1,1,59,0,0.128221," ","integrate(x^5*arccot(a*x),x, algorithm=""giac"")","\frac{1}{90} \, {\left(\frac{15 \, x^{6} \arctan\left(\frac{1}{a x}\right)}{a} - \frac{x^{5} {\left(\frac{5}{a^{2} x^{2}} - \frac{15}{a^{4} x^{4}} - 3\right)}}{a^{2}} + \frac{15 \, \arctan\left(\frac{1}{a x}\right)}{a^{7}}\right)} a"," ",0,"1/90*(15*x^6*arctan(1/(a*x))/a - x^5*(5/(a^2*x^2) - 15/(a^4*x^4) - 3)/a^2 + 15*arctan(1/(a*x))/a^7)*a","A",0
2,1,74,0,0.122720," ","integrate(x^4*arccot(a*x),x, algorithm=""giac"")","\frac{1}{20} \, {\left(\frac{4 \, x^{5} \arctan\left(\frac{1}{a x}\right)}{a} - \frac{x^{4} {\left(\frac{2}{a^{2} x^{2}} - \frac{3}{a^{4} x^{4}} - 1\right)}}{a^{2}} + \frac{2 \, \log\left(\frac{1}{a^{2} x^{2}} + 1\right)}{a^{6}} - \frac{2 \, \log\left(\frac{1}{a^{2} x^{2}}\right)}{a^{6}}\right)} a"," ",0,"1/20*(4*x^5*arctan(1/(a*x))/a - x^4*(2/(a^2*x^2) - 3/(a^4*x^4) - 1)/a^2 + 2*log(1/(a^2*x^2) + 1)/a^6 - 2*log(1/(a^2*x^2))/a^6)*a","A",0
3,1,51,0,0.128355," ","integrate(x^3*arccot(a*x),x, algorithm=""giac"")","\frac{1}{12} \, {\left(\frac{3 \, x^{4} \arctan\left(\frac{1}{a x}\right)}{a} - \frac{x^{3} {\left(\frac{3}{a^{2} x^{2}} - 1\right)}}{a^{2}} - \frac{3 \, \arctan\left(\frac{1}{a x}\right)}{a^{5}}\right)} a"," ",0,"1/12*(3*x^4*arctan(1/(a*x))/a - x^3*(3/(a^2*x^2) - 1)/a^2 - 3*arctan(1/(a*x))/a^5)*a","A",0
4,1,64,0,0.115295," ","integrate(x^2*arccot(a*x),x, algorithm=""giac"")","\frac{1}{6} \, {\left(\frac{2 \, x^{3} \arctan\left(\frac{1}{a x}\right)}{a} - \frac{x^{2} {\left(\frac{1}{a^{2} x^{2}} - 1\right)}}{a^{2}} - \frac{\log\left(\frac{1}{a^{2} x^{2}} + 1\right)}{a^{4}} + \frac{\log\left(\frac{1}{a^{2} x^{2}}\right)}{a^{4}}\right)} a"," ",0,"1/6*(2*x^3*arctan(1/(a*x))/a - x^2*(1/(a^2*x^2) - 1)/a^2 - log(1/(a^2*x^2) + 1)/a^4 + log(1/(a^2*x^2))/a^4)*a","A",0
5,1,36,0,0.131289," ","integrate(x*arccot(a*x),x, algorithm=""giac"")","\frac{1}{2} \, {\left(\frac{x^{2} \arctan\left(\frac{1}{a x}\right)}{a} + \frac{x}{a^{2}} + \frac{\arctan\left(\frac{1}{a x}\right)}{a^{3}}\right)} a"," ",0,"1/2*(x^2*arctan(1/(a*x))/a + x/a^2 + arctan(1/(a*x))/a^3)*a","A",0
6,1,45,0,0.108384," ","integrate(arccot(a*x),x, algorithm=""giac"")","\frac{1}{2} \, a {\left(\frac{2 \, x \arctan\left(\frac{1}{a x}\right)}{a} + \frac{\log\left(\frac{1}{a^{2} x^{2}} + 1\right)}{a^{2}} - \frac{\log\left(\frac{1}{a^{2} x^{2}}\right)}{a^{2}}\right)}"," ",0,"1/2*a*(2*x*arctan(1/(a*x))/a + log(1/(a^2*x^2) + 1)/a^2 - log(1/(a^2*x^2))/a^2)","B",0
7,1,38,0,0.127557," ","integrate(arccot(a*x)/x,x, algorithm=""giac"")","-\frac{1}{2} \, {\left(\frac{x^{2} \arctan\left(\frac{1}{a x}\right)}{a} + \frac{x}{a^{2}} + \frac{\arctan\left(\frac{1}{a x}\right)}{a^{3}}\right)} a^{2}"," ",0,"-1/2*(x^2*arctan(1/(a*x))/a + x/a^2 + arctan(1/(a*x))/a^3)*a^2","A",0
8,1,32,0,0.126434," ","integrate(arccot(a*x)/x^2,x, algorithm=""giac"")","-\frac{1}{2} \, a {\left(\frac{2 \, \arctan\left(\frac{1}{a x}\right)}{a x} - \log\left(\frac{1}{a^{2} x^{2}} + 1\right)\right)}"," ",0,"-1/2*a*(2*arctan(1/(a*x))/(a*x) - log(1/(a^2*x^2) + 1))","A",0
9,1,40,0,0.110584," ","integrate(arccot(a*x)/x^3,x, algorithm=""giac"")","\frac{1}{2} \, {\left(a {\left(\frac{1}{a x} - \arctan\left(\frac{1}{a x}\right)\right)} - \frac{\arctan\left(\frac{1}{a x}\right)}{a x^{2}}\right)} a"," ",0,"1/2*(a*(1/(a*x) - arctan(1/(a*x))) - arctan(1/(a*x))/(a*x^2))*a","A",0
10,1,44,0,0.126418," ","integrate(arccot(a*x)/x^4,x, algorithm=""giac"")","\frac{1}{6} \, {\left(a^{2} {\left(\frac{1}{a^{2} x^{2}} - \log\left(\frac{1}{a^{2} x^{2}} + 1\right)\right)} - \frac{2 \, \arctan\left(\frac{1}{a x}\right)}{a x^{3}}\right)} a"," ",0,"1/6*(a^2*(1/(a^2*x^2) - log(1/(a^2*x^2) + 1)) - 2*arctan(1/(a*x))/(a*x^3))*a","A",0
11,1,51,0,0.114864," ","integrate(arccot(a*x)/x^5,x, algorithm=""giac"")","-\frac{1}{12} \, {\left(a^{3} {\left(\frac{3}{a x} - \frac{1}{a^{3} x^{3}} - 3 \, \arctan\left(\frac{1}{a x}\right)\right)} + \frac{3 \, \arctan\left(\frac{1}{a x}\right)}{a x^{4}}\right)} a"," ",0,"-1/12*(a^3*(3/(a*x) - 1/(a^3*x^3) - 3*arctan(1/(a*x))) + 3*arctan(1/(a*x))/(a*x^4))*a","A",0
12,0,0,0,0.000000," ","integrate(x^5*arccot(a*x)^2,x, algorithm=""giac"")","\int x^{5} \operatorname{arccot}\left(a x\right)^{2}\,{d x}"," ",0,"integrate(x^5*arccot(a*x)^2, x)","F",0
13,0,0,0,0.000000," ","integrate(x^4*arccot(a*x)^2,x, algorithm=""giac"")","\int x^{4} \operatorname{arccot}\left(a x\right)^{2}\,{d x}"," ",0,"integrate(x^4*arccot(a*x)^2, x)","F",0
14,0,0,0,0.000000," ","integrate(x^3*arccot(a*x)^2,x, algorithm=""giac"")","\int x^{3} \operatorname{arccot}\left(a x\right)^{2}\,{d x}"," ",0,"integrate(x^3*arccot(a*x)^2, x)","F",0
15,0,0,0,0.000000," ","integrate(x^2*arccot(a*x)^2,x, algorithm=""giac"")","\int x^{2} \operatorname{arccot}\left(a x\right)^{2}\,{d x}"," ",0,"integrate(x^2*arccot(a*x)^2, x)","F",0
16,0,0,0,0.000000," ","integrate(x*arccot(a*x)^2,x, algorithm=""giac"")","\int x \operatorname{arccot}\left(a x\right)^{2}\,{d x}"," ",0,"integrate(x*arccot(a*x)^2, x)","F",0
17,0,0,0,0.000000," ","integrate(arccot(a*x)^2,x, algorithm=""giac"")","\int \operatorname{arccot}\left(a x\right)^{2}\,{d x}"," ",0,"integrate(arccot(a*x)^2, x)","F",0
18,0,0,0,0.000000," ","integrate(arccot(a*x)^2/x,x, algorithm=""giac"")","\int \frac{\operatorname{arccot}\left(a x\right)^{2}}{x}\,{d x}"," ",0,"integrate(arccot(a*x)^2/x, x)","F",0
19,0,0,0,0.000000," ","integrate(arccot(a*x)^2/x^2,x, algorithm=""giac"")","\int \frac{\operatorname{arccot}\left(a x\right)^{2}}{x^{2}}\,{d x}"," ",0,"integrate(arccot(a*x)^2/x^2, x)","F",0
20,1,60,0,0.122194," ","integrate(arccot(a*x)^2/x^3,x, algorithm=""giac"")","-\frac{1}{2} \, {\left({\left(\arctan\left(\frac{1}{a x}\right)^{2} - \frac{2 \, \arctan\left(\frac{1}{a x}\right)}{a x} + \log\left(\frac{1}{a^{2} x^{2}} + 1\right)\right)} a + \frac{\arctan\left(\frac{1}{a x}\right)^{2}}{a x^{2}}\right)} a"," ",0,"-1/2*((arctan(1/(a*x))^2 - 2*arctan(1/(a*x))/(a*x) + log(1/(a^2*x^2) + 1))*a + arctan(1/(a*x))^2/(a*x^2))*a","A",0
21,0,0,0,0.000000," ","integrate(arccot(a*x)^2/x^4,x, algorithm=""giac"")","\int \frac{\operatorname{arccot}\left(a x\right)^{2}}{x^{4}}\,{d x}"," ",0,"integrate(arccot(a*x)^2/x^4, x)","F",0
22,1,91,0,0.121353," ","integrate(arccot(a*x)^2/x^5,x, algorithm=""giac"")","\frac{1}{12} \, {\left({\left(3 \, \arctan\left(\frac{1}{a x}\right)^{2} - \frac{6 \, \arctan\left(\frac{1}{a x}\right)}{a x} - \frac{1}{a^{2} x^{2}} + \frac{2 \, \arctan\left(\frac{1}{a x}\right)}{a^{3} x^{3}} + 4 \, \log\left(\frac{1}{a^{2} x^{2}} + 1\right)\right)} a^{3} - \frac{3 \, \arctan\left(\frac{1}{a x}\right)^{2}}{a x^{4}}\right)} a"," ",0,"1/12*((3*arctan(1/(a*x))^2 - 6*arctan(1/(a*x))/(a*x) - 1/(a^2*x^2) + 2*arctan(1/(a*x))/(a^3*x^3) + 4*log(1/(a^2*x^2) + 1))*a^3 - 3*arctan(1/(a*x))^2/(a*x^4))*a","A",0
23,0,0,0,0.000000," ","integrate(x^5*arccot(a*x)^3,x, algorithm=""giac"")","\int x^{5} \operatorname{arccot}\left(a x\right)^{3}\,{d x}"," ",0,"integrate(x^5*arccot(a*x)^3, x)","F",0
24,0,0,0,0.000000," ","integrate(x^4*arccot(a*x)^3,x, algorithm=""giac"")","\int x^{4} \operatorname{arccot}\left(a x\right)^{3}\,{d x}"," ",0,"integrate(x^4*arccot(a*x)^3, x)","F",0
25,0,0,0,0.000000," ","integrate(x^3*arccot(a*x)^3,x, algorithm=""giac"")","\int x^{3} \operatorname{arccot}\left(a x\right)^{3}\,{d x}"," ",0,"integrate(x^3*arccot(a*x)^3, x)","F",0
26,0,0,0,0.000000," ","integrate(x^2*arccot(a*x)^3,x, algorithm=""giac"")","\int x^{2} \operatorname{arccot}\left(a x\right)^{3}\,{d x}"," ",0,"integrate(x^2*arccot(a*x)^3, x)","F",0
27,0,0,0,0.000000," ","integrate(x*arccot(a*x)^3,x, algorithm=""giac"")","\int x \operatorname{arccot}\left(a x\right)^{3}\,{d x}"," ",0,"integrate(x*arccot(a*x)^3, x)","F",0
28,0,0,0,0.000000," ","integrate(arccot(a*x)^3,x, algorithm=""giac"")","\int \operatorname{arccot}\left(a x\right)^{3}\,{d x}"," ",0,"integrate(arccot(a*x)^3, x)","F",0
29,0,0,0,0.000000," ","integrate(arccot(a*x)^3/x,x, algorithm=""giac"")","\int \frac{\operatorname{arccot}\left(a x\right)^{3}}{x}\,{d x}"," ",0,"integrate(arccot(a*x)^3/x, x)","F",0
30,0,0,0,0.000000," ","integrate(arccot(a*x)^3/x^2,x, algorithm=""giac"")","\int \frac{\operatorname{arccot}\left(a x\right)^{3}}{x^{2}}\,{d x}"," ",0,"integrate(arccot(a*x)^3/x^2, x)","F",0
31,1,29,0,0.146070," ","integrate(arccot(a*x)^3/x^3,x, algorithm=""giac"")","-\frac{1}{2} \, a \arctan\left(\frac{1}{a x}\right)^{3} - \frac{\arctan\left(\frac{1}{a x}\right)^{3}}{2 \, x^{2}}"," ",0,"-1/2*a*arctan(1/(a*x))^3 - 1/2*arctan(1/(a*x))^3/x^2","A",0
32,0,0,0,0.000000," ","integrate(arccot(a*x)^3/x^4,x, algorithm=""giac"")","\int \frac{\operatorname{arccot}\left(a x\right)^{3}}{x^{4}}\,{d x}"," ",0,"integrate(arccot(a*x)^3/x^4, x)","F",0
33,0,0,0,0.000000," ","integrate(arccot(a*x)^3/x^5,x, algorithm=""giac"")","\int \frac{\operatorname{arccot}\left(a x\right)^{3}}{x^{5}}\,{d x}"," ",0,"integrate(arccot(a*x)^3/x^5, x)","F",0
34,0,0,0,0.000000," ","integrate(x^m*arccot(a*x)^3,x, algorithm=""giac"")","\int x^{m} \operatorname{arccot}\left(a x\right)^{3}\,{d x}"," ",0,"integrate(x^m*arccot(a*x)^3, x)","F",0
35,0,0,0,0.000000," ","integrate(x^m*arccot(a*x)^2,x, algorithm=""giac"")","\int x^{m} \operatorname{arccot}\left(a x\right)^{2}\,{d x}"," ",0,"integrate(x^m*arccot(a*x)^2, x)","F",0
36,0,0,0,0.000000," ","integrate(x^m*arccot(a*x),x, algorithm=""giac"")","\int x^{m} \operatorname{arccot}\left(a x\right)\,{d x}"," ",0,"integrate(x^m*arccot(a*x), x)","F",0
37,0,0,0,0.000000," ","integrate(x^4*arccot(x)/(x^2+1),x, algorithm=""giac"")","\int \frac{x^{4} \operatorname{arccot}\left(x\right)}{x^{2} + 1}\,{d x}"," ",0,"integrate(x^4*arccot(x)/(x^2 + 1), x)","F",0
38,0,0,0,0.000000," ","integrate(x^3*arccot(x)/(x^2+1),x, algorithm=""giac"")","\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
39,0,0,0,0.000000," ","integrate(x^2*arccot(x)/(x^2+1),x, algorithm=""giac"")","\int \frac{x^{2} \operatorname{arccot}\left(x\right)}{x^{2} + 1}\,{d x}"," ",0,"integrate(x^2*arccot(x)/(x^2 + 1), x)","F",0
40,0,0,0,0.000000," ","integrate(x*arccot(x)/(x^2+1),x, algorithm=""giac"")","\int \frac{x \operatorname{arccot}\left(x\right)}{x^{2} + 1}\,{d x}"," ",0,"integrate(x*arccot(x)/(x^2 + 1), x)","F",0
41,1,8,0,0.110119," ","integrate(arccot(x)/(x^2+1),x, algorithm=""giac"")","-\frac{1}{2} \, \arctan\left(\frac{1}{x}\right)^{2}"," ",0,"-1/2*arctan(1/x)^2","A",0
42,0,0,0,0.000000," ","integrate(arccot(x)/x/(x^2+1),x, algorithm=""giac"")","\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
43,1,26,0,0.113303," ","integrate(arccot(x)/x^2/(x^2+1),x, algorithm=""giac"")","\frac{1}{2} \, \arctan\left(\frac{1}{x}\right)^{2} - \frac{\arctan\left(\frac{1}{x}\right)}{x} + \frac{1}{2} \, \log\left(\frac{1}{x^{2}} + 1\right)"," ",0,"1/2*arctan(1/x)^2 - arctan(1/x)/x + 1/2*log(1/x^2 + 1)","A",0
44,0,0,0,0.000000," ","integrate(arccot(x)/x^3/(x^2+1),x, algorithm=""giac"")","\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
45,1,39,0,0.115617," ","integrate(arccot(x)/x^4/(x^2+1),x, algorithm=""giac"")","-\frac{1}{2} \, \arctan\left(\frac{1}{x}\right)^{2} + \frac{\arctan\left(\frac{1}{x}\right)}{x} + \frac{1}{6 \, x^{2}} - \frac{\arctan\left(\frac{1}{x}\right)}{3 \, x^{3}} - \frac{2}{3} \, \log\left(\frac{1}{x^{2}} + 1\right)"," ",0,"-1/2*arctan(1/x)^2 + arctan(1/x)/x + 1/6/x^2 - 1/3*arctan(1/x)/x^3 - 2/3*log(1/x^2 + 1)","A",0
46,0,0,0,0.000000," ","integrate(x^2*arccot(c*x)/(x^2+1),x, algorithm=""giac"")","\int \frac{x^{2} \operatorname{arccot}\left(c x\right)}{x^{2} + 1}\,{d x}"," ",0,"integrate(x^2*arccot(c*x)/(x^2 + 1), x)","F",0
47,0,0,0,0.000000," ","integrate(x*arccot(c*x)/(x^2+1),x, algorithm=""giac"")","\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
48,0,0,0,0.000000," ","integrate(arccot(c*x)/(x^2+1),x, algorithm=""giac"")","\int \frac{\operatorname{arccot}\left(c x\right)}{x^{2} + 1}\,{d x}"," ",0,"integrate(arccot(c*x)/(x^2 + 1), x)","F",0
49,0,0,0,0.000000," ","integrate(arccot(c*x)/x/(x^2+1),x, algorithm=""giac"")","\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
50,0,0,0,0.000000," ","integrate(arccot(c*x)/x^2/(x^2+1),x, algorithm=""giac"")","\int \frac{\operatorname{arccot}\left(c x\right)}{{\left(x^{2} + 1\right)} x^{2}}\,{d x}"," ",0,"integrate(arccot(c*x)/((x^2 + 1)*x^2), x)","F",0
51,1,8,0,0.122905," ","integrate(1/(x^2+1)/arccot(x),x, algorithm=""giac"")","-\log\left({\left| \arctan\left(\frac{1}{x}\right) \right|}\right)"," ",0,"-log(abs(arctan(1/x)))","A",0
52,1,15,0,0.123754," ","integrate(arccot(x)^n/(x^2+1),x, algorithm=""giac"")","-\frac{\arctan\left(\frac{1}{x}\right)^{n + 1}}{n + 1}"," ",0,"-arctan(1/x)^(n + 1)/(n + 1)","A",0
53,1,347,0,0.146491," ","integrate((d*x^2+c)^4*arccot(a*x),x, algorithm=""giac"")","\frac{1}{7560} \, {\left(\frac{24 \, {\left(35 \, d^{4} + \frac{180 \, c d^{3}}{x^{2}} + \frac{378 \, c^{2} d^{2}}{x^{4}} + \frac{420 \, c^{3} d}{x^{6}} + \frac{315 \, c^{4}}{x^{8}}\right)} x^{9} \arctan\left(\frac{1}{a x}\right)}{a} + \frac{{\left(105 \, d^{4} + \frac{720 \, c d^{3}}{x^{2}} + \frac{2268 \, c^{2} d^{2}}{x^{4}} - \frac{140 \, d^{4}}{a^{2} x^{2}} + \frac{5040 \, c^{3} d}{x^{6}} - \frac{1080 \, c d^{3}}{a^{2} x^{4}} + \frac{7875 \, c^{4}}{x^{8}} - \frac{4536 \, c^{2} d^{2}}{a^{2} x^{6}} + \frac{210 \, d^{4}}{a^{4} x^{4}} - \frac{10500 \, c^{3} d}{a^{2} x^{8}} + \frac{2160 \, c d^{3}}{a^{4} x^{6}} + \frac{9450 \, c^{2} d^{2}}{a^{4} x^{8}} - \frac{420 \, d^{4}}{a^{6} x^{6}} - \frac{4500 \, c d^{3}}{a^{6} x^{8}} + \frac{875 \, d^{4}}{a^{8} x^{8}}\right)} x^{8}}{a^{2}} + \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(\frac{1}{a^{2} x^{2}} + 1\right)}{a^{10}} - \frac{12 \, {\left(315 \, a^{8} c^{4} - 420 \, a^{6} c^{3} d + 378 \, a^{4} c^{2} d^{2} - 180 \, a^{2} c d^{3} + 35 \, d^{4}\right)} \log\left(\frac{1}{a^{2} x^{2}}\right)}{a^{10}}\right)} a"," ",0,"1/7560*(24*(35*d^4 + 180*c*d^3/x^2 + 378*c^2*d^2/x^4 + 420*c^3*d/x^6 + 315*c^4/x^8)*x^9*arctan(1/(a*x))/a + (105*d^4 + 720*c*d^3/x^2 + 2268*c^2*d^2/x^4 - 140*d^4/(a^2*x^2) + 5040*c^3*d/x^6 - 1080*c*d^3/(a^2*x^4) + 7875*c^4/x^8 - 4536*c^2*d^2/(a^2*x^6) + 210*d^4/(a^4*x^4) - 10500*c^3*d/(a^2*x^8) + 2160*c*d^3/(a^4*x^6) + 9450*c^2*d^2/(a^4*x^8) - 420*d^4/(a^6*x^6) - 4500*c*d^3/(a^6*x^8) + 875*d^4/(a^8*x^8))*x^8/a^2 + 12*(315*a^8*c^4 - 420*a^6*c^3*d + 378*a^4*c^2*d^2 - 180*a^2*c*d^3 + 35*d^4)*log(1/(a^2*x^2) + 1)/a^10 - 12*(315*a^8*c^4 - 420*a^6*c^3*d + 378*a^4*c^2*d^2 - 180*a^2*c*d^3 + 35*d^4)*log(1/(a^2*x^2))/a^10)*a","A",0
54,1,252,0,0.141113," ","integrate((d*x^2+c)^3*arccot(a*x),x, algorithm=""giac"")","\frac{1}{420} \, {\left(\frac{12 \, {\left(5 \, d^{3} + \frac{21 \, c d^{2}}{x^{2}} + \frac{35 \, c^{2} d}{x^{4}} + \frac{35 \, c^{3}}{x^{6}}\right)} x^{7} \arctan\left(\frac{1}{a x}\right)}{a} + \frac{{\left(10 \, d^{3} + \frac{63 \, c d^{2}}{x^{2}} + \frac{210 \, c^{2} d}{x^{4}} - \frac{15 \, d^{3}}{a^{2} x^{2}} + \frac{385 \, c^{3}}{x^{6}} - \frac{126 \, c d^{2}}{a^{2} x^{4}} - \frac{385 \, c^{2} d}{a^{2} x^{6}} + \frac{30 \, d^{3}}{a^{4} x^{4}} + \frac{231 \, c d^{2}}{a^{4} x^{6}} - \frac{55 \, d^{3}}{a^{6} x^{6}}\right)} x^{6}}{a^{2}} + \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(\frac{1}{a^{2} x^{2}} + 1\right)}{a^{8}} - \frac{6 \, {\left(35 \, a^{6} c^{3} - 35 \, a^{4} c^{2} d + 21 \, a^{2} c d^{2} - 5 \, d^{3}\right)} \log\left(\frac{1}{a^{2} x^{2}}\right)}{a^{8}}\right)} a"," ",0,"1/420*(12*(5*d^3 + 21*c*d^2/x^2 + 35*c^2*d/x^4 + 35*c^3/x^6)*x^7*arctan(1/(a*x))/a + (10*d^3 + 63*c*d^2/x^2 + 210*c^2*d/x^4 - 15*d^3/(a^2*x^2) + 385*c^3/x^6 - 126*c*d^2/(a^2*x^4) - 385*c^2*d/(a^2*x^6) + 30*d^3/(a^4*x^4) + 231*c*d^2/(a^4*x^6) - 55*d^3/(a^6*x^6))*x^6/a^2 + 6*(35*a^6*c^3 - 35*a^4*c^2*d + 21*a^2*c*d^2 - 5*d^3)*log(1/(a^2*x^2) + 1)/a^8 - 6*(35*a^6*c^3 - 35*a^4*c^2*d + 21*a^2*c*d^2 - 5*d^3)*log(1/(a^2*x^2))/a^8)*a","A",0
55,1,171,0,0.143340," ","integrate((d*x^2+c)^2*arccot(a*x),x, algorithm=""giac"")","\frac{1}{60} \, {\left(\frac{4 \, {\left(3 \, d^{2} + \frac{10 \, c d}{x^{2}} + \frac{15 \, c^{2}}{x^{4}}\right)} x^{5} \arctan\left(\frac{1}{a x}\right)}{a} + \frac{{\left(3 \, d^{2} + \frac{20 \, c d}{x^{2}} + \frac{45 \, c^{2}}{x^{4}} - \frac{6 \, d^{2}}{a^{2} x^{2}} - \frac{30 \, c d}{a^{2} x^{4}} + \frac{9 \, d^{2}}{a^{4} x^{4}}\right)} x^{4}}{a^{2}} + \frac{2 \, {\left(15 \, a^{4} c^{2} - 10 \, a^{2} c d + 3 \, d^{2}\right)} \log\left(\frac{1}{a^{2} x^{2}} + 1\right)}{a^{6}} - \frac{2 \, {\left(15 \, a^{4} c^{2} - 10 \, a^{2} c d + 3 \, d^{2}\right)} \log\left(\frac{1}{a^{2} x^{2}}\right)}{a^{6}}\right)} a"," ",0,"1/60*(4*(3*d^2 + 10*c*d/x^2 + 15*c^2/x^4)*x^5*arctan(1/(a*x))/a + (3*d^2 + 20*c*d/x^2 + 45*c^2/x^4 - 6*d^2/(a^2*x^2) - 30*c*d/(a^2*x^4) + 9*d^2/(a^4*x^4))*x^4/a^2 + 2*(15*a^4*c^2 - 10*a^2*c*d + 3*d^2)*log(1/(a^2*x^2) + 1)/a^6 - 2*(15*a^4*c^2 - 10*a^2*c*d + 3*d^2)*log(1/(a^2*x^2))/a^6)*a","A",0
56,1,99,0,0.117033," ","integrate((d*x^2+c)*arccot(a*x),x, algorithm=""giac"")","\frac{1}{6} \, {\left(\frac{2 \, {\left(d + \frac{3 \, c}{x^{2}}\right)} x^{3} \arctan\left(\frac{1}{a x}\right)}{a} + \frac{{\left(d + \frac{3 \, c}{x^{2}} - \frac{d}{a^{2} x^{2}}\right)} x^{2}}{a^{2}} + \frac{{\left(3 \, a^{2} c - d\right)} \log\left(\frac{1}{a^{2} x^{2}} + 1\right)}{a^{4}} - \frac{{\left(3 \, a^{2} c - d\right)} \log\left(\frac{1}{a^{2} x^{2}}\right)}{a^{4}}\right)} a"," ",0,"1/6*(2*(d + 3*c/x^2)*x^3*arctan(1/(a*x))/a + (d + 3*c/x^2 - d/(a^2*x^2))*x^2/a^2 + (3*a^2*c - d)*log(1/(a^2*x^2) + 1)/a^4 - (3*a^2*c - d)*log(1/(a^2*x^2))/a^4)*a","A",0
57,0,0,0,0.000000," ","integrate(arccot(a*x)/(d*x^2+c),x, algorithm=""giac"")","\int \frac{\operatorname{arccot}\left(a x\right)}{d x^{2} + c}\,{d x}"," ",0,"integrate(arccot(a*x)/(d*x^2 + c), x)","F",0
58,0,0,0,0.000000," ","integrate(arccot(a*x)/(d*x^2+c)^2,x, algorithm=""giac"")","\int \frac{\operatorname{arccot}\left(a x\right)}{{\left(d x^{2} + c\right)}^{2}}\,{d x}"," ",0,"integrate(arccot(a*x)/(d*x^2 + c)^2, x)","F",0
59,0,0,0,0.000000," ","integrate((d*x^2+c)^(1/2)*arccot(a*x),x, algorithm=""giac"")","\int \sqrt{d x^{2} + c} \operatorname{arccot}\left(a x\right)\,{d x}"," ",0,"integrate(sqrt(d*x^2 + c)*arccot(a*x), x)","F",0
60,0,0,0,0.000000," ","integrate(arccot(a*x)/(d*x^2+c)^(1/2),x, algorithm=""giac"")","\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
61,1,59,0,0.169886," ","integrate(arccot(a*x)/(d*x^2+c)^(3/2),x, algorithm=""giac"")","\frac{x \arctan\left(\frac{1}{a x}\right)}{\sqrt{d x^{2} + c} c} + \frac{\arctan\left(\frac{\sqrt{d x^{2} + c} a}{\sqrt{-a^{2} c + d}}\right)}{\sqrt{-a^{2} c + d} c}"," ",0,"x*arctan(1/(a*x))/(sqrt(d*x^2 + c)*c) + arctan(sqrt(d*x^2 + c)*a/sqrt(-a^2*c + d))/(sqrt(-a^2*c + d)*c)","A",0
62,1,126,0,0.156117," ","integrate(arccot(a*x)/(d*x^2+c)^(5/2),x, algorithm=""giac"")","\frac{1}{3} \, a {\left(\frac{{\left(3 \, a^{2} c - 2 \, d\right)} \arctan\left(\frac{\sqrt{d x^{2} + c} a}{\sqrt{-a^{2} c + d}}\right)}{{\left(a^{2} c^{3} - c^{2} d\right)} \sqrt{-a^{2} c + d} a} + \frac{1}{{\left(a^{2} c^{2} - c d\right)} \sqrt{d x^{2} + c}}\right)} + \frac{x {\left(\frac{2 \, d x^{2}}{c^{2}} + \frac{3}{c}\right)} \arctan\left(\frac{1}{a x}\right)}{3 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}}}"," ",0,"1/3*a*((3*a^2*c - 2*d)*arctan(sqrt(d*x^2 + c)*a/sqrt(-a^2*c + d))/((a^2*c^3 - c^2*d)*sqrt(-a^2*c + d)*a) + 1/((a^2*c^2 - c*d)*sqrt(d*x^2 + c))) + 1/3*x*(2*d*x^2/c^2 + 3/c)*arctan(1/(a*x))/(d*x^2 + c)^(3/2)","A",0
63,1,208,0,0.173457," ","integrate(arccot(a*x)/(d*x^2+c)^(7/2),x, algorithm=""giac"")","\frac{1}{15} \, a {\left(\frac{{\left(15 \, a^{4} c^{2} - 20 \, a^{2} c d + 8 \, d^{2}\right)} \arctan\left(\frac{\sqrt{d x^{2} + c} a}{\sqrt{-a^{2} c + d}}\right)}{{\left(a^{4} c^{5} - 2 \, a^{2} c^{4} d + c^{3} d^{2}\right)} \sqrt{-a^{2} c + d} a} + \frac{7 \, {\left(d x^{2} + c\right)} a^{2} c + a^{2} c^{2} - 4 \, {\left(d x^{2} + c\right)} d - c d}{{\left(a^{4} c^{4} - 2 \, a^{2} c^{3} d + c^{2} d^{2}\right)} {\left(d x^{2} + c\right)}^{\frac{3}{2}}}\right)} + \frac{{\left(4 \, x^{2} {\left(\frac{2 \, d^{2} x^{2}}{c^{3}} + \frac{5 \, d}{c^{2}}\right)} + \frac{15}{c}\right)} x \arctan\left(\frac{1}{a x}\right)}{15 \, {\left(d x^{2} + c\right)}^{\frac{5}{2}}}"," ",0,"1/15*a*((15*a^4*c^2 - 20*a^2*c*d + 8*d^2)*arctan(sqrt(d*x^2 + c)*a/sqrt(-a^2*c + d))/((a^4*c^5 - 2*a^2*c^4*d + c^3*d^2)*sqrt(-a^2*c + d)*a) + (7*(d*x^2 + c)*a^2*c + a^2*c^2 - 4*(d*x^2 + c)*d - c*d)/((a^4*c^4 - 2*a^2*c^3*d + c^2*d^2)*(d*x^2 + c)^(3/2))) + 1/15*(4*x^2*(2*d^2*x^2/c^3 + 5*d/c^2) + 15/c)*x*arctan(1/(a*x))/(d*x^2 + c)^(5/2)","A",0
64,1,340,0,0.179032," ","integrate(arccot(a*x)/(d*x^2+c)^(9/2),x, algorithm=""giac"")","\frac{1}{105} \, a {\left(\frac{3 \, {\left(35 \, a^{6} c^{3} - 70 \, a^{4} c^{2} d + 56 \, a^{2} c d^{2} - 16 \, d^{3}\right)} \arctan\left(\frac{\sqrt{d x^{2} + c} a}{\sqrt{-a^{2} c + d}}\right)}{{\left(a^{6} c^{7} - 3 \, a^{4} c^{6} d + 3 \, a^{2} c^{5} d^{2} - c^{4} d^{3}\right)} \sqrt{-a^{2} c + d} a} + \frac{57 \, {\left(d x^{2} + c\right)}^{2} a^{4} c^{2} + 11 \, {\left(d x^{2} + c\right)} a^{4} c^{3} + 3 \, a^{4} c^{4} - 66 \, {\left(d x^{2} + c\right)}^{2} a^{2} c d - 17 \, {\left(d x^{2} + c\right)} a^{2} c^{2} d - 6 \, a^{2} c^{3} d + 24 \, {\left(d x^{2} + c\right)}^{2} d^{2} + 6 \, {\left(d x^{2} + c\right)} c d^{2} + 3 \, c^{2} d^{2}}{{\left(a^{6} c^{6} - 3 \, a^{4} c^{5} d + 3 \, a^{2} c^{4} d^{2} - c^{3} d^{3}\right)} {\left(d x^{2} + c\right)}^{\frac{5}{2}}}\right)} + \frac{{\left(2 \, {\left(4 \, x^{2} {\left(\frac{2 \, d^{3} x^{2}}{c^{4}} + \frac{7 \, d^{2}}{c^{3}}\right)} + \frac{35 \, d}{c^{2}}\right)} x^{2} + \frac{35}{c}\right)} x \arctan\left(\frac{1}{a x}\right)}{35 \, {\left(d x^{2} + c\right)}^{\frac{7}{2}}}"," ",0,"1/105*a*(3*(35*a^6*c^3 - 70*a^4*c^2*d + 56*a^2*c*d^2 - 16*d^3)*arctan(sqrt(d*x^2 + c)*a/sqrt(-a^2*c + d))/((a^6*c^7 - 3*a^4*c^6*d + 3*a^2*c^5*d^2 - c^4*d^3)*sqrt(-a^2*c + d)*a) + (57*(d*x^2 + c)^2*a^4*c^2 + 11*(d*x^2 + c)*a^4*c^3 + 3*a^4*c^4 - 66*(d*x^2 + c)^2*a^2*c*d - 17*(d*x^2 + c)*a^2*c^2*d - 6*a^2*c^3*d + 24*(d*x^2 + c)^2*d^2 + 6*(d*x^2 + c)*c*d^2 + 3*c^2*d^2)/((a^6*c^6 - 3*a^4*c^5*d + 3*a^2*c^4*d^2 - c^3*d^3)*(d*x^2 + c)^(5/2))) + 1/35*(2*(4*x^2*(2*d^3*x^2/c^4 + 7*d^2/c^3) + 35*d/c^2)*x^2 + 35/c)*x*arctan(1/(a*x))/(d*x^2 + c)^(7/2)","A",0
