1,1,48,0,1.217780," ","integrate(x**5*acot(a*x),x)","\begin{cases} \frac{x^{6} \operatorname{acot}{\left(a x \right)}}{6} + \frac{x^{5}}{30 a} - \frac{x^{3}}{18 a^{3}} + \frac{x}{6 a^{5}} + \frac{\operatorname{acot}{\left(a x \right)}}{6 a^{6}} & \text{for}\: a \neq 0 \\\frac{\pi x^{6}}{12} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x**6*acot(a*x)/6 + x**5/(30*a) - x**3/(18*a**3) + x/(6*a**5) + acot(a*x)/(6*a**6), Ne(a, 0)), (pi*x**6/12, True))","A",0
2,1,46,0,0.874388," ","integrate(x**4*acot(a*x),x)","\begin{cases} \frac{x^{5} \operatorname{acot}{\left(a x \right)}}{5} + \frac{x^{4}}{20 a} - \frac{x^{2}}{10 a^{3}} + \frac{\log{\left(a^{2} x^{2} + 1 \right)}}{10 a^{5}} & \text{for}\: a \neq 0 \\\frac{\pi x^{5}}{10} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x**5*acot(a*x)/5 + x**4/(20*a) - x**2/(10*a**3) + log(a**2*x**2 + 1)/(10*a**5), Ne(a, 0)), (pi*x**5/10, True))","A",0
3,1,39,0,0.680308," ","integrate(x**3*acot(a*x),x)","\begin{cases} \frac{x^{4} \operatorname{acot}{\left(a x \right)}}{4} + \frac{x^{3}}{12 a} - \frac{x}{4 a^{3}} - \frac{\operatorname{acot}{\left(a x \right)}}{4 a^{4}} & \text{for}\: a \neq 0 \\\frac{\pi x^{4}}{8} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x**4*acot(a*x)/4 + x**3/(12*a) - x/(4*a**3) - acot(a*x)/(4*a**4), Ne(a, 0)), (pi*x**4/8, True))","A",0
4,1,37,0,0.476213," ","integrate(x**2*acot(a*x),x)","\begin{cases} \frac{x^{3} \operatorname{acot}{\left(a x \right)}}{3} + \frac{x^{2}}{6 a} - \frac{\log{\left(a^{2} x^{2} + 1 \right)}}{6 a^{3}} & \text{for}\: a \neq 0 \\\frac{\pi x^{3}}{6} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x**3*acot(a*x)/3 + x**2/(6*a) - log(a**2*x**2 + 1)/(6*a**3), Ne(a, 0)), (pi*x**3/6, True))","A",0
5,1,31,0,0.338527," ","integrate(x*acot(a*x),x)","\begin{cases} \frac{x^{2} \operatorname{acot}{\left(a x \right)}}{2} + \frac{x}{2 a} + \frac{\operatorname{acot}{\left(a x \right)}}{2 a^{2}} & \text{for}\: a \neq 0 \\\frac{\pi x^{2}}{4} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x**2*acot(a*x)/2 + x/(2*a) + acot(a*x)/(2*a**2), Ne(a, 0)), (pi*x**2/4, True))","A",0
6,1,24,0,0.214351," ","integrate(acot(a*x),x)","\begin{cases} x \operatorname{acot}{\left(a x \right)} + \frac{\log{\left(a^{2} x^{2} + 1 \right)}}{2 a} & \text{for}\: a \neq 0 \\\frac{\pi x}{2} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x*acot(a*x) + log(a**2*x**2 + 1)/(2*a), Ne(a, 0)), (pi*x/2, True))","A",0
7,0,0,0,0.000000," ","integrate(acot(a*x)/x,x)","\int \frac{\operatorname{acot}{\left(a x \right)}}{x}\, dx"," ",0,"Integral(acot(a*x)/x, x)","F",0
8,1,24,0,0.283376," ","integrate(acot(a*x)/x**2,x)","- a \log{\left(x \right)} + \frac{a \log{\left(a^{2} x^{2} + 1 \right)}}{2} - \frac{\operatorname{acot}{\left(a x \right)}}{x}"," ",0,"-a*log(x) + a*log(a**2*x**2 + 1)/2 - acot(a*x)/x","A",0
9,1,24,0,0.477321," ","integrate(acot(a*x)/x**3,x)","- \frac{a^{2} \operatorname{acot}{\left(a x \right)}}{2} + \frac{a}{2 x} - \frac{\operatorname{acot}{\left(a x \right)}}{2 x^{2}}"," ",0,"-a**2*acot(a*x)/2 + a/(2*x) - acot(a*x)/(2*x**2)","A",0
10,1,39,0,0.591851," ","integrate(acot(a*x)/x**4,x)","\frac{a^{3} \log{\left(x \right)}}{3} - \frac{a^{3} \log{\left(a^{2} x^{2} + 1 \right)}}{6} + \frac{a}{6 x^{2}} - \frac{\operatorname{acot}{\left(a x \right)}}{3 x^{3}}"," ",0,"a**3*log(x)/3 - a**3*log(a**2*x**2 + 1)/6 + a/(6*x**2) - acot(a*x)/(3*x**3)","A",0
11,1,32,0,0.749327," ","integrate(acot(a*x)/x**5,x)","\frac{a^{4} \operatorname{acot}{\left(a x \right)}}{4} - \frac{a^{3}}{4 x} + \frac{a}{12 x^{3}} - \frac{\operatorname{acot}{\left(a x \right)}}{4 x^{4}}"," ",0,"a**4*acot(a*x)/4 - a**3/(4*x) + a/(12*x**3) - acot(a*x)/(4*x**4)","A",0
12,1,104,0,1.763408," ","integrate(x**5*acot(a*x)**2,x)","\begin{cases} \frac{x^{6} \operatorname{acot}^{2}{\left(a x \right)}}{6} + \frac{x^{5} \operatorname{acot}{\left(a x \right)}}{15 a} + \frac{x^{4}}{60 a^{2}} - \frac{x^{3} \operatorname{acot}{\left(a x \right)}}{9 a^{3}} - \frac{4 x^{2}}{45 a^{4}} + \frac{x \operatorname{acot}{\left(a x \right)}}{3 a^{5}} + \frac{23 \log{\left(a^{2} x^{2} + 1 \right)}}{90 a^{6}} + \frac{\operatorname{acot}^{2}{\left(a x \right)}}{6 a^{6}} & \text{for}\: a \neq 0 \\\frac{\pi^{2} x^{6}}{24} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x**6*acot(a*x)**2/6 + x**5*acot(a*x)/(15*a) + x**4/(60*a**2) - x**3*acot(a*x)/(9*a**3) - 4*x**2/(45*a**4) + x*acot(a*x)/(3*a**5) + 23*log(a**2*x**2 + 1)/(90*a**6) + acot(a*x)**2/(6*a**6), Ne(a, 0)), (pi**2*x**6/24, True))","A",0
13,0,0,0,0.000000," ","integrate(x**4*acot(a*x)**2,x)","\int x^{4} \operatorname{acot}^{2}{\left(a x \right)}\, dx"," ",0,"Integral(x**4*acot(a*x)**2, x)","F",0
14,1,78,0,1.034830," ","integrate(x**3*acot(a*x)**2,x)","\begin{cases} \frac{x^{4} \operatorname{acot}^{2}{\left(a x \right)}}{4} + \frac{x^{3} \operatorname{acot}{\left(a x \right)}}{6 a} + \frac{x^{2}}{12 a^{2}} - \frac{x \operatorname{acot}{\left(a x \right)}}{2 a^{3}} - \frac{\log{\left(a^{2} x^{2} + 1 \right)}}{3 a^{4}} - \frac{\operatorname{acot}^{2}{\left(a x \right)}}{4 a^{4}} & \text{for}\: a \neq 0 \\\frac{\pi^{2} x^{4}}{16} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x**4*acot(a*x)**2/4 + x**3*acot(a*x)/(6*a) + x**2/(12*a**2) - x*acot(a*x)/(2*a**3) - log(a**2*x**2 + 1)/(3*a**4) - acot(a*x)**2/(4*a**4), Ne(a, 0)), (pi**2*x**4/16, True))","A",0
15,0,0,0,0.000000," ","integrate(x**2*acot(a*x)**2,x)","\int x^{2} \operatorname{acot}^{2}{\left(a x \right)}\, dx"," ",0,"Integral(x**2*acot(a*x)**2, x)","F",0
16,1,54,0,0.480015," ","integrate(x*acot(a*x)**2,x)","\begin{cases} \frac{x^{2} \operatorname{acot}^{2}{\left(a x \right)}}{2} + \frac{x \operatorname{acot}{\left(a x \right)}}{a} + \frac{\log{\left(a^{2} x^{2} + 1 \right)}}{2 a^{2}} + \frac{\operatorname{acot}^{2}{\left(a x \right)}}{2 a^{2}} & \text{for}\: a \neq 0 \\\frac{\pi^{2} x^{2}}{8} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x**2*acot(a*x)**2/2 + x*acot(a*x)/a + log(a**2*x**2 + 1)/(2*a**2) + acot(a*x)**2/(2*a**2), Ne(a, 0)), (pi**2*x**2/8, True))","A",0
17,0,0,0,0.000000," ","integrate(acot(a*x)**2,x)","\int \operatorname{acot}^{2}{\left(a x \right)}\, dx"," ",0,"Integral(acot(a*x)**2, x)","F",0
18,0,0,0,0.000000," ","integrate(acot(a*x)**2/x,x)","\int \frac{\operatorname{acot}^{2}{\left(a x \right)}}{x}\, dx"," ",0,"Integral(acot(a*x)**2/x, x)","F",0
19,0,0,0,0.000000," ","integrate(acot(a*x)**2/x**2,x)","\int \frac{\operatorname{acot}^{2}{\left(a x \right)}}{x^{2}}\, dx"," ",0,"Integral(acot(a*x)**2/x**2, x)","F",0
20,1,53,0,0.502018," ","integrate(acot(a*x)**2/x**3,x)","a^{2} \log{\left(x \right)} - \frac{a^{2} \log{\left(a^{2} x^{2} + 1 \right)}}{2} - \frac{a^{2} \operatorname{acot}^{2}{\left(a x \right)}}{2} + \frac{a \operatorname{acot}{\left(a x \right)}}{x} - \frac{\operatorname{acot}^{2}{\left(a x \right)}}{2 x^{2}}"," ",0,"a**2*log(x) - a**2*log(a**2*x**2 + 1)/2 - a**2*acot(a*x)**2/2 + a*acot(a*x)/x - acot(a*x)**2/(2*x**2)","A",0
21,0,0,0,0.000000," ","integrate(acot(a*x)**2/x**4,x)","\int \frac{\operatorname{acot}^{2}{\left(a x \right)}}{x^{4}}\, dx"," ",0,"Integral(acot(a*x)**2/x**4, x)","F",0
22,1,80,0,0.814071," ","integrate(acot(a*x)**2/x**5,x)","- \frac{2 a^{4} \log{\left(x \right)}}{3} + \frac{a^{4} \log{\left(a^{2} x^{2} + 1 \right)}}{3} + \frac{a^{4} \operatorname{acot}^{2}{\left(a x \right)}}{4} - \frac{a^{3} \operatorname{acot}{\left(a x \right)}}{2 x} - \frac{a^{2}}{12 x^{2}} + \frac{a \operatorname{acot}{\left(a x \right)}}{6 x^{3}} - \frac{\operatorname{acot}^{2}{\left(a x \right)}}{4 x^{4}}"," ",0,"-2*a**4*log(x)/3 + a**4*log(a**2*x**2 + 1)/3 + a**4*acot(a*x)**2/4 - a**3*acot(a*x)/(2*x) - a**2/(12*x**2) + a*acot(a*x)/(6*x**3) - acot(a*x)**2/(4*x**4)","A",0
23,0,0,0,0.000000," ","integrate(x**5*acot(a*x)**3,x)","\int x^{5} \operatorname{acot}^{3}{\left(a x \right)}\, dx"," ",0,"Integral(x**5*acot(a*x)**3, x)","F",0
24,0,0,0,0.000000," ","integrate(x**4*acot(a*x)**3,x)","\int x^{4} \operatorname{acot}^{3}{\left(a x \right)}\, dx"," ",0,"Integral(x**4*acot(a*x)**3, x)","F",0
25,0,0,0,0.000000," ","integrate(x**3*acot(a*x)**3,x)","\int x^{3} \operatorname{acot}^{3}{\left(a x \right)}\, dx"," ",0,"Integral(x**3*acot(a*x)**3, x)","F",0
26,0,0,0,0.000000," ","integrate(x**2*acot(a*x)**3,x)","\int x^{2} \operatorname{acot}^{3}{\left(a x \right)}\, dx"," ",0,"Integral(x**2*acot(a*x)**3, x)","F",0
27,0,0,0,0.000000," ","integrate(x*acot(a*x)**3,x)","\int x \operatorname{acot}^{3}{\left(a x \right)}\, dx"," ",0,"Integral(x*acot(a*x)**3, x)","F",0
28,0,0,0,0.000000," ","integrate(acot(a*x)**3,x)","\int \operatorname{acot}^{3}{\left(a x \right)}\, dx"," ",0,"Integral(acot(a*x)**3, x)","F",0
29,0,0,0,0.000000," ","integrate(acot(a*x)**3/x,x)","\int \frac{\operatorname{acot}^{3}{\left(a x \right)}}{x}\, dx"," ",0,"Integral(acot(a*x)**3/x, x)","F",0
30,0,0,0,0.000000," ","integrate(acot(a*x)**3/x**2,x)","\int \frac{\operatorname{acot}^{3}{\left(a x \right)}}{x^{2}}\, dx"," ",0,"Integral(acot(a*x)**3/x**2, x)","F",0
31,0,0,0,0.000000," ","integrate(acot(a*x)**3/x**3,x)","\int \frac{\operatorname{acot}^{3}{\left(a x \right)}}{x^{3}}\, dx"," ",0,"Integral(acot(a*x)**3/x**3, x)","F",0
32,0,0,0,0.000000," ","integrate(acot(a*x)**3/x**4,x)","\int \frac{\operatorname{acot}^{3}{\left(a x \right)}}{x^{4}}\, dx"," ",0,"Integral(acot(a*x)**3/x**4, x)","F",0
33,0,0,0,0.000000," ","integrate(acot(a*x)**3/x**5,x)","\int \frac{\operatorname{acot}^{3}{\left(a x \right)}}{x^{5}}\, dx"," ",0,"Integral(acot(a*x)**3/x**5, x)","F",0
34,0,0,0,0.000000," ","integrate(x**m*acot(a*x)**3,x)","\int x^{m} \operatorname{acot}^{3}{\left(a x \right)}\, dx"," ",0,"Integral(x**m*acot(a*x)**3, x)","F",0
