1,0,0,0,0.000000," ","integrate((A+C*cot(d*x+c)^2)/(b*tan(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{C \cot\left(d x + c\right)^{2} + A}{\sqrt{b \tan\left(d x + c\right)}}\,{d x}"," ",0,"integrate((C*cot(d*x + c)^2 + A)/sqrt(b*tan(d*x + c)), x)","F",0
2,1,40,0,0.192326," ","integrate(a+b*cot(d*x+c)^2,x, algorithm=""giac"")","a x - \frac{{\left(2 \, d x + 2 \, c + \frac{1}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)} - \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} b}{2 \, d}"," ",0,"a*x - 1/2*(2*d*x + 2*c + 1/tan(1/2*d*x + 1/2*c) - tan(1/2*d*x + 1/2*c))*b/d","A",0
3,1,114,0,0.253604," ","integrate((a+b*cot(d*x+c)^2)^2,x, algorithm=""giac"")","\frac{b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 24 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 15 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 24 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} {\left(d x + c\right)} - \frac{24 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 15 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + b^{2}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3}}}{24 \, d}"," ",0,"1/24*(b^2*tan(1/2*d*x + 1/2*c)^3 + 24*a*b*tan(1/2*d*x + 1/2*c) - 15*b^2*tan(1/2*d*x + 1/2*c) + 24*(a^2 - 2*a*b + b^2)*(d*x + c) - (24*a*b*tan(1/2*d*x + 1/2*c)^2 - 15*b^2*tan(1/2*d*x + 1/2*c)^2 + b^2)/tan(1/2*d*x + 1/2*c)^3)/d","B",0
4,1,229,0,0.371398," ","integrate((a+b*cot(d*x+c)^2)^3,x, algorithm=""giac"")","\frac{3 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 60 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 35 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 720 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 900 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 330 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 480 \, {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} {\left(d x + c\right)} - \frac{720 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 900 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 330 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 60 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 35 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 3 \, b^{3}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5}}}{480 \, d}"," ",0,"1/480*(3*b^3*tan(1/2*d*x + 1/2*c)^5 + 60*a*b^2*tan(1/2*d*x + 1/2*c)^3 - 35*b^3*tan(1/2*d*x + 1/2*c)^3 + 720*a^2*b*tan(1/2*d*x + 1/2*c) - 900*a*b^2*tan(1/2*d*x + 1/2*c) + 330*b^3*tan(1/2*d*x + 1/2*c) + 480*(a^3 - 3*a^2*b + 3*a*b^2 - b^3)*(d*x + c) - (720*a^2*b*tan(1/2*d*x + 1/2*c)^4 - 900*a*b^2*tan(1/2*d*x + 1/2*c)^4 + 330*b^3*tan(1/2*d*x + 1/2*c)^4 + 60*a*b^2*tan(1/2*d*x + 1/2*c)^2 - 35*b^3*tan(1/2*d*x + 1/2*c)^2 + 3*b^3)/tan(1/2*d*x + 1/2*c)^5)/d","B",0
5,1,65,0,0.187491," ","integrate(1/(a+b*cot(d*x+c)^2),x, algorithm=""giac"")","-\frac{\frac{{\left(\pi \left \lfloor \frac{d x + c}{\pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(d x + c\right)}{\sqrt{a b}}\right)\right)} b}{\sqrt{a b} {\left(a - b\right)}} - \frac{d x + c}{a - b}}{d}"," ",0,"-((pi*floor((d*x + c)/pi + 1/2)*sgn(a) + arctan(a*tan(d*x + c)/sqrt(a*b)))*b/(sqrt(a*b)*(a - b)) - (d*x + c)/(a - b))/d","A",0
6,1,123,0,0.266711," ","integrate(1/(a+b*cot(d*x+c)^2)^2,x, algorithm=""giac"")","-\frac{\frac{{\left(\pi \left \lfloor \frac{d x + c}{\pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(d x + c\right)}{\sqrt{a b}}\right)\right)} {\left(3 \, a b - b^{2}\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}} - \frac{b \tan\left(d x + c\right)}{{\left(a \tan\left(d x + c\right)^{2} + b\right)} {\left(a^{2} - a b\right)}}}{2 \, d}"," ",0,"-1/2*((pi*floor((d*x + c)/pi + 1/2)*sgn(a) + arctan(a*tan(d*x + c)/sqrt(a*b)))*(3*a*b - b^2)/((a^3 - 2*a^2*b + a*b^2)*sqrt(a*b)) - 2*(d*x + c)/(a^2 - 2*a*b + b^2) - b*tan(d*x + c)/((a*tan(d*x + c)^2 + b)*(a^2 - a*b)))/d","A",0
7,1,206,0,0.712796," ","integrate(1/(a+b*cot(d*x+c)^2)^3,x, algorithm=""giac"")","-\frac{\frac{{\left(15 \, a^{2} b - 10 \, a b^{2} + 3 \, b^{3}\right)} {\left(\pi \left \lfloor \frac{d x + c}{\pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(d x + c\right)}{\sqrt{a b}}\right)\right)}}{{\left(a^{5} - 3 \, a^{4} b + 3 \, a^{3} b^{2} - a^{2} b^{3}\right)} \sqrt{a b}} - \frac{8 \, {\left(d x + c\right)}}{a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}} - \frac{9 \, a^{2} b \tan\left(d x + c\right)^{3} - 5 \, a b^{2} \tan\left(d x + c\right)^{3} + 7 \, a b^{2} \tan\left(d x + c\right) - 3 \, b^{3} \tan\left(d x + c\right)}{{\left(a^{4} - 2 \, a^{3} b + a^{2} b^{2}\right)} {\left(a \tan\left(d x + c\right)^{2} + b\right)}^{2}}}{8 \, d}"," ",0,"-1/8*((15*a^2*b - 10*a*b^2 + 3*b^3)*(pi*floor((d*x + c)/pi + 1/2)*sgn(a) + 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)) - 8*(d*x + c)/(a^3 - 3*a^2*b + 3*a*b^2 - b^3) - (9*a^2*b*tan(d*x + c)^3 - 5*a*b^2*tan(d*x + c)^3 + 7*a*b^2*tan(d*x + c) - 3*b^3*tan(d*x + c))/((a^4 - 2*a^3*b + a^2*b^2)*(a*tan(d*x + c)^2 + b)^2))/d","A",0
8,1,32,0,0.182877," ","integrate((1+cot(x)^2)^(3/2),x, algorithm=""giac"")","\frac{1}{4} \, {\left(\frac{2 \, \cos\left(x\right)}{\cos\left(x\right)^{2} - 1} - \log\left(\cos\left(x\right) + 1\right) + \log\left(-\cos\left(x\right) + 1\right)\right)} \mathrm{sgn}\left(\sin\left(x\right)\right)"," ",0,"1/4*(2*cos(x)/(cos(x)^2 - 1) - log(cos(x) + 1) + log(-cos(x) + 1))*sgn(sin(x))","A",0
9,0,0,0,0.000000," ","integrate((1+cot(x)^2)^(1/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
10,0,0,0,0.000000," ","integrate(1/(1+cot(x)^2)^(1/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
11,0,0,0,0.000000," ","integrate((-1-cot(x)^2)^(3/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
12,0,0,0,0.000000," ","integrate((-1-cot(x)^2)^(1/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
13,0,0,0,0.000000," ","integrate(1/(-1-cot(x)^2)^(1/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
14,1,30,0,0.180295," ","integrate(cot(x)^3/(a+a*cot(x)^2)^(1/2),x, algorithm=""giac"")","-\frac{\sqrt{-a \cos\left(x\right)^{2} + a} + \frac{a}{\sqrt{-a \cos\left(x\right)^{2} + a}}}{a}"," ",0,"-(sqrt(-a*cos(x)^2 + a) + a/sqrt(-a*cos(x)^2 + a))/a","A",0
15,0,0,0,0.000000," ","integrate(cot(x)^2/(a+a*cot(x)^2)^(1/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
16,1,12,0,0.203366," ","integrate(cot(x)/(a+a*cot(x)^2)^(1/2),x, algorithm=""giac"")","\frac{\sqrt{a \sin\left(x\right)^{2}}}{a}"," ",0,"sqrt(a*sin(x)^2)/a","A",0
17,1,42,0,0.192179," ","integrate(tan(x)/(a+a*cot(x)^2)^(1/2),x, algorithm=""giac"")","-\frac{\arctan\left(\frac{\sqrt{-a \cos\left(x\right)^{2} + a}}{\sqrt{-a}}\right)}{\sqrt{-a}} - \frac{\sqrt{-a \cos\left(x\right)^{2} + a}}{a}"," ",0,"-arctan(sqrt(-a*cos(x)^2 + a)/sqrt(-a))/sqrt(-a) - sqrt(-a*cos(x)^2 + a)/a","A",0
18,0,0,0,0.000000," ","integrate(tan(x)^2/(a+a*cot(x)^2)^(1/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
19,-2,0,0,0.000000," ","integrate(cot(x)^3*(a+b*cot(x)^2)^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(sin(x))]Warning, choosing root of [1,0,%%%{-2,[1,2,0]%%%}+%%%{-2,[1,0,0]%%%}+%%%{2,[0,2,1]%%%},0,%%%{1,[2,4,0]%%%}+%%%{-2,[2,2,0]%%%}+%%%{1,[2,0,0]%%%}+%%%{-2,[1,4,1]%%%}+%%%{6,[1,2,1]%%%}+%%%{-4,[1,0,1]%%%}+%%%{1,[0,4,2]%%%}+%%%{-4,[0,2,2]%%%}+%%%{4,[0,0,2]%%%}] at parameters values [86,-97,-82]Warning, choosing root of [1,0,%%%{-2,[1,0]%%%},0,%%%{1,[2,0]%%%}+%%%{-4,[1,1]%%%}+%%%{4,[0,2]%%%}] at parameters values [90.79236355,54.1277311612]Warning, choosing root of [1,0,%%%{-2,[1,0]%%%},0,%%%{1,[2,0]%%%}+%%%{-4,[1,1]%%%}+%%%{4,[0,2]%%%}] at parameters values [69.8278764193,63.4443001123]Warning, choosing root of [1,0,%%%{-2,[1,0]%%%},0,%%%{1,[2,0]%%%}+%%%{-4,[1,1]%%%}+%%%{4,[0,2]%%%}] at parameters values [108.020125429,82.1195442914]Warning, choosing root of [1,0,%%%{-2,[1,0]%%%},0,%%%{1,[2,0]%%%}+%%%{-4,[1,1]%%%}+%%%{4,[0,2]%%%}] at parameters values [26.4357969165,7.79369851155]Warning, choosing root of [1,0,%%%{-2,[1,0]%%%},0,%%%{1,[2,0]%%%}+%%%{-4,[1,1]%%%}+%%%{4,[0,2]%%%}] at parameters values [150.357303702,71.707969239]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b]=[b+63,75]Unable to convert to real 75.0*(b+63.0)-5625.0 Error: Bad Argument ValueWarning, choosing root of [1,0,%%%{-2,[1,2,0]%%%}+%%%{-2,[1,0,0]%%%}+%%%{2,[0,2,1]%%%},0,%%%{1,[2,4,0]%%%}+%%%{-2,[2,2,0]%%%}+%%%{1,[2,0,0]%%%}+%%%{-2,[1,4,1]%%%}+%%%{6,[1,2,1]%%%}+%%%{-4,[1,0,1]%%%}+%%%{1,[0,4,2]%%%}+%%%{-4,[0,2,2]%%%}+%%%{4,[0,0,2]%%%}] at parameters values [18,-49,-33]Warning, choosing root of [1,0,%%%{-2,[1,0]%%%},0,%%%{1,[2,0]%%%}+%%%{-4,[1,1]%%%}+%%%{4,[0,2]%%%}] at parameters values [70.2095400225,15.451549686]Warning, choosing root of [1,0,%%%{-2,[1,0]%%%},0,%%%{1,[2,0]%%%}+%%%{-4,[1,1]%%%}+%%%{4,[0,2]%%%}] at parameters values [100.356811349,81.9516051291]Warning, choosing root of [1,0,%%%{-2,[1,0]%%%},0,%%%{1,[2,0]%%%}+%%%{-4,[1,1]%%%}+%%%{4,[0,2]%%%}] at parameters values [133.032670634,51.6443148847]Warning, choosing root of [1,0,%%%{-2,[1,0]%%%},0,%%%{1,[2,0]%%%}+%%%{-4,[1,1]%%%}+%%%{4,[0,2]%%%}] at parameters values [42.28121641,31.8503101398]Warning, choosing root of [1,0,%%%{-2,[1,0]%%%},0,%%%{1,[2,0]%%%}+%%%{-4,[1,1]%%%}+%%%{4,[0,2]%%%}] at parameters values [92.8262473457,64.3995612673]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b]=[b+66,40]Unable to convert to real 40.0*(b+66.0)-1600.0 Error: Bad Argument ValueUnable to cancel step at 0 of 2*(((3*a-6*b)*sqrt(a-b)*(sqrt(a*sin(x)^2-b*sin(x)^2+b)-sqrt(a-b)*sin(x))^4+6*b^2*sqrt(a-b)*(sqrt(a*sin(x)^2-b*sin(x)^2+b)-sqrt(a-b)*sin(x))^2+(a*b^2-4*b^3)*sqrt(a-b))/3/((sqrt(a*sin(x)^2-b*sin(x)^2+b)-sqrt(a-b)*sin(x))^2-b)^3+sqrt(a-b)/4*ln((sqrt(a*sin(x)^2-b*sin(x)^2+b)-sqrt(a-b)*sin(x))^2))--2*(((3*a-6*b)*sqrt(a-b)*(sqrt(a*sin(x)^2-b*sin(x)^2+b)-sqrt(a-b)*sin(x))^4+6*b^2*sqrt(a-b)*(sqrt(a*sin(x)^2-b*sin(x)^2+b)-sqrt(a-b)*sin(x))^2+(a*b^2-4*b^3)*sqrt(a-b))/3/((sqrt(a*sin(x)^2-b*sin(x)^2+b)-sqrt(a-b)*sin(x))^2-b)^3+sqrt(a-b)/4*ln((sqrt(a*sin(x)^2-b*sin(x)^2+b)-sqrt(a-b)*sin(x))^2))Discontinuities at zeroes of sin(x) were not checkedEvaluation time: 0.8Done","F(-2)",0
20,1,95,0,0.800775," ","integrate(cot(x)*(a+b*cot(x)^2)^(1/2),x, algorithm=""giac"")","-\frac{1}{2} \, {\left(\sqrt{a - b} \log\left({\left(\sqrt{a - b} \sin\left(x\right) - \sqrt{a \sin\left(x\right)^{2} - b \sin\left(x\right)^{2} + b}\right)}^{2}\right) - \frac{4 \, \sqrt{a - b} b}{{\left(\sqrt{a - b} \sin\left(x\right) - \sqrt{a \sin\left(x\right)^{2} - b \sin\left(x\right)^{2} + b}\right)}^{2} - b}\right)} \mathrm{sgn}\left(\sin\left(x\right)\right)"," ",0,"-1/2*(sqrt(a - b)*log((sqrt(a - b)*sin(x) - sqrt(a*sin(x)^2 - b*sin(x)^2 + b))^2) - 4*sqrt(a - b)*b/((sqrt(a - b)*sin(x) - sqrt(a*sin(x)^2 - b*sin(x)^2 + b))^2 - b))*sgn(sin(x))","B",0
21,1,187,0,0.736280," ","integrate((a+b*cot(x)^2)^(1/2)*tan(x),x, algorithm=""giac"")","\frac{1}{2} \, {\left(\frac{2 \, \sqrt{a - b} a \arctan\left(\frac{{\left(\sqrt{a - b} \sin\left(x\right) - \sqrt{a \sin\left(x\right)^{2} - b \sin\left(x\right)^{2} + b}\right)}^{2} - 2 \, a + b}{2 \, \sqrt{-a^{2} + a b}}\right)}{\sqrt{-a^{2} + a b}} + \sqrt{a - b} \log\left({\left(\sqrt{a - b} \sin\left(x\right) - \sqrt{a \sin\left(x\right)^{2} - b \sin\left(x\right)^{2} + b}\right)}^{2}\right)\right)} \mathrm{sgn}\left(\sin\left(x\right)\right) - \frac{{\left(2 \, \sqrt{a - b} a \arctan\left(-\frac{a - b}{\sqrt{-a^{2} + a b}}\right) + \sqrt{-a^{2} + a b} \sqrt{a - b} \log\left(b\right)\right)} \mathrm{sgn}\left(\sin\left(x\right)\right)}{2 \, \sqrt{-a^{2} + a b}}"," ",0,"1/2*(2*sqrt(a - b)*a*arctan(1/2*((sqrt(a - b)*sin(x) - sqrt(a*sin(x)^2 - b*sin(x)^2 + b))^2 - 2*a + b)/sqrt(-a^2 + a*b))/sqrt(-a^2 + a*b) + sqrt(a - b)*log((sqrt(a - b)*sin(x) - sqrt(a*sin(x)^2 - b*sin(x)^2 + b))^2))*sgn(sin(x)) - 1/2*(2*sqrt(a - b)*a*arctan(-(a - b)/sqrt(-a^2 + a*b)) + sqrt(-a^2 + a*b)*sqrt(a - b)*log(b))*sgn(sin(x))/sqrt(-a^2 + a*b)","B",0
22,-2,0,0,0.000000," ","integrate(cot(x)^2*(a+b*cot(x)^2)^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(sin(x))]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
