1,-2,0,0,0.000000," ","integrate(sin(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(sin(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(sin(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(sin(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
5,1,15,0,0.711814," ","integrate(csc(x)/(I+cot(x)),x, algorithm=""maxima"")","\frac{2}{\frac{\sin\left(x\right)}{\cos\left(x\right) + 1} - i}"," ",0,"2/(sin(x)/(cos(x) + 1) - I)","A",0
6,1,7,0,1.077366," ","integrate(csc(x)^2/(I+cot(x)),x, algorithm=""maxima"")","-\log\left(\cot\left(x\right) + i\right)"," ",0,"-log(cot(x) + I)","A",0
7,1,33,0,0.543877," ","integrate(csc(x)^3/(I+cot(x)),x, algorithm=""maxima"")","-\frac{\cos\left(x\right) + 1}{2 \, \sin\left(x\right)} - \frac{\sin\left(x\right)}{2 \, {\left(\cos\left(x\right) + 1\right)}} - i \, \log\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1}\right)"," ",0,"-1/2*(cos(x) + 1)/sin(x) - 1/2*sin(x)/(cos(x) + 1) - I*log(sin(x)/(cos(x) + 1))","B",0
8,1,12,0,1.023868," ","integrate(csc(x)^4/(I+cot(x)),x, algorithm=""maxima"")","\frac{2 i \, \tan\left(x\right) - 1}{2 \, \tan\left(x\right)^{2}}"," ",0,"1/2*(2*I*tan(x) - 1)/tan(x)^2","A",0
9,1,83,0,0.361995," ","integrate(csc(x)^5/(I+cot(x)),x, algorithm=""maxima"")","-\frac{{\left(-\frac{6 i \, \sin\left(x\right)}{\cos\left(x\right) + 1} + \frac{6 \, \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + 2\right)} {\left(\cos\left(x\right) + 1\right)}^{3}}{48 \, \sin\left(x\right)^{3}} - \frac{\sin\left(x\right)}{8 \, {\left(\cos\left(x\right) + 1\right)}} - \frac{i \, \sin\left(x\right)^{2}}{8 \, {\left(\cos\left(x\right) + 1\right)}^{2}} - \frac{\sin\left(x\right)^{3}}{24 \, {\left(\cos\left(x\right) + 1\right)}^{3}} - \frac{1}{2} i \, \log\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1}\right)"," ",0,"-1/48*(-6*I*sin(x)/(cos(x) + 1) + 6*sin(x)^2/(cos(x) + 1)^2 + 2)*(cos(x) + 1)^3/sin(x)^3 - 1/8*sin(x)/(cos(x) + 1) - 1/8*I*sin(x)^2/(cos(x) + 1)^2 - 1/24*sin(x)^3/(cos(x) + 1)^3 - 1/2*I*log(sin(x)/(cos(x) + 1))","B",0
10,1,24,0,0.641490," ","integrate(csc(x)^6/(I+cot(x)),x, algorithm=""maxima"")","\frac{12 i \, \tan\left(x\right)^{3} - 6 \, \tan\left(x\right)^{2} + 4 i \, \tan\left(x\right) - 3}{12 \, \tan\left(x\right)^{4}}"," ",0,"1/12*(12*I*tan(x)^3 - 6*tan(x)^2 + 4*I*tan(x) - 3)/tan(x)^4","A",0
11,1,131,0,0.417546," ","integrate(csc(x)^7/(I+cot(x)),x, algorithm=""maxima"")","-\frac{{\left(-\frac{15 i \, \sin\left(x\right)}{\cos\left(x\right) + 1} + \frac{30 \, \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} - \frac{120 i \, \sin\left(x\right)^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}} + \frac{60 \, \sin\left(x\right)^{4}}{{\left(\cos\left(x\right) + 1\right)}^{4}} + 6\right)} {\left(\cos\left(x\right) + 1\right)}^{5}}{960 \, \sin\left(x\right)^{5}} - \frac{\sin\left(x\right)}{16 \, {\left(\cos\left(x\right) + 1\right)}} - \frac{i \, \sin\left(x\right)^{2}}{8 \, {\left(\cos\left(x\right) + 1\right)}^{2}} - \frac{\sin\left(x\right)^{3}}{32 \, {\left(\cos\left(x\right) + 1\right)}^{3}} - \frac{i \, \sin\left(x\right)^{4}}{64 \, {\left(\cos\left(x\right) + 1\right)}^{4}} - \frac{\sin\left(x\right)^{5}}{160 \, {\left(\cos\left(x\right) + 1\right)}^{5}} - \frac{3}{8} i \, \log\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1}\right)"," ",0,"-1/960*(-15*I*sin(x)/(cos(x) + 1) + 30*sin(x)^2/(cos(x) + 1)^2 - 120*I*sin(x)^3/(cos(x) + 1)^3 + 60*sin(x)^4/(cos(x) + 1)^4 + 6)*(cos(x) + 1)^5/sin(x)^5 - 1/16*sin(x)/(cos(x) + 1) - 1/8*I*sin(x)^2/(cos(x) + 1)^2 - 1/32*sin(x)^3/(cos(x) + 1)^3 - 1/64*I*sin(x)^4/(cos(x) + 1)^4 - 1/160*sin(x)^5/(cos(x) + 1)^5 - 3/8*I*log(sin(x)/(cos(x) + 1))","B",0
