1,1,83,0,0.481461," ","integrate(sin(b*x+a)*sin(2*b*x+2*a)^7,x, algorithm=""fricas"")","\frac{128 \, {\left(429 \, \cos\left(b x + a\right)^{14} - 1518 \, \cos\left(b x + a\right)^{12} + 1854 \, \cos\left(b x + a\right)^{10} - 800 \, \cos\left(b x + a\right)^{8} + 5 \, \cos\left(b x + a\right)^{6} + 6 \, \cos\left(b x + a\right)^{4} + 8 \, \cos\left(b x + a\right)^{2} + 16\right)} \sin\left(b x + a\right)}{6435 \, b}"," ",0,"128/6435*(429*cos(b*x + a)^14 - 1518*cos(b*x + a)^12 + 1854*cos(b*x + a)^10 - 800*cos(b*x + a)^8 + 5*cos(b*x + a)^6 + 6*cos(b*x + a)^4 + 8*cos(b*x + a)^2 + 16)*sin(b*x + a)/b","A",0
2,1,46,0,0.428569," ","integrate(sin(b*x+a)*sin(2*b*x+2*a)^6,x, algorithm=""fricas"")","\frac{64 \, {\left(231 \, \cos\left(b x + a\right)^{13} - 819 \, \cos\left(b x + a\right)^{11} + 1001 \, \cos\left(b x + a\right)^{9} - 429 \, \cos\left(b x + a\right)^{7}\right)}}{3003 \, b}"," ",0,"64/3003*(231*cos(b*x + a)^13 - 819*cos(b*x + a)^11 + 1001*cos(b*x + a)^9 - 429*cos(b*x + a)^7)/b","A",0
3,1,63,0,0.415325," ","integrate(sin(b*x+a)*sin(2*b*x+2*a)^5,x, algorithm=""fricas"")","-\frac{32 \, {\left(63 \, \cos\left(b x + a\right)^{10} - 161 \, \cos\left(b x + a\right)^{8} + 113 \, \cos\left(b x + a\right)^{6} - 3 \, \cos\left(b x + a\right)^{4} - 4 \, \cos\left(b x + a\right)^{2} - 8\right)} \sin\left(b x + a\right)}{693 \, b}"," ",0,"-32/693*(63*cos(b*x + a)^10 - 161*cos(b*x + a)^8 + 113*cos(b*x + a)^6 - 3*cos(b*x + a)^4 - 4*cos(b*x + a)^2 - 8)*sin(b*x + a)/b","A",0
4,1,36,0,0.414679," ","integrate(sin(b*x+a)*sin(2*b*x+2*a)^4,x, algorithm=""fricas"")","-\frac{16 \, {\left(35 \, \cos\left(b x + a\right)^{9} - 90 \, \cos\left(b x + a\right)^{7} + 63 \, \cos\left(b x + a\right)^{5}\right)}}{315 \, b}"," ",0,"-16/315*(35*cos(b*x + a)^9 - 90*cos(b*x + a)^7 + 63*cos(b*x + a)^5)/b","A",0
5,1,41,0,0.472868," ","integrate(sin(b*x+a)*sin(2*b*x+2*a)^3,x, algorithm=""fricas"")","\frac{8 \, {\left(5 \, \cos\left(b x + a\right)^{6} - 8 \, \cos\left(b x + a\right)^{4} + \cos\left(b x + a\right)^{2} + 2\right)} \sin\left(b x + a\right)}{35 \, b}"," ",0,"8/35*(5*cos(b*x + a)^6 - 8*cos(b*x + a)^4 + cos(b*x + a)^2 + 2)*sin(b*x + a)/b","A",0
6,1,26,0,0.507973," ","integrate(sin(b*x+a)*sin(2*b*x+2*a)^2,x, algorithm=""fricas"")","\frac{4 \, {\left(3 \, \cos\left(b x + a\right)^{5} - 5 \, \cos\left(b x + a\right)^{3}\right)}}{15 \, b}"," ",0,"4/15*(3*cos(b*x + a)^5 - 5*cos(b*x + a)^3)/b","A",0
7,1,21,0,0.436395," ","integrate(sin(b*x+a)*sin(2*b*x+2*a),x, algorithm=""fricas"")","-\frac{2 \, {\left(\cos\left(b x + a\right)^{2} - 1\right)} \sin\left(b x + a\right)}{3 \, b}"," ",0,"-2/3*(cos(b*x + a)^2 - 1)*sin(b*x + a)/b","A",0
8,1,28,0,0.484790," ","integrate(csc(2*b*x+2*a)*sin(b*x+a),x, algorithm=""fricas"")","\frac{\log\left(\sin\left(b x + a\right) + 1\right) - \log\left(-\sin\left(b x + a\right) + 1\right)}{4 \, b}"," ",0,"1/4*(log(sin(b*x + a) + 1) - log(-sin(b*x + a) + 1))/b","B",0
9,1,52,0,0.451215," ","integrate(csc(2*b*x+2*a)^2*sin(b*x+a),x, algorithm=""fricas"")","-\frac{\cos\left(b x + a\right) \log\left(\frac{1}{2} \, \cos\left(b x + a\right) + \frac{1}{2}\right) - \cos\left(b x + a\right) \log\left(-\frac{1}{2} \, \cos\left(b x + a\right) + \frac{1}{2}\right) - 2}{8 \, b \cos\left(b x + a\right)}"," ",0,"-1/8*(cos(b*x + a)*log(1/2*cos(b*x + a) + 1/2) - cos(b*x + a)*log(-1/2*cos(b*x + a) + 1/2) - 2)/(b*cos(b*x + a))","B",0
10,1,85,0,0.493671," ","integrate(csc(2*b*x+2*a)^3*sin(b*x+a),x, algorithm=""fricas"")","\frac{3 \, \cos\left(b x + a\right)^{2} \log\left(\sin\left(b x + a\right) + 1\right) \sin\left(b x + a\right) - 3 \, \cos\left(b x + a\right)^{2} \log\left(-\sin\left(b x + a\right) + 1\right) \sin\left(b x + a\right) - 6 \, \cos\left(b x + a\right)^{2} + 2}{32 \, b \cos\left(b x + a\right)^{2} \sin\left(b x + a\right)}"," ",0,"1/32*(3*cos(b*x + a)^2*log(sin(b*x + a) + 1)*sin(b*x + a) - 3*cos(b*x + a)^2*log(-sin(b*x + a) + 1)*sin(b*x + a) - 6*cos(b*x + a)^2 + 2)/(b*cos(b*x + a)^2*sin(b*x + a))","A",0
11,1,112,0,0.478738," ","integrate(csc(2*b*x+2*a)^4*sin(b*x+a),x, algorithm=""fricas"")","\frac{30 \, \cos\left(b x + a\right)^{4} - 20 \, \cos\left(b x + a\right)^{2} - 15 \, {\left(\cos\left(b x + a\right)^{5} - \cos\left(b x + a\right)^{3}\right)} \log\left(\frac{1}{2} \, \cos\left(b x + a\right) + \frac{1}{2}\right) + 15 \, {\left(\cos\left(b x + a\right)^{5} - \cos\left(b x + a\right)^{3}\right)} \log\left(-\frac{1}{2} \, \cos\left(b x + a\right) + \frac{1}{2}\right) - 4}{192 \, {\left(b \cos\left(b x + a\right)^{5} - b \cos\left(b x + a\right)^{3}\right)}}"," ",0,"1/192*(30*cos(b*x + a)^4 - 20*cos(b*x + a)^2 - 15*(cos(b*x + a)^5 - cos(b*x + a)^3)*log(1/2*cos(b*x + a) + 1/2) + 15*(cos(b*x + a)^5 - cos(b*x + a)^3)*log(-1/2*cos(b*x + a) + 1/2) - 4)/(b*cos(b*x + a)^5 - b*cos(b*x + a)^3)","A",0
12,1,140,0,0.514788," ","integrate(csc(2*b*x+2*a)^5*sin(b*x+a),x, algorithm=""fricas"")","-\frac{210 \, \cos\left(b x + a\right)^{6} - 280 \, \cos\left(b x + a\right)^{4} - 105 \, {\left(\cos\left(b x + a\right)^{6} - \cos\left(b x + a\right)^{4}\right)} \log\left(\sin\left(b x + a\right) + 1\right) \sin\left(b x + a\right) + 105 \, {\left(\cos\left(b x + a\right)^{6} - \cos\left(b x + a\right)^{4}\right)} \log\left(-\sin\left(b x + a\right) + 1\right) \sin\left(b x + a\right) + 42 \, \cos\left(b x + a\right)^{2} + 12}{1536 \, {\left(b \cos\left(b x + a\right)^{6} - b \cos\left(b x + a\right)^{4}\right)} \sin\left(b x + a\right)}"," ",0,"-1/1536*(210*cos(b*x + a)^6 - 280*cos(b*x + a)^4 - 105*(cos(b*x + a)^6 - cos(b*x + a)^4)*log(sin(b*x + a) + 1)*sin(b*x + a) + 105*(cos(b*x + a)^6 - cos(b*x + a)^4)*log(-sin(b*x + a) + 1)*sin(b*x + a) + 42*cos(b*x + a)^2 + 12)/((b*cos(b*x + a)^6 - b*cos(b*x + a)^4)*sin(b*x + a))","A",0
13,1,46,0,0.478590," ","integrate(sin(b*x+a)^2*sin(2*b*x+2*a)^5,x, algorithm=""fricas"")","\frac{4 \, {\left(10 \, \cos\left(b x + a\right)^{12} - 36 \, \cos\left(b x + a\right)^{10} + 45 \, \cos\left(b x + a\right)^{8} - 20 \, \cos\left(b x + a\right)^{6}\right)}}{15 \, b}"," ",0,"4/15*(10*cos(b*x + a)^12 - 36*cos(b*x + a)^10 + 45*cos(b*x + a)^8 - 20*cos(b*x + a)^6)/b","A",0
14,1,67,0,0.624179," ","integrate(sin(b*x+a)^2*sin(2*b*x+2*a)^4,x, algorithm=""fricas"")","\frac{15 \, b x - {\left(128 \, \cos\left(b x + a\right)^{9} - 336 \, \cos\left(b x + a\right)^{7} + 248 \, \cos\left(b x + a\right)^{5} - 10 \, \cos\left(b x + a\right)^{3} - 15 \, \cos\left(b x + a\right)\right)} \sin\left(b x + a\right)}{80 \, b}"," ",0,"1/80*(15*b*x - (128*cos(b*x + a)^9 - 336*cos(b*x + a)^7 + 248*cos(b*x + a)^5 - 10*cos(b*x + a)^3 - 15*cos(b*x + a))*sin(b*x + a))/b","A",0
15,1,36,0,0.455109," ","integrate(sin(b*x+a)^2*sin(2*b*x+2*a)^3,x, algorithm=""fricas"")","-\frac{3 \, \cos\left(b x + a\right)^{8} - 8 \, \cos\left(b x + a\right)^{6} + 6 \, \cos\left(b x + a\right)^{4}}{3 \, b}"," ",0,"-1/3*(3*cos(b*x + a)^8 - 8*cos(b*x + a)^6 + 6*cos(b*x + a)^4)/b","A",0
16,1,46,0,0.493467," ","integrate(sin(b*x+a)^2*sin(2*b*x+2*a)^2,x, algorithm=""fricas"")","\frac{3 \, b x + {\left(8 \, \cos\left(b x + a\right)^{5} - 14 \, \cos\left(b x + a\right)^{3} + 3 \, \cos\left(b x + a\right)\right)} \sin\left(b x + a\right)}{12 \, b}"," ",0,"1/12*(3*b*x + (8*cos(b*x + a)^5 - 14*cos(b*x + a)^3 + 3*cos(b*x + a))*sin(b*x + a))/b","A",0
17,1,24,0,0.520363," ","integrate(sin(b*x+a)^2*sin(2*b*x+2*a),x, algorithm=""fricas"")","\frac{\cos\left(b x + a\right)^{4} - 2 \, \cos\left(b x + a\right)^{2}}{2 \, b}"," ",0,"1/2*(cos(b*x + a)^4 - 2*cos(b*x + a)^2)/b","A",0
18,1,14,0,0.444059," ","integrate(csc(2*b*x+2*a)*sin(b*x+a)^2,x, algorithm=""fricas"")","-\frac{\log\left(-\cos\left(b x + a\right)\right)}{2 \, b}"," ",0,"-1/2*log(-cos(b*x + a))/b","A",0
19,1,19,0,0.404562," ","integrate(csc(2*b*x+2*a)^2*sin(b*x+a)^2,x, algorithm=""fricas"")","\frac{\sin\left(b x + a\right)}{4 \, b \cos\left(b x + a\right)}"," ",0,"1/4*sin(b*x + a)/(b*cos(b*x + a))","A",0
20,1,56,0,0.427982," ","integrate(csc(2*b*x+2*a)^3*sin(b*x+a)^2,x, algorithm=""fricas"")","-\frac{\cos\left(b x + a\right)^{2} \log\left(\cos\left(b x + a\right)^{2}\right) - \cos\left(b x + a\right)^{2} \log\left(-\frac{1}{4} \, \cos\left(b x + a\right)^{2} + \frac{1}{4}\right) - 1}{16 \, b \cos\left(b x + a\right)^{2}}"," ",0,"-1/16*(cos(b*x + a)^2*log(cos(b*x + a)^2) - cos(b*x + a)^2*log(-1/4*cos(b*x + a)^2 + 1/4) - 1)/(b*cos(b*x + a)^2)","B",0
21,1,43,0,0.393283," ","integrate(csc(2*b*x+2*a)^4*sin(b*x+a)^2,x, algorithm=""fricas"")","-\frac{8 \, \cos\left(b x + a\right)^{4} - 4 \, \cos\left(b x + a\right)^{2} - 1}{48 \, b \cos\left(b x + a\right)^{3} \sin\left(b x + a\right)}"," ",0,"-1/48*(8*cos(b*x + a)^4 - 4*cos(b*x + a)^2 - 1)/(b*cos(b*x + a)^3*sin(b*x + a))","A",0
22,1,112,0,0.430322," ","integrate(csc(2*b*x+2*a)^5*sin(b*x+a)^2,x, algorithm=""fricas"")","\frac{6 \, \cos\left(b x + a\right)^{4} - 3 \, \cos\left(b x + a\right)^{2} - 6 \, {\left(\cos\left(b x + a\right)^{6} - \cos\left(b x + a\right)^{4}\right)} \log\left(\cos\left(b x + a\right)^{2}\right) + 6 \, {\left(\cos\left(b x + a\right)^{6} - \cos\left(b x + a\right)^{4}\right)} \log\left(-\frac{1}{4} \, \cos\left(b x + a\right)^{2} + \frac{1}{4}\right) - 1}{128 \, {\left(b \cos\left(b x + a\right)^{6} - b \cos\left(b x + a\right)^{4}\right)}}"," ",0,"1/128*(6*cos(b*x + a)^4 - 3*cos(b*x + a)^2 - 6*(cos(b*x + a)^6 - cos(b*x + a)^4)*log(cos(b*x + a)^2) + 6*(cos(b*x + a)^6 - cos(b*x + a)^4)*log(-1/4*cos(b*x + a)^2 + 1/4) - 1)/(b*cos(b*x + a)^6 - b*cos(b*x + a)^4)","B",0
23,1,73,0,0.423474," ","integrate(sin(b*x+a)^3*sin(2*b*x+2*a)^5,x, algorithm=""fricas"")","\frac{32 \, {\left(99 \, \cos\left(b x + a\right)^{12} - 360 \, \cos\left(b x + a\right)^{10} + 458 \, \cos\left(b x + a\right)^{8} - 212 \, \cos\left(b x + a\right)^{6} + 3 \, \cos\left(b x + a\right)^{4} + 4 \, \cos\left(b x + a\right)^{2} + 8\right)} \sin\left(b x + a\right)}{1287 \, b}"," ",0,"32/1287*(99*cos(b*x + a)^12 - 360*cos(b*x + a)^10 + 458*cos(b*x + a)^8 - 212*cos(b*x + a)^6 + 3*cos(b*x + a)^4 + 4*cos(b*x + a)^2 + 8)*sin(b*x + a)/b","A",0
24,1,46,0,0.422163," ","integrate(sin(b*x+a)^3*sin(2*b*x+2*a)^4,x, algorithm=""fricas"")","\frac{16 \, {\left(105 \, \cos\left(b x + a\right)^{11} - 385 \, \cos\left(b x + a\right)^{9} + 495 \, \cos\left(b x + a\right)^{7} - 231 \, \cos\left(b x + a\right)^{5}\right)}}{1155 \, b}"," ",0,"16/1155*(105*cos(b*x + a)^11 - 385*cos(b*x + a)^9 + 495*cos(b*x + a)^7 - 231*cos(b*x + a)^5)/b","A",0
25,1,53,0,0.412555," ","integrate(sin(b*x+a)^3*sin(2*b*x+2*a)^3,x, algorithm=""fricas"")","-\frac{8 \, {\left(7 \, \cos\left(b x + a\right)^{8} - 19 \, \cos\left(b x + a\right)^{6} + 15 \, \cos\left(b x + a\right)^{4} - \cos\left(b x + a\right)^{2} - 2\right)} \sin\left(b x + a\right)}{63 \, b}"," ",0,"-8/63*(7*cos(b*x + a)^8 - 19*cos(b*x + a)^6 + 15*cos(b*x + a)^4 - cos(b*x + a)^2 - 2)*sin(b*x + a)/b","A",0
26,1,36,0,0.445335," ","integrate(sin(b*x+a)^3*sin(2*b*x+2*a)^2,x, algorithm=""fricas"")","-\frac{4 \, {\left(15 \, \cos\left(b x + a\right)^{7} - 42 \, \cos\left(b x + a\right)^{5} + 35 \, \cos\left(b x + a\right)^{3}\right)}}{105 \, b}"," ",0,"-4/105*(15*cos(b*x + a)^7 - 42*cos(b*x + a)^5 + 35*cos(b*x + a)^3)/b","A",0
27,1,31,0,0.458009," ","integrate(sin(b*x+a)^3*sin(2*b*x+2*a),x, algorithm=""fricas"")","\frac{2 \, {\left(\cos\left(b x + a\right)^{4} - 2 \, \cos\left(b x + a\right)^{2} + 1\right)} \sin\left(b x + a\right)}{5 \, b}"," ",0,"2/5*(cos(b*x + a)^4 - 2*cos(b*x + a)^2 + 1)*sin(b*x + a)/b","B",0
28,1,36,0,0.488923," ","integrate(csc(2*b*x+2*a)*sin(b*x+a)^3,x, algorithm=""fricas"")","\frac{\log\left(\sin\left(b x + a\right) + 1\right) - \log\left(-\sin\left(b x + a\right) + 1\right) - 2 \, \sin\left(b x + a\right)}{4 \, b}"," ",0,"1/4*(log(sin(b*x + a) + 1) - log(-sin(b*x + a) + 1) - 2*sin(b*x + a))/b","A",0
29,1,13,0,0.439803," ","integrate(csc(2*b*x+2*a)^2*sin(b*x+a)^3,x, algorithm=""fricas"")","\frac{1}{4 \, b \cos\left(b x + a\right)}"," ",0,"1/4/(b*cos(b*x + a))","A",0
30,1,61,0,0.450755," ","integrate(csc(2*b*x+2*a)^3*sin(b*x+a)^3,x, algorithm=""fricas"")","\frac{\cos\left(b x + a\right)^{2} \log\left(\sin\left(b x + a\right) + 1\right) - \cos\left(b x + a\right)^{2} \log\left(-\sin\left(b x + a\right) + 1\right) + 2 \, \sin\left(b x + a\right)}{32 \, b \cos\left(b x + a\right)^{2}}"," ",0,"1/32*(cos(b*x + a)^2*log(sin(b*x + a) + 1) - cos(b*x + a)^2*log(-sin(b*x + a) + 1) + 2*sin(b*x + a))/(b*cos(b*x + a)^2)","B",0
31,1,67,0,0.484073," ","integrate(csc(2*b*x+2*a)^4*sin(b*x+a)^3,x, algorithm=""fricas"")","-\frac{3 \, \cos\left(b x + a\right)^{3} \log\left(\frac{1}{2} \, \cos\left(b x + a\right) + \frac{1}{2}\right) - 3 \, \cos\left(b x + a\right)^{3} \log\left(-\frac{1}{2} \, \cos\left(b x + a\right) + \frac{1}{2}\right) - 6 \, \cos\left(b x + a\right)^{2} - 2}{96 \, b \cos\left(b x + a\right)^{3}}"," ",0,"-1/96*(3*cos(b*x + a)^3*log(1/2*cos(b*x + a) + 1/2) - 3*cos(b*x + a)^3*log(-1/2*cos(b*x + a) + 1/2) - 6*cos(b*x + a)^2 - 2)/(b*cos(b*x + a)^3)","A",0
32,1,95,0,0.594781," ","integrate(csc(2*b*x+2*a)^5*sin(b*x+a)^3,x, algorithm=""fricas"")","\frac{15 \, \cos\left(b x + a\right)^{4} \log\left(\sin\left(b x + a\right) + 1\right) \sin\left(b x + a\right) - 15 \, \cos\left(b x + a\right)^{4} \log\left(-\sin\left(b x + a\right) + 1\right) \sin\left(b x + a\right) - 30 \, \cos\left(b x + a\right)^{4} + 10 \, \cos\left(b x + a\right)^{2} + 4}{512 \, b \cos\left(b x + a\right)^{4} \sin\left(b x + a\right)}"," ",0,"1/512*(15*cos(b*x + a)^4*log(sin(b*x + a) + 1)*sin(b*x + a) - 15*cos(b*x + a)^4*log(-sin(b*x + a) + 1)*sin(b*x + a) - 30*cos(b*x + a)^4 + 10*cos(b*x + a)^2 + 4)/(b*cos(b*x + a)^4*sin(b*x + a))","A",0
33,1,46,0,0.514195," ","integrate(csc(b*x+a)*sin(2*b*x+2*a)^8,x, algorithm=""fricas"")","\frac{256 \, {\left(429 \, \cos\left(b x + a\right)^{15} - 1485 \, \cos\left(b x + a\right)^{13} + 1755 \, \cos\left(b x + a\right)^{11} - 715 \, \cos\left(b x + a\right)^{9}\right)}}{6435 \, b}"," ",0,"256/6435*(429*cos(b*x + a)^15 - 1485*cos(b*x + a)^13 + 1755*cos(b*x + a)^11 - 715*cos(b*x + a)^9)/b","A",0
34,1,73,0,0.457531," ","integrate(csc(b*x+a)*sin(2*b*x+2*a)^7,x, algorithm=""fricas"")","-\frac{128 \, {\left(231 \, \cos\left(b x + a\right)^{12} - 567 \, \cos\left(b x + a\right)^{10} + 371 \, \cos\left(b x + a\right)^{8} - 5 \, \cos\left(b x + a\right)^{6} - 6 \, \cos\left(b x + a\right)^{4} - 8 \, \cos\left(b x + a\right)^{2} - 16\right)} \sin\left(b x + a\right)}{3003 \, b}"," ",0,"-128/3003*(231*cos(b*x + a)^12 - 567*cos(b*x + a)^10 + 371*cos(b*x + a)^8 - 5*cos(b*x + a)^6 - 6*cos(b*x + a)^4 - 8*cos(b*x + a)^2 - 16)*sin(b*x + a)/b","A",0
35,1,36,0,0.437761," ","integrate(csc(b*x+a)*sin(2*b*x+2*a)^6,x, algorithm=""fricas"")","-\frac{64 \, {\left(63 \, \cos\left(b x + a\right)^{11} - 154 \, \cos\left(b x + a\right)^{9} + 99 \, \cos\left(b x + a\right)^{7}\right)}}{693 \, b}"," ",0,"-64/693*(63*cos(b*x + a)^11 - 154*cos(b*x + a)^9 + 99*cos(b*x + a)^7)/b","A",0
36,1,53,0,0.445562," ","integrate(csc(b*x+a)*sin(2*b*x+2*a)^5,x, algorithm=""fricas"")","\frac{32 \, {\left(35 \, \cos\left(b x + a\right)^{8} - 50 \, \cos\left(b x + a\right)^{6} + 3 \, \cos\left(b x + a\right)^{4} + 4 \, \cos\left(b x + a\right)^{2} + 8\right)} \sin\left(b x + a\right)}{315 \, b}"," ",0,"32/315*(35*cos(b*x + a)^8 - 50*cos(b*x + a)^6 + 3*cos(b*x + a)^4 + 4*cos(b*x + a)^2 + 8)*sin(b*x + a)/b","A",0
