1,1,41,0,0.908254," ","integrate(x^5*arccot(a*x),x, algorithm=""fricas"")","\frac{3 \, a^{5} x^{5} - 5 \, a^{3} x^{3} + 15 \, a x + 15 \, {\left(a^{6} x^{6} + 1\right)} \operatorname{arccot}\left(a x\right)}{90 \, a^{6}}"," ",0,"1/90*(3*a^5*x^5 - 5*a^3*x^3 + 15*a*x + 15*(a^6*x^6 + 1)*arccot(a*x))/a^6","A",0
2,1,45,0,0.535703," ","integrate(x^4*arccot(a*x),x, algorithm=""fricas"")","\frac{4 \, a^{5} x^{5} \operatorname{arccot}\left(a x\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*(4*a^5*x^5*arccot(a*x) + a^4*x^4 - 2*a^2*x^2 + 2*log(a^2*x^2 + 1))/a^5","A",0
3,1,32,0,1.014829," ","integrate(x^3*arccot(a*x),x, algorithm=""fricas"")","\frac{a^{3} x^{3} - 3 \, a x + 3 \, {\left(a^{4} x^{4} - 1\right)} \operatorname{arccot}\left(a x\right)}{12 \, a^{4}}"," ",0,"1/12*(a^3*x^3 - 3*a*x + 3*(a^4*x^4 - 1)*arccot(a*x))/a^4","A",0
4,1,37,0,0.729549," ","integrate(x^2*arccot(a*x),x, algorithm=""fricas"")","\frac{2 \, a^{3} x^{3} \operatorname{arccot}\left(a x\right) + a^{2} x^{2} - \log\left(a^{2} x^{2} + 1\right)}{6 \, a^{3}}"," ",0,"1/6*(2*a^3*x^3*arccot(a*x) + a^2*x^2 - log(a^2*x^2 + 1))/a^3","A",0
5,1,23,0,0.675884," ","integrate(x*arccot(a*x),x, algorithm=""fricas"")","\frac{a x + {\left(a^{2} x^{2} + 1\right)} \operatorname{arccot}\left(a x\right)}{2 \, a^{2}}"," ",0,"1/2*(a*x + (a^2*x^2 + 1)*arccot(a*x))/a^2","A",0
6,1,24,0,0.752664," ","integrate(arccot(a*x),x, algorithm=""fricas"")","\frac{2 \, a x \operatorname{arccot}\left(a x\right) + \log\left(a^{2} x^{2} + 1\right)}{2 \, a}"," ",0,"1/2*(2*a*x*arccot(a*x) + log(a^2*x^2 + 1))/a","A",0
7,0,0,0,0.978658," ","integrate(arccot(a*x)/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{arccot}\left(a x\right)}{x}, x\right)"," ",0,"integral(arccot(a*x)/x, x)","F",0
8,1,31,0,0.783325," ","integrate(arccot(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) - 2 \, \operatorname{arccot}\left(a x\right)}{2 \, x}"," ",0,"1/2*(a*x*log(a^2*x^2 + 1) - 2*a*x*log(x) - 2*arccot(a*x))/x","A",0
9,1,24,0,0.572562," ","integrate(arccot(a*x)/x^3,x, algorithm=""fricas"")","\frac{a x - {\left(a^{2} x^{2} + 1\right)} \operatorname{arccot}\left(a x\right)}{2 \, x^{2}}"," ",0,"1/2*(a*x - (a^2*x^2 + 1)*arccot(a*x))/x^2","A",0
10,1,43,0,0.620880," ","integrate(arccot(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 + 2 \, \operatorname{arccot}\left(a x\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 + 2*arccot(a*x))/x^3","A",0
11,1,33,0,0.702150," ","integrate(arccot(a*x)/x^5,x, algorithm=""fricas"")","-\frac{3 \, a^{3} x^{3} - a x - 3 \, {\left(a^{4} x^{4} - 1\right)} \operatorname{arccot}\left(a x\right)}{12 \, x^{4}}"," ",0,"-1/12*(3*a^3*x^3 - a*x - 3*(a^4*x^4 - 1)*arccot(a*x))/x^4","A",0
12,1,78,0,0.607374," ","integrate(x^5*arccot(a*x)^2,x, algorithm=""fricas"")","\frac{3 \, a^{4} x^{4} - 16 \, a^{2} x^{2} + 30 \, {\left(a^{6} x^{6} + 1\right)} \operatorname{arccot}\left(a x\right)^{2} + 4 \, {\left(3 \, a^{5} x^{5} - 5 \, a^{3} x^{3} + 15 \, a x\right)} \operatorname{arccot}\left(a x\right) + 46 \, \log\left(a^{2} x^{2} + 1\right)}{180 \, a^{6}}"," ",0,"1/180*(3*a^4*x^4 - 16*a^2*x^2 + 30*(a^6*x^6 + 1)*arccot(a*x)^2 + 4*(3*a^5*x^5 - 5*a^3*x^3 + 15*a*x)*arccot(a*x) + 46*log(a^2*x^2 + 1))/a^6","A",0
13,0,0,0,0.650764," ","integrate(x^4*arccot(a*x)^2,x, algorithm=""fricas"")","{\rm integral}\left(x^{4} \operatorname{arccot}\left(a x\right)^{2}, x\right)"," ",0,"integral(x^4*arccot(a*x)^2, x)","F",0
14,1,60,0,0.643930," ","integrate(x^3*arccot(a*x)^2,x, algorithm=""fricas"")","\frac{a^{2} x^{2} + 3 \, {\left(a^{4} x^{4} - 1\right)} \operatorname{arccot}\left(a x\right)^{2} + 2 \, {\left(a^{3} x^{3} - 3 \, a x\right)} \operatorname{arccot}\left(a x\right) - 4 \, \log\left(a^{2} x^{2} + 1\right)}{12 \, a^{4}}"," ",0,"1/12*(a^2*x^2 + 3*(a^4*x^4 - 1)*arccot(a*x)^2 + 2*(a^3*x^3 - 3*a*x)*arccot(a*x) - 4*log(a^2*x^2 + 1))/a^4","A",0
15,0,0,0,0.627933," ","integrate(x^2*arccot(a*x)^2,x, algorithm=""fricas"")","{\rm integral}\left(x^{2} \operatorname{arccot}\left(a x\right)^{2}, x\right)"," ",0,"integral(x^2*arccot(a*x)^2, x)","F",0
16,1,40,0,0.586077," ","integrate(x*arccot(a*x)^2,x, algorithm=""fricas"")","\frac{2 \, a x \operatorname{arccot}\left(a x\right) + {\left(a^{2} x^{2} + 1\right)} \operatorname{arccot}\left(a x\right)^{2} + \log\left(a^{2} x^{2} + 1\right)}{2 \, a^{2}}"," ",0,"1/2*(2*a*x*arccot(a*x) + (a^2*x^2 + 1)*arccot(a*x)^2 + log(a^2*x^2 + 1))/a^2","A",0
17,0,0,0,0.593467," ","integrate(arccot(a*x)^2,x, algorithm=""fricas"")","{\rm integral}\left(\operatorname{arccot}\left(a x\right)^{2}, x\right)"," ",0,"integral(arccot(a*x)^2, x)","F",0
18,0,0,0,0.563695," ","integrate(arccot(a*x)^2/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{arccot}\left(a x\right)^{2}}{x}, x\right)"," ",0,"integral(arccot(a*x)^2/x, x)","F",0
19,0,0,0,0.556057," ","integrate(arccot(a*x)^2/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{arccot}\left(a x\right)^{2}}{x^{2}}, x\right)"," ",0,"integral(arccot(a*x)^2/x^2, x)","F",0
20,1,57,0,0.713787," ","integrate(arccot(a*x)^2/x^3,x, algorithm=""fricas"")","-\frac{a^{2} x^{2} \log\left(a^{2} x^{2} + 1\right) - 2 \, a^{2} x^{2} \log\left(x\right) - 2 \, a x \operatorname{arccot}\left(a x\right) + {\left(a^{2} x^{2} + 1\right)} \operatorname{arccot}\left(a x\right)^{2}}{2 \, x^{2}}"," ",0,"-1/2*(a^2*x^2*log(a^2*x^2 + 1) - 2*a^2*x^2*log(x) - 2*a*x*arccot(a*x) + (a^2*x^2 + 1)*arccot(a*x)^2)/x^2","A",0
21,0,0,0,0.678141," ","integrate(arccot(a*x)^2/x^4,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{arccot}\left(a x\right)^{2}}{x^{4}}, x\right)"," ",0,"integral(arccot(a*x)^2/x^4, x)","F",0
22,1,78,0,0.860934," ","integrate(arccot(a*x)^2/x^5,x, algorithm=""fricas"")","\frac{4 \, a^{4} x^{4} \log\left(a^{2} x^{2} + 1\right) - 8 \, a^{4} x^{4} \log\left(x\right) - a^{2} x^{2} + 3 \, {\left(a^{4} x^{4} - 1\right)} \operatorname{arccot}\left(a x\right)^{2} - 2 \, {\left(3 \, a^{3} x^{3} - a x\right)} \operatorname{arccot}\left(a x\right)}{12 \, x^{4}}"," ",0,"1/12*(4*a^4*x^4*log(a^2*x^2 + 1) - 8*a^4*x^4*log(x) - a^2*x^2 + 3*(a^4*x^4 - 1)*arccot(a*x)^2 - 2*(3*a^3*x^3 - a*x)*arccot(a*x))/x^4","A",0
23,0,0,0,0.975331," ","integrate(x^5*arccot(a*x)^3,x, algorithm=""fricas"")","{\rm integral}\left(x^{5} \operatorname{arccot}\left(a x\right)^{3}, x\right)"," ",0,"integral(x^5*arccot(a*x)^3, x)","F",0
24,0,0,0,1.133386," ","integrate(x^4*arccot(a*x)^3,x, algorithm=""fricas"")","{\rm integral}\left(x^{4} \operatorname{arccot}\left(a x\right)^{3}, x\right)"," ",0,"integral(x^4*arccot(a*x)^3, x)","F",0
25,0,0,0,0.548593," ","integrate(x^3*arccot(a*x)^3,x, algorithm=""fricas"")","{\rm integral}\left(x^{3} \operatorname{arccot}\left(a x\right)^{3}, x\right)"," ",0,"integral(x^3*arccot(a*x)^3, x)","F",0
26,0,0,0,0.603316," ","integrate(x^2*arccot(a*x)^3,x, algorithm=""fricas"")","{\rm integral}\left(x^{2} \operatorname{arccot}\left(a x\right)^{3}, x\right)"," ",0,"integral(x^2*arccot(a*x)^3, x)","F",0
27,0,0,0,0.700206," ","integrate(x*arccot(a*x)^3,x, algorithm=""fricas"")","{\rm integral}\left(x \operatorname{arccot}\left(a x\right)^{3}, x\right)"," ",0,"integral(x*arccot(a*x)^3, x)","F",0
28,0,0,0,0.540454," ","integrate(arccot(a*x)^3,x, algorithm=""fricas"")","{\rm integral}\left(\operatorname{arccot}\left(a x\right)^{3}, x\right)"," ",0,"integral(arccot(a*x)^3, x)","F",0
29,0,0,0,0.623760," ","integrate(arccot(a*x)^3/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{arccot}\left(a x\right)^{3}}{x}, x\right)"," ",0,"integral(arccot(a*x)^3/x, x)","F",0
30,0,0,0,0.857075," ","integrate(arccot(a*x)^3/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{arccot}\left(a x\right)^{3}}{x^{2}}, x\right)"," ",0,"integral(arccot(a*x)^3/x^2, x)","F",0
31,0,0,0,0.768236," ","integrate(arccot(a*x)^3/x^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{arccot}\left(a x\right)^{3}}{x^{3}}, x\right)"," ",0,"integral(arccot(a*x)^3/x^3, x)","F",0
32,0,0,0,0.528567," ","integrate(arccot(a*x)^3/x^4,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{arccot}\left(a x\right)^{3}}{x^{4}}, x\right)"," ",0,"integral(arccot(a*x)^3/x^4, x)","F",0
33,0,0,0,0.726390," ","integrate(arccot(a*x)^3/x^5,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{arccot}\left(a x\right)^{3}}{x^{5}}, x\right)"," ",0,"integral(arccot(a*x)^3/x^5, x)","F",0
34,0,0,0,0.545804," ","integrate(x^m*arccot(a*x)^3,x, algorithm=""fricas"")","{\rm integral}\left(x^{m} \operatorname{arccot}\left(a x\right)^{3}, x\right)"," ",0,"integral(x^m*arccot(a*x)^3, x)","F",0
35,0,0,0,0.578116," ","integrate(x^m*arccot(a*x)^2,x, algorithm=""fricas"")","{\rm integral}\left(x^{m} \operatorname{arccot}\left(a x\right)^{2}, x\right)"," ",0,"integral(x^m*arccot(a*x)^2, x)","F",0
36,0,0,0,0.622141," ","integrate(x^m*arccot(a*x),x, algorithm=""fricas"")","{\rm integral}\left(x^{m} \operatorname{arccot}\left(a x\right), x\right)"," ",0,"integral(x^m*arccot(a*x), x)","F",0
37,1,31,0,0.607176," ","integrate(x^4*arccot(x)/(x^2+1),x, algorithm=""fricas"")","\frac{1}{6} \, x^{2} + \frac{1}{3} \, {\left(x^{3} - 3 \, x\right)} \operatorname{arccot}\left(x\right) - \frac{1}{2} \, \operatorname{arccot}\left(x\right)^{2} - \frac{2}{3} \, \log\left(x^{2} + 1\right)"," ",0,"1/6*x^2 + 1/3*(x^3 - 3*x)*arccot(x) - 1/2*arccot(x)^2 - 2/3*log(x^2 + 1)","A",0
38,0,0,0,0.394253," ","integrate(x^3*arccot(x)/(x^2+1),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{3} \operatorname{arccot}\left(x\right)}{x^{2} + 1}, x\right)"," ",0,"integral(x^3*arccot(x)/(x^2 + 1), x)","F",0
39,1,19,0,0.559471," ","integrate(x^2*arccot(x)/(x^2+1),x, algorithm=""fricas"")","x \operatorname{arccot}\left(x\right) + \frac{1}{2} \, \operatorname{arccot}\left(x\right)^{2} + \frac{1}{2} \, \log\left(x^{2} + 1\right)"," ",0,"x*arccot(x) + 1/2*arccot(x)^2 + 1/2*log(x^2 + 1)","A",0
40,0,0,0,0.633211," ","integrate(x*arccot(x)/(x^2+1),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x \operatorname{arccot}\left(x\right)}{x^{2} + 1}, x\right)"," ",0,"integral(x*arccot(x)/(x^2 + 1), x)","F",0
41,1,6,0,0.644586," ","integrate(arccot(x)/(x^2+1),x, algorithm=""fricas"")","-\frac{1}{2} \, \operatorname{arccot}\left(x\right)^{2}"," ",0,"-1/2*arccot(x)^2","A",0
42,0,0,0,0.395884," ","integrate(arccot(x)/x/(x^2+1),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{arccot}\left(x\right)}{x^{3} + x}, x\right)"," ",0,"integral(arccot(x)/(x^3 + x), x)","F",0
43,1,29,0,1.018461," ","integrate(arccot(x)/x^2/(x^2+1),x, algorithm=""fricas"")","\frac{x \operatorname{arccot}\left(x\right)^{2} + x \log\left(x^{2} + 1\right) - 2 \, x \log\left(x\right) - 2 \, \operatorname{arccot}\left(x\right)}{2 \, x}"," ",0,"1/2*(x*arccot(x)^2 + x*log(x^2 + 1) - 2*x*log(x) - 2*arccot(x))/x","A",0
44,0,0,0,1.505396," ","integrate(arccot(x)/x^3/(x^2+1),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{arccot}\left(x\right)}{x^{5} + x^{3}}, x\right)"," ",0,"integral(arccot(x)/(x^5 + x^3), x)","F",0
45,1,47,0,0.661910," ","integrate(arccot(x)/x^4/(x^2+1),x, algorithm=""fricas"")","-\frac{3 \, x^{3} \operatorname{arccot}\left(x\right)^{2} + 4 \, x^{3} \log\left(x^{2} + 1\right) - 8 \, x^{3} \log\left(x\right) - 2 \, {\left(3 \, x^{2} - 1\right)} \operatorname{arccot}\left(x\right) - x}{6 \, x^{3}}"," ",0,"-1/6*(3*x^3*arccot(x)^2 + 4*x^3*log(x^2 + 1) - 8*x^3*log(x) - 2*(3*x^2 - 1)*arccot(x) - x)/x^3","A",0
46,0,0,0,0.551249," ","integrate(x^2*arccot(c*x)/(x^2+1),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{2} \operatorname{arccot}\left(c x\right)}{x^{2} + 1}, x\right)"," ",0,"integral(x^2*arccot(c*x)/(x^2 + 1), x)","F",0
47,0,0,0,2.915456," ","integrate(x*arccot(c*x)/(x^2+1),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x \operatorname{arccot}\left(c x\right)}{x^{2} + 1}, x\right)"," ",0,"integral(x*arccot(c*x)/(x^2 + 1), x)","F",0
48,0,0,0,0.598780," ","integrate(arccot(c*x)/(x^2+1),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{arccot}\left(c x\right)}{x^{2} + 1}, x\right)"," ",0,"integral(arccot(c*x)/(x^2 + 1), x)","F",0
49,0,0,0,1.462312," ","integrate(arccot(c*x)/x/(x^2+1),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{arccot}\left(c x\right)}{x^{3} + x}, x\right)"," ",0,"integral(arccot(c*x)/(x^3 + x), x)","F",0
50,0,0,0,0.489243," ","integrate(arccot(c*x)/x^2/(x^2+1),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{arccot}\left(c x\right)}{x^{4} + x^{2}}, x\right)"," ",0,"integral(arccot(c*x)/(x^4 + x^2), x)","F",0
51,1,5,0,0.463693," ","integrate(1/(x^2+1)/arccot(x),x, algorithm=""fricas"")","-\log\left(\operatorname{arccot}\left(x\right)\right)"," ",0,"-log(arccot(x))","A",0
52,1,13,0,0.461775," ","integrate(arccot(x)^n/(x^2+1),x, algorithm=""fricas"")","-\frac{\operatorname{arccot}\left(x\right)^{n} \operatorname{arccot}\left(x\right)}{n + 1}"," ",0,"-arccot(x)^n*arccot(x)/(n + 1)","A",0
53,1,237,0,0.491050," ","integrate((d*x^2+c)^4*arccot(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} + 24 \, {\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)} \operatorname{arccot}\left(a x\right) + 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)}{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 + 24*(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)*arccot(a*x) + 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))/a^9","A",0
54,1,167,0,1.434286," ","integrate((d*x^2+c)^3*arccot(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} + 12 \, {\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)} \operatorname{arccot}\left(a x\right) + 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)}{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 + 12*(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)*arccot(a*x) + 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))/a^7","A",0
55,1,108,0,1.523464," ","integrate((d*x^2+c)^2*arccot(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} + 4 \, {\left(3 \, a^{5} d^{2} x^{5} + 10 \, a^{5} c d x^{3} + 15 \, a^{5} c^{2} x\right)} \operatorname{arccot}\left(a x\right) + 2 \, {\left(15 \, a^{4} c^{2} - 10 \, a^{2} c d + 3 \, d^{2}\right)} \log\left(a^{2} x^{2} + 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 + 4*(3*a^5*d^2*x^5 + 10*a^5*c*d*x^3 + 15*a^5*c^2*x)*arccot(a*x) + 2*(15*a^4*c^2 - 10*a^2*c*d + 3*d^2)*log(a^2*x^2 + 1))/a^5","A",0
56,1,57,0,0.974498," ","integrate((d*x^2+c)*arccot(a*x),x, algorithm=""fricas"")","\frac{a^{2} d x^{2} + 2 \, {\left(a^{3} d x^{3} + 3 \, a^{3} c x\right)} \operatorname{arccot}\left(a x\right) + {\left(3 \, a^{2} c - d\right)} \log\left(a^{2} x^{2} + 1\right)}{6 \, a^{3}}"," ",0,"1/6*(a^2*d*x^2 + 2*(a^3*d*x^3 + 3*a^3*c*x)*arccot(a*x) + (3*a^2*c - d)*log(a^2*x^2 + 1))/a^3","A",0
57,0,0,0,0.585933," ","integrate(arccot(a*x)/(d*x^2+c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{arccot}\left(a x\right)}{d x^{2} + c}, x\right)"," ",0,"integral(arccot(a*x)/(d*x^2 + c), x)","F",0
58,0,0,0,0.693772," ","integrate(arccot(a*x)/(d*x^2+c)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{arccot}\left(a x\right)}{d^{2} x^{4} + 2 \, c d x^{2} + c^{2}}, x\right)"," ",0,"integral(arccot(a*x)/(d^2*x^4 + 2*c*d*x^2 + c^2), x)","F",0
59,0,0,0,0.589993," ","integrate((d*x^2+c)^(1/2)*arccot(a*x),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{d x^{2} + c} \operatorname{arccot}\left(a x\right), x\right)"," ",0,"integral(sqrt(d*x^2 + c)*arccot(a*x), x)","F",0
60,0,0,0,0.957000," ","integrate(arccot(a*x)/(d*x^2+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{arccot}\left(a x\right)}{\sqrt{d x^{2} + c}}, x\right)"," ",0,"integral(arccot(a*x)/sqrt(d*x^2 + c), x)","F",0
61,1,349,0,1.467036," ","integrate(arccot(a*x)/(d*x^2+c)^(3/2),x, algorithm=""fricas"")","\left[\frac{4 \, {\left(a^{2} c - d\right)} \sqrt{d x^{2} + c} x \operatorname{arccot}\left(a x\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{2 \, {\left(a^{2} c - d\right)} \sqrt{d x^{2} + c} x \operatorname{arccot}\left(a x\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*(4*(a^2*c - d)*sqrt(d*x^2 + c)*x*arccot(a*x) + 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*(2*(a^2*c - d)*sqrt(d*x^2 + c)*x*arccot(a*x) - 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
62,1,712,0,1.156591," ","integrate(arccot(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) + 4 \, {\left(a^{3} c^{3} - a c^{2} d + {\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)} \operatorname{arccot}\left(a x\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) - 2 \, {\left(a^{3} c^{3} - a c^{2} d + {\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)} \operatorname{arccot}\left(a x\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)) + 4*(a^3*c^3 - a*c^2*d + (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)*arccot(a*x))*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 - a*c^2*d + (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)*arccot(a*x))*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
63,1,1278,0,1.406183," ","integrate(arccot(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) + 4 \, {\left(8 \, a^{5} c^{5} - 13 \, a^{3} c^{4} d + 5 \, a c^{3} d^{2} + {\left(7 \, a^{5} c^{3} d^{2} - 11 \, a^{3} c^{2} d^{3} + 4 \, a c d^{4}\right)} x^{4} + 3 \, {\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)} \operatorname{arccot}\left(a x\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) - 2 \, {\left(8 \, a^{5} c^{5} - 13 \, a^{3} c^{4} d + 5 \, a c^{3} d^{2} + {\left(7 \, a^{5} c^{3} d^{2} - 11 \, a^{3} c^{2} d^{3} + 4 \, a c d^{4}\right)} x^{4} + 3 \, {\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)} \operatorname{arccot}\left(a x\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)) + 4*(8*a^5*c^5 - 13*a^3*c^4*d + 5*a*c^3*d^2 + (7*a^5*c^3*d^2 - 11*a^3*c^2*d^3 + 4*a*c*d^4)*x^4 + 3*(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)*arccot(a*x))*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)) - 2*(8*a^5*c^5 - 13*a^3*c^4*d + 5*a*c^3*d^2 + (7*a^5*c^3*d^2 - 11*a^3*c^2*d^3 + 4*a*c*d^4)*x^4 + 3*(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)*arccot(a*x))*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
64,1,1986,0,1.588648," ","integrate(arccot(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) + 4 \, {\left(71 \, a^{7} c^{7} - 160 \, a^{5} c^{6} d + 122 \, a^{3} c^{5} d^{2} - 33 \, a c^{4} d^{3} + 3 \, {\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} + {\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} + {\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)} \operatorname{arccot}\left(a x\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) - 2 \, {\left(71 \, a^{7} c^{7} - 160 \, a^{5} c^{6} d + 122 \, a^{3} c^{5} d^{2} - 33 \, a c^{4} d^{3} + 3 \, {\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} + {\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} + {\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)} \operatorname{arccot}\left(a x\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)) + 4*(71*a^7*c^7 - 160*a^5*c^6*d + 122*a^3*c^5*d^2 - 33*a*c^4*d^3 + 3*(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 + (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 + (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)*arccot(a*x))*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)) - 2*(71*a^7*c^7 - 160*a^5*c^6*d + 122*a^3*c^5*d^2 - 33*a*c^4*d^3 + 3*(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 + (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 + (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)*arccot(a*x))*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
65,0,0,0,1.642365," ","integrate((a*x^2+a)^(1/2)*arccot(x),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{a x^{2} + a} \operatorname{arccot}\left(x\right), x\right)"," ",0,"integral(sqrt(a*x^2 + a)*arccot(x), x)","F",0
66,0,0,0,0.575118," ","integrate(arccot(x)/(a*x^2+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{arccot}\left(x\right)}{\sqrt{a x^{2} + a}}, x\right)"," ",0,"integral(arccot(x)/sqrt(a*x^2 + a), x)","F",0
67,1,29,0,3.041022," ","integrate(arccot(x)/(a*x^2+a)^(3/2),x, algorithm=""fricas"")","\frac{\sqrt{a x^{2} + a} {\left(x \operatorname{arccot}\left(x\right) - 1\right)}}{a^{2} x^{2} + a^{2}}"," ",0,"sqrt(a*x^2 + a)*(x*arccot(x) - 1)/(a^2*x^2 + a^2)","A",0
68,1,52,0,0.538098," ","integrate(arccot(x)/(a*x^2+a)^(5/2),x, algorithm=""fricas"")","-\frac{\sqrt{a x^{2} + a} {\left(6 \, x^{2} - 3 \, {\left(2 \, x^{3} + 3 \, x\right)} \operatorname{arccot}\left(x\right) + 7\right)}}{9 \, {\left(a^{3} x^{4} + 2 \, a^{3} x^{2} + a^{3}\right)}}"," ",0,"-1/9*sqrt(a*x^2 + a)*(6*x^2 - 3*(2*x^3 + 3*x)*arccot(x) + 7)/(a^3*x^4 + 2*a^3*x^2 + a^3)","A",0
69,1,70,0,0.622683," ","integrate(arccot(x)/(a*x^2+a)^(7/2),x, algorithm=""fricas"")","-\frac{{\left(120 \, x^{4} + 260 \, x^{2} - 15 \, {\left(8 \, x^{5} + 20 \, x^{3} + 15 \, x\right)} \operatorname{arccot}\left(x\right) + 149\right)} \sqrt{a x^{2} + a}}{225 \, {\left(a^{4} x^{6} + 3 \, a^{4} x^{4} + 3 \, a^{4} x^{2} + a^{4}\right)}}"," ",0,"-1/225*(120*x^4 + 260*x^2 - 15*(8*x^5 + 20*x^3 + 15*x)*arccot(x) + 149)*sqrt(a*x^2 + a)/(a^4*x^6 + 3*a^4*x^4 + 3*a^4*x^2 + a^4)","A",0
70,1,21,0,0.674666," ","integrate(x*arccot(x)/(x^2+1)^2,x, algorithm=""fricas"")","\frac{{\left(x^{2} - 1\right)} \operatorname{arccot}\left(x\right) - x}{4 \, {\left(x^{2} + 1\right)}}"," ",0,"1/4*((x^2 - 1)*arccot(x) - x)/(x^2 + 1)","A",0
71,1,39,0,1.965417," ","integrate(x*arccot(x)/(x^2+1)^3,x, algorithm=""fricas"")","-\frac{3 \, x^{3} - {\left(3 \, x^{4} + 6 \, x^{2} - 5\right)} \operatorname{arccot}\left(x\right) + 5 \, x}{32 \, {\left(x^{4} + 2 \, x^{2} + 1\right)}}"," ",0,"-1/32*(3*x^3 - (3*x^4 + 6*x^2 - 5)*arccot(x) + 5*x)/(x^4 + 2*x^2 + 1)","A",0
72,1,26,0,1.336742," ","integrate(arccot(x)/(x^2+1)^2,x, algorithm=""fricas"")","-\frac{{\left(x^{2} + 1\right)} \operatorname{arccot}\left(x\right)^{2} - 2 \, x \operatorname{arccot}\left(x\right) + 1}{4 \, {\left(x^{2} + 1\right)}}"," ",0,"-1/4*((x^2 + 1)*arccot(x)^2 - 2*x*arccot(x) + 1)/(x^2 + 1)","A",0
73,1,40,0,0.654829," ","integrate(arccot(x)^2/(x^2+1)^2,x, algorithm=""fricas"")","-\frac{2 \, {\left(x^{2} + 1\right)} \operatorname{arccot}\left(x\right)^{3} - 6 \, x \operatorname{arccot}\left(x\right)^{2} - 3 \, {\left(x^{2} - 1\right)} \operatorname{arccot}\left(x\right) + 3 \, x}{12 \, {\left(x^{2} + 1\right)}}"," ",0,"-1/12*(2*(x^2 + 1)*arccot(x)^3 - 6*x*arccot(x)^2 - 3*(x^2 - 1)*arccot(x) + 3*x)/(x^2 + 1)","A",0
74,1,39,0,1.557130," ","integrate(x^5*arccot(a*x^2),x, algorithm=""fricas"")","\frac{2 \, a^{3} x^{6} \operatorname{arccot}\left(a x^{2}\right) + a^{2} x^{4} - \log\left(a^{2} x^{4} + 1\right)}{12 \, a^{3}}"," ",0,"1/12*(2*a^3*x^6*arccot(a*x^2) + a^2*x^4 - log(a^2*x^4 + 1))/a^3","A",0
75,1,27,0,0.736764," ","integrate(x^3*arccot(a*x^2),x, algorithm=""fricas"")","\frac{a x^{2} + {\left(a^{2} x^{4} + 1\right)} \operatorname{arccot}\left(a x^{2}\right)}{4 \, a^{2}}"," ",0,"1/4*(a*x^2 + (a^2*x^4 + 1)*arccot(a*x^2))/a^2","A",0
76,1,28,0,0.981310," ","integrate(x*arccot(a*x^2),x, algorithm=""fricas"")","\frac{2 \, a x^{2} \operatorname{arccot}\left(a x^{2}\right) + \log\left(a^{2} x^{4} + 1\right)}{4 \, a}"," ",0,"1/4*(2*a*x^2*arccot(a*x^2) + log(a^2*x^4 + 1))/a","A",0
77,0,0,0,0.609760," ","integrate(arccot(a*x^2)/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{arccot}\left(a x^{2}\right)}{x}, x\right)"," ",0,"integral(arccot(a*x^2)/x, x)","F",0
78,1,37,0,0.677374," ","integrate(arccot(a*x^2)/x^3,x, algorithm=""fricas"")","\frac{a x^{2} \log\left(a^{2} x^{4} + 1\right) - 4 \, a x^{2} \log\left(x\right) - 2 \, \operatorname{arccot}\left(a x^{2}\right)}{4 \, x^{2}}"," ",0,"1/4*(a*x^2*log(a^2*x^4 + 1) - 4*a*x^2*log(x) - 2*arccot(a*x^2))/x^2","A",0
79,1,28,0,0.492764," ","integrate(arccot(a*x^2)/x^5,x, algorithm=""fricas"")","\frac{a x^{2} - {\left(a^{2} x^{4} + 1\right)} \operatorname{arccot}\left(a x^{2}\right)}{4 \, x^{4}}"," ",0,"1/4*(a*x^2 - (a^2*x^4 + 1)*arccot(a*x^2))/x^4","A",0
80,1,239,0,0.558099," ","integrate(x^4*arccot(a*x^2),x, algorithm=""fricas"")","\frac{12 \, a x^{5} \arctan\left(\frac{1}{a x^{2}}\right) + 8 \, x^{3} + 12 \, \sqrt{2} a \frac{1}{a^{10}}^{\frac{1}{4}} \arctan\left(-\sqrt{2} a^{3} \frac{1}{a^{10}}^{\frac{1}{4}} x + \sqrt{2} \sqrt{\sqrt{2} a^{7} \frac{1}{a^{10}}^{\frac{3}{4}} x + a^{4} \sqrt{\frac{1}{a^{10}}} + x^{2}} a^{3} \frac{1}{a^{10}}^{\frac{1}{4}} - 1\right) + 12 \, \sqrt{2} a \frac{1}{a^{10}}^{\frac{1}{4}} \arctan\left(-\sqrt{2} a^{3} \frac{1}{a^{10}}^{\frac{1}{4}} x + \sqrt{2} \sqrt{-\sqrt{2} a^{7} \frac{1}{a^{10}}^{\frac{3}{4}} x + a^{4} \sqrt{\frac{1}{a^{10}}} + x^{2}} a^{3} \frac{1}{a^{10}}^{\frac{1}{4}} + 1\right) + 3 \, \sqrt{2} a \frac{1}{a^{10}}^{\frac{1}{4}} \log\left(\sqrt{2} a^{7} \frac{1}{a^{10}}^{\frac{3}{4}} x + a^{4} \sqrt{\frac{1}{a^{10}}} + x^{2}\right) - 3 \, \sqrt{2} a \frac{1}{a^{10}}^{\frac{1}{4}} \log\left(-\sqrt{2} a^{7} \frac{1}{a^{10}}^{\frac{3}{4}} x + a^{4} \sqrt{\frac{1}{a^{10}}} + x^{2}\right)}{60 \, a}"," ",0,"1/60*(12*a*x^5*arctan(1/(a*x^2)) + 8*x^3 + 12*sqrt(2)*a*(a^(-10))^(1/4)*arctan(-sqrt(2)*a^3*(a^(-10))^(1/4)*x + sqrt(2)*sqrt(sqrt(2)*a^7*(a^(-10))^(3/4)*x + a^4*sqrt(a^(-10)) + x^2)*a^3*(a^(-10))^(1/4) - 1) + 12*sqrt(2)*a*(a^(-10))^(1/4)*arctan(-sqrt(2)*a^3*(a^(-10))^(1/4)*x + sqrt(2)*sqrt(-sqrt(2)*a^7*(a^(-10))^(3/4)*x + a^4*sqrt(a^(-10)) + x^2)*a^3*(a^(-10))^(1/4) + 1) + 3*sqrt(2)*a*(a^(-10))^(1/4)*log(sqrt(2)*a^7*(a^(-10))^(3/4)*x + a^4*sqrt(a^(-10)) + x^2) - 3*sqrt(2)*a*(a^(-10))^(1/4)*log(-sqrt(2)*a^7*(a^(-10))^(3/4)*x + a^4*sqrt(a^(-10)) + x^2))/a","B",0
81,1,228,0,0.806988," ","integrate(x^2*arccot(a*x^2),x, algorithm=""fricas"")","\frac{4 \, a x^{3} \arctan\left(\frac{1}{a x^{2}}\right) + 4 \, \sqrt{2} a \frac{1}{a^{6}}^{\frac{1}{4}} \arctan\left(-\sqrt{2} a^{5} \frac{1}{a^{6}}^{\frac{3}{4}} x + \sqrt{2} \sqrt{\sqrt{2} a \frac{1}{a^{6}}^{\frac{1}{4}} x + a^{2} \sqrt{\frac{1}{a^{6}}} + x^{2}} a^{5} \frac{1}{a^{6}}^{\frac{3}{4}} - 1\right) + 4 \, \sqrt{2} a \frac{1}{a^{6}}^{\frac{1}{4}} \arctan\left(-\sqrt{2} a^{5} \frac{1}{a^{6}}^{\frac{3}{4}} x + \sqrt{2} \sqrt{-\sqrt{2} a \frac{1}{a^{6}}^{\frac{1}{4}} x + a^{2} \sqrt{\frac{1}{a^{6}}} + x^{2}} a^{5} \frac{1}{a^{6}}^{\frac{3}{4}} + 1\right) - \sqrt{2} a \frac{1}{a^{6}}^{\frac{1}{4}} \log\left(\sqrt{2} a \frac{1}{a^{6}}^{\frac{1}{4}} x + a^{2} \sqrt{\frac{1}{a^{6}}} + x^{2}\right) + \sqrt{2} a \frac{1}{a^{6}}^{\frac{1}{4}} \log\left(-\sqrt{2} a \frac{1}{a^{6}}^{\frac{1}{4}} x + a^{2} \sqrt{\frac{1}{a^{6}}} + x^{2}\right) + 8 \, x}{12 \, a}"," ",0,"1/12*(4*a*x^3*arctan(1/(a*x^2)) + 4*sqrt(2)*a*(a^(-6))^(1/4)*arctan(-sqrt(2)*a^5*(a^(-6))^(3/4)*x + sqrt(2)*sqrt(sqrt(2)*a*(a^(-6))^(1/4)*x + a^2*sqrt(a^(-6)) + x^2)*a^5*(a^(-6))^(3/4) - 1) + 4*sqrt(2)*a*(a^(-6))^(1/4)*arctan(-sqrt(2)*a^5*(a^(-6))^(3/4)*x + sqrt(2)*sqrt(-sqrt(2)*a*(a^(-6))^(1/4)*x + a^2*sqrt(a^(-6)) + x^2)*a^5*(a^(-6))^(3/4) + 1) - sqrt(2)*a*(a^(-6))^(1/4)*log(sqrt(2)*a*(a^(-6))^(1/4)*x + a^2*sqrt(a^(-6)) + x^2) + sqrt(2)*a*(a^(-6))^(1/4)*log(-sqrt(2)*a*(a^(-6))^(1/4)*x + a^2*sqrt(a^(-6)) + x^2) + 8*x)/a","B",0
82,1,189,0,0.620170," ","integrate(arccot(a*x^2),x, algorithm=""fricas"")","x \arctan\left(\frac{1}{a x^{2}}\right) - \sqrt{2} \frac{1}{a^{2}}^{\frac{1}{4}} \arctan\left(-\sqrt{2} a \frac{1}{a^{2}}^{\frac{1}{4}} x + \sqrt{2} \sqrt{\sqrt{2} a \frac{1}{a^{2}}^{\frac{3}{4}} x + x^{2} + \sqrt{\frac{1}{a^{2}}}} a \frac{1}{a^{2}}^{\frac{1}{4}} - 1\right) - \sqrt{2} \frac{1}{a^{2}}^{\frac{1}{4}} \arctan\left(-\sqrt{2} a \frac{1}{a^{2}}^{\frac{1}{4}} x + \sqrt{2} \sqrt{-\sqrt{2} a \frac{1}{a^{2}}^{\frac{3}{4}} x + x^{2} + \sqrt{\frac{1}{a^{2}}}} a \frac{1}{a^{2}}^{\frac{1}{4}} + 1\right) - \frac{1}{4} \, \sqrt{2} \frac{1}{a^{2}}^{\frac{1}{4}} \log\left(\sqrt{2} a \frac{1}{a^{2}}^{\frac{3}{4}} x + x^{2} + \sqrt{\frac{1}{a^{2}}}\right) + \frac{1}{4} \, \sqrt{2} \frac{1}{a^{2}}^{\frac{1}{4}} \log\left(-\sqrt{2} a \frac{1}{a^{2}}^{\frac{3}{4}} x + x^{2} + \sqrt{\frac{1}{a^{2}}}\right)"," ",0,"x*arctan(1/(a*x^2)) - sqrt(2)*(a^(-2))^(1/4)*arctan(-sqrt(2)*a*(a^(-2))^(1/4)*x + sqrt(2)*sqrt(sqrt(2)*a*(a^(-2))^(3/4)*x + x^2 + sqrt(a^(-2)))*a*(a^(-2))^(1/4) - 1) - sqrt(2)*(a^(-2))^(1/4)*arctan(-sqrt(2)*a*(a^(-2))^(1/4)*x + sqrt(2)*sqrt(-sqrt(2)*a*(a^(-2))^(3/4)*x + x^2 + sqrt(a^(-2)))*a*(a^(-2))^(1/4) + 1) - 1/4*sqrt(2)*(a^(-2))^(1/4)*log(sqrt(2)*a*(a^(-2))^(3/4)*x + x^2 + sqrt(a^(-2))) + 1/4*sqrt(2)*(a^(-2))^(1/4)*log(-sqrt(2)*a*(a^(-2))^(3/4)*x + x^2 + sqrt(a^(-2)))","A",0
83,1,227,0,1.532724," ","integrate(arccot(a*x^2)/x^2,x, algorithm=""fricas"")","\frac{4 \, \sqrt{2} {\left(a^{2}\right)}^{\frac{1}{4}} x \arctan\left(-\frac{\sqrt{2} {\left(a^{2}\right)}^{\frac{3}{4}} a x + a^{2} - \sqrt{2} \sqrt{a^{2} x^{2} + \sqrt{2} {\left(a^{2}\right)}^{\frac{1}{4}} a x + \sqrt{a^{2}}} {\left(a^{2}\right)}^{\frac{3}{4}}}{a^{2}}\right) + 4 \, \sqrt{2} {\left(a^{2}\right)}^{\frac{1}{4}} x \arctan\left(-\frac{\sqrt{2} {\left(a^{2}\right)}^{\frac{3}{4}} a x - a^{2} - \sqrt{2} \sqrt{a^{2} x^{2} - \sqrt{2} {\left(a^{2}\right)}^{\frac{1}{4}} a x + \sqrt{a^{2}}} {\left(a^{2}\right)}^{\frac{3}{4}}}{a^{2}}\right) - \sqrt{2} {\left(a^{2}\right)}^{\frac{1}{4}} x \log\left(a^{2} x^{2} + \sqrt{2} {\left(a^{2}\right)}^{\frac{1}{4}} a x + \sqrt{a^{2}}\right) + \sqrt{2} {\left(a^{2}\right)}^{\frac{1}{4}} x \log\left(a^{2} x^{2} - \sqrt{2} {\left(a^{2}\right)}^{\frac{1}{4}} a x + \sqrt{a^{2}}\right) - 4 \, \arctan\left(\frac{1}{a x^{2}}\right)}{4 \, x}"," ",0,"1/4*(4*sqrt(2)*(a^2)^(1/4)*x*arctan(-(sqrt(2)*(a^2)^(3/4)*a*x + a^2 - sqrt(2)*sqrt(a^2*x^2 + sqrt(2)*(a^2)^(1/4)*a*x + sqrt(a^2))*(a^2)^(3/4))/a^2) + 4*sqrt(2)*(a^2)^(1/4)*x*arctan(-(sqrt(2)*(a^2)^(3/4)*a*x - a^2 - sqrt(2)*sqrt(a^2*x^2 - sqrt(2)*(a^2)^(1/4)*a*x + sqrt(a^2))*(a^2)^(3/4))/a^2) - sqrt(2)*(a^2)^(1/4)*x*log(a^2*x^2 + sqrt(2)*(a^2)^(1/4)*a*x + sqrt(a^2)) + sqrt(2)*(a^2)^(1/4)*x*log(a^2*x^2 - sqrt(2)*(a^2)^(1/4)*a*x + sqrt(a^2)) - 4*arctan(1/(a*x^2)))/x","B",0
