1,1,110,0,3.139228," ","integrate(sin(b*x+a)*sin(2*b*x+2*a)^7,x, algorithm=""giac"")","\frac{\sin\left(15 \, b x + 15 \, a\right)}{1920 \, b} - \frac{\sin\left(13 \, b x + 13 \, a\right)}{1664 \, b} - \frac{7 \, \sin\left(11 \, b x + 11 \, a\right)}{1408 \, b} + \frac{7 \, \sin\left(9 \, b x + 9 \, a\right)}{1152 \, b} + \frac{3 \, \sin\left(7 \, b x + 7 \, a\right)}{128 \, b} - \frac{21 \, \sin\left(5 \, b x + 5 \, a\right)}{640 \, b} - \frac{35 \, \sin\left(3 \, b x + 3 \, a\right)}{384 \, b} + \frac{35 \, \sin\left(b x + a\right)}{128 \, b}"," ",0,"1/1920*sin(15*b*x + 15*a)/b - 1/1664*sin(13*b*x + 13*a)/b - 7/1408*sin(11*b*x + 11*a)/b + 7/1152*sin(9*b*x + 9*a)/b + 3/128*sin(7*b*x + 7*a)/b - 21/640*sin(5*b*x + 5*a)/b - 35/384*sin(3*b*x + 3*a)/b + 35/128*sin(b*x + a)/b","B",0
2,1,96,0,1.905972," ","integrate(sin(b*x+a)*sin(2*b*x+2*a)^6,x, algorithm=""giac"")","\frac{\cos\left(13 \, b x + 13 \, a\right)}{832 \, b} - \frac{\cos\left(11 \, b x + 11 \, a\right)}{704 \, b} - \frac{\cos\left(9 \, b x + 9 \, a\right)}{96 \, b} + \frac{3 \, \cos\left(7 \, b x + 7 \, a\right)}{224 \, b} + \frac{3 \, \cos\left(5 \, b x + 5 \, a\right)}{64 \, b} - \frac{5 \, \cos\left(3 \, b x + 3 \, a\right)}{64 \, b} - \frac{5 \, \cos\left(b x + a\right)}{16 \, b}"," ",0,"1/832*cos(13*b*x + 13*a)/b - 1/704*cos(11*b*x + 11*a)/b - 1/96*cos(9*b*x + 9*a)/b + 3/224*cos(7*b*x + 7*a)/b + 3/64*cos(5*b*x + 5*a)/b - 5/64*cos(3*b*x + 3*a)/b - 5/16*cos(b*x + a)/b","A",0
3,1,82,0,0.709103," ","integrate(sin(b*x+a)*sin(2*b*x+2*a)^5,x, algorithm=""giac"")","-\frac{\sin\left(11 \, b x + 11 \, a\right)}{352 \, b} + \frac{\sin\left(9 \, b x + 9 \, a\right)}{288 \, b} + \frac{5 \, \sin\left(7 \, b x + 7 \, a\right)}{224 \, b} - \frac{\sin\left(5 \, b x + 5 \, a\right)}{32 \, b} - \frac{5 \, \sin\left(3 \, b x + 3 \, a\right)}{48 \, b} + \frac{5 \, \sin\left(b x + a\right)}{16 \, b}"," ",0,"-1/352*sin(11*b*x + 11*a)/b + 1/288*sin(9*b*x + 9*a)/b + 5/224*sin(7*b*x + 7*a)/b - 1/32*sin(5*b*x + 5*a)/b - 5/48*sin(3*b*x + 3*a)/b + 5/16*sin(b*x + a)/b","B",0
4,1,68,0,0.449368," ","integrate(sin(b*x+a)*sin(2*b*x+2*a)^4,x, algorithm=""giac"")","-\frac{\cos\left(9 \, b x + 9 \, a\right)}{144 \, b} + \frac{\cos\left(7 \, b x + 7 \, a\right)}{112 \, b} + \frac{\cos\left(5 \, b x + 5 \, a\right)}{20 \, b} - \frac{\cos\left(3 \, b x + 3 \, a\right)}{12 \, b} - \frac{3 \, \cos\left(b x + a\right)}{8 \, b}"," ",0,"-1/144*cos(9*b*x + 9*a)/b + 1/112*cos(7*b*x + 7*a)/b + 1/20*cos(5*b*x + 5*a)/b - 1/12*cos(3*b*x + 3*a)/b - 3/8*cos(b*x + a)/b","A",0
5,1,54,0,0.374250," ","integrate(sin(b*x+a)*sin(2*b*x+2*a)^3,x, algorithm=""giac"")","\frac{\sin\left(7 \, b x + 7 \, a\right)}{56 \, b} - \frac{\sin\left(5 \, b x + 5 \, a\right)}{40 \, b} - \frac{\sin\left(3 \, b x + 3 \, a\right)}{8 \, b} + \frac{3 \, \sin\left(b x + a\right)}{8 \, b}"," ",0,"1/56*sin(7*b*x + 7*a)/b - 1/40*sin(5*b*x + 5*a)/b - 1/8*sin(3*b*x + 3*a)/b + 3/8*sin(b*x + a)/b","A",0
6,1,40,0,0.352695," ","integrate(sin(b*x+a)*sin(2*b*x+2*a)^2,x, algorithm=""giac"")","\frac{\cos\left(5 \, b x + 5 \, a\right)}{20 \, b} - \frac{\cos\left(3 \, b x + 3 \, a\right)}{12 \, b} - \frac{\cos\left(b x + a\right)}{2 \, b}"," ",0,"1/20*cos(5*b*x + 5*a)/b - 1/12*cos(3*b*x + 3*a)/b - 1/2*cos(b*x + a)/b","A",0
7,1,26,0,0.320819," ","integrate(sin(b*x+a)*sin(2*b*x+2*a),x, algorithm=""giac"")","-\frac{\sin\left(3 \, b x + 3 \, a\right)}{6 \, b} + \frac{\sin\left(b x + a\right)}{2 \, b}"," ",0,"-1/6*sin(3*b*x + 3*a)/b + 1/2*sin(b*x + a)/b","A",0
8,1,174,0,0.801334," ","integrate(csc(2*b*x+2*a)*sin(b*x+a),x, algorithm=""giac"")","\frac{\log\left({\left| \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{3} + 3 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{2} - \tan\left(\frac{1}{2} \, a\right)^{3} - 3 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right) + 3 \, \tan\left(\frac{1}{2} \, a\right)^{2} - \tan\left(\frac{1}{2} \, b x + 2 \, a\right) + 3 \, \tan\left(\frac{1}{2} \, a\right) - 1 \right|}\right) - \log\left({\left| \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{3} - 3 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{2} + \tan\left(\frac{1}{2} \, a\right)^{3} - 3 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right) + 3 \, \tan\left(\frac{1}{2} \, a\right)^{2} + \tan\left(\frac{1}{2} \, b x + 2 \, a\right) - 3 \, \tan\left(\frac{1}{2} \, a\right) - 1 \right|}\right)}{2 \, b}"," ",0,"1/2*(log(abs(tan(1/2*b*x + 2*a)*tan(1/2*a)^3 + 3*tan(1/2*b*x + 2*a)*tan(1/2*a)^2 - tan(1/2*a)^3 - 3*tan(1/2*b*x + 2*a)*tan(1/2*a) + 3*tan(1/2*a)^2 - tan(1/2*b*x + 2*a) + 3*tan(1/2*a) - 1)) - log(abs(tan(1/2*b*x + 2*a)*tan(1/2*a)^3 - 3*tan(1/2*b*x + 2*a)*tan(1/2*a)^2 + tan(1/2*a)^3 - 3*tan(1/2*b*x + 2*a)*tan(1/2*a) + 3*tan(1/2*a)^2 + tan(1/2*b*x + 2*a) - 3*tan(1/2*a) - 1)))/b","B",0
9,1,412,0,2.370837," ","integrate(csc(2*b*x+2*a)^2*sin(b*x+a),x, algorithm=""giac"")","-\frac{\frac{2 \, {\left(6 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{11} - \tan\left(\frac{1}{2} \, a\right)^{12} - 2 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{9} + 12 \, \tan\left(\frac{1}{2} \, a\right)^{10} - 36 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{7} + 27 \, \tan\left(\frac{1}{2} \, a\right)^{8} - 36 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{5} - 2 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{3} - 27 \, \tan\left(\frac{1}{2} \, a\right)^{4} + 6 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right) - 12 \, \tan\left(\frac{1}{2} \, a\right)^{2} + 1\right)}}{{\left(\tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{6} - 15 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{4} + 12 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{5} - \tan\left(\frac{1}{2} \, a\right)^{6} + 15 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} - 40 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{3} + 15 \, \tan\left(\frac{1}{2} \, a\right)^{4} - \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} + 12 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right) - 15 \, \tan\left(\frac{1}{2} \, a\right)^{2} + 1\right)} {\left(\tan\left(\frac{1}{2} \, a\right)^{6} - 15 \, \tan\left(\frac{1}{2} \, a\right)^{4} + 15 \, \tan\left(\frac{1}{2} \, a\right)^{2} - 1\right)}} + \log\left({\left| \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{3} - 3 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right) + 3 \, \tan\left(\frac{1}{2} \, a\right)^{2} - 1 \right|}\right) - \log\left({\left| 3 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{2} - \tan\left(\frac{1}{2} \, a\right)^{3} - \tan\left(\frac{1}{2} \, b x + 2 \, a\right) + 3 \, \tan\left(\frac{1}{2} \, a\right) \right|}\right)}{4 \, b}"," ",0,"-1/4*(2*(6*tan(1/2*b*x + 2*a)*tan(1/2*a)^11 - tan(1/2*a)^12 - 2*tan(1/2*b*x + 2*a)*tan(1/2*a)^9 + 12*tan(1/2*a)^10 - 36*tan(1/2*b*x + 2*a)*tan(1/2*a)^7 + 27*tan(1/2*a)^8 - 36*tan(1/2*b*x + 2*a)*tan(1/2*a)^5 - 2*tan(1/2*b*x + 2*a)*tan(1/2*a)^3 - 27*tan(1/2*a)^4 + 6*tan(1/2*b*x + 2*a)*tan(1/2*a) - 12*tan(1/2*a)^2 + 1)/((tan(1/2*b*x + 2*a)^2*tan(1/2*a)^6 - 15*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^4 + 12*tan(1/2*b*x + 2*a)*tan(1/2*a)^5 - tan(1/2*a)^6 + 15*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^2 - 40*tan(1/2*b*x + 2*a)*tan(1/2*a)^3 + 15*tan(1/2*a)^4 - tan(1/2*b*x + 2*a)^2 + 12*tan(1/2*b*x + 2*a)*tan(1/2*a) - 15*tan(1/2*a)^2 + 1)*(tan(1/2*a)^6 - 15*tan(1/2*a)^4 + 15*tan(1/2*a)^2 - 1)) + log(abs(tan(1/2*b*x + 2*a)*tan(1/2*a)^3 - 3*tan(1/2*b*x + 2*a)*tan(1/2*a) + 3*tan(1/2*a)^2 - 1)) - log(abs(3*tan(1/2*b*x + 2*a)*tan(1/2*a)^2 - tan(1/2*a)^3 - tan(1/2*b*x + 2*a) + 3*tan(1/2*a))))/b","B",0
10,1,1421,0,4.654468," ","integrate(csc(2*b*x+2*a)^3*sin(b*x+a),x, algorithm=""giac"")","-\frac{\frac{\tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{12} - 12 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{10} + 6 \, \tan\left(\frac{1}{2} \, a\right)^{11} - 27 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{8} - 2 \, \tan\left(\frac{1}{2} \, a\right)^{9} - 36 \, \tan\left(\frac{1}{2} \, a\right)^{7} + 27 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{4} - 36 \, \tan\left(\frac{1}{2} \, a\right)^{5} + 12 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, a\right)^{3} - \tan\left(\frac{1}{2} \, b x + 2 \, a\right) + 6 \, \tan\left(\frac{1}{2} \, a\right)}{{\left(3 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{5} - \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{6} - 10 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{3} + 15 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{4} - 3 \, \tan\left(\frac{1}{2} \, a\right)^{5} + 3 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right) - 15 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{2} + 10 \, \tan\left(\frac{1}{2} \, a\right)^{3} + \tan\left(\frac{1}{2} \, b x + 2 \, a\right) - 3 \, \tan\left(\frac{1}{2} \, a\right)\right)} {\left(3 \, \tan\left(\frac{1}{2} \, a\right)^{5} - 10 \, \tan\left(\frac{1}{2} \, a\right)^{3} + 3 \, \tan\left(\frac{1}{2} \, a\right)\right)}} + \frac{2 \, {\left(\tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{24} + 30 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{22} - 6 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{23} + \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{24} - 756 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{20} + 614 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{21} - 114 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{22} + 6 \, \tan\left(\frac{1}{2} \, a\right)^{23} + 2058 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{18} - 4578 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{19} + 1932 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{20} - 182 \, \tan\left(\frac{1}{2} \, a\right)^{21} - 27 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{16} + 6210 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{17} - 7462 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{18} + 1554 \, \tan\left(\frac{1}{2} \, a\right)^{19} - 9396 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{14} + 15588 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{15} - 2331 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{16} - 2178 \, \tan\left(\frac{1}{2} \, a\right)^{17} - 21924 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{13} + 26028 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{14} - 5668 \, \tan\left(\frac{1}{2} \, a\right)^{15} + 9396 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{10} - 21924 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{11} + 6468 \, \tan\left(\frac{1}{2} \, a\right)^{13} + 27 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{8} + 15588 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{9} - 26028 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{10} + 6468 \, \tan\left(\frac{1}{2} \, a\right)^{11} - 2058 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{6} + 6210 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{7} + 2331 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{8} - 5668 \, \tan\left(\frac{1}{2} \, a\right)^{9} + 756 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{4} - 4578 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{5} + 7462 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{6} - 2178 \, \tan\left(\frac{1}{2} \, a\right)^{7} - 30 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{2} + 614 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{3} - 1932 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{4} + 1554 \, \tan\left(\frac{1}{2} \, a\right)^{5} - \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} - 6 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right) + 114 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{2} - 182 \, \tan\left(\frac{1}{2} \, a\right)^{3} - \tan\left(\frac{1}{2} \, b x + 2 \, a\right) + 6 \, \tan\left(\frac{1}{2} \, a\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, a\right)^{12} - 30 \, \tan\left(\frac{1}{2} \, a\right)^{10} + 255 \, \tan\left(\frac{1}{2} \, a\right)^{8} - 452 \, \tan\left(\frac{1}{2} \, a\right)^{6} + 255 \, \tan\left(\frac{1}{2} \, a\right)^{4} - 30 \, \tan\left(\frac{1}{2} \, a\right)^{2} + 1\right)} {\left(\tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{6} - 15 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{4} + 12 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{5} - \tan\left(\frac{1}{2} \, a\right)^{6} + 15 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} - 40 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{3} + 15 \, \tan\left(\frac{1}{2} \, a\right)^{4} - \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} + 12 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right) - 15 \, \tan\left(\frac{1}{2} \, a\right)^{2} + 1\right)}^{2}} - 3 \, \log\left({\left| \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{3} + 3 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{2} - \tan\left(\frac{1}{2} \, a\right)^{3} - 3 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right) + 3 \, \tan\left(\frac{1}{2} \, a\right)^{2} - \tan\left(\frac{1}{2} \, b x + 2 \, a\right) + 3 \, \tan\left(\frac{1}{2} \, a\right) - 1 \right|}\right) + 3 \, \log\left({\left| \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{3} - 3 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{2} + \tan\left(\frac{1}{2} \, a\right)^{3} - 3 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right) + 3 \, \tan\left(\frac{1}{2} \, a\right)^{2} + \tan\left(\frac{1}{2} \, b x + 2 \, a\right) - 3 \, \tan\left(\frac{1}{2} \, a\right) - 1 \right|}\right)}{16 \, b}"," ",0,"-1/16*((tan(1/2*b*x + 2*a)*tan(1/2*a)^12 - 12*tan(1/2*b*x + 2*a)*tan(1/2*a)^10 + 6*tan(1/2*a)^11 - 27*tan(1/2*b*x + 2*a)*tan(1/2*a)^8 - 2*tan(1/2*a)^9 - 36*tan(1/2*a)^7 + 27*tan(1/2*b*x + 2*a)*tan(1/2*a)^4 - 36*tan(1/2*a)^5 + 12*tan(1/2*b*x + 2*a)*tan(1/2*a)^2 - 2*tan(1/2*a)^3 - tan(1/2*b*x + 2*a) + 6*tan(1/2*a))/((3*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^5 - tan(1/2*b*x + 2*a)*tan(1/2*a)^6 - 10*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^3 + 15*tan(1/2*b*x + 2*a)*tan(1/2*a)^4 - 3*tan(1/2*a)^5 + 3*tan(1/2*b*x + 2*a)^2*tan(1/2*a) - 15*tan(1/2*b*x + 2*a)*tan(1/2*a)^2 + 10*tan(1/2*a)^3 + tan(1/2*b*x + 2*a) - 3*tan(1/2*a))*(3*tan(1/2*a)^5 - 10*tan(1/2*a)^3 + 3*tan(1/2*a))) + 2*(tan(1/2*b*x + 2*a)^3*tan(1/2*a)^24 + 30*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^22 - 6*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^23 + tan(1/2*b*x + 2*a)*tan(1/2*a)^24 - 756*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^20 + 614*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^21 - 114*tan(1/2*b*x + 2*a)*tan(1/2*a)^22 + 6*tan(1/2*a)^23 + 2058*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^18 - 4578*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^19 + 1932*tan(1/2*b*x + 2*a)*tan(1/2*a)^20 - 182*tan(1/2*a)^21 - 27*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^16 + 6210*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^17 - 7462*tan(1/2*b*x + 2*a)*tan(1/2*a)^18 + 1554*tan(1/2*a)^19 - 9396*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^14 + 15588*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^15 - 2331*tan(1/2*b*x + 2*a)*tan(1/2*a)^16 - 2178*tan(1/2*a)^17 - 21924*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^13 + 26028*tan(1/2*b*x + 2*a)*tan(1/2*a)^14 - 5668*tan(1/2*a)^15 + 9396*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^10 - 21924*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^11 + 6468*tan(1/2*a)^13 + 27*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^8 + 15588*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^9 - 26028*tan(1/2*b*x + 2*a)*tan(1/2*a)^10 + 6468*tan(1/2*a)^11 - 2058*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^6 + 6210*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^7 + 2331*tan(1/2*b*x + 2*a)*tan(1/2*a)^8 - 5668*tan(1/2*a)^9 + 756*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^4 - 4578*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^5 + 7462*tan(1/2*b*x + 2*a)*tan(1/2*a)^6 - 2178*tan(1/2*a)^7 - 30*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^2 + 614*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^3 - 1932*tan(1/2*b*x + 2*a)*tan(1/2*a)^4 + 1554*tan(1/2*a)^5 - tan(1/2*b*x + 2*a)^3 - 6*tan(1/2*b*x + 2*a)^2*tan(1/2*a) + 114*tan(1/2*b*x + 2*a)*tan(1/2*a)^2 - 182*tan(1/2*a)^3 - tan(1/2*b*x + 2*a) + 6*tan(1/2*a))/((tan(1/2*a)^12 - 30*tan(1/2*a)^10 + 255*tan(1/2*a)^8 - 452*tan(1/2*a)^6 + 255*tan(1/2*a)^4 - 30*tan(1/2*a)^2 + 1)*(tan(1/2*b*x + 2*a)^2*tan(1/2*a)^6 - 15*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^4 + 12*tan(1/2*b*x + 2*a)*tan(1/2*a)^5 - tan(1/2*a)^6 + 15*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^2 - 40*tan(1/2*b*x + 2*a)*tan(1/2*a)^3 + 15*tan(1/2*a)^4 - tan(1/2*b*x + 2*a)^2 + 12*tan(1/2*b*x + 2*a)*tan(1/2*a) - 15*tan(1/2*a)^2 + 1)^2) - 3*log(abs(tan(1/2*b*x + 2*a)*tan(1/2*a)^3 + 3*tan(1/2*b*x + 2*a)*tan(1/2*a)^2 - tan(1/2*a)^3 - 3*tan(1/2*b*x + 2*a)*tan(1/2*a) + 3*tan(1/2*a)^2 - tan(1/2*b*x + 2*a) + 3*tan(1/2*a) - 1)) + 3*log(abs(tan(1/2*b*x + 2*a)*tan(1/2*a)^3 - 3*tan(1/2*b*x + 2*a)*tan(1/2*a)^2 + tan(1/2*a)^3 - 3*tan(1/2*b*x + 2*a)*tan(1/2*a) + 3*tan(1/2*a)^2 + tan(1/2*b*x + 2*a) - 3*tan(1/2*a) - 1)))/b","B",0
11,1,3028,0,8.638808," ","integrate(csc(2*b*x+2*a)^4*sin(b*x+a),x, algorithm=""giac"")","-\frac{\frac{3 \, {\left(6 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{23} - \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{24} - 74 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{21} + 60 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{22} - 6 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{23} + 798 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{19} - 924 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{20} + 290 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{21} - 18 \, \tan\left(\frac{1}{2} \, a\right)^{22} - 1170 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{17} + 3892 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{18} - 2310 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{19} + 336 \, \tan\left(\frac{1}{2} \, a\right)^{20} - 3188 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{15} + 1467 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{16} + 3186 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{17} - 1190 \, \tan\left(\frac{1}{2} \, a\right)^{18} + 2604 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{13} - 12744 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{14} + 8148 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{15} - 288 \, \tan\left(\frac{1}{2} \, a\right)^{16} + 2604 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{11} - 10332 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{13} + 4428 \, \tan\left(\frac{1}{2} \, a\right)^{14} - 3188 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{9} + 12744 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{10} - 10332 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{11} - 1170 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{7} - 1467 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{8} + 8148 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{9} - 4428 \, \tan\left(\frac{1}{2} \, a\right)^{10} + 798 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{5} - 3892 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{6} + 3186 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{7} + 288 \, \tan\left(\frac{1}{2} \, a\right)^{8} - 74 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{3} + 924 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{4} - 2310 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{5} + 1190 \, \tan\left(\frac{1}{2} \, a\right)^{6} + 6 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right) - 60 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} + 290 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{3} - 336 \, \tan\left(\frac{1}{2} \, a\right)^{4} + \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} - 6 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right) + 18 \, \tan\left(\frac{1}{2} \, a\right)^{2}\right)}}{{\left(9 \, \tan\left(\frac{1}{2} \, a\right)^{10} - 60 \, \tan\left(\frac{1}{2} \, a\right)^{8} + 118 \, \tan\left(\frac{1}{2} \, a\right)^{6} - 60 \, \tan\left(\frac{1}{2} \, a\right)^{4} + 9 \, \tan\left(\frac{1}{2} \, a\right)^{2}\right)} {\left(3 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{5} - \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{6} - 10 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{3} + 15 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{4} - 3 \, \tan\left(\frac{1}{2} \, a\right)^{5} + 3 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right) - 15 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{2} + 10 \, \tan\left(\frac{1}{2} \, a\right)^{3} + \tan\left(\frac{1}{2} \, b x + 2 \, a\right) - 3 \, \tan\left(\frac{1}{2} \, a\right)\right)}^{2}} + \frac{16 \, {\left(54 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{35} - 9 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{36} - 2610 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{33} + 1620 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{34} - 252 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{35} + 12 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{36} + 52920 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{31} - 58455 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{32} + 19956 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{33} - 2808 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{34} + 198 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{35} - 7 \, \tan\left(\frac{1}{2} \, a\right)^{36} - 573912 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{29} + 942984 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{30} - 503568 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{31} + 112068 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{32} - 11298 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{33} + 468 \, \tan\left(\frac{1}{2} \, a\right)^{34} + 3241488 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{27} - 7636140 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{28} + 5941584 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{29} - 1893936 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{30} + 257976 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{31} - 12969 \, \tan\left(\frac{1}{2} \, a\right)^{32} - 6862752 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{25} + 27168408 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{26} - 32370944 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{27} + 15361632 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{28} - 2923992 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{29} + 188808 \, \tan\left(\frac{1}{2} \, a\right)^{30} - 1663560 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{23} - 24990420 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{24} + 67201056 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{25} - 54063504 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{26} + 16195152 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{27} - 1484964 \, \tan\left(\frac{1}{2} \, a\right)^{28} + 20436072 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{21} - 57467160 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{22} + 13860720 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{23} + 50019840 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{24} - 33931872 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{25} + 5559192 \, \tan\left(\frac{1}{2} \, a\right)^{26} - 14627700 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{19} + 112971402 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{20} - 204830640 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{21} + 114114960 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{22} - 7584840 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{23} - 4921020 \, \tan\left(\frac{1}{2} \, a\right)^{24} - 14627700 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{17} + 150157800 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{19} - 227062440 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{20} + 102261096 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{21} - 11686680 \, \tan\left(\frac{1}{2} \, a\right)^{22} + 20436072 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{15} - 112971402 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{16} + 150157800 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{17} - 74262420 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{19} + 22278726 \, \tan\left(\frac{1}{2} \, a\right)^{20} - 1663560 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{13} + 57467160 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{14} - 204830640 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{15} + 227062440 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{16} - 74262420 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{17} - 6862752 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{11} + 24990420 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{12} + 13860720 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{13} - 114114960 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{14} + 102261096 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{15} - 22278726 \, \tan\left(\frac{1}{2} \, a\right)^{16} + 3241488 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{9} - 27168408 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{10} + 67201056 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{11} - 50019840 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{12} - 7584840 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{13} + 11686680 \, \tan\left(\frac{1}{2} \, a\right)^{14} - 573912 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{7} + 7636140 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{8} - 32370944 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{9} + 54063504 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{10} - 33931872 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{11} + 4921020 \, \tan\left(\frac{1}{2} \, a\right)^{12} + 52920 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{5} - 942984 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{6} + 5941584 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{7} - 15361632 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{8} + 16195152 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{9} - 5559192 \, \tan\left(\frac{1}{2} \, a\right)^{10} - 2610 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{3} + 58455 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{4} - 503568 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{5} + 1893936 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{6} - 2923992 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{7} + 1484964 \, \tan\left(\frac{1}{2} \, a\right)^{8} + 54 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right) - 1620 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{2} + 19956 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{3} - 112068 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{4} + 257976 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{5} - 188808 \, \tan\left(\frac{1}{2} \, a\right)^{6} + 9 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} - 252 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right) + 2808 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} - 11298 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{3} + 12969 \, \tan\left(\frac{1}{2} \, a\right)^{4} - 12 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} + 198 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right) - 468 \, \tan\left(\frac{1}{2} \, a\right)^{2} + 7\right)}}{{\left(\tan\left(\frac{1}{2} \, a\right)^{18} - 45 \, \tan\left(\frac{1}{2} \, a\right)^{16} + 720 \, \tan\left(\frac{1}{2} \, a\right)^{14} - 4728 \, \tan\left(\frac{1}{2} \, a\right)^{12} + 10890 \, \tan\left(\frac{1}{2} \, a\right)^{10} - 10890 \, \tan\left(\frac{1}{2} \, a\right)^{8} + 4728 \, \tan\left(\frac{1}{2} \, a\right)^{6} - 720 \, \tan\left(\frac{1}{2} \, a\right)^{4} + 45 \, \tan\left(\frac{1}{2} \, a\right)^{2} - 1\right)} {\left(\tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{6} - 15 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{4} + 12 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{5} - \tan\left(\frac{1}{2} \, a\right)^{6} + 15 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} - 40 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{3} + 15 \, \tan\left(\frac{1}{2} \, a\right)^{4} - \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} + 12 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right) - 15 \, \tan\left(\frac{1}{2} \, a\right)^{2} + 1\right)}^{3}} + 60 \, \log\left({\left| \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{3} - 3 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right) + 3 \, \tan\left(\frac{1}{2} \, a\right)^{2} - 1 \right|}\right) - 60 \, \log\left({\left| 3 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{2} - \tan\left(\frac{1}{2} \, a\right)^{3} - \tan\left(\frac{1}{2} \, b x + 2 \, a\right) + 3 \, \tan\left(\frac{1}{2} \, a\right) \right|}\right)}{384 \, b}"," ",0,"-1/384*(3*(6*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^23 - tan(1/2*b*x + 2*a)^2*tan(1/2*a)^24 - 74*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^21 + 60*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^22 - 6*tan(1/2*b*x + 2*a)*tan(1/2*a)^23 + 798*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^19 - 924*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^20 + 290*tan(1/2*b*x + 2*a)*tan(1/2*a)^21 - 18*tan(1/2*a)^22 - 1170*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^17 + 3892*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^18 - 2310*tan(1/2*b*x + 2*a)*tan(1/2*a)^19 + 336*tan(1/2*a)^20 - 3188*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^15 + 1467*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^16 + 3186*tan(1/2*b*x + 2*a)*tan(1/2*a)^17 - 1190*tan(1/2*a)^18 + 2604*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^13 - 12744*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^14 + 8148*tan(1/2*b*x + 2*a)*tan(1/2*a)^15 - 288*tan(1/2*a)^16 + 2604*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^11 - 10332*tan(1/2*b*x + 2*a)*tan(1/2*a)^13 + 4428*tan(1/2*a)^14 - 3188*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^9 + 12744*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^10 - 10332*tan(1/2*b*x + 2*a)*tan(1/2*a)^11 - 1170*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^7 - 1467*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^8 + 8148*tan(1/2*b*x + 2*a)*tan(1/2*a)^9 - 4428*tan(1/2*a)^10 + 798*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^5 - 3892*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^6 + 3186*tan(1/2*b*x + 2*a)*tan(1/2*a)^7 + 288*tan(1/2*a)^8 - 74*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^3 + 924*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^4 - 2310*tan(1/2*b*x + 2*a)*tan(1/2*a)^5 + 1190*tan(1/2*a)^6 + 6*tan(1/2*b*x + 2*a)^3*tan(1/2*a) - 60*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^2 + 290*tan(1/2*b*x + 2*a)*tan(1/2*a)^3 - 336*tan(1/2*a)^4 + tan(1/2*b*x + 2*a)^2 - 6*tan(1/2*b*x + 2*a)*tan(1/2*a) + 18*tan(1/2*a)^2)/((9*tan(1/2*a)^10 - 60*tan(1/2*a)^8 + 118*tan(1/2*a)^6 - 60*tan(1/2*a)^4 + 9*tan(1/2*a)^2)*(3*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^5 - tan(1/2*b*x + 2*a)*tan(1/2*a)^6 - 10*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^3 + 15*tan(1/2*b*x + 2*a)*tan(1/2*a)^4 - 3*tan(1/2*a)^5 + 3*tan(1/2*b*x + 2*a)^2*tan(1/2*a) - 15*tan(1/2*b*x + 2*a)*tan(1/2*a)^2 + 10*tan(1/2*a)^3 + tan(1/2*b*x + 2*a) - 3*tan(1/2*a))^2) + 16*(54*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^35 - 9*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^36 - 2610*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^33 + 1620*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^34 - 252*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^35 + 12*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^36 + 52920*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^31 - 58455*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^32 + 19956*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^33 - 2808*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^34 + 198*tan(1/2*b*x + 2*a)*tan(1/2*a)^35 - 7*tan(1/2*a)^36 - 573912*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^29 + 942984*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^30 - 503568*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^31 + 112068*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^32 - 11298*tan(1/2*b*x + 2*a)*tan(1/2*a)^33 + 468*tan(1/2*a)^34 + 3241488*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^27 - 7636140*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^28 + 5941584*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^29 - 1893936*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^30 + 257976*tan(1/2*b*x + 2*a)*tan(1/2*a)^31 - 12969*tan(1/2*a)^32 - 6862752*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^25 + 27168408*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^26 - 32370944*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^27 + 15361632*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^28 - 2923992*tan(1/2*b*x + 2*a)*tan(1/2*a)^29 + 188808*tan(1/2*a)^30 - 1663560*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^23 - 24990420*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^24 + 67201056*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^25 - 54063504*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^26 + 16195152*tan(1/2*b*x + 2*a)*tan(1/2*a)^27 - 1484964*tan(1/2*a)^28 + 20436072*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^21 - 57467160*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^22 + 13860720*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^23 + 50019840*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^24 - 33931872*tan(1/2*b*x + 2*a)*tan(1/2*a)^25 + 5559192*tan(1/2*a)^26 - 14627700*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^19 + 112971402*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^20 - 204830640*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^21 + 114114960*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^22 - 7584840*tan(1/2*b*x + 2*a)*tan(1/2*a)^23 - 4921020*tan(1/2*a)^24 - 14627700*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^17 + 150157800*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^19 - 227062440*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^20 + 102261096*tan(1/2*b*x + 2*a)*tan(1/2*a)^21 - 11686680*tan(1/2*a)^22 + 20436072*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^15 - 112971402*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^16 + 150157800*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^17 - 74262420*tan(1/2*b*x + 2*a)*tan(1/2*a)^19 + 22278726*tan(1/2*a)^20 - 1663560*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^13 + 57467160*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^14 - 204830640*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^15 + 227062440*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^16 - 74262420*tan(1/2*b*x + 2*a)*tan(1/2*a)^17 - 6862752*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^11 + 24990420*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^12 + 13860720*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^13 - 114114960*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^14 + 102261096*tan(1/2*b*x + 2*a)*tan(1/2*a)^15 - 22278726*tan(1/2*a)^16 + 3241488*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^9 - 27168408*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^10 + 67201056*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^11 - 50019840*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^12 - 7584840*tan(1/2*b*x + 2*a)*tan(1/2*a)^13 + 11686680*tan(1/2*a)^14 - 573912*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^7 + 7636140*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^8 - 32370944*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^9 + 54063504*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^10 - 33931872*tan(1/2*b*x + 2*a)*tan(1/2*a)^11 + 4921020*tan(1/2*a)^12 + 52920*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^5 - 942984*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^6 + 5941584*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^7 - 15361632*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^8 + 16195152*tan(1/2*b*x + 2*a)*tan(1/2*a)^9 - 5559192*tan(1/2*a)^10 - 2610*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^3 + 58455*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^4 - 503568*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^5 + 1893936*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^6 - 2923992*tan(1/2*b*x + 2*a)*tan(1/2*a)^7 + 1484964*tan(1/2*a)^8 + 54*tan(1/2*b*x + 2*a)^5*tan(1/2*a) - 1620*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^2 + 19956*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^3 - 112068*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^4 + 257976*tan(1/2*b*x + 2*a)*tan(1/2*a)^5 - 188808*tan(1/2*a)^6 + 9*tan(1/2*b*x + 2*a)^4 - 252*tan(1/2*b*x + 2*a)^3*tan(1/2*a) + 2808*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^2 - 11298*tan(1/2*b*x + 2*a)*tan(1/2*a)^3 + 12969*tan(1/2*a)^4 - 12*tan(1/2*b*x + 2*a)^2 + 198*tan(1/2*b*x + 2*a)*tan(1/2*a) - 468*tan(1/2*a)^2 + 7)/((tan(1/2*a)^18 - 45*tan(1/2*a)^16 + 720*tan(1/2*a)^14 - 4728*tan(1/2*a)^12 + 10890*tan(1/2*a)^10 - 10890*tan(1/2*a)^8 + 4728*tan(1/2*a)^6 - 720*tan(1/2*a)^4 + 45*tan(1/2*a)^2 - 1)*(tan(1/2*b*x + 2*a)^2*tan(1/2*a)^6 - 15*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^4 + 12*tan(1/2*b*x + 2*a)*tan(1/2*a)^5 - tan(1/2*a)^6 + 15*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^2 - 40*tan(1/2*b*x + 2*a)*tan(1/2*a)^3 + 15*tan(1/2*a)^4 - tan(1/2*b*x + 2*a)^2 + 12*tan(1/2*b*x + 2*a)*tan(1/2*a) - 15*tan(1/2*a)^2 + 1)^3) + 60*log(abs(tan(1/2*b*x + 2*a)*tan(1/2*a)^3 - 3*tan(1/2*b*x + 2*a)*tan(1/2*a) + 3*tan(1/2*a)^2 - 1)) - 60*log(abs(3*tan(1/2*b*x + 2*a)*tan(1/2*a)^2 - tan(1/2*a)^3 - tan(1/2*b*x + 2*a) + 3*tan(1/2*a))))/b","B",0
12,1,5647,0,12.384105," ","integrate(csc(2*b*x+2*a)^5*sin(b*x+a),x, algorithm=""giac"")","-\frac{\frac{27 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{34} - 9 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{35} + \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{36} + 2574 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{32} - 1563 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{33} + 234 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{34} + 9 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{35} - 74706 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{30} + 88434 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{31} - 32229 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{32} + 3669 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{33} + 27 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{34} + 598014 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{28} - 1170882 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{29} + 730596 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{30} - 178020 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{31} + 14238 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{32} + 54 \, \tan\left(\frac{1}{2} \, a\right)^{33} - 1958598 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{26} + 6055062 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{27} - 5907096 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{28} + 2329236 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{29} - 370194 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{30} + 17442 \, \tan\left(\frac{1}{2} \, a\right)^{31} + 1859910 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{24} - 12207078 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{25} + 19818828 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{26} - 12113616 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{27} + 2973582 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{28} - 240066 \, \tan\left(\frac{1}{2} \, a\right)^{29} + 3993750 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{22} - 1879110 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{23} - 18713760 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{24} + 24499800 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{25} - 9845190 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{26} + 1208842 \, \tan\left(\frac{1}{2} \, a\right)^{27} - 8882730 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{20} + 38331030 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{21} - 41093100 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{22} + 3908700 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{23} + 9319830 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{24} - 2402946 \, \tan\left(\frac{1}{2} \, a\right)^{25} - 29609100 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{19} + 87376914 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{20} - 76707084 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{21} + 20211030 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{22} - 319590 \, \tan\left(\frac{1}{2} \, a\right)^{23} + 8882730 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{16} - 29609100 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{17} + 58847130 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{19} - 44106714 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{20} + 7594374 \, \tan\left(\frac{1}{2} \, a\right)^{21} - 3993750 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{14} + 38331030 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{15} - 87376914 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{16} + 58847130 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{17} - 6185790 \, \tan\left(\frac{1}{2} \, a\right)^{19} - 1859910 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{12} - 1879110 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{13} + 41093100 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{14} - 76707084 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{15} + 44106714 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{16} - 6185790 \, \tan\left(\frac{1}{2} \, a\right)^{17} + 1958598 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{10} - 12207078 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{11} + 18713760 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{12} + 3908700 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{13} - 20211030 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{14} + 7594374 \, \tan\left(\frac{1}{2} \, a\right)^{15} - 598014 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{8} + 6055062 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{9} - 19818828 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{10} + 24499800 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{11} - 9319830 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{12} - 319590 \, \tan\left(\frac{1}{2} \, a\right)^{13} + 74706 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{6} - 1170882 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{7} + 5907096 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{8} - 12113616 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{9} + 9845190 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{10} - 2402946 \, \tan\left(\frac{1}{2} \, a\right)^{11} - 2574 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{4} + 88434 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{5} - 730596 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{6} + 2329236 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{7} - 2973582 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{8} + 1208842 \, \tan\left(\frac{1}{2} \, a\right)^{9} - 27 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{2} - 1563 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{3} + 32229 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{4} - 178020 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{5} + 370194 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{6} - 240066 \, \tan\left(\frac{1}{2} \, a\right)^{7} - 9 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right) - 234 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{2} + 3669 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{3} - 14238 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{4} + 17442 \, \tan\left(\frac{1}{2} \, a\right)^{5} - \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} + 9 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right) - 27 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{2} + 54 \, \tan\left(\frac{1}{2} \, a\right)^{3}}{{\left(27 \, \tan\left(\frac{1}{2} \, a\right)^{15} - 270 \, \tan\left(\frac{1}{2} \, a\right)^{13} + 981 \, \tan\left(\frac{1}{2} \, a\right)^{11} - 1540 \, \tan\left(\frac{1}{2} \, a\right)^{9} + 981 \, \tan\left(\frac{1}{2} \, a\right)^{7} - 270 \, \tan\left(\frac{1}{2} \, a\right)^{5} + 27 \, \tan\left(\frac{1}{2} \, a\right)^{3}\right)} {\left(3 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{5} - \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{6} - 10 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{3} + 15 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{4} - 3 \, \tan\left(\frac{1}{2} \, a\right)^{5} + 3 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right) - 15 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{2} + 10 \, \tan\left(\frac{1}{2} \, a\right)^{3} + \tan\left(\frac{1}{2} \, b x + 2 \, a\right) - 3 \, \tan\left(\frac{1}{2} \, a\right)\right)}^{3}} + \frac{6 \, {\left(13 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{7} \tan\left(\frac{1}{2} \, a\right)^{48} - 174 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{7} \tan\left(\frac{1}{2} \, a\right)^{46} + 162 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{47} - 5 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{48} - 21522 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{7} \tan\left(\frac{1}{2} \, a\right)^{44} + 13014 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{45} - 2514 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{46} + 234 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{47} - 5 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{48} + 942746 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{7} \tan\left(\frac{1}{2} \, a\right)^{42} - 1100574 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{43} + 453762 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{44} - 87234 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{45} + 8718 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{46} - 474 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{47} + 13 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{48} - 17981508 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{7} \tan\left(\frac{1}{2} \, a\right)^{40} + 30574566 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{41} - 18985626 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{42} + 5680314 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{43} - 906750 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{44} + 80834 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{45} - 3918 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{46} + 78 \, \tan\left(\frac{1}{2} \, a\right)^{47} + 193013886 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{7} \tan\left(\frac{1}{2} \, a\right)^{38} - 441566530 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{39} + 374555556 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{40} - 153629730 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{41} + 33577926 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{42} - 4014234 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{43} + 252270 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{44} - 6614 \, \tan\left(\frac{1}{2} \, a\right)^{45} - 1202084806 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{7} \tan\left(\frac{1}{2} \, a\right)^{36} + 3626590890 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{37} - 4076849790 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{38} + 2214510870 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{39} - 633112668 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{40} + 97266546 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{41} - 7629702 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{42} + 243198 \, \tan\left(\frac{1}{2} \, a\right)^{43} + 4119245478 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{7} \tan\left(\frac{1}{2} \, a\right)^{34} - 16824081618 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{35} + 25189696662 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{36} - 18102012318 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{37} + 6776146338 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{38} - 1334518022 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{39} + 130749372 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{40} - 5045814 \, \tan\left(\frac{1}{2} \, a\right)^{41} - 6836731551 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{7} \tan\left(\frac{1}{2} \, a\right)^{32} + 41573675178 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{33} - 86629166118 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{34} + 84079436982 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{35} - 41858006762 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{36} + 10786903998 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{37} - 1346794722 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{38} + 64179762 \, \tan\left(\frac{1}{2} \, a\right)^{39} + 267313972 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{7} \tan\left(\frac{1}{2} \, a\right)^{30} - 37264510188 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{31} + 143316996039 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{32} - 208138130542 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{33} + 144563703930 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{34} - 50381554230 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{35} + 8311517370 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{36} - 507068874 \, \tan\left(\frac{1}{2} \, a\right)^{37} + 17351751084 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{7} \tan\left(\frac{1}{2} \, a\right)^{28} - 56502600420 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{29} - 5710349876 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{30} + 186100588644 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{31} - 239405365305 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{32} + 125386031934 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{33} - 29001178170 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{34} + 2392888914 \, \tan\left(\frac{1}{2} \, a\right)^{35} - 22757749308 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{7} \tan\left(\frac{1}{2} \, a\right)^{26} + 164419919188 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{27} - 363804236364 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{28} + 282793219500 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{29} + 8521880716 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{30} - 111637405764 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{31} + 48133667169 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{32} - 6017063802 \, \tan\left(\frac{1}{2} \, a\right)^{33} - 98616913668 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{25} + 478784400444 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{26} - 821763522748 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{27} + 607022398644 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{28} - 171137317932 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{29} - 1237805836 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{30} + 5308170444 \, \tan\left(\frac{1}{2} \, a\right)^{31} + 22757749308 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{7} \tan\left(\frac{1}{2} \, a\right)^{22} - 98616913668 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{23} + 492829728300 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{25} - 795918156804 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{26} + 492162548604 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{27} - 121726145364 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{28} + 8269813092 \, \tan\left(\frac{1}{2} \, a\right)^{29} - 17351751084 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{7} \tan\left(\frac{1}{2} \, a\right)^{20} + 164419919188 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{21} - 478784400444 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{22} + 492829728300 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{23} - 293938021260 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{25} + 158215581828 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{26} - 23358680596 \, \tan\left(\frac{1}{2} \, a\right)^{27} - 267313972 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{7} \tan\left(\frac{1}{2} \, a\right)^{18} - 56502600420 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{19} + 363804236364 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{20} - 821763522748 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{21} + 795918156804 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{22} - 293938021260 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{23} + 13852570212 \, \tan\left(\frac{1}{2} \, a\right)^{25} + 6836731551 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{7} \tan\left(\frac{1}{2} \, a\right)^{16} - 37264510188 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{17} + 5710349876 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{18} + 282793219500 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{19} - 607022398644 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{20} + 492162548604 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{21} - 158215581828 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{22} + 13852570212 \, \tan\left(\frac{1}{2} \, a\right)^{23} - 4119245478 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{7} \tan\left(\frac{1}{2} \, a\right)^{14} + 41573675178 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{15} - 143316996039 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{16} + 186100588644 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{17} - 8521880716 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{18} - 171137317932 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{19} + 121726145364 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{20} - 23358680596 \, \tan\left(\frac{1}{2} \, a\right)^{21} + 1202084806 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{7} \tan\left(\frac{1}{2} \, a\right)^{12} - 16824081618 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{13} + 86629166118 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{14} - 208138130542 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{15} + 239405365305 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{16} - 111637405764 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{17} + 1237805836 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{18} + 8269813092 \, \tan\left(\frac{1}{2} \, a\right)^{19} - 193013886 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{7} \tan\left(\frac{1}{2} \, a\right)^{10} + 3626590890 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{11} - 25189696662 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{12} + 84079436982 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{13} - 144563703930 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{14} + 125386031934 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{15} - 48133667169 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{16} + 5308170444 \, \tan\left(\frac{1}{2} \, a\right)^{17} + 17981508 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{7} \tan\left(\frac{1}{2} \, a\right)^{8} - 441566530 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{9} + 4076849790 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{10} - 18102012318 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{11} + 41858006762 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{12} - 50381554230 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{13} + 29001178170 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{14} - 6017063802 \, \tan\left(\frac{1}{2} \, a\right)^{15} - 942746 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{7} \tan\left(\frac{1}{2} \, a\right)^{6} + 30574566 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{7} - 374555556 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{8} + 2214510870 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{9} - 6776146338 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{10} + 10786903998 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{11} - 8311517370 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{12} + 2392888914 \, \tan\left(\frac{1}{2} \, a\right)^{13} + 21522 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{7} \tan\left(\frac{1}{2} \, a\right)^{4} - 1100574 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{5} + 18985626 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{6} - 153629730 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{7} + 633112668 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{8} - 1334518022 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{9} + 1346794722 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{10} - 507068874 \, \tan\left(\frac{1}{2} \, a\right)^{11} + 174 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{7} \tan\left(\frac{1}{2} \, a\right)^{2} + 13014 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{3} - 453762 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{4} + 5680314 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{5} - 33577926 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{6} + 97266546 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{7} - 130749372 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{8} + 64179762 \, \tan\left(\frac{1}{2} \, a\right)^{9} - 13 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{7} + 162 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right) + 2514 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{2} - 87234 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{3} + 906750 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{4} - 4014234 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{5} + 7629702 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{6} - 5045814 \, \tan\left(\frac{1}{2} \, a\right)^{7} + 5 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} + 234 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right) - 8718 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{2} + 80834 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{3} - 252270 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{4} + 243198 \, \tan\left(\frac{1}{2} \, a\right)^{5} + 5 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} - 474 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right) + 3918 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{2} - 6614 \, \tan\left(\frac{1}{2} \, a\right)^{3} - 13 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) + 78 \, \tan\left(\frac{1}{2} \, a\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, a\right)^{24} - 60 \, \tan\left(\frac{1}{2} \, a\right)^{22} + 1410 \, \tan\left(\frac{1}{2} \, a\right)^{20} - 16204 \, \tan\left(\frac{1}{2} \, a\right)^{18} + 92655 \, \tan\left(\frac{1}{2} \, a\right)^{16} - 245880 \, \tan\left(\frac{1}{2} \, a\right)^{14} + 336156 \, \tan\left(\frac{1}{2} \, a\right)^{12} - 245880 \, \tan\left(\frac{1}{2} \, a\right)^{10} + 92655 \, \tan\left(\frac{1}{2} \, a\right)^{8} - 16204 \, \tan\left(\frac{1}{2} \, a\right)^{6} + 1410 \, \tan\left(\frac{1}{2} \, a\right)^{4} - 60 \, \tan\left(\frac{1}{2} \, a\right)^{2} + 1\right)} {\left(\tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{6} - 15 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{4} + 12 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{5} - \tan\left(\frac{1}{2} \, a\right)^{6} + 15 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} - 40 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{3} + 15 \, \tan\left(\frac{1}{2} \, a\right)^{4} - \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} + 12 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right) - 15 \, \tan\left(\frac{1}{2} \, a\right)^{2} + 1\right)}^{4}} - 105 \, \log\left({\left| \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{3} + 3 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{2} - \tan\left(\frac{1}{2} \, a\right)^{3} - 3 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right) + 3 \, \tan\left(\frac{1}{2} \, a\right)^{2} - \tan\left(\frac{1}{2} \, b x + 2 \, a\right) + 3 \, \tan\left(\frac{1}{2} \, a\right) - 1 \right|}\right) + 105 \, \log\left({\left| \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{3} - 3 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{2} + \tan\left(\frac{1}{2} \, a\right)^{3} - 3 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right) + 3 \, \tan\left(\frac{1}{2} \, a\right)^{2} + \tan\left(\frac{1}{2} \, b x + 2 \, a\right) - 3 \, \tan\left(\frac{1}{2} \, a\right) - 1 \right|}\right)}{768 \, b}"," ",0,"-1/768*((27*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^34 - 9*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^35 + tan(1/2*b*x + 2*a)^3*tan(1/2*a)^36 + 2574*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^32 - 1563*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^33 + 234*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^34 + 9*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^35 - 74706*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^30 + 88434*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^31 - 32229*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^32 + 3669*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^33 + 27*tan(1/2*b*x + 2*a)*tan(1/2*a)^34 + 598014*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^28 - 1170882*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^29 + 730596*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^30 - 178020*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^31 + 14238*tan(1/2*b*x + 2*a)*tan(1/2*a)^32 + 54*tan(1/2*a)^33 - 1958598*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^26 + 6055062*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^27 - 5907096*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^28 + 2329236*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^29 - 370194*tan(1/2*b*x + 2*a)*tan(1/2*a)^30 + 17442*tan(1/2*a)^31 + 1859910*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^24 - 12207078*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^25 + 19818828*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^26 - 12113616*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^27 + 2973582*tan(1/2*b*x + 2*a)*tan(1/2*a)^28 - 240066*tan(1/2*a)^29 + 3993750*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^22 - 1879110*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^23 - 18713760*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^24 + 24499800*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^25 - 9845190*tan(1/2*b*x + 2*a)*tan(1/2*a)^26 + 1208842*tan(1/2*a)^27 - 8882730*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^20 + 38331030*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^21 - 41093100*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^22 + 3908700*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^23 + 9319830*tan(1/2*b*x + 2*a)*tan(1/2*a)^24 - 2402946*tan(1/2*a)^25 - 29609100*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^19 + 87376914*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^20 - 76707084*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^21 + 20211030*tan(1/2*b*x + 2*a)*tan(1/2*a)^22 - 319590*tan(1/2*a)^23 + 8882730*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^16 - 29609100*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^17 + 58847130*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^19 - 44106714*tan(1/2*b*x + 2*a)*tan(1/2*a)^20 + 7594374*tan(1/2*a)^21 - 3993750*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^14 + 38331030*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^15 - 87376914*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^16 + 58847130*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^17 - 6185790*tan(1/2*a)^19 - 1859910*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^12 - 1879110*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^13 + 41093100*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^14 - 76707084*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^15 + 44106714*tan(1/2*b*x + 2*a)*tan(1/2*a)^16 - 6185790*tan(1/2*a)^17 + 1958598*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^10 - 12207078*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^11 + 18713760*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^12 + 3908700*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^13 - 20211030*tan(1/2*b*x + 2*a)*tan(1/2*a)^14 + 7594374*tan(1/2*a)^15 - 598014*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^8 + 6055062*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^9 - 19818828*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^10 + 24499800*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^11 - 9319830*tan(1/2*b*x + 2*a)*tan(1/2*a)^12 - 319590*tan(1/2*a)^13 + 74706*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^6 - 1170882*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^7 + 5907096*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^8 - 12113616*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^9 + 9845190*tan(1/2*b*x + 2*a)*tan(1/2*a)^10 - 2402946*tan(1/2*a)^11 - 2574*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^4 + 88434*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^5 - 730596*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^6 + 2329236*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^7 - 2973582*tan(1/2*b*x + 2*a)*tan(1/2*a)^8 + 1208842*tan(1/2*a)^9 - 27*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^2 - 1563*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^3 + 32229*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^4 - 178020*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^5 + 370194*tan(1/2*b*x + 2*a)*tan(1/2*a)^6 - 240066*tan(1/2*a)^7 - 9*tan(1/2*b*x + 2*a)^4*tan(1/2*a) - 234*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^2 + 3669*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^3 - 14238*tan(1/2*b*x + 2*a)*tan(1/2*a)^4 + 17442*tan(1/2*a)^5 - tan(1/2*b*x + 2*a)^3 + 9*tan(1/2*b*x + 2*a)^2*tan(1/2*a) - 27*tan(1/2*b*x + 2*a)*tan(1/2*a)^2 + 54*tan(1/2*a)^3)/((27*tan(1/2*a)^15 - 270*tan(1/2*a)^13 + 981*tan(1/2*a)^11 - 1540*tan(1/2*a)^9 + 981*tan(1/2*a)^7 - 270*tan(1/2*a)^5 + 27*tan(1/2*a)^3)*(3*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^5 - tan(1/2*b*x + 2*a)*tan(1/2*a)^6 - 10*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^3 + 15*tan(1/2*b*x + 2*a)*tan(1/2*a)^4 - 3*tan(1/2*a)^5 + 3*tan(1/2*b*x + 2*a)^2*tan(1/2*a) - 15*tan(1/2*b*x + 2*a)*tan(1/2*a)^2 + 10*tan(1/2*a)^3 + tan(1/2*b*x + 2*a) - 3*tan(1/2*a))^3) + 6*(13*tan(1/2*b*x + 2*a)^7*tan(1/2*a)^48 - 174*tan(1/2*b*x + 2*a)^7*tan(1/2*a)^46 + 162*tan(1/2*b*x + 2*a)^6*tan(1/2*a)^47 - 5*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^48 - 21522*tan(1/2*b*x + 2*a)^7*tan(1/2*a)^44 + 13014*tan(1/2*b*x + 2*a)^6*tan(1/2*a)^45 - 2514*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^46 + 234*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^47 - 5*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^48 + 942746*tan(1/2*b*x + 2*a)^7*tan(1/2*a)^42 - 1100574*tan(1/2*b*x + 2*a)^6*tan(1/2*a)^43 + 453762*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^44 - 87234*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^45 + 8718*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^46 - 474*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^47 + 13*tan(1/2*b*x + 2*a)*tan(1/2*a)^48 - 17981508*tan(1/2*b*x + 2*a)^7*tan(1/2*a)^40 + 30574566*tan(1/2*b*x + 2*a)^6*tan(1/2*a)^41 - 18985626*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^42 + 5680314*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^43 - 906750*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^44 + 80834*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^45 - 3918*tan(1/2*b*x + 2*a)*tan(1/2*a)^46 + 78*tan(1/2*a)^47 + 193013886*tan(1/2*b*x + 2*a)^7*tan(1/2*a)^38 - 441566530*tan(1/2*b*x + 2*a)^6*tan(1/2*a)^39 + 374555556*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^40 - 153629730*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^41 + 33577926*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^42 - 4014234*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^43 + 252270*tan(1/2*b*x + 2*a)*tan(1/2*a)^44 - 6614*tan(1/2*a)^45 - 1202084806*tan(1/2*b*x + 2*a)^7*tan(1/2*a)^36 + 3626590890*tan(1/2*b*x + 2*a)^6*tan(1/2*a)^37 - 4076849790*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^38 + 2214510870*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^39 - 633112668*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^40 + 97266546*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^41 - 7629702*tan(1/2*b*x + 2*a)*tan(1/2*a)^42 + 243198*tan(1/2*a)^43 + 4119245478*tan(1/2*b*x + 2*a)^7*tan(1/2*a)^34 - 16824081618*tan(1/2*b*x + 2*a)^6*tan(1/2*a)^35 + 25189696662*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^36 - 18102012318*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^37 + 6776146338*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^38 - 1334518022*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^39 + 130749372*tan(1/2*b*x + 2*a)*tan(1/2*a)^40 - 5045814*tan(1/2*a)^41 - 6836731551*tan(1/2*b*x + 2*a)^7*tan(1/2*a)^32 + 41573675178*tan(1/2*b*x + 2*a)^6*tan(1/2*a)^33 - 86629166118*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^34 + 84079436982*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^35 - 41858006762*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^36 + 10786903998*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^37 - 1346794722*tan(1/2*b*x + 2*a)*tan(1/2*a)^38 + 64179762*tan(1/2*a)^39 + 267313972*tan(1/2*b*x + 2*a)^7*tan(1/2*a)^30 - 37264510188*tan(1/2*b*x + 2*a)^6*tan(1/2*a)^31 + 143316996039*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^32 - 208138130542*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^33 + 144563703930*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^34 - 50381554230*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^35 + 8311517370*tan(1/2*b*x + 2*a)*tan(1/2*a)^36 - 507068874*tan(1/2*a)^37 + 17351751084*tan(1/2*b*x + 2*a)^7*tan(1/2*a)^28 - 56502600420*tan(1/2*b*x + 2*a)^6*tan(1/2*a)^29 - 5710349876*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^30 + 186100588644*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^31 - 239405365305*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^32 + 125386031934*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^33 - 29001178170*tan(1/2*b*x + 2*a)*tan(1/2*a)^34 + 2392888914*tan(1/2*a)^35 - 22757749308*tan(1/2*b*x + 2*a)^7*tan(1/2*a)^26 + 164419919188*tan(1/2*b*x + 2*a)^6*tan(1/2*a)^27 - 363804236364*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^28 + 282793219500*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^29 + 8521880716*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^30 - 111637405764*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^31 + 48133667169*tan(1/2*b*x + 2*a)*tan(1/2*a)^32 - 6017063802*tan(1/2*a)^33 - 98616913668*tan(1/2*b*x + 2*a)^6*tan(1/2*a)^25 + 478784400444*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^26 - 821763522748*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^27 + 607022398644*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^28 - 171137317932*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^29 - 1237805836*tan(1/2*b*x + 2*a)*tan(1/2*a)^30 + 5308170444*tan(1/2*a)^31 + 22757749308*tan(1/2*b*x + 2*a)^7*tan(1/2*a)^22 - 98616913668*tan(1/2*b*x + 2*a)^6*tan(1/2*a)^23 + 492829728300*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^25 - 795918156804*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^26 + 492162548604*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^27 - 121726145364*tan(1/2*b*x + 2*a)*tan(1/2*a)^28 + 8269813092*tan(1/2*a)^29 - 17351751084*tan(1/2*b*x + 2*a)^7*tan(1/2*a)^20 + 164419919188*tan(1/2*b*x + 2*a)^6*tan(1/2*a)^21 - 478784400444*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^22 + 492829728300*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^23 - 293938021260*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^25 + 158215581828*tan(1/2*b*x + 2*a)*tan(1/2*a)^26 - 23358680596*tan(1/2*a)^27 - 267313972*tan(1/2*b*x + 2*a)^7*tan(1/2*a)^18 - 56502600420*tan(1/2*b*x + 2*a)^6*tan(1/2*a)^19 + 363804236364*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^20 - 821763522748*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^21 + 795918156804*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^22 - 293938021260*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^23 + 13852570212*tan(1/2*a)^25 + 6836731551*tan(1/2*b*x + 2*a)^7*tan(1/2*a)^16 - 37264510188*tan(1/2*b*x + 2*a)^6*tan(1/2*a)^17 + 5710349876*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^18 + 282793219500*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^19 - 607022398644*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^20 + 492162548604*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^21 - 158215581828*tan(1/2*b*x + 2*a)*tan(1/2*a)^22 + 13852570212*tan(1/2*a)^23 - 4119245478*tan(1/2*b*x + 2*a)^7*tan(1/2*a)^14 + 41573675178*tan(1/2*b*x + 2*a)^6*tan(1/2*a)^15 - 143316996039*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^16 + 186100588644*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^17 - 8521880716*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^18 - 171137317932*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^19 + 121726145364*tan(1/2*b*x + 2*a)*tan(1/2*a)^20 - 23358680596*tan(1/2*a)^21 + 1202084806*tan(1/2*b*x + 2*a)^7*tan(1/2*a)^12 - 16824081618*tan(1/2*b*x + 2*a)^6*tan(1/2*a)^13 + 86629166118*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^14 - 208138130542*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^15 + 239405365305*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^16 - 111637405764*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^17 + 1237805836*tan(1/2*b*x + 2*a)*tan(1/2*a)^18 + 8269813092*tan(1/2*a)^19 - 193013886*tan(1/2*b*x + 2*a)^7*tan(1/2*a)^10 + 3626590890*tan(1/2*b*x + 2*a)^6*tan(1/2*a)^11 - 25189696662*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^12 + 84079436982*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^13 - 144563703930*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^14 + 125386031934*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^15 - 48133667169*tan(1/2*b*x + 2*a)*tan(1/2*a)^16 + 5308170444*tan(1/2*a)^17 + 17981508*tan(1/2*b*x + 2*a)^7*tan(1/2*a)^8 - 441566530*tan(1/2*b*x + 2*a)^6*tan(1/2*a)^9 + 4076849790*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^10 - 18102012318*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^11 + 41858006762*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^12 - 50381554230*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^13 + 29001178170*tan(1/2*b*x + 2*a)*tan(1/2*a)^14 - 6017063802*tan(1/2*a)^15 - 942746*tan(1/2*b*x + 2*a)^7*tan(1/2*a)^6 + 30574566*tan(1/2*b*x + 2*a)^6*tan(1/2*a)^7 - 374555556*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^8 + 2214510870*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^9 - 6776146338*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^10 + 10786903998*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^11 - 8311517370*tan(1/2*b*x + 2*a)*tan(1/2*a)^12 + 2392888914*tan(1/2*a)^13 + 21522*tan(1/2*b*x + 2*a)^7*tan(1/2*a)^4 - 1100574*tan(1/2*b*x + 2*a)^6*tan(1/2*a)^5 + 18985626*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^6 - 153629730*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^7 + 633112668*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^8 - 1334518022*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^9 + 1346794722*tan(1/2*b*x + 2*a)*tan(1/2*a)^10 - 507068874*tan(1/2*a)^11 + 174*tan(1/2*b*x + 2*a)^7*tan(1/2*a)^2 + 13014*tan(1/2*b*x + 2*a)^6*tan(1/2*a)^3 - 453762*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^4 + 5680314*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^5 - 33577926*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^6 + 97266546*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^7 - 130749372*tan(1/2*b*x + 2*a)*tan(1/2*a)^8 + 64179762*tan(1/2*a)^9 - 13*tan(1/2*b*x + 2*a)^7 + 162*tan(1/2*b*x + 2*a)^6*tan(1/2*a) + 2514*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^2 - 87234*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^3 + 906750*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^4 - 4014234*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^5 + 7629702*tan(1/2*b*x + 2*a)*tan(1/2*a)^6 - 5045814*tan(1/2*a)^7 + 5*tan(1/2*b*x + 2*a)^5 + 234*tan(1/2*b*x + 2*a)^4*tan(1/2*a) - 8718*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^2 + 80834*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^3 - 252270*tan(1/2*b*x + 2*a)*tan(1/2*a)^4 + 243198*tan(1/2*a)^5 + 5*tan(1/2*b*x + 2*a)^3 - 474*tan(1/2*b*x + 2*a)^2*tan(1/2*a) + 3918*tan(1/2*b*x + 2*a)*tan(1/2*a)^2 - 6614*tan(1/2*a)^3 - 13*tan(1/2*b*x + 2*a) + 78*tan(1/2*a))/((tan(1/2*a)^24 - 60*tan(1/2*a)^22 + 1410*tan(1/2*a)^20 - 16204*tan(1/2*a)^18 + 92655*tan(1/2*a)^16 - 245880*tan(1/2*a)^14 + 336156*tan(1/2*a)^12 - 245880*tan(1/2*a)^10 + 92655*tan(1/2*a)^8 - 16204*tan(1/2*a)^6 + 1410*tan(1/2*a)^4 - 60*tan(1/2*a)^2 + 1)*(tan(1/2*b*x + 2*a)^2*tan(1/2*a)^6 - 15*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^4 + 12*tan(1/2*b*x + 2*a)*tan(1/2*a)^5 - tan(1/2*a)^6 + 15*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^2 - 40*tan(1/2*b*x + 2*a)*tan(1/2*a)^3 + 15*tan(1/2*a)^4 - tan(1/2*b*x + 2*a)^2 + 12*tan(1/2*b*x + 2*a)*tan(1/2*a) - 15*tan(1/2*a)^2 + 1)^4) - 105*log(abs(tan(1/2*b*x + 2*a)*tan(1/2*a)^3 + 3*tan(1/2*b*x + 2*a)*tan(1/2*a)^2 - tan(1/2*a)^3 - 3*tan(1/2*b*x + 2*a)*tan(1/2*a) + 3*tan(1/2*a)^2 - tan(1/2*b*x + 2*a) + 3*tan(1/2*a) - 1)) + 105*log(abs(tan(1/2*b*x + 2*a)*tan(1/2*a)^3 - 3*tan(1/2*b*x + 2*a)*tan(1/2*a)^2 + tan(1/2*a)^3 - 3*tan(1/2*b*x + 2*a)*tan(1/2*a) + 3*tan(1/2*a)^2 + tan(1/2*b*x + 2*a) - 3*tan(1/2*a) - 1)))/b","B",0
13,1,85,0,0.761403," ","integrate(sin(b*x+a)^2*sin(2*b*x+2*a)^5,x, algorithm=""giac"")","\frac{\cos\left(12 \, b x + 12 \, a\right)}{768 \, b} - \frac{\cos\left(10 \, b x + 10 \, a\right)}{320 \, b} - \frac{\cos\left(8 \, b x + 8 \, a\right)}{128 \, b} + \frac{5 \, \cos\left(6 \, b x + 6 \, a\right)}{192 \, b} + \frac{5 \, \cos\left(4 \, b x + 4 \, a\right)}{256 \, b} - \frac{5 \, \cos\left(2 \, b x + 2 \, a\right)}{32 \, b}"," ",0,"1/768*cos(12*b*x + 12*a)/b - 1/320*cos(10*b*x + 10*a)/b - 1/128*cos(8*b*x + 8*a)/b + 5/192*cos(6*b*x + 6*a)/b + 5/256*cos(4*b*x + 4*a)/b - 5/32*cos(2*b*x + 2*a)/b","B",0
14,1,74,0,0.598906," ","integrate(sin(b*x+a)^2*sin(2*b*x+2*a)^4,x, algorithm=""giac"")","\frac{3}{16} \, x - \frac{\sin\left(10 \, b x + 10 \, a\right)}{320 \, b} + \frac{\sin\left(8 \, b x + 8 \, a\right)}{128 \, b} + \frac{\sin\left(6 \, b x + 6 \, a\right)}{64 \, b} - \frac{\sin\left(4 \, b x + 4 \, a\right)}{16 \, b} - \frac{\sin\left(2 \, b x + 2 \, a\right)}{32 \, b}"," ",0,"3/16*x - 1/320*sin(10*b*x + 10*a)/b + 1/128*sin(8*b*x + 8*a)/b + 1/64*sin(6*b*x + 6*a)/b - 1/16*sin(4*b*x + 4*a)/b - 1/32*sin(2*b*x + 2*a)/b","A",0
