1,1,179,0,1.973204," ","integrate((A+C*cot(d*x+c)^2)/(b*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{3 \, {\left(2 \, \sqrt{2} \sqrt{b} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{b} + 2 \, \sqrt{b \tan\left(d x + c\right)}\right)}}{2 \, \sqrt{b}}\right) + 2 \, \sqrt{2} \sqrt{b} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{b} - 2 \, \sqrt{b \tan\left(d x + c\right)}\right)}}{2 \, \sqrt{b}}\right) + \sqrt{2} \sqrt{b} \log\left(b \tan\left(d x + c\right) + \sqrt{2} \sqrt{b \tan\left(d x + c\right)} \sqrt{b} + b\right) - \sqrt{2} \sqrt{b} \log\left(b \tan\left(d x + c\right) - \sqrt{2} \sqrt{b \tan\left(d x + c\right)} \sqrt{b} + b\right)\right)} {\left(A - C\right)} - \frac{8 \, C b^{2}}{\left(b \tan\left(d x + c\right)\right)^{\frac{3}{2}}}}{12 \, b d}"," ",0,"1/12*(3*(2*sqrt(2)*sqrt(b)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(b) + 2*sqrt(b*tan(d*x + c)))/sqrt(b)) + 2*sqrt(2)*sqrt(b)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(b) - 2*sqrt(b*tan(d*x + c)))/sqrt(b)) + sqrt(2)*sqrt(b)*log(b*tan(d*x + c) + sqrt(2)*sqrt(b*tan(d*x + c))*sqrt(b) + b) - sqrt(2)*sqrt(b)*log(b*tan(d*x + c) - sqrt(2)*sqrt(b*tan(d*x + c))*sqrt(b) + b))*(A - C) - 8*C*b^2/(b*tan(d*x + c))^(3/2))/(b*d)","A",0
2,1,23,0,1.144453," ","integrate(a+b*cot(d*x+c)^2,x, algorithm=""maxima"")","a x - \frac{{\left(d x + c + \frac{1}{\tan\left(d x + c\right)}\right)} b}{d}"," ",0,"a*x - (d*x + c + 1/tan(d*x + c))*b/d","A",0
3,1,63,0,0.755701," ","integrate((a+b*cot(d*x+c)^2)^2,x, algorithm=""maxima"")","a^{2} x - \frac{2 \, {\left(d x + c + \frac{1}{\tan\left(d x + c\right)}\right)} a b}{d} + \frac{{\left(3 \, d x + 3 \, c + \frac{3 \, \tan\left(d x + c\right)^{2} - 1}{\tan\left(d x + c\right)^{3}}\right)} b^{2}}{3 \, d}"," ",0,"a^2*x - 2*(d*x + c + 1/tan(d*x + c))*a*b/d + 1/3*(3*d*x + 3*c + (3*tan(d*x + c)^2 - 1)/tan(d*x + c)^3)*b^2/d","A",0
4,1,112,0,0.928140," ","integrate((a+b*cot(d*x+c)^2)^3,x, algorithm=""maxima"")","a^{3} x - \frac{3 \, {\left(d x + c + \frac{1}{\tan\left(d x + c\right)}\right)} a^{2} b}{d} + \frac{{\left(3 \, d x + 3 \, c + \frac{3 \, \tan\left(d x + c\right)^{2} - 1}{\tan\left(d x + c\right)^{3}}\right)} a b^{2}}{d} - \frac{{\left(15 \, d x + 15 \, c + \frac{15 \, \tan\left(d x + c\right)^{4} - 5 \, \tan\left(d x + c\right)^{2} + 3}{\tan\left(d x + c\right)^{5}}\right)} b^{3}}{15 \, d}"," ",0,"a^3*x - 3*(d*x + c + 1/tan(d*x + c))*a^2*b/d + (3*d*x + 3*c + (3*tan(d*x + c)^2 - 1)/tan(d*x + c)^3)*a*b^2/d - 1/15*(15*d*x + 15*c + (15*tan(d*x + c)^4 - 5*tan(d*x + c)^2 + 3)/tan(d*x + c)^5)*b^3/d","A",0
5,1,48,0,0.885105," ","integrate(1/(a+b*cot(d*x+c)^2),x, algorithm=""maxima"")","-\frac{\frac{b \arctan\left(\frac{a \tan\left(d x + c\right)}{\sqrt{a b}}\right)}{\sqrt{a b} {\left(a - b\right)}} - \frac{d x + c}{a - b}}{d}"," ",0,"-(b*arctan(a*tan(d*x + c)/sqrt(a*b))/(sqrt(a*b)*(a - b)) - (d*x + c)/(a - b))/d","A",0