37,1,26,0,0.473169," ","integrate(csc(b*x+a)*sin(2*b*x+2*a)^4,x, algorithm=""fricas"")","\frac{16 \, {\left(5 \, \cos\left(b x + a\right)^{7} - 7 \, \cos\left(b x + a\right)^{5}\right)}}{35 \, b}"," ",0,"16/35*(5*cos(b*x + a)^7 - 7*cos(b*x + a)^5)/b","A",0
38,1,33,0,0.439466," ","integrate(csc(b*x+a)*sin(2*b*x+2*a)^3,x, algorithm=""fricas"")","-\frac{8 \, {\left(3 \, \cos\left(b x + a\right)^{4} - \cos\left(b x + a\right)^{2} - 2\right)} \sin\left(b x + a\right)}{15 \, b}"," ",0,"-8/15*(3*cos(b*x + a)^4 - cos(b*x + a)^2 - 2)*sin(b*x + a)/b","A",0
39,1,13,0,0.437643," ","integrate(csc(b*x+a)*sin(2*b*x+2*a)^2,x, algorithm=""fricas"")","-\frac{4 \, \cos\left(b x + a\right)^{3}}{3 \, b}"," ",0,"-4/3*cos(b*x + a)^3/b","A",0
40,1,11,0,0.473081," ","integrate(csc(b*x+a)*sin(2*b*x+2*a),x, algorithm=""fricas"")","\frac{2 \, \sin\left(b x + a\right)}{b}"," ",0,"2*sin(b*x + a)/b","A",0
41,1,50,0,0.426038," ","integrate(csc(b*x+a)*csc(2*b*x+2*a),x, algorithm=""fricas"")","\frac{\log\left(\sin\left(b x + a\right) + 1\right) \sin\left(b x + a\right) - \log\left(-\sin\left(b x + a\right) + 1\right) \sin\left(b x + a\right) - 2}{4 \, b \sin\left(b x + a\right)}"," ",0,"1/4*(log(sin(b*x + a) + 1)*sin(b*x + a) - log(-sin(b*x + a) + 1)*sin(b*x + a) - 2)/(b*sin(b*x + a))","B",0
42,1,96,0,0.438433," ","integrate(csc(b*x+a)*csc(2*b*x+2*a)^2,x, algorithm=""fricas"")","\frac{6 \, \cos\left(b x + a\right)^{2} - 3 \, {\left(\cos\left(b x + a\right)^{3} - \cos\left(b x + a\right)\right)} \log\left(\frac{1}{2} \, \cos\left(b x + a\right) + \frac{1}{2}\right) + 3 \, {\left(\cos\left(b x + a\right)^{3} - \cos\left(b x + a\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(b x + a\right) + \frac{1}{2}\right) - 4}{16 \, {\left(b \cos\left(b x + a\right)^{3} - b \cos\left(b x + a\right)\right)}}"," ",0,"1/16*(6*cos(b*x + a)^2 - 3*(cos(b*x + a)^3 - cos(b*x + a))*log(1/2*cos(b*x + a) + 1/2) + 3*(cos(b*x + a)^3 - cos(b*x + a))*log(-1/2*cos(b*x + a) + 1/2) - 4)/(b*cos(b*x + a)^3 - b*cos(b*x + a))","B",0
43,1,130,0,0.472858," ","integrate(csc(b*x+a)*csc(2*b*x+2*a)^3,x, algorithm=""fricas"")","-\frac{30 \, \cos\left(b x + a\right)^{4} - 15 \, {\left(\cos\left(b x + a\right)^{4} - \cos\left(b x + a\right)^{2}\right)} \log\left(\sin\left(b x + a\right) + 1\right) \sin\left(b x + a\right) + 15 \, {\left(\cos\left(b x + a\right)^{4} - \cos\left(b x + a\right)^{2}\right)} \log\left(-\sin\left(b x + a\right) + 1\right) \sin\left(b x + a\right) - 40 \, \cos\left(b x + a\right)^{2} + 6}{96 \, {\left(b \cos\left(b x + a\right)^{4} - b \cos\left(b x + a\right)^{2}\right)} \sin\left(b x + a\right)}"," ",0,"-1/96*(30*cos(b*x + a)^4 - 15*(cos(b*x + a)^4 - cos(b*x + a)^2)*log(sin(b*x + a) + 1)*sin(b*x + a) + 15*(cos(b*x + a)^4 - cos(b*x + a)^2)*log(-sin(b*x + a) + 1)*sin(b*x + a) - 40*cos(b*x + a)^2 + 6)/((b*cos(b*x + a)^4 - b*cos(b*x + a)^2)*sin(b*x + a))","B",0
44,1,148,0,0.494113," ","integrate(csc(b*x+a)*csc(2*b*x+2*a)^4,x, algorithm=""fricas"")","\frac{210 \, \cos\left(b x + a\right)^{6} - 350 \, \cos\left(b x + a\right)^{4} + 112 \, \cos\left(b x + a\right)^{2} - 105 \, {\left(\cos\left(b x + a\right)^{7} - 2 \, \cos\left(b x + a\right)^{5} + \cos\left(b x + a\right)^{3}\right)} \log\left(\frac{1}{2} \, \cos\left(b x + a\right) + \frac{1}{2}\right) + 105 \, {\left(\cos\left(b x + a\right)^{7} - 2 \, \cos\left(b x + a\right)^{5} + \cos\left(b x + a\right)^{3}\right)} \log\left(-\frac{1}{2} \, \cos\left(b x + a\right) + \frac{1}{2}\right) + 16}{768 \, {\left(b \cos\left(b x + a\right)^{7} - 2 \, b \cos\left(b x + a\right)^{5} + b \cos\left(b x + a\right)^{3}\right)}}"," ",0,"1/768*(210*cos(b*x + a)^6 - 350*cos(b*x + a)^4 + 112*cos(b*x + a)^2 - 105*(cos(b*x + a)^7 - 2*cos(b*x + a)^5 + cos(b*x + a)^3)*log(1/2*cos(b*x + a) + 1/2) + 105*(cos(b*x + a)^7 - 2*cos(b*x + a)^5 + cos(b*x + a)^3)*log(-1/2*cos(b*x + a) + 1/2) + 16)/(b*cos(b*x + a)^7 - 2*b*cos(b*x + a)^5 + b*cos(b*x + a)^3)","A",0
45,1,87,0,0.458151," ","integrate(csc(b*x+a)^2*sin(2*b*x+2*a)^8,x, algorithm=""fricas"")","\frac{105 \, b x - {\left(3072 \, \cos\left(b x + a\right)^{13} - 7424 \, \cos\left(b x + a\right)^{11} + 4736 \, \cos\left(b x + a\right)^{9} - 48 \, \cos\left(b x + a\right)^{7} - 56 \, \cos\left(b x + a\right)^{5} - 70 \, \cos\left(b x + a\right)^{3} - 105 \, \cos\left(b x + a\right)\right)} \sin\left(b x + a\right)}{168 \, b}"," ",0,"1/168*(105*b*x - (3072*cos(b*x + a)^13 - 7424*cos(b*x + a)^11 + 4736*cos(b*x + a)^9 - 48*cos(b*x + a)^7 - 56*cos(b*x + a)^5 - 70*cos(b*x + a)^3 - 105*cos(b*x + a))*sin(b*x + a))/b","A",0
46,1,36,0,0.423758," ","integrate(csc(b*x+a)^2*sin(2*b*x+2*a)^7,x, algorithm=""fricas"")","-\frac{16 \, {\left(10 \, \cos\left(b x + a\right)^{12} - 24 \, \cos\left(b x + a\right)^{10} + 15 \, \cos\left(b x + a\right)^{8}\right)}}{15 \, b}"," ",0,"-16/15*(10*cos(b*x + a)^12 - 24*cos(b*x + a)^10 + 15*cos(b*x + a)^8)/b","A",0
47,1,66,0,0.457580," ","integrate(csc(b*x+a)^2*sin(2*b*x+2*a)^6,x, algorithm=""fricas"")","\frac{15 \, b x + {\left(128 \, \cos\left(b x + a\right)^{9} - 176 \, \cos\left(b x + a\right)^{7} + 8 \, \cos\left(b x + a\right)^{5} + 10 \, \cos\left(b x + a\right)^{3} + 15 \, \cos\left(b x + a\right)\right)} \sin\left(b x + a\right)}{20 \, b}"," ",0,"1/20*(15*b*x + (128*cos(b*x + a)^9 - 176*cos(b*x + a)^7 + 8*cos(b*x + a)^5 + 10*cos(b*x + a)^3 + 15*cos(b*x + a))*sin(b*x + a))/b","A",0
48,1,26,0,0.418469," ","integrate(csc(b*x+a)^2*sin(2*b*x+2*a)^5,x, algorithm=""fricas"")","\frac{4 \, {\left(3 \, \cos\left(b x + a\right)^{8} - 4 \, \cos\left(b x + a\right)^{6}\right)}}{3 \, b}"," ",0,"4/3*(3*cos(b*x + a)^8 - 4*cos(b*x + a)^6)/b","A",0
49,1,47,0,0.458714," ","integrate(csc(b*x+a)^2*sin(2*b*x+2*a)^4,x, algorithm=""fricas"")","\frac{3 \, b x - {\left(8 \, \cos\left(b x + a\right)^{5} - 2 \, \cos\left(b x + a\right)^{3} - 3 \, \cos\left(b x + a\right)\right)} \sin\left(b x + a\right)}{3 \, b}"," ",0,"1/3*(3*b*x - (8*cos(b*x + a)^5 - 2*cos(b*x + a)^3 - 3*cos(b*x + a))*sin(b*x + a))/b","A",0
50,1,13,0,0.449074," ","integrate(csc(b*x+a)^2*sin(2*b*x+2*a)^3,x, algorithm=""fricas"")","-\frac{2 \, \cos\left(b x + a\right)^{4}}{b}"," ",0,"-2*cos(b*x + a)^4/b","A",0
51,1,22,0,0.410016," ","integrate(csc(b*x+a)^2*sin(2*b*x+2*a)^2,x, algorithm=""fricas"")","\frac{2 \, {\left(b x + \cos\left(b x + a\right) \sin\left(b x + a\right)\right)}}{b}"," ",0,"2*(b*x + cos(b*x + a)*sin(b*x + a))/b","A",0
52,1,14,0,0.450939," ","integrate(csc(b*x+a)^2*sin(2*b*x+2*a),x, algorithm=""fricas"")","\frac{2 \, \log\left(\frac{1}{2} \, \sin\left(b x + a\right)\right)}{b}"," ",0,"2*log(1/2*sin(b*x + a))/b","A",0
53,1,65,0,0.432866," ","integrate(csc(b*x+a)^2*csc(2*b*x+2*a),x, algorithm=""fricas"")","-\frac{{\left(\cos\left(b x + a\right)^{2} - 1\right)} \log\left(\cos\left(b x + a\right)^{2}\right) - {\left(\cos\left(b x + a\right)^{2} - 1\right)} \log\left(-\frac{1}{4} \, \cos\left(b x + a\right)^{2} + \frac{1}{4}\right) - 1}{4 \, {\left(b \cos\left(b x + a\right)^{2} - b\right)}}"," ",0,"-1/4*((cos(b*x + a)^2 - 1)*log(cos(b*x + a)^2) - (cos(b*x + a)^2 - 1)*log(-1/4*cos(b*x + a)^2 + 1/4) - 1)/(b*cos(b*x + a)^2 - b)","B",0
54,1,54,0,0.427277," ","integrate(csc(b*x+a)^2*csc(2*b*x+2*a)^2,x, algorithm=""fricas"")","-\frac{8 \, \cos\left(b x + a\right)^{4} - 12 \, \cos\left(b x + a\right)^{2} + 3}{12 \, {\left(b \cos\left(b x + a\right)^{3} - b \cos\left(b x + a\right)\right)} \sin\left(b x + a\right)}"," ",0,"-1/12*(8*cos(b*x + a)^4 - 12*cos(b*x + a)^2 + 3)/((b*cos(b*x + a)^3 - b*cos(b*x + a))*sin(b*x + a))","A",0
55,1,138,0,0.512491," ","integrate(csc(b*x+a)^2*csc(2*b*x+2*a)^3,x, algorithm=""fricas"")","\frac{6 \, \cos\left(b x + a\right)^{4} - 9 \, \cos\left(b x + a\right)^{2} - 6 \, {\left(\cos\left(b x + a\right)^{6} - 2 \, \cos\left(b x + a\right)^{4} + \cos\left(b x + a\right)^{2}\right)} \log\left(\cos\left(b x + a\right)^{2}\right) + 6 \, {\left(\cos\left(b x + a\right)^{6} - 2 \, \cos\left(b x + a\right)^{4} + \cos\left(b x + a\right)^{2}\right)} \log\left(-\frac{1}{4} \, \cos\left(b x + a\right)^{2} + \frac{1}{4}\right) + 2}{32 \, {\left(b \cos\left(b x + a\right)^{6} - 2 \, b \cos\left(b x + a\right)^{4} + b \cos\left(b x + a\right)^{2}\right)}}"," ",0,"1/32*(6*cos(b*x + a)^4 - 9*cos(b*x + a)^2 - 6*(cos(b*x + a)^6 - 2*cos(b*x + a)^4 + cos(b*x + a)^2)*log(cos(b*x + a)^2) + 6*(cos(b*x + a)^6 - 2*cos(b*x + a)^4 + cos(b*x + a)^2)*log(-1/4*cos(b*x + a)^2 + 1/4) + 2)/(b*cos(b*x + a)^6 - 2*b*cos(b*x + a)^4 + b*cos(b*x + a)^2)","B",0
56,1,86,0,0.416599," ","integrate(csc(b*x+a)^2*csc(2*b*x+2*a)^4,x, algorithm=""fricas"")","-\frac{128 \, \cos\left(b x + a\right)^{8} - 320 \, \cos\left(b x + a\right)^{6} + 240 \, \cos\left(b x + a\right)^{4} - 40 \, \cos\left(b x + a\right)^{2} - 5}{240 \, {\left(b \cos\left(b x + a\right)^{7} - 2 \, b \cos\left(b x + a\right)^{5} + b \cos\left(b x + a\right)^{3}\right)} \sin\left(b x + a\right)}"," ",0,"-1/240*(128*cos(b*x + a)^8 - 320*cos(b*x + a)^6 + 240*cos(b*x + a)^4 - 40*cos(b*x + a)^2 - 5)/((b*cos(b*x + a)^7 - 2*b*cos(b*x + a)^5 + b*cos(b*x + a)^3)*sin(b*x + a))","A",0
57,1,194,0,0.566117," ","integrate(csc(b*x+a)^2*csc(2*b*x+2*a)^5,x, algorithm=""fricas"")","\frac{60 \, \cos\left(b x + a\right)^{8} - 150 \, \cos\left(b x + a\right)^{6} + 110 \, \cos\left(b x + a\right)^{4} - 15 \, \cos\left(b x + a\right)^{2} - 60 \, {\left(\cos\left(b x + a\right)^{10} - 3 \, \cos\left(b x + a\right)^{8} + 3 \, \cos\left(b x + a\right)^{6} - \cos\left(b x + a\right)^{4}\right)} \log\left(\cos\left(b x + a\right)^{2}\right) + 60 \, {\left(\cos\left(b x + a\right)^{10} - 3 \, \cos\left(b x + a\right)^{8} + 3 \, \cos\left(b x + a\right)^{6} - \cos\left(b x + a\right)^{4}\right)} \log\left(-\frac{1}{4} \, \cos\left(b x + a\right)^{2} + \frac{1}{4}\right) - 3}{384 \, {\left(b \cos\left(b x + a\right)^{10} - 3 \, b \cos\left(b x + a\right)^{8} + 3 \, b \cos\left(b x + a\right)^{6} - b \cos\left(b x + a\right)^{4}\right)}}"," ",0,"1/384*(60*cos(b*x + a)^8 - 150*cos(b*x + a)^6 + 110*cos(b*x + a)^4 - 15*cos(b*x + a)^2 - 60*(cos(b*x + a)^10 - 3*cos(b*x + a)^8 + 3*cos(b*x + a)^6 - cos(b*x + a)^4)*log(cos(b*x + a)^2) + 60*(cos(b*x + a)^10 - 3*cos(b*x + a)^8 + 3*cos(b*x + a)^6 - cos(b*x + a)^4)*log(-1/4*cos(b*x + a)^2 + 1/4) - 3)/(b*cos(b*x + a)^10 - 3*b*cos(b*x + a)^8 + 3*b*cos(b*x + a)^6 - b*cos(b*x + a)^4)","B",0
58,1,118,0,0.511068," ","integrate(csc(b*x+a)^2*csc(2*b*x+2*a)^6,x, algorithm=""fricas"")","-\frac{1024 \, \cos\left(b x + a\right)^{12} - 3584 \, \cos\left(b x + a\right)^{10} + 4480 \, \cos\left(b x + a\right)^{8} - 2240 \, \cos\left(b x + a\right)^{6} + 280 \, \cos\left(b x + a\right)^{4} + 28 \, \cos\left(b x + a\right)^{2} + 7}{2240 \, {\left(b \cos\left(b x + a\right)^{11} - 3 \, b \cos\left(b x + a\right)^{9} + 3 \, b \cos\left(b x + a\right)^{7} - b \cos\left(b x + a\right)^{5}\right)} \sin\left(b x + a\right)}"," ",0,"-1/2240*(1024*cos(b*x + a)^12 - 3584*cos(b*x + a)^10 + 4480*cos(b*x + a)^8 - 2240*cos(b*x + a)^6 + 280*cos(b*x + a)^4 + 28*cos(b*x + a)^2 + 7)/((b*cos(b*x + a)^11 - 3*b*cos(b*x + a)^9 + 3*b*cos(b*x + a)^7 - b*cos(b*x + a)^5)*sin(b*x + a))","A",0
59,1,46,0,0.652144," ","integrate(csc(b*x+a)^3*sin(2*b*x+2*a)^10,x, algorithm=""fricas"")","\frac{1024 \, {\left(715 \, \cos\left(b x + a\right)^{17} - 2431 \, \cos\left(b x + a\right)^{15} + 2805 \, \cos\left(b x + a\right)^{13} - 1105 \, \cos\left(b x + a\right)^{11}\right)}}{12155 \, b}"," ",0,"1024/12155*(715*cos(b*x + a)^17 - 2431*cos(b*x + a)^15 + 2805*cos(b*x + a)^13 - 1105*cos(b*x + a)^11)/b","A",0
60,1,83,0,0.480734," ","integrate(csc(b*x+a)^3*sin(2*b*x+2*a)^9,x, algorithm=""fricas"")","-\frac{512 \, {\left(3003 \, \cos\left(b x + a\right)^{14} - 7161 \, \cos\left(b x + a\right)^{12} + 4473 \, \cos\left(b x + a\right)^{10} - 35 \, \cos\left(b x + a\right)^{8} - 40 \, \cos\left(b x + a\right)^{6} - 48 \, \cos\left(b x + a\right)^{4} - 64 \, \cos\left(b x + a\right)^{2} - 128\right)} \sin\left(b x + a\right)}{45045 \, b}"," ",0,"-512/45045*(3003*cos(b*x + a)^14 - 7161*cos(b*x + a)^12 + 4473*cos(b*x + a)^10 - 35*cos(b*x + a)^8 - 40*cos(b*x + a)^6 - 48*cos(b*x + a)^4 - 64*cos(b*x + a)^2 - 128)*sin(b*x + a)/b","A",0
61,1,36,0,0.445290," ","integrate(csc(b*x+a)^3*sin(2*b*x+2*a)^8,x, algorithm=""fricas"")","-\frac{256 \, {\left(99 \, \cos\left(b x + a\right)^{13} - 234 \, \cos\left(b x + a\right)^{11} + 143 \, \cos\left(b x + a\right)^{9}\right)}}{1287 \, b}"," ",0,"-256/1287*(99*cos(b*x + a)^13 - 234*cos(b*x + a)^11 + 143*cos(b*x + a)^9)/b","A",0
62,1,63,0,0.425860," ","integrate(csc(b*x+a)^3*sin(2*b*x+2*a)^7,x, algorithm=""fricas"")","\frac{128 \, {\left(105 \, \cos\left(b x + a\right)^{10} - 140 \, \cos\left(b x + a\right)^{8} + 5 \, \cos\left(b x + a\right)^{6} + 6 \, \cos\left(b x + a\right)^{4} + 8 \, \cos\left(b x + a\right)^{2} + 16\right)} \sin\left(b x + a\right)}{1155 \, b}"," ",0,"128/1155*(105*cos(b*x + a)^10 - 140*cos(b*x + a)^8 + 5*cos(b*x + a)^6 + 6*cos(b*x + a)^4 + 8*cos(b*x + a)^2 + 16)*sin(b*x + a)/b","A",0
63,1,26,0,0.437872," ","integrate(csc(b*x+a)^3*sin(2*b*x+2*a)^6,x, algorithm=""fricas"")","\frac{64 \, {\left(7 \, \cos\left(b x + a\right)^{9} - 9 \, \cos\left(b x + a\right)^{7}\right)}}{63 \, b}"," ",0,"64/63*(7*cos(b*x + a)^9 - 9*cos(b*x + a)^7)/b","A",0
64,1,43,0,0.689691," ","integrate(csc(b*x+a)^3*sin(2*b*x+2*a)^5,x, algorithm=""fricas"")","-\frac{32 \, {\left(15 \, \cos\left(b x + a\right)^{6} - 3 \, \cos\left(b x + a\right)^{4} - 4 \, \cos\left(b x + a\right)^{2} - 8\right)} \sin\left(b x + a\right)}{105 \, b}"," ",0,"-32/105*(15*cos(b*x + a)^6 - 3*cos(b*x + a)^4 - 4*cos(b*x + a)^2 - 8)*sin(b*x + a)/b","A",0
65,1,13,0,0.506085," ","integrate(csc(b*x+a)^3*sin(2*b*x+2*a)^4,x, algorithm=""fricas"")","-\frac{16 \, \cos\left(b x + a\right)^{5}}{5 \, b}"," ",0,"-16/5*cos(b*x + a)^5/b","A",0
66,1,21,0,0.643836," ","integrate(csc(b*x+a)^3*sin(2*b*x+2*a)^3,x, algorithm=""fricas"")","\frac{8 \, {\left(\cos\left(b x + a\right)^{2} + 2\right)} \sin\left(b x + a\right)}{3 \, b}"," ",0,"8/3*(cos(b*x + a)^2 + 2)*sin(b*x + a)/b","A",0
67,1,38,0,0.622835," ","integrate(csc(b*x+a)^3*sin(2*b*x+2*a)^2,x, algorithm=""fricas"")","\frac{2 \, {\left(2 \, \cos\left(b x + a\right) - \log\left(\frac{1}{2} \, \cos\left(b x + a\right) + \frac{1}{2}\right) + \log\left(-\frac{1}{2} \, \cos\left(b x + a\right) + \frac{1}{2}\right)\right)}}{b}"," ",0,"2*(2*cos(b*x + a) - log(1/2*cos(b*x + a) + 1/2) + log(-1/2*cos(b*x + a) + 1/2))/b","A",0
68,1,13,0,0.518262," ","integrate(csc(b*x+a)^3*sin(2*b*x+2*a),x, algorithm=""fricas"")","-\frac{2}{b \sin\left(b x + a\right)}"," ",0,"-2/(b*sin(b*x + a))","A",0
69,1,94,0,0.433640," ","integrate(csc(b*x+a)^3*csc(2*b*x+2*a),x, algorithm=""fricas"")","\frac{3 \, {\left(\cos\left(b x + a\right)^{2} - 1\right)} \log\left(\sin\left(b x + a\right) + 1\right) \sin\left(b x + a\right) - 3 \, {\left(\cos\left(b x + a\right)^{2} - 1\right)} \log\left(-\sin\left(b x + a\right) + 1\right) \sin\left(b x + a\right) - 6 \, \cos\left(b x + a\right)^{2} + 8}{12 \, {\left(b \cos\left(b x + a\right)^{2} - b\right)} \sin\left(b x + a\right)}"," ",0,"1/12*(3*(cos(b*x + a)^2 - 1)*log(sin(b*x + a) + 1)*sin(b*x + a) - 3*(cos(b*x + a)^2 - 1)*log(-sin(b*x + a) + 1)*sin(b*x + a) - 6*cos(b*x + a)^2 + 8)/((b*cos(b*x + a)^2 - b)*sin(b*x + a))","B",0
