1,1,19,0,0.853864," ","integrate(cot(b*x+a),x, algorithm=""fricas"")","\frac{\log\left(-\frac{1}{2} \, \cos\left(2 \, b x + 2 \, a\right) + \frac{1}{2}\right)}{2 \, b}"," ",0,"1/2*log(-1/2*cos(2*b*x + 2*a) + 1/2)/b","A",0
2,1,39,0,0.434666," ","integrate(cot(b*x+a)^2,x, algorithm=""fricas"")","-\frac{b x \sin\left(2 \, b x + 2 \, a\right) + \cos\left(2 \, b x + 2 \, a\right) + 1}{b \sin\left(2 \, b x + 2 \, a\right)}"," ",0,"-(b*x*sin(2*b*x + 2*a) + cos(2*b*x + 2*a) + 1)/(b*sin(2*b*x + 2*a))","B",0
3,1,47,0,0.542259," ","integrate(cot(b*x+a)^3,x, algorithm=""fricas"")","-\frac{{\left(\cos\left(2 \, b x + 2 \, a\right) - 1\right)} \log\left(-\frac{1}{2} \, \cos\left(2 \, b x + 2 \, a\right) + \frac{1}{2}\right) - 2}{2 \, {\left(b \cos\left(2 \, b x + 2 \, a\right) - b\right)}}"," ",0,"-1/2*((cos(2*b*x + 2*a) - 1)*log(-1/2*cos(2*b*x + 2*a) + 1/2) - 2)/(b*cos(2*b*x + 2*a) - b)","A",0
4,1,84,0,0.442525," ","integrate(cot(b*x+a)^4,x, algorithm=""fricas"")","\frac{4 \, \cos\left(2 \, b x + 2 \, a\right)^{2} + 3 \, {\left(b x \cos\left(2 \, b x + 2 \, a\right) - b x\right)} \sin\left(2 \, b x + 2 \, a\right) + 2 \, \cos\left(2 \, b x + 2 \, a\right) - 2}{3 \, {\left(b \cos\left(2 \, b x + 2 \, a\right) - b\right)} \sin\left(2 \, b x + 2 \, a\right)}"," ",0,"1/3*(4*cos(2*b*x + 2*a)^2 + 3*(b*x*cos(2*b*x + 2*a) - b*x)*sin(2*b*x + 2*a) + 2*cos(2*b*x + 2*a) - 2)/((b*cos(2*b*x + 2*a) - b)*sin(2*b*x + 2*a))","B",0
5,1,83,0,0.456556," ","integrate(cot(b*x+a)^5,x, algorithm=""fricas"")","\frac{{\left(\cos\left(2 \, b x + 2 \, a\right)^{2} - 2 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \log\left(-\frac{1}{2} \, \cos\left(2 \, b x + 2 \, a\right) + \frac{1}{2}\right) - 4 \, \cos\left(2 \, b x + 2 \, a\right) + 2}{2 \, {\left(b \cos\left(2 \, b x + 2 \, a\right)^{2} - 2 \, b \cos\left(2 \, b x + 2 \, a\right) + b\right)}}"," ",0,"1/2*((cos(2*b*x + 2*a)^2 - 2*cos(2*b*x + 2*a) + 1)*log(-1/2*cos(2*b*x + 2*a) + 1/2) - 4*cos(2*b*x + 2*a) + 2)/(b*cos(2*b*x + 2*a)^2 - 2*b*cos(2*b*x + 2*a) + b)","B",0
6,1,123,0,0.614028," ","integrate(cot(b*x+a)^6,x, algorithm=""fricas"")","-\frac{23 \, \cos\left(2 \, b x + 2 \, a\right)^{3} - \cos\left(2 \, b x + 2 \, a\right)^{2} + 15 \, {\left(b x \cos\left(2 \, b x + 2 \, a\right)^{2} - 2 \, b x \cos\left(2 \, b x + 2 \, a\right) + b x\right)} \sin\left(2 \, b x + 2 \, a\right) - 11 \, \cos\left(2 \, b x + 2 \, a\right) + 13}{15 \, {\left(b \cos\left(2 \, b x + 2 \, a\right)^{2} - 2 \, b \cos\left(2 \, b x + 2 \, a\right) + b\right)} \sin\left(2 \, b x + 2 \, a\right)}"," ",0,"-1/15*(23*cos(2*b*x + 2*a)^3 - cos(2*b*x + 2*a)^2 + 15*(b*x*cos(2*b*x + 2*a)^2 - 2*b*x*cos(2*b*x + 2*a) + b*x)*sin(2*b*x + 2*a) - 11*cos(2*b*x + 2*a) + 13)/((b*cos(2*b*x + 2*a)^2 - 2*b*cos(2*b*x + 2*a) + b)*sin(2*b*x + 2*a))","B",0
