 1}\right) - \frac{1}{4} \, x^{2} \log\left(\cosh\left(x\right) + \sinh\left(x\right) + 1\right) + \frac{1}{4} \, x^{2} \log\left(-\cosh\left(x\right) - \sinh\left(x\right) + 1\right) + \frac{1}{2} \, x {\rm Li}_2\left(\cosh\left(x\right) + \sinh\left(x\right)\right) - \frac{1}{2} \, x {\rm Li}_2\left(-\cosh\left(x\right) - \sinh\left(x\right)\right) - \frac{1}{2} \, {\rm polylog}\left(3, \cosh\left(x\right) + \sinh\left(x\right)\right) + \frac{1}{2} \, {\rm polylog}\left(3, -\cosh\left(x\right) - \sinh\left(x\right)\right)"," ",0,"1/4*x^2*log((cosh(x) + sinh(x) + 1)/(cosh(x) + sinh(x) - 1)) - 1/4*x^2*log(cosh(x) + sinh(x) + 1) + 1/4*x^2*log(-cosh(x) - sinh(x) + 1) + 1/2*x*dilog(cosh(x) + sinh(x)) - 1/2*x*dilog(-cosh(x) - sinh(x)) - 1/2*polylog(3, cosh(x) + sinh(x)) + 1/2*polylog(3, -cosh(x) - sinh(x))","C",0
285,1,119,0,0.687487," ","integrate(x^2*arccoth(exp(x)),x, algorithm=""fricas"")","\frac{1}{6} \, x^{3} \log\left(\frac{\cosh\left(x\right) + \sinh\left(x\right) + 1}{\cosh\left(x\right) + \sinh\left(x\right) - 1}\right) - \frac{1}{6} \, x^{3} \log\left(\cosh\left(x\right) + \sinh\left(x\right) + 1\right) + \frac{1}{6} \, x^{3} \log\left(-\cosh\left(x\right) - \sinh\left(x\right) + 1\right) + \frac{1}{2} \, x^{2} {\rm Li}_2\left(\cosh\left(x\right) + \sinh\left(x\right)\right) - \frac{1}{2} \, x^{2} {\rm Li}_2\left(-\cosh\left(x\right) - \sinh\left(x\right)\right) - x {\rm polylog}\left(3, \cosh\left(x\right) + \sinh\left(x\right)\right) + x {\rm polylog}\left(3, -\cosh\left(x\right) - \sinh\left(x\right)\right) + {\rm polylog}\left(4, \cosh\left(x\right) + \sinh\left(x\right)\right) - {\rm polylog}\left(4, -\cosh\left(x\right) - \sinh\left(x\right)\right)"," ",0,"1/6*x^3*log((cosh(x) + sinh(x) + 1)/(cosh(x) + sinh(x) - 1)) - 1/6*x^3*log(cosh(x) + sinh(x) + 1) + 1/6*x^3*log(-cosh(x) - sinh(x) + 1) + 1/2*x^2*dilog(cosh(x) + sinh(x)) - 1/2*x^2*dilog(-cosh(x) - sinh(x)) - x*polylog(3, cosh(x) + sinh(x)) + x*polylog(3, -cosh(x) - sinh(x)) + polylog(4, cosh(x) + sinh(x)) - polylog(4, -cosh(x) - sinh(x))","C",0
286,1,137,0,0.629951," ","integrate(arccoth(exp(b*x+a)),x, algorithm=""fricas"")","\frac{b x \log\left(\frac{\cosh\left(b x + a\right) + \sinh\left(b x + a\right) + 1}{\cosh\left(b x + a\right) + \sinh\left(b x + a\right) - 1}\right) - b x \log\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right) + 1\right) - a \log\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right) - 1\right) + {\left(b x + a\right)} \log\left(-\cosh\left(b x + a\right) - \sinh\left(b x + a\right) + 1\right) + {\rm Li}_2\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right) - {\rm