1,1,29,0,0.154470," ","integrate(cot(b*x+a),x)","\begin{cases} - \frac{\log{\left(\tan^{2}{\left(a + b x \right)} + 1 \right)}}{2 b} + \frac{\log{\left(\tan{\left(a + b x \right)} \right)}}{b} & \text{for}\: b \neq 0 \\x \cot{\left(a \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-log(tan(a + b*x)**2 + 1)/(2*b) + log(tan(a + b*x))/b, Ne(b, 0)), (x*cot(a), True))","A",0
2,1,17,0,0.127009," ","integrate(cot(b*x+a)**2,x)","\begin{cases} - x - \frac{\cot{\left(a + b x \right)}}{b} & \text{for}\: b \neq 0 \\x \cot^{2}{\left(a \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-x - cot(a + b*x)/b, Ne(b, 0)), (x*cot(a)**2, True))","A",0
3,1,58,0,0.434265," ","integrate(cot(b*x+a)**3,x)","\begin{cases} \tilde{\infty} x & \text{for}\: \left(a = 0 \vee a = - b x\right) \wedge \left(a = - b x \vee b = 0\right) \\x \cot^{3}{\left(a \right)} & \text{for}\: b = 0 \\\frac{\log{\left(\tan^{2}{\left(a + b x \right)} + 1 \right)}}{2 b} - \frac{\log{\left(\tan{\left(a + b x \right)} \right)}}{b} - \frac{1}{2 b \tan^{2}{\left(a + b x \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*x, (Eq(a, 0) | Eq(a, -b*x)) & (Eq(b, 0) | Eq(a, -b*x))), (x*cot(a)**3, Eq(b, 0)), (log(tan(a + b*x)**2 + 1)/(2*b) - log(tan(a + b*x))/b - 1/(2*b*tan(a + b*x)**2), True))","A",0
4,1,27,0,0.192099," ","integrate(cot(b*x+a)**4,x)","\begin{cases} x - \frac{\cot^{3}{\left(a + b x \right)}}{3 b} + \frac{\cot{\left(a + b x \right)}}{b} & \text{for}\: b \neq 0 \\x \cot^{4}{\left(a \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x - cot(a + b*x)**3/(3*b) + cot(a + b*x)/b, Ne(b, 0)), (x*cot(a)**4, True))","A",0
5,1,71,0,0.770816," ","integrate(cot(b*x+a)**5,x)","\begin{cases} \tilde{\infty} x & \text{for}\: \left(a = 0 \vee a = - b x\right) \wedge \left(a = - b x \vee b = 0\right) \\x \cot^{5}{\left(a \right)} & \text{for}\: b = 0 \\- \frac{\log{\left(\tan^{2}{\left(a + b x \right)} + 1 \right)}}{2 b} + \frac{\log{\left(\tan{\left(a + b x \right)} \right)}}{b} + \frac{1}{2 b \tan^{2}{\left(a + b x \right)}} - \frac{1}{4 b \tan^{4}{\left(a + b x \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*x, (Eq(a, 0) | Eq(a, -b*x)) & (Eq(b, 0) | Eq(a, -b*x))), (x*cot(a)**5, Eq(b, 0)), (-log(tan(a + b*x)**2 + 1)/(2*b) + log(tan(a + b*x))/b + 1/(2*b*tan(a + b*x)**2) - 1/(4*b*tan(a + b*x)**4), True))","A",0
6,1,39,0,0.407379," ","integrate(cot(b*x+a)**6,x)","\begin{cases} - x - \frac{\cot^{5}{\left(a + b x \right)}}{5 b} + \frac{\cot^{3}{\left(a + b x \right)}}{3 b} - \frac{\cot{\left(a + b x \right)}}{b} & \text{for}\: b \neq 0 \\x \cot^{6}{\left(a \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-x - cot(a + b*x)**5/(5*b) + cot(a + b*x)**3/(3*b) - cot(a + b*x)/b, Ne(b, 0)), (x*cot(a)**6, True))","A",0
