1,1,55,51,0.804990,"\text{Not used}","int(x^5*acot(a*x),x)","\left\{\begin{array}{cl} \frac{\pi \,x^6}{12} & \text{\ if\ \ }a=0\\ \frac{x^6\,\mathrm{acot}\left(a\,x\right)}{6}-\frac{\frac{\mathrm{atan}\left(a\,x\right)}{6}-\frac{a\,x}{6}+\frac{a^3\,x^3}{18}-\frac{a^5\,x^5}{30}}{a^6} & \text{\ if\ \ }a\neq 0 \end{array}\right.","Not used",1,"piecewise(a == 0, (x^6*pi)/12, a ~= 0, - (atan(a*x)/6 - (a*x)/6 + (a^3*x^3)/18 - (a^5*x^5)/30)/a^6 + (x^6*acot(a*x))/6)","B"
2,1,56,49,0.700048,"\text{Not used}","int(x^4*acot(a*x),x)","\left\{\begin{array}{cl} \frac{\pi \,x^5}{10} & \text{\ if\ \ }a=0\\ \frac{2\,\ln\left(a^2\,x^2+1\right)-2\,a^2\,x^2+a^4\,x^4}{20\,a^5}+\frac{x^5\,\mathrm{acot}\left(a\,x\right)}{5} & \text{\ if\ \ }a\neq 0 \end{array}\right.","Not used",1,"piecewise(a == 0, (x^5*pi)/10, a ~= 0, (2*log(a^2*x^2 + 1) - 2*a^2*x^2 + a^4*x^4)/(20*a^5) + (x^5*acot(a*x))/5)","B"
3,1,46,41,0.720526,"\text{Not used}","int(x^3*acot(a*x),x)","\left\{\begin{array}{cl} \frac{\pi \,x^4}{8} & \text{\ if\ \ }a=0\\ \frac{3\,\mathrm{atan}\left(a\,x\right)-3\,a\,x+a^3\,x^3}{12\,a^4}+\frac{x^4\,\mathrm{acot}\left(a\,x\right)}{4} & \text{\ if\ \ }a\neq 0 \end{array}\right.","Not used",1,"piecewise(a == 0, (x^4*pi)/8, a ~= 0, (3*atan(a*x) - 3*a*x + a^3*x^3)/(12*a^4) + (x^4*acot(a*x))/4)","B"
4,1,49,39,0.688122,"\text{Not used}","int(x^2*acot(a*x),x)","\left\{\begin{array}{cl} \frac{\pi \,x^3}{6} & \text{\ if\ \ }a=0\\ \frac{\frac{x^2}{2}-\frac{\ln\left(a^2\,x^2+1\right)}{2\,a^2}}{3\,a}+\frac{x^3\,\mathrm{acot}\left(a\,x\right)}{3} & \text{\ if\ \ }a\neq 0 \end{array}\right.","Not used",1,"piecewise(a == 0, (x^3*pi)/6, a ~= 0, (x^2/2 - log(a^2*x^2 + 1)/(2*a^2))/(3*a) + (x^3*acot(a*x))/3)","B"
5,1,39,31,0.757390,"\text{Not used}","int(x*acot(a*x),x)","\left\{\begin{array}{cl} \frac{\pi \,x^2}{4} & \text{\ if\ \ }a=0\\ \frac{x-\frac{\mathrm{atan}\left(a\,x\right)}{a}}{2\,a}+\frac{x^2\,\mathrm{acot}\left(a\,x\right)}{2} & \text{\ if\ \ }a\neq 0 \end{array}\right.","Not used",1,"piecewise(a == 0, (x^2*pi)/4, a ~= 0, (x - atan(a*x)/a)/(2*a) + (x^2*acot(a*x))/2)","B"
6,1,22,24,0.136453,"\text{Not used}","int(acot(a*x),x)","x\,\mathrm{acot}\left(a\,x\right)+\frac{\ln\left(a^2\,x^2+1\right)}{2\,a}","Not used",1,"x*acot(a*x) + log(a^2*x^2 + 1)/(2*a)","B"
7,0,-1,37,0.000000,"\text{Not used}","int(acot(a*x)/x,x)","\int \frac{\mathrm{acot}\left(a\,x\right)}{x} \,d x","Not used",1,"int(acot(a*x)/x, x)","F"
8,1,28,30,0.234525,"\text{Not used}","int(acot(a*x)/x^2,x)","\frac{a\,\left(\ln\left(a^2\,x^2+1\right)-2\,\ln\left(x\right)\right)}{2}-\frac{\mathrm{acot}\left(a\,x\right)}{x}","Not used",1,"(a*(log(a^2*x^2 + 1) - 2*log(x)))/2 - acot(a*x)/x","B"
9,1,44,31,0.700601,"\text{Not used}","int(acot(a*x)/x^3,x)","\left\{\begin{array}{cl} -\frac{\pi }{4\,x^2} & \text{\ if\ \ }a=0\\ \frac{a^3\,\mathrm{atan}\left(a\,x\right)+\frac{a^2}{x}}{2\,a}-\frac{\mathrm{acot}\left(a\,x\right)}{2\,x^2} & \text{\ if\ \ }a\neq 0 \end{array}\right.","Not used",1,"piecewise(a == 0, -pi/(4*x^2), a ~= 0, (a^3*atan(a*x) + a^2/x)/(2*a) - acot(a*x)/(2*x^2))","B"
10,1,58,46,0.850321,"\text{Not used}","int(acot(a*x)/x^4,x)","\left\{\begin{array}{cl} -\frac{\pi }{6\,x^3} & \text{\ if\ \ }a=0\\ \frac{a^4\,\ln\left(x\right)-\frac{a^4\,\ln\left(a^2\,x^2+1\right)}{2}+\frac{a^2}{2\,x^2}}{3\,a}-\frac{\mathrm{acot}\left(a\,x\right)}{3\,x^3} & \text{\ if\ \ }a\neq 0 \end{array}\right.","Not used",1,"piecewise(a == 0, -pi/(6*x^3), a ~= 0, (a^4*log(x) - (a^4*log(a^2*x^2 + 1))/2 + a^2/(2*x^2))/(3*a) - acot(a*x)/(3*x^3))","B"
11,1,47,41,0.704386,"\text{Not used}","int(acot(a*x)/x^5,x)","\left\{\begin{array}{cl} -\frac{\pi }{8\,x^4} & \text{\ if\ \ }a=0\\ -\frac{a^4\,\mathrm{atan}\left(a\,x\right)}{4}-\frac{\frac{\mathrm{acot}\left(a\,x\right)}{4}-\frac{a\,x}{12}+\frac{a^3\,x^3}{4}}{x^4} & \text{\ if\ \ }a\neq 0 \end{array}\right.","Not used",1,"piecewise(a == 0, -pi/(8*x^4), a ~= 0, - (a^4*atan(a*x))/4 - (acot(a*x)/4 - (a*x)/12 + (a^3*x^3)/4)/x^4)","B"
12,1,85,104,0.809249,"\text{Not used}","int(x^5*acot(a*x)^2,x)","\frac{x^6\,{\mathrm{acot}\left(a\,x\right)}^2}{6}+\frac{\frac{23\,\ln\left(a^2\,x^2+1\right)}{90}-\frac{4\,a^2\,x^2}{45}+\frac{a^4\,x^4}{60}+\frac{{\mathrm{acot}\left(a\,x\right)}^2}{6}-\frac{a^3\,x^3\,\mathrm{acot}\left(a\,x\right)}{9}+\frac{a^5\,x^5\,\mathrm{acot}\left(a\,x\right)}{15}+\frac{a\,x\,\mathrm{acot}\left(a\,x\right)}{3}}{a^6}","Not used",1,"(x^6*acot(a*x)^2)/6 + ((23*log(a^2*x^2 + 1))/90 - (4*a^2*x^2)/45 + (a^4*x^4)/60 + acot(a*x)^2/6 - (a^3*x^3*acot(a*x))/9 + (a^5*x^5*acot(a*x))/15 + (a*x*acot(a*x))/3)/a^6","B"
13,0,-1,135,0.000000,"\text{Not used}","int(x^4*acot(a*x)^2,x)","\int x^4\,{\mathrm{acot}\left(a\,x\right)}^2 \,d x","Not used",1,"int(x^4*acot(a*x)^2, x)","F"
14,1,66,80,0.204269,"\text{Not used}","int(x^3*acot(a*x)^2,x)","\frac{x^4\,{\mathrm{acot}\left(a\,x\right)}^2}{4}-\frac{\frac{\ln\left(a^2\,x^2+1\right)}{3}-\frac{a^2\,x^2}{12}+\frac{{\mathrm{acot}\left(a\,x\right)}^2}{4}-\frac{a^3\,x^3\,\mathrm{acot}\left(a\,x\right)}{6}+\frac{a\,x\,\mathrm{acot}\left(a\,x\right)}{2}}{a^4}","Not used",1,"(x^4*acot(a*x)^2)/4 - (log(a^2*x^2 + 1)/3 - (a^2*x^2)/12 + acot(a*x)^2/4 - (a^3*x^3*acot(a*x))/6 + (a*x*acot(a*x))/2)/a^4","B"
15,0,-1,111,0.000000,"\text{Not used}","int(x^2*acot(a*x)^2,x)","\int x^2\,{\mathrm{acot}\left(a\,x\right)}^2 \,d x","Not used",1,"int(x^2*acot(a*x)^2, x)","F"
16,1,44,53,0.136970,"\text{Not used}","int(x*acot(a*x)^2,x)","\frac{x^2\,{\mathrm{acot}\left(a\,x\right)}^2}{2}+\frac{\frac{{\mathrm{acot}\left(a\,x\right)}^2}{2}+a\,x\,\mathrm{acot}\left(a\,x\right)+\frac{\ln\left(a^2\,x^2+1\right)}{2}}{a^2}","Not used",1,"(x^2*acot(a*x)^2)/2 + (log(a^2*x^2 + 1)/2 + acot(a*x)^2/2 + a*x*acot(a*x))/a^2","B"
17,1,55,67,0.591015,"\text{Not used}","int(acot(a*x)^2,x)","\frac{-2\,\ln\left(1-{\mathrm{e}}^{\mathrm{acot}\left(a\,x\right)\,2{}\mathrm{i}}\right)\,\mathrm{acot}\left(a\,x\right)+\mathrm{polylog}\left(2,{\mathrm{e}}^{\mathrm{acot}\left(a\,x\right)\,2{}\mathrm{i}}\right)\,1{}\mathrm{i}+{\mathrm{acot}\left(a\,x\right)}^2\,1{}\mathrm{i}}{a}+x\,{\mathrm{acot}\left(a\,x\right)}^2","Not used",1,"(polylog(2, exp(acot(a*x)*2i))*1i - 2*log(1 - exp(acot(a*x)*2i))*acot(a*x) + acot(a*x)^2*1i)/a + x*acot(a*x)^2","B"
18,0,-1,116,0.000000,"\text{Not used}","int(acot(a*x)^2/x,x)","\int \frac{{\mathrm{acot}\left(a\,x\right)}^2}{x} \,d x","Not used",1,"int(acot(a*x)^2/x, x)","F"
19,0,-1,66,0.000000,"\text{Not used}","int(acot(a*x)^2/x^2,x)","\int \frac{{\mathrm{acot}\left(a\,x\right)}^2}{x^2} \,d x","Not used",1,"int(acot(a*x)^2/x^2, x)","F"
20,1,50,59,0.660272,"\text{Not used}","int(acot(a*x)^2/x^3,x)","a^2\,\ln\left(x\right)-{\mathrm{acot}\left(a\,x\right)}^2\,\left(\frac{a^2}{2}+\frac{1}{2\,x^2}\right)-\frac{a^2\,\ln\left(a^2\,x^2+1\right)}{2}+\frac{a\,\mathrm{acot}\left(a\,x\right)}{x}","Not used",1,"a^2*log(x) - acot(a*x)^2*(a^2/2 + 1/(2*x^2)) - (a^2*log(a^2*x^2 + 1))/2 + (a*acot(a*x))/x","B"
21,0,-1,113,0.000000,"\text{Not used}","int(acot(a*x)^2/x^4,x)","\int \frac{{\mathrm{acot}\left(a\,x\right)}^2}{x^4} \,d x","Not used",1,"int(acot(a*x)^2/x^4, x)","F"
22,1,73,89,0.699238,"\text{Not used}","int(acot(a*x)^2/x^5,x)","{\mathrm{acot}\left(a\,x\right)}^2\,\left(\frac{a^4}{4}-\frac{1}{4\,x^4}\right)-\frac{2\,a^4\,\ln\left(x\right)}{3}+\frac{a^4\,\ln\left(a^2\,x^2+1\right)}{3}-\frac{a^2}{12\,x^2}-\frac{a^2\,\mathrm{acot}\left(a\,x\right)\,\left(\frac{a\,x^2}{2}-\frac{1}{6\,a}\right)}{x^3}","Not used",1,"acot(a*x)^2*(a^4/4 - 1/(4*x^4)) - (2*a^4*log(x))/3 + (a^4*log(a^2*x^2 + 1))/3 - a^2/(12*x^2) - (a^2*acot(a*x)*((a*x^2)/2 - 1/(6*a)))/x^3","B"
23,0,-1,194,0.000000,"\text{Not used}","int(x^5*acot(a*x)^3,x)","\int x^5\,{\mathrm{acot}\left(a\,x\right)}^3 \,d x","Not used",1,"int(x^5*acot(a*x)^3, x)","F"
24,0,-1,205,0.000000,"\text{Not used}","int(x^4*acot(a*x)^3,x)","\int x^4\,{\mathrm{acot}\left(a\,x\right)}^3 \,d x","Not used",1,"int(x^4*acot(a*x)^3, x)","F"
25,0,-1,148,0.000000,"\text{Not used}","int(x^3*acot(a*x)^3,x)","\int x^3\,{\mathrm{acot}\left(a\,x\right)}^3 \,d x","Not used",1,"int(x^3*acot(a*x)^3, x)","F"
26,0,-1,157,0.000000,"\text{Not used}","int(x^2*acot(a*x)^3,x)","\int x^2\,{\mathrm{acot}\left(a\,x\right)}^3 \,d x","Not used",1,"int(x^2*acot(a*x)^3, x)","F"
27,0,-1,103,0.000000,"\text{Not used}","int(x*acot(a*x)^3,x)","\int x\,{\mathrm{acot}\left(a\,x\right)}^3 \,d x","Not used",1,"int(x*acot(a*x)^3, x)","F"
28,0,-1,96,0.000000,"\text{Not used}","int(acot(a*x)^3,x)","\int {\mathrm{acot}\left(a\,x\right)}^3 \,d x","Not used",1,"int(acot(a*x)^3, x)","F"
29,0,-1,178,0.000000,"\text{Not used}","int(acot(a*x)^3/x,x)","\int \frac{{\mathrm{acot}\left(a\,x\right)}^3}{x} \,d x","Not used",1,"int(acot(a*x)^3/x, x)","F"
30,0,-1,93,0.000000,"\text{Not used}","int(acot(a*x)^3/x^2,x)","\int \frac{{\mathrm{acot}\left(a\,x\right)}^3}{x^2} \,d x","Not used",1,"int(acot(a*x)^3/x^2, x)","F"
31,0,-1,105,0.000000,"\text{Not used}","int(acot(a*x)^3/x^3,x)","\int \frac{{\mathrm{acot}\left(a\,x\right)}^3}{x^3} \,d x","Not used",1,"int(acot(a*x)^3/x^3, x)","F"
32,0,-1,167,0.000000,"\text{Not used}","int(acot(a*x)^3/x^4,x)","\int \frac{{\mathrm{acot}\left(a\,x\right)}^3}{x^4} \,d x","Not used",1,"int(acot(a*x)^3/x^4, x)","F"
33,0,-1,152,0.000000,"\text{Not used}","int(acot(a*x)^3/x^5,x)","\int \frac{{\mathrm{acot}\left(a\,x\right)}^3}{x^5} \,d x","Not used",1,"int(acot(a*x)^3/x^5, x)","F"
34,0,-1,13,0.000000,"\text{Not used}","int(x^m*acot(a*x)^3,x)","\int x^m\,{\mathrm{acot}\left(a\,x\right)}^3 \,d x","Not used",0,"int(x^m*acot(a*x)^3, x)","F"