Li}_2\left(-\cosh\left(b x + a\right) - \sinh\left(b x + a\right)\right)}{2 \, b}"," ",0,"1/2*(b*x*log((cosh(b*x + a) + sinh(b*x + a) + 1)/(cosh(b*x + a) + sinh(b*x + a) - 1)) - b*x*log(cosh(b*x + a) + sinh(b*x + a) + 1) - a*log(cosh(b*x + a) + sinh(b*x + a) - 1) + (b*x + a)*log(-cosh(b*x + a) - sinh(b*x + a) + 1) + dilog(cosh(b*x + a) + sinh(b*x + a)) - dilog(-cosh(b*x + a) - sinh(b*x + a)))/b","B",0
287,1,198,0,0.642873," ","integrate(x*arccoth(exp(b*x+a)),x, algorithm=""fricas"")","\frac{b^{2} x^{2} \log\left(\frac{\cosh\left(b x + a\right) + \sinh\left(b x + a\right) + 1}{\cosh\left(b x + a\right) + \sinh\left(b x + a\right) - 1}\right) - b^{2} x^{2} \log\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right) + 1\right) + 2 \, b x {\rm Li}_2\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right) - 2 \, b x {\rm Li}_2\left(-\cosh\left(b x + a\right) - \sinh\left(b x + a\right)\right) + a^{2} \log\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right) - 1\right) + {\left(b^{2} x^{2} - a^{2}\right)} \log\left(-\cosh\left(b x + a\right) - \sinh\left(b x + a\right) + 1\right) - 2 \, {\rm polylog}\left(3, \cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right) + 2 \, {\rm polylog}\left(3, -\cosh\left(b x + a\right) - \sinh\left(b x + a\right)\right)}{4 \, b^{2}}"," ",0,"1/4*(b^2*x^2*log((cosh(b*x + a) + sinh(b*x + a) + 1)/(cosh(b*x + a) + sinh(b*x + a) - 1)) - b^2*x^2*log(cosh(b*x + a) + sinh(b*x + a) + 1) + 2*b*x*dilog(cosh(b*x + a) + sinh(b*x + a)) - 2*b*x*dilog(-cosh(b*x + a) - sinh(b*x + a)) + a^2*log(cosh(b*x + a) + sinh(b*x + a) - 1) + (b^2*x^2 - a^2)*log(-cosh(b*x + a) - sinh(b*x + a) + 1) - 2*polylog(3, cosh(b*x + a) + sinh(b*x + a)) + 2*polylog(3, -cosh(b*x + a) - sinh(b*x + a)))/b^2","C",0
288,1,247,0,0.572681," ","integrate(x^2*arccoth(exp(b*x+a)),x, algorithm=""fricas"")","\frac{b^{3} x^{3} \log\left(\frac{\cosh\left(b x + a\right) + \sinh\left(b x + a\right) + 1}{\cosh\left(b x + a\right) + \sinh\left(b x + a\right) - 1}\right) - b^{3} x^{3} \log\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right) + 1\right) + 3 \, b^{2} x^{2} {\rm Li}_2\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right) - 3 \, b^{2} x^{2} {\rm Li}_2\left(-\cosh\left(b x + a\right) - \sinh\left(b x + a\right)\right) - a^{3} \log\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right) - 1\right) - 6 \, b x {\rm polylog}\left(3, \cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right) + 6 \, b x {\rm polylog}\left(3, -\cosh\left(b x + a\right) - \sinh\left(b x + a\right)\right) + {\left(b^{3} x^{3} + a^{3}\right)} \log\left(-\cosh\left(b