15,1,57,0,0.502385," ","integrate(sin(b*x+a)^2*sin(2*b*x+2*a)^3,x, algorithm=""giac"")","-\frac{\cos\left(8 \, b x + 8 \, a\right)}{128 \, b} + \frac{\cos\left(6 \, b x + 6 \, a\right)}{48 \, b} + \frac{\cos\left(4 \, b x + 4 \, a\right)}{32 \, b} - \frac{3 \, \cos\left(2 \, b x + 2 \, a\right)}{16 \, b}"," ",0,"-1/128*cos(8*b*x + 8*a)/b + 1/48*cos(6*b*x + 6*a)/b + 1/32*cos(4*b*x + 4*a)/b - 3/16*cos(2*b*x + 2*a)/b","B",0
16,1,46,0,0.417804," ","integrate(sin(b*x+a)^2*sin(2*b*x+2*a)^2,x, algorithm=""giac"")","\frac{1}{4} \, x + \frac{\sin\left(6 \, b x + 6 \, a\right)}{48 \, b} - \frac{\sin\left(4 \, b x + 4 \, a\right)}{16 \, b} - \frac{\sin\left(2 \, b x + 2 \, a\right)}{16 \, b}"," ",0,"1/4*x + 1/48*sin(6*b*x + 6*a)/b - 1/16*sin(4*b*x + 4*a)/b - 1/16*sin(2*b*x + 2*a)/b","A",0
17,1,29,0,0.459088," ","integrate(sin(b*x+a)^2*sin(2*b*x+2*a),x, algorithm=""giac"")","\frac{\cos\left(4 \, b x + 4 \, a\right)}{16 \, b} - \frac{\cos\left(2 \, b x + 2 \, a\right)}{4 \, b}"," ",0,"1/16*cos(4*b*x + 4*a)/b - 1/4*cos(2*b*x + 2*a)/b","B",0
18,1,95,0,0.770424," ","integrate(csc(2*b*x+2*a)*sin(b*x+a)^2,x, algorithm=""giac"")","\frac{\log\left(\tan\left(b x + 4 \, a\right)^{2} + 1\right) - 2 \, \log\left({\left| 6 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{5} - \tan\left(\frac{1}{2} \, a\right)^{6} - 20 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{3} + 15 \, \tan\left(\frac{1}{2} \, a\right)^{4} + 6 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right) - 15 \, \tan\left(\frac{1}{2} \, a\right)^{2} + 1 \right|}\right)}{4 \, b}"," ",0,"1/4*(log(tan(b*x + 4*a)^2 + 1) - 2*log(abs(6*tan(b*x + 4*a)*tan(1/2*a)^5 - tan(1/2*a)^6 - 20*tan(b*x + 4*a)*tan(1/2*a)^3 + 15*tan(1/2*a)^4 + 6*tan(b*x + 4*a)*tan(1/2*a) - 15*tan(1/2*a)^2 + 1)))/b","B",0
19,1,152,0,1.521545," ","integrate(csc(2*b*x+2*a)^2*sin(b*x+a)^2,x, algorithm=""giac"")","-\frac{\tan\left(\frac{1}{2} \, a\right)^{12} + 6 \, \tan\left(\frac{1}{2} \, a\right)^{10} + 15 \, \tan\left(\frac{1}{2} \, a\right)^{8} + 20 \, \tan\left(\frac{1}{2} \, a\right)^{6} + 15 \, \tan\left(\frac{1}{2} \, a\right)^{4} + 6 \, \tan\left(\frac{1}{2} \, a\right)^{2} + 1}{8 \, {\left(6 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{5} - \tan\left(\frac{1}{2} \, a\right)^{6} - 20 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{3} + 15 \, \tan\left(\frac{1}{2} \, a\right)^{4} + 6 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right) - 15 \, \tan\left(\frac{1}{2} \, a\right)^{2} + 1\right)} {\left(3 \, \tan\left(\frac{1}{2} \, a\right)^{5} - 10 \, \tan\left(\frac{1}{2} \, a\right)^{3} + 3 \, \tan\left(\frac{1}{2} \, a\right)\right)} b}"," ",0,"-1/8*(tan(1/2*a)^12 + 6*tan(1/2*a)^10 + 15*tan(1/2*a)^8 + 20*tan(1/2*a)^6 + 15*tan(1/2*a)^4 + 6*tan(1/2*a)^2 + 1)/((6*tan(b*x + 4*a)*tan(1/2*a)^5 - tan(1/2*a)^6 - 20*tan(b*x + 4*a)*tan(1/2*a)^3 + 15*tan(1/2*a)^4 + 6*tan(b*x + 4*a)*tan(1/2*a) - 15*tan(1/2*a)^2 + 1)*(3*tan(1/2*a)^5 - 10*tan(1/2*a)^3 + 3*tan(1/2*a))*b)","B",0
20,1,734,0,3.551395," ","integrate(csc(2*b*x+2*a)^3*sin(b*x+a)^2,x, algorithm=""giac"")","\frac{\frac{12 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{23} - \tan\left(\frac{1}{2} \, a\right)^{24} + 3888 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{20} - 1444 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{21} + 168 \, \tan\left(\frac{1}{2} \, a\right)^{22} - 51840 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{18} + 32052 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{19} - 4074 \, \tan\left(\frac{1}{2} \, a\right)^{20} + 274752 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{16} - 260028 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{17} + 49480 \, \tan\left(\frac{1}{2} \, a\right)^{18} - 731520 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{14} + 979064 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{15} - 276687 \, \tan\left(\frac{1}{2} \, a\right)^{16} + 1021728 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{12} - 1873128 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{13} + 737808 \, \tan\left(\frac{1}{2} \, a\right)^{14} - 731520 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{10} + 1873128 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{11} - 1009292 \, \tan\left(\frac{1}{2} \, a\right)^{12} + 274752 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{8} - 979064 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{9} + 737808 \, \tan\left(\frac{1}{2} \, a\right)^{10} - 51840 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{6} + 260028 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{7} - 276687 \, \tan\left(\frac{1}{2} \, a\right)^{8} + 3888 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{4} - 32052 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{5} + 49480 \, \tan\left(\frac{1}{2} \, a\right)^{6} + 1444 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{3} - 4074 \, \tan\left(\frac{1}{2} \, a\right)^{4} - 12 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right) + 168 \, \tan\left(\frac{1}{2} \, a\right)^{2} - 1}{{\left(9 \, \tan\left(\frac{1}{2} \, a\right)^{10} - 60 \, \tan\left(\frac{1}{2} \, a\right)^{8} + 118 \, \tan\left(\frac{1}{2} \, a\right)^{6} - 60 \, \tan\left(\frac{1}{2} \, a\right)^{4} + 9 \, \tan\left(\frac{1}{2} \, a\right)^{2}\right)} {\left(6 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{5} - \tan\left(\frac{1}{2} \, a\right)^{6} - 20 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{3} + 15 \, \tan\left(\frac{1}{2} \, a\right)^{4} + 6 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right) - 15 \, \tan\left(\frac{1}{2} \, a\right)^{2} + 1\right)}^{2}} + 8 \, \log\left({\left| \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{6} - 15 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{4} + 6 \, \tan\left(\frac{1}{2} \, a\right)^{5} + 15 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{2} - 20 \, \tan\left(\frac{1}{2} \, a\right)^{3} - \tan\left(b x + 4 \, a\right) + 6 \, \tan\left(\frac{1}{2} \, a\right) \right|}\right) - 8 \, \log\left({\left| 6 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{5} - \tan\left(\frac{1}{2} \, a\right)^{6} - 20 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{3} + 15 \, \tan\left(\frac{1}{2} \, a\right)^{4} + 6 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right) - 15 \, \tan\left(\frac{1}{2} \, a\right)^{2} + 1 \right|}\right)}{64 \, b}"," ",0,"1/64*((12*tan(b*x + 4*a)*tan(1/2*a)^23 - tan(1/2*a)^24 + 3888*tan(b*x + 4*a)^2*tan(1/2*a)^20 - 1444*tan(b*x + 4*a)*tan(1/2*a)^21 + 168*tan(1/2*a)^22 - 51840*tan(b*x + 4*a)^2*tan(1/2*a)^18 + 32052*tan(b*x + 4*a)*tan(1/2*a)^19 - 4074*tan(1/2*a)^20 + 274752*tan(b*x + 4*a)^2*tan(1/2*a)^16 - 260028*tan(b*x + 4*a)*tan(1/2*a)^17 + 49480*tan(1/2*a)^18 - 731520*tan(b*x + 4*a)^2*tan(1/2*a)^14 + 979064*tan(b*x + 4*a)*tan(1/2*a)^15 - 276687*tan(1/2*a)^16 + 1021728*tan(b*x + 4*a)^2*tan(1/2*a)^12 - 1873128*tan(b*x + 4*a)*tan(1/2*a)^13 + 737808*tan(1/2*a)^14 - 731520*tan(b*x + 4*a)^2*tan(1/2*a)^10 + 1873128*tan(b*x + 4*a)*tan(1/2*a)^11 - 1009292*tan(1/2*a)^12 + 274752*tan(b*x + 4*a)^2*tan(1/2*a)^8 - 979064*tan(b*x + 4*a)*tan(1/2*a)^9 + 737808*tan(1/2*a)^10 - 51840*tan(b*x + 4*a)^2*tan(1/2*a)^6 + 260028*tan(b*x + 4*a)*tan(1/2*a)^7 - 276687*tan(1/2*a)^8 + 3888*tan(b*x + 4*a)^2*tan(1/2*a)^4 - 32052*tan(b*x + 4*a)*tan(1/2*a)^5 + 49480*tan(1/2*a)^6 + 1444*tan(b*x + 4*a)*tan(1/2*a)^3 - 4074*tan(1/2*a)^4 - 12*tan(b*x + 4*a)*tan(1/2*a) + 168*tan(1/2*a)^2 - 1)/((9*tan(1/2*a)^10 - 60*tan(1/2*a)^8 + 118*tan(1/2*a)^6 - 60*tan(1/2*a)^4 + 9*tan(1/2*a)^2)*(6*tan(b*x + 4*a)*tan(1/2*a)^5 - tan(1/2*a)^6 - 20*tan(b*x + 4*a)*tan(1/2*a)^3 + 15*tan(1/2*a)^4 + 6*tan(b*x + 4*a)*tan(1/2*a) - 15*tan(1/2*a)^2 + 1)^2) + 8*log(abs(tan(b*x + 4*a)*tan(1/2*a)^6 - 15*tan(b*x + 4*a)*tan(1/2*a)^4 + 6*tan(1/2*a)^5 + 15*tan(b*x + 4*a)*tan(1/2*a)^2 - 20*tan(1/2*a)^3 - tan(b*x + 4*a) + 6*tan(1/2*a))) - 8*log(abs(6*tan(b*x + 4*a)*tan(1/2*a)^5 - tan(1/2*a)^6 - 20*tan(b*x + 4*a)*tan(1/2*a)^3 + 15*tan(1/2*a)^4 + 6*tan(b*x + 4*a)*tan(1/2*a) - 15*tan(1/2*a)^2 + 1)))/b","B",0
21,1,1034,0,2.259841," ","integrate(csc(2*b*x+2*a)^4*sin(b*x+a)^2,x, algorithm=""giac"")","-\frac{\frac{24 \, {\left(\tan\left(\frac{1}{2} \, a\right)^{12} + 6 \, \tan\left(\frac{1}{2} \, a\right)^{10} + 15 \, \tan\left(\frac{1}{2} \, a\right)^{8} + 20 \, \tan\left(\frac{1}{2} \, a\right)^{6} + 15 \, \tan\left(\frac{1}{2} \, a\right)^{4} + 6 \, \tan\left(\frac{1}{2} \, a\right)^{2} + 1\right)}}{{\left(\tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{6} - 15 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{4} + 6 \, \tan\left(\frac{1}{2} \, a\right)^{5} + 15 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{2} - 20 \, \tan\left(\frac{1}{2} \, a\right)^{3} - \tan\left(b x + 4 \, a\right) + 6 \, \tan\left(\frac{1}{2} \, a\right)\right)} {\left(\tan\left(\frac{1}{2} \, a\right)^{6} - 15 \, \tan\left(\frac{1}{2} \, a\right)^{4} + 15 \, \tan\left(\frac{1}{2} \, a\right)^{2} - 1\right)}} + \frac{108 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{34} - 18 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{35} + \tan\left(\frac{1}{2} \, a\right)^{36} + 4464 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{32} - 1182 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{33} + 126 \, \tan\left(\frac{1}{2} \, a\right)^{34} - 28608 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{30} + 26208 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{31} - 3159 \, \tan\left(\frac{1}{2} \, a\right)^{32} + 14544 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{28} - 81216 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{29} + 29232 \, \tan\left(\frac{1}{2} \, a\right)^{30} + 197136 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{26} - 130344 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{27} - 26460 \, \tan\left(\frac{1}{2} \, a\right)^{28} - 230160 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{24} + 657288 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{25} - 228600 \, \tan\left(\frac{1}{2} \, a\right)^{26} - 753984 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{22} + 419328 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{23} + 237588 \, \tan\left(\frac{1}{2} \, a\right)^{24} + 604368 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{20} - 2188128 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{21} + 944208 \, \tan\left(\frac{1}{2} \, a\right)^{22} + 1957128 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{18} - 1928412 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{19} - 142434 \, \tan\left(\frac{1}{2} \, a\right)^{20} + 604368 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{16} + 1928412 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{17} - 1358860 \, \tan\left(\frac{1}{2} \, a\right)^{18} - 753984 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{14} + 2188128 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{15} - 142434 \, \tan\left(\frac{1}{2} \, a\right)^{16} - 230160 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{12} - 419328 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{13} + 944208 \, \tan\left(\frac{1}{2} \, a\right)^{14} + 197136 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{10} - 657288 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{11} + 237588 \, \tan\left(\frac{1}{2} \, a\right)^{12} + 14544 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{8} + 130344 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{9} - 228600 \, \tan\left(\frac{1}{2} \, a\right)^{10} - 28608 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{6} + 81216 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{7} - 26460 \, \tan\left(\frac{1}{2} \, a\right)^{8} + 4464 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{4} - 26208 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{5} + 29232 \, \tan\left(\frac{1}{2} \, a\right)^{6} + 108 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} + 1182 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{3} - 3159 \, \tan\left(\frac{1}{2} \, a\right)^{4} + 18 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right) + 126 \, \tan\left(\frac{1}{2} \, a\right)^{2} + 1}{{\left(27 \, \tan\left(\frac{1}{2} \, a\right)^{15} - 270 \, \tan\left(\frac{1}{2} \, a\right)^{13} + 981 \, \tan\left(\frac{1}{2} \, a\right)^{11} - 1540 \, \tan\left(\frac{1}{2} \, a\right)^{9} + 981 \, \tan\left(\frac{1}{2} \, a\right)^{7} - 270 \, \tan\left(\frac{1}{2} \, a\right)^{5} + 27 \, \tan\left(\frac{1}{2} \, a\right)^{3}\right)} {\left(6 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{5} - \tan\left(\frac{1}{2} \, a\right)^{6} - 20 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{3} + 15 \, \tan\left(\frac{1}{2} \, a\right)^{4} + 6 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right) - 15 \, \tan\left(\frac{1}{2} \, a\right)^{2} + 1\right)}^{3}}}{384 \, b}"," ",0,"-1/384*(24*(tan(1/2*a)^12 + 6*tan(1/2*a)^10 + 15*tan(1/2*a)^8 + 20*tan(1/2*a)^6 + 15*tan(1/2*a)^4 + 6*tan(1/2*a)^2 + 1)/((tan(b*x + 4*a)*tan(1/2*a)^6 - 15*tan(b*x + 4*a)*tan(1/2*a)^4 + 6*tan(1/2*a)^5 + 15*tan(b*x + 4*a)*tan(1/2*a)^2 - 20*tan(1/2*a)^3 - tan(b*x + 4*a) + 6*tan(1/2*a))*(tan(1/2*a)^6 - 15*tan(1/2*a)^4 + 15*tan(1/2*a)^2 - 1)) + (108*tan(b*x + 4*a)^2*tan(1/2*a)^34 - 18*tan(b*x + 4*a)*tan(1/2*a)^35 + tan(1/2*a)^36 + 4464*tan(b*x + 4*a)^2*tan(1/2*a)^32 - 1182*tan(b*x + 4*a)*tan(1/2*a)^33 + 126*tan(1/2*a)^34 - 28608*tan(b*x + 4*a)^2*tan(1/2*a)^30 + 26208*tan(b*x + 4*a)*tan(1/2*a)^31 - 3159*tan(1/2*a)^32 + 14544*tan(b*x + 4*a)^2*tan(1/2*a)^28 - 81216*tan(b*x + 4*a)*tan(1/2*a)^29 + 29232*tan(1/2*a)^30 + 197136*tan(b*x + 4*a)^2*tan(1/2*a)^26 - 130344*tan(b*x + 4*a)*tan(1/2*a)^27 - 26460*tan(1/2*a)^28 - 230160*tan(b*x + 4*a)^2*tan(1/2*a)^24 + 657288*tan(b*x + 4*a)*tan(1/2*a)^25 - 228600*tan(1/2*a)^26 - 753984*tan(b*x + 4*a)^2*tan(1/2*a)^22 + 419328*tan(b*x + 4*a)*tan(1/2*a)^23 + 237588*tan(1/2*a)^24 + 604368*tan(b*x + 4*a)^2*tan(1/2*a)^20 - 2188128*tan(b*x + 4*a)*tan(1/2*a)^21 + 944208*tan(1/2*a)^22 + 1957128*tan(b*x + 4*a)^2*tan(1/2*a)^18 - 1928412*tan(b*x + 4*a)*tan(1/2*a)^19 - 142434*tan(1/2*a)^20 + 604368*tan(b*x + 4*a)^2*tan(1/2*a)^16 + 1928412*tan(b*x + 4*a)*tan(1/2*a)^17 - 1358860*tan(1/2*a)^18 - 753984*tan(b*x + 4*a)^2*tan(1/2*a)^14 + 2188128*tan(b*x + 4*a)*tan(1/2*a)^15 - 142434*tan(1/2*a)^16 - 230160*tan(b*x + 4*a)^2*tan(1/2*a)^12 - 419328*tan(b*x + 4*a)*tan(1/2*a)^13 + 944208*tan(1/2*a)^14 + 197136*tan(b*x + 4*a)^2*tan(1/2*a)^10 - 657288*tan(b*x + 4*a)*tan(1/2*a)^11 + 237588*tan(1/2*a)^12 + 14544*tan(b*x + 4*a)^2*tan(1/2*a)^8 + 130344*tan(b*x + 4*a)*tan(1/2*a)^9 - 228600*tan(1/2*a)^10 - 28608*tan(b*x + 4*a)^2*tan(1/2*a)^6 + 81216*tan(b*x + 4*a)*tan(1/2*a)^7 - 26460*tan(1/2*a)^8 + 4464*tan(b*x + 4*a)^2*tan(1/2*a)^4 - 26208*tan(b*x + 4*a)*tan(1/2*a)^5 + 29232*tan(1/2*a)^6 + 108*tan(b*x + 4*a)^2*tan(1/2*a)^2 + 1182*tan(b*x + 4*a)*tan(1/2*a)^3 - 3159*tan(1/2*a)^4 + 18*tan(b*x + 4*a)*tan(1/2*a) + 126*tan(1/2*a)^2 + 1)/((27*tan(1/2*a)^15 - 270*tan(1/2*a)^13 + 981*tan(1/2*a)^11 - 1540*tan(1/2*a)^9 + 981*tan(1/2*a)^7 - 270*tan(1/2*a)^5 + 27*tan(1/2*a)^3)*(6*tan(b*x + 4*a)*tan(1/2*a)^5 - tan(1/2*a)^6 - 20*tan(b*x + 4*a)*tan(1/2*a)^3 + 15*tan(1/2*a)^4 + 6*tan(b*x + 4*a)*tan(1/2*a) - 15*tan(1/2*a)^2 + 1)^3))/b","B",0
22,1,2657,0,2.354259," ","integrate(csc(2*b*x+2*a)^5*sin(b*x+a)^2,x, algorithm=""giac"")","-\frac{\frac{32 \, {\left(9 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{24} - 540 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{22} + 96 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{23} + \tan\left(\frac{1}{2} \, a\right)^{24} + 12690 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{20} - 5072 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{21} + 264 \, \tan\left(\frac{1}{2} \, a\right)^{22} - 145836 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{18} + 94416 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{19} - 11766 \, \tan\left(\frac{1}{2} \, a\right)^{20} + 833895 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{16} - 775584 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{17} + 152744 \, \tan\left(\frac{1}{2} \, a\right)^{18} - 2212920 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{14} + 2952832 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{15} - 825777 \, \tan\left(\frac{1}{2} \, a\right)^{16} + 3025404 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{12} - 5609184 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{13} + 2205264 \, \tan\left(\frac{1}{2} \, a\right)^{14} - 2212920 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{10} + 5609184 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{11} - 3045556 \, \tan\left(\frac{1}{2} \, a\right)^{12} + 833895 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{8} - 2952832 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{9} + 2205264 \, \tan\left(\frac{1}{2} \, a\right)^{10} - 145836 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{6} + 775584 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{7} - 825777 \, \tan\left(\frac{1}{2} \, a\right)^{8} + 12690 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{4} - 94416 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{5} + 152744 \, \tan\left(\frac{1}{2} \, a\right)^{6} - 540 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} + 5072 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{3} - 11766 \, \tan\left(\frac{1}{2} \, a\right)^{4} + 9 \, \tan\left(b x + 4 \, a\right)^{2} - 96 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right) + 264 \, \tan\left(\frac{1}{2} \, a\right)^{2} + 1\right)}}{{\left(\tan\left(\frac{1}{2} \, a\right)^{12} - 30 \, \tan\left(\frac{1}{2} \, a\right)^{10} + 255 \, \tan\left(\frac{1}{2} \, a\right)^{8} - 452 \, \tan\left(\frac{1}{2} \, a\right)^{6} + 255 \, \tan\left(\frac{1}{2} \, a\right)^{4} - 30 \, \tan\left(\frac{1}{2} \, a\right)^{2} + 1\right)} {\left(\tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{6} - 15 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{4} + 6 \, \tan\left(\frac{1}{2} \, a\right)^{5} + 15 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{2} - 20 \, \tan\left(\frac{1}{2} \, a\right)^{3} - \tan\left(b x + 4 \, a\right) + 6 \, \tan\left(\frac{1}{2} \, a\right)\right)}^{2}} - \frac{864 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{45} - 216 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{46} + 24 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{47} - \tan\left(\frac{1}{2} \, a\right)^{48} + 50976 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{43} - 18000 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{44} + 2584 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{45} - 96 \, \tan\left(\frac{1}{2} \, a\right)^{46} + 41990400 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{40} - 29618496 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{41} + 8128920 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{42} - 1000584 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{43} + 46860 \, \tan\left(\frac{1}{2} \, a\right)^{44} - 1119744000 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{38} + 1086111040 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{39} - 365239008 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{40} + 52636536 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{41} - 2775328 \, \tan\left(\frac{1}{2} \, a\right)^{42} + 13399603200 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{36} - 16982062752 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{37} + 7267900536 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{38} - 1271292760 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{39} + 78743742 \, \tan\left(\frac{1}{2} \, a\right)^{40} - 94929408000 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{34} + 150936080928 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{35} - 81088683024 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{36} + 17523815592 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{37} - 1302867360 \, \tan\left(\frac{1}{2} \, a\right)^{38} + 442437811200 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{32} - 858638750464 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{33} + 567089250120 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{34} - 150754238328 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{35} + 13639996380 \, \tan\left(\frac{1}{2} \, a\right)^{36} - 1426650624000 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{30} + 3319597849344 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{31} - 2647648010880 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{32} + 854992222856 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{33} - 94087910880 \, \tan\left(\frac{1}{2} \, a\right)^{34} + 3262626662400 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{28} - 9004992609600 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{29} + 8563235603472 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{30} - 3316579144464 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{31} + 440072542737 \, \tan\left(\frac{1}{2} \, a\right)^{32} - 5349143040000 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{26} + 17420327827008 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{27} - 19596982709664 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{28} + 9014744094960 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{29} - 1427870886848 \, \tan\left(\frac{1}{2} \, a\right)^{30} + 6307092928000 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{24} - 24202990429056 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{25} + 32094110324592 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{26} - 17430945047632 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{27} + 3269665274136 \, \tan\left(\frac{1}{2} \, a\right)^{28} - 5349143040000 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{22} + 24202990429056 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{23} - 37811152430400 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{24} + 24188717892528 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{25} - 5348679038784 \, \tan\left(\frac{1}{2} \, a\right)^{26} + 3262626662400 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{20} - 17420327827008 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{21} + 32094110324592 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{22} - 24188717892528 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{23} + 6296990528100 \, \tan\left(\frac{1}{2} \, a\right)^{24} - 1426650624000 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{18} + 9004992609600 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{19} - 19596982709664 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{20} + 17430945047632 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{21} - 5348679038784 \, \tan\left(\frac{1}{2} \, a\right)^{22} + 442437811200 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{16} - 3319597849344 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{17} + 8563235603472 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{18} - 9014744094960 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{19} + 3269665274136 \, \tan\left(\frac{1}{2} \, a\right)^{20} - 94929408000 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{14} + 858638750464 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{15} - 2647648010880 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{16} + 3316579144464 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{17} - 1427870886848 \, \tan\left(\frac{1}{2} \, a\right)^{18} + 13399603200 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{12} - 150936080928 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{13} + 567089250120 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{14} - 854992222856 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{15} + 440072542737 \, \tan\left(\frac{1}{2} \, a\right)^{16} - 1119744000 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{10} + 16982062752 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{11} - 81088683024 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{12} + 150754238328 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{13} - 94087910880 \, \tan\left(\frac{1}{2} \, a\right)^{14} + 41990400 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{8} - 1086111040 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{9} + 7267900536 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{10} - 17523815592 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{11} + 13639996380 \, \tan\left(\frac{1}{2} \, a\right)^{12} + 29618496 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{7} - 365239008 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{8} + 1271292760 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{9} - 1302867360 \, \tan\left(\frac{1}{2} \, a\right)^{10} - 50976 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{5} + 8128920 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{6} - 52636536 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{7} + 78743742 \, \tan\left(\frac{1}{2} \, a\right)^{8} - 864 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{3} - 18000 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{4} + 1000584 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{5} - 2775328 \, \tan\left(\frac{1}{2} \, a\right)^{6} - 216 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} - 2584 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{3} + 46860 \, \tan\left(\frac{1}{2} \, a\right)^{4} - 24 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right) - 96 \, \tan\left(\frac{1}{2} \, a\right)^{2} - 1}{{\left(81 \, \tan\left(\frac{1}{2} \, a\right)^{20} - 1080 \, \tan\left(\frac{1}{2} \, a\right)^{18} + 5724 \, \tan\left(\frac{1}{2} \, a\right)^{16} - 15240 \, \tan\left(\frac{1}{2} \, a\right)^{14} + 21286 \, \tan\left(\frac{1}{2} \, a\right)^{12} - 15240 \, \tan\left(\frac{1}{2} \, a\right)^{10} + 5724 \, \tan\left(\frac{1}{2} \, a\right)^{8} - 1080 \, \tan\left(\frac{1}{2} \, a\right)^{6} + 81 \, \tan\left(\frac{1}{2} \, a\right)^{4}\right)} {\left(6 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{5} - \tan\left(\frac{1}{2} \, a\right)^{6} - 20 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{3} + 15 \, \tan\left(\frac{1}{2} \, a\right)^{4} + 6 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right) - 15 \, \tan\left(\frac{1}{2} \, a\right)^{2} + 1\right)}^{4}} - 192 \, \log\left({\left| \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{6} - 15 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{4} + 6 \, \tan\left(\frac{1}{2} \, a\right)^{5} + 15 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{2} - 20 \, \tan\left(\frac{1}{2} \, a\right)^{3} - \tan\left(b x + 4 \, a\right) + 6 \, \tan\left(\frac{1}{2} \, a\right) \right|}\right) + 192 \, \log\left({\left| 6 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{5} - \tan\left(\frac{1}{2} \, a\right)^{6} - 20 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{3} + 15 \, \tan\left(\frac{1}{2} \, a\right)^{4} + 6 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right) - 15 \, \tan\left(\frac{1}{2} \, a\right)^{2} + 1 \right|}\right)}{2048 \, b}"," ",0,"-1/2048*(32*(9*tan(b*x + 4*a)^2*tan(1/2*a)^24 - 540*tan(b*x + 4*a)^2*tan(1/2*a)^22 + 96*tan(b*x + 4*a)*tan(1/2*a)^23 + tan(1/2*a)^24 + 12690*tan(b*x + 4*a)^2*tan(1/2*a)^20 - 5072*tan(b*x + 4*a)*tan(1/2*a)^21 + 264*tan(1/2*a)^22 - 145836*tan(b*x + 4*a)^2*tan(1/2*a)^18 + 94416*tan(b*x + 4*a)*tan(1/2*a)^19 - 11766*tan(1/2*a)^20 + 833895*tan(b*x + 4*a)^2*tan(1/2*a)^16 - 775584*tan(b*x + 4*a)*tan(1/2*a)^17 + 152744*tan(1/2*a)^18 - 2212920*tan(b*x + 4*a)^2*tan(1/2*a)^14 + 2952832*tan(b*x + 4*a)*tan(1/2*a)^15 - 825777*tan(1/2*a)^16 + 3025404*tan(b*x + 4*a)^2*tan(1/2*a)^12 - 5609184*tan(b*x + 4*a)*tan(1/2*a)^13 + 2205264*tan(1/2*a)^14 - 2212920*tan(b*x + 4*a)^2*tan(1/2*a)^10 + 5609184*tan(b*x + 4*a)*tan(1/2*a)^11 - 3045556*tan(1/2*a)^12 + 833895*tan(b*x + 4*a)^2*tan(1/2*a)^8 - 2952832*tan(b*x + 4*a)*tan(1/2*a)^9 + 2205264*tan(1/2*a)^10 - 145836*tan(b*x + 4*a)^2*tan(1/2*a)^6 + 775584*tan(b*x + 4*a)*tan(1/2*a)^7 - 825777*tan(1/2*a)^8 + 12690*tan(b*x + 4*a)^2*tan(1/2*a)^4 - 94416*tan(b*x + 4*a)*tan(1/2*a)^5 + 152744*tan(1/2*a)^6 - 540*tan(b*x + 4*a)^2*tan(1/2*a)^2 + 5072*tan(b*x + 4*a)*tan(1/2*a)^3 - 11766*tan(1/2*a)^4 + 9*tan(b*x + 4*a)^2 - 96*tan(b*x + 4*a)*tan(1/2*a) + 264*tan(1/2*a)^2 + 1)/((tan(1/2*a)^12 - 30*tan(1/2*a)^10 + 255*tan(1/2*a)^8 - 452*tan(1/2*a)^6 + 255*tan(1/2*a)^4 - 30*tan(1/2*a)^2 + 1)*(tan(b*x + 4*a)*tan(1/2*a)^6 - 15*tan(b*x + 4*a)*tan(1/2*a)^4 + 6*tan(1/2*a)^5 + 15*tan(b*x + 4*a)*tan(1/2*a)^2 - 20*tan(1/2*a)^3 - tan(b*x + 4*a) + 6*tan(1/2*a))^2) - (864*tan(b*x + 4*a)^3*tan(1/2*a)^45 - 216*tan(b*x + 4*a)^2*tan(1/2*a)^46 + 24*tan(b*x + 4*a)*tan(1/2*a)^47 - tan(1/2*a)^48 + 50976*tan(b*x + 4*a)^3*tan(1/2*a)^43 - 18000*tan(b*x + 4*a)^2*tan(1/2*a)^44 + 2584*tan(b*x + 4*a)*tan(1/2*a)^45 - 96*tan(1/2*a)^46 + 41990400*tan(b*x + 4*a)^4*tan(1/2*a)^40 - 29618496*tan(b*x + 4*a)^3*tan(1/2*a)^41 + 8128920*tan(b*x + 4*a)^2*tan(1/2*a)^42 - 1000584*tan(b*x + 4*a)*tan(1/2*a)^43 + 46860*tan(1/2*a)^44 - 1119744000*tan(b*x + 4*a)^4*tan(1/2*a)^38 + 1086111040*tan(b*x + 4*a)^3*tan(1/2*a)^39 - 365239008*tan(b*x + 4*a)^2*tan(1/2*a)^40 + 52636536*tan(b*x + 4*a)*tan(1/2*a)^41 - 2775328*tan(1/2*a)^42 + 13399603200*tan(b*x + 4*a)^4*tan(1/2*a)^36 - 16982062752*tan(b*x + 4*a)^3*tan(1/2*a)^37 + 7267900536*tan(b*x + 4*a)^2*tan(1/2*a)^38 - 1271292760*tan(b*x + 4*a)*tan(1/2*a)^39 + 78743742*tan(1/2*a)^40 - 94929408000*tan(b*x + 4*a)^4*tan(1/2*a)^34 + 150936080928*tan(b*x + 4*a)^3*tan(1/2*a)^35 - 81088683024*tan(b*x + 4*a)^2*tan(1/2*a)^36 + 17523815592*tan(b*x + 4*a)*tan(1/2*a)^37 - 1302867360*tan(1/2*a)^38 + 442437811200*tan(b*x + 4*a)^4*tan(1/2*a)^32 - 858638750464*tan(b*x + 4*a)^3*tan(1/2*a)^33 + 567089250120*tan(b*x + 4*a)^2*tan(1/2*a)^34 - 150754238328*tan(b*x + 4*a)*tan(1/2*a)^35 + 13639996380*tan(1/2*a)^36 - 1426650624000*tan(b*x + 4*a)^4*tan(1/2*a)^30 + 3319597849344*tan(b*x + 4*a)^3*tan(1/2*a)^31 - 2647648010880*tan(b*x + 4*a)^2*tan(1/2*a)^32 + 854992222856*tan(b*x + 4*a)*tan(1/2*a)^33 - 94087910880*tan(1/2*a)^34 + 3262626662400*tan(b*x + 4*a)^4*tan(1/2*a)^28 - 9004992609600*tan(b*x + 4*a)^3*tan(1/2*a)^29 + 8563235603472*tan(b*x + 4*a)^2*tan(1/2*a)^30 - 3316579144464*tan(b*x + 4*a)*tan(1/2*a)^31 + 440072542737*tan(1/2*a)^32 - 5349143040000*tan(b*x + 4*a)^4*tan(1/2*a)^26 + 17420327827008*tan(b*x + 4*a)^3*tan(1/2*a)^27 - 19596982709664*tan(b*x + 4*a)^2*tan(1/2*a)^28 + 9014744094960*tan(b*x + 4*a)*tan(1/2*a)^29 - 1427870886848*tan(1/2*a)^30 + 6307092928000*tan(b*x + 4*a)^4*tan(1/2*a)^24 - 24202990429056*tan(b*x + 4*a)^3*tan(1/2*a)^25 + 32094110324592*tan(b*x + 4*a)^2*tan(1/2*a)^26 - 17430945047632*tan(b*x + 4*a)*tan(1/2*a)^27 + 3269665274136*tan(1/2*a)^28 - 5349143040000*tan(b*x + 4*a)^4*tan(1/2*a)^22 + 24202990429056*tan(b*x + 4*a)^3*tan(1/2*a)^23 - 37811152430400*tan(b*x + 4*a)^2*tan(1/2*a)^24 + 24188717892528*tan(b*x + 4*a)*tan(1/2*a)^25 - 5348679038784*tan(1/2*a)^26 + 3262626662400*tan(b*x + 4*a)^4*tan(1/2*a)^20 - 17420327827008*tan(b*x + 4*a)^3*tan(1/2*a)^21 + 32094110324592*tan(b*x + 4*a)^2*tan(1/2*a)^22 - 24188717892528*tan(b*x + 4*a)*tan(1/2*a)^23 + 6296990528100*tan(1/2*a)^24 - 1426650624000*tan(b*x + 4*a)^4*tan(1/2*a)^18 + 9004992609600*tan(b*x + 4*a)^3*tan(1/2*a)^19 - 19596982709664*tan(b*x + 4*a)^2*tan(1/2*a)^20 + 17430945047632*tan(b*x + 4*a)*tan(1/2*a)^21 - 5348679038784*tan(1/2*a)^22 + 442437811200*tan(b*x + 4*a)^4*tan(1/2*a)^16 - 3319597849344*tan(b*x + 4*a)^3*tan(1/2*a)^17 + 8563235603472*tan(b*x + 4*a)^2*tan(1/2*a)^18 - 9014744094960*tan(b*x + 4*a)*tan(1/2*a)^19 + 3269665274136*tan(1/2*a)^20 - 94929408000*tan(b*x + 4*a)^4*tan(1/2*a)^14 + 858638750464*tan(b*x + 4*a)^3*tan(1/2*a)^15 - 2647648010880*tan(b*x + 4*a)^2*tan(1/2*a)^16 + 3316579144464*tan(b*x + 4*a)*tan(1/2*a)^17 - 1427870886848*tan(1/2*a)^18 + 13399603200*tan(b*x + 4*a)^4*tan(1/2*a)^12 - 150936080928*tan(b*x + 4*a)^3*tan(1/2*a)^13 + 567089250120*tan(b*x + 4*a)^2*tan(1/2*a)^14 - 854992222856*tan(b*x + 4*a)*tan(1/2*a)^15 + 440072542737*tan(1/2*a)^16 - 1119744000*tan(b*x + 4*a)^4*tan(1/2*a)^10 + 16982062752*tan(b*x + 4*a)^3*tan(1/2*a)^11 - 81088683024*tan(b*x + 4*a)^2*tan(1/2*a)^12 + 150754238328*tan(b*x + 4*a)*tan(1/2*a)^13 - 94087910880*tan(1/2*a)^14 + 41990400*tan(b*x + 4*a)^4*tan(1/2*a)^8 - 1086111040*tan(b*x + 4*a)^3*tan(1/2*a)^9 + 7267900536*tan(b*x + 4*a)^2*tan(1/2*a)^10 - 17523815592*tan(b*x + 4*a)*tan(1/2*a)^11 + 13639996380*tan(1/2*a)^12 + 29618496*tan(b*x + 4*a)^3*tan(1/2*a)^7 - 365239008*tan(b*x + 4*a)^2*tan(1/2*a)^8 + 1271292760*tan(b*x + 4*a)*tan(1/2*a)^9 - 1302867360*tan(1/2*a)^10 - 50976*tan(b*x + 4*a)^3*tan(1/2*a)^5 + 8128920*tan(b*x + 4*a)^2*tan(1/2*a)^6 - 52636536*tan(b*x + 4*a)*tan(1/2*a)^7 + 78743742*tan(1/2*a)^8 - 864*tan(b*x + 4*a)^3*tan(1/2*a)^3 - 18000*tan(b*x + 4*a)^2*tan(1/2*a)^4 + 1000584*tan(b*x + 4*a)*tan(1/2*a)^5 - 2775328*tan(1/2*a)^6 - 216*tan(b*x + 4*a)^2*tan(1/2*a)^2 - 2584*tan(b*x + 4*a)*tan(1/2*a)^3 + 46860*tan(1/2*a)^4 - 24*tan(b*x + 4*a)*tan(1/2*a) - 96*tan(1/2*a)^2 - 1)/((81*tan(1/2*a)^20 - 1080*tan(1/2*a)^18 + 5724*tan(1/2*a)^16 - 15240*tan(1/2*a)^14 + 21286*tan(1/2*a)^12 - 15240*tan(1/2*a)^10 + 5724*tan(1/2*a)^8 - 1080*tan(1/2*a)^6 + 81*tan(1/2*a)^4)*(6*tan(b*x + 4*a)*tan(1/2*a)^5 - tan(1/2*a)^6 - 20*tan(b*x + 4*a)*tan(1/2*a)^3 + 15*tan(1/2*a)^4 + 6*tan(b*x + 4*a)*tan(1/2*a) - 15*tan(1/2*a)^2 + 1)^4) - 192*log(abs(tan(b*x + 4*a)*tan(1/2*a)^6 - 15*tan(b*x + 4*a)*tan(1/2*a)^4 + 6*tan(1/2*a)^5 + 15*tan(b*x + 4*a)*tan(1/2*a)^2 - 20*tan(1/2*a)^3 - tan(b*x + 4*a) + 6*tan(1/2*a))) + 192*log(abs(6*tan(b*x + 4*a)*tan(1/2*a)^5 - tan(1/2*a)^6 - 20*tan(b*x + 4*a)*tan(1/2*a)^3 + 15*tan(1/2*a)^4 + 6*tan(b*x + 4*a)*tan(1/2*a) - 15*tan(1/2*a)^2 + 1)))/b","B",0
23,1,96,0,0.618128," ","integrate(sin(b*x+a)^3*sin(2*b*x+2*a)^5,x, algorithm=""giac"")","\frac{\sin\left(13 \, b x + 13 \, a\right)}{1664 \, b} - \frac{3 \, \sin\left(11 \, b x + 11 \, a\right)}{1408 \, b} - \frac{\sin\left(9 \, b x + 9 \, a\right)}{576 \, b} + \frac{\sin\left(7 \, b x + 7 \, a\right)}{64 \, b} - \frac{\sin\left(5 \, b x + 5 \, a\right)}{128 \, b} - \frac{25 \, \sin\left(3 \, b x + 3 \, a\right)}{384 \, b} + \frac{5 \, \sin\left(b x + a\right)}{32 \, b}"," ",0,"1/1664*sin(13*b*x + 13*a)/b - 3/1408*sin(11*b*x + 11*a)/b - 1/576*sin(9*b*x + 9*a)/b + 1/64*sin(7*b*x + 7*a)/b - 1/128*sin(5*b*x + 5*a)/b - 25/384*sin(3*b*x + 3*a)/b + 5/32*sin(b*x + a)/b","B",0
24,1,82,0,0.798208," ","integrate(sin(b*x+a)^3*sin(2*b*x+2*a)^4,x, algorithm=""giac"")","\frac{\cos\left(11 \, b x + 11 \, a\right)}{704 \, b} - \frac{\cos\left(9 \, b x + 9 \, a\right)}{192 \, b} - \frac{\cos\left(7 \, b x + 7 \, a\right)}{448 \, b} + \frac{11 \, \cos\left(5 \, b x + 5 \, a\right)}{320 \, b} - \frac{\cos\left(3 \, b x + 3 \, a\right)}{32 \, b} - \frac{7 \, \cos\left(b x + a\right)}{32 \, b}"," ",0,"1/704*cos(11*b*x + 11*a)/b - 1/192*cos(9*b*x + 9*a)/b - 1/448*cos(7*b*x + 7*a)/b + 11/320*cos(5*b*x + 5*a)/b - 1/32*cos(3*b*x + 3*a)/b - 7/32*cos(b*x + a)/b","A",0
25,1,54,0,0.448391," ","integrate(sin(b*x+a)^3*sin(2*b*x+2*a)^3,x, algorithm=""giac"")","-\frac{\sin\left(9 \, b x + 9 \, a\right)}{288 \, b} + \frac{3 \, \sin\left(7 \, b x + 7 \, a\right)}{224 \, b} - \frac{\sin\left(3 \, b x + 3 \, a\right)}{12 \, b} + \frac{3 \, \sin\left(b x + a\right)}{16 \, b}"," ",0,"-1/288*sin(9*b*x + 9*a)/b + 3/224*sin(7*b*x + 7*a)/b - 1/12*sin(3*b*x + 3*a)/b + 3/16*sin(b*x + a)/b","A",0
26,1,54,0,0.327926," ","integrate(sin(b*x+a)^3*sin(2*b*x+2*a)^2,x, algorithm=""giac"")","-\frac{\cos\left(7 \, b x + 7 \, a\right)}{112 \, b} + \frac{3 \, \cos\left(5 \, b x + 5 \, a\right)}{80 \, b} - \frac{\cos\left(3 \, b x + 3 \, a\right)}{48 \, b} - \frac{5 \, \cos\left(b x + a\right)}{16 \, b}"," ",0,"-1/112*cos(7*b*x + 7*a)/b + 3/80*cos(5*b*x + 5*a)/b - 1/48*cos(3*b*x + 3*a)/b - 5/16*cos(b*x + a)/b","A",0
27,1,40,0,0.333329," ","integrate(sin(b*x+a)^3*sin(2*b*x+2*a),x, algorithm=""giac"")","\frac{\sin\left(5 \, b x + 5 \, a\right)}{40 \, b} - \frac{\sin\left(3 \, b x + 3 \, a\right)}{8 \, b} + \frac{\sin\left(b x + a\right)}{4 \, b}"," ",0,"1/40*sin(5*b*x + 5*a)/b - 1/8*sin(3*b*x + 3*a)/b + 1/4*sin(b*x + a)/b","B",0
28,1,618,0,0.986408," ","integrate(csc(2*b*x+2*a)*sin(b*x+a)^3,x, algorithm=""giac"")","\frac{\frac{{\left(\tan\left(\frac{1}{2} \, a\right)^{15} + 3 \, \tan\left(\frac{1}{2} \, a\right)^{14} + 3 \, \tan\left(\frac{1}{2} \, a\right)^{13} + 17 \, \tan\left(\frac{1}{2} \, a\right)^{12} - 3 \, \tan\left(\frac{1}{2} \, a\right)^{11} + 39 \, \tan\left(\frac{1}{2} \, a\right)^{10} - 25 \, \tan\left(\frac{1}{2} \, a\right)^{9} + 45 \, \tan\left(\frac{1}{2} \, a\right)^{8} - 45 \, \tan\left(\frac{1}{2} \, a\right)^{7} + 25 \, \tan\left(\frac{1}{2} \, a\right)^{6} - 39 \, \tan\left(\frac{1}{2} \, a\right)^{5} + 3 \, \tan\left(\frac{1}{2} \, a\right)^{4} - 17 \, \tan\left(\frac{1}{2} \, a\right)^{3} - 3 \, \tan\left(\frac{1}{2} \, a\right)^{2} - 3 \, \tan\left(\frac{1}{2} \, a\right) - 1\right)} \log\left({\left| \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{3} + 3 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{2} - \tan\left(\frac{1}{2} \, a\right)^{3} - 3 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right) + 3 \, \tan\left(\frac{1}{2} \, a\right)^{2} - \tan\left(\frac{1}{2} \, b x + 2 \, a\right) + 3 \, \tan\left(\frac{1}{2} \, a\right) - 1 \right|}\right)}{\tan\left(\frac{1}{2} \, a\right)^{3} + 3 \, \tan\left(\frac{1}{2} \, a\right)^{2} - 3 \, \tan\left(\frac{1}{2} \, a\right) - 1} - \frac{{\left(\tan\left(\frac{1}{2} \, a\right)^{15} - 3 \, \tan\left(\frac{1}{2} \, a\right)^{14} + 3 \, \tan\left(\frac{1}{2} \, a\right)^{13} - 17 \, \tan\left(\frac{1}{2} \, a\right)^{12} - 3 \, \tan\left(\frac{1}{2} \, a\right)^{11} - 39 \, \tan\left(\frac{1}{2} \, a\right)^{10} - 25 \, \tan\left(\frac{1}{2} \, a\right)^{9} - 45 \, \tan\left(\frac{1}{2} \, a\right)^{8} - 45 \, \tan\left(\frac{1}{2} \, a\right)^{7} - 25 \, \tan\left(\frac{1}{2} \, a\right)^{6} - 39 \, \tan\left(\frac{1}{2} \, a\right)^{5} - 3 \, \tan\left(\frac{1}{2} \, a\right)^{4} - 17 \, \tan\left(\frac{1}{2} \, a\right)^{3} + 3 \, \tan\left(\frac{1}{2} \, a\right)^{2} - 3 \, \tan\left(\frac{1}{2} \, a\right) + 1\right)} \log\left({\left| \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{3} - 3 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{2} + \tan\left(\frac{1}{2} \, a\right)^{3} - 3 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right) + 3 \, \tan\left(\frac{1}{2} \, a\right)^{2} + \tan\left(\frac{1}{2} \, b x + 2 \, a\right) - 3 \, \tan\left(\frac{1}{2} \, a\right) - 1 \right|}\right)}{\tan\left(\frac{1}{2} \, a\right)^{3} - 3 \, \tan\left(\frac{1}{2} \, a\right)^{2} - 3 \, \tan\left(\frac{1}{2} \, a\right) + 1} + \frac{2 \, {\left(\tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{12} - 12 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{10} + 6 \, \tan\left(\frac{1}{2} \, a\right)^{11} - 27 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{8} - 2 \, \tan\left(\frac{1}{2} \, a\right)^{9} - 36 \, \tan\left(\frac{1}{2} \, a\right)^{7} + 27 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{4} - 36 \, \tan\left(\frac{1}{2} \, a\right)^{5} + 12 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, a\right)^{3} - \tan\left(\frac{1}{2} \, b x + 2 \, a\right) + 6 \, \tan\left(\frac{1}{2} \, a\right)\right)}}{\tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} + 1}}{2 \, b}"," ",0,"1/2*((tan(1/2*a)^15 + 3*tan(1/2*a)^14 + 3*tan(1/2*a)^13 + 17*tan(1/2*a)^12 - 3*tan(1/2*a)^11 + 39*tan(1/2*a)^10 - 25*tan(1/2*a)^9 + 45*tan(1/2*a)^8 - 45*tan(1/2*a)^7 + 25*tan(1/2*a)^6 - 39*tan(1/2*a)^5 + 3*tan(1/2*a)^4 - 17*tan(1/2*a)^3 - 3*tan(1/2*a)^2 - 3*tan(1/2*a) - 1)*log(abs(tan(1/2*b*x + 2*a)*tan(1/2*a)^3 + 3*tan(1/2*b*x + 2*a)*tan(1/2*a)^2 - tan(1/2*a)^3 - 3*tan(1/2*b*x + 2*a)*tan(1/2*a) + 3*tan(1/2*a)^2 - tan(1/2*b*x + 2*a) + 3*tan(1/2*a) - 1))/(tan(1/2*a)^3 + 3*tan(1/2*a)^2 - 3*tan(1/2*a) - 1) - (tan(1/2*a)^15 - 3*tan(1/2*a)^14 + 3*tan(1/2*a)^13 - 17*tan(1/2*a)^12 - 3*tan(1/2*a)^11 - 39*tan(1/2*a)^10 - 25*tan(1/2*a)^9 - 45*tan(1/2*a)^8 - 45*tan(1/2*a)^7 - 25*tan(1/2*a)^6 - 39*tan(1/2*a)^5 - 3*tan(1/2*a)^4 - 17*tan(1/2*a)^3 + 3*tan(1/2*a)^2 - 3*tan(1/2*a) + 1)*log(abs(tan(1/2*b*x + 2*a)*tan(1/2*a)^3 - 3*tan(1/2*b*x + 2*a)*tan(1/2*a)^2 + tan(1/2*a)^3 - 3*tan(1/2*b*x + 2*a)*tan(1/2*a) + 3*tan(1/2*a)^2 + tan(1/2*b*x + 2*a) - 3*tan(1/2*a) - 1))/(tan(1/2*a)^3 - 3*tan(1/2*a)^2 - 3*tan(1/2*a) + 1) + 2*(tan(1/2*b*x + 2*a)*tan(1/2*a)^12 - 12*tan(1/2*b*x + 2*a)*tan(1/2*a)^10 + 6*tan(1/2*a)^11 - 27*tan(1/2*b*x + 2*a)*tan(1/2*a)^8 - 2*tan(1/2*a)^9 - 36*tan(1/2*a)^7 + 27*tan(1/2*b*x + 2*a)*tan(1/2*a)^4 - 36*tan(1/2*a)^5 + 12*tan(1/2*b*x + 2*a)*tan(1/2*a)^2 - 2*tan(1/2*a)^3 - tan(1/2*b*x + 2*a) + 6*tan(1/2*a))/(tan(1/2*b*x + 2*a)^2 + 1))/b","B",0
29,1,319,0,3.869479," ","integrate(csc(2*b*x+2*a)^2*sin(b*x+a)^3,x, algorithm=""giac"")","-\frac{6 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{11} - \tan\left(\frac{1}{2} \, a\right)^{12} - 2 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{9} + 12 \, \tan\left(\frac{1}{2} \, a\right)^{10} - 36 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{7} + 27 \, \tan\left(\frac{1}{2} \, a\right)^{8} - 36 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{5} - 2 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{3} - 27 \, \tan\left(\frac{1}{2} \, a\right)^{4} + 6 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right) - 12 \, \tan\left(\frac{1}{2} \, a\right)^{2} + 1}{2 \, {\left(\tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{6} - 15 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{4} + 12 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{5} - \tan\left(\frac{1}{2} \, a\right)^{6} + 15 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} - 40 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{3} + 15 \, \tan\left(\frac{1}{2} \, a\right)^{4} - \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} + 12 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right) - 15 \, \tan\left(\frac{1}{2} \, a\right)^{2} + 1\right)} {\left(\tan\left(\frac{1}{2} \, a\right)^{6} - 15 \, \tan\left(\frac{1}{2} \, a\right)^{4} + 15 \, \tan\left(\frac{1}{2} \, a\right)^{2} - 1\right)} b}"," ",0,"-1/2*(6*tan(1/2*b*x + 2*a)*tan(1/2*a)^11 - tan(1/2*a)^12 - 2*tan(1/2*b*x + 2*a)*tan(1/2*a)^9 + 12*tan(1/2*a)^10 - 36*tan(1/2*b*x + 2*a)*tan(1/2*a)^7 + 27*tan(1/2*a)^8 - 36*tan(1/2*b*x + 2*a)*tan(1/2*a)^5 - 2*tan(1/2*b*x + 2*a)*tan(1/2*a)^3 - 27*tan(1/2*a)^4 + 6*tan(1/2*b*x + 2*a)*tan(1/2*a) - 12*tan(1/2*a)^2 + 1)/((tan(1/2*b*x + 2*a)^2*tan(1/2*a)^6 - 15*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^4 + 12*tan(1/2*b*x + 2*a)*tan(1/2*a)^5 - tan(1/2*a)^6 + 15*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^2 - 40*tan(1/2*b*x + 2*a)*tan(1/2*a)^3 + 15*tan(1/2*a)^4 - tan(1/2*b*x + 2*a)^2 + 12*tan(1/2*b*x + 2*a)*tan(1/2*a) - 15*tan(1/2*a)^2 + 1)*(tan(1/2*a)^6 - 15*tan(1/2*a)^4 + 15*tan(1/2*a)^2 - 1)*b)","B",0
30,1,1111,0,2.945009," ","integrate(csc(2*b*x+2*a)^3*sin(b*x+a)^3,x, algorithm=""giac"")","-\frac{\frac{2 \, {\left(\tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{24} + 30 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{22} - 6 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{23} + \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{24} - 756 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{20} + 614 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{21} - 114 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{22} + 6 \, \tan\left(\frac{1}{2} \, a\right)^{23} + 2058 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{18} - 4578 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{19} + 1932 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{20} - 182 \, \tan\left(\frac{1}{2} \, a\right)^{21} - 27 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{16} + 6210 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{17} - 7462 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{18} + 1554 \, \tan\left(\frac{1}{2} \, a\right)^{19} - 9396 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{14} + 15588 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{15} - 2331 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{16} - 2178 \, \tan\left(\frac{1}{2} \, a\right)^{17} - 21924 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{13} + 26028 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{14} - 5668 \, \tan\left(\frac{1}{2} \, a\right)^{15} + 9396 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{10} - 21924 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{11} + 6468 \, \tan\left(\frac{1}{2} \, a\right)^{13} + 27 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{8} + 15588 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{9} - 26028 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{10} + 6468 \, \tan\left(\frac{1}{2} \, a\right)^{11} - 2058 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{6} + 6210 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{7} + 2331 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{8} - 5668 \, \tan\left(\frac{1}{2} \, a\right)^{9} + 756 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{4} - 4578 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{5} + 7462 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{6} - 2178 \, \tan\left(\frac{1}{2} \, a\right)^{7} - 30 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{2} + 614 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{3} - 1932 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{4} + 1554 \, \tan\left(\frac{1}{2} \, a\right)^{5} - \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} - 6 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right) + 114 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{2} - 182 \, \tan\left(\frac{1}{2} \, a\right)^{3} - \tan\left(\frac{1}{2} \, b x + 2 \, a\right) + 6 \, \tan\left(\frac{1}{2} \, a\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, a\right)^{12} - 30 \, \tan\left(\frac{1}{2} \, a\right)^{10} + 255 \, \tan\left(\frac{1}{2} \, a\right)^{8} - 452 \, \tan\left(\frac{1}{2} \, a\right)^{6} + 255 \, \tan\left(\frac{1}{2} \, a\right)^{4} - 30 \, \tan\left(\frac{1}{2} \, a\right)^{2} + 1\right)} {\left(\tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{6} - 15 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{4} + 12 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{5} - \tan\left(\frac{1}{2} \, a\right)^{6} + 15 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} - 40 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{3} + 15 \, \tan\left(\frac{1}{2} \, a\right)^{4} - \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} + 12 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right) - 15 \, \tan\left(\frac{1}{2} \, a\right)^{2} + 1\right)}^{2}} - \log\left({\left| \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{3} + 3 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{2} - \tan\left(\frac{1}{2} \, a\right)^{3} - 3 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right) + 3 \, \tan\left(\frac{1}{2} \, a\right)^{2} - \tan\left(\frac{1}{2} \, b x + 2 \, a\right) + 3 \, \tan\left(\frac{1}{2} \, a\right) - 1 \right|}\right) + \log\left({\left| \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{3} - 3 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{2} + \tan\left(\frac{1}{2} \, a\right)^{3} - 3 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right) + 3 \, \tan\left(\frac{1}{2} \, a\right)^{2} + \tan\left(\frac{1}{2} \, b x + 2 \, a\right) - 3 \, \tan\left(\frac{1}{2} \, a\right) - 1 \right|}\right)}{16 \, b}"," ",0,"-1/16*(2*(tan(1/2*b*x + 2*a)^3*tan(1/2*a)^24 + 30*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^22 - 6*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^23 + tan(1/2*b*x + 2*a)*tan(1/2*a)^24 - 756*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^20 + 614*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^21 - 114*tan(1/2*b*x + 2*a)*tan(1/2*a)^22 + 6*tan(1/2*a)^23 + 2058*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^18 - 4578*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^19 + 1932*tan(1/2*b*x + 2*a)*tan(1/2*a)^20 - 182*tan(1/2*a)^21 - 27*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^16 + 6210*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^17 - 7462*tan(1/2*b*x + 2*a)*tan(1/2*a)^18 + 1554*tan(1/2*a)^19 - 9396*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^14 + 15588*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^15 - 2331*tan(1/2*b*x + 2*a)*tan(1/2*a)^16 - 2178*tan(1/2*a)^17 - 21924*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^13 + 26028*tan(1/2*b*x + 2*a)*tan(1/2*a)^14 - 5668*tan(1/2*a)^15 + 9396*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^10 - 21924*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^11 + 6468*tan(1/2*a)^13 + 27*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^8 + 15588*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^9 - 26028*tan(1/2*b*x + 2*a)*tan(1/2*a)^10 + 6468*tan(1/2*a)^11 - 2058*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^6 + 6210*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^7 + 2331*tan(1/2*b*x + 2*a)*tan(1/2*a)^8 - 5668*tan(1/2*a)^9 + 756*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^4 - 4578*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^5 + 7462*tan(1/2*b*x + 2*a)*tan(1/2*a)^6 - 2178*tan(1/2*a)^7 - 30*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^2 + 614*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^3 - 1932*tan(1/2*b*x + 2*a)*tan(1/2*a)^4 + 1554*tan(1/2*a)^5 - tan(1/2*b*x + 2*a)^3 - 6*tan(1/2*b*x + 2*a)^2*tan(1/2*a) + 114*tan(1/2*b*x + 2*a)*tan(1/2*a)^2 - 182*tan(1/2*a)^3 - tan(1/2*b*x + 2*a) + 6*tan(1/2*a))/((tan(1/2*a)^12 - 30*tan(1/2*a)^10 + 255*tan(1/2*a)^8 - 452*tan(1/2*a)^6 + 255*tan(1/2*a)^4 - 30*tan(1/2*a)^2 + 1)*(tan(1/2*b*x + 2*a)^2*tan(1/2*a)^6 - 15*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^4 + 12*tan(1/2*b*x + 2*a)*tan(1/2*a)^5 - tan(1/2*a)^6 + 15*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^2 - 40*tan(1/2*b*x + 2*a)*tan(1/2*a)^3 + 15*tan(1/2*a)^4 - tan(1/2*b*x + 2*a)^2 + 12*tan(1/2*b*x + 2*a)*tan(1/2*a) - 15*tan(1/2*a)^2 + 1)^2) - log(abs(tan(1/2*b*x + 2*a)*tan(1/2*a)^3 + 3*tan(1/2*b*x + 2*a)*tan(1/2*a)^2 - tan(1/2*a)^3 - 3*tan(1/2*b*x + 2*a)*tan(1/2*a) + 3*tan(1/2*a)^2 - tan(1/2*b*x + 2*a) + 3*tan(1/2*a) - 1)) + log(abs(tan(1/2*b*x + 2*a)*tan(1/2*a)^3 - 3*tan(1/2*b*x + 2*a)*tan(1/2*a)^2 + tan(1/2*a)^3 - 3*tan(1/2*b*x + 2*a)*tan(1/2*a) + 3*tan(1/2*a)^2 + tan(1/2*b*x + 2*a) - 3*tan(1/2*a) - 1)))/b","B",0
31,1,2114,0,6.790236," ","integrate(csc(2*b*x+2*a)^4*sin(b*x+a)^3,x, algorithm=""giac"")","-\frac{\frac{4 \, {\left(18 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{35} - 3 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{36} - 762 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{33} + 486 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{34} - 72 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{35} + 3 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{36} + 13644 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{31} - 15561 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{32} + 5424 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{33} - 756 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{34} + 54 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{35} - 2 \, \tan\left(\frac{1}{2} \, a\right)^{36} - 140076 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{29} + 233916 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{30} - 126936 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{31} + 28701 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{32} - 2934 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{33} + 126 \, \tan\left(\frac{1}{2} \, a\right)^{34} + 811140 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{27} - 1893744 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{28} + 1474776 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{29} - 471816 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{30} + 64908 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{31} - 3330 \, \tan\left(\frac{1}{2} \, a\right)^{32} - 1739556 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{25} + 6839316 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{26} - 8095576 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{27} + 3832164 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{28} - 727596 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{29} + 47148 \, \tan\left(\frac{1}{2} \, a\right)^{30} - 461700 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{23} - 6247800 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{24} + 16873272 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{25} - 13541976 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{26} + 4049556 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{27} - 368892 \, \tan\left(\frac{1}{2} \, a\right)^{28} + 5103972 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{21} - 14529780 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{22} + 3596040 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{23} + 12515100 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{24} - 8506836 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{25} + 1396836 \, \tan\left(\frac{1}{2} \, a\right)^{26} - 3586680 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{19} + 28026162 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{20} - 51234312 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{21} + 28649880 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{22} - 1942020 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{23} - 1226940 \, \tan\left(\frac{1}{2} \, a\right)^{24} - 3586680 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{17} + 37245240 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{19} - 56612142 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{20} + 25560228 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{21} - 2935620 \, \tan\left(\frac{1}{2} \, a\right)^{22} + 5103972 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{15} - 28026162 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{16} + 37245240 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{17} - 18495360 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{19} + 5548608 \, \tan\left(\frac{1}{2} \, a\right)^{20} - 461700 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{13} + 14529780 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{14} - 51234312 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{15} + 56612142 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{16} - 18495360 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{17} - 1739556 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{11} + 6247800 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{12} + 3596040 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{13} - 28649880 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{14} + 25560228 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{15} - 5548608 \, \tan\left(\frac{1}{2} \, a\right)^{16} + 811140 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{9} - 6839316 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{10} + 16873272 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{11} - 12515100 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{12} - 1942020 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{13} + 2935620 \, \tan\left(\frac{1}{2} \, a\right)^{14} - 140076 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{7} + 1893744 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{8} - 8095576 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{9} + 13541976 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{10} - 8506836 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{11} + 1226940 \, \tan\left(\frac{1}{2} \, a\right)^{12} + 13644 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{5} - 233916 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{6} + 1474776 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{7} - 3832164 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{8} + 4049556 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{9} - 1396836 \, \tan\left(\frac{1}{2} \, a\right)^{10} - 762 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{3} + 15561 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{4} - 126936 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{5} + 471816 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{6} - 727596 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{7} + 368892 \, \tan\left(\frac{1}{2} \, a\right)^{8} + 18 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right) - 486 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{2} + 5424 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{3} - 28701 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{4} + 64908 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{5} - 47148 \, \tan\left(\frac{1}{2} \, a\right)^{6} + 3 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} - 72 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right) + 756 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} - 2934 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{3} + 3330 \, \tan\left(\frac{1}{2} \, a\right)^{4} - 3 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} + 54 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right) - 126 \, \tan\left(\frac{1}{2} \, a\right)^{2} + 2\right)}}{{\left(\tan\left(\frac{1}{2} \, a\right)^{18} - 45 \, \tan\left(\frac{1}{2} \, a\right)^{16} + 720 \, \tan\left(\frac{1}{2} \, a\right)^{14} - 4728 \, \tan\left(\frac{1}{2} \, a\right)^{12} + 10890 \, \tan\left(\frac{1}{2} \, a\right)^{10} - 10890 \, \tan\left(\frac{1}{2} \, a\right)^{8} + 4728 \, \tan\left(\frac{1}{2} \, a\right)^{6} - 720 \, \tan\left(\frac{1}{2} \, a\right)^{4} + 45 \, \tan\left(\frac{1}{2} \, a\right)^{2} - 1\right)} {\left(\tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{6} - 15 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{4} + 12 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{5} - \tan\left(\frac{1}{2} \, a\right)^{6} + 15 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} - 40 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{3} + 15 \, \tan\left(\frac{1}{2} \, a\right)^{4} - \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} + 12 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right) - 15 \, \tan\left(\frac{1}{2} \, a\right)^{2} + 1\right)}^{3}} + 3 \, \log\left({\left| \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{3} - 3 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right) + 3 \, \tan\left(\frac{1}{2} \, a\right)^{2} - 1 \right|}\right) - 3 \, \log\left({\left| 3 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{2} - \tan\left(\frac{1}{2} \, a\right)^{3} - \tan\left(\frac{1}{2} \, b x + 2 \, a\right) + 3 \, \tan\left(\frac{1}{2} \, a\right) \right|}\right)}{48 \, b}"," ",0,"-1/48*(4*(18*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^35 - 3*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^36 - 762*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^33 + 486*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^34 - 72*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^35 + 3*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^36 + 13644*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^31 - 15561*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^32 + 5424*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^33 - 756*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^34 + 54*tan(1/2*b*x + 2*a)*tan(1/2*a)^35 - 2*tan(1/2*a)^36 - 140076*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^29 + 233916*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^30 - 126936*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^31 + 28701*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^32 - 2934*tan(1/2*b*x + 2*a)*tan(1/2*a)^33 + 126*tan(1/2*a)^34 + 811140*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^27 - 1893744*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^28 + 1474776*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^29 - 471816*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^30 + 64908*tan(1/2*b*x + 2*a)*tan(1/2*a)^31 - 3330*tan(1/2*a)^32 - 1739556*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^25 + 6839316*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^26 - 8095576*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^27 + 3832164*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^28 - 727596*tan(1/2*b*x + 2*a)*tan(1/2*a)^29 + 47148*tan(1/2*a)^30 - 461700*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^23 - 6247800*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^24 + 16873272*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^25 - 13541976*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^26 + 4049556*tan(1/2*b*x + 2*a)*tan(1/2*a)^27 - 368892*tan(1/2*a)^28 + 5103972*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^21 - 14529780*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^22 + 3596040*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^23 + 12515100*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^24 - 8506836*tan(1/2*b*x + 2*a)*tan(1/2*a)^25 + 1396836*tan(1/2*a)^26 - 3586680*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^19 + 28026162*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^20 - 51234312*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^21 + 28649880*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^22 - 1942020*tan(1/2*b*x + 2*a)*tan(1/2*a)^23 - 1226940*tan(1/2*a)^24 - 3586680*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^17 + 37245240*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^19 - 56612142*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^20 + 25560228*tan(1/2*b*x + 2*a)*tan(1/2*a)^21 - 2935620*tan(1/2*a)^22 + 5103972*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^15 - 28026162*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^16 + 37245240*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^17 - 18495360*tan(1/2*b*x + 2*a)*tan(1/2*a)^19 + 5548608*tan(1/2*a)^20 - 461700*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^13 + 14529780*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^14 - 51234312*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^15 + 56612142*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^16 - 18495360*tan(1/2*b*x + 2*a)*tan(1/2*a)^17 - 1739556*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^11 + 6247800*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^12 + 3596040*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^13 - 28649880*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^14 + 25560228*tan(1/2*b*x + 2*a)*tan(1/2*a)^15 - 5548608*tan(1/2*a)^16 + 811140*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^9 - 6839316*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^10 + 16873272*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^11 - 12515100*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^12 - 1942020*tan(1/2*b*x + 2*a)*tan(1/2*a)^13 + 2935620*tan(1/2*a)^14 - 140076*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^7 + 1893744*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^8 - 8095576*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^9 + 13541976*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^10 - 8506836*tan(1/2*b*x + 2*a)*tan(1/2*a)^11 + 1226940*tan(1/2*a)^12 + 13644*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^5 - 233916*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^6 + 1474776*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^7 - 3832164*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^8 + 4049556*tan(1/2*b*x + 2*a)*tan(1/2*a)^9 - 1396836*tan(1/2*a)^10 - 762*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^3 + 15561*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^4 - 126936*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^5 + 471816*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^6 - 727596*tan(1/2*b*x + 2*a)*tan(1/2*a)^7 + 368892*tan(1/2*a)^8 + 18*tan(1/2*b*x + 2*a)^5*tan(1/2*a) - 486*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^2 + 5424*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^3 - 28701*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^4 + 64908*tan(1/2*b*x + 2*a)*tan(1/2*a)^5 - 47148*tan(1/2*a)^6 + 3*tan(1/2*b*x + 2*a)^4 - 72*tan(1/2*b*x + 2*a)^3*tan(1/2*a) + 756*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^2 - 2934*tan(1/2*b*x + 2*a)*tan(1/2*a)^3 + 3330*tan(1/2*a)^4 - 3*tan(1/2*b*x + 2*a)^2 + 54*tan(1/2*b*x + 2*a)*tan(1/2*a) - 126*tan(1/2*a)^2 + 2)/((tan(1/2*a)^18 - 45*tan(1/2*a)^16 + 720*tan(1/2*a)^14 - 4728*tan(1/2*a)^12 + 10890*tan(1/2*a)^10 - 10890*tan(1/2*a)^8 + 4728*tan(1/2*a)^6 - 720*tan(1/2*a)^4 + 45*tan(1/2*a)^2 - 1)*(tan(1/2*b*x + 2*a)^2*tan(1/2*a)^6 - 15*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^4 + 12*tan(1/2*b*x + 2*a)*tan(1/2*a)^5 - tan(1/2*a)^6 + 15*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^2 - 40*tan(1/2*b*x + 2*a)*tan(1/2*a)^3 + 15*tan(1/2*a)^4 - tan(1/2*b*x + 2*a)^2 + 12*tan(1/2*b*x + 2*a)*tan(1/2*a) - 15*tan(1/2*a)^2 + 1)^3) + 3*log(abs(tan(1/2*b*x + 2*a)*tan(1/2*a)^3 - 3*tan(1/2*b*x + 2*a)*tan(1/2*a) + 3*tan(1/2*a)^2 - 1)) - 3*log(abs(3*tan(1/2*b*x + 2*a)*tan(1/2*a)^2 - tan(1/2*a)^3 - tan(1/2*b*x + 2*a) + 3*tan(1/2*a))))/b","B",0
32,1,4032,0,14.593328," ","integrate(csc(2*b*x+2*a)^5*sin(b*x+a)^3,x, algorithm=""giac"")","-\frac{\frac{4 \, {\left(\tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{12} - 12 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{10} + 6 \, \tan\left(\frac{1}{2} \, a\right)^{11} - 27 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{8} - 2 \, \tan\left(\frac{1}{2} \, a\right)^{9} - 36 \, \tan\left(\frac{1}{2} \, a\right)^{7} + 27 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{4} - 36 \, \tan\left(\frac{1}{2} \, a\right)^{5} + 12 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, a\right)^{3} - \tan\left(\frac{1}{2} \, b x + 2 \, a\right) + 6 \, \tan\left(\frac{1}{2} \, a\right)\right)}}{{\left(3 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{5} - \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{6} - 10 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{3} + 15 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{4} - 3 \, \tan\left(\frac{1}{2} \, a\right)^{5} + 3 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right) - 15 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{2} + 10 \, \tan\left(\frac{1}{2} \, a\right)^{3} + \tan\left(\frac{1}{2} \, b x + 2 \, a\right) - 3 \, \tan\left(\frac{1}{2} \, a\right)\right)} {\left(3 \, \tan\left(\frac{1}{2} \, a\right)^{5} - 10 \, \tan\left(\frac{1}{2} \, a\right)^{3} + 3 \, \tan\left(\frac{1}{2} \, a\right)\right)}} + \frac{2 \, {\left(9 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{7} \tan\left(\frac{1}{2} \, a\right)^{48} - 54 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{7} \tan\left(\frac{1}{2} \, a\right)^{46} + 90 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{47} - \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{48} - 16938 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{7} \tan\left(\frac{1}{2} \, a\right)^{44} + 10878 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{45} - 2058 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{46} + 162 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{47} - \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{48} + 648690 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{7} \tan\left(\frac{1}{2} \, a\right)^{42} - 772902 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{43} + 320922 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{44} - 59994 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{45} + 5718 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{46} - 306 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{47} + 9 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{48} - 11649780 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{7} \tan\left(\frac{1}{2} \, a\right)^{40} + 20073870 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{41} - 12606642 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{42} + 3790962 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{43} - 601830 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{44} + 53562 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{45} - 2646 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{46} + 54 \, \tan\left(\frac{1}{2} \, a\right)^{47} + 122301894 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{7} \tan\left(\frac{1}{2} \, a\right)^{38} - 281501690 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{39} + 240373332 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{40} - 99232506 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{41} + 21805614 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{42} - 2617650 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{43} + 166230 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{44} - 4446 \, \tan\left(\frac{1}{2} \, a\right)^{45} - 762446542 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{7} \tan\left(\frac{1}{2} \, a\right)^{36} + 2299471746 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{37} - 2589365766 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{38} + 1410179550 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{39} - 404516268 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{40} + 62438634 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{41} - 4933038 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{42} + 159462 \, \tan\left(\frac{1}{2} \, a\right)^{43} + 2624819022 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{7} \tan\left(\frac{1}{2} \, a\right)^{34} - 10699256970 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{35} + 16002520222 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{36} - 11500345350 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{37} + 4307714970 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{38} - 849637038 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{39} + 83542284 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{40} - 3248766 \, \tan\left(\frac{1}{2} \, a\right)^{41} - 4363726131 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{7} \tan\left(\frac{1}{2} \, a\right)^{32} + 26510577474 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{33} - 55167038478 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{34} + 53489761470 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{35} - 26616485090 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{36} + 6857208774 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{37} - 856321050 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{38} + 40894922 \, \tan\left(\frac{1}{2} \, a\right)^{39} + 148294628 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{7} \tan\left(\frac{1}{2} \, a\right)^{30} - 23718089916 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{31} + 91329113691 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{32} - 132573864918 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{33} + 92023852050 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{34} - 32055103710 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{35} + 5284344754 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{36} - 322093122 \, \tan\left(\frac{1}{2} \, a\right)^{37} + 11061475644 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{7} \tan\left(\frac{1}{2} \, a\right)^{28} - 36130112340 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{29} - 3422040164 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{30} + 118445882004 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{31} - 152452905381 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{32} + 79837550214 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{33} - 18462316050 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{34} + 1522201770 \, \tan\left(\frac{1}{2} \, a\right)^{35} - 14430929868 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{7} \tan\left(\frac{1}{2} \, a\right)^{26} + 104533629188 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{27} - 231729549276 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{28} + 180365650620 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{29} + 5258310492 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{30} - 71047415988 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{31} + 30651378381 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{32} - 3833122290 \, \tan\left(\frac{1}{2} \, a\right)^{33} - 62534029428 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{25} + 304139029068 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{26} - 522734622092 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{27} + 386477003556 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{28} - 109057608828 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{29} - 750175580 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{30} + 3377366748 \, \tan\left(\frac{1}{2} \, a\right)^{31} + 14430929868 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{7} \tan\left(\frac{1}{2} \, a\right)^{22} - 62534029428 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{23} + 313058642364 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{25} - 506043183348 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{26} + 313110921612 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{27} - 77490791364 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{28} + 5273542932 \, \tan\left(\frac{1}{2} \, a\right)^{29} - 11061475644 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{7} \tan\left(\frac{1}{2} \, a\right)^{20} + 104533629188 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{21} - 304139029068 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{22} + 313058642364 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{23} - 186855789276 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{25} + 100600780788 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{26} - 14857714436 \, \tan\left(\frac{1}{2} \, a\right)^{27} - 148294628 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{7} \tan\left(\frac{1}{2} \, a\right)^{18} - 36130112340 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{19} + 231729549276 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{20} - 522734622092 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{21} + 506043183348 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{22} - 186855789276 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{23} + 8802017172 \, \tan\left(\frac{1}{2} \, a\right)^{25} + 4363726131 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{7} \tan\left(\frac{1}{2} \, a\right)^{16} - 23718089916 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{17} + 3422040164 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{18} + 180365650620 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{19} - 386477003556 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{20} + 313110921612 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{21} - 100600780788 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{22} + 8802017172 \, \tan\left(\frac{1}{2} \, a\right)^{23} - 2624819022 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{7} \tan\left(\frac{1}{2} \, a\right)^{14} + 26510577474 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{15} - 91329113691 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{16} + 118445882004 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{17} - 5258310492 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{18} - 109057608828 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{19} + 77490791364 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{20} - 14857714436 \, \tan\left(\frac{1}{2} \, a\right)^{21} + 762446542 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{7} \tan\left(\frac{1}{2} \, a\right)^{12} - 10699256970 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{13} + 55167038478 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{14} - 132573864918 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{15} + 152452905381 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{16} - 71047415988 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{17} + 750175580 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{18} + 5273542932 \, \tan\left(\frac{1}{2} \, a\right)^{19} - 122301894 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{7} \tan\left(\frac{1}{2} \, a\right)^{10} + 2299471746 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{11} - 16002520222 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{12} + 53489761470 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{13} - 92023852050 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{14} + 79837550214 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{15} - 30651378381 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{16} + 3377366748 \, \tan\left(\frac{1}{2} \, a\right)^{17} + 11649780 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{7} \tan\left(\frac{1}{2} \, a\right)^{8} - 281501690 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{9} + 2589365766 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{10} - 11500345350 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{11} + 26616485090 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{12} - 32055103710 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{13} + 18462316050 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{14} - 3833122290 \, \tan\left(\frac{1}{2} \, a\right)^{15} - 648690 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{7} \tan\left(\frac{1}{2} \, a\right)^{6} + 20073870 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{7} - 240373332 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{8} + 1410179550 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{9} - 4307714970 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{10} + 6857208774 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{11} - 5284344754 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{12} + 1522201770 \, \tan\left(\frac{1}{2} \, a\right)^{13} + 16938 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{7} \tan\left(\frac{1}{2} \, a\right)^{4} - 772902 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{5} + 12606642 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{6} - 99232506 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{7} + 404516268 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{8} - 849637038 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{9} + 856321050 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{10} - 322093122 \, \tan\left(\frac{1}{2} \, a\right)^{11} + 54 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{7} \tan\left(\frac{1}{2} \, a\right)^{2} + 10878 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{3} - 320922 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{4} + 3790962 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{5} - 21805614 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{6} + 62438634 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{7} - 83542284 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{8} + 40894922 \, \tan\left(\frac{1}{2} \, a\right)^{9} - 9 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{7} + 90 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right) + 2058 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{2} - 59994 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{3} + 601830 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{4} - 2617650 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{5} + 