1,1,351,0,0.393769," ","integrate((a+b*csc(d*x+c)^2)^4,x, algorithm=""giac"")","\frac{15 \, b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 336 \, a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 147 \, b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 3360 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2800 \, a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 735 \, b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 13440 \, {\left(d x + c\right)} a^{4} + 26880 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 30240 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 16800 \, a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3675 \, b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{26880 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 30240 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 16800 \, a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 3675 \, b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 3360 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 2800 \, a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 735 \, b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 336 \, a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 147 \, b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 15 \, b^{4}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7}}}{13440 \, d}"," ",0,"1/13440*(15*b^4*tan(1/2*d*x + 1/2*c)^7 + 336*a*b^3*tan(1/2*d*x + 1/2*c)^5 + 147*b^4*tan(1/2*d*x + 1/2*c)^5 + 3360*a^2*b^2*tan(1/2*d*x + 1/2*c)^3 + 2800*a*b^3*tan(1/2*d*x + 1/2*c)^3 + 735*b^4*tan(1/2*d*x + 1/2*c)^3 + 13440*(d*x + c)*a^4 + 26880*a^3*b*tan(1/2*d*x + 1/2*c) + 30240*a^2*b^2*tan(1/2*d*x + 1/2*c) + 16800*a*b^3*tan(1/2*d*x + 1/2*c) + 3675*b^4*tan(1/2*d*x + 1/2*c) - (26880*a^3*b*tan(1/2*d*x + 1/2*c)^6 + 30240*a^2*b^2*tan(1/2*d*x + 1/2*c)^6 + 16800*a*b^3*tan(1/2*d*x + 1/2*c)^6 + 3675*b^4*tan(1/2*d*x + 1/2*c)^6 + 3360*a^2*b^2*tan(1/2*d*x + 1/2*c)^4 + 2800*a*b^3*tan(1/2*d*x + 1/2*c)^4 + 735*b^4*tan(1/2*d*x + 1/2*c)^4 + 336*a*b^3*tan(1/2*d*x + 1/2*c)^2 + 147*b^4*tan(1/2*d*x + 1/2*c)^2 + 15*b^4)/tan(1/2*d*x + 1/2*c)^7)/d","B",0
2,1,211,0,0.362677," ","integrate((a+b*csc(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} + 25 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 480 \, {\left(d x + c\right)} a^{3} + 720 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 540 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 150 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{720 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 540 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 150 \, 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} + 25 \, 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 + 25*b^3*tan(1/2*d*x + 1/2*c)^3 + 480*(d*x + c)*a^3 + 720*a^2*b*tan(1/2*d*x + 1/2*c) + 540*a*b^2*tan(1/2*d*x + 1/2*c) + 150*b^3*tan(1/2*d*x + 1/2*c) - (720*a^2*b*tan(1/2*d*x + 1/2*c)^4 + 540*a*b^2*tan(1/2*d*x + 1/2*c)^4 + 150*b^3*tan(1/2*d*x + 1/2*c)^4 + 60*a*b^2*tan(1/2*d*x + 1/2*c)^2 + 25*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
