1,1,157,0,0.423167," ","integrate(cos(x)^4/(a+a*csc(x)),x, algorithm=""maxima"")","\frac{\frac{3 \, \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 \, \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 \, \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 \, \sin\left(x\right)^{7}}{{\left(\cos\left(x\right) + 1\right)}^{7}} - 8}{12 \, {\left(a + \frac{4 \, a \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + \frac{6 \, a \sin\left(x\right)^{4}}{{\left(\cos\left(x\right) + 1\right)}^{4}} + \frac{4 \, a \sin\left(x\right)^{6}}{{\left(\cos\left(x\right) + 1\right)}^{6}} + \frac{a \sin\left(x\right)^{8}}{{\left(\cos\left(x\right) + 1\right)}^{8}}\right)}} - \frac{\arctan\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1}\right)}{4 \, a}"," ",0,"1/12*(3*sin(x)/(cos(x) + 1) - 8*sin(x)^2/(cos(x) + 1)^2 - 21*sin(x)^3/(cos(x) + 1)^3 - 24*sin(x)^4/(cos(x) + 1)^4 + 21*sin(x)^5/(cos(x) + 1)^5 - 24*sin(x)^6/(cos(x) + 1)^6 - 3*sin(x)^7/(cos(x) + 1)^7 - 8)/(a + 4*a*sin(x)^2/(cos(x) + 1)^2 + 6*a*sin(x)^4/(cos(x) + 1)^4 + 4*a*sin(x)^6/(cos(x) + 1)^6 + a*sin(x)^8/(cos(x) + 1)^8) - 1/4*arctan(sin(x)/(cos(x) + 1))/a","B",0
2,1,18,0,0.323901," ","integrate(cos(x)^3/(a+a*csc(x)),x, algorithm=""maxima"")","-\frac{2 \, \sin\left(x\right)^{3} - 3 \, \sin\left(x\right)^{2}}{6 \, a}"," ",0,"-1/6*(2*sin(x)^3 - 3*sin(x)^2)/a","A",0
3,1,81,0,0.423249," ","integrate(cos(x)^2/(a+a*csc(x)),x, algorithm=""maxima"")","\frac{\frac{\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{\sin\left(x\right)^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}} - 2}{a + \frac{2 \, a \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + \frac{a \sin\left(x\right)^{4}}{{\left(\cos\left(x\right) + 1\right)}^{4}}} - \frac{\arctan\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1}\right)}{a}"," ",0,"(sin(x)/(cos(x) + 1) - 2*sin(x)^2/(cos(x) + 1)^2 - sin(x)^3/(cos(x) + 1)^3 - 2)/(a + 2*a*sin(x)^2/(cos(x) + 1)^2 + a*sin(x)^4/(cos(x) + 1)^4) - arctan(sin(x)/(cos(x) + 1))/a","B",0
4,1,17,0,0.312574," ","integrate(cos(x)/(a+a*csc(x)),x, algorithm=""maxima"")","-\frac{\log\left(\sin\left(x\right) + 1\right)}{a} + \frac{\sin\left(x\right)}{a}"," ",0,"-log(sin(x) + 1)/a + sin(x)/a","A",0
5,1,31,0,0.310221," ","integrate(sec(x)/(a+a*csc(x)),x, algorithm=""maxima"")","\frac{\log\left(\sin\left(x\right) + 1\right)}{4 \, a} - \frac{\log\left(\sin\left(x\right) - 1\right)}{4 \, a} + \frac{1}{2 \, {\left(a \sin\left(x\right) + a\right)}}"," ",0,"1/4*log(sin(x) + 1)/a - 1/4*log(sin(x) - 1)/a + 1/2/(a*sin(x) + a)","A",0
6,1,67,0,0.311883," ","integrate(sec(x)^2/(a+a*csc(x)),x, algorithm=""maxima"")","\frac{2 \, {\left(\frac{2 \, \sin\left(x\right)}{\cos\left(x\right) + 1} + \frac{3 \, \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + 1\right)}}{3 \, {\left(a + \frac{2 \, a \sin\left(x\right)}{\cos\left(x\right) + 1} - \frac{2 \, a \sin\left(x\right)^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}} - \frac{a \sin\left(x\right)^{4}}{{\left(\cos\left(x\right) + 1\right)}^{4}}\right)}}"," ",0,"2/3*(2*sin(x)/(cos(x) + 1) + 3*sin(x)^2/(cos(x) + 1)^2 + 1)/(a + 2*a*sin(x)/(cos(x) + 1) - 2*a*sin(x)^3/(cos(x) + 1)^3 - a*sin(x)^4/(cos(x) + 1)^4)","B",0
7,1,54,0,0.376163," ","integrate(sec(x)^3/(a+a*csc(x)),x, algorithm=""maxima"")","-\frac{\sin\left(x\right)^{2} + \sin\left(x\right) + 2}{8 \, {\left(a \sin\left(x\right)^{3} + a \sin\left(x\right)^{2} - a \sin\left(x\right) - a\right)}} + \frac{\log\left(\sin\left(x\right) + 1\right)}{16 \, a} - \frac{\log\left(\sin\left(x\right) - 1\right)}{16 \, a}"," ",0,"-1/8*(sin(x)^2 + sin(x) + 2)/(a*sin(x)^3 + a*sin(x)^2 - a*sin(x) - a) + 1/16*log(sin(x) + 1)/a - 1/16*log(sin(x) - 1)/a","A",0