12,1,106,0,0.380118," ","integrate(csc(x)^6/(a+b*cot(x)),x, algorithm=""maxima"")","-\frac{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \log\left(a \tan\left(x\right) + b\right)}{b^{5}} + \frac{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \log\left(\tan\left(x\right)\right)}{b^{5}} + \frac{4 \, a b^{2} \tan\left(x\right) + 12 \, {\left(a^{3} + 2 \, a b^{2}\right)} \tan\left(x\right)^{3} - 3 \, b^{3} - 6 \, {\left(a^{2} b + 2 \, b^{3}\right)} \tan\left(x\right)^{2}}{12 \, b^{4} \tan\left(x\right)^{4}}"," ",0,"-(a^4 + 2*a^2*b^2 + b^4)*log(a*tan(x) + b)/b^5 + (a^4 + 2*a^2*b^2 + b^4)*log(tan(x))/b^5 + 1/12*(4*a*b^2*tan(x) + 12*(a^3 + 2*a*b^2)*tan(x)^3 - 3*b^3 - 6*(a^2*b + 2*b^3)*tan(x)^2)/(b^4*tan(x)^4)","A",0
13,1,52,0,0.548734," ","integrate(csc(x)^4/(a+b*cot(x)),x, algorithm=""maxima"")","-\frac{{\left(a^{2} + b^{2}\right)} \log\left(a \tan\left(x\right) + b\right)}{b^{3}} + \frac{{\left(a^{2} + b^{2}\right)} \log\left(\tan\left(x\right)\right)}{b^{3}} + \frac{2 \, a \tan\left(x\right) - b}{2 \, b^{2} \tan\left(x\right)^{2}}"," ",0,"-(a^2 + b^2)*log(a*tan(x) + b)/b^3 + (a^2 + b^2)*log(tan(x))/b^3 + 1/2*(2*a*tan(x) - b)/(b^2*tan(x)^2)","A",0
14,1,12,0,0.687704," ","integrate(csc(x)^2/(a+b*cot(x)),x, algorithm=""maxima"")","-\frac{\log\left(b \cot\left(x\right) + a\right)}{b}"," ",0,"-log(b*cot(x) + a)/b","A",0
15,1,120,0,0.937641," ","integrate(sin(x)^2/(a+b*cot(x)),x, algorithm=""maxima"")","-\frac{b^{3} \log\left(a \tan\left(x\right) + b\right)}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} + \frac{b^{3} \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} + 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,"-b^3*log(a*tan(x) + b)/(a^4 + 2*a^2*b^2 + b^4) + 1/2*b^3*log(tan(x)^2 + 1)/(a^4 + 2*a^2*b^2 + b^4) + 1/2*(a^3 + 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
16,1,244,0,0.684976," ","integrate(sin(x)^4/(a+b*cot(x)),x, algorithm=""maxima"")","-\frac{b^{5} \log\left(a \tan\left(x\right) + b\right)}{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}} + \frac{b^{5} \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} + 10 \, a^{3} b^{2} + 15 \, a b^{4}\right)} x}{8 \, {\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)}} - \frac{{\left(5 \, a^{3} + 9 \, a b^{2}\right)} \tan\left(x\right)^{3} - 2 \, a^{2} b - 6 \, b^{3} - 4 \, {\left(a^{2} b + 2 \, b^{3}\right)} \tan\left(x\right)^{2} + {\left(3 \, a^{3} + 7 \, 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,"-b^5*log(a*tan(x) + b)/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) + 1/2*b^5*log(tan(x)^2 + 1)/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) + 1/8*(3*a^5 + 10*a^3*b^2 + 15*a*b^4)*x/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) - 1/8*((5*a^3 + 9*a*b^2)*tan(x)^3 - 2*a^2*b - 6*b^3 - 4*(a^2*b + 2*b^3)*tan(x)^2 + (3*a^3 + 7*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)","B",0