65,0,0,0,0.000000," ","integrate((a*x^2+a)^(1/2)*arccot(x),x, algorithm=""giac"")","\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=""giac"")","\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
67,1,33,0,0.150684," ","integrate(arccot(x)/(a*x^2+a)^(3/2),x, algorithm=""giac"")","\frac{x \arctan\left(\frac{1}{x}\right)}{\sqrt{a x^{2} + a} a} - \frac{1}{\sqrt{a x^{2} + a} a}"," ",0,"x*arctan(1/x)/(sqrt(a*x^2 + a)*a) - 1/(sqrt(a*x^2 + a)*a)","A",0
68,1,55,0,0.149078," ","integrate(arccot(x)/(a*x^2+a)^(5/2),x, algorithm=""giac"")","\frac{x {\left(\frac{2 \, x^{2}}{a} + \frac{3}{a}\right)} \arctan\left(\frac{1}{x}\right)}{3 \, {\left(a x^{2} + a\right)}^{\frac{3}{2}}} - \frac{6 \, a x^{2} + 7 \, a}{9 \, {\left(a x^{2} + a\right)}^{\frac{3}{2}} a^{2}}"," ",0,"1/3*x*(2*x^2/a + 3/a)*arctan(1/x)/(a*x^2 + a)^(3/2) - 1/9*(6*a*x^2 + 7*a)/((a*x^2 + a)^(3/2)*a^2)","A",0
69,1,83,0,0.168304," ","integrate(arccot(x)/(a*x^2+a)^(7/2),x, algorithm=""giac"")","\frac{{\left(4 \, x^{2} {\left(\frac{2 \, x^{2}}{a} + \frac{5}{a}\right)} + \frac{15}{a}\right)} x \arctan\left(\frac{1}{x}\right)}{15 \, {\left(a x^{2} + a\right)}^{\frac{5}{2}}} - \frac{120 \, {\left(a x^{2} + a\right)}^{2} + 20 \, {\left(a x^{2} + a\right)} a + 9 \, a^{2}}{225 \, {\left(a x^{2} + a\right)}^{\frac{5}{2}} a^{3}}"," ",0,"1/15*(4*x^2*(2*x^2/a + 5/a) + 15/a)*x*arctan(1/x)/(a*x^2 + a)^(5/2) - 1/225*(120*(a*x^2 + a)^2 + 20*(a*x^2 + a)*a + 9*a^2)/((a*x^2 + a)^(5/2)*a^3)","A",0
70,1,32,0,0.132974," ","integrate(x*arccot(x)/(x^2+1)^2,x, algorithm=""giac"")","-\frac{\arctan\left(\frac{1}{x}\right)}{2 \, {\left(x^{2} + 1\right)}} - \frac{1}{4 \, x {\left(\frac{1}{x^{2}} + 1\right)}} + \frac{1}{4} \, \arctan\left(\frac{1}{x}\right)"," ",0,"-1/2*arctan(1/x)/(x^2 + 1) - 1/4/(x*(1/x^2 + 1)) + 1/4*arctan(1/x)","A",0
71,1,40,0,0.131064," ","integrate(x*arccot(x)/(x^2+1)^3,x, algorithm=""giac"")","-\frac{\frac{3}{x} + \frac{5}{x^{3}}}{32 \, {\left(\frac{1}{x^{2}} + 1\right)}^{2}} - \frac{\arctan\left(\frac{1}{x}\right)}{4 \, {\left(x^{2} + 1\right)}^{2}} + \frac{3}{32} \, \arctan\left(\frac{1}{x}\right)"," ",0,"-1/32*(3/x + 5/x^3)/(1/x^2 + 1)^2 - 1/4*arctan(1/x)/(x^2 + 1)^2 + 3/32*arctan(1/x)","A",0
72,0,0,0,0.000000," ","integrate(arccot(x)/(x^2+1)^2,x, algorithm=""giac"")","\int \frac{\operatorname{arccot}\left(x\right)}{{\left(x^{2} + 1\right)}^{2}}\,{d x}"," ",0,"integrate(arccot(x)/(x^2 + 1)^2, x)","F",0
73,0,0,0,0.000000," ","integrate(arccot(x)^2/(x^2+1)^2,x, algorithm=""giac"")","\int \frac{\operatorname{arccot}\left(x\right)^{2}}{{\left(x^{2} + 1\right)}^{2}}\,{d x}"," ",0,"integrate(arccot(x)^2/(x^2 + 1)^2, x)","F",0
74,1,40,0,0.133522," ","integrate(x^5*arccot(a*x^2),x, algorithm=""giac"")","\frac{1}{6} \, x^{6} \arctan\left(\frac{1}{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*arctan(1/(a*x^2)) + 1/12*(x^4/a^2 - log(a^2*x^4 + 1)/a^4)*a","A",0
75,1,38,0,0.112347," ","integrate(x^3*arccot(a*x^2),x, algorithm=""giac"")","\frac{1}{4} \, {\left(\frac{x^{4} \arctan\left(\frac{1}{a x^{2}}\right)}{a} + \frac{x^{2}}{a^{2}} + \frac{\arctan\left(\frac{1}{a x^{2}}\right)}{a^{3}}\right)} a"," ",0,"1/4*(x^4*arctan(1/(a*x^2))/a + x^2/a^2 + arctan(1/(a*x^2))/a^3)*a","A",0
76,1,47,0,0.131442," ","integrate(x*arccot(a*x^2),x, algorithm=""giac"")","\frac{1}{4} \, {\left(\frac{2 \, x^{2} \arctan\left(\frac{1}{a x^{2}}\right)}{a} + \frac{\log\left(\frac{1}{a^{2} x^{4}} + 1\right)}{a^{2}} - \frac{\log\left(\frac{1}{a^{2} x^{4}}\right)}{a^{2}}\right)} a"," ",0,"1/4*(2*x^2*arctan(1/(a*x^2))/a + log(1/(a^2*x^4) + 1)/a^2 - log(1/(a^2*x^4))/a^2)*a","A",0
77,0,0,0,0.000000," ","integrate(arccot(a*x^2)/x,x, algorithm=""giac"")","\int \frac{\operatorname{arccot}\left(a x^{2}\right)}{x}\,{d x}"," ",0,"integrate(arccot(a*x^2)/x, x)","F",0
78,1,34,0,0.123308," ","integrate(arccot(a*x^2)/x^3,x, algorithm=""giac"")","\frac{1}{4} \, a {\left(\log\left(a^{2} x^{4} + 1\right) - \log\left(x^{4}\right)\right)} - \frac{\arctan\left(\frac{1}{a x^{2}}\right)}{2 \, x^{2}}"," ",0,"1/4*a*(log(a^2*x^4 + 1) - log(x^4)) - 1/2*arctan(1/(a*x^2))/x^2","A",0
79,1,29,0,0.121060," ","integrate(arccot(a*x^2)/x^5,x, algorithm=""giac"")","\frac{1}{4} \, {\left(a \arctan\left(a x^{2}\right) + \frac{1}{x^{2}}\right)} a - \frac{\arctan\left(\frac{1}{a x^{2}}\right)}{4 \, x^{4}}"," ",0,"1/4*(a*arctan(a*x^2) + 1/x^2)*a - 1/4*arctan(1/(a*x^2))/x^4","A",0
80,1,156,0,0.146946," ","integrate(x^4*arccot(a*x^2),x, algorithm=""giac"")","\frac{1}{5} \, x^{5} \arctan\left(\frac{1}{a x^{2}}\right) + \frac{1}{60} \, a {\left(\frac{8 \, x^{3}}{a^{2}} - \frac{6 \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(2 \, x + \frac{\sqrt{2}}{\sqrt{{\left| a \right|}}}\right)} \sqrt{{\left| a \right|}}\right)}{a^{2} {\left| a \right|}^{\frac{3}{2}}} - \frac{6 \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(2 \, x - \frac{\sqrt{2}}{\sqrt{{\left| a \right|}}}\right)} \sqrt{{\left| a \right|}}\right)}{a^{2} {\left| a \right|}^{\frac{3}{2}}} + \frac{3 \, \sqrt{2} \sqrt{{\left| a \right|}} \log\left(x^{2} + \frac{\sqrt{2} x}{\sqrt{{\left| a \right|}}} + \frac{1}{{\left| a \right|}}\right)}{a^{4}} - \frac{3 \, \sqrt{2} \log\left(x^{2} - \frac{\sqrt{2} x}{\sqrt{{\left| a \right|}}} + \frac{1}{{\left| a \right|}}\right)}{a^{2} {\left| a \right|}^{\frac{3}{2}}}\right)}"," ",0,"1/5*x^5*arctan(1/(a*x^2)) + 1/60*a*(8*x^3/a^2 - 6*sqrt(2)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)/sqrt(abs(a)))*sqrt(abs(a)))/(a^2*abs(a)^(3/2)) - 6*sqrt(2)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)/sqrt(abs(a)))*sqrt(abs(a)))/(a^2*abs(a)^(3/2)) + 3*sqrt(2)*sqrt(abs(a))*log(x^2 + sqrt(2)*x/sqrt(abs(a)) + 1/abs(a))/a^4 - 3*sqrt(2)*log(x^2 - sqrt(2)*x/sqrt(abs(a)) + 1/abs(a))/(a^2*abs(a)^(3/2)))","A",0
81,1,153,0,0.138421," ","integrate(x^2*arccot(a*x^2),x, algorithm=""giac"")","\frac{1}{3} \, x^{3} \arctan\left(\frac{1}{a x^{2}}\right) + \frac{1}{12} \, a {\left(\frac{8 \, x}{a^{2}} - \frac{2 \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(2 \, x + \frac{\sqrt{2}}{\sqrt{{\left| a \right|}}}\right)} \sqrt{{\left| a \right|}}\right)}{a^{2} \sqrt{{\left| a \right|}}} - \frac{2 \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(2 \, x - \frac{\sqrt{2}}{\sqrt{{\left| a \right|}}}\right)} \sqrt{{\left| a \right|}}\right)}{a^{2} \sqrt{{\left| a \right|}}} - \frac{\sqrt{2} \log\left(x^{2} + \frac{\sqrt{2} x}{\sqrt{{\left| a \right|}}} + \frac{1}{{\left| a \right|}}\right)}{a^{2} \sqrt{{\left| a \right|}}} + \frac{\sqrt{2} \log\left(x^{2} - \frac{\sqrt{2} x}{\sqrt{{\left| a \right|}}} + \frac{1}{{\left| a \right|}}\right)}{a^{2} \sqrt{{\left| a \right|}}}\right)}"," ",0,"1/3*x^3*arctan(1/(a*x^2)) + 1/12*a*(8*x/a^2 - 2*sqrt(2)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)/sqrt(abs(a)))*sqrt(abs(a)))/(a^2*sqrt(abs(a))) - 2*sqrt(2)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)/sqrt(abs(a)))*sqrt(abs(a)))/(a^2*sqrt(abs(a))) - sqrt(2)*log(x^2 + sqrt(2)*x/sqrt(abs(a)) + 1/abs(a))/(a^2*sqrt(abs(a))) + sqrt(2)*log(x^2 - sqrt(2)*x/sqrt(abs(a)) + 1/abs(a))/(a^2*sqrt(abs(a))))","A",0
82,1,144,0,0.136475," ","integrate(arccot(a*x^2),x, algorithm=""giac"")","\frac{1}{4} \, a {\left(\frac{2 \, \sqrt{2} \sqrt{{\left| a \right|}} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(2 \, x + \frac{\sqrt{2}}{\sqrt{{\left| a \right|}}}\right)} \sqrt{{\left| a \right|}}\right)}{a^{2}} + \frac{2 \, \sqrt{2} \sqrt{{\left| a \right|}} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(2 \, x - \frac{\sqrt{2}}{\sqrt{{\left| a \right|}}}\right)} \sqrt{{\left| a \right|}}\right)}{a^{2}} - \frac{\sqrt{2} \sqrt{{\left| a \right|}} \log\left(x^{2} + \frac{\sqrt{2} x}{\sqrt{{\left| a \right|}}} + \frac{1}{{\left| a \right|}}\right)}{a^{2}} + \frac{\sqrt{2} \sqrt{{\left| a \right|}} \log\left(x^{2} - \frac{\sqrt{2} x}{\sqrt{{\left| a \right|}}} + \frac{1}{{\left| a \right|}}\right)}{a^{2}}\right)} + x \arctan\left(\frac{1}{a x^{2}}\right)"," ",0,"1/4*a*(2*sqrt(2)*sqrt(abs(a))*arctan(1/2*sqrt(2)*(2*x + sqrt(2)/sqrt(abs(a)))*sqrt(abs(a)))/a^2 + 2*sqrt(2)*sqrt(abs(a))*arctan(1/2*sqrt(2)*(2*x - sqrt(2)/sqrt(abs(a)))*sqrt(abs(a)))/a^2 - sqrt(2)*sqrt(abs(a))*log(x^2 + sqrt(2)*x/sqrt(abs(a)) + 1/abs(a))/a^2 + sqrt(2)*sqrt(abs(a))*log(x^2 - sqrt(2)*x/sqrt(abs(a)) + 1/abs(a))/a^2) + x*arctan(1/(a*x^2))","A",0
83,1,135,0,0.137360," ","integrate(arccot(a*x^2)/x^2,x, algorithm=""giac"")","-\frac{1}{4} \, a {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(2 \, x + \frac{\sqrt{2}}{\sqrt{{\left| a \right|}}}\right)} \sqrt{{\left| a \right|}}\right)}{\sqrt{{\left| a \right|}}} + \frac{2 \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(2 \, x - \frac{\sqrt{2}}{\sqrt{{\left| a \right|}}}\right)} \sqrt{{\left| a \right|}}\right)}{\sqrt{{\left| a \right|}}} + \frac{\sqrt{2} \log\left(x^{2} + \frac{\sqrt{2} x}{\sqrt{{\left| a \right|}}} + \frac{1}{{\left| a \right|}}\right)}{\sqrt{{\left| a \right|}}} - \frac{\sqrt{2} \log\left(x^{2} - \frac{\sqrt{2} x}{\sqrt{{\left| a \right|}}} + \frac{1}{{\left| a \right|}}\right)}{\sqrt{{\left| a \right|}}}\right)} - \frac{\arctan\left(\frac{1}{a x^{2}}\right)}{x}"," ",0,"-1/4*a*(2*sqrt(2)*arctan(1/2*sqrt(2)*(2*x + sqrt(2)/sqrt(abs(a)))*sqrt(abs(a)))/sqrt(abs(a)) + 2*sqrt(2)*arctan(1/2*sqrt(2)*(2*x - sqrt(2)/sqrt(abs(a)))*sqrt(abs(a)))/sqrt(abs(a)) + sqrt(2)*log(x^2 + sqrt(2)*x/sqrt(abs(a)) + 1/abs(a))/sqrt(abs(a)) - sqrt(2)*log(x^2 - sqrt(2)*x/sqrt(abs(a)) + 1/abs(a))/sqrt(abs(a))) - arctan(1/(a*x^2))/x","A",0
84,1,149,0,0.129991," ","integrate(arccot(a*x^2)/x^4,x, algorithm=""giac"")","\frac{1}{12} \, {\left(\frac{2 \, \sqrt{2} a^{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(2 \, x + \frac{\sqrt{2}}{\sqrt{{\left| a \right|}}}\right)} \sqrt{{\left| a \right|}}\right)}{{\left| a \right|}^{\frac{3}{2}}} + \frac{2 \, \sqrt{2} a^{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(2 \, x - \frac{\sqrt{2}}{\sqrt{{\left| a \right|}}}\right)} \sqrt{{\left| a \right|}}\right)}{{\left| a \right|}^{\frac{3}{2}}} - \sqrt{2} \sqrt{{\left| a \right|}} \log\left(x^{2} + \frac{\sqrt{2} x}{\sqrt{{\left| a \right|}}} + \frac{1}{{\left| a \right|}}\right) + \frac{\sqrt{2} a^{2} \log\left(x^{2} - \frac{\sqrt{2} x}{\sqrt{{\left| a \right|}}} + \frac{1}{{\left| a \right|}}\right)}{{\left| a \right|}^{\frac{3}{2}}} + \frac{8}{x}\right)} a - \frac{\arctan\left(\frac{1}{a x^{2}}\right)}{3 \, x^{3}}"," ",0,"1/12*(2*sqrt(2)*a^2*arctan(1/2*sqrt(2)*(2*x + sqrt(2)/sqrt(abs(a)))*sqrt(abs(a)))/abs(a)^(3/2) + 2*sqrt(2)*a^2*arctan(1/2*sqrt(2)*(2*x - sqrt(2)/sqrt(abs(a)))*sqrt(abs(a)))/abs(a)^(3/2) - sqrt(2)*sqrt(abs(a))*log(x^2 + sqrt(2)*x/sqrt(abs(a)) + 1/abs(a)) + sqrt(2)*a^2*log(x^2 - sqrt(2)*x/sqrt(abs(a)) + 1/abs(a))/abs(a)^(3/2) + 8/x)*a - 1/3*arctan(1/(a*x^2))/x^3","A",0
85,1,33,0,0.119399," ","integrate(x^2*arccot(x^(1/2)),x, algorithm=""giac"")","\frac{1}{3} \, x^{3} \arctan\left(\frac{1}{\sqrt{x}}\right) - \frac{1}{45} \, x^{\frac{5}{2}} {\left(\frac{5}{x} - \frac{15}{x^{2}} - 3\right)} + \frac{1}{3} \, \arctan\left(\frac{1}{\sqrt{x}}\right)"," ",0,"1/3*x^3*arctan(1/sqrt(x)) - 1/45*x^(5/2)*(5/x - 15/x^2 - 3) + 1/3*arctan(1/sqrt(x))","A",0
86,1,28,0,0.144187," ","integrate(x*arccot(x^(1/2)),x, algorithm=""giac"")","\frac{1}{2} \, x^{2} \arctan\left(\frac{1}{\sqrt{x}}\right) - \frac{1}{6} \, x^{\frac{3}{2}} {\left(\frac{3}{x} - 1\right)} - \frac{1}{2} \, \arctan\left(\frac{1}{\sqrt{x}}\right)"," ",0,"1/2*x^2*arctan(1/sqrt(x)) - 1/6*x^(3/2)*(3/x - 1) - 1/2*arctan(1/sqrt(x))","A",0
87,1,14,0,0.115404," ","integrate(arccot(x^(1/2)),x, algorithm=""giac"")","x \arctan\left(\frac{1}{\sqrt{x}}\right) + \sqrt{x} + \arctan\left(\frac{1}{\sqrt{x}}\right)"," ",0,"x*arctan(1/sqrt(x)) + sqrt(x) + arctan(1/sqrt(x))","A",0
88,1,19,0,0.151878," ","integrate(arccot(x^(1/2))/x,x, algorithm=""giac"")","-x \arctan\left(\frac{1}{\sqrt{x}}\right) - \sqrt{x} - \arctan\left(\frac{1}{\sqrt{x}}\right)"," ",0,"-x*arctan(1/sqrt(x)) - sqrt(x) - arctan(1/sqrt(x))","A",0
89,1,19,0,0.133623," ","integrate(arccot(x^(1/2))/x^2,x, algorithm=""giac"")","-\frac{\arctan\left(\frac{1}{\sqrt{x}}\right)}{x} + \frac{1}{\sqrt{x}} - \arctan\left(\frac{1}{\sqrt{x}}\right)"," ",0,"-arctan(1/sqrt(x))/x + 1/sqrt(x) - arctan(1/sqrt(x))","A",0
90,1,26,0,0.120952," ","integrate(arccot(x^(1/2))/x^3,x, algorithm=""giac"")","-\frac{1}{2 \, \sqrt{x}} - \frac{\arctan\left(\frac{1}{\sqrt{x}}\right)}{2 \, x^{2}} + \frac{1}{6 \, x^{\frac{3}{2}}} + \frac{1}{2} \, \arctan\left(\frac{1}{\sqrt{x}}\right)"," ",0,"-1/2/sqrt(x) - 1/2*arctan(1/sqrt(x))/x^2 + 1/6/x^(3/2) + 1/2*arctan(1/sqrt(x))","A",0
91,1,39,0,0.129164," ","integrate(x^(3/2)*arccot(x^(1/2)),x, algorithm=""giac"")","\frac{2}{5} \, x^{\frac{5}{2}} \arctan\left(\frac{1}{\sqrt{x}}\right) - \frac{1}{10} \, x^{2} {\left(\frac{2}{x} - \frac{3}{x^{2}} - 1\right)} + \frac{1}{5} \, \log\left(x\right) + \frac{1}{5} \, \log\left(\frac{1}{x} + 1\right)"," ",0,"2/5*x^(5/2)*arctan(1/sqrt(x)) - 1/10*x^2*(2/x - 3/x^2 - 1) + 1/5*log(x) + 1/5*log(1/x + 1)","A",0
92,1,30,0,0.119138," ","integrate(x^(1/2)*arccot(x^(1/2)),x, algorithm=""giac"")","\frac{2}{3} \, x^{\frac{3}{2}} \arctan\left(\frac{1}{\sqrt{x}}\right) - \frac{1}{3} \, x {\left(\frac{1}{x} - 1\right)} - \frac{1}{3} \, \log\left(x\right) - \frac{1}{3} \, \log\left(\frac{1}{x} + 1\right)"," ",0,"2/3*x^(3/2)*arctan(1/sqrt(x)) - 1/3*x*(1/x - 1) - 1/3*log(x) - 1/3*log(1/x + 1)","A",0
93,1,18,0,0.115033," ","integrate(arccot(x^(1/2))/x^(1/2),x, algorithm=""giac"")","2 \, \sqrt{x} \arctan\left(\frac{1}{\sqrt{x}}\right) + \log\left(x\right) + \log\left(\frac{1}{x} + 1\right)"," ",0,"2*sqrt(x)*arctan(1/sqrt(x)) + log(x) + log(1/x + 1)","A",0
94,1,16,0,0.135069," ","integrate(arccot(x^(1/2))/x^(3/2),x, algorithm=""giac"")","-\frac{2 \, \arctan\left(\frac{1}{\sqrt{x}}\right)}{\sqrt{x}} + \log\left(\frac{1}{x} + 1\right)"," ",0,"-2*arctan(1/sqrt(x))/sqrt(x) + log(1/x + 1)","A",0
95,1,23,0,0.129492," ","integrate(arccot(x^(1/2))/x^(5/2),x, algorithm=""giac"")","-\frac{2 \, \arctan\left(\frac{1}{\sqrt{x}}\right)}{3 \, x^{\frac{3}{2}}} + \frac{1}{3 \, x} - \frac{1}{3} \, \log\left(\frac{1}{x} + 1\right)"," ",0,"-2/3*arctan(1/sqrt(x))/x^(3/2) + 1/3/x - 1/3*log(1/x + 1)","A",0
96,1,13,0,0.122119," ","integrate(arccot(1/x),x, algorithm=""giac"")","x \arctan\left(x\right) - \frac{1}{2} \, \log\left(x^{2} + 1\right)"," ",0,"x*arctan(x) - 1/2*log(x^2 + 1)","A",0
97,0,0,0,0.000000," ","integrate(arccot(a*x^n)/x,x, algorithm=""giac"")","\int \frac{\operatorname{arccot}\left(a x^{n}\right)}{x}\,{d x}"," ",0,"integrate(arccot(a*x^n)/x, x)","F",0
98,0,0,0,0.000000," ","integrate(arccot(a*x^5)/x,x, algorithm=""giac"")","\int \frac{\operatorname{arccot}\left(a x^{5}\right)}{x}\,{d x}"," ",0,"integrate(arccot(a*x^5)/x, x)","F",0
99,1,617,0,0.981242," ","integrate(x^3*arccot(b*x+a),x, algorithm=""giac"")","\frac{96 \, a^{3} \arctan\left(\frac{1}{b x + a}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{5} + 72 \, a^{2} \arctan\left(\frac{1}{b x + a}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{6} + 24 \, a \arctan\left(\frac{1}{b x + a}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{7} + 3 \, \arctan\left(\frac{1}{b x + a}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{8} + 96 \, a^{3} \log\left(\frac{16 \, \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{2}}{\tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{4} - 96 \, a^{3} \arctan\left(\frac{1}{b x + a}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{3} + 144 \, a^{2} \arctan\left(\frac{1}{b x + a}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{4} - 144 \, a^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{5} - 72 \, a \arctan\left(\frac{1}{b x + a}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{5} - 24 \, a \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{6} - 12 \, \arctan\left(\frac{1}{b x + a}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{6} - 2 \, \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{7} - 96 \, a \log\left(\frac{16 \, \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{2}}{\tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{4} + 72 \, a^{2} \arctan\left(\frac{1}{b x + a}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{2} + 144 \, a^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{3} + 72 \, a \arctan\left(\frac{1}{b x + a}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{3} - 48 \, a \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{4} - 30 \, \arctan\left(\frac{1}{b x + a}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{4} + 30 \, \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{5} - 24 \, a \arctan\left(\frac{1}{b x + a}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right) - 24 \, a \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{2} - 12 \, \arctan\left(\frac{1}{b x + a}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{2} - 30 \, \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{3} + 3 \, \arctan\left(\frac{1}{b x + a}\right) + 2 \, \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)}{192 \, b^{4} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{4}}"," ",0,"1/192*(96*a^3*arctan(1/(b*x + a))*tan(1/2*arctan(1/(b*x + a)))^5 + 72*a^2*arctan(1/(b*x + a))*tan(1/2*arctan(1/(b*x + a)))^6 + 24*a*arctan(1/(b*x + a))*tan(1/2*arctan(1/(b*x + a)))^7 + 3*arctan(1/(b*x + a))*tan(1/2*arctan(1/(b*x + a)))^8 + 96*a^3*log(16*tan(1/2*arctan(1/(b*x + a)))^2/(tan(1/2*arctan(1/(b*x + a)))^4 + 2*tan(1/2*arctan(1/(b*x + a)))^2 + 1))*tan(1/2*arctan(1/(b*x + a)))^4 - 96*a^3*arctan(1/(b*x + a))*tan(1/2*arctan(1/(b*x + a)))^3 + 144*a^2*arctan(1/(b*x + a))*tan(1/2*arctan(1/(b*x + a)))^4 - 144*a^2*tan(1/2*arctan(1/(b*x + a)))^5 - 72*a*arctan(1/(b*x + a))*tan(1/2*arctan(1/(b*x + a)))^5 - 24*a*tan(1/2*arctan(1/(b*x + a)))^6 - 12*arctan(1/(b*x + a))*tan(1/2*arctan(1/(b*x + a)))^6 - 2*tan(1/2*arctan(1/(b*x + a)))^7 - 96*a*log(16*tan(1/2*arctan(1/(b*x + a)))^2/(tan(1/2*arctan(1/(b*x + a)))^4 + 2*tan(1/2*arctan(1/(b*x + a)))^2 + 1))*tan(1/2*arctan(1/(b*x + a)))^4 + 72*a^2*arctan(1/(b*x + a))*tan(1/2*arctan(1/(b*x + a)))^2 + 144*a^2*tan(1/2*arctan(1/(b*x + a)))^3 + 72*a*arctan(1/(b*x + a))*tan(1/2*arctan(1/(b*x + a)))^3 - 48*a*tan(1/2*arctan(1/(b*x + a)))^4 - 30*arctan(1/(b*x + a))*tan(1/2*arctan(1/(b*x + a)))^4 + 30*tan(1/2*arctan(1/(b*x + a)))^5 - 24*a*arctan(1/(b*x + a))*tan(1/2*arctan(1/(b*x + a))) - 24*a*tan(1/2*arctan(1/(b*x + a)))^2 - 12*arctan(1/(b*x + a))*tan(1/2*arctan(1/(b*x + a)))^2 - 30*tan(1/2*arctan(1/(b*x + a)))^3 + 3*arctan(1/(b*x + a)) + 2*tan(1/2*arctan(1/(b*x + a))))/(b^4*tan(1/2*arctan(1/(b*x + a)))^4)","B",0
100,1,423,0,0.846745," ","integrate(x^2*arccot(b*x+a),x, algorithm=""giac"")","-\frac{12 \, a^{2} \arctan\left(\frac{1}{b x + a}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{4} + 6 \, a \arctan\left(\frac{1}{b x + a}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{5} + \arctan\left(\frac{1}{b x + a}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{6} + 12 \, a^{2} \log\left(\frac{16 \, \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{2}}{\tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{3} - 12 \, a^{2} \arctan\left(\frac{1}{b x + a}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{2} + 12 \, a \arctan\left(\frac{1}{b x + a}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{3} - 12 \, a \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{4} - 3 \, \arctan\left(\frac{1}{b x + a}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{4} - \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{5} - 4 \, \log\left(\frac{16 \, \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{2}}{\tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{3} + 6 \, a \arctan\left(\frac{1}{b x + a}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right) + 12 \, a \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{2} + 3 \, \arctan\left(\frac{1}{b x + a}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{3} - \arctan\left(\frac{1}{b x + a}\right) - \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)}{24 \, b^{3} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{3}}"," ",0,"-1/24*(12*a^2*arctan(1/(b*x + a))*tan(1/2*arctan(1/(b*x + a)))^4 + 6*a*arctan(1/(b*x + a))*tan(1/2*arctan(1/(b*x + a)))^5 + arctan(1/(b*x + a))*tan(1/2*arctan(1/(b*x + a)))^6 + 12*a^2*log(16*tan(1/2*arctan(1/(b*x + a)))^2/(tan(1/2*arctan(1/(b*x + a)))^4 + 2*tan(1/2*arctan(1/(b*x + a)))^2 + 1))*tan(1/2*arctan(1/(b*x + a)))^3 - 12*a^2*arctan(1/(b*x + a))*tan(1/2*arctan(1/(b*x + a)))^2 + 12*a*arctan(1/(b*x + a))*tan(1/2*arctan(1/(b*x + a)))^3 - 12*a*tan(1/2*arctan(1/(b*x + a)))^4 - 3*arctan(1/(b*x + a))*tan(1/2*arctan(1/(b*x + a)))^4 - tan(1/2*arctan(1/(b*x + a)))^5 - 4*log(16*tan(1/2*arctan(1/(b*x + a)))^2/(tan(1/2*arctan(1/(b*x + a)))^4 + 2*tan(1/2*arctan(1/(b*x + a)))^2 + 1))*tan(1/2*arctan(1/(b*x + a)))^3 + 6*a*arctan(1/(b*x + a))*tan(1/2*arctan(1/(b*x + a))) + 12*a*tan(1/2*arctan(1/(b*x + a)))^2 + 3*arctan(1/(b*x + a))*tan(1/2*arctan(1/(b*x + a)))^2 - 2*tan(1/2*arctan(1/(b*x + a)))^3 - arctan(1/(b*x + a)) - tan(1/2*arctan(1/(b*x + a))))/(b^3*tan(1/2*arctan(1/(b*x + a)))^3)","B",0