4933038 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{6} - 3248766 \, \tan\left(\frac{1}{2} \, a\right)^{7} + \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} + 162 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right) - 5718 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{2} + 53562 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{3} - 166230 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{4} + 159462 \, \tan\left(\frac{1}{2} \, a\right)^{5} + \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} - 306 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right) + 2646 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{2} - 4446 \, \tan\left(\frac{1}{2} \, a\right)^{3} - 9 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) + 54 \, \tan\left(\frac{1}{2} \, a\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, a\right)^{24} - 60 \, \tan\left(\frac{1}{2} \, a\right)^{22} + 1410 \, \tan\left(\frac{1}{2} \, a\right)^{20} - 16204 \, \tan\left(\frac{1}{2} \, a\right)^{18} + 92655 \, \tan\left(\frac{1}{2} \, a\right)^{16} - 245880 \, \tan\left(\frac{1}{2} \, a\right)^{14} + 336156 \, \tan\left(\frac{1}{2} \, a\right)^{12} - 245880 \, \tan\left(\frac{1}{2} \, a\right)^{10} + 92655 \, \tan\left(\frac{1}{2} \, a\right)^{8} - 16204 \, \tan\left(\frac{1}{2} \, a\right)^{6} + 1410 \, \tan\left(\frac{1}{2} \, a\right)^{4} - 60 \, \tan\left(\frac{1}{2} \, a\right)^{2} + 1\right)} {\left(\tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{6} - 15 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{4} + 12 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{5} - \tan\left(\frac{1}{2} \, a\right)^{6} + 15 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} - 40 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{3} + 15 \, \tan\left(\frac{1}{2} \, a\right)^{4} - \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} + 12 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right) - 15 \, \tan\left(\frac{1}{2} \, a\right)^{2} + 1\right)}^{4}} - 15 \, \log\left({\left| \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{3} + 3 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{2} - \tan\left(\frac{1}{2} \, a\right)^{3} - 3 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right) + 3 \, \tan\left(\frac{1}{2} \, a\right)^{2} - \tan\left(\frac{1}{2} \, b x + 2 \, a\right) + 3 \, \tan\left(\frac{1}{2} \, a\right) - 1 \right|}\right) + 15 \, \log\left({\left| \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{3} - 3 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{2} + \tan\left(\frac{1}{2} \, a\right)^{3} - 3 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right) + 3 \, \tan\left(\frac{1}{2} \, a\right)^{2} + \tan\left(\frac{1}{2} \, b x + 2 \, a\right) - 3 \, \tan\left(\frac{1}{2} \, a\right) - 1 \right|}\right)}{256 \, b}"," ",0,"-1/256*(4*(tan(1/2*b*x + 2*a)*tan(1/2*a)^12 - 12*tan(1/2*b*x + 2*a)*tan(1/2*a)^10 + 6*tan(1/2*a)^11 - 27*tan(1/2*b*x + 2*a)*tan(1/2*a)^8 - 2*tan(1/2*a)^9 - 36*tan(1/2*a)^7 + 27*tan(1/2*b*x + 2*a)*tan(1/2*a)^4 - 36*tan(1/2*a)^5 + 12*tan(1/2*b*x + 2*a)*tan(1/2*a)^2 - 2*tan(1/2*a)^3 - tan(1/2*b*x + 2*a) + 6*tan(1/2*a))/((3*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^5 - tan(1/2*b*x + 2*a)*tan(1/2*a)^6 - 10*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^3 + 15*tan(1/2*b*x + 2*a)*tan(1/2*a)^4 - 3*tan(1/2*a)^5 + 3*tan(1/2*b*x + 2*a)^2*tan(1/2*a) - 15*tan(1/2*b*x + 2*a)*tan(1/2*a)^2 + 10*tan(1/2*a)^3 + tan(1/2*b*x + 2*a) - 3*tan(1/2*a))*(3*tan(1/2*a)^5 - 10*tan(1/2*a)^3 + 3*tan(1/2*a))) + 2*(9*tan(1/2*b*x + 2*a)^7*tan(1/2*a)^48 - 54*tan(1/2*b*x + 2*a)^7*tan(1/2*a)^46 + 90*tan(1/2*b*x + 2*a)^6*tan(1/2*a)^47 - tan(1/2*b*x + 2*a)^5*tan(1/2*a)^48 - 16938*tan(1/2*b*x + 2*a)^7*tan(1/2*a)^44 + 10878*tan(1/2*b*x + 2*a)^6*tan(1/2*a)^45 - 2058*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^46 + 162*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^47 - tan(1/2*b*x + 2*a)^3*tan(1/2*a)^48 + 648690*tan(1/2*b*x + 2*a)^7*tan(1/2*a)^42 - 772902*tan(1/2*b*x + 2*a)^6*tan(1/2*a)^43 + 320922*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^44 - 59994*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^45 + 5718*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^46 - 306*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^47 + 9*tan(1/2*b*x + 2*a)*tan(1/2*a)^48 - 11649780*tan(1/2*b*x + 2*a)^7*tan(1/2*a)^40 + 20073870*tan(1/2*b*x + 2*a)^6*tan(1/2*a)^41 - 12606642*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^42 + 3790962*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^43 - 601830*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^44 + 53562*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^45 - 2646*tan(1/2*b*x + 2*a)*tan(1/2*a)^46 + 54*tan(1/2*a)^47 + 122301894*tan(1/2*b*x + 2*a)^7*tan(1/2*a)^38 - 281501690*tan(1/2*b*x + 2*a)^6*tan(1/2*a)^39 + 240373332*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^40 - 99232506*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^41 + 21805614*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^42 - 2617650*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^43 + 166230*tan(1/2*b*x + 2*a)*tan(1/2*a)^44 - 4446*tan(1/2*a)^45 - 762446542*tan(1/2*b*x + 2*a)^7*tan(1/2*a)^36 + 2299471746*tan(1/2*b*x + 2*a)^6*tan(1/2*a)^37 - 2589365766*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^38 + 1410179550*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^39 - 404516268*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^40 + 62438634*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^41 - 4933038*tan(1/2*b*x + 2*a)*tan(1/2*a)^42 + 159462*tan(1/2*a)^43 + 2624819022*tan(1/2*b*x + 2*a)^7*tan(1/2*a)^34 - 10699256970*tan(1/2*b*x + 2*a)^6*tan(1/2*a)^35 + 16002520222*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^36 - 11500345350*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^37 + 4307714970*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^38 - 849637038*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^39 + 83542284*tan(1/2*b*x + 2*a)*tan(1/2*a)^40 - 3248766*tan(1/2*a)^41 - 4363726131*tan(1/2*b*x + 2*a)^7*tan(1/2*a)^32 + 26510577474*tan(1/2*b*x + 2*a)^6*tan(1/2*a)^33 - 55167038478*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^34 + 53489761470*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^35 - 26616485090*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^36 + 6857208774*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^37 - 856321050*tan(1/2*b*x + 2*a)*tan(1/2*a)^38 + 40894922*tan(1/2*a)^39 + 148294628*tan(1/2*b*x + 2*a)^7*tan(1/2*a)^30 - 23718089916*tan(1/2*b*x + 2*a)^6*tan(1/2*a)^31 + 91329113691*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^32 - 132573864918*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^33 + 92023852050*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^34 - 32055103710*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^35 + 5284344754*tan(1/2*b*x + 2*a)*tan(1/2*a)^36 - 322093122*tan(1/2*a)^37 + 11061475644*tan(1/2*b*x + 2*a)^7*tan(1/2*a)^28 - 36130112340*tan(1/2*b*x + 2*a)^6*tan(1/2*a)^29 - 3422040164*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^30 + 118445882004*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^31 - 152452905381*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^32 + 79837550214*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^33 - 18462316050*tan(1/2*b*x + 2*a)*tan(1/2*a)^34 + 1522201770*tan(1/2*a)^35 - 14430929868*tan(1/2*b*x + 2*a)^7*tan(1/2*a)^26 + 104533629188*tan(1/2*b*x + 2*a)^6*tan(1/2*a)^27 - 231729549276*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^28 + 180365650620*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^29 + 5258310492*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^30 - 71047415988*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^31 + 30651378381*tan(1/2*b*x + 2*a)*tan(1/2*a)^32 - 3833122290*tan(1/2*a)^33 - 62534029428*tan(1/2*b*x + 2*a)^6*tan(1/2*a)^25 + 304139029068*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^26 - 522734622092*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^27 + 386477003556*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^28 - 109057608828*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^29 - 750175580*tan(1/2*b*x + 2*a)*tan(1/2*a)^30 + 3377366748*tan(1/2*a)^31 + 14430929868*tan(1/2*b*x + 2*a)^7*tan(1/2*a)^22 - 62534029428*tan(1/2*b*x + 2*a)^6*tan(1/2*a)^23 + 313058642364*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^25 - 506043183348*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^26 + 313110921612*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^27 - 77490791364*tan(1/2*b*x + 2*a)*tan(1/2*a)^28 + 5273542932*tan(1/2*a)^29 - 11061475644*tan(1/2*b*x + 2*a)^7*tan(1/2*a)^20 + 104533629188*tan(1/2*b*x + 2*a)^6*tan(1/2*a)^21 - 304139029068*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^22 + 313058642364*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^23 - 186855789276*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^25 + 100600780788*tan(1/2*b*x + 2*a)*tan(1/2*a)^26 - 14857714436*tan(1/2*a)^27 - 148294628*tan(1/2*b*x + 2*a)^7*tan(1/2*a)^18 - 36130112340*tan(1/2*b*x + 2*a)^6*tan(1/2*a)^19 + 231729549276*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^20 - 522734622092*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^21 + 506043183348*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^22 - 186855789276*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^23 + 8802017172*tan(1/2*a)^25 + 4363726131*tan(1/2*b*x + 2*a)^7*tan(1/2*a)^16 - 23718089916*tan(1/2*b*x + 2*a)^6*tan(1/2*a)^17 + 3422040164*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^18 + 180365650620*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^19 - 386477003556*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^20 + 313110921612*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^21 - 100600780788*tan(1/2*b*x + 2*a)*tan(1/2*a)^22 + 8802017172*tan(1/2*a)^23 - 2624819022*tan(1/2*b*x + 2*a)^7*tan(1/2*a)^14 + 26510577474*tan(1/2*b*x + 2*a)^6*tan(1/2*a)^15 - 91329113691*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^16 + 118445882004*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^17 - 5258310492*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^18 - 109057608828*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^19 + 77490791364*tan(1/2*b*x + 2*a)*tan(1/2*a)^20 - 14857714436*tan(1/2*a)^21 + 762446542*tan(1/2*b*x + 2*a)^7*tan(1/2*a)^12 - 10699256970*tan(1/2*b*x + 2*a)^6*tan(1/2*a)^13 + 55167038478*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^14 - 132573864918*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^15 + 152452905381*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^16 - 71047415988*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^17 + 750175580*tan(1/2*b*x + 2*a)*tan(1/2*a)^18 + 5273542932*tan(1/2*a)^19 - 122301894*tan(1/2*b*x + 2*a)^7*tan(1/2*a)^10 + 2299471746*tan(1/2*b*x + 2*a)^6*tan(1/2*a)^11 - 16002520222*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^12 + 53489761470*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^13 - 92023852050*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^14 + 79837550214*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^15 - 30651378381*tan(1/2*b*x + 2*a)*tan(1/2*a)^16 + 3377366748*tan(1/2*a)^17 + 11649780*tan(1/2*b*x + 2*a)^7*tan(1/2*a)^8 - 281501690*tan(1/2*b*x + 2*a)^6*tan(1/2*a)^9 + 2589365766*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^10 - 11500345350*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^11 + 26616485090*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^12 - 32055103710*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^13 + 18462316050*tan(1/2*b*x + 2*a)*tan(1/2*a)^14 - 3833122290*tan(1/2*a)^15 - 648690*tan(1/2*b*x + 2*a)^7*tan(1/2*a)^6 + 20073870*tan(1/2*b*x + 2*a)^6*tan(1/2*a)^7 - 240373332*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^8 + 1410179550*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^9 - 4307714970*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^10 + 6857208774*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^11 - 5284344754*tan(1/2*b*x + 2*a)*tan(1/2*a)^12 + 1522201770*tan(1/2*a)^13 + 16938*tan(1/2*b*x + 2*a)^7*tan(1/2*a)^4 - 772902*tan(1/2*b*x + 2*a)^6*tan(1/2*a)^5 + 12606642*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^6 - 99232506*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^7 + 404516268*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^8 - 849637038*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^9 + 856321050*tan(1/2*b*x + 2*a)*tan(1/2*a)^10 - 322093122*tan(1/2*a)^11 + 54*tan(1/2*b*x + 2*a)^7*tan(1/2*a)^2 + 10878*tan(1/2*b*x + 2*a)^6*tan(1/2*a)^3 - 320922*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^4 + 3790962*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^5 - 21805614*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^6 + 62438634*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^7 - 83542284*tan(1/2*b*x + 2*a)*tan(1/2*a)^8 + 40894922*tan(1/2*a)^9 - 9*tan(1/2*b*x + 2*a)^7 + 90*tan(1/2*b*x + 2*a)^6*tan(1/2*a) + 2058*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^2 - 59994*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^3 + 601830*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^4 - 2617650*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^5 + 4933038*tan(1/2*b*x + 2*a)*tan(1/2*a)^6 - 3248766*tan(1/2*a)^7 + tan(1/2*b*x + 2*a)^5 + 162*tan(1/2*b*x + 2*a)^4*tan(1/2*a) - 5718*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^2 + 53562*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^3 - 166230*tan(1/2*b*x + 2*a)*tan(1/2*a)^4 + 159462*tan(1/2*a)^5 + tan(1/2*b*x + 2*a)^3 - 306*tan(1/2*b*x + 2*a)^2*tan(1/2*a) + 2646*tan(1/2*b*x + 2*a)*tan(1/2*a)^2 - 4446*tan(1/2*a)^3 - 9*tan(1/2*b*x + 2*a) + 54*tan(1/2*a))/((tan(1/2*a)^24 - 60*tan(1/2*a)^22 + 1410*tan(1/2*a)^20 - 16204*tan(1/2*a)^18 + 92655*tan(1/2*a)^16 - 245880*tan(1/2*a)^14 + 336156*tan(1/2*a)^12 - 245880*tan(1/2*a)^10 + 92655*tan(1/2*a)^8 - 16204*tan(1/2*a)^6 + 1410*tan(1/2*a)^4 - 60*tan(1/2*a)^2 + 1)*(tan(1/2*b*x + 2*a)^2*tan(1/2*a)^6 - 15*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^4 + 12*tan(1/2*b*x + 2*a)*tan(1/2*a)^5 - tan(1/2*a)^6 + 15*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^2 - 40*tan(1/2*b*x + 2*a)*tan(1/2*a)^3 + 15*tan(1/2*a)^4 - tan(1/2*b*x + 2*a)^2 + 12*tan(1/2*b*x + 2*a)*tan(1/2*a) - 15*tan(1/2*a)^2 + 1)^4) - 15*log(abs(tan(1/2*b*x + 2*a)*tan(1/2*a)^3 + 3*tan(1/2*b*x + 2*a)*tan(1/2*a)^2 - tan(1/2*a)^3 - 3*tan(1/2*b*x + 2*a)*tan(1/2*a) + 3*tan(1/2*a)^2 - tan(1/2*b*x + 2*a) + 3*tan(1/2*a) - 1)) + 15*log(abs(tan(1/2*b*x + 2*a)*tan(1/2*a)^3 - 3*tan(1/2*b*x + 2*a)*tan(1/2*a)^2 + tan(1/2*a)^3 - 3*tan(1/2*b*x + 2*a)*tan(1/2*a) + 3*tan(1/2*a)^2 + tan(1/2*b*x + 2*a) - 3*tan(1/2*a) - 1)))/b","B",0
33,1,270,0,1.177922," ","integrate(csc(b*x+a)*sin(2*b*x+2*a)^8,x, algorithm=""giac"")","-\frac{8192 \, {\left(\frac{15 \, {\left(\cos\left(b x + a\right) - 1\right)}}{\cos\left(b x + a\right) + 1} - \frac{105 \, {\left(\cos\left(b x + a\right) - 1\right)}^{2}}{{\left(\cos\left(b x + a\right) + 1\right)}^{2}} + \frac{455 \, {\left(\cos\left(b x + a\right) - 1\right)}^{3}}{{\left(\cos\left(b x + a\right) + 1\right)}^{3}} + \frac{5070 \, {\left(\cos\left(b x + a\right) - 1\right)}^{4}}{{\left(\cos\left(b x + a\right) + 1\right)}^{4}} + \frac{30030 \, {\left(\cos\left(b x + a\right) - 1\right)}^{5}}{{\left(\cos\left(b x + a\right) + 1\right)}^{5}} + \frac{70070 \, {\left(\cos\left(b x + a\right) - 1\right)}^{6}}{{\left(\cos\left(b x + a\right) + 1\right)}^{6}} + \frac{115830 \, {\left(\cos\left(b x + a\right) - 1\right)}^{7}}{{\left(\cos\left(b x + a\right) + 1\right)}^{7}} + \frac{109395 \, {\left(\cos\left(b x + a\right) - 1\right)}^{8}}{{\left(\cos\left(b x + a\right) + 1\right)}^{8}} + \frac{75075 \, {\left(\cos\left(b x + a\right) - 1\right)}^{9}}{{\left(\cos\left(b x + a\right) + 1\right)}^{9}} + \frac{27027 \, {\left(\cos\left(b x + a\right) - 1\right)}^{10}}{{\left(\cos\left(b x + a\right) + 1\right)}^{10}} + \frac{6435 \, {\left(\cos\left(b x + a\right) - 1\right)}^{11}}{{\left(\cos\left(b x + a\right) + 1\right)}^{11}} - 1\right)}}{6435 \, b {\left(\frac{\cos\left(b x + a\right) - 1}{\cos\left(b x + a\right) + 1} - 1\right)}^{15}}"," ",0,"-8192/6435*(15*(cos(b*x + a) - 1)/(cos(b*x + a) + 1) - 105*(cos(b*x + a) - 1)^2/(cos(b*x + a) + 1)^2 + 455*(cos(b*x + a) - 1)^3/(cos(b*x + a) + 1)^3 + 5070*(cos(b*x + a) - 1)^4/(cos(b*x + a) + 1)^4 + 30030*(cos(b*x + a) - 1)^5/(cos(b*x + a) + 1)^5 + 70070*(cos(b*x + a) - 1)^6/(cos(b*x + a) + 1)^6 + 115830*(cos(b*x + a) - 1)^7/(cos(b*x + a) + 1)^7 + 109395*(cos(b*x + a) - 1)^8/(cos(b*x + a) + 1)^8 + 75075*(cos(b*x + a) - 1)^9/(cos(b*x + a) + 1)^9 + 27027*(cos(b*x + a) - 1)^10/(cos(b*x + a) + 1)^10 + 6435*(cos(b*x + a) - 1)^11/(cos(b*x + a) + 1)^11 - 1)/(b*((cos(b*x + a) - 1)/(cos(b*x + a) + 1) - 1)^15)","B",0
34,1,46,0,0.989799," ","integrate(csc(b*x+a)*sin(2*b*x+2*a)^7,x, algorithm=""giac"")","-\frac{128 \, {\left(231 \, \sin\left(b x + a\right)^{13} - 819 \, \sin\left(b x + a\right)^{11} + 1001 \, \sin\left(b x + a\right)^{9} - 429 \, \sin\left(b x + a\right)^{7}\right)}}{3003 \, b}"," ",0,"-128/3003*(231*sin(b*x + a)^13 - 819*sin(b*x + a)^11 + 1001*sin(b*x + a)^9 - 429*sin(b*x + a)^7)/b","A",0
35,1,204,0,0.808035," ","integrate(csc(b*x+a)*sin(2*b*x+2*a)^6,x, algorithm=""giac"")","-\frac{1024 \, {\left(\frac{11 \, {\left(\cos\left(b x + a\right) - 1\right)}}{\cos\left(b x + a\right) + 1} - \frac{55 \, {\left(\cos\left(b x + a\right) - 1\right)}^{2}}{{\left(\cos\left(b x + a\right) + 1\right)}^{2}} - \frac{297 \, {\left(\cos\left(b x + a\right) - 1\right)}^{3}}{{\left(\cos\left(b x + a\right) + 1\right)}^{3}} - \frac{1485 \, {\left(\cos\left(b x + a\right) - 1\right)}^{4}}{{\left(\cos\left(b x + a\right) + 1\right)}^{4}} - \frac{2079 \, {\left(\cos\left(b x + a\right) - 1\right)}^{5}}{{\left(\cos\left(b x + a\right) + 1\right)}^{5}} - \frac{2541 \, {\left(\cos\left(b x + a\right) - 1\right)}^{6}}{{\left(\cos\left(b x + a\right) + 1\right)}^{6}} - \frac{1155 \, {\left(\cos\left(b x + a\right) - 1\right)}^{7}}{{\left(\cos\left(b x + a\right) + 1\right)}^{7}} - \frac{462 \, {\left(\cos\left(b x + a\right) - 1\right)}^{8}}{{\left(\cos\left(b x + a\right) + 1\right)}^{8}} - 1\right)}}{693 \, b {\left(\frac{\cos\left(b x + a\right) - 1}{\cos\left(b x + a\right) + 1} - 1\right)}^{11}}"," ",0,"-1024/693*(11*(cos(b*x + a) - 1)/(cos(b*x + a) + 1) - 55*(cos(b*x + a) - 1)^2/(cos(b*x + a) + 1)^2 - 297*(cos(b*x + a) - 1)^3/(cos(b*x + a) + 1)^3 - 1485*(cos(b*x + a) - 1)^4/(cos(b*x + a) + 1)^4 - 2079*(cos(b*x + a) - 1)^5/(cos(b*x + a) + 1)^5 - 2541*(cos(b*x + a) - 1)^6/(cos(b*x + a) + 1)^6 - 1155*(cos(b*x + a) - 1)^7/(cos(b*x + a) + 1)^7 - 462*(cos(b*x + a) - 1)^8/(cos(b*x + a) + 1)^8 - 1)/(b*((cos(b*x + a) - 1)/(cos(b*x + a) + 1) - 1)^11)","B",0
36,1,36,0,0.651156," ","integrate(csc(b*x+a)*sin(2*b*x+2*a)^5,x, algorithm=""giac"")","\frac{32 \, {\left(35 \, \sin\left(b x + a\right)^{9} - 90 \, \sin\left(b x + a\right)^{7} + 63 \, \sin\left(b x + a\right)^{5}\right)}}{315 \, b}"," ",0,"32/315*(35*sin(b*x + a)^9 - 90*sin(b*x + a)^7 + 63*sin(b*x + a)^5)/b","A",0
37,1,138,0,0.562430," ","integrate(csc(b*x+a)*sin(2*b*x+2*a)^4,x, algorithm=""giac"")","-\frac{64 \, {\left(\frac{7 \, {\left(\cos\left(b x + a\right) - 1\right)}}{\cos\left(b x + a\right) + 1} + \frac{14 \, {\left(\cos\left(b x + a\right) - 1\right)}^{2}}{{\left(\cos\left(b x + a\right) + 1\right)}^{2}} + \frac{70 \, {\left(\cos\left(b x + a\right) - 1\right)}^{3}}{{\left(\cos\left(b x + a\right) + 1\right)}^{3}} + \frac{35 \, {\left(\cos\left(b x + a\right) - 1\right)}^{4}}{{\left(\cos\left(b x + a\right) + 1\right)}^{4}} + \frac{35 \, {\left(\cos\left(b x + a\right) - 1\right)}^{5}}{{\left(\cos\left(b x + a\right) + 1\right)}^{5}} - 1\right)}}{35 \, b {\left(\frac{\cos\left(b x + a\right) - 1}{\cos\left(b x + a\right) + 1} - 1\right)}^{7}}"," ",0,"-64/35*(7*(cos(b*x + a) - 1)/(cos(b*x + a) + 1) + 14*(cos(b*x + a) - 1)^2/(cos(b*x + a) + 1)^2 + 70*(cos(b*x + a) - 1)^3/(cos(b*x + a) + 1)^3 + 35*(cos(b*x + a) - 1)^4/(cos(b*x + a) + 1)^4 + 35*(cos(b*x + a) - 1)^5/(cos(b*x + a) + 1)^5 - 1)/(b*((cos(b*x + a) - 1)/(cos(b*x + a) + 1) - 1)^7)","B",0
38,1,26,0,0.361447," ","integrate(csc(b*x+a)*sin(2*b*x+2*a)^3,x, algorithm=""giac"")","-\frac{8 \, {\left(3 \, \sin\left(b x + a\right)^{5} - 5 \, \sin\left(b x + a\right)^{3}\right)}}{15 \, b}"," ",0,"-8/15*(3*sin(b*x + a)^5 - 5*sin(b*x + a)^3)/b","A",0
39,1,52,0,0.371982," ","integrate(csc(b*x+a)*sin(2*b*x+2*a)^2,x, algorithm=""giac"")","\frac{8 \, {\left(\frac{3 \, {\left(\cos\left(b x + a\right) - 1\right)}^{2}}{{\left(\cos\left(b x + a\right) + 1\right)}^{2}} + 1\right)}}{3 \, b {\left(\frac{\cos\left(b x + a\right) - 1}{\cos\left(b x + a\right) + 1} - 1\right)}^{3}}"," ",0,"8/3*(3*(cos(b*x + a) - 1)^2/(cos(b*x + a) + 1)^2 + 1)/(b*((cos(b*x + a) - 1)/(cos(b*x + a) + 1) - 1)^3)","B",0
40,1,11,0,0.361501," ","integrate(csc(b*x+a)*sin(2*b*x+2*a),x, algorithm=""giac"")","\frac{2 \, \sin\left(b x + a\right)}{b}"," ",0,"2*sin(b*x + a)/b","A",0
41,1,484,0,1.695549," ","integrate(csc(b*x+a)*csc(2*b*x+2*a),x, algorithm=""giac"")","-\frac{\frac{\tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{12} - 12 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{10} + 6 \, \tan\left(\frac{1}{2} \, a\right)^{11} - 27 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{8} - 2 \, \tan\left(\frac{1}{2} \, a\right)^{9} - 36 \, \tan\left(\frac{1}{2} \, a\right)^{7} + 27 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{4} - 36 \, \tan\left(\frac{1}{2} \, a\right)^{5} + 12 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, a\right)^{3} - \tan\left(\frac{1}{2} \, b x + 2 \, a\right) + 6 \, \tan\left(\frac{1}{2} \, a\right)}{{\left(3 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{5} - \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{6} - 10 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{3} + 15 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{4} - 3 \, \tan\left(\frac{1}{2} \, a\right)^{5} + 3 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right) - 15 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{2} + 10 \, \tan\left(\frac{1}{2} \, a\right)^{3} + \tan\left(\frac{1}{2} \, b x + 2 \, a\right) - 3 \, \tan\left(\frac{1}{2} \, a\right)\right)} {\left(3 \, \tan\left(\frac{1}{2} \, a\right)^{5} - 10 \, \tan\left(\frac{1}{2} \, a\right)^{3} + 3 \, \tan\left(\frac{1}{2} \, a\right)\right)}} - 2 \, \log\left({\left| \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{3} + 3 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{2} - \tan\left(\frac{1}{2} \, a\right)^{3} - 3 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right) + 3 \, \tan\left(\frac{1}{2} \, a\right)^{2} - \tan\left(\frac{1}{2} \, b x + 2 \, a\right) + 3 \, \tan\left(\frac{1}{2} \, a\right) - 1 \right|}\right) + 2 \, \log\left({\left| \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{3} - 3 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{2} + \tan\left(\frac{1}{2} \, a\right)^{3} - 3 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right) + 3 \, \tan\left(\frac{1}{2} \, a\right)^{2} + \tan\left(\frac{1}{2} \, b x + 2 \, a\right) - 3 \, \tan\left(\frac{1}{2} \, a\right) - 1 \right|}\right)}{4 \, b}"," ",0,"-1/4*((tan(1/2*b*x + 2*a)*tan(1/2*a)^12 - 12*tan(1/2*b*x + 2*a)*tan(1/2*a)^10 + 6*tan(1/2*a)^11 - 27*tan(1/2*b*x + 2*a)*tan(1/2*a)^8 - 2*tan(1/2*a)^9 - 36*tan(1/2*a)^7 + 27*tan(1/2*b*x + 2*a)*tan(1/2*a)^4 - 36*tan(1/2*a)^5 + 12*tan(1/2*b*x + 2*a)*tan(1/2*a)^2 - 2*tan(1/2*a)^3 - tan(1/2*b*x + 2*a) + 6*tan(1/2*a))/((3*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^5 - tan(1/2*b*x + 2*a)*tan(1/2*a)^6 - 10*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^3 + 15*tan(1/2*b*x + 2*a)*tan(1/2*a)^4 - 3*tan(1/2*a)^5 + 3*tan(1/2*b*x + 2*a)^2*tan(1/2*a) - 15*tan(1/2*b*x + 2*a)*tan(1/2*a)^2 + 10*tan(1/2*a)^3 + tan(1/2*b*x + 2*a) - 3*tan(1/2*a))*(3*tan(1/2*a)^5 - 10*tan(1/2*a)^3 + 3*tan(1/2*a))) - 2*log(abs(tan(1/2*b*x + 2*a)*tan(1/2*a)^3 + 3*tan(1/2*b*x + 2*a)*tan(1/2*a)^2 - tan(1/2*a)^3 - 3*tan(1/2*b*x + 2*a)*tan(1/2*a) + 3*tan(1/2*a)^2 - tan(1/2*b*x + 2*a) + 3*tan(1/2*a) - 1)) + 2*log(abs(tan(1/2*b*x + 2*a)*tan(1/2*a)^3 - 3*tan(1/2*b*x + 2*a)*tan(1/2*a)^2 + tan(1/2*a)^3 - 3*tan(1/2*b*x + 2*a)*tan(1/2*a) + 3*tan(1/2*a)^2 + tan(1/2*b*x + 2*a) - 3*tan(1/2*a) - 1)))/b","B",0
42,1,1327,0,1.607150," ","integrate(csc(b*x+a)*csc(2*b*x+2*a)^2,x, algorithm=""giac"")","-\frac{\frac{16 \, {\left(6 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{11} - \tan\left(\frac{1}{2} \, a\right)^{12} - 2 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{9} + 12 \, \tan\left(\frac{1}{2} \, a\right)^{10} - 36 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{7} + 27 \, \tan\left(\frac{1}{2} \, a\right)^{8} - 36 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{5} - 2 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{3} - 27 \, \tan\left(\frac{1}{2} \, a\right)^{4} + 6 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right) - 12 \, \tan\left(\frac{1}{2} \, a\right)^{2} + 1\right)}}{{\left(\tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{6} - 15 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{4} + 12 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{5} - \tan\left(\frac{1}{2} \, a\right)^{6} + 15 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} - 40 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{3} + 15 \, \tan\left(\frac{1}{2} \, a\right)^{4} - \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} + 12 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right) - 15 \, \tan\left(\frac{1}{2} \, a\right)^{2} + 1\right)} {\left(\tan\left(\frac{1}{2} \, a\right)^{6} - 15 \, \tan\left(\frac{1}{2} \, a\right)^{4} + 15 \, \tan\left(\frac{1}{2} \, a\right)^{2} - 1\right)}} + \frac{6 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{23} - \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{24} - 74 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{21} + 60 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{22} - 6 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{23} + 798 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{19} - 924 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{20} + 290 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{21} - 18 \, \tan\left(\frac{1}{2} \, a\right)^{22} - 1170 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{17} + 3892 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{18} - 2310 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{19} + 336 \, \tan\left(\frac{1}{2} \, a\right)^{20} - 3188 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{15} + 1467 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{16} + 3186 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{17} - 1190 \, \tan\left(\frac{1}{2} \, a\right)^{18} + 2604 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{13} - 12744 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{14} + 8148 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{15} - 288 \, \tan\left(\frac{1}{2} \, a\right)^{16} + 2604 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{11} - 10332 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{13} + 4428 \, \tan\left(\frac{1}{2} \, a\right)^{14} - 3188 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{9} + 12744 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{10} - 10332 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{11} - 1170 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{7} - 1467 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{8} + 8148 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{9} - 4428 \, \tan\left(\frac{1}{2} \, a\right)^{10} + 798 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{5} - 3892 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{6} + 3186 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{7} + 288 \, \tan\left(\frac{1}{2} \, a\right)^{8} - 74 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{3} + 924 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{4} - 2310 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{5} + 1190 \, \tan\left(\frac{1}{2} \, a\right)^{6} + 6 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right) - 60 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} + 290 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{3} - 336 \, \tan\left(\frac{1}{2} \, a\right)^{4} + \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} - 6 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right) + 18 \, \tan\left(\frac{1}{2} \, a\right)^{2}}{{\left(9 \, \tan\left(\frac{1}{2} \, a\right)^{10} - 60 \, \tan\left(\frac{1}{2} \, a\right)^{8} + 118 \, \tan\left(\frac{1}{2} \, a\right)^{6} - 60 \, \tan\left(\frac{1}{2} \, a\right)^{4} + 9 \, \tan\left(\frac{1}{2} \, a\right)^{2}\right)} {\left(3 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{5} - \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{6} - 10 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{3} + 15 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{4} - 3 \, \tan\left(\frac{1}{2} \, a\right)^{5} + 3 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right) - 15 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{2} + 10 \, \tan\left(\frac{1}{2} \, a\right)^{3} + \tan\left(\frac{1}{2} \, b x + 2 \, a\right) - 3 \, \tan\left(\frac{1}{2} \, a\right)\right)}^{2}} + 12 \, \log\left({\left| \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{3} - 3 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right) + 3 \, \tan\left(\frac{1}{2} \, a\right)^{2} - 1 \right|}\right) - 12 \, \log\left({\left| 3 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{2} - \tan\left(\frac{1}{2} \, a\right)^{3} - \tan\left(\frac{1}{2} \, b x + 2 \, a\right) + 3 \, \tan\left(\frac{1}{2} \, a\right) \right|}\right)}{32 \, b}"," ",0,"-1/32*(16*(6*tan(1/2*b*x + 2*a)*tan(1/2*a)^11 - tan(1/2*a)^12 - 2*tan(1/2*b*x + 2*a)*tan(1/2*a)^9 + 12*tan(1/2*a)^10 - 36*tan(1/2*b*x + 2*a)*tan(1/2*a)^7 + 27*tan(1/2*a)^8 - 36*tan(1/2*b*x + 2*a)*tan(1/2*a)^5 - 2*tan(1/2*b*x + 2*a)*tan(1/2*a)^3 - 27*tan(1/2*a)^4 + 6*tan(1/2*b*x + 2*a)*tan(1/2*a) - 12*tan(1/2*a)^2 + 1)/((tan(1/2*b*x + 2*a)^2*tan(1/2*a)^6 - 15*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^4 + 12*tan(1/2*b*x + 2*a)*tan(1/2*a)^5 - tan(1/2*a)^6 + 15*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^2 - 40*tan(1/2*b*x + 2*a)*tan(1/2*a)^3 + 15*tan(1/2*a)^4 - tan(1/2*b*x + 2*a)^2 + 12*tan(1/2*b*x + 2*a)*tan(1/2*a) - 15*tan(1/2*a)^2 + 1)*(tan(1/2*a)^6 - 15*tan(1/2*a)^4 + 15*tan(1/2*a)^2 - 1)) + (6*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^23 - tan(1/2*b*x + 2*a)^2*tan(1/2*a)^24 - 74*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^21 + 60*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^22 - 6*tan(1/2*b*x + 2*a)*tan(1/2*a)^23 + 798*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^19 - 924*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^20 + 290*tan(1/2*b*x + 2*a)*tan(1/2*a)^21 - 18*tan(1/2*a)^22 - 1170*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^17 + 3892*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^18 - 2310*tan(1/2*b*x + 2*a)*tan(1/2*a)^19 + 336*tan(1/2*a)^20 - 3188*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^15 + 1467*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^16 + 3186*tan(1/2*b*x + 2*a)*tan(1/2*a)^17 - 1190*tan(1/2*a)^18 + 2604*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^13 - 12744*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^14 + 8148*tan(1/2*b*x + 2*a)*tan(1/2*a)^15 - 288*tan(1/2*a)^16 + 2604*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^11 - 10332*tan(1/2*b*x + 2*a)*tan(1/2*a)^13 + 4428*tan(1/2*a)^14 - 3188*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^9 + 12744*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^10 - 10332*tan(1/2*b*x + 2*a)*tan(1/2*a)^11 - 1170*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^7 - 1467*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^8 + 8148*tan(1/2*b*x + 2*a)*tan(1/2*a)^9 - 4428*tan(1/2*a)^10 + 798*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^5 - 3892*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^6 + 3186*tan(1/2*b*x + 2*a)*tan(1/2*a)^7 + 288*tan(1/2*a)^8 - 74*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^3 + 924*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^4 - 2310*tan(1/2*b*x + 2*a)*tan(1/2*a)^5 + 1190*tan(1/2*a)^6 + 6*tan(1/2*b*x + 2*a)^3*tan(1/2*a) - 60*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^2 + 290*tan(1/2*b*x + 2*a)*tan(1/2*a)^3 - 336*tan(1/2*a)^4 + tan(1/2*b*x + 2*a)^2 - 6*tan(1/2*b*x + 2*a)*tan(1/2*a) + 18*tan(1/2*a)^2)/((9*tan(1/2*a)^10 - 60*tan(1/2*a)^8 + 118*tan(1/2*a)^6 - 60*tan(1/2*a)^4 + 9*tan(1/2*a)^2)*(3*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^5 - tan(1/2*b*x + 2*a)*tan(1/2*a)^6 - 10*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^3 + 15*tan(1/2*b*x + 2*a)*tan(1/2*a)^4 - 3*tan(1/2*a)^5 + 3*tan(1/2*b*x + 2*a)^2*tan(1/2*a) - 15*tan(1/2*b*x + 2*a)*tan(1/2*a)^2 + 10*tan(1/2*a)^3 + tan(1/2*b*x + 2*a) - 3*tan(1/2*a))^2) + 12*log(abs(tan(1/2*b*x + 2*a)*tan(1/2*a)^3 - 3*tan(1/2*b*x + 2*a)*tan(1/2*a) + 3*tan(1/2*a)^2 - 1)) - 12*log(abs(3*tan(1/2*b*x + 2*a)*tan(1/2*a)^2 - tan(1/2*a)^3 - tan(1/2*b*x + 2*a) + 3*tan(1/2*a))))/b","B",0
43,1,3033,0,3.944176," ","integrate(csc(b*x+a)*csc(2*b*x+2*a)^3,x, algorithm=""giac"")","-\frac{\frac{24 \, {\left(\tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{24} + 30 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{22} - 6 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{23} + \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{24} - 756 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{20} + 614 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{21} - 114 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{22} + 6 \, \tan\left(\frac{1}{2} \, a\right)^{23} + 2058 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{18} - 4578 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{19} + 1932 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{20} - 182 \, \tan\left(\frac{1}{2} \, a\right)^{21} - 27 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{16} + 6210 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{17} - 7462 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{18} + 1554 \, \tan\left(\frac{1}{2} \, a\right)^{19} - 9396 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{14} + 15588 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{15} - 2331 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{16} - 2178 \, \tan\left(\frac{1}{2} \, a\right)^{17} - 21924 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{13} + 26028 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{14} - 5668 \, \tan\left(\frac{1}{2} \, a\right)^{15} + 9396 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{10} - 21924 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{11} + 6468 \, \tan\left(\frac{1}{2} \, a\right)^{13} + 27 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{8} + 15588 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{9} - 26028 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{10} + 6468 \, \tan\left(\frac{1}{2} \, a\right)^{11} - 2058 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{6} + 6210 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{7} + 2331 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{8} - 5668 \, \tan\left(\frac{1}{2} \, a\right)^{9} + 756 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{4} - 4578 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{5} + 7462 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{6} - 2178 \, \tan\left(\frac{1}{2} \, a\right)^{7} - 30 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{2} + 614 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{3} - 1932 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{4} + 1554 \, \tan\left(\frac{1}{2} \, a\right)^{5} - \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} - 6 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right) + 114 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{2} - 182 \, \tan\left(\frac{1}{2} \, a\right)^{3} - \tan\left(\frac{1}{2} \, b x + 2 \, a\right) + 6 \, \tan\left(\frac{1}{2} \, a\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, a\right)^{12} - 30 \, \tan\left(\frac{1}{2} \, a\right)^{10} + 255 \, \tan\left(\frac{1}{2} \, a\right)^{8} - 452 \, \tan\left(\frac{1}{2} \, a\right)^{6} + 255 \, \tan\left(\frac{1}{2} \, a\right)^{4} - 30 \, \tan\left(\frac{1}{2} \, a\right)^{2} + 1\right)} {\left(\tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{6} - 15 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{4} + 12 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{5} - \tan\left(\frac{1}{2} \, a\right)^{6} + 15 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} - 40 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{3} + 15 \, \tan\left(\frac{1}{2} \, a\right)^{4} - \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} + 12 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right) - 15 \, \tan\left(\frac{1}{2} \, a\right)^{2} + 1\right)}^{2}} + \frac{27 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{34} - 9 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{35} + \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{36} + 1602 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{32} - 915 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{33} + 126 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{34} + 9 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{35} - 50082 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{30} + 58626 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{31} - 21141 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{32} + 2373 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{33} + 27 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{34} + 400050 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{28} - 783810 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{29} + 487692 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{30} - 118404 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{31} + 9378 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{32} + 54 \, \tan\left(\frac{1}{2} \, a\right)^{33} - 1301382 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{26} + 4035870 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{27} - 3943944 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{28} + 1555092 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{29} - 247074 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{30} + 11610 \, \tan\left(\frac{1}{2} \, a\right)^{31} + 1238250 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{24} - 8115822 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{25} + 13194468 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{26} - 8075232 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{27} + 1983762 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{28} - 160362 \, \tan\left(\frac{1}{2} \, a\right)^{29} + 2642310 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{22} - 1212390 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{23} - 12476880 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{24} + 16317288 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{25} - 6559110 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{26} + 805786 \, \tan\left(\frac{1}{2} \, a\right)^{27} - 5947398 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{20} + 25548198 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{21} - 27336420 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{22} + 2575260 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{23} + 6211530 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{24} - 1599858 \, \tan\left(\frac{1}{2} \, a\right)^{25} - 19824660 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{19} + 58330530 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{20} - 51141420 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{21} + 13453830 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{22} - 209790 \, \tan\left(\frac{1}{2} \, a\right)^{23} + 5947398 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{16} - 19824660 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{17} + 39278250 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{19} - 29430054 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{20} + 5059854 \, \tan\left(\frac{1}{2} \, a\right)^{21} - 2642310 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{14} + 25548198 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{15} - 58330530 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{16} + 39278250 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{17} - 4136670 \, \tan\left(\frac{1}{2} \, a\right)^{19} - 1238250 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{12} - 1212390 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{13} + 27336420 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{14} - 51141420 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{15} + 29430054 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{16} - 4136670 \, \tan\left(\frac{1}{2} \, a\right)^{17} + 1301382 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{10} - 8115822 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{11} + 12476880 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{12} + 2575260 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{13} - 13453830 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{14} + 5059854 \, \tan\left(\frac{1}{2} \, a\right)^{15} - 400050 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{8} + 4035870 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{9} - 13194468 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{10} + 16317288 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{11} - 6211530 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{12} - 209790 \, \tan\left(\frac{1}{2} \, a\right)^{13} + 50082 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{6} - 783810 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{7} + 3943944 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{8} - 8075232 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{9} + 6559110 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{10} - 1599858 \, \tan\left(\frac{1}{2} \, a\right)^{11} - 1602 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{4} + 58626 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{5} - 487692 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{6} + 1555092 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{7} - 1983762 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{8} + 805786 \, \tan\left(\frac{1}{2} \, a\right)^{9} - 27 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{2} - 915 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{3} + 21141 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{4} - 118404 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{5} + 247074 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{6} - 160362 \, \tan\left(\frac{1}{2} \, a\right)^{7} - 9 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right) - 126 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{2} + 2373 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{3} - 9378 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{4} + 11610 \, \tan\left(\frac{1}{2} \, a\right)^{5} - \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} + 9 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right) - 27 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{2} + 54 \, \tan\left(\frac{1}{2} \, a\right)^{3}}{{\left(27 \, \tan\left(\frac{1}{2} \, a\right)^{15} - 270 \, \tan\left(\frac{1}{2} \, a\right)^{13} + 981 \, \tan\left(\frac{1}{2} \, a\right)^{11} - 1540 \, \tan\left(\frac{1}{2} \, a\right)^{9} + 981 \, \tan\left(\frac{1}{2} \, a\right)^{7} - 270 \, \tan\left(\frac{1}{2} \, a\right)^{5} + 27 \, \tan\left(\frac{1}{2} \, a\right)^{3}\right)} {\left(3 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{5} - \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{6} - 10 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{3} + 15 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{4} - 3 \, \tan\left(\frac{1}{2} \, a\right)^{5} + 3 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right) - 15 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{2} + 10 \, \tan\left(\frac{1}{2} \, a\right)^{3} + \tan\left(\frac{1}{2} \, b x + 2 \, a\right) - 3 \, \tan\left(\frac{1}{2} \, a\right)\right)}^{3}} - 60 \, \log\left({\left| \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{3} + 3 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{2} - \tan\left(\frac{1}{2} \, a\right)^{3} - 3 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right) + 3 \, \tan\left(\frac{1}{2} \, a\right)^{2} - \tan\left(\frac{1}{2} \, b x + 2 \, a\right) + 3 \, \tan\left(\frac{1}{2} \, a\right) - 1 \right|}\right) + 60 \, \log\left({\left| \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{3} - 3 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{2} + \tan\left(\frac{1}{2} \, a\right)^{3} - 3 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right) + 3 \, \tan\left(\frac{1}{2} \, a\right)^{2} + \tan\left(\frac{1}{2} \, b x + 2 \, a\right) - 3 \, \tan\left(\frac{1}{2} \, a\right) - 1 \right|}\right)}{192 \, b}"," ",0,"-1/192*(24*(tan(1/2*b*x + 2*a)^3*tan(1/2*a)^24 + 30*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^22 - 6*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^23 + tan(1/2*b*x + 2*a)*tan(1/2*a)^24 - 756*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^20 + 614*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^21 - 114*tan(1/2*b*x + 2*a)*tan(1/2*a)^22 + 6*tan(1/2*a)^23 + 2058*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^18 - 4578*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^19 + 1932*tan(1/2*b*x + 2*a)*tan(1/2*a)^20 - 182*tan(1/2*a)^21 - 27*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^16 + 6210*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^17 - 7462*tan(1/2*b*x + 2*a)*tan(1/2*a)^18 + 1554*tan(1/2*a)^19 - 9396*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^14 + 15588*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^15 - 2331*tan(1/2*b*x + 2*a)*tan(1/2*a)^16 - 2178*tan(1/2*a)^17 - 21924*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^13 + 26028*tan(1/2*b*x + 2*a)*tan(1/2*a)^14 - 5668*tan(1/2*a)^15 + 9396*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^10 - 21924*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^11 + 6468*tan(1/2*a)^13 + 27*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^8 + 15588*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^9 - 26028*tan(1/2*b*x + 2*a)*tan(1/2*a)^10 + 6468*tan(1/2*a)^11 - 2058*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^6 + 6210*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^7 + 2331*tan(1/2*b*x + 2*a)*tan(1/2*a)^8 - 5668*tan(1/2*a)^9 + 756*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^4 - 4578*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^5 + 7462*tan(1/2*b*x + 2*a)*tan(1/2*a)^6 - 2178*tan(1/2*a)^7 - 30*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^2 + 614*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^3 - 1932*tan(1/2*b*x + 2*a)*tan(1/2*a)^4 + 1554*tan(1/2*a)^5 - tan(1/2*b*x + 2*a)^3 - 6*tan(1/2*b*x + 2*a)^2*tan(1/2*a) + 114*tan(1/2*b*x + 2*a)*tan(1/2*a)^2 - 182*tan(1/2*a)^3 - tan(1/2*b*x + 2*a) + 6*tan(1/2*a))/((tan(1/2*a)^12 - 30*tan(1/2*a)^10 + 255*tan(1/2*a)^8 - 452*tan(1/2*a)^6 + 255*tan(1/2*a)^4 - 30*tan(1/2*a)^2 + 1)*(tan(1/2*b*x + 2*a)^2*tan(1/2*a)^6 - 15*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^4 + 12*tan(1/2*b*x + 2*a)*tan(1/2*a)^5 - tan(1/2*a)^6 + 15*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^2 - 40*tan(1/2*b*x + 2*a)*tan(1/2*a)^3 + 15*tan(1/2*a)^4 - tan(1/2*b*x + 2*a)^2 + 12*tan(1/2*b*x + 2*a)*tan(1/2*a) - 15*tan(1/2*a)^2 + 1)^2) + (27*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^34 - 9*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^35 + tan(1/2*b*x + 2*a)^3*tan(1/2*a)^36 + 1602*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^32 - 915*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^33 + 126*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^34 + 9*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^35 - 50082*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^30 + 58626*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^31 - 21141*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^32 + 2373*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^33 + 27*tan(1/2*b*x + 2*a)*tan(1/2*a)^34 + 400050*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^28 - 783810*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^29 + 487692*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^30 - 118404*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^31 + 9378*tan(1/2*b*x + 2*a)*tan(1/2*a)^32 + 54*tan(1/2*a)^33 - 1301382*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^26 + 4035870*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^27 - 3943944*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^28 + 1555092*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^29 - 247074*tan(1/2*b*x + 2*a)*tan(1/2*a)^30 + 11610*tan(1/2*a)^31 + 1238250*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^24 - 8115822*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^25 + 13194468*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^26 - 8075232*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^27 + 1983762*tan(1/2*b*x + 2*a)*tan(1/2*a)^28 - 160362*tan(1/2*a)^29 + 2642310*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^22 - 1212390*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^23 - 12476880*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^24 + 16317288*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^25 - 6559110*tan(1/2*b*x + 2*a)*tan(1/2*a)^26 + 805786*tan(1/2*a)^27 - 5947398*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^20 + 25548198*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^21 - 27336420*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^22 + 2575260*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^23 + 6211530*tan(1/2*b*x + 2*a)*tan(1/2*a)^24 - 1599858*tan(1/2*a)^25 - 19824660*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^19 + 58330530*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^20 - 51141420*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^21 + 13453830*tan(1/2*b*x + 2*a)*tan(1/2*a)^22 - 209790*tan(1/2*a)^23 + 5947398*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^16 - 19824660*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^17 + 39278250*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^19 - 29430054*tan(1/2*b*x + 2*a)*tan(1/2*a)^20 + 5059854*tan(1/2*a)^21 - 2642310*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^14 + 25548198*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^15 - 58330530*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^16 + 39278250*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^17 - 4136670*tan(1/2*a)^19 - 1238250*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^12 - 1212390*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^13 + 27336420*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^14 - 51141420*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^15 + 29430054*tan(1/2*b*x + 2*a)*tan(1/2*a)^16 - 4136670*tan(1/2*a)^17 + 1301382*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^10 - 8115822*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^11 + 12476880*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^12 + 2575260*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^13 - 13453830*tan(1/2*b*x + 2*a)*tan(1/2*a)^14 + 5059854*tan(1/2*a)^15 - 400050*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^8 + 4035870*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^9 - 13194468*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^10 + 16317288*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^11 - 6211530*tan(1/2*b*x + 2*a)*tan(1/2*a)^12 - 209790*tan(1/2*a)^13 + 50082*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^6 - 783810*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^7 + 3943944*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^8 - 8075232*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^9 + 6559110*tan(1/2*b*x + 2*a)*tan(1/2*a)^10 - 1599858*tan(1/2*a)^11 - 1602*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^4 + 58626*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^5 - 487692*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^6 + 1555092*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^7 - 1983762*tan(1/2*b*x + 2*a)*tan(1/2*a)^8 + 805786*tan(1/2*a)^9 - 27*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^2 - 915*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^3 + 21141*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^4 - 118404*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^5 + 247074*tan(1/2*b*x + 2*a)*tan(1/2*a)^6 - 160362*tan(1/2*a)^7 - 9*tan(1/2*b*x + 2*a)^4*tan(1/2*a) - 126*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^2 + 2373*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^3 - 9378*tan(1/2*b*x + 2*a)*tan(1/2*a)^4 + 11610*tan(1/2*a)^5 - tan(1/2*b*x + 2*a)^3 + 9*tan(1/2*b*x + 2*a)^2*tan(1/2*a) - 27*tan(1/2*b*x + 2*a)*tan(1/2*a)^2 + 54*tan(1/2*a)^3)/((27*tan(1/2*a)^15 - 270*tan(1/2*a)^13 + 981*tan(1/2*a)^11 - 1540*tan(1/2*a)^9 + 981*tan(1/2*a)^7 - 270*tan(1/2*a)^5 + 27*tan(1/2*a)^3)*(3*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^5 - tan(1/2*b*x + 2*a)*tan(1/2*a)^6 - 10*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^3 + 15*tan(1/2*b*x + 2*a)*tan(1/2*a)^4 - 3*tan(1/2*a)^5 + 3*tan(1/2*b*x + 2*a)^2*tan(1/2*a) - 15*tan(1/2*b*x + 2*a)*tan(1/2*a)^2 + 10*tan(1/2*a)^3 + tan(1/2*b*x + 2*a) - 3*tan(1/2*a))^3) - 60*log(abs(tan(1/2*b*x + 2*a)*tan(1/2*a)^3 + 3*tan(1/2*b*x + 2*a)*tan(1/2*a)^2 - tan(1/2*a)^3 - 3*tan(1/2*b*x + 2*a)*tan(1/2*a) + 3*tan(1/2*a)^2 - tan(1/2*b*x + 2*a) + 3*tan(1/2*a) - 1)) + 60*log(abs(tan(1/2*b*x + 2*a)*tan(1/2*a)^3 - 3*tan(1/2*b*x + 2*a)*tan(1/2*a)^2 + tan(1/2*a)^3 - 3*tan(1/2*b*x + 2*a)*tan(1/2*a) + 3*tan(1/2*a)^2 + tan(1/2*b*x + 2*a) - 3*tan(1/2*a) - 1)))/b","B",0
44,1,5476,0,10.215770," ","integrate(csc(b*x+a)*csc(2*b*x+2*a)^4,x, algorithm=""giac"")","-\frac{\frac{256 \, {\left(36 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{35} - 6 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{36} - 1848 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{33} + 1134 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{34} - 180 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{35} + 9 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{36} + 39276 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{31} - 42894 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{32} + 14532 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{33} - 2052 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{34} + 144 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{35} - 5 \, \tan\left(\frac{1}{2} \, a\right)^{36} - 433836 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{29} + 709068 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{30} - 376632 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{31} + 83367 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{32} - 8364 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{33} + 342 \, \tan\left(\frac{1}{2} \, a\right)^{34} + 2430348 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{27} - 5742396 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{28} + 4466808 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{29} - 1422120 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{30} + 193068 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{31} - 9639 \, \tan\left(\frac{1}{2} \, a\right)^{32} - 5123196 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{25} + 20329092 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{26} - 24275368 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{27} + 11529468 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{28} - 2196396 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{29} + 141660 \, \tan\left(\frac{1}{2} \, a\right)^{30} - 1201860 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{23} - 18742620 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{24} + 50327784 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{25} - 40521528 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{26} + 12145596 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{27} - 1116072 \, \tan\left(\frac{1}{2} \, a\right)^{28} + 15332100 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{21} - 42937380 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{22} + 10264680 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{23} + 37504740 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{24} - 25425036 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{25} + 4162356 \, \tan\left(\frac{1}{2} \, a\right)^{26} - 11041020 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{19} + 84945240 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{20} - 153596328 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{21} + 85465080 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{22} - 5642820 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{23} - 3694080 \, \tan\left(\frac{1}{2} \, a\right)^{24} - 11041020 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{17} + 112912560 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{19} - 170450298 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{20} + 76700868 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{21} - 8751060 \, \tan\left(\frac{1}{2} \, a\right)^{22} + 15332100 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{15} - 84945240 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{16} + 112912560 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{17} - 55767060 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{19} + 16730118 \, \tan\left(\frac{1}{2} \, a\right)^{20} - 1201860 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{13} + 42937380 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{14} - 153596328 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{15} + 170450298 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{16} - 55767060 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{17} - 5123196 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{11} + 18742620 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{12} + 10264680 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{13} - 85465080 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{14} + 76700868 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{15} - 16730118 \, \tan\left(\frac{1}{2} \, a\right)^{16} + 2430348 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{9} - 20329092 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{10} + 50327784 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{11} - 37504740 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{12} - 5642820 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{13} + 8751060 \, \tan\left(\frac{1}{2} \, a\right)^{14} - 433836 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{7} + 5742396 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{8} - 24275368 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{9} + 40521528 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{10} - 25425036 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{11} + 3694080 \, \tan\left(\frac{1}{2} \, a\right)^{12} + 39276 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{5} - 709068 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{6} + 4466808 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{7} - 11529468 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{8} + 12145596 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{9} - 4162356 \, \tan\left(\frac{1}{2} \, a\right)^{10} - 1848 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{3} + 42894 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{4} - 376632 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{5} + 1422120 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{6} - 2196396 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{7} + 1116072 \, \tan\left(\frac{1}{2} \, a\right)^{8} + 36 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right) - 1134 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{2} + 14532 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{3} - 83367 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{4} + 193068 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{5} - 141660 \, \tan\left(\frac{1}{2} \, a\right)^{6} + 6 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} - 180 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right) + 2052 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} - 8364 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{3} + 9639 \, \tan\left(\frac{1}{2} \, a\right)^{4} - 9 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} + 144 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right) - 342 \, \tan\left(\frac{1}{2} \, a\right)^{2} + 5\right)}}{{\left(\tan\left(\frac{1}{2} \, a\right)^{18} - 45 \, \tan\left(\frac{1}{2} \, a\right)^{16} + 720 \, \tan\left(\frac{1}{2} \, a\right)^{14} - 4728 \, \tan\left(\frac{1}{2} \, a\right)^{12} + 10890 \, \tan\left(\frac{1}{2} \, a\right)^{10} - 10890 \, \tan\left(\frac{1}{2} \, a\right)^{8} + 4728 \, \tan\left(\frac{1}{2} \, a\right)^{6} - 720 \, \tan\left(\frac{1}{2} \, a\right)^{4} + 45 \, \tan\left(\frac{1}{2} \, a\right)^{2} - 1\right)} {\left(\tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{6} - 15 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{4} + 12 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{5} - \tan\left(\frac{1}{2} \, a\right)^{6} + 15 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} - 40 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{3} + 15 \, \tan\left(\frac{1}{2} \, a\right)^{4} - \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} + 12 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right) - 15 \, \tan\left(\frac{1}{2} \, a\right)^{2} + 1\right)}^{3}} + \frac{3 \, {\left(108 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{7} \tan\left(\frac{1}{2} \, a\right)^{45} - 54 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{46} + 12 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{47} - \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{48} + 8316 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{7} \tan\left(\frac{1}{2} \, a\right)^{43} - 6120 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{44} + 1400 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{45} - 24 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{46} - 12 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{47} - 253008 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{7} \tan\left(\frac{1}{2} \, a\right)^{41} + 354774 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{42} - 165384 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{43} + 30180 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{44} - 1400 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{45} - 54 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{46} + 3918128 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{7} \tan\left(\frac{1}{2} \, a\right)^{39} - 7606080 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{40} + 5365548 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{41} - 1698920 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{42} + 235368 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{43} - 10008 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{44} - 108 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{45} - 32664372 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{7} \tan\left(\frac{1}{2} \, a\right)^{37} + 85352514 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{38} - 82649988 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{39} + 37937604 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{40} - 8596476 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{41} + 879006 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{42} - 27756 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{43} - 162 \, \tan\left(\frac{1}{2} \, a\right)^{44} + 150470268 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{7} \tan\left(\frac{1}{2} \, a\right)^{35} - 527449208 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{36} + 684424728 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{37} - 427365432 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{38} + 137583540 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{39} - 22235328 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{40} + 1556784 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{41} - 28944 \, \tan\left(\frac{1}{2} \, a\right)^{42} - 369285568 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{7} \tan\left(\frac{1}{2} \, a\right)^{33} + 1800957150 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{34} - 3157829352 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{35} + 2638274028 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{36} - 1145015352 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{37} + 257818938 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{38} - 27438800 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{39} + 1015632 \, \tan\left(\frac{1}{2} \, a\right)^{40} + 332678976 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{7} \tan\left(\frac{1}{2} \, a\right)^{31} - 2973661056 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{32} + 7767810012 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{33} - 9003276360 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{34} + 5266355688 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{35} - 1589641352 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{36} + 231030852 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{37} - 12400752 \, \tan\left(\frac{1}{2} \, a\right)^{38} + 498198168 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{7} \tan\left(\frac{1}{2} \, a\right)^{29} + 141213844 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{30} - 6978686184 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{31} + 14860730619 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{32} - 12919461276 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{33} + 5392538622 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{34} - 1054828476 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{35} + 76246378 \, \tan\left(\frac{1}{2} \, a\right)^{36} - 1473564360 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{7} \tan\left(\frac{1}{2} \, a\right)^{27} + 7565433072 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{28} - 10492595088 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{29} - 707654192 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{30} + 11624633640 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{31} - 8882796672 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{32} + 2571218880 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{33} - 256007232 \, \tan\left(\frac{1}{2} \, a\right)^{34} + 883677600 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{7} \tan\left(\frac{1}{2} \, a\right)^{25} - 10018470420 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{26} + 30880710896 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{27} - 37780516920 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{28} + 17392225680 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{29} + 478350836 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{30} - 2321948736 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{31} + 420191712 \, \tan\left(\frac{1}{2} \, a\right)^{32} + 883677600 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{7} \tan\left(\frac{1}{2} \, a\right)^{23} - 18623765160 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{25} + 50161528368 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{26} - 51515325744 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{27} + 22607976720 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{28} - 3433884120 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{29} - 26975424 \, \tan\left(\frac{1}{2} \, a\right)^{30} - 1473564360 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{7} \tan\left(\frac{1}{2} \, a\right)^{21} + 10018470420 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{22} - 18623765160 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{23} + 31169987784 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{25} - 30241452708 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{26} + 10324445736 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{27} - 1070628372 \, \tan\left(\frac{1}{2} \, a\right)^{28} + 498198168 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{7} \tan\left(\frac{1}{2} \, a\right)^{19} - 7565433072 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{20} + 30880710896 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{21} - 50161528368 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{22} + 31169987784 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{23} - 6296940000 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{25} + 1453140000 \, \tan\left(\frac{1}{2} \, a\right)^{26} + 332678976 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{7} \tan\left(\frac{1}{2} \, a\right)^{17} - 141213844 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{18} - 10492595088 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{19} + 37780516920 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{20} - 51515325744 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{21} + 30241452708 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{22} - 6296940000 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{23} - 369285568 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{7} \tan\left(\frac{1}{2} \, a\right)^{15} + 2973661056 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{16} - 6978686184 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{17} + 707654192 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{18} + 17392225680 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{19} - 22607976720 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{20} + 10324445736 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{21} - 1453140000 \, \tan\left(\frac{1}{2} \, a\right)^{22} + 150470268 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{7} \tan\left(\frac{1}{2} \, a\right)^{13} - 1800957150 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{14} + 7767810012 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{15} - 14860730619 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{16} + 11624633640 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{17} - 478350836 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{18} - 3433884120 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{19} + 1070628372 \, \tan\left(\frac{1}{2} \, a\right)^{20} - 32664372 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{7} \tan\left(\frac{1}{2} \, a\right)^{11} + 527449208 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{12} - 3157829352 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{13} + 9003276360 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{14} - 12919461276 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{15} + 8882796672 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{16} - 2321948736 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{17} + 26975424 \, \tan\left(\frac{1}{2} \, a\right)^{18} + 3918128 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{7} \tan\left(\frac{1}{2} \, a\right)^{9} - 85352514 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{10} + 684424728 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{11} - 2638274028 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{12} + 5266355688 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{13} - 5392538622 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{14} + 2571218880 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{15} - 420191712 \, \tan\left(\frac{1}{2} \, a\right)^{16} - 253008 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{7} \tan\left(\frac{1}{2} \, a\right)^{7} + 7606080 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{8} - 82649988 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{9} + 427365432 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{10} - 1145015352 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{11} + 1589641352 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{12} - 1054828476 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{13} + 256007232 \, \tan\left(\frac{1}{2} \, a\right)^{14} + 8316 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{7} \tan\left(\frac{1}{2} \, a\right)^{5} - 354774 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{6} + 5365548 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{7} - 37937604 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{8} + 137583540 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{9} - 257818938 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{10} + 231030852 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{11} - 76246378 \, \tan\left(\frac{1}{2} \, a\right)^{12} + 108 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{7} \tan\left(\frac{1}{2} \, a\right)^{3} + 6120 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{4} - 165384 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{5} + 1698920 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{6} - 8596476 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{7} + 22235328 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{8} - 27438800 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{9} + 12400752 \, \tan\left(\frac{1}{2} \, a\right)^{10} + 54 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{2} + 1400 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{3} - 30180 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{4} + 235368 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{5} - 879006 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{6} + 1556784 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{7} - 1015632 \, \tan\left(\frac{1}{2} \, a\right)^{8} + 12 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right) + 24 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{2} - 1400 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{3} + 10008 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{4} - 27756 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{5} + 28944 \, \tan\left(\frac{1}{2} \, a\right)^{6} + \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} - 12 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right) + 54 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} - 108 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{3} + 162 \, \tan\left(\frac{1}{2} \, a\right)^{4}\right)}}{{\left(81 \, \tan\left(\frac{1}{2} \, a\right)^{20} - 1080 \, \tan\left(\frac{1}{2} \, a\right)^{18} + 5724 \, \tan\left(\frac{1}{2} \, a\right)^{16} - 15240 \, \tan\left(\frac{1}{2} \, a\right)^{14} + 21286 \, \tan\left(\frac{1}{2} \, a\right)^{12} - 15240 \, \tan\left(\frac{1}{2} \, a\right)^{10} + 5724 \, \tan\left(\frac{1}{2} \, a\right)^{8} - 1080 \, \tan\left(\frac{1}{2} \, a\right)^{6} + 81 \, \tan\left(\frac{1}{2} \, a\right)^{4}\right)} {\left(3 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{5} - \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{6} - 10 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{3} + 15 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{4} - 3 \, \tan\left(\frac{1}{2} \, a\right)^{5} + 3 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right) - 15 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{2} + 10 \, \tan\left(\frac{1}{2} \, a\right)^{3} + \tan\left(\frac{1}{2} \, b x + 2 \, a\right) - 3 \, \tan\left(\frac{1}{2} \, a\right)\right)}^{4}} + 840 \, \log\left({\left| \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{3} - 3 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right) + 3 \, \tan\left(\frac{1}{2} \, a\right)^{2} - 1 \right|}\right) - 840 \, \log\left({\left| 3 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{2} - \tan\left(\frac{1}{2} \, a\right)^{3} - \tan\left(\frac{1}{2} \, b x + 2 \, a\right) + 3 \, \tan\left(\frac{1}{2} \, a\right) \right|}\right)}{3072 \, b}"," ",0,"-1/3072*(256*(36*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^35 - 6*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^36 - 1848*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^33 + 1134*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^34 - 180*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^35 + 9*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^36 + 39276*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^31 - 42894*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^32 + 14532*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^33 - 2052*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^34 + 144*tan(1/2*b*x + 2*a)*tan(1/2*a)^35 - 5*tan(1/2*a)^36 - 433836*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^29 + 709068*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^30 - 376632*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^31 + 83367*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^32 - 8364*tan(1/2*b*x + 2*a)*tan(1/2*a)^33 + 342*tan(1/2*a)^34 + 2430348*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^27 - 5742396*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^28 + 4466808*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^29 - 1422120*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^30 + 193068*tan(1/2*b*x + 2*a)*tan(1/2*a)^31 - 9639*tan(1/2*a)^32 - 5123196*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^25 + 20329092*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^26 - 24275368*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^27 + 11529468*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^28 - 2196396*tan(1/2*b*x + 2*a)*tan(1/2*a)^29 + 141660*tan(1/2*a)^30 - 1201860*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^23 - 18742620*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^24 + 50327784*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^25 - 40521528*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^26 + 12145596*tan(1/2*b*x + 2*a)*tan(1/2*a)^27 - 1116072*tan(1/2*a)^28 + 15332100*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^21 - 42937380*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^22 + 10264680*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^23 + 37504740*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^24 - 25425036*tan(1/2*b*x + 2*a)*tan(1/2*a)^25 + 4162356*tan(1/2*a)^26 - 11041020*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^19 + 84945240*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^20 - 153596328*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^21 + 85465080*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^22 - 5642820*tan(1/2*b*x + 2*a)*tan(1/2*a)^23 - 3694080*tan(1/2*a)^24 - 11041020*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^17 + 112912560*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^19 - 170450298*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^20 + 76700868*tan(1/2*b*x + 2*a)*tan(1/2*a)^21 - 8751060*tan(1/2*a)^22 + 15332100*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^15 - 84945240*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^16 + 112912560*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^17 - 55767060*tan(1/2*b*x + 2*a)*tan(1/2*a)^19 + 16730118*tan(1/2*a)^20 - 