6,1,115,0,0.985689," ","integrate(1/(a+b*cot(d*x+c)^2)^2,x, algorithm=""maxima"")","\frac{\frac{b \tan\left(d x + c\right)}{a^{2} b - a b^{2} + {\left(a^{3} - a^{2} b\right)} \tan\left(d x + c\right)^{2}} - \frac{{\left(3 \, a b - b^{2}\right)} \arctan\left(\frac{a \tan\left(d x + c\right)}{\sqrt{a b}}\right)}{{\left(a^{3} - 2 \, a^{2} b + a b^{2}\right)} \sqrt{a b}} + \frac{2 \, {\left(d x + c\right)}}{a^{2} - 2 \, a b + b^{2}}}{2 \, d}"," ",0,"1/2*(b*tan(d*x + c)/(a^2*b - a*b^2 + (a^3 - a^2*b)*tan(d*x + c)^2) - (3*a*b - b^2)*arctan(a*tan(d*x + c)/sqrt(a*b))/((a^3 - 2*a^2*b + a*b^2)*sqrt(a*b)) + 2*(d*x + c)/(a^2 - 2*a*b + b^2))/d","A",0
7,1,228,0,1.642212," ","integrate(1/(a+b*cot(d*x+c)^2)^3,x, algorithm=""maxima"")","-\frac{\frac{{\left(15 \, a^{2} b - 10 \, a b^{2} + 3 \, b^{3}\right)} \arctan\left(\frac{a \tan\left(d x + c\right)}{\sqrt{a b}}\right)}{{\left(a^{5} - 3 \, a^{4} b + 3 \, a^{3} b^{2} - a^{2} b^{3}\right)} \sqrt{a b}} - \frac{{\left(9 \, a^{2} b - 5 \, a b^{2}\right)} \tan\left(d x + c\right)^{3} + {\left(7 \, a b^{2} - 3 \, b^{3}\right)} \tan\left(d x + c\right)}{a^{4} b^{2} - 2 \, a^{3} b^{3} + a^{2} b^{4} + {\left(a^{6} - 2 \, a^{5} b + a^{4} b^{2}\right)} \tan\left(d x + c\right)^{4} + 2 \, {\left(a^{5} b - 2 \, a^{4} b^{2} + a^{3} b^{3}\right)} \tan\left(d x + c\right)^{2}} - \frac{8 \, {\left(d x + c\right)}}{a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}}}{8 \, d}"," ",0,"-1/8*((15*a^2*b - 10*a*b^2 + 3*b^3)*arctan(a*tan(d*x + c)/sqrt(a*b))/((a^5 - 3*a^4*b + 3*a^3*b^2 - a^2*b^3)*sqrt(a*b)) - ((9*a^2*b - 5*a*b^2)*tan(d*x + c)^3 + (7*a*b^2 - 3*b^3)*tan(d*x + c))/(a^4*b^2 - 2*a^3*b^3 + a^2*b^4 + (a^6 - 2*a^5*b + a^4*b^2)*tan(d*x + c)^4 + 2*(a^5*b - 2*a^4*b^2 + a^3*b^3)*tan(d*x + c)^2) - 8*(d*x + c)/(a^3 - 3*a^2*b + 3*a*b^2 - b^3))/d","A",0
8,1,300,0,1.100886," ","integrate((1+cot(x)^2)^(3/2),x, algorithm=""maxima"")","-\frac{4 \, {\left(\cos\left(3 \, x\right) + \cos\left(x\right)\right)} \cos\left(4 \, x\right) - 4 \, {\left(2 \, \cos\left(2 \, x\right) - 1\right)} \cos\left(3 \, x\right) - 8 \, \cos\left(2 \, x\right) \cos\left(x\right) + {\left(2 \, {\left(2 \, \cos\left(2 \, x\right) - 1\right)} \cos\left(4 \, x\right) - \cos\left(4 \, x\right)^{2} - 4 \, \cos\left(2 \, x\right)^{2} - \sin\left(4 \, x\right)^{2} + 4 \, \sin\left(4 \, x\right) \sin\left(2 \, x\right) - 4 \, \sin\left(2 \, x\right)^{2} + 4 \, \cos\left(2 \, x\right) - 1\right)} \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} + 2 \, \cos\left(x\right) + 1\right) - {\left(2 \, {\left(2 \, \cos\left(2 \, x\right) - 1\right)} \cos\left(4 \, x\right) - \cos\left(4 \, x\right)^{2} - 4 \, \cos\left(2 \, x\right)^{2} - \sin\left(4 \, x\right)^{2} + 4 \, \sin\left(4 \, x\right) \sin\left(2 \, x\right) - 4 \, \sin\left(2 \, x\right)^{2} + 4 \, \cos\left(2 \, x\right) - 1\right)} \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} - 2 \, \cos\left(x\right) + 1\right) + 4 \, {\left(\sin\left(3 \, x\right) + \sin\left(x\right)\right)} \sin\left(4 \, x\right) - 8 \, \sin\left(3 \, x\right) \sin\left(2 \, x\right) - 8 \, \sin\left(2 \, x\right) \sin\left(x\right) + 4 \, \cos\left(x\right)}{4 \, {\left(2 \, {\left(2 \, \cos\left(2 \, x\right) - 1\right)} \cos\left(4 \, x\right) - \cos\left(4 \, x\right)^{2} - 4 \, \cos\left(2 \, x\right)^{2} - \sin\left(4 \, x\right)^{2} + 4 \, \sin\left(4 \, x\right) \sin\left(2 \, x\right) - 4 \, \sin\left(2 \, x\right)^{2} + 4 \, \cos\left(2 \, x\right) - 1\right)}}"," ",0,"-1/4*(4*(cos(3*x) + cos(x))*cos(4*x) - 4*(2*cos(2*x) - 1)*cos(3*x) - 8*cos(2*x)*cos(x) + (2*(2*cos(2*x) - 1)*cos(4*x) - cos(4*x)^2 - 4*cos(2*x)^2 - sin(4*x)^2 + 4*sin(4*x)*sin(2*x) - 4*sin(2*x)^2 + 4*cos(2*x) - 1)*log(cos(x)^2 + sin(x)^2 + 2*cos(x) + 1) - (2*(2*cos(2*x) - 1)*cos(4*x) - cos(4*x)^2 - 4*cos(2*x)^2 - sin(4*x)^2 + 4*sin(4*x)*sin(2*x) - 4*sin(2*x)^2 + 4*cos(2*x) - 1)*log(cos(x)^2 + sin(x)^2 - 2*cos(x) + 1) + 4*(sin(3*x) + sin(x))*sin(4*x) - 8*sin(3*x)*sin(2*x) - 8*sin(2*x)*sin(x) + 4*cos(x))/(2*(2*cos(2*x) - 1)*cos(4*x) - cos(4*x)^2 - 4*cos(2*x)^2 - sin(4*x)^2 + 4*sin(4*x)*sin(2*x) - 4*sin(2*x)^2 + 4*cos(2*x) - 1)","B",0
9,1,35,0,1.002804," ","integrate((1+cot(x)^2)^(1/2),x, algorithm=""maxima"")","-\frac{1}{2} \, \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} + 2 \, \cos\left(x\right) + 1\right) + \frac{1}{2} \, \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} - 2 \, \cos\left(x\right) + 1\right)"," ",0,"-1/2*log(cos(x)^2 + sin(x)^2 + 2*cos(x) + 1) + 1/2*log(cos(x)^2 + sin(x)^2 - 2*cos(x) + 1)","B",0
10,1,10,0,0.831012," ","integrate(1/(1+cot(x)^2)^(1/2),x, algorithm=""maxima"")","-\frac{1}{\sqrt{\tan\left(x\right)^{2} + 1}}"," ",0,"-1/sqrt(tan(x)^2 + 1)","A",0
11,1,284,0,1.007931," ","integrate((-1-cot(x)^2)^(3/2),x, algorithm=""maxima"")","\frac{{\left(2 \, {\left(2 \, \cos\left(2 \, x\right) - 1\right)} \cos\left(4 \, x\right) - \cos\left(4 \, x\right)^{2} - 4 \, \cos\left(2 \, x\right)^{2} - \sin\left(4 \, x\right)^{2} + 4 \, \sin\left(4 \, x\right) \sin\left(2 \, x\right) - 4 \, \sin\left(2 \, x\right)^{2} + 4 \, \cos\left(2 \, x\right) - 1\right)} \arctan\left(\sin\left(x\right), \cos\left(x\right) + 1\right) - {\left(2 \, {\left(2 \, \cos\left(2 \, x\right) - 1\right)} \cos\left(4 \, x\right) - \cos\left(4 \, x\right)^{2} - 4 \, \cos\left(2 \, x\right)^{2} - \sin\left(4 \, x\right)^{2} + 4 \, \sin\left(4 \, x\right) \sin\left(2 \, x\right) - 4 \, \sin\left(2 \, x\right)^{2} + 4 \, \cos\left(2 \, x\right) - 1\right)} \arctan\left(\sin\left(x\right), \cos\left(x\right) - 1\right) + 2 \, {\left(\sin\left(3 \, x\right) + \sin\left(x\right)\right)} \cos\left(4 \, x\right) - 2 \, {\left(\cos\left(3 \, x\right) + \cos\left(x\right)\right)} \sin\left(4 \, x\right) - 2 \, {\left(2 \, \cos\left(2 \, x\right) - 1\right)} \sin\left(3 \, x\right) + 4 \, \cos\left(3 \, x\right) \sin\left(2 \, x\right) + 