101,1,210,0,0.271768," ","integrate(x*arccot(b*x+a),x, algorithm=""giac"")","\frac{4 \, a \arctan\left(\frac{1}{b x + a}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{3} + \arctan\left(\frac{1}{b x + a}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{4} + 4 \, a \log\left(\frac{16 \, \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{2}}{\tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{2} - 4 \, a \arctan\left(\frac{1}{b x + a}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right) + 2 \, \arctan\left(\frac{1}{b x + a}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{3} + \arctan\left(\frac{1}{b x + a}\right) + 2 \, \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)}{8 \, b^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{2}}"," ",0,"1/8*(4*a*arctan(1/(b*x + a))*tan(1/2*arctan(1/(b*x + a)))^3 + arctan(1/(b*x + a))*tan(1/2*arctan(1/(b*x + a)))^4 + 4*a*log(16*tan(1/2*arctan(1/(b*x + a)))^2/(tan(1/2*arctan(1/(b*x + a)))^4 + 2*tan(1/2*arctan(1/(b*x + a)))^2 + 1))*tan(1/2*arctan(1/(b*x + a)))^2 - 4*a*arctan(1/(b*x + a))*tan(1/2*arctan(1/(b*x + a))) + 2*arctan(1/(b*x + a))*tan(1/2*arctan(1/(b*x + a)))^2 - 2*tan(1/2*arctan(1/(b*x + a)))^3 + arctan(1/(b*x + a)) + 2*tan(1/2*arctan(1/(b*x + a))))/(b^2*tan(1/2*arctan(1/(b*x + a)))^2)","B",0
102,1,111,0,0.191920," ","integrate(arccot(b*x+a),x, algorithm=""giac"")","-\frac{\arctan\left(\frac{1}{b x + a}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{2} + \log\left(\frac{16 \, \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{2}}{\tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right) - \arctan\left(\frac{1}{b x + a}\right)}{2 \, b \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)}"," ",0,"-1/2*(arctan(1/(b*x + a))*tan(1/2*arctan(1/(b*x + a)))^2 + log(16*tan(1/2*arctan(1/(b*x + a)))^2/(tan(1/2*arctan(1/(b*x + a)))^4 + 2*tan(1/2*arctan(1/(b*x + a)))^2 + 1))*tan(1/2*arctan(1/(b*x + a))) - arctan(1/(b*x + a)))/(b*tan(1/2*arctan(1/(b*x + a))))","B",0
103,0,0,0,0.000000," ","integrate(arccot(b*x+a)/x,x, algorithm=""giac"")","\int \frac{\operatorname{arccot}\left(b x + a\right)}{x}\,{d x}"," ",0,"integrate(arccot(b*x + a)/x, x)","F",0
104,1,498,0,0.366953," ","integrate(arccot(b*x+a)/x^2,x, algorithm=""giac"")","-\frac{{\left(2 \, a \arctan\left(\frac{1}{b x + a}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{2} + 2 \, a \log\left(\frac{4 \, {\left(4 \, a^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{2} + 4 \, a \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{3} + \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{4} - 4 \, a \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right) - 2 \, \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{2} + 1\right)}}{\tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right) + \log\left(\frac{4 \, {\left(4 \, a^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{2} + 4 \, a \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{3} + \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{4} - 4 \, a \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right) - 2 \, \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{2} + 1\right)}}{\tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{2} - 2 \, a \arctan\left(\frac{1}{b x + a}\right) - 4 \, \arctan\left(\frac{1}{b x + a}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right) - \log\left(\frac{4 \, {\left(4 \, a^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{2} + 4 \, a \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{3} + \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{4} - 4 \, a \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right) - 2 \, \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{2} + 1\right)}}{\tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{2} + 1}\right)\right)} b}{2 \, {\left(2 \, a^{3} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right) + a^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{2} - a^{2} + 2 \, a \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right) + \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{2} - 1\right)}}"," ",0,"-1/2*(2*a*arctan(1/(b*x + a))*tan(1/2*arctan(1/(b*x + a)))^2 + 2*a*log(4*(4*a^2*tan(1/2*arctan(1/(b*x + a)))^2 + 4*a*tan(1/2*arctan(1/(b*x + a)))^3 + tan(1/2*arctan(1/(b*x + a)))^4 - 4*a*tan(1/2*arctan(1/(b*x + a))) - 2*tan(1/2*arctan(1/(b*x + a)))^2 + 1)/(tan(1/2*arctan(1/(b*x + a)))^4 + 2*tan(1/2*arctan(1/(b*x + a)))^2 + 1))*tan(1/2*arctan(1/(b*x + a))) + log(4*(4*a^2*tan(1/2*arctan(1/(b*x + a)))^2 + 4*a*tan(1/2*arctan(1/(b*x + a)))^3 + tan(1/2*arctan(1/(b*x + a)))^4 - 4*a*tan(1/2*arctan(1/(b*x + a))) - 2*tan(1/2*arctan(1/(b*x + a)))^2 + 1)/(tan(1/2*arctan(1/(b*x + a)))^4 + 2*tan(1/2*arctan(1/(b*x + a)))^2 + 1))*tan(1/2*arctan(1/(b*x + a)))^2 - 2*a*arctan(1/(b*x + a)) - 4*arctan(1/(b*x + a))*tan(1/2*arctan(1/(b*x + a))) - log(4*(4*a^2*tan(1/2*arctan(1/(b*x + a)))^2 + 4*a*tan(1/2*arctan(1/(b*x + a)))^3 + tan(1/2*arctan(1/(b*x + a)))^4 - 4*a*tan(1/2*arctan(1/(b*x + a))) - 2*tan(1/2*arctan(1/(b*x + a)))^2 + 1)/(tan(1/2*arctan(1/(b*x + a)))^4 + 2*tan(1/2*arctan(1/(b*x + a)))^2 + 1)))*b/(2*a^3*tan(1/2*arctan(1/(b*x + a))) + a^2*tan(1/2*arctan(1/(b*x + a)))^2 - a^2 + 2*a*tan(1/2*arctan(1/(b*x + a))) + tan(1/2*arctan(1/(b*x + a)))^2 - 1)","B",0
105,1,1309,0,0.712252," ","integrate(arccot(b*x+a)/x^3,x, algorithm=""giac"")","\frac{{\left(4 \, a^{3} b \arctan\left(\frac{1}{b x + a}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{3} + a^{2} b \arctan\left(\frac{1}{b x + a}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{4} + 4 \, a^{3} b \log\left(\frac{4 \, {\left(4 \, a^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{2} + 4 \, a \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{3} + \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{4} - 4 \, a \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right) - 2 \, \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{2} + 1\right)}}{\tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{2} + 4 \, a^{2} b \log\left(\frac{4 \, {\left(4 \, a^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{2} + 4 \, a \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{3} + \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{4} - 4 \, a \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right) - 2 \, \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{2} + 1\right)}}{\tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{3} + a b \log\left(\frac{4 \, {\left(4 \, a^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{2} + 4 \, a \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{3} + \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{4} - 4 \, a \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right) - 2 \, \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{2} + 1\right)}}{\tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{4} - 4 \, a^{3} b \arctan\left(\frac{1}{b x + a}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right) - 14 \, a^{2} b \arctan\left(\frac{1}{b x + a}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{2} + 2 \, a^{2} b \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{3} - 4 \, a b \arctan\left(\frac{1}{b x + a}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{3} + a b \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{4} - b \arctan\left(\frac{1}{b x + a}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{4} - 4 \, a^{2} b \log\left(\frac{4 \, {\left(4 \, a^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{2} + 4 \, a \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{3} + \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{4} - 4 \, a \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right) - 2 \, \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{2} + 1\right)}}{\tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right) - 2 \, a b \log\left(\frac{4 \, {\left(4 \, a^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{2} + 4 \, a \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{3} + \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{4} - 4 \, a \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right) - 2 \, \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{2} + 1\right)}}{\tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{2} + a^{2} b \arctan\left(\frac{1}{b x + a}\right) - 2 \, a^{2} b \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right) + 4 \, a b \arctan\left(\frac{1}{b x + a}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right) - 6 \, a b \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{2} - 2 \, b \arctan\left(\frac{1}{b x + a}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{2} - 2 \, b \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{3} + a b \log\left(\frac{4 \, {\left(4 \, a^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{2} + 4 \, a \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{3} + \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{4} - 4 \, a \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right) - 2 \, \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{2} + 1\right)}}{\tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{2} + 1}\right) + a b - b \arctan\left(\frac{1}{b x + a}\right) + 2 \, b \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)\right)} b}{2 \, {\left(4 \, a^{6} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{2} + 4 \, a^{5} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{3} + a^{4} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{4} - 4 \, a^{5} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right) + 6 \, a^{4} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{2} + 8 \, a^{3} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{3} + 2 \, a^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{4} + a^{4} - 8 \, a^{3} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right) + 4 \, a \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{3} + \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{4} + 2 \, a^{2} - 4 \, a \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right) - 2 \, \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{2} + 1\right)}}"," ",0,"1/2*(4*a^3*b*arctan(1/(b*x + a))*tan(1/2*arctan(1/(b*x + a)))^3 + a^2*b*arctan(1/(b*x + a))*tan(1/2*arctan(1/(b*x + a)))^4 + 4*a^3*b*log(4*(4*a^2*tan(1/2*arctan(1/(b*x + a)))^2 + 4*a*tan(1/2*arctan(1/(b*x + a)))^3 + tan(1/2*arctan(1/(b*x + a)))^4 - 4*a*tan(1/2*arctan(1/(b*x + a))) - 2*tan(1/2*arctan(1/(b*x + a)))^2 + 1)/(tan(1/2*arctan(1/(b*x + a)))^4 + 2*tan(1/2*arctan(1/(b*x + a)))^2 + 1))*tan(1/2*arctan(1/(b*x + a)))^2 + 4*a^2*b*log(4*(4*a^2*tan(1/2*arctan(1/(b*x + a)))^2 + 4*a*tan(1/2*arctan(1/(b*x + a)))^3 + tan(1/2*arctan(1/(b*x + a)))^4 - 4*a*tan(1/2*arctan(1/(b*x + a))) - 2*tan(1/2*arctan(1/(b*x + a)))^2 + 1)/(tan(1/2*arctan(1/(b*x + a)))^4 + 2*tan(1/2*arctan(1/(b*x + a)))^2 + 1))*tan(1/2*arctan(1/(b*x + a)))^3 + a*b*log(4*(4*a^2*tan(1/2*arctan(1/(b*x + a)))^2 + 4*a*tan(1/2*arctan(1/(b*x + a)))^3 + tan(1/2*arctan(1/(b*x + a)))^4 - 4*a*tan(1/2*arctan(1/(b*x + a))) - 2*tan(1/2*arctan(1/(b*x + a)))^2 + 1)/(tan(1/2*arctan(1/(b*x + a)))^4 + 2*tan(1/2*arctan(1/(b*x + a)))^2 + 1))*tan(1/2*arctan(1/(b*x + a)))^4 - 4*a^3*b*arctan(1/(b*x + a))*tan(1/2*arctan(1/(b*x + a))) - 14*a^2*b*arctan(1/(b*x + a))*tan(1/2*arctan(1/(b*x + a)))^2 + 2*a^2*b*tan(1/2*arctan(1/(b*x + a)))^3 - 4*a*b*arctan(1/(b*x + a))*tan(1/2*arctan(1/(b*x + a)))^3 + a*b*tan(1/2*arctan(1/(b*x + a)))^4 - b*arctan(1/(b*x + a))*tan(1/2*arctan(1/(b*x + a)))^4 - 4*a^2*b*log(4*(4*a^2*tan(1/2*arctan(1/(b*x + a)))^2 + 4*a*tan(1/2*arctan(1/(b*x + a)))^3 + tan(1/2*arctan(1/(b*x + a)))^4 - 4*a*tan(1/2*arctan(1/(b*x + a))) - 2*tan(1/2*arctan(1/(b*x + a)))^2 + 1)/(tan(1/2*arctan(1/(b*x + a)))^4 + 2*tan(1/2*arctan(1/(b*x + a)))^2 + 1))*tan(1/2*arctan(1/(b*x + a))) - 2*a*b*log(4*(4*a^2*tan(1/2*arctan(1/(b*x + a)))^2 + 4*a*tan(1/2*arctan(1/(b*x + a)))^3 + tan(1/2*arctan(1/(b*x + a)))^4 - 4*a*tan(1/2*arctan(1/(b*x + a))) - 2*tan(1/2*arctan(1/(b*x + a)))^2 + 1)/(tan(1/2*arctan(1/(b*x + a)))^4 + 2*tan(1/2*arctan(1/(b*x + a)))^2 + 1))*tan(1/2*arctan(1/(b*x + a)))^2 + a^2*b*arctan(1/(b*x + a)) - 2*a^2*b*tan(1/2*arctan(1/(b*x + a))) + 4*a*b*arctan(1/(b*x + a))*tan(1/2*arctan(1/(b*x + a))) - 6*a*b*tan(1/2*arctan(1/(b*x + a)))^2 - 2*b*arctan(1/(b*x + a))*tan(1/2*arctan(1/(b*x + a)))^2 - 2*b*tan(1/2*arctan(1/(b*x + a)))^3 + a*b*log(4*(4*a^2*tan(1/2*arctan(1/(b*x + a)))^2 + 4*a*tan(1/2*arctan(1/(b*x + a)))^3 + tan(1/2*arctan(1/(b*x + a)))^4 - 4*a*tan(1/2*arctan(1/(b*x + a))) - 2*tan(1/2*arctan(1/(b*x + a)))^2 + 1)/(tan(1/2*arctan(1/(b*x + a)))^4 + 2*tan(1/2*arctan(1/(b*x + a)))^2 + 1)) + a*b - b*arctan(1/(b*x + a)) + 2*b*tan(1/2*arctan(1/(b*x + a))))*b/(4*a^6*tan(1/2*arctan(1/(b*x + a)))^2 + 4*a^5*tan(1/2*arctan(1/(b*x + a)))^3 + a^4*tan(1/2*arctan(1/(b*x + a)))^4 - 4*a^5*tan(1/2*arctan(1/(b*x + a))) + 6*a^4*tan(1/2*arctan(1/(b*x + a)))^2 + 8*a^3*tan(1/2*arctan(1/(b*x + a)))^3 + 2*a^2*tan(1/2*arctan(1/(b*x + a)))^4 + a^4 - 8*a^3*tan(1/2*arctan(1/(b*x + a))) + 4*a*tan(1/2*arctan(1/(b*x + a)))^3 + tan(1/2*arctan(1/(b*x + a)))^4 + 2*a^2 - 4*a*tan(1/2*arctan(1/(b*x + a))) - 2*tan(1/2*arctan(1/(b*x + a)))^2 + 1)","B",0
106,1,3449,0,2.611609," ","integrate(arccot(b*x+a)/x^4,x, algorithm=""giac"")","-\frac{{\left(24 \, a^{5} b^{2} \arctan\left(\frac{1}{b x + a}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{4} + 12 \, a^{4} b^{2} \arctan\left(\frac{1}{b x + a}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{5} + 2 \, a^{3} b^{2} \arctan\left(\frac{1}{b x + a}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{6} + 24 \, a^{5} b^{2} \log\left(\frac{4 \, {\left(4 \, a^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{2} + 4 \, a \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{3} + \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{4} - 4 \, a \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right) - 2 \, \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{2} + 1\right)}}{\tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{3} + 36 \, a^{4} b^{2} \log\left(\frac{4 \, {\left(4 \, a^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{2} + 4 \, a \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{3} + \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{4} - 4 \, a \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right) - 2 \, \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{2} + 1\right)}}{\tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{4} + 18 \, a^{3} b^{2} \log\left(\frac{4 \, {\left(4 \, a^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{2} + 4 \, a \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{3} + \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{4} - 4 \, a \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right) - 2 \, \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{2} + 1\right)}}{\tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{5} + 3 \, a^{2} b^{2} \log\left(\frac{4 \, {\left(4 \, a^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{2} + 4 \, a \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{3} + \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{4} - 4 \, a \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right) - 2 \, \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{2} + 1\right)}}{\tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{6} - 24 \, a^{5} b^{2} \arctan\left(\frac{1}{b x + a}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{2} - 120 \, a^{4} b^{2} \arctan\left(\frac{1}{b x + a}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{3} + 24 \, a^{4} b^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{4} - 78 \, a^{3} b^{2} \arctan\left(\frac{1}{b x + a}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{4} + 22 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{5} - 36 \, a^{2} b^{2} \arctan\left(\frac{1}{b x + a}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{5} + 5 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{6} - 6 \, a b^{2} \arctan\left(\frac{1}{b x + a}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{6} - 36 \, a^{4} b^{2} \log\left(\frac{4 \, {\left(4 \, a^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{2} + 4 \, a \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{3} + \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{4} - 4 \, a \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right) - 2 \, \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{2} + 1\right)}}{\tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{2} - 44 \, a^{3} b^{2} \log\left(\frac{4 \, {\left(4 \, a^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{2} + 4 \, a \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{3} + \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{4} - 4 \, a \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right) - 2 \, \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{2} + 1\right)}}{\tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{3} - 21 \, a^{2} b^{2} \log\left(\frac{4 \, {\left(4 \, a^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{2} + 4 \, a \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{3} + \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{4} - 4 \, a \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right) - 2 \, \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{2} + 1\right)}}{\tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{4} - 6 \, a b^{2} \log\left(\frac{4 \, {\left(4 \, a^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{2} + 4 \, a \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{3} + \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{4} - 4 \, a \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right) - 2 \, \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{2} + 1\right)}}{\tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{5} - b^{2} \log\left(\frac{4 \, {\left(4 \, a^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{2} + 4 \, a \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{3} + \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{4} - 4 \, a \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right) - 2 \, \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{2} + 1\right)}}{\tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{6} + 12 \, a^{4} b^{2} \arctan\left(\frac{1}{b x + a}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right) - 24 \, a^{4} b^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{2} + 78 \, a^{3} b^{2} \arctan\left(\frac{1}{b x + a}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{2} - 100 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{3} + 24 \, a^{2} b^{2} \arctan\left(\frac{1}{b x + a}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{3} - 67 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{4} + 18 \, a b^{2} \arctan\left(\frac{1}{b x + a}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{4} - 14 \, a b^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{5} - b^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{6} + 18 \, a^{3} b^{2} \log\left(\frac{4 \, {\left(4 \, a^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{2} + 4 \, a \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{3} + \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{4} - 4 \, a \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right) - 2 \, \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{2} + 1\right)}}{\tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right) + 21 \, a^{2} b^{2} \log\left(\frac{4 \, {\left(4 \, a^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{2} + 4 \, a \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{3} + \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{4} - 4 \, a \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right) - 2 \, \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{2} + 1\right)}}{\tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{2} + 12 \, a b^{2} \log\left(\frac{4 \, {\left(4 \, a^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{2} + 4 \, a \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{3} + \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{4} - 4 \, a \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right) - 2 \, \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{2} + 1\right)}}{\tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{3} + 3 \, b^{2} \log\left(\frac{4 \, {\left(4 \, a^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{2} + 4 \, a \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{3} + \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{4} - 4 \, a \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right) - 2 \, \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{2} + 1\right)}}{\tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{4} - 2 \, a^{3} b^{2} \arctan\left(\frac{1}{b x + a}\right) + 22 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right) - 36 \, a^{2} b^{2} \arctan\left(\frac{1}{b x + a}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right) + 67 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{2} - 18 \, a b^{2} \arctan\left(\frac{1}{b x + a}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{2} + 20 \, a b^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{3} - 16 \, b^{2} \arctan\left(\frac{1}{b x + a}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{3} - b^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{4} - 3 \, a^{2} b^{2} \log\left(\frac{4 \, {\left(4 \, a^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{2} + 4 \, a \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{3} + \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{4} - 4 \, a \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right) - 2 \, \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{2} + 