35,0,-1,13,0.000000,"\text{Not used}","int(x^m*acot(a*x)^2,x)","\int x^m\,{\mathrm{acot}\left(a\,x\right)}^2 \,d x","Not used",0,"int(x^m*acot(a*x)^2, x)","F"
36,0,-1,57,0.000000,"\text{Not used}","int(x^m*acot(a*x),x)","\int x^m\,\mathrm{acot}\left(a\,x\right) \,d x","Not used",1,"int(x^m*acot(a*x), x)","F"
37,1,32,40,0.733581,"\text{Not used}","int((x^4*acot(x))/(x^2 + 1),x)","\frac{x^3\,\mathrm{acot}\left(x\right)}{3}-\frac{2\,\ln\left(x^2+1\right)}{3}-\frac{{\mathrm{acot}\left(x\right)}^2}{2}-x\,\mathrm{acot}\left(x\right)+\frac{x^2}{6}","Not used",1,"(x^3*acot(x))/3 - (2*log(x^2 + 1))/3 - acot(x)^2/2 - x*acot(x) + x^2/6","B"
38,0,-1,67,0.000000,"\text{Not used}","int((x^3*acot(x))/(x^2 + 1),x)","\int \frac{x^3\,\mathrm{acot}\left(x\right)}{x^2+1} \,d x","Not used",1,"int((x^3*acot(x))/(x^2 + 1), x)","F"
39,1,19,23,0.635804,"\text{Not used}","int((x^2*acot(x))/(x^2 + 1),x)","\frac{{\mathrm{acot}\left(x\right)}^2}{2}+x\,\mathrm{acot}\left(x\right)+\frac{\ln\left(x^2+1\right)}{2}","Not used",1,"log(x^2 + 1)/2 + acot(x)^2/2 + x*acot(x)","B"
40,0,-1,48,0.000000,"\text{Not used}","int((x*acot(x))/(x^2 + 1),x)","\int \frac{x\,\mathrm{acot}\left(x\right)}{x^2+1} \,d x","Not used",1,"int((x*acot(x))/(x^2 + 1), x)","F"
41,1,6,8,0.617087,"\text{Not used}","int(acot(x)/(x^2 + 1),x)","-\frac{{\mathrm{acot}\left(x\right)}^2}{2}","Not used",1,"-acot(x)^2/2","B"
42,0,-1,49,0.000000,"\text{Not used}","int(acot(x)/(x*(x^2 + 1)),x)","\int \frac{\mathrm{acot}\left(x\right)}{x\,\left(x^2+1\right)} \,d x","Not used",1,"int(acot(x)/(x*(x^2 + 1)), x)","F"
43,1,26,30,0.092087,"\text{Not used}","int(acot(x)/(x^2*(x^2 + 1)),x)","\frac{\ln\left(x^2+1\right)}{2}-\ln\left(x\right)-\frac{\mathrm{acot}\left(x\right)}{x}+\frac{{\mathrm{acot}\left(x\right)}^2}{2}","Not used",1,"log(x^2 + 1)/2 - log(x) - acot(x)/x + acot(x)^2/2","B"
44,0,-1,72,0.000000,"\text{Not used}","int(acot(x)/(x^3*(x^2 + 1)),x)","\int \frac{\mathrm{acot}\left(x\right)}{x^3\,\left(x^2+1\right)} \,d x","Not used",1,"int(acot(x)/(x^3*(x^2 + 1)), x)","F"
45,1,35,47,0.097042,"\text{Not used}","int(acot(x)/(x^4*(x^2 + 1)),x)","\frac{4\,\ln\left(x\right)}{3}-\frac{2\,\ln\left(x^2+1\right)}{3}-\frac{{\mathrm{acot}\left(x\right)}^2}{2}+\frac{1}{6\,x^2}+\frac{\mathrm{acot}\left(x\right)\,\left(x^2-\frac{1}{3}\right)}{x^3}","Not used",1,"(4*log(x))/3 - (2*log(x^2 + 1))/3 - acot(x)^2/2 + 1/(6*x^2) + (acot(x)*(x^2 - 1/3))/x^3","B"
46,0,-1,206,0.000000,"\text{Not used}","int((x^2*acot(c*x))/(x^2 + 1),x)","\int \frac{x^2\,\mathrm{acot}\left(c\,x\right)}{x^2+1} \,d x","Not used",1,"int((x^2*acot(c*x))/(x^2 + 1), x)","F"
47,0,-1,188,0.000000,"\text{Not used}","int((x*acot(c*x))/(x^2 + 1),x)","\int \frac{x\,\mathrm{acot}\left(c\,x\right)}{x^2+1} \,d x","Not used",1,"int((x*acot(c*x))/(x^2 + 1), x)","F"
48,0,-1,183,0.000000,"\text{Not used}","int(acot(c*x)/(x^2 + 1),x)","\int \frac{\mathrm{acot}\left(c\,x\right)}{x^2+1} \,d x","Not used",1,"int(acot(c*x)/(x^2 + 1), x)","F"
49,0,-1,223,0.000000,"\text{Not used}","int(acot(c*x)/(x*(x^2 + 1)),x)","\int \frac{\mathrm{acot}\left(c\,x\right)}{x\,\left(x^2+1\right)} \,d x","Not used",1,"int(acot(c*x)/(x*(x^2 + 1)), x)","F"
50,0,-1,212,0.000000,"\text{Not used}","int(acot(c*x)/(x^2*(x^2 + 1)),x)","\int \frac{\mathrm{acot}\left(c\,x\right)}{x^2\,\left(x^2+1\right)} \,d x","Not used",1,"int(acot(c*x)/(x^2*(x^2 + 1)), x)","F"
51,1,5,5,0.588958,"\text{Not used}","int(1/(acot(x)*(x^2 + 1)),x)","-\ln\left(\mathrm{acot}\left(x\right)\right)","Not used",1,"-log(acot(x))","B"
52,1,13,13,0.605639,"\text{Not used}","int(acot(x)^n/(x^2 + 1),x)","-\frac{{\mathrm{acot}\left(x\right)}^{n+1}}{n+1}","Not used",1,"-acot(x)^(n + 1)/(n + 1)","B"
53,1,234,244,0.216540,"\text{Not used}","int(acot(a*x)*(c + d*x^2)^4,x)","\mathrm{acot}\left(a\,x\right)\,\left(c^4\,x+\frac{4\,c^3\,d\,x^3}{3}+\frac{6\,c^2\,d^2\,x^5}{5}+\frac{4\,c\,d^3\,x^7}{7}+\frac{d^4\,x^9}{9}\right)-x^2\,\left(\frac{\frac{\frac{d^4}{9\,a^3}-\frac{4\,c\,d^3}{7\,a}}{a^2}+\frac{6\,c^2\,d^2}{5\,a}}{2\,a^2}-\frac{2\,c^3\,d}{3\,a}\right)-x^6\,\left(\frac{d^4}{54\,a^3}-\frac{2\,c\,d^3}{21\,a}\right)+x^4\,\left(\frac{\frac{d^4}{9\,a^3}-\frac{4\,c\,d^3}{7\,a}}{4\,a^2}+\frac{3\,c^2\,d^2}{10\,a}\right)+\frac{\ln\left(a^2\,x^2+1\right)\,\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)}{630\,a^9}+\frac{d^4\,x^8}{72\,a}","Not used",1,"acot(a*x)*(c^4*x + (d^4*x^9)/9 + (4*c^3*d*x^3)/3 + (4*c*d^3*x^7)/7 + (6*c^2*d^2*x^5)/5) - x^2*(((d^4/(9*a^3) - (4*c*d^3)/(7*a))/a^2 + (6*c^2*d^2)/(5*a))/(2*a^2) - (2*c^3*d)/(3*a)) - x^6*(d^4/(54*a^3) - (2*c*d^3)/(21*a)) + x^4*((d^4/(9*a^3) - (4*c*d^3)/(7*a))/(4*a^2) + (3*c^2*d^2)/(10*a)) + (log(a^2*x^2 + 1)*(35*d^4 + 315*a^8*c^4 - 180*a^2*c*d^3 - 420*a^6*c^3*d + 378*a^4*c^2*d^2))/(630*a^9) + (d^4*x^8)/(72*a)","B"
54,1,190,168,1.016134,"\text{Not used}","int(acot(a*x)*(c + d*x^2)^3,x)","c^3\,x\,\mathrm{acot}\left(a\,x\right)+\frac{d^3\,x^7\,\mathrm{acot}\left(a\,x\right)}{7}+\frac{c^3\,\ln\left(a^2\,x^2+1\right)}{2\,a}-\frac{d^3\,\ln\left(a^2\,x^2+1\right)}{14\,a^7}+\frac{d^3\,x^6}{42\,a}-\frac{d^3\,x^4}{28\,a^3}+\frac{d^3\,x^2}{14\,a^5}-\frac{c^2\,d\,\ln\left(a^2\,x^2+1\right)}{2\,a^3}+\frac{3\,c\,d^2\,\ln\left(a^2\,x^2+1\right)}{10\,a^5}+\frac{c^2\,d\,x^2}{2\,a}+\frac{3\,c\,d^2\,x^4}{20\,a}-\frac{3\,c\,d^2\,x^2}{10\,a^3}+c^2\,d\,x^3\,\mathrm{acot}\left(a\,x\right)+\frac{3\,c\,d^2\,x^5\,\mathrm{acot}\left(a\,x\right)}{5}","Not used",1,"c^3*x*acot(a*x) + (d^3*x^7*acot(a*x))/7 + (c^3*log(a^2*x^2 + 1))/(2*a) - (d^3*log(a^2*x^2 + 1))/(14*a^7) + (d^3*x^6)/(42*a) - (d^3*x^4)/(28*a^3) + (d^3*x^2)/(14*a^5) - (c^2*d*log(a^2*x^2 + 1))/(2*a^3) + (3*c*d^2*log(a^2*x^2 + 1))/(10*a^5) + (c^2*d*x^2)/(2*a) + (3*c*d^2*x^4)/(20*a) - (3*c*d^2*x^2)/(10*a^3) + c^2*d*x^3*acot(a*x) + (3*c*d^2*x^5*acot(a*x))/5","B"
55,1,116,109,0.843777,"\text{Not used}","int(acot(a*x)*(c + d*x^2)^2,x)","\frac{a^4\,\left(\frac{c^2\,\ln\left(a^2\,x^2+1\right)}{2}+\frac{d^2\,x^4}{20}+\frac{c\,d\,x^2}{3}\right)-a^2\,\left(\frac{d^2\,x^2}{10}+\frac{c\,d\,\ln\left(a^2\,x^2+1\right)}{3}\right)+\frac{d^2\,\ln\left(a^2\,x^2+1\right)}{10}}{a^5}+c^2\,x\,\mathrm{acot}\left(a\,x\right)+\frac{d^2\,x^5\,\mathrm{acot}\left(a\,x\right)}{5}+\frac{2\,c\,d\,x^3\,\mathrm{acot}\left(a\,x\right)}{3}","Not used",1,"(a^4*((c^2*log(a^2*x^2 + 1))/2 + (d^2*x^4)/20 + (c*d*x^2)/3) - a^2*((d^2*x^2)/10 + (c*d*log(a^2*x^2 + 1))/3) + (d^2*log(a^2*x^2 + 1))/10)/a^5 + c^2*x*acot(a*x) + (d^2*x^5*acot(a*x))/5 + (2*c*d*x^3*acot(a*x))/3","B"
56,1,62,58,0.786028,"\text{Not used}","int(acot(a*x)*(c + d*x^2),x)","\frac{d\,x^3\,\mathrm{acot}\left(a\,x\right)}{3}-\frac{\frac{d\,\ln\left(a^2\,x^2+1\right)}{6}-a^2\,\left(\frac{c\,\ln\left(a^2\,x^2+1\right)}{2}+\frac{d\,x^2}{6}\right)}{a^3}+c\,x\,\mathrm{acot}\left(a\,x\right)","Not used",1,"(d*x^3*acot(a*x))/3 - ((d*log(a^2*x^2 + 1))/6 - a^2*((c*log(a^2*x^2 + 1))/2 + (d*x^2)/6))/a^3 + c*x*acot(a*x)","B"
57,0,-1,403,0.000000,"\text{Not used}","int(acot(a*x)/(c + d*x^2),x)","\int \frac{\mathrm{acot}\left(a\,x\right)}{d\,x^2+c} \,d x","Not used",1,"int(acot(a*x)/(c + d*x^2), x)","F"
58,0,-1,801,0.000000,"\text{Not used}","int(acot(a*x)/(c + d*x^2)^2,x)","\int \frac{\mathrm{acot}\left(a\,x\right)}{{\left(d\,x^2+c\right)}^2} \,d x","Not used",1,"int(acot(a*x)/(c + d*x^2)^2, x)","F"
59,0,-1,19,0.000000,"\text{Not used}","int(acot(a*x)*(c + d*x^2)^(1/2),x)","\int \mathrm{acot}\left(a\,x\right)\,\sqrt{d\,x^2+c} \,d x","Not used",0,"int(acot(a*x)*(c + d*x^2)^(1/2), x)","F"
60,0,-1,19,0.000000,"\text{Not used}","int(acot(a*x)/(c + d*x^2)^(1/2),x)","\int \frac{\mathrm{acot}\left(a\,x\right)}{\sqrt{d\,x^2+c}} \,d x","Not used",0,"int(acot(a*x)/(c + d*x^2)^(1/2), x)","F"
61,0,-1,66,0.000000,"\text{Not used}","int(acot(a*x)/(c + d*x^2)^(3/2),x)","\int \frac{\mathrm{acot}\left(a\,x\right)}{{\left(d\,x^2+c\right)}^{3/2}} \,d x","Not used",1,"int(acot(a*x)/(c + d*x^2)^(3/2), x)","F"
62,0,-1,134,0.000000,"\text{Not used}","int(acot(a*x)/(c + d*x^2)^(5/2),x)","\int \frac{\mathrm{acot}\left(a\,x\right)}{{\left(d\,x^2+c\right)}^{5/2}} \,d x","Not used",1,"int(acot(a*x)/(c + d*x^2)^(5/2), x)","F"
63,0,-1,208,0.000000,"\text{Not used}","int(acot(a*x)/(c + d*x^2)^(7/2),x)","\int \frac{\mathrm{acot}\left(a\,x\right)}{{\left(d\,x^2+c\right)}^{7/2}} \,d x","Not used",1,"int(acot(a*x)/(c + d*x^2)^(7/2), x)","F"
64,0,-1,293,0.000000,"\text{Not used}","int(acot(a*x)/(c + d*x^2)^(9/2),x)","\int \frac{\mathrm{acot}\left(a\,x\right)}{{\left(d\,x^2+c\right)}^{9/2}} \,d x","Not used",1,"int(acot(a*x)/(c + d*x^2)^(9/2), x)","F"
65,0,-1,195,0.000000,"\text{Not used}","int(acot(x)*(a + a*x^2)^(1/2),x)","\int \mathrm{acot}\left(x\right)\,\sqrt{a\,x^2+a} \,d x","Not used",1,"int(acot(x)*(a + a*x^2)^(1/2), x)","F"
66,0,-1,155,0.000000,"\text{Not used}","int(acot(x)/(a + a*x^2)^(1/2),x)","\int \frac{\mathrm{acot}\left(x\right)}{\sqrt{a\,x^2+a}} \,d x","Not used",1,"int(acot(x)/(a + a*x^2)^(1/2), x)","F"
67,0,-1,35,0.000000,"\text{Not used}","int(acot(x)/(a + a*x^2)^(3/2),x)","\int \frac{\mathrm{acot}\left(x\right)}{{\left(a\,x^2+a\right)}^{3/2}} \,d x","Not used",1,"int(acot(x)/(a + a*x^2)^(3/2), x)","F"
68,0,-1,79,0.000000,"\text{Not used}","int(acot(x)/(a + a*x^2)^(5/2),x)","\int \frac{\mathrm{acot}\left(x\right)}{{\left(a\,x^2+a\right)}^{5/2}} \,d x","Not used",1,"int(acot(x)/(a + a*x^2)^(5/2), x)","F"
69,0,-1,118,0.000000,"\text{Not used}","int(acot(x)/(a + a*x^2)^(7/2),x)","\int \frac{\mathrm{acot}\left(x\right)}{{\left(a\,x^2+a\right)}^{7/2}} \,d x","Not used",1,"int(acot(x)/(a + a*x^2)^(7/2), x)","F"
70,1,22,32,0.073068,"\text{Not used}","int((x*acot(x))/(x^2 + 1)^2,x)","\frac{\mathrm{acot}\left(x\right)}{4}-\frac{\frac{x}{4}+\frac{\mathrm{acot}\left(x\right)}{2}}{x^2+1}","Not used",1,"acot(x)/4 - (x/4 + acot(x)/2)/(x^2 + 1)","B"