35,0,0,0,0.000000," ","integrate(x**m*acot(a*x)**2,x)","\int x^{m} \operatorname{acot}^{2}{\left(a x \right)}\, dx"," ",0,"Integral(x**m*acot(a*x)**2, x)","F",0
36,0,0,0,0.000000," ","integrate(x**m*acot(a*x),x)","\int x^{m} \operatorname{acot}{\left(a x \right)}\, dx"," ",0,"Integral(x**m*acot(a*x), x)","F",0
37,1,34,0,0.506013," ","integrate(x**4*acot(x)/(x**2+1),x)","\frac{x^{3} \operatorname{acot}{\left(x \right)}}{3} + \frac{x^{2}}{6} - x \operatorname{acot}{\left(x \right)} - \frac{2 \log{\left(x^{2} + 1 \right)}}{3} - \frac{\operatorname{acot}^{2}{\left(x \right)}}{2}"," ",0,"x**3*acot(x)/3 + x**2/6 - x*acot(x) - 2*log(x**2 + 1)/3 - acot(x)**2/2","A",0
38,0,0,0,0.000000," ","integrate(x**3*acot(x)/(x**2+1),x)","\int \frac{x^{3} \operatorname{acot}{\left(x \right)}}{x^{2} + 1}\, dx"," ",0,"Integral(x**3*acot(x)/(x**2 + 1), x)","F",0
39,1,19,0,0.296146," ","integrate(x**2*acot(x)/(x**2+1),x)","x \operatorname{acot}{\left(x \right)} + \frac{\log{\left(x^{2} + 1 \right)}}{2} + \frac{\operatorname{acot}^{2}{\left(x \right)}}{2}"," ",0,"x*acot(x) + log(x**2 + 1)/2 + acot(x)**2/2","A",0
40,0,0,0,0.000000," ","integrate(x*acot(x)/(x**2+1),x)","\int \frac{x \operatorname{acot}{\left(x \right)}}{x^{2} + 1}\, dx"," ",0,"Integral(x*acot(x)/(x**2 + 1), x)","F",0
41,1,7,0,0.876553," ","integrate(acot(x)/(x**2+1),x)","- \frac{\operatorname{acot}^{2}{\left(x \right)}}{2}"," ",0,"-acot(x)**2/2","A",0
42,0,0,0,0.000000," ","integrate(acot(x)/x/(x**2+1),x)","\int \frac{\operatorname{acot}{\left(x \right)}}{x \left(x^{2} + 1\right)}\, dx"," ",0,"Integral(acot(x)/(x*(x**2 + 1)), x)","F",0
43,1,22,0,0.432523," ","integrate(acot(x)/x**2/(x**2+1),x)","- \log{\left(x \right)} + \frac{\log{\left(x^{2} + 1 \right)}}{2} + \frac{\operatorname{acot}^{2}{\left(x \right)}}{2} - \frac{\operatorname{acot}{\left(x \right)}}{x}"," ",0,"-log(x) + log(x**2 + 1)/2 + acot(x)**2/2 - acot(x)/x","A",0
44,0,0,0,0.000000," ","integrate(acot(x)/x**3/(x**2+1),x)","\int \frac{\operatorname{acot}{\left(x \right)}}{x^{3} \left(x^{2} + 1\right)}\, dx"," ",0,"Integral(acot(x)/(x**3*(x**2 + 1)), x)","F",0
45,1,42,0,0.847520," ","integrate(acot(x)/x**4/(x**2+1),x)","\frac{4 \log{\left(x \right)}}{3} - \frac{2 \log{\left(x^{2} + 1 \right)}}{3} - \frac{\operatorname{acot}^{2}{\left(x \right)}}{2} + \frac{\operatorname{acot}{\left(x \right)}}{x} + \frac{1}{6 x^{2}} - \frac{\operatorname{acot}{\left(x \right)}}{3 x^{3}}"," ",0,"4*log(x)/3 - 2*log(x**2 + 1)/3 - acot(x)**2/2 + acot(x)/x + 1/(6*x**2) - acot(x)/(3*x**3)","A",0
46,0,0,0,0.000000," ","integrate(x**2*acot(c*x)/(x**2+1),x)","\int \frac{x^{2} \operatorname{acot}{\left(c x \right)}}{x^{2} + 1}\, dx"," ",0,"Integral(x**2*acot(c*x)/(x**2 + 1), x)","F",0
47,0,0,0,0.000000," ","integrate(x*acot(c*x)/(x**2+1),x)","\int \frac{x \operatorname{acot}{\left(c x \right)}}{x^{2} + 1}\, dx"," ",0,"Integral(x*acot(c*x)/(x**2 + 1), x)","F",0
48,0,0,0,0.000000," ","integrate(acot(c*x)/(x**2+1),x)","\int \frac{\operatorname{acot}{\left(c x \right)}}{x^{2} + 1}\, dx"," ",0,"Integral(acot(c*x)/(x**2 + 1), x)","F",0
49,0,0,0,0.000000," ","integrate(acot(c*x)/x/(x**2+1),x)","\int \frac{\operatorname{acot}{\left(c x \right)}}{x \left(x^{2} + 1\right)}\, dx"," ",0,"Integral(acot(c*x)/(x*(x**2 + 1)), x)","F",0
50,0,0,0,0.000000," ","integrate(acot(c*x)/x**2/(x**2+1),x)","\int \frac{\operatorname{acot}{\left(c x \right)}}{x^{2} \left(x^{2} + 1\right)}\, dx"," ",0,"Integral(acot(c*x)/(x**2*(x**2 + 1)), x)","F",0
51,1,5,0,0.243093," ","integrate(1/(x**2+1)/acot(x),x)","- \log{\left(\operatorname{acot}{\left(x \right)} \right)}"," ",0,"-log(acot(x))","A",0
52,1,17,0,1.447146," ","integrate(acot(x)**n/(x**2+1),x)","- \begin{cases} \frac{\operatorname{acot}^{n + 1}{\left(x \right)}}{n + 1} & \text{for}\: n \neq -1 \\\log{\left(\operatorname{acot}{\left(x \right)} \right)} & \text{otherwise} \end{cases}"," ",0,"-Piecewise((acot(x)**(n + 1)/(n + 1), Ne(n, -1)), (log(acot(x)), True))","A",0
53,1,367,0,4.358967," ","integrate((d*x**2+c)**4*acot(a*x),x)","\begin{cases} c^{4} x \operatorname{acot}{\left(a x \right)} + \frac{4 c^{3} d x^{3} \operatorname{acot}{\left(a x \right)}}{3} + \frac{6 c^{2} d^{2} x^{5} \operatorname{acot}{\left(a x \right)}}{5} + \frac{4 c d^{3} x^{7} \operatorname{acot}{\left(a x \right)}}{7} + \frac{d^{4} x^{9} \operatorname{acot}{\left(a x \right)}}{9} + \frac{c^{4} \log{\left(x^{2} + \frac{1}{a^{2}} \right)}}{2 a} + \frac{2 c^{3} d x^{2}}{3 a} + \frac{3 c^{2} d^{2} x^{4}}{10 a} + \frac{2 c d^{3} x^{6}}{21 a} + \frac{d^{4} x^{8}}{72 a} - \frac{2 c^{3} d \log{\left(x^{2} + \frac{1}{a^{2}} \right)}}{3 a^{3}} - \frac{3 c^{2} d^{2} x^{2}}{5 a^{3}} - \frac{c d^{3} x^{4}}{7 a^{3}} - \frac{d^{4} x^{6}}{54 a^{3}} + \frac{3 c^{2} d^{2} \log{\left(x^{2} + \frac{1}{a^{2}} \right)}}{5 a^{5}} + \frac{2 c d^{3} x^{2}}{7 a^{5}} + \frac{d^{4} x^{4}}{36 a^{5}} - \frac{2 c d^{3} \log{\left(x^{2} + \frac{1}{a^{2}} \right)}}{7 a^{7}} - \frac{d^{4} x^{2}}{18 a^{7}} + \frac{d^{4} \log{\left(x^{2} + \frac{1}{a^{2}} \right)}}{18 a^{9}} & \text{for}\: a \neq 0 \\\frac{\pi \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)}{2} & \text{otherwise} \end{cases}"," ",0,"Piecewise((c**4*x*acot(a*x) + 4*c**3*d*x**3*acot(a*x)/3 + 6*c**2*d**2*x**5*acot(a*x)/5 + 4*c*d**3*x**7*acot(a*x)/7 + d**4*x**9*acot(a*x)/9 + c**4*log(x**2 + a**(-2))/(2*a) + 2*c**3*d*x**2/(3*a) + 3*c**2*d**2*x**4/(10*a) + 2*c*d**3*x**6/(21*a) + d**4*x**8/(72*a) - 2*c**3*d*log(x**2 + a**(-2))/(3*a**3) - 3*c**2*d**2*x**2/(5*a**3) - c*d**3*x**4/(7*a**3) - d**4*x**6/(54*a**3) + 3*c**2*d**2*log(x**2 + a**(-2))/(5*a**5) + 2*c*d**3*x**2/(7*a**5) + d**4*x**4/(36*a**5) - 2*c*d**3*log(x**2 + a**(-2))/(7*a**7) - d**4*x**2/(18*a**7) + d**4*log(x**2 + a**(-2))/(18*a**9), Ne(a, 0)), (pi*(c**4*x + 4*c**3*d*x**3/3 + 6*c**2*d**2*x**5/5 + 4*c*d**3*x**7/7 + d**4*x**9/9)/2, True))","A",0
54,1,243,0,2.500512," ","integrate((d*x**2+c)**3*acot(a*x),x)","\begin{cases} c^{3} x \operatorname{acot}{\left(a x \right)} + c^{2} d x^{3} \operatorname{acot}{\left(a x \right)} + \frac{3 c d^{2} x^{5} \operatorname{acot}{\left(a x \right)}}{5} + \frac{d^{3} x^{7} \operatorname{acot}{\left(a x \right)}}{7} + \frac{c^{3} \log{\left(x^{2} + \frac{1}{a^{2}} \right)}}{2 a} + \frac{c^{2} d x^{2}}{2 a} + \frac{3 c d^{2} x^{4}}{20 a} + \frac{d^{3} x^{6}}{42 a} - \frac{c^{2} d \log{\left(x^{2} + \frac{1}{a^{2}} \right)}}{2 a^{3}} - \frac{3 c d^{2} x^{2}}{10 a^{3}} - \frac{d^{3} x^{4}}{28 a^{3}} + \frac{3 c d^{2} \log{\left(x^{2} + \frac{1}{a^{2}} \right)}}{10 a^{5}} + \frac{d^{3} x^{2}}{14 a^{5}} - \frac{d^{3} \log{\left(x^{2} + \frac{1}{a^{2}} \right)}}{14 a^{7}} & \text{for}\: a \neq 0 \\\frac{\pi \left(c^{3} x + c^{2} d x^{3} + \frac{3 c d^{2} x^{5}}{5} + \frac{d^{3} x^{7}}{7}\right)}{2} & \text{otherwise} \end{cases}"," ",0,"Piecewise((c**3*x*acot(a*x) + c**2*d*x**3*acot(a*x) + 3*c*d**2*x**5*acot(a*x)/5 + d**3*x**7*acot(a*x)/7 + c**3*log(x**2 + a**(-2))/(2*a) + c**2*d*x**2/(2*a) + 3*c*d**2*x**4/(20*a) + d**3*x**6/(42*a) - c**2*d*log(x**2 + a**(-2))/(2*a**3) - 3*c*d**2*x**2/(10*a**3) - d**3*x**4/(28*a**3) + 3*c*d**2*log(x**2 + a**(-2))/(10*a**5) + d**3*x**2/(14*a**5) - d**3*log(x**2 + a**(-2))/(14*a**7), Ne(a, 0)), (pi*(c**3*x + c**2*d*x**3 + 3*c*d**2*x**5/5 + d**3*x**7/7)/2, True))","A",0
55,1,151,0,1.361218," ","integrate((d*x**2+c)**2*acot(a*x),x)","\begin{cases} c^{2} x \operatorname{acot}{\left(a x \right)} + \frac{2 c d x^{3} \operatorname{acot}{\left(a x \right)}}{3} + \frac{d^{2} x^{5} \operatorname{acot}{\left(a x \right)}}{5} + \frac{c^{2} \log{\left(x^{2} + \frac{1}{a^{2}} \right)}}{2 a} + \frac{c d x^{2}}{3 a} + \frac{d^{2} x^{4}}{20 a} - \frac{c d \log{\left(x^{2} + \frac{1}{a^{2}} \right)}}{3 a^{3}} - \frac{d^{2} x^{2}}{10 a^{3}} + \frac{d^{2} \log{\left(x^{2} + \frac{1}{a^{2}} \right)}}{10 a^{5}} & \text{for}\: a \neq 0 \\\frac{\pi \left(c^{2} x + \frac{2 c d x^{3}}{3} + \frac{d^{2} x^{5}}{5}\right)}{2} & \text{otherwise} \end{cases}"," ",0,"Piecewise((c**2*x*acot(a*x) + 2*c*d*x**3*acot(a*x)/3 + d**2*x**5*acot(a*x)/5 + c**2*log(x**2 + a**(-2))/(2*a) + c*d*x**2/(3*a) + d**2*x**4/(20*a) - c*d*log(x**2 + a**(-2))/(3*a**3) - d**2*x**2/(10*a**3) + d**2*log(x**2 + a**(-2))/(10*a**5), Ne(a, 0)), (pi*(c**2*x + 2*c*d*x**3/3 + d**2*x**5/5)/2, True))","A",0
56,1,73,0,0.617171," ","integrate((d*x**2+c)*acot(a*x),x)","\begin{cases} c x \operatorname{acot}{\left(a x \right)} + \frac{d x^{3} \operatorname{acot}{\left(a x \right)}}{3} + \frac{c \log{\left(x^{2} + \frac{1}{a^{2}} \right)}}{2 a} + \frac{d x^{2}}{6 a} - \frac{d \log{\left(x^{2} + \frac{1}{a^{2}} \right)}}{6 a^{3}} & \text{for}\: a \neq 0 \\\frac{\pi \left(c x + \frac{d x^{3}}{3}\right)}{2} & \text{otherwise} \end{cases}"," ",0,"Piecewise((c*x*acot(a*x) + d*x**3*acot(a*x)/3 + c*log(x**2 + a**(-2))/(2*a) + d*x**2/(6*a) - d*log(x**2 + a**(-2))/(6*a**3), Ne(a, 0)), (pi*(c*x + d*x**3/3)/2, True))","A",0
57,0,0,0,0.000000," ","integrate(acot(a*x)/(d*x**2+c),x)","\int \frac{\operatorname{acot}{\left(a x \right)}}{c + d x^{2}}\, dx"," ",0,"Integral(acot(a*x)/(c + d*x**2), x)","F",0
58,-1,0,0,0.000000," ","integrate(acot(a*x)/(d*x**2+c)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
59,0,0,0,0.000000," ","integrate((d*x**2+c)**(1/2)*acot(a*x),x)","\int \sqrt{c + d x^{2}} \operatorname{acot}{\left(a x \right)}\, dx"," ",0,"Integral(sqrt(c + d*x**2)*acot(a*x), x)","F",0
60,0,0,0,0.000000," ","integrate(acot(a*x)/(d*x**2+c)**(1/2),x)","\int \frac{\operatorname{acot}{\left(a x \right)}}{\sqrt{c + d x^{2}}}\, dx"," ",0,"Integral(acot(a*x)/sqrt(c + d*x**2), x)","F",0