1\right)}}{\tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{2} + 1}\right) - 6 \, a b^{2} \log\left(\frac{4 \, {\left(4 \, a^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{2} + 4 \, a \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{3} + \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{4} - 4 \, a \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right) - 2 \, \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{2} + 1\right)}}{\tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right) - 3 \, b^{2} \log\left(\frac{4 \, {\left(4 \, a^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{2} + 4 \, a \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{3} + \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{4} - 4 \, a \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right) - 2 \, \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{2} + 1\right)}}{\tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{2} - 5 \, a^{2} b^{2} + 6 \, a b^{2} \arctan\left(\frac{1}{b x + a}\right) - 14 \, a b^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right) + b^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{2} + b^{2} \log\left(\frac{4 \, {\left(4 \, a^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{2} + 4 \, a \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{3} + \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{4} - 4 \, a \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right) - 2 \, \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{2} + 1\right)}}{\tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{2} + 1}\right) + b^{2}\right)} b}{6 \, {\left(8 \, a^{9} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{3} + 12 \, a^{8} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{4} + 6 \, a^{7} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{5} + a^{6} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{6} - 12 \, a^{8} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{2} + 12 \, a^{7} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{3} + 33 \, a^{6} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{4} + 18 \, a^{5} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{5} + 3 \, a^{4} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{6} + 6 \, a^{7} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right) - 33 \, a^{6} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{2} - 12 \, a^{5} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{3} + 27 \, a^{4} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{4} + 18 \, a^{3} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{5} + 3 \, a^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{6} - a^{6} + 18 \, a^{5} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right) - 27 \, a^{4} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{2} - 28 \, a^{3} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{3} + 3 \, a^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{4} + 6 \, a \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{5} + \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{6} - 3 \, a^{4} + 18 \, a^{3} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right) - 3 \, a^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{2} - 12 \, a \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{3} - 3 \, \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{4} - 3 \, a^{2} + 6 \, a \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right) + 3 \, \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{2} - 1\right)}}"," ",0,"-1/6*(24*a^5*b^2*arctan(1/(b*x + a))*tan(1/2*arctan(1/(b*x + a)))^4 + 12*a^4*b^2*arctan(1/(b*x + a))*tan(1/2*arctan(1/(b*x + a)))^5 + 2*a^3*b^2*arctan(1/(b*x + a))*tan(1/2*arctan(1/(b*x + a)))^6 + 24*a^5*b^2*log(4*(4*a^2*tan(1/2*arctan(1/(b*x + a)))^2 + 4*a*tan(1/2*arctan(1/(b*x + a)))^3 + tan(1/2*arctan(1/(b*x + a)))^4 - 4*a*tan(1/2*arctan(1/(b*x + a))) - 2*tan(1/2*arctan(1/(b*x + a)))^2 + 1)/(tan(1/2*arctan(1/(b*x + a)))^4 + 2*tan(1/2*arctan(1/(b*x + a)))^2 + 1))*tan(1/2*arctan(1/(b*x + a)))^3 + 36*a^4*b^2*log(4*(4*a^2*tan(1/2*arctan(1/(b*x + a)))^2 + 4*a*tan(1/2*arctan(1/(b*x + a)))^3 + tan(1/2*arctan(1/(b*x + a)))^4 - 4*a*tan(1/2*arctan(1/(b*x + a))) - 2*tan(1/2*arctan(1/(b*x + a)))^2 + 1)/(tan(1/2*arctan(1/(b*x + a)))^4 + 2*tan(1/2*arctan(1/(b*x + a)))^2 + 1))*tan(1/2*arctan(1/(b*x + a)))^4 + 18*a^3*b^2*log(4*(4*a^2*tan(1/2*arctan(1/(b*x + a)))^2 + 4*a*tan(1/2*arctan(1/(b*x + a)))^3 + tan(1/2*arctan(1/(b*x + a)))^4 - 4*a*tan(1/2*arctan(1/(b*x + a))) - 2*tan(1/2*arctan(1/(b*x + a)))^2 + 1)/(tan(1/2*arctan(1/(b*x + a)))^4 + 2*tan(1/2*arctan(1/(b*x + a)))^2 + 1))*tan(1/2*arctan(1/(b*x + a)))^5 + 3*a^2*b^2*log(4*(4*a^2*tan(1/2*arctan(1/(b*x + a)))^2 + 4*a*tan(1/2*arctan(1/(b*x + a)))^3 + tan(1/2*arctan(1/(b*x + a)))^4 - 4*a*tan(1/2*arctan(1/(b*x + a))) - 2*tan(1/2*arctan(1/(b*x + a)))^2 + 1)/(tan(1/2*arctan(1/(b*x + a)))^4 + 2*tan(1/2*arctan(1/(b*x + a)))^2 + 1))*tan(1/2*arctan(1/(b*x + a)))^6 - 24*a^5*b^2*arctan(1/(b*x + a))*tan(1/2*arctan(1/(b*x + a)))^2 - 120*a^4*b^2*arctan(1/(b*x + a))*tan(1/2*arctan(1/(b*x + a)))^3 + 24*a^4*b^2*tan(1/2*arctan(1/(b*x + a)))^4 - 78*a^3*b^2*arctan(1/(b*x + a))*tan(1/2*arctan(1/(b*x + a)))^4 + 22*a^3*b^2*tan(1/2*arctan(1/(b*x + a)))^5 - 36*a^2*b^2*arctan(1/(b*x + a))*tan(1/2*arctan(1/(b*x + a)))^5 + 5*a^2*b^2*tan(1/2*arctan(1/(b*x + a)))^6 - 6*a*b^2*arctan(1/(b*x + a))*tan(1/2*arctan(1/(b*x + a)))^6 - 36*a^4*b^2*log(4*(4*a^2*tan(1/2*arctan(1/(b*x + a)))^2 + 4*a*tan(1/2*arctan(1/(b*x + a)))^3 + tan(1/2*arctan(1/(b*x + a)))^4 - 4*a*tan(1/2*arctan(1/(b*x + a))) - 2*tan(1/2*arctan(1/(b*x + a)))^2 + 1)/(tan(1/2*arctan(1/(b*x + a)))^4 + 2*tan(1/2*arctan(1/(b*x + a)))^2 + 1))*tan(1/2*arctan(1/(b*x + a)))^2 - 44*a^3*b^2*log(4*(4*a^2*tan(1/2*arctan(1/(b*x + a)))^2 + 4*a*tan(1/2*arctan(1/(b*x + a)))^3 + tan(1/2*arctan(1/(b*x + a)))^4 - 4*a*tan(1/2*arctan(1/(b*x + a))) - 2*tan(1/2*arctan(1/(b*x + a)))^2 + 1)/(tan(1/2*arctan(1/(b*x + a)))^4 + 2*tan(1/2*arctan(1/(b*x + a)))^2 + 1))*tan(1/2*arctan(1/(b*x + a)))^3 - 21*a^2*b^2*log(4*(4*a^2*tan(1/2*arctan(1/(b*x + a)))^2 + 4*a*tan(1/2*arctan(1/(b*x + a)))^3 + tan(1/2*arctan(1/(b*x + a)))^4 - 4*a*tan(1/2*arctan(1/(b*x + a))) - 2*tan(1/2*arctan(1/(b*x + a)))^2 + 1)/(tan(1/2*arctan(1/(b*x + a)))^4 + 2*tan(1/2*arctan(1/(b*x + a)))^2 + 1))*tan(1/2*arctan(1/(b*x + a)))^4 - 6*a*b^2*log(4*(4*a^2*tan(1/2*arctan(1/(b*x + a)))^2 + 4*a*tan(1/2*arctan(1/(b*x + a)))^3 + tan(1/2*arctan(1/(b*x + a)))^4 - 4*a*tan(1/2*arctan(1/(b*x + a))) - 2*tan(1/2*arctan(1/(b*x + a)))^2 + 1)/(tan(1/2*arctan(1/(b*x + a)))^4 + 2*tan(1/2*arctan(1/(b*x + a)))^2 + 1))*tan(1/2*arctan(1/(b*x + a)))^5 - b^2*log(4*(4*a^2*tan(1/2*arctan(1/(b*x + a)))^2 + 4*a*tan(1/2*arctan(1/(b*x + a)))^3 + tan(1/2*arctan(1/(b*x + a)))^4 - 4*a*tan(1/2*arctan(1/(b*x + a))) - 2*tan(1/2*arctan(1/(b*x + a)))^2 + 1)/(tan(1/2*arctan(1/(b*x + a)))^4 + 2*tan(1/2*arctan(1/(b*x + a)))^2 + 1))*tan(1/2*arctan(1/(b*x + a)))^6 + 12*a^4*b^2*arctan(1/(b*x + a))*tan(1/2*arctan(1/(b*x + a))) - 24*a^4*b^2*tan(1/2*arctan(1/(b*x + a)))^2 + 78*a^3*b^2*arctan(1/(b*x + a))*tan(1/2*arctan(1/(b*x + a)))^2 - 100*a^3*b^2*tan(1/2*arctan(1/(b*x + a)))^3 + 24*a^2*b^2*arctan(1/(b*x + a))*tan(1/2*arctan(1/(b*x + a)))^3 - 67*a^2*b^2*tan(1/2*arctan(1/(b*x + a)))^4 + 18*a*b^2*arctan(1/(b*x + a))*tan(1/2*arctan(1/(b*x + a)))^4 - 14*a*b^2*tan(1/2*arctan(1/(b*x + a)))^5 - b^2*tan(1/2*arctan(1/(b*x + a)))^6 + 18*a^3*b^2*log(4*(4*a^2*tan(1/2*arctan(1/(b*x + a)))^2 + 4*a*tan(1/2*arctan(1/(b*x + a)))^3 + tan(1/2*arctan(1/(b*x + a)))^4 - 4*a*tan(1/2*arctan(1/(b*x + a))) - 2*tan(1/2*arctan(1/(b*x + a)))^2 + 1)/(tan(1/2*arctan(1/(b*x + a)))^4 + 2*tan(1/2*arctan(1/(b*x + a)))^2 + 1))*tan(1/2*arctan(1/(b*x + a))) + 21*a^2*b^2*log(4*(4*a^2*tan(1/2*arctan(1/(b*x + a)))^2 + 4*a*tan(1/2*arctan(1/(b*x + a)))^3 + tan(1/2*arctan(1/(b*x + a)))^4 - 4*a*tan(1/2*arctan(1/(b*x + a))) - 2*tan(1/2*arctan(1/(b*x + a)))^2 + 1)/(tan(1/2*arctan(1/(b*x + a)))^4 + 2*tan(1/2*arctan(1/(b*x + a)))^2 + 1))*tan(1/2*arctan(1/(b*x + a)))^2 + 12*a*b^2*log(4*(4*a^2*tan(1/2*arctan(1/(b*x + a)))^2 + 4*a*tan(1/2*arctan(1/(b*x + a)))^3 + tan(1/2*arctan(1/(b*x + a)))^4 - 4*a*tan(1/2*arctan(1/(b*x + a))) - 2*tan(1/2*arctan(1/(b*x + a)))^2 + 1)/(tan(1/2*arctan(1/(b*x + a)))^4 + 2*tan(1/2*arctan(1/(b*x + a)))^2 + 1))*tan(1/2*arctan(1/(b*x + a)))^3 + 3*b^2*log(4*(4*a^2*tan(1/2*arctan(1/(b*x + a)))^2 + 4*a*tan(1/2*arctan(1/(b*x + a)))^3 + tan(1/2*arctan(1/(b*x + a)))^4 - 4*a*tan(1/2*arctan(1/(b*x + a))) - 2*tan(1/2*arctan(1/(b*x + a)))^2 + 1)/(tan(1/2*arctan(1/(b*x + a)))^4 + 2*tan(1/2*arctan(1/(b*x + a)))^2 + 1))*tan(1/2*arctan(1/(b*x + a)))^4 - 2*a^3*b^2*arctan(1/(b*x + a)) + 22*a^3*b^2*tan(1/2*arctan(1/(b*x + a))) - 36*a^2*b^2*arctan(1/(b*x + a))*tan(1/2*arctan(1/(b*x + a))) + 67*a^2*b^2*tan(1/2*arctan(1/(b*x + a)))^2 - 18*a*b^2*arctan(1/(b*x + a))*tan(1/2*arctan(1/(b*x + a)))^2 + 20*a*b^2*tan(1/2*arctan(1/(b*x + a)))^3 - 16*b^2*arctan(1/(b*x + a))*tan(1/2*arctan(1/(b*x + a)))^3 - b^2*tan(1/2*arctan(1/(b*x + a)))^4 - 3*a^2*b^2*log(4*(4*a^2*tan(1/2*arctan(1/(b*x + a)))^2 + 4*a*tan(1/2*arctan(1/(b*x + a)))^3 + tan(1/2*arctan(1/(b*x + a)))^4 - 4*a*tan(1/2*arctan(1/(b*x + a))) - 2*tan(1/2*arctan(1/(b*x + a)))^2 + 1)/(tan(1/2*arctan(1/(b*x + a)))^4 + 2*tan(1/2*arctan(1/(b*x + a)))^2 + 1)) - 6*a*b^2*log(4*(4*a^2*tan(1/2*arctan(1/(b*x + a)))^2 + 4*a*tan(1/2*arctan(1/(b*x + a)))^3 + tan(1/2*arctan(1/(b*x + a)))^4 - 4*a*tan(1/2*arctan(1/(b*x + a))) - 2*tan(1/2*arctan(1/(b*x + a)))^2 + 1)/(tan(1/2*arctan(1/(b*x + a)))^4 + 2*tan(1/2*arctan(1/(b*x + a)))^2 + 1))*tan(1/2*arctan(1/(b*x + a))) - 3*b^2*log(4*(4*a^2*tan(1/2*arctan(1/(b*x + a)))^2 + 4*a*tan(1/2*arctan(1/(b*x + a)))^3 + tan(1/2*arctan(1/(b*x + a)))^4 - 4*a*tan(1/2*arctan(1/(b*x + a))) - 2*tan(1/2*arctan(1/(b*x + a)))^2 + 1)/(tan(1/2*arctan(1/(b*x + a)))^4 + 2*tan(1/2*arctan(1/(b*x + a)))^2 + 1))*tan(1/2*arctan(1/(b*x + a)))^2 - 5*a^2*b^2 + 6*a*b^2*arctan(1/(b*x + a)) - 14*a*b^2*tan(1/2*arctan(1/(b*x + a))) + b^2*tan(1/2*arctan(1/(b*x + a)))^2 + b^2*log(4*(4*a^2*tan(1/2*arctan(1/(b*x + a)))^2 + 4*a*tan(1/2*arctan(1/(b*x + a)))^3 + tan(1/2*arctan(1/(b*x + a)))^4 - 4*a*tan(1/2*arctan(1/(b*x + a))) - 2*tan(1/2*arctan(1/(b*x + a)))^2 + 1)/(tan(1/2*arctan(1/(b*x + a)))^4 + 2*tan(1/2*arctan(1/(b*x + a)))^2 + 1)) + b^2)*b/(8*a^9*tan(1/2*arctan(1/(b*x + a)))^3 + 12*a^8*tan(1/2*arctan(1/(b*x + a)))^4 + 6*a^7*tan(1/2*arctan(1/(b*x + a)))^5 + a^6*tan(1/2*arctan(1/(b*x + a)))^6 - 12*a^8*tan(1/2*arctan(1/(b*x + a)))^2 + 12*a^7*tan(1/2*arctan(1/(b*x + a)))^3 + 33*a^6*tan(1/2*arctan(1/(b*x + a)))^4 + 18*a^5*tan(1/2*arctan(1/(b*x + a)))^5 + 3*a^4*tan(1/2*arctan(1/(b*x + a)))^6 + 6*a^7*tan(1/2*arctan(1/(b*x + a))) - 33*a^6*tan(1/2*arctan(1/(b*x + a)))^2 - 12*a^5*tan(1/2*arctan(1/(b*x + a)))^3 + 27*a^4*tan(1/2*arctan(1/(b*x + a)))^4 + 18*a^3*tan(1/2*arctan(1/(b*x + a)))^5 + 3*a^2*tan(1/2*arctan(1/(b*x + a)))^6 - a^6 + 18*a^5*tan(1/2*arctan(1/(b*x + a))) - 27*a^4*tan(1/2*arctan(1/(b*x + a)))^2 - 28*a^3*tan(1/2*arctan(1/(b*x + a)))^3 + 3*a^2*tan(1/2*arctan(1/(b*x + a)))^4 + 6*a*tan(1/2*arctan(1/(b*x + a)))^5 + tan(1/2*arctan(1/(b*x + a)))^6 - 3*a^4 + 18*a^3*tan(1/2*arctan(1/(b*x + a))) - 3*a^2*tan(1/2*arctan(1/(b*x + a)))^2 - 12*a*tan(1/2*arctan(1/(b*x + a)))^3 - 3*tan(1/2*arctan(1/(b*x + a)))^4 - 3*a^2 + 6*a*tan(1/2*arctan(1/(b*x + a))) + 3*tan(1/2*arctan(1/(b*x + a)))^2 - 1)","B",0
107,-1,0,0,0.000000," ","integrate(arccot(b*x+a)/(d*x^2+c),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
108,0,0,0,0.000000," ","integrate(arccot(b*x+a)/(d*x+c),x, algorithm=""giac"")","\int \frac{\operatorname{arccot}\left(b x + a\right)}{d x + c}\,{d x}"," ",0,"integrate(arccot(b*x + a)/(d*x + c), x)","F",0
109,0,0,0,0.000000," ","integrate(arccot(b*x+a)/(c+d/x),x, algorithm=""giac"")","\int \frac{\operatorname{arccot}\left(b x + a\right)}{c + \frac{d}{x}}\,{d x}"," ",0,"integrate(arccot(b*x + a)/(c + d/x), x)","F",0
110,-1,0,0,0.000000," ","integrate(arccot(b*x+a)/(c+d/x^2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
111,-1,0,0,0.000000," ","integrate(arccot(b*x+a)/(c+d*x^(1/2)),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
112,-1,0,0,0.000000," ","integrate(arccot(b*x+a)/(c+d/x^(1/2)),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
113,-1,0,0,0.000000," ","integrate(arccot(e*x+d)/(c*x^2+b*x+a),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",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=""giac"")","\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=""giac"")","\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=""giac"")","\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=""giac"")","\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=""giac"")","\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=""giac"")","\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=""giac"")","\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=""giac"")","\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
122,1,203,0,0.307988," ","integrate((b*x+a)^2*arccot(b*x+a),x, algorithm=""giac"")","-\frac{\arctan\left(\frac{1}{b x + a}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{6} - 3 \, \arctan\left(\frac{1}{b x + a}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{4} - \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{5} - 4 \, \log\left(\frac{16 \, \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{2}}{\tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{3} + 3 \, \arctan\left(\frac{1}{b x + a}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{3} - \arctan\left(\frac{1}{b x + a}\right) - \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)}{24 \, b \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{3}}"," ",0,"-1/24*(arctan(1/(b*x + a))*tan(1/2*arctan(1/(b*x + a)))^6 - 3*arctan(1/(b*x + a))*tan(1/2*arctan(1/(b*x + a)))^4 - tan(1/2*arctan(1/(b*x + a)))^5 - 4*log(16*tan(1/2*arctan(1/(b*x + a)))^2/(tan(1/2*arctan(1/(b*x + a)))^4 + 2*tan(1/2*arctan(1/(b*x + a)))^2 + 1))*tan(1/2*arctan(1/(b*x + a)))^3 + 3*arctan(1/(b*x + a))*tan(1/2*arctan(1/(b*x + a)))^2 - 2*tan(1/2*arctan(1/(b*x + a)))^3 - arctan(1/(b*x + a)) - tan(1/2*arctan(1/(b*x + a))))/(b*tan(1/2*arctan(1/(b*x + a)))^3)","B",0
123,1,100,0,0.178755," ","integrate((b*x+a)*arccot(b*x+a),x, algorithm=""giac"")","\frac{\arctan\left(\frac{1}{b x + a}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{4} + 2 \, \arctan\left(\frac{1}{b x + a}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{3} + \arctan\left(\frac{1}{b x + a}\right) + 2 \, \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)}{8 \, b \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{2}}"," ",0,"1/8*(arctan(1/(b*x + a))*tan(1/2*arctan(1/(b*x + a)))^4 + 2*arctan(1/(b*x + a))*tan(1/2*arctan(1/(b*x + a)))^2 - 2*tan(1/2*arctan(1/(b*x + a)))^3 + arctan(1/(b*x + a)) + 2*tan(1/2*arctan(1/(b*x + a))))/(b*tan(1/2*arctan(1/(b*x + a)))^2)","B",0
124,1,100,0,0.549780," ","integrate(arccot(b*x+a)/(b*x+a),x, algorithm=""giac"")","-\frac{\arctan\left(\frac{1}{b x + a}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{4} + 2 \, \arctan\left(\frac{1}{b x + a}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{3} + \arctan\left(\frac{1}{b x + a}\right) + 2 \, \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)}{8 \, b^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{2}}"," ",0,"-1/8*(arctan(1/(b*x + a))*tan(1/2*arctan(1/(b*x + a)))^4 + 2*arctan(1/(b*x + a))*tan(1/2*arctan(1/(b*x + a)))^2 - 2*tan(1/2*arctan(1/(b*x + a)))^3 + arctan(1/(b*x + a)) + 2*tan(1/2*arctan(1/(b*x + a))))/(b^2*tan(1/2*arctan(1/(b*x + a)))^2)","B",0
125,1,238,0,0.172675," ","integrate(arccot(b*x+a)/(b*x+a)^2,x, algorithm=""giac"")","-\frac{\arctan\left(\frac{1}{b x + a}\right)^{2} - \frac{\arctan\left(\frac{1}{b x + a}\right)^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{2} - \log\left(\frac{4 \, {\left(\tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{4} - 2 \, \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{2} + 1\right)}}{\tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{2} - \arctan\left(\frac{1}{b x + a}\right)^{2} + 4 \, \arctan\left(\frac{1}{b x + a}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right) + \log\left(\frac{4 \, {\left(\tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{4} - 2 \, \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{2} + 1\right)}}{\tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{2} + 1}\right)}{\tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{2} - 1}}{2 \, b}"," ",0,"-1/2*(arctan(1/(b*x + a))^2 - (arctan(1/(b*x + a))^2*tan(1/2*arctan(1/(b*x + a)))^2 - log(4*(tan(1/2*arctan(1/(b*x + a)))^4 - 2*tan(1/2*arctan(1/(b*x + a)))^2 + 1)/(tan(1/2*arctan(1/(b*x + a)))^4 + 2*tan(1/2*arctan(1/(b*x + a)))^2 + 1))*tan(1/2*arctan(1/(b*x + a)))^2 - arctan(1/(b*x + a))^2 + 4*arctan(1/(b*x + a))*tan(1/2*arctan(1/(b*x + a))) + log(4*(tan(1/2*arctan(1/(b*x + a)))^4 - 2*tan(1/2*arctan(1/(b*x + a)))^2 + 1)/(tan(1/2*arctan(1/(b*x + a)))^4 + 2*tan(1/2*arctan(1/(b*x + a)))^2 + 1)))/(tan(1/2*arctan(1/(b*x + a)))^2 - 1))/b","B",0
126,1,26,0,0.159441," ","integrate(arccot(1+x)/(2+2*x),x, algorithm=""giac"")","-\frac{1}{4} \, {\left(x + 1\right)}^{2} \arctan\left(\frac{1}{x + 1}\right) - \frac{1}{4} \, x - \frac{1}{4} \, \arctan\left(\frac{1}{x + 1}\right) - \frac{1}{4}"," ",0,"-1/4*(x + 1)^2*arctan(1/(x + 1)) - 1/4*x - 1/4*arctan(1/(x + 1)) - 1/4","A",0
127,1,103,0,0.687992," ","integrate(arccot(b*x+a)/(a*d/b+d*x),x, algorithm=""giac"")","-\frac{\arctan\left(\frac{1}{b x + a}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{4} + 2 \, \arctan\left(\frac{1}{b x + a}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{3} + \arctan\left(\frac{1}{b x + a}\right) + 2 \, \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)}{8 \, b d \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x + a}\right)\right)^{2}}"," ",0,"-1/8*(arctan(1/(b*x + a))*tan(1/2*arctan(1/(b*x + a)))^4 + 2*arctan(1/(b*x + a))*tan(1/2*arctan(1/(b*x + a)))^2 - 2*tan(1/2*arctan(1/(b*x + a)))^3 + arctan(1/(b*x + a)) + 2*tan(1/2*arctan(1/(b*x + a))))/(b*d*tan(1/2*arctan(1/(b*x + a)))^2)","B",0
128,0,0,0,0.000000," ","integrate((b*x+a)^2*arccot(b*x+a)^(1/2),x, algorithm=""giac"")","\int {\left(b x + a\right)}^{2} \sqrt{\operatorname{arccot}\left(b x + a\right)}\,{d x}"," ",0,"integrate((b*x + a)^2*sqrt(arccot(b*x + a)), x)","F",0
129,1,2272,0,2.762334," ","integrate((f*x+e)^3*(a+b*arccot(d*x+c)),x, algorithm=""giac"")","\frac{96 \, b c^{3} f^{3} \arctan\left(\frac{1}{d x + c}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{5} - 288 \, b c^{2} d f^{2} \arctan\left(\frac{1}{d x + c}\right) e \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{5} + 72 \, b c^{2} f^{3} \arctan\left(\frac{1}{d x + c}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{6} - 144 \, b c d f^{2} \arctan\left(\frac{1}{d x + c}\right) e \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{6} + 24 \, b c f^{3} \arctan\left(\frac{1}{d x + c}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{7} - 24 \, b d f^{2} \arctan\left(\frac{1}{d x + c}\right) e \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{7} + 3 \, b f^{3} \arctan\left(\frac{1}{d x + c}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{8} + 96 \, b c^{3} f^{3} \log\left(\frac{16 \, \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2}}{\tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{4} - 288 \, b c^{2} d f^{2} e \log\left(\frac{16 \, \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2}}{\tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{4} + 96 \, a c^{3} f^{3} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{5} + 288 \, b c d^{2} f \arctan\left(\frac{1}{d x + c}\right) e^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{5} - 288 \, a c^{2} d f^{2} e \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{5} + 72 \, a c^{2} f^{3} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{6} + 72 \, b d^{2} f \arctan\left(\frac{1}{d x + c}\right) e^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{6} - 144 \, a c d f^{2} e \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{6} + 24 \, a c f^{3} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{7} - 24 \, a d f^{2} e \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{7} + 3 \, a f^{3} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{8} - 96 \, b c^{3} f^{3} \arctan\left(\frac{1}{d x + c}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{3} + 288 \, b c^{2} d f^{2} \arctan\left(\frac{1}{d x + c}\right) e \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{3} + 144 \, b c^{2} f^{3} \arctan\left(\frac{1}{d x + c}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{4} - 288 \, b c d f^{2} \arctan\left(\frac{1}{d x + c}\right) e \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{4} + 288 \, b c d^{2} f e^{2} \log\left(\frac{16 \, \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2}}{\tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{4} - 144 \, b c^{2} f^{3} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{5} - 72 \, b c f^{3} \arctan\left(\frac{1}{d x + c}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{5} - 96 \, b d^{3} \arctan\left(\frac{1}{d x + c}\right) e^{3} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{5} + 288 \, a c d^{2} f e^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{5} + 288 \, b c d f^{2} e \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{5} + 72 \, b d f^{2} \arctan\left(\frac{1}{d x + c}\right) e \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{5} - 24 \, b c f^{3} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{6} - 12 \, b