71,1,27,44,0.601348,"\text{Not used}","int((x*acot(x))/(x^2 + 1)^3,x)","-\frac{3\,\mathrm{atan}\left(x\right)}{32}-\frac{\frac{5\,x}{32}+\frac{\mathrm{acot}\left(x\right)}{4}+\frac{3\,x^3}{32}}{{\left(x^2+1\right)}^2}","Not used",1,"- (3*atan(x))/32 - ((5*x)/32 + acot(x)/4 + (3*x^3)/32)/(x^2 + 1)^2","B"
72,1,22,34,0.614069,"\text{Not used}","int(acot(x)/(x^2 + 1)^2,x)","\frac{\frac{x\,\mathrm{acot}\left(x\right)}{2}-\frac{1}{4}}{x^2+1}-\frac{{\mathrm{acot}\left(x\right)}^2}{4}","Not used",1,"((x*acot(x))/2 - 1/4)/(x^2 + 1) - acot(x)^2/4","B"
73,1,51,56,0.062482,"\text{Not used}","int(acot(x)^2/(x^2 + 1)^2,x)","\frac{x\,{\mathrm{acot}\left(x\right)}^2}{2\,\left(x^2+1\right)}-\frac{{\mathrm{acot}\left(x\right)}^3}{6}-\frac{x}{4\,\left(x^2+1\right)}-\frac{\mathrm{acot}\left(x\right)}{2\,\left(x^2+1\right)}-\frac{\mathrm{atan}\left(x\right)}{4}","Not used",1,"(x*acot(x)^2)/(2*(x^2 + 1)) - acot(x)^3/6 - x/(4*(x^2 + 1)) - acot(x)/(2*(x^2 + 1)) - atan(x)/4","B"
74,1,35,41,0.645378,"\text{Not used}","int(x^5*acot(a*x^2),x)","\frac{x^6\,\mathrm{acot}\left(a\,x^2\right)}{6}-\frac{\ln\left(a^2\,x^4+1\right)}{12\,a^3}+\frac{x^4}{12\,a}","Not used",1,"(x^6*acot(a*x^2))/6 - log(a^2*x^4 + 1)/(12*a^3) + x^4/(12*a)","B"
75,1,31,37,0.612085,"\text{Not used}","int(x^3*acot(a*x^2),x)","\frac{x^4\,\mathrm{acot}\left(a\,x^2\right)}{4}-\frac{\mathrm{atan}\left(a\,x^2\right)}{4\,a^2}+\frac{x^2}{4\,a}","Not used",1,"(x^4*acot(a*x^2))/4 - atan(a*x^2)/(4*a^2) + x^2/(4*a)","B"
76,1,27,31,0.595505,"\text{Not used}","int(x*acot(a*x^2),x)","\frac{x^2\,\mathrm{acot}\left(a\,x^2\right)}{2}+\frac{\ln\left(a^2\,x^4+1\right)}{4\,a}","Not used",1,"(x^2*acot(a*x^2))/2 + log(a^2*x^4 + 1)/(4*a)","B"
77,0,-1,37,0.000000,"\text{Not used}","int(acot(a*x^2)/x,x)","\int \frac{\mathrm{acot}\left(a\,x^2\right)}{x} \,d x","Not used",1,"int(acot(a*x^2)/x, x)","F"
78,1,31,34,0.659528,"\text{Not used}","int(acot(a*x^2)/x^3,x)","\frac{a\,\ln\left(-a^2\,x^4-1\right)}{4}-\frac{\mathrm{acot}\left(a\,x^2\right)}{2\,x^2}-a\,\ln\left(x\right)","Not used",1,"(a*log(- a^2*x^4 - 1))/4 - acot(a*x^2)/(2*x^2) - a*log(x)","B"
79,1,32,35,0.648969,"\text{Not used}","int(acot(a*x^2)/x^5,x)","\frac{a\,x^2-\mathrm{acot}\left(a\,x^2\right)+a^2\,x^4\,\mathrm{atan}\left(a\,x^2\right)}{4\,x^4}","Not used",1,"(a*x^2 - acot(a*x^2) + a^2*x^4*atan(a*x^2))/(4*x^4)","B"
80,1,54,152,0.443256,"\text{Not used}","int(x^4*acot(a*x^2),x)","\frac{x^5\,\mathrm{acot}\left(a\,x^2\right)}{5}+\frac{2\,x^3}{15\,a}-\frac{{\left(-1\right)}^{1/4}\,\mathrm{atan}\left({\left(-1\right)}^{1/4}\,\sqrt{a}\,x\right)}{5\,a^{5/2}}-\frac{{\left(-1\right)}^{1/4}\,\mathrm{atan}\left({\left(-1\right)}^{1/4}\,\sqrt{a}\,x\,1{}\mathrm{i}\right)\,1{}\mathrm{i}}{5\,a^{5/2}}","Not used",1,"(x^5*acot(a*x^2))/5 + (2*x^3)/(15*a) - ((-1)^(1/4)*atan((-1)^(1/4)*a^(1/2)*x))/(5*a^(5/2)) - ((-1)^(1/4)*atan((-1)^(1/4)*a^(1/2)*x*1i)*1i)/(5*a^(5/2))","B"
81,1,52,150,0.700089,"\text{Not used}","int(x^2*acot(a*x^2),x)","\frac{x^3\,\mathrm{acot}\left(a\,x^2\right)}{3}+\frac{2\,x}{3\,a}+\frac{{\left(-1\right)}^{1/4}\,\mathrm{atan}\left({\left(-1\right)}^{1/4}\,\sqrt{a}\,x\right)\,1{}\mathrm{i}}{3\,a^{3/2}}+\frac{{\left(-1\right)}^{1/4}\,\mathrm{atan}\left({\left(-1\right)}^{1/4}\,\sqrt{a}\,x\,1{}\mathrm{i}\right)}{3\,a^{3/2}}","Not used",1,"(x^3*acot(a*x^2))/3 + (2*x)/(3*a) + ((-1)^(1/4)*atan((-1)^(1/4)*a^(1/2)*x)*1i)/(3*a^(3/2)) + ((-1)^(1/4)*atan((-1)^(1/4)*a^(1/2)*x*1i))/(3*a^(3/2))","B"
82,1,42,132,0.129449,"\text{Not used}","int(acot(a*x^2),x)","x\,\mathrm{acot}\left(a\,x^2\right)+\frac{{\left(-1\right)}^{1/4}\,\mathrm{atan}\left({\left(-1\right)}^{1/4}\,\sqrt{a}\,x\right)}{\sqrt{a}}-\frac{{\left(-1\right)}^{1/4}\,\mathrm{atanh}\left({\left(-1\right)}^{1/4}\,\sqrt{a}\,x\right)}{\sqrt{a}}","Not used",1,"x*acot(a*x^2) + ((-1)^(1/4)*atan((-1)^(1/4)*a^(1/2)*x))/a^(1/2) - ((-1)^(1/4)*atanh((-1)^(1/4)*a^(1/2)*x))/a^(1/2)","B"
83,1,44,135,0.683179,"\text{Not used}","int(acot(a*x^2)/x^2,x)","-\frac{\mathrm{acot}\left(a\,x^2\right)}{x}+{\left(-1\right)}^{1/4}\,\sqrt{a}\,\mathrm{atan}\left({\left(-1\right)}^{1/4}\,\sqrt{a}\,x\right)\,1{}\mathrm{i}+{\left(-1\right)}^{1/4}\,\sqrt{a}\,\mathrm{atanh}\left({\left(-1\right)}^{1/4}\,\sqrt{a}\,x\right)\,1{}\mathrm{i}","Not used",1,"(-1)^(1/4)*a^(1/2)*atan((-1)^(1/4)*a^(1/2)*x)*1i - acot(a*x^2)/x + (-1)^(1/4)*a^(1/2)*atanh((-1)^(1/4)*a^(1/2)*x)*1i","B"
84,1,52,150,0.714617,"\text{Not used}","int(acot(a*x^2)/x^4,x)","\frac{2\,a}{3\,x}-\frac{\mathrm{acot}\left(a\,x^2\right)}{3\,x^3}+\frac{{\left(-1\right)}^{1/4}\,a^{3/2}\,\mathrm{atan}\left({\left(-1\right)}^{1/4}\,\sqrt{a}\,x\right)}{3}+\frac{{\left(-1\right)}^{1/4}\,a^{3/2}\,\mathrm{atan}\left({\left(-1\right)}^{1/4}\,\sqrt{a}\,x\,1{}\mathrm{i}\right)\,1{}\mathrm{i}}{3}","Not used",1,"(2*a)/(3*x) - acot(a*x^2)/(3*x^3) + ((-1)^(1/4)*a^(3/2)*atan((-1)^(1/4)*a^(1/2)*x))/3 + ((-1)^(1/4)*a^(3/2)*atan((-1)^(1/4)*a^(1/2)*x*1i)*1i)/3","B"
85,1,31,51,0.650290,"\text{Not used}","int(x^2*acot(x^(1/2)),x)","\frac{x^3\,\mathrm{acot}\left(\sqrt{x}\right)}{3}-\frac{\mathrm{atan}\left(\sqrt{x}\right)}{3}+\frac{\sqrt{x}}{3}-\frac{x^{3/2}}{9}+\frac{x^{5/2}}{15}","Not used",1,"(x^3*acot(x^(1/2)))/3 - atan(x^(1/2))/3 + x^(1/2)/3 - x^(3/2)/9 + x^(5/2)/15","B"
86,1,26,42,0.658828,"\text{Not used}","int(x*acot(x^(1/2)),x)","\frac{\mathrm{atan}\left(\sqrt{x}\right)}{2}+\frac{x^2\,\mathrm{acot}\left(\sqrt{x}\right)}{2}-\frac{\sqrt{x}}{2}+\frac{x^{3/2}}{6}","Not used",1,"atan(x^(1/2))/2 + (x^2*acot(x^(1/2)))/2 - x^(1/2)/2 + x^(3/2)/6","B"
87,1,16,22,0.631200,"\text{Not used}","int(acot(x^(1/2)),x)","x\,\mathrm{acot}\left(\sqrt{x}\right)-\mathrm{atan}\left(\sqrt{x}\right)+\sqrt{x}","Not used",1,"x*acot(x^(1/2)) - atan(x^(1/2)) + x^(1/2)","B"
88,0,-1,31,0.000000,"\text{Not used}","int(acot(x^(1/2))/x,x)","\int \frac{\mathrm{acot}\left(\sqrt{x}\right)}{x} \,d x","Not used",1,"int(acot(x^(1/2))/x, x)","F"
89,1,17,23,0.642243,"\text{Not used}","int(acot(x^(1/2))/x^2,x)","\mathrm{atan}\left(\sqrt{x}\right)-\frac{\mathrm{acot}\left(\sqrt{x}\right)}{x}+\frac{1}{\sqrt{x}}","Not used",1,"atan(x^(1/2)) - acot(x^(1/2))/x + 1/x^(1/2)","B"
90,1,24,42,0.646360,"\text{Not used}","int(acot(x^(1/2))/x^3,x)","-\frac{\mathrm{atan}\left(\sqrt{x}\right)}{2}-\frac{x-\frac{1}{3}}{2\,x^{3/2}}-\frac{\mathrm{acot}\left(\sqrt{x}\right)}{2\,x^2}","Not used",1,"- atan(x^(1/2))/2 - (x - 1/3)/(2*x^(3/2)) - acot(x^(1/2))/(2*x^2)","B"
91,1,24,36,0.646400,"\text{Not used}","int(x^(3/2)*acot(x^(1/2)),x)","\frac{\ln\left(x+1\right)}{5}-\frac{x}{5}+\frac{2\,x^{5/2}\,\mathrm{acot}\left(\sqrt{x}\right)}{5}+\frac{x^2}{10}","Not used",1,"log(x + 1)/5 - x/5 + (2*x^(5/2)*acot(x^(1/2)))/5 + x^2/10","B"
92,0,-1,29,0.000000,"\text{Not used}","int(x^(1/2)*acot(x^(1/2)),x)","\int \sqrt{x}\,\mathrm{acot}\left(\sqrt{x}\right) \,d x","Not used",1,"int(x^(1/2)*acot(x^(1/2)), x)","F"
93,1,14,18,0.769865,"\text{Not used}","int(acot(x^(1/2))/x^(1/2),x)","\ln\left(x+1\right)+2\,\sqrt{x}\,\mathrm{acot}\left(\sqrt{x}\right)","Not used",1,"log(x + 1) + 2*x^(1/2)*acot(x^(1/2))","B"
94,1,20,22,0.665309,"\text{Not used}","int(acot(x^(1/2))/x^(3/2),x)","\ln\left(x+1\right)-2\,\ln\left(\sqrt{x}\right)-\frac{2\,\mathrm{acot}\left(\sqrt{x}\right)}{\sqrt{x}}","Not used",1,"log(x + 1) - 2*log(x^(1/2)) - (2*acot(x^(1/2)))/x^(1/2)","B"
95,1,27,37,0.649913,"\text{Not used}","int(acot(x^(1/2))/x^(5/2),x)","\frac{2\,\ln\left(\sqrt{x}\right)}{3}-\frac{\ln\left(x+1\right)}{3}-\frac{2\,\mathrm{acot}\left(\sqrt{x}\right)}{3\,x^{3/2}}+\frac{1}{3\,x}","Not used",1,"(2*log(x^(1/2)))/3 - log(x + 1)/3 - (2*acot(x^(1/2)))/(3*x^(3/2)) + 1/(3*x)","B"
96,1,15,17,0.055798,"\text{Not used}","int(acot(1/x),x)","x\,\mathrm{acot}\left(\frac{1}{x}\right)-\frac{\ln\left(x^2+1\right)}{2}","Not used",1,"x*acot(1/x) - log(x^2 + 1)/2","B"
97,0,-1,47,0.000000,"\text{Not used}","int(acot(a*x^n)/x,x)","\int \frac{\mathrm{acot}\left(a\,x^n\right)}{x} \,d x","Not used",1,"int(acot(a*x^n)/x, x)","F"
98,0,-1,37,0.000000,"\text{Not used}","int(acot(a*x^5)/x,x)","\int \frac{\mathrm{acot}\left(a\,x^5\right)}{x} \,d x","Not used",1,"int(acot(a*x^5)/x, x)","F"
99,1,133,106,0.774584,"\text{Not used}","int(x^3*acot(a + b*x),x)","\frac{\mathrm{atan}\left(a+b\,x\right)}{4\,b^4}+\frac{x^4\,\mathrm{acot}\left(a+b\,x\right)}{4}-\frac{x}{4\,b^3}+\frac{x^3}{12\,b}-\frac{a^3\,\ln\left(a^2+2\,a\,b\,x+b^2\,x^2+1\right)}{2\,b^4}-\frac{3\,a^2\,\mathrm{atan}\left(a+b\,x\right)}{2\,b^4}+\frac{a^4\,\mathrm{atan}\left(a+b\,x\right)}{4\,b^4}-\frac{a\,x^2}{4\,b^2}+\frac{3\,a^2\,x}{4\,b^3}+\frac{a\,\ln\left(a^2+2\,a\,b\,x+b^2\,x^2+1\right)}{2\,b^4}","Not used",1,"atan(a + b*x)/(4*b^4) + (x^4*acot(a + b*x))/4 - x/(4*b^3) + x^3/(12*b) - (a^3*log(a^2 + b^2*x^2 + 2*a*b*x + 1))/(2*b^4) - (3*a^2*atan(a + b*x))/(2*b^4) + (a^4*atan(a + b*x))/(4*b^4) - (a*x^2)/(4*b^2) + (3*a^2*x)/(4*b^3) + (a*log(a^2 + b^2*x^2 + 2*a*b*x + 1))/(2*b^4)","B"
100,1,101,80,1.335413,"\text{Not used}","int(x^2*acot(a + b*x),x)","\frac{x^3\,\mathrm{acot}\left(a+b\,x\right)}{3}-\frac{\ln\left(a^2+2\,a\,b\,x+b^2\,x^2+1\right)}{6\,b^3}+\frac{x^2}{6\,b}+\frac{a^2\,\ln\left(a^2+2\,a\,b\,x+b^2\,x^2+1\right)}{2\,b^3}-\frac{a^3\,\mathrm{atan}\left(a+b\,x\right)}{3\,b^3}+\frac{a\,\mathrm{atan}\left(a+b\,x\right)}{b^3}-\frac{2\,a\,x}{3\,b^2}","Not used",1,"(x^3*acot(a + b*x))/3 - log(a^2 + b^2*x^2 + 2*a*b*x + 1)/(6*b^3) + x^2/(6*b) + (a^2*log(a^2 + b^2*x^2 + 2*a*b*x + 1))/(2*b^3) - (a^3*atan(a + b*x))/(3*b^3) + (a*atan(a + b*x))/b^3 - (2*a*x)/(3*b^2)","B"