84,1,269,0,1.044030," ","integrate(arccot(a*x^2)/x^4,x, algorithm=""fricas"")","-\frac{4 \, \sqrt{2} {\left(a^{6}\right)}^{\frac{1}{4}} x^{3} \arctan\left(-\frac{\sqrt{2} {\left(a^{6}\right)}^{\frac{1}{4}} a^{5} x + a^{6} - \sqrt{2} \sqrt{a^{10} x^{2} + \sqrt{2} {\left(a^{6}\right)}^{\frac{3}{4}} a^{5} x + \sqrt{a^{6}} a^{6}} {\left(a^{6}\right)}^{\frac{1}{4}}}{a^{6}}\right) + 4 \, \sqrt{2} {\left(a^{6}\right)}^{\frac{1}{4}} x^{3} \arctan\left(-\frac{\sqrt{2} {\left(a^{6}\right)}^{\frac{1}{4}} a^{5} x - a^{6} - \sqrt{2} \sqrt{a^{10} x^{2} - \sqrt{2} {\left(a^{6}\right)}^{\frac{3}{4}} a^{5} x + \sqrt{a^{6}} a^{6}} {\left(a^{6}\right)}^{\frac{1}{4}}}{a^{6}}\right) + \sqrt{2} {\left(a^{6}\right)}^{\frac{1}{4}} x^{3} \log\left(a^{10} x^{2} + \sqrt{2} {\left(a^{6}\right)}^{\frac{3}{4}} a^{5} x + \sqrt{a^{6}} a^{6}\right) - \sqrt{2} {\left(a^{6}\right)}^{\frac{1}{4}} x^{3} \log\left(a^{10} x^{2} - \sqrt{2} {\left(a^{6}\right)}^{\frac{3}{4}} a^{5} x + \sqrt{a^{6}} a^{6}\right) - 8 \, a x^{2} + 4 \, \arctan\left(\frac{1}{a x^{2}}\right)}{12 \, x^{3}}"," ",0,"-1/12*(4*sqrt(2)*(a^6)^(1/4)*x^3*arctan(-(sqrt(2)*(a^6)^(1/4)*a^5*x + a^6 - sqrt(2)*sqrt(a^10*x^2 + sqrt(2)*(a^6)^(3/4)*a^5*x + sqrt(a^6)*a^6)*(a^6)^(1/4))/a^6) + 4*sqrt(2)*(a^6)^(1/4)*x^3*arctan(-(sqrt(2)*(a^6)^(1/4)*a^5*x - a^6 - sqrt(2)*sqrt(a^10*x^2 - sqrt(2)*(a^6)^(3/4)*a^5*x + sqrt(a^6)*a^6)*(a^6)^(1/4))/a^6) + sqrt(2)*(a^6)^(1/4)*x^3*log(a^10*x^2 + sqrt(2)*(a^6)^(3/4)*a^5*x + sqrt(a^6)*a^6) - sqrt(2)*(a^6)^(1/4)*x^3*log(a^10*x^2 - sqrt(2)*(a^6)^(3/4)*a^5*x + sqrt(a^6)*a^6) - 8*a*x^2 + 4*arctan(1/(a*x^2)))/x^3","B",0
85,1,27,0,1.393209," ","integrate(x^2*arccot(x^(1/2)),x, algorithm=""fricas"")","\frac{1}{3} \, {\left(x^{3} + 1\right)} \operatorname{arccot}\left(\sqrt{x}\right) + \frac{1}{45} \, {\left(3 \, x^{2} - 5 \, x + 15\right)} \sqrt{x}"," ",0,"1/3*(x^3 + 1)*arccot(sqrt(x)) + 1/45*(3*x^2 - 5*x + 15)*sqrt(x)","A",0
86,1,20,0,0.626222," ","integrate(x*arccot(x^(1/2)),x, algorithm=""fricas"")","\frac{1}{2} \, {\left(x^{2} - 1\right)} \operatorname{arccot}\left(\sqrt{x}\right) + \frac{1}{6} \, {\left(x - 3\right)} \sqrt{x}"," ",0,"1/2*(x^2 - 1)*arccot(sqrt(x)) + 1/6*(x - 3)*sqrt(x)","A",0
87,1,12,0,0.568252," ","integrate(arccot(x^(1/2)),x, algorithm=""fricas"")","{\left(x + 1\right)} \operatorname{arccot}\left(\sqrt{x}\right) + \sqrt{x}"," ",0,"(x + 1)*arccot(sqrt(x)) + sqrt(x)","A",0
88,0,0,0,0.613060," ","integrate(arccot(x^(1/2))/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{arccot}\left(\sqrt{x}\right)}{x}, x\right)"," ",0,"integral(arccot(sqrt(x))/x, x)","F",0
89,1,19,0,0.672817," ","integrate(arccot(x^(1/2))/x^2,x, algorithm=""fricas"")","-\frac{{\left(x + 1\right)} \operatorname{arccot}\left(\sqrt{x}\right) - \sqrt{x}}{x}"," ",0,"-((x + 1)*arccot(sqrt(x)) - sqrt(x))/x","A",0
90,1,27,0,0.526555," ","integrate(arccot(x^(1/2))/x^3,x, algorithm=""fricas"")","\frac{3 \, {\left(x^{2} - 1\right)} \operatorname{arccot}\left(\sqrt{x}\right) - {\left(3 \, x - 1\right)} \sqrt{x}}{6 \, x^{2}}"," ",0,"1/6*(3*(x^2 - 1)*arccot(sqrt(x)) - (3*x - 1)*sqrt(x))/x^2","A",0
91,1,24,0,1.458151," ","integrate(x^(3/2)*arccot(x^(1/2)),x, algorithm=""fricas"")","\frac{2}{5} \, x^{\frac{5}{2}} \operatorname{arccot}\left(\sqrt{x}\right) + \frac{1}{10} \, x^{2} - \frac{1}{5} \, x + \frac{1}{5} \, \log\left(x + 1\right)"," ",0,"2/5*x^(5/2)*arccot(sqrt(x)) + 1/10*x^2 - 1/5*x + 1/5*log(x + 1)","A",0
92,1,19,0,1.126265," ","integrate(x^(1/2)*arccot(x^(1/2)),x, algorithm=""fricas"")","\frac{2}{3} \, x^{\frac{3}{2}} \operatorname{arccot}\left(\sqrt{x}\right) + \frac{1}{3} \, x - \frac{1}{3} \, \log\left(x + 1\right)"," ",0,"2/3*x^(3/2)*arccot(sqrt(x)) + 1/3*x - 1/3*log(x + 1)","A",0
93,1,14,0,0.785365," ","integrate(arccot(x^(1/2))/x^(1/2),x, algorithm=""fricas"")","2 \, \sqrt{x} \operatorname{arccot}\left(\sqrt{x}\right) + \log\left(x + 1\right)"," ",0,"2*sqrt(x)*arccot(sqrt(x)) + log(x + 1)","A",0
94,1,25,0,2.094512," ","integrate(arccot(x^(1/2))/x^(3/2),x, algorithm=""fricas"")","\frac{x \log\left(x + 1\right) - x \log\left(x\right) - 2 \, \sqrt{x} \operatorname{arccot}\left(\sqrt{x}\right)}{x}"," ",0,"(x*log(x + 1) - x*log(x) - 2*sqrt(x)*arccot(sqrt(x)))/x","A",0
95,1,33,0,0.471206," ","integrate(arccot(x^(1/2))/x^(5/2),x, algorithm=""fricas"")","-\frac{x^{2} \log\left(x + 1\right) - x^{2} \log\left(x\right) + 2 \, \sqrt{x} \operatorname{arccot}\left(\sqrt{x}\right) - x}{3 \, x^{2}}"," ",0,"-1/3*(x^2*log(x + 1) - x^2*log(x) + 2*sqrt(x)*arccot(sqrt(x)) - x)/x^2","A",0
96,1,15,0,0.481568," ","integrate(arccot(1/x),x, algorithm=""fricas"")","x \operatorname{arccot}\left(\frac{1}{x}\right) - \frac{1}{2} \, \log\left(x^{2} + 1\right)"," ",0,"x*arccot(1/x) - 1/2*log(x^2 + 1)","A",0
97,1,63,0,2.580035," ","integrate(arccot(a*x^n)/x,x, algorithm=""fricas"")","\frac{2 \, n \operatorname{arccot}\left(a x^{n}\right) \log\left(x\right) - i \, n \log\left(i \, a x^{n} + 1\right) \log\left(x\right) + i \, n \log\left(-i \, a x^{n} + 1\right) \log\left(x\right) + i \, {\rm Li}_2\left(i \, a x^{n}\right) - i \, {\rm Li}_2\left(-i \, a x^{n}\right)}{2 \, n}"," ",0,"1/2*(2*n*arccot(a*x^n)*log(x) - I*n*log(I*a*x^n + 1)*log(x) + I*n*log(-I*a*x^n + 1)*log(x) + I*dilog(I*a*x^n) - I*dilog(-I*a*x^n))/n","A",0
98,0,0,0,1.070041," ","integrate(arccot(a*x^5)/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{arccot}\left(a x^{5}\right)}{x}, x\right)"," ",0,"integral(arccot(a*x^5)/x, x)","F",0
99,1,92,0,0.699884," ","integrate(x^3*arccot(b*x+a),x, algorithm=""fricas"")","\frac{3 \, b^{4} x^{4} \operatorname{arccot}\left(b x + a\right) + b^{3} x^{3} - 3 \, a b^{2} x^{2} + 3 \, {\left(3 \, a^{2} - 1\right)} b x + 3 \, {\left(a^{4} - 6 \, a^{2} + 1\right)} \arctan\left(b x + a\right) - 6 \, {\left(a^{3} - a\right)} \log\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}{12 \, b^{4}}"," ",0,"1/12*(3*b^4*x^4*arccot(b*x + a) + b^3*x^3 - 3*a*b^2*x^2 + 3*(3*a^2 - 1)*b*x + 3*(a^4 - 6*a^2 + 1)*arctan(b*x + a) - 6*(a^3 - a)*log(b^2*x^2 + 2*a*b*x + a^2 + 1))/b^4","A",0
100,1,73,0,2.252992," ","integrate(x^2*arccot(b*x+a),x, algorithm=""fricas"")","\frac{2 \, b^{3} x^{3} \operatorname{arccot}\left(b x + a\right) + b^{2} x^{2} - 4 \, a b x - 2 \, {\left(a^{3} - 3 \, a\right)} \arctan\left(b x + a\right) + {\left(3 \, a^{2} - 1\right)} \log\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}{6 \, b^{3}}"," ",0,"1/6*(2*b^3*x^3*arccot(b*x + a) + b^2*x^2 - 4*a*b*x - 2*(a^3 - 3*a)*arctan(b*x + a) + (3*a^2 - 1)*log(b^2*x^2 + 2*a*b*x + a^2 + 1))/b^3","A",0
101,1,55,0,1.054788," ","integrate(x*arccot(b*x+a),x, algorithm=""fricas"")","\frac{b^{2} x^{2} \operatorname{arccot}\left(b x + a\right) + b x + {\left(a^{2} - 1\right)} \arctan\left(b x + a\right) - a \log\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}{2 \, b^{2}}"," ",0,"1/2*(b^2*x^2*arccot(b*x + a) + b*x + (a^2 - 1)*arctan(b*x + a) - a*log(b^2*x^2 + 2*a*b*x + a^2 + 1))/b^2","A",0
102,1,43,0,0.585126," ","integrate(arccot(b*x+a),x, algorithm=""fricas"")","\frac{2 \, b x \operatorname{arccot}\left(b x + a\right) - 2 \, a \arctan\left(b x + a\right) + \log\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}{2 \, b}"," ",0,"1/2*(2*b*x*arccot(b*x + a) - 2*a*arctan(b*x + a) + log(b^2*x^2 + 2*a*b*x + a^2 + 1))/b","A",0
103,0,0,0,0.534263," ","integrate(arccot(b*x+a)/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{arccot}\left(b x + a\right)}{x}, x\right)"," ",0,"integral(arccot(b*x + a)/x, x)","F",0
104,1,64,0,0.519647," ","integrate(arccot(b*x+a)/x^2,x, algorithm=""fricas"")","\frac{2 \, a b x \arctan\left(b x + a\right) + b x \log\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right) - 2 \, b x \log\left(x\right) - 2 \, {\left(a^{2} + 1\right)} \operatorname{arccot}\left(b x + a\right)}{2 \, {\left(a^{2} + 1\right)} x}"," ",0,"1/2*(2*a*b*x*arctan(b*x + a) + b*x*log(b^2*x^2 + 2*a*b*x + a^2 + 1) - 2*b*x*log(x) - 2*(a^2 + 1)*arccot(b*x + a))/((a^2 + 1)*x)","A",0
105,1,99,0,0.743980," ","integrate(arccot(b*x+a)/x^3,x, algorithm=""fricas"")","-\frac{{\left(a^{2} - 1\right)} b^{2} x^{2} \arctan\left(b x + a\right) + a b^{2} x^{2} \log\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right) - 2 \, a b^{2} x^{2} \log\left(x\right) - {\left(a^{2} + 1\right)} b x + {\left(a^{4} + 2 \, a^{2} + 1\right)} \operatorname{arccot}\left(b x + a\right)}{2 \, {\left(a^{4} + 2 \, a^{2} + 1\right)} x^{2}}"," ",0,"-1/2*((a^2 - 1)*b^2*x^2*arctan(b*x + a) + a*b^2*x^2*log(b^2*x^2 + 2*a*b*x + a^2 + 1) - 2*a*b^2*x^2*log(x) - (a^2 + 1)*b*x + (a^4 + 2*a^2 + 1)*arccot(b*x + a))/((a^4 + 2*a^2 + 1)*x^2)","A",0
106,1,142,0,0.587300," ","integrate(arccot(b*x+a)/x^4,x, algorithm=""fricas"")","\frac{2 \, {\left(a^{3} - 3 \, a\right)} b^{3} x^{3} \arctan\left(b x + a\right) + {\left(3 \, a^{2} - 1\right)} b^{3} x^{3} \log\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right) - 2 \, {\left(3 \, a^{2} - 1\right)} b^{3} x^{3} \log\left(x\right) - 4 \, {\left(a^{3} + a\right)} b^{2} x^{2} + {\left(a^{4} + 2 \, a^{2} + 1\right)} b x - 2 \, {\left(a^{6} + 3 \, a^{4} + 3 \, a^{2} + 1\right)} \operatorname{arccot}\left(b x + a\right)}{6 \, {\left(a^{6} + 3 \, a^{4} + 3 \, a^{2} + 1\right)} x^{3}}"," ",0,"1/6*(2*(a^3 - 3*a)*b^3*x^3*arctan(b*x + a) + (3*a^2 - 1)*b^3*x^3*log(b^2*x^2 + 2*a*b*x + a^2 + 1) - 2*(3*a^2 - 1)*b^3*x^3*log(x) - 4*(a^3 + a)*b^2*x^2 + (a^4 + 2*a^2 + 1)*b*x - 2*(a^6 + 3*a^4 + 3*a^2 + 1)*arccot(b*x + a))/((a^6 + 3*a^4 + 3*a^2 + 1)*x^3)","A",0
107,0,0,0,1.500436," ","integrate(arccot(b*x+a)/(d*x^2+c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{arccot}\left(b x + a\right)}{d x^{2} + c}, x\right)"," ",0,"integral(arccot(b*x + a)/(d*x^2 + c), x)","F",0
108,0,0,0,2.519807," ","integrate(arccot(b*x+a)/(d*x+c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{arccot}\left(b x + a\right)}{d x + c}, x\right)"," ",0,"integral(arccot(b*x + a)/(d*x + c), x)","F",0
109,0,0,0,1.686218," ","integrate(arccot(b*x+a)/(c+d/x),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x \operatorname{arccot}\left(b x + a\right)}{c x + d}, x\right)"," ",0,"integral(x*arccot(b*x + a)/(c*x + d), x)","F",0
110,0,0,0,0.659080," ","integrate(arccot(b*x+a)/(c+d/x^2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{2} \operatorname{arccot}\left(b x + a\right)}{c x^{2} + d}, x\right)"," ",0,"integral(x^2*arccot(b*x + a)/(c*x^2 + d), x)","F",0
111,0,0,0,0.564981," ","integrate(arccot(b*x+a)/(c+d*x^(1/2)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{d \sqrt{x} \operatorname{arccot}\left(b x + a\right) - c \operatorname{arccot}\left(b x + a\right)}{d^{2} x - c^{2}}, x\right)"," ",0,"integral((d*sqrt(x)*arccot(b*x + a) - c*arccot(b*x + a))/(d^2*x - c^2), x)","F",0
112,0,0,0,0.647848," ","integrate(arccot(b*x+a)/(c+d/x^(1/2)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{c x \operatorname{arccot}\left(b x + a\right) - d \sqrt{x} \operatorname{arccot}\left(b x + a\right)}{c^{2} x - d^{2}}, x\right)"," ",0,"integral((c*x*arccot(b*x + a) - d*sqrt(x)*arccot(b*x + a))/(c^2*x - d^2), x)","F",0
113,0,0,0,0.642217," ","integrate(arccot(e*x+d)/(c*x^2+b*x+a),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{arccot}\left(e x + d\right)}{c x^{2} + b x + a}, x\right)"," ",0,"integral(arccot(e*x + d)/(c*x^2 + b*x + a), x)","F",0
114,0,0,0,0.626037," ","integrate(arccot(b*x+a)/(b^2*x^2+2*a*b*x+a^2+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{arccot}\left(b x + a\right)}{\sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}, x\right)"," ",0,"integral(arccot(b*x + a)/sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1), x)","F",0
115,0,0,0,0.607201," ","integrate(arccot(b*x+a)/((a^2+1)*c+2*a*b*c*x+c*x^2*b^2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{arccot}\left(b x + a\right)}{\sqrt{b^{2} c x^{2} + 2 \, a b c x + {\left(a^{2} + 1\right)} c}}, x\right)"," ",0,"integral(arccot(b*x + a)/sqrt(b^2*c*x^2 + 2*a*b*c*x + (a^2 + 1)*c), x)","F",0
116,0,0,0,1.413283," ","integrate(arccot(b*x+a)/(b^2*x^2+2*a*b*x+a^2+1)^(1/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{arccot}\left(b x + a\right)}{{\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}^{\frac{1}{3}}}, x\right)"," ",0,"integral(arccot(b*x + a)/(b^2*x^2 + 2*a*b*x + a^2 + 1)^(1/3), x)","F",0
117,0,0,0,2.421940," ","integrate(arccot(b*x+a)/((a^2+1)*c+2*a*b*c*x+c*x^2*b^2)^(1/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{arccot}\left(b x + a\right)}{{\left(b^{2} c x^{2} + 2 \, a b c x + {\left(a^{2} + 1\right)} c\right)}^{\frac{1}{3}}}, x\right)"," ",0,"integral(arccot(b*x + a)/(b^2*c*x^2 + 2*a*b*c*x + (a^2 + 1)*c)^(1/3), x)","F",0
118,0,0,0,2.103364," ","integrate((b*x+a)^2*arccot(b*x+a)/(b^2*x^2+2*a*b*x+a^2+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)} \operatorname{arccot}\left(b x + a\right)}{\sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}, x\right)"," ",0,"integral((b^2*x^2 + 2*a*b*x + a^2)*arccot(b*x + a)/sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1), x)","F",0
119,0,0,0,1.094982," ","integrate((b*x+a)^2*arccot(b*x+a)/((a^2+1)*c+2*a*b*c*x+c*x^2*b^2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)} \operatorname{arccot}\left(b x + a\right)}{\sqrt{b^{2} c x^{2} + 2 \, a b c x + {\left(a^{2} + 1\right)} c}}, x\right)"," ",0,"integral((b^2*x^2 + 2*a*b*x + a^2)*arccot(b*x + a)/sqrt(b^2*c*x^2 + 2*a*b*c*x + (a^2 + 1)*c), x)","F",0
120,0,0,0,0.571696," ","integrate((b*x+a)^2*arccot(b*x+a)/(b^2*x^2+2*a*b*x+a^2+1)^(1/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)} \operatorname{arccot}\left(b x + a\right)}{{\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}^{\frac{1}{3}}}, x\right)"," ",0,"integral((b^2*x^2 + 2*a*b*x + a^2)*arccot(b*x + a)/(b^2*x^2 + 2*a*b*x + a^2 + 1)^(1/3), x)","F",0
121,0,0,0,0.672910," ","integrate((b*x+a)^2*arccot(b*x+a)/((a^2+1)*c+2*a*b*c*x+c*x^2*b^2)^(1/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b^{2} x^{2} + 2 \, a b x + a^{2}\right)} \operatorname{arccot}\left(b x + a\right)}{{\left(b^{2} c x^{2} + 2 \, a b c x + {\left(a^{2} + 1\right)} c\right)}^{\frac{1}{3}}}, x\right)"," ",0,"integral((b^2*x^2 + 2*a*b*x + a^2)*arccot(b*x + a)/(b^2*c*x^2 + 2*a*b*c*x + (a^2 + 1)*c)^(1/3), x)","F",0
122,1,81,0,0.553730," ","integrate((b*x+a)^2*arccot(b*x+a),x, algorithm=""fricas"")","\frac{b^{2} x^{2} - 2 \, a^{3} \arctan\left(b x + a\right) + 2 \, a b x + 2 \, {\left(b^{3} x^{3} + 3 \, a b^{2} x^{2} + 3 \, a^{2} b x\right)} \operatorname{arccot}\left(b x + a\right) - \log\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}{6 \, b}"," ",0,"1/6*(b^2*x^2 - 2*a^3*arctan(b*x + a) + 2*a*b*x + 2*(b^3*x^3 + 3*a*b^2*x^2 + 3*a^2*b*x)*arccot(b*x + a) - log(b^2*x^2 + 2*a*b*x + a^2 + 1))/b","A",0
123,1,33,0,0.518134," ","integrate((b*x+a)*arccot(b*x+a),x, algorithm=""fricas"")","\frac{b x + {\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)} \operatorname{arccot}\left(b x + a\right)}{2 \, b}"," ",0,"1/2*(b*x + (b^2*x^2 + 2*a*b*x + a^2 + 1)*arccot(b*x + a))/b","A",0
124,0,0,0,0.614956," ","integrate(arccot(b*x+a)/(b*x+a),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{arccot}\left(b x + a\right)}{b x + a}, x\right)"," ",0,"integral(arccot(b*x + a)/(b*x + a), x)","F",0
125,1,59,0,0.558119," ","integrate(arccot(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) - 2 \, \operatorname{arccot}\left(b x + a\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) - 2*arccot(b*x + a))/(b^2*x + a*b)","A",0
126,0,0,0,2.080843," ","integrate(arccot(1+x)/(2+2*x),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{arccot}\left(x + 1\right)}{2 \, {\left(x + 1\right)}}, x\right)"," ",0,"integral(1/2*arccot(x + 1)/(x + 1), x)","F",0
127,0,0,0,1.728779," ","integrate(arccot(b*x+a)/(a*d/b+d*x),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \operatorname{arccot}\left(b x + a\right)}{b d x + a d}, x\right)"," ",0,"integral(b*arccot(b*x + a)/(b*d*x + a*d), x)","F",0
128,-2,0,0,0.000000," ","integrate((b*x+a)^2*arccot(b*x+a)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
129,1,325,0,1.936547," ","integrate((f*x+e)^3*(a+b*arccot(d*x+c)),x, algorithm=""fricas"")","\frac{3 \, a d^{4} f^{3} x^{4} + {\left(12 \, a d^{4} e f^{2} + b d^{3} f^{3}\right)} x^{3} + 3 \, {\left(6 \, a d^{4} e^{2} f + 2 \, b d^{3} e f^{2} - b c d^{2} f^{3}\right)} x^{2} + 3 \, {\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(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)} \operatorname{arccot}\left(d x + c\right) - 3 \, {\left(4 \, b c d^{3} e^{3} - 6 \, {\left(b c^{2} - b\right)} d^{2} e^{2} f + 4 \, {\left(b c^{3} - 3 \, b c\right)} d e f^{2} - {\left(b c^{4} - 6 \, b c^{2} + b\right)} f^{3}\right)} \arctan\left(d x + c\right) + 6 \, {\left(b d^{3} e^{3} - 3 \, b c d^{2} e^{2} f + {\left(3 \, b c^{2} - b\right)} d e f^{2} - {\left(b c^{3} - b c\right)} f^{3}\right)} \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}{12 \, d^{4}}"," ",0,"1/12*(3*a*d^4*f^3*x^4 + (12*a*d^4*e*f^2 + b*d^3*f^3)*x^3 + 3*(6*a*d^4*e^2*f + 2*b*d^3*e*f^2 - b*c*d^2*f^3)*x^2 + 3*(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*(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)*arccot(d*x + c) - 3*(4*b*c*d^3*e^3 - 6*(b*c^2 - b)*d^2*e^2*f + 4*(b*c^3 - 3*b*c)*d*e*f^2 - (b*c^4 - 6*b*c^2 + b)*f^3)*arctan(d*x + c) + 6*(b*d^3*e^3 - 3*b*c*d^2*e^2*f + (3*b*c^2 - b)*d*e*f^2 - (b*c^3 - b*c)*f^3)*log(d^2*x^2 + 2*c*d*x + c^2 + 1))/d^4","A",0
130,1,206,0,0.735029," ","integrate((f*x+e)^2*(a+b*arccot(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 + 2 \, {\left(b d^{3} f^{2} x^{3} + 3 \, b d^{3} e f x^{2} + 3 \, b d^{3} e^{2} x\right)} \operatorname{arccot}\left(d x + c\right) - 2 \, {\left(3 \, b c d^{2} e^{2} - 3 \, {\left(b c^{2} - b\right)} d e f + {\left(b c^{3} - 3 \, b c\right)} f^{2}\right)} \arctan\left(d x + c\right) + {\left(3 \, b d^{2} e^{2} - 6 \, b c d e f + {\left(3 \, b c^{2} - b\right)} f^{2}\right)} \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 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 + 2*(b*d^3*f^2*x^3 + 3*b*d^3*e*f*x^2 + 3*b*d^3*e^2*x)*arccot(d*x + c) - 2*(3*b*c*d^2*e^2 - 3*(b*c^2 - b)*d*e*f + (b*c^3 - 3*b*c)*f^2)*arctan(d*x + c) + (3*b*d^2*e^2 - 6*b*c*d*e*f + (3*b*c^2 - b)*f^2)*log(d^2*x^2 + 2*c*d*x + c^2 + 1))/d^3","A",0
131,1,110,0,0.519755," ","integrate((f*x+e)*(a+b*arccot(d*x+c)),x, algorithm=""fricas"")","\frac{a d^{2} f x^{2} + {\left(2 \, a d^{2} e + b d f\right)} x + {\left(b d^{2} f x^{2} + 2 \, b d^{2} e x\right)} \operatorname{arccot}\left(d x + c\right) - {\left(2 \, b c d e - {\left(b c^{2} - b\right)} f\right)} \arctan\left(d x + c\right) + {\left(b d e - b c f\right)} \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}{2 \, d^{2}}"," ",0,"1/2*(a*d^2*f*x^2 + (2*a*d^2*e + b*d*f)*x + (b*d^2*f*x^2 + 2*b*d^2*e*x)*arccot(d*x + c) - (2*b*c*d*e - (b*c^2 - b)*f)*arctan(d*x + c) + (b*d*e - b*c*f)*log(d^2*x^2 + 2*c*d*x + c^2 + 1))/d^2","A",0
132,1,52,0,0.693773," ","integrate(a+b*arccot(d*x+c),x, algorithm=""fricas"")","\frac{2 \, b d x \operatorname{arccot}\left(d x + c\right) + 2 \, a d x - 2 \, b c \arctan\left(d x + c\right) + b \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}{2 \, d}"," ",0,"1/2*(2*b*d*x*arccot(d*x + c) + 2*a*d*x - 2*b*c*arctan(d*x + c) + b*log(d^2*x^2 + 2*c*d*x + c^2 + 1))/d","A",0
133,0,0,0,0.524909," ","integrate((a+b*arccot(d*x+c))/(f*x+e),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \operatorname{arccot}\left(d x + c\right) + a}{f x + e}, x\right)"," ",0,"integral((b*arccot(d*x + c) + a)/(f*x + e), x)","F",0
134,1,223,0,1.124779," ","integrate((a+b*arccot(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} + 2 \, {\left(b d^{2} e^{2} - 2 \, b c d e f + {\left(b c^{2} + b\right)} f^{2}\right)} \operatorname{arccot}\left(d x + c\right) + 2 \, {\left(b d^{2} e^{2} - b c d e f + {\left(b d^{2} e f - b c d f^{2}\right)} x\right)} \arctan\left(d x + c\right) - {\left(b d f^{2} x + b d e f\right)} \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right) + 2 \, {\left(b d f^{2} x + b d e f\right)} \log\left(f x + e\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 + 2*(b*d^2*e^2 - 2*b*c*d*e*f + (b*c^2 + b)*f^2)*arccot(d*x + c) + 2*(b*d^2*e^2 - b*c*d*e*f + (b*d^2*e*f - b*c*d*f^2)*x)*arctan(d*x + c) - (b*d*f^2*x + b*d*e*f)*log(d^2*x^2 + 2*c*d*x + c^2 + 1) + 2*(b*d*f^2*x + b*d*e*f)*log(f*x + e))/(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)","A",0
135,1,728,0,3.214680," ","integrate((a+b*arccot(d*x+c))/(f*x+e)^3,x, algorithm=""fricas"")","-\frac{a d^{4} e^{4} - {\left(4 \, a c + b\right)} d^{3} e^{3} f + 2 \, {\left(3 \, a c^{2} + b c + a\right)} d^{2} e^{2} f^{2} - {\left(4 \, a c^{3} + b c^{2} + 4 \, a c + b\right)} d e f^{3} + {\left(a c^{4} + 2 \, a c^{2} + a\right)} f^{4} - {\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} - 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)} \operatorname{arccot}\left(d x + c\right) + {\left(b d^{4} e^{4} - 2 \, b c d^{3} e^{3} f + {\left(b c^{2} - b\right)} d^{2} e^{2} f^{2} + {\left(b d^{4} e^{2} f^{2} - 2 \, b c d^{3} e f^{3} + {\left(b c^{2} - b\right)} d^{2} f^{4}\right)} x^{2} + 2 \, {\left(b d^{4} e^{3} f - 2 \, b c d^{3} e^{2} f^{2} + {\left(b c^{2} - b\right)} d^{2} e f^{3}\right)} x\right)} \arctan\left(d x + c\right) - {\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(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right) + 2 \, {\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)}{2 \, {\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,"-1/2*(a*d^4*e^4 - (4*a*c + b)*d^3*e^3*f + 2*(3*a*c^2 + b*c + a)*d^2*e^2*f^2 - (4*a*c^3 + b*c^2 + 4*a*c + b)*d*e*f^3 + (a*c^4 + 2*a*c^2 + a)*f^4 - (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 - 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)*arccot(d*x + c) + (b*d^4*e^4 - 2*b*c*d^3*e^3*f + (b*c^2 - b)*d^2*e^2*f^2 + (b*d^4*e^2*f^2 - 2*b*c*d^3*e*f^3 + (b*c^2 - b)*d^2*f^4)*x^2 + 2*(b*d^4*e^3*f - 2*b*c*d^3*e^2*f^2 + (b*c^2 - b)*d^2*e*f^3)*x)*arctan(d*x + c) - (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(d^2*x^2 + 2*c*d*x + c^2 + 1) + 2*(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))/(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
136,0,0,0,0.623482," ","integrate((f*x+e)^2*(a+b*arccot(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{arccot}\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{arccot}\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)*arccot(d*x + c)^2 + 2*(a*b*f^2*x^2 + 2*a*b*e*f*x + a*b*e^2)*arccot(d*x + c), x)","F",0
137,0,0,0,0.541424," ","integrate((f*x+e)*(a+b*arccot(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{arccot}\left(d x + c\right)^{2} + 2 \, {\left(a b f x + a b e\right)} \operatorname{arccot}\left(d x + c\right), x\right)"," ",0,"integral(a^2*f*x + a^2*e + (b^2*f*x + b^2*e)*arccot(d*x + c)^2 + 2*(a*b*f*x + a*b*e)*arccot(d*x + c), x)","F",0
138,0,0,0,0.623706," ","integrate((a+b*arccot(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(b^{2} \operatorname{arccot}\left(d x + c\right)^{2} + 2 \, a b \operatorname{arccot}\left(d x + c\right) + a^{2}, x\right)"," ",0,"integral(b^2*arccot(d*x + c)^2 + 2*a*b*arccot(d*x + c) + a^2, x)","F",0
139,0,0,0,0.667093," ","integrate((a+b*arccot(d*x+c))^2/(f*x+e),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} \operatorname{arccot}\left(d x + c\right)^{2} + 2 \, a b \operatorname{arccot}\left(d x + c\right) + a^{2}}{f x + e}, x\right)"," ",0,"integral((b^2*arccot(d*x + c)^2 + 2*a*b*arccot(d*x + c) + a^2)/(f*x + e), x)","F",0
140,0,0,0,0.833374," ","integrate((a+b*arccot(d*x+c))^2/(f*x+e)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{2} \operatorname{arccot}\left(d x + c\right)^{2} + 2 \, a b \operatorname{arccot}\left(d x + c\right) + a^{2}}{f^{2} x^{2} + 2 \, e f x + e^{2}}, x\right)"," ",0,"integral((b^2*arccot(d*x + c)^2 + 2*a*b*arccot(d*x + c) + a^2)/(f^2*x^2 + 2*e*f*x + e^2), x)","F",0
141,0,0,0,0.587634," ","integrate((f*x+e)^2*(a+b*arccot(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{arccot}\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{arccot}\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{arccot}\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)*arccot(d*x + c)^3 + 3*(a*b^2*f^2*x^2 + 2*a*b^2*e*f*x + a*b^2*e^2)*arccot(d*x + c)^2 + 3*(a^2*b*f^2*x^2 + 2*a^2*b*e*f*x + a^2*b*e^2)*arccot(d*x + c), x)","F",0
142,0,0,0,0.590993," ","integrate((f*x+e)*(a+b*arccot(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{arccot}\left(d x + c\right)^{3} + 3 \, {\left(a b^{2} f x + a b^{2} e\right)} \operatorname{arccot}\left(d x + c\right)^{2} + 3 \, {\left(a^{2} b f x + a^{2} b e\right)} \operatorname{arccot}\left(d x + c\right), x\right)"," ",0,"integral(a^3*f*x + a^3*e + (b^3*f*x + b^3*e)*arccot(d*x + c)^3 + 3*(a*b^2*f*x + a*b^2*e)*arccot(d*x + c)^2 + 3*(a^2*b*f*x + a^2*b*e)*arccot(d*x + c), x)","F",0
143,0,0,0,0.727225," ","integrate((a+b*arccot(d*x+c))^3,x, algorithm=""fricas"")","{\rm integral}\left(b^{3} \operatorname{arccot}\left(d x + c\right)^{3} + 3 \, a b^{2} \operatorname{arccot}\left(d x + c\right)^{2} + 3 \, a^{2} b \operatorname{arccot}\left(d x + c\right) + a^{3}, x\right)"," ",0,"integral(b^3*arccot(d*x + c)^3 + 3*a*b^2*arccot(d*x + c)^2 + 3*a^2*b*arccot(d*x + c) + a^3, x)","F",0
144,0,0,0,0.477452," ","integrate((a+b*arccot(d*x+c))^3/(f*x+e),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{3} \operatorname{arccot}\left(d x + c\right)^{3} + 3 \, a b^{2} \operatorname{arccot}\left(d x + c\right)^{2} + 3 \, a^{2} b \operatorname{arccot}\left(d x + c\right) + a^{3}}{f x + e}, x\right)"," ",0,"integral((b^3*arccot(d*x + c)^3 + 3*a*b^2*arccot(d*x + c)^2 + 3*a^2*b*arccot(d*x + c) + a^3)/(f*x + e), x)","F",0
145,0,0,0,0.725839," ","integrate((a+b*arccot(d*x+c))^3/(f*x+e)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b^{3} \operatorname{arccot}\left(d x + c\right)^{3} + 3 \, a b^{2} \operatorname{arccot}\left(d x + c\right)^{2} + 3 \, a^{2} b \operatorname{arccot}\left(d x + c\right) + a^{3}}{f^{2} x^{2} + 2 \, e f x + e^{2}}, x\right)"," ",0,"integral((b^3*arccot(d*x + c)^3 + 3*a*b^2*arccot(d*x + c)^2 + 3*a^2*b*arccot(d*x + c) + a^3)/(f^2*x^2 + 2*e*f*x + e^2), x)","F",0
146,0,0,0,0.580690," ","integrate((f*x+e)^m*(a+b*arccot(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(b \operatorname{arccot}\left(d x + c\right) + a\right)} {\left(f x + e\right)}^{m}, x\right)"," ",0,"integral((b*arccot(d*x + c) + a)*(f*x + e)^m, x)","F",0
147,0,0,0,0.774090," ","integrate((f*x+e)^m*(a+b*arccot(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{2} \operatorname{arccot}\left(d x + c\right)^{2} + 2 \, a b \operatorname{arccot}\left(d x + c\right) + a^{2}\right)} {\left(f x + e\right)}^{m}, x\right)"," ",0,"integral((b^2*arccot(d*x + c)^2 + 2*a*b*arccot(d*x + c) + a^2)*(f*x + e)^m, x)","F",0
148,0,0,0,0.540264," ","integrate((f*x+e)^m*(a+b*arccot(d*x+c))^3,x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{3} \operatorname{arccot}\left(d x + c\right)^{3} + 3 \, a b^{2} \operatorname{arccot}\left(d x + c\right)^{2} + 3 \, a^{2} b \operatorname{arccot}\left(d x + c\right) + a^{3}\right)} {\left(f x + e\right)}^{m}, x\right)"," ",0,"integral((b^3*arccot(d*x + c)^3 + 3*a*b^2*arccot(d*x + c)^2 + 3*a^2*b*arccot(d*x + c) + a^3)*(f*x + e)^m, x)","F",0
149,1,51,0,0.678571," ","integrate(x^3*arccot(b*x^4+a),x, algorithm=""fricas"")","\frac{2 \, b x^{4} \operatorname{arccot}\left(b x^{4} + a\right) - 2 \, a \arctan\left(b x^{4} + a\right) + \log\left(b^{2} x^{8} + 2 \, a b x^{4} + a^{2} + 1\right)}{8 \, b}"," ",0,"1/8*(2*b*x^4*arccot(b*x^4 + a) - 2*a*arctan(b*x^4 + a) + log(b^2*x^8 + 2*a*b*x^4 + a^2 + 1))/b","A",0
150,1,56,0,0.607759," ","integrate(x^(-1+n)*arccot(a+b*x^n),x, algorithm=""fricas"")","\frac{2 \, b x^{n} \operatorname{arccot}\left(b x^{n} + a\right) - 2 \, a \arctan\left(b x^{n} + a\right) + \log\left(b^{2} x^{2 \, n} + 2 \, a b x^{n} + a^{2} + 1\right)}{2 \, b n}"," ",0,"1/2*(2*b*x^n*arccot(b*x^n + a) - 2*a*arctan(b*x^n + a) + log(b^2*x^(2*n) + 2*a*b*x^n + a^2 + 1))/(b*n)","A",0
151,0,0,0,0.621225," ","integrate((a+b*arccot((-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{arccot}\left(\frac{\sqrt{-c x + 1}}{\sqrt{c x + 1}}\right) + a\right)}^{n}}{c^{2} x^{2} - 1}, x\right)"," ",0,"integral(-(b*arccot(sqrt(-c*x + 1)/sqrt(c*x + 1)) + a)^n/(c^2*x^2 - 1), x)","F",0
152,0,0,0,0.543684," ","integrate((a+b*arccot((-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{arccot}\left(\frac{\sqrt{-c x + 1}}{\sqrt{c x + 1}}\right)^{3} + 3 \, a b^{2} \operatorname{arccot}\left(\frac{\sqrt{-c x + 1}}{\sqrt{c x + 1}}\right)^{2} + 3 \, a^{2} b \operatorname{arccot}\left(\frac{\sqrt{-c x + 1}}{\sqrt{c x + 1}}\right) + a^{3}}{c^{2} x^{2} - 1}, x\right)"," ",0,"integral(-(b^3*arccot(sqrt(-c*x + 1)/sqrt(c*x + 1))^3 + 3*a*b^2*arccot(sqrt(-c*x + 1)/sqrt(c*x + 1))^2 + 3*a^2*b*arccot(sqrt(-c*x + 1)/sqrt(c*x + 1)) + a^3)/(c^2*x^2 - 1), x)","F",0
153,0,0,0,0.608201," ","integrate((a+b*arccot((-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{arccot}\left(\frac{\sqrt{-c x + 1}}{\sqrt{c x + 1}}\right)^{2} + 2 \, a b \operatorname{arccot}\left(\frac{\sqrt{-c x + 1}}{\sqrt{c x + 1}}\right) + a^{2}}{c^{2} x^{2} - 1}, x\right)"," ",0,"integral(-(b^2*arccot(sqrt(-c*x + 1)/sqrt(c*x + 1))^2 + 2*a*b*arccot(sqrt(-c*x + 1)/sqrt(c*x + 1)) + a^2)/(c^2*x^2 - 1), x)","F",0
154,0,0,0,0.603109," ","integrate((a+b*arccot((-c*x+1)^(1/2)/(c*x+1)^(1/2)))/(-c^2*x^2+1),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{b \operatorname{arccot}\left(\frac{\sqrt{-c x + 1}}{\sqrt{c x + 1}}\right) + a}{c^{2} x^{2} - 1}, x\right)"," ",0,"integral(-(b*arccot(sqrt(-c*x + 1)/sqrt(c*x + 1)) + a)/(c^2*x^2 - 1), x)","F",0
155,0,0,0,0.734028," ","integrate(1/(-c^2*x^2+1)/(a+b*arccot((-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{arccot}\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)*arccot(sqrt(-c*x + 1)/sqrt(c*x + 1)) - a), x)","F",0
156,0,0,0,0.736870," ","integrate(1/(-c^2*x^2+1)/(a+b*arccot((-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{arccot}\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{arccot}\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)*arccot(sqrt(-c*x + 1)/sqrt(c*x + 1))^2 - a^2 + 2*(a*b*c^2*x^2 - a*b)*arccot(sqrt(-c*x + 1)/sqrt(c*x + 1))), x)","F",0
157,1,15,0,0.682811," ","integrate(1/2*pi-arctan(tan(b*x+a)),x, algorithm=""fricas"")","-\frac{1}{2} \, b x^{2} + \frac{1}{2} \, {\left(\pi - 2 \, a\right)} x"," ",0,"-1/2*b*x^2 + 1/2*(pi - 2*a)*x","A",0