23,1,210,0,2.641770," ","integrate((a+b*cot(x)^2)^(1/2),x, algorithm=""giac"")","-\frac{1}{2} \, {\left(\frac{2 \, \sqrt{-a + b} b \arctan\left(\frac{{\left(\sqrt{-a + b} \cos\left(x\right) - \sqrt{-a \cos\left(x\right)^{2} + b \cos\left(x\right)^{2} + a}\right)}^{2} + a - 2 \, b}{2 \, \sqrt{a b - b^{2}}}\right)}{\sqrt{a b - b^{2}}} + \sqrt{-a + b} \log\left({\left(\sqrt{-a + b} \cos\left(x\right) - \sqrt{-a \cos\left(x\right)^{2} + b \cos\left(x\right)^{2} + a}\right)}^{2}\right)\right)} \mathrm{sgn}\left(\sin\left(x\right)\right) - \frac{{\left(2 \, \sqrt{-a + b} b \arctan\left(\frac{\sqrt{-a + b} \sqrt{b}}{\sqrt{a b - b^{2}}}\right) - \sqrt{a b - b^{2}} \sqrt{-a + b} \log\left(-a - 2 \, \sqrt{-a + b} \sqrt{b} + 2 \, b\right)\right)} \mathrm{sgn}\left(\sin\left(x\right)\right)}{2 \, \sqrt{a b - b^{2}}}"," ",0,"-1/2*(2*sqrt(-a + b)*b*arctan(1/2*((sqrt(-a + b)*cos(x) - sqrt(-a*cos(x)^2 + b*cos(x)^2 + a))^2 + a - 2*b)/sqrt(a*b - b^2))/sqrt(a*b - b^2) + sqrt(-a + b)*log((sqrt(-a + b)*cos(x) - sqrt(-a*cos(x)^2 + b*cos(x)^2 + a))^2))*sgn(sin(x)) - 1/2*(2*sqrt(-a + b)*b*arctan(sqrt(-a + b)*sqrt(b)/sqrt(a*b - b^2)) - sqrt(a*b - b^2)*sqrt(-a + b)*log(-a - 2*sqrt(-a + b)*sqrt(b) + 2*b))*sgn(sin(x))/sqrt(a*b - b^2)","B",0
24,1,239,0,0.495191," ","integrate((a+b*cot(x)^2)^(1/2)*tan(x)^2,x, algorithm=""giac"")","\frac{1}{2} \, {\left(\sqrt{-a + b} \log\left({\left(\sqrt{-a + b} \cos\left(x\right) - \sqrt{-a \cos\left(x\right)^{2} + b \cos\left(x\right)^{2} + a}\right)}^{2}\right) - \frac{4 \, a \sqrt{-a + b}}{{\left(\sqrt{-a + b} \cos\left(x\right) - \sqrt{-a \cos\left(x\right)^{2} + b \cos\left(x\right)^{2} + a}\right)}^{2} - a}\right)} \mathrm{sgn}\left(\sin\left(x\right)\right) - \frac{{\left(a \sqrt{-a + b} \log\left(-a - 2 \, \sqrt{-a + b} \sqrt{b} + 2 \, b\right) - a \sqrt{b} \log\left(-a - 2 \, \sqrt{-a + b} \sqrt{b} + 2 \, b\right) - \sqrt{-a + b} b \log\left(-a - 2 \, \sqrt{-a + b} \sqrt{b} + 2 \, b\right) + b^{\frac{3}{2}} \log\left(-a - 2 \, \sqrt{-a + b} \sqrt{b} + 2 \, b\right) + 2 \, a \sqrt{-a + b}\right)} \mathrm{sgn}\left(\sin\left(x\right)\right)}{2 \, {\left(a + \sqrt{-a + b} \sqrt{b} - b\right)}}"," ",0,"1/2*(sqrt(-a + b)*log((sqrt(-a + b)*cos(x) - sqrt(-a*cos(x)^2 + b*cos(x)^2 + a))^2) - 4*a*sqrt(-a + b)/((sqrt(-a + b)*cos(x) - sqrt(-a*cos(x)^2 + b*cos(x)^2 + a))^2 - a))*sgn(sin(x)) - 1/2*(a*sqrt(-a + b)*log(-a - 2*sqrt(-a + b)*sqrt(b) + 2*b) - a*sqrt(b)*log(-a - 2*sqrt(-a + b)*sqrt(b) + 2*b) - sqrt(-a + b)*b*log(-a - 2*sqrt(-a + b)*sqrt(b) + 2*b) + b^(3/2)*log(-a - 2*sqrt(-a + b)*sqrt(b) + 2*b) + 2*a*sqrt(-a + b))*sgn(sin(x))/(a + sqrt(-a + b)*sqrt(b) - b)","B",0
25,1,476,0,0.250656," ","integrate((a+b*cot(x)^2)^(1/2)*tan(x)^4,x, algorithm=""giac"")","-\frac{1}{6} \, {\left(3 \, \sqrt{-a + b} \log\left({\left(\sqrt{-a + b} \cos\left(x\right) - \sqrt{-a \cos\left(x\right)^{2} + b \cos\left(x\right)^{2} + a}\right)}^{2}\right) - \frac{4 \, {\left(3 \, {\left(\sqrt{-a + b} \cos\left(x\right) - \sqrt{-a \cos\left(x\right)^{2} + b \cos\left(x\right)^{2} + a}\right)}^{4} {\left(2 \, a - b\right)} \sqrt{-a + b} - 6 \, {\left(\sqrt{-a + b} \cos\left(x\right) - \sqrt{-a \cos\left(x\right)^{2} + b \cos\left(x\right)^{2} + a}\right)}^{2} a^{2} \sqrt{-a + b} + {\left(4 \, a^{3} - a^{2} b\right)} \sqrt{-a + b}\right)}}{{\left({\left(\sqrt{-a + b} \cos\left(x\right) - \sqrt{-a \cos\left(x\right)^{2} + b \cos\left(x\right)^{2} + a}\right)}^{2} - a\right)}^{3}}\right)} \mathrm{sgn}\left(\sin\left(x\right)\right) + \frac{{\left(3 \, a^{2} \sqrt{-a + b} \log\left(-a - 2 \, \sqrt{-a + b} \sqrt{b} + 2 \, b\right) - 9 \, a^{2} \sqrt{b} \log\left(-a - 2 \, \sqrt{-a + b} \sqrt{b} + 2 \, b\right) - 15 \, a \sqrt{-a + b} b \log\left(-a - 2 \, \sqrt{-a + b} \sqrt{b} + 2 \, b\right) + 21 \, a b^{\frac{3}{2}} \log\left(-a - 2 \, \sqrt{-a + b} \sqrt{b} + 2 \, b\right) + 12 \, \sqrt{-a + b} b^{2} \log\left(-a - 2 \, \sqrt{-a + b} \sqrt{b} + 2 \, b\right) - 12 \, b^{\frac{5}{2}} \log\left(-a - 2 \, \sqrt{-a + b} \sqrt{b} + 2 \, b\right) + 8 \, a^{2} \sqrt{-a + b} - 18 \, a^{2} \sqrt{b} - 24 \, a \sqrt{-a + b} b + 30 \, a b^{\frac{3}{2}} + 12 \, \sqrt{-a + b} b^{2} - 12 \, b^{\frac{5}{2}}\right)} \mathrm{sgn}\left(\sin\left(x\right)\right)}{6 \, {\left(a^{2} + 3 \, a \sqrt{-a + b} \sqrt{b} - 5 \, a b - 4 \, \sqrt{-a + b} b^{\frac{3}{2}} + 4 \, b^{2}\right)}}"," ",0,"-1/6*(3*sqrt(-a + b)*log((sqrt(-a + b)*cos(x) - sqrt(-a*cos(x)^2 + b*cos(x)^2 + a))^2) - 4*(3*(sqrt(-a + b)*cos(x) - sqrt(-a*cos(x)^2 + b*cos(x)^2 + a))^4*(2*a - b)*sqrt(-a + b) - 6*(sqrt(-a + b)*cos(x) - sqrt(-a*cos(x)^2 + b*cos(x)^2 + a))^2*a^2*sqrt(-a + b) + (4*a^3 - a^2*b)*sqrt(-a + b))/((sqrt(-a + b)*cos(x) - sqrt(-a*cos(x)^2 + b*cos(x)^2 + a))^2 - a)^3)*sgn(sin(x)) + 1/6*(3*a^2*sqrt(-a + b)*log(-a - 2*sqrt(-a + b)*sqrt(b) + 2*b) - 9*a^2*sqrt(b)*log(-a - 2*sqrt(-a + b)*sqrt(b) + 2*b) - 15*a*sqrt(-a + b)*b*log(-a - 2*sqrt(-a + b)*sqrt(b) + 2*b) + 21*a*b^(3/2)*log(-a - 2*sqrt(-a + b)*sqrt(b) + 2*b) + 12*sqrt(-a + b)*b^2*log(-a - 2*sqrt(-a + b)*sqrt(b) + 2*b) - 12*b^(5/2)*log(-a - 2*sqrt(-a + b)*sqrt(b) + 2*b) + 8*a^2*sqrt(-a + b) - 18*a^2*sqrt(b) - 24*a*sqrt(-a + b)*b + 30*a*b^(3/2) + 12*sqrt(-a + b)*b^2 - 12*b^(5/2))*sgn(sin(x))/(a^2 + 3*a*sqrt(-a + b)*sqrt(b) - 5*a*b - 4*sqrt(-a + b)*b^(3/2) + 4*b^2)","B",0
26,-2,0,0,0.000000," ","integrate(cot(x)^3*(a+b*cot(x)^2)^(3/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(sin(x))]Warning, choosing root of [1,0,%%%{-2,[1,2,0]%%%}+%%%{-2,[1,0,0]%%%}+%%%{2,[0,2,1]%%%},0,%%%{1,[2,4,0]%%%}+%%%{-2,[2,2,0]%%%}+%%%{1,[2,0,0]%%%}+%%%{-2,[1,4,1]%%%}+%%%{6,[1,2,1]%%%}+%%%{-4,[1,0,1]%%%}+%%%{1,[0,4,2]%%%}+%%%{-4,[0,2,2]%%%}+%%%{4,[0,0,2]%%%}] at parameters values [86,-97,-82]Warning, choosing root of [1,0,%%%{-2,[1,0]%%%},0,%%%{1,[2,0]%%%}+%%%{-4,[1,1]%%%}+%%%{4,[0,2]%%%}] at parameters values [90.79236355,54.1277311612]Warning, choosing root of [1,0,%%%{-2,[1,0]%%%},0,%%%{1,[2,0]%%%}+%%%{-4,[1,1]%%%}+%%%{4,[0,2]%%%}] at parameters values [69.8278764193,63.4443001123]Warning, choosing root of [1,0,%%%{-2,[1,0]%%%},0,%%%{1,[2,0]%%%}+%%%{-4,[1,1]%%%}+%%%{4,[0,2]%%%}] at parameters values [108.020125429,82.1195442914]Warning, choosing root of [1,0,%%%{-2,[1,0]%%%},0,%%%{1,[2,0]%%%}+%%%{-4,[1,1]%%%}+%%%{4,[0,2]%%%}] at parameters values [26.4357969165,7.79369851155]Warning, choosing root of [1,0,%%%{-2,[1,0]%%%},0,%%%{1,[2,0]%%%}+%%%{-4,[1,1]%%%}+%%%{4,[0,2]%%%}] at parameters values [150.357303702,71.707969239]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b]=[b+46,44]Unable to convert to real 44.0*(b+46.0)-1936.0 Error: Bad Argument ValueWarning, choosing root of [1,0,%%%{-2,[1,0]%%%},0,%%%{1,[2,0]%%%}+%%%{-4,[1,1]%%%}+%%%{4,[0,2]%%%}] at parameters values [135.979061965,73.519035968]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b]=[b+75,47]Unable to convert to real 47.0*(b+75.0)-2209.0 Error: Bad Argument ValueWarning, choosing root of [1,0,%%%{-2,[1,0]%%%},0,%%%{1,[2,0]%%%}+%%%{-4,[1,1]%%%}+%%%{4,[0,2]%%%}] at parameters values [141.604341501,50.5901726987]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b]=[b+15,55]Unable to convert to real 55.0*(b+15.0)-3025.0 Error: Bad Argument ValueWarning, choosing root of [1,0,%%%{-2,[1,2,0]%%%}+%%%{-2,[1,0,0]%%%}+%%%{2,[0,2,1]%%%},0,%%%{1,[2,4,0]%%%}+%%%{-2,[2,2,0]%%%}+%%%{1,[2,0,0]%%%}+%%%{-2,[1,4,1]%%%}+%%%{6,[1,2,1]%%%}+%%%{-4,[1,0,1]%%%}+%%%{1,[0,4,2]%%%}+%%%{-4,[0,2,2]%%%}+%%%{4,[0,0,2]%%%}] at parameters values [63,-64,2]Warning, choosing root of [1,0,%%%{-2,[1,0]%%%},0,%%%{1,[2,0]%%%}+%%%{-4,[1,1]%%%}+%%%{4,[0,2]%%%}] at parameters values [113.238665889,81.3883557492]Warning, choosing root of [1,0,%%%{-2,[1,0]%%%},0,%%%{1,[2,0]%%%}+%%%{-4,[1,1]%%%}+%%%{4,[0,2]%%%}] at parameters values [49.4233726808,10.4309062702]Warning, choosing root of [1,0,%%%{-2,[1,0]%%%},0,%%%{1,[2,0]%%%}+%%%{-4,[1,1]%%%}+%%%{4,[0,2]%%%}] at parameters values [90.7803645204,82.7280518371]Warning, choosing root of [1,0,%%%{-2,[1,0]%%%},0,%%%{1,[2,0]%%%}+%%%{-4,[1,1]%%%}+%%%{4,[0,2]%%%}] at parameters values [92.8262473457,64.3995612673]Warning, choosing root of [1,0,%%%{-2,[1,0]%%%},0,%%%{1,[2,0]%%%}+%%%{-4,[1,1]%%%}+%%%{4,[0,2]%%%}] at parameters values [106.159791361,66.1769613782]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b]=[b+95,89]Unable to convert to real 89.0*(b+95.0)-7921.0 Error: Bad Argument ValueWarning, choosing root of [1,0,%%%{-2,[1,0]%%%},0,%%%{1,[2,0]%%%}+%%%{-4,[1,1]%%%}+%%%{4,[0,2]%%%}] at parameters values [101.17473746,17.6881634681]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b]=[b+53,39]Unable to convert to real 39.0*(b+53.0)-1521.0 Error: Bad Argument ValueWarning, choosing root of [1,0,%%%{-2,[1,0]%%%},0,%%%{1,[2,0]%%%}+%%%{-4,[1,1]%%%}+%%%{4,[0,2]%%%}] at parameters values [96.452219774,89.629912049]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b]=[b+46,66]Unable to convert to real 66.0*(b+46.0)-4356.0 Error: Bad Argument ValueUnable to cancel step at 0 of 2*(((15*a^2-60*a*b+45*b^2)*sqrt(a-b)*(sqrt(a*sin(x)^2-b*sin(x)^2+b)-sqrt(a-b)*sin(x))^8+(90*a*b^2-90*b^3)*sqrt(a-b)*(sqrt(a*sin(x)^2-b*sin(x)^2+b)-sqrt(a-b)*sin(x))^6+(30*a^2*b^2-170*a*b^3+140*b^4)*sqrt(a-b)*(sqrt(a*sin(x)^2-b*sin(x)^2+b)-sqrt(a-b)*sin(x))^4+(70*a*b^4-70*b^5)*sqrt(a-b)*(sqrt(a*sin(x)^2-b*sin(x)^2+b)-sqrt(a-b)*sin(x))^2+(3*a^2*b^4-26*a*b^5+23*b^6)*sqrt(a-b))/15/((sqrt(a*sin(x)^2-b*sin(x)^2+b)-sqrt(a-b)*sin(x))^2-b)^5+(a-b)*sqrt(a-b)/4*ln((sqrt(a*sin(x)^2-b*sin(x)^2+b)-sqrt(a-b)*sin(x))^2))--2*(((15*a^2-60*a*b+45*b^2)*sqrt(a-b)*(sqrt(a*sin(x)^2-b*sin(x)^2+b)-sqrt(a-b)*sin(x))^8+(90*a*b^2-90*b^3)*sqrt(a-b)*(sqrt(a*sin(x)^2-b*sin(x)^2+b)-sqrt(a-b)*sin(x))^6+(30*a^2*b^2-170*a*b^3+140*b^4)*sqrt(a-b)*(sqrt(a*sin(x)^2-b*sin(x)^2+b)-sqrt(a-b)*sin(x))^4+(70*a*b^4-70*b^5)*sqrt(a-b)*(sqrt(a*sin(x)^2-b*sin(x)^2+b)-sqrt(a-b)*sin(x))^2+(3*a^2*b^4-26*a*b^5+23*b^6)*sqrt(a-b))/15/((sqrt(a*sin(x)^2-b*sin(x)^2+b)-sqrt(a-b)*sin(x))^2-b)^5+(a-b)*sqrt(a-b)/4*ln((sqrt(a*sin(x)^2-b*sin(x)^2+b)-sqrt(a-b)*sin(x))^2))Discontinuities at zeroes of sin(x) were not checkedEvaluation time: 2.44Done","F(-2)",0
27,-2,0,0,0.000000," ","integrate(cot(x)^2*(a+b*cot(x)^2)^(3/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(sin(x))]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
28,-2,0,0,0.000000," ","integrate(cot(x)*(a+b*cot(x)^2)^(3/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(sin(x))]Warning, choosing root of [1,0,%%%{-2,[1,2,0]%%%}+%%%{-2,[1,0,0]%%%}+%%%{2,[0,2,1]%%%},0,%%%{1,[2,4,0]%%%}+%%%{-2,[2,2,0]%%%}+%%%{1,[2,0,0]%%%}+%%%{-2,[1,4,1]%%%}+%%%{6,[1,2,1]%%%}+%%%{-4,[1,0,1]%%%}+%%%{1,[0,4,2]%%%}+%%%{-4,[0,2,2]%%%}+%%%{4,[0,0,2]%%%}] at parameters values [86,-97,-82]Warning, choosing root of [1,0,%%%{-2,[1,0]%%%},0,%%%{1,[2,0]%%%}+%%%{-4,[1,1]%%%}+%%%{4,[0,2]%%%}] at parameters values [90.79236355,54.1277311612]Warning, choosing root of [1,0,%%%{-2,[1,0]%%%},0,%%%{1,[2,0]%%%}+%%%{-4,[1,1]%%%}+%%%{4,[0,2]%%%}] at parameters values [69.8278764193,63.4443001123]Warning, choosing root of [1,0,%%%{-2,[1,0]%%%},0,%%%{1,[2,0]%%%}+%%%{-4,[1,1]%%%}+%%%{4,[0,2]%%%}] at parameters values [108.020125429,82.1195442914]Warning, choosing root of [1,0,%%%{-2,[1,0]%%%},0,%%%{1,[2,0]%%%}+%%%{-4,[1,1]%%%}+%%%{4,[0,2]%%%}] at parameters values [26.4357969165,7.79369851155]Warning, choosing root of [1,0,%%%{-2,[1,0]%%%},0,%%%{1,[2,0]%%%}+%%%{-4,[1,1]%%%}+%%%{4,[0,2]%%%}] at parameters values [150.357303702,71.707969239]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b]=[b+63,75]Unable to convert to real 75.0*(b+63.0)-5625.0 Error: Bad Argument ValueWarning, choosing root of [1,0,%%%{-2,[1,2,0]%%%}+%%%{-2,[1,0,0]%%%}+%%%{2,[0,2,1]%%%},0,%%%{1,[2,4,0]%%%}+%%%{-2,[2,2,0]%%%}+%%%{1,[2,0,0]%%%}+%%%{-2,[1,4,1]%%%}+%%%{6,[1,2,1]%%%}+%%%{-4,[1,0,1]%%%}+%%%{1,[0,4,2]%%%}+%%%{-4,[0,2,2]%%%}+%%%{4,[0,0,2]%%%}] at parameters values [18,-49,-33]Warning, choosing root of [1,0,%%%{-2,[1,0]%%%},0,%%%{1,[2,0]%%%}+%%%{-4,[1,1]%%%}+%%%{4,[0,2]%%%}] at parameters values [70.2095400225,15.451549686]Warning, choosing root of [1,0,%%%{-2,[1,0]%%%},0,%%%{1,[2,0]%%%}+%%%{-4,[1,1]%%%}+%%%{4,[0,2]%%%}] at parameters values [100.356811349,81.9516051291]Warning, choosing root of [1,0,%%%{-2,[1,0]%%%},0,%%%{1,[2,0]%%%}+%%%{-4,[1,1]%%%}+%%%{4,[0,2]%%%}] at parameters values [133.032670634,51.6443148847]Warning, choosing root of [1,0,%%%{-2,[1,0]%%%},0,%%%{1,[2,0]%%%}+%%%{-4,[1,1]%%%}+%%%{4,[0,2]%%%}] at parameters values [42.28121641,31.8503101398]Warning, choosing root of [1,0,%%%{-2,[1,0]%%%},0,%%%{1,[2,0]%%%}+%%%{-4,[1,1]%%%}+%%%{4,[0,2]%%%}] at parameters values [92.8262473457,64.3995612673]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b]=[b+66,40]Unable to convert to real 40.0*(b+66.0)-1600.0 Error: Bad Argument ValueUnable to cancel step at 0 of 2*(((6*a*b-6*b^2)*sqrt(a-b)*(sqrt(a*sin(x)^2-b*sin(x)^2+b)-sqrt(a-b)*sin(x))^4+(-6*a*b^2+6*b^3)*sqrt(a-b)*(sqrt(a*sin(x)^2-b*sin(x)^2+b)-sqrt(a-b)*sin(x))^2+(4*a*b^3-4*b^4)*sqrt(a-b))/3/((sqrt(a*sin(x)^2-b*sin(x)^2+b)-sqrt(a-b)*sin(x))^2-b)^3+(-a+b)*sqrt(a-b)/4*ln((sqrt(a*sin(x)^2-b*sin(x)^2+b)-sqrt(a-b)*sin(x))^2))--2*(((6*a*b-6*b^2)*sqrt(a-b)*(sqrt(a*sin(x)^2-b*sin(x)^2+b)-sqrt(a-b)*sin(x))^4+(-6*a*b^2+6*b^3)*sqrt(a-b)*(sqrt(a*sin(x)^2-b*sin(x)^2+b)-sqrt(a-b)*sin(x))^2+(4*a*b^3-4*b^4)*sqrt(a-b))/3/((sqrt(a*sin(x)^2-b*sin(x)^2+b)-sqrt(a-b)*sin(x))^2-b)^3+(-a+b)*sqrt(a-b)/4*ln((sqrt(a*sin(x)^2-b*sin(x)^2+b)-sqrt(a-b)*sin(x))^2))Discontinuities at zeroes of sin(x) were not checkedEvaluation time: 0.72Done","F(-2)",0