101,1,61,60,0.973472,"\text{Not used}","int(x*acot(a + b*x),x)","\frac{x^2\,\mathrm{acot}\left(a+b\,x\right)}{2}+\frac{\frac{\mathrm{acot}\left(a+b\,x\right)}{2}+\frac{b\,x}{2}-\frac{a^2\,\mathrm{acot}\left(a+b\,x\right)}{2}-\frac{a\,\ln\left(a^2+2\,a\,b\,x+b^2\,x^2+1\right)}{2}}{b^2}","Not used",1,"(x^2*acot(a + b*x))/2 + (acot(a + b*x)/2 + (b*x)/2 - (a^2*acot(a + b*x))/2 - (a*log(a^2 + b^2*x^2 + 2*a*b*x + 1))/2)/b^2","B"
102,1,42,33,1.196929,"\text{Not used}","int(acot(a + b*x),x)","\frac{\frac{\ln\left(a^2+2\,a\,b\,x+b^2\,x^2+1\right)}{2}+a\,\mathrm{acot}\left(a+b\,x\right)}{b}+x\,\mathrm{acot}\left(a+b\,x\right)","Not used",1,"(log(a^2 + b^2*x^2 + 2*a*b*x + 1)/2 + a*acot(a + b*x))/b + x*acot(a + b*x)","B"
103,0,-1,120,0.000000,"\text{Not used}","int(acot(a + b*x)/x,x)","\int \frac{\mathrm{acot}\left(a+b\,x\right)}{x} \,d x","Not used",1,"int(acot(a + b*x)/x, x)","F"
104,1,62,62,1.221661,"\text{Not used}","int(acot(a + b*x)/x^2,x)","-\frac{\mathrm{acot}\left(a+b\,x\right)}{x}-\frac{b\,x\,\ln\left(x\right)-\frac{b\,x\,\ln\left(a^2+2\,a\,b\,x+b^2\,x^2+1\right)}{2}+a\,b\,x\,\mathrm{acot}\left(a+b\,x\right)}{x\,\left(a^2+1\right)}","Not used",1,"- acot(a + b*x)/x - (b*x*log(x) - (b*x*log(a^2 + b^2*x^2 + 2*a*b*x + 1))/2 + a*b*x*acot(a + b*x))/(x*(a^2 + 1))","B"
105,1,230,95,1.385672,"\text{Not used}","int(acot(a + b*x)/x^3,x)","\frac{\mathrm{atan}\left(\frac{2\,x\,b^2+2\,a\,b}{2\,\sqrt{b^2\,\left(a^2+1\right)-a^2\,b^2}}\right)\,\left(b^3-a^2\,b^3\right)}{\sqrt{b^2}\,\left(2\,a^4+4\,a^2+2\right)}-\frac{a\,b^2\,\ln\left(a^2+2\,a\,b\,x+b^2\,x^2+1\right)}{2\,{\left(a^2+1\right)}^2}-\frac{\mathrm{acot}\left(a+b\,x\right)\,\left(\frac{a^2}{2}+\frac{1}{2}\right)-\frac{b\,x}{2}+\frac{b^2\,x^2\,\mathrm{acot}\left(a+b\,x\right)}{2}-\frac{x^3\,\left(b^3-3\,a^2\,b^3\right)}{2\,\left(a^4+2\,a^2+1\right)}+\frac{a\,b^4\,x^4}{{\left(a^2+1\right)}^2}+a\,b\,x\,\mathrm{acot}\left(a+b\,x\right)}{a^2\,x^2+2\,a\,b\,x^3+b^2\,x^4+x^2}+\frac{a\,b^2\,\ln\left(x\right)}{{\left(a^2+1\right)}^2}","Not used",1,"(atan((2*a*b + 2*b^2*x)/(2*(b^2*(a^2 + 1) - a^2*b^2)^(1/2)))*(b^3 - a^2*b^3))/((b^2)^(1/2)*(4*a^2 + 2*a^4 + 2)) - (a*b^2*log(a^2 + b^2*x^2 + 2*a*b*x + 1))/(2*(a^2 + 1)^2) - (acot(a + b*x)*(a^2/2 + 1/2) - (b*x)/2 + (b^2*x^2*acot(a + b*x))/2 - (x^3*(b^3 - 3*a^2*b^3))/(2*(2*a^2 + a^4 + 1)) + (a*b^4*x^4)/(a^2 + 1)^2 + a*b*x*acot(a + b*x))/(x^2 + a^2*x^2 + b^2*x^4 + 2*a*b*x^3) + (a*b^2*log(x))/(a^2 + 1)^2","B"
106,1,285,129,1.240394,"\text{Not used}","int(acot(a + b*x)/x^4,x)","\frac{\ln\left(x\right)\,\left(\frac{b^3}{3}-a^2\,b^3\right)}{a^6+3\,a^4+3\,a^2+1}-\frac{\mathrm{acot}\left(a+b\,x\right)\,\left(\frac{a^2}{3}+\frac{1}{3}\right)-\frac{b\,x}{6}+\frac{b^2\,x^2\,\mathrm{acot}\left(a+b\,x\right)}{3}-\frac{x^3\,\left(b^3-7\,a^2\,b^3\right)}{6\,\left(a^4+2\,a^2+1\right)}+\frac{a\,b^2\,x^2}{3\,\left(a^2+1\right)}+\frac{2\,a\,b^4\,x^4}{3\,{\left(a^2+1\right)}^2}+\frac{2\,a\,b\,x\,\mathrm{acot}\left(a+b\,x\right)}{3}}{a^2\,x^3+2\,a\,b\,x^4+b^2\,x^5+x^3}+\frac{b^3\,\ln\left(a^2+2\,a\,b\,x+b^2\,x^2+1\right)\,\left(3\,a^2-1\right)}{6\,\left(a^6+3\,a^4+3\,a^2+1\right)}+\frac{a\,\mathrm{atan}\left(\frac{2\,x\,b^2+2\,a\,b}{2\,\sqrt{b^2\,\left(a^2+1\right)-a^2\,b^2}}\right)\,\left(a^2-3\right)\,{\left(b^2\right)}^{3/2}}{3\,\left(a^6+3\,a^4+3\,a^2+1\right)}","Not used",1,"(log(x)*(b^3/3 - a^2*b^3))/(3*a^2 + 3*a^4 + a^6 + 1) - (acot(a + b*x)*(a^2/3 + 1/3) - (b*x)/6 + (b^2*x^2*acot(a + b*x))/3 - (x^3*(b^3 - 7*a^2*b^3))/(6*(2*a^2 + a^4 + 1)) + (a*b^2*x^2)/(3*(a^2 + 1)) + (2*a*b^4*x^4)/(3*(a^2 + 1)^2) + (2*a*b*x*acot(a + b*x))/3)/(x^3 + a^2*x^3 + b^2*x^5 + 2*a*b*x^4) + (b^3*log(a^2 + b^2*x^2 + 2*a*b*x + 1)*(3*a^2 - 1))/(6*(3*a^2 + 3*a^4 + a^6 + 1)) + (a*atan((2*a*b + 2*b^2*x)/(2*(b^2*(a^2 + 1) - a^2*b^2)^(1/2)))*(a^2 - 3)*(b^2)^(3/2))/(3*(3*a^2 + 3*a^4 + a^6 + 1))","B"
107,0,-1,642,0.000000,"\text{Not used}","int(acot(a + b*x)/(c + d*x^2),x)","\int \frac{\mathrm{acot}\left(a+b\,x\right)}{d\,x^2+c} \,d x","Not used",1,"int(acot(a + b*x)/(c + d*x^2), x)","F"
108,0,-1,152,0.000000,"\text{Not used}","int(acot(a + b*x)/(c + d*x),x)","\int \frac{\mathrm{acot}\left(a+b\,x\right)}{c+d\,x} \,d x","Not used",1,"int(acot(a + b*x)/(c + d*x), x)","F"
109,0,-1,338,0.000000,"\text{Not used}","int(acot(a + b*x)/(c + d/x),x)","\int \frac{\mathrm{acot}\left(a+b\,x\right)}{c+\frac{d}{x}} \,d x","Not used",1,"int(acot(a + b*x)/(c + d/x), x)","F"
110,0,-1,735,0.000000,"\text{Not used}","int(acot(a + b*x)/(c + d/x^2),x)","\int \frac{\mathrm{acot}\left(a+b\,x\right)}{c+\frac{d}{x^2}} \,d x","Not used",1,"int(acot(a + b*x)/(c + d/x^2), x)","F"
111,0,-1,693,0.000000,"\text{Not used}","int(acot(a + b*x)/(c + d*x^(1/2)),x)","\int \frac{\mathrm{acot}\left(a+b\,x\right)}{c+d\,\sqrt{x}} \,d x","Not used",1,"int(acot(a + b*x)/(c + d*x^(1/2)), x)","F"
112,0,-1,830,0.000000,"\text{Not used}","int(acot(a + b*x)/(c + d/x^(1/2)),x)","\int \frac{\mathrm{acot}\left(a+b\,x\right)}{c+\frac{d}{\sqrt{x}}} \,d x","Not used",1,"int(acot(a + b*x)/(c + d/x^(1/2)), x)","F"
113,0,-1,367,0.000000,"\text{Not used}","int(acot(d + e*x)/(a + b*x + c*x^2),x)","\int \frac{\mathrm{acot}\left(d+e\,x\right)}{c\,x^2+b\,x+a} \,d x","Not used",1,"int(acot(d + e*x)/(a + b*x + c*x^2), x)","F"
114,0,-1,132,0.000000,"\text{Not used}","int(acot(a + b*x)/(a^2 + b^2*x^2 + 2*a*b*x + 1)^(1/2),x)","\int \frac{\mathrm{acot}\left(a+b\,x\right)}{\sqrt{a^2+2\,a\,b\,x+b^2\,x^2+1}} \,d x","Not used",1,"int(acot(a + b*x)/(a^2 + b^2*x^2 + 2*a*b*x + 1)^(1/2), x)","F"
115,0,-1,216,0.000000,"\text{Not used}","int(acot(a + b*x)/(c*(a^2 + 1) + b^2*c*x^2 + 2*a*b*c*x)^(1/2),x)","\int \frac{\mathrm{acot}\left(a+b\,x\right)}{\sqrt{c\,b^2\,x^2+2\,a\,c\,b\,x+c\,\left(a^2+1\right)}} \,d x","Not used",1,"int(acot(a + b*x)/(c*(a^2 + 1) + b^2*c*x^2 + 2*a*b*c*x)^(1/2), x)","F"
116,0,-1,23,0.000000,"\text{Not used}","int(acot(a + b*x)/(a^2 + b^2*x^2 + 2*a*b*x + 1)^(1/3),x)","\int \frac{\mathrm{acot}\left(a+b\,x\right)}{{\left(a^2+2\,a\,b\,x+b^2\,x^2+1\right)}^{1/3}} \,d x","Not used",0,"int(acot(a + b*x)/(a^2 + b^2*x^2 + 2*a*b*x + 1)^(1/3), x)","F"
117,0,-1,25,0.000000,"\text{Not used}","int(acot(a + b*x)/(c*(a^2 + 1) + b^2*c*x^2 + 2*a*b*c*x)^(1/3),x)","\int \frac{\mathrm{acot}\left(a+b\,x\right)}{{\left(c\,b^2\,x^2+2\,a\,c\,b\,x+c\,\left(a^2+1\right)\right)}^{1/3}} \,d x","Not used",0,"int(acot(a + b*x)/(c*(a^2 + 1) + b^2*c*x^2 + 2*a*b*c*x)^(1/3), x)","F"
118,0,-1,187,0.000000,"\text{Not used}","int((acot(a + b*x)*(a + b*x)^2)/(a^2 + b^2*x^2 + 2*a*b*x + 1)^(1/2),x)","\int \frac{\mathrm{acot}\left(a+b\,x\right)\,{\left(a+b\,x\right)}^2}{\sqrt{a^2+2\,a\,b\,x+b^2\,x^2+1}} \,d x","Not used",1,"int((acot(a + b*x)*(a + b*x)^2)/(a^2 + b^2*x^2 + 2*a*b*x + 1)^(1/2), x)","F"
119,0,-1,281,0.000000,"\text{Not used}","int((acot(a + b*x)*(a + b*x)^2)/(c*(a^2 + 1) + b^2*c*x^2 + 2*a*b*c*x)^(1/2),x)","\int \frac{\mathrm{acot}\left(a+b\,x\right)\,{\left(a+b\,x\right)}^2}{\sqrt{c\,b^2\,x^2+2\,a\,c\,b\,x+c\,\left(a^2+1\right)}} \,d x","Not used",1,"int((acot(a + b*x)*(a + b*x)^2)/(c*(a^2 + 1) + b^2*c*x^2 + 2*a*b*c*x)^(1/2), x)","F"
120,0,-1,30,0.000000,"\text{Not used}","int((acot(a + b*x)*(a + b*x)^2)/(a^2 + b^2*x^2 + 2*a*b*x + 1)^(1/3),x)","\int \frac{\mathrm{acot}\left(a+b\,x\right)\,{\left(a+b\,x\right)}^2}{{\left(a^2+2\,a\,b\,x+b^2\,x^2+1\right)}^{1/3}} \,d x","Not used",0,"int((acot(a + b*x)*(a + b*x)^2)/(a^2 + b^2*x^2 + 2*a*b*x + 1)^(1/3), x)","F"
121,0,-1,32,0.000000,"\text{Not used}","int((acot(a + b*x)*(a + b*x)^2)/(c*(a^2 + 1) + b^2*c*x^2 + 2*a*b*c*x)^(1/3),x)","\int \frac{\mathrm{acot}\left(a+b\,x\right)\,{\left(a+b\,x\right)}^2}{{\left(c\,b^2\,x^2+2\,a\,c\,b\,x+c\,\left(a^2+1\right)\right)}^{1/3}} \,d x","Not used",0,"int((acot(a + b*x)*(a + b*x)^2)/(c*(a^2 + 1) + b^2*c*x^2 + 2*a*b*c*x)^(1/3), x)","F"
122,1,85,52,0.153279,"\text{Not used}","int(acot(a + b*x)*(a + b*x)^2,x)","\frac{a\,x}{3}-\frac{\ln\left(a^2+2\,a\,b\,x+b^2\,x^2+1\right)}{6\,b}+\frac{b\,x^2}{6}-\frac{a^3\,\mathrm{atan}\left(a+b\,x\right)}{3\,b}+\frac{b^2\,x^3\,\mathrm{acot}\left(a+b\,x\right)}{3}+a^2\,x\,\mathrm{acot}\left(a+b\,x\right)+a\,b\,x^2\,\mathrm{acot}\left(a+b\,x\right)","Not used",1,"(a*x)/3 - log(a^2 + b^2*x^2 + 2*a*b*x + 1)/(6*b) + (b*x^2)/6 - (a^3*atan(a + b*x))/(3*b) + (b^2*x^3*acot(a + b*x))/3 + a^2*x*acot(a + b*x) + a*b*x^2*acot(a + b*x)","B"
123,1,49,39,1.509939,"\text{Not used}","int(acot(a + b*x)*(a + b*x),x)","\frac{x}{2}+\frac{\frac{\mathrm{acot}\left(a+b\,x\right)}{2}+\frac{a^2\,\mathrm{acot}\left(a+b\,x\right)}{2}}{b}+a\,x\,\mathrm{acot}\left(a+b\,x\right)+\frac{b\,x^2\,\mathrm{acot}\left(a+b\,x\right)}{2}","Not used",1,"x/2 + (acot(a + b*x)/2 + (a^2*acot(a + b*x))/2)/b + a*x*acot(a + b*x) + (b*x^2*acot(a + b*x))/2","B"
124,0,-1,45,0.000000,"\text{Not used}","int(acot(a + b*x)/(a + b*x),x)","\int \frac{\mathrm{acot}\left(a+b\,x\right)}{a+b\,x} \,d x","Not used",1,"int(acot(a + b*x)/(a + b*x), x)","F"
125,1,57,47,0.773994,"\text{Not used}","int(acot(a + b*x)/(a + b*x)^2,x)","\frac{\ln\left(-a^2-2\,a\,b\,x-b^2\,x^2-1\right)}{2\,b}-\frac{\ln\left(a+b\,x\right)}{b}-\frac{\mathrm{acot}\left(a+b\,x\right)}{x\,b^2+a\,b}","Not used",1,"log(- a^2 - b^2*x^2 - 2*a*b*x - 1)/(2*b) - log(a + b*x)/b - acot(a + b*x)/(a*b + b^2*x)","B"
126,0,-1,35,0.000000,"\text{Not used}","int(acot(x + 1)/(2*x + 2),x)","\int \frac{\mathrm{acot}\left(x+1\right)}{2\,x+2} \,d x","Not used",1,"int(acot(x + 1)/(2*x + 2), x)","F"
127,0,-1,45,0.000000,"\text{Not used}","int(acot(a + b*x)/(d*x + (a*d)/b),x)","\int \frac{\mathrm{acot}\left(a+b\,x\right)}{d\,x+\frac{a\,d}{b}} \,d x","Not used",1,"int(acot(a + b*x)/(d*x + (a*d)/b), x)","F"