1201860*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^13 + 42937380*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^14 - 153596328*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^15 + 170450298*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^16 - 55767060*tan(1/2*b*x + 2*a)*tan(1/2*a)^17 - 5123196*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^11 + 18742620*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^12 + 10264680*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^13 - 85465080*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^14 + 76700868*tan(1/2*b*x + 2*a)*tan(1/2*a)^15 - 16730118*tan(1/2*a)^16 + 2430348*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^9 - 20329092*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^10 + 50327784*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^11 - 37504740*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^12 - 5642820*tan(1/2*b*x + 2*a)*tan(1/2*a)^13 + 8751060*tan(1/2*a)^14 - 433836*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^7 + 5742396*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^8 - 24275368*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^9 + 40521528*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^10 - 25425036*tan(1/2*b*x + 2*a)*tan(1/2*a)^11 + 3694080*tan(1/2*a)^12 + 39276*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^5 - 709068*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^6 + 4466808*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^7 - 11529468*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^8 + 12145596*tan(1/2*b*x + 2*a)*tan(1/2*a)^9 - 4162356*tan(1/2*a)^10 - 1848*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^3 + 42894*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^4 - 376632*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^5 + 1422120*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^6 - 2196396*tan(1/2*b*x + 2*a)*tan(1/2*a)^7 + 1116072*tan(1/2*a)^8 + 36*tan(1/2*b*x + 2*a)^5*tan(1/2*a) - 1134*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^2 + 14532*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^3 - 83367*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^4 + 193068*tan(1/2*b*x + 2*a)*tan(1/2*a)^5 - 141660*tan(1/2*a)^6 + 6*tan(1/2*b*x + 2*a)^4 - 180*tan(1/2*b*x + 2*a)^3*tan(1/2*a) + 2052*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^2 - 8364*tan(1/2*b*x + 2*a)*tan(1/2*a)^3 + 9639*tan(1/2*a)^4 - 9*tan(1/2*b*x + 2*a)^2 + 144*tan(1/2*b*x + 2*a)*tan(1/2*a) - 342*tan(1/2*a)^2 + 5)/((tan(1/2*a)^18 - 45*tan(1/2*a)^16 + 720*tan(1/2*a)^14 - 4728*tan(1/2*a)^12 + 10890*tan(1/2*a)^10 - 10890*tan(1/2*a)^8 + 4728*tan(1/2*a)^6 - 720*tan(1/2*a)^4 + 45*tan(1/2*a)^2 - 1)*(tan(1/2*b*x + 2*a)^2*tan(1/2*a)^6 - 15*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^4 + 12*tan(1/2*b*x + 2*a)*tan(1/2*a)^5 - tan(1/2*a)^6 + 15*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^2 - 40*tan(1/2*b*x + 2*a)*tan(1/2*a)^3 + 15*tan(1/2*a)^4 - tan(1/2*b*x + 2*a)^2 + 12*tan(1/2*b*x + 2*a)*tan(1/2*a) - 15*tan(1/2*a)^2 + 1)^3) + 3*(108*tan(1/2*b*x + 2*a)^7*tan(1/2*a)^45 - 54*tan(1/2*b*x + 2*a)^6*tan(1/2*a)^46 + 12*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^47 - tan(1/2*b*x + 2*a)^4*tan(1/2*a)^48 + 8316*tan(1/2*b*x + 2*a)^7*tan(1/2*a)^43 - 6120*tan(1/2*b*x + 2*a)^6*tan(1/2*a)^44 + 1400*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^45 - 24*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^46 - 12*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^47 - 253008*tan(1/2*b*x + 2*a)^7*tan(1/2*a)^41 + 354774*tan(1/2*b*x + 2*a)^6*tan(1/2*a)^42 - 165384*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^43 + 30180*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^44 - 1400*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^45 - 54*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^46 + 3918128*tan(1/2*b*x + 2*a)^7*tan(1/2*a)^39 - 7606080*tan(1/2*b*x + 2*a)^6*tan(1/2*a)^40 + 5365548*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^41 - 1698920*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^42 + 235368*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^43 - 10008*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^44 - 108*tan(1/2*b*x + 2*a)*tan(1/2*a)^45 - 32664372*tan(1/2*b*x + 2*a)^7*tan(1/2*a)^37 + 85352514*tan(1/2*b*x + 2*a)^6*tan(1/2*a)^38 - 82649988*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^39 + 37937604*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^40 - 8596476*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^41 + 879006*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^42 - 27756*tan(1/2*b*x + 2*a)*tan(1/2*a)^43 - 162*tan(1/2*a)^44 + 150470268*tan(1/2*b*x + 2*a)^7*tan(1/2*a)^35 - 527449208*tan(1/2*b*x + 2*a)^6*tan(1/2*a)^36 + 684424728*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^37 - 427365432*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^38 + 137583540*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^39 - 22235328*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^40 + 1556784*tan(1/2*b*x + 2*a)*tan(1/2*a)^41 - 28944*tan(1/2*a)^42 - 369285568*tan(1/2*b*x + 2*a)^7*tan(1/2*a)^33 + 1800957150*tan(1/2*b*x + 2*a)^6*tan(1/2*a)^34 - 3157829352*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^35 + 2638274028*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^36 - 1145015352*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^37 + 257818938*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^38 - 27438800*tan(1/2*b*x + 2*a)*tan(1/2*a)^39 + 1015632*tan(1/2*a)^40 + 332678976*tan(1/2*b*x + 2*a)^7*tan(1/2*a)^31 - 2973661056*tan(1/2*b*x + 2*a)^6*tan(1/2*a)^32 + 7767810012*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^33 - 9003276360*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^34 + 5266355688*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^35 - 1589641352*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^36 + 231030852*tan(1/2*b*x + 2*a)*tan(1/2*a)^37 - 12400752*tan(1/2*a)^38 + 498198168*tan(1/2*b*x + 2*a)^7*tan(1/2*a)^29 + 141213844*tan(1/2*b*x + 2*a)^6*tan(1/2*a)^30 - 6978686184*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^31 + 14860730619*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^32 - 12919461276*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^33 + 5392538622*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^34 - 1054828476*tan(1/2*b*x + 2*a)*tan(1/2*a)^35 + 76246378*tan(1/2*a)^36 - 1473564360*tan(1/2*b*x + 2*a)^7*tan(1/2*a)^27 + 7565433072*tan(1/2*b*x + 2*a)^6*tan(1/2*a)^28 - 10492595088*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^29 - 707654192*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^30 + 11624633640*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^31 - 8882796672*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^32 + 2571218880*tan(1/2*b*x + 2*a)*tan(1/2*a)^33 - 256007232*tan(1/2*a)^34 + 883677600*tan(1/2*b*x + 2*a)^7*tan(1/2*a)^25 - 10018470420*tan(1/2*b*x + 2*a)^6*tan(1/2*a)^26 + 30880710896*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^27 - 37780516920*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^28 + 17392225680*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^29 + 478350836*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^30 - 2321948736*tan(1/2*b*x + 2*a)*tan(1/2*a)^31 + 420191712*tan(1/2*a)^32 + 883677600*tan(1/2*b*x + 2*a)^7*tan(1/2*a)^23 - 18623765160*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^25 + 50161528368*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^26 - 51515325744*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^27 + 22607976720*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^28 - 3433884120*tan(1/2*b*x + 2*a)*tan(1/2*a)^29 - 26975424*tan(1/2*a)^30 - 1473564360*tan(1/2*b*x + 2*a)^7*tan(1/2*a)^21 + 10018470420*tan(1/2*b*x + 2*a)^6*tan(1/2*a)^22 - 18623765160*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^23 + 31169987784*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^25 - 30241452708*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^26 + 10324445736*tan(1/2*b*x + 2*a)*tan(1/2*a)^27 - 1070628372*tan(1/2*a)^28 + 498198168*tan(1/2*b*x + 2*a)^7*tan(1/2*a)^19 - 7565433072*tan(1/2*b*x + 2*a)^6*tan(1/2*a)^20 + 30880710896*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^21 - 50161528368*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^22 + 31169987784*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^23 - 6296940000*tan(1/2*b*x + 2*a)*tan(1/2*a)^25 + 1453140000*tan(1/2*a)^26 + 332678976*tan(1/2*b*x + 2*a)^7*tan(1/2*a)^17 - 141213844*tan(1/2*b*x + 2*a)^6*tan(1/2*a)^18 - 10492595088*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^19 + 37780516920*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^20 - 51515325744*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^21 + 30241452708*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^22 - 6296940000*tan(1/2*b*x + 2*a)*tan(1/2*a)^23 - 369285568*tan(1/2*b*x + 2*a)^7*tan(1/2*a)^15 + 2973661056*tan(1/2*b*x + 2*a)^6*tan(1/2*a)^16 - 6978686184*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^17 + 707654192*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^18 + 17392225680*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^19 - 22607976720*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^20 + 10324445736*tan(1/2*b*x + 2*a)*tan(1/2*a)^21 - 1453140000*tan(1/2*a)^22 + 150470268*tan(1/2*b*x + 2*a)^7*tan(1/2*a)^13 - 1800957150*tan(1/2*b*x + 2*a)^6*tan(1/2*a)^14 + 7767810012*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^15 - 14860730619*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^16 + 11624633640*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^17 - 478350836*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^18 - 3433884120*tan(1/2*b*x + 2*a)*tan(1/2*a)^19 + 1070628372*tan(1/2*a)^20 - 32664372*tan(1/2*b*x + 2*a)^7*tan(1/2*a)^11 + 527449208*tan(1/2*b*x + 2*a)^6*tan(1/2*a)^12 - 3157829352*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^13 + 9003276360*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^14 - 12919461276*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^15 + 8882796672*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^16 - 2321948736*tan(1/2*b*x + 2*a)*tan(1/2*a)^17 + 26975424*tan(1/2*a)^18 + 3918128*tan(1/2*b*x + 2*a)^7*tan(1/2*a)^9 - 85352514*tan(1/2*b*x + 2*a)^6*tan(1/2*a)^10 + 684424728*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^11 - 2638274028*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^12 + 5266355688*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^13 - 5392538622*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^14 + 2571218880*tan(1/2*b*x + 2*a)*tan(1/2*a)^15 - 420191712*tan(1/2*a)^16 - 253008*tan(1/2*b*x + 2*a)^7*tan(1/2*a)^7 + 7606080*tan(1/2*b*x + 2*a)^6*tan(1/2*a)^8 - 82649988*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^9 + 427365432*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^10 - 1145015352*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^11 + 1589641352*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^12 - 1054828476*tan(1/2*b*x + 2*a)*tan(1/2*a)^13 + 256007232*tan(1/2*a)^14 + 8316*tan(1/2*b*x + 2*a)^7*tan(1/2*a)^5 - 354774*tan(1/2*b*x + 2*a)^6*tan(1/2*a)^6 + 5365548*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^7 - 37937604*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^8 + 137583540*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^9 - 257818938*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^10 + 231030852*tan(1/2*b*x + 2*a)*tan(1/2*a)^11 - 76246378*tan(1/2*a)^12 + 108*tan(1/2*b*x + 2*a)^7*tan(1/2*a)^3 + 6120*tan(1/2*b*x + 2*a)^6*tan(1/2*a)^4 - 165384*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^5 + 1698920*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^6 - 8596476*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^7 + 22235328*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^8 - 27438800*tan(1/2*b*x + 2*a)*tan(1/2*a)^9 + 12400752*tan(1/2*a)^10 + 54*tan(1/2*b*x + 2*a)^6*tan(1/2*a)^2 + 1400*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^3 - 30180*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^4 + 235368*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^5 - 879006*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^6 + 1556784*tan(1/2*b*x + 2*a)*tan(1/2*a)^7 - 1015632*tan(1/2*a)^8 + 12*tan(1/2*b*x + 2*a)^5*tan(1/2*a) + 24*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^2 - 1400*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^3 + 10008*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^4 - 27756*tan(1/2*b*x + 2*a)*tan(1/2*a)^5 + 28944*tan(1/2*a)^6 + tan(1/2*b*x + 2*a)^4 - 12*tan(1/2*b*x + 2*a)^3*tan(1/2*a) + 54*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^2 - 108*tan(1/2*b*x + 2*a)*tan(1/2*a)^3 + 162*tan(1/2*a)^4)/((81*tan(1/2*a)^20 - 1080*tan(1/2*a)^18 + 5724*tan(1/2*a)^16 - 15240*tan(1/2*a)^14 + 21286*tan(1/2*a)^12 - 15240*tan(1/2*a)^10 + 5724*tan(1/2*a)^8 - 1080*tan(1/2*a)^6 + 81*tan(1/2*a)^4)*(3*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^5 - tan(1/2*b*x + 2*a)*tan(1/2*a)^6 - 10*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^3 + 15*tan(1/2*b*x + 2*a)*tan(1/2*a)^4 - 3*tan(1/2*a)^5 + 3*tan(1/2*b*x + 2*a)^2*tan(1/2*a) - 15*tan(1/2*b*x + 2*a)*tan(1/2*a)^2 + 10*tan(1/2*a)^3 + tan(1/2*b*x + 2*a) - 3*tan(1/2*a))^4) + 840*log(abs(tan(1/2*b*x + 2*a)*tan(1/2*a)^3 - 3*tan(1/2*b*x + 2*a)*tan(1/2*a) + 3*tan(1/2*a)^2 - 1)) - 840*log(abs(3*tan(1/2*b*x + 2*a)*tan(1/2*a)^2 - tan(1/2*a)^3 - tan(1/2*b*x + 2*a) + 3*tan(1/2*a))))/b","B",0
45,1,95,0,1.613559," ","integrate(csc(b*x+a)^2*sin(2*b*x+2*a)^8,x, algorithm=""giac"")","\frac{105 \, b x + 105 \, a + \frac{105 \, \tan\left(b x + a\right)^{13} + 700 \, \tan\left(b x + a\right)^{11} + 1981 \, \tan\left(b x + a\right)^{9} + 3072 \, \tan\left(b x + a\right)^{7} - 1981 \, \tan\left(b x + a\right)^{5} - 700 \, \tan\left(b x + a\right)^{3} - 105 \, \tan\left(b x + a\right)}{{\left(\tan\left(b x + a\right)^{2} + 1\right)}^{7}}}{168 \, b}"," ",0,"1/168*(105*b*x + 105*a + (105*tan(b*x + a)^13 + 700*tan(b*x + a)^11 + 1981*tan(b*x + a)^9 + 3072*tan(b*x + a)^7 - 1981*tan(b*x + a)^5 - 700*tan(b*x + a)^3 - 105*tan(b*x + a))/(tan(b*x + a)^2 + 1)^7)/b","A",0
46,1,183,0,0.994602," ","integrate(csc(b*x+a)^2*sin(2*b*x+2*a)^7,x, algorithm=""giac"")","-\frac{4096 \, {\left(\frac{5 \, {\left(\cos\left(b x + a\right) - 1\right)}^{3}}{{\left(\cos\left(b x + a\right) + 1\right)}^{3}} + \frac{15 \, {\left(\cos\left(b x + a\right) - 1\right)}^{4}}{{\left(\cos\left(b x + a\right) + 1\right)}^{4}} + \frac{39 \, {\left(\cos\left(b x + a\right) - 1\right)}^{5}}{{\left(\cos\left(b x + a\right) + 1\right)}^{5}} + \frac{42 \, {\left(\cos\left(b x + a\right) - 1\right)}^{6}}{{\left(\cos\left(b x + a\right) + 1\right)}^{6}} + \frac{39 \, {\left(\cos\left(b x + a\right) - 1\right)}^{7}}{{\left(\cos\left(b x + a\right) + 1\right)}^{7}} + \frac{15 \, {\left(\cos\left(b x + a\right) - 1\right)}^{8}}{{\left(\cos\left(b x + a\right) + 1\right)}^{8}} + \frac{5 \, {\left(\cos\left(b x + a\right) - 1\right)}^{9}}{{\left(\cos\left(b x + a\right) + 1\right)}^{9}}\right)}}{15 \, b {\left(\frac{\cos\left(b x + a\right) - 1}{\cos\left(b x + a\right) + 1} - 1\right)}^{12}}"," ",0,"-4096/15*(5*(cos(b*x + a) - 1)^3/(cos(b*x + a) + 1)^3 + 15*(cos(b*x + a) - 1)^4/(cos(b*x + a) + 1)^4 + 39*(cos(b*x + a) - 1)^5/(cos(b*x + a) + 1)^5 + 42*(cos(b*x + a) - 1)^6/(cos(b*x + a) + 1)^6 + 39*(cos(b*x + a) - 1)^7/(cos(b*x + a) + 1)^7 + 15*(cos(b*x + a) - 1)^8/(cos(b*x + a) + 1)^8 + 5*(cos(b*x + a) - 1)^9/(cos(b*x + a) + 1)^9)/(b*((cos(b*x + a) - 1)/(cos(b*x + a) + 1) - 1)^12)","B",0
47,1,75,0,1.021114," ","integrate(csc(b*x+a)^2*sin(2*b*x+2*a)^6,x, algorithm=""giac"")","\frac{15 \, b x + 15 \, a + \frac{15 \, \tan\left(b x + a\right)^{9} + 70 \, \tan\left(b x + a\right)^{7} + 128 \, \tan\left(b x + a\right)^{5} - 70 \, \tan\left(b x + a\right)^{3} - 15 \, \tan\left(b x + a\right)}{{\left(\tan\left(b x + a\right)^{2} + 1\right)}^{5}}}{20 \, b}"," ",0,"1/20*(15*b*x + 15*a + (15*tan(b*x + a)^9 + 70*tan(b*x + a)^7 + 128*tan(b*x + a)^5 - 70*tan(b*x + a)^3 - 15*tan(b*x + a))/(tan(b*x + a)^2 + 1)^5)/b","A",0
48,1,139,0,0.675754," ","integrate(csc(b*x+a)^2*sin(2*b*x+2*a)^5,x, algorithm=""giac"")","\frac{128 \, {\left(\frac{3 \, {\left(\cos\left(b x + a\right) - 1\right)}^{2}}{{\left(\cos\left(b x + a\right) + 1\right)}^{2}} + \frac{4 \, {\left(\cos\left(b x + a\right) - 1\right)}^{3}}{{\left(\cos\left(b x + a\right) + 1\right)}^{3}} + \frac{10 \, {\left(\cos\left(b x + a\right) - 1\right)}^{4}}{{\left(\cos\left(b x + a\right) + 1\right)}^{4}} + \frac{4 \, {\left(\cos\left(b x + a\right) - 1\right)}^{5}}{{\left(\cos\left(b x + a\right) + 1\right)}^{5}} + \frac{3 \, {\left(\cos\left(b x + a\right) - 1\right)}^{6}}{{\left(\cos\left(b x + a\right) + 1\right)}^{6}}\right)}}{3 \, b {\left(\frac{\cos\left(b x + a\right) - 1}{\cos\left(b x + a\right) + 1} - 1\right)}^{8}}"," ",0,"128/3*(3*(cos(b*x + a) - 1)^2/(cos(b*x + a) + 1)^2 + 4*(cos(b*x + a) - 1)^3/(cos(b*x + a) + 1)^3 + 10*(cos(b*x + a) - 1)^4/(cos(b*x + a) + 1)^4 + 4*(cos(b*x + a) - 1)^5/(cos(b*x + a) + 1)^5 + 3*(cos(b*x + a) - 1)^6/(cos(b*x + a) + 1)^6)/(b*((cos(b*x + a) - 1)/(cos(b*x + a) + 1) - 1)^8)","B",0
49,1,55,0,0.768531," ","integrate(csc(b*x+a)^2*sin(2*b*x+2*a)^4,x, algorithm=""giac"")","\frac{3 \, b x + 3 \, a + \frac{3 \, \tan\left(b x + a\right)^{5} + 8 \, \tan\left(b x + a\right)^{3} - 3 \, \tan\left(b x + a\right)}{{\left(\tan\left(b x + a\right)^{2} + 1\right)}^{3}}}{3 \, b}"," ",0,"1/3*(3*b*x + 3*a + (3*tan(b*x + a)^5 + 8*tan(b*x + a)^3 - 3*tan(b*x + a))/(tan(b*x + a)^2 + 1)^3)/b","A",0
50,1,69,0,0.489674," ","integrate(csc(b*x+a)^2*sin(2*b*x+2*a)^3,x, algorithm=""giac"")","-\frac{16 \, {\left(\frac{\cos\left(b x + a\right) - 1}{\cos\left(b x + a\right) + 1} + \frac{{\left(\cos\left(b x + a\right) - 1\right)}^{3}}{{\left(\cos\left(b x + a\right) + 1\right)}^{3}}\right)}}{b {\left(\frac{\cos\left(b x + a\right) - 1}{\cos\left(b x + a\right) + 1} - 1\right)}^{4}}"," ",0,"-16*((cos(b*x + a) - 1)/(cos(b*x + a) + 1) + (cos(b*x + a) - 1)^3/(cos(b*x + a) + 1)^3)/(b*((cos(b*x + a) - 1)/(cos(b*x + a) + 1) - 1)^4)","B",0
51,1,29,0,0.493914," ","integrate(csc(b*x+a)^2*sin(2*b*x+2*a)^2,x, algorithm=""giac"")","\frac{2 \, {\left(b x + a + \frac{\tan\left(b x + a\right)}{\tan\left(b x + a\right)^{2} + 1}\right)}}{b}"," ",0,"2*(b*x + a + tan(b*x + a)/(tan(b*x + a)^2 + 1))/b","A",0
52,1,55,0,0.985809," ","integrate(csc(b*x+a)^2*sin(2*b*x+2*a),x, algorithm=""giac"")","\frac{\log\left(\frac{{\left| -\cos\left(b x + a\right) + 1 \right|}}{{\left| \cos\left(b x + a\right) + 1 \right|}}\right) - 2 \, \log\left({\left| -\frac{\cos\left(b x + a\right) - 1}{\cos\left(b x + a\right) + 1} + 1 \right|}\right)}{b}"," ",0,"(log(abs(-cos(b*x + a) + 1)/abs(cos(b*x + a) + 1)) - 2*log(abs(-(cos(b*x + a) - 1)/(cos(b*x + a) + 1) + 1)))/b","B",0
53,1,813,0,1.006810," ","integrate(csc(b*x+a)^2*csc(2*b*x+2*a),x, algorithm=""giac"")","-\frac{\frac{3 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{24} - 180 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{22} + 24 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{23} + \tan\left(\frac{1}{2} \, a\right)^{24} + 4230 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{20} - 1592 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{21} + 48 \, \tan\left(\frac{1}{2} \, a\right)^{22} - 48612 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{18} + 31704 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{19} - 3846 \, \tan\left(\frac{1}{2} \, a\right)^{20} + 277965 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{16} - 259128 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{17} + 51632 \, \tan\left(\frac{1}{2} \, a\right)^{18} - 737640 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{14} + 982192 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{15} - 274545 \, \tan\left(\frac{1}{2} \, a\right)^{16} + 1008468 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{12} - 1871088 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{13} + 733728 \, \tan\left(\frac{1}{2} \, a\right)^{14} - 737640 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{10} + 1871088 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{11} - 1018132 \, \tan\left(\frac{1}{2} \, a\right)^{12} + 277965 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{8} - 982192 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{9} + 733728 \, \tan\left(\frac{1}{2} \, a\right)^{10} - 48612 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{6} + 259128 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{7} - 274545 \, \tan\left(\frac{1}{2} \, a\right)^{8} + 4230 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{4} - 31704 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{5} + 51632 \, \tan\left(\frac{1}{2} \, a\right)^{6} - 180 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} + 1592 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{3} - 3846 \, \tan\left(\frac{1}{2} \, a\right)^{4} + 3 \, \tan\left(b x + 4 \, a\right)^{2} - 24 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right) + 48 \, \tan\left(\frac{1}{2} \, a\right)^{2} + 1}{{\left(\tan\left(\frac{1}{2} \, a\right)^{12} - 30 \, \tan\left(\frac{1}{2} \, a\right)^{10} + 255 \, \tan\left(\frac{1}{2} \, a\right)^{8} - 452 \, \tan\left(\frac{1}{2} \, a\right)^{6} + 255 \, \tan\left(\frac{1}{2} \, a\right)^{4} - 30 \, \tan\left(\frac{1}{2} \, a\right)^{2} + 1\right)} {\left(\tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{6} - 15 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{4} + 6 \, \tan\left(\frac{1}{2} \, a\right)^{5} + 15 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{2} - 20 \, \tan\left(\frac{1}{2} \, a\right)^{3} - \tan\left(b x + 4 \, a\right) + 6 \, \tan\left(\frac{1}{2} \, a\right)\right)}^{2}} - 2 \, \log\left({\left| \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{6} - 15 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{4} + 6 \, \tan\left(\frac{1}{2} \, a\right)^{5} + 15 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{2} - 20 \, \tan\left(\frac{1}{2} \, a\right)^{3} - \tan\left(b x + 4 \, a\right) + 6 \, \tan\left(\frac{1}{2} \, a\right) \right|}\right) + 2 \, \log\left({\left| 6 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{5} - \tan\left(\frac{1}{2} \, a\right)^{6} - 20 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{3} + 15 \, \tan\left(\frac{1}{2} \, a\right)^{4} + 6 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right) - 15 \, \tan\left(\frac{1}{2} \, a\right)^{2} + 1 \right|}\right)}{4 \, b}"," ",0,"-1/4*((3*tan(b*x + 4*a)^2*tan(1/2*a)^24 - 180*tan(b*x + 4*a)^2*tan(1/2*a)^22 + 24*tan(b*x + 4*a)*tan(1/2*a)^23 + tan(1/2*a)^24 + 4230*tan(b*x + 4*a)^2*tan(1/2*a)^20 - 1592*tan(b*x + 4*a)*tan(1/2*a)^21 + 48*tan(1/2*a)^22 - 48612*tan(b*x + 4*a)^2*tan(1/2*a)^18 + 31704*tan(b*x + 4*a)*tan(1/2*a)^19 - 3846*tan(1/2*a)^20 + 277965*tan(b*x + 4*a)^2*tan(1/2*a)^16 - 259128*tan(b*x + 4*a)*tan(1/2*a)^17 + 51632*tan(1/2*a)^18 - 737640*tan(b*x + 4*a)^2*tan(1/2*a)^14 + 982192*tan(b*x + 4*a)*tan(1/2*a)^15 - 274545*tan(1/2*a)^16 + 1008468*tan(b*x + 4*a)^2*tan(1/2*a)^12 - 1871088*tan(b*x + 4*a)*tan(1/2*a)^13 + 733728*tan(1/2*a)^14 - 737640*tan(b*x + 4*a)^2*tan(1/2*a)^10 + 1871088*tan(b*x + 4*a)*tan(1/2*a)^11 - 1018132*tan(1/2*a)^12 + 277965*tan(b*x + 4*a)^2*tan(1/2*a)^8 - 982192*tan(b*x + 4*a)*tan(1/2*a)^9 + 733728*tan(1/2*a)^10 - 48612*tan(b*x + 4*a)^2*tan(1/2*a)^6 + 259128*tan(b*x + 4*a)*tan(1/2*a)^7 - 274545*tan(1/2*a)^8 + 4230*tan(b*x + 4*a)^2*tan(1/2*a)^4 - 31704*tan(b*x + 4*a)*tan(1/2*a)^5 + 51632*tan(1/2*a)^6 - 180*tan(b*x + 4*a)^2*tan(1/2*a)^2 + 1592*tan(b*x + 4*a)*tan(1/2*a)^3 - 3846*tan(1/2*a)^4 + 3*tan(b*x + 4*a)^2 - 24*tan(b*x + 4*a)*tan(1/2*a) + 48*tan(1/2*a)^2 + 1)/((tan(1/2*a)^12 - 30*tan(1/2*a)^10 + 255*tan(1/2*a)^8 - 452*tan(1/2*a)^6 + 255*tan(1/2*a)^4 - 30*tan(1/2*a)^2 + 1)*(tan(b*x + 4*a)*tan(1/2*a)^6 - 15*tan(b*x + 4*a)*tan(1/2*a)^4 + 6*tan(1/2*a)^5 + 15*tan(b*x + 4*a)*tan(1/2*a)^2 - 20*tan(1/2*a)^3 - tan(b*x + 4*a) + 6*tan(1/2*a))^2) - 2*log(abs(tan(b*x + 4*a)*tan(1/2*a)^6 - 15*tan(b*x + 4*a)*tan(1/2*a)^4 + 6*tan(1/2*a)^5 + 15*tan(b*x + 4*a)*tan(1/2*a)^2 - 20*tan(1/2*a)^3 - tan(b*x + 4*a) + 6*tan(1/2*a))) + 2*log(abs(6*tan(b*x + 4*a)*tan(1/2*a)^5 - tan(1/2*a)^6 - 20*tan(b*x + 4*a)*tan(1/2*a)^3 + 15*tan(1/2*a)^4 + 6*tan(b*x + 4*a)*tan(1/2*a) - 15*tan(1/2*a)^2 + 1)))/b","B",0
54,1,1079,0,1.806437," ","integrate(csc(b*x+a)^2*csc(2*b*x+2*a)^2,x, algorithm=""giac"")","-\frac{\frac{3 \, {\left(\tan\left(\frac{1}{2} \, a\right)^{12} + 6 \, \tan\left(\frac{1}{2} \, a\right)^{10} + 15 \, \tan\left(\frac{1}{2} \, a\right)^{8} + 20 \, \tan\left(\frac{1}{2} \, a\right)^{6} + 15 \, \tan\left(\frac{1}{2} \, a\right)^{4} + 6 \, \tan\left(\frac{1}{2} \, a\right)^{2} + 1\right)}}{{\left(6 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{5} - \tan\left(\frac{1}{2} \, a\right)^{6} - 20 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{3} + 15 \, \tan\left(\frac{1}{2} \, a\right)^{4} + 6 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right) - 15 \, \tan\left(\frac{1}{2} \, a\right)^{2} + 1\right)} {\left(3 \, \tan\left(\frac{1}{2} \, a\right)^{5} - 10 \, \tan\left(\frac{1}{2} \, a\right)^{3} + 3 \, \tan\left(\frac{1}{2} \, a\right)\right)}} + \frac{2 \, {\left(6 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{36} - 216 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{34} + 54 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{35} + \tan\left(\frac{1}{2} \, a\right)^{36} + 3078 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{32} - 1638 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{33} + 126 \, \tan\left(\frac{1}{2} \, a\right)^{34} - 23328 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{30} + 19872 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{31} - 3159 \, \tan\left(\frac{1}{2} \, a\right)^{32} + 62856 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{28} - 100224 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{29} + 29232 \, \tan\left(\frac{1}{2} \, a\right)^{30} + 328608 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{26} - 127176 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{27} - 26460 \, \tan\left(\frac{1}{2} \, a\right)^{28} - 96504 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{24} + 808488 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{25} - 228600 \, \tan\left(\frac{1}{2} \, a\right)^{26} - 879840 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{22} + 833472 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{23} + 237588 \, \tan\left(\frac{1}{2} \, a\right)^{24} + 30564 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{20} - 1653792 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{21} + 944208 \, \tan\left(\frac{1}{2} \, a\right)^{22} + 1149552 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{18} - 1673388 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{19} - 142434 \, \tan\left(\frac{1}{2} \, a\right)^{20} + 30564 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{16} + 1673388 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{17} - 1358860 \, \tan\left(\frac{1}{2} \, a\right)^{18} - 879840 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{14} + 1653792 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{15} - 142434 \, \tan\left(\frac{1}{2} \, a\right)^{16} - 96504 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{12} - 833472 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{13} + 944208 \, \tan\left(\frac{1}{2} \, a\right)^{14} + 328608 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{10} - 808488 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{11} + 237588 \, \tan\left(\frac{1}{2} \, a\right)^{12} + 62856 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{8} + 127176 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{9} - 228600 \, \tan\left(\frac{1}{2} \, a\right)^{10} - 23328 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{6} + 100224 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{7} - 26460 \, \tan\left(\frac{1}{2} \, a\right)^{8} + 3078 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{4} - 19872 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{5} + 29232 \, \tan\left(\frac{1}{2} \, a\right)^{6} - 216 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} + 1638 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{3} - 3159 \, \tan\left(\frac{1}{2} \, a\right)^{4} + 6 \, \tan\left(b x + 4 \, a\right)^{2} - 54 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right) + 126 \, \tan\left(\frac{1}{2} \, a\right)^{2} + 1\right)}}{{\left(\tan\left(\frac{1}{2} \, a\right)^{18} - 45 \, \tan\left(\frac{1}{2} \, a\right)^{16} + 720 \, \tan\left(\frac{1}{2} \, a\right)^{14} - 4728 \, \tan\left(\frac{1}{2} \, a\right)^{12} + 10890 \, \tan\left(\frac{1}{2} \, a\right)^{10} - 10890 \, \tan\left(\frac{1}{2} \, a\right)^{8} + 4728 \, \tan\left(\frac{1}{2} \, a\right)^{6} - 720 \, \tan\left(\frac{1}{2} \, a\right)^{4} + 45 \, \tan\left(\frac{1}{2} \, a\right)^{2} - 1\right)} {\left(\tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{6} - 15 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{4} + 6 \, \tan\left(\frac{1}{2} \, a\right)^{5} + 15 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{2} - 20 \, \tan\left(\frac{1}{2} \, a\right)^{3} - \tan\left(b x + 4 \, a\right) + 6 \, \tan\left(\frac{1}{2} \, a\right)\right)}^{3}}}{24 \, b}"," ",0,"-1/24*(3*(tan(1/2*a)^12 + 6*tan(1/2*a)^10 + 15*tan(1/2*a)^8 + 20*tan(1/2*a)^6 + 15*tan(1/2*a)^4 + 6*tan(1/2*a)^2 + 1)/((6*tan(b*x + 4*a)*tan(1/2*a)^5 - tan(1/2*a)^6 - 20*tan(b*x + 4*a)*tan(1/2*a)^3 + 15*tan(1/2*a)^4 + 6*tan(b*x + 4*a)*tan(1/2*a) - 15*tan(1/2*a)^2 + 1)*(3*tan(1/2*a)^5 - 10*tan(1/2*a)^3 + 3*tan(1/2*a))) + 2*(6*tan(b*x + 4*a)^2*tan(1/2*a)^36 - 216*tan(b*x + 4*a)^2*tan(1/2*a)^34 + 54*tan(b*x + 4*a)*tan(1/2*a)^35 + tan(1/2*a)^36 + 3078*tan(b*x + 4*a)^2*tan(1/2*a)^32 - 1638*tan(b*x + 4*a)*tan(1/2*a)^33 + 126*tan(1/2*a)^34 - 23328*tan(b*x + 4*a)^2*tan(1/2*a)^30 + 19872*tan(b*x + 4*a)*tan(1/2*a)^31 - 3159*tan(1/2*a)^32 + 62856*tan(b*x + 4*a)^2*tan(1/2*a)^28 - 100224*tan(b*x + 4*a)*tan(1/2*a)^29 + 29232*tan(1/2*a)^30 + 328608*tan(b*x + 4*a)^2*tan(1/2*a)^26 - 127176*tan(b*x + 4*a)*tan(1/2*a)^27 - 26460*tan(1/2*a)^28 - 96504*tan(b*x + 4*a)^2*tan(1/2*a)^24 + 808488*tan(b*x + 4*a)*tan(1/2*a)^25 - 228600*tan(1/2*a)^26 - 879840*tan(b*x + 4*a)^2*tan(1/2*a)^22 + 833472*tan(b*x + 4*a)*tan(1/2*a)^23 + 237588*tan(1/2*a)^24 + 30564*tan(b*x + 4*a)^2*tan(1/2*a)^20 - 1653792*tan(b*x + 4*a)*tan(1/2*a)^21 + 944208*tan(1/2*a)^22 + 1149552*tan(b*x + 4*a)^2*tan(1/2*a)^18 - 1673388*tan(b*x + 4*a)*tan(1/2*a)^19 - 142434*tan(1/2*a)^20 + 30564*tan(b*x + 4*a)^2*tan(1/2*a)^16 + 1673388*tan(b*x + 4*a)*tan(1/2*a)^17 - 1358860*tan(1/2*a)^18 - 879840*tan(b*x + 4*a)^2*tan(1/2*a)^14 + 1653792*tan(b*x + 4*a)*tan(1/2*a)^15 - 142434*tan(1/2*a)^16 - 96504*tan(b*x + 4*a)^2*tan(1/2*a)^12 - 833472*tan(b*x + 4*a)*tan(1/2*a)^13 + 944208*tan(1/2*a)^14 + 328608*tan(b*x + 4*a)^2*tan(1/2*a)^10 - 808488*tan(b*x + 4*a)*tan(1/2*a)^11 + 237588*tan(1/2*a)^12 + 62856*tan(b*x + 4*a)^2*tan(1/2*a)^8 + 127176*tan(b*x + 4*a)*tan(1/2*a)^9 - 228600*tan(1/2*a)^10 - 23328*tan(b*x + 4*a)^2*tan(1/2*a)^6 + 100224*tan(b*x + 4*a)*tan(1/2*a)^7 - 26460*tan(1/2*a)^8 + 3078*tan(b*x + 4*a)^2*tan(1/2*a)^4 - 19872*tan(b*x + 4*a)*tan(1/2*a)^5 + 29232*tan(1/2*a)^6 - 216*tan(b*x + 4*a)^2*tan(1/2*a)^2 + 1638*tan(b*x + 4*a)*tan(1/2*a)^3 - 3159*tan(1/2*a)^4 + 6*tan(b*x + 4*a)^2 - 54*tan(b*x + 4*a)*tan(1/2*a) + 126*tan(1/2*a)^2 + 1)/((tan(1/2*a)^18 - 45*tan(1/2*a)^16 + 720*tan(1/2*a)^14 - 4728*tan(1/2*a)^12 + 10890*tan(1/2*a)^10 - 10890*tan(1/2*a)^8 + 4728*tan(1/2*a)^6 - 720*tan(1/2*a)^4 + 45*tan(1/2*a)^2 - 1)*(tan(b*x + 4*a)*tan(1/2*a)^6 - 15*tan(b*x + 4*a)*tan(1/2*a)^4 + 6*tan(1/2*a)^5 + 15*tan(b*x + 4*a)*tan(1/2*a)^2 - 20*tan(1/2*a)^3 - tan(b*x + 4*a) + 6*tan(1/2*a))^3))/b","B",0
55,1,2808,0,3.363771," ","integrate(csc(b*x+a)^2*csc(2*b*x+2*a)^3,x, algorithm=""giac"")","\frac{\frac{12 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{23} - \tan\left(\frac{1}{2} \, a\right)^{24} + 11664 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{20} - 4036 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{21} + 384 \, \tan\left(\frac{1}{2} \, a\right)^{22} - 155520 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{18} + 96852 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{19} - 11994 \, \tan\left(\frac{1}{2} \, a\right)^{20} + 824256 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{16} - 781884 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{17} + 150592 \, \tan\left(\frac{1}{2} \, a\right)^{18} - 2194560 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{14} + 2930936 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{15} - 827919 \, \tan\left(\frac{1}{2} \, a\right)^{16} + 3065184 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{12} - 5623464 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{13} + 2209344 \, \tan\left(\frac{1}{2} \, a\right)^{14} - 2194560 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{10} + 5623464 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{11} - 3036716 \, \tan\left(\frac{1}{2} \, a\right)^{12} + 824256 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{8} - 2930936 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{9} + 2209344 \, \tan\left(\frac{1}{2} \, a\right)^{10} - 155520 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{6} + 781884 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{7} - 827919 \, \tan\left(\frac{1}{2} \, a\right)^{8} + 11664 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{4} - 96852 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{5} + 150592 \, \tan\left(\frac{1}{2} \, a\right)^{6} + 4036 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{3} - 11994 \, \tan\left(\frac{1}{2} \, a\right)^{4} - 12 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right) + 384 \, \tan\left(\frac{1}{2} \, a\right)^{2} - 1}{{\left(9 \, \tan\left(\frac{1}{2} \, a\right)^{10} - 60 \, \tan\left(\frac{1}{2} \, a\right)^{8} + 118 \, \tan\left(\frac{1}{2} \, a\right)^{6} - 60 \, \tan\left(\frac{1}{2} \, a\right)^{4} + 9 \, \tan\left(\frac{1}{2} \, a\right)^{2}\right)} {\left(6 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{5} - \tan\left(\frac{1}{2} \, a\right)^{6} - 20 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{3} + 15 \, \tan\left(\frac{1}{2} \, a\right)^{4} + 6 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right) - 15 \, \tan\left(\frac{1}{2} \, a\right)^{2} + 1\right)}^{2}} - \frac{2 \, {\left(25 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{48} - 3000 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{46} + 528 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{47} + 6 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{48} + 160500 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{44} - 60656 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{45} + 4032 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{46} + 48 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{47} + \tan\left(\frac{1}{2} \, a\right)^{48} - 5040200 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{42} + 2998224 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{43} - 459720 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{44} + 13808 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{45} + 96 \, \tan\left(\frac{1}{2} \, a\right)^{46} + 102947250 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{40} - 84754224 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{41} + 20740800 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{42} - 1553616 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{43} + 17940 \, \tan\left(\frac{1}{2} \, a\right)^{44} - 1432641000 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{38} + 1525423600 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{39} - 518242932 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{40} + 62627184 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{41} - 1976672 \, \tan\left(\frac{1}{2} \, a\right)^{42} + 13850865700 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{36} - 18347115792 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{37} + 8061782976 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{38} - 1352088880 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{39} + 69043458 \, \tan\left(\frac{1}{2} \, a\right)^{40} - 93424383000 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{34} + 150554954928 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{35} - 82205969064 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{36} + 17773339152 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{37} - 1252335840 \, \tan\left(\frac{1}{2} \, a\right)^{38} + 438276972375 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{32} - 849352828496 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{33} + 563338964160 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{34} - 150682961328 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{35} + 13569524420 \, \tan\left(\frac{1}{2} \, a\right)^{36} - 1429067476400 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{30} + 3312518959776 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{31} - 2637116003430 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{32} + 853300409104 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{33} - 94325029920 \, \tan\left(\frac{1}{2} \, a\right)^{34} + 3274543905000 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{28} - 9029526276960 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{29} + 8569312295808 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{30} - 3315261850656 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{31} + 440742337263 \, \tan\left(\frac{1}{2} \, a\right)^{32} - 5348018130000 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{26} + 17444688475680 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{27} - 19627171727760 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{28} + 9019269429600 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{29} - 1427485388352 \, \tan\left(\frac{1}{2} \, a\right)^{30} + 6290345645500 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{24} - 24168979539936 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{25} + 32090952253824 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{26} - 17435372647456 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{27} + 3267744813864 \, \tan\left(\frac{1}{2} \, a\right)^{28} - 5348018130000 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{22} + 24168979539936 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{23} - 37769347277400 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{24} + 24182504468064 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{25} - 5348887137216 \, \tan\left(\frac{1}{2} \, a\right)^{26} + 3274543905000 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{20} - 17444688475680 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{21} + 32090952253824 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{22} - 24182504468064 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{23} + 6299635484700 \, \tan\left(\frac{1}{2} \, a\right)^{24} - 1429067476400 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{18} + 9029526276960 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{19} - 19627171727760 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{20} + 17435372647456 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{21} - 5348887137216 \, \tan\left(\frac{1}{2} \, a\right)^{22} + 438276972375 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{16} - 3312518959776 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{17} + 8569312295808 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{18} - 9019269429600 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{19} + 3267744813864 \, \tan\left(\frac{1}{2} \, a\right)^{20} - 93424383000 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{14} + 849352828496 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{15} - 2637116003430 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{16} + 3315261850656 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{17} - 1427485388352 \, \tan\left(\frac{1}{2} \, a\right)^{18} + 13850865700 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{12} - 150554954928 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{13} + 563338964160 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{14} - 853300409104 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{15} + 440742337263 \, \tan\left(\frac{1}{2} \, a\right)^{16} - 1432641000 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{10} + 18347115792 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{11} - 82205969064 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{12} + 150682961328 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{13} - 94325029920 \, \tan\left(\frac{1}{2} \, a\right)^{14} + 102947250 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{8} - 1525423600 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{9} + 8061782976 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{10} - 17773339152 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{11} + 13569524420 \, \tan\left(\frac{1}{2} \, a\right)^{12} - 5040200 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{6} + 84754224 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{7} - 518242932 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{8} + 1352088880 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{9} - 1252335840 \, \tan\left(\frac{1}{2} \, a\right)^{10} + 160500 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{4} - 2998224 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{5} + 20740800 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{6} - 62627184 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{7} + 69043458 \, \tan\left(\frac{1}{2} \, a\right)^{8} - 3000 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{2} + 60656 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{3} - 459720 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{4} + 1553616 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{5} - 1976672 \, \tan\left(\frac{1}{2} \, a\right)^{6} + 25 \, \tan\left(b x + 4 \, a\right)^{4} - 528 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right) + 4032 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} - 13808 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{3} + 17940 \, \tan\left(\frac{1}{2} \, a\right)^{4} + 6 \, \tan\left(b x + 4 \, a\right)^{2} - 48 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right) + 96 \, \tan\left(\frac{1}{2} \, a\right)^{2} + 1\right)}}{{\left(\tan\left(\frac{1}{2} \, a\right)^{24} - 60 \, \tan\left(\frac{1}{2} \, a\right)^{22} + 1410 \, \tan\left(\frac{1}{2} \, a\right)^{20} - 16204 \, \tan\left(\frac{1}{2} \, a\right)^{18} + 92655 \, \tan\left(\frac{1}{2} \, a\right)^{16} - 245880 \, \tan\left(\frac{1}{2} \, a\right)^{14} + 336156 \, \tan\left(\frac{1}{2} \, a\right)^{12} - 245880 \, \tan\left(\frac{1}{2} \, a\right)^{10} + 92655 \, \tan\left(\frac{1}{2} \, a\right)^{8} - 16204 \, \tan\left(\frac{1}{2} \, a\right)^{6} + 1410 \, \tan\left(\frac{1}{2} \, a\right)^{4} - 60 \, \tan\left(\frac{1}{2} \, a\right)^{2} + 1\right)} {\left(\tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{6} - 15 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{4} + 6 \, \tan\left(\frac{1}{2} \, a\right)^{5} + 15 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{2} - 20 \, \tan\left(\frac{1}{2} \, a\right)^{3} - \tan\left(b x + 4 \, a\right) + 6 \, \tan\left(\frac{1}{2} \, a\right)\right)}^{4}} + 24 \, \log\left({\left| \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{6} - 15 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{4} + 6 \, \tan\left(\frac{1}{2} \, a\right)^{5} + 15 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{2} - 20 \, \tan\left(\frac{1}{2} \, a\right)^{3} - \tan\left(b x + 4 \, a\right) + 6 \, \tan\left(\frac{1}{2} \, a\right) \right|}\right) - 24 \, \log\left({\left| 6 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{5} - \tan\left(\frac{1}{2} \, a\right)^{6} - 20 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{3} + 15 \, \tan\left(\frac{1}{2} \, a\right)^{4} + 6 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right) - 15 \, \tan\left(\frac{1}{2} \, a\right)^{2} + 1 \right|}\right)}{64 \, b}"," ",0,"1/64*((12*tan(b*x + 4*a)*tan(1/2*a)^23 - tan(1/2*a)^24 + 11664*tan(b*x + 4*a)^2*tan(1/2*a)^20 - 4036*tan(b*x + 4*a)*tan(1/2*a)^21 + 384*tan(1/2*a)^22 - 155520*tan(b*x + 4*a)^2*tan(1/2*a)^18 + 96852*tan(b*x + 4*a)*tan(1/2*a)^19 - 11994*tan(1/2*a)^20 + 824256*tan(b*x + 4*a)^2*tan(1/2*a)^16 - 781884*tan(b*x + 4*a)*tan(1/2*a)^17 + 150592*tan(1/2*a)^18 - 2194560*tan(b*x + 4*a)^2*tan(1/2*a)^14 + 2930936*tan(b*x + 4*a)*tan(1/2*a)^15 - 827919*tan(1/2*a)^16 + 3065184*tan(b*x + 4*a)^2*tan(1/2*a)^12 - 5623464*tan(b*x + 4*a)*tan(1/2*a)^13 + 2209344*tan(1/2*a)^14 - 2194560*tan(b*x + 4*a)^2*tan(1/2*a)^10 + 5623464*tan(b*x + 4*a)*tan(1/2*a)^11 - 3036716*tan(1/2*a)^12 + 824256*tan(b*x + 4*a)^2*tan(1/2*a)^8 - 2930936*tan(b*x + 4*a)*tan(1/2*a)^9 + 2209344*tan(1/2*a)^10 - 155520*tan(b*x + 4*a)^2*tan(1/2*a)^6 + 781884*tan(b*x + 4*a)*tan(1/2*a)^7 - 827919*tan(1/2*a)^8 + 11664*tan(b*x + 4*a)^2*tan(1/2*a)^4 - 96852*tan(b*x + 4*a)*tan(1/2*a)^5 + 150592*tan(1/2*a)^6 + 4036*tan(b*x + 4*a)*tan(1/2*a)^3 - 11994*tan(1/2*a)^4 - 12*tan(b*x + 4*a)*tan(1/2*a) + 384*tan(1/2*a)^2 - 1)/((9*tan(1/2*a)^10 - 60*tan(1/2*a)^8 + 118*tan(1/2*a)^6 - 60*tan(1/2*a)^4 + 9*tan(1/2*a)^2)*(6*tan(b*x + 4*a)*tan(1/2*a)^5 - tan(1/2*a)^6 - 20*tan(b*x + 4*a)*tan(1/2*a)^3 + 15*tan(1/2*a)^4 + 6*tan(b*x + 4*a)*tan(1/2*a) - 15*tan(1/2*a)^2 + 1)^2) - 2*(25*tan(b*x + 4*a)^4*tan(1/2*a)^48 - 3000*tan(b*x + 4*a)^4*tan(1/2*a)^46 + 528*tan(b*x + 4*a)^3*tan(1/2*a)^47 + 6*tan(b*x + 4*a)^2*tan(1/2*a)^48 + 160500*tan(b*x + 4*a)^4*tan(1/2*a)^44 - 60656*tan(b*x + 4*a)^3*tan(1/2*a)^45 + 4032*tan(b*x + 4*a)^2*tan(1/2*a)^46 + 48*tan(b*x + 4*a)*tan(1/2*a)^47 + tan(1/2*a)^48 - 5040200*tan(b*x + 4*a)^4*tan(1/2*a)^42 + 2998224*tan(b*x + 4*a)^3*tan(1/2*a)^43 - 459720*tan(b*x + 4*a)^2*tan(1/2*a)^44 + 13808*tan(b*x + 4*a)*tan(1/2*a)^45 + 96*tan(1/2*a)^46 + 102947250*tan(b*x + 4*a)^4*tan(1/2*a)^40 - 84754224*tan(b*x + 4*a)^3*tan(1/2*a)^41 + 20740800*tan(b*x + 4*a)^2*tan(1/2*a)^42 - 1553616*tan(b*x + 4*a)*tan(1/2*a)^43 + 17940*tan(1/2*a)^44 - 1432641000*tan(b*x + 4*a)^4*tan(1/2*a)^38 + 1525423600*tan(b*x + 4*a)^3*tan(1/2*a)^39 - 518242932*tan(b*x + 4*a)^2*tan(1/2*a)^40 + 62627184*tan(b*x + 4*a)*tan(1/2*a)^41 - 1976672*tan(1/2*a)^42 + 13850865700*tan(b*x + 4*a)^4*tan(1/2*a)^36 - 18347115792*tan(b*x + 4*a)^3*tan(1/2*a)^37 + 8061782976*tan(b*x + 4*a)^2*tan(1/2*a)^38 - 1352088880*tan(b*x + 4*a)*tan(1/2*a)^39 + 69043458*tan(1/2*a)^40 - 93424383000*tan(b*x + 4*a)^4*tan(1/2*a)^34 + 150554954928*tan(b*x + 4*a)^3*tan(1/2*a)^35 - 82205969064*tan(b*x + 4*a)^2*tan(1/2*a)^36 + 17773339152*tan(b*x + 4*a)*tan(1/2*a)^37 - 1252335840*tan(1/2*a)^38 + 438276972375*tan(b*x + 4*a)^4*tan(1/2*a)^32 - 849352828496*tan(b*x + 4*a)^3*tan(1/2*a)^33 + 563338964160*tan(b*x + 4*a)^2*tan(1/2*a)^34 - 150682961328*tan(b*x + 4*a)*tan(1/2*a)^35 + 13569524420*tan(1/2*a)^36 - 1429067476400*tan(b*x + 4*a)^4*tan(1/2*a)^30 + 3312518959776*tan(b*x + 4*a)^3*tan(1/2*a)^31 - 2637116003430*tan(b*x + 4*a)^2*tan(1/2*a)^32 + 853300409104*tan(b*x + 4*a)*tan(1/2*a)^33 - 94325029920*tan(1/2*a)^34 + 3274543905000*tan(b*x + 4*a)^4*tan(1/2*a)^28 - 9029526276960*tan(b*x + 4*a)^3*tan(1/2*a)^29 + 8569312295808*tan(b*x + 4*a)^2*tan(1/2*a)^30 - 3315261850656*tan(b*x + 4*a)*tan(1/2*a)^31 + 440742337263*tan(1/2*a)^32 - 5348018130000*tan(b*x + 4*a)^4*tan(1/2*a)^26 + 17444688475680*tan(b*x + 4*a)^3*tan(1/2*a)^27 - 19627171727760*tan(b*x + 4*a)^2*tan(1/2*a)^28 + 9019269429600*tan(b*x + 4*a)*tan(1/2*a)^29 - 1427485388352*tan(1/2*a)^30 + 6290345645500*tan(b*x + 4*a)^4*tan(1/2*a)^24 - 24168979539936*tan(b*x + 4*a)^3*tan(1/2*a)^25 + 32090952253824*tan(b*x + 4*a)^2*tan(1/2*a)^26 - 17435372647456*tan(b*x + 4*a)*tan(1/2*a)^27 + 3267744813864*tan(1/2*a)^28 - 5348018130000*tan(b*x + 4*a)^4*tan(1/2*a)^22 + 24168979539936*tan(b*x + 4*a)^3*tan(1/2*a)^23 - 37769347277400*tan(b*x + 4*a)^2*tan(1/2*a)^24 + 24182504468064*tan(b*x + 4*a)*tan(1/2*a)^25 - 5348887137216*tan(1/2*a)^26 + 3274543905000*tan(b*x + 4*a)^4*tan(1/2*a)^20 - 17444688475680*tan(b*x + 4*a)^3*tan(1/2*a)^21 + 32090952253824*tan(b*x + 4*a)^2*tan(1/2*a)^22 - 24182504468064*tan(b*x + 4*a)*tan(1/2*a)^23 + 6299635484700*tan(1/2*a)^24 - 1429067476400*tan(b*x + 4*a)^4*tan(1/2*a)^18 + 9029526276960*tan(b*x + 4*a)^3*tan(1/2*a)^19 - 19627171727760*tan(b*x + 4*a)^2*tan(1/2*a)^20 + 17435372647456*tan(b*x + 4*a)*tan(1/2*a)^21 - 5348887137216*tan(1/2*a)^22 + 438276972375*tan(b*x + 4*a)^4*tan(1/2*a)^16 - 3312518959776*tan(b*x + 4*a)^3*tan(1/2*a)^17 + 8569312295808*tan(b*x + 4*a)^2*tan(1/2*a)^18 - 9019269429600*tan(b*x + 4*a)*tan(1/2*a)^19 + 3267744813864*tan(1/2*a)^20 - 93424383000*tan(b*x + 4*a)^4*tan(1/2*a)^14 + 849352828496*tan(b*x + 4*a)^3*tan(1/2*a)^15 - 2637116003430*tan(b*x + 4*a)^2*tan(1/2*a)^16 + 3315261850656*tan(b*x + 4*a)*tan(1/2*a)^17 - 1427485388352*tan(1/2*a)^18 + 13850865700*tan(b*x + 4*a)^4*tan(1/2*a)^12 - 150554954928*tan(b*x + 4*a)^3*tan(1/2*a)^13 + 563338964160*tan(b*x + 4*a)^2*tan(1/2*a)^14 - 853300409104*tan(b*x + 4*a)*tan(1/2*a)^15 + 440742337263*tan(1/2*a)^16 - 1432641000*tan(b*x + 4*a)^4*tan(1/2*a)^10 + 18347115792*tan(b*x + 4*a)^3*tan(1/2*a)^11 - 82205969064*tan(b*x + 4*a)^2*tan(1/2*a)^12 + 150682961328*tan(b*x + 4*a)*tan(1/2*a)^13 - 94325029920*tan(1/2*a)^14 + 102947250*tan(b*x + 4*a)^4*tan(1/2*a)^8 - 1525423600*tan(b*x + 4*a)^3*tan(1/2*a)^9 + 8061782976*tan(b*x + 4*a)^2*tan(1/2*a)^10 - 17773339152*tan(b*x + 4*a)*tan(1/2*a)^11 + 13569524420*tan(1/2*a)^12 - 5040200*tan(b*x + 4*a)^4*tan(1/2*a)^6 + 84754224*tan(b*x + 4*a)^3*tan(1/2*a)^7 - 518242932*tan(b*x + 4*a)^2*tan(1/2*a)^8 + 1352088880*tan(b*x + 4*a)*tan(1/2*a)^9 - 1252335840*tan(1/2*a)^10 + 160500*tan(b*x + 4*a)^4*tan(1/2*a)^4 - 2998224*tan(b*x + 4*a)^3*tan(1/2*a)^5 + 20740800*tan(b*x + 4*a)^2*tan(1/2*a)^6 - 62627184*tan(b*x + 4*a)*tan(1/2*a)^7 + 69043458*tan(1/2*a)^8 - 3000*tan(b*x + 4*a)^4*tan(1/2*a)^2 + 60656*tan(b*x + 4*a)^3*tan(1/2*a)^3 - 459720*tan(b*x + 4*a)^2*tan(1/2*a)^4 + 1553616*tan(b*x + 4*a)*tan(1/2*a)^5 - 1976672*tan(1/2*a)^6 + 25*tan(b*x + 4*a)^4 - 528*tan(b*x + 4*a)^3*tan(1/2*a) + 4032*tan(b*x + 4*a)^2*tan(1/2*a)^2 - 13808*tan(b*x + 4*a)*tan(1/2*a)^3 + 17940*tan(1/2*a)^4 + 6*tan(b*x + 4*a)^2 - 48*tan(b*x + 4*a)*tan(1/2*a) + 96*tan(1/2*a)^2 + 1)/((tan(1/2*a)^24 - 60*tan(1/2*a)^22 + 1410*tan(1/2*a)^20 - 16204*tan(1/2*a)^18 + 92655*tan(1/2*a)^16 - 245880*tan(1/2*a)^14 + 336156*tan(1/2*a)^12 - 245880*tan(1/2*a)^10 + 92655*tan(1/2*a)^8 - 16204*tan(1/2*a)^6 + 1410*tan(1/2*a)^4 - 60*tan(1/2*a)^2 + 1)*(tan(b*x + 4*a)*tan(1/2*a)^6 - 15*tan(b*x + 4*a)*tan(1/2*a)^4 + 6*tan(1/2*a)^5 + 15*tan(b*x + 4*a)*tan(1/2*a)^2 - 20*tan(1/2*a)^3 - tan(b*x + 4*a) + 6*tan(1/2*a))^4) + 24*log(abs(tan(b*x + 4*a)*tan(1/2*a)^6 - 15*tan(b*x + 4*a)*tan(1/2*a)^4 + 6*tan(1/2*a)^5 + 15*tan(b*x + 4*a)*tan(1/2*a)^2 - 20*tan(1/2*a)^3 - tan(b*x + 4*a) + 6*tan(1/2*a))) - 24*log(abs(6*tan(b*x + 4*a)*tan(1/2*a)^5 - tan(1/2*a)^6 - 20*tan(b*x + 4*a)*tan(1/2*a)^3 + 15*tan(1/2*a)^4 + 6*tan(b*x + 4*a)*tan(1/2*a) - 15*tan(1/2*a)^2 + 1)))/b","B",0
56,1,3445,0,2.834429," ","integrate(csc(b*x+a)^2*csc(2*b*x+2*a)^4,x, algorithm=""giac"")","-\frac{\frac{5 \, {\left(108 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{34} - 18 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{35} + \tan\left(\frac{1}{2} \, a\right)^{36} + 12240 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{32} - 3774 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{33} + 342 \, \tan\left(\frac{1}{2} \, a\right)^{34} - 85632 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{30} + 75456 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{31} - 9783 \, \tan\left(\frac{1}{2} \, a\right)^{32} + 58608 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{28} - 253152 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{29} + 86064 \, \tan\left(\frac{1}{2} \, a\right)^{30} + 631440 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{26} - 389448 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{27} - 85500 \, \tan\left(\frac{1}{2} \, a\right)^{28} - 679344 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{24} + 2047464 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{25} - 702936 \, \tan\left(\frac{1}{2} \, a\right)^{26} - 2420352 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{22} + 1465056 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{23} + 675636 \, \tan\left(\frac{1}{2} \, a\right)^{24} + 1394928 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{20} - 6297216 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{21} + 2768976 \, \tan\left(\frac{1}{2} \, a\right)^{22} + 5321736 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{18} - 5657724 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{19} - 514818 \, \tan\left(\frac{1}{2} \, a\right)^{20} + 1394928 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{16} + 5657724 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{17} - 4173820 \, \tan\left(\frac{1}{2} \, a\right)^{18} - 2420352 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{14} + 6297216 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{15} - 514818 \, \tan\left(\frac{1}{2} \, a\right)^{16} - 679344 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{12} - 1465056 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{13} + 2768976 \, \tan\left(\frac{1}{2} \, a\right)^{14} + 631440 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{10} - 2047464 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{11} + 675636 \, \tan\left(\frac{1}{2} \, a\right)^{12} + 58608 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{8} + 389448 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{9} - 702936 \, \tan\left(\frac{1}{2} \, a\right)^{10} - 85632 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{6} + 253152 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{7} - 85500 \, \tan\left(\frac{1}{2} \, a\right)^{8} + 12240 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{4} - 75456 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{5} + 86064 \, \tan\left(\frac{1}{2} \, a\right)^{6} + 108 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} + 3774 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{3} - 9783 \, \tan\left(\frac{1}{2} \, a\right)^{4} + 18 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right) + 342 \, \tan\left(\frac{1}{2} \, a\right)^{2} + 1\right)}}{{\left(27 \, \tan\left(\frac{1}{2} \, a\right)^{15} - 270 \, \tan\left(\frac{1}{2} \, a\right)^{13} + 981 \, \tan\left(\frac{1}{2} \, a\right)^{11} - 1540 \, \tan\left(\frac{1}{2} \, a\right)^{9} + 981 \, \tan\left(\frac{1}{2} \, a\right)^{7} - 270 \, \tan\left(\frac{1}{2} \, a\right)^{5} + 27 \, \tan\left(\frac{1}{2} \, a\right)^{3}\right)} {\left(6 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{5} - \tan\left(\frac{1}{2} \, a\right)^{6} - 20 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{3} + 15 \, \tan\left(\frac{1}{2} \, a\right)^{4} + 6 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right) - 15 \, \tan\left(\frac{1}{2} \, a\right)^{2} + 1\right)}^{3}} + \frac{8 \, {\left(90 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{60} - 8100 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{58} + 1800 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{59} + 20 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{60} + 337950 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{56} - 151800 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{57} + 13200 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{58} + 150 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{59} + 3 \, \tan\left(\frac{1}{2} \, a\right)^{60} - 8558760 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{54} + 5856480 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{55} - 1068900 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{56} + 44050 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{57} + 270 \, \tan\left(\frac{1}{2} \, a\right)^{58} + 143179650 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{52} - 133967520 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{53} + 37650400 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{54} - 3349740 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{55} + 56265 \, \tan\left(\frac{1}{2} \, a\right)^{56} - 1610662860 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{50} + 1962664200 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{51} - 761504220 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{52} + 105669900 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{53} - 3921700 \, \tan\left(\frac{1}{2} \, a\right)^{54} + 11902135590 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{48} - 18613230840 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{49} + 9508215600 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{50} - 1840189110 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{51} + 108499095 \, \tan\left(\frac{1}{2} \, a\right)^{52} - 53242909200 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{46} + 109725269760 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{47} - 73309882260 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{48} + 18891597150 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{49} - 1563175302 \, \tan\left(\frac{1}{2} \, a\right)^{50} + 107646377490 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{44} - 347626321920 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{45} + 324785269440 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{46} - 112787150040 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{47} + 12602922605 \, \tan\left(\frac{1}{2} \, a\right)^{48} + 100499354940 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{42} + 243954351720 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{43} - 614500276860 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{44} + 342870428760 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{45} - 54544776360 \, \tan\left(\frac{1}{2} \, a\right)^{46} - 720524857050 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{40} + 1552622504040 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{41} - 592670717680 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{42} - 221864573610 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{43} + 98588733975 \, \tan\left(\frac{1}{2} \, a\right)^{44} + 545843494440 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{38} - 3402462596640 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{39} + 4208031154860 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{40} - 1502042255310 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{41} + 99097279550 \, \tan\left(\frac{1}{2} \, a\right)^{42} + 1394520156090 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{36} - 1060535913120 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{37} - 3399607142880 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{38} + 3367956274060 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{39} - 681790695915 \, \tan\left(\frac{1}{2} \, a\right)^{40} - 2195406541260 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{34} + 8940274641000 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{35} - 8188018122860 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{36} + 893802691860 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{37} + 583218519780 \, \tan\left(\frac{1}{2} \, a\right)^{38} - 793687329810 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{32} - 4368381430680 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{33} + 13505898965040 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{34} - 8980226310150 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{35} + 1327591075915 \, \tan\left(\frac{1}{2} \, a\right)^{36} + 3207851661600 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{30} - 10136128700160 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{31} + 4668559700220 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{32} + 4628264277390 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{33} - 2309792723910 \, \tan\left(\frac{1}{2} \, a\right)^{34} - 793687329810 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{28} + 10136128700160 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{29} - 19695904506240 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{30} + 10330657752240 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{31} - 756295285575 \, \tan\left(\frac{1}{2} \, a\right)^{32} - 2195406541260 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{26} + 4368381430680 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{27} + 4668559700220 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{28} - 10330657752240 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{29} + 3368788208080 \, \tan\left(\frac{1}{2} \, a\right)^{30} + 1394520156090 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{24} - 8940274641000 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{25} + 13505898965040 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{26} - 4628264277390 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{27} - 756295285575 \, \tan\left(\frac{1}{2} \, a\right)^{28} + 545843494440 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{22} + 1060535913120 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{23} - 8188018122860 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{24} + 8980226310150 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{25} - 2309792723910 \, \tan\left(\frac{1}{2} \, a\right)^{26} - 720524857050 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{20} + 3402462596640 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{21} - 3399607142880 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{22} - 893802691860 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{23} + 1327591075915 \, \tan\left(\frac{1}{2} \, a\right)^{24} + 100499354940 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{18} - 1552622504040 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{19} + 4208031154860 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{20} - 3367956274060 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{21} + 583218519780 \, \tan\left(\frac{1}{2} \, a\right)^{22} + 107646377490 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{16} - 243954351720 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{17} - 592670717680 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{18} + 1502042255310 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{19} - 681790695915 \, \tan\left(\frac{1}{2} \, a\right)^{20} - 53242909200 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{14} + 347626321920 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{15} - 614500276860 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{16} + 221864573610 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{17} + 99097279550 \, \tan\left(\frac{1}{2} \, a\right)^{18} + 11902135590 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{12} - 109725269760 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{13} + 324785269440 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{14} - 342870428760 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{15} + 98588733975 \, \tan\left(\frac{1}{2} \, a\right)^{16} - 1610662860 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{10} + 18613230840 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{11} - 73309882260 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{12} + 112787150040 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{13} - 54544776360 \, \tan\left(\frac{1}{2} \, a\right)^{14} + 143179650 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{8} - 1962664200 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{9} + 9508215600 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{10} - 18891597150 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{11} + 12602922605 \, \tan\left(\frac{1}{2} \, a\right)^{12} - 8558760 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{6} + 133967520 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{7} - 761504220 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{8} + 1840189110 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{9} - 1563175302 \, \tan\left(\frac{1}{2} \, a\right)^{10} + 337950 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{4} - 5856480 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{5} + 37650400 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{6} - 105669900 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{7} + 108499095 \, \tan\left(\frac{1}{2} \, a\right)^{8} - 8100 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{2} + 151800 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{3} - 1068900 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{4} + 3349740 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{5} - 3921700 \, \tan\left(\frac{1}{2} \, a\right)^{6} + 90 \, \tan\left(b x + 4 \, a\right)^{4} - 1800 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right) + 13200 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} - 44050 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{3} + 56265 \, \tan\left(\frac{1}{2} \, a\right)^{4} + 20 \, \tan\left(b x + 4 \, a\right)^{2} - 150 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right) + 270 \, \tan\left(\frac{1}{2} \, a\right)^{2} + 3\right)}}{{\left(\tan\left(\frac{1}{2} \, a\right)^{30} - 75 \, \tan\left(\frac{1}{2} \, a\right)^{28} + 2325 \, \tan\left(\frac{1}{2} \, a\right)^{26} - 38255 \, \tan\left(\frac{1}{2} \, a\right)^{24} + 356925 \, \tan\left(\frac{1}{2} \, a\right)^{22} - 1880175 \, \tan\left(\frac{1}{2} \, a\right)^{20} + 5430385 \, \tan\left(\frac{1}{2} \, a\right)^{18} - 9069075 \, \tan\left(\frac{1}{2} \, a\right)^{16} + 9069075 \, \tan\left(\frac{1}{2} \, a\right)^{14} - 5430385 \, \tan\left(\frac{1}{2} \, a\right)^{12} + 1880175 \, \tan\left(\frac{1}{2} \, a\right)^{10} - 356925 \, \tan\left(\frac{1}{2} \, a\right)^{8} + 38255 \, \tan\left(\frac{1}{2} \, a\right)^{6} - 2325 \, \tan\left(\frac{1}{2} \, a\right)^{4} + 75 \, \tan\left(\frac{1}{2} \, a\right)^{2} - 1\right)} {\left(\tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{6} - 15 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{4} + 6 \, \tan\left(\frac{1}{2} \, a\right)^{5} + 15 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{2} - 20 \, \tan\left(\frac{1}{2} \, a\right)^{3} - \tan\left(b x + 4 \, a\right) + 6 \, \tan\left(\frac{1}{2} \, a\right)\right)}^{5}}}{1920 \, b}"," ",0,"-1/1920*(5*(108*tan(b*x + 4*a)^2*tan(1/2*a)^34 - 18*tan(b*x + 4*a)*tan(1/2*a)^35 + tan(1/2*a)^36 + 12240*tan(b*x + 4*a)^2*tan(1/2*a)^32 - 3774*tan(b*x + 4*a)*tan(1/2*a)^33 + 342*tan(1/2*a)^34 - 85632*tan(b*x + 4*a)^2*tan(1/2*a)^30 + 75456*tan(b*x + 4*a)*tan(1/2*a)^31 - 9783*tan(1/2*a)^32 + 58608*tan(b*x + 4*a)^2*tan(1/2*a)^28 - 253152*tan(b*x + 4*a)*tan(1/2*a)^29 + 86064*tan(1/2*a)^30 + 631440*tan(b*x + 4*a)^2*tan(1/2*a)^26 - 389448*tan(b*x + 4*a)*tan(1/2*a)^27 - 85500*tan(1/2*a)^28 - 679344*tan(b*x + 4*a)^2*tan(1/2*a)^24 + 2047464*tan(b*x + 4*a)*tan(1/2*a)^25 - 702936*tan(1/2*a)^26 - 2420352*tan(b*x + 4*a)^2*tan(1/2*a)^22 + 1465056*tan(b*x + 4*a)*tan(1/2*a)^23 + 675636*tan(1/2*a)^24 + 1394928*tan(b*x + 4*a)^2*tan(1/2*a)^20 - 6297216*tan(b*x + 4*a)*tan(1/2*a)^21 + 2768976*tan(1/2*a)^22 + 5321736*tan(b*x + 4*a)^2*tan(1/2*a)^18 - 5657724*tan(b*x + 4*a)*tan(1/2*a)^19 - 514818*tan(1/2*a)^20 + 1394928*tan(b*x + 4*a)^2*tan(1/2*a)^16 + 5657724*tan(b*x + 4*a)*tan(1/2*a)^17 - 4173820*tan(1/2*a)^18 - 2420352*tan(b*x + 4*a)^2*tan(1/2*a)^14 + 6297216*tan(b*x + 4*a)*tan(1/2*a)^15 - 514818*tan(1/2*a)^16 - 679344*tan(b*x + 4*a)^2*tan(1/2*a)^12 - 1465056*tan(b*x + 4*a)*tan(1/2*a)^13 + 2768976*tan(1/2*a)^14 + 631440*tan(b*x + 4*a)^2*tan(1/2*a)^10 - 2047464*tan(b*x + 4*a)*tan(1/2*a)^11 + 675636*tan(1/2*a)^12 + 58608*tan(b*x + 4*a)^2*tan(1/2*a)^8 + 389448*tan(b*x + 4*a)*tan(1/2*a)^9 - 702936*tan(1/2*a)^10 - 85632*tan(b*x + 4*a)^2*tan(1/2*a)^6 + 253152*tan(b*x + 4*a)*tan(1/2*a)^7 - 85500*tan(1/2*a)^8 + 12240*tan(b*x + 4*a)^2*tan(1/2*a)^4 - 75456*tan(b*x + 4*a)*tan(1/2*a)^5 + 86064*tan(1/2*a)^6 + 108*tan(b*x + 4*a)^2*tan(1/2*a)^2 + 3774*tan(b*x + 4*a)*tan(1/2*a)^3 - 9783*tan(1/2*a)^4 + 18*tan(b*x + 4*a)*tan(1/2*a) + 342*tan(1/2*a)^2 + 1)/((27*tan(1/2*a)^15 - 270*tan(1/2*a)^13 + 981*tan(1/2*a)^11 - 1540*tan(1/2*a)^9 + 981*tan(1/2*a)^7 - 270*tan(1/2*a)^5 + 27*tan(1/2*a)^3)*(6*tan(b*x + 4*a)*tan(1/2*a)^5 - tan(1/2*a)^6 - 20*tan(b*x + 4*a)*tan(1/2*a)^3 + 15*tan(1/2*a)^4 + 6*tan(b*x + 4*a)*tan(1/2*a) - 15*tan(1/2*a)^2 + 1)^3) + 8*(90*tan(b*x + 4*a)^4*tan(1/2*a)^60 - 8100*tan(b*x + 4*a)^4*tan(1/2*a)^58 + 1800*tan(b*x + 4*a)^3*tan(1/2*a)^59 + 20*tan(b*x + 4*a)^2*tan(1/2*a)^60 + 337950*tan(b*x + 4*a)^4*tan(1/2*a)^56 - 151800*tan(b*x + 4*a)^3*tan(1/2*a)^57 + 13200*tan(b*x + 4*a)^2*tan(1/2*a)^58 + 150*tan(b*x + 4*a)*tan(1/2*a)^59 + 3*tan(1/2*a)^60 - 8558760*tan(b*x + 4*a)^4*tan(1/2*a)^54 + 5856480*tan(b*x + 4*a)^3*tan(1/2*a)^55 - 1068900*tan(b*x + 4*a)^2*tan(1/2*a)^56 + 44050*tan(b*x + 4*a)*tan(1/2*a)^57 + 270*tan(1/2*a)^58 + 143179650*tan(b*x + 4*a)^4*tan(1/2*a)^52 - 133967520*tan(b*x + 4*a)^3*tan(1/2*a)^53 + 37650400*tan(b*x + 4*a)^2*tan(1/2*a)^54 - 3349740*tan(b*x + 4*a)*tan(1/2*a)^55 + 56265*tan(1/2*a)^56 - 1610662860*tan(b*x + 4*a)^4*tan(1/2*a)^50 + 1962664200*tan(b*x + 4*a)^3*tan(1/2*a)^51 - 761504220*tan(b*x + 4*a)^2*tan(1/2*a)^52 + 105669900*tan(b*x + 4*a)*tan(1/2*a)^53 - 3921700*tan(1/2*a)^54 + 11902135590*tan(b*x + 4*a)^4*tan(1/2*a)^48 - 18613230840*tan(b*x + 4*a)^3*tan(1/2*a)^49 + 9508215600*tan(b*x + 4*a)^2*tan(1/2*a)^50 - 1840189110*tan(b*x + 4*a)*tan(1/2*a)^51 + 108499095*tan(1/2*a)^52 - 53242909200*tan(b*x + 4*a)^4*tan(1/2*a)^46 + 109725269760*tan(b*x + 4*a)^3*tan(1/2*a)^47 - 73309882260*tan(b*x + 4*a)^2*tan(1/2*a)^48 + 18891597150*tan(b*x + 4*a)*tan(1/2*a)^49 - 1563175302*tan(1/2*a)^50 + 107646377490*tan(b*x + 4*a)^4*tan(1/2*a)^44 - 347626321920*tan(b*x + 4*a)^3*tan(1/2*a)^45 + 324785269440*tan(b*x + 4*a)^2*tan(1/2*a)^46 - 112787150040*tan(b*x + 4*a)*tan(1/2*a)^47 + 12602922605*tan(1/2*a)^48 + 100499354940*tan(b*x + 4*a)^4*tan(1/2*a)^42 + 243954351720*tan(b*x + 4*a)^3*tan(1/2*a)^43 - 614500276860*tan(b*x + 4*a)^2*tan(1/2*a)^44 + 342870428760*tan(b*x + 4*a)*tan(1/2*a)^45 - 54544776360*tan(1/2*a)^46 - 720524857050*tan(b*x + 4*a)^4*tan(1/2*a)^40 + 1552622504040*tan(b*x + 4*a)^3*tan(1/2*a)^41 - 592670717680*tan(b*x + 4*a)^2*tan(1/2*a)^42 - 221864573610*tan(b*x + 4*a)*tan(1/2*a)^43 + 98588733975*tan(1/2*a)^44 + 545843494440*tan(b*x + 4*a)^4*tan(1/2*a)^38 - 3402462596640*tan(b*x + 4*a)^3*tan(1/2*a)^39 + 4208031154860*tan(b*x + 4*a)^2*tan(1/2*a)^40 - 1502042255310*tan(b*x + 4*a)*tan(1/2*a)^41 + 99097279550*tan(1/2*a)^42 + 1394520156090*tan(b*x + 4*a)^4*tan(1/2*a)^36 - 1060535913120*tan(b*x + 4*a)^3*tan(1/2*a)^37 - 3399607142880*tan(b*x + 4*a)^2*tan(1/2*a)^38 + 3367956274060*tan(b*x + 4*a)*tan(1/2*a)^39 - 681790695915*tan(1/2*a)^40 - 2195406541260*tan(b*x + 4*a)^4*tan(1/2*a)^34 + 8940274641000*tan(b*x + 4*a)^3*tan(1/2*a)^35 - 8188018122860*tan(b*x + 4*a)^2*tan(1/2*a)^36 + 893802691860*tan(b*x + 4*a)*tan(1/2*a)^37 + 583218519780*tan(1/2*a)^38 - 793687329810*tan(b*x + 4*a)^4*tan(1/2*a)^32 - 4368381430680*tan(b*x + 4*a)^3*tan(1/2*a)^33 + 13505898965040*tan(b*x + 4*a)^2*tan(1/2*a)^34 - 8980226310150*tan(b*x + 4*a)*tan(1/2*a)^35 + 1327591075915*tan(1/2*a)^36 + 3207851661600*tan(b*x + 4*a)^4*tan(1/2*a)^30 - 10136128700160*tan(b*x + 4*a)^3*tan(1/2*a)^31 + 4668559700220*tan(b*x + 4*a)^2*tan(1/2*a)^32 + 4628264277390*tan(b*x + 4*a)*tan(1/2*a)^33 - 2309792723910*tan(1/2*a)^34 - 793687329810*tan(b*x + 4*a)^4*tan(1/2*a)^28 + 10136128700160*tan(b*x + 4*a)^3*tan(1/2*a)^29 - 19695904506240*tan(b*x + 4*a)^2*tan(1/2*a)^30 + 10330657752240*tan(b*x + 4*a)*tan(1/2*a)^31 - 756295285575*tan(1/2*a)^32 - 2195406541260*tan(b*x + 4*a)^4*tan(1/2*a)^26 + 4368381430680*tan(b*x + 4*a)^3*tan(1/2*a)^27 + 4668559700220*tan(b*x + 4*a)^2*tan(1/2*a)^28 - 10330657752240*tan(b*x + 4*a)*tan(1/2*a)^29 + 3368788208080*tan(1/2*a)^30 + 1394520156090*tan(b*x + 4*a)^4*tan(1/2*a)^24 - 8940274641000*tan(b*x + 4*a)^3*tan(1/2*a)^25 + 13505898965040*tan(b*x + 4*a)^2*tan(1/2*a)^26 - 4628264277390*tan(b*x + 4*a)*tan(1/2*a)^27 - 756295285575*tan(1/2*a)^28 + 545843494440*tan(b*x + 4*a)^4*tan(1/2*a)^22 + 1060535913120*tan(b*x + 4*a)^3*tan(1/2*a)^23 - 8188018122860*tan(b*x + 4*a)^2*tan(1/2*a)^24 + 8980226310150*tan(b*x + 4*a)*tan(1/2*a)^25 - 2309792723910*tan(1/2*a)^26 - 720524857050*tan(b*x + 4*a)^4*tan(1/2*a)^20 + 3402462596640*tan(b*x + 4*a)^3*tan(1/2*a)^21 - 3399607142880*tan(b*x + 4*a)^2*tan(1/2*a)^22 - 893802691860*tan(b*x + 4*a)*tan(1/2*a)^23 + 1327591075915*tan(1/2*a)^24 + 100499354940*tan(b*x + 4*a)^4*tan(1/2*a)^18 - 1552622504040*tan(b*x + 4*a)^3*tan(1/2*a)^19 + 4208031154860*tan(b*x + 4*a)^2*tan(1/2*a)^20 - 3367956274060*tan(b*x + 4*a)*tan(1/2*a)^21 + 583218519780*tan(1/2*a)^22 + 107646377490*tan(b*x + 4*a)^4*tan(1/2*a)^16 - 243954351720*tan(b*x + 4*a)^3*tan(1/2*a)^17 - 592670717680*tan(b*x + 4*a)^2*tan(1/2*a)^18 + 1502042255310*tan(b*x + 4*a)*tan(1/2*a)^19 - 681790695915*tan(1/2*a)^20 - 53242909200*tan(b*x + 4*a)^4*tan(1/2*a)^14 + 347626321920*tan(b*x + 4*a)^3*tan(1/2*a)^15 - 614500276860*tan(b*x + 4*a)^2*tan(1/2*a)^16 + 221864573610*tan(b*x + 4*a)*tan(1/2*a)^17 + 99097279550*tan(1/2*a)^18 + 11902135590*tan(b*x + 4*a)^4*tan(1/2*a)^12 - 109725269760*tan(b*x + 4*a)^3*tan(1/2*a)^13 + 324785269440*tan(b*x + 4*a)^2*tan(1/2*a)^14 - 342870428760*tan(b*x + 4*a)*tan(1/2*a)^15 + 98588733975*tan(1/2*a)^16 - 1610662860*tan(b*x + 4*a)^4*tan(1/2*a)^10 + 18613230840*tan(b*x + 4*a)^3*tan(1/2*a)^11 - 73309882260*tan(b*x + 4*a)^2*tan(1/2*a)^12 + 112787150040*tan(b*x + 4*a)*tan(1/2*a)^13 - 54544776360*tan(1/2*a)^14 + 143179650*tan(b*x + 4*a)^4*tan(1/2*a)^8 - 1962664200*tan(b*x + 4*a)^3*tan(1/2*a)^9 + 9508215600*tan(b*x + 4*a)^2*tan(1/2*a)^10 - 18891597150*tan(b*x + 4*a)*tan(1/2*a)^11 + 12602922605*tan(1/2*a)^12 - 8558760*tan(b*x + 4*a)^4*tan(1/2*a)^6 + 133967520*tan(b*x + 4*a)^3*tan(1/2*a)^7 - 761504220*tan(b*x + 4*a)^2*tan(1/2*a)^8 + 1840189110*tan(b*x + 4*a)*tan(1/2*a)^9 - 1563175302*tan(1/2*a)^10 + 337950*tan(b*x + 4*a)^4*tan(1/2*a)^4 - 5856480*tan(b*x + 4*a)^3*tan(1/2*a)^5 + 37650400*tan(b*x + 4*a)^2*tan(1/2*a)^6 - 105669900*tan(b*x + 4*a)*tan(1/2*a)^7 + 108499095*tan(1/2*a)^8 - 8100*tan(b*x + 4*a)^4*tan(1/2*a)^2 + 151800*tan(b*x + 4*a)^3*tan(1/2*a)^3 - 1068900*tan(b*x + 4*a)^2*tan(1/2*a)^4 + 3349740*tan(b*x + 4*a)*tan(1/2*a)^5 - 3921700*tan(1/2*a)^6 + 90*tan(b*x + 4*a)^4 - 1800*tan(b*x + 4*a)^3*tan(1/2*a) + 13200*tan(b*x + 4*a)^2*tan(1/2*a)^2 - 44050*tan(b*x + 4*a)*tan(1/2*a)^3 + 56265*tan(1/2*a)^4 + 20*tan(b*x + 4*a)^2 - 150*tan(b*x + 4*a)*tan(1/2*a) + 270*tan(1/2*a)^2 + 3)/((tan(1/2*a)^30 - 75*tan(1/2*a)^28 + 2325*tan(1/2*a)^26 - 38255*tan(1/2*a)^24 + 356925*tan(1/2*a)^22 - 1880175*tan(1/2*a)^20 + 5430385*tan(1/2*a)^18 - 9069075*tan(1/2*a)^16 + 9069075*tan(1/2*a)^14 - 5430385*tan(1/2*a)^12 + 1880175*tan(1/2*a)^10 - 356925*tan(1/2*a)^8 + 38255*tan(1/2*a)^6 - 2325*tan(1/2*a)^4 + 75*tan(1/2*a)^2 - 1)*(tan(b*x + 4*a)*tan(1/2*a)^6 - 15*tan(b*x + 4*a)*tan(1/2*a)^4 + 6*tan(1/2*a)^5 + 15*tan(b*x + 4*a)*tan(1/2*a)^2 - 20*tan(1/2*a)^3 - tan(b*x + 4*a) + 6*tan(1/2*a))^5))/b","B",0