7,1,85,0,1.221575," ","integrate(cot(b*x+a)**7,x)","\begin{cases} \tilde{\infty} x & \text{for}\: \left(a = 0 \vee a = - b x\right) \wedge \left(a = - b x \vee b = 0\right) \\x \cot^{7}{\left(a \right)} & \text{for}\: b = 0 \\\frac{\log{\left(\tan^{2}{\left(a + b x \right)} + 1 \right)}}{2 b} - \frac{\log{\left(\tan{\left(a + b x \right)} \right)}}{b} - \frac{1}{2 b \tan^{2}{\left(a + b x \right)}} + \frac{1}{4 b \tan^{4}{\left(a + b x \right)}} - \frac{1}{6 b \tan^{6}{\left(a + b x \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*x, (Eq(a, 0) | Eq(a, -b*x)) & (Eq(b, 0) | Eq(a, -b*x))), (x*cot(a)**7, Eq(b, 0)), (log(tan(a + b*x)**2 + 1)/(2*b) - log(tan(a + b*x))/b - 1/(2*b*tan(a + b*x)**2) + 1/(4*b*tan(a + b*x)**4) - 1/(6*b*tan(a + b*x)**6), True))","A",0
8,1,51,0,0.776990," ","integrate(cot(b*x+a)**8,x)","\begin{cases} x - \frac{\cot^{7}{\left(a + b x \right)}}{7 b} + \frac{\cot^{5}{\left(a + b x \right)}}{5 b} - \frac{\cot^{3}{\left(a + b x \right)}}{3 b} + \frac{\cot{\left(a + b x \right)}}{b} & \text{for}\: b \neq 0 \\x \cot^{8}{\left(a \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x - cot(a + b*x)**7/(7*b) + cot(a + b*x)**5/(5*b) - cot(a + b*x)**3/(3*b) + cot(a + b*x)/b, Ne(b, 0)), (x*cot(a)**8, True))","A",0
9,0,0,0,0.000000," ","integrate((c*cot(b*x+a))**(7/2),x)","\int \left(c \cot{\left(a + b x \right)}\right)^{\frac{7}{2}}\, dx"," ",0,"Integral((c*cot(a + b*x))**(7/2), x)","F",0
10,0,0,0,0.000000," ","integrate((c*cot(b*x+a))**(5/2),x)","\int \left(c \cot{\left(a + b x \right)}\right)^{\frac{5}{2}}\, dx"," ",0,"Integral((c*cot(a + b*x))**(5/2), x)","F",0
11,0,0,0,0.000000," ","integrate((c*cot(b*x+a))**(3/2),x)","\int \left(c \cot{\left(a + b x \right)}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((c*cot(a + b*x))**(3/2), x)","F",0
12,0,0,0,0.000000," ","integrate((c*cot(b*x+a))**(1/2),x)","\int \sqrt{c \cot{\left(a + b x \right)}}\, dx"," ",0,"Integral(sqrt(c*cot(a + b*x)), x)","F",0
13,0,0,0,0.000000," ","integrate(1/(c*cot(b*x+a))**(1/2),x)","\int \frac{1}{\sqrt{c \cot{\left(a + b x \right)}}}\, dx"," ",0,"Integral(1/sqrt(c*cot(a + b*x)), x)","F",0
14,0,0,0,0.000000," ","integrate(1/(c*cot(b*x+a))**(3/2),x)","\int \frac{1}{\left(c \cot{\left(a + b x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((c*cot(a + b*x))**(-3/2), x)","F",0
15,0,0,0,0.000000," ","integrate(1/(c*cot(b*x+a))**(5/2),x)","\int \frac{1}{\left(c \cot{\left(a + b x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((c*cot(a + b*x))**(-5/2), x)","F",0
16,0,0,0,0.000000," ","integrate(1/(c*cot(b*x+a))**(7/2),x)","\int \frac{1}{\left(c \cot{\left(a + b x \right)}\right)^{\frac{7}{2}}}\, dx"," ",0,"Integral((c*cot(a + b*x))**(-7/2), x)","F",0
17,0,0,0,0.000000," ","integrate((c*cot(b*x+a))**(4/3),x)","\int \left(c \cot{\left(a + b x \right)}\right)^{\frac{4}{3}}\, dx"," ",0,"Integral((c*cot(a + b*x))**(4/3), x)","F",0
18,0,0,0,0.000000," ","integrate((c*cot(b*x+a))**(2/3),x)","\int \left(c \cot{\left(a + b x \right)}\right)^{\frac{2}{3}}\, dx"," ",0,"Integral((c*cot(a + b*x))**(2/3), x)","F",0
19,0,0,0,0.000000," ","integrate((c*cot(b*x+a))**(1/3),x)","\int \sqrt[3]{c \cot{\left(a + b x \right)}}\, dx"," ",0,"Integral((c*cot(a + b*x))**(1/3), x)","F",0
20,0,0,0,0.000000," ","integrate(1/(c*cot(b*x+a))**(1/3),x)","\int \frac{1}{\sqrt[3]{c \cot{\left(a + b x \right)}}}\, dx"," ",0,"Integral((c*cot(a + b*x))**(-1/3), x)","F",0