128,0,-1,21,0.000000,"\text{Not used}","int(acot(a + b*x)^(1/2)*(a + b*x)^2,x)","\int \sqrt{\mathrm{acot}\left(a+b\,x\right)}\,{\left(a+b\,x\right)}^2 \,d x","Not used",0,"int(acot(a + b*x)^(1/2)*(a + b*x)^2, x)","F"
129,1,783,233,1.194432,"\text{Not used}","int((e + f*x)^3*(a + b*acot(c + d*x)),x)","\mathrm{acot}\left(c+d\,x\right)\,\left(b\,e^3\,x+\frac{3\,b\,e^2\,f\,x^2}{2}+b\,e\,f^2\,x^3+\frac{b\,f^3\,x^4}{4}\right)+x\,\left(\frac{e\,\left(6\,a\,c^2\,f^2+12\,a\,c\,d\,e\,f+2\,a\,d^2\,e^2+3\,b\,d\,e\,f+6\,a\,f^2\right)}{2\,d^2}-\frac{\left(4\,c^2+4\right)\,\left(\frac{f^2\,\left(b\,f+8\,a\,c\,f+12\,a\,d\,e\right)}{4\,d}-\frac{2\,a\,c\,f^3}{d}\right)}{4\,d^2}+\frac{2\,c\,\left(\frac{2\,c\,\left(\frac{f^2\,\left(b\,f+8\,a\,c\,f+12\,a\,d\,e\right)}{4\,d}-\frac{2\,a\,c\,f^3}{d}\right)}{d}-\frac{4\,a\,c^2\,f^3+24\,a\,c\,d\,e\,f^2+12\,a\,d^2\,e^2\,f+4\,b\,d\,e\,f^2+4\,a\,f^3}{4\,d^2}+\frac{a\,f^3\,\left(4\,c^2+4\right)}{4\,d^2}\right)}{d}\right)-x^2\,\left(\frac{c\,\left(\frac{f^2\,\left(b\,f+8\,a\,c\,f+12\,a\,d\,e\right)}{4\,d}-\frac{2\,a\,c\,f^3}{d}\right)}{d}-\frac{4\,a\,c^2\,f^3+24\,a\,c\,d\,e\,f^2+12\,a\,d^2\,e^2\,f+4\,b\,d\,e\,f^2+4\,a\,f^3}{8\,d^2}+\frac{a\,f^3\,\left(4\,c^2+4\right)}{8\,d^2}\right)+x^3\,\left(\frac{f^2\,\left(b\,f+8\,a\,c\,f+12\,a\,d\,e\right)}{12\,d}-\frac{2\,a\,c\,f^3}{3\,d}\right)+\frac{a\,f^3\,x^4}{4}+\frac{\ln\left(c^2+2\,c\,d\,x+d^2\,x^2+1\right)\,\left(-64\,b\,c^3\,d^4\,f^3+192\,b\,c^2\,d^5\,e\,f^2-192\,b\,c\,d^6\,e^2\,f+64\,b\,c\,d^4\,f^3+64\,b\,d^7\,e^3-64\,b\,d^5\,e\,f^2\right)}{128\,d^8}+\frac{b\,\mathrm{atan}\left(\frac{4\,d^3\,\left(\frac{c\,\left(c^4\,f^3-4\,c^3\,d\,e\,f^2+6\,c^2\,d^2\,e^2\,f-6\,c^2\,f^3-4\,c\,d^3\,e^3+12\,c\,d\,e\,f^2-6\,d^2\,e^2\,f+f^3\right)}{4\,d^3}+\frac{x\,\left(c^4\,f^3-4\,c^3\,d\,e\,f^2+6\,c^2\,d^2\,e^2\,f-6\,c^2\,f^3-4\,c\,d^3\,e^3+12\,c\,d\,e\,f^2-6\,d^2\,e^2\,f+f^3\right)}{4\,d^2}\right)}{c^4\,f^3-4\,c^3\,d\,e\,f^2+6\,c^2\,d^2\,e^2\,f-6\,c^2\,f^3-4\,c\,d^3\,e^3+12\,c\,d\,e\,f^2-6\,d^2\,e^2\,f+f^3}\right)\,\left(c^4\,f^3-4\,c^3\,d\,e\,f^2+6\,c^2\,d^2\,e^2\,f-6\,c^2\,f^3-4\,c\,d^3\,e^3+12\,c\,d\,e\,f^2-6\,d^2\,e^2\,f+f^3\right)}{4\,d^4}","Not used",1,"acot(c + d*x)*((b*f^3*x^4)/4 + b*e^3*x + (3*b*e^2*f*x^2)/2 + b*e*f^2*x^3) + x*((e*(6*a*f^2 + 6*a*c^2*f^2 + 2*a*d^2*e^2 + 3*b*d*e*f + 12*a*c*d*e*f))/(2*d^2) - ((4*c^2 + 4)*((f^2*(b*f + 8*a*c*f + 12*a*d*e))/(4*d) - (2*a*c*f^3)/d))/(4*d^2) + (2*c*((2*c*((f^2*(b*f + 8*a*c*f + 12*a*d*e))/(4*d) - (2*a*c*f^3)/d))/d - (4*a*f^3 + 4*a*c^2*f^3 + 4*b*d*e*f^2 + 12*a*d^2*e^2*f + 24*a*c*d*e*f^2)/(4*d^2) + (a*f^3*(4*c^2 + 4))/(4*d^2)))/d) - x^2*((c*((f^2*(b*f + 8*a*c*f + 12*a*d*e))/(4*d) - (2*a*c*f^3)/d))/d - (4*a*f^3 + 4*a*c^2*f^3 + 4*b*d*e*f^2 + 12*a*d^2*e^2*f + 24*a*c*d*e*f^2)/(8*d^2) + (a*f^3*(4*c^2 + 4))/(8*d^2)) + x^3*((f^2*(b*f + 8*a*c*f + 12*a*d*e))/(12*d) - (2*a*c*f^3)/(3*d)) + (a*f^3*x^4)/4 + (log(c^2 + d^2*x^2 + 2*c*d*x + 1)*(64*b*d^7*e^3 - 64*b*c^3*d^4*f^3 + 64*b*c*d^4*f^3 - 64*b*d^5*e*f^2 - 192*b*c*d^6*e^2*f + 192*b*c^2*d^5*e*f^2))/(128*d^8) + (b*atan((4*d^3*((c*(f^3 - 6*c^2*f^3 + c^4*f^3 - 4*c*d^3*e^3 - 6*d^2*e^2*f + 6*c^2*d^2*e^2*f + 12*c*d*e*f^2 - 4*c^3*d*e*f^2))/(4*d^3) + (x*(f^3 - 6*c^2*f^3 + c^4*f^3 - 4*c*d^3*e^3 - 6*d^2*e^2*f + 6*c^2*d^2*e^2*f + 12*c*d*e*f^2 - 4*c^3*d*e*f^2))/(4*d^2)))/(f^3 - 6*c^2*f^3 + c^4*f^3 - 4*c*d^3*e^3 - 6*d^2*e^2*f + 6*c^2*d^2*e^2*f + 12*c*d*e*f^2 - 4*c^3*d*e*f^2))*(f^3 - 6*c^2*f^3 + c^4*f^3 - 4*c*d^3*e^3 - 6*d^2*e^2*f + 6*c^2*d^2*e^2*f + 12*c*d*e*f^2 - 4*c^3*d*e*f^2))/(4*d^4)","B"
130,1,409,154,0.955681,"\text{Not used}","int((e + f*x)^2*(a + b*acot(c + d*x)),x)","x^2\,\left(\frac{f\,\left(b\,f+6\,a\,c\,f+6\,a\,d\,e\right)}{6\,d}-\frac{a\,c\,f^2}{d}\right)-x\,\left(\frac{2\,c\,\left(\frac{f\,\left(b\,f+6\,a\,c\,f+6\,a\,d\,e\right)}{3\,d}-\frac{2\,a\,c\,f^2}{d}\right)}{d}-\frac{3\,a\,c^2\,f^2+12\,a\,c\,d\,e\,f+3\,a\,d^2\,e^2+3\,b\,d\,e\,f+3\,a\,f^2}{3\,d^2}+\frac{a\,f^2\,\left(3\,c^2+3\right)}{3\,d^2}\right)+\mathrm{acot}\left(c+d\,x\right)\,\left(b\,e^2\,x+b\,e\,f\,x^2+\frac{b\,f^2\,x^3}{3}\right)+\frac{a\,f^2\,x^3}{3}+\frac{\ln\left(c^2+2\,c\,d\,x+d^2\,x^2+1\right)\,\left(36\,b\,c^2\,d^3\,f^2-72\,b\,c\,d^4\,e\,f+36\,b\,d^5\,e^2-12\,b\,d^3\,f^2\right)}{72\,d^6}-\frac{b\,\mathrm{atan}\left(\frac{3\,d^2\,\left(\frac{c\,\left(c^3\,f^2-3\,c^2\,d\,e\,f+3\,c\,d^2\,e^2-3\,c\,f^2+3\,d\,e\,f\right)}{3\,d^2}+\frac{x\,\left(c^3\,f^2-3\,c^2\,d\,e\,f+3\,c\,d^2\,e^2-3\,c\,f^2+3\,d\,e\,f\right)}{3\,d}\right)}{c^3\,f^2-3\,c^2\,d\,e\,f+3\,c\,d^2\,e^2-3\,c\,f^2+3\,d\,e\,f}\right)\,\left(c^3\,f^2-3\,c^2\,d\,e\,f+3\,c\,d^2\,e^2-3\,c\,f^2+3\,d\,e\,f\right)}{3\,d^3}","Not used",1,"x^2*((f*(b*f + 6*a*c*f + 6*a*d*e))/(6*d) - (a*c*f^2)/d) - x*((2*c*((f*(b*f + 6*a*c*f + 6*a*d*e))/(3*d) - (2*a*c*f^2)/d))/d - (3*a*f^2 + 3*a*c^2*f^2 + 3*a*d^2*e^2 + 3*b*d*e*f + 12*a*c*d*e*f)/(3*d^2) + (a*f^2*(3*c^2 + 3))/(3*d^2)) + acot(c + d*x)*((b*f^2*x^3)/3 + b*e^2*x + b*e*f*x^2) + (a*f^2*x^3)/3 + (log(c^2 + d^2*x^2 + 2*c*d*x + 1)*(36*b*d^5*e^2 - 12*b*d^3*f^2 + 36*b*c^2*d^3*f^2 - 72*b*c*d^4*e*f))/(72*d^6) - (b*atan((3*d^2*((c*(c^3*f^2 - 3*c*f^2 + 3*c*d^2*e^2 + 3*d*e*f - 3*c^2*d*e*f))/(3*d^2) + (x*(c^3*f^2 - 3*c*f^2 + 3*c*d^2*e^2 + 3*d*e*f - 3*c^2*d*e*f))/(3*d)))/(c^3*f^2 - 3*c*f^2 + 3*c*d^2*e^2 + 3*d*e*f - 3*c^2*d*e*f))*(c^3*f^2 - 3*c*f^2 + 3*c*d^2*e^2 + 3*d*e*f - 3*c^2*d*e*f))/(3*d^3)","B"
131,1,136,97,1.452927,"\text{Not used}","int((e + f*x)*(a + b*acot(c + d*x)),x)","a\,e\,x+\frac{a\,f\,x^2}{2}+\frac{b\,e\,\ln\left(c^2+2\,c\,d\,x+d^2\,x^2+1\right)}{2\,d}+\frac{b\,f\,\mathrm{acot}\left(c+d\,x\right)}{2\,d^2}+\frac{b\,f\,x^2\,\mathrm{acot}\left(c+d\,x\right)}{2}+\frac{b\,f\,x}{2\,d}+b\,e\,x\,\mathrm{acot}\left(c+d\,x\right)-\frac{b\,c^2\,f\,\mathrm{acot}\left(c+d\,x\right)}{2\,d^2}-\frac{b\,c\,f\,\ln\left(c^2+2\,c\,d\,x+d^2\,x^2+1\right)}{2\,d^2}+\frac{b\,c\,e\,\mathrm{acot}\left(c+d\,x\right)}{d}","Not used",1,"a*e*x + (a*f*x^2)/2 + (b*e*log(c^2 + d^2*x^2 + 2*c*d*x + 1))/(2*d) + (b*f*acot(c + d*x))/(2*d^2) + (b*f*x^2*acot(c + d*x))/2 + (b*f*x)/(2*d) + b*e*x*acot(c + d*x) - (b*c^2*f*acot(c + d*x))/(2*d^2) - (b*c*f*log(c^2 + d^2*x^2 + 2*c*d*x + 1))/(2*d^2) + (b*c*e*acot(c + d*x))/d","B"
132,1,48,38,1.285169,"\text{Not used}","int(a + b*acot(c + d*x),x)","a\,x+\frac{\frac{b\,\ln\left(c^2+2\,c\,d\,x+d^2\,x^2+1\right)}{2}+b\,c\,\mathrm{acot}\left(c+d\,x\right)}{d}+b\,x\,\mathrm{acot}\left(c+d\,x\right)","Not used",1,"a*x + ((b*log(c^2 + d^2*x^2 + 2*c*d*x + 1))/2 + b*c*acot(c + d*x))/d + b*x*acot(c + d*x)","B"
133,0,-1,162,0.000000,"\text{Not used}","int((a + b*acot(c + d*x))/(e + f*x),x)","\int \frac{a+b\,\mathrm{acot}\left(c+d\,x\right)}{e+f\,x} \,d x","Not used",1,"int((a + b*acot(c + d*x))/(e + f*x), x)","F"
134,1,128,153,2.084301,"\text{Not used}","int((a + b*acot(c + d*x))/(e + f*x)^2,x)","-\frac{a}{x\,f^2+e\,f}-\frac{b\,\mathrm{acot}\left(c+d\,x\right)}{f\,\left(e+f\,x\right)}-\frac{b\,d\,\ln\left(e+f\,x\right)}{d^2\,e^2-2\,c\,d\,e\,f+\left(c^2+1\right)\,f^2}+\frac{b\,d\,\ln\left(c+d\,x-\mathrm{i}\right)\,1{}\mathrm{i}}{2\,f\,\left(d\,e-c\,f+f\,1{}\mathrm{i}\right)}+\frac{b\,d\,\ln\left(c+d\,x+1{}\mathrm{i}\right)}{2\,f\,\left(f-c\,f\,1{}\mathrm{i}+d\,e\,1{}\mathrm{i}\right)}","Not used",1,"(b*d*log(c + d*x - 1i)*1i)/(2*f*(f*1i - c*f + d*e)) - (b*acot(c + d*x))/(f*(e + f*x)) - (b*d*log(e + f*x))/(f^2*(c^2 + 1) + d^2*e^2 - 2*c*d*e*f) - a/(e*f + f^2*x) + (b*d*log(c + d*x + 1i))/(2*f*(f - c*f*1i + d*e*1i))","B"
135,1,399,228,7.329473,"\text{Not used}","int((a + b*acot(c + d*x))/(e + f*x)^3,x)","\frac{b\,d\,e}{2\,{\left(e+f\,x\right)}^2\,\left(c^2\,f^2-2\,c\,d\,e\,f+d^2\,e^2+f^2\right)}-\frac{a\,f}{2\,{\left(e+f\,x\right)}^2\,\left(c^2\,f^2-2\,c\,d\,e\,f+d^2\,e^2+f^2\right)}-\frac{b\,\mathrm{acot}\left(c+d\,x\right)}{2\,f\,{\left(e+f\,x\right)}^2}-\frac{a\,c^2\,f}{2\,{\left(e+f\,x\right)}^2\,\left(c^2\,f^2-2\,c\,d\,e\,f+d^2\,e^2+f^2\right)}-\frac{b\,d^3\,e\,\ln\left(e+f\,x\right)}{{\left(c^2\,f^2-2\,c\,d\,e\,f+d^2\,e^2+f^2\right)}^2}+\frac{b\,c\,d^2\,f\,\ln\left(e+f\,x\right)}{{\left(c^2\,f^2-2\,c\,d\,e\,f+d^2\,e^2+f^2\right)}^2}+\frac{a\,c\,d\,e}{{\left(e+f\,x\right)}^2\,\left(c^2\,f^2-2\,c\,d\,e\,f+d^2\,e^2+f^2\right)}+\frac{b\,d\,f\,x}{2\,{\left(e+f\,x\right)}^2\,\left(c^2\,f^2-2\,c\,d\,e\,f+d^2\,e^2+f^2\right)}-\frac{a\,d^2\,e^2}{2\,f\,{\left(e+f\,x\right)}^2\,\left(c^2\,f^2-2\,c\,d\,e\,f+d^2\,e^2+f^2\right)}+\frac{b\,d^2\,\ln\left(c+d\,x-\mathrm{i}\right)\,1{}\mathrm{i}}{4\,f\,{\left(d\,e-c\,f+f\,1{}\mathrm{i}\right)}^2}-\frac{b\,d^2\,\ln\left(c+d\,x+1{}\mathrm{i}\right)\,1{}\mathrm{i}}{4\,f\,{\left(c\,f-d\,e+f\,1{}\mathrm{i}\right)}^2}","Not used",1,"(b*d*e)/(2*(e + f*x)^2*(f^2 + c^2*f^2 + d^2*e^2 - 2*c*d*e*f)) - (a*f)/(2*(e + f*x)^2*(f^2 + c^2*f^2 + d^2*e^2 - 2*c*d*e*f)) - (b*acot(c + d*x))/(2*f*(e + f*x)^2) + (b*d^2*log(c + d*x - 1i)*1i)/(4*f*(f*1i - c*f + d*e)^2) - (b*d^2*log(c + d*x + 1i)*1i)/(4*f*(f*1i + c*f - d*e)^2) - (a*c^2*f)/(2*(e + f*x)^2*(f^2 + c^2*f^2 + d^2*e^2 - 2*c*d*e*f)) - (b*d^3*e*log(e + f*x))/(f^2 + c^2*f^2 + d^2*e^2 - 2*c*d*e*f)^2 + (b*c*d^2*f*log(e + f*x))/(f^2 + c^2*f^2 + d^2*e^2 - 2*c*d*e*f)^2 + (a*c*d*e)/((e + f*x)^2*(f^2 + c^2*f^2 + d^2*e^2 - 2*c*d*e*f)) + (b*d*f*x)/(2*(e + f*x)^2*(f^2 + c^2*f^2 + d^2*e^2 - 2*c*d*e*f)) - (a*d^2*e^2)/(2*f*(e + f*x)^2*(f^2 + c^2*f^2 + d^2*e^2 - 2*c*d*e*f))","B"
136,0,-1,382,0.000000,"\text{Not used}","int((e + f*x)^2*(a + b*acot(c + d*x))^2,x)","\int {\left(e+f\,x\right)}^2\,{\left(a+b\,\mathrm{acot}\left(c+d\,x\right)\right)}^2 \,d x","Not used",1,"int((e + f*x)^2*(a + b*acot(c + d*x))^2, x)","F"
137,0,-1,220,0.000000,"\text{Not used}","int((e + f*x)*(a + b*acot(c + d*x))^2,x)","\int \left(e+f\,x\right)\,{\left(a+b\,\mathrm{acot}\left(c+d\,x\right)\right)}^2 \,d x","Not used",1,"int((e + f*x)*(a + b*acot(c + d*x))^2, x)","F"