70,1,132,0,0.443326," ","integrate(csc(b*x+a)^3*csc(2*b*x+2*a)^2,x, algorithm=""fricas"")","\frac{30 \, \cos\left(b x + a\right)^{4} - 50 \, \cos\left(b x + a\right)^{2} - 15 \, {\left(\cos\left(b x + a\right)^{5} - 2 \, \cos\left(b x + a\right)^{3} + \cos\left(b x + a\right)\right)} \log\left(\frac{1}{2} \, \cos\left(b x + a\right) + \frac{1}{2}\right) + 15 \, {\left(\cos\left(b x + a\right)^{5} - 2 \, \cos\left(b x + a\right)^{3} + \cos\left(b x + a\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(b x + a\right) + \frac{1}{2}\right) + 16}{64 \, {\left(b \cos\left(b x + a\right)^{5} - 2 \, b \cos\left(b x + a\right)^{3} + b \cos\left(b x + a\right)\right)}}"," ",0,"1/64*(30*cos(b*x + a)^4 - 50*cos(b*x + a)^2 - 15*(cos(b*x + a)^5 - 2*cos(b*x + a)^3 + cos(b*x + a))*log(1/2*cos(b*x + a) + 1/2) + 15*(cos(b*x + a)^5 - 2*cos(b*x + a)^3 + cos(b*x + a))*log(-1/2*cos(b*x + a) + 1/2) + 16)/(b*cos(b*x + a)^5 - 2*b*cos(b*x + a)^3 + b*cos(b*x + a))","B",0
71,1,166,0,0.563915," ","integrate(csc(b*x+a)^3*csc(2*b*x+2*a)^3,x, algorithm=""fricas"")","-\frac{210 \, \cos\left(b x + a\right)^{6} - 490 \, \cos\left(b x + a\right)^{4} - 105 \, {\left(\cos\left(b x + a\right)^{6} - 2 \, \cos\left(b x + a\right)^{4} + \cos\left(b x + a\right)^{2}\right)} \log\left(\sin\left(b x + a\right) + 1\right) \sin\left(b x + a\right) + 105 \, {\left(\cos\left(b x + a\right)^{6} - 2 \, \cos\left(b x + a\right)^{4} + \cos\left(b x + a\right)^{2}\right)} \log\left(-\sin\left(b x + a\right) + 1\right) \sin\left(b x + a\right) + 322 \, \cos\left(b x + a\right)^{2} - 30}{480 \, {\left(b \cos\left(b x + a\right)^{6} - 2 \, b \cos\left(b x + a\right)^{4} + b \cos\left(b x + a\right)^{2}\right)} \sin\left(b x + a\right)}"," ",0,"-1/480*(210*cos(b*x + a)^6 - 490*cos(b*x + a)^4 - 105*(cos(b*x + a)^6 - 2*cos(b*x + a)^4 + cos(b*x + a)^2)*log(sin(b*x + a) + 1)*sin(b*x + a) + 105*(cos(b*x + a)^6 - 2*cos(b*x + a)^4 + cos(b*x + a)^2)*log(-sin(b*x + a) + 1)*sin(b*x + a) + 322*cos(b*x + a)^2 - 30)/((b*cos(b*x + a)^6 - 2*b*cos(b*x + a)^4 + b*cos(b*x + a)^2)*sin(b*x + a))","B",0
72,1,194,0,0.554174," ","integrate(csc(b*x+a)^3*csc(2*b*x+2*a)^4,x, algorithm=""fricas"")","\frac{630 \, \cos\left(b x + a\right)^{8} - 1680 \, \cos\left(b x + a\right)^{6} + 1386 \, \cos\left(b x + a\right)^{4} - 288 \, \cos\left(b x + a\right)^{2} - 315 \, {\left(\cos\left(b x + a\right)^{9} - 3 \, \cos\left(b x + a\right)^{7} + 3 \, \cos\left(b x + a\right)^{5} - \cos\left(b x + a\right)^{3}\right)} \log\left(\frac{1}{2} \, \cos\left(b x + a\right) + \frac{1}{2}\right) + 315 \, {\left(\cos\left(b x + a\right)^{9} - 3 \, \cos\left(b x + a\right)^{7} + 3 \, \cos\left(b x + a\right)^{5} - \cos\left(b x + a\right)^{3}\right)} \log\left(-\frac{1}{2} \, \cos\left(b x + a\right) + \frac{1}{2}\right) - 32}{1536 \, {\left(b \cos\left(b x + a\right)^{9} - 3 \, b \cos\left(b x + a\right)^{7} + 3 \, b \cos\left(b x + a\right)^{5} - b \cos\left(b x + a\right)^{3}\right)}}"," ",0,"1/1536*(630*cos(b*x + a)^8 - 1680*cos(b*x + a)^6 + 1386*cos(b*x + a)^4 - 288*cos(b*x + a)^2 - 315*(cos(b*x + a)^9 - 3*cos(b*x + a)^7 + 3*cos(b*x + a)^5 - cos(b*x + a)^3)*log(1/2*cos(b*x + a) + 1/2) + 315*(cos(b*x + a)^9 - 3*cos(b*x + a)^7 + 3*cos(b*x + a)^5 - cos(b*x + a)^3)*log(-1/2*cos(b*x + a) + 1/2) - 32)/(b*cos(b*x + a)^9 - 3*b*cos(b*x + a)^7 + 3*b*cos(b*x + a)^5 - b*cos(b*x + a)^3)","A",0
73,1,291,0,0.621819," ","integrate(sin(b*x+a)*sin(2*b*x+2*a)^(5/2),x, algorithm=""fricas"")","\frac{8 \, \sqrt{2} {\left(32 \, \cos\left(b x + a\right)^{5} - 52 \, \cos\left(b x + a\right)^{3} + 5 \, \cos\left(b x + a\right)\right)} \sqrt{\cos\left(b x + a\right) \sin\left(b x + a\right)} + 30 \, \arctan\left(-\frac{\sqrt{2} \sqrt{\cos\left(b x + a\right) \sin\left(b x + a\right)} {\left(\cos\left(b x + a\right) - \sin\left(b x + a\right)\right)} + \cos\left(b x + a\right) \sin\left(b x + a\right)}{\cos\left(b x + a\right)^{2} + 2 \, \cos\left(b x + a\right) \sin\left(b x + a\right) - 1}\right) - 30 \, \arctan\left(-\frac{2 \, \sqrt{2} \sqrt{\cos\left(b x + a\right) \sin\left(b x + a\right)} - \cos\left(b x + a\right) - \sin\left(b x + a\right)}{\cos\left(b x + a\right) - \sin\left(b x + a\right)}\right) - 15 \, \log\left(-32 \, \cos\left(b x + a\right)^{4} + 4 \, \sqrt{2} {\left(4 \, \cos\left(b x + a\right)^{3} - {\left(4 \, \cos\left(b x + a\right)^{2} + 1\right)} \sin\left(b x + a\right) - 5 \, \cos\left(b x + a\right)\right)} \sqrt{\cos\left(b x + a\right) \sin\left(b x + a\right)} + 32 \, \cos\left(b x + a\right)^{2} + 16 \, \cos\left(b x + a\right) \sin\left(b x + a\right) + 1\right)}{384 \, b}"," ",0,"1/384*(8*sqrt(2)*(32*cos(b*x + a)^5 - 52*cos(b*x + a)^3 + 5*cos(b*x + a))*sqrt(cos(b*x + a)*sin(b*x + a)) + 30*arctan(-(sqrt(2)*sqrt(cos(b*x + a)*sin(b*x + a))*(cos(b*x + a) - sin(b*x + a)) + cos(b*x + a)*sin(b*x + a))/(cos(b*x + a)^2 + 2*cos(b*x + a)*sin(b*x + a) - 1)) - 30*arctan(-(2*sqrt(2)*sqrt(cos(b*x + a)*sin(b*x + a)) - cos(b*x + a) - sin(b*x + a))/(cos(b*x + a) - sin(b*x + a))) - 15*log(-32*cos(b*x + a)^4 + 4*sqrt(2)*(4*cos(b*x + a)^3 - (4*cos(b*x + a)^2 + 1)*sin(b*x + a) - 5*cos(b*x + a))*sqrt(cos(b*x + a)*sin(b*x + a)) + 32*cos(b*x + a)^2 + 16*cos(b*x + a)*sin(b*x + a) + 1))/b","B",0
74,1,280,0,0.480546," ","integrate(sin(b*x+a)*sin(2*b*x+2*a)^(3/2),x, algorithm=""fricas"")","-\frac{8 \, \sqrt{2} {\left(4 \, \cos\left(b x + a\right)^{2} - 3\right)} \sqrt{\cos\left(b x + a\right) \sin\left(b x + a\right)} \sin\left(b x + a\right) - 6 \, \arctan\left(-\frac{\sqrt{2} \sqrt{\cos\left(b x + a\right) \sin\left(b x + a\right)} {\left(\cos\left(b x + a\right) - \sin\left(b x + a\right)\right)} + \cos\left(b x + a\right) \sin\left(b x + a\right)}{\cos\left(b x + a\right)^{2} + 2 \, \cos\left(b x + a\right) \sin\left(b x + a\right) - 1}\right) + 6 \, \arctan\left(-\frac{2 \, \sqrt{2} \sqrt{\cos\left(b x + a\right) \sin\left(b x + a\right)} - \cos\left(b x + a\right) - \sin\left(b x + a\right)}{\cos\left(b x + a\right) - \sin\left(b x + a\right)}\right) - 3 \, \log\left(-32 \, \cos\left(b x + a\right)^{4} + 4 \, \sqrt{2} {\left(4 \, \cos\left(b x + a\right)^{3} - {\left(4 \, \cos\left(b x + a\right)^{2} + 1\right)} \sin\left(b x + a\right) - 5 \, \cos\left(b x + a\right)\right)} \sqrt{\cos\left(b x + a\right) \sin\left(b x + a\right)} + 32 \, \cos\left(b x + a\right)^{2} + 16 \, \cos\left(b x + a\right) \sin\left(b x + a\right) + 1\right)}{64 \, b}"," ",0,"-1/64*(8*sqrt(2)*(4*cos(b*x + a)^2 - 3)*sqrt(cos(b*x + a)*sin(b*x + a))*sin(b*x + a) - 6*arctan(-(sqrt(2)*sqrt(cos(b*x + a)*sin(b*x + a))*(cos(b*x + a) - sin(b*x + a)) + cos(b*x + a)*sin(b*x + a))/(cos(b*x + a)^2 + 2*cos(b*x + a)*sin(b*x + a) - 1)) + 6*arctan(-(2*sqrt(2)*sqrt(cos(b*x + a)*sin(b*x + a)) - cos(b*x + a) - sin(b*x + a))/(cos(b*x + a) - sin(b*x + a))) - 3*log(-32*cos(b*x + a)^4 + 4*sqrt(2)*(4*cos(b*x + a)^3 - (4*cos(b*x + a)^2 + 1)*sin(b*x + a) - 5*cos(b*x + a))*sqrt(cos(b*x + a)*sin(b*x + a)) + 32*cos(b*x + a)^2 + 16*cos(b*x + a)*sin(b*x + a) + 1))/b","B",0
75,1,266,0,0.780545," ","integrate(sin(b*x+a)*sin(2*b*x+2*a)^(1/2),x, algorithm=""fricas"")","-\frac{8 \, \sqrt{2} \sqrt{\cos\left(b x + a\right) \sin\left(b x + a\right)} \cos\left(b x + a\right) - 2 \, \arctan\left(-\frac{\sqrt{2} \sqrt{\cos\left(b x + a\right) \sin\left(b x + a\right)} {\left(\cos\left(b x + a\right) - \sin\left(b x + a\right)\right)} + \cos\left(b x + a\right) \sin\left(b x + a\right)}{\cos\left(b x + a\right)^{2} + 2 \, \cos\left(b x + a\right) \sin\left(b x + a\right) - 1}\right) + 2 \, \arctan\left(-\frac{2 \, \sqrt{2} \sqrt{\cos\left(b x + a\right) \sin\left(b x + a\right)} - \cos\left(b x + a\right) - \sin\left(b x + a\right)}{\cos\left(b x + a\right) - \sin\left(b x + a\right)}\right) + \log\left(-32 \, \cos\left(b x + a\right)^{4} + 4 \, \sqrt{2} {\left(4 \, \cos\left(b x + a\right)^{3} - {\left(4 \, \cos\left(b x + a\right)^{2} + 1\right)} \sin\left(b x + a\right) - 5 \, \cos\left(b x + a\right)\right)} \sqrt{\cos\left(b x + a\right) \sin\left(b x + a\right)} + 32 \, \cos\left(b x + a\right)^{2} + 16 \, \cos\left(b x + a\right) \sin\left(b x + a\right) + 1\right)}{16 \, b}"," ",0,"-1/16*(8*sqrt(2)*sqrt(cos(b*x + a)*sin(b*x + a))*cos(b*x + a) - 2*arctan(-(sqrt(2)*sqrt(cos(b*x + a)*sin(b*x + a))*(cos(b*x + a) - sin(b*x + a)) + cos(b*x + a)*sin(b*x + a))/(cos(b*x + a)^2 + 2*cos(b*x + a)*sin(b*x + a) - 1)) + 2*arctan(-(2*sqrt(2)*sqrt(cos(b*x + a)*sin(b*x + a)) - cos(b*x + a) - sin(b*x + a))/(cos(b*x + a) - sin(b*x + a))) + log(-32*cos(b*x + a)^4 + 4*sqrt(2)*(4*cos(b*x + a)^3 - (4*cos(b*x + a)^2 + 1)*sin(b*x + a) - 5*cos(b*x + a))*sqrt(cos(b*x + a)*sin(b*x + a)) + 32*cos(b*x + a)^2 + 16*cos(b*x + a)*sin(b*x + a) + 1))/b","B",0
76,1,240,0,0.494302," ","integrate(sin(b*x+a)/sin(2*b*x+2*a)^(1/2),x, algorithm=""fricas"")","\frac{2 \, \arctan\left(-\frac{\sqrt{2} \sqrt{\cos\left(b x + a\right) \sin\left(b x + a\right)} {\left(\cos\left(b x + a\right) - \sin\left(b x + a\right)\right)} + \cos\left(b x + a\right) \sin\left(b x + a\right)}{\cos\left(b x + a\right)^{2} + 2 \, \cos\left(b x + a\right) \sin\left(b x + a\right) - 1}\right) - 2 \, \arctan\left(-\frac{2 \, \sqrt{2} \sqrt{\cos\left(b x + a\right) \sin\left(b x + a\right)} - \cos\left(b x + a\right) - \sin\left(b x + a\right)}{\cos\left(b x + a\right) - \sin\left(b x + a\right)}\right) + \log\left(-32 \, \cos\left(b x + a\right)^{4} + 4 \, \sqrt{2} {\left(4 \, \cos\left(b x + a\right)^{3} - {\left(4 \, \cos\left(b x + a\right)^{2} + 1\right)} \sin\left(b x + a\right) - 5 \, \cos\left(b x + a\right)\right)} \sqrt{\cos\left(b x + a\right) \sin\left(b x + a\right)} + 32 \, \cos\left(b x + a\right)^{2} + 16 \, \cos\left(b x + a\right) \sin\left(b x + a\right) + 1\right)}{8 \, b}"," ",0,"1/8*(2*arctan(-(sqrt(2)*sqrt(cos(b*x + a)*sin(b*x + a))*(cos(b*x + a) - sin(b*x + a)) + cos(b*x + a)*sin(b*x + a))/(cos(b*x + a)^2 + 2*cos(b*x + a)*sin(b*x + a) - 1)) - 2*arctan(-(2*sqrt(2)*sqrt(cos(b*x + a)*sin(b*x + a)) - cos(b*x + a) - sin(b*x + a))/(cos(b*x + a) - sin(b*x + a))) + log(-32*cos(b*x + a)^4 + 4*sqrt(2)*(4*cos(b*x + a)^3 - (4*cos(b*x + a)^2 + 1)*sin(b*x + a) - 5*cos(b*x + a))*sqrt(cos(b*x + a)*sin(b*x + a)) + 32*cos(b*x + a)^2 + 16*cos(b*x + a)*sin(b*x + a) + 1))/b","B",0
77,1,39,0,0.472987," ","integrate(sin(b*x+a)/sin(2*b*x+2*a)^(3/2),x, algorithm=""fricas"")","\frac{\sqrt{2} \sqrt{\cos\left(b x + a\right) \sin\left(b x + a\right)} + \cos\left(b x + a\right)}{2 \, b \cos\left(b x + a\right)}"," ",0,"1/2*(sqrt(2)*sqrt(cos(b*x + a)*sin(b*x + a)) + cos(b*x + a))/(b*cos(b*x + a))","A",0
78,1,69,0,0.451291," ","integrate(sin(b*x+a)/sin(2*b*x+2*a)^(5/2),x, algorithm=""fricas"")","-\frac{4 \, \cos\left(b x + a\right)^{2} \sin\left(b x + a\right) + \sqrt{2} {\left(4 \, \cos\left(b x + a\right)^{2} - 1\right)} \sqrt{\cos\left(b x + a\right) \sin\left(b x + a\right)}}{12 \, b \cos\left(b x + a\right)^{2} \sin\left(b x + a\right)}"," ",0,"-1/12*(4*cos(b*x + a)^2*sin(b*x + a) + sqrt(2)*(4*cos(b*x + a)^2 - 1)*sqrt(cos(b*x + a)*sin(b*x + a)))/(b*cos(b*x + a)^2*sin(b*x + a))","A",0
79,1,88,0,0.431595," ","integrate(sin(b*x+a)/sin(2*b*x+2*a)^(7/2),x, algorithm=""fricas"")","\frac{32 \, \cos\left(b x + a\right)^{5} - 32 \, \cos\left(b x + a\right)^{3} + \sqrt{2} {\left(32 \, \cos\left(b x + a\right)^{4} - 24 \, \cos\left(b x + a\right)^{2} - 3\right)} \sqrt{\cos\left(b x + a\right) \sin\left(b x + a\right)}}{120 \, {\left(b \cos\left(b x + a\right)^{5} - b \cos\left(b x + a\right)^{3}\right)}}"," ",0,"1/120*(32*cos(b*x + a)^5 - 32*cos(b*x + a)^3 + sqrt(2)*(32*cos(b*x + a)^4 - 24*cos(b*x + a)^2 - 3)*sqrt(cos(b*x + a)*sin(b*x + a)))/(b*cos(b*x + a)^5 - b*cos(b*x + a)^3)","A",0
80,1,113,0,0.453024," ","integrate(sin(b*x+a)/sin(2*b*x+2*a)^(9/2),x, algorithm=""fricas"")","-\frac{\sqrt{2} {\left(128 \, \cos\left(b x + a\right)^{6} - 160 \, \cos\left(b x + a\right)^{4} + 20 \, \cos\left(b x + a\right)^{2} + 5\right)} \sqrt{\cos\left(b x + a\right) \sin\left(b x + a\right)} + 128 \, {\left(\cos\left(b x + a\right)^{6} - \cos\left(b x + a\right)^{4}\right)} \sin\left(b x + a\right)}{560 \, {\left(b \cos\left(b x + a\right)^{6} - b \cos\left(b x + a\right)^{4}\right)} \sin\left(b x + a\right)}"," ",0,"-1/560*(sqrt(2)*(128*cos(b*x + a)^6 - 160*cos(b*x + a)^4 + 20*cos(b*x + a)^2 + 5)*sqrt(cos(b*x + a)*sin(b*x + a)) + 128*(cos(b*x + a)^6 - cos(b*x + a)^4)*sin(b*x + a))/((b*cos(b*x + a)^6 - b*cos(b*x + a)^4)*sin(b*x + a))","A",0
81,0,0,0,0.572733," ","integrate(sin(b*x+a)^2*sin(2*b*x+2*a)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left({\left({\left(\cos\left(b x + a\right)^{2} - 1\right)} \cos\left(2 \, b x + 2 \, a\right)^{2} - \cos\left(b x + a\right)^{2} + 1\right)} \sin\left(2 \, b x + 2 \, a\right)^{\frac{3}{2}}, x\right)"," ",0,"integral(((cos(b*x + a)^2 - 1)*cos(2*b*x + 2*a)^2 - cos(b*x + a)^2 + 1)*sin(2*b*x + 2*a)^(3/2), x)","F",0
82,0,0,0,0.521396," ","integrate(sin(b*x+a)^2*sin(2*b*x+2*a)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left({\left({\left(\cos\left(b x + a\right)^{2} - 1\right)} \cos\left(2 \, b x + 2 \, a\right)^{2} - \cos\left(b x + a\right)^{2} + 1\right)} \sqrt{\sin\left(2 \, b x + 2 \, a\right)}, x\right)"," ",0,"integral(((cos(b*x + a)^2 - 1)*cos(2*b*x + 2*a)^2 - cos(b*x + a)^2 + 1)*sqrt(sin(2*b*x + 2*a)), x)","F",0
83,0,0,0,0.440971," ","integrate(sin(b*x+a)^2*sin(2*b*x+2*a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(-{\left(\cos\left(b x + a\right)^{2} - 1\right)} \sin\left(2 \, b x + 2 \, a\right)^{\frac{3}{2}}, x\right)"," ",0,"integral(-(cos(b*x + a)^2 - 1)*sin(2*b*x + 2*a)^(3/2), x)","F",0
84,0,0,0,0.468464," ","integrate(sin(b*x+a)^2*sin(2*b*x+2*a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-{\left(\cos\left(b x + a\right)^{2} - 1\right)} \sqrt{\sin\left(2 \, b x + 2 \, a\right)}, x\right)"," ",0,"integral(-(cos(b*x + a)^2 - 1)*sqrt(sin(2*b*x + 2*a)), x)","F",0
85,0,0,0,0.448030," ","integrate(sin(b*x+a)^2/sin(2*b*x+2*a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\cos\left(b x + a\right)^{2} - 1}{\sqrt{\sin\left(2 \, b x + 2 \, a\right)}}, x\right)"," ",0,"integral(-(cos(b*x + a)^2 - 1)/sqrt(sin(2*b*x + 2*a)), x)","F",0
86,0,0,0,0.449398," ","integrate(sin(b*x+a)^2/sin(2*b*x+2*a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(\cos\left(b x + a\right)^{2} - 1\right)} \sqrt{\sin\left(2 \, b x + 2 \, a\right)}}{\cos\left(2 \, b x + 2 \, a\right)^{2} - 1}, x\right)"," ",0,"integral((cos(b*x + a)^2 - 1)*sqrt(sin(2*b*x + 2*a))/(cos(2*b*x + 2*a)^2 - 1), x)","F",0
87,0,0,0,0.451602," ","integrate(sin(b*x+a)^2/sin(2*b*x+2*a)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\cos\left(b x + a\right)^{2} - 1}{{\left(\cos\left(2 \, b x + 2 \, a\right)^{2} - 1\right)} \sqrt{\sin\left(2 \, b x + 2 \, a\right)}}, x\right)"," ",0,"integral((cos(b*x + a)^2 - 1)/((cos(2*b*x + 2*a)^2 - 1)*sqrt(sin(2*b*x + 2*a))), x)","F",0
88,0,0,0,0.432214," ","integrate(sin(b*x+a)^2/sin(2*b*x+2*a)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(\cos\left(b x + a\right)^{2} - 1\right)} \sqrt{\sin\left(2 \, b x + 2 \, a\right)}}{\cos\left(2 \, b x + 2 \, a\right)^{4} - 2 \, \cos\left(2 \, b x + 2 \, a\right)^{2} + 1}, x\right)"," ",0,"integral(-(cos(b*x + a)^2 - 1)*sqrt(sin(2*b*x + 2*a))/(cos(2*b*x + 2*a)^4 - 2*cos(2*b*x + 2*a)^2 + 1), x)","F",0
