1,1,47,0,0.412013," ","integrate(x^5*arccot(a*x),x, algorithm=""maxima"")","\frac{1}{6} \, x^{6} \operatorname{arccot}\left(a x\right) + \frac{1}{90} \, a {\left(\frac{3 \, a^{4} x^{5} - 5 \, a^{2} x^{3} + 15 \, x}{a^{6}} - \frac{15 \, \arctan\left(a x\right)}{a^{7}}\right)}"," ",0,"1/6*x^6*arccot(a*x) + 1/90*a*((3*a^4*x^5 - 5*a^2*x^3 + 15*x)/a^6 - 15*arctan(a*x)/a^7)","A",0
2,1,46,0,0.311164," ","integrate(x^4*arccot(a*x),x, algorithm=""maxima"")","\frac{1}{5} \, x^{5} \operatorname{arccot}\left(a x\right) + \frac{1}{20} \, a {\left(\frac{a^{2} x^{4} - 2 \, x^{2}}{a^{4}} + \frac{2 \, \log\left(a^{2} x^{2} + 1\right)}{a^{6}}\right)}"," ",0,"1/5*x^5*arccot(a*x) + 1/20*a*((a^2*x^4 - 2*x^2)/a^4 + 2*log(a^2*x^2 + 1)/a^6)","A",0
3,1,38,0,0.408749," ","integrate(x^3*arccot(a*x),x, algorithm=""maxima"")","\frac{1}{4} \, x^{4} \operatorname{arccot}\left(a x\right) + \frac{1}{12} \, a {\left(\frac{a^{2} x^{3} - 3 \, x}{a^{4}} + \frac{3 \, \arctan\left(a x\right)}{a^{5}}\right)}"," ",0,"1/4*x^4*arccot(a*x) + 1/12*a*((a^2*x^3 - 3*x)/a^4 + 3*arctan(a*x)/a^5)","A",0
4,1,36,0,0.308930," ","integrate(x^2*arccot(a*x),x, algorithm=""maxima"")","\frac{1}{3} \, x^{3} \operatorname{arccot}\left(a x\right) + \frac{1}{6} \, a {\left(\frac{x^{2}}{a^{2}} - \frac{\log\left(a^{2} x^{2} + 1\right)}{a^{4}}\right)}"," ",0,"1/3*x^3*arccot(a*x) + 1/6*a*(x^2/a^2 - log(a^2*x^2 + 1)/a^4)","A",0
5,1,28,0,0.406841," ","integrate(x*arccot(a*x),x, algorithm=""maxima"")","\frac{1}{2} \, x^{2} \operatorname{arccot}\left(a x\right) + \frac{1}{2} \, a {\left(\frac{x}{a^{2}} - \frac{\arctan\left(a x\right)}{a^{3}}\right)}"," ",0,"1/2*x^2*arccot(a*x) + 1/2*a*(x/a^2 - arctan(a*x)/a^3)","A",0
6,1,24,0,0.319573," ","integrate(arccot(a*x),x, algorithm=""maxima"")","\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
7,1,56,0,0.456821," ","integrate(arccot(a*x)/x,x, algorithm=""maxima"")","\frac{1}{4} \, \pi \log\left(a^{2} x^{2} + 1\right) - \arctan\left(a x\right) \log\left(a x\right) + \operatorname{arccot}\left(a x\right) \log\left(x\right) + \arctan\left(a x\right) \log\left(x\right) + \frac{1}{2} i \, {\rm Li}_2\left(i \, a x + 1\right) - \frac{1}{2} i \, {\rm Li}_2\left(-i \, a x + 1\right)"," ",0,"1/4*pi*log(a^2*x^2 + 1) - arctan(a*x)*log(a*x) + arccot(a*x)*log(x) + arctan(a*x)*log(x) + 1/2*I*dilog(I*a*x + 1) - 1/2*I*dilog(-I*a*x + 1)","B",0
8,1,30,0,0.307778," ","integrate(arccot(a*x)/x^2,x, algorithm=""maxima"")","\frac{1}{2} \, a {\left(\log\left(a^{2} x^{2} + 1\right) - \log\left(x^{2}\right)\right)} - \frac{\operatorname{arccot}\left(a x\right)}{x}"," ",0,"1/2*a*(log(a^2*x^2 + 1) - log(x^2)) - arccot(a*x)/x","A",0
9,1,23,0,0.412657," ","integrate(arccot(a*x)/x^3,x, algorithm=""maxima"")","\frac{1}{2} \, {\left(a \arctan\left(a x\right) + \frac{1}{x}\right)} a - \frac{\operatorname{arccot}\left(a x\right)}{2 \, x^{2}}"," ",0,"1/2*(a*arctan(a*x) + 1/x)*a - 1/2*arccot(a*x)/x^2","A",0
10,1,42,0,0.307892," ","integrate(arccot(a*x)/x^4,x, algorithm=""maxima"")","-\frac{1}{6} \, {\left(a^{2} \log\left(a^{2} x^{2} + 1\right) - a^{2} \log\left(x^{2}\right) - \frac{1}{x^{2}}\right)} a - \frac{\operatorname{arccot}\left(a x\right)}{3 \, x^{3}}"," ",0,"-1/6*(a^2*log(a^2*x^2 + 1) - a^2*log(x^2) - 1/x^2)*a - 1/3*arccot(a*x)/x^3","A",0
11,1,37,0,0.412590," ","integrate(arccot(a*x)/x^5,x, algorithm=""maxima"")","-\frac{1}{12} \, {\left(3 \, a^{3} \arctan\left(a x\right) + \frac{3 \, a^{2} x^{2} - 1}{x^{3}}\right)} a - \frac{\operatorname{arccot}\left(a x\right)}{4 \, x^{4}}"," ",0,"-1/12*(3*a^3*arctan(a*x) + (3*a^2*x^2 - 1)/x^3)*a - 1/4*arccot(a*x)/x^4","A",0
12,1,95,0,0.426447," ","integrate(x^5*arccot(a*x)^2,x, algorithm=""maxima"")","\frac{1}{6} \, x^{6} \operatorname{arccot}\left(a x\right)^{2} + \frac{1}{45} \, a {\left(\frac{3 \, a^{4} x^{5} - 5 \, a^{2} x^{3} + 15 \, x}{a^{6}} - \frac{15 \, \arctan\left(a x\right)}{a^{7}}\right)} \operatorname{arccot}\left(a x\right) + \frac{3 \, a^{4} x^{4} - 16 \, a^{2} x^{2} - 30 \, \arctan\left(a x\right)^{2} + 46 \, \log\left(a^{2} x^{2} + 1\right)}{180 \, a^{6}}"," ",0,"1/6*x^6*arccot(a*x)^2 + 1/45*a*((3*a^4*x^5 - 5*a^2*x^3 + 15*x)/a^6 - 15*arctan(a*x)/a^7)*arccot(a*x) + 1/180*(3*a^4*x^4 - 16*a^2*x^2 - 30*arctan(a*x)^2 + 46*log(a^2*x^2 + 1))/a^6","A",0
13,0,0,0,0.000000," ","integrate(x^4*arccot(a*x)^2,x, algorithm=""maxima"")","\frac{1}{20} \, x^{5} \arctan\left(1, a x\right)^{2} - \frac{1}{80} \, x^{5} \log\left(a^{2} x^{2} + 1\right)^{2} + \int \frac{60 \, a^{2} x^{6} \arctan\left(1, a x\right)^{2} + 4 \, a^{2} x^{6} \log\left(a^{2} x^{2} + 1\right) + 8 \, a x^{5} \arctan\left(1, a x\right) + 60 \, x^{4} \arctan\left(1, a x\right)^{2} + 5 \, {\left(a^{2} x^{6} + x^{4}\right)} \log\left(a^{2} x^{2} + 1\right)^{2}}{80 \, {\left(a^{2} x^{2} + 1\right)}}\,{d x}"," ",0,"1/20*x^5*arctan2(1, a*x)^2 - 1/80*x^5*log(a^2*x^2 + 1)^2 + integrate(1/80*(60*a^2*x^6*arctan2(1, a*x)^2 + 4*a^2*x^6*log(a^2*x^2 + 1) + 8*a*x^5*arctan2(1, a*x) + 60*x^4*arctan2(1, a*x)^2 + 5*(a^2*x^6 + x^4)*log(a^2*x^2 + 1)^2)/(a^2*x^2 + 1), x)","F",0
14,1,77,0,0.415183," ","integrate(x^3*arccot(a*x)^2,x, algorithm=""maxima"")","\frac{1}{4} \, x^{4} \operatorname{arccot}\left(a x\right)^{2} + \frac{1}{6} \, a {\left(\frac{a^{2} x^{3} - 3 \, x}{a^{4}} + \frac{3 \, \arctan\left(a x\right)}{a^{5}}\right)} \operatorname{arccot}\left(a x\right) + \frac{a^{2} x^{2} + 3 \, \arctan\left(a x\right)^{2} - 4 \, \log\left(a^{2} x^{2} + 1\right)}{12 \, a^{4}}"," ",0,"1/4*x^4*arccot(a*x)^2 + 1/6*a*((a^2*x^3 - 3*x)/a^4 + 3*arctan(a*x)/a^5)*arccot(a*x) + 1/12*(a^2*x^2 + 3*arctan(a*x)^2 - 4*log(a^2*x^2 + 1))/a^4","A",0
15,0,0,0,0.000000," ","integrate(x^2*arccot(a*x)^2,x, algorithm=""maxima"")","\frac{1}{12} \, x^{3} \arctan\left(1, a x\right)^{2} - \frac{1}{48} \, x^{3} \log\left(a^{2} x^{2} + 1\right)^{2} + \int \frac{36 \, a^{2} x^{4} \arctan\left(1, a x\right)^{2} + 4 \, a^{2} x^{4} \log\left(a^{2} x^{2} + 1\right) + 8 \, a x^{3} \arctan\left(1, a x\right) + 36 \, x^{2} \arctan\left(1, a x\right)^{2} + 3 \, {\left(a^{2} x^{4} + x^{2}\right)} \log\left(a^{2} x^{2} + 1\right)^{2}}{48 \, {\left(a^{2} x^{2} + 1\right)}}\,{d x}"," ",0,"1/12*x^3*arctan2(1, a*x)^2 - 1/48*x^3*log(a^2*x^2 + 1)^2 + integrate(1/48*(36*a^2*x^4*arctan2(1, a*x)^2 + 4*a^2*x^4*log(a^2*x^2 + 1) + 8*a*x^3*arctan2(1, a*x) + 36*x^2*arctan2(1, a*x)^2 + 3*(a^2*x^4 + x^2)*log(a^2*x^2 + 1)^2)/(a^2*x^2 + 1), x)","F",0
16,1,57,0,0.418764," ","integrate(x*arccot(a*x)^2,x, algorithm=""maxima"")","\frac{1}{2} \, x^{2} \operatorname{arccot}\left(a x\right)^{2} + a {\left(\frac{x}{a^{2}} - \frac{\arctan\left(a x\right)}{a^{3}}\right)} \operatorname{arccot}\left(a x\right) - \frac{\arctan\left(a x\right)^{2} - \log\left(a^{2} x^{2} + 1\right)}{2 \, a^{2}}"," ",0,"1/2*x^2*arccot(a*x)^2 + a*(x/a^2 - arctan(a*x)/a^3)*arccot(a*x) - 1/2*(arctan(a*x)^2 - log(a^2*x^2 + 1))/a^2","A",0
17,0,0,0,0.000000," ","integrate(arccot(a*x)^2,x, algorithm=""maxima"")","\frac{1}{4} \, x \arctan\left(1, a x\right)^{2} + 12 \, a^{2} \int \frac{x^{2} \arctan\left(\frac{1}{a x}\right)^{2}}{16 \, {\left(a^{2} x^{2} + 1\right)}}\,{d x} + a^{2} \int \frac{x^{2} \log\left(a^{2} x^{2} + 1\right)^{2}}{16 \, {\left(a^{2} x^{2} + 1\right)}}\,{d x} + 4 \, a^{2} \int \frac{x^{2} \log\left(a^{2} x^{2} + 1\right)}{16 \, {\left(a^{2} x^{2} + 1\right)}}\,{d x} - \frac{1}{16} \, x \log\left(a^{2} x^{2} + 1\right)^{2} + \frac{\arctan\left(a x\right)^{3}}{4 \, a} + \frac{3 \, \arctan\left(a x\right)^{2} \arctan\left(\frac{1}{a x}\right)}{4 \, a} + \frac{3 \, \arctan\left(a x\right) \arctan\left(\frac{1}{a x}\right)^{2}}{4 \, a} + 8 \, a \int \frac{x \arctan\left(\frac{1}{a x}\right)}{16 \, {\left(a^{2} x^{2} + 1\right)}}\,{d x} + \int \frac{\log\left(a^{2} x^{2} + 1\right)^{2}}{16 \, {\left(a^{2} x^{2} + 1\right)}}\,{d x}"," ",0,"1/4*x*arctan2(1, a*x)^2 + 12*a^2*integrate(1/16*x^2*arctan(1/(a*x))^2/(a^2*x^2 + 1), x) + a^2*integrate(1/16*x^2*log(a^2*x^2 + 1)^2/(a^2*x^2 + 1), x) + 4*a^2*integrate(1/16*x^2*log(a^2*x^2 + 1)/(a^2*x^2 + 1), x) - 1/16*x*log(a^2*x^2 + 1)^2 + 1/4*arctan(a*x)^3/a + 3/4*arctan(a*x)^2*arctan(1/(a*x))/a + 3/4*arctan(a*x)*arctan(1/(a*x))^2/a + 8*a*integrate(1/16*x*arctan(1/(a*x))/(a^2*x^2 + 1), x) + integrate(1/16*log(a^2*x^2 + 1)^2/(a^2*x^2 + 1), x)","F",0
18,0,0,0,0.000000," ","integrate(arccot(a*x)^2/x,x, algorithm=""maxima"")","\int \frac{\operatorname{arccot}\left(a x\right)^{2}}{x}\,{d x}"," ",0,"integrate(arccot(a*x)^2/x, x)","F",0
19,-1,0,0,0.000000," ","integrate(arccot(a*x)^2/x^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
20,1,56,0,0.424078," ","integrate(arccot(a*x)^2/x^3,x, algorithm=""maxima"")","\frac{1}{2} \, {\left(\arctan\left(a x\right)^{2} - \log\left(a^{2} x^{2} + 1\right) + 2 \, \log\left(x\right)\right)} a^{2} + {\left(a \arctan\left(a x\right) + \frac{1}{x}\right)} a \operatorname{arccot}\left(a x\right) - \frac{\operatorname{arccot}\left(a x\right)^{2}}{2 \, x^{2}}"," ",0,"1/2*(arctan(a*x)^2 - log(a^2*x^2 + 1) + 2*log(x))*a^2 + (a*arctan(a*x) + 1/x)*a*arccot(a*x) - 1/2*arccot(a*x)^2/x^2","A",0
21,-1,0,0,0.000000," ","integrate(arccot(a*x)^2/x^4,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
22,1,95,0,0.429492," ","integrate(arccot(a*x)^2/x^5,x, algorithm=""maxima"")","-\frac{1}{6} \, {\left(3 \, a^{3} \arctan\left(a x\right) + \frac{3 \, a^{2} x^{2} - 1}{x^{3}}\right)} a \operatorname{arccot}\left(a x\right) - \frac{{\left(3 \, a^{2} x^{2} \arctan\left(a x\right)^{2} - 4 \, a^{2} x^{2} \log\left(a^{2} x^{2} + 1\right) + 8 \, a^{2} x^{2} \log\left(x\right) + 1\right)} a^{2}}{12 \, x^{2}} - \frac{\operatorname{arccot}\left(a x\right)^{2}}{4 \, x^{4}}"," ",0,"-1/6*(3*a^3*arctan(a*x) + (3*a^2*x^2 - 1)/x^3)*a*arccot(a*x) - 1/12*(3*a^2*x^2*arctan(a*x)^2 - 4*a^2*x^2*log(a^2*x^2 + 1) + 8*a^2*x^2*log(x) + 1)*a^2/x^2 - 1/4*arccot(a*x)^2/x^4","A",0
23,-1,0,0,0.000000," ","integrate(x^5*arccot(a*x)^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
24,0,0,0,0.000000," ","integrate(x^4*arccot(a*x)^3,x, algorithm=""maxima"")","\frac{1}{40} \, x^{5} \arctan\left(1, a x\right)^{3} - \frac{3}{160} \, x^{5} \arctan\left(1, a x\right) \log\left(a^{2} x^{2} + 1\right)^{2} + \int \frac{140 \, a^{2} x^{6} \arctan\left(1, a x\right)^{3} + 12 \, a^{2} x^{6} \arctan\left(1, a x\right) \log\left(a^{2} x^{2} + 1\right) + 12 \, a x^{5} \arctan\left(1, a x\right)^{2} + 140 \, x^{4} \arctan\left(1, a x\right)^{3} + 3 \, {\left(5 \, a^{2} x^{6} \arctan\left(1, a x\right) - a x^{5} + 5 \, x^{4} \arctan\left(1, a x\right)\right)} \log\left(a^{2} x^{2} + 1\right)^{2}}{160 \, {\left(a^{2} x^{2} + 1\right)}}\,{d x}"," ",0,"1/40*x^5*arctan2(1, a*x)^3 - 3/160*x^5*arctan2(1, a*x)*log(a^2*x^2 + 1)^2 + integrate(1/160*(140*a^2*x^6*arctan2(1, a*x)^3 + 12*a^2*x^6*arctan2(1, a*x)*log(a^2*x^2 + 1) + 12*a*x^5*arctan2(1, a*x)^2 + 140*x^4*arctan2(1, a*x)^3 + 3*(5*a^2*x^6*arctan2(1, a*x) - a*x^5 + 5*x^4*arctan2(1, a*x))*log(a^2*x^2 + 1)^2)/(a^2*x^2 + 1), x)","F",0
25,-1,0,0,0.000000," ","integrate(x^3*arccot(a*x)^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
26,0,0,0,0.000000," ","integrate(x^2*arccot(a*x)^3,x, algorithm=""maxima"")","\frac{1}{24} \, x^{3} \arctan\left(1, a x\right)^{3} - \frac{1}{32} \, x^{3} \arctan\left(1, a x\right) \log\left(a^{2} x^{2} + 1\right)^{2} + \int \frac{28 \, a^{2} x^{4} \arctan\left(1, a x\right)^{3} + 4 \, a^{2} x^{4} \arctan\left(1, a x\right) \log\left(a^{2} x^{2} + 1\right) + 4 \, a x^{3} \arctan\left(1, a x\right)^{2} + 28 \, x^{2} \arctan\left(1, a x\right)^{3} + {\left(3 \, a^{2} x^{4} \arctan\left(1, a x\right) - a x^{3} + 3 \, x^{2} \arctan\left(1, a x\right)\right)} \log\left(a^{2} x^{2} + 1\right)^{2}}{32 \, {\left(a^{2} x^{2} + 1\right)}}\,{d x}"," ",0,"1/24*x^3*arctan2(1, a*x)^3 - 1/32*x^3*arctan2(1, a*x)*log(a^2*x^2 + 1)^2 + integrate(1/32*(28*a^2*x^4*arctan2(1, a*x)^3 + 4*a^2*x^4*arctan2(1, a*x)*log(a^2*x^2 + 1) + 4*a*x^3*arctan2(1, a*x)^2 + 28*x^2*arctan2(1, a*x)^3 + (3*a^2*x^4*arctan2(1, a*x) - a*x^3 + 3*x^2*arctan2(1, a*x))*log(a^2*x^2 + 1)^2)/(a^2*x^2 + 1), x)","F",0
27,-1,0,0,0.000000," ","integrate(x*arccot(a*x)^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
28,0,0,0,0.000000," ","integrate(arccot(a*x)^3,x, algorithm=""maxima"")","\frac{1}{8} \, x \arctan\left(1, a x\right)^{3} - \frac{3}{32} \, x \arctan\left(1, a x\right) \log\left(a^{2} x^{2} + 1\right)^{2} + \frac{21 \, \arctan\left(a x\right)^{2} \arctan\left(\frac{1}{a x}\right)^{2}}{16 \, a} + \frac{7 \, \arctan\left(a x\right) \arctan\left(\frac{1}{a x}\right)^{3}}{8 \, a} + 28 \, a^{2} \int \frac{x^{2} \arctan\left(\frac{1}{a x}\right)^{3}}{32 \, {\left(a^{2} x^{2} + 1\right)}}\,{d x} + 3 \, a^{2} \int \frac{x^{2} \arctan\left(\frac{1}{a x}\right) \log\left(a^{2} x^{2} + 1\right)^{2}}{32 \, {\left(a^{2} x^{2} + 1\right)}}\,{d x} + 12 \, a^{2} \int \frac{x^{2} \arctan\left(\frac{1}{a x}\right) \log\left(a^{2} x^{2} + 1\right)}{32 \, {\left(a^{2} x^{2} + 1\right)}}\,{d x} + 12 \, a \int \frac{x \arctan\left(\frac{1}{a x}\right)^{2}}{32 \, {\left(a^{2} x^{2} + 1\right)}}\,{d x} - 3 \, a \int \frac{x \log\left(a^{2} x^{2} + 1\right)^{2}}{32 \, {\left(a^{2} x^{2} + 1\right)}}\,{d x} + \frac{7 \, {\left(a \arctan\left(a x\right)^{4} + 4 \, a \arctan\left(a x\right)^{3} \arctan\left(\frac{1}{a x}\right)\right)}}{32 \, a^{2}} + 3 \, \int \frac{\arctan\left(\frac{1}{a x}\right) \log\left(a^{2} x^{2} + 1\right)^{2}}{32 \, {\left(a^{2} x^{2} + 1\right)}}\,{d x}"," ",0,"1/8*x*arctan2(1, a*x)^3 - 3/32*x*arctan2(1, a*x)*log(a^2*x^2 + 1)^2 + 21/16*arctan(a*x)^2*arctan(1/(a*x))^2/a + 7/8*arctan(a*x)*arctan(1/(a*x))^3/a + 28*a^2*integrate(1/32*x^2*arctan(1/(a*x))^3/(a^2*x^2 + 1), x) + 3*a^2*integrate(1/32*x^2*arctan(1/(a*x))*log(a^2*x^2 + 1)^2/(a^2*x^2 + 1), x) + 12*a^2*integrate(1/32*x^2*arctan(1/(a*x))*log(a^2*x^2 + 1)/(a^2*x^2 + 1), x) + 12*a*integrate(1/32*x*arctan(1/(a*x))^2/(a^2*x^2 + 1), x) - 3*a*integrate(1/32*x*log(a^2*x^2 + 1)^2/(a^2*x^2 + 1), x) + 7/32*(a*arctan(a*x)^4 + 4*a*arctan(a*x)^3*arctan(1/(a*x)))/a^2 + 3*integrate(1/32*arctan(1/(a*x))*log(a^2*x^2 + 1)^2/(a^2*x^2 + 1), x)","F",0
29,0,0,0,0.000000," ","integrate(arccot(a*x)^3/x,x, algorithm=""maxima"")","\int \frac{\operatorname{arccot}\left(a x\right)^{3}}{x}\,{d x}"," ",0,"integrate(arccot(a*x)^3/x, x)","F",0
30,-1,0,0,0.000000," ","integrate(arccot(a*x)^3/x^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
31,-1,0,0,0.000000," ","integrate(arccot(a*x)^3/x^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
32,-1,0,0,0.000000," ","integrate(arccot(a*x)^3/x^4,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
33,-1,0,0,0.000000," ","integrate(arccot(a*x)^3/x^5,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
34,0,0,0,0.000000," ","integrate(x^m*arccot(a*x)^3,x, algorithm=""maxima"")","\frac{\frac{15}{2} \, x x^{m} \arctan\left(1, a x\right)^{3} - \frac{21}{8} \, x x^{m} \arctan\left(1, a x\right) \log\left(a^{2} x^{2} + 1\right)^{2} + {\left(m + 1\right)} \int \frac{84 \, a^{2} x^{2} x^{m} \arctan\left(1, a x\right) \log\left(a^{2} x^{2} + 1\right) + 21 \, {\left({\left(a^{2} m \arctan\left(1, a x\right) + a^{2} \arctan\left(1, a x\right)\right)} x^{2} - a x + m \arctan\left(1, a x\right) + \arctan\left(1, a x\right)\right)} x^{m} \log\left(a^{2} x^{2} + 1\right)^{2} + 4 \, {\left(45 \, a x \arctan\left(1, a x\right)^{2} + 49 \, m \arctan\left(1, a x\right)^{3} + 49 \, {\left(a^{2} m \arctan\left(1, a x\right)^{3} + a^{2} \arctan\left(1, a x\right)^{3}\right)} x^{2} + 49 \, \arctan\left(1, a x\right)^{3}\right)} x^{m}}{8 \, {\left({\left(a^{2} m + a^{2}\right)} x^{2} + m + 1\right)}}\,{d x}}{32 \, {\left(m + 1\right)}}"," ",0,"1/32*(4*x*x^m*arctan2(1, a*x)^3 - 3*x*x^m*arctan2(1, a*x)*log(a^2*x^2 + 1)^2 + 32*(m + 1)*integrate(1/32*(12*a^2*x^2*x^m*arctan2(1, a*x)*log(a^2*x^2 + 1) + 3*((a^2*m*arctan2(1, a*x) + a^2*arctan2(1, a*x))*x^2 - a*x + m*arctan2(1, a*x) + arctan2(1, a*x))*x^m*log(a^2*x^2 + 1)^2 + 4*(3*a*x*arctan2(1, a*x)^2 + 7*m*arctan2(1, a*x)^3 + 7*(a^2*m*arctan2(1, a*x)^3 + a^2*arctan2(1, a*x)^3)*x^2 + 7*arctan2(1, a*x)^3)*x^m)/((a^2*m + a^2)*x^2 + m + 1), x))/(m + 1)","F",0
35,0,0,0,0.000000," ","integrate(x^m*arccot(a*x)^2,x, algorithm=""maxima"")","\frac{7 \, x x^{m} \arctan\left(1, a x\right)^{2} - \frac{3}{4} \, x x^{m} \log\left(a^{2} x^{2} + 1\right)^{2} + {\left(m + 1\right)} \int \frac{12 \, a^{2} x^{2} x^{m} \log\left(a^{2} x^{2} + 1\right) + 3 \, {\left({\left(a^{2} m + a^{2}\right)} x^{2} + m + 1\right)} x^{m} \log\left(a^{2} x^{2} + 1\right)^{2} + 4 \, {\left(9 \, {\left(a^{2} m \arctan\left(1, a x\right)^{2} + a^{2} \arctan\left(1, a x\right)^{2}\right)} x^{2} + 14 \, a x \arctan\left(1, a x\right) + 9 \, m \arctan\left(1, a x\right)^{2} + 9 \, \arctan\left(1, a x\right)^{2}\right)} x^{m}}{4 \, {\left({\left(a^{2} m + a^{2}\right)} x^{2} + m + 1\right)}}\,{d x}}{16 \, {\left(m + 1\right)}}"," ",0,"1/16*(4*x*x^m*arctan2(1, a*x)^2 - x*x^m*log(a^2*x^2 + 1)^2 + 16*(m + 1)*integrate(1/16*(4*a^2*x^2*x^m*log(a^2*x^2 + 1) + ((a^2*m + a^2)*x^2 + m + 1)*x^m*log(a^2*x^2 + 1)^2 + 4*(3*(a^2*m*arctan2(1, a*x)^2 + a^2*arctan2(1, a*x)^2)*x^2 + 2*a*x*arctan2(1, a*x) + 3*m*arctan2(1, a*x)^2 + 3*arctan2(1, a*x)^2)*x^m)/((a^2*m + a^2)*x^2 + m + 1), x))/(m + 1)","F",0
36,0,0,0,0.000000," ","integrate(x^m*arccot(a*x),x, algorithm=""maxima"")","\frac{x x^{m} \arctan\left(1, a x\right) + {\left(a m + a\right)} \int \frac{x x^{m}}{{\left(a^{2} m + a^{2}\right)} x^{2} + m + 1}\,{d x}}{m + 1}"," ",0,"(x*x^m*arctan2(1, a*x) + (a*m + a)*integrate(x*x^m/((a^2*m + a^2)*x^2 + m + 1), x))/(m + 1)","F",0
37,1,35,0,0.423986," ","integrate(x^4*arccot(x)/(x^2+1),x, algorithm=""maxima"")","\frac{1}{6} \, x^{2} + \frac{1}{3} \, {\left(x^{3} - 3 \, x + 3 \, \arctan\left(x\right)\right)} \operatorname{arccot}\left(x\right) + \frac{1}{2} \, \arctan\left(x\right)^{2} - \frac{2}{3} \, \log\left(x^{2} + 1\right)"," ",0,"1/6*x^2 + 1/3*(x^3 - 3*x + 3*arctan(x))*arccot(x) + 1/2*arctan(x)^2 - 2/3*log(x^2 + 1)","A",0
38,0,0,0,0.000000," ","integrate(x^3*arccot(x)/(x^2+1),x, algorithm=""maxima"")","\int \frac{x^{3} \operatorname{arccot}\left(x\right)}{x^{2} + 1}\,{d x}"," ",0,"integrate(x^3*arccot(x)/(x^2 + 1), x)","F",0
39,1,24,0,0.432799," ","integrate(x^2*arccot(x)/(x^2+1),x, algorithm=""maxima"")","{\left(x - \arctan\left(x\right)\right)} \operatorname{arccot}\left(x\right) - \frac{1}{2} \, \arctan\left(x\right)^{2} + \frac{1}{2} \, \log\left(x^{2} + 1\right)"," ",0,"(x - arctan(x))*arccot(x) - 1/2*arctan(x)^2 + 1/2*log(x^2 + 1)","A",0
40,0,0,0,0.000000," ","integrate(x*arccot(x)/(x^2+1),x, algorithm=""maxima"")","\int \frac{x \operatorname{arccot}\left(x\right)}{x^{2} + 1}\,{d x}"," ",0,"integrate(x*arccot(x)/(x^2 + 1), x)","F",0
41,1,6,0,0.309973," ","integrate(arccot(x)/(x^2+1),x, algorithm=""maxima"")","-\frac{1}{2} \, \operatorname{arccot}\left(x\right)^{2}"," ",0,"-1/2*arccot(x)^2","A",0
42,0,0,0,0.000000," ","integrate(arccot(x)/x/(x^2+1),x, algorithm=""maxima"")","\int \frac{\operatorname{arccot}\left(x\right)}{{\left(x^{2} + 1\right)} x}\,{d x}"," ",0,"integrate(arccot(x)/((x^2 + 1)*x), x)","F",0
43,1,29,0,0.419857," ","integrate(arccot(x)/x^2/(x^2+1),x, algorithm=""maxima"")","-{\left(\frac{1}{x} + \arctan\left(x\right)\right)} \operatorname{arccot}\left(x\right) - \frac{1}{2} \, \arctan\left(x\right)^{2} + \frac{1}{2} \, \log\left(x^{2} + 1\right) - \log\left(x\right)"," ",0,"-(1/x + arctan(x))*arccot(x) - 1/2*arctan(x)^2 + 1/2*log(x^2 + 1) - log(x)","A",0
44,0,0,0,0.000000," ","integrate(arccot(x)/x^3/(x^2+1),x, algorithm=""maxima"")","\int \frac{\operatorname{arccot}\left(x\right)}{{\left(x^{2} + 1\right)} x^{3}}\,{d x}"," ",0,"integrate(arccot(x)/((x^2 + 1)*x^3), x)","F",0
45,1,55,0,0.416717," ","integrate(arccot(x)/x^4/(x^2+1),x, algorithm=""maxima"")","\frac{1}{3} \, {\left(\frac{3 \, x^{2} - 1}{x^{3}} + 3 \, \arctan\left(x\right)\right)} \operatorname{arccot}\left(x\right) + \frac{3 \, x^{2} \arctan\left(x\right)^{2} - 4 \, x^{2} \log\left(x^{2} + 1\right) + 8 \, x^{2} \log\left(x\right) + 1}{6 \, x^{2}}"," ",0,"1/3*((3*x^2 - 1)/x^3 + 3*arctan(x))*arccot(x) + 1/6*(3*x^2*arctan(x)^2 - 4*x^2*log(x^2 + 1) + 8*x^2*log(x) + 1)/x^2","A",0
46,1,189,0,0.450538," ","integrate(x^2*arccot(c*x)/(x^2+1),x, algorithm=""maxima"")","{\left(x - \arctan\left(x\right)\right)} \operatorname{arccot}\left(c x\right) - \frac{4 \, c \arctan\left(c x\right) \arctan\left(x\right) - 4 \, c \arctan\left(x\right) \arctan\left(\frac{c x}{c - 1}, -\frac{1}{c - 1}\right) + c \log\left(x^{2} + 1\right) \log\left(\frac{c^{2} x^{2} + 1}{c^{2} + 2 \, c + 1}\right) - c \log\left(x^{2} + 1\right) \log\left(\frac{c^{2} x^{2} + 1}{c^{2} - 2 \, c + 1}\right) + 2 \, c {\rm Li}_2\left(\frac{i \, c x + c}{c + 1}\right) + 2 \, c {\rm Li}_2\left(-\frac{i \, c x - c}{c + 1}\right) - 2 \, c {\rm Li}_2\left(\frac{i \, c x + c}{c - 1}\right) - 2 \, c {\rm Li}_2\left(-\frac{i \, c x - c}{c - 1}\right) - 4 \, \log\left(c^{2} x^{2} + 1\right)}{8 \, c}"," ",0,"(x - arctan(x))*arccot(c*x) - 1/8*(4*c*arctan(c*x)*arctan(x) - 4*c*arctan(x)*arctan2(c*x/(c - 1), -1/(c - 1)) + c*log(x^2 + 1)*log((c^2*x^2 + 1)/(c^2 + 2*c + 1)) - c*log(x^2 + 1)*log((c^2*x^2 + 1)/(c^2 - 2*c + 1)) + 2*c*dilog((I*c*x + c)/(c + 1)) + 2*c*dilog(-(I*c*x - c)/(c + 1)) - 2*c*dilog((I*c*x + c)/(c - 1)) - 2*c*dilog(-(I*c*x - c)/(c - 1)) - 4*log(c^2*x^2 + 1))/c","A",0
47,0,0,0,0.000000," ","integrate(x*arccot(c*x)/(x^2+1),x, algorithm=""maxima"")","\int \frac{x \operatorname{arccot}\left(c x\right)}{x^{2} + 1}\,{d x}"," ",0,"integrate(x*arccot(c*x)/(x^2 + 1), x)","F",0
48,1,187,0,0.440413," ","integrate(arccot(c*x)/(x^2+1),x, algorithm=""maxima"")","-\frac{1}{8} \, c {\left(\frac{8 \, \arctan\left(c x\right) \arctan\left(x\right)}{c} - \frac{4 \, \arctan\left(c x\right) \arctan\left(x\right) - 4 \, \arctan\left(x\right) \arctan\left(\frac{c x}{c - 1}, -\frac{1}{c - 1}\right) + \log\left(x^{2} + 1\right) \log\left(\frac{c^{2} x^{2} + 1}{c^{2} + 2 \, c + 1}\right) - \log\left(x^{2} + 1\right) \log\left(\frac{c^{2} x^{2} + 1}{c^{2} - 2 \, c + 1}\right) + 2 \, {\rm Li}_2\left(\frac{i \, c x + c}{c + 1}\right) + 2 \, {\rm Li}_2\left(-\frac{i \, c x - c}{c + 1}\right) - 2 \, {\rm Li}_2\left(\frac{i \, c x + c}{c - 1}\right) - 2 \, {\rm Li}_2\left(-\frac{i \, c x - c}{c - 1}\right)}{c}\right)} + \operatorname{arccot}\left(c x\right) \arctan\left(x\right) + \arctan\left(c x\right) \arctan\left(x\right)"," ",0,"-1/8*c*(8*arctan(c*x)*arctan(x)/c - (4*arctan(c*x)*arctan(x) - 4*arctan(x)*arctan2(c*x/(c - 1), -1/(c - 1)) + log(x^2 + 1)*log((c^2*x^2 + 1)/(c^2 + 2*c + 1)) - log(x^2 + 1)*log((c^2*x^2 + 1)/(c^2 - 2*c + 1)) + 2*dilog((I*c*x + c)/(c + 1)) + 2*dilog(-(I*c*x - c)/(c + 1)) - 2*dilog((I*c*x + c)/(c - 1)) - 2*dilog(-(I*c*x - c)/(c - 1)))/c) + arccot(c*x)*arctan(x) + arctan(c*x)*arctan(x)","A",0
49,0,0,0,0.000000," ","integrate(arccot(c*x)/x/(x^2+1),x, algorithm=""maxima"")","\int \frac{\operatorname{arccot}\left(c x\right)}{{\left(x^{2} + 1\right)} x}\,{d x}"," ",0,"integrate(arccot(c*x)/((x^2 + 1)*x), x)","F",0
50,1,183,0,0.445858," ","integrate(arccot(c*x)/x^2/(x^2+1),x, algorithm=""maxima"")","-{\left(\frac{1}{x} + \arctan\left(x\right)\right)} \operatorname{arccot}\left(c x\right) - \frac{1}{2} \, \arctan\left(c x\right) \arctan\left(x\right) + \frac{1}{2} \, \arctan\left(x\right) \arctan\left(\frac{c x}{c - 1}, -\frac{1}{c - 1}\right) + \frac{1}{2} \, c \log\left(c^{2} x^{2} + 1\right) - c \log\left(x\right) - \frac{1}{8} \, \log\left(x^{2} + 1\right) \log\left(\frac{c^{2} x^{2} + 1}{c^{2} + 2 \, c + 1}\right) + \frac{1}{8} \, \log\left(x^{2} + 1\right) \log\left(\frac{c^{2} x^{2} + 1}{c^{2} - 2 \, c + 1}\right) - \frac{1}{4} \, {\rm Li}_2\left(\frac{i \, c x + c}{c + 1}\right) - \frac{1}{4} \, {\rm Li}_2\left(-\frac{i \, c x - c}{c + 1}\right) + \frac{1}{4} \, {\rm Li}_2\left(\frac{i \, c x + c}{c - 1}\right) + \frac{1}{4} \, {\rm Li}_2\left(-\frac{i \, c x - c}{c - 1}\right)"," ",0,"-(1/x + arctan(x))*arccot(c*x) - 1/2*arctan(c*x)*arctan(x) + 1/2*arctan(x)*arctan2(c*x/(c - 1), -1/(c - 1)) + 1/2*c*log(c^2*x^2 + 1) - c*log(x) - 1/8*log(x^2 + 1)*log((c^2*x^2 + 1)/(c^2 + 2*c + 1)) + 1/8*log(x^2 + 1)*log((c^2*x^2 + 1)/(c^2 - 2*c + 1)) - 1/4*dilog((I*c*x + c)/(c + 1)) - 1/4*dilog(-(I*c*x - c)/(c + 1)) + 1/4*dilog((I*c*x + c)/(c - 1)) + 1/4*dilog(-(I*c*x - c)/(c - 1))","A",0
51,1,5,0,0.324438," ","integrate(1/(x^2+1)/arccot(x),x, algorithm=""maxima"")","-\log\left(\operatorname{arccot}\left(x\right)\right)"," ",0,"-log(arccot(x))","A",0
52,1,13,0,0.319400," ","integrate(arccot(x)^n/(x^2+1),x, algorithm=""maxima"")","-\frac{\operatorname{arccot}\left(x\right)^{n + 1}}{n + 1}"," ",0,"-arccot(x)^(n + 1)/(n + 1)","A",0
53,1,226,0,0.320923," ","integrate((d*x^2+c)^4*arccot(a*x),x, algorithm=""maxima"")","\frac{1}{7560} \, a {\left(\frac{105 \, a^{6} d^{4} x^{8} + 20 \, {\left(36 \, a^{6} c d^{3} - 7 \, a^{4} d^{4}\right)} x^{6} + 6 \, {\left(378 \, a^{6} c^{2} d^{2} - 180 \, a^{4} c d^{3} + 35 \, a^{2} d^{4}\right)} x^{4} + 12 \, {\left(420 \, a^{6} c^{3} d - 378 \, a^{4} c^{2} d^{2} + 180 \, a^{2} c d^{3} - 35 \, d^{4}\right)} x^{2}}{a^{8}} + \frac{12 \, {\left(315 \, a^{8} c^{4} - 420 \, a^{6} c^{3} d + 378 \, a^{4} c^{2} d^{2} - 180 \, a^{2} c d^{3} + 35 \, d^{4}\right)} \log\left(a^{2} x^{2} + 1\right)}{a^{10}}\right)} + \frac{1}{315} \, {\left(35 \, d^{4} x^{9} + 180 \, c d^{3} x^{7} + 378 \, c^{2} d^{2} x^{5} + 420 \, c^{3} d x^{3} + 315 \, c^{4} x\right)} \operatorname{arccot}\left(a x\right)"," ",0,"1/7560*a*((105*a^6*d^4*x^8 + 20*(36*a^6*c*d^3 - 7*a^4*d^4)*x^6 + 6*(378*a^6*c^2*d^2 - 180*a^4*c*d^3 + 35*a^2*d^4)*x^4 + 12*(420*a^6*c^3*d - 378*a^4*c^2*d^2 + 180*a^2*c*d^3 - 35*d^4)*x^2)/a^8 + 12*(315*a^8*c^4 - 420*a^6*c^3*d + 378*a^4*c^2*d^2 - 180*a^2*c*d^3 + 35*d^4)*log(a^2*x^2 + 1)/a^10) + 1/315*(35*d^4*x^9 + 180*c*d^3*x^7 + 378*c^2*d^2*x^5 + 420*c^3*d*x^3 + 315*c^4*x)*arccot(a*x)","A",0
54,1,159,0,0.329709," ","integrate((d*x^2+c)^3*arccot(a*x),x, algorithm=""maxima"")","\frac{1}{420} \, a {\left(\frac{10 \, a^{4} d^{3} x^{6} + 3 \, {\left(21 \, a^{4} c d^{2} - 5 \, a^{2} d^{3}\right)} x^{4} + 6 \, {\left(35 \, a^{4} c^{2} d - 21 \, a^{2} c d^{2} + 5 \, d^{3}\right)} x^{2}}{a^{6}} + \frac{6 \, {\left(35 \, a^{6} c^{3} - 35 \, a^{4} c^{2} d + 21 \, a^{2} c d^{2} - 5 \, d^{3}\right)} \log\left(a^{2} x^{2} + 1\right)}{a^{8}}\right)} + \frac{1}{35} \, {\left(5 \, d^{3} x^{7} + 21 \, c d^{2} x^{5} + 35 \, c^{2} d x^{3} + 35 \, c^{3} x\right)} \operatorname{arccot}\left(a x\right)"," ",0,"1/420*a*((10*a^4*d^3*x^6 + 3*(21*a^4*c*d^2 - 5*a^2*d^3)*x^4 + 6*(35*a^4*c^2*d - 21*a^2*c*d^2 + 5*d^3)*x^2)/a^6 + 6*(35*a^6*c^3 - 35*a^4*c^2*d + 21*a^2*c*d^2 - 5*d^3)*log(a^2*x^2 + 1)/a^8) + 1/35*(5*d^3*x^7 + 21*c*d^2*x^5 + 35*c^2*d*x^3 + 35*c^3*x)*arccot(a*x)","A",0
55,1,103,0,0.314054," ","integrate((d*x^2+c)^2*arccot(a*x),x, algorithm=""maxima"")","\frac{1}{60} \, a {\left(\frac{3 \, a^{2} d^{2} x^{4} + 2 \, {\left(10 \, a^{2} c d - 3 \, d^{2}\right)} x^{2}}{a^{4}} + \frac{2 \, {\left(15 \, a^{4} c^{2} - 10 \, a^{2} c d + 3 \, d^{2}\right)} \log\left(a^{2} x^{2} + 1\right)}{a^{6}}\right)} + \frac{1}{15} \, {\left(3 \, d^{2} x^{5} + 10 \, c d x^{3} + 15 \, c^{2} x\right)} \operatorname{arccot}\left(a x\right)"," ",0,"1/60*a*((3*a^2*d^2*x^4 + 2*(10*a^2*c*d - 3*d^2)*x^2)/a^4 + 2*(15*a^4*c^2 - 10*a^2*c*d + 3*d^2)*log(a^2*x^2 + 1)/a^6) + 1/15*(3*d^2*x^5 + 10*c*d*x^3 + 15*c^2*x)*arccot(a*x)","A",0
56,1,53,0,0.318946," ","integrate((d*x^2+c)*arccot(a*x),x, algorithm=""maxima"")","\frac{1}{6} \, a {\left(\frac{d x^{2}}{a^{2}} + \frac{{\left(3 \, a^{2} c - d\right)} \log\left(a^{2} x^{2} + 1\right)}{a^{4}}\right)} + \frac{1}{3} \, {\left(d x^{3} + 3 \, c x\right)} \operatorname{arccot}\left(a x\right)"," ",0,"1/6*a*(d*x^2/a^2 + (3*a^2*c - d)*log(a^2*x^2 + 1)/a^4) + 1/3*(d*x^3 + 3*c*x)*arccot(a*x)","A",0
57,1,528,0,0.645259," ","integrate(arccot(a*x)/(d*x^2+c),x, algorithm=""maxima"")","-\frac{a {\left(\frac{8 \, \arctan\left(a x\right) \arctan\left(\frac{d x}{\sqrt{c d}}\right)}{a} - \frac{4 \, \arctan\left(a x\right) \arctan\left(\frac{\sqrt{d} x}{\sqrt{c}}\right) + 4 \, \arctan\left(\frac{\sqrt{d} x}{\sqrt{c}}\right) \arctan\left(-\frac{a \sqrt{d} x}{a \sqrt{c} - \sqrt{d}}, -\frac{\sqrt{d}}{a \sqrt{c} - \sqrt{d}}\right) + \log\left(d x^{2} + c\right) \log\left(\frac{a^{2} c d + {\left(a^{4} c d + a^{2} d^{2}\right)} x^{2} + 2 \, {\left(a^{3} d x^{2} + a d\right)} \sqrt{c} \sqrt{d} + d^{2}}{a^{4} c^{2} + 6 \, a^{2} c d + 4 \, {\left(a^{3} c + a d\right)} \sqrt{c} \sqrt{d} + d^{2}}\right) - \log\left(d x^{2} + c\right) \log\left(\frac{a^{2} c d + {\left(a^{4} c d + a^{2} d^{2}\right)} x^{2} - 2 \, {\left(a^{3} d x^{2} + a d\right)} \sqrt{c} \sqrt{d} + d^{2}}{a^{4} c^{2} + 6 \, a^{2} c d - 4 \, {\left(a^{3} c + a d\right)} \sqrt{c} \sqrt{d} + d^{2}}\right) + 2 \, {\rm Li}_2\left(\frac{a^{2} c + i \, a d x + {\left(i \, a^{2} x + a\right)} \sqrt{c} \sqrt{d}}{a^{2} c + 2 \, a \sqrt{c} \sqrt{d} + d}\right) + 2 \, {\rm Li}_2\left(\frac{a^{2} c - i \, a d x - {\left(i \, a^{2} x - a\right)} \sqrt{c} \sqrt{d}}{a^{2} c + 2 \, a \sqrt{c} \sqrt{d} + d}\right) - 2 \, {\rm Li}_2\left(\frac{a^{2} c + i \, a d x - {\left(i \, a^{2} x + a\right)} \sqrt{c} \sqrt{d}}{a^{2} c - 2 \, a \sqrt{c} \sqrt{d} + d}\right) - 2 \, {\rm Li}_2\left(\frac{a^{2} c - i \, a d x + {\left(i \, a^{2} x - a\right)} \sqrt{c} \sqrt{d}}{a^{2} c - 2 \, a \sqrt{c} \sqrt{d} + d}\right)}{a}\right)}}{8 \, \sqrt{c d}} + \frac{\operatorname{arccot}\left(a x\right) \arctan\left(\frac{d x}{\sqrt{c d}}\right)}{\sqrt{c d}} + \frac{\arctan\left(a x\right) \arctan\left(\frac{d x}{\sqrt{c d}}\right)}{\sqrt{c d}}"," ",0,"-1/8*a*(8*arctan(a*x)*arctan(d*x/sqrt(c*d))/a - (4*arctan(a*x)*arctan(sqrt(d)*x/sqrt(c)) + 4*arctan(sqrt(d)*x/sqrt(c))*arctan2(-a*sqrt(d)*x/(a*sqrt(c) - sqrt(d)), -sqrt(d)/(a*sqrt(c) - sqrt(d))) + log(d*x^2 + c)*log((a^2*c*d + (a^4*c*d + a^2*d^2)*x^2 + 2*(a^3*d*x^2 + a*d)*sqrt(c)*sqrt(d) + d^2)/(a^4*c^2 + 6*a^2*c*d + 4*(a^3*c + a*d)*sqrt(c)*sqrt(d) + d^2)) - log(d*x^2 + c)*log((a^2*c*d + (a^4*c*d + a^2*d^2)*x^2 - 2*(a^3*d*x^2 + a*d)*sqrt(c)*sqrt(d) + d^2)/(a^4*c^2 + 6*a^2*c*d - 4*(a^3*c + a*d)*sqrt(c)*sqrt(d) + d^2)) + 2*dilog((a^2*c + I*a*d*x + (I*a^2*x + a)*sqrt(c)*sqrt(d))/(a^2*c + 2*a*sqrt(c)*sqrt(d) + d)) + 2*dilog((a^2*c - I*a*d*x - (I*a^2*x - a)*sqrt(c)*sqrt(d))/(a^2*c + 2*a*sqrt(c)*sqrt(d) + d)) - 2*dilog((a^2*c + I*a*d*x - (I*a^2*x + a)*sqrt(c)*sqrt(d))/(a^2*c - 2*a*sqrt(c)*sqrt(d) + d)) - 2*dilog((a^2*c - I*a*d*x + (I*a^2*x - a)*sqrt(c)*sqrt(d))/(a^2*c - 2*a*sqrt(c)*sqrt(d) + d)))/a)/sqrt(c*d) + arccot(a*x)*arctan(d*x/sqrt(c*d))/sqrt(c*d) + arctan(a*x)*arctan(d*x/sqrt(c*d))/sqrt(c*d)","A",0
58,1,628,0,0.546008," ","integrate(arccot(a*x)/(d*x^2+c)^2,x, algorithm=""maxima"")","\frac{1}{2} \, {\left(\frac{x}{c d x^{2} + c^{2}} + \frac{\arctan\left(\frac{d x}{\sqrt{c d}}\right)}{\sqrt{c d} c}\right)} \operatorname{arccot}\left(a x\right) + \frac{{\left(4 \, a c d \log\left(a^{2} x^{2} + 1\right) - 4 \, a c d \log\left(d x^{2} + c\right) + {\left(4 \, {\left(a^{2} c - d\right)} \arctan\left(a x\right) \arctan\left(\frac{\sqrt{d} x}{\sqrt{c}}\right) + 4 \, {\left(a^{2} c - d\right)} \arctan\left(\frac{\sqrt{d} x}{\sqrt{c}}\right) \arctan\left(-\frac{a \sqrt{d} x}{a \sqrt{c} - \sqrt{d}}, -\frac{\sqrt{d}}{a \sqrt{c} - \sqrt{d}}\right) + {\left(a^{2} c - d\right)} \log\left(d x^{2} + c\right) \log\left(\frac{a^{2} c d + {\left(a^{4} c d + a^{2} d^{2}\right)} x^{2} + 2 \, {\left(a^{3} d x^{2} + a d\right)} \sqrt{c} \sqrt{d} + d^{2}}{a^{4} c^{2} + 6 \, a^{2} c d + 4 \, {\left(a^{3} c + a d\right)} \sqrt{c} \sqrt{d} + d^{2}}\right) - {\left(a^{2} c - d\right)} \log\left(d x^{2} + c\right) \log\left(\frac{a^{2} c d + {\left(a^{4} c d + a^{2} d^{2}\right)} x^{2} - 2 \, {\left(a^{3} d x^{2} + a d\right)} \sqrt{c} \sqrt{d} + d^{2}}{a^{4} c^{2} + 6 \, a^{2} c d - 4 \, {\left(a^{3} c + a d\right)} \sqrt{c} \sqrt{d} + d^{2}}\right) + 2 \, {\left(a^{2} c - d\right)} {\rm Li}_2\left(\frac{a^{2} c + i \, a d x + {\left(i \, a^{2} x + a\right)} \sqrt{c} \sqrt{d}}{a^{2} c + 2 \, a \sqrt{c} \sqrt{d} + d}\right) + 2 \, {\left(a^{2} c - d\right)} {\rm Li}_2\left(\frac{a^{2} c - i \, a d x - {\left(i \, a^{2} x - a\right)} \sqrt{c} \sqrt{d}}{a^{2} c + 2 \, a \sqrt{c} \sqrt{d} + d}\right) - 2 \, {\left(a^{2} c - d\right)} {\rm Li}_2\left(\frac{a^{2} c + i \, a d x - {\left(i \, a^{2} x + a\right)} \sqrt{c} \sqrt{d}}{a^{2} c - 2 \, a \sqrt{c} \sqrt{d} + d}\right) - 2 \, {\left(a^{2} c - d\right)} {\rm Li}_2\left(\frac{a^{2} c - i \, a d x + {\left(i \, a^{2} x - a\right)} \sqrt{c} \sqrt{d}}{a^{2} c - 2 \, a \sqrt{c} \sqrt{d} + d}\right)\right)} \sqrt{c} \sqrt{d}\right)} a}{16 \, {\left(a^{3} c^{3} d - a c^{2} d^{2}\right)}}"," ",0,"1/2*(x/(c*d*x^2 + c^2) + arctan(d*x/sqrt(c*d))/(sqrt(c*d)*c))*arccot(a*x) + 1/16*(4*a*c*d*log(a^2*x^2 + 1) - 4*a*c*d*log(d*x^2 + c) + (4*(a^2*c - d)*arctan(a*x)*arctan(sqrt(d)*x/sqrt(c)) + 4*(a^2*c - d)*arctan(sqrt(d)*x/sqrt(c))*arctan2(-a*sqrt(d)*x/(a*sqrt(c) - sqrt(d)), -sqrt(d)/(a*sqrt(c) - sqrt(d))) + (a^2*c - d)*log(d*x^2 + c)*log((a^2*c*d + (a^4*c*d + a^2*d^2)*x^2 + 2*(a^3*d*x^2 + a*d)*sqrt(c)*sqrt(d) + d^2)/(a^4*c^2 + 6*a^2*c*d + 4*(a^3*c + a*d)*sqrt(c)*sqrt(d) + d^2)) - (a^2*c - d)*log(d*x^2 + c)*log((a^2*c*d + (a^4*c*d + a^2*d^2)*x^2 - 2*(a^3*d*x^2 + a*d)*sqrt(c)*sqrt(d) + d^2)/(a^4*c^2 + 6*a^2*c*d - 4*(a^3*c + a*d)*sqrt(c)*sqrt(d) + d^2)) + 2*(a^2*c - d)*dilog((a^2*c + I*a*d*x + (I*a^2*x + a)*sqrt(c)*sqrt(d))/(a^2*c + 2*a*sqrt(c)*sqrt(d) + d)) + 2*(a^2*c - d)*dilog((a^2*c - I*a*d*x - (I*a^2*x - a)*sqrt(c)*sqrt(d))/(a^2*c + 2*a*sqrt(c)*sqrt(d) + d)) - 2*(a^2*c - d)*dilog((a^2*c + I*a*d*x - (I*a^2*x + a)*sqrt(c)*sqrt(d))/(a^2*c - 2*a*sqrt(c)*sqrt(d) + d)) - 2*(a^2*c - d)*dilog((a^2*c - I*a*d*x + (I*a^2*x - a)*sqrt(c)*sqrt(d))/(a^2*c - 2*a*sqrt(c)*sqrt(d) + d)))*sqrt(c)*sqrt(d))*a/(a^3*c^3*d - a*c^2*d^2)","A",0
59,-2,0,0,0.000000," ","integrate((d*x^2+c)^(1/2)*arccot(a*x),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(d-a^2*c>0)', see `assume?` for more details)Is d-a^2*c positive or negative?","F(-2)",0
60,0,0,0,0.000000," ","integrate(arccot(a*x)/(d*x^2+c)^(1/2),x, algorithm=""maxima"")","\int \frac{\operatorname{arccot}\left(a x\right)}{\sqrt{d x^{2} + c}}\,{d x}"," ",0,"integrate(arccot(a*x)/sqrt(d*x^2 + c), x)","F",0
61,-2,0,0,0.000000," ","integrate(arccot(a*x)/(d*x^2+c)^(3/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(d-a^2*c>0)', see `assume?` for more details)Is d-a^2*c positive or negative?","F(-2)",0