x + a\right) - \sinh\left(b x + a\right) + 1\right) + 6 \, {\rm polylog}\left(4, \cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right) - 6 \, {\rm polylog}\left(4, -\cosh\left(b x + a\right) - \sinh\left(b x + a\right)\right)}{6 \, b^{3}}"," ",0,"1/6*(b^3*x^3*log((cosh(b*x + a) + sinh(b*x + a) + 1)/(cosh(b*x + a) + sinh(b*x + a) - 1)) - b^3*x^3*log(cosh(b*x + a) + sinh(b*x + a) + 1) + 3*b^2*x^2*dilog(cosh(b*x + a) + sinh(b*x + a)) - 3*b^2*x^2*dilog(-cosh(b*x + a) - sinh(b*x + a)) - a^3*log(cosh(b*x + a) + sinh(b*x + a) - 1) - 6*b*x*polylog(3, cosh(b*x + a) + sinh(b*x + a)) + 6*b*x*polylog(3, -cosh(b*x + a) - sinh(b*x + a)) + (b^3*x^3 + a^3)*log(-cosh(b*x + a) - sinh(b*x + a) + 1) + 6*polylog(4, cosh(b*x + a) + sinh(b*x + a)) - 6*polylog(4, -cosh(b*x + a) - sinh(b*x + a)))/b^3","C",0
289,1,283,0,0.578553," ","integrate(arccoth(a+b*f^(d*x+c)),x, algorithm=""fricas"")","\frac{d x \log\left(f\right) \log\left(\frac{b \cosh\left({\left(d x + c\right)} \log\left(f\right)\right) + b \sinh\left({\left(d x + c\right)} \log\left(f\right)\right) + a + 1}{b \cosh\left({\left(d x + c\right)} \log\left(f\right)\right) + b \sinh\left({\left(d x + c\right)} \log\left(f\right)\right) + a - 1}\right) + c \log\left(b \cosh\left({\left(d x + c\right)} \log\left(f\right)\right) + b \sinh\left({\left(d x + c\right)} \log\left(f\right)\right) + a + 1\right) \log\left(f\right) - c \log\left(b \cosh\left({\left(d x + c\right)} \log\left(f\right)\right) + b \sinh\left({\left(d x + c\right)} \log\left(f\right)\right) + a - 1\right) \log\left(f\right) - {\left(d x + c\right)} \log\left(f\right) \log\left(\frac{b \cosh\left({\left(d x + c\right)} \log\left(f\right)\right) + b \sinh\left({\left(d x + c\right)} \log\left(f\right)\right) + a + 1}{a + 1}\right) + {\left(d x + c\right)} \log\left(f\right) \log\left(\frac{b \cosh\left({\left(d x + c\right)} \log\left(f\right)\right) + b \sinh\left({\left(d x + c\right)} \log\left(f\right)\right) + a - 1}{a - 1}\right) - {\rm Li}_2\left(-\frac{b \cosh\left({\left(d x + c\right)} \log\left(f\right)\right) + b \sinh\left({\left(d x + c\right)} \log\left(f\right)\right) + a + 1}{a + 1} + 1\right) + {\rm Li}_2\left(-\frac{b \cosh\left({\left(d x + c\right)} \log\left(f\right)\right) + b \sinh\left({\left(d x + c\right)} \log\left(f\right)\right) + a - 1}{a - 1} + 1\right)}{2 \, d \log\left(f\right)}"," ",0,"1/2*(d*x*log(f)*log((b*cosh((d*x + c)*log(f)) + b*sinh((d*x + c)*log(f)) + a + 1)/(b*cosh((d*x + c)*log(f)) + b*sinh((d*x + c)*log(f)) + a - 1)) + c*log(b*cosh((d*x + c)*log(f)) + b*sinh((d*x + c)*log(f)) + a + 1)*log(f) - c*log(b*cosh((d*x + c)*log(f)) + b*sinh((d*x + c)*log(f)) + a - 1)*log(f) - (d*x + c)*log(f)*log((b*cosh((d*x + c)*log(f)) + b*sinh((d*x + c)*log(f)) + a + 1)/(a + 1)) + (d*x + c)*log(f)*log((b*cosh((d*x + c)*log(f)) + b*sinh((d*x + c)*log(f)) + a - 1)/(a - 1)) - dilog(-(b*cosh((d*x + c)*log(f)) + b*sinh((d*x + c)*log(f)) + a + 1)/(a + 1) + 1) + dilog(-(b*cosh((d*x + c)*log(f)) + b*sinh((d*x + c)*log(f)) + a - 1)/(a - 1) + 1))/(d*log(f))","A",0
290,1,395,0,0.659161," ","integrate(x*arccoth(a+b*f^(d*x+c)),x, algorithm=""fricas"")","\frac{d^{2} x^{2} \log\left(f\right)^{2} \log\left(\frac{b \cosh\left({\left(d x + c\right)} \log\left(f\right)\right) + b \sinh\left({\left(d x + c\right)} \log\left(f\right)\right) + a + 1}{b \cosh\left({\left(d x + c\right)} \log\left(f\right)\right) + b \sinh\left({\left(d x + c\right)} \log\left(f\right)\right) + a - 1}\right) - c^{2} \log\left(b \cosh\left({\left(d x + c\right)} \log\left(f\right)\right) + b \sinh\left({\left(d x + c\right)} \log\left(f\right)\right) + a + 1\right) \log\left(f\right)^{2} + c^{2} \log\left(b \cosh\left({\left(d x + c\right)} \log\left(f\right)\right) + b \sinh\left({\left(d x + c\right)} \log\left(f\right)\right) + a - 1\right) \log\left(f\right)^{2} - 2 \, d x {\rm Li}_2\left(-\frac{b \cosh\left({\left(d x + c\right)} \log\left(f\right)\right) + b \sinh\left({\left(d x + c\right)} \log\left(f\right)\right) + a + 1}{a + 1} + 1\right) \log\left(f\right) + 2 \, d x {\rm Li}_2\left(-\frac{b \cosh\left({\left(d x + c\right)} \log\left(f\right)\right) + b \sinh\left({\left(d x + c\right)} \log\left(f\right)\right) + a - 1}{a - 1} + 1\right) \log\left(f\right) - {\left(d^{2} x^{2} - c^{2}\right)} \log\left(f\right)^{2} \log\left(\frac{b \cosh\left({\left(d x + c\right)} \log\left(f\right)\right) + b \sinh\left({\left(d x + c\right)} \log\left(f\right)\right) + a + 1}{a + 1}\right) + {\left(d^{2} x^{2} - c^{2}\right)} \log\left(f\right)^{2} \log\left(\frac{b \cosh\left({\left(d x + c\right)} \log\left(f\right)\right) + b \sinh\left({\left(d x + c\right)} \log\left(f\right)\right) + a - 1}{a - 1}\right) + 2 \, {\rm polylog}\left(3, -\frac{b \cosh\left({\left(d x + c\right)} \log\left(f\right)\right) + b \sinh\left({\left(d x + c\right)} \log\left(f\right)\right)}{a + 1}\right) - 2 \, {\rm polylog}\left(3, -\frac{b \cosh\left({\left(d x + c\right)} \log\left(f\right)\right) + b \sinh\left({\left(d x + c\right)} \log\left(f\right)\right)}{a - 1}\right)}{4 \, d^{2} \log\left(f\right)^{2}}"," ",0,"1/4*(d^2*x^2*log(f)^2*log((b*cosh((d*x + c)*log(f)) + b*sinh((d*x + c)*log(f)) + a + 1)/(b*cosh((d*x + c)*log(f)) + b*sinh((d*x + c)*log(f)) + a - 1)) - c^2*log(b*cosh((d*x + c)*log(f)) + b*sinh((d*x + c)*log(f)) + a + 1)*log(f)^2 + c^2*log(b*cosh((d*x + c)*log(f)) + b*sinh((d*x + c)*log(f)) + a - 1)*log(f)^2 - 2*d*x*dilog(-(b*cosh((d*x + c)*log(f)) + b*sinh((d*x + c)*log(f)) + a + 1)/(a + 1) + 1)*log(f) + 2*d*x*dilog(-(b*cosh((d*x + c)*log(f)) + b*sinh((d*x + c)*log(f)) + a - 1)/(a - 1) + 1)*log(f) - (d^2*x^2 - c^2)*log(f)^2*log((b*cosh((d*x + c)*log(f)) + b*sinh((d*x + c)*log(f)) + a + 1)/(a + 1)) + (d^2*x^2 - c^2)*log(f)^2*log((b*cosh((d*x + c)*log(f)) + b*sinh((d*x + c)*log(f)) + a - 1)/(a - 1)) + 2*polylog(3, -(b*cosh((d*x + c)*log(f)) + b*sinh((d*x + c)*log(f)))/(a + 1)) - 2*polylog(3, -(b*cosh((d*x + c)*log(f)) + b*sinh((d*x + c)*log(f)))/(a - 1)))/(d^2*log(f)^2)","C",0
291,1,479,0,0.704967," ","integrate(x^2*arccoth(a+b*f^(d*x+c)),x, algorithm=""fricas"")","\frac{d^{3} x^{3} \log\left(f\right)^{3} \log\left(\frac{b \cosh\left({\left(d x + c\right)} \log\left(f\right)\right) + b \sinh\left({\left(d x + c\right)} \log\left(f\right)\right) + a + 1}{b \cosh\left({\left(d x + c\right)} \log\left(f\right)\right) + b \sinh\left({\left(d x + c\right)} \log\left(f\right)\right) + a - 1}\right) - 3 \, d^{2} x^{2} {\rm Li}_2\left(-\frac{b \cosh\left({\left(d x + c\right)} \log\left(f\right)\right) + b \sinh\left({\left(d x + c\right)} \log\left(f\right)\right) + a + 1}{a + 1} + 1\right) \log\left(f\right)^{2} + 3 \, d^{2} x^{2} {\rm Li}_2\left(-\frac{b \cosh\left({\left(d x + c\right)} \log\left(f\right)\right) + b \sinh\left({\left(d x + c\right)} \log\left(f\right)\right) + a - 1}{a - 1} + 1\right) \log\left(f\right)^{2} + c^{3} \log\left(b \cosh\left({\left(d x + c\right)} \log\left(f\right)\right) + b \sinh\left({\left(d x + c\right)} \log\left(f\right)\right) + a + 1\right) \log\left(f\right)^{3} - c^{3} \log\left(b \cosh\left({\left(d x + c\right)} \log\left(f\right)\right) + b \sinh\left({\left(d x + c\right)} \log\left(f\right)\right) + a - 1\right) \log\left(f\right)^{3} - {\left(d^{3} x^{3} + c^{3}\right)} \log\left(f\right)^{3} \log\left(\frac{b \cosh\left({\left(d x + c\right)} \log\left(f\right)\right) + b \sinh\left({\left(d x + c\right)} \log\left(f\right)\right) + a + 1}{a + 1}\right) + {\left(d^{3} x^{3} + c^{3}\right)} \log\left(f\right)^{3} \log\left(\frac{b \cosh\left({\left(d x + c\right)} \log\left(f\right)\right) + b \sinh\left({\left(d x + c\right)} \log\left(f\right)\right) + a - 1}{a - 1}\right) + 6 \, d x \log\left(f\right) {\rm polylog}\left(3, -\frac{b \cosh\left({\left(d x + c\right)} \log\left(f\right)\right) + b \sinh\left({\left(d x + c\right)} \log\left(f\right)\right)}{a + 1}\right) - 6 \, d x \log\left(f\right) {\rm polylog}\left(3, -\frac{b \cosh\left({\left(d x + c\right)} \log\left(f\right)\right) + b \sinh\left({\left(d x + c\right)} \log\left(f\right)\right)}{a - 1}\right) - 6 \, {\rm polylog}\left(4, -\frac{b \cosh\left({\left(d x + c\right)} \log\left(f\right)\right) + b \sinh\left({\left(d x + c\right)} \log\left(f\right)\right)}{a + 1}\right) + 6 \, {\rm polylog}\left(4, -\frac{b \cosh\left({\left(d x + c\right)} \log\left(f\right)\right) + b \sinh\left({\left(d x + c\right)} \log\left(f\right)\right)}{a - 1}\right)}{6 \, d^{3} \log\left(f\right)^{3}}"," ",0,"1/6*(d^3*x^3*log(f)^3*log((b*cosh((d*x + c)*log(f)) + b*sinh((d*x + c)*log(f)) + a + 1)/(b*cosh((d*x + c)*log(f)) + b*sinh((d*x + c)*log(f)) + a - 1)) - 3*d^2*x^2*dilog(-(b*cosh((d*x + c)*log(f)) + b*sinh((d*x + c)*log(f)) + a + 1)/(a + 1) + 1)*log(f)^2 + 3*d^2*x^2*dilog(-(b*cosh((d*x + c)*log(f)) + b*sinh((d*x + c)*log(f)) + a - 1)/(a - 1) + 1)*log(f)^2 + c^3*log(b*cosh((d*x + c)*log(f)) + b*sinh((d*x + c)*log(f)) + a + 1)*log(f)^3 - c^3*log(b*cosh((d*x + c)*log(f)) + b*sinh((d*x + c)*log(f)) + a - 1)*log(f)^3 - (d^3*x^3 + c^3)*log(f)^3*log((b*cosh((d*x + c)*log(f)) + b*sinh((d*x + c)*log(f)) + a + 1)/(a + 1)) + (d^3*x^3 + c^3)*log(f)^3*log((b*cosh((d*x + c)*log(f)) + b*sinh((d*x + c)*log(f)) + a - 1)/(a - 1)) + 6*d*x*log(f)*polylog(3, -(b*cosh((d*x + c)*log(f)) + b*sinh((d*x + c)*log(f)))/(a + 1)) - 6*d*x*log(f)*polylog(3, -(b*cosh((d*x + c)*log(f)) + b*sinh((d*x + c)*log(f)))/(a - 1)) - 6*polylog(4, -(b*cosh((d*x + c)*log(f)) + b*sinh((d*x + c)*log(f)))/(a + 1)) + 6*polylog(4, -(b*cosh((d*x + c)*log(f)) + b*sinh((d*x + c)*log(f)))/(a - 1)))/(d^3*log(f)^3)","C",0
292,1,21,0,0.730174," ","integrate(1/(-a*x^2+a)/(b-2*b*arccoth(x)),x, algorithm=""fricas"")","-\frac{\log\left(\log\left(\frac{x + 1}{x - 1}\right) - 1\right)}{2 \, a b}"," ",0,"-1/2*log(log((x + 1)/(x - 1)) - 1)/(a*b)","A",0
293,1,58,0,0.606601," ","integrate(x^3*arccoth(b*x^4+a),x, algorithm=""fricas"")","\frac{b x^{4} \log\left(\frac{b x^{4} + a + 1}{b x^{4} + a - 1}\right) + {\left(a + 1\right)} \log\left(b x^{4} + a + 1\right) - {\left(a - 1\right)} \log\left(b x^{4} + a - 1\right)}{8 \, b}"," ",0,"1/8*(b*x^4*log((b*x^4 + a + 1)/(b*x^4 + a - 1)) + (a + 1)*log(b*x^4 + a + 1) - (a - 1)*log(b*x^4 + a - 1))/b","A",0
