1,1,115,0,0.297337," ","integrate(tan(x)^4/(a+a*cos(x)),x, algorithm=""maxima"")","-\frac{\frac{3 \, \sin\left(x\right)}{\cos\left(x\right) + 1} - \frac{8 \, \sin\left(x\right)^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}} - \frac{3 \, \sin\left(x\right)^{5}}{{\left(\cos\left(x\right) + 1\right)}^{5}}}{3 \, {\left(a - \frac{3 \, a \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + \frac{3 \, a \sin\left(x\right)^{4}}{{\left(\cos\left(x\right) + 1\right)}^{4}} - \frac{a \sin\left(x\right)^{6}}{{\left(\cos\left(x\right) + 1\right)}^{6}}\right)}} + \frac{\log\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1} + 1\right)}{2 \, a} - \frac{\log\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1} - 1\right)}{2 \, a}"," ",0,"-1/3*(3*sin(x)/(cos(x) + 1) - 8*sin(x)^3/(cos(x) + 1)^3 - 3*sin(x)^5/(cos(x) + 1)^5)/(a - 3*a*sin(x)^2/(cos(x) + 1)^2 + 3*a*sin(x)^4/(cos(x) + 1)^4 - a*sin(x)^6/(cos(x) + 1)^6) + 1/2*log(sin(x)/(cos(x) + 1) + 1)/a - 1/2*log(sin(x)/(cos(x) + 1) - 1)/a","B",0
2,1,15,0,0.660834," ","integrate(tan(x)^3/(a+a*cos(x)),x, algorithm=""maxima"")","-\frac{2 \, \cos\left(x\right) - 1}{2 \, a \cos\left(x\right)^{2}}"," ",0,"-1/2*(2*cos(x) - 1)/(a*cos(x)^2)","A",0
3,1,61,0,0.935158," ","integrate(tan(x)^2/(a+a*cos(x)),x, algorithm=""maxima"")","-\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} + \frac{2 \, \sin\left(x\right)}{{\left(a - \frac{a \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}}\right)} {\left(\cos\left(x\right) + 1\right)}}"," ",0,"-log(sin(x)/(cos(x) + 1) + 1)/a + log(sin(x)/(cos(x) + 1) - 1)/a + 2*sin(x)/((a - a*sin(x)^2/(cos(x) + 1)^2)*(cos(x) + 1))","B",0
4,1,18,0,0.783139," ","integrate(tan(x)/(a+a*cos(x)),x, algorithm=""maxima"")","\frac{\log\left(\cos\left(x\right) + 1\right)}{a} - \frac{\log\left(\cos\left(x\right)\right)}{a}"," ",0,"log(cos(x) + 1)/a - log(cos(x))/a","A",0
5,1,31,0,0.300393," ","integrate(cot(x)/(a+a*cos(x)),x, algorithm=""maxima"")","-\frac{\log\left(\cos\left(x\right) + 1\right)}{4 \, a} + \frac{\log\left(\cos\left(x\right) - 1\right)}{4 \, a} - \frac{1}{2 \, {\left(a \cos\left(x\right) + a\right)}}"," ",0,"-1/4*log(cos(x) + 1)/a + 1/4*log(cos(x) - 1)/a - 1/2/(a*cos(x) + a)","A",0
6,1,42,0,0.295239," ","integrate(cot(x)^2/(a+a*cos(x)),x, algorithm=""maxima"")","-\frac{\frac{6 \, \sin\left(x\right)}{\cos\left(x\right) + 1} - \frac{\sin\left(x\right)^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}}}{12 \, a} - \frac{\cos\left(x\right) + 1}{4 \, a \sin\left(x\right)}"," ",0,"-1/12*(6*sin(x)/(cos(x) + 1) - sin(x)^3/(cos(x) + 1)^3)/a - 1/4*(cos(x) + 1)/(a*sin(x))","A",0