62,-2,0,0,0.000000," ","integrate(arccot(a*x)/(d*x^2+c)^(5/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(d-a^2*c>0)', see `assume?` for more details)Is d-a^2*c positive or negative?","F(-2)",0
63,-2,0,0,0.000000," ","integrate(arccot(a*x)/(d*x^2+c)^(7/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(d-a^2*c>0)', see `assume?` for more details)Is d-a^2*c positive or negative?","F(-2)",0
64,-2,0,0,0.000000," ","integrate(arccot(a*x)/(d*x^2+c)^(9/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(d-a^2*c>0)', see `assume?` for more details)Is d-a^2*c positive or negative?","F(-2)",0
65,0,0,0,0.000000," ","integrate((a*x^2+a)^(1/2)*arccot(x),x, algorithm=""maxima"")","\int \sqrt{a x^{2} + a} \operatorname{arccot}\left(x\right)\,{d x}"," ",0,"integrate(sqrt(a*x^2 + a)*arccot(x), x)","F",0
66,0,0,0,0.000000," ","integrate(arccot(x)/(a*x^2+a)^(1/2),x, algorithm=""maxima"")","\int \frac{\operatorname{arccot}\left(x\right)}{\sqrt{a x^{2} + a}}\,{d x}"," ",0,"integrate(arccot(x)/sqrt(a*x^2 + a), x)","F",0
67,1,31,0,0.479858," ","integrate(arccot(x)/(a*x^2+a)^(3/2),x, algorithm=""maxima"")","\frac{x \operatorname{arccot}\left(x\right)}{\sqrt{a x^{2} + a} a} - \frac{1}{\sqrt{a x^{2} + a} a}"," ",0,"x*arccot(x)/(sqrt(a*x^2 + a)*a) - 1/(sqrt(a*x^2 + a)*a)","A",0
68,1,63,0,0.450442," ","integrate(arccot(x)/(a*x^2+a)^(5/2),x, algorithm=""maxima"")","\frac{1}{3} \, {\left(\frac{2 \, x}{\sqrt{a x^{2} + a} a^{2}} + \frac{x}{{\left(a x^{2} + a\right)}^{\frac{3}{2}} a}\right)} \operatorname{arccot}\left(x\right) - \frac{2}{3 \, \sqrt{a x^{2} + a} a^{2}} - \frac{1}{9 \, {\left(a x^{2} + a\right)}^{\frac{3}{2}} a}"," ",0,"1/3*(2*x/(sqrt(a*x^2 + a)*a^2) + x/((a*x^2 + a)^(3/2)*a))*arccot(x) - 2/3/(sqrt(a*x^2 + a)*a^2) - 1/9/((a*x^2 + a)^(3/2)*a)","A",0
69,1,93,0,0.454689," ","integrate(arccot(x)/(a*x^2+a)^(7/2),x, algorithm=""maxima"")","\frac{1}{15} \, {\left(\frac{8 \, x}{\sqrt{a x^{2} + a} a^{3}} + \frac{4 \, x}{{\left(a x^{2} + a\right)}^{\frac{3}{2}} a^{2}} + \frac{3 \, x}{{\left(a x^{2} + a\right)}^{\frac{5}{2}} a}\right)} \operatorname{arccot}\left(x\right) - \frac{8}{15 \, \sqrt{a x^{2} + a} a^{3}} - \frac{4}{45 \, {\left(a x^{2} + a\right)}^{\frac{3}{2}} a^{2}} - \frac{1}{25 \, {\left(a x^{2} + a\right)}^{\frac{5}{2}} a}"," ",0,"1/15*(8*x/(sqrt(a*x^2 + a)*a^3) + 4*x/((a*x^2 + a)^(3/2)*a^2) + 3*x/((a*x^2 + a)^(5/2)*a))*arccot(x) - 8/15/(sqrt(a*x^2 + a)*a^3) - 4/45/((a*x^2 + a)^(3/2)*a^2) - 1/25/((a*x^2 + a)^(5/2)*a)","A",0
70,1,26,0,0.446754," ","integrate(x*arccot(x)/(x^2+1)^2,x, algorithm=""maxima"")","-\frac{x}{4 \, {\left(x^{2} + 1\right)}} - \frac{\operatorname{arccot}\left(x\right)}{2 \, {\left(x^{2} + 1\right)}} - \frac{1}{4} \, \arctan\left(x\right)"," ",0,"-1/4*x/(x^2 + 1) - 1/2*arccot(x)/(x^2 + 1) - 1/4*arctan(x)","A",0
71,1,39,0,0.438339," ","integrate(x*arccot(x)/(x^2+1)^3,x, algorithm=""maxima"")","-\frac{3 \, x^{3} + 5 \, x}{32 \, {\left(x^{4} + 2 \, x^{2} + 1\right)}} - \frac{\operatorname{arccot}\left(x\right)}{4 \, {\left(x^{2} + 1\right)}^{2}} - \frac{3}{32} \, \arctan\left(x\right)"," ",0,"-1/32*(3*x^3 + 5*x)/(x^4 + 2*x^2 + 1) - 1/4*arccot(x)/(x^2 + 1)^2 - 3/32*arctan(x)","A",0
72,1,38,0,0.419365," ","integrate(arccot(x)/(x^2+1)^2,x, algorithm=""maxima"")","\frac{1}{2} \, {\left(\frac{x}{x^{2} + 1} + \arctan\left(x\right)\right)} \operatorname{arccot}\left(x\right) + \frac{{\left(x^{2} + 1\right)} \arctan\left(x\right)^{2} - 1}{4 \, {\left(x^{2} + 1\right)}}"," ",0,"1/2*(x/(x^2 + 1) + arctan(x))*arccot(x) + 1/4*((x^2 + 1)*arctan(x)^2 - 1)/(x^2 + 1)","A",0
73,1,75,0,0.430319," ","integrate(arccot(x)^2/(x^2+1)^2,x, algorithm=""maxima"")","\frac{1}{2} \, {\left(\frac{x}{x^{2} + 1} + \arctan\left(x\right)\right)} \operatorname{arccot}\left(x\right)^{2} + \frac{{\left({\left(x^{2} + 1\right)} \arctan\left(x\right)^{2} - 1\right)} \operatorname{arccot}\left(x\right)}{2 \, {\left(x^{2} + 1\right)}} + \frac{2 \, {\left(x^{2} + 1\right)} \arctan\left(x\right)^{3} - 3 \, {\left(x^{2} + 1\right)} \arctan\left(x\right) - 3 \, x}{12 \, {\left(x^{2} + 1\right)}}"," ",0,"1/2*(x/(x^2 + 1) + arctan(x))*arccot(x)^2 + 1/2*((x^2 + 1)*arctan(x)^2 - 1)*arccot(x)/(x^2 + 1) + 1/12*(2*(x^2 + 1)*arctan(x)^3 - 3*(x^2 + 1)*arctan(x) - 3*x)/(x^2 + 1)","A",0
74,1,38,0,0.315147," ","integrate(x^5*arccot(a*x^2),x, algorithm=""maxima"")","\frac{1}{6} \, x^{6} \operatorname{arccot}\left(a x^{2}\right) + \frac{1}{12} \, {\left(\frac{x^{4}}{a^{2}} - \frac{\log\left(a^{2} x^{4} + 1\right)}{a^{4}}\right)} a"," ",0,"1/6*x^6*arccot(a*x^2) + 1/12*(x^4/a^2 - log(a^2*x^4 + 1)/a^4)*a","A",0
75,1,34,0,0.416918," ","integrate(x^3*arccot(a*x^2),x, algorithm=""maxima"")","\frac{1}{4} \, x^{4} \operatorname{arccot}\left(a x^{2}\right) + \frac{1}{4} \, a {\left(\frac{x^{2}}{a^{2}} - \frac{\arctan\left(a x^{2}\right)}{a^{3}}\right)}"," ",0,"1/4*x^4*arccot(a*x^2) + 1/4*a*(x^2/a^2 - arctan(a*x^2)/a^3)","A",0
76,1,28,0,0.323013," ","integrate(x*arccot(a*x^2),x, algorithm=""maxima"")","\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
77,1,68,0,0.480377," ","integrate(arccot(a*x^2)/x,x, algorithm=""maxima"")","\frac{1}{8} \, \pi \log\left(a^{2} x^{4} + 1\right) - \frac{1}{2} \, \arctan\left(a x^{2}\right) \log\left(a x^{2}\right) + \operatorname{arccot}\left(a x^{2}\right) \log\left(x\right) + \arctan\left(a x^{2}\right) \log\left(x\right) + \frac{1}{4} i \, {\rm Li}_2\left(i \, a x^{2} + 1\right) - \frac{1}{4} i \, {\rm Li}_2\left(-i \, a x^{2} + 1\right)"," ",0,"1/8*pi*log(a^2*x^4 + 1) - 1/2*arctan(a*x^2)*log(a*x^2) + arccot(a*x^2)*log(x) + arctan(a*x^2)*log(x) + 1/4*I*dilog(I*a*x^2 + 1) - 1/4*I*dilog(-I*a*x^2 + 1)","B",0
78,1,32,0,0.316601," ","integrate(arccot(a*x^2)/x^3,x, algorithm=""maxima"")","\frac{1}{4} \, a {\left(\log\left(a^{2} x^{4} + 1\right) - \log\left(x^{4}\right)\right)} - \frac{\operatorname{arccot}\left(a x^{2}\right)}{2 \, x^{2}}"," ",0,"1/4*a*(log(a^2*x^4 + 1) - log(x^4)) - 1/2*arccot(a*x^2)/x^2","A",0
79,1,27,0,0.408470," ","integrate(arccot(a*x^2)/x^5,x, algorithm=""maxima"")","\frac{1}{4} \, {\left(a \arctan\left(a x^{2}\right) + \frac{1}{x^{2}}\right)} a - \frac{\operatorname{arccot}\left(a x^{2}\right)}{4 \, x^{4}}"," ",0,"1/4*(a*arctan(a*x^2) + 1/x^2)*a - 1/4*arccot(a*x^2)/x^4","A",0
80,1,137,0,0.406341," ","integrate(x^4*arccot(a*x^2),x, algorithm=""maxima"")","\frac{1}{5} \, x^{5} \operatorname{arccot}\left(a x^{2}\right) + \frac{1}{60} \, a {\left(\frac{8 \, x^{3}}{a^{2}} - \frac{3 \, {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(2 \, a x + \sqrt{2} \sqrt{a}\right)}}{2 \, \sqrt{a}}\right)}{a^{\frac{3}{2}}} + \frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(2 \, a x - \sqrt{2} \sqrt{a}\right)}}{2 \, \sqrt{a}}\right)}{a^{\frac{3}{2}}} - \frac{\sqrt{2} \log\left(a x^{2} + \sqrt{2} \sqrt{a} x + 1\right)}{a^{\frac{3}{2}}} + \frac{\sqrt{2} \log\left(a x^{2} - \sqrt{2} \sqrt{a} x + 1\right)}{a^{\frac{3}{2}}}\right)}}{a^{2}}\right)}"," ",0,"1/5*x^5*arccot(a*x^2) + 1/60*a*(8*x^3/a^2 - 3*(2*sqrt(2)*arctan(1/2*sqrt(2)*(2*a*x + sqrt(2)*sqrt(a))/sqrt(a))/a^(3/2) + 2*sqrt(2)*arctan(1/2*sqrt(2)*(2*a*x - sqrt(2)*sqrt(a))/sqrt(a))/a^(3/2) - sqrt(2)*log(a*x^2 + sqrt(2)*sqrt(a)*x + 1)/a^(3/2) + sqrt(2)*log(a*x^2 - sqrt(2)*sqrt(a)*x + 1)/a^(3/2))/a^2)","A",0
81,1,135,0,0.409564," ","integrate(x^2*arccot(a*x^2),x, algorithm=""maxima"")","\frac{1}{3} \, x^{3} \operatorname{arccot}\left(a x^{2}\right) + \frac{1}{12} \, a {\left(\frac{8 \, x}{a^{2}} - \frac{\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(2 \, a x + \sqrt{2} \sqrt{a}\right)}}{2 \, \sqrt{a}}\right)}{\sqrt{a}} + \frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(2 \, a x - \sqrt{2} \sqrt{a}\right)}}{2 \, \sqrt{a}}\right)}{\sqrt{a}} + \frac{\sqrt{2} \log\left(a x^{2} + \sqrt{2} \sqrt{a} x + 1\right)}{\sqrt{a}} - \frac{\sqrt{2} \log\left(a x^{2} - \sqrt{2} \sqrt{a} x + 1\right)}{\sqrt{a}}}{a^{2}}\right)}"," ",0,"1/3*x^3*arccot(a*x^2) + 1/12*a*(8*x/a^2 - (2*sqrt(2)*arctan(1/2*sqrt(2)*(2*a*x + sqrt(2)*sqrt(a))/sqrt(a))/sqrt(a) + 2*sqrt(2)*arctan(1/2*sqrt(2)*(2*a*x - sqrt(2)*sqrt(a))/sqrt(a))/sqrt(a) + sqrt(2)*log(a*x^2 + sqrt(2)*sqrt(a)*x + 1)/sqrt(a) - sqrt(2)*log(a*x^2 - sqrt(2)*sqrt(a)*x + 1)/sqrt(a))/a^2)","A",0
82,1,120,0,0.412687," ","integrate(arccot(a*x^2),x, algorithm=""maxima"")","\frac{1}{4} \, a {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(2 \, a x + \sqrt{2} \sqrt{a}\right)}}{2 \, \sqrt{a}}\right)}{a^{\frac{3}{2}}} + \frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(2 \, a x - \sqrt{2} \sqrt{a}\right)}}{2 \, \sqrt{a}}\right)}{a^{\frac{3}{2}}} - \frac{\sqrt{2} \log\left(a x^{2} + \sqrt{2} \sqrt{a} x + 1\right)}{a^{\frac{3}{2}}} + \frac{\sqrt{2} \log\left(a x^{2} - \sqrt{2} \sqrt{a} x + 1\right)}{a^{\frac{3}{2}}}\right)} + x \operatorname{arccot}\left(a x^{2}\right)"," ",0,"1/4*a*(2*sqrt(2)*arctan(1/2*sqrt(2)*(2*a*x + sqrt(2)*sqrt(a))/sqrt(a))/a^(3/2) + 2*sqrt(2)*arctan(1/2*sqrt(2)*(2*a*x - sqrt(2)*sqrt(a))/sqrt(a))/a^(3/2) - sqrt(2)*log(a*x^2 + sqrt(2)*sqrt(a)*x + 1)/a^(3/2) + sqrt(2)*log(a*x^2 - sqrt(2)*sqrt(a)*x + 1)/a^(3/2)) + x*arccot(a*x^2)","A",0
83,1,123,0,0.411068," ","integrate(arccot(a*x^2)/x^2,x, algorithm=""maxima"")","-\frac{1}{4} \, a {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(2 \, a x + \sqrt{2} \sqrt{a}\right)}}{2 \, \sqrt{a}}\right)}{\sqrt{a}} + \frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(2 \, a x - \sqrt{2} \sqrt{a}\right)}}{2 \, \sqrt{a}}\right)}{\sqrt{a}} + \frac{\sqrt{2} \log\left(a x^{2} + \sqrt{2} \sqrt{a} x + 1\right)}{\sqrt{a}} - \frac{\sqrt{2} \log\left(a x^{2} - \sqrt{2} \sqrt{a} x + 1\right)}{\sqrt{a}}\right)} - \frac{\operatorname{arccot}\left(a x^{2}\right)}{x}"," ",0,"-1/4*a*(2*sqrt(2)*arctan(1/2*sqrt(2)*(2*a*x + sqrt(2)*sqrt(a))/sqrt(a))/sqrt(a) + 2*sqrt(2)*arctan(1/2*sqrt(2)*(2*a*x - sqrt(2)*sqrt(a))/sqrt(a))/sqrt(a) + sqrt(2)*log(a*x^2 + sqrt(2)*sqrt(a)*x + 1)/sqrt(a) - sqrt(2)*log(a*x^2 - sqrt(2)*sqrt(a)*x + 1)/sqrt(a)) - arccot(a*x^2)/x","A",0
84,1,133,0,0.414914," ","integrate(arccot(a*x^2)/x^4,x, algorithm=""maxima"")","\frac{1}{12} \, {\left(a^{2} {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(2 \, a x + \sqrt{2} \sqrt{a}\right)}}{2 \, \sqrt{a}}\right)}{a^{\frac{3}{2}}} + \frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(2 \, a x - \sqrt{2} \sqrt{a}\right)}}{2 \, \sqrt{a}}\right)}{a^{\frac{3}{2}}} - \frac{\sqrt{2} \log\left(a x^{2} + \sqrt{2} \sqrt{a} x + 1\right)}{a^{\frac{3}{2}}} + \frac{\sqrt{2} \log\left(a x^{2} - \sqrt{2} \sqrt{a} x + 1\right)}{a^{\frac{3}{2}}}\right)} + \frac{8}{x}\right)} a - \frac{\operatorname{arccot}\left(a x^{2}\right)}{3 \, x^{3}}"," ",0,"1/12*(a^2*(2*sqrt(2)*arctan(1/2*sqrt(2)*(2*a*x + sqrt(2)*sqrt(a))/sqrt(a))/a^(3/2) + 2*sqrt(2)*arctan(1/2*sqrt(2)*(2*a*x - sqrt(2)*sqrt(a))/sqrt(a))/a^(3/2) - sqrt(2)*log(a*x^2 + sqrt(2)*sqrt(a)*x + 1)/a^(3/2) + sqrt(2)*log(a*x^2 - sqrt(2)*sqrt(a)*x + 1)/a^(3/2)) + 8/x)*a - 1/3*arccot(a*x^2)/x^3","A",0
85,1,31,0,0.564362," ","integrate(x^2*arccot(x^(1/2)),x, algorithm=""maxima"")","\frac{1}{3} \, x^{3} \operatorname{arccot}\left(\sqrt{x}\right) + \frac{1}{15} \, x^{\frac{5}{2}} - \frac{1}{9} \, x^{\frac{3}{2}} + \frac{1}{3} \, \sqrt{x} - \frac{1}{3} \, \arctan\left(\sqrt{x}\right)"," ",0,"1/3*x^3*arccot(sqrt(x)) + 1/15*x^(5/2) - 1/9*x^(3/2) + 1/3*sqrt(x) - 1/3*arctan(sqrt(x))","A",0
86,1,26,0,0.416179," ","integrate(x*arccot(x^(1/2)),x, algorithm=""maxima"")","\frac{1}{2} \, x^{2} \operatorname{arccot}\left(\sqrt{x}\right) + \frac{1}{6} \, x^{\frac{3}{2}} - \frac{1}{2} \, \sqrt{x} + \frac{1}{2} \, \arctan\left(\sqrt{x}\right)"," ",0,"1/2*x^2*arccot(sqrt(x)) + 1/6*x^(3/2) - 1/2*sqrt(x) + 1/2*arctan(sqrt(x))","A",0
87,1,16,0,0.414488," ","integrate(arccot(x^(1/2)),x, algorithm=""maxima"")","x \operatorname{arccot}\left(\sqrt{x}\right) + \sqrt{x} - \arctan\left(\sqrt{x}\right)"," ",0,"x*arccot(sqrt(x)) + sqrt(x) - arctan(sqrt(x))","A",0
88,1,35,0,0.452900," ","integrate(arccot(x^(1/2))/x,x, algorithm=""maxima"")","\frac{1}{2} \, \pi \log\left(x + 1\right) + \operatorname{arccot}\left(\sqrt{x}\right) \log\left(x\right) + i \, {\rm Li}_2\left(i \, \sqrt{x} + 1\right) - i \, {\rm Li}_2\left(-i \, \sqrt{x} + 1\right)"," ",0,"1/2*pi*log(x + 1) + arccot(sqrt(x))*log(x) + I*dilog(I*sqrt(x) + 1) - I*dilog(-I*sqrt(x) + 1)","B",0
89,1,17,0,0.433846," ","integrate(arccot(x^(1/2))/x^2,x, algorithm=""maxima"")","-\frac{\operatorname{arccot}\left(\sqrt{x}\right)}{x} + \frac{1}{\sqrt{x}} + \arctan\left(\sqrt{x}\right)"," ",0,"-arccot(sqrt(x))/x + 1/sqrt(x) + arctan(sqrt(x))","A",0
90,1,26,0,0.412040," ","integrate(arccot(x^(1/2))/x^3,x, algorithm=""maxima"")","-\frac{3 \, x - 1}{6 \, x^{\frac{3}{2}}} - \frac{\operatorname{arccot}\left(\sqrt{x}\right)}{2 \, x^{2}} - \frac{1}{2} \, \arctan\left(\sqrt{x}\right)"," ",0,"-1/6*(3*x - 1)/x^(3/2) - 1/2*arccot(sqrt(x))/x^2 - 1/2*arctan(sqrt(x))","A",0
91,1,24,0,0.328260," ","integrate(x^(3/2)*arccot(x^(1/2)),x, algorithm=""maxima"")","\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
92,1,19,0,0.314932," ","integrate(x^(1/2)*arccot(x^(1/2)),x, algorithm=""maxima"")","\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
93,1,14,0,0.312932," ","integrate(arccot(x^(1/2))/x^(1/2),x, algorithm=""maxima"")","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
94,1,18,0,0.329596," ","integrate(arccot(x^(1/2))/x^(3/2),x, algorithm=""maxima"")","-\frac{2 \, \operatorname{arccot}\left(\sqrt{x}\right)}{\sqrt{x}} + \log\left(x + 1\right) - \log\left(x\right)"," ",0,"-2*arccot(sqrt(x))/sqrt(x) + log(x + 1) - log(x)","A",0
95,1,25,0,0.324518," ","integrate(arccot(x^(1/2))/x^(5/2),x, algorithm=""maxima"")","-\frac{2 \, \operatorname{arccot}\left(\sqrt{x}\right)}{3 \, x^{\frac{3}{2}}} + \frac{1}{3 \, x} - \frac{1}{3} \, \log\left(x + 1\right) + \frac{1}{3} \, \log\left(x\right)"," ",0,"-2/3*arccot(sqrt(x))/x^(3/2) + 1/3/x - 1/3*log(x + 1) + 1/3*log(x)","A",0
96,1,15,0,0.331650," ","integrate(arccot(1/x),x, algorithm=""maxima"")","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
97,0,0,0,0.000000," ","integrate(arccot(a*x^n)/x,x, algorithm=""maxima"")","a n \int \frac{x^{n} \log\left(x\right)}{a^{2} x x^{2 \, n} + x}\,{d x} + \arctan\left(\frac{1}{a x^{n}}\right) \log\left(x\right)"," ",0,"a*n*integrate(x^n*log(x)/(a^2*x*x^(2*n) + x), x) + arctan(1/(a*x^n))*log(x)","F",0
98,1,68,0,0.561659," ","integrate(arccot(a*x^5)/x,x, algorithm=""maxima"")","\frac{1}{20} \, \pi \log\left(a^{2} x^{10} + 1\right) - \frac{1}{5} \, \arctan\left(a x^{5}\right) \log\left(a x^{5}\right) + \operatorname{arccot}\left(a x^{5}\right) \log\left(x\right) + \arctan\left(a x^{5}\right) \log\left(x\right) + \frac{1}{10} i \, {\rm Li}_2\left(i \, a x^{5} + 1\right) - \frac{1}{10} i \, {\rm Li}_2\left(-i \, a x^{5} + 1\right)"," ",0,"1/20*pi*log(a^2*x^10 + 1) - 1/5*arctan(a*x^5)*log(a*x^5) + arccot(a*x^5)*log(x) + arctan(a*x^5)*log(x) + 1/10*I*dilog(I*a*x^5 + 1) - 1/10*I*dilog(-I*a*x^5 + 1)","B",0
99,1,104,0,0.430743," ","integrate(x^3*arccot(b*x+a),x, algorithm=""maxima"")","\frac{1}{4} \, x^{4} \operatorname{arccot}\left(b x + a\right) + \frac{1}{12} \, b {\left(\frac{b^{2} x^{3} - 3 \, a b x^{2} + 3 \, {\left(3 \, a^{2} - 1\right)} x}{b^{4}} + \frac{3 \, {\left(a^{4} - 6 \, a^{2} + 1\right)} \arctan\left(\frac{b^{2} x + a b}{b}\right)}{b^{5}} - \frac{6 \, {\left(a^{3} - a\right)} \log\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}{b^{5}}\right)}"," ",0,"1/4*x^4*arccot(b*x + a) + 1/12*b*((b^2*x^3 - 3*a*b*x^2 + 3*(3*a^2 - 1)*x)/b^4 + 3*(a^4 - 6*a^2 + 1)*arctan((b^2*x + a*b)/b)/b^5 - 6*(a^3 - a)*log(b^2*x^2 + 2*a*b*x + a^2 + 1)/b^5)","A",0
100,1,85,0,0.444370," ","integrate(x^2*arccot(b*x+a),x, algorithm=""maxima"")","\frac{1}{3} \, x^{3} \operatorname{arccot}\left(b x + a\right) + \frac{1}{6} \, b {\left(\frac{b x^{2} - 4 \, a x}{b^{3}} - \frac{2 \, {\left(a^{3} - 3 \, a\right)} \arctan\left(\frac{b^{2} x + a b}{b}\right)}{b^{4}} + \frac{{\left(3 \, a^{2} - 1\right)} \log\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}{b^{4}}\right)}"," ",0,"1/3*x^3*arccot(b*x + a) + 1/6*b*((b*x^2 - 4*a*x)/b^3 - 2*(a^3 - 3*a)*arctan((b^2*x + a*b)/b)/b^4 + (3*a^2 - 1)*log(b^2*x^2 + 2*a*b*x + a^2 + 1)/b^4)","A",0
101,1,68,0,0.429155," ","integrate(x*arccot(b*x+a),x, algorithm=""maxima"")","\frac{1}{2} \, x^{2} \operatorname{arccot}\left(b x + a\right) + \frac{1}{2} \, b {\left(\frac{x}{b^{2}} + \frac{{\left(a^{2} - 1\right)} \arctan\left(\frac{b^{2} x + a b}{b}\right)}{b^{3}} - \frac{a \log\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}{b^{3}}\right)}"," ",0,"1/2*x^2*arccot(b*x + a) + 1/2*b*(x/b^2 + (a^2 - 1)*arctan((b^2*x + a*b)/b)/b^3 - a*log(b^2*x^2 + 2*a*b*x + a^2 + 1)/b^3)","A",0
102,1,29,0,0.372514," ","integrate(arccot(b*x+a),x, algorithm=""maxima"")","\frac{2 \, {\left(b x + a\right)} \operatorname{arccot}\left(b x + a\right) + \log\left({\left(b x + a\right)}^{2} + 1\right)}{2 \, b}"," ",0,"1/2*(2*(b*x + a)*arccot(b*x + a) + log((b*x + a)^2 + 1))/b","A",0
103,1,133,0,0.483371," ","integrate(arccot(b*x+a)/x,x, algorithm=""maxima"")","\frac{1}{2} \, \arctan\left(\frac{b x}{a^{2} + 1}, -\frac{a b x}{a^{2} + 1}\right) \log\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right) - \frac{1}{2} \, \arctan\left(b x + a\right) \log\left(\frac{b^{2} x^{2}}{a^{2} + 1}\right) + \operatorname{arccot}\left(b x + a\right) \log\left(x\right) + \arctan\left(\frac{b^{2} x + a b}{b}\right) \log\left(x\right) + \frac{1}{2} i \, {\rm Li}_2\left(\frac{i \, b x + i \, a + 1}{i \, a + 1}\right) - \frac{1}{2} i \, {\rm Li}_2\left(\frac{i \, b x + i \, a - 1}{i \, a - 1}\right)"," ",0,"1/2*arctan2(b*x/(a^2 + 1), -a*b*x/(a^2 + 1))*log(b^2*x^2 + 2*a*b*x + a^2 + 1) - 1/2*arctan(b*x + a)*log(b^2*x^2/(a^2 + 1)) + arccot(b*x + a)*log(x) + arctan((b^2*x + a*b)/b)*log(x) + 1/2*I*dilog((I*b*x + I*a + 1)/(I*a + 1)) - 1/2*I*dilog((I*b*x + I*a - 1)/(I*a - 1))","A",0
104,1,77,0,0.424686," ","integrate(arccot(b*x+a)/x^2,x, algorithm=""maxima"")","\frac{1}{2} \, b {\left(\frac{2 \, a \arctan\left(\frac{b^{2} x + a b}{b}\right)}{a^{2} + 1} + \frac{\log\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}{a^{2} + 1} - \frac{2 \, \log\left(x\right)}{a^{2} + 1}\right)} - \frac{\operatorname{arccot}\left(b x + a\right)}{x}"," ",0,"1/2*b*(2*a*arctan((b^2*x + a*b)/b)/(a^2 + 1) + log(b^2*x^2 + 2*a*b*x + a^2 + 1)/(a^2 + 1) - 2*log(x)/(a^2 + 1)) - arccot(b*x + a)/x","A",0
105,1,112,0,0.421959," ","integrate(arccot(b*x+a)/x^3,x, algorithm=""maxima"")","-\frac{1}{2} \, {\left(\frac{{\left(a^{2} - 1\right)} b \arctan\left(\frac{b^{2} x + a b}{b}\right)}{a^{4} + 2 \, a^{2} + 1} + \frac{a b \log\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}{a^{4} + 2 \, a^{2} + 1} - \frac{2 \, a b \log\left(x\right)}{a^{4} + 2 \, a^{2} + 1} - \frac{1}{{\left(a^{2} + 1\right)} x}\right)} b - \frac{\operatorname{arccot}\left(b x + a\right)}{2 \, x^{2}}"," ",0,"-1/2*((a^2 - 1)*b*arctan((b^2*x + a*b)/b)/(a^4 + 2*a^2 + 1) + a*b*log(b^2*x^2 + 2*a*b*x + a^2 + 1)/(a^4 + 2*a^2 + 1) - 2*a*b*log(x)/(a^4 + 2*a^2 + 1) - 1/((a^2 + 1)*x))*b - 1/2*arccot(b*x + a)/x^2","A",0
106,1,165,0,0.416635," ","integrate(arccot(b*x+a)/x^4,x, algorithm=""maxima"")","\frac{1}{6} \, {\left(\frac{2 \, {\left(a^{3} - 3 \, a\right)} b^{2} \arctan\left(\frac{b^{2} x + a b}{b}\right)}{a^{6} + 3 \, a^{4} + 3 \, a^{2} + 1} + \frac{{\left(3 \, a^{2} - 1\right)} b^{2} \log\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}{a^{6} + 3 \, a^{4} + 3 \, a^{2} + 1} - \frac{2 \, {\left(3 \, a^{2} - 1\right)} b^{2} \log\left(x\right)}{a^{6} + 3 \, a^{4} + 3 \, a^{2} + 1} - \frac{4 \, a b x - a^{2} - 1}{{\left(a^{4} + 2 \, a^{2} + 1\right)} x^{2}}\right)} b - \frac{\operatorname{arccot}\left(b x + a\right)}{3 \, x^{3}}"," ",0,"1/6*(2*(a^3 - 3*a)*b^2*arctan((b^2*x + a*b)/b)/(a^6 + 3*a^4 + 3*a^2 + 1) + (3*a^2 - 1)*b^2*log(b^2*x^2 + 2*a*b*x + a^2 + 1)/(a^6 + 3*a^4 + 3*a^2 + 1) - 2*(3*a^2 - 1)*b^2*log(x)/(a^6 + 3*a^4 + 3*a^2 + 1) - (4*a*b*x - a^2 - 1)/((a^4 + 2*a^2 + 1)*x^2))*b - 1/3*arccot(b*x + a)/x^3","A",0
107,1,8519,0,5.977929," ","integrate(arccot(b*x+a)/(d*x^2+c),x, algorithm=""maxima"")","-\frac{b {\left(\frac{8 \, \arctan\left(\frac{d x}{\sqrt{c d}}\right) \arctan\left(\frac{b^{2} x + a b}{b}\right)}{b} - \frac{4 \, \arctan\left(\frac{\sqrt{d} x}{\sqrt{c}}\right) \arctan\left(\frac{2 \, a b^{2} c d + {\left(a b^{3} c + {\left(a^{3} + a\right)} b d + {\left(b^{4} c + {\left(a^{2} + 3\right)} b^{2} d\right)} x\right)} \sqrt{c} \sqrt{d} + {\left(3 \, b^{3} c d + {\left(a^{2} + 1\right)} b d^{2}\right)} x}{b^{4} c^{2} + 2 \, {\left(a^{2} + 3\right)} b^{2} c d + {\left(a^{4} + 2 \, a^{2} + 1\right)} d^{2} + 4 \, {\left(b^{3} c + {\left(a^{2} + 1\right)} b d\right)} \sqrt{c} \sqrt{d}}, \frac{{\left(a^{2} + 3\right)} b^{2} c d + {\left(a^{4} + 2 \, a^{2} + 1\right)} d^{2} + {\left(2 \, a b^{2} d x + b^{3} c + 3 \, {\left(a^{2} + 1\right)} b d\right)} \sqrt{c} \sqrt{d} + {\left(a b^{3} c d + {\left(a^{3} + a\right)} b d^{2}\right)} x}{b^{4} c^{2} + 2 \, {\left(a^{2} + 3\right)} b^{2} c d + {\left(a^{4} + 2 \, a^{2} + 1\right)} d^{2} + 4 \, {\left(b^{3} c + {\left(a^{2} + 1\right)} b d\right)} \sqrt{c} \sqrt{d}}\right) + 4 \, \arctan\left(\frac{\sqrt{d} x}{\sqrt{c}}\right) \arctan\left(\frac{2 \, a b^{2} c d - {\left(a b^{3} c + {\left(a^{3} + a\right)} b d + {\left(b^{4} c + {\left(a^{2} + 3\right)} b^{2} d\right)} x\right)} \sqrt{c} \sqrt{d} + {\left(3 \, b^{3} c d + {\left(a^{2} + 1\right)} b d^{2}\right)} x}{b^{4} c^{2} + 2 \, {\left(a^{2} + 3\right)} b^{2} c d + {\left(a^{4} + 2 \, a^{2} + 1\right)} d^{2} - 4 \, {\left(b^{3} c + {\left(a^{2} + 1\right)} b d\right)} \sqrt{c} \sqrt{d}}, \frac{{\left(a^{2} + 3\right)} b^{2} c d + {\left(a^{4} + 2 \, a^{2} + 1\right)} d^{2} - {\left(2 \, a b^{2} d x + b^{3} c + 3 \, {\left(a^{2} + 1\right)} b d\right)} \sqrt{c} \sqrt{d} + {\left(a b^{3} c d + {\left(a^{3} + a\right)} b d^{2}\right)} x}{b^{4} c^{2} + 2 \, {\left(a^{2} + 3\right)} b^{2} c d + {\left(a^{4} + 2 \, a^{2} + 1\right)} d^{2} - 4 \, {\left(b^{3} c + {\left(a^{2} + 1\right)} b d\right)} \sqrt{c} \sqrt{d}}\right) + \log\left(d x^{2} + c\right) \log\left(\frac{{\left(a^{2} + 1\right)} b^{22} c^{11} d + 11 \, {\left(a^{4} + 22 \, a^{2} + 21\right)} b^{20} c^{10} d^{2} + 55 \, {\left(a^{6} + 39 \, a^{4} + 171 \, a^{2} + 133\right)} b^{18} c^{9} d^{3} + 33 \, {\left(5 \, a^{8} + 260 \, a^{6} + 1870 \, a^{4} + 3876 \, a^{2} + 2261\right)} b^{16} c^{8} d^{4} + 330 \, {\left(a^{10} + 61 \, a^{8} + 570 \, a^{6} + 1802 \, a^{4} + 2261 \, a^{2} + 969\right)} b^{14} c^{7} d^{5} + 22 \, {\left(21 \, a^{12} + 1386 \, a^{10} + 15015 \, a^{8} + 60060 \, a^{6} + 109395 \, a^{4} + 92378 \, a^{2} + 29393\right)} b^{12} c^{6} d^{6} + 22 \, {\left(21 \, a^{14} + 1407 \, a^{12} + 16401 \, a^{10} + 75075 \, a^{8} + 169455 \, a^{6} + 201773 \, a^{4} + 121771 \, a^{2} + 29393\right)} b^{10} c^{5} d^{7} + 330 \, {\left(a^{16} + 64 \, a^{14} + 756 \, a^{12} + 3696 \, a^{10} + 9438 \, a^{8} + 13728 \, a^{6} + 11492 \, a^{4} + 5168 \, a^{2} + 969\right)} b^{8} c^{4} d^{8} + 33 \, {\left(5 \, a^{18} + 285 \, a^{16} + 3220 \, a^{14} + 15876 \, a^{12} + 42966 \, a^{10} + 70070 \, a^{8} + 70980 \, a^{6} + 43860 \, a^{4} + 15181 \, a^{2} + 2261\right)} b^{6} c^{3} d^{9} + 55 \, {\left(a^{20} + 46 \, a^{18} + 465 \, a^{16} + 2184 \, a^{14} + 5922 \, a^{12} + 10164 \, a^{10} + 11466 \, a^{8} + 8520 \, a^{6} + 4029 \, a^{4} + 1102 \, a^{2} + 133\right)} b^{4} c^{2} d^{10} + 11 \, {\left(a^{22} + 31 \, a^{20} + 255 \, a^{18} + 1065 \, a^{16} + 2730 \, a^{14} + 4662 \, a^{12} + 5502 \, a^{10} + 4530 \, a^{8} + 2565 \, a^{6} + 955 \, a^{4} + 211 \, a^{2} + 21\right)} b^{2} c d^{11} + {\left(a^{24} + 12 \, a^{22} + 66 \, a^{20} + 220 \, a^{18} + 495 \, a^{16} + 792 \, a^{14} + 924 \, a^{12} + 792 \, a^{10} + 495 \, a^{8} + 220 \, a^{6} + 66 \, a^{4} + 12 \, a^{2} + 1\right)} d^{12} + {\left(b^{24} c^{11} d + 11 \, {\left(a^{2} + 21\right)} b^{22} c^{10} d^{2} + 55 \, {\left(a^{4} + 38 \, a^{2} + 133\right)} b^{20} c^{9} d^{3} + 33 \, {\left(5 \, a^{6} + 255 \, a^{4} + 1615 \, a^{2} + 2261\right)} b^{18} c^{8} d^{4} + 330 \, {\left(a^{8} + 60 \, a^{6} + 510 \, a^{4} + 1292 \, a^{2} + 969\right)} b^{16} c^{7} d^{5} + 22 \, {\left(21 \, a^{10} + 1365 \, a^{8} + 13650 \, a^{6} + 46410 \, a^{4} + 62985 \, a^{2} + 29393\right)} b^{14} c^{6} d^{6} + 22 \, {\left(21 \, a^{12} + 1386 \, a^{10} + 15015 \, a^{8} + 60060 \, a^{6} + 109395 \, a^{4} + 92378 \, a^{2} + 29393\right)} b^{12} c^{5} d^{7} + 330 \, {\left(a^{14} + 63 \, a^{12} + 693 \, a^{10} + 3003 \, a^{8} + 6435 \, a^{6} + 7293 \, a^{4} + 4199 \, a^{2} + 969\right)} b^{10} c^{4} d^{8} + 33 \, {\left(5 \, a^{16} + 280 \, a^{14} + 2940 \, a^{12} + 12936 \, a^{10} + 30030 \, a^{8} + 40040 \, a^{6} + 30940 \, a^{4} + 12920 \, a^{2} + 2261\right)} b^{8} c^{3} d^{9} + 55 \, {\left(a^{18} + 45 \, a^{16} + 420 \, a^{14} + 1764 \, a^{12} + 4158 \, a^{10} + 6006 \, a^{8} + 5460 \, a^{6} + 3060 \, a^{4} + 969 \, a^{2} + 133\right)} b^{6} c^{2} d^{10} + 11 \, {\left(a^{20} + 30 \, a^{18} + 225 \, a^{16} + 840 \, a^{14} + 1890 \, a^{12} + 2772 \, a^{10} + 2730 \, a^{8} + 1800 \, a^{6} + 765 \, a^{4} + 190 \, a^{2} + 21\right)} b^{4} c d^{11} + {\left(a^{22} + 11 \, a^{20} + 55 \, a^{18} + 165 \, a^{16} + 330 \, a^{14} + 462 \, a^{12} + 462 \, a^{10} + 330 \, a^{8} + 165 \, a^{6} + 55 \, a^{4} + 11 \, a^{2} + 1\right)} b^{2} d^{12}\right)} x^{2} + 2 \, {\left(11 \, {\left(a^{2} + 1\right)} b^{21} c^{10} d + 110 \, {\left(a^{4} + 8 \, a^{2} + 7\right)} b^{19} c^{9} d^{2} + 33 \, {\left(15 \, a^{6} + 205 \, a^{4} + 589 \, a^{2} + 399\right)} b^{17} c^{8} d^{3} + 264 \, {\left(5 \, a^{8} + 90 \, a^{6} + 408 \, a^{4} + 646 \, a^{2} + 323\right)} b^{15} c^{7} d^{4} + 110 \, {\left(21 \, a^{10} + 441 \, a^{8} + 2562 \, a^{6} + 6018 \, a^{4} + 6137 \, a^{2} + 2261\right)} b^{13} c^{6} d^{5} + 4 \, {\left(693 \, a^{12} + 15708 \, a^{10} + 105105 \, a^{8} + 308880 \, a^{6} + 449735 \, a^{4} + 319124 \, a^{2} + 88179\right)} b^{11} c^{5} d^{6} + 110 \, {\left(21 \, a^{14} + 483 \, a^{12} + 3465 \, a^{10} + 11583 \, a^{8} + 20735 \, a^{6} + 20553 \, a^{4} + 10659 \, a^{2} + 2261\right)} b^{9} c^{4} d^{7} + 264 \, {\left(5 \, a^{16} + 110 \, a^{14} + 798 \, a^{12} + 2838 \, a^{10} + 5720 \, a^{8} + 6890 \, a^{6} + 4930 \, a^{4} + 1938 \, a^{2} + 323\right)} b^{7} c^{3} d^{8} + 33 \, {\left(15 \, a^{18} + 295 \, a^{16} + 2044 \, a^{14} + 7308 \, a^{12} + 15554 \, a^{10} + 20930 \, a^{8} + 18060 \, a^{6} + 9724 \, a^{4} + 2983 \, a^{2} + 399\right)} b^{5} c^{2} d^{9} + 110 \, {\left(a^{20} + 16 \, a^{18} + 99 \, a^{16} + 336 \, a^{14} + 714 \, a^{12} + 1008 \, a^{10} + 966 \, a^{8} + 624 \, a^{6} + 261 \, a^{4} + 64 \, a^{2} + 7\right)} b^{3} c d^{10} + 11 \, {\left(a^{22} + 11 \, a^{20} + 55 \, a^{18} + 165 \, a^{16} + 330 \, a^{14} + 462 \, a^{12} + 462 \, a^{10} + 330 \, a^{8} + 165 \, a^{6} + 55 \, a^{4} + 11 \, a^{2} + 1\right)} b d^{11} + {\left(11 \, b^{23} c^{10} d + 110 \, {\left(a^{2} + 7\right)} b^{21} c^{9} d^{2} + 33 \, {\left(15 \, a^{4} + 190 \, a^{2} + 399\right)} b^{19} c^{8} d^{3} + 264 \, {\left(5 \, a^{6} + 85 \, a^{4} + 323 \, a^{2} + 323\right)} b^{17} c^{7} d^{4} + 110 \, {\left(21 \, a^{8} + 420 \, a^{6} + 2142 \, a^{4} + 3876 \, a^{2} + 2261\right)} b^{15} c^{6} d^{5} + 4 \, {\left(693 \, a^{10} + 15015 \, a^{8} + 90090 \, a^{6} + 218790 \, a^{4} + 230945 \, a^{2} + 88179\right)} b^{13} c^{5} d^{6} + 110 \, {\left(21 \, a^{12} + 462 \, a^{10} + 3003 \, a^{8} + 8580 \, a^{6} + 12155 \, a^{4} + 8398 \, a^{2} + 2261\right)} b^{11} c^{4} d^{7} + 264 \, {\left(5 \, a^{14} + 105 \, a^{12} + 693 \, a^{10} + 2145 \, a^{8} + 3575 \, a^{6} + 3315 \, a^{4} + 1615 \, a^{2} + 323\right)} b^{9} c^{3} d^{8} + 33 \, {\left(15 \, a^{16} + 280 \, a^{14} + 1764 \, a^{12} + 5544 \, a^{10} + 10010 \, a^{8} + 10920 \, a^{6} + 7140 \, a^{4} + 2584 \, a^{2} + 399\right)} b^{7} c^{2} d^{9} + 110 \, {\left(a^{18} + 15 \, a^{16} + 84 \, a^{14} + 252 \, a^{12} + 462 \, a^{10} + 546 \, a^{8} + 420 \, a^{6} + 204 \, a^{4} + 57 \, a^{2} + 7\right)} b^{5} c d^{10} + 11 \, {\left(a^{20} + 10 \, a^{18} + 45 \, a^{16} + 120 \, a^{14} + 210 \, a^{12} + 252 \, a^{10} + 210 \, a^{8} + 120 \, a^{6} + 45 \, a^{4} + 10 \, a^{2} + 1\right)} b^{3} d^{11}\right)} x^{2} + 2 \, {\left(11 \, a b^{22} c^{10} d + 110 \, {\left(a^{3} + 7 \, a\right)} b^{20} c^{9} d^{2} + 33 \, {\left(15 \, a^{5} + 190 \, a^{3} + 399 \, a\right)} b^{18} c^{8} d^{3} + 264 \, {\left(5 \, a^{7} + 85 \, a^{5} + 323 \, a^{3} + 323 \, a\right)} b^{16} c^{7} d^{4} + 110 \, {\left(21 \, a^{9} + 420 \, a^{7} + 2142 \, a^{5} + 3876 \, a^{3} + 2261 \, a\right)} b^{14} c^{6} d^{5} + 4 \, {\left(693 \, a^{11} + 15015 \, a^{9} + 90090 \, a^{7} + 218790 \, a^{5} + 230945 \, a^{3} + 88179 \, a\right)} b^{12} c^{5} d^{6} + 110 \, {\left(21 \, a^{13} + 462 \, a^{11} + 3003 \, a^{9} + 8580 \, a^{7} + 12155 \, a^{5} + 8398 \, a^{3} + 2261 \, a\right)} b^{10} c^{4} d^{7} + 264 \, {\left(5 \, a^{15} + 105 \, a^{13} + 693 \, a^{11} + 2145 \, a^{9} + 3575 \, a^{7} + 3315 \, a^{5} + 1615 \, a^{3} + 323 \, a\right)} b^{8} c^{3} d^{8} + 33 \, {\left(15 \, a^{17} + 280 \, a^{15} + 1764 \, a^{13} + 5544 \, a^{11} + 10010 \, a^{9} + 10920 \, a^{7} + 7140 \, a^{5} + 2584 \, a^{3} + 399 \, a\right)} b^{6} c^{2} d^{9} + 110 \, {\left(a^{19} + 15 \, a^{17} + 84 \, a^{15} + 252 \, a^{13} + 462 \, a^{11} + 546 \, a^{9} + 420 \, a^{7} + 204 \, a^{5} + 57 \, a^{3} + 7 \, a\right)} b^{4} c d^{10} + 11 \, {\left(a^{21} + 10 \, a^{19} + 45 \, a^{17} + 120 \, a^{15} + 210 \, a^{13} + 252 \, a^{11} + 210 \, a^{9} + 120 \, a^{7} + 45 \, a^{5} + 10 \, a^{3} + a\right)} b^{2} d^{11}\right)} x\right)} \sqrt{c} \sqrt{d} + 2 \, {\left(a b^{23} c^{11} d + 11 \, {\left(a^{3} + 21 \, a\right)} b^{21} c^{10} d^{2} + 55 \, {\left(a^{5} + 38 \, a^{3} + 133 \, a\right)} b^{19} c^{9} d^{3} + 33 \, {\left(5 \, a^{7} + 255 \, a^{5} + 1615 \, a^{3} + 2261 \, a\right)} b^{17} c^{8} d^{4} + 330 \, {\left(a^{9} + 60 \, a^{7} + 510 \, a^{5} + 1292 \, a^{3} + 969 \, a\right)} b^{15} c^{7} d^{5} + 22 \, {\left(21 \, a^{11} + 1365 \, a^{9} + 13650 \, a^{7} + 46410 \, a^{5} + 62985 \, a^{3} + 29393 \, a\right)} b^{13} c^{6} d^{6} + 22 \, {\left(21 \, a^{13} + 1386 \, a^{11} + 15015 \, a^{9} + 60060 \, a^{7} + 109395 \, a^{5} + 92378 \, a^{3} + 29393 \, a\right)} b^{11} c^{5} d^{7} + 330 \, {\left(a^{15} + 63 \, a^{13} + 693 \, a^{11} + 3003 \, a^{9} + 6435 \, a^{7} + 7293 \, a^{5} + 4199 \, a^{3} + 969 \, a\right)} b^{9} c^{4} d^{8} + 33 \, {\left(5 \, a^{17} + 280 \, a^{15} + 2940 \, a^{13} + 12936 \, a^{11} + 30030 \, a^{9} + 40040 \, a^{7} + 30940 \, a^{5} + 12920 \, a^{3} + 2261 \, a\right)} b^{7} c^{3} d^{9} + 55 \, {\left(a^{19} + 45 \, a^{17} + 420 \, a^{15} + 1764 \, a^{13} + 4158 \, a^{11} + 6006 \, a^{9} + 5460 \, a^{7} + 3060 \, a^{5} + 969 \, a^{3} + 133 \, a\right)} b^{5} c^{2} d^{10} + 11 \, {\left(a^{21} + 30 \, a^{19} + 225 \, a^{17} + 840 \, a^{15} + 1890 \, a^{13} + 2772 \, a^{11} + 2730 \, a^{9} + 1800 \, a^{7} + 765 \, a^{5} + 190 \, a^{3} + 21 \, a\right)} b^{3} c d^{11} + {\left(a^{23} + 11 \, a^{21} + 55 \, a^{19} + 165 \, a^{17} + 330 \, a^{15} + 462 \, a^{13} + 462 \, a^{11} + 330 \, a^{9} + 165 \, a^{7} + 55 \, a^{5} + 11 \, a^{3} + a\right)} b d^{12}\right)} x}{b^{24} c^{12} + 12 \, {\left(a^{2} + 23\right)} b^{22} c^{11} d + 66 \, {\left(a^{4} + 42 \, a^{2} + 161\right)} b^{20} c^{10} d^{2} + 44 \, {\left(5 \, a^{6} + 285 \, a^{4} + 1995 \, a^{2} + 3059\right)} b^{18} c^{9} d^{3} + 99 \, {\left(5 \, a^{8} + 340 \, a^{6} + 3230 \, a^{4} + 9044 \, a^{2} + 7429\right)} b^{16} c^{8} d^{4} + 264 \, {\left(3 \, a^{10} + 225 \, a^{8} + 2550 \, a^{6} + 9690 \, a^{4} + 14535 \, a^{2} + 7429\right)} b^{14} c^{7} d^{5} + 4 \, {\left(231 \, a^{12} + 18018 \, a^{10} + 225225 \, a^{8} + 1021020 \, a^{6} + 2078505 \, a^{4} + 1939938 \, a^{2} + 676039\right)} b^{12} c^{6} d^{6} + 264 \, {\left(3 \, a^{14} + 231 \, a^{12} + 3003 \, a^{10} + 15015 \, a^{8} + 36465 \, a^{6} + 46189 \, a^{4} + 29393 \, a^{2} + 7429\right)} b^{10} c^{5} d^{7} + 99 \, {\left(5 \, a^{16} + 360 \, a^{14} + 4620 \, a^{12} + 24024 \, a^{10} + 64350 \, a^{8} + 97240 \, a^{6} + 83980 \, a^{4} + 38760 \, a^{2} + 7429\right)} b^{8} c^{4} d^{8} + 44 \, {\left(5 \, a^{18} + 315 \, a^{16} + 3780 \, a^{14} + 19404 \, a^{12} + 54054 \, a^{10} + 90090 \, a^{8} + 92820 \, a^{6} + 58140 \, a^{4} + 20349 \, a^{2} + 3059\right)} b^{6} c^{3} d^{9} + 66 \, {\left(a^{20} + 50 \, a^{18} + 525 \, a^{16} + 2520 \, a^{14} + 6930 \, a^{12} + 12012 \, a^{10} + 13650 \, a^{8} + 10200 \, a^{6} + 4845 \, a^{4} + 1330 \, a^{2} + 161\right)} b^{4} c^{2} d^{10} + 12 \, {\left(a^{22} + 33 \, a^{20} + 275 \, a^{18} + 1155 \, a^{16} + 2970 \, a^{14} + 5082 \, a^{12} + 6006 \, a^{10} + 4950 \, a^{8} + 2805 \, a^{6} + 1045 \, a^{4} + 231 \, a^{2} + 23\right)} b^{2} c d^{11} + {\left(a^{24} + 12 \, a^{22} + 66 \, a^{20} + 220 \, a^{18} + 495 \, a^{16} + 792 \, a^{14} + 924 \, a^{12} + 792 \, a^{10} + 495 \, a^{8} + 220 \, a^{6} + 66 \, a^{4} + 12 \, a^{2} + 1\right)} d^{12} + 8 \, {\left(3 \, b^{23} c^{11} + 11 \, {\left(3 \, a^{2} + 23\right)} b^{21} c^{10} d + 33 \, {\left(5 \, a^{4} + 70 \, a^{2} + 161\right)} b^{19} c^{9} d^{2} + 99 \, {\left(5 \, a^{6} + 95 \, a^{4} + 399 \, a^{2} + 437\right)} b^{17} c^{8} d^{3} + 22 \, {\left(45 \, a^{8} + 1020 \, a^{6} + 5814 \, a^{4} + 11628 \, a^{2} + 7429\right)} b^{15} c^{7} d^{4} + 6 \, {\left(231 \, a^{10} + 5775 \, a^{8} + 39270 \, a^{6} + 106590 \, a^{4} + 124355 \, a^{2} + 52003\right)} b^{13} c^{6} d^{5} + 6 \, {\left(231 \, a^{12} + 6006 \, a^{10} + 45045 \, a^{8} + 145860 \, a^{6} + 230945 \, a^{4} + 176358 \, a^{2} + 52003\right)} b^{11} c^{5} d^{6} + 22 \, {\left(45 \, a^{14} + 1155 \, a^{12} + 9009 \, a^{10} + 32175 \, a^{8} + 60775 \, a^{6} + 62985 \, a^{4} + 33915 \, a^{2} + 7429\right)} b^{9} c^{4} d^{7} + 99 \, {\left(5 \, a^{16} + 120 \, a^{14} + 924 \, a^{12} + 3432 \, a^{10} + 7150 \, a^{8} + 8840 \, a^{6} + 6460 \, a^{4} + 2584 \, a^{2} + 437\right)} b^{7} c^{3} d^{8} + 33 \, {\left(5 \, a^{18} + 105 \, a^{16} + 756 \, a^{14} + 2772 \, a^{12} + 6006 \, a^{10} + 8190 \, a^{8} + 7140 \, a^{6} + 3876 \, a^{4} + 1197 \, a^{2} + 161\right)} b^{5} c^{2} d^{9} + 11 \, {\left(3 \, a^{20} + 50 \, a^{18} + 315 \, a^{16} + 1080 \, a^{14} + 2310 \, a^{12} + 3276 \, a^{10} + 3150 \, a^{8} + 2040 \, a^{6} + 855 \, a^{4} + 210 \, a^{2} + 23\right)} b^{3} c d^{10} + 3 \, {\left(a^{22} + 11 \, a^{20} + 55 \, a^{18} + 165 \, a^{16} + 330 \, a^{14} + 462 \, a^{12} + 462 \, a^{10} + 330 \, a^{8} + 165 \, a^{6} + 55 \, a^{4} + 11 \, a^{2} + 1\right)} b d^{11}\right)} \sqrt{c} \sqrt{d}}\right) - \log\left(d x^{2} + c\right) \log\left(\frac{{\left(a^{2} + 1\right)} b^{22} c^{11} d + 11 \, {\left(a^{4} + 22 \, a^{2} + 21\right)} b^{20} c^{10} d^{2} + 55 \, {\left(a^{6} + 39 \, a^{4} + 171 \, a^{2} + 133\right)} b^{18} c^{9} d^{3} + 33 \, {\left(5 \, a^{8} + 260 \, a^{6} + 1870 \, a^{4} + 3876 \, a^{2} + 2261\right)} b^{16} c^{8} d^{4} + 330 \, {\left(a^{10} + 61 \, a^{8} + 570 \, a^{6} + 1802 \, a^{4} + 2261 \, a^{2} + 969\right)} b^{14} c^{7} d^{5} + 22 \, {\left(21 \, a^{12} + 1386 \, a^{10} + 15015 \, a^{8} + 60060 \, a^{6} + 109395 \, a^{4} + 92378 \, a^{2} + 29393\right)} b^{12} c^{6} d^{6} + 22 \, {\left(21 \, a^{14} + 1407 \, a^{12} + 16401 \, a^{10} + 75075 \, a^{8} + 169455 \, a^{6} + 201773 \, a^{4} + 121771 \, a^{2} + 29393\right)} b^{10} c^{5} d^{7} + 330 \, {\left(a^{16} + 64 \, a^{14} + 756 \, a^{12} + 3696 \, a^{10} + 9438 \, a^{8} + 13728 \, a^{6} + 11492 \, a^{4} + 5168 \, a^{2} + 969\right)} b^{8} c^{4} d^{8} + 33 \, {\left(5 \, a^{18} + 285 \, a^{16} + 3220 \, a^{14} + 15876 \, a^{12} + 42966 \, a^{10} + 70070 \, a^{8} + 70980 \, a^{6} + 43860 \, a^{4} + 15181 \, a^{2} + 2261\right)} b^{6} c^{3} d^{9} + 55 \, {\left(a^{20} + 46 \, a^{18} + 465 \, a^{16} + 2184 \, a^{14} + 5922 \, a^{12} + 10164 \, a^{10} + 11466 \, a^{8} + 8520 \, a^{6} + 4029 \, a^{4} + 1102 \, a^{2} + 133\right)} b^{4} c^{2} d^{10} + 11 \, {\left(a^{22} + 31 \, a^{20} + 255 \, a^{18} + 1065 \, a^{16} + 2730 \, a^{14} + 4662 \, a^{12} + 5502 \, a^{10} + 4530 \, a^{8} + 2565 \, a^{6} + 955 \, a^{4} + 211 \, a^{2} + 21\right)} b^{2} c d^{11} + {\left(a^{24} + 12 \, a^{22} + 66 \, a^{20} + 220 \, a^{18} + 495 \, a^{16} + 792 \, a^{14} + 924 \, a^{12} + 792 \, a^{10} + 495 \, a^{8} + 220 \, a^{6} + 66 \, a^{4} + 12 \, a^{2} + 1\right)} d^{12} + {\left(b^{24} c^{11} d + 11 \, {\left(a^{2} + 21\right)} b^{22} c^{10} d^{2} + 55 \, {\left(a^{4} + 38 \, a^{2} + 133\right)} b^{20} c^{9} d^{3} + 33 \, {\left(5 \, a^{6} + 255 \, a^{4} + 1615 \, a^{2} + 2261\right)} b^{18} c^{8} d^{4} + 330 \, {\left(a^{8} + 60 \, a^{6} + 510 \, a^{4} + 1292 \, a^{2} + 969\right)} b^{16} c^{7} d^{5} + 22 \, {\left(21 \, a^{10} + 1365 \, a^{8} + 13650 \, a^{6} + 46410 \, a^{4} + 62985 \, a^{2} + 29393\right)} b^{14} c^{6} d^{6} + 22 \, {\left(21 \, a^{12} + 1386 \, a^{10} + 15015 \, a^{8} + 60060 \, a^{6} + 109395 \, a^{4} + 92378 \, a^{2} + 29393\right)} b^{12} c^{5} d^{7} + 330 \, {\left(a^{14} + 63 \, a^{12} + 693 \, a^{10} + 3003 \, a^{8} + 6435 \, a^{6} + 7293 \, a^{4} + 4199 \, a^{2} + 969\right)} b^{10} c^{4} d^{8} + 33 \, {\left(5 \, a^{16} + 280 \, a^{14} + 2940 \, a^{12} + 12936 \, a^{10} + 30030 \, a^{8} + 40040 \, a^{6} + 30940 \, a^{4} + 12920 \, a^{2} + 2261\right)} b^{8} c^{3} d^{9} + 55 \, {\left(a^{18} + 45 \, a^{16} + 420 \, a^{14} + 1764 \, a^{12} + 4158 \, a^{10} + 6006 \, a^{8} + 5460 \, a^{6} + 3060 \, a^{4} + 969 \, a^{2} + 133\right)} b^{6} c^{2} d^{10} + 11 \, {\left(a^{20} + 30 \, a^{18} + 225 \, a^{16} + 840 \, a^{14} + 1890 \, a^{12} + 2772 \, a^{10} + 2730 \, a^{8} + 1800 \, a^{6} + 765 \, a^{4} + 190 \, a^{2} + 21\right)} b^{4} c d^{11} + {\left(a^{22} + 11 \, a^{20} + 55 \, a^{18} + 165 \, a^{16} + 330 \, a^{14} + 462 \, a^{12} + 462 \, a^{10} + 330 \, a^{8} + 165 \, a^{6} + 55 \, a^{4} + 11 \, a^{2} + 1\right)} b^{2} d^{12}\right)} x^{2} - 2 \, {\left(11 \, {\left(a^{2} + 1\right)} b^{21} c^{10} d + 110 \, {\left(a^{4} + 8 \, a^{2} + 7\right)} b^{19} c^{9} d^{2} + 33 \, {\left(15 \, a^{6} + 205 \, a^{4} + 589 \, a^{2} + 399\right)} b^{17} c^{8} d^{3} + 264 \, {\left(5 \, a^{8} + 90 \, a^{6} + 408 \, a^{4} + 646 \, a^{2} + 323\right)} b^{15} c^{7} d^{4} + 110 \, {\left(21 \, a^{10} + 441 \, a^{8} + 2562 \, a^{6} + 6018 \, a^{4} + 6137 \, a^{2} + 2261\right)} b^{13} c^{6} d^{5} + 4 \, {\left(693 \, a^{12} + 15708 \, a^{10} + 105105 \, a^{8} + 308880 \, a^{6} + 449735 \, a^{4} + 319124 \, a^{2} + 88179\right)} b^{11} c^{5} d^{6} + 110 \, {\left(21 \, a^{14} + 483 \, a^{12} + 3465 \, a^{10} + 11583 \, a^{8} + 20735 \, a^{6} + 20553 \, a^{4} + 10659 \, a^{2} + 2261\right)} b^{9} c^{4} d^{7} + 264 \, {\left(5 \, a^{16} + 110 \, a^{14} + 798 \, a^{12} + 2838 \, a^{10} + 5720 \, a^{8} + 6890 \, a^{6} + 4930 \, a^{4} + 1938 \, a^{2} + 323\right)} b^{7} c^{3} d^{8} + 33 \, {\left(15 \, a^{18} + 295 \, a^{16} + 2044 \, a^{14} + 7308 \, a^{12} + 15554 \, a^{10} + 20930 \, a^{8} + 18060 \, a^{6} + 9724 \, a^{4} + 2983 \, a^{2} + 399\right)} b^{5} c^{2} d^{9} + 110 \, {\left(a^{20} + 16 \, a^{18} + 99 \, a^{16} + 336 \, a^{14} + 714 \, a^{12} + 1008 \, a^{10} + 966 \, a^{8} + 624 \, a^{6} + 261 \, a^{4} + 64 \, a^{2} + 7\right)} b^{3} c d^{10} + 11 \, {\left(a^{22} + 11 \, a^{20} + 55 \, a^{18} + 165 \, a^{16} + 330 \, a^{14} + 462 \, a^{12} + 462 \, a^{10} + 330 \, a^{8} + 165 \, a^{6} + 55 \, a^{4} + 11 \, a^{2} + 1\right)} b d^{11} + {\left(11 \, b^{23} c^{10} d + 110 \, {\left(a^{2} + 7\right)} b^{21} c^{9} d^{2} + 33 \, {\left(15 \, a^{4} + 190 \, a^{2} + 399\right)} b^{19} c^{8} d^{3} + 264 \, {\left(5 \, a^{6} + 85 \, a^{4} + 323 \, a^{2} + 323\right)} b^{17} c^{7} d^{4} + 110 \, {\left(21 \, a^{8} + 420 \, a^{6} + 2142 \, a^{4} + 3876 \, a^{2} + 2261\right)} b^{15} c^{6} d^{5} + 4 \, {\left(693 \, a^{10} + 15015 \, a^{8} + 90090 \, a^{6} + 218790 \, a^{4} + 230945 \, a^{2} + 88179\right)} b^{13} c^{5} d^{6} + 110 \, {\left(21 \, a^{12} + 462 \, a^{10} + 3003 \, a^{8} + 8580 \, a^{6} + 12155 \, a^{4} + 8398 \, a^{2} + 2261\right)} b^{11} c^{4} d^{7} + 264 \, {\left(5 \, a^{14} + 105 \, a^{12} + 693 \, a^{10} + 2145 \, a^{8} + 3575 \, a^{6} + 3315 \, a^{4} + 1615 \, a^{2} + 323\right)} b^{9} c^{3} d^{8} + 33 \, {\left(15 \, a^{16} + 280 \, a^{14} + 1764 \, a^{12} + 5544 \, a^{10} + 10010 \, a^{8} + 10920 \, a^{6} + 7140 \, a^{4} + 2584 \, a^{2} + 399\right)} b^{7} c^{2} d^{9} + 110 \, {\left(a^{18} + 15 \, a^{16} + 84 \, a^{14} + 252 \, a^{12} + 462 \, a^{10} + 546 \, a^{8} + 420 \, a^{6} + 204 \, a^{4} + 57 \, a^{2} + 7\right)} b^{5} c d^{10} + 11 \, {\left(a^{20} + 10 \, a^{18} + 45 \, a^{16} + 120 \, a^{14} + 210 \, a^{12} + 252 \, a^{10} + 210 \, a^{8} + 120 \, a^{6} + 45 \, a^{4} + 10 \, a^{2} + 1\right)} b^{3} d^{11}\right)} x^{2} + 2 \, {\left(11 \, a b^{22} c^{10} d + 110 \, {\left(a^{3} + 7 \, a\right)} b^{20} c^{9} d^{2} + 33 \, {\left(15 \, a^{5} + 190 \, a^{3} + 399 \, a\right)} b^{18} c^{8} d^{3} + 264 \, {\left(5 \, a^{7} + 85 \, a^{5} + 323 \, a^{3} + 323 \, a\right)} b^{16} c^{7} d^{4} + 110 \, {\left(21 \, a^{9} + 420 \, a^{7} + 2142 \, a^{5} + 3876 \, a^{3} + 2261 \, a\right)} b^{14} c^{6} d^{5} + 4 \, {\left(693 \, a^{11} + 15015 \, a^{9} + 90090 \, a^{7} + 218790 \, a^{5} + 230945 \, a^{3} + 88179 \, a\right)} b^{12} c^{5} d^{6} + 110 \, {\left(21 \, a^{13} + 462 \, a^{11} + 3003 \, a^{9} + 8580 \, a^{7} + 12155 \, a^{5} + 8398 \, a^{3} + 2261 \, a\right)} b^{10} c^{4} d^{7} + 264 \, {\left(5 \, a^{15} + 105 \, a^{13} + 693 \, a^{11} + 2145 \, a^{9} + 3575 \, a^{7} + 3315 \, a^{5} + 1615 \, a^{3} + 323 \, a\right)} b^{8} c^{3} d^{8} + 33 \, {\left(15 \, a^{17} + 280 \, a^{15} + 1764 \, a^{13} + 5544 \, a^{11} + 10010 \, a^{9} + 10920 \, a^{7} + 7140 \, a^{5} + 2584 \, a^{3} + 399 \, a\right)} b^{6} c^{2} d^{9} + 110 \, {\left(a^{19} + 15 \, a^{17} + 84 \, a^{15} + 252 \, a^{13} + 462 \, a^{11} + 546 \, a^{9} + 420 \, a^{7} + 204 \, a^{5} + 57 \, a^{3} + 7 \, a\right)} b^{4} c d^{10} + 11 \, {\left(a^{21} + 10 \, a^{19} + 45 \, a^{17} + 120 \, a^{15} + 210 \, a^{13} + 252 \, a^{11} + 210 \, a^{9} + 120 \, a^{7} + 45 \, a^{5} + 10 \, a^{3} + a\right)} b^{2} d^{11}\right)} x\right)} \sqrt{c} \sqrt{d} + 2 \, {\left(a b^{23} c^{11} d + 11 \, {\left(a^{3} + 21 \, a\right)} b^{21} c^{10} d^{2} + 55 \, {\left(a^{5} + 38 \, a^{3} + 133 \, a\right)} b^{19} c^{9} d^{3} + 33 \, {\left(5 \, a^{7} + 255 \, a^{5} + 1615 \, a^{3} + 2261 \, a\right)} b^{17} c^{8} d^{4} + 330 \, {\left(a^{9} + 60 \, a^{7} + 510 \, a^{5} + 1292 \, a^{3} + 969 \, a\right)} b^{15} c^{7} d^{5} + 22 \, {\left(21 \, a^{11} + 1365 \, a^{9} + 13650 \, a^{7} + 46410 \, a^{5} + 62985 \, a^{3} + 29393 \, a\right)} b^{13} c^{6} d^{6} + 22 \, {\left(21 \, a^{13} + 1386 \, a^{11} + 15015 \, a^{9} + 60060 \, a^{7} + 109395 \, a^{5} + 92378 \, a^{3} + 29393 \, a\right)} b^{11} c^{5} d^{7} + 330 \, {\left(a^{15} + 63 \, a^{13} + 693 \, a^{11} + 3003 \, a^{9} + 6435 \, a^{7} + 7293 \, a^{5} + 4199 \, a^{3} + 969 \, a\right)} b^{9} c^{4} d^{8} + 33 \, {\left(5 \, a^{17} + 280 \, a^{15} + 2940 \, a^{13} + 12936 \, a^{11} + 30030 \, a^{9} + 40040 \, a^{7} + 30940 \, a^{5} + 12920 \, a^{3} + 2261 \, a\right)} b^{7} c^{3} d^{9} + 55 \, {\left(a^{19} + 45 \, a^{17} + 420 \, a^{15} + 1764 \, a^{13} + 4158 \, a^{11} + 6006 \, a^{9} + 5460 \, a^{7} + 3060 \, a^{5} + 969 \, a^{3} + 133 \, a\right)} b^{5} c^{2} d^{10} + 11 \, {\left(a^{21} + 30 \, a^{19} + 225 \, a^{17} + 840 \, a^{15} + 1890 \, a^{13} + 2772 \, a^{11} + 2730 \, a^{9} + 1800 \, a^{7} + 765 \, a^{5} + 190 \, a^{3} + 21 \, a\right)} b^{3} c d^{11} + {\left(a^{23} + 11 \, a^{21} + 55 \, a^{19} + 165 \, a^{17} + 330 \, a^{15} + 462 \, a^{13} + 462 \, a^{11} + 330 \, a^{9} + 165 \, a^{7} + 55 \, a^{5} + 11 \, a^{3} + a\right)} b d^{12}\right)} x}{b^{24} c^{12} + 12 \, {\left(a^{2} + 23\right)} b^{22} c^{11} d + 66 \, {\left(a^{4} + 42 \, a^{2} + 161\right)} b^{20} c^{10} d^{2} + 44 \, {\left(5 \, a^{6} + 285 \, a^{4} + 1995 \, a^{2} + 3059\right)} b^{18} c^{9} d^{3} + 99 \, {\left(5 \, a^{8} + 340 \, a^{6} + 3230 \, a^{4} + 9044 \, a^{2} + 7429\right)} b^{16} c^{8} d^{4} + 264 \, {\left(3 \, a^{10} + 225 \, a^{8} + 2550 \, a^{6} + 9690 \, a^{4} + 14535 \, a^{2} + 7429\right)} b^{14} c^{7} d^{5} + 4 \, {\left(231 \, a^{12} + 18018 \, a^{10} + 225225 \, a^{8} + 1021020 \, a^{6} + 2078505 \, a^{4} + 1939938 \, a^{2} + 676039\right)} b^{12} c^{6} d^{6} + 264 \, {\left(3 \, a^{14} + 231 \, a^{12} + 3003 \, a^{10} + 15015 \, a^{8} + 36465 \, a^{6} + 46189 \, a^{4} + 29393 \, a^{2} + 7429\right)} b^{10} c^{5} d^{7} + 99 \, {\left(5 \, a^{16} + 360 \, a^{14} + 4620 \, a^{12} + 24024 \, a^{10} + 64350 \, a^{8} + 97240 \, a^{6} + 83980 \, a^{4} + 38760 \, a^{2} + 7429\right)} b^{8} c^{4} d^{8} + 44 \, {\left(5 \, a^{18} + 315 \, a^{16} + 3780 \, a^{14} + 19404 \, a^{12} + 54054 \, a^{10} + 90090 \, a^{8} + 92820 \, a^{6} + 58140 \, a^{4} + 20349 \, a^{2} + 3059\right)} b^{6} c^{3} d^{9} + 66 \, {\left(a^{20} + 50 \, a^{18} + 525 \, a^{16} + 2520 \, a^{14} + 6930 \, a^{12} + 12012 \, a^{10} + 13650 \, a^{8} + 10200 \, a^{6} + 4845 \, a^{4} + 1330 \, a^{2} + 161\right)} b^{4} c^{2} d^{10} + 12 \, {\left(a^{22} + 33 \, a^{20} + 275 \, a^{18} + 1155 \, a^{16} + 2970 \, a^{14} + 5082 \, a^{12} + 6006 \, a^{10} + 4950 \, a^{8} + 2805 \, a^{6} + 1045 \, a^{4} + 231 \, a^{2} + 23\right)} b^{2} c d^{11} + {\left(a^{24} + 12 \, a^{22} + 66 \, a^{20} + 220 \, a^{18} + 495 \, a^{16} + 792 \, a^{14} + 924 \, a^{12} + 792 \, a^{10} + 495 \, a^{8} + 220 \, a^{6} + 66 \, a^{4} + 12 \, a^{2} + 1\right)} d^{12} - 8 \, {\left(3 \, b^{23} c^{11} + 11 \, {\left(3 \, a^{2} + 23\right)} b^{21} c^{10} d + 33 \, {\left(5 \, a^{4} + 70 \, a^{2} + 161\right)} b^{19} c^{9} d^{2} + 99 \, {\left(5 \, a^{6} + 95 \, a^{4} + 399 \, a^{2} + 437\right)} b^{17} c^{8} d^{3} + 22 \, {\left(45 \, a^{8} + 1020 \, a^{6} + 5814 \, a^{4} + 11628 \, a^{2} + 7429\right)} b^{15} c^{7} d^{4} + 6 \, {\left(231 \, a^{10} + 5775 \, a^{8} + 39270 \, a^{6} + 106590 \, a^{4} + 124355 \, a^{2} + 52003\right)} b^{13} c^{6} d^{5} + 6 \, {\left(231 \, a^{12} + 6006 \, a^{10} + 45045 \, a^{8} + 145860 \, a^{6} + 230945 \, a^{4} + 176358 \, a^{2} + 52003\right)} b^{11} c^{5} d^{6} + 22 \, {\left(45 \, a^{14} + 1155 \, a^{12} + 9009 \, a^{10} + 32175 \, a^{8} + 60775 \, a^{6} + 62985 \, a^{4} + 33915 \, a^{2} + 7429\right)} b^{9} c^{4} d^{7} + 99 \, {\left(5 \, a^{16} + 120 \, a^{14} + 924 \, a^{12} + 3432 \, a^{10} + 7150 \, a^{8} + 8840 \, a^{6} + 6460 \, a^{4} + 2584 \, a^{2} + 437\right)} b^{7} c^{3} d^{8} + 33 \, {\left(5 \, a^{18} + 105 \, a^{16} + 756 \, a^{14} + 2772 \, a^{12} + 6006 \, a^{10} + 8190 \, a^{8} + 7140 \, a^{6} + 3876 \, a^{4} + 1197 \, a^{2} + 161\right)} b^{5} c^{2} d^{9} + 11 \, {\left(3 \, a^{20} + 50 \, a^{18} + 315 \, a^{16} + 1080 \, a^{14} + 2310 \, a^{12} + 3276 \, a^{10} + 3150 \, a^{8} + 2040 \, a^{6} + 855 \, a^{4} + 210 \, a^{2} + 23\right)} b^{3} c d^{10} + 3 \, {\left(a^{22} + 11 \, a^{20} + 55 \, a^{18} + 165 \, a^{16} + 330 \, a^{14} + 462 \, a^{12} + 462 \, a^{10} + 330 \, a^{8} + 165 \, a^{6} + 55 \, a^{4} + 11 \, a^{2} + 1\right)} b d^{11}\right)} \sqrt{c} \sqrt{d}}\right) + 2 \, {\rm Li}_2\left(\frac{{\left(a + i\right)} b d x + b^{2} c + {\left(i \, b^{2} x + {\left(-i \, a + 1\right)} b\right)} \sqrt{c} \sqrt{d}}{b^{2} c + 2 \, {\left(-i \, a + 1\right)} b \sqrt{c} \sqrt{d} - {\left(a^{2} + 2 i \, a - 1\right)} d}\right) - 2 \, {\rm Li}_2\left(\frac{{\left(a + i\right)} b d x + b^{2} c - {\left(i \, b^{2} x + {\left(-i \, a + 1\right)} b\right)} \sqrt{c} \sqrt{d}}{b^{2} c - 2 \, {\left(-i \, a + 1\right)} b \sqrt{c} \sqrt{d} - {\left(a^{2} + 2 i \, a - 1\right)} d}\right) - 2 \, {\rm Li}_2\left(\frac{{\left(a - i\right)} b d x + b^{2} c + {\left(i \, b^{2} x + {\left(-i \, a - 1\right)} b\right)} \sqrt{c} \sqrt{d}}{b^{2} c + 2 \, {\left(-i \, a - 1\right)} b \sqrt{c} \sqrt{d} - {\left(a^{2} - 2 i \, a - 1\right)} d}\right) + 2 \, {\rm Li}_2\left(\frac{{\left(a - i\right)} b d x + b^{2} c - {\left(i \, b^{2} x + {\left(-i \, a - 1\right)} b\right)} \sqrt{c} \sqrt{d}}{b^{2} c - 2 \, {\left(-i \, a - 1\right)} b \sqrt{c} \sqrt{d} - {\left(a^{2} - 2 i \, a - 1\right)} d}\right)}{b}\right)}}{8 \, \sqrt{c d}} + \frac{\operatorname{arccot}\left(b x + a\right) \arctan\left(\frac{d x}{\sqrt{c d}}\right)}{\sqrt{c d}} + \frac{\arctan\left(\frac{d x}{\sqrt{c d}}\right) \arctan\left(\frac{b^{2} x + a b}{b}\right)}{\sqrt{c d}}"," ",0,"-1/8*b*(8*arctan(d*x/sqrt(c*d))*arctan((b^2*x + a*b)/b)/b - (4*arctan(sqrt(d)*x/sqrt(c))*arctan2((2*a*b^2*c*d + (a*b^3*c + (a^3 + a)*b*d + (b^4*c + (a^2 + 3)*b^2*d)*x)*sqrt(c)*sqrt(d) + (3*b^3*c*d + (a^2 + 1)*b*d^2)*x)/(b^4*c^2 + 2*(a^2 + 3)*b^2*c*d + (a^4 + 2*a^2 + 1)*d^2 + 4*(b^3*c + (a^2 + 1)*b*d)*sqrt(c)*sqrt(d)), ((a^2 + 3)*b^2*c*d + (a^4 + 2*a^2 + 1)*d^2 + (2*a*b^2*d*x + b^3*c + 3*(a^2 + 1)*b*d)*sqrt(c)*sqrt(d) + (a*b^3*c*d + (a^3 + a)*b*d^2)*x)/(b^4*c^2 + 2*(a^2 + 3)*b^2*c*d + (a^4 + 2*a^2 + 1)*d^2 + 4*(b^3*c + (a^2 + 1)*b*d)*sqrt(c)*sqrt(d))) + 4*arctan(sqrt(d)*x/sqrt(c))*arctan2((2*a*b^2*c*d - (a*b^3*c + (a^3 + a)*b*d + (b^4*c + (a^2 + 3)*b^2*d)*x)*sqrt(c)*sqrt(d) + (3*b^3*c*d + (a^2 + 1)*b*d^2)*x)/(b^4*c^2 + 2*(a^2 + 3)*b^2*c*d + (a^4 + 2*a^2 + 1)*d^2 - 4*(b^3*c + (a^2 + 1)*b*d)*sqrt(c)*sqrt(d)), ((a^2 + 3)*b^2*c*d + (a^4 + 2*a^2 + 1)*d^2 - (2*a*b^2*d*x + b^3*c + 3*(a^2 + 1)*b*d)*sqrt(c)*sqrt(d) + (a*b^3*c*d + (a^3 + a)*b*d^2)*x)/(b^4*c^2 + 2*(a^2 + 3)*b^2*c*d + (a^4 + 2*a^2 + 1)*d^2 - 4*(b^3*c + (a^2 + 1)*b*d)*sqrt(c)*sqrt(d))) + log(d*x^2 + c)*log(((a^2 + 1)*b^22*c^11*d + 11*(a^4 + 22*a^2 + 21)*b^20*c^10*d^2 + 55*(a^6 + 39*a^4 + 171*a^2 + 133)*b^18*c^9*d^3 + 33*(5*a^8 + 260*a^6 + 1870*a^4 + 3876*a^2 + 2261)*b^16*c^8*d^4 + 330*(a^10 + 61*a^8 + 570*a^6 + 1802*a^4 + 2261*a^2 + 969)*b^14*c^7*d^5 + 22*(21*a^12 + 1386*a^10 + 15015*a^8 + 60060*a^6 + 109395*a^4 + 92378*a^2 + 29393)*b^12*c^6*d^6 + 22*(21*a^14 + 1407*a^12 + 16401*a^10 + 75075*a^8 + 169455*a^6 + 201773*a^4 + 121771*a^2 + 29393)*b^10*c^5*d^7 + 330*(a^16 + 64*a^14 + 756*a^12 + 3696*a^10 + 9438*a^8 + 13728*a^6 + 11492*a^4 + 5168*a^2 + 969)*b^8*c^4*d^8 + 33*(5*a^18 + 285*a^16 + 3220*a^14 + 15876*a^12 + 42966*a^10 + 70070*a^8 + 70980*a^6 + 43860*a^4 + 15181*a^2 + 2261)*b^6*c^3*d^9 + 55*(a^20 + 46*a^18 + 465*a^16 + 2184*a^14 + 5922*a^12 + 10164*a^10 + 11466*a^8 + 8520*a^6 + 4029*a^4 + 1102*a^2 + 133)*b^4*c^2*d^10 + 11*(a^22 + 31*a^20 + 255*a^18 + 1065*a^16 + 2730*a^14 + 4662*a^12 + 5502*a^10 + 4530*a^8 + 2565*a^6 + 955*a^4 + 211*a^2 + 21)*b^2*c*d^11 + (a^24 + 12*a^22 + 66*a^20 + 220*a^18 + 495*a^16 + 792*a^14 + 924*a^12 + 792*a^10 + 495*a^8 + 220*a^6 + 66*a^4 + 12*a^2 + 1)*d^12 + (b^24*c^11*d + 11*(a^2 + 21)*b^22*c^10*d^2 + 55*(a^4 + 38*a^2 + 133)*b^20*c^9*d^3 + 33*(5*a^6 + 255*a^4 + 1615*a^2 + 2261)*b^18*c^8*d^4 + 330*(a^8 + 60*a^6 + 510*a^4 + 1292*a^2 + 969)*b^16*c^7*d^5 + 22*(21*a^10 + 1365*a^8 + 13650*a^6 + 46410*a^4 + 62985*a^2 + 29393)*b^14*c^6*d^6 + 22*(21*a^12 + 1386*a^10 + 15015*a^8 + 60060*a^6 + 109395*a^4 + 92378*a^2 + 29393)*b^12*c^5*d^7 + 330*(a^14 + 63*a^12 + 693*a^10 + 3003*a^8 + 6435*a^6 + 7293*a^4 + 4199*a^2 + 969)*b^10*c^4*d^8 + 33*(5*a^16 + 280*a^14 + 2940*a^12 + 12936*a^10 + 30030*a^8 + 40040*a^6 + 30940*a^4 + 12920*a^2 + 2261)*b^8*c^3*d^9 + 55*(a^18 + 45*a^16 + 420*a^14 + 1764*a^12 + 4158*a^10 + 6006*a^8 + 5460*a^6 + 3060*a^4 + 969*a^2 + 133)*b^6*c^2*d^10 + 11*(a^20 + 30*a^18 + 225*a^16 + 840*a^14 + 1890*a^12 + 2772*a^10 + 2730*a^8 + 1800*a^6 + 765*a^4 + 190*a^2 + 21)*b^4*c*d^11 + (a^22 + 11*a^20 + 55*a^18 + 165*a^16 + 330*a^14 + 462*a^12 + 462*a^10 + 330*a^8 + 165*a^6 + 55*a^4 + 11*a^2 + 1)*b^2*d^12)*x^2 + 2*(11*(a^2 + 1)*b^21*c^10*d + 110*(a^4 + 8*a^2 + 7)*b^19*c^9*d^2 + 33*(15*a^6 + 205*a^4 + 589*a^2 + 399)*b^17*c^8*d^3 + 264*(5*a^8 + 90*a^6 + 408*a^4 + 646*a^2 + 323)*b^15*c^7*d^4 + 110*(21*a^10 + 441*a^8 + 2562*a^6 + 6018*a^4 + 6137*a^2 + 2261)*b^13*c^6*d^5 + 4*(693*a^12 + 15708*a^10 + 105105*a^8 + 308880*a^6 + 449735*a^4 + 319124*a^2 + 88179)*b^11*c^5*d^6 + 110*(21*a^14 + 483*a^12 + 3465*a^10 + 11583*a^8 + 20735*a^6 + 20553*a^4 + 10659*a^2 + 2261)*b^9*c^4*d^7 + 264*(5*a^16 + 110*a^14 + 798*a^12 + 2838*a^10 + 5720*a^8 + 6890*a^6 + 4930*a^4 + 1938*a^2 + 323)*b^7*c^3*d^8 + 33*(15*a^18 + 295*a^16 + 2044*a^14 + 7308*a^12 + 15554*a^10 + 20930*a^8 + 18060*a^6 + 9724*a^4 + 2983*a^2 + 399)*b^5*c^2*d^9 + 110*(a^20 + 16*a^18 + 99*a^16 + 336*a^14 + 714*a^12 + 1008*a^10 + 966*a^8 + 624*a^6 + 261*a^4 + 64*a^2 + 7)*b^3*c*d^10 + 11*(a^22 + 11*a^20 + 55*a^18 + 165*a^16 + 330*a^14 + 462*a^12 + 462*a^10 + 330*a^8 + 165*a^6 + 55*a^4 + 11*a^2 + 1)*b*d^11 + (11*b^23*c^10*d + 110*(a^2 + 7)*b^21*c^9*d^2 + 33*(15*a^4 + 190*a^2 + 399)*b^19*c^8*d^3 + 264*(5*a^6 + 85*a^4 + 323*a^2 + 323)*b^17*c^7*d^4 + 110*(21*a^8 + 420*a^6 + 2142*a^4 + 3876*a^2 + 2261)*b^15*c^6*d^5 + 4*(693*a^10 + 15015*a^8 + 90090*a^6 + 218790*a^4 + 230945*a^2 + 88179)*b^13*c^5*d^6 + 110*(21*a^12 + 462*a^10 + 3003*a^8 + 8580*a^6 + 12155*a^4 + 8398*a^2 + 2261)*b^11*c^4*d^7 + 264*(5*a^14 + 105*a^12 + 693*a^10 + 2145*a^8 + 3575*a^6 + 3315*a^4 + 1615*a^2 + 323)*b^9*c^3*d^8 + 33*(15*a^16 + 280*a^14 + 1764*a^12 + 5544*a^10 + 10010*a^8 + 10920*a^6 + 7140*a^4 + 2584*a^2 + 399)*b^7*c^2*d^9 + 110*(a^18 + 15*a^16 + 84*a^14 + 252*a^12 + 462*a^10 + 546*a^8 + 420*a^6 + 204*a^4 + 57*a^2 + 7)*b^5*c*d^10 + 11*(a^20 + 10*a^18 + 45*a^16 + 120*a^14 + 210*a^12 + 252*a^10 + 210*a^8 + 120*a^6 + 45*a^4 + 10*a^2 + 1)*b^3*d^11)*x^2 + 2*(11*a*b^22*c^10*d + 110*(a^3 + 7*a)*b^20*c^9*d^2 + 33*(15*a^5 + 190*a^3 + 399*a)*b^18*c^8*d^3 + 264*(5*a^7 + 85*a^5 + 323*a^3 + 323*a)*b^16*c^7*d^4 + 110*(21*a^9 + 420*a^7 + 2142*a^5 + 3876*a^3 + 2261*a)*b^14*c^6*d^5 + 4*(693*a^11 + 15015*a^9 + 90090*a^7 + 218790*a^5 + 230945*a^3 + 88179*a)*b^12*c^5*d^6 + 110*(21*a^13 + 462*a^11 + 3003*a^9 + 8580*a^7 + 12155*a^5 + 8398*a^3 + 2261*a)*b^10*c^4*d^7 + 264*(5*a^15 + 105*a^13 + 693*a^11 + 2145*a^9 + 3575*a^7 + 3315*a^5 + 1615*a^3 + 323*a)*b^8*c^3*d^8 + 33*(15*a^17 + 280*a^15 + 1764*a^13 + 5544*a^11 + 10010*a^9 + 10920*a^7 + 7140*a^5 + 2584*a^3 + 399*a)*b^6*c^2*d^9 + 110*(a^19 + 15*a^17 + 84*a^15 + 252*a^13 + 462*a^11 + 546*a^9 + 420*a^7 + 204*a^5 + 57*a^3 + 7*a)*b^4*c*d^10 + 11*(a^21 + 10*a^19 + 45*a^17 + 120*a^15 + 210*a^13 + 252*a^11 + 210*a^9 + 120*a^7 + 45*a^5 + 10*a^3 + a)*b^2*d^11)*x)*sqrt(c)*sqrt(d) + 2*(a*b^23*c^11*d + 11*(a^3 + 21*a)*b^21*c^10*d^2 + 55*(a^5 + 38*a^3 + 133*a)*b^19*c^9*d^3 + 33*(5*a^7 + 255*a^5 + 1615*a^3 + 2261*a)*b^17*c^8*d^4 + 330*(a^9 + 60*a^7 + 510*a^5 + 1292*a^3 + 969*a)*b^15*c^7*d^5 + 22*(21*a^11 + 1365*a^9 + 13650*a^7 + 46410*a^5 + 62985*a^3 + 29393*a)*b^13*c^6*d^6 + 22*(21*a^13 + 1386*a^11 + 15015*a^9 + 60060*a^7 + 109395*a^5 + 92378*a^3 + 29393*a)*b^11*c^5*d^7 + 330*(a^15 + 63*a^13 + 693*a^11 + 3003*a^9 + 6435*a^7 + 7293*a^5 + 4199*a^3 + 969*a)*b^9*c^4*d^8 + 33*(5*a^17 + 280*a^15 + 2940*a^13 + 12936*a^11 + 30030*a^9 + 40040*a^7 + 30940*a^5 + 12920*a^3 + 2261*a)*b^7*c^3*d^9 + 55*(a^19 + 45*a^17 + 420*a^15 + 1764*a^13 + 4158*a^11 + 6006*a^9 + 5460*a^7 + 3060*a^5 + 969*a^3 + 133*a)*b^5*c^2*d^10 + 11*(a^21 + 30*a^19 + 225*a^17 + 840*a^15 + 1890*a^13 + 2772*a^11 + 2730*a^9 + 1800*a^7 + 765*a^5 + 190*a^3 + 21*a)*b^3*c*d^11 + (a^23 + 11*a^21 + 55*a^19 + 165*a^17 + 330*a^15 + 462*a^13 + 462*a^11 + 330*a^9 + 165*a^7 + 55*a^5 + 11*a^3 + a)*b*d^12)*x)/(b^24*c^12 + 12*(a^2 + 23)*b^22*c^11*d + 66*(a^4 + 42*a^2 + 161)*b^20*c^10*d^2 + 44*(5*a^6 + 285*a^4 + 1995*a^2 + 3059)*b^18*c^9*d^3 + 99*(5*a^8 + 340*a^6 + 3230*a^4 + 9044*a^2 + 7429)*b^16*c^8*d^4 + 264*(3*a^10 + 225*a^8 + 2550*a^6 + 9690*a^4 + 14535*a^2 + 7429)*b^14*c^7*d^5 + 4*(231*a^12 + 18018*a^10 + 225225*a^8 + 1021020*a^6 + 2078505*a^4 + 1939938*a^2 + 676039)*b^12*c^6*d^6 + 264*(3*a^14 + 231*a^12 + 3003*a^10 + 15015*a^8 + 36465*a^6 + 46189*a^4 + 29393*a^2 + 7429)*b^10*c^5*d^7 + 99*(5*a^16 + 360*a^14 + 4620*a^12 + 24024*a^10 + 64350*a^8 + 97240*a^6 + 83980*a^4 + 38760*a^2 + 7429)*b^8*c^4*d^8 + 44*(5*a^18 + 315*a^16 + 3780*a^14 + 19404*a^12 + 54054*a^10 + 90090*a^8 + 92820*a^6 + 58140*a^4 + 20349*a^2 + 3059)*b^6*c^3*d^9 + 66*(a^20 + 50*a^18 + 525*a^16 + 2520*a^14 + 6930*a^12 + 12012*a^10 + 13650*a^8 + 10200*a^6 + 4845*a^4 + 1330*a^2 + 161)*b^4*c^2*d^10 + 12*(a^22 + 33*a^20 + 275*a^18 + 1155*a^16 + 2970*a^14 + 5082*a^12 + 6006*a^10 + 4950*a^8 + 2805*a^6 + 1045*a^4 + 231*a^2 + 23)*b^2*c*d^11 + (a^24 + 12*a^22 + 66*a^20 + 220*a^18 + 495*a^16 + 792*a^14 + 924*a^12 + 792*a^10 + 495*a^8 + 220*a^6 + 66*a^4 + 12*a^2 + 1)*d^12 + 8*(3*b^23*c^11 + 11*(3*a^2 + 23)*b^21*c^10*d + 33*(5*a^4 + 70*a^2 + 161)*b^19*c^9*d^2 + 99*(5*a^6 + 95*a^4 + 399*a^2 + 437)*b^17*c^8*d^3 + 22*(45*a^8 + 1020*a^6 + 5814*a^4 + 11628*a^2 + 7429)*b^15*c^7*d^4 + 6*(231*a^10 + 5775*a^8 + 39270*a^6 + 106590*a^4 + 124355*a^2 + 52003)*b^13*c^6*d^5 + 6*(231*a^12 + 6006*a^10 + 45045*a^8 + 145860*a^6 + 230945*a^4 + 176358*a^2 + 52003)*b^11*c^5*d^6 + 22*(45*a^14 + 1155*a^12 + 9009*a^10 + 32175*a^8 + 60775*a^6 + 62985*a^4 + 33915*a^2 + 7429)*b^9*c^4*d^7 + 99*(5*a^16 + 120*a^14 + 924*a^12 + 3432*a^10 + 7150*a^8 + 8840*a^6 + 6460*a^4 + 2584*a^2 + 437)*b^7*c^3*d^8 + 33*(5*a^18 + 105*a^16 + 756*a^14 + 2772*a^12 + 6006*a^10 + 8190*a^8 + 7140*a^6 + 3876*a^4 + 1197*a^2 + 161)*b^5*c^2*d^9 + 11*(3*a^20 + 50*a^18 + 315*a^16 + 1080*a^14 + 2310*a^12 + 3276*a^10 + 3150*a^8 + 2040*a^6 + 855*a^4 + 210*a^2 + 23)*b^3*c*d^10 + 3*(a^22 + 11*a^20 + 55*a^18 + 165*a^16 + 330*a^14 + 462*a^12 + 462*a^10 + 330*a^8 + 165*a^6 + 55*a^4 + 11*a^2 + 1)*b*d^11)*sqrt(c)*sqrt(d))) - log(d*x^2 + c)*log(((a^2 + 1)*b^22*c^11*d + 11*(a^4 + 22*a^2 + 21)*b^20*c^10*d^2 + 55*(a^6 + 39*a^4 + 171*a^2 + 133)*b^18*c^9*d^3 + 33*(5*a^8 + 260*a^6 + 1870*a^4 + 3876*a^2 + 2261)*b^16*c^8*d^4 + 330*(a^10 + 61*a^8 + 570*a^6 + 1802*a^4 + 2261*a^2 + 969)*b^14*c^7*d^5 + 22*(21*a^12 + 1386*a^10 + 15015*a^8 + 60060*a^6 + 109395*a^4 + 92378*a^2 + 29393)*b^12*c^6*d^6 + 22*(21*a^14 + 1407*a^12 + 16401*a^10 + 75075*a^8 + 169455*a^6 + 201773*a^4 + 121771*a^2 + 29393)*b^10*c^5*d^7 + 330*(a^16 + 64*a^14 + 756*a^12 + 3696*a^10 + 9438*a^8 + 13728*a^6 + 11492*a^4 + 5168*a^2 + 969)*b^8*c^4*d^8 + 33*(5*a^18 + 285*a^16 + 3220*a^14 + 15876*a^12 + 42966*a^10 + 70070*a^8 + 70980*a^6 + 43860*a^4 + 15181*a^2 + 2261)*b^6*c^3*d^9 + 55*(a^20 + 46*a^18 + 465*a^16 + 2184*a^14 + 5922*a^12 + 10164*a^10 + 11466*a^8 + 8520*a^6 + 4029*a^4 + 1102*a^2 + 133)*b^4*c^2*d^10 + 11*(a^22 + 31*a^20 + 255*a^18 + 1065*a^16 + 2730*a^14 + 4662*a^12 + 5502*a^10 + 4530*a^8 + 2565*a^6 + 955*a^4 + 211*a^2 + 21)*b^2*c*d^11 + (a^24 + 12*a^22 + 66*a^20 + 220*a^18 + 495*a^16 + 792*a^14 + 924*a^12 + 792*a^10 + 495*a^8 + 220*a^6 + 66*a^4 + 12*a^2 + 1)*d^12 + (b^24*c^11*d + 11*(a^2 + 21)*b^22*c^10*d^2 + 55*(a^4 + 38*a^2 + 133)*b^20*c^9*d^3 + 33*(5*a^6 + 255*a^4 + 1615*a^2 + 2261)*b^18*c^8*d^4 + 330*(a^8 + 60*a^6 + 510*a^4 + 1292*a^2 + 969)*b^16*c^7*d^5 + 22*(21*a^10 + 1365*a^8 + 13650*a^6 + 46410*a^4 + 62985*a^2 + 29393)*b^14*c^6*d^6 + 22*(21*a^12 + 1386*a^10 + 15015*a^8 + 60060*a^6 + 109395*a^4 + 92378*a^2 + 29393)*b^12*c^5*d^7 + 330*(a^14 + 63*a^12 + 693*a^10 + 3003*a^8 + 6435*a^6 + 7293*a^4 + 4199*a^2 + 969)*b^10*c^4*d^8 + 33*(5*a^16 + 280*a^14 + 2940*a^12 + 12936*a^10 + 30030*a^8 + 40040*a^6 + 30940*a^4 + 12920*a^2 + 2261)*b^8*c^3*d^9 + 55*(a^18 + 45*a^16 + 420*a^14 + 1764*a^12 + 4158*a^10 + 6006*a^8 + 5460*a^6 + 3060*a^4 + 969*a^2 + 133)*b^6*c^2*d^10 + 11*(a^20 + 30*a^18 + 225*a^16 + 840*a^14 + 1890*a^12 + 2772*a^10 + 2730*a^8 + 1800*a^6 + 765*a^4 + 190*a^2 + 21)*b^4*c*d^11 + (a^22 + 11*a^20 + 55*a^18 + 165*a^16 + 330*a^14 + 462*a^12 + 462*a^10 + 330*a^8 + 165*a^6 + 55*a^4 + 11*a^2 + 1)*b^2*d^12)*x^2 - 2*(11*(a^2 + 1)*b^21*c^10*d + 110*(a^4 + 8*a^2 + 7)*b^19*c^9*d^2 + 33*(15*a^6 + 205*a^4 + 589*a^2 + 399)*b^17*c^8*d^3 + 264*(5*a^8 + 90*a^6 + 408*a^4 + 646*a^2 + 323)*b^15*c^7*d^4 + 110*(21*a^10 + 441*a^8 + 2562*a^6 + 6018*a^4 + 6137*a^2 + 2261)*b^13*c^6*d^5 + 4*(693*a^12 + 15708*a^10 + 105105*a^8 + 308880*a^6 + 449735*a^4 + 319124*a^2 + 88179)*b^11*c^5*d^6 + 110*(21*a^14 + 483*a^12 + 3465*a^10 + 11583*a^8 + 20735*a^6 + 20553*a^4 + 10659*a^2 + 2261)*b^9*c^4*d^7 + 264*(5*a^16 + 110*a^14 + 798*a^12 + 2838*a^10 + 5720*a^8 + 6890*a^6 + 4930*a^4 + 1938*a^2 + 323)*b^7*c^3*d^8 + 33*(15*a^18 + 295*a^16 + 2044*a^14 + 7308*a^12 + 15554*a^10 + 20930*a^8 + 18060*a^6 + 9724*a^4 + 2983*a^2 + 399)*b^5*c^2*d^9 + 110*(a^20 + 16*a^18 + 99*a^16 + 336*a^14 + 714*a^12 + 1008*a^10 + 966*a^8 + 624*a^6 + 261*a^4 + 64*a^2 + 7)*b^3*c*d^10 + 11*(a^22 + 11*a^20 + 55*a^18 + 165*a^16 + 330*a^14 + 462*a^12 + 462*a^10 + 330*a^8 + 165*a^6 + 55*a^4 + 11*a^2 + 1)*b*d^11 + (11*b^23*c^10*d + 110*(a^2 + 7)*b^21*c^9*d^2 + 33*(15*a^4 + 190*a^2 + 399)*b^19*c^8*d^3 + 264*(5*a^6 + 85*a^4 + 323*a^2 + 323)*b^17*c^7*d^4 + 110*(21*a^8 + 420*a^6 + 2142*a^4 + 3876*a^2 + 2261)*b^15*c^6*d^5 + 4*(693*a^10 + 15015*a^8 + 90090*a^6 + 218790*a^4 + 230945*a^2 + 88179)*b^13*c^5*d^6 + 110*(21*a^12 + 462*a^10 + 3003*a^8 + 8580*a^6 + 12155*a^4 + 8398*a^2 + 2261)*b^11*c^4*d^7 + 264*(5*a^14 + 105*a^12 + 693*a^10 + 2145*a^8 + 3575*a^6 + 3315*a^4 + 1615*a^2 + 323)*b^9*c^3*d^8 + 33*(15*a^16 + 280*a^14 + 1764*a^12 + 5544*a^10 + 10010*a^8 + 10920*a^6 + 7140*a^4 + 2584*a^2 + 399)*b^7*c^2*d^9 + 110*(a^18 + 15*a^16 + 84*a^14 + 252*a^12 + 462*a^10 + 546*a^8 + 420*a^6 + 204*a^4 + 57*a^2 + 7)*b^5*c*d^10 + 11*(a^20 + 10*a^18 + 45*a^16 + 120*a^14 + 210*a^12 + 252*a^10 + 210*a^8 + 120*a^6 + 45*a^4 + 10*a^2 + 1)*b^3*d^11)*x^2 + 2*(11*a*b^22*c^10*d + 110*(a^3 + 7*a)*b^20*c^9*d^2 + 33*(15*a^5 + 190*a^3 + 399*a)*b^18*c^8*d^3 + 264*(5*a^7 + 85*a^5 + 323*a^3 + 323*a)*b^16*c^7*d^4 + 110*(21*a^9 + 420*a^7 + 2142*a^5 + 3876*a^3 + 2261*a)*b^14*c^6*d^5 + 4*(693*a^11 + 15015*a^9 + 90090*a^7 + 218790*a^5 + 230945*a^3 + 88179*a)*b^12*c^5*d^6 + 110*(21*a^13 + 462*a^11 + 3003*a^9 + 8580*a^7 + 12155*a^5 + 8398*a^3 + 2261*a)*b^10*c^4*d^7 + 264*(5*a^15 + 105*a^13 + 693*a^11 + 2145*a^9 + 3575*a^7 + 3315*a^5 + 1615*a^3 + 323*a)*b^8*c^3*d^8 + 33*(15*a^17 + 280*a^15 + 1764*a^13 + 5544*a^11 + 10010*a^9 + 10920*a^7 + 7140*a^5 + 2584*a^3 + 399*a)*b^6*c^2*d^9 + 110*(a^19 + 15*a^17 + 84*a^15 + 252*a^13 + 462*a^11 + 546*a^9 + 420*a^7 + 204*a^5 + 57*a^3 + 7*a)*b^4*c*d^10 + 11*(a^21 + 10*a^19 + 45*a^17 + 120*a^15 + 210*a^13 + 252*a^11 + 210*a^9 + 120*a^7 + 45*a^5 + 10*a^3 + a)*b^2*d^11)*x)*sqrt(c)*sqrt(d) + 2*(a*b^23*c^11*d + 11*(a^3 + 21*a)*b^21*c^10*d^2 + 55*(a^5 + 38*a^3 + 133*a)*b^19*c^9*d^3 + 33*(5*a^7 + 255*a^5 + 1615*a^3 + 2261*a)*b^17*c^8*d^4 + 330*(a^9 + 60*a^7 + 510*a^5 + 1292*a^3 + 969*a)*b^15*c^7*d^5 + 22*(21*a^11 + 1365*a^9 + 13650*a^7 + 46410*a^5 + 62985*a^3 + 29393*a)*b^13*c^6*d^6 + 22*(21*a^13 + 1386*a^11 + 15015*a^9 + 60060*a^7 + 109395*a^5 + 92378*a^3 + 29393*a)*b^11*c^5*d^7 + 330*(a^15 + 63*a^13 + 693*a^11 + 3003*a^9 + 6435*a^7 + 7293*a^5 + 4199*a^3 + 969*a)*b^9*c^4*d^8 + 33*(5*a^17 + 280*a^15 + 2940*a^13 + 12936*a^11 + 30030*a^9 + 40040*a^7 + 30940*a^5 + 12920*a^3 + 2261*a)*b^7*c^3*d^9 + 55*(a^19 + 45*a^17 + 420*a^15 + 1764*a^13 + 4158*a^11 + 6006*a^9 + 5460*a^7 + 3060*a^5 + 969*a^3 + 133*a)*b^5*c^2*d^10 + 11*(a^21 + 30*a^19 + 225*a^17 + 840*a^15 + 1890*a^13 + 2772*a^11 + 2730*a^9 + 1800*a^7 + 765*a^5 + 190*a^3 + 21*a)*b^3*c*d^11 + (a^23 + 11*a^21 + 55*a^19 + 165*a^17 + 330*a^15 + 462*a^13 + 462*a^11 + 330*a^9 + 165*a^7 + 55*a^5 + 11*a^3 + a)*b*d^12)*x)/(b^24*c^12 + 12*(a^2 + 23)*b^22*c^11*d + 66*(a^4 + 42*a^2 + 161)*b^20*c^10*d^2 + 44*(5*a^6 + 285*a^4 + 1995*a^2 + 3059)*b^18*c^9*d^3 + 99*(5*a^8 + 340*a^6 + 3230*a^4 + 9044*a^2 + 7429)*b^16*c^8*d^4 + 264*(3*a^10 + 225*a^8 + 2550*a^6 + 9690*a^4 + 14535*a^2 + 7429)*b^14*c^7*d^5 + 4*(231*a^12 + 18018*a^10 + 225225*a^8 + 1021020*a^6 + 2078505*a^4 + 1939938*a^2 + 676039)*b^12*c^6*d^6 + 264*(3*a^14 + 231*a^12 + 3003*a^10 + 15015*a^8 + 36465*a^6 + 46189*a^4 + 29393*a^2 + 7429)*b^10*c^5*d^7 + 99*(5*a^16 + 360*a^14 + 4620*a^12 + 24024*a^10 + 64350*a^8 + 97240*a^6 + 83980*a^4 + 38760*a^2 + 7429)*b^8*c^4*d^8 + 44*(5*a^18 + 315*a^16 + 3780*a^14 + 19404*a^12 + 54054*a^10 + 90090*a^8 + 92820*a^6 + 58140*a^4 + 20349*a^2 + 3059)*b^6*c^3*d^9 + 66*(a^20 + 50*a^18 + 525*a^16 + 2520*a^14 + 6930*a^12 + 12012*a^10 + 13650*a^8 + 10200*a^6 + 4845*a^4 + 1330*a^2 + 161)*b^4*c^2*d^10 + 12*(a^22 + 33*a^20 + 275*a^18 + 1155*a^16 + 2970*a^14 + 5082*a^12 + 6006*a^10 + 4950*a^8 + 2805*a^6 + 1045*a^4 + 231*a^2 + 23)*b^2*c*d^11 + (a^24 + 12*a^22 + 66*a^20 + 220*a^18 + 495*a^16 + 792*a^14 + 924*a^12 + 792*a^10 + 495*a^8 + 220*a^6 + 66*a^4 + 12*a^2 + 1)*d^12 - 8*(3*b^23*c^11 + 11*(3*a^2 + 23)*b^21*c^10*d + 33*(5*a^4 + 70*a^2 + 161)*b^19*c^9*d^2 + 99*(5*a^6 + 95*a^4 + 399*a^2 + 437)*b^17*c^8*d^3 + 22*(45*a^8 + 1020*a^6 + 5814*a^4 + 11628*a^2 + 7429)*b^15*c^7*d^4 + 6*(231*a^10 + 5775*a^8 + 39270*a^6 + 106590*a^4 + 124355*a^2 + 52003)*b^13*c^6*d^5 + 6*(231*a^12 + 6006*a^10 + 45045*a^8 + 145860*a^6 + 230945*a^4 + 176358*a^2 + 52003)*b^11*c^5*d^6 + 22*(45*a^14 + 1155*a^12 + 9009*a^10 + 32175*a^8 + 60775*a^6 + 62985*a^4 + 33915*a^2 + 7429)*b^9*c^4*d^7 + 99*(5*a^16 + 120*a^14 + 924*a^12 + 3432*a^10 + 7150*a^8 + 8840*a^6 + 6460*a^4 + 2584*a^2 + 437)*b^7*c^3*d^8 + 33*(5*a^18 + 105*a^16 + 756*a^14 + 2772*a^12 + 6006*a^10 + 8190*a^8 + 7140*a^6 + 3876*a^4 + 1197*a^2 + 161)*b^5*c^2*d^9 + 11*(3*a^20 + 50*a^18 + 315*a^16 + 1080*a^14 + 2310*a^12 + 3276*a^10 + 3150*a^8 + 2040*a^6 + 855*a^4 + 210*a^2 + 23)*b^3*c*d^10 + 3*(a^22 + 11*a^20 + 55*a^18 + 165*a^16 + 330*a^14 + 462*a^12 + 462*a^10 + 330*a^8 + 165*a^6 + 55*a^4 + 11*a^2 + 1)*b*d^11)*sqrt(c)*sqrt(d))) + 2*dilog(((a + I)*b*d*x + b^2*c + (I*b^2*x + (-I*a + 1)*b)*sqrt(c)*sqrt(d))/(b^2*c + 2*(-I*a + 1)*b*sqrt(c)*sqrt(d) - (a^2 + 2*I*a - 1)*d)) - 2*dilog(((a + I)*b*d*x + b^2*c - (I*b^2*x + (-I*a + 1)*b)*sqrt(c)*sqrt(d))/(b^2*c - 2*(-I*a + 1)*b*sqrt(c)*sqrt(d) - (a^2 + 2*I*a - 1)*d)) - 2*dilog(((a - I)*b*d*x + b^2*c + (I*b^2*x + (-I*a - 1)*b)*sqrt(c)*sqrt(d))/(b^2*c + 2*(-I*a - 1)*b*sqrt(c)*sqrt(d) - (a^2 - 2*I*a - 1)*d)) + 2*dilog(((a - I)*b*d*x + b^2*c - (I*b^2*x + (-I*a - 1)*b)*sqrt(c)*sqrt(d))/(b^2*c - 2*(-I*a - 1)*b*sqrt(c)*sqrt(d) - (a^2 - 2*I*a - 1)*d)))/b)/sqrt(c*d) + arccot(b*x + a)*arctan(d*x/sqrt(c*d))/sqrt(c*d) + arctan(d*x/sqrt(c*d))*arctan((b^2*x + a*b)/b)/sqrt(c*d)","B",0
108,1,283,0,0.549876," ","integrate(arccot(b*x+a)/(d*x+c),x, algorithm=""maxima"")","\frac{\operatorname{arccot}\left(b x + a\right) \log\left(d x + c\right)}{d} + \frac{\arctan\left(\frac{b^{2} x + a b}{b}\right) \log\left(d x + c\right)}{d} + \frac{\arctan\left(\frac{b d^{2} x + b c d}{b^{2} c^{2} - 2 \, a b c d + {\left(a^{2} + 1\right)} d^{2}}, \frac{b^{2} c^{2} - a b c d + {\left(b^{2} c d - a b d^{2}\right)} x}{b^{2} c^{2} - 2 \, a b c d + {\left(a^{2} + 1\right)} d^{2}}\right) \log\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right) - \arctan\left(b x + a\right) \log\left(\frac{b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}}{b^{2} c^{2} - 2 \, a b c d + {\left(a^{2} + 1\right)} d^{2}}\right) + i \, {\rm Li}_2\left(\frac{i \, b d x + {\left(i \, a + 1\right)} d}{-i \, b c + {\left(i \, a + 1\right)} d}\right) - i \, {\rm Li}_2\left(\frac{i \, b d x + {\left(i \, a - 1\right)} d}{-i \, b c + {\left(i \, a - 1\right)} d}\right)}{2 \, d}"," ",0,"arccot(b*x + a)*log(d*x + c)/d + arctan((b^2*x + a*b)/b)*log(d*x + c)/d + 1/2*(arctan2((b*d^2*x + b*c*d)/(b^2*c^2 - 2*a*b*c*d + (a^2 + 1)*d^2), (b^2*c^2 - a*b*c*d + (b^2*c*d - a*b*d^2)*x)/(b^2*c^2 - 2*a*b*c*d + (a^2 + 1)*d^2))*log(b^2*x^2 + 2*a*b*x + a^2 + 1) - arctan(b*x + a)*log((b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)/(b^2*c^2 - 2*a*b*c*d + (a^2 + 1)*d^2)) + I*dilog((I*b*d*x + (I*a + 1)*d)/(-I*b*c + (I*a + 1)*d)) - I*dilog((I*b*d*x + (I*a - 1)*d)/(-I*b*c + (I*a - 1)*d)))/d","B",0
109,1,280,0,0.553908," ","integrate(arccot(b*x+a)/(c+d/x),x, algorithm=""maxima"")","\frac{2 \, b c x \arctan\left(1, b x + a\right) - b d \arctan\left(1, b x + a\right) \log\left(-\frac{b^{2} c^{2} x^{2} + 2 \, b^{2} c d x + b^{2} d^{2}}{2 \, a b c d - b^{2} d^{2} - {\left(a^{2} + 1\right)} c^{2}}\right) - 2 \, a c \arctan\left(b x + a\right) + i \, b d {\rm Li}_2\left(\frac{b c x + {\left(a + i\right)} c}{{\left(a + i\right)} c - b d}\right) - i \, b d {\rm Li}_2\left(\frac{b c x + {\left(a - i\right)} c}{{\left(a - i\right)} c - b d}\right) - {\left(b d \arctan\left(-\frac{b c^{2} x + b c d}{2 \, a b c d - b^{2} d^{2} - {\left(a^{2} + 1\right)} c^{2}}, \frac{a b c d - b^{2} d^{2} + {\left(a b c^{2} - b^{2} c d\right)} x}{2 \, a b c d - b^{2} d^{2} - {\left(a^{2} + 1\right)} c^{2}}\right) - c\right)} \log\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}{2 \, b c^{2}}"," ",0,"1/2*(2*b*c*x*arctan2(1, b*x + a) - b*d*arctan2(1, b*x + a)*log(-(b^2*c^2*x^2 + 2*b^2*c*d*x + b^2*d^2)/(2*a*b*c*d - b^2*d^2 - (a^2 + 1)*c^2)) - 2*a*c*arctan(b*x + a) + I*b*d*dilog((b*c*x + (a + I)*c)/((a + I)*c - b*d)) - I*b*d*dilog((b*c*x + (a - I)*c)/((a - I)*c - b*d)) - (b*d*arctan2(-(b*c^2*x + b*c*d)/(2*a*b*c*d - b^2*d^2 - (a^2 + 1)*c^2), (a*b*c*d - b^2*d^2 + (a*b*c^2 - b^2*c*d)*x)/(2*a*b*c*d - b^2*d^2 - (a^2 + 1)*c^2)) - c)*log(b^2*x^2 + 2*a*b*x + a^2 + 1))/(b*c^2)","A",0