158,1,1973,0,0.806397," ","integrate(x^2*arccot(c+d*tan(b*x+a)),x, algorithm=""fricas"")","\frac{16 \, b^{3} x^{3} \operatorname{arccot}\left(d \tan\left(b x + a\right) + c\right) - 6 \, b^{2} x^{2} {\rm Li}_2\left(\frac{2 \, {\left(i \, c d - d^{2} + d\right)} \tan\left(b x + a\right)^{2} - 2 \, c^{2} - 2 i \, c d - {\left(-2 i \, c^{2} + 4 \, c d + 2 i \, d^{2} - 2 i\right)} \tan\left(b x + a\right) + 2 \, d - 2}{{\left(c^{2} + d^{2} - 2 \, d + 1\right)} \tan\left(b x + a\right)^{2} + c^{2} + d^{2} - 2 \, d + 1} + 1\right) + 6 \, b^{2} x^{2} {\rm Li}_2\left(\frac{2 \, {\left(i \, c d - d^{2} - d\right)} \tan\left(b x + a\right)^{2} - 2 \, c^{2} - 2 i \, c d - {\left(-2 i \, c^{2} + 4 \, c d + 2 i \, d^{2} - 2 i\right)} \tan\left(b x + a\right) - 2 \, d - 2}{{\left(c^{2} + d^{2} + 2 \, d + 1\right)} \tan\left(b x + a\right)^{2} + c^{2} + d^{2} + 2 \, d + 1} + 1\right) - 6 \, b^{2} x^{2} {\rm Li}_2\left(\frac{2 \, {\left(-i \, c d - d^{2} + d\right)} \tan\left(b x + a\right)^{2} - 2 \, c^{2} + 2 i \, c d - {\left(2 i \, c^{2} + 4 \, c d - 2 i \, d^{2} + 2 i\right)} \tan\left(b x + a\right) + 2 \, d - 2}{{\left(c^{2} + d^{2} - 2 \, d + 1\right)} \tan\left(b x + a\right)^{2} + c^{2} + d^{2} - 2 \, d + 1} + 1\right) + 6 \, b^{2} x^{2} {\rm Li}_2\left(\frac{2 \, {\left(-i \, c d - d^{2} - d\right)} \tan\left(b x + a\right)^{2} - 2 \, c^{2} + 2 i \, c d - {\left(2 i \, c^{2} + 4 \, c d - 2 i \, d^{2} + 2 i\right)} \tan\left(b x + a\right) - 2 \, d - 2}{{\left(c^{2} + d^{2} + 2 \, d + 1\right)} \tan\left(b x + a\right)^{2} + c^{2} + d^{2} + 2 \, d + 1} + 1\right) - 4 i \, a^{3} \log\left(\frac{{\left(i \, c d + d^{2} + d\right)} \tan\left(b x + a\right)^{2} - c^{2} + i \, c d + {\left(i \, c^{2} + i \, d^{2} + 2 i \, d + i\right)} \tan\left(b x + a\right) - d - 1}{\tan\left(b x + a\right)^{2} + 1}\right) + 4 i \, a^{3} \log\left(\frac{{\left(i \, c d + d^{2} - d\right)} \tan\left(b x + a\right)^{2} - c^{2} + i \, c d + {\left(i \, c^{2} + i \, d^{2} - 2 i \, d + i\right)} \tan\left(b x + a\right) + d - 1}{\tan\left(b x + a\right)^{2} + 1}\right) - 4 i \, a^{3} \log\left(\frac{{\left(i \, c d - d^{2} + d\right)} \tan\left(b x + a\right)^{2} + c^{2} + i \, c d + {\left(i \, c^{2} + i \, d^{2} - 2 i \, d + i\right)} \tan\left(b x + a\right) - d + 1}{\tan\left(b x + a\right)^{2} + 1}\right) + 4 i \, a^{3} \log\left(\frac{{\left(i \, c d - d^{2} - d\right)} \tan\left(b x + a\right)^{2} + c^{2} + i \, c d + {\left(i \, c^{2} + i \, d^{2} + 2 i \, d + i\right)} \tan\left(b x + a\right) + d + 1}{\tan\left(b x + a\right)^{2} + 1}\right) - 6 i \, b x {\rm polylog}\left(3, \frac{{\left(c^{2} + 2 i \, c d - d^{2} + 1\right)} \tan\left(b x + a\right)^{2} - c^{2} - 2 i \, c d + d^{2} + {\left(2 i \, c^{2} - 4 \, c d - 2 i \, d^{2} + 2 i\right)} \tan\left(b x + a\right) - 1}{{\left(c^{2} + d^{2} + 2 \, d + 1\right)} \tan\left(b x + a\right)^{2} + c^{2} + d^{2} + 2 \, d + 1}\right) + 6 i \, b x {\rm polylog}\left(3, \frac{{\left(c^{2} - 2 i \, c d - d^{2} + 1\right)} \tan\left(b x + a\right)^{2} - c^{2} + 2 i \, c d + d^{2} + {\left(-2 i \, c^{2} - 4 \, c d + 2 i \, d^{2} - 2 i\right)} \tan\left(b x + a\right) - 1}{{\left(c^{2} + d^{2} + 2 \, d + 1\right)} \tan\left(b x + a\right)^{2} + c^{2} + d^{2} + 2 \, d + 1}\right) + 6 i \, b x {\rm polylog}\left(3, \frac{{\left(c^{2} + 2 i \, c d - d^{2} + 1\right)} \tan\left(b x + a\right)^{2} - c^{2} - 2 i \, c d + d^{2} + {\left(2 i \, c^{2} - 4 \, c d - 2 i \, d^{2} + 2 i\right)} \tan\left(b x + a\right) - 1}{{\left(c^{2} + d^{2} - 2 \, d + 1\right)} \tan\left(b x + a\right)^{2} + c^{2} + d^{2} - 2 \, d + 1}\right) - 6 i \, b x {\rm polylog}\left(3, \frac{{\left(c^{2} - 2 i \, c d - d^{2} + 1\right)} \tan\left(b x + a\right)^{2} - c^{2} + 2 i \, c d + d^{2} + {\left(-2 i \, c^{2} - 4 \, c d + 2 i \, d^{2} - 2 i\right)} \tan\left(b x + a\right) - 1}{{\left(c^{2} + d^{2} - 2 \, d + 1\right)} \tan\left(b x + a\right)^{2} + c^{2} + d^{2} - 2 \, d + 1}\right) + {\left(4 i \, b^{3} x^{3} + 4 i \, a^{3}\right)} \log\left(-\frac{2 \, {\left(i \, c d - d^{2} + d\right)} \tan\left(b x + a\right)^{2} - 2 \, c^{2} - 2 i \, c d - {\left(-2 i \, c^{2} + 4 \, c d + 2 i \, d^{2} - 2 i\right)} \tan\left(b x + a\right) + 2 \, d - 2}{{\left(c^{2} + d^{2} - 2 \, d + 1\right)} \tan\left(b x + a\right)^{2} + c^{2} + d^{2} - 2 \, d + 1}\right) + {\left(-4 i \, b^{3} x^{3} - 4 i \, a^{3}\right)} \log\left(-\frac{2 \, {\left(i \, c d - d^{2} - d\right)} \tan\left(b x + a\right)^{2} - 2 \, c^{2} - 2 i \, c d - {\left(-2 i \, c^{2} + 4 \, c d + 2 i \, d^{2} - 2 i\right)} \tan\left(b x + a\right) - 2 \, d - 2}{{\left(c^{2} + d^{2} + 2 \, d + 1\right)} \tan\left(b x + a\right)^{2} + c^{2} + d^{2} + 2 \, d + 1}\right) + {\left(-4 i \, b^{3} x^{3} - 4 i \, a^{3}\right)} \log\left(-\frac{2 \, {\left(-i \, c d - d^{2} + d\right)} \tan\left(b x + a\right)^{2} - 2 \, c^{2} + 2 i \, c d - {\left(2 i \, c^{2} + 4 \, c d - 2 i \, d^{2} + 2 i\right)} \tan\left(b x + a\right) + 2 \, d - 2}{{\left(c^{2} + d^{2} - 2 \, d + 1\right)} \tan\left(b x + a\right)^{2} + c^{2} + d^{2} - 2 \, d + 1}\right) + {\left(4 i \, b^{3} x^{3} + 4 i \, a^{3}\right)} \log\left(-\frac{2 \, {\left(-i \, c d - d^{2} - d\right)} \tan\left(b x + a\right)^{2} - 2 \, c^{2} + 2 i \, c d - {\left(2 i \, c^{2} + 4 \, c d - 2 i \, d^{2} + 2 i\right)} \tan\left(b x + a\right) - 2 \, d - 2}{{\left(c^{2} + d^{2} + 2 \, d + 1\right)} \tan\left(b x + a\right)^{2} + c^{2} + d^{2} + 2 \, d + 1}\right) - 3 \, {\rm polylog}\left(4, \frac{{\left(c^{2} + 2 i \, c d - d^{2} + 1\right)} \tan\left(b x + a\right)^{2} - c^{2} - 2 i \, c d + d^{2} + {\left(2 i \, c^{2} - 4 \, c d - 2 i \, d^{2} + 2 i\right)} \tan\left(b x + a\right) - 1}{{\left(c^{2} + d^{2} + 2 \, d + 1\right)} \tan\left(b x + a\right)^{2} + c^{2} + d^{2} + 2 \, d + 1}\right) - 3 \, {\rm polylog}\left(4, \frac{{\left(c^{2} - 2 i \, c d - d^{2} + 1\right)} \tan\left(b x + a\right)^{2} - c^{2} + 2 i \, c d + d^{2} + {\left(-2 i \, c^{2} - 4 \, c d + 2 i \, d^{2} - 2 i\right)} \tan\left(b x + a\right) - 1}{{\left(c^{2} + d^{2} + 2 \, d + 1\right)} \tan\left(b x + a\right)^{2} + c^{2} + d^{2} + 2 \, d + 1}\right) + 3 \, {\rm polylog}\left(4, \frac{{\left(c^{2} + 2 i \, c d - d^{2} + 1\right)} \tan\left(b x + a\right)^{2} - c^{2} - 2 i \, c d + d^{2} + {\left(2 i \, c^{2} - 4 \, c d - 2 i \, d^{2} + 2 i\right)} \tan\left(b x + a\right) - 1}{{\left(c^{2} + d^{2} - 2 \, d + 1\right)} \tan\left(b x + a\right)^{2} + c^{2} + d^{2} - 2 \, d + 1}\right) + 3 \, {\rm polylog}\left(4, \frac{{\left(c^{2} - 2 i \, c d - d^{2} + 1\right)} \tan\left(b x + a\right)^{2} - c^{2} + 2 i \, c d + d^{2} + {\left(-2 i \, c^{2} - 4 \, c d + 2 i \, d^{2} - 2 i\right)} \tan\left(b x + a\right) - 1}{{\left(c^{2} + d^{2} - 2 \, d + 1\right)} \tan\left(b x + a\right)^{2} + c^{2} + d^{2} - 2 \, d + 1}\right)}{48 \, b^{3}}"," ",0,"1/48*(16*b^3*x^3*arccot(d*tan(b*x + a) + c) - 6*b^2*x^2*dilog((2*(I*c*d - d^2 + d)*tan(b*x + a)^2 - 2*c^2 - 2*I*c*d - (-2*I*c^2 + 4*c*d + 2*I*d^2 - 2*I)*tan(b*x + a) + 2*d - 2)/((c^2 + d^2 - 2*d + 1)*tan(b*x + a)^2 + c^2 + d^2 - 2*d + 1) + 1) + 6*b^2*x^2*dilog((2*(I*c*d - d^2 - d)*tan(b*x + a)^2 - 2*c^2 - 2*I*c*d - (-2*I*c^2 + 4*c*d + 2*I*d^2 - 2*I)*tan(b*x + a) - 2*d - 2)/((c^2 + d^2 + 2*d + 1)*tan(b*x + a)^2 + c^2 + d^2 + 2*d + 1) + 1) - 6*b^2*x^2*dilog((2*(-I*c*d - d^2 + d)*tan(b*x + a)^2 - 2*c^2 + 2*I*c*d - (2*I*c^2 + 4*c*d - 2*I*d^2 + 2*I)*tan(b*x + a) + 2*d - 2)/((c^2 + d^2 - 2*d + 1)*tan(b*x + a)^2 + c^2 + d^2 - 2*d + 1) + 1) + 6*b^2*x^2*dilog((2*(-I*c*d - d^2 - d)*tan(b*x + a)^2 - 2*c^2 + 2*I*c*d - (2*I*c^2 + 4*c*d - 2*I*d^2 + 2*I)*tan(b*x + a) - 2*d - 2)/((c^2 + d^2 + 2*d + 1)*tan(b*x + a)^2 + c^2 + d^2 + 2*d + 1) + 1) - 4*I*a^3*log(((I*c*d + d^2 + d)*tan(b*x + a)^2 - c^2 + I*c*d + (I*c^2 + I*d^2 + 2*I*d + I)*tan(b*x + a) - d - 1)/(tan(b*x + a)^2 + 1)) + 4*I*a^3*log(((I*c*d + d^2 - d)*tan(b*x + a)^2 - c^2 + I*c*d + (I*c^2 + I*d^2 - 2*I*d + I)*tan(b*x + a) + d - 1)/(tan(b*x + a)^2 + 1)) - 4*I*a^3*log(((I*c*d - d^2 + d)*tan(b*x + a)^2 + c^2 + I*c*d + (I*c^2 + I*d^2 - 2*I*d + I)*tan(b*x + a) - d + 1)/(tan(b*x + a)^2 + 1)) + 4*I*a^3*log(((I*c*d - d^2 - d)*tan(b*x + a)^2 + c^2 + I*c*d + (I*c^2 + I*d^2 + 2*I*d + I)*tan(b*x + a) + d + 1)/(tan(b*x + a)^2 + 1)) - 6*I*b*x*polylog(3, ((c^2 + 2*I*c*d - d^2 + 1)*tan(b*x + a)^2 - c^2 - 2*I*c*d + d^2 + (2*I*c^2 - 4*c*d - 2*I*d^2 + 2*I)*tan(b*x + a) - 1)/((c^2 + d^2 + 2*d + 1)*tan(b*x + a)^2 + c^2 + d^2 + 2*d + 1)) + 6*I*b*x*polylog(3, ((c^2 - 2*I*c*d - d^2 + 1)*tan(b*x + a)^2 - c^2 + 2*I*c*d + d^2 + (-2*I*c^2 - 4*c*d + 2*I*d^2 - 2*I)*tan(b*x + a) - 1)/((c^2 + d^2 + 2*d + 1)*tan(b*x + a)^2 + c^2 + d^2 + 2*d + 1)) + 6*I*b*x*polylog(3, ((c^2 + 2*I*c*d - d^2 + 1)*tan(b*x + a)^2 - c^2 - 2*I*c*d + d^2 + (2*I*c^2 - 4*c*d - 2*I*d^2 + 2*I)*tan(b*x + a) - 1)/((c^2 + d^2 - 2*d + 1)*tan(b*x + a)^2 + c^2 + d^2 - 2*d + 1)) - 6*I*b*x*polylog(3, ((c^2 - 2*I*c*d - d^2 + 1)*tan(b*x + a)^2 - c^2 + 2*I*c*d + d^2 + (-2*I*c^2 - 4*c*d + 2*I*d^2 - 2*I)*tan(b*x + a) - 1)/((c^2 + d^2 - 2*d + 1)*tan(b*x + a)^2 + c^2 + d^2 - 2*d + 1)) + (4*I*b^3*x^3 + 4*I*a^3)*log(-(2*(I*c*d - d^2 + d)*tan(b*x + a)^2 - 2*c^2 - 2*I*c*d - (-2*I*c^2 + 4*c*d + 2*I*d^2 - 2*I)*tan(b*x + a) + 2*d - 2)/((c^2 + d^2 - 2*d + 1)*tan(b*x + a)^2 + c^2 + d^2 - 2*d + 1)) + (-4*I*b^3*x^3 - 4*I*a^3)*log(-(2*(I*c*d - d^2 - d)*tan(b*x + a)^2 - 2*c^2 - 2*I*c*d - (-2*I*c^2 + 4*c*d + 2*I*d^2 - 2*I)*tan(b*x + a) - 2*d - 2)/((c^2 + d^2 + 2*d + 1)*tan(b*x + a)^2 + c^2 + d^2 + 2*d + 1)) + (-4*I*b^3*x^3 - 4*I*a^3)*log(-(2*(-I*c*d - d^2 + d)*tan(b*x + a)^2 - 2*c^2 + 2*I*c*d - (2*I*c^2 + 4*c*d - 2*I*d^2 + 2*I)*tan(b*x + a) + 2*d - 2)/((c^2 + d^2 - 2*d + 1)*tan(b*x + a)^2 + c^2 + d^2 - 2*d + 1)) + (4*I*b^3*x^3 + 4*I*a^3)*log(-(2*(-I*c*d - d^2 - d)*tan(b*x + a)^2 - 2*c^2 + 2*I*c*d - (2*I*c^2 + 4*c*d - 2*I*d^2 + 2*I)*tan(b*x + a) - 2*d - 2)/((c^2 + d^2 + 2*d + 1)*tan(b*x + a)^2 + c^2 + d^2 + 2*d + 1)) - 3*polylog(4, ((c^2 + 2*I*c*d - d^2 + 1)*tan(b*x + a)^2 - c^2 - 2*I*c*d + d^2 + (2*I*c^2 - 4*c*d - 2*I*d^2 + 2*I)*tan(b*x + a) - 1)/((c^2 + d^2 + 2*d + 1)*tan(b*x + a)^2 + c^2 + d^2 + 2*d + 1)) - 3*polylog(4, ((c^2 - 2*I*c*d - d^2 + 1)*tan(b*x + a)^2 - c^2 + 2*I*c*d + d^2 + (-2*I*c^2 - 4*c*d + 2*I*d^2 - 2*I)*tan(b*x + a) - 1)/((c^2 + d^2 + 2*d + 1)*tan(b*x + a)^2 + c^2 + d^2 + 2*d + 1)) + 3*polylog(4, ((c^2 + 2*I*c*d - d^2 + 1)*tan(b*x + a)^2 - c^2 - 2*I*c*d + d^2 + (2*I*c^2 - 4*c*d - 2*I*d^2 + 2*I)*tan(b*x + a) - 1)/((c^2 + d^2 - 2*d + 1)*tan(b*x + a)^2 + c^2 + d^2 - 2*d + 1)) + 3*polylog(4, ((c^2 - 2*I*c*d - d^2 + 1)*tan(b*x + a)^2 - c^2 + 2*I*c*d + d^2 + (-2*I*c^2 - 4*c*d + 2*I*d^2 - 2*I)*tan(b*x + a) - 1)/((c^2 + d^2 - 2*d + 1)*tan(b*x + a)^2 + c^2 + d^2 - 2*d + 1)))/b^3","C",0
159,1,1557,0,0.851065," ","integrate(x*arccot(c+d*tan(b*x+a)),x, algorithm=""fricas"")","\frac{8 \, b^{2} x^{2} \operatorname{arccot}\left(d \tan\left(b x + a\right) + c\right) - 2 \, b x {\rm Li}_2\left(\frac{2 \, {\left(i \, c d - d^{2} + d\right)} \tan\left(b x + a\right)^{2} - 2 \, c^{2} - 2 i \, c d - {\left(-2 i \, c^{2} + 4 \, c d + 2 i \, d^{2} - 2 i\right)} \tan\left(b x + a\right) + 2 \, d - 2}{{\left(c^{2} + d^{2} - 2 \, d + 1\right)} \tan\left(b x + a\right)^{2} + c^{2} + d^{2} - 2 \, d + 1} + 1\right) + 2 \, b x {\rm Li}_2\left(\frac{2 \, {\left(i \, c d - d^{2} - d\right)} \tan\left(b x + a\right)^{2} - 2 \, c^{2} - 2 i \, c d - {\left(-2 i \, c^{2} + 4 \, c d + 2 i \, d^{2} - 2 i\right)} \tan\left(b x + a\right) - 2 \, d - 2}{{\left(c^{2} + d^{2} + 2 \, d + 1\right)} \tan\left(b x + a\right)^{2} + c^{2} + d^{2} + 2 \, d + 1} + 1\right) - 2 \, b x {\rm Li}_2\left(\frac{2 \, {\left(-i \, c d - d^{2} + d\right)} \tan\left(b x + a\right)^{2} - 2 \, c^{2} + 2 i \, c d - {\left(2 i \, c^{2} + 4 \, c d - 2 i \, d^{2} + 2 i\right)} \tan\left(b x + a\right) + 2 \, d - 2}{{\left(c^{2} + d^{2} - 2 \, d + 1\right)} \tan\left(b x + a\right)^{2} + c^{2} + d^{2} - 2 \, d + 1} + 1\right) + 2 \, b x {\rm Li}_2\left(\frac{2 \, {\left(-i \, c d - d^{2} - d\right)} \tan\left(b x + a\right)^{2} - 2 \, c^{2} + 2 i \, c d - {\left(2 i \, c^{2} + 4 \, c d - 2 i \, d^{2} + 2 i\right)} \tan\left(b x + a\right) - 2 \, d - 2}{{\left(c^{2} + d^{2} + 2 \, d + 1\right)} \tan\left(b x + a\right)^{2} + c^{2} + d^{2} + 2 \, d + 1} + 1\right) + 2 i \, a^{2} \log\left(\frac{{\left(i \, c d + d^{2} + d\right)} \tan\left(b x + a\right)^{2} - c^{2} + i \, c d + {\left(i \, c^{2} + i \, d^{2} + 2 i \, d + i\right)} \tan\left(b x + a\right) - d - 1}{\tan\left(b x + a\right)^{2} + 1}\right) - 2 i \, a^{2} \log\left(\frac{{\left(i \, c d + d^{2} - d\right)} \tan\left(b x + a\right)^{2} - c^{2} + i \, c d + {\left(i \, c^{2} + i \, d^{2} - 2 i \, d + i\right)} \tan\left(b x + a\right) + d - 1}{\tan\left(b x + a\right)^{2} + 1}\right) + 2 i \, a^{2} \log\left(\frac{{\left(i \, c d - d^{2} + d\right)} \tan\left(b x + a\right)^{2} + c^{2} + i \, c d + {\left(i \, c^{2} + i \, d^{2} - 2 i \, d + i\right)} \tan\left(b x + a\right) - d + 1}{\tan\left(b x + a\right)^{2} + 1}\right) - 2 i \, a^{2} \log\left(\frac{{\left(i \, c d - d^{2} - d\right)} \tan\left(b x + a\right)^{2} + c^{2} + i \, c d + {\left(i \, c^{2} + i \, d^{2} + 2 i \, d + i\right)} \tan\left(b x + a\right) + d + 1}{\tan\left(b x + a\right)^{2} + 1}\right) + {\left(2 i \, b^{2} x^{2} - 2 i \, a^{2}\right)} \log\left(-\frac{2 \, {\left(i \, c d - d^{2} + d\right)} \tan\left(b x + a\right)^{2} - 2 \, c^{2} - 2 i \, c d - {\left(-2 i \, c^{2} + 4 \, c d + 2 i \, d^{2} - 2 i\right)} \tan\left(b x + a\right) + 2 \, d - 2}{{\left(c^{2} + d^{2} - 2 \, d + 1\right)} \tan\left(b x + a\right)^{2} + c^{2} + d^{2} - 2 \, d + 1}\right) + {\left(-2 i \, b^{2} x^{2} + 2 i \, a^{2}\right)} \log\left(-\frac{2 \, {\left(i \, c d - d^{2} - d\right)} \tan\left(b x + a\right)^{2} - 2 \, c^{2} - 2 i \, c d - {\left(-2 i \, c^{2} + 4 \, c d + 2 i \, d^{2} - 2 i\right)} \tan\left(b x + a\right) - 2 \, d - 2}{{\left(c^{2} + d^{2} + 2 \, d + 1\right)} \tan\left(b x + a\right)^{2} + c^{2} + d^{2} + 2 \, d + 1}\right) + {\left(-2 i \, b^{2} x^{2} + 2 i \, a^{2}\right)} \log\left(-\frac{2 \, {\left(-i \, c d - d^{2} + d\right)} \tan\left(b x + a\right)^{2} - 2 \, c^{2} + 2 i \, c d - {\left(2 i \, c^{2} + 4 \, c d - 2 i \, d^{2} + 2 i\right)} \tan\left(b x + a\right) + 2 \, d - 2}{{\left(c^{2} + d^{2} - 2 \, d + 1\right)} \tan\left(b x + a\right)^{2} + c^{2} + d^{2} - 2 \, d + 1}\right) + {\left(2 i \, b^{2} x^{2} - 2 i \, a^{2}\right)} \log\left(-\frac{2 \, {\left(-i \, c d - d^{2} - d\right)} \tan\left(b x + a\right)^{2} - 2 \, c^{2} + 2 i \, c d - {\left(2 i \, c^{2} + 4 \, c d - 2 i \, d^{2} + 2 i\right)} \tan\left(b x + a\right) - 2 \, d - 2}{{\left(c^{2} + d^{2} + 2 \, d + 1\right)} \tan\left(b x + a\right)^{2} + c^{2} + d^{2} + 2 \, d + 1}\right) - i \, {\rm polylog}\left(3, \frac{{\left(c^{2} + 2 i \, c d - d^{2} + 1\right)} \tan\left(b x + a\right)^{2} - c^{2} - 2 i \, c d + d^{2} + {\left(2 i \, c^{2} - 4 \, c d - 2 i \, d^{2} + 2 i\right)} \tan\left(b x + a\right) - 1}{{\left(c^{2} + d^{2} + 2 \, d + 1\right)} \tan\left(b x + a\right)^{2} + c^{2} + d^{2} + 2 \, d + 1}\right) + i \, {\rm polylog}\left(3, \frac{{\left(c^{2} - 2 i \, c d - d^{2} + 1\right)} \tan\left(b x + a\right)^{2} - c^{2} + 2 i \, c d + d^{2} + {\left(-2 i \, c^{2} - 4 \, c d + 2 i \, d^{2} - 2 i\right)} \tan\left(b x + a\right) - 1}{{\left(c^{2} + d^{2} + 2 \, d + 1\right)} \tan\left(b x + a\right)^{2} + c^{2} + d^{2} + 2 \, d + 1}\right) + i \, {\rm polylog}\left(3, \frac{{\left(c^{2} + 2 i \, c d - d^{2} + 1\right)} \tan\left(b x + a\right)^{2} - c^{2} - 2 i \, c d + d^{2} + {\left(2 i \, c^{2} - 4 \, c d - 2 i \, d^{2} + 2 i\right)} \tan\left(b x + a\right) - 1}{{\left(c^{2} + d^{2} - 2 \, d + 1\right)} \tan\left(b x + a\right)^{2} + c^{2} + d^{2} - 2 \, d + 1}\right) - i \, {\rm polylog}\left(3, \frac{{\left(c^{2} - 2 i \, c d - d^{2} + 1\right)} \tan\left(b x + a\right)^{2} - c^{2} + 2 i \, c d + d^{2} + {\left(-2 i \, c^{2} - 4 \, c d + 2 i \, d^{2} - 2 i\right)} \tan\left(b x + a\right) - 1}{{\left(c^{2} + d^{2} - 2 \, d + 1\right)} \tan\left(b x + a\right)^{2} + c^{2} + d^{2} - 2 \, d + 1}\right)}{16 \, b^{2}}"," ",0,"1/16*(8*b^2*x^2*arccot(d*tan(b*x + a) + c) - 2*b*x*dilog((2*(I*c*d - d^2 + d)*tan(b*x + a)^2 - 2*c^2 - 2*I*c*d - (-2*I*c^2 + 4*c*d + 2*I*d^2 - 2*I)*tan(b*x + a) + 2*d - 2)/((c^2 + d^2 - 2*d + 1)*tan(b*x + a)^2 + c^2 + d^2 - 2*d + 1) + 1) + 2*b*x*dilog((2*(I*c*d - d^2 - d)*tan(b*x + a)^2 - 2*c^2 - 2*I*c*d - (-2*I*c^2 + 4*c*d + 2*I*d^2 - 2*I)*tan(b*x + a) - 2*d - 2)/((c^2 + d^2 + 2*d + 1)*tan(b*x + a)^2 + c^2 + d^2 + 2*d + 1) + 1) - 2*b*x*dilog((2*(-I*c*d - d^2 + d)*tan(b*x + a)^2 - 2*c^2 + 2*I*c*d - (2*I*c^2 + 4*c*d - 2*I*d^2 + 2*I)*tan(b*x + a) + 2*d - 2)/((c^2 + d^2 - 2*d + 1)*tan(b*x + a)^2 + c^2 + d^2 - 2*d + 1) + 1) + 2*b*x*dilog((2*(-I*c*d - d^2 - d)*tan(b*x + a)^2 - 2*c^2 + 2*I*c*d - (2*I*c^2 + 4*c*d - 2*I*d^2 + 2*I)*tan(b*x + a) - 2*d - 2)/((c^2 + d^2 + 2*d + 1)*tan(b*x + a)^2 + c^2 + d^2 + 2*d + 1) + 1) + 2*I*a^2*log(((I*c*d + d^2 + d)*tan(b*x + a)^2 - c^2 + I*c*d + (I*c^2 + I*d^2 + 2*I*d + I)*tan(b*x + a) - d - 1)/(tan(b*x + a)^2 + 1)) - 2*I*a^2*log(((I*c*d + d^2 - d)*tan(b*x + a)^2 - c^2 + I*c*d + (I*c^2 + I*d^2 - 2*I*d + I)*tan(b*x + a) + d - 1)/(tan(b*x + a)^2 + 1)) + 2*I*a^2*log(((I*c*d - d^2 + d)*tan(b*x + a)^2 + c^2 + I*c*d + (I*c^2 + I*d^2 - 2*I*d + I)*tan(b*x + a) - d + 1)/(tan(b*x + a)^2 + 1)) - 2*I*a^2*log(((I*c*d - d^2 - d)*tan(b*x + a)^2 + c^2 + I*c*d + (I*c^2 + I*d^2 + 2*I*d + I)*tan(b*x + a) + d + 1)/(tan(b*x + a)^2 + 1)) + (2*I*b^2*x^2 - 2*I*a^2)*log(-(2*(I*c*d - d^2 + d)*tan(b*x + a)^2 - 2*c^2 - 2*I*c*d - (-2*I*c^2 + 4*c*d + 2*I*d^2 - 2*I)*tan(b*x + a) + 2*d - 2)/((c^2 + d^2 - 2*d + 1)*tan(b*x + a)^2 + c^2 + d^2 - 2*d + 1)) + (-2*I*b^2*x^2 + 2*I*a^2)*log(-(2*(I*c*d - d^2 - d)*tan(b*x + a)^2 - 2*c^2 - 2*I*c*d - (-2*I*c^2 + 4*c*d + 2*I*d^2 - 2*I)*tan(b*x + a) - 2*d - 2)/((c^2 + d^2 + 2*d + 1)*tan(b*x + a)^2 + c^2 + d^2 + 2*d + 1)) + (-2*I*b^2*x^2 + 2*I*a^2)*log(-(2*(-I*c*d - d^2 + d)*tan(b*x + a)^2 - 2*c^2 + 2*I*c*d - (2*I*c^2 + 4*c*d - 2*I*d^2 + 2*I)*tan(b*x + a) + 2*d - 2)/((c^2 + d^2 - 2*d + 1)*tan(b*x + a)^2 + c^2 + d^2 - 2*d + 1)) + (2*I*b^2*x^2 - 2*I*a^2)*log(-(2*(-I*c*d - d^2 - d)*tan(b*x + a)^2 - 2*c^2 + 2*I*c*d - (2*I*c^2 + 4*c*d - 2*I*d^2 + 2*I)*tan(b*x + a) - 2*d - 2)/((c^2 + d^2 + 2*d + 1)*tan(b*x + a)^2 + c^2 + d^2 + 2*d + 1)) - I*polylog(3, ((c^2 + 2*I*c*d - d^2 + 1)*tan(b*x + a)^2 - c^2 - 2*I*c*d + d^2 + (2*I*c^2 - 4*c*d - 2*I*d^2 + 2*I)*tan(b*x + a) - 1)/((c^2 + d^2 + 2*d + 1)*tan(b*x + a)^2 + c^2 + d^2 + 2*d + 1)) + I*polylog(3, ((c^2 - 2*I*c*d - d^2 + 1)*tan(b*x + a)^2 - c^2 + 2*I*c*d + d^2 + (-2*I*c^2 - 4*c*d + 2*I*d^2 - 2*I)*tan(b*x + a) - 1)/((c^2 + d^2 + 2*d + 1)*tan(b*x + a)^2 + c^2 + d^2 + 2*d + 1)) + I*polylog(3, ((c^2 + 2*I*c*d - d^2 + 1)*tan(b*x + a)^2 - c^2 - 2*I*c*d + d^2 + (2*I*c^2 - 4*c*d - 2*I*d^2 + 2*I)*tan(b*x + a) - 1)/((c^2 + d^2 - 2*d + 1)*tan(b*x + a)^2 + c^2 + d^2 - 2*d + 1)) - I*polylog(3, ((c^2 - 2*I*c*d - d^2 + 1)*tan(b*x + a)^2 - c^2 + 2*I*c*d + d^2 + (-2*I*c^2 - 4*c*d + 2*I*d^2 - 2*I)*tan(b*x + a) - 1)/((c^2 + d^2 - 2*d + 1)*tan(b*x + a)^2 + c^2 + d^2 - 2*d + 1)))/b^2","C",0
160,1,1117,0,1.113247," ","integrate(arccot(c+d*tan(b*x+a)),x, algorithm=""fricas"")","\frac{8 \, b x \operatorname{arccot}\left(d \tan\left(b x + a\right) + c\right) + {\left(2 i \, b x + 2 i \, a\right)} \log\left(-\frac{2 \, {\left(i \, c d - d^{2} + d\right)} \tan\left(b x + a\right)^{2} - 2 \, c^{2} - 2 i \, c d - {\left(-2 i \, c^{2} + 4 \, c d + 2 i \, d^{2} - 2 i\right)} \tan\left(b x + a\right) + 2 \, d - 2}{{\left(c^{2} + d^{2} - 2 \, d + 1\right)} \tan\left(b x + a\right)^{2} + c^{2} + d^{2} - 2 \, d + 1}\right) + {\left(-2 i \, b x - 2 i \, a\right)} \log\left(-\frac{2 \, {\left(i \, c d - d^{2} - d\right)} \tan\left(b x + a\right)^{2} - 2 \, c^{2} - 2 i \, c d - {\left(-2 i \, c^{2} + 4 \, c d + 2 i \, d^{2} - 2 i\right)} \tan\left(b x + a\right) - 2 \, d - 2}{{\left(c^{2} + d^{2} + 2 \, d + 1\right)} \tan\left(b x + a\right)^{2} + c^{2} + d^{2} + 2 \, d + 1}\right) + {\left(-2 i \, b x - 2 i \, a\right)} \log\left(-\frac{2 \, {\left(-i \, c d - d^{2} + d\right)} \tan\left(b x + a\right)^{2} - 2 \, c^{2} + 2 i \, c d - {\left(2 i \, c^{2} + 4 \, c d - 2 i \, d^{2} + 2 i\right)} \tan\left(b x + a\right) + 2 \, d - 2}{{\left(c^{2} + d^{2} - 2 \, d + 1\right)} \tan\left(b x + a\right)^{2} + c^{2} + d^{2} - 2 \, d + 1}\right) + {\left(2 i \, b x + 2 i \, a\right)} \log\left(-\frac{2 \, {\left(-i \, c d - d^{2} - d\right)} \tan\left(b x + a\right)^{2} - 2 \, c^{2} + 2 i \, c d - {\left(2 i \, c^{2} + 4 \, c d - 2 i \, d^{2} + 2 i\right)} \tan\left(b x + a\right) - 2 \, d - 2}{{\left(c^{2} + d^{2} + 2 \, d + 1\right)} \tan\left(b x + a\right)^{2} + c^{2} + d^{2} + 2 \, d + 1}\right) - 2 i \, a \log\left(\frac{{\left(i \, c d + d^{2} + d\right)} \tan\left(b x + a\right)^{2} - c^{2} + i \, c d + {\left(i \, c^{2} + i \, d^{2} + 2 i \, d + i\right)} \tan\left(b x + a\right) - d - 1}{\tan\left(b x + a\right)^{2} + 1}\right) + 2 i \, a \log\left(\frac{{\left(i \, c d + d^{2} - d\right)} \tan\left(b x + a\right)^{2} - c^{2} + i \, c d + {\left(i \, c^{2} + i \, d^{2} - 2 i \, d + i\right)} \tan\left(b x + a\right) + d - 1}{\tan\left(b x + a\right)^{2} + 1}\right) - 2 i \, a \log\left(\frac{{\left(i \, c d - d^{2} + d\right)} \tan\left(b x + a\right)^{2} + c^{2} + i \, c d + {\left(i \, c^{2} + i \, d^{2} - 2 i \, d + i\right)} \tan\left(b x + a\right) - d + 1}{\tan\left(b x + a\right)^{2} + 1}\right) + 2 i \, a \log\left(\frac{{\left(i \, c d - d^{2} - d\right)} \tan\left(b x + a\right)^{2} + c^{2} + i \, c d + {\left(i \, c^{2} + i \, d^{2} + 2 i \, d + i\right)} \tan\left(b x + a\right) + d + 1}{\tan\left(b x + a\right)^{2} + 1}\right) - {\rm Li}_2\left(\frac{2 \, {\left(i \, c d - d^{2} + d\right)} \tan\left(b x + a\right)^{2} - 2 \, c^{2} - 2 i \, c d - {\left(-2 i \, c^{2} + 4 \, c d + 2 i \, d^{2} - 2 i\right)} \tan\left(b x + a\right) + 2 \, d - 2}{{\left(c^{2} + d^{2} - 2 \, d + 1\right)} \tan\left(b x + a\right)^{2} + c^{2} + d^{2} - 2 \, d + 1} + 1\right) + {\rm Li}_2\left(\frac{2 \, {\left(i \, c d - d^{2} - d\right)} \tan\left(b x + a\right)^{2} - 2 \, c^{2} - 2 i \, c d - {\left(-2 i \, c^{2} + 4 \, c d + 2 i \, d^{2} - 2 i\right)} \tan\left(b x + a\right) - 2 \, d - 2}{{\left(c^{2} + d^{2} + 2 \, d + 1\right)} \tan\left(b x + a\right)^{2} + c^{2} + d^{2} + 2 \, d + 1} + 1\right) - {\rm Li}_2\left(\frac{2 \, {\left(-i \, c d - d^{2} + d\right)} \tan\left(b x + a\right)^{2} - 2 \, c^{2} + 2 i \, c d - {\left(2 i \, c^{2} + 4 \, c d - 2 i \, d^{2} + 2 i\right)} \tan\left(b x + a\right) + 2 \, d - 2}{{\left(c^{2} + d^{2} - 2 \, d + 1\right)} \tan\left(b x + a\right)^{2} + c^{2} + d^{2} - 2 \, d + 1} + 1\right) + {\rm Li}_2\left(\frac{2 \, {\left(-i \, c d - d^{2} - d\right)} \tan\left(b x + a\right)^{2} - 2 \, c^{2} + 2 i \, c d - {\left(2 i \, c^{2} + 4 \, c d - 2 i \, d^{2} + 2 i\right)} \tan\left(b x + a\right) - 2 \, d - 2}{{\left(c^{2} + d^{2} + 2 \, d + 1\right)} \tan\left(b x + a\right)^{2} + c^{2} + d^{2} + 2 \, d + 1} + 1\right)}{8 \, b}"," ",0,"1/8*(8*b*x*arccot(d*tan(b*x + a) + c) + (2*I*b*x + 2*I*a)*log(-(2*(I*c*d - d^2 + d)*tan(b*x + a)^2 - 2*c^2 - 2*I*c*d - (-2*I*c^2 + 4*c*d + 2*I*d^2 - 2*I)*tan(b*x + a) + 2*d - 2)/((c^2 + d^2 - 2*d + 1)*tan(b*x + a)^2 + c^2 + d^2 - 2*d + 1)) + (-2*I*b*x - 2*I*a)*log(-(2*(I*c*d - d^2 - d)*tan(b*x + a)^2 - 2*c^2 - 2*I*c*d - (-2*I*c^2 + 4*c*d + 2*I*d^2 - 2*I)*tan(b*x + a) - 2*d - 2)/((c^2 + d^2 + 2*d + 1)*tan(b*x + a)^2 + c^2 + d^2 + 2*d + 1)) + (-2*I*b*x - 2*I*a)*log(-(2*(-I*c*d - d^2 + d)*tan(b*x + a)^2 - 2*c^2 + 2*I*c*d - (2*I*c^2 + 4*c*d - 2*I*d^2 + 2*I)*tan(b*x + a) + 2*d - 2)/((c^2 + d^2 - 2*d + 1)*tan(b*x + a)^2 + c^2 + d^2 - 2*d + 1)) + (2*I*b*x + 2*I*a)*log(-(2*(-I*c*d - d^2 - d)*tan(b*x + a)^2 - 2*c^2 + 2*I*c*d - (2*I*c^2 + 4*c*d - 2*I*d^2 + 2*I)*tan(b*x + a) - 2*d - 2)/((c^2 + d^2 + 2*d + 1)*tan(b*x + a)^2 + c^2 + d^2 + 2*d + 1)) - 2*I*a*log(((I*c*d + d^2 + d)*tan(b*x + a)^2 - c^2 + I*c*d + (I*c^2 + I*d^2 + 2*I*d + I)*tan(b*x + a) - d - 1)/(tan(b*x + a)^2 + 1)) + 2*I*a*log(((I*c*d + d^2 - d)*tan(b*x + a)^2 - c^2 + I*c*d + (I*c^2 + I*d^2 - 2*I*d + I)*tan(b*x + a) + d - 1)/(tan(b*x + a)^2 + 1)) - 2*I*a*log(((I*c*d - d^2 + d)*tan(b*x + a)^2 + c^2 + I*c*d + (I*c^2 + I*d^2 - 2*I*d + I)*tan(b*x + a) - d + 1)/(tan(b*x + a)^2 + 1)) + 2*I*a*log(((I*c*d - d^2 - d)*tan(b*x + a)^2 + c^2 + I*c*d + (I*c^2 + I*d^2 + 2*I*d + I)*tan(b*x + a) + d + 1)/(tan(b*x + a)^2 + 1)) - dilog((2*(I*c*d - d^2 + d)*tan(b*x + a)^2 - 2*c^2 - 2*I*c*d - (-2*I*c^2 + 4*c*d + 2*I*d^2 - 2*I)*tan(b*x + a) + 2*d - 2)/((c^2 + d^2 - 2*d + 1)*tan(b*x + a)^2 + c^2 + d^2 - 2*d + 1) + 1) + dilog((2*(I*c*d - d^2 - d)*tan(b*x + a)^2 - 2*c^2 - 2*I*c*d - (-2*I*c^2 + 4*c*d + 2*I*d^2 - 2*I)*tan(b*x + a) - 2*d - 2)/((c^2 + d^2 + 2*d + 1)*tan(b*x + a)^2 + c^2 + d^2 + 2*d + 1) + 1) - dilog((2*(-I*c*d - d^2 + d)*tan(b*x + a)^2 - 2*c^2 + 2*I*c*d - (2*I*c^2 + 4*c*d - 2*I*d^2 + 2*I)*tan(b*x + a) + 2*d - 2)/((c^2 + d^2 - 2*d + 1)*tan(b*x + a)^2 + c^2 + d^2 - 2*d + 1) + 1) + dilog((2*(-I*c*d - d^2 - d)*tan(b*x + a)^2 - 2*c^2 + 2*I*c*d - (2*I*c^2 + 4*c*d - 2*I*d^2 + 2*I)*tan(b*x + a) - 2*d - 2)/((c^2 + d^2 + 2*d + 1)*tan(b*x + a)^2 + c^2 + d^2 + 2*d + 1) + 1))/b","B",0
161,0,0,0,0.495834," ","integrate(arccot(c+d*tan(b*x+a))/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{arccot}\left(d \tan\left(b x + a\right) + c\right)}{x}, x\right)"," ",0,"integral(arccot(d*tan(b*x + a) + c)/x, x)","F",0
162,1,319,0,0.592287," ","integrate(x^2*arccot(c+(1+I*c)*tan(b*x+a)),x, algorithm=""fricas"")","\frac{b^{4} x^{4} - 2 i \, b^{3} x^{3} \log\left(\frac{{\left(c e^{\left(2 i \, b x + 2 i \, a\right)} + i\right)} e^{\left(-2 i \, b x - 2 i \, a\right)}}{c - i}\right) + 6 \, b^{2} x^{2} {\rm Li}_2\left(\frac{1}{2} \, \sqrt{4 i \, c} e^{\left(i \, b x + i \, a\right)}\right) + 6 \, b^{2} x^{2} {\rm Li}_2\left(-\frac{1}{2} \, \sqrt{4 i \, c} e^{\left(i \, b x + i \, a\right)}\right) - a^{4} - 2 i \, a^{3} \log\left(\frac{2 \, c e^{\left(i \, b x + i \, a\right)} + i \, \sqrt{4 i \, c}}{2 \, c}\right) - 2 i \, a^{3} \log\left(\frac{2 \, c e^{\left(i \, b x + i \, a\right)} - i \, \sqrt{4 i \, c}}{2 \, c}\right) + 12 i \, b x {\rm polylog}\left(3, \frac{1}{2} \, \sqrt{4 i \, c} e^{\left(i \, b x + i \, a\right)}\right) + 12 i \, b x {\rm polylog}\left(3, -\frac{1}{2} \, \sqrt{4 i \, c} e^{\left(i \, b x + i \, a\right)}\right) + {\left(2 i \, b^{3} x^{3} + 2 i \, a^{3}\right)} \log\left(\frac{1}{2} \, \sqrt{4 i \, c} e^{\left(i \, b x + i \, a\right)} + 1\right) + {\left(2 i \, b^{3} x^{3} + 2 i \, a^{3}\right)} \log\left(-\frac{1}{2} \, \sqrt{4 i \, c} e^{\left(i \, b x + i \, a\right)} + 1\right) - 12 \, {\rm polylog}\left(4, \frac{1}{2} \, \sqrt{4 i \, c} e^{\left(i \, b x + i \, a\right)}\right) - 12 \, {\rm polylog}\left(4, -\frac{1}{2} \, \sqrt{4 i \, c} e^{\left(i \, b x + i \, a\right)}\right)}{12 \, b^{3}}"," ",0,"1/12*(b^4*x^4 - 2*I*b^3*x^3*log((c*e^(2*I*b*x + 2*I*a) + I)*e^(-2*I*b*x - 2*I*a)/(c - I)) + 6*b^2*x^2*dilog(1/2*sqrt(4*I*c)*e^(I*b*x + I*a)) + 6*b^2*x^2*dilog(-1/2*sqrt(4*I*c)*e^(I*b*x + I*a)) - a^4 - 2*I*a^3*log(1/2*(2*c*e^(I*b*x + I*a) + I*sqrt(4*I*c))/c) - 2*I*a^3*log(1/2*(2*c*e^(I*b*x + I*a) - I*sqrt(4*I*c))/c) + 12*I*b*x*polylog(3, 1/2*sqrt(4*I*c)*e^(I*b*x + I*a)) + 12*I*b*x*polylog(3, -1/2*sqrt(4*I*c)*e^(I*b*x + I*a)) + (2*I*b^3*x^3 + 2*I*a^3)*log(1/2*sqrt(4*I*c)*e^(I*b*x + I*a) + 1) + (2*I*b^3*x^3 + 2*I*a^3)*log(-1/2*sqrt(4*I*c)*e^(I*b*x + I*a) + 1) - 12*polylog(4, 1/2*sqrt(4*I*c)*e^(I*b*x + I*a)) - 12*polylog(4, -1/2*sqrt(4*I*c)*e^(I*b*x + I*a)))/b^3","C",0
163,1,268,0,0.721478," ","integrate(x*arccot(c+(1+I*c)*tan(b*x+a)),x, algorithm=""fricas"")","\frac{2 \, b^{3} x^{3} - 3 i \, b^{2} x^{2} \log\left(\frac{{\left(c e^{\left(2 i \, b x + 2 i \, a\right)} + i\right)} e^{\left(-2 i \, b x - 2 i \, a\right)}}{c - i}\right) + 2 \, a^{3} + 6 \, b x {\rm Li}_2\left(\frac{1}{2} \, \sqrt{4 i \, c} e^{\left(i \, b x + i \, a\right)}\right) + 6 \, b x {\rm Li}_2\left(-\frac{1}{2} \, \sqrt{4 i \, c} e^{\left(i \, b x + i \, a\right)}\right) + 3 i \, a^{2} \log\left(\frac{2 \, c e^{\left(i \, b x + i \, a\right)} + i \, \sqrt{4 i \, c}}{2 \, c}\right) + 3 i \, a^{2} \log\left(\frac{2 \, c e^{\left(i \, b x + i \, a\right)} - i \, \sqrt{4 i \, c}}{2 \, c}\right) + {\left(3 i \, b^{2} x^{2} - 3 i \, a^{2}\right)} \log\left(\frac{1}{2} \, \sqrt{4 i \, c} e^{\left(i \, b x + i \, a\right)} + 1\right) + {\left(3 i \, b^{2} x^{2} - 3 i \, a^{2}\right)} \log\left(-\frac{1}{2} \, \sqrt{4 i \, c} e^{\left(i \, b x + i \, a\right)} + 1\right) + 6 i \, {\rm polylog}\left(3, \frac{1}{2} \, \sqrt{4 i \, c} e^{\left(i \, b x + i \, a\right)}\right) + 6 i \, {\rm polylog}\left(3, -\frac{1}{2} \, \sqrt{4 i \, c} e^{\left(i \, b x + i \, a\right)}\right)}{12 \, b^{2}}"," ",0,"1/12*(2*b^3*x^3 - 3*I*b^2*x^2*log((c*e^(2*I*b*x + 2*I*a) + I)*e^(-2*I*b*x - 2*I*a)/(c - I)) + 2*a^3 + 6*b*x*dilog(1/2*sqrt(4*I*c)*e^(I*b*x + I*a)) + 6*b*x*dilog(-1/2*sqrt(4*I*c)*e^(I*b*x + I*a)) + 3*I*a^2*log(1/2*(2*c*e^(I*b*x + I*a) + I*sqrt(4*I*c))/c) + 3*I*a^2*log(1/2*(2*c*e^(I*b*x + I*a) - I*sqrt(4*I*c))/c) + (3*I*b^2*x^2 - 3*I*a^2)*log(1/2*sqrt(4*I*c)*e^(I*b*x + I*a) + 1) + (3*I*b^2*x^2 - 3*I*a^2)*log(-1/2*sqrt(4*I*c)*e^(I*b*x + I*a) + 1) + 6*I*polylog(3, 1/2*sqrt(4*I*c)*e^(I*b*x + I*a)) + 6*I*polylog(3, -1/2*sqrt(4*I*c)*e^(I*b*x + I*a)))/b^2","C",0
164,1,199,0,0.681762," ","integrate(arccot(c+(1+I*c)*tan(b*x+a)),x, algorithm=""fricas"")","\frac{b^{2} x^{2} - i \, b x \log\left(\frac{{\left(c e^{\left(2 i \, b x + 2 i \, a\right)} + i\right)} e^{\left(-2 i \, b x - 2 i \, a\right)}}{c - i}\right) - a^{2} + {\left(i \, b x + i \, a\right)} \log\left(\frac{1}{2} \, \sqrt{4 i \, c} e^{\left(i \, b x + i \, a\right)} + 1\right) + {\left(i \, b x + i \, a\right)} \log\left(-\frac{1}{2} \, \sqrt{4 i \, c} e^{\left(i \, b x + i \, a\right)} + 1\right) - i \, a \log\left(\frac{2 \, c e^{\left(i \, b x + i \, a\right)} + i \, \sqrt{4 i \, c}}{2 \, c}\right) - i \, a \log\left(\frac{2 \, c e^{\left(i \, b x + i \, a\right)} - i \, \sqrt{4 i \, c}}{2 \, c}\right) + {\rm Li}_2\left(\frac{1}{2} \, \sqrt{4 i \, c} e^{\left(i \, b x + i \, a\right)}\right) + {\rm Li}_2\left(-\frac{1}{2} \, \sqrt{4 i \, c} e^{\left(i \, b x + i \, a\right)}\right)}{2 \, b}"," ",0,"1/2*(b^2*x^2 - I*b*x*log((c*e^(2*I*b*x + 2*I*a) + I)*e^(-2*I*b*x - 2*I*a)/(c - I)) - a^2 + (I*b*x + I*a)*log(1/2*sqrt(4*I*c)*e^(I*b*x + I*a) + 1) + (I*b*x + I*a)*log(-1/2*sqrt(4*I*c)*e^(I*b*x + I*a) + 1) - I*a*log(1/2*(2*c*e^(I*b*x + I*a) + I*sqrt(4*I*c))/c) - I*a*log(1/2*(2*c*e^(I*b*x + I*a) - I*sqrt(4*I*c))/c) + dilog(1/2*sqrt(4*I*c)*e^(I*b*x + I*a)) + dilog(-1/2*sqrt(4*I*c)*e^(I*b*x + I*a)))/b","B",0