57,1,6374,0,7.125518," ","integrate(csc(b*x+a)^2*csc(2*b*x+2*a)^5,x, algorithm=""giac"")","\frac{\frac{2592 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{45} - 648 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{46} + 72 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{47} - 3 \, \tan\left(\frac{1}{2} \, a\right)^{48} + 339552 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{43} - 131760 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{44} + 18120 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{45} - 720 \, \tan\left(\frac{1}{2} \, a\right)^{46} + 419904000 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{40} - 289600704 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{41} + 76838472 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{42} - 9139608 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{43} + 409140 \, \tan\left(\frac{1}{2} \, a\right)^{44} - 11197440000 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{38} + 10808414400 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{39} - 3590371872 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{40} + 507604968 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{41} - 26159856 \, \tan\left(\frac{1}{2} \, a\right)^{42} + 133996032000 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{36} - 169676010720 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{37} + 72375177960 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{38} - 12560378760 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{39} + 768063258 \, \tan\left(\frac{1}{2} \, a\right)^{40} - 949294080000 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{34} + 1509418412640 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{35} - 810503332080 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{36} + 174786910200 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{37} - 12927376560 \, \tan\left(\frac{1}{2} \, a\right)^{38} + 4424378112000 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{32} - 8587351903488 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{33} + 5672266009560 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{34} - 1507689425640 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{35} + 136259884900 \, \tan\left(\frac{1}{2} \, a\right)^{36} - 14266506240000 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{30} + 33196837729536 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{31} - 26480349456768 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{32} + 8552959192472 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{33} - 941351504400 \, \tan\left(\frac{1}{2} \, a\right)^{34} + 32626266624000 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{28} - 90047346555840 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{29} + 85630491456048 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{30} - 33168296242992 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{31} + 4402067046579 \, \tan\left(\frac{1}{2} \, a\right)^{32} - 53491430400000 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{26} + 174200110235840 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{27} - 195958049148000 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{28} + 90139253610960 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{29} - 14277938470432 \, \tan\left(\frac{1}{2} \, a\right)^{30} + 63070929280000 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{24} - 242033974687872 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{25} + 320941776763728 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{26} - 174300870723312 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{27} + 32692804970088 \, \tan\left(\frac{1}{2} \, a\right)^{28} - 53491430400000 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{22} + 242033974687872 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{23} - 378128484292800 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{24} + 241898880641040 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{25} - 53487220641120 \, \tan\left(\frac{1}{2} \, a\right)^{26} + 32626266624000 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{20} - 174200110235840 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{21} + 320941776763728 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{22} - 241898880641040 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{23} + 62975177889900 \, \tan\left(\frac{1}{2} \, a\right)^{24} - 14266506240000 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{18} + 90047346555840 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{19} - 195958049148000 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{20} + 174300870723312 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{21} - 53487220641120 \, \tan\left(\frac{1}{2} \, a\right)^{22} + 4424378112000 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{16} - 33196837729536 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{17} + 85630491456048 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{18} - 90139253610960 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{19} + 32692804970088 \, \tan\left(\frac{1}{2} \, a\right)^{20} - 949294080000 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{14} + 8587351903488 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{15} - 26480349456768 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{16} + 33168296242992 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{17} - 14277938470432 \, \tan\left(\frac{1}{2} \, a\right)^{18} + 133996032000 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{12} - 1509418412640 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{13} + 5672266009560 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{14} - 8552959192472 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{15} + 4402067046579 \, \tan\left(\frac{1}{2} \, a\right)^{16} - 11197440000 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{10} + 169676010720 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{11} - 810503332080 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{12} + 1507689425640 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{13} - 941351504400 \, \tan\left(\frac{1}{2} \, a\right)^{14} + 419904000 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{8} - 10808414400 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{9} + 72375177960 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{10} - 174786910200 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{11} + 136259884900 \, \tan\left(\frac{1}{2} \, a\right)^{12} + 289600704 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{7} - 3590371872 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{8} + 12560378760 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{9} - 12927376560 \, \tan\left(\frac{1}{2} \, a\right)^{10} - 339552 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{5} + 76838472 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{6} - 507604968 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{7} + 768063258 \, \tan\left(\frac{1}{2} \, a\right)^{8} - 2592 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{3} - 131760 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{4} + 9139608 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{5} - 26159856 \, \tan\left(\frac{1}{2} \, a\right)^{6} - 648 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} - 18120 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{3} + 409140 \, \tan\left(\frac{1}{2} \, a\right)^{4} - 72 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right) - 720 \, \tan\left(\frac{1}{2} \, a\right)^{2} - 3}{{\left(81 \, \tan\left(\frac{1}{2} \, a\right)^{20} - 1080 \, \tan\left(\frac{1}{2} \, a\right)^{18} + 5724 \, \tan\left(\frac{1}{2} \, a\right)^{16} - 15240 \, \tan\left(\frac{1}{2} \, a\right)^{14} + 21286 \, \tan\left(\frac{1}{2} \, a\right)^{12} - 15240 \, \tan\left(\frac{1}{2} \, a\right)^{10} + 5724 \, \tan\left(\frac{1}{2} \, a\right)^{8} - 1080 \, \tan\left(\frac{1}{2} \, a\right)^{6} + 81 \, \tan\left(\frac{1}{2} \, a\right)^{4}\right)} {\left(6 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{5} - \tan\left(\frac{1}{2} \, a\right)^{6} - 20 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{3} + 15 \, \tan\left(\frac{1}{2} \, a\right)^{4} + 6 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right) - 15 \, \tan\left(\frac{1}{2} \, a\right)^{2} + 1\right)}^{4}} - \frac{16 \, {\left(294 \, \tan\left(b x + 4 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{72} - 52920 \, \tan\left(b x + 4 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{70} + 9864 \, \tan\left(b x + 4 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{71} + 60 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{72} + 4418820 \, \tan\left(b x + 4 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{68} - 1699320 \, \tan\left(b x + 4 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{69} + 133920 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{70} + 1080 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{71} + 15 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{72} - 227030328 \, \tan\left(b x + 4 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{66} + 134207352 \, \tan\left(b x + 4 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{67} - 22587480 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{68} + 963000 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{69} + 7020 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{70} + 108 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{71} + 2 \, \tan\left(\frac{1}{2} \, a\right)^{72} + 8027289270 \, \tan\left(b x + 4 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{64} - 6460519176 \, \tan\left(b x + 4 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{65} + 1686348960 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{66} - 159789240 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{67} + 3912570 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{68} + 20700 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{69} + 180 \, \tan\left(\frac{1}{2} \, a\right)^{70} - 206987901120 \, \tan\left(b x + 4 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{62} + 212284461120 \, \tan\left(b x + 4 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{63} - 75682808100 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{64} + 11222034120 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{65} - 635709780 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{66} + 8559972 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{67} + 23220 \, \tan\left(\frac{1}{2} \, a\right)^{68} + 4024901399904 \, \tan\left(b x + 4 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{60} - 5048602582464 \, \tan\left(b x + 4 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{61} + 2296406448000 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{62} - 466347413440 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{63} + 41675854455 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{64} - 1349403948 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{65} + 7900020 \, \tan\left(\frac{1}{2} \, a\right)^{66} - 60212793009600 \, \tan\left(b x + 4 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{58} + 89880504373440 \, \tan\left(b x + 4 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{59} - 50018473204800 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{60} + 12967578538560 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{61} - 1590087843360 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{62} + 81753694560 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{63} - 1193590350 \, \tan\left(\frac{1}{2} \, a\right)^{64} + 701137434828600 \, \tan\left(b x + 4 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{56} - 1222155524626752 \, \tan\left(b x + 4 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{57} + 809309015383680 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{58} - 256626846135360 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{59} + 40162301142000 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{60} - 2834816578848 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{61} + 66006729504 \, \tan\left(\frac{1}{2} \, a\right)^{62} - 6393695038795680 \, \tan\left(b x + 4 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{54} + 12843489105103968 \, \tan\left(b x + 4 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{55} - 9928727737010640 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{56} + 3743548943593920 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{57} - 715723706535840 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{58} + 64379802333600 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{59} - 2055305635104 \, \tan\left(\frac{1}{2} \, a\right)^{60} + 45773543210194800 \, \tan\left(b x + 4 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{52} - 105001341586308000 \, \tan\left(b x + 4 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{53} + 93508763139878400 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{54} - 41119960482804960 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{55} + 9332822656724940 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{56} - 1023101781887712 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{57} + 41487214960800 \, \tan\left(\frac{1}{2} \, a\right)^{58} - 257401775291824800 \, \tan\left(b x + 4 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{50} + 670176117430046880 \, \tan\left(b x + 4 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{51} - 681255358380496800 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{52} + 344752124474645280 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{53} - 91096096904718960 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{54} + 11822570313904656 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{55} - 581936260957848 \, \tan\left(\frac{1}{2} \, a\right)^{56} + 1137175039130480280 \, \tan\left(b x + 4 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{48} - 3346975359162280800 \, \tan\left(b x + 4 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{49} + 3859521230041977600 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{50} - 2227011325606075680 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{51} + 675970919512787160 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{52} - 101853310806506160 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{53} + 5911352313614320 \, \tan\left(\frac{1}{2} \, a\right)^{54} - 3952573715797761600 \, \tan\left(b x + 4 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{46} + 13113192238126665408 \, \tan\left(b x + 4 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{47} - 17080215895273086480 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{48} + 11166956763854634720 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{49} - 3858112452887270640 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{50} + 666075670217316912 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{51} - 44716273127011152 \, \tan\left(\frac{1}{2} \, a\right)^{52} + 10845567549201117600 \, \tan\left(b x + 4 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{44} - 40458410119612759872 \, \tan\left(b x + 4 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{45} + 59335425213582061440 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{46} - 43761763235235147840 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{47} + 17102501830780473660 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{48} - 3353178363149270160 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{49} + 257119896646635120 \, \tan\left(\frac{1}{2} \, a\right)^{50} - 23606655837981910848 \, \tan\left(b x + 4 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{42} + 98782934174733211200 \, \tan\left(b x + 4 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{43} - 162685440260092255680 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{44} + 134910442121291395520 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{45} - 59381984929519133280 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{46} + 13143687759024316704 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{47} - 1141633895066211960 \, \tan\left(\frac{1}{2} \, a\right)^{48} + 40965300945895635540 \, \tan\left(b x + 4 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{40} - 191862094942696932288 \, \tan\left(b x + 4 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{41} + 353993803428323256960 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{42} - 329207698514963712960 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{43} + 162688248623415050640 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{44} - 40487960376937634400 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{45} + 3961883425271202144 \, \tan\left(\frac{1}{2} \, a\right)^{46} - 56916645144484965840 \, \tan\left(b x + 4 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{38} + 297814271756856799920 \, \tan\left(b x + 4 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{39} - 614369141282401310520 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{40} + 639362819497412266560 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{41} - 353888122537448556000 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{42} + 98742097283990220000 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{43} - 10846128270028623840 \, \tan\left(\frac{1}{2} \, a\right)^{44} + 63490416681595775256 \, \tan\left(b x + 4 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{36} - 370709550220416445008 \, \tan\left(b x + 4 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{37} + 853812888586853302080 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{38} - 992663809176983006640 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{39} + 614257138968343735410 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{40} - 191755286425161694368 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{41} + 23585525195746656480 \, \tan\left(\frac{1}{2} \, a\right)^{42} - 56916645144484965840 \, \tan\left(b x + 4 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{34} + 370709550220416445008 \, \tan\left(b x + 4 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{35} - 952539854421972061200 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{36} + 1235898837202727952720 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{37} - 853875925497859030200 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{38} + 297783419266886959560 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{39} - 40942896085716296868 \, \tan\left(\frac{1}{2} \, a\right)^{40} + 40965300945895635540 \, \tan\left(b x + 4 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{32} - 297814271756856799920 \, \tan\left(b x + 4 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{33} + 853812888586853302080 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{34} - 1235898837202727952720 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{35} + 952725450920718220380 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{36} - 370830295637238771864 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{37} + 56929249131035815800 \, \tan\left(\frac{1}{2} \, a\right)^{38} - 23606655837981910848 \, \tan\left(b x + 4 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{30} + 191862094942696932288 \, \tan\left(b x + 4 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{31} - 614369141282401310520 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{32} + 992663809176983006640 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{33} - 853875925497859030200 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{34} + 370830295637238771864 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{35} - 63527544212529374408 \, \tan\left(\frac{1}{2} \, a\right)^{36} + 10845567549201117600 \, \tan\left(b x + 4 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{28} - 98782934174733211200 \, \tan\left(b x + 4 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{29} + 353993803428323256960 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{30} - 639362819497412266560 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{31} + 614257138968343735410 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{32} - 297783419266886959560 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{33} + 56929249131035815800 \, \tan\left(\frac{1}{2} \, a\right)^{34} - 3952573715797761600 \, \tan\left(b x + 4 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{26} + 40458410119612759872 \, \tan\left(b x + 4 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{27} - 162685440260092255680 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{28} + 329207698514963712960 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{29} - 353888122537448556000 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{30} + 191755286425161694368 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{31} - 40942896085716296868 \, \tan\left(\frac{1}{2} \, a\right)^{32} + 1137175039130480280 \, \tan\left(b x + 4 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{24} - 13113192238126665408 \, \tan\left(b x + 4 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{25} + 59335425213582061440 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{26} - 134910442121291395520 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{27} + 162688248623415050640 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{28} - 98742097283990220000 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{29} + 23585525195746656480 \, \tan\left(\frac{1}{2} \, a\right)^{30} - 257401775291824800 \, \tan\left(b x + 4 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{22} + 3346975359162280800 \, \tan\left(b x + 4 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{23} - 17080215895273086480 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{24} + 43761763235235147840 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{25} - 59381984929519133280 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{26} + 40487960376937634400 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{27} - 10846128270028623840 \, \tan\left(\frac{1}{2} \, a\right)^{28} + 45773543210194800 \, \tan\left(b x + 4 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{20} - 670176117430046880 \, \tan\left(b x + 4 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{21} + 3859521230041977600 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{22} - 11166956763854634720 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{23} + 17102501830780473660 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{24} - 13143687759024316704 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{25} + 3961883425271202144 \, \tan\left(\frac{1}{2} \, a\right)^{26} - 6393695038795680 \, \tan\left(b x + 4 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{18} + 105001341586308000 \, \tan\left(b x + 4 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{19} - 681255358380496800 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{20} + 2227011325606075680 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{21} - 3858112452887270640 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{22} + 3353178363149270160 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{23} - 1141633895066211960 \, \tan\left(\frac{1}{2} \, a\right)^{24} + 701137434828600 \, \tan\left(b x + 4 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{16} - 12843489105103968 \, \tan\left(b x + 4 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{17} + 93508763139878400 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{18} - 344752124474645280 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{19} + 675970919512787160 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{20} - 666075670217316912 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{21} + 257119896646635120 \, \tan\left(\frac{1}{2} \, a\right)^{22} - 60212793009600 \, \tan\left(b x + 4 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{14} + 1222155524626752 \, \tan\left(b x + 4 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{15} - 9928727737010640 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{16} + 41119960482804960 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{17} - 91096096904718960 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{18} + 101853310806506160 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{19} - 44716273127011152 \, \tan\left(\frac{1}{2} \, a\right)^{20} + 4024901399904 \, \tan\left(b x + 4 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{12} - 89880504373440 \, \tan\left(b x + 4 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{13} + 809309015383680 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{14} - 3743548943593920 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{15} + 9332822656724940 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{16} - 11822570313904656 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{17} + 5911352313614320 \, \tan\left(\frac{1}{2} \, a\right)^{18} - 206987901120 \, \tan\left(b x + 4 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{10} + 5048602582464 \, \tan\left(b x + 4 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{11} - 50018473204800 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{12} + 256626846135360 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{13} - 715723706535840 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{14} + 1023101781887712 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{15} - 581936260957848 \, \tan\left(\frac{1}{2} \, a\right)^{16} + 8027289270 \, \tan\left(b x + 4 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{8} - 212284461120 \, \tan\left(b x + 4 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{9} + 2296406448000 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{10} - 12967578538560 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{11} + 40162301142000 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{12} - 64379802333600 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{13} + 41487214960800 \, \tan\left(\frac{1}{2} \, a\right)^{14} - 227030328 \, \tan\left(b x + 4 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{6} + 6460519176 \, \tan\left(b x + 4 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{7} - 75682808100 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{8} + 466347413440 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{9} - 1590087843360 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{10} + 2834816578848 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{11} - 2055305635104 \, \tan\left(\frac{1}{2} \, a\right)^{12} + 4418820 \, \tan\left(b x + 4 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{4} - 134207352 \, \tan\left(b x + 4 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{5} + 1686348960 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{6} - 11222034120 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{7} + 41675854455 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{8} - 81753694560 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{9} + 66006729504 \, \tan\left(\frac{1}{2} \, a\right)^{10} - 52920 \, \tan\left(b x + 4 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{2} + 1699320 \, \tan\left(b x + 4 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{3} - 22587480 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{4} + 159789240 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{5} - 635709780 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{6} + 1349403948 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{7} - 1193590350 \, \tan\left(\frac{1}{2} \, a\right)^{8} + 294 \, \tan\left(b x + 4 \, a\right)^{6} - 9864 \, \tan\left(b x + 4 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right) + 133920 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{2} - 963000 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{3} + 3912570 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{4} - 8559972 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{5} + 7900020 \, \tan\left(\frac{1}{2} \, a\right)^{6} + 60 \, \tan\left(b x + 4 \, a\right)^{4} - 1080 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right) + 7020 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} - 20700 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{3} + 23220 \, \tan\left(\frac{1}{2} \, a\right)^{4} + 15 \, \tan\left(b x + 4 \, a\right)^{2} - 108 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right) + 180 \, \tan\left(\frac{1}{2} \, a\right)^{2} + 2\right)}}{{\left(\tan\left(\frac{1}{2} \, a\right)^{36} - 90 \, \tan\left(\frac{1}{2} \, a\right)^{34} + 3465 \, \tan\left(\frac{1}{2} \, a\right)^{32} - 74256 \, \tan\left(\frac{1}{2} \, a\right)^{30} + 965700 \, \tan\left(\frac{1}{2} \, a\right)^{28} - 7810200 \, \tan\left(\frac{1}{2} \, a\right)^{26} + 39025140 \, \tan\left(\frac{1}{2} \, a\right)^{24} - 119084400 \, \tan\left(\frac{1}{2} \, a\right)^{22} + 228441150 \, \tan\left(\frac{1}{2} \, a\right)^{20} - 282933020 \, \tan\left(\frac{1}{2} \, a\right)^{18} + 228441150 \, \tan\left(\frac{1}{2} \, a\right)^{16} - 119084400 \, \tan\left(\frac{1}{2} \, a\right)^{14} + 39025140 \, \tan\left(\frac{1}{2} \, a\right)^{12} - 7810200 \, \tan\left(\frac{1}{2} \, a\right)^{10} + 965700 \, \tan\left(\frac{1}{2} \, a\right)^{8} - 74256 \, \tan\left(\frac{1}{2} \, a\right)^{6} + 3465 \, \tan\left(\frac{1}{2} \, a\right)^{4} - 90 \, \tan\left(\frac{1}{2} \, a\right)^{2} + 1\right)} {\left(\tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{6} - 15 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{4} + 6 \, \tan\left(\frac{1}{2} \, a\right)^{5} + 15 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{2} - 20 \, \tan\left(\frac{1}{2} \, a\right)^{3} - \tan\left(b x + 4 \, a\right) + 6 \, \tan\left(\frac{1}{2} \, a\right)\right)}^{6}} + 1920 \, \log\left({\left| \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{6} - 15 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{4} + 6 \, \tan\left(\frac{1}{2} \, a\right)^{5} + 15 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{2} - 20 \, \tan\left(\frac{1}{2} \, a\right)^{3} - \tan\left(b x + 4 \, a\right) + 6 \, \tan\left(\frac{1}{2} \, a\right) \right|}\right) - 1920 \, \log\left({\left| 6 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{5} - \tan\left(\frac{1}{2} \, a\right)^{6} - 20 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{3} + 15 \, \tan\left(\frac{1}{2} \, a\right)^{4} + 6 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right) - 15 \, \tan\left(\frac{1}{2} \, a\right)^{2} + 1 \right|}\right)}{6144 \, b}"," ",0,"1/6144*((2592*tan(b*x + 4*a)^3*tan(1/2*a)^45 - 648*tan(b*x + 4*a)^2*tan(1/2*a)^46 + 72*tan(b*x + 4*a)*tan(1/2*a)^47 - 3*tan(1/2*a)^48 + 339552*tan(b*x + 4*a)^3*tan(1/2*a)^43 - 131760*tan(b*x + 4*a)^2*tan(1/2*a)^44 + 18120*tan(b*x + 4*a)*tan(1/2*a)^45 - 720*tan(1/2*a)^46 + 419904000*tan(b*x + 4*a)^4*tan(1/2*a)^40 - 289600704*tan(b*x + 4*a)^3*tan(1/2*a)^41 + 76838472*tan(b*x + 4*a)^2*tan(1/2*a)^42 - 9139608*tan(b*x + 4*a)*tan(1/2*a)^43 + 409140*tan(1/2*a)^44 - 11197440000*tan(b*x + 4*a)^4*tan(1/2*a)^38 + 10808414400*tan(b*x + 4*a)^3*tan(1/2*a)^39 - 3590371872*tan(b*x + 4*a)^2*tan(1/2*a)^40 + 507604968*tan(b*x + 4*a)*tan(1/2*a)^41 - 26159856*tan(1/2*a)^42 + 133996032000*tan(b*x + 4*a)^4*tan(1/2*a)^36 - 169676010720*tan(b*x + 4*a)^3*tan(1/2*a)^37 + 72375177960*tan(b*x + 4*a)^2*tan(1/2*a)^38 - 12560378760*tan(b*x + 4*a)*tan(1/2*a)^39 + 768063258*tan(1/2*a)^40 - 949294080000*tan(b*x + 4*a)^4*tan(1/2*a)^34 + 1509418412640*tan(b*x + 4*a)^3*tan(1/2*a)^35 - 810503332080*tan(b*x + 4*a)^2*tan(1/2*a)^36 + 174786910200*tan(b*x + 4*a)*tan(1/2*a)^37 - 12927376560*tan(1/2*a)^38 + 4424378112000*tan(b*x + 4*a)^4*tan(1/2*a)^32 - 8587351903488*tan(b*x + 4*a)^3*tan(1/2*a)^33 + 5672266009560*tan(b*x + 4*a)^2*tan(1/2*a)^34 - 1507689425640*tan(b*x + 4*a)*tan(1/2*a)^35 + 136259884900*tan(1/2*a)^36 - 14266506240000*tan(b*x + 4*a)^4*tan(1/2*a)^30 + 33196837729536*tan(b*x + 4*a)^3*tan(1/2*a)^31 - 26480349456768*tan(b*x + 4*a)^2*tan(1/2*a)^32 + 8552959192472*tan(b*x + 4*a)*tan(1/2*a)^33 - 941351504400*tan(1/2*a)^34 + 32626266624000*tan(b*x + 4*a)^4*tan(1/2*a)^28 - 90047346555840*tan(b*x + 4*a)^3*tan(1/2*a)^29 + 85630491456048*tan(b*x + 4*a)^2*tan(1/2*a)^30 - 33168296242992*tan(b*x + 4*a)*tan(1/2*a)^31 + 4402067046579*tan(1/2*a)^32 - 53491430400000*tan(b*x + 4*a)^4*tan(1/2*a)^26 + 174200110235840*tan(b*x + 4*a)^3*tan(1/2*a)^27 - 195958049148000*tan(b*x + 4*a)^2*tan(1/2*a)^28 + 90139253610960*tan(b*x + 4*a)*tan(1/2*a)^29 - 14277938470432*tan(1/2*a)^30 + 63070929280000*tan(b*x + 4*a)^4*tan(1/2*a)^24 - 242033974687872*tan(b*x + 4*a)^3*tan(1/2*a)^25 + 320941776763728*tan(b*x + 4*a)^2*tan(1/2*a)^26 - 174300870723312*tan(b*x + 4*a)*tan(1/2*a)^27 + 32692804970088*tan(1/2*a)^28 - 53491430400000*tan(b*x + 4*a)^4*tan(1/2*a)^22 + 242033974687872*tan(b*x + 4*a)^3*tan(1/2*a)^23 - 378128484292800*tan(b*x + 4*a)^2*tan(1/2*a)^24 + 241898880641040*tan(b*x + 4*a)*tan(1/2*a)^25 - 53487220641120*tan(1/2*a)^26 + 32626266624000*tan(b*x + 4*a)^4*tan(1/2*a)^20 - 174200110235840*tan(b*x + 4*a)^3*tan(1/2*a)^21 + 320941776763728*tan(b*x + 4*a)^2*tan(1/2*a)^22 - 241898880641040*tan(b*x + 4*a)*tan(1/2*a)^23 + 62975177889900*tan(1/2*a)^24 - 14266506240000*tan(b*x + 4*a)^4*tan(1/2*a)^18 + 90047346555840*tan(b*x + 4*a)^3*tan(1/2*a)^19 - 195958049148000*tan(b*x + 4*a)^2*tan(1/2*a)^20 + 174300870723312*tan(b*x + 4*a)*tan(1/2*a)^21 - 53487220641120*tan(1/2*a)^22 + 4424378112000*tan(b*x + 4*a)^4*tan(1/2*a)^16 - 33196837729536*tan(b*x + 4*a)^3*tan(1/2*a)^17 + 85630491456048*tan(b*x + 4*a)^2*tan(1/2*a)^18 - 90139253610960*tan(b*x + 4*a)*tan(1/2*a)^19 + 32692804970088*tan(1/2*a)^20 - 949294080000*tan(b*x + 4*a)^4*tan(1/2*a)^14 + 8587351903488*tan(b*x + 4*a)^3*tan(1/2*a)^15 - 26480349456768*tan(b*x + 4*a)^2*tan(1/2*a)^16 + 33168296242992*tan(b*x + 4*a)*tan(1/2*a)^17 - 14277938470432*tan(1/2*a)^18 + 133996032000*tan(b*x + 4*a)^4*tan(1/2*a)^12 - 1509418412640*tan(b*x + 4*a)^3*tan(1/2*a)^13 + 5672266009560*tan(b*x + 4*a)^2*tan(1/2*a)^14 - 8552959192472*tan(b*x + 4*a)*tan(1/2*a)^15 + 4402067046579*tan(1/2*a)^16 - 11197440000*tan(b*x + 4*a)^4*tan(1/2*a)^10 + 169676010720*tan(b*x + 4*a)^3*tan(1/2*a)^11 - 810503332080*tan(b*x + 4*a)^2*tan(1/2*a)^12 + 1507689425640*tan(b*x + 4*a)*tan(1/2*a)^13 - 941351504400*tan(1/2*a)^14 + 419904000*tan(b*x + 4*a)^4*tan(1/2*a)^8 - 10808414400*tan(b*x + 4*a)^3*tan(1/2*a)^9 + 72375177960*tan(b*x + 4*a)^2*tan(1/2*a)^10 - 174786910200*tan(b*x + 4*a)*tan(1/2*a)^11 + 136259884900*tan(1/2*a)^12 + 289600704*tan(b*x + 4*a)^3*tan(1/2*a)^7 - 3590371872*tan(b*x + 4*a)^2*tan(1/2*a)^8 + 12560378760*tan(b*x + 4*a)*tan(1/2*a)^9 - 12927376560*tan(1/2*a)^10 - 339552*tan(b*x + 4*a)^3*tan(1/2*a)^5 + 76838472*tan(b*x + 4*a)^2*tan(1/2*a)^6 - 507604968*tan(b*x + 4*a)*tan(1/2*a)^7 + 768063258*tan(1/2*a)^8 - 2592*tan(b*x + 4*a)^3*tan(1/2*a)^3 - 131760*tan(b*x + 4*a)^2*tan(1/2*a)^4 + 9139608*tan(b*x + 4*a)*tan(1/2*a)^5 - 26159856*tan(1/2*a)^6 - 648*tan(b*x + 4*a)^2*tan(1/2*a)^2 - 18120*tan(b*x + 4*a)*tan(1/2*a)^3 + 409140*tan(1/2*a)^4 - 72*tan(b*x + 4*a)*tan(1/2*a) - 720*tan(1/2*a)^2 - 3)/((81*tan(1/2*a)^20 - 1080*tan(1/2*a)^18 + 5724*tan(1/2*a)^16 - 15240*tan(1/2*a)^14 + 21286*tan(1/2*a)^12 - 15240*tan(1/2*a)^10 + 5724*tan(1/2*a)^8 - 1080*tan(1/2*a)^6 + 81*tan(1/2*a)^4)*(6*tan(b*x + 4*a)*tan(1/2*a)^5 - tan(1/2*a)^6 - 20*tan(b*x + 4*a)*tan(1/2*a)^3 + 15*tan(1/2*a)^4 + 6*tan(b*x + 4*a)*tan(1/2*a) - 15*tan(1/2*a)^2 + 1)^4) - 16*(294*tan(b*x + 4*a)^6*tan(1/2*a)^72 - 52920*tan(b*x + 4*a)^6*tan(1/2*a)^70 + 9864*tan(b*x + 4*a)^5*tan(1/2*a)^71 + 60*tan(b*x + 4*a)^4*tan(1/2*a)^72 + 4418820*tan(b*x + 4*a)^6*tan(1/2*a)^68 - 1699320*tan(b*x + 4*a)^5*tan(1/2*a)^69 + 133920*tan(b*x + 4*a)^4*tan(1/2*a)^70 + 1080*tan(b*x + 4*a)^3*tan(1/2*a)^71 + 15*tan(b*x + 4*a)^2*tan(1/2*a)^72 - 227030328*tan(b*x + 4*a)^6*tan(1/2*a)^66 + 134207352*tan(b*x + 4*a)^5*tan(1/2*a)^67 - 22587480*tan(b*x + 4*a)^4*tan(1/2*a)^68 + 963000*tan(b*x + 4*a)^3*tan(1/2*a)^69 + 7020*tan(b*x + 4*a)^2*tan(1/2*a)^70 + 108*tan(b*x + 4*a)*tan(1/2*a)^71 + 2*tan(1/2*a)^72 + 8027289270*tan(b*x + 4*a)^6*tan(1/2*a)^64 - 6460519176*tan(b*x + 4*a)^5*tan(1/2*a)^65 + 1686348960*tan(b*x + 4*a)^4*tan(1/2*a)^66 - 159789240*tan(b*x + 4*a)^3*tan(1/2*a)^67 + 3912570*tan(b*x + 4*a)^2*tan(1/2*a)^68 + 20700*tan(b*x + 4*a)*tan(1/2*a)^69 + 180*tan(1/2*a)^70 - 206987901120*tan(b*x + 4*a)^6*tan(1/2*a)^62 + 212284461120*tan(b*x + 4*a)^5*tan(1/2*a)^63 - 75682808100*tan(b*x + 4*a)^4*tan(1/2*a)^64 + 11222034120*tan(b*x + 4*a)^3*tan(1/2*a)^65 - 635709780*tan(b*x + 4*a)^2*tan(1/2*a)^66 + 8559972*tan(b*x + 4*a)*tan(1/2*a)^67 + 23220*tan(1/2*a)^68 + 4024901399904*tan(b*x + 4*a)^6*tan(1/2*a)^60 - 5048602582464*tan(b*x + 4*a)^5*tan(1/2*a)^61 + 2296406448000*tan(b*x + 4*a)^4*tan(1/2*a)^62 - 466347413440*tan(b*x + 4*a)^3*tan(1/2*a)^63 + 41675854455*tan(b*x + 4*a)^2*tan(1/2*a)^64 - 1349403948*tan(b*x + 4*a)*tan(1/2*a)^65 + 7900020*tan(1/2*a)^66 - 60212793009600*tan(b*x + 4*a)^6*tan(1/2*a)^58 + 89880504373440*tan(b*x + 4*a)^5*tan(1/2*a)^59 - 50018473204800*tan(b*x + 4*a)^4*tan(1/2*a)^60 + 12967578538560*tan(b*x + 4*a)^3*tan(1/2*a)^61 - 1590087843360*tan(b*x + 4*a)^2*tan(1/2*a)^62 + 81753694560*tan(b*x + 4*a)*tan(1/2*a)^63 - 1193590350*tan(1/2*a)^64 + 701137434828600*tan(b*x + 4*a)^6*tan(1/2*a)^56 - 1222155524626752*tan(b*x + 4*a)^5*tan(1/2*a)^57 + 809309015383680*tan(b*x + 4*a)^4*tan(1/2*a)^58 - 256626846135360*tan(b*x + 4*a)^3*tan(1/2*a)^59 + 40162301142000*tan(b*x + 4*a)^2*tan(1/2*a)^60 - 2834816578848*tan(b*x + 4*a)*tan(1/2*a)^61 + 66006729504*tan(1/2*a)^62 - 6393695038795680*tan(b*x + 4*a)^6*tan(1/2*a)^54 + 12843489105103968*tan(b*x + 4*a)^5*tan(1/2*a)^55 - 9928727737010640*tan(b*x + 4*a)^4*tan(1/2*a)^56 + 3743548943593920*tan(b*x + 4*a)^3*tan(1/2*a)^57 - 715723706535840*tan(b*x + 4*a)^2*tan(1/2*a)^58 + 64379802333600*tan(b*x + 4*a)*tan(1/2*a)^59 - 2055305635104*tan(1/2*a)^60 + 45773543210194800*tan(b*x + 4*a)^6*tan(1/2*a)^52 - 105001341586308000*tan(b*x + 4*a)^5*tan(1/2*a)^53 + 93508763139878400*tan(b*x + 4*a)^4*tan(1/2*a)^54 - 41119960482804960*tan(b*x + 4*a)^3*tan(1/2*a)^55 + 9332822656724940*tan(b*x + 4*a)^2*tan(1/2*a)^56 - 1023101781887712*tan(b*x + 4*a)*tan(1/2*a)^57 + 41487214960800*tan(1/2*a)^58 - 257401775291824800*tan(b*x + 4*a)^6*tan(1/2*a)^50 + 670176117430046880*tan(b*x + 4*a)^5*tan(1/2*a)^51 - 681255358380496800*tan(b*x + 4*a)^4*tan(1/2*a)^52 + 344752124474645280*tan(b*x + 4*a)^3*tan(1/2*a)^53 - 91096096904718960*tan(b*x + 4*a)^2*tan(1/2*a)^54 + 11822570313904656*tan(b*x + 4*a)*tan(1/2*a)^55 - 581936260957848*tan(1/2*a)^56 + 1137175039130480280*tan(b*x + 4*a)^6*tan(1/2*a)^48 - 3346975359162280800*tan(b*x + 4*a)^5*tan(1/2*a)^49 + 3859521230041977600*tan(b*x + 4*a)^4*tan(1/2*a)^50 - 2227011325606075680*tan(b*x + 4*a)^3*tan(1/2*a)^51 + 675970919512787160*tan(b*x + 4*a)^2*tan(1/2*a)^52 - 101853310806506160*tan(b*x + 4*a)*tan(1/2*a)^53 + 5911352313614320*tan(1/2*a)^54 - 3952573715797761600*tan(b*x + 4*a)^6*tan(1/2*a)^46 + 13113192238126665408*tan(b*x + 4*a)^5*tan(1/2*a)^47 - 17080215895273086480*tan(b*x + 4*a)^4*tan(1/2*a)^48 + 11166956763854634720*tan(b*x + 4*a)^3*tan(1/2*a)^49 - 3858112452887270640*tan(b*x + 4*a)^2*tan(1/2*a)^50 + 666075670217316912*tan(b*x + 4*a)*tan(1/2*a)^51 - 44716273127011152*tan(1/2*a)^52 + 10845567549201117600*tan(b*x + 4*a)^6*tan(1/2*a)^44 - 40458410119612759872*tan(b*x + 4*a)^5*tan(1/2*a)^45 + 59335425213582061440*tan(b*x + 4*a)^4*tan(1/2*a)^46 - 43761763235235147840*tan(b*x + 4*a)^3*tan(1/2*a)^47 + 17102501830780473660*tan(b*x + 4*a)^2*tan(1/2*a)^48 - 3353178363149270160*tan(b*x + 4*a)*tan(1/2*a)^49 + 257119896646635120*tan(1/2*a)^50 - 23606655837981910848*tan(b*x + 4*a)^6*tan(1/2*a)^42 + 98782934174733211200*tan(b*x + 4*a)^5*tan(1/2*a)^43 - 162685440260092255680*tan(b*x + 4*a)^4*tan(1/2*a)^44 + 134910442121291395520*tan(b*x + 4*a)^3*tan(1/2*a)^45 - 59381984929519133280*tan(b*x + 4*a)^2*tan(1/2*a)^46 + 13143687759024316704*tan(b*x + 4*a)*tan(1/2*a)^47 - 1141633895066211960*tan(1/2*a)^48 + 40965300945895635540*tan(b*x + 4*a)^6*tan(1/2*a)^40 - 191862094942696932288*tan(b*x + 4*a)^5*tan(1/2*a)^41 + 353993803428323256960*tan(b*x + 4*a)^4*tan(1/2*a)^42 - 329207698514963712960*tan(b*x + 4*a)^3*tan(1/2*a)^43 + 162688248623415050640*tan(b*x + 4*a)^2*tan(1/2*a)^44 - 40487960376937634400*tan(b*x + 4*a)*tan(1/2*a)^45 + 3961883425271202144*tan(1/2*a)^46 - 56916645144484965840*tan(b*x + 4*a)^6*tan(1/2*a)^38 + 297814271756856799920*tan(b*x + 4*a)^5*tan(1/2*a)^39 - 614369141282401310520*tan(b*x + 4*a)^4*tan(1/2*a)^40 + 639362819497412266560*tan(b*x + 4*a)^3*tan(1/2*a)^41 - 353888122537448556000*tan(b*x + 4*a)^2*tan(1/2*a)^42 + 98742097283990220000*tan(b*x + 4*a)*tan(1/2*a)^43 - 10846128270028623840*tan(1/2*a)^44 + 63490416681595775256*tan(b*x + 4*a)^6*tan(1/2*a)^36 - 370709550220416445008*tan(b*x + 4*a)^5*tan(1/2*a)^37 + 853812888586853302080*tan(b*x + 4*a)^4*tan(1/2*a)^38 - 992663809176983006640*tan(b*x + 4*a)^3*tan(1/2*a)^39 + 614257138968343735410*tan(b*x + 4*a)^2*tan(1/2*a)^40 - 191755286425161694368*tan(b*x + 4*a)*tan(1/2*a)^41 + 23585525195746656480*tan(1/2*a)^42 - 56916645144484965840*tan(b*x + 4*a)^6*tan(1/2*a)^34 + 370709550220416445008*tan(b*x + 4*a)^5*tan(1/2*a)^35 - 952539854421972061200*tan(b*x + 4*a)^4*tan(1/2*a)^36 + 1235898837202727952720*tan(b*x + 4*a)^3*tan(1/2*a)^37 - 853875925497859030200*tan(b*x + 4*a)^2*tan(1/2*a)^38 + 297783419266886959560*tan(b*x + 4*a)*tan(1/2*a)^39 - 40942896085716296868*tan(1/2*a)^40 + 40965300945895635540*tan(b*x + 4*a)^6*tan(1/2*a)^32 - 297814271756856799920*tan(b*x + 4*a)^5*tan(1/2*a)^33 + 853812888586853302080*tan(b*x + 4*a)^4*tan(1/2*a)^34 - 1235898837202727952720*tan(b*x + 4*a)^3*tan(1/2*a)^35 + 952725450920718220380*tan(b*x + 4*a)^2*tan(1/2*a)^36 - 370830295637238771864*tan(b*x + 4*a)*tan(1/2*a)^37 + 56929249131035815800*tan(1/2*a)^38 - 23606655837981910848*tan(b*x + 4*a)^6*tan(1/2*a)^30 + 191862094942696932288*tan(b*x + 4*a)^5*tan(1/2*a)^31 - 614369141282401310520*tan(b*x + 4*a)^4*tan(1/2*a)^32 + 992663809176983006640*tan(b*x + 4*a)^3*tan(1/2*a)^33 - 853875925497859030200*tan(b*x + 4*a)^2*tan(1/2*a)^34 + 370830295637238771864*tan(b*x + 4*a)*tan(1/2*a)^35 - 63527544212529374408*tan(1/2*a)^36 + 10845567549201117600*tan(b*x + 4*a)^6*tan(1/2*a)^28 - 98782934174733211200*tan(b*x + 4*a)^5*tan(1/2*a)^29 + 353993803428323256960*tan(b*x + 4*a)^4*tan(1/2*a)^30 - 639362819497412266560*tan(b*x + 4*a)^3*tan(1/2*a)^31 + 614257138968343735410*tan(b*x + 4*a)^2*tan(1/2*a)^32 - 297783419266886959560*tan(b*x + 4*a)*tan(1/2*a)^33 + 56929249131035815800*tan(1/2*a)^34 - 3952573715797761600*tan(b*x + 4*a)^6*tan(1/2*a)^26 + 40458410119612759872*tan(b*x + 4*a)^5*tan(1/2*a)^27 - 162685440260092255680*tan(b*x + 4*a)^4*tan(1/2*a)^28 + 329207698514963712960*tan(b*x + 4*a)^3*tan(1/2*a)^29 - 353888122537448556000*tan(b*x + 4*a)^2*tan(1/2*a)^30 + 191755286425161694368*tan(b*x + 4*a)*tan(1/2*a)^31 - 40942896085716296868*tan(1/2*a)^32 + 1137175039130480280*tan(b*x + 4*a)^6*tan(1/2*a)^24 - 13113192238126665408*tan(b*x + 4*a)^5*tan(1/2*a)^25 + 59335425213582061440*tan(b*x + 4*a)^4*tan(1/2*a)^26 - 134910442121291395520*tan(b*x + 4*a)^3*tan(1/2*a)^27 + 162688248623415050640*tan(b*x + 4*a)^2*tan(1/2*a)^28 - 98742097283990220000*tan(b*x + 4*a)*tan(1/2*a)^29 + 23585525195746656480*tan(1/2*a)^30 - 257401775291824800*tan(b*x + 4*a)^6*tan(1/2*a)^22 + 3346975359162280800*tan(b*x + 4*a)^5*tan(1/2*a)^23 - 17080215895273086480*tan(b*x + 4*a)^4*tan(1/2*a)^24 + 43761763235235147840*tan(b*x + 4*a)^3*tan(1/2*a)^25 - 59381984929519133280*tan(b*x + 4*a)^2*tan(1/2*a)^26 + 40487960376937634400*tan(b*x + 4*a)*tan(1/2*a)^27 - 10846128270028623840*tan(1/2*a)^28 + 45773543210194800*tan(b*x + 4*a)^6*tan(1/2*a)^20 - 670176117430046880*tan(b*x + 4*a)^5*tan(1/2*a)^21 + 3859521230041977600*tan(b*x + 4*a)^4*tan(1/2*a)^22 - 11166956763854634720*tan(b*x + 4*a)^3*tan(1/2*a)^23 + 17102501830780473660*tan(b*x + 4*a)^2*tan(1/2*a)^24 - 13143687759024316704*tan(b*x + 4*a)*tan(1/2*a)^25 + 3961883425271202144*tan(1/2*a)^26 - 6393695038795680*tan(b*x + 4*a)^6*tan(1/2*a)^18 + 105001341586308000*tan(b*x + 4*a)^5*tan(1/2*a)^19 - 681255358380496800*tan(b*x + 4*a)^4*tan(1/2*a)^20 + 2227011325606075680*tan(b*x + 4*a)^3*tan(1/2*a)^21 - 3858112452887270640*tan(b*x + 4*a)^2*tan(1/2*a)^22 + 3353178363149270160*tan(b*x + 4*a)*tan(1/2*a)^23 - 1141633895066211960*tan(1/2*a)^24 + 701137434828600*tan(b*x + 4*a)^6*tan(1/2*a)^16 - 12843489105103968*tan(b*x + 4*a)^5*tan(1/2*a)^17 + 93508763139878400*tan(b*x + 4*a)^4*tan(1/2*a)^18 - 344752124474645280*tan(b*x + 4*a)^3*tan(1/2*a)^19 + 675970919512787160*tan(b*x + 4*a)^2*tan(1/2*a)^20 - 666075670217316912*tan(b*x + 4*a)*tan(1/2*a)^21 + 257119896646635120*tan(1/2*a)^22 - 60212793009600*tan(b*x + 4*a)^6*tan(1/2*a)^14 + 1222155524626752*tan(b*x + 4*a)^5*tan(1/2*a)^15 - 9928727737010640*tan(b*x + 4*a)^4*tan(1/2*a)^16 + 41119960482804960*tan(b*x + 4*a)^3*tan(1/2*a)^17 - 91096096904718960*tan(b*x + 4*a)^2*tan(1/2*a)^18 + 101853310806506160*tan(b*x + 4*a)*tan(1/2*a)^19 - 44716273127011152*tan(1/2*a)^20 + 4024901399904*tan(b*x + 4*a)^6*tan(1/2*a)^12 - 89880504373440*tan(b*x + 4*a)^5*tan(1/2*a)^13 + 809309015383680*tan(b*x + 4*a)^4*tan(1/2*a)^14 - 3743548943593920*tan(b*x + 4*a)^3*tan(1/2*a)^15 + 9332822656724940*tan(b*x + 4*a)^2*tan(1/2*a)^16 - 11822570313904656*tan(b*x + 4*a)*tan(1/2*a)^17 + 5911352313614320*tan(1/2*a)^18 - 206987901120*tan(b*x + 4*a)^6*tan(1/2*a)^10 + 5048602582464*tan(b*x + 4*a)^5*tan(1/2*a)^11 - 50018473204800*tan(b*x + 4*a)^4*tan(1/2*a)^12 + 256626846135360*tan(b*x + 4*a)^3*tan(1/2*a)^13 - 715723706535840*tan(b*x + 4*a)^2*tan(1/2*a)^14 + 1023101781887712*tan(b*x + 4*a)*tan(1/2*a)^15 - 581936260957848*tan(1/2*a)^16 + 8027289270*tan(b*x + 4*a)^6*tan(1/2*a)^8 - 212284461120*tan(b*x + 4*a)^5*tan(1/2*a)^9 + 2296406448000*tan(b*x + 4*a)^4*tan(1/2*a)^10 - 12967578538560*tan(b*x + 4*a)^3*tan(1/2*a)^11 + 40162301142000*tan(b*x + 4*a)^2*tan(1/2*a)^12 - 64379802333600*tan(b*x + 4*a)*tan(1/2*a)^13 + 41487214960800*tan(1/2*a)^14 - 227030328*tan(b*x + 4*a)^6*tan(1/2*a)^6 + 6460519176*tan(b*x + 4*a)^5*tan(1/2*a)^7 - 75682808100*tan(b*x + 4*a)^4*tan(1/2*a)^8 + 466347413440*tan(b*x + 4*a)^3*tan(1/2*a)^9 - 1590087843360*tan(b*x + 4*a)^2*tan(1/2*a)^10 + 2834816578848*tan(b*x + 4*a)*tan(1/2*a)^11 - 2055305635104*tan(1/2*a)^12 + 4418820*tan(b*x + 4*a)^6*tan(1/2*a)^4 - 134207352*tan(b*x + 4*a)^5*tan(1/2*a)^5 + 1686348960*tan(b*x + 4*a)^4*tan(1/2*a)^6 - 11222034120*tan(b*x + 4*a)^3*tan(1/2*a)^7 + 41675854455*tan(b*x + 4*a)^2*tan(1/2*a)^8 - 81753694560*tan(b*x + 4*a)*tan(1/2*a)^9 + 66006729504*tan(1/2*a)^10 - 52920*tan(b*x + 4*a)^6*tan(1/2*a)^2 + 1699320*tan(b*x + 4*a)^5*tan(1/2*a)^3 - 22587480*tan(b*x + 4*a)^4*tan(1/2*a)^4 + 159789240*tan(b*x + 4*a)^3*tan(1/2*a)^5 - 635709780*tan(b*x + 4*a)^2*tan(1/2*a)^6 + 1349403948*tan(b*x + 4*a)*tan(1/2*a)^7 - 1193590350*tan(1/2*a)^8 + 294*tan(b*x + 4*a)^6 - 9864*tan(b*x + 4*a)^5*tan(1/2*a) + 133920*tan(b*x + 4*a)^4*tan(1/2*a)^2 - 963000*tan(b*x + 4*a)^3*tan(1/2*a)^3 + 3912570*tan(b*x + 4*a)^2*tan(1/2*a)^4 - 8559972*tan(b*x + 4*a)*tan(1/2*a)^5 + 7900020*tan(1/2*a)^6 + 60*tan(b*x + 4*a)^4 - 1080*tan(b*x + 4*a)^3*tan(1/2*a) + 7020*tan(b*x + 4*a)^2*tan(1/2*a)^2 - 20700*tan(b*x + 4*a)*tan(1/2*a)^3 + 23220*tan(1/2*a)^4 + 15*tan(b*x + 4*a)^2 - 108*tan(b*x + 4*a)*tan(1/2*a) + 180*tan(1/2*a)^2 + 2)/((tan(1/2*a)^36 - 90*tan(1/2*a)^34 + 3465*tan(1/2*a)^32 - 74256*tan(1/2*a)^30 + 965700*tan(1/2*a)^28 - 7810200*tan(1/2*a)^26 + 39025140*tan(1/2*a)^24 - 119084400*tan(1/2*a)^22 + 228441150*tan(1/2*a)^20 - 282933020*tan(1/2*a)^18 + 228441150*tan(1/2*a)^16 - 119084400*tan(1/2*a)^14 + 39025140*tan(1/2*a)^12 - 7810200*tan(1/2*a)^10 + 965700*tan(1/2*a)^8 - 74256*tan(1/2*a)^6 + 3465*tan(1/2*a)^4 - 90*tan(1/2*a)^2 + 1)*(tan(b*x + 4*a)*tan(1/2*a)^6 - 15*tan(b*x + 4*a)*tan(1/2*a)^4 + 6*tan(1/2*a)^5 + 15*tan(b*x + 4*a)*tan(1/2*a)^2 - 20*tan(1/2*a)^3 - tan(b*x + 4*a) + 6*tan(1/2*a))^6) + 1920*log(abs(tan(b*x + 4*a)*tan(1/2*a)^6 - 15*tan(b*x + 4*a)*tan(1/2*a)^4 + 6*tan(1/2*a)^5 + 15*tan(b*x + 4*a)*tan(1/2*a)^2 - 20*tan(1/2*a)^3 - tan(b*x + 4*a) + 6*tan(1/2*a))) - 1920*log(abs(6*tan(b*x + 4*a)*tan(1/2*a)^5 - tan(1/2*a)^6 - 20*tan(b*x + 4*a)*tan(1/2*a)^3 + 15*tan(1/2*a)^4 + 6*tan(b*x + 4*a)*tan(1/2*a) - 15*tan(1/2*a)^2 + 1)))/b","B",0
58,1,7477,0,12.220706," ","integrate(csc(b*x+a)^2*csc(2*b*x+2*a)^6,x, algorithm=""giac"")","-\frac{\frac{7 \, {\left(6480 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{56} - 2160 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{57} + 360 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{58} - 30 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{59} + \tan\left(\frac{1}{2} \, a\right)^{60} + 963360 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{54} - 451440 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{55} + 84000 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{56} - 6650 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{57} + 210 \, \tan\left(\frac{1}{2} \, a\right)^{58} + 76410000 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{52} - 46604880 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{53} + 11606800 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{54} - 1351380 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{55} + 61875 \, \tan\left(\frac{1}{2} \, a\right)^{56} - 1737755520 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{50} + 1779239600 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{51} - 594557280 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{52} + 84179700 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{53} - 4366140 \, \tan\left(\frac{1}{2} \, a\right)^{54} + 14743616480 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{48} - 21984264480 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{49} + 10388004600 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{50} - 1902997490 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{51} + 120469005 \, \tan\left(\frac{1}{2} \, a\right)^{52} - 61028652480 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{46} + 130174560480 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{47} - 86273730880 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{48} + 21462983130 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{49} - 1737306714 \, \tan\left(\frac{1}{2} \, a\right)^{50} + 103180381920 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{44} - 371517010400 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{45} + 365221080480 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{46} - 127981989480 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{47} + 14001839215 \, \tan\left(\frac{1}{2} \, a\right)^{48} + 111160976000 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{42} + 211586603040 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{43} - 637111944000 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{44} + 376048838120 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{45} - 60608749080 \, \tan\left(\frac{1}{2} \, a\right)^{46} - 724773023760 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{40} + 1597018455600 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{41} - 663483964760 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{42} - 227449079550 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{43} + 109533462525 \, \tan\left(\frac{1}{2} \, a\right)^{44} + 663892404960 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{38} - 3633046154960 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{39} + 4442053139040 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{40} - 1628950998330 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{41} + 110076988450 \, \tan\left(\frac{1}{2} \, a\right)^{42} + 1382243479600 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{36} - 662161010160 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{37} - 3947253799440 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{38} + 3687432890100 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{39} - 757631165865 \, \tan\left(\frac{1}{2} \, a\right)^{40} - 2679939290880 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{34} + 9953265569040 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{35} - 8576804580640 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{36} + 813320615340 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{37} + 647844828540 \, \tan\left(\frac{1}{2} \, a\right)^{38} - 755338211520 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{32} - 5830705497280 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{33} + 15767445241080 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{34} - 9992067869250 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{35} + 1474839074345 \, \tan\left(\frac{1}{2} \, a\right)^{36} + 3975568027520 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{30} - 11953155299520 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{31} + 4861415944320 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{32} + 5463157048330 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{33} - 2566729120410 \, \tan\left(\frac{1}{2} \, a\right)^{34} - 755338211520 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{28} + 11953155299520 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{29} - 23059287629120 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{30} + 11707093056720 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{31} - 840595305645 \, \tan\left(\frac{1}{2} \, a\right)^{32} - 2679939290880 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{26} + 5830705497280 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{27} + 4861415944320 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{28} - 11707093056720 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{29} + 3742852321200 \, \tan\left(\frac{1}{2} \, a\right)^{30} + 1382243479600 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{24} - 9953265569040 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{25} + 15767445241080 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{26} - 5463157048330 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{27} - 840595305645 \, \tan\left(\frac{1}{2} \, a\right)^{28} + 663892404960 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{22} + 662161010160 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{23} - 8576804580640 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{24} + 9992067869250 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{25} - 2566729120410 \, \tan\left(\frac{1}{2} \, a\right)^{26} - 724773023760 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{20} + 3633046154960 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{21} - 3947253799440 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{22} - 813320615340 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{23} + 1474839074345 \, \tan\left(\frac{1}{2} \, a\right)^{24} + 111160976000 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{18} - 1597018455600 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{19} + 4442053139040 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{20} - 3687432890100 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{21} + 647844828540 \, \tan\left(\frac{1}{2} \, a\right)^{22} + 103180381920 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{16} - 211586603040 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{17} - 663483964760 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{18} + 1628950998330 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{19} - 757631165865 \, \tan\left(\frac{1}{2} \, a\right)^{20} - 61028652480 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{14} + 371517010400 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{15} - 637111944000 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{16} + 227449079550 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{17} + 110076988450 \, \tan\left(\frac{1}{2} \, a\right)^{18} + 14743616480 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{12} - 130174560480 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{13} + 365221080480 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{14} - 376048838120 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{15} + 109533462525 \, \tan\left(\frac{1}{2} \, a\right)^{16} - 1737755520 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{10} + 21984264480 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{11} - 86273730880 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{12} + 127981989480 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{13} - 60608749080 \, \tan\left(\frac{1}{2} \, a\right)^{14} + 76410000 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{8} - 1779239600 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{9} + 10388004600 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{10} - 21462983130 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{11} + 14001839215 \, \tan\left(\frac{1}{2} \, a\right)^{12} + 963360 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{6} + 46604880 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{7} - 594557280 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{8} + 1902997490 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{9} - 1737306714 \, \tan\left(\frac{1}{2} \, a\right)^{10} + 6480 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{4} + 451440 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{5} + 11606800 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{6} - 84179700 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{7} + 120469005 \, \tan\left(\frac{1}{2} \, a\right)^{8} + 2160 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{3} + 84000 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{4} + 1351380 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{5} - 4366140 \, \tan\left(\frac{1}{2} \, a\right)^{6} + 360 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} + 6650 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{3} + 61875 \, \tan\left(\frac{1}{2} \, a\right)^{4} + 30 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right) + 210 \, \tan\left(\frac{1}{2} \, a\right)^{2} + 1\right)}}{{\left(243 \, \tan\left(\frac{1}{2} \, a\right)^{25} - 4050 \, \tan\left(\frac{1}{2} \, a\right)^{23} + 28215 \, \tan\left(\frac{1}{2} \, a\right)^{21} - 106200 \, \tan\left(\frac{1}{2} \, a\right)^{19} + 233430 \, \tan\left(\frac{1}{2} \, a\right)^{17} - 304300 \, \tan\left(\frac{1}{2} \, a\right)^{15} + 233430 \, \tan\left(\frac{1}{2} \, a\right)^{13} - 106200 \, \tan\left(\frac{1}{2} \, a\right)^{11} + 28215 \, \tan\left(\frac{1}{2} \, a\right)^{9} - 4050 \, \tan\left(\frac{1}{2} \, a\right)^{7} + 243 \, \tan\left(\frac{1}{2} \, a\right)^{5}\right)} {\left(6 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{5} - \tan\left(\frac{1}{2} \, a\right)^{6} - 20 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{3} + 15 \, \tan\left(\frac{1}{2} \, a\right)^{4} + 6 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right) - 15 \, \tan\left(\frac{1}{2} \, a\right)^{2} + 1\right)}^{5}} + \frac{32 \, {\left(700 \, \tan\left(b x + 4 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{84} - 102900 \, \tan\left(b x + 4 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{82} + 22050 \, \tan\left(b x + 4 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{83} + 175 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{84} + 7200060 \, \tan\left(b x + 4 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{80} - 3103170 \, \tan\left(b x + 4 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{81} + 280770 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{82} + 2940 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{83} + 42 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{84} - 316457680 \, \tan\left(b x + 4 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{78} + 206229240 \, \tan\left(b x + 4 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{79} - 38821965 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{80} + 1904140 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{81} + 17640 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{82} + 294 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{83} + 5 \, \tan\left(\frac{1}{2} \, a\right)^{84} + 9709765800 \, \tan\left(b x + 4 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{76} - 8530152120 \, \tan\left(b x + 4 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{77} + 2449598200 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{78} - 259255080 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{79} + 7360290 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{80} + 47530 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{81} + 462 \, \tan\left(\frac{1}{2} \, a\right)^{82} - 218895118680 \, \tan\left(b x + 4 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{74} + 243907782300 \, \tan\left(b x + 4 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{75} - 94820555130 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{76} + 15442018200 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{77} - 976159968 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{78} + 15463224 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{79} + 47985 \, \tan\left(\frac{1}{2} \, a\right)^{80} + 3722263347880 \, \tan\left(b x + 4 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{72} - 5072116579740 \, \tan\left(b x + 4 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{73} + 2508017550780 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{74} - 555145935120 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{75} + 54416410020 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{76} - 1964255832 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{77} + 13827464 \, \tan\left(\frac{1}{2} \, a\right)^{78} - 48306853319760 \, \tan\left(b x + 4 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{70} + 78691575627000 \, \tan\left(b x + 4 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{71} - 47699227086490 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{72} + 13463793136080 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{73} - 1800097458768 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{74} + 101416919940 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{75} - 1647303294 \, \tan\left(\frac{1}{2} \, a\right)^{76} + 478852179070860 \, \tan\left(b x + 4 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{68} - 920259549793080 \, \tan\left(b x + 4 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{69} + 668627834124600 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{70} - 231870649855320 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{71} + 39617163658212 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{72} - 3053123538948 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{73} + 77871263652 \, \tan\left(\frac{1}{2} \, a\right)^{74} - 3590491658734820 \, \tan\left(b x + 4 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{66} + 8099233169503770 \, \tan\left(b x + 4 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{67} - 6967640085374745 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{68} + 2903918016468840 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{69} - 610729793019360 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{70} + 60236954245272 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{71} - 2105389907166 \, \tan\left(\frac{1}{2} \, a\right)^{72} + 19896259338686220 \, \tan\left(b x + 4 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{64} - 52908136354185210 \, \tan\left(b x + 4 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{65} + 53736728263219610 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{66} - 26624174150101500 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{67} + 6746600775679002 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{68} - 820187477390456 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{69} + 36705931718472 \, \tan\left(\frac{1}{2} \, a\right)^{70} - 77771578076512320 \, \tan\left(b x + 4 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{62} + 248694609613265760 \, \tan\left(b x + 4 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{63} - 300960195956707245 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{64} + 177302439156331860 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{65} - 53651600975241528 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{66} + 7877252164835550 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{67} - 434705306175315 \, \tan\left(\frac{1}{2} \, a\right)^{68} + 192844994494822880 \, \tan\left(b x + 4 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{60} - 787509809051626080 \, \tan\left(b x + 4 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{61} + 1173510851306099040 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{62} - 835950959826956960 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{63} + 303563975744062530 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{64} - 53507434964136174 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{65} + 3573865030470070 \, \tan\left(\frac{1}{2} \, a\right)^{66} - 200273988698142240 \, \tan\left(b x + 4 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{58} + 1398151947986755920 \, \tan\left(b x + 4 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{59} - 2880661846092155160 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{60} + 2628180105420371040 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{61} - 1179839882273931648 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{62} + 252811149558104928 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{63} - 20413710218743023 \, \tan\left(\frac{1}{2} \, a\right)^{64} - 371753255147504160 \, \tan\left(b x + 4 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{56} - 100566683363511120 \, \tan\left(b x + 4 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{57} + 2954417021031525840 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{58} - 4615789529427552000 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{59} + 2869139270141795952 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{60} - 789182123619651552 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{61} + 79047902485397664 \, \tan\left(\frac{1}{2} \, a\right)^{62} + 1588175918421104320 \, \tan\left(b x + 4 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{54} - 5705288320074446880 \, \tan\left(b x + 4 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{55} + 5543116031154667560 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{56} + 291827962982908800 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{57} - 2907035119602048960 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{58} + 1372067944595797680 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{59} - 190524603741625608 \, \tan\left(\frac{1}{2} \, a\right)^{60} - 1764268417682817480 \, \tan\left(b x + 4 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{52} + 11851507413382482720 \, \tan\left(b x + 4 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{53} - 23636877153497649440 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{54} + 18852555003710349600 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{55} - 5514689294400576528 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{56} - 74535612123099568 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{57} + 190797055644582576 \, \tan\left(\frac{1}{2} \, a\right)^{58} - 1248453345588419880 \, \tan\left(b x + 4 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{50} - 4107878664125019420 \, \tan\left(b x + 4 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{51} + 26521780108972032990 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{52} - 39323126797282860000 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{53} + 23453137263033690240 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{54} - 5608964036362402464 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{55} + 366017355229752504 \, \tan\left(\frac{1}{2} \, a\right)^{56} + 5286270479895116600 \, \tan\left(b x + 4 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{48} - 21060700379637099300 \, \tan\left(b x + 4 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{49} + 18283250157335063460 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{50} + 14094690574782962200 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{51} - 26565501133755260460 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{52} + 11739546935802688800 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{53} - 1551520053876868320 \, \tan\left(\frac{1}{2} \, a\right)^{54} - 4019457841895096160 \, \tan\left(b x + 4 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{46} + 33873365085581604240 \, \tan\left(b x + 4 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{47} - 79355355678133689210 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{48} + 69758331625489475640 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{49} - 17832092647389129648 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{50} - 4344999459760312724 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{51} + 1772974039101333642 \, \tan\left(\frac{1}{2} \, a\right)^{52} - 3363472645057689360 \, \tan\left(b x + 4 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{44} - 4196346243738904080 \, \tan\left(b x + 4 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{45} + 61023004440064909200 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{46} - 113594005549024014000 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{47} + 79397061913802193540 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{48} - 20785250550683362380 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{49} + 1158344161574237820 \, \tan\left(\frac{1}{2} \, a\right)^{50} + 7922839707121600240 \, \tan\left(b x + 4 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{42} - 40062672006803795160 \, \tan\left(b x + 4 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{43} + 50479097014227689220 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{44} + 14711499739562948560 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{45} - 61779677247183389760 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{46} + 34283272085462710800 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{47} - 5294375878659948990 \, \tan\left(\frac{1}{2} \, a\right)^{48} - 3363472645057689360 \, \tan\left(b x + 4 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{40} + 40062672006803795160 \, \tan\left(b x + 4 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{41} - 119703426365609444120 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{42} + 134372289532573058400 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{43} - 50496361003895322600 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{44} - 4643613116469393360 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{45} + 4170913759258711920 \, \tan\left(\frac{1}{2} \, a\right)^{46} - 4019457841895096160 \, \tan\left(b x + 4 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{38} + 4196346243738904080 \, \tan\left(b x + 4 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{39} + 50479097014227689220 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{40} - 134372289532573058400 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{41} + 120599543530513343520 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{42} - 40569490418667454440 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{43} + 3366765108190708140 \, \tan\left(\frac{1}{2} \, a\right)^{44} + 5286270479895116600 \, \tan\left(b x + 4 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{36} - 33873365085581604240 \, \tan\left(b x + 4 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{37} + 61023004440064909200 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{38} - 14711499739562948560 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{39} - 50496361003895322600 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{40} + 40569490418667454440 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{41} - 8102375952750405800 \, \tan\left(\frac{1}{2} \, a\right)^{42} - 1248453345588419880 \, \tan\left(b x + 4 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{34} + 21060700379637099300 \, \tan\left(b x + 4 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{35} - 79355355678133689210 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{36} + 113594005549024014000 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{37} - 61779677247183389760 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{38} + 4643613116469393360 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{39} + 3366765108190708140 \, \tan\left(\frac{1}{2} \, a\right)^{40} - 1764268417682817480 \, \tan\left(b x + 4 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{32} + 4107878664125019420 \, \tan\left(b x + 4 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{33} + 18283250157335063460 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{34} - 69758331625489475640 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{35} + 79397061913802193540 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{36} - 34283272085462710800 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{37} + 4170913759258711920 \, \tan\left(\frac{1}{2} \, a\right)^{38} + 1588175918421104320 \, \tan\left(b x + 4 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{30} - 11851507413382482720 \, \tan\left(b x + 4 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{31} + 26521780108972032990 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{32} - 14094690574782962200 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{33} - 17832092647389129648 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{34} + 20785250550683362380 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{35} - 5294375878659948990 \, \tan\left(\frac{1}{2} \, a\right)^{36} - 371753255147504160 \, \tan\left(b x + 4 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{28} + 5705288320074446880 \, \tan\left(b x + 4 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{29} - 23636877153497649440 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{30} + 39323126797282860000 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{31} - 26565501133755260460 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{32} + 4344999459760312724 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{33} + 1158344161574237820 \, \tan\left(\frac{1}{2} \, a\right)^{34} - 200273988698142240 \, \tan\left(b x + 4 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{26} + 100566683363511120 \, \tan\left(b x + 4 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{27} + 5543116031154667560 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{28} - 18852555003710349600 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{29} + 23453137263033690240 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{30} - 11739546935802688800 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{31} + 1772974039101333642 \, \tan\left(\frac{1}{2} \, a\right)^{32} + 192844994494822880 \, \tan\left(b x + 4 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{24} - 1398151947986755920 \, \tan\left(b x + 4 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{25} + 2954417021031525840 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{26} - 291827962982908800 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{27} - 5514689294400576528 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{28} + 5608964036362402464 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{29} - 1551520053876868320 \, \tan\left(\frac{1}{2} \, a\right)^{30} - 77771578076512320 \, \tan\left(b x + 4 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{22} + 787509809051626080 \, \tan\left(b x + 4 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{23} - 2880661846092155160 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{24} + 4615789529427552000 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{25} - 2907035119602048960 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{26} + 74535612123099568 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{27} + 366017355229752504 \, \tan\left(\frac{1}{2} \, a\right)^{28} + 19896259338686220 \, \tan\left(b x + 4 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{20} - 248694609613265760 \, \tan\left(b x + 4 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{21} + 1173510851306099040 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{22} - 2628180105420371040 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{23} + 2869139270141795952 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{24} - 1372067944595797680 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{25} + 190797055644582576 \, \tan\left(\frac{1}{2} \, a\right)^{26} - 3590491658734820 \, \tan\left(b x + 4 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{18} + 52908136354185210 \, \tan\left(b x + 4 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{19} - 300960195956707245 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{20} + 835950959826956960 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{21} - 1179839882273931648 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{22} + 789182123619651552 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{23} - 190524603741625608 \, \tan\left(\frac{1}{2} \, a\right)^{24} + 478852179070860 \, \tan\left(b x + 4 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{16} - 8099233169503770 \, \tan\left(b x + 4 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{17} + 53736728263219610 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{18} - 177302439156331860 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{19} + 303563975744062530 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{20} - 252811149558104928 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{21} + 79047902485397664 \, \tan\left(\frac{1}{2} \, a\right)^{22} - 48306853319760 \, \tan\left(b x + 4 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{14} + 920259549793080 \, \tan\left(b x + 4 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{15} - 6967640085374745 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{16} + 26624174150101500 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{17} - 53651600975241528 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{18} + 53507434964136174 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{19} - 20413710218743023 \, \tan\left(\frac{1}{2} \, a\right)^{20} + 3722263347880 \, \tan\left(b x + 4 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{12} - 78691575627000 \, \tan\left(b x + 4 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{13} + 668627834124600 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{14} - 2903918016468840 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{15} + 6746600775679002 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{16} - 7877252164835550 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{17} + 3573865030470070 \, \tan\left(\frac{1}{2} \, a\right)^{18} - 218895118680 \, \tan\left(b x + 4 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{10} + 5072116579740 \, \tan\left(b x + 4 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{11} - 47699227086490 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{12} + 231870649855320 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{13} - 610729793019360 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{14} + 820187477390456 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{15} - 434705306175315 \, \tan\left(\frac{1}{2} \, a\right)^{16} + 9709765800 \, \tan\left(b x + 4 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{8} - 243907782300 \, \tan\left(b x + 4 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{9} + 2508017550780 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{10} - 13463793136080 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{11} + 39617163658212 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{12} - 60236954245272 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{13} + 36705931718472 \, \tan\left(\frac{1}{2} \, a\right)^{14} - 316457680 \, \tan\left(b x + 4 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{6} + 8530152120 \, \tan\left(b x + 4 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{7} - 94820555130 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{8} + 555145935120 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{9} - 1800097458768 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{10} + 3053123538948 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{11} - 2105389907166 \, \tan\left(\frac{1}{2} \, a\right)^{12} + 7200060 \, \tan\left(b x + 4 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{4} - 206229240 \, \tan\left(b x + 4 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{5} + 2449598200 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{6} - 15442018200 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{7} + 54416410020 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{8} - 101416919940 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{9} + 77871263652 \, \tan\left(\frac{1}{2} \, a\right)^{10} - 102900 \, \tan\left(b x + 4 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{2} + 3103170 \, \tan\left(b x + 4 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{3} - 38821965 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{4} + 259255080 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{5} - 976159968 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{6} + 1964255832 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{7} - 1647303294 \, \tan\left(\frac{1}{2} \, a\right)^{8} + 700 \, \tan\left(b x + 4 \, a\right)^{6} - 22050 \, \tan\left(b x + 4 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right) + 280770 \, \tan\left(b x + 4 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{2} - 1904140 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{3} + 7360290 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{4} - 15463224 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{5} + 13827464 \, \tan\left(\frac{1}{2} \, a\right)^{6} + 175 \, \tan\left(b x + 4 \, a\right)^{4} - 2940 \, \tan\left(b x + 4 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right) + 17640 \, \tan\left(b x + 4 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} - 47530 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{3} + 47985 \, \tan\left(\frac{1}{2} \, a\right)^{4} + 42 \, \tan\left(b x + 4 \, a\right)^{2} - 294 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right) + 462 \, \tan\left(\frac{1}{2} \, a\right)^{2} + 5\right)}}{{\left(\tan\left(\frac{1}{2} \, a\right)^{42} - 105 \, \tan\left(\frac{1}{2} \, a\right)^{40} + 4830 \, \tan\left(\frac{1}{2} \, a\right)^{38} - 127582 \, \tan\left(\frac{1}{2} \, a\right)^{36} + 2131605 \, \tan\left(\frac{1}{2} \, a\right)^{34} - 23413005 \, \tan\left(\frac{1}{2} \, a\right)^{32} + 170737896 \, \tan\left(\frac{1}{2} \, a\right)^{30} - 822580200 \, \tan\left(\frac{1}{2} \, a\right)^{28} + 2607894450 \, \tan\left(\frac{1}{2} \, a\right)^{26} - 5534841410 \, \tan\left(\frac{1}{2} \, a\right)^{24} + 8018138100 \, \tan\left(\frac{1}{2} \, a\right)^{22} - 8018138100 \, \tan\left(\frac{1}{2} \, a\right)^{20} + 5534841410 \, \tan\left(\frac{1}{2} \, a\right)^{18} - 2607894450 \, \tan\left(\frac{1}{2} \, a\right)^{16} + 822580200 \, \tan\left(\frac{1}{2} \, a\right)^{14} - 170737896 \, \tan\left(\frac{1}{2} \, a\right)^{12} + 23413005 \, \tan\left(\frac{1}{2} \, a\right)^{10} - 2131605 \, \tan\left(\frac{1}{2} \, a\right)^{8} + 127582 \, \tan\left(\frac{1}{2} \, a\right)^{6} - 4830 \, \tan\left(\frac{1}{2} \, a\right)^{4} + 105 \, \tan\left(\frac{1}{2} \, a\right)^{2} - 1\right)} {\left(\tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{6} - 15 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{4} + 6 \, \tan\left(\frac{1}{2} \, a\right)^{5} + 15 \, \tan\left(b x + 4 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{2} - 20 \, \tan\left(\frac{1}{2} \, a\right)^{3} - \tan\left(b x + 4 \, a\right) + 6 \, \tan\left(\frac{1}{2} \, a\right)\right)}^{7}}}{71680 \, b}"," ",0,"-1/71680*(7*(6480*tan(b*x + 4*a)^4*tan(1/2*a)^56 - 2160*tan(b*x + 4*a)^3*tan(1/2*a)^57 + 360*tan(b*x + 4*a)^2*tan(1/2*a)^58 - 30*tan(b*x + 4*a)*tan(1/2*a)^59 + tan(1/2*a)^60 + 963360*tan(b*x + 4*a)^4*tan(1/2*a)^54 - 451440*tan(b*x + 4*a)^3*tan(1/2*a)^55 + 84000*tan(b*x + 4*a)^2*tan(1/2*a)^56 - 6650*tan(b*x + 4*a)*tan(1/2*a)^57 + 210*tan(1/2*a)^58 + 76410000*tan(b*x + 4*a)^4*tan(1/2*a)^52 - 46604880*tan(b*x + 4*a)^3*tan(1/2*a)^53 + 11606800*tan(b*x + 4*a)^2*tan(1/2*a)^54 - 1351380*tan(b*x + 4*a)*tan(1/2*a)^55 + 61875*tan(1/2*a)^56 - 1737755520*tan(b*x + 4*a)^4*tan(1/2*a)^50 + 1779239600*tan(b*x + 4*a)^3*tan(1/2*a)^51 - 594557280*tan(b*x + 4*a)^2*tan(1/2*a)^52 + 84179700*tan(b*x + 4*a)*tan(1/2*a)^53 - 4366140*tan(1/2*a)^54 + 14743616480*tan(b*x + 4*a)^4*tan(1/2*a)^48 - 21984264480*tan(b*x + 4*a)^3*tan(1/2*a)^49 + 10388004600*tan(b*x + 4*a)^2*tan(1/2*a)^50 - 1902997490*tan(b*x + 4*a)*tan(1/2*a)^51 + 120469005*tan(1/2*a)^52 - 61028652480*tan(b*x + 4*a)^4*tan(1/2*a)^46 + 130174560480*tan(b*x + 4*a)^3*tan(1/2*a)^47 - 86273730880*tan(b*x + 4*a)^2*tan(1/2*a)^48 + 21462983130*tan(b*x + 4*a)*tan(1/2*a)^49 - 1737306714*tan(1/2*a)^50 + 103180381920*tan(b*x + 4*a)^4*tan(1/2*a)^44 - 371517010400*tan(b*x + 4*a)^3*tan(1/2*a)^45 + 365221080480*tan(b*x + 4*a)^2*tan(1/2*a)^46 - 127981989480*tan(b*x + 4*a)*tan(1/2*a)^47 + 14001839215*tan(1/2*a)^48 + 111160976000*tan(b*x + 4*a)^4*tan(1/2*a)^42 + 211586603040*tan(b*x + 4*a)^3*tan(1/2*a)^43 - 637111944000*tan(b*x + 4*a)^2*tan(1/2*a)^44 + 376048838120*tan(b*x + 4*a)*tan(1/2*a)^45 - 60608749080*tan(1/2*a)^46 - 724773023760*tan(b*x + 4*a)^4*tan(1/2*a)^40 + 1597018455600*tan(b*x + 4*a)^3*tan(1/2*a)^41 - 663483964760*tan(b*x + 4*a)^2*tan(1/2*a)^42 - 227449079550*tan(b*x + 4*a)*tan(1/2*a)^43 + 109533462525*tan(1/2*a)^44 + 663892404960*tan(b*x + 4*a)^4*tan(1/2*a)^38 - 3633046154960*tan(b*x + 4*a)^3*tan(1/2*a)^39 + 4442053139040*tan(b*x + 4*a)^2*tan(1/2*a)^40 - 1628950998330*tan(b*x + 4*a)*tan(1/2*a)^41 + 110076988450*tan(1/2*a)^42 + 1382243479600*tan(b*x + 4*a)^4*tan(1/2*a)^36 - 662161010160*tan(b*x + 4*a)^3*tan(1/2*a)^37 - 3947253799440*tan(b*x + 4*a)^2*tan(1/2*a)^38 + 3687432890100*tan(b*x + 4*a)*tan(1/2*a)^39 - 757631165865*tan(1/2*a)^40 - 2679939290880*tan(b*x + 4*a)^4*tan(1/2*a)^34 + 9953265569040*tan(b*x + 4*a)^3*tan(1/2*a)^35 - 8576804580640*tan(b*x + 4*a)^2*tan(1/2*a)^36 + 813320615340*tan(b*x + 4*a)*tan(1/2*a)^37 + 647844828540*tan(1/2*a)^38 - 755338211520*tan(b*x + 4*a)^4*tan(1/2*a)^32 - 5830705497280*tan(b*x + 4*a)^3*tan(1/2*a)^33 + 15767445241080*tan(b*x + 4*a)^2*tan(1/2*a)^34 - 9992067869250*tan(b*x + 4*a)*tan(1/2*a)^35 + 1474839074345*tan(1/2*a)^36 + 3975568027520*tan(b*x + 4*a)^4*tan(1/2*a)^30 - 11953155299520*tan(b*x + 4*a)^3*tan(1/2*a)^31 + 4861415944320*tan(b*x + 4*a)^2*tan(1/2*a)^32 + 5463157048330*tan(b*x + 4*a)*tan(1/2*a)^33 - 2566729120410*tan(1/2*a)^34 - 755338211520*tan(b*x + 4*a)^4*tan(1/2*a)^28 + 11953155299520*tan(b*x + 4*a)^3*tan(1/2*a)^29 - 23059287629120*tan(b*x + 4*a)^2*tan(1/2*a)^30 + 11707093056720*tan(b*x + 4*a)*tan(1/2*a)^31 - 840595305645*tan(1/2*a)^32 - 2679939290880*tan(b*x + 4*a)^4*tan(1/2*a)^26 + 5830705497280*tan(b*x + 4*a)^3*tan(1/2*a)^27 + 4861415944320*tan(b*x + 4*a)^2*tan(1/2*a)^28 - 11707093056720*tan(b*x + 4*a)*tan(1/2*a)^29 + 3742852321200*tan(1/2*a)^30 + 1382243479600*tan(b*x + 4*a)^4*tan(1/2*a)^24 - 9953265569040*tan(b*x + 4*a)^3*tan(1/2*a)^25 + 15767445241080*tan(b*x + 4*a)^2*tan(1/2*a)^26 - 5463157048330*tan(b*x + 4*a)*tan(1/2*a)^27 - 840595305645*tan(1/2*a)^28 + 663892404960*tan(b*x + 4*a)^4*tan(1/2*a)^22 + 662161010160*tan(b*x + 4*a)^3*tan(1/2*a)^23 - 8576804580640*tan(b*x + 4*a)^2*tan(1/2*a)^24 + 9992067869250*tan(b*x + 4*a)*tan(1/2*a)^25 - 2566729120410*tan(1/2*a)^26 - 724773023760*tan(b*x + 4*a)^4*tan(1/2*a)^20 + 3633046154960*tan(b*x + 4*a)^3*tan(1/2*a)^21 - 3947253799440*tan(b*x + 4*a)^2*tan(1/2*a)^22 - 813320615340*tan(b*x + 4*a)*tan(1/2*a)^23 + 1474839074345*tan(1/2*a)^24 + 111160976000*tan(b*x + 4*a)^4*tan(1/2*a)^18 - 1597018455600*tan(b*x + 4*a)^3*tan(1/2*a)^19 + 4442053139040*tan(b*x + 4*a)^2*tan(1/2*a)^20 - 3687432890100*tan(b*x + 4*a)*tan(1/2*a)^21 + 647844828540*tan(1/2*a)^22 + 103180381920*tan(b*x + 4*a)^4*tan(1/2*a)^16 - 211586603040*tan(b*x + 4*a)^3*tan(1/2*a)^17 - 663483964760*tan(b*x + 4*a)^2*tan(1/2*a)^18 + 1628950998330*tan(b*x + 4*a)*tan(1/2*a)^19 - 757631165865*tan(1/2*a)^20 - 61028652480*tan(b*x + 4*a)^4*tan(1/2*a)^14 + 371517010400*tan(b*x + 4*a)^3*tan(1/2*a)^15 - 637111944000*tan(b*x + 4*a)^2*tan(1/2*a)^16 + 227449079550*tan(b*x + 4*a)*tan(1/2*a)^17 + 110076988450*tan(1/2*a)^18 + 14743616480*tan(b*x + 4*a)^4*tan(1/2*a)^12 - 130174560480*tan(b*x + 4*a)^3*tan(1/2*a)^13 + 365221080480*tan(b*x + 4*a)^2*tan(1/2*a)^14 - 376048838120*tan(b*x + 4*a)*tan(1/2*a)^15 + 109533462525*tan(1/2*a)^16 - 1737755520*tan(b*x + 4*a)^4*tan(1/2*a)^10 + 21984264480*tan(b*x + 4*a)^3*tan(1/2*a)^11 - 86273730880*tan(b*x + 4*a)^2*tan(1/2*a)^12 + 127981989480*tan(b*x + 4*a)*tan(1/2*a)^13 - 60608749080*tan(1/2*a)^14 + 76410000*tan(b*x + 4*a)^4*tan(1/2*a)^8 - 1779239600*tan(b*x + 4*a)^3*tan(1/2*a)^9 + 10388004600*tan(b*x + 4*a)^2*tan(1/2*a)^10 - 21462983130*tan(b*x + 4*a)*tan(1/2*a)^11 + 14001839215*tan(1/2*a)^12 + 963360*tan(b*x + 4*a)^4*tan(1/2*a)^6 + 46604880*tan(b*x + 4*a)^3*tan(1/2*a)^7 - 594557280*tan(b*x + 4*a)^2*tan(1/2*a)^8 + 1902997490*tan(b*x + 4*a)*tan(1/2*a)^9 - 1737306714*tan(1/2*a)^10 + 6480*tan(b*x + 4*a)^4*tan(1/2*a)^4 + 451440*tan(b*x + 4*a)^3*tan(1/2*a)^5 + 11606800*tan(b*x + 4*a)^2*tan(1/2*a)^6 - 84179700*tan(b*x + 4*a)*tan(1/2*a)^7 + 120469005*tan(1/2*a)^8 + 2160*tan(b*x + 4*a)^3*tan(1/2*a)^3 + 84000*tan(b*x + 4*a)^2*tan(1/2*a)^4 + 1351380*tan(b*x + 4*a)*tan(1/2*a)^5 - 4366140*tan(1/2*a)^6 + 360*tan(b*x + 4*a)^2*tan(1/2*a)^2 + 6650*tan(b*x + 4*a)*tan(1/2*a)^3 + 61875*tan(1/2*a)^4 + 30*tan(b*x + 4*a)*tan(1/2*a) + 210*tan(1/2*a)^2 + 1)/((243*tan(1/2*a)^25 - 4050*tan(1/2*a)^23 + 28215*tan(1/2*a)^21 - 106200*tan(1/2*a)^19 + 233430*tan(1/2*a)^17 - 304300*tan(1/2*a)^15 + 233430*tan(1/2*a)^13 - 106200*tan(1/2*a)^11 + 28215*tan(1/2*a)^9 - 4050*tan(1/2*a)^7 + 243*tan(1/2*a)^5)*(6*tan(b*x + 4*a)*tan(1/2*a)^5 - tan(1/2*a)^6 - 20*tan(b*x + 4*a)*tan(1/2*a)^3 + 15*tan(1/2*a)^4 + 6*tan(b*x + 4*a)*tan(1/2*a) - 15*tan(1/2*a)^2 + 1)^5) + 32*(700*tan(b*x + 4*a)^6*tan(1/2*a)^84 - 102900*tan(b*x + 4*a)^6*tan(1/2*a)^82 + 22050*tan(b*x + 4*a)^5*tan(1/2*a)^83 + 175*tan(b*x + 4*a)^4*tan(1/2*a)^84 + 7200060*tan(b*x + 4*a)^6*tan(1/2*a)^80 - 3103170*tan(b*x + 4*a)^5*tan(1/2*a)^81 + 280770*tan(b*x + 4*a)^4*tan(1/2*a)^82 + 2940*tan(b*x + 4*a)^3*tan(1/2*a)^83 + 42*tan(b*x + 4*a)^2*tan(1/2*a)^84 - 316457680*tan(b*x + 4*a)^6*tan(1/2*a)^78 + 206229240*tan(b*x + 4*a)^5*tan(1/2*a)^79 - 38821965*tan(b*x + 4*a)^4*tan(1/2*a)^80 + 1904140*tan(b*x + 4*a)^3*tan(1/2*a)^81 + 17640*tan(b*x + 4*a)^2*tan(1/2*a)^82 + 294*tan(b*x + 4*a)*tan(1/2*a)^83 + 5*tan(1/2*a)^84 + 9709765800*tan(b*x + 4*a)^6*tan(1/2*a)^76 - 8530152120*tan(b*x + 4*a)^5*tan(1/2*a)^77 + 2449598200*tan(b*x + 4*a)^4*tan(1/2*a)^78 - 259255080*tan(b*x + 4*a)^3*tan(1/2*a)^79 + 7360290*tan(b*x + 4*a)^2*tan(1/2*a)^80 + 47530*tan(b*x + 4*a)*tan(1/2*a)^81 + 462*tan(1/2*a)^82 - 218895118680*tan(b*x + 4*a)^6*tan(1/2*a)^74 + 243907782300*tan(b*x + 4*a)^5*tan(1/2*a)^75 - 94820555130*tan(b*x + 4*a)^4*tan(1/2*a)^76 + 15442018200*tan(b*x + 4*a)^3*tan(1/2*a)^77 - 976159968*tan(b*x + 4*a)^2*tan(1/2*a)^78 + 15463224*tan(b*x + 4*a)*tan(1/2*a)^79 + 47985*tan(1/2*a)^80 + 3722263347880*tan(b*x + 4*a)^6*tan(1/2*a)^72 - 5072116579740*tan(b*x + 4*a)^5*tan(1/2*a)^73 + 2508017550780*tan(b*x + 4*a)^4*tan(1/2*a)^74 - 555145935120*tan(b*x + 4*a)^3*tan(1/2*a)^75 + 54416410020*tan(b*x + 4*a)^2*tan(1/2*a)^76 - 1964255832*tan(b*x + 4*a)*tan(1/2*a)^77 + 13827464*tan(1/2*a)^78 - 48306853319760*tan(b*x + 4*a)^6*tan(1/2*a)^70 + 78691575627000*tan(b*x + 4*a)^5*tan(1/2*a)^71 - 47699227086490*tan(b*x + 4*a)^4*tan(1/2*a)^72 + 13463793136080*tan(b*x + 4*a)^3*tan(1/2*a)^73 - 1800097458768*tan(b*x + 4*a)^2*tan(1/2*a)^74 + 101416919940*tan(b*x + 4*a)*tan(1/2*a)^75 - 1647303294*tan(1/2*a)^76 + 478852179070860*tan(b*x + 4*a)^6*tan(1/2*a)^68 - 920259549793080*tan(b*x + 4*a)^5*tan(1/2*a)^69 + 668627834124600*tan(b*x + 4*a)^4*tan(1/2*a)^70 - 231870649855320*tan(b*x + 4*a)^3*tan(1/2*a)^71 + 39617163658212*tan(b*x + 4*a)^2*tan(1/2*a)^72 - 3053123538948*tan(b*x + 4*a)*tan(1/2*a)^73 + 77871263652*tan(1/2*a)^74 - 3590491658734820*tan(b*x + 4*a)^6*tan(1/2*a)^66 + 8099233169503770*tan(b*x + 4*a)^5*tan(1/2*a)^67 - 6967640085374745*tan(b*x + 4*a)^4*tan(1/2*a)^68 + 2903918016468840*tan(b*x + 4*a)^3*tan(1/2*a)^69 - 610729793019360*tan(b*x + 4*a)^2*tan(1/2*a)^70 + 60236954245272*tan(b*x + 4*a)*tan(1/2*a)^71 - 2105389907166*tan(1/2*a)^72 + 19896259338686220*tan(b*x + 4*a)^6*tan(1/2*a)^64 - 52908136354185210*tan(b*x + 4*a)^5*tan(1/2*a)^65 + 53736728263219610*tan(b*x + 4*a)^4*tan(1/2*a)^66 - 26624174150101500*tan(b*x + 4*a)^3*tan(1/2*a)^67 + 6746600775679002*tan(b*x + 4*a)^2*tan(1/2*a)^68 - 820187477390456*tan(b*x + 4*a)*tan(1/2*a)^69 + 36705931718472*tan(1/2*a)^70 - 77771578076512320*tan(b*x + 4*a)^6*tan(1/2*a)^62 + 248694609613265760*tan(b*x + 4*a)^5*tan(1/2*a)^63 - 300960195956707245*tan(b*x + 4*a)^4*tan(1/2*a)^64 + 177302439156331860*tan(b*x + 4*a)^3*tan(1/2*a)^65 - 53651600975241528*tan(b*x + 4*a)^2*tan(1/2*a)^66 + 7877252164835550*tan(b*x + 4*a)*tan(1/2*a)^67 - 434705306175315*tan(1/2*a)^68 + 192844994494822880*tan(b*x + 4*a)^6*tan(1/2*a)^60 - 787509809051626080*tan(b*x + 4*a)^5*tan(1/2*a)^61 + 1173510851306099040*tan(b*x + 4*a)^4*tan(1/2*a)^62 - 835950959826956960*tan(b*x + 4*a)^3*tan(1/2*a)^63 + 303563975744062530*tan(b*x + 4*a)^2*tan(1/2*a)^64 - 53507434964136174*tan(b*x + 4*a)*tan(1/2*a)^65 + 3573865030470070*tan(1/2*a)^66 - 200273988698142240*tan(b*x + 4*a)^6*tan(1/2*a)^58 + 1398151947986755920*tan(b*x + 4*a)^5*tan(1/2*a)^59 - 2880661846092155160*tan(b*x + 4*a)^4*tan(1/2*a)^60 + 2628180105420371040*tan(b*x + 4*a)^3*tan(1/2*a)^61 - 1179839882273931648*tan(b*x + 4*a)^2*tan(1/2*a)^62 + 252811149558104928*tan(b*x + 4*a)*tan(1/2*a)^63 - 20413710218743023*tan(1/2*a)^64 - 371753255147504160*tan(b*x + 4*a)^6*tan(1/2*a)^56 - 100566683363511120*tan(b*x + 4*a)^5*tan(1/2*a)^57 + 2954417021031525840*tan(b*x + 4*a)^4*tan(1/2*a)^58 - 4615789529427552000*tan(b*x + 4*a)^3*tan(1/2*a)^59 + 2869139270141795952*tan(b*x + 4*a)^2*tan(1/2*a)^60 - 789182123619651552*tan(b*x + 4*a)*tan(1/2*a)^61 + 79047902485397664*tan(1/2*a)^62 + 1588175918421104320*tan(b*x + 4*a)^6*tan(1/2*a)^54 - 5705288320074446880*tan(b*x + 4*a)^5*tan(1/2*a)^55 + 5543116031154667560*tan(b*x + 4*a)^4*tan(1/2*a)^56 + 291827962982908800*tan(b*x + 4*a)^3*tan(1/2*a)^57 - 2907035119602048960*tan(b*x + 4*a)^2*tan(1/2*a)^58 + 1372067944595797680*tan(b*x + 4*a)*tan(1/2*a)^59 - 190524603741625608*tan(1/2*a)^60 - 1764268417682817480*tan(b*x + 4*a)^6*tan(1/2*a)^52 + 11851507413382482720*tan(b*x + 4*a)^5*tan(1/2*a)^53 - 23636877153497649440*tan(b*x + 4*a)^4*tan(1/2*a)^54 + 18852555003710349600*tan(b*x + 4*a)^3*tan(1/2*a)^55 - 5514689294400576528*tan(b*x + 4*a)^2*tan(1/2*a)^56 - 74535612123099568*tan(b*x + 4*a)*tan(1/2*a)^57 + 190797055644582576*tan(1/2*a)^58 - 1248453345588419880*tan(b*x + 4*a)^6*tan(1/2*a)^50 - 4107878664125019420*tan(b*x + 4*a)^5*tan(1/2*a)^51 + 26521780108972032990*tan(b*x + 4*a)^4*tan(1/2*a)^52 - 39323126797282860000*tan(b*x + 4*a)^3*tan(1/2*a)^53 + 23453137263033690240*tan(b*x + 4*a)^2*tan(1/2*a)^54 - 5608964036362402464*tan(b*x + 4*a)*tan(1/2*a)^55 + 366017355229752504*tan(1/2*a)^56 + 5286270479895116600*tan(b*x + 4*a)^6*tan(1/2*a)^48 - 21060700379637099300*tan(b*x + 4*a)^5*tan(1/2*a)^49 + 18283250157335063460*tan(b*x + 4*a)^4*tan(1/2*a)^50 + 14094690574782962200*tan(b*x + 4*a)^3*tan(1/2*a)^51 - 26565501133755260460*tan(b*x + 4*a)^2*tan(1/2*a)^52 + 11739546935802688800*tan(b*x + 4*a)*tan(1/2*a)^53 - 1551520053876868320*tan(1/2*a)^54 - 4019457841895096160*tan(b*x + 4*a)^6*tan(1/2*a)^46 + 33873365085581604240*tan(b*x + 4*a)^5*tan(1/2*a)^47 - 79355355678133689210*tan(b*x + 4*a)^4*tan(1/2*a)^48 + 69758331625489475640*tan(b*x + 4*a)^3*tan(1/2*a)^49 - 17832092647389129648*tan(b*x + 4*a)^2*tan(1/2*a)^50 - 4344999459760312724*tan(b*x + 4*a)*tan(1/2*a)^51 + 1772974039101333642*tan(1/2*a)^52 - 3363472645057689360*tan(b*x + 4*a)^6*tan(1/2*a)^44 - 4196346243738904080*tan(b*x + 4*a)^5*tan(1/2*a)^45 + 61023004440064909200*tan(b*x + 4*a)^4*tan(1/2*a)^46 - 113594005549024014000*tan(b*x + 4*a)^3*tan(1/2*a)^47 + 79397061913802193540*tan(b*x + 4*a)^2*tan(1/2*a)^48 - 20785250550683362380*tan(b*x + 4*a)*tan(1/2*a)^49 + 1158344161574237820*tan(1/2*a)^50 + 7922839707121600240*tan(b*x + 4*a)^6*tan(1/2*a)^42 - 40062672006803795160*tan(b*x + 4*a)^5*tan(1/2*a)^43 + 50479097014227689220*tan(b*x + 4*a)^4*tan(1/2*a)^44 + 14711499739562948560*tan(b*x + 4*a)^3*tan(1/2*a)^45 - 61779677247183389760*tan(b*x + 4*a)^2*tan(1/2*a)^46 + 34283272085462710800*tan(b*x + 4*a)*tan(1/2*a)^47 - 5294375878659948990*tan(1/2*a)^48 - 3363472645057689360*tan(b*x + 4*a)^6*tan(1/2*a)^40 + 40062672006803795160*tan(b*x + 4*a)^5*tan(1/2*a)^41 - 119703426365609444120*tan(b*x + 4*a)^4*tan(1/2*a)^42 + 134372289532573058400*tan(b*x + 4*a)^3*tan(1/2*a)^43 - 50496361003895322600*tan(b*x + 4*a)^2*tan(1/2*a)^44 - 4643613116469393360*tan(b*x + 4*a)*tan(1/2*a)^45 + 4170913759258711920*tan(1/2*a)^46 - 4019457841895096160*tan(b*x + 4*a)^6*tan(1/2*a)^38 + 4196346243738904080*tan(b*x + 4*a)^5*tan(1/2*a)^39 + 50479097014227689220*tan(b*x + 4*a)^4*tan(1/2*a)^40 - 134372289532573058400*tan(b*x + 4*a)^3*tan(1/2*a)^41 + 120599543530513343520*tan(b*x + 4*a)^2*tan(1/2*a)^42 - 40569490418667454440*tan(b*x + 4*a)*tan(1/2*a)^43 + 3366765108190708140*tan(1/2*a)^44 + 5286270479895116600*tan(b*x + 4*a)^6*tan(1/2*a)^36 - 33873365085581604240*tan(b*x + 4*a)^5*tan(1/2*a)^37 + 61023004440064909200*tan(b*x + 4*a)^4*tan(1/2*a)^38 - 14711499739562948560*tan(b*x + 4*a)^3*tan(1/2*a)^39 - 50496361003895322600*tan(b*x + 4*a)^2*tan(1/2*a)^40 + 40569490418667454440*tan(b*x + 4*a)*tan(1/2*a)^41 - 8102375952750405800*tan(1/2*a)^42 - 1248453345588419880*tan(b*x + 4*a)^6*tan(1/2*a)^34 + 21060700379637099300*tan(b*x + 4*a)^5*tan(1/2*a)^35 - 79355355678133689210*tan(b*x + 4*a)^4*tan(1/2*a)^36 + 113594005549024014000*tan(b*x + 4*a)^3*tan(1/2*a)^37 - 61779677247183389760*tan(b*x + 4*a)^2*tan(1/2*a)^38 + 4643613116469393360*tan(b*x + 4*a)*tan(1/2*a)^39 + 3366765108190708140*tan(1/2*a)^40 - 1764268417682817480*tan(b*x + 4*a)^6*tan(1/2*a)^32 + 4107878664125019420*tan(b*x + 4*a)^5*tan(1/2*a)^33 + 18283250157335063460*tan(b*x + 4*a)^4*tan(1/2*a)^34 - 69758331625489475640*tan(b*x + 4*a)^3*tan(1/2*a)^35 + 79397061913802193540*tan(b*x + 4*a)^2*tan(1/2*a)^36 - 34283272085462710800*tan(b*x + 4*a)*tan(1/2*a)^37 + 4170913759258711920*tan(1/2*a)^38 + 1588175918421104320*tan(b*x + 4*a)^6*tan(1/2*a)^30 - 11851507413382482720*tan(b*x + 4*a)^5*tan(1/2*a)^31 + 26521780108972032990*tan(b*x + 4*a)^4*tan(1/2*a)^32 - 14094690574782962200*tan(b*x + 4*a)^3*tan(1/2*a)^33 - 17832092647389129648*tan(b*x + 4*a)^2*tan(1/2*a)^34 + 20785250550683362380*tan(b*x + 4*a)*tan(1/2*a)^35 - 5294375878659948990*tan(1/2*a)^36 - 371753255147504160*tan(b*x + 4*a)^6*tan(1/2*a)^28 + 5705288320074446880*tan(b*x + 4*a)^5*tan(1/2*a)^29 - 23636877153497649440*tan(b*x + 4*a)^4*tan(1/2*a)^30 + 39323126797282860000*tan(b*x + 4*a)^3*tan(1/2*a)^31 - 26565501133755260460*tan(b*x + 4*a)^2*tan(1/2*a)^32 + 4344999459760312724*tan(b*x + 4*a)*tan(1/2*a)^33 + 1158344161574237820*tan(1/2*a)^34 - 200273988698142240*tan(b*x + 4*a)^6*tan(1/2*a)^26 + 100566683363511120*tan(b*x + 4*a)^5*tan(1/2*a)^27 + 5543116031154667560*tan(b*x + 4*a)^4*tan(1/2*a)^28 - 18852555003710349600*tan(b*x + 4*a)^3*tan(1/2*a)^29 + 23453137263033690240*tan(b*x + 4*a)^2*tan(1/2*a)^30 - 11739546935802688800*tan(b*x + 4*a)*tan(1/2*a)^31 + 1772974039101333642*tan(1/2*a)^32 + 192844994494822880*tan(b*x + 4*a)^6*tan(1/2*a)^24 - 1398151947986755920*tan(b*x + 4*a)^5*tan(1/2*a)^25 + 2954417021031525840*tan(b*x + 4*a)^4*tan(1/2*a)^26 - 291827962982908800*tan(b*x + 4*a)^3*tan(1/2*a)^27 - 5514689294400576528*tan(b*x + 4*a)^2*tan(1/2*a)^28 + 5608964036362402464*tan(b*x + 4*a)*tan(1/2*a)^29 - 1551520053876868320*tan(1/2*a)^30 - 77771578076512320*tan(b*x + 4*a)^6*tan(1/2*a)^22 + 787509809051626080*tan(b*x + 4*a)^5*tan(1/2*a)^23 - 2880661846092155160*tan(b*x + 4*a)^4*tan(1/2*a)^24 + 4615789529427552000*tan(b*x + 4*a)^3*tan(1/2*a)^25 - 2907035119602048960*tan(b*x + 4*a)^2*tan(1/2*a)^26 + 74535612123099568*tan(b*x + 4*a)*tan(1/2*a)^27 + 366017355229752504*tan(1/2*a)^28 + 19896259338686220*tan(b*x + 4*a)^6*tan(1/2*a)^20 - 248694609613265760*tan(b*x + 4*a)^5*tan(1/2*a)^21 + 1173510851306099040*tan(b*x + 4*a)^4*tan(1/2*a)^22 - 2628180105420371040*tan(b*x + 4*a)^3*tan(1/2*a)^23 + 2869139270141795952*tan(b*x + 4*a)^2*tan(1/2*a)^24 - 1372067944595797680*tan(b*x + 4*a)*tan(1/2*a)^25 + 190797055644582576*tan(1/2*a)^26 - 3590491658734820*tan(b*x + 4*a)^6*tan(1/2*a)^18 + 52908136354185210*tan(b*x + 4*a)^5*tan(1/2*a)^19 - 300960195956707245*tan(b*x + 4*a)^4*tan(1/2*a)^20 + 835950959826956960*tan(b*x + 4*a)^3*tan(1/2*a)^21 - 1179839882273931648*tan(b*x + 4*a)^2*tan(1/2*a)^22 + 789182123619651552*tan(b*x + 4*a)*tan(1/2*a)^23 - 190524603741625608*tan(1/2*a)^24 + 478852179070860*tan(b*x + 4*a)^6*tan(1/2*a)^16 - 8099233169503770*tan(b*x + 4*a)^5*tan(1/2*a)^17 + 53736728263219610*tan(b*x + 4*a)^4*tan(1/2*a)^18 - 177302439156331860*tan(b*x + 4*a)^3*tan(1/2*a)^19 + 303563975744062530*tan(b*x + 4*a)^2*tan(1/2*a)^20 - 252811149558104928*tan(b*x + 4*a)*tan(1/2*a)^21 + 79047902485397664*tan(1/2*a)^22 - 48306853319760*tan(b*x + 4*a)^6*tan(1/2*a)^14 + 920259549793080*tan(b*x + 4*a)^5*tan(1/2*a)^15 - 6967640085374745*tan(b*x + 4*a)^4*tan(1/2*a)^16 + 26624174150101500*tan(b*x + 4*a)^3*tan(1/2*a)^17 - 53651600975241528*tan(b*x + 4*a)^2*tan(1/2*a)^18 + 53507434964136174*tan(b*x + 4*a)*tan(1/2*a)^19 - 20413710218743023*tan(1/2*a)^20 + 3722263347880*tan(b*x + 4*a)^6*tan(1/2*a)^12 - 78691575627000*tan(b*x + 4*a)^5*tan(1/2*a)^13 + 668627834124600*tan(b*x + 4*a)^4*tan(1/2*a)^14 - 2903918016468840*tan(b*x + 4*a)^3*tan(1/2*a)^15 + 6746600775679002*tan(b*x + 4*a)^2*tan(1/2*a)^16 - 7877252164835550*tan(b*x + 4*a)*tan(1/2*a)^17 + 3573865030470070*tan(1/2*a)^18 - 218895118680*tan(b*x + 4*a)^6*tan(1/2*a)^10 + 5072116579740*tan(b*x + 4*a)^5*tan(1/2*a)^11 - 47699227086490*tan(b*x + 4*a)^4*tan(1/2*a)^12 + 231870649855320*tan(b*x + 4*a)^3*tan(1/2*a)^13 - 610729793019360*tan(b*x + 4*a)^2*tan(1/2*a)^14 + 820187477390456*tan(b*x + 4*a)*tan(1/2*a)^15 - 434705306175315*tan(1/2*a)^16 + 9709765800*tan(b*x + 4*a)^6*tan(1/2*a)^8 - 243907782300*tan(b*x + 4*a)^5*tan(1/2*a)^9 + 2508017550780*tan(b*x + 4*a)^4*tan(1/2*a)^10 - 13463793136080*tan(b*x + 4*a)^3*tan(1/2*a)^11 + 39617163658212*tan(b*x + 4*a)^2*tan(1/2*a)^12 - 60236954245272*tan(b*x + 4*a)*tan(1/2*a)^13 + 36705931718472*tan(1/2*a)^14 - 316457680*tan(b*x + 4*a)^6*tan(1/2*a)^6 + 8530152120*tan(b*x + 4*a)^5*tan(1/2*a)^7 - 94820555130*tan(b*x + 4*a)^4*tan(1/2*a)^8 + 555145935120*tan(b*x + 4*a)^3*tan(1/2*a)^9 - 1800097458768*tan(b*x + 4*a)^2*tan(1/2*a)^10 + 3053123538948*tan(b*x + 4*a)*tan(1/2*a)^11 - 2105389907166*tan(1/2*a)^12 + 7200060*tan(b*x + 4*a)^6*tan(1/2*a)^4 - 206229240*tan(b*x + 4*a)^5*tan(1/2*a)^5 + 2449598200*tan(b*x + 4*a)^4*tan(1/2*a)^6 - 15442018200*tan(b*x + 4*a)^3*tan(1/2*a)^7 + 54416410020*tan(b*x + 4*a)^2*tan(1/2*a)^8 - 101416919940*tan(b*x + 4*a)*tan(1/2*a)^9 + 77871263652*tan(1/2*a)^10 - 102900*tan(b*x + 4*a)^6*tan(1/2*a)^2 + 3103170*tan(b*x + 4*a)^5*tan(1/2*a)^3 - 38821965*tan(b*x + 4*a)^4*tan(1/2*a)^4 + 259255080*tan(b*x + 4*a)^3*tan(1/2*a)^5 - 976159968*tan(b*x + 4*a)^2*tan(1/2*a)^6 + 1964255832*tan(b*x + 4*a)*tan(1/2*a)^7 - 1647303294*tan(1/2*a)^8 + 700*tan(b*x + 4*a)^6 - 22050*tan(b*x + 4*a)^5*tan(1/2*a) + 280770*tan(b*x + 4*a)^4*tan(1/2*a)^2 - 1904140*tan(b*x + 4*a)^3*tan(1/2*a)^3 + 7360290*tan(b*x + 4*a)^2*tan(1/2*a)^4 - 15463224*tan(b*x + 4*a)*tan(1/2*a)^5 + 13827464*tan(1/2*a)^6 + 175*tan(b*x + 4*a)^4 - 2940*tan(b*x + 4*a)^3*tan(1/2*a) + 17640*tan(b*x + 4*a)^2*tan(1/2*a)^2 - 47530*tan(b*x + 4*a)*tan(1/2*a)^3 + 47985*tan(1/2*a)^4 + 42*tan(b*x + 4*a)^2 - 294*tan(b*x + 4*a)*tan(1/2*a) + 462*tan(1/2*a)^2 + 5)/((tan(1/2*a)^42 - 105*tan(1/2*a)^40 + 4830*tan(1/2*a)^38 - 127582*tan(1/2*a)^36 + 2131605*tan(1/2*a)^34 - 23413005*tan(1/2*a)^32 + 170737896*tan(1/2*a)^30 - 822580200*tan(1/2*a)^28 + 2607894450*tan(1/2*a)^26 - 5534841410*tan(1/2*a)^24 + 8018138100*tan(1/2*a)^22 - 8018138100*tan(1/2*a)^20 + 5534841410*tan(1/2*a)^18 - 2607894450*tan(1/2*a)^16 + 822580200*tan(1/2*a)^14 - 170737896*tan(1/2*a)^12 + 23413005*tan(1/2*a)^10 - 2131605*tan(1/2*a)^8 + 127582*tan(1/2*a)^6 - 4830*tan(1/2*a)^4 + 105*tan(1/2*a)^2 - 1)*(tan(b*x + 4*a)*tan(1/2*a)^6 - 15*tan(b*x + 4*a)*tan(1/2*a)^4 + 6*tan(1/2*a)^5 + 15*tan(b*x + 4*a)*tan(1/2*a)^2 - 20*tan(1/2*a)^3 - tan(b*x + 4*a) + 6*tan(1/2*a))^7))/b","B",0
59,1,314,0,3.296916," ","integrate(csc(b*x+a)^3*sin(2*b*x+2*a)^10,x, algorithm=""giac"")","-\frac{32768 \, {\left(\frac{17 \, {\left(\cos\left(b x + a\right) - 1\right)}}{\cos\left(b x + a\right) + 1} - \frac{136 \, {\left(\cos\left(b x + a\right) - 1\right)}^{2}}{{\left(\cos\left(b x + a\right) + 1\right)}^{2}} + \frac{680 \, {\left(\cos\left(b x + a\right) - 1\right)}^{3}}{{\left(\cos\left(b x + a\right) + 1\right)}^{3}} + \frac{9775 \, {\left(\cos\left(b x + a\right) - 1\right)}^{4}}{{\left(\cos\left(b x + a\right) + 1\right)}^{4}} + \frac{71825 \, {\left(\cos\left(b x + a\right) - 1\right)}^{5}}{{\left(\cos\left(b x + a\right) + 1\right)}^{5}} + \frac{221000 \, {\left(\cos\left(b x + a\right) - 1\right)}^{6}}{{\left(\cos\left(b x + a\right) + 1\right)}^{6}} + \frac{486200 \, {\left(\cos\left(b x + a\right) - 1\right)}^{7}}{{\left(\cos\left(b x + a\right) + 1\right)}^{7}} + \frac{668525 \, {\left(\cos\left(b x + a\right) - 1\right)}^{8}}{{\left(\cos\left(b x + a\right) + 1\right)}^{8}} + \frac{692835 \, {\left(\cos\left(b x + a\right) - 1\right)}^{9}}{{\left(\cos\left(b x + a\right) + 1\right)}^{9}} + \frac{466752 \, {\left(\cos\left(b x + a\right) - 1\right)}^{10}}{{\left(\cos\left(b x + a\right) + 1\right)}^{10}} + \frac{233376 \, {\left(\cos\left(b x + a\right) - 1\right)}^{11}}{{\left(\cos\left(b x + a\right) + 1\right)}^{11}} + \frac{65637 \, {\left(\cos\left(b x + a\right) - 1\right)}^{12}}{{\left(\cos\left(b x + a\right) + 1\right)}^{12}} + \frac{12155 \, {\left(\cos\left(b x + a\right) - 1\right)}^{13}}{{\left(\cos\left(b x + a\right) + 1\right)}^{13}} - 1\right)}}{12155 \, b {\left(\frac{\cos\left(b x + a\right) - 1}{\cos\left(b x + a\right) + 1} - 1\right)}^{17}}"," ",0,"-32768/12155*(17*(cos(b*x + a) - 1)/(cos(b*x + a) + 1) - 136*(cos(b*x + a) - 1)^2/(cos(b*x + a) + 1)^2 + 680*(cos(b*x + a) - 1)^3/(cos(b*x + a) + 1)^3 + 9775*(cos(b*x + a) - 1)^4/(cos(b*x + a) + 1)^4 + 71825*(cos(b*x + a) - 1)^5/(cos(b*x + a) + 1)^5 + 221000*(cos(b*x + a) - 1)^6/(cos(b*x + a) + 1)^6 + 486200*(cos(b*x + a) - 1)^7/(cos(b*x + a) + 1)^7 + 668525*(cos(b*x + a) - 1)^8/(cos(b*x + a) + 1)^8 + 692835*(cos(b*x + a) - 1)^9/(cos(b*x + a) + 1)^9 + 466752*(cos(b*x + a) - 1)^10/(cos(b*x + a) + 1)^10 + 233376*(cos(b*x + a) - 1)^11/(cos(b*x + a) + 1)^11 + 65637*(cos(b*x + a) - 1)^12/(cos(b*x + a) + 1)^12 + 12155*(cos(b*x + a) - 1)^13/(cos(b*x + a) + 1)^13 - 1)/(b*((cos(b*x + a) - 1)/(cos(b*x + a) + 1) - 1)^17)","B",0
60,1,56,0,1.931077," ","integrate(csc(b*x+a)^3*sin(2*b*x+2*a)^9,x, algorithm=""giac"")","\frac{512 \, {\left(3003 \, \sin\left(b x + a\right)^{15} - 13860 \, \sin\left(b x + a\right)^{13} + 24570 \, \sin\left(b x + a\right)^{11} - 20020 \, \sin\left(b x + a\right)^{9} + 6435 \, \sin\left(b x + a\right)^{7}\right)}}{45045 \, b}"," ",0,"512/45045*(3003*sin(b*x + a)^15 - 13860*sin(b*x + a)^13 + 24570*sin(b*x + a)^11 - 20020*sin(b*x + a)^9 + 6435*sin(b*x + a)^7)/b","A",0
61,1,248,0,1.343716," ","integrate(csc(b*x+a)^3*sin(2*b*x+2*a)^8,x, algorithm=""giac"")","-\frac{4096 \, {\left(\frac{13 \, {\left(\cos\left(b x + a\right) - 1\right)}}{\cos\left(b x + a\right) + 1} - \frac{78 \, {\left(\cos\left(b x + a\right) - 1\right)}^{2}}{{\left(\cos\left(b x + a\right) + 1\right)}^{2}} - \frac{572 \, {\left(\cos\left(b x + a\right) - 1\right)}^{3}}{{\left(\cos\left(b x + a\right) + 1\right)}^{3}} - \frac{3718 \, {\left(\cos\left(b x + a\right) - 1\right)}^{4}}{{\left(\cos\left(b x + a\right) + 1\right)}^{4}} - \frac{7722 \, {\left(\cos\left(b x + a\right) - 1\right)}^{5}}{{\left(\cos\left(b x + a\right) + 1\right)}^{5}} - \frac{13728 \, {\left(\cos\left(b x + a\right) - 1\right)}^{6}}{{\left(\cos\left(b x + a\right) + 1\right)}^{6}} - \frac{12012 \, {\left(\cos\left(b x + a\right) - 1\right)}^{7}}{{\left(\cos\left(b x + a\right) + 1\right)}^{7}} - \frac{9009 \, {\left(\cos\left(b x + a\right) - 1\right)}^{8}}{{\left(\cos\left(b x + a\right) + 1\right)}^{8}} - \frac{3003 \, {\left(\cos\left(b x + a\right) - 1\right)}^{9}}{{\left(\cos\left(b x + a\right) + 1\right)}^{9}} - \frac{858 \, {\left(\cos\left(b x + a\right) - 1\right)}^{10}}{{\left(\cos\left(b x + a\right) + 1\right)}^{10}} - 1\right)}}{1287 \, b {\left(\frac{\cos\left(b x + a\right) - 1}{\cos\left(b x + a\right) + 1} - 1\right)}^{13}}"," ",0,"-4096/1287*(13*(cos(b*x + a) - 1)/(cos(b*x + a) + 1) - 78*(cos(b*x + a) - 1)^2/(cos(b*x + a) + 1)^2 - 572*(cos(b*x + a) - 1)^3/(cos(b*x + a) + 1)^3 - 3718*(cos(b*x + a) - 1)^4/(cos(b*x + a) + 1)^4 - 7722*(cos(b*x + a) - 1)^5/(cos(b*x + a) + 1)^5 - 13728*(cos(b*x + a) - 1)^6/(cos(b*x + a) + 1)^6 - 12012*(cos(b*x + a) - 1)^7/(cos(b*x + a) + 1)^7 - 9009*(cos(b*x + a) - 1)^8/(cos(b*x + a) + 1)^8 - 3003*(cos(b*x + a) - 1)^9/(cos(b*x + a) + 1)^9 - 858*(cos(b*x + a) - 1)^10/(cos(b*x + a) + 1)^10 - 1)/(b*((cos(b*x + a) - 1)/(cos(b*x + a) + 1) - 1)^13)","B",0
62,1,46,0,1.338507," ","integrate(csc(b*x+a)^3*sin(2*b*x+2*a)^7,x, algorithm=""giac"")","-\frac{128 \, {\left(105 \, \sin\left(b x + a\right)^{11} - 385 \, \sin\left(b x + a\right)^{9} + 495 \, \sin\left(b x + a\right)^{7} - 231 \, \sin\left(b x + a\right)^{5}\right)}}{1155 \, b}"," ",0,"-128/1155*(105*sin(b*x + a)^11 - 385*sin(b*x + a)^9 + 495*sin(b*x + a)^7 - 231*sin(b*x + a)^5)/b","A",0
63,1,182,0,1.443391," ","integrate(csc(b*x+a)^3*sin(2*b*x+2*a)^6,x, algorithm=""giac"")","-\frac{256 \, {\left(\frac{9 \, {\left(\cos\left(b x + a\right) - 1\right)}}{\cos\left(b x + a\right) + 1} + \frac{27 \, {\left(\cos\left(b x + a\right) - 1\right)}^{2}}{{\left(\cos\left(b x + a\right) + 1\right)}^{2}} + \frac{189 \, {\left(\cos\left(b x + a\right) - 1\right)}^{3}}{{\left(\cos\left(b x + a\right) + 1\right)}^{3}} + \frac{189 \, {\left(\cos\left(b x + a\right) - 1\right)}^{4}}{{\left(\cos\left(b x + a\right) + 1\right)}^{4}} + \frac{315 \, {\left(\cos\left(b x + a\right) - 1\right)}^{5}}{{\left(\cos\left(b x + a\right) + 1\right)}^{5}} + \frac{105 \, {\left(\cos\left(b x + a\right) - 1\right)}^{6}}{{\left(\cos\left(b x + a\right) + 1\right)}^{6}} + \frac{63 \, {\left(\cos\left(b x + a\right) - 1\right)}^{7}}{{\left(\cos\left(b x + a\right) + 1\right)}^{7}} - 1\right)}}{63 \, b {\left(\frac{\cos\left(b x + a\right) - 1}{\cos\left(b x + a\right) + 1} - 1\right)}^{9}}"," ",0,"-256/63*(9*(cos(b*x + a) - 1)/(cos(b*x + a) + 1) + 27*(cos(b*x + a) - 1)^2/(cos(b*x + a) + 1)^2 + 189*(cos(b*x + a) - 1)^3/(cos(b*x + a) + 1)^3 + 189*(cos(b*x + a) - 1)^4/(cos(b*x + a) + 1)^4 + 315*(cos(b*x + a) - 1)^5/(cos(b*x + a) + 1)^5 + 105*(cos(b*x + a) - 1)^6/(cos(b*x + a) + 1)^6 + 63*(cos(b*x + a) - 1)^7/(cos(b*x + a) + 1)^7 - 1)/(b*((cos(b*x + a) - 1)/(cos(b*x + a) + 1) - 1)^9)","B",0
64,1,36,0,0.776212," ","integrate(csc(b*x+a)^3*sin(2*b*x+2*a)^5,x, algorithm=""giac"")","\frac{32 \, {\left(15 \, \sin\left(b x + a\right)^{7} - 42 \, \sin\left(b x + a\right)^{5} + 35 \, \sin\left(b x + a\right)^{3}\right)}}{105 \, b}"," ",0,"32/105*(15*sin(b*x + a)^7 - 42*sin(b*x + a)^5 + 35*sin(b*x + a)^3)/b","A",0
65,1,74,0,0.978974," ","integrate(csc(b*x+a)^3*sin(2*b*x+2*a)^4,x, algorithm=""giac"")","\frac{32 \, {\left(\frac{10 \, {\left(\cos\left(b x + a\right) - 1\right)}^{2}}{{\left(\cos\left(b x + a\right) + 1\right)}^{2}} + \frac{5 \, {\left(\cos\left(b x + a\right) - 1\right)}^{4}}{{\left(\cos\left(b x + a\right) + 1\right)}^{4}} + 1\right)}}{5 \, b {\left(\frac{\cos\left(b x + a\right) - 1}{\cos\left(b x + a\right) + 1} - 1\right)}^{5}}"," ",0,"32/5*(10*(cos(b*x + a) - 1)^2/(cos(b*x + a) + 1)^2 + 5*(cos(b*x + a) - 1)^4/(cos(b*x + a) + 1)^4 + 1)/(b*((cos(b*x + a) - 1)/(cos(b*x + a) + 1) - 1)^5)","B",0
66,1,22,0,0.505427," ","integrate(csc(b*x+a)^3*sin(2*b*x+2*a)^3,x, algorithm=""giac"")","-\frac{8 \, {\left(\sin\left(b x + a\right)^{3} - 3 \, \sin\left(b x + a\right)\right)}}{3 \, b}"," ",0,"-8/3*(sin(b*x + a)^3 - 3*sin(b*x + a))/b","A",0
67,1,57,0,0.573680," ","integrate(csc(b*x+a)^3*sin(2*b*x+2*a)^2,x, algorithm=""giac"")","-\frac{2 \, {\left(\frac{4}{\frac{\cos\left(b x + a\right) - 1}{\cos\left(b x + a\right) + 1} - 1} - \log\left(\frac{{\left| -\cos\left(b x + a\right) + 1 \right|}}{{\left| \cos\left(b x + a\right) + 1 \right|}}\right)\right)}}{b}"," ",0,"-2*(4/((cos(b*x + a) - 1)/(cos(b*x + a) + 1) - 1) - log(abs(-cos(b*x + a) + 1)/abs(cos(b*x + a) + 1)))/b","B",0
68,1,13,0,0.347772," ","integrate(csc(b*x+a)^3*sin(2*b*x+2*a),x, algorithm=""giac"")","-\frac{2}{b \sin\left(b x + a\right)}"," ",0,"-2/(b*sin(b*x + a))","A",0
69,1,2096,0,1.074800," ","integrate(csc(b*x+a)^3*csc(2*b*x+2*a),x, algorithm=""giac"")","-\frac{\frac{27 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{34} - 9 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{35} + \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{36} + 630 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{32} - 267 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{33} + 18 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{34} + 9 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{35} - 25458 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{30} + 28818 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{31} - 10053 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{32} + 1077 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{33} + 27 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{34} + 202086 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{28} - 396738 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{29} + 244788 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{30} - 58788 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{31} + 4518 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{32} + 54 \, \tan\left(\frac{1}{2} \, a\right)^{33} - 644166 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{26} + 2016678 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{27} - 1980792 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{28} + 780948 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{29} - 123954 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{30} + 5778 \, \tan\left(\frac{1}{2} \, a\right)^{31} + 616590 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{24} - 4024566 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{25} + 6570108 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{26} - 4036848 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{27} + 993942 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{28} - 80658 \, \tan\left(\frac{1}{2} \, a\right)^{29} + 1290870 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{22} - 545670 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{23} - 6240000 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{24} + 8134776 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{25} - 3273030 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{26} + 402730 \, \tan\left(\frac{1}{2} \, a\right)^{27} - 3012066 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{20} + 12765366 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{21} - 13579740 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{22} + 1241820 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{23} + 3103230 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{24} - 796770 \, \tan\left(\frac{1}{2} \, a\right)^{25} - 10040220 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{19} + 29284146 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{20} - 25575756 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{21} + 6696630 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{22} - 99990 \, \tan\left(\frac{1}{2} \, a\right)^{23} + 3012066 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{16} - 10040220 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{17} + 19709370 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{19} - 14753394 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{20} + 2525334 \, \tan\left(\frac{1}{2} \, a\right)^{21} - 1290870 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{14} + 12765366 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{15} - 29284146 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{16} + 19709370 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{17} - 2087550 \, \tan\left(\frac{1}{2} \, a\right)^{19} - 616590 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{12} - 545670 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{13} + 13579740 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{14} - 25575756 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{15} + 14753394 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{16} - 2087550 \, \tan\left(\frac{1}{2} \, a\right)^{17} + 644166 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{10} - 4024566 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{11} + 6240000 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{12} + 1241820 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{13} - 6696630 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{14} + 2525334 \, \tan\left(\frac{1}{2} \, a\right)^{15} - 202086 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{8} + 2016678 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{9} - 6570108 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{10} + 8134776 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{11} - 3103230 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{12} - 99990 \, \tan\left(\frac{1}{2} \, a\right)^{13} + 25458 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{6} - 396738 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{7} + 1980792 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{8} - 4036848 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{9} + 3273030 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{10} - 796770 \, \tan\left(\frac{1}{2} \, a\right)^{11} - 630 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{4} + 28818 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{5} - 244788 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{6} + 780948 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{7} - 993942 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{8} + 402730 \, \tan\left(\frac{1}{2} \, a\right)^{9} - 27 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{2} - 267 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{3} + 10053 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{4} - 58788 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{5} + 123954 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{6} - 80658 \, \tan\left(\frac{1}{2} \, a\right)^{7} - 9 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right) - 18 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{2} + 1077 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{3} - 4518 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{4} + 5778 \, \tan\left(\frac{1}{2} \, a\right)^{5} - \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} + 9 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right) - 27 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{2} + 54 \, \tan\left(\frac{1}{2} \, a\right)^{3}}{{\left(27 \, \tan\left(\frac{1}{2} \, a\right)^{15} - 270 \, \tan\left(\frac{1}{2} \, a\right)^{13} + 981 \, \tan\left(\frac{1}{2} \, a\right)^{11} - 1540 \, \tan\left(\frac{1}{2} \, a\right)^{9} + 981 \, \tan\left(\frac{1}{2} \, a\right)^{7} - 270 \, \tan\left(\frac{1}{2} \, a\right)^{5} + 27 \, \tan\left(\frac{1}{2} \, a\right)^{3}\right)} {\left(3 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{5} - \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{6} - 10 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{3} + 15 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{4} - 3 \, \tan\left(\frac{1}{2} \, a\right)^{5} + 3 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right) - 15 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{2} + 10 \, \tan\left(\frac{1}{2} \, a\right)^{3} + \tan\left(\frac{1}{2} \, b x + 2 \, a\right) - 3 \, \tan\left(\frac{1}{2} \, a\right)\right)}^{3}} - 24 \, \log\left({\left| \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{3} + 3 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{2} - \tan\left(\frac{1}{2} \, a\right)^{3} - 3 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right) + 3 \, \tan\left(\frac{1}{2} \, a\right)^{2} - \tan\left(\frac{1}{2} \, b x + 2 \, a\right) + 3 \, \tan\left(\frac{1}{2} \, a\right) - 1 \right|}\right) + 24 \, \log\left({\left| \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{3} - 3 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{2} + \tan\left(\frac{1}{2} \, a\right)^{3} - 3 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right) + 3 \, \tan\left(\frac{1}{2} \, a\right)^{2} + \tan\left(\frac{1}{2} \, b x + 2 \, a\right) - 3 \, \tan\left(\frac{1}{2} \, a\right) - 1 \right|}\right)}{48 \, b}"," ",0,"-1/48*((27*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^34 - 9*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^35 + tan(1/2*b*x + 2*a)^3*tan(1/2*a)^36 + 630*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^32 - 267*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^33 + 18*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^34 + 9*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^35 - 25458*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^30 + 28818*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^31 - 10053*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^32 + 1077*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^33 + 27*tan(1/2*b*x + 2*a)*tan(1/2*a)^34 + 202086*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^28 - 396738*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^29 + 244788*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^30 - 58788*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^31 + 4518*tan(1/2*b*x + 2*a)*tan(1/2*a)^32 + 54*tan(1/2*a)^33 - 644166*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^26 + 2016678*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^27 - 1980792*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^28 + 780948*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^29 - 123954*tan(1/2*b*x + 2*a)*tan(1/2*a)^30 + 5778*tan(1/2*a)^31 + 616590*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^24 - 4024566*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^25 + 6570108*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^26 - 4036848*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^27 + 993942*tan(1/2*b*x + 2*a)*tan(1/2*a)^28 - 80658*tan(1/2*a)^29 + 1290870*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^22 - 545670*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^23 - 6240000*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^24 + 8134776*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^25 - 3273030*tan(1/2*b*x + 2*a)*tan(1/2*a)^26 + 402730*tan(1/2*a)^27 - 3012066*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^20 + 12765366*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^21 - 13579740*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^22 + 1241820*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^23 + 3103230*tan(1/2*b*x + 2*a)*tan(1/2*a)^24 - 796770*tan(1/2*a)^25 - 10040220*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^19 + 29284146*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^20 - 25575756*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^21 + 6696630*tan(1/2*b*x + 2*a)*tan(1/2*a)^22 - 99990*tan(1/2*a)^23 + 3012066*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^16 - 10040220*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^17 + 19709370*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^19 - 14753394*tan(1/2*b*x + 2*a)*tan(1/2*a)^20 + 2525334*tan(1/2*a)^21 - 1290870*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^14 + 12765366*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^15 - 29284146*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^16 + 19709370*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^17 - 2087550*tan(1/2*a)^19 - 616590*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^12 - 545670*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^13 + 13579740*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^14 - 25575756*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^15 + 14753394*tan(1/2*b*x + 2*a)*tan(1/2*a)^16 - 2087550*tan(1/2*a)^17 + 644166*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^10 - 4024566*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^11 + 6240000*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^12 + 1241820*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^13 - 6696630*tan(1/2*b*x + 2*a)*tan(1/2*a)^14 + 2525334*tan(1/2*a)^15 - 202086*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^8 + 2016678*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^9 - 6570108*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^10 + 8134776*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^11 - 3103230*tan(1/2*b*x + 2*a)*tan(1/2*a)^12 - 99990*tan(1/2*a)^13 + 25458*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^6 - 396738*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^7 + 1980792*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^8 - 4036848*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^9 + 3273030*tan(1/2*b*x + 2*a)*tan(1/2*a)^10 - 796770*tan(1/2*a)^11 - 630*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^4 + 28818*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^5 - 244788*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^6 + 780948*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^7 - 993942*tan(1/2*b*x + 2*a)*tan(1/2*a)^8 + 402730*tan(1/2*a)^9 - 27*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^2 - 267*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^3 + 10053*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^4 - 58788*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^5 + 123954*tan(1/2*b*x + 2*a)*tan(1/2*a)^6 - 80658*tan(1/2*a)^7 - 9*tan(1/2*b*x + 2*a)^4*tan(1/2*a) - 18*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^2 + 1077*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^3 - 4518*tan(1/2*b*x + 2*a)*tan(1/2*a)^4 + 5778*tan(1/2*a)^5 - tan(1/2*b*x + 2*a)^3 + 9*tan(1/2*b*x + 2*a)^2*tan(1/2*a) - 27*tan(1/2*b*x + 2*a)*tan(1/2*a)^2 + 54*tan(1/2*a)^3)/((27*tan(1/2*a)^15 - 270*tan(1/2*a)^13 + 981*tan(1/2*a)^11 - 1540*tan(1/2*a)^9 + 981*tan(1/2*a)^7 - 270*tan(1/2*a)^5 + 27*tan(1/2*a)^3)*(3*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^5 - tan(1/2*b*x + 2*a)*tan(1/2*a)^6 - 10*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^3 + 15*tan(1/2*b*x + 2*a)*tan(1/2*a)^4 - 3*tan(1/2*a)^5 + 3*tan(1/2*b*x + 2*a)^2*tan(1/2*a) - 15*tan(1/2*b*x + 2*a)*tan(1/2*a)^2 + 10*tan(1/2*a)^3 + tan(1/2*b*x + 2*a) - 3*tan(1/2*a))^3) - 24*log(abs(tan(1/2*b*x + 2*a)*tan(1/2*a)^3 + 3*tan(1/2*b*x + 2*a)*tan(1/2*a)^2 - tan(1/2*a)^3 - 3*tan(1/2*b*x + 2*a)*tan(1/2*a) + 3*tan(1/2*a)^2 - tan(1/2*b*x + 2*a) + 3*tan(1/2*a) - 1)) + 24*log(abs(tan(1/2*b*x + 2*a)*tan(1/2*a)^3 - 3*tan(1/2*b*x + 2*a)*tan(1/2*a)^2 + tan(1/2*a)^3 - 3*tan(1/2*b*x + 2*a)*tan(1/2*a) + 3*tan(1/2*a)^2 + tan(1/2*b*x + 2*a) - 3*tan(1/2*a) - 1)))/b","B",0
70,1,3775,0,4.385639," ","integrate(csc(b*x+a)^3*csc(2*b*x+2*a)^2,x, algorithm=""giac"")","-\frac{\frac{128 \, {\left(6 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{11} - \tan\left(\frac{1}{2} \, a\right)^{12} - 2 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{9} + 12 \, \tan\left(\frac{1}{2} \, a\right)^{10} - 36 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{7} + 27 \, \tan\left(\frac{1}{2} \, a\right)^{8} - 36 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{5} - 2 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{3} - 27 \, \tan\left(\frac{1}{2} \, a\right)^{4} + 6 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right) - 12 \, \tan\left(\frac{1}{2} \, a\right)^{2} + 1\right)}}{{\left(\tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{6} - 15 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{4} + 12 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{5} - \tan\left(\frac{1}{2} \, a\right)^{6} + 15 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} - 40 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{3} + 15 \, \tan\left(\frac{1}{2} \, a\right)^{4} - \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} + 12 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right) - 15 \, \tan\left(\frac{1}{2} \, a\right)^{2} + 1\right)} {\left(\tan\left(\frac{1}{2} \, a\right)^{6} - 15 \, \tan\left(\frac{1}{2} \, a\right)^{4} + 15 \, \tan\left(\frac{1}{2} \, a\right)^{2} - 1\right)}} + \frac{108 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{7} \tan\left(\frac{1}{2} \, a\right)^{45} - 54 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{46} + 12 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{47} - \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{48} + 4428 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{7} \tan\left(\frac{1}{2} \, a\right)^{43} - 2880 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{44} + 536 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{45} + 48 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{46} - 12 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{47} - 153216 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{7} \tan\left(\frac{1}{2} \, a\right)^{41} + 210486 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{42} - 95832 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{43} + 16740 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{44} - 536 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{45} - 54 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{46} + 2486912 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{7} \tan\left(\frac{1}{2} \, a\right)^{39} - 4777344 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{40} + 3337020 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{41} - 1046736 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{42} + 142488 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{43} - 5472 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{44} - 108 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{45} - 20891364 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{7} \tan\left(\frac{1}{2} \, a\right)^{37} + 54465762 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{38} - 52518388 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{39} + 23995332 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{40} - 5409324 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{41} + 546366 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{42} - 16092 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{43} - 162 \, \tan\left(\frac{1}{2} \, a\right)^{44} + 95841468 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{7} \tan\left(\frac{1}{2} \, a\right)^{35} - 336486592 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{36} + 436639944 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{37} - 272279280 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{38} + 87480580 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{39} - 14094720 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{40} + 977472 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{41} - 17280 \, \tan\left(\frac{1}{2} \, a\right)^{42} - 234315648 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{7} \tan\left(\frac{1}{2} \, a\right)^{33} + 1144864350 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{34} - 2010477960 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{35} + 1680996460 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{36} - 729548040 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{37} + 164195226 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{38} - 17453120 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{39} + 642384 \, \tan\left(\frac{1}{2} \, a\right)^{40} + 211641984 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{7} \tan\left(\frac{1}{2} \, a\right)^{31} - 1888388352 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{32} + 4935828252 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{33} - 5726288880 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{34} + 3352125960 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{35} - 1012326432 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{36} + 147189588 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{37} - 7902336 \, \tan\left(\frac{1}{2} \, a\right)^{38} + 314808792 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{7} \tan\left(\frac{1}{2} \, a\right)^{29} + 96589076 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{30} - 4440981672 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{31} + 9447759099 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{32} - 8215340892 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{33} + 3430559358 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{34} - 671389308 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{35} + 48570730 \, \tan\left(\frac{1}{2} \, a\right)^{36} - 939066728 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{7} \tan\left(\frac{1}{2} \, a\right)^{27} + 4808309376 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{28} - 6655212048 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{29} - 466539808 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{30} + 7397865576 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{31} - 5649253632 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{32} + 1635149568 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{33} - 162842112 \, \tan\left(\frac{1}{2} \, a\right)^{34} + 564924672 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{7} \tan\left(\frac{1}{2} \, a\right)^{25} - 6391344852 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{26} + 19663795984 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{27} - 24029264184 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{28} + 11050166160 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{29} + 310355316 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{30} - 1477416960 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{31} + 267141600 \, \tan\left(\frac{1}{2} \, a\right)^{32} + 564924672 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{7} \tan\left(\frac{1}{2} \, a\right)^{23} - 11879791560 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{25} + 31957055712 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{26} - 32793412368 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{27} + 14381865792 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{28} - 2181545880 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{29} - 17553920 \, \tan\left(\frac{1}{2} \, a\right)^{30} - 939066728 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{7} \tan\left(\frac{1}{2} \, a\right)^{21} + 6391344852 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{22} - 11879791560 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{23} + 19856454696 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{25} - 19258200036 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{26} + 6571946504 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{27} - 680794644 \, \tan\left(\frac{1}{2} \, a\right)^{28} + 314808792 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{7} \tan\left(\frac{1}{2} \, a\right)^{19} - 4808309376 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{20} + 19663795984 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{21} - 31957055712 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{22} + 19856454696 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{23} - 4012160256 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{25} + 925883136 \, \tan\left(\frac{1}{2} \, a\right)^{26} + 211641984 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{7} \tan\left(\frac{1}{2} \, a\right)^{17} - 96589076 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{18} - 6655212048 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{19} + 24029264184 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{20} - 32793412368 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{21} + 19258200036 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{22} - 4012160256 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{23} - 234315648 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{7} \tan\left(\frac{1}{2} \, a\right)^{15} + 1888388352 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{16} - 4440981672 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{17} + 466539808 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{18} + 11050166160 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{19} - 14381865792 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{20} + 6571946504 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{21} - 925883136 \, \tan\left(\frac{1}{2} \, a\right)^{22} + 95841468 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{7} \tan\left(\frac{1}{2} \, a\right)^{13} - 1144864350 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{14} + 4935828252 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{15} - 9447759099 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{16} + 7397865576 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{17} - 310355316 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{18} - 2181545880 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{19} + 680794644 \, \tan\left(\frac{1}{2} \, a\right)^{20} - 20891364 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{7} \tan\left(\frac{1}{2} \, a\right)^{11} + 336486592 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{12} - 2010477960 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{13} + 5726288880 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{14} - 8215340892 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{15} + 5649253632 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{16} - 1477416960 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{17} + 17553920 \, \tan\left(\frac{1}{2} \, a\right)^{18} + 2486912 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{7} \tan\left(\frac{1}{2} \, a\right)^{9} - 54465762 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{10} + 436639944 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{11} - 1680996460 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{12} + 3352125960 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{13} - 3430559358 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{14} + 1635149568 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{15} - 267141600 \, \tan\left(\frac{1}{2} \, a\right)^{16} - 153216 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{7} \tan\left(\frac{1}{2} \, a\right)^{7} + 4777344 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{8} - 52518388 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{9} + 272279280 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{10} - 729548040 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{11} + 1012326432 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{12} - 671389308 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{13} + 162842112 \, \tan\left(\frac{1}{2} \, a\right)^{14} + 4428 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{7} \tan\left(\frac{1}{2} \, a\right)^{5} - 210486 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{6} + 3337020 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{7} - 23995332 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{8} + 87480580 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{9} - 164195226 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{10} + 147189588 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{11} - 48570730 \, \tan\left(\frac{1}{2} \, a\right)^{12} + 108 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{7} \tan\left(\frac{1}{2} \, a\right)^{3} + 2880 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{4} - 95832 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{5} + 1046736 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{6} - 5409324 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{7} + 14094720 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{8} - 17453120 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{9} + 7902336 \, \tan\left(\frac{1}{2} \, a\right)^{10} + 54 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{2} + 536 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{3} - 16740 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{4} + 142488 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{5} - 546366 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{6} + 977472 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{7} - 642384 \, \tan\left(\frac{1}{2} \, a\right)^{8} + 12 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right) - 48 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{2} - 536 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{3} + 5472 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{4} - 16092 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{5} + 17280 \, \tan\left(\frac{1}{2} \, a\right)^{6} + \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} - 12 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right) + 54 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} - 108 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{3} + 162 \, \tan\left(\frac{1}{2} \, a\right)^{4}}{{\left(81 \, \tan\left(\frac{1}{2} \, a\right)^{20} - 1080 \, \tan\left(\frac{1}{2} \, a\right)^{18} + 5724 \, \tan\left(\frac{1}{2} \, a\right)^{16} - 15240 \, \tan\left(\frac{1}{2} \, a\right)^{14} + 21286 \, \tan\left(\frac{1}{2} \, a\right)^{12} - 15240 \, \tan\left(\frac{1}{2} \, a\right)^{10} + 5724 \, \tan\left(\frac{1}{2} \, a\right)^{8} - 1080 \, \tan\left(\frac{1}{2} \, a\right)^{6} + 81 \, \tan\left(\frac{1}{2} \, a\right)^{4}\right)} {\left(3 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{5} - \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{6} - 10 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{3} + 15 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{4} - 3 \, \tan\left(\frac{1}{2} \, a\right)^{5} + 3 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right) - 15 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{2} + 10 \, \tan\left(\frac{1}{2} \, a\right)^{3} + \tan\left(\frac{1}{2} \, b x + 2 \, a\right) - 3 \, \tan\left(\frac{1}{2} \, a\right)\right)}^{4}} + 120 \, \log\left({\left| \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{3} - 3 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right) + 3 \, \tan\left(\frac{1}{2} \, a\right)^{2} - 1 \right|}\right) - 120 \, \log\left({\left| 3 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{2} - \tan\left(\frac{1}{2} \, a\right)^{3} - \tan\left(\frac{1}{2} \, b x + 2 \, a\right) + 3 \, \tan\left(\frac{1}{2} \, a\right) \right|}\right)}{256 \, b}"," ",0,"-1/256*(128*(6*tan(1/2*b*x + 2*a)*tan(1/2*a)^11 - tan(1/2*a)^12 - 2*tan(1/2*b*x + 2*a)*tan(1/2*a)^9 + 12*tan(1/2*a)^10 - 36*tan(1/2*b*x + 2*a)*tan(1/2*a)^7 + 27*tan(1/2*a)^8 - 36*tan(1/2*b*x + 2*a)*tan(1/2*a)^5 - 2*tan(1/2*b*x + 2*a)*tan(1/2*a)^3 - 27*tan(1/2*a)^4 + 6*tan(1/2*b*x + 2*a)*tan(1/2*a) - 12*tan(1/2*a)^2 + 1)/((tan(1/2*b*x + 2*a)^2*tan(1/2*a)^6 - 15*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^4 + 12*tan(1/2*b*x + 2*a)*tan(1/2*a)^5 - tan(1/2*a)^6 + 15*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^2 - 40*tan(1/2*b*x + 2*a)*tan(1/2*a)^3 + 15*tan(1/2*a)^4 - tan(1/2*b*x + 2*a)^2 + 12*tan(1/2*b*x + 2*a)*tan(1/2*a) - 15*tan(1/2*a)^2 + 1)*(tan(1/2*a)^6 - 15*tan(1/2*a)^4 + 15*tan(1/2*a)^2 - 1)) + (108*tan(1/2*b*x + 2*a)^7*tan(1/2*a)^45 - 54*tan(1/2*b*x + 2*a)^6*tan(1/2*a)^46 + 12*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^47 - tan(1/2*b*x + 2*a)^4*tan(1/2*a)^48 + 4428*tan(1/2*b*x + 2*a)^7*tan(1/2*a)^43 - 2880*tan(1/2*b*x + 2*a)^6*tan(1/2*a)^44 + 536*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^45 + 48*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^46 - 12*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^47 - 153216*tan(1/2*b*x + 2*a)^7*tan(1/2*a)^41 + 210486*tan(1/2*b*x + 2*a)^6*tan(1/2*a)^42 - 95832*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^43 + 16740*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^44 - 536*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^45 - 54*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^46 + 2486912*tan(1/2*b*x + 2*a)^7*tan(1/2*a)^39 - 4777344*tan(1/2*b*x + 2*a)^6*tan(1/2*a)^40 + 3337020*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^41 - 1046736*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^42 + 142488*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^43 - 5472*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^44 - 108*tan(1/2*b*x + 2*a)*tan(1/2*a)^45 - 20891364*tan(1/2*b*x + 2*a)^7*tan(1/2*a)^37 + 54465762*tan(1/2*b*x + 2*a)^6*tan(1/2*a)^38 - 52518388*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^39 + 23995332*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^40 - 5409324*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^41 + 546366*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^42 - 16092*tan(1/2*b*x + 2*a)*tan(1/2*a)^43 - 162*tan(1/2*a)^44 + 95841468*tan(1/2*b*x + 2*a)^7*tan(1/2*a)^35 - 336486592*tan(1/2*b*x + 2*a)^6*tan(1/2*a)^36 + 436639944*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^37 - 272279280*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^38 + 87480580*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^39 - 14094720*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^40 + 977472*tan(1/2*b*x + 2*a)*tan(1/2*a)^41 - 17280*tan(1/2*a)^42 - 234315648*tan(1/2*b*x + 2*a)^7*tan(1/2*a)^33 + 1144864350*tan(1/2*b*x + 2*a)^6*tan(1/2*a)^34 - 2010477960*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^35 + 1680996460*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^36 - 729548040*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^37 + 164195226*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^38 - 17453120*tan(1/2*b*x + 2*a)*tan(1/2*a)^39 + 642384*tan(1/2*a)^40 + 211641984*tan(1/2*b*x + 2*a)^7*tan(1/2*a)^31 - 1888388352*tan(1/2*b*x + 2*a)^6*tan(1/2*a)^32 + 4935828252*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^33 - 5726288880*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^34 + 3352125960*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^35 - 1012326432*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^36 + 147189588*tan(1/2*b*x + 2*a)*tan(1/2*a)^37 - 7902336*tan(1/2*a)^38 + 314808792*tan(1/2*b*x + 2*a)^7*tan(1/2*a)^29 + 96589076*tan(1/2*b*x + 2*a)^6*tan(1/2*a)^30 - 4440981672*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^31 + 9447759099*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^32 - 8215340892*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^33 + 3430559358*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^34 - 671389308*tan(1/2*b*x + 2*a)*tan(1/2*a)^35 + 48570730*tan(1/2*a)^36 - 939066728*tan(1/2*b*x + 2*a)^7*tan(1/2*a)^27 + 4808309376*tan(1/2*b*x + 2*a)^6*tan(1/2*a)^28 - 6655212048*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^29 - 466539808*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^30 + 7397865576*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^31 - 5649253632*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^32 + 1635149568*tan(1/2*b*x + 2*a)*tan(1/2*a)^33 - 162842112*tan(1/2*a)^34 + 564924672*tan(1/2*b*x + 2*a)^7*tan(1/2*a)^25 - 6391344852*tan(1/2*b*x + 2*a)^6*tan(1/2*a)^26 + 19663795984*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^27 - 24029264184*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^28 + 11050166160*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^29 + 310355316*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^30 - 1477416960*tan(1/2*b*x + 2*a)*tan(1/2*a)^31 + 267141600*tan(1/2*a)^32 + 564924672*tan(1/2*b*x + 2*a)^7*tan(1/2*a)^23 - 11879791560*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^25 + 31957055712*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^26 - 32793412368*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^27 + 14381865792*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^28 - 2181545880*tan(1/2*b*x + 2*a)*tan(1/2*a)^29 - 17553920*tan(1/2*a)^30 - 939066728*tan(1/2*b*x + 2*a)^7*tan(1/2*a)^21 + 6391344852*tan(1/2*b*x + 2*a)^6*tan(1/2*a)^22 - 11879791560*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^23 + 19856454696*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^25 - 19258200036*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^26 + 6571946504*tan(1/2*b*x + 2*a)*tan(1/2*a)^27 - 680794644*tan(1/2*a)^28 + 314808792*tan(1/2*b*x + 2*a)^7*tan(1/2*a)^19 - 4808309376*tan(1/2*b*x + 2*a)^6*tan(1/2*a)^20 + 19663795984*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^21 - 31957055712*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^22 + 19856454696*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^23 - 4012160256*tan(1/2*b*x + 2*a)*tan(1/2*a)^25 + 925883136*tan(1/2*a)^26 + 211641984*tan(1/2*b*x + 2*a)^7*tan(1/2*a)^17 - 96589076*tan(1/2*b*x + 2*a)^6*tan(1/2*a)^18 - 6655212048*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^19 + 24029264184*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^20 - 32793412368*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^21 + 19258200036*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^22 - 4012160256*tan(1/2*b*x + 2*a)*tan(1/2*a)^23 - 234315648*tan(1/2*b*x + 2*a)^7*tan(1/2*a)^15 + 1888388352*tan(1/2*b*x + 2*a)^6*tan(1/2*a)^16 - 4440981672*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^17 + 466539808*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^18 + 11050166160*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^19 - 14381865792*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^20 + 6571946504*tan(1/2*b*x + 2*a)*tan(1/2*a)^21 - 925883136*tan(1/2*a)^22 + 95841468*tan(1/2*b*x + 2*a)^7*tan(1/2*a)^13 - 1144864350*tan(1/2*b*x + 2*a)^6*tan(1/2*a)^14 + 4935828252*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^15 - 9447759099*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^16 + 7397865576*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^17 - 310355316*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^18 - 2181545880*tan(1/2*b*x + 2*a)*tan(1/2*a)^19 + 680794644*tan(1/2*a)^20 - 20891364*tan(1/2*b*x + 2*a)^7*tan(1/2*a)^11 + 336486592*tan(1/2*b*x + 2*a)^6*tan(1/2*a)^12 - 2010477960*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^13 + 5726288880*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^14 - 8215340892*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^15 + 5649253632*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^16 - 1477416960*tan(1/2*b*x + 2*a)*tan(1/2*a)^17 + 17553920*tan(1/2*a)^18 + 2486912*tan(1/2*b*x + 2*a)^7*tan(1/2*a)^9 - 54465762*tan(1/2*b*x + 2*a)^6*tan(1/2*a)^10 + 436639944*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^11 - 1680996460*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^12 + 3352125960*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^13 - 3430559358*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^14 + 1635149568*tan(1/2*b*x + 2*a)*tan(1/2*a)^15 - 267141600*tan(1/2*a)^16 - 153216*tan(1/2*b*x + 2*a)^7*tan(1/2*a)^7 + 4777344*tan(1/2*b*x + 2*a)^6*tan(1/2*a)^8 - 52518388*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^9 + 272279280*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^10 - 729548040*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^11 + 1012326432*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^12 - 671389308*tan(1/2*b*x + 2*a)*tan(1/2*a)^13 + 162842112*tan(1/2*a)^14 + 4428*tan(1/2*b*x + 2*a)^7*tan(1/2*a)^5 - 210486*tan(1/2*b*x + 2*a)^6*tan(1/2*a)^6 + 3337020*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^7 - 23995332*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^8 + 87480580*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^9 - 164195226*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^10 + 147189588*tan(1/2*b*x + 2*a)*tan(1/2*a)^11 - 48570730*tan(1/2*a)^12 + 108*tan(1/2*b*x + 2*a)^7*tan(1/2*a)^3 + 2880*tan(1/2*b*x + 2*a)^6*tan(1/2*a)^4 - 95832*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^5 + 1046736*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^6 - 5409324*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^7 + 14094720*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^8 - 17453120*tan(1/2*b*x + 2*a)*tan(1/2*a)^9 + 7902336*tan(1/2*a)^10 + 54*tan(1/2*b*x + 2*a)^6*tan(1/2*a)^2 + 536*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^3 - 16740*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^4 + 142488*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^5 - 546366*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^6 + 977472*tan(1/2*b*x + 2*a)*tan(1/2*a)^7 - 642384*tan(1/2*a)^8 + 12*tan(1/2*b*x + 2*a)^5*tan(1/2*a) - 48*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^2 - 536*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^3 + 5472*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^4 - 16092*tan(1/2*b*x + 2*a)*tan(1/2*a)^5 + 17280*tan(1/2*a)^6 + tan(1/2*b*x + 2*a)^4 - 12*tan(1/2*b*x + 2*a)^3*tan(1/2*a) + 54*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^2 - 108*tan(1/2*b*x + 2*a)*tan(1/2*a)^3 + 162*tan(1/2*a)^4)/((81*tan(1/2*a)^20 - 1080*tan(1/2*a)^18 + 5724*tan(1/2*a)^16 - 15240*tan(1/2*a)^14 + 21286*tan(1/2*a)^12 - 15240*tan(1/2*a)^10 + 5724*tan(1/2*a)^8 - 1080*tan(1/2*a)^6 + 81*tan(1/2*a)^4)*(3*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^5 - tan(1/2*b*x + 2*a)*tan(1/2*a)^6 - 10*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^3 + 15*tan(1/2*b*x + 2*a)*tan(1/2*a)^4 - 3*tan(1/2*a)^5 + 3*tan(1/2*b*x + 2*a)^2*tan(1/2*a) - 15*tan(1/2*b*x + 2*a)*tan(1/2*a)^2 + 10*tan(1/2*a)^3 + tan(1/2*b*x + 2*a) - 3*tan(1/2*a))^4) + 120*log(abs(tan(1/2*b*x + 2*a)*tan(1/2*a)^3 - 3*tan(1/2*b*x + 2*a)*tan(1/2*a) + 3*tan(1/2*a)^2 - 1)) - 120*log(abs(3*tan(1/2*b*x + 2*a)*tan(1/2*a)^2 - tan(1/2*a)^3 - tan(1/2*b*x + 2*a) + 3*tan(1/2*a))))/b","B",0