21,0,0,0,0.000000," ","integrate(1/(c*cot(b*x+a))**(2/3),x)","\int \frac{1}{\left(c \cot{\left(a + b x \right)}\right)^{\frac{2}{3}}}\, dx"," ",0,"Integral((c*cot(a + b*x))**(-2/3), x)","F",0
22,0,0,0,0.000000," ","integrate(1/(c*cot(b*x+a))**(4/3),x)","\int \frac{1}{\left(c \cot{\left(a + b x \right)}\right)^{\frac{4}{3}}}\, dx"," ",0,"Integral((c*cot(a + b*x))**(-4/3), x)","F",0
23,0,0,0,0.000000," ","integrate(cot(b*x+a)**n,x)","\int \cot^{n}{\left(a + b x \right)}\, dx"," ",0,"Integral(cot(a + b*x)**n, x)","F",0
24,0,0,0,0.000000," ","integrate((b*cot(d*x+c))**n,x)","\int \left(b \cot{\left(c + d x \right)}\right)^{n}\, dx"," ",0,"Integral((b*cot(c + d*x))**n, x)","F",0
25,0,0,0,0.000000," ","integrate((a*cot(x)**2)**(3/2),x)","\int \left(a \cot^{2}{\left(x \right)}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((a*cot(x)**2)**(3/2), x)","F",0
26,0,0,0,0.000000," ","integrate((a*cot(x)**2)**(1/2),x)","\int \sqrt{a \cot^{2}{\left(x \right)}}\, dx"," ",0,"Integral(sqrt(a*cot(x)**2), x)","F",0
27,0,0,0,0.000000," ","integrate(1/(a*cot(x)**2)**(1/2),x)","\int \frac{1}{\sqrt{a \cot^{2}{\left(x \right)}}}\, dx"," ",0,"Integral(1/sqrt(a*cot(x)**2), x)","F",0
28,0,0,0,0.000000," ","integrate(1/(a*cot(x)**2)**(3/2),x)","\int \frac{1}{\left(a \cot^{2}{\left(x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a*cot(x)**2)**(-3/2), x)","F",0
29,0,0,0,0.000000," ","integrate((a*cot(x)**3)**(3/2),x)","\int \left(a \cot^{3}{\left(x \right)}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((a*cot(x)**3)**(3/2), x)","F",0
30,0,0,0,0.000000," ","integrate((a*cot(x)**3)**(1/2),x)","\int \sqrt{a \cot^{3}{\left(x \right)}}\, dx"," ",0,"Integral(sqrt(a*cot(x)**3), x)","F",0
31,0,0,0,0.000000," ","integrate(1/(a*cot(x)**3)**(1/2),x)","\int \frac{1}{\sqrt{a \cot^{3}{\left(x \right)}}}\, dx"," ",0,"Integral(1/sqrt(a*cot(x)**3), x)","F",0
32,0,0,0,0.000000," ","integrate(1/(a*cot(x)**3)**(3/2),x)","\int \frac{1}{\left(a \cot^{3}{\left(x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a*cot(x)**3)**(-3/2), x)","F",0
33,0,0,0,0.000000," ","integrate((a*cot(x)**4)**(3/2),x)","\int \left(a \cot^{4}{\left(x \right)}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((a*cot(x)**4)**(3/2), x)","F",0
34,0,0,0,0.000000," ","integrate((a*cot(x)**4)**(1/2),x)","\int \sqrt{a \cot^{4}{\left(x \right)}}\, dx"," ",0,"Integral(sqrt(a*cot(x)**4), x)","F",0
35,0,0,0,0.000000," ","integrate(1/(a*cot(x)**4)**(1/2),x)","\int \frac{1}{\sqrt{a \cot^{4}{\left(x \right)}}}\, dx"," ",0,"Integral(1/sqrt(a*cot(x)**4), x)","F",0
36,0,0,0,0.000000," ","integrate(1/(a*cot(x)**4)**(3/2),x)","\int \frac{1}{\left(a \cot^{4}{\left(x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a*cot(x)**4)**(-3/2), x)","F",0
37,0,0,0,0.000000," ","integrate((b*cot(d*x+c)**p)**n,x)","\int \left(b \cot^{p}{\left(c + d x \right)}\right)^{n}\, dx"," ",0,"Integral((b*cot(c + d*x)**p)**n, x)","F",0
38,0,0,0,0.000000," ","integrate((a*(b*cot(d*x+c))**p)**n,x)","\int \left(a \left(b \cot{\left(c + d x \right)}\right)^{p}\right)^{n}\, dx"," ",0,"Integral((a*(b*cot(c + d*x))**p)**n, x)","F",0