4 \, \cos\left(x\right) \sin\left(2 \, x\right) - 4 \, \cos\left(2 \, x\right) \sin\left(x\right) + 2 \, \sin\left(x\right)}{2 \, {\left(2 \, {\left(2 \, \cos\left(2 \, x\right) - 1\right)} \cos\left(4 \, x\right) - \cos\left(4 \, x\right)^{2} - 4 \, \cos\left(2 \, x\right)^{2} - \sin\left(4 \, x\right)^{2} + 4 \, \sin\left(4 \, x\right) \sin\left(2 \, x\right) - 4 \, \sin\left(2 \, x\right)^{2} + 4 \, \cos\left(2 \, x\right) - 1\right)}}"," ",0,"1/2*((2*(2*cos(2*x) - 1)*cos(4*x) - cos(4*x)^2 - 4*cos(2*x)^2 - sin(4*x)^2 + 4*sin(4*x)*sin(2*x) - 4*sin(2*x)^2 + 4*cos(2*x) - 1)*arctan2(sin(x), cos(x) + 1) - (2*(2*cos(2*x) - 1)*cos(4*x) - cos(4*x)^2 - 4*cos(2*x)^2 - sin(4*x)^2 + 4*sin(4*x)*sin(2*x) - 4*sin(2*x)^2 + 4*cos(2*x) - 1)*arctan2(sin(x), cos(x) - 1) + 2*(sin(3*x) + sin(x))*cos(4*x) - 2*(cos(3*x) + cos(x))*sin(4*x) - 2*(2*cos(2*x) - 1)*sin(3*x) + 4*cos(3*x)*sin(2*x) + 4*cos(x)*sin(2*x) - 4*cos(2*x)*sin(x) + 2*sin(x))/(2*(2*cos(2*x) - 1)*cos(4*x) - cos(4*x)^2 - 4*cos(2*x)^2 - sin(4*x)^2 + 4*sin(4*x)*sin(2*x) - 4*sin(2*x)^2 + 4*cos(2*x) - 1)","B",0
12,1,17,0,1.030939," ","integrate((-1-cot(x)^2)^(1/2),x, algorithm=""maxima"")","-\arctan\left(\sin\left(x\right), \cos\left(x\right) + 1\right) + \arctan\left(\sin\left(x\right), \cos\left(x\right) - 1\right)"," ",0,"-arctan2(sin(x), cos(x) + 1) + arctan2(sin(x), cos(x) - 1)","A",0
13,1,12,0,0.498873," ","integrate(1/(-1-cot(x)^2)^(1/2),x, algorithm=""maxima"")","-\frac{1}{\sqrt{-\tan\left(x\right)^{2} - 1}}"," ",0,"-1/sqrt(-tan(x)^2 - 1)","A",0
14,1,24,0,0.744774," ","integrate(cot(x)^3/(a+a*cot(x)^2)^(1/2),x, algorithm=""maxima"")","-\frac{1}{\sqrt{\frac{a}{\sin\left(x\right)^{2}}}} - \frac{\sqrt{\frac{a}{\sin\left(x\right)^{2}}}}{a}"," ",0,"-1/sqrt(a/sin(x)^2) - sqrt(a/sin(x)^2)/a","A",0
15,1,27,0,0.769695," ","integrate(cot(x)^2/(a+a*cot(x)^2)^(1/2),x, algorithm=""maxima"")","-\frac{\sqrt{-a} {\left(\arctan\left(\sin\left(x\right), \cos\left(x\right) + 1\right) - \arctan\left(\sin\left(x\right), \cos\left(x\right) - 1\right)\right)}}{a}"," ",0,"-sqrt(-a)*(arctan2(sin(x), cos(x) + 1) - arctan2(sin(x), cos(x) - 1))/a","A",0
16,1,8,0,0.547269," ","integrate(cot(x)/(a+a*cot(x)^2)^(1/2),x, algorithm=""maxima"")","\frac{1}{\sqrt{\frac{a}{\sin\left(x\right)^{2}}}}"," ",0,"1/sqrt(a/sin(x)^2)","A",0
17,1,52,0,0.653100," ","integrate(tan(x)/(a+a*cot(x)^2)^(1/2),x, algorithm=""maxima"")","-\frac{1}{2} \, a {\left(\frac{\log\left(-\frac{\sqrt{a} - \sqrt{\frac{a}{\sin\left(x\right)^{2}}}}{\sqrt{a} + \sqrt{\frac{a}{\sin\left(x\right)^{2}}}}\right)}{a^{\frac{3}{2}}} + \frac{2}{a \sqrt{\frac{a}{\sin\left(x\right)^{2}}}}\right)}"," ",0,"-1/2*a*(log(-(sqrt(a) - sqrt(a/sin(x)^2))/(sqrt(a) + sqrt(a/sin(x)^2)))/a^(3/2) + 2/(a*sqrt(a/sin(x)^2)))","A",0
18,1,18,0,0.520462," ","integrate(tan(x)^2/(a+a*cot(x)^2)^(1/2),x, algorithm=""maxima"")","\frac{\tan\left(x\right)^{2} + 2}{\sqrt{\tan\left(x\right)^{2} + 1} \sqrt{a}}"," ",0,"(tan(x)^2 + 2)/(sqrt(tan(x)^2 + 1)*sqrt(a))","A",0