71,1,6318,0,9.366558," ","integrate(csc(b*x+a)^3*csc(2*b*x+2*a)^3,x, algorithm=""giac"")","-\frac{\frac{480 \, {\left(\tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{24} + 30 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{22} - 6 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{23} + \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{24} - 756 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{20} + 614 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{21} - 114 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{22} + 6 \, \tan\left(\frac{1}{2} \, a\right)^{23} + 2058 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{18} - 4578 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{19} + 1932 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{20} - 182 \, \tan\left(\frac{1}{2} \, a\right)^{21} - 27 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{16} + 6210 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{17} - 7462 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{18} + 1554 \, \tan\left(\frac{1}{2} \, a\right)^{19} - 9396 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{14} + 15588 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{15} - 2331 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{16} - 2178 \, \tan\left(\frac{1}{2} \, a\right)^{17} - 21924 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{13} + 26028 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{14} - 5668 \, \tan\left(\frac{1}{2} \, a\right)^{15} + 9396 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{10} - 21924 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{11} + 6468 \, \tan\left(\frac{1}{2} \, a\right)^{13} + 27 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{8} + 15588 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{9} - 26028 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{10} + 6468 \, \tan\left(\frac{1}{2} \, a\right)^{11} - 2058 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{6} + 6210 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{7} + 2331 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{8} - 5668 \, \tan\left(\frac{1}{2} \, a\right)^{9} + 756 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{4} - 4578 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{5} + 7462 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{6} - 2178 \, \tan\left(\frac{1}{2} \, a\right)^{7} - 30 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{2} + 614 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{3} - 1932 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{4} + 1554 \, \tan\left(\frac{1}{2} \, a\right)^{5} - \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} - 6 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right) + 114 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{2} - 182 \, \tan\left(\frac{1}{2} \, a\right)^{3} - \tan\left(\frac{1}{2} \, b x + 2 \, a\right) + 6 \, \tan\left(\frac{1}{2} \, a\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, a\right)^{12} - 30 \, \tan\left(\frac{1}{2} \, a\right)^{10} + 255 \, \tan\left(\frac{1}{2} \, a\right)^{8} - 452 \, \tan\left(\frac{1}{2} \, a\right)^{6} + 255 \, \tan\left(\frac{1}{2} \, a\right)^{4} - 30 \, \tan\left(\frac{1}{2} \, a\right)^{2} + 1\right)} {\left(\tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{6} - 15 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{4} + 12 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{5} - \tan\left(\frac{1}{2} \, a\right)^{6} + 15 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} - 40 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{3} + 15 \, \tan\left(\frac{1}{2} \, a\right)^{4} - \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} + 12 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right) - 15 \, \tan\left(\frac{1}{2} \, a\right)^{2} + 1\right)}^{2}} + \frac{1215 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{9} \tan\left(\frac{1}{2} \, a\right)^{56} - 810 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{8} \tan\left(\frac{1}{2} \, a\right)^{57} + 270 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{7} \tan\left(\frac{1}{2} \, a\right)^{58} - 45 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{59} + 3 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{60} + 71280 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{9} \tan\left(\frac{1}{2} \, a\right)^{54} - 59940 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{8} \tan\left(\frac{1}{2} \, a\right)^{55} + 17640 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{7} \tan\left(\frac{1}{2} \, a\right)^{56} - 795 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{57} - 360 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{58} + 45 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{59} + 2407725 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{9} \tan\left(\frac{1}{2} \, a\right)^{52} - 2568780 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{8} \tan\left(\frac{1}{2} \, a\right)^{53} + 1013880 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{7} \tan\left(\frac{1}{2} \, a\right)^{54} - 144900 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{55} - 1635 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{56} + 795 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{57} + 270 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{58} - 164020320 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{9} \tan\left(\frac{1}{2} \, a\right)^{50} + 294234150 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{8} \tan\left(\frac{1}{2} \, a\right)^{51} - 204257160 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{7} \tan\left(\frac{1}{2} \, a\right)^{52} + 68740740 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{53} - 10958240 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{54} + 567720 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{55} + 17640 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{56} + 810 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{57} + 2847265170 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{9} \tan\left(\frac{1}{2} \, a\right)^{48} - 7061366340 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{8} \tan\left(\frac{1}{2} \, a\right)^{49} + 6848508750 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{7} \tan\left(\frac{1}{2} \, a\right)^{50} - 3360350485 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{51} + 882126585 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{52} - 115984800 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{53} + 5446200 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{54} + 86670 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{55} + 1215 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{56} - 25466109120 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{9} \tan\left(\frac{1}{2} \, a\right)^{46} + 82199042640 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{8} \tan\left(\frac{1}{2} \, a\right)^{47} - 104745094160 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{7} \tan\left(\frac{1}{2} \, a\right)^{48} + 68829859005 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{49} - 25315144296 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{50} + 5205627685 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{51} - 546245640 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{52} + 20895030 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{53} + 187920 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{54} + 1458 \, \tan\left(\frac{1}{2} \, a\right)^{55} + 137905936830 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{9} \tan\left(\frac{1}{2} \, a\right)^{44} - 562989334800 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{8} \tan\left(\frac{1}{2} \, a\right)^{45} + 911808828960 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{7} \tan\left(\frac{1}{2} \, a\right)^{46} - 768698936880 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{47} + 370049962295 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{48} - 104054449965 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{49} + 16540981710 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{50} - 1323596190 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{51} + 37166445 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{52} + 172530 \, \tan\left(\frac{1}{2} \, a\right)^{53} - 472782926880 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{9} \tan\left(\frac{1}{2} \, a\right)^{42} + 2429658984060 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{8} \tan\left(\frac{1}{2} \, a\right)^{43} - 4936681833840 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{7} \tan\left(\frac{1}{2} \, a\right)^{44} + 5227899617200 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{45} - 3184356059520 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{46} + 1153540125240 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{47} - 245839387280 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{48} + 28942646220 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{49} - 1600947360 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{50} + 25793640 \, \tan\left(\frac{1}{2} \, a\right)^{51} + 985566407445 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{9} \tan\left(\frac{1}{2} \, a\right)^{40} - 6594701846310 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{8} \tan\left(\frac{1}{2} \, a\right)^{41} + 17020352439990 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{7} \tan\left(\frac{1}{2} \, a\right)^{42} - 22628389243545 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{43} + 17235607351635 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{44} - 7834375816360 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{45} + 2124636283680 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{46} - 329145687420 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{47} + 25919270610 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{48} - 753655320 \, \tan\left(\frac{1}{2} \, a\right)^{49} - 941937351120 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{9} \tan\left(\frac{1}{2} \, a\right)^{38} + 10024213003740 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{8} \tan\left(\frac{1}{2} \, a\right)^{39} - 35619165658440 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{7} \tan\left(\frac{1}{2} \, a\right)^{40} + 61660501611345 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{41} - 59571399047240 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{42} + 33928676906985 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{43} - 11501138427120 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{44} + 2245614722020 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{45} - 228535536960 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{46} + 9122039460 \, \tan\left(\frac{1}{2} \, a\right)^{47} - 756859069305 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{9} \tan\left(\frac{1}{2} \, a\right)^{36} - 2938166946540 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{8} \tan\left(\frac{1}{2} \, a\right)^{37} + 33963536732760 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{7} \tan\left(\frac{1}{2} \, a\right)^{38} - 93824947269780 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{39} + 124880209066749 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{40} - 92522313305985 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{41} + 39714192559670 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{42} - 9707168584980 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{43} + 1237500036990 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{44} - 62831824476 \, \tan\left(\frac{1}{2} \, a\right)^{45} + 3403775131200 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{9} \tan\left(\frac{1}{2} \, a\right)^{34} - 19290846651030 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{8} \tan\left(\frac{1}{2} \, a\right)^{35} + 27663473408040 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{7} \tan\left(\frac{1}{2} \, a\right)^{36} + 27109136872980 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{37} - 118939479927840 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{38} + 140811947469040 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{39} - 83200102704840 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{40} + 26404824927630 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{41} - 4255065187040 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{42} + 270445183560 \, \tan\left(\frac{1}{2} \, a\right)^{43} - 3650513198580 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{9} \tan\left(\frac{1}{2} \, a\right)^{32} + 36323787336840 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{8} \tan\left(\frac{1}{2} \, a\right)^{33} - 122659045084170 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{7} \tan\left(\frac{1}{2} \, a\right)^{34} + 180766125659295 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{35} - 97447951446495 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{36} - 40571312613240 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{37} + 79276457792280 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{38} - 40160124218470 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{39} + 8888251621845 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{40} - 731644643640 \, \tan\left(\frac{1}{2} \, a\right)^{41} - 19469403725760 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{8} \tan\left(\frac{1}{2} \, a\right)^{31} + 130628272644000 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{7} \tan\left(\frac{1}{2} \, a\right)^{32} - 338314460497335 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{33} + 429435328442040 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{34} - 271342502839935 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{35} + 64809044724520 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{36} + 11678391455970 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{37} - 8484705136560 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{38} + 1111051397230 \, \tan\left(\frac{1}{2} \, a\right)^{39} + 3650513198580 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{9} \tan\left(\frac{1}{2} \, a\right)^{28} - 19469403725760 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{8} \tan\left(\frac{1}{2} \, a\right)^{29} + 180715347146880 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{31} - 456090384021345 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{32} + 507272799301335 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{33} - 286258153276170 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{34} + 77334987640230 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{35} - 6866537353465 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{36} - 329444622930 \, \tan\left(\frac{1}{2} \, a\right)^{37} - 3403775131200 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{9} \tan\left(\frac{1}{2} \, a\right)^{26} + 36323787336840 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{8} \tan\left(\frac{1}{2} \, a\right)^{27} - 130628272644000 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{7} \tan\left(\frac{1}{2} \, a\right)^{28} + 180715347146880 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{29} - 270808903495440 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{31} + 304337156718240 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{32} - 145126844230520 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{33} + 30650585964480 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{34} - 2135547006768 \, \tan\left(\frac{1}{2} \, a\right)^{35} + 756859069305 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{9} \tan\left(\frac{1}{2} \, a\right)^{24} - 19290846651030 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{8} \tan\left(\frac{1}{2} \, a\right)^{25} + 122659045084170 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{7} \tan\left(\frac{1}{2} \, a\right)^{26} - 338314460497335 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{27} + 456090384021345 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{28} - 270808903495440 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{29} + 77638534829400 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{31} - 32750159843700 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{32} + 4042939650000 \, \tan\left(\frac{1}{2} \, a\right)^{33} + 941937351120 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{9} \tan\left(\frac{1}{2} \, a\right)^{22} - 2938166946540 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{8} \tan\left(\frac{1}{2} \, a\right)^{23} - 27663473408040 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{7} \tan\left(\frac{1}{2} \, a\right)^{24} + 180766125659295 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{25} - 429435328442040 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{26} + 507272799301335 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{27} - 304337156718240 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{28} + 77638534829400 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{29} - 2175308641800 \, \tan\left(\frac{1}{2} \, a\right)^{31} - 985566407445 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{9} \tan\left(\frac{1}{2} \, a\right)^{20} + 10024213003740 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{8} \tan\left(\frac{1}{2} \, a\right)^{21} - 33963536732760 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{7} \tan\left(\frac{1}{2} \, a\right)^{22} + 27109136872980 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{23} + 97447951446495 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{24} - 271342502839935 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{25} + 286258153276170 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{26} - 145126844230520 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{27} + 32750159843700 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{28} - 2175308641800 \, \tan\left(\frac{1}{2} \, a\right)^{29} + 472782926880 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{9} \tan\left(\frac{1}{2} \, a\right)^{18} - 6594701846310 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{8} \tan\left(\frac{1}{2} \, a\right)^{19} + 35619165658440 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{7} \tan\left(\frac{1}{2} \, a\right)^{20} - 93824947269780 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{21} + 118939479927840 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{22} - 40571312613240 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{23} - 64809044724520 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{24} + 77334987640230 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{25} - 30650585964480 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{26} + 4042939650000 \, \tan\left(\frac{1}{2} \, a\right)^{27} - 137905936830 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{9} \tan\left(\frac{1}{2} \, a\right)^{16} + 2429658984060 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{8} \tan\left(\frac{1}{2} \, a\right)^{17} - 17020352439990 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{7} \tan\left(\frac{1}{2} \, a\right)^{18} + 61660501611345 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{19} - 124880209066749 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{20} + 140811947469040 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{21} - 79276457792280 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{22} + 11678391455970 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{23} + 6866537353465 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{24} - 2135547006768 \, \tan\left(\frac{1}{2} \, a\right)^{25} + 25466109120 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{9} \tan\left(\frac{1}{2} \, a\right)^{14} - 562989334800 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{8} \tan\left(\frac{1}{2} \, a\right)^{15} + 4936681833840 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{7} \tan\left(\frac{1}{2} \, a\right)^{16} - 22628389243545 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{17} + 59571399047240 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{18} - 92522313305985 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{19} + 83200102704840 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{20} - 40160124218470 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{21} + 8484705136560 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{22} - 329444622930 \, \tan\left(\frac{1}{2} \, a\right)^{23} - 2847265170 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{9} \tan\left(\frac{1}{2} \, a\right)^{12} + 82199042640 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{8} \tan\left(\frac{1}{2} \, a\right)^{13} - 911808828960 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{7} \tan\left(\frac{1}{2} \, a\right)^{14} + 5227899617200 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{15} - 17235607351635 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{16} + 33928676906985 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{17} - 39714192559670 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{18} + 26404824927630 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{19} - 8888251621845 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{20} + 1111051397230 \, \tan\left(\frac{1}{2} \, a\right)^{21} + 164020320 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{9} \tan\left(\frac{1}{2} \, a\right)^{10} - 7061366340 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{8} \tan\left(\frac{1}{2} \, a\right)^{11} + 104745094160 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{7} \tan\left(\frac{1}{2} \, a\right)^{12} - 768698936880 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{13} + 3184356059520 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{14} - 7834375816360 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{15} + 11501138427120 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{16} - 9707168584980 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{17} + 4255065187040 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{18} - 731644643640 \, \tan\left(\frac{1}{2} \, a\right)^{19} - 2407725 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{9} \tan\left(\frac{1}{2} \, a\right)^{8} + 294234150 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{8} \tan\left(\frac{1}{2} \, a\right)^{9} - 6848508750 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{7} \tan\left(\frac{1}{2} \, a\right)^{10} + 68829859005 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{11} - 370049962295 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{12} + 1153540125240 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{13} - 2124636283680 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{14} + 2245614722020 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{15} - 1237500036990 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{16} + 270445183560 \, \tan\left(\frac{1}{2} \, a\right)^{17} - 71280 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{9} \tan\left(\frac{1}{2} \, a\right)^{6} - 2568780 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{8} \tan\left(\frac{1}{2} \, a\right)^{7} + 204257160 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{7} \tan\left(\frac{1}{2} \, a\right)^{8} - 3360350485 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{9} + 25315144296 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{10} - 104054449965 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{11} + 245839387280 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{12} - 329145687420 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{13} + 228535536960 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{14} - 62831824476 \, \tan\left(\frac{1}{2} \, a\right)^{15} - 1215 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{9} \tan\left(\frac{1}{2} \, a\right)^{4} - 59940 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{8} \tan\left(\frac{1}{2} \, a\right)^{5} - 1013880 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{7} \tan\left(\frac{1}{2} \, a\right)^{6} + 68740740 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{7} - 882126585 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{8} + 5205627685 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{9} - 16540981710 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{10} + 28942646220 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{11} - 25919270610 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{12} + 9122039460 \, \tan\left(\frac{1}{2} \, a\right)^{13} - 810 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{8} \tan\left(\frac{1}{2} \, a\right)^{3} - 17640 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{7} \tan\left(\frac{1}{2} \, a\right)^{4} - 144900 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{5} + 10958240 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{6} - 115984800 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{7} + 546245640 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{8} - 1323596190 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{9} + 1600947360 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{10} - 753655320 \, \tan\left(\frac{1}{2} \, a\right)^{11} - 270 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{7} \tan\left(\frac{1}{2} \, a\right)^{2} - 795 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{3} + 1635 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{4} + 567720 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{5} - 5446200 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{6} + 20895030 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{7} - 37166445 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{8} + 25793640 \, \tan\left(\frac{1}{2} \, a\right)^{9} - 45 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{6} \tan\left(\frac{1}{2} \, a\right) + 360 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{2} + 795 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{3} - 17640 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{4} + 86670 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{5} - 187920 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{6} + 172530 \, \tan\left(\frac{1}{2} \, a\right)^{7} - 3 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{5} + 45 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{4} \tan\left(\frac{1}{2} \, a\right) - 270 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{2} + 810 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{3} - 1215 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{4} + 1458 \, \tan\left(\frac{1}{2} \, a\right)^{5}}{{\left(243 \, \tan\left(\frac{1}{2} \, a\right)^{25} - 4050 \, \tan\left(\frac{1}{2} \, a\right)^{23} + 28215 \, \tan\left(\frac{1}{2} \, a\right)^{21} - 106200 \, \tan\left(\frac{1}{2} \, a\right)^{19} + 233430 \, \tan\left(\frac{1}{2} \, a\right)^{17} - 304300 \, \tan\left(\frac{1}{2} \, a\right)^{15} + 233430 \, \tan\left(\frac{1}{2} \, a\right)^{13} - 106200 \, \tan\left(\frac{1}{2} \, a\right)^{11} + 28215 \, \tan\left(\frac{1}{2} \, a\right)^{9} - 4050 \, \tan\left(\frac{1}{2} \, a\right)^{7} + 243 \, \tan\left(\frac{1}{2} \, a\right)^{5}\right)} {\left(3 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{5} - \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{6} - 10 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{3} + 15 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{4} - 3 \, \tan\left(\frac{1}{2} \, a\right)^{5} + 3 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right) - 15 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{2} + 10 \, \tan\left(\frac{1}{2} \, a\right)^{3} + \tan\left(\frac{1}{2} \, b x + 2 \, a\right) - 3 \, \tan\left(\frac{1}{2} \, a\right)\right)}^{5}} - 1680 \, \log\left({\left| \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{3} + 3 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{2} - \tan\left(\frac{1}{2} \, a\right)^{3} - 3 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right) + 3 \, \tan\left(\frac{1}{2} \, a\right)^{2} - \tan\left(\frac{1}{2} \, b x + 2 \, a\right) + 3 \, \tan\left(\frac{1}{2} \, a\right) - 1 \right|}\right) + 1680 \, \log\left({\left| \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{3} - 3 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{2} + \tan\left(\frac{1}{2} \, a\right)^{3} - 3 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right) + 3 \, \tan\left(\frac{1}{2} \, a\right)^{2} + \tan\left(\frac{1}{2} \, b x + 2 \, a\right) - 3 \, \tan\left(\frac{1}{2} \, a\right) - 1 \right|}\right)}{3840 \, b}"," ",0,"-1/3840*(480*(tan(1/2*b*x + 2*a)^3*tan(1/2*a)^24 + 30*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^22 - 6*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^23 + tan(1/2*b*x + 2*a)*tan(1/2*a)^24 - 756*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^20 + 614*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^21 - 114*tan(1/2*b*x + 2*a)*tan(1/2*a)^22 + 6*tan(1/2*a)^23 + 2058*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^18 - 4578*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^19 + 1932*tan(1/2*b*x + 2*a)*tan(1/2*a)^20 - 182*tan(1/2*a)^21 - 27*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^16 + 6210*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^17 - 7462*tan(1/2*b*x + 2*a)*tan(1/2*a)^18 + 1554*tan(1/2*a)^19 - 9396*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^14 + 15588*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^15 - 2331*tan(1/2*b*x + 2*a)*tan(1/2*a)^16 - 2178*tan(1/2*a)^17 - 21924*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^13 + 26028*tan(1/2*b*x + 2*a)*tan(1/2*a)^14 - 5668*tan(1/2*a)^15 + 9396*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^10 - 21924*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^11 + 6468*tan(1/2*a)^13 + 27*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^8 + 15588*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^9 - 26028*tan(1/2*b*x + 2*a)*tan(1/2*a)^10 + 6468*tan(1/2*a)^11 - 2058*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^6 + 6210*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^7 + 2331*tan(1/2*b*x + 2*a)*tan(1/2*a)^8 - 5668*tan(1/2*a)^9 + 756*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^4 - 4578*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^5 + 7462*tan(1/2*b*x + 2*a)*tan(1/2*a)^6 - 2178*tan(1/2*a)^7 - 30*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^2 + 614*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^3 - 1932*tan(1/2*b*x + 2*a)*tan(1/2*a)^4 + 1554*tan(1/2*a)^5 - tan(1/2*b*x + 2*a)^3 - 6*tan(1/2*b*x + 2*a)^2*tan(1/2*a) + 114*tan(1/2*b*x + 2*a)*tan(1/2*a)^2 - 182*tan(1/2*a)^3 - tan(1/2*b*x + 2*a) + 6*tan(1/2*a))/((tan(1/2*a)^12 - 30*tan(1/2*a)^10 + 255*tan(1/2*a)^8 - 452*tan(1/2*a)^6 + 255*tan(1/2*a)^4 - 30*tan(1/2*a)^2 + 1)*(tan(1/2*b*x + 2*a)^2*tan(1/2*a)^6 - 15*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^4 + 12*tan(1/2*b*x + 2*a)*tan(1/2*a)^5 - tan(1/2*a)^6 + 15*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^2 - 40*tan(1/2*b*x + 2*a)*tan(1/2*a)^3 + 15*tan(1/2*a)^4 - tan(1/2*b*x + 2*a)^2 + 12*tan(1/2*b*x + 2*a)*tan(1/2*a) - 15*tan(1/2*a)^2 + 1)^2) + (1215*tan(1/2*b*x + 2*a)^9*tan(1/2*a)^56 - 810*tan(1/2*b*x + 2*a)^8*tan(1/2*a)^57 + 270*tan(1/2*b*x + 2*a)^7*tan(1/2*a)^58 - 45*tan(1/2*b*x + 2*a)^6*tan(1/2*a)^59 + 3*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^60 + 71280*tan(1/2*b*x + 2*a)^9*tan(1/2*a)^54 - 59940*tan(1/2*b*x + 2*a)^8*tan(1/2*a)^55 + 17640*tan(1/2*b*x + 2*a)^7*tan(1/2*a)^56 - 795*tan(1/2*b*x + 2*a)^6*tan(1/2*a)^57 - 360*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^58 + 45*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^59 + 2407725*tan(1/2*b*x + 2*a)^9*tan(1/2*a)^52 - 2568780*tan(1/2*b*x + 2*a)^8*tan(1/2*a)^53 + 1013880*tan(1/2*b*x + 2*a)^7*tan(1/2*a)^54 - 144900*tan(1/2*b*x + 2*a)^6*tan(1/2*a)^55 - 1635*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^56 + 795*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^57 + 270*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^58 - 164020320*tan(1/2*b*x + 2*a)^9*tan(1/2*a)^50 + 294234150*tan(1/2*b*x + 2*a)^8*tan(1/2*a)^51 - 204257160*tan(1/2*b*x + 2*a)^7*tan(1/2*a)^52 + 68740740*tan(1/2*b*x + 2*a)^6*tan(1/2*a)^53 - 10958240*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^54 + 567720*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^55 + 17640*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^56 + 810*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^57 + 2847265170*tan(1/2*b*x + 2*a)^9*tan(1/2*a)^48 - 7061366340*tan(1/2*b*x + 2*a)^8*tan(1/2*a)^49 + 6848508750*tan(1/2*b*x + 2*a)^7*tan(1/2*a)^50 - 3360350485*tan(1/2*b*x + 2*a)^6*tan(1/2*a)^51 + 882126585*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^52 - 115984800*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^53 + 5446200*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^54 + 86670*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^55 + 1215*tan(1/2*b*x + 2*a)*tan(1/2*a)^56 - 25466109120*tan(1/2*b*x + 2*a)^9*tan(1/2*a)^46 + 82199042640*tan(1/2*b*x + 2*a)^8*tan(1/2*a)^47 - 104745094160*tan(1/2*b*x + 2*a)^7*tan(1/2*a)^48 + 68829859005*tan(1/2*b*x + 2*a)^6*tan(1/2*a)^49 - 25315144296*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^50 + 5205627685*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^51 - 546245640*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^52 + 20895030*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^53 + 187920*tan(1/2*b*x + 2*a)*tan(1/2*a)^54 + 1458*tan(1/2*a)^55 + 137905936830*tan(1/2*b*x + 2*a)^9*tan(1/2*a)^44 - 562989334800*tan(1/2*b*x + 2*a)^8*tan(1/2*a)^45 + 911808828960*tan(1/2*b*x + 2*a)^7*tan(1/2*a)^46 - 768698936880*tan(1/2*b*x + 2*a)^6*tan(1/2*a)^47 + 370049962295*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^48 - 104054449965*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^49 + 16540981710*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^50 - 1323596190*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^51 + 37166445*tan(1/2*b*x + 2*a)*tan(1/2*a)^52 + 172530*tan(1/2*a)^53 - 472782926880*tan(1/2*b*x + 2*a)^9*tan(1/2*a)^42 + 2429658984060*tan(1/2*b*x + 2*a)^8*tan(1/2*a)^43 - 4936681833840*tan(1/2*b*x + 2*a)^7*tan(1/2*a)^44 + 5227899617200*tan(1/2*b*x + 2*a)^6*tan(1/2*a)^45 - 3184356059520*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^46 + 1153540125240*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^47 - 245839387280*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^48 + 28942646220*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^49 - 1600947360*tan(1/2*b*x + 2*a)*tan(1/2*a)^50 + 25793640*tan(1/2*a)^51 + 985566407445*tan(1/2*b*x + 2*a)^9*tan(1/2*a)^40 - 6594701846310*tan(1/2*b*x + 2*a)^8*tan(1/2*a)^41 + 17020352439990*tan(1/2*b*x + 2*a)^7*tan(1/2*a)^42 - 22628389243545*tan(1/2*b*x + 2*a)^6*tan(1/2*a)^43 + 17235607351635*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^44 - 7834375816360*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^45 + 2124636283680*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^46 - 329145687420*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^47 + 25919270610*tan(1/2*b*x + 2*a)*tan(1/2*a)^48 - 753655320*tan(1/2*a)^49 - 941937351120*tan(1/2*b*x + 2*a)^9*tan(1/2*a)^38 + 10024213003740*tan(1/2*b*x + 2*a)^8*tan(1/2*a)^39 - 35619165658440*tan(1/2*b*x + 2*a)^7*tan(1/2*a)^40 + 61660501611345*tan(1/2*b*x + 2*a)^6*tan(1/2*a)^41 - 59571399047240*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^42 + 33928676906985*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^43 - 11501138427120*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^44 + 2245614722020*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^45 - 228535536960*tan(1/2*b*x + 2*a)*tan(1/2*a)^46 + 9122039460*tan(1/2*a)^47 - 756859069305*tan(1/2*b*x + 2*a)^9*tan(1/2*a)^36 - 2938166946540*tan(1/2*b*x + 2*a)^8*tan(1/2*a)^37 + 33963536732760*tan(1/2*b*x + 2*a)^7*tan(1/2*a)^38 - 93824947269780*tan(1/2*b*x + 2*a)^6*tan(1/2*a)^39 + 124880209066749*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^40 - 92522313305985*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^41 + 39714192559670*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^42 - 9707168584980*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^43 + 1237500036990*tan(1/2*b*x + 2*a)*tan(1/2*a)^44 - 62831824476*tan(1/2*a)^45 + 3403775131200*tan(1/2*b*x + 2*a)^9*tan(1/2*a)^34 - 19290846651030*tan(1/2*b*x + 2*a)^8*tan(1/2*a)^35 + 27663473408040*tan(1/2*b*x + 2*a)^7*tan(1/2*a)^36 + 27109136872980*tan(1/2*b*x + 2*a)^6*tan(1/2*a)^37 - 118939479927840*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^38 + 140811947469040*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^39 - 83200102704840*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^40 + 26404824927630*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^41 - 4255065187040*tan(1/2*b*x + 2*a)*tan(1/2*a)^42 + 270445183560*tan(1/2*a)^43 - 3650513198580*tan(1/2*b*x + 2*a)^9*tan(1/2*a)^32 + 36323787336840*tan(1/2*b*x + 2*a)^8*tan(1/2*a)^33 - 122659045084170*tan(1/2*b*x + 2*a)^7*tan(1/2*a)^34 + 180766125659295*tan(1/2*b*x + 2*a)^6*tan(1/2*a)^35 - 97447951446495*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^36 - 40571312613240*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^37 + 79276457792280*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^38 - 40160124218470*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^39 + 8888251621845*tan(1/2*b*x + 2*a)*tan(1/2*a)^40 - 731644643640*tan(1/2*a)^41 - 19469403725760*tan(1/2*b*x + 2*a)^8*tan(1/2*a)^31 + 130628272644000*tan(1/2*b*x + 2*a)^7*tan(1/2*a)^32 - 338314460497335*tan(1/2*b*x + 2*a)^6*tan(1/2*a)^33 + 429435328442040*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^34 - 271342502839935*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^35 + 64809044724520*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^36 + 11678391455970*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^37 - 8484705136560*tan(1/2*b*x + 2*a)*tan(1/2*a)^38 + 1111051397230*tan(1/2*a)^39 + 3650513198580*tan(1/2*b*x + 2*a)^9*tan(1/2*a)^28 - 19469403725760*tan(1/2*b*x + 2*a)^8*tan(1/2*a)^29 + 180715347146880*tan(1/2*b*x + 2*a)^6*tan(1/2*a)^31 - 456090384021345*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^32 + 507272799301335*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^33 - 286258153276170*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^34 + 77334987640230*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^35 - 6866537353465*tan(1/2*b*x + 2*a)*tan(1/2*a)^36 - 329444622930*tan(1/2*a)^37 - 3403775131200*tan(1/2*b*x + 2*a)^9*tan(1/2*a)^26 + 36323787336840*tan(1/2*b*x + 2*a)^8*tan(1/2*a)^27 - 130628272644000*tan(1/2*b*x + 2*a)^7*tan(1/2*a)^28 + 180715347146880*tan(1/2*b*x + 2*a)^6*tan(1/2*a)^29 - 270808903495440*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^31 + 304337156718240*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^32 - 145126844230520*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^33 + 30650585964480*tan(1/2*b*x + 2*a)*tan(1/2*a)^34 - 2135547006768*tan(1/2*a)^35 + 756859069305*tan(1/2*b*x + 2*a)^9*tan(1/2*a)^24 - 19290846651030*tan(1/2*b*x + 2*a)^8*tan(1/2*a)^25 + 122659045084170*tan(1/2*b*x + 2*a)^7*tan(1/2*a)^26 - 338314460497335*tan(1/2*b*x + 2*a)^6*tan(1/2*a)^27 + 456090384021345*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^28 - 270808903495440*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^29 + 77638534829400*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^31 - 32750159843700*tan(1/2*b*x + 2*a)*tan(1/2*a)^32 + 4042939650000*tan(1/2*a)^33 + 941937351120*tan(1/2*b*x + 2*a)^9*tan(1/2*a)^22 - 2938166946540*tan(1/2*b*x + 2*a)^8*tan(1/2*a)^23 - 27663473408040*tan(1/2*b*x + 2*a)^7*tan(1/2*a)^24 + 180766125659295*tan(1/2*b*x + 2*a)^6*tan(1/2*a)^25 - 429435328442040*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^26 + 507272799301335*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^27 - 304337156718240*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^28 + 77638534829400*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^29 - 2175308641800*tan(1/2*a)^31 - 985566407445*tan(1/2*b*x + 2*a)^9*tan(1/2*a)^20 + 10024213003740*tan(1/2*b*x + 2*a)^8*tan(1/2*a)^21 - 33963536732760*tan(1/2*b*x + 2*a)^7*tan(1/2*a)^22 + 27109136872980*tan(1/2*b*x + 2*a)^6*tan(1/2*a)^23 + 97447951446495*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^24 - 271342502839935*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^25 + 286258153276170*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^26 - 145126844230520*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^27 + 32750159843700*tan(1/2*b*x + 2*a)*tan(1/2*a)^28 - 2175308641800*tan(1/2*a)^29 + 472782926880*tan(1/2*b*x + 2*a)^9*tan(1/2*a)^18 - 6594701846310*tan(1/2*b*x + 2*a)^8*tan(1/2*a)^19 + 35619165658440*tan(1/2*b*x + 2*a)^7*tan(1/2*a)^20 - 93824947269780*tan(1/2*b*x + 2*a)^6*tan(1/2*a)^21 + 118939479927840*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^22 - 40571312613240*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^23 - 64809044724520*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^24 + 77334987640230*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^25 - 30650585964480*tan(1/2*b*x + 2*a)*tan(1/2*a)^26 + 4042939650000*tan(1/2*a)^27 - 137905936830*tan(1/2*b*x + 2*a)^9*tan(1/2*a)^16 + 2429658984060*tan(1/2*b*x + 2*a)^8*tan(1/2*a)^17 - 17020352439990*tan(1/2*b*x + 2*a)^7*tan(1/2*a)^18 + 61660501611345*tan(1/2*b*x + 2*a)^6*tan(1/2*a)^19 - 124880209066749*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^20 + 140811947469040*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^21 - 79276457792280*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^22 + 11678391455970*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^23 + 6866537353465*tan(1/2*b*x + 2*a)*tan(1/2*a)^24 - 2135547006768*tan(1/2*a)^25 + 25466109120*tan(1/2*b*x + 2*a)^9*tan(1/2*a)^14 - 562989334800*tan(1/2*b*x + 2*a)^8*tan(1/2*a)^15 + 4936681833840*tan(1/2*b*x + 2*a)^7*tan(1/2*a)^16 - 22628389243545*tan(1/2*b*x + 2*a)^6*tan(1/2*a)^17 + 59571399047240*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^18 - 92522313305985*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^19 + 83200102704840*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^20 - 40160124218470*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^21 + 8484705136560*tan(1/2*b*x + 2*a)*tan(1/2*a)^22 - 329444622930*tan(1/2*a)^23 - 2847265170*tan(1/2*b*x + 2*a)^9*tan(1/2*a)^12 + 82199042640*tan(1/2*b*x + 2*a)^8*tan(1/2*a)^13 - 911808828960*tan(1/2*b*x + 2*a)^7*tan(1/2*a)^14 + 5227899617200*tan(1/2*b*x + 2*a)^6*tan(1/2*a)^15 - 17235607351635*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^16 + 33928676906985*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^17 - 39714192559670*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^18 + 26404824927630*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^19 - 8888251621845*tan(1/2*b*x + 2*a)*tan(1/2*a)^20 + 1111051397230*tan(1/2*a)^21 + 164020320*tan(1/2*b*x + 2*a)^9*tan(1/2*a)^10 - 7061366340*tan(1/2*b*x + 2*a)^8*tan(1/2*a)^11 + 104745094160*tan(1/2*b*x + 2*a)^7*tan(1/2*a)^12 - 768698936880*tan(1/2*b*x + 2*a)^6*tan(1/2*a)^13 + 3184356059520*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^14 - 7834375816360*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^15 + 11501138427120*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^16 - 9707168584980*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^17 + 4255065187040*tan(1/2*b*x + 2*a)*tan(1/2*a)^18 - 731644643640*tan(1/2*a)^19 - 2407725*tan(1/2*b*x + 2*a)^9*tan(1/2*a)^8 + 294234150*tan(1/2*b*x + 2*a)^8*tan(1/2*a)^9 - 6848508750*tan(1/2*b*x + 2*a)^7*tan(1/2*a)^10 + 68829859005*tan(1/2*b*x + 2*a)^6*tan(1/2*a)^11 - 370049962295*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^12 + 1153540125240*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^13 - 2124636283680*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^14 + 2245614722020*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^15 - 1237500036990*tan(1/2*b*x + 2*a)*tan(1/2*a)^16 + 270445183560*tan(1/2*a)^17 - 71280*tan(1/2*b*x + 2*a)^9*tan(1/2*a)^6 - 2568780*tan(1/2*b*x + 2*a)^8*tan(1/2*a)^7 + 204257160*tan(1/2*b*x + 2*a)^7*tan(1/2*a)^8 - 3360350485*tan(1/2*b*x + 2*a)^6*tan(1/2*a)^9 + 25315144296*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^10 - 104054449965*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^11 + 245839387280*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^12 - 329145687420*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^13 + 228535536960*tan(1/2*b*x + 2*a)*tan(1/2*a)^14 - 62831824476*tan(1/2*a)^15 - 1215*tan(1/2*b*x + 2*a)^9*tan(1/2*a)^4 - 59940*tan(1/2*b*x + 2*a)^8*tan(1/2*a)^5 - 1013880*tan(1/2*b*x + 2*a)^7*tan(1/2*a)^6 + 68740740*tan(1/2*b*x + 2*a)^6*tan(1/2*a)^7 - 882126585*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^8 + 5205627685*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^9 - 16540981710*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^10 + 28942646220*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^11 - 25919270610*tan(1/2*b*x + 2*a)*tan(1/2*a)^12 + 9122039460*tan(1/2*a)^13 - 810*tan(1/2*b*x + 2*a)^8*tan(1/2*a)^3 - 17640*tan(1/2*b*x + 2*a)^7*tan(1/2*a)^4 - 144900*tan(1/2*b*x + 2*a)^6*tan(1/2*a)^5 + 10958240*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^6 - 115984800*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^7 + 546245640*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^8 - 1323596190*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^9 + 1600947360*tan(1/2*b*x + 2*a)*tan(1/2*a)^10 - 753655320*tan(1/2*a)^11 - 270*tan(1/2*b*x + 2*a)^7*tan(1/2*a)^2 - 795*tan(1/2*b*x + 2*a)^6*tan(1/2*a)^3 + 1635*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^4 + 567720*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^5 - 5446200*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^6 + 20895030*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^7 - 37166445*tan(1/2*b*x + 2*a)*tan(1/2*a)^8 + 25793640*tan(1/2*a)^9 - 45*tan(1/2*b*x + 2*a)^6*tan(1/2*a) + 360*tan(1/2*b*x + 2*a)^5*tan(1/2*a)^2 + 795*tan(1/2*b*x + 2*a)^4*tan(1/2*a)^3 - 17640*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^4 + 86670*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^5 - 187920*tan(1/2*b*x + 2*a)*tan(1/2*a)^6 + 172530*tan(1/2*a)^7 - 3*tan(1/2*b*x + 2*a)^5 + 45*tan(1/2*b*x + 2*a)^4*tan(1/2*a) - 270*tan(1/2*b*x + 2*a)^3*tan(1/2*a)^2 + 810*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^3 - 1215*tan(1/2*b*x + 2*a)*tan(1/2*a)^4 + 1458*tan(1/2*a)^5)/((243*tan(1/2*a)^25 - 4050*tan(1/2*a)^23 + 28215*tan(1/2*a)^21 - 106200*tan(1/2*a)^19 + 233430*tan(1/2*a)^17 - 304300*tan(1/2*a)^15 + 233430*tan(1/2*a)^13 - 106200*tan(1/2*a)^11 + 28215*tan(1/2*a)^9 - 4050*tan(1/2*a)^7 + 243*tan(1/2*a)^5)*(3*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^5 - tan(1/2*b*x + 2*a)*tan(1/2*a)^6 - 10*tan(1/2*b*x + 2*a)^2*tan(1/2*a)^3 + 15*tan(1/2*b*x + 2*a)*tan(1/2*a)^4 - 3*tan(1/2*a)^5 + 3*tan(1/2*b*x + 2*a)^2*tan(1/2*a) - 15*tan(1/2*b*x + 2*a)*tan(1/2*a)^2 + 10*tan(1/2*a)^3 + tan(1/2*b*x + 2*a) - 3*tan(1/2*a))^5) - 1680*log(abs(tan(1/2*b*x + 2*a)*tan(1/2*a)^3 + 3*tan(1/2*b*x + 2*a)*tan(1/2*a)^2 - tan(1/2*a)^3 - 3*tan(1/2*b*x + 2*a)*tan(1/2*a) + 3*tan(1/2*a)^2 - tan(1/2*b*x + 2*a) + 3*tan(1/2*a) - 1)) + 1680*log(abs(tan(1/2*b*x + 2*a)*tan(1/2*a)^3 - 3*tan(1/2*b*x + 2*a)*tan(1/2*a)^2 + tan(1/2*a)^3 - 3*tan(1/2*b*x + 2*a)*tan(1/2*a) + 3*tan(1/2*a)^2 + tan(1/2*b*x + 2*a) - 3*tan(1/2*a) - 1)))/b","B",0
72,-1,0,0,0.000000," ","integrate(csc(b*x+a)^3*csc(2*b*x+2*a)^4,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
73,-1,0,0,0.000000," ","integrate(sin(b*x+a)*sin(2*b*x+2*a)^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
74,0,0,0,0.000000," ","integrate(sin(b*x+a)*sin(2*b*x+2*a)^(3/2),x, algorithm=""giac"")","\int \sin\left(2 \, b x + 2 \, a\right)^{\frac{3}{2}} \sin\left(b x + a\right)\,{d x}"," ",0,"integrate(sin(2*b*x + 2*a)^(3/2)*sin(b*x + a), x)","F",0
75,0,0,0,0.000000," ","integrate(sin(b*x+a)*sin(2*b*x+2*a)^(1/2),x, algorithm=""giac"")","\int \sqrt{\sin\left(2 \, b x + 2 \, a\right)} \sin\left(b x + a\right)\,{d x}"," ",0,"integrate(sqrt(sin(2*b*x + 2*a))*sin(b*x + a), x)","F",0
76,-1,0,0,0.000000," ","integrate(sin(b*x+a)/sin(2*b*x+2*a)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
77,-1,0,0,0.000000," ","integrate(sin(b*x+a)/sin(2*b*x+2*a)^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
78,-1,0,0,0.000000," ","integrate(sin(b*x+a)/sin(2*b*x+2*a)^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
79,-1,0,0,0.000000," ","integrate(sin(b*x+a)/sin(2*b*x+2*a)^(7/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
80,-1,0,0,0.000000," ","integrate(sin(b*x+a)/sin(2*b*x+2*a)^(9/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
81,-1,0,0,0.000000," ","integrate(sin(b*x+a)^2*sin(2*b*x+2*a)^(7/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
82,-1,0,0,0.000000," ","integrate(sin(b*x+a)^2*sin(2*b*x+2*a)^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
83,-1,0,0,0.000000," ","integrate(sin(b*x+a)^2*sin(2*b*x+2*a)^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
84,0,0,0,0.000000," ","integrate(sin(b*x+a)^2*sin(2*b*x+2*a)^(1/2),x, algorithm=""giac"")","\int \sqrt{\sin\left(2 \, b x + 2 \, a\right)} \sin\left(b x + a\right)^{2}\,{d x}"," ",0,"integrate(sqrt(sin(2*b*x + 2*a))*sin(b*x + a)^2, x)","F",0
85,-1,0,0,0.000000," ","integrate(sin(b*x+a)^2/sin(2*b*x+2*a)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
86,-1,0,0,0.000000," ","integrate(sin(b*x+a)^2/sin(2*b*x+2*a)^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
87,-1,0,0,0.000000," ","integrate(sin(b*x+a)^2/sin(2*b*x+2*a)^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
88,-1,0,0,0.000000," ","integrate(sin(b*x+a)^2/sin(2*b*x+2*a)^(7/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
89,-1,0,0,0.000000," ","integrate(sin(b*x+a)^3*sin(2*b*x+2*a)^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
90,-2,0,0,0.000000," ","integrate(sin(b*x+a)^3*sin(2*b*x+2*a)^(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:ext_reduce Error: Bad Argument TypeEvaluation time: 0.47Done","F(-2)",0
91,-1,0,0,0.000000," ","integrate(sin(b*x+a)^3/sin(2*b*x+2*a)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
92,-1,0,0,0.000000," ","integrate(sin(b*x+a)^3/sin(2*b*x+2*a)^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
93,-1,0,0,0.000000," ","integrate(sin(b*x+a)^3/sin(2*b*x+2*a)^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
94,-1,0,0,0.000000," ","integrate(sin(b*x+a)^3/sin(2*b*x+2*a)^(7/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
95,-1,0,0,0.000000," ","integrate(sin(b*x+a)^3/sin(2*b*x+2*a)^(9/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
96,-1,0,0,0.000000," ","integrate(sin(b*x+a)^3/sin(2*b*x+2*a)^(11/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
97,-1,0,0,0.000000," ","integrate(csc(b*x+a)*sin(2*b*x+2*a)^(7/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
98,-1,0,0,0.000000," ","integrate(csc(b*x+a)*sin(2*b*x+2*a)^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
99,0,0,0,0.000000," ","integrate(csc(b*x+a)*sin(2*b*x+2*a)^(3/2),x, algorithm=""giac"")","\int \csc\left(b x + a\right) \sin\left(2 \, b x + 2 \, a\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate(csc(b*x + a)*sin(2*b*x + 2*a)^(3/2), x)","F",0
100,0,0,0,0.000000," ","integrate(csc(b*x+a)*sin(2*b*x+2*a)^(1/2),x, algorithm=""giac"")","\int \csc\left(b x + a\right) \sqrt{\sin\left(2 \, b x + 2 \, a\right)}\,{d x}"," ",0,"integrate(csc(b*x + a)*sqrt(sin(2*b*x + 2*a)), x)","F",0
101,0,0,0,0.000000," ","integrate(csc(b*x+a)/sin(2*b*x+2*a)^(1/2),x, algorithm=""giac"")","\int \frac{\csc\left(b x + a\right)}{\sqrt{\sin\left(2 \, b x + 2 \, a\right)}}\,{d x}"," ",0,"integrate(csc(b*x + a)/sqrt(sin(2*b*x + 2*a)), x)","F",0
102,0,0,0,0.000000," ","integrate(csc(b*x+a)/sin(2*b*x+2*a)^(3/2),x, algorithm=""giac"")","\int \frac{\csc\left(b x + a\right)}{\sin\left(2 \, b x + 2 \, a\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(csc(b*x + a)/sin(2*b*x + 2*a)^(3/2), x)","F",0
103,0,0,0,0.000000," ","integrate(csc(b*x+a)/sin(2*b*x+2*a)^(5/2),x, algorithm=""giac"")","\int \frac{\csc\left(b x + a\right)}{\sin\left(2 \, b x + 2 \, a\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(csc(b*x + a)/sin(2*b*x + 2*a)^(5/2), x)","F",0
104,0,0,0,0.000000," ","integrate(csc(b*x+a)/sin(2*b*x+2*a)^(7/2),x, algorithm=""giac"")","\int \frac{\csc\left(b x + a\right)}{\sin\left(2 \, b x + 2 \, a\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(csc(b*x + a)/sin(2*b*x + 2*a)^(7/2), x)","F",0
105,-1,0,0,0.000000," ","integrate(csc(b*x+a)^2*sin(2*b*x+2*a)^(9/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
106,-1,0,0,0.000000," ","integrate(csc(b*x+a)^2*sin(2*b*x+2*a)^(7/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
107,-1,0,0,0.000000," ","integrate(csc(b*x+a)^2*sin(2*b*x+2*a)^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
108,0,0,0,0.000000," ","integrate(csc(b*x+a)^2*sin(2*b*x+2*a)^(3/2),x, algorithm=""giac"")","\int \csc\left(b x + a\right)^{2} \sin\left(2 \, b x + 2 \, a\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate(csc(b*x + a)^2*sin(2*b*x + 2*a)^(3/2), x)","F",0
109,0,0,0,0.000000," ","integrate(csc(b*x+a)^2*sin(2*b*x+2*a)^(1/2),x, algorithm=""giac"")","\int \csc\left(b x + a\right)^{2} \sqrt{\sin\left(2 \, b x + 2 \, a\right)}\,{d x}"," ",0,"integrate(csc(b*x + a)^2*sqrt(sin(2*b*x + 2*a)), x)","F",0
110,0,0,0,0.000000," ","integrate(csc(b*x+a)^2/sin(2*b*x+2*a)^(1/2),x, algorithm=""giac"")","\int \frac{\csc\left(b x + a\right)^{2}}{\sqrt{\sin\left(2 \, b x + 2 \, a\right)}}\,{d x}"," ",0,"integrate(csc(b*x + a)^2/sqrt(sin(2*b*x + 2*a)), x)","F",0
111,0,0,0,0.000000," ","integrate(csc(b*x+a)^2/sin(2*b*x+2*a)^(3/2),x, algorithm=""giac"")","\int \frac{\csc\left(b x + a\right)^{2}}{\sin\left(2 \, b x + 2 \, a\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(csc(b*x + a)^2/sin(2*b*x + 2*a)^(3/2), x)","F",0
112,0,0,0,0.000000," ","integrate(csc(b*x+a)^2/sin(2*b*x+2*a)^(5/2),x, algorithm=""giac"")","\int \frac{\csc\left(b x + a\right)^{2}}{\sin\left(2 \, b x + 2 \, a\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(csc(b*x + a)^2/sin(2*b*x + 2*a)^(5/2), x)","F",0
113,0,0,0,0.000000," ","integrate(csc(b*x+a)^2/sin(2*b*x+2*a)^(7/2),x, algorithm=""giac"")","\int \frac{\csc\left(b x + a\right)^{2}}{\sin\left(2 \, b x + 2 \, a\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(csc(b*x + a)^2/sin(2*b*x + 2*a)^(7/2), x)","F",0
114,0,0,0,0.000000," ","integrate(csc(b*x+a)^2/sin(2*b*x+2*a)^(9/2),x, algorithm=""giac"")","\int \frac{\csc\left(b x + a\right)^{2}}{\sin\left(2 \, b x + 2 \, a\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate(csc(b*x + a)^2/sin(2*b*x + 2*a)^(9/2), x)","F",0
115,-1,0,0,0.000000," ","integrate(csc(b*x+a)^3*sin(2*b*x+2*a)^(9/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
116,-1,0,0,0.000000," ","integrate(csc(b*x+a)^3*sin(2*b*x+2*a)^(7/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
117,-1,0,0,0.000000," ","integrate(csc(b*x+a)^3*sin(2*b*x+2*a)^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
118,0,0,0,0.000000," ","integrate(csc(b*x+a)^3*sin(2*b*x+2*a)^(3/2),x, algorithm=""giac"")","\int \csc\left(b x + a\right)^{3} \sin\left(2 \, b x + 2 \, a\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate(csc(b*x + a)^3*sin(2*b*x + 2*a)^(3/2), x)","F",0
119,0,0,0,0.000000," ","integrate(csc(b*x+a)^3*sin(2*b*x+2*a)^(1/2),x, algorithm=""giac"")","\int \csc\left(b x + a\right)^{3} \sqrt{\sin\left(2 \, b x + 2 \, a\right)}\,{d x}"," ",0,"integrate(csc(b*x + a)^3*sqrt(sin(2*b*x + 2*a)), x)","F",0
120,0,0,0,0.000000," ","integrate(csc(b*x+a)^3/sin(2*b*x+2*a)^(1/2),x, algorithm=""giac"")","\int \frac{\csc\left(b x + a\right)^{3}}{\sqrt{\sin\left(2 \, b x + 2 \, a\right)}}\,{d x}"," ",0,"integrate(csc(b*x + a)^3/sqrt(sin(2*b*x + 2*a)), x)","F",0
121,0,0,0,0.000000," ","integrate(csc(b*x+a)^3/sin(2*b*x+2*a)^(3/2),x, algorithm=""giac"")","\int \frac{\csc\left(b x + a\right)^{3}}{\sin\left(2 \, b x + 2 \, a\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(csc(b*x + a)^3/sin(2*b*x + 2*a)^(3/2), x)","F",0
122,0,0,0,0.000000," ","integrate(csc(b*x+a)^3/sin(2*b*x+2*a)^(5/2),x, algorithm=""giac"")","\int \frac{\csc\left(b x + a\right)^{3}}{\sin\left(2 \, b x + 2 \, a\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(csc(b*x + a)^3/sin(2*b*x + 2*a)^(5/2), x)","F",0
123,0,0,0,0.000000," ","integrate(sin(b*x+a)^3*sin(2*b*x+2*a)^m,x, algorithm=""giac"")","\int \sin\left(2 \, b x + 2 \, a\right)^{m} \sin\left(b x + a\right)^{3}\,{d x}"," ",0,"integrate(sin(2*b*x + 2*a)^m*sin(b*x + a)^3, x)","F",0
124,0,0,0,0.000000," ","integrate(sin(b*x+a)^2*sin(2*b*x+2*a)^m,x, algorithm=""giac"")","\int \sin\left(2 \, b x + 2 \, a\right)^{m} \sin\left(b x + a\right)^{2}\,{d x}"," ",0,"integrate(sin(2*b*x + 2*a)^m*sin(b*x + a)^2, x)","F",0
125,0,0,0,0.000000," ","integrate(sin(b*x+a)*sin(2*b*x+2*a)^m,x, algorithm=""giac"")","\int \sin\left(2 \, b x + 2 \, a\right)^{m} \sin\left(b x + a\right)\,{d x}"," ",0,"integrate(sin(2*b*x + 2*a)^m*sin(b*x + a), x)","F",0
126,-1,0,0,0.000000," ","integrate(csc(b*x+a)*sin(2*b*x+2*a)^m,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
127,-1,0,0,0.000000," ","integrate(csc(b*x+a)^2*sin(2*b*x+2*a)^m,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
128,-1,0,0,0.000000," ","integrate(csc(b*x+a)^3*sin(2*b*x+2*a)^m,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
129,1,110,0,2.903458," ","integrate(cos(b*x+a)*sin(2*b*x+2*a)^7,x, algorithm=""giac"")","\frac{\cos\left(15 \, b x + 15 \, a\right)}{1920 \, b} + \frac{\cos\left(13 \, b x + 13 \, a\right)}{1664 \, b} - \frac{7 \, \cos\left(11 \, b x + 11 \, a\right)}{1408 \, b} - \frac{7 \, \cos\left(9 \, b x + 9 \, a\right)}{1152 \, b} + \frac{3 \, \cos\left(7 \, b x + 7 \, a\right)}{128 \, b} + \frac{21 \, \cos\left(5 \, b x + 5 \, a\right)}{640 \, b} - \frac{35 \, \cos\left(3 \, b x + 3 \, a\right)}{384 \, b} - \frac{35 \, \cos\left(b x + a\right)}{128 \, b}"," ",0,"1/1920*cos(15*b*x + 15*a)/b + 1/1664*cos(13*b*x + 13*a)/b - 7/1408*cos(11*b*x + 11*a)/b - 7/1152*cos(9*b*x + 9*a)/b + 3/128*cos(7*b*x + 7*a)/b + 21/640*cos(5*b*x + 5*a)/b - 35/384*cos(3*b*x + 3*a)/b - 35/128*cos(b*x + a)/b","B",0
130,1,96,0,1.726415," ","integrate(cos(b*x+a)*sin(2*b*x+2*a)^6,x, algorithm=""giac"")","-\frac{\sin\left(13 \, b x + 13 \, a\right)}{832 \, b} - \frac{\sin\left(11 \, b x + 11 \, a\right)}{704 \, b} + \frac{\sin\left(9 \, b x + 9 \, a\right)}{96 \, b} + \frac{3 \, \sin\left(7 \, b x + 7 \, a\right)}{224 \, b} - \frac{3 \, \sin\left(5 \, b x + 5 \, a\right)}{64 \, b} - \frac{5 \, \sin\left(3 \, b x + 3 \, a\right)}{64 \, b} + \frac{5 \, \sin\left(b x + a\right)}{16 \, b}"," ",0,"-1/832*sin(13*b*x + 13*a)/b - 1/704*sin(11*b*x + 11*a)/b + 1/96*sin(9*b*x + 9*a)/b + 3/224*sin(7*b*x + 7*a)/b - 3/64*sin(5*b*x + 5*a)/b - 5/64*sin(3*b*x + 3*a)/b + 5/16*sin(b*x + a)/b","A",0
131,1,82,0,0.942661," ","integrate(cos(b*x+a)*sin(2*b*x+2*a)^5,x, algorithm=""giac"")","-\frac{\cos\left(11 \, b x + 11 \, a\right)}{352 \, b} - \frac{\cos\left(9 \, b x + 9 \, a\right)}{288 \, b} + \frac{5 \, \cos\left(7 \, b x + 7 \, a\right)}{224 \, b} + \frac{\cos\left(5 \, b x + 5 \, a\right)}{32 \, b} - \frac{5 \, \cos\left(3 \, b x + 3 \, a\right)}{48 \, b} - \frac{5 \, \cos\left(b x + a\right)}{16 \, b}"," ",0,"-1/352*cos(11*b*x + 11*a)/b - 1/288*cos(9*b*x + 9*a)/b + 5/224*cos(7*b*x + 7*a)/b + 1/32*cos(5*b*x + 5*a)/b - 5/48*cos(3*b*x + 3*a)/b - 5/16*cos(b*x + a)/b","B",0
132,1,68,0,2.924605," ","integrate(cos(b*x+a)*sin(2*b*x+2*a)^4,x, algorithm=""giac"")","\frac{\sin\left(9 \, b x + 9 \, a\right)}{144 \, b} + \frac{\sin\left(7 \, b x + 7 \, a\right)}{112 \, b} - \frac{\sin\left(5 \, b x + 5 \, a\right)}{20 \, b} - \frac{\sin\left(3 \, b x + 3 \, a\right)}{12 \, b} + \frac{3 \, \sin\left(b x + a\right)}{8 \, b}"," ",0,"1/144*sin(9*b*x + 9*a)/b + 1/112*sin(7*b*x + 7*a)/b - 1/20*sin(5*b*x + 5*a)/b - 1/12*sin(3*b*x + 3*a)/b + 3/8*sin(b*x + a)/b","A",0
133,1,54,0,0.290418," ","integrate(cos(b*x+a)*sin(2*b*x+2*a)^3,x, algorithm=""giac"")","\frac{\cos\left(7 \, b x + 7 \, a\right)}{56 \, b} + \frac{\cos\left(5 \, b x + 5 \, a\right)}{40 \, b} - \frac{\cos\left(3 \, b x + 3 \, a\right)}{8 \, b} - \frac{3 \, \cos\left(b x + a\right)}{8 \, b}"," ",0,"1/56*cos(7*b*x + 7*a)/b + 1/40*cos(5*b*x + 5*a)/b - 1/8*cos(3*b*x + 3*a)/b - 3/8*cos(b*x + a)/b","A",0
134,1,40,0,0.455131," ","integrate(cos(b*x+a)*sin(2*b*x+2*a)^2,x, algorithm=""giac"")","-\frac{\sin\left(5 \, b x + 5 \, a\right)}{20 \, b} - \frac{\sin\left(3 \, b x + 3 \, a\right)}{12 \, b} + \frac{\sin\left(b x + a\right)}{2 \, b}"," ",0,"-1/20*sin(5*b*x + 5*a)/b - 1/12*sin(3*b*x + 3*a)/b + 1/2*sin(b*x + a)/b","A",0
135,1,26,0,0.277994," ","integrate(cos(b*x+a)*sin(2*b*x+2*a),x, algorithm=""giac"")","-\frac{\cos\left(3 \, b x + 3 \, a\right)}{6 \, b} - \frac{\cos\left(b x + a\right)}{2 \, b}"," ",0,"-1/6*cos(3*b*x + 3*a)/b - 1/2*cos(b*x + a)/b","A",0
136,1,16,0,0.223439," ","integrate(cos(b*x+a)/sin(2*b*x+2*a),x, algorithm=""giac"")","\frac{\log\left({\left| \tan\left(\frac{1}{2} \, b x + \frac{1}{2} \, a\right) \right|}\right)}{2 \, b}"," ",0,"1/2*log(abs(tan(1/2*b*x + 1/2*a)))/b","A",0
137,1,38,0,0.271287," ","integrate(cos(b*x+a)/sin(2*b*x+2*a)^2,x, algorithm=""giac"")","-\frac{\frac{2}{\sin\left(b x + a\right)} - \log\left({\left| \sin\left(b x + a\right) + 1 \right|}\right) + \log\left({\left| \sin\left(b x + a\right) - 1 \right|}\right)}{8 \, b}"," ",0,"-1/8*(2/sin(b*x + a) - log(abs(sin(b*x + a) + 1)) + log(abs(sin(b*x + a) - 1)))/b","A",0
138,1,140,0,0.411786," ","integrate(cos(b*x+a)/sin(2*b*x+2*a)^3,x, algorithm=""giac"")","\frac{\frac{\frac{14 \, {\left(\cos\left(b x + a\right) - 1\right)}}{\cos\left(b x + a\right) + 1} - \frac{3 \, {\left(\cos\left(b x + a\right) - 1\right)}^{2}}{{\left(\cos\left(b x + a\right) + 1\right)}^{2}} + 1}{\frac{\cos\left(b x + a\right) - 1}{\cos\left(b x + a\right) + 1} + \frac{{\left(\cos\left(b x + a\right) - 1\right)}^{2}}{{\left(\cos\left(b x + a\right) + 1\right)}^{2}}} - \frac{\cos\left(b x + a\right) - 1}{\cos\left(b x + a\right) + 1} + 6 \, \log\left(\frac{{\left| -\cos\left(b x + a\right) + 1 \right|}}{{\left| \cos\left(b x + a\right) + 1 \right|}}\right)}{64 \, b}"," ",0,"1/64*((14*(cos(b*x + a) - 1)/(cos(b*x + a) + 1) - 3*(cos(b*x + a) - 1)^2/(cos(b*x + a) + 1)^2 + 1)/((cos(b*x + a) - 1)/(cos(b*x + a) + 1) + (cos(b*x + a) - 1)^2/(cos(b*x + a) + 1)^2) - (cos(b*x + a) - 1)/(cos(b*x + a) + 1) + 6*log(abs(-cos(b*x + a) + 1)/abs(cos(b*x + a) + 1)))/b","B",0
139,1,72,0,0.436957," ","integrate(cos(b*x+a)/sin(2*b*x+2*a)^4,x, algorithm=""giac"")","-\frac{\frac{6 \, \sin\left(b x + a\right)}{\sin\left(b x + a\right)^{2} - 1} + \frac{4 \, {\left(6 \, \sin\left(b x + a\right)^{2} + 1\right)}}{\sin\left(b x + a\right)^{3}} - 15 \, \log\left({\left| \sin\left(b x + a\right) + 1 \right|}\right) + 15 \, \log\left({\left| \sin\left(b x + a\right) - 1 \right|}\right)}{192 \, b}"," ",0,"-1/192*(6*sin(b*x + a)/(sin(b*x + a)^2 - 1) + 4*(6*sin(b*x + a)^2 + 1)/sin(b*x + a)^3 - 15*log(abs(sin(b*x + a) + 1)) + 15*log(abs(sin(b*x + a) - 1)))/b","A",0
140,1,209,0,0.642542," ","integrate(cos(b*x+a)/sin(2*b*x+2*a)^5,x, algorithm=""giac"")","\frac{\frac{3 \, {\left(\frac{24 \, {\left(\cos\left(b x + a\right) - 1\right)}}{\cos\left(b x + a\right) + 1} - \frac{210 \, {\left(\cos\left(b x + a\right) - 1\right)}^{2}}{{\left(\cos\left(b x + a\right) + 1\right)}^{2}} - 1\right)} {\left(\cos\left(b x + a\right) + 1\right)}^{2}}{{\left(\cos\left(b x + a\right) - 1\right)}^{2}} - \frac{72 \, {\left(\cos\left(b x + a\right) - 1\right)}}{\cos\left(b x + a\right) + 1} + \frac{3 \, {\left(\cos\left(b x + a\right) - 1\right)}^{2}}{{\left(\cos\left(b x + a\right) + 1\right)}^{2}} + \frac{256 \, {\left(\frac{9 \, {\left(\cos\left(b x + a\right) - 1\right)}}{\cos\left(b x + a\right) + 1} + \frac{6 \, {\left(\cos\left(b x + a\right) - 1\right)}^{2}}{{\left(\cos\left(b x + a\right) + 1\right)}^{2}} + 5\right)}}{{\left(\frac{\cos\left(b x + a\right) - 1}{\cos\left(b x + a\right) + 1} + 1\right)}^{3}} + 420 \, \log\left(\frac{{\left| -\cos\left(b x + a\right) + 1 \right|}}{{\left| \cos\left(b x + a\right) + 1 \right|}}\right)}{6144 \, b}"," ",0,"1/6144*(3*(24*(cos(b*x + a) - 1)/(cos(b*x + a) + 1) - 210*(cos(b*x + a) - 1)^2/(cos(b*x + a) + 1)^2 - 1)*(cos(b*x + a) + 1)^2/(cos(b*x + a) - 1)^2 - 72*(cos(b*x + a) - 1)/(cos(b*x + a) + 1) + 3*(cos(b*x + a) - 1)^2/(cos(b*x + a) + 1)^2 + 256*(9*(cos(b*x + a) - 1)/(cos(b*x + a) + 1) + 6*(cos(b*x + a) - 1)^2/(cos(b*x + a) + 1)^2 + 5)/((cos(b*x + a) - 1)/(cos(b*x + a) + 1) + 1)^3 + 420*log(abs(-cos(b*x + a) + 1)/abs(cos(b*x + a) + 1)))/b","B",0
141,1,85,0,0.493260," ","integrate(cos(b*x+a)^2*sin(2*b*x+2*a)^5,x, algorithm=""giac"")","-\frac{\cos\left(12 \, b x + 12 \, a\right)}{768 \, b} - \frac{\cos\left(10 \, b x + 10 \, a\right)}{320 \, b} + \frac{\cos\left(8 \, b x + 8 \, a\right)}{128 \, b} + \frac{5 \, \cos\left(6 \, b x + 6 \, a\right)}{192 \, b} - \frac{5 \, \cos\left(4 \, b x + 4 \, a\right)}{256 \, b} - \frac{5 \, \cos\left(2 \, b x + 2 \, a\right)}{32 \, b}"," ",0,"-1/768*cos(12*b*x + 12*a)/b - 1/320*cos(10*b*x + 10*a)/b + 1/128*cos(8*b*x + 8*a)/b + 5/192*cos(6*b*x + 6*a)/b - 5/256*cos(4*b*x + 4*a)/b - 5/32*cos(2*b*x + 2*a)/b","B",0
142,1,74,0,0.398407," ","integrate(cos(b*x+a)^2*sin(2*b*x+2*a)^4,x, algorithm=""giac"")","\frac{3}{16} \, x + \frac{\sin\left(10 \, b x + 10 \, a\right)}{320 \, b} + \frac{\sin\left(8 \, b x + 8 \, a\right)}{128 \, b} - \frac{\sin\left(6 \, b x + 6 \, a\right)}{64 \, b} - \frac{\sin\left(4 \, b x + 4 \, a\right)}{16 \, b} + \frac{\sin\left(2 \, b x + 2 \, a\right)}{32 \, b}"," ",0,"3/16*x + 1/320*sin(10*b*x + 10*a)/b + 1/128*sin(8*b*x + 8*a)/b - 1/64*sin(6*b*x + 6*a)/b - 1/16*sin(4*b*x + 4*a)/b + 1/32*sin(2*b*x + 2*a)/b","A",0
143,1,57,0,0.319520," ","integrate(cos(b*x+a)^2*sin(2*b*x+2*a)^3,x, algorithm=""giac"")","\frac{\cos\left(8 \, b x + 8 \, a\right)}{128 \, b} + \frac{\cos\left(6 \, b x + 6 \, a\right)}{48 \, b} - \frac{\cos\left(4 \, b x + 4 \, a\right)}{32 \, b} - \frac{3 \, \cos\left(2 \, b x + 2 \, a\right)}{16 \, b}"," ",0,"1/128*cos(8*b*x + 8*a)/b + 1/48*cos(6*b*x + 6*a)/b - 1/32*cos(4*b*x + 4*a)/b - 3/16*cos(2*b*x + 2*a)/b","B",0
144,1,46,0,0.191460," ","integrate(cos(b*x+a)^2*sin(2*b*x+2*a)^2,x, algorithm=""giac"")","\frac{1}{4} \, x - \frac{\sin\left(6 \, b x + 6 \, a\right)}{48 \, b} - \frac{\sin\left(4 \, b x + 4 \, a\right)}{16 \, b} + \frac{\sin\left(2 \, b x + 2 \, a\right)}{16 \, b}"," ",0,"1/4*x - 1/48*sin(6*b*x + 6*a)/b - 1/16*sin(4*b*x + 4*a)/b + 1/16*sin(2*b*x + 2*a)/b","A",0
145,1,29,0,0.495965," ","integrate(cos(b*x+a)^2*sin(2*b*x+2*a),x, algorithm=""giac"")","-\frac{\cos\left(4 \, b x + 4 \, a\right)}{16 \, b} - \frac{\cos\left(2 \, b x + 2 \, a\right)}{4 \, b}"," ",0,"-1/16*cos(4*b*x + 4*a)/b - 1/4*cos(2*b*x + 2*a)/b","B",0
146,1,56,0,0.223812," ","integrate(cos(b*x+a)^2/sin(2*b*x+2*a),x, algorithm=""giac"")","\frac{\log\left(\frac{{\left| -\cos\left(b x + a\right) + 1 \right|}}{{\left| \cos\left(b x + a\right) + 1 \right|}}\right) - 2 \, \log\left({\left| -\frac{\cos\left(b x + a\right) - 1}{\cos\left(b x + a\right) + 1} + 1 \right|}\right)}{4 \, b}"," ",0,"1/4*(log(abs(-cos(b*x + a) + 1)/abs(cos(b*x + a) + 1)) - 2*log(abs(-(cos(b*x + a) - 1)/(cos(b*x + a) + 1) + 1)))/b","B",0
147,1,13,0,0.229628," ","integrate(cos(b*x+a)^2/sin(2*b*x+2*a)^2,x, algorithm=""giac"")","-\frac{1}{4 \, b \tan\left(b x + a\right)}"," ",0,"-1/4/(b*tan(b*x + a))","A",0
148,1,119,0,0.360514," ","integrate(cos(b*x+a)^2/sin(2*b*x+2*a)^3,x, algorithm=""giac"")","-\frac{\frac{{\left(\frac{4 \, {\left(\cos\left(b x + a\right) - 1\right)}}{\cos\left(b x + a\right) + 1} - 1\right)} {\left(\cos\left(b x + a\right) + 1\right)}}{\cos\left(b x + a\right) - 1} - \frac{\cos\left(b x + a\right) - 1}{\cos\left(b x + a\right) + 1} - 4 \, \log\left(\frac{{\left| -\cos\left(b x + a\right) + 1 \right|}}{{\left| \cos\left(b x + a\right) + 1 \right|}}\right) + 8 \, \log\left({\left| -\frac{\cos\left(b x + a\right) - 1}{\cos\left(b x + a\right) + 1} - 1 \right|}\right)}{64 \, b}"," ",0,"-1/64*((4*(cos(b*x + a) - 1)/(cos(b*x + a) + 1) - 1)*(cos(b*x + a) + 1)/(cos(b*x + a) - 1) - (cos(b*x + a) - 1)/(cos(b*x + a) + 1) - 4*log(abs(-cos(b*x + a) + 1)/abs(cos(b*x + a) + 1)) + 8*log(abs(-(cos(b*x + a) - 1)/(cos(b*x + a) + 1) - 1)))/b","B",0
149,1,35,0,0.495426," ","integrate(cos(b*x+a)^2/sin(2*b*x+2*a)^4,x, algorithm=""giac"")","-\frac{\frac{6 \, \tan\left(b x + a\right)^{2} + 1}{\tan\left(b x + a\right)^{3}} - 3 \, \tan\left(b x + a\right)}{48 \, b}"," ",0,"-1/48*((6*tan(b*x + a)^2 + 1)/tan(b*x + a)^3 - 3*tan(b*x + a))/b","A",0
150,1,232,0,0.739410," ","integrate(cos(b*x+a)^2/sin(2*b*x+2*a)^5,x, algorithm=""giac"")","\frac{\frac{20 \, {\left(\cos\left(b x + a\right) - 1\right)}}{\cos\left(b x + a\right) + 1} - \frac{{\left(\cos\left(b x + a\right) - 1\right)}^{2}}{{\left(\cos\left(b x + a\right) + 1\right)}^{2}} + \frac{\frac{18 \, {\left(\cos\left(b x + a\right) - 1\right)}}{\cos\left(b x + a\right) + 1} + \frac{111 \, {\left(\cos\left(b x + a\right) - 1\right)}^{2}}{{\left(\cos\left(b x + a\right) + 1\right)}^{2}} + \frac{36 \, {\left(\cos\left(b x + a\right) - 1\right)}^{3}}{{\left(\cos\left(b x + a\right) + 1\right)}^{3}} + \frac{72 \, {\left(\cos\left(b x + a\right) - 1\right)}^{4}}{{\left(\cos\left(b x + a\right) + 1\right)}^{4}} - 1}{{\left(\frac{\cos\left(b x + a\right) - 1}{\cos\left(b x + a\right) + 1} + \frac{{\left(\cos\left(b x + a\right) - 1\right)}^{2}}{{\left(\cos\left(b x + a\right) + 1\right)}^{2}}\right)}^{2}} + 96 \, \log\left(\frac{{\left| -\cos\left(b x + a\right) + 1 \right|}}{{\left| \cos\left(b x + a\right) + 1 \right|}}\right) - 192 \, \log\left({\left| -\frac{\cos\left(b x + a\right) - 1}{\cos\left(b x + a\right) + 1} - 1 \right|}\right)}{2048 \, b}"," ",0,"1/2048*(20*(cos(b*x + a) - 1)/(cos(b*x + a) + 1) - (cos(b*x + a) - 1)^2/(cos(b*x + a) + 1)^2 + (18*(cos(b*x + a) - 1)/(cos(b*x + a) + 1) + 111*(cos(b*x + a) - 1)^2/(cos(b*x + a) + 1)^2 + 36*(cos(b*x + a) - 1)^3/(cos(b*x + a) + 1)^3 + 72*(cos(b*x + a) - 1)^4/(cos(b*x + a) + 1)^4 - 1)/((cos(b*x + a) - 1)/(cos(b*x + a) + 1) + (cos(b*x + a) - 1)^2/(cos(b*x + a) + 1)^2)^2 + 96*log(abs(-cos(b*x + a) + 1)/abs(cos(b*x + a) + 1)) - 192*log(abs(-(cos(b*x + a) - 1)/(cos(b*x + a) + 1) - 1)))/b","B",0
151,1,96,0,0.597578," ","integrate(cos(b*x+a)^3*sin(2*b*x+2*a)^5,x, algorithm=""giac"")","-\frac{\cos\left(13 \, b x + 13 \, a\right)}{1664 \, b} - \frac{3 \, \cos\left(11 \, b x + 11 \, a\right)}{1408 \, b} + \frac{\cos\left(9 \, b x + 9 \, a\right)}{576 \, b} + \frac{\cos\left(7 \, b x + 7 \, a\right)}{64 \, b} + \frac{\cos\left(5 \, b x + 5 \, a\right)}{128 \, b} - \frac{25 \, \cos\left(3 \, b x + 3 \, a\right)}{384 \, b} - \frac{5 \, \cos\left(b x + a\right)}{32 \, b}"," ",0,"-1/1664*cos(13*b*x + 13*a)/b - 3/1408*cos(11*b*x + 11*a)/b + 1/576*cos(9*b*x + 9*a)/b + 1/64*cos(7*b*x + 7*a)/b + 1/128*cos(5*b*x + 5*a)/b - 25/384*cos(3*b*x + 3*a)/b - 5/32*cos(b*x + a)/b","B",0
152,1,82,0,0.370559," ","integrate(cos(b*x+a)^3*sin(2*b*x+2*a)^4,x, algorithm=""giac"")","\frac{\sin\left(11 \, b x + 11 \, a\right)}{704 \, b} + \frac{\sin\left(9 \, b x + 9 \, a\right)}{192 \, b} - \frac{\sin\left(7 \, b x + 7 \, a\right)}{448 \, b} - \frac{11 \, \sin\left(5 \, b x + 5 \, a\right)}{320 \, b} - \frac{\sin\left(3 \, b x + 3 \, a\right)}{32 \, b} + \frac{7 \, \sin\left(b x + a\right)}{32 \, b}"," ",0,"1/704*sin(11*b*x + 11*a)/b + 1/192*sin(9*b*x + 9*a)/b - 1/448*sin(7*b*x + 7*a)/b - 11/320*sin(5*b*x + 5*a)/b - 1/32*sin(3*b*x + 3*a)/b + 7/32*sin(b*x + a)/b","A",0
153,1,54,0,0.374132," ","integrate(cos(b*x+a)^3*sin(2*b*x+2*a)^3,x, algorithm=""giac"")","\frac{\cos\left(9 \, b x + 9 \, a\right)}{288 \, b} + \frac{3 \, \cos\left(7 \, b x + 7 \, a\right)}{224 \, b} - \frac{\cos\left(3 \, b x + 3 \, a\right)}{12 \, b} - \frac{3 \, \cos\left(b x + a\right)}{16 \, b}"," ",0,"1/288*cos(9*b*x + 9*a)/b + 3/224*cos(7*b*x + 7*a)/b - 1/12*cos(3*b*x + 3*a)/b - 3/16*cos(b*x + a)/b","A",0
154,1,54,0,0.226243," ","integrate(cos(b*x+a)^3*sin(2*b*x+2*a)^2,x, algorithm=""giac"")","-\frac{\sin\left(7 \, b x + 7 \, a\right)}{112 \, b} - \frac{3 \, \sin\left(5 \, b x + 5 \, a\right)}{80 \, b} - \frac{\sin\left(3 \, b x + 3 \, a\right)}{48 \, b} + \frac{5 \, \sin\left(b x + a\right)}{16 \, b}"," ",0,"-1/112*sin(7*b*x + 7*a)/b - 3/80*sin(5*b*x + 5*a)/b - 1/48*sin(3*b*x + 3*a)/b + 5/16*sin(b*x + a)/b","A",0
155,1,40,0,0.177937," ","integrate(cos(b*x+a)^3*sin(2*b*x+2*a),x, algorithm=""giac"")","-\frac{\cos\left(5 \, b x + 5 \, a\right)}{40 \, b} - \frac{\cos\left(3 \, b x + 3 \, a\right)}{8 \, b} - \frac{\cos\left(b x + a\right)}{4 \, b}"," ",0,"-1/40*cos(5*b*x + 5*a)/b - 1/8*cos(3*b*x + 3*a)/b - 1/4*cos(b*x + a)/b","B",0
156,1,57,0,0.691174," ","integrate(cos(b*x+a)^3/sin(2*b*x+2*a),x, algorithm=""giac"")","-\frac{\frac{4}{\frac{\cos\left(b x + a\right) - 1}{\cos\left(b x + a\right) + 1} - 1} - \log\left(\frac{{\left| -\cos\left(b x + a\right) + 1 \right|}}{{\left| \cos\left(b x + a\right) + 1 \right|}}\right)}{4 \, b}"," ",0,"-1/4*(4/((cos(b*x + a) - 1)/(cos(b*x + a) + 1) - 1) - log(abs(-cos(b*x + a) + 1)/abs(cos(b*x + a) + 1)))/b","B",0
157,1,13,0,0.249636," ","integrate(cos(b*x+a)^3/sin(2*b*x+2*a)^2,x, algorithm=""giac"")","-\frac{1}{4 \, b \sin\left(b x + a\right)}"," ",0,"-1/4/(b*sin(b*x + a))","A",0
158,1,92,0,0.657420," ","integrate(cos(b*x+a)^3/sin(2*b*x+2*a)^3,x, algorithm=""giac"")","-\frac{\frac{{\left(\frac{2 \, {\left(\cos\left(b x + a\right) - 1\right)}}{\cos\left(b x + a\right) + 1} - 1\right)} {\left(\cos\left(b x + a\right) + 1\right)}}{\cos\left(b x + a\right) - 1} + \frac{\cos\left(b x + a\right) - 1}{\cos\left(b x + a\right) + 1} - 2 \, \log\left(\frac{{\left| -\cos\left(b x + a\right) + 1 \right|}}{{\left| \cos\left(b x + a\right) + 1 \right|}}\right)}{64 \, b}"," ",0,"-1/64*((2*(cos(b*x + a) - 1)/(cos(b*x + a) + 1) - 1)*(cos(b*x + a) + 1)/(cos(b*x + a) - 1) + (cos(b*x + a) - 1)/(cos(b*x + a) + 1) - 2*log(abs(-cos(b*x + a) + 1)/abs(cos(b*x + a) + 1)))/b","B",0
159,1,52,0,0.928525," ","integrate(cos(b*x+a)^3/sin(2*b*x+2*a)^4,x, algorithm=""giac"")","-\frac{\frac{2 \, {\left(3 \, \sin\left(b x + a\right)^{2} + 1\right)}}{\sin\left(b x + a\right)^{3}} - 3 \, \log\left({\left| \sin\left(b x + a\right) + 1 \right|}\right) + 3 \, \log\left({\left| \sin\left(b x + a\right) - 1 \right|}\right)}{96 \, b}"," ",0,"-1/96*(2*(3*sin(b*x + a)^2 + 1)/sin(b*x + a)^3 - 3*log(abs(sin(b*x + a) + 1)) + 3*log(abs(sin(b*x + a) - 1)))/b","A",0
160,1,163,0,0.824538," ","integrate(cos(b*x+a)^3/sin(2*b*x+2*a)^5,x, algorithm=""giac"")","\frac{\frac{{\left(\frac{16 \, {\left(\cos\left(b x + a\right) - 1\right)}}{\cos\left(b x + a\right) + 1} - \frac{90 \, {\left(\cos\left(b x + a\right) - 1\right)}^{2}}{{\left(\cos\left(b x + a\right) + 1\right)}^{2}} - 1\right)} {\left(\cos\left(b x + a\right) + 1\right)}^{2}}{{\left(\cos\left(b x + a\right) - 1\right)}^{2}} - \frac{16 \, {\left(\cos\left(b x + a\right) - 1\right)}}{\cos\left(b x + a\right) + 1} + \frac{{\left(\cos\left(b x + a\right) - 1\right)}^{2}}{{\left(\cos\left(b x + a\right) + 1\right)}^{2}} + \frac{128}{\frac{\cos\left(b x + a\right) - 1}{\cos\left(b x + a\right) + 1} + 1} + 60 \, \log\left(\frac{{\left| -\cos\left(b x + a\right) + 1 \right|}}{{\left| \cos\left(b x + a\right) + 1 \right|}}\right)}{2048 \, b}"," ",0,"1/2048*((16*(cos(b*x + a) - 1)/(cos(b*x + a) + 1) - 90*(cos(b*x + a) - 1)^2/(cos(b*x + a) + 1)^2 - 1)*(cos(b*x + a) + 1)^2/(cos(b*x + a) - 1)^2 - 16*(cos(b*x + a) - 1)/(cos(b*x + a) + 1) + (cos(b*x + a) - 1)^2/(cos(b*x + a) + 1)^2 + 128/((cos(b*x + a) - 1)/(cos(b*x + a) + 1) + 1) + 60*log(abs(-cos(b*x + a) + 1)/abs(cos(b*x + a) + 1)))/b","B",0
161,-1,0,0,0.000000," ","integrate(cos(b*x+a)*sin(2*b*x+2*a)^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
162,0,0,0,0.000000," ","integrate(cos(b*x+a)*sin(2*b*x+2*a)^(3/2),x, algorithm=""giac"")","\int \cos\left(b x + a\right) \sin\left(2 \, b x + 2 \, a\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate(cos(b*x + a)*sin(2*b*x + 2*a)^(3/2), x)","F",0
163,0,0,0,0.000000," ","integrate(cos(b*x+a)*sin(2*b*x+2*a)^(1/2),x, algorithm=""giac"")","\int \cos\left(b x + a\right) \sqrt{\sin\left(2 \, b x + 2 \, a\right)}\,{d x}"," ",0,"integrate(cos(b*x + a)*sqrt(sin(2*b*x + 2*a)), x)","F",0
164,0,0,0,0.000000," ","integrate(cos(b*x+a)/sin(2*b*x+2*a)^(1/2),x, algorithm=""giac"")","\int \frac{\cos\left(b x + a\right)}{\sqrt{\sin\left(2 \, b x + 2 \, a\right)}}\,{d x}"," ",0,"integrate(cos(b*x + a)/sqrt(sin(2*b*x + 2*a)), x)","F",0
165,0,0,0,0.000000," ","integrate(cos(b*x+a)/sin(2*b*x+2*a)^(3/2),x, algorithm=""giac"")","\int \frac{\cos\left(b x + a\right)}{\sin\left(2 \, b x + 2 \, a\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(cos(b*x + a)/sin(2*b*x + 2*a)^(3/2), x)","F",0
166,0,0,0,0.000000," ","integrate(cos(b*x+a)/sin(2*b*x+2*a)^(5/2),x, algorithm=""giac"")","\int \frac{\cos\left(b x + a\right)}{\sin\left(2 \, b x + 2 \, a\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(cos(b*x + a)/sin(2*b*x + 2*a)^(5/2), x)","F",0
167,0,0,0,0.000000," ","integrate(cos(b*x+a)/sin(2*b*x+2*a)^(7/2),x, algorithm=""giac"")","\int \frac{\cos\left(b x + a\right)}{\sin\left(2 \, b x + 2 \, a\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(cos(b*x + a)/sin(2*b*x + 2*a)^(7/2), x)","F",0
168,0,0,0,0.000000," ","integrate(cos(b*x+a)/sin(2*b*x+2*a)^(9/2),x, algorithm=""giac"")","\int \frac{\cos\left(b x + a\right)}{\sin\left(2 \, b x + 2 \, a\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate(cos(b*x + a)/sin(2*b*x + 2*a)^(9/2), x)","F",0
169,-1,0,0,0.000000," ","integrate(cos(b*x+a)^2*sin(2*b*x+2*a)^(7/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
170,-1,0,0,0.000000," ","integrate(cos(b*x+a)^2*sin(2*b*x+2*a)^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
171,-1,0,0,0.000000," ","integrate(cos(b*x+a)^2*sin(2*b*x+2*a)^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
172,0,0,0,0.000000," ","integrate(cos(b*x+a)^2*sin(2*b*x+2*a)^(1/2),x, algorithm=""giac"")","\int \cos\left(b x + a\right)^{2} \sqrt{\sin\left(2 \, b x + 2 \, a\right)}\,{d x}"," ",0,"integrate(cos(b*x + a)^2*sqrt(sin(2*b*x + 2*a)), x)","F",0
173,0,0,0,0.000000," ","integrate(cos(b*x+a)^2/sin(2*b*x+2*a)^(1/2),x, algorithm=""giac"")","\int \frac{\cos\left(b x + a\right)^{2}}{\sqrt{\sin\left(2 \, b x + 2 \, a\right)}}\,{d x}"," ",0,"integrate(cos(b*x + a)^2/sqrt(sin(2*b*x + 2*a)), x)","F",0
174,0,0,0,0.000000," ","integrate(cos(b*x+a)^2/sin(2*b*x+2*a)^(3/2),x, algorithm=""giac"")","\int \frac{\cos\left(b x + a\right)^{2}}{\sin\left(2 \, b x + 2 \, a\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(cos(b*x + a)^2/sin(2*b*x + 2*a)^(3/2), x)","F",0
175,0,0,0,0.000000," ","integrate(cos(b*x+a)^2/sin(2*b*x+2*a)^(5/2),x, algorithm=""giac"")","\int \frac{\cos\left(b x + a\right)^{2}}{\sin\left(2 \, b x + 2 \, a\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(cos(b*x + a)^2/sin(2*b*x + 2*a)^(5/2), x)","F",0
176,0,0,0,0.000000," ","integrate(cos(b*x+a)^2/sin(2*b*x+2*a)^(7/2),x, algorithm=""giac"")","\int \frac{\cos\left(b x + a\right)^{2}}{\sin\left(2 \, b x + 2 \, a\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(cos(b*x + a)^2/sin(2*b*x + 2*a)^(7/2), x)","F",0
177,-1,0,0,0.000000," ","integrate(cos(b*x+a)^3*sin(2*b*x+2*a)^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
178,-2,0,0,0.000000," ","integrate(cos(b*x+a)^3*sin(2*b*x+2*a)^(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:ext_reduce Error: Bad Argument TypeEvaluation time: 0.48Done","F(-2)",0
179,0,0,0,0.000000," ","integrate(cos(b*x+a)^3/sin(2*b*x+2*a)^(1/2),x, algorithm=""giac"")","\int \frac{\cos\left(b x + a\right)^{3}}{\sqrt{\sin\left(2 \, b x + 2 \, a\right)}}\,{d x}"," ",0,"integrate(cos(b*x + a)^3/sqrt(sin(2*b*x + 2*a)), x)","F",0
180,0,0,0,0.000000," ","integrate(cos(b*x+a)^3/sin(2*b*x+2*a)^(3/2),x, algorithm=""giac"")","\int \frac{\cos\left(b x + a\right)^{3}}{\sin\left(2 \, b x + 2 \, a\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(cos(b*x + a)^3/sin(2*b*x + 2*a)^(3/2), x)","F",0
181,0,0,0,0.000000," ","integrate(cos(b*x+a)^3/sin(2*b*x+2*a)^(5/2),x, algorithm=""giac"")","\int \frac{\cos\left(b x + a\right)^{3}}{\sin\left(2 \, b x + 2 \, a\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(cos(b*x + a)^3/sin(2*b*x + 2*a)^(5/2), x)","F",0
182,0,0,0,0.000000," ","integrate(cos(b*x+a)^3/sin(2*b*x+2*a)^(7/2),x, algorithm=""giac"")","\int \frac{\cos\left(b x + a\right)^{3}}{\sin\left(2 \, b x + 2 \, a\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(cos(b*x + a)^3/sin(2*b*x + 2*a)^(7/2), x)","F",0
183,0,0,0,0.000000," ","integrate(cos(b*x+a)^3/sin(2*b*x+2*a)^(9/2),x, algorithm=""giac"")","\int \frac{\cos\left(b x + a\right)^{3}}{\sin\left(2 \, b x + 2 \, a\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate(cos(b*x + a)^3/sin(2*b*x + 2*a)^(9/2), x)","F",0
184,0,0,0,0.000000," ","integrate(cos(b*x+a)^3/sin(2*b*x+2*a)^(11/2),x, algorithm=""giac"")","\int \frac{\cos\left(b x + a\right)^{3}}{\sin\left(2 \, b x + 2 \, a\right)^{\frac{11}{2}}}\,{d x}"," ",0,"integrate(cos(b*x + a)^3/sin(2*b*x + 2*a)^(11/2), x)","F",0
185,0,0,0,0.000000," ","integrate(cos(x)/sin(2*x)^(1/2),x, algorithm=""giac"")","\int \frac{\cos\left(x\right)}{\sqrt{\sin\left(2 \, x\right)}}\,{d x}"," ",0,"integrate(cos(x)/sqrt(sin(2*x)), x)","F",0
186,0,0,0,0.000000," ","integrate(csc(x)*sin(2*x)^(1/2),x, algorithm=""giac"")","\int \csc\left(x\right) \sqrt{\sin\left(2 \, x\right)}\,{d x}"," ",0,"integrate(csc(x)*sqrt(sin(2*x)), x)","F",0
187,0,0,0,0.000000," ","integrate(cos(b*x+a)^3*sin(2*b*x+2*a)^m,x, algorithm=""giac"")","\int \sin\left(2 \, b x + 2 \, a\right)^{m} \cos\left(b x + a\right)^{3}\,{d x}"," ",0,"integrate(sin(2*b*x + 2*a)^m*cos(b*x + a)^3, x)","F",0
188,0,0,0,0.000000," ","integrate(cos(b*x+a)^2*sin(2*b*x+2*a)^m,x, algorithm=""giac"")","\int \sin\left(2 \, b x + 2 \, a\right)^{m} \cos\left(b x + a\right)^{2}\,{d x}"," ",0,"integrate(sin(2*b*x + 2*a)^m*cos(b*x + a)^2, x)","F",0
189,0,0,0,0.000000," ","integrate(cos(b*x+a)*sin(2*b*x+2*a)^m,x, algorithm=""giac"")","\int \sin\left(2 \, b x + 2 \, a\right)^{m} \cos\left(b x + a\right)\,{d x}"," ",0,"integrate(sin(2*b*x + 2*a)^m*cos(b*x + a), x)","F",0
190,1,68,0,0.638342," ","integrate(cos(b*x+a)^2*sin(b*x+a)^3*sin(2*b*x+2*a)^2,x, algorithm=""giac"")","-\frac{\cos\left(9 \, b x + 9 \, a\right)}{576 \, b} + \frac{\cos\left(7 \, b x + 7 \, a\right)}{448 \, b} + \frac{\cos\left(5 \, b x + 5 \, a\right)}{80 \, b} - \frac{\cos\left(3 \, b x + 3 \, a\right)}{48 \, b} - \frac{3 \, \cos\left(b x + a\right)}{32 \, b}"," ",0,"-1/576*cos(9*b*x + 9*a)/b + 1/448*cos(7*b*x + 7*a)/b + 1/80*cos(5*b*x + 5*a)/b - 1/48*cos(3*b*x + 3*a)/b - 3/32*cos(b*x + a)/b","A",0
191,0,0,0,0.000000," ","integrate(sin(b*x+a)*sin(d*x+c)^n,x, algorithm=""giac"")","\int \sin\left(d x + c\right)^{n} \sin\left(b x + a\right)\,{d x}"," ",0,"integrate(sin(d*x + c)^n*sin(b*x + a), x)","F",0
192,1,84,0,0.745098," ","integrate(sin(b*x+a)*sin(d*x+c)^3,x, algorithm=""giac"")","\frac{\sin\left(b x + 3 \, d x + a + 3 \, c\right)}{8 \, {\left(b + 3 \, d\right)}} - \frac{3 \, \sin\left(b x + d x + a + c\right)}{8 \, {\left(b + d\right)}} + \frac{3 \, \sin\left(b x - d x + a - c\right)}{8 \, {\left(b - d\right)}} - \frac{\sin\left(b x - 3 \, d x + a - 3 \, c\right)}{8 \, {\left(b - 3 \, d\right)}}"," ",0,"1/8*sin(b*x + 3*d*x + a + 3*c)/(b + 3*d) - 3/8*sin(b*x + d*x + a + c)/(b + d) + 3/8*sin(b*x - d*x + a - c)/(b - d) - 1/8*sin(b*x - 3*d*x + a - 3*c)/(b - 3*d)","A",0
193,1,56,0,0.187669," ","integrate(sin(b*x+a)*sin(d*x+c)^2,x, algorithm=""giac"")","\frac{\cos\left(b x + 2 \, d x + a + 2 \, c\right)}{4 \, {\left(b + 2 \, d\right)}} + \frac{\cos\left(b x - 2 \, d x + a - 2 \, c\right)}{4 \, {\left(b - 2 \, d\right)}} - \frac{\cos\left(b x + a\right)}{2 \, b}"," ",0,"1/4*cos(b*x + 2*d*x + a + 2*c)/(b + 2*d) + 1/4*cos(b*x - 2*d*x + a - 2*c)/(b - 2*d) - 1/2*cos(b*x + a)/b","A",0
194,1,40,0,0.363092," ","integrate(sin(b*x+a)*sin(d*x+c),x, algorithm=""giac"")","-\frac{\sin\left(b x + d x + a + c\right)}{2 \, {\left(b + d\right)}} + \frac{\sin\left(b x - d x + a - c\right)}{2 \, {\left(b - d\right)}}"," ",0,"-1/2*sin(b*x + d*x + a + c)/(b + d) + 1/2*sin(b*x - d*x + a - c)/(b - d)","A",0
195,-2,0,0,0.000000," ","integrate(csc(b*x+c)*sin(b*x+a),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)2/b*((tan(a/2)^2*tan(c/2)-tan(a/2)*tan(c/2)^2+tan(a/2)-tan(c/2))/(tan(a/2)^2*tan(c/2)^2+tan(a/2)^2+tan(c/2)^2+1)*ln(abs(tan((b*x+c)/2)))+(-tan(a/2)^2*tan(c/2)+tan(a/2)*tan(c/2)^2-tan(a/2)+tan(c/2))/(tan(a/2)^2*tan(c/2)^2+tan(a/2)^2+tan(c/2)^2+1)*ln(tan((b*x+c)/2)^2+1)+(2*tan(a/2)^2*tan(c/2)^2-2*tan(a/2)^2+8*tan(a/2)*tan(c/2)-2*tan(c/2)^2+2)*1/2/(tan(a/2)^2*tan(c/2)^2+tan(a/2)^2+tan(c/2)^2+1)*(b*x+c)/2)","F(-2)",0
196,-2,0,0,0.000000," ","integrate(csc(b*x+c)^2*sin(b*x+a),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)2/b*((-tan((b*x+c)/2)*tan(a/2)^2*tan(c/2)+tan((b*x+c)/2)*tan(a/2)*tan(c/2)^2-tan((b*x+c)/2)*tan(a/2)+tan((b*x+c)/2)*tan(c/2))/(2*tan(a/2)^2*tan(c/2)^2+2*tan(a/2)^2+2*tan(c/2)^2+2)+(-tan((b*x+c)/2)*tan(a/2)^2*tan(c/2)^2+tan((b*x+c)/2)*tan(a/2)^2-4*tan((b*x+c)/2)*tan(a/2)*tan(c/2)+tan((b*x+c)/2)*tan(c/2)^2-tan((b*x+c)/2)-tan(a/2)^2*tan(c/2)+tan(a/2)*tan(c/2)^2-tan(a/2)+tan(c/2))/(2*tan(a/2)^2*tan(c/2)^2+2*tan(a/2)^2+2*tan(c/2)^2+2)/tan((b*x+c)/2)+(tan(a/2)^2*tan(c/2)^2-tan(a/2)^2+4*tan(a/2)*tan(c/2)-tan(c/2)^2+1)/(2*tan(a/2)^2*tan(c/2)^2+2*tan(a/2)^2+2*tan(c/2)^2+2)*ln(abs(tan((b*x+c)/2))))","F(-2)",0
197,1,145,0,0.214907," ","integrate(csc(b*x+c)^3*sin(b*x+a),x, algorithm=""giac"")","-\frac{\tan\left(b x + c\right) \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - \tan\left(b x + c\right) \tan\left(\frac{1}{2} \, a\right)^{2} + 4 \, \tan\left(b x + c\right) \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{1}{2} \, c\right) + \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, c\right) - \tan\left(b x + c\right) \tan\left(\frac{1}{2} \, c\right)^{2} - \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(b x + c\right) + \tan\left(\frac{1}{2} \, a\right) - \tan\left(\frac{1}{2} \, c\right)}{{\left(\tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, a\right)^{2} + \tan\left(\frac{1}{2} \, c\right)^{2} + 1\right)} b \tan\left(b x + c\right)^{2}}"," ",0,"-(tan(b*x + c)*tan(1/2*a)^2*tan(1/2*c)^2 - tan(b*x + c)*tan(1/2*a)^2 + 4*tan(b*x + c)*tan(1/2*a)*tan(1/2*c) + tan(1/2*a)^2*tan(1/2*c) - tan(b*x + c)*tan(1/2*c)^2 - tan(1/2*a)*tan(1/2*c)^2 + tan(b*x + c) + tan(1/2*a) - tan(1/2*c))/((tan(1/2*a)^2*tan(1/2*c)^2 + tan(1/2*a)^2 + tan(1/2*c)^2 + 1)*b*tan(b*x + c)^2)","B",0
198,-2,0,0,0.000000," ","integrate(csc(b*x+c)^4*sin(b*x+a),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)2/b*((-64/3*tan((b*x+c)/2)^3*tan(a/2)^6*tan(c/2)^5-128/3*tan((b*x+c)/2)^3*tan(a/2)^6*tan(c/2)^3-64/3*tan((b*x+c)/2)^3*tan(a/2)^6*tan(c/2)+64/3*tan((b*x+c)/2)^3*tan(a/2)^5*tan(c/2)^6+64/3*tan((b*x+c)/2)^3*tan(a/2)^5*tan(c/2)^4-64/3*tan((b*x+c)/2)^3*tan(a/2)^5*tan(c/2)^2-64/3*tan((b*x+c)/2)^3*tan(a/2)^5-64/3*tan((b*x+c)/2)^3*tan(a/2)^4*tan(c/2)^5-128/3*tan((b*x+c)/2)^3*tan(a/2)^4*tan(c/2)^3-64/3*tan((b*x+c)/2)^3*tan(a/2)^4*tan(c/2)+128/3*tan((b*x+c)/2)^3*tan(a/2)^3*tan(c/2)^6+128/3*tan((b*x+c)/2)^3*tan(a/2)^3*tan(c/2)^4-128/3*tan((b*x+c)/2)^3*tan(a/2)^3*tan(c/2)^2-128/3*tan((b*x+c)/2)^3*tan(a/2)^3+64/3*tan((b*x+c)/2)^3*tan(a/2)^2*tan(c/2)^5+128/3*tan((b*x+c)/2)^3*tan(a/2)^2*tan(c/2)^3+64/3*tan((b*x+c)/2)^3*tan(a/2)^2*tan(c/2)+64/3*tan((b*x+c)/2)^3*tan(a/2)*tan(c/2)^6+64/3*tan((b*x+c)/2)^3*tan(a/2)*tan(c/2)^4-64/3*tan((b*x+c)/2)^3*tan(a/2)*tan(c/2)^2-64/3*tan((b*x+c)/2)^3*tan(a/2)+64/3*tan((b*x+c)/2)^3*tan(c/2)^5+128/3*tan((b*x+c)/2)^3*tan(c/2)^3+64/3*tan((b*x+c)/2)^3*tan(c/2)+32*tan((b*x+c)/2)^2*tan(a/2)^6*tan(c/2)^6+32*tan((b*x+c)/2)^2*tan(a/2)^6*tan(c/2)^4-32*tan((b*x+c)/2)^2*tan(a/2)^6*tan(c/2)^2-32*tan((b*x+c)/2)^2*tan(a/2)^6+128*tan((b*x+c)/2)^2*tan(a/2)^5*tan(c/2)^5+256*tan((b*x+c)/2)^2*tan(a/2)^5*tan(c/2)^3+128*tan((b*x+c)/2)^2*tan(a/2)^5*tan(c/2)+32*tan((b*x+c)/2)^2*tan(a/2)^4*tan(c/2)^6+32*tan((b*x+c)/2)^2*tan(a/2)^4*tan(c/2)^4-32*tan((b*x+c)/2)^2*tan(a/2)^4*tan(c/2)^2-32*tan((b*x+c)/2)^2*tan(a/2)^4+256*tan((b*x+c)/2)^2*tan(a/2)^3*tan(c/2)^5+512*tan((b*x+c)/2)^2*tan(a/2)^3*tan(c/2)^3+256*tan((b*x+c)/2)^2*tan(a/2)^3*tan(c/2)-32*tan((b*x+c)/2)^2*tan(a/2)^2*tan(c/2)^6-32*tan((b*x+c)/2)^2*tan(a/2)^2*tan(c/2)^4+32*tan((b*x+c)/2)^2*tan(a/2)^2*tan(c/2)^2+32*tan((b*x+c)/2)^2*tan(a/2)^2+128*tan((b*x+c)/2)^2*tan(a/2)*tan(c/2)^5+256*tan((b*x+c)/2)^2*tan(a/2)*tan(c/2)^3+128*tan((b*x+c)/2)^2*tan(a/2)*tan(c/2)-32*tan((b*x+c)/2)^2*tan(c/2)^6-32*tan((b*x+c)/2)^2*tan(c/2)^4+32*tan((b*x+c)/2)^2*tan(c/2)^2+32*tan((b*x+c)/2)^2-64*tan((b*x+c)/2)*tan(a/2)^6*tan(c/2)^5-128*tan((b*x+c)/2)*tan(a/2)^6*tan(c/2)^3-64*tan((b*x+c)/2)*tan(a/2)^6*tan(c/2)+64*tan((b*x+c)/2)*tan(a/2)^5*tan(c/2)^6+64*tan((b*x+c)/2)*tan(a/2)^5*tan(c/2)^4-64*tan((b*x+c)/2)*tan(a/2)^5*tan(c/2)^2-64*tan((b*x+c)/2)*tan(a/2)^5-64*tan((b*x+c)/2)*tan(a/2)^4*tan(c/2)^5-128*tan((b*x+c)/2)*tan(a/2)^4*tan(c/2)^3-64*tan((b*x+c)/2)*tan(a/2)^4*tan(c/2)+128*tan((b*x+c)/2)*tan(a/2)^3*tan(c/2)^6+128*tan((b*x+c)/2)*tan(a/2)^3*tan(c/2)^4-128*tan((b*x+c)/2)*tan(a/2)^3*tan(c/2)^2-128*tan((b*x+c)/2)*tan(a/2)^3+64*tan((b*x+c)/2)*tan(a/2)^2*tan(c/2)^5+128*tan((b*x+c)/2)*tan(a/2)^2*tan(c/2)^3+64*tan((b*x+c)/2)*tan(a/2)^2*tan(c/2)+64*tan((b*x+c)/2)*tan(a/2)*tan(c/2)^6+64*tan((b*x+c)/2)*tan(a/2)*tan(c/2)^4-64*tan((b*x+c)/2)*tan(a/2)*tan(c/2)^2-64*tan((b*x+c)/2)*tan(a/2)+64*tan((b*x+c)/2)*tan(c/2)^5+128*tan((b*x+c)/2)*tan(c/2)^3+64*tan((b*x+c)/2)*tan(c/2))/(512*tan(a/2)^6*tan(c/2)^6+1536*tan(a/2)^6*tan(c/2)^4+1536*tan(a/2)^6*tan(c/2)^2+512*tan(a/2)^6+1536*tan(a/2)^4*tan(c/2)^6+4608*tan(a/2)^4*tan(c/2)^4+4608*tan(a/2)^4*tan(c/2)^2+1536*tan(a/2)^4+1536*tan(a/2)^2*tan(c/2)^6+4608*tan(a/2)^2*tan(c/2)^4+4608*tan(a/2)^2*tan(c/2)^2+1536*tan(a/2)^2+512*tan(c/2)^6+1536*tan(c/2)^4+1536*tan(c/2)^2+512)+(-22*tan((b*x+c)/2)^3*tan(a/2)^2*tan(c/2)^2+22*tan((b*x+c)/2)^3*tan(a/2)^2-88*tan((b*x+c)/2)^3*tan(a/2)*tan(c/2)+22*tan((b*x+c)/2)^3*tan(c/2)^2-22*tan((b*x+c)/2)^3-6*tan((b*x+c)/2)^2*tan(a/2)^2*tan(c/2)+6*tan((b*x+c)/2)^2*tan(a/2)*tan(c/2)^2-6*tan((b*x+c)/2)^2*tan(a/2)+6*tan((b*x+c)/2)^2*tan(c/2)-3*tan((b*x+c)/2)*tan(a/2)^2*tan(c/2)^2+3*tan((b*x+c)/2)*tan(a/2)^2-12*tan((b*x+c)/2)*tan(a/2)*tan(c/2)+3*tan((b*x+c)/2)*tan(c/2)^2-3*tan((b*x+c)/2)-2*tan(a/2)^2*tan(c/2)+2*tan(a/2)*tan(c/2)^2-2*tan(a/2)+2*tan(c/2))/(48*tan(a/2)^2*tan(c/2)^2+48*tan(a/2)^2+48*tan(c/2)^2+48)/tan((b*x+c)/2)^3+(tan(a/2)^2*tan(c/2)^2-tan(a/2)^2+4*tan(a/2)*tan(c/2)-tan(c/2)^2+1)/(4*tan(a/2)^2*tan(c/2)^2+4*tan(a/2)^2+4*tan(c/2)^2+4)*ln(abs(tan((b*x+c)/2))))","F(-2)",0