7,1,56,0,0.469131," ","integrate(cot(x)^3/(a+a*cos(x)),x, algorithm=""maxima"")","\frac{5 \, \cos\left(x\right)^{2} + \cos\left(x\right) - 2}{8 \, {\left(a \cos\left(x\right)^{3} + a \cos\left(x\right)^{2} - a \cos\left(x\right) - a\right)}} + \frac{3 \, \log\left(\cos\left(x\right) + 1\right)}{16 \, a} - \frac{3 \, \log\left(\cos\left(x\right) - 1\right)}{16 \, a}"," ",0,"1/8*(5*cos(x)^2 + cos(x) - 2)/(a*cos(x)^3 + a*cos(x)^2 - a*cos(x) - a) + 3/16*log(cos(x) + 1)/a - 3/16*log(cos(x) - 1)/a","A",0
8,1,70,0,1.717756," ","integrate(cot(x)^4/(a+a*cos(x)),x, algorithm=""maxima"")","\frac{\frac{90 \, \sin\left(x\right)}{\cos\left(x\right) + 1} - \frac{20 \, \sin\left(x\right)^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(x\right)^{5}}{{\left(\cos\left(x\right) + 1\right)}^{5}}}{240 \, a} + \frac{{\left(\frac{12 \, \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} - 1\right)} {\left(\cos\left(x\right) + 1\right)}^{3}}{48 \, a \sin\left(x\right)^{3}}"," ",0,"1/240*(90*sin(x)/(cos(x) + 1) - 20*sin(x)^3/(cos(x) + 1)^3 + 3*sin(x)^5/(cos(x) + 1)^5)/a + 1/48*(12*sin(x)^2/(cos(x) + 1)^2 - 1)*(cos(x) + 1)^3/(a*sin(x)^3)","B",0
9,1,27,0,0.574372," ","integrate(tan(3*x)/(1+cos(3*x))^2,x, algorithm=""maxima"")","-\frac{1}{3 \, {\left(\cos\left(3 \, x\right) + 1\right)}} + \frac{1}{3} \, \log\left(\cos\left(3 \, x\right) + 1\right) - \frac{1}{3} \, \log\left(\cos\left(3 \, x\right)\right)"," ",0,"-1/3/(cos(3*x) + 1) + 1/3*log(cos(3*x) + 1) - 1/3*log(cos(3*x))","A",0
10,-2,0,0,0.000000," ","integrate(tan(x)^4/(a+b*cos(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*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
11,1,56,0,0.503799," ","integrate(tan(x)^3/(a+b*cos(x)),x, algorithm=""maxima"")","-\frac{{\left(a^{2} - b^{2}\right)} \log\left(b \cos\left(x\right) + a\right)}{a^{3}} + \frac{{\left(a^{2} - b^{2}\right)} \log\left(\cos\left(x\right)\right)}{a^{3}} - \frac{2 \, b \cos\left(x\right) - a}{2 \, a^{2} \cos\left(x\right)^{2}}"," ",0,"-(a^2 - b^2)*log(b*cos(x) + a)/a^3 + (a^2 - b^2)*log(cos(x))/a^3 - 1/2*(2*b*cos(x) - a)/(a^2*cos(x)^2)","A",0
12,-2,0,0,0.000000," ","integrate(tan(x)^2/(a+b*cos(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*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
13,1,20,0,0.342844," ","integrate(tan(x)/(a+b*cos(x)),x, algorithm=""maxima"")","\frac{\log\left(b \cos\left(x\right) + a\right)}{a} - \frac{\log\left(\cos\left(x\right)\right)}{a}"," ",0,"log(b*cos(x) + a)/a - log(cos(x))/a","A",0
14,1,48,0,0.656868," ","integrate(cot(x)/(a+b*cos(x)),x, algorithm=""maxima"")","-\frac{a \log\left(b \cos\left(x\right) + a\right)}{a^{2} - b^{2}} + \frac{\log\left(\cos\left(x\right) + 1\right)}{2 \, {\left(a - b\right)}} + \frac{\log\left(\cos\left(x\right) - 1\right)}{2 \, {\left(a + b\right)}}"," ",0,"-a*log(b*cos(x) + a)/(a^2 - b^2) + 1/2*log(cos(x) + 1)/(a - b) + 1/2*log(cos(x) - 1)/(a + b)","A",0