19,-2,0,0,0.000000," ","integrate(cot(x)^3*(a+b*cot(x)^2)^(1/2),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-4*b>0)', see `assume?` for more details)Is 4*a-4*b positive or negative?","F(-2)",0
20,-2,0,0,0.000000," ","integrate(cot(x)*(a+b*cot(x)^2)^(1/2),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-4*b>0)', see `assume?` for more details)Is 4*a-4*b positive or negative?","F(-2)",0
21,0,0,0,0.000000," ","integrate((a+b*cot(x)^2)^(1/2)*tan(x),x, algorithm=""maxima"")","\int \sqrt{b \cot\left(x\right)^{2} + a} \tan\left(x\right)\,{d x}"," ",0,"integrate(sqrt(b*cot(x)^2 + a)*tan(x), x)","F",0
22,0,0,0,0.000000," ","integrate(cot(x)^2*(a+b*cot(x)^2)^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \cot\left(x\right)^{2} + a} \cot\left(x\right)^{2}\,{d x}"," ",0,"integrate(sqrt(b*cot(x)^2 + a)*cot(x)^2, x)","F",0
23,-2,0,0,0.000000," ","integrate((a+b*cot(x)^2)^(1/2),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(b-a>0)', see `assume?` for more details)Is b-a positive or negative?","F(-2)",0
24,0,0,0,0.000000," ","integrate((a+b*cot(x)^2)^(1/2)*tan(x)^2,x, algorithm=""maxima"")","\int \sqrt{b \cot\left(x\right)^{2} + a} \tan\left(x\right)^{2}\,{d x}"," ",0,"integrate(sqrt(b*cot(x)^2 + a)*tan(x)^2, x)","F",0
25,0,0,0,0.000000," ","integrate((a+b*cot(x)^2)^(1/2)*tan(x)^4,x, algorithm=""maxima"")","\int \sqrt{b \cot\left(x\right)^{2} + a} \tan\left(x\right)^{4}\,{d x}"," ",0,"integrate(sqrt(b*cot(x)^2 + a)*tan(x)^4, x)","F",0
26,-2,0,0,0.000000," ","integrate(cot(x)^3*(a+b*cot(x)^2)^(3/2),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-4*b>0)', see `assume?` for more details)Is 4*a-4*b positive or negative?","F(-2)",0
27,0,0,0,0.000000," ","integrate(cot(x)^2*(a+b*cot(x)^2)^(3/2),x, algorithm=""maxima"")","\int {\left(b \cot\left(x\right)^{2} + a\right)}^{\frac{3}{2}} \cot\left(x\right)^{2}\,{d x}"," ",0,"integrate((b*cot(x)^2 + a)^(3/2)*cot(x)^2, x)","F",0
28,-2,0,0,0.000000," ","integrate(cot(x)*(a+b*cot(x)^2)^(3/2),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-4*b>0)', see `assume?` for more details)Is 4*a-4*b positive or negative?","F(-2)",0
29,0,0,0,0.000000," ","integrate((a+b*cot(x)^2)^(3/2)*tan(x),x, algorithm=""maxima"")","\int {\left(b \cot\left(x\right)^{2} + a\right)}^{\frac{3}{2}} \tan\left(x\right)\,{d x}"," ",0,"integrate((b*cot(x)^2 + a)^(3/2)*tan(x), x)","F",0
30,0,0,0,0.000000," ","integrate((a+b*cot(x)^2)^(3/2)*tan(x)^2,x, algorithm=""maxima"")","\int {\left(b \cot\left(x\right)^{2} + a\right)}^{\frac{3}{2}} \tan\left(x\right)^{2}\,{d x}"," ",0,"integrate((b*cot(x)^2 + a)^(3/2)*tan(x)^2, x)","F",0
31,0,0,0,0.000000," ","integrate((a+b*cot(d*x+c)^2)^(5/2),x, algorithm=""maxima"")","\int {\left(b \cot\left(d x + c\right)^{2} + a\right)}^{\frac{5}{2}}\,{d x}"," ",0,"integrate((b*cot(d*x + c)^2 + a)^(5/2), x)","F",0