29,-2,0,0,0.000000," ","integrate((a+b*cot(x)^2)^(3/2)*tan(x),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(sin(x))]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
30,-1,0,0,0.000000," ","integrate((a+b*cot(x)^2)^(3/2)*tan(x)^2,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
31,-2,0,0,0.000000," ","integrate((a+b*cot(d*x+c)^2)^(5/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(sin(d*x+c))]Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Evaluation time: 2Error: Bad Argument Type","F(-2)",0
32,-2,0,0,0.000000," ","integrate((a+b*cot(d*x+c)^2)^(3/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(sin(d*x+c))]Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Evaluation time: 0.71Error: Bad Argument Type","F(-2)",0
33,-2,0,0,0.000000," ","integrate((a+b*cot(d*x+c)^2)^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(sin(d*x+c))]Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Warning, replacing 0 by ` u`, a substitution variable should perhaps be purged.Warning, replacing 0 by ` u`, a substitution variable should perhaps be purged.Warning, replacing 0 by ` u`, a substitution variable should perhaps be purged.Warning, replacing 0 by ` u`, a substitution variable should perhaps be purged.Warning, replacing 0 by ` u`, a substitution variable should perhaps be purged.Warning, replacing 0 by ` u`, a substitution variable should perhaps be purged.Warning, replacing 0 by ` u`, a substitution variable should perhaps be purged.Warning, replacing 0 by ` u`, a substitution variable should perhaps be purged.Warning, replacing 0 by ` u`, a substitution variable should perhaps be purged.Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep)]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.Non regular value [0] was discarded and replaced randomly by 0=[-92]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.Non regular value [0] was discarded and replaced randomly by 0=[4]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.Non regular value [0] was discarded and replaced randomly by 0=[69]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.Non regular value [0] was discarded and replaced randomly by 0=[-99]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.Non regular value [0] was discarded and replaced randomly by 0=[94]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.Non regular value [0] was discarded and replaced randomly by 0=[-94]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.Non regular value [0] was discarded and replaced randomly by 0=[-41]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.Non regular value [0] was discarded and replaced randomly by 0=[-81]Precision problem choosing root in common_EXT, current precision 14Evaluation time: 0.63index.cc index_m operator + Error: Bad Argument Value","F(-2)",0
34,1,88,0,4.941287," ","integrate(1/(a+b*cot(d*x+c)^2)^(1/2),x, algorithm=""giac"")","\frac{2 \, \arctan\left(-\frac{\sqrt{b} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - \sqrt{b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 4 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + b} + \sqrt{b}}{2 \, \sqrt{a - b}}\right)}{\sqrt{a - b} d}"," ",0,"2*arctan(-1/2*(sqrt(b)*tan(1/2*d*x + 1/2*c)^2 - sqrt(b*tan(1/2*d*x + 1/2*c)^4 + 4*a*tan(1/2*d*x + 1/2*c)^2 - 2*b*tan(1/2*d*x + 1/2*c)^2 + b) + sqrt(b))/sqrt(a - b))/(sqrt(a - b)*d)","B",0
35,1,348,0,10.137198," ","integrate(1/(a+b*cot(d*x+c)^2)^(3/2),x, algorithm=""giac"")","-\frac{\frac{\frac{{\left(a^{2} b \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) - 2 \, a b^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + b^{3} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}}{a^{4} - 3 \, a^{3} b + 3 \, a^{2} b^{2} - a b^{3}} - \frac{a^{2} b \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) - 2 \, a b^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + b^{3} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{a^{4} - 3 \, a^{3} b + 3 \, a^{2} b^{2} - a b^{3}}}{\sqrt{b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 4 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + b}} + \frac{\sqrt{b} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{a^{2} - a b} - \frac{2 \, \arctan\left(-\frac{\sqrt{b} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - \sqrt{b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 4 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + b} + \sqrt{b}}{2 \, \sqrt{a - b}}\right)}{{\left(a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) - b \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)} \sqrt{a - b}}}{d}"," ",0,"-(((a^2*b*sgn(tan(1/2*d*x + 1/2*c)) - 2*a*b^2*sgn(tan(1/2*d*x + 1/2*c)) + b^3*sgn(tan(1/2*d*x + 1/2*c)))*tan(1/2*d*x + 1/2*c)^2/(a^4 - 3*a^3*b + 3*a^2*b^2 - a*b^3) - (a^2*b*sgn(tan(1/2*d*x + 1/2*c)) - 2*a*b^2*sgn(tan(1/2*d*x + 1/2*c)) + b^3*sgn(tan(1/2*d*x + 1/2*c)))/(a^4 - 3*a^3*b + 3*a^2*b^2 - a*b^3))/sqrt(b*tan(1/2*d*x + 1/2*c)^4 + 4*a*tan(1/2*d*x + 1/2*c)^2 - 2*b*tan(1/2*d*x + 1/2*c)^2 + b) + sqrt(b)*sgn(tan(1/2*d*x + 1/2*c))/(a^2 - a*b) - 2*arctan(-1/2*(sqrt(b)*tan(1/2*d*x + 1/2*c)^2 - sqrt(b*tan(1/2*d*x + 1/2*c)^4 + 4*a*tan(1/2*d*x + 1/2*c)^2 - 2*b*tan(1/2*d*x + 1/2*c)^2 + b) + sqrt(b))/sqrt(a - b))/((a*sgn(tan(1/2*d*x + 1/2*c)) - b*sgn(tan(1/2*d*x + 1/2*c)))*sqrt(a - b)))/d","B",0
36,1,1341,0,13.770206," ","integrate(1/(a+b*cot(d*x+c)^2)^(5/2),x, algorithm=""giac"")","-\frac{\frac{{\left(5 \, a b - 2 \, b^{2}\right)} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{a^{4} \sqrt{b} - 2 \, a^{3} b^{\frac{3}{2}} + a^{2} b^{\frac{5}{2}}} + \frac{{\left({\left(\frac{{\left(5 \, a^{9} b^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) - 42 \, a^{8} b^{3} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 156 \, a^{7} b^{4} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) - 336 \, a^{6} b^{5} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 462 \, a^{5} b^{6} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) - 420 \, a^{4} b^{7} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 252 \, a^{3} b^{8} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) - 96 \, a^{2} b^{9} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 21 \, a b^{10} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) - 2 \, b^{11} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}}{a^{12} - 10 \, a^{11} b + 45 \, a^{10} b^{2} - 120 \, a^{9} b^{3} + 210 \, a^{8} b^{4} - 252 \, a^{7} b^{5} + 210 \, a^{6} b^{6} - 120 \, a^{5} b^{7} + 45 \, a^{4} b^{8} - 10 \, a^{3} b^{9} + a^{2} b^{10}} + \frac{3 \, {\left(8 \, a^{10} b \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) - 73 \, a^{9} b^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 298 \, a^{8} b^{3} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) - 716 \, a^{7} b^{4} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 1120 \, a^{6} b^{5} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) - 1190 \, a^{5} b^{6} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 868 \, a^{4} b^{7} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) - 428 \, a^{3} b^{8} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 136 \, a^{2} b^{9} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) - 25 \, a b^{10} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 2 \, b^{11} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)}}{a^{12} - 10 \, a^{11} b + 45 \, a^{10} b^{2} - 120 \, a^{9} b^{3} + 210 \, a^{8} b^{4} - 252 \, a^{7} b^{5} + 210 \, a^{6} b^{6} - 120 \, a^{5} b^{7} + 45 \, a^{4} b^{8} - 10 \, a^{3} b^{9} + a^{2} b^{10}}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - \frac{3 \, {\left(8 \, a^{10} b \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) - 73 \, a^{9} b^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 298 \, a^{8} b^{3} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) - 716 \, a^{7} b^{4} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 1120 \, a^{6} b^{5} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) - 1190 \, a^{5} b^{6} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 868 \, a^{4} b^{7} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) - 428 \, a^{3} b^{8} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 136 \, a^{2} b^{9} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) - 25 \, a b^{10} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 2 \, b^{11} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)}}{a^{12} - 10 \, a^{11} b + 45 \, a^{10} b^{2} - 120 \, a^{9} b^{3} + 210 \, a^{8} b^{4} - 252 \, a^{7} b^{5} + 210 \, a^{6} b^{6} - 120 \, a^{5} b^{7} + 45 \, a^{4} b^{8} - 10 \, a^{3} b^{9} + a^{2} b^{10}}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - \frac{5 \, a^{9} b^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) - 42 \, a^{8} b^{3} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 156 \, a^{7} b^{4} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) - 336 \, a^{6} b^{5} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 462 \, a^{5} b^{6} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) - 420 \, a^{4} b^{7} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 252 \, a^{3} b^{8} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) - 96 \, a^{2} b^{9} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 21 \, a b^{10} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) - 2 \, b^{11} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{a^{12} - 10 \, a^{11} b + 45 \, a^{10} b^{2} - 120 \, a^{9} b^{3} + 210 \, a^{8} b^{4} - 252 \, a^{7} b^{5} + 210 \, a^{6} b^{6} - 120 \, a^{5} b^{7} + 45 \, a^{4} b^{8} - 10 \, a^{3} b^{9} + a^{2} b^{10}}}{{\left(b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 4 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + b\right)}^{\frac{3}{2}}} - \frac{6 \, \arctan\left(-\frac{\sqrt{b} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - \sqrt{b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 4 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + b} + \sqrt{b}}{2 \, \sqrt{a - b}}\right)}{{\left(a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) - 2 \, a b \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + b^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)} \sqrt{a - b}}}{3 \, d}"," ",0,"-1/3*((5*a*b - 2*b^2)*sgn(tan(1/2*d*x + 1/2*c))/(a^4*sqrt(b) - 2*a^3*b^(3/2) + a^2*b^(5/2)) + ((((5*a^9*b^2*sgn(tan(1/2*d*x + 1/2*c)) - 42*a^8*b^3*sgn(tan(1/2*d*x + 1/2*c)) + 156*a^7*b^4*sgn(tan(1/2*d*x + 1/2*c)) - 336*a^6*b^5*sgn(tan(1/2*d*x + 1/2*c)) + 462*a^5*b^6*sgn(tan(1/2*d*x + 1/2*c)) - 420*a^4*b^7*sgn(tan(1/2*d*x + 1/2*c)) + 252*a^3*b^8*sgn(tan(1/2*d*x + 1/2*c)) - 96*a^2*b^9*sgn(tan(1/2*d*x + 1/2*c)) + 21*a*b^10*sgn(tan(1/2*d*x + 1/2*c)) - 2*b^11*sgn(tan(1/2*d*x + 1/2*c)))*tan(1/2*d*x + 1/2*c)^2/(a^12 - 10*a^11*b + 45*a^10*b^2 - 120*a^9*b^3 + 210*a^8*b^4 - 252*a^7*b^5 + 210*a^6*b^6 - 120*a^5*b^7 + 45*a^4*b^8 - 10*a^3*b^9 + a^2*b^10) + 3*(8*a^10*b*sgn(tan(1/2*d*x + 1/2*c)) - 73*a^9*b^2*sgn(tan(1/2*d*x + 1/2*c)) + 298*a^8*b^3*sgn(tan(1/2*d*x + 1/2*c)) - 716*a^7*b^4*sgn(tan(1/2*d*x + 1/2*c)) + 1120*a^6*b^5*sgn(tan(1/2*d*x + 1/2*c)) - 1190*a^5*b^6*sgn(tan(1/2*d*x + 1/2*c)) + 868*a^4*b^7*sgn(tan(1/2*d*x + 1/2*c)) - 428*a^3*b^8*sgn(tan(1/2*d*x + 1/2*c)) + 136*a^2*b^9*sgn(tan(1/2*d*x + 1/2*c)) - 25*a*b^10*sgn(tan(1/2*d*x + 1/2*c)) + 2*b^11*sgn(tan(1/2*d*x + 1/2*c)))/(a^12 - 10*a^11*b + 45*a^10*b^2 - 120*a^9*b^3 + 210*a^8*b^4 - 252*a^7*b^5 + 210*a^6*b^6 - 120*a^5*b^7 + 45*a^4*b^8 - 10*a^3*b^9 + a^2*b^10))*tan(1/2*d*x + 1/2*c)^2 - 3*(8*a^10*b*sgn(tan(1/2*d*x + 1/2*c)) - 73*a^9*b^2*sgn(tan(1/2*d*x + 1/2*c)) + 298*a^8*b^3*sgn(tan(1/2*d*x + 1/2*c)) - 716*a^7*b^4*sgn(tan(1/2*d*x + 1/2*c)) + 1120*a^6*b^5*sgn(tan(1/2*d*x + 1/2*c)) - 1190*a^5*b^6*sgn(tan(1/2*d*x + 1/2*c)) + 868*a^4*b^7*sgn(tan(1/2*d*x + 1/2*c)) - 428*a^3*b^8*sgn(tan(1/2*d*x + 1/2*c)) + 136*a^2*b^9*sgn(tan(1/2*d*x + 1/2*c)) - 25*a*b^10*sgn(tan(1/2*d*x + 1/2*c)) + 2*b^11*sgn(tan(1/2*d*x + 1/2*c)))/(a^12 - 10*a^11*b + 45*a^10*b^2 - 120*a^9*b^3 + 210*a^8*b^4 - 252*a^7*b^5 + 210*a^6*b^6 - 120*a^5*b^7 + 45*a^4*b^8 - 10*a^3*b^9 + a^2*b^10))*tan(1/2*d*x + 1/2*c)^2 - (5*a^9*b^2*sgn(tan(1/2*d*x + 1/2*c)) - 42*a^8*b^3*sgn(tan(1/2*d*x + 1/2*c)) + 156*a^7*b^4*sgn(tan(1/2*d*x + 1/2*c)) - 336*a^6*b^5*sgn(tan(1/2*d*x + 1/2*c)) + 462*a^5*b^6*sgn(tan(1/2*d*x + 1/2*c)) - 420*a^4*b^7*sgn(tan(1/2*d*x + 1/2*c)) + 252*a^3*b^8*sgn(tan(1/2*d*x + 1/2*c)) - 96*a^2*b^9*sgn(tan(1/2*d*x + 1/2*c)) + 21*a*b^10*sgn(tan(1/2*d*x + 1/2*c)) - 2*b^11*sgn(tan(1/2*d*x + 1/2*c)))/(a^12 - 10*a^11*b + 45*a^10*b^2 - 120*a^9*b^3 + 210*a^8*b^4 - 252*a^7*b^5 + 210*a^6*b^6 - 120*a^5*b^7 + 45*a^4*b^8 - 10*a^3*b^9 + a^2*b^10))/(b*tan(1/2*d*x + 1/2*c)^4 + 4*a*tan(1/2*d*x + 1/2*c)^2 - 2*b*tan(1/2*d*x + 1/2*c)^2 + b)^(3/2) - 6*arctan(-1/2*(sqrt(b)*tan(1/2*d*x + 1/2*c)^2 - sqrt(b*tan(1/2*d*x + 1/2*c)^4 + 4*a*tan(1/2*d*x + 1/2*c)^2 - 2*b*tan(1/2*d*x + 1/2*c)^2 + b) + sqrt(b))/sqrt(a - b))/((a^2*sgn(tan(1/2*d*x + 1/2*c)) - 2*a*b*sgn(tan(1/2*d*x + 1/2*c)) + b^2*sgn(tan(1/2*d*x + 1/2*c)))*sqrt(a - b)))/d","B",0