89,1,290,0,0.469310," ","integrate(sin(b*x+a)^3*sin(2*b*x+2*a)^(3/2),x, algorithm=""fricas"")","\frac{8 \, \sqrt{2} {\left(32 \, \cos\left(b x + a\right)^{4} - 60 \, \cos\left(b x + a\right)^{2} + 21\right)} \sqrt{\cos\left(b x + a\right) \sin\left(b x + a\right)} \sin\left(b x + a\right) + 42 \, \arctan\left(-\frac{\sqrt{2} \sqrt{\cos\left(b x + a\right) \sin\left(b x + a\right)} {\left(\cos\left(b x + a\right) - \sin\left(b x + a\right)\right)} + \cos\left(b x + a\right) \sin\left(b x + a\right)}{\cos\left(b x + a\right)^{2} + 2 \, \cos\left(b x + a\right) \sin\left(b x + a\right) - 1}\right) - 42 \, \arctan\left(-\frac{2 \, \sqrt{2} \sqrt{\cos\left(b x + a\right) \sin\left(b x + a\right)} - \cos\left(b x + a\right) - \sin\left(b x + a\right)}{\cos\left(b x + a\right) - \sin\left(b x + a\right)}\right) + 21 \, \log\left(-32 \, \cos\left(b x + a\right)^{4} + 4 \, \sqrt{2} {\left(4 \, \cos\left(b x + a\right)^{3} - {\left(4 \, \cos\left(b x + a\right)^{2} + 1\right)} \sin\left(b x + a\right) - 5 \, \cos\left(b x + a\right)\right)} \sqrt{\cos\left(b x + a\right) \sin\left(b x + a\right)} + 32 \, \cos\left(b x + a\right)^{2} + 16 \, \cos\left(b x + a\right) \sin\left(b x + a\right) + 1\right)}{768 \, b}"," ",0,"1/768*(8*sqrt(2)*(32*cos(b*x + a)^4 - 60*cos(b*x + a)^2 + 21)*sqrt(cos(b*x + a)*sin(b*x + a))*sin(b*x + a) + 42*arctan(-(sqrt(2)*sqrt(cos(b*x + a)*sin(b*x + a))*(cos(b*x + a) - sin(b*x + a)) + cos(b*x + a)*sin(b*x + a))/(cos(b*x + a)^2 + 2*cos(b*x + a)*sin(b*x + a) - 1)) - 42*arctan(-(2*sqrt(2)*sqrt(cos(b*x + a)*sin(b*x + a)) - cos(b*x + a) - sin(b*x + a))/(cos(b*x + a) - sin(b*x + a))) + 21*log(-32*cos(b*x + a)^4 + 4*sqrt(2)*(4*cos(b*x + a)^3 - (4*cos(b*x + a)^2 + 1)*sin(b*x + a) - 5*cos(b*x + a))*sqrt(cos(b*x + a)*sin(b*x + a)) + 32*cos(b*x + a)^2 + 16*cos(b*x + a)*sin(b*x + a) + 1))/b","B",0
90,1,281,0,0.506634," ","integrate(sin(b*x+a)^3*sin(2*b*x+2*a)^(1/2),x, algorithm=""fricas"")","\frac{8 \, \sqrt{2} {\left(4 \, \cos\left(b x + a\right)^{3} - 9 \, \cos\left(b x + a\right)\right)} \sqrt{\cos\left(b x + a\right) \sin\left(b x + a\right)} + 10 \, \arctan\left(-\frac{\sqrt{2} \sqrt{\cos\left(b x + a\right) \sin\left(b x + a\right)} {\left(\cos\left(b x + a\right) - \sin\left(b x + a\right)\right)} + \cos\left(b x + a\right) \sin\left(b x + a\right)}{\cos\left(b x + a\right)^{2} + 2 \, \cos\left(b x + a\right) \sin\left(b x + a\right) - 1}\right) - 10 \, \arctan\left(-\frac{2 \, \sqrt{2} \sqrt{\cos\left(b x + a\right) \sin\left(b x + a\right)} - \cos\left(b x + a\right) - \sin\left(b x + a\right)}{\cos\left(b x + a\right) - \sin\left(b x + a\right)}\right) - 5 \, \log\left(-32 \, \cos\left(b x + a\right)^{4} + 4 \, \sqrt{2} {\left(4 \, \cos\left(b x + a\right)^{3} - {\left(4 \, \cos\left(b x + a\right)^{2} + 1\right)} \sin\left(b x + a\right) - 5 \, \cos\left(b x + a\right)\right)} \sqrt{\cos\left(b x + a\right) \sin\left(b x + a\right)} + 32 \, \cos\left(b x + a\right)^{2} + 16 \, \cos\left(b x + a\right) \sin\left(b x + a\right) + 1\right)}{128 \, b}"," ",0,"1/128*(8*sqrt(2)*(4*cos(b*x + a)^3 - 9*cos(b*x + a))*sqrt(cos(b*x + a)*sin(b*x + a)) + 10*arctan(-(sqrt(2)*sqrt(cos(b*x + a)*sin(b*x + a))*(cos(b*x + a) - sin(b*x + a)) + cos(b*x + a)*sin(b*x + a))/(cos(b*x + a)^2 + 2*cos(b*x + a)*sin(b*x + a) - 1)) - 10*arctan(-(2*sqrt(2)*sqrt(cos(b*x + a)*sin(b*x + a)) - cos(b*x + a) - sin(b*x + a))/(cos(b*x + a) - sin(b*x + a))) - 5*log(-32*cos(b*x + a)^4 + 4*sqrt(2)*(4*cos(b*x + a)^3 - (4*cos(b*x + a)^2 + 1)*sin(b*x + a) - 5*cos(b*x + a))*sqrt(cos(b*x + a)*sin(b*x + a)) + 32*cos(b*x + a)^2 + 16*cos(b*x + a)*sin(b*x + a) + 1))/b","B",0
91,1,268,0,0.487651," ","integrate(sin(b*x+a)^3/sin(2*b*x+2*a)^(1/2),x, algorithm=""fricas"")","-\frac{8 \, \sqrt{2} \sqrt{\cos\left(b x + a\right) \sin\left(b x + a\right)} \sin\left(b x + a\right) - 6 \, \arctan\left(-\frac{\sqrt{2} \sqrt{\cos\left(b x + a\right) \sin\left(b x + a\right)} {\left(\cos\left(b x + a\right) - \sin\left(b x + a\right)\right)} + \cos\left(b x + a\right) \sin\left(b x + a\right)}{\cos\left(b x + a\right)^{2} + 2 \, \cos\left(b x + a\right) \sin\left(b x + a\right) - 1}\right) + 6 \, \arctan\left(-\frac{2 \, \sqrt{2} \sqrt{\cos\left(b x + a\right) \sin\left(b x + a\right)} - \cos\left(b x + a\right) - \sin\left(b x + a\right)}{\cos\left(b x + a\right) - \sin\left(b x + a\right)}\right) - 3 \, \log\left(-32 \, \cos\left(b x + a\right)^{4} + 4 \, \sqrt{2} {\left(4 \, \cos\left(b x + a\right)^{3} - {\left(4 \, \cos\left(b x + a\right)^{2} + 1\right)} \sin\left(b x + a\right) - 5 \, \cos\left(b x + a\right)\right)} \sqrt{\cos\left(b x + a\right) \sin\left(b x + a\right)} + 32 \, \cos\left(b x + a\right)^{2} + 16 \, \cos\left(b x + a\right) \sin\left(b x + a\right) + 1\right)}{32 \, b}"," ",0,"-1/32*(8*sqrt(2)*sqrt(cos(b*x + a)*sin(b*x + a))*sin(b*x + a) - 6*arctan(-(sqrt(2)*sqrt(cos(b*x + a)*sin(b*x + a))*(cos(b*x + a) - sin(b*x + a)) + cos(b*x + a)*sin(b*x + a))/(cos(b*x + a)^2 + 2*cos(b*x + a)*sin(b*x + a) - 1)) + 6*arctan(-(2*sqrt(2)*sqrt(cos(b*x + a)*sin(b*x + a)) - cos(b*x + a) - sin(b*x + a))/(cos(b*x + a) - sin(b*x + a))) - 3*log(-32*cos(b*x + a)^4 + 4*sqrt(2)*(4*cos(b*x + a)^3 - (4*cos(b*x + a)^2 + 1)*sin(b*x + a) - 5*cos(b*x + a))*sqrt(cos(b*x + a)*sin(b*x + a)) + 32*cos(b*x + a)^2 + 16*cos(b*x + a)*sin(b*x + a) + 1))/b","B",0
92,1,296,0,0.463940," ","integrate(sin(b*x+a)^3/sin(2*b*x+2*a)^(3/2),x, algorithm=""fricas"")","-\frac{2 \, \arctan\left(-\frac{\sqrt{2} \sqrt{\cos\left(b x + a\right) \sin\left(b x + a\right)} {\left(\cos\left(b x + a\right) - \sin\left(b x + a\right)\right)} + \cos\left(b x + a\right) \sin\left(b x + a\right)}{\cos\left(b x + a\right)^{2} + 2 \, \cos\left(b x + a\right) \sin\left(b x + a\right) - 1}\right) \cos\left(b x + a\right) - 2 \, \arctan\left(-\frac{2 \, \sqrt{2} \sqrt{\cos\left(b x + a\right) \sin\left(b x + a\right)} - \cos\left(b x + a\right) - \sin\left(b x + a\right)}{\cos\left(b x + a\right) - \sin\left(b x + a\right)}\right) \cos\left(b x + a\right) - \cos\left(b x + a\right) \log\left(-32 \, \cos\left(b x + a\right)^{4} + 4 \, \sqrt{2} {\left(4 \, \cos\left(b x + a\right)^{3} - {\left(4 \, \cos\left(b x + a\right)^{2} + 1\right)} \sin\left(b x + a\right) - 5 \, \cos\left(b x + a\right)\right)} \sqrt{\cos\left(b x + a\right) \sin\left(b x + a\right)} + 32 \, \cos\left(b x + a\right)^{2} + 16 \, \cos\left(b x + a\right) \sin\left(b x + a\right) + 1\right) - 8 \, \sqrt{2} \sqrt{\cos\left(b x + a\right) \sin\left(b x + a\right)} - 8 \, \cos\left(b x + a\right)}{16 \, b \cos\left(b x + a\right)}"," ",0,"-1/16*(2*arctan(-(sqrt(2)*sqrt(cos(b*x + a)*sin(b*x + a))*(cos(b*x + a) - sin(b*x + a)) + cos(b*x + a)*sin(b*x + a))/(cos(b*x + a)^2 + 2*cos(b*x + a)*sin(b*x + a) - 1))*cos(b*x + a) - 2*arctan(-(2*sqrt(2)*sqrt(cos(b*x + a)*sin(b*x + a)) - cos(b*x + a) - sin(b*x + a))/(cos(b*x + a) - sin(b*x + a)))*cos(b*x + a) - cos(b*x + a)*log(-32*cos(b*x + a)^4 + 4*sqrt(2)*(4*cos(b*x + a)^3 - (4*cos(b*x + a)^2 + 1)*sin(b*x + a) - 5*cos(b*x + a))*sqrt(cos(b*x + a)*sin(b*x + a)) + 32*cos(b*x + a)^2 + 16*cos(b*x + a)*sin(b*x + a) + 1) - 8*sqrt(2)*sqrt(cos(b*x + a)*sin(b*x + a)) - 8*cos(b*x + a))/(b*cos(b*x + a))","B",0
93,1,48,0,0.449700," ","integrate(sin(b*x+a)^3/sin(2*b*x+2*a)^(5/2),x, algorithm=""fricas"")","-\frac{\cos\left(b x + a\right)^{2} - \sqrt{2} \sqrt{\cos\left(b x + a\right) \sin\left(b x + a\right)} \sin\left(b x + a\right)}{12 \, b \cos\left(b x + a\right)^{2}}"," ",0,"-1/12*(cos(b*x + a)^2 - sqrt(2)*sqrt(cos(b*x + a)*sin(b*x + a))*sin(b*x + a))/(b*cos(b*x + a)^2)","A",0
94,1,55,0,0.486390," ","integrate(sin(b*x+a)^3/sin(2*b*x+2*a)^(7/2),x, algorithm=""fricas"")","\frac{4 \, \cos\left(b x + a\right)^{3} + \sqrt{2} {\left(4 \, \cos\left(b x + a\right)^{2} + 1\right)} \sqrt{\cos\left(b x + a\right) \sin\left(b x + a\right)}}{40 \, b \cos\left(b x + a\right)^{3}}"," ",0,"1/40*(4*cos(b*x + a)^3 + sqrt(2)*(4*cos(b*x + a)^2 + 1)*sqrt(cos(b*x + a)*sin(b*x + a)))/(b*cos(b*x + a)^3)","A",0
95,1,79,0,0.428936," ","integrate(sin(b*x+a)^3/sin(2*b*x+2*a)^(9/2),x, algorithm=""fricas"")","-\frac{32 \, \cos\left(b x + a\right)^{4} \sin\left(b x + a\right) + \sqrt{2} {\left(32 \, \cos\left(b x + a\right)^{4} - 8 \, \cos\left(b x + a\right)^{2} - 3\right)} \sqrt{\cos\left(b x + a\right) \sin\left(b x + a\right)}}{336 \, b \cos\left(b x + a\right)^{4} \sin\left(b x + a\right)}"," ",0,"-1/336*(32*cos(b*x + a)^4*sin(b*x + a) + sqrt(2)*(32*cos(b*x + a)^4 - 8*cos(b*x + a)^2 - 3)*sqrt(cos(b*x + a)*sin(b*x + a)))/(b*cos(b*x + a)^4*sin(b*x + a))","A",0
96,1,98,0,0.446878," ","integrate(sin(b*x+a)^3/sin(2*b*x+2*a)^(11/2),x, algorithm=""fricas"")","\frac{128 \, \cos\left(b x + a\right)^{7} - 128 \, \cos\left(b x + a\right)^{5} + \sqrt{2} {\left(128 \, \cos\left(b x + a\right)^{6} - 96 \, \cos\left(b x + a\right)^{4} - 12 \, \cos\left(b x + a\right)^{2} - 5\right)} \sqrt{\cos\left(b x + a\right) \sin\left(b x + a\right)}}{1440 \, {\left(b \cos\left(b x + a\right)^{7} - b \cos\left(b x + a\right)^{5}\right)}}"," ",0,"1/1440*(128*cos(b*x + a)^7 - 128*cos(b*x + a)^5 + sqrt(2)*(128*cos(b*x + a)^6 - 96*cos(b*x + a)^4 - 12*cos(b*x + a)^2 - 5)*sqrt(cos(b*x + a)*sin(b*x + a)))/(b*cos(b*x + a)^7 - b*cos(b*x + a)^5)","A",0
97,1,290,0,0.448260," ","integrate(csc(b*x+a)*sin(2*b*x+2*a)^(7/2),x, algorithm=""fricas"")","-\frac{8 \, \sqrt{2} {\left(32 \, \cos\left(b x + a\right)^{4} - 12 \, \cos\left(b x + a\right)^{2} - 15\right)} \sqrt{\cos\left(b x + a\right) \sin\left(b x + a\right)} \sin\left(b x + a\right) - 30 \, \arctan\left(-\frac{\sqrt{2} \sqrt{\cos\left(b x + a\right) \sin\left(b x + a\right)} {\left(\cos\left(b x + a\right) - \sin\left(b x + a\right)\right)} + \cos\left(b x + a\right) \sin\left(b x + a\right)}{\cos\left(b x + a\right)^{2} + 2 \, \cos\left(b x + a\right) \sin\left(b x + a\right) - 1}\right) + 30 \, \arctan\left(-\frac{2 \, \sqrt{2} \sqrt{\cos\left(b x + a\right) \sin\left(b x + a\right)} - \cos\left(b x + a\right) - \sin\left(b x + a\right)}{\cos\left(b x + a\right) - \sin\left(b x + a\right)}\right) - 15 \, \log\left(-32 \, \cos\left(b x + a\right)^{4} + 4 \, \sqrt{2} {\left(4 \, \cos\left(b x + a\right)^{3} - {\left(4 \, \cos\left(b x + a\right)^{2} + 1\right)} \sin\left(b x + a\right) - 5 \, \cos\left(b x + a\right)\right)} \sqrt{\cos\left(b x + a\right) \sin\left(b x + a\right)} + 32 \, \cos\left(b x + a\right)^{2} + 16 \, \cos\left(b x + a\right) \sin\left(b x + a\right) + 1\right)}{192 \, b}"," ",0,"-1/192*(8*sqrt(2)*(32*cos(b*x + a)^4 - 12*cos(b*x + a)^2 - 15)*sqrt(cos(b*x + a)*sin(b*x + a))*sin(b*x + a) - 30*arctan(-(sqrt(2)*sqrt(cos(b*x + a)*sin(b*x + a))*(cos(b*x + a) - sin(b*x + a)) + cos(b*x + a)*sin(b*x + a))/(cos(b*x + a)^2 + 2*cos(b*x + a)*sin(b*x + a) - 1)) + 30*arctan(-(2*sqrt(2)*sqrt(cos(b*x + a)*sin(b*x + a)) - cos(b*x + a) - sin(b*x + a))/(cos(b*x + a) - sin(b*x + a))) - 15*log(-32*cos(b*x + a)^4 + 4*sqrt(2)*(4*cos(b*x + a)^3 - (4*cos(b*x + a)^2 + 1)*sin(b*x + a) - 5*cos(b*x + a))*sqrt(cos(b*x + a)*sin(b*x + a)) + 32*cos(b*x + a)^2 + 16*cos(b*x + a)*sin(b*x + a) + 1))/b","B",0
98,1,281,0,0.461830," ","integrate(csc(b*x+a)*sin(2*b*x+2*a)^(5/2),x, algorithm=""fricas"")","-\frac{8 \, \sqrt{2} {\left(4 \, \cos\left(b x + a\right)^{3} - \cos\left(b x + a\right)\right)} \sqrt{\cos\left(b x + a\right) \sin\left(b x + a\right)} - 6 \, \arctan\left(-\frac{\sqrt{2} \sqrt{\cos\left(b x + a\right) \sin\left(b x + a\right)} {\left(\cos\left(b x + a\right) - \sin\left(b x + a\right)\right)} + \cos\left(b x + a\right) \sin\left(b x + a\right)}{\cos\left(b x + a\right)^{2} + 2 \, \cos\left(b x + a\right) \sin\left(b x + a\right) - 1}\right) + 6 \, \arctan\left(-\frac{2 \, \sqrt{2} \sqrt{\cos\left(b x + a\right) \sin\left(b x + a\right)} - \cos\left(b x + a\right) - \sin\left(b x + a\right)}{\cos\left(b x + a\right) - \sin\left(b x + a\right)}\right) + 3 \, \log\left(-32 \, \cos\left(b x + a\right)^{4} + 4 \, \sqrt{2} {\left(4 \, \cos\left(b x + a\right)^{3} - {\left(4 \, \cos\left(b x + a\right)^{2} + 1\right)} \sin\left(b x + a\right) - 5 \, \cos\left(b x + a\right)\right)} \sqrt{\cos\left(b x + a\right) \sin\left(b x + a\right)} + 32 \, \cos\left(b x + a\right)^{2} + 16 \, \cos\left(b x + a\right) \sin\left(b x + a\right) + 1\right)}{32 \, b}"," ",0,"-1/32*(8*sqrt(2)*(4*cos(b*x + a)^3 - cos(b*x + a))*sqrt(cos(b*x + a)*sin(b*x + a)) - 6*arctan(-(sqrt(2)*sqrt(cos(b*x + a)*sin(b*x + a))*(cos(b*x + a) - sin(b*x + a)) + cos(b*x + a)*sin(b*x + a))/(cos(b*x + a)^2 + 2*cos(b*x + a)*sin(b*x + a) - 1)) + 6*arctan(-(2*sqrt(2)*sqrt(cos(b*x + a)*sin(b*x + a)) - cos(b*x + a) - sin(b*x + a))/(cos(b*x + a) - sin(b*x + a))) + 3*log(-32*cos(b*x + a)^4 + 4*sqrt(2)*(4*cos(b*x + a)^3 - (4*cos(b*x + a)^2 + 1)*sin(b*x + a) - 5*cos(b*x + a))*sqrt(cos(b*x + a)*sin(b*x + a)) + 32*cos(b*x + a)^2 + 16*cos(b*x + a)*sin(b*x + a) + 1))/b","B",0
99,1,266,0,0.473656," ","integrate(csc(b*x+a)*sin(2*b*x+2*a)^(3/2),x, algorithm=""fricas"")","\frac{8 \, \sqrt{2} \sqrt{\cos\left(b x + a\right) \sin\left(b x + a\right)} \sin\left(b x + a\right) + 2 \, \arctan\left(-\frac{\sqrt{2} \sqrt{\cos\left(b x + a\right) \sin\left(b x + a\right)} {\left(\cos\left(b x + a\right) - \sin\left(b x + a\right)\right)} + \cos\left(b x + a\right) \sin\left(b x + a\right)}{\cos\left(b x + a\right)^{2} + 2 \, \cos\left(b x + a\right) \sin\left(b x + a\right) - 1}\right) - 2 \, \arctan\left(-\frac{2 \, \sqrt{2} \sqrt{\cos\left(b x + a\right) \sin\left(b x + a\right)} - \cos\left(b x + a\right) - \sin\left(b x + a\right)}{\cos\left(b x + a\right) - \sin\left(b x + a\right)}\right) + \log\left(-32 \, \cos\left(b x + a\right)^{4} + 4 \, \sqrt{2} {\left(4 \, \cos\left(b x + a\right)^{3} - {\left(4 \, \cos\left(b x + a\right)^{2} + 1\right)} \sin\left(b x + a\right) - 5 \, \cos\left(b x + a\right)\right)} \sqrt{\cos\left(b x + a\right) \sin\left(b x + a\right)} + 32 \, \cos\left(b x + a\right)^{2} + 16 \, \cos\left(b x + a\right) \sin\left(b x + a\right) + 1\right)}{8 \, b}"," ",0,"1/8*(8*sqrt(2)*sqrt(cos(b*x + a)*sin(b*x + a))*sin(b*x + a) + 2*arctan(-(sqrt(2)*sqrt(cos(b*x + a)*sin(b*x + a))*(cos(b*x + a) - sin(b*x + a)) + cos(b*x + a)*sin(b*x + a))/(cos(b*x + a)^2 + 2*cos(b*x + a)*sin(b*x + a) - 1)) - 2*arctan(-(2*sqrt(2)*sqrt(cos(b*x + a)*sin(b*x + a)) - cos(b*x + a) - sin(b*x + a))/(cos(b*x + a) - sin(b*x + a))) + log(-32*cos(b*x + a)^4 + 4*sqrt(2)*(4*cos(b*x + a)^3 - (4*cos(b*x + a)^2 + 1)*sin(b*x + a) - 5*cos(b*x + a))*sqrt(cos(b*x + a)*sin(b*x + a)) + 32*cos(b*x + a)^2 + 16*cos(b*x + a)*sin(b*x + a) + 1))/b","B",0
100,1,242,0,0.488096," ","integrate(csc(b*x+a)*sin(2*b*x+2*a)^(1/2),x, algorithm=""fricas"")","\frac{2 \, \arctan\left(-\frac{\sqrt{2} \sqrt{\cos\left(b x + a\right) \sin\left(b x + a\right)} {\left(\cos\left(b x + a\right) - \sin\left(b x + a\right)\right)} + \cos\left(b x + a\right) \sin\left(b x + a\right)}{\cos\left(b x + a\right)^{2} + 2 \, \cos\left(b x + a\right) \sin\left(b x + a\right) - 1}\right) - 2 \, \arctan\left(-\frac{2 \, \sqrt{2} \sqrt{\cos\left(b x + a\right) \sin\left(b x + a\right)} - \cos\left(b x + a\right) - \sin\left(b x + a\right)}{\cos\left(b x + a\right) - \sin\left(b x + a\right)}\right) - \log\left(-32 \, \cos\left(b x + a\right)^{4} + 4 \, \sqrt{2} {\left(4 \, \cos\left(b x + a\right)^{3} - {\left(4 \, \cos\left(b x + a\right)^{2} + 1\right)} \sin\left(b x + a\right) - 5 \, \cos\left(b x + a\right)\right)} \sqrt{\cos\left(b x + a\right) \sin\left(b x + a\right)} + 32 \, \cos\left(b x + a\right)^{2} + 16 \, \cos\left(b x + a\right) \sin\left(b x + a\right) + 1\right)}{4 \, b}"," ",0,"1/4*(2*arctan(-(sqrt(2)*sqrt(cos(b*x + a)*sin(b*x + a))*(cos(b*x + a) - sin(b*x + a)) + cos(b*x + a)*sin(b*x + a))/(cos(b*x + a)^2 + 2*cos(b*x + a)*sin(b*x + a) - 1)) - 2*arctan(-(2*sqrt(2)*sqrt(cos(b*x + a)*sin(b*x + a)) - cos(b*x + a) - sin(b*x + a))/(cos(b*x + a) - sin(b*x + a))) - log(-32*cos(b*x + a)^4 + 4*sqrt(2)*(4*cos(b*x + a)^3 - (4*cos(b*x + a)^2 + 1)*sin(b*x + a) - 5*cos(b*x + a))*sqrt(cos(b*x + a)*sin(b*x + a)) + 32*cos(b*x + a)^2 + 16*cos(b*x + a)*sin(b*x + a) + 1))/b","B",0