110,1,8518,0,1.363999," ","integrate(arccot(b*x+a)/(c+d/x^2),x, algorithm=""maxima"")","-{\left(\frac{d \arctan\left(\frac{c x}{\sqrt{c d}}\right)}{\sqrt{c d} c} - \frac{x}{c}\right)} \operatorname{arccot}\left(b x + a\right) - \frac{8 \, a c \arctan\left(b x + a\right) + {\left(4 \, b \arctan\left(\frac{\sqrt{c} x}{\sqrt{d}}\right) \arctan\left(\frac{2 \, a b^{2} c d + {\left(a b^{3} d + {\left(a^{3} + a\right)} b c + {\left(b^{4} d + {\left(a^{2} + 3\right)} b^{2} c\right)} x\right)} \sqrt{c} \sqrt{d} + {\left(3 \, b^{3} c d + {\left(a^{2} + 1\right)} b c^{2}\right)} x}{b^{4} d^{2} + 2 \, {\left(a^{2} + 3\right)} b^{2} c d + {\left(a^{4} + 2 \, a^{2} + 1\right)} c^{2} + 4 \, {\left(b^{3} d + {\left(a^{2} + 1\right)} b c\right)} \sqrt{c} \sqrt{d}}, \frac{{\left(a^{2} + 3\right)} b^{2} c d + {\left(a^{4} + 2 \, a^{2} + 1\right)} c^{2} + {\left(2 \, a b^{2} c x + b^{3} d + 3 \, {\left(a^{2} + 1\right)} b c\right)} \sqrt{c} \sqrt{d} + {\left(a b^{3} c d + {\left(a^{3} + a\right)} b c^{2}\right)} x}{b^{4} d^{2} + 2 \, {\left(a^{2} + 3\right)} b^{2} c d + {\left(a^{4} + 2 \, a^{2} + 1\right)} c^{2} + 4 \, {\left(b^{3} d + {\left(a^{2} + 1\right)} b c\right)} \sqrt{c} \sqrt{d}}\right) + 4 \, b \arctan\left(\frac{\sqrt{c} x}{\sqrt{d}}\right) \arctan\left(\frac{2 \, a b^{2} c d - {\left(a b^{3} d + {\left(a^{3} + a\right)} b c + {\left(b^{4} d + {\left(a^{2} + 3\right)} b^{2} c\right)} x\right)} \sqrt{c} \sqrt{d} + {\left(3 \, b^{3} c d + {\left(a^{2} + 1\right)} b c^{2}\right)} x}{b^{4} d^{2} + 2 \, {\left(a^{2} + 3\right)} b^{2} c d + {\left(a^{4} + 2 \, a^{2} + 1\right)} c^{2} - 4 \, {\left(b^{3} d + {\left(a^{2} + 1\right)} b c\right)} \sqrt{c} \sqrt{d}}, \frac{{\left(a^{2} + 3\right)} b^{2} c d + {\left(a^{4} + 2 \, a^{2} + 1\right)} c^{2} - {\left(2 \, a b^{2} c x + b^{3} d + 3 \, {\left(a^{2} + 1\right)} b c\right)} \sqrt{c} \sqrt{d} + {\left(a b^{3} c d + {\left(a^{3} + a\right)} b c^{2}\right)} x}{b^{4} d^{2} + 2 \, {\left(a^{2} + 3\right)} b^{2} c d + {\left(a^{4} + 2 \, a^{2} + 1\right)} c^{2} - 4 \, {\left(b^{3} d + {\left(a^{2} + 1\right)} b c\right)} \sqrt{c} \sqrt{d}}\right) + b \log\left(c x^{2} + d\right) \log\left(\frac{{\left(a^{2} + 1\right)} b^{22} c d^{11} + 11 \, {\left(a^{4} + 22 \, a^{2} + 21\right)} b^{20} c^{2} d^{10} + 55 \, {\left(a^{6} + 39 \, a^{4} + 171 \, a^{2} + 133\right)} b^{18} c^{3} d^{9} + 33 \, {\left(5 \, a^{8} + 260 \, a^{6} + 1870 \, a^{4} + 3876 \, a^{2} + 2261\right)} b^{16} c^{4} d^{8} + 330 \, {\left(a^{10} + 61 \, a^{8} + 570 \, a^{6} + 1802 \, a^{4} + 2261 \, a^{2} + 969\right)} b^{14} c^{5} d^{7} + 22 \, {\left(21 \, a^{12} + 1386 \, a^{10} + 15015 \, a^{8} + 60060 \, a^{6} + 109395 \, a^{4} + 92378 \, a^{2} + 29393\right)} b^{12} c^{6} d^{6} + 22 \, {\left(21 \, a^{14} + 1407 \, a^{12} + 16401 \, a^{10} + 75075 \, a^{8} + 169455 \, a^{6} + 201773 \, a^{4} + 121771 \, a^{2} + 29393\right)} b^{10} c^{7} d^{5} + 330 \, {\left(a^{16} + 64 \, a^{14} + 756 \, a^{12} + 3696 \, a^{10} + 9438 \, a^{8} + 13728 \, a^{6} + 11492 \, a^{4} + 5168 \, a^{2} + 969\right)} b^{8} c^{8} d^{4} + 33 \, {\left(5 \, a^{18} + 285 \, a^{16} + 3220 \, a^{14} + 15876 \, a^{12} + 42966 \, a^{10} + 70070 \, a^{8} + 70980 \, a^{6} + 43860 \, a^{4} + 15181 \, a^{2} + 2261\right)} b^{6} c^{9} d^{3} + 55 \, {\left(a^{20} + 46 \, a^{18} + 465 \, a^{16} + 2184 \, a^{14} + 5922 \, a^{12} + 10164 \, a^{10} + 11466 \, a^{8} + 8520 \, a^{6} + 4029 \, a^{4} + 1102 \, a^{2} + 133\right)} b^{4} c^{10} d^{2} + 11 \, {\left(a^{22} + 31 \, a^{20} + 255 \, a^{18} + 1065 \, a^{16} + 2730 \, a^{14} + 4662 \, a^{12} + 5502 \, a^{10} + 4530 \, a^{8} + 2565 \, a^{6} + 955 \, a^{4} + 211 \, a^{2} + 21\right)} b^{2} c^{11} d + {\left(a^{24} + 12 \, a^{22} + 66 \, a^{20} + 220 \, a^{18} + 495 \, a^{16} + 792 \, a^{14} + 924 \, a^{12} + 792 \, a^{10} + 495 \, a^{8} + 220 \, a^{6} + 66 \, a^{4} + 12 \, a^{2} + 1\right)} c^{12} + {\left(b^{24} c d^{11} + 11 \, {\left(a^{2} + 21\right)} b^{22} c^{2} d^{10} + 55 \, {\left(a^{4} + 38 \, a^{2} + 133\right)} b^{20} c^{3} d^{9} + 33 \, {\left(5 \, a^{6} + 255 \, a^{4} + 1615 \, a^{2} + 2261\right)} b^{18} c^{4} d^{8} + 330 \, {\left(a^{8} + 60 \, a^{6} + 510 \, a^{4} + 1292 \, a^{2} + 969\right)} b^{16} c^{5} d^{7} + 22 \, {\left(21 \, a^{10} + 1365 \, a^{8} + 13650 \, a^{6} + 46410 \, a^{4} + 62985 \, a^{2} + 29393\right)} b^{14} c^{6} d^{6} + 22 \, {\left(21 \, a^{12} + 1386 \, a^{10} + 15015 \, a^{8} + 60060 \, a^{6} + 109395 \, a^{4} + 92378 \, a^{2} + 29393\right)} b^{12} c^{7} d^{5} + 330 \, {\left(a^{14} + 63 \, a^{12} + 693 \, a^{10} + 3003 \, a^{8} + 6435 \, a^{6} + 7293 \, a^{4} + 4199 \, a^{2} + 969\right)} b^{10} c^{8} d^{4} + 33 \, {\left(5 \, a^{16} + 280 \, a^{14} + 2940 \, a^{12} + 12936 \, a^{10} + 30030 \, a^{8} + 40040 \, a^{6} + 30940 \, a^{4} + 12920 \, a^{2} + 2261\right)} b^{8} c^{9} d^{3} + 55 \, {\left(a^{18} + 45 \, a^{16} + 420 \, a^{14} + 1764 \, a^{12} + 4158 \, a^{10} + 6006 \, a^{8} + 5460 \, a^{6} + 3060 \, a^{4} + 969 \, a^{2} + 133\right)} b^{6} c^{10} d^{2} + 11 \, {\left(a^{20} + 30 \, a^{18} + 225 \, a^{16} + 840 \, a^{14} + 1890 \, a^{12} + 2772 \, a^{10} + 2730 \, a^{8} + 1800 \, a^{6} + 765 \, a^{4} + 190 \, a^{2} + 21\right)} b^{4} c^{11} d + {\left(a^{22} + 11 \, a^{20} + 55 \, a^{18} + 165 \, a^{16} + 330 \, a^{14} + 462 \, a^{12} + 462 \, a^{10} + 330 \, a^{8} + 165 \, a^{6} + 55 \, a^{4} + 11 \, a^{2} + 1\right)} b^{2} c^{12}\right)} x^{2} + 2 \, {\left(11 \, {\left(a^{2} + 1\right)} b^{21} c d^{10} + 110 \, {\left(a^{4} + 8 \, a^{2} + 7\right)} b^{19} c^{2} d^{9} + 33 \, {\left(15 \, a^{6} + 205 \, a^{4} + 589 \, a^{2} + 399\right)} b^{17} c^{3} d^{8} + 264 \, {\left(5 \, a^{8} + 90 \, a^{6} + 408 \, a^{4} + 646 \, a^{2} + 323\right)} b^{15} c^{4} d^{7} + 110 \, {\left(21 \, a^{10} + 441 \, a^{8} + 2562 \, a^{6} + 6018 \, a^{4} + 6137 \, a^{2} + 2261\right)} b^{13} c^{5} d^{6} + 4 \, {\left(693 \, a^{12} + 15708 \, a^{10} + 105105 \, a^{8} + 308880 \, a^{6} + 449735 \, a^{4} + 319124 \, a^{2} + 88179\right)} b^{11} c^{6} d^{5} + 110 \, {\left(21 \, a^{14} + 483 \, a^{12} + 3465 \, a^{10} + 11583 \, a^{8} + 20735 \, a^{6} + 20553 \, a^{4} + 10659 \, a^{2} + 2261\right)} b^{9} c^{7} d^{4} + 264 \, {\left(5 \, a^{16} + 110 \, a^{14} + 798 \, a^{12} + 2838 \, a^{10} + 5720 \, a^{8} + 6890 \, a^{6} + 4930 \, a^{4} + 1938 \, a^{2} + 323\right)} b^{7} c^{8} d^{3} + 33 \, {\left(15 \, a^{18} + 295 \, a^{16} + 2044 \, a^{14} + 7308 \, a^{12} + 15554 \, a^{10} + 20930 \, a^{8} + 18060 \, a^{6} + 9724 \, a^{4} + 2983 \, a^{2} + 399\right)} b^{5} c^{9} d^{2} + 110 \, {\left(a^{20} + 16 \, a^{18} + 99 \, a^{16} + 336 \, a^{14} + 714 \, a^{12} + 1008 \, a^{10} + 966 \, a^{8} + 624 \, a^{6} + 261 \, a^{4} + 64 \, a^{2} + 7\right)} b^{3} c^{10} d + 11 \, {\left(a^{22} + 11 \, a^{20} + 55 \, a^{18} + 165 \, a^{16} + 330 \, a^{14} + 462 \, a^{12} + 462 \, a^{10} + 330 \, a^{8} + 165 \, a^{6} + 55 \, a^{4} + 11 \, a^{2} + 1\right)} b c^{11} + {\left(11 \, b^{23} c d^{10} + 110 \, {\left(a^{2} + 7\right)} b^{21} c^{2} d^{9} + 33 \, {\left(15 \, a^{4} + 190 \, a^{2} + 399\right)} b^{19} c^{3} d^{8} + 264 \, {\left(5 \, a^{6} + 85 \, a^{4} + 323 \, a^{2} + 323\right)} b^{17} c^{4} d^{7} + 110 \, {\left(21 \, a^{8} + 420 \, a^{6} + 2142 \, a^{4} + 3876 \, a^{2} + 2261\right)} b^{15} c^{5} d^{6} + 4 \, {\left(693 \, a^{10} + 15015 \, a^{8} + 90090 \, a^{6} + 218790 \, a^{4} + 230945 \, a^{2} + 88179\right)} b^{13} c^{6} d^{5} + 110 \, {\left(21 \, a^{12} + 462 \, a^{10} + 3003 \, a^{8} + 8580 \, a^{6} + 12155 \, a^{4} + 8398 \, a^{2} + 2261\right)} b^{11} c^{7} d^{4} + 264 \, {\left(5 \, a^{14} + 105 \, a^{12} + 693 \, a^{10} + 2145 \, a^{8} + 3575 \, a^{6} + 3315 \, a^{4} + 1615 \, a^{2} + 323\right)} b^{9} c^{8} d^{3} + 33 \, {\left(15 \, a^{16} + 280 \, a^{14} + 1764 \, a^{12} + 5544 \, a^{10} + 10010 \, a^{8} + 10920 \, a^{6} + 7140 \, a^{4} + 2584 \, a^{2} + 399\right)} b^{7} c^{9} d^{2} + 110 \, {\left(a^{18} + 15 \, a^{16} + 84 \, a^{14} + 252 \, a^{12} + 462 \, a^{10} + 546 \, a^{8} + 420 \, a^{6} + 204 \, a^{4} + 57 \, a^{2} + 7\right)} b^{5} c^{10} d + 11 \, {\left(a^{20} + 10 \, a^{18} + 45 \, a^{16} + 120 \, a^{14} + 210 \, a^{12} + 252 \, a^{10} + 210 \, a^{8} + 120 \, a^{6} + 45 \, a^{4} + 10 \, a^{2} + 1\right)} b^{3} c^{11}\right)} x^{2} + 2 \, {\left(11 \, a b^{22} c d^{10} + 110 \, {\left(a^{3} + 7 \, a\right)} b^{20} c^{2} d^{9} + 33 \, {\left(15 \, a^{5} + 190 \, a^{3} + 399 \, a\right)} b^{18} c^{3} d^{8} + 264 \, {\left(5 \, a^{7} + 85 \, a^{5} + 323 \, a^{3} + 323 \, a\right)} b^{16} c^{4} d^{7} + 110 \, {\left(21 \, a^{9} + 420 \, a^{7} + 2142 \, a^{5} + 3876 \, a^{3} + 2261 \, a\right)} b^{14} c^{5} d^{6} + 4 \, {\left(693 \, a^{11} + 15015 \, a^{9} + 90090 \, a^{7} + 218790 \, a^{5} + 230945 \, a^{3} + 88179 \, a\right)} b^{12} c^{6} d^{5} + 110 \, {\left(21 \, a^{13} + 462 \, a^{11} + 3003 \, a^{9} + 8580 \, a^{7} + 12155 \, a^{5} + 8398 \, a^{3} + 2261 \, a\right)} b^{10} c^{7} d^{4} + 264 \, {\left(5 \, a^{15} + 105 \, a^{13} + 693 \, a^{11} + 2145 \, a^{9} + 3575 \, a^{7} + 3315 \, a^{5} + 1615 \, a^{3} + 323 \, a\right)} b^{8} c^{8} d^{3} + 33 \, {\left(15 \, a^{17} + 280 \, a^{15} + 1764 \, a^{13} + 5544 \, a^{11} + 10010 \, a^{9} + 10920 \, a^{7} + 7140 \, a^{5} + 2584 \, a^{3} + 399 \, a\right)} b^{6} c^{9} d^{2} + 110 \, {\left(a^{19} + 15 \, a^{17} + 84 \, a^{15} + 252 \, a^{13} + 462 \, a^{11} + 546 \, a^{9} + 420 \, a^{7} + 204 \, a^{5} + 57 \, a^{3} + 7 \, a\right)} b^{4} c^{10} d + 11 \, {\left(a^{21} + 10 \, a^{19} + 45 \, a^{17} + 120 \, a^{15} + 210 \, a^{13} + 252 \, a^{11} + 210 \, a^{9} + 120 \, a^{7} + 45 \, a^{5} + 10 \, a^{3} + a\right)} b^{2} c^{11}\right)} x\right)} \sqrt{c} \sqrt{d} + 2 \, {\left(a b^{23} c d^{11} + 11 \, {\left(a^{3} + 21 \, a\right)} b^{21} c^{2} d^{10} + 55 \, {\left(a^{5} + 38 \, a^{3} + 133 \, a\right)} b^{19} c^{3} d^{9} + 33 \, {\left(5 \, a^{7} + 255 \, a^{5} + 1615 \, a^{3} + 2261 \, a\right)} b^{17} c^{4} d^{8} + 330 \, {\left(a^{9} + 60 \, a^{7} + 510 \, a^{5} + 1292 \, a^{3} + 969 \, a\right)} b^{15} c^{5} d^{7} + 22 \, {\left(21 \, a^{11} + 1365 \, a^{9} + 13650 \, a^{7} + 46410 \, a^{5} + 62985 \, a^{3} + 29393 \, a\right)} b^{13} c^{6} d^{6} + 22 \, {\left(21 \, a^{13} + 1386 \, a^{11} + 15015 \, a^{9} + 60060 \, a^{7} + 109395 \, a^{5} + 92378 \, a^{3} + 29393 \, a\right)} b^{11} c^{7} d^{5} + 330 \, {\left(a^{15} + 63 \, a^{13} + 693 \, a^{11} + 3003 \, a^{9} + 6435 \, a^{7} + 7293 \, a^{5} + 4199 \, a^{3} + 969 \, a\right)} b^{9} c^{8} d^{4} + 33 \, {\left(5 \, a^{17} + 280 \, a^{15} + 2940 \, a^{13} + 12936 \, a^{11} + 30030 \, a^{9} + 40040 \, a^{7} + 30940 \, a^{5} + 12920 \, a^{3} + 2261 \, a\right)} b^{7} c^{9} d^{3} + 55 \, {\left(a^{19} + 45 \, a^{17} + 420 \, a^{15} + 1764 \, a^{13} + 4158 \, a^{11} + 6006 \, a^{9} + 5460 \, a^{7} + 3060 \, a^{5} + 969 \, a^{3} + 133 \, a\right)} b^{5} c^{10} d^{2} + 11 \, {\left(a^{21} + 30 \, a^{19} + 225 \, a^{17} + 840 \, a^{15} + 1890 \, a^{13} + 2772 \, a^{11} + 2730 \, a^{9} + 1800 \, a^{7} + 765 \, a^{5} + 190 \, a^{3} + 21 \, a\right)} b^{3} c^{11} d + {\left(a^{23} + 11 \, a^{21} + 55 \, a^{19} + 165 \, a^{17} + 330 \, a^{15} + 462 \, a^{13} + 462 \, a^{11} + 330 \, a^{9} + 165 \, a^{7} + 55 \, a^{5} + 11 \, a^{3} + a\right)} b c^{12}\right)} x}{b^{24} d^{12} + 12 \, {\left(a^{2} + 23\right)} b^{22} c d^{11} + 66 \, {\left(a^{4} + 42 \, a^{2} + 161\right)} b^{20} c^{2} d^{10} + 44 \, {\left(5 \, a^{6} + 285 \, a^{4} + 1995 \, a^{2} + 3059\right)} b^{18} c^{3} d^{9} + 99 \, {\left(5 \, a^{8} + 340 \, a^{6} + 3230 \, a^{4} + 9044 \, a^{2} + 7429\right)} b^{16} c^{4} d^{8} + 264 \, {\left(3 \, a^{10} + 225 \, a^{8} + 2550 \, a^{6} + 9690 \, a^{4} + 14535 \, a^{2} + 7429\right)} b^{14} c^{5} d^{7} + 4 \, {\left(231 \, a^{12} + 18018 \, a^{10} + 225225 \, a^{8} + 1021020 \, a^{6} + 2078505 \, a^{4} + 1939938 \, a^{2} + 676039\right)} b^{12} c^{6} d^{6} + 264 \, {\left(3 \, a^{14} + 231 \, a^{12} + 3003 \, a^{10} + 15015 \, a^{8} + 36465 \, a^{6} + 46189 \, a^{4} + 29393 \, a^{2} + 7429\right)} b^{10} c^{7} d^{5} + 99 \, {\left(5 \, a^{16} + 360 \, a^{14} + 4620 \, a^{12} + 24024 \, a^{10} + 64350 \, a^{8} + 97240 \, a^{6} + 83980 \, a^{4} + 38760 \, a^{2} + 7429\right)} b^{8} c^{8} d^{4} + 44 \, {\left(5 \, a^{18} + 315 \, a^{16} + 3780 \, a^{14} + 19404 \, a^{12} + 54054 \, a^{10} + 90090 \, a^{8} + 92820 \, a^{6} + 58140 \, a^{4} + 20349 \, a^{2} + 3059\right)} b^{6} c^{9} d^{3} + 66 \, {\left(a^{20} + 50 \, a^{18} + 525 \, a^{16} + 2520 \, a^{14} + 6930 \, a^{12} + 12012 \, a^{10} + 13650 \, a^{8} + 10200 \, a^{6} + 4845 \, a^{4} + 1330 \, a^{2} + 161\right)} b^{4} c^{10} d^{2} + 12 \, {\left(a^{22} + 33 \, a^{20} + 275 \, a^{18} + 1155 \, a^{16} + 2970 \, a^{14} + 5082 \, a^{12} + 6006 \, a^{10} + 4950 \, a^{8} + 2805 \, a^{6} + 1045 \, a^{4} + 231 \, a^{2} + 23\right)} b^{2} c^{11} d + {\left(a^{24} + 12 \, a^{22} + 66 \, a^{20} + 220 \, a^{18} + 495 \, a^{16} + 792 \, a^{14} + 924 \, a^{12} + 792 \, a^{10} + 495 \, a^{8} + 220 \, a^{6} + 66 \, a^{4} + 12 \, a^{2} + 1\right)} c^{12} + 8 \, {\left(3 \, b^{23} d^{11} + 11 \, {\left(3 \, a^{2} + 23\right)} b^{21} c d^{10} + 33 \, {\left(5 \, a^{4} + 70 \, a^{2} + 161\right)} b^{19} c^{2} d^{9} + 99 \, {\left(5 \, a^{6} + 95 \, a^{4} + 399 \, a^{2} + 437\right)} b^{17} c^{3} d^{8} + 22 \, {\left(45 \, a^{8} + 1020 \, a^{6} + 5814 \, a^{4} + 11628 \, a^{2} + 7429\right)} b^{15} c^{4} d^{7} + 6 \, {\left(231 \, a^{10} + 5775 \, a^{8} + 39270 \, a^{6} + 106590 \, a^{4} + 124355 \, a^{2} + 52003\right)} b^{13} c^{5} d^{6} + 6 \, {\left(231 \, a^{12} + 6006 \, a^{10} + 45045 \, a^{8} + 145860 \, a^{6} + 230945 \, a^{4} + 176358 \, a^{2} + 52003\right)} b^{11} c^{6} d^{5} + 22 \, {\left(45 \, a^{14} + 1155 \, a^{12} + 9009 \, a^{10} + 32175 \, a^{8} + 60775 \, a^{6} + 62985 \, a^{4} + 33915 \, a^{2} + 7429\right)} b^{9} c^{7} d^{4} + 99 \, {\left(5 \, a^{16} + 120 \, a^{14} + 924 \, a^{12} + 3432 \, a^{10} + 7150 \, a^{8} + 8840 \, a^{6} + 6460 \, a^{4} + 2584 \, a^{2} + 437\right)} b^{7} c^{8} d^{3} + 33 \, {\left(5 \, a^{18} + 105 \, a^{16} + 756 \, a^{14} + 2772 \, a^{12} + 6006 \, a^{10} + 8190 \, a^{8} + 7140 \, a^{6} + 3876 \, a^{4} + 1197 \, a^{2} + 161\right)} b^{5} c^{9} d^{2} + 11 \, {\left(3 \, a^{20} + 50 \, a^{18} + 315 \, a^{16} + 1080 \, a^{14} + 2310 \, a^{12} + 3276 \, a^{10} + 3150 \, a^{8} + 2040 \, a^{6} + 855 \, a^{4} + 210 \, a^{2} + 23\right)} b^{3} c^{10} d + 3 \, {\left(a^{22} + 11 \, a^{20} + 55 \, a^{18} + 165 \, a^{16} + 330 \, a^{14} + 462 \, a^{12} + 462 \, a^{10} + 330 \, a^{8} + 165 \, a^{6} + 55 \, a^{4} + 11 \, a^{2} + 1\right)} b c^{11}\right)} \sqrt{c} \sqrt{d}}\right) - b \log\left(c x^{2} + d\right) \log\left(\frac{{\left(a^{2} + 1\right)} b^{22} c d^{11} + 11 \, {\left(a^{4} + 22 \, a^{2} + 21\right)} b^{20} c^{2} d^{10} + 55 \, {\left(a^{6} + 39 \, a^{4} + 171 \, a^{2} + 133\right)} b^{18} c^{3} d^{9} + 33 \, {\left(5 \, a^{8} + 260 \, a^{6} + 1870 \, a^{4} + 3876 \, a^{2} + 2261\right)} b^{16} c^{4} d^{8} + 330 \, {\left(a^{10} + 61 \, a^{8} + 570 \, a^{6} + 1802 \, a^{4} + 2261 \, a^{2} + 969\right)} b^{14} c^{5} d^{7} + 22 \, {\left(21 \, a^{12} + 1386 \, a^{10} + 15015 \, a^{8} + 60060 \, a^{6} + 109395 \, a^{4} + 92378 \, a^{2} + 29393\right)} b^{12} c^{6} d^{6} + 22 \, {\left(21 \, a^{14} + 1407 \, a^{12} + 16401 \, a^{10} + 75075 \, a^{8} + 169455 \, a^{6} + 201773 \, a^{4} + 121771 \, a^{2} + 29393\right)} b^{10} c^{7} d^{5} + 330 \, {\left(a^{16} + 64 \, a^{14} + 756 \, a^{12} + 3696 \, a^{10} + 9438 \, a^{8} + 13728 \, a^{6} + 11492 \, a^{4} + 5168 \, a^{2} + 969\right)} b^{8} c^{8} d^{4} + 33 \, {\left(5 \, a^{18} + 285 \, a^{16} + 3220 \, a^{14} + 15876 \, a^{12} + 42966 \, a^{10} + 70070 \, a^{8} + 70980 \, a^{6} + 43860 \, a^{4} + 15181 \, a^{2} + 2261\right)} b^{6} c^{9} d^{3} + 55 \, {\left(a^{20} + 46 \, a^{18} + 465 \, a^{16} + 2184 \, a^{14} + 5922 \, a^{12} + 10164 \, a^{10} + 11466 \, a^{8} + 8520 \, a^{6} + 4029 \, a^{4} + 1102 \, a^{2} + 133\right)} b^{4} c^{10} d^{2} + 11 \, {\left(a^{22} + 31 \, a^{20} + 255 \, a^{18} + 1065 \, a^{16} + 2730 \, a^{14} + 4662 \, a^{12} + 5502 \, a^{10} + 4530 \, a^{8} + 2565 \, a^{6} + 955 \, a^{4} + 211 \, a^{2} + 21\right)} b^{2} c^{11} d + {\left(a^{24} + 12 \, a^{22} + 66 \, a^{20} + 220 \, a^{18} + 495 \, a^{16} + 792 \, a^{14} + 924 \, a^{12} + 792 \, a^{10} + 495 \, a^{8} + 220 \, a^{6} + 66 \, a^{4} + 12 \, a^{2} + 1\right)} c^{12} + {\left(b^{24} c d^{11} + 11 \, {\left(a^{2} + 21\right)} b^{22} c^{2} d^{10} + 55 \, {\left(a^{4} + 38 \, a^{2} + 133\right)} b^{20} c^{3} d^{9} + 33 \, {\left(5 \, a^{6} + 255 \, a^{4} + 1615 \, a^{2} + 2261\right)} b^{18} c^{4} d^{8} + 330 \, {\left(a^{8} + 60 \, a^{6} + 510 \, a^{4} + 1292 \, a^{2} + 969\right)} b^{16} c^{5} d^{7} + 22 \, {\left(21 \, a^{10} + 1365 \, a^{8} + 13650 \, a^{6} + 46410 \, a^{4} + 62985 \, a^{2} + 29393\right)} b^{14} c^{6} d^{6} + 22 \, {\left(21 \, a^{12} + 1386 \, a^{10} + 15015 \, a^{8} + 60060 \, a^{6} + 109395 \, a^{4} + 92378 \, a^{2} + 29393\right)} b^{12} c^{7} d^{5} + 330 \, {\left(a^{14} + 63 \, a^{12} + 693 \, a^{10} + 3003 \, a^{8} + 6435 \, a^{6} + 7293 \, a^{4} + 4199 \, a^{2} + 969\right)} b^{10} c^{8} d^{4} + 33 \, {\left(5 \, a^{16} + 280 \, a^{14} + 2940 \, a^{12} + 12936 \, a^{10} + 30030 \, a^{8} + 40040 \, a^{6} + 30940 \, a^{4} + 12920 \, a^{2} + 2261\right)} b^{8} c^{9} d^{3} + 55 \, {\left(a^{18} + 45 \, a^{16} + 420 \, a^{14} + 1764 \, a^{12} + 4158 \, a^{10} + 6006 \, a^{8} + 5460 \, a^{6} + 3060 \, a^{4} + 969 \, a^{2} + 133\right)} b^{6} c^{10} d^{2} + 11 \, {\left(a^{20} + 30 \, a^{18} + 225 \, a^{16} + 840 \, a^{14} + 1890 \, a^{12} + 2772 \, a^{10} + 2730 \, a^{8} + 1800 \, a^{6} + 765 \, a^{4} + 190 \, a^{2} + 21\right)} b^{4} c^{11} d + {\left(a^{22} + 11 \, a^{20} + 55 \, a^{18} + 165 \, a^{16} + 330 \, a^{14} + 462 \, a^{12} + 462 \, a^{10} + 330 \, a^{8} + 165 \, a^{6} + 55 \, a^{4} + 11 \, a^{2} + 1\right)} b^{2} c^{12}\right)} x^{2} - 2 \, {\left(11 \, {\left(a^{2} + 1\right)} b^{21} c d^{10} + 110 \, {\left(a^{4} + 8 \, a^{2} + 7\right)} b^{19} c^{2} d^{9} + 33 \, {\left(15 \, a^{6} + 205 \, a^{4} + 589 \, a^{2} + 399\right)} b^{17} c^{3} d^{8} + 264 \, {\left(5 \, a^{8} + 90 \, a^{6} + 408 \, a^{4} + 646 \, a^{2} + 323\right)} b^{15} c^{4} d^{7} + 110 \, {\left(21 \, a^{10} + 441 \, a^{8} + 2562 \, a^{6} + 6018 \, a^{4} + 6137 \, a^{2} + 2261\right)} b^{13} c^{5} d^{6} + 4 \, {\left(693 \, a^{12} + 15708 \, a^{10} + 105105 \, a^{8} + 308880 \, a^{6} + 449735 \, a^{4} + 319124 \, a^{2} + 88179\right)} b^{11} c^{6} d^{5} + 110 \, {\left(21 \, a^{14} + 483 \, a^{12} + 3465 \, a^{10} + 11583 \, a^{8} + 20735 \, a^{6} + 20553 \, a^{4} + 10659 \, a^{2} + 2261\right)} b^{9} c^{7} d^{4} + 264 \, {\left(5 \, a^{16} + 110 \, a^{14} + 798 \, a^{12} + 2838 \, a^{10} + 5720 \, a^{8} + 6890 \, a^{6} + 4930 \, a^{4} + 1938 \, a^{2} + 323\right)} b^{7} c^{8} d^{3} + 33 \, {\left(15 \, a^{18} + 295 \, a^{16} + 2044 \, a^{14} + 7308 \, a^{12} + 15554 \, a^{10} + 20930 \, a^{8} + 18060 \, a^{6} + 9724 \, a^{4} + 2983 \, a^{2} + 399\right)} b^{5} c^{9} d^{2} + 110 \, {\left(a^{20} + 16 \, a^{18} + 99 \, a^{16} + 336 \, a^{14} + 714 \, a^{12} + 1008 \, a^{10} + 966 \, a^{8} + 624 \, a^{6} + 261 \, a^{4} + 64 \, a^{2} + 7\right)} b^{3} c^{10} d + 11 \, {\left(a^{22} + 11 \, a^{20} + 55 \, a^{18} + 165 \, a^{16} + 330 \, a^{14} + 462 \, a^{12} + 462 \, a^{10} + 330 \, a^{8} + 165 \, a^{6} + 55 \, a^{4} + 11 \, a^{2} + 1\right)} b c^{11} + {\left(11 \, b^{23} c d^{10} + 110 \, {\left(a^{2} + 7\right)} b^{21} c^{2} d^{9} + 33 \, {\left(15 \, a^{4} + 190 \, a^{2} + 399\right)} b^{19} c^{3} d^{8} + 264 \, {\left(5 \, a^{6} + 85 \, a^{4} + 323 \, a^{2} + 323\right)} b^{17} c^{4} d^{7} + 110 \, {\left(21 \, a^{8} + 420 \, a^{6} + 2142 \, a^{4} + 3876 \, a^{2} + 2261\right)} b^{15} c^{5} d^{6} + 4 \, {\left(693 \, a^{10} + 15015 \, a^{8} + 90090 \, a^{6} + 218790 \, a^{4} + 230945 \, a^{2} + 88179\right)} b^{13} c^{6} d^{5} + 110 \, {\left(21 \, a^{12} + 462 \, a^{10} + 3003 \, a^{8} + 8580 \, a^{6} + 12155 \, a^{4} + 8398 \, a^{2} + 2261\right)} b^{11} c^{7} d^{4} + 264 \, {\left(5 \, a^{14} + 105 \, a^{12} + 693 \, a^{10} + 2145 \, a^{8} + 3575 \, a^{6} + 3315 \, a^{4} + 1615 \, a^{2} + 323\right)} b^{9} c^{8} d^{3} + 33 \, {\left(15 \, a^{16} + 280 \, a^{14} + 1764 \, a^{12} + 5544 \, a^{10} + 10010 \, a^{8} + 10920 \, a^{6} + 7140 \, a^{4} + 2584 \, a^{2} + 399\right)} b^{7} c^{9} d^{2} + 110 \, {\left(a^{18} + 15 \, a^{16} + 84 \, a^{14} + 252 \, a^{12} + 462 \, a^{10} + 546 \, a^{8} + 420 \, a^{6} + 204 \, a^{4} + 57 \, a^{2} + 7\right)} b^{5} c^{10} d + 11 \, {\left(a^{20} + 10 \, a^{18} + 45 \, a^{16} + 120 \, a^{14} + 210 \, a^{12} + 252 \, a^{10} + 210 \, a^{8} + 120 \, a^{6} + 45 \, a^{4} + 10 \, a^{2} + 1\right)} b^{3} c^{11}\right)} x^{2} + 2 \, {\left(11 \, a b^{22} c d^{10} + 110 \, {\left(a^{3} + 7 \, a\right)} b^{20} c^{2} d^{9} + 33 \, {\left(15 \, a^{5} + 190 \, a^{3} + 399 \, a\right)} b^{18} c^{3} d^{8} + 264 \, {\left(5 \, a^{7} + 85 \, a^{5} + 323 \, a^{3} + 323 \, a\right)} b^{16} c^{4} d^{7} + 110 \, {\left(21 \, a^{9} + 420 \, a^{7} + 2142 \, a^{5} + 3876 \, a^{3} + 2261 \, a\right)} b^{14} c^{5} d^{6} + 4 \, {\left(693 \, a^{11} + 15015 \, a^{9} + 90090 \, a^{7} + 218790 \, a^{5} + 230945 \, a^{3} + 88179 \, a\right)} b^{12} c^{6} d^{5} + 110 \, {\left(21 \, a^{13} + 462 \, a^{11} + 3003 \, a^{9} + 8580 \, a^{7} + 12155 \, a^{5} + 8398 \, a^{3} + 2261 \, a\right)} b^{10} c^{7} d^{4} + 264 \, {\left(5 \, a^{15} + 105 \, a^{13} + 693 \, a^{11} + 2145 \, a^{9} + 3575 \, a^{7} + 3315 \, a^{5} + 1615 \, a^{3} + 323 \, a\right)} b^{8} c^{8} d^{3} + 33 \, {\left(15 \, a^{17} + 280 \, a^{15} + 1764 \, a^{13} + 5544 \, a^{11} + 10010 \, a^{9} + 10920 \, a^{7} + 7140 \, a^{5} + 2584 \, a^{3} + 399 \, a\right)} b^{6} c^{9} d^{2} + 110 \, {\left(a^{19} + 15 \, a^{17} + 84 \, a^{15} + 252 \, a^{13} + 462 \, a^{11} + 546 \, a^{9} + 420 \, a^{7} + 204 \, a^{5} + 57 \, a^{3} + 7 \, a\right)} b^{4} c^{10} d + 11 \, {\left(a^{21} + 10 \, a^{19} + 45 \, a^{17} + 120 \, a^{15} + 210 \, a^{13} + 252 \, a^{11} + 210 \, a^{9} + 120 \, a^{7} + 45 \, a^{5} + 10 \, a^{3} + a\right)} b^{2} c^{11}\right)} x\right)} \sqrt{c} \sqrt{d} + 2 \, {\left(a b^{23} c d^{11} + 11 \, {\left(a^{3} + 21 \, a\right)} b^{21} c^{2} d^{10} + 55 \, {\left(a^{5} + 38 \, a^{3} + 133 \, a\right)} b^{19} c^{3} d^{9} + 33 \, {\left(5 \, a^{7} + 255 \, a^{5} + 1615 \, a^{3} + 2261 \, a\right)} b^{17} c^{4} d^{8} + 330 \, {\left(a^{9} + 60 \, a^{7} + 510 \, a^{5} + 1292 \, a^{3} + 969 \, a\right)} b^{15} c^{5} d^{7} + 22 \, {\left(21 \, a^{11} + 1365 \, a^{9} + 13650 \, a^{7} + 46410 \, a^{5} + 62985 \, a^{3} + 29393 \, a\right)} b^{13} c^{6} d^{6} + 22 \, {\left(21 \, a^{13} + 1386 \, a^{11} + 15015 \, a^{9} + 60060 \, a^{7} + 109395 \, a^{5} + 92378 \, a^{3} + 29393 \, a\right)} b^{11} c^{7} d^{5} + 330 \, {\left(a^{15} + 63 \, a^{13} + 693 \, a^{11} + 3003 \, a^{9} + 6435 \, a^{7} + 7293 \, a^{5} + 4199 \, a^{3} + 969 \, a\right)} b^{9} c^{8} d^{4} + 33 \, {\left(5 \, a^{17} + 280 \, a^{15} + 2940 \, a^{13} + 12936 \, a^{11} + 30030 \, a^{9} + 40040 \, a^{7} + 30940 \, a^{5} + 12920 \, a^{3} + 2261 \, a\right)} b^{7} c^{9} d^{3} + 55 \, {\left(a^{19} + 45 \, a^{17} + 420 \, a^{15} + 1764 \, a^{13} + 4158 \, a^{11} + 6006 \, a^{9} + 5460 \, a^{7} + 3060 \, a^{5} + 969 \, a^{3} + 133 \, a\right)} b^{5} c^{10} d^{2} + 11 \, {\left(a^{21} + 30 \, a^{19} + 225 \, a^{17} + 840 \, a^{15} + 1890 \, a^{13} + 2772 \, a^{11} + 2730 \, a^{9} + 1800 \, a^{7} + 765 \, a^{5} + 190 \, a^{3} + 21 \, a\right)} b^{3} c^{11} d + {\left(a^{23} + 11 \, a^{21} + 55 \, a^{19} + 165 \, a^{17} + 330 \, a^{15} + 462 \, a^{13} + 462 \, a^{11} + 330 \, a^{9} + 165 \, a^{7} + 55 \, a^{5} + 11 \, a^{3} + a\right)} b c^{12}\right)} x}{b^{24} d^{12} + 12 \, {\left(a^{2} + 23\right)} b^{22} c d^{11} + 66 \, {\left(a^{4} + 42 \, a^{2} + 161\right)} b^{20} c^{2} d^{10} + 44 \, {\left(5 \, a^{6} + 285 \, a^{4} + 1995 \, a^{2} + 3059\right)} b^{18} c^{3} d^{9} + 99 \, {\left(5 \, a^{8} + 340 \, a^{6} + 3230 \, a^{4} + 9044 \, a^{2} + 7429\right)} b^{16} c^{4} d^{8} + 264 \, {\left(3 \, a^{10} + 225 \, a^{8} + 2550 \, a^{6} + 9690 \, a^{4} + 14535 \, a^{2} + 7429\right)} b^{14} c^{5} d^{7} + 4 \, {\left(231 \, a^{12} + 18018 \, a^{10} + 225225 \, a^{8} + 1021020 \, a^{6} + 2078505 \, a^{4} + 1939938 \, a^{2} + 676039\right)} b^{12} c^{6} d^{6} + 264 \, {\left(3 \, a^{14} + 231 \, a^{12} + 3003 \, a^{10} + 15015 \, a^{8} + 36465 \, a^{6} + 46189 \, a^{4} + 29393 \, a^{2} + 7429\right)} b^{10} c^{7} d^{5} + 99 \, {\left(5 \, a^{16} + 360 \, a^{14} + 4620 \, a^{12} + 24024 \, a^{10} + 64350 \, a^{8} + 97240 \, a^{6} + 83980 \, a^{4} + 38760 \, a^{2} + 7429\right)} b^{8} c^{8} d^{4} + 44 \, {\left(5 \, a^{18} + 315 \, a^{16} + 3780 \, a^{14} + 19404 \, a^{12} + 54054 \, a^{10} + 90090 \, a^{8} + 92820 \, a^{6} + 58140 \, a^{4} + 20349 \, a^{2} + 3059\right)} b^{6} c^{9} d^{3} + 66 \, {\left(a^{20} + 50 \, a^{18} + 525 \, a^{16} + 2520 \, a^{14} + 6930 \, a^{12} + 12012 \, a^{10} + 13650 \, a^{8} + 10200 \, a^{6} + 4845 \, a^{4} + 1330 \, a^{2} + 161\right)} b^{4} c^{10} d^{2} + 12 \, {\left(a^{22} + 33 \, a^{20} + 275 \, a^{18} + 1155 \, a^{16} + 2970 \, a^{14} + 5082 \, a^{12} + 6006 \, a^{10} + 4950 \, a^{8} + 2805 \, a^{6} + 1045 \, a^{4} + 231 \, a^{2} + 23\right)} b^{2} c^{11} d + {\left(a^{24} + 12 \, a^{22} + 66 \, a^{20} + 220 \, a^{18} + 495 \, a^{16} + 792 \, a^{14} + 924 \, a^{12} + 792 \, a^{10} + 495 \, a^{8} + 220 \, a^{6} + 66 \, a^{4} + 12 \, a^{2} + 1\right)} c^{12} - 8 \, {\left(3 \, b^{23} d^{11} + 11 \, {\left(3 \, a^{2} + 23\right)} b^{21} c d^{10} + 33 \, {\left(5 \, a^{4} + 70 \, a^{2} + 161\right)} b^{19} c^{2} d^{9} + 99 \, {\left(5 \, a^{6} + 95 \, a^{4} + 399 \, a^{2} + 437\right)} b^{17} c^{3} d^{8} + 22 \, {\left(45 \, a^{8} + 1020 \, a^{6} + 5814 \, a^{4} + 11628 \, a^{2} + 7429\right)} b^{15} c^{4} d^{7} + 6 \, {\left(231 \, a^{10} + 5775 \, a^{8} + 39270 \, a^{6} + 106590 \, a^{4} + 124355 \, a^{2} + 52003\right)} b^{13} c^{5} d^{6} + 6 \, {\left(231 \, a^{12} + 6006 \, a^{10} + 45045 \, a^{8} + 145860 \, a^{6} + 230945 \, a^{4} + 176358 \, a^{2} + 52003\right)} b^{11} c^{6} d^{5} + 22 \, {\left(45 \, a^{14} + 1155 \, a^{12} + 9009 \, a^{10} + 32175 \, a^{8} + 60775 \, a^{6} + 62985 \, a^{4} + 33915 \, a^{2} + 7429\right)} b^{9} c^{7} d^{4} + 99 \, {\left(5 \, a^{16} + 120 \, a^{14} + 924 \, a^{12} + 3432 \, a^{10} + 7150 \, a^{8} + 8840 \, a^{6} + 6460 \, a^{4} + 2584 \, a^{2} + 437\right)} b^{7} c^{8} d^{3} + 33 \, {\left(5 \, a^{18} + 105 \, a^{16} + 756 \, a^{14} + 2772 \, a^{12} + 6006 \, a^{10} + 8190 \, a^{8} + 7140 \, a^{6} + 3876 \, a^{4} + 1197 \, a^{2} + 161\right)} b^{5} c^{9} d^{2} + 11 \, {\left(3 \, a^{20} + 50 \, a^{18} + 315 \, a^{16} + 1080 \, a^{14} + 2310 \, a^{12} + 3276 \, a^{10} + 3150 \, a^{8} + 2040 \, a^{6} + 855 \, a^{4} + 210 \, a^{2} + 23\right)} b^{3} c^{10} d + 3 \, {\left(a^{22} + 11 \, a^{20} + 55 \, a^{18} + 165 \, a^{16} + 330 \, a^{14} + 462 \, a^{12} + 462 \, a^{10} + 330 \, a^{8} + 165 \, a^{6} + 55 \, a^{4} + 11 \, a^{2} + 1\right)} b c^{11}\right)} \sqrt{c} \sqrt{d}}\right) + 2 \, b {\rm Li}_2\left(\frac{{\left(a + i\right)} b c x + b^{2} d + {\left(i \, b^{2} x + {\left(-i \, a + 1\right)} b\right)} \sqrt{c} \sqrt{d}}{2 \, {\left(-i \, a + 1\right)} b \sqrt{c} \sqrt{d} + b^{2} d - {\left(a^{2} + 2 i \, a - 1\right)} c}\right) - 2 \, b {\rm Li}_2\left(-\frac{{\left(a + i\right)} b c x + b^{2} d - {\left(i \, b^{2} x + {\left(-i \, a + 1\right)} b\right)} \sqrt{c} \sqrt{d}}{2 \, {\left(-i \, a + 1\right)} b \sqrt{c} \sqrt{d} - b^{2} d + {\left(a^{2} + 2 i \, a - 1\right)} c}\right) - 2 \, b {\rm Li}_2\left(\frac{{\left(a - i\right)} b c x + b^{2} d + {\left(i \, b^{2} x + {\left(-i \, a - 1\right)} b\right)} \sqrt{c} \sqrt{d}}{2 \, {\left(-i \, a - 1\right)} b \sqrt{c} \sqrt{d} + b^{2} d - {\left(a^{2} - 2 i \, a - 1\right)} c}\right) + 2 \, b {\rm Li}_2\left(-\frac{{\left(a - i\right)} b c x + b^{2} d - {\left(i \, b^{2} x + {\left(-i \, a - 1\right)} b\right)} \sqrt{c} \sqrt{d}}{2 \, {\left(-i \, a - 1\right)} b \sqrt{c} \sqrt{d} - b^{2} d + {\left(a^{2} - 2 i \, a - 1\right)} c}\right)\right)} \sqrt{c} \sqrt{d} - 4 \, c \log\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}{8 \, b c^{2}}"," ",0,"-(d*arctan(c*x/sqrt(c*d))/(sqrt(c*d)*c) - x/c)*arccot(b*x + a) - 1/8*(8*a*c*arctan(b*x + a) + (4*b*arctan(sqrt(c)*x/sqrt(d))*arctan2((2*a*b^2*c*d + (a*b^3*d + (a^3 + a)*b*c + (b^4*d + (a^2 + 3)*b^2*c)*x)*sqrt(c)*sqrt(d) + (3*b^3*c*d + (a^2 + 1)*b*c^2)*x)/(b^4*d^2 + 2*(a^2 + 3)*b^2*c*d + (a^4 + 2*a^2 + 1)*c^2 + 4*(b^3*d + (a^2 + 1)*b*c)*sqrt(c)*sqrt(d)), ((a^2 + 3)*b^2*c*d + (a^4 + 2*a^2 + 1)*c^2 + (2*a*b^2*c*x + b^3*d + 3*(a^2 + 1)*b*c)*sqrt(c)*sqrt(d) + (a*b^3*c*d + (a^3 + a)*b*c^2)*x)/(b^4*d^2 + 2*(a^2 + 3)*b^2*c*d + (a^4 + 2*a^2 + 1)*c^2 + 4*(b^3*d + (a^2 + 1)*b*c)*sqrt(c)*sqrt(d))) + 4*b*arctan(sqrt(c)*x/sqrt(d))*arctan2((2*a*b^2*c*d - (a*b^3*d + (a^3 + a)*b*c + (b^4*d + (a^2 + 3)*b^2*c)*x)*sqrt(c)*sqrt(d) + (3*b^3*c*d + (a^2 + 1)*b*c^2)*x)/(b^4*d^2 + 2*(a^2 + 3)*b^2*c*d + (a^4 + 2*a^2 + 1)*c^2 - 4*(b^3*d + (a^2 + 1)*b*c)*sqrt(c)*sqrt(d)), ((a^2 + 3)*b^2*c*d + (a^4 + 2*a^2 + 1)*c^2 - (2*a*b^2*c*x + b^3*d + 3*(a^2 + 1)*b*c)*sqrt(c)*sqrt(d) + (a*b^3*c*d + (a^3 + a)*b*c^2)*x)/(b^4*d^2 + 2*(a^2 + 3)*b^2*c*d + (a^4 + 2*a^2 + 1)*c^2 - 4*(b^3*d + (a^2 + 1)*b*c)*sqrt(c)*sqrt(d))) + b*log(c*x^2 + d)*log(((a^2 + 1)*b^22*c*d^11 + 11*(a^4 + 22*a^2 + 21)*b^20*c^2*d^10 + 55*(a^6 + 39*a^4 + 171*a^2 + 133)*b^18*c^3*d^9 + 33*(5*a^8 + 260*a^6 + 1870*a^4 + 3876*a^2 + 2261)*b^16*c^4*d^8 + 330*(a^10 + 61*a^8 + 570*a^6 + 1802*a^4 + 2261*a^2 + 969)*b^14*c^5*d^7 + 22*(21*a^12 + 1386*a^10 + 15015*a^8 + 60060*a^6 + 109395*a^4 + 92378*a^2 + 29393)*b^12*c^6*d^6 + 22*(21*a^14 + 1407*a^12 + 16401*a^10 + 75075*a^8 + 169455*a^6 + 201773*a^4 + 121771*a^2 + 29393)*b^10*c^7*d^5 + 330*(a^16 + 64*a^14 + 756*a^12 + 3696*a^10 + 9438*a^8 + 13728*a^6 + 11492*a^4 + 5168*a^2 + 969)*b^8*c^8*d^4 + 33*(5*a^18 + 285*a^16 + 3220*a^14 + 15876*a^12 + 42966*a^10 + 70070*a^8 + 70980*a^6 + 43860*a^4 + 15181*a^2 + 2261)*b^6*c^9*d^3 + 55*(a^20 + 46*a^18 + 465*a^16 + 2184*a^14 + 5922*a^12 + 10164*a^10 + 11466*a^8 + 8520*a^6 + 4029*a^4 + 1102*a^2 + 133)*b^4*c^10*d^2 + 11*(a^22 + 31*a^20 + 255*a^18 + 1065*a^16 + 2730*a^14 + 4662*a^12 + 5502*a^10 + 4530*a^8 + 2565*a^6 + 955*a^4 + 211*a^2 + 21)*b^2*c^11*d + (a^24 + 12*a^22 + 66*a^20 + 220*a^18 + 495*a^16 + 792*a^14 + 924*a^12 + 792*a^10 + 495*a^8 + 220*a^6 + 66*a^4 + 12*a^2 + 1)*c^12 + (b^24*c*d^11 + 11*(a^2 + 21)*b^22*c^2*d^10 + 55*(a^4 + 38*a^2 + 133)*b^20*c^3*d^9 + 33*(5*a^6 + 255*a^4 + 1615*a^2 + 2261)*b^18*c^4*d^8 + 330*(a^8 + 60*a^6 + 510*a^4 + 1292*a^2 + 969)*b^16*c^5*d^7 + 22*(21*a^10 + 1365*a^8 + 13650*a^6 + 46410*a^4 + 62985*a^2 + 29393)*b^14*c^6*d^6 + 22*(21*a^12 + 1386*a^10 + 15015*a^8 + 60060*a^6 + 109395*a^4 + 92378*a^2 + 29393)*b^12*c^7*d^5 + 330*(a^14 + 63*a^12 + 693*a^10 + 3003*a^8 + 6435*a^6 + 7293*a^4 + 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33*(15*a^18 + 295*a^16 + 2044*a^14 + 7308*a^12 + 15554*a^10 + 20930*a^8 + 18060*a^6 + 9724*a^4 + 2983*a^2 + 399)*b^5*c^9*d^2 + 110*(a^20 + 16*a^18 + 99*a^16 + 336*a^14 + 714*a^12 + 1008*a^10 + 966*a^8 + 624*a^6 + 261*a^4 + 64*a^2 + 7)*b^3*c^10*d + 11*(a^22 + 11*a^20 + 55*a^18 + 165*a^16 + 330*a^14 + 462*a^12 + 462*a^10 + 330*a^8 + 165*a^6 + 55*a^4 + 11*a^2 + 1)*b*c^11 + (11*b^23*c*d^10 + 110*(a^2 + 7)*b^21*c^2*d^9 + 33*(15*a^4 + 190*a^2 + 399)*b^19*c^3*d^8 + 264*(5*a^6 + 85*a^4 + 323*a^2 + 323)*b^17*c^4*d^7 + 110*(21*a^8 + 420*a^6 + 2142*a^4 + 3876*a^2 + 2261)*b^15*c^5*d^6 + 4*(693*a^10 + 15015*a^8 + 90090*a^6 + 218790*a^4 + 230945*a^2 + 88179)*b^13*c^6*d^5 + 110*(21*a^12 + 462*a^10 + 3003*a^8 + 8580*a^6 + 12155*a^4 + 8398*a^2 + 2261)*b^11*c^7*d^4 + 264*(5*a^14 + 105*a^12 + 693*a^10 + 2145*a^8 + 3575*a^6 + 3315*a^4 + 1615*a^2 + 323)*b^9*c^8*d^3 + 33*(15*a^16 + 280*a^14 + 1764*a^12 + 5544*a^10 + 10010*a^8 + 10920*a^6 + 7140*a^4 + 2584*a^2 + 399)*b^7*c^9*d^2 + 110*(a^18 + 15*a^16 + 84*a^14 + 252*a^12 + 462*a^10 + 546*a^8 + 420*a^6 + 204*a^4 + 57*a^2 + 7)*b^5*c^10*d + 11*(a^20 + 10*a^18 + 45*a^16 + 120*a^14 + 210*a^12 + 252*a^10 + 210*a^8 + 120*a^6 + 45*a^4 + 10*a^2 + 1)*b^3*c^11)*x^2 + 2*(11*a*b^22*c*d^10 + 110*(a^3 + 7*a)*b^20*c^2*d^9 + 33*(15*a^5 + 190*a^3 + 399*a)*b^18*c^3*d^8 + 264*(5*a^7 + 85*a^5 + 323*a^3 + 323*a)*b^16*c^4*d^7 + 110*(21*a^9 + 420*a^7 + 2142*a^5 + 3876*a^3 + 2261*a)*b^14*c^5*d^6 + 4*(693*a^11 + 15015*a^9 + 90090*a^7 + 218790*a^5 + 230945*a^3 + 88179*a)*b^12*c^6*d^5 + 110*(21*a^13 + 462*a^11 + 3003*a^9 + 8580*a^7 + 12155*a^5 + 8398*a^3 + 2261*a)*b^10*c^7*d^4 + 264*(5*a^15 + 105*a^13 + 693*a^11 + 2145*a^9 + 3575*a^7 + 3315*a^5 + 1615*a^3 + 323*a)*b^8*c^8*d^3 + 33*(15*a^17 + 280*a^15 + 1764*a^13 + 5544*a^11 + 10010*a^9 + 10920*a^7 + 7140*a^5 + 2584*a^3 + 399*a)*b^6*c^9*d^2 + 110*(a^19 + 15*a^17 + 84*a^15 + 252*a^13 + 462*a^11 + 546*a^9 + 420*a^7 + 204*a^5 + 57*a^3 + 7*a)*b^4*c^10*d + 11*(a^21 + 10*a^19 + 45*a^17 + 120*a^15 + 210*a^13 + 252*a^11 + 210*a^9 + 120*a^7 + 45*a^5 + 10*a^3 + a)*b^2*c^11)*x)*sqrt(c)*sqrt(d) + 2*(a*b^23*c*d^11 + 11*(a^3 + 21*a)*b^21*c^2*d^10 + 55*(a^5 + 38*a^3 + 133*a)*b^19*c^3*d^9 + 33*(5*a^7 + 255*a^5 + 1615*a^3 + 2261*a)*b^17*c^4*d^8 + 330*(a^9 + 60*a^7 + 510*a^5 + 1292*a^3 + 969*a)*b^15*c^5*d^7 + 22*(21*a^11 + 1365*a^9 + 13650*a^7 + 46410*a^5 + 62985*a^3 + 29393*a)*b^13*c^6*d^6 + 22*(21*a^13 + 1386*a^11 + 15015*a^9 + 60060*a^7 + 109395*a^5 + 92378*a^3 + 29393*a)*b^11*c^7*d^5 + 330*(a^15 + 63*a^13 + 693*a^11 + 3003*a^9 + 6435*a^7 + 7293*a^5 + 4199*a^3 + 969*a)*b^9*c^8*d^4 + 33*(5*a^17 + 280*a^15 + 2940*a^13 + 12936*a^11 + 30030*a^9 + 40040*a^7 + 30940*a^5 + 12920*a^3 + 2261*a)*b^7*c^9*d^3 + 55*(a^19 + 45*a^17 + 420*a^15 + 1764*a^13 + 4158*a^11 + 6006*a^9 + 5460*a^7 + 3060*a^5 + 969*a^3 + 133*a)*b^5*c^10*d^2 + 11*(a^21 + 30*a^19 + 225*a^17 + 840*a^15 + 1890*a^13 + 2772*a^11 + 2730*a^9 + 1800*a^7 + 765*a^5 + 190*a^3 + 21*a)*b^3*c^11*d + (a^23 + 11*a^21 + 55*a^19 + 165*a^17 + 330*a^15 + 462*a^13 + 462*a^11 + 330*a^9 + 165*a^7 + 55*a^5 + 11*a^3 + a)*b*c^12)*x)/(b^24*d^12 + 12*(a^2 + 23)*b^22*c*d^11 + 66*(a^4 + 42*a^2 + 161)*b^20*c^2*d^10 + 44*(5*a^6 + 285*a^4 + 1995*a^2 + 3059)*b^18*c^3*d^9 + 99*(5*a^8 + 340*a^6 + 3230*a^4 + 9044*a^2 + 7429)*b^16*c^4*d^8 + 264*(3*a^10 + 225*a^8 + 2550*a^6 + 9690*a^4 + 14535*a^2 + 7429)*b^14*c^5*d^7 + 4*(231*a^12 + 18018*a^10 + 225225*a^8 + 1021020*a^6 + 2078505*a^4 + 1939938*a^2 + 676039)*b^12*c^6*d^6 + 264*(3*a^14 + 231*a^12 + 3003*a^10 + 15015*a^8 + 36465*a^6 + 46189*a^4 + 29393*a^2 + 7429)*b^10*c^7*d^5 + 99*(5*a^16 + 360*a^14 + 4620*a^12 + 24024*a^10 + 64350*a^8 + 97240*a^6 + 83980*a^4 + 38760*a^2 + 7429)*b^8*c^8*d^4 + 44*(5*a^18 + 315*a^16 + 3780*a^14 + 19404*a^12 + 54054*a^10 + 90090*a^8 + 92820*a^6 + 58140*a^4 + 20349*a^2 + 3059)*b^6*c^9*d^3 + 66*(a^20 + 50*a^18 + 525*a^16 + 2520*a^14 + 6930*a^12 + 12012*a^10 + 13650*a^8 + 10200*a^6 + 4845*a^4 + 1330*a^2 + 161)*b^4*c^10*d^2 + 12*(a^22 + 33*a^20 + 275*a^18 + 1155*a^16 + 2970*a^14 + 5082*a^12 + 6006*a^10 + 4950*a^8 + 2805*a^6 + 1045*a^4 + 231*a^2 + 23)*b^2*c^11*d + (a^24 + 12*a^22 + 66*a^20 + 220*a^18 + 495*a^16 + 792*a^14 + 924*a^12 + 792*a^10 + 495*a^8 + 220*a^6 + 66*a^4 + 12*a^2 + 1)*c^12 - 8*(3*b^23*d^11 + 11*(3*a^2 + 23)*b^21*c*d^10 + 33*(5*a^4 + 70*a^2 + 161)*b^19*c^2*d^9 + 99*(5*a^6 + 95*a^4 + 399*a^2 + 437)*b^17*c^3*d^8 + 22*(45*a^8 + 1020*a^6 + 5814*a^4 + 11628*a^2 + 7429)*b^15*c^4*d^7 + 6*(231*a^10 + 5775*a^8 + 39270*a^6 + 106590*a^4 + 124355*a^2 + 52003)*b^13*c^5*d^6 + 6*(231*a^12 + 6006*a^10 + 45045*a^8 + 145860*a^6 + 230945*a^4 + 176358*a^2 + 52003)*b^11*c^6*d^5 + 22*(45*a^14 + 1155*a^12 + 9009*a^10 + 32175*a^8 + 60775*a^6 + 62985*a^4 + 33915*a^2 + 7429)*b^9*c^7*d^4 + 99*(5*a^16 + 120*a^14 + 924*a^12 + 3432*a^10 + 7150*a^8 + 8840*a^6 + 6460*a^4 + 2584*a^2 + 437)*b^7*c^8*d^3 + 33*(5*a^18 + 105*a^16 + 756*a^14 + 2772*a^12 + 6006*a^10 + 8190*a^8 + 7140*a^6 + 3876*a^4 + 1197*a^2 + 161)*b^5*c^9*d^2 + 11*(3*a^20 + 50*a^18 + 315*a^16 + 1080*a^14 + 2310*a^12 + 3276*a^10 + 3150*a^8 + 2040*a^6 + 855*a^4 + 210*a^2 + 23)*b^3*c^10*d + 3*(a^22 + 11*a^20 + 55*a^18 + 165*a^16 + 330*a^14 + 462*a^12 + 462*a^10 + 330*a^8 + 165*a^6 + 55*a^4 + 11*a^2 + 1)*b*c^11)*sqrt(c)*sqrt(d))) + 2*b*dilog(((a + I)*b*c*x + b^2*d + (I*b^2*x + (-I*a + 1)*b)*sqrt(c)*sqrt(d))/(2*(-I*a + 1)*b*sqrt(c)*sqrt(d) + b^2*d - (a^2 + 2*I*a - 1)*c)) - 2*b*dilog(-((a + I)*b*c*x + b^2*d - (I*b^2*x + (-I*a + 1)*b)*sqrt(c)*sqrt(d))/(2*(-I*a + 1)*b*sqrt(c)*sqrt(d) - b^2*d + (a^2 + 2*I*a - 1)*c)) - 2*b*dilog(((a - I)*b*c*x + b^2*d + (I*b^2*x + (-I*a - 1)*b)*sqrt(c)*sqrt(d))/(2*(-I*a - 1)*b*sqrt(c)*sqrt(d) + b^2*d - (a^2 - 2*I*a - 1)*c)) + 2*b*dilog(-((a - I)*b*c*x + b^2*d - (I*b^2*x + (-I*a - 1)*b)*sqrt(c)*sqrt(d))/(2*(-I*a - 1)*b*sqrt(c)*sqrt(d) - b^2*d + (a^2 - 2*I*a - 1)*c)))*sqrt(c)*sqrt(d) - 4*c*log(b^2*x^2 + 2*a*b*x + a^2 + 1))/(b*c^2)","B",0
