1,1,194,0,0.419107," ","integrate(tan(x)^4/(a+a*csc(x)),x, algorithm=""maxima"")","\frac{2 \, {\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1} - \frac{46 \, \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} - \frac{13 \, \sin\left(x\right)^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}} + \frac{100 \, \sin\left(x\right)^{4}}{{\left(\cos\left(x\right) + 1\right)}^{4}} + \frac{35 \, \sin\left(x\right)^{5}}{{\left(\cos\left(x\right) + 1\right)}^{5}} - \frac{30 \, \sin\left(x\right)^{6}}{{\left(\cos\left(x\right) + 1\right)}^{6}} - \frac{15 \, \sin\left(x\right)^{7}}{{\left(\cos\left(x\right) + 1\right)}^{7}} + 8\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)}} + \frac{2 \, \arctan\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1}\right)}{a}"," ",0,"2/15*(sin(x)/(cos(x) + 1) - 46*sin(x)^2/(cos(x) + 1)^2 - 13*sin(x)^3/(cos(x) + 1)^3 + 100*sin(x)^4/(cos(x) + 1)^4 + 35*sin(x)^5/(cos(x) + 1)^5 - 30*sin(x)^6/(cos(x) + 1)^6 - 15*sin(x)^7/(cos(x) + 1)^7 + 8)/(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) + 2*arctan(sin(x)/(cos(x) + 1))/a","B",0
2,1,58,0,0.320001," ","integrate(tan(x)^3/(a+a*csc(x)),x, algorithm=""maxima"")","\frac{5 \, \sin\left(x\right)^{2} - 3 \, \sin\left(x\right) - 6}{8 \, {\left(a \sin\left(x\right)^{3} + a \sin\left(x\right)^{2} - a \sin\left(x\right) - a\right)}} + \frac{11 \, \log\left(\sin\left(x\right) + 1\right)}{16 \, a} + \frac{5 \, \log\left(\sin\left(x\right) - 1\right)}{16 \, a}"," ",0,"1/8*(5*sin(x)^2 - 3*sin(x) - 6)/(a*sin(x)^3 + a*sin(x)^2 - a*sin(x) - a) + 11/16*log(sin(x) + 1)/a + 5/16*log(sin(x) - 1)/a","A",0
3,1,94,0,0.423056," ","integrate(tan(x)^2/(a+a*csc(x)),x, algorithm=""maxima"")","-\frac{2 \, {\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1} - \frac{6 \, \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} - \frac{3 \, \sin\left(x\right)^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}} + 2\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)}} - \frac{2 \, \arctan\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1}\right)}{a}"," ",0,"-2/3*(sin(x)/(cos(x) + 1) - 6*sin(x)^2/(cos(x) + 1)^2 - 3*sin(x)^3/(cos(x) + 1)^3 + 2)/(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) - 2*arctan(sin(x)/(cos(x) + 1))/a","B",0
4,1,31,0,0.322134," ","integrate(tan(x)/(a+a*csc(x)),x, algorithm=""maxima"")","-\frac{3 \, \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,"-3/4*log(sin(x) + 1)/a - 1/4*log(sin(x) - 1)/a - 1/2/(a*sin(x) + a)","A",0
5,1,9,0,0.317560," ","integrate(cot(x)/(a+a*csc(x)),x, algorithm=""maxima"")","\frac{\log\left(\sin\left(x\right) + 1\right)}{a}"," ",0,"log(sin(x) + 1)/a","A",0
6,1,30,0,0.426224," ","integrate(cot(x)^2/(a+a*csc(x)),x, algorithm=""maxima"")","-\frac{2 \, \arctan\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1}\right)}{a} + \frac{\log\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1}\right)}{a}"," ",0,"-2*arctan(sin(x)/(cos(x) + 1))/a + log(sin(x)/(cos(x) + 1))/a","A",0
7,1,18,0,0.322381," ","integrate(cot(x)^3/(a+a*csc(x)),x, algorithm=""maxima"")","-\frac{\log\left(\sin\left(x\right)\right)}{a} - \frac{1}{a \sin\left(x\right)}"," ",0,"-log(sin(x))/a - 1/(a*sin(x))","A",0
8,1,86,0,0.418618," ","integrate(cot(x)^4/(a+a*csc(x)),x, algorithm=""maxima"")","-\frac{\frac{4 \, \sin\left(x\right)}{\cos\left(x\right) + 1} - \frac{\sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}}}{8 \, a} + \frac{2 \, \arctan\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1}\right)}{a} - \frac{\log\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1}\right)}{2 \, a} + \frac{{\left(\frac{4 \, \sin\left(x\right)}{\cos\left(x\right) + 1} - 1\right)} {\left(\cos\left(x\right) + 1\right)}^{2}}{8 \, a \sin\left(x\right)^{2}}"," ",0,"-1/8*(4*sin(x)/(cos(x) + 1) - sin(x)^2/(cos(x) + 1)^2)/a + 2*arctan(sin(x)/(cos(x) + 1))/a - 1/2*log(sin(x)/(cos(x) + 1))/a + 1/8*(4*sin(x)/(cos(x) + 1) - 1)*(cos(x) + 1)^2/(a*sin(x)^2)","B",0