199,1,301,0,3.250404," ","integrate(csc(b*x+c)^5*sin(b*x+a),x, algorithm=""giac"")","-\frac{6 \, \tan\left(b x + c\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 6 \, \tan\left(b x + c\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{2} + 24 \, \tan\left(b x + c\right)^{3} \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{1}{2} \, c\right) + 6 \, \tan\left(b x + c\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, c\right) - 6 \, \tan\left(b x + c\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{2} - 6 \, \tan\left(b x + c\right)^{2} \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(b x + c\right) \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 6 \, \tan\left(b x + c\right)^{3} + 6 \, \tan\left(b x + c\right)^{2} \tan\left(\frac{1}{2} \, a\right) - 2 \, \tan\left(b x + c\right) \tan\left(\frac{1}{2} \, a\right)^{2} - 6 \, \tan\left(b x + c\right)^{2} \tan\left(\frac{1}{2} \, c\right) + 8 \, \tan\left(b x + c\right) \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{1}{2} \, c\right) + 3 \, \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, c\right) - 2 \, \tan\left(b x + c\right) \tan\left(\frac{1}{2} \, c\right)^{2} - 3 \, \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(b x + c\right) + 3 \, \tan\left(\frac{1}{2} \, a\right) - 3 \, \tan\left(\frac{1}{2} \, c\right)}{6 \, {\left(\tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, a\right)^{2} + \tan\left(\frac{1}{2} \, c\right)^{2} + 1\right)} b \tan\left(b x + c\right)^{4}}"," ",0,"-1/6*(6*tan(b*x + c)^3*tan(1/2*a)^2*tan(1/2*c)^2 - 6*tan(b*x + c)^3*tan(1/2*a)^2 + 24*tan(b*x + c)^3*tan(1/2*a)*tan(1/2*c) + 6*tan(b*x + c)^2*tan(1/2*a)^2*tan(1/2*c) - 6*tan(b*x + c)^3*tan(1/2*c)^2 - 6*tan(b*x + c)^2*tan(1/2*a)*tan(1/2*c)^2 + 2*tan(b*x + c)*tan(1/2*a)^2*tan(1/2*c)^2 + 6*tan(b*x + c)^3 + 6*tan(b*x + c)^2*tan(1/2*a) - 2*tan(b*x + c)*tan(1/2*a)^2 - 6*tan(b*x + c)^2*tan(1/2*c) + 8*tan(b*x + c)*tan(1/2*a)*tan(1/2*c) + 3*tan(1/2*a)^2*tan(1/2*c) - 2*tan(b*x + c)*tan(1/2*c)^2 - 3*tan(1/2*a)*tan(1/2*c)^2 + 2*tan(b*x + c) + 3*tan(1/2*a) - 3*tan(1/2*c))/((tan(1/2*a)^2*tan(1/2*c)^2 + tan(1/2*a)^2 + tan(1/2*c)^2 + 1)*b*tan(b*x + c)^4)","B",0
200,-2,0,0,0.000000," ","integrate(csc(b*x+c)^6*sin(b*x+a),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)2/b*((-1048576/5*tan((b*x+c)/2)^5*tan(a/2)^10*tan(c/2)^9-4194304/5*tan((b*x+c)/2)^5*tan(a/2)^10*tan(c/2)^7-6291456/5*tan((b*x+c)/2)^5*tan(a/2)^10*tan(c/2)^5-4194304/5*tan((b*x+c)/2)^5*tan(a/2)^10*tan(c/2)^3-1048576/5*tan((b*x+c)/2)^5*tan(a/2)^10*tan(c/2)+1048576/5*tan((b*x+c)/2)^5*tan(a/2)^9*tan(c/2)^10+3145728/5*tan((b*x+c)/2)^5*tan(a/2)^9*tan(c/2)^8+2097152/5*tan((b*x+c)/2)^5*tan(a/2)^9*tan(c/2)^6-2097152/5*tan((b*x+c)/2)^5*tan(a/2)^9*tan(c/2)^4-3145728/5*tan((b*x+c)/2)^5*tan(a/2)^9*tan(c/2)^2-1048576/5*tan((b*x+c)/2)^5*tan(a/2)^9-3145728/5*tan((b*x+c)/2)^5*tan(a/2)^8*tan(c/2)^9-12582912/5*tan((b*x+c)/2)^5*tan(a/2)^8*tan(c/2)^7-18874368/5*tan((b*x+c)/2)^5*tan(a/2)^8*tan(c/2)^5-12582912/5*tan((b*x+c)/2)^5*tan(a/2)^8*tan(c/2)^3-3145728/5*tan((b*x+c)/2)^5*tan(a/2)^8*tan(c/2)+4194304/5*tan((b*x+c)/2)^5*tan(a/2)^7*tan(c/2)^10+12582912/5*tan((b*x+c)/2)^5*tan(a/2)^7*tan(c/2)^8+8388608/5*tan((b*x+c)/2)^5*tan(a/2)^7*tan(c/2)^6-8388608/5*tan((b*x+c)/2)^5*tan(a/2)^7*tan(c/2)^4-12582912/5*tan((b*x+c)/2)^5*tan(a/2)^7*tan(c/2)^2-4194304/5*tan((b*x+c)/2)^5*tan(a/2)^7-2097152/5*tan((b*x+c)/2)^5*tan(a/2)^6*tan(c/2)^9-8388608/5*tan((b*x+c)/2)^5*tan(a/2)^6*tan(c/2)^7-12582912/5*tan((b*x+c)/2)^5*tan(a/2)^6*tan(c/2)^5-8388608/5*tan((b*x+c)/2)^5*tan(a/2)^6*tan(c/2)^3-2097152/5*tan((b*x+c)/2)^5*tan(a/2)^6*tan(c/2)+6291456/5*tan((b*x+c)/2)^5*tan(a/2)^5*tan(c/2)^10+18874368/5*tan((b*x+c)/2)^5*tan(a/2)^5*tan(c/2)^8+12582912/5*tan((b*x+c)/2)^5*tan(a/2)^5*tan(c/2)^6-12582912/5*tan((b*x+c)/2)^5*tan(a/2)^5*tan(c/2)^4-18874368/5*tan((b*x+c)/2)^5*tan(a/2)^5*tan(c/2)^2-6291456/5*tan((b*x+c)/2)^5*tan(a/2)^5+2097152/5*tan((b*x+c)/2)^5*tan(a/2)^4*tan(c/2)^9+8388608/5*tan((b*x+c)/2)^5*tan(a/2)^4*tan(c/2)^7+12582912/5*tan((b*x+c)/2)^5*tan(a/2)^4*tan(c/2)^5+8388608/5*tan((b*x+c)/2)^5*tan(a/2)^4*tan(c/2)^3+2097152/5*tan((b*x+c)/2)^5*tan(a/2)^4*tan(c/2)+4194304/5*tan((b*x+c)/2)^5*tan(a/2)^3*tan(c/2)^10+12582912/5*tan((b*x+c)/2)^5*tan(a/2)^3*tan(c/2)^8+8388608/5*tan((b*x+c)/2)^5*tan(a/2)^3*tan(c/2)^6-8388608/5*tan((b*x+c)/2)^5*tan(a/2)^3*tan(c/2)^4-12582912/5*tan((b*x+c)/2)^5*tan(a/2)^3*tan(c/2)^2-4194304/5*tan((b*x+c)/2)^5*tan(a/2)^3+3145728/5*tan((b*x+c)/2)^5*tan(a/2)^2*tan(c/2)^9+12582912/5*tan((b*x+c)/2)^5*tan(a/2)^2*tan(c/2)^7+18874368/5*tan((b*x+c)/2)^5*tan(a/2)^2*tan(c/2)^5+12582912/5*tan((b*x+c)/2)^5*tan(a/2)^2*tan(c/2)^3+3145728/5*tan((b*x+c)/2)^5*tan(a/2)^2*tan(c/2)+1048576/5*tan((b*x+c)/2)^5*tan(a/2)*tan(c/2)^10+3145728/5*tan((b*x+c)/2)^5*tan(a/2)*tan(c/2)^8+2097152/5*tan((b*x+c)/2)^5*tan(a/2)*tan(c/2)^6-2097152/5*tan((b*x+c)/2)^5*tan(a/2)*tan(c/2)^4-3145728/5*tan((b*x+c)/2)^5*tan(a/2)*tan(c/2)^2-1048576/5*tan((b*x+c)/2)^5*tan(a/2)+1048576/5*tan((b*x+c)/2)^5*tan(c/2)^9+4194304/5*tan((b*x+c)/2)^5*tan(c/2)^7+6291456/5*tan((b*x+c)/2)^5*tan(c/2)^5+4194304/5*tan((b*x+c)/2)^5*tan(c/2)^3+1048576/5*tan((b*x+c)/2)^5*tan(c/2)+262144*tan((b*x+c)/2)^4*tan(a/2)^10*tan(c/2)^10+786432*tan((b*x+c)/2)^4*tan(a/2)^10*tan(c/2)^8+524288*tan((b*x+c)/2)^4*tan(a/2)^10*tan(c/2)^6-524288*tan((b*x+c)/2)^4*tan(a/2)^10*tan(c/2)^4-786432*tan((b*x+c)/2)^4*tan(a/2)^10*tan(c/2)^2-262144*tan((b*x+c)/2)^4*tan(a/2)^10+1048576*tan((b*x+c)/2)^4*tan(a/2)^9*tan(c/2)^9+4194304*tan((b*x+c)/2)^4*tan(a/2)^9*tan(c/2)^7+6291456*tan((b*x+c)/2)^4*tan(a/2)^9*tan(c/2)^5+4194304*tan((b*x+c)/2)^4*tan(a/2)^9*tan(c/2)^3+1048576*tan((b*x+c)/2)^4*tan(a/2)^9*tan(c/2)+786432*tan((b*x+c)/2)^4*tan(a/2)^8*tan(c/2)^10+2359296*tan((b*x+c)/2)^4*tan(a/2)^8*tan(c/2)^8+1572864*tan((b*x+c)/2)^4*tan(a/2)^8*tan(c/2)^6-1572864*tan((b*x+c)/2)^4*tan(a/2)^8*tan(c/2)^4-2359296*tan((b*x+c)/2)^4*tan(a/2)^8*tan(c/2)^2-786432*tan((b*x+c)/2)^4*tan(a/2)^8+4194304*tan((b*x+c)/2)^4*tan(a/2)^7*tan(c/2)^9+16777216*tan((b*x+c)/2)^4*tan(a/2)^7*tan(c/2)^7+25165824*tan((b*x+c)/2)^4*tan(a/2)^7*tan(c/2)^5+16777216*tan((b*x+c)/2)^4*tan(a/2)^7*tan(c/2)^3+4194304*tan((b*x+c)/2)^4*tan(a/2)^7*tan(c/2)+524288*tan((b*x+c)/2)^4*tan(a/2)^6*tan(c/2)^10+1572864*tan((b*x+c)/2)^4*tan(a/2)^6*tan(c/2)^8+1048576*tan((b*x+c)/2)^4*tan(a/2)^6*tan(c/2)^6-1048576*tan((b*x+c)/2)^4*tan(a/2)^6*tan(c/2)^4-1572864*tan((b*x+c)/2)^4*tan(a/2)^6*tan(c/2)^2-524288*tan((b*x+c)/2)^4*tan(a/2)^6+6291456*tan((b*x+c)/2)^4*tan(a/2)^5*tan(c/2)^9+25165824*tan((b*x+c)/2)^4*tan(a/2)^5*tan(c/2)^7+37748736*tan((b*x+c)/2)^4*tan(a/2)^5*tan(c/2)^5+25165824*tan((b*x+c)/2)^4*tan(a/2)^5*tan(c/2)^3+6291456*tan((b*x+c)/2)^4*tan(a/2)^5*tan(c/2)-524288*tan((b*x+c)/2)^4*tan(a/2)^4*tan(c/2)^10-1572864*tan((b*x+c)/2)^4*tan(a/2)^4*tan(c/2)^8-1048576*tan((b*x+c)/2)^4*tan(a/2)^4*tan(c/2)^6+1048576*tan((b*x+c)/2)^4*tan(a/2)^4*tan(c/2)^4+1572864*tan((b*x+c)/2)^4*tan(a/2)^4*tan(c/2)^2+524288*tan((b*x+c)/2)^4*tan(a/2)^4+4194304*tan((b*x+c)/2)^4*tan(a/2)^3*tan(c/2)^9+16777216*tan((b*x+c)/2)^4*tan(a/2)^3*tan(c/2)^7+25165824*tan((b*x+c)/2)^4*tan(a/2)^3*tan(c/2)^5+16777216*tan((b*x+c)/2)^4*tan(a/2)^3*tan(c/2)^3+4194304*tan((b*x+c)/2)^4*tan(a/2)^3*tan(c/2)-786432*tan((b*x+c)/2)^4*tan(a/2)^2*tan(c/2)^10-2359296*tan((b*x+c)/2)^4*tan(a/2)^2*tan(c/2)^8-1572864*tan((b*x+c)/2)^4*tan(a/2)^2*tan(c/2)^6+1572864*tan((b*x+c)/2)^4*tan(a/2)^2*tan(c/2)^4+2359296*tan((b*x+c)/2)^4*tan(a/2)^2*tan(c/2)^2+786432*tan((b*x+c)/2)^4*tan(a/2)^2+1048576*tan((b*x+c)/2)^4*tan(a/2)*tan(c/2)^9+4194304*tan((b*x+c)/2)^4*tan(a/2)*tan(c/2)^7+6291456*tan((b*x+c)/2)^4*tan(a/2)*tan(c/2)^5+4194304*tan((b*x+c)/2)^4*tan(a/2)*tan(c/2)^3+1048576*tan((b*x+c)/2)^4*tan(a/2)*tan(c/2)-262144*tan((b*x+c)/2)^4*tan(c/2)^10-786432*tan((b*x+c)/2)^4*tan(c/2)^8-524288*tan((b*x+c)/2)^4*tan(c/2)^6+524288*tan((b*x+c)/2)^4*tan(c/2)^4+786432*tan((b*x+c)/2)^4*tan(c/2)^2+262144*tan((b*x+c)/2)^4-1048576*tan((b*x+c)/2)^3*tan(a/2)^10*tan(c/2)^9-4194304*tan((b*x+c)/2)^3*tan(a/2)^10*tan(c/2)^7-6291456*tan((b*x+c)/2)^3*tan(a/2)^10*tan(c/2)^5-4194304*tan((b*x+c)/2)^3*tan(a/2)^10*tan(c/2)^3-1048576*tan((b*x+c)/2)^3*tan(a/2)^10*tan(c/2)+1048576*tan((b*x+c)/2)^3*tan(a/2)^9*tan(c/2)^10+3145728*tan((b*x+c)/2)^3*tan(a/2)^9*tan(c/2)^8+2097152*tan((b*x+c)/2)^3*tan(a/2)^9*tan(c/2)^6-2097152*tan((b*x+c)/2)^3*tan(a/2)^9*tan(c/2)^4-3145728*tan((b*x+c)/2)^3*tan(a/2)^9*tan(c/2)^2-1048576*tan((b*x+c)/2)^3*tan(a/2)^9-3145728*tan((b*x+c)/2)^3*tan(a/2)^8*tan(c/2)^9-12582912*tan((b*x+c)/2)^3*tan(a/2)^8*tan(c/2)^7-18874368*tan((b*x+c)/2)^3*tan(a/2)^8*tan(c/2)^5-12582912*tan((b*x+c)/2)^3*tan(a/2)^8*tan(c/2)^3-3145728*tan((b*x+c)/2)^3*tan(a/2)^8*tan(c/2)+4194304*tan((b*x+c)/2)^3*tan(a/2)^7*tan(c/2)^10+12582912*tan((b*x+c)/2)^3*tan(a/2)^7*tan(c/2)^8+8388608*tan((b*x+c)/2)^3*tan(a/2)^7*tan(c/2)^6-8388608*tan((b*x+c)/2)^3*tan(a/2)^7*tan(c/2)^4-12582912*tan((b*x+c)/2)^3*tan(a/2)^7*tan(c/2)^2-4194304*tan((b*x+c)/2)^3*tan(a/2)^7-2097152*tan((b*x+c)/2)^3*tan(a/2)^6*tan(c/2)^9-8388608*tan((b*x+c)/2)^3*tan(a/2)^6*tan(c/2)^7-12582912*tan((b*x+c)/2)^3*tan(a/2)^6*tan(c/2)^5-8388608*tan((b*x+c)/2)^3*tan(a/2)^6*tan(c/2)^3-2097152*tan((b*x+c)/2)^3*tan(a/2)^6*tan(c/2)+6291456*tan((b*x+c)/2)^3*tan(a/2)^5*tan(c/2)^10+18874368*tan((b*x+c)/2)^3*tan(a/2)^5*tan(c/2)^8+12582912*tan((b*x+c)/2)^3*tan(a/2)^5*tan(c/2)^6-12582912*tan((b*x+c)/2)^3*tan(a/2)^5*tan(c/2)^4-18874368*tan((b*x+c)/2)^3*tan(a/2)^5*tan(c/2)^2-6291456*tan((b*x+c)/2)^3*tan(a/2)^5+2097152*tan((b*x+c)/2)^3*tan(a/2)^4*tan(c/2)^9+8388608*tan((b*x+c)/2)^3*tan(a/2)^4*tan(c/2)^7+12582912*tan((b*x+c)/2)^3*tan(a/2)^4*tan(c/2)^5+8388608*tan((b*x+c)/2)^3*tan(a/2)^4*tan(c/2)^3+2097152*tan((b*x+c)/2)^3*tan(a/2)^4*tan(c/2)+4194304*tan((b*x+c)/2)^3*tan(a/2)^3*tan(c/2)^10+12582912*tan((b*x+c)/2)^3*tan(a/2)^3*tan(c/2)^8+8388608*tan((b*x+c)/2)^3*tan(a/2)^3*tan(c/2)^6-8388608*tan((b*x+c)/2)^3*tan(a/2)^3*tan(c/2)^4-12582912*tan((b*x+c)/2)^3*tan(a/2)^3*tan(c/2)^2-4194304*tan((b*x+c)/2)^3*tan(a/2)^3+3145728*tan((b*x+c)/2)^3*tan(a/2)^2*tan(c/2)^9+12582912*tan((b*x+c)/2)^3*tan(a/2)^2*tan(c/2)^7+18874368*tan((b*x+c)/2)^3*tan(a/2)^2*tan(c/2)^5+12582912*tan((b*x+c)/2)^3*tan(a/2)^2*tan(c/2)^3+3145728*tan((b*x+c)/2)^3*tan(a/2)^2*tan(c/2)+1048576*tan((b*x+c)/2)^3*tan(a/2)*tan(c/2)^10+3145728*tan((b*x+c)/2)^3*tan(a/2)*tan(c/2)^8+2097152*tan((b*x+c)/2)^3*tan(a/2)*tan(c/2)^6-2097152*tan((b*x+c)/2)^3*tan(a/2)*tan(c/2)^4-3145728*tan((b*x+c)/2)^3*tan(a/2)*tan(c/2)^2-1048576*tan((b*x+c)/2)^3*tan(a/2)+1048576*tan((b*x+c)/2)^3*tan(c/2)^9+4194304*tan((b*x+c)/2)^3*tan(c/2)^7+6291456*tan((b*x+c)/2)^3*tan(c/2)^5+4194304*tan((b*x+c)/2)^3*tan(c/2)^3+1048576*tan((b*x+c)/2)^3*tan(c/2)+2097152*tan((b*x+c)/2)^2*tan(a/2)^10*tan(c/2)^10+6291456*tan((b*x+c)/2)^2*tan(a/2)^10*tan(c/2)^8+4194304*tan((b*x+c)/2)^2*tan(a/2)^10*tan(c/2)^6-4194304*tan((b*x+c)/2)^2*tan(a/2)^10*tan(c/2)^4-6291456*tan((b*x+c)/2)^2*tan(a/2)^10*tan(c/2)^2-2097152*tan((b*x+c)/2)^2*tan(a/2)^10+8388608*tan((b*x+c)/2)^2*tan(a/2)^9*tan(c/2)^9+33554432*tan((b*x+c)/2)^2*tan(a/2)^9*tan(c/2)^7+50331648*tan((b*x+c)/2)^2*tan(a/2)^9*tan(c/2)^5+33554432*tan((b*x+c)/2)^2*tan(a/2)^9*tan(c/2)^3+8388608*tan((b*x+c)/2)^2*tan(a/2)^9*tan(c/2)+6291456*tan((b*x+c)/2)^2*tan(a/2)^8*tan(c/2)^10+18874368*tan((b*x+c)/2)^2*tan(a/2)^8*tan(c/2)^8+12582912*tan((b*x+c)/2)^2*tan(a/2)^8*tan(c/2)^6-12582912*tan((b*x+c)/2)^2*tan(a/2)^8*tan(c/2)^4-18874368*tan((b*x+c)/2)^2*tan(a/2)^8*tan(c/2)^2-6291456*tan((b*x+c)/2)^2*tan(a/2)^8+33554432*tan((b*x+c)/2)^2*tan(a/2)^7*tan(c/2)^9+134217728*tan((b*x+c)/2)^2*tan(a/2)^7*tan(c/2)^7+201326592*tan((b*x+c)/2)^2*tan(a/2)^7*tan(c/2)^5+134217728*tan((b*x+c)/2)^2*tan(a/2)^7*tan(c/2)^3+33554432*tan((b*x+c)/2)^2*tan(a/2)^7*tan(c/2)+4194304*tan((b*x+c)/2)^2*tan(a/2)^6*tan(c/2)^10+12582912*tan((b*x+c)/2)^2*tan(a/2)^6*tan(c/2)^8+8388608*tan((b*x+c)/2)^2*tan(a/2)^6*tan(c/2)^6-8388608*tan((b*x+c)/2)^2*tan(a/2)^6*tan(c/2)^4-12582912*tan((b*x+c)/2)^2*tan(a/2)^6*tan(c/2)^2-4194304*tan((b*x+c)/2)^2*tan(a/2)^6+50331648*tan((b*x+c)/2)^2*tan(a/2)^5*tan(c/2)^9+201326592*tan((b*x+c)/2)^2*tan(a/2)^5*tan(c/2)^7+301989888*tan((b*x+c)/2)^2*tan(a/2)^5*tan(c/2)^5+201326592*tan((b*x+c)/2)^2*tan(a/2)^5*tan(c/2)^3+50331648*tan((b*x+c)/2)^2*tan(a/2)^5*tan(c/2)-4194304*tan((b*x+c)/2)^2*tan(a/2)^4*tan(c/2)^10-12582912*tan((b*x+c)/2)^2*tan(a/2)^4*tan(c/2)^8-8388608*tan((b*x+c)/2)^2*tan(a/2)^4*tan(c/2)^6+8388608*tan((b*x+c)/2)^2*tan(a/2)^4*tan(c/2)^4+12582912*tan((b*x+c)/2)^2*tan(a/2)^4*tan(c/2)^2+4194304*tan((b*x+c)/2)^2*tan(a/2)^4+33554432*tan((b*x+c)/2)^2*tan(a/2)^3*tan(c/2)^9+134217728*tan((b*x+c)/2)^2*tan(a/2)^3*tan(c/2)^7+201326592*tan((b*x+c)/2)^2*tan(a/2)^3*tan(c/2)^5+134217728*tan((b*x+c)/2)^2*tan(a/2)^3*tan(c/2)^3+33554432*tan((b*x+c)/2)^2*tan(a/2)^3*tan(c/2)-6291456*tan((b*x+c)/2)^2*tan(a/2)^2*tan(c/2)^10-18874368*tan((b*x+c)/2)^2*tan(a/2)^2*tan(c/2)^8-12582912*tan((b*x+c)/2)^2*tan(a/2)^2*tan(c/2)^6+12582912*tan((b*x+c)/2)^2*tan(a/2)^2*tan(c/2)^4+18874368*tan((b*x+c)/2)^2*tan(a/2)^2*tan(c/2)^2+6291456*tan((b*x+c)/2)^2*tan(a/2)^2+8388608*tan((b*x+c)/2)^2*tan(a/2)*tan(c/2)^9+33554432*tan((b*x+c)/2)^2*tan(a/2)*tan(c/2)^7+50331648*tan((b*x+c)/2)^2*tan(a/2)*tan(c/2)^5+33554432*tan((b*x+c)/2)^2*tan(a/2)*tan(c/2)^3+8388608*tan((b*x+c)/2)^2*tan(a/2)*tan(c/2)-2097152*tan((b*x+c)/2)^2*tan(c/2)^10-6291456*tan((b*x+c)/2)^2*tan(c/2)^8-4194304*tan((b*x+c)/2)^2*tan(c/2)^6+4194304*tan((b*x+c)/2)^2*tan(c/2)^4+6291456*tan((b*x+c)/2)^2*tan(c/2)^2+2097152*tan((b*x+c)/2)^2-2097152*tan((b*x+c)/2)*tan(a/2)^10*tan(c/2)^9-8388608*tan((b*x+c)/2)*tan(a/2)^10*tan(c/2)^7-12582912*tan((b*x+c)/2)*tan(a/2)^10*tan(c/2)^5-8388608*tan((b*x+c)/2)*tan(a/2)^10*tan(c/2)^3-2097152*tan((b*x+c)/2)*tan(a/2)^10*tan(c/2)+2097152*tan((b*x+c)/2)*tan(a/2)^9*tan(c/2)^10+6291456*tan((b*x+c)/2)*tan(a/2)^9*tan(c/2)^8+4194304*tan((b*x+c)/2)*tan(a/2)^9*tan(c/2)^6-4194304*tan((b*x+c)/2)*tan(a/2)^9*tan(c/2)^4-6291456*tan((b*x+c)/2)*tan(a/2)^9*tan(c/2)^2-2097152*tan((b*x+c)/2)*tan(a/2)^9-6291456*tan((b*x+c)/2)*tan(a/2)^8*tan(c/2)^9-25165824*tan((b*x+c)/2)*tan(a/2)^8*tan(c/2)^7-37748736*tan((b*x+c)/2)*tan(a/2)^8*tan(c/2)^5-25165824*tan((b*x+c)/2)*tan(a/2)^8*tan(c/2)^3-6291456*tan((b*x+c)/2)*tan(a/2)^8*tan(c/2)+8388608*tan((b*x+c)/2)*tan(a/2)^7*tan(c/2)^10+25165824*tan((b*x+c)/2)*tan(a/2)^7*tan(c/2)^8+16777216*tan((b*x+c)/2)*tan(a/2)^7*tan(c/2)^6-16777216*tan((b*x+c)/2)*tan(a/2)^7*tan(c/2)^4-25165824*tan((b*x+c)/2)*tan(a/2)^7*tan(c/2)^2-8388608*tan((b*x+c)/2)*tan(a/2)^7-4194304*tan((b*x+c)/2)*tan(a/2)^6*tan(c/2)^9-16777216*tan((b*x+c)/2)*tan(a/2)^6*tan(c/2)^7-25165824*tan((b*x+c)/2)*tan(a/2)^6*tan(c/2)^5-16777216*tan((b*x+c)/2)*tan(a/2)^6*tan(c/2)^3-4194304*tan((b*x+c)/2)*tan(a/2)^6*tan(c/2)+12582912*tan((b*x+c)/2)*tan(a/2)^5*tan(c/2)^10+37748736*tan((b*x+c)/2)*tan(a/2)^5*tan(c/2)^8+25165824*tan((b*x+c)/2)*tan(a/2)^5*tan(c/2)^6-25165824*tan((b*x+c)/2)*tan(a/2)^5*tan(c/2)^4-37748736*tan((b*x+c)/2)*tan(a/2)^5*tan(c/2)^2-12582912*tan((b*x+c)/2)*tan(a/2)^5+4194304*tan((b*x+c)/2)*tan(a/2)^4*tan(c/2)^9+16777216*tan((b*x+c)/2)*tan(a/2)^4*tan(c/2)^7+25165824*tan((b*x+c)/2)*tan(a/2)^4*tan(c/2)^5+16777216*tan((b*x+c)/2)*tan(a/2)^4*tan(c/2)^3+4194304*tan((b*x+c)/2)*tan(a/2)^4*tan(c/2)+8388608*tan((b*x+c)/2)*tan(a/2)^3*tan(c/2)^10+25165824*tan((b*x+c)/2)*tan(a/2)^3*tan(c/2)^8+16777216*tan((b*x+c)/2)*tan(a/2)^3*tan(c/2)^6-16777216*tan((b*x+c)/2)*tan(a/2)^3*tan(c/2)^4-25165824*tan((b*x+c)/2)*tan(a/2)^3*tan(c/2)^2-8388608*tan((b*x+c)/2)*tan(a/2)^3+6291456*tan((b*x+c)/2)*tan(a/2)^2*tan(c/2)^9+25165824*tan((b*x+c)/2)*tan(a/2)^2*tan(c/2)^7+37748736*tan((b*x+c)/2)*tan(a/2)^2*tan(c/2)^5+25165824*tan((b*x+c)/2)*tan(a/2)^2*tan(c/2)^3+6291456*tan((b*x+c)/2)*tan(a/2)^2*tan(c/2)+2097152*tan((b*x+c)/2)*tan(a/2)*tan(c/2)^10+6291456*tan((b*x+c)/2)*tan(a/2)*tan(c/2)^8+4194304*tan((b*x+c)/2)*tan(a/2)*tan(c/2)^6-4194304*tan((b*x+c)/2)*tan(a/2)*tan(c/2)^4-6291456*tan((b*x+c)/2)*tan(a/2)*tan(c/2)^2-2097152*tan((b*x+c)/2)*tan(a/2)+2097152*tan((b*x+c)/2)*tan(c/2)^9+8388608*tan((b*x+c)/2)*tan(c/2)^7+12582912*tan((b*x+c)/2)*tan(c/2)^5+8388608*tan((b*x+c)/2)*tan(c/2)^3+2097152*tan((b*x+c)/2)*tan(c/2))/(33554432*tan(a/2)^10*tan(c/2)^10+167772160*tan(a/2)^10*tan(c/2)^8+335544320*tan(a/2)^10*tan(c/2)^6+335544320*tan(a/2)^10*tan(c/2)^4+167772160*tan(a/2)^10*tan(c/2)^2+33554432*tan(a/2)^10+167772160*tan(a/2)^8*tan(c/2)^10+838860800*tan(a/2)^8*tan(c/2)^8+1677721600*tan(a/2)^8*tan(c/2)^6+1677721600*tan(a/2)^8*tan(c/2)^4+838860800*tan(a/2)^8*tan(c/2)^2+167772160*tan(a/2)^8+335544320*tan(a/2)^6*tan(c/2)^10+1677721600*tan(a/2)^6*tan(c/2)^8+3355443200*tan(a/2)^6*tan(c/2)^6+3355443200*tan(a/2)^6*tan(c/2)^4+1677721600*tan(a/2)^6*tan(c/2)^2+335544320*tan(a/2)^6+335544320*tan(a/2)^4*tan(c/2)^10+1677721600*tan(a/2)^4*tan(c/2)^8+3355443200*tan(a/2)^4*tan(c/2)^6+3355443200*tan(a/2)^4*tan(c/2)^4+1677721600*tan(a/2)^4*tan(c/2)^2+335544320*tan(a/2)^4+167772160*tan(a/2)^2*tan(c/2)^10+838860800*tan(a/2)^2*tan(c/2)^8+1677721600*tan(a/2)^2*tan(c/2)^6+1677721600*tan(a/2)^2*tan(c/2)^4+838860800*tan(a/2)^2*tan(c/2)^2+167772160*tan(a/2)^2+33554432*tan(c/2)^10+167772160*tan(c/2)^8+335544320*tan(c/2)^6+335544320*tan(c/2)^4+167772160*tan(c/2)^2+33554432)+(-274*tan((b*x+c)/2)^5*tan(a/2)^2*tan(c/2)^2+274*tan((b*x+c)/2)^5*tan(a/2)^2-1096*tan((b*x+c)/2)^5*tan(a/2)*tan(c/2)+274*tan((b*x+c)/2)^5*tan(c/2)^2-274*tan((b*x+c)/2)^5-40*tan((b*x+c)/2)^4*tan(a/2)^2*tan(c/2)+40*tan((b*x+c)/2)^4*tan(a/2)*tan(c/2)^2-40*tan((b*x+c)/2)^4*tan(a/2)+40*tan((b*x+c)/2)^4*tan(c/2)-40*tan((b*x+c)/2)^3*tan(a/2)^2*tan(c/2)^2+40*tan((b*x+c)/2)^3*tan(a/2)^2-160*tan((b*x+c)/2)^3*tan(a/2)*tan(c/2)+40*tan((b*x+c)/2)^3*tan(c/2)^2-40*tan((b*x+c)/2)^3-20*tan((b*x+c)/2)^2*tan(a/2)^2*tan(c/2)+20*tan((b*x+c)/2)^2*tan(a/2)*tan(c/2)^2-20*tan((b*x+c)/2)^2*tan(a/2)+20*tan((b*x+c)/2)^2*tan(c/2)-5*tan((b*x+c)/2)*tan(a/2)^2*tan(c/2)^2+5*tan((b*x+c)/2)*tan(a/2)^2-20*tan((b*x+c)/2)*tan(a/2)*tan(c/2)+5*tan((b*x+c)/2)*tan(c/2)^2-5*tan((b*x+c)/2)-4*tan(a/2)^2*tan(c/2)+4*tan(a/2)*tan(c/2)^2-4*tan(a/2)+4*tan(c/2))/(640*tan(a/2)^2*tan(c/2)^2+640*tan(a/2)^2+640*tan(c/2)^2+640)/tan((b*x+c)/2)^5+(3*tan(a/2)^2*tan(c/2)^2-3*tan(a/2)^2+12*tan(a/2)*tan(c/2)-3*tan(c/2)^2+3)/(16*tan(a/2)^2*tan(c/2)^2+16*tan(a/2)^2+16*tan(c/2)^2+16)*ln(abs(tan((b*x+c)/2))))","F(-2)",0
201,0,0,0,0.000000," ","integrate(sin(b*x+a)^2*sin(d*x+c)^n,x, algorithm=""giac"")","\int \sin\left(d x + c\right)^{n} \sin\left(b x + a\right)^{2}\,{d x}"," ",0,"integrate(sin(d*x + c)^n*sin(b*x + a)^2, x)","F",0
202,1,61,0,0.202395," ","integrate(sin(b*x+a)^2*sin(d*x+c),x, algorithm=""giac"")","\frac{\cos\left(2 \, b x + d x + 2 \, a + c\right)}{4 \, {\left(2 \, b + d\right)}} - \frac{\cos\left(2 \, b x - d x + 2 \, a - c\right)}{4 \, {\left(2 \, b - d\right)}} - \frac{\cos\left(d x + c\right)}{2 \, d}"," ",0,"1/4*cos(2*b*x + d*x + 2*a + c)/(2*b + d) - 1/4*cos(2*b*x - d*x + 2*a - c)/(2*b - d) - 1/2*cos(d*x + c)/d","A",0
203,1,80,0,0.183640," ","integrate(sin(b*x+a)^2*sin(d*x+c)^2,x, algorithm=""giac"")","\frac{1}{4} \, x + \frac{\sin\left(2 \, b x + 2 \, d x + 2 \, a + 2 \, c\right)}{16 \, {\left(b + d\right)}} + \frac{\sin\left(2 \, b x - 2 \, d x + 2 \, a - 2 \, c\right)}{16 \, {\left(b - d\right)}} - \frac{\sin\left(2 \, b x + 2 \, a\right)}{8 \, b} - \frac{\sin\left(2 \, d x + 2 \, c\right)}{8 \, d}"," ",0,"1/4*x + 1/16*sin(2*b*x + 2*d*x + 2*a + 2*c)/(b + d) + 1/16*sin(2*b*x - 2*d*x + 2*a - 2*c)/(b - d) - 1/8*sin(2*b*x + 2*a)/b - 1/8*sin(2*d*x + 2*c)/d","A",0
204,1,129,0,2.527268," ","integrate(sin(b*x+a)^2*sin(d*x+c)^3,x, algorithm=""giac"")","-\frac{\cos\left(2 \, b x + 3 \, d x + 2 \, a + 3 \, c\right)}{16 \, {\left(2 \, b + 3 \, d\right)}} + \frac{3 \, \cos\left(2 \, b x + d x + 2 \, a + c\right)}{16 \, {\left(2 \, b + d\right)}} - \frac{3 \, \cos\left(2 \, b x - d x + 2 \, a - c\right)}{16 \, {\left(2 \, b - d\right)}} + \frac{\cos\left(2 \, b x - 3 \, d x + 2 \, a - 3 \, c\right)}{16 \, {\left(2 \, b - 3 \, d\right)}} + \frac{\cos\left(3 \, d x + 3 \, c\right)}{24 \, d} - \frac{3 \, \cos\left(d x + c\right)}{8 \, d}"," ",0,"-1/16*cos(2*b*x + 3*d*x + 2*a + 3*c)/(2*b + 3*d) + 3/16*cos(2*b*x + d*x + 2*a + c)/(2*b + d) - 3/16*cos(2*b*x - d*x + 2*a - c)/(2*b - d) + 1/16*cos(2*b*x - 3*d*x + 2*a - 3*c)/(2*b - 3*d) + 1/24*cos(3*d*x + 3*c)/d - 3/8*cos(d*x + c)/d","A",0
205,0,0,0,0.000000," ","integrate(sin(b*x+a)^3*sin(d*x+c)^n,x, algorithm=""giac"")","\int \sin\left(d x + c\right)^{n} \sin\left(b x + a\right)^{3}\,{d x}"," ",0,"integrate(sin(d*x + c)^n*sin(b*x + a)^3, x)","F",0
206,1,89,0,1.460267," ","integrate(sin(b*x+a)^3*sin(d*x+c),x, algorithm=""giac"")","\frac{\sin\left(3 \, b x + d x + 3 \, a + c\right)}{8 \, {\left(3 \, b + d\right)}} - \frac{\sin\left(3 \, b x - d x + 3 \, a - c\right)}{8 \, {\left(3 \, b - d\right)}} - \frac{3 \, \sin\left(b x + d x + a + c\right)}{8 \, {\left(b + d\right)}} + \frac{3 \, \sin\left(b x - d x + a - c\right)}{8 \, {\left(b - d\right)}}"," ",0,"1/8*sin(3*b*x + d*x + 3*a + c)/(3*b + d) - 1/8*sin(3*b*x - d*x + 3*a - c)/(3*b - d) - 3/8*sin(b*x + d*x + a + c)/(b + d) + 3/8*sin(b*x - d*x + a - c)/(b - d)","A",0
207,1,124,0,0.183211," ","integrate(sin(b*x+a)^3*sin(d*x+c)^2,x, algorithm=""giac"")","-\frac{\cos\left(3 \, b x + 2 \, d x + 3 \, a + 2 \, c\right)}{16 \, {\left(3 \, b + 2 \, d\right)}} - \frac{\cos\left(3 \, b x - 2 \, d x + 3 \, a - 2 \, c\right)}{16 \, {\left(3 \, b - 2 \, d\right)}} + \frac{\cos\left(3 \, b x + 3 \, a\right)}{24 \, b} + \frac{3 \, \cos\left(b x + 2 \, d x + a + 2 \, c\right)}{16 \, {\left(b + 2 \, d\right)}} + \frac{3 \, \cos\left(b x - 2 \, d x + a - 2 \, c\right)}{16 \, {\left(b - 2 \, d\right)}} - \frac{3 \, \cos\left(b x + a\right)}{8 \, b}"," ",0,"-1/16*cos(3*b*x + 2*d*x + 3*a + 2*c)/(3*b + 2*d) - 1/16*cos(3*b*x - 2*d*x + 3*a - 2*c)/(3*b - 2*d) + 1/24*cos(3*b*x + 3*a)/b + 3/16*cos(b*x + 2*d*x + a + 2*c)/(b + 2*d) + 3/16*cos(b*x - 2*d*x + a - 2*c)/(b - 2*d) - 3/8*cos(b*x + a)/b","A",0
208,1,181,0,0.178428," ","integrate(sin(b*x+a)^3*sin(d*x+c)^3,x, algorithm=""giac"")","-\frac{\sin\left(3 \, b x + 3 \, d x + 3 \, a + 3 \, c\right)}{96 \, {\left(b + d\right)}} + \frac{3 \, \sin\left(3 \, b x + d x + 3 \, a + c\right)}{32 \, {\left(3 \, b + d\right)}} - \frac{3 \, \sin\left(3 \, b x - d x + 3 \, a - c\right)}{32 \, {\left(3 \, b - d\right)}} + \frac{\sin\left(3 \, b x - 3 \, d x + 3 \, a - 3 \, c\right)}{96 \, {\left(b - d\right)}} + \frac{3 \, \sin\left(b x + 3 \, d x + a + 3 \, c\right)}{32 \, {\left(b + 3 \, d\right)}} - \frac{9 \, \sin\left(b x + d x + a + c\right)}{32 \, {\left(b + d\right)}} + \frac{9 \, \sin\left(b x - d x + a - c\right)}{32 \, {\left(b - d\right)}} - \frac{3 \, \sin\left(b x - 3 \, d x + a - 3 \, c\right)}{32 \, {\left(b - 3 \, d\right)}}"," ",0,"-1/96*sin(3*b*x + 3*d*x + 3*a + 3*c)/(b + d) + 3/32*sin(3*b*x + d*x + 3*a + c)/(3*b + d) - 3/32*sin(3*b*x - d*x + 3*a - c)/(3*b - d) + 1/96*sin(3*b*x - 3*d*x + 3*a - 3*c)/(b - d) + 3/32*sin(b*x + 3*d*x + a + 3*c)/(b + 3*d) - 9/32*sin(b*x + d*x + a + c)/(b + d) + 9/32*sin(b*x - d*x + a - c)/(b - d) - 3/32*sin(b*x - 3*d*x + a - 3*c)/(b - 3*d)","A",0
209,0,0,0,0.000000," ","integrate(cos(d*x+c)^n*sin(b*x+a),x, algorithm=""giac"")","\int \cos\left(d x + c\right)^{n} \sin\left(b x + a\right)\,{d x}"," ",0,"integrate(cos(d*x + c)^n*sin(b*x + a), x)","F",0
210,1,84,0,1.920019," ","integrate(cos(d*x+c)^3*sin(b*x+a),x, algorithm=""giac"")","-\frac{\cos\left(b x + 3 \, d x + a + 3 \, c\right)}{8 \, {\left(b + 3 \, d\right)}} - \frac{3 \, \cos\left(b x + d x + a + c\right)}{8 \, {\left(b + d\right)}} - \frac{3 \, \cos\left(b x - d x + a - c\right)}{8 \, {\left(b - d\right)}} - \frac{\cos\left(b x - 3 \, d x + a - 3 \, c\right)}{8 \, {\left(b - 3 \, d\right)}}"," ",0,"-1/8*cos(b*x + 3*d*x + a + 3*c)/(b + 3*d) - 3/8*cos(b*x + d*x + a + c)/(b + d) - 3/8*cos(b*x - d*x + a - c)/(b - d) - 1/8*cos(b*x - 3*d*x + a - 3*c)/(b - 3*d)","A",0
211,1,56,0,5.904244," ","integrate(cos(d*x+c)^2*sin(b*x+a),x, algorithm=""giac"")","-\frac{\cos\left(b x + 2 \, d x + a + 2 \, c\right)}{4 \, {\left(b + 2 \, d\right)}} - \frac{\cos\left(b x - 2 \, d x + a - 2 \, c\right)}{4 \, {\left(b - 2 \, d\right)}} - \frac{\cos\left(b x + a\right)}{2 \, b}"," ",0,"-1/4*cos(b*x + 2*d*x + a + 2*c)/(b + 2*d) - 1/4*cos(b*x - 2*d*x + a - 2*c)/(b - 2*d) - 1/2*cos(b*x + a)/b","A",0
212,1,40,0,0.262421," ","integrate(cos(d*x+c)*sin(b*x+a),x, algorithm=""giac"")","-\frac{\cos\left(b x + d x + a + c\right)}{2 \, {\left(b + d\right)}} - \frac{\cos\left(b x - d x + a - c\right)}{2 \, {\left(b - d\right)}}"," ",0,"-1/2*cos(b*x + d*x + a + c)/(b + d) - 1/2*cos(b*x - d*x + a - c)/(b - d)","A",0
213,1,158,0,0.203483," ","integrate(sec(b*x+c)*sin(b*x+a),x, algorithm=""giac"")","\frac{\frac{4 \, {\left(\tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, c\right) - \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, a\right) - \tan\left(\frac{1}{2} \, c\right)\right)} {\left(b x + c\right)}}{\tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, a\right)^{2} + \tan\left(\frac{1}{2} \, c\right)^{2} + 1} + \frac{{\left(\tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - \tan\left(\frac{1}{2} \, a\right)^{2} + 4 \, \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{1}{2} \, c\right) - \tan\left(\frac{1}{2} \, c\right)^{2} + 1\right)} \log\left(\tan\left(b x + c\right)^{2} + 1\right)}{\tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, a\right)^{2} + \tan\left(\frac{1}{2} \, c\right)^{2} + 1}}{2 \, b}"," ",0,"1/2*(4*(tan(1/2*a)^2*tan(1/2*c) - tan(1/2*a)*tan(1/2*c)^2 + tan(1/2*a) - tan(1/2*c))*(b*x + c)/(tan(1/2*a)^2*tan(1/2*c)^2 + tan(1/2*a)^2 + tan(1/2*c)^2 + 1) + (tan(1/2*a)^2*tan(1/2*c)^2 - tan(1/2*a)^2 + 4*tan(1/2*a)*tan(1/2*c) - tan(1/2*c)^2 + 1)*log(tan(b*x + c)^2 + 1)/(tan(1/2*a)^2*tan(1/2*c)^2 + tan(1/2*a)^2 + tan(1/2*c)^2 + 1))/b","B",0
214,-2,0,0,0.000000," ","integrate(sec(b*x+c)^2*sin(b*x+a),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)2/b*((tan(a/2)^2*tan(c/2)-tan(a/2)*tan(c/2)^2+tan(a/2)-tan(c/2))/(-tan(a/2)^2*tan(c/2)^2-tan(a/2)^2-tan(c/2)^2-1)*ln(abs(tan((b*x+c)/2)-1))+(tan(a/2)^2*tan(c/2)-tan(a/2)*tan(c/2)^2+tan(a/2)-tan(c/2))/(tan(a/2)^2*tan(c/2)^2+tan(a/2)^2+tan(c/2)^2+1)*ln(abs(tan((b*x+c)/2)+1))+(tan(a/2)^2*tan(c/2)^2-tan(a/2)^2+4*tan(a/2)*tan(c/2)-tan(c/2)^2+1)/(-tan(a/2)^2*tan(c/2)^2-tan(a/2)^2-tan(c/2)^2-1)/(tan((b*x+c)/2)^2-1))","F(-2)",0
215,1,174,0,3.852168," ","integrate(sec(b*x+c)^3*sin(b*x+a),x, algorithm=""giac"")","\frac{\tan\left(b x + c\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - \tan\left(b x + c\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} + 4 \, \tan\left(b x + c\right)^{2} \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{1}{2} \, c\right) + 4 \, \tan\left(b x + c\right) \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, c\right) - \tan\left(b x + c\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 4 \, \tan\left(b x + c\right) \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(b x + c\right)^{2} + 4 \, \tan\left(b x + c\right) \tan\left(\frac{1}{2} \, a\right) - 4 \, \tan\left(b x + c\right) \tan\left(\frac{1}{2} \, c\right)}{2 \, {\left(\tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, a\right)^{2} + \tan\left(\frac{1}{2} \, c\right)^{2} + 1\right)} b}"," ",0,"1/2*(tan(b*x + c)^2*tan(1/2*a)^2*tan(1/2*c)^2 - tan(b*x + c)^2*tan(1/2*a)^2 + 4*tan(b*x + c)^2*tan(1/2*a)*tan(1/2*c) + 4*tan(b*x + c)*tan(1/2*a)^2*tan(1/2*c) - tan(b*x + c)^2*tan(1/2*c)^2 - 4*tan(b*x + c)*tan(1/2*a)*tan(1/2*c)^2 + tan(b*x + c)^2 + 4*tan(b*x + c)*tan(1/2*a) - 4*tan(b*x + c)*tan(1/2*c))/((tan(1/2*a)^2*tan(1/2*c)^2 + tan(1/2*a)^2 + tan(1/2*c)^2 + 1)*b)","B",0
216,-2,0,0,0.000000," ","integrate(sec(b*x+c)^4*sin(b*x+a),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)2/b*((tan(a/2)^2*tan(c/2)-tan(a/2)*tan(c/2)^2+tan(a/2)-tan(c/2))/(-2*tan(a/2)^2*tan(c/2)^2-2*tan(a/2)^2-2*tan(c/2)^2-2)*ln(abs(tan((b*x+c)/2)-1))+(tan(a/2)^2*tan(c/2)-tan(a/2)*tan(c/2)^2+tan(a/2)-tan(c/2))/(2*tan(a/2)^2*tan(c/2)^2+2*tan(a/2)^2+2*tan(c/2)^2+2)*ln(abs(tan((b*x+c)/2)+1))+(-3*tan((b*x+c)/2)^5*tan(a/2)^2*tan(c/2)+3*tan((b*x+c)/2)^5*tan(a/2)*tan(c/2)^2-3*tan((b*x+c)/2)^5*tan(a/2)+3*tan((b*x+c)/2)^5*tan(c/2)+3*tan((b*x+c)/2)^4*tan(a/2)^2*tan(c/2)^2-3*tan((b*x+c)/2)^4*tan(a/2)^2+12*tan((b*x+c)/2)^4*tan(a/2)*tan(c/2)-3*tan((b*x+c)/2)^4*tan(c/2)^2+3*tan((b*x+c)/2)^4+3*tan((b*x+c)/2)*tan(a/2)^2*tan(c/2)-3*tan((b*x+c)/2)*tan(a/2)*tan(c/2)^2+3*tan((b*x+c)/2)*tan(a/2)-3*tan((b*x+c)/2)*tan(c/2)+tan(a/2)^2*tan(c/2)^2-tan(a/2)^2+4*tan(a/2)*tan(c/2)-tan(c/2)^2+1)/(-3*tan(a/2)^2*tan(c/2)^2-3*tan(a/2)^2-3*tan(c/2)^2-3)/(tan((b*x+c)/2)^2-1)^3)","F(-2)",0
217,1,327,0,0.230377," ","integrate(sec(b*x+c)^5*sin(b*x+a),x, algorithm=""giac"")","\frac{3 \, \tan\left(b x + c\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 3 \, \tan\left(b x + c\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{2} + 12 \, \tan\left(b x + c\right)^{4} \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{1}{2} \, c\right) + 8 \, \tan\left(b x + c\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, c\right) - 3 \, \tan\left(b x + c\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{2} - 8 \, \tan\left(b x + c\right)^{3} \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 6 \, \tan\left(b x + c\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 3 \, \tan\left(b x + c\right)^{4} + 8 \, \tan\left(b x + c\right)^{3} \tan\left(\frac{1}{2} \, a\right) - 6 \, \tan\left(b x + c\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} - 8 \, \tan\left(b x + c\right)^{3} \tan\left(\frac{1}{2} \, c\right) + 24 \, \tan\left(b x + c\right)^{2} \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{1}{2} \, c\right) + 24 \, \tan\left(b x + c\right) \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, c\right) - 6 \, \tan\left(b x + c\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 24 \, \tan\left(b x + c\right) \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 6 \, \tan\left(b x + c\right)^{2} + 24 \, \tan\left(b x + c\right) \tan\left(\frac{1}{2} \, a\right) - 24 \, \tan\left(b x + c\right) \tan\left(\frac{1}{2} \, c\right)}{12 \, {\left(\tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, a\right)^{2} + \tan\left(\frac{1}{2} \, c\right)^{2} + 1\right)} b}"," ",0,"1/12*(3*tan(b*x + c)^4*tan(1/2*a)^2*tan(1/2*c)^2 - 3*tan(b*x + c)^4*tan(1/2*a)^2 + 12*tan(b*x + c)^4*tan(1/2*a)*tan(1/2*c) + 8*tan(b*x + c)^3*tan(1/2*a)^2*tan(1/2*c) - 3*tan(b*x + c)^4*tan(1/2*c)^2 - 8*tan(b*x + c)^3*tan(1/2*a)*tan(1/2*c)^2 + 6*tan(b*x + c)^2*tan(1/2*a)^2*tan(1/2*c)^2 + 3*tan(b*x + c)^4 + 8*tan(b*x + c)^3*tan(1/2*a) - 6*tan(b*x + c)^2*tan(1/2*a)^2 - 8*tan(b*x + c)^3*tan(1/2*c) + 24*tan(b*x + c)^2*tan(1/2*a)*tan(1/2*c) + 24*tan(b*x + c)*tan(1/2*a)^2*tan(1/2*c) - 6*tan(b*x + c)^2*tan(1/2*c)^2 - 24*tan(b*x + c)*tan(1/2*a)*tan(1/2*c)^2 + 6*tan(b*x + c)^2 + 24*tan(b*x + c)*tan(1/2*a) - 24*tan(b*x + c)*tan(1/2*c))/((tan(1/2*a)^2*tan(1/2*c)^2 + tan(1/2*a)^2 + tan(1/2*c)^2 + 1)*b)","B",0
218,-2,0,0,0.000000," ","integrate(sec(b*x+c)^6*sin(b*x+a),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)2/b*((3*tan(a/2)^2*tan(c/2)-3*tan(a/2)*tan(c/2)^2+3*tan(a/2)-3*tan(c/2))/(-8*tan(a/2)^2*tan(c/2)^2-8*tan(a/2)^2-8*tan(c/2)^2-8)*ln(abs(tan((b*x+c)/2)-1))+(3*tan(a/2)^2*tan(c/2)-3*tan(a/2)*tan(c/2)^2+3*tan(a/2)-3*tan(c/2))/(8*tan(a/2)^2*tan(c/2)^2+8*tan(a/2)^2+8*tan(c/2)^2+8)*ln(abs(tan((b*x+c)/2)+1))+(-25*tan((b*x+c)/2)^9*tan(a/2)^2*tan(c/2)+25*tan((b*x+c)/2)^9*tan(a/2)*tan(c/2)^2-25*tan((b*x+c)/2)^9*tan(a/2)+25*tan((b*x+c)/2)^9*tan(c/2)+20*tan((b*x+c)/2)^8*tan(a/2)^2*tan(c/2)^2-20*tan((b*x+c)/2)^8*tan(a/2)^2+80*tan((b*x+c)/2)^8*tan(a/2)*tan(c/2)-20*tan((b*x+c)/2)^8*tan(c/2)^2+20*tan((b*x+c)/2)^8+10*tan((b*x+c)/2)^7*tan(a/2)^2*tan(c/2)-10*tan((b*x+c)/2)^7*tan(a/2)*tan(c/2)^2+10*tan((b*x+c)/2)^7*tan(a/2)-10*tan((b*x+c)/2)^7*tan(c/2)+40*tan((b*x+c)/2)^4*tan(a/2)^2*tan(c/2)^2-40*tan((b*x+c)/2)^4*tan(a/2)^2+160*tan((b*x+c)/2)^4*tan(a/2)*tan(c/2)-40*tan((b*x+c)/2)^4*tan(c/2)^2+40*tan((b*x+c)/2)^4-10*tan((b*x+c)/2)^3*tan(a/2)^2*tan(c/2)+10*tan((b*x+c)/2)^3*tan(a/2)*tan(c/2)^2-10*tan((b*x+c)/2)^3*tan(a/2)+10*tan((b*x+c)/2)^3*tan(c/2)+25*tan((b*x+c)/2)*tan(a/2)^2*tan(c/2)-25*tan((b*x+c)/2)*tan(a/2)*tan(c/2)^2+25*tan((b*x+c)/2)*tan(a/2)-25*tan((b*x+c)/2)*tan(c/2)+4*tan(a/2)^2*tan(c/2)^2-4*tan(a/2)^2+16*tan(a/2)*tan(c/2)-4*tan(c/2)^2+4)/(-20*tan(a/2)^2*tan(c/2)^2-20*tan(a/2)^2-20*tan(c/2)^2-20)/(tan((b*x+c)/2)^2-1)^5)","F(-2)",0
219,0,0,0,0.000000," ","integrate(cos(d*x+c)^n*sin(b*x+a)^2,x, algorithm=""giac"")","\int \cos\left(d x + c\right)^{n} \sin\left(b x + a\right)^{2}\,{d x}"," ",0,"integrate(cos(d*x + c)^n*sin(b*x + a)^2, x)","F",0
220,1,61,0,0.196077," ","integrate(cos(d*x+c)*sin(b*x+a)^2,x, algorithm=""giac"")","-\frac{\sin\left(2 \, b x + d x + 2 \, a + c\right)}{4 \, {\left(2 \, b + d\right)}} - \frac{\sin\left(2 \, b x - d x + 2 \, a - c\right)}{4 \, {\left(2 \, b - d\right)}} + \frac{\sin\left(d x + c\right)}{2 \, d}"," ",0,"-1/4*sin(2*b*x + d*x + 2*a + c)/(2*b + d) - 1/4*sin(2*b*x - d*x + 2*a - c)/(2*b - d) + 1/2*sin(d*x + c)/d","A",0
221,1,80,0,0.197665," ","integrate(cos(d*x+c)^2*sin(b*x+a)^2,x, algorithm=""giac"")","\frac{1}{4} \, x - \frac{\sin\left(2 \, b x + 2 \, d x + 2 \, a + 2 \, c\right)}{16 \, {\left(b + d\right)}} - \frac{\sin\left(2 \, b x - 2 \, d x + 2 \, a - 2 \, c\right)}{16 \, {\left(b - d\right)}} - \frac{\sin\left(2 \, b x + 2 \, a\right)}{8 \, b} + \frac{\sin\left(2 \, d x + 2 \, c\right)}{8 \, d}"," ",0,"1/4*x - 1/16*sin(2*b*x + 2*d*x + 2*a + 2*c)/(b + d) - 1/16*sin(2*b*x - 2*d*x + 2*a - 2*c)/(b - d) - 1/8*sin(2*b*x + 2*a)/b + 1/8*sin(2*d*x + 2*c)/d","A",0
222,1,129,0,0.277754," ","integrate(cos(d*x+c)^3*sin(b*x+a)^2,x, algorithm=""giac"")","-\frac{\sin\left(2 \, b x + 3 \, d x + 2 \, a + 3 \, c\right)}{16 \, {\left(2 \, b + 3 \, d\right)}} - \frac{3 \, \sin\left(2 \, b x + d x + 2 \, a + c\right)}{16 \, {\left(2 \, b + d\right)}} - \frac{3 \, \sin\left(2 \, b x - d x + 2 \, a - c\right)}{16 \, {\left(2 \, b - d\right)}} - \frac{\sin\left(2 \, b x - 3 \, d x + 2 \, a - 3 \, c\right)}{16 \, {\left(2 \, b - 3 \, d\right)}} + \frac{\sin\left(3 \, d x + 3 \, c\right)}{24 \, d} + \frac{3 \, \sin\left(d x + c\right)}{8 \, d}"," ",0,"-1/16*sin(2*b*x + 3*d*x + 2*a + 3*c)/(2*b + 3*d) - 3/16*sin(2*b*x + d*x + 2*a + c)/(2*b + d) - 3/16*sin(2*b*x - d*x + 2*a - c)/(2*b - d) - 1/16*sin(2*b*x - 3*d*x + 2*a - 3*c)/(2*b - 3*d) + 1/24*sin(3*d*x + 3*c)/d + 3/8*sin(d*x + c)/d","A",0
223,0,0,0,0.000000," ","integrate(cos(d*x+c)^n*sin(b*x+a)^3,x, algorithm=""giac"")","\int \cos\left(d x + c\right)^{n} \sin\left(b x + a\right)^{3}\,{d x}"," ",0,"integrate(cos(d*x + c)^n*sin(b*x + a)^3, x)","F",0
224,1,89,0,0.248585," ","integrate(cos(d*x+c)*sin(b*x+a)^3,x, algorithm=""giac"")","\frac{\cos\left(3 \, b x + d x + 3 \, a + c\right)}{8 \, {\left(3 \, b + d\right)}} + \frac{\cos\left(3 \, b x - d x + 3 \, a - c\right)}{8 \, {\left(3 \, b - d\right)}} - \frac{3 \, \cos\left(b x + d x + a + c\right)}{8 \, {\left(b + d\right)}} - \frac{3 \, \cos\left(b x - d x + a - c\right)}{8 \, {\left(b - d\right)}}"," ",0,"1/8*cos(3*b*x + d*x + 3*a + c)/(3*b + d) + 1/8*cos(3*b*x - d*x + 3*a - c)/(3*b - d) - 3/8*cos(b*x + d*x + a + c)/(b + d) - 3/8*cos(b*x - d*x + a - c)/(b - d)","A",0
225,1,124,0,0.194661," ","integrate(cos(d*x+c)^2*sin(b*x+a)^3,x, algorithm=""giac"")","\frac{\cos\left(3 \, b x + 2 \, d x + 3 \, a + 2 \, c\right)}{16 \, {\left(3 \, b + 2 \, d\right)}} + \frac{\cos\left(3 \, b x - 2 \, d x + 3 \, a - 2 \, c\right)}{16 \, {\left(3 \, b - 2 \, d\right)}} + \frac{\cos\left(3 \, b x + 3 \, a\right)}{24 \, b} - \frac{3 \, \cos\left(b x + 2 \, d x + a + 2 \, c\right)}{16 \, {\left(b + 2 \, d\right)}} - \frac{3 \, \cos\left(b x - 2 \, d x + a - 2 \, c\right)}{16 \, {\left(b - 2 \, d\right)}} - \frac{3 \, \cos\left(b x + a\right)}{8 \, b}"," ",0,"1/16*cos(3*b*x + 2*d*x + 3*a + 2*c)/(3*b + 2*d) + 1/16*cos(3*b*x - 2*d*x + 3*a - 2*c)/(3*b - 2*d) + 1/24*cos(3*b*x + 3*a)/b - 3/16*cos(b*x + 2*d*x + a + 2*c)/(b + 2*d) - 3/16*cos(b*x - 2*d*x + a - 2*c)/(b - 2*d) - 3/8*cos(b*x + a)/b","A",0
226,1,181,0,0.281689," ","integrate(cos(d*x+c)^3*sin(b*x+a)^3,x, algorithm=""giac"")","\frac{\cos\left(3 \, b x + 3 \, d x + 3 \, a + 3 \, c\right)}{96 \, {\left(b + d\right)}} + \frac{3 \, \cos\left(3 \, b x + d x + 3 \, a + c\right)}{32 \, {\left(3 \, b + d\right)}} + \frac{3 \, \cos\left(3 \, b x - d x + 3 \, a - c\right)}{32 \, {\left(3 \, b - d\right)}} + \frac{\cos\left(3 \, b x - 3 \, d x + 3 \, a - 3 \, c\right)}{96 \, {\left(b - d\right)}} - \frac{3 \, \cos\left(b x + 3 \, d x + a + 3 \, c\right)}{32 \, {\left(b + 3 \, d\right)}} - \frac{9 \, \cos\left(b x + d x + a + c\right)}{32 \, {\left(b + d\right)}} - \frac{9 \, \cos\left(b x - d x + a - c\right)}{32 \, {\left(b - d\right)}} - \frac{3 \, \cos\left(b x - 3 \, d x + a - 3 \, c\right)}{32 \, {\left(b - 3 \, d\right)}}"," ",0,"1/96*cos(3*b*x + 3*d*x + 3*a + 3*c)/(b + d) + 3/32*cos(3*b*x + d*x + 3*a + c)/(3*b + d) + 3/32*cos(3*b*x - d*x + 3*a - c)/(3*b - d) + 1/96*cos(3*b*x - 3*d*x + 3*a - 3*c)/(b - d) - 3/32*cos(b*x + 3*d*x + a + 3*c)/(b + 3*d) - 9/32*cos(b*x + d*x + a + c)/(b + d) - 9/32*cos(b*x - d*x + a - c)/(b - d) - 3/32*cos(b*x - 3*d*x + a - 3*c)/(b - 3*d)","A",0
227,1,482,0,1.556461," ","integrate(cos(b*x+a)/sin(b*x+c),x, algorithm=""giac"")","-\frac{\frac{4 \, {\left(\tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, c\right) - \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, a\right) - \tan\left(\frac{1}{2} \, c\right)\right)} {\left(b x + a\right)}}{\tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, a\right)^{2} + \tan\left(\frac{1}{2} \, c\right)^{2} + 1} + \frac{{\left(\tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - \tan\left(\frac{1}{2} \, a\right)^{2} + 4 \, \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{1}{2} \, c\right) - \tan\left(\frac{1}{2} \, c\right)^{2} + 1\right)} \log\left(\tan\left(b x + a\right)^{2} + 1\right)}{\tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, a\right)^{2} + \tan\left(\frac{1}{2} \, c\right)^{2} + 1} - \frac{2 \, {\left(\tan\left(\frac{1}{2} \, a\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{4} - 2 \, \tan\left(\frac{1}{2} \, a\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{2} + 8 \, \tan\left(\frac{1}{2} \, a\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{3} - 2 \, \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{4} + \tan\left(\frac{1}{2} \, a\right)^{4} - 8 \, \tan\left(\frac{1}{2} \, a\right)^{3} \tan\left(\frac{1}{2} \, c\right) + 20 \, \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 8 \, \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{1}{2} \, c\right)^{3} + \tan\left(\frac{1}{2} \, c\right)^{4} - 2 \, \tan\left(\frac{1}{2} \, a\right)^{2} + 8 \, \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{1}{2} \, c\right) - 2 \, \tan\left(\frac{1}{2} \, c\right)^{2} + 1\right)} \log\left({\left| \tan\left(b x + a\right) \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - \tan\left(b x + a\right) \tan\left(\frac{1}{2} \, a\right)^{2} + 4 \, \tan\left(b x + a\right) \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{1}{2} \, c\right) - 2 \, \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, c\right) - \tan\left(b x + a\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(b x + a\right) - 2 \, \tan\left(\frac{1}{2} \, a\right) + 2 \, \tan\left(\frac{1}{2} \, c\right) \right|}\right)}{\tan\left(\frac{1}{2} \, a\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{4} + 4 \, \tan\left(\frac{1}{2} \, a\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{3} - \tan\left(\frac{1}{2} \, a\right)^{4} + 4 \, \tan\left(\frac{1}{2} \, a\right)^{3} \tan\left(\frac{1}{2} \, c\right) + 4 \, \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{1}{2} \, c\right)^{3} - \tan\left(\frac{1}{2} \, c\right)^{4} + 4 \, \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{1}{2} \, c\right) + 1}}{2 \, b}"," ",0,"-1/2*(4*(tan(1/2*a)^2*tan(1/2*c) - tan(1/2*a)*tan(1/2*c)^2 + tan(1/2*a) - tan(1/2*c))*(b*x + a)/(tan(1/2*a)^2*tan(1/2*c)^2 + tan(1/2*a)^2 + tan(1/2*c)^2 + 1) + (tan(1/2*a)^2*tan(1/2*c)^2 - tan(1/2*a)^2 + 4*tan(1/2*a)*tan(1/2*c) - tan(1/2*c)^2 + 1)*log(tan(b*x + a)^2 + 1)/(tan(1/2*a)^2*tan(1/2*c)^2 + tan(1/2*a)^2 + tan(1/2*c)^2 + 1) - 2*(tan(1/2*a)^4*tan(1/2*c)^4 - 2*tan(1/2*a)^4*tan(1/2*c)^2 + 8*tan(1/2*a)^3*tan(1/2*c)^3 - 2*tan(1/2*a)^2*tan(1/2*c)^4 + tan(1/2*a)^4 - 8*tan(1/2*a)^3*tan(1/2*c) + 20*tan(1/2*a)^2*tan(1/2*c)^2 - 8*tan(1/2*a)*tan(1/2*c)^3 + tan(1/2*c)^4 - 2*tan(1/2*a)^2 + 8*tan(1/2*a)*tan(1/2*c) - 2*tan(1/2*c)^2 + 1)*log(abs(tan(b*x + a)*tan(1/2*a)^2*tan(1/2*c)^2 - tan(b*x + a)*tan(1/2*a)^2 + 4*tan(b*x + a)*tan(1/2*a)*tan(1/2*c) - 2*tan(1/2*a)^2*tan(1/2*c) - tan(b*x + a)*tan(1/2*c)^2 + 2*tan(1/2*a)*tan(1/2*c)^2 + tan(b*x + a) - 2*tan(1/2*a) + 2*tan(1/2*c)))/(tan(1/2*a)^4*tan(1/2*c)^4 + 4*tan(1/2*a)^3*tan(1/2*c)^3 - tan(1/2*a)^4 + 4*tan(1/2*a)^3*tan(1/2*c) + 4*tan(1/2*a)*tan(1/2*c)^3 - tan(1/2*c)^4 + 4*tan(1/2*a)*tan(1/2*c) + 1))/b","B",0
228,1,893,0,0.465927," ","integrate(cos(b*x+a)/sin(b*x+c)^2,x, algorithm=""giac"")","-\frac{\frac{4 \, {\left(\tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, c\right) - \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, a\right) - \tan\left(\frac{1}{2} \, c\right)\right)} \log\left(\frac{{\left| 2 \, \tan\left(\frac{1}{2} \, b x + \frac{1}{2} \, a\right) \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, c\right) - 2 \, \tan\left(\frac{1}{2} \, b x + \frac{1}{2} \, a\right) \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, b x + \frac{1}{2} \, a\right) \tan\left(\frac{1}{2} \, a\right) - 2 \, \tan\left(\frac{1}{2} \, a\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, b x + \frac{1}{2} \, a\right) \tan\left(\frac{1}{2} \, c\right) + 4 \, \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{1}{2} \, c\right) - 2 \, \tan\left(\frac{1}{2} \, c\right)^{2} \right|}}{{\left| 2 \, \tan\left(\frac{1}{2} \, b x + \frac{1}{2} \, a\right) \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, c\right) - 2 \, \tan\left(\frac{1}{2} \, b x + \frac{1}{2} \, a\right) \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, b x + \frac{1}{2} \, a\right) \tan\left(\frac{1}{2} \, a\right) - 2 \, \tan\left(\frac{1}{2} \, b x + \frac{1}{2} \, a\right) \tan\left(\frac{1}{2} \, c\right) + 4 \, \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{1}{2} \, c\right) + 2 \right|}}\right)}{\tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, a\right)^{2} + \tan\left(\frac{1}{2} \, c\right)^{2} + 1} - \frac{\tan\left(\frac{1}{2} \, b x + \frac{1}{2} \, a\right) \tan\left(\frac{1}{2} \, a\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{4} - 2 \, \tan\left(\frac{1}{2} \, b x + \frac{1}{2} \, a\right) \tan\left(\frac{1}{2} \, a\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{2} + 8 \, \tan\left(\frac{1}{2} \, b x + \frac{1}{2} \, a\right) \tan\left(\frac{1}{2} \, a\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{3} - 2 \, \tan\left(\frac{1}{2} \, a\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{3} - 2 \, \tan\left(\frac{1}{2} \, b x + \frac{1}{2} \, a\right) \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, a\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{4} + \tan\left(\frac{1}{2} \, b x + \frac{1}{2} \, a\right) \tan\left(\frac{1}{2} \, a\right)^{4} - 8 \, \tan\left(\frac{1}{2} \, b x + \frac{1}{2} \, a\right) \tan\left(\frac{1}{2} \, a\right)^{3} \tan\left(\frac{1}{2} \, c\right) + 2 \, \tan\left(\frac{1}{2} \, a\right)^{4} \tan\left(\frac{1}{2} \, c\right) + 20 \, \tan\left(\frac{1}{2} \, b x + \frac{1}{2} \, a\right) \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 12 \, \tan\left(\frac{1}{2} \, a\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{2} - 8 \, \tan\left(\frac{1}{2} \, b x + \frac{1}{2} \, a\right) \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{1}{2} \, c\right)^{3} + 12 \, \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{3} + \tan\left(\frac{1}{2} \, b x + \frac{1}{2} \, a\right) \tan\left(\frac{1}{2} \, c\right)^{4} - 2 \, \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{1}{2} \, c\right)^{4} - 2 \, \tan\left(\frac{1}{2} \, b x + \frac{1}{2} \, a\right) \tan\left(\frac{1}{2} \, a\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, a\right)^{3} + 8 \, \tan\left(\frac{1}{2} \, b x + \frac{1}{2} \, a\right) \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{1}{2} \, c\right) - 12 \, \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, c\right) - 2 \, \tan\left(\frac{1}{2} \, b x + \frac{1}{2} \, a\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 12 \, \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, c\right)^{3} + \tan\left(\frac{1}{2} \, b x + \frac{1}{2} \, a\right) - 2 \, \tan\left(\frac{1}{2} \, a\right) + 2 \, \tan\left(\frac{1}{2} \, c\right)}{{\left(\tan\left(\frac{1}{2} \, b x + \frac{1}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, c\right) - \tan\left(\frac{1}{2} \, b x + \frac{1}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, b x + \frac{1}{2} \, a\right) \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, b x + \frac{1}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right) - \tan\left(\frac{1}{2} \, b x + \frac{1}{2} \, a\right) \tan\left(\frac{1}{2} \, a\right)^{2} - \tan\left(\frac{1}{2} \, b x + \frac{1}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, c\right) + 4 \, \tan\left(\frac{1}{2} \, b x + \frac{1}{2} \, a\right) \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{1}{2} \, c\right) - \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, c\right) - \tan\left(\frac{1}{2} \, b x + \frac{1}{2} \, a\right) \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, b x + \frac{1}{2} \, a\right) - \tan\left(\frac{1}{2} \, a\right) + \tan\left(\frac{1}{2} \, c\right)\right)} {\left(\tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, c\right) - \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, a\right) - \tan\left(\frac{1}{2} \, c\right)\right)}}}{2 \, b}"," ",0,"-1/2*(4*(tan(1/2*a)^2*tan(1/2*c) - tan(1/2*a)*tan(1/2*c)^2 + tan(1/2*a) - tan(1/2*c))*log(abs(2*tan(1/2*b*x + 1/2*a)*tan(1/2*a)^2*tan(1/2*c) - 2*tan(1/2*b*x + 1/2*a)*tan(1/2*a)*tan(1/2*c)^2 + 2*tan(1/2*b*x + 1/2*a)*tan(1/2*a) - 2*tan(1/2*a)^2 - 2*tan(1/2*b*x + 1/2*a)*tan(1/2*c) + 4*tan(1/2*a)*tan(1/2*c) - 2*tan(1/2*c)^2)/abs(2*tan(1/2*b*x + 1/2*a)*tan(1/2*a)^2*tan(1/2*c) - 2*tan(1/2*b*x + 1/2*a)*tan(1/2*a)*tan(1/2*c)^2 + 2*tan(1/2*a)^2*tan(1/2*c)^2 + 2*tan(1/2*b*x + 1/2*a)*tan(1/2*a) - 2*tan(1/2*b*x + 1/2*a)*tan(1/2*c) + 4*tan(1/2*a)*tan(1/2*c) + 2))/(tan(1/2*a)^2*tan(1/2*c)^2 + tan(1/2*a)^2 + tan(1/2*c)^2 + 1) - (tan(1/2*b*x + 1/2*a)*tan(1/2*a)^4*tan(1/2*c)^4 - 2*tan(1/2*b*x + 1/2*a)*tan(1/2*a)^4*tan(1/2*c)^2 + 8*tan(1/2*b*x + 1/2*a)*tan(1/2*a)^3*tan(1/2*c)^3 - 2*tan(1/2*a)^4*tan(1/2*c)^3 - 2*tan(1/2*b*x + 1/2*a)*tan(1/2*a)^2*tan(1/2*c)^4 + 2*tan(1/2*a)^3*tan(1/2*c)^4 + tan(1/2*b*x + 1/2*a)*tan(1/2*a)^4 - 8*tan(1/2*b*x + 1/2*a)*tan(1/2*a)^3*tan(1/2*c) + 2*tan(1/2*a)^4*tan(1/2*c) + 20*tan(1/2*b*x + 1/2*a)*tan(1/2*a)^2*tan(1/2*c)^2 - 12*tan(1/2*a)^3*tan(1/2*c)^2 - 8*tan(1/2*b*x + 1/2*a)*tan(1/2*a)*tan(1/2*c)^3 + 12*tan(1/2*a)^2*tan(1/2*c)^3 + tan(1/2*b*x + 1/2*a)*tan(1/2*c)^4 - 2*tan(1/2*a)*tan(1/2*c)^4 - 2*tan(1/2*b*x + 1/2*a)*tan(1/2*a)^2 + 2*tan(1/2*a)^3 + 8*tan(1/2*b*x + 1/2*a)*tan(1/2*a)*tan(1/2*c) - 12*tan(1/2*a)^2*tan(1/2*c) - 2*tan(1/2*b*x + 1/2*a)*tan(1/2*c)^2 + 12*tan(1/2*a)*tan(1/2*c)^2 - 2*tan(1/2*c)^3 + tan(1/2*b*x + 1/2*a) - 2*tan(1/2*a) + 2*tan(1/2*c))/((tan(1/2*b*x + 1/2*a)^2*tan(1/2*a)^2*tan(1/2*c) - tan(1/2*b*x + 1/2*a)^2*tan(1/2*a)*tan(1/2*c)^2 + tan(1/2*b*x + 1/2*a)*tan(1/2*a)^2*tan(1/2*c)^2 + tan(1/2*b*x + 1/2*a)^2*tan(1/2*a) - tan(1/2*b*x + 1/2*a)*tan(1/2*a)^2 - tan(1/2*b*x + 1/2*a)^2*tan(1/2*c) + 4*tan(1/2*b*x + 1/2*a)*tan(1/2*a)*tan(1/2*c) - tan(1/2*a)^2*tan(1/2*c) - tan(1/2*b*x + 1/2*a)*tan(1/2*c)^2 + tan(1/2*a)*tan(1/2*c)^2 + tan(1/2*b*x + 1/2*a) - tan(1/2*a) + tan(1/2*c))*(tan(1/2*a)^2*tan(1/2*c) - tan(1/2*a)*tan(1/2*c)^2 + tan(1/2*a) - tan(1/2*c))))/b","B",0
229,1,327,0,0.285396," ","integrate(cos(b*x+a)/sin(b*x+c)^3,x, algorithm=""giac"")","-\frac{\tan\left(\frac{1}{2} \, a\right)^{6} \tan\left(\frac{1}{2} \, c\right)^{6} + 3 \, \tan\left(\frac{1}{2} \, a\right)^{6} \tan\left(\frac{1}{2} \, c\right)^{4} + 3 \, \tan\left(\frac{1}{2} \, a\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{6} + 3 \, \tan\left(\frac{1}{2} \, a\right)^{6} \tan\left(\frac{1}{2} \, c\right)^{2} + 9 \, \tan\left(\frac{1}{2} \, a\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{4} + 3 \, \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{6} + \tan\left(\frac{1}{2} \, a\right)^{6} + 9 \, \tan\left(\frac{1}{2} \, a\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{2} + 9 \, \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{4} + \tan\left(\frac{1}{2} \, c\right)^{6} + 3 \, \tan\left(\frac{1}{2} \, a\right)^{4} + 9 \, \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 3 \, \tan\left(\frac{1}{2} \, c\right)^{4} + 3 \, \tan\left(\frac{1}{2} \, a\right)^{2} + 3 \, \tan\left(\frac{1}{2} \, c\right)^{2} + 1}{2 \, {\left(\tan\left(b x + a\right) \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - \tan\left(b x + a\right) \tan\left(\frac{1}{2} \, a\right)^{2} + 4 \, \tan\left(b x + a\right) \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{1}{2} \, c\right) - 2 \, \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, c\right) - \tan\left(b x + a\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(b x + a\right) - 2 \, \tan\left(\frac{1}{2} \, a\right) + 2 \, \tan\left(\frac{1}{2} \, c\right)\right)}^{2} {\left(\tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - \tan\left(\frac{1}{2} \, a\right)^{2} + 4 \, \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{1}{2} \, c\right) - \tan\left(\frac{1}{2} \, c\right)^{2} + 1\right)} b}"," ",0,"-1/2*(tan(1/2*a)^6*tan(1/2*c)^6 + 3*tan(1/2*a)^6*tan(1/2*c)^4 + 3*tan(1/2*a)^4*tan(1/2*c)^6 + 3*tan(1/2*a)^6*tan(1/2*c)^2 + 9*tan(1/2*a)^4*tan(1/2*c)^4 + 3*tan(1/2*a)^2*tan(1/2*c)^6 + tan(1/2*a)^6 + 9*tan(1/2*a)^4*tan(1/2*c)^2 + 9*tan(1/2*a)^2*tan(1/2*c)^4 + tan(1/2*c)^6 + 3*tan(1/2*a)^4 + 9*tan(1/2*a)^2*tan(1/2*c)^2 + 3*tan(1/2*c)^4 + 3*tan(1/2*a)^2 + 3*tan(1/2*c)^2 + 1)/((tan(b*x + a)*tan(1/2*a)^2*tan(1/2*c)^2 - tan(b*x + a)*tan(1/2*a)^2 + 4*tan(b*x + a)*tan(1/2*a)*tan(1/2*c) - 2*tan(1/2*a)^2*tan(1/2*c) - tan(b*x + a)*tan(1/2*c)^2 + 2*tan(1/2*a)*tan(1/2*c)^2 + tan(b*x + a) - 2*tan(1/2*a) + 2*tan(1/2*c))^2*(tan(1/2*a)^2*tan(1/2*c)^2 - tan(1/2*a)^2 + 4*tan(1/2*a)*tan(1/2*c) - tan(1/2*c)^2 + 1)*b)","B",0
230,0,0,0,0.000000," ","integrate(sin(b*x+a)*tan(b*x+c)^3,x, algorithm=""giac"")","\int \sin\left(b x + a\right) \tan\left(b x + c\right)^{3}\,{d x}"," ",0,"integrate(sin(b*x + a)*tan(b*x + c)^3, x)","F",0
231,0,0,0,0.000000," ","integrate(sin(b*x+a)*tan(b*x+c)^2,x, algorithm=""giac"")","\int \sin\left(b x + a\right) \tan\left(b x + c\right)^{2}\,{d x}"," ",0,"integrate(sin(b*x + a)*tan(b*x + c)^2, x)","F",0
232,0,0,0,0.000000," ","integrate(sin(b*x+a)*tan(b*x+c),x, algorithm=""giac"")","\int \sin\left(b x + a\right) \tan\left(b x + c\right)\,{d x}"," ",0,"integrate(sin(b*x + a)*tan(b*x + c), x)","F",0
233,-2,0,0,0.000000," ","integrate(cot(b*x+c)*sin(b*x+a),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)2/b*((-tan(a/2)^2*tan(c/2)+tan(a/2)*tan(c/2)^2-tan(a/2)+tan(c/2))/(-tan(a/2)^2*tan(c/2)^2-tan(a/2)^2-tan(c/2)^2-1)*ln(abs(tan(b*x/2)+tan(c/2)))+(-tan(a/2)^2*tan(c/2)^2+tan(a/2)*tan(c/2)^3-tan(a/2)*tan(c/2)+tan(c/2)^2)/(tan(a/2)^2*tan(c/2)^3+tan(a/2)^2*tan(c/2)+tan(c/2)^3+tan(c/2))*ln(abs(tan(b*x/2)*tan(c/2)-1))+(-tan(b*x/2)*tan(a/2)^2+tan(b*x/2)+2*tan(a/2))/(tan(a/2)^2+1)/(tan(b*x/2)^2+1))","F(-2)",0
234,-2,0,0,0.000000," ","integrate(cot(b*x+c)^2*sin(b*x+a),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)2/b*((tan(c/2)^2*tan(a/2)^2-tan(c/2)^2+4*tan(c/2)*tan(a/2)-tan(a/2)^2+1)/(2*tan(c/2)^2*tan(a/2)^2+2*tan(c/2)^2+2*tan(a/2)^2+2)*ln(abs(tan(b*x/2)+tan(c/2)))+(tan(c/2)^3*tan(a/2)^2-tan(c/2)^3+4*tan(c/2)^2*tan(a/2)-tan(c/2)*tan(a/2)^2+tan(c/2))/(-2*tan(c/2)^3*tan(a/2)^2-2*tan(c/2)^3-2*tan(c/2)*tan(a/2)^2-2*tan(c/2))*ln(abs(tan(b*x/2)*tan(c/2)-1))+(-tan(b*x/2)^3*tan(c/2)^4*tan(a/2)+tan(b*x/2)^3*tan(c/2)^3*tan(a/2)^2-tan(b*x/2)^3*tan(c/2)^3+6*tan(b*x/2)^3*tan(c/2)^2*tan(a/2)-tan(b*x/2)^3*tan(c/2)*tan(a/2)^2+tan(b*x/2)^3*tan(c/2)-tan(b*x/2)^3*tan(a/2)+6*tan(b*x/2)^2*tan(c/2)^3*tan(a/2)-6*tan(b*x/2)^2*tan(c/2)*tan(a/2)-tan(b*x/2)*tan(c/2)^4*tan(a/2)+3*tan(b*x/2)*tan(c/2)^3*tan(a/2)^2-3*tan(b*x/2)*tan(c/2)^3-2*tan(b*x/2)*tan(c/2)^2*tan(a/2)-3*tan(b*x/2)*tan(c/2)*tan(a/2)^2+3*tan(b*x/2)*tan(c/2)-tan(b*x/2)*tan(a/2)+2*tan(c/2)^3*tan(a/2)-4*tan(c/2)^2*tan(a/2)^2+4*tan(c/2)^2-2*tan(c/2)*tan(a/2))/(-2*tan(c/2)*tan(a/2)^2-2*tan(c/2))/(tan(b*x/2)^4*tan(c/2)+tan(b*x/2)^3*tan(c/2)^2-tan(b*x/2)^3+tan(b*x/2)*tan(c/2)^2-tan(b*x/2)-tan(c/2)))","F(-2)",0
235,-2,0,0,0.000000," ","integrate(cot(b*x+c)^3*sin(b*x+a),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)2/b*((tan(b*x/2)*tan(a/2)^2-tan(b*x/2)-2*tan(a/2))/(tan(a/2)^2+1)/(tan(b*x/2)^2+1)+(2*tan(b*x/2)^3*tan(c/2)^7*tan(a/2)+6*tan(b*x/2)^3*tan(c/2)^5*tan(a/2)-4*tan(b*x/2)^3*tan(c/2)^4*tan(a/2)^2+4*tan(b*x/2)^3*tan(c/2)^4-6*tan(b*x/2)^3*tan(c/2)^3*tan(a/2)-2*tan(b*x/2)^3*tan(c/2)*tan(a/2)+tan(b*x/2)^2*tan(c/2)^8*tan(a/2)+tan(b*x/2)^2*tan(c/2)^7*tan(a/2)^2-tan(b*x/2)^2*tan(c/2)^7+2*tan(b*x/2)^2*tan(c/2)^6*tan(a/2)-5*tan(b*x/2)^2*tan(c/2)^5*tan(a/2)^2+5*tan(b*x/2)^2*tan(c/2)^5-22*tan(b*x/2)^2*tan(c/2)^4*tan(a/2)+5*tan(b*x/2)^2*tan(c/2)^3*tan(a/2)^2-5*tan(b*x/2)^2*tan(c/2)^3+2*tan(b*x/2)^2*tan(c/2)^2*tan(a/2)-tan(b*x/2)^2*tan(c/2)*tan(a/2)^2+tan(b*x/2)^2*tan(c/2)+tan(b*x/2)^2*tan(a/2)-2*tan(b*x/2)*tan(c/2)^7*tan(a/2)-4*tan(b*x/2)*tan(c/2)^6*tan(a/2)^2+4*tan(b*x/2)*tan(c/2)^6-14*tan(b*x/2)*tan(c/2)^5*tan(a/2)+4*tan(b*x/2)*tan(c/2)^4*tan(a/2)^2-4*tan(b*x/2)*tan(c/2)^4+14*tan(b*x/2)*tan(c/2)^3*tan(a/2)-4*tan(b*x/2)*tan(c/2)^2*tan(a/2)^2+4*tan(b*x/2)*tan(c/2)^2+2*tan(b*x/2)*tan(c/2)*tan(a/2)+2*tan(c/2)^6*tan(a/2)+2*tan(c/2)^5*tan(a/2)^2-2*tan(c/2)^5+12*tan(c/2)^4*tan(a/2)-2*tan(c/2)^3*tan(a/2)^2+2*tan(c/2)^3+2*tan(c/2)^2*tan(a/2))/(-8*tan(c/2)^2*tan(a/2)^2-8*tan(c/2)^2)/(tan(b*x/2)^2*tan(c/2)+tan(b*x/2)*tan(c/2)^2-tan(b*x/2)-tan(c/2))^2+(-3*tan(c/2)^2*tan(a/2)+3*tan(c/2)*tan(a/2)^2-3*tan(c/2)+3*tan(a/2))/(-2*tan(c/2)^2*tan(a/2)^2-2*tan(c/2)^2-2*tan(a/2)^2-2)*ln(abs(tan(b*x/2)+tan(c/2)))+(-3*tan(c/2)^3*tan(a/2)+3*tan(c/2)^2*tan(a/2)^2-3*tan(c/2)^2+3*tan(c/2)*tan(a/2))/(2*tan(c/2)^3*tan(a/2)^2+2*tan(c/2)^3+2*tan(c/2)*tan(a/2)^2+2*tan(c/2))*ln(abs(tan(b*x/2)*tan(c/2)-1)))","F(-2)",0
236,0,0,0,0.000000," ","integrate(sin(b*x+a)*tan(d*x+c),x, algorithm=""giac"")","\int \sin\left(b x + a\right) \tan\left(d x + c\right)\,{d x}"," ",0,"integrate(sin(b*x + a)*tan(d*x + c), x)","F",0
237,0,0,0,0.000000," ","integrate(cot(d*x+c)*sin(b*x+a),x, algorithm=""giac"")","\int \cot\left(d x + c\right) \sin\left(b x + a\right)\,{d x}"," ",0,"integrate(cot(d*x + c)*sin(b*x + a), x)","F",0
238,1,84,0,5.945406," ","integrate(cos(b*x+a)*cos(d*x+c)^3,x, algorithm=""giac"")","\frac{\sin\left(b x + 3 \, d x + a + 3 \, c\right)}{8 \, {\left(b + 3 \, d\right)}} + \frac{3 \, \sin\left(b x + d x + a + c\right)}{8 \, {\left(b + d\right)}} + \frac{3 \, \sin\left(b x - d x + a - c\right)}{8 \, {\left(b - d\right)}} + \frac{\sin\left(b x - 3 \, d x + a - 3 \, c\right)}{8 \, {\left(b - 3 \, d\right)}}"," ",0,"1/8*sin(b*x + 3*d*x + a + 3*c)/(b + 3*d) + 3/8*sin(b*x + d*x + a + c)/(b + d) + 3/8*sin(b*x - d*x + a - c)/(b - d) + 1/8*sin(b*x - 3*d*x + a - 3*c)/(b - 3*d)","A",0
239,1,56,0,0.195716," ","integrate(cos(b*x+a)*cos(d*x+c)^2,x, algorithm=""giac"")","\frac{\sin\left(b x + 2 \, d x + a + 2 \, c\right)}{4 \, {\left(b + 2 \, d\right)}} + \frac{\sin\left(b x - 2 \, d x + a - 2 \, c\right)}{4 \, {\left(b - 2 \, d\right)}} + \frac{\sin\left(b x + a\right)}{2 \, b}"," ",0,"1/4*sin(b*x + 2*d*x + a + 2*c)/(b + 2*d) + 1/4*sin(b*x - 2*d*x + a - 2*c)/(b - 2*d) + 1/2*sin(b*x + a)/b","A",0
240,1,40,0,0.819844," ","integrate(cos(b*x+a)*cos(d*x+c),x, algorithm=""giac"")","\frac{\sin\left(b x + d x + a + c\right)}{2 \, {\left(b + d\right)}} + \frac{\sin\left(b x - d x + a - c\right)}{2 \, {\left(b - d\right)}}"," ",0,"1/2*sin(b*x + d*x + a + c)/(b + d) + 1/2*sin(b*x - d*x + a - c)/(b - d)","A",0
241,1,440,0,0.260915," ","integrate(cos(b*x+a)*sec(b*x+c),x, algorithm=""giac"")","\frac{\frac{{\left(\tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - \tan\left(\frac{1}{2} \, a\right)^{2} + 4 \, \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{1}{2} \, c\right) - \tan\left(\frac{1}{2} \, c\right)^{2} + 1\right)} {\left(b x + a\right)}}{\tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, a\right)^{2} + \tan\left(\frac{1}{2} \, c\right)^{2} + 1} - \frac{{\left(\tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, c\right) - \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, a\right) - \tan\left(\frac{1}{2} \, c\right)\right)} \log\left(\tan\left(b x + a\right)^{2} + 1\right)}{\tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, a\right)^{2} + \tan\left(\frac{1}{2} \, c\right)^{2} + 1} + \frac{2 \, {\left(\tan\left(\frac{1}{2} \, a\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, a\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{3} + \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, a\right)^{3} \tan\left(\frac{1}{2} \, c\right) - 4 \, \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{1}{2} \, c\right)^{3} + \tan\left(\frac{1}{2} \, a\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{1}{2} \, c\right) + \tan\left(\frac{1}{2} \, c\right)^{2}\right)} \log\left({\left| 2 \, \tan\left(b x + a\right) \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, c\right) - 2 \, \tan\left(b x + a\right) \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(b x + a\right) \tan\left(\frac{1}{2} \, a\right) - \tan\left(\frac{1}{2} \, a\right)^{2} - 2 \, \tan\left(b x + a\right) \tan\left(\frac{1}{2} \, c\right) + 4 \, \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{1}{2} \, c\right) - \tan\left(\frac{1}{2} \, c\right)^{2} + 1 \right|}\right)}{\tan\left(\frac{1}{2} \, a\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{3} - \tan\left(\frac{1}{2} \, a\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{4} + \tan\left(\frac{1}{2} \, a\right)^{4} \tan\left(\frac{1}{2} \, c\right) - \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{1}{2} \, c\right)^{4} + \tan\left(\frac{1}{2} \, a\right)^{3} - \tan\left(\frac{1}{2} \, c\right)^{3} + \tan\left(\frac{1}{2} \, a\right) - \tan\left(\frac{1}{2} \, c\right)}}{b}"," ",0,"((tan(1/2*a)^2*tan(1/2*c)^2 - tan(1/2*a)^2 + 4*tan(1/2*a)*tan(1/2*c) - tan(1/2*c)^2 + 1)*(b*x + a)/(tan(1/2*a)^2*tan(1/2*c)^2 + tan(1/2*a)^2 + tan(1/2*c)^2 + 1) - (tan(1/2*a)^2*tan(1/2*c) - tan(1/2*a)*tan(1/2*c)^2 + tan(1/2*a) - tan(1/2*c))*log(tan(b*x + a)^2 + 1)/(tan(1/2*a)^2*tan(1/2*c)^2 + tan(1/2*a)^2 + tan(1/2*c)^2 + 1) + 2*(tan(1/2*a)^4*tan(1/2*c)^2 - 2*tan(1/2*a)^3*tan(1/2*c)^3 + tan(1/2*a)^2*tan(1/2*c)^4 + 2*tan(1/2*a)^3*tan(1/2*c) - 4*tan(1/2*a)^2*tan(1/2*c)^2 + 2*tan(1/2*a)*tan(1/2*c)^3 + tan(1/2*a)^2 - 2*tan(1/2*a)*tan(1/2*c) + tan(1/2*c)^2)*log(abs(2*tan(b*x + a)*tan(1/2*a)^2*tan(1/2*c) - 2*tan(b*x + a)*tan(1/2*a)*tan(1/2*c)^2 + tan(1/2*a)^2*tan(1/2*c)^2 + 2*tan(b*x + a)*tan(1/2*a) - tan(1/2*a)^2 - 2*tan(b*x + a)*tan(1/2*c) + 4*tan(1/2*a)*tan(1/2*c) - tan(1/2*c)^2 + 1))/(tan(1/2*a)^4*tan(1/2*c)^3 - tan(1/2*a)^3*tan(1/2*c)^4 + tan(1/2*a)^4*tan(1/2*c) - tan(1/2*a)*tan(1/2*c)^4 + tan(1/2*a)^3 - tan(1/2*c)^3 + tan(1/2*a) - tan(1/2*c)))/b","B",0
242,1,1341,0,1.829122," ","integrate(cos(b*x+a)*sec(b*x+c)^2,x, algorithm=""giac"")","-\frac{\frac{{\left(\tan\left(\frac{1}{2} \, a\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{3} - \tan\left(\frac{1}{2} \, a\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{3} - \tan\left(\frac{1}{2} \, a\right)^{3} \tan\left(\frac{1}{2} \, c\right) + 5 \, \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{1}{2} \, c\right)^{3} + \tan\left(\frac{1}{2} \, a\right)^{3} - 5 \, \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, c\right) + 5 \, \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{1}{2} \, c\right)^{2} - \tan\left(\frac{1}{2} \, c\right)^{3} - \tan\left(\frac{1}{2} \, a\right)^{2} + 5 \, \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{1}{2} \, c\right) - \tan\left(\frac{1}{2} \, c\right)^{2} - \tan\left(\frac{1}{2} \, a\right) + \tan\left(\frac{1}{2} \, c\right) + 1\right)} \log\left({\left| -\tan\left(\frac{1}{2} \, b x + \frac{1}{2} \, a\right) \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{1}{2} \, c\right) + \tan\left(\frac{1}{2} \, b x + \frac{1}{2} \, a\right) \tan\left(\frac{1}{2} \, a\right) - \tan\left(\frac{1}{2} \, b x + \frac{1}{2} \, a\right) \tan\left(\frac{1}{2} \, c\right) + \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{1}{2} \, c\right) - \tan\left(\frac{1}{2} \, b x + \frac{1}{2} \, a\right) + \tan\left(\frac{1}{2} \, a\right) - \tan\left(\frac{1}{2} \, c\right) + 1 \right|}\right)}{\tan\left(\frac{1}{2} \, a\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{3} - \tan\left(\frac{1}{2} \, a\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{3} + \tan\left(\frac{1}{2} \, a\right)^{3} \tan\left(\frac{1}{2} \, c\right) + \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{1}{2} \, c\right)^{3} - \tan\left(\frac{1}{2} \, a\right)^{3} + \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, c\right) - \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, c\right)^{3} + \tan\left(\frac{1}{2} \, a\right)^{2} + \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{1}{2} \, c\right) + \tan\left(\frac{1}{2} \, c\right)^{2} - \tan\left(\frac{1}{2} \, a\right) + \tan\left(\frac{1}{2} \, c\right) + 1} - \frac{{\left(\tan\left(\frac{1}{2} \, a\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{3} + \tan\left(\frac{1}{2} \, a\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{2} - \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{3} - \tan\left(\frac{1}{2} \, a\right)^{3} \tan\left(\frac{1}{2} \, c\right) + 5 \, \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{1}{2} \, c\right)^{3} - \tan\left(\frac{1}{2} \, a\right)^{3} + 5 \, \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, c\right) - 5 \, \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, c\right)^{3} - \tan\left(\frac{1}{2} \, a\right)^{2} + 5 \, \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{1}{2} \, c\right) - \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, a\right) - \tan\left(\frac{1}{2} \, c\right) + 1\right)} \log\left({\left| -\tan\left(\frac{1}{2} \, b x + \frac{1}{2} \, a\right) \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{1}{2} \, c\right) - \tan\left(\frac{1}{2} \, b x + \frac{1}{2} \, a\right) \tan\left(\frac{1}{2} \, a\right) + \tan\left(\frac{1}{2} \, b x + \frac{1}{2} \, a\right) \tan\left(\frac{1}{2} \, c\right) - \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{1}{2} \, c\right) - \tan\left(\frac{1}{2} \, b x + \frac{1}{2} \, a\right) + \tan\left(\frac{1}{2} \, a\right) - \tan\left(\frac{1}{2} \, c\right) - 1 \right|}\right)}{\tan\left(\frac{1}{2} \, a\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{3} + \tan\left(\frac{1}{2} \, a\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{2} - \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{3} + \tan\left(\frac{1}{2} \, a\right)^{3} \tan\left(\frac{1}{2} \, c\right) + \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{1}{2} \, c\right)^{3} + \tan\left(\frac{1}{2} \, a\right)^{3} - \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, c\right) + \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{1}{2} \, c\right)^{2} - \tan\left(\frac{1}{2} \, c\right)^{3} + \tan\left(\frac{1}{2} \, a\right)^{2} + \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{1}{2} \, c\right) + \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, a\right) - \tan\left(\frac{1}{2} \, c\right) + 1} - \frac{4 \, {\left(2 \, \tan\left(\frac{1}{2} \, b x + \frac{1}{2} \, a\right) \tan\left(\frac{1}{2} \, a\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{2} - 4 \, \tan\left(\frac{1}{2} \, b x + \frac{1}{2} \, a\right) \tan\left(\frac{1}{2} \, a\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{3} + \tan\left(\frac{1}{2} \, a\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{3} + 2 \, \tan\left(\frac{1}{2} \, b x + \frac{1}{2} \, a\right) \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{4} - \tan\left(\frac{1}{2} \, a\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{4} + 4 \, \tan\left(\frac{1}{2} \, b x + \frac{1}{2} \, a\right) \tan\left(\frac{1}{2} \, a\right)^{3} \tan\left(\frac{1}{2} \, c\right) - \tan\left(\frac{1}{2} \, a\right)^{4} \tan\left(\frac{1}{2} \, c\right) - 8 \, \tan\left(\frac{1}{2} \, b x + \frac{1}{2} \, a\right) \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 6 \, \tan\left(\frac{1}{2} \, a\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{2} + 4 \, \tan\left(\frac{1}{2} \, b x + \frac{1}{2} \, a\right) \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{1}{2} \, c\right)^{3} - 6 \, \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{3} + \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{1}{2} \, c\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, b x + \frac{1}{2} \, a\right) \tan\left(\frac{1}{2} \, a\right)^{2} - \tan\left(\frac{1}{2} \, a\right)^{3} - 4 \, \tan\left(\frac{1}{2} \, b x + \frac{1}{2} \, a\right) \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{1}{2} \, c\right) + 6 \, \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, c\right) + 2 \, \tan\left(\frac{1}{2} \, b x + \frac{1}{2} \, a\right) \tan\left(\frac{1}{2} \, c\right)^{2} - 6 \, \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, c\right)^{3} + \tan\left(\frac{1}{2} \, a\right) - \tan\left(\frac{1}{2} \, c\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, b x + \frac{1}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - \tan\left(\frac{1}{2} \, b x + \frac{1}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} + 4 \, \tan\left(\frac{1}{2} \, b x + \frac{1}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{1}{2} \, c\right) - 4 \, \tan\left(\frac{1}{2} \, b x + \frac{1}{2} \, a\right) \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, c\right) - \tan\left(\frac{1}{2} \, b x + \frac{1}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 4 \, \tan\left(\frac{1}{2} \, b x + \frac{1}{2} \, a\right) \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{1}{2} \, c\right)^{2} - \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, b x + \frac{1}{2} \, a\right)^{2} - 4 \, \tan\left(\frac{1}{2} \, b x + \frac{1}{2} \, a\right) \tan\left(\frac{1}{2} \, a\right) + \tan\left(\frac{1}{2} \, a\right)^{2} + 4 \, \tan\left(\frac{1}{2} \, b x + \frac{1}{2} \, a\right) \tan\left(\frac{1}{2} \, c\right) - 4 \, \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{1}{2} \, c\right) + \tan\left(\frac{1}{2} \, c\right)^{2} - 1\right)} {\left(\tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - \tan\left(\frac{1}{2} \, a\right)^{2} + 4 \, \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{1}{2} \, c\right) - \tan\left(\frac{1}{2} \, c\right)^{2} + 1\right)}}}{b}"," ",0,"-((tan(1/2*a)^3*tan(1/2*c)^3 - tan(1/2*a)^3*tan(1/2*c)^2 + tan(1/2*a)^2*tan(1/2*c)^3 - tan(1/2*a)^3*tan(1/2*c) + 5*tan(1/2*a)^2*tan(1/2*c)^2 - tan(1/2*a)*tan(1/2*c)^3 + tan(1/2*a)^3 - 5*tan(1/2*a)^2*tan(1/2*c) + 5*tan(1/2*a)*tan(1/2*c)^2 - tan(1/2*c)^3 - tan(1/2*a)^2 + 5*tan(1/2*a)*tan(1/2*c) - tan(1/2*c)^2 - tan(1/2*a) + tan(1/2*c) + 1)*log(abs(-tan(1/2*b*x + 1/2*a)*tan(1/2*a)*tan(1/2*c) + tan(1/2*b*x + 1/2*a)*tan(1/2*a) - tan(1/2*b*x + 1/2*a)*tan(1/2*c) + tan(1/2*a)*tan(1/2*c) - tan(1/2*b*x + 1/2*a) + tan(1/2*a) - tan(1/2*c) + 1))/(tan(1/2*a)^3*tan(1/2*c)^3 - tan(1/2*a)^3*tan(1/2*c)^2 + tan(1/2*a)^2*tan(1/2*c)^3 + tan(1/2*a)^3*tan(1/2*c) + tan(1/2*a)^2*tan(1/2*c)^2 + tan(1/2*a)*tan(1/2*c)^3 - tan(1/2*a)^3 + tan(1/2*a)^2*tan(1/2*c) - tan(1/2*a)*tan(1/2*c)^2 + tan(1/2*c)^3 + tan(1/2*a)^2 + tan(1/2*a)*tan(1/2*c) + tan(1/2*c)^2 - tan(1/2*a) + tan(1/2*c) + 1) - (tan(1/2*a)^3*tan(1/2*c)^3 + tan(1/2*a)^3*tan(1/2*c)^2 - tan(1/2*a)^2*tan(1/2*c)^3 - tan(1/2*a)^3*tan(1/2*c) + 5*tan(1/2*a)^2*tan(1/2*c)^2 - tan(1/2*a)*tan(1/2*c)^3 - tan(1/2*a)^3 + 5*tan(1/2*a)^2*tan(1/2*c) - 5*tan(1/2*a)*tan(1/2*c)^2 + tan(1/2*c)^3 - tan(1/2*a)^2 + 5*tan(1/2*a)*tan(1/2*c) - tan(1/2*c)^2 + tan(1/2*a) - tan(1/2*c) + 1)*log(abs(-tan(1/2*b*x + 1/2*a)*tan(1/2*a)*tan(1/2*c) - tan(1/2*b*x + 1/2*a)*tan(1/2*a) + tan(1/2*b*x + 1/2*a)*tan(1/2*c) - tan(1/2*a)*tan(1/2*c) - tan(1/2*b*x + 1/2*a) + tan(1/2*a) - tan(1/2*c) - 1))/(tan(1/2*a)^3*tan(1/2*c)^3 + tan(1/2*a)^3*tan(1/2*c)^2 - tan(1/2*a)^2*tan(1/2*c)^3 + tan(1/2*a)^3*tan(1/2*c) + tan(1/2*a)^2*tan(1/2*c)^2 + tan(1/2*a)*tan(1/2*c)^3 + tan(1/2*a)^3 - tan(1/2*a)^2*tan(1/2*c) + tan(1/2*a)*tan(1/2*c)^2 - tan(1/2*c)^3 + tan(1/2*a)^2 + tan(1/2*a)*tan(1/2*c) + tan(1/2*c)^2 + tan(1/2*a) - tan(1/2*c) + 1) - 4*(2*tan(1/2*b*x + 1/2*a)*tan(1/2*a)^4*tan(1/2*c)^2 - 4*tan(1/2*b*x + 1/2*a)*tan(1/2*a)^3*tan(1/2*c)^3 + tan(1/2*a)^4*tan(1/2*c)^3 + 2*tan(1/2*b*x + 1/2*a)*tan(1/2*a)^2*tan(1/2*c)^4 - tan(1/2*a)^3*tan(1/2*c)^4 + 4*tan(1/2*b*x + 1/2*a)*tan(1/2*a)^3*tan(1/2*c) - tan(1/2*a)^4*tan(1/2*c) - 8*tan(1/2*b*x + 1/2*a)*tan(1/2*a)^2*tan(1/2*c)^2 + 6*tan(1/2*a)^3*tan(1/2*c)^2 + 4*tan(1/2*b*x + 1/2*a)*tan(1/2*a)*tan(1/2*c)^3 - 6*tan(1/2*a)^2*tan(1/2*c)^3 + tan(1/2*a)*tan(1/2*c)^4 + 2*tan(1/2*b*x + 1/2*a)*tan(1/2*a)^2 - tan(1/2*a)^3 - 4*tan(1/2*b*x + 1/2*a)*tan(1/2*a)*tan(1/2*c) + 6*tan(1/2*a)^2*tan(1/2*c) + 2*tan(1/2*b*x + 1/2*a)*tan(1/2*c)^2 - 6*tan(1/2*a)*tan(1/2*c)^2 + tan(1/2*c)^3 + tan(1/2*a) - tan(1/2*c))/((tan(1/2*b*x + 1/2*a)^2*tan(1/2*a)^2*tan(1/2*c)^2 - tan(1/2*b*x + 1/2*a)^2*tan(1/2*a)^2 + 4*tan(1/2*b*x + 1/2*a)^2*tan(1/2*a)*tan(1/2*c) - 4*tan(1/2*b*x + 1/2*a)*tan(1/2*a)^2*tan(1/2*c) - tan(1/2*b*x + 1/2*a)^2*tan(1/2*c)^2 + 4*tan(1/2*b*x + 1/2*a)*tan(1/2*a)*tan(1/2*c)^2 - tan(1/2*a)^2*tan(1/2*c)^2 + tan(1/2*b*x + 1/2*a)^2 - 4*tan(1/2*b*x + 1/2*a)*tan(1/2*a) + tan(1/2*a)^2 + 4*tan(1/2*b*x + 1/2*a)*tan(1/2*c) - 4*tan(1/2*a)*tan(1/2*c) + tan(1/2*c)^2 - 1)*(tan(1/2*a)^2*tan(1/2*c)^2 - tan(1/2*a)^2 + 4*tan(1/2*a)*tan(1/2*c) - tan(1/2*c)^2 + 1)))/b","B",0
243,1,315,0,5.751871," ","integrate(cos(b*x+a)*sec(b*x+c)^3,x, algorithm=""giac"")","-\frac{\tan\left(\frac{1}{2} \, a\right)^{6} \tan\left(\frac{1}{2} \, c\right)^{6} + 3 \, \tan\left(\frac{1}{2} \, a\right)^{6} \tan\left(\frac{1}{2} \, c\right)^{4} + 3 \, \tan\left(\frac{1}{2} \, a\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{6} + 3 \, \tan\left(\frac{1}{2} \, a\right)^{6} \tan\left(\frac{1}{2} \, c\right)^{2} + 9 \, \tan\left(\frac{1}{2} \, a\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{4} + 3 \, \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{6} + \tan\left(\frac{1}{2} \, a\right)^{6} + 9 \, \tan\left(\frac{1}{2} \, a\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{2} + 9 \, \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{4} + \tan\left(\frac{1}{2} \, c\right)^{6} + 3 \, \tan\left(\frac{1}{2} \, a\right)^{4} + 9 \, \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 3 \, \tan\left(\frac{1}{2} \, c\right)^{4} + 3 \, \tan\left(\frac{1}{2} \, a\right)^{2} + 3 \, \tan\left(\frac{1}{2} \, c\right)^{2} + 1}{4 \, {\left(2 \, \tan\left(b x + a\right) \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, c\right) - 2 \, \tan\left(b x + a\right) \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(b x + a\right) \tan\left(\frac{1}{2} \, a\right) - \tan\left(\frac{1}{2} \, a\right)^{2} - 2 \, \tan\left(b x + a\right) \tan\left(\frac{1}{2} \, c\right) + 4 \, \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{1}{2} \, c\right) - \tan\left(\frac{1}{2} \, c\right)^{2} + 1\right)}^{2} {\left(\tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, c\right) - \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, a\right) - \tan\left(\frac{1}{2} \, c\right)\right)} b}"," ",0,"-1/4*(tan(1/2*a)^6*tan(1/2*c)^6 + 3*tan(1/2*a)^6*tan(1/2*c)^4 + 3*tan(1/2*a)^4*tan(1/2*c)^6 + 3*tan(1/2*a)^6*tan(1/2*c)^2 + 9*tan(1/2*a)^4*tan(1/2*c)^4 + 3*tan(1/2*a)^2*tan(1/2*c)^6 + tan(1/2*a)^6 + 9*tan(1/2*a)^4*tan(1/2*c)^2 + 9*tan(1/2*a)^2*tan(1/2*c)^4 + tan(1/2*c)^6 + 3*tan(1/2*a)^4 + 9*tan(1/2*a)^2*tan(1/2*c)^2 + 3*tan(1/2*c)^4 + 3*tan(1/2*a)^2 + 3*tan(1/2*c)^2 + 1)/((2*tan(b*x + a)*tan(1/2*a)^2*tan(1/2*c) - 2*tan(b*x + a)*tan(1/2*a)*tan(1/2*c)^2 + tan(1/2*a)^2*tan(1/2*c)^2 + 2*tan(b*x + a)*tan(1/2*a) - tan(1/2*a)^2 - 2*tan(b*x + a)*tan(1/2*c) + 4*tan(1/2*a)*tan(1/2*c) - tan(1/2*c)^2 + 1)^2*(tan(1/2*a)^2*tan(1/2*c) - tan(1/2*a)*tan(1/2*c)^2 + tan(1/2*a) - tan(1/2*c))*b)","B",0
244,1,129,0,4.935411," ","integrate(cos(b*x+a)^2*cos(d*x+c)^3,x, algorithm=""giac"")","\frac{\sin\left(2 \, b x + 3 \, d x + 2 \, a + 3 \, c\right)}{16 \, {\left(2 \, b + 3 \, d\right)}} + \frac{3 \, \sin\left(2 \, b x + d x + 2 \, a + c\right)}{16 \, {\left(2 \, b + d\right)}} + \frac{3 \, \sin\left(2 \, b x - d x + 2 \, a - c\right)}{16 \, {\left(2 \, b - d\right)}} + \frac{\sin\left(2 \, b x - 3 \, d x + 2 \, a - 3 \, c\right)}{16 \, {\left(2 \, b - 3 \, d\right)}} + \frac{\sin\left(3 \, d x + 3 \, c\right)}{24 \, d} + \frac{3 \, \sin\left(d x + c\right)}{8 \, d}"," ",0,"1/16*sin(2*b*x + 3*d*x + 2*a + 3*c)/(2*b + 3*d) + 3/16*sin(2*b*x + d*x + 2*a + c)/(2*b + d) + 3/16*sin(2*b*x - d*x + 2*a - c)/(2*b - d) + 1/16*sin(2*b*x - 3*d*x + 2*a - 3*c)/(2*b - 3*d) + 1/24*sin(3*d*x + 3*c)/d + 3/8*sin(d*x + c)/d","A",0
245,1,80,0,1.985325," ","integrate(cos(b*x+a)^2*cos(d*x+c)^2,x, algorithm=""giac"")","\frac{1}{4} \, x + \frac{\sin\left(2 \, b x + 2 \, d x + 2 \, a + 2 \, c\right)}{16 \, {\left(b + d\right)}} + \frac{\sin\left(2 \, b x - 2 \, d x + 2 \, a - 2 \, c\right)}{16 \, {\left(b - d\right)}} + \frac{\sin\left(2 \, b x + 2 \, a\right)}{8 \, b} + \frac{\sin\left(2 \, d x + 2 \, c\right)}{8 \, d}"," ",0,"1/4*x + 1/16*sin(2*b*x + 2*d*x + 2*a + 2*c)/(b + d) + 1/16*sin(2*b*x - 2*d*x + 2*a - 2*c)/(b - d) + 1/8*sin(2*b*x + 2*a)/b + 1/8*sin(2*d*x + 2*c)/d","A",0
246,1,181,0,0.174152," ","integrate(cos(b*x+a)^3*cos(d*x+c)^3,x, algorithm=""giac"")","\frac{\sin\left(3 \, b x + 3 \, d x + 3 \, a + 3 \, c\right)}{96 \, {\left(b + d\right)}} + \frac{3 \, \sin\left(3 \, b x + d x + 3 \, a + c\right)}{32 \, {\left(3 \, b + d\right)}} + \frac{3 \, \sin\left(3 \, b x - d x + 3 \, a - c\right)}{32 \, {\left(3 \, b - d\right)}} + \frac{\sin\left(3 \, b x - 3 \, d x + 3 \, a - 3 \, c\right)}{96 \, {\left(b - d\right)}} + \frac{3 \, \sin\left(b x + 3 \, d x + a + 3 \, c\right)}{32 \, {\left(b + 3 \, d\right)}} + \frac{9 \, \sin\left(b x + d x + a + c\right)}{32 \, {\left(b + d\right)}} + \frac{9 \, \sin\left(b x - d x + a - c\right)}{32 \, {\left(b - d\right)}} + \frac{3 \, \sin\left(b x - 3 \, d x + a - 3 \, c\right)}{32 \, {\left(b - 3 \, d\right)}}"," ",0,"1/96*sin(3*b*x + 3*d*x + 3*a + 3*c)/(b + d) + 3/32*sin(3*b*x + d*x + 3*a + c)/(3*b + d) + 3/32*sin(3*b*x - d*x + 3*a - c)/(3*b - d) + 1/96*sin(3*b*x - 3*d*x + 3*a - 3*c)/(b - d) + 3/32*sin(b*x + 3*d*x + a + 3*c)/(b + 3*d) + 9/32*sin(b*x + d*x + a + c)/(b + d) + 9/32*sin(b*x - d*x + a - c)/(b - d) + 3/32*sin(b*x - 3*d*x + a - 3*c)/(b - 3*d)","A",0
247,0,0,0,0.000000," ","integrate(cos(b*x+a)*tan(b*x+c)^3,x, algorithm=""giac"")","\int \cos\left(b x + a\right) \tan\left(b x + c\right)^{3}\,{d x}"," ",0,"integrate(cos(b*x + a)*tan(b*x + c)^3, x)","F",0
248,0,0,0,0.000000," ","integrate(cos(b*x+a)*tan(b*x+c)^2,x, algorithm=""giac"")","\int \cos\left(b x + a\right) \tan\left(b x + c\right)^{2}\,{d x}"," ",0,"integrate(cos(b*x + a)*tan(b*x + c)^2, x)","F",0
249,0,0,0,0.000000," ","integrate(cos(b*x+a)*tan(b*x+c),x, algorithm=""giac"")","\int \cos\left(b x + a\right) \tan\left(b x + c\right)\,{d x}"," ",0,"integrate(cos(b*x + a)*tan(b*x + c), x)","F",0
250,-2,0,0,0.000000," ","integrate(cos(b*x+a)*cot(b*x+c),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)2/b*((-tan(a/2)^2*tan(c/2)^2+tan(a/2)^2-4*tan(a/2)*tan(c/2)+tan(c/2)^2-1)/(-2*tan(a/2)^2*tan(c/2)^2-2*tan(a/2)^2-2*tan(c/2)^2-2)*ln(abs(tan(b*x/2)+tan(c/2)))+(-tan(a/2)^2*tan(c/2)^3+tan(a/2)^2*tan(c/2)-4*tan(a/2)*tan(c/2)^2+tan(c/2)^3-tan(c/2))/(2*tan(a/2)^2*tan(c/2)^3+2*tan(a/2)^2*tan(c/2)+2*tan(c/2)^3+2*tan(c/2))*ln(abs(tan(b*x/2)*tan(c/2)-1))+(-2*tan(b*x/2)*tan(a/2)-tan(a/2)^2+1)/(tan(a/2)^2+1)/(tan(b*x/2)^2+1))","F(-2)",0
251,-2,0,0,0.000000," ","integrate(cos(b*x+a)*cot(b*x+c)^2,x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)2/b*((tan(c/2)^2*tan(a/2)-tan(c/2)*tan(a/2)^2+tan(c/2)-tan(a/2))/(tan(c/2)^2*tan(a/2)^2+tan(c/2)^2+tan(a/2)^2+1)*ln(abs(tan(b*x/2)+tan(c/2)))+(tan(c/2)^3*tan(a/2)-tan(c/2)^2*tan(a/2)^2+tan(c/2)^2-tan(c/2)*tan(a/2))/(-tan(c/2)^3*tan(a/2)^2-tan(c/2)^3-tan(c/2)*tan(a/2)^2-tan(c/2))*ln(abs(tan(b*x/2)*tan(c/2)-1))+(tan(b*x/2)^3*tan(c/2)^4*tan(a/2)^2-tan(b*x/2)^3*tan(c/2)^4+4*tan(b*x/2)^3*tan(c/2)^3*tan(a/2)-6*tan(b*x/2)^3*tan(c/2)^2*tan(a/2)^2+6*tan(b*x/2)^3*tan(c/2)^2-4*tan(b*x/2)^3*tan(c/2)*tan(a/2)+tan(b*x/2)^3*tan(a/2)^2-tan(b*x/2)^3-6*tan(b*x/2)^2*tan(c/2)^3*tan(a/2)^2+6*tan(b*x/2)^2*tan(c/2)^3+6*tan(b*x/2)^2*tan(c/2)*tan(a/2)^2-6*tan(b*x/2)^2*tan(c/2)+tan(b*x/2)*tan(c/2)^4*tan(a/2)^2-tan(b*x/2)*tan(c/2)^4+12*tan(b*x/2)*tan(c/2)^3*tan(a/2)+2*tan(b*x/2)*tan(c/2)^2*tan(a/2)^2-2*tan(b*x/2)*tan(c/2)^2-12*tan(b*x/2)*tan(c/2)*tan(a/2)+tan(b*x/2)*tan(a/2)^2-tan(b*x/2)-2*tan(c/2)^3*tan(a/2)^2+2*tan(c/2)^3-16*tan(c/2)^2*tan(a/2)+2*tan(c/2)*tan(a/2)^2-2*tan(c/2))/(-4*tan(c/2)*tan(a/2)^2-4*tan(c/2))/(tan(b*x/2)^4*tan(c/2)+tan(b*x/2)^3*tan(c/2)^2-tan(b*x/2)^3+tan(b*x/2)*tan(c/2)^2-tan(b*x/2)-tan(c/2)))","F(-2)",0
252,-2,0,0,0.000000," ","integrate(cos(b*x+a)*cot(b*x+c)^3,x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)2/b*((2*tan(b*x/2)*tan(a/2)+tan(a/2)^2-1)/(tan(a/2)^2+1)/(tan(b*x/2)^2+1)+(-2*tan(b*x/2)^3*tan(c/2)^7*tan(a/2)^2+2*tan(b*x/2)^3*tan(c/2)^7-6*tan(b*x/2)^3*tan(c/2)^5*tan(a/2)^2+6*tan(b*x/2)^3*tan(c/2)^5-16*tan(b*x/2)^3*tan(c/2)^4*tan(a/2)+6*tan(b*x/2)^3*tan(c/2)^3*tan(a/2)^2-6*tan(b*x/2)^3*tan(c/2)^3+2*tan(b*x/2)^3*tan(c/2)*tan(a/2)^2-2*tan(b*x/2)^3*tan(c/2)-tan(b*x/2)^2*tan(c/2)^8*tan(a/2)^2+tan(b*x/2)^2*tan(c/2)^8+4*tan(b*x/2)^2*tan(c/2)^7*tan(a/2)-2*tan(b*x/2)^2*tan(c/2)^6*tan(a/2)^2+2*tan(b*x/2)^2*tan(c/2)^6-20*tan(b*x/2)^2*tan(c/2)^5*tan(a/2)+22*tan(b*x/2)^2*tan(c/2)^4*tan(a/2)^2-22*tan(b*x/2)^2*tan(c/2)^4+20*tan(b*x/2)^2*tan(c/2)^3*tan(a/2)-2*tan(b*x/2)^2*tan(c/2)^2*tan(a/2)^2+2*tan(b*x/2)^2*tan(c/2)^2-4*tan(b*x/2)^2*tan(c/2)*tan(a/2)-tan(b*x/2)^2*tan(a/2)^2+tan(b*x/2)^2+2*tan(b*x/2)*tan(c/2)^7*tan(a/2)^2-2*tan(b*x/2)*tan(c/2)^7-16*tan(b*x/2)*tan(c/2)^6*tan(a/2)+14*tan(b*x/2)*tan(c/2)^5*tan(a/2)^2-14*tan(b*x/2)*tan(c/2)^5+16*tan(b*x/2)*tan(c/2)^4*tan(a/2)-14*tan(b*x/2)*tan(c/2)^3*tan(a/2)^2+14*tan(b*x/2)*tan(c/2)^3-16*tan(b*x/2)*tan(c/2)^2*tan(a/2)-2*tan(b*x/2)*tan(c/2)*tan(a/2)^2+2*tan(b*x/2)*tan(c/2)-2*tan(c/2)^6*tan(a/2)^2+2*tan(c/2)^6+8*tan(c/2)^5*tan(a/2)-12*tan(c/2)^4*tan(a/2)^2+12*tan(c/2)^4-8*tan(c/2)^3*tan(a/2)-2*tan(c/2)^2*tan(a/2)^2+2*tan(c/2)^2)/(-16*tan(c/2)^2*tan(a/2)^2-16*tan(c/2)^2)/(tan(b*x/2)^2*tan(c/2)+tan(b*x/2)*tan(c/2)^2-tan(b*x/2)-tan(c/2))^2+(3*tan(c/2)^2*tan(a/2)^2-3*tan(c/2)^2+12*tan(c/2)*tan(a/2)-3*tan(a/2)^2+3)/(-4*tan(c/2)^2*tan(a/2)^2-4*tan(c/2)^2-4*tan(a/2)^2-4)*ln(abs(tan(b*x/2)+tan(c/2)))+(3*tan(c/2)^3*tan(a/2)^2-3*tan(c/2)^3+12*tan(c/2)^2*tan(a/2)-3*tan(c/2)*tan(a/2)^2+3*tan(c/2))/(4*tan(c/2)^3*tan(a/2)^2+4*tan(c/2)^3+4*tan(c/2)*tan(a/2)^2+4*tan(c/2))*ln(abs(tan(b*x/2)*tan(c/2)-1)))","F(-2)",0
253,0,0,0,0.000000," ","integrate(cos(b*x+a)*tan(d*x+c),x, algorithm=""giac"")","\int \cos\left(b x + a\right) \tan\left(d x + c\right)\,{d x}"," ",0,"integrate(cos(b*x + a)*tan(d*x + c), x)","F",0
254,0,0,0,0.000000," ","integrate(cos(b*x+a)*cot(d*x+c),x, algorithm=""giac"")","\int \cos\left(b x + a\right) \cot\left(d x + c\right)\,{d x}"," ",0,"integrate(cos(b*x + a)*cot(d*x + c), x)","F",0