3,1,106,0,0.517099," ","integrate((a+b*csc(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 \, {\left(d x + c\right)} a^{2} + 24 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 9 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{24 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 9 \, 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*(d*x + c)*a^2 + 24*a*b*tan(1/2*d*x + 1/2*c) + 9*b^2*tan(1/2*d*x + 1/2*c) - (24*a*b*tan(1/2*d*x + 1/2*c)^2 + 9*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
4,1,18,0,0.697643," ","integrate(a+b*csc(d*x+c)^2,x, algorithm=""giac"")","a x - \frac{b}{d \tan\left(d x + c\right)}"," ",0,"a*x - b/(d*tan(d*x + c))","A",0
5,1,81,0,0.585436," ","integrate(1/(a+b*csc(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(2 \, a + 2 \, b\right) + \arctan\left(\frac{a \tan\left(d x + c\right) + b \tan\left(d x + c\right)}{\sqrt{a b + b^{2}}}\right)\right)} b}{\sqrt{a b + b^{2}} a} - \frac{d x + c}{a}}{d}"," ",0,"-((pi*floor((d*x + c)/pi + 1/2)*sgn(2*a + 2*b) + arctan((a*tan(d*x + c) + b*tan(d*x + c))/sqrt(a*b + b^2)))*b/(sqrt(a*b + b^2)*a) - (d*x + c)/a)/d","B",0
6,1,140,0,0.343420," ","integrate(1/(a+b*csc(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(2 \, a + 2 \, b\right) + \arctan\left(\frac{a \tan\left(d x + c\right) + b \tan\left(d x + c\right)}{\sqrt{a b + b^{2}}}\right)\right)} {\left(3 \, a b + 2 \, b^{2}\right)}}{{\left(a^{3} + a^{2} b\right)} \sqrt{a b + b^{2}}} - \frac{b \tan\left(d x + c\right)}{{\left(a \tan\left(d x + c\right)^{2} + b \tan\left(d x + c\right)^{2} + b\right)} {\left(a^{2} + a b\right)}} - \frac{2 \, {\left(d x + c\right)}}{a^{2}}}{2 \, d}"," ",0,"-1/2*((pi*floor((d*x + c)/pi + 1/2)*sgn(2*a + 2*b) + arctan((a*tan(d*x + c) + b*tan(d*x + c))/sqrt(a*b + b^2)))*(3*a*b + 2*b^2)/((a^3 + a^2*b)*sqrt(a*b + b^2)) - b*tan(d*x + c)/((a*tan(d*x + c)^2 + b*tan(d*x + c)^2 + b)*(a^2 + a*b)) - 2*(d*x + c)/a^2)/d","A",0
7,1,224,0,0.960075," ","integrate(1/(a+b*csc(d*x+c)^2)^3,x, algorithm=""giac"")","-\frac{\frac{{\left(15 \, a^{2} b + 20 \, a b^{2} + 8 \, b^{3}\right)} {\left(\pi \left \lfloor \frac{d x + c}{\pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(2 \, a + 2 \, b\right) + \arctan\left(\frac{a \tan\left(d x + c\right) + b \tan\left(d x + c\right)}{\sqrt{a b + b^{2}}}\right)\right)}}{{\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \sqrt{a b + b^{2}}} - \frac{9 \, a^{2} b \tan\left(d x + c\right)^{3} + 13 \, a b^{2} \tan\left(d x + c\right)^{3} + 4 \, b^{3} \tan\left(d x + c\right)^{3} + 7 \, a b^{2} \tan\left(d x + c\right) + 4 \, 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 \tan\left(d x + c\right)^{2} + b\right)}^{2}} - \frac{8 \, {\left(d x + c\right)}}{a^{3}}}{8 \, d}"," ",0,"-1/8*((15*a^2*b + 20*a*b^2 + 8*b^3)*(pi*floor((d*x + c)/pi + 1/2)*sgn(2*a + 2*b) + arctan((a*tan(d*x + c) + b*tan(d*x + c))/sqrt(a*b + b^2)))/((a^5 + 2*a^4*b + a^3*b^2)*sqrt(a*b + b^2)) - (9*a^2*b*tan(d*x + c)^3 + 13*a*b^2*tan(d*x + c)^3 + 4*b^3*tan(d*x + c)^3 + 7*a*b^2*tan(d*x + c) + 4*b^3*tan(d*x + c))/((a^4 + 2*a^3*b + a^2*b^2)*(a*tan(d*x + c)^2 + b*tan(d*x + c)^2 + b)^2) - 8*(d*x + c)/a^3)/d","A",0