9,1,29,0,0.313867," ","integrate(cot(x)^5/(a+a*csc(x)),x, algorithm=""maxima"")","\frac{\log\left(\sin\left(x\right)\right)}{a} + \frac{6 \, \sin\left(x\right)^{2} + 3 \, \sin\left(x\right) - 2}{6 \, a \sin\left(x\right)^{3}}"," ",0,"log(sin(x))/a + 1/6*(6*sin(x)^2 + 3*sin(x) - 2)/(a*sin(x)^3)","A",0
10,1,134,0,0.418139," ","integrate(cot(x)^6/(a+a*csc(x)),x, algorithm=""maxima"")","\frac{\frac{120 \, \sin\left(x\right)}{\cos\left(x\right) + 1} - \frac{24 \, \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{3 \, \sin\left(x\right)^{4}}{{\left(\cos\left(x\right) + 1\right)}^{4}}}{192 \, a} - \frac{2 \, \arctan\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1}\right)}{a} + \frac{3 \, \log\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1}\right)}{8 \, a} + \frac{{\left(\frac{8 \, \sin\left(x\right)}{\cos\left(x\right) + 1} + \frac{24 \, \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} - \frac{120 \, \sin\left(x\right)^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}} - 3\right)} {\left(\cos\left(x\right) + 1\right)}^{4}}{192 \, a \sin\left(x\right)^{4}}"," ",0,"1/192*(120*sin(x)/(cos(x) + 1) - 24*sin(x)^2/(cos(x) + 1)^2 - 8*sin(x)^3/(cos(x) + 1)^3 + 3*sin(x)^4/(cos(x) + 1)^4)/a - 2*arctan(sin(x)/(cos(x) + 1))/a + 3/8*log(sin(x)/(cos(x) + 1))/a + 1/192*(8*sin(x)/(cos(x) + 1) + 24*sin(x)^2/(cos(x) + 1)^2 - 120*sin(x)^3/(cos(x) + 1)^3 - 3)*(cos(x) + 1)^4/(a*sin(x)^4)","B",0
11,1,42,0,0.315735," ","integrate(cot(x)^7/(a+a*csc(x)),x, algorithm=""maxima"")","-\frac{\log\left(\sin\left(x\right)\right)}{a} - \frac{60 \, \sin\left(x\right)^{4} + 60 \, \sin\left(x\right)^{3} - 40 \, \sin\left(x\right)^{2} - 15 \, \sin\left(x\right) + 12}{60 \, a \sin\left(x\right)^{5}}"," ",0,"-log(sin(x))/a - 1/60*(60*sin(x)^4 + 60*sin(x)^3 - 40*sin(x)^2 - 15*sin(x) + 12)/(a*sin(x)^5)","A",0
12,1,251,0,0.331949," ","integrate(tan(x)^5/(a+b*csc(x)),x, algorithm=""maxima"")","\frac{b^{6} \log\left(a \sin\left(x\right) + b\right)}{a^{7} - 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} - a b^{6}} - \frac{{\left(8 \, a^{2} - 21 \, a b + 15 \, b^{2}\right)} \log\left(\sin\left(x\right) + 1\right)}{16 \, {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)}} - \frac{{\left(8 \, a^{2} + 21 \, a b + 15 \, b^{2}\right)} \log\left(\sin\left(x\right) - 1\right)}{16 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)}} - \frac{{\left(5 \, a^{2} b - 9 \, b^{3}\right)} \sin\left(x\right)^{3} + 6 \, a^{3} - 10 \, a b^{2} - 4 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} \sin\left(x\right)^{2} - {\left(3 \, a^{2} b - 7 \, b^{3}\right)} \sin\left(x\right)}{8 \, {\left({\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \sin\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)} \sin\left(x\right)^{2}\right)}}"," ",0,"b^6*log(a*sin(x) + b)/(a^7 - 3*a^5*b^2 + 3*a^3*b^4 - a*b^6) - 1/16*(8*a^2 - 21*a*b + 15*b^2)*log(sin(x) + 1)/(a^3 - 3*a^2*b + 3*a*b^2 - b^3) - 1/16*(8*a^2 + 21*a*b + 15*b^2)*log(sin(x) - 1)/(a^3 + 3*a^2*b + 3*a*b^2 + b^3) - 1/8*((5*a^2*b - 9*b^3)*sin(x)^3 + 6*a^3 - 10*a*b^2 - 4*(2*a^3 - 3*a*b^2)*sin(x)^2 - (3*a^2*b - 7*b^3)*sin(x))/((a^4 - 2*a^2*b^2 + b^4)*sin(x)^4 + a^4 - 2*a^2*b^2 + b^4 - 2*(a^4 - 2*a^2*b^2 + b^4)*sin(x)^2)","A",0