32,0,0,0,0.000000," ","integrate((a+b*cot(d*x+c)^2)^(3/2),x, algorithm=""maxima"")","\int {\left(b \cot\left(d x + c\right)^{2} + a\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((b*cot(d*x + c)^2 + a)^(3/2), x)","F",0
33,-2,0,0,0.000000," ","integrate((a+b*cot(d*x+c)^2)^(1/2),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(b-a>0)', see `assume?` for more details)Is b-a positive or negative?","F(-2)",0
34,-2,0,0,0.000000," ","integrate(1/(a+b*cot(d*x+c)^2)^(1/2),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(b-a>0)', see `assume?` for more details)Is b-a positive or negative?","F(-2)",0
35,-2,0,0,0.000000," ","integrate(1/(a+b*cot(d*x+c)^2)^(3/2),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(b-a>0)', see `assume?` for more details)Is b-a positive or negative?","F(-2)",0
36,-2,0,0,0.000000," ","integrate(1/(a+b*cot(d*x+c)^2)^(5/2),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(b-a>0)', see `assume?` for more details)Is b-a positive or negative?","F(-2)",0
37,-2,0,0,0.000000," ","integrate(1/(a+b*cot(d*x+c)^2)^(7/2),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(b-a>0)', see `assume?` for more details)Is b-a positive or negative?","F(-2)",0
38,0,0,0,0.000000," ","integrate((1-cot(x)^2)^(3/2),x, algorithm=""maxima"")","\int {\left(-\cot\left(x\right)^{2} + 1\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((-cot(x)^2 + 1)^(3/2), x)","F",0
39,-2,0,0,0.000000," ","integrate((1-cot(x)^2)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: sign: argument cannot be imaginary; found %i","F(-2)",0
40,1,90,0,0.506476," ","integrate(1/(1-cot(x)^2)^(1/2),x, algorithm=""maxima"")","\frac{1}{4} \, \sqrt{2} \arctan\left({\left(\cos\left(4 \, x\right)^{2} + \sin\left(4 \, x\right)^{2} + 2 \, \cos\left(4 \, x\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, x\right), \cos\left(4 \, x\right) + 1\right)\right) + \sin\left(2 \, x\right), {\left(\cos\left(4 \, x\right)^{2} + \sin\left(4 \, x\right)^{2} + 2 \, \cos\left(4 \, x\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, x\right), \cos\left(4 \, x\right) + 1\right)\right) + \cos\left(2 \, x\right)\right)"," ",0,"1/4*sqrt(2)*arctan2((cos(4*x)^2 + sin(4*x)^2 + 2*cos(4*x) + 1)^(1/4)*sin(1/2*arctan2(sin(4*x), cos(4*x) + 1)) + sin(2*x), (cos(4*x)^2 + sin(4*x)^2 + 2*cos(4*x) + 1)^(1/4)*cos(1/2*arctan2(sin(4*x), cos(4*x) + 1)) + cos(2*x))","B",0
41,0,0,0,0.000000," ","integrate((-1+cot(x)^2)^(3/2),x, algorithm=""maxima"")","\int {\left(\cot\left(x\right)^{2} - 1\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((cot(x)^2 - 1)^(3/2), x)","F",0
42,-2,0,0,0.000000," ","integrate((-1+cot(x)^2)^(1/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: sign: argument cannot be imaginary; found %i","F(-2)",0