111,0,0,0,0.000000," ","integrate(arccot(b*x+a)/(c+d*x^(1/2)),x, algorithm=""maxima"")","\int \frac{\operatorname{arccot}\left(b x + a\right)}{d \sqrt{x} + c}\,{d x}"," ",0,"integrate(arccot(b*x + a)/(d*sqrt(x) + c), x)","F",0
112,0,0,0,0.000000," ","integrate(arccot(b*x+a)/(c+d/x^(1/2)),x, algorithm=""maxima"")","\int \frac{\operatorname{arccot}\left(b x + a\right)}{c + \frac{d}{\sqrt{x}}}\,{d x}"," ",0,"integrate(arccot(b*x + a)/(c + d/sqrt(x)), x)","F",0
113,-2,0,0,0.000000," ","integrate(arccot(e*x+d)/(c*x^2+b*x+a),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a*c-b^2>0)', see `assume?` for more details)Is 4*a*c-b^2 positive or negative?","F(-2)",0
114,0,0,0,0.000000," ","integrate(arccot(b*x+a)/(b^2*x^2+2*a*b*x+a^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{\operatorname{arccot}\left(b x + a\right)}{\sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}\,{d x}"," ",0,"integrate(arccot(b*x + a)/sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1), x)","F",0
115,0,0,0,0.000000," ","integrate(arccot(b*x+a)/((a^2+1)*c+2*a*b*c*x+c*x^2*b^2)^(1/2),x, algorithm=""maxima"")","\int \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}}\,{d x}"," ",0,"integrate(arccot(b*x + a)/sqrt(b^2*c*x^2 + 2*a*b*c*x + (a^2 + 1)*c), x)","F",0
116,0,0,0,0.000000," ","integrate(arccot(b*x+a)/(b^2*x^2+2*a*b*x+a^2+1)^(1/3),x, algorithm=""maxima"")","\int \frac{\operatorname{arccot}\left(b x + a\right)}{{\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(arccot(b*x + a)/(b^2*x^2 + 2*a*b*x + a^2 + 1)^(1/3), x)","F",0
117,0,0,0,0.000000," ","integrate(arccot(b*x+a)/((a^2+1)*c+2*a*b*c*x+c*x^2*b^2)^(1/3),x, algorithm=""maxima"")","\int \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}}}\,{d x}"," ",0,"integrate(arccot(b*x + a)/(b^2*c*x^2 + 2*a*b*c*x + (a^2 + 1)*c)^(1/3), x)","F",0
118,0,0,0,0.000000," ","integrate((b*x+a)^2*arccot(b*x+a)/(b^2*x^2+2*a*b*x+a^2+1)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(b x + a\right)}^{2} \operatorname{arccot}\left(b x + a\right)}{\sqrt{b^{2} x^{2} + 2 \, a b x + a^{2} + 1}}\,{d x}"," ",0,"integrate((b*x + a)^2*arccot(b*x + a)/sqrt(b^2*x^2 + 2*a*b*x + a^2 + 1), x)","F",0
119,0,0,0,0.000000," ","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=""maxima"")","\int \frac{{\left(b x + a\right)}^{2} \operatorname{arccot}\left(b x + a\right)}{\sqrt{b^{2} c x^{2} + 2 \, a b c x + {\left(a^{2} + 1\right)} c}}\,{d x}"," ",0,"integrate((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
120,0,0,0,0.000000," ","integrate((b*x+a)^2*arccot(b*x+a)/(b^2*x^2+2*a*b*x+a^2+1)^(1/3),x, algorithm=""maxima"")","\int \frac{{\left(b x + a\right)}^{2} \operatorname{arccot}\left(b x + a\right)}{{\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((b*x + a)^2*arccot(b*x + a)/(b^2*x^2 + 2*a*b*x + a^2 + 1)^(1/3), x)","F",0
121,0,0,0,0.000000," ","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=""maxima"")","\int \frac{{\left(b x + a\right)}^{2} \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}}}\,{d x}"," ",0,"integrate((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
122,1,93,0,0.431825," ","integrate((b*x+a)^2*arccot(b*x+a),x, algorithm=""maxima"")","-\frac{1}{6} \, {\left(\frac{2 \, a^{3} \arctan\left(\frac{b^{2} x + a b}{b}\right)}{b^{2}} - \frac{b x^{2} + 2 \, a x}{b} + \frac{\log\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}{b^{2}}\right)} b + \frac{1}{3} \, {\left(b^{2} x^{3} + 3 \, a b x^{2} + 3 \, a^{2} x\right)} \operatorname{arccot}\left(b x + a\right)"," ",0,"-1/6*(2*a^3*arctan((b^2*x + a*b)/b)/b^2 - (b*x^2 + 2*a*x)/b + log(b^2*x^2 + 2*a*b*x + a^2 + 1)/b^2)*b + 1/3*(b^2*x^3 + 3*a*b*x^2 + 3*a^2*x)*arccot(b*x + a)","B",0
123,1,52,0,0.425475," ","integrate((b*x+a)*arccot(b*x+a),x, algorithm=""maxima"")","\frac{1}{2} \, b {\left(\frac{x}{b} - \frac{{\left(a^{2} + 1\right)} \arctan\left(\frac{b^{2} x + a b}{b}\right)}{b^{2}}\right)} + \frac{1}{2} \, {\left(b x^{2} + 2 \, a x\right)} \operatorname{arccot}\left(b x + a\right)"," ",0,"1/2*b*(x/b - (a^2 + 1)*arctan((b^2*x + a*b)/b)/b^2) + 1/2*(b*x^2 + 2*a*x)*arccot(b*x + a)","A",0
124,1,112,0,0.479561," ","integrate(arccot(b*x+a)/(b*x+a),x, algorithm=""maxima"")","\frac{\operatorname{arccot}\left(b x + a\right) \log\left(b x + a\right)}{b} + \frac{\arctan\left(\frac{b^{2} x + a b}{b}\right) \log\left(b x + a\right)}{b} + \frac{\arctan\left(b x + a, 0\right) \log\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right) - 2 \, \arctan\left(b x + a\right) \log\left({\left| b x + a \right|}\right) + i \, {\rm Li}_2\left(i \, b x + i \, a + 1\right) - i \, {\rm Li}_2\left(-i \, b x - i \, a + 1\right)}{2 \, b}"," ",0,"arccot(b*x + a)*log(b*x + a)/b + arctan((b^2*x + a*b)/b)*log(b*x + a)/b + 1/2*(arctan2(b*x + a, 0)*log(b^2*x^2 + 2*a*b*x + a^2 + 1) - 2*arctan(b*x + a)*log(abs(b*x + a)) + I*dilog(I*b*x + I*a + 1) - I*dilog(-I*b*x - I*a + 1))/b","B",0
125,1,53,0,0.320110," ","integrate(arccot(b*x+a)/(b*x+a)^2,x, algorithm=""maxima"")","\frac{\log\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right)}{2 \, b} - \frac{\log\left(b x + a\right)}{b} - \frac{\operatorname{arccot}\left(b x + a\right)}{{\left(b x + a\right)} b}"," ",0,"1/2*log(b^2*x^2 + 2*a*b*x + a^2 + 1)/b - log(b*x + a)/b - arccot(b*x + a)/((b*x + a)*b)","A",0
126,1,64,0,0.458250," ","integrate(arccot(1+x)/(2+2*x),x, algorithm=""maxima"")","\frac{1}{4} \, \arctan\left(x + 1, 0\right) \log\left(x^{2} + 2 \, x + 2\right) + \frac{1}{2} \, \operatorname{arccot}\left(x + 1\right) \log\left(x + 1\right) + \frac{1}{2} \, \arctan\left(x + 1\right) \log\left(x + 1\right) - \frac{1}{2} \, \arctan\left(x + 1\right) \log\left({\left| x + 1 \right|}\right) + \frac{1}{4} i \, {\rm Li}_2\left(i \, x + i + 1\right) - \frac{1}{4} i \, {\rm Li}_2\left(-i \, x - i + 1\right)"," ",0,"1/4*arctan2(x + 1, 0)*log(x^2 + 2*x + 2) + 1/2*arccot(x + 1)*log(x + 1) + 1/2*arctan(x + 1)*log(x + 1) - 1/2*arctan(x + 1)*log(abs(x + 1)) + 1/4*I*dilog(I*x + I + 1) - 1/4*I*dilog(-I*x - I + 1)","B",0
127,1,122,0,0.479783," ","integrate(arccot(b*x+a)/(a*d/b+d*x),x, algorithm=""maxima"")","\frac{\operatorname{arccot}\left(b x + a\right) \log\left(d x + \frac{a d}{b}\right)}{d} + \frac{\arctan\left(\frac{b^{2} x + a b}{b}\right) \log\left(d x + \frac{a d}{b}\right)}{d} + \frac{\arctan\left(b x + a, 0\right) \log\left(b^{2} x^{2} + 2 \, a b x + a^{2} + 1\right) - 2 \, \arctan\left(b x + a\right) \log\left({\left| b x + a \right|}\right) + i \, {\rm Li}_2\left(i \, b x + i \, a + 1\right) - i \, {\rm Li}_2\left(-i \, b x - i \, a + 1\right)}{2 \, d}"," ",0,"arccot(b*x + a)*log(d*x + a*d/b)/d + arctan((b^2*x + a*b)/b)*log(d*x + a*d/b)/d + 1/2*(arctan2(b*x + a, 0)*log(b^2*x^2 + 2*a*b*x + a^2 + 1) - 2*arctan(b*x + a)*log(abs(b*x + a)) + I*dilog(I*b*x + I*a + 1) - I*dilog(-I*b*x - I*a + 1))/d","B",0
128,-2,0,0,0.000000," ","integrate((b*x+a)^2*arccot(b*x+a)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
129,1,341,0,0.449022," ","integrate((f*x+e)^3*(a+b*arccot(d*x+c)),x, algorithm=""maxima"")","\frac{1}{4} \, a f^{3} x^{4} + a e f^{2} x^{3} + \frac{3}{2} \, a e^{2} f x^{2} + \frac{3}{2} \, {\left(x^{2} \operatorname{arccot}\left(d x + c\right) + d {\left(\frac{x}{d^{2}} + \frac{{\left(c^{2} - 1\right)} \arctan\left(\frac{d^{2} x + c d}{d}\right)}{d^{3}} - \frac{c \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}{d^{3}}\right)}\right)} b e^{2} f + \frac{1}{2} \, {\left(2 \, x^{3} \operatorname{arccot}\left(d x + c\right) + d {\left(\frac{d x^{2} - 4 \, c x}{d^{3}} - \frac{2 \, {\left(c^{3} - 3 \, c\right)} \arctan\left(\frac{d^{2} x + c d}{d}\right)}{d^{4}} + \frac{{\left(3 \, c^{2} - 1\right)} \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}{d^{4}}\right)}\right)} b e f^{2} + \frac{1}{12} \, {\left(3 \, x^{4} \operatorname{arccot}\left(d x + c\right) + d {\left(\frac{d^{2} x^{3} - 3 \, c d x^{2} + 3 \, {\left(3 \, c^{2} - 1\right)} x}{d^{4}} + \frac{3 \, {\left(c^{4} - 6 \, c^{2} + 1\right)} \arctan\left(\frac{d^{2} x + c d}{d}\right)}{d^{5}} - \frac{6 \, {\left(c^{3} - c\right)} \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}{d^{5}}\right)}\right)} b f^{3} + a e^{3} x + \frac{{\left(2 \, {\left(d x + c\right)} \operatorname{arccot}\left(d x + c\right) + \log\left({\left(d x + c\right)}^{2} + 1\right)\right)} b e^{3}}{2 \, d}"," ",0,"1/4*a*f^3*x^4 + a*e*f^2*x^3 + 3/2*a*e^2*f*x^2 + 3/2*(x^2*arccot(d*x + c) + d*(x/d^2 + (c^2 - 1)*arctan((d^2*x + c*d)/d)/d^3 - c*log(d^2*x^2 + 2*c*d*x + c^2 + 1)/d^3))*b*e^2*f + 1/2*(2*x^3*arccot(d*x + c) + d*((d*x^2 - 4*c*x)/d^3 - 2*(c^3 - 3*c)*arctan((d^2*x + c*d)/d)/d^4 + (3*c^2 - 1)*log(d^2*x^2 + 2*c*d*x + c^2 + 1)/d^4))*b*e*f^2 + 1/12*(3*x^4*arccot(d*x + c) + d*((d^2*x^3 - 3*c*d*x^2 + 3*(3*c^2 - 1)*x)/d^4 + 3*(c^4 - 6*c^2 + 1)*arctan((d^2*x + c*d)/d)/d^5 - 6*(c^3 - c)*log(d^2*x^2 + 2*c*d*x + c^2 + 1)/d^5))*b*f^3 + a*e^3*x + 1/2*(2*(d*x + c)*arccot(d*x + c) + log((d*x + c)^2 + 1))*b*e^3/d","A",0
130,1,216,0,0.425902," ","integrate((f*x+e)^2*(a+b*arccot(d*x+c)),x, algorithm=""maxima"")","\frac{1}{3} \, a f^{2} x^{3} + a e f x^{2} + {\left(x^{2} \operatorname{arccot}\left(d x + c\right) + d {\left(\frac{x}{d^{2}} + \frac{{\left(c^{2} - 1\right)} \arctan\left(\frac{d^{2} x + c d}{d}\right)}{d^{3}} - \frac{c \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}{d^{3}}\right)}\right)} b e f + \frac{1}{6} \, {\left(2 \, x^{3} \operatorname{arccot}\left(d x + c\right) + d {\left(\frac{d x^{2} - 4 \, c x}{d^{3}} - \frac{2 \, {\left(c^{3} - 3 \, c\right)} \arctan\left(\frac{d^{2} x + c d}{d}\right)}{d^{4}} + \frac{{\left(3 \, c^{2} - 1\right)} \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}{d^{4}}\right)}\right)} b f^{2} + a e^{2} x + \frac{{\left(2 \, {\left(d x + c\right)} \operatorname{arccot}\left(d x + c\right) + \log\left({\left(d x + c\right)}^{2} + 1\right)\right)} b e^{2}}{2 \, d}"," ",0,"1/3*a*f^2*x^3 + a*e*f*x^2 + (x^2*arccot(d*x + c) + d*(x/d^2 + (c^2 - 1)*arctan((d^2*x + c*d)/d)/d^3 - c*log(d^2*x^2 + 2*c*d*x + c^2 + 1)/d^3))*b*e*f + 1/6*(2*x^3*arccot(d*x + c) + d*((d*x^2 - 4*c*x)/d^3 - 2*(c^3 - 3*c)*arctan((d^2*x + c*d)/d)/d^4 + (3*c^2 - 1)*log(d^2*x^2 + 2*c*d*x + c^2 + 1)/d^4))*b*f^2 + a*e^2*x + 1/2*(2*(d*x + c)*arccot(d*x + c) + log((d*x + c)^2 + 1))*b*e^2/d","A",0
131,1,113,0,0.426277," ","integrate((f*x+e)*(a+b*arccot(d*x+c)),x, algorithm=""maxima"")","\frac{1}{2} \, a f x^{2} + \frac{1}{2} \, {\left(x^{2} \operatorname{arccot}\left(d x + c\right) + d {\left(\frac{x}{d^{2}} + \frac{{\left(c^{2} - 1\right)} \arctan\left(\frac{d^{2} x + c d}{d}\right)}{d^{3}} - \frac{c \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}{d^{3}}\right)}\right)} b f + a e x + \frac{{\left(2 \, {\left(d x + c\right)} \operatorname{arccot}\left(d x + c\right) + \log\left({\left(d x + c\right)}^{2} + 1\right)\right)} b e}{2 \, d}"," ",0,"1/2*a*f*x^2 + 1/2*(x^2*arccot(d*x + c) + d*(x/d^2 + (c^2 - 1)*arctan((d^2*x + c*d)/d)/d^3 - c*log(d^2*x^2 + 2*c*d*x + c^2 + 1)/d^3))*b*f + a*e*x + 1/2*(2*(d*x + c)*arccot(d*x + c) + log((d*x + c)^2 + 1))*b*e/d","A",0
132,1,34,0,0.309898," ","integrate(a+b*arccot(d*x+c),x, algorithm=""maxima"")","a x + \frac{{\left(2 \, {\left(d x + c\right)} \operatorname{arccot}\left(d x + c\right) + \log\left({\left(d x + c\right)}^{2} + 1\right)\right)} b}{2 \, d}"," ",0,"a*x + 1/2*(2*(d*x + c)*arccot(d*x + c) + log((d*x + c)^2 + 1))*b/d","A",0
133,0,0,0,0.000000," ","integrate((a+b*arccot(d*x+c))/(f*x+e),x, algorithm=""maxima"")","2 \, b \int \frac{\arctan\left(1, d x + c\right)}{2 \, {\left(f x + e\right)}}\,{d x} + \frac{a \log\left(f x + e\right)}{f}"," ",0,"2*b*integrate(1/2*arctan2(1, d*x + c)/(f*x + e), x) + a*log(f*x + e)/f","F",0
134,1,177,0,0.440856," ","integrate((a+b*arccot(d*x+c))/(f*x+e)^2,x, algorithm=""maxima"")","-\frac{1}{2} \, {\left(d {\left(\frac{2 \, {\left(d^{2} e - c d f\right)} \arctan\left(\frac{d^{2} x + c d}{d}\right)}{{\left(d^{2} e^{2} f - 2 \, c d e f^{2} + {\left(c^{2} + 1\right)} f^{3}\right)} d} - \frac{\log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}{d^{2} e^{2} - 2 \, c d e f + {\left(c^{2} + 1\right)} f^{2}} + \frac{2 \, \log\left(f x + e\right)}{d^{2} e^{2} - 2 \, c d e f + {\left(c^{2} + 1\right)} f^{2}}\right)} + \frac{2 \, \operatorname{arccot}\left(d x + c\right)}{f^{2} x + e f}\right)} b - \frac{a}{f^{2} x + e f}"," ",0,"-1/2*(d*(2*(d^2*e - c*d*f)*arctan((d^2*x + c*d)/d)/((d^2*e^2*f - 2*c*d*e*f^2 + (c^2 + 1)*f^3)*d) - log(d^2*x^2 + 2*c*d*x + c^2 + 1)/(d^2*e^2 - 2*c*d*e*f + (c^2 + 1)*f^2) + 2*log(f*x + e)/(d^2*e^2 - 2*c*d*e*f + (c^2 + 1)*f^2)) + 2*arccot(d*x + c)/(f^2*x + e*f))*b - a/(f^2*x + e*f)","A",0
135,1,410,0,0.451999," ","integrate((a+b*arccot(d*x+c))/(f*x+e)^3,x, algorithm=""maxima"")","\frac{1}{2} \, {\left(d {\left(\frac{{\left(d^{2} e - c d f\right)} \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}{d^{4} e^{4} - 4 \, c d^{3} e^{3} f + 2 \, {\left(3 \, c^{2} + 1\right)} d^{2} e^{2} f^{2} - 4 \, {\left(c^{3} + c\right)} d e f^{3} + {\left(c^{4} + 2 \, c^{2} + 1\right)} f^{4}} - \frac{2 \, {\left(d^{2} e - c d f\right)} \log\left(f x + e\right)}{d^{4} e^{4} - 4 \, c d^{3} e^{3} f + 2 \, {\left(3 \, c^{2} + 1\right)} d^{2} e^{2} f^{2} - 4 \, {\left(c^{3} + c\right)} d e f^{3} + {\left(c^{4} + 2 \, c^{2} + 1\right)} f^{4}} - \frac{{\left(d^{4} e^{2} - 2 \, c d^{3} e f + {\left(c^{2} - 1\right)} d^{2} f^{2}\right)} \arctan\left(\frac{d^{2} x + c d}{d}\right)}{{\left(d^{4} e^{4} f - 4 \, c d^{3} e^{3} f^{2} + 2 \, {\left(3 \, c^{2} + 1\right)} d^{2} e^{2} f^{3} - 4 \, {\left(c^{3} + c\right)} d e f^{4} + {\left(c^{4} + 2 \, c^{2} + 1\right)} f^{5}\right)} d} + \frac{1}{d^{2} e^{3} - 2 \, c d e^{2} f + {\left(c^{2} + 1\right)} e f^{2} + {\left(d^{2} e^{2} f - 2 \, c d e f^{2} + {\left(c^{2} + 1\right)} f^{3}\right)} x}\right)} - \frac{\operatorname{arccot}\left(d x + c\right)}{f^{3} x^{2} + 2 \, e f^{2} x + e^{2} f}\right)} b - \frac{a}{2 \, {\left(f^{3} x^{2} + 2 \, e f^{2} x + e^{2} f\right)}}"," ",0,"1/2*(d*((d^2*e - c*d*f)*log(d^2*x^2 + 2*c*d*x + c^2 + 1)/(d^4*e^4 - 4*c*d^3*e^3*f + 2*(3*c^2 + 1)*d^2*e^2*f^2 - 4*(c^3 + c)*d*e*f^3 + (c^4 + 2*c^2 + 1)*f^4) - 2*(d^2*e - c*d*f)*log(f*x + e)/(d^4*e^4 - 4*c*d^3*e^3*f + 2*(3*c^2 + 1)*d^2*e^2*f^2 - 4*(c^3 + c)*d*e*f^3 + (c^4 + 2*c^2 + 1)*f^4) - (d^4*e^2 - 2*c*d^3*e*f + (c^2 - 1)*d^2*f^2)*arctan((d^2*x + c*d)/d)/((d^4*e^4*f - 4*c*d^3*e^3*f^2 + 2*(3*c^2 + 1)*d^2*e^2*f^3 - 4*(c^3 + c)*d*e*f^4 + (c^4 + 2*c^2 + 1)*f^5)*d) + 1/(d^2*e^3 - 2*c*d*e^2*f + (c^2 + 1)*e*f^2 + (d^2*e^2*f - 2*c*d*e*f^2 + (c^2 + 1)*f^3)*x)) - arccot(d*x + c)/(f^3*x^2 + 2*e*f^2*x + e^2*f))*b - 1/2*a/(f^3*x^2 + 2*e*f^2*x + e^2*f)","A",0
136,0,0,0,0.000000," ","integrate((f*x+e)^2*(a+b*arccot(d*x+c))^2,x, algorithm=""maxima"")","\frac{1}{12} \, b^{2} f^{2} x^{3} \arctan\left(1, d x + c\right)^{2} + \frac{1}{4} \, b^{2} e f x^{2} \arctan\left(1, d x + c\right)^{2} + \frac{1}{3} \, a^{2} f^{2} x^{3} + \frac{1}{4} \, b^{2} e^{2} x \arctan\left(1, d x + c\right)^{2} + a^{2} e f x^{2} + 2 \, {\left(x^{2} \operatorname{arccot}\left(d x + c\right) + d {\left(\frac{x}{d^{2}} + \frac{{\left(c^{2} - 1\right)} \arctan\left(\frac{d^{2} x + c d}{d}\right)}{d^{3}} - \frac{c \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}{d^{3}}\right)}\right)} a b e f + \frac{1}{3} \, {\left(2 \, x^{3} \operatorname{arccot}\left(d x + c\right) + d {\left(\frac{d x^{2} - 4 \, c x}{d^{3}} - \frac{2 \, {\left(c^{3} - 3 \, c\right)} \arctan\left(\frac{d^{2} x + c d}{d}\right)}{d^{4}} + \frac{{\left(3 \, c^{2} - 1\right)} \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}{d^{4}}\right)}\right)} a b f^{2} + a^{2} e^{2} x + \frac{{\left(2 \, {\left(d x + c\right)} \operatorname{arccot}\left(d x + c\right) + \log\left({\left(d x + c\right)}^{2} + 1\right)\right)} a b e^{2}}{d} - \frac{1}{48} \, {\left(b^{2} f^{2} x^{3} + 3 \, b^{2} e f x^{2} + 3 \, b^{2} e^{2} x\right)} \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)^{2} + \int \frac{36 \, b^{2} d^{2} f^{2} x^{4} \arctan\left(1, d x + c\right)^{2} + 8 \, {\left(9 \, b^{2} d^{2} e f \arctan\left(1, d x + c\right)^{2} + {\left(9 \, b^{2} c \arctan\left(1, d x + c\right)^{2} + b^{2} \arctan\left(1, d x + c\right)\right)} d f^{2}\right)} x^{3} + 36 \, {\left(b^{2} c^{2} \arctan\left(1, d x + c\right)^{2} + b^{2} \arctan\left(1, d x + c\right)^{2}\right)} e^{2} + 12 \, {\left(3 \, b^{2} d^{2} e^{2} \arctan\left(1, d x + c\right)^{2} + 2 \, {\left(6 \, b^{2} c \arctan\left(1, d x + c\right)^{2} + b^{2} \arctan\left(1, d x + c\right)\right)} d e f + 3 \, {\left(b^{2} c^{2} \arctan\left(1, d x + c\right)^{2} + b^{2} \arctan\left(1, d x + c\right)^{2}\right)} f^{2}\right)} x^{2} + 3 \, {\left(b^{2} d^{2} f^{2} x^{4} + 2 \, {\left(b^{2} d^{2} e f + b^{2} c d f^{2}\right)} x^{3} + {\left(b^{2} c^{2} + b^{2}\right)} e^{2} + {\left(b^{2} d^{2} e^{2} + 4 \, b^{2} c d e f + {\left(b^{2} c^{2} + b^{2}\right)} f^{2}\right)} x^{2} + 2 \, {\left(b^{2} c d e^{2} + {\left(b^{2} c^{2} + b^{2}\right)} e f\right)} x\right)} \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)^{2} + 24 \, {\left({\left(3 \, b^{2} c \arctan\left(1, d x + c\right)^{2} + b^{2} \arctan\left(1, d x + c\right)\right)} d e^{2} + 3 \, {\left(b^{2} c^{2} \arctan\left(1, d x + c\right)^{2} + b^{2} \arctan\left(1, d x + c\right)^{2}\right)} e f\right)} x + 4 \, {\left(b^{2} d^{2} f^{2} x^{4} + 3 \, b^{2} c d e^{2} x + {\left(3 \, b^{2} d^{2} e f + b^{2} c d f^{2}\right)} x^{3} + 3 \, {\left(b^{2} d^{2} e^{2} + b^{2} c d e f\right)} x^{2}\right)} \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}{48 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x}"," ",0,"1/12*b^2*f^2*x^3*arctan2(1, d*x + c)^2 + 1/4*b^2*e*f*x^2*arctan2(1, d*x + c)^2 + 1/3*a^2*f^2*x^3 + 1/4*b^2*e^2*x*arctan2(1, d*x + c)^2 + a^2*e*f*x^2 + 2*(x^2*arccot(d*x + c) + d*(x/d^2 + (c^2 - 1)*arctan((d^2*x + c*d)/d)/d^3 - c*log(d^2*x^2 + 2*c*d*x + c^2 + 1)/d^3))*a*b*e*f + 1/3*(2*x^3*arccot(d*x + c) + d*((d*x^2 - 4*c*x)/d^3 - 2*(c^3 - 3*c)*arctan((d^2*x + c*d)/d)/d^4 + (3*c^2 - 1)*log(d^2*x^2 + 2*c*d*x + c^2 + 1)/d^4))*a*b*f^2 + a^2*e^2*x + (2*(d*x + c)*arccot(d*x + c) + log((d*x + c)^2 + 1))*a*b*e^2/d - 1/48*(b^2*f^2*x^3 + 3*b^2*e*f*x^2 + 3*b^2*e^2*x)*log(d^2*x^2 + 2*c*d*x + c^2 + 1)^2 + integrate(1/48*(36*b^2*d^2*f^2*x^4*arctan2(1, d*x + c)^2 + 8*(9*b^2*d^2*e*f*arctan2(1, d*x + c)^2 + (9*b^2*c*arctan2(1, d*x + c)^2 + b^2*arctan2(1, d*x + c))*d*f^2)*x^3 + 36*(b^2*c^2*arctan2(1, d*x + c)^2 + b^2*arctan2(1, d*x + c)^2)*e^2 + 12*(3*b^2*d^2*e^2*arctan2(1, d*x + c)^2 + 2*(6*b^2*c*arctan2(1, d*x + c)^2 + b^2*arctan2(1, d*x + c))*d*e*f + 3*(b^2*c^2*arctan2(1, d*x + c)^2 + b^2*arctan2(1, d*x + c)^2)*f^2)*x^2 + 3*(b^2*d^2*f^2*x^4 + 2*(b^2*d^2*e*f + b^2*c*d*f^2)*x^3 + (b^2*c^2 + b^2)*e^2 + (b^2*d^2*e^2 + 4*b^2*c*d*e*f + (b^2*c^2 + b^2)*f^2)*x^2 + 2*(b^2*c*d*e^2 + (b^2*c^2 + b^2)*e*f)*x)*log(d^2*x^2 + 2*c*d*x + c^2 + 1)^2 + 24*((3*b^2*c*arctan2(1, d*x + c)^2 + b^2*arctan2(1, d*x + c))*d*e^2 + 3*(b^2*c^2*arctan2(1, d*x + c)^2 + b^2*arctan2(1, d*x + c)^2)*e*f)*x + 4*(b^2*d^2*f^2*x^4 + 3*b^2*c*d*e^2*x + (3*b^2*d^2*e*f + b^2*c*d*f^2)*x^3 + 3*(b^2*d^2*e^2 + b^2*c*d*e*f)*x^2)*log(d^2*x^2 + 2*c*d*x + c^2 + 1))/(d^2*x^2 + 2*c*d*x + c^2 + 1), x)","F",0
137,0,0,0,0.000000," ","integrate((f*x+e)*(a+b*arccot(d*x+c))^2,x, algorithm=""maxima"")","\frac{1}{8} \, b^{2} f x^{2} \arctan\left(1, d x + c\right)^{2} + \frac{1}{4} \, b^{2} e x \arctan\left(1, d x + c\right)^{2} + \frac{1}{2} \, a^{2} f x^{2} + {\left(x^{2} \operatorname{arccot}\left(d x + c\right) + d {\left(\frac{x}{d^{2}} + \frac{{\left(c^{2} - 1\right)} \arctan\left(\frac{d^{2} x + c d}{d}\right)}{d^{3}} - \frac{c \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}{d^{3}}\right)}\right)} a b f + a^{2} e x + \frac{{\left(2 \, {\left(d x + c\right)} \operatorname{arccot}\left(d x + c\right) + \log\left({\left(d x + c\right)}^{2} + 1\right)\right)} a b e}{d} - \frac{1}{32} \, {\left(b^{2} f x^{2} + 2 \, b^{2} e x\right)} \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)^{2} + \int \frac{12 \, b^{2} d^{2} f x^{3} \arctan\left(1, d x + c\right)^{2} + 4 \, {\left(3 \, b^{2} d^{2} e \arctan\left(1, d x + c\right)^{2} + {\left(6 \, b^{2} c \arctan\left(1, d x + c\right)^{2} + b^{2} \arctan\left(1, d x + c\right)\right)} d f\right)} x^{2} + {\left(b^{2} d^{2} f x^{3} + {\left(b^{2} d^{2} e + 2 \, b^{2} c d f\right)} x^{2} + {\left(b^{2} c^{2} + b^{2}\right)} e + {\left(2 \, b^{2} c d e + {\left(b^{2} c^{2} + b^{2}\right)} f\right)} x\right)} \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)^{2} + 12 \, {\left(b^{2} c^{2} \arctan\left(1, d x + c\right)^{2} + b^{2} \arctan\left(1, d x + c\right)^{2}\right)} e + 4 \, {\left(2 \, {\left(3 \, b^{2} c \arctan\left(1, d x + c\right)^{2} + b^{2} \arctan\left(1, d x + c\right)\right)} d e + 3 \, {\left(b^{2} c^{2} \arctan\left(1, d x + c\right)^{2} + b^{2} \arctan\left(1, d x + c\right)^{2}\right)} f\right)} x + 2 \, {\left(b^{2} d^{2} f x^{3} + 2 \, b^{2} c d e x + {\left(2 \, b^{2} d^{2} e + b^{2} c d f\right)} x^{2}\right)} \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}{16 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x}"," ",0,"1/8*b^2*f*x^2*arctan2(1, d*x + c)^2 + 1/4*b^2*e*x*arctan2(1, d*x + c)^2 + 1/2*a^2*f*x^2 + (x^2*arccot(d*x + c) + d*(x/d^2 + (c^2 - 1)*arctan((d^2*x + c*d)/d)/d^3 - c*log(d^2*x^2 + 2*c*d*x + c^2 + 1)/d^3))*a*b*f + a^2*e*x + (2*(d*x + c)*arccot(d*x + c) + log((d*x + c)^2 + 1))*a*b*e/d - 1/32*(b^2*f*x^2 + 2*b^2*e*x)*log(d^2*x^2 + 2*c*d*x + c^2 + 1)^2 + integrate(1/16*(12*b^2*d^2*f*x^3*arctan2(1, d*x + c)^2 + 4*(3*b^2*d^2*e*arctan2(1, d*x + c)^2 + (6*b^2*c*arctan2(1, d*x + c)^2 + b^2*arctan2(1, d*x + c))*d*f)*x^2 + (b^2*d^2*f*x^3 + (b^2*d^2*e + 2*b^2*c*d*f)*x^2 + (b^2*c^2 + b^2)*e + (2*b^2*c*d*e + (b^2*c^2 + b^2)*f)*x)*log(d^2*x^2 + 2*c*d*x + c^2 + 1)^2 + 12*(b^2*c^2*arctan2(1, d*x + c)^2 + b^2*arctan2(1, d*x + c)^2)*e + 4*(2*(3*b^2*c*arctan2(1, d*x + c)^2 + b^2*arctan2(1, d*x + c))*d*e + 3*(b^2*c^2*arctan2(1, d*x + c)^2 + b^2*arctan2(1, d*x + c)^2)*f)*x + 2*(b^2*d^2*f*x^3 + 2*b^2*c*d*e*x + (2*b^2*d^2*e + b^2*c*d*f)*x^2)*log(d^2*x^2 + 2*c*d*x + c^2 + 1))/(d^2*x^2 + 2*c*d*x + c^2 + 1), x)","F",0
138,0,0,0,0.000000," ","integrate((a+b*arccot(d*x+c))^2,x, algorithm=""maxima"")","\frac{1}{16} \, {\left(4 \, x \arctan\left(1, d x + c\right)^{2} - x \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)^{2} + 16 \, \int \frac{12 \, d^{2} x^{2} \arctan\left(1, d x + c\right)^{2} + 12 \, c^{2} \arctan\left(1, d x + c\right)^{2} + 8 \, {\left(3 \, c \arctan\left(1, d x + c\right)^{2} + \arctan\left(1, d x + c\right)\right)} d x + {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)} \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)^{2} + 12 \, \arctan\left(1, d x + c\right)^{2} + 4 \, {\left(d^{2} x^{2} + c d x\right)} \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}{16 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x}\right)} b^{2} + a^{2} x + \frac{{\left(2 \, {\left(d x + c\right)} \operatorname{arccot}\left(d x + c\right) + \log\left({\left(d x + c\right)}^{2} + 1\right)\right)} a b}{d}"," ",0,"1/16*(4*x*arctan2(1, d*x + c)^2 - x*log(d^2*x^2 + 2*c*d*x + c^2 + 1)^2 + 16*integrate(1/16*(12*d^2*x^2*arctan2(1, d*x + c)^2 + 12*c^2*arctan2(1, d*x + c)^2 + 8*(3*c*arctan2(1, d*x + c)^2 + arctan2(1, d*x + c))*d*x + (d^2*x^2 + 2*c*d*x + c^2 + 1)*log(d^2*x^2 + 2*c*d*x + c^2 + 1)^2 + 12*arctan2(1, d*x + c)^2 + 4*(d^2*x^2 + c*d*x)*log(d^2*x^2 + 2*c*d*x + c^2 + 1))/(d^2*x^2 + 2*c*d*x + c^2 + 1), x))*b^2 + a^2*x + (2*(d*x + c)*arccot(d*x + c) + log((d*x + c)^2 + 1))*a*b/d","F",0
139,0,0,0,0.000000," ","integrate((a+b*arccot(d*x+c))^2/(f*x+e),x, algorithm=""maxima"")","\frac{a^{2} \log\left(f x + e\right)}{f} + \int \frac{12 \, b^{2} \arctan\left(1, d x + c\right)^{2} + b^{2} \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)^{2} + 32 \, a b \arctan\left(1, d x + c\right)}{16 \, {\left(f x + e\right)}}\,{d x}"," ",0,"a^2*log(f*x + e)/f + integrate(1/16*(12*b^2*arctan2(1, d*x + c)^2 + b^2*log(d^2*x^2 + 2*c*d*x + c^2 + 1)^2 + 32*a*b*arctan2(1, d*x + c))/(f*x + e), x)","F",0
140,0,0,0,0.000000," ","integrate((a+b*arccot(d*x+c))^2/(f*x+e)^2,x, algorithm=""maxima"")","-{\left(d {\left(\frac{2 \, {\left(d^{2} e - c d f\right)} \arctan\left(\frac{d^{2} x + c d}{d}\right)}{{\left(d^{2} e^{2} f - 2 \, c d e f^{2} + {\left(c^{2} + 1\right)} f^{3}\right)} d} - \frac{\log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}{d^{2} e^{2} - 2 \, c d e f + {\left(c^{2} + 1\right)} f^{2}} + \frac{2 \, \log\left(f x + e\right)}{d^{2} e^{2} - 2 \, c d e f + {\left(c^{2} + 1\right)} f^{2}}\right)} + \frac{2 \, \operatorname{arccot}\left(d x + c\right)}{f^{2} x + e f}\right)} a b - \frac{\frac{1}{4} \, {\left(28 \, \arctan\left(1, d x + c\right)^{2} - 4 \, {\left(f^{2} x + e f\right)} \int \frac{36 \, d^{2} f x^{2} \arctan\left(1, d x + c\right)^{2} + 8 \, {\left(9 \, c \arctan\left(1, d x + c\right)^{2} - 7 \, \arctan\left(1, d x + c\right)\right)} d f x - 56 \, d e \arctan\left(1, d x + c\right) + 3 \, {\left(d^{2} f x^{2} + 2 \, c d f x + {\left(c^{2} + 1\right)} f\right)} \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)^{2} + 36 \, {\left(c^{2} \arctan\left(1, d x + c\right)^{2} + \arctan\left(1, d x + c\right)^{2}\right)} f - 12 \, {\left(d^{2} f x^{2} + c d e + {\left(d^{2} e + c d f\right)} x\right)} \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}{4 \, {\left(d^{2} f^{3} x^{4} + {\left(c^{2} + 1\right)} e^{2} f + 2 \, {\left(d^{2} e f^{2} + c d f^{3}\right)} x^{3} + {\left(d^{2} e^{2} f + 4 \, c d e f^{2} + {\left(c^{2} + 1\right)} f^{3}\right)} x^{2} + 2 \, {\left(c d e^{2} f + {\left(c^{2} + 1\right)} e f^{2}\right)} x\right)}}\,{d x} - 3 \, \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)^{2}\right)} b^{2}}{16 \, {\left(f^{2} x + e f\right)}} - \frac{a^{2}}{f^{2} x + e f}"," ",0,"-(d*(2*(d^2*e - c*d*f)*arctan((d^2*x + c*d)/d)/((d^2*e^2*f - 2*c*d*e*f^2 + (c^2 + 1)*f^3)*d) - log(d^2*x^2 + 2*c*d*x + c^2 + 1)/(d^2*e^2 - 2*c*d*e*f + (c^2 + 1)*f^2) + 2*log(f*x + e)/(d^2*e^2 - 2*c*d*e*f + (c^2 + 1)*f^2)) + 2*arccot(d*x + c)/(f^2*x + e*f))*a*b - 1/16*(4*arctan2(1, d*x + c)^2 - 16*(f^2*x + e*f)*integrate(1/16*(12*d^2*f*x^2*arctan2(1, d*x + c)^2 + 8*(3*c*arctan2(1, d*x + c)^2 - arctan2(1, d*x + c))*d*f*x - 8*d*e*arctan2(1, d*x + c) + (d^2*f*x^2 + 2*c*d*f*x + (c^2 + 1)*f)*log(d^2*x^2 + 2*c*d*x + c^2 + 1)^2 + 12*(c^2*arctan2(1, d*x + c)^2 + arctan2(1, d*x + c)^2)*f - 4*(d^2*f*x^2 + c*d*e + (d^2*e + c*d*f)*x)*log(d^2*x^2 + 2*c*d*x + c^2 + 1))/(d^2*f^3*x^4 + (c^2 + 1)*e^2*f + 2*(d^2*e*f^2 + c*d*f^3)*x^3 + (d^2*e^2*f + 4*c*d*e*f^2 + (c^2 + 1)*f^3)*x^2 + 2*(c*d*e^2*f + (c^2 + 1)*e*f^2)*x), x) - log(d^2*x^2 + 2*c*d*x + c^2 + 1)^2)*b^2/(f^2*x + e*f) - a^2/(f^2*x + e*f)","F",0
141,0,0,0,0.000000," ","integrate((f*x+e)^2*(a+b*arccot(d*x+c))^3,x, algorithm=""maxima"")","\frac{1}{24} \, b^{3} f^{2} x^{3} \arctan\left(1, d x + c\right)^{3} + \frac{1}{8} \, b^{3} e f x^{2} \arctan\left(1, d x + c\right)^{3} + \frac{1}{8} \, b^{3} e^{2} x \arctan\left(1, d x + c\right)^{3} + \frac{1}{3} \, a^{3} f^{2} x^{3} + a^{3} e f x^{2} + 3 \, {\left(x^{2} \operatorname{arccot}\left(d x + c\right) + d {\left(\frac{x}{d^{2}} + \frac{{\left(c^{2} - 1\right)} \arctan\left(\frac{d^{2} x + c d}{d}\right)}{d^{3}} - \frac{c \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}{d^{3}}\right)}\right)} a^{2} b e f + \frac{1}{2} \, {\left(2 \, x^{3} \operatorname{arccot}\left(d x + c\right) + d {\left(\frac{d x^{2} - 4 \, c x}{d^{3}} - \frac{2 \, {\left(c^{3} - 3 \, c\right)} \arctan\left(\frac{d^{2} x + c d}{d}\right)}{d^{4}} + \frac{{\left(3 \, c^{2} - 1\right)} \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}{d^{4}}\right)}\right)} a^{2} b f^{2} + a^{3} e^{2} x + \frac{3 \, {\left(2 \, {\left(d x + c\right)} \operatorname{arccot}\left(d x + c\right) + \log\left({\left(d x + c\right)}^{2} + 1\right)\right)} a^{2} b e^{2}}{2 \, d} - \frac{1}{32} \, {\left(b^{3} f^{2} x^{3} \arctan\left(1, d x + c\right) + 3 \, b^{3} e f x^{2} \arctan\left(1, d x + c\right) + 3 \, b^{3} e^{2} x \arctan\left(1, d x + c\right)\right)} \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)^{2} + \int \frac{4 \, {\left(7 \, b^{3} \arctan\left(1, d x + c\right)^{3} + 24 \, a b^{2} \arctan\left(1, d x + c\right)^{2}\right)} d^{2} f^{2} x^{4} + 4 \, {\left(2 \, {\left(7 \, b^{3} \arctan\left(1, d x + c\right)^{3} + 24 \, a b^{2} \arctan\left(1, d x + c\right)^{2}\right)} d^{2} e f + {\left(b^{3} \arctan\left(1, d x + c\right)^{2} + 2 \, {\left(7 \, b^{3} \arctan\left(1, d x + c\right)^{3} + 24 \, a b^{2} \arctan\left(1, d x + c\right)^{2}\right)} c\right)} d f^{2}\right)} x^{3} + 4 \, {\left(7 \, b^{3} \arctan\left(1, d x + c\right)^{3} + 24 \, a b^{2} \arctan\left(1, d x + c\right)^{2} + {\left(7 \, b^{3} \arctan\left(1, d x + c\right)^{3} + 24 \, a b^{2} \arctan\left(1, d x + c\right)^{2}\right)} c^{2}\right)} e^{2} + 4 \, {\left({\left(7 \, b^{3} \arctan\left(1, d x + c\right)^{3} + 24 \, a b^{2} \arctan\left(1, d x + c\right)^{2}\right)} d^{2} e^{2} + {\left(3 \, b^{3} \arctan\left(1, d x + c\right)^{2} + 4 \, {\left(7 \, b^{3} \arctan\left(1, d x + c\right)^{3} + 24 \, a b^{2} \arctan\left(1, d x + c\right)^{2}\right)} c\right)} d e f + {\left(7 \, b^{3} \arctan\left(1, d x + c\right)^{3} + 24 \, a b^{2} \arctan\left(1, d x + c\right)^{2} + {\left(7 \, b^{3} \arctan\left(1, d x + c\right)^{3} + 24 \, a b^{2} \arctan\left(1, d x + c\right)^{2}\right)} c^{2}\right)} f^{2}\right)} x^{2} + {\left(3 \, b^{3} d^{2} f^{2} x^{4} \arctan\left(1, d x + c\right) + {\left(6 \, b^{3} d^{2} e f \arctan\left(1, d x + c\right) + {\left(6 \, b^{3} c \arctan\left(1, d x + c\right) - b^{3}\right)} d f^{2}\right)} x^{3} + 3 \, {\left(b^{3} c^{2} \arctan\left(1, d x + c\right) + b^{3} \arctan\left(1, d x + c\right)\right)} e^{2} + 3 \, {\left(b^{3} d^{2} e^{2} \arctan\left(1, d x + c\right) + {\left(4 \, b^{3} c \arctan\left(1, d x + c\right) - b^{3}\right)} d e f + {\left(b^{3} c^{2} \arctan\left(1, d x + c\right) + b^{3} \arctan\left(1, d x + c\right)\right)} f^{2}\right)} x^{2} + 3 \, {\left({\left(2 \, b^{3} c \arctan\left(1, d x + c\right) - b^{3}\right)} d e^{2} + 2 \, {\left(b^{3} c^{2} \arctan\left(1, d x + c\right) + b^{3} \arctan\left(1, d x + c\right)\right)} e f\right)} x\right)} \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)^{2} + 4 \, {\left({\left(3 \, b^{3} \arctan\left(1, d x + c\right)^{2} + 2 \, {\left(7 \, b^{3} \arctan\left(1, d x + c\right)^{3} + 24 \, a b^{2} \arctan\left(1, d x + c\right)^{2}\right)} c\right)} d e^{2} + 2 \, {\left(7 \, b^{3} \arctan\left(1, d x + c\right)^{3} + 24 \, a b^{2} \arctan\left(1, d x + c\right)^{2} + {\left(7 \, b^{3} \arctan\left(1, d x + c\right)^{3} + 24 \, a b^{2} \arctan\left(1, d x + c\right)^{2}\right)} c^{2}\right)} e f\right)} x + 4 \, {\left(b^{3} d^{2} f^{2} x^{4} \arctan\left(1, d x + c\right) + 3 \, b^{3} c d e^{2} x \arctan\left(1, d x + c\right) + {\left(3 \, b^{3} d^{2} e f \arctan\left(1, d x + c\right) + b^{3} c d f^{2} \arctan\left(1, d x + c\right)\right)} x^{3} + 3 \, {\left(b^{3} d^{2} e^{2} \arctan\left(1, d x + c\right) + b^{3} c d e f \arctan\left(1, d x + c\right)\right)} x^{2}\right)} \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}{32 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x}"," ",0,"1/24*b^3*f^2*x^3*arctan2(1, d*x + c)^3 + 1/8*b^3*e*f*x^2*arctan2(1, d*x + c)^3 + 1/8*b^3*e^2*x*arctan2(1, d*x + c)^3 + 1/3*a^3*f^2*x^3 + a^3*e*f*x^2 + 3*(x^2*arccot(d*x + c) + d*(x/d^2 + (c^2 - 1)*arctan((d^2*x + c*d)/d)/d^3 - c*log(d^2*x^2 + 2*c*d*x + c^2 + 1)/d^3))*a^2*b*e*f + 1/2*(2*x^3*arccot(d*x + c) + d*((d*x^2 - 4*c*x)/d^3 - 2*(c^3 - 3*c)*arctan((d^2*x + c*d)/d)/d^4 + (3*c^2 - 1)*log(d^2*x^2 + 2*c*d*x + c^2 + 1)/d^4))*a^2*b*f^2 + a^3*e^2*x + 3/2*(2*(d*x + c)*arccot(d*x + c) + log((d*x + c)^2 + 1))*a^2*b*e^2/d - 1/32*(b^3*f^2*x^3*arctan2(1, d*x + c) + 3*b^3*e*f*x^2*arctan2(1, d*x + c) + 3*b^3*e^2*x*arctan2(1, d*x + c))*log(d^2*x^2 + 2*c*d*x + c^2 + 1)^2 + integrate(1/32*(4*(7*b^3*arctan2(1, d*x + c)^3 + 24*a*b^2*arctan2(1, d*x + c)^2)*d^2*f^2*x^4 + 4*(2*(7*b^3*arctan2(1, d*x + c)^3 + 24*a*b^2*arctan2(1, d*x + c)^2)*d^2*e*f + (b^3*arctan2(1, d*x + c)^2 + 2*(7*b^3*arctan2(1, d*x + c)^3 + 24*a*b^2*arctan2(1, d*x + c)^2)*c)*d*f^2)*x^3 + 4*(7*b^3*arctan2(1, d*x + c)^3 + 24*a*b^2*arctan2(1, d*x + c)^2 + (7*b^3*arctan2(1, d*x + c)^3 + 24*a*b^2*arctan2(1, d*x + c)^2)*c^2)*e^2 + 4*((7*b^3*arctan2(1, d*x + c)^3 + 24*a*b^2*arctan2(1, d*x + c)^2)*d^2*e^2 + (3*b^3*arctan2(1, d*x + c)^2 + 4*(7*b^3*arctan2(1, d*x + c)^3 + 24*a*b^2*arctan2(1, d*x + c)^2)*c)*d*e*f + (7*b^3*arctan2(1, d*x + c)^3 + 24*a*b^2*arctan2(1, d*x + c)^2 + (7*b^3*arctan2(1, d*x + c)^3 + 24*a*b^2*arctan2(1, d*x + c)^2)*c^2)*f^2)*x^2 + (3*b^3*d^2*f^2*x^4*arctan2(1, d*x + c) + (6*b^3*d^2*e*f*arctan2(1, d*x + c) + (6*b^3*c*arctan2(1, d*x + c) - b^3)*d*f^2)*x^3 + 3*(b^3*c^2*arctan2(1, d*x + c) + b^3*arctan2(1, d*x + c))*e^2 + 3*(b^3*d^2*e^2*arctan2(1, d*x + c) + (4*b^3*c*arctan2(1, d*x + c) - b^3)*d*e*f + (b^3*c^2*arctan2(1, d*x + c) + b^3*arctan2(1, d*x + c))*f^2)*x^2 + 3*((2*b^3*c*arctan2(1, d*x + c) - b^3)*d*e^2 + 2*(b^3*c^2*arctan2(1, d*x + c) + b^3*arctan2(1, d*x + c))*e*f)*x)*log(d^2*x^2 + 2*c*d*x + c^2 + 1)^2 + 4*((3*b^3*arctan2(1, d*x + c)^2 + 2*(7*b^3*arctan2(1, d*x + c)^3 + 24*a*b^2*arctan2(1, d*x + c)^2)*c)*d*e^2 + 2*(7*b^3*arctan2(1, d*x + c)^3 + 24*a*b^2*arctan2(1, d*x + c)^2 + (7*b^3*arctan2(1, d*x + c)^3 + 24*a*b^2*arctan2(1, d*x + c)^2)*c^2)*e*f)*x + 4*(b^3*d^2*f^2*x^4*arctan2(1, d*x + c) + 3*b^3*c*d*e^2*x*arctan2(1, d*x + c) + (3*b^3*d^2*e*f*arctan2(1, d*x + c) + b^3*c*d*f^2*arctan2(1, d*x + c))*x^3 + 3*(b^3*d^2*e^2*arctan2(1, d*x + c) + b^3*c*d*e*f*arctan2(1, d*x + c))*x^2)*log(d^2*x^2 + 2*c*d*x + c^2 + 1))/(d^2*x^2 + 2*c*d*x + c^2 + 1), x)","F",0