7,1,126,0,0.496914," ","integrate(cot(b*x+a)^7,x, algorithm=""fricas"")","\frac{18 \, \cos\left(2 \, b x + 2 \, a\right)^{2} - 3 \, {\left(\cos\left(2 \, b x + 2 \, a\right)^{3} - 3 \, \cos\left(2 \, b x + 2 \, a\right)^{2} + 3 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \log\left(-\frac{1}{2} \, \cos\left(2 \, b x + 2 \, a\right) + \frac{1}{2}\right) - 18 \, \cos\left(2 \, b x + 2 \, a\right) + 8}{6 \, {\left(b \cos\left(2 \, b x + 2 \, a\right)^{3} - 3 \, b \cos\left(2 \, b x + 2 \, a\right)^{2} + 3 \, b \cos\left(2 \, b x + 2 \, a\right) - b\right)}}"," ",0,"1/6*(18*cos(2*b*x + 2*a)^2 - 3*(cos(2*b*x + 2*a)^3 - 3*cos(2*b*x + 2*a)^2 + 3*cos(2*b*x + 2*a) - 1)*log(-1/2*cos(2*b*x + 2*a) + 1/2) - 18*cos(2*b*x + 2*a) + 8)/(b*cos(2*b*x + 2*a)^3 - 3*b*cos(2*b*x + 2*a)^2 + 3*b*cos(2*b*x + 2*a) - b)","B",0
8,1,168,0,0.528253," ","integrate(cot(b*x+a)^8,x, algorithm=""fricas"")","\frac{176 \, \cos\left(2 \, b x + 2 \, a\right)^{4} - 108 \, \cos\left(2 \, b x + 2 \, a\right)^{3} + 20 \, \cos\left(2 \, b x + 2 \, a\right)^{2} + 105 \, {\left(b x \cos\left(2 \, b x + 2 \, a\right)^{3} - 3 \, b x \cos\left(2 \, b x + 2 \, a\right)^{2} + 3 \, b x \cos\left(2 \, b x + 2 \, a\right) - b x\right)} \sin\left(2 \, b x + 2 \, a\right) + 228 \, \cos\left(2 \, b x + 2 \, a\right) - 76}{105 \, {\left(b \cos\left(2 \, b x + 2 \, a\right)^{3} - 3 \, b \cos\left(2 \, b x + 2 \, a\right)^{2} + 3 \, b \cos\left(2 \, b x + 2 \, a\right) - b\right)} \sin\left(2 \, b x + 2 \, a\right)}"," ",0,"1/105*(176*cos(2*b*x + 2*a)^4 - 108*cos(2*b*x + 2*a)^3 + 20*cos(2*b*x + 2*a)^2 + 105*(b*x*cos(2*b*x + 2*a)^3 - 3*b*x*cos(2*b*x + 2*a)^2 + 3*b*x*cos(2*b*x + 2*a) - b*x)*sin(2*b*x + 2*a) + 228*cos(2*b*x + 2*a) - 76)/((b*cos(2*b*x + 2*a)^3 - 3*b*cos(2*b*x + 2*a)^2 + 3*b*cos(2*b*x + 2*a) - b)*sin(2*b*x + 2*a))","B",0
9,-2,0,0,0.000000," ","integrate((c*cot(b*x+a))^(7/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   catdef: division by zero","F(-2)",0
10,-2,0,0,0.000000," ","integrate((c*cot(b*x+a))^(5/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   catdef: division by zero","F(-2)",0
11,-2,0,0,0.000000," ","integrate((c*cot(b*x+a))^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   catdef: division by zero","F(-2)",0
12,-2,0,0,0.000000," ","integrate((c*cot(b*x+a))^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   catdef: division by zero","F(-2)",0
13,-2,0,0,0.000000," ","integrate(1/(c*cot(b*x+a))^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   catdef: division by zero","F(-2)",0
14,-2,0,0,0.000000," ","integrate(1/(c*cot(b*x+a))^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   catdef: division by zero","F(-2)",0
15,-2,0,0,0.000000," ","integrate(1/(c*cot(b*x+a))^(5/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   catdef: division by zero","F(-2)",0