101,1,39,0,0.448145," ","integrate(csc(b*x+a)/sin(2*b*x+2*a)^(1/2),x, algorithm=""fricas"")","-\frac{\sqrt{2} \sqrt{\cos\left(b x + a\right) \sin\left(b x + a\right)} + \sin\left(b x + a\right)}{b \sin\left(b x + a\right)}"," ",0,"-(sqrt(2)*sqrt(cos(b*x + a)*sin(b*x + a)) + sin(b*x + a))/(b*sin(b*x + a))","A",0
102,1,74,0,0.522319," ","integrate(csc(b*x+a)/sin(2*b*x+2*a)^(3/2),x, algorithm=""fricas"")","\frac{4 \, \cos\left(b x + a\right)^{3} + \sqrt{2} {\left(4 \, \cos\left(b x + a\right)^{2} - 3\right)} \sqrt{\cos\left(b x + a\right) \sin\left(b x + a\right)} - 4 \, \cos\left(b x + a\right)}{6 \, {\left(b \cos\left(b x + a\right)^{3} - b \cos\left(b x + a\right)\right)}}"," ",0,"1/6*(4*cos(b*x + a)^3 + sqrt(2)*(4*cos(b*x + a)^2 - 3)*sqrt(cos(b*x + a)*sin(b*x + a)) - 4*cos(b*x + a))/(b*cos(b*x + a)^3 - b*cos(b*x + a))","A",0
103,1,103,0,0.555461," ","integrate(csc(b*x+a)/sin(2*b*x+2*a)^(5/2),x, algorithm=""fricas"")","-\frac{\sqrt{2} {\left(32 \, \cos\left(b x + a\right)^{4} - 40 \, \cos\left(b x + a\right)^{2} + 5\right)} \sqrt{\cos\left(b x + a\right) \sin\left(b x + a\right)} + 32 \, {\left(\cos\left(b x + a\right)^{4} - \cos\left(b x + a\right)^{2}\right)} \sin\left(b x + a\right)}{60 \, {\left(b \cos\left(b x + a\right)^{4} - b \cos\left(b x + a\right)^{2}\right)} \sin\left(b x + a\right)}"," ",0,"-1/60*(sqrt(2)*(32*cos(b*x + a)^4 - 40*cos(b*x + a)^2 + 5)*sqrt(cos(b*x + a)*sin(b*x + a)) + 32*(cos(b*x + a)^4 - cos(b*x + a)^2)*sin(b*x + a))/((b*cos(b*x + a)^4 - b*cos(b*x + a)^2)*sin(b*x + a))","A",0
104,1,118,0,0.460207," ","integrate(csc(b*x+a)/sin(2*b*x+2*a)^(7/2),x, algorithm=""fricas"")","\frac{128 \, \cos\left(b x + a\right)^{7} - 256 \, \cos\left(b x + a\right)^{5} + 128 \, \cos\left(b x + a\right)^{3} + \sqrt{2} {\left(128 \, \cos\left(b x + a\right)^{6} - 224 \, \cos\left(b x + a\right)^{4} + 84 \, \cos\left(b x + a\right)^{2} + 7\right)} \sqrt{\cos\left(b x + a\right) \sin\left(b x + a\right)}}{280 \, {\left(b \cos\left(b x + a\right)^{7} - 2 \, b \cos\left(b x + a\right)^{5} + b \cos\left(b x + a\right)^{3}\right)}}"," ",0,"1/280*(128*cos(b*x + a)^7 - 256*cos(b*x + a)^5 + 128*cos(b*x + a)^3 + sqrt(2)*(128*cos(b*x + a)^6 - 224*cos(b*x + a)^4 + 84*cos(b*x + a)^2 + 7)*sqrt(cos(b*x + a)*sin(b*x + a)))/(b*cos(b*x + a)^7 - 2*b*cos(b*x + a)^5 + b*cos(b*x + a)^3)","A",0
105,0,0,0,0.519306," ","integrate(csc(b*x+a)^2*sin(2*b*x+2*a)^(9/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(\cos\left(2 \, b x + 2 \, a\right)^{4} - 2 \, \cos\left(2 \, b x + 2 \, a\right)^{2} + 1\right)} \csc\left(b x + a\right)^{2} \sqrt{\sin\left(2 \, b x + 2 \, a\right)}, x\right)"," ",0,"integral((cos(2*b*x + 2*a)^4 - 2*cos(2*b*x + 2*a)^2 + 1)*csc(b*x + a)^2*sqrt(sin(2*b*x + 2*a)), x)","F",0
106,0,0,0,0.460236," ","integrate(csc(b*x+a)^2*sin(2*b*x+2*a)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(-{\left(\cos\left(2 \, b x + 2 \, a\right)^{2} - 1\right)} \csc\left(b x + a\right)^{2} \sin\left(2 \, b x + 2 \, a\right)^{\frac{3}{2}}, x\right)"," ",0,"integral(-(cos(2*b*x + 2*a)^2 - 1)*csc(b*x + a)^2*sin(2*b*x + 2*a)^(3/2), x)","F",0
107,0,0,0,0.471584," ","integrate(csc(b*x+a)^2*sin(2*b*x+2*a)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-{\left(\cos\left(2 \, b x + 2 \, a\right)^{2} - 1\right)} \csc\left(b x + a\right)^{2} \sqrt{\sin\left(2 \, b x + 2 \, a\right)}, x\right)"," ",0,"integral(-(cos(2*b*x + 2*a)^2 - 1)*csc(b*x + a)^2*sqrt(sin(2*b*x + 2*a)), x)","F",0
108,0,0,0,0.456680," ","integrate(csc(b*x+a)^2*sin(2*b*x+2*a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\csc\left(b x + a\right)^{2} \sin\left(2 \, b x + 2 \, a\right)^{\frac{3}{2}}, x\right)"," ",0,"integral(csc(b*x + a)^2*sin(2*b*x + 2*a)^(3/2), x)","F",0
109,0,0,0,0.436323," ","integrate(csc(b*x+a)^2*sin(2*b*x+2*a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\csc\left(b x + a\right)^{2} \sqrt{\sin\left(2 \, b x + 2 \, a\right)}, x\right)"," ",0,"integral(csc(b*x + a)^2*sqrt(sin(2*b*x + 2*a)), x)","F",0
110,0,0,0,0.497044," ","integrate(csc(b*x+a)^2/sin(2*b*x+2*a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\csc\left(b x + a\right)^{2}}{\sqrt{\sin\left(2 \, b x + 2 \, a\right)}}, x\right)"," ",0,"integral(csc(b*x + a)^2/sqrt(sin(2*b*x + 2*a)), x)","F",0
111,0,0,0,0.466738," ","integrate(csc(b*x+a)^2/sin(2*b*x+2*a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\csc\left(b x + a\right)^{2} \sqrt{\sin\left(2 \, b x + 2 \, a\right)}}{\cos\left(2 \, b x + 2 \, a\right)^{2} - 1}, x\right)"," ",0,"integral(-csc(b*x + a)^2*sqrt(sin(2*b*x + 2*a))/(cos(2*b*x + 2*a)^2 - 1), x)","F",0
112,0,0,0,0.543754," ","integrate(csc(b*x+a)^2/sin(2*b*x+2*a)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\csc\left(b x + a\right)^{2}}{{\left(\cos\left(2 \, b x + 2 \, a\right)^{2} - 1\right)} \sqrt{\sin\left(2 \, b x + 2 \, a\right)}}, x\right)"," ",0,"integral(-csc(b*x + a)^2/((cos(2*b*x + 2*a)^2 - 1)*sqrt(sin(2*b*x + 2*a))), x)","F",0
113,0,0,0,0.522726," ","integrate(csc(b*x+a)^2/sin(2*b*x+2*a)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\csc\left(b x + a\right)^{2} \sqrt{\sin\left(2 \, b x + 2 \, a\right)}}{\cos\left(2 \, b x + 2 \, a\right)^{4} - 2 \, \cos\left(2 \, b x + 2 \, a\right)^{2} + 1}, x\right)"," ",0,"integral(csc(b*x + a)^2*sqrt(sin(2*b*x + 2*a))/(cos(2*b*x + 2*a)^4 - 2*cos(2*b*x + 2*a)^2 + 1), x)","F",0
114,0,0,0,0.476006," ","integrate(csc(b*x+a)^2/sin(2*b*x+2*a)^(9/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\csc\left(b x + a\right)^{2}}{{\left(\cos\left(2 \, b x + 2 \, a\right)^{4} - 2 \, \cos\left(2 \, b x + 2 \, a\right)^{2} + 1\right)} \sqrt{\sin\left(2 \, b x + 2 \, a\right)}}, x\right)"," ",0,"integral(csc(b*x + a)^2/((cos(2*b*x + 2*a)^4 - 2*cos(2*b*x + 2*a)^2 + 1)*sqrt(sin(2*b*x + 2*a))), x)","F",0
115,1,291,0,0.490129," ","integrate(csc(b*x+a)^3*sin(2*b*x+2*a)^(9/2),x, algorithm=""fricas"")","-\frac{8 \, \sqrt{2} {\left(32 \, \cos\left(b x + a\right)^{5} - 4 \, \cos\left(b x + a\right)^{3} - 7 \, \cos\left(b x + a\right)\right)} \sqrt{\cos\left(b x + a\right) \sin\left(b x + a\right)} - 42 \, \arctan\left(-\frac{\sqrt{2} \sqrt{\cos\left(b x + a\right) \sin\left(b x + a\right)} {\left(\cos\left(b x + a\right) - \sin\left(b x + a\right)\right)} + \cos\left(b x + a\right) \sin\left(b x + a\right)}{\cos\left(b x + a\right)^{2} + 2 \, \cos\left(b x + a\right) \sin\left(b x + a\right) - 1}\right) + 42 \, \arctan\left(-\frac{2 \, \sqrt{2} \sqrt{\cos\left(b x + a\right) \sin\left(b x + a\right)} - \cos\left(b x + a\right) - \sin\left(b x + a\right)}{\cos\left(b x + a\right) - \sin\left(b x + a\right)}\right) + 21 \, \log\left(-32 \, \cos\left(b x + a\right)^{4} + 4 \, \sqrt{2} {\left(4 \, \cos\left(b x + a\right)^{3} - {\left(4 \, \cos\left(b x + a\right)^{2} + 1\right)} \sin\left(b x + a\right) - 5 \, \cos\left(b x + a\right)\right)} \sqrt{\cos\left(b x + a\right) \sin\left(b x + a\right)} + 32 \, \cos\left(b x + a\right)^{2} + 16 \, \cos\left(b x + a\right) \sin\left(b x + a\right) + 1\right)}{96 \, b}"," ",0,"-1/96*(8*sqrt(2)*(32*cos(b*x + a)^5 - 4*cos(b*x + a)^3 - 7*cos(b*x + a))*sqrt(cos(b*x + a)*sin(b*x + a)) - 42*arctan(-(sqrt(2)*sqrt(cos(b*x + a)*sin(b*x + a))*(cos(b*x + a) - sin(b*x + a)) + cos(b*x + a)*sin(b*x + a))/(cos(b*x + a)^2 + 2*cos(b*x + a)*sin(b*x + a) - 1)) + 42*arctan(-(2*sqrt(2)*sqrt(cos(b*x + a)*sin(b*x + a)) - cos(b*x + a) - sin(b*x + a))/(cos(b*x + a) - sin(b*x + a))) + 21*log(-32*cos(b*x + a)^4 + 4*sqrt(2)*(4*cos(b*x + a)^3 - (4*cos(b*x + a)^2 + 1)*sin(b*x + a) - 5*cos(b*x + a))*sqrt(cos(b*x + a)*sin(b*x + a)) + 32*cos(b*x + a)^2 + 16*cos(b*x + a)*sin(b*x + a) + 1))/b","A",0
116,1,280,0,0.677711," ","integrate(csc(b*x+a)^3*sin(2*b*x+2*a)^(7/2),x, algorithm=""fricas"")","\frac{8 \, \sqrt{2} {\left(4 \, \cos\left(b x + a\right)^{2} + 5\right)} \sqrt{\cos\left(b x + a\right) \sin\left(b x + a\right)} \sin\left(b x + a\right) + 10 \, \arctan\left(-\frac{\sqrt{2} \sqrt{\cos\left(b x + a\right) \sin\left(b x + a\right)} {\left(\cos\left(b x + a\right) - \sin\left(b x + a\right)\right)} + \cos\left(b x + a\right) \sin\left(b x + a\right)}{\cos\left(b x + a\right)^{2} + 2 \, \cos\left(b x + a\right) \sin\left(b x + a\right) - 1}\right) - 10 \, \arctan\left(-\frac{2 \, \sqrt{2} \sqrt{\cos\left(b x + a\right) \sin\left(b x + a\right)} - \cos\left(b x + a\right) - \sin\left(b x + a\right)}{\cos\left(b x + a\right) - \sin\left(b x + a\right)}\right) + 5 \, \log\left(-32 \, \cos\left(b x + a\right)^{4} + 4 \, \sqrt{2} {\left(4 \, \cos\left(b x + a\right)^{3} - {\left(4 \, \cos\left(b x + a\right)^{2} + 1\right)} \sin\left(b x + a\right) - 5 \, \cos\left(b x + a\right)\right)} \sqrt{\cos\left(b x + a\right) \sin\left(b x + a\right)} + 32 \, \cos\left(b x + a\right)^{2} + 16 \, \cos\left(b x + a\right) \sin\left(b x + a\right) + 1\right)}{16 \, b}"," ",0,"1/16*(8*sqrt(2)*(4*cos(b*x + a)^2 + 5)*sqrt(cos(b*x + a)*sin(b*x + a))*sin(b*x + a) + 10*arctan(-(sqrt(2)*sqrt(cos(b*x + a)*sin(b*x + a))*(cos(b*x + a) - sin(b*x + a)) + cos(b*x + a)*sin(b*x + a))/(cos(b*x + a)^2 + 2*cos(b*x + a)*sin(b*x + a) - 1)) - 10*arctan(-(2*sqrt(2)*sqrt(cos(b*x + a)*sin(b*x + a)) - cos(b*x + a) - sin(b*x + a))/(cos(b*x + a) - sin(b*x + a))) + 5*log(-32*cos(b*x + a)^4 + 4*sqrt(2)*(4*cos(b*x + a)^3 - (4*cos(b*x + a)^2 + 1)*sin(b*x + a) - 5*cos(b*x + a))*sqrt(cos(b*x + a)*sin(b*x + a)) + 32*cos(b*x + a)^2 + 16*cos(b*x + a)*sin(b*x + a) + 1))/b","A",0
117,1,268,0,0.573611," ","integrate(csc(b*x+a)^3*sin(2*b*x+2*a)^(5/2),x, algorithm=""fricas"")","\frac{8 \, \sqrt{2} \sqrt{\cos\left(b x + a\right) \sin\left(b x + a\right)} \cos\left(b x + a\right) + 6 \, \arctan\left(-\frac{\sqrt{2} \sqrt{\cos\left(b x + a\right) \sin\left(b x + a\right)} {\left(\cos\left(b x + a\right) - \sin\left(b x + a\right)\right)} + \cos\left(b x + a\right) \sin\left(b x + a\right)}{\cos\left(b x + a\right)^{2} + 2 \, \cos\left(b x + a\right) \sin\left(b x + a\right) - 1}\right) - 6 \, \arctan\left(-\frac{2 \, \sqrt{2} \sqrt{\cos\left(b x + a\right) \sin\left(b x + a\right)} - \cos\left(b x + a\right) - \sin\left(b x + a\right)}{\cos\left(b x + a\right) - \sin\left(b x + a\right)}\right) - 3 \, \log\left(-32 \, \cos\left(b x + a\right)^{4} + 4 \, \sqrt{2} {\left(4 \, \cos\left(b x + a\right)^{3} - {\left(4 \, \cos\left(b x + a\right)^{2} + 1\right)} \sin\left(b x + a\right) - 5 \, \cos\left(b x + a\right)\right)} \sqrt{\cos\left(b x + a\right) \sin\left(b x + a\right)} + 32 \, \cos\left(b x + a\right)^{2} + 16 \, \cos\left(b x + a\right) \sin\left(b x + a\right) + 1\right)}{4 \, b}"," ",0,"1/4*(8*sqrt(2)*sqrt(cos(b*x + a)*sin(b*x + a))*cos(b*x + a) + 6*arctan(-(sqrt(2)*sqrt(cos(b*x + a)*sin(b*x + a))*(cos(b*x + a) - sin(b*x + a)) + cos(b*x + a)*sin(b*x + a))/(cos(b*x + a)^2 + 2*cos(b*x + a)*sin(b*x + a) - 1)) - 6*arctan(-(2*sqrt(2)*sqrt(cos(b*x + a)*sin(b*x + a)) - cos(b*x + a) - sin(b*x + a))/(cos(b*x + a) - sin(b*x + a))) - 3*log(-32*cos(b*x + a)^4 + 4*sqrt(2)*(4*cos(b*x + a)^3 - (4*cos(b*x + a)^2 + 1)*sin(b*x + a) - 5*cos(b*x + a))*sqrt(cos(b*x + a)*sin(b*x + a)) + 32*cos(b*x + a)^2 + 16*cos(b*x + a)*sin(b*x + a) + 1))/b","B",0
118,1,295,0,0.540892," ","integrate(csc(b*x+a)^3*sin(2*b*x+2*a)^(3/2),x, algorithm=""fricas"")","-\frac{2 \, \arctan\left(-\frac{\sqrt{2} \sqrt{\cos\left(b x + a\right) \sin\left(b x + a\right)} {\left(\cos\left(b x + a\right) - \sin\left(b x + a\right)\right)} + \cos\left(b x + a\right) \sin\left(b x + a\right)}{\cos\left(b x + a\right)^{2} + 2 \, \cos\left(b x + a\right) \sin\left(b x + a\right) - 1}\right) \sin\left(b x + a\right) - 2 \, \arctan\left(-\frac{2 \, \sqrt{2} \sqrt{\cos\left(b x + a\right) \sin\left(b x + a\right)} - \cos\left(b x + a\right) - \sin\left(b x + a\right)}{\cos\left(b x + a\right) - \sin\left(b x + a\right)}\right) \sin\left(b x + a\right) + \log\left(-32 \, \cos\left(b x + a\right)^{4} + 4 \, \sqrt{2} {\left(4 \, \cos\left(b x + a\right)^{3} - {\left(4 \, \cos\left(b x + a\right)^{2} + 1\right)} \sin\left(b x + a\right) - 5 \, \cos\left(b x + a\right)\right)} \sqrt{\cos\left(b x + a\right) \sin\left(b x + a\right)} + 32 \, \cos\left(b x + a\right)^{2} + 16 \, \cos\left(b x + a\right) \sin\left(b x + a\right) + 1\right) \sin\left(b x + a\right) + 8 \, \sqrt{2} \sqrt{\cos\left(b x + a\right) \sin\left(b x + a\right)} + 8 \, \sin\left(b x + a\right)}{2 \, b \sin\left(b x + a\right)}"," ",0,"-1/2*(2*arctan(-(sqrt(2)*sqrt(cos(b*x + a)*sin(b*x + a))*(cos(b*x + a) - sin(b*x + a)) + cos(b*x + a)*sin(b*x + a))/(cos(b*x + a)^2 + 2*cos(b*x + a)*sin(b*x + a) - 1))*sin(b*x + a) - 2*arctan(-(2*sqrt(2)*sqrt(cos(b*x + a)*sin(b*x + a)) - cos(b*x + a) - sin(b*x + a))/(cos(b*x + a) - sin(b*x + a)))*sin(b*x + a) + log(-32*cos(b*x + a)^4 + 4*sqrt(2)*(4*cos(b*x + a)^3 - (4*cos(b*x + a)^2 + 1)*sin(b*x + a) - 5*cos(b*x + a))*sqrt(cos(b*x + a)*sin(b*x + a)) + 32*cos(b*x + a)^2 + 16*cos(b*x + a)*sin(b*x + a) + 1)*sin(b*x + a) + 8*sqrt(2)*sqrt(cos(b*x + a)*sin(b*x + a)) + 8*sin(b*x + a))/(b*sin(b*x + a))","B",0
119,1,53,0,0.457398," ","integrate(csc(b*x+a)^3*sin(2*b*x+2*a)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(\sqrt{2} \sqrt{\cos\left(b x + a\right) \sin\left(b x + a\right)} \cos\left(b x + a\right) + \cos\left(b x + a\right)^{2} - 1\right)}}{3 \, {\left(b \cos\left(b x + a\right)^{2} - b\right)}}"," ",0,"2/3*(sqrt(2)*sqrt(cos(b*x + a)*sin(b*x + a))*cos(b*x + a) + cos(b*x + a)^2 - 1)/(b*cos(b*x + a)^2 - b)","B",0
120,1,76,0,0.475030," ","integrate(csc(b*x+a)^3/sin(2*b*x+2*a)^(1/2),x, algorithm=""fricas"")","-\frac{\sqrt{2} {\left(4 \, \cos\left(b x + a\right)^{2} - 5\right)} \sqrt{\cos\left(b x + a\right) \sin\left(b x + a\right)} + 4 \, {\left(\cos\left(b x + a\right)^{2} - 1\right)} \sin\left(b x + a\right)}{5 \, {\left(b \cos\left(b x + a\right)^{2} - b\right)} \sin\left(b x + a\right)}"," ",0,"-1/5*(sqrt(2)*(4*cos(b*x + a)^2 - 5)*sqrt(cos(b*x + a)*sin(b*x + a)) + 4*(cos(b*x + a)^2 - 1)*sin(b*x + a))/((b*cos(b*x + a)^2 - b)*sin(b*x + a))","A",0
121,1,104,0,0.512373," ","integrate(csc(b*x+a)^3/sin(2*b*x+2*a)^(3/2),x, algorithm=""fricas"")","\frac{32 \, \cos\left(b x + a\right)^{5} - 64 \, \cos\left(b x + a\right)^{3} + \sqrt{2} {\left(32 \, \cos\left(b x + a\right)^{4} - 56 \, \cos\left(b x + a\right)^{2} + 21\right)} \sqrt{\cos\left(b x + a\right) \sin\left(b x + a\right)} + 32 \, \cos\left(b x + a\right)}{42 \, {\left(b \cos\left(b x + a\right)^{5} - 2 \, b \cos\left(b x + a\right)^{3} + b \cos\left(b x + a\right)\right)}}"," ",0,"1/42*(32*cos(b*x + a)^5 - 64*cos(b*x + a)^3 + sqrt(2)*(32*cos(b*x + a)^4 - 56*cos(b*x + a)^2 + 21)*sqrt(cos(b*x + a)*sin(b*x + a)) + 32*cos(b*x + a))/(b*cos(b*x + a)^5 - 2*b*cos(b*x + a)^3 + b*cos(b*x + a))","A",0