165,0,0,0,0.771880," ","integrate(arccot(c+(1+I*c)*tan(b*x+a))/x,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{i \, \log\left(\frac{{\left(c e^{\left(2 i \, b x + 2 i \, a\right)} + i\right)} e^{\left(-2 i \, b x - 2 i \, a\right)}}{c - i}\right)}{2 \, x}, x\right)"," ",0,"integral(-1/2*I*log((c*e^(2*I*b*x + 2*I*a) + I)*e^(-2*I*b*x - 2*I*a)/(c - I))/x, x)","F",0
166,1,321,0,0.724189," ","integrate(x^2*arccot(c-(1-I*c)*tan(b*x+a)),x, algorithm=""fricas"")","-\frac{b^{4} x^{4} + 2 i \, b^{3} x^{3} \log\left(\frac{{\left(c + i\right)} e^{\left(2 i \, b x + 2 i \, a\right)}}{c e^{\left(2 i \, b x + 2 i \, a\right)} - i}\right) + 6 \, b^{2} x^{2} {\rm Li}_2\left(\frac{1}{2} \, \sqrt{-4 i \, c} e^{\left(i \, b x + i \, a\right)}\right) + 6 \, b^{2} x^{2} {\rm Li}_2\left(-\frac{1}{2} \, \sqrt{-4 i \, c} e^{\left(i \, b x + i \, a\right)}\right) - a^{4} - 2 i \, a^{3} \log\left(\frac{2 \, c e^{\left(i \, b x + i \, a\right)} + i \, \sqrt{-4 i \, c}}{2 \, c}\right) - 2 i \, a^{3} \log\left(\frac{2 \, c e^{\left(i \, b x + i \, a\right)} - i \, \sqrt{-4 i \, c}}{2 \, c}\right) + 12 i \, b x {\rm polylog}\left(3, \frac{1}{2} \, \sqrt{-4 i \, c} e^{\left(i \, b x + i \, a\right)}\right) + 12 i \, b x {\rm polylog}\left(3, -\frac{1}{2} \, \sqrt{-4 i \, c} e^{\left(i \, b x + i \, a\right)}\right) - {\left(-2 i \, b^{3} x^{3} - 2 i \, a^{3}\right)} \log\left(\frac{1}{2} \, \sqrt{-4 i \, c} e^{\left(i \, b x + i \, a\right)} + 1\right) - {\left(-2 i \, b^{3} x^{3} - 2 i \, a^{3}\right)} \log\left(-\frac{1}{2} \, \sqrt{-4 i \, c} e^{\left(i \, b x + i \, a\right)} + 1\right) - 12 \, {\rm polylog}\left(4, \frac{1}{2} \, \sqrt{-4 i \, c} e^{\left(i \, b x + i \, a\right)}\right) - 12 \, {\rm polylog}\left(4, -\frac{1}{2} \, \sqrt{-4 i \, c} e^{\left(i \, b x + i \, a\right)}\right)}{12 \, b^{3}}"," ",0,"-1/12*(b^4*x^4 + 2*I*b^3*x^3*log((c + I)*e^(2*I*b*x + 2*I*a)/(c*e^(2*I*b*x + 2*I*a) - I)) + 6*b^2*x^2*dilog(1/2*sqrt(-4*I*c)*e^(I*b*x + I*a)) + 6*b^2*x^2*dilog(-1/2*sqrt(-4*I*c)*e^(I*b*x + I*a)) - a^4 - 2*I*a^3*log(1/2*(2*c*e^(I*b*x + I*a) + I*sqrt(-4*I*c))/c) - 2*I*a^3*log(1/2*(2*c*e^(I*b*x + I*a) - I*sqrt(-4*I*c))/c) + 12*I*b*x*polylog(3, 1/2*sqrt(-4*I*c)*e^(I*b*x + I*a)) + 12*I*b*x*polylog(3, -1/2*sqrt(-4*I*c)*e^(I*b*x + I*a)) - (-2*I*b^3*x^3 - 2*I*a^3)*log(1/2*sqrt(-4*I*c)*e^(I*b*x + I*a) + 1) - (-2*I*b^3*x^3 - 2*I*a^3)*log(-1/2*sqrt(-4*I*c)*e^(I*b*x + I*a) + 1) - 12*polylog(4, 1/2*sqrt(-4*I*c)*e^(I*b*x + I*a)) - 12*polylog(4, -1/2*sqrt(-4*I*c)*e^(I*b*x + I*a)))/b^3","C",0
167,1,270,0,0.618969," ","integrate(x*arccot(c-(1-I*c)*tan(b*x+a)),x, algorithm=""fricas"")","-\frac{2 \, b^{3} x^{3} + 3 i \, b^{2} x^{2} \log\left(\frac{{\left(c + i\right)} e^{\left(2 i \, b x + 2 i \, a\right)}}{c e^{\left(2 i \, b x + 2 i \, a\right)} - i}\right) + 2 \, a^{3} + 6 \, b x {\rm Li}_2\left(\frac{1}{2} \, \sqrt{-4 i \, c} e^{\left(i \, b x + i \, a\right)}\right) + 6 \, b x {\rm Li}_2\left(-\frac{1}{2} \, \sqrt{-4 i \, c} e^{\left(i \, b x + i \, a\right)}\right) + 3 i \, a^{2} \log\left(\frac{2 \, c e^{\left(i \, b x + i \, a\right)} + i \, \sqrt{-4 i \, c}}{2 \, c}\right) + 3 i \, a^{2} \log\left(\frac{2 \, c e^{\left(i \, b x + i \, a\right)} - i \, \sqrt{-4 i \, c}}{2 \, c}\right) - {\left(-3 i \, b^{2} x^{2} + 3 i \, a^{2}\right)} \log\left(\frac{1}{2} \, \sqrt{-4 i \, c} e^{\left(i \, b x + i \, a\right)} + 1\right) - {\left(-3 i \, b^{2} x^{2} + 3 i \, a^{2}\right)} \log\left(-\frac{1}{2} \, \sqrt{-4 i \, c} e^{\left(i \, b x + i \, a\right)} + 1\right) + 6 i \, {\rm polylog}\left(3, \frac{1}{2} \, \sqrt{-4 i \, c} e^{\left(i \, b x + i \, a\right)}\right) + 6 i \, {\rm polylog}\left(3, -\frac{1}{2} \, \sqrt{-4 i \, c} e^{\left(i \, b x + i \, a\right)}\right)}{12 \, b^{2}}"," ",0,"-1/12*(2*b^3*x^3 + 3*I*b^2*x^2*log((c + I)*e^(2*I*b*x + 2*I*a)/(c*e^(2*I*b*x + 2*I*a) - I)) + 2*a^3 + 6*b*x*dilog(1/2*sqrt(-4*I*c)*e^(I*b*x + I*a)) + 6*b*x*dilog(-1/2*sqrt(-4*I*c)*e^(I*b*x + I*a)) + 3*I*a^2*log(1/2*(2*c*e^(I*b*x + I*a) + I*sqrt(-4*I*c))/c) + 3*I*a^2*log(1/2*(2*c*e^(I*b*x + I*a) - I*sqrt(-4*I*c))/c) - (-3*I*b^2*x^2 + 3*I*a^2)*log(1/2*sqrt(-4*I*c)*e^(I*b*x + I*a) + 1) - (-3*I*b^2*x^2 + 3*I*a^2)*log(-1/2*sqrt(-4*I*c)*e^(I*b*x + I*a) + 1) + 6*I*polylog(3, 1/2*sqrt(-4*I*c)*e^(I*b*x + I*a)) + 6*I*polylog(3, -1/2*sqrt(-4*I*c)*e^(I*b*x + I*a)))/b^2","C",0
168,1,201,0,0.577669," ","integrate(arccot(c-(1-I*c)*tan(b*x+a)),x, algorithm=""fricas"")","-\frac{b^{2} x^{2} + i \, b x \log\left(\frac{{\left(c + i\right)} e^{\left(2 i \, b x + 2 i \, a\right)}}{c e^{\left(2 i \, b x + 2 i \, a\right)} - i}\right) - a^{2} - {\left(-i \, b x - i \, a\right)} \log\left(\frac{1}{2} \, \sqrt{-4 i \, c} e^{\left(i \, b x + i \, a\right)} + 1\right) - {\left(-i \, b x - i \, a\right)} \log\left(-\frac{1}{2} \, \sqrt{-4 i \, c} e^{\left(i \, b x + i \, a\right)} + 1\right) - i \, a \log\left(\frac{2 \, c e^{\left(i \, b x + i \, a\right)} + i \, \sqrt{-4 i \, c}}{2 \, c}\right) - i \, a \log\left(\frac{2 \, c e^{\left(i \, b x + i \, a\right)} - i \, \sqrt{-4 i \, c}}{2 \, c}\right) + {\rm Li}_2\left(\frac{1}{2} \, \sqrt{-4 i \, c} e^{\left(i \, b x + i \, a\right)}\right) + {\rm Li}_2\left(-\frac{1}{2} \, \sqrt{-4 i \, c} e^{\left(i \, b x + i \, a\right)}\right)}{2 \, b}"," ",0,"-1/2*(b^2*x^2 + I*b*x*log((c + I)*e^(2*I*b*x + 2*I*a)/(c*e^(2*I*b*x + 2*I*a) - I)) - a^2 - (-I*b*x - I*a)*log(1/2*sqrt(-4*I*c)*e^(I*b*x + I*a) + 1) - (-I*b*x - I*a)*log(-1/2*sqrt(-4*I*c)*e^(I*b*x + I*a) + 1) - I*a*log(1/2*(2*c*e^(I*b*x + I*a) + I*sqrt(-4*I*c))/c) - I*a*log(1/2*(2*c*e^(I*b*x + I*a) - I*sqrt(-4*I*c))/c) + dilog(1/2*sqrt(-4*I*c)*e^(I*b*x + I*a)) + dilog(-1/2*sqrt(-4*I*c)*e^(I*b*x + I*a)))/b","B",0
169,0,0,0,0.580851," ","integrate(arccot(c-(1-I*c)*tan(b*x+a))/x,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{i \, \log\left(\frac{{\left(c + i\right)} e^{\left(2 i \, b x + 2 i \, a\right)}}{c e^{\left(2 i \, b x + 2 i \, a\right)} - i}\right)}{2 \, x}, x\right)"," ",0,"integral(-1/2*I*log((c + I)*e^(2*I*b*x + 2*I*a)/(c*e^(2*I*b*x + 2*I*a) - I))/x, x)","F",0
170,1,10,0,0.631036," ","integrate(arccot(cot(b*x+a)),x, algorithm=""fricas"")","\frac{1}{2} x^{2} b + x a"," ",0,"1/2*x^2*b + x*a","A",0
171,1,1585,0,0.887730," ","integrate(x^2*arccot(c+d*cot(b*x+a)),x, algorithm=""fricas"")","\frac{16 \, b^{3} x^{3} \operatorname{arccot}\left(d \cot\left(b x + a\right) + c\right) - 6 \, b^{2} x^{2} {\rm Li}_2\left(-\frac{c^{2} + d^{2} - {\left(c^{2} + 2 i \, c d - d^{2} + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(-i \, c^{2} + 2 \, c d + i \, d^{2} - i\right)} \sin\left(2 \, b x + 2 \, a\right) + 2 \, d + 1}{c^{2} + d^{2} + 2 \, d + 1} + 1\right) - 6 \, b^{2} x^{2} {\rm Li}_2\left(-\frac{c^{2} + d^{2} - {\left(c^{2} - 2 i \, c d - d^{2} + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(i \, c^{2} + 2 \, c d - i \, d^{2} + i\right)} \sin\left(2 \, b x + 2 \, a\right) + 2 \, d + 1}{c^{2} + d^{2} + 2 \, d + 1} + 1\right) + 6 \, b^{2} x^{2} {\rm Li}_2\left(-\frac{c^{2} + d^{2} - {\left(c^{2} + 2 i \, c d - d^{2} + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(-i \, c^{2} + 2 \, c d + i \, d^{2} - i\right)} \sin\left(2 \, b x + 2 \, a\right) - 2 \, d + 1}{c^{2} + d^{2} - 2 \, d + 1} + 1\right) + 6 \, b^{2} x^{2} {\rm Li}_2\left(-\frac{c^{2} + d^{2} - {\left(c^{2} - 2 i \, c d - d^{2} + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(i \, c^{2} + 2 \, c d - i \, d^{2} + i\right)} \sin\left(2 \, b x + 2 \, a\right) - 2 \, d + 1}{c^{2} + d^{2} - 2 \, d + 1} + 1\right) + 4 i \, a^{3} \log\left(\frac{1}{2} \, c^{2} + i \, c d - \frac{1}{2} \, d^{2} - \frac{1}{2} \, {\left(c^{2} + d^{2} + 2 \, d + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + \frac{1}{2} \, {\left(i \, c^{2} + i \, d^{2} + 2 i \, d + i\right)} \sin\left(2 \, b x + 2 \, a\right) + \frac{1}{2}\right) - 4 i \, a^{3} \log\left(\frac{1}{2} \, c^{2} + i \, c d - \frac{1}{2} \, d^{2} - \frac{1}{2} \, {\left(c^{2} + d^{2} - 2 \, d + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + \frac{1}{2} \, {\left(i \, c^{2} + i \, d^{2} - 2 i \, d + i\right)} \sin\left(2 \, b x + 2 \, a\right) + \frac{1}{2}\right) - 4 i \, a^{3} \log\left(-\frac{1}{2} \, c^{2} + i \, c d + \frac{1}{2} \, d^{2} + \frac{1}{2} \, {\left(c^{2} + d^{2} + 2 \, d + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + \frac{1}{2} \, {\left(i \, c^{2} + i \, d^{2} + 2 i \, d + i\right)} \sin\left(2 \, b x + 2 \, a\right) - \frac{1}{2}\right) + 4 i \, a^{3} \log\left(-\frac{1}{2} \, c^{2} + i \, c d + \frac{1}{2} \, d^{2} + \frac{1}{2} \, {\left(c^{2} + d^{2} - 2 \, d + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + \frac{1}{2} \, {\left(i \, c^{2} + i \, d^{2} - 2 i \, d + i\right)} \sin\left(2 \, b x + 2 \, a\right) - \frac{1}{2}\right) - 6 i \, b x {\rm polylog}\left(3, \frac{{\left(c^{2} + 2 i \, c d - d^{2} + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(i \, c^{2} - 2 \, c d - i \, d^{2} + i\right)} \sin\left(2 \, b x + 2 \, a\right)}{c^{2} + d^{2} + 2 \, d + 1}\right) + 6 i \, b x {\rm polylog}\left(3, \frac{{\left(c^{2} + 2 i \, c d - d^{2} + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(i \, c^{2} - 2 \, c d - i \, d^{2} + i\right)} \sin\left(2 \, b x + 2 \, a\right)}{c^{2} + d^{2} - 2 \, d + 1}\right) + 6 i \, b x {\rm polylog}\left(3, \frac{{\left(c^{2} - 2 i \, c d - d^{2} + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(-i \, c^{2} - 2 \, c d + i \, d^{2} - i\right)} \sin\left(2 \, b x + 2 \, a\right)}{c^{2} + d^{2} + 2 \, d + 1}\right) - 6 i \, b x {\rm polylog}\left(3, \frac{{\left(c^{2} - 2 i \, c d - d^{2} + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(-i \, c^{2} - 2 \, c d + i \, d^{2} - i\right)} \sin\left(2 \, b x + 2 \, a\right)}{c^{2} + d^{2} - 2 \, d + 1}\right) + {\left(-4 i \, b^{3} x^{3} - 4 i \, a^{3}\right)} \log\left(\frac{c^{2} + d^{2} - {\left(c^{2} + 2 i \, c d - d^{2} + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(-i \, c^{2} + 2 \, c d + i \, d^{2} - i\right)} \sin\left(2 \, b x + 2 \, a\right) + 2 \, d + 1}{c^{2} + d^{2} + 2 \, d + 1}\right) + {\left(4 i \, b^{3} x^{3} + 4 i \, a^{3}\right)} \log\left(\frac{c^{2} + d^{2} - {\left(c^{2} - 2 i \, c d - d^{2} + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(i \, c^{2} + 2 \, c d - i \, d^{2} + i\right)} \sin\left(2 \, b x + 2 \, a\right) + 2 \, d + 1}{c^{2} + d^{2} + 2 \, d + 1}\right) + {\left(4 i \, b^{3} x^{3} + 4 i \, a^{3}\right)} \log\left(\frac{c^{2} + d^{2} - {\left(c^{2} + 2 i \, c d - d^{2} + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(-i \, c^{2} + 2 \, c d + i \, d^{2} - i\right)} \sin\left(2 \, b x + 2 \, a\right) - 2 \, d + 1}{c^{2} + d^{2} - 2 \, d + 1}\right) + {\left(-4 i \, b^{3} x^{3} - 4 i \, a^{3}\right)} \log\left(\frac{c^{2} + d^{2} - {\left(c^{2} - 2 i \, c d - d^{2} + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(i \, c^{2} + 2 \, c d - i \, d^{2} + i\right)} \sin\left(2 \, b x + 2 \, a\right) - 2 \, d + 1}{c^{2} + d^{2} - 2 \, d + 1}\right) + 3 \, {\rm polylog}\left(4, \frac{{\left(c^{2} + 2 i \, c d - d^{2} + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(i \, c^{2} - 2 \, c d - i \, d^{2} + i\right)} \sin\left(2 \, b x + 2 \, a\right)}{c^{2} + d^{2} + 2 \, d + 1}\right) - 3 \, {\rm polylog}\left(4, \frac{{\left(c^{2} + 2 i \, c d - d^{2} + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(i \, c^{2} - 2 \, c d - i \, d^{2} + i\right)} \sin\left(2 \, b x + 2 \, a\right)}{c^{2} + d^{2} - 2 \, d + 1}\right) + 3 \, {\rm polylog}\left(4, \frac{{\left(c^{2} - 2 i \, c d - d^{2} + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(-i \, c^{2} - 2 \, c d + i \, d^{2} - i\right)} \sin\left(2 \, b x + 2 \, a\right)}{c^{2} + d^{2} + 2 \, d + 1}\right) - 3 \, {\rm polylog}\left(4, \frac{{\left(c^{2} - 2 i \, c d - d^{2} + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(-i \, c^{2} - 2 \, c d + i \, d^{2} - i\right)} \sin\left(2 \, b x + 2 \, a\right)}{c^{2} + d^{2} - 2 \, d + 1}\right)}{48 \, b^{3}}"," ",0,"1/48*(16*b^3*x^3*arccot(d*cot(b*x + a) + c) - 6*b^2*x^2*dilog(-(c^2 + d^2 - (c^2 + 2*I*c*d - d^2 + 1)*cos(2*b*x + 2*a) + (-I*c^2 + 2*c*d + I*d^2 - I)*sin(2*b*x + 2*a) + 2*d + 1)/(c^2 + d^2 + 2*d + 1) + 1) - 6*b^2*x^2*dilog(-(c^2 + d^2 - (c^2 - 2*I*c*d - d^2 + 1)*cos(2*b*x + 2*a) + (I*c^2 + 2*c*d - I*d^2 + I)*sin(2*b*x + 2*a) + 2*d + 1)/(c^2 + d^2 + 2*d + 1) + 1) + 6*b^2*x^2*dilog(-(c^2 + d^2 - (c^2 + 2*I*c*d - d^2 + 1)*cos(2*b*x + 2*a) + (-I*c^2 + 2*c*d + I*d^2 - I)*sin(2*b*x + 2*a) - 2*d + 1)/(c^2 + d^2 - 2*d + 1) + 1) + 6*b^2*x^2*dilog(-(c^2 + d^2 - (c^2 - 2*I*c*d - d^2 + 1)*cos(2*b*x + 2*a) + (I*c^2 + 2*c*d - I*d^2 + I)*sin(2*b*x + 2*a) - 2*d + 1)/(c^2 + d^2 - 2*d + 1) + 1) + 4*I*a^3*log(1/2*c^2 + I*c*d - 1/2*d^2 - 1/2*(c^2 + d^2 + 2*d + 1)*cos(2*b*x + 2*a) + 1/2*(I*c^2 + I*d^2 + 2*I*d + I)*sin(2*b*x + 2*a) + 1/2) - 4*I*a^3*log(1/2*c^2 + I*c*d - 1/2*d^2 - 1/2*(c^2 + d^2 - 2*d + 1)*cos(2*b*x + 2*a) + 1/2*(I*c^2 + I*d^2 - 2*I*d + I)*sin(2*b*x + 2*a) + 1/2) - 4*I*a^3*log(-1/2*c^2 + I*c*d + 1/2*d^2 + 1/2*(c^2 + d^2 + 2*d + 1)*cos(2*b*x + 2*a) + 1/2*(I*c^2 + I*d^2 + 2*I*d + I)*sin(2*b*x + 2*a) - 1/2) + 4*I*a^3*log(-1/2*c^2 + I*c*d + 1/2*d^2 + 1/2*(c^2 + d^2 - 2*d + 1)*cos(2*b*x + 2*a) + 1/2*(I*c^2 + I*d^2 - 2*I*d + I)*sin(2*b*x + 2*a) - 1/2) - 6*I*b*x*polylog(3, ((c^2 + 2*I*c*d - d^2 + 1)*cos(2*b*x + 2*a) + (I*c^2 - 2*c*d - I*d^2 + I)*sin(2*b*x + 2*a))/(c^2 + d^2 + 2*d + 1)) + 6*I*b*x*polylog(3, ((c^2 + 2*I*c*d - d^2 + 1)*cos(2*b*x + 2*a) + (I*c^2 - 2*c*d - I*d^2 + I)*sin(2*b*x + 2*a))/(c^2 + d^2 - 2*d + 1)) + 6*I*b*x*polylog(3, ((c^2 - 2*I*c*d - d^2 + 1)*cos(2*b*x + 2*a) + (-I*c^2 - 2*c*d + I*d^2 - I)*sin(2*b*x + 2*a))/(c^2 + d^2 + 2*d + 1)) - 6*I*b*x*polylog(3, ((c^2 - 2*I*c*d - d^2 + 1)*cos(2*b*x + 2*a) + (-I*c^2 - 2*c*d + I*d^2 - I)*sin(2*b*x + 2*a))/(c^2 + d^2 - 2*d + 1)) + (-4*I*b^3*x^3 - 4*I*a^3)*log((c^2 + d^2 - (c^2 + 2*I*c*d - d^2 + 1)*cos(2*b*x + 2*a) + (-I*c^2 + 2*c*d + I*d^2 - I)*sin(2*b*x + 2*a) + 2*d + 1)/(c^2 + d^2 + 2*d + 1)) + (4*I*b^3*x^3 + 4*I*a^3)*log((c^2 + d^2 - (c^2 - 2*I*c*d - d^2 + 1)*cos(2*b*x + 2*a) + (I*c^2 + 2*c*d - I*d^2 + I)*sin(2*b*x + 2*a) + 2*d + 1)/(c^2 + d^2 + 2*d + 1)) + (4*I*b^3*x^3 + 4*I*a^3)*log((c^2 + d^2 - (c^2 + 2*I*c*d - d^2 + 1)*cos(2*b*x + 2*a) + (-I*c^2 + 2*c*d + I*d^2 - I)*sin(2*b*x + 2*a) - 2*d + 1)/(c^2 + d^2 - 2*d + 1)) + (-4*I*b^3*x^3 - 4*I*a^3)*log((c^2 + d^2 - (c^2 - 2*I*c*d - d^2 + 1)*cos(2*b*x + 2*a) + (I*c^2 + 2*c*d - I*d^2 + I)*sin(2*b*x + 2*a) - 2*d + 1)/(c^2 + d^2 - 2*d + 1)) + 3*polylog(4, ((c^2 + 2*I*c*d - d^2 + 1)*cos(2*b*x + 2*a) + (I*c^2 - 2*c*d - I*d^2 + I)*sin(2*b*x + 2*a))/(c^2 + d^2 + 2*d + 1)) - 3*polylog(4, ((c^2 + 2*I*c*d - d^2 + 1)*cos(2*b*x + 2*a) + (I*c^2 - 2*c*d - I*d^2 + I)*sin(2*b*x + 2*a))/(c^2 + d^2 - 2*d + 1)) + 3*polylog(4, ((c^2 - 2*I*c*d - d^2 + 1)*cos(2*b*x + 2*a) + (-I*c^2 - 2*c*d + I*d^2 - I)*sin(2*b*x + 2*a))/(c^2 + d^2 + 2*d + 1)) - 3*polylog(4, ((c^2 - 2*I*c*d - d^2 + 1)*cos(2*b*x + 2*a) + (-I*c^2 - 2*c*d + I*d^2 - I)*sin(2*b*x + 2*a))/(c^2 + d^2 - 2*d + 1)))/b^3","C",0
172,1,1285,0,1.076206," ","integrate(x*arccot(c+d*cot(b*x+a)),x, algorithm=""fricas"")","\frac{8 \, b^{2} x^{2} \operatorname{arccot}\left(d \cot\left(b x + a\right) + c\right) - 2 \, b x {\rm Li}_2\left(-\frac{c^{2} + d^{2} - {\left(c^{2} + 2 i \, c d - d^{2} + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(-i \, c^{2} + 2 \, c d + i \, d^{2} - i\right)} \sin\left(2 \, b x + 2 \, a\right) + 2 \, d + 1}{c^{2} + d^{2} + 2 \, d + 1} + 1\right) - 2 \, b x {\rm Li}_2\left(-\frac{c^{2} + d^{2} - {\left(c^{2} - 2 i \, c d - d^{2} + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(i \, c^{2} + 2 \, c d - i \, d^{2} + i\right)} \sin\left(2 \, b x + 2 \, a\right) + 2 \, d + 1}{c^{2} + d^{2} + 2 \, d + 1} + 1\right) + 2 \, b x {\rm Li}_2\left(-\frac{c^{2} + d^{2} - {\left(c^{2} + 2 i \, c d - d^{2} + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(-i \, c^{2} + 2 \, c d + i \, d^{2} - i\right)} \sin\left(2 \, b x + 2 \, a\right) - 2 \, d + 1}{c^{2} + d^{2} - 2 \, d + 1} + 1\right) + 2 \, b x {\rm Li}_2\left(-\frac{c^{2} + d^{2} - {\left(c^{2} - 2 i \, c d - d^{2} + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(i \, c^{2} + 2 \, c d - i \, d^{2} + i\right)} \sin\left(2 \, b x + 2 \, a\right) - 2 \, d + 1}{c^{2} + d^{2} - 2 \, d + 1} + 1\right) - 2 i \, a^{2} \log\left(\frac{1}{2} \, c^{2} + i \, c d - \frac{1}{2} \, d^{2} - \frac{1}{2} \, {\left(c^{2} + d^{2} + 2 \, d + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + \frac{1}{2} \, {\left(i \, c^{2} + i \, d^{2} + 2 i \, d + i\right)} \sin\left(2 \, b x + 2 \, a\right) + \frac{1}{2}\right) + 2 i \, a^{2} \log\left(\frac{1}{2} \, c^{2} + i \, c d - \frac{1}{2} \, d^{2} - \frac{1}{2} \, {\left(c^{2} + d^{2} - 2 \, d + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + \frac{1}{2} \, {\left(i \, c^{2} + i \, d^{2} - 2 i \, d + i\right)} \sin\left(2 \, b x + 2 \, a\right) + \frac{1}{2}\right) + 2 i \, a^{2} \log\left(-\frac{1}{2} \, c^{2} + i \, c d + \frac{1}{2} \, d^{2} + \frac{1}{2} \, {\left(c^{2} + d^{2} + 2 \, d + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + \frac{1}{2} \, {\left(i \, c^{2} + i \, d^{2} + 2 i \, d + i\right)} \sin\left(2 \, b x + 2 \, a\right) - \frac{1}{2}\right) - 2 i \, a^{2} \log\left(-\frac{1}{2} \, c^{2} + i \, c d + \frac{1}{2} \, d^{2} + \frac{1}{2} \, {\left(c^{2} + d^{2} - 2 \, d + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + \frac{1}{2} \, {\left(i \, c^{2} + i \, d^{2} - 2 i \, d + i\right)} \sin\left(2 \, b x + 2 \, a\right) - \frac{1}{2}\right) + {\left(-2 i \, b^{2} x^{2} + 2 i \, a^{2}\right)} \log\left(\frac{c^{2} + d^{2} - {\left(c^{2} + 2 i \, c d - d^{2} + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(-i \, c^{2} + 2 \, c d + i \, d^{2} - i\right)} \sin\left(2 \, b x + 2 \, a\right) + 2 \, d + 1}{c^{2} + d^{2} + 2 \, d + 1}\right) + {\left(2 i \, b^{2} x^{2} - 2 i \, a^{2}\right)} \log\left(\frac{c^{2} + d^{2} - {\left(c^{2} - 2 i \, c d - d^{2} + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(i \, c^{2} + 2 \, c d - i \, d^{2} + i\right)} \sin\left(2 \, b x + 2 \, a\right) + 2 \, d + 1}{c^{2} + d^{2} + 2 \, d + 1}\right) + {\left(2 i \, b^{2} x^{2} - 2 i \, a^{2}\right)} \log\left(\frac{c^{2} + d^{2} - {\left(c^{2} + 2 i \, c d - d^{2} + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(-i \, c^{2} + 2 \, c d + i \, d^{2} - i\right)} \sin\left(2 \, b x + 2 \, a\right) - 2 \, d + 1}{c^{2} + d^{2} - 2 \, d + 1}\right) + {\left(-2 i \, b^{2} x^{2} + 2 i \, a^{2}\right)} \log\left(\frac{c^{2} + d^{2} - {\left(c^{2} - 2 i \, c d - d^{2} + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(i \, c^{2} + 2 \, c d - i \, d^{2} + i\right)} \sin\left(2 \, b x + 2 \, a\right) - 2 \, d + 1}{c^{2} + d^{2} - 2 \, d + 1}\right) - i \, {\rm polylog}\left(3, \frac{{\left(c^{2} + 2 i \, c d - d^{2} + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(i \, c^{2} - 2 \, c d - i \, d^{2} + i\right)} \sin\left(2 \, b x + 2 \, a\right)}{c^{2} + d^{2} + 2 \, d + 1}\right) + i \, {\rm polylog}\left(3, \frac{{\left(c^{2} + 2 i \, c d - d^{2} + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(i \, c^{2} - 2 \, c d - i \, d^{2} + i\right)} \sin\left(2 \, b x + 2 \, a\right)}{c^{2} + d^{2} - 2 \, d + 1}\right) + i \, {\rm polylog}\left(3, \frac{{\left(c^{2} - 2 i \, c d - d^{2} + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(-i \, c^{2} - 2 \, c d + i \, d^{2} - i\right)} \sin\left(2 \, b x + 2 \, a\right)}{c^{2} + d^{2} + 2 \, d + 1}\right) - i \, {\rm polylog}\left(3, \frac{{\left(c^{2} - 2 i \, c d - d^{2} + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(-i \, c^{2} - 2 \, c d + i \, d^{2} - i\right)} \sin\left(2 \, b x + 2 \, a\right)}{c^{2} + d^{2} - 2 \, d + 1}\right)}{16 \, b^{2}}"," ",0,"1/16*(8*b^2*x^2*arccot(d*cot(b*x + a) + c) - 2*b*x*dilog(-(c^2 + d^2 - (c^2 + 2*I*c*d - d^2 + 1)*cos(2*b*x + 2*a) + (-I*c^2 + 2*c*d + I*d^2 - I)*sin(2*b*x + 2*a) + 2*d + 1)/(c^2 + d^2 + 2*d + 1) + 1) - 2*b*x*dilog(-(c^2 + d^2 - (c^2 - 2*I*c*d - d^2 + 1)*cos(2*b*x + 2*a) + (I*c^2 + 2*c*d - I*d^2 + I)*sin(2*b*x + 2*a) + 2*d + 1)/(c^2 + d^2 + 2*d + 1) + 1) + 2*b*x*dilog(-(c^2 + d^2 - (c^2 + 2*I*c*d - d^2 + 1)*cos(2*b*x + 2*a) + (-I*c^2 + 2*c*d + I*d^2 - I)*sin(2*b*x + 2*a) - 2*d + 1)/(c^2 + d^2 - 2*d + 1) + 1) + 2*b*x*dilog(-(c^2 + d^2 - (c^2 - 2*I*c*d - d^2 + 1)*cos(2*b*x + 2*a) + (I*c^2 + 2*c*d - I*d^2 + I)*sin(2*b*x + 2*a) - 2*d + 1)/(c^2 + d^2 - 2*d + 1) + 1) - 2*I*a^2*log(1/2*c^2 + I*c*d - 1/2*d^2 - 1/2*(c^2 + d^2 + 2*d + 1)*cos(2*b*x + 2*a) + 1/2*(I*c^2 + I*d^2 + 2*I*d + I)*sin(2*b*x + 2*a) + 1/2) + 2*I*a^2*log(1/2*c^2 + I*c*d - 1/2*d^2 - 1/2*(c^2 + d^2 - 2*d + 1)*cos(2*b*x + 2*a) + 1/2*(I*c^2 + I*d^2 - 2*I*d + I)*sin(2*b*x + 2*a) + 1/2) + 2*I*a^2*log(-1/2*c^2 + I*c*d + 1/2*d^2 + 1/2*(c^2 + d^2 + 2*d + 1)*cos(2*b*x + 2*a) + 1/2*(I*c^2 + I*d^2 + 2*I*d + I)*sin(2*b*x + 2*a) - 1/2) - 2*I*a^2*log(-1/2*c^2 + I*c*d + 1/2*d^2 + 1/2*(c^2 + d^2 - 2*d + 1)*cos(2*b*x + 2*a) + 1/2*(I*c^2 + I*d^2 - 2*I*d + I)*sin(2*b*x + 2*a) - 1/2) + (-2*I*b^2*x^2 + 2*I*a^2)*log((c^2 + d^2 - (c^2 + 2*I*c*d - d^2 + 1)*cos(2*b*x + 2*a) + (-I*c^2 + 2*c*d + I*d^2 - I)*sin(2*b*x + 2*a) + 2*d + 1)/(c^2 + d^2 + 2*d + 1)) + (2*I*b^2*x^2 - 2*I*a^2)*log((c^2 + d^2 - (c^2 - 2*I*c*d - d^2 + 1)*cos(2*b*x + 2*a) + (I*c^2 + 2*c*d - I*d^2 + I)*sin(2*b*x + 2*a) + 2*d + 1)/(c^2 + d^2 + 2*d + 1)) + (2*I*b^2*x^2 - 2*I*a^2)*log((c^2 + d^2 - (c^2 + 2*I*c*d - d^2 + 1)*cos(2*b*x + 2*a) + (-I*c^2 + 2*c*d + I*d^2 - I)*sin(2*b*x + 2*a) - 2*d + 1)/(c^2 + d^2 - 2*d + 1)) + (-2*I*b^2*x^2 + 2*I*a^2)*log((c^2 + d^2 - (c^2 - 2*I*c*d - d^2 + 1)*cos(2*b*x + 2*a) + (I*c^2 + 2*c*d - I*d^2 + I)*sin(2*b*x + 2*a) - 2*d + 1)/(c^2 + d^2 - 2*d + 1)) - I*polylog(3, ((c^2 + 2*I*c*d - d^2 + 1)*cos(2*b*x + 2*a) + (I*c^2 - 2*c*d - I*d^2 + I)*sin(2*b*x + 2*a))/(c^2 + d^2 + 2*d + 1)) + I*polylog(3, ((c^2 + 2*I*c*d - d^2 + 1)*cos(2*b*x + 2*a) + (I*c^2 - 2*c*d - I*d^2 + I)*sin(2*b*x + 2*a))/(c^2 + d^2 - 2*d + 1)) + I*polylog(3, ((c^2 - 2*I*c*d - d^2 + 1)*cos(2*b*x + 2*a) + (-I*c^2 - 2*c*d + I*d^2 - I)*sin(2*b*x + 2*a))/(c^2 + d^2 + 2*d + 1)) - I*polylog(3, ((c^2 - 2*I*c*d - d^2 + 1)*cos(2*b*x + 2*a) + (-I*c^2 - 2*c*d + I*d^2 - I)*sin(2*b*x + 2*a))/(c^2 + d^2 - 2*d + 1)))/b^2","C",0
173,1,961,0,0.978353," ","integrate(arccot(c+d*cot(b*x+a)),x, algorithm=""fricas"")","\frac{8 \, b x \operatorname{arccot}\left(d \cot\left(b x + a\right) + c\right) + 2 i \, a \log\left(\frac{1}{2} \, c^{2} + i \, c d - \frac{1}{2} \, d^{2} - \frac{1}{2} \, {\left(c^{2} + d^{2} + 2 \, d + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + \frac{1}{2} \, {\left(i \, c^{2} + i \, d^{2} + 2 i \, d + i\right)} \sin\left(2 \, b x + 2 \, a\right) + \frac{1}{2}\right) - 2 i \, a \log\left(\frac{1}{2} \, c^{2} + i \, c d - \frac{1}{2} \, d^{2} - \frac{1}{2} \, {\left(c^{2} + d^{2} - 2 \, d + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + \frac{1}{2} \, {\left(i \, c^{2} + i \, d^{2} - 2 i \, d + i\right)} \sin\left(2 \, b x + 2 \, a\right) + \frac{1}{2}\right) - 2 i \, a \log\left(-\frac{1}{2} \, c^{2} + i \, c d + \frac{1}{2} \, d^{2} + \frac{1}{2} \, {\left(c^{2} + d^{2} + 2 \, d + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + \frac{1}{2} \, {\left(i \, c^{2} + i \, d^{2} + 2 i \, d + i\right)} \sin\left(2 \, b x + 2 \, a\right) - \frac{1}{2}\right) + 2 i \, a \log\left(-\frac{1}{2} \, c^{2} + i \, c d + \frac{1}{2} \, d^{2} + \frac{1}{2} \, {\left(c^{2} + d^{2} - 2 \, d + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + \frac{1}{2} \, {\left(i \, c^{2} + i \, d^{2} - 2 i \, d + i\right)} \sin\left(2 \, b x + 2 \, a\right) - \frac{1}{2}\right) + {\left(-2 i \, b x - 2 i \, a\right)} \log\left(\frac{c^{2} + d^{2} - {\left(c^{2} + 2 i \, c d - d^{2} + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(-i \, c^{2} + 2 \, c d + i \, d^{2} - i\right)} \sin\left(2 \, b x + 2 \, a\right) + 2 \, d + 1}{c^{2} + d^{2} + 2 \, d + 1}\right) + {\left(2 i \, b x + 2 i \, a\right)} \log\left(\frac{c^{2} + d^{2} - {\left(c^{2} - 2 i \, c d - d^{2} + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(i \, c^{2} + 2 \, c d - i \, d^{2} + i\right)} \sin\left(2 \, b x + 2 \, a\right) + 2 \, d + 1}{c^{2} + d^{2} + 2 \, d + 1}\right) + {\left(2 i \, b x + 2 i \, a\right)} \log\left(\frac{c^{2} + d^{2} - {\left(c^{2} + 2 i \, c d - d^{2} + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(-i \, c^{2} + 2 \, c d + i \, d^{2} - i\right)} \sin\left(2 \, b x + 2 \, a\right) - 2 \, d + 1}{c^{2} + d^{2} - 2 \, d + 1}\right) + {\left(-2 i \, b x - 2 i \, a\right)} \log\left(\frac{c^{2} + d^{2} - {\left(c^{2} - 2 i \, c d - d^{2} + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(i \, c^{2} + 2 \, c d - i \, d^{2} + i\right)} \sin\left(2 \, b x + 2 \, a\right) - 2 \, d + 1}{c^{2} + d^{2} - 2 \, d + 1}\right) - {\rm Li}_2\left(-\frac{c^{2} + d^{2} - {\left(c^{2} + 2 i \, c d - d^{2} + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(-i \, c^{2} + 2 \, c d + i \, d^{2} - i\right)} \sin\left(2 \, b x + 2 \, a\right) + 2 \, d + 1}{c^{2} + d^{2} + 2 \, d + 1} + 1\right) - {\rm Li}_2\left(-\frac{c^{2} + d^{2} - {\left(c^{2} - 2 i \, c d - d^{2} + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(i \, c^{2} + 2 \, c d - i \, d^{2} + i\right)} \sin\left(2 \, b x + 2 \, a\right) + 2 \, d + 1}{c^{2} + d^{2} + 2 \, d + 1} + 1\right) + {\rm Li}_2\left(-\frac{c^{2} + d^{2} - {\left(c^{2} + 2 i \, c d - d^{2} + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(-i \, c^{2} + 2 \, c d + i \, d^{2} - i\right)} \sin\left(2 \, b x + 2 \, a\right) - 2 \, d + 1}{c^{2} + d^{2} - 2 \, d + 1} + 1\right) + {\rm Li}_2\left(-\frac{c^{2} + d^{2} - {\left(c^{2} - 2 i \, c d - d^{2} + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(i \, c^{2} + 2 \, c d - i \, d^{2} + i\right)} \sin\left(2 \, b x + 2 \, a\right) - 2 \, d + 1}{c^{2} + d^{2} - 2 \, d + 1} + 1\right)}{8 \, b}"," ",0,"1/8*(8*b*x*arccot(d*cot(b*x + a) + c) + 2*I*a*log(1/2*c^2 + I*c*d - 1/2*d^2 - 1/2*(c^2 + d^2 + 2*d + 1)*cos(2*b*x + 2*a) + 1/2*(I*c^2 + I*d^2 + 2*I*d + I)*sin(2*b*x + 2*a) + 1/2) - 2*I*a*log(1/2*c^2 + I*c*d - 1/2*d^2 - 1/2*(c^2 + d^2 - 2*d + 1)*cos(2*b*x + 2*a) + 1/2*(I*c^2 + I*d^2 - 2*I*d + I)*sin(2*b*x + 2*a) + 1/2) - 2*I*a*log(-1/2*c^2 + I*c*d + 1/2*d^2 + 1/2*(c^2 + d^2 + 2*d + 1)*cos(2*b*x + 2*a) + 1/2*(I*c^2 + I*d^2 + 2*I*d + I)*sin(2*b*x + 2*a) - 1/2) + 2*I*a*log(-1/2*c^2 + I*c*d + 1/2*d^2 + 1/2*(c^2 + d^2 - 2*d + 1)*cos(2*b*x + 2*a) + 1/2*(I*c^2 + I*d^2 - 2*I*d + I)*sin(2*b*x + 2*a) - 1/2) + (-2*I*b*x - 2*I*a)*log((c^2 + d^2 - (c^2 + 2*I*c*d - d^2 + 1)*cos(2*b*x + 2*a) + (-I*c^2 + 2*c*d + I*d^2 - I)*sin(2*b*x + 2*a) + 2*d + 1)/(c^2 + d^2 + 2*d + 1)) + (2*I*b*x + 2*I*a)*log((c^2 + d^2 - (c^2 - 2*I*c*d - d^2 + 1)*cos(2*b*x + 2*a) + (I*c^2 + 2*c*d - I*d^2 + I)*sin(2*b*x + 2*a) + 2*d + 1)/(c^2 + d^2 + 2*d + 1)) + (2*I*b*x + 2*I*a)*log((c^2 + d^2 - (c^2 + 2*I*c*d - d^2 + 1)*cos(2*b*x + 2*a) + (-I*c^2 + 2*c*d + I*d^2 - I)*sin(2*b*x + 2*a) - 2*d + 1)/(c^2 + d^2 - 2*d + 1)) + (-2*I*b*x - 2*I*a)*log((c^2 + d^2 - (c^2 - 2*I*c*d - d^2 + 1)*cos(2*b*x + 2*a) + (I*c^2 + 2*c*d - I*d^2 + I)*sin(2*b*x + 2*a) - 2*d + 1)/(c^2 + d^2 - 2*d + 1)) - dilog(-(c^2 + d^2 - (c^2 + 2*I*c*d - d^2 + 1)*cos(2*b*x + 2*a) + (-I*c^2 + 2*c*d + I*d^2 - I)*sin(2*b*x + 2*a) + 2*d + 1)/(c^2 + d^2 + 2*d + 1) + 1) - dilog(-(c^2 + d^2 - (c^2 - 2*I*c*d - d^2 + 1)*cos(2*b*x + 2*a) + (I*c^2 + 2*c*d - I*d^2 + I)*sin(2*b*x + 2*a) + 2*d + 1)/(c^2 + d^2 + 2*d + 1) + 1) + dilog(-(c^2 + d^2 - (c^2 + 2*I*c*d - d^2 + 1)*cos(2*b*x + 2*a) + (-I*c^2 + 2*c*d + I*d^2 - I)*sin(2*b*x + 2*a) - 2*d + 1)/(c^2 + d^2 - 2*d + 1) + 1) + dilog(-(c^2 + d^2 - (c^2 - 2*I*c*d - d^2 + 1)*cos(2*b*x + 2*a) + (I*c^2 + 2*c*d - I*d^2 + I)*sin(2*b*x + 2*a) - 2*d + 1)/(c^2 + d^2 - 2*d + 1) + 1))/b","B",0
174,0,0,0,0.517520," ","integrate(arccot(c+d*cot(b*x+a))/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{arccot}\left(d \cot\left(b x + a\right) + c\right)}{x}, x\right)"," ",0,"integral(arccot(d*cot(b*x + a) + c)/x, x)","F",0
175,1,174,0,0.722900," ","integrate(x^2*(pi-arccot(-c-(1-I*c)*cot(b*x+a))),x, algorithm=""fricas"")","-\frac{2 \, b^{4} x^{4} - 8 \, \pi b^{3} x^{3} - 4 i \, b^{3} x^{3} \log\left(\frac{{\left(c e^{\left(2 i \, b x + 2 i \, a\right)} + i\right)} e^{\left(-2 i \, b x - 2 i \, a\right)}}{c + i}\right) + 6 \, b^{2} x^{2} {\rm Li}_2\left(i \, c e^{\left(2 i \, b x + 2 i \, a\right)}\right) - 2 \, a^{4} - 4 i \, a^{3} \log\left(\frac{c e^{\left(2 i \, b x + 2 i \, a\right)} + i}{c}\right) + 6 i \, b x {\rm polylog}\left(3, i \, c e^{\left(2 i \, b x + 2 i \, a\right)}\right) - {\left(-4 i \, b^{3} x^{3} - 4 i \, a^{3}\right)} \log\left(-i \, c e^{\left(2 i \, b x + 2 i \, a\right)} + 1\right) - 3 \, {\rm polylog}\left(4, i \, c e^{\left(2 i \, b x + 2 i \, a\right)}\right)}{24 \, b^{3}}"," ",0,"-1/24*(2*b^4*x^4 - 8*pi*b^3*x^3 - 4*I*b^3*x^3*log((c*e^(2*I*b*x + 2*I*a) + I)*e^(-2*I*b*x - 2*I*a)/(c + I)) + 6*b^2*x^2*dilog(I*c*e^(2*I*b*x + 2*I*a)) - 2*a^4 - 4*I*a^3*log((c*e^(2*I*b*x + 2*I*a) + I)/c) + 6*I*b*x*polylog(3, I*c*e^(2*I*b*x + 2*I*a)) - (-4*I*b^3*x^3 - 4*I*a^3)*log(-I*c*e^(2*I*b*x + 2*I*a) + 1) - 3*polylog(4, I*c*e^(2*I*b*x + 2*I*a)))/b^3","C",0
176,1,152,0,0.425946," ","integrate(x*(pi-arccot(-c-(1-I*c)*cot(b*x+a))),x, algorithm=""fricas"")","-\frac{4 \, b^{3} x^{3} - 12 \, \pi b^{2} x^{2} - 6 i \, b^{2} x^{2} \log\left(\frac{{\left(c e^{\left(2 i \, b x + 2 i \, a\right)} + i\right)} e^{\left(-2 i \, b x - 2 i \, a\right)}}{c + i}\right) + 4 \, a^{3} + 6 \, b x {\rm Li}_2\left(i \, c e^{\left(2 i \, b x + 2 i \, a\right)}\right) + 6 i \, a^{2} \log\left(\frac{c e^{\left(2 i \, b x + 2 i \, a\right)} + i}{c}\right) - {\left(-6 i \, b^{2} x^{2} + 6 i \, a^{2}\right)} \log\left(-i \, c e^{\left(2 i \, b x + 2 i \, a\right)} + 1\right) + 3 i \, {\rm polylog}\left(3, i \, c e^{\left(2 i \, b x + 2 i \, a\right)}\right)}{24 \, b^{2}}"," ",0,"-1/24*(4*b^3*x^3 - 12*pi*b^2*x^2 - 6*I*b^2*x^2*log((c*e^(2*I*b*x + 2*I*a) + I)*e^(-2*I*b*x - 2*I*a)/(c + I)) + 4*a^3 + 6*b*x*dilog(I*c*e^(2*I*b*x + 2*I*a)) + 6*I*a^2*log((c*e^(2*I*b*x + 2*I*a) + I)/c) - (-6*I*b^2*x^2 + 6*I*a^2)*log(-I*c*e^(2*I*b*x + 2*I*a) + 1) + 3*I*polylog(3, I*c*e^(2*I*b*x + 2*I*a)))/b^2","C",0