8,1,354,0,0.743314," ","integrate(1/(a+b*csc(d*x+c)^2)^4,x, algorithm=""giac"")","-\frac{\frac{3 \, {\left(35 \, a^{3} b + 70 \, a^{2} b^{2} + 56 \, a b^{3} + 16 \, b^{4}\right)} {\left(\pi \left \lfloor \frac{d x + c}{\pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(2 \, a + 2 \, b\right) + \arctan\left(\frac{a \tan\left(d x + c\right) + b \tan\left(d x + c\right)}{\sqrt{a b + b^{2}}}\right)\right)}}{{\left(a^{7} + 3 \, a^{6} b + 3 \, a^{5} b^{2} + a^{4} b^{3}\right)} \sqrt{a b + b^{2}}} - \frac{87 \, a^{4} b \tan\left(d x + c\right)^{5} + 252 \, a^{3} b^{2} \tan\left(d x + c\right)^{5} + 267 \, a^{2} b^{3} \tan\left(d x + c\right)^{5} + 126 \, a b^{4} \tan\left(d x + c\right)^{5} + 24 \, b^{5} \tan\left(d x + c\right)^{5} + 136 \, a^{3} b^{2} \tan\left(d x + c\right)^{3} + 280 \, a^{2} b^{3} \tan\left(d x + c\right)^{3} + 192 \, a b^{4} \tan\left(d x + c\right)^{3} + 48 \, b^{5} \tan\left(d x + c\right)^{3} + 57 \, a^{2} b^{3} \tan\left(d x + c\right) + 66 \, a b^{4} \tan\left(d x + c\right) + 24 \, b^{5} \tan\left(d x + c\right)}{{\left(a^{6} + 3 \, a^{5} b + 3 \, a^{4} b^{2} + a^{3} b^{3}\right)} {\left(a \tan\left(d x + c\right)^{2} + b \tan\left(d x + c\right)^{2} + b\right)}^{3}} - \frac{48 \, {\left(d x + c\right)}}{a^{4}}}{48 \, d}"," ",0,"-1/48*(3*(35*a^3*b + 70*a^2*b^2 + 56*a*b^3 + 16*b^4)*(pi*floor((d*x + c)/pi + 1/2)*sgn(2*a + 2*b) + arctan((a*tan(d*x + c) + b*tan(d*x + c))/sqrt(a*b + b^2)))/((a^7 + 3*a^6*b + 3*a^5*b^2 + a^4*b^3)*sqrt(a*b + b^2)) - (87*a^4*b*tan(d*x + c)^5 + 252*a^3*b^2*tan(d*x + c)^5 + 267*a^2*b^3*tan(d*x + c)^5 + 126*a*b^4*tan(d*x + c)^5 + 24*b^5*tan(d*x + c)^5 + 136*a^3*b^2*tan(d*x + c)^3 + 280*a^2*b^3*tan(d*x + c)^3 + 192*a*b^4*tan(d*x + c)^3 + 48*b^5*tan(d*x + c)^3 + 57*a^2*b^3*tan(d*x + c) + 66*a*b^4*tan(d*x + c) + 24*b^5*tan(d*x + c))/((a^6 + 3*a^5*b + 3*a^4*b^2 + a^3*b^3)*(a*tan(d*x + c)^2 + b*tan(d*x + c)^2 + b)^3) - 48*(d*x + c)/a^4)/d","A",0
9,-2,0,0,0.000000," ","integrate((a+b*csc(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))]Evaluation time: 0.76Error: Bad Argument Type","F(-2)",0
10,-2,0,0,0.000000," ","integrate((a+b*csc(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))]Error: Bad Argument Type","F(-2)",0
11,-2,0,0,0.000000," ","integrate((a+b*csc(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))]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, 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=[97]Evaluation time: 70.94Conj Error: Bad Argument Type","F(-2)",0