142,0,0,0,0.000000," ","integrate((f*x+e)*(a+b*arccot(d*x+c))^3,x, algorithm=""maxima"")","\frac{1}{16} \, b^{3} f x^{2} \arctan\left(1, d x + c\right)^{3} + \frac{1}{8} \, b^{3} e x \arctan\left(1, d x + c\right)^{3} + \frac{1}{2} \, a^{3} f x^{2} + \frac{3}{2} \, {\left(x^{2} \operatorname{arccot}\left(d x + c\right) + d {\left(\frac{x}{d^{2}} + \frac{{\left(c^{2} - 1\right)} \arctan\left(\frac{d^{2} x + c d}{d}\right)}{d^{3}} - \frac{c \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}{d^{3}}\right)}\right)} a^{2} b f + a^{3} e x + \frac{3 \, {\left(2 \, {\left(d x + c\right)} \operatorname{arccot}\left(d x + c\right) + \log\left({\left(d x + c\right)}^{2} + 1\right)\right)} a^{2} b e}{2 \, d} - \frac{3}{64} \, {\left(b^{3} f x^{2} \arctan\left(1, d x + c\right) + 2 \, b^{3} e x \arctan\left(1, d x + c\right)\right)} \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)^{2} + \int \frac{8 \, {\left(7 \, b^{3} \arctan\left(1, d x + c\right)^{3} + 24 \, a b^{2} \arctan\left(1, d x + c\right)^{2}\right)} d^{2} f x^{3} + 4 \, {\left(2 \, {\left(7 \, b^{3} \arctan\left(1, d x + c\right)^{3} + 24 \, a b^{2} \arctan\left(1, d x + c\right)^{2}\right)} d^{2} e + {\left(3 \, b^{3} \arctan\left(1, d x + c\right)^{2} + 4 \, {\left(7 \, b^{3} \arctan\left(1, d x + c\right)^{3} + 24 \, a b^{2} \arctan\left(1, d x + c\right)^{2}\right)} c\right)} d f\right)} x^{2} + 3 \, {\left(2 \, b^{3} d^{2} f x^{3} \arctan\left(1, d x + c\right) + {\left(2 \, b^{3} d^{2} e \arctan\left(1, d x + c\right) + {\left(4 \, b^{3} c \arctan\left(1, d x + c\right) - b^{3}\right)} d f\right)} x^{2} + 2 \, {\left(b^{3} c^{2} \arctan\left(1, d x + c\right) + b^{3} \arctan\left(1, d x + c\right)\right)} e + 2 \, {\left({\left(2 \, b^{3} c \arctan\left(1, d x + c\right) - b^{3}\right)} d e + {\left(b^{3} c^{2} \arctan\left(1, d x + c\right) + b^{3} \arctan\left(1, d x + c\right)\right)} f\right)} x\right)} \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)^{2} + 8 \, {\left(7 \, b^{3} \arctan\left(1, d x + c\right)^{3} + 24 \, a b^{2} \arctan\left(1, d x + c\right)^{2} + {\left(7 \, b^{3} \arctan\left(1, d x + c\right)^{3} + 24 \, a b^{2} \arctan\left(1, d x + c\right)^{2}\right)} c^{2}\right)} e + 8 \, {\left({\left(3 \, b^{3} \arctan\left(1, d x + c\right)^{2} + 2 \, {\left(7 \, b^{3} \arctan\left(1, d x + c\right)^{3} + 24 \, a b^{2} \arctan\left(1, d x + c\right)^{2}\right)} c\right)} d e + {\left(7 \, b^{3} \arctan\left(1, d x + c\right)^{3} + 24 \, a b^{2} \arctan\left(1, d x + c\right)^{2} + {\left(7 \, b^{3} \arctan\left(1, d x + c\right)^{3} + 24 \, a b^{2} \arctan\left(1, d x + c\right)^{2}\right)} c^{2}\right)} f\right)} x + 12 \, {\left(b^{3} d^{2} f x^{3} \arctan\left(1, d x + c\right) + 2 \, b^{3} c d e x \arctan\left(1, d x + c\right) + {\left(2 \, b^{3} d^{2} e \arctan\left(1, d x + c\right) + b^{3} c d f \arctan\left(1, d x + c\right)\right)} x^{2}\right)} \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}{64 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x}"," ",0,"1/16*b^3*f*x^2*arctan2(1, d*x + c)^3 + 1/8*b^3*e*x*arctan2(1, d*x + c)^3 + 1/2*a^3*f*x^2 + 3/2*(x^2*arccot(d*x + c) + d*(x/d^2 + (c^2 - 1)*arctan((d^2*x + c*d)/d)/d^3 - c*log(d^2*x^2 + 2*c*d*x + c^2 + 1)/d^3))*a^2*b*f + a^3*e*x + 3/2*(2*(d*x + c)*arccot(d*x + c) + log((d*x + c)^2 + 1))*a^2*b*e/d - 3/64*(b^3*f*x^2*arctan2(1, d*x + c) + 2*b^3*e*x*arctan2(1, d*x + c))*log(d^2*x^2 + 2*c*d*x + c^2 + 1)^2 + integrate(1/64*(8*(7*b^3*arctan2(1, d*x + c)^3 + 24*a*b^2*arctan2(1, d*x + c)^2)*d^2*f*x^3 + 4*(2*(7*b^3*arctan2(1, d*x + c)^3 + 24*a*b^2*arctan2(1, d*x + c)^2)*d^2*e + (3*b^3*arctan2(1, d*x + c)^2 + 4*(7*b^3*arctan2(1, d*x + c)^3 + 24*a*b^2*arctan2(1, d*x + c)^2)*c)*d*f)*x^2 + 3*(2*b^3*d^2*f*x^3*arctan2(1, d*x + c) + (2*b^3*d^2*e*arctan2(1, d*x + c) + (4*b^3*c*arctan2(1, d*x + c) - b^3)*d*f)*x^2 + 2*(b^3*c^2*arctan2(1, d*x + c) + b^3*arctan2(1, d*x + c))*e + 2*((2*b^3*c*arctan2(1, d*x + c) - b^3)*d*e + (b^3*c^2*arctan2(1, d*x + c) + b^3*arctan2(1, d*x + c))*f)*x)*log(d^2*x^2 + 2*c*d*x + c^2 + 1)^2 + 8*(7*b^3*arctan2(1, d*x + c)^3 + 24*a*b^2*arctan2(1, d*x + c)^2 + (7*b^3*arctan2(1, d*x + c)^3 + 24*a*b^2*arctan2(1, d*x + c)^2)*c^2)*e + 8*((3*b^3*arctan2(1, d*x + c)^2 + 2*(7*b^3*arctan2(1, d*x + c)^3 + 24*a*b^2*arctan2(1, d*x + c)^2)*c)*d*e + (7*b^3*arctan2(1, d*x + c)^3 + 24*a*b^2*arctan2(1, d*x + c)^2 + (7*b^3*arctan2(1, d*x + c)^3 + 24*a*b^2*arctan2(1, d*x + c)^2)*c^2)*f)*x + 12*(b^3*d^2*f*x^3*arctan2(1, d*x + c) + 2*b^3*c*d*e*x*arctan2(1, d*x + c) + (2*b^3*d^2*e*arctan2(1, d*x + c) + b^3*c*d*f*arctan2(1, d*x + c))*x^2)*log(d^2*x^2 + 2*c*d*x + c^2 + 1))/(d^2*x^2 + 2*c*d*x + c^2 + 1), x)","F",0
143,0,0,0,0.000000," ","integrate((a+b*arccot(d*x+c))^3,x, algorithm=""maxima"")","\frac{1}{8} \, b^{3} x \arctan\left(1, d x + c\right)^{3} - \frac{3}{32} \, b^{3} x \arctan\left(1, d x + c\right) \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)^{2} + a^{3} x + \frac{3 \, {\left(2 \, {\left(d x + c\right)} \operatorname{arccot}\left(d x + c\right) + \log\left({\left(d x + c\right)}^{2} + 1\right)\right)} a^{2} b}{2 \, d} + \int \frac{28 \, b^{3} \arctan\left(1, d x + c\right)^{3} + 4 \, {\left(7 \, b^{3} \arctan\left(1, d x + c\right)^{3} + 24 \, a b^{2} \arctan\left(1, d x + c\right)^{2}\right)} d^{2} x^{2} + 96 \, a b^{2} \arctan\left(1, d x + c\right)^{2} + 4 \, {\left(7 \, b^{3} \arctan\left(1, d x + c\right)^{3} + 24 \, a b^{2} \arctan\left(1, d x + c\right)^{2}\right)} c^{2} + 4 \, {\left(3 \, b^{3} \arctan\left(1, d x + c\right)^{2} + 2 \, {\left(7 \, b^{3} \arctan\left(1, d x + c\right)^{3} + 24 \, a b^{2} \arctan\left(1, d x + c\right)^{2}\right)} c\right)} d x + 3 \, {\left(b^{3} d^{2} x^{2} \arctan\left(1, d x + c\right) + b^{3} c^{2} \arctan\left(1, d x + c\right) + b^{3} \arctan\left(1, d x + c\right) + {\left(2 \, b^{3} c \arctan\left(1, d x + c\right) - b^{3}\right)} d x\right)} \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)^{2} + 12 \, {\left(b^{3} d^{2} x^{2} \arctan\left(1, d x + c\right) + b^{3} c d x \arctan\left(1, d x + c\right)\right)} \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}{32 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}}\,{d x}"," ",0,"1/8*b^3*x*arctan2(1, d*x + c)^3 - 3/32*b^3*x*arctan2(1, d*x + c)*log(d^2*x^2 + 2*c*d*x + c^2 + 1)^2 + a^3*x + 3/2*(2*(d*x + c)*arccot(d*x + c) + log((d*x + c)^2 + 1))*a^2*b/d + integrate(1/32*(28*b^3*arctan2(1, d*x + c)^3 + 4*(7*b^3*arctan2(1, d*x + c)^3 + 24*a*b^2*arctan2(1, d*x + c)^2)*d^2*x^2 + 96*a*b^2*arctan2(1, d*x + c)^2 + 4*(7*b^3*arctan2(1, d*x + c)^3 + 24*a*b^2*arctan2(1, d*x + c)^2)*c^2 + 4*(3*b^3*arctan2(1, d*x + c)^2 + 2*(7*b^3*arctan2(1, d*x + c)^3 + 24*a*b^2*arctan2(1, d*x + c)^2)*c)*d*x + 3*(b^3*d^2*x^2*arctan2(1, d*x + c) + b^3*c^2*arctan2(1, d*x + c) + b^3*arctan2(1, d*x + c) + (2*b^3*c*arctan2(1, d*x + c) - b^3)*d*x)*log(d^2*x^2 + 2*c*d*x + c^2 + 1)^2 + 12*(b^3*d^2*x^2*arctan2(1, d*x + c) + b^3*c*d*x*arctan2(1, d*x + c))*log(d^2*x^2 + 2*c*d*x + c^2 + 1))/(d^2*x^2 + 2*c*d*x + c^2 + 1), x)","F",0
144,0,0,0,0.000000," ","integrate((a+b*arccot(d*x+c))^3/(f*x+e),x, algorithm=""maxima"")","\frac{a^{3} \log\left(f x + e\right)}{f} + \int \frac{28 \, b^{3} \arctan\left(1, d x + c\right)^{3} + 3 \, b^{3} \arctan\left(1, d x + c\right) \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)^{2} + 96 \, a b^{2} \arctan\left(1, d x + c\right)^{2} + 96 \, a^{2} b \arctan\left(1, d x + c\right)}{32 \, {\left(f x + e\right)}}\,{d x}"," ",0,"a^3*log(f*x + e)/f + integrate(1/32*(28*b^3*arctan2(1, d*x + c)^3 + 3*b^3*arctan2(1, d*x + c)*log(d^2*x^2 + 2*c*d*x + c^2 + 1)^2 + 96*a*b^2*arctan2(1, d*x + c)^2 + 96*a^2*b*arctan2(1, d*x + c))/(f*x + e), x)","F",0
145,0,0,0,0.000000," ","integrate((a+b*arccot(d*x+c))^3/(f*x+e)^2,x, algorithm=""maxima"")","-\frac{3}{2} \, {\left(d {\left(\frac{2 \, {\left(d^{2} e - c d f\right)} \arctan\left(\frac{d^{2} x + c d}{d}\right)}{{\left(d^{2} e^{2} f - 2 \, c d e f^{2} + {\left(c^{2} + 1\right)} f^{3}\right)} d} - \frac{\log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}{d^{2} e^{2} - 2 \, c d e f + {\left(c^{2} + 1\right)} f^{2}} + \frac{2 \, \log\left(f x + e\right)}{d^{2} e^{2} - 2 \, c d e f + {\left(c^{2} + 1\right)} f^{2}}\right)} + \frac{2 \, \operatorname{arccot}\left(d x + c\right)}{f^{2} x + e f}\right)} a^{2} b - \frac{a^{3}}{f^{2} x + e f} - \frac{\frac{15}{2} \, b^{3} \arctan\left(1, d x + c\right)^{3} - \frac{21}{8} \, b^{3} \arctan\left(1, d x + c\right) \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)^{2} - {\left(f^{2} x + e f\right)} \int -\frac{180 \, b^{3} d e \arctan\left(1, d x + c\right)^{2} - 4 \, {\left(49 \, b^{3} \arctan\left(1, d x + c\right)^{3} + 192 \, a b^{2} \arctan\left(1, d x + c\right)^{2}\right)} d^{2} f x^{2} + 4 \, {\left(45 \, b^{3} \arctan\left(1, d x + c\right)^{2} - 2 \, {\left(49 \, b^{3} \arctan\left(1, d x + c\right)^{3} + 192 \, a b^{2} \arctan\left(1, d x + c\right)^{2}\right)} c\right)} d f x - 21 \, {\left(b^{3} d^{2} f x^{2} \arctan\left(1, d x + c\right) + b^{3} d e + {\left(2 \, b^{3} c \arctan\left(1, d x + c\right) + b^{3}\right)} d f x + {\left(b^{3} c^{2} \arctan\left(1, d x + c\right) + b^{3} \arctan\left(1, d x + c\right)\right)} f\right)} \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)^{2} - 4 \, {\left(49 \, b^{3} \arctan\left(1, d x + c\right)^{3} + 192 \, a b^{2} \arctan\left(1, d x + c\right)^{2} + {\left(49 \, b^{3} \arctan\left(1, d x + c\right)^{3} + 192 \, a b^{2} \arctan\left(1, d x + c\right)^{2}\right)} c^{2}\right)} f + 84 \, {\left(b^{3} d^{2} f x^{2} \arctan\left(1, d x + c\right) + b^{3} c d e \arctan\left(1, d x + c\right) + {\left(b^{3} d^{2} e \arctan\left(1, d x + c\right) + b^{3} c d f \arctan\left(1, d x + c\right)\right)} x\right)} \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)}{8 \, {\left(d^{2} f^{3} x^{4} + {\left(c^{2} + 1\right)} e^{2} f + 2 \, {\left(d^{2} e f^{2} + c d f^{3}\right)} x^{3} + {\left(d^{2} e^{2} f + 4 \, c d e f^{2} + {\left(c^{2} + 1\right)} f^{3}\right)} x^{2} + 2 \, {\left(c d e^{2} f + {\left(c^{2} + 1\right)} e f^{2}\right)} x\right)}}\,{d x}}{32 \, {\left(f^{2} x + e f\right)}}"," ",0,"-3/2*(d*(2*(d^2*e - c*d*f)*arctan((d^2*x + c*d)/d)/((d^2*e^2*f - 2*c*d*e*f^2 + (c^2 + 1)*f^3)*d) - log(d^2*x^2 + 2*c*d*x + c^2 + 1)/(d^2*e^2 - 2*c*d*e*f + (c^2 + 1)*f^2) + 2*log(f*x + e)/(d^2*e^2 - 2*c*d*e*f + (c^2 + 1)*f^2)) + 2*arccot(d*x + c)/(f^2*x + e*f))*a^2*b - a^3/(f^2*x + e*f) - 1/32*(4*b^3*arctan2(1, d*x + c)^3 - 3*b^3*arctan2(1, d*x + c)*log(d^2*x^2 + 2*c*d*x + c^2 + 1)^2 - 32*(f^2*x + e*f)*integrate(-1/32*(12*b^3*d*e*arctan2(1, d*x + c)^2 - 4*(7*b^3*arctan2(1, d*x + c)^3 + 24*a*b^2*arctan2(1, d*x + c)^2)*d^2*f*x^2 + 4*(3*b^3*arctan2(1, d*x + c)^2 - 2*(7*b^3*arctan2(1, d*x + c)^3 + 24*a*b^2*arctan2(1, d*x + c)^2)*c)*d*f*x - 3*(b^3*d^2*f*x^2*arctan2(1, d*x + c) + b^3*d*e + (2*b^3*c*arctan2(1, d*x + c) + b^3)*d*f*x + (b^3*c^2*arctan2(1, d*x + c) + b^3*arctan2(1, d*x + c))*f)*log(d^2*x^2 + 2*c*d*x + c^2 + 1)^2 - 4*(7*b^3*arctan2(1, d*x + c)^3 + 24*a*b^2*arctan2(1, d*x + c)^2 + (7*b^3*arctan2(1, d*x + c)^3 + 24*a*b^2*arctan2(1, d*x + c)^2)*c^2)*f + 12*(b^3*d^2*f*x^2*arctan2(1, d*x + c) + b^3*c*d*e*arctan2(1, d*x + c) + (b^3*d^2*e*arctan2(1, d*x + c) + b^3*c*d*f*arctan2(1, d*x + c))*x)*log(d^2*x^2 + 2*c*d*x + c^2 + 1))/(d^2*f^3*x^4 + (c^2 + 1)*e^2*f + 2*(d^2*e*f^2 + c*d*f^3)*x^3 + (d^2*e^2*f + 4*c*d*e*f^2 + (c^2 + 1)*f^3)*x^2 + 2*(c*d*e^2*f + (c^2 + 1)*e*f^2)*x), x))/(f^2*x + e*f)","F",0
146,0,0,0,0.000000," ","integrate((f*x+e)^m*(a+b*arccot(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{1}{2} \, {\left(3 \, {\left(f x \arctan\left(1, d x + c\right) + e \arctan\left(1, d x + c\right)\right)} {\left(f x + e\right)}^{m} + 2 \, {\left(f m + f\right)} \int \frac{{\left({\left(c^{2} \arctan\left(1, d x + c\right) + \arctan\left(1, d x + c\right)\right)} f m + {\left(d^{2} f m \arctan\left(1, d x + c\right) + d^{2} f \arctan\left(1, d x + c\right)\right)} x^{2} + 3 \, d e + {\left(c^{2} \arctan\left(1, d x + c\right) + \arctan\left(1, d x + c\right)\right)} f + {\left(2 \, c d f m \arctan\left(1, d x + c\right) + {\left(2 \, c \arctan\left(1, d x + c\right) + 3\right)} d f\right)} x\right)} {\left(f x + e\right)}^{m}}{2 \, {\left({\left(c^{2} + 1\right)} f m + {\left(d^{2} f m + d^{2} f\right)} x^{2} + {\left(c^{2} + 1\right)} f + 2 \, {\left(c d f m + c d f\right)} x\right)}}\,{d x}\right)} b}{2 \, {\left(f m + f\right)}} + \frac{{\left(f x + e\right)}^{m + 1} a}{f {\left(m + 1\right)}}"," ",0,"1/2*((f*x*arctan2(1, d*x + c) + e*arctan2(1, d*x + c))*(f*x + e)^m + 2*(f*m + f)*integrate(1/2*((c^2*arctan2(1, d*x + c) + arctan2(1, d*x + c))*f*m + (d^2*f*m*arctan2(1, d*x + c) + d^2*f*arctan2(1, d*x + c))*x^2 + d*e + (c^2*arctan2(1, d*x + c) + arctan2(1, d*x + c))*f + (2*c*d*f*m*arctan2(1, d*x + c) + (2*c*arctan2(1, d*x + c) + 1)*d*f)*x)*(f*x + e)^m/((c^2 + 1)*f*m + (d^2*f*m + d^2*f)*x^2 + (c^2 + 1)*f + 2*(c*d*f*m + c*d*f)*x), x))*b/(f*m + f) + (f*x + e)^(m + 1)*a/(f*(m + 1))","F",0
147,0,0,0,0.000000," ","integrate((f*x+e)^m*(a+b*arccot(d*x+c))^2,x, algorithm=""maxima"")","\frac{{\left(f x + e\right)}^{m + 1} a^{2}}{f {\left(m + 1\right)}} - \frac{\frac{3}{4} \, {\left(b^{2} f x + b^{2} e\right)} {\left(f x + e\right)}^{m} \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)^{2} - 7 \, {\left(b^{2} f x \arctan\left(1, d x + c\right)^{2} + b^{2} e \arctan\left(1, d x + c\right)^{2}\right)} {\left(f x + e\right)}^{m} - {\left(f m + f\right)} \int \frac{3 \, {\left({\left(b^{2} c^{2} + b^{2}\right)} f m + {\left(b^{2} d^{2} f m + b^{2} d^{2} f\right)} x^{2} + {\left(b^{2} c^{2} + b^{2}\right)} f + 2 \, {\left(b^{2} c d f m + b^{2} c d f\right)} x\right)} {\left(f x + e\right)}^{m} \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)^{2} + 12 \, {\left(b^{2} d^{2} f x^{2} + b^{2} c d e + {\left(b^{2} d^{2} e + b^{2} c d f\right)} x\right)} {\left(f x + e\right)}^{m} \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right) + 4 \, {\left(14 \, b^{2} d e \arctan\left(1, d x + c\right) + {\left(9 \, b^{2} \arctan\left(1, d x + c\right)^{2} + {\left(9 \, b^{2} \arctan\left(1, d x + c\right)^{2} + 32 \, a b \arctan\left(1, d x + c\right)\right)} c^{2} + 32 \, a b \arctan\left(1, d x + c\right)\right)} f m + {\left({\left(9 \, b^{2} \arctan\left(1, d x + c\right)^{2} + 32 \, a b \arctan\left(1, d x + c\right)\right)} d^{2} f m + {\left(9 \, b^{2} \arctan\left(1, d x + c\right)^{2} + 32 \, a b \arctan\left(1, d x + c\right)\right)} d^{2} f\right)} x^{2} + {\left(9 \, b^{2} \arctan\left(1, d x + c\right)^{2} + {\left(9 \, b^{2} \arctan\left(1, d x + c\right)^{2} + 32 \, a b \arctan\left(1, d x + c\right)\right)} c^{2} + 32 \, a b \arctan\left(1, d x + c\right)\right)} f + 2 \, {\left({\left(9 \, b^{2} \arctan\left(1, d x + c\right)^{2} + 32 \, a b \arctan\left(1, d x + c\right)\right)} c d f m + {\left(7 \, b^{2} \arctan\left(1, d x + c\right) + {\left(9 \, b^{2} \arctan\left(1, d x + c\right)^{2} + 32 \, a b \arctan\left(1, d x + c\right)\right)} c\right)} d f\right)} x\right)} {\left(f x + e\right)}^{m}}{4 \, {\left({\left(c^{2} + 1\right)} f m + {\left(d^{2} f m + d^{2} f\right)} x^{2} + {\left(c^{2} + 1\right)} f + 2 \, {\left(c d f m + c d f\right)} x\right)}}\,{d x}}{16 \, {\left(f m + f\right)}}"," ",0,"(f*x + e)^(m + 1)*a^2/(f*(m + 1)) - 1/16*((b^2*f*x + b^2*e)*(f*x + e)^m*log(d^2*x^2 + 2*c*d*x + c^2 + 1)^2 - 4*(b^2*f*x*arctan2(1, d*x + c)^2 + b^2*e*arctan2(1, d*x + c)^2)*(f*x + e)^m - 16*(f*m + f)*integrate(1/16*(((b^2*c^2 + b^2)*f*m + (b^2*d^2*f*m + b^2*d^2*f)*x^2 + (b^2*c^2 + b^2)*f + 2*(b^2*c*d*f*m + b^2*c*d*f)*x)*(f*x + e)^m*log(d^2*x^2 + 2*c*d*x + c^2 + 1)^2 + 4*(b^2*d^2*f*x^2 + b^2*c*d*e + (b^2*d^2*e + b^2*c*d*f)*x)*(f*x + e)^m*log(d^2*x^2 + 2*c*d*x + c^2 + 1) + 4*(2*b^2*d*e*arctan2(1, d*x + c) + (3*b^2*arctan2(1, d*x + c)^2 + (3*b^2*arctan2(1, d*x + c)^2 + 8*a*b*arctan2(1, d*x + c))*c^2 + 8*a*b*arctan2(1, d*x + c))*f*m + ((3*b^2*arctan2(1, d*x + c)^2 + 8*a*b*arctan2(1, d*x + c))*d^2*f*m + (3*b^2*arctan2(1, d*x + c)^2 + 8*a*b*arctan2(1, d*x + c))*d^2*f)*x^2 + (3*b^2*arctan2(1, d*x + c)^2 + (3*b^2*arctan2(1, d*x + c)^2 + 8*a*b*arctan2(1, d*x + c))*c^2 + 8*a*b*arctan2(1, d*x + c))*f + 2*((3*b^2*arctan2(1, d*x + c)^2 + 8*a*b*arctan2(1, d*x + c))*c*d*f*m + (b^2*arctan2(1, d*x + c) + (3*b^2*arctan2(1, d*x + c)^2 + 8*a*b*arctan2(1, d*x + c))*c)*d*f)*x)*(f*x + e)^m)/((c^2 + 1)*f*m + (d^2*f*m + d^2*f)*x^2 + (c^2 + 1)*f + 2*(c*d*f*m + c*d*f)*x), x))/(f*m + f)","F",0
148,0,0,0,0.000000," ","integrate((f*x+e)^m*(a+b*arccot(d*x+c))^3,x, algorithm=""maxima"")","\frac{{\left(f x + e\right)}^{m + 1} a^{3}}{f {\left(m + 1\right)}} - \frac{\frac{21}{8} \, {\left(b^{3} f x \arctan\left(1, d x + c\right) + b^{3} e \arctan\left(1, d x + c\right)\right)} {\left(f x + e\right)}^{m} \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)^{2} - \frac{15}{2} \, {\left(b^{3} f x \arctan\left(1, d x + c\right)^{3} + b^{3} e \arctan\left(1, d x + c\right)^{3}\right)} {\left(f x + e\right)}^{m} - {\left(f m + f\right)} \int -\frac{21 \, {\left(b^{3} d e - {\left(b^{3} c^{2} \arctan\left(1, d x + c\right) + b^{3} \arctan\left(1, d x + c\right)\right)} f m - {\left(b^{3} d^{2} f m \arctan\left(1, d x + c\right) + b^{3} d^{2} f \arctan\left(1, d x + c\right)\right)} x^{2} - {\left(b^{3} c^{2} \arctan\left(1, d x + c\right) + b^{3} \arctan\left(1, d x + c\right)\right)} f - {\left(2 \, b^{3} c d f m \arctan\left(1, d x + c\right) + {\left(2 \, b^{3} c \arctan\left(1, d x + c\right) - b^{3}\right)} d f\right)} x\right)} {\left(f x + e\right)}^{m} \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right)^{2} - 84 \, {\left(b^{3} d^{2} f x^{2} \arctan\left(1, d x + c\right) + b^{3} c d e \arctan\left(1, d x + c\right) + {\left(b^{3} d^{2} e \arctan\left(1, d x + c\right) + b^{3} c d f \arctan\left(1, d x + c\right)\right)} x\right)} {\left(f x + e\right)}^{m} \log\left(d^{2} x^{2} + 2 \, c d x + c^{2} + 1\right) - 4 \, {\left(45 \, b^{3} d e \arctan\left(1, d x + c\right)^{2} + {\left(49 \, b^{3} \arctan\left(1, d x + c\right)^{3} + 192 \, a b^{2} \arctan\left(1, d x + c\right)^{2} + 192 \, a^{2} b \arctan\left(1, d x + c\right) + {\left(49 \, b^{3} \arctan\left(1, d x + c\right)^{3} + 192 \, a b^{2} \arctan\left(1, d x + c\right)^{2} + 192 \, a^{2} b \arctan\left(1, d x + c\right)\right)} c^{2}\right)} f m + {\left({\left(49 \, b^{3} \arctan\left(1, d x + c\right)^{3} + 192 \, a b^{2} \arctan\left(1, d x + c\right)^{2} + 192 \, a^{2} b \arctan\left(1, d x + c\right)\right)} d^{2} f m + {\left(49 \, b^{3} \arctan\left(1, d x + c\right)^{3} + 192 \, a b^{2} \arctan\left(1, d x + c\right)^{2} + 192 \, a^{2} b \arctan\left(1, d x + c\right)\right)} d^{2} f\right)} x^{2} + {\left(49 \, b^{3} \arctan\left(1, d x + c\right)^{3} + 192 \, a b^{2} \arctan\left(1, d x + c\right)^{2} + 192 \, a^{2} b \arctan\left(1, d x + c\right) + {\left(49 \, b^{3} \arctan\left(1, d x + c\right)^{3} + 192 \, a b^{2} \arctan\left(1, d x + c\right)^{2} + 192 \, a^{2} b \arctan\left(1, d x + c\right)\right)} c^{2}\right)} f + {\left(2 \, {\left(49 \, b^{3} \arctan\left(1, d x + c\right)^{3} + 192 \, a b^{2} \arctan\left(1, d x + c\right)^{2} + 192 \, a^{2} b \arctan\left(1, d x + c\right)\right)} c d f m + {\left(45 \, b^{3} \arctan\left(1, d x + c\right)^{2} + 2 \, {\left(49 \, b^{3} \arctan\left(1, d x + c\right)^{3} + 192 \, a b^{2} \arctan\left(1, d x + c\right)^{2} + 192 \, a^{2} b \arctan\left(1, d x + c\right)\right)} c\right)} d f\right)} x\right)} {\left(f x + e\right)}^{m}}{8 \, {\left({\left(c^{2} + 1\right)} f m + {\left(d^{2} f m + d^{2} f\right)} x^{2} + {\left(c^{2} + 1\right)} f + 2 \, {\left(c d f m + c d f\right)} x\right)}}\,{d x}}{32 \, {\left(f m + f\right)}}"," ",0,"(f*x + e)^(m + 1)*a^3/(f*(m + 1)) - 1/32*(3*(b^3*f*x*arctan2(1, d*x + c) + b^3*e*arctan2(1, d*x + c))*(f*x + e)^m*log(d^2*x^2 + 2*c*d*x + c^2 + 1)^2 - 4*(b^3*f*x*arctan2(1, d*x + c)^3 + b^3*e*arctan2(1, d*x + c)^3)*(f*x + e)^m - 32*(f*m + f)*integrate(-1/32*(3*(b^3*d*e - (b^3*c^2*arctan2(1, d*x + c) + b^3*arctan2(1, d*x + c))*f*m - (b^3*d^2*f*m*arctan2(1, d*x + c) + b^3*d^2*f*arctan2(1, d*x + c))*x^2 - (b^3*c^2*arctan2(1, d*x + c) + b^3*arctan2(1, d*x + c))*f - (2*b^3*c*d*f*m*arctan2(1, d*x + c) + (2*b^3*c*arctan2(1, d*x + c) - b^3)*d*f)*x)*(f*x + e)^m*log(d^2*x^2 + 2*c*d*x + c^2 + 1)^2 - 12*(b^3*d^2*f*x^2*arctan2(1, d*x + c) + b^3*c*d*e*arctan2(1, d*x + c) + (b^3*d^2*e*arctan2(1, d*x + c) + b^3*c*d*f*arctan2(1, d*x + c))*x)*(f*x + e)^m*log(d^2*x^2 + 2*c*d*x + c^2 + 1) - 4*(3*b^3*d*e*arctan2(1, d*x + c)^2 + (7*b^3*arctan2(1, d*x + c)^3 + 24*a*b^2*arctan2(1, d*x + c)^2 + 24*a^2*b*arctan2(1, d*x + c) + (7*b^3*arctan2(1, d*x + c)^3 + 24*a*b^2*arctan2(1, d*x + c)^2 + 24*a^2*b*arctan2(1, d*x + c))*c^2)*f*m + ((7*b^3*arctan2(1, d*x + c)^3 + 24*a*b^2*arctan2(1, d*x + c)^2 + 24*a^2*b*arctan2(1, d*x + c))*d^2*f*m + (7*b^3*arctan2(1, d*x + c)^3 + 24*a*b^2*arctan2(1, d*x + c)^2 + 24*a^2*b*arctan2(1, d*x + c))*d^2*f)*x^2 + (7*b^3*arctan2(1, d*x + c)^3 + 24*a*b^2*arctan2(1, d*x + c)^2 + 24*a^2*b*arctan2(1, d*x + c) + (7*b^3*arctan2(1, d*x + c)^3 + 24*a*b^2*arctan2(1, d*x + c)^2 + 24*a^2*b*arctan2(1, d*x + c))*c^2)*f + (2*(7*b^3*arctan2(1, d*x + c)^3 + 24*a*b^2*arctan2(1, d*x + c)^2 + 24*a^2*b*arctan2(1, d*x + c))*c*d*f*m + (3*b^3*arctan2(1, d*x + c)^2 + 2*(7*b^3*arctan2(1, d*x + c)^3 + 24*a*b^2*arctan2(1, d*x + c)^2 + 24*a^2*b*arctan2(1, d*x + c))*c)*d*f)*x)*(f*x + e)^m)/((c^2 + 1)*f*m + (d^2*f*m + d^2*f)*x^2 + (c^2 + 1)*f + 2*(c*d*f*m + c*d*f)*x), x))/(f*m + f)","F",0
149,1,35,0,0.319263," ","integrate(x^3*arccot(b*x^4+a),x, algorithm=""maxima"")","\frac{2 \, {\left(b x^{4} + a\right)} \operatorname{arccot}\left(b x^{4} + a\right) + \log\left({\left(b x^{4} + a\right)}^{2} + 1\right)}{8 \, b}"," ",0,"1/8*(2*(b*x^4 + a)*arccot(b*x^4 + a) + log((b*x^4 + a)^2 + 1))/b","A",0
150,1,38,0,0.316803," ","integrate(x^(-1+n)*arccot(a+b*x^n),x, algorithm=""maxima"")","\frac{2 \, {\left(b x^{n} + a\right)} \operatorname{arccot}\left(b x^{n} + a\right) + \log\left({\left(b x^{n} + a\right)}^{2} + 1\right)}{2 \, b n}"," ",0,"1/2*(2*(b*x^n + a)*arccot(b*x^n + a) + log((b*x^n + a)^2 + 1))/(b*n)","A",0
151,0,0,0,0.000000," ","integrate((a+b*arccot((-c*x+1)^(1/2)/(c*x+1)^(1/2)))^n/(-c^2*x^2+1),x, algorithm=""maxima"")","-\int \frac{{\left(b \operatorname{arccot}\left(\frac{\sqrt{-c x + 1}}{\sqrt{c x + 1}}\right) + a\right)}^{n}}{c^{2} x^{2} - 1}\,{d x}"," ",0,"-integrate((b*arccot(sqrt(-c*x + 1)/sqrt(c*x + 1)) + a)^n/(c^2*x^2 - 1), x)","F",0
152,0,0,0,0.000000," ","integrate((a+b*arccot((-c*x+1)^(1/2)/(c*x+1)^(1/2)))^3/(-c^2*x^2+1),x, algorithm=""maxima"")","\frac{1}{2} \, a^{3} {\left(\frac{\log\left(c x + 1\right)}{c} - \frac{\log\left(c x - 1\right)}{c}\right)} + \frac{\frac{15}{2} \, {\left(b^{3} \log\left(c x + 1\right) - b^{3} \log\left(-c x + 1\right)\right)} \arctan\left(\sqrt{c x + 1}, \sqrt{-c x + 1}\right)^{3} - \frac{45}{8} \, {\left(b^{3} \log\left(2\right)^{2} \log\left(c x + 1\right) - b^{3} \log\left(2\right)^{2} \log\left(-c x + 1\right)\right)} \arctan\left(\sqrt{c x + 1}, \sqrt{-c x + 1}\right) + \frac{1}{2} \, c \int -\frac{784 \, b^{3} \arctan\left(\sqrt{c x + 1}, \sqrt{-c x + 1}\right)^{3} + 3072 \, a b^{2} \arctan\left(\sqrt{c x + 1}, \sqrt{-c x + 1}\right)^{2} + 45 \, {\left(b^{3} \log\left(2\right)^{2} \log\left(c x + 1\right) - b^{3} \log\left(2\right)^{2} \log\left(-c x + 1\right) - 4 \, {\left(b^{3} \log\left(c x + 1\right) - b^{3} \log\left(-c x + 1\right)\right)} \arctan\left(\sqrt{c x + 1}, \sqrt{-c x + 1}\right)^{2}\right)} \sqrt{c x + 1} \sqrt{-c x + 1} + 12 \, {\left(15 \, b^{3} \log\left(2\right)^{2} + 256 \, a^{2} b\right)} \arctan\left(\sqrt{c x + 1}, \sqrt{-c x + 1}\right)}{8 \, {\left(c^{2} x^{2} - 1\right)}}\,{d x}}{64 \, c}"," ",0,"1/2*a^3*(log(c*x + 1)/c - log(c*x - 1)/c) + 1/64*(4*(b^3*log(c*x + 1) - b^3*log(-c*x + 1))*arctan2(sqrt(c*x + 1), sqrt(-c*x + 1))^3 - 3*(b^3*log(2)^2*log(c*x + 1) - b^3*log(2)^2*log(-c*x + 1))*arctan2(sqrt(c*x + 1), sqrt(-c*x + 1)) + 64*c*integrate(-1/128*(112*b^3*arctan2(sqrt(c*x + 1), sqrt(-c*x + 1))^3 + 384*a*b^2*arctan2(sqrt(c*x + 1), sqrt(-c*x + 1))^2 + 3*(b^3*log(2)^2*log(c*x + 1) - b^3*log(2)^2*log(-c*x + 1) - 4*(b^3*log(c*x + 1) - b^3*log(-c*x + 1))*arctan2(sqrt(c*x + 1), sqrt(-c*x + 1))^2)*sqrt(c*x + 1)*sqrt(-c*x + 1) + 12*(b^3*log(2)^2 + 32*a^2*b)*arctan2(sqrt(c*x + 1), sqrt(-c*x + 1)))/(c^2*x^2 - 1), x))/c","F",0
153,0,0,0,0.000000," ","integrate((a+b*arccot((-c*x+1)^(1/2)/(c*x+1)^(1/2)))^2/(-c^2*x^2+1),x, algorithm=""maxima"")","\frac{1}{2} \, a^{2} {\left(\frac{\log\left(c x + 1\right)}{c} - \frac{\log\left(c x - 1\right)}{c}\right)} - \frac{b^{2} \log\left(2\right)^{2} \log\left(c x + 1\right) - b^{2} \log\left(2\right)^{2} \log\left(-c x + 1\right) - 4 \, {\left(b^{2} \log\left(c x + 1\right) - b^{2} \log\left(-c x + 1\right)\right)} \arctan\left(\sqrt{c x + 1}, \sqrt{-c x + 1}\right)^{2} - {\left(12 \, b^{2} {\left(\frac{\log\left(c x + 1\right)}{c} - \frac{\log\left(c x - 1\right)}{c}\right)} \arctan\left(\frac{\sqrt{c x + 1}}{\sqrt{-c x + 1}}\right)^{2} + b^{2} {\left(\frac{\log\left(c x + 1\right)}{c} - \frac{\log\left(c x - 1\right)}{c}\right)} \log\left(2\right)^{2} + 4 \, b^{2} \int \frac{\sqrt{c x + 1} \sqrt{-c x + 1} \arctan\left(\frac{\sqrt{c x + 1}}{\sqrt{-c x + 1}}\right) \log\left(c x + 1\right)}{c^{2} x^{2} - 1}\,{d x} - 4 \, b^{2} \int \frac{\sqrt{c x + 1} \sqrt{-c x + 1} \arctan\left(\frac{\sqrt{c x + 1}}{\sqrt{-c x + 1}}\right) \log\left(-c x + 1\right)}{c^{2} x^{2} - 1}\,{d x} + \frac{32 \, {\left({\left(\log\left(c x + 1\right) - \log\left(-c x + 1\right)\right)} \arctan\left(\sqrt{c x + 1}, \sqrt{-c x + 1}\right) + c \int \frac{e^{\left(\frac{1}{2} \, \log\left(c x + 1\right) + \frac{1}{2} \, \log\left(-c x + 1\right)\right)} \log\left(c x + 1\right) - e^{\left(\frac{1}{2} \, \log\left(c x + 1\right) + \frac{1}{2} \, \log\left(-c x + 1\right)\right)} \log\left(-c x + 1\right)}{{\left(c^{2} x^{2} - 1\right)} {\left(c x + 1\right)} - {\left(c^{2} x^{2} - 1\right)} {\left(c x - 1\right)}}\,{d x}\right)} a b}{c}\right)} c}{32 \, c}"," ",0,"1/2*a^2*(log(c*x + 1)/c - log(c*x - 1)/c) - 1/32*(b^2*log(2)^2*log(c*x + 1) - b^2*log(2)^2*log(-c*x + 1) - 4*(b^2*log(c*x + 1) - b^2*log(-c*x + 1))*arctan2(sqrt(c*x + 1), sqrt(-c*x + 1))^2 - (b^2*(log(c*x + 1)/c - log(c*x - 1)/c)*log(2)^2 + 64*b^2*integrate(1/16*sqrt(c*x + 1)*sqrt(-c*x + 1)*arctan(sqrt(c*x + 1)/sqrt(-c*x + 1))*log(c*x + 1)/(c^2*x^2 - 1), x) - 64*b^2*integrate(1/16*sqrt(c*x + 1)*sqrt(-c*x + 1)*arctan(sqrt(c*x + 1)/sqrt(-c*x + 1))*log(-c*x + 1)/(c^2*x^2 - 1), x) - 384*b^2*integrate(1/16*arctan(sqrt(c*x + 1)/sqrt(-c*x + 1))^2/(c^2*x^2 - 1), x) - 1024*a*b*integrate(1/16*arctan(sqrt(c*x + 1)/sqrt(-c*x + 1))/(c^2*x^2 - 1), x))*c)/c","F",0
154,0,0,0,0.000000," ","integrate((a+b*arccot((-c*x+1)^(1/2)/(c*x+1)^(1/2)))/(-c^2*x^2+1),x, algorithm=""maxima"")","\frac{1}{2} \, a {\left(\frac{\log\left(c x + 1\right)}{c} - \frac{\log\left(c x - 1\right)}{c}\right)} + \frac{{\left({\left(\log\left(c x + 1\right) - \log\left(-c x + 1\right)\right)} \arctan\left(\sqrt{c x + 1}, \sqrt{-c x + 1}\right) + c \int \frac{e^{\left(\frac{1}{2} \, \log\left(c x + 1\right) + \frac{1}{2} \, \log\left(-c x + 1\right)\right)} \log\left(c x + 1\right) - e^{\left(\frac{1}{2} \, \log\left(c x + 1\right) + \frac{1}{2} \, \log\left(-c x + 1\right)\right)} \log\left(-c x + 1\right)}{{\left(c^{2} x^{2} - 1\right)} {\left(c x + 1\right)} - {\left(c^{2} x^{2} - 1\right)} {\left(c x - 1\right)}}\,{d x}\right)} b}{2 \, c}"," ",0,"1/2*a*(log(c*x + 1)/c - log(c*x - 1)/c) + 1/2*((log(c*x + 1) - log(-c*x + 1))*arctan2(sqrt(c*x + 1), sqrt(-c*x + 1)) + 2*c*integrate(1/2*(e^(1/2*log(c*x + 1) + 1/2*log(-c*x + 1))*log(c*x + 1) - e^(1/2*log(c*x + 1) + 1/2*log(-c*x + 1))*log(-c*x + 1))/((c^2*x^2 - 1)*(c*x + 1) - (c^2*x^2 - 1)*(c*x - 1)), x))*b/c","F",0
155,0,0,0,0.000000," ","integrate(1/(-c^2*x^2+1)/(a+b*arccot((-c*x+1)^(1/2)/(c*x+1)^(1/2))),x, algorithm=""maxima"")","-\int \frac{1}{{\left(c^{2} x^{2} - 1\right)} {\left(b \operatorname{arccot}\left(\frac{\sqrt{-c x + 1}}{\sqrt{c x + 1}}\right) + a\right)}}\,{d x}"," ",0,"-integrate(1/((c^2*x^2 - 1)*(b*arccot(sqrt(-c*x + 1)/sqrt(c*x + 1)) + a)), x)","F",0
156,0,0,0,0.000000," ","integrate(1/(-c^2*x^2+1)/(a+b*arccot((-c*x+1)^(1/2)/(c*x+1)^(1/2)))^2,x, algorithm=""maxima"")","-\frac{2 \, {\left({\left(b^{2} c^{2} \arctan\left(\sqrt{c x + 1}, \sqrt{-c x + 1}\right) + a b c^{2}\right)} \sqrt{c x + 1} \sqrt{-c x + 1} \int \frac{x}{{\left(a b c^{2} x^{2} - a b + {\left(b^{2} c^{2} x^{2} - b^{2}\right)} \arctan\left(\sqrt{c x + 1}, \sqrt{-c x + 1}\right)\right)} \sqrt{c x + 1} \sqrt{-c x + 1}}\,{d x} + 1\right)}}{{\left(b^{2} c \arctan\left(\sqrt{c x + 1}, \sqrt{-c x + 1}\right) + a b c\right)} \sqrt{c x + 1} \sqrt{-c x + 1}}"," ",0,"-2*(2*(b^2*c^2*arctan2(sqrt(c*x + 1), sqrt(-c*x + 1)) + a*b*c^2)*sqrt(c*x + 1)*sqrt(-c*x + 1)*integrate(1/2*x/((a*b*c^2*x^2 - a*b + (b^2*c^2*x^2 - b^2)*arctan2(sqrt(c*x + 1), sqrt(-c*x + 1)))*sqrt(c*x + 1)*sqrt(-c*x + 1)), x) + 1)/((b^2*c*arctan2(sqrt(c*x + 1), sqrt(-c*x + 1)) + a*b*c)*sqrt(c*x + 1)*sqrt(-c*x + 1))","F",0
157,1,17,0,0.314543," ","integrate(1/2*pi-arctan(tan(b*x+a)),x, algorithm=""maxima"")","\frac{1}{2} \, \pi x - \frac{{\left(b x + a\right)}^{2}}{2 \, b}"," ",0,"1/2*pi*x - 1/2*(b*x + a)^2/b","A",0
158,0,0,0,0.000000," ","integrate(x^2*arccot(c+d*tan(b*x+a)),x, algorithm=""maxima"")","\frac{1}{6} \, x^{3} \arctan\left(-{\left(d + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + c \sin\left(2 \, b x + 2 \, a\right) + d - 1, -c \cos\left(2 \, b x + 2 \, a\right) - {\left(d + 1\right)} \sin\left(2 \, b x + 2 \, a\right) - c\right) - \frac{1}{6} \, x^{3} \arctan\left(-{\left(d - 1\right)} \cos\left(2 \, b x + 2 \, a\right) + c \sin\left(2 \, b x + 2 \, a\right) + d + 1, -c \cos\left(2 \, b x + 2 \, a\right) - {\left(d - 1\right)} \sin\left(2 \, b x + 2 \, a\right) - c\right) - 4 \, b d \int -\frac{2 \, {\left(c^{2} + d^{2} + 1\right)} x^{3} \cos\left(2 \, b x + 2 \, a\right)^{2} + 2 \, c d x^{3} \sin\left(2 \, b x + 2 \, a\right) + 2 \, {\left(c^{2} + d^{2} + 1\right)} x^{3} \sin\left(2 \, b x + 2 \, a\right)^{2} + {\left(c^{2} - d^{2} + 1\right)} x^{3} \cos\left(2 \, b x + 2 \, a\right) - {\left(2 \, c d x^{3} \sin\left(2 \, b x + 2 \, a\right) - {\left(c^{2} - d^{2} + 1\right)} x^{3} \cos\left(2 \, b x + 2 \, a\right)\right)} \cos\left(4 \, b x + 4 \, a\right) + {\left(2 \, c d x^{3} \cos\left(2 \, b x + 2 \, a\right) + {\left(c^{2} - d^{2} + 1\right)} x^{3} \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(4 \, b x + 4 \, a\right)}{3 \, {\left(c^{4} + d^{4} + 2 \, {\left(c^{2} - 1\right)} d^{2} + {\left(c^{4} + d^{4} + 2 \, {\left(c^{2} - 1\right)} d^{2} + 2 \, c^{2} + 1\right)} \cos\left(4 \, b x + 4 \, a\right)^{2} + 4 \, {\left(c^{4} + d^{4} + 2 \, {\left(c^{2} + 1\right)} d^{2} + 2 \, c^{2} + 1\right)} \cos\left(2 \, b x + 2 \, a\right)^{2} + {\left(c^{4} + d^{4} + 2 \, {\left(c^{2} - 1\right)} d^{2} + 2 \, c^{2} + 1\right)} \sin\left(4 \, b x + 4 \, a\right)^{2} + 4 \, {\left(c^{4} + d^{4} + 2 \, {\left(c^{2} + 1\right)} d^{2} + 2 \, c^{2} + 1\right)} \sin\left(2 \, b x + 2 \, a\right)^{2} + 2 \, c^{2} + 2 \, {\left(c^{4} + d^{4} - 2 \, {\left(3 \, c^{2} + 1\right)} d^{2} + 2 \, c^{2} + 2 \, {\left(c^{4} - d^{4} + 2 \, c^{2} + 1\right)} \cos\left(2 \, b x + 2 \, a\right) - 4 \, {\left(c d^{3} + {\left(c^{3} + c\right)} d\right)} \sin\left(2 \, b x + 2 \, a\right) + 1\right)} \cos\left(4 \, b x + 4 \, a\right) + 4 \, {\left(c^{4} - d^{4} + 2 \, c^{2} + 1\right)} \cos\left(2 \, b x + 2 \, a\right) - 4 \, {\left(2 \, c d^{3} - 2 \, {\left(c^{3} + c\right)} d - 2 \, {\left(c d^{3} + {\left(c^{3} + c\right)} d\right)} \cos\left(2 \, b x + 2 \, a\right) - {\left(c^{4} - d^{4} + 2 \, c^{2} + 1\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(4 \, b x + 4 \, a\right) + 8 \, {\left(c d^{3} + {\left(c^{3} + c\right)} d\right)} \sin\left(2 \, b x + 2 \, a\right) + 1\right)}}\,{d x}"," ",0,"1/6*x^3*arctan2(-(d + 1)*cos(2*b*x + 2*a) + c*sin(2*b*x + 2*a) + d - 1, -c*cos(2*b*x + 2*a) - (d + 1)*sin(2*b*x + 2*a) - c) - 1/6*x^3*arctan2(-(d - 1)*cos(2*b*x + 2*a) + c*sin(2*b*x + 2*a) + d + 1, -c*cos(2*b*x + 2*a) - (d - 1)*sin(2*b*x + 2*a) - c) - 4*b*d*integrate(-1/3*(2*(c^2 + d^2 + 1)*x^3*cos(2*b*x + 2*a)^2 + 2*c*d*x^3*sin(2*b*x + 2*a) + 2*(c^2 + d^2 + 1)*x^3*sin(2*b*x + 2*a)^2 + (c^2 - d^2 + 1)*x^3*cos(2*b*x + 2*a) - (2*c*d*x^3*sin(2*b*x + 2*a) - (c^2 - d^2 + 1)*x^3*cos(2*b*x + 2*a))*cos(4*b*x + 4*a) + (2*c*d*x^3*cos(2*b*x + 2*a) + (c^2 - d^2 + 1)*x^3*sin(2*b*x + 2*a))*sin(4*b*x + 4*a))/(c^4 + d^4 + 2*(c^2 - 1)*d^2 + (c^4 + d^4 + 2*(c^2 - 1)*d^2 + 2*c^2 + 1)*cos(4*b*x + 4*a)^2 + 4*(c^4 + d^4 + 2*(c^2 + 1)*d^2 + 2*c^2 + 1)*cos(2*b*x + 2*a)^2 + (c^4 + d^4 + 2*(c^2 - 1)*d^2 + 2*c^2 + 1)*sin(4*b*x + 4*a)^2 + 4*(c^4 + d^4 + 2*(c^2 + 1)*d^2 + 2*c^2 + 1)*sin(2*b*x + 2*a)^2 + 2*c^2 + 2*(c^4 + d^4 - 2*(3*c^2 + 1)*d^2 + 2*c^2 + 2*(c^4 - d^4 + 2*c^2 + 1)*cos(2*b*x + 2*a) - 4*(c*d^3 + (c^3 + c)*d)*sin(2*b*x + 2*a) + 1)*cos(4*b*x + 4*a) + 4*(c^4 - d^4 + 2*c^2 + 1)*cos(2*b*x + 2*a) - 4*(2*c*d^3 - 2*(c^3 + c)*d - 2*(c*d^3 + (c^3 + c)*d)*cos(2*b*x + 2*a) - (c^4 - d^4 + 2*c^2 + 1)*sin(2*b*x + 2*a))*sin(4*b*x + 4*a) + 8*(c*d^3 + (c^3 + c)*d)*sin(2*b*x + 2*a) + 1), x)","F",0