177,1,116,0,0.411692," ","integrate(pi-arccot(-c-(1-I*c)*cot(b*x+a)),x, algorithm=""fricas"")","-\frac{2 \, b^{2} x^{2} - 4 \, \pi b x - 2 i \, b x \log\left(\frac{{\left(c e^{\left(2 i \, b x + 2 i \, a\right)} + i\right)} e^{\left(-2 i \, b x - 2 i \, a\right)}}{c + i}\right) - 2 \, a^{2} - {\left(-2 i \, b x - 2 i \, a\right)} \log\left(-i \, c e^{\left(2 i \, b x + 2 i \, a\right)} + 1\right) - 2 i \, a \log\left(\frac{c e^{\left(2 i \, b x + 2 i \, a\right)} + i}{c}\right) + {\rm Li}_2\left(i \, c e^{\left(2 i \, b x + 2 i \, a\right)}\right)}{4 \, b}"," ",0,"-1/4*(2*b^2*x^2 - 4*pi*b*x - 2*I*b*x*log((c*e^(2*I*b*x + 2*I*a) + I)*e^(-2*I*b*x - 2*I*a)/(c + I)) - 2*a^2 - (-2*I*b*x - 2*I*a)*log(-I*c*e^(2*I*b*x + 2*I*a) + 1) - 2*I*a*log((c*e^(2*I*b*x + 2*I*a) + I)/c) + dilog(I*c*e^(2*I*b*x + 2*I*a)))/b","A",0
178,0,0,0,0.527390," ","integrate((pi-arccot(-c-(1-I*c)*cot(b*x+a)))/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{2 \, \pi + i \, \log\left(\frac{{\left(c e^{\left(2 i \, b x + 2 i \, a\right)} + i\right)} e^{\left(-2 i \, b x - 2 i \, a\right)}}{c + i}\right)}{2 \, x}, x\right)"," ",0,"integral(1/2*(2*pi + I*log((c*e^(2*I*b*x + 2*I*a) + I)*e^(-2*I*b*x - 2*I*a)/(c + I)))/x, x)","F",0
179,1,173,0,0.811713," ","integrate(x^2*(pi-arccot(-c+(1+I*c)*cot(b*x+a))),x, algorithm=""fricas"")","\frac{2 \, b^{4} x^{4} + 8 \, \pi b^{3} x^{3} + 4 i \, b^{3} x^{3} \log\left(\frac{{\left(c - i\right)} e^{\left(2 i \, b x + 2 i \, a\right)}}{c e^{\left(2 i \, b x + 2 i \, a\right)} - i}\right) + 6 \, b^{2} x^{2} {\rm Li}_2\left(-i \, c e^{\left(2 i \, b x + 2 i \, a\right)}\right) - 2 \, a^{4} - 4 i \, a^{3} \log\left(\frac{c e^{\left(2 i \, b x + 2 i \, a\right)} - i}{c}\right) + 6 i \, b x {\rm polylog}\left(3, -i \, c e^{\left(2 i \, b x + 2 i \, a\right)}\right) + {\left(4 i \, b^{3} x^{3} + 4 i \, a^{3}\right)} \log\left(i \, c e^{\left(2 i \, b x + 2 i \, a\right)} + 1\right) - 3 \, {\rm polylog}\left(4, -i \, c e^{\left(2 i \, b x + 2 i \, a\right)}\right)}{24 \, b^{3}}"," ",0,"1/24*(2*b^4*x^4 + 8*pi*b^3*x^3 + 4*I*b^3*x^3*log((c - I)*e^(2*I*b*x + 2*I*a)/(c*e^(2*I*b*x + 2*I*a) - I)) + 6*b^2*x^2*dilog(-I*c*e^(2*I*b*x + 2*I*a)) - 2*a^4 - 4*I*a^3*log((c*e^(2*I*b*x + 2*I*a) - I)/c) + 6*I*b*x*polylog(3, -I*c*e^(2*I*b*x + 2*I*a)) + (4*I*b^3*x^3 + 4*I*a^3)*log(I*c*e^(2*I*b*x + 2*I*a) + 1) - 3*polylog(4, -I*c*e^(2*I*b*x + 2*I*a)))/b^3","C",0
180,1,151,0,0.689667," ","integrate(x*(pi-arccot(-c+(1+I*c)*cot(b*x+a))),x, algorithm=""fricas"")","\frac{4 \, b^{3} x^{3} + 12 \, \pi b^{2} x^{2} + 6 i \, b^{2} x^{2} \log\left(\frac{{\left(c - i\right)} e^{\left(2 i \, b x + 2 i \, a\right)}}{c e^{\left(2 i \, b x + 2 i \, a\right)} - i}\right) + 4 \, a^{3} + 6 \, b x {\rm Li}_2\left(-i \, c e^{\left(2 i \, b x + 2 i \, a\right)}\right) + 6 i \, a^{2} \log\left(\frac{c e^{\left(2 i \, b x + 2 i \, a\right)} - i}{c}\right) + {\left(6 i \, b^{2} x^{2} - 6 i \, a^{2}\right)} \log\left(i \, c e^{\left(2 i \, b x + 2 i \, a\right)} + 1\right) + 3 i \, {\rm polylog}\left(3, -i \, c e^{\left(2 i \, b x + 2 i \, a\right)}\right)}{24 \, b^{2}}"," ",0,"1/24*(4*b^3*x^3 + 12*pi*b^2*x^2 + 6*I*b^2*x^2*log((c - I)*e^(2*I*b*x + 2*I*a)/(c*e^(2*I*b*x + 2*I*a) - I)) + 4*a^3 + 6*b*x*dilog(-I*c*e^(2*I*b*x + 2*I*a)) + 6*I*a^2*log((c*e^(2*I*b*x + 2*I*a) - I)/c) + (6*I*b^2*x^2 - 6*I*a^2)*log(I*c*e^(2*I*b*x + 2*I*a) + 1) + 3*I*polylog(3, -I*c*e^(2*I*b*x + 2*I*a)))/b^2","C",0
181,1,115,0,0.819000," ","integrate(pi-arccot(-c+(1+I*c)*cot(b*x+a)),x, algorithm=""fricas"")","\frac{2 \, b^{2} x^{2} + 4 \, \pi b x + 2 i \, b x \log\left(\frac{{\left(c - i\right)} e^{\left(2 i \, b x + 2 i \, a\right)}}{c e^{\left(2 i \, b x + 2 i \, a\right)} - i}\right) - 2 \, a^{2} + {\left(2 i \, b x + 2 i \, a\right)} \log\left(i \, c e^{\left(2 i \, b x + 2 i \, a\right)} + 1\right) - 2 i \, a \log\left(\frac{c e^{\left(2 i \, b x + 2 i \, a\right)} - i}{c}\right) + {\rm Li}_2\left(-i \, c e^{\left(2 i \, b x + 2 i \, a\right)}\right)}{4 \, b}"," ",0,"1/4*(2*b^2*x^2 + 4*pi*b*x + 2*I*b*x*log((c - I)*e^(2*I*b*x + 2*I*a)/(c*e^(2*I*b*x + 2*I*a) - I)) - 2*a^2 + (2*I*b*x + 2*I*a)*log(I*c*e^(2*I*b*x + 2*I*a) + 1) - 2*I*a*log((c*e^(2*I*b*x + 2*I*a) - I)/c) + dilog(-I*c*e^(2*I*b*x + 2*I*a)))/b","A",0
182,0,0,0,0.507552," ","integrate((pi-arccot(-c+(1+I*c)*cot(b*x+a)))/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{2 \, \pi + i \, \log\left(\frac{{\left(c - i\right)} e^{\left(2 i \, b x + 2 i \, a\right)}}{c e^{\left(2 i \, b x + 2 i \, a\right)} - i}\right)}{2 \, x}, x\right)"," ",0,"integral(1/2*(2*pi + I*log((c - I)*e^(2*I*b*x + 2*I*a)/(c*e^(2*I*b*x + 2*I*a) - I)))/x, x)","F",0
183,1,1448,0,0.971105," ","integrate((f*x+e)^3*arccot(tanh(b*x+a)),x, algorithm=""fricas"")","\frac{-24 i \, f^{3} {\rm polylog}\left(5, \frac{1}{2} \, \sqrt{4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - 24 i \, f^{3} {\rm polylog}\left(5, -\frac{1}{2} \, \sqrt{4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + 24 i \, f^{3} {\rm polylog}\left(5, \frac{1}{2} \, \sqrt{-4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + 24 i \, f^{3} {\rm polylog}\left(5, -\frac{1}{2} \, \sqrt{-4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\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\right)} \arctan\left(\frac{\cosh\left(b x + a\right)}{\sinh\left(b x + 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(\frac{1}{2} \, \sqrt{4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\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(-\frac{1}{2} \, \sqrt{4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\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(\frac{1}{2} \, \sqrt{-4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\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(-\frac{1}{2} \, \sqrt{-4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + {\left(i \, b^{4} f^{3} x^{4} + 4 i \, b^{4} e f^{2} x^{3} + 6 i \, b^{4} e^{2} f x^{2} + 4 i \, b^{4} e^{3} x + 4 i \, a b^{3} e^{3} - 6 i \, a^{2} b^{2} e^{2} f + 4 i \, a^{3} b e f^{2} - i \, a^{4} f^{3}\right)} \log\left(\frac{1}{2} \, \sqrt{4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) + {\left(i \, b^{4} f^{3} x^{4} + 4 i \, b^{4} e f^{2} x^{3} + 6 i \, b^{4} e^{2} f x^{2} + 4 i \, b^{4} e^{3} x + 4 i \, a b^{3} e^{3} - 6 i \, a^{2} b^{2} e^{2} f + 4 i \, a^{3} b e f^{2} - i \, a^{4} f^{3}\right)} \log\left(-\frac{1}{2} \, \sqrt{4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) + {\left(-i \, b^{4} f^{3} x^{4} - 4 i \, b^{4} e f^{2} x^{3} - 6 i \, b^{4} e^{2} f x^{2} - 4 i \, b^{4} e^{3} x - 4 i \, a b^{3} e^{3} + 6 i \, a^{2} b^{2} e^{2} f - 4 i \, a^{3} b e f^{2} + i \, a^{4} f^{3}\right)} \log\left(\frac{1}{2} \, \sqrt{-4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) + {\left(-i \, b^{4} f^{3} x^{4} - 4 i \, b^{4} e f^{2} x^{3} - 6 i \, b^{4} e^{2} f x^{2} - 4 i \, b^{4} e^{3} x - 4 i \, a b^{3} e^{3} + 6 i \, a^{2} b^{2} e^{2} f - 4 i \, a^{3} b e f^{2} + i \, a^{4} f^{3}\right)} \log\left(-\frac{1}{2} \, \sqrt{-4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) + {\left(-4 i \, a b^{3} e^{3} + 6 i \, a^{2} b^{2} e^{2} f - 4 i \, a^{3} b e f^{2} + i \, a^{4} f^{3}\right)} \log\left(i \, \sqrt{4 i} + 2 \, \cosh\left(b x + a\right) + 2 \, \sinh\left(b x + a\right)\right) + {\left(-4 i \, a b^{3} e^{3} + 6 i \, a^{2} b^{2} e^{2} f - 4 i \, a^{3} b e f^{2} + i \, a^{4} f^{3}\right)} \log\left(-i \, \sqrt{4 i} + 2 \, \cosh\left(b x + a\right) + 2 \, \sinh\left(b x + a\right)\right) + {\left(4 i \, a b^{3} e^{3} - 6 i \, a^{2} b^{2} e^{2} f + 4 i \, a^{3} b e f^{2} - i \, a^{4} f^{3}\right)} \log\left(i \, \sqrt{-4 i} + 2 \, \cosh\left(b x + a\right) + 2 \, \sinh\left(b x + a\right)\right) + {\left(4 i \, a b^{3} e^{3} - 6 i \, a^{2} b^{2} e^{2} f + 4 i \, a^{3} b e f^{2} - i \, a^{4} f^{3}\right)} \log\left(-i \, \sqrt{-4 i} + 2 \, \cosh\left(b x + a\right) + 2 \, \sinh\left(b x + a\right)\right) + {\left(24 i \, b f^{3} x + 24 i \, b e f^{2}\right)} {\rm polylog}\left(4, \frac{1}{2} \, \sqrt{4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + {\left(24 i \, b f^{3} x + 24 i \, b e f^{2}\right)} {\rm polylog}\left(4, -\frac{1}{2} \, \sqrt{4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + {\left(-24 i \, b f^{3} x - 24 i \, b e f^{2}\right)} {\rm polylog}\left(4, \frac{1}{2} \, \sqrt{-4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + {\left(-24 i \, b f^{3} x - 24 i \, b e f^{2}\right)} {\rm polylog}\left(4, -\frac{1}{2} \, \sqrt{-4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + {\left(-12 i \, b^{2} f^{3} x^{2} - 24 i \, b^{2} e f^{2} x - 12 i \, b^{2} e^{2} f\right)} {\rm polylog}\left(3, \frac{1}{2} \, \sqrt{4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + {\left(-12 i \, b^{2} f^{3} x^{2} - 24 i \, b^{2} e f^{2} x - 12 i \, b^{2} e^{2} f\right)} {\rm polylog}\left(3, -\frac{1}{2} \, \sqrt{4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + {\left(12 i \, b^{2} f^{3} x^{2} + 24 i \, b^{2} e f^{2} x + 12 i \, b^{2} e^{2} f\right)} {\rm polylog}\left(3, \frac{1}{2} \, \sqrt{-4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + {\left(12 i \, b^{2} f^{3} x^{2} + 24 i \, b^{2} e f^{2} x + 12 i \, b^{2} e^{2} f\right)} {\rm polylog}\left(3, -\frac{1}{2} \, \sqrt{-4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right)}{8 \, b^{4}}"," ",0,"1/8*(-24*I*f^3*polylog(5, 1/2*sqrt(4*I)*(cosh(b*x + a) + sinh(b*x + a))) - 24*I*f^3*polylog(5, -1/2*sqrt(4*I)*(cosh(b*x + a) + sinh(b*x + a))) + 24*I*f^3*polylog(5, 1/2*sqrt(-4*I)*(cosh(b*x + a) + sinh(b*x + a))) + 24*I*f^3*polylog(5, -1/2*sqrt(-4*I)*(cosh(b*x + a) + sinh(b*x + a))) + 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)*arctan(cosh(b*x + a)/sinh(b*x + 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(1/2*sqrt(4*I)*(cosh(b*x + a) + sinh(b*x + 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(-1/2*sqrt(4*I)*(cosh(b*x + a) + sinh(b*x + 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(1/2*sqrt(-4*I)*(cosh(b*x + a) + sinh(b*x + 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(-1/2*sqrt(-4*I)*(cosh(b*x + a) + sinh(b*x + a))) + (I*b^4*f^3*x^4 + 4*I*b^4*e*f^2*x^3 + 6*I*b^4*e^2*f*x^2 + 4*I*b^4*e^3*x + 4*I*a*b^3*e^3 - 6*I*a^2*b^2*e^2*f + 4*I*a^3*b*e*f^2 - I*a^4*f^3)*log(1/2*sqrt(4*I)*(cosh(b*x + a) + sinh(b*x + a)) + 1) + (I*b^4*f^3*x^4 + 4*I*b^4*e*f^2*x^3 + 6*I*b^4*e^2*f*x^2 + 4*I*b^4*e^3*x + 4*I*a*b^3*e^3 - 6*I*a^2*b^2*e^2*f + 4*I*a^3*b*e*f^2 - I*a^4*f^3)*log(-1/2*sqrt(4*I)*(cosh(b*x + a) + sinh(b*x + a)) + 1) + (-I*b^4*f^3*x^4 - 4*I*b^4*e*f^2*x^3 - 6*I*b^4*e^2*f*x^2 - 4*I*b^4*e^3*x - 4*I*a*b^3*e^3 + 6*I*a^2*b^2*e^2*f - 4*I*a^3*b*e*f^2 + I*a^4*f^3)*log(1/2*sqrt(-4*I)*(cosh(b*x + a) + sinh(b*x + a)) + 1) + (-I*b^4*f^3*x^4 - 4*I*b^4*e*f^2*x^3 - 6*I*b^4*e^2*f*x^2 - 4*I*b^4*e^3*x - 4*I*a*b^3*e^3 + 6*I*a^2*b^2*e^2*f - 4*I*a^3*b*e*f^2 + I*a^4*f^3)*log(-1/2*sqrt(-4*I)*(cosh(b*x + a) + sinh(b*x + a)) + 1) + (-4*I*a*b^3*e^3 + 6*I*a^2*b^2*e^2*f - 4*I*a^3*b*e*f^2 + I*a^4*f^3)*log(I*sqrt(4*I) + 2*cosh(b*x + a) + 2*sinh(b*x + a)) + (-4*I*a*b^3*e^3 + 6*I*a^2*b^2*e^2*f - 4*I*a^3*b*e*f^2 + I*a^4*f^3)*log(-I*sqrt(4*I) + 2*cosh(b*x + a) + 2*sinh(b*x + a)) + (4*I*a*b^3*e^3 - 6*I*a^2*b^2*e^2*f + 4*I*a^3*b*e*f^2 - I*a^4*f^3)*log(I*sqrt(-4*I) + 2*cosh(b*x + a) + 2*sinh(b*x + a)) + (4*I*a*b^3*e^3 - 6*I*a^2*b^2*e^2*f + 4*I*a^3*b*e*f^2 - I*a^4*f^3)*log(-I*sqrt(-4*I) + 2*cosh(b*x + a) + 2*sinh(b*x + a)) + (24*I*b*f^3*x + 24*I*b*e*f^2)*polylog(4, 1/2*sqrt(4*I)*(cosh(b*x + a) + sinh(b*x + a))) + (24*I*b*f^3*x + 24*I*b*e*f^2)*polylog(4, -1/2*sqrt(4*I)*(cosh(b*x + a) + sinh(b*x + a))) + (-24*I*b*f^3*x - 24*I*b*e*f^2)*polylog(4, 1/2*sqrt(-4*I)*(cosh(b*x + a) + sinh(b*x + a))) + (-24*I*b*f^3*x - 24*I*b*e*f^2)*polylog(4, -1/2*sqrt(-4*I)*(cosh(b*x + a) + sinh(b*x + a))) + (-12*I*b^2*f^3*x^2 - 24*I*b^2*e*f^2*x - 12*I*b^2*e^2*f)*polylog(3, 1/2*sqrt(4*I)*(cosh(b*x + a) + sinh(b*x + a))) + (-12*I*b^2*f^3*x^2 - 24*I*b^2*e*f^2*x - 12*I*b^2*e^2*f)*polylog(3, -1/2*sqrt(4*I)*(cosh(b*x + a) + sinh(b*x + a))) + (12*I*b^2*f^3*x^2 + 24*I*b^2*e*f^2*x + 12*I*b^2*e^2*f)*polylog(3, 1/2*sqrt(-4*I)*(cosh(b*x + a) + sinh(b*x + a))) + (12*I*b^2*f^3*x^2 + 24*I*b^2*e*f^2*x + 12*I*b^2*e^2*f)*polylog(3, -1/2*sqrt(-4*I)*(cosh(b*x + a) + sinh(b*x + a))))/b^4","C",0
184,1,994,0,0.779869," ","integrate((f*x+e)^2*arccot(tanh(b*x+a)),x, algorithm=""fricas"")","\frac{6 i \, f^{2} {\rm polylog}\left(4, \frac{1}{2} \, \sqrt{4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + 6 i \, f^{2} {\rm polylog}\left(4, -\frac{1}{2} \, \sqrt{4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - 6 i \, f^{2} {\rm polylog}\left(4, \frac{1}{2} \, \sqrt{-4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - 6 i \, f^{2} {\rm polylog}\left(4, -\frac{1}{2} \, \sqrt{-4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + 2 \, {\left(b^{3} f^{2} x^{3} + 3 \, b^{3} e f x^{2} + 3 \, b^{3} e^{2} x\right)} \arctan\left(\frac{\cosh\left(b x + a\right)}{\sinh\left(b x + a\right)}\right) + {\left(3 i \, b^{2} f^{2} x^{2} + 6 i \, b^{2} e f x + 3 i \, b^{2} e^{2}\right)} {\rm Li}_2\left(\frac{1}{2} \, \sqrt{4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + {\left(3 i \, b^{2} f^{2} x^{2} + 6 i \, b^{2} e f x + 3 i \, b^{2} e^{2}\right)} {\rm Li}_2\left(-\frac{1}{2} \, \sqrt{4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + {\left(-3 i \, b^{2} f^{2} x^{2} - 6 i \, b^{2} e f x - 3 i \, b^{2} e^{2}\right)} {\rm Li}_2\left(\frac{1}{2} \, \sqrt{-4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + {\left(-3 i \, b^{2} f^{2} x^{2} - 6 i \, b^{2} e f x - 3 i \, b^{2} e^{2}\right)} {\rm Li}_2\left(-\frac{1}{2} \, \sqrt{-4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + {\left(i \, b^{3} f^{2} x^{3} + 3 i \, b^{3} e f x^{2} + 3 i \, b^{3} e^{2} x + 3 i \, a b^{2} e^{2} - 3 i \, a^{2} b e f + i \, a^{3} f^{2}\right)} \log\left(\frac{1}{2} \, \sqrt{4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) + {\left(i \, b^{3} f^{2} x^{3} + 3 i \, b^{3} e f x^{2} + 3 i \, b^{3} e^{2} x + 3 i \, a b^{2} e^{2} - 3 i \, a^{2} b e f + i \, a^{3} f^{2}\right)} \log\left(-\frac{1}{2} \, \sqrt{4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) + {\left(-i \, b^{3} f^{2} x^{3} - 3 i \, b^{3} e f x^{2} - 3 i \, b^{3} e^{2} x - 3 i \, a b^{2} e^{2} + 3 i \, a^{2} b e f - i \, a^{3} f^{2}\right)} \log\left(\frac{1}{2} \, \sqrt{-4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) + {\left(-i \, b^{3} f^{2} x^{3} - 3 i \, b^{3} e f x^{2} - 3 i \, b^{3} e^{2} x - 3 i \, a b^{2} e^{2} + 3 i \, a^{2} b e f - i \, a^{3} f^{2}\right)} \log\left(-\frac{1}{2} \, \sqrt{-4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) + {\left(-3 i \, a b^{2} e^{2} + 3 i \, a^{2} b e f - i \, a^{3} f^{2}\right)} \log\left(i \, \sqrt{4 i} + 2 \, \cosh\left(b x + a\right) + 2 \, \sinh\left(b x + a\right)\right) + {\left(-3 i \, a b^{2} e^{2} + 3 i \, a^{2} b e f - i \, a^{3} f^{2}\right)} \log\left(-i \, \sqrt{4 i} + 2 \, \cosh\left(b x + a\right) + 2 \, \sinh\left(b x + a\right)\right) + {\left(3 i \, a b^{2} e^{2} - 3 i \, a^{2} b e f + i \, a^{3} f^{2}\right)} \log\left(i \, \sqrt{-4 i} + 2 \, \cosh\left(b x + a\right) + 2 \, \sinh\left(b x + a\right)\right) + {\left(3 i \, a b^{2} e^{2} - 3 i \, a^{2} b e f + i \, a^{3} f^{2}\right)} \log\left(-i \, \sqrt{-4 i} + 2 \, \cosh\left(b x + a\right) + 2 \, \sinh\left(b x + a\right)\right) + {\left(-6 i \, b f^{2} x - 6 i \, b e f\right)} {\rm polylog}\left(3, \frac{1}{2} \, \sqrt{4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + {\left(-6 i \, b f^{2} x - 6 i \, b e f\right)} {\rm polylog}\left(3, -\frac{1}{2} \, \sqrt{4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + {\left(6 i \, b f^{2} x + 6 i \, b e f\right)} {\rm polylog}\left(3, \frac{1}{2} \, \sqrt{-4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + {\left(6 i \, b f^{2} x + 6 i \, b e f\right)} {\rm polylog}\left(3, -\frac{1}{2} \, \sqrt{-4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right)}{6 \, b^{3}}"," ",0,"1/6*(6*I*f^2*polylog(4, 1/2*sqrt(4*I)*(cosh(b*x + a) + sinh(b*x + a))) + 6*I*f^2*polylog(4, -1/2*sqrt(4*I)*(cosh(b*x + a) + sinh(b*x + a))) - 6*I*f^2*polylog(4, 1/2*sqrt(-4*I)*(cosh(b*x + a) + sinh(b*x + a))) - 6*I*f^2*polylog(4, -1/2*sqrt(-4*I)*(cosh(b*x + a) + sinh(b*x + a))) + 2*(b^3*f^2*x^3 + 3*b^3*e*f*x^2 + 3*b^3*e^2*x)*arctan(cosh(b*x + a)/sinh(b*x + a)) + (3*I*b^2*f^2*x^2 + 6*I*b^2*e*f*x + 3*I*b^2*e^2)*dilog(1/2*sqrt(4*I)*(cosh(b*x + a) + sinh(b*x + a))) + (3*I*b^2*f^2*x^2 + 6*I*b^2*e*f*x + 3*I*b^2*e^2)*dilog(-1/2*sqrt(4*I)*(cosh(b*x + a) + sinh(b*x + a))) + (-3*I*b^2*f^2*x^2 - 6*I*b^2*e*f*x - 3*I*b^2*e^2)*dilog(1/2*sqrt(-4*I)*(cosh(b*x + a) + sinh(b*x + a))) + (-3*I*b^2*f^2*x^2 - 6*I*b^2*e*f*x - 3*I*b^2*e^2)*dilog(-1/2*sqrt(-4*I)*(cosh(b*x + a) + sinh(b*x + a))) + (I*b^3*f^2*x^3 + 3*I*b^3*e*f*x^2 + 3*I*b^3*e^2*x + 3*I*a*b^2*e^2 - 3*I*a^2*b*e*f + I*a^3*f^2)*log(1/2*sqrt(4*I)*(cosh(b*x + a) + sinh(b*x + a)) + 1) + (I*b^3*f^2*x^3 + 3*I*b^3*e*f*x^2 + 3*I*b^3*e^2*x + 3*I*a*b^2*e^2 - 3*I*a^2*b*e*f + I*a^3*f^2)*log(-1/2*sqrt(4*I)*(cosh(b*x + a) + sinh(b*x + a)) + 1) + (-I*b^3*f^2*x^3 - 3*I*b^3*e*f*x^2 - 3*I*b^3*e^2*x - 3*I*a*b^2*e^2 + 3*I*a^2*b*e*f - I*a^3*f^2)*log(1/2*sqrt(-4*I)*(cosh(b*x + a) + sinh(b*x + a)) + 1) + (-I*b^3*f^2*x^3 - 3*I*b^3*e*f*x^2 - 3*I*b^3*e^2*x - 3*I*a*b^2*e^2 + 3*I*a^2*b*e*f - I*a^3*f^2)*log(-1/2*sqrt(-4*I)*(cosh(b*x + a) + sinh(b*x + a)) + 1) + (-3*I*a*b^2*e^2 + 3*I*a^2*b*e*f - I*a^3*f^2)*log(I*sqrt(4*I) + 2*cosh(b*x + a) + 2*sinh(b*x + a)) + (-3*I*a*b^2*e^2 + 3*I*a^2*b*e*f - I*a^3*f^2)*log(-I*sqrt(4*I) + 2*cosh(b*x + a) + 2*sinh(b*x + a)) + (3*I*a*b^2*e^2 - 3*I*a^2*b*e*f + I*a^3*f^2)*log(I*sqrt(-4*I) + 2*cosh(b*x + a) + 2*sinh(b*x + a)) + (3*I*a*b^2*e^2 - 3*I*a^2*b*e*f + I*a^3*f^2)*log(-I*sqrt(-4*I) + 2*cosh(b*x + a) + 2*sinh(b*x + a)) + (-6*I*b*f^2*x - 6*I*b*e*f)*polylog(3, 1/2*sqrt(4*I)*(cosh(b*x + a) + sinh(b*x + a))) + (-6*I*b*f^2*x - 6*I*b*e*f)*polylog(3, -1/2*sqrt(4*I)*(cosh(b*x + a) + sinh(b*x + a))) + (6*I*b*f^2*x + 6*I*b*e*f)*polylog(3, 1/2*sqrt(-4*I)*(cosh(b*x + a) + sinh(b*x + a))) + (6*I*b*f^2*x + 6*I*b*e*f)*polylog(3, -1/2*sqrt(-4*I)*(cosh(b*x + a) + sinh(b*x + a))))/b^3","C",0
185,1,596,0,0.835243," ","integrate((f*x+e)*arccot(tanh(b*x+a)),x, algorithm=""fricas"")","\frac{2 \, {\left(b^{2} f x^{2} + 2 \, b^{2} e x\right)} \arctan\left(\frac{\cosh\left(b x + a\right)}{\sinh\left(b x + a\right)}\right) + {\left(2 i \, b f x + 2 i \, b e\right)} {\rm Li}_2\left(\frac{1}{2} \, \sqrt{4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + {\left(2 i \, b f x + 2 i \, b e\right)} {\rm Li}_2\left(-\frac{1}{2} \, \sqrt{4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + {\left(-2 i \, b f x - 2 i \, b e\right)} {\rm Li}_2\left(\frac{1}{2} \, \sqrt{-4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + {\left(-2 i \, b f x - 2 i \, b e\right)} {\rm Li}_2\left(-\frac{1}{2} \, \sqrt{-4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + {\left(i \, b^{2} f x^{2} + 2 i \, b^{2} e x + 2 i \, a b e - i \, a^{2} f\right)} \log\left(\frac{1}{2} \, \sqrt{4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) + {\left(i \, b^{2} f x^{2} + 2 i \, b^{2} e x + 2 i \, a b e - i \, a^{2} f\right)} \log\left(-\frac{1}{2} \, \sqrt{4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) + {\left(-i \, b^{2} f x^{2} - 2 i \, b^{2} e x - 2 i \, a b e + i \, a^{2} f\right)} \log\left(\frac{1}{2} \, \sqrt{-4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) + {\left(-i \, b^{2} f x^{2} - 2 i \, b^{2} e x - 2 i \, a b e + i \, a^{2} f\right)} \log\left(-\frac{1}{2} \, \sqrt{-4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) + {\left(-2 i \, a b e + i \, a^{2} f\right)} \log\left(i \, \sqrt{4 i} + 2 \, \cosh\left(b x + a\right) + 2 \, \sinh\left(b x + a\right)\right) + {\left(-2 i \, a b e + i \, a^{2} f\right)} \log\left(-i \, \sqrt{4 i} + 2 \, \cosh\left(b x + a\right) + 2 \, \sinh\left(b x + a\right)\right) + {\left(2 i \, a b e - i \, a^{2} f\right)} \log\left(i \, \sqrt{-4 i} + 2 \, \cosh\left(b x + a\right) + 2 \, \sinh\left(b x + a\right)\right) + {\left(2 i \, a b e - i \, a^{2} f\right)} \log\left(-i \, \sqrt{-4 i} + 2 \, \cosh\left(b x + a\right) + 2 \, \sinh\left(b x + a\right)\right) - 2 i \, f {\rm polylog}\left(3, \frac{1}{2} \, \sqrt{4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - 2 i \, f {\rm polylog}\left(3, -\frac{1}{2} \, \sqrt{4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + 2 i \, f {\rm polylog}\left(3, \frac{1}{2} \, \sqrt{-4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + 2 i \, f {\rm polylog}\left(3, -\frac{1}{2} \, \sqrt{-4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right)}{4 \, b^{2}}"," ",0,"1/4*(2*(b^2*f*x^2 + 2*b^2*e*x)*arctan(cosh(b*x + a)/sinh(b*x + a)) + (2*I*b*f*x + 2*I*b*e)*dilog(1/2*sqrt(4*I)*(cosh(b*x + a) + sinh(b*x + a))) + (2*I*b*f*x + 2*I*b*e)*dilog(-1/2*sqrt(4*I)*(cosh(b*x + a) + sinh(b*x + a))) + (-2*I*b*f*x - 2*I*b*e)*dilog(1/2*sqrt(-4*I)*(cosh(b*x + a) + sinh(b*x + a))) + (-2*I*b*f*x - 2*I*b*e)*dilog(-1/2*sqrt(-4*I)*(cosh(b*x + a) + sinh(b*x + a))) + (I*b^2*f*x^2 + 2*I*b^2*e*x + 2*I*a*b*e - I*a^2*f)*log(1/2*sqrt(4*I)*(cosh(b*x + a) + sinh(b*x + a)) + 1) + (I*b^2*f*x^2 + 2*I*b^2*e*x + 2*I*a*b*e - I*a^2*f)*log(-1/2*sqrt(4*I)*(cosh(b*x + a) + sinh(b*x + a)) + 1) + (-I*b^2*f*x^2 - 2*I*b^2*e*x - 2*I*a*b*e + I*a^2*f)*log(1/2*sqrt(-4*I)*(cosh(b*x + a) + sinh(b*x + a)) + 1) + (-I*b^2*f*x^2 - 2*I*b^2*e*x - 2*I*a*b*e + I*a^2*f)*log(-1/2*sqrt(-4*I)*(cosh(b*x + a) + sinh(b*x + a)) + 1) + (-2*I*a*b*e + I*a^2*f)*log(I*sqrt(4*I) + 2*cosh(b*x + a) + 2*sinh(b*x + a)) + (-2*I*a*b*e + I*a^2*f)*log(-I*sqrt(4*I) + 2*cosh(b*x + a) + 2*sinh(b*x + a)) + (2*I*a*b*e - I*a^2*f)*log(I*sqrt(-4*I) + 2*cosh(b*x + a) + 2*sinh(b*x + a)) + (2*I*a*b*e - I*a^2*f)*log(-I*sqrt(-4*I) + 2*cosh(b*x + a) + 2*sinh(b*x + a)) - 2*I*f*polylog(3, 1/2*sqrt(4*I)*(cosh(b*x + a) + sinh(b*x + a))) - 2*I*f*polylog(3, -1/2*sqrt(4*I)*(cosh(b*x + a) + sinh(b*x + a))) + 2*I*f*polylog(3, 1/2*sqrt(-4*I)*(cosh(b*x + a) + sinh(b*x + a))) + 2*I*f*polylog(3, -1/2*sqrt(-4*I)*(cosh(b*x + a) + sinh(b*x + a))))/b^2","C",0
186,1,334,0,0.599054," ","integrate(arccot(tanh(b*x+a)),x, algorithm=""fricas"")","\frac{2 \, b x \arctan\left(\frac{\cosh\left(b x + a\right)}{\sinh\left(b x + a\right)}\right) + {\left(i \, b x + i \, a\right)} \log\left(\frac{1}{2} \, \sqrt{4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) + {\left(i \, b x + i \, a\right)} \log\left(-\frac{1}{2} \, \sqrt{4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) + {\left(-i \, b x - i \, a\right)} \log\left(\frac{1}{2} \, \sqrt{-4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) + {\left(-i \, b x - i \, a\right)} \log\left(-\frac{1}{2} \, \sqrt{-4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) - i \, a \log\left(i \, \sqrt{4 i} + 2 \, \cosh\left(b x + a\right) + 2 \, \sinh\left(b x + a\right)\right) - i \, a \log\left(-i \, \sqrt{4 i} + 2 \, \cosh\left(b x + a\right) + 2 \, \sinh\left(b x + a\right)\right) + i \, a \log\left(i \, \sqrt{-4 i} + 2 \, \cosh\left(b x + a\right) + 2 \, \sinh\left(b x + a\right)\right) + i \, a \log\left(-i \, \sqrt{-4 i} + 2 \, \cosh\left(b x + a\right) + 2 \, \sinh\left(b x + a\right)\right) + i \, {\rm Li}_2\left(\frac{1}{2} \, \sqrt{4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + i \, {\rm Li}_2\left(-\frac{1}{2} \, \sqrt{4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - i \, {\rm Li}_2\left(\frac{1}{2} \, \sqrt{-4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - i \, {\rm Li}_2\left(-\frac{1}{2} \, \sqrt{-4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right)}{2 \, b}"," ",0,"1/2*(2*b*x*arctan(cosh(b*x + a)/sinh(b*x + a)) + (I*b*x + I*a)*log(1/2*sqrt(4*I)*(cosh(b*x + a) + sinh(b*x + a)) + 1) + (I*b*x + I*a)*log(-1/2*sqrt(4*I)*(cosh(b*x + a) + sinh(b*x + a)) + 1) + (-I*b*x - I*a)*log(1/2*sqrt(-4*I)*(cosh(b*x + a) + sinh(b*x + a)) + 1) + (-I*b*x - I*a)*log(-1/2*sqrt(-4*I)*(cosh(b*x + a) + sinh(b*x + a)) + 1) - I*a*log(I*sqrt(4*I) + 2*cosh(b*x + a) + 2*sinh(b*x + a)) - I*a*log(-I*sqrt(4*I) + 2*cosh(b*x + a) + 2*sinh(b*x + a)) + I*a*log(I*sqrt(-4*I) + 2*cosh(b*x + a) + 2*sinh(b*x + a)) + I*a*log(-I*sqrt(-4*I) + 2*cosh(b*x + a) + 2*sinh(b*x + a)) + I*dilog(1/2*sqrt(4*I)*(cosh(b*x + a) + sinh(b*x + a))) + I*dilog(-1/2*sqrt(4*I)*(cosh(b*x + a) + sinh(b*x + a))) - I*dilog(1/2*sqrt(-4*I)*(cosh(b*x + a) + sinh(b*x + a))) - I*dilog(-1/2*sqrt(-4*I)*(cosh(b*x + a) + sinh(b*x + a))))/b","B",0
187,0,0,0,0.772609," ","integrate(arccot(tanh(b*x+a))/(f*x+e),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{arccot}\left(\tanh\left(b x + a\right)\right)}{f x + e}, x\right)"," ",0,"integral(arccot(tanh(b*x + a))/(f*x + e), x)","F",0
188,1,1335,0,0.723160," ","integrate(x^2*arccot(c+d*tanh(b*x+a)),x, algorithm=""fricas"")","\frac{2 \, b^{3} x^{3} \arctan\left(\frac{\cosh\left(b x + a\right)}{c \cosh\left(b x + a\right) + d \sinh\left(b x + a\right)}\right) - 3 i \, b^{2} x^{2} {\rm Li}_2\left(\frac{1}{2} \, \sqrt{-\frac{4 \, c^{2} - 4 \, d^{2} + 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - 3 i \, b^{2} x^{2} {\rm Li}_2\left(-\frac{1}{2} \, \sqrt{-\frac{4 \, c^{2} - 4 \, d^{2} + 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + 3 i \, b^{2} x^{2} {\rm Li}_2\left(\frac{1}{2} \, \sqrt{-\frac{4 \, c^{2} - 4 \, d^{2} - 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + 3 i \, b^{2} x^{2} {\rm Li}_2\left(-\frac{1}{2} \, \sqrt{-\frac{4 \, c^{2} - 4 \, d^{2} - 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + i \, a^{3} \log\left(2 \, {\left(c^{2} + 2 \, c d + d^{2} + 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(c^{2} + 2 \, c d + d^{2} + 1\right)} \sinh\left(b x + a\right) + {\left(c^{2} - d^{2} - 2 i \, d + 1\right)} \sqrt{-\frac{4 \, c^{2} - 4 \, d^{2} + 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}}\right) + i \, a^{3} \log\left(2 \, {\left(c^{2} + 2 \, c d + d^{2} + 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(c^{2} + 2 \, c d + d^{2} + 1\right)} \sinh\left(b x + a\right) - {\left(c^{2} - d^{2} - 2 i \, d + 1\right)} \sqrt{-\frac{4 \, c^{2} - 4 \, d^{2} + 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}}\right) - i \, a^{3} \log\left(2 \, {\left(c^{2} + 2 \, c d + d^{2} + 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(c^{2} + 2 \, c d + d^{2} + 1\right)} \sinh\left(b x + a\right) + {\left(c^{2} - d^{2} + 2 i \, d + 1\right)} \sqrt{-\frac{4 \, c^{2} - 4 \, d^{2} - 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}}\right) - i \, a^{3} \log\left(2 \, {\left(c^{2} + 2 \, c d + d^{2} + 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(c^{2} + 2 \, c d + d^{2} + 1\right)} \sinh\left(b x + a\right) - {\left(c^{2} - d^{2} + 2 i \, d + 1\right)} \sqrt{-\frac{4 \, c^{2} - 4 \, d^{2} - 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}}\right) + 6 i \, b x {\rm polylog}\left(3, \frac{1}{2} \, \sqrt{-\frac{4 \, c^{2} - 4 \, d^{2} + 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + 6 i \, b x {\rm polylog}\left(3, -\frac{1}{2} \, \sqrt{-\frac{4 \, c^{2} - 4 \, d^{2} + 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - 6 i \, b x {\rm polylog}\left(3, \frac{1}{2} \, \sqrt{-\frac{4 \, c^{2} - 4 \, d^{2} - 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - 6 i \, b x {\rm polylog}\left(3, -\frac{1}{2} \, \sqrt{-\frac{4 \, c^{2} - 4 \, d^{2} - 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + {\left(-i \, b^{3} x^{3} - i \, a^{3}\right)} \log\left(\frac{1}{2} \, \sqrt{-\frac{4 \, c^{2} - 4 \, d^{2} + 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) + {\left(-i \, b^{3} x^{3} - i \, a^{3}\right)} \log\left(-\frac{1}{2} \, \sqrt{-\frac{4 \, c^{2} - 4 \, d^{2} + 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) + {\left(i \, b^{3} x^{3} + i \, a^{3}\right)} \log\left(\frac{1}{2} \, \sqrt{-\frac{4 \, c^{2} - 4 \, d^{2} - 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) + {\left(i \, b^{3} x^{3} + i \, a^{3}\right)} \log\left(-\frac{1}{2} \, \sqrt{-\frac{4 \, c^{2} - 4 \, d^{2} - 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) - 6 i \, {\rm polylog}\left(4, \frac{1}{2} \, \sqrt{-\frac{4 \, c^{2} - 4 \, d^{2} + 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - 6 i \, {\rm polylog}\left(4, -\frac{1}{2} \, \sqrt{-\frac{4 \, c^{2} - 4 \, d^{2} + 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + 6 i \, {\rm polylog}\left(4, \frac{1}{2} \, \sqrt{-\frac{4 \, c^{2} - 4 \, d^{2} - 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + 6 i \, {\rm polylog}\left(4, -\frac{1}{2} \, \sqrt{-\frac{4 \, c^{2} - 4 \, d^{2} - 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right)}{6 \, b^{3}}"," ",0,"1/6*(2*b^3*x^3*arctan(cosh(b*x + a)/(c*cosh(b*x + a) + d*sinh(b*x + a))) - 3*I*b^2*x^2*dilog(1/2*sqrt(-(4*c^2 - 4*d^2 + 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))*(cosh(b*x + a) + sinh(b*x + a))) - 3*I*b^2*x^2*dilog(-1/2*sqrt(-(4*c^2 - 4*d^2 + 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))*(cosh(b*x + a) + sinh(b*x + a))) + 3*I*b^2*x^2*dilog(1/2*sqrt(-(4*c^2 - 4*d^2 - 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))*(cosh(b*x + a) + sinh(b*x + a))) + 3*I*b^2*x^2*dilog(-1/2*sqrt(-(4*c^2 - 4*d^2 - 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))*(cosh(b*x + a) + sinh(b*x + a))) + I*a^3*log(2*(c^2 + 2*c*d + d^2 + 1)*cosh(b*x + a) + 2*(c^2 + 2*c*d + d^2 + 1)*sinh(b*x + a) + (c^2 - d^2 - 2*I*d + 1)*sqrt(-(4*c^2 - 4*d^2 + 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))) + I*a^3*log(2*(c^2 + 2*c*d + d^2 + 1)*cosh(b*x + a) + 2*(c^2 + 2*c*d + d^2 + 1)*sinh(b*x + a) - (c^2 - d^2 - 2*I*d + 1)*sqrt(-(4*c^2 - 4*d^2 + 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))) - I*a^3*log(2*(c^2 + 2*c*d + d^2 + 1)*cosh(b*x + a) + 2*(c^2 + 2*c*d + d^2 + 1)*sinh(b*x + a) + (c^2 - d^2 + 2*I*d + 1)*sqrt(-(4*c^2 - 4*d^2 - 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))) - I*a^3*log(2*(c^2 + 2*c*d + d^2 + 1)*cosh(b*x + a) + 2*(c^2 + 2*c*d + d^2 + 1)*sinh(b*x + a) - (c^2 - d^2 + 2*I*d + 1)*sqrt(-(4*c^2 - 4*d^2 - 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))) + 6*I*b*x*polylog(3, 1/2*sqrt(-(4*c^2 - 4*d^2 + 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))*(cosh(b*x + a) + sinh(b*x + a))) + 6*I*b*x*polylog(3, -1/2*sqrt(-(4*c^2 - 4*d^2 + 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))*(cosh(b*x + a) + sinh(b*x + a))) - 6*I*b*x*polylog(3, 1/2*sqrt(-(4*c^2 - 4*d^2 - 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))*(cosh(b*x + a) + sinh(b*x + a))) - 6*I*b*x*polylog(3, -1/2*sqrt(-(4*c^2 - 4*d^2 - 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))*(cosh(b*x + a) + sinh(b*x + a))) + (-I*b^3*x^3 - I*a^3)*log(1/2*sqrt(-(4*c^2 - 4*d^2 + 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))*(cosh(b*x + a) + sinh(b*x + a)) + 1) + (-I*b^3*x^3 - I*a^3)*log(-1/2*sqrt(-(4*c^2 - 4*d^2 + 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))*(cosh(b*x + a) + sinh(b*x + a)) + 1) + (I*b^3*x^3 + I*a^3)*log(1/2*sqrt(-(4*c^2 - 4*d^2 - 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))*(cosh(b*x + a) + sinh(b*x + a)) + 1) + (I*b^3*x^3 + I*a^3)*log(-1/2*sqrt(-(4*c^2 - 4*d^2 - 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))*(cosh(b*x + a) + sinh(b*x + a)) + 1) - 6*I*polylog(4, 1/2*sqrt(-(4*c^2 - 4*d^2 + 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))*(cosh(b*x + a) + sinh(b*x + a))) - 6*I*polylog(4, -1/2*sqrt(-(4*c^2 - 4*d^2 + 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))*(cosh(b*x + a) + sinh(b*x + a))) + 6*I*polylog(4, 1/2*sqrt(-(4*c^2 - 4*d^2 - 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))*(cosh(b*x + a) + sinh(b*x + a))) + 6*I*polylog(4, -1/2*sqrt(-(4*c^2 - 4*d^2 - 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))*(cosh(b*x + a) + sinh(b*x + a))))/b^3","C",0