61,0,0,0,0.000000," ","integrate(acot(a*x)/(d*x**2+c)**(3/2),x)","\int \frac{\operatorname{acot}{\left(a x \right)}}{\left(c + d x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(acot(a*x)/(c + d*x**2)**(3/2), x)","F",0
62,0,0,0,0.000000," ","integrate(acot(a*x)/(d*x**2+c)**(5/2),x)","\int \frac{\operatorname{acot}{\left(a x \right)}}{\left(c + d x^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(acot(a*x)/(c + d*x**2)**(5/2), x)","F",0
63,0,0,0,0.000000," ","integrate(acot(a*x)/(d*x**2+c)**(7/2),x)","\int \frac{\operatorname{acot}{\left(a x \right)}}{\left(c + d x^{2}\right)^{\frac{7}{2}}}\, dx"," ",0,"Integral(acot(a*x)/(c + d*x**2)**(7/2), x)","F",0
64,0,0,0,0.000000," ","integrate(acot(a*x)/(d*x**2+c)**(9/2),x)","\int \frac{\operatorname{acot}{\left(a x \right)}}{\left(c + d x^{2}\right)^{\frac{9}{2}}}\, dx"," ",0,"Integral(acot(a*x)/(c + d*x**2)**(9/2), x)","F",0
65,0,0,0,0.000000," ","integrate((a*x**2+a)**(1/2)*acot(x),x)","\int \sqrt{a \left(x^{2} + 1\right)} \operatorname{acot}{\left(x \right)}\, dx"," ",0,"Integral(sqrt(a*(x**2 + 1))*acot(x), x)","F",0
66,0,0,0,0.000000," ","integrate(acot(x)/(a*x**2+a)**(1/2),x)","\int \frac{\operatorname{acot}{\left(x \right)}}{\sqrt{a \left(x^{2} + 1\right)}}\, dx"," ",0,"Integral(acot(x)/sqrt(a*(x**2 + 1)), x)","F",0
67,0,0,0,0.000000," ","integrate(acot(x)/(a*x**2+a)**(3/2),x)","\int \frac{\operatorname{acot}{\left(x \right)}}{\left(a \left(x^{2} + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(acot(x)/(a*(x**2 + 1))**(3/2), x)","F",0
68,0,0,0,0.000000," ","integrate(acot(x)/(a*x**2+a)**(5/2),x)","\int \frac{\operatorname{acot}{\left(x \right)}}{\left(a \left(x^{2} + 1\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(acot(x)/(a*(x**2 + 1))**(5/2), x)","F",0
69,0,0,0,0.000000," ","integrate(acot(x)/(a*x**2+a)**(7/2),x)","\int \frac{\operatorname{acot}{\left(x \right)}}{\left(a \left(x^{2} + 1\right)\right)^{\frac{7}{2}}}\, dx"," ",0,"Integral(acot(x)/(a*(x**2 + 1))**(7/2), x)","F",0
70,1,31,0,0.496572," ","integrate(x*acot(x)/(x**2+1)**2,x)","\frac{x^{2} \operatorname{acot}{\left(x \right)}}{4 x^{2} + 4} - \frac{x}{4 x^{2} + 4} - \frac{\operatorname{acot}{\left(x \right)}}{4 x^{2} + 4}"," ",0,"x**2*acot(x)/(4*x**2 + 4) - x/(4*x**2 + 4) - acot(x)/(4*x**2 + 4)","A",0
71,1,88,0,0.797361," ","integrate(x*acot(x)/(x**2+1)**3,x)","\frac{3 x^{4} \operatorname{acot}{\left(x \right)}}{32 x^{4} + 64 x^{2} + 32} - \frac{3 x^{3}}{32 x^{4} + 64 x^{2} + 32} + \frac{6 x^{2} \operatorname{acot}{\left(x \right)}}{32 x^{4} + 64 x^{2} + 32} - \frac{5 x}{32 x^{4} + 64 x^{2} + 32} - \frac{5 \operatorname{acot}{\left(x \right)}}{32 x^{4} + 64 x^{2} + 32}"," ",0,"3*x**4*acot(x)/(32*x**4 + 64*x**2 + 32) - 3*x**3/(32*x**4 + 64*x**2 + 32) + 6*x**2*acot(x)/(32*x**4 + 64*x**2 + 32) - 5*x/(32*x**4 + 64*x**2 + 32) - 5*acot(x)/(32*x**4 + 64*x**2 + 32)","B",0
72,-2,0,0,0.000000," ","integrate(acot(x)/(x**2+1)**2,x)","\text{Exception raised: RecursionError}"," ",0,"Exception raised: RecursionError","F(-2)",0
73,0,0,0,0.000000," ","integrate(acot(x)**2/(x**2+1)**2,x)","\int \frac{\operatorname{acot}^{2}{\left(x \right)}}{\left(x^{2} + 1\right)^{2}}\, dx"," ",0,"Integral(acot(x)**2/(x**2 + 1)**2, x)","F",0
74,1,39,0,1.781004," ","integrate(x**5*acot(a*x**2),x)","\begin{cases} \frac{x^{6} \operatorname{acot}{\left(a x^{2} \right)}}{6} + \frac{x^{4}}{12 a} - \frac{\log{\left(a^{2} x^{4} + 1 \right)}}{12 a^{3}} & \text{for}\: a \neq 0 \\\frac{\pi x^{6}}{12} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x**6*acot(a*x**2)/6 + x**4/(12*a) - log(a**2*x**4 + 1)/(12*a**3), Ne(a, 0)), (pi*x**6/12, True))","A",0
75,1,36,0,1.033419," ","integrate(x**3*acot(a*x**2),x)","\begin{cases} \frac{x^{4} \operatorname{acot}{\left(a x^{2} \right)}}{4} + \frac{x^{2}}{4 a} + \frac{\operatorname{acot}{\left(a x^{2} \right)}}{4 a^{2}} & \text{for}\: a \neq 0 \\\frac{\pi x^{4}}{8} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x**4*acot(a*x**2)/4 + x**2/(4*a) + acot(a*x**2)/(4*a**2), Ne(a, 0)), (pi*x**4/8, True))","A",0
76,1,31,0,0.581081," ","integrate(x*acot(a*x**2),x)","\begin{cases} \frac{x^{2} \operatorname{acot}{\left(a x^{2} \right)}}{2} + \frac{\log{\left(a^{2} x^{4} + 1 \right)}}{4 a} & \text{for}\: a \neq 0 \\\frac{\pi x^{2}}{4} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x**2*acot(a*x**2)/2 + log(a**2*x**4 + 1)/(4*a), Ne(a, 0)), (pi*x**2/4, True))","A",0
77,0,0,0,0.000000," ","integrate(acot(a*x**2)/x,x)","\int \frac{\operatorname{acot}{\left(a x^{2} \right)}}{x}\, dx"," ",0,"Integral(acot(a*x**2)/x, x)","F",0
78,1,29,0,0.696105," ","integrate(acot(a*x**2)/x**3,x)","- a \log{\left(x \right)} + \frac{a \log{\left(a^{2} x^{4} + 1 \right)}}{4} - \frac{\operatorname{acot}{\left(a x^{2} \right)}}{2 x^{2}}"," ",0,"-a*log(x) + a*log(a**2*x**4 + 1)/4 - acot(a*x**2)/(2*x**2)","A",0
79,1,29,0,1.045095," ","integrate(acot(a*x**2)/x**5,x)","- \frac{a^{2} \operatorname{acot}{\left(a x^{2} \right)}}{4} + \frac{a}{4 x^{2}} - \frac{\operatorname{acot}{\left(a x^{2} \right)}}{4 x^{4}}"," ",0,"-a**2*acot(a*x**2)/4 + a/(4*x**2) - acot(a*x**2)/(4*x**4)","A",0
80,1,167,0,30.120550," ","integrate(x**4*acot(a*x**2),x)","\begin{cases} \frac{x^{5} \operatorname{acot}{\left(a x^{2} \right)}}{5} + \frac{2 x^{3}}{15 a} - \frac{\sqrt[4]{-1} \sqrt[4]{\frac{1}{a^{2}}} \operatorname{acot}{\left(a x^{2} \right)}}{5 a^{2}} + \frac{\left(-1\right)^{\frac{3}{4}} \log{\left(x - \sqrt[4]{-1} \sqrt[4]{\frac{1}{a^{2}}} \right)}}{5 a^{3} \sqrt[4]{\frac{1}{a^{2}}}} - \frac{\left(-1\right)^{\frac{3}{4}} \log{\left(x^{2} + i \sqrt{\frac{1}{a^{2}}} \right)}}{10 a^{3} \sqrt[4]{\frac{1}{a^{2}}}} - \frac{\left(-1\right)^{\frac{3}{4}} \operatorname{atan}{\left(\frac{\left(-1\right)^{\frac{3}{4}} x}{\sqrt[4]{\frac{1}{a^{2}}}} \right)}}{5 a^{3} \sqrt[4]{\frac{1}{a^{2}}}} & \text{for}\: a \neq 0 \\\frac{\pi x^{5}}{10} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x**5*acot(a*x**2)/5 + 2*x**3/(15*a) - (-1)**(1/4)*(a**(-2))**(1/4)*acot(a*x**2)/(5*a**2) + (-1)**(3/4)*log(x - (-1)**(1/4)*(a**(-2))**(1/4))/(5*a**3*(a**(-2))**(1/4)) - (-1)**(3/4)*log(x**2 + I*sqrt(a**(-2)))/(10*a**3*(a**(-2))**(1/4)) - (-1)**(3/4)*atan((-1)**(3/4)*x/(a**(-2))**(1/4))/(5*a**3*(a**(-2))**(1/4)), Ne(a, 0)), (pi*x**5/10, True))","A",0
81,1,156,0,17.159930," ","integrate(x**2*acot(a*x**2),x)","\begin{cases} \frac{x^{3} \operatorname{acot}{\left(a x^{2} \right)}}{3} + \frac{\left(-1\right)^{\frac{3}{4}} \left(\frac{1}{a^{2}}\right)^{\frac{3}{4}} \operatorname{acot}{\left(a x^{2} \right)}}{3} + \frac{2 x}{3 a} + \frac{\sqrt[4]{-1} \sqrt[4]{\frac{1}{a^{2}}} \log{\left(x - \sqrt[4]{-1} \sqrt[4]{\frac{1}{a^{2}}} \right)}}{3 a} - \frac{\sqrt[4]{-1} \sqrt[4]{\frac{1}{a^{2}}} \log{\left(x^{2} + i \sqrt{\frac{1}{a^{2}}} \right)}}{6 a} + \frac{\sqrt[4]{-1} \sqrt[4]{\frac{1}{a^{2}}} \operatorname{atan}{\left(\frac{\left(-1\right)^{\frac{3}{4}} x}{\sqrt[4]{\frac{1}{a^{2}}}} \right)}}{3 a} & \text{for}\: a \neq 0 \\\frac{\pi x^{3}}{6} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x**3*acot(a*x**2)/3 + (-1)**(3/4)*(a**(-2))**(3/4)*acot(a*x**2)/3 + 2*x/(3*a) + (-1)**(1/4)*(a**(-2))**(1/4)*log(x - (-1)**(1/4)*(a**(-2))**(1/4))/(3*a) - (-1)**(1/4)*(a**(-2))**(1/4)*log(x**2 + I*sqrt(a**(-2)))/(6*a) + (-1)**(1/4)*(a**(-2))**(1/4)*atan((-1)**(3/4)*x/(a**(-2))**(1/4))/(3*a), Ne(a, 0)), (pi*x**3/6, True))","A",0
82,1,139,0,9.454142," ","integrate(acot(a*x**2),x)","\begin{cases} x \operatorname{acot}{\left(a x^{2} \right)} + \sqrt[4]{-1} \sqrt[4]{\frac{1}{a^{2}}} \operatorname{acot}{\left(a x^{2} \right)} - \frac{\left(-1\right)^{\frac{3}{4}} \log{\left(x - \sqrt[4]{-1} \sqrt[4]{\frac{1}{a^{2}}} \right)}}{a \sqrt[4]{\frac{1}{a^{2}}}} + \frac{\left(-1\right)^{\frac{3}{4}} \log{\left(x^{2} + i \sqrt{\frac{1}{a^{2}}} \right)}}{2 a \sqrt[4]{\frac{1}{a^{2}}}} + \frac{\left(-1\right)^{\frac{3}{4}} \operatorname{atan}{\left(\frac{\left(-1\right)^{\frac{3}{4}} x}{\sqrt[4]{\frac{1}{a^{2}}}} \right)}}{a \sqrt[4]{\frac{1}{a^{2}}}} & \text{for}\: a \neq 0 \\\frac{\pi x}{2} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x*acot(a*x**2) + (-1)**(1/4)*(a**(-2))**(1/4)*acot(a*x**2) - (-1)**(3/4)*log(x - (-1)**(1/4)*(a**(-2))**(1/4))/(a*(a**(-2))**(1/4)) + (-1)**(3/4)*log(x**2 + I*sqrt(a**(-2)))/(2*a*(a**(-2))**(1/4)) + (-1)**(3/4)*atan((-1)**(3/4)*x/(a**(-2))**(1/4))/(a*(a**(-2))**(1/4)), Ne(a, 0)), (pi*x/2, True))","A",0
83,1,144,0,19.964437," ","integrate(acot(a*x**2)/x**2,x)","\begin{cases} \left(-1\right)^{\frac{3}{4}} a^{2} \left(\frac{1}{a^{2}}\right)^{\frac{3}{4}} \operatorname{acot}{\left(a x^{2} \right)} + \sqrt[4]{-1} a \sqrt[4]{\frac{1}{a^{2}}} \log{\left(x - \sqrt[4]{-1} \sqrt[4]{\frac{1}{a^{2}}} \right)} - \frac{\sqrt[4]{-1} a \sqrt[4]{\frac{1}{a^{2}}} \log{\left(x^{2} + i \sqrt{\frac{1}{a^{2}}} \right)}}{2} + \sqrt[4]{-1} a \sqrt[4]{\frac{1}{a^{2}}} \operatorname{atan}{\left(\frac{\left(-1\right)^{\frac{3}{4}} x}{\sqrt[4]{\frac{1}{a^{2}}}} \right)} - \frac{\operatorname{acot}{\left(a x^{2} \right)}}{x} & \text{for}\: a \neq 0 \\- \frac{\pi}{2 x} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((-1)**(3/4)*a**2*(a**(-2))**(3/4)*acot(a*x**2) + (-1)**(1/4)*a*(a**(-2))**(1/4)*log(x - (-1)**(1/4)*(a**(-2))**(1/4)) - (-1)**(1/4)*a*(a**(-2))**(1/4)*log(x**2 + I*sqrt(a**(-2)))/2 + (-1)**(1/4)*a*(a**(-2))**(1/4)*atan((-1)**(3/4)*x/(a**(-2))**(1/4)) - acot(a*x**2)/x, Ne(a, 0)), (-pi/(2*x), True))","A",0