16,-2,0,0,0.000000," ","integrate(1/(c*cot(b*x+a))^(7/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   catdef: division by zero","F(-2)",0
17,-2,0,0,0.000000," ","integrate((c*cot(b*x+a))^(4/3),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   catdef: division by zero","F(-2)",0
18,-2,0,0,0.000000," ","integrate((c*cot(b*x+a))^(2/3),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   catdef: division by zero","F(-2)",0
19,1,211,0,0.652000," ","integrate((c*cot(b*x+a))^(1/3),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{3} c^{\frac{1}{3}} \arctan\left(-\frac{\sqrt{3} c - 2 \, \sqrt{3} c^{\frac{1}{3}} \left(\frac{c \cos\left(2 \, b x + 2 \, a\right) + c}{\sin\left(2 \, b x + 2 \, a\right)}\right)^{\frac{2}{3}}}{3 \, c}\right) - 2 \, c^{\frac{1}{3}} \log\left(c^{\frac{2}{3}} + \left(\frac{c \cos\left(2 \, b x + 2 \, a\right) + c}{\sin\left(2 \, b x + 2 \, a\right)}\right)^{\frac{2}{3}}\right) + c^{\frac{1}{3}} \log\left(\frac{c^{\frac{4}{3}} \sin\left(2 \, b x + 2 \, a\right) - c^{\frac{2}{3}} \left(\frac{c \cos\left(2 \, b x + 2 \, a\right) + c}{\sin\left(2 \, b x + 2 \, a\right)}\right)^{\frac{2}{3}} \sin\left(2 \, b x + 2 \, a\right) + {\left(c \cos\left(2 \, b x + 2 \, a\right) + c\right)} \left(\frac{c \cos\left(2 \, b x + 2 \, a\right) + c}{\sin\left(2 \, b x + 2 \, a\right)}\right)^{\frac{1}{3}}}{\sin\left(2 \, b x + 2 \, a\right)}\right)}{4 \, b}"," ",0,"-1/4*(2*sqrt(3)*c^(1/3)*arctan(-1/3*(sqrt(3)*c - 2*sqrt(3)*c^(1/3)*((c*cos(2*b*x + 2*a) + c)/sin(2*b*x + 2*a))^(2/3))/c) - 2*c^(1/3)*log(c^(2/3) + ((c*cos(2*b*x + 2*a) + c)/sin(2*b*x + 2*a))^(2/3)) + c^(1/3)*log((c^(4/3)*sin(2*b*x + 2*a) - c^(2/3)*((c*cos(2*b*x + 2*a) + c)/sin(2*b*x + 2*a))^(2/3)*sin(2*b*x + 2*a) + (c*cos(2*b*x + 2*a) + c)*((c*cos(2*b*x + 2*a) + c)/sin(2*b*x + 2*a))^(1/3))/sin(2*b*x + 2*a)))/b","B",0
20,1,639,0,0.766244," ","integrate(1/(c*cot(b*x+a))^(1/3),x, algorithm=""fricas"")","\left[\frac{\sqrt{3} c \sqrt{\frac{\left(-c\right)^{\frac{1}{3}}}{c}} \log\left(\frac{1}{2} \, \sqrt{3} {\left(\left(-c\right)^{\frac{2}{3}} \left(\frac{c \cos\left(2 \, b x + 2 \, a\right) + c}{\sin\left(2 \, b x + 2 \, a\right)}\right)^{\frac{2}{3}} {\left(\cos\left(2 \, b x + 2 \, a\right) - 1\right)} - 2 \, c \left(\frac{c \cos\left(2 \, b x + 2 \, a\right) + c}{\sin\left(2 \, b x + 2 \, a\right)}\right)^{\frac{1}{3}} \sin\left(2 \, b x + 2 \, a\right) + {\left(c \cos\left(2 \, b x + 2 \, a\right) - c\right)} \left(-c\right)^{\frac{1}{3}}\right)} \sqrt{\frac{\left(-c\right)^{\frac{1}{3}}}{c}} - \frac{3}{2} \, \left(-c\right)^{\frac{1}{3}} \left(\frac{c \cos\left(2 \, b x + 2 \, a\right) + c}{\sin\left(2 \, b x + 2 \, a\right)}\right)^{\frac{2}{3}} {\left(\cos\left(2 \, b x + 2 \, a\right) - 1\right)} + \frac{3}{2} \, c \cos\left(2 \, b x + 2 \, a\right) + \frac{1}{2} \, c\right) - 2 \, \left(-c\right)^{\frac{2}{3}} \log\left(\left(-c\right)^{\frac{2}{3}} + \left(\frac{c \cos\left(2 \, b x + 2 \, a\right) + c}{\sin\left(2 \, b x + 2 \, a\right)}\right)^{\frac{2}{3}}\right) + \left(-c\right)^{\frac{2}{3}} \log\left(-\frac{\left(-c\right)^{\frac{1}{3}} c \sin\left(2 \, b x + 2 \, a\right) + \left(-c\right)^{\frac{2}{3}} \left(\frac{c \cos\left(2 \, b x + 2 \, a\right) + c}{\sin\left(2 \, b x + 2 \, a\right)}\right)^{\frac{2}{3}} \sin\left(2 \, b x + 2 \, a\right) - {\left(c \cos\left(2 \, b x + 2 \, a\right) + c\right)} \left(\frac{c \cos\left(2 \, b x + 2 \, a\right) + c}{\sin\left(2 \, b x + 2 \, a\right)}\right)^{\frac{1}{3}}}{\sin\left(2 \, b x + 2 \, a\right)}\right)}{4 \, b c}, -\frac{2 \, \sqrt{3} c \sqrt{-\frac{\left(-c\right)^{\frac{1}{3}}}{c}} \arctan\left(\frac{\sqrt{3} \left(-c\right)^{\frac{1}{3}} c \sqrt{-\frac{\left(-c\right)^{\frac{1}{3}}}{c}} + 2 \, \sqrt{3} \left(-c\right)^{\frac{2}{3}} \left(\frac{c \cos\left(2 \, b x + 2 \, a\right) + c}{\sin\left(2 \, b x + 2 \, a\right)}\right)^{\frac{2}{3}} \sqrt{-\frac{\left(-c\right)^{\frac{1}{3}}}{c}}}{3 \, c}\right) + 2 \, \left(-c\right)^{\frac{2}{3}} \log\left(\left(-c\right)^{\frac{2}{3}} + \left(\frac{c \cos\left(2 \, b x + 2 \, a\right) + c}{\sin\left(2 \, b x + 2 \, a\right)}\right)^{\frac{2}{3}}\right) - \left(-c\right)^{\frac{2}{3}} \log\left(-\frac{\left(-c\right)^{\frac{1}{3}} c \sin\left(2 \, b x + 2 \, a\right) + \left(-c\right)^{\frac{2}{3}} \left(\frac{c \cos\left(2 \, b x + 2 \, a\right) + c}{\sin\left(2 \, b x + 2 \, a\right)}\right)^{\frac{2}{3}} \sin\left(2 \, b x + 2 \, a\right) - {\left(c \cos\left(2 \, b x + 2 \, a\right) + c\right)} \left(\frac{c \cos\left(2 \, b x + 2 \, a\right) + c}{\sin\left(2 \, b x + 2 \, a\right)}\right)^{\frac{1}{3}}}{\sin\left(2 \, b x + 2 \, a\right)}\right)}{4 \, b c}\right]"," ",0,"[1/4*(sqrt(3)*c*sqrt((-c)^(1/3)/c)*log(1/2*sqrt(3)*((-c)^(2/3)*((c*cos(2*b*x + 2*a) + c)/sin(2*b*x + 2*a))^(2/3)*(cos(2*b*x + 2*a) - 1) - 2*c*((c*cos(2*b*x + 2*a) + c)/sin(2*b*x + 2*a))^(1/3)*sin(2*b*x + 2*a) + (c*cos(2*b*x + 2*a) - c)*(-c)^(1/3))*sqrt((-c)^(1/3)/c) - 3/2*(-c)^(1/3)*((c*cos(2*b*x + 2*a) + c)/sin(2*b*x + 2*a))^(2/3)*(cos(2*b*x + 2*a) - 1) + 3/2*c*cos(2*b*x + 2*a) + 1/2*c) - 2*(-c)^(2/3)*log((-c)^(2/3) + ((c*cos(2*b*x + 2*a) + c)/sin(2*b*x + 2*a))^(2/3)) + (-c)^(2/3)*log(-((-c)^(1/3)*c*sin(2*b*x + 2*a) + (-c)^(2/3)*((c*cos(2*b*x + 2*a) + c)/sin(2*b*x + 2*a))^(2/3)*sin(2*b*x + 2*a) - (c*cos(2*b*x + 2*a) + c)*((c*cos(2*b*x + 2*a) + c)/sin(2*b*x + 2*a))^(1/3))/sin(2*b*x + 2*a)))/(b*c), -1/4*(2*sqrt(3)*c*sqrt(-(-c)^(1/3)/c)*arctan(1/3*(sqrt(3)*(-c)^(1/3)*c*sqrt(-(-c)^(1/3)/c) + 2*sqrt(3)*(-c)^(2/3)*((c*cos(2*b*x + 2*a) + c)/sin(2*b*x + 2*a))^(2/3)*sqrt(-(-c)^(1/3)/c))/c) + 2*(-c)^(2/3)*log((-c)^(2/3) + ((c*cos(2*b*x + 2*a) + c)/sin(2*b*x + 2*a))^(2/3)) - (-c)^(2/3)*log(-((-c)^(1/3)*c*sin(2*b*x + 2*a) + (-c)^(2/3)*((c*cos(2*b*x + 2*a) + c)/sin(2*b*x + 2*a))^(2/3)*sin(2*b*x + 2*a) - (c*cos(2*b*x + 2*a) + c)*((c*cos(2*b*x + 2*a) + c)/sin(2*b*x + 2*a))^(1/3))/sin(2*b*x + 2*a)))/(b*c)]","B",0
