1,-2,0,0,0.000000," ","integrate(cos(x)^4/(I+cot(x)),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
2,-2,0,0,0.000000," ","integrate(cos(x)^3/(I+cot(x)),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
3,-2,0,0,0.000000," ","integrate(cos(x)^2/(I+cot(x)),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
4,-2,0,0,0.000000," ","integrate(cos(x)/(I+cot(x)),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
5,1,45,0,0.569448," ","integrate(sec(x)/(I+cot(x)),x, algorithm=""maxima"")","-\frac{2}{\frac{i \, \sin\left(x\right)}{\cos\left(x\right) + 1} + 1} - i \, \log\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1} + 1\right) + i \, \log\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1} - 1\right)"," ",0,"-2/(I*sin(x)/(cos(x) + 1) + 1) - I*log(sin(x)/(cos(x) + 1) + 1) + I*log(sin(x)/(cos(x) + 1) - 1)","B",0
6,1,12,0,0.351062," ","integrate(sec(x)^2/(I+cot(x)),x, algorithm=""maxima"")","\log\left(i \, \tan\left(x\right) + 1\right) - i \, \tan\left(x\right)"," ",0,"log(I*tan(x) + 1) - I*tan(x)","A",0
7,1,94,0,0.482701," ","integrate(sec(x)^3/(I+cot(x)),x, algorithm=""maxima"")","\frac{\frac{i \, \sin\left(x\right)}{\cos\left(x\right) + 1} + \frac{2 \, \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + \frac{i \, \sin\left(x\right)^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}} - 2}{\frac{2 \, \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} - \frac{\sin\left(x\right)^{4}}{{\left(\cos\left(x\right) + 1\right)}^{4}} - 1} + \frac{1}{2} i \, \log\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1} + 1\right) - \frac{1}{2} i \, \log\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1} - 1\right)"," ",0,"(I*sin(x)/(cos(x) + 1) + 2*sin(x)^2/(cos(x) + 1)^2 + I*sin(x)^3/(cos(x) + 1)^3 - 2)/(2*sin(x)^2/(cos(x) + 1)^2 - sin(x)^4/(cos(x) + 1)^4 - 1) + 1/2*I*log(sin(x)/(cos(x) + 1) + 1) - 1/2*I*log(sin(x)/(cos(x) + 1) - 1)","B",0
8,1,13,0,0.691516," ","integrate(sec(x)^4/(I+cot(x)),x, algorithm=""maxima"")","-\frac{1}{3} i \, \tan\left(x\right)^{3} + \frac{1}{2} \, \tan\left(x\right)^{2}"," ",0,"-1/3*I*tan(x)^3 + 1/2*tan(x)^2","A",0
9,1,167,0,0.354129," ","integrate(sec(x)^5/(I+cot(x)),x, algorithm=""maxima"")","-\frac{-\frac{3 i \, \sin\left(x\right)}{\cos\left(x\right) + 1} - \frac{8 \, \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} - \frac{21 i \, \sin\left(x\right)^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}} + \frac{24 \, \sin\left(x\right)^{4}}{{\left(\cos\left(x\right) + 1\right)}^{4}} - \frac{21 i \, \sin\left(x\right)^{5}}{{\left(\cos\left(x\right) + 1\right)}^{5}} - \frac{24 \, \sin\left(x\right)^{6}}{{\left(\cos\left(x\right) + 1\right)}^{6}} - \frac{3 i \, \sin\left(x\right)^{7}}{{\left(\cos\left(x\right) + 1\right)}^{7}} + 8}{12 \, {\left(\frac{4 \, \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} - \frac{6 \, \sin\left(x\right)^{4}}{{\left(\cos\left(x\right) + 1\right)}^{4}} + \frac{4 \, \sin\left(x\right)^{6}}{{\left(\cos\left(x\right) + 