189,1,1103,0,0.709909," ","integrate(x*arccot(c+d*tanh(b*x+a)),x, algorithm=""fricas"")","\frac{2 \, b^{2} x^{2} \arctan\left(\frac{\cosh\left(b x + a\right)}{c \cosh\left(b x + a\right) + d \sinh\left(b x + a\right)}\right) - 2 i \, b x {\rm Li}_2\left(\frac{1}{2} \, \sqrt{-\frac{4 \, c^{2} - 4 \, d^{2} + 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - 2 i \, b x {\rm Li}_2\left(-\frac{1}{2} \, \sqrt{-\frac{4 \, c^{2} - 4 \, d^{2} + 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + 2 i \, b x {\rm Li}_2\left(\frac{1}{2} \, \sqrt{-\frac{4 \, c^{2} - 4 \, d^{2} - 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + 2 i \, b x {\rm Li}_2\left(-\frac{1}{2} \, \sqrt{-\frac{4 \, c^{2} - 4 \, d^{2} - 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - i \, a^{2} \log\left(2 \, {\left(c^{2} + 2 \, c d + d^{2} + 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(c^{2} + 2 \, c d + d^{2} + 1\right)} \sinh\left(b x + a\right) + {\left(c^{2} - d^{2} - 2 i \, d + 1\right)} \sqrt{-\frac{4 \, c^{2} - 4 \, d^{2} + 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}}\right) - i \, a^{2} \log\left(2 \, {\left(c^{2} + 2 \, c d + d^{2} + 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(c^{2} + 2 \, c d + d^{2} + 1\right)} \sinh\left(b x + a\right) - {\left(c^{2} - d^{2} - 2 i \, d + 1\right)} \sqrt{-\frac{4 \, c^{2} - 4 \, d^{2} + 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}}\right) + i \, a^{2} \log\left(2 \, {\left(c^{2} + 2 \, c d + d^{2} + 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(c^{2} + 2 \, c d + d^{2} + 1\right)} \sinh\left(b x + a\right) + {\left(c^{2} - d^{2} + 2 i \, d + 1\right)} \sqrt{-\frac{4 \, c^{2} - 4 \, d^{2} - 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}}\right) + i \, a^{2} \log\left(2 \, {\left(c^{2} + 2 \, c d + d^{2} + 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(c^{2} + 2 \, c d + d^{2} + 1\right)} \sinh\left(b x + a\right) - {\left(c^{2} - d^{2} + 2 i \, d + 1\right)} \sqrt{-\frac{4 \, c^{2} - 4 \, d^{2} - 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}}\right) + {\left(-i \, b^{2} x^{2} + i \, a^{2}\right)} \log\left(\frac{1}{2} \, \sqrt{-\frac{4 \, c^{2} - 4 \, d^{2} + 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) + {\left(-i \, b^{2} x^{2} + i \, a^{2}\right)} \log\left(-\frac{1}{2} \, \sqrt{-\frac{4 \, c^{2} - 4 \, d^{2} + 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) + {\left(i \, b^{2} x^{2} - i \, a^{2}\right)} \log\left(\frac{1}{2} \, \sqrt{-\frac{4 \, c^{2} - 4 \, d^{2} - 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) + {\left(i \, b^{2} x^{2} - i \, a^{2}\right)} \log\left(-\frac{1}{2} \, \sqrt{-\frac{4 \, c^{2} - 4 \, d^{2} - 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) + 2 i \, {\rm polylog}\left(3, \frac{1}{2} \, \sqrt{-\frac{4 \, c^{2} - 4 \, d^{2} + 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + 2 i \, {\rm polylog}\left(3, -\frac{1}{2} \, \sqrt{-\frac{4 \, c^{2} - 4 \, d^{2} + 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - 2 i \, {\rm polylog}\left(3, \frac{1}{2} \, \sqrt{-\frac{4 \, c^{2} - 4 \, d^{2} - 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - 2 i \, {\rm polylog}\left(3, -\frac{1}{2} \, \sqrt{-\frac{4 \, c^{2} - 4 \, d^{2} - 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right)}{4 \, b^{2}}"," ",0,"1/4*(2*b^2*x^2*arctan(cosh(b*x + a)/(c*cosh(b*x + a) + d*sinh(b*x + a))) - 2*I*b*x*dilog(1/2*sqrt(-(4*c^2 - 4*d^2 + 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))*(cosh(b*x + a) + sinh(b*x + a))) - 2*I*b*x*dilog(-1/2*sqrt(-(4*c^2 - 4*d^2 + 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))*(cosh(b*x + a) + sinh(b*x + a))) + 2*I*b*x*dilog(1/2*sqrt(-(4*c^2 - 4*d^2 - 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))*(cosh(b*x + a) + sinh(b*x + a))) + 2*I*b*x*dilog(-1/2*sqrt(-(4*c^2 - 4*d^2 - 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))*(cosh(b*x + a) + sinh(b*x + a))) - I*a^2*log(2*(c^2 + 2*c*d + d^2 + 1)*cosh(b*x + a) + 2*(c^2 + 2*c*d + d^2 + 1)*sinh(b*x + a) + (c^2 - d^2 - 2*I*d + 1)*sqrt(-(4*c^2 - 4*d^2 + 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))) - I*a^2*log(2*(c^2 + 2*c*d + d^2 + 1)*cosh(b*x + a) + 2*(c^2 + 2*c*d + d^2 + 1)*sinh(b*x + a) - (c^2 - d^2 - 2*I*d + 1)*sqrt(-(4*c^2 - 4*d^2 + 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))) + I*a^2*log(2*(c^2 + 2*c*d + d^2 + 1)*cosh(b*x + a) + 2*(c^2 + 2*c*d + d^2 + 1)*sinh(b*x + a) + (c^2 - d^2 + 2*I*d + 1)*sqrt(-(4*c^2 - 4*d^2 - 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))) + I*a^2*log(2*(c^2 + 2*c*d + d^2 + 1)*cosh(b*x + a) + 2*(c^2 + 2*c*d + d^2 + 1)*sinh(b*x + a) - (c^2 - d^2 + 2*I*d + 1)*sqrt(-(4*c^2 - 4*d^2 - 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))) + (-I*b^2*x^2 + I*a^2)*log(1/2*sqrt(-(4*c^2 - 4*d^2 + 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))*(cosh(b*x + a) + sinh(b*x + a)) + 1) + (-I*b^2*x^2 + I*a^2)*log(-1/2*sqrt(-(4*c^2 - 4*d^2 + 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))*(cosh(b*x + a) + sinh(b*x + a)) + 1) + (I*b^2*x^2 - I*a^2)*log(1/2*sqrt(-(4*c^2 - 4*d^2 - 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))*(cosh(b*x + a) + sinh(b*x + a)) + 1) + (I*b^2*x^2 - I*a^2)*log(-1/2*sqrt(-(4*c^2 - 4*d^2 - 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))*(cosh(b*x + a) + sinh(b*x + a)) + 1) + 2*I*polylog(3, 1/2*sqrt(-(4*c^2 - 4*d^2 + 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))*(cosh(b*x + a) + sinh(b*x + a))) + 2*I*polylog(3, -1/2*sqrt(-(4*c^2 - 4*d^2 + 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))*(cosh(b*x + a) + sinh(b*x + a))) - 2*I*polylog(3, 1/2*sqrt(-(4*c^2 - 4*d^2 - 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))*(cosh(b*x + a) + sinh(b*x + a))) - 2*I*polylog(3, -1/2*sqrt(-(4*c^2 - 4*d^2 - 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))*(cosh(b*x + a) + sinh(b*x + a))))/b^2","C",0
190,1,851,0,1.651338," ","integrate(arccot(c+d*tanh(b*x+a)),x, algorithm=""fricas"")","\frac{2 \, b x \arctan\left(\frac{\cosh\left(b x + a\right)}{c \cosh\left(b x + a\right) + d \sinh\left(b x + a\right)}\right) + i \, a \log\left(2 \, {\left(c^{2} + 2 \, c d + d^{2} + 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(c^{2} + 2 \, c d + d^{2} + 1\right)} \sinh\left(b x + a\right) + {\left(c^{2} - d^{2} - 2 i \, d + 1\right)} \sqrt{-\frac{4 \, c^{2} - 4 \, d^{2} + 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}}\right) + i \, a \log\left(2 \, {\left(c^{2} + 2 \, c d + d^{2} + 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(c^{2} + 2 \, c d + d^{2} + 1\right)} \sinh\left(b x + a\right) - {\left(c^{2} - d^{2} - 2 i \, d + 1\right)} \sqrt{-\frac{4 \, c^{2} - 4 \, d^{2} + 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}}\right) - i \, a \log\left(2 \, {\left(c^{2} + 2 \, c d + d^{2} + 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(c^{2} + 2 \, c d + d^{2} + 1\right)} \sinh\left(b x + a\right) + {\left(c^{2} - d^{2} + 2 i \, d + 1\right)} \sqrt{-\frac{4 \, c^{2} - 4 \, d^{2} - 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}}\right) - i \, a \log\left(2 \, {\left(c^{2} + 2 \, c d + d^{2} + 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(c^{2} + 2 \, c d + d^{2} + 1\right)} \sinh\left(b x + a\right) - {\left(c^{2} - d^{2} + 2 i \, d + 1\right)} \sqrt{-\frac{4 \, c^{2} - 4 \, d^{2} - 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}}\right) + {\left(-i \, b x - i \, a\right)} \log\left(\frac{1}{2} \, \sqrt{-\frac{4 \, c^{2} - 4 \, d^{2} + 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) + {\left(-i \, b x - i \, a\right)} \log\left(-\frac{1}{2} \, \sqrt{-\frac{4 \, c^{2} - 4 \, d^{2} + 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) + {\left(i \, b x + i \, a\right)} \log\left(\frac{1}{2} \, \sqrt{-\frac{4 \, c^{2} - 4 \, d^{2} - 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) + {\left(i \, b x + i \, a\right)} \log\left(-\frac{1}{2} \, \sqrt{-\frac{4 \, c^{2} - 4 \, d^{2} - 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) - i \, {\rm Li}_2\left(\frac{1}{2} \, \sqrt{-\frac{4 \, c^{2} - 4 \, d^{2} + 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - i \, {\rm Li}_2\left(-\frac{1}{2} \, \sqrt{-\frac{4 \, c^{2} - 4 \, d^{2} + 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + i \, {\rm Li}_2\left(\frac{1}{2} \, \sqrt{-\frac{4 \, c^{2} - 4 \, d^{2} - 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + i \, {\rm Li}_2\left(-\frac{1}{2} \, \sqrt{-\frac{4 \, c^{2} - 4 \, d^{2} - 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right)}{2 \, b}"," ",0,"1/2*(2*b*x*arctan(cosh(b*x + a)/(c*cosh(b*x + a) + d*sinh(b*x + a))) + I*a*log(2*(c^2 + 2*c*d + d^2 + 1)*cosh(b*x + a) + 2*(c^2 + 2*c*d + d^2 + 1)*sinh(b*x + a) + (c^2 - d^2 - 2*I*d + 1)*sqrt(-(4*c^2 - 4*d^2 + 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))) + I*a*log(2*(c^2 + 2*c*d + d^2 + 1)*cosh(b*x + a) + 2*(c^2 + 2*c*d + d^2 + 1)*sinh(b*x + a) - (c^2 - d^2 - 2*I*d + 1)*sqrt(-(4*c^2 - 4*d^2 + 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))) - I*a*log(2*(c^2 + 2*c*d + d^2 + 1)*cosh(b*x + a) + 2*(c^2 + 2*c*d + d^2 + 1)*sinh(b*x + a) + (c^2 - d^2 + 2*I*d + 1)*sqrt(-(4*c^2 - 4*d^2 - 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))) - I*a*log(2*(c^2 + 2*c*d + d^2 + 1)*cosh(b*x + a) + 2*(c^2 + 2*c*d + d^2 + 1)*sinh(b*x + a) - (c^2 - d^2 + 2*I*d + 1)*sqrt(-(4*c^2 - 4*d^2 - 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))) + (-I*b*x - I*a)*log(1/2*sqrt(-(4*c^2 - 4*d^2 + 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))*(cosh(b*x + a) + sinh(b*x + a)) + 1) + (-I*b*x - I*a)*log(-1/2*sqrt(-(4*c^2 - 4*d^2 + 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))*(cosh(b*x + a) + sinh(b*x + a)) + 1) + (I*b*x + I*a)*log(1/2*sqrt(-(4*c^2 - 4*d^2 - 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))*(cosh(b*x + a) + sinh(b*x + a)) + 1) + (I*b*x + I*a)*log(-1/2*sqrt(-(4*c^2 - 4*d^2 - 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))*(cosh(b*x + a) + sinh(b*x + a)) + 1) - I*dilog(1/2*sqrt(-(4*c^2 - 4*d^2 + 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))*(cosh(b*x + a) + sinh(b*x + a))) - I*dilog(-1/2*sqrt(-(4*c^2 - 4*d^2 + 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))*(cosh(b*x + a) + sinh(b*x + a))) + I*dilog(1/2*sqrt(-(4*c^2 - 4*d^2 - 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))*(cosh(b*x + a) + sinh(b*x + a))) + I*dilog(-1/2*sqrt(-(4*c^2 - 4*d^2 - 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))*(cosh(b*x + a) + sinh(b*x + a))))/b","B",0
191,0,0,0,0.584925," ","integrate(arccot(c+d*tanh(b*x+a))/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{arccot}\left(d \tanh\left(b x + a\right) + c\right)}{x}, x\right)"," ",0,"integral(arccot(d*tanh(b*x + a) + c)/x, x)","F",0
192,1,290,0,0.840354," ","integrate(x^2*arccot(c+(I+c)*tanh(b*x+a)),x, algorithm=""fricas"")","\frac{i \, b^{4} x^{4} + 2 i \, b^{3} x^{3} \log\left(\frac{{\left(c e^{\left(2 \, b x + 2 \, a\right)} - i\right)} e^{\left(-2 \, b x - 2 \, a\right)}}{c + i}\right) - 6 i \, b^{2} x^{2} {\rm Li}_2\left(\frac{1}{2} \, \sqrt{-4 i \, c} e^{\left(b x + a\right)}\right) - 6 i \, b^{2} x^{2} {\rm Li}_2\left(-\frac{1}{2} \, \sqrt{-4 i \, c} e^{\left(b x + a\right)}\right) - i \, a^{4} + 2 i \, a^{3} \log\left(\frac{2 \, c e^{\left(b x + a\right)} + i \, \sqrt{-4 i \, c}}{2 \, c}\right) + 2 i \, a^{3} \log\left(\frac{2 \, c e^{\left(b x + a\right)} - i \, \sqrt{-4 i \, c}}{2 \, c}\right) + 12 i \, b x {\rm polylog}\left(3, \frac{1}{2} \, \sqrt{-4 i \, c} e^{\left(b x + a\right)}\right) + 12 i \, b x {\rm polylog}\left(3, -\frac{1}{2} \, \sqrt{-4 i \, c} e^{\left(b x + a\right)}\right) + {\left(-2 i \, b^{3} x^{3} - 2 i \, a^{3}\right)} \log\left(\frac{1}{2} \, \sqrt{-4 i \, c} e^{\left(b x + a\right)} + 1\right) + {\left(-2 i \, b^{3} x^{3} - 2 i \, a^{3}\right)} \log\left(-\frac{1}{2} \, \sqrt{-4 i \, c} e^{\left(b x + a\right)} + 1\right) - 12 i \, {\rm polylog}\left(4, \frac{1}{2} \, \sqrt{-4 i \, c} e^{\left(b x + a\right)}\right) - 12 i \, {\rm polylog}\left(4, -\frac{1}{2} \, \sqrt{-4 i \, c} e^{\left(b x + a\right)}\right)}{12 \, b^{3}}"," ",0,"1/12*(I*b^4*x^4 + 2*I*b^3*x^3*log((c*e^(2*b*x + 2*a) - I)*e^(-2*b*x - 2*a)/(c + I)) - 6*I*b^2*x^2*dilog(1/2*sqrt(-4*I*c)*e^(b*x + a)) - 6*I*b^2*x^2*dilog(-1/2*sqrt(-4*I*c)*e^(b*x + a)) - I*a^4 + 2*I*a^3*log(1/2*(2*c*e^(b*x + a) + I*sqrt(-4*I*c))/c) + 2*I*a^3*log(1/2*(2*c*e^(b*x + a) - I*sqrt(-4*I*c))/c) + 12*I*b*x*polylog(3, 1/2*sqrt(-4*I*c)*e^(b*x + a)) + 12*I*b*x*polylog(3, -1/2*sqrt(-4*I*c)*e^(b*x + a)) + (-2*I*b^3*x^3 - 2*I*a^3)*log(1/2*sqrt(-4*I*c)*e^(b*x + a) + 1) + (-2*I*b^3*x^3 - 2*I*a^3)*log(-1/2*sqrt(-4*I*c)*e^(b*x + a) + 1) - 12*I*polylog(4, 1/2*sqrt(-4*I*c)*e^(b*x + a)) - 12*I*polylog(4, -1/2*sqrt(-4*I*c)*e^(b*x + a)))/b^3","C",0
193,1,244,0,0.425104," ","integrate(x*arccot(c+(I+c)*tanh(b*x+a)),x, algorithm=""fricas"")","\frac{2 i \, b^{3} x^{3} + 3 i \, b^{2} x^{2} \log\left(\frac{{\left(c e^{\left(2 \, b x + 2 \, a\right)} - i\right)} e^{\left(-2 \, b x - 2 \, a\right)}}{c + i}\right) + 2 i \, a^{3} - 6 i \, b x {\rm Li}_2\left(\frac{1}{2} \, \sqrt{-4 i \, c} e^{\left(b x + a\right)}\right) - 6 i \, b x {\rm Li}_2\left(-\frac{1}{2} \, \sqrt{-4 i \, c} e^{\left(b x + a\right)}\right) - 3 i \, a^{2} \log\left(\frac{2 \, c e^{\left(b x + a\right)} + i \, \sqrt{-4 i \, c}}{2 \, c}\right) - 3 i \, a^{2} \log\left(\frac{2 \, c e^{\left(b x + a\right)} - i \, \sqrt{-4 i \, c}}{2 \, c}\right) + {\left(-3 i \, b^{2} x^{2} + 3 i \, a^{2}\right)} \log\left(\frac{1}{2} \, \sqrt{-4 i \, c} e^{\left(b x + a\right)} + 1\right) + {\left(-3 i \, b^{2} x^{2} + 3 i \, a^{2}\right)} \log\left(-\frac{1}{2} \, \sqrt{-4 i \, c} e^{\left(b x + a\right)} + 1\right) + 6 i \, {\rm polylog}\left(3, \frac{1}{2} \, \sqrt{-4 i \, c} e^{\left(b x + a\right)}\right) + 6 i \, {\rm polylog}\left(3, -\frac{1}{2} \, \sqrt{-4 i \, c} e^{\left(b x + a\right)}\right)}{12 \, b^{2}}"," ",0,"1/12*(2*I*b^3*x^3 + 3*I*b^2*x^2*log((c*e^(2*b*x + 2*a) - I)*e^(-2*b*x - 2*a)/(c + I)) + 2*I*a^3 - 6*I*b*x*dilog(1/2*sqrt(-4*I*c)*e^(b*x + a)) - 6*I*b*x*dilog(-1/2*sqrt(-4*I*c)*e^(b*x + a)) - 3*I*a^2*log(1/2*(2*c*e^(b*x + a) + I*sqrt(-4*I*c))/c) - 3*I*a^2*log(1/2*(2*c*e^(b*x + a) - I*sqrt(-4*I*c))/c) + (-3*I*b^2*x^2 + 3*I*a^2)*log(1/2*sqrt(-4*I*c)*e^(b*x + a) + 1) + (-3*I*b^2*x^2 + 3*I*a^2)*log(-1/2*sqrt(-4*I*c)*e^(b*x + a) + 1) + 6*I*polylog(3, 1/2*sqrt(-4*I*c)*e^(b*x + a)) + 6*I*polylog(3, -1/2*sqrt(-4*I*c)*e^(b*x + a)))/b^2","C",0
194,1,186,0,0.581706," ","integrate(arccot(c+(I+c)*tanh(b*x+a)),x, algorithm=""fricas"")","\frac{i \, b^{2} x^{2} + i \, b x \log\left(\frac{{\left(c e^{\left(2 \, b x + 2 \, a\right)} - i\right)} e^{\left(-2 \, b x - 2 \, a\right)}}{c + i}\right) - i \, a^{2} + {\left(-i \, b x - i \, a\right)} \log\left(\frac{1}{2} \, \sqrt{-4 i \, c} e^{\left(b x + a\right)} + 1\right) + {\left(-i \, b x - i \, a\right)} \log\left(-\frac{1}{2} \, \sqrt{-4 i \, c} e^{\left(b x + a\right)} + 1\right) + i \, a \log\left(\frac{2 \, c e^{\left(b x + a\right)} + i \, \sqrt{-4 i \, c}}{2 \, c}\right) + i \, a \log\left(\frac{2 \, c e^{\left(b x + a\right)} - i \, \sqrt{-4 i \, c}}{2 \, c}\right) - i \, {\rm Li}_2\left(\frac{1}{2} \, \sqrt{-4 i \, c} e^{\left(b x + a\right)}\right) - i \, {\rm Li}_2\left(-\frac{1}{2} \, \sqrt{-4 i \, c} e^{\left(b x + a\right)}\right)}{2 \, b}"," ",0,"1/2*(I*b^2*x^2 + I*b*x*log((c*e^(2*b*x + 2*a) - I)*e^(-2*b*x - 2*a)/(c + I)) - I*a^2 + (-I*b*x - I*a)*log(1/2*sqrt(-4*I*c)*e^(b*x + a) + 1) + (-I*b*x - I*a)*log(-1/2*sqrt(-4*I*c)*e^(b*x + a) + 1) + I*a*log(1/2*(2*c*e^(b*x + a) + I*sqrt(-4*I*c))/c) + I*a*log(1/2*(2*c*e^(b*x + a) - I*sqrt(-4*I*c))/c) - I*dilog(1/2*sqrt(-4*I*c)*e^(b*x + a)) - I*dilog(-1/2*sqrt(-4*I*c)*e^(b*x + a)))/b","B",0
195,0,0,0,0.647890," ","integrate(arccot(c+(I+c)*tanh(b*x+a))/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{i \, \log\left(\frac{{\left(c e^{\left(2 \, b x + 2 \, a\right)} - i\right)} e^{\left(-2 \, b x - 2 \, a\right)}}{c + i}\right)}{2 \, x}, x\right)"," ",0,"integral(1/2*I*log((c*e^(2*b*x + 2*a) - I)*e^(-2*b*x - 2*a)/(c + I))/x, x)","F",0
196,1,290,0,0.654264," ","integrate(x^2*arccot(c-(I-c)*tanh(b*x+a)),x, algorithm=""fricas"")","\frac{-i \, b^{4} x^{4} + 2 i \, b^{3} x^{3} \log\left(\frac{{\left(c - i\right)} e^{\left(2 \, b x + 2 \, a\right)}}{c e^{\left(2 \, b x + 2 \, a\right)} + i}\right) + 6 i \, b^{2} x^{2} {\rm Li}_2\left(\frac{1}{2} \, \sqrt{4 i \, c} e^{\left(b x + a\right)}\right) + 6 i \, b^{2} x^{2} {\rm Li}_2\left(-\frac{1}{2} \, \sqrt{4 i \, c} e^{\left(b x + a\right)}\right) + i \, a^{4} - 2 i \, a^{3} \log\left(\frac{2 \, c e^{\left(b x + a\right)} + i \, \sqrt{4 i \, c}}{2 \, c}\right) - 2 i \, a^{3} \log\left(\frac{2 \, c e^{\left(b x + a\right)} - i \, \sqrt{4 i \, c}}{2 \, c}\right) - 12 i \, b x {\rm polylog}\left(3, \frac{1}{2} \, \sqrt{4 i \, c} e^{\left(b x + a\right)}\right) - 12 i \, b x {\rm polylog}\left(3, -\frac{1}{2} \, \sqrt{4 i \, c} e^{\left(b x + a\right)}\right) + {\left(2 i \, b^{3} x^{3} + 2 i \, a^{3}\right)} \log\left(\frac{1}{2} \, \sqrt{4 i \, c} e^{\left(b x + a\right)} + 1\right) + {\left(2 i \, b^{3} x^{3} + 2 i \, a^{3}\right)} \log\left(-\frac{1}{2} \, \sqrt{4 i \, c} e^{\left(b x + a\right)} + 1\right) + 12 i \, {\rm polylog}\left(4, \frac{1}{2} \, \sqrt{4 i \, c} e^{\left(b x + a\right)}\right) + 12 i \, {\rm polylog}\left(4, -\frac{1}{2} \, \sqrt{4 i \, c} e^{\left(b x + a\right)}\right)}{12 \, b^{3}}"," ",0,"1/12*(-I*b^4*x^4 + 2*I*b^3*x^3*log((c - I)*e^(2*b*x + 2*a)/(c*e^(2*b*x + 2*a) + I)) + 6*I*b^2*x^2*dilog(1/2*sqrt(4*I*c)*e^(b*x + a)) + 6*I*b^2*x^2*dilog(-1/2*sqrt(4*I*c)*e^(b*x + a)) + I*a^4 - 2*I*a^3*log(1/2*(2*c*e^(b*x + a) + I*sqrt(4*I*c))/c) - 2*I*a^3*log(1/2*(2*c*e^(b*x + a) - I*sqrt(4*I*c))/c) - 12*I*b*x*polylog(3, 1/2*sqrt(4*I*c)*e^(b*x + a)) - 12*I*b*x*polylog(3, -1/2*sqrt(4*I*c)*e^(b*x + a)) + (2*I*b^3*x^3 + 2*I*a^3)*log(1/2*sqrt(4*I*c)*e^(b*x + a) + 1) + (2*I*b^3*x^3 + 2*I*a^3)*log(-1/2*sqrt(4*I*c)*e^(b*x + a) + 1) + 12*I*polylog(4, 1/2*sqrt(4*I*c)*e^(b*x + a)) + 12*I*polylog(4, -1/2*sqrt(4*I*c)*e^(b*x + a)))/b^3","C",0
197,1,244,0,0.657851," ","integrate(x*arccot(c-(I-c)*tanh(b*x+a)),x, algorithm=""fricas"")","\frac{-2 i \, b^{3} x^{3} + 3 i \, b^{2} x^{2} \log\left(\frac{{\left(c - i\right)} e^{\left(2 \, b x + 2 \, a\right)}}{c e^{\left(2 \, b x + 2 \, a\right)} + i}\right) - 2 i \, a^{3} + 6 i \, b x {\rm Li}_2\left(\frac{1}{2} \, \sqrt{4 i \, c} e^{\left(b x + a\right)}\right) + 6 i \, b x {\rm Li}_2\left(-\frac{1}{2} \, \sqrt{4 i \, c} e^{\left(b x + a\right)}\right) + 3 i \, a^{2} \log\left(\frac{2 \, c e^{\left(b x + a\right)} + i \, \sqrt{4 i \, c}}{2 \, c}\right) + 3 i \, a^{2} \log\left(\frac{2 \, c e^{\left(b x + a\right)} - i \, \sqrt{4 i \, c}}{2 \, c}\right) + {\left(3 i \, b^{2} x^{2} - 3 i \, a^{2}\right)} \log\left(\frac{1}{2} \, \sqrt{4 i \, c} e^{\left(b x + a\right)} + 1\right) + {\left(3 i \, b^{2} x^{2} - 3 i \, a^{2}\right)} \log\left(-\frac{1}{2} \, \sqrt{4 i \, c} e^{\left(b x + a\right)} + 1\right) - 6 i \, {\rm polylog}\left(3, \frac{1}{2} \, \sqrt{4 i \, c} e^{\left(b x + a\right)}\right) - 6 i \, {\rm polylog}\left(3, -\frac{1}{2} \, \sqrt{4 i \, c} e^{\left(b x + a\right)}\right)}{12 \, b^{2}}"," ",0,"1/12*(-2*I*b^3*x^3 + 3*I*b^2*x^2*log((c - I)*e^(2*b*x + 2*a)/(c*e^(2*b*x + 2*a) + I)) - 2*I*a^3 + 6*I*b*x*dilog(1/2*sqrt(4*I*c)*e^(b*x + a)) + 6*I*b*x*dilog(-1/2*sqrt(4*I*c)*e^(b*x + a)) + 3*I*a^2*log(1/2*(2*c*e^(b*x + a) + I*sqrt(4*I*c))/c) + 3*I*a^2*log(1/2*(2*c*e^(b*x + a) - I*sqrt(4*I*c))/c) + (3*I*b^2*x^2 - 3*I*a^2)*log(1/2*sqrt(4*I*c)*e^(b*x + a) + 1) + (3*I*b^2*x^2 - 3*I*a^2)*log(-1/2*sqrt(4*I*c)*e^(b*x + a) + 1) - 6*I*polylog(3, 1/2*sqrt(4*I*c)*e^(b*x + a)) - 6*I*polylog(3, -1/2*sqrt(4*I*c)*e^(b*x + a)))/b^2","C",0
198,1,186,0,0.738673," ","integrate(arccot(c-(I-c)*tanh(b*x+a)),x, algorithm=""fricas"")","\frac{-i \, b^{2} x^{2} + i \, b x \log\left(\frac{{\left(c - i\right)} e^{\left(2 \, b x + 2 \, a\right)}}{c e^{\left(2 \, b x + 2 \, a\right)} + i}\right) + i \, a^{2} + {\left(i \, b x + i \, a\right)} \log\left(\frac{1}{2} \, \sqrt{4 i \, c} e^{\left(b x + a\right)} + 1\right) + {\left(i \, b x + i \, a\right)} \log\left(-\frac{1}{2} \, \sqrt{4 i \, c} e^{\left(b x + a\right)} + 1\right) - i \, a \log\left(\frac{2 \, c e^{\left(b x + a\right)} + i \, \sqrt{4 i \, c}}{2 \, c}\right) - i \, a \log\left(\frac{2 \, c e^{\left(b x + a\right)} - i \, \sqrt{4 i \, c}}{2 \, c}\right) + i \, {\rm Li}_2\left(\frac{1}{2} \, \sqrt{4 i \, c} e^{\left(b x + a\right)}\right) + i \, {\rm Li}_2\left(-\frac{1}{2} \, \sqrt{4 i \, c} e^{\left(b x + a\right)}\right)}{2 \, b}"," ",0,"1/2*(-I*b^2*x^2 + I*b*x*log((c - I)*e^(2*b*x + 2*a)/(c*e^(2*b*x + 2*a) + I)) + I*a^2 + (I*b*x + I*a)*log(1/2*sqrt(4*I*c)*e^(b*x + a) + 1) + (I*b*x + I*a)*log(-1/2*sqrt(4*I*c)*e^(b*x + a) + 1) - I*a*log(1/2*(2*c*e^(b*x + a) + I*sqrt(4*I*c))/c) - I*a*log(1/2*(2*c*e^(b*x + a) - I*sqrt(4*I*c))/c) + I*dilog(1/2*sqrt(4*I*c)*e^(b*x + a)) + I*dilog(-1/2*sqrt(4*I*c)*e^(b*x + a)))/b","B",0
199,0,0,0,0.744798," ","integrate(arccot(c-(I-c)*tanh(b*x+a))/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{i \, \log\left(\frac{{\left(c - i\right)} e^{\left(2 \, b x + 2 \, a\right)}}{c e^{\left(2 \, b x + 2 \, a\right)} + i}\right)}{2 \, x}, x\right)"," ",0,"integral(1/2*I*log((c - I)*e^(2*b*x + 2*a)/(c*e^(2*b*x + 2*a) + I))/x, x)","F",0
200,1,1448,0,0.753302," ","integrate((f*x+e)^3*arccot(coth(b*x+a)),x, algorithm=""fricas"")","\frac{24 i \, f^{3} {\rm polylog}\left(5, \frac{1}{2} \, \sqrt{4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + 24 i \, f^{3} {\rm polylog}\left(5, -\frac{1}{2} \, \sqrt{4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - 24 i \, f^{3} {\rm polylog}\left(5, \frac{1}{2} \, \sqrt{-4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - 24 i \, f^{3} {\rm polylog}\left(5, -\frac{1}{2} \, \sqrt{-4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\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\right)} \arctan\left(\frac{\sinh\left(b x + a\right)}{\cosh\left(b x + 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(\frac{1}{2} \, \sqrt{4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\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(-\frac{1}{2} \, \sqrt{4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\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(\frac{1}{2} \, \sqrt{-4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\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(-\frac{1}{2} \, \sqrt{-4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + {\left(-i \, b^{4} f^{3} x^{4} - 4 i \, b^{4} e f^{2} x^{3} - 6 i \, b^{4} e^{2} f x^{2} - 4 i \, b^{4} e^{3} x - 4 i \, a b^{3} e^{3} + 6 i \, a^{2} b^{2} e^{2} f - 4 i \, a^{3} b e f^{2} + i \, a^{4} f^{3}\right)} \log\left(\frac{1}{2} \, \sqrt{4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) + {\left(-i \, b^{4} f^{3} x^{4} - 4 i \, b^{4} e f^{2} x^{3} - 6 i \, b^{4} e^{2} f x^{2} - 4 i \, b^{4} e^{3} x - 4 i \, a b^{3} e^{3} + 6 i \, a^{2} b^{2} e^{2} f - 4 i \, a^{3} b e f^{2} + i \, a^{4} f^{3}\right)} \log\left(-\frac{1}{2} \, \sqrt{4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) + {\left(i \, b^{4} f^{3} x^{4} + 4 i \, b^{4} e f^{2} x^{3} + 6 i \, b^{4} e^{2} f x^{2} + 4 i \, b^{4} e^{3} x + 4 i \, a b^{3} e^{3} - 6 i \, a^{2} b^{2} e^{2} f + 4 i \, a^{3} b e f^{2} - i \, a^{4} f^{3}\right)} \log\left(\frac{1}{2} \, \sqrt{-4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) + {\left(i \, b^{4} f^{3} x^{4} + 4 i \, b^{4} e f^{2} x^{3} + 6 i \, b^{4} e^{2} f x^{2} + 4 i \, b^{4} e^{3} x + 4 i \, a b^{3} e^{3} - 6 i \, a^{2} b^{2} e^{2} f + 4 i \, a^{3} b e f^{2} - i \, a^{4} f^{3}\right)} \log\left(-\frac{1}{2} \, \sqrt{-4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) + {\left(4 i \, a b^{3} e^{3} - 6 i \, a^{2} b^{2} e^{2} f + 4 i \, a^{3} b e f^{2} - i \, a^{4} f^{3}\right)} \log\left(i \, \sqrt{4 i} + 2 \, \cosh\left(b x + a\right) + 2 \, \sinh\left(b x + a\right)\right) + {\left(4 i \, a b^{3} e^{3} - 6 i \, a^{2} b^{2} e^{2} f + 4 i \, a^{3} b e f^{2} - i \, a^{4} f^{3}\right)} \log\left(-i \, \sqrt{4 i} + 2 \, \cosh\left(b x + a\right) + 2 \, \sinh\left(b x + a\right)\right) + {\left(-4 i \, a b^{3} e^{3} + 6 i \, a^{2} b^{2} e^{2} f - 4 i \, a^{3} b e f^{2} + i \, a^{4} f^{3}\right)} \log\left(i \, \sqrt{-4 i} + 2 \, \cosh\left(b x + a\right) + 2 \, \sinh\left(b x + a\right)\right) + {\left(-4 i \, a b^{3} e^{3} + 6 i \, a^{2} b^{2} e^{2} f - 4 i \, a^{3} b e f^{2} + i \, a^{4} f^{3}\right)} \log\left(-i \, \sqrt{-4 i} + 2 \, \cosh\left(b x + a\right) + 2 \, \sinh\left(b x + a\right)\right) + {\left(-24 i \, b f^{3} x - 24 i \, b e f^{2}\right)} {\rm polylog}\left(4, \frac{1}{2} \, \sqrt{4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + {\left(-24 i \, b f^{3} x - 24 i \, b e f^{2}\right)} {\rm polylog}\left(4, -\frac{1}{2} \, \sqrt{4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + {\left(24 i \, b f^{3} x + 24 i \, b e f^{2}\right)} {\rm polylog}\left(4, \frac{1}{2} \, \sqrt{-4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + {\left(24 i \, b f^{3} x + 24 i \, b e f^{2}\right)} {\rm polylog}\left(4, -\frac{1}{2} \, \sqrt{-4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + {\left(12 i \, b^{2} f^{3} x^{2} + 24 i \, b^{2} e f^{2} x + 12 i \, b^{2} e^{2} f\right)} {\rm polylog}\left(3, \frac{1}{2} \, \sqrt{4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + {\left(12 i \, b^{2} f^{3} x^{2} + 24 i \, b^{2} e f^{2} x + 12 i \, b^{2} e^{2} f\right)} {\rm polylog}\left(3, -\frac{1}{2} \, \sqrt{4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + {\left(-12 i \, b^{2} f^{3} x^{2} - 24 i \, b^{2} e f^{2} x - 12 i \, b^{2} e^{2} f\right)} {\rm polylog}\left(3, \frac{1}{2} \, \sqrt{-4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + {\left(-12 i \, b^{2} f^{3} x^{2} - 24 i \, b^{2} e f^{2} x - 12 i \, b^{2} e^{2} f\right)} {\rm polylog}\left(3, -\frac{1}{2} \, \sqrt{-4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right)}{8 \, b^{4}}"," ",0,"1/8*(24*I*f^3*polylog(5, 1/2*sqrt(4*I)*(cosh(b*x + a) + sinh(b*x + a))) + 24*I*f^3*polylog(5, -1/2*sqrt(4*I)*(cosh(b*x + a) + sinh(b*x + a))) - 24*I*f^3*polylog(5, 1/2*sqrt(-4*I)*(cosh(b*x + a) + sinh(b*x + a))) - 24*I*f^3*polylog(5, -1/2*sqrt(-4*I)*(cosh(b*x + a) + sinh(b*x + a))) + 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)*arctan(sinh(b*x + a)/cosh(b*x + 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(1/2*sqrt(4*I)*(cosh(b*x + a) + sinh(b*x + 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(-1/2*sqrt(4*I)*(cosh(b*x + a) + sinh(b*x + 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(1/2*sqrt(-4*I)*(cosh(b*x + a) + sinh(b*x + 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(-1/2*sqrt(-4*I)*(cosh(b*x + a) + sinh(b*x + a))) + (-I*b^4*f^3*x^4 - 4*I*b^4*e*f^2*x^3 - 6*I*b^4*e^2*f*x^2 - 4*I*b^4*e^3*x - 4*I*a*b^3*e^3 + 6*I*a^2*b^2*e^2*f - 4*I*a^3*b*e*f^2 + I*a^4*f^3)*log(1/2*sqrt(4*I)*(cosh(b*x + a) + sinh(b*x + a)) + 1) + (-I*b^4*f^3*x^4 - 4*I*b^4*e*f^2*x^3 - 6*I*b^4*e^2*f*x^2 - 4*I*b^4*e^3*x - 4*I*a*b^3*e^3 + 6*I*a^2*b^2*e^2*f - 4*I*a^3*b*e*f^2 + I*a^4*f^3)*log(-1/2*sqrt(4*I)*(cosh(b*x + a) + sinh(b*x + a)) + 1) + (I*b^4*f^3*x^4 + 4*I*b^4*e*f^2*x^3 + 6*I*b^4*e^2*f*x^2 + 4*I*b^4*e^3*x + 4*I*a*b^3*e^3 - 6*I*a^2*b^2*e^2*f + 4*I*a^3*b*e*f^2 - I*a^4*f^3)*log(1/2*sqrt(-4*I)*(cosh(b*x + a) + sinh(b*x + a)) + 1) + (I*b^4*f^3*x^4 + 4*I*b^4*e*f^2*x^3 + 6*I*b^4*e^2*f*x^2 + 4*I*b^4*e^3*x + 4*I*a*b^3*e^3 - 6*I*a^2*b^2*e^2*f + 4*I*a^3*b*e*f^2 - I*a^4*f^3)*log(-1/2*sqrt(-4*I)*(cosh(b*x + a) + sinh(b*x + a)) + 1) + (4*I*a*b^3*e^3 - 6*I*a^2*b^2*e^2*f + 4*I*a^3*b*e*f^2 - I*a^4*f^3)*log(I*sqrt(4*I) + 2*cosh(b*x + a) + 2*sinh(b*x + a)) + (4*I*a*b^3*e^3 - 6*I*a^2*b^2*e^2*f + 4*I*a^3*b*e*f^2 - I*a^4*f^3)*log(-I*sqrt(4*I) + 2*cosh(b*x + a) + 2*sinh(b*x + a)) + (-4*I*a*b^3*e^3 + 6*I*a^2*b^2*e^2*f - 4*I*a^3*b*e*f^2 + I*a^4*f^3)*log(I*sqrt(-4*I) + 2*cosh(b*x + a) + 2*sinh(b*x + a)) + (-4*I*a*b^3*e^3 + 6*I*a^2*b^2*e^2*f - 4*I*a^3*b*e*f^2 + I*a^4*f^3)*log(-I*sqrt(-4*I) + 2*cosh(b*x + a) + 2*sinh(b*x + a)) + (-24*I*b*f^3*x - 24*I*b*e*f^2)*polylog(4, 1/2*sqrt(4*I)*(cosh(b*x + a) + sinh(b*x + a))) + (-24*I*b*f^3*x - 24*I*b*e*f^2)*polylog(4, -1/2*sqrt(4*I)*(cosh(b*x + a) + sinh(b*x + a))) + (24*I*b*f^3*x + 24*I*b*e*f^2)*polylog(4, 1/2*sqrt(-4*I)*(cosh(b*x + a) + sinh(b*x + a))) + (24*I*b*f^3*x + 24*I*b*e*f^2)*polylog(4, -1/2*sqrt(-4*I)*(cosh(b*x + a) + sinh(b*x + a))) + (12*I*b^2*f^3*x^2 + 24*I*b^2*e*f^2*x + 12*I*b^2*e^2*f)*polylog(3, 1/2*sqrt(4*I)*(cosh(b*x + a) + sinh(b*x + a))) + (12*I*b^2*f^3*x^2 + 24*I*b^2*e*f^2*x + 12*I*b^2*e^2*f)*polylog(3, -1/2*sqrt(4*I)*(cosh(b*x + a) + sinh(b*x + a))) + (-12*I*b^2*f^3*x^2 - 24*I*b^2*e*f^2*x - 12*I*b^2*e^2*f)*polylog(3, 1/2*sqrt(-4*I)*(cosh(b*x + a) + sinh(b*x + a))) + (-12*I*b^2*f^3*x^2 - 24*I*b^2*e*f^2*x - 12*I*b^2*e^2*f)*polylog(3, -1/2*sqrt(-4*I)*(cosh(b*x + a) + sinh(b*x + a))))/b^4","C",0