f^{3} \arctan\left(\frac{1}{d x + c}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{6} + 72 \, a d^{2} f e^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{6} + 24 \, b d f^{2} e \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{6} - 2 \, b f^{3} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{7} - 96 \, a c^{3} f^{3} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{3} - 288 \, b c d^{2} f \arctan\left(\frac{1}{d x + c}\right) e^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{3} + 288 \, a c^{2} d f^{2} e \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{3} + 144 \, a c^{2} f^{3} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{4} + 144 \, b d^{2} f \arctan\left(\frac{1}{d x + c}\right) e^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{4} - 288 \, a c d f^{2} e \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{4} - 96 \, b c f^{3} \log\left(\frac{16 \, \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2}}{\tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{4} - 96 \, b d^{3} e^{3} \log\left(\frac{16 \, \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2}}{\tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{4} + 96 \, b d f^{2} e \log\left(\frac{16 \, \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2}}{\tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{4} - 72 \, a c f^{3} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{5} - 96 \, a d^{3} e^{3} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{5} - 144 \, b d^{2} f e^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{5} + 72 \, a d f^{2} e \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{5} - 12 \, a f^{3} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{6} + 72 \, b c^{2} f^{3} \arctan\left(\frac{1}{d x + c}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} - 144 \, b c d f^{2} \arctan\left(\frac{1}{d x + c}\right) e \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} + 144 \, b c^{2} f^{3} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{3} + 72 \, b c f^{3} \arctan\left(\frac{1}{d x + c}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{3} + 96 \, b d^{3} \arctan\left(\frac{1}{d x + c}\right) e^{3} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{3} - 288 \, a c d^{2} f e^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{3} - 288 \, b c d f^{2} e \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{3} - 72 \, b d f^{2} \arctan\left(\frac{1}{d x + c}\right) e \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{3} - 48 \, b c f^{3} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{4} - 30 \, b f^{3} \arctan\left(\frac{1}{d x + c}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{4} + 144 \, a d^{2} f e^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{4} + 48 \, b d f^{2} e \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{4} + 30 \, b f^{3} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{5} + 72 \, a c^{2} f^{3} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} + 72 \, b d^{2} f \arctan\left(\frac{1}{d x + c}\right) e^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} - 144 \, a c d f^{2} e \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} + 72 \, a c f^{3} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{3} + 96 \, a d^{3} e^{3} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{3} + 144 \, b d^{2} f e^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{3} - 72 \, a d f^{2} e \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{3} - 30 \, a f^{3} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{4} - 24 \, b c f^{3} \arctan\left(\frac{1}{d x + c}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right) + 24 \, b d f^{2} \arctan\left(\frac{1}{d x + c}\right) e \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right) - 24 \, b c f^{3} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} - 12 \, b f^{3} \arctan\left(\frac{1}{d x + c}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} + 72 \, a d^{2} f e^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} + 24 \, b d f^{2} e \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} - 30 \, b f^{3} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{3} - 24 \, a c f^{3} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right) + 24 \, a d f^{2} e \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right) - 12 \, a f^{3} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} + 3 \, b f^{3} \arctan\left(\frac{1}{d x + c}\right) + 2 \, b f^{3} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right) + 3 \, a f^{3}}{192 \, d^{4} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{4}}"," ",0,"1/192*(96*b*c^3*f^3*arctan(1/(d*x + c))*tan(1/2*arctan(1/(d*x + c)))^5 - 288*b*c^2*d*f^2*arctan(1/(d*x + c))*e*tan(1/2*arctan(1/(d*x + c)))^5 + 72*b*c^2*f^3*arctan(1/(d*x + c))*tan(1/2*arctan(1/(d*x + c)))^6 - 144*b*c*d*f^2*arctan(1/(d*x + c))*e*tan(1/2*arctan(1/(d*x + c)))^6 + 24*b*c*f^3*arctan(1/(d*x + c))*tan(1/2*arctan(1/(d*x + c)))^7 - 24*b*d*f^2*arctan(1/(d*x + c))*e*tan(1/2*arctan(1/(d*x + c)))^7 + 3*b*f^3*arctan(1/(d*x + c))*tan(1/2*arctan(1/(d*x + c)))^8 + 96*b*c^3*f^3*log(16*tan(1/2*arctan(1/(d*x + c)))^2/(tan(1/2*arctan(1/(d*x + c)))^4 + 2*tan(1/2*arctan(1/(d*x + c)))^2 + 1))*tan(1/2*arctan(1/(d*x + c)))^4 - 288*b*c^2*d*f^2*e*log(16*tan(1/2*arctan(1/(d*x + c)))^2/(tan(1/2*arctan(1/(d*x + c)))^4 + 2*tan(1/2*arctan(1/(d*x + c)))^2 + 1))*tan(1/2*arctan(1/(d*x + c)))^4 + 96*a*c^3*f^3*tan(1/2*arctan(1/(d*x + c)))^5 + 288*b*c*d^2*f*arctan(1/(d*x + c))*e^2*tan(1/2*arctan(1/(d*x + c)))^5 - 288*a*c^2*d*f^2*e*tan(1/2*arctan(1/(d*x + c)))^5 + 72*a*c^2*f^3*tan(1/2*arctan(1/(d*x + c)))^6 + 72*b*d^2*f*arctan(1/(d*x + c))*e^2*tan(1/2*arctan(1/(d*x + c)))^6 - 144*a*c*d*f^2*e*tan(1/2*arctan(1/(d*x + c)))^6 + 24*a*c*f^3*tan(1/2*arctan(1/(d*x + c)))^7 - 24*a*d*f^2*e*tan(1/2*arctan(1/(d*x + c)))^7 + 3*a*f^3*tan(1/2*arctan(1/(d*x + c)))^8 - 96*b*c^3*f^3*arctan(1/(d*x + c))*tan(1/2*arctan(1/(d*x + c)))^3 + 288*b*c^2*d*f^2*arctan(1/(d*x + c))*e*tan(1/2*arctan(1/(d*x + c)))^3 + 144*b*c^2*f^3*arctan(1/(d*x + c))*tan(1/2*arctan(1/(d*x + c)))^4 - 288*b*c*d*f^2*arctan(1/(d*x + c))*e*tan(1/2*arctan(1/(d*x + c)))^4 + 288*b*c*d^2*f*e^2*log(16*tan(1/2*arctan(1/(d*x + c)))^2/(tan(1/2*arctan(1/(d*x + c)))^4 + 2*tan(1/2*arctan(1/(d*x + c)))^2 + 1))*tan(1/2*arctan(1/(d*x + c)))^4 - 144*b*c^2*f^3*tan(1/2*arctan(1/(d*x + c)))^5 - 72*b*c*f^3*arctan(1/(d*x + c))*tan(1/2*arctan(1/(d*x + c)))^5 - 96*b*d^3*arctan(1/(d*x + c))*e^3*tan(1/2*arctan(1/(d*x + c)))^5 + 288*a*c*d^2*f*e^2*tan(1/2*arctan(1/(d*x + c)))^5 + 288*b*c*d*f^2*e*tan(1/2*arctan(1/(d*x + c)))^5 + 72*b*d*f^2*arctan(1/(d*x + c))*e*tan(1/2*arctan(1/(d*x + c)))^5 - 24*b*c*f^3*tan(1/2*arctan(1/(d*x + c)))^6 - 12*b*f^3*arctan(1/(d*x + c))*tan(1/2*arctan(1/(d*x + c)))^6 + 72*a*d^2*f*e^2*tan(1/2*arctan(1/(d*x + c)))^6 + 24*b*d*f^2*e*tan(1/2*arctan(1/(d*x + c)))^6 - 2*b*f^3*tan(1/2*arctan(1/(d*x + c)))^7 - 96*a*c^3*f^3*tan(1/2*arctan(1/(d*x + c)))^3 - 288*b*c*d^2*f*arctan(1/(d*x + c))*e^2*tan(1/2*arctan(1/(d*x + c)))^3 + 288*a*c^2*d*f^2*e*tan(1/2*arctan(1/(d*x + c)))^3 + 144*a*c^2*f^3*tan(1/2*arctan(1/(d*x + c)))^4 + 144*b*d^2*f*arctan(1/(d*x + c))*e^2*tan(1/2*arctan(1/(d*x + c)))^4 - 288*a*c*d*f^2*e*tan(1/2*arctan(1/(d*x + c)))^4 - 96*b*c*f^3*log(16*tan(1/2*arctan(1/(d*x + c)))^2/(tan(1/2*arctan(1/(d*x + c)))^4 + 2*tan(1/2*arctan(1/(d*x + c)))^2 + 1))*tan(1/2*arctan(1/(d*x + c)))^4 - 96*b*d^3*e^3*log(16*tan(1/2*arctan(1/(d*x + c)))^2/(tan(1/2*arctan(1/(d*x + c)))^4 + 2*tan(1/2*arctan(1/(d*x + c)))^2 + 1))*tan(1/2*arctan(1/(d*x + c)))^4 + 96*b*d*f^2*e*log(16*tan(1/2*arctan(1/(d*x + c)))^2/(tan(1/2*arctan(1/(d*x + c)))^4 + 2*tan(1/2*arctan(1/(d*x + c)))^2 + 1))*tan(1/2*arctan(1/(d*x + c)))^4 - 72*a*c*f^3*tan(1/2*arctan(1/(d*x + c)))^5 - 96*a*d^3*e^3*tan(1/2*arctan(1/(d*x + c)))^5 - 144*b*d^2*f*e^2*tan(1/2*arctan(1/(d*x + c)))^5 + 72*a*d*f^2*e*tan(1/2*arctan(1/(d*x + c)))^5 - 12*a*f^3*tan(1/2*arctan(1/(d*x + c)))^6 + 72*b*c^2*f^3*arctan(1/(d*x + c))*tan(1/2*arctan(1/(d*x + c)))^2 - 144*b*c*d*f^2*arctan(1/(d*x + c))*e*tan(1/2*arctan(1/(d*x + c)))^2 + 144*b*c^2*f^3*tan(1/2*arctan(1/(d*x + c)))^3 + 72*b*c*f^3*arctan(1/(d*x + c))*tan(1/2*arctan(1/(d*x + c)))^3 + 96*b*d^3*arctan(1/(d*x + c))*e^3*tan(1/2*arctan(1/(d*x + c)))^3 - 288*a*c*d^2*f*e^2*tan(1/2*arctan(1/(d*x + c)))^3 - 288*b*c*d*f^2*e*tan(1/2*arctan(1/(d*x + c)))^3 - 72*b*d*f^2*arctan(1/(d*x + c))*e*tan(1/2*arctan(1/(d*x + c)))^3 - 48*b*c*f^3*tan(1/2*arctan(1/(d*x + c)))^4 - 30*b*f^3*arctan(1/(d*x + c))*tan(1/2*arctan(1/(d*x + c)))^4 + 144*a*d^2*f*e^2*tan(1/2*arctan(1/(d*x + c)))^4 + 48*b*d*f^2*e*tan(1/2*arctan(1/(d*x + c)))^4 + 30*b*f^3*tan(1/2*arctan(1/(d*x + c)))^5 + 72*a*c^2*f^3*tan(1/2*arctan(1/(d*x + c)))^2 + 72*b*d^2*f*arctan(1/(d*x + c))*e^2*tan(1/2*arctan(1/(d*x + c)))^2 - 144*a*c*d*f^2*e*tan(1/2*arctan(1/(d*x + c)))^2 + 72*a*c*f^3*tan(1/2*arctan(1/(d*x + c)))^3 + 96*a*d^3*e^3*tan(1/2*arctan(1/(d*x + c)))^3 + 144*b*d^2*f*e^2*tan(1/2*arctan(1/(d*x + c)))^3 - 72*a*d*f^2*e*tan(1/2*arctan(1/(d*x + c)))^3 - 30*a*f^3*tan(1/2*arctan(1/(d*x + c)))^4 - 24*b*c*f^3*arctan(1/(d*x + c))*tan(1/2*arctan(1/(d*x + c))) + 24*b*d*f^2*arctan(1/(d*x + c))*e*tan(1/2*arctan(1/(d*x + c))) - 24*b*c*f^3*tan(1/2*arctan(1/(d*x + c)))^2 - 12*b*f^3*arctan(1/(d*x + c))*tan(1/2*arctan(1/(d*x + c)))^2 + 72*a*d^2*f*e^2*tan(1/2*arctan(1/(d*x + c)))^2 + 24*b*d*f^2*e*tan(1/2*arctan(1/(d*x + c)))^2 - 30*b*f^3*tan(1/2*arctan(1/(d*x + c)))^3 - 24*a*c*f^3*tan(1/2*arctan(1/(d*x + c))) + 24*a*d*f^2*e*tan(1/2*arctan(1/(d*x + c))) - 12*a*f^3*tan(1/2*arctan(1/(d*x + c)))^2 + 3*b*f^3*arctan(1/(d*x + c)) + 2*b*f^3*tan(1/2*arctan(1/(d*x + c))) + 3*a*f^3)/(d^4*tan(1/2*arctan(1/(d*x + c)))^4)","B",0
130,1,1169,0,1.879844," ","integrate((f*x+e)^2*(a+b*arccot(d*x+c)),x, algorithm=""giac"")","-\frac{12 \, b c^{2} f^{2} \arctan\left(\frac{1}{d x + c}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{4} - 24 \, b c d f \arctan\left(\frac{1}{d x + c}\right) e \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{4} + 6 \, b c f^{2} \arctan\left(\frac{1}{d x + c}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{5} - 6 \, b d f \arctan\left(\frac{1}{d x + c}\right) e \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{5} + b f^{2} \arctan\left(\frac{1}{d x + c}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{6} + 12 \, b c^{2} f^{2} \log\left(\frac{16 \, \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2}}{\tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{3} - 24 \, b c d f e \log\left(\frac{16 \, \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2}}{\tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{3} + 12 \, a c^{2} f^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{4} + 12 \, b d^{2} \arctan\left(\frac{1}{d x + c}\right) e^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{4} - 24 \, a c d f e \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{4} + 6 \, a c f^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{5} - 6 \, a d f e \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{5} + a f^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{6} - 12 \, b c^{2} f^{2} \arctan\left(\frac{1}{d x + c}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} + 24 \, b c d f \arctan\left(\frac{1}{d x + c}\right) e \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} + 12 \, b c f^{2} \arctan\left(\frac{1}{d x + c}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{3} - 12 \, b d f \arctan\left(\frac{1}{d x + c}\right) e \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{3} + 12 \, b d^{2} e^{2} \log\left(\frac{16 \, \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2}}{\tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{3} - 12 \, b c f^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{4} - 3 \, b f^{2} \arctan\left(\frac{1}{d x + c}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{4} + 12 \, a d^{2} e^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{4} + 12 \, b d f e \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{4} - b f^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{5} - 12 \, a c^{2} f^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} - 12 \, b d^{2} \arctan\left(\frac{1}{d x + c}\right) e^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} + 24 \, a c d f e \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} + 12 \, a c f^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{3} - 12 \, a d f e \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{3} - 4 \, b f^{2} \log\left(\frac{16 \, \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2}}{\tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{3} - 3 \, a f^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{4} + 6 \, b c f^{2} \arctan\left(\frac{1}{d x + c}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right) - 6 \, b d f \arctan\left(\frac{1}{d x + c}\right) e \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right) + 12 \, b c f^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} + 3 \, b f^{2} \arctan\left(\frac{1}{d x + c}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} - 12 \, a d^{2} e^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} - 12 \, b d f e \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} - 2 \, b f^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{3} + 6 \, a c f^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right) - 6 \, a d f e \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right) + 3 \, a f^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} - b f^{2} \arctan\left(\frac{1}{d x + c}\right) - b f^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right) - a f^{2}}{24 \, d^{3} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{3}}"," ",0,"-1/24*(12*b*c^2*f^2*arctan(1/(d*x + c))*tan(1/2*arctan(1/(d*x + c)))^4 - 24*b*c*d*f*arctan(1/(d*x + c))*e*tan(1/2*arctan(1/(d*x + c)))^4 + 6*b*c*f^2*arctan(1/(d*x + c))*tan(1/2*arctan(1/(d*x + c)))^5 - 6*b*d*f*arctan(1/(d*x + c))*e*tan(1/2*arctan(1/(d*x + c)))^5 + b*f^2*arctan(1/(d*x + c))*tan(1/2*arctan(1/(d*x + c)))^6 + 12*b*c^2*f^2*log(16*tan(1/2*arctan(1/(d*x + c)))^2/(tan(1/2*arctan(1/(d*x + c)))^4 + 2*tan(1/2*arctan(1/(d*x + c)))^2 + 1))*tan(1/2*arctan(1/(d*x + c)))^3 - 24*b*c*d*f*e*log(16*tan(1/2*arctan(1/(d*x + c)))^2/(tan(1/2*arctan(1/(d*x + c)))^4 + 2*tan(1/2*arctan(1/(d*x + c)))^2 + 1))*tan(1/2*arctan(1/(d*x + c)))^3 + 12*a*c^2*f^2*tan(1/2*arctan(1/(d*x + c)))^4 + 12*b*d^2*arctan(1/(d*x + c))*e^2*tan(1/2*arctan(1/(d*x + c)))^4 - 24*a*c*d*f*e*tan(1/2*arctan(1/(d*x + c)))^4 + 6*a*c*f^2*tan(1/2*arctan(1/(d*x + c)))^5 - 6*a*d*f*e*tan(1/2*arctan(1/(d*x + c)))^5 + a*f^2*tan(1/2*arctan(1/(d*x + c)))^6 - 12*b*c^2*f^2*arctan(1/(d*x + c))*tan(1/2*arctan(1/(d*x + c)))^2 + 24*b*c*d*f*arctan(1/(d*x + c))*e*tan(1/2*arctan(1/(d*x + c)))^2 + 12*b*c*f^2*arctan(1/(d*x + c))*tan(1/2*arctan(1/(d*x + c)))^3 - 12*b*d*f*arctan(1/(d*x + c))*e*tan(1/2*arctan(1/(d*x + c)))^3 + 12*b*d^2*e^2*log(16*tan(1/2*arctan(1/(d*x + c)))^2/(tan(1/2*arctan(1/(d*x + c)))^4 + 2*tan(1/2*arctan(1/(d*x + c)))^2 + 1))*tan(1/2*arctan(1/(d*x + c)))^3 - 12*b*c*f^2*tan(1/2*arctan(1/(d*x + c)))^4 - 3*b*f^2*arctan(1/(d*x + c))*tan(1/2*arctan(1/(d*x + c)))^4 + 12*a*d^2*e^2*tan(1/2*arctan(1/(d*x + c)))^4 + 12*b*d*f*e*tan(1/2*arctan(1/(d*x + c)))^4 - b*f^2*tan(1/2*arctan(1/(d*x + c)))^5 - 12*a*c^2*f^2*tan(1/2*arctan(1/(d*x + c)))^2 - 12*b*d^2*arctan(1/(d*x + c))*e^2*tan(1/2*arctan(1/(d*x + c)))^2 + 24*a*c*d*f*e*tan(1/2*arctan(1/(d*x + c)))^2 + 12*a*c*f^2*tan(1/2*arctan(1/(d*x + c)))^3 - 12*a*d*f*e*tan(1/2*arctan(1/(d*x + c)))^3 - 4*b*f^2*log(16*tan(1/2*arctan(1/(d*x + c)))^2/(tan(1/2*arctan(1/(d*x + c)))^4 + 2*tan(1/2*arctan(1/(d*x + c)))^2 + 1))*tan(1/2*arctan(1/(d*x + c)))^3 - 3*a*f^2*tan(1/2*arctan(1/(d*x + c)))^4 + 6*b*c*f^2*arctan(1/(d*x + c))*tan(1/2*arctan(1/(d*x + c))) - 6*b*d*f*arctan(1/(d*x + c))*e*tan(1/2*arctan(1/(d*x + c))) + 12*b*c*f^2*tan(1/2*arctan(1/(d*x + c)))^2 + 3*b*f^2*arctan(1/(d*x + c))*tan(1/2*arctan(1/(d*x + c)))^2 - 12*a*d^2*e^2*tan(1/2*arctan(1/(d*x + c)))^2 - 12*b*d*f*e*tan(1/2*arctan(1/(d*x + c)))^2 - 2*b*f^2*tan(1/2*arctan(1/(d*x + c)))^3 + 6*a*c*f^2*tan(1/2*arctan(1/(d*x + c))) - 6*a*d*f*e*tan(1/2*arctan(1/(d*x + c))) + 3*a*f^2*tan(1/2*arctan(1/(d*x + c)))^2 - b*f^2*arctan(1/(d*x + c)) - b*f^2*tan(1/2*arctan(1/(d*x + c))) - a*f^2)/(d^3*tan(1/2*arctan(1/(d*x + c)))^3)","B",0
131,1,452,0,0.341958," ","integrate((f*x+e)*(a+b*arccot(d*x+c)),x, algorithm=""giac"")","\frac{4 \, b c f \arctan\left(\frac{1}{d x + c}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{3} - 4 \, b d \arctan\left(\frac{1}{d x + c}\right) e \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{3} + b f \arctan\left(\frac{1}{d x + c}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{4} + 4 \, b c f \log\left(\frac{16 \, \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2}}{\tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} - 4 \, b d e \log\left(\frac{16 \, \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2}}{\tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} + 4 \, a c f \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{3} - 4 \, a d e \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{3} + a f \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{4} - 4 \, b c f \arctan\left(\frac{1}{d x + c}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right) + 4 \, b d \arctan\left(\frac{1}{d x + c}\right) e \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right) + 2 \, b f \arctan\left(\frac{1}{d x + c}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} - 2 \, b f \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{3} - 4 \, a c f \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right) + 4 \, a d e \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right) + 2 \, a f \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} + b f \arctan\left(\frac{1}{d x + c}\right) + 2 \, b f \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right) + a f}{8 \, d^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2}}"," ",0,"1/8*(4*b*c*f*arctan(1/(d*x + c))*tan(1/2*arctan(1/(d*x + c)))^3 - 4*b*d*arctan(1/(d*x + c))*e*tan(1/2*arctan(1/(d*x + c)))^3 + b*f*arctan(1/(d*x + c))*tan(1/2*arctan(1/(d*x + c)))^4 + 4*b*c*f*log(16*tan(1/2*arctan(1/(d*x + c)))^2/(tan(1/2*arctan(1/(d*x + c)))^4 + 2*tan(1/2*arctan(1/(d*x + c)))^2 + 1))*tan(1/2*arctan(1/(d*x + c)))^2 - 4*b*d*e*log(16*tan(1/2*arctan(1/(d*x + c)))^2/(tan(1/2*arctan(1/(d*x + c)))^4 + 2*tan(1/2*arctan(1/(d*x + c)))^2 + 1))*tan(1/2*arctan(1/(d*x + c)))^2 + 4*a*c*f*tan(1/2*arctan(1/(d*x + c)))^3 - 4*a*d*e*tan(1/2*arctan(1/(d*x + c)))^3 + a*f*tan(1/2*arctan(1/(d*x + c)))^4 - 4*b*c*f*arctan(1/(d*x + c))*tan(1/2*arctan(1/(d*x + c))) + 4*b*d*arctan(1/(d*x + c))*e*tan(1/2*arctan(1/(d*x + c))) + 2*b*f*arctan(1/(d*x + c))*tan(1/2*arctan(1/(d*x + c)))^2 - 2*b*f*tan(1/2*arctan(1/(d*x + c)))^3 - 4*a*c*f*tan(1/2*arctan(1/(d*x + c))) + 4*a*d*e*tan(1/2*arctan(1/(d*x + c))) + 2*a*f*tan(1/2*arctan(1/(d*x + c)))^2 + b*f*arctan(1/(d*x + c)) + 2*b*f*tan(1/2*arctan(1/(d*x + c))) + a*f)/(d^2*tan(1/2*arctan(1/(d*x + c)))^2)","B",0
132,1,116,0,0.214527," ","integrate(a+b*arccot(d*x+c),x, algorithm=""giac"")","a x - \frac{{\left(\arctan\left(\frac{1}{d x + c}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} + \log\left(\frac{16 \, \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2}}{\tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right) - \arctan\left(\frac{1}{d x + c}\right)\right)} b}{2 \, d \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)}"," ",0,"a*x - 1/2*(arctan(1/(d*x + c))*tan(1/2*arctan(1/(d*x + c)))^2 + log(16*tan(1/2*arctan(1/(d*x + c)))^2/(tan(1/2*arctan(1/(d*x + c)))^4 + 2*tan(1/2*arctan(1/(d*x + c)))^2 + 1))*tan(1/2*arctan(1/(d*x + c))) - arctan(1/(d*x + c)))*b/(d*tan(1/2*arctan(1/(d*x + c))))","B",0
133,0,0,0,0.000000," ","integrate((a+b*arccot(d*x+c))/(f*x+e),x, algorithm=""giac"")","\int \frac{b \operatorname{arccot}\left(d x + c\right) + a}{f x + e}\,{d x}"," ",0,"integrate((b*arccot(d*x + c) + a)/(f*x + e), x)","F",0