138,1,123,102,0.966081,"\text{Not used}","int((a + b*acot(c + d*x))^2,x)","a^2\,x+\frac{a\,b\,\left(\ln\left({\left(c+d\,x\right)}^2+1\right)+2\,\mathrm{acot}\left(c+d\,x\right)\,\left(c+d\,x\right)\right)}{d}-\frac{2\,b^2\,\ln\left(1-{\mathrm{e}}^{\mathrm{acot}\left(c+d\,x\right)\,2{}\mathrm{i}}\right)\,\mathrm{acot}\left(c+d\,x\right)}{d}+\frac{b^2\,{\mathrm{acot}\left(c+d\,x\right)}^2\,\left(c+d\,x\right)}{d}+\frac{b^2\,\mathrm{polylog}\left(2,{\mathrm{e}}^{\mathrm{acot}\left(c+d\,x\right)\,2{}\mathrm{i}}\right)\,1{}\mathrm{i}}{d}+\frac{b^2\,{\mathrm{acot}\left(c+d\,x\right)}^2\,1{}\mathrm{i}}{d}","Not used",1,"a^2*x + (b^2*polylog(2, exp(acot(c + d*x)*2i))*1i)/d + (b^2*acot(c + d*x)^2*1i)/d + (a*b*(log((c + d*x)^2 + 1) + 2*acot(c + d*x)*(c + d*x)))/d - (2*b^2*log(1 - exp(acot(c + d*x)*2i))*acot(c + d*x))/d + (b^2*acot(c + d*x)^2*(c + d*x))/d","B"
139,0,-1,261,0.000000,"\text{Not used}","int((a + b*acot(c + d*x))^2/(e + f*x),x)","\int \frac{{\left(a+b\,\mathrm{acot}\left(c+d\,x\right)\right)}^2}{e+f\,x} \,d x","Not used",1,"int((a + b*acot(c + d*x))^2/(e + f*x), x)","F"
140,0,-1,567,0.000000,"\text{Not used}","int((a + b*acot(c + d*x))^2/(e + f*x)^2,x)","\int \frac{{\left(a+b\,\mathrm{acot}\left(c+d\,x\right)\right)}^2}{{\left(e+f\,x\right)}^2} \,d x","Not used",1,"int((a + b*acot(c + d*x))^2/(e + f*x)^2, x)","F"
141,0,-1,565,0.000000,"\text{Not used}","int((e + f*x)^2*(a + b*acot(c + d*x))^3,x)","\int {\left(e+f\,x\right)}^2\,{\left(a+b\,\mathrm{acot}\left(c+d\,x\right)\right)}^3 \,d x","Not used",1,"int((e + f*x)^2*(a + b*acot(c + d*x))^3, x)","F"
142,0,-1,337,0.000000,"\text{Not used}","int((e + f*x)*(a + b*acot(c + d*x))^3,x)","\int \left(e+f\,x\right)\,{\left(a+b\,\mathrm{acot}\left(c+d\,x\right)\right)}^3 \,d x","Not used",1,"int((e + f*x)*(a + b*acot(c + d*x))^3, x)","F"
143,0,-1,143,0.000000,"\text{Not used}","int((a + b*acot(c + d*x))^3,x)","\int {\left(a+b\,\mathrm{acot}\left(c+d\,x\right)\right)}^3 \,d x","Not used",1,"int((a + b*acot(c + d*x))^3, x)","F"
144,0,-1,372,0.000000,"\text{Not used}","int((a + b*acot(c + d*x))^3/(e + f*x),x)","\int \frac{{\left(a+b\,\mathrm{acot}\left(c+d\,x\right)\right)}^3}{e+f\,x} \,d x","Not used",1,"int((a + b*acot(c + d*x))^3/(e + f*x), x)","F"
145,0,-1,1233,0.000000,"\text{Not used}","int((a + b*acot(c + d*x))^3/(e + f*x)^2,x)","\int \frac{{\left(a+b\,\mathrm{acot}\left(c+d\,x\right)\right)}^3}{{\left(e+f\,x\right)}^2} \,d x","Not used",1,"int((a + b*acot(c + d*x))^3/(e + f*x)^2, x)","F"
146,0,-1,177,0.000000,"\text{Not used}","int((e + f*x)^m*(a + b*acot(c + d*x)),x)","\int {\left(e+f\,x\right)}^m\,\left(a+b\,\mathrm{acot}\left(c+d\,x\right)\right) \,d x","Not used",1,"int((e + f*x)^m*(a + b*acot(c + d*x)), x)","F"
147,0,-1,23,0.000000,"\text{Not used}","int((e + f*x)^m*(a + b*acot(c + d*x))^2,x)","\int {\left(e+f\,x\right)}^m\,{\left(a+b\,\mathrm{acot}\left(c+d\,x\right)\right)}^2 \,d x","Not used",0,"int((e + f*x)^m*(a + b*acot(c + d*x))^2, x)","F"
148,0,-1,23,0.000000,"\text{Not used}","int((e + f*x)^m*(a + b*acot(c + d*x))^3,x)","\int {\left(e+f\,x\right)}^m\,{\left(a+b\,\mathrm{acot}\left(c+d\,x\right)\right)}^3 \,d x","Not used",0,"int((e + f*x)^m*(a + b*acot(c + d*x))^3, x)","F"
149,1,230,42,0.762555,"\text{Not used}","int(x^3*acot(a + b*x^4),x)","\frac{\ln\left(a^2+2\,a\,b\,x^4+b^2\,x^8+1\right)}{8\,b}+\frac{x^4\,\mathrm{acot}\left(b\,x^4+a\right)}{4}-\frac{a\,\mathrm{atan}\left(\frac{a}{a^6+3\,a^4+3\,a^2+1}+\frac{3\,a^3}{a^6+3\,a^4+3\,a^2+1}+\frac{3\,a^5}{a^6+3\,a^4+3\,a^2+1}+\frac{a^7}{a^6+3\,a^4+3\,a^2+1}+\frac{b\,x^4}{a^6+3\,a^4+3\,a^2+1}+\frac{3\,a^2\,b\,x^4}{a^6+3\,a^4+3\,a^2+1}+\frac{3\,a^4\,b\,x^4}{a^6+3\,a^4+3\,a^2+1}+\frac{a^6\,b\,x^4}{a^6+3\,a^4+3\,a^2+1}\right)}{4\,b}","Not used",1,"log(a^2 + b^2*x^8 + 2*a*b*x^4 + 1)/(8*b) + (x^4*acot(a + b*x^4))/4 - (a*atan(a/(3*a^2 + 3*a^4 + a^6 + 1) + (3*a^3)/(3*a^2 + 3*a^4 + a^6 + 1) + (3*a^5)/(3*a^2 + 3*a^4 + a^6 + 1) + a^7/(3*a^2 + 3*a^4 + a^6 + 1) + (b*x^4)/(3*a^2 + 3*a^4 + a^6 + 1) + (3*a^2*b*x^4)/(3*a^2 + 3*a^4 + a^6 + 1) + (3*a^4*b*x^4)/(3*a^2 + 3*a^4 + a^6 + 1) + (a^6*b*x^4)/(3*a^2 + 3*a^4 + a^6 + 1)))/(4*b)","B"
150,1,58,45,1.376540,"\text{Not used}","int(x^(n - 1)*acot(a + b*x^n),x)","\frac{\frac{\ln\left(a^2+b^2\,x^{2\,n}+2\,a\,b\,x^n+1\right)}{2}+a\,\mathrm{acot}\left(a+b\,x^n\right)}{b\,n}+\frac{x^n\,\mathrm{acot}\left(a+b\,x^n\right)}{n}","Not used",1,"(log(a^2 + b^2*x^(2*n) + 2*a*b*x^n + 1)/2 + a*acot(a + b*x^n))/(b*n) + (x^n*acot(a + b*x^n))/n","B"
151,0,-1,43,0.000000,"\text{Not used}","int(-(a + b*acot((1 - c*x)^(1/2)/(c*x + 1)^(1/2)))^n/(c^2*x^2 - 1),x)","-\int \frac{{\left(a+b\,\mathrm{acot}\left(\frac{\sqrt{1-c\,x}}{\sqrt{c\,x+1}}\right)\right)}^n}{c^2\,x^2-1} \,d x","Not used",0,"-int((a + b*acot((1 - c*x)^(1/2)/(c*x + 1)^(1/2)))^n/(c^2*x^2 - 1), x)","F"
152,0,-1,488,0.000000,"\text{Not used}","int(-(a + b*acot((1 - c*x)^(1/2)/(c*x + 1)^(1/2)))^3/(c^2*x^2 - 1),x)","\int -\frac{{\left(a+b\,\mathrm{acot}\left(\frac{\sqrt{1-c\,x}}{\sqrt{c\,x+1}}\right)\right)}^3}{c^2\,x^2-1} \,d x","Not used",1,"int(-(a + b*acot((1 - c*x)^(1/2)/(c*x + 1)^(1/2)))^3/(c^2*x^2 - 1), x)","F"
153,0,-1,321,0.000000,"\text{Not used}","int(-(a + b*acot((1 - c*x)^(1/2)/(c*x + 1)^(1/2)))^2/(c^2*x^2 - 1),x)","\int -\frac{{\left(a+b\,\mathrm{acot}\left(\frac{\sqrt{1-c\,x}}{\sqrt{c\,x+1}}\right)\right)}^2}{c^2\,x^2-1} \,d x","Not used",1,"int(-(a + b*acot((1 - c*x)^(1/2)/(c*x + 1)^(1/2)))^2/(c^2*x^2 - 1), x)","F"
154,0,-1,98,0.000000,"\text{Not used}","int(-(a + b*acot((1 - c*x)^(1/2)/(c*x + 1)^(1/2)))/(c^2*x^2 - 1),x)","\int -\frac{a+b\,\mathrm{acot}\left(\frac{\sqrt{1-c\,x}}{\sqrt{c\,x+1}}\right)}{c^2\,x^2-1} \,d x","Not used",1,"int(-(a + b*acot((1 - c*x)^(1/2)/(c*x + 1)^(1/2)))/(c^2*x^2 - 1), x)","F"
155,0,-1,43,0.000000,"\text{Not used}","int(-1/((a + b*acot((1 - c*x)^(1/2)/(c*x + 1)^(1/2)))*(c^2*x^2 - 1)),x)","-\int \frac{1}{\left(a+b\,\mathrm{acot}\left(\frac{\sqrt{1-c\,x}}{\sqrt{c\,x+1}}\right)\right)\,\left(c^2\,x^2-1\right)} \,d x","Not used",0,"-int(1/((a + b*acot((1 - c*x)^(1/2)/(c*x + 1)^(1/2)))*(c^2*x^2 - 1)), x)","F"
156,0,-1,43,0.000000,"\text{Not used}","int(-1/((a + b*acot((1 - c*x)^(1/2)/(c*x + 1)^(1/2)))^2*(c^2*x^2 - 1)),x)","-\int \frac{1}{{\left(a+b\,\mathrm{acot}\left(\frac{\sqrt{1-c\,x}}{\sqrt{c\,x+1}}\right)\right)}^2\,\left(c^2\,x^2-1\right)} \,d x","Not used",0,"-int(1/((a + b*acot((1 - c*x)^(1/2)/(c*x + 1)^(1/2)))^2*(c^2*x^2 - 1)), x)","F"
157,1,21,16,0.076629,"\text{Not used}","int(Pi/2 - atan(tan(a + b*x)),x)","\frac{\Pi \,x}{2}+\frac{b\,x^2}{2}-x\,\mathrm{atan}\left(\mathrm{tan}\left(a+b\,x\right)\right)","Not used",1,"(Pi*x)/2 + (b*x^2)/2 - x*atan(tan(a + b*x))","B"
158,0,-1,403,0.000000,"\text{Not used}","int(x^2*acot(c + d*tan(a + b*x)),x)","\int x^2\,\mathrm{acot}\left(c+d\,\mathrm{tan}\left(a+b\,x\right)\right) \,d x","Not used",1,"int(x^2*acot(c + d*tan(a + b*x)), x)","F"
159,0,-1,305,0.000000,"\text{Not used}","int(x*acot(c + d*tan(a + b*x)),x)","\int x\,\mathrm{acot}\left(c+d\,\mathrm{tan}\left(a+b\,x\right)\right) \,d x","Not used",1,"int(x*acot(c + d*tan(a + b*x)), x)","F"
160,0,-1,198,0.000000,"\text{Not used}","int(acot(c + d*tan(a + b*x)),x)","\int \mathrm{acot}\left(c+d\,\mathrm{tan}\left(a+b\,x\right)\right) \,d x","Not used",1,"int(acot(c + d*tan(a + b*x)), x)","F"
161,0,-1,18,0.000000,"\text{Not used}","int(acot(c + d*tan(a + b*x))/x,x)","\int \frac{\mathrm{acot}\left(c+d\,\mathrm{tan}\left(a+b\,x\right)\right)}{x} \,d x","Not used",0,"int(acot(c + d*tan(a + b*x))/x, x)","F"
162,0,-1,154,0.000000,"\text{Not used}","int(x^2*acot(c + tan(a + b*x)*(c*1i + 1)),x)","\int x^2\,\mathrm{acot}\left(c+\mathrm{tan}\left(a+b\,x\right)\,\left(1+c\,1{}\mathrm{i}\right)\right) \,d x","Not used",1,"int(x^2*acot(c + tan(a + b*x)*(c*1i + 1)), x)","F"
163,0,-1,123,0.000000,"\text{Not used}","int(x*acot(c + tan(a + b*x)*(c*1i + 1)),x)","\int x\,\mathrm{acot}\left(c+\mathrm{tan}\left(a+b\,x\right)\,\left(1+c\,1{}\mathrm{i}\right)\right) \,d x","Not used",1,"int(x*acot(c + tan(a + b*x)*(c*1i + 1)), x)","F"
164,0,-1,85,0.000000,"\text{Not used}","int(acot(c + tan(a + b*x)*(c*1i + 1)),x)","\int \mathrm{acot}\left(c+\mathrm{tan}\left(a+b\,x\right)\,\left(1+c\,1{}\mathrm{i}\right)\right) \,d x","Not used",1,"int(acot(c + tan(a + b*x)*(c*1i + 1)), x)","F"
165,0,-1,24,0.000000,"\text{Not used}","int(acot(c + tan(a + b*x)*(c*1i + 1))/x,x)","\int \frac{\mathrm{acot}\left(c+\mathrm{tan}\left(a+b\,x\right)\,\left(1+c\,1{}\mathrm{i}\right)\right)}{x} \,d x","Not used",0,"int(acot(c + tan(a + b*x)*(c*1i + 1))/x, x)","F"
166,0,-1,155,0.000000,"\text{Not used}","int(x^2*acot(c + tan(a + b*x)*(c*1i - 1)),x)","\int x^2\,\mathrm{acot}\left(c+\mathrm{tan}\left(a+b\,x\right)\,\left(-1+c\,1{}\mathrm{i}\right)\right) \,d x","Not used",1,"int(x^2*acot(c + tan(a + b*x)*(c*1i - 1)), x)","F"
167,0,-1,124,0.000000,"\text{Not used}","int(x*acot(c + tan(a + b*x)*(c*1i - 1)),x)","\int x\,\mathrm{acot}\left(c+\mathrm{tan}\left(a+b\,x\right)\,\left(-1+c\,1{}\mathrm{i}\right)\right) \,d x","Not used",1,"int(x*acot(c + tan(a + b*x)*(c*1i - 1)), x)","F"
168,0,-1,86,0.000000,"\text{Not used}","int(acot(c + tan(a + b*x)*(c*1i - 1)),x)","\int \mathrm{acot}\left(c+\mathrm{tan}\left(a+b\,x\right)\,\left(-1+c\,1{}\mathrm{i}\right)\right) \,d x","Not used",1,"int(acot(c + tan(a + b*x)*(c*1i - 1)), x)","F"
169,0,-1,25,0.000000,"\text{Not used}","int(acot(c + tan(a + b*x)*(c*1i - 1))/x,x)","\int \frac{\mathrm{acot}\left(c+\mathrm{tan}\left(a+b\,x\right)\,\left(-1+c\,1{}\mathrm{i}\right)\right)}{x} \,d x","Not used",0,"int(acot(c + tan(a + b*x)*(c*1i - 1))/x, x)","F"