201,1,994,0,0.837007," ","integrate((f*x+e)^2*arccot(coth(b*x+a)),x, algorithm=""fricas"")","\frac{-6 i \, f^{2} {\rm polylog}\left(4, \frac{1}{2} \, \sqrt{4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - 6 i \, f^{2} {\rm polylog}\left(4, -\frac{1}{2} \, \sqrt{4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + 6 i \, f^{2} {\rm polylog}\left(4, \frac{1}{2} \, \sqrt{-4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + 6 i \, f^{2} {\rm polylog}\left(4, -\frac{1}{2} \, \sqrt{-4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + 2 \, {\left(b^{3} f^{2} x^{3} + 3 \, b^{3} e f x^{2} + 3 \, b^{3} e^{2} x\right)} \arctan\left(\frac{\sinh\left(b x + a\right)}{\cosh\left(b x + a\right)}\right) + {\left(-3 i \, b^{2} f^{2} x^{2} - 6 i \, b^{2} e f x - 3 i \, b^{2} e^{2}\right)} {\rm Li}_2\left(\frac{1}{2} \, \sqrt{4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + {\left(-3 i \, b^{2} f^{2} x^{2} - 6 i \, b^{2} e f x - 3 i \, b^{2} e^{2}\right)} {\rm Li}_2\left(-\frac{1}{2} \, \sqrt{4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + {\left(3 i \, b^{2} f^{2} x^{2} + 6 i \, b^{2} e f x + 3 i \, b^{2} e^{2}\right)} {\rm Li}_2\left(\frac{1}{2} \, \sqrt{-4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + {\left(3 i \, b^{2} f^{2} x^{2} + 6 i \, b^{2} e f x + 3 i \, b^{2} e^{2}\right)} {\rm Li}_2\left(-\frac{1}{2} \, \sqrt{-4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + {\left(-i \, b^{3} f^{2} x^{3} - 3 i \, b^{3} e f x^{2} - 3 i \, b^{3} e^{2} x - 3 i \, a b^{2} e^{2} + 3 i \, a^{2} b e f - i \, a^{3} f^{2}\right)} \log\left(\frac{1}{2} \, \sqrt{4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) + {\left(-i \, b^{3} f^{2} x^{3} - 3 i \, b^{3} e f x^{2} - 3 i \, b^{3} e^{2} x - 3 i \, a b^{2} e^{2} + 3 i \, a^{2} b e f - i \, a^{3} f^{2}\right)} \log\left(-\frac{1}{2} \, \sqrt{4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) + {\left(i \, b^{3} f^{2} x^{3} + 3 i \, b^{3} e f x^{2} + 3 i \, b^{3} e^{2} x + 3 i \, a b^{2} e^{2} - 3 i \, a^{2} b e f + i \, a^{3} f^{2}\right)} \log\left(\frac{1}{2} \, \sqrt{-4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) + {\left(i \, b^{3} f^{2} x^{3} + 3 i \, b^{3} e f x^{2} + 3 i \, b^{3} e^{2} x + 3 i \, a b^{2} e^{2} - 3 i \, a^{2} b e f + i \, a^{3} f^{2}\right)} \log\left(-\frac{1}{2} \, \sqrt{-4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) + {\left(3 i \, a b^{2} e^{2} - 3 i \, a^{2} b e f + i \, a^{3} f^{2}\right)} \log\left(i \, \sqrt{4 i} + 2 \, \cosh\left(b x + a\right) + 2 \, \sinh\left(b x + a\right)\right) + {\left(3 i \, a b^{2} e^{2} - 3 i \, a^{2} b e f + i \, a^{3} f^{2}\right)} \log\left(-i \, \sqrt{4 i} + 2 \, \cosh\left(b x + a\right) + 2 \, \sinh\left(b x + a\right)\right) + {\left(-3 i \, a b^{2} e^{2} + 3 i \, a^{2} b e f - i \, a^{3} f^{2}\right)} \log\left(i \, \sqrt{-4 i} + 2 \, \cosh\left(b x + a\right) + 2 \, \sinh\left(b x + a\right)\right) + {\left(-3 i \, a b^{2} e^{2} + 3 i \, a^{2} b e f - i \, a^{3} f^{2}\right)} \log\left(-i \, \sqrt{-4 i} + 2 \, \cosh\left(b x + a\right) + 2 \, \sinh\left(b x + a\right)\right) + {\left(6 i \, b f^{2} x + 6 i \, b e f\right)} {\rm polylog}\left(3, \frac{1}{2} \, \sqrt{4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + {\left(6 i \, b f^{2} x + 6 i \, b e f\right)} {\rm polylog}\left(3, -\frac{1}{2} \, \sqrt{4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + {\left(-6 i \, b f^{2} x - 6 i \, b e f\right)} {\rm polylog}\left(3, \frac{1}{2} \, \sqrt{-4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + {\left(-6 i \, b f^{2} x - 6 i \, b e f\right)} {\rm polylog}\left(3, -\frac{1}{2} \, \sqrt{-4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right)}{6 \, b^{3}}"," ",0,"1/6*(-6*I*f^2*polylog(4, 1/2*sqrt(4*I)*(cosh(b*x + a) + sinh(b*x + a))) - 6*I*f^2*polylog(4, -1/2*sqrt(4*I)*(cosh(b*x + a) + sinh(b*x + a))) + 6*I*f^2*polylog(4, 1/2*sqrt(-4*I)*(cosh(b*x + a) + sinh(b*x + a))) + 6*I*f^2*polylog(4, -1/2*sqrt(-4*I)*(cosh(b*x + a) + sinh(b*x + a))) + 2*(b^3*f^2*x^3 + 3*b^3*e*f*x^2 + 3*b^3*e^2*x)*arctan(sinh(b*x + a)/cosh(b*x + a)) + (-3*I*b^2*f^2*x^2 - 6*I*b^2*e*f*x - 3*I*b^2*e^2)*dilog(1/2*sqrt(4*I)*(cosh(b*x + a) + sinh(b*x + a))) + (-3*I*b^2*f^2*x^2 - 6*I*b^2*e*f*x - 3*I*b^2*e^2)*dilog(-1/2*sqrt(4*I)*(cosh(b*x + a) + sinh(b*x + a))) + (3*I*b^2*f^2*x^2 + 6*I*b^2*e*f*x + 3*I*b^2*e^2)*dilog(1/2*sqrt(-4*I)*(cosh(b*x + a) + sinh(b*x + a))) + (3*I*b^2*f^2*x^2 + 6*I*b^2*e*f*x + 3*I*b^2*e^2)*dilog(-1/2*sqrt(-4*I)*(cosh(b*x + a) + sinh(b*x + a))) + (-I*b^3*f^2*x^3 - 3*I*b^3*e*f*x^2 - 3*I*b^3*e^2*x - 3*I*a*b^2*e^2 + 3*I*a^2*b*e*f - I*a^3*f^2)*log(1/2*sqrt(4*I)*(cosh(b*x + a) + sinh(b*x + a)) + 1) + (-I*b^3*f^2*x^3 - 3*I*b^3*e*f*x^2 - 3*I*b^3*e^2*x - 3*I*a*b^2*e^2 + 3*I*a^2*b*e*f - I*a^3*f^2)*log(-1/2*sqrt(4*I)*(cosh(b*x + a) + sinh(b*x + a)) + 1) + (I*b^3*f^2*x^3 + 3*I*b^3*e*f*x^2 + 3*I*b^3*e^2*x + 3*I*a*b^2*e^2 - 3*I*a^2*b*e*f + I*a^3*f^2)*log(1/2*sqrt(-4*I)*(cosh(b*x + a) + sinh(b*x + a)) + 1) + (I*b^3*f^2*x^3 + 3*I*b^3*e*f*x^2 + 3*I*b^3*e^2*x + 3*I*a*b^2*e^2 - 3*I*a^2*b*e*f + I*a^3*f^2)*log(-1/2*sqrt(-4*I)*(cosh(b*x + a) + sinh(b*x + a)) + 1) + (3*I*a*b^2*e^2 - 3*I*a^2*b*e*f + I*a^3*f^2)*log(I*sqrt(4*I) + 2*cosh(b*x + a) + 2*sinh(b*x + a)) + (3*I*a*b^2*e^2 - 3*I*a^2*b*e*f + I*a^3*f^2)*log(-I*sqrt(4*I) + 2*cosh(b*x + a) + 2*sinh(b*x + a)) + (-3*I*a*b^2*e^2 + 3*I*a^2*b*e*f - I*a^3*f^2)*log(I*sqrt(-4*I) + 2*cosh(b*x + a) + 2*sinh(b*x + a)) + (-3*I*a*b^2*e^2 + 3*I*a^2*b*e*f - I*a^3*f^2)*log(-I*sqrt(-4*I) + 2*cosh(b*x + a) + 2*sinh(b*x + a)) + (6*I*b*f^2*x + 6*I*b*e*f)*polylog(3, 1/2*sqrt(4*I)*(cosh(b*x + a) + sinh(b*x + a))) + (6*I*b*f^2*x + 6*I*b*e*f)*polylog(3, -1/2*sqrt(4*I)*(cosh(b*x + a) + sinh(b*x + a))) + (-6*I*b*f^2*x - 6*I*b*e*f)*polylog(3, 1/2*sqrt(-4*I)*(cosh(b*x + a) + sinh(b*x + a))) + (-6*I*b*f^2*x - 6*I*b*e*f)*polylog(3, -1/2*sqrt(-4*I)*(cosh(b*x + a) + sinh(b*x + a))))/b^3","C",0
202,1,596,0,0.822245," ","integrate((f*x+e)*arccot(coth(b*x+a)),x, algorithm=""fricas"")","\frac{2 \, {\left(b^{2} f x^{2} + 2 \, b^{2} e x\right)} \arctan\left(\frac{\sinh\left(b x + a\right)}{\cosh\left(b x + a\right)}\right) + {\left(-2 i \, b f x - 2 i \, b e\right)} {\rm Li}_2\left(\frac{1}{2} \, \sqrt{4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + {\left(-2 i \, b f x - 2 i \, b e\right)} {\rm Li}_2\left(-\frac{1}{2} \, \sqrt{4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + {\left(2 i \, b f x + 2 i \, b e\right)} {\rm Li}_2\left(\frac{1}{2} \, \sqrt{-4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + {\left(2 i \, b f x + 2 i \, b e\right)} {\rm Li}_2\left(-\frac{1}{2} \, \sqrt{-4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + {\left(-i \, b^{2} f x^{2} - 2 i \, b^{2} e x - 2 i \, a b e + i \, a^{2} f\right)} \log\left(\frac{1}{2} \, \sqrt{4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) + {\left(-i \, b^{2} f x^{2} - 2 i \, b^{2} e x - 2 i \, a b e + i \, a^{2} f\right)} \log\left(-\frac{1}{2} \, \sqrt{4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) + {\left(i \, b^{2} f x^{2} + 2 i \, b^{2} e x + 2 i \, a b e - i \, a^{2} f\right)} \log\left(\frac{1}{2} \, \sqrt{-4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) + {\left(i \, b^{2} f x^{2} + 2 i \, b^{2} e x + 2 i \, a b e - i \, a^{2} f\right)} \log\left(-\frac{1}{2} \, \sqrt{-4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) + {\left(2 i \, a b e - i \, a^{2} f\right)} \log\left(i \, \sqrt{4 i} + 2 \, \cosh\left(b x + a\right) + 2 \, \sinh\left(b x + a\right)\right) + {\left(2 i \, a b e - i \, a^{2} f\right)} \log\left(-i \, \sqrt{4 i} + 2 \, \cosh\left(b x + a\right) + 2 \, \sinh\left(b x + a\right)\right) + {\left(-2 i \, a b e + i \, a^{2} f\right)} \log\left(i \, \sqrt{-4 i} + 2 \, \cosh\left(b x + a\right) + 2 \, \sinh\left(b x + a\right)\right) + {\left(-2 i \, a b e + i \, a^{2} f\right)} \log\left(-i \, \sqrt{-4 i} + 2 \, \cosh\left(b x + a\right) + 2 \, \sinh\left(b x + a\right)\right) + 2 i \, f {\rm polylog}\left(3, \frac{1}{2} \, \sqrt{4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + 2 i \, f {\rm polylog}\left(3, -\frac{1}{2} \, \sqrt{4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - 2 i \, f {\rm polylog}\left(3, \frac{1}{2} \, \sqrt{-4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - 2 i \, f {\rm polylog}\left(3, -\frac{1}{2} \, \sqrt{-4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right)}{4 \, b^{2}}"," ",0,"1/4*(2*(b^2*f*x^2 + 2*b^2*e*x)*arctan(sinh(b*x + a)/cosh(b*x + a)) + (-2*I*b*f*x - 2*I*b*e)*dilog(1/2*sqrt(4*I)*(cosh(b*x + a) + sinh(b*x + a))) + (-2*I*b*f*x - 2*I*b*e)*dilog(-1/2*sqrt(4*I)*(cosh(b*x + a) + sinh(b*x + a))) + (2*I*b*f*x + 2*I*b*e)*dilog(1/2*sqrt(-4*I)*(cosh(b*x + a) + sinh(b*x + a))) + (2*I*b*f*x + 2*I*b*e)*dilog(-1/2*sqrt(-4*I)*(cosh(b*x + a) + sinh(b*x + a))) + (-I*b^2*f*x^2 - 2*I*b^2*e*x - 2*I*a*b*e + I*a^2*f)*log(1/2*sqrt(4*I)*(cosh(b*x + a) + sinh(b*x + a)) + 1) + (-I*b^2*f*x^2 - 2*I*b^2*e*x - 2*I*a*b*e + I*a^2*f)*log(-1/2*sqrt(4*I)*(cosh(b*x + a) + sinh(b*x + a)) + 1) + (I*b^2*f*x^2 + 2*I*b^2*e*x + 2*I*a*b*e - I*a^2*f)*log(1/2*sqrt(-4*I)*(cosh(b*x + a) + sinh(b*x + a)) + 1) + (I*b^2*f*x^2 + 2*I*b^2*e*x + 2*I*a*b*e - I*a^2*f)*log(-1/2*sqrt(-4*I)*(cosh(b*x + a) + sinh(b*x + a)) + 1) + (2*I*a*b*e - I*a^2*f)*log(I*sqrt(4*I) + 2*cosh(b*x + a) + 2*sinh(b*x + a)) + (2*I*a*b*e - I*a^2*f)*log(-I*sqrt(4*I) + 2*cosh(b*x + a) + 2*sinh(b*x + a)) + (-2*I*a*b*e + I*a^2*f)*log(I*sqrt(-4*I) + 2*cosh(b*x + a) + 2*sinh(b*x + a)) + (-2*I*a*b*e + I*a^2*f)*log(-I*sqrt(-4*I) + 2*cosh(b*x + a) + 2*sinh(b*x + a)) + 2*I*f*polylog(3, 1/2*sqrt(4*I)*(cosh(b*x + a) + sinh(b*x + a))) + 2*I*f*polylog(3, -1/2*sqrt(4*I)*(cosh(b*x + a) + sinh(b*x + a))) - 2*I*f*polylog(3, 1/2*sqrt(-4*I)*(cosh(b*x + a) + sinh(b*x + a))) - 2*I*f*polylog(3, -1/2*sqrt(-4*I)*(cosh(b*x + a) + sinh(b*x + a))))/b^2","C",0
203,1,334,0,0.829064," ","integrate(arccot(coth(b*x+a)),x, algorithm=""fricas"")","\frac{2 \, b x \arctan\left(\frac{\sinh\left(b x + a\right)}{\cosh\left(b x + a\right)}\right) + {\left(-i \, b x - i \, a\right)} \log\left(\frac{1}{2} \, \sqrt{4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) + {\left(-i \, b x - i \, a\right)} \log\left(-\frac{1}{2} \, \sqrt{4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) + {\left(i \, b x + i \, a\right)} \log\left(\frac{1}{2} \, \sqrt{-4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) + {\left(i \, b x + i \, a\right)} \log\left(-\frac{1}{2} \, \sqrt{-4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) + i \, a \log\left(i \, \sqrt{4 i} + 2 \, \cosh\left(b x + a\right) + 2 \, \sinh\left(b x + a\right)\right) + i \, a \log\left(-i \, \sqrt{4 i} + 2 \, \cosh\left(b x + a\right) + 2 \, \sinh\left(b x + a\right)\right) - i \, a \log\left(i \, \sqrt{-4 i} + 2 \, \cosh\left(b x + a\right) + 2 \, \sinh\left(b x + a\right)\right) - i \, a \log\left(-i \, \sqrt{-4 i} + 2 \, \cosh\left(b x + a\right) + 2 \, \sinh\left(b x + a\right)\right) - i \, {\rm Li}_2\left(\frac{1}{2} \, \sqrt{4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - i \, {\rm Li}_2\left(-\frac{1}{2} \, \sqrt{4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + i \, {\rm Li}_2\left(\frac{1}{2} \, \sqrt{-4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + i \, {\rm Li}_2\left(-\frac{1}{2} \, \sqrt{-4 i} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right)}{2 \, b}"," ",0,"1/2*(2*b*x*arctan(sinh(b*x + a)/cosh(b*x + a)) + (-I*b*x - I*a)*log(1/2*sqrt(4*I)*(cosh(b*x + a) + sinh(b*x + a)) + 1) + (-I*b*x - I*a)*log(-1/2*sqrt(4*I)*(cosh(b*x + a) + sinh(b*x + a)) + 1) + (I*b*x + I*a)*log(1/2*sqrt(-4*I)*(cosh(b*x + a) + sinh(b*x + a)) + 1) + (I*b*x + I*a)*log(-1/2*sqrt(-4*I)*(cosh(b*x + a) + sinh(b*x + a)) + 1) + I*a*log(I*sqrt(4*I) + 2*cosh(b*x + a) + 2*sinh(b*x + a)) + I*a*log(-I*sqrt(4*I) + 2*cosh(b*x + a) + 2*sinh(b*x + a)) - I*a*log(I*sqrt(-4*I) + 2*cosh(b*x + a) + 2*sinh(b*x + a)) - I*a*log(-I*sqrt(-4*I) + 2*cosh(b*x + a) + 2*sinh(b*x + a)) - I*dilog(1/2*sqrt(4*I)*(cosh(b*x + a) + sinh(b*x + a))) - I*dilog(-1/2*sqrt(4*I)*(cosh(b*x + a) + sinh(b*x + a))) + I*dilog(1/2*sqrt(-4*I)*(cosh(b*x + a) + sinh(b*x + a))) + I*dilog(-1/2*sqrt(-4*I)*(cosh(b*x + a) + sinh(b*x + a))))/b","B",0
204,0,0,0,0.625470," ","integrate(arccot(coth(b*x+a))/(f*x+e),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{arccot}\left(\coth\left(b x + a\right)\right)}{f x + e}, x\right)"," ",0,"integral(arccot(coth(b*x + a))/(f*x + e), x)","F",0
205,1,1315,0,1.179259," ","integrate(x^2*arccot(c+d*coth(b*x+a)),x, algorithm=""fricas"")","\frac{2 \, b^{3} x^{3} \arctan\left(\frac{\sinh\left(b x + a\right)}{d \cosh\left(b x + a\right) + c \sinh\left(b x + a\right)}\right) - 3 i \, b^{2} x^{2} {\rm Li}_2\left(\frac{1}{2} \, \sqrt{\frac{4 \, c^{2} - 4 \, d^{2} + 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - 3 i \, b^{2} x^{2} {\rm Li}_2\left(-\frac{1}{2} \, \sqrt{\frac{4 \, c^{2} - 4 \, d^{2} + 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + 3 i \, b^{2} x^{2} {\rm Li}_2\left(\frac{1}{2} \, \sqrt{\frac{4 \, c^{2} - 4 \, d^{2} - 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + 3 i \, b^{2} x^{2} {\rm Li}_2\left(-\frac{1}{2} \, \sqrt{\frac{4 \, c^{2} - 4 \, d^{2} - 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + i \, a^{3} \log\left(2 \, {\left(c^{2} + 2 \, c d + d^{2} + 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(c^{2} + 2 \, c d + d^{2} + 1\right)} \sinh\left(b x + a\right) + {\left(c^{2} - d^{2} - 2 i \, d + 1\right)} \sqrt{\frac{4 \, c^{2} - 4 \, d^{2} + 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}}\right) + i \, a^{3} \log\left(2 \, {\left(c^{2} + 2 \, c d + d^{2} + 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(c^{2} + 2 \, c d + d^{2} + 1\right)} \sinh\left(b x + a\right) - {\left(c^{2} - d^{2} - 2 i \, d + 1\right)} \sqrt{\frac{4 \, c^{2} - 4 \, d^{2} + 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}}\right) - i \, a^{3} \log\left(2 \, {\left(c^{2} + 2 \, c d + d^{2} + 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(c^{2} + 2 \, c d + d^{2} + 1\right)} \sinh\left(b x + a\right) + {\left(c^{2} - d^{2} + 2 i \, d + 1\right)} \sqrt{\frac{4 \, c^{2} - 4 \, d^{2} - 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}}\right) - i \, a^{3} \log\left(2 \, {\left(c^{2} + 2 \, c d + d^{2} + 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(c^{2} + 2 \, c d + d^{2} + 1\right)} \sinh\left(b x + a\right) - {\left(c^{2} - d^{2} + 2 i \, d + 1\right)} \sqrt{\frac{4 \, c^{2} - 4 \, d^{2} - 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}}\right) + 6 i \, b x {\rm polylog}\left(3, \frac{1}{2} \, \sqrt{\frac{4 \, c^{2} - 4 \, d^{2} + 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + 6 i \, b x {\rm polylog}\left(3, -\frac{1}{2} \, \sqrt{\frac{4 \, c^{2} - 4 \, d^{2} + 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - 6 i \, b x {\rm polylog}\left(3, \frac{1}{2} \, \sqrt{\frac{4 \, c^{2} - 4 \, d^{2} - 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - 6 i \, b x {\rm polylog}\left(3, -\frac{1}{2} \, \sqrt{\frac{4 \, c^{2} - 4 \, d^{2} - 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + {\left(-i \, b^{3} x^{3} - i \, a^{3}\right)} \log\left(\frac{1}{2} \, \sqrt{\frac{4 \, c^{2} - 4 \, d^{2} + 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) + {\left(-i \, b^{3} x^{3} - i \, a^{3}\right)} \log\left(-\frac{1}{2} \, \sqrt{\frac{4 \, c^{2} - 4 \, d^{2} + 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) + {\left(i \, b^{3} x^{3} + i \, a^{3}\right)} \log\left(\frac{1}{2} \, \sqrt{\frac{4 \, c^{2} - 4 \, d^{2} - 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) + {\left(i \, b^{3} x^{3} + i \, a^{3}\right)} \log\left(-\frac{1}{2} \, \sqrt{\frac{4 \, c^{2} - 4 \, d^{2} - 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) - 6 i \, {\rm polylog}\left(4, \frac{1}{2} \, \sqrt{\frac{4 \, c^{2} - 4 \, d^{2} + 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - 6 i \, {\rm polylog}\left(4, -\frac{1}{2} \, \sqrt{\frac{4 \, c^{2} - 4 \, d^{2} + 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + 6 i \, {\rm polylog}\left(4, \frac{1}{2} \, \sqrt{\frac{4 \, c^{2} - 4 \, d^{2} - 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + 6 i \, {\rm polylog}\left(4, -\frac{1}{2} \, \sqrt{\frac{4 \, c^{2} - 4 \, d^{2} - 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right)}{6 \, b^{3}}"," ",0,"1/6*(2*b^3*x^3*arctan(sinh(b*x + a)/(d*cosh(b*x + a) + c*sinh(b*x + a))) - 3*I*b^2*x^2*dilog(1/2*sqrt((4*c^2 - 4*d^2 + 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))*(cosh(b*x + a) + sinh(b*x + a))) - 3*I*b^2*x^2*dilog(-1/2*sqrt((4*c^2 - 4*d^2 + 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))*(cosh(b*x + a) + sinh(b*x + a))) + 3*I*b^2*x^2*dilog(1/2*sqrt((4*c^2 - 4*d^2 - 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))*(cosh(b*x + a) + sinh(b*x + a))) + 3*I*b^2*x^2*dilog(-1/2*sqrt((4*c^2 - 4*d^2 - 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))*(cosh(b*x + a) + sinh(b*x + a))) + I*a^3*log(2*(c^2 + 2*c*d + d^2 + 1)*cosh(b*x + a) + 2*(c^2 + 2*c*d + d^2 + 1)*sinh(b*x + a) + (c^2 - d^2 - 2*I*d + 1)*sqrt((4*c^2 - 4*d^2 + 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))) + I*a^3*log(2*(c^2 + 2*c*d + d^2 + 1)*cosh(b*x + a) + 2*(c^2 + 2*c*d + d^2 + 1)*sinh(b*x + a) - (c^2 - d^2 - 2*I*d + 1)*sqrt((4*c^2 - 4*d^2 + 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))) - I*a^3*log(2*(c^2 + 2*c*d + d^2 + 1)*cosh(b*x + a) + 2*(c^2 + 2*c*d + d^2 + 1)*sinh(b*x + a) + (c^2 - d^2 + 2*I*d + 1)*sqrt((4*c^2 - 4*d^2 - 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))) - I*a^3*log(2*(c^2 + 2*c*d + d^2 + 1)*cosh(b*x + a) + 2*(c^2 + 2*c*d + d^2 + 1)*sinh(b*x + a) - (c^2 - d^2 + 2*I*d + 1)*sqrt((4*c^2 - 4*d^2 - 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))) + 6*I*b*x*polylog(3, 1/2*sqrt((4*c^2 - 4*d^2 + 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))*(cosh(b*x + a) + sinh(b*x + a))) + 6*I*b*x*polylog(3, -1/2*sqrt((4*c^2 - 4*d^2 + 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))*(cosh(b*x + a) + sinh(b*x + a))) - 6*I*b*x*polylog(3, 1/2*sqrt((4*c^2 - 4*d^2 - 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))*(cosh(b*x + a) + sinh(b*x + a))) - 6*I*b*x*polylog(3, -1/2*sqrt((4*c^2 - 4*d^2 - 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))*(cosh(b*x + a) + sinh(b*x + a))) + (-I*b^3*x^3 - I*a^3)*log(1/2*sqrt((4*c^2 - 4*d^2 + 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))*(cosh(b*x + a) + sinh(b*x + a)) + 1) + (-I*b^3*x^3 - I*a^3)*log(-1/2*sqrt((4*c^2 - 4*d^2 + 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))*(cosh(b*x + a) + sinh(b*x + a)) + 1) + (I*b^3*x^3 + I*a^3)*log(1/2*sqrt((4*c^2 - 4*d^2 - 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))*(cosh(b*x + a) + sinh(b*x + a)) + 1) + (I*b^3*x^3 + I*a^3)*log(-1/2*sqrt((4*c^2 - 4*d^2 - 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))*(cosh(b*x + a) + sinh(b*x + a)) + 1) - 6*I*polylog(4, 1/2*sqrt((4*c^2 - 4*d^2 + 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))*(cosh(b*x + a) + sinh(b*x + a))) - 6*I*polylog(4, -1/2*sqrt((4*c^2 - 4*d^2 + 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))*(cosh(b*x + a) + sinh(b*x + a))) + 6*I*polylog(4, 1/2*sqrt((4*c^2 - 4*d^2 - 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))*(cosh(b*x + a) + sinh(b*x + a))) + 6*I*polylog(4, -1/2*sqrt((4*c^2 - 4*d^2 - 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))*(cosh(b*x + a) + sinh(b*x + a))))/b^3","C",0
206,1,1087,0,1.082181," ","integrate(x*arccot(c+d*coth(b*x+a)),x, algorithm=""fricas"")","\frac{2 \, b^{2} x^{2} \arctan\left(\frac{\sinh\left(b x + a\right)}{d \cosh\left(b x + a\right) + c \sinh\left(b x + a\right)}\right) - 2 i \, b x {\rm Li}_2\left(\frac{1}{2} \, \sqrt{\frac{4 \, c^{2} - 4 \, d^{2} + 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - 2 i \, b x {\rm Li}_2\left(-\frac{1}{2} \, \sqrt{\frac{4 \, c^{2} - 4 \, d^{2} + 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + 2 i \, b x {\rm Li}_2\left(\frac{1}{2} \, \sqrt{\frac{4 \, c^{2} - 4 \, d^{2} - 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + 2 i \, b x {\rm Li}_2\left(-\frac{1}{2} \, \sqrt{\frac{4 \, c^{2} - 4 \, d^{2} - 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - i \, a^{2} \log\left(2 \, {\left(c^{2} + 2 \, c d + d^{2} + 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(c^{2} + 2 \, c d + d^{2} + 1\right)} \sinh\left(b x + a\right) + {\left(c^{2} - d^{2} - 2 i \, d + 1\right)} \sqrt{\frac{4 \, c^{2} - 4 \, d^{2} + 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}}\right) - i \, a^{2} \log\left(2 \, {\left(c^{2} + 2 \, c d + d^{2} + 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(c^{2} + 2 \, c d + d^{2} + 1\right)} \sinh\left(b x + a\right) - {\left(c^{2} - d^{2} - 2 i \, d + 1\right)} \sqrt{\frac{4 \, c^{2} - 4 \, d^{2} + 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}}\right) + i \, a^{2} \log\left(2 \, {\left(c^{2} + 2 \, c d + d^{2} + 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(c^{2} + 2 \, c d + d^{2} + 1\right)} \sinh\left(b x + a\right) + {\left(c^{2} - d^{2} + 2 i \, d + 1\right)} \sqrt{\frac{4 \, c^{2} - 4 \, d^{2} - 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}}\right) + i \, a^{2} \log\left(2 \, {\left(c^{2} + 2 \, c d + d^{2} + 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(c^{2} + 2 \, c d + d^{2} + 1\right)} \sinh\left(b x + a\right) - {\left(c^{2} - d^{2} + 2 i \, d + 1\right)} \sqrt{\frac{4 \, c^{2} - 4 \, d^{2} - 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}}\right) + {\left(-i \, b^{2} x^{2} + i \, a^{2}\right)} \log\left(\frac{1}{2} \, \sqrt{\frac{4 \, c^{2} - 4 \, d^{2} + 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) + {\left(-i \, b^{2} x^{2} + i \, a^{2}\right)} \log\left(-\frac{1}{2} \, \sqrt{\frac{4 \, c^{2} - 4 \, d^{2} + 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) + {\left(i \, b^{2} x^{2} - i \, a^{2}\right)} \log\left(\frac{1}{2} \, \sqrt{\frac{4 \, c^{2} - 4 \, d^{2} - 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) + {\left(i \, b^{2} x^{2} - i \, a^{2}\right)} \log\left(-\frac{1}{2} \, \sqrt{\frac{4 \, c^{2} - 4 \, d^{2} - 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) + 2 i \, {\rm polylog}\left(3, \frac{1}{2} \, \sqrt{\frac{4 \, c^{2} - 4 \, d^{2} + 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + 2 i \, {\rm polylog}\left(3, -\frac{1}{2} \, \sqrt{\frac{4 \, c^{2} - 4 \, d^{2} + 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - 2 i \, {\rm polylog}\left(3, \frac{1}{2} \, \sqrt{\frac{4 \, c^{2} - 4 \, d^{2} - 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - 2 i \, {\rm polylog}\left(3, -\frac{1}{2} \, \sqrt{\frac{4 \, c^{2} - 4 \, d^{2} - 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right)}{4 \, b^{2}}"," ",0,"1/4*(2*b^2*x^2*arctan(sinh(b*x + a)/(d*cosh(b*x + a) + c*sinh(b*x + a))) - 2*I*b*x*dilog(1/2*sqrt((4*c^2 - 4*d^2 + 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))*(cosh(b*x + a) + sinh(b*x + a))) - 2*I*b*x*dilog(-1/2*sqrt((4*c^2 - 4*d^2 + 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))*(cosh(b*x + a) + sinh(b*x + a))) + 2*I*b*x*dilog(1/2*sqrt((4*c^2 - 4*d^2 - 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))*(cosh(b*x + a) + sinh(b*x + a))) + 2*I*b*x*dilog(-1/2*sqrt((4*c^2 - 4*d^2 - 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))*(cosh(b*x + a) + sinh(b*x + a))) - I*a^2*log(2*(c^2 + 2*c*d + d^2 + 1)*cosh(b*x + a) + 2*(c^2 + 2*c*d + d^2 + 1)*sinh(b*x + a) + (c^2 - d^2 - 2*I*d + 1)*sqrt((4*c^2 - 4*d^2 + 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))) - I*a^2*log(2*(c^2 + 2*c*d + d^2 + 1)*cosh(b*x + a) + 2*(c^2 + 2*c*d + d^2 + 1)*sinh(b*x + a) - (c^2 - d^2 - 2*I*d + 1)*sqrt((4*c^2 - 4*d^2 + 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))) + I*a^2*log(2*(c^2 + 2*c*d + d^2 + 1)*cosh(b*x + a) + 2*(c^2 + 2*c*d + d^2 + 1)*sinh(b*x + a) + (c^2 - d^2 + 2*I*d + 1)*sqrt((4*c^2 - 4*d^2 - 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))) + I*a^2*log(2*(c^2 + 2*c*d + d^2 + 1)*cosh(b*x + a) + 2*(c^2 + 2*c*d + d^2 + 1)*sinh(b*x + a) - (c^2 - d^2 + 2*I*d + 1)*sqrt((4*c^2 - 4*d^2 - 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))) + (-I*b^2*x^2 + I*a^2)*log(1/2*sqrt((4*c^2 - 4*d^2 + 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))*(cosh(b*x + a) + sinh(b*x + a)) + 1) + (-I*b^2*x^2 + I*a^2)*log(-1/2*sqrt((4*c^2 - 4*d^2 + 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))*(cosh(b*x + a) + sinh(b*x + a)) + 1) + (I*b^2*x^2 - I*a^2)*log(1/2*sqrt((4*c^2 - 4*d^2 - 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))*(cosh(b*x + a) + sinh(b*x + a)) + 1) + (I*b^2*x^2 - I*a^2)*log(-1/2*sqrt((4*c^2 - 4*d^2 - 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))*(cosh(b*x + a) + sinh(b*x + a)) + 1) + 2*I*polylog(3, 1/2*sqrt((4*c^2 - 4*d^2 + 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))*(cosh(b*x + a) + sinh(b*x + a))) + 2*I*polylog(3, -1/2*sqrt((4*c^2 - 4*d^2 + 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))*(cosh(b*x + a) + sinh(b*x + a))) - 2*I*polylog(3, 1/2*sqrt((4*c^2 - 4*d^2 - 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))*(cosh(b*x + a) + sinh(b*x + a))) - 2*I*polylog(3, -1/2*sqrt((4*c^2 - 4*d^2 - 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))*(cosh(b*x + a) + sinh(b*x + a))))/b^2","C",0
207,1,839,0,1.414001," ","integrate(arccot(c+d*coth(b*x+a)),x, algorithm=""fricas"")","\frac{2 \, b x \arctan\left(\frac{\sinh\left(b x + a\right)}{d \cosh\left(b x + a\right) + c \sinh\left(b x + a\right)}\right) + i \, a \log\left(2 \, {\left(c^{2} + 2 \, c d + d^{2} + 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(c^{2} + 2 \, c d + d^{2} + 1\right)} \sinh\left(b x + a\right) + {\left(c^{2} - d^{2} - 2 i \, d + 1\right)} \sqrt{\frac{4 \, c^{2} - 4 \, d^{2} + 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}}\right) + i \, a \log\left(2 \, {\left(c^{2} + 2 \, c d + d^{2} + 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(c^{2} + 2 \, c d + d^{2} + 1\right)} \sinh\left(b x + a\right) - {\left(c^{2} - d^{2} - 2 i \, d + 1\right)} \sqrt{\frac{4 \, c^{2} - 4 \, d^{2} + 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}}\right) - i \, a \log\left(2 \, {\left(c^{2} + 2 \, c d + d^{2} + 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(c^{2} + 2 \, c d + d^{2} + 1\right)} \sinh\left(b x + a\right) + {\left(c^{2} - d^{2} + 2 i \, d + 1\right)} \sqrt{\frac{4 \, c^{2} - 4 \, d^{2} - 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}}\right) - i \, a \log\left(2 \, {\left(c^{2} + 2 \, c d + d^{2} + 1\right)} \cosh\left(b x + a\right) + 2 \, {\left(c^{2} + 2 \, c d + d^{2} + 1\right)} \sinh\left(b x + a\right) - {\left(c^{2} - d^{2} + 2 i \, d + 1\right)} \sqrt{\frac{4 \, c^{2} - 4 \, d^{2} - 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}}\right) + {\left(-i \, b x - i \, a\right)} \log\left(\frac{1}{2} \, \sqrt{\frac{4 \, c^{2} - 4 \, d^{2} + 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) + {\left(-i \, b x - i \, a\right)} \log\left(-\frac{1}{2} \, \sqrt{\frac{4 \, c^{2} - 4 \, d^{2} + 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) + {\left(i \, b x + i \, a\right)} \log\left(\frac{1}{2} \, \sqrt{\frac{4 \, c^{2} - 4 \, d^{2} - 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) + {\left(i \, b x + i \, a\right)} \log\left(-\frac{1}{2} \, \sqrt{\frac{4 \, c^{2} - 4 \, d^{2} - 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)} + 1\right) - i \, {\rm Li}_2\left(\frac{1}{2} \, \sqrt{\frac{4 \, c^{2} - 4 \, d^{2} + 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) - i \, {\rm Li}_2\left(-\frac{1}{2} \, \sqrt{\frac{4 \, c^{2} - 4 \, d^{2} + 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + i \, {\rm Li}_2\left(\frac{1}{2} \, \sqrt{\frac{4 \, c^{2} - 4 \, d^{2} - 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right) + i \, {\rm Li}_2\left(-\frac{1}{2} \, \sqrt{\frac{4 \, c^{2} - 4 \, d^{2} - 8 i \, d + 4}{c^{2} - 2 \, c d + d^{2} + 1}} {\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right)}\right)}{2 \, b}"," ",0,"1/2*(2*b*x*arctan(sinh(b*x + a)/(d*cosh(b*x + a) + c*sinh(b*x + a))) + I*a*log(2*(c^2 + 2*c*d + d^2 + 1)*cosh(b*x + a) + 2*(c^2 + 2*c*d + d^2 + 1)*sinh(b*x + a) + (c^2 - d^2 - 2*I*d + 1)*sqrt((4*c^2 - 4*d^2 + 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))) + I*a*log(2*(c^2 + 2*c*d + d^2 + 1)*cosh(b*x + a) + 2*(c^2 + 2*c*d + d^2 + 1)*sinh(b*x + a) - (c^2 - d^2 - 2*I*d + 1)*sqrt((4*c^2 - 4*d^2 + 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))) - I*a*log(2*(c^2 + 2*c*d + d^2 + 1)*cosh(b*x + a) + 2*(c^2 + 2*c*d + d^2 + 1)*sinh(b*x + a) + (c^2 - d^2 + 2*I*d + 1)*sqrt((4*c^2 - 4*d^2 - 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))) - I*a*log(2*(c^2 + 2*c*d + d^2 + 1)*cosh(b*x + a) + 2*(c^2 + 2*c*d + d^2 + 1)*sinh(b*x + a) - (c^2 - d^2 + 2*I*d + 1)*sqrt((4*c^2 - 4*d^2 - 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))) + (-I*b*x - I*a)*log(1/2*sqrt((4*c^2 - 4*d^2 + 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))*(cosh(b*x + a) + sinh(b*x + a)) + 1) + (-I*b*x - I*a)*log(-1/2*sqrt((4*c^2 - 4*d^2 + 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))*(cosh(b*x + a) + sinh(b*x + a)) + 1) + (I*b*x + I*a)*log(1/2*sqrt((4*c^2 - 4*d^2 - 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))*(cosh(b*x + a) + sinh(b*x + a)) + 1) + (I*b*x + I*a)*log(-1/2*sqrt((4*c^2 - 4*d^2 - 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))*(cosh(b*x + a) + sinh(b*x + a)) + 1) - I*dilog(1/2*sqrt((4*c^2 - 4*d^2 + 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))*(cosh(b*x + a) + sinh(b*x + a))) - I*dilog(-1/2*sqrt((4*c^2 - 4*d^2 + 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))*(cosh(b*x + a) + sinh(b*x + a))) + I*dilog(1/2*sqrt((4*c^2 - 4*d^2 - 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))*(cosh(b*x + a) + sinh(b*x + a))) + I*dilog(-1/2*sqrt((4*c^2 - 4*d^2 - 8*I*d + 4)/(c^2 - 2*c*d + d^2 + 1))*(cosh(b*x + a) + sinh(b*x + a))))/b","B",0
208,0,0,0,0.580470," ","integrate(arccot(c+d*coth(b*x+a))/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{arccot}\left(d \coth\left(b x + a\right) + c\right)}{x}, x\right)"," ",0,"integral(arccot(d*coth(b*x + a) + c)/x, x)","F",0