43,1,143,0,0.498868," ","integrate(1/(-1+cot(x)^2)^(1/2),x, algorithm=""maxima"")","-\frac{1}{8} \, \sqrt{2} {\left(2 \, \operatorname{arsinh}\left(1\right) + \log\left(\cos\left(2 \, x\right)^{2} + \sin\left(2 \, x\right)^{2} + \sqrt{\cos\left(4 \, x\right)^{2} + \sin\left(4 \, x\right)^{2} + 2 \, \cos\left(4 \, x\right) + 1} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, x\right), \cos\left(4 \, x\right) + 1\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, x\right), \cos\left(4 \, x\right) + 1\right)\right)^{2}\right)} + 2 \, {\left(\cos\left(4 \, x\right)^{2} + \sin\left(4 \, x\right)^{2} + 2 \, \cos\left(4 \, x\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(2 \, x\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, x\right), \cos\left(4 \, x\right) + 1\right)\right) + \sin\left(2 \, x\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(4 \, x\right), \cos\left(4 \, x\right) + 1\right)\right)\right)}\right)\right)}"," ",0,"-1/8*sqrt(2)*(2*arcsinh(1) + log(cos(2*x)^2 + sin(2*x)^2 + sqrt(cos(4*x)^2 + sin(4*x)^2 + 2*cos(4*x) + 1)*(cos(1/2*arctan2(sin(4*x), cos(4*x) + 1))^2 + sin(1/2*arctan2(sin(4*x), cos(4*x) + 1))^2) + 2*(cos(4*x)^2 + sin(4*x)^2 + 2*cos(4*x) + 1)^(1/4)*(cos(2*x)*cos(1/2*arctan2(sin(4*x), cos(4*x) + 1)) + sin(2*x)*sin(1/2*arctan2(sin(4*x), cos(4*x) + 1)))))","B",0
44,-2,0,0,0.000000," ","integrate(cot(x)^3/(a+b*cot(x)^2)^(1/2),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-4*b>0)', see `assume?` for more details)Is 4*a-4*b positive or negative?","F(-2)",0
45,0,0,0,0.000000," ","integrate(cot(x)^2/(a+b*cot(x)^2)^(1/2),x, algorithm=""maxima"")","\int \frac{\cot\left(x\right)^{2}}{\sqrt{b \cot\left(x\right)^{2} + a}}\,{d x}"," ",0,"integrate(cot(x)^2/sqrt(b*cot(x)^2 + a), x)","F",0
46,-2,0,0,0.000000," ","integrate(cot(x)/(a+b*cot(x)^2)^(1/2),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-4*b>0)', see `assume?` for more details)Is 4*a-4*b positive or negative?","F(-2)",0
47,0,0,0,0.000000," ","integrate(tan(x)/(a+b*cot(x)^2)^(1/2),x, algorithm=""maxima"")","\int \frac{\tan\left(x\right)}{\sqrt{b \cot\left(x\right)^{2} + a}}\,{d x}"," ",0,"integrate(tan(x)/sqrt(b*cot(x)^2 + a), x)","F",0
48,0,0,0,0.000000," ","integrate(tan(x)^2/(a+b*cot(x)^2)^(1/2),x, algorithm=""maxima"")","\int \frac{\tan\left(x\right)^{2}}{\sqrt{b \cot\left(x\right)^{2} + a}}\,{d x}"," ",0,"integrate(tan(x)^2/sqrt(b*cot(x)^2 + a), x)","F",0
49,-2,0,0,0.000000," ","integrate(cot(x)^3/(a+b*cot(x)^2)^(3/2),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-4*b>0)', see `assume?` for more details)Is 4*a-4*b positive or negative?","F(-2)",0
50,-2,0,0,0.000000," ","integrate(cot(x)^2/(a+b*cot(x)^2)^(3/2),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(b-a>0)', see `assume?` for more details)Is b-a positive or negative?","F(-2)",0
51,-2,0,0,0.000000," ","integrate(cot(x)/(a+b*cot(x)^2)^(3/2),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-4*b>0)', see `assume?` for more details)Is 4*a-4*b positive or negative?","F(-2)",0