159,0,0,0,0.000000," ","integrate(x*arccot(c+d*tan(b*x+a)),x, algorithm=""maxima"")","\frac{1}{4} \, x^{2} \arctan\left(-{\left(d + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + c \sin\left(2 \, b x + 2 \, a\right) + d - 1, -c \cos\left(2 \, b x + 2 \, a\right) - {\left(d + 1\right)} \sin\left(2 \, b x + 2 \, a\right) - c\right) - \frac{1}{4} \, x^{2} \arctan\left(-{\left(d - 1\right)} \cos\left(2 \, b x + 2 \, a\right) + c \sin\left(2 \, b x + 2 \, a\right) + d + 1, -c \cos\left(2 \, b x + 2 \, a\right) - {\left(d - 1\right)} \sin\left(2 \, b x + 2 \, a\right) - c\right) - 2 \, b d \int -\frac{2 \, {\left(c^{2} + d^{2} + 1\right)} x^{2} \cos\left(2 \, b x + 2 \, a\right)^{2} + 2 \, c d x^{2} \sin\left(2 \, b x + 2 \, a\right) + 2 \, {\left(c^{2} + d^{2} + 1\right)} x^{2} \sin\left(2 \, b x + 2 \, a\right)^{2} + {\left(c^{2} - d^{2} + 1\right)} x^{2} \cos\left(2 \, b x + 2 \, a\right) - {\left(2 \, c d x^{2} \sin\left(2 \, b x + 2 \, a\right) - {\left(c^{2} - d^{2} + 1\right)} x^{2} \cos\left(2 \, b x + 2 \, a\right)\right)} \cos\left(4 \, b x + 4 \, a\right) + {\left(2 \, c d x^{2} \cos\left(2 \, b x + 2 \, a\right) + {\left(c^{2} - d^{2} + 1\right)} x^{2} \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(4 \, b x + 4 \, a\right)}{c^{4} + d^{4} + 2 \, {\left(c^{2} - 1\right)} d^{2} + {\left(c^{4} + d^{4} + 2 \, {\left(c^{2} - 1\right)} d^{2} + 2 \, c^{2} + 1\right)} \cos\left(4 \, b x + 4 \, a\right)^{2} + 4 \, {\left(c^{4} + d^{4} + 2 \, {\left(c^{2} + 1\right)} d^{2} + 2 \, c^{2} + 1\right)} \cos\left(2 \, b x + 2 \, a\right)^{2} + {\left(c^{4} + d^{4} + 2 \, {\left(c^{2} - 1\right)} d^{2} + 2 \, c^{2} + 1\right)} \sin\left(4 \, b x + 4 \, a\right)^{2} + 4 \, {\left(c^{4} + d^{4} + 2 \, {\left(c^{2} + 1\right)} d^{2} + 2 \, c^{2} + 1\right)} \sin\left(2 \, b x + 2 \, a\right)^{2} + 2 \, c^{2} + 2 \, {\left(c^{4} + d^{4} - 2 \, {\left(3 \, c^{2} + 1\right)} d^{2} + 2 \, c^{2} + 2 \, {\left(c^{4} - d^{4} + 2 \, c^{2} + 1\right)} \cos\left(2 \, b x + 2 \, a\right) - 4 \, {\left(c d^{3} + {\left(c^{3} + c\right)} d\right)} \sin\left(2 \, b x + 2 \, a\right) + 1\right)} \cos\left(4 \, b x + 4 \, a\right) + 4 \, {\left(c^{4} - d^{4} + 2 \, c^{2} + 1\right)} \cos\left(2 \, b x + 2 \, a\right) - 4 \, {\left(2 \, c d^{3} - 2 \, {\left(c^{3} + c\right)} d - 2 \, {\left(c d^{3} + {\left(c^{3} + c\right)} d\right)} \cos\left(2 \, b x + 2 \, a\right) - {\left(c^{4} - d^{4} + 2 \, c^{2} + 1\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(4 \, b x + 4 \, a\right) + 8 \, {\left(c d^{3} + {\left(c^{3} + c\right)} d\right)} \sin\left(2 \, b x + 2 \, a\right) + 1}\,{d x}"," ",0,"1/4*x^2*arctan2(-(d + 1)*cos(2*b*x + 2*a) + c*sin(2*b*x + 2*a) + d - 1, -c*cos(2*b*x + 2*a) - (d + 1)*sin(2*b*x + 2*a) - c) - 1/4*x^2*arctan2(-(d - 1)*cos(2*b*x + 2*a) + c*sin(2*b*x + 2*a) + d + 1, -c*cos(2*b*x + 2*a) - (d - 1)*sin(2*b*x + 2*a) - c) - 2*b*d*integrate(-(2*(c^2 + d^2 + 1)*x^2*cos(2*b*x + 2*a)^2 + 2*c*d*x^2*sin(2*b*x + 2*a) + 2*(c^2 + d^2 + 1)*x^2*sin(2*b*x + 2*a)^2 + (c^2 - d^2 + 1)*x^2*cos(2*b*x + 2*a) - (2*c*d*x^2*sin(2*b*x + 2*a) - (c^2 - d^2 + 1)*x^2*cos(2*b*x + 2*a))*cos(4*b*x + 4*a) + (2*c*d*x^2*cos(2*b*x + 2*a) + (c^2 - d^2 + 1)*x^2*sin(2*b*x + 2*a))*sin(4*b*x + 4*a))/(c^4 + d^4 + 2*(c^2 - 1)*d^2 + (c^4 + d^4 + 2*(c^2 - 1)*d^2 + 2*c^2 + 1)*cos(4*b*x + 4*a)^2 + 4*(c^4 + d^4 + 2*(c^2 + 1)*d^2 + 2*c^2 + 1)*cos(2*b*x + 2*a)^2 + (c^4 + d^4 + 2*(c^2 - 1)*d^2 + 2*c^2 + 1)*sin(4*b*x + 4*a)^2 + 4*(c^4 + d^4 + 2*(c^2 + 1)*d^2 + 2*c^2 + 1)*sin(2*b*x + 2*a)^2 + 2*c^2 + 2*(c^4 + d^4 - 2*(3*c^2 + 1)*d^2 + 2*c^2 + 2*(c^4 - d^4 + 2*c^2 + 1)*cos(2*b*x + 2*a) - 4*(c*d^3 + (c^3 + c)*d)*sin(2*b*x + 2*a) + 1)*cos(4*b*x + 4*a) + 4*(c^4 - d^4 + 2*c^2 + 1)*cos(2*b*x + 2*a) - 4*(2*c*d^3 - 2*(c^3 + c)*d - 2*(c*d^3 + (c^3 + c)*d)*cos(2*b*x + 2*a) - (c^4 - d^4 + 2*c^2 + 1)*sin(2*b*x + 2*a))*sin(4*b*x + 4*a) + 8*(c*d^3 + (c^3 + c)*d)*sin(2*b*x + 2*a) + 1), x)","F",0
160,1,433,0,0.536746," ","integrate(arccot(c+d*tan(b*x+a)),x, algorithm=""maxima"")","-\frac{d {\left(\frac{8 \, {\left(b x + a\right)} \arctan\left(\frac{d^{2} \tan\left(b x + a\right) + c d}{d}\right)}{d} - \frac{4 \, {\left(b x + a\right)} \arctan\left(\frac{c d + {\left(d^{2} + d\right)} \tan\left(b x + a\right)}{c^{2} + d^{2} + 2 \, d + 1}, \frac{c d \tan\left(b x + a\right) + c^{2} + d + 1}{c^{2} + d^{2} + 2 \, d + 1}\right) - 4 \, {\left(b x + a\right)} \arctan\left(\frac{c d + {\left(d^{2} - d\right)} \tan\left(b x + a\right)}{c^{2} + d^{2} - 2 \, d + 1}, \frac{c d \tan\left(b x + a\right) + c^{2} - d + 1}{c^{2} + d^{2} - 2 \, d + 1}\right) + \log\left(\tan\left(b x + a\right)^{2} + 1\right) \log\left(\frac{d^{2} \tan\left(b x + a\right)^{2} + 2 \, c d \tan\left(b x + a\right) + c^{2} + 1}{c^{2} + d^{2} + 2 \, d + 1}\right) - \log\left(\tan\left(b x + a\right)^{2} + 1\right) \log\left(\frac{d^{2} \tan\left(b x + a\right)^{2} + 2 \, c d \tan\left(b x + a\right) + c^{2} + 1}{c^{2} + d^{2} - 2 \, d + 1}\right) + 2 \, {\rm Li}_2\left(-\frac{i \, d \tan\left(b x + a\right) - d}{i \, c + d + 1}\right) - 2 \, {\rm Li}_2\left(-\frac{i \, d \tan\left(b x + a\right) - d}{i \, c + d - 1}\right) + 2 \, {\rm Li}_2\left(\frac{i \, d \tan\left(b x + a\right) + d}{-i \, c + d + 1}\right) - 2 \, {\rm Li}_2\left(\frac{i \, d \tan\left(b x + a\right) + d}{-i \, c + d - 1}\right)}{d}\right)} - 8 \, {\left(b x + a\right)} \operatorname{arccot}\left(d \tan\left(b x + a\right) + c\right) - 8 \, {\left(b x + a\right)} \arctan\left(\frac{d^{2} \tan\left(b x + a\right) + c d}{d}\right)}{8 \, b}"," ",0,"-1/8*(d*(8*(b*x + a)*arctan((d^2*tan(b*x + a) + c*d)/d)/d - (4*(b*x + a)*arctan2((c*d + (d^2 + d)*tan(b*x + a))/(c^2 + d^2 + 2*d + 1), (c*d*tan(b*x + a) + c^2 + d + 1)/(c^2 + d^2 + 2*d + 1)) - 4*(b*x + a)*arctan2((c*d + (d^2 - d)*tan(b*x + a))/(c^2 + d^2 - 2*d + 1), (c*d*tan(b*x + a) + c^2 - d + 1)/(c^2 + d^2 - 2*d + 1)) + log(tan(b*x + a)^2 + 1)*log((d^2*tan(b*x + a)^2 + 2*c*d*tan(b*x + a) + c^2 + 1)/(c^2 + d^2 + 2*d + 1)) - log(tan(b*x + a)^2 + 1)*log((d^2*tan(b*x + a)^2 + 2*c*d*tan(b*x + a) + c^2 + 1)/(c^2 + d^2 - 2*d + 1)) + 2*dilog(-(I*d*tan(b*x + a) - d)/(I*c + d + 1)) - 2*dilog(-(I*d*tan(b*x + a) - d)/(I*c + d - 1)) + 2*dilog((I*d*tan(b*x + a) + d)/(-I*c + d + 1)) - 2*dilog((I*d*tan(b*x + a) + d)/(-I*c + d - 1)))/d) - 8*(b*x + a)*arccot(d*tan(b*x + a) + c) - 8*(b*x + a)*arctan((d^2*tan(b*x + a) + c*d)/d))/b","B",0
161,-1,0,0,0.000000," ","integrate(arccot(c+d*tan(b*x+a))/x,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
162,1,309,0,0.368453," ","integrate(x^2*arccot(c+(1+I*c)*tan(b*x+a)),x, algorithm=""maxima"")","\frac{\frac{{\left({\left(b x + a\right)}^{3} - 3 \, {\left(b x + a\right)}^{2} a + 3 \, {\left(b x + a\right)} a^{2}\right)} \operatorname{arccot}\left({\left(i \, c + 1\right)} \tan\left(b x + a\right) + c\right)}{b^{2}} - \frac{3 \, {\left(-3 i \, {\left(b x + a\right)}^{4} + 12 i \, {\left(b x + a\right)}^{3} a - 18 i \, {\left(b x + a\right)}^{2} a^{2} + {\left(-8 i \, {\left(b x + a\right)}^{3} + 18 i \, {\left(b x + a\right)}^{2} a - 18 i \, {\left(b x + a\right)} a^{2}\right)} \arctan\left(c \cos\left(2 \, b x + 2 \, a\right), c \sin\left(2 \, b x + 2 \, a\right) + 1\right) + {\left(-12 i \, {\left(b x + a\right)}^{2} + 18 i \, {\left(b x + a\right)} a - 9 i \, a^{2}\right)} {\rm Li}_2\left(i \, c e^{\left(2 i \, b x + 2 i \, a\right)}\right) + {\left(4 \, {\left(b x + a\right)}^{3} - 9 \, {\left(b x + a\right)}^{2} a + 9 \, {\left(b x + a\right)} a^{2}\right)} \log\left(c^{2} \cos\left(2 \, b x + 2 \, a\right)^{2} + c^{2} \sin\left(2 \, b x + 2 \, a\right)^{2} + 2 \, c \sin\left(2 \, b x + 2 \, a\right) + 1\right) + 3 \, {\left(4 \, b x + a\right)} {\rm Li}_{3}(i \, c e^{\left(2 i \, b x + 2 i \, a\right)}) + 6 i \, {\rm Li}_{4}(i \, c e^{\left(2 i \, b x + 2 i \, a\right)})\right)} {\left(-i \, c - 1\right)}}{b^{2} {\left(12 \, c - 12 i\right)}}}{3 \, b}"," ",0,"1/3*(((b*x + a)^3 - 3*(b*x + a)^2*a + 3*(b*x + a)*a^2)*arccot((I*c + 1)*tan(b*x + a) + c)/b^2 - 3*(-3*I*(b*x + a)^4 + 12*I*(b*x + a)^3*a - 18*I*(b*x + a)^2*a^2 + (-8*I*(b*x + a)^3 + 18*I*(b*x + a)^2*a - 18*I*(b*x + a)*a^2)*arctan2(c*cos(2*b*x + 2*a), c*sin(2*b*x + 2*a) + 1) + (-12*I*(b*x + a)^2 + 18*I*(b*x + a)*a - 9*I*a^2)*dilog(I*c*e^(2*I*b*x + 2*I*a)) + (4*(b*x + a)^3 - 9*(b*x + a)^2*a + 9*(b*x + a)*a^2)*log(c^2*cos(2*b*x + 2*a)^2 + c^2*sin(2*b*x + 2*a)^2 + 2*c*sin(2*b*x + 2*a) + 1) + 3*(4*b*x + a)*polylog(3, I*c*e^(2*I*b*x + 2*I*a)) + 6*I*polylog(4, I*c*e^(2*I*b*x + 2*I*a)))*(-I*c - 1)/(b^2*(12*c - 12*I)))/b","B",0
163,1,218,0,0.344666," ","integrate(x*arccot(c+(1+I*c)*tan(b*x+a)),x, algorithm=""maxima"")","\frac{\frac{{\left({\left(b x + a\right)}^{2} - 2 \, {\left(b x + a\right)} a\right)} \operatorname{arccot}\left({\left(i \, c + 1\right)} \tan\left(b x + a\right) + c\right)}{b} - \frac{2 \, {\left(-4 i \, {\left(b x + a\right)}^{3} + 12 i \, {\left(b x + a\right)}^{2} a - 6 i \, b x {\rm Li}_2\left(i \, c e^{\left(2 i \, b x + 2 i \, a\right)}\right) + {\left(-6 i \, {\left(b x + a\right)}^{2} + 12 i \, {\left(b x + a\right)} a\right)} \arctan\left(c \cos\left(2 \, b x + 2 \, a\right), c \sin\left(2 \, b x + 2 \, a\right) + 1\right) + 3 \, {\left({\left(b x + a\right)}^{2} - 2 \, {\left(b x + a\right)} a\right)} \log\left(c^{2} \cos\left(2 \, b x + 2 \, a\right)^{2} + c^{2} \sin\left(2 \, b x + 2 \, a\right)^{2} + 2 \, c \sin\left(2 \, b x + 2 \, a\right) + 1\right) + 3 \, {\rm Li}_{3}(i \, c e^{\left(2 i \, b x + 2 i \, a\right)})\right)} {\left(-i \, c - 1\right)}}{b {\left(12 \, c - 12 i\right)}}}{2 \, b}"," ",0,"1/2*(((b*x + a)^2 - 2*(b*x + a)*a)*arccot((I*c + 1)*tan(b*x + a) + c)/b - 2*(-4*I*(b*x + a)^3 + 12*I*(b*x + a)^2*a - 6*I*b*x*dilog(I*c*e^(2*I*b*x + 2*I*a)) + (-6*I*(b*x + a)^2 + 12*I*(b*x + a)*a)*arctan2(c*cos(2*b*x + 2*a), c*sin(2*b*x + 2*a) + 1) + 3*((b*x + a)^2 - 2*(b*x + a)*a)*log(c^2*cos(2*b*x + 2*a)^2 + c^2*sin(2*b*x + 2*a)^2 + 2*c*sin(2*b*x + 2*a) + 1) + 3*polylog(3, I*c*e^(2*I*b*x + 2*I*a)))*(-I*c - 1)/(b*(12*c - 12*I)))/b","B",0
164,1,455,0,0.454396," ","integrate(arccot(c+(1+I*c)*tan(b*x+a)),x, algorithm=""maxima"")","-\frac{{\left(-i \, c - 1\right)} {\left(\frac{4 i \, {\left(b x + a\right)} \log\left(\frac{2 i \, c^{2} - 2 \, {\left(c^{2} - 2 i \, c - 1\right)} \tan\left(b x + a\right) + 4 \, c - 2 i}{2 i \, c^{2} - 2 \, {\left(c^{2} - 2 i \, c - 1\right)} \tan\left(b x + a\right) + 2 i}\right)}{i \, c + 1} - \frac{i \, {\left(4 \, {\left(b x + a\right)} {\left(\log\left(-i \, c^{2} + {\left(c^{2} - 2 i \, c - 1\right)} \tan\left(b x + a\right) - 2 \, c + i\right) - \log\left(-i \, c^{2} + {\left(c^{2} - 2 i \, c - 1\right)} \tan\left(b x + a\right) - i\right)\right)} + i \, \log\left(-i \, c^{2} + {\left(c^{2} - 2 i \, c - 1\right)} \tan\left(b x + a\right) - 2 \, c + i\right)^{2} - 2 i \, \log\left(-i \, c^{2} + {\left(c^{2} - 2 i \, c - 1\right)} \tan\left(b x + a\right) - i\right) \log\left(-\frac{1}{2} \, {\left(c - i\right)} \tan\left(b x + a\right) + \frac{1}{2} i \, c + \frac{1}{2}\right) + 2 i \, \log\left(-i \, c^{2} + {\left(c^{2} - 2 i \, c - 1\right)} \tan\left(b x + a\right) - i\right) \log\left(-\frac{{\left(i \, c + 1\right)} \tan\left(b x + a\right) + c + i}{2 \, c} + 1\right) - 2 i \, \log\left(-i \, c^{2} + {\left(c^{2} - 2 i \, c - 1\right)} \tan\left(b x + a\right) - 2 \, c + i\right) \log\left(-\frac{1}{2} i \, \tan\left(b x + a\right) + \frac{1}{2}\right) - 2 i \, {\rm Li}_2\left(\frac{1}{2} \, {\left(c - i\right)} \tan\left(b x + a\right) - \frac{1}{2} i \, c + \frac{1}{2}\right) + 2 i \, {\rm Li}_2\left(\frac{{\left(i \, c + 1\right)} \tan\left(b x + a\right) + c + i}{2 \, c}\right) - 2 i \, {\rm Li}_2\left(\frac{1}{2} i \, \tan\left(b x + a\right) + \frac{1}{2}\right)\right)}}{i \, c + 1}\right)} - 8 \, {\left(b x + a\right)} \operatorname{arccot}\left({\left(i \, c + 1\right)} \tan\left(b x + a\right) + c\right) - \frac{4 \, {\left(b x + a\right)} {\left(c - i\right)} \log\left(\frac{2 i \, c^{2} - 2 \, {\left(c^{2} - 2 i \, c - 1\right)} \tan\left(b x + a\right) + 4 \, c - 2 i}{2 i \, c^{2} - 2 \, {\left(c^{2} - 2 i \, c - 1\right)} \tan\left(b x + a\right) + 2 i}\right)}{i \, c + 1}}{8 \, b}"," ",0,"-1/8*((-I*c - 1)*(4*I*(b*x + a)*log((2*I*c^2 - 2*(c^2 - 2*I*c - 1)*tan(b*x + a) + 4*c - 2*I)/(2*I*c^2 - 2*(c^2 - 2*I*c - 1)*tan(b*x + a) + 2*I))/(I*c + 1) - I*(4*(b*x + a)*(log(-I*c^2 + (c^2 - 2*I*c - 1)*tan(b*x + a) - 2*c + I) - log(-I*c^2 + (c^2 - 2*I*c - 1)*tan(b*x + a) - I)) + I*log(-I*c^2 + (c^2 - 2*I*c - 1)*tan(b*x + a) - 2*c + I)^2 - 2*I*log(-I*c^2 + (c^2 - 2*I*c - 1)*tan(b*x + a) - I)*log(-1/2*(c - I)*tan(b*x + a) + 1/2*I*c + 1/2) + 2*I*log(-I*c^2 + (c^2 - 2*I*c - 1)*tan(b*x + a) - I)*log(-1/2*((I*c + 1)*tan(b*x + a) + c + I)/c + 1) - 2*I*log(-I*c^2 + (c^2 - 2*I*c - 1)*tan(b*x + a) - 2*c + I)*log(-1/2*I*tan(b*x + a) + 1/2) - 2*I*dilog(1/2*(c - I)*tan(b*x + a) - 1/2*I*c + 1/2) + 2*I*dilog(1/2*((I*c + 1)*tan(b*x + a) + c + I)/c) - 2*I*dilog(1/2*I*tan(b*x + a) + 1/2))/(I*c + 1)) - 8*(b*x + a)*arccot((I*c + 1)*tan(b*x + a) + c) - 4*(b*x + a)*(c - I)*log((2*I*c^2 - 2*(c^2 - 2*I*c - 1)*tan(b*x + a) + 4*c - 2*I)/(2*I*c^2 - 2*(c^2 - 2*I*c - 1)*tan(b*x + a) + 2*I))/(I*c + 1))/b","B",0
165,-2,0,0,0.000000," ","integrate(arccot(c+(1+I*c)*tan(b*x+a))/x,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(c-1>0)', see `assume?` for more details)Is c-1 zero or nonzero?","F(-2)",0
166,1,312,0,0.366740," ","integrate(x^2*arccot(c-(1-I*c)*tan(b*x+a)),x, algorithm=""maxima"")","-\frac{\frac{{\left({\left(b x + a\right)}^{3} - 3 \, {\left(b x + a\right)}^{2} a + 3 \, {\left(b x + a\right)} a^{2}\right)} \operatorname{arccot}\left({\left(-i \, c + 1\right)} \tan\left(b x + a\right) - c\right)}{b^{2}} + \frac{3 \, {\left(-3 i \, {\left(b x + a\right)}^{4} + 12 i \, {\left(b x + a\right)}^{3} a - 18 i \, {\left(b x + a\right)}^{2} a^{2} + {\left(8 i \, {\left(b x + a\right)}^{3} - 18 i \, {\left(b x + a\right)}^{2} a + 18 i \, {\left(b x + a\right)} a^{2}\right)} \arctan\left(c \cos\left(2 \, b x + 2 \, a\right), -c \sin\left(2 \, b x + 2 \, a\right) + 1\right) + {\left(-12 i \, {\left(b x + a\right)}^{2} + 18 i \, {\left(b x + a\right)} a - 9 i \, a^{2}\right)} {\rm Li}_2\left(-i \, c e^{\left(2 i \, b x + 2 i \, a\right)}\right) + {\left(4 \, {\left(b x + a\right)}^{3} - 9 \, {\left(b x + a\right)}^{2} a + 9 \, {\left(b x + a\right)} a^{2}\right)} \log\left(c^{2} \cos\left(2 \, b x + 2 \, a\right)^{2} + c^{2} \sin\left(2 \, b x + 2 \, a\right)^{2} - 2 \, c \sin\left(2 \, b x + 2 \, a\right) + 1\right) + 3 \, {\left(4 \, b x + a\right)} {\rm Li}_{3}(-i \, c e^{\left(2 i \, b x + 2 i \, a\right)}) + 6 i \, {\rm Li}_{4}(-i \, c e^{\left(2 i \, b x + 2 i \, a\right)})\right)} {\left(i \, c - 1\right)}}{b^{2} {\left(12 \, c + 12 i\right)}}}{3 \, b}"," ",0,"-1/3*(((b*x + a)^3 - 3*(b*x + a)^2*a + 3*(b*x + a)*a^2)*arccot((-I*c + 1)*tan(b*x + a) - c)/b^2 + 3*(-3*I*(b*x + a)^4 + 12*I*(b*x + a)^3*a - 18*I*(b*x + a)^2*a^2 + (8*I*(b*x + a)^3 - 18*I*(b*x + a)^2*a + 18*I*(b*x + a)*a^2)*arctan2(c*cos(2*b*x + 2*a), -c*sin(2*b*x + 2*a) + 1) + (-12*I*(b*x + a)^2 + 18*I*(b*x + a)*a - 9*I*a^2)*dilog(-I*c*e^(2*I*b*x + 2*I*a)) + (4*(b*x + a)^3 - 9*(b*x + a)^2*a + 9*(b*x + a)*a^2)*log(c^2*cos(2*b*x + 2*a)^2 + c^2*sin(2*b*x + 2*a)^2 - 2*c*sin(2*b*x + 2*a) + 1) + 3*(4*b*x + a)*polylog(3, -I*c*e^(2*I*b*x + 2*I*a)) + 6*I*polylog(4, -I*c*e^(2*I*b*x + 2*I*a)))*(I*c - 1)/(b^2*(12*c + 12*I)))/b","B",0
167,1,221,0,0.367924," ","integrate(x*arccot(c-(1-I*c)*tan(b*x+a)),x, algorithm=""maxima"")","-\frac{\frac{{\left({\left(b x + a\right)}^{2} - 2 \, {\left(b x + a\right)} a\right)} \operatorname{arccot}\left({\left(-i \, c + 1\right)} \tan\left(b x + a\right) - c\right)}{b} + \frac{2 \, {\left(-4 i \, {\left(b x + a\right)}^{3} + 12 i \, {\left(b x + a\right)}^{2} a - 6 i \, b x {\rm Li}_2\left(-i \, c e^{\left(2 i \, b x + 2 i \, a\right)}\right) + {\left(6 i \, {\left(b x + a\right)}^{2} - 12 i \, {\left(b x + a\right)} a\right)} \arctan\left(c \cos\left(2 \, b x + 2 \, a\right), -c \sin\left(2 \, b x + 2 \, a\right) + 1\right) + 3 \, {\left({\left(b x + a\right)}^{2} - 2 \, {\left(b x + a\right)} a\right)} \log\left(c^{2} \cos\left(2 \, b x + 2 \, a\right)^{2} + c^{2} \sin\left(2 \, b x + 2 \, a\right)^{2} - 2 \, c \sin\left(2 \, b x + 2 \, a\right) + 1\right) + 3 \, {\rm Li}_{3}(-i \, c e^{\left(2 i \, b x + 2 i \, a\right)})\right)} {\left(i \, c - 1\right)}}{b {\left(12 \, c + 12 i\right)}}}{2 \, b}"," ",0,"-1/2*(((b*x + a)^2 - 2*(b*x + a)*a)*arccot((-I*c + 1)*tan(b*x + a) - c)/b + 2*(-4*I*(b*x + a)^3 + 12*I*(b*x + a)^2*a - 6*I*b*x*dilog(-I*c*e^(2*I*b*x + 2*I*a)) + (6*I*(b*x + a)^2 - 12*I*(b*x + a)*a)*arctan2(c*cos(2*b*x + 2*a), -c*sin(2*b*x + 2*a) + 1) + 3*((b*x + a)^2 - 2*(b*x + a)*a)*log(c^2*cos(2*b*x + 2*a)^2 + c^2*sin(2*b*x + 2*a)^2 - 2*c*sin(2*b*x + 2*a) + 1) + 3*polylog(3, -I*c*e^(2*I*b*x + 2*I*a)))*(I*c - 1)/(b*(12*c + 12*I)))/b","B",0
168,1,450,0,0.465941," ","integrate(arccot(c-(1-I*c)*tan(b*x+a)),x, algorithm=""maxima"")","\frac{{\left(i \, c - 1\right)} {\left(\frac{4 i \, {\left(b x + a\right)} \log\left(\frac{2 i \, c^{2} - 2 \, {\left(c^{2} + 2 i \, c - 1\right)} \tan\left(b x + a\right) + 2 i}{2 i \, c^{2} - 2 \, {\left(c^{2} + 2 i \, c - 1\right)} \tan\left(b x + a\right) - 4 \, c - 2 i}\right)}{i \, c - 1} + \frac{i \, {\left(4 \, {\left(b x + a\right)} {\left(\log\left(-i \, c^{2} + {\left(c^{2} + 2 i \, c - 1\right)} \tan\left(b x + a\right) + 2 \, c + i\right) - \log\left(-i \, c^{2} + {\left(c^{2} + 2 i \, c - 1\right)} \tan\left(b x + a\right) - i\right)\right)} + i \, \log\left(-i \, c^{2} + {\left(c^{2} + 2 i \, c - 1\right)} \tan\left(b x + a\right) + 2 \, c + i\right)^{2} - 2 i \, \log\left(-i \, c^{2} + {\left(c^{2} + 2 i \, c - 1\right)} \tan\left(b x + a\right) - i\right) \log\left(\frac{1}{2} \, {\left(c + i\right)} \tan\left(b x + a\right) - \frac{1}{2} i \, c + \frac{1}{2}\right) + 2 i \, \log\left(-i \, c^{2} + {\left(c^{2} + 2 i \, c - 1\right)} \tan\left(b x + a\right) - i\right) \log\left(-\frac{{\left(i \, c - 1\right)} \tan\left(b x + a\right) + c - i}{2 \, c} + 1\right) - 2 i \, \log\left(-i \, c^{2} + {\left(c^{2} + 2 i \, c - 1\right)} \tan\left(b x + a\right) + 2 \, c + i\right) \log\left(-\frac{1}{2} i \, \tan\left(b x + a\right) + \frac{1}{2}\right) - 2 i \, {\rm Li}_2\left(-\frac{1}{2} \, {\left(c + i\right)} \tan\left(b x + a\right) + \frac{1}{2} i \, c + \frac{1}{2}\right) + 2 i \, {\rm Li}_2\left(\frac{{\left(i \, c - 1\right)} \tan\left(b x + a\right) + c - i}{2 \, c}\right) - 2 i \, {\rm Li}_2\left(\frac{1}{2} i \, \tan\left(b x + a\right) + \frac{1}{2}\right)\right)}}{i \, c - 1}\right)} - 8 \, {\left(b x + a\right)} \operatorname{arccot}\left({\left(-i \, c + 1\right)} \tan\left(b x + a\right) - c\right) + 4 \, {\left(-i \, b x - i \, a\right)} \log\left(\frac{2 i \, c^{2} - 2 \, {\left(c^{2} + 2 i \, c - 1\right)} \tan\left(b x + a\right) + 2 i}{2 i \, c^{2} - 2 \, {\left(c^{2} + 2 i \, c - 1\right)} \tan\left(b x + a\right) - 4 \, c - 2 i}\right)}{8 \, b}"," ",0,"1/8*((I*c - 1)*(4*I*(b*x + a)*log((2*I*c^2 - 2*(c^2 + 2*I*c - 1)*tan(b*x + a) + 2*I)/(2*I*c^2 - 2*(c^2 + 2*I*c - 1)*tan(b*x + a) - 4*c - 2*I))/(I*c - 1) + I*(4*(b*x + a)*(log(-I*c^2 + (c^2 + 2*I*c - 1)*tan(b*x + a) + 2*c + I) - log(-I*c^2 + (c^2 + 2*I*c - 1)*tan(b*x + a) - I)) + I*log(-I*c^2 + (c^2 + 2*I*c - 1)*tan(b*x + a) + 2*c + I)^2 - 2*I*log(-I*c^2 + (c^2 + 2*I*c - 1)*tan(b*x + a) - I)*log(1/2*(c + I)*tan(b*x + a) - 1/2*I*c + 1/2) + 2*I*log(-I*c^2 + (c^2 + 2*I*c - 1)*tan(b*x + a) - I)*log(-1/2*((I*c - 1)*tan(b*x + a) + c - I)/c + 1) - 2*I*log(-I*c^2 + (c^2 + 2*I*c - 1)*tan(b*x + a) + 2*c + I)*log(-1/2*I*tan(b*x + a) + 1/2) - 2*I*dilog(-1/2*(c + I)*tan(b*x + a) + 1/2*I*c + 1/2) + 2*I*dilog(1/2*((I*c - 1)*tan(b*x + a) + c - I)/c) - 2*I*dilog(1/2*I*tan(b*x + a) + 1/2))/(I*c - 1)) - 8*(b*x + a)*arccot((-I*c + 1)*tan(b*x + a) - c) + 4*(-I*b*x - I*a)*log((2*I*c^2 - 2*(c^2 + 2*I*c - 1)*tan(b*x + a) + 2*I)/(2*I*c^2 - 2*(c^2 + 2*I*c - 1)*tan(b*x + a) - 4*c - 2*I)))/b","B",0
169,-2,0,0,0.000000," ","integrate(arccot(c-(1-I*c)*tan(b*x+a))/x,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(c-1>0)', see `assume?` for more details)Is c-1 zero or nonzero?","F(-2)",0
170,1,10,0,0.322082," ","integrate(arccot(cot(b*x+a)),x, algorithm=""maxima"")","\frac{1}{2} \, b x^{2} + a x"," ",0,"1/2*b*x^2 + a*x","A",0
171,0,0,0,0.000000," ","integrate(x^2*arccot(c+d*cot(b*x+a)),x, algorithm=""maxima"")","\frac{1}{6} \, x^{3} \arctan\left({\left(d + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + c \sin\left(2 \, b x + 2 \, a\right) + d - 1, c \cos\left(2 \, b x + 2 \, a\right) - {\left(d + 1\right)} \sin\left(2 \, b x + 2 \, a\right) - c\right) - \frac{1}{6} \, x^{3} \arctan\left({\left(d - 1\right)} \cos\left(2 \, b x + 2 \, a\right) + c \sin\left(2 \, b x + 2 \, a\right) + d + 1, c \cos\left(2 \, b x + 2 \, a\right) - {\left(d - 1\right)} \sin\left(2 \, b x + 2 \, a\right) - c\right) - 4 \, b d \int \frac{2 \, {\left(c^{2} + d^{2} + 1\right)} x^{3} \cos\left(2 \, b x + 2 \, a\right)^{2} + 2 \, c d x^{3} \sin\left(2 \, b x + 2 \, a\right) + 2 \, {\left(c^{2} + d^{2} + 1\right)} x^{3} \sin\left(2 \, b x + 2 \, a\right)^{2} - {\left(c^{2} - d^{2} + 1\right)} x^{3} \cos\left(2 \, b x + 2 \, a\right) - {\left(2 \, c d x^{3} \sin\left(2 \, b x + 2 \, a\right) + {\left(c^{2} - d^{2} + 1\right)} x^{3} \cos\left(2 \, b x + 2 \, a\right)\right)} \cos\left(4 \, b x + 4 \, a\right) + {\left(2 \, c d x^{3} \cos\left(2 \, b x + 2 \, a\right) - {\left(c^{2} - d^{2} + 1\right)} x^{3} \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(4 \, b x + 4 \, a\right)}{3 \, {\left(c^{4} + d^{4} + 2 \, {\left(c^{2} - 1\right)} d^{2} + {\left(c^{4} + d^{4} + 2 \, {\left(c^{2} - 1\right)} d^{2} + 2 \, c^{2} + 1\right)} \cos\left(4 \, b x + 4 \, a\right)^{2} + 4 \, {\left(c^{4} + d^{4} + 2 \, {\left(c^{2} + 1\right)} d^{2} + 2 \, c^{2} + 1\right)} \cos\left(2 \, b x + 2 \, a\right)^{2} + {\left(c^{4} + d^{4} + 2 \, {\left(c^{2} - 1\right)} d^{2} + 2 \, c^{2} + 1\right)} \sin\left(4 \, b x + 4 \, a\right)^{2} + 4 \, {\left(c^{4} + d^{4} + 2 \, {\left(c^{2} + 1\right)} d^{2} + 2 \, c^{2} + 1\right)} \sin\left(2 \, b x + 2 \, a\right)^{2} + 2 \, c^{2} + 2 \, {\left(c^{4} + d^{4} - 2 \, {\left(3 \, c^{2} + 1\right)} d^{2} + 2 \, c^{2} - 2 \, {\left(c^{4} - d^{4} + 2 \, c^{2} + 1\right)} \cos\left(2 \, b x + 2 \, a\right) - 4 \, {\left(c d^{3} + {\left(c^{3} + c\right)} d\right)} \sin\left(2 \, b x + 2 \, a\right) + 1\right)} \cos\left(4 \, b x + 4 \, a\right) - 4 \, {\left(c^{4} - d^{4} + 2 \, c^{2} + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + 4 \, {\left(2 \, c d^{3} - 2 \, {\left(c^{3} + c\right)} d + 2 \, {\left(c d^{3} + {\left(c^{3} + c\right)} d\right)} \cos\left(2 \, b x + 2 \, a\right) - {\left(c^{4} - d^{4} + 2 \, c^{2} + 1\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(4 \, b x + 4 \, a\right) + 8 \, {\left(c d^{3} + {\left(c^{3} + c\right)} d\right)} \sin\left(2 \, b x + 2 \, a\right) + 1\right)}}\,{d x}"," ",0,"1/6*x^3*arctan2((d + 1)*cos(2*b*x + 2*a) + c*sin(2*b*x + 2*a) + d - 1, c*cos(2*b*x + 2*a) - (d + 1)*sin(2*b*x + 2*a) - c) - 1/6*x^3*arctan2((d - 1)*cos(2*b*x + 2*a) + c*sin(2*b*x + 2*a) + d + 1, c*cos(2*b*x + 2*a) - (d - 1)*sin(2*b*x + 2*a) - c) - 4*b*d*integrate(1/3*(2*(c^2 + d^2 + 1)*x^3*cos(2*b*x + 2*a)^2 + 2*c*d*x^3*sin(2*b*x + 2*a) + 2*(c^2 + d^2 + 1)*x^3*sin(2*b*x + 2*a)^2 - (c^2 - d^2 + 1)*x^3*cos(2*b*x + 2*a) - (2*c*d*x^3*sin(2*b*x + 2*a) + (c^2 - d^2 + 1)*x^3*cos(2*b*x + 2*a))*cos(4*b*x + 4*a) + (2*c*d*x^3*cos(2*b*x + 2*a) - (c^2 - d^2 + 1)*x^3*sin(2*b*x + 2*a))*sin(4*b*x + 4*a))/(c^4 + d^4 + 2*(c^2 - 1)*d^2 + (c^4 + d^4 + 2*(c^2 - 1)*d^2 + 2*c^2 + 1)*cos(4*b*x + 4*a)^2 + 4*(c^4 + d^4 + 2*(c^2 + 1)*d^2 + 2*c^2 + 1)*cos(2*b*x + 2*a)^2 + (c^4 + d^4 + 2*(c^2 - 1)*d^2 + 2*c^2 + 1)*sin(4*b*x + 4*a)^2 + 4*(c^4 + d^4 + 2*(c^2 + 1)*d^2 + 2*c^2 + 1)*sin(2*b*x + 2*a)^2 + 2*c^2 + 2*(c^4 + d^4 - 2*(3*c^2 + 1)*d^2 + 2*c^2 - 2*(c^4 - d^4 + 2*c^2 + 1)*cos(2*b*x + 2*a) - 4*(c*d^3 + (c^3 + c)*d)*sin(2*b*x + 2*a) + 1)*cos(4*b*x + 4*a) - 4*(c^4 - d^4 + 2*c^2 + 1)*cos(2*b*x + 2*a) + 4*(2*c*d^3 - 2*(c^3 + c)*d + 2*(c*d^3 + (c^3 + c)*d)*cos(2*b*x + 2*a) - (c^4 - d^4 + 2*c^2 + 1)*sin(2*b*x + 2*a))*sin(4*b*x + 4*a) + 8*(c*d^3 + (c^3 + c)*d)*sin(2*b*x + 2*a) + 1), x)","F",0
172,0,0,0,0.000000," ","integrate(x*arccot(c+d*cot(b*x+a)),x, algorithm=""maxima"")","\frac{1}{4} \, x^{2} \arctan\left({\left(d + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + c \sin\left(2 \, b x + 2 \, a\right) + d - 1, c \cos\left(2 \, b x + 2 \, a\right) - {\left(d + 1\right)} \sin\left(2 \, b x + 2 \, a\right) - c\right) - \frac{1}{4} \, x^{2} \arctan\left({\left(d - 1\right)} \cos\left(2 \, b x + 2 \, a\right) + c \sin\left(2 \, b x + 2 \, a\right) + d + 1, c \cos\left(2 \, b x + 2 \, a\right) - {\left(d - 1\right)} \sin\left(2 \, b x + 2 \, a\right) - c\right) - 2 \, b d \int \frac{2 \, {\left(c^{2} + d^{2} + 1\right)} x^{2} \cos\left(2 \, b x + 2 \, a\right)^{2} + 2 \, c d x^{2} \sin\left(2 \, b x + 2 \, a\right) + 2 \, {\left(c^{2} + d^{2} + 1\right)} x^{2} \sin\left(2 \, b x + 2 \, a\right)^{2} - {\left(c^{2} - d^{2} + 1\right)} x^{2} \cos\left(2 \, b x + 2 \, a\right) - {\left(2 \, c d x^{2} \sin\left(2 \, b x + 2 \, a\right) + {\left(c^{2} - d^{2} + 1\right)} x^{2} \cos\left(2 \, b x + 2 \, a\right)\right)} \cos\left(4 \, b x + 4 \, a\right) + {\left(2 \, c d x^{2} \cos\left(2 \, b x + 2 \, a\right) - {\left(c^{2} - d^{2} + 1\right)} x^{2} \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(4 \, b x + 4 \, a\right)}{c^{4} + d^{4} + 2 \, {\left(c^{2} - 1\right)} d^{2} + {\left(c^{4} + d^{4} + 2 \, {\left(c^{2} - 1\right)} d^{2} + 2 \, c^{2} + 1\right)} \cos\left(4 \, b x + 4 \, a\right)^{2} + 4 \, {\left(c^{4} + d^{4} + 2 \, {\left(c^{2} + 1\right)} d^{2} + 2 \, c^{2} + 1\right)} \cos\left(2 \, b x + 2 \, a\right)^{2} + {\left(c^{4} + d^{4} + 2 \, {\left(c^{2} - 1\right)} d^{2} + 2 \, c^{2} + 1\right)} \sin\left(4 \, b x + 4 \, a\right)^{2} + 4 \, {\left(c^{4} + d^{4} + 2 \, {\left(c^{2} + 1\right)} d^{2} + 2 \, c^{2} + 1\right)} \sin\left(2 \, b x + 2 \, a\right)^{2} + 2 \, c^{2} + 2 \, {\left(c^{4} + d^{4} - 2 \, {\left(3 \, c^{2} + 1\right)} d^{2} + 2 \, c^{2} - 2 \, {\left(c^{4} - d^{4} + 2 \, c^{2} + 1\right)} \cos\left(2 \, b x + 2 \, a\right) - 4 \, {\left(c d^{3} + {\left(c^{3} + c\right)} d\right)} \sin\left(2 \, b x + 2 \, a\right) + 1\right)} \cos\left(4 \, b x + 4 \, a\right) - 4 \, {\left(c^{4} - d^{4} + 2 \, c^{2} + 1\right)} \cos\left(2 \, b x + 2 \, a\right) + 4 \, {\left(2 \, c d^{3} - 2 \, {\left(c^{3} + c\right)} d + 2 \, {\left(c d^{3} + {\left(c^{3} + c\right)} d\right)} \cos\left(2 \, b x + 2 \, a\right) - {\left(c^{4} - d^{4} + 2 \, c^{2} + 1\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(4 \, b x + 4 \, a\right) + 8 \, {\left(c d^{3} + {\left(c^{3} + c\right)} d\right)} \sin\left(2 \, b x + 2 \, a\right) + 1}\,{d x}"," ",0,"1/4*x^2*arctan2((d + 1)*cos(2*b*x + 2*a) + c*sin(2*b*x + 2*a) + d - 1, c*cos(2*b*x + 2*a) - (d + 1)*sin(2*b*x + 2*a) - c) - 1/4*x^2*arctan2((d - 1)*cos(2*b*x + 2*a) + c*sin(2*b*x + 2*a) + d + 1, c*cos(2*b*x + 2*a) - (d - 1)*sin(2*b*x + 2*a) - c) - 2*b*d*integrate((2*(c^2 + d^2 + 1)*x^2*cos(2*b*x + 2*a)^2 + 2*c*d*x^2*sin(2*b*x + 2*a) + 2*(c^2 + d^2 + 1)*x^2*sin(2*b*x + 2*a)^2 - (c^2 - d^2 + 1)*x^2*cos(2*b*x + 2*a) - (2*c*d*x^2*sin(2*b*x + 2*a) + (c^2 - d^2 + 1)*x^2*cos(2*b*x + 2*a))*cos(4*b*x + 4*a) + (2*c*d*x^2*cos(2*b*x + 2*a) - (c^2 - d^2 + 1)*x^2*sin(2*b*x + 2*a))*sin(4*b*x + 4*a))/(c^4 + d^4 + 2*(c^2 - 1)*d^2 + (c^4 + d^4 + 2*(c^2 - 1)*d^2 + 2*c^2 + 1)*cos(4*b*x + 4*a)^2 + 4*(c^4 + d^4 + 2*(c^2 + 1)*d^2 + 2*c^2 + 1)*cos(2*b*x + 2*a)^2 + (c^4 + d^4 + 2*(c^2 - 1)*d^2 + 2*c^2 + 1)*sin(4*b*x + 4*a)^2 + 4*(c^4 + d^4 + 2*(c^2 + 1)*d^2 + 2*c^2 + 1)*sin(2*b*x + 2*a)^2 + 2*c^2 + 2*(c^4 + d^4 - 2*(3*c^2 + 1)*d^2 + 2*c^2 - 2*(c^4 - d^4 + 2*c^2 + 1)*cos(2*b*x + 2*a) - 4*(c*d^3 + (c^3 + c)*d)*sin(2*b*x + 2*a) + 1)*cos(4*b*x + 4*a) - 4*(c^4 - d^4 + 2*c^2 + 1)*cos(2*b*x + 2*a) + 4*(2*c*d^3 - 2*(c^3 + c)*d + 2*(c*d^3 + (c^3 + c)*d)*cos(2*b*x + 2*a) - (c^4 - d^4 + 2*c^2 + 1)*sin(2*b*x + 2*a))*sin(4*b*x + 4*a) + 8*(c*d^3 + (c^3 + c)*d)*sin(2*b*x + 2*a) + 1), x)","F",0
173,1,532,0,0.540517," ","integrate(arccot(c+d*cot(b*x+a)),x, algorithm=""maxima"")","\frac{d {\left(\frac{8 \, {\left(b x + a\right)} \arctan\left(\frac{c d + {\left(c^{2} + 1\right)} \tan\left(b x + a\right)}{d}\right)}{d} - \frac{8 \, {\left(b x + a\right)} \arctan\left(\frac{c d + {\left(c^{2} + 1\right)} \tan\left(b x + a\right)}{d}\right) - 4 \, \arctan\left(\frac{c d + {\left(c^{2} + 1\right)} \tan\left(b x + a\right)}{d}\right) \arctan\left(\frac{c d + {\left(c^{2} + d + 1\right)} \tan\left(b x + a\right)}{c^{2} + d^{2} + 2 \, d + 1}, -\frac{c d \tan\left(b x + a\right) - c^{2} - d - 1}{c^{2} + d^{2} + 2 \, d + 1}\right) + 4 \, \arctan\left(\frac{c d + {\left(c^{2} + 1\right)} \tan\left(b x + a\right)}{d}\right) \arctan\left(-\frac{c d + {\left(c^{2} - d + 1\right)} \tan\left(b x + a\right)}{c^{2} + d^{2} - 2 \, d + 1}, -\frac{c d \tan\left(b x + a\right) - c^{2} + d - 1}{c^{2} + d^{2} - 2 \, d + 1}\right) - {\left(\log\left(\frac{{\left(c^{2} + 1\right)} \tan\left(b x + a\right)^{2} + c^{2} + 1}{c^{2} + d^{2} + 2 \, d + 1}\right) - \log\left(\frac{{\left(c^{2} + 1\right)} \tan\left(b x + a\right)^{2} + c^{2} + 1}{c^{2} + d^{2} - 2 \, d + 1}\right)\right)} \log\left({\left(c^{2} + 1\right)} d^{2} + 2 \, {\left(c^{3} + c\right)} d \tan\left(b x + a\right) + {\left(c^{4} + 2 \, c^{2} + 1\right)} \tan\left(b x + a\right)^{2}\right) - 2 \, {\rm Li}_2\left(\frac{{\left(i \, c - 1\right)} \tan\left(b x + a\right) + i \, d}{c + i \, d + i}\right) + 2 \, {\rm Li}_2\left(\frac{{\left(i \, c + 1\right)} \tan\left(b x + a\right) + i \, d}{c + i \, d - i}\right) + 2 \, {\rm Li}_2\left(-\frac{{\left(i \, c - 1\right)} \tan\left(b x + a\right) + i \, d}{c - i \, d + i}\right) - 2 \, {\rm Li}_2\left(-\frac{{\left(i \, c + 1\right)} \tan\left(b x + a\right) + i \, d}{c - i \, d - i}\right)}{d}\right)} + 8 \, {\left(b x + a\right)} \operatorname{arccot}\left(c + \frac{d}{\tan\left(b x + a\right)}\right) - 8 \, {\left(b x + a\right)} \arctan\left(\frac{c d + {\left(c^{2} + 1\right)} \tan\left(b x + a\right)}{d}\right)}{8 \, b}"," ",0,"1/8*(d*(8*(b*x + a)*arctan((c*d + (c^2 + 1)*tan(b*x + a))/d)/d - (8*(b*x + a)*arctan((c*d + (c^2 + 1)*tan(b*x + a))/d) - 4*arctan((c*d + (c^2 + 1)*tan(b*x + a))/d)*arctan2((c*d + (c^2 + d + 1)*tan(b*x + a))/(c^2 + d^2 + 2*d + 1), -(c*d*tan(b*x + a) - c^2 - d - 1)/(c^2 + d^2 + 2*d + 1)) + 4*arctan((c*d + (c^2 + 1)*tan(b*x + a))/d)*arctan2(-(c*d + (c^2 - d + 1)*tan(b*x + a))/(c^2 + d^2 - 2*d + 1), -(c*d*tan(b*x + a) - c^2 + d - 1)/(c^2 + d^2 - 2*d + 1)) - (log(((c^2 + 1)*tan(b*x + a)^2 + c^2 + 1)/(c^2 + d^2 + 2*d + 1)) - log(((c^2 + 1)*tan(b*x + a)^2 + c^2 + 1)/(c^2 + d^2 - 2*d + 1)))*log((c^2 + 1)*d^2 + 2*(c^3 + c)*d*tan(b*x + a) + (c^4 + 2*c^2 + 1)*tan(b*x + a)^2) - 2*dilog(((I*c - 1)*tan(b*x + a) + I*d)/(c + I*d + I)) + 2*dilog(((I*c + 1)*tan(b*x + a) + I*d)/(c + I*d - I)) + 2*dilog(-((I*c - 1)*tan(b*x + a) + I*d)/(c - I*d + I)) - 2*dilog(-((I*c + 1)*tan(b*x + a) + I*d)/(c - I*d - I)))/d) + 8*(b*x + a)*arccot(c + d/tan(b*x + a)) - 8*(b*x + a)*arctan((c*d + (c^2 + 1)*tan(b*x + a))/d))/b","B",0
174,-1,0,0,0.000000," ","integrate(arccot(c+d*cot(b*x+a))/x,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
175,-2,0,0,0.000000," ","integrate(x^2*(pi-arccot(-c-(1-I*c)*cot(b*x+a))),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(c-1>0)', see `assume?` for more details)Is c-1 zero or nonzero?","F(-2)",0
176,-2,0,0,0.000000," ","integrate(x*(pi-arccot(-c-(1-I*c)*cot(b*x+a))),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(c-1>0)', see `assume?` for more details)Is c-1 zero or nonzero?","F(-2)",0
177,-2,0,0,0.000000," ","integrate(pi-arccot(-c-(1-I*c)*cot(b*x+a)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(c-1>0)', see `assume?` for more details)Is c-1 zero or nonzero?","F(-2)",0
178,-2,0,0,0.000000," ","integrate((pi-arccot(-c-(1-I*c)*cot(b*x+a)))/x,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(c-1>0)', see `assume?` for more details)Is c-1 zero or nonzero?","F(-2)",0
179,-2,0,0,0.000000," ","integrate(x^2*(pi-arccot(-c+(1+I*c)*cot(b*x+a))),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(c-1>0)', see `assume?` for more details)Is c-1 zero or nonzero?","F(-2)",0
180,-2,0,0,0.000000," ","integrate(x*(pi-arccot(-c+(1+I*c)*cot(b*x+a))),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(c-1>0)', see `assume?` for more details)Is c-1 zero or nonzero?","F(-2)",0
181,-2,0,0,0.000000," ","integrate(pi-arccot(-c+(1+I*c)*cot(b*x+a)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(c-1>0)', see `assume?` for more details)Is c-1 zero or nonzero?","F(-2)",0
182,-2,0,0,0.000000," ","integrate((pi-arccot(-c+(1+I*c)*cot(b*x+a)))/x,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(c-1>0)', see `assume?` for more details)Is c-1 zero or nonzero?","F(-2)",0