12,-2,0,0,0.000000," ","integrate(1/(a+b*csc(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=[-77]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=[82]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=[15]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=[-24]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=[16]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=[-59]Evaluation time: 0.66index.cc index_m operator + Error: Bad Argument Value","F(-2)",0
13,-2,0,0,0.000000," ","integrate(1/(a+b*csc(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*t_nostep+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=[15]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=[-24]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=[16]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=[-59]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=[80]Evaluation time: 0.78index.cc index_m operator + Error: Bad Argument Value","F(-2)",0
14,-2,0,0,0.000000," ","integrate(1/(a+b*csc(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*t_nostep+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=[15]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=[-24]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=[16]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=[-59]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=[80]Evaluation time: 0.96index.cc index_m operator + Error: Bad Argument Value","F(-2)",0
15,-2,0,0,0.000000," ","integrate(1/(a+b*csc(d*x+c)^2)^(7/2),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*t_nostep+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=[15]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=[-24]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=[16]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=[-59]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=[80]Evaluation time: 1.23index.cc index_m operator + Error: Bad Argument Value","F(-2)",0
16,1,232,0,0.477209," ","integrate((1+csc(x)^2)^(3/2),x, algorithm=""giac"")","2 \, \arctan\left(-\frac{1}{2} \, \tan\left(\frac{1}{2} \, x\right)^{2} + \frac{1}{2} \, \sqrt{\tan\left(\frac{1}{2} \, x\right)^{4} + 6 \, \tan\left(\frac{1}{2} \, x\right)^{2} + 1} - \frac{1}{2}\right) \mathrm{sgn}\left(\sin\left(x\right)\right) - \log\left(\tan\left(\frac{1}{2} \, x\right)^{2} - \sqrt{\tan\left(\frac{1}{2} \, x\right)^{4} + 6 \, \tan\left(\frac{1}{2} \, x\right)^{2} + 1} + 3\right) \mathrm{sgn}\left(\sin\left(x\right)\right) - \log\left(-\tan\left(\frac{1}{2} \, x\right)^{2} + \sqrt{\tan\left(\frac{1}{2} \, x\right)^{4} + 6 \, \tan\left(\frac{1}{2} \, x\right)^{2} + 1} + 1\right) \mathrm{sgn}\left(\sin\left(x\right)\right) + \log\left(-\tan\left(\frac{1}{2} \, x\right)^{2} + \sqrt{\tan\left(\frac{1}{2} \, x\right)^{4} + 6 \, \tan\left(\frac{1}{2} \, x\right)^{2} + 1} - 1\right) \mathrm{sgn}\left(\sin\left(x\right)\right) + \frac{1}{8} \, \sqrt{\tan\left(\frac{1}{2} \, x\right)^{4} + 6 \, \tan\left(\frac{1}{2} \, x\right)^{2} + 1} \mathrm{sgn}\left(\sin\left(x\right)\right) + \frac{3 \, {\left(\tan\left(\frac{1}{2} \, x\right)^{2} - \sqrt{\tan\left(\frac{1}{2} \, x\right)^{4} + 