52,0,0,0,0.000000," ","integrate(tan(x)/(a+b*cot(x)^2)^(3/2),x, algorithm=""maxima"")","\int \frac{\tan\left(x\right)}{{\left(b \cot\left(x\right)^{2} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(tan(x)/(b*cot(x)^2 + a)^(3/2), x)","F",0
53,0,0,0,0.000000," ","integrate(tan(x)^2/(a+b*cot(x)^2)^(3/2),x, algorithm=""maxima"")","\int \frac{\tan\left(x\right)^{2}}{{\left(b \cot\left(x\right)^{2} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(tan(x)^2/(b*cot(x)^2 + a)^(3/2), x)","F",0
54,-2,0,0,0.000000," ","integrate(cot(x)^3/(a+b*cot(x)^2)^(5/2),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-4*b>0)', see `assume?` for more details)Is 4*a-4*b positive or negative?","F(-2)",0
55,-2,0,0,0.000000," ","integrate(cot(x)^2/(a+b*cot(x)^2)^(5/2),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(b-a>0)', see `assume?` for more details)Is b-a positive or negative?","F(-2)",0
56,-2,0,0,0.000000," ","integrate(cot(x)/(a+b*cot(x)^2)^(5/2),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-4*b>0)', see `assume?` for more details)Is 4*a-4*b positive or negative?","F(-2)",0
57,0,0,0,0.000000," ","integrate(tan(x)/(a+b*cot(x)^2)^(5/2),x, algorithm=""maxima"")","\int \frac{\tan\left(x\right)}{{\left(b \cot\left(x\right)^{2} + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(tan(x)/(b*cot(x)^2 + a)^(5/2), x)","F",0
58,-1,0,0,0.000000," ","integrate(tan(x)^2/(a+b*cot(x)^2)^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
59,1,33,0,0.416960," ","integrate(1/(1+cot(x)^3),x, algorithm=""maxima"")","\frac{1}{2} \, x + \frac{1}{3} \, \log\left(\tan\left(x\right)^{2} - \tan\left(x\right) + 1\right) - \frac{1}{4} \, \log\left(\tan\left(x\right)^{2} + 1\right) - \frac{1}{6} \, \log\left(\tan\left(x\right) + 1\right)"," ",0,"1/2*x + 1/3*log(tan(x)^2 - tan(x) + 1) - 1/4*log(tan(x)^2 + 1) - 1/6*log(tan(x) + 1)","A",0
60,0,0,0,0.000000," ","integrate(cot(x)*(a+b*cot(x)^4)^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \cot\left(x\right)^{4} + a} \cot\left(x\right)\,{d x}"," ",0,"integrate(sqrt(b*cot(x)^4 + a)*cot(x), x)","F",0
61,0,0,0,0.000000," ","integrate(cot(x)*(a+b*cot(x)^4)^(3/2),x, algorithm=""maxima"")","\int {\left(b \cot\left(x\right)^{4} + a\right)}^{\frac{3}{2}} \cot\left(x\right)\,{d x}"," ",0,"integrate((b*cot(x)^4 + a)^(3/2)*cot(x), x)","F",0
62,0,0,0,0.000000," ","integrate(cot(x)/(a+b*cot(x)^4)^(1/2),x, algorithm=""maxima"")","\int \frac{\cot\left(x\right)}{\sqrt{b \cot\left(x\right)^{4} + a}}\,{d x}"," ",0,"integrate(cot(x)/sqrt(b*cot(x)^4 + a), x)","F",0
63,0,0,0,0.000000," ","integrate(cot(x)/(a+b*cot(x)^4)^(3/2),x, algorithm=""maxima"")","\int \frac{\cot\left(x\right)}{{\left(b \cot\left(x\right)^{4} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(cot(x)/(b*cot(x)^4 + a)^(3/2), x)","F",0
64,0,0,0,0.000000," ","integrate(cot(x)/(a+b*cot(x)^4)^(5/2),x, algorithm=""maxima"")","\int \frac{\cot\left(x\right)}{{\left(b \cot\left(x\right)^{4} + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(cot(x)/(b*cot(x)^4 + a)^(5/2), x)","F",0