122,1,131,0,0.607301," ","integrate(csc(b*x+a)^3/sin(2*b*x+2*a)^(5/2),x, algorithm=""fricas"")","-\frac{\sqrt{2} {\left(128 \, \cos\left(b x + a\right)^{6} - 288 \, \cos\left(b x + a\right)^{4} + 180 \, \cos\left(b x + a\right)^{2} - 15\right)} \sqrt{\cos\left(b x + a\right) \sin\left(b x + a\right)} + 128 \, {\left(\cos\left(b x + a\right)^{6} - 2 \, \cos\left(b x + a\right)^{4} + \cos\left(b x + a\right)^{2}\right)} \sin\left(b x + a\right)}{180 \, {\left(b \cos\left(b x + a\right)^{6} - 2 \, b \cos\left(b x + a\right)^{4} + b \cos\left(b x + a\right)^{2}\right)} \sin\left(b x + a\right)}"," ",0,"-1/180*(sqrt(2)*(128*cos(b*x + a)^6 - 288*cos(b*x + a)^4 + 180*cos(b*x + a)^2 - 15)*sqrt(cos(b*x + a)*sin(b*x + a)) + 128*(cos(b*x + a)^6 - 2*cos(b*x + a)^4 + cos(b*x + a)^2)*sin(b*x + a))/((b*cos(b*x + a)^6 - 2*b*cos(b*x + a)^4 + b*cos(b*x + a)^2)*sin(b*x + a))","A",0
123,0,0,0,0.508102," ","integrate(sin(b*x+a)^3*sin(2*b*x+2*a)^m,x, algorithm=""fricas"")","{\rm integral}\left(-{\left(\cos\left(b x + a\right)^{2} - 1\right)} \sin\left(2 \, b x + 2 \, a\right)^{m} \sin\left(b x + a\right), x\right)"," ",0,"integral(-(cos(b*x + a)^2 - 1)*sin(2*b*x + 2*a)^m*sin(b*x + a), x)","F",0
124,0,0,0,0.533280," ","integrate(sin(b*x+a)^2*sin(2*b*x+2*a)^m,x, algorithm=""fricas"")","{\rm integral}\left(-{\left(\cos\left(b x + a\right)^{2} - 1\right)} \sin\left(2 \, b x + 2 \, a\right)^{m}, x\right)"," ",0,"integral(-(cos(b*x + a)^2 - 1)*sin(2*b*x + 2*a)^m, x)","F",0
125,0,0,0,0.501705," ","integrate(sin(b*x+a)*sin(2*b*x+2*a)^m,x, algorithm=""fricas"")","{\rm integral}\left(\sin\left(2 \, b x + 2 \, a\right)^{m} \sin\left(b x + a\right), x\right)"," ",0,"integral(sin(2*b*x + 2*a)^m*sin(b*x + a), x)","F",0
126,0,0,0,0.574713," ","integrate(csc(b*x+a)*sin(2*b*x+2*a)^m,x, algorithm=""fricas"")","{\rm integral}\left(\sin\left(2 \, b x + 2 \, a\right)^{m} \csc\left(b x + a\right), x\right)"," ",0,"integral(sin(2*b*x + 2*a)^m*csc(b*x + a), x)","F",0
127,0,0,0,0.506443," ","integrate(csc(b*x+a)^2*sin(2*b*x+2*a)^m,x, algorithm=""fricas"")","{\rm integral}\left(\sin\left(2 \, b x + 2 \, a\right)^{m} \csc\left(b x + a\right)^{2}, x\right)"," ",0,"integral(sin(2*b*x + 2*a)^m*csc(b*x + a)^2, x)","F",0
128,0,0,0,0.475988," ","integrate(csc(b*x+a)^3*sin(2*b*x+2*a)^m,x, algorithm=""fricas"")","{\rm integral}\left(\sin\left(2 \, b x + 2 \, a\right)^{m} \csc\left(b x + a\right)^{3}, x\right)"," ",0,"integral(sin(2*b*x + 2*a)^m*csc(b*x + a)^3, x)","F",0
129,1,46,0,0.467649," ","integrate(cos(b*x+a)*sin(2*b*x+2*a)^7,x, algorithm=""fricas"")","\frac{128 \, {\left(429 \, \cos\left(b x + a\right)^{15} - 1485 \, \cos\left(b x + a\right)^{13} + 1755 \, \cos\left(b x + a\right)^{11} - 715 \, \cos\left(b x + a\right)^{9}\right)}}{6435 \, b}"," ",0,"128/6435*(429*cos(b*x + a)^15 - 1485*cos(b*x + a)^13 + 1755*cos(b*x + a)^11 - 715*cos(b*x + a)^9)/b","A",0
130,1,73,0,0.509688," ","integrate(cos(b*x+a)*sin(2*b*x+2*a)^6,x, algorithm=""fricas"")","-\frac{64 \, {\left(231 \, \cos\left(b x + a\right)^{12} - 567 \, \cos\left(b x + a\right)^{10} + 371 \, \cos\left(b x + a\right)^{8} - 5 \, \cos\left(b x + a\right)^{6} - 6 \, \cos\left(b x + a\right)^{4} - 8 \, \cos\left(b x + a\right)^{2} - 16\right)} \sin\left(b x + a\right)}{3003 \, b}"," ",0,"-64/3003*(231*cos(b*x + a)^12 - 567*cos(b*x + a)^10 + 371*cos(b*x + a)^8 - 5*cos(b*x + a)^6 - 6*cos(b*x + a)^4 - 8*cos(b*x + a)^2 - 16)*sin(b*x + a)/b","A",0
131,1,36,0,0.462959," ","integrate(cos(b*x+a)*sin(2*b*x+2*a)^5,x, algorithm=""fricas"")","-\frac{32 \, {\left(63 \, \cos\left(b x + a\right)^{11} - 154 \, \cos\left(b x + a\right)^{9} + 99 \, \cos\left(b x + a\right)^{7}\right)}}{693 \, b}"," ",0,"-32/693*(63*cos(b*x + a)^11 - 154*cos(b*x + a)^9 + 99*cos(b*x + a)^7)/b","A",0
132,1,53,0,0.410423," ","integrate(cos(b*x+a)*sin(2*b*x+2*a)^4,x, algorithm=""fricas"")","\frac{16 \, {\left(35 \, \cos\left(b x + a\right)^{8} - 50 \, \cos\left(b x + a\right)^{6} + 3 \, \cos\left(b x + a\right)^{4} + 4 \, \cos\left(b x + a\right)^{2} + 8\right)} \sin\left(b x + a\right)}{315 \, b}"," ",0,"16/315*(35*cos(b*x + a)^8 - 50*cos(b*x + a)^6 + 3*cos(b*x + a)^4 + 4*cos(b*x + a)^2 + 8)*sin(b*x + a)/b","A",0
133,1,26,0,0.451897," ","integrate(cos(b*x+a)*sin(2*b*x+2*a)^3,x, algorithm=""fricas"")","\frac{8 \, {\left(5 \, \cos\left(b x + a\right)^{7} - 7 \, \cos\left(b x + a\right)^{5}\right)}}{35 \, b}"," ",0,"8/35*(5*cos(b*x + a)^7 - 7*cos(b*x + a)^5)/b","A",0
134,1,33,0,0.420366," ","integrate(cos(b*x+a)*sin(2*b*x+2*a)^2,x, algorithm=""fricas"")","-\frac{4 \, {\left(3 \, \cos\left(b x + a\right)^{4} - \cos\left(b x + a\right)^{2} - 2\right)} \sin\left(b x + a\right)}{15 \, b}"," ",0,"-4/15*(3*cos(b*x + a)^4 - cos(b*x + a)^2 - 2)*sin(b*x + a)/b","A",0
135,1,13,0,0.480149," ","integrate(cos(b*x+a)*sin(2*b*x+2*a),x, algorithm=""fricas"")","-\frac{2 \, \cos\left(b x + a\right)^{3}}{3 \, b}"," ",0,"-2/3*cos(b*x + a)^3/b","A",0
136,1,30,0,0.596633," ","integrate(cos(b*x+a)/sin(2*b*x+2*a),x, algorithm=""fricas"")","-\frac{\log\left(\frac{1}{2} \, \cos\left(b x + a\right) + \frac{1}{2}\right) - \log\left(-\frac{1}{2} \, \cos\left(b x + a\right) + \frac{1}{2}\right)}{4 \, b}"," ",0,"-1/4*(log(1/2*cos(b*x + a) + 1/2) - log(-1/2*cos(b*x + a) + 1/2))/b","B",0
137,1,50,0,0.473564," ","integrate(cos(b*x+a)/sin(2*b*x+2*a)^2,x, algorithm=""fricas"")","\frac{\log\left(\sin\left(b x + a\right) + 1\right) \sin\left(b x + a\right) - \log\left(-\sin\left(b x + a\right) + 1\right) \sin\left(b x + a\right) - 2}{8 \, b \sin\left(b x + a\right)}"," ",0,"1/8*(log(sin(b*x + a) + 1)*sin(b*x + a) - log(-sin(b*x + a) + 1)*sin(b*x + a) - 2)/(b*sin(b*x + a))","B",0
138,1,96,0,0.468253," ","integrate(cos(b*x+a)/sin(2*b*x+2*a)^3,x, algorithm=""fricas"")","\frac{6 \, \cos\left(b x + a\right)^{2} - 3 \, {\left(\cos\left(b x + a\right)^{3} - \cos\left(b x + a\right)\right)} \log\left(\frac{1}{2} \, \cos\left(b x + a\right) + \frac{1}{2}\right) + 3 \, {\left(\cos\left(b x + a\right)^{3} - \cos\left(b x + a\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(b x + a\right) + \frac{1}{2}\right) - 4}{32 \, {\left(b \cos\left(b x + a\right)^{3} - b \cos\left(b x + a\right)\right)}}"," ",0,"1/32*(6*cos(b*x + a)^2 - 3*(cos(b*x + a)^3 - cos(b*x + a))*log(1/2*cos(b*x + a) + 1/2) + 3*(cos(b*x + a)^3 - cos(b*x + a))*log(-1/2*cos(b*x + a) + 1/2) - 4)/(b*cos(b*x + a)^3 - b*cos(b*x + a))","B",0
139,1,130,0,0.465525," ","integrate(cos(b*x+a)/sin(2*b*x+2*a)^4,x, algorithm=""fricas"")","-\frac{30 \, \cos\left(b x + a\right)^{4} - 15 \, {\left(\cos\left(b x + a\right)^{4} - \cos\left(b x + a\right)^{2}\right)} \log\left(\sin\left(b x + a\right) + 1\right) \sin\left(b x + a\right) + 15 \, {\left(\cos\left(b x + a\right)^{4} - \cos\left(b x + a\right)^{2}\right)} \log\left(-\sin\left(b x + a\right) + 1\right) \sin\left(b x + a\right) - 40 \, \cos\left(b x + a\right)^{2} + 6}{192 \, {\left(b \cos\left(b x + a\right)^{4} - b \cos\left(b x + a\right)^{2}\right)} \sin\left(b x + a\right)}"," ",0,"-1/192*(30*cos(b*x + a)^4 - 15*(cos(b*x + a)^4 - cos(b*x + a)^2)*log(sin(b*x + a) + 1)*sin(b*x + a) + 15*(cos(b*x + a)^4 - cos(b*x + a)^2)*log(-sin(b*x + a) + 1)*sin(b*x + a) - 40*cos(b*x + a)^2 + 6)/((b*cos(b*x + a)^4 - b*cos(b*x + a)^2)*sin(b*x + a))","B",0
140,1,148,0,0.476909," ","integrate(cos(b*x+a)/sin(2*b*x+2*a)^5,x, algorithm=""fricas"")","\frac{210 \, \cos\left(b x + a\right)^{6} - 350 \, \cos\left(b x + a\right)^{4} + 112 \, \cos\left(b x + a\right)^{2} - 105 \, {\left(\cos\left(b x + a\right)^{7} - 2 \, \cos\left(b x + a\right)^{5} + \cos\left(b x + a\right)^{3}\right)} \log\left(\frac{1}{2} \, \cos\left(b x + a\right) + \frac{1}{2}\right) + 105 \, {\left(\cos\left(b x + a\right)^{7} - 2 \, \cos\left(b x + a\right)^{5} + \cos\left(b x + a\right)^{3}\right)} \log\left(-\frac{1}{2} \, \cos\left(b x + a\right) + \frac{1}{2}\right) + 16}{1536 \, {\left(b \cos\left(b x + a\right)^{7} - 2 \, b \cos\left(b x + a\right)^{5} + b \cos\left(b x + a\right)^{3}\right)}}"," ",0,"1/1536*(210*cos(b*x + a)^6 - 350*cos(b*x + a)^4 + 112*cos(b*x + a)^2 - 105*(cos(b*x + a)^7 - 2*cos(b*x + a)^5 + cos(b*x + a)^3)*log(1/2*cos(b*x + a) + 1/2) + 105*(cos(b*x + a)^7 - 2*cos(b*x + a)^5 + cos(b*x + a)^3)*log(-1/2*cos(b*x + a) + 1/2) + 16)/(b*cos(b*x + a)^7 - 2*b*cos(b*x + a)^5 + b*cos(b*x + a)^3)","A",0
141,1,36,0,0.459461," ","integrate(cos(b*x+a)^2*sin(2*b*x+2*a)^5,x, algorithm=""fricas"")","-\frac{4 \, {\left(10 \, \cos\left(b x + a\right)^{12} - 24 \, \cos\left(b x + a\right)^{10} + 15 \, \cos\left(b x + a\right)^{8}\right)}}{15 \, b}"," ",0,"-4/15*(10*cos(b*x + a)^12 - 24*cos(b*x + a)^10 + 15*cos(b*x + a)^8)/b","A",0
142,1,66,0,0.464815," ","integrate(cos(b*x+a)^2*sin(2*b*x+2*a)^4,x, algorithm=""fricas"")","\frac{15 \, b x + {\left(128 \, \cos\left(b x + a\right)^{9} - 176 \, \cos\left(b x + a\right)^{7} + 8 \, \cos\left(b x + a\right)^{5} + 10 \, \cos\left(b x + a\right)^{3} + 15 \, \cos\left(b x + a\right)\right)} \sin\left(b x + a\right)}{80 \, b}"," ",0,"1/80*(15*b*x + (128*cos(b*x + a)^9 - 176*cos(b*x + a)^7 + 8*cos(b*x + a)^5 + 10*cos(b*x + a)^3 + 15*cos(b*x + a))*sin(b*x + a))/b","A",0
143,1,26,0,0.652331," ","integrate(cos(b*x+a)^2*sin(2*b*x+2*a)^3,x, algorithm=""fricas"")","\frac{3 \, \cos\left(b x + a\right)^{8} - 4 \, \cos\left(b x + a\right)^{6}}{3 \, b}"," ",0,"1/3*(3*cos(b*x + a)^8 - 4*cos(b*x + a)^6)/b","A",0
144,1,47,0,0.500691," ","integrate(cos(b*x+a)^2*sin(2*b*x+2*a)^2,x, algorithm=""fricas"")","\frac{3 \, b x - {\left(8 \, \cos\left(b x + a\right)^{5} - 2 \, \cos\left(b x + a\right)^{3} - 3 \, \cos\left(b x + a\right)\right)} \sin\left(b x + a\right)}{12 \, b}"," ",0,"1/12*(3*b*x - (8*cos(b*x + a)^5 - 2*cos(b*x + a)^3 - 3*cos(b*x + a))*sin(b*x + a))/b","A",0
145,1,13,0,0.517785," ","integrate(cos(b*x+a)^2*sin(2*b*x+2*a),x, algorithm=""fricas"")","-\frac{\cos\left(b x + a\right)^{4}}{2 \, b}"," ",0,"-1/2*cos(b*x + a)^4/b","A",0
146,1,14,0,0.518433," ","integrate(cos(b*x+a)^2/sin(2*b*x+2*a),x, algorithm=""fricas"")","\frac{\log\left(\frac{1}{2} \, \sin\left(b x + a\right)\right)}{2 \, b}"," ",0,"1/2*log(1/2*sin(b*x + a))/b","A",0
147,1,19,0,0.515393," ","integrate(cos(b*x+a)^2/sin(2*b*x+2*a)^2,x, algorithm=""fricas"")","-\frac{\cos\left(b x + a\right)}{4 \, b \sin\left(b x + a\right)}"," ",0,"-1/4*cos(b*x + a)/(b*sin(b*x + a))","A",0
148,1,65,0,0.584928," ","integrate(cos(b*x+a)^2/sin(2*b*x+2*a)^3,x, algorithm=""fricas"")","-\frac{{\left(\cos\left(b x + a\right)^{2} - 1\right)} \log\left(\cos\left(b x + a\right)^{2}\right) - {\left(\cos\left(b x + a\right)^{2} - 1\right)} \log\left(-\frac{1}{4} \, \cos\left(b x + a\right)^{2} + \frac{1}{4}\right) - 1}{16 \, {\left(b \cos\left(b x + a\right)^{2} - b\right)}}"," ",0,"-1/16*((cos(b*x + a)^2 - 1)*log(cos(b*x + a)^2) - (cos(b*x + a)^2 - 1)*log(-1/4*cos(b*x + a)^2 + 1/4) - 1)/(b*cos(b*x + a)^2 - b)","B",0
149,1,54,0,0.459011," ","integrate(cos(b*x+a)^2/sin(2*b*x+2*a)^4,x, algorithm=""fricas"")","-\frac{8 \, \cos\left(b x + a\right)^{4} - 12 \, \cos\left(b x + a\right)^{2} + 3}{48 \, {\left(b \cos\left(b x + a\right)^{3} - b \cos\left(b x + a\right)\right)} \sin\left(b x + a\right)}"," ",0,"-1/48*(8*cos(b*x + a)^4 - 12*cos(b*x + a)^2 + 3)/((b*cos(b*x + a)^3 - b*cos(b*x + a))*sin(b*x + a))","A",0
150,1,138,0,0.465616," ","integrate(cos(b*x+a)^2/sin(2*b*x+2*a)^5,x, algorithm=""fricas"")","\frac{6 \, \cos\left(b x + a\right)^{4} - 9 \, \cos\left(b x + a\right)^{2} - 6 \, {\left(\cos\left(b x + a\right)^{6} - 2 \, \cos\left(b x + a\right)^{4} + \cos\left(b x + a\right)^{2}\right)} \log\left(\cos\left(b x + a\right)^{2}\right) + 6 \, {\left(\cos\left(b x + a\right)^{6} - 2 \, \cos\left(b x + a\right)^{4} + \cos\left(b x + a\right)^{2}\right)} \log\left(-\frac{1}{4} \, \cos\left(b x + a\right)^{2} + \frac{1}{4}\right) + 2}{128 \, {\left(b \cos\left(b x + a\right)^{6} - 2 \, b \cos\left(b x + a\right)^{4} + b \cos\left(b x + a\right)^{2}\right)}}"," ",0,"1/128*(6*cos(b*x + a)^4 - 9*cos(b*x + a)^2 - 6*(cos(b*x + a)^6 - 2*cos(b*x + a)^4 + cos(b*x + a)^2)*log(cos(b*x + a)^2) + 6*(cos(b*x + a)^6 - 2*cos(b*x + a)^4 + cos(b*x + a)^2)*log(-1/4*cos(b*x + a)^2 + 1/4) + 2)/(b*cos(b*x + a)^6 - 2*b*cos(b*x + a)^4 + b*cos(b*x + a)^2)","B",0
151,1,36,0,0.445724," ","integrate(cos(b*x+a)^3*sin(2*b*x+2*a)^5,x, algorithm=""fricas"")","-\frac{32 \, {\left(99 \, \cos\left(b x + a\right)^{13} - 234 \, \cos\left(b x + a\right)^{11} + 143 \, \cos\left(b x + a\right)^{9}\right)}}{1287 \, b}"," ",0,"-32/1287*(99*cos(b*x + a)^13 - 234*cos(b*x + a)^11 + 143*cos(b*x + a)^9)/b","A",0
152,1,63,0,0.483882," ","integrate(cos(b*x+a)^3*sin(2*b*x+2*a)^4,x, algorithm=""fricas"")","\frac{16 \, {\left(105 \, \cos\left(b x + a\right)^{10} - 140 \, \cos\left(b x + a\right)^{8} + 5 \, \cos\left(b x + a\right)^{6} + 6 \, \cos\left(b x + a\right)^{4} + 8 \, \cos\left(b x + a\right)^{2} + 16\right)} \sin\left(b x + a\right)}{1155 \, b}"," ",0,"16/1155*(105*cos(b*x + a)^10 - 140*cos(b*x + a)^8 + 5*cos(b*x + a)^6 + 6*cos(b*x + a)^4 + 8*cos(b*x + a)^2 + 16)*sin(b*x + a)/b","A",0
153,1,26,0,0.422979," ","integrate(cos(b*x+a)^3*sin(2*b*x+2*a)^3,x, algorithm=""fricas"")","\frac{8 \, {\left(7 \, \cos\left(b x + a\right)^{9} - 9 \, \cos\left(b x + a\right)^{7}\right)}}{63 \, b}"," ",0,"8/63*(7*cos(b*x + a)^9 - 9*cos(b*x + a)^7)/b","A",0
154,1,43,0,0.414147," ","integrate(cos(b*x+a)^3*sin(2*b*x+2*a)^2,x, algorithm=""fricas"")","-\frac{4 \, {\left(15 \, \cos\left(b x + a\right)^{6} - 3 \, \cos\left(b x + a\right)^{4} - 4 \, \cos\left(b x + a\right)^{2} - 8\right)} \sin\left(b x + a\right)}{105 \, b}"," ",0,"-4/105*(15*cos(b*x + a)^6 - 3*cos(b*x + a)^4 - 4*cos(b*x + a)^2 - 8)*sin(b*x + a)/b","A",0
155,1,13,0,0.454751," ","integrate(cos(b*x+a)^3*sin(2*b*x+2*a),x, algorithm=""fricas"")","-\frac{2 \, \cos\left(b x + a\right)^{5}}{5 \, b}"," ",0,"-2/5*cos(b*x + a)^5/b","A",0
156,1,38,0,0.494543," ","integrate(cos(b*x+a)^3/sin(2*b*x+2*a),x, algorithm=""fricas"")","\frac{2 \, \cos\left(b x + a\right) - \log\left(\frac{1}{2} \, \cos\left(b x + a\right) + \frac{1}{2}\right) + \log\left(-\frac{1}{2} \, \cos\left(b x + a\right) + \frac{1}{2}\right)}{4 \, b}"," ",0,"1/4*(2*cos(b*x + a) - log(1/2*cos(b*x + a) + 1/2) + log(-1/2*cos(b*x + a) + 1/2))/b","A",0
157,1,13,0,0.462600," ","integrate(cos(b*x+a)^3/sin(2*b*x+2*a)^2,x, algorithm=""fricas"")","-\frac{1}{4 \, b \sin\left(b x + a\right)}"," ",0,"-1/4/(b*sin(b*x + a))","A",0
158,1,72,0,0.477541," ","integrate(cos(b*x+a)^3/sin(2*b*x+2*a)^3,x, algorithm=""fricas"")","-\frac{{\left(\cos\left(b x + a\right)^{2} - 1\right)} \log\left(\frac{1}{2} \, \cos\left(b x + a\right) + \frac{1}{2}\right) - {\left(\cos\left(b x + a\right)^{2} - 1\right)} \log\left(-\frac{1}{2} \, \cos\left(b x + a\right) + \frac{1}{2}\right) - 2 \, \cos\left(b x + a\right)}{32 \, {\left(b \cos\left(b x + a\right)^{2} - b\right)}}"," ",0,"-1/32*((cos(b*x + a)^2 - 1)*log(1/2*cos(b*x + a) + 1/2) - (cos(b*x + a)^2 - 1)*log(-1/2*cos(b*x + a) + 1/2) - 2*cos(b*x + a))/(b*cos(b*x + a)^2 - b)","B",0
159,1,94,0,0.446749," ","integrate(cos(b*x+a)^3/sin(2*b*x+2*a)^4,x, algorithm=""fricas"")","\frac{3 \, {\left(\cos\left(b x + a\right)^{2} - 1\right)} \log\left(\sin\left(b x + a\right) + 1\right) \sin\left(b x + a\right) - 3 \, {\left(\cos\left(b x + a\right)^{2} - 1\right)} \log\left(-\sin\left(b x + a\right) + 1\right) \sin\left(b x + a\right) - 6 \, \cos\left(b x + a\right)^{2} + 8}{96 \, {\left(b \cos\left(b x + a\right)^{2} - b\right)} \sin\left(b x + a\right)}"," ",0,"1/96*(3*(cos(b*x + a)^2 - 1)*log(sin(b*x + a) + 1)*sin(b*x + a) - 3*(cos(b*x + a)^2 - 1)*log(-sin(b*x + a) + 1)*sin(b*x + a) - 6*cos(b*x + a)^2 + 8)/((b*cos(b*x + a)^2 - b)*sin(b*x + a))","B",0