84,1,162,0,37.993337," ","integrate(acot(a*x**2)/x**4,x)","\begin{cases} \frac{\sqrt[4]{-1} a^{2} \sqrt[4]{\frac{1}{a^{2}}} \operatorname{acot}{\left(a x^{2} \right)}}{3} - \frac{\left(-1\right)^{\frac{3}{4}} a \log{\left(x - \sqrt[4]{-1} \sqrt[4]{\frac{1}{a^{2}}} \right)}}{3 \sqrt[4]{\frac{1}{a^{2}}}} + \frac{\left(-1\right)^{\frac{3}{4}} a \log{\left(x^{2} + i \sqrt{\frac{1}{a^{2}}} \right)}}{6 \sqrt[4]{\frac{1}{a^{2}}}} + \frac{\left(-1\right)^{\frac{3}{4}} a \operatorname{atan}{\left(\frac{\left(-1\right)^{\frac{3}{4}} x}{\sqrt[4]{\frac{1}{a^{2}}}} \right)}}{3 \sqrt[4]{\frac{1}{a^{2}}}} + \frac{2 a}{3 x} - \frac{\operatorname{acot}{\left(a x^{2} \right)}}{3 x^{3}} & \text{for}\: a \neq 0 \\- \frac{\pi}{6 x^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((-1)**(1/4)*a**2*(a**(-2))**(1/4)*acot(a*x**2)/3 - (-1)**(3/4)*a*log(x - (-1)**(1/4)*(a**(-2))**(1/4))/(3*(a**(-2))**(1/4)) + (-1)**(3/4)*a*log(x**2 + I*sqrt(a**(-2)))/(6*(a**(-2))**(1/4)) + (-1)**(3/4)*a*atan((-1)**(3/4)*x/(a**(-2))**(1/4))/(3*(a**(-2))**(1/4)) + 2*a/(3*x) - acot(a*x**2)/(3*x**3), Ne(a, 0)), (-pi/(6*x**3), True))","A",0
85,1,39,0,2.000019," ","integrate(x**2*acot(x**(1/2)),x)","\frac{x^{\frac{5}{2}}}{15} - \frac{x^{\frac{3}{2}}}{9} + \frac{\sqrt{x}}{3} + \frac{x^{3} \operatorname{acot}{\left(\sqrt{x} \right)}}{3} - \frac{\operatorname{atan}{\left(\sqrt{x} \right)}}{3}"," ",0,"x**(5/2)/15 - x**(3/2)/9 + sqrt(x)/3 + x**3*acot(sqrt(x))/3 - atan(sqrt(x))/3","A",0
86,1,32,0,1.294772," ","integrate(x*acot(x**(1/2)),x)","\frac{x^{\frac{3}{2}}}{6} - \frac{\sqrt{x}}{2} + \frac{x^{2} \operatorname{acot}{\left(\sqrt{x} \right)}}{2} + \frac{\operatorname{atan}{\left(\sqrt{x} \right)}}{2}"," ",0,"x**(3/2)/6 - sqrt(x)/2 + x**2*acot(sqrt(x))/2 + atan(sqrt(x))/2","A",0
87,1,19,0,1.180749," ","integrate(acot(x**(1/2)),x)","\sqrt{x} + x \operatorname{acot}{\left(\sqrt{x} \right)} - \operatorname{atan}{\left(\sqrt{x} \right)}"," ",0,"sqrt(x) + x*acot(sqrt(x)) - atan(sqrt(x))","A",0
88,0,0,0,0.000000," ","integrate(acot(x**(1/2))/x,x)","\int \frac{\operatorname{acot}{\left(\sqrt{x} \right)}}{x}\, dx"," ",0,"Integral(acot(sqrt(x))/x, x)","F",0
89,1,92,0,1.941507," ","integrate(acot(x**(1/2))/x**2,x)","- \frac{x^{\frac{5}{2}} \operatorname{acot}{\left(\sqrt{x} \right)}}{x^{\frac{5}{2}} + x^{\frac{3}{2}}} - \frac{2 x^{\frac{3}{2}} \operatorname{acot}{\left(\sqrt{x} \right)}}{x^{\frac{5}{2}} + x^{\frac{3}{2}}} - \frac{\sqrt{x} \operatorname{acot}{\left(\sqrt{x} \right)}}{x^{\frac{5}{2}} + x^{\frac{3}{2}}} + \frac{x^{2}}{x^{\frac{5}{2}} + x^{\frac{3}{2}}} + \frac{x}{x^{\frac{5}{2}} + x^{\frac{3}{2}}}"," ",0,"-x**(5/2)*acot(sqrt(x))/(x**(5/2) + x**(3/2)) - 2*x**(3/2)*acot(sqrt(x))/(x**(5/2) + x**(3/2)) - sqrt(x)*acot(sqrt(x))/(x**(5/2) + x**(3/2)) + x**2/(x**(5/2) + x**(3/2)) + x/(x**(5/2) + x**(3/2))","B",0
90,1,160,0,4.945576," ","integrate(acot(x**(1/2))/x**3,x)","\frac{3 x^{\frac{7}{2}} \operatorname{acot}{\left(\sqrt{x} \right)}}{6 x^{\frac{7}{2}} + 6 x^{\frac{5}{2}}} + \frac{3 x^{\frac{5}{2}} \operatorname{acot}{\left(\sqrt{x} \right)}}{6 x^{\frac{7}{2}} + 6 x^{\frac{5}{2}}} - \frac{3 x^{\frac{3}{2}} \operatorname{acot}{\left(\sqrt{x} \right)}}{6 x^{\frac{7}{2}} + 6 x^{\frac{5}{2}}} - \frac{3 \sqrt{x} \operatorname{acot}{\left(\sqrt{x} \right)}}{6 x^{\frac{7}{2}} + 6 x^{\frac{5}{2}}} - \frac{3 x^{3}}{6 x^{\frac{7}{2}} + 6 x^{\frac{5}{2}}} - \frac{2 x^{2}}{6 x^{\frac{7}{2}} + 6 x^{\frac{5}{2}}} + \frac{x}{6 x^{\frac{7}{2}} + 6 x^{\frac{5}{2}}}"," ",0,"3*x**(7/2)*acot(sqrt(x))/(6*x**(7/2) + 6*x**(5/2)) + 3*x**(5/2)*acot(sqrt(x))/(6*x**(7/2) + 6*x**(5/2)) - 3*x**(3/2)*acot(sqrt(x))/(6*x**(7/2) + 6*x**(5/2)) - 3*sqrt(x)*acot(sqrt(x))/(6*x**(7/2) + 6*x**(5/2)) - 3*x**3/(6*x**(7/2) + 6*x**(5/2)) - 2*x**2/(6*x**(7/2) + 6*x**(5/2)) + x/(6*x**(7/2) + 6*x**(5/2))","B",0
91,1,85,0,4.964684," ","integrate(x**(3/2)*acot(x**(1/2)),x)","\frac{4 x^{\frac{7}{2}} \operatorname{acot}{\left(\sqrt{x} \right)}}{10 x + 10} + \frac{4 x^{\frac{5}{2}} \operatorname{acot}{\left(\sqrt{x} \right)}}{10 x + 10} + \frac{x^{3}}{10 x + 10} - \frac{x^{2}}{10 x + 10} + \frac{2 x \log{\left(x + 1 \right)}}{10 x + 10} + \frac{2 \log{\left(x + 1 \right)}}{10 x + 10} + \frac{2}{10 x + 10}"," ",0,"4*x**(7/2)*acot(sqrt(x))/(10*x + 10) + 4*x**(5/2)*acot(sqrt(x))/(10*x + 10) + x**3/(10*x + 10) - x**2/(10*x + 10) + 2*x*log(x + 1)/(10*x + 10) + 2*log(x + 1)/(10*x + 10) + 2/(10*x + 10)","B",0
92,1,24,0,1.274213," ","integrate(x**(1/2)*acot(x**(1/2)),x)","\frac{2 x^{\frac{3}{2}} \operatorname{acot}{\left(\sqrt{x} \right)}}{3} + \frac{x}{3} - \frac{\log{\left(x + 1 \right)}}{3}"," ",0,"2*x**(3/2)*acot(sqrt(x))/3 + x/3 - log(x + 1)/3","A",0
93,1,17,0,0.339980," ","integrate(acot(x**(1/2))/x**(1/2),x)","2 \sqrt{x} \operatorname{acot}{\left(\sqrt{x} \right)} + \log{\left(x + 1 \right)}"," ",0,"2*sqrt(x)*acot(sqrt(x)) + log(x + 1)","A",0
94,1,20,0,1.182952," ","integrate(acot(x**(1/2))/x**(3/2),x)","- \log{\left(x \right)} + \log{\left(x + 1 \right)} - \frac{2 \operatorname{acot}{\left(\sqrt{x} \right)}}{\sqrt{x}}"," ",0,"-log(x) + log(x + 1) - 2*acot(sqrt(x))/sqrt(x)","A",0
95,1,143,0,4.920297," ","integrate(acot(x**(1/2))/x**(5/2),x)","- \frac{2 x^{\frac{3}{2}} \operatorname{acot}{\left(\sqrt{x} \right)}}{3 x^{3} + 3 x^{2}} - \frac{2 \sqrt{x} \operatorname{acot}{\left(\sqrt{x} \right)}}{3 x^{3} + 3 x^{2}} + \frac{x^{3} \log{\left(x \right)}}{3 x^{3} + 3 x^{2}} - \frac{x^{3} \log{\left(x + 1 \right)}}{3 x^{3} + 3 x^{2}} + \frac{x^{2} \log{\left(x \right)}}{3 x^{3} + 3 x^{2}} - \frac{x^{2} \log{\left(x + 1 \right)}}{3 x^{3} + 3 x^{2}} + \frac{x^{2}}{3 x^{3} + 3 x^{2}} + \frac{x}{3 x^{3} + 3 x^{2}}"," ",0,"-2*x**(3/2)*acot(sqrt(x))/(3*x**3 + 3*x**2) - 2*sqrt(x)*acot(sqrt(x))/(3*x**3 + 3*x**2) + x**3*log(x)/(3*x**3 + 3*x**2) - x**3*log(x + 1)/(3*x**3 + 3*x**2) + x**2*log(x)/(3*x**3 + 3*x**2) - x**2*log(x + 1)/(3*x**3 + 3*x**2) + x**2/(3*x**3 + 3*x**2) + x/(3*x**3 + 3*x**2)","B",0
96,1,14,0,0.152021," ","integrate(acot(1/x),x)","x \operatorname{acot}{\left(\frac{1}{x} \right)} - \frac{\log{\left(x^{2} + 1 \right)}}{2}"," ",0,"x*acot(1/x) - log(x**2 + 1)/2","A",0
97,0,0,0,0.000000," ","integrate(acot(a*x**n)/x,x)","\int \frac{\operatorname{acot}{\left(a x^{n} \right)}}{x}\, dx"," ",0,"Integral(acot(a*x**n)/x, x)","F",0
98,0,0,0,0.000000," ","integrate(acot(a*x**5)/x,x)","\int \frac{\operatorname{acot}{\left(a x^{5} \right)}}{x}\, dx"," ",0,"Integral(acot(a*x**5)/x, x)","F",0
99,1,155,0,1.453199," ","integrate(x**3*acot(b*x+a),x)","\begin{cases} - \frac{a^{4} \operatorname{acot}{\left(a + b x \right)}}{4 b^{4}} - \frac{a^{3} \log{\left(a^{2} + 2 a b x + b^{2} x^{2} + 1 \right)}}{2 b^{4}} + \frac{3 a^{2} x}{4 b^{3}} + \frac{3 a^{2} \operatorname{acot}{\left(a + b x \right)}}{2 b^{4}} - \frac{a x^{2}}{4 b^{2}} + \frac{a \log{\left(a^{2} + 2 a b x + b^{2} x^{2} + 1 \right)}}{2 b^{4}} + \frac{x^{4} \operatorname{acot}{\left(a + b x \right)}}{4} + \frac{x^{3}}{12 b} - \frac{x}{4 b^{3}} - \frac{\operatorname{acot}{\left(a + b x \right)}}{4 b^{4}} & \text{for}\: b \neq 0 \\\frac{x^{4} \operatorname{acot}{\left(a \right)}}{4} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a**4*acot(a + b*x)/(4*b**4) - a**3*log(a**2 + 2*a*b*x + b**2*x**2 + 1)/(2*b**4) + 3*a**2*x/(4*b**3) + 3*a**2*acot(a + b*x)/(2*b**4) - a*x**2/(4*b**2) + a*log(a**2 + 2*a*b*x + b**2*x**2 + 1)/(2*b**4) + x**4*acot(a + b*x)/4 + x**3/(12*b) - x/(4*b**3) - acot(a + b*x)/(4*b**4), Ne(b, 0)), (x**4*acot(a)/4, True))","A",0
100,1,117,0,0.995589," ","integrate(x**2*acot(b*x+a),x)","\begin{cases} \frac{a^{3} \operatorname{acot}{\left(a + b x \right)}}{3 b^{3}} + \frac{a^{2} \log{\left(a^{2} + 2 a b x + b^{2} x^{2} + 1 \right)}}{2 b^{3}} - \frac{2 a x}{3 b^{2}} - \frac{a \operatorname{acot}{\left(a + b x \right)}}{b^{3}} + \frac{x^{3} \operatorname{acot}{\left(a + b x \right)}}{3} + \frac{x^{2}}{6 b} - \frac{\log{\left(a^{2} + 2 a b x + b^{2} x^{2} + 1 \right)}}{6 b^{3}} & \text{for}\: b \neq 0 \\\frac{x^{3} \operatorname{acot}{\left(a \right)}}{3} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**3*acot(a + b*x)/(3*b**3) + a**2*log(a**2 + 2*a*b*x + b**2*x**2 + 1)/(2*b**3) - 2*a*x/(3*b**2) - a*acot(a + b*x)/b**3 + x**3*acot(a + b*x)/3 + x**2/(6*b) - log(a**2 + 2*a*b*x + b**2*x**2 + 1)/(6*b**3), Ne(b, 0)), (x**3*acot(a)/3, True))","A",0
101,1,78,0,0.612536," ","integrate(x*acot(b*x+a),x)","\begin{cases} - \frac{a^{2} \operatorname{acot}{\left(a + b x \right)}}{2 b^{2}} - \frac{a \log{\left(a^{2} + 2 a b x + b^{2} x^{2} + 1 \right)}}{2 b^{2}} + \frac{x^{2} \operatorname{acot}{\left(a + b x \right)}}{2} + \frac{x}{2 b} + \frac{\operatorname{acot}{\left(a + b x \right)}}{2 b^{2}} & \text{for}\: b \neq 0 \\\frac{x^{2} \operatorname{acot}{\left(a \right)}}{2} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a**2*acot(a + b*x)/(2*b**2) - a*log(a**2 + 2*a*b*x + b**2*x**2 + 1)/(2*b**2) + x**2*acot(a + b*x)/2 + x/(2*b) + acot(a + b*x)/(2*b**2), Ne(b, 0)), (x**2*acot(a)/2, True))","A",0
102,1,46,0,0.383227," ","integrate(acot(b*x+a),x)","\begin{cases} \frac{a \operatorname{acot}{\left(a + b x \right)}}{b} + x \operatorname{acot}{\left(a + b x \right)} + \frac{\log{\left(a^{2} + 2 a b x + b^{2} x^{2} + 1 \right)}}{2 b} & \text{for}\: b \neq 0 \\x \operatorname{acot}{\left(a \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*acot(a + b*x)/b + x*acot(a + b*x) + log(a**2 + 2*a*b*x + b**2*x**2 + 1)/(2*b), Ne(b, 0)), (x*acot(a), True))","A",0
103,-1,0,0,0.000000," ","integrate(acot(b*x+a)/x,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