37,1,3719,0,31.531965," ","integrate(1/(a+b*cot(d*x+c)^2)^(7/2),x, algorithm=""giac"")","-\frac{\frac{{\left(33 \, a^{2} b - 26 \, a b^{2} + 8 \, b^{3}\right)} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{a^{6} \sqrt{b} - 3 \, a^{5} b^{\frac{3}{2}} + 3 \, a^{4} b^{\frac{5}{2}} - a^{3} b^{\frac{7}{2}}} - \frac{30 \, \arctan\left(-\frac{\sqrt{b} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - \sqrt{b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 4 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + b} + \sqrt{b}}{2 \, \sqrt{a - b}}\right)}{{\left(a^{3} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) - 3 \, a^{2} b \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 3 \, a b^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) - b^{3} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)} \sqrt{a - b}} + \frac{{\left({\left({\left({\left(\frac{{\left(33 \, a^{20} b^{3} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) - 620 \, a^{19} b^{4} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 5525 \, a^{18} b^{5} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) - 31050 \, a^{17} b^{6} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 123420 \, a^{16} b^{7} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) - 368832 \, a^{15} b^{8} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 859860 \, a^{14} b^{9} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) - 1601400 \, a^{13} b^{10} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 2419950 \, a^{12} b^{11} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) - 2996760 \, a^{11} b^{12} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 3058198 \, a^{10} b^{13} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) - 2576860 \, a^{9} b^{14} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 1790100 \, a^{8} b^{15} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) - 1020000 \, a^{7} b^{16} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 472260 \, a^{6} b^{17} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) - 175032 \, a^{5} b^{18} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 50745 \, a^{4} b^{19} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) - 11100 \, a^{3} b^{20} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 1725 \, a^{2} b^{21} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) - 170 \, a b^{22} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 8 \, b^{23} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}}{a^{24} - 21 \, a^{23} b + 210 \, a^{22} b^{2} - 1330 \, a^{21} b^{3} + 5985 \, a^{20} b^{4} - 20349 \, a^{19} b^{5} + 54264 \, a^{18} b^{6} - 116280 \, a^{17} b^{7} + 203490 \, a^{16} b^{8} - 293930 \, a^{15} b^{9} + 352716 \, a^{14} b^{10} - 352716 \, a^{13} b^{11} + 293930 \, a^{12} b^{12} - 203490 \, a^{11} b^{13} + 116280 \, a^{10} b^{14} - 54264 \, a^{9} b^{15} + 20349 \, a^{8} b^{16} - 5985 \, a^{7} b^{17} + 1330 \, a^{6} b^{18} - 210 \, a^{5} b^{19} + 21 \, a^{4} b^{20} - a^{3} b^{21}} + \frac{5 \, {\left(60 \, a^{21} b^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) - 1165 \, a^{20} b^{3} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 10752 \, a^{19} b^{4} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) - 62729 \, a^{18} b^{5} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 259530 \, a^{17} b^{6} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) - 809676 \, a^{16} b^{7} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 1977168 \, a^{15} b^{8} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) - 3871716 \, a^{14} b^{9} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 6178752 \, a^{13} b^{10} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) - 8121750 \, a^{12} b^{11} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 8850608 \, a^{11} b^{12} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) - 8020974 \, a^{10} b^{13} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 6045676 \, a^{9} b^{14} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) - 3778692 \, a^{8} b^{15} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 1946160 \, a^{7} b^{16} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) - 817428 \, a^{6} b^{17} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 275604 \, a^{5} b^{18} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) - 72837 \, a^{4} b^{19} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 14544 \, a^{3} b^{20} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) - 2065 \, a^{2} b^{21} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 186 \, a b^{22} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) - 8 \, b^{23} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)}}{a^{24} - 21 \, a^{23} b + 210 \, a^{22} b^{2} - 1330 \, a^{21} b^{3} + 5985 \, a^{20} b^{4} - 20349 \, a^{19} b^{5} + 54264 \, a^{18} b^{6} - 116280 \, a^{17} b^{7} + 203490 \, a^{16} b^{8} - 293930 \, a^{15} b^{9} + 352716 \, a^{14} b^{10} - 352716 \, a^{13} b^{11} + 293930 \, a^{12} b^{12} - 203490 \, a^{11} b^{13} + 116280 \, a^{10} b^{14} - 54264 \, a^{9} b^{15} + 20349 \, a^{8} b^{16} - 5985 \, a^{7} b^{17} + 1330 \, a^{6} b^{18} - 210 \, a^{5} b^{19} + 21 \, a^{4} b^{20} - a^{3} b^{21}}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \frac{10 \, {\left(72 \, a^{22} b \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) - 1458 \, a^{21} b^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 14067 \, a^{20} b^{3} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) - 86018 \, a^{19} b^{4} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 374075 \, a^{18} b^{5} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) - 1230570 \, a^{17} b^{6} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 3179748 \, a^{16} b^{7} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) - 6614904 \, a^{15} b^{8} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 11265084 \, a^{14} b^{9} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) - 15882420 \, a^{13} b^{10} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 18674058 \, a^{12} b^{11} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) - 18386316 \, a^{11} b^{12} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 15180490 \, a^{10} b^{13} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) - 10497364 \, a^{9} b^{14} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 6055740 \, a^{8} b^{15} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) - 2893944 \, a^{7} b^{16} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 1133220 \, a^{6} b^{17} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) - 357786 \, a^{5} b^{18} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 88923 \, a^{4} b^{19} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) - 16770 \, a^{3} b^{20} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 2259 \, a^{2} b^{21} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) - 194 \, a b^{22} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 8 \, b^{23} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)}}{a^{24} - 21 \, a^{23} b + 210 \, a^{22} b^{2} - 1330 \, a^{21} b^{3} + 5985 \, a^{20} b^{4} - 20349 \, a^{19} b^{5} + 54264 \, a^{18} b^{6} - 116280 \, a^{17} b^{7} + 203490 \, a^{16} b^{8} - 293930 \, a^{15} b^{9} + 352716 \, a^{14} b^{10} - 352716 \, a^{13} b^{11} + 293930 \, a^{12} b^{12} - 203490 \, a^{11} b^{13} + 116280 \, a^{10} b^{14} - 54264 \, a^{9} b^{15} + 20349 \, a^{8} b^{16} - 5985 \, a^{7} b^{17} + 1330 \, a^{6} b^{18} - 210 \, a^{5} b^{19} + 21 \, a^{4} b^{20} - a^{3} b^{21}}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - \frac{10 \, {\left(72 \, a^{22} b \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) - 1458 \, a^{21} b^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 14067 \, a^{20} b^{3} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) - 86018 \, a^{19} b^{4} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 374075 \, a^{18} b^{5} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) - 1230570 \, a^{17} b^{6} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 3179748 \, a^{16} b^{7} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) - 6614904 \, a^{15} b^{8} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 11265084 \, a^{14} b^{9} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) - 15882420 \, a^{13} b^{10} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 18674058 \, a^{12} b^{11} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) - 18386316 \, a^{11} b^{12} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 15180490 \, a^{10} b^{13} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) - 10497364 \, a^{9} b^{14} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 6055740 \, a^{8} b^{15} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) - 2893944 \, a^{7} b^{16} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 1133220 \, a^{6} b^{17} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) - 357786 \, a^{5} b^{18} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 88923 \, a^{4} b^{19} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) - 16770 \, a^{3} b^{20} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 2259 \, a^{2} b^{21} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) - 194 \, a b^{22} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 8 \, b^{23} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)}}{a^{24} - 21 \, a^{23} b + 210 \, a^{22} b^{2} - 1330 \, a^{21} b^{3} + 5985 \, a^{20} b^{4} - 20349 \, a^{19} b^{5} + 54264 \, a^{18} b^{6} - 116280 \, a^{17} b^{7} + 203490 \, a^{16} b^{8} - 293930 \, a^{15} b^{9} + 352716 \, a^{14} b^{10} - 352716 \, a^{13} b^{11} + 293930 \, a^{12} b^{12} - 203490 \, a^{11} b^{13} + 116280 \, a^{10} b^{14} - 54264 \, a^{9} b^{15} + 20349 \, a^{8} b^{16} - 5985 \, a^{7} b^{17} + 1330 \, a^{6} b^{18} - 210 \, a^{5} b^{19} + 21 \, a^{4} b^{20} - a^{3} b^{21}}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - \frac{5 \, {\left(60 \, a^{21} b^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) - 1165 \, a^{20} b^{3} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 10752 \, a^{19} b^{4} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) - 62729 \, a^{18} b^{5} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 259530 \, a^{17} b^{6} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) - 809676 \, a^{16} b^{7} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 1977168 \, a^{15} b^{8} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) - 3871716 \, a^{14} b^{9} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 6178752 \, a^{13} b^{10} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) - 8121750 \, a^{12} b^{11} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 8850608 \, a^{11} b^{12} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) - 8020974 \, a^{10} b^{13} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 6045676 \, a^{9} b^{14} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) - 3778692 \, a^{8} b^{15} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 1946160 \, a^{7} b^{16} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) - 817428 \, a^{6} b^{17} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 275604 \, a^{5} b^{18} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) - 72837 \, a^{4} b^{19} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 14544 \, a^{3} b^{20} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) - 2065 \, a^{2} b^{21} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 186 \, a