13,1,120,0,0.319977," ","integrate(tan(x)^3/(a+b*csc(x)),x, algorithm=""maxima"")","\frac{b^{4} \log\left(a \sin\left(x\right) + b\right)}{a^{5} - 2 \, a^{3} b^{2} + a b^{4}} + \frac{{\left(2 \, a - 3 \, b\right)} \log\left(\sin\left(x\right) + 1\right)}{4 \, {\left(a^{2} - 2 \, a b + b^{2}\right)}} + \frac{{\left(2 \, a + 3 \, b\right)} \log\left(\sin\left(x\right) - 1\right)}{4 \, {\left(a^{2} + 2 \, a b + b^{2}\right)}} + \frac{b \sin\left(x\right) - a}{2 \, {\left({\left(a^{2} - b^{2}\right)} \sin\left(x\right)^{2} - a^{2} + b^{2}\right)}}"," ",0,"b^4*log(a*sin(x) + b)/(a^5 - 2*a^3*b^2 + a*b^4) + 1/4*(2*a - 3*b)*log(sin(x) + 1)/(a^2 - 2*a*b + b^2) + 1/4*(2*a + 3*b)*log(sin(x) - 1)/(a^2 + 2*a*b + b^2) + 1/2*(b*sin(x) - a)/((a^2 - b^2)*sin(x)^2 - a^2 + b^2)","A",0
14,1,50,0,0.316928," ","integrate(tan(x)/(a+b*csc(x)),x, algorithm=""maxima"")","\frac{b^{2} \log\left(a \sin\left(x\right) + b\right)}{a^{3} - a 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^2*log(a*sin(x) + b)/(a^3 - a*b^2) - 1/2*log(sin(x) + 1)/(a - b) - 1/2*log(sin(x) - 1)/(a + b)","A",0
15,1,11,0,0.314305," ","integrate(cot(x)/(a+b*csc(x)),x, algorithm=""maxima"")","\frac{\log\left(a \sin\left(x\right) + b\right)}{a}"," ",0,"log(a*sin(x) + b)/a","A",0
16,1,42,0,0.310582," ","integrate(cot(x)^3/(a+b*csc(x)),x, algorithm=""maxima"")","-\frac{a \log\left(\sin\left(x\right)\right)}{b^{2}} + \frac{{\left(a^{2} - b^{2}\right)} \log\left(a \sin\left(x\right) + b\right)}{a b^{2}} - \frac{1}{b \sin\left(x\right)}"," ",0,"-a*log(sin(x))/b^2 + (a^2 - b^2)*log(a*sin(x) + b)/(a*b^2) - 1/(b*sin(x))","A",0
17,1,84,0,0.311307," ","integrate(cot(x)^5/(a+b*csc(x)),x, algorithm=""maxima"")","-\frac{{\left(a^{3} - 2 \, a b^{2}\right)} \log\left(\sin\left(x\right)\right)}{b^{4}} + \frac{{\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \log\left(a \sin\left(x\right) + b\right)}{a b^{4}} + \frac{3 \, a b \sin\left(x\right) - 6 \, {\left(a^{2} - 2 \, b^{2}\right)} \sin\left(x\right)^{2} - 2 \, b^{2}}{6 \, b^{3} \sin\left(x\right)^{3}}"," ",0,"-(a^3 - 2*a*b^2)*log(sin(x))/b^4 + (a^4 - 2*a^2*b^2 + b^4)*log(a*sin(x) + b)/(a*b^4) + 1/6*(3*a*b*sin(x) - 6*(a^2 - 2*b^2)*sin(x)^2 - 2*b^2)/(b^3*sin(x)^3)","A",0
18,1,149,0,0.316042," ","integrate(cot(x)^7/(a+b*csc(x)),x, algorithm=""maxima"")","-\frac{{\left(a^{5} - 3 \, a^{3} b^{2} + 3 \, a b^{4}\right)} \log\left(\sin\left(x\right)\right)}{b^{6}} + \frac{{\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} \log\left(a \sin\left(x\right) + b\right)}{a b^{6}} + \frac{15 \, a b^{3} \sin\left(x\right) - 60 \, {\left(a^{4} - 3 \, a^{2} b^{2} + 3 \, b^{4}\right)} \sin\left(x\right)^{4} - 12 \, b^{4} + 30 \, {\left(a^{3} b - 3 \, a b^{3}\right)} \sin\left(x\right)^{3} - 20 \, {\left(a^{2} b^{2} - 3 \, b^{4}\right)} \sin\left(x\right)^{2}}{60 \, b^{5} \sin\left(x\right)^{5}}"," ",0,"-(a^5 - 3*a^3*b^2 + 3*a*b^4)*log(sin(x))/b^6 + (a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*log(a*sin(x) + b)/(a*b^6) + 1/60*(15*a*b^3*sin(x) - 60*(a^4 - 3*a^2*b^2 + 3*b^4)*sin(x)^4 - 12*b^4 + 30*(a^3*b - 3*a*b^3)*sin(x)^3 - 20*(a^2*b^2 - 3*b^4)*sin(x)^2)/(b^5*sin(x)^5)","A",0
19,-2,0,0,0.000000," ","integrate(tan(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
20,-2,0,0,0.000000," ","integrate(tan(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
21,-2,0,0,0.000000," ","integrate(cot(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
22,-2,0,0,0.000000," ","integrate(cot(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
23,-2,0,0,0.000000," ","integrate(cot(x)^6/(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