183,0,0,0,0.000000," ","integrate((f*x+e)^3*arccot(tanh(b*x+a)),x, algorithm=""maxima"")","\frac{1}{4} \, {\left(f^{3} x^{4} + 4 \, e f^{2} x^{3} + 6 \, e^{2} f x^{2} + 4 \, e^{3} x\right)} \arctan\left(e^{\left(2 \, b x + 2 \, a\right)} + 1, e^{\left(2 \, b x + 2 \, a\right)} - 1\right) + \int \frac{{\left(b f^{3} x^{4} e^{\left(2 \, a\right)} + 4 \, b e f^{2} x^{3} e^{\left(2 \, a\right)} + 6 \, b e^{2} f x^{2} e^{\left(2 \, a\right)} + 4 \, b e^{3} x e^{\left(2 \, a\right)}\right)} e^{\left(2 \, b x\right)}}{2 \, {\left(e^{\left(4 \, b x + 4 \, a\right)} + 1\right)}}\,{d x}"," ",0,"1/4*(f^3*x^4 + 4*e*f^2*x^3 + 6*e^2*f*x^2 + 4*e^3*x)*arctan2(e^(2*b*x + 2*a) + 1, e^(2*b*x + 2*a) - 1) + integrate(1/2*(b*f^3*x^4*e^(2*a) + 4*b*e*f^2*x^3*e^(2*a) + 6*b*e^2*f*x^2*e^(2*a) + 4*b*e^3*x*e^(2*a))*e^(2*b*x)/(e^(4*b*x + 4*a) + 1), x)","F",0
184,0,0,0,0.000000," ","integrate((f*x+e)^2*arccot(tanh(b*x+a)),x, algorithm=""maxima"")","\frac{1}{3} \, {\left(f^{2} x^{3} + 3 \, e f x^{2} + 3 \, e^{2} x\right)} \arctan\left(e^{\left(2 \, b x + 2 \, a\right)} + 1, e^{\left(2 \, b x + 2 \, a\right)} - 1\right) + \int \frac{2 \, {\left(b f^{2} x^{3} e^{\left(2 \, a\right)} + 3 \, b e f x^{2} e^{\left(2 \, a\right)} + 3 \, b e^{2} x e^{\left(2 \, a\right)}\right)} e^{\left(2 \, b x\right)}}{3 \, {\left(e^{\left(4 \, b x + 4 \, a\right)} + 1\right)}}\,{d x}"," ",0,"1/3*(f^2*x^3 + 3*e*f*x^2 + 3*e^2*x)*arctan2(e^(2*b*x + 2*a) + 1, e^(2*b*x + 2*a) - 1) + integrate(2/3*(b*f^2*x^3*e^(2*a) + 3*b*e*f*x^2*e^(2*a) + 3*b*e^2*x*e^(2*a))*e^(2*b*x)/(e^(4*b*x + 4*a) + 1), x)","F",0
185,0,0,0,0.000000," ","integrate((f*x+e)*arccot(tanh(b*x+a)),x, algorithm=""maxima"")","\frac{1}{2} \, {\left(f x^{2} + 2 \, e x\right)} \arctan\left(e^{\left(2 \, b x + 2 \, a\right)} + 1, e^{\left(2 \, b x + 2 \, a\right)} - 1\right) + \int \frac{{\left(b f x^{2} e^{\left(2 \, a\right)} + 2 \, b e x e^{\left(2 \, a\right)}\right)} e^{\left(2 \, b x\right)}}{e^{\left(4 \, b x + 4 \, a\right)} + 1}\,{d x}"," ",0,"1/2*(f*x^2 + 2*e*x)*arctan2(e^(2*b*x + 2*a) + 1, e^(2*b*x + 2*a) - 1) + integrate((b*f*x^2*e^(2*a) + 2*b*e*x*e^(2*a))*e^(2*b*x)/(e^(4*b*x + 4*a) + 1), x)","F",0
186,0,0,0,0.000000," ","integrate(arccot(tanh(b*x+a)),x, algorithm=""maxima"")","x \arctan\left(e^{\left(2 \, b x + 2 \, a\right)} + 1, e^{\left(2 \, b x + 2 \, a\right)} - 1\right) + 2 \, b \int \frac{x e^{\left(2 \, b x + 2 \, a\right)}}{e^{\left(4 \, b x + 4 \, a\right)} + 1}\,{d x}"," ",0,"x*arctan2(e^(2*b*x + 2*a) + 1, e^(2*b*x + 2*a) - 1) + 2*b*integrate(x*e^(2*b*x + 2*a)/(e^(4*b*x + 4*a) + 1), x)","F",0
187,0,0,0,0.000000," ","integrate(arccot(tanh(b*x+a))/(f*x+e),x, algorithm=""maxima"")","\int \frac{\operatorname{arccot}\left(\tanh\left(b x + a\right)\right)}{f x + e}\,{d x}"," ",0,"integrate(arccot(tanh(b*x + a))/(f*x + e), x)","F",0
188,0,0,0,0.000000," ","integrate(x^2*arccot(c+d*tanh(b*x+a)),x, algorithm=""maxima"")","\frac{1}{3} \, x^{3} \arctan\left(e^{\left(2 \, b x + 2 \, a\right)} + 1, {\left(c e^{\left(2 \, a\right)} + d e^{\left(2 \, a\right)}\right)} e^{\left(2 \, b x\right)} + c - d\right) + 4 \, b d \int \frac{x^{3} e^{\left(2 \, b x + 2 \, a\right)}}{3 \, {\left(c^{2} - 2 \, c d + d^{2} + {\left(c^{2} e^{\left(4 \, a\right)} + 2 \, c d e^{\left(4 \, a\right)} + d^{2} e^{\left(4 \, a\right)} + e^{\left(4 \, a\right)}\right)} e^{\left(4 \, b x\right)} + 2 \, {\left(c^{2} e^{\left(2 \, a\right)} - d^{2} e^{\left(2 \, a\right)} + e^{\left(2 \, a\right)}\right)} e^{\left(2 \, b x\right)} + 1\right)}}\,{d x}"," ",0,"1/3*x^3*arctan2(e^(2*b*x + 2*a) + 1, (c*e^(2*a) + d*e^(2*a))*e^(2*b*x) + c - d) + 4*b*d*integrate(1/3*x^3*e^(2*b*x + 2*a)/(c^2 - 2*c*d + d^2 + (c^2*e^(4*a) + 2*c*d*e^(4*a) + d^2*e^(4*a) + e^(4*a))*e^(4*b*x) + 2*(c^2*e^(2*a) - d^2*e^(2*a) + e^(2*a))*e^(2*b*x) + 1), x)","F",0
189,0,0,0,0.000000," ","integrate(x*arccot(c+d*tanh(b*x+a)),x, algorithm=""maxima"")","\frac{1}{2} \, x^{2} \arctan\left(e^{\left(2 \, b x + 2 \, a\right)} + 1, {\left(c e^{\left(2 \, a\right)} + d e^{\left(2 \, a\right)}\right)} e^{\left(2 \, b x\right)} + c - d\right) + 2 \, b d \int \frac{x^{2} e^{\left(2 \, b x + 2 \, a\right)}}{c^{2} - 2 \, c d + d^{2} + {\left(c^{2} e^{\left(4 \, a\right)} + 2 \, c d e^{\left(4 \, a\right)} + d^{2} e^{\left(4 \, a\right)} + e^{\left(4 \, a\right)}\right)} e^{\left(4 \, b x\right)} + 2 \, {\left(c^{2} e^{\left(2 \, a\right)} - d^{2} e^{\left(2 \, a\right)} + e^{\left(2 \, a\right)}\right)} e^{\left(2 \, b x\right)} + 1}\,{d x}"," ",0,"1/2*x^2*arctan2(e^(2*b*x + 2*a) + 1, (c*e^(2*a) + d*e^(2*a))*e^(2*b*x) + c - d) + 2*b*d*integrate(x^2*e^(2*b*x + 2*a)/(c^2 - 2*c*d + d^2 + (c^2*e^(4*a) + 2*c*d*e^(4*a) + d^2*e^(4*a) + e^(4*a))*e^(4*b*x) + 2*(c^2*e^(2*a) - d^2*e^(2*a) + e^(2*a))*e^(2*b*x) + 1), x)","F",0
190,0,0,0,0.000000," ","integrate(arccot(c+d*tanh(b*x+a)),x, algorithm=""maxima"")","4 \, b d \int \frac{x e^{\left(2 \, b x + 2 \, a\right)}}{c^{2} - 2 \, c d + d^{2} + {\left(c^{2} e^{\left(4 \, a\right)} + 2 \, c d e^{\left(4 \, a\right)} + d^{2} e^{\left(4 \, a\right)} + e^{\left(4 \, a\right)}\right)} e^{\left(4 \, b x\right)} + 2 \, {\left(c^{2} e^{\left(2 \, a\right)} - d^{2} e^{\left(2 \, a\right)} + e^{\left(2 \, a\right)}\right)} e^{\left(2 \, b x\right)} + 1}\,{d x} + x \arctan\left(e^{\left(2 \, b x + 2 \, a\right)} + 1, {\left(c e^{\left(2 \, a\right)} + d e^{\left(2 \, a\right)}\right)} e^{\left(2 \, b x\right)} + c - d\right)"," ",0,"4*b*d*integrate(x*e^(2*b*x + 2*a)/(c^2 - 2*c*d + d^2 + (c^2*e^(4*a) + 2*c*d*e^(4*a) + d^2*e^(4*a) + e^(4*a))*e^(4*b*x) + 2*(c^2*e^(2*a) - d^2*e^(2*a) + e^(2*a))*e^(2*b*x) + 1), x) + x*arctan2(e^(2*b*x + 2*a) + 1, (c*e^(2*a) + d*e^(2*a))*e^(2*b*x) + c - d)","F",0
191,0,0,0,0.000000," ","integrate(arccot(c+d*tanh(b*x+a))/x,x, algorithm=""maxima"")","\int \frac{\operatorname{arccot}\left(d \tanh\left(b x + a\right) + c\right)}{x}\,{d x}"," ",0,"integrate(arccot(d*tanh(b*x + a) + c)/x, x)","F",0
192,1,129,0,2.100040," ","integrate(x^2*arccot(c+(I+c)*tanh(b*x+a)),x, algorithm=""maxima"")","\frac{1}{3} \, x^{3} \operatorname{arccot}\left({\left(c + i\right)} \tanh\left(b x + a\right) + c\right) - \frac{4}{9} \, {\left(\frac{3 \, x^{4}}{4 i \, c - 4} - \frac{4 \, b^{3} x^{3} \log\left(i \, c e^{\left(2 \, b x + 2 \, a\right)} + 1\right) + 6 \, b^{2} x^{2} {\rm Li}_2\left(-i \, c e^{\left(2 \, b x + 2 \, a\right)}\right) - 6 \, b x {\rm Li}_{3}(-i \, c e^{\left(2 \, b x + 2 \, a\right)}) + 3 \, {\rm Li}_{4}(-i \, c e^{\left(2 \, b x + 2 \, a\right)})}{-2 \, b^{4} {\left(-i \, c + 1\right)}}\right)} b {\left(c + i\right)}"," ",0,"1/3*x^3*arccot((c + I)*tanh(b*x + a) + c) - 4/9*(3*x^4/(4*I*c - 4) - (4*b^3*x^3*log(I*c*e^(2*b*x + 2*a) + 1) + 6*b^2*x^2*dilog(-I*c*e^(2*b*x + 2*a)) - 6*b*x*polylog(3, -I*c*e^(2*b*x + 2*a)) + 3*polylog(4, -I*c*e^(2*b*x + 2*a)))/(b^4*(2*I*c - 2)))*b*(c + I)","A",0
193,1,107,0,2.018669," ","integrate(x*arccot(c+(I+c)*tanh(b*x+a)),x, algorithm=""maxima"")","-{\left(\frac{2 \, x^{3}}{3 i \, c - 3} - \frac{2 \, b^{2} x^{2} \log\left(i \, c e^{\left(2 \, b x + 2 \, a\right)} + 1\right) + 2 \, b x {\rm Li}_2\left(-i \, c e^{\left(2 \, b x + 2 \, a\right)}\right) - {\rm Li}_{3}(-i \, c e^{\left(2 \, b x + 2 \, a\right)})}{-2 \, b^{3} {\left(-i \, c + 1\right)}}\right)} b {\left(c + i\right)} + \frac{1}{2} \, x^{2} \operatorname{arccot}\left({\left(c + i\right)} \tanh\left(b x + a\right) + c\right)"," ",0,"-(2*x^3/(3*I*c - 3) - (2*b^2*x^2*log(I*c*e^(2*b*x + 2*a) + 1) + 2*b*x*dilog(-I*c*e^(2*b*x + 2*a)) - polylog(3, -I*c*e^(2*b*x + 2*a)))/(b^3*(2*I*c - 2)))*b*(c + I) + 1/2*x^2*arccot((c + I)*tanh(b*x + a) + c)","A",0
194,1,80,0,1.988883," ","integrate(arccot(c+(I+c)*tanh(b*x+a)),x, algorithm=""maxima"")","-2 \, b {\left(c + i\right)} {\left(\frac{2 \, x^{2}}{2 i \, c - 2} - \frac{2 \, b x \log\left(i \, c e^{\left(2 \, b x + 2 \, a\right)} + 1\right) + {\rm Li}_2\left(-i \, c e^{\left(2 \, b x + 2 \, a\right)}\right)}{-2 \, b^{2} {\left(-i \, c + 1\right)}}\right)} + x \operatorname{arccot}\left({\left(c + i\right)} \tanh\left(b x + a\right) + c\right)"," ",0,"-2*b*(c + I)*(2*x^2/(2*I*c - 2) - (2*b*x*log(I*c*e^(2*b*x + 2*a) + 1) + dilog(-I*c*e^(2*b*x + 2*a)))/(b^2*(2*I*c - 2))) + x*arccot((c + I)*tanh(b*x + a) + c)","A",0
195,0,0,0,0.000000," ","integrate(arccot(c+(I+c)*tanh(b*x+a))/x,x, algorithm=""maxima"")","-i \, b x - \frac{1}{2} \, \pi \log\left(x\right) - \frac{1}{4} \, {\left(2 \, \pi + 4 i \, a - 2 \, \arctan\left(\frac{1}{c}\right) + i \, \log\left(c^{2} + 1\right)\right)} \log\left(x\right) + \frac{1}{2} \, \int \frac{\arctan\left(\frac{e^{\left(-2 \, b x - 2 \, a\right)}}{c}\right)}{x}\,{d x} + \frac{1}{4} i \, \int \frac{\log\left(c^{2} e^{\left(4 \, b x + 4 \, a\right)} + 1\right)}{x}\,{d x}"," ",0,"-I*b*x - 1/2*pi*log(x) - 1/4*(2*pi + 4*I*a - 2*arctan(1/c) + I*log(c^2 + 1))*log(x) + 1/2*integrate(arctan(e^(-2*b*x - 2*a)/c)/x, x) + 1/4*I*integrate(log(c^2*e^(4*b*x + 4*a) + 1)/x, x)","F",0
196,1,129,0,2.002946," ","integrate(x^2*arccot(c-(I-c)*tanh(b*x+a)),x, algorithm=""maxima"")","\frac{1}{3} \, x^{3} \operatorname{arccot}\left({\left(c - i\right)} \tanh\left(b x + a\right) + c\right) + \frac{4}{9} \, {\left(\frac{3 \, x^{4}}{4 i \, c + 4} - \frac{4 \, b^{3} x^{3} \log\left(-i \, c e^{\left(2 \, b x + 2 \, a\right)} + 1\right) + 6 \, b^{2} x^{2} {\rm Li}_2\left(i \, c e^{\left(2 \, b x + 2 \, a\right)}\right) - 6 \, b x {\rm Li}_{3}(i \, c e^{\left(2 \, b x + 2 \, a\right)}) + 3 \, {\rm Li}_{4}(i \, c e^{\left(2 \, b x + 2 \, a\right)})}{-2 \, b^{4} {\left(-i \, c - 1\right)}}\right)} b {\left(c - i\right)}"," ",0,"1/3*x^3*arccot((c - I)*tanh(b*x + a) + c) + 4/9*(3*x^4/(4*I*c + 4) - (4*b^3*x^3*log(-I*c*e^(2*b*x + 2*a) + 1) + 6*b^2*x^2*dilog(I*c*e^(2*b*x + 2*a)) - 6*b*x*polylog(3, I*c*e^(2*b*x + 2*a)) + 3*polylog(4, I*c*e^(2*b*x + 2*a)))/(b^4*(2*I*c + 2)))*b*(c - I)","A",0
197,1,106,0,2.015123," ","integrate(x*arccot(c-(I-c)*tanh(b*x+a)),x, algorithm=""maxima"")","{\left(\frac{2 \, x^{3}}{3 i \, c + 3} - \frac{2 \, b^{2} x^{2} \log\left(-i \, c e^{\left(2 \, b x + 2 \, a\right)} + 1\right) + 2 \, b x {\rm Li}_2\left(i \, c e^{\left(2 \, b x + 2 \, a\right)}\right) - {\rm Li}_{3}(i \, c e^{\left(2 \, b x + 2 \, a\right)})}{-2 \, b^{3} {\left(-i \, c - 1\right)}}\right)} b {\left(c - i\right)} + \frac{1}{2} \, x^{2} \operatorname{arccot}\left({\left(c - i\right)} \tanh\left(b x + a\right) + c\right)"," ",0,"(2*x^3/(3*I*c + 3) - (2*b^2*x^2*log(-I*c*e^(2*b*x + 2*a) + 1) + 2*b*x*dilog(I*c*e^(2*b*x + 2*a)) - polylog(3, I*c*e^(2*b*x + 2*a)))/(b^3*(2*I*c + 2)))*b*(c - I) + 1/2*x^2*arccot((c - I)*tanh(b*x + a) + c)","A",0
198,1,80,0,2.006398," ","integrate(arccot(c-(I-c)*tanh(b*x+a)),x, algorithm=""maxima"")","2 \, b {\left(c - i\right)} {\left(\frac{2 \, x^{2}}{2 i \, c + 2} - \frac{2 \, b x \log\left(-i \, c e^{\left(2 \, b x + 2 \, a\right)} + 1\right) + {\rm Li}_2\left(i \, c e^{\left(2 \, b x + 2 \, a\right)}\right)}{-2 \, b^{2} {\left(-i \, c - 1\right)}}\right)} + x \operatorname{arccot}\left({\left(c - i\right)} \tanh\left(b x + a\right) + c\right)"," ",0,"2*b*(c - I)*(2*x^2/(2*I*c + 2) - (2*b*x*log(-I*c*e^(2*b*x + 2*a) + 1) + dilog(I*c*e^(2*b*x + 2*a)))/(b^2*(2*I*c + 2))) + x*arccot((c - I)*tanh(b*x + a) + c)","A",0
199,0,0,0,0.000000," ","integrate(arccot(c-(I-c)*tanh(b*x+a))/x,x, algorithm=""maxima"")","i \, b x - \frac{1}{4} \, {\left(-4 i \, a - 2 \, \arctan\left(\frac{1}{c}\right) - i \, \log\left(c^{2} + 1\right)\right)} \log\left(x\right) + \frac{1}{2} \, \int \frac{\arctan\left(\frac{e^{\left(-2 \, b x - 2 \, a\right)}}{c}\right)}{x}\,{d x} - \frac{1}{4} i \, \int \frac{\log\left(c^{2} e^{\left(4 \, b x + 4 \, a\right)} + 1\right)}{x}\,{d x}"," ",0,"I*b*x - 1/4*(-4*I*a - 2*arctan(1/c) - I*log(c^2 + 1))*log(x) + 1/2*integrate(arctan(e^(-2*b*x - 2*a)/c)/x, x) - 1/4*I*integrate(log(c^2*e^(4*b*x + 4*a) + 1)/x, x)","F",0
200,0,0,0,0.000000," ","integrate((f*x+e)^3*arccot(coth(b*x+a)),x, algorithm=""maxima"")","\frac{1}{4} \, {\left(f^{3} x^{4} + 4 \, e f^{2} x^{3} + 6 \, e^{2} f x^{2} + 4 \, e^{3} x\right)} \arctan\left(\frac{e^{\left(2 \, b x + 2 \, a\right)} - 1}{e^{\left(2 \, b x + 2 \, a\right)} + 1}\right) - \int \frac{{\left(b f^{3} x^{4} e^{\left(2 \, a\right)} + 4 \, b e f^{2} x^{3} e^{\left(2 \, a\right)} + 6 \, b e^{2} f x^{2} e^{\left(2 \, a\right)} + 4 \, b e^{3} x e^{\left(2 \, a\right)}\right)} e^{\left(2 \, b x\right)}}{2 \, {\left(e^{\left(4 \, b x + 4 \, a\right)} + 1\right)}}\,{d x}"," ",0,"1/4*(f^3*x^4 + 4*e*f^2*x^3 + 6*e^2*f*x^2 + 4*e^3*x)*arctan((e^(2*b*x + 2*a) - 1)/(e^(2*b*x + 2*a) + 1)) - integrate(1/2*(b*f^3*x^4*e^(2*a) + 4*b*e*f^2*x^3*e^(2*a) + 6*b*e^2*f*x^2*e^(2*a) + 4*b*e^3*x*e^(2*a))*e^(2*b*x)/(e^(4*b*x + 4*a) + 1), x)","F",0
201,0,0,0,0.000000," ","integrate((f*x+e)^2*arccot(coth(b*x+a)),x, algorithm=""maxima"")","\frac{1}{3} \, {\left(f^{2} x^{3} + 3 \, e f x^{2} + 3 \, e^{2} x\right)} \arctan\left(\frac{e^{\left(2 \, b x + 2 \, a\right)} - 1}{e^{\left(2 \, b x + 2 \, a\right)} + 1}\right) - \int \frac{2 \, {\left(b f^{2} x^{3} e^{\left(2 \, a\right)} + 3 \, b e f x^{2} e^{\left(2 \, a\right)} + 3 \, b e^{2} x e^{\left(2 \, a\right)}\right)} e^{\left(2 \, b x\right)}}{3 \, {\left(e^{\left(4 \, b x + 4 \, a\right)} + 1\right)}}\,{d x}"," ",0,"1/3*(f^2*x^3 + 3*e*f*x^2 + 3*e^2*x)*arctan((e^(2*b*x + 2*a) - 1)/(e^(2*b*x + 2*a) + 1)) - integrate(2/3*(b*f^2*x^3*e^(2*a) + 3*b*e*f*x^2*e^(2*a) + 3*b*e^2*x*e^(2*a))*e^(2*b*x)/(e^(4*b*x + 4*a) + 1), x)","F",0
202,0,0,0,0.000000," ","integrate((f*x+e)*arccot(coth(b*x+a)),x, algorithm=""maxima"")","\frac{1}{2} \, {\left(f x^{2} + 2 \, e x\right)} \arctan\left(\frac{e^{\left(2 \, b x + 2 \, a\right)} - 1}{e^{\left(2 \, b x + 2 \, a\right)} + 1}\right) - \int \frac{{\left(b f x^{2} e^{\left(2 \, a\right)} + 2 \, b e x e^{\left(2 \, a\right)}\right)} e^{\left(2 \, b x\right)}}{e^{\left(4 \, b x + 4 \, a\right)} + 1}\,{d x}"," ",0,"1/2*(f*x^2 + 2*e*x)*arctan((e^(2*b*x + 2*a) - 1)/(e^(2*b*x + 2*a) + 1)) - integrate((b*f*x^2*e^(2*a) + 2*b*e*x*e^(2*a))*e^(2*b*x)/(e^(4*b*x + 4*a) + 1), x)","F",0
203,0,0,0,0.000000," ","integrate(arccot(coth(b*x+a)),x, algorithm=""maxima"")","x \arctan\left(\frac{e^{\left(2 \, b x + 2 \, a\right)} - 1}{e^{\left(2 \, b x + 2 \, a\right)} + 1}\right) - 2 \, b \int \frac{x e^{\left(2 \, b x + 2 \, a\right)}}{e^{\left(4 \, b x + 4 \, a\right)} + 1}\,{d x}"," ",0,"x*arctan((e^(2*b*x + 2*a) - 1)/(e^(2*b*x + 2*a) + 1)) - 2*b*integrate(x*e^(2*b*x + 2*a)/(e^(4*b*x + 4*a) + 1), x)","F",0
204,0,0,0,0.000000," ","integrate(arccot(coth(b*x+a))/(f*x+e),x, algorithm=""maxima"")","\int \frac{\operatorname{arccot}\left(\coth\left(b x + a\right)\right)}{f x + e}\,{d x}"," ",0,"integrate(arccot(coth(b*x + a))/(f*x + e), x)","F",0
205,0,0,0,0.000000," ","integrate(x^2*arccot(c+d*coth(b*x+a)),x, algorithm=""maxima"")","\frac{1}{3} \, x^{3} \arctan\left(e^{\left(2 \, b x + 2 \, a\right)} - 1, {\left(c e^{\left(2 \, a\right)} + d e^{\left(2 \, a\right)}\right)} e^{\left(2 \, b x\right)} - c + d\right) - 4 \, b d \int \frac{x^{3} e^{\left(2 \, b x + 2 \, a\right)}}{3 \, {\left(c^{2} - 2 \, c d + d^{2} + {\left(c^{2} e^{\left(4 \, a\right)} + 2 \, c d e^{\left(4 \, a\right)} + d^{2} e^{\left(4 \, a\right)} + e^{\left(4 \, a\right)}\right)} e^{\left(4 \, b x\right)} - 2 \, {\left(c^{2} e^{\left(2 \, a\right)} - d^{2} e^{\left(2 \, a\right)} + e^{\left(2 \, a\right)}\right)} e^{\left(2 \, b x\right)} + 1\right)}}\,{d x}"," ",0,"1/3*x^3*arctan2(e^(2*b*x + 2*a) - 1, (c*e^(2*a) + d*e^(2*a))*e^(2*b*x) - c + d) - 4*b*d*integrate(1/3*x^3*e^(2*b*x + 2*a)/(c^2 - 2*c*d + d^2 + (c^2*e^(4*a) + 2*c*d*e^(4*a) + d^2*e^(4*a) + e^(4*a))*e^(4*b*x) - 2*(c^2*e^(2*a) - d^2*e^(2*a) + e^(2*a))*e^(2*b*x) + 1), x)","F",0
206,0,0,0,0.000000," ","integrate(x*arccot(c+d*coth(b*x+a)),x, algorithm=""maxima"")","\frac{1}{2} \, x^{2} \arctan\left(e^{\left(2 \, b x + 2 \, a\right)} - 1, {\left(c e^{\left(2 \, a\right)} + d e^{\left(2 \, a\right)}\right)} e^{\left(2 \, b x\right)} - c + d\right) - 2 \, b d \int \frac{x^{2} e^{\left(2 \, b x + 2 \, a\right)}}{c^{2} - 2 \, c d + d^{2} + {\left(c^{2} e^{\left(4 \, a\right)} + 2 \, c d e^{\left(4 \, a\right)} + d^{2} e^{\left(4 \, a\right)} + e^{\left(4 \, a\right)}\right)} e^{\left(4 \, b x\right)} - 2 \, {\left(c^{2} e^{\left(2 \, a\right)} - d^{2} e^{\left(2 \, a\right)} + e^{\left(2 \, a\right)}\right)} e^{\left(2 \, b x\right)} + 1}\,{d x}"," ",0,"1/2*x^2*arctan2(e^(2*b*x + 2*a) - 1, (c*e^(2*a) + d*e^(2*a))*e^(2*b*x) - c + d) - 2*b*d*integrate(x^2*e^(2*b*x + 2*a)/(c^2 - 2*c*d + d^2 + (c^2*e^(4*a) + 2*c*d*e^(4*a) + d^2*e^(4*a) + e^(4*a))*e^(4*b*x) - 2*(c^2*e^(2*a) - d^2*e^(2*a) + e^(2*a))*e^(2*b*x) + 1), x)","F",0
207,0,0,0,0.000000," ","integrate(arccot(c+d*coth(b*x+a)),x, algorithm=""maxima"")","-4 \, b d \int \frac{x e^{\left(2 \, b x + 2 \, a\right)}}{c^{2} - 2 \, c d + d^{2} + {\left(c^{2} e^{\left(4 \, a\right)} + 2 \, c d e^{\left(4 \, a\right)} + d^{2} e^{\left(4 \, a\right)} + e^{\left(4 \, a\right)}\right)} e^{\left(4 \, b x\right)} - 2 \, {\left(c^{2} e^{\left(2 \, a\right)} - d^{2} e^{\left(2 \, a\right)} + e^{\left(2 \, a\right)}\right)} e^{\left(2 \, b x\right)} + 1}\,{d x} + x \arctan\left(e^{\left(2 \, b x + 2 \, a\right)} - 1, {\left(c e^{\left(2 \, a\right)} + d e^{\left(2 \, a\right)}\right)} e^{\left(2 \, b x\right)} - c + d\right)"," ",0,"-4*b*d*integrate(x*e^(2*b*x + 2*a)/(c^2 - 2*c*d + d^2 + (c^2*e^(4*a) + 2*c*d*e^(4*a) + d^2*e^(4*a) + e^(4*a))*e^(4*b*x) - 2*(c^2*e^(2*a) - d^2*e^(2*a) + e^(2*a))*e^(2*b*x) + 1), x) + x*arctan2(e^(2*b*x + 2*a) - 1, (c*e^(2*a) + d*e^(2*a))*e^(2*b*x) - c + d)","F",0
208,0,0,0,0.000000," ","integrate(arccot(c+d*coth(b*x+a))/x,x, algorithm=""maxima"")","\int \frac{\operatorname{arccot}\left(d \coth\left(b x + a\right) + c\right)}{x}\,{d x}"," ",0,"integrate(arccot(d*coth(b*x + a) + c)/x, x)","F",0
209,1,129,0,2.009942," ","integrate(x^2*arccot(c+(I+c)*coth(b*x+a)),x, algorithm=""maxima"")","\frac{1}{3} \, x^{3} \operatorname{arccot}\left({\left(c + i\right)} \coth\left(b x + a\right) + c\right) - \frac{4}{9} \, {\left(\frac{3 \, x^{4}}{4 i \, c - 4} - \frac{4 \, b^{3} x^{3} \log\left(-i \, c e^{\left(2 \, b x + 2 \, a\right)} + 1\right) + 6 \, b^{2} x^{2} {\rm Li}_2\left(i \, c e^{\left(2 \, b x + 2 \, a\right)}\right) - 6 \, b x {\rm Li}_{3}(i \, c e^{\left(2 \, b x + 2 \, a\right)}) + 3 \, {\rm Li}_{4}(i \, c e^{\left(2 \, b x + 2 \, a\right)})}{-2 \, b^{4} {\left(-i \, c + 1\right)}}\right)} b {\left(c + i\right)}"," ",0,"1/3*x^3*arccot((c + I)*coth(b*x + a) + c) - 4/9*(3*x^4/(4*I*c - 4) - (4*b^3*x^3*log(-I*c*e^(2*b*x + 2*a) + 1) + 6*b^2*x^2*dilog(I*c*e^(2*b*x + 2*a)) - 6*b*x*polylog(3, I*c*e^(2*b*x + 2*a)) + 3*polylog(4, I*c*e^(2*b*x + 2*a)))/(b^4*(2*I*c - 2)))*b*(c + I)","A",0
210,1,107,0,1.977201," ","integrate(x*arccot(c+(I+c)*coth(b*x+a)),x, algorithm=""maxima"")","-{\left(\frac{2 \, x^{3}}{3 i \, c - 3} - \frac{2 \, b^{2} x^{2} \log\left(-i \, c e^{\left(2 \, b x + 2 \, a\right)} + 1\right) + 2 \, b x {\rm Li}_2\left(i \, c e^{\left(2 \, b x + 2 \, a\right)}\right) - {\rm Li}_{3}(i \, c e^{\left(2 \, b x + 2 \, a\right)})}{-2 \, b^{3} {\left(-i \, c + 1\right)}}\right)} b {\left(c + i\right)} + \frac{1}{2} \, x^{2} \operatorname{arccot}\left({\left(c + i\right)} \coth\left(b x + a\right) + c\right)"," ",0,"-(2*x^3/(3*I*c - 3) - (2*b^2*x^2*log(-I*c*e^(2*b*x + 2*a) + 1) + 2*b*x*dilog(I*c*e^(2*b*x + 2*a)) - polylog(3, I*c*e^(2*b*x + 2*a)))/(b^3*(2*I*c - 2)))*b*(c + I) + 1/2*x^2*arccot((c + I)*coth(b*x + a) + c)","A",0
211,1,80,0,2.008280," ","integrate(arccot(c+(I+c)*coth(b*x+a)),x, algorithm=""maxima"")","-2 \, b {\left(c + i\right)} {\left(\frac{2 \, x^{2}}{2 i \, c - 2} - \frac{2 \, b x \log\left(-i \, c e^{\left(2 \, b x + 2 \, a\right)} + 1\right) + {\rm Li}_2\left(i \, c e^{\left(2 \, b x + 2 \, a\right)}\right)}{-2 \, b^{2} {\left(-i \, c + 1\right)}}\right)} + x \operatorname{arccot}\left({\left(c + i\right)} \coth\left(b x + a\right) + c\right)"," ",0,"-2*b*(c + I)*(2*x^2/(2*I*c - 2) - (2*b*x*log(-I*c*e^(2*b*x + 2*a) + 1) + dilog(I*c*e^(2*b*x + 2*a)))/(b^2*(2*I*c - 2))) + x*arccot((c + I)*coth(b*x + a) + c)","A",0
212,0,0,0,0.000000," ","integrate(arccot(c+(I+c)*coth(b*x+a))/x,x, algorithm=""maxima"")","-i \, b x + \frac{1}{4} \, {\left(-4 i \, a + 2 \, \arctan\left(\frac{1}{c}\right) - i \, \log\left(c^{2} + 1\right)\right)} \log\left(x\right) - \frac{1}{2} \, \int \frac{\arctan\left(\frac{e^{\left(-2 \, b x - 2 \, a\right)}}{c}\right)}{x}\,{d x} + \frac{1}{4} i \, \int \frac{\log\left(c^{2} e^{\left(4 \, b x + 4 \, a\right)} + 1\right)}{x}\,{d x}"," ",0,"-I*b*x + 1/4*(-4*I*a + 2*arctan(1/c) - I*log(c^2 + 1))*log(x) - 1/2*integrate(arctan(e^(-2*b*x - 2*a)/c)/x, x) + 1/4*I*integrate(log(c^2*e^(4*b*x + 4*a) + 1)/x, x)","F",0
213,1,129,0,2.012156," ","integrate(x^2*arccot(c-(I-c)*coth(b*x+a)),x, algorithm=""maxima"")","\frac{1}{3} \, x^{3} \operatorname{arccot}\left({\left(c - i\right)} \coth\left(b x + a\right) + c\right) + \frac{4}{9} \, {\left(\frac{3 \, x^{4}}{4 i \, c + 4} - \frac{4 \, b^{3} x^{3} \log\left(i \, c e^{\left(2 \, b x + 2 \, a\right)} + 1\right) + 6 \, b^{2} x^{2} {\rm Li}_2\left(-i \, c e^{\left(2 \, b x + 2 \, a\right)}\right) - 6 \, b x {\rm Li}_{3}(-i \, c e^{\left(2 \, b x + 2 \, a\right)}) + 3 \, {\rm Li}_{4}(-i \, c e^{\left(2 \, b x + 2 \, a\right)})}{-2 \, b^{4} {\left(-i \, c - 1\right)}}\right)} b {\left(c - i\right)}"," ",0,"1/3*x^3*arccot((c - I)*coth(b*x + a) + c) + 4/9*(3*x^4/(4*I*c + 4) - (4*b^3*x^3*log(I*c*e^(2*b*x + 2*a) + 1) + 6*b^2*x^2*dilog(-I*c*e^(2*b*x + 2*a)) - 6*b*x*polylog(3, -I*c*e^(2*b*x + 2*a)) + 3*polylog(4, -I*c*e^(2*b*x + 2*a)))/(b^4*(2*I*c + 2)))*b*(c - I)","A",0
214,1,106,0,2.005535," ","integrate(x*arccot(c-(I-c)*coth(b*x+a)),x, algorithm=""maxima"")","{\left(\frac{2 \, x^{3}}{3 i \, c + 3} - \frac{2 \, b^{2} x^{2} \log\left(i \, c e^{\left(2 \, b x + 2 \, a\right)} + 1\right) + 2 \, b x {\rm Li}_2\left(-i \, c e^{\left(2 \, b x + 2 \, a\right)}\right) - {\rm Li}_{3}(-i \, c e^{\left(2 \, b x + 2 \, a\right)})}{-2 \, b^{3} {\left(-i \, c - 1\right)}}\right)} b {\left(c - i\right)} + \frac{1}{2} \, x^{2} \operatorname{arccot}\left({\left(c - i\right)} \coth\left(b x + a\right) + c\right)"," ",0,"(2*x^3/(3*I*c + 3) - (2*b^2*x^2*log(I*c*e^(2*b*x + 2*a) + 1) + 2*b*x*dilog(-I*c*e^(2*b*x + 2*a)) - polylog(3, -I*c*e^(2*b*x + 2*a)))/(b^3*(2*I*c + 2)))*b*(c - I) + 1/2*x^2*arccot((c - I)*coth(b*x + a) + c)","A",0
215,1,80,0,2.031616," ","integrate(arccot(c-(I-c)*coth(b*x+a)),x, algorithm=""maxima"")","2 \, b {\left(c - i\right)} {\left(\frac{2 \, x^{2}}{2 i \, c + 2} - \frac{2 \, b x \log\left(i \, c e^{\left(2 \, b x + 2 \, a\right)} + 1\right) + {\rm Li}_2\left(-i \, c e^{\left(2 \, b x + 2 \, a\right)}\right)}{-2 \, b^{2} {\left(-i \, c - 1\right)}}\right)} + x \operatorname{arccot}\left({\left(c - i\right)} \coth\left(b x + a\right) + c\right)"," ",0,"2*b*(c - I)*(2*x^2/(2*I*c + 2) - (2*b*x*log(I*c*e^(2*b*x + 2*a) + 1) + dilog(-I*c*e^(2*b*x + 2*a)))/(b^2*(2*I*c + 2))) + x*arccot((c - I)*coth(b*x + a) + c)","A",0
216,0,0,0,0.000000," ","integrate(arccot(c-(I-c)*coth(b*x+a))/x,x, algorithm=""maxima"")","i \, b x + \frac{1}{2} \, \pi \log\left(x\right) - \frac{1}{4} \, {\left(2 \, \pi - 4 i \, a - 2 \, \arctan\left(\frac{1}{c}\right) - i \, \log\left(c^{2} + 1\right)\right)} \log\left(x\right) - \frac{1}{2} \, \int \frac{\arctan\left(\frac{e^{\left(-2 \, b x - 2 \, a\right)}}{c}\right)}{x}\,{d x} - \frac{1}{4} i \, \int \frac{\log\left(c^{2} e^{\left(4 \, b x + 4 \, a\right)} + 1\right)}{x}\,{d x}"," ",0,"I*b*x + 1/2*pi*log(x) - 1/4*(2*pi - 4*I*a - 2*arctan(1/c) - I*log(c^2 + 1))*log(x) - 1/2*integrate(arctan(e^(-2*b*x - 2*a)/c)/x, x) - 1/4*I*integrate(log(c^2*e^(4*b*x + 4*a) + 1)/x, x)","F",0
217,0,0,0,0.000000," ","integrate((a+b*arccot(c*x^n))*(d+e*log(f*x^m))/x,x, algorithm=""maxima"")","\frac{a e \log\left(f x^{m}\right)^{2}}{2 \, m} + a d \log\left(x\right) - \frac{1}{2} \, {\left(b e m \log\left(x\right)^{2} - 2 \, b e \log\left(x\right) \log\left(x^{m}\right) - 2 \, {\left(b e \log\left(f\right) + b d\right)} \log\left(x\right)\right)} \arctan\left(\frac{1}{c x^{n}}\right) + \int -\frac{b c e m n x^{n} \log\left(x\right)^{2} - 2 \, b c e n x^{n} \log\left(x\right) \log\left(x^{m}\right) - 2 \, {\left(b c e \log\left(f\right) + b c d\right)} n x^{n} \log\left(x\right)}{2 \, {\left(c^{2} x x^{2 \, n} + x\right)}}\,{d x}"," ",0,"1/2*a*e*log(f*x^m)^2/m + a*d*log(x) - 1/2*(b*e*m*log(x)^2 - 2*b*e*log(x)*log(x^m) - 2*(b*e*log(f) + b*d)*log(x))*arctan(1/(c*x^n)) + integrate(-1/2*(b*c*e*m*n*x^n*log(x)^2 - 2*b*c*e*n*x^n*log(x)*log(x^m) - 2*(b*c*e*log(f) + b*c*d)*n*x^n*log(x))/(c^2*x*x^(2*n) + x), x)","F",0
218,1,34,0,0.454686," ","integrate(arccot(exp(x)),x, algorithm=""maxima"")","x \operatorname{arccot}\left(e^{x}\right) + \frac{1}{4} \, \pi \log\left(e^{\left(2 \, x\right)} + 1\right) + \frac{1}{2} i \, {\rm Li}_2\left(i \, e^{x} + 1\right) - \frac{1}{2} i \, {\rm Li}_2\left(-i \, e^{x} + 1\right)"," ",0,"x*arccot(e^x) + 1/4*pi*log(e^(2*x) + 1) + 1/2*I*dilog(I*e^x + 1) - 1/2*I*dilog(-I*e^x + 1)","A",0
219,0,0,0,0.000000," ","integrate(x*arccot(exp(x)),x, algorithm=""maxima"")","\frac{1}{2} \, x^{2} \arctan\left(e^{\left(-x\right)}\right) + \int \frac{x^{2} e^{x}}{2 \, {\left(e^{\left(2 \, x\right)} + 1\right)}}\,{d x}"," ",0,"1/2*x^2*arctan(e^(-x)) + integrate(1/2*x^2*e^x/(e^(2*x) + 1), x)","F",0
220,0,0,0,0.000000," ","integrate(x^2*arccot(exp(x)),x, algorithm=""maxima"")","\frac{1}{3} \, x^{3} \arctan\left(e^{\left(-x\right)}\right) + \int \frac{x^{3} e^{x}}{3 \, {\left(e^{\left(2 \, x\right)} + 1\right)}}\,{d x}"," ",0,"1/3*x^3*arctan(e^(-x)) + integrate(1/3*x^3*e^x/(e^(2*x) + 1), x)","F",0
221,1,63,0,0.463105," ","integrate(arccot(exp(b*x+a)),x, algorithm=""maxima"")","\frac{{\left(b x + a\right)} \operatorname{arccot}\left(e^{\left(b x + a\right)}\right)}{b} + \frac{\pi \log\left(e^{\left(2 \, b x + 2 \, a\right)} + 1\right) + 2 i \, {\rm Li}_2\left(i \, e^{\left(b x + a\right)} + 1\right) - 2 i \, {\rm Li}_2\left(-i \, e^{\left(b x + a\right)} + 1\right)}{4 \, b}"," ",0,"(b*x + a)*arccot(e^(b*x + a))/b + 1/4*(pi*log(e^(2*b*x + 2*a) + 1) + 2*I*dilog(I*e^(b*x + a) + 1) - 2*I*dilog(-I*e^(b*x + a) + 1))/b","A",0
222,0,0,0,0.000000," ","integrate(x*arccot(exp(b*x+a)),x, algorithm=""maxima"")","\frac{1}{2} \, x^{2} \arctan\left(e^{\left(-b x - a\right)}\right) + b \int \frac{x^{2} e^{\left(b x + a\right)}}{2 \, {\left(e^{\left(2 \, b x + 2 \, a\right)} + 1\right)}}\,{d x}"," ",0,"1/2*x^2*arctan(e^(-b*x - a)) + b*integrate(1/2*x^2*e^(b*x + a)/(e^(2*b*x + 2*a) + 1), x)","F",0
223,0,0,0,0.000000," ","integrate(x^2*arccot(exp(b*x+a)),x, algorithm=""maxima"")","\frac{1}{3} \, x^{3} \arctan\left(e^{\left(-b x - a\right)}\right) + b \int \frac{x^{3} e^{\left(b x + a\right)}}{3 \, {\left(e^{\left(2 \, b x + 2 \, a\right)} + 1\right)}}\,{d x}"," ",0,"1/3*x^3*arctan(e^(-b*x - a)) + b*integrate(1/3*x^3*e^(b*x + a)/(e^(2*b*x + 2*a) + 1), x)","F",0
224,1,189,0,0.513631," ","integrate(arccot(a+b*f^(d*x+c)),x, algorithm=""maxima"")","\frac{{\left(d x + c\right)} \operatorname{arccot}\left(b f^{d x + c} + a\right)}{d} + \frac{2 \, {\left(d x + c\right)} \arctan\left(\frac{b^{2} f^{d x + c} + a b}{b}\right) \log\left(f\right) + {\left(\pi - \arctan\left(\frac{1}{a}\right)\right)} \log\left(b^{2} f^{2 \, d x + 2 \, c} + 2 \, a b f^{d x + c} + a^{2} + 1\right) - \arctan\left(b f^{d x + c} + a\right) \log\left(\frac{b^{2} f^{2 \, d x + 2 \, c}}{a^{2} + 1}\right) + i \, {\rm Li}_2\left(\frac{i \, b f^{d x + c} + i \, a + 1}{i \, a + 1}\right) - i \, {\rm Li}_2\left(\frac{i \, b f^{d x + c} + i \, a - 1}{i \, a - 1}\right)}{2 \, d \log\left(f\right)}"," ",0,"(d*x + c)*arccot(b*f^(d*x + c) + a)/d + 1/2*(2*(d*x + c)*arctan((b^2*f^(d*x + c) + a*b)/b)*log(f) + (pi - arctan(1/a))*log(b^2*f^(2*d*x + 2*c) + 2*a*b*f^(d*x + c) + a^2 + 1) - arctan(b*f^(d*x + c) + a)*log(b^2*f^(2*d*x + 2*c)/(a^2 + 1)) + I*dilog((I*b*f^(d*x + c) + I*a + 1)/(I*a + 1)) - I*dilog((I*b*f^(d*x + c) + I*a - 1)/(I*a - 1)))/(d*log(f))","A",0
225,0,0,0,0.000000," ","integrate(x*arccot(a+b*f^(d*x+c)),x, algorithm=""maxima"")","b d f^{c} \int \frac{f^{d x} x^{2}}{2 \, {\left(b^{2} f^{2 \, d x} f^{2 \, c} + 2 \, a b f^{d x} f^{c} + a^{2} + 1\right)}}\,{d x} \log\left(f\right) + \frac{1}{2} \, x^{2} \arctan\left(\frac{1}{b f^{d x} f^{c} + a}\right)"," ",0,"b*d*f^c*integrate(1/2*f^(d*x)*x^2/(b^2*f^(2*d*x)*f^(2*c) + 2*a*b*f^(d*x)*f^c + a^2 + 1), x)*log(f) + 1/2*x^2*arctan(1/(b*f^(d*x)*f^c + a))","F",0
226,0,0,0,0.000000," ","integrate(x^2*arccot(a+b*f^(d*x+c)),x, algorithm=""maxima"")","b d f^{c} \int \frac{f^{d x} x^{3}}{3 \, {\left(b^{2} f^{2 \, d x} f^{2 \, c} + 2 \, a b f^{d x} f^{c} + a^{2} + 1\right)}}\,{d x} \log\left(f\right) + \frac{1}{3} \, x^{3} \arctan\left(\frac{1}{b f^{d x} f^{c} + a}\right)"," ",0,"b*d*f^c*integrate(1/3*f^(d*x)*x^3/(b^2*f^(2*d*x)*f^(2*c) + 2*a*b*f^(d*x)*f^c + a^2 + 1), x)*log(f) + 1/3*x^3*arctan(1/(b*f^(d*x)*f^c + a))","F",0
227,1,19,0,0.336580," ","integrate(arccot(exp(x))/exp(x),x, algorithm=""maxima"")","-\operatorname{arccot}\left(e^{x}\right) e^{\left(-x\right)} + \frac{1}{2} \, \log\left(e^{\left(-2 \, x\right)} + 1\right)"," ",0,"-arccot(e^x)*e^(-x) + 1/2*log(e^(-2*x) + 1)","A",0
228,1,17,0,0.356152," ","integrate(1/(a*x^2+a)/(b-2*b*arccot(x)),x, algorithm=""maxima"")","\frac{\log\left({\left| 2 \, \arctan\left(1, x\right) - 1 \right|}\right)}{2 \, a b}"," ",0,"1/2*log(abs(2*arctan2(1, x) - 1))/(a*b)","A",0
229,1,47,0,0.440738," ","integrate(exp(c*(b*x+a))*arccot(sinh(b*c*x+a*c)),x, algorithm=""maxima"")","\frac{\operatorname{arccot}\left(\sinh\left(b c x + a c\right)\right) e^{\left({\left(b x + a\right)} c\right)}}{b c} + \frac{\log\left(e^{\left(2 \, b c x + 2 \, a c\right)} + 1\right)}{b c}"," ",0,"arccot(sinh(b*c*x + a*c))*e^((b*x + a)*c)/(b*c) + log(e^(2*b*c*x + 2*a*c) + 1)/(b*c)","A",0
230,1,131,0,0.451369," ","integrate(exp(c*(b*x+a))*arccot(cosh(b*c*x+a*c)),x, algorithm=""maxima"")","\frac{\operatorname{arccot}\left(\cosh\left(b c x + a c\right)\right) e^{\left({\left(b x + a\right)} c\right)}}{b c} + \frac{\sqrt{2} \log\left(-\frac{2 \, \sqrt{2} - e^{\left(-2 \, b c x - 2 \, a c\right)} - 3}{2 \, \sqrt{2} + e^{\left(-2 \, b c x - 2 \, a c\right)} + 3}\right)}{2 \, b c} + \frac{2 \, {\left(b c x + a c\right)}}{b c} + \frac{\log\left(6 \, e^{\left(-2 \, b c x - 2 \, a c\right)} + e^{\left(-4 \, b c x - 4 \, a c\right)} + 1\right)}{2 \, b c}"," ",0,"arccot(cosh(b*c*x + a*c))*e^((b*x + a)*c)/(b*c) + 1/2*sqrt(2)*log(-(2*sqrt(2) - e^(-2*b*c*x - 2*a*c) - 3)/(2*sqrt(2) + e^(-2*b*c*x - 2*a*c) + 3))/(b*c) + 2*(b*c*x + a*c)/(b*c) + 1/2*log(6*e^(-2*b*c*x - 2*a*c) + e^(-4*b*c*x - 4*a*c) + 1)/(b*c)","A",0
231,1,167,0,0.431563," ","integrate(exp(c*(b*x+a))*arccot(tanh(b*c*x+a*c)),x, algorithm=""maxima"")","\frac{\operatorname{arccot}\left(\tanh\left(b c x + a c\right)\right) e^{\left({\left(b x + a\right)} c\right)}}{b c} + \frac{\sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + 2 \, e^{\left(b c x + a c\right)}\right)}\right)}{2 \, b c} + \frac{\sqrt{2} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - 2 \, e^{\left(b c x + a c\right)}\right)}\right)}{2 \, b c} - \frac{\sqrt{2} \log\left(\sqrt{2} e^{\left(b c x + a c\right)} + e^{\left(2 \, b c x + 2 \, a c\right)} + 1\right)}{4 \, b c} + \frac{\sqrt{2} \log\left(-\sqrt{2} e^{\left(b c x + a c\right)} + e^{\left(2 \, b c x + 2 \, a c\right)} + 1\right)}{4 \, b c}"," ",0,"arccot(tanh(b*c*x + a*c))*e^((b*x + a)*c)/(b*c) + 1/2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*e^(b*c*x + a*c)))/(b*c) + 1/2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*e^(b*c*x + a*c)))/(b*c) - 1/4*sqrt(2)*log(sqrt(2)*e^(b*c*x + a*c) + e^(2*b*c*x + 2*a*c) + 1)/(b*c) + 1/4*sqrt(2)*log(-sqrt(2)*e^(b*c*x + a*c) + e^(2*b*c*x + 2*a*c) + 1)/(b*c)","A",0
232,1,167,0,0.444689," ","integrate(exp(c*(b*x+a))*arccot(coth(b*c*x+a*c)),x, algorithm=""maxima"")","\frac{\operatorname{arccot}\left(\coth\left(b c x + a c\right)\right) e^{\left({\left(b x + a\right)} c\right)}}{b c} - \frac{\sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + 2 \, e^{\left(b c x + a c\right)}\right)}\right)}{2 \, b c} - \frac{\sqrt{2} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - 2 \, e^{\left(b c x + a c\right)}\right)}\right)}{2 \, b c} + \frac{\sqrt{2} \log\left(\sqrt{2} e^{\left(b c x + a c\right)} + e^{\left(2 \, b c x + 2 \, a c\right)} + 1\right)}{4 \, b c} - \frac{\sqrt{2} \log\left(-\sqrt{2} e^{\left(b c x + a c\right)} + e^{\left(2 \, b c x + 2 \, a c\right)} + 1\right)}{4 \, b c}"," ",0,"arccot(coth(b*c*x + a*c))*e^((b*x + a)*c)/(b*c) - 1/2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*e^(b*c*x + a*c)))/(b*c) - 1/2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*e^(b*c*x + a*c)))/(b*c) + 1/4*sqrt(2)*log(sqrt(2)*e^(b*c*x + a*c) + e^(2*b*c*x + 2*a*c) + 1)/(b*c) - 1/4*sqrt(2)*log(-sqrt(2)*e^(b*c*x + a*c) + e^(2*b*c*x + 2*a*c) + 1)/(b*c)","A",0
233,1,169,0,0.483224," ","integrate(exp(c*(b*x+a))*arccot(sech(b*c*x+a*c)),x, algorithm=""maxima"")","\frac{\operatorname{arccot}\left(\operatorname{sech}\left(b c x + a c\right)\right) e^{\left({\left(b x + a\right)} c\right)}}{b c} + \frac{3 \, \sqrt{2} \log\left(-\frac{2 \, \sqrt{2} - e^{\left(2 \, b c x + 2 \, a c\right)} - 3}{2 \, \sqrt{2} + e^{\left(2 \, b c x + 2 \, a c\right)} + 3}\right)}{8 \, b c} - \frac{\sqrt{2} \log\left(-\frac{2 \, \sqrt{2} - e^{\left(-2 \, b c x - 2 \, a c\right)} - 3}{2 \, \sqrt{2} + e^{\left(-2 \, b c x - 2 \, a c\right)} + 3}\right)}{8 \, b c} - \frac{\log\left(e^{\left(4 \, b c x + 4 \, a c\right)} + 6 \, e^{\left(2 \, b c x + 2 \, a c\right)} + 1\right)}{2 \, b c}"," ",0,"arccot(sech(b*c*x + a*c))*e^((b*x + a)*c)/(b*c) + 3/8*sqrt(2)*log(-(2*sqrt(2) - e^(2*b*c*x + 2*a*c) - 3)/(2*sqrt(2) + e^(2*b*c*x + 2*a*c) + 3))/(b*c) - 1/8*sqrt(2)*log(-(2*sqrt(2) - e^(-2*b*c*x - 2*a*c) - 3)/(2*sqrt(2) + e^(-2*b*c*x - 2*a*c) + 3))/(b*c) - 1/2*log(e^(4*b*c*x + 4*a*c) + 6*e^(2*b*c*x + 2*a*c) + 1)/(b*c)","A",0
234,1,48,0,0.435822," ","integrate(exp(c*(b*x+a))*arccot(csch(b*c*x+a*c)),x, algorithm=""maxima"")","\frac{\operatorname{arccot}\left(\operatorname{csch}\left(b c x + a c\right)\right) e^{\left({\left(b x + a\right)} c\right)}}{b c} - \frac{\log\left(e^{\left(2 \, b c x + 2 \, a c\right)} + 1\right)}{b c}"," ",0,"arccot(csch(b*c*x + a*c))*e^((b*x + a)*c)/(b*c) - log(e^(2*b*c*x + 2*a*c) + 1)/(b*c)","A",0