134,1,1278,0,0.866796," ","integrate((a+b*arccot(d*x+c))/(f*x+e)^2,x, algorithm=""giac"")","-\frac{{\left(2 \, b c f \arctan\left(\frac{1}{d x + c}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} - 2 \, b d \arctan\left(\frac{1}{d x + c}\right) e \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} + 2 \, b c f \log\left(\frac{4 \, {\left(4 \, c^{2} f^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} - 8 \, c d f e \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} + 4 \, c f^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{3} - 4 \, d f e \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{3} + f^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{4} + 4 \, d^{2} e^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} - 4 \, c f^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right) + 4 \, d f e \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right) - 2 \, f^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} + f^{2}\right)}}{\tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right) - 2 \, b d e \log\left(\frac{4 \, {\left(4 \, c^{2} f^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} - 8 \, c d f e \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} + 4 \, c f^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{3} - 4 \, d f e \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{3} + f^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{4} + 4 \, d^{2} e^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} - 4 \, c f^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right) + 4 \, d f e \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right) - 2 \, f^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} + f^{2}\right)}}{\tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right) + 2 \, a c f \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} - 2 \, a d e \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} + b f \log\left(\frac{4 \, {\left(4 \, c^{2} f^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} - 8 \, c d f e \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} + 4 \, c f^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{3} - 4 \, d f e \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{3} + f^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{4} + 4 \, d^{2} e^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} - 4 \, c f^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right) + 4 \, d f e \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right) - 2 \, f^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} + f^{2}\right)}}{\tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} - 2 \, b c f \arctan\left(\frac{1}{d x + c}\right) + 2 \, b d \arctan\left(\frac{1}{d x + c}\right) e - 4 \, b f \arctan\left(\frac{1}{d x + c}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right) - 2 \, a c f + 2 \, a d e - b f \log\left(\frac{4 \, {\left(4 \, c^{2} f^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} - 8 \, c d f e \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} + 4 \, c f^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{3} - 4 \, d f e \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{3} + f^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{4} + 4 \, d^{2} e^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} - 4 \, c f^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right) + 4 \, d f e \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right) - 2 \, f^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} + f^{2}\right)}}{\tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} + 1}\right) - 4 \, a f \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)\right)} d}{2 \, {\left(2 \, c^{3} f^{3} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right) - 6 \, c^{2} d f^{2} e \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right) + c^{2} f^{3} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} - 2 \, c d f^{2} e \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} + 6 \, c d^{2} f e^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right) + d^{2} f e^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} - c^{2} f^{3} + 2 \, c d f^{2} e + 2 \, c f^{3} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right) - 2 \, d^{3} e^{3} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right) - 2 \, d f^{2} e \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right) + f^{3} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} - d^{2} f e^{2} - f^{3}\right)}}"," ",0,"-1/2*(2*b*c*f*arctan(1/(d*x + c))*tan(1/2*arctan(1/(d*x + c)))^2 - 2*b*d*arctan(1/(d*x + c))*e*tan(1/2*arctan(1/(d*x + c)))^2 + 2*b*c*f*log(4*(4*c^2*f^2*tan(1/2*arctan(1/(d*x + c)))^2 - 8*c*d*f*e*tan(1/2*arctan(1/(d*x + c)))^2 + 4*c*f^2*tan(1/2*arctan(1/(d*x + c)))^3 - 4*d*f*e*tan(1/2*arctan(1/(d*x + c)))^3 + f^2*tan(1/2*arctan(1/(d*x + c)))^4 + 4*d^2*e^2*tan(1/2*arctan(1/(d*x + c)))^2 - 4*c*f^2*tan(1/2*arctan(1/(d*x + c))) + 4*d*f*e*tan(1/2*arctan(1/(d*x + c))) - 2*f^2*tan(1/2*arctan(1/(d*x + c)))^2 + f^2)/(tan(1/2*arctan(1/(d*x + c)))^4 + 2*tan(1/2*arctan(1/(d*x + c)))^2 + 1))*tan(1/2*arctan(1/(d*x + c))) - 2*b*d*e*log(4*(4*c^2*f^2*tan(1/2*arctan(1/(d*x + c)))^2 - 8*c*d*f*e*tan(1/2*arctan(1/(d*x + c)))^2 + 4*c*f^2*tan(1/2*arctan(1/(d*x + c)))^3 - 4*d*f*e*tan(1/2*arctan(1/(d*x + c)))^3 + f^2*tan(1/2*arctan(1/(d*x + c)))^4 + 4*d^2*e^2*tan(1/2*arctan(1/(d*x + c)))^2 - 4*c*f^2*tan(1/2*arctan(1/(d*x + c))) + 4*d*f*e*tan(1/2*arctan(1/(d*x + c))) - 2*f^2*tan(1/2*arctan(1/(d*x + c)))^2 + f^2)/(tan(1/2*arctan(1/(d*x + c)))^4 + 2*tan(1/2*arctan(1/(d*x + c)))^2 + 1))*tan(1/2*arctan(1/(d*x + c))) + 2*a*c*f*tan(1/2*arctan(1/(d*x + c)))^2 - 2*a*d*e*tan(1/2*arctan(1/(d*x + c)))^2 + b*f*log(4*(4*c^2*f^2*tan(1/2*arctan(1/(d*x + c)))^2 - 8*c*d*f*e*tan(1/2*arctan(1/(d*x + c)))^2 + 4*c*f^2*tan(1/2*arctan(1/(d*x + c)))^3 - 4*d*f*e*tan(1/2*arctan(1/(d*x + c)))^3 + f^2*tan(1/2*arctan(1/(d*x + c)))^4 + 4*d^2*e^2*tan(1/2*arctan(1/(d*x + c)))^2 - 4*c*f^2*tan(1/2*arctan(1/(d*x + c))) + 4*d*f*e*tan(1/2*arctan(1/(d*x + c))) - 2*f^2*tan(1/2*arctan(1/(d*x + c)))^2 + f^2)/(tan(1/2*arctan(1/(d*x + c)))^4 + 2*tan(1/2*arctan(1/(d*x + c)))^2 + 1))*tan(1/2*arctan(1/(d*x + c)))^2 - 2*b*c*f*arctan(1/(d*x + c)) + 2*b*d*arctan(1/(d*x + c))*e - 4*b*f*arctan(1/(d*x + c))*tan(1/2*arctan(1/(d*x + c))) - 2*a*c*f + 2*a*d*e - b*f*log(4*(4*c^2*f^2*tan(1/2*arctan(1/(d*x + c)))^2 - 8*c*d*f*e*tan(1/2*arctan(1/(d*x + c)))^2 + 4*c*f^2*tan(1/2*arctan(1/(d*x + c)))^3 - 4*d*f*e*tan(1/2*arctan(1/(d*x + c)))^3 + f^2*tan(1/2*arctan(1/(d*x + c)))^4 + 4*d^2*e^2*tan(1/2*arctan(1/(d*x + c)))^2 - 4*c*f^2*tan(1/2*arctan(1/(d*x + c))) + 4*d*f*e*tan(1/2*arctan(1/(d*x + c))) - 2*f^2*tan(1/2*arctan(1/(d*x + c)))^2 + f^2)/(tan(1/2*arctan(1/(d*x + c)))^4 + 2*tan(1/2*arctan(1/(d*x + c)))^2 + 1)) - 4*a*f*tan(1/2*arctan(1/(d*x + c))))*d/(2*c^3*f^3*tan(1/2*arctan(1/(d*x + c))) - 6*c^2*d*f^2*e*tan(1/2*arctan(1/(d*x + c))) + c^2*f^3*tan(1/2*arctan(1/(d*x + c)))^2 - 2*c*d*f^2*e*tan(1/2*arctan(1/(d*x + c)))^2 + 6*c*d^2*f*e^2*tan(1/2*arctan(1/(d*x + c))) + d^2*f*e^2*tan(1/2*arctan(1/(d*x + c)))^2 - c^2*f^3 + 2*c*d*f^2*e + 2*c*f^3*tan(1/2*arctan(1/(d*x + c))) - 2*d^3*e^3*tan(1/2*arctan(1/(d*x + c))) - 2*d*f^2*e*tan(1/2*arctan(1/(d*x + c))) + f^3*tan(1/2*arctan(1/(d*x + c)))^2 - d^2*f*e^2 - f^3)","B",0
135,1,6190,0,4.697761," ","integrate((a+b*arccot(d*x+c))/(f*x+e)^3,x, algorithm=""giac"")","\frac{{\left(4 \, b c^{3} d f^{3} \arctan\left(\frac{1}{d x + c}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{3} - 12 \, b c^{2} d^{2} f^{2} \arctan\left(\frac{1}{d x + c}\right) e \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{3} + b c^{2} d f^{3} \arctan\left(\frac{1}{d x + c}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{4} - 2 \, b c d^{2} f^{2} \arctan\left(\frac{1}{d x + c}\right) e \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{4} + 4 \, b c^{3} d f^{3} \log\left(\frac{4 \, {\left(4 \, c^{2} f^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} - 8 \, c d f e \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} + 4 \, c f^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{3} - 4 \, d f e \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{3} + f^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{4} + 4 \, d^{2} e^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} - 4 \, c f^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right) + 4 \, d f e \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right) - 2 \, f^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} + f^{2}\right)}}{\tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} - 12 \, b c^{2} d^{2} f^{2} e \log\left(\frac{4 \, {\left(4 \, c^{2} f^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} - 8 \, c d f e \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} + 4 \, c f^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{3} - 4 \, d f e \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{3} + f^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{4} + 4 \, d^{2} e^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} - 4 \, c f^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right) + 4 \, d f e \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right) - 2 \, f^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} + f^{2}\right)}}{\tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} + 4 \, a c^{3} d f^{3} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{3} + 12 \, b c d^{3} f \arctan\left(\frac{1}{d x + c}\right) e^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{3} - 12 \, a c^{2} d^{2} f^{2} e \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{3} + 4 \, b c^{2} d f^{3} \log\left(\frac{4 \, {\left(4 \, c^{2} f^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} - 8 \, c d f e \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} + 4 \, c f^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{3} - 4 \, d f e \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{3} + f^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{4} + 4 \, d^{2} e^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} - 4 \, c f^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right) + 4 \, d f e \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right) - 2 \, f^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} + f^{2}\right)}}{\tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{3} - 8 \, b c d^{2} f^{2} e \log\left(\frac{4 \, {\left(4 \, c^{2} f^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} - 8 \, c d f e \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} + 4 \, c f^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{3} - 4 \, d f e \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{3} + f^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{4} + 4 \, d^{2} e^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} - 4 \, c f^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right) + 4 \, d f e \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right) - 2 \, f^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} + f^{2}\right)}}{\tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{3} + a c^{2} d f^{3} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{4} + b d^{3} f \arctan\left(\frac{1}{d x + c}\right) e^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{4} - 2 \, a c d^{2} f^{2} e \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{4} + b c d f^{3} \log\left(\frac{4 \, {\left(4 \, c^{2} f^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} - 8 \, c d f e \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} + 4 \, c f^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{3} - 4 \, d f e \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{3} + f^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{4} + 4 \, d^{2} e^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} - 4 \, c f^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right) + 4 \, d f e \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right) - 2 \, f^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} + f^{2}\right)}}{\tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{4} - b d^{2} f^{2} e \log\left(\frac{4 \, {\left(4 \, c^{2} f^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} - 8 \, c d f e \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} + 4 \, c f^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{3} - 4 \, d f e \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{3} + f^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{4} + 4 \, d^{2} e^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} - 4 \, c f^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right) + 4 \, d f e \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right) - 2 \, f^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} + f^{2}\right)}}{\tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{4} - 4 \, b c^{3} d f^{3} \arctan\left(\frac{1}{d x + c}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right) + 12 \, b c^{2} d^{2} f^{2} \arctan\left(\frac{1}{d x + c}\right) e \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right) - 14 \, b c^{2} d f^{3} \arctan\left(\frac{1}{d x + c}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} + 28 \, b c d^{2} f^{2} \arctan\left(\frac{1}{d x + c}\right) e \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} + 12 \, b c d^{3} f e^{2} \log\left(\frac{4 \, {\left(4 \, c^{2} f^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} - 8 \, c d f e \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} + 4 \, c f^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{3} - 4 \, d f e \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{3} + f^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{4} + 4 \, d^{2} e^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} - 4 \, c f^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right) + 4 \, d f e \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right) - 2 \, f^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} + f^{2}\right)}}{\tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} + 2 \, b c^{2} d f^{3} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{3} - 4 \, b c d f^{3} \arctan\left(\frac{1}{d x + c}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{3} - 4 \, b d^{4} \arctan\left(\frac{1}{d x + c}\right) e^{3} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{3} + 12 \, a c d^{3} f e^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{3} - 4 \, b c d^{2} f^{2} e \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{3} + 4 \, b d^{2} f^{2} \arctan\left(\frac{1}{d x + c}\right) e \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{3} + 4 \, b d^{3} f e^{2} \log\left(\frac{4 \, {\left(4 \, c^{2} f^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} - 8 \, c d f e \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} + 4 \, c f^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{3} - 4 \, d f e \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{3} + f^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{4} + 4 \, d^{2} e^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} - 4 \, c f^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right) + 4 \, d f e \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right) - 2 \, f^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} + f^{2}\right)}}{\tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{3} + b c d f^{3} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{4} - b d f^{3} \arctan\left(\frac{1}{d x + c}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{4} + a d^{3} f e^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{4} - b d^{2} f^{2} e \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{4} - 4 \, a c^{3} d f^{3} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right) - 12 \, b c d^{3} f \arctan\left(\frac{1}{d x + c}\right) e^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right) + 12 \, a c^{2} d^{2} f^{2} e \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right) - 4 \, b c^{2} d f^{3} \log\left(\frac{4 \, {\left(4 \, c^{2} f^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} - 8 \, c d f e \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} + 4 \, c f^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{3} - 4 \, d f e \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{3} + f^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{4} + 4 \, d^{2} e^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} - 4 \, c f^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right) + 4 \, d f e \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right) - 2 \, f^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} + f^{2}\right)}}{\tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right) + 8 \, b c d^{2} f^{2} e \log\left(\frac{4 \, {\left(4 \, c^{2} f^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} - 8 \, c d f e \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} + 4 \, c f^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{3} - 4 \, d f e \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{3} + f^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{4} + 4 \, d^{2} e^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} - 4 \, c f^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right) + 4 \, d f e \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right) - 2 \, f^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} + f^{2}\right)}}{\tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right) - 14 \, a c^{2} d f^{3} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} - 14 \, b d^{3} f \arctan\left(\frac{1}{d x + c}\right) e^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} + 28 \, a c d^{2} f^{2} e \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} - 2 \, b c d f^{3} \log\left(\frac{4 \, {\left(4 \, c^{2} f^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} - 8 \, c d f e \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} + 4 \, c f^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{3} - 4 \, d f e \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{3} + f^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{4} + 4 \, d^{2} e^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} - 4 \, c f^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right) + 4 \, d f e \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right) - 2 \, f^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} + f^{2}\right)}}{\tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} - 4 \, b d^{4} e^{3} \log\left(\frac{4 \, {\left(4 \, c^{2} f^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} - 8 \, c d f e \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} + 4 \, c f^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{3} - 4 \, d f e \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{3} + f^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{4} + 4 \, d^{2} e^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} - 4 \, c f^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right) + 4 \, d f e \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right) - 2 \, f^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} + f^{2}\right)}}{\tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} + 2 \, b d^{2} f^{2} e \log\left(\frac{4 \, {\left(4 \, c^{2} f^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} - 8 \, c d f e \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} + 4 \, c f^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{3} - 4 \, d f e \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{3} + f^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{4} + 4 \, d^{2} e^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} - 4 \, c f^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right) + 4 \, d f e \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right) - 2 \, f^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} + f^{2}\right)}}{\tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} - 4 \, a c d f^{3} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{3} - 4 \, a d^{4} e^{3} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{3} + 2 \, b d^{3} f e^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{3} + 4 \, a d^{2} f^{2} e \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{3} - a d f^{3} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{4} + b c^{2} d f^{3} \arctan\left(\frac{1}{d x + c}\right) - 2 \, b c d^{2} f^{2} \arctan\left(\frac{1}{d x + c}\right) e - 2 \, b c^{2} d f^{3} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right) + 4 \, b c d f^{3} \arctan\left(\frac{1}{d x + c}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right) + 4 \, b d^{4} \arctan\left(\frac{1}{d x + c}\right) e^{3} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right) - 12 \, a c d^{3} f e^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right) + 4 \, b c d^{2} f^{2} e \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right) - 4 \, b d^{2} f^{2} \arctan\left(\frac{1}{d x + c}\right) e \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right) - 4 \, b d^{3} f e^{2} \log\left(\frac{4 \, {\left(4 \, c^{2} f^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} - 8 \, c d f e \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} + 4 \, c f^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{3} - 4 \, d f e \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{3} + f^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{4} + 4 \, d^{2} e^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} - 4 \, c f^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right) + 4 \, d f e \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right) - 2 \, f^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} + f^{2}\right)}}{\tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right) - 6 \, b c d f^{3} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} - 2 \, b d f^{3} \arctan\left(\frac{1}{d x + c}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} - 14 \, a d^{3} f e^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} + 6 \, b d^{2} f^{2} e \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} - 2 \, b d f^{3} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{3} + a c^{2} d f^{3} + b d^{3} f \arctan\left(\frac{1}{d x + c}\right) e^{2} - 2 \, a c d^{2} f^{2} e + b c d f^{3} \log\left(\frac{4 \, {\left(4 \, c^{2} f^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} - 8 \, c d f e \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} + 4 \, c f^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{3} - 4 \, d f e \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{3} + f^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{4} + 4 \, d^{2} e^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} - 4 \, c f^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right) + 4 \, d f e \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right) - 2 \, f^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} + f^{2}\right)}}{\tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} + 1}\right) - b d^{2} f^{2} e \log\left(\frac{4 \, {\left(4 \, c^{2} f^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} - 8 \, c d f e \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} + 4 \, c f^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{3} - 4 \, d f e \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{3} + f^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{4} + 4 \, d^{2} e^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} - 4 \, c f^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right) + 4 \, d f e \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right) - 2 \, f^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} + f^{2}\right)}}{\tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} + 1}\right) + 4 \, a c d f^{3} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right) + 4 \, a d^{4} e^{3} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right) - 2 \, b d^{3} f e^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right) - 4 \, a d^{2} f^{2} e \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right) - 2 \, a d f^{3} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} + b c d f^{3} - b d f^{3} \arctan\left(\frac{1}{d x + c}\right) + a d^{3} f e^{2} - b d^{2} f^{2} e + 2 \, b d f^{3} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right) - a d f^{3}\right)} d}{2 \, {\left(4 \, c^{6} f^{6} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} - 24 \, c^{5} d f^{5} e \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} + 4 \, c^{5} f^{6} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{3} - 20 \, c^{4} d f^{5} e \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{3} + c^{4} f^{6} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{4} - 4 \, c^{3} d f^{5} e \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{4} + 60 \, c^{4} d^{2} f^{4} e^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} + 40 \, c^{3} d^{2} f^{4} e^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{3} + 6 \, c^{2} d^{2} f^{4} e^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{4} - 4 \, c^{5} f^{6} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right) + 20 \, c^{4} d f^{5} e \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right) + 6 \, c^{4} f^{6} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} - 80 \, c^{3} d^{3} f^{3} e^{3} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} - 24 \, c^{3} d f^{5} e \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} + 8 \, c^{3} f^{6} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{3} - 40 \, c^{2} d^{3} f^{3} e^{3} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{3} - 24 \, c^{2} d f^{5} e \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{3} + 2 \, c^{2} f^{6} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{4} - 4 \, c d^{3} f^{3} e^{3} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{4} - 4 \, c d f^{5} e \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{4} - 40 \, c^{3} d^{2} f^{4} e^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right) + 60 \, c^{2} d^{4} f^{2} e^{4} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} + 36 \, c^{2} d^{2} f^{4} e^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} + 20 \, c d^{4} f^{2} e^{4} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{3} + 24 \, c d^{2} f^{4} e^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{3} + d^{4} f^{2} e^{4} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{4} + 2 \, d^{2} f^{4} e^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{4} + c^{4} f^{6} - 4 \, c^{3} d f^{5} e - 8 \, c^{3} f^{6} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right) + 40 \, c^{2} d^{3} f^{3} e^{3} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right) + 24 \, c^{2} d f^{5} e \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right) - 24 \, c d^{5} f e^{5} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} - 24 \, c d^{3} f^{3} e^{3} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} + 4 \, c f^{6} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{3} - 4 \, d^{5} f e^{5} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{3} - 8 \, d^{3} f^{3} e^{3} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{3} - 4 \, d f^{5} e \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{3} + f^{6} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{4} + 6 \, c^{2} d^{2} f^{4} e^{2} - 20 \, c d^{4} f^{2} e^{4} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right) - 24 \, c d^{2} f^{4} e^{2} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right) + 4 \, d^{6} e^{6} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} + 6 \, d^{4} f^{2} e^{4} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} + 2 \, c^{2} f^{6} - 4 \, c d^{3} f^{3} e^{3} - 4 \, c d f^{5} e - 4 \, c f^{6} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right) + 4 \, d^{5} f e^{5} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right) + 8 \, d^{3} f^{3} e^{3} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right) + 4 \, d f^{5} e \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right) - 2 \, f^{6} \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{d x + c}\right)\right)^{2} + d^{4} f^{2} e^{4} + 2 \, d^{2} f^{4} e^{2} + f^{6}\right)}}"," ",0,"1/2*(4*b*c^3*d*f^3*arctan(1/(d*x + c))*tan(1/2*arctan(1/(d*x + c)))^3 - 12*b*c^2*d^2*f^2*arctan(1/(d*x + c))*e*tan(1/2*arctan(1/(d*x + c)))^3 + b*c^2*d*f^3*arctan(1/(d*x + c))*tan(1/2*arctan(1/(d*x + c)))^4 - 2*b*c*d^2*f^2*arctan(1/(d*x + c))*e*tan(1/2*arctan(1/(d*x + c)))^4 + 4*b*c^3*d*f^3*log(4*(4*c^2*f^2*tan(1/2*arctan(1/(d*x + c)))^2 - 8*c*d*f*e*tan(1/2*arctan(1/(d*x + c)))^2 + 4*c*f^2*tan(1/2*arctan(1/(d*x + c)))^3 - 4*d*f*e*tan(1/2*arctan(1/(d*x + c)))^3 + f^2*tan(1/2*arctan(1/(d*x + c)))^4 + 4*d^2*e^2*tan(1/2*arctan(1/(d*x + c)))^2 - 4*c*f^2*tan(1/2*arctan(1/(d*x + c))) + 4*d*f*e*tan(1/2*arctan(1/(d*x + c))) - 2*f^2*tan(1/2*arctan(1/(d*x + c)))^2 + f^2)/(tan(1/2*arctan(1/(d*x + c)))^4 + 2*tan(1/2*arctan(1/(d*x + c)))^2 + 1))*tan(1/2*arctan(1/(d*x + c)))^2 - 12*b*c^2*d^2*f^2*e*log(4*(4*c^2*f^2*tan(1/2*arctan(1/(d*x + c)))^2 - 8*c*d*f*e*tan(1/2*arctan(1/(d*x + c)))^2 + 4*c*f^2*tan(1/2*arctan(1/(d*x + c)))^3 - 4*d*f*e*tan(1/2*arctan(1/(d*x + c)))^3 + f^2*tan(1/2*arctan(1/(d*x + c)))^4 + 4*d^2*e^2*tan(1/2*arctan(1/(d*x + c)))^2 - 4*c*f^2*tan(1/2*arctan(1/(d*x + c))) + 4*d*f*e*tan(1/2*arctan(1/(d*x + c))) - 2*f^2*tan(1/2*arctan(1/(d*x + c)))^2 + f^2)/(tan(1/2*arctan(1/(d*x + c)))^4 + 2*tan(1/2*arctan(1/(d*x + c)))^2 + 1))*tan(1/2*arctan(1/(d*x + c)))^2 + 4*a*c^3*d*f^3*tan(1/2*arctan(1/(d*x + c)))^3 + 12*b*c*d^3*f*arctan(1/(d*x + c))*e^2*tan(1/2*arctan(1/(d*x + c)))^3 - 12*a*c^2*d^2*f^2*e*tan(1/2*arctan(1/(d*x + c)))^3 + 4*b*c^2*d*f^3*log(4*(4*c^2*f^2*tan(1/2*arctan(1/(d*x + c)))^2 - 8*c*d*f*e*tan(1/2*arctan(1/(d*x + c)))^2 + 4*c*f^2*tan(1/2*arctan(1/(d*x + c)))^3 - 4*d*f*e*tan(1/2*arctan(1/(d*x + c)))^3 + f^2*tan(1/2*arctan(1/(d*x + c)))^4 + 4*d^2*e^2*tan(1/2*arctan(1/(d*x + c)))^2 - 4*c*f^2*tan(1/2*arctan(1/(d*x + c))) + 4*d*f*e*tan(1/2*arctan(1/(d*x + c))) - 2*f^2*tan(1/2*arctan(1/(d*x + c)))^2 + f^2)/(tan(1/2*arctan(1/(d*x + c)))^4 + 2*tan(1/2*arctan(1/(d*x + c)))^2 + 1))*tan(1/2*arctan(1/(d*x + c)))^3 - 8*b*c*d^2*f^2*e*log(4*(4*c^2*f^2*tan(1/2*arctan(1/(d*x + c)))^2 - 8*c*d*f*e*tan(1/2*arctan(1/(d*x + c)))^2 + 4*c*f^2*tan(1/2*arctan(1/(d*x + c)))^3 - 4*d*f*e*tan(1/2*arctan(1/(d*x + c)))^3 + f^2*tan(1/2*arctan(1/(d*x + c)))^4 + 4*d^2*e^2*tan(1/2*arctan(1/(d*x + c)))^2 - 4*c*f^2*tan(1/2*arctan(1/(d*x + c))) + 4*d*f*e*tan(1/2*arctan(1/(d*x + c))) - 2*f^2*tan(1/2*arctan(1/(d*x + c)))^2 + f^2)/(tan(1/2*arctan(1/(d*x + c)))^4 + 2*tan(1/2*arctan(1/(d*x + c)))^2 + 1))*tan(1/2*arctan(1/(d*x + c)))^3 + a*c^2*d*f^3*tan(1/2*arctan(1/(d*x + c)))^4 + b*d^3*f*arctan(1/(d*x + c))*e^2*tan(1/2*arctan(1/(d*x + c)))^4 - 2*a*c*d^2*f^2*e*tan(1/2*arctan(1/(d*x + c)))^4 + b*c*d*f^3*log(4*(4*c^2*f^2*tan(1/2*arctan(1/(d*x + c)))^2 - 8*c*d*f*e*tan(1/2*arctan(1/(d*x + c)))^2 + 4*c*f^2*tan(1/2*arctan(1/(d*x + c)))^3 - 4*d*f*e*tan(1/2*arctan(1/(d*x + c)))^3 + f^2*tan(1/2*arctan(1/(d*x + c)))^4 + 4*d^2*e^2*tan(1/2*arctan(1/(d*x + c)))^2 - 4*c*f^2*tan(1/2*arctan(1/(d*x + c))) + 4*d*f*e*tan(1/2*arctan(1/(d*x + c))) - 2*f^2*tan(1/2*arctan(1/(d*x + c)))^2 + f^2)/(tan(1/2*arctan(1/(d*x + c)))^4 + 2*tan(1/2*arctan(1/(d*x + c)))^2 + 1))*tan(1/2*arctan(1/(d*x + c)))^4 - b*d^2*f^2*e*log(4*(4*c^2*f^2*tan(1/2*arctan(1/(d*x + c)))^2 - 8*c*d*f*e*tan(1/2*arctan(1/(d*x + c)))^2 + 4*c*f^2*tan(1/2*arctan(1/(d*x + c)))^3 - 4*d*f*e*tan(1/2*arctan(1/(d*x + c)))^3 + f^2*tan(1/2*arctan(1/(d*x + c)))^4 + 4*d^2*e^2*tan(1/2*arctan(1/(d*x + c)))^2 - 4*c*f^2*tan(1/2*arctan(1/(d*x + c))) + 4*d*f*e*tan(1/2*arctan(1/(d*x + c))) - 2*f^2*tan(1/2*arctan(1/(d*x + c)))^2 + f^2)/(tan(1/2*arctan(1/(d*x + c)))^4 + 2*tan(1/2*arctan(1/(d*x + c)))^2 + 1))*tan(1/2*arctan(1/(d*x + c)))^4 - 4*b*c^3*d*f^3*arctan(1/(d*x + c))*tan(1/2*arctan(1/(d*x + c))) + 12*b*c^2*d^2*f^2*arctan(1/(d*x + c))*e*tan(1/2*arctan(1/(d*x + c))) - 14*b*c^2*d*f^3*arctan(1/(d*x + c))*tan(1/2*arctan(1/(d*x + c)))^2 + 28*b*c*d^2*f^2*arctan(1/(d*x + c))*e*tan(1/2*arctan(1/(d*x + c)))^2 + 12*b*c*d^3*f*e^2*log(4*(4*c^2*f^2*tan(1/2*arctan(1/(d*x + c)))^2 - 8*c*d*f*e*tan(1/2*arctan(1/(d*x + c)))^2 + 4*c*f^2*tan(1/2*arctan(1/(d*x + c)))^3 - 4*d*f*e*tan(1/2*arctan(1/(d*x + c)))^3 + f^2*tan(1/2*arctan(1/(d*x + c)))^4 + 4*d^2*e^2*tan(1/2*arctan(1/(d*x + c)))^2 - 4*c*f^2*tan(1/2*arctan(1/(d*x + c))) + 4*d*f*e*tan(1/2*arctan(1/(d*x + c))) - 2*f^2*tan(1/2*arctan(1/(d*x + c)))^2 + f^2)/(tan(1/2*arctan(1/(d*x + c)))^4 + 2*tan(1/2*arctan(1/(d*x + c)))^2 + 1))*tan(1/2*arctan(1/(d*x + c)))^2 + 2*b*c^2*d*f^3*tan(1/2*arctan(1/(d*x + c)))^3 - 4*b*c*d*f^3*arctan(1/(d*x + c))*tan(1/2*arctan(1/(d*x + c)))^3 - 4*b*d^4*arctan(1/(d*x + c))*e^3*tan(1/2*arctan(1/(d*x + c)))^3 + 12*a*c*d^3*f*e^2*tan(1/2*arctan(1/(d*x + c)))^3 - 4*b*c*d^2*f^2*e*tan(1/2*arctan(1/(d*x + c)))^3 + 4*b*d^2*f^2*arctan(1/(d*x + c))*e*tan(1/2*arctan(1/(d*x + c)))^3 + 4*b*d^3*f*e^2*log(4*(4*c^2*f^2*tan(1/2*arctan(1/(d*x + c)))^2 - 8*c*d*f*e*tan(1/2*arctan(1/(d*x + c)))^2 + 4*c*f^2*tan(1/2*arctan(1/(d*x + c)))^3 - 4*d*f*e*tan(1/2*arctan(1/(d*x + c)))^3 + f^2*tan(1/2*arctan(1/(d*x + c)))^4 + 4*d^2*e^2*tan(1/2*arctan(1/(d*x + c)))^2 - 4*c*f^2*tan(1/2*arctan(1/(d*x + c))) + 4*d*f*e*tan(1/2*arctan(1/(d*x + c))) - 2*f^2*tan(1/2*arctan(1/(d*x + c)))^2 + f^2)/(tan(1/2*arctan(1/(d*x + c)))^4 + 2*tan(1/2*arctan(1/(d*x + c)))^2 + 1))*tan(1/2*arctan(1/(d*x + c)))^3 + b*c*d*f^3*tan(1/2*arctan(1/(d*x + c)))^4 - b*d*f^3*arctan(1/(d*x + c))*tan(1/2*arctan(1/(d*x + c)))^4 + a*d^3*f*e^2*tan(1/2*arctan(1/(d*x + c)))^4 - b*d^2*f^2*e*tan(1/2*arctan(1/(d*x + c)))^4 - 4*a*c^3*d*f^3*tan(1/2*arctan(1/(d*x + c))) - 12*b*c*d^3*f*arctan(1/(d*x + c))*e^2*tan(1/2*arctan(1/(d*x + c))) + 12*a*c^2*d^2*f^2*e*tan(1/2*arctan(1/(d*x + c))) - 4*b*c^2*d*f^3*log(4*(4*c^2*f^2*tan(1/2*arctan(1/(d*x + c)))^2 - 8*c*d*f*e*tan(1/2*arctan(1/(d*x + c)))^2 + 4*c*f^2*tan(1/2*arctan(1/(d*x + c)))^3 - 4*d*f*e*tan(1/2*arctan(1/(d*x + c)))^3 + f^2*tan(1/2*arctan(1/(d*x + c)))^4 + 4*d^2*e^2*tan(1/2*arctan(1/(d*x + c)))^2 - 4*c*f^2*tan(1/2*arctan(1/(d*x + c))) + 4*d*f*e*tan(1/2*arctan(1/(d*x + c))) - 2*f^2*tan(1/2*arctan(1/(d*x + c)))^2 + f^2)/(tan(1/2*arctan(1/(d*x + c)))^4 + 2*tan(1/2*arctan(1/(d*x + c)))^2 + 1))*tan(1/2*arctan(1/(d*x + c))) + 8*b*c*d^2*f^2*e*log(4*(4*c^2*f^2*tan(1/2*arctan(1/(d*x + c)))^2 - 8*c*d*f*e*tan(1/2*arctan(1/(d*x + c)))^2 + 4*c*f^2*tan(1/2*arctan(1/(d*x + c)))^3 - 4*d*f*e*tan(1/2*arctan(1/(d*x + c)))^3 + f^2*tan(1/2*arctan(1/(d*x + c)))^4 + 4*d^2*e^2*tan(1/2*arctan(1/(d*x + c)))^2 - 4*c*f^2*tan(1/2*arctan(1/(d*x + c))) + 4*d*f*e*tan(1/2*arctan(1/(d*x + c))) - 2*f^2*tan(1/2*arctan(1/(d*x + c)))^2 + f^2)/(tan(1/2*arctan(1/(d*x + c)))^4 + 2*tan(1/2*arctan(1/(d*x + c)))^2 + 1))*tan(1/2*arctan(1/(d*x + c))) - 14*a*c^2*d*f^3*tan(1/2*arctan(1/(d*x + c)))^2 - 14*b*d^3*f*arctan(1/(d*x + c))*e^2*tan(1/2*arctan(1/(d*x + c)))^2 + 28*a*c*d^2*f^2*e*tan(1/2*arctan(1/(d*x + c)))^2 - 2*b*c*d*f^3*log(4*(4*c^2*f^2*tan(1/2*arctan(1/(d*x + c)))^2 - 8*c*d*f*e*tan(1/2*arctan(1/(d*x + c)))^2 + 4*c*f^2*tan(1/2*arctan(1/(d*x + c)))^3 - 4*d*f*e*tan(1/2*arctan(1/(d*x + c)))^3 + f^2*tan(1/2*arctan(1/(d*x + c)))^4 + 4*d^2*e^2*tan(1/2*arctan(1/(d*x + c)))^2 - 4*c*f^2*tan(1/2*arctan(1/(d*x + c))) + 4*d*f*e*tan(1/2*arctan(1/(d*x + c))) - 2*f^2*tan(1/2*arctan(1/(d*x + c)))^2 + f^2)/(tan(1/2*arctan(1/(d*x + c)))^4 + 2*tan(1/2*arctan(1/(d*x + c)))^2 + 1))*tan(1/2*arctan(1/(d*x + c)))^2 - 4*b*d^4*e^3*log(4*(4*c^2*f^2*tan(1/2*arctan(1/(d*x + c)))^2 - 8*c*d*f*e*tan(1/2*arctan(1/(d*x + c)))^2 + 4*c*f^2*tan(1/2*arctan(1/(d*x + c)))^3 - 4*d*f*e*tan(1/2*arctan(1/(d*x + c)))^3 + f^2*tan(1/2*arctan(1/(d*x + c)))^4 + 4*d^2*e^2*tan(1/2*arctan(1/(d*x + c)))^2 - 4*c*f^2*tan(1/2*arctan(1/(d*x + c))) + 4*d*f*e*tan(1/2*arctan(1/(d*x + c))) - 2*f^2*tan(1/2*arctan(1/(d*x + c)))^2 + f^2)/(tan(1/2*arctan(1/(d*x + c)))^4 + 2*tan(1/2*arctan(1/(d*x + c)))^2 + 1))*tan(1/2*arctan(1/(d*x + c)))^2 + 2*b*d^2*f^2*e*log(4*(4*c^2*f^2*tan(1/2*arctan(1/(d*x + c)))^2 - 8*c*d*f*e*tan(1/2*arctan(1/(d*x + c)))^2 + 4*c*f^2*tan(1/2*arctan(1/(d*x + c)))^3 - 4*d*f*e*tan(1/2*arctan(1/(d*x + c)))^3 + f^2*tan(1/2*arctan(1/(d*x + c)))^4 + 4*d^2*e^2*tan(1/2*arctan(1/(d*x + c)))^2 - 4*c*f^2*tan(1/2*arctan(1/(d*x + c))) + 4*d*f*e*tan(1/2*arctan(1/(d*x + c))) - 2*f^2*tan(1/2*arctan(1/(d*x + c)))^2 + f^2)/(tan(1/2*arctan(1/(d*x + c)))^4 + 2*tan(1/2*arctan(1/(d*x + c)))^2 + 1))*tan(1/2*arctan(1/(d*x + c)))^2 - 4*a*c*d*f^3*tan(1/2*arctan(1/(d*x + c)))^3 - 4*a*d^4*e^3*tan(1/2*arctan(1/(d*x + c)))^3 + 2*b*d^3*f*e^2*tan(1/2*arctan(1/(d*x + c)))^3 + 4*a*d^2*f^2*e*tan(1/2*arctan(1/(d*x + c)))^3 - a*d*f^3*tan(1/2*arctan(1/(d*x + c)))^4 + b*c^2*d*f^3*arctan(1/(d*x + c)) - 2*b*c*d^2*f^2*arctan(1/(d*x + c))*e - 2*b*c^2*d*f^3*tan(1/2*arctan(1/(d*x + c))) + 4*b*c*d*f^3*arctan(1/(d*x + c))*tan(1/2*arctan(1/(d*x + c))) + 4*b*d^4*arctan(1/(d*x + c))*e^3*tan(1/2*arctan(1/(d*x + c))) - 12*a*c*d^3*f*e^2*tan(1/2*arctan(1/(d*x + c))) + 4*b*c*d^2*f^2*e*tan(1/2*arctan(1/(d*x + c))) - 4*b*d^2*f^2*arctan(1/(d*x + c))*e*tan(1/2*arctan(1/(d*x + c))) - 4*b*d^3*f*e^2*log(4*(4*c^2*f^2*tan(1/2*arctan(1/(d*x + c)))^2 - 8*c*d*f*e*tan(1/2*arctan(1/(d*x + c)))^2 + 4*c*f^2*tan(1/2*arctan(1/(d*x + c)))^3 - 4*d*f*e*tan(1/2*arctan(1/(d*x + c)))^3 + f^2*tan(1/2*arctan(1/(d*x + c)))^4 + 4*d^2*e^2*tan(1/2*arctan(1/(d*x + c)))^2 - 4*c*f^2*tan(1/2*arctan(1/(d*x + c))) + 4*d*f*e*tan(1/2*arctan(1/(d*x + c))) - 2*f^2*tan(1/2*arctan(1/(d*x + c)))^2 + f^2)/(tan(1/2*arctan(1/(d*x + c)))^4 + 2*tan(1/2*arctan(1/(d*x + c)))^2 + 1))*tan(1/2*arctan(1/(d*x + c))) - 6*b*c*d*f^3*tan(1/2*arctan(1/(d*x + c)))^2 - 2*b*d*f^3*arctan(1/(d*x + c))*tan(1/2*arctan(1/(d*x + c)))^2 - 14*a*d^3*f*e^2*tan(1/2*arctan(1/(d*x + c)))^2 + 6*b*d^2*f^2*e*tan(1/2*arctan(1/(d*x + c)))^2 - 2*b*d*f^3*tan(1/2*arctan(1/(d*x + c)))^3 + a*c^2*d*f^3 + b*d^3*f*arctan(1/(d*x + c))*e^2 - 2*a*c*d^2*f^2*e + b*c*d*f^3*log(4*(4*c^2*f^2*tan(1/2*arctan(1/(d*x + c)))^2 - 8*c*d*f*e*tan(1/2*arctan(1/(d*x + c)))^2 + 4*c*f^2*tan(1/2*arctan(1/(d*x + c)))^3 - 4*d*f*e*tan(1/2*arctan(1/(d*x + c)))^3 + f^2*tan(1/2*arctan(1/(d*x + c)))^4 + 4*d^2*e^2*tan(1/2*arctan(1/(d*x + c)))^2 - 4*c*f^2*tan(1/2*arctan(1/(d*x + c))) + 4*d*f*e*tan(1/2*arctan(1/(d*x + c))) - 2*f^2*tan(1/2*arctan(1/(d*x + c)))^2 + f^2)/(tan(1/2*arctan(1/(d*x + c)))^4 + 2*tan(1/2*arctan(1/(d*x + c)))^2 + 1)) - b*d^2*f^2*e*log(4*(4*c^2*f^2*tan(1/2*arctan(1/(d*x + c)))^2 - 8*c*d*f*e*tan(1/2*arctan(1/(d*x + c)))^2 + 4*c*f^2*tan(1/2*arctan(1/(d*x + c)))^3 - 4*d*f*e*tan(1/2*arctan(1/(d*x + c)))^3 + f^2*tan(1/2*arctan(1/(d*x + c)))^4 + 4*d^2*e^2*tan(1/2*arctan(1/(d*x + c)))^2 - 4*c*f^2*tan(1/2*arctan(1/(d*x + c))) + 4*d*f*e*tan(1/2*arctan(1/(d*x + c))) - 2*f^2*tan(1/2*arctan(1/(d*x + c)))^2 + f^2)/(tan(1/2*arctan(1/(d*x + c)))^4 + 2*tan(1/2*arctan(1/(d*x + c)))^2 + 1)) + 4*a*c*d*f^3*tan(1/2*arctan(1/(d*x + c))) + 4*a*d^4*e^3*tan(1/2*arctan(1/(d*x + c))) - 2*b*d^3*f*e^2*tan(1/2*arctan(1/(d*x + c))) - 4*a*d^2*f^2*e*tan(1/2*arctan(1/(d*x + c))) - 2*a*d*f^3*tan(1/2*arctan(1/(d*x + c)))^2 + b*c*d*f^3 - b*d*f^3*arctan(1/(d*x + c)) + a*d^3*f*e^2 - b*d^2*f^2*e + 2*b*d*f^3*tan(1/2*arctan(1/(d*x + c))) - a*d*f^3)*d/(4*c^6*f^6*tan(1/2*arctan(1/(d*x + c)))^2 - 24*c^5*d*f^5*e*tan(1/2*arctan(1/(d*x + c)))^2 + 4*c^5*f^6*tan(1/2*arctan(1/(d*x + c)))^3 - 20*c^4*d*f^5*e*tan(1/2*arctan(1/(d*x + c)))^3 + c^4*f^6*tan(1/2*arctan(1/(d*x + c)))^4 - 4*c^3*d*f^5*e*tan(1/2*arctan(1/(d*x + c)))^4 + 60*c^4*d^2*f^4*e^2*tan(1/2*arctan(1/(d*x + c)))^2 + 40*c^3*d^2*f^4*e^2*tan(1/2*arctan(1/(d*x + c)))^3 + 6*c^2*d^2*f^4*e^2*tan(1/2*arctan(1/(d*x + c)))^4 - 4*c^5*f^6*tan(1/2*arctan(1/(d*x + c))) + 20*c^4*d*f^5*e*tan(1/2*arctan(1/(d*x + c))) + 6*c^4*f^6*tan(1/2*arctan(1/(d*x + c)))^2 - 80*c^3*d^3*f^3*e^3*tan(1/2*arctan(1/(d*x + c)))^2 - 24*c^3*d*f^5*e*tan(1/2*arctan(1/(d*x + c)))^2 + 8*c^3*f^6*tan(1/2*arctan(1/(d*x + c)))^3 - 40*c^2*d^3*f^3*e^3*tan(1/2*arctan(1/(d*x + c)))^3 - 24*c^2*d*f^5*e*tan(1/2*arctan(1/(d*x + c)))^3 + 2*c^2*f^6*tan(1/2*arctan(1/(d*x + c)))^4 - 4*c*d^3*f^3*e^3*tan(1/2*arctan(1/(d*x + c)))^4 - 4*c*d*f^5*e*tan(1/2*arctan(1/(d*x + c)))^4 - 40*c^3*d^2*f^4*e^2*tan(1/2*arctan(1/(d*x + c))) + 60*c^2*d^4*f^2*e^4*tan(1/2*arctan(1/(d*x + c)))^2 + 36*c^2*d^2*f^4*e^2*tan(1/2*arctan(1/(d*x + c)))^2 + 20*c*d^4*f^2*e^4*tan(1/2*arctan(1/(d*x + c)))^3 + 24*c*d^2*f^4*e^2*tan(1/2*arctan(1/(d*x + c)))^3 + d^4*f^2*e^4*tan(1/2*arctan(1/(d*x + c)))^4 + 2*d^2*f^4*e^2*tan(1/2*arctan(1/(d*x + c)))^4 + c^4*f^6 - 4*c^3*d*f^5*e - 8*c^3*f^6*tan(1/2*arctan(1/(d*x + c))) + 40*c^2*d^3*f^3*e^3*tan(1/2*arctan(1/(d*x + c))) + 24*c^2*d*f^5*e*tan(1/2*arctan(1/(d*x + c))) - 24*c*d^5*f*e^5*tan(1/2*arctan(1/(d*x + c)))^2 - 24*c*d^3*f^3*e^3*tan(1/2*arctan(1/(d*x + c)))^2 + 4*c*f^6*tan(1/2*arctan(1/(d*x + c)))^3 - 4*d^5*f*e^5*tan(1/2*arctan(1/(d*x + c)))^3 - 8*d^3*f^3*e^3*tan(1/2*arctan(1/(d*x + c)))^3 - 4*d*f^5*e*tan(1/2*arctan(1/(d*x + c)))^3 + f^6*tan(1/2*arctan(1/(d*x + c)))^4 + 6*c^2*d^2*f^4*e^2 - 20*c*d^4*f^2*e^4*tan(1/2*arctan(1/(d*x + c))) - 24*c*d^2*f^4*e^2*tan(1/2*arctan(1/(d*x + c))) + 4*d^6*e^6*tan(1/2*arctan(1/(d*x + c)))^2 + 6*d^4*f^2*e^4*tan(1/2*arctan(1/(d*x + c)))^2 + 2*c^2*f^6 - 4*c*d^3*f^3*e^3 - 4*c*d*f^5*e - 4*c*f^6*tan(1/2*arctan(1/(d*x + c))) + 4*d^5*f*e^5*tan(1/2*arctan(1/(d*x + c))) + 8*d^3*f^3*e^3*tan(1/2*arctan(1/(d*x + c))) + 4*d*f^5*e*tan(1/2*arctan(1/(d*x + c))) - 2*f^6*tan(1/2*arctan(1/(d*x + c)))^2 + d^4*f^2*e^4 + 2*d^2*f^4*e^2 + f^6)","B",0
136,0,0,0,0.000000," ","integrate((f*x+e)^2*(a+b*arccot(d*x+c))^2,x, algorithm=""giac"")","\int {\left(f x + e\right)}^{2} {\left(b \operatorname{arccot}\left(d x + c\right) + a\right)}^{2}\,{d x}"," ",0,"integrate((f*x + e)^2*(b*arccot(d*x + c) + a)^2, x)","F",0
137,0,0,0,0.000000," ","integrate((f*x+e)*(a+b*arccot(d*x+c))^2,x, algorithm=""giac"")","\int {\left(f x + e\right)} {\left(b \operatorname{arccot}\left(d x + c\right) + a\right)}^{2}\,{d x}"," ",0,"integrate((f*x + e)*(b*arccot(d*x + c) + a)^2, x)","F",0
138,0,0,0,0.000000," ","integrate((a+b*arccot(d*x+c))^2,x, algorithm=""giac"")","\int {\left(b \operatorname{arccot}\left(d x + c\right) + a\right)}^{2}\,{d x}"," ",0,"integrate((b*arccot(d*x + c) + a)^2, x)","F",0
139,-1,0,0,0.000000," ","integrate((a+b*arccot(d*x+c))^2/(f*x+e),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
140,-1,0,0,0.000000," ","integrate((a+b*arccot(d*x+c))^2/(f*x+e)^2,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
141,0,0,0,0.000000," ","integrate((f*x+e)^2*(a+b*arccot(d*x+c))^3,x, algorithm=""giac"")","\int {\left(f x + e\right)}^{2} {\left(b \operatorname{arccot}\left(d x + c\right) + a\right)}^{3}\,{d x}"," ",0,"integrate((f*x + e)^2*(b*arccot(d*x + c) + a)^3, x)","F",0
142,0,0,0,0.000000," ","integrate((f*x+e)*(a+b*arccot(d*x+c))^3,x, algorithm=""giac"")","\int {\left(f x + e\right)} {\left(b \operatorname{arccot}\left(d x + c\right) + a\right)}^{3}\,{d x}"," ",0,"integrate((f*x + e)*(b*arccot(d*x + c) + a)^3, x)","F",0
143,0,0,0,0.000000," ","integrate((a+b*arccot(d*x+c))^3,x, algorithm=""giac"")","\int {\left(b \operatorname{arccot}\left(d x + c\right) + a\right)}^{3}\,{d x}"," ",0,"integrate((b*arccot(d*x + c) + a)^3, x)","F",0
144,-1,0,0,0.000000," ","integrate((a+b*arccot(d*x+c))^3/(f*x+e),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
145,-2,0,0,0.000000," ","integrate((a+b*arccot(d*x+c))^3/(f*x+e)^2,x, algorithm=""giac"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> An error occurred running a Giac command:INPUT:sage2OUTPUT:Evaluation time: 42.28Not invertible Error: Bad Argument Value","F(-2)",0
146,0,0,0,0.000000," ","integrate((f*x+e)^m*(a+b*arccot(d*x+c)),x, algorithm=""giac"")","\int {\left(b \operatorname{arccot}\left(d x + c\right) + a\right)} {\left(f x + e\right)}^{m}\,{d x}"," ",0,"integrate((b*arccot(d*x + c) + a)*(f*x + e)^m, x)","F",0
147,0,0,0,0.000000," ","integrate((f*x+e)^m*(a+b*arccot(d*x+c))^2,x, algorithm=""giac"")","\int {\left(b \operatorname{arccot}\left(d x + c\right) + a\right)}^{2} {\left(f x + e\right)}^{m}\,{d x}"," ",0,"integrate((b*arccot(d*x + c) + a)^2*(f*x + e)^m, x)","F",0
148,0,0,0,0.000000," ","integrate((f*x+e)^m*(a+b*arccot(d*x+c))^3,x, algorithm=""giac"")","\int {\left(b \operatorname{arccot}\left(d x + c\right) + a\right)}^{3} {\left(f x + e\right)}^{m}\,{d x}"," ",0,"integrate((b*arccot(d*x + c) + a)^3*(f*x + e)^m, x)","F",0