b^{22} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) - 8 \, b^{23} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)}}{a^{24} - 21 \, a^{23} b + 210 \, a^{22} b^{2} - 1330 \, a^{21} b^{3} + 5985 \, a^{20} b^{4} - 20349 \, a^{19} b^{5} + 54264 \, a^{18} b^{6} - 116280 \, a^{17} b^{7} + 203490 \, a^{16} b^{8} - 293930 \, a^{15} b^{9} + 352716 \, a^{14} b^{10} - 352716 \, a^{13} b^{11} + 293930 \, a^{12} b^{12} - 203490 \, a^{11} b^{13} + 116280 \, a^{10} b^{14} - 54264 \, a^{9} b^{15} + 20349 \, a^{8} b^{16} - 5985 \, a^{7} b^{17} + 1330 \, a^{6} b^{18} - 210 \, a^{5} b^{19} + 21 \, a^{4} b^{20} - a^{3} b^{21}}\right)} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - \frac{33 \, a^{20} b^{3} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) - 620 \, a^{19} b^{4} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 5525 \, a^{18} b^{5} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) - 31050 \, a^{17} b^{6} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 123420 \, a^{16} b^{7} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) - 368832 \, a^{15} b^{8} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 859860 \, a^{14} b^{9} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) - 1601400 \, a^{13} b^{10} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 2419950 \, a^{12} b^{11} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) - 2996760 \, a^{11} b^{12} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 3058198 \, a^{10} b^{13} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) - 2576860 \, a^{9} b^{14} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 1790100 \, a^{8} b^{15} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) - 1020000 \, a^{7} b^{16} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 472260 \, a^{6} b^{17} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) - 175032 \, a^{5} b^{18} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 50745 \, a^{4} b^{19} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) - 11100 \, a^{3} b^{20} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 1725 \, a^{2} b^{21} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) - 170 \, a b^{22} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 8 \, b^{23} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{a^{24} - 21 \, a^{23} b + 210 \, a^{22} b^{2} - 1330 \, a^{21} b^{3} + 5985 \, a^{20} b^{4} - 20349 \, a^{19} b^{5} + 54264 \, a^{18} b^{6} - 116280 \, a^{17} b^{7} + 203490 \, a^{16} b^{8} - 293930 \, a^{15} b^{9} + 352716 \, a^{14} b^{10} - 352716 \, a^{13} b^{11} + 293930 \, a^{12} b^{12} - 203490 \, a^{11} b^{13} + 116280 \, a^{10} b^{14} - 54264 \, a^{9} b^{15} + 20349 \, a^{8} b^{16} - 5985 \, a^{7} b^{17} + 1330 \, a^{6} b^{18} - 210 \, a^{5} b^{19} + 21 \, a^{4} b^{20} - a^{3} b^{21}}}{{\left(b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 4 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + b\right)}^{\frac{5}{2}}}}{15 \, d}"," ",0,"-1/15*((33*a^2*b - 26*a*b^2 + 8*b^3)*sgn(tan(1/2*d*x + 1/2*c))/(a^6*sqrt(b) - 3*a^5*b^(3/2) + 3*a^4*b^(5/2) - a^3*b^(7/2)) - 30*arctan(-1/2*(sqrt(b)*tan(1/2*d*x + 1/2*c)^2 - sqrt(b*tan(1/2*d*x + 1/2*c)^4 + 4*a*tan(1/2*d*x + 1/2*c)^2 - 2*b*tan(1/2*d*x + 1/2*c)^2 + b) + sqrt(b))/sqrt(a - b))/((a^3*sgn(tan(1/2*d*x + 1/2*c)) - 3*a^2*b*sgn(tan(1/2*d*x + 1/2*c)) + 3*a*b^2*sgn(tan(1/2*d*x + 1/2*c)) - b^3*sgn(tan(1/2*d*x + 1/2*c)))*sqrt(a - b)) + ((((((33*a^20*b^3*sgn(tan(1/2*d*x + 1/2*c)) - 620*a^19*b^4*sgn(tan(1/2*d*x + 1/2*c)) + 5525*a^18*b^5*sgn(tan(1/2*d*x + 1/2*c)) - 31050*a^17*b^6*sgn(tan(1/2*d*x + 1/2*c)) + 123420*a^16*b^7*sgn(tan(1/2*d*x + 1/2*c)) - 368832*a^15*b^8*sgn(tan(1/2*d*x + 1/2*c)) + 859860*a^14*b^9*sgn(tan(1/2*d*x + 1/2*c)) - 1601400*a^13*b^10*sgn(tan(1/2*d*x + 1/2*c)) + 2419950*a^12*b^11*sgn(tan(1/2*d*x + 1/2*c)) - 2996760*a^11*b^12*sgn(tan(1/2*d*x + 1/2*c)) + 3058198*a^10*b^13*sgn(tan(1/2*d*x + 1/2*c)) - 2576860*a^9*b^14*sgn(tan(1/2*d*x + 1/2*c)) + 1790100*a^8*b^15*sgn(tan(1/2*d*x + 1/2*c)) - 1020000*a^7*b^16*sgn(tan(1/2*d*x + 1/2*c)) + 472260*a^6*b^17*sgn(tan(1/2*d*x + 1/2*c)) - 175032*a^5*b^18*sgn(tan(1/2*d*x + 1/2*c)) + 50745*a^4*b^19*sgn(tan(1/2*d*x + 1/2*c)) - 11100*a^3*b^20*sgn(tan(1/2*d*x + 1/2*c)) + 1725*a^2*b^21*sgn(tan(1/2*d*x + 1/2*c)) - 170*a*b^22*sgn(tan(1/2*d*x + 1/2*c)) + 8*b^23*sgn(tan(1/2*d*x + 1/2*c)))*tan(1/2*d*x + 1/2*c)^2/(a^24 - 21*a^23*b + 210*a^22*b^2 - 1330*a^21*b^3 + 5985*a^20*b^4 - 20349*a^19*b^5 + 54264*a^18*b^6 - 116280*a^17*b^7 + 203490*a^16*b^8 - 293930*a^15*b^9 + 352716*a^14*b^10 - 352716*a^13*b^11 + 293930*a^12*b^12 - 203490*a^11*b^13 + 116280*a^10*b^14 - 54264*a^9*b^15 + 20349*a^8*b^16 - 5985*a^7*b^17 + 1330*a^6*b^18 - 210*a^5*b^19 + 21*a^4*b^20 - a^3*b^21) + 5*(60*a^21*b^2*sgn(tan(1/2*d*x + 1/2*c)) - 1165*a^20*b^3*sgn(tan(1/2*d*x + 1/2*c)) + 10752*a^19*b^4*sgn(tan(1/2*d*x + 1/2*c)) - 62729*a^18*b^5*sgn(tan(1/2*d*x + 1/2*c)) + 259530*a^17*b^6*sgn(tan(1/2*d*x + 1/2*c)) - 809676*a^16*b^7*sgn(tan(1/2*d*x + 1/2*c)) + 1977168*a^15*b^8*sgn(tan(1/2*d*x + 1/2*c)) - 3871716*a^14*b^9*sgn(tan(1/2*d*x + 1/2*c)) + 6178752*a^13*b^10*sgn(tan(1/2*d*x + 1/2*c)) - 8121750*a^12*b^11*sgn(tan(1/2*d*x + 1/2*c)) + 8850608*a^11*b^12*sgn(tan(1/2*d*x + 1/2*c)) - 8020974*a^10*b^13*sgn(tan(1/2*d*x + 1/2*c)) + 6045676*a^9*b^14*sgn(tan(1/2*d*x + 1/2*c)) - 3778692*a^8*b^15*sgn(tan(1/2*d*x + 1/2*c)) + 1946160*a^7*b^16*sgn(tan(1/2*d*x + 1/2*c)) - 817428*a^6*b^17*sgn(tan(1/2*d*x + 1/2*c)) + 275604*a^5*b^18*sgn(tan(1/2*d*x + 1/2*c)) - 72837*a^4*b^19*sgn(tan(1/2*d*x + 1/2*c)) + 14544*a^3*b^20*sgn(tan(1/2*d*x + 1/2*c)) - 2065*a^2*b^21*sgn(tan(1/2*d*x + 1/2*c)) + 186*a*b^22*sgn(tan(1/2*d*x + 1/2*c)) - 8*b^23*sgn(tan(1/2*d*x + 1/2*c)))/(a^24 - 21*a^23*b + 210*a^22*b^2 - 1330*a^21*b^3 + 5985*a^20*b^4 - 20349*a^19*b^5 + 54264*a^18*b^6 - 116280*a^17*b^7 + 203490*a^16*b^8 - 293930*a^15*b^9 + 352716*a^14*b^10 - 352716*a^13*b^11 + 293930*a^12*b^12 - 203490*a^11*b^13 + 116280*a^10*b^14 - 54264*a^9*b^15 + 20349*a^8*b^16 - 5985*a^7*b^17 + 1330*a^6*b^18 - 210*a^5*b^19 + 21*a^4*b^20 - a^3*b^21))*tan(1/2*d*x + 1/2*c)^2 + 10*(72*a^22*b*sgn(tan(1/2*d*x + 1/2*c)) - 1458*a^21*b^2*sgn(tan(1/2*d*x + 1/2*c)) + 14067*a^20*b^3*sgn(tan(1/2*d*x + 1/2*c)) - 86018*a^19*b^4*sgn(tan(1/2*d*x + 1/2*c)) + 374075*a^18*b^5*sgn(tan(1/2*d*x + 1/2*c)) - 1230570*a^17*b^6*sgn(tan(1/2*d*x + 1/2*c)) + 3179748*a^16*b^7*sgn(tan(1/2*d*x + 1/2*c)) - 6614904*a^15*b^8*sgn(tan(1/2*d*x + 1/2*c)) + 11265084*a^14*b^9*sgn(tan(1/2*d*x + 1/2*c)) - 15882420*a^13*b^10*sgn(tan(1/2*d*x + 1/2*c)) + 18674058*a^12*b^11*sgn(tan(1/2*d*x + 1/2*c)) - 18386316*a^11*b^12*sgn(tan(1/2*d*x + 1/2*c)) + 15180490*a^10*b^13*sgn(tan(1/2*d*x + 1/2*c)) - 10497364*a^9*b^14*sgn(tan(1/2*d*x + 1/2*c)) + 6055740*a^8*b^15*sgn(tan(1/2*d*x + 1/2*c)) - 2893944*a^7*b^16*sgn(tan(1/2*d*x + 1/2*c)) + 1133220*a^6*b^17*sgn(tan(1/2*d*x + 1/2*c)) - 357786*a^5*b^18*sgn(tan(1/2*d*x + 1/2*c)) + 88923*a^4*b^19*sgn(tan(1/2*d*x + 1/2*c)) - 16770*a^3*b^20*sgn(tan(1/2*d*x + 1/2*c)) + 2259*a^2*b^21*sgn(tan(1/2*d*x + 1/2*c)) - 194*a*b^22*sgn(tan(1/2*d*x + 1/2*c)) + 8*b^23*sgn(tan(1/2*d*x + 1/2*c)))/(a^24 - 21*a^23*b + 210*a^22*b^2 - 1330*a^21*b^3 + 5985*a^20*b^4 - 20349*a^19*b^5 + 54264*a^18*b^6 - 116280*a^17*b^7 + 203490*a^16*b^8 - 293930*a^15*b^9 + 352716*a^14*b^10 - 352716*a^13*b^11 + 293930*a^12*b^12 - 203490*a^11*b^13 + 116280*a^10*b^14 - 54264*a^9*b^15 + 20349*a^8*b^16 - 5985*a^7*b^17 + 1330*a^6*b^18 - 210*a^5*b^19 + 21*a^4*b^20 - a^3*b^21))*tan(1/2*d*x + 1/2*c)^2 - 10*(72*a^22*b*sgn(tan(1/2*d*x + 1/2*c)) - 1458*a^21*b^2*sgn(tan(1/2*d*x + 1/2*c)) + 14067*a^20*b^3*sgn(tan(1/2*d*x + 1/2*c)) - 86018*a^19*b^4*sgn(tan(1/2*d*x + 1/2*c)) + 374075*a^18*b^5*sgn(tan(1/2*d*x + 1/2*c)) - 1230570*a^17*b^6*sgn(tan(1/2*d*x + 1/2*c)) + 3179748*a^16*b^7*sgn(tan(1/2*d*x + 1/2*c)) - 6614904*a^15*b^8*sgn(tan(1/2*d*x + 1/2*c)) + 11265084*a^14*b^9*sgn(tan(1/2*d*x + 1/2*c)) - 15882420*a^13*b^10*sgn(tan(1/2*d*x + 1/2*c)) + 18674058*a^12*b^11*sgn(tan(1/2*d*x + 1/2*c)) - 18386316*a^11*b^12*sgn(tan(1/2*d*x + 1/2*c)) + 15180490*a^10*b^13*sgn(tan(1/2*d*x + 1/2*c)) - 10497364*a^9*b^14*sgn(tan(1/2*d*x + 1/2*c)) + 6055740*a^8*b^15*sgn(tan(1/2*d*x + 1/2*c)) - 2893944*a^7*b^16*sgn(tan(1/2*d*x + 1/2*c)) + 1133220*a^6*b^17*sgn(tan(1/2*d*x + 1/2*c)) - 357786*a^5*b^18*sgn(tan(1/2*d*x + 1/2*c)) + 88923*a^4*b^19*sgn(tan(1/2*d*x + 1/2*c)) - 16770*a^3*b^20*sgn(tan(1/2*d*x + 1/2*c)) + 2259*a^2*b^21*sgn(tan(1/2*d*x + 1/2*c)) - 194*a*b^22*sgn(tan(1/2*d*x + 1/2*c)) + 8*b^23*sgn(tan(1/2*d*x + 1/2*c)))/(a^24 - 21*a^23*b + 210*a^22*b^2 - 1330*a^21*b^3 + 5985*a^20*b^4 - 20349*a^19*b^5 + 54264*a^18*b^6 - 116280*a^17*b^7 + 203490*a^16*b^8 - 293930*a^15*b^9 + 352716*a^14*b^10 - 352716*a^13*b^11 + 293930*a^12*b^12 - 203490*a^11*b^13 + 116280*a^10*b^14 - 54264*a^9*b^15 + 20349*a^8*b^16 - 5985*a^7*b^17 + 1330*a^6*b^18 - 210*a^5*b^19 + 21*a^4*b^20 - a^3*b^21))*tan(1/2*d*x + 1/2*c)^2 - 5*(60*a^21*b^2*sgn(tan(1/2*d*x + 1/2*c)) - 1165*a^20*b^3*sgn(tan(1/2*d*x + 1/2*c)) + 10752*a^19*b^4*sgn(tan(1/2*d*x + 1/2*c)) - 62729*a^18*b^5*sgn(tan(1/2*d*x + 1/2*c)) + 259530*a^17*b^6*sgn(tan(1/2*d*x + 1/2*c)) - 809676*a^16*b^7*sgn(tan(1/2*d*x + 1/2*c)) + 1977168*a^15*b^8*sgn(tan(1/2*d*x + 1/2*c)) - 3871716*a^14*b^9*sgn(tan(1/2*d*x + 1/2*c)) + 6178752*a^13*b^10*sgn(tan(1/2*d*x + 1/2*c)) - 8121750*a^12*b^11*sgn(tan(1/2*d*x + 1/2*c)) + 8850608*a^11*b^12*sgn(tan(1/2*d*x + 1/2*c)) - 8020974*a^10*b^13*sgn(tan(1/2*d*x + 1/2*c)) + 6045676*a^9*b^14*sgn(tan(1/2*d*x + 1/2*c)) - 3778692*a^8*b^15*sgn(tan(1/2*d*x + 1/2*c)) + 1946160*a^7*b^16*sgn(tan(1/2*d*x + 1/2*c)) - 817428*a^6*b^17*sgn(tan(1/2*d*x + 1/2*c)) + 275604*a^5*b^18*sgn(tan(1/2*d*x + 1/2*c)) - 72837*a^4*b^19*sgn(tan(1/2*d*x + 1/2*c)) + 14544*a^3*b^20*sgn(tan(1/2*d*x + 1/2*c)) - 2065*a^2*b^21*sgn(tan(1/2*d*x + 1/2*c)) + 186*a*b^22*sgn(tan(1/2*d*x + 1/2*c)) - 8*b^23*sgn(tan(1/2*d*x + 1/2*c)))/(a^24 - 21*a^23*b + 210*a^22*b^2 - 1330*a^21*b^3 + 5985*a^20*b^4 - 20349*a^19*b^5 + 54264*a^18*b^6 - 116280*a^17*b^7 + 203490*a^16*b^8 - 293930*a^15*b^9 + 352716*a^14*b^10 - 352716*a^13*b^11 + 293930*a^12*b^12 - 203490*a^11*b^13 + 116280*a^10*b^14 - 54264*a^9*b^15 + 20349*a^8*b^16 - 5985*a^7*b^17 + 1330*a^6*b^18 - 210*a^5*b^19 + 21*a^4*b^20 - a^3*b^21))*tan(1/2*d*x + 1/2*c)^2 - (33*a^20*b^3*sgn(tan(1/2*d*x + 1/2*c)) - 620*a^19*b^4*sgn(tan(1/2*d*x + 1/2*c)) + 5525*a^18*b^5*sgn(tan(1/2*d*x + 1/2*c)) - 31050*a^17*b^6*sgn(tan(1/2*d*x + 1/2*c)) + 123420*a^16*b^7*sgn(tan(1/2*d*x + 1/2*c)) - 368832*a^15*b^8*sgn(tan(1/2*d*x + 1/2*c)) + 859860*a^14*b^9*sgn(tan(1/2*d*x + 1/2*c)) - 1601400*a^13*b^10*sgn(tan(1/2*d*x + 1/2*c)) + 2419950*a^12*b^11*sgn(tan(1/2*d*x + 1/2*c)) - 2996760*a^11*b^12*sgn(tan(1/2*d*x + 1/2*c)) + 3058198*a^10*b^13*sgn(tan(1/2*d*x + 1/2*c)) - 2576860*a^9*b^14*sgn(tan(1/2*d*x + 1/2*c)) + 1790100*a^8*b^15*sgn(tan(1/2*d*x + 1/2*c)) - 1020000*a^7*b^16*sgn(tan(1/2*d*x + 1/2*c)) + 472260*a^6*b^17*sgn(tan(1/2*d*x + 1/2*c)) - 175032*a^5*b^18*sgn(tan(1/2*d*x + 1/2*c)) + 50745*a^4*b^19*sgn(tan(1/2*d*x + 1/2*c)) - 11100*a^3*b^20*sgn(tan(1/2*d*x + 1/2*c)) + 1725*a^2*b^21*sgn(tan(1/2*d*x + 1/2*c)) - 170*a*b^22*sgn(tan(1/2*d*x + 1/2*c)) + 8*b^23*sgn(tan(1/2*d*x + 1/2*c)))/(a^24 - 21*a^23*b + 210*a^22*b^2 - 1330*a^21*b^3 + 5985*a^20*b^4 - 20349*a^19*b^5 + 54264*a^18*b^6 - 116280*a^17*b^7 + 203490*a^16*b^8 - 293930*a^15*b^9 + 352716*a^14*b^10 - 352716*a^13*b^11 + 293930*a^12*b^12 - 203490*a^11*b^13 + 116280*a^10*b^14 - 54264*a^9*b^15 + 20349*a^8*b^16 - 5985*a^7*b^17 + 1330*a^6*b^18 - 210*a^5*b^19 + 21*a^4*b^20 - a^3*b^21))/(b*tan(1/2*d*x + 1/2*c)^4 + 4*a*tan(1/2*d*x + 1/2*c)^2 - 2*b*tan(1/2*d*x + 1/2*c)^2 + b)^(5/2))/d","B",0
38,1,257,0,0.282653," ","integrate((1-cot(x)^2)^(3/2),x, algorithm=""giac"")","\frac{1}{4} \, {\left(5 \, \pi \mathrm{sgn}\left(\cos\left(x\right)\right) - 4 \, \sqrt{2} {\left(\pi \mathrm{sgn}\left(\cos\left(x\right)\right) + 2 \, \arctan\left(-\frac{{\left(\frac{{\left(\sqrt{2} \sqrt{-2 \, \cos\left(x\right)^{2} + 1} - \sqrt{2}\right)}^{2}}{\cos\left(x\right)^{2}} - 4\right)} \cos\left(x\right)}{4 \, {\left(\sqrt{2} \sqrt{-2 \, \cos\left(x\right)^{2} + 1} - \sqrt{2}\right)}}\right)\right)} + \frac{4 \, \sqrt{2} {\left(\frac{\sqrt{2} \sqrt{-2 \, \cos\left(x\right)^{2} + 1} - \sqrt{2}}{\cos\left(x\right)} - \frac{4 \, \cos\left(x\right)}{\sqrt{2} \sqrt{-2 \, \cos\left(x\right)^{2} + 1} - \sqrt{2}}\right)}}{{\left(\frac{\sqrt{2} \sqrt{-2 \, \cos\left(x\right)^{2} + 1} - \sqrt{2}}{\cos\left(x\right)} - \frac{4 \, \cos\left(x\right)}{\sqrt{2} \sqrt{-2 \, \cos\left(x\right)^{2} + 1} - \sqrt{2}}\right)}^{2} + 8} + 10 \, \arctan\left(-\frac{\sqrt{2} {\left(\frac{{\left(\sqrt{2} \sqrt{-2 \, \cos\left(x\right)^{2} + 1} - \sqrt{2}\right)}^{2}}{\cos\left(x\right)^{2}} - 4\right)} \cos\left(x\right)}{4 \, {\left(\sqrt{2} \sqrt{-2 \, \cos\left(x\right)^{2} + 1} - \sqrt{2}\right)}}\right)\right)} \mathrm{sgn}\left(\sin\left(x\right)\right)"," ",0,"1/4*(5*pi*sgn(cos(x)) - 4*sqrt(2)*(pi*sgn(cos(x)) + 2*arctan(-1/4*((sqrt(2)*sqrt(-2*cos(x)^2 + 1) - sqrt(2))^2/cos(x)^2 - 4)*cos(x)/(sqrt(2)*sqrt(-2*cos(x)^2 + 1) - sqrt(2)))) + 4*sqrt(2)*((sqrt(2)*sqrt(-2*cos(x)^2 + 1) - sqrt(2))/cos(x) - 4*cos(x)/(sqrt(2)*sqrt(-2*cos(x)^2 + 1) - sqrt(2)))/(((sqrt(2)*sqrt(-2*cos(x)^2 + 1) - sqrt(2))/cos(x) - 4*cos(x)/(sqrt(2)*sqrt(-2*cos(x)^2 + 1) - sqrt(2)))^2 + 8) + 10*arctan(-1/4*sqrt(2)*((sqrt(2)*sqrt(-2*cos(x)^2 + 1) - sqrt(2))^2/cos(x)^2 - 4)*cos(x)/(sqrt(2)*sqrt(-2*cos(x)^2 + 1) - sqrt(2))))*sgn(sin(x))","B",0