21,-2,0,0,0.000000," ","integrate(1/(c*cot(b*x+a))^(2/3),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   catdef: division by zero","F(-2)",0
22,-2,0,0,0.000000," ","integrate(1/(c*cot(b*x+a))^(4/3),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   catdef: division by zero","F(-2)",0
23,0,0,0,1.027816," ","integrate(cot(b*x+a)^n,x, algorithm=""fricas"")","{\rm integral}\left(\cot\left(b x + a\right)^{n}, x\right)"," ",0,"integral(cot(b*x + a)^n, x)","F",0
24,0,0,0,2.993591," ","integrate((b*cot(d*x+c))^n,x, algorithm=""fricas"")","{\rm integral}\left(\left(b \cot\left(d x + c\right)\right)^{n}, x\right)"," ",0,"integral((b*cot(d*x + c))^n, x)","F",0
25,1,52,0,1.316940," ","integrate((a*cot(x)^2)^(3/2),x, algorithm=""fricas"")","\frac{{\left({\left(a \cos\left(2 \, x\right) - a\right)} \log\left(-\frac{1}{2} \, \cos\left(2 \, x\right) + \frac{1}{2}\right) - 2 \, a\right)} \sqrt{-\frac{a \cos\left(2 \, x\right) + a}{\cos\left(2 \, x\right) - 1}}}{2 \, \sin\left(2 \, x\right)}"," ",0,"1/2*((a*cos(2*x) - a)*log(-1/2*cos(2*x) + 1/2) - 2*a)*sqrt(-(a*cos(2*x) + a)/(cos(2*x) - 1))/sin(2*x)","A",0
26,1,43,0,0.752663," ","integrate((a*cot(x)^2)^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{-\frac{a \cos\left(2 \, x\right) + a}{\cos\left(2 \, x\right) - 1}} \log\left(-\frac{1}{2} \, \cos\left(2 \, x\right) + \frac{1}{2}\right) \sin\left(2 \, x\right)}{2 \, {\left(\cos\left(2 \, x\right) + 1\right)}}"," ",0,"1/2*sqrt(-(a*cos(2*x) + a)/(cos(2*x) - 1))*log(-1/2*cos(2*x) + 1/2)*sin(2*x)/(cos(2*x) + 1)","B",0
27,1,45,0,0.704901," ","integrate(1/(a*cot(x)^2)^(1/2),x, algorithm=""fricas"")","-\frac{\sqrt{-\frac{a \cos\left(2 \, x\right) + a}{\cos\left(2 \, x\right) - 1}} \log\left(\frac{1}{2} \, \cos\left(2 \, x\right) + \frac{1}{2}\right) \sin\left(2 \, x\right)}{2 \, {\left(a \cos\left(2 \, x\right) + a\right)}}"," ",0,"-1/2*sqrt(-(a*cos(2*x) + a)/(cos(2*x) - 1))*log(1/2*cos(2*x) + 1/2)*sin(2*x)/(a*cos(2*x) + a)","B",0
28,1,74,0,0.585660," ","integrate(1/(a*cot(x)^2)^(3/2),x, algorithm=""fricas"")","\frac{{\left({\left(\cos\left(2 \, x\right) + 1\right)} \log\left(\frac{1}{2} \, \cos\left(2 \, x\right) + \frac{1}{2}\right) \sin\left(2 \, x\right) + 2 \, \sin\left(2 \, x\right)\right)} \sqrt{-\frac{a \cos\left(2 \, x\right) + a}{\cos\left(2 \, x\right) - 1}}}{2 \, {\left(a^{2} \cos\left(2 \, x\right)^{2} + 2 \, a^{2} \cos\left(2 \, x\right) + a^{2}\right)}}"," ",0,"1/2*((cos(2*x) + 1)*log(1/2*cos(2*x) + 1/2)*sin(2*x) + 2*sin(2*x))*sqrt(-(a*cos(2*x) + a)/(cos(2*x) - 1))/(a^2*cos(2*x)^2 + 2*a^2*cos(2*x) + a^2)","B",0
29,-1,0,0,0.000000," ","integrate((a*cot(x)^3)^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