294,1,108,0,0.636641," ","integrate(x^(-1+n)*arccoth(a+b*x^n),x, algorithm=""fricas"")","\frac{{\left(a + 1\right)} \log\left(b \cosh\left(n \log\left(x\right)\right) + b \sinh\left(n \log\left(x\right)\right) + a + 1\right) - {\left(a - 1\right)} \log\left(b \cosh\left(n \log\left(x\right)\right) + b \sinh\left(n \log\left(x\right)\right) + a - 1\right) + {\left(b \cosh\left(n \log\left(x\right)\right) + b \sinh\left(n \log\left(x\right)\right)\right)} \log\left(\frac{b \cosh\left(n \log\left(x\right)\right) + b \sinh\left(n \log\left(x\right)\right) + a + 1}{b \cosh\left(n \log\left(x\right)\right) + b \sinh\left(n \log\left(x\right)\right) + a - 1}\right)}{2 \, b n}"," ",0,"1/2*((a + 1)*log(b*cosh(n*log(x)) + b*sinh(n*log(x)) + a + 1) - (a - 1)*log(b*cosh(n*log(x)) + b*sinh(n*log(x)) + a - 1) + (b*cosh(n*log(x)) + b*sinh(n*log(x)))*log((b*cosh(n*log(x)) + b*sinh(n*log(x)) + a + 1)/(b*cosh(n*log(x)) + b*sinh(n*log(x)) + a - 1)))/(b*n)","B",0
295,1,233,0,0.589660," ","integrate(exp(c*(b*x+a))*arccoth(sinh(b*c*x+a*c)),x, algorithm=""fricas"")","\frac{{\left(\cosh\left(b c x + a c\right) + \sinh\left(b c x + a c\right)\right)} \log\left(\frac{\sinh\left(b c x + a c\right) + 1}{\sinh\left(b c x + a c\right) - 1}\right) + \sqrt{2} \log\left(\frac{3 \, {\left(2 \, \sqrt{2} + 3\right)} \cosh\left(b c x + a c\right)^{2} - 4 \, {\left(3 \, \sqrt{2} + 4\right)} \cosh\left(b c x + a c\right) \sinh\left(b c x + a c\right) + 3 \, {\left(2 \, \sqrt{2} + 3\right)} \sinh\left(b c x + a c\right)^{2} - 2 \, \sqrt{2} - 3}{\cosh\left(b c x + a c\right)^{2} + \sinh\left(b c x + a c\right)^{2} - 3}\right) + \log\left(\frac{2 \, {\left(\cosh\left(b c x + a c\right)^{2} + \sinh\left(b c x + a c\right)^{2} - 3\right)}}{\cosh\left(b c x + a c\right)^{2} - 2 \, \cosh\left(b c x + a c\right) \sinh\left(b c x + a c\right) + \sinh\left(b c x + a c\right)^{2}}\right)}{2 \, b c}"," ",0,"1/2*((cosh(b*c*x + a*c) + sinh(b*c*x + a*c))*log((sinh(b*c*x + a*c) + 1)/(sinh(b*c*x + a*c) - 1)) + sqrt(2)*log((3*(2*sqrt(2) + 3)*cosh(b*c*x + a*c)^2 - 4*(3*sqrt(2) + 4)*cosh(b*c*x + a*c)*sinh(b*c*x + a*c) + 3*(2*sqrt(2) + 3)*sinh(b*c*x + a*c)^2 - 2*sqrt(2) - 3)/(cosh(b*c*x + a*c)^2 + sinh(b*c*x + a*c)^2 - 3)) + log(2*(cosh(b*c*x + a*c)^2 + sinh(b*c*x + a*c)^2 - 3)/(cosh(b*c*x + a*c)^2 - 2*cosh(b*c*x + a*c)*sinh(b*c*x + a*c) + sinh(b*c*x + a*c)^2)))/(b*c)","B",0
296,1,92,0,0.496269," ","integrate(exp(c*(b*x+a))*arccoth(cosh(b*c*x+a*c)),x, algorithm=""fricas"")","\frac{{\left(\cosh\left(b c x + a c\right) + \sinh\left(b c x + a c\right)\right)} \log\left(\frac{\cosh\left(b c x + a c\right) + 1}{\cosh\left(b c x + a c\right) - 1}\right) + 2 \, \log\left(\frac{2 \, \sinh\left(b c x + a c\right)}{\cosh\left(b c x + a c\right) - \sinh\left(b c x + a c\right)}\right)}{2 \, b c}"," ",0,"1/2*((cosh(b*c*x + a*c) + sinh(b*c*x + a*c))*log((cosh(b*c*x + a*c) + 1)/(cosh(b*c*x + a*c) - 1)) + 2*log(2*sinh(b*c*x + a*c)/(cosh(b*c*x + a*c) - sinh(b*c*x + a*c))))/(b*c)","A",0