149,1,127,0,0.230311," ","integrate(x^3*arccot(b*x^4+a),x, algorithm=""giac"")","-\frac{\arctan\left(\frac{1}{b x^{4} + a}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x^{4} + a}\right)\right)^{2} + \log\left(\frac{16 \, \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x^{4} + a}\right)\right)^{2}}{\tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x^{4} + a}\right)\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x^{4} + a}\right)\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x^{4} + a}\right)\right) - \arctan\left(\frac{1}{b x^{4} + a}\right)}{8 \, b \tan\left(\frac{1}{2} \, \arctan\left(\frac{1}{b x^{4} + a}\right)\right)}"," ",0,"-1/8*(arctan(1/(b*x^4 + a))*tan(1/2*arctan(1/(b*x^4 + a)))^2 + log(16*tan(1/2*arctan(1/(b*x^4 + a)))^2/(tan(1/2*arctan(1/(b*x^4 + a)))^4 + 2*tan(1/2*arctan(1/(b*x^4 + a)))^2 + 1))*tan(1/2*arctan(1/(b*x^4 + a))) - arctan(1/(b*x^4 + a)))/(b*tan(1/2*arctan(1/(b*x^4 + a))))","B",0
150,1,60,0,0.376768," ","integrate(x^(-1+n)*arccot(a+b*x^n),x, algorithm=""giac"")","\frac{b {\left(\frac{2 \, {\left(b x^{n} + a\right)} \arctan\left(\frac{1}{b x^{n} + a}\right)}{b^{2}} + \frac{\log\left(\frac{1}{{\left(b x^{n} + a\right)}^{2}} + 1\right)}{b^{2}} - \frac{\log\left(\frac{1}{{\left(b x^{n} + a\right)}^{2}}\right)}{b^{2}}\right)}}{2 \, n}"," ",0,"1/2*b*(2*(b*x^n + a)*arctan(1/(b*x^n + a))/b^2 + log(1/(b*x^n + a)^2 + 1)/b^2 - log((b*x^n + a)^(-2))/b^2)/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=""giac"")","\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=""giac"")","\int -\frac{{\left(b \operatorname{arccot}\left(\frac{\sqrt{-c x + 1}}{\sqrt{c x + 1}}\right) + a\right)}^{3}}{c^{2} x^{2} - 1}\,{d x}"," ",0,"integrate(-(b*arccot(sqrt(-c*x + 1)/sqrt(c*x + 1)) + a)^3/(c^2*x^2 - 1), x)","F",0
153,0,0,0,0.000000," ","integrate((a+b*arccot((-c*x+1)^(1/2)/(c*x+1)^(1/2)))^2/(-c^2*x^2+1),x, algorithm=""giac"")","\int -\frac{{\left(b \operatorname{arccot}\left(\frac{\sqrt{-c x + 1}}{\sqrt{c x + 1}}\right) + a\right)}^{2}}{c^{2} x^{2} - 1}\,{d x}"," ",0,"integrate(-(b*arccot(sqrt(-c*x + 1)/sqrt(c*x + 1)) + a)^2/(c^2*x^2 - 1), x)","F",0
154,0,0,0,0.000000," ","integrate((a+b*arccot((-c*x+1)^(1/2)/(c*x+1)^(1/2)))/(-c^2*x^2+1),x, algorithm=""giac"")","\int -\frac{b \operatorname{arccot}\left(\frac{\sqrt{-c x + 1}}{\sqrt{c x + 1}}\right) + a}{c^{2} x^{2} - 1}\,{d x}"," ",0,"integrate(-(b*arccot(sqrt(-c*x + 1)/sqrt(c*x + 1)) + a)/(c^2*x^2 - 1), x)","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=""giac"")","\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=""giac"")","\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)}^{2}}\,{d x}"," ",0,"integrate(-1/((c^2*x^2 - 1)*(b*arccot(sqrt(-c*x + 1)/sqrt(c*x + 1)) + a)^2), x)","F",0
157,1,30,0,0.206671," ","integrate(1/2*pi-arctan(tan(b*x+a)),x, algorithm=""giac"")","-\frac{1}{2} \, b x^{2} + \pi x \left \lfloor \frac{b x + a}{\pi} + \frac{1}{2} \right \rfloor + \frac{1}{2} \, \pi x - a x"," ",0,"-1/2*b*x^2 + pi*x*floor((b*x + a)/pi + 1/2) + 1/2*pi*x - a*x","A",0
158,0,0,0,0.000000," ","integrate(x^2*arccot(c+d*tan(b*x+a)),x, algorithm=""giac"")","\int x^{2} \operatorname{arccot}\left(d \tan\left(b x + a\right) + c\right)\,{d x}"," ",0,"integrate(x^2*arccot(d*tan(b*x + a) + c), x)","F",0
159,0,0,0,0.000000," ","integrate(x*arccot(c+d*tan(b*x+a)),x, algorithm=""giac"")","\int x \operatorname{arccot}\left(d \tan\left(b x + a\right) + c\right)\,{d x}"," ",0,"integrate(x*arccot(d*tan(b*x + a) + c), x)","F",0
160,0,0,0,0.000000," ","integrate(arccot(c+d*tan(b*x+a)),x, algorithm=""giac"")","\int \operatorname{arccot}\left(d \tan\left(b x + a\right) + c\right)\,{d x}"," ",0,"integrate(arccot(d*tan(b*x + a) + c), x)","F",0
161,0,0,0,0.000000," ","integrate(arccot(c+d*tan(b*x+a))/x,x, algorithm=""giac"")","\int \frac{\operatorname{arccot}\left(d \tan\left(b x + a\right) + c\right)}{x}\,{d x}"," ",0,"integrate(arccot(d*tan(b*x + a) + c)/x, x)","F",0
162,0,0,0,0.000000," ","integrate(x^2*arccot(c+(1+I*c)*tan(b*x+a)),x, algorithm=""giac"")","\int x^{2} \operatorname{arccot}\left({\left(i \, c + 1\right)} \tan\left(b x + a\right) + c\right)\,{d x}"," ",0,"integrate(x^2*arccot((I*c + 1)*tan(b*x + a) + c), x)","F",0
163,0,0,0,0.000000," ","integrate(x*arccot(c+(1+I*c)*tan(b*x+a)),x, algorithm=""giac"")","\int x \operatorname{arccot}\left({\left(i \, c + 1\right)} \tan\left(b x + a\right) + c\right)\,{d x}"," ",0,"integrate(x*arccot((I*c + 1)*tan(b*x + a) + c), x)","F",0
164,0,0,0,0.000000," ","integrate(arccot(c+(1+I*c)*tan(b*x+a)),x, algorithm=""giac"")","\int \operatorname{arccot}\left({\left(i \, c + 1\right)} \tan\left(b x + a\right) + c\right)\,{d x}"," ",0,"integrate(arccot((I*c + 1)*tan(b*x + a) + c), x)","F",0
165,0,0,0,0.000000," ","integrate(arccot(c+(1+I*c)*tan(b*x+a))/x,x, algorithm=""giac"")","\int \frac{\operatorname{arccot}\left({\left(i \, c + 1\right)} \tan\left(b x + a\right) + c\right)}{x}\,{d x}"," ",0,"integrate(arccot((I*c + 1)*tan(b*x + a) + c)/x, x)","F",0
166,0,0,0,0.000000," ","integrate(x^2*arccot(c-(1-I*c)*tan(b*x+a)),x, algorithm=""giac"")","\int x^{2} \operatorname{arccot}\left(-{\left(-i \, c + 1\right)} \tan\left(b x + a\right) + c\right)\,{d x}"," ",0,"integrate(x^2*arccot(-(-I*c + 1)*tan(b*x + a) + c), x)","F",0
167,0,0,0,0.000000," ","integrate(x*arccot(c-(1-I*c)*tan(b*x+a)),x, algorithm=""giac"")","\int x \operatorname{arccot}\left(-{\left(-i \, c + 1\right)} \tan\left(b x + a\right) + c\right)\,{d x}"," ",0,"integrate(x*arccot(-(-I*c + 1)*tan(b*x + a) + c), x)","F",0
168,0,0,0,0.000000," ","integrate(arccot(c-(1-I*c)*tan(b*x+a)),x, algorithm=""giac"")","\int \operatorname{arccot}\left(-{\left(-i \, c + 1\right)} \tan\left(b x + a\right) + c\right)\,{d x}"," ",0,"integrate(arccot(-(-I*c + 1)*tan(b*x + a) + c), x)","F",0
169,0,0,0,0.000000," ","integrate(arccot(c-(1-I*c)*tan(b*x+a))/x,x, algorithm=""giac"")","\int \frac{\operatorname{arccot}\left(-{\left(-i \, c + 1\right)} \tan\left(b x + a\right) + c\right)}{x}\,{d x}"," ",0,"integrate(arccot(-(-I*c + 1)*tan(b*x + a) + c)/x, x)","F",0
170,1,10,0,0.123166," ","integrate(arccot(cot(b*x+a)),x, algorithm=""giac"")","\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=""giac"")","\int x^{2} \operatorname{arccot}\left(d \cot\left(b x + a\right) + c\right)\,{d x}"," ",0,"integrate(x^2*arccot(d*cot(b*x + a) + c), x)","F",0
172,0,0,0,0.000000," ","integrate(x*arccot(c+d*cot(b*x+a)),x, algorithm=""giac"")","\int x \operatorname{arccot}\left(d \cot\left(b x + a\right) + c\right)\,{d x}"," ",0,"integrate(x*arccot(d*cot(b*x + a) + c), x)","F",0
173,0,0,0,0.000000," ","integrate(arccot(c+d*cot(b*x+a)),x, algorithm=""giac"")","\int \operatorname{arccot}\left(d \cot\left(b x + a\right) + c\right)\,{d x}"," ",0,"integrate(arccot(d*cot(b*x + a) + c), x)","F",0
174,0,0,0,0.000000," ","integrate(arccot(c+d*cot(b*x+a))/x,x, algorithm=""giac"")","\int \frac{\operatorname{arccot}\left(d \cot\left(b x + a\right) + c\right)}{x}\,{d x}"," ",0,"integrate(arccot(d*cot(b*x + a) + c)/x, x)","F",0
175,0,0,0,0.000000," ","integrate(x^2*(pi-arccot(-c-(1-I*c)*cot(b*x+a))),x, algorithm=""giac"")","\int {\left(\pi - \operatorname{arccot}\left(-{\left(-i \, c + 1\right)} \cot\left(b x + a\right) - c\right)\right)} x^{2}\,{d x}"," ",0,"integrate((pi - arccot(-(-I*c + 1)*cot(b*x + a) - c))*x^2, x)","F",0
176,0,0,0,0.000000," ","integrate(x*(pi-arccot(-c-(1-I*c)*cot(b*x+a))),x, algorithm=""giac"")","\int {\left(\pi - \operatorname{arccot}\left(-{\left(-i \, c + 1\right)} \cot\left(b x + a\right) - c\right)\right)} x\,{d x}"," ",0,"integrate((pi - arccot(-(-I*c + 1)*cot(b*x + a) - c))*x, x)","F",0
177,0,0,0,0.000000," ","integrate(pi-arccot(-c-(1-I*c)*cot(b*x+a)),x, algorithm=""giac"")","\int \pi - \operatorname{arccot}\left(-{\left(-i \, c + 1\right)} \cot\left(b x + a\right) - c\right)\,{d x}"," ",0,"integrate(pi - arccot(-(-I*c + 1)*cot(b*x + a) - c), x)","F",0
178,0,0,0,0.000000," ","integrate((pi-arccot(-c-(1-I*c)*cot(b*x+a)))/x,x, algorithm=""giac"")","\int \frac{\pi - \operatorname{arccot}\left(-{\left(-i \, c + 1\right)} \cot\left(b x + a\right) - c\right)}{x}\,{d x}"," ",0,"integrate((pi - arccot(-(-I*c + 1)*cot(b*x + a) - c))/x, x)","F",0
179,0,0,0,0.000000," ","integrate(x^2*(pi-arccot(-c+(1+I*c)*cot(b*x+a))),x, algorithm=""giac"")","\int {\left(\pi - \operatorname{arccot}\left({\left(i \, c + 1\right)} \cot\left(b x + a\right) - c\right)\right)} x^{2}\,{d x}"," ",0,"integrate((pi - arccot((I*c + 1)*cot(b*x + a) - c))*x^2, x)","F",0
180,0,0,0,0.000000," ","integrate(x*(pi-arccot(-c+(1+I*c)*cot(b*x+a))),x, algorithm=""giac"")","\int {\left(\pi - \operatorname{arccot}\left({\left(i \, c + 1\right)} \cot\left(b x + a\right) - c\right)\right)} x\,{d x}"," ",0,"integrate((pi - arccot((I*c + 1)*cot(b*x + a) - c))*x, x)","F",0
181,0,0,0,0.000000," ","integrate(pi-arccot(-c+(1+I*c)*cot(b*x+a)),x, algorithm=""giac"")","\int \pi - \operatorname{arccot}\left({\left(i \, c + 1\right)} \cot\left(b x + a\right) - c\right)\,{d x}"," ",0,"integrate(pi - arccot((I*c + 1)*cot(b*x + a) - c), x)","F",0
182,0,0,0,0.000000," ","integrate((pi-arccot(-c+(1+I*c)*cot(b*x+a)))/x,x, algorithm=""giac"")","\int \frac{\pi - \operatorname{arccot}\left({\left(i \, c + 1\right)} \cot\left(b x + a\right) - c\right)}{x}\,{d x}"," ",0,"integrate((pi - arccot((I*c + 1)*cot(b*x + a) - c))/x, x)","F",0
183,-1,0,0,0.000000," ","integrate((f*x+e)^3*arccot(tanh(b*x+a)),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
184,-1,0,0,0.000000," ","integrate((f*x+e)^2*arccot(tanh(b*x+a)),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
185,0,0,0,0.000000," ","integrate((f*x+e)*arccot(tanh(b*x+a)),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
186,0,0,0,0.000000," ","integrate(arccot(tanh(b*x+a)),x, algorithm=""giac"")","\int \operatorname{arccot}\left(\tanh\left(b x + a\right)\right)\,{d x}"," ",0,"integrate(arccot(tanh(b*x + a)), x)","F",0
187,0,0,0,0.000000," ","integrate(arccot(tanh(b*x+a))/(f*x+e),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
188,0,0,0,0.000000," ","integrate(x^2*arccot(c+d*tanh(b*x+a)),x, algorithm=""giac"")","\int x^{2} \operatorname{arccot}\left(d \tanh\left(b x + a\right) + c\right)\,{d x}"," ",0,"integrate(x^2*arccot(d*tanh(b*x + a) + c), x)","F",0
189,0,0,0,0.000000," ","integrate(x*arccot(c+d*tanh(b*x+a)),x, algorithm=""giac"")","\int x \operatorname{arccot}\left(d \tanh\left(b x + a\right) + c\right)\,{d x}"," ",0,"integrate(x*arccot(d*tanh(b*x + a) + c), x)","F",0
190,0,0,0,0.000000," ","integrate(arccot(c+d*tanh(b*x+a)),x, algorithm=""giac"")","\int \operatorname{arccot}\left(d \tanh\left(b x + a\right) + c\right)\,{d x}"," ",0,"integrate(arccot(d*tanh(b*x + a) + c), x)","F",0
191,0,0,0,0.000000," ","integrate(arccot(c+d*tanh(b*x+a))/x,x, algorithm=""giac"")","\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
192,0,0,0,0.000000," ","integrate(x^2*arccot(c+(I+c)*tanh(b*x+a)),x, algorithm=""giac"")","\int x^{2} \operatorname{arccot}\left({\left(c + i\right)} \tanh\left(b x + a\right) + c\right)\,{d x}"," ",0,"integrate(x^2*arccot((c + I)*tanh(b*x + a) + c), x)","F",0
193,0,0,0,0.000000," ","integrate(x*arccot(c+(I+c)*tanh(b*x+a)),x, algorithm=""giac"")","\int x \operatorname{arccot}\left({\left(c + i\right)} \tanh\left(b x + a\right) + c\right)\,{d x}"," ",0,"integrate(x*arccot((c + I)*tanh(b*x + a) + c), x)","F",0
194,0,0,0,0.000000," ","integrate(arccot(c+(I+c)*tanh(b*x+a)),x, algorithm=""giac"")","\int \operatorname{arccot}\left({\left(c + i\right)} \tanh\left(b x + a\right) + c\right)\,{d x}"," ",0,"integrate(arccot((c + I)*tanh(b*x + a) + c), x)","F",0
195,0,0,0,0.000000," ","integrate(arccot(c+(I+c)*tanh(b*x+a))/x,x, algorithm=""giac"")","\int \frac{\operatorname{arccot}\left({\left(c + i\right)} \tanh\left(b x + a\right) + c\right)}{x}\,{d x}"," ",0,"integrate(arccot((c + I)*tanh(b*x + a) + c)/x, x)","F",0
196,0,0,0,0.000000," ","integrate(x^2*arccot(c-(I-c)*tanh(b*x+a)),x, algorithm=""giac"")","\int x^{2} \operatorname{arccot}\left({\left(c - i\right)} \tanh\left(b x + a\right) + c\right)\,{d x}"," ",0,"integrate(x^2*arccot((c - I)*tanh(b*x + a) + c), x)","F",0
197,0,0,0,0.000000," ","integrate(x*arccot(c-(I-c)*tanh(b*x+a)),x, algorithm=""giac"")","\int x \operatorname{arccot}\left({\left(c - i\right)} \tanh\left(b x + a\right) + c\right)\,{d x}"," ",0,"integrate(x*arccot((c - I)*tanh(b*x + a) + c), x)","F",0
198,0,0,0,0.000000," ","integrate(arccot(c-(I-c)*tanh(b*x+a)),x, algorithm=""giac"")","\int \operatorname{arccot}\left({\left(c - i\right)} \tanh\left(b x + a\right) + c\right)\,{d x}"," ",0,"integrate(arccot((c - I)*tanh(b*x + a) + c), x)","F",0
199,0,0,0,0.000000," ","integrate(arccot(c-(I-c)*tanh(b*x+a))/x,x, algorithm=""giac"")","\int \frac{\operatorname{arccot}\left({\left(c - i\right)} \tanh\left(b x + a\right) + c\right)}{x}\,{d x}"," ",0,"integrate(arccot((c - I)*tanh(b*x + a) + c)/x, x)","F",0
200,-1,0,0,0.000000," ","integrate((f*x+e)^3*arccot(coth(b*x+a)),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
201,-1,0,0,0.000000," ","integrate((f*x+e)^2*arccot(coth(b*x+a)),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
202,-1,0,0,0.000000," ","integrate((f*x+e)*arccot(coth(b*x+a)),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
203,0,0,0,0.000000," ","integrate(arccot(coth(b*x+a)),x, algorithm=""giac"")","\int \operatorname{arccot}\left(\coth\left(b x + a\right)\right)\,{d x}"," ",0,"integrate(arccot(coth(b*x + a)), x)","F",0
204,0,0,0,0.000000," ","integrate(arccot(coth(b*x+a))/(f*x+e),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
205,0,0,0,0.000000," ","integrate(x^2*arccot(c+d*coth(b*x+a)),x, algorithm=""giac"")","\int x^{2} \operatorname{arccot}\left(d \coth\left(b x + a\right) + c\right)\,{d x}"," ",0,"integrate(x^2*arccot(d*coth(b*x + a) + c), x)","F",0
206,0,0,0,0.000000," ","integrate(x*arccot(c+d*coth(b*x+a)),x, algorithm=""giac"")","\int x \operatorname{arccot}\left(d \coth\left(b x + a\right) + c\right)\,{d x}"," ",0,"integrate(x*arccot(d*coth(b*x + a) + c), x)","F",0
207,0,0,0,0.000000," ","integrate(arccot(c+d*coth(b*x+a)),x, algorithm=""giac"")","\int \operatorname{arccot}\left(d \coth\left(b x + a\right) + c\right)\,{d x}"," ",0,"integrate(arccot(d*coth(b*x + a) + c), x)","F",0
208,0,0,0,0.000000," ","integrate(arccot(c+d*coth(b*x+a))/x,x, algorithm=""giac"")","\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
209,0,0,0,0.000000," ","integrate(x^2*arccot(c+(I+c)*coth(b*x+a)),x, algorithm=""giac"")","\int x^{2} \operatorname{arccot}\left({\left(c + i\right)} \coth\left(b x + a\right) + c\right)\,{d x}"," ",0,"integrate(x^2*arccot((c + I)*coth(b*x + a) + c), x)","F",0
210,0,0,0,0.000000," ","integrate(x*arccot(c+(I+c)*coth(b*x+a)),x, algorithm=""giac"")","\int x \operatorname{arccot}\left({\left(c + i\right)} \coth\left(b x + a\right) + c\right)\,{d x}"," ",0,"integrate(x*arccot((c + I)*coth(b*x + a) + c), x)","F",0
211,0,0,0,0.000000," ","integrate(arccot(c+(I+c)*coth(b*x+a)),x, algorithm=""giac"")","\int \operatorname{arccot}\left({\left(c + i\right)} \coth\left(b x + a\right) + c\right)\,{d x}"," ",0,"integrate(arccot((c + I)*coth(b*x + a) + c), x)","F",0
212,0,0,0,0.000000," ","integrate(arccot(c+(I+c)*coth(b*x+a))/x,x, algorithm=""giac"")","\int \frac{\operatorname{arccot}\left({\left(c + i\right)} \coth\left(b x + a\right) + c\right)}{x}\,{d x}"," ",0,"integrate(arccot((c + I)*coth(b*x + a) + c)/x, x)","F",0
213,0,0,0,0.000000," ","integrate(x^2*arccot(c-(I-c)*coth(b*x+a)),x, algorithm=""giac"")","\int x^{2} \operatorname{arccot}\left({\left(c - i\right)} \coth\left(b x + a\right) + c\right)\,{d x}"," ",0,"integrate(x^2*arccot((c - I)*coth(b*x + a) + c), x)","F",0
214,0,0,0,0.000000," ","integrate(x*arccot(c-(I-c)*coth(b*x+a)),x, algorithm=""giac"")","\int x \operatorname{arccot}\left({\left(c - i\right)} \coth\left(b x + a\right) + c\right)\,{d x}"," ",0,"integrate(x*arccot((c - I)*coth(b*x + a) + c), x)","F",0
215,0,0,0,0.000000," ","integrate(arccot(c-(I-c)*coth(b*x+a)),x, algorithm=""giac"")","\int \operatorname{arccot}\left({\left(c - i\right)} \coth\left(b x + a\right) + c\right)\,{d x}"," ",0,"integrate(arccot((c - I)*coth(b*x + a) + c), x)","F",0
216,0,0,0,0.000000," ","integrate(arccot(c-(I-c)*coth(b*x+a))/x,x, algorithm=""giac"")","\int \frac{\operatorname{arccot}\left({\left(c - i\right)} \coth\left(b x + a\right) + c\right)}{x}\,{d x}"," ",0,"integrate(arccot((c - I)*coth(b*x + a) + c)/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=""giac"")","\int \frac{{\left(b \operatorname{arccot}\left(c x^{n}\right) + a\right)} {\left(e \log\left(f x^{m}\right) + d\right)}}{x}\,{d x}"," ",0,"integrate((b*arccot(c*x^n) + a)*(e*log(f*x^m) + d)/x, x)","F",0
218,0,0,0,0.000000," ","integrate(arccot(exp(x)),x, algorithm=""giac"")","\int \operatorname{arccot}\left(e^{x}\right)\,{d x}"," ",0,"integrate(arccot(e^x), x)","F",0
219,0,0,0,0.000000," ","integrate(x*arccot(exp(x)),x, algorithm=""giac"")","\int x \operatorname{arccot}\left(e^{x}\right)\,{d x}"," ",0,"integrate(x*arccot(e^x), x)","F",0
220,0,0,0,0.000000," ","integrate(x^2*arccot(exp(x)),x, algorithm=""giac"")","\int x^{2} \operatorname{arccot}\left(e^{x}\right)\,{d x}"," ",0,"integrate(x^2*arccot(e^x), x)","F",0
221,0,0,0,0.000000," ","integrate(arccot(exp(b*x+a)),x, algorithm=""giac"")","\int \operatorname{arccot}\left(e^{\left(b x + a\right)}\right)\,{d x}"," ",0,"integrate(arccot(e^(b*x + a)), x)","F",0
222,0,0,0,0.000000," ","integrate(x*arccot(exp(b*x+a)),x, algorithm=""giac"")","\int x \operatorname{arccot}\left(e^{\left(b x + a\right)}\right)\,{d x}"," ",0,"integrate(x*arccot(e^(b*x + a)), x)","F",0
223,0,0,0,0.000000," ","integrate(x^2*arccot(exp(b*x+a)),x, algorithm=""giac"")","\int x^{2} \operatorname{arccot}\left(e^{\left(b x + a\right)}\right)\,{d x}"," ",0,"integrate(x^2*arccot(e^(b*x + a)), x)","F",0
224,0,0,0,0.000000," ","integrate(arccot(a+b*f^(d*x+c)),x, algorithm=""giac"")","\int \operatorname{arccot}\left(b f^{d x + c} + a\right)\,{d x}"," ",0,"integrate(arccot(b*f^(d*x + c) + a), x)","F",0
225,0,0,0,0.000000," ","integrate(x*arccot(a+b*f^(d*x+c)),x, algorithm=""giac"")","\int x \operatorname{arccot}\left(b f^{d x + c} + a\right)\,{d x}"," ",0,"integrate(x*arccot(b*f^(d*x + c) + a), x)","F",0
226,0,0,0,0.000000," ","integrate(x^2*arccot(a+b*f^(d*x+c)),x, algorithm=""giac"")","\int x^{2} \operatorname{arccot}\left(b f^{d x + c} + a\right)\,{d x}"," ",0,"integrate(x^2*arccot(b*f^(d*x + c) + a), x)","F",0
227,1,21,0,0.123061," ","integrate(arccot(exp(x))/exp(x),x, algorithm=""giac"")","-\arctan\left(e^{\left(-x\right)}\right) e^{\left(-x\right)} + \frac{1}{2} \, \log\left(e^{\left(-2 \, x\right)} + 1\right)"," ",0,"-arctan(e^(-x))*e^(-x) + 1/2*log(e^(-2*x) + 1)","A",0
228,1,18,0,0.107979," ","integrate(1/(a*x^2+a)/(b-2*b*arccot(x)),x, algorithm=""giac"")","\frac{\log\left({\left| 2 \, \arctan\left(\frac{1}{x}\right) - 1 \right|}\right)}{2 \, a b}"," ",0,"1/2*log(abs(2*arctan(1/x) - 1))/(a*b)","A",0
229,1,66,0,0.127174," ","integrate(exp(c*(b*x+a))*arccot(sinh(b*c*x+a*c)),x, algorithm=""giac"")","\frac{{\left(\arctan\left(\frac{2}{e^{\left(b c x + a c\right)} - e^{\left(-b c x - a c\right)}}\right) e^{\left(b c x\right)} + e^{\left(-a c\right)} \log\left(e^{\left(2 \, b c x + 2 \, a c\right)} + 1\right)\right)} e^{\left(a c\right)}}{b c}"," ",0,"(arctan(2/(e^(b*c*x + a*c) - e^(-b*c*x - a*c)))*e^(b*c*x) + e^(-a*c)*log(e^(2*b*c*x + 2*a*c) + 1))*e^(a*c)/(b*c)","A",0
230,1,154,0,0.135886," ","integrate(exp(c*(b*x+a))*arccot(cosh(b*c*x+a*c)),x, algorithm=""giac"")","-\frac{{\left(\sqrt{2} e^{\left(-a c\right)} \log\left(-\frac{2 \, \sqrt{2} e^{\left(2 \, a c\right)} - e^{\left(2 \, b c x + 4 \, a c\right)} - 3 \, e^{\left(2 \, a c\right)}}{2 \, \sqrt{2} e^{\left(2 \, a c\right)} + e^{\left(2 \, b c x + 4 \, a c\right)} + 3 \, e^{\left(2 \, a c\right)}}\right) - 2 \, \arctan\left(\frac{2}{e^{\left(b c x + a c\right)} + e^{\left(-b c x - a c\right)}}\right) e^{\left(b c x\right)} - e^{\left(-a c\right)} \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)\right)} e^{\left(a c\right)}}{2 \, b c}"," ",0,"-1/2*(sqrt(2)*e^(-a*c)*log(-(2*sqrt(2)*e^(2*a*c) - e^(2*b*c*x + 4*a*c) - 3*e^(2*a*c))/(2*sqrt(2)*e^(2*a*c) + e^(2*b*c*x + 4*a*c) + 3*e^(2*a*c))) - 2*arctan(2/(e^(b*c*x + a*c) + e^(-b*c*x - a*c)))*e^(b*c*x) - e^(-a*c)*log(e^(4*b*c*x + 4*a*c) + 6*e^(2*b*c*x + 2*a*c) + 1))*e^(a*c)/(b*c)","A",0
231,0,0,0,0.000000," ","integrate(exp(c*(b*x+a))*arccot(tanh(b*c*x+a*c)),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
232,0,0,0,0.000000," ","integrate(exp(c*(b*x+a))*arccot(coth(b*c*x+a*c)),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
233,1,154,0,0.126772," ","integrate(exp(c*(b*x+a))*arccot(sech(b*c*x+a*c)),x, algorithm=""giac"")","\frac{{\left(\sqrt{2} e^{\left(-a c\right)} \log\left(-\frac{2 \, \sqrt{2} e^{\left(2 \, a c\right)} - e^{\left(2 \, b c x + 4 \, a c\right)} - 3 \, e^{\left(2 \, a c\right)}}{2 \, \sqrt{2} e^{\left(2 \, a c\right)} + e^{\left(2 \, b c x + 4 \, a c\right)} + 3 \, e^{\left(2 \, a c\right)}}\right) + 2 \, \arctan\left(\frac{1}{2} \, e^{\left(b c x + a c\right)} + \frac{1}{2} \, e^{\left(-b c x - a c\right)}\right) e^{\left(b c x\right)} - e^{\left(-a c\right)} \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)\right)} e^{\left(a c\right)}}{2 \, b c}"," ",0,"1/2*(sqrt(2)*e^(-a*c)*log(-(2*sqrt(2)*e^(2*a*c) - e^(2*b*c*x + 4*a*c) - 3*e^(2*a*c))/(2*sqrt(2)*e^(2*a*c) + e^(2*b*c*x + 4*a*c) + 3*e^(2*a*c))) + 2*arctan(1/2*e^(b*c*x + a*c) + 1/2*e^(-b*c*x - a*c))*e^(b*c*x) - e^(-a*c)*log(e^(4*b*c*x + 4*a*c) + 6*e^(2*b*c*x + 2*a*c) + 1))*e^(a*c)/(b*c)","A",0
234,1,65,0,0.127788," ","integrate(exp(c*(b*x+a))*arccot(csch(b*c*x+a*c)),x, algorithm=""giac"")","\frac{{\left(\arctan\left(\frac{1}{2} \, e^{\left(b c x + a c\right)} - \frac{1}{2} \, e^{\left(-b c x - a c\right)}\right) e^{\left(b c x\right)} - e^{\left(-a c\right)} \log\left(e^{\left(2 \, b c x + 2 \, a c\right)} + 1\right)\right)} e^{\left(a c\right)}}{b c}"," ",0,"(arctan(1/2*e^(b*c*x + a*c) - 1/2*e^(-b*c*x - a*c))*e^(b*c*x) - e^(-a*c)*log(e^(2*b*c*x + 2*a*c) + 1))*e^(a*c)/(b*c)","A",0