30,-1,0,0,0.000000," ","integrate((a*cot(x)^3)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
31,-1,0,0,0.000000," ","integrate(1/(a*cot(x)^3)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
32,-1,0,0,0.000000," ","integrate(1/(a*cot(x)^3)^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
33,1,110,0,1.392338," ","integrate((a*cot(x)^4)^(3/2),x, algorithm=""fricas"")","\frac{{\left(23 \, a \cos\left(2 \, x\right)^{3} - a \cos\left(2 \, x\right)^{2} - 11 \, a \cos\left(2 \, x\right) + 15 \, {\left(a x \cos\left(2 \, x\right)^{2} - 2 \, a x \cos\left(2 \, x\right) + a x\right)} \sin\left(2 \, x\right) + 13 \, a\right)} \sqrt{\frac{a \cos\left(2 \, x\right)^{2} + 2 \, a \cos\left(2 \, x\right) + a}{\cos\left(2 \, x\right)^{2} - 2 \, \cos\left(2 \, x\right) + 1}}}{15 \, {\left(\cos\left(2 \, x\right)^{2} - 1\right)} \sin\left(2 \, x\right)}"," ",0,"1/15*(23*a*cos(2*x)^3 - a*cos(2*x)^2 - 11*a*cos(2*x) + 15*(a*x*cos(2*x)^2 - 2*a*x*cos(2*x) + a*x)*sin(2*x) + 13*a)*sqrt((a*cos(2*x)^2 + 2*a*cos(2*x) + a)/(cos(2*x)^2 - 2*cos(2*x) + 1))/((cos(2*x)^2 - 1)*sin(2*x))","A",0
34,1,61,0,1.414737," ","integrate((a*cot(x)^4)^(1/2),x, algorithm=""fricas"")","\frac{{\left(x \cos\left(2 \, x\right) - x - \sin\left(2 \, x\right)\right)} \sqrt{\frac{a \cos\left(2 \, x\right)^{2} + 2 \, a \cos\left(2 \, x\right) + a}{\cos\left(2 \, x\right)^{2} - 2 \, \cos\left(2 \, x\right) + 1}}}{\cos\left(2 \, x\right) + 1}"," ",0,"(x*cos(2*x) - x - sin(2*x))*sqrt((a*cos(2*x)^2 + 2*a*cos(2*x) + a)/(cos(2*x)^2 - 2*cos(2*x) + 1))/(cos(2*x) + 1)","B",0
35,1,80,0,1.347569," ","integrate(1/(a*cot(x)^4)^(1/2),x, algorithm=""fricas"")","\frac{{\left(x \cos\left(2 \, x\right)^{2} - {\left(\cos\left(2 \, x\right) - 1\right)} \sin\left(2 \, x\right) - x\right)} \sqrt{\frac{a \cos\left(2 \, x\right)^{2} + 2 \, a \cos\left(2 \, x\right) + a}{\cos\left(2 \, x\right)^{2} - 2 \, \cos\left(2 \, x\right) + 1}}}{a \cos\left(2 \, x\right)^{2} + 2 \, a \cos\left(2 \, x\right) + a}"," ",0,"(x*cos(2*x)^2 - (cos(2*x) - 1)*sin(2*x) - x)*sqrt((a*cos(2*x)^2 + 2*a*cos(2*x) + a)/(cos(2*x)^2 - 2*cos(2*x) + 1))/(a*cos(2*x)^2 + 2*a*cos(2*x) + a)","B",0
36,1,142,0,1.369468," ","integrate(1/(a*cot(x)^4)^(3/2),x, algorithm=""fricas"")","\frac{{\left(15 \, x \cos\left(2 \, x\right)^{4} + 30 \, x \cos\left(2 \, x\right)^{3} - 30 \, x \cos\left(2 \, x\right) - {\left(23 \, \cos\left(2 \, x\right)^{3} + \cos\left(2 \, x\right)^{2} - 11 \, \cos\left(2 \, x\right) - 13\right)} \sin\left(2 \, x\right) - 15 \, x\right)} \sqrt{\frac{a \cos\left(2 \, x\right)^{2} + 2 \, a \cos\left(2 \, x\right) + a}{\cos\left(2 \, x\right)^{2} - 2 \, \cos\left(2 \, x\right) + 1}}}{15 \, {\left(a^{2} \cos\left(2 \, x\right)^{4} + 4 \, a^{2} \cos\left(2 \, x\right)^{3} + 6 \, a^{2} \cos\left(2 \, x\right)^{2} + 4 \, a^{2} \cos\left(2 \, x\right) + a^{2}\right)}}"," ",0,"1/15*(15*x*cos(2*x)^4 + 30*x*cos(2*x)^3 - 30*x*cos(2*x) - (23*cos(2*x)^3 + cos(2*x)^2 - 11*cos(2*x) - 13)*sin(2*x) - 15*x)*sqrt((a*cos(2*x)^2 + 2*a*cos(2*x) + a)/(cos(2*x)^2 - 2*cos(2*x) + 1))/(a^2*cos(2*x)^4 + 4*a^2*cos(2*x)^3 + 6*a^2*cos(2*x)^2 + 4*a^2*cos(2*x) + a^2)","B",0