160,1,132,0,0.435344," ","integrate(cos(b*x+a)^3/sin(2*b*x+2*a)^5,x, algorithm=""fricas"")","\frac{30 \, \cos\left(b x + a\right)^{4} - 50 \, \cos\left(b x + a\right)^{2} - 15 \, {\left(\cos\left(b x + a\right)^{5} - 2 \, \cos\left(b x + a\right)^{3} + \cos\left(b x + a\right)\right)} \log\left(\frac{1}{2} \, \cos\left(b x + a\right) + \frac{1}{2}\right) + 15 \, {\left(\cos\left(b x + a\right)^{5} - 2 \, \cos\left(b x + a\right)^{3} + \cos\left(b x + a\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(b x + a\right) + \frac{1}{2}\right) + 16}{512 \, {\left(b \cos\left(b x + a\right)^{5} - 2 \, b \cos\left(b x + a\right)^{3} + b \cos\left(b x + a\right)\right)}}"," ",0,"1/512*(30*cos(b*x + a)^4 - 50*cos(b*x + a)^2 - 15*(cos(b*x + a)^5 - 2*cos(b*x + a)^3 + cos(b*x + a))*log(1/2*cos(b*x + a) + 1/2) + 15*(cos(b*x + a)^5 - 2*cos(b*x + a)^3 + cos(b*x + a))*log(-1/2*cos(b*x + a) + 1/2) + 16)/(b*cos(b*x + a)^5 - 2*b*cos(b*x + a)^3 + b*cos(b*x + a))","B",0
161,1,290,0,0.496387," ","integrate(cos(b*x+a)*sin(2*b*x+2*a)^(5/2),x, algorithm=""fricas"")","-\frac{8 \, \sqrt{2} {\left(32 \, \cos\left(b x + a\right)^{4} - 12 \, \cos\left(b x + a\right)^{2} - 15\right)} \sqrt{\cos\left(b x + a\right) \sin\left(b x + a\right)} \sin\left(b x + a\right) - 30 \, \arctan\left(-\frac{\sqrt{2} \sqrt{\cos\left(b x + a\right) \sin\left(b x + a\right)} {\left(\cos\left(b x + a\right) - \sin\left(b x + a\right)\right)} + \cos\left(b x + a\right) \sin\left(b x + a\right)}{\cos\left(b x + a\right)^{2} + 2 \, \cos\left(b x + a\right) \sin\left(b x + a\right) - 1}\right) + 30 \, \arctan\left(-\frac{2 \, \sqrt{2} \sqrt{\cos\left(b x + a\right) \sin\left(b x + a\right)} - \cos\left(b x + a\right) - \sin\left(b x + a\right)}{\cos\left(b x + a\right) - \sin\left(b x + a\right)}\right) - 15 \, \log\left(-32 \, \cos\left(b x + a\right)^{4} + 4 \, \sqrt{2} {\left(4 \, \cos\left(b x + a\right)^{3} - {\left(4 \, \cos\left(b x + a\right)^{2} + 1\right)} \sin\left(b x + a\right) - 5 \, \cos\left(b x + a\right)\right)} \sqrt{\cos\left(b x + a\right) \sin\left(b x + a\right)} + 32 \, \cos\left(b x + a\right)^{2} + 16 \, \cos\left(b x + a\right) \sin\left(b x + a\right) + 1\right)}{384 \, b}"," ",0,"-1/384*(8*sqrt(2)*(32*cos(b*x + a)^4 - 12*cos(b*x + a)^2 - 15)*sqrt(cos(b*x + a)*sin(b*x + a))*sin(b*x + a) - 30*arctan(-(sqrt(2)*sqrt(cos(b*x + a)*sin(b*x + a))*(cos(b*x + a) - sin(b*x + a)) + cos(b*x + a)*sin(b*x + a))/(cos(b*x + a)^2 + 2*cos(b*x + a)*sin(b*x + a) - 1)) + 30*arctan(-(2*sqrt(2)*sqrt(cos(b*x + a)*sin(b*x + a)) - cos(b*x + a) - sin(b*x + a))/(cos(b*x + a) - sin(b*x + a))) - 15*log(-32*cos(b*x + a)^4 + 4*sqrt(2)*(4*cos(b*x + a)^3 - (4*cos(b*x + a)^2 + 1)*sin(b*x + a) - 5*cos(b*x + a))*sqrt(cos(b*x + a)*sin(b*x + a)) + 32*cos(b*x + a)^2 + 16*cos(b*x + a)*sin(b*x + a) + 1))/b","B",0
162,1,281,0,0.497156," ","integrate(cos(b*x+a)*sin(2*b*x+2*a)^(3/2),x, algorithm=""fricas"")","-\frac{8 \, \sqrt{2} {\left(4 \, \cos\left(b x + a\right)^{3} - \cos\left(b x + a\right)\right)} \sqrt{\cos\left(b x + a\right) \sin\left(b x + a\right)} - 6 \, \arctan\left(-\frac{\sqrt{2} \sqrt{\cos\left(b x + a\right) \sin\left(b x + a\right)} {\left(\cos\left(b x + a\right) - \sin\left(b x + a\right)\right)} + \cos\left(b x + a\right) \sin\left(b x + a\right)}{\cos\left(b x + a\right)^{2} + 2 \, \cos\left(b x + a\right) \sin\left(b x + a\right) - 1}\right) + 6 \, \arctan\left(-\frac{2 \, \sqrt{2} \sqrt{\cos\left(b x + a\right) \sin\left(b x + a\right)} - \cos\left(b x + a\right) - \sin\left(b x + a\right)}{\cos\left(b x + a\right) - \sin\left(b x + a\right)}\right) + 3 \, \log\left(-32 \, \cos\left(b x + a\right)^{4} + 4 \, \sqrt{2} {\left(4 \, \cos\left(b x + a\right)^{3} - {\left(4 \, \cos\left(b x + a\right)^{2} + 1\right)} \sin\left(b x + a\right) - 5 \, \cos\left(b x + a\right)\right)} \sqrt{\cos\left(b x + a\right) \sin\left(b x + a\right)} + 32 \, \cos\left(b x + a\right)^{2} + 16 \, \cos\left(b x + a\right) \sin\left(b x + a\right) + 1\right)}{64 \, b}"," ",0,"-1/64*(8*sqrt(2)*(4*cos(b*x + a)^3 - cos(b*x + a))*sqrt(cos(b*x + a)*sin(b*x + a)) - 6*arctan(-(sqrt(2)*sqrt(cos(b*x + a)*sin(b*x + a))*(cos(b*x + a) - sin(b*x + a)) + cos(b*x + a)*sin(b*x + a))/(cos(b*x + a)^2 + 2*cos(b*x + a)*sin(b*x + a) - 1)) + 6*arctan(-(2*sqrt(2)*sqrt(cos(b*x + a)*sin(b*x + a)) - cos(b*x + a) - sin(b*x + a))/(cos(b*x + a) - sin(b*x + a))) + 3*log(-32*cos(b*x + a)^4 + 4*sqrt(2)*(4*cos(b*x + a)^3 - (4*cos(b*x + a)^2 + 1)*sin(b*x + a) - 5*cos(b*x + a))*sqrt(cos(b*x + a)*sin(b*x + a)) + 32*cos(b*x + a)^2 + 16*cos(b*x + a)*sin(b*x + a) + 1))/b","B",0
163,1,266,0,0.532531," ","integrate(cos(b*x+a)*sin(2*b*x+2*a)^(1/2),x, algorithm=""fricas"")","\frac{8 \, \sqrt{2} \sqrt{\cos\left(b x + a\right) \sin\left(b x + a\right)} \sin\left(b x + a\right) + 2 \, \arctan\left(-\frac{\sqrt{2} \sqrt{\cos\left(b x + a\right) \sin\left(b x + a\right)} {\left(\cos\left(b x + a\right) - \sin\left(b x + a\right)\right)} + \cos\left(b x + a\right) \sin\left(b x + a\right)}{\cos\left(b x + a\right)^{2} + 2 \, \cos\left(b x + a\right) \sin\left(b x + a\right) - 1}\right) - 2 \, \arctan\left(-\frac{2 \, \sqrt{2} \sqrt{\cos\left(b x + a\right) \sin\left(b x + a\right)} - \cos\left(b x + a\right) - \sin\left(b x + a\right)}{\cos\left(b x + a\right) - \sin\left(b x + a\right)}\right) + \log\left(-32 \, \cos\left(b x + a\right)^{4} + 4 \, \sqrt{2} {\left(4 \, \cos\left(b x + a\right)^{3} - {\left(4 \, \cos\left(b x + a\right)^{2} + 1\right)} \sin\left(b x + a\right) - 5 \, \cos\left(b x + a\right)\right)} \sqrt{\cos\left(b x + a\right) \sin\left(b x + a\right)} + 32 \, \cos\left(b x + a\right)^{2} + 16 \, \cos\left(b x + a\right) \sin\left(b x + a\right) + 1\right)}{16 \, b}"," ",0,"1/16*(8*sqrt(2)*sqrt(cos(b*x + a)*sin(b*x + a))*sin(b*x + a) + 2*arctan(-(sqrt(2)*sqrt(cos(b*x + a)*sin(b*x + a))*(cos(b*x + a) - sin(b*x + a)) + cos(b*x + a)*sin(b*x + a))/(cos(b*x + a)^2 + 2*cos(b*x + a)*sin(b*x + a) - 1)) - 2*arctan(-(2*sqrt(2)*sqrt(cos(b*x + a)*sin(b*x + a)) - cos(b*x + a) - sin(b*x + a))/(cos(b*x + a) - sin(b*x + a))) + log(-32*cos(b*x + a)^4 + 4*sqrt(2)*(4*cos(b*x + a)^3 - (4*cos(b*x + a)^2 + 1)*sin(b*x + a) - 5*cos(b*x + a))*sqrt(cos(b*x + a)*sin(b*x + a)) + 32*cos(b*x + a)^2 + 16*cos(b*x + a)*sin(b*x + a) + 1))/b","B",0
164,1,242,0,0.440883," ","integrate(cos(b*x+a)/sin(2*b*x+2*a)^(1/2),x, algorithm=""fricas"")","\frac{2 \, \arctan\left(-\frac{\sqrt{2} \sqrt{\cos\left(b x + a\right) \sin\left(b x + a\right)} {\left(\cos\left(b x + a\right) - \sin\left(b x + a\right)\right)} + \cos\left(b x + a\right) \sin\left(b x + a\right)}{\cos\left(b x + a\right)^{2} + 2 \, \cos\left(b x + a\right) \sin\left(b x + a\right) - 1}\right) - 2 \, \arctan\left(-\frac{2 \, \sqrt{2} \sqrt{\cos\left(b x + a\right) \sin\left(b x + a\right)} - \cos\left(b x + a\right) - \sin\left(b x + a\right)}{\cos\left(b x + a\right) - \sin\left(b x + a\right)}\right) - \log\left(-32 \, \cos\left(b x + a\right)^{4} + 4 \, \sqrt{2} {\left(4 \, \cos\left(b x + a\right)^{3} - {\left(4 \, \cos\left(b x + a\right)^{2} + 1\right)} \sin\left(b x + a\right) - 5 \, \cos\left(b x + a\right)\right)} \sqrt{\cos\left(b x + a\right) \sin\left(b x + a\right)} + 32 \, \cos\left(b x + a\right)^{2} + 16 \, \cos\left(b x + a\right) \sin\left(b x + a\right) + 1\right)}{8 \, b}"," ",0,"1/8*(2*arctan(-(sqrt(2)*sqrt(cos(b*x + a)*sin(b*x + a))*(cos(b*x + a) - sin(b*x + a)) + cos(b*x + a)*sin(b*x + a))/(cos(b*x + a)^2 + 2*cos(b*x + a)*sin(b*x + a) - 1)) - 2*arctan(-(2*sqrt(2)*sqrt(cos(b*x + a)*sin(b*x + a)) - cos(b*x + a) - sin(b*x + a))/(cos(b*x + a) - sin(b*x + a))) - log(-32*cos(b*x + a)^4 + 4*sqrt(2)*(4*cos(b*x + a)^3 - (4*cos(b*x + a)^2 + 1)*sin(b*x + a) - 5*cos(b*x + a))*sqrt(cos(b*x + a)*sin(b*x + a)) + 32*cos(b*x + a)^2 + 16*cos(b*x + a)*sin(b*x + a) + 1))/b","B",0
165,1,39,0,0.502595," ","integrate(cos(b*x+a)/sin(2*b*x+2*a)^(3/2),x, algorithm=""fricas"")","-\frac{\sqrt{2} \sqrt{\cos\left(b x + a\right) \sin\left(b x + a\right)} + \sin\left(b x + a\right)}{2 \, b \sin\left(b x + a\right)}"," ",0,"-1/2*(sqrt(2)*sqrt(cos(b*x + a)*sin(b*x + a)) + sin(b*x + a))/(b*sin(b*x + a))","A",0
166,1,74,0,0.591676," ","integrate(cos(b*x+a)/sin(2*b*x+2*a)^(5/2),x, algorithm=""fricas"")","\frac{4 \, \cos\left(b x + a\right)^{3} + \sqrt{2} {\left(4 \, \cos\left(b x + a\right)^{2} - 3\right)} \sqrt{\cos\left(b x + a\right) \sin\left(b x + a\right)} - 4 \, \cos\left(b x + a\right)}{12 \, {\left(b \cos\left(b x + a\right)^{3} - b \cos\left(b x + a\right)\right)}}"," ",0,"1/12*(4*cos(b*x + a)^3 + sqrt(2)*(4*cos(b*x + a)^2 - 3)*sqrt(cos(b*x + a)*sin(b*x + a)) - 4*cos(b*x + a))/(b*cos(b*x + a)^3 - b*cos(b*x + a))","A",0
167,1,103,0,0.457741," ","integrate(cos(b*x+a)/sin(2*b*x+2*a)^(7/2),x, algorithm=""fricas"")","-\frac{\sqrt{2} {\left(32 \, \cos\left(b x + a\right)^{4} - 40 \, \cos\left(b x + a\right)^{2} + 5\right)} \sqrt{\cos\left(b x + a\right) \sin\left(b x + a\right)} + 32 \, {\left(\cos\left(b x + a\right)^{4} - \cos\left(b x + a\right)^{2}\right)} \sin\left(b x + a\right)}{120 \, {\left(b \cos\left(b x + a\right)^{4} - b \cos\left(b x + a\right)^{2}\right)} \sin\left(b x + a\right)}"," ",0,"-1/120*(sqrt(2)*(32*cos(b*x + a)^4 - 40*cos(b*x + a)^2 + 5)*sqrt(cos(b*x + a)*sin(b*x + a)) + 32*(cos(b*x + a)^4 - cos(b*x + a)^2)*sin(b*x + a))/((b*cos(b*x + a)^4 - b*cos(b*x + a)^2)*sin(b*x + a))","A",0
168,1,118,0,0.432847," ","integrate(cos(b*x+a)/sin(2*b*x+2*a)^(9/2),x, algorithm=""fricas"")","\frac{128 \, \cos\left(b x + a\right)^{7} - 256 \, \cos\left(b x + a\right)^{5} + 128 \, \cos\left(b x + a\right)^{3} + \sqrt{2} {\left(128 \, \cos\left(b x + a\right)^{6} - 224 \, \cos\left(b x + a\right)^{4} + 84 \, \cos\left(b x + a\right)^{2} + 7\right)} \sqrt{\cos\left(b x + a\right) \sin\left(b x + a\right)}}{560 \, {\left(b \cos\left(b x + a\right)^{7} - 2 \, b \cos\left(b x + a\right)^{5} + b \cos\left(b x + a\right)^{3}\right)}}"," ",0,"1/560*(128*cos(b*x + a)^7 - 256*cos(b*x + a)^5 + 128*cos(b*x + a)^3 + sqrt(2)*(128*cos(b*x + a)^6 - 224*cos(b*x + a)^4 + 84*cos(b*x + a)^2 + 7)*sqrt(cos(b*x + a)*sin(b*x + a)))/(b*cos(b*x + a)^7 - 2*b*cos(b*x + a)^5 + b*cos(b*x + a)^3)","A",0
169,0,0,0,0.555458," ","integrate(cos(b*x+a)^2*sin(2*b*x+2*a)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(-{\left(\cos\left(2 \, b x + 2 \, a\right)^{2} \cos\left(b x + a\right)^{2} - \cos\left(b x + a\right)^{2}\right)} \sin\left(2 \, b x + 2 \, a\right)^{\frac{3}{2}}, x\right)"," ",0,"integral(-(cos(2*b*x + 2*a)^2*cos(b*x + a)^2 - cos(b*x + a)^2)*sin(2*b*x + 2*a)^(3/2), x)","F",0
170,0,0,0,0.551194," ","integrate(cos(b*x+a)^2*sin(2*b*x+2*a)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-{\left(\cos\left(2 \, b x + 2 \, a\right)^{2} \cos\left(b x + a\right)^{2} - \cos\left(b x + a\right)^{2}\right)} \sqrt{\sin\left(2 \, b x + 2 \, a\right)}, x\right)"," ",0,"integral(-(cos(2*b*x + 2*a)^2*cos(b*x + a)^2 - cos(b*x + a)^2)*sqrt(sin(2*b*x + 2*a)), x)","F",0
171,0,0,0,0.483545," ","integrate(cos(b*x+a)^2*sin(2*b*x+2*a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\cos\left(b x + a\right)^{2} \sin\left(2 \, b x + 2 \, a\right)^{\frac{3}{2}}, x\right)"," ",0,"integral(cos(b*x + a)^2*sin(2*b*x + 2*a)^(3/2), x)","F",0
172,0,0,0,0.542009," ","integrate(cos(b*x+a)^2*sin(2*b*x+2*a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\cos\left(b x + a\right)^{2} \sqrt{\sin\left(2 \, b x + 2 \, a\right)}, x\right)"," ",0,"integral(cos(b*x + a)^2*sqrt(sin(2*b*x + 2*a)), x)","F",0
173,0,0,0,0.599855," ","integrate(cos(b*x+a)^2/sin(2*b*x+2*a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\cos\left(b x + a\right)^{2}}{\sqrt{\sin\left(2 \, b x + 2 \, a\right)}}, x\right)"," ",0,"integral(cos(b*x + a)^2/sqrt(sin(2*b*x + 2*a)), x)","F",0
174,0,0,0,0.615829," ","integrate(cos(b*x+a)^2/sin(2*b*x+2*a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\cos\left(b x + a\right)^{2} \sqrt{\sin\left(2 \, b x + 2 \, a\right)}}{\cos\left(2 \, b x + 2 \, a\right)^{2} - 1}, x\right)"," ",0,"integral(-cos(b*x + a)^2*sqrt(sin(2*b*x + 2*a))/(cos(2*b*x + 2*a)^2 - 1), x)","F",0
175,0,0,0,0.520164," ","integrate(cos(b*x+a)^2/sin(2*b*x+2*a)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\cos\left(b x + a\right)^{2}}{{\left(\cos\left(2 \, b x + 2 \, a\right)^{2} - 1\right)} \sqrt{\sin\left(2 \, b x + 2 \, a\right)}}, x\right)"," ",0,"integral(-cos(b*x + a)^2/((cos(2*b*x + 2*a)^2 - 1)*sqrt(sin(2*b*x + 2*a))), x)","F",0
176,0,0,0,0.553695," ","integrate(cos(b*x+a)^2/sin(2*b*x+2*a)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\cos\left(b x + a\right)^{2} \sqrt{\sin\left(2 \, b x + 2 \, a\right)}}{\cos\left(2 \, b x + 2 \, a\right)^{4} - 2 \, \cos\left(2 \, b x + 2 \, a\right)^{2} + 1}, x\right)"," ",0,"integral(cos(b*x + a)^2*sqrt(sin(2*b*x + 2*a))/(cos(2*b*x + 2*a)^4 - 2*cos(2*b*x + 2*a)^2 + 1), x)","F",0
177,1,291,0,0.458982," ","integrate(cos(b*x+a)^3*sin(2*b*x+2*a)^(3/2),x, algorithm=""fricas"")","-\frac{8 \, \sqrt{2} {\left(32 \, \cos\left(b x + a\right)^{5} - 4 \, \cos\left(b x + a\right)^{3} - 7 \, \cos\left(b x + a\right)\right)} \sqrt{\cos\left(b x + a\right) \sin\left(b x + a\right)} - 42 \, \arctan\left(-\frac{\sqrt{2} \sqrt{\cos\left(b x + a\right) \sin\left(b x + a\right)} {\left(\cos\left(b x + a\right) - \sin\left(b x + a\right)\right)} + \cos\left(b x + a\right) \sin\left(b x + a\right)}{\cos\left(b x + a\right)^{2} + 2 \, \cos\left(b x + a\right) \sin\left(b x + a\right) - 1}\right) + 42 \, \arctan\left(-\frac{2 \, \sqrt{2} \sqrt{\cos\left(b x + a\right) \sin\left(b x + a\right)} - \cos\left(b x + a\right) - \sin\left(b x + a\right)}{\cos\left(b x + a\right) - \sin\left(b x + a\right)}\right) + 21 \, \log\left(-32 \, \cos\left(b x + a\right)^{4} + 4 \, \sqrt{2} {\left(4 \, \cos\left(b x + a\right)^{3} - {\left(4 \, \cos\left(b x + a\right)^{2} + 1\right)} \sin\left(b x + a\right) - 5 \, \cos\left(b x + a\right)\right)} \sqrt{\cos\left(b x + a\right) \sin\left(b x + a\right)} + 32 \, \cos\left(b x + a\right)^{2} + 16 \, \cos\left(b x + a\right) \sin\left(b x + a\right) + 1\right)}{768 \, b}"," ",0,"-1/768*(8*sqrt(2)*(32*cos(b*x + a)^5 - 4*cos(b*x + a)^3 - 7*cos(b*x + a))*sqrt(cos(b*x + a)*sin(b*x + a)) - 42*arctan(-(sqrt(2)*sqrt(cos(b*x + a)*sin(b*x + a))*(cos(b*x + a) - sin(b*x + a)) + cos(b*x + a)*sin(b*x + a))/(cos(b*x + a)^2 + 2*cos(b*x + a)*sin(b*x + a) - 1)) + 42*arctan(-(2*sqrt(2)*sqrt(cos(b*x + a)*sin(b*x + a)) - cos(b*x + a) - sin(b*x + a))/(cos(b*x + a) - sin(b*x + a))) + 21*log(-32*cos(b*x + a)^4 + 4*sqrt(2)*(4*cos(b*x + a)^3 - (4*cos(b*x + a)^2 + 1)*sin(b*x + a) - 5*cos(b*x + a))*sqrt(cos(b*x + a)*sin(b*x + a)) + 32*cos(b*x + a)^2 + 16*cos(b*x + a)*sin(b*x + a) + 1))/b","B",0