297,1,25,0,0.583654," ","integrate(exp(c*(b*x+a))*arccoth(tanh(b*c*x+a*c)),x, algorithm=""fricas"")","\frac{{\left(b c x + a c - 1\right)} e^{\left(b c x + a c\right)}}{b c}"," ",0,"(b*c*x + a*c - 1)*e^(b*c*x + a*c)/(b*c)","A",0
298,1,25,0,0.526272," ","integrate(exp(c*(b*x+a))*arccoth(coth(b*c*x+a*c)),x, algorithm=""fricas"")","\frac{{\left(b c x + a c - 1\right)} e^{\left(b c x + a c\right)}}{b c}"," ",0,"(b*c*x + a*c - 1)*e^(b*c*x + a*c)/(b*c)","A",0
299,1,93,0,0.666528," ","integrate(exp(c*(b*x+a))*arccoth(sech(b*c*x+a*c)),x, algorithm=""fricas"")","\frac{{\left(\cosh\left(b c x + a c\right) + \sinh\left(b c x + a c\right)\right)} \log\left(-\frac{\cosh\left(b c x + a c\right) + 1}{\cosh\left(b c x + a c\right) - 1}\right) + 2 \, \log\left(\frac{2 \, \sinh\left(b c x + a c\right)}{\cosh\left(b c x + a c\right) - \sinh\left(b c x + a c\right)}\right)}{2 \, b c}"," ",0,"1/2*((cosh(b*c*x + a*c) + sinh(b*c*x + a*c))*log(-(cosh(b*c*x + a*c) + 1)/(cosh(b*c*x + a*c) - 1)) + 2*log(2*sinh(b*c*x + a*c)/(cosh(b*c*x + a*c) - sinh(b*c*x + a*c))))/(b*c)","A",0
300,1,234,0,0.459594," ","integrate(exp(c*(b*x+a))*arccoth(csch(b*c*x+a*c)),x, algorithm=""fricas"")","\frac{{\left(\cosh\left(b c x + a c\right) + \sinh\left(b c x + a c\right)\right)} \log\left(-\frac{\sinh\left(b c x + a c\right) + 1}{\sinh\left(b c x + a c\right) - 1}\right) + \sqrt{2} \log\left(\frac{3 \, {\left(2 \, \sqrt{2} + 3\right)} \cosh\left(b c x + a c\right)^{2} - 4 \, {\left(3 \, \sqrt{2} + 4\right)} \cosh\left(b c x + a c\right) \sinh\left(b c x + a c\right) + 3 \, {\left(2 \, \sqrt{2} + 3\right)} \sinh\left(b c x + a c\right)^{2} - 2 \, \sqrt{2} - 3}{\cosh\left(b c x + a c\right)^{2} + \sinh\left(b c x + a c\right)^{2} - 3}\right) + \log\left(\frac{2 \, {\left(\cosh\left(b c x + a c\right)^{2} + \sinh\left(b c x + a c\right)^{2} - 3\right)}}{\cosh\left(b c x + a c\right)^{2} - 2 \, \cosh\left(b c x + a c\right) \sinh\left(b c x + a c\right) + \sinh\left(b c x + a c\right)^{2}}\right)}{2 \, b c}"," ",0,"1/2*((cosh(b*c*x + a*c) + sinh(b*c*x + a*c))*log(-(sinh(b*c*x + a*c) + 1)/(sinh(b*c*x + a*c) - 1)) + sqrt(2)*log((3*(2*sqrt(2) + 3)*cosh(b*c*x + a*c)^2 - 4*(3*sqrt(2) + 4)*cosh(b*c*x + a*c)*sinh(b*c*x + a*c) + 3*(2*sqrt(2) + 3)*sinh(b*c*x + a*c)^2 - 2*sqrt(2) - 3)/(cosh(b*c*x + a*c)^2 + sinh(b*c*x + a*c)^2 - 3)) + log(2*(cosh(b*c*x + a*c)^2 + sinh(b*c*x + a*c)^2 - 3)/(cosh(b*c*x + a*c)^2 - 2*cosh(b*c*x + a*c)*sinh(b*c*x + a*c) + sinh(b*c*x + a*c)^2)))/(b*c)","B",0