104,1,167,0,1.771348," ","integrate(acot(b*x+a)/x**2,x)","\begin{cases} - \frac{i b \operatorname{acot}{\left(b x - i \right)}}{2} - \frac{\operatorname{acot}{\left(b x - i \right)}}{x} + \frac{i}{2 x} & \text{for}\: a = - i \\\frac{i b \operatorname{acot}{\left(b x + i \right)}}{2} - \frac{\operatorname{acot}{\left(b x + i \right)}}{x} - \frac{i}{2 x} & \text{for}\: a = i \\- \frac{2 a^{2} \operatorname{acot}{\left(a + b x \right)}}{2 a^{2} x + 2 x} - \frac{2 a b x \operatorname{acot}{\left(a + b x \right)}}{2 a^{2} x + 2 x} - \frac{2 b x \log{\left(x \right)}}{2 a^{2} x + 2 x} + \frac{b x \log{\left(a^{2} + 2 a b x + b^{2} x^{2} + 1 \right)}}{2 a^{2} x + 2 x} - \frac{2 \operatorname{acot}{\left(a + b x \right)}}{2 a^{2} x + 2 x} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-I*b*acot(b*x - I)/2 - acot(b*x - I)/x + I/(2*x), Eq(a, -I)), (I*b*acot(b*x + I)/2 - acot(b*x + I)/x - I/(2*x), Eq(a, I)), (-2*a**2*acot(a + b*x)/(2*a**2*x + 2*x) - 2*a*b*x*acot(a + b*x)/(2*a**2*x + 2*x) - 2*b*x*log(x)/(2*a**2*x + 2*x) + b*x*log(a**2 + 2*a*b*x + b**2*x**2 + 1)/(2*a**2*x + 2*x) - 2*acot(a + b*x)/(2*a**2*x + 2*x), True))","B",0
105,1,381,0,2.831012," ","integrate(acot(b*x+a)/x**3,x)","\begin{cases} - \frac{b^{2} \operatorname{acot}{\left(b x - i \right)}}{8} + \frac{b}{8 x} - \frac{\operatorname{acot}{\left(b x - i \right)}}{2 x^{2}} + \frac{i}{8 x^{2}} & \text{for}\: a = - i \\- \frac{b^{2} \operatorname{acot}{\left(b x + i \right)}}{8} + \frac{b}{8 x} - \frac{\operatorname{acot}{\left(b x + i \right)}}{2 x^{2}} - \frac{i}{8 x^{2}} & \text{for}\: a = i \\- \frac{a^{4} \operatorname{acot}{\left(a + b x \right)}}{2 a^{4} x^{2} + 4 a^{2} x^{2} + 2 x^{2}} + \frac{a^{2} b^{2} x^{2} \operatorname{acot}{\left(a + b x \right)}}{2 a^{4} x^{2} + 4 a^{2} x^{2} + 2 x^{2}} + \frac{a^{2} b x}{2 a^{4} x^{2} + 4 a^{2} x^{2} + 2 x^{2}} - \frac{2 a^{2} \operatorname{acot}{\left(a + b x \right)}}{2 a^{4} x^{2} + 4 a^{2} x^{2} + 2 x^{2}} + \frac{2 a b^{2} x^{2} \log{\left(x \right)}}{2 a^{4} x^{2} + 4 a^{2} x^{2} + 2 x^{2}} - \frac{a b^{2} x^{2} \log{\left(a^{2} + 2 a b x + b^{2} x^{2} + 1 \right)}}{2 a^{4} x^{2} + 4 a^{2} x^{2} + 2 x^{2}} - \frac{b^{2} x^{2} \operatorname{acot}{\left(a + b x \right)}}{2 a^{4} x^{2} + 4 a^{2} x^{2} + 2 x^{2}} + \frac{b x}{2 a^{4} x^{2} + 4 a^{2} x^{2} + 2 x^{2}} - \frac{\operatorname{acot}{\left(a + b x \right)}}{2 a^{4} x^{2} + 4 a^{2} x^{2} + 2 x^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-b**2*acot(b*x - I)/8 + b/(8*x) - acot(b*x - I)/(2*x**2) + I/(8*x**2), Eq(a, -I)), (-b**2*acot(b*x + I)/8 + b/(8*x) - acot(b*x + I)/(2*x**2) - I/(8*x**2), Eq(a, I)), (-a**4*acot(a + b*x)/(2*a**4*x**2 + 4*a**2*x**2 + 2*x**2) + a**2*b**2*x**2*acot(a + b*x)/(2*a**4*x**2 + 4*a**2*x**2 + 2*x**2) + a**2*b*x/(2*a**4*x**2 + 4*a**2*x**2 + 2*x**2) - 2*a**2*acot(a + b*x)/(2*a**4*x**2 + 4*a**2*x**2 + 2*x**2) + 2*a*b**2*x**2*log(x)/(2*a**4*x**2 + 4*a**2*x**2 + 2*x**2) - a*b**2*x**2*log(a**2 + 2*a*b*x + b**2*x**2 + 1)/(2*a**4*x**2 + 4*a**2*x**2 + 2*x**2) - b**2*x**2*acot(a + b*x)/(2*a**4*x**2 + 4*a**2*x**2 + 2*x**2) + b*x/(2*a**4*x**2 + 4*a**2*x**2 + 2*x**2) - acot(a + b*x)/(2*a**4*x**2 + 4*a**2*x**2 + 2*x**2), True))","B",0
106,1,760,0,4.505835," ","integrate(acot(b*x+a)/x**4,x)","\begin{cases} \frac{i b^{3} \operatorname{acot}{\left(b x - i \right)}}{24} - \frac{i b^{2}}{24 x} + \frac{b}{24 x^{2}} - \frac{\operatorname{acot}{\left(b x - i \right)}}{3 x^{3}} + \frac{i}{18 x^{3}} & \text{for}\: a = - i \\- \frac{i b^{3} \operatorname{acot}{\left(b x + i \right)}}{24} + \frac{i b^{2}}{24 x} + \frac{b}{24 x^{2}} - \frac{\operatorname{acot}{\left(b x + i \right)}}{3 x^{3}} - \frac{i}{18 x^{3}} & \text{for}\: a = i \\- \frac{2 a^{6} \operatorname{acot}{\left(a + b x \right)}}{6 a^{6} x^{3} + 18 a^{4} x^{3} + 18 a^{2} x^{3} + 6 x^{3}} + \frac{a^{4} b x}{6 a^{6} x^{3} + 18 a^{4} x^{3} + 18 a^{2} x^{3} + 6 x^{3}} - \frac{6 a^{4} \operatorname{acot}{\left(a + b x \right)}}{6 a^{6} x^{3} + 18 a^{4} x^{3} + 18 a^{2} x^{3} + 6 x^{3}} - \frac{2 a^{3} b^{3} x^{3} \operatorname{acot}{\left(a + b x \right)}}{6 a^{6} x^{3} + 18 a^{4} x^{3} + 18 a^{2} x^{3} + 6 x^{3}} - \frac{4 a^{3} b^{2} x^{2}}{6 a^{6} x^{3} + 18 a^{4} x^{3} + 18 a^{2} x^{3} + 6 x^{3}} - \frac{6 a^{2} b^{3} x^{3} \log{\left(x \right)}}{6 a^{6} x^{3} + 18 a^{4} x^{3} + 18 a^{2} x^{3} + 6 x^{3}} + \frac{3 a^{2} b^{3} x^{3} \log{\left(a^{2} + 2 a b x + b^{2} x^{2} + 1 \right)}}{6 a^{6} x^{3} + 18 a^{4} x^{3} + 18 a^{2} x^{3} + 6 x^{3}} + \frac{2 a^{2} b x}{6 a^{6} x^{3} + 18 a^{4} x^{3} + 18 a^{2} x^{3} + 6 x^{3}} - \frac{6 a^{2} \operatorname{acot}{\left(a + b x \right)}}{6 a^{6} x^{3} + 18 a^{4} x^{3} + 18 a^{2} x^{3} + 6 x^{3}} + \frac{6 a b^{3} x^{3} \operatorname{acot}{\left(a + b x \right)}}{6 a^{6} x^{3} + 18 a^{4} x^{3} + 18 a^{2} x^{3} + 6 x^{3}} - \frac{4 a b^{2} x^{2}}{6 a^{6} x^{3} + 18 a^{4} x^{3} + 18 a^{2} x^{3} + 6 x^{3}} + \frac{2 b^{3} x^{3} \log{\left(x \right)}}{6 a^{6} x^{3} + 18 a^{4} x^{3} + 18 a^{2} x^{3} + 6 x^{3}} - \frac{b^{3} x^{3} \log{\left(a^{2} + 2 a b x + b^{2} x^{2} + 1 \right)}}{6 a^{6} x^{3} + 18 a^{4} x^{3} + 18 a^{2} x^{3} + 6 x^{3}} + \frac{b x}{6 a^{6} x^{3} + 18 a^{4} x^{3} + 18 a^{2} x^{3} + 6 x^{3}} - \frac{2 \operatorname{acot}{\left(a + b x \right)}}{6 a^{6} x^{3} + 18 a^{4} x^{3} + 18 a^{2} x^{3} + 6 x^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((I*b**3*acot(b*x - I)/24 - I*b**2/(24*x) + b/(24*x**2) - acot(b*x - I)/(3*x**3) + I/(18*x**3), Eq(a, -I)), (-I*b**3*acot(b*x + I)/24 + I*b**2/(24*x) + b/(24*x**2) - acot(b*x + I)/(3*x**3) - I/(18*x**3), Eq(a, I)), (-2*a**6*acot(a + b*x)/(6*a**6*x**3 + 18*a**4*x**3 + 18*a**2*x**3 + 6*x**3) + a**4*b*x/(6*a**6*x**3 + 18*a**4*x**3 + 18*a**2*x**3 + 6*x**3) - 6*a**4*acot(a + b*x)/(6*a**6*x**3 + 18*a**4*x**3 + 18*a**2*x**3 + 6*x**3) - 2*a**3*b**3*x**3*acot(a + b*x)/(6*a**6*x**3 + 18*a**4*x**3 + 18*a**2*x**3 + 6*x**3) - 4*a**3*b**2*x**2/(6*a**6*x**3 + 18*a**4*x**3 + 18*a**2*x**3 + 6*x**3) - 6*a**2*b**3*x**3*log(x)/(6*a**6*x**3 + 18*a**4*x**3 + 18*a**2*x**3 + 6*x**3) + 3*a**2*b**3*x**3*log(a**2 + 2*a*b*x + b**2*x**2 + 1)/(6*a**6*x**3 + 18*a**4*x**3 + 18*a**2*x**3 + 6*x**3) + 2*a**2*b*x/(6*a**6*x**3 + 18*a**4*x**3 + 18*a**2*x**3 + 6*x**3) - 6*a**2*acot(a + b*x)/(6*a**6*x**3 + 18*a**4*x**3 + 18*a**2*x**3 + 6*x**3) + 6*a*b**3*x**3*acot(a + b*x)/(6*a**6*x**3 + 18*a**4*x**3 + 18*a**2*x**3 + 6*x**3) - 4*a*b**2*x**2/(6*a**6*x**3 + 18*a**4*x**3 + 18*a**2*x**3 + 6*x**3) + 2*b**3*x**3*log(x)/(6*a**6*x**3 + 18*a**4*x**3 + 18*a**2*x**3 + 6*x**3) - b**3*x**3*log(a**2 + 2*a*b*x + b**2*x**2 + 1)/(6*a**6*x**3 + 18*a**4*x**3 + 18*a**2*x**3 + 6*x**3) + b*x/(6*a**6*x**3 + 18*a**4*x**3 + 18*a**2*x**3 + 6*x**3) - 2*acot(a + b*x)/(6*a**6*x**3 + 18*a**4*x**3 + 18*a**2*x**3 + 6*x**3), True))","B",0
107,-1,0,0,0.000000," ","integrate(acot(b*x+a)/(d*x**2+c),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
108,-1,0,0,0.000000," ","integrate(acot(b*x+a)/(d*x+c),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
109,-1,0,0,0.000000," ","integrate(acot(b*x+a)/(c+d/x),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
110,-1,0,0,0.000000," ","integrate(acot(b*x+a)/(c+d/x**2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
111,-1,0,0,0.000000," ","integrate(acot(b*x+a)/(c+d*x**(1/2)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
112,-1,0,0,0.000000," ","integrate(acot(b*x+a)/(c+d/x**(1/2)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
113,-1,0,0,0.000000," ","integrate(acot(e*x+d)/(c*x**2+b*x+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
114,0,0,0,0.000000," ","integrate(acot(b*x+a)/(b**2*x**2+2*a*b*x+a**2+1)**(1/2),x)","\int \frac{\operatorname{acot}{\left(a + b x \right)}}{\sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1}}\, dx"," ",0,"Integral(acot(a + b*x)/sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1), x)","F",0
115,0,0,0,0.000000," ","integrate(acot(b*x+a)/((a**2+1)*c+2*a*b*c*x+c*x**2*b**2)**(1/2),x)","\int \frac{\operatorname{acot}{\left(a + b x \right)}}{\sqrt{c \left(a^{2} + 2 a b x + b^{2} x^{2} + 1\right)}}\, dx"," ",0,"Integral(acot(a + b*x)/sqrt(c*(a**2 + 2*a*b*x + b**2*x**2 + 1)), x)","F",0
116,0,0,0,0.000000," ","integrate(acot(b*x+a)/(b**2*x**2+2*a*b*x+a**2+1)**(1/3),x)","\int \frac{\operatorname{acot}{\left(a + b x \right)}}{\sqrt[3]{a^{2} + 2 a b x + b^{2} x^{2} + 1}}\, dx"," ",0,"Integral(acot(a + b*x)/(a**2 + 2*a*b*x + b**2*x**2 + 1)**(1/3), x)","F",0
117,0,0,0,0.000000," ","integrate(acot(b*x+a)/((a**2+1)*c+2*a*b*c*x+c*x**2*b**2)**(1/3),x)","\int \frac{\operatorname{acot}{\left(a + b x \right)}}{\sqrt[3]{c \left(a^{2} + 2 a b x + b^{2} x^{2} + 1\right)}}\, dx"," ",0,"Integral(acot(a + b*x)/(c*(a**2 + 2*a*b*x + b**2*x**2 + 1))**(1/3), x)","F",0
118,0,0,0,0.000000," ","integrate((b*x+a)**2*acot(b*x+a)/(b**2*x**2+2*a*b*x+a**2+1)**(1/2),x)","\int \frac{\left(a + b x\right)^{2} \operatorname{acot}{\left(a + b x \right)}}{\sqrt{a^{2} + 2 a b x + b^{2} x^{2} + 1}}\, dx"," ",0,"Integral((a + b*x)**2*acot(a + b*x)/sqrt(a**2 + 2*a*b*x + b**2*x**2 + 1), x)","F",0
119,0,0,0,0.000000," ","integrate((b*x+a)**2*acot(b*x+a)/((a**2+1)*c+2*a*b*c*x+c*x**2*b**2)**(1/2),x)","\int \frac{\left(a + b x\right)^{2} \operatorname{acot}{\left(a + b x \right)}}{\sqrt{c \left(a^{2} + 2 a b x + b^{2} x^{2} + 1\right)}}\, dx"," ",0,"Integral((a + b*x)**2*acot(a + b*x)/sqrt(c*(a**2 + 2*a*b*x + b**2*x**2 + 1)), x)","F",0
120,0,0,0,0.000000," ","integrate((b*x+a)**2*acot(b*x+a)/(b**2*x**2+2*a*b*x+a**2+1)**(1/3),x)","\int \frac{\left(a + b x\right)^{2} \operatorname{acot}{\left(a + b x \right)}}{\sqrt[3]{a^{2} + 2 a b x + b^{2} x^{2} + 1}}\, dx"," ",0,"Integral((a + b*x)**2*acot(a + b*x)/(a**2 + 2*a*b*x + b**2*x**2 + 1)**(1/3), x)","F",0