37,0,0,0,1.204136," ","integrate((b*cot(d*x+c)^p)^n,x, algorithm=""fricas"")","{\rm integral}\left(\left(b \cot\left(d x + c\right)^{p}\right)^{n}, x\right)"," ",0,"integral((b*cot(d*x + c)^p)^n, x)","F",0
38,0,0,0,1.174417," ","integrate((a*(b*cot(d*x+c))^p)^n,x, algorithm=""fricas"")","{\rm integral}\left(\left(\left(b \cot\left(d x + c\right)\right)^{p} a\right)^{n}, x\right)"," ",0,"integral(((b*cot(d*x + c))^p*a)^n, x)","F",0
39,0,0,0,1.315845," ","integrate((b*cot(f*x+e))^n*(a*sin(f*x+e))^m,x, algorithm=""fricas"")","{\rm integral}\left(\left(b \cot\left(f x + e\right)\right)^{n} \left(a \sin\left(f x + e\right)\right)^{m}, x\right)"," ",0,"integral((b*cot(f*x + e))^n*(a*sin(f*x + e))^m, x)","F",0
40,0,0,0,0.556983," ","integrate((a*cos(f*x+e))^m*(b*cot(f*x+e))^n,x, algorithm=""fricas"")","{\rm integral}\left(\left(a \cos\left(f x + e\right)\right)^{m} \left(b \cot\left(f x + e\right)\right)^{n}, x\right)"," ",0,"integral((a*cos(f*x + e))^m*(b*cot(f*x + e))^n, x)","F",0
41,0,0,0,1.193593," ","integrate((a*cot(f*x+e))^m*(b*cot(f*x+e))^n,x, algorithm=""fricas"")","{\rm integral}\left(\left(a \cot\left(f x + e\right)\right)^{m} \left(b \cot\left(f x + e\right)\right)^{n}, x\right)"," ",0,"integral((a*cot(f*x + e))^m*(b*cot(f*x + e))^n, x)","F",0
42,0,0,0,2.774133," ","integrate((b*cot(f*x+e))^n*(a*sec(f*x+e))^m,x, algorithm=""fricas"")","{\rm integral}\left(\left(b \cot\left(f x + e\right)\right)^{n} \left(a \sec\left(f x + e\right)\right)^{m}, x\right)"," ",0,"integral((b*cot(f*x + e))^n*(a*sec(f*x + e))^m, x)","F",0
43,1,145,0,0.945127," ","integrate((d*cot(f*x+e))^n*csc(f*x+e)^6,x, algorithm=""fricas"")","-\frac{{\left(8 \, \cos\left(f x + e\right)^{5} - 4 \, {\left(n + 5\right)} \cos\left(f x + e\right)^{3} + {\left(n^{2} + 8 \, n + 15\right)} \cos\left(f x + e\right)\right)} \left(\frac{d \cos\left(f x + e\right)}{\sin\left(f x + e\right)}\right)^{n}}{{\left({\left(f n^{3} + 9 \, f n^{2} + 23 \, f n + 15 \, f\right)} \cos\left(f x + e\right)^{4} + f n^{3} + 9 \, f n^{2} - 2 \, {\left(f n^{3} + 9 \, f n^{2} + 23 \, f n + 15 \, f\right)} \cos\left(f x + e\right)^{2} + 23 \, f n + 15 \, f\right)} \sin\left(f x + e\right)}"," ",0,"-(8*cos(f*x + e)^5 - 4*(n + 5)*cos(f*x + e)^3 + (n^2 + 8*n + 15)*cos(f*x + e))*(d*cos(f*x + e)/sin(f*x + e))^n/(((f*n^3 + 9*f*n^2 + 23*f*n + 15*f)*cos(f*x + e)^4 + f*n^3 + 9*f*n^2 - 2*(f*n^3 + 9*f*n^2 + 23*f*n + 15*f)*cos(f*x + e)^2 + 23*f*n + 15*f)*sin(f*x + e))","A",0