170,1,16,16,0.636688,"\text{Not used}","int(acot(cot(a + b*x)),x)","x\,\mathrm{acot}\left(\mathrm{cot}\left(a+b\,x\right)\right)-\frac{b\,x^2}{2}","Not used",1,"x*acot(cot(a + b*x)) - (b*x^2)/2","B"
171,0,-1,399,0.000000,"\text{Not used}","int(x^2*acot(c + d*cot(a + b*x)),x)","\int x^2\,\mathrm{acot}\left(c+d\,\mathrm{cot}\left(a+b\,x\right)\right) \,d x","Not used",1,"int(x^2*acot(c + d*cot(a + b*x)), x)","F"
172,0,-1,303,0.000000,"\text{Not used}","int(x*acot(c + d*cot(a + b*x)),x)","\int x\,\mathrm{acot}\left(c+d\,\mathrm{cot}\left(a+b\,x\right)\right) \,d x","Not used",1,"int(x*acot(c + d*cot(a + b*x)), x)","F"
173,0,-1,198,0.000000,"\text{Not used}","int(acot(c + d*cot(a + b*x)),x)","\int \mathrm{acot}\left(c+d\,\mathrm{cot}\left(a+b\,x\right)\right) \,d x","Not used",1,"int(acot(c + d*cot(a + b*x)), x)","F"
174,0,-1,18,0.000000,"\text{Not used}","int(acot(c + d*cot(a + b*x))/x,x)","\int \frac{\mathrm{acot}\left(c+d\,\mathrm{cot}\left(a+b\,x\right)\right)}{x} \,d x","Not used",0,"int(acot(c + d*cot(a + b*x))/x, x)","F"
175,0,-1,154,0.000000,"\text{Not used}","int(x^2*(Pi + acot(c - cot(a + b*x)*(c*1i - 1))),x)","\int x^2\,\left(\Pi +\mathrm{acot}\left(c-\mathrm{cot}\left(a+b\,x\right)\,\left(-1+c\,1{}\mathrm{i}\right)\right)\right) \,d x","Not used",1,"int(x^2*(Pi + acot(c - cot(a + b*x)*(c*1i - 1))), x)","F"
176,0,-1,123,0.000000,"\text{Not used}","int(x*(Pi + acot(c - cot(a + b*x)*(c*1i - 1))),x)","\int x\,\left(\Pi +\mathrm{acot}\left(c-\mathrm{cot}\left(a+b\,x\right)\,\left(-1+c\,1{}\mathrm{i}\right)\right)\right) \,d x","Not used",1,"int(x*(Pi + acot(c - cot(a + b*x)*(c*1i - 1))), x)","F"
177,0,-1,85,0.000000,"\text{Not used}","int(Pi + acot(c - cot(a + b*x)*(c*1i - 1)),x)","\int \Pi +\mathrm{acot}\left(c-\mathrm{cot}\left(a+b\,x\right)\,\left(-1+c\,1{}\mathrm{i}\right)\right) \,d x","Not used",1,"int(Pi + acot(c - cot(a + b*x)*(c*1i - 1)), x)","F"
178,0,-1,24,0.000000,"\text{Not used}","int((Pi + acot(c - cot(a + b*x)*(c*1i - 1)))/x,x)","\int \frac{\Pi +\mathrm{acot}\left(c-\mathrm{cot}\left(a+b\,x\right)\,\left(-1+c\,1{}\mathrm{i}\right)\right)}{x} \,d x","Not used",0,"int((Pi + acot(c - cot(a + b*x)*(c*1i - 1)))/x, x)","F"
179,0,-1,155,0.000000,"\text{Not used}","int(x^2*(Pi + acot(c - cot(a + b*x)*(c*1i + 1))),x)","\int x^2\,\left(\Pi +\mathrm{acot}\left(c-\mathrm{cot}\left(a+b\,x\right)\,\left(1+c\,1{}\mathrm{i}\right)\right)\right) \,d x","Not used",1,"int(x^2*(Pi + acot(c - cot(a + b*x)*(c*1i + 1))), x)","F"
180,0,-1,124,0.000000,"\text{Not used}","int(x*(Pi + acot(c - cot(a + b*x)*(c*1i + 1))),x)","\int x\,\left(\Pi +\mathrm{acot}\left(c-\mathrm{cot}\left(a+b\,x\right)\,\left(1+c\,1{}\mathrm{i}\right)\right)\right) \,d x","Not used",1,"int(x*(Pi + acot(c - cot(a + b*x)*(c*1i + 1))), x)","F"
181,0,-1,86,0.000000,"\text{Not used}","int(Pi + acot(c - cot(a + b*x)*(c*1i + 1)),x)","\int \Pi +\mathrm{acot}\left(c-\mathrm{cot}\left(a+b\,x\right)\,\left(1+c\,1{}\mathrm{i}\right)\right) \,d x","Not used",1,"int(Pi + acot(c - cot(a + b*x)*(c*1i + 1)), x)","F"
182,0,-1,25,0.000000,"\text{Not used}","int((Pi + acot(c - cot(a + b*x)*(c*1i + 1)))/x,x)","\int \frac{\Pi +\mathrm{acot}\left(c-\mathrm{cot}\left(a+b\,x\right)\,\left(1+c\,1{}\mathrm{i}\right)\right)}{x} \,d x","Not used",0,"int((Pi + acot(c - cot(a + b*x)*(c*1i + 1)))/x, x)","F"
183,0,-1,299,0.000000,"\text{Not used}","int(acot(tanh(a + b*x))*(e + f*x)^3,x)","\int \mathrm{acot}\left(\mathrm{tanh}\left(a+b\,x\right)\right)\,{\left(e+f\,x\right)}^3 \,d x","Not used",1,"int(acot(tanh(a + b*x))*(e + f*x)^3, x)","F"
184,0,-1,229,0.000000,"\text{Not used}","int(acot(tanh(a + b*x))*(e + f*x)^2,x)","\int \mathrm{acot}\left(\mathrm{tanh}\left(a+b\,x\right)\right)\,{\left(e+f\,x\right)}^2 \,d x","Not used",1,"int(acot(tanh(a + b*x))*(e + f*x)^2, x)","F"
185,0,-1,159,0.000000,"\text{Not used}","int(acot(tanh(a + b*x))*(e + f*x),x)","\int \mathrm{acot}\left(\mathrm{tanh}\left(a+b\,x\right)\right)\,\left(e+f\,x\right) \,d x","Not used",1,"int(acot(tanh(a + b*x))*(e + f*x), x)","F"
186,0,-1,73,0.000000,"\text{Not used}","int(acot(tanh(a + b*x)),x)","\int \mathrm{acot}\left(\mathrm{tanh}\left(a+b\,x\right)\right) \,d x","Not used",1,"int(acot(tanh(a + b*x)), x)","F"
187,0,-1,18,0.000000,"\text{Not used}","int(acot(tanh(a + b*x))/(e + f*x),x)","\int \frac{\mathrm{acot}\left(\mathrm{tanh}\left(a+b\,x\right)\right)}{e+f\,x} \,d x","Not used",0,"int(acot(tanh(a + b*x))/(e + f*x), x)","F"
188,0,-1,355,0.000000,"\text{Not used}","int(x^2*acot(c + d*tanh(a + b*x)),x)","\int x^2\,\mathrm{acot}\left(c+d\,\mathrm{tanh}\left(a+b\,x\right)\right) \,d x","Not used",1,"int(x^2*acot(c + d*tanh(a + b*x)), x)","F"
189,0,-1,267,0.000000,"\text{Not used}","int(x*acot(c + d*tanh(a + b*x)),x)","\int x\,\mathrm{acot}\left(c+d\,\mathrm{tanh}\left(a+b\,x\right)\right) \,d x","Not used",1,"int(x*acot(c + d*tanh(a + b*x)), x)","F"
190,0,-1,174,0.000000,"\text{Not used}","int(acot(c + d*tanh(a + b*x)),x)","\int \mathrm{acot}\left(c+d\,\mathrm{tanh}\left(a+b\,x\right)\right) \,d x","Not used",1,"int(acot(c + d*tanh(a + b*x)), x)","F"
191,0,-1,18,0.000000,"\text{Not used}","int(acot(c + d*tanh(a + b*x))/x,x)","\int \frac{\mathrm{acot}\left(c+d\,\mathrm{tanh}\left(a+b\,x\right)\right)}{x} \,d x","Not used",0,"int(acot(c + d*tanh(a + b*x))/x, x)","F"
192,0,-1,142,0.000000,"\text{Not used}","int(x^2*acot(c + tanh(a + b*x)*(c + 1i)),x)","\int x^2\,\mathrm{acot}\left(c+\mathrm{tanh}\left(a+b\,x\right)\,\left(c+1{}\mathrm{i}\right)\right) \,d x","Not used",1,"int(x^2*acot(c + tanh(a + b*x)*(c + 1i)), x)","F"
193,0,-1,113,0.000000,"\text{Not used}","int(x*acot(c + tanh(a + b*x)*(c + 1i)),x)","\int x\,\mathrm{acot}\left(c+\mathrm{tanh}\left(a+b\,x\right)\,\left(c+1{}\mathrm{i}\right)\right) \,d x","Not used",1,"int(x*acot(c + tanh(a + b*x)*(c + 1i)), x)","F"
194,0,-1,79,0.000000,"\text{Not used}","int(acot(c + tanh(a + b*x)*(c + 1i)),x)","\int \mathrm{acot}\left(c+\mathrm{tanh}\left(a+b\,x\right)\,\left(c+1{}\mathrm{i}\right)\right) \,d x","Not used",1,"int(acot(c + tanh(a + b*x)*(c + 1i)), x)","F"
195,0,-1,22,0.000000,"\text{Not used}","int(acot(c + tanh(a + b*x)*(c + 1i))/x,x)","\int \frac{\mathrm{acot}\left(c+\mathrm{tanh}\left(a+b\,x\right)\,\left(c+1{}\mathrm{i}\right)\right)}{x} \,d x","Not used",0,"int(acot(c + tanh(a + b*x)*(c + 1i))/x, x)","F"
196,0,-1,145,0.000000,"\text{Not used}","int(x^2*acot(c + tanh(a + b*x)*(c - 1i)),x)","\int x^2\,\mathrm{acot}\left(c+\mathrm{tanh}\left(a+b\,x\right)\,\left(c-\mathrm{i}\right)\right) \,d x","Not used",1,"int(x^2*acot(c + tanh(a + b*x)*(c - 1i)), x)","F"
197,0,-1,116,0.000000,"\text{Not used}","int(x*acot(c + tanh(a + b*x)*(c - 1i)),x)","\int x\,\mathrm{acot}\left(c+\mathrm{tanh}\left(a+b\,x\right)\,\left(c-\mathrm{i}\right)\right) \,d x","Not used",1,"int(x*acot(c + tanh(a + b*x)*(c - 1i)), x)","F"
198,0,-1,82,0.000000,"\text{Not used}","int(acot(c + tanh(a + b*x)*(c - 1i)),x)","\int \mathrm{acot}\left(c+\mathrm{tanh}\left(a+b\,x\right)\,\left(c-\mathrm{i}\right)\right) \,d x","Not used",1,"int(acot(c + tanh(a + b*x)*(c - 1i)), x)","F"
199,0,-1,25,0.000000,"\text{Not used}","int(acot(c + tanh(a + b*x)*(c - 1i))/x,x)","\int \frac{\mathrm{acot}\left(c+\mathrm{tanh}\left(a+b\,x\right)\,\left(c-\mathrm{i}\right)\right)}{x} \,d x","Not used",0,"int(acot(c + tanh(a + b*x)*(c - 1i))/x, x)","F"
200,0,-1,299,0.000000,"\text{Not used}","int(acot(coth(a + b*x))*(e + f*x)^3,x)","\int \mathrm{acot}\left(\mathrm{coth}\left(a+b\,x\right)\right)\,{\left(e+f\,x\right)}^3 \,d x","Not used",1,"int(acot(coth(a + b*x))*(e + f*x)^3, x)","F"
201,0,-1,229,0.000000,"\text{Not used}","int(acot(coth(a + b*x))*(e + f*x)^2,x)","\int \mathrm{acot}\left(\mathrm{coth}\left(a+b\,x\right)\right)\,{\left(e+f\,x\right)}^2 \,d x","Not used",1,"int(acot(coth(a + b*x))*(e + f*x)^2, x)","F"
202,0,-1,159,0.000000,"\text{Not used}","int(acot(coth(a + b*x))*(e + f*x),x)","\int \mathrm{acot}\left(\mathrm{coth}\left(a+b\,x\right)\right)\,\left(e+f\,x\right) \,d x","Not used",1,"int(acot(coth(a + b*x))*(e + f*x), x)","F"
203,0,-1,74,0.000000,"\text{Not used}","int(acot(coth(a + b*x)),x)","\int \mathrm{acot}\left(\mathrm{coth}\left(a+b\,x\right)\right) \,d x","Not used",1,"int(acot(coth(a + b*x)), x)","F"
204,0,-1,18,0.000000,"\text{Not used}","int(acot(coth(a + b*x))/(e + f*x),x)","\int \frac{\mathrm{acot}\left(\mathrm{coth}\left(a+b\,x\right)\right)}{e+f\,x} \,d x","Not used",0,"int(acot(coth(a + b*x))/(e + f*x), x)","F"
205,0,-1,351,0.000000,"\text{Not used}","int(x^2*acot(c + d*coth(a + b*x)),x)","\int x^2\,\mathrm{acot}\left(c+d\,\mathrm{coth}\left(a+b\,x\right)\right) \,d x","Not used",1,"int(x^2*acot(c + d*coth(a + b*x)), x)","F"
206,0,-1,265,0.000000,"\text{Not used}","int(x*acot(c + d*coth(a + b*x)),x)","\int x\,\mathrm{acot}\left(c+d\,\mathrm{coth}\left(a+b\,x\right)\right) \,d x","Not used",1,"int(x*acot(c + d*coth(a + b*x)), x)","F"
207,0,-1,174,0.000000,"\text{Not used}","int(acot(c + d*coth(a + b*x)),x)","\int \mathrm{acot}\left(c+d\,\mathrm{coth}\left(a+b\,x\right)\right) \,d x","Not used",1,"int(acot(c + d*coth(a + b*x)), x)","F"
208,0,-1,18,0.000000,"\text{Not used}","int(acot(c + d*coth(a + b*x))/x,x)","\int \frac{\mathrm{acot}\left(c+d\,\mathrm{coth}\left(a+b\,x\right)\right)}{x} \,d x","Not used",0,"int(acot(c + d*coth(a + b*x))/x, x)","F"
209,0,-1,142,0.000000,"\text{Not used}","int(x^2*acot(c + coth(a + b*x)*(c + 1i)),x)","\int x^2\,\mathrm{acot}\left(c+\mathrm{coth}\left(a+b\,x\right)\,\left(c+1{}\mathrm{i}\right)\right) \,d x","Not used",1,"int(x^2*acot(c + coth(a + b*x)*(c + 1i)), x)","F"