8,1,167,0,0.320902," ","integrate(sec(x)^4/(a+a*csc(x)),x, algorithm=""maxima"")","\frac{2 \, {\left(\frac{6 \, \sin\left(x\right)}{\cos\left(x\right) + 1} + \frac{9 \, \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} - \frac{8 \, \sin\left(x\right)^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}} + \frac{5 \, \sin\left(x\right)^{4}}{{\left(\cos\left(x\right) + 1\right)}^{4}} + \frac{10 \, \sin\left(x\right)^{5}}{{\left(\cos\left(x\right) + 1\right)}^{5}} + \frac{15 \, \sin\left(x\right)^{6}}{{\left(\cos\left(x\right) + 1\right)}^{6}} + 3\right)}}{15 \, {\left(a + \frac{2 \, a \sin\left(x\right)}{\cos\left(x\right) + 1} - \frac{2 \, a \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} - \frac{6 \, a \sin\left(x\right)^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}} + \frac{6 \, a \sin\left(x\right)^{5}}{{\left(\cos\left(x\right) + 1\right)}^{5}} + \frac{2 \, a \sin\left(x\right)^{6}}{{\left(\cos\left(x\right) + 1\right)}^{6}} - \frac{2 \, a \sin\left(x\right)^{7}}{{\left(\cos\left(x\right) + 1\right)}^{7}} - \frac{a \sin\left(x\right)^{8}}{{\left(\cos\left(x\right) + 1\right)}^{8}}\right)}}"," ",0,"2/15*(6*sin(x)/(cos(x) + 1) + 9*sin(x)^2/(cos(x) + 1)^2 - 8*sin(x)^3/(cos(x) + 1)^3 + 5*sin(x)^4/(cos(x) + 1)^4 + 10*sin(x)^5/(cos(x) + 1)^5 + 15*sin(x)^6/(cos(x) + 1)^6 + 3)/(a + 2*a*sin(x)/(cos(x) + 1) - 2*a*sin(x)^2/(cos(x) + 1)^2 - 6*a*sin(x)^3/(cos(x) + 1)^3 + 6*a*sin(x)^5/(cos(x) + 1)^5 + 2*a*sin(x)^6/(cos(x) + 1)^6 - 2*a*sin(x)^7/(cos(x) + 1)^7 - a*sin(x)^8/(cos(x) + 1)^8)","B",0
9,-2,0,0,0.000000," ","integrate(cos(x)^4/(a+b*csc(x)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
10,1,60,0,0.330009," ","integrate(cos(x)^3/(a+b*csc(x)),x, algorithm=""maxima"")","-\frac{2 \, a^{2} \sin\left(x\right)^{3} - 3 \, a b \sin\left(x\right)^{2} - 6 \, {\left(a^{2} - b^{2}\right)} \sin\left(x\right)}{6 \, a^{3}} - \frac{{\left(a^{2} b - b^{3}\right)} \log\left(a \sin\left(x\right) + b\right)}{a^{4}}"," ",0,"-1/6*(2*a^2*sin(x)^3 - 3*a*b*sin(x)^2 - 6*(a^2 - b^2)*sin(x))/a^3 - (a^2*b - b^3)*log(a*sin(x) + b)/a^4","A",0
11,-2,0,0,0.000000," ","integrate(cos(x)^2/(a+b*csc(x)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
12,1,20,0,0.315988," ","integrate(cos(x)/(a+b*csc(x)),x, algorithm=""maxima"")","-\frac{b \log\left(a \sin\left(x\right) + b\right)}{a^{2}} + \frac{\sin\left(x\right)}{a}"," ",0,"-b*log(a*sin(x) + b)/a^2 + sin(x)/a","A",0
13,1,48,0,0.310652," ","integrate(sec(x)/(a+b*csc(x)),x, algorithm=""maxima"")","-\frac{b \log\left(a \sin\left(x\right) + b\right)}{a^{2} - b^{2}} + \frac{\log\left(\sin\left(x\right) + 1\right)}{2 \, {\left(a - b\right)}} - \frac{\log\left(\sin\left(x\right) - 1\right)}{2 \, {\left(a + b\right)}}"," ",0,"-b*log(a*sin(x) + b)/(a^2 - b^2) + 1/2*log(sin(x) + 1)/(a - b) - 1/2*log(sin(x) - 1)/(a + b)","A",0
14,-2,0,0,0.000000," ","integrate(sec(x)^2/(a+b*csc(x)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
15,1,108,0,0.316918," ","integrate(sec(x)^3/(a+b*csc(x)),x, algorithm=""maxima"")","-\frac{a^{2} b \log\left(a \sin\left(x\right) + b\right)}{a^{4} - 2 \, a^{2} b^{2} + b^{4}} + \frac{a \log\left(\sin\left(x\right) + 1\right)}{4 \, {\left(a^{2} - 2 \, a b + b^{2}\right)}} - \frac{a \log\left(\sin\left(x\right) - 1\right)}{4 \, {\left(a^{2} + 2 \, a b + b^{2}\right)}} - \frac{a \sin\left(x\right) - b}{2 \, {\left({\left(a^{2} - b^{2}\right)} \sin\left(x\right)^{2} - a^{2} + b^{2}\right)}}"," ",0,"-a^2*b*log(a*sin(x) + b)/(a^4 - 2*a^2*b^2 + b^4) + 1/4*a*log(sin(x) + 1)/(a^2 - 2*a*b + b^2) - 1/4*a*log(sin(x) - 1)/(a^2 + 2*a*b + b^2) - 1/2*(a*sin(x) - b)/((a^2 - b^2)*sin(x)^2 - a^2 + b^2)","A",0
16,-2,0,0,0.000000," ","integrate(sec(x)^4/(a+b*csc(x)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