6 \, \tan\left(\frac{1}{2} \, x\right)^{2} + 1}\right)} \mathrm{sgn}\left(\sin\left(x\right)\right) + \mathrm{sgn}\left(\sin\left(x\right)\right)}{4 \, {\left({\left(\tan\left(\frac{1}{2} \, x\right)^{2} - \sqrt{\tan\left(\frac{1}{2} \, x\right)^{4} + 6 \, \tan\left(\frac{1}{2} \, x\right)^{2} + 1}\right)}^{2} - 1\right)}}"," ",0,"2*arctan(-1/2*tan(1/2*x)^2 + 1/2*sqrt(tan(1/2*x)^4 + 6*tan(1/2*x)^2 + 1) - 1/2)*sgn(sin(x)) - log(tan(1/2*x)^2 - sqrt(tan(1/2*x)^4 + 6*tan(1/2*x)^2 + 1) + 3)*sgn(sin(x)) - log(-tan(1/2*x)^2 + sqrt(tan(1/2*x)^4 + 6*tan(1/2*x)^2 + 1) + 1)*sgn(sin(x)) + log(-tan(1/2*x)^2 + sqrt(tan(1/2*x)^4 + 6*tan(1/2*x)^2 + 1) - 1)*sgn(sin(x)) + 1/8*sqrt(tan(1/2*x)^4 + 6*tan(1/2*x)^2 + 1)*sgn(sin(x)) + 1/4*(3*(tan(1/2*x)^2 - sqrt(tan(1/2*x)^4 + 6*tan(1/2*x)^2 + 1))*sgn(sin(x)) + sgn(sin(x)))/((tan(1/2*x)^2 - sqrt(tan(1/2*x)^4 + 6*tan(1/2*x)^2 + 1))^2 - 1)","B",0
17,1,130,0,0.424346," ","integrate((1+csc(x)^2)^(1/2),x, algorithm=""giac"")","\frac{1}{2} \, {\left(4 \, \arctan\left(-\frac{1}{2} \, \tan\left(\frac{1}{2} \, x\right)^{2} + \frac{1}{2} \, \sqrt{\tan\left(\frac{1}{2} \, x\right)^{4} + 6 \, \tan\left(\frac{1}{2} \, x\right)^{2} + 1} - \frac{1}{2}\right) - \log\left(\tan\left(\frac{1}{2} \, x\right)^{2} - \sqrt{\tan\left(\frac{1}{2} \, x\right)^{4} + 6 \, \tan\left(\frac{1}{2} \, x\right)^{2} + 1} + 3\right) - \log\left(-\tan\left(\frac{1}{2} \, x\right)^{2} + \sqrt{\tan\left(\frac{1}{2} \, x\right)^{4} + 6 \, \tan\left(\frac{1}{2} \, x\right)^{2} + 1} + 1\right) + \log\left(-\tan\left(\frac{1}{2} \, x\right)^{2} + \sqrt{\tan\left(\frac{1}{2} \, x\right)^{4} + 6 \, \tan\left(\frac{1}{2} \, x\right)^{2} + 1} - 1\right)\right)} \mathrm{sgn}\left(\sin\left(x\right)\right)"," ",0,"1/2*(4*arctan(-1/2*tan(1/2*x)^2 + 1/2*sqrt(tan(1/2*x)^4 + 6*tan(1/2*x)^2 + 1) - 1/2) - log(tan(1/2*x)^2 - sqrt(tan(1/2*x)^4 + 6*tan(1/2*x)^2 + 1) + 3) - log(-tan(1/2*x)^2 + sqrt(tan(1/2*x)^4 + 6*tan(1/2*x)^2 + 1) + 1) + log(-tan(1/2*x)^2 + sqrt(tan(1/2*x)^4 + 6*tan(1/2*x)^2 + 1) - 1))*sgn(sin(x))","B",0
18,1,33,0,0.618657," ","integrate(1/(1+csc(x)^2)^(1/2),x, algorithm=""giac"")","2 \, \arctan\left(-\frac{1}{2} \, \tan\left(\frac{1}{2} \, x\right)^{2} + \frac{1}{2} \, \sqrt{\tan\left(\frac{1}{2} \, x\right)^{4} + 6 \, \tan\left(\frac{1}{2} \, x\right)^{2} + 1} - \frac{1}{2}\right)"," ",0,"2*arctan(-1/2*tan(1/2*x)^2 + 1/2*sqrt(tan(1/2*x)^4 + 6*tan(1/2*x)^2 + 1) - 1/2)","B",0
19,1,47,0,0.414792," ","integrate((1-csc(x)^2)^(3/2),x, algorithm=""giac"")","\frac{1}{8} i \, \tan\left(\frac{1}{2} \, x\right)^{2} - \frac{4 i \, \tan\left(\frac{1}{2} \, x\right)^{2} - i}{8 \, \tan\left(\frac{1}{2} \, x\right)^{2}} - i \, \log\left(\tan\left(\frac{1}{2} \, x\right)^{2} + 1\right) + \frac{1}{2} i \, \log\left(\tan\left(\frac{1}{2} \, x\right)^{2}\right)"," ",0,"1/8*I*tan(1/2*x)^2 - 1/8*(4*I*tan(1/2*x)^2 - I)/tan(1/2*x)^2 - I*log(tan(1/2*x)^2 + 1) + 1/2*I*log(tan(1/2*x)^2)","C",0