210,0,-1,113,0.000000,"\text{Not used}","int(x*acot(c + coth(a + b*x)*(c + 1i)),x)","\int x\,\mathrm{acot}\left(c+\mathrm{coth}\left(a+b\,x\right)\,\left(c+1{}\mathrm{i}\right)\right) \,d x","Not used",1,"int(x*acot(c + coth(a + b*x)*(c + 1i)), x)","F"
211,0,-1,79,0.000000,"\text{Not used}","int(acot(c + coth(a + b*x)*(c + 1i)),x)","\int \mathrm{acot}\left(c+\mathrm{coth}\left(a+b\,x\right)\,\left(c+1{}\mathrm{i}\right)\right) \,d x","Not used",1,"int(acot(c + coth(a + b*x)*(c + 1i)), x)","F"
212,0,-1,22,0.000000,"\text{Not used}","int(acot(c + coth(a + b*x)*(c + 1i))/x,x)","\int \frac{\mathrm{acot}\left(c+\mathrm{coth}\left(a+b\,x\right)\,\left(c+1{}\mathrm{i}\right)\right)}{x} \,d x","Not used",0,"int(acot(c + coth(a + b*x)*(c + 1i))/x, x)","F"
213,0,-1,145,0.000000,"\text{Not used}","int(x^2*acot(c + coth(a + b*x)*(c - 1i)),x)","\int x^2\,\mathrm{acot}\left(c+\mathrm{coth}\left(a+b\,x\right)\,\left(c-\mathrm{i}\right)\right) \,d x","Not used",1,"int(x^2*acot(c + coth(a + b*x)*(c - 1i)), x)","F"
214,0,-1,116,0.000000,"\text{Not used}","int(x*acot(c + coth(a + b*x)*(c - 1i)),x)","\int x\,\mathrm{acot}\left(c+\mathrm{coth}\left(a+b\,x\right)\,\left(c-\mathrm{i}\right)\right) \,d x","Not used",1,"int(x*acot(c + coth(a + b*x)*(c - 1i)), x)","F"
215,0,-1,82,0.000000,"\text{Not used}","int(acot(c + coth(a + b*x)*(c - 1i)),x)","\int \mathrm{acot}\left(c+\mathrm{coth}\left(a+b\,x\right)\,\left(c-\mathrm{i}\right)\right) \,d x","Not used",1,"int(acot(c + coth(a + b*x)*(c - 1i)), x)","F"
216,0,-1,25,0.000000,"\text{Not used}","int(acot(c + coth(a + b*x)*(c - 1i))/x,x)","\int \frac{\mathrm{acot}\left(c+\mathrm{coth}\left(a+b\,x\right)\,\left(c-\mathrm{i}\right)\right)}{x} \,d x","Not used",0,"int(acot(c + coth(a + b*x)*(c - 1i))/x, x)","F"
217,0,-1,187,0.000000,"\text{Not used}","int(((a + b*acot(c*x^n))*(d + e*log(f*x^m)))/x,x)","\int \frac{\left(a+b\,\mathrm{acot}\left(c\,x^n\right)\right)\,\left(d+e\,\ln\left(f\,x^m\right)\right)}{x} \,d x","Not used",1,"int(((a + b*acot(c*x^n))*(d + e*log(f*x^m)))/x, x)","F"
218,0,-1,35,0.000000,"\text{Not used}","int(acot(exp(x)),x)","\int \mathrm{acot}\left({\mathrm{e}}^x\right) \,d x","Not used",1,"int(acot(exp(x)), x)","F"
219,0,-1,71,0.000000,"\text{Not used}","int(x*acot(exp(x)),x)","\int x\,\mathrm{acot}\left({\mathrm{e}}^x\right) \,d x","Not used",1,"int(x*acot(exp(x)), x)","F"
220,0,-1,103,0.000000,"\text{Not used}","int(x^2*acot(exp(x)),x)","\int x^2\,\mathrm{acot}\left({\mathrm{e}}^x\right) \,d x","Not used",1,"int(x^2*acot(exp(x)), x)","F"
221,0,-1,51,0.000000,"\text{Not used}","int(acot(exp(a + b*x)),x)","\int \mathrm{acot}\left({\mathrm{e}}^{a+b\,x}\right) \,d x","Not used",1,"int(acot(exp(a + b*x)), x)","F"
222,0,-1,103,0.000000,"\text{Not used}","int(x*acot(exp(a + b*x)),x)","\int x\,\mathrm{acot}\left({\mathrm{e}}^{a+b\,x}\right) \,d x","Not used",1,"int(x*acot(exp(a + b*x)), x)","F"
223,0,-1,151,0.000000,"\text{Not used}","int(x^2*acot(exp(a + b*x)),x)","\int x^2\,\mathrm{acot}\left({\mathrm{e}}^{a+b\,x}\right) \,d x","Not used",1,"int(x^2*acot(exp(a + b*x)), x)","F"
224,0,-1,196,0.000000,"\text{Not used}","int(acot(a + b*f^(c + d*x)),x)","\int \mathrm{acot}\left(a+b\,f^{c+d\,x}\right) \,d x","Not used",1,"int(acot(a + b*f^(c + d*x)), x)","F"
225,0,-1,250,0.000000,"\text{Not used}","int(x*acot(a + b*f^(c + d*x)),x)","\int x\,\mathrm{acot}\left(a+b\,f^{c+d\,x}\right) \,d x","Not used",1,"int(x*acot(a + b*f^(c + d*x)), x)","F"
226,0,-1,313,0.000000,"\text{Not used}","int(x^2*acot(a + b*f^(c + d*x)),x)","\int x^2\,\mathrm{acot}\left(a+b\,f^{c+d\,x}\right) \,d x","Not used",1,"int(x^2*acot(a + b*f^(c + d*x)), x)","F"
227,1,22,27,0.093251,"\text{Not used}","int(acot(exp(x))*exp(-x),x)","\frac{\ln\left({\mathrm{e}}^{2\,x}+1\right)}{2}-x-\mathrm{acot}\left({\mathrm{e}}^x\right)\,{\mathrm{e}}^{-x}","Not used",1,"log(exp(2*x) + 1)/2 - x - acot(exp(x))*exp(-x)","B"
228,1,15,17,0.127118,"\text{Not used}","int(1/((a + a*x^2)*(b - 2*b*acot(x))),x)","\frac{\ln\left(2\,\mathrm{acot}\left(x\right)-1\right)}{2\,a\,b}","Not used",1,"log(2*acot(x) - 1)/(2*a*b)","B"
229,1,65,47,0.730190,"\text{Not used}","int(exp(c*(a + b*x))*acot(sinh(a*c + b*c*x)),x)","\frac{\ln\left({\mathrm{e}}^{2\,b\,c\,x}\,{\mathrm{e}}^{2\,a\,c}+1\right)}{b\,c}+\frac{{\mathrm{e}}^{b\,c\,x}\,{\mathrm{e}}^{a\,c}\,\mathrm{acot}\left(\frac{{\mathrm{e}}^{b\,c\,x}\,{\mathrm{e}}^{a\,c}}{2}-\frac{{\mathrm{e}}^{-b\,c\,x}\,{\mathrm{e}}^{-a\,c}}{2}\right)}{b\,c}","Not used",1,"log(exp(2*b*c*x)*exp(2*a*c) + 1)/(b*c) + (exp(b*c*x)*exp(a*c)*acot((exp(b*c*x)*exp(a*c))/2 - (exp(-b*c*x)*exp(-a*c))/2))/(b*c)","B"
230,1,133,103,0.855337,"\text{Not used}","int(exp(c*(a + b*x))*acot(cosh(a*c + b*c*x)),x)","\frac{\ln\left(8\,{\mathrm{e}}^{2\,c\,\left(a+b\,x\right)}-2\,\sqrt{2}-6\,\sqrt{2}\,{\mathrm{e}}^{2\,c\,\left(a+b\,x\right)}\right)\,\left(\sqrt{2}+1\right)}{2\,b\,c}-\frac{\ln\left(8\,{\mathrm{e}}^{2\,c\,\left(a+b\,x\right)}+2\,\sqrt{2}+6\,\sqrt{2}\,{\mathrm{e}}^{2\,c\,\left(a+b\,x\right)}\right)\,\left(\sqrt{2}-1\right)}{2\,b\,c}+\frac{{\mathrm{e}}^{a\,c+b\,c\,x}\,\mathrm{acot}\left(\frac{{\mathrm{e}}^{b\,c\,x}\,{\mathrm{e}}^{a\,c}}{2}+\frac{{\mathrm{e}}^{-b\,c\,x}\,{\mathrm{e}}^{-a\,c}}{2}\right)}{b\,c}","Not used",1,"(log(8*exp(2*c*(a + b*x)) - 2*2^(1/2) - 6*2^(1/2)*exp(2*c*(a + b*x)))*(2^(1/2) + 1))/(2*b*c) - (log(8*exp(2*c*(a + b*x)) + 2*2^(1/2) + 6*2^(1/2)*exp(2*c*(a + b*x)))*(2^(1/2) - 1))/(2*b*c) + (exp(a*c + b*c*x)*acot((exp(b*c*x)*exp(a*c))/2 + (exp(-b*c*x)*exp(-a*c))/2))/(b*c)","B"
231,1,164,180,2.563651,"\text{Not used}","int(exp(c*(a + b*x))*acot(tanh(a*c + b*c*x)),x)","\frac{4\,{\mathrm{e}}^{a\,c+b\,c\,x}\,\mathrm{acot}\left(\frac{{\mathrm{e}}^{2\,b\,c\,x}\,{\mathrm{e}}^{2\,a\,c}-1}{{\mathrm{e}}^{2\,b\,c\,x}\,{\mathrm{e}}^{2\,a\,c}+1}\right)+\sqrt{2}\,\ln\left(\sqrt{2}\,\left(-4-4{}\mathrm{i}\right)-{\mathrm{e}}^{b\,c\,x}\,{\mathrm{e}}^{a\,c}\,8{}\mathrm{i}\right)\,\left(-1-\mathrm{i}\right)+\sqrt{2}\,\ln\left(\sqrt{2}\,\left(-4+4{}\mathrm{i}\right)+{\mathrm{e}}^{b\,c\,x}\,{\mathrm{e}}^{a\,c}\,8{}\mathrm{i}\right)\,\left(-1+1{}\mathrm{i}\right)+\sqrt{2}\,\ln\left(\sqrt{2}\,\left(4-4{}\mathrm{i}\right)+{\mathrm{e}}^{b\,c\,x}\,{\mathrm{e}}^{a\,c}\,8{}\mathrm{i}\right)\,\left(1-\mathrm{i}\right)+\sqrt{2}\,\ln\left(\sqrt{2}\,\left(4+4{}\mathrm{i}\right)-{\mathrm{e}}^{b\,c\,x}\,{\mathrm{e}}^{a\,c}\,8{}\mathrm{i}\right)\,\left(1+1{}\mathrm{i}\right)}{4\,b\,c}","Not used",1,"(2^(1/2)*log(2^(1/2)*(4 - 4i) + exp(b*c*x)*exp(a*c)*8i)*(1 - 1i) - 2^(1/2)*log(exp(b*c*x)*exp(a*c)*8i - 2^(1/2)*(4 - 4i))*(1 - 1i) - 2^(1/2)*log(- 2^(1/2)*(4 + 4i) - exp(b*c*x)*exp(a*c)*8i)*(1 + 1i) + 2^(1/2)*log(2^(1/2)*(4 + 4i) - exp(b*c*x)*exp(a*c)*8i)*(1 + 1i) + 4*exp(a*c + b*c*x)*acot((exp(2*b*c*x)*exp(2*a*c) - 1)/(exp(2*b*c*x)*exp(2*a*c) + 1)))/(4*b*c)","B"
232,1,164,180,2.371706,"\text{Not used}","int(exp(c*(a + b*x))*acot(coth(a*c + b*c*x)),x)","\frac{4\,{\mathrm{e}}^{a\,c+b\,c\,x}\,\mathrm{acot}\left(\frac{{\mathrm{e}}^{2\,b\,c\,x}\,{\mathrm{e}}^{2\,a\,c}+1}{{\mathrm{e}}^{2\,b\,c\,x}\,{\mathrm{e}}^{2\,a\,c}-1}\right)+\sqrt{2}\,\ln\left(\sqrt{2}\,\left(-4-4{}\mathrm{i}\right)+{\mathrm{e}}^{b\,c\,x}\,{\mathrm{e}}^{a\,c}\,8{}\mathrm{i}\right)\,\left(-1-\mathrm{i}\right)+\sqrt{2}\,\ln\left(\sqrt{2}\,\left(-4+4{}\mathrm{i}\right)-{\mathrm{e}}^{b\,c\,x}\,{\mathrm{e}}^{a\,c}\,8{}\mathrm{i}\right)\,\left(-1+1{}\mathrm{i}\right)+\sqrt{2}\,\ln\left(\sqrt{2}\,\left(4-4{}\mathrm{i}\right)-{\mathrm{e}}^{b\,c\,x}\,{\mathrm{e}}^{a\,c}\,8{}\mathrm{i}\right)\,\left(1-\mathrm{i}\right)+\sqrt{2}\,\ln\left(\sqrt{2}\,\left(4+4{}\mathrm{i}\right)+{\mathrm{e}}^{b\,c\,x}\,{\mathrm{e}}^{a\,c}\,8{}\mathrm{i}\right)\,\left(1+1{}\mathrm{i}\right)}{4\,b\,c}","Not used",1,"(2^(1/2)*log(2^(1/2)*(4 - 4i) - exp(b*c*x)*exp(a*c)*8i)*(1 - 1i) - 2^(1/2)*log(- 2^(1/2)*(4 - 4i) - exp(b*c*x)*exp(a*c)*8i)*(1 - 1i) - 2^(1/2)*log(exp(b*c*x)*exp(a*c)*8i - 2^(1/2)*(4 + 4i))*(1 + 1i) + 2^(1/2)*log(2^(1/2)*(4 + 4i) + exp(b*c*x)*exp(a*c)*8i)*(1 + 1i) + 4*exp(a*c + b*c*x)*acot((exp(2*b*c*x)*exp(2*a*c) + 1)/(exp(2*b*c*x)*exp(2*a*c) - 1)))/(4*b*c)","B"
233,1,135,103,0.834970,"\text{Not used}","int(acot(1/cosh(a*c + b*c*x))*exp(c*(a + b*x)),x)","\frac{{\mathrm{e}}^{a\,c+b\,c\,x}\,\mathrm{acot}\left(\frac{1}{\frac{{\mathrm{e}}^{b\,c\,x}\,{\mathrm{e}}^{a\,c}}{2}+\frac{{\mathrm{e}}^{-b\,c\,x}\,{\mathrm{e}}^{-a\,c}}{2}}\right)}{b\,c}+\frac{\ln\left(-8\,{\mathrm{e}}^{2\,c\,\left(a+b\,x\right)}-2\,\sqrt{2}-6\,\sqrt{2}\,{\mathrm{e}}^{2\,c\,\left(a+b\,x\right)}\right)\,\left(\sqrt{2}-1\right)}{2\,b\,c}-\frac{\ln\left(2\,\sqrt{2}-8\,{\mathrm{e}}^{2\,c\,\left(a+b\,x\right)}+6\,\sqrt{2}\,{\mathrm{e}}^{2\,c\,\left(a+b\,x\right)}\right)\,\left(\sqrt{2}+1\right)}{2\,b\,c}","Not used",1,"(exp(a*c + b*c*x)*acot(1/((exp(b*c*x)*exp(a*c))/2 + (exp(-b*c*x)*exp(-a*c))/2)))/(b*c) + (log(- 8*exp(2*c*(a + b*x)) - 2*2^(1/2) - 6*2^(1/2)*exp(2*c*(a + b*x)))*(2^(1/2) - 1))/(2*b*c) - (log(2*2^(1/2) - 8*exp(2*c*(a + b*x)) + 6*2^(1/2)*exp(2*c*(a + b*x)))*(2^(1/2) + 1))/(2*b*c)","B"
234,1,68,48,0.706407,"\text{Not used}","int(acot(1/sinh(a*c + b*c*x))*exp(c*(a + b*x)),x)","\frac{{\mathrm{e}}^{b\,c\,x}\,{\mathrm{e}}^{a\,c}\,\mathrm{acot}\left(\frac{1}{\frac{{\mathrm{e}}^{b\,c\,x}\,{\mathrm{e}}^{a\,c}}{2}-\frac{{\mathrm{e}}^{-b\,c\,x}\,{\mathrm{e}}^{-a\,c}}{2}}\right)}{b\,c}-\frac{\ln\left({\mathrm{e}}^{2\,b\,c\,x}\,{\mathrm{e}}^{2\,a\,c}+1\right)}{b\,c}","Not used",1,"(exp(b*c*x)*exp(a*c)*acot(1/((exp(b*c*x)*exp(a*c))/2 - (exp(-b*c*x)*exp(-a*c))/2)))/(b*c) - log(exp(2*b*c*x)*exp(2*a*c) + 1)/(b*c)","B"