39,1,170,0,0.261590," ","integrate((1-cot(x)^2)^(1/2),x, algorithm=""giac"")","-\frac{1}{2} \, {\left(\pi - \sqrt{2} \pi - 2 \, \sqrt{2} \arctan\left(-\frac{1}{2} i \, \sqrt{2}\right) + 2 \, \arctan\left(-i\right)\right)} \mathrm{sgn}\left(\sin\left(x\right)\right) + \frac{1}{2} \, {\left(\pi \mathrm{sgn}\left(\cos\left(x\right)\right) - \sqrt{2} {\left(\pi \mathrm{sgn}\left(\cos\left(x\right)\right) + 2 \, \arctan\left(-\frac{{\left(\frac{{\left(\sqrt{2} \sqrt{-2 \, \cos\left(x\right)^{2} + 1} - \sqrt{2}\right)}^{2}}{\cos\left(x\right)^{2}} - 4\right)} \cos\left(x\right)}{4 \, {\left(\sqrt{2} \sqrt{-2 \, \cos\left(x\right)^{2} + 1} - \sqrt{2}\right)}}\right)\right)} + 2 \, \arctan\left(-\frac{\sqrt{2} {\left(\frac{{\left(\sqrt{2} \sqrt{-2 \, \cos\left(x\right)^{2} + 1} - \sqrt{2}\right)}^{2}}{\cos\left(x\right)^{2}} - 4\right)} \cos\left(x\right)}{4 \, {\left(\sqrt{2} \sqrt{-2 \, \cos\left(x\right)^{2} + 1} - \sqrt{2}\right)}}\right)\right)} \mathrm{sgn}\left(\sin\left(x\right)\right)"," ",0,"-1/2*(pi - sqrt(2)*pi - 2*sqrt(2)*arctan(-1/2*I*sqrt(2)) + 2*arctan(-I))*sgn(sin(x)) + 1/2*(pi*sgn(cos(x)) - sqrt(2)*(pi*sgn(cos(x)) + 2*arctan(-1/4*((sqrt(2)*sqrt(-2*cos(x)^2 + 1) - sqrt(2))^2/cos(x)^2 - 4)*cos(x)/(sqrt(2)*sqrt(-2*cos(x)^2 + 1) - sqrt(2)))) + 2*arctan(-1/4*sqrt(2)*((sqrt(2)*sqrt(-2*cos(x)^2 + 1) - sqrt(2))^2/cos(x)^2 - 4)*cos(x)/(sqrt(2)*sqrt(-2*cos(x)^2 + 1) - sqrt(2))))*sgn(sin(x))","C",0
40,1,34,0,0.210104," ","integrate(1/(1-cot(x)^2)^(1/2),x, algorithm=""giac"")","-\frac{1}{2} i \, \sqrt{2} \log\left(i \, \sqrt{2} + i\right) \mathrm{sgn}\left(\sin\left(x\right)\right) - \frac{\sqrt{2} \arcsin\left(\sqrt{2} \cos\left(x\right)\right)}{2 \, \mathrm{sgn}\left(\sin\left(x\right)\right)}"," ",0,"-1/2*I*sqrt(2)*log(I*sqrt(2) + I)*sgn(sin(x)) - 1/2*sqrt(2)*arcsin(sqrt(2)*cos(x))/sgn(sin(x))","C",0
41,1,179,0,0.664765," ","integrate((-1+cot(x)^2)^(3/2),x, algorithm=""giac"")","\frac{1}{4} \, {\left(4 \, \sqrt{2} \log\left({\left(\sqrt{2} \cos\left(x\right) - \sqrt{2 \, \cos\left(x\right)^{2} - 1}\right)}^{2}\right) - \frac{4 \, \sqrt{2} {\left(3 \, {\left(\sqrt{2} \cos\left(x\right) - \sqrt{2 \, \cos\left(x\right)^{2} - 1}\right)}^{2} - 1\right)}}{{\left(\sqrt{2} \cos\left(x\right) - \sqrt{2 \, \cos\left(x\right)^{2} - 1}\right)}^{4} - 6 \, {\left(\sqrt{2} \cos\left(x\right) - \sqrt{2 \, \cos\left(x\right)^{2} - 1}\right)}^{2} + 1} + 5 \, \log\left(\frac{{\left| 2 \, {\left(\sqrt{2} \cos\left(x\right) - \sqrt{2 \, \cos\left(x\right)^{2} - 1}\right)}^{2} - 4 \, \sqrt{2} - 6 \right|}}{{\left| 2 \, {\left(\sqrt{2} \cos\left(x\right) - \sqrt{2 \, \cos\left(x\right)^{2} - 1}\right)}^{2} + 4 \, \sqrt{2} - 6 \right|}}\right)\right)} \mathrm{sgn}\left(\sin\left(x\right)\right)"," ",0,"1/4*(4*sqrt(2)*log((sqrt(2)*cos(x) - sqrt(2*cos(x)^2 - 1))^2) - 4*sqrt(2)*(3*(sqrt(2)*cos(x) - sqrt(2*cos(x)^2 - 1))^2 - 1)/((sqrt(2)*cos(x) - sqrt(2*cos(x)^2 - 1))^4 - 6*(sqrt(2)*cos(x) - sqrt(2*cos(x)^2 - 1))^2 + 1) + 5*log(abs(2*(sqrt(2)*cos(x) - sqrt(2*cos(x)^2 - 1))^2 - 4*sqrt(2) - 6)/abs(2*(sqrt(2)*cos(x) - sqrt(2*cos(x)^2 - 1))^2 + 4*sqrt(2) - 6)))*sgn(sin(x))","B",0
42,-1,0,0,0.000000," ","integrate((-1+cot(x)^2)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
43,1,45,0,4.067658," ","integrate(1/(-1+cot(x)^2)^(1/2),x, algorithm=""giac"")","-\frac{1}{2} \, \sqrt{2} \log\left(\sqrt{2} - 1\right) \mathrm{sgn}\left(\sin\left(x\right)\right) + \frac{\sqrt{2} \log\left({\left| -\sqrt{2} \cos\left(x\right) + \sqrt{2 \, \cos\left(x\right)^{2} - 1} \right|}\right)}{2 \, \mathrm{sgn}\left(\sin\left(x\right)\right)}"," ",0,"-1/2*sqrt(2)*log(sqrt(2) - 1)*sgn(sin(x)) + 1/2*sqrt(2)*log(abs(-sqrt(2)*cos(x) + sqrt(2*cos(x)^2 - 1)))/sgn(sin(x))","B",0
44,1,127,0,4.909565," ","integrate(cot(x)^3/(a+b*cot(x)^2)^(1/2),x, algorithm=""giac"")","-\frac{\log\left({\left| 2 \, {\left(\sqrt{a - b} \cos\left(x\right)^{2} - \sqrt{a \cos\left(x\right)^{4} - b \cos\left(x\right)^{4} - 2 \, a \cos\left(x\right)^{2} + b \cos\left(x\right)^{2} + a}\right)} \sqrt{a - b} - 2 \, a + b \right|}\right)}{2 \, \sqrt{a - b}} + \frac{1}{\sqrt{a - b} \cos\left(x\right)^{2} - \sqrt{a \cos\left(x\right)^{4} - b \cos\left(x\right)^{4} - 2 \, a \cos\left(x\right)^{2} + b \cos\left(x\right)^{2} + a} - \sqrt{a - b}}"," ",0,"-1/2*log(abs(2*(sqrt(a - b)*cos(x)^2 - sqrt(a*cos(x)^4 - b*cos(x)^4 - 2*a*cos(x)^2 + b*cos(x)^2 + a))*sqrt(a - b) - 2*a + b))/sqrt(a - b) + 1/(sqrt(a - b)*cos(x)^2 - sqrt(a*cos(x)^4 - b*cos(x)^4 - 2*a*cos(x)^2 + b*cos(x)^2 + a) - sqrt(a - b))","B",0
45,-2,0,0,0.000000," ","integrate(cot(x)^2/(a+b*cot(x)^2)^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(sin(t_nostep))]Discontinuities at zeroes of sin(t_nostep) were not checkedWarning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep)]Error: Bad Argument Type","F(-2)",0
46,1,70,0,0.562539," ","integrate(cot(x)/(a+b*cot(x)^2)^(1/2),x, algorithm=""giac"")","\frac{\log\left({\left| 2 \, {\left(\sqrt{a - b} \cos\left(x\right)^{2} - \sqrt{a \cos\left(x\right)^{4} - b \cos\left(x\right)^{4} - 2 \, a \cos\left(x\right)^{2} + b \cos\left(x\right)^{2} + a}\right)} \sqrt{a - b} - 2 \, a + b \right|}\right)}{2 \, \sqrt{a - b}}"," ",0,"1/2*log(abs(2*(sqrt(a - b)*cos(x)^2 - sqrt(a*cos(x)^4 - b*cos(x)^4 - 2*a*cos(x)^2 + b*cos(x)^2 + a))*sqrt(a - b) - 2*a + b))/sqrt(a - b)","B",0
47,1,140,0,0.384686," ","integrate(tan(x)/(a+b*cot(x)^2)^(1/2),x, algorithm=""giac"")","-\frac{\arctan\left(-\frac{\sqrt{a - b} \cos\left(x\right)^{2} - \sqrt{a \cos\left(x\right)^{4} - b \cos\left(x\right)^{4} - 2 \, a \cos\left(x\right)^{2} + b \cos\left(x\right)^{2} + a}}{\sqrt{-a}}\right)}{\sqrt{-a}} - \frac{\log\left({\left| -2 \, {\left(\sqrt{a - b} \cos\left(x\right)^{2} - \sqrt{a \cos\left(x\right)^{4} - b \cos\left(x\right)^{4} - 2 \, a \cos\left(x\right)^{2} + b \cos\left(x\right)^{2} + a}\right)} {\left(a - b\right)} + {\left(2 \, a - b\right)} \sqrt{a - b} \right|}\right)}{2 \, \sqrt{a - b}}"," ",0,"-arctan(-(sqrt(a - b)*cos(x)^2 - sqrt(a*cos(x)^4 - b*cos(x)^4 - 2*a*cos(x)^2 + b*cos(x)^2 + a))/sqrt(-a))/sqrt(-a) - 1/2*log(abs(-2*(sqrt(a - b)*cos(x)^2 - sqrt(a*cos(x)^4 - b*cos(x)^4 - 2*a*cos(x)^2 + b*cos(x)^2 + a))*(a - b) + (2*a - b)*sqrt(a - b)))/sqrt(a - b)","B",0
48,-2,0,0,0.000000," ","integrate(tan(x)^2/(a+b*cot(x)^2)^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(sin(t_nostep))]Discontinuities at zeroes of sin(t_nostep) were not checkedWarning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep)]Error: Bad Argument Type","F(-2)",0
49,-2,0,0,0.000000," ","integrate(cot(x)^3/(a+b*cot(x)^2)^(3/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to divide, perhaps due to rounding error%%%{%%{[%%%{2,[1,2]%%%}+%%%{-2,[0,3]%%%},0]:[1,0,%%%{-1,[1,0]%%%}+%%%{1,[0,1]%%%}]%%},[2]%%%}+%%%{%%%{4,[2,2]%%%}+%%%{-4,[1,3]%%%},[1]%%%}+%%%{%%{[%%%{2,[2,2]%%%},0]:[1,0,%%%{-1,[1,0]%%%}+%%%{1,[0,1]%%%}]%%},[0]%%%} / %%%{%%%{1,[2,0]%%%}+%%%{-2,[1,1]%%%}+%%%{1,[0,2]%%%},[2]%%%}+%%%{%%{[%%%{2,[2,0]%%%}+%%%{-2,[1,1]%%%},0]:[1,0,%%%{-1,[1,0]%%%}+%%%{1,[0,1]%%%}]%%},[1]%%%}+%%%{%%%{1,[3,0]%%%}+%%%{-1,[2,1]%%%},[0]%%%} Error: Bad Argument Value","F(-2)",0
50,1,259,0,1.098629," ","integrate(cot(x)^2/(a+b*cot(x)^2)^(3/2),x, algorithm=""giac"")","\frac{\frac{{\left(a^{3} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, x\right)\right) - 2 \, a^{2} b \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, x\right)\right) + a b^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, x\right)\right)\right)} \tan\left(\frac{1}{2} \, x\right)^{2}}{a^{4} - 3 \, a^{3} b + 3 \, a^{2} b^{2} - a b^{3}} - \frac{a^{3} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, x\right)\right) - 2 \, a^{2} b \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, x\right)\right) + a b^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, x\right)\right)}{a^{4} - 3 \, a^{3} b + 3 \, a^{2} b^{2} - a b^{3}}}{\sqrt{b \tan\left(\frac{1}{2} \, x\right)^{4} + 4 \, a \tan\left(\frac{1}{2} \, x\right)^{2} - 2 \, b \tan\left(\frac{1}{2} \, x\right)^{2} + b}} + \frac{\sqrt{b} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, x\right)\right)}{a b - b^{2}} - \frac{2 \, \arctan\left(-\frac{\sqrt{b} \tan\left(\frac{1}{2} \, x\right)^{2} - \sqrt{b \tan\left(\frac{1}{2} \, x\right)^{4} + 4 \, a \tan\left(\frac{1}{2} \, x\right)^{2} - 2 \, b \tan\left(\frac{1}{2} \, x\right)^{2} + b} + \sqrt{b}}{2 \, \sqrt{a - b}}\right)}{{\left(a \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, x\right)\right) - b \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, x\right)\right)\right)} \sqrt{a - b}}"," ",0,"((a^3*sgn(tan(1/2*x)) - 2*a^2*b*sgn(tan(1/2*x)) + a*b^2*sgn(tan(1/2*x)))*tan(1/2*x)^2/(a^4 - 3*a^3*b + 3*a^2*b^2 - a*b^3) - (a^3*sgn(tan(1/2*x)) - 2*a^2*b*sgn(tan(1/2*x)) + a*b^2*sgn(tan(1/2*x)))/(a^4 - 3*a^3*b + 3*a^2*b^2 - a*b^3))/sqrt(b*tan(1/2*x)^4 + 4*a*tan(1/2*x)^2 - 2*b*tan(1/2*x)^2 + b) + sqrt(b)*sgn(tan(1/2*x))/(a*b - b^2) - 2*arctan(-1/2*(sqrt(b)*tan(1/2*x)^2 - sqrt(b*tan(1/2*x)^4 + 4*a*tan(1/2*x)^2 - 2*b*tan(1/2*x)^2 + b) + sqrt(b))/sqrt(a - b))/((a*sgn(tan(1/2*x)) - b*sgn(tan(1/2*x)))*sqrt(a - b))","B",0
51,-2,0,0,0.000000," ","integrate(cot(x)/(a+b*cot(x)^2)^(3/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to divide, perhaps due to rounding error%%%{%%{[%%%{2,[1,2]%%%}+%%%{-2,[0,3]%%%},0]:[1,0,%%%{-1,[1,0]%%%}+%%%{1,[0,1]%%%}]%%},[2]%%%}+%%%{%%%{4,[2,2]%%%}+%%%{-4,[1,3]%%%},[1]%%%}+%%%{%%{[%%%{2,[2,2]%%%},0]:[1,0,%%%{-1,[1,0]%%%}+%%%{1,[0,1]%%%}]%%},[0]%%%} / %%%{%%%{1,[2,0]%%%}+%%%{-2,[1,1]%%%}+%%%{1,[0,2]%%%},[2]%%%}+%%%{%%{[%%%{2,[2,0]%%%}+%%%{-2,[1,1]%%%},0]:[1,0,%%%{-1,[1,0]%%%}+%%%{1,[0,1]%%%}]%%},[1]%%%}+%%%{%%%{1,[3,0]%%%}+%%%{-1,[2,1]%%%},[0]%%%} Error: Bad Argument Value","F(-2)",0
52,-2,0,0,0.000000," ","integrate(tan(x)/(a+b*cot(x)^2)^(3/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, replacing 0 by ` u`, a substitution variable should perhaps be purged.Warning, replacing 0 by ` u`, a substitution variable should perhaps be purged.Warning, replacing 0 by ` u`, a substitution variable should perhaps be purged.Warning, replacing 0 by ` u`, a substitution variable should perhaps be purged.Warning, replacing 0 by ` u`, a substitution variable should perhaps be purged.Warning, replacing 0 by ` u`, a substitution variable should perhaps be purged.Warning, replacing 0 by ` u`, a substitution variable should perhaps be purged.Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep)]Error: Bad Argument Type","F(-2)",0
53,-2,0,0,0.000000," ","integrate(tan(x)^2/(a+b*cot(x)^2)^(3/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(sin(t_nostep))]Discontinuities at zeroes of sin(t_nostep) were not checkedWarning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep)]Evaluation time: 0.48Error: Bad Argument Type","F(-2)",0
54,-2,0,0,0.000000," ","integrate(cot(x)^3/(a+b*cot(x)^2)^(5/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:index.cc index_m i_lex_is_greater Error: Bad Argument Value","F(-2)",0