20,1,48,0,1.259246," ","integrate((1-csc(x)^2)^(1/2),x, algorithm=""giac"")","-\frac{1}{2} \, {\left(2 i \, \log\left(\tan\left(\frac{1}{2} \, x\right)^{2} + 1\right) \mathrm{sgn}\left(-\tan\left(\frac{1}{2} \, x\right)^{4} + 1\right) - i \, \log\left(\tan\left(\frac{1}{2} \, x\right)^{2}\right) \mathrm{sgn}\left(-\tan\left(\frac{1}{2} \, x\right)^{4} + 1\right)\right)} \mathrm{sgn}\left(\sin\left(x\right)\right)"," ",0,"-1/2*(2*I*log(tan(1/2*x)^2 + 1)*sgn(-tan(1/2*x)^4 + 1) - I*log(tan(1/2*x)^2)*sgn(-tan(1/2*x)^4 + 1))*sgn(sin(x))","C",0
21,1,24,0,0.640495," ","integrate(1/(1-csc(x)^2)^(1/2),x, algorithm=""giac"")","-i \, \log\left(\tan\left(\frac{1}{2} \, x\right)^{2} + 1\right) + i \, \log\left({\left| \tan\left(\frac{1}{2} \, x\right)^{2} - 1 \right|}\right)"," ",0,"-I*log(tan(1/2*x)^2 + 1) + I*log(abs(tan(1/2*x)^2 - 1))","C",0
22,1,47,0,0.385493," ","integrate((-1+csc(x)^2)^(3/2),x, algorithm=""giac"")","\frac{1}{8} \, \tan\left(\frac{1}{2} \, x\right)^{2} - \frac{4 \, \tan\left(\frac{1}{2} \, x\right)^{2} - 1}{8 \, \tan\left(\frac{1}{2} \, x\right)^{2}} - \log\left(\tan\left(\frac{1}{2} \, x\right)^{2} + 1\right) + \frac{1}{2} \, \log\left(\tan\left(\frac{1}{2} \, x\right)^{2}\right)"," ",0,"1/8*tan(1/2*x)^2 - 1/8*(4*tan(1/2*x)^2 - 1)/tan(1/2*x)^2 - log(tan(1/2*x)^2 + 1) + 1/2*log(tan(1/2*x)^2)","A",0
23,1,44,0,0.575784," ","integrate((-1+csc(x)^2)^(1/2),x, algorithm=""giac"")","\frac{1}{2} \, {\left(2 \, \log\left(\tan\left(\frac{1}{2} \, x\right)^{2} + 1\right) \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, x\right)^{4} - 1\right) - \log\left(\tan\left(\frac{1}{2} \, x\right)^{2}\right) \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, x\right)^{4} - 1\right)\right)} \mathrm{sgn}\left(\sin\left(x\right)\right)"," ",0,"1/2*(2*log(tan(1/2*x)^2 + 1)*sgn(tan(1/2*x)^4 - 1) - log(tan(1/2*x)^2)*sgn(tan(1/2*x)^4 - 1))*sgn(sin(x))","B",0
24,1,22,0,0.764518," ","integrate(1/(-1+csc(x)^2)^(1/2),x, algorithm=""giac"")","-\log\left(\tan\left(\frac{1}{2} \, x\right)^{2} + 1\right) + \log\left({\left| \tan\left(\frac{1}{2} \, x\right)^{2} - 1 \right|}\right)"," ",0,"-log(tan(1/2*x)^2 + 1) + log(abs(tan(1/2*x)^2 - 1))","A",0
25,0,0,0,0.000000," ","integrate((-1-csc(x)^2)^(3/2),x, algorithm=""giac"")","\int {\left(-\csc\left(x\right)^{2} - 1\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((-csc(x)^2 - 1)^(3/2), x)","F",0
26,-2,0,0,0.000000," ","integrate((-1-csc(x)^2)^(1/2),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: i/2*(2*(2*atan(1/2*(-tan(1/2*x)^2+sqrt(tan(1/2*x)^4+6*tan(1/2*x)^2+1)-1))-1/2*ln(-tan(1/2*x)^2+sqrt(tan(1/2*x)^4+6*tan(1/2*x)^2+1)+1)+1/2*ln(-tan(1/2*x)^2+sqrt(tan(1/2*x)^4+6*tan(1/2*x)^2+1)-1)-1/2*ln(-tan(1/2*x)^2+sqrt(tan(1/2*x)^4+6*tan(1/2*x)^2+1)-3))-4*atan(i)+ln(2+2*i)+ln(-2+2*i)-ln(2*i))*sign(sin(x))","F(-2)",0
27,0,0,0,0.000000," ","integrate(1/(-1-csc(x)^2)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{-\csc\left(x\right)^{2} - 1}}\,{d x}"," ",0,"integrate(1/sqrt(-csc(x)^2 - 1), x)","F",0