121,0,0,0,0.000000," ","integrate((b*x+a)**2*acot(b*x+a)/((a**2+1)*c+2*a*b*c*x+c*x**2*b**2)**(1/3),x)","\int \frac{\left(a + b x\right)^{2} \operatorname{acot}{\left(a + b x \right)}}{\sqrt[3]{c \left(a^{2} + 2 a b x + b^{2} x^{2} + 1\right)}}\, dx"," ",0,"Integral((a + b*x)**2*acot(a + b*x)/(c*(a**2 + 2*a*b*x + b**2*x**2 + 1))**(1/3), x)","F",0
122,1,99,0,2.910341," ","integrate((b*x+a)**2*acot(b*x+a),x)","\begin{cases} \frac{a^{3} \operatorname{acot}{\left(a + b x \right)}}{3 b} + a^{2} x \operatorname{acot}{\left(a + b x \right)} + a b x^{2} \operatorname{acot}{\left(a + b x \right)} + \frac{a x}{3} + \frac{b^{2} x^{3} \operatorname{acot}{\left(a + b x \right)}}{3} + \frac{b x^{2}}{6} - \frac{\log{\left(\frac{a}{b} + x - \frac{i}{b} \right)}}{3 b} - \frac{i \operatorname{acot}{\left(a + b x \right)}}{3 b} & \text{for}\: b \neq 0 \\a^{2} x \operatorname{acot}{\left(a \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**3*acot(a + b*x)/(3*b) + a**2*x*acot(a + b*x) + a*b*x**2*acot(a + b*x) + a*x/3 + b**2*x**3*acot(a + b*x)/3 + b*x**2/6 - log(a/b + x - I/b)/(3*b) - I*acot(a + b*x)/(3*b), Ne(b, 0)), (a**2*x*acot(a), True))","A",0
123,1,56,0,1.774208," ","integrate((b*x+a)*acot(b*x+a),x)","\begin{cases} \frac{a^{2} \operatorname{acot}{\left(a + b x \right)}}{2 b} + a x \operatorname{acot}{\left(a + b x \right)} + \frac{b x^{2} \operatorname{acot}{\left(a + b x \right)}}{2} + \frac{x}{2} + \frac{\operatorname{acot}{\left(a + b x \right)}}{2 b} & \text{for}\: b \neq 0 \\a x \operatorname{acot}{\left(a \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*acot(a + b*x)/(2*b) + a*x*acot(a + b*x) + b*x**2*acot(a + b*x)/2 + x/2 + acot(a + b*x)/(2*b), Ne(b, 0)), (a*x*acot(a), True))","A",0
124,0,0,0,0.000000," ","integrate(acot(b*x+a)/(b*x+a),x)","\int \frac{\operatorname{acot}{\left(a + b x \right)}}{a + b x}\, dx"," ",0,"Integral(acot(a + b*x)/(a + b*x), x)","F",0
125,1,151,0,6.136667," ","integrate(acot(b*x+a)/(b*x+a)**2,x)","\begin{cases} \frac{a \log{\left(\frac{a}{b} + x \right)}}{- a b - b^{2} x} - \frac{a \log{\left(\frac{a}{b} + x - \frac{i}{b} \right)}}{- a b - b^{2} x} - \frac{i a \operatorname{acot}{\left(a + b x \right)}}{- a b - b^{2} x} + \frac{b x \log{\left(\frac{a}{b} + x \right)}}{- a b - b^{2} x} - \frac{b x \log{\left(\frac{a}{b} + x - \frac{i}{b} \right)}}{- a b - b^{2} x} - \frac{i b x \operatorname{acot}{\left(a + b x \right)}}{- a b - b^{2} x} + \frac{\operatorname{acot}{\left(a + b x \right)}}{- a b - b^{2} x} & \text{for}\: b \neq 0 \\\frac{x \operatorname{acot}{\left(a \right)}}{a^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*log(a/b + x)/(-a*b - b**2*x) - a*log(a/b + x - I/b)/(-a*b - b**2*x) - I*a*acot(a + b*x)/(-a*b - b**2*x) + b*x*log(a/b + x)/(-a*b - b**2*x) - b*x*log(a/b + x - I/b)/(-a*b - b**2*x) - I*b*x*acot(a + b*x)/(-a*b - b**2*x) + acot(a + b*x)/(-a*b - b**2*x), Ne(b, 0)), (x*acot(a)/a**2, True))","A",0
126,0,0,0,0.000000," ","integrate(acot(1+x)/(2+2*x),x)","\frac{\int \frac{\operatorname{acot}{\left(x + 1 \right)}}{x + 1}\, dx}{2}"," ",0,"Integral(acot(x + 1)/(x + 1), x)/2","F",0
127,0,0,0,0.000000," ","integrate(acot(b*x+a)/(a*d/b+d*x),x)","\frac{b \int \frac{\operatorname{acot}{\left(a + b x \right)}}{a + b x}\, dx}{d}"," ",0,"b*Integral(acot(a + b*x)/(a + b*x), x)/d","F",0
128,0,0,0,0.000000," ","integrate((b*x+a)**2*acot(b*x+a)**(1/2),x)","\int \left(a + b x\right)^{2} \sqrt{\operatorname{acot}{\left(a + b x \right)}}\, dx"," ",0,"Integral((a + b*x)**2*sqrt(acot(a + b*x)), x)","F",0
129,1,654,0,26.449358," ","integrate((f*x+e)**3*(a+b*acot(d*x+c)),x)","\begin{cases} a e^{3} x + \frac{3 a e^{2} f x^{2}}{2} + a e f^{2} x^{3} + \frac{a f^{3} x^{4}}{4} - \frac{b c^{4} f^{3} \operatorname{acot}{\left(c + d x \right)}}{4 d^{4}} + \frac{b c^{3} e f^{2} \operatorname{acot}{\left(c + d x \right)}}{d^{3}} - \frac{b c^{3} f^{3} \log{\left(\frac{c}{d} + x - \frac{i}{d} \right)}}{d^{4}} - \frac{i b c^{3} f^{3} \operatorname{acot}{\left(c + d x \right)}}{d^{4}} - \frac{3 b c^{2} e^{2} f \operatorname{acot}{\left(c + d x \right)}}{2 d^{2}} + \frac{3 b c^{2} e f^{2} \log{\left(\frac{c}{d} + x - \frac{i}{d} \right)}}{d^{3}} + \frac{3 i b c^{2} e f^{2} \operatorname{acot}{\left(c + d x \right)}}{d^{3}} + \frac{3 b c^{2} f^{3} x}{4 d^{3}} + \frac{3 b c^{2} f^{3} \operatorname{acot}{\left(c + d x \right)}}{2 d^{4}} + \frac{b c e^{3} \operatorname{acot}{\left(c + d x \right)}}{d} - \frac{3 b c e^{2} f \log{\left(\frac{c}{d} + x - \frac{i}{d} \right)}}{d^{2}} - \frac{3 i b c e^{2} f \operatorname{acot}{\left(c + d x \right)}}{d^{2}} - \frac{2 b c e f^{2} x}{d^{2}} - \frac{b c f^{3} x^{2}}{4 d^{2}} - \frac{3 b c e f^{2} \operatorname{acot}{\left(c + d x \right)}}{d^{3}} + \frac{b c f^{3} \log{\left(\frac{c}{d} + x - \frac{i}{d} \right)}}{d^{4}} + \frac{i b c f^{3} \operatorname{acot}{\left(c + d x \right)}}{d^{4}} + b e^{3} x \operatorname{acot}{\left(c + d x \right)} + \frac{3 b e^{2} f x^{2} \operatorname{acot}{\left(c + d x \right)}}{2} + b e f^{2} x^{3} \operatorname{acot}{\left(c + d x \right)} + \frac{b f^{3} x^{4} \operatorname{acot}{\left(c + d x \right)}}{4} + \frac{b e^{3} \log{\left(\frac{c}{d} + x - \frac{i}{d} \right)}}{d} + \frac{i b e^{3} \operatorname{acot}{\left(c + d x \right)}}{d} + \frac{3 b e^{2} f x}{2 d} + \frac{b e f^{2} x^{2}}{2 d} + \frac{b f^{3} x^{3}}{12 d} + \frac{3 b e^{2} f \operatorname{acot}{\left(c + d x \right)}}{2 d^{2}} - \frac{b e f^{2} \log{\left(\frac{c}{d} + x - \frac{i}{d} \right)}}{d^{3}} - \frac{i b e f^{2} \operatorname{acot}{\left(c + d x \right)}}{d^{3}} - \frac{b f^{3} x}{4 d^{3}} - \frac{b f^{3} \operatorname{acot}{\left(c + d x \right)}}{4 d^{4}} & \text{for}\: d \neq 0 \\\left(a + b \operatorname{acot}{\left(c \right)}\right) \left(e^{3} x + \frac{3 e^{2} f x^{2}}{2} + e f^{2} x^{3} + \frac{f^{3} x^{4}}{4}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*e**3*x + 3*a*e**2*f*x**2/2 + a*e*f**2*x**3 + a*f**3*x**4/4 - b*c**4*f**3*acot(c + d*x)/(4*d**4) + b*c**3*e*f**2*acot(c + d*x)/d**3 - b*c**3*f**3*log(c/d + x - I/d)/d**4 - I*b*c**3*f**3*acot(c + d*x)/d**4 - 3*b*c**2*e**2*f*acot(c + d*x)/(2*d**2) + 3*b*c**2*e*f**2*log(c/d + x - I/d)/d**3 + 3*I*b*c**2*e*f**2*acot(c + d*x)/d**3 + 3*b*c**2*f**3*x/(4*d**3) + 3*b*c**2*f**3*acot(c + d*x)/(2*d**4) + b*c*e**3*acot(c + d*x)/d - 3*b*c*e**2*f*log(c/d + x - I/d)/d**2 - 3*I*b*c*e**2*f*acot(c + d*x)/d**2 - 2*b*c*e*f**2*x/d**2 - b*c*f**3*x**2/(4*d**2) - 3*b*c*e*f**2*acot(c + d*x)/d**3 + b*c*f**3*log(c/d + x - I/d)/d**4 + I*b*c*f**3*acot(c + d*x)/d**4 + b*e**3*x*acot(c + d*x) + 3*b*e**2*f*x**2*acot(c + d*x)/2 + b*e*f**2*x**3*acot(c + d*x) + b*f**3*x**4*acot(c + d*x)/4 + b*e**3*log(c/d + x - I/d)/d + I*b*e**3*acot(c + d*x)/d + 3*b*e**2*f*x/(2*d) + b*e*f**2*x**2/(2*d) + b*f**3*x**3/(12*d) + 3*b*e**2*f*acot(c + d*x)/(2*d**2) - b*e*f**2*log(c/d + x - I/d)/d**3 - I*b*e*f**2*acot(c + d*x)/d**3 - b*f**3*x/(4*d**3) - b*f**3*acot(c + d*x)/(4*d**4), Ne(d, 0)), ((a + b*acot(c))*(e**3*x + 3*e**2*f*x**2/2 + e*f**2*x**3 + f**3*x**4/4), True))","A",0
130,1,376,0,11.140970," ","integrate((f*x+e)**2*(a+b*acot(d*x+c)),x)","\begin{cases} a e^{2} x + a e f x^{2} + \frac{a f^{2} x^{3}}{3} + \frac{b c^{3} f^{2} \operatorname{acot}{\left(c + d x \right)}}{3 d^{3}} - \frac{b c^{2} e f \operatorname{acot}{\left(c + d x \right)}}{d^{2}} + \frac{b c^{2} f^{2} \log{\left(\frac{c}{d} + x - \frac{i}{d} \right)}}{d^{3}} + \frac{i b c^{2} f^{2} \operatorname{acot}{\left(c + d x \right)}}{d^{3}} + \frac{b c e^{2} \operatorname{acot}{\left(c + d x \right)}}{d} - \frac{2 b c e f \log{\left(\frac{c}{d} + x - \frac{i}{d} \right)}}{d^{2}} - \frac{2 i b c e f \operatorname{acot}{\left(c + d x \right)}}{d^{2}} - \frac{2 b c f^{2} x}{3 d^{2}} - \frac{b c f^{2} \operatorname{acot}{\left(c + d x \right)}}{d^{3}} + b e^{2} x \operatorname{acot}{\left(c + d x \right)} + b e f x^{2} \operatorname{acot}{\left(c + d x \right)} + \frac{b f^{2} x^{3} \operatorname{acot}{\left(c + d x \right)}}{3} + \frac{b e^{2} \log{\left(\frac{c}{d} + x - \frac{i}{d} \right)}}{d} + \frac{i b e^{2} \operatorname{acot}{\left(c + d x \right)}}{d} + \frac{b e f x}{d} + \frac{b f^{2} x^{2}}{6 d} + \frac{b e f \operatorname{acot}{\left(c + d x \right)}}{d^{2}} - \frac{b f^{2} \log{\left(\frac{c}{d} + x - \frac{i}{d} \right)}}{3 d^{3}} - \frac{i b f^{2} \operatorname{acot}{\left(c + d x \right)}}{3 d^{3}} & \text{for}\: d \neq 0 \\\left(a + b \operatorname{acot}{\left(c \right)}\right) \left(e^{2} x + e f x^{2} + \frac{f^{2} x^{3}}{3}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*e**2*x + a*e*f*x**2 + a*f**2*x**3/3 + b*c**3*f**2*acot(c + d*x)/(3*d**3) - b*c**2*e*f*acot(c + d*x)/d**2 + b*c**2*f**2*log(c/d + x - I/d)/d**3 + I*b*c**2*f**2*acot(c + d*x)/d**3 + b*c*e**2*acot(c + d*x)/d - 2*b*c*e*f*log(c/d + x - I/d)/d**2 - 2*I*b*c*e*f*acot(c + d*x)/d**2 - 2*b*c*f**2*x/(3*d**2) - b*c*f**2*acot(c + d*x)/d**3 + b*e**2*x*acot(c + d*x) + b*e*f*x**2*acot(c + d*x) + b*f**2*x**3*acot(c + d*x)/3 + b*e**2*log(c/d + x - I/d)/d + I*b*e**2*acot(c + d*x)/d + b*e*f*x/d + b*f**2*x**2/(6*d) + b*e*f*acot(c + d*x)/d**2 - b*f**2*log(c/d + x - I/d)/(3*d**3) - I*b*f**2*acot(c + d*x)/(3*d**3), Ne(d, 0)), ((a + b*acot(c))*(e**2*x + e*f*x**2 + f**2*x**3/3), True))","A",0