55,1,1025,0,2.397777," ","integrate(cot(x)^2/(a+b*cot(x)^2)^(5/2),x, algorithm=""giac"")","\frac{{\left(2 \, a + b\right)} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, x\right)\right)}{3 \, {\left(a^{3} \sqrt{b} - 2 \, a^{2} b^{\frac{3}{2}} + a b^{\frac{5}{2}}\right)}} + \frac{{\left({\left(\frac{{\left(2 \, a^{10} b \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, x\right)\right) - 15 \, a^{9} b^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, x\right)\right) + 48 \, a^{8} b^{3} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, x\right)\right) - 84 \, a^{7} b^{4} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, x\right)\right) + 84 \, a^{6} b^{5} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, x\right)\right) - 42 \, a^{5} b^{6} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, x\right)\right) + 12 \, a^{3} b^{8} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, x\right)\right) - 6 \, a^{2} b^{9} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, x\right)\right) + a b^{10} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, x\right)\right)\right)} \tan\left(\frac{1}{2} \, x\right)^{2}}{a^{12} - 10 \, a^{11} b + 45 \, a^{10} b^{2} - 120 \, a^{9} b^{3} + 210 \, a^{8} b^{4} - 252 \, a^{7} b^{5} + 210 \, a^{6} b^{6} - 120 \, a^{5} b^{7} + 45 \, a^{4} b^{8} - 10 \, a^{3} b^{9} + a^{2} b^{10}} + \frac{3 \, {\left(4 \, a^{11} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, x\right)\right) - 34 \, a^{10} b \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, x\right)\right) + 127 \, a^{9} b^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, x\right)\right) - 272 \, a^{8} b^{3} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, x\right)\right) + 364 \, a^{7} b^{4} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, x\right)\right) - 308 \, a^{6} b^{5} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, x\right)\right) + 154 \, a^{5} b^{6} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, x\right)\right) - 32 \, a^{4} b^{7} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, x\right)\right) - 8 \, a^{3} b^{8} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, x\right)\right) + 6 \, a^{2} b^{9} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, x\right)\right) - a b^{10} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, x\right)\right)\right)}}{a^{12} - 10 \, a^{11} b + 45 \, a^{10} b^{2} - 120 \, a^{9} b^{3} + 210 \, a^{8} b^{4} - 252 \, a^{7} b^{5} + 210 \, a^{6} b^{6} - 120 \, a^{5} b^{7} + 45 \, a^{4} b^{8} - 10 \, a^{3} b^{9} + a^{2} b^{10}}\right)} \tan\left(\frac{1}{2} \, x\right)^{2} - \frac{3 \, {\left(4 \, a^{11} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, x\right)\right) - 34 \, a^{10} b \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, x\right)\right) + 127 \, a^{9} b^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, x\right)\right) - 272 \, a^{8} b^{3} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, x\right)\right) + 364 \, a^{7} b^{4} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, x\right)\right) - 308 \, a^{6} b^{5} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, x\right)\right) + 154 \, a^{5} b^{6} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, x\right)\right) - 32 \, a^{4} b^{7} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, x\right)\right) - 8 \, a^{3} b^{8} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, x\right)\right) + 6 \, a^{2} b^{9} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, x\right)\right) - a b^{10} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, x\right)\right)\right)}}{a^{12} - 10 \, a^{11} b + 45 \, a^{10} b^{2} - 120 \, a^{9} b^{3} + 210 \, a^{8} b^{4} - 252 \, a^{7} b^{5} + 210 \, a^{6} b^{6} - 120 \, a^{5} b^{7} + 45 \, a^{4} b^{8} - 10 \, a^{3} b^{9} + a^{2} b^{10}}\right)} \tan\left(\frac{1}{2} \, x\right)^{2} - \frac{2 \, a^{10} b \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, x\right)\right) - 15 \, a^{9} b^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, x\right)\right) + 48 \, a^{8} b^{3} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, x\right)\right) - 84 \, a^{7} b^{4} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, x\right)\right) + 84 \, a^{6} b^{5} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, x\right)\right) - 42 \, a^{5} b^{6} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, x\right)\right) + 12 \, a^{3} b^{8} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, x\right)\right) - 6 \, a^{2} b^{9} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, x\right)\right) + a b^{10} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, x\right)\right)}{a^{12} - 10 \, a^{11} b + 45 \, a^{10} b^{2} - 120 \, a^{9} b^{3} + 210 \, a^{8} b^{4} - 252 \, a^{7} b^{5} + 210 \, a^{6} b^{6} - 120 \, a^{5} b^{7} + 45 \, a^{4} b^{8} - 10 \, a^{3} b^{9} + a^{2} b^{10}}}{3 \, {\left(b \tan\left(\frac{1}{2} \, x\right)^{4} + 4 \, a \tan\left(\frac{1}{2} \, x\right)^{2} - 2 \, b \tan\left(\frac{1}{2} \, x\right)^{2} + b\right)}^{\frac{3}{2}}} - \frac{2 \, \arctan\left(-\frac{\sqrt{b} \tan\left(\frac{1}{2} \, x\right)^{2} - \sqrt{b \tan\left(\frac{1}{2} \, x\right)^{4} + 4 \, a \tan\left(\frac{1}{2} \, x\right)^{2} - 2 \, b \tan\left(\frac{1}{2} \, x\right)^{2} + b} + \sqrt{b}}{2 \, \sqrt{a - b}}\right)}{{\left(a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, x\right)\right) - 2 \, a b \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, x\right)\right) + b^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, x\right)\right)\right)} \sqrt{a - b}}"," ",0,"1/3*(2*a + b)*sgn(tan(1/2*x))/(a^3*sqrt(b) - 2*a^2*b^(3/2) + a*b^(5/2)) + 1/3*((((2*a^10*b*sgn(tan(1/2*x)) - 15*a^9*b^2*sgn(tan(1/2*x)) + 48*a^8*b^3*sgn(tan(1/2*x)) - 84*a^7*b^4*sgn(tan(1/2*x)) + 84*a^6*b^5*sgn(tan(1/2*x)) - 42*a^5*b^6*sgn(tan(1/2*x)) + 12*a^3*b^8*sgn(tan(1/2*x)) - 6*a^2*b^9*sgn(tan(1/2*x)) + a*b^10*sgn(tan(1/2*x)))*tan(1/2*x)^2/(a^12 - 10*a^11*b + 45*a^10*b^2 - 120*a^9*b^3 + 210*a^8*b^4 - 252*a^7*b^5 + 210*a^6*b^6 - 120*a^5*b^7 + 45*a^4*b^8 - 10*a^3*b^9 + a^2*b^10) + 3*(4*a^11*sgn(tan(1/2*x)) - 34*a^10*b*sgn(tan(1/2*x)) + 127*a^9*b^2*sgn(tan(1/2*x)) - 272*a^8*b^3*sgn(tan(1/2*x)) + 364*a^7*b^4*sgn(tan(1/2*x)) - 308*a^6*b^5*sgn(tan(1/2*x)) + 154*a^5*b^6*sgn(tan(1/2*x)) - 32*a^4*b^7*sgn(tan(1/2*x)) - 8*a^3*b^8*sgn(tan(1/2*x)) + 6*a^2*b^9*sgn(tan(1/2*x)) - a*b^10*sgn(tan(1/2*x)))/(a^12 - 10*a^11*b + 45*a^10*b^2 - 120*a^9*b^3 + 210*a^8*b^4 - 252*a^7*b^5 + 210*a^6*b^6 - 120*a^5*b^7 + 45*a^4*b^8 - 10*a^3*b^9 + a^2*b^10))*tan(1/2*x)^2 - 3*(4*a^11*sgn(tan(1/2*x)) - 34*a^10*b*sgn(tan(1/2*x)) + 127*a^9*b^2*sgn(tan(1/2*x)) - 272*a^8*b^3*sgn(tan(1/2*x)) + 364*a^7*b^4*sgn(tan(1/2*x)) - 308*a^6*b^5*sgn(tan(1/2*x)) + 154*a^5*b^6*sgn(tan(1/2*x)) - 32*a^4*b^7*sgn(tan(1/2*x)) - 8*a^3*b^8*sgn(tan(1/2*x)) + 6*a^2*b^9*sgn(tan(1/2*x)) - a*b^10*sgn(tan(1/2*x)))/(a^12 - 10*a^11*b + 45*a^10*b^2 - 120*a^9*b^3 + 210*a^8*b^4 - 252*a^7*b^5 + 210*a^6*b^6 - 120*a^5*b^7 + 45*a^4*b^8 - 10*a^3*b^9 + a^2*b^10))*tan(1/2*x)^2 - (2*a^10*b*sgn(tan(1/2*x)) - 15*a^9*b^2*sgn(tan(1/2*x)) + 48*a^8*b^3*sgn(tan(1/2*x)) - 84*a^7*b^4*sgn(tan(1/2*x)) + 84*a^6*b^5*sgn(tan(1/2*x)) - 42*a^5*b^6*sgn(tan(1/2*x)) + 12*a^3*b^8*sgn(tan(1/2*x)) - 6*a^2*b^9*sgn(tan(1/2*x)) + a*b^10*sgn(tan(1/2*x)))/(a^12 - 10*a^11*b + 45*a^10*b^2 - 120*a^9*b^3 + 210*a^8*b^4 - 252*a^7*b^5 + 210*a^6*b^6 - 120*a^5*b^7 + 45*a^4*b^8 - 10*a^3*b^9 + a^2*b^10))/(b*tan(1/2*x)^4 + 4*a*tan(1/2*x)^2 - 2*b*tan(1/2*x)^2 + b)^(3/2) - 2*arctan(-1/2*(sqrt(b)*tan(1/2*x)^2 - sqrt(b*tan(1/2*x)^4 + 4*a*tan(1/2*x)^2 - 2*b*tan(1/2*x)^2 + b) + sqrt(b))/sqrt(a - b))/((a^2*sgn(tan(1/2*x)) - 2*a*b*sgn(tan(1/2*x)) + b^2*sgn(tan(1/2*x)))*sqrt(a - b))","B",0
56,-2,0,0,0.000000," ","integrate(cot(x)/(a+b*cot(x)^2)^(5/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:index.cc index_m i_lex_is_greater Error: Bad Argument Value","F(-2)",0
57,-2,0,0,0.000000," ","integrate(tan(x)/(a+b*cot(x)^2)^(5/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, replacing 0 by ` u`, a substitution variable should perhaps be purged.Warning, replacing 0 by ` u`, a substitution variable should perhaps be purged.Warning, replacing 0 by ` u`, a substitution variable should perhaps be purged.Warning, replacing 0 by ` u`, a substitution variable should perhaps be purged.Warning, replacing 0 by ` u`, a substitution variable should perhaps be purged.Warning, replacing 0 by ` u`, a substitution variable should perhaps be purged.Warning, replacing 0 by ` u`, a substitution variable should perhaps be purged.Warning, replacing 0 by ` u`, a substitution variable should perhaps be purged.Warning, replacing 0 by ` u`, a substitution variable should perhaps be purged.Warning, replacing 0 by ` u`, a substitution variable should perhaps be purged.Warning, replacing 0 by ` u`, a substitution variable should perhaps be purged.Warning, replacing 0 by ` u`, a substitution variable should perhaps be purged.Warning, replacing 0 by ` u`, a substitution variable should perhaps be purged.Warning, replacing 0 by ` u`, a substitution variable should perhaps be purged.Warning, replacing 0 by ` u`, a substitution variable should perhaps be purged.Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep)]Evaluation time: 0.79Error: Bad Argument Type","F(-2)",0
58,1,1242,0,4.940577," ","integrate(tan(x)^2/(a+b*cot(x)^2)^(5/2),x, algorithm=""giac"")","\frac{{\left(8 \, a b^{2} - 5 \, b^{3}\right)} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, x\right)\right)}{3 \, {\left(a^{5} \sqrt{b} - 2 \, a^{4} b^{\frac{3}{2}} + a^{3} b^{\frac{5}{2}}\right)}} + \frac{{\left({\left(\frac{{\left(8 \, a^{16} b^{3} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, x\right)\right) - 69 \, a^{15} b^{4} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, x\right)\right) + 264 \, a^{14} b^{5} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, x\right)\right) - 588 \, a^{13} b^{6} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, x\right)\right) + 840 \, a^{12} b^{7} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, x\right)\right) - 798 \, a^{11} b^{8} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, x\right)\right) + 504 \, a^{10} b^{9} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, x\right)\right) - 204 \, a^{9} b^{10} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, x\right)\right) + 48 \, a^{8} b^{11} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, x\right)\right) - 5 \, a^{7} b^{12} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, x\right)\right)\right)} \tan\left(\frac{1}{2} \, x\right)^{2}}{a^{20} - 10 \, a^{19} b + 45 \, a^{18} b^{2} - 120 \, a^{17} b^{3} + 210 \, a^{16} b^{4} - 252 \, a^{15} b^{5} + 210 \, a^{14} b^{6} - 120 \, a^{13} b^{7} + 45 \, a^{12} b^{8} - 10 \, a^{11} b^{9} + a^{10} b^{10}} + \frac{3 \, {\left(12 \, a^{17} b^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, x\right)\right) - 112 \, a^{16} b^{3} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, x\right)\right) + 469 \, a^{15} b^{4} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, x\right)\right) - 1160 \, a^{14} b^{5} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, x\right)\right) + 1876 \, a^{13} b^{6} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, x\right)\right) - 2072 \, a^{12} b^{7} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, x\right)\right) + 1582 \, a^{11} b^{8} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, x\right)\right) - 824 \, a^{10} b^{9} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, x\right)\right) + 280 \, a^{9} b^{10} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, x\right)\right) - 56 \, a^{8} b^{11} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, x\right)\right) + 5 \, a^{7} b^{12} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, x\right)\right)\right)}}{a^{20} - 10 \, a^{19} b + 45 \, a^{18} b^{2} - 120 \, a^{17} b^{3} + 210 \, a^{16} b^{4} - 252 \, a^{15} b^{5} + 210 \, a^{14} b^{6} - 120 \, a^{13} b^{7} + 45 \, a^{12} b^{8} - 10 \, a^{11} b^{9} + a^{10} b^{10}}\right)} \tan\left(\frac{1}{2} \, x\right)^{2} - \frac{3 \, {\left(12 \, a^{17} b^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, x\right)\right) - 112 \, a^{16} b^{3} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, x\right)\right) + 469 \, a^{15} b^{4} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, x\right)\right) - 1160 \, a^{14} b^{5} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, x\right)\right) + 1876 \, a^{13} b^{6} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, x\right)\right) - 2072 \, a^{12} b^{7} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, x\right)\right) + 1582 \, a^{11} b^{8} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, x\right)\right) - 824 \, a^{10} b^{9} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, x\right)\right) + 280 \, a^{9} b^{10} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, x\right)\right) - 56 \, a^{8} b^{11} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, x\right)\right) + 5 \, a^{7} b^{12} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, x\right)\right)\right)}}{a^{20} - 10 \, a^{19} b + 45 \, a^{18} b^{2} - 