44,1,87,0,0.925616," ","integrate((d*cot(f*x+e))^n*csc(f*x+e)^4,x, algorithm=""fricas"")","\frac{{\left(2 \, \cos\left(f x + e\right)^{3} - {\left(n + 3\right)} \cos\left(f x + e\right)\right)} \left(\frac{d \cos\left(f x + e\right)}{\sin\left(f x + e\right)}\right)^{n}}{{\left(f n^{2} - {\left(f n^{2} + 4 \, f n + 3 \, f\right)} \cos\left(f x + e\right)^{2} + 4 \, f n + 3 \, f\right)} \sin\left(f x + e\right)}"," ",0,"(2*cos(f*x + e)^3 - (n + 3)*cos(f*x + e))*(d*cos(f*x + e)/sin(f*x + e))^n/((f*n^2 - (f*n^2 + 4*f*n + 3*f)*cos(f*x + e)^2 + 4*f*n + 3*f)*sin(f*x + e))","A",0
45,1,41,0,1.318555," ","integrate((d*cot(f*x+e))^n*csc(f*x+e)^2,x, algorithm=""fricas"")","-\frac{\left(\frac{d \cos\left(f x + e\right)}{\sin\left(f x + e\right)}\right)^{n} \cos\left(f x + e\right)}{{\left(f n + f\right)} \sin\left(f x + e\right)}"," ",0,"-(d*cos(f*x + e)/sin(f*x + e))^n*cos(f*x + e)/((f*n + f)*sin(f*x + e))","A",0
46,0,0,0,1.419194," ","integrate((d*cot(f*x+e))^n*sin(f*x+e)^2,x, algorithm=""fricas"")","{\rm integral}\left(-{\left(\cos\left(f x + e\right)^{2} - 1\right)} \left(d \cot\left(f x + e\right)\right)^{n}, x\right)"," ",0,"integral(-(cos(f*x + e)^2 - 1)*(d*cot(f*x + e))^n, x)","F",0
47,0,0,0,1.065318," ","integrate((d*cot(f*x+e))^n*sin(f*x+e)^4,x, algorithm=""fricas"")","{\rm integral}\left({\left(\cos\left(f x + e\right)^{4} - 2 \, \cos\left(f x + e\right)^{2} + 1\right)} \left(d \cot\left(f x + e\right)\right)^{n}, x\right)"," ",0,"integral((cos(f*x + e)^4 - 2*cos(f*x + e)^2 + 1)*(d*cot(f*x + e))^n, x)","F",0
48,0,0,0,0.835688," ","integrate((d*cot(f*x+e))^n*csc(f*x+e)^3,x, algorithm=""fricas"")","{\rm integral}\left(\left(d \cot\left(f x + e\right)\right)^{n} \csc\left(f x + e\right)^{3}, x\right)"," ",0,"integral((d*cot(f*x + e))^n*csc(f*x + e)^3, x)","F",0
49,0,0,0,1.099383," ","integrate((d*cot(f*x+e))^n*csc(f*x+e),x, algorithm=""fricas"")","{\rm integral}\left(\left(d \cot\left(f x + e\right)\right)^{n} \csc\left(f x + e\right), x\right)"," ",0,"integral((d*cot(f*x + e))^n*csc(f*x + e), x)","F",0
50,0,0,0,0.775954," ","integrate((d*cot(f*x+e))^n*sin(f*x+e),x, algorithm=""fricas"")","{\rm integral}\left(\left(d \cot\left(f x + e\right)\right)^{n} \sin\left(f x + e\right), x\right)"," ",0,"integral((d*cot(f*x + e))^n*sin(f*x + e), x)","F",0
51,0,0,0,0.617859," ","integrate((d*cot(f*x+e))^n*sin(f*x+e)^3,x, algorithm=""fricas"")","{\rm integral}\left(-{\left(\cos\left(f x + e\right)^{2} - 1\right)} \left(d \cot\left(f x + e\right)\right)^{n} \sin\left(f x + e\right), x\right)"," ",0,"integral(-(cos(f*x + e)^2 - 1)*(d*cot(f*x + e))^n*sin(f*x + e), x)","F",0
52,0,0,0,0.621372," ","integrate((b*cot(f*x+e))^n*(a*csc(f*x+e))^m,x, algorithm=""fricas"")","{\rm integral}\left(\left(b \cot\left(f x + e\right)\right)^{n} \left(a \csc\left(f x + e\right)\right)^{m}, x\right)"," ",0,"integral((b*cot(f*x + e))^n*(a*csc(f*x + e))^m, x)","F",0