131,1,177,0,4.757839," ","integrate((f*x+e)*(a+b*acot(d*x+c)),x)","\begin{cases} a e x + \frac{a f x^{2}}{2} - \frac{b c^{2} f \operatorname{acot}{\left(c + d x \right)}}{2 d^{2}} + \frac{b c e \operatorname{acot}{\left(c + d x \right)}}{d} - \frac{b c f \log{\left(\frac{c}{d} + x - \frac{i}{d} \right)}}{d^{2}} - \frac{i b c f \operatorname{acot}{\left(c + d x \right)}}{d^{2}} + b e x \operatorname{acot}{\left(c + d x \right)} + \frac{b f x^{2} \operatorname{acot}{\left(c + d x \right)}}{2} + \frac{b e \log{\left(\frac{c}{d} + x - \frac{i}{d} \right)}}{d} + \frac{i b e \operatorname{acot}{\left(c + d x \right)}}{d} + \frac{b f x}{2 d} + \frac{b f \operatorname{acot}{\left(c + d x \right)}}{2 d^{2}} & \text{for}\: d \neq 0 \\\left(a + b \operatorname{acot}{\left(c \right)}\right) \left(e x + \frac{f x^{2}}{2}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*e*x + a*f*x**2/2 - b*c**2*f*acot(c + d*x)/(2*d**2) + b*c*e*acot(c + d*x)/d - b*c*f*log(c/d + x - I/d)/d**2 - I*b*c*f*acot(c + d*x)/d**2 + b*e*x*acot(c + d*x) + b*f*x**2*acot(c + d*x)/2 + b*e*log(c/d + x - I/d)/d + I*b*e*acot(c + d*x)/d + b*f*x/(2*d) + b*f*acot(c + d*x)/(2*d**2), Ne(d, 0)), ((a + b*acot(c))*(e*x + f*x**2/2), True))","A",0
132,1,51,0,0.387113," ","integrate(a+b*acot(d*x+c),x)","a x + b \left(\begin{cases} \frac{c \operatorname{acot}{\left(c + d x \right)}}{d} + x \operatorname{acot}{\left(c + d x \right)} + \frac{\log{\left(c^{2} + 2 c d x + d^{2} x^{2} + 1 \right)}}{2 d} & \text{for}\: d \neq 0 \\x \operatorname{acot}{\left(c \right)} & \text{otherwise} \end{cases}\right)"," ",0,"a*x + b*Piecewise((c*acot(c + d*x)/d + x*acot(c + d*x) + log(c**2 + 2*c*d*x + d**2*x**2 + 1)/(2*d), Ne(d, 0)), (x*acot(c), True))","A",0
133,-1,0,0,0.000000," ","integrate((a+b*acot(d*x+c))/(f*x+e),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
134,-1,0,0,0.000000," ","integrate((a+b*acot(d*x+c))/(f*x+e)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
135,-1,0,0,0.000000," ","integrate((a+b*acot(d*x+c))/(f*x+e)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
136,0,0,0,0.000000," ","integrate((f*x+e)**2*(a+b*acot(d*x+c))**2,x)","\int \left(a + b \operatorname{acot}{\left(c + d x \right)}\right)^{2} \left(e + f x\right)^{2}\, dx"," ",0,"Integral((a + b*acot(c + d*x))**2*(e + f*x)**2, x)","F",0
137,0,0,0,0.000000," ","integrate((f*x+e)*(a+b*acot(d*x+c))**2,x)","\int \left(a + b \operatorname{acot}{\left(c + d x \right)}\right)^{2} \left(e + f x\right)\, dx"," ",0,"Integral((a + b*acot(c + d*x))**2*(e + f*x), x)","F",0
138,0,0,0,0.000000," ","integrate((a+b*acot(d*x+c))**2,x)","\int \left(a + b \operatorname{acot}{\left(c + d x \right)}\right)^{2}\, dx"," ",0,"Integral((a + b*acot(c + d*x))**2, x)","F",0
139,-1,0,0,0.000000," ","integrate((a+b*acot(d*x+c))**2/(f*x+e),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
140,-1,0,0,0.000000," ","integrate((a+b*acot(d*x+c))**2/(f*x+e)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
141,0,0,0,0.000000," ","integrate((f*x+e)**2*(a+b*acot(d*x+c))**3,x)","\int \left(a + b \operatorname{acot}{\left(c + d x \right)}\right)^{3} \left(e + f x\right)^{2}\, dx"," ",0,"Integral((a + b*acot(c + d*x))**3*(e + f*x)**2, x)","F",0
142,0,0,0,0.000000," ","integrate((f*x+e)*(a+b*acot(d*x+c))**3,x)","\int \left(a + b \operatorname{acot}{\left(c + d x \right)}\right)^{3} \left(e + f x\right)\, dx"," ",0,"Integral((a + b*acot(c + d*x))**3*(e + f*x), x)","F",0
143,0,0,0,0.000000," ","integrate((a+b*acot(d*x+c))**3,x)","\int \left(a + b \operatorname{acot}{\left(c + d x \right)}\right)^{3}\, dx"," ",0,"Integral((a + b*acot(c + d*x))**3, x)","F",0
144,-1,0,0,0.000000," ","integrate((a+b*acot(d*x+c))**3/(f*x+e),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
145,-1,0,0,0.000000," ","integrate((a+b*acot(d*x+c))**3/(f*x+e)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
146,-1,0,0,0.000000," ","integrate((f*x+e)**m*(a+b*acot(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
147,-1,0,0,0.000000," ","integrate((f*x+e)**m*(a+b*acot(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
148,-1,0,0,0.000000," ","integrate((f*x+e)**m*(a+b*acot(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
149,1,60,0,3.338991," ","integrate(x**3*acot(b*x**4+a),x)","\begin{cases} \frac{a \operatorname{acot}{\left(a + b x^{4} \right)}}{4 b} + \frac{x^{4} \operatorname{acot}{\left(a + b x^{4} \right)}}{4} + \frac{\log{\left(a^{2} + 2 a b x^{4} + b^{2} x^{8} + 1 \right)}}{8 b} & \text{for}\: b \neq 0 \\\frac{x^{4} \operatorname{acot}{\left(a \right)}}{4} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*acot(a + b*x**4)/(4*b) + x**4*acot(a + b*x**4)/4 + log(a**2 + 2*a*b*x**4 + b**2*x**8 + 1)/(8*b), Ne(b, 0)), (x**4*acot(a)/4, True))","A",0
150,-1,0,0,0.000000," ","integrate(x**(-1+n)*acot(a+b*x**n),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
151,0,0,0,0.000000," ","integrate((a+b*acot((-c*x+1)**(1/2)/(c*x+1)**(1/2)))**n/(-c**2*x**2+1),x)","- \int \frac{\left(a + b \operatorname{acot}{\left(\frac{\sqrt{- c x + 1}}{\sqrt{c x + 1}} \right)}\right)^{n}}{c^{2} x^{2} - 1}\, dx"," ",0,"-Integral((a + b*acot(sqrt(-c*x + 1)/sqrt(c*x + 1)))**n/(c**2*x**2 - 1), x)","F",0
152,-1,0,0,0.000000," ","integrate((a+b*acot((-c*x+1)**(1/2)/(c*x+1)**(1/2)))**3/(-c**2*x**2+1),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
153,-1,0,0,0.000000," ","integrate((a+b*acot((-c*x+1)**(1/2)/(c*x+1)**(1/2)))**2/(-c**2*x**2+1),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
154,-1,0,0,0.000000," ","integrate((a+b*acot((-c*x+1)**(1/2)/(c*x+1)**(1/2)))/(-c**2*x**2+1),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
155,0,0,0,0.000000," ","integrate(1/(-c**2*x**2+1)/(a+b*acot((-c*x+1)**(1/2)/(c*x+1)**(1/2))),x)","- \int \frac{1}{a c^{2} x^{2} - a + b c^{2} x^{2} \operatorname{acot}{\left(\frac{\sqrt{- c x + 1}}{\sqrt{c x + 1}} \right)} - b \operatorname{acot}{\left(\frac{\sqrt{- c x + 1}}{\sqrt{c x + 1}} \right)}}\, dx"," ",0,"-Integral(1/(a*c**2*x**2 - a + b*c**2*x**2*acot(sqrt(-c*x + 1)/sqrt(c*x + 1)) - b*acot(sqrt(-c*x + 1)/sqrt(c*x + 1))), x)","F",0
156,0,0,0,0.000000," ","integrate(1/(-c**2*x**2+1)/(a+b*acot((-c*x+1)**(1/2)/(c*x+1)**(1/2)))**2,x)","- \int \frac{1}{a^{2} c^{2} x^{2} - a^{2} + 2 a b c^{2} x^{2} \operatorname{acot}{\left(\frac{\sqrt{- c x + 1}}{\sqrt{c x + 1}} \right)} - 2 a b \operatorname{acot}{\left(\frac{\sqrt{- c x + 1}}{\sqrt{c x + 1}} \right)} + b^{2} c^{2} x^{2} \operatorname{acot}^{2}{\left(\frac{\sqrt{- c x + 1}}{\sqrt{c x + 1}} \right)} - b^{2} \operatorname{acot}^{2}{\left(\frac{\sqrt{- c x + 1}}{\sqrt{c x + 1}} \right)}}\, dx"," ",0,"-Integral(1/(a**2*c**2*x**2 - a**2 + 2*a*b*c**2*x**2*acot(sqrt(-c*x + 1)/sqrt(c*x + 1)) - 2*a*b*acot(sqrt(-c*x + 1)/sqrt(c*x + 1)) + b**2*c**2*x**2*acot(sqrt(-c*x + 1)/sqrt(c*x + 1))**2 - b**2*acot(sqrt(-c*x + 1)/sqrt(c*x + 1))**2), x)","F",0
157,1,48,0,0.137393," ","integrate(1/2*pi-atan(tan(b*x+a)),x)","\frac{\pi x}{2} - \begin{cases} \frac{\left(\operatorname{atan}{\left(\tan{\left(a + b x \right)} \right)} + \pi \left\lfloor{\frac{a + b x - \frac{\pi}{2}}{\pi}}\right\rfloor\right)^{2}}{2 b} & \text{for}\: b \neq 0 \\x \left(\operatorname{atan}{\left(\tan{\left(a \right)} \right)} + \pi \left\lfloor{\frac{a - \frac{\pi}{2}}{\pi}}\right\rfloor\right) & \text{otherwise} \end{cases}"," ",0,"pi*x/2 - Piecewise(((atan(tan(a + b*x)) + pi*floor((a + b*x - pi/2)/pi))**2/(2*b), Ne(b, 0)), (x*(atan(tan(a)) + pi*floor((a - pi/2)/pi)), True))","B",0
158,-1,0,0,0.000000," ","integrate(x**2*acot(c+d*tan(b*x+a)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
159,-1,0,0,0.000000," ","integrate(x*acot(c+d*tan(b*x+a)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
160,0,0,0,0.000000," ","integrate(acot(c+d*tan(b*x+a)),x)","\int \operatorname{acot}{\left(c + d \tan{\left(a + b x \right)} \right)}\, dx"," ",0,"Integral(acot(c + d*tan(a + b*x)), x)","F",0
161,0,0,0,0.000000," ","integrate(acot(c+d*tan(b*x+a))/x,x)","\int \frac{\operatorname{acot}{\left(c + d \tan{\left(a + b x \right)} \right)}}{x}\, dx"," ",0,"Integral(acot(c + d*tan(a + b*x))/x, x)","F",0
162,-2,0,0,0.000000," ","integrate(x**2*acot(c+(1+I*c)*tan(b*x+a)),x)","\text{Exception raised: CoercionFailed}"," ",0,"Exception raised: CoercionFailed","F(-2)",0
163,-2,0,0,0.000000," ","integrate(x*acot(c+(1+I*c)*tan(b*x+a)),x)","\text{Exception raised: CoercionFailed}"," ",0,"Exception raised: CoercionFailed","F(-2)",0
164,-2,0,0,0.000000," ","integrate(acot(c+(1+I*c)*tan(b*x+a)),x)","\text{Exception raised: CoercionFailed}"," ",0,"Exception raised: CoercionFailed","F(-2)",0
165,-1,0,0,0.000000," ","integrate(acot(c+(1+I*c)*tan(b*x+a))/x,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
166,-2,0,0,0.000000," ","integrate(x**2*acot(c-(1-I*c)*tan(b*x+a)),x)","\text{Exception raised: CoercionFailed}"," ",0,"Exception raised: CoercionFailed","F(-2)",0
167,-2,0,0,0.000000," ","integrate(x*acot(c-(1-I*c)*tan(b*x+a)),x)","\text{Exception raised: CoercionFailed}"," ",0,"Exception raised: CoercionFailed","F(-2)",0
168,-2,0,0,0.000000," ","integrate(acot(c-(1-I*c)*tan(b*x+a)),x)","\text{Exception raised: CoercionFailed}"," ",0,"Exception raised: CoercionFailed","F(-2)",0
169,-1,0,0,0.000000," ","integrate(acot(c-(1-I*c)*tan(b*x+a))/x,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
170,1,19,0,0.123989," ","integrate(acot(cot(b*x+a)),x)","\begin{cases} \frac{\operatorname{acot}^{2}{\left(\cot{\left(a + b x \right)} \right)}}{2 b} & \text{for}\: b \neq 0 \\x \operatorname{acot}{\left(\cot{\left(a \right)} \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((acot(cot(a + b*x))**2/(2*b), Ne(b, 0)), (x*acot(cot(a)), True))","A",0
171,-1,0,0,0.000000," ","integrate(x**2*acot(c+d*cot(b*x+a)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
172,-1,0,0,0.000000," ","integrate(x*acot(c+d*cot(b*x+a)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
173,-1,0,0,0.000000," ","integrate(acot(c+d*cot(b*x+a)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
174,-1,0,0,0.000000," ","integrate(acot(c+d*cot(b*x+a))/x,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