1\right)}^{6}} - \frac{\sin\left(x\right)^{8}}{{\left(\cos\left(x\right) + 1\right)}^{8}} - 1\right)}} + \frac{1}{8} i \, \log\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1} + 1\right) - \frac{1}{8} i \, \log\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1} - 1\right)"," ",0,"-1/12*(-3*I*sin(x)/(cos(x) + 1) - 8*sin(x)^2/(cos(x) + 1)^2 - 21*I*sin(x)^3/(cos(x) + 1)^3 + 24*sin(x)^4/(cos(x) + 1)^4 - 21*I*sin(x)^5/(cos(x) + 1)^5 - 24*sin(x)^6/(cos(x) + 1)^6 - 3*I*sin(x)^7/(cos(x) + 1)^7 + 8)/(4*sin(x)^2/(cos(x) + 1)^2 - 6*sin(x)^4/(cos(x) + 1)^4 + 4*sin(x)^6/(cos(x) + 1)^6 - sin(x)^8/(cos(x) + 1)^8 - 1) + 1/8*I*log(sin(x)/(cos(x) + 1) + 1) - 1/8*I*log(sin(x)/(cos(x) + 1) - 1)","B",0
10,1,25,0,0.857023," ","integrate(sec(x)^6/(I+cot(x)),x, algorithm=""maxima"")","-\frac{1}{5} i \, \tan\left(x\right)^{5} + \frac{1}{4} \, \tan\left(x\right)^{4} - \frac{1}{3} i \, \tan\left(x\right)^{3} + \frac{1}{2} \, \tan\left(x\right)^{2}"," ",0,"-1/5*I*tan(x)^5 + 1/4*tan(x)^4 - 1/3*I*tan(x)^3 + 1/2*tan(x)^2","A",0
11,1,240,0,0.527158," ","integrate(cos(x)^4/(a+b*cot(x)),x, algorithm=""maxima"")","-\frac{a^{4} b \log\left(a \tan\left(x\right) + b\right)}{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}} + \frac{a^{4} b \log\left(\tan\left(x\right)^{2} + 1\right)}{2 \, {\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)}} + \frac{{\left(3 \, a^{5} - 6 \, a^{3} b^{2} - a b^{4}\right)} x}{8 \, {\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)}} - \frac{4 \, a^{2} b \tan\left(x\right)^{2} - {\left(3 \, a^{3} - a b^{2}\right)} \tan\left(x\right)^{3} + 6 \, a^{2} b + 2 \, b^{3} - {\left(5 \, a^{3} + a b^{2}\right)} \tan\left(x\right)}{8 \, {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \tan\left(x\right)^{4} + a^{4} + 2 \, a^{2} b^{2} + b^{4} + 2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \tan\left(x\right)^{2}\right)}}"," ",0,"-a^4*b*log(a*tan(x) + b)/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) + 1/2*a^4*b*log(tan(x)^2 + 1)/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) + 1/8*(3*a^5 - 6*a^3*b^2 - a*b^4)*x/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) - 1/8*(4*a^2*b*tan(x)^2 - (3*a^3 - a*b^2)*tan(x)^3 + 6*a^2*b + 2*b^3 - (5*a^3 + a*b^2)*tan(x))/((a^4 + 2*a^2*b^2 + b^4)*tan(x)^4 + a^4 + 2*a^2*b^2 + b^4 + 2*(a^4 + 2*a^2*b^2 + b^4)*tan(x)^2)","A",0
12,1,279,0,0.491218," ","integrate(cos(x)^3/(a+b*cot(x)),x, algorithm=""maxima"")","\frac{a^{3} b \log\left(\frac{a - \frac{b \sin\left(x\right)}{\cos\left(x\right) + 1} + \sqrt{a^{2} + b^{2}}}{a - \frac{b \sin\left(x\right)}{\cos\left(x\right) + 1} - \sqrt{a^{2} + b^{2}}}\right)}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \sqrt{a^{2} + b^{2}}} - \frac{2 \, {\left(4 \, a^{2} b + b^{3} - \frac{3 \, a^{3} \sin\left(x\right)}{\cos\left(x\right) + 1} + \frac{6 \, a^{2} b \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} - \frac{3 \, a^{3} \sin\left(x\right)^{5}}{{\left(\cos\left(x\right) + 1\right)}^{5}} - \frac{2 \, {\left(a^{3} - 2 \, a b^{2}\right)} \sin\left(x\right)^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}} + \frac{3 \, {\left(2 \, a^{2} b + b^{3}\right)} \sin\left(x\right)^{4}}{{\left(\cos\left(x\right) + 1\right)}^{4}}\right)}}{3 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4} + \frac{3 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + \frac{3 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \sin\left(x\right)^{4}}{{\left(\cos\left(x\right) + 1\right)}^{4}} + \frac{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \sin\left(x\right)^{6}}{{\left(\cos\left(x\right) + 1\right)}^{6}}\right)}}"," ",0,"a^3*b*log((a - b*sin(x)/(cos(x) + 1) + sqrt(a^2 + b^2))/(a - b*sin(x)/(cos(x) + 1) - sqrt(a^2 + b^2)))/((a^4 + 2*a^2*b^2 + b^4)*sqrt(a^2 + b^2)) - 2/3*(4*a^2*b + b^3 - 3*a^3*sin(x)/(cos(x) + 1) + 6*a^2*b*sin(x)^2/(cos(x) + 1)^2 - 3*a^3*sin(x)^5/(cos(x) + 1)^5 - 2*(a^3 - 2*a*b^2)*sin(x)^3/(cos(x) + 1)^3 + 3*(2*a^2*b + b^3)*sin(x)^4/(cos(x) + 1)^4)/(a^4 + 2*a^2*b^2 + b^4 + 3*(a^4 + 2*a^2*b^2 + b^4)*sin(x)^2/(cos(x) + 1)^2 + 3*(a^4 + 2*a^2*b^2 + b^4)*sin(x)^4/(cos(x) + 1)^4 + (a^4 + 2*a^2*b^2 + b^4)*sin(x)^6/(cos(x) + 1)^6)","B",0
13,1,122,0,0.716984," ","integrate(cos(x)^2/(a+b*cot(x)),x, algorithm=""maxima"")","-\frac{a^{2} b \log\left(a \tan\left(x\right) + b\right)}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} + \frac{a^{2} b \log\left(\tan\left(x\right)^{2} + 1\right)}{2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)}} + \frac{{\left(a^{3} - a b^{2}\right)} x}{2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)}} + \frac{a \tan\left(x\right) - b}{2 \, {\left({\left(a^{2} + b^{2}\right)} \tan\left(x\right)^{2} + a^{2} + b^{2}\right)}}"," ",0,"-a^2*b*log(a*tan(x) + b)/(a^4 + 2*a^2*b^2 + b^4) + 1/2*a^2*b*log(tan(x)^2 + 1)/(a^4 + 2*a^2*b^2 + b^4) + 1/2*(a^3 - a*b^2)*x/(a^4 + 2*a^2*b^2 + b^4) + 1/2*(a*tan(x) - b)/((a^2 + b^2)*tan(x)^2 + a^2 + b^2)","A",0
14,1,105,0,0.589494," ","integrate(cos(x)/(a+b*cot(x)),x, algorithm=""maxima"")","\frac{a b \log\left(\frac{a - \frac{b \sin\left(x\right)}{\cos\left(x\right) + 1} + \sqrt{a^{2} + b^{2}}}{a - \frac{b \sin\left(x\right)}{\cos\left(x\right) + 1} - \sqrt{a^{2} + b^{2}}}\right)}{{\left(a^{2} + b^{2}\right)}^{\frac{3}{2}}} - \frac{2 \, {\left(b - \frac{a \sin\left(x\right)}{\cos\left(x\right) + 1}\right)}}{a^{2} + b^{2} + \frac{{\left(a^{2} + b^{2}\right)} \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}}}"," ",0,"a*b*log((a - b*sin(x)/(cos(x) + 1) + sqrt(a^2 + b^2))/(a - b*sin(x)/(cos(x) + 1) - sqrt(a^2 + b^2)))/(a^2 + b^2)^(3/2) - 2*(b - a*sin(x)/(cos(x) + 1))/(a^2 + b^2 + (a^2 + b^2)*sin(x)^2/(cos(x) + 1)^2)","A",0