39,0,0,0,0.000000," ","integrate((b*cot(f*x+e))**n*(a*sin(f*x+e))**m,x)","\int \left(a \sin{\left(e + f x \right)}\right)^{m} \left(b \cot{\left(e + f x \right)}\right)^{n}\, dx"," ",0,"Integral((a*sin(e + f*x))**m*(b*cot(e + f*x))**n, x)","F",0
40,0,0,0,0.000000," ","integrate((a*cos(f*x+e))**m*(b*cot(f*x+e))**n,x)","\int \left(a \cos{\left(e + f x \right)}\right)^{m} \left(b \cot{\left(e + f x \right)}\right)^{n}\, dx"," ",0,"Integral((a*cos(e + f*x))**m*(b*cot(e + f*x))**n, x)","F",0
41,0,0,0,0.000000," ","integrate((a*cot(f*x+e))**m*(b*cot(f*x+e))**n,x)","\int \left(a \cot{\left(e + f x \right)}\right)^{m} \left(b \cot{\left(e + f x \right)}\right)^{n}\, dx"," ",0,"Integral((a*cot(e + f*x))**m*(b*cot(e + f*x))**n, x)","F",0
42,0,0,0,0.000000," ","integrate((b*cot(f*x+e))**n*(a*sec(f*x+e))**m,x)","\int \left(a \sec{\left(e + f x \right)}\right)^{m} \left(b \cot{\left(e + f x \right)}\right)^{n}\, dx"," ",0,"Integral((a*sec(e + f*x))**m*(b*cot(e + f*x))**n, x)","F",0
43,-1,0,0,0.000000," ","integrate((d*cot(f*x+e))**n*csc(f*x+e)**6,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
44,0,0,0,0.000000," ","integrate((d*cot(f*x+e))**n*csc(f*x+e)**4,x)","\int \left(d \cot{\left(e + f x \right)}\right)^{n} \csc^{4}{\left(e + f x \right)}\, dx"," ",0,"Integral((d*cot(e + f*x))**n*csc(e + f*x)**4, x)","F",0
45,0,0,0,0.000000," ","integrate((d*cot(f*x+e))**n*csc(f*x+e)**2,x)","\int \left(d \cot{\left(e + f x \right)}\right)^{n} \csc^{2}{\left(e + f x \right)}\, dx"," ",0,"Integral((d*cot(e + f*x))**n*csc(e + f*x)**2, x)","F",0
46,0,0,0,0.000000," ","integrate((d*cot(f*x+e))**n*sin(f*x+e)**2,x)","\int \left(d \cot{\left(e + f x \right)}\right)^{n} \sin^{2}{\left(e + f x \right)}\, dx"," ",0,"Integral((d*cot(e + f*x))**n*sin(e + f*x)**2, x)","F",0
47,0,0,0,0.000000," ","integrate((d*cot(f*x+e))**n*sin(f*x+e)**4,x)","\int \left(d \cot{\left(e + f x \right)}\right)^{n} \sin^{4}{\left(e + f x \right)}\, dx"," ",0,"Integral((d*cot(e + f*x))**n*sin(e + f*x)**4, x)","F",0
48,0,0,0,0.000000," ","integrate((d*cot(f*x+e))**n*csc(f*x+e)**3,x)","\int \left(d \cot{\left(e + f x \right)}\right)^{n} \csc^{3}{\left(e + f x \right)}\, dx"," ",0,"Integral((d*cot(e + f*x))**n*csc(e + f*x)**3, x)","F",0
49,0,0,0,0.000000," ","integrate((d*cot(f*x+e))**n*csc(f*x+e),x)","\int \left(d \cot{\left(e + f x \right)}\right)^{n} \csc{\left(e + f x \right)}\, dx"," ",0,"Integral((d*cot(e + f*x))**n*csc(e + f*x), x)","F",0
50,0,0,0,0.000000," ","integrate((d*cot(f*x+e))**n*sin(f*x+e),x)","\int \left(d \cot{\left(e + f x \right)}\right)^{n} \sin{\left(e + f x \right)}\, dx"," ",0,"Integral((d*cot(e + f*x))**n*sin(e + f*x), x)","F",0
51,-1,0,0,0.000000," ","integrate((d*cot(f*x+e))**n*sin(f*x+e)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
52,0,0,0,0.000000," ","integrate((b*cot(f*x+e))**n*(a*csc(f*x+e))**m,x)","\int \left(a \csc{\left(e + f x \right)}\right)^{m} \left(b \cot{\left(e + f x \right)}\right)^{n}\, dx"," ",0,"Integral((a*csc(e + f*x))**m*(b*cot(e + f*x))**n, x)","F",0