175,-2,0,0,0.000000," ","integrate(x**2*(pi-acot(-c-(1-I*c)*cot(b*x+a))),x)","\text{Exception raised: CoercionFailed}"," ",0,"Exception raised: CoercionFailed","F(-2)",0
176,-2,0,0,0.000000," ","integrate(x*(pi-acot(-c-(1-I*c)*cot(b*x+a))),x)","\text{Exception raised: CoercionFailed}"," ",0,"Exception raised: CoercionFailed","F(-2)",0
177,-2,0,0,0.000000," ","integrate(pi-acot(-c-(1-I*c)*cot(b*x+a)),x)","\text{Exception raised: CoercionFailed}"," ",0,"Exception raised: CoercionFailed","F(-2)",0
178,-1,0,0,0.000000," ","integrate((pi-acot(-c-(1-I*c)*cot(b*x+a)))/x,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
179,-2,0,0,0.000000," ","integrate(x**2*(pi-acot(-c+(1+I*c)*cot(b*x+a))),x)","\text{Exception raised: CoercionFailed}"," ",0,"Exception raised: CoercionFailed","F(-2)",0
180,-2,0,0,0.000000," ","integrate(x*(pi-acot(-c+(1+I*c)*cot(b*x+a))),x)","\text{Exception raised: CoercionFailed}"," ",0,"Exception raised: CoercionFailed","F(-2)",0
181,-2,0,0,0.000000," ","integrate(pi-acot(-c+(1+I*c)*cot(b*x+a)),x)","\text{Exception raised: CoercionFailed}"," ",0,"Exception raised: CoercionFailed","F(-2)",0
182,-1,0,0,0.000000," ","integrate((pi-acot(-c+(1+I*c)*cot(b*x+a)))/x,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
183,0,0,0,0.000000," ","integrate((f*x+e)**3*acot(tanh(b*x+a)),x)","\int \left(e + f x\right)^{3} \operatorname{acot}{\left(\tanh{\left(a + b x \right)} \right)}\, dx"," ",0,"Integral((e + f*x)**3*acot(tanh(a + b*x)), x)","F",0
184,0,0,0,0.000000," ","integrate((f*x+e)**2*acot(tanh(b*x+a)),x)","\int \left(e + f x\right)^{2} \operatorname{acot}{\left(\tanh{\left(a + b x \right)} \right)}\, dx"," ",0,"Integral((e + f*x)**2*acot(tanh(a + b*x)), x)","F",0
185,0,0,0,0.000000," ","integrate((f*x+e)*acot(tanh(b*x+a)),x)","\int \left(e + f x\right) \operatorname{acot}{\left(\tanh{\left(a + b x \right)} \right)}\, dx"," ",0,"Integral((e + f*x)*acot(tanh(a + b*x)), x)","F",0
186,0,0,0,0.000000," ","integrate(acot(tanh(b*x+a)),x)","\int \operatorname{acot}{\left(\tanh{\left(a + b x \right)} \right)}\, dx"," ",0,"Integral(acot(tanh(a + b*x)), x)","F",0
187,0,0,0,0.000000," ","integrate(acot(tanh(b*x+a))/(f*x+e),x)","\int \frac{\operatorname{acot}{\left(\tanh{\left(a + b x \right)} \right)}}{e + f x}\, dx"," ",0,"Integral(acot(tanh(a + b*x))/(e + f*x), x)","F",0
188,-1,0,0,0.000000," ","integrate(x**2*acot(c+d*tanh(b*x+a)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
189,-1,0,0,0.000000," ","integrate(x*acot(c+d*tanh(b*x+a)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
190,0,0,0,0.000000," ","integrate(acot(c+d*tanh(b*x+a)),x)","\int \operatorname{acot}{\left(c + d \tanh{\left(a + b x \right)} \right)}\, dx"," ",0,"Integral(acot(c + d*tanh(a + b*x)), x)","F",0
191,-1,0,0,0.000000," ","integrate(acot(c+d*tanh(b*x+a))/x,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
192,-2,0,0,0.000000," ","integrate(x**2*acot(c+(I+c)*tanh(b*x+a)),x)","\text{Exception raised: CoercionFailed}"," ",0,"Exception raised: CoercionFailed","F(-2)",0
193,-2,0,0,0.000000," ","integrate(x*acot(c+(I+c)*tanh(b*x+a)),x)","\text{Exception raised: CoercionFailed}"," ",0,"Exception raised: CoercionFailed","F(-2)",0
194,-2,0,0,0.000000," ","integrate(acot(c+(I+c)*tanh(b*x+a)),x)","\text{Exception raised: CoercionFailed}"," ",0,"Exception raised: CoercionFailed","F(-2)",0
195,-1,0,0,0.000000," ","integrate(acot(c+(I+c)*tanh(b*x+a))/x,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
196,-2,0,0,0.000000," ","integrate(x**2*acot(c-(I-c)*tanh(b*x+a)),x)","\text{Exception raised: CoercionFailed}"," ",0,"Exception raised: CoercionFailed","F(-2)",0
197,-2,0,0,0.000000," ","integrate(x*acot(c-(I-c)*tanh(b*x+a)),x)","\text{Exception raised: CoercionFailed}"," ",0,"Exception raised: CoercionFailed","F(-2)",0
198,-2,0,0,0.000000," ","integrate(acot(c-(I-c)*tanh(b*x+a)),x)","\text{Exception raised: CoercionFailed}"," ",0,"Exception raised: CoercionFailed","F(-2)",0
199,-1,0,0,0.000000," ","integrate(acot(c-(I-c)*tanh(b*x+a))/x,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
200,0,0,0,0.000000," ","integrate((f*x+e)**3*acot(coth(b*x+a)),x)","\int \left(e + f x\right)^{3} \operatorname{acot}{\left(\coth{\left(a + b x \right)} \right)}\, dx"," ",0,"Integral((e + f*x)**3*acot(coth(a + b*x)), x)","F",0
201,0,0,0,0.000000," ","integrate((f*x+e)**2*acot(coth(b*x+a)),x)","\int \left(e + f x\right)^{2} \operatorname{acot}{\left(\coth{\left(a + b x \right)} \right)}\, dx"," ",0,"Integral((e + f*x)**2*acot(coth(a + b*x)), x)","F",0
202,0,0,0,0.000000," ","integrate((f*x+e)*acot(coth(b*x+a)),x)","\int \left(e + f x\right) \operatorname{acot}{\left(\coth{\left(a + b x \right)} \right)}\, dx"," ",0,"Integral((e + f*x)*acot(coth(a + b*x)), x)","F",0
203,0,0,0,0.000000," ","integrate(acot(coth(b*x+a)),x)","\int \operatorname{acot}{\left(\coth{\left(a + b x \right)} \right)}\, dx"," ",0,"Integral(acot(coth(a + b*x)), x)","F",0
204,-1,0,0,0.000000," ","integrate(acot(coth(b*x+a))/(f*x+e),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
205,-1,0,0,0.000000," ","integrate(x**2*acot(c+d*coth(b*x+a)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
206,-1,0,0,0.000000," ","integrate(x*acot(c+d*coth(b*x+a)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
207,-1,0,0,0.000000," ","integrate(acot(c+d*coth(b*x+a)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
208,-1,0,0,0.000000," ","integrate(acot(c+d*coth(b*x+a))/x,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
209,-2,0,0,0.000000," ","integrate(x**2*acot(c+(I+c)*coth(b*x+a)),x)","\text{Exception raised: CoercionFailed}"," ",0,"Exception raised: CoercionFailed","F(-2)",0
210,-2,0,0,0.000000," ","integrate(x*acot(c+(I+c)*coth(b*x+a)),x)","\text{Exception raised: CoercionFailed}"," ",0,"Exception raised: CoercionFailed","F(-2)",0
211,-2,0,0,0.000000," ","integrate(acot(c+(I+c)*coth(b*x+a)),x)","\text{Exception raised: CoercionFailed}"," ",0,"Exception raised: CoercionFailed","F(-2)",0
212,-1,0,0,0.000000," ","integrate(acot(c+(I+c)*coth(b*x+a))/x,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
213,-2,0,0,0.000000," ","integrate(x**2*acot(c-(I-c)*coth(b*x+a)),x)","\text{Exception raised: CoercionFailed}"," ",0,"Exception raised: CoercionFailed","F(-2)",0
214,-2,0,0,0.000000," ","integrate(x*acot(c-(I-c)*coth(b*x+a)),x)","\text{Exception raised: CoercionFailed}"," ",0,"Exception raised: CoercionFailed","F(-2)",0
215,-2,0,0,0.000000," ","integrate(acot(c-(I-c)*coth(b*x+a)),x)","\text{Exception raised: CoercionFailed}"," ",0,"Exception raised: CoercionFailed","F(-2)",0
216,-1,0,0,0.000000," ","integrate(acot(c-(I-c)*coth(b*x+a))/x,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
217,-1,0,0,0.000000," ","integrate((a+b*acot(c*x**n))*(d+e*ln(f*x**m))/x,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
218,0,0,0,0.000000," ","integrate(acot(exp(x)),x)","\int \operatorname{acot}{\left(e^{x} \right)}\, dx"," ",0,"Integral(acot(exp(x)), x)","F",0
219,0,0,0,0.000000," ","integrate(x*acot(exp(x)),x)","\int x \operatorname{acot}{\left(e^{x} \right)}\, dx"," ",0,"Integral(x*acot(exp(x)), x)","F",0
220,0,0,0,0.000000," ","integrate(x**2*acot(exp(x)),x)","\int x^{2} \operatorname{acot}{\left(e^{x} \right)}\, dx"," ",0,"Integral(x**2*acot(exp(x)), x)","F",0
221,0,0,0,0.000000," ","integrate(acot(exp(b*x+a)),x)","\int \operatorname{acot}{\left(e^{a + b x} \right)}\, dx"," ",0,"Integral(acot(exp(a + b*x)), x)","F",0
222,0,0,0,0.000000," ","integrate(x*acot(exp(b*x+a)),x)","\int x \operatorname{acot}{\left(e^{a} e^{b x} \right)}\, dx"," ",0,"Integral(x*acot(exp(a)*exp(b*x)), x)","F",0
223,0,0,0,0.000000," ","integrate(x**2*acot(exp(b*x+a)),x)","\int x^{2} \operatorname{acot}{\left(e^{a} e^{b x} \right)}\, dx"," ",0,"Integral(x**2*acot(exp(a)*exp(b*x)), x)","F",0
224,-1,0,0,0.000000," ","integrate(acot(a+b*f**(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
225,-1,0,0,0.000000," ","integrate(x*acot(a+b*f**(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
226,-1,0,0,0.000000," ","integrate(x**2*acot(a+b*f**(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
227,1,19,0,6.091766," ","integrate(acot(exp(x))/exp(x),x)","- x + \frac{\log{\left(e^{2 x} + 1 \right)}}{2} - e^{- x} \operatorname{acot}{\left(e^{x} \right)}"," ",0,"-x + log(exp(2*x) + 1)/2 - exp(-x)*acot(exp(x))","A",0
228,1,12,0,0.527484," ","integrate(1/(a*x**2+a)/(b-2*b*acot(x)),x)","\frac{\log{\left(\operatorname{acot}{\left(x \right)} - \frac{1}{2} \right)}}{2 a b}"," ",0,"log(acot(x) - 1/2)/(2*a*b)","A",0
229,-1,0,0,0.000000," ","integrate(exp(c*(b*x+a))*acot(sinh(b*c*x+a*c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
230,-1,0,0,0.000000," ","integrate(exp(c*(b*x+a))*acot(cosh(b*c*x+a*c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
231,-1,0,0,0.000000," ","integrate(exp(c*(b*x+a))*acot(tanh(b*c*x+a*c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
232,0,0,0,0.000000," ","integrate(exp(c*(b*x+a))*acot(coth(b*c*x+a*c)),x)","e^{a c} \int e^{b c x} \operatorname{acot}{\left(\coth{\left(a c + b c x \right)} \right)}\, dx"," ",0,"exp(a*c)*Integral(exp(b*c*x)*acot(coth(a*c + b*c*x)), x)","F",0
233,-1,0,0,0.000000," ","integrate(exp(c*(b*x+a))*acot(sech(b*c*x+a*c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
234,0,0,0,0.000000," ","integrate(exp(c*(b*x+a))*acot(csch(b*c*x+a*c)),x)","e^{a c} \int e^{b c x} \operatorname{acot}{\left(\operatorname{csch}{\left(a c + b c x \right)} \right)}\, dx"," ",0,"exp(a*c)*Integral(exp(b*c*x)*acot(csch(a*c + b*c*x)), x)","F",0