15,-2,0,0,0.000000," ","integrate(cot(x)^2/(a+b*cos(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*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
16,1,116,0,0.872900," ","integrate(cot(x)^3/(a+b*cos(x)),x, algorithm=""maxima"")","\frac{a^{3} \log\left(b \cos\left(x\right) + a\right)}{a^{4} - 2 \, a^{2} b^{2} + b^{4}} - \frac{{\left(2 \, a - b\right)} \log\left(\cos\left(x\right) + 1\right)}{4 \, {\left(a^{2} - 2 \, a b + b^{2}\right)}} - \frac{{\left(2 \, a + b\right)} \log\left(\cos\left(x\right) - 1\right)}{4 \, {\left(a^{2} + 2 \, a b + b^{2}\right)}} - \frac{b \cos\left(x\right) - a}{2 \, {\left({\left(a^{2} - b^{2}\right)} \cos\left(x\right)^{2} - a^{2} + b^{2}\right)}}"," ",0,"a^3*log(b*cos(x) + a)/(a^4 - 2*a^2*b^2 + b^4) - 1/4*(2*a - b)*log(cos(x) + 1)/(a^2 - 2*a*b + b^2) - 1/4*(2*a + b)*log(cos(x) - 1)/(a^2 + 2*a*b + b^2) - 1/2*(b*cos(x) - a)/((a^2 - b^2)*cos(x)^2 - a^2 + b^2)","A",0
17,-2,0,0,0.000000," ","integrate(cot(x)^4/(a+b*cos(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*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
18,1,63,0,2.535760," ","integrate(cot(x)/(3-cos(x))^(1/2),x, algorithm=""maxima"")","\frac{1}{4} \, \sqrt{2} \log\left(-\frac{\sqrt{2} - \sqrt{-\cos\left(x\right) + 3}}{\sqrt{2} + \sqrt{-\cos\left(x\right) + 3}}\right) - \frac{1}{4} \, \log\left(\sqrt{-\cos\left(x\right) + 3} + 2\right) + \frac{1}{4} \, \log\left(\sqrt{-\cos\left(x\right) + 3} - 2\right)"," ",0,"1/4*sqrt(2)*log(-(sqrt(2) - sqrt(-cos(x) + 3))/(sqrt(2) + sqrt(-cos(x) + 3))) - 1/4*log(sqrt(-cos(x) + 3) + 2) + 1/4*log(sqrt(-cos(x) + 3) - 2)","A",0
19,1,46,0,1.672987," ","integrate((a+b*cos(x))^(1/2)*tan(x),x, algorithm=""maxima"")","-\sqrt{a} \log\left(\frac{\sqrt{b \cos\left(x\right) + a} - \sqrt{a}}{\sqrt{b \cos\left(x\right) + a} + \sqrt{a}}\right) - 2 \, \sqrt{b \cos\left(x\right) + a}"," ",0,"-sqrt(a)*log((sqrt(b*cos(x) + a) - sqrt(a))/(sqrt(b*cos(x) + a) + sqrt(a))) - 2*sqrt(b*cos(x) + a)","A",0
20,1,35,0,1.176547," ","integrate(tan(x)/(a+b*cos(x))^(1/2),x, algorithm=""maxima"")","-\frac{\log\left(\frac{\sqrt{b \cos\left(x\right) + a} - \sqrt{a}}{\sqrt{b \cos\left(x\right) + a} + \sqrt{a}}\right)}{\sqrt{a}}"," ",0,"-log((sqrt(b*cos(x) + a) - sqrt(a))/(sqrt(b*cos(x) + a) + sqrt(a)))/sqrt(a)","A",0
21,0,0,0,0.000000," ","integrate((e*tan(d*x+c))^(1/2)/(a+b*cos(d*x+c)),x, algorithm=""maxima"")","\int \frac{\sqrt{e \tan\left(d x + c\right)}}{b \cos\left(d x + c\right) + a}\,{d x}"," ",0,"integrate(sqrt(e*tan(d*x + c))/(b*cos(d*x + c) + a), x)","F",0
22,0,0,0,0.000000," ","integrate((a+b*cos(f*x+e))^m*(g*tan(f*x+e))^p,x, algorithm=""maxima"")","\int {\left(b \cos\left(f x + e\right) + a\right)}^{m} \left(g \tan\left(f x + e\right)\right)^{p}\,{d x}"," ",0,"integrate((b*cos(f*x + e) + a)^m*(g*tan(f*x + e))^p, x)","F",0