120 \, a^{17} b^{3} + 210 \, a^{16} b^{4} - 252 \, a^{15} b^{5} + 210 \, a^{14} b^{6} - 120 \, a^{13} b^{7} + 45 \, a^{12} b^{8} - 10 \, a^{11} b^{9} + a^{10} b^{10}}\right)} \tan\left(\frac{1}{2} \, x\right)^{2} - \frac{8 \, a^{16} b^{3} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, x\right)\right) - 69 \, a^{15} b^{4} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, x\right)\right) + 264 \, a^{14} b^{5} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, x\right)\right) - 588 \, a^{13} b^{6} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, x\right)\right) + 840 \, a^{12} b^{7} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, x\right)\right) - 798 \, a^{11} b^{8} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, x\right)\right) + 504 \, a^{10} b^{9} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, x\right)\right) - 204 \, a^{9} b^{10} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, x\right)\right) + 48 \, a^{8} b^{11} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, x\right)\right) - 5 \, a^{7} b^{12} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, x\right)\right)}{a^{20} - 10 \, a^{19} b + 45 \, a^{18} b^{2} - 120 \, a^{17} b^{3} + 210 \, a^{16} b^{4} - 252 \, a^{15} b^{5} + 210 \, a^{14} b^{6} - 120 \, a^{13} b^{7} + 45 \, a^{12} b^{8} - 10 \, a^{11} b^{9} + a^{10} b^{10}}}{3 \, {\left(b \tan\left(\frac{1}{2} \, x\right)^{4} + 4 \, a \tan\left(\frac{1}{2} \, x\right)^{2} - 2 \, b \tan\left(\frac{1}{2} \, x\right)^{2} + b\right)}^{\frac{3}{2}}} - \frac{2 \, \arctan\left(-\frac{\sqrt{b} \tan\left(\frac{1}{2} \, x\right)^{2} - \sqrt{b \tan\left(\frac{1}{2} \, x\right)^{4} + 4 \, a \tan\left(\frac{1}{2} \, x\right)^{2} - 2 \, b \tan\left(\frac{1}{2} \, x\right)^{2} + b} + \sqrt{b}}{2 \, \sqrt{a - b}}\right)}{{\left(a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, x\right)\right) - 2 \, a b \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, x\right)\right) + b^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, x\right)\right)\right)} \sqrt{a - b}} + \frac{4 \, {\left(\sqrt{b} \tan\left(\frac{1}{2} \, x\right)^{2} - \sqrt{b \tan\left(\frac{1}{2} \, x\right)^{4} + 4 \, a \tan\left(\frac{1}{2} \, x\right)^{2} - 2 \, b \tan\left(\frac{1}{2} \, x\right)^{2} + b} + \sqrt{b}\right)}}{{\left({\left(\sqrt{b} \tan\left(\frac{1}{2} \, x\right)^{2} - \sqrt{b \tan\left(\frac{1}{2} \, x\right)^{4} + 4 \, a \tan\left(\frac{1}{2} \, x\right)^{2} - 2 \, b \tan\left(\frac{1}{2} \, x\right)^{2} + b}\right)}^{2} - 2 \, {\left(\sqrt{b} \tan\left(\frac{1}{2} \, x\right)^{2} - \sqrt{b \tan\left(\frac{1}{2} \, x\right)^{4} + 4 \, a \tan\left(\frac{1}{2} \, x\right)^{2} - 2 \, b \tan\left(\frac{1}{2} \, x\right)^{2} + b}\right)} \sqrt{b} - 4 \, a + b\right)} a^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, x\right)\right)}"," ",0,"1/3*(8*a*b^2 - 5*b^3)*sgn(tan(1/2*x))/(a^5*sqrt(b) - 2*a^4*b^(3/2) + a^3*b^(5/2)) + 1/3*((((8*a^16*b^3*sgn(tan(1/2*x)) - 69*a^15*b^4*sgn(tan(1/2*x)) + 264*a^14*b^5*sgn(tan(1/2*x)) - 588*a^13*b^6*sgn(tan(1/2*x)) + 840*a^12*b^7*sgn(tan(1/2*x)) - 798*a^11*b^8*sgn(tan(1/2*x)) + 504*a^10*b^9*sgn(tan(1/2*x)) - 204*a^9*b^10*sgn(tan(1/2*x)) + 48*a^8*b^11*sgn(tan(1/2*x)) - 5*a^7*b^12*sgn(tan(1/2*x)))*tan(1/2*x)^2/(a^20 - 10*a^19*b + 45*a^18*b^2 - 120*a^17*b^3 + 210*a^16*b^4 - 252*a^15*b^5 + 210*a^14*b^6 - 120*a^13*b^7 + 45*a^12*b^8 - 10*a^11*b^9 + a^10*b^10) + 3*(12*a^17*b^2*sgn(tan(1/2*x)) - 112*a^16*b^3*sgn(tan(1/2*x)) + 469*a^15*b^4*sgn(tan(1/2*x)) - 1160*a^14*b^5*sgn(tan(1/2*x)) + 1876*a^13*b^6*sgn(tan(1/2*x)) - 2072*a^12*b^7*sgn(tan(1/2*x)) + 1582*a^11*b^8*sgn(tan(1/2*x)) - 824*a^10*b^9*sgn(tan(1/2*x)) + 280*a^9*b^10*sgn(tan(1/2*x)) - 56*a^8*b^11*sgn(tan(1/2*x)) + 5*a^7*b^12*sgn(tan(1/2*x)))/(a^20 - 10*a^19*b + 45*a^18*b^2 - 120*a^17*b^3 + 210*a^16*b^4 - 252*a^15*b^5 + 210*a^14*b^6 - 120*a^13*b^7 + 45*a^12*b^8 - 10*a^11*b^9 + a^10*b^10))*tan(1/2*x)^2 - 3*(12*a^17*b^2*sgn(tan(1/2*x)) - 112*a^16*b^3*sgn(tan(1/2*x)) + 469*a^15*b^4*sgn(tan(1/2*x)) - 1160*a^14*b^5*sgn(tan(1/2*x)) + 1876*a^13*b^6*sgn(tan(1/2*x)) - 2072*a^12*b^7*sgn(tan(1/2*x)) + 1582*a^11*b^8*sgn(tan(1/2*x)) - 824*a^10*b^9*sgn(tan(1/2*x)) + 280*a^9*b^10*sgn(tan(1/2*x)) - 56*a^8*b^11*sgn(tan(1/2*x)) + 5*a^7*b^12*sgn(tan(1/2*x)))/(a^20 - 10*a^19*b + 45*a^18*b^2 - 120*a^17*b^3 + 210*a^16*b^4 - 252*a^15*b^5 + 210*a^14*b^6 - 120*a^13*b^7 + 45*a^12*b^8 - 10*a^11*b^9 + a^10*b^10))*tan(1/2*x)^2 - (8*a^16*b^3*sgn(tan(1/2*x)) - 69*a^15*b^4*sgn(tan(1/2*x)) + 264*a^14*b^5*sgn(tan(1/2*x)) - 588*a^13*b^6*sgn(tan(1/2*x)) + 840*a^12*b^7*sgn(tan(1/2*x)) - 798*a^11*b^8*sgn(tan(1/2*x)) + 504*a^10*b^9*sgn(tan(1/2*x)) - 204*a^9*b^10*sgn(tan(1/2*x)) + 48*a^8*b^11*sgn(tan(1/2*x)) - 5*a^7*b^12*sgn(tan(1/2*x)))/(a^20 - 10*a^19*b + 45*a^18*b^2 - 120*a^17*b^3 + 210*a^16*b^4 - 252*a^15*b^5 + 210*a^14*b^6 - 120*a^13*b^7 + 45*a^12*b^8 - 10*a^11*b^9 + a^10*b^10))/(b*tan(1/2*x)^4 + 4*a*tan(1/2*x)^2 - 2*b*tan(1/2*x)^2 + b)^(3/2) - 2*arctan(-1/2*(sqrt(b)*tan(1/2*x)^2 - sqrt(b*tan(1/2*x)^4 + 4*a*tan(1/2*x)^2 - 2*b*tan(1/2*x)^2 + b) + sqrt(b))/sqrt(a - b))/((a^2*sgn(tan(1/2*x)) - 2*a*b*sgn(tan(1/2*x)) + b^2*sgn(tan(1/2*x)))*sqrt(a - b)) + 4*(sqrt(b)*tan(1/2*x)^2 - sqrt(b*tan(1/2*x)^4 + 4*a*tan(1/2*x)^2 - 2*b*tan(1/2*x)^2 + b) + sqrt(b))/(((sqrt(b)*tan(1/2*x)^2 - sqrt(b*tan(1/2*x)^4 + 4*a*tan(1/2*x)^2 - 2*b*tan(1/2*x)^2 + b))^2 - 2*(sqrt(b)*tan(1/2*x)^2 - sqrt(b*tan(1/2*x)^4 + 4*a*tan(1/2*x)^2 - 2*b*tan(1/2*x)^2 + b))*sqrt(b) - 4*a + b)*a^2*sgn(tan(1/2*x)))","B",0
59,1,34,0,0.424721," ","integrate(1/(1+cot(x)^3),x, algorithm=""giac"")","\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({\left| \tan\left(x\right) + 1 \right|}\right)"," ",0,"1/2*x + 1/3*log(tan(x)^2 - tan(x) + 1) - 1/4*log(tan(x)^2 + 1) - 1/6*log(abs(tan(x) + 1))","A",0
60,1,204,0,0.446552," ","integrate(cot(x)*(a+b*cot(x)^4)^(1/2),x, algorithm=""giac"")","-\frac{b \arctan\left(-\frac{\sqrt{a + b} \sin\left(x\right)^{2} - \sqrt{a \sin\left(x\right)^{4} + b \sin\left(x\right)^{4} - 2 \, b \sin\left(x\right)^{2} + b}}{\sqrt{-b}}\right)}{\sqrt{-b}} - \frac{1}{2} \, \sqrt{a + b} \log\left({\left| -{\left(\sqrt{a + b} \sin\left(x\right)^{2} - \sqrt{a \sin\left(x\right)^{4} + b \sin\left(x\right)^{4} - 2 \, b \sin\left(x\right)^{2} + b}\right)} {\left(a + b\right)} + \sqrt{a + b} b \right|}\right) - \frac{{\left(\sqrt{a + b} \sin\left(x\right)^{2} - \sqrt{a \sin\left(x\right)^{4} + b \sin\left(x\right)^{4} - 2 \, b \sin\left(x\right)^{2} + b}\right)} b - \sqrt{a + b} b}{{\left(\sqrt{a + b} \sin\left(x\right)^{2} - \sqrt{a \sin\left(x\right)^{4} + b \sin\left(x\right)^{4} - 2 \, b \sin\left(x\right)^{2} + b}\right)}^{2} - b}"," ",0,"-b*arctan(-(sqrt(a + b)*sin(x)^2 - sqrt(a*sin(x)^4 + b*sin(x)^4 - 2*b*sin(x)^2 + b))/sqrt(-b))/sqrt(-b) - 1/2*sqrt(a + b)*log(abs(-(sqrt(a + b)*sin(x)^2 - sqrt(a*sin(x)^4 + b*sin(x)^4 - 2*b*sin(x)^2 + b))*(a + b) + sqrt(a + b)*b)) - ((sqrt(a + b)*sin(x)^2 - sqrt(a*sin(x)^4 + b*sin(x)^4 - 2*b*sin(x)^2 + b))*b - sqrt(a + b)*b)/((sqrt(a + b)*sin(x)^2 - sqrt(a*sin(x)^4 + b*sin(x)^4 - 2*b*sin(x)^2 + b))^2 - b)","B",0
61,1,445,0,1.798712," ","integrate(cot(x)*(a+b*cot(x)^4)^(3/2),x, algorithm=""giac"")","-\frac{{\left(3 \, a b + 2 \, b^{2}\right)} \arctan\left(-\frac{\sqrt{a + b} \sin\left(x\right)^{2} - \sqrt{a \sin\left(x\right)^{4} + b \sin\left(x\right)^{4} - 2 \, b \sin\left(x\right)^{2} + b}}{\sqrt{-b}}\right)}{2 \, \sqrt{-b}} - \frac{{\left(a^{2} + 2 \, a b + b^{2}\right)} \log\left({\left| -{\left(\sqrt{a + b} \sin\left(x\right)^{2} - \sqrt{a \sin\left(x\right)^{4} + b \sin\left(x\right)^{4} - 2 \, b \sin\left(x\right)^{2} + b}\right)} {\left(a + b\right)} + \sqrt{a + b} b \right|}\right)}{2 \, \sqrt{a + b}} - \frac{3 \, {\left(\sqrt{a + b} \sin\left(x\right)^{2} - \sqrt{a \sin\left(x\right)^{4} + b \sin\left(x\right)^{4} - 2 \, b \sin\left(x\right)^{2} + b}\right)}^{5} {\left(5 \, a b + 6 \, b^{2}\right)} + 8 \, {\left(\sqrt{a + b} \sin\left(x\right)^{2} - \sqrt{a \sin\left(x\right)^{4} + b \sin\left(x\right)^{4} - 2 \, b \sin\left(x\right)^{2} + b}\right)}^{3} b^{3} - 12 \, {\left(\sqrt{a + b} \sin\left(x\right)^{2} - \sqrt{a \sin\left(x\right)^{4} + b \sin\left(x\right)^{4} - 2 \, b \sin\left(x\right)^{2} + b}\right)}^{4} {\left(a b + 3 \, b^{2}\right)} \sqrt{a + b} + 12 \, {\left(a b^{2} + b^{3}\right)} {\left(\sqrt{a + b} \sin\left(x\right)^{2} - \sqrt{a \sin\left(x\right)^{4} + b \sin\left(x\right)^{4} - 2 \, b \sin\left(x\right)^{2} + b}\right)}^{2} \sqrt{a + b} + 3 \, {\left(3 \, a b^{3} + 2 \, b^{4}\right)} {\left(\sqrt{a + b} \sin\left(x\right)^{2} - \sqrt{a \sin\left(x\right)^{4} + b \sin\left(x\right)^{4} - 2 \, b \sin\left(x\right)^{2} + b}\right)} - 8 \, {\left(a b^{3} + b^{4}\right)} \sqrt{a + b}}{6 \, {\left({\left(\sqrt{a + b} \sin\left(x\right)^{2} - \sqrt{a \sin\left(x\right)^{4} + b \sin\left(x\right)^{4} - 2 \, b \sin\left(x\right)^{2} + b}\right)}^{2} - b\right)}^{3}}"," ",0,"-1/2*(3*a*b + 2*b^2)*arctan(-(sqrt(a + b)*sin(x)^2 - sqrt(a*sin(x)^4 + b*sin(x)^4 - 2*b*sin(x)^2 + b))/sqrt(-b))/sqrt(-b) - 1/2*(a^2 + 2*a*b + b^2)*log(abs(-(sqrt(a + b)*sin(x)^2 - sqrt(a*sin(x)^4 + b*sin(x)^4 - 2*b*sin(x)^2 + b))*(a + b) + sqrt(a + b)*b))/sqrt(a + b) - 1/6*(3*(sqrt(a + b)*sin(x)^2 - sqrt(a*sin(x)^4 + b*sin(x)^4 - 2*b*sin(x)^2 + b))^5*(5*a*b + 6*b^2) + 8*(sqrt(a + b)*sin(x)^2 - sqrt(a*sin(x)^4 + b*sin(x)^4 - 2*b*sin(x)^2 + b))^3*b^3 - 12*(sqrt(a + b)*sin(x)^2 - sqrt(a*sin(x)^4 + b*sin(x)^4 - 2*b*sin(x)^2 + b))^4*(a*b + 3*b^2)*sqrt(a + b) + 12*(a*b^2 + b^3)*(sqrt(a + b)*sin(x)^2 - sqrt(a*sin(x)^4 + b*sin(x)^4 - 2*b*sin(x)^2 + b))^2*sqrt(a + b) + 3*(3*a*b^3 + 2*b^4)*(sqrt(a + b)*sin(x)^2 - sqrt(a*sin(x)^4 + b*sin(x)^4 - 2*b*sin(x)^2 + b)) - 8*(a*b^3 + b^4)*sqrt(a + b))/((sqrt(a + b)*sin(x)^2 - sqrt(a*sin(x)^4 + b*sin(x)^4 - 2*b*sin(x)^2 + b))^2 - b)^3","B",0
62,1,58,0,0.383353," ","integrate(cot(x)/(a+b*cot(x)^4)^(1/2),x, algorithm=""giac"")","\frac{\log\left({\left| -{\left(\sqrt{a + b} \cos\left(x\right)^{2} - \sqrt{a \cos\left(x\right)^{4} + b \cos\left(x\right)^{4} - 2 \, a \cos\left(x\right)^{2} + a}\right)} {\left(a + b\right)} + \sqrt{a + b} a \right|}\right)}{2 \, \sqrt{a + b}}"," ",0,"1/2*log(abs(-(sqrt(a + b)*cos(x)^2 - sqrt(a*cos(x)^4 + b*cos(x)^4 - 2*a*cos(x)^2 + a))*(a + b) + sqrt(a + b)*a))/sqrt(a + b)","A",0
63,1,111,0,0.444086," ","integrate(cot(x)/(a+b*cot(x)^4)^(3/2),x, algorithm=""giac"")","-\frac{\frac{{\left(a - b\right)} \sin\left(x\right)^{2}}{a^{2} + a b} + \frac{b}{a^{2} + a b}}{2 \, \sqrt{a \sin\left(x\right)^{4} + b \sin\left(x\right)^{4} - 2 \, b \sin\left(x\right)^{2} + b}} - \frac{\log\left({\left| -{\left(\sqrt{a + b} \sin\left(x\right)^{2} - \sqrt{a \sin\left(x\right)^{4} + b \sin\left(x\right)^{4} - 2 \, b \sin\left(x\right)^{2} + b}\right)} \sqrt{a + b} + b \right|}\right)}{2 \, {\left(a + b\right)}^{\frac{3}{2}}}"," ",0,"-1/2*((a - b)*sin(x)^2/(a^2 + a*b) + b/(a^2 + a*b))/sqrt(a*sin(x)^4 + b*sin(x)^4 - 2*b*sin(x)^2 + b) - 1/2*log(abs(-(sqrt(a + b)*sin(x)^2 - sqrt(a*sin(x)^4 + b*sin(x)^4 - 2*b*sin(x)^2 + b))*sqrt(a + b) + b))/(a + b)^(3/2)","A",0
64,1,276,0,0.484636," ","integrate(cot(x)/(a+b*cot(x)^4)^(5/2),x, algorithm=""giac"")","-\frac{{\left(2 \, {\left(\frac{{\left(2 \, a^{3} b - a^{2} b^{2} - 4 \, a b^{3} - b^{4}\right)} \sin\left(x\right)^{2}}{a^{4} b + 2 \, a^{3} b^{2} + a^{2} b^{3}} + \frac{3 \, {\left(3 \, a b^{3} + b^{4}\right)}}{a^{4} b + 2 \, a^{3} b^{2} + a^{2} b^{3}}\right)} \sin\left(x\right)^{2} + \frac{3 \, {\left(a^{2} b^{2} - 5 \, a b^{3} - 2 \, b^{4}\right)}}{a^{4} b + 2 \, a^{3} b^{2} + a^{2} b^{3}}\right)} \sin\left(x\right)^{2} + \frac{5 \, a b^{3} + 2 \, b^{4}}{a^{4} b + 2 \, a^{3} b^{2} + a^{2} b^{3}}}{6 \, {\left(a \sin\left(x\right)^{4} + b \sin\left(x\right)^{4} - 2 \, b \sin\left(x\right)^{2} + b\right)}^{\frac{3}{2}}} - \frac{\log\left({\left| -{\left(\sqrt{a + b} \sin\left(x\right)^{2} - \sqrt{a \sin\left(x\right)^{4} + b \sin\left(x\right)^{4} - 2 \, b \sin\left(x\right)^{2} + b}\right)} \sqrt{a + b} + b \right|}\right)}{2 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \sqrt{a + b}}"," ",0,"-1/6*((2*((2*a^3*b - a^2*b^2 - 4*a*b^3 - b^4)*sin(x)^2/(a^4*b + 2*a^3*b^2 + a^2*b^3) + 3*(3*a*b^3 + b^4)/(a^4*b + 2*a^3*b^2 + a^2*b^3))*sin(x)^2 + 3*(a^2*b^2 - 5*a*b^3 - 2*b^4)/(a^4*b + 2*a^3*b^2 + a^2*b^3))*sin(x)^2 + (5*a*b^3 + 2*b^4)/(a^4*b + 2*a^3*b^2 + a^2*b^3))/(a*sin(x)^4 + b*sin(x)^4 - 2*b*sin(x)^2 + b)^(3/2) - 1/2*log(abs(-(sqrt(a + b)*sin(x)^2 - sqrt(a*sin(x)^4 + b*sin(x)^4 - 2*b*sin(x)^2 + b))*sqrt(a + b) + b))/((a^2 + 2*a*b + b^2)*sqrt(a + b))","B",0