15,1,98,0,0.728662," ","integrate(sec(x)/(a+b*cot(x)),x, algorithm=""maxima"")","\frac{b \log\left(\frac{a - \frac{b \sin\left(x\right)}{\cos\left(x\right) + 1} + \sqrt{a^{2} + b^{2}}}{a - \frac{b \sin\left(x\right)}{\cos\left(x\right) + 1} - \sqrt{a^{2} + b^{2}}}\right)}{\sqrt{a^{2} + b^{2}} a} + \frac{\log\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1} + 1\right)}{a} - \frac{\log\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1} - 1\right)}{a}"," ",0,"b*log((a - b*sin(x)/(cos(x) + 1) + sqrt(a^2 + b^2))/(a - b*sin(x)/(cos(x) + 1) - sqrt(a^2 + b^2)))/(sqrt(a^2 + b^2)*a) + log(sin(x)/(cos(x) + 1) + 1)/a - log(sin(x)/(cos(x) + 1) - 1)/a","B",0
16,1,20,0,0.390452," ","integrate(sec(x)^2/(a+b*cot(x)),x, algorithm=""maxima"")","-\frac{b \log\left(a \tan\left(x\right) + b\right)}{a^{2}} + \frac{\tan\left(x\right)}{a}"," ",0,"-b*log(a*tan(x) + b)/a^2 + tan(x)/a","A",0
17,1,203,0,0.650843," ","integrate(sec(x)^3/(a+b*cot(x)),x, algorithm=""maxima"")","-\frac{2 \, b - \frac{a \sin\left(x\right)}{\cos\left(x\right) + 1} - \frac{2 \, b \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} - \frac{a \sin\left(x\right)^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}}}{a^{2} - \frac{2 \, a^{2} \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + \frac{a^{2} \sin\left(x\right)^{4}}{{\left(\cos\left(x\right) + 1\right)}^{4}}} + \frac{{\left(a^{2} + 2 \, b^{2}\right)} \log\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1} + 1\right)}{2 \, a^{3}} - \frac{{\left(a^{2} + 2 \, b^{2}\right)} \log\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1} - 1\right)}{2 \, a^{3}} + \frac{{\left(a^{2} b + b^{3}\right)} \log\left(\frac{a - \frac{b \sin\left(x\right)}{\cos\left(x\right) + 1} + \sqrt{a^{2} + b^{2}}}{a - \frac{b \sin\left(x\right)}{\cos\left(x\right) + 1} - \sqrt{a^{2} + b^{2}}}\right)}{\sqrt{a^{2} + b^{2}} a^{3}}"," ",0,"-(2*b - a*sin(x)/(cos(x) + 1) - 2*b*sin(x)^2/(cos(x) + 1)^2 - a*sin(x)^3/(cos(x) + 1)^3)/(a^2 - 2*a^2*sin(x)^2/(cos(x) + 1)^2 + a^2*sin(x)^4/(cos(x) + 1)^4) + 1/2*(a^2 + 2*b^2)*log(sin(x)/(cos(x) + 1) + 1)/a^3 - 1/2*(a^2 + 2*b^2)*log(sin(x)/(cos(x) + 1) - 1)/a^3 + (a^2*b + b^3)*log((a - b*sin(x)/(cos(x) + 1) + sqrt(a^2 + b^2))/(a - b*sin(x)/(cos(x) + 1) - sqrt(a^2 + b^2)))/(sqrt(a^2 + b^2)*a^3)","B",0
18,1,56,0,0.370514," ","integrate(sec(x)^4/(a+b*cot(x)),x, algorithm=""maxima"")","\frac{2 \, a^{2} \tan\left(x\right)^{3} - 3 \, a b \tan\left(x\right)^{2} + 6 \, {\left(a^{2} + b^{2}\right)} \tan\left(x\right)}{6 \, a^{3}} - \frac{{\left(a^{2} b + b^{3}\right)} \log\left(a \tan\left(x\right) + b\right)}{a^{4}}"," ",0,"1/6*(2*a^2*tan(x)^3 - 3*a*b*tan(x)^2 + 6*(a^2 + b^2)*tan(x))/a^3 - (a^2*b + b^3)*log(a*tan(x) + b)/a^4","A",0
19,1,67,0,0.652496," ","integrate(sec(x)/(1+2*cot(x)),x, algorithm=""maxima"")","\frac{2}{5} \, \sqrt{5} \log\left(-\frac{\sqrt{5} - \frac{2 \, \sin\left(x\right)}{\cos\left(x\right) + 1} + 1}{\sqrt{5} + \frac{2 \, \sin\left(x\right)}{\cos\left(x\right) + 1} - 1}\right) + \log\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1} + 1\right) - \log\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1} - 1\right)"," ",0,"2/5*sqrt(5)*log(-(sqrt(5) - 2*sin(x)/(cos(x) + 1) + 1)/(sqrt(5) + 2*sin(x)/(cos(x) + 1) - 1)) + log(sin(x)/(cos(x) + 1) + 1) - log(sin(x)/(cos(x) + 1) - 1)","B",0