209,1,290,0,0.806624," ","integrate(x^2*arccot(c+(I+c)*coth(b*x+a)),x, algorithm=""fricas"")","\frac{i \, b^{4} x^{4} + 2 i \, b^{3} x^{3} \log\left(\frac{{\left(c e^{\left(2 \, b x + 2 \, a\right)} + i\right)} e^{\left(-2 \, b x - 2 \, a\right)}}{c + i}\right) - 6 i \, b^{2} x^{2} {\rm Li}_2\left(\frac{1}{2} \, \sqrt{4 i \, c} e^{\left(b x + a\right)}\right) - 6 i \, b^{2} x^{2} {\rm Li}_2\left(-\frac{1}{2} \, \sqrt{4 i \, c} e^{\left(b x + a\right)}\right) - i \, a^{4} + 2 i \, a^{3} \log\left(\frac{2 \, c e^{\left(b x + a\right)} + i \, \sqrt{4 i \, c}}{2 \, c}\right) + 2 i \, a^{3} \log\left(\frac{2 \, c e^{\left(b x + a\right)} - i \, \sqrt{4 i \, c}}{2 \, c}\right) + 12 i \, b x {\rm polylog}\left(3, \frac{1}{2} \, \sqrt{4 i \, c} e^{\left(b x + a\right)}\right) + 12 i \, b x {\rm polylog}\left(3, -\frac{1}{2} \, \sqrt{4 i \, c} e^{\left(b x + a\right)}\right) + {\left(-2 i \, b^{3} x^{3} - 2 i \, a^{3}\right)} \log\left(\frac{1}{2} \, \sqrt{4 i \, c} e^{\left(b x + a\right)} + 1\right) + {\left(-2 i \, b^{3} x^{3} - 2 i \, a^{3}\right)} \log\left(-\frac{1}{2} \, \sqrt{4 i \, c} e^{\left(b x + a\right)} + 1\right) - 12 i \, {\rm polylog}\left(4, \frac{1}{2} \, \sqrt{4 i \, c} e^{\left(b x + a\right)}\right) - 12 i \, {\rm polylog}\left(4, -\frac{1}{2} \, \sqrt{4 i \, c} e^{\left(b x + a\right)}\right)}{12 \, b^{3}}"," ",0,"1/12*(I*b^4*x^4 + 2*I*b^3*x^3*log((c*e^(2*b*x + 2*a) + I)*e^(-2*b*x - 2*a)/(c + I)) - 6*I*b^2*x^2*dilog(1/2*sqrt(4*I*c)*e^(b*x + a)) - 6*I*b^2*x^2*dilog(-1/2*sqrt(4*I*c)*e^(b*x + a)) - I*a^4 + 2*I*a^3*log(1/2*(2*c*e^(b*x + a) + I*sqrt(4*I*c))/c) + 2*I*a^3*log(1/2*(2*c*e^(b*x + a) - I*sqrt(4*I*c))/c) + 12*I*b*x*polylog(3, 1/2*sqrt(4*I*c)*e^(b*x + a)) + 12*I*b*x*polylog(3, -1/2*sqrt(4*I*c)*e^(b*x + a)) + (-2*I*b^3*x^3 - 2*I*a^3)*log(1/2*sqrt(4*I*c)*e^(b*x + a) + 1) + (-2*I*b^3*x^3 - 2*I*a^3)*log(-1/2*sqrt(4*I*c)*e^(b*x + a) + 1) - 12*I*polylog(4, 1/2*sqrt(4*I*c)*e^(b*x + a)) - 12*I*polylog(4, -1/2*sqrt(4*I*c)*e^(b*x + a)))/b^3","C",0
210,1,244,0,0.845170," ","integrate(x*arccot(c+(I+c)*coth(b*x+a)),x, algorithm=""fricas"")","\frac{2 i \, b^{3} x^{3} + 3 i \, b^{2} x^{2} \log\left(\frac{{\left(c e^{\left(2 \, b x + 2 \, a\right)} + i\right)} e^{\left(-2 \, b x - 2 \, a\right)}}{c + i}\right) + 2 i \, a^{3} - 6 i \, b x {\rm Li}_2\left(\frac{1}{2} \, \sqrt{4 i \, c} e^{\left(b x + a\right)}\right) - 6 i \, b x {\rm Li}_2\left(-\frac{1}{2} \, \sqrt{4 i \, c} e^{\left(b x + a\right)}\right) - 3 i \, a^{2} \log\left(\frac{2 \, c e^{\left(b x + a\right)} + i \, \sqrt{4 i \, c}}{2 \, c}\right) - 3 i \, a^{2} \log\left(\frac{2 \, c e^{\left(b x + a\right)} - i \, \sqrt{4 i \, c}}{2 \, c}\right) + {\left(-3 i \, b^{2} x^{2} + 3 i \, a^{2}\right)} \log\left(\frac{1}{2} \, \sqrt{4 i \, c} e^{\left(b x + a\right)} + 1\right) + {\left(-3 i \, b^{2} x^{2} + 3 i \, a^{2}\right)} \log\left(-\frac{1}{2} \, \sqrt{4 i \, c} e^{\left(b x + a\right)} + 1\right) + 6 i \, {\rm polylog}\left(3, \frac{1}{2} \, \sqrt{4 i \, c} e^{\left(b x + a\right)}\right) + 6 i \, {\rm polylog}\left(3, -\frac{1}{2} \, \sqrt{4 i \, c} e^{\left(b x + a\right)}\right)}{12 \, b^{2}}"," ",0,"1/12*(2*I*b^3*x^3 + 3*I*b^2*x^2*log((c*e^(2*b*x + 2*a) + I)*e^(-2*b*x - 2*a)/(c + I)) + 2*I*a^3 - 6*I*b*x*dilog(1/2*sqrt(4*I*c)*e^(b*x + a)) - 6*I*b*x*dilog(-1/2*sqrt(4*I*c)*e^(b*x + a)) - 3*I*a^2*log(1/2*(2*c*e^(b*x + a) + I*sqrt(4*I*c))/c) - 3*I*a^2*log(1/2*(2*c*e^(b*x + a) - I*sqrt(4*I*c))/c) + (-3*I*b^2*x^2 + 3*I*a^2)*log(1/2*sqrt(4*I*c)*e^(b*x + a) + 1) + (-3*I*b^2*x^2 + 3*I*a^2)*log(-1/2*sqrt(4*I*c)*e^(b*x + a) + 1) + 6*I*polylog(3, 1/2*sqrt(4*I*c)*e^(b*x + a)) + 6*I*polylog(3, -1/2*sqrt(4*I*c)*e^(b*x + a)))/b^2","C",0
211,1,186,0,0.697901," ","integrate(arccot(c+(I+c)*coth(b*x+a)),x, algorithm=""fricas"")","\frac{i \, b^{2} x^{2} + i \, b x \log\left(\frac{{\left(c e^{\left(2 \, b x + 2 \, a\right)} + i\right)} e^{\left(-2 \, b x - 2 \, a\right)}}{c + i}\right) - i \, a^{2} + {\left(-i \, b x - i \, a\right)} \log\left(\frac{1}{2} \, \sqrt{4 i \, c} e^{\left(b x + a\right)} + 1\right) + {\left(-i \, b x - i \, a\right)} \log\left(-\frac{1}{2} \, \sqrt{4 i \, c} e^{\left(b x + a\right)} + 1\right) + i \, a \log\left(\frac{2 \, c e^{\left(b x + a\right)} + i \, \sqrt{4 i \, c}}{2 \, c}\right) + i \, a \log\left(\frac{2 \, c e^{\left(b x + a\right)} - i \, \sqrt{4 i \, c}}{2 \, c}\right) - i \, {\rm Li}_2\left(\frac{1}{2} \, \sqrt{4 i \, c} e^{\left(b x + a\right)}\right) - i \, {\rm Li}_2\left(-\frac{1}{2} \, \sqrt{4 i \, c} e^{\left(b x + a\right)}\right)}{2 \, b}"," ",0,"1/2*(I*b^2*x^2 + I*b*x*log((c*e^(2*b*x + 2*a) + I)*e^(-2*b*x - 2*a)/(c + I)) - I*a^2 + (-I*b*x - I*a)*log(1/2*sqrt(4*I*c)*e^(b*x + a) + 1) + (-I*b*x - I*a)*log(-1/2*sqrt(4*I*c)*e^(b*x + a) + 1) + I*a*log(1/2*(2*c*e^(b*x + a) + I*sqrt(4*I*c))/c) + I*a*log(1/2*(2*c*e^(b*x + a) - I*sqrt(4*I*c))/c) - I*dilog(1/2*sqrt(4*I*c)*e^(b*x + a)) - I*dilog(-1/2*sqrt(4*I*c)*e^(b*x + a)))/b","B",0
212,0,0,0,0.671828," ","integrate(arccot(c+(I+c)*coth(b*x+a))/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{i \, \log\left(\frac{{\left(c e^{\left(2 \, b x + 2 \, a\right)} + i\right)} e^{\left(-2 \, b x - 2 \, a\right)}}{c + i}\right)}{2 \, x}, x\right)"," ",0,"integral(1/2*I*log((c*e^(2*b*x + 2*a) + I)*e^(-2*b*x - 2*a)/(c + I))/x, x)","F",0
213,1,290,0,0.607702," ","integrate(x^2*arccot(c-(I-c)*coth(b*x+a)),x, algorithm=""fricas"")","\frac{-i \, b^{4} x^{4} + 2 i \, b^{3} x^{3} \log\left(\frac{{\left(c - i\right)} e^{\left(2 \, b x + 2 \, a\right)}}{c e^{\left(2 \, b x + 2 \, a\right)} - i}\right) + 6 i \, b^{2} x^{2} {\rm Li}_2\left(\frac{1}{2} \, \sqrt{-4 i \, c} e^{\left(b x + a\right)}\right) + 6 i \, b^{2} x^{2} {\rm Li}_2\left(-\frac{1}{2} \, \sqrt{-4 i \, c} e^{\left(b x + a\right)}\right) + i \, a^{4} - 2 i \, a^{3} \log\left(\frac{2 \, c e^{\left(b x + a\right)} + i \, \sqrt{-4 i \, c}}{2 \, c}\right) - 2 i \, a^{3} \log\left(\frac{2 \, c e^{\left(b x + a\right)} - i \, \sqrt{-4 i \, c}}{2 \, c}\right) - 12 i \, b x {\rm polylog}\left(3, \frac{1}{2} \, \sqrt{-4 i \, c} e^{\left(b x + a\right)}\right) - 12 i \, b x {\rm polylog}\left(3, -\frac{1}{2} \, \sqrt{-4 i \, c} e^{\left(b x + a\right)}\right) + {\left(2 i \, b^{3} x^{3} + 2 i \, a^{3}\right)} \log\left(\frac{1}{2} \, \sqrt{-4 i \, c} e^{\left(b x + a\right)} + 1\right) + {\left(2 i \, b^{3} x^{3} + 2 i \, a^{3}\right)} \log\left(-\frac{1}{2} \, \sqrt{-4 i \, c} e^{\left(b x + a\right)} + 1\right) + 12 i \, {\rm polylog}\left(4, \frac{1}{2} \, \sqrt{-4 i \, c} e^{\left(b x + a\right)}\right) + 12 i \, {\rm polylog}\left(4, -\frac{1}{2} \, \sqrt{-4 i \, c} e^{\left(b x + a\right)}\right)}{12 \, b^{3}}"," ",0,"1/12*(-I*b^4*x^4 + 2*I*b^3*x^3*log((c - I)*e^(2*b*x + 2*a)/(c*e^(2*b*x + 2*a) - I)) + 6*I*b^2*x^2*dilog(1/2*sqrt(-4*I*c)*e^(b*x + a)) + 6*I*b^2*x^2*dilog(-1/2*sqrt(-4*I*c)*e^(b*x + a)) + I*a^4 - 2*I*a^3*log(1/2*(2*c*e^(b*x + a) + I*sqrt(-4*I*c))/c) - 2*I*a^3*log(1/2*(2*c*e^(b*x + a) - I*sqrt(-4*I*c))/c) - 12*I*b*x*polylog(3, 1/2*sqrt(-4*I*c)*e^(b*x + a)) - 12*I*b*x*polylog(3, -1/2*sqrt(-4*I*c)*e^(b*x + a)) + (2*I*b^3*x^3 + 2*I*a^3)*log(1/2*sqrt(-4*I*c)*e^(b*x + a) + 1) + (2*I*b^3*x^3 + 2*I*a^3)*log(-1/2*sqrt(-4*I*c)*e^(b*x + a) + 1) + 12*I*polylog(4, 1/2*sqrt(-4*I*c)*e^(b*x + a)) + 12*I*polylog(4, -1/2*sqrt(-4*I*c)*e^(b*x + a)))/b^3","C",0
214,1,244,0,0.670784," ","integrate(x*arccot(c-(I-c)*coth(b*x+a)),x, algorithm=""fricas"")","\frac{-2 i \, b^{3} x^{3} + 3 i \, b^{2} x^{2} \log\left(\frac{{\left(c - i\right)} e^{\left(2 \, b x + 2 \, a\right)}}{c e^{\left(2 \, b x + 2 \, a\right)} - i}\right) - 2 i \, a^{3} + 6 i \, b x {\rm Li}_2\left(\frac{1}{2} \, \sqrt{-4 i \, c} e^{\left(b x + a\right)}\right) + 6 i \, b x {\rm Li}_2\left(-\frac{1}{2} \, \sqrt{-4 i \, c} e^{\left(b x + a\right)}\right) + 3 i \, a^{2} \log\left(\frac{2 \, c e^{\left(b x + a\right)} + i \, \sqrt{-4 i \, c}}{2 \, c}\right) + 3 i \, a^{2} \log\left(\frac{2 \, c e^{\left(b x + a\right)} - i \, \sqrt{-4 i \, c}}{2 \, c}\right) + {\left(3 i \, b^{2} x^{2} - 3 i \, a^{2}\right)} \log\left(\frac{1}{2} \, \sqrt{-4 i \, c} e^{\left(b x + a\right)} + 1\right) + {\left(3 i \, b^{2} x^{2} - 3 i \, a^{2}\right)} \log\left(-\frac{1}{2} \, \sqrt{-4 i \, c} e^{\left(b x + a\right)} + 1\right) - 6 i \, {\rm polylog}\left(3, \frac{1}{2} \, \sqrt{-4 i \, c} e^{\left(b x + a\right)}\right) - 6 i \, {\rm polylog}\left(3, -\frac{1}{2} \, \sqrt{-4 i \, c} e^{\left(b x + a\right)}\right)}{12 \, b^{2}}"," ",0,"1/12*(-2*I*b^3*x^3 + 3*I*b^2*x^2*log((c - I)*e^(2*b*x + 2*a)/(c*e^(2*b*x + 2*a) - I)) - 2*I*a^3 + 6*I*b*x*dilog(1/2*sqrt(-4*I*c)*e^(b*x + a)) + 6*I*b*x*dilog(-1/2*sqrt(-4*I*c)*e^(b*x + a)) + 3*I*a^2*log(1/2*(2*c*e^(b*x + a) + I*sqrt(-4*I*c))/c) + 3*I*a^2*log(1/2*(2*c*e^(b*x + a) - I*sqrt(-4*I*c))/c) + (3*I*b^2*x^2 - 3*I*a^2)*log(1/2*sqrt(-4*I*c)*e^(b*x + a) + 1) + (3*I*b^2*x^2 - 3*I*a^2)*log(-1/2*sqrt(-4*I*c)*e^(b*x + a) + 1) - 6*I*polylog(3, 1/2*sqrt(-4*I*c)*e^(b*x + a)) - 6*I*polylog(3, -1/2*sqrt(-4*I*c)*e^(b*x + a)))/b^2","C",0
215,1,186,0,0.721636," ","integrate(arccot(c-(I-c)*coth(b*x+a)),x, algorithm=""fricas"")","\frac{-i \, b^{2} x^{2} + i \, b x \log\left(\frac{{\left(c - i\right)} e^{\left(2 \, b x + 2 \, a\right)}}{c e^{\left(2 \, b x + 2 \, a\right)} - i}\right) + i \, a^{2} + {\left(i \, b x + i \, a\right)} \log\left(\frac{1}{2} \, \sqrt{-4 i \, c} e^{\left(b x + a\right)} + 1\right) + {\left(i \, b x + i \, a\right)} \log\left(-\frac{1}{2} \, \sqrt{-4 i \, c} e^{\left(b x + a\right)} + 1\right) - i \, a \log\left(\frac{2 \, c e^{\left(b x + a\right)} + i \, \sqrt{-4 i \, c}}{2 \, c}\right) - i \, a \log\left(\frac{2 \, c e^{\left(b x + a\right)} - i \, \sqrt{-4 i \, c}}{2 \, c}\right) + i \, {\rm Li}_2\left(\frac{1}{2} \, \sqrt{-4 i \, c} e^{\left(b x + a\right)}\right) + i \, {\rm Li}_2\left(-\frac{1}{2} \, \sqrt{-4 i \, c} e^{\left(b x + a\right)}\right)}{2 \, b}"," ",0,"1/2*(-I*b^2*x^2 + I*b*x*log((c - I)*e^(2*b*x + 2*a)/(c*e^(2*b*x + 2*a) - I)) + I*a^2 + (I*b*x + I*a)*log(1/2*sqrt(-4*I*c)*e^(b*x + a) + 1) + (I*b*x + I*a)*log(-1/2*sqrt(-4*I*c)*e^(b*x + a) + 1) - I*a*log(1/2*(2*c*e^(b*x + a) + I*sqrt(-4*I*c))/c) - I*a*log(1/2*(2*c*e^(b*x + a) - I*sqrt(-4*I*c))/c) + I*dilog(1/2*sqrt(-4*I*c)*e^(b*x + a)) + I*dilog(-1/2*sqrt(-4*I*c)*e^(b*x + a)))/b","B",0
216,0,0,0,0.717116," ","integrate(arccot(c-(I-c)*coth(b*x+a))/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{i \, \log\left(\frac{{\left(c - i\right)} e^{\left(2 \, b x + 2 \, a\right)}}{c e^{\left(2 \, b x + 2 \, a\right)} - i}\right)}{2 \, x}, x\right)"," ",0,"integral(1/2*I*log((c - I)*e^(2*b*x + 2*a)/(c*e^(2*b*x + 2*a) - I))/x, x)","F",0
217,1,246,0,0.821495," ","integrate((a+b*arccot(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 i \, b e m {\rm polylog}\left(3, i \, c x^{n}\right) + 2 i \, b e m {\rm polylog}\left(3, -i \, c x^{n}\right) + 2 \, {\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)} \operatorname{arccot}\left(c x^{n}\right) + {\left(2 i \, b e m n \log\left(x\right) + 2 i \, b e n \log\left(f\right) + 2 i \, b d n\right)} {\rm Li}_2\left(i \, c x^{n}\right) + {\left(-2 i \, b e m n \log\left(x\right) - 2 i \, b e n \log\left(f\right) - 2 i \, b d n\right)} {\rm Li}_2\left(-i \, c x^{n}\right) + {\left(-i \, b e m n^{2} \log\left(x\right)^{2} + {\left(-2 i \, b e n^{2} \log\left(f\right) - 2 i \, b d n^{2}\right)} \log\left(x\right)\right)} \log\left(i \, c x^{n} + 1\right) + {\left(i \, b e m n^{2} \log\left(x\right)^{2} + {\left(2 i \, b e n^{2} \log\left(f\right) + 2 i \, b d n^{2}\right)} \log\left(x\right)\right)} \log\left(-i \, c x^{n} + 1\right) + 4 \, {\left(a e n^{2} \log\left(f\right) + a d n^{2}\right)} \log\left(x\right)}{4 \, n^{2}}"," ",0,"1/4*(2*a*e*m*n^2*log(x)^2 - 2*I*b*e*m*polylog(3, I*c*x^n) + 2*I*b*e*m*polylog(3, -I*c*x^n) + 2*(b*e*m*n^2*log(x)^2 + 2*(b*e*n^2*log(f) + b*d*n^2)*log(x))*arccot(c*x^n) + (2*I*b*e*m*n*log(x) + 2*I*b*e*n*log(f) + 2*I*b*d*n)*dilog(I*c*x^n) + (-2*I*b*e*m*n*log(x) - 2*I*b*e*n*log(f) - 2*I*b*d*n)*dilog(-I*c*x^n) + (-I*b*e*m*n^2*log(x)^2 + (-2*I*b*e*n^2*log(f) - 2*I*b*d*n^2)*log(x))*log(I*c*x^n + 1) + (I*b*e*m*n^2*log(x)^2 + (2*I*b*e*n^2*log(f) + 2*I*b*d*n^2)*log(x))*log(-I*c*x^n + 1) + 4*(a*e*n^2*log(f) + a*d*n^2)*log(x))/n^2","C",0
218,1,40,0,0.493838," ","integrate(arccot(exp(x)),x, algorithm=""fricas"")","x \operatorname{arccot}\left(e^{x}\right) - \frac{1}{2} i \, x \log\left(i \, e^{x} + 1\right) + \frac{1}{2} i \, x \log\left(-i \, e^{x} + 1\right) + \frac{1}{2} i \, {\rm Li}_2\left(i \, e^{x}\right) - \frac{1}{2} i \, {\rm Li}_2\left(-i \, e^{x}\right)"," ",0,"x*arccot(e^x) - 1/2*I*x*log(I*e^x + 1) + 1/2*I*x*log(-I*e^x + 1) + 1/2*I*dilog(I*e^x) - 1/2*I*dilog(-I*e^x)","B",0
219,1,65,0,0.673602," ","integrate(x*arccot(exp(x)),x, algorithm=""fricas"")","\frac{1}{2} \, x^{2} \operatorname{arccot}\left(e^{x}\right) - \frac{1}{4} i \, x^{2} \log\left(i \, e^{x} + 1\right) + \frac{1}{4} i \, x^{2} \log\left(-i \, e^{x} + 1\right) + \frac{1}{2} i \, x {\rm Li}_2\left(i \, e^{x}\right) - \frac{1}{2} i \, x {\rm Li}_2\left(-i \, e^{x}\right) - \frac{1}{2} i \, {\rm polylog}\left(3, i \, e^{x}\right) + \frac{1}{2} i \, {\rm polylog}\left(3, -i \, e^{x}\right)"," ",0,"1/2*x^2*arccot(e^x) - 1/4*I*x^2*log(I*e^x + 1) + 1/4*I*x^2*log(-I*e^x + 1) + 1/2*I*x*dilog(I*e^x) - 1/2*I*x*dilog(-I*e^x) - 1/2*I*polylog(3, I*e^x) + 1/2*I*polylog(3, -I*e^x)","C",0
220,1,87,0,0.575178," ","integrate(x^2*arccot(exp(x)),x, algorithm=""fricas"")","\frac{1}{3} \, x^{3} \operatorname{arccot}\left(e^{x}\right) - \frac{1}{6} i \, x^{3} \log\left(i \, e^{x} + 1\right) + \frac{1}{6} i \, x^{3} \log\left(-i \, e^{x} + 1\right) + \frac{1}{2} i \, x^{2} {\rm Li}_2\left(i \, e^{x}\right) - \frac{1}{2} i \, x^{2} {\rm Li}_2\left(-i \, e^{x}\right) - i \, x {\rm polylog}\left(3, i \, e^{x}\right) + i \, x {\rm polylog}\left(3, -i \, e^{x}\right) + i \, {\rm polylog}\left(4, i \, e^{x}\right) - i \, {\rm polylog}\left(4, -i \, e^{x}\right)"," ",0,"1/3*x^3*arccot(e^x) - 1/6*I*x^3*log(I*e^x + 1) + 1/6*I*x^3*log(-I*e^x + 1) + 1/2*I*x^2*dilog(I*e^x) - 1/2*I*x^2*dilog(-I*e^x) - I*x*polylog(3, I*e^x) + I*x*polylog(3, -I*e^x) + I*polylog(4, I*e^x) - I*polylog(4, -I*e^x)","C",0
221,1,103,0,0.749209," ","integrate(arccot(exp(b*x+a)),x, algorithm=""fricas"")","\frac{2 \, b x \operatorname{arccot}\left(e^{\left(b x + a\right)}\right) - i \, a \log\left(e^{\left(b x + a\right)} + i\right) + i \, a \log\left(e^{\left(b x + a\right)} - i\right) + {\left(-i \, b x - i \, a\right)} \log\left(i \, e^{\left(b x + a\right)} + 1\right) + {\left(i \, b x + i \, a\right)} \log\left(-i \, e^{\left(b x + a\right)} + 1\right) + i \, {\rm Li}_2\left(i \, e^{\left(b x + a\right)}\right) - i \, {\rm Li}_2\left(-i \, e^{\left(b x + a\right)}\right)}{2 \, b}"," ",0,"1/2*(2*b*x*arccot(e^(b*x + a)) - I*a*log(e^(b*x + a) + I) + I*a*log(e^(b*x + a) - I) + (-I*b*x - I*a)*log(I*e^(b*x + a) + 1) + (I*b*x + I*a)*log(-I*e^(b*x + a) + 1) + I*dilog(I*e^(b*x + a)) - I*dilog(-I*e^(b*x + a)))/b","B",0
222,1,151,0,0.658582," ","integrate(x*arccot(exp(b*x+a)),x, algorithm=""fricas"")","\frac{2 \, b^{2} x^{2} \operatorname{arccot}\left(e^{\left(b x + a\right)}\right) + 2 i \, b x {\rm Li}_2\left(i \, e^{\left(b x + a\right)}\right) - 2 i \, b x {\rm Li}_2\left(-i \, e^{\left(b x + a\right)}\right) + i \, a^{2} \log\left(e^{\left(b x + a\right)} + i\right) - i \, a^{2} \log\left(e^{\left(b x + a\right)} - i\right) + {\left(-i \, b^{2} x^{2} + i \, a^{2}\right)} \log\left(i \, e^{\left(b x + a\right)} + 1\right) + {\left(i \, b^{2} x^{2} - i \, a^{2}\right)} \log\left(-i \, e^{\left(b x + a\right)} + 1\right) - 2 i \, {\rm polylog}\left(3, i \, e^{\left(b x + a\right)}\right) + 2 i \, {\rm polylog}\left(3, -i \, e^{\left(b x + a\right)}\right)}{4 \, b^{2}}"," ",0,"1/4*(2*b^2*x^2*arccot(e^(b*x + a)) + 2*I*b*x*dilog(I*e^(b*x + a)) - 2*I*b*x*dilog(-I*e^(b*x + a)) + I*a^2*log(e^(b*x + a) + I) - I*a^2*log(e^(b*x + a) - I) + (-I*b^2*x^2 + I*a^2)*log(I*e^(b*x + a) + 1) + (I*b^2*x^2 - I*a^2)*log(-I*e^(b*x + a) + 1) - 2*I*polylog(3, I*e^(b*x + a)) + 2*I*polylog(3, -I*e^(b*x + a)))/b^2","C",0
223,1,187,0,0.815587," ","integrate(x^2*arccot(exp(b*x+a)),x, algorithm=""fricas"")","\frac{2 \, b^{3} x^{3} \operatorname{arccot}\left(e^{\left(b x + a\right)}\right) + 3 i \, b^{2} x^{2} {\rm Li}_2\left(i \, e^{\left(b x + a\right)}\right) - 3 i \, b^{2} x^{2} {\rm Li}_2\left(-i \, e^{\left(b x + a\right)}\right) - i \, a^{3} \log\left(e^{\left(b x + a\right)} + i\right) + i \, a^{3} \log\left(e^{\left(b x + a\right)} - i\right) - 6 i \, b x {\rm polylog}\left(3, i \, e^{\left(b x + a\right)}\right) + 6 i \, b x {\rm polylog}\left(3, -i \, e^{\left(b x + a\right)}\right) + {\left(-i \, b^{3} x^{3} - i \, a^{3}\right)} \log\left(i \, e^{\left(b x + a\right)} + 1\right) + {\left(i \, b^{3} x^{3} + i \, a^{3}\right)} \log\left(-i \, e^{\left(b x + a\right)} + 1\right) + 6 i \, {\rm polylog}\left(4, i \, e^{\left(b x + a\right)}\right) - 6 i \, {\rm polylog}\left(4, -i \, e^{\left(b x + a\right)}\right)}{6 \, b^{3}}"," ",0,"1/6*(2*b^3*x^3*arccot(e^(b*x + a)) + 3*I*b^2*x^2*dilog(I*e^(b*x + a)) - 3*I*b^2*x^2*dilog(-I*e^(b*x + a)) - I*a^3*log(e^(b*x + a) + I) + I*a^3*log(e^(b*x + a) - I) - 6*I*b*x*polylog(3, I*e^(b*x + a)) + 6*I*b*x*polylog(3, -I*e^(b*x + a)) + (-I*b^3*x^3 - I*a^3)*log(I*e^(b*x + a) + 1) + (I*b^3*x^3 + I*a^3)*log(-I*e^(b*x + a) + 1) + 6*I*polylog(4, I*e^(b*x + a)) - 6*I*polylog(4, -I*e^(b*x + a)))/b^3","C",0
224,1,212,0,1.526490," ","integrate(arccot(a+b*f^(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, d x \operatorname{arccot}\left(b f^{d x + c} + a\right) \log\left(f\right) - i \, c \log\left(b f^{d x + c} + a + i\right) \log\left(f\right) + i \, c \log\left(b f^{d x + c} + a - i\right) \log\left(f\right) + {\left(-i \, d x - i \, c\right)} \log\left(f\right) \log\left(\frac{a^{2} + {\left(a b + i \, b\right)} f^{d x + c} + 1}{a^{2} + 1}\right) + {\left(i \, d x + i \, c\right)} \log\left(f\right) \log\left(\frac{a^{2} + {\left(a b - i \, b\right)} f^{d x + c} + 1}{a^{2} + 1}\right) - i \, {\rm Li}_2\left(-\frac{a^{2} + {\left(a b + i \, b\right)} f^{d x + c} + 1}{a^{2} + 1} + 1\right) + i \, {\rm Li}_2\left(-\frac{a^{2} + {\left(a b - i \, b\right)} f^{d x + c} + 1}{a^{2} + 1} + 1\right)}{2 \, d \log\left(f\right)}"," ",0,"1/2*(2*d*x*arccot(b*f^(d*x + c) + a)*log(f) - I*c*log(b*f^(d*x + c) + a + I)*log(f) + I*c*log(b*f^(d*x + c) + a - I)*log(f) + (-I*d*x - I*c)*log(f)*log((a^2 + (a*b + I*b)*f^(d*x + c) + 1)/(a^2 + 1)) + (I*d*x + I*c)*log(f)*log((a^2 + (a*b - I*b)*f^(d*x + c) + 1)/(a^2 + 1)) - I*dilog(-(a^2 + (a*b + I*b)*f^(d*x + c) + 1)/(a^2 + 1) + 1) + I*dilog(-(a^2 + (a*b - I*b)*f^(d*x + c) + 1)/(a^2 + 1) + 1))/(d*log(f))","A",0
225,1,304,0,0.695267," ","integrate(x*arccot(a+b*f^(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, d^{2} x^{2} \operatorname{arccot}\left(b f^{d x + c} + a\right) \log\left(f\right)^{2} + i \, c^{2} \log\left(b f^{d x + c} + a + i\right) \log\left(f\right)^{2} - i \, c^{2} \log\left(b f^{d x + c} + a - i\right) \log\left(f\right)^{2} - 2 i \, d x {\rm Li}_2\left(-\frac{a^{2} + {\left(a b + i \, b\right)} f^{d x + c} + 1}{a^{2} + 1} + 1\right) \log\left(f\right) + 2 i \, d x {\rm Li}_2\left(-\frac{a^{2} + {\left(a b - i \, b\right)} f^{d x + c} + 1}{a^{2} + 1} + 1\right) \log\left(f\right) + {\left(-i \, d^{2} x^{2} + i \, c^{2}\right)} \log\left(f\right)^{2} \log\left(\frac{a^{2} + {\left(a b + i \, b\right)} f^{d x + c} + 1}{a^{2} + 1}\right) + {\left(i \, d^{2} x^{2} - i \, c^{2}\right)} \log\left(f\right)^{2} \log\left(\frac{a^{2} + {\left(a b - i \, b\right)} f^{d x + c} + 1}{a^{2} + 1}\right) + 2 i \, {\rm polylog}\left(3, -\frac{{\left(a b + i \, b\right)} f^{d x + c}}{a^{2} + 1}\right) - 2 i \, {\rm polylog}\left(3, -\frac{{\left(a b - i \, b\right)} f^{d x + c}}{a^{2} + 1}\right)}{4 \, d^{2} \log\left(f\right)^{2}}"," ",0,"1/4*(2*d^2*x^2*arccot(b*f^(d*x + c) + a)*log(f)^2 + I*c^2*log(b*f^(d*x + c) + a + I)*log(f)^2 - I*c^2*log(b*f^(d*x + c) + a - I)*log(f)^2 - 2*I*d*x*dilog(-(a^2 + (a*b + I*b)*f^(d*x + c) + 1)/(a^2 + 1) + 1)*log(f) + 2*I*d*x*dilog(-(a^2 + (a*b - I*b)*f^(d*x + c) + 1)/(a^2 + 1) + 1)*log(f) + (-I*d^2*x^2 + I*c^2)*log(f)^2*log((a^2 + (a*b + I*b)*f^(d*x + c) + 1)/(a^2 + 1)) + (I*d^2*x^2 - I*c^2)*log(f)^2*log((a^2 + (a*b - I*b)*f^(d*x + c) + 1)/(a^2 + 1)) + 2*I*polylog(3, -(a*b + I*b)*f^(d*x + c)/(a^2 + 1)) - 2*I*polylog(3, -(a*b - I*b)*f^(d*x + c)/(a^2 + 1)))/(d^2*log(f)^2)","C",0
226,1,378,0,0.794224," ","integrate(x^2*arccot(a+b*f^(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, d^{3} x^{3} \operatorname{arccot}\left(b f^{d x + c} + a\right) \log\left(f\right)^{3} - 3 i \, d^{2} x^{2} {\rm Li}_2\left(-\frac{a^{2} + {\left(a b + i \, b\right)} f^{d x + c} + 1}{a^{2} + 1} + 1\right) \log\left(f\right)^{2} + 3 i \, d^{2} x^{2} {\rm Li}_2\left(-\frac{a^{2} + {\left(a b - i \, b\right)} f^{d x + c} + 1}{a^{2} + 1} + 1\right) \log\left(f\right)^{2} - i \, c^{3} \log\left(b f^{d x + c} + a + i\right) \log\left(f\right)^{3} + i \, c^{3} \log\left(b f^{d x + c} + a - i\right) \log\left(f\right)^{3} + {\left(-i \, d^{3} x^{3} - i \, c^{3}\right)} \log\left(f\right)^{3} \log\left(\frac{a^{2} + {\left(a b + i \, b\right)} f^{d x + c} + 1}{a^{2} + 1}\right) + {\left(i \, d^{3} x^{3} + i \, c^{3}\right)} \log\left(f\right)^{3} \log\left(\frac{a^{2} + {\left(a b - i \, b\right)} f^{d x + c} + 1}{a^{2} + 1}\right) + 6 i \, d x \log\left(f\right) {\rm polylog}\left(3, -\frac{{\left(a b + i \, b\right)} f^{d x + c}}{a^{2} + 1}\right) - 6 i \, d x \log\left(f\right) {\rm polylog}\left(3, -\frac{{\left(a b - i \, b\right)} f^{d x + c}}{a^{2} + 1}\right) - 6 i \, {\rm polylog}\left(4, -\frac{{\left(a b + i \, b\right)} f^{d x + c}}{a^{2} + 1}\right) + 6 i \, {\rm polylog}\left(4, -\frac{{\left(a b - i \, b\right)} f^{d x + c}}{a^{2} + 1}\right)}{6 \, d^{3} \log\left(f\right)^{3}}"," ",0,"1/6*(2*d^3*x^3*arccot(b*f^(d*x + c) + a)*log(f)^3 - 3*I*d^2*x^2*dilog(-(a^2 + (a*b + I*b)*f^(d*x + c) + 1)/(a^2 + 1) + 1)*log(f)^2 + 3*I*d^2*x^2*dilog(-(a^2 + (a*b - I*b)*f^(d*x + c) + 1)/(a^2 + 1) + 1)*log(f)^2 - I*c^3*log(b*f^(d*x + c) + a + I)*log(f)^3 + I*c^3*log(b*f^(d*x + c) + a - I)*log(f)^3 + (-I*d^3*x^3 - I*c^3)*log(f)^3*log((a^2 + (a*b + I*b)*f^(d*x + c) + 1)/(a^2 + 1)) + (I*d^3*x^3 + I*c^3)*log(f)^3*log((a^2 + (a*b - I*b)*f^(d*x + c) + 1)/(a^2 + 1)) + 6*I*d*x*log(f)*polylog(3, -(a*b + I*b)*f^(d*x + c)/(a^2 + 1)) - 6*I*d*x*log(f)*polylog(3, -(a*b - I*b)*f^(d*x + c)/(a^2 + 1)) - 6*I*polylog(4, -(a*b + I*b)*f^(d*x + c)/(a^2 + 1)) + 6*I*polylog(4, -(a*b - I*b)*f^(d*x + c)/(a^2 + 1)))/(d^3*log(f)^3)","C",0
227,1,28,0,0.521190," ","integrate(arccot(exp(x))/exp(x),x, algorithm=""fricas"")","-\frac{1}{2} \, {\left(2 \, x e^{x} - e^{x} \log\left(e^{\left(2 \, x\right)} + 1\right) + 2 \, \operatorname{arccot}\left(e^{x}\right)\right)} e^{\left(-x\right)}"," ",0,"-1/2*(2*x*e^x - e^x*log(e^(2*x) + 1) + 2*arccot(e^x))*e^(-x)","A",0
228,1,15,0,0.642744," ","integrate(1/(a*x^2+a)/(b-2*b*arccot(x)),x, algorithm=""fricas"")","\frac{\log\left(2 \, \operatorname{arccot}\left(x\right) - 1\right)}{2 \, a b}"," ",0,"1/2*log(2*arccot(x) - 1)/(a*b)","A",0
229,1,131,0,0.624766," ","integrate(exp(c*(b*x+a))*arccot(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)} \arctan\left(\frac{2 \, {\left(\cosh\left(b c x + a c\right) + \sinh\left(b c x + a c\right)\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} - 1}\right) + \log\left(\frac{2 \, \cosh\left(b c x + a c\right)}{\cosh\left(b c x + a c\right) - \sinh\left(b c x + a c\right)}\right)}{b c}"," ",0,"((cosh(b*c*x + a*c) + sinh(b*c*x + a*c))*arctan(2*(cosh(b*c*x + a*c) + sinh(b*c*x + a*c))/(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 - 1)) + log(2*cosh(b*c*x + a*c)/(cosh(b*c*x + a*c) - sinh(b*c*x + a*c))))/(b*c)","B",0
230,1,276,0,0.672526," ","integrate(exp(c*(b*x+a))*arccot(cosh(b*c*x+a*c)),x, algorithm=""fricas"")","\frac{2 \, {\left(\cosh\left(b c x + a c\right) + \sinh\left(b c x + a c\right)\right)} \arctan\left(\frac{2 \, {\left(\cosh\left(b c x + a c\right) + \sinh\left(b c x + a c\right)\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} + 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*(2*(cosh(b*c*x + a*c) + sinh(b*c*x + a*c))*arctan(2*(cosh(b*c*x + a*c) + sinh(b*c*x + a*c))/(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 + 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
231,1,431,0,0.709785," ","integrate(exp(c*(b*x+a))*arccot(tanh(b*c*x+a*c)),x, algorithm=""fricas"")","-\frac{4 \, \sqrt{2} b c \left(\frac{1}{b^{4} c^{4}}\right)^{\frac{1}{4}} \arctan\left(-\sqrt{2} b c \left(\frac{1}{b^{4} c^{4}}\right)^{\frac{1}{4}} e^{\left(b c x + a c\right)} + \sqrt{2} \sqrt{\sqrt{2} b^{3} c^{3} \left(\frac{1}{b^{4} c^{4}}\right)^{\frac{3}{4}} e^{\left(b c x + a c\right)} + b^{2} c^{2} \sqrt{\frac{1}{b^{4} c^{4}}} + e^{\left(2 \, b c x + 2 \, a c\right)}} b c \left(\frac{1}{b^{4} c^{4}}\right)^{\frac{1}{4}} - 1\right) + 4 \, \sqrt{2} b c \left(\frac{1}{b^{4} c^{4}}\right)^{\frac{1}{4}} \arctan\left(-\sqrt{2} b c \left(\frac{1}{b^{4} c^{4}}\right)^{\frac{1}{4}} e^{\left(b c x + a c\right)} + \sqrt{2} \sqrt{-\sqrt{2} b^{3} c^{3} \left(\frac{1}{b^{4} c^{4}}\right)^{\frac{3}{4}} e^{\left(b c x + a c\right)} + b^{2} c^{2} \sqrt{\frac{1}{b^{4} c^{4}}} + e^{\left(2 \, b c x + 2 \, a c\right)}} b c \left(\frac{1}{b^{4} c^{4}}\right)^{\frac{1}{4}} + 1\right) + \sqrt{2} b c \left(\frac{1}{b^{4} c^{4}}\right)^{\frac{1}{4}} \log\left(\sqrt{2} b^{3} c^{3} \left(\frac{1}{b^{4} c^{4}}\right)^{\frac{3}{4}} e^{\left(b c x + a c\right)} + b^{2} c^{2} \sqrt{\frac{1}{b^{4} c^{4}}} + e^{\left(2 \, b c x + 2 \, a c\right)}\right) - \sqrt{2} b c \left(\frac{1}{b^{4} c^{4}}\right)^{\frac{1}{4}} \log\left(-\sqrt{2} b^{3} c^{3} \left(\frac{1}{b^{4} c^{4}}\right)^{\frac{3}{4}} e^{\left(b c x + a c\right)} + b^{2} c^{2} \sqrt{\frac{1}{b^{4} c^{4}}} + e^{\left(2 \, b c x + 2 \, a c\right)}\right) - 4 \, \arctan\left(\frac{e^{\left(2 \, b c x + 2 \, a c\right)} + 1}{e^{\left(2 \, b c x + 2 \, a c\right)} - 1}\right) e^{\left(b c x + a c\right)}}{4 \, b c}"," ",0,"-1/4*(4*sqrt(2)*b*c*(1/(b^4*c^4))^(1/4)*arctan(-sqrt(2)*b*c*(1/(b^4*c^4))^(1/4)*e^(b*c*x + a*c) + sqrt(2)*sqrt(sqrt(2)*b^3*c^3*(1/(b^4*c^4))^(3/4)*e^(b*c*x + a*c) + b^2*c^2*sqrt(1/(b^4*c^4)) + e^(2*b*c*x + 2*a*c))*b*c*(1/(b^4*c^4))^(1/4) - 1) + 4*sqrt(2)*b*c*(1/(b^4*c^4))^(1/4)*arctan(-sqrt(2)*b*c*(1/(b^4*c^4))^(1/4)*e^(b*c*x + a*c) + sqrt(2)*sqrt(-sqrt(2)*b^3*c^3*(1/(b^4*c^4))^(3/4)*e^(b*c*x + a*c) + b^2*c^2*sqrt(1/(b^4*c^4)) + e^(2*b*c*x + 2*a*c))*b*c*(1/(b^4*c^4))^(1/4) + 1) + sqrt(2)*b*c*(1/(b^4*c^4))^(1/4)*log(sqrt(2)*b^3*c^3*(1/(b^4*c^4))^(3/4)*e^(b*c*x + a*c) + b^2*c^2*sqrt(1/(b^4*c^4)) + e^(2*b*c*x + 2*a*c)) - sqrt(2)*b*c*(1/(b^4*c^4))^(1/4)*log(-sqrt(2)*b^3*c^3*(1/(b^4*c^4))^(3/4)*e^(b*c*x + a*c) + b^2*c^2*sqrt(1/(b^4*c^4)) + e^(2*b*c*x + 2*a*c)) - 4*arctan((e^(2*b*c*x + 2*a*c) + 1)/(e^(2*b*c*x + 2*a*c) - 1))*e^(b*c*x + a*c))/(b*c)","B",0
232,1,431,0,0.680411," ","integrate(exp(c*(b*x+a))*arccot(coth(b*c*x+a*c)),x, algorithm=""fricas"")","\frac{4 \, \sqrt{2} b c \left(\frac{1}{b^{4} c^{4}}\right)^{\frac{1}{4}} \arctan\left(-\sqrt{2} b c \left(\frac{1}{b^{4} c^{4}}\right)^{\frac{1}{4}} e^{\left(b c x + a c\right)} + \sqrt{2} \sqrt{\sqrt{2} b^{3} c^{3} \left(\frac{1}{b^{4} c^{4}}\right)^{\frac{3}{4}} e^{\left(b c x + a c\right)} + b^{2} c^{2} \sqrt{\frac{1}{b^{4} c^{4}}} + e^{\left(2 \, b c x + 2 \, a c\right)}} b c \left(\frac{1}{b^{4} c^{4}}\right)^{\frac{1}{4}} - 1\right) + 4 \, \sqrt{2} b c \left(\frac{1}{b^{4} c^{4}}\right)^{\frac{1}{4}} \arctan\left(-\sqrt{2} b c \left(\frac{1}{b^{4} c^{4}}\right)^{\frac{1}{4}} e^{\left(b c x + a c\right)} + \sqrt{2} \sqrt{-\sqrt{2} b^{3} c^{3} \left(\frac{1}{b^{4} c^{4}}\right)^{\frac{3}{4}} e^{\left(b c x + a c\right)} + b^{2} c^{2} \sqrt{\frac{1}{b^{4} c^{4}}} + e^{\left(2 \, b c x + 2 \, a c\right)}} b c \left(\frac{1}{b^{4} c^{4}}\right)^{\frac{1}{4}} + 1\right) + \sqrt{2} b c \left(\frac{1}{b^{4} c^{4}}\right)^{\frac{1}{4}} \log\left(\sqrt{2} b^{3} c^{3} \left(\frac{1}{b^{4} c^{4}}\right)^{\frac{3}{4}} e^{\left(b c x + a c\right)} + b^{2} c^{2} \sqrt{\frac{1}{b^{4} c^{4}}} + e^{\left(2 \, b c x + 2 \, a c\right)}\right) - \sqrt{2} b c \left(\frac{1}{b^{4} c^{4}}\right)^{\frac{1}{4}} \log\left(-\sqrt{2} b^{3} c^{3} \left(\frac{1}{b^{4} c^{4}}\right)^{\frac{3}{4}} e^{\left(b c x + a c\right)} + b^{2} c^{2} \sqrt{\frac{1}{b^{4} c^{4}}} + e^{\left(2 \, b c x + 2 \, a c\right)}\right) + 4 \, \arctan\left(\frac{e^{\left(2 \, b c x + 2 \, a c\right)} - 1}{e^{\left(2 \, b c x + 2 \, a c\right)} + 1}\right) e^{\left(b c x + a c\right)}}{4 \, b c}"," ",0,"1/4*(4*sqrt(2)*b*c*(1/(b^4*c^4))^(1/4)*arctan(-sqrt(2)*b*c*(1/(b^4*c^4))^(1/4)*e^(b*c*x + a*c) + sqrt(2)*sqrt(sqrt(2)*b^3*c^3*(1/(b^4*c^4))^(3/4)*e^(b*c*x + a*c) + b^2*c^2*sqrt(1/(b^4*c^4)) + e^(2*b*c*x + 2*a*c))*b*c*(1/(b^4*c^4))^(1/4) - 1) + 4*sqrt(2)*b*c*(1/(b^4*c^4))^(1/4)*arctan(-sqrt(2)*b*c*(1/(b^4*c^4))^(1/4)*e^(b*c*x + a*c) + sqrt(2)*sqrt(-sqrt(2)*b^3*c^3*(1/(b^4*c^4))^(3/4)*e^(b*c*x + a*c) + b^2*c^2*sqrt(1/(b^4*c^4)) + e^(2*b*c*x + 2*a*c))*b*c*(1/(b^4*c^4))^(1/4) + 1) + sqrt(2)*b*c*(1/(b^4*c^4))^(1/4)*log(sqrt(2)*b^3*c^3*(1/(b^4*c^4))^(3/4)*e^(b*c*x + a*c) + b^2*c^2*sqrt(1/(b^4*c^4)) + e^(2*b*c*x + 2*a*c)) - sqrt(2)*b*c*(1/(b^4*c^4))^(1/4)*log(-sqrt(2)*b^3*c^3*(1/(b^4*c^4))^(3/4)*e^(b*c*x + a*c) + b^2*c^2*sqrt(1/(b^4*c^4)) + e^(2*b*c*x + 2*a*c)) + 4*arctan((e^(2*b*c*x + 2*a*c) - 1)/(e^(2*b*c*x + 2*a*c) + 1))*e^(b*c*x + a*c))/(b*c)","B",0
233,1,221,0,0.445418," ","integrate(exp(c*(b*x+a))*arccot(sech(b*c*x+a*c)),x, algorithm=""fricas"")","\frac{2 \, {\left(\cosh\left(b c x + a c\right) + \sinh\left(b c x + a c\right)\right)} \arctan\left(\cosh\left(b c x + a c\right)\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*(2*(cosh(b*c*x + a*c) + sinh(b*c*x + a*c))*arctan(cosh(b*c*x + a*c)) + 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
234,1,75,0,0.624766," ","integrate(exp(c*(b*x+a))*arccot(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)} \arctan\left(\sinh\left(b c x + a c\right)\right) - \log\left(\frac{2 \, \cosh\left(b c x + a c\right)}{\cosh\left(b c x + a c\right) - \sinh\left(b c x + a c\right)}\right)}{b c}"," ",0,"((cosh(b*c*x + a*c) + sinh(b*c*x + a*c))*arctan(sinh(b*c*x + a*c)) - log(2*cosh(b*c*x + a*c)/(cosh(b*c*x + a*c) - sinh(b*c*x + a*c))))/(b*c)","A",0