17,1,216,0,0.607365," ","integrate(csc(x)^5/(a+b*cot(x)),x, algorithm=""maxima"")","-\frac{\frac{3 \, a b \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + \frac{b^{2} \sin\left(x\right)^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}} + \frac{3 \, {\left(4 \, a^{2} + 5 \, b^{2}\right)} \sin\left(x\right)}{\cos\left(x\right) + 1}}{24 \, b^{3}} - \frac{{\left(2 \, a^{3} + 3 \, a b^{2}\right)} \log\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1}\right)}{2 \, b^{4}} - \frac{{\left(b^{2} - \frac{3 \, a b \sin\left(x\right)}{\cos\left(x\right) + 1} + \frac{3 \, {\left(4 \, a^{2} + 5 \, b^{2}\right)} \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}}\right)} {\left(\cos\left(x\right) + 1\right)}^{3}}{24 \, b^{3} \sin\left(x\right)^{3}} - \frac{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\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}} b^{4}}"," ",0,"-1/24*(3*a*b*sin(x)^2/(cos(x) + 1)^2 + b^2*sin(x)^3/(cos(x) + 1)^3 + 3*(4*a^2 + 5*b^2)*sin(x)/(cos(x) + 1))/b^3 - 1/2*(2*a^3 + 3*a*b^2)*log(sin(x)/(cos(x) + 1))/b^4 - 1/24*(b^2 - 3*a*b*sin(x)/(cos(x) + 1) + 3*(4*a^2 + 5*b^2)*sin(x)^2/(cos(x) + 1)^2)*(cos(x) + 1)^3/(b^3*sin(x)^3) - (a^4 + 2*a^2*b^2 + b^4)*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)*b^4)","B",0
18,1,107,0,1.120300," ","integrate(csc(x)^3/(a+b*cot(x)),x, algorithm=""maxima"")","-\frac{a \log\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1}\right)}{b^{2}} - \frac{\sqrt{a^{2} + b^{2}} \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)}{b^{2}} - \frac{\cos\left(x\right) + 1}{2 \, b \sin\left(x\right)} - \frac{\sin\left(x\right)}{2 \, b {\left(\cos\left(x\right) + 1\right)}}"," ",0,"-a*log(sin(x)/(cos(x) + 1))/b^2 - sqrt(a^2 + b^2)*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)))/b^2 - 1/2*(cos(x) + 1)/(b*sin(x)) - 1/2*sin(x)/(b*(cos(x) + 1))","B",0
19,1,61,0,1.883349," ","integrate(csc(x)/(a+b*cot(x)),x, algorithm=""maxima"")","-\frac{\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}}}"," ",0,"-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",0
20,1,106,0,0.693138," ","integrate(sin(x)/(a+b*cot(x)),x, algorithm=""maxima"")","-\frac{b^{2} \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(a + \frac{b \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,"-b^2*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*(a + b*sin(x)/(cos(x) + 1))/(a^2 + b^2 + (a^2 + b^2)*sin(x)^2/(cos(x) + 1)^2)","A",0
21,1,283,0,0.787891," ","integrate(sin(x)^3/(a+b*cot(x)),x, algorithm=""maxima"")","-\frac{b^{4} \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(2 \, a^{3} + 5 \, a b^{2} + \frac{3 \, b^{3} \sin\left(x\right)}{\cos\left(x\right) + 1} + \frac{3 \, a b^{2} \sin\left(x\right)^{4}}{{\left(\cos\left(x\right) + 1\right)}^{4}} + \frac{3 \, b^{3} \sin\left(x\right)^{5}}{{\left(\cos\left(x\right) + 1\right)}^{5}} + \frac{6 \, {\left(a^{3} + 2 \, a b^{2}\right)} \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + \frac{2 \, {\left(2 \, a^{2} b + 5 \, b^{3}\right)} \sin\left(x\right)^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}}\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,"-b^4*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*(2*a^3 + 5*a*b^2 + 3*b^3*sin(x)/(cos(x) + 1) + 3*a*b^2*sin(x)^4/(cos(x) + 1)^4 + 3*b^3*sin(x)^5/(cos(x) + 1)^5 + 6*(a^3 + 2*a*b^2)*sin(x)^2/(cos(x) + 1)^2 + 2*(2*a^2*b + 5*b^3)*sin(x)^3/(cos(x) + 1)^3)/(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
22,1,12,0,0.753602," ","integrate(csc(x)^2/(a+b*cot(x))^2,x, algorithm=""maxima"")","\frac{1}{{\left(b \cot\left(x\right) + a\right)} b}"," ",0,"1/((b*cot(x) + a)*b)","A",0
23,1,20,0,0.322411," ","integrate((a+b*cot(x))^n*csc(x)^2,x, algorithm=""maxima"")","-\frac{{\left(b \cot\left(x\right) + a\right)}^{n + 1}}{b {\left(n + 1\right)}}"," ",0,"-(b*cot(x) + a)^(n + 1)/(b*(n + 1))","A",0