178,1,280,0,0.564691," ","integrate(cos(b*x+a)^3*sin(2*b*x+2*a)^(1/2),x, algorithm=""fricas"")","\frac{8 \, \sqrt{2} {\left(4 \, \cos\left(b x + a\right)^{2} + 5\right)} \sqrt{\cos\left(b x + a\right) \sin\left(b x + a\right)} \sin\left(b x + a\right) + 10 \, \arctan\left(-\frac{\sqrt{2} \sqrt{\cos\left(b x + a\right) \sin\left(b x + a\right)} {\left(\cos\left(b x + a\right) - \sin\left(b x + a\right)\right)} + \cos\left(b x + a\right) \sin\left(b x + a\right)}{\cos\left(b x + a\right)^{2} + 2 \, \cos\left(b x + a\right) \sin\left(b x + a\right) - 1}\right) - 10 \, \arctan\left(-\frac{2 \, \sqrt{2} \sqrt{\cos\left(b x + a\right) \sin\left(b x + a\right)} - \cos\left(b x + a\right) - \sin\left(b x + a\right)}{\cos\left(b x + a\right) - \sin\left(b x + a\right)}\right) + 5 \, \log\left(-32 \, \cos\left(b x + a\right)^{4} + 4 \, \sqrt{2} {\left(4 \, \cos\left(b x + a\right)^{3} - {\left(4 \, \cos\left(b x + a\right)^{2} + 1\right)} \sin\left(b x + a\right) - 5 \, \cos\left(b x + a\right)\right)} \sqrt{\cos\left(b x + a\right) \sin\left(b x + a\right)} + 32 \, \cos\left(b x + a\right)^{2} + 16 \, \cos\left(b x + a\right) \sin\left(b x + a\right) + 1\right)}{128 \, b}"," ",0,"1/128*(8*sqrt(2)*(4*cos(b*x + a)^2 + 5)*sqrt(cos(b*x + a)*sin(b*x + a))*sin(b*x + a) + 10*arctan(-(sqrt(2)*sqrt(cos(b*x + a)*sin(b*x + a))*(cos(b*x + a) - sin(b*x + a)) + cos(b*x + a)*sin(b*x + a))/(cos(b*x + a)^2 + 2*cos(b*x + a)*sin(b*x + a) - 1)) - 10*arctan(-(2*sqrt(2)*sqrt(cos(b*x + a)*sin(b*x + a)) - cos(b*x + a) - sin(b*x + a))/(cos(b*x + a) - sin(b*x + a))) + 5*log(-32*cos(b*x + a)^4 + 4*sqrt(2)*(4*cos(b*x + a)^3 - (4*cos(b*x + a)^2 + 1)*sin(b*x + a) - 5*cos(b*x + a))*sqrt(cos(b*x + a)*sin(b*x + a)) + 32*cos(b*x + a)^2 + 16*cos(b*x + a)*sin(b*x + a) + 1))/b","B",0
179,1,268,0,0.725312," ","integrate(cos(b*x+a)^3/sin(2*b*x+2*a)^(1/2),x, algorithm=""fricas"")","\frac{8 \, \sqrt{2} \sqrt{\cos\left(b x + a\right) \sin\left(b x + a\right)} \cos\left(b x + a\right) + 6 \, \arctan\left(-\frac{\sqrt{2} \sqrt{\cos\left(b x + a\right) \sin\left(b x + a\right)} {\left(\cos\left(b x + a\right) - \sin\left(b x + a\right)\right)} + \cos\left(b x + a\right) \sin\left(b x + a\right)}{\cos\left(b x + a\right)^{2} + 2 \, \cos\left(b x + a\right) \sin\left(b x + a\right) - 1}\right) - 6 \, \arctan\left(-\frac{2 \, \sqrt{2} \sqrt{\cos\left(b x + a\right) \sin\left(b x + a\right)} - \cos\left(b x + a\right) - \sin\left(b x + a\right)}{\cos\left(b x + a\right) - \sin\left(b x + a\right)}\right) - 3 \, \log\left(-32 \, \cos\left(b x + a\right)^{4} + 4 \, \sqrt{2} {\left(4 \, \cos\left(b x + a\right)^{3} - {\left(4 \, \cos\left(b x + a\right)^{2} + 1\right)} \sin\left(b x + a\right) - 5 \, \cos\left(b x + a\right)\right)} \sqrt{\cos\left(b x + a\right) \sin\left(b x + a\right)} + 32 \, \cos\left(b x + a\right)^{2} + 16 \, \cos\left(b x + a\right) \sin\left(b x + a\right) + 1\right)}{32 \, b}"," ",0,"1/32*(8*sqrt(2)*sqrt(cos(b*x + a)*sin(b*x + a))*cos(b*x + a) + 6*arctan(-(sqrt(2)*sqrt(cos(b*x + a)*sin(b*x + a))*(cos(b*x + a) - sin(b*x + a)) + cos(b*x + a)*sin(b*x + a))/(cos(b*x + a)^2 + 2*cos(b*x + a)*sin(b*x + a) - 1)) - 6*arctan(-(2*sqrt(2)*sqrt(cos(b*x + a)*sin(b*x + a)) - cos(b*x + a) - sin(b*x + a))/(cos(b*x + a) - sin(b*x + a))) - 3*log(-32*cos(b*x + a)^4 + 4*sqrt(2)*(4*cos(b*x + a)^3 - (4*cos(b*x + a)^2 + 1)*sin(b*x + a) - 5*cos(b*x + a))*sqrt(cos(b*x + a)*sin(b*x + a)) + 32*cos(b*x + a)^2 + 16*cos(b*x + a)*sin(b*x + a) + 1))/b","B",0
180,1,295,0,0.542372," ","integrate(cos(b*x+a)^3/sin(2*b*x+2*a)^(3/2),x, algorithm=""fricas"")","-\frac{2 \, \arctan\left(-\frac{\sqrt{2} \sqrt{\cos\left(b x + a\right) \sin\left(b x + a\right)} {\left(\cos\left(b x + a\right) - \sin\left(b x + a\right)\right)} + \cos\left(b x + a\right) \sin\left(b x + a\right)}{\cos\left(b x + a\right)^{2} + 2 \, \cos\left(b x + a\right) \sin\left(b x + a\right) - 1}\right) \sin\left(b x + a\right) - 2 \, \arctan\left(-\frac{2 \, \sqrt{2} \sqrt{\cos\left(b x + a\right) \sin\left(b x + a\right)} - \cos\left(b x + a\right) - \sin\left(b x + a\right)}{\cos\left(b x + a\right) - \sin\left(b x + a\right)}\right) \sin\left(b x + a\right) + \log\left(-32 \, \cos\left(b x + a\right)^{4} + 4 \, \sqrt{2} {\left(4 \, \cos\left(b x + a\right)^{3} - {\left(4 \, \cos\left(b x + a\right)^{2} + 1\right)} \sin\left(b x + a\right) - 5 \, \cos\left(b x + a\right)\right)} \sqrt{\cos\left(b x + a\right) \sin\left(b x + a\right)} + 32 \, \cos\left(b x + a\right)^{2} + 16 \, \cos\left(b x + a\right) \sin\left(b x + a\right) + 1\right) \sin\left(b x + a\right) + 8 \, \sqrt{2} \sqrt{\cos\left(b x + a\right) \sin\left(b x + a\right)} + 8 \, \sin\left(b x + a\right)}{16 \, b \sin\left(b x + a\right)}"," ",0,"-1/16*(2*arctan(-(sqrt(2)*sqrt(cos(b*x + a)*sin(b*x + a))*(cos(b*x + a) - sin(b*x + a)) + cos(b*x + a)*sin(b*x + a))/(cos(b*x + a)^2 + 2*cos(b*x + a)*sin(b*x + a) - 1))*sin(b*x + a) - 2*arctan(-(2*sqrt(2)*sqrt(cos(b*x + a)*sin(b*x + a)) - cos(b*x + a) - sin(b*x + a))/(cos(b*x + a) - sin(b*x + a)))*sin(b*x + a) + log(-32*cos(b*x + a)^4 + 4*sqrt(2)*(4*cos(b*x + a)^3 - (4*cos(b*x + a)^2 + 1)*sin(b*x + a) - 5*cos(b*x + a))*sqrt(cos(b*x + a)*sin(b*x + a)) + 32*cos(b*x + a)^2 + 16*cos(b*x + a)*sin(b*x + a) + 1)*sin(b*x + a) + 8*sqrt(2)*sqrt(cos(b*x + a)*sin(b*x + a)) + 8*sin(b*x + a))/(b*sin(b*x + a))","B",0
181,1,53,0,0.644519," ","integrate(cos(b*x+a)^3/sin(2*b*x+2*a)^(5/2),x, algorithm=""fricas"")","\frac{\sqrt{2} \sqrt{\cos\left(b x + a\right) \sin\left(b x + a\right)} \cos\left(b x + a\right) + \cos\left(b x + a\right)^{2} - 1}{12 \, {\left(b \cos\left(b x + a\right)^{2} - b\right)}}"," ",0,"1/12*(sqrt(2)*sqrt(cos(b*x + a)*sin(b*x + a))*cos(b*x + a) + cos(b*x + a)^2 - 1)/(b*cos(b*x + a)^2 - b)","B",0
182,1,76,0,0.469935," ","integrate(cos(b*x+a)^3/sin(2*b*x+2*a)^(7/2),x, algorithm=""fricas"")","-\frac{\sqrt{2} {\left(4 \, \cos\left(b x + a\right)^{2} - 5\right)} \sqrt{\cos\left(b x + a\right) \sin\left(b x + a\right)} + 4 \, {\left(\cos\left(b x + a\right)^{2} - 1\right)} \sin\left(b x + a\right)}{40 \, {\left(b \cos\left(b x + a\right)^{2} - b\right)} \sin\left(b x + a\right)}"," ",0,"-1/40*(sqrt(2)*(4*cos(b*x + a)^2 - 5)*sqrt(cos(b*x + a)*sin(b*x + a)) + 4*(cos(b*x + a)^2 - 1)*sin(b*x + a))/((b*cos(b*x + a)^2 - b)*sin(b*x + a))","A",0
183,1,104,0,0.518480," ","integrate(cos(b*x+a)^3/sin(2*b*x+2*a)^(9/2),x, algorithm=""fricas"")","\frac{32 \, \cos\left(b x + a\right)^{5} - 64 \, \cos\left(b x + a\right)^{3} + \sqrt{2} {\left(32 \, \cos\left(b x + a\right)^{4} - 56 \, \cos\left(b x + a\right)^{2} + 21\right)} \sqrt{\cos\left(b x + a\right) \sin\left(b x + a\right)} + 32 \, \cos\left(b x + a\right)}{336 \, {\left(b \cos\left(b x + a\right)^{5} - 2 \, b \cos\left(b x + a\right)^{3} + b \cos\left(b x + a\right)\right)}}"," ",0,"1/336*(32*cos(b*x + a)^5 - 64*cos(b*x + a)^3 + sqrt(2)*(32*cos(b*x + a)^4 - 56*cos(b*x + a)^2 + 21)*sqrt(cos(b*x + a)*sin(b*x + a)) + 32*cos(b*x + a))/(b*cos(b*x + a)^5 - 2*b*cos(b*x + a)^3 + b*cos(b*x + a))","A",0
184,1,131,0,0.481822," ","integrate(cos(b*x+a)^3/sin(2*b*x+2*a)^(11/2),x, algorithm=""fricas"")","-\frac{\sqrt{2} {\left(128 \, \cos\left(b x + a\right)^{6} - 288 \, \cos\left(b x + a\right)^{4} + 180 \, \cos\left(b x + a\right)^{2} - 15\right)} \sqrt{\cos\left(b x + a\right) \sin\left(b x + a\right)} + 128 \, {\left(\cos\left(b x + a\right)^{6} - 2 \, \cos\left(b x + a\right)^{4} + \cos\left(b x + a\right)^{2}\right)} \sin\left(b x + a\right)}{1440 \, {\left(b \cos\left(b x + a\right)^{6} - 2 \, b \cos\left(b x + a\right)^{4} + b \cos\left(b x + a\right)^{2}\right)} \sin\left(b x + a\right)}"," ",0,"-1/1440*(sqrt(2)*(128*cos(b*x + a)^6 - 288*cos(b*x + a)^4 + 180*cos(b*x + a)^2 - 15)*sqrt(cos(b*x + a)*sin(b*x + a)) + 128*(cos(b*x + a)^6 - 2*cos(b*x + a)^4 + cos(b*x + a)^2)*sin(b*x + a))/((b*cos(b*x + a)^6 - 2*b*cos(b*x + a)^4 + b*cos(b*x + a)^2)*sin(b*x + a))","A",0
185,1,137,0,0.487046," ","integrate(cos(x)/sin(2*x)^(1/2),x, algorithm=""fricas"")","\frac{1}{4} \, \arctan\left(-\frac{\sqrt{2} \sqrt{\cos\left(x\right) \sin\left(x\right)} {\left(\cos\left(x\right) - \sin\left(x\right)\right)} + \cos\left(x\right) \sin\left(x\right)}{\cos\left(x\right)^{2} + 2 \, \cos\left(x\right) \sin\left(x\right) - 1}\right) - \frac{1}{4} \, \arctan\left(-\frac{2 \, \sqrt{2} \sqrt{\cos\left(x\right) \sin\left(x\right)} - \cos\left(x\right) - \sin\left(x\right)}{\cos\left(x\right) - \sin\left(x\right)}\right) - \frac{1}{8} \, \log\left(-32 \, \cos\left(x\right)^{4} + 4 \, \sqrt{2} {\left(4 \, \cos\left(x\right)^{3} - {\left(4 \, \cos\left(x\right)^{2} + 1\right)} \sin\left(x\right) - 5 \, \cos\left(x\right)\right)} \sqrt{\cos\left(x\right) \sin\left(x\right)} + 32 \, \cos\left(x\right)^{2} + 16 \, \cos\left(x\right) \sin\left(x\right) + 1\right)"," ",0,"1/4*arctan(-(sqrt(2)*sqrt(cos(x)*sin(x))*(cos(x) - sin(x)) + cos(x)*sin(x))/(cos(x)^2 + 2*cos(x)*sin(x) - 1)) - 1/4*arctan(-(2*sqrt(2)*sqrt(cos(x)*sin(x)) - cos(x) - sin(x))/(cos(x) - sin(x))) - 1/8*log(-32*cos(x)^4 + 4*sqrt(2)*(4*cos(x)^3 - (4*cos(x)^2 + 1)*sin(x) - 5*cos(x))*sqrt(cos(x)*sin(x)) + 32*cos(x)^2 + 16*cos(x)*sin(x) + 1)","B",0
186,1,137,0,0.452616," ","integrate(csc(x)*sin(2*x)^(1/2),x, algorithm=""fricas"")","\frac{1}{2} \, \arctan\left(-\frac{\sqrt{2} \sqrt{\cos\left(x\right) \sin\left(x\right)} {\left(\cos\left(x\right) - \sin\left(x\right)\right)} + \cos\left(x\right) \sin\left(x\right)}{\cos\left(x\right)^{2} + 2 \, \cos\left(x\right) \sin\left(x\right) - 1}\right) - \frac{1}{2} \, \arctan\left(-\frac{2 \, \sqrt{2} \sqrt{\cos\left(x\right) \sin\left(x\right)} - \cos\left(x\right) - \sin\left(x\right)}{\cos\left(x\right) - \sin\left(x\right)}\right) - \frac{1}{4} \, \log\left(-32 \, \cos\left(x\right)^{4} + 4 \, \sqrt{2} {\left(4 \, \cos\left(x\right)^{3} - {\left(4 \, \cos\left(x\right)^{2} + 1\right)} \sin\left(x\right) - 5 \, \cos\left(x\right)\right)} \sqrt{\cos\left(x\right) \sin\left(x\right)} + 32 \, \cos\left(x\right)^{2} + 16 \, \cos\left(x\right) \sin\left(x\right) + 1\right)"," ",0,"1/2*arctan(-(sqrt(2)*sqrt(cos(x)*sin(x))*(cos(x) - sin(x)) + cos(x)*sin(x))/(cos(x)^2 + 2*cos(x)*sin(x) - 1)) - 1/2*arctan(-(2*sqrt(2)*sqrt(cos(x)*sin(x)) - cos(x) - sin(x))/(cos(x) - sin(x))) - 1/4*log(-32*cos(x)^4 + 4*sqrt(2)*(4*cos(x)^3 - (4*cos(x)^2 + 1)*sin(x) - 5*cos(x))*sqrt(cos(x)*sin(x)) + 32*cos(x)^2 + 16*cos(x)*sin(x) + 1)","B",0
187,0,0,0,0.432423," ","integrate(cos(b*x+a)^3*sin(2*b*x+2*a)^m,x, algorithm=""fricas"")","{\rm integral}\left(\sin\left(2 \, b x + 2 \, a\right)^{m} \cos\left(b x + a\right)^{3}, x\right)"," ",0,"integral(sin(2*b*x + 2*a)^m*cos(b*x + a)^3, x)","F",0
188,0,0,0,0.431011," ","integrate(cos(b*x+a)^2*sin(2*b*x+2*a)^m,x, algorithm=""fricas"")","{\rm integral}\left(\sin\left(2 \, b x + 2 \, a\right)^{m} \cos\left(b x + a\right)^{2}, x\right)"," ",0,"integral(sin(2*b*x + 2*a)^m*cos(b*x + a)^2, x)","F",0
189,0,0,0,0.476846," ","integrate(cos(b*x+a)*sin(2*b*x+2*a)^m,x, algorithm=""fricas"")","{\rm integral}\left(\sin\left(2 \, b x + 2 \, a\right)^{m} \cos\left(b x + a\right), x\right)"," ",0,"integral(sin(2*b*x + 2*a)^m*cos(b*x + a), x)","F",0
190,1,36,0,0.530718," ","integrate(cos(b*x+a)^2*sin(b*x+a)^3*sin(2*b*x+2*a)^2,x, algorithm=""fricas"")","-\frac{4 \, {\left(35 \, \cos\left(b x + a\right)^{9} - 90 \, \cos\left(b x + a\right)^{7} + 63 \, \cos\left(b x + a\right)^{5}\right)}}{315 \, b}"," ",0,"-4/315*(35*cos(b*x + a)^9 - 90*cos(b*x + a)^7 + 63*cos(b*x + a)^5)/b","A",0
191,0,0,0,0.449951," ","integrate(sin(b*x+a)*sin(d*x+c)^n,x, algorithm=""fricas"")","{\rm integral}\left(\sin\left(d x + c\right)^{n} \sin\left(b x + a\right), x\right)"," ",0,"integral(sin(d*x + c)^n*sin(b*x + a), x)","F",0
192,1,122,0,0.572388," ","integrate(sin(b*x+a)*sin(d*x+c)^3,x, algorithm=""fricas"")","-\frac{3 \, {\left({\left(b^{2} d - d^{3}\right)} \cos\left(d x + c\right)^{3} - {\left(b^{2} d - 3 \, d^{3}\right)} \cos\left(d x + c\right)\right)} \sin\left(b x + a\right) - {\left({\left(b^{3} - b d^{2}\right)} \cos\left(b x + a\right) \cos\left(d x + c\right)^{2} - {\left(b^{3} - 7 \, b d^{2}\right)} \cos\left(b x + a\right)\right)} \sin\left(d x + c\right)}{b^{4} - 10 \, b^{2} d^{2} + 9 \, d^{4}}"," ",0,"-(3*((b^2*d - d^3)*cos(d*x + c)^3 - (b^2*d - 3*d^3)*cos(d*x + c))*sin(b*x + a) - ((b^3 - b*d^2)*cos(b*x + a)*cos(d*x + c)^2 - (b^3 - 7*b*d^2)*cos(b*x + a))*sin(d*x + c))/(b^4 - 10*b^2*d^2 + 9*d^4)","A",0
193,1,71,0,0.426090," ","integrate(sin(b*x+a)*sin(d*x+c)^2,x, algorithm=""fricas"")","\frac{b^{2} \cos\left(b x + a\right) \cos\left(d x + c\right)^{2} + 2 \, b d \cos\left(d x + c\right) \sin\left(b x + a\right) \sin\left(d x + c\right) - {\left(b^{2} - 2 \, d^{2}\right)} \cos\left(b x + a\right)}{b^{3} - 4 \, b d^{2}}"," ",0,"(b^2*cos(b*x + a)*cos(d*x + c)^2 + 2*b*d*cos(d*x + c)*sin(b*x + a)*sin(d*x + c) - (b^2 - 2*d^2)*cos(b*x + a))/(b^3 - 4*b*d^2)","A",0
194,1,42,0,0.427619," ","integrate(sin(b*x+a)*sin(d*x+c),x, algorithm=""fricas"")","\frac{d \cos\left(d x + c\right) \sin\left(b x + a\right) - b \cos\left(b x + a\right) \sin\left(d x + c\right)}{b^{2} - d^{2}}"," ",0,"(d*cos(d*x + c)*sin(b*x + a) - b*cos(b*x + a)*sin(d*x + c))/(b^2 - d^2)","A",0
195,1,31,0,0.423676," ","integrate(csc(b*x+c)*sin(b*x+a),x, algorithm=""fricas"")","\frac{b x \cos\left(-a + c\right) - \log\left(\frac{1}{2} \, \sin\left(b x + c\right)\right) \sin\left(-a + c\right)}{b}"," ",0,"(b*x*cos(-a + c) - log(1/2*sin(b*x + c))*sin(-a + c))/b","A",0
196,1,71,0,0.508986," ","integrate(csc(b*x+c)^2*sin(b*x+a),x, algorithm=""fricas"")","-\frac{\cos\left(-a + c\right) \log\left(\frac{1}{2} \, \cos\left(b x + c\right) + \frac{1}{2}\right) \sin\left(b x + c\right) - \cos\left(-a + c\right) \log\left(-\frac{1}{2} \, \cos\left(b x + c\right) + \frac{1}{2}\right) \sin\left(b x + c\right) - 2 \, \sin\left(-a + c\right)}{2 \, b \sin\left(b x + c\right)}"," ",0,"-1/2*(cos(-a + c)*log(1/2*cos(b*x + c) + 1/2)*sin(b*x + c) - cos(-a + c)*log(-1/2*cos(b*x + c) + 1/2)*sin(b*x + c) - 2*sin(-a + c))/(b*sin(b*x + c))","A",0
197,1,47,0,0.433170," ","integrate(csc(b*x+c)^3*sin(b*x+a),x, algorithm=""fricas"")","\frac{2 \, \cos\left(b x + c\right) \cos\left(-a + c\right) \sin\left(b x + c\right) - \sin\left(-a + c\right)}{2 \, {\left(b \cos\left(b x + c\right)^{2} - b\right)}}"," ",0,"1/2*(2*cos(b*x + c)*cos(-a + c)*sin(b*x + c) - sin(-a + c))/(b*cos(b*x + c)^2 - b)","A",0
198,1,141,0,0.651154," ","integrate(csc(b*x+c)^4*sin(b*x+a),x, algorithm=""fricas"")","\frac{6 \, \cos\left(b x + c\right) \cos\left(-a + c\right) \sin\left(b x + c\right) - 3 \, {\left(\cos\left(b x + c\right)^{2} \cos\left(-a + c\right) - \cos\left(-a + c\right)\right)} \log\left(\frac{1}{2} \, \cos\left(b x + c\right) + \frac{1}{2}\right) \sin\left(b x + c\right) + 3 \, {\left(\cos\left(b x + c\right)^{2} \cos\left(-a + c\right) - \cos\left(-a + c\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(b x + c\right) + \frac{1}{2}\right) \sin\left(b x + c\right) - 4 \, \sin\left(-a + c\right)}{12 \, {\left(b \cos\left(b x + c\right)^{2} - b\right)} \sin\left(b x + c\right)}"," ",0,"1/12*(6*cos(b*x + c)*cos(-a + c)*sin(b*x + c) - 3*(cos(b*x + c)^2*cos(-a + c) - cos(-a + c))*log(1/2*cos(b*x + c) + 1/2)*sin(b*x + c) + 3*(cos(b*x + c)^2*cos(-a + c) - cos(-a + c))*log(-1/2*cos(b*x + c) + 1/2)*sin(b*x + c) - 4*sin(-a + c))/((b*cos(b*x + c)^2 - b)*sin(b*x + c))","B",0
199,1,75,0,0.573030," ","integrate(csc(b*x+c)^5*sin(b*x+a),x, algorithm=""fricas"")","\frac{4 \, {\left(2 \, \cos\left(b x + c\right)^{3} \cos\left(-a + c\right) - 3 \, \cos\left(b x + c\right) \cos\left(-a + c\right)\right)} \sin\left(b x + c\right) + 3 \, \sin\left(-a + c\right)}{12 \, {\left(b \cos\left(b x + c\right)^{4} - 2 \, b \cos\left(b x + c\right)^{2} + b\right)}}"," ",0,"1/12*(4*(2*cos(b*x + c)^3*cos(-a + c) - 3*cos(b*x + c)*cos(-a + c))*sin(b*x + c) + 3*sin(-a + c))/(b*cos(b*x + c)^4 - 2*b*cos(b*x + c)^2 + b)","A",0
200,1,197,0,0.492212," ","integrate(csc(b*x+c)^6*sin(b*x+a),x, algorithm=""fricas"")","-\frac{15 \, {\left(\cos\left(b x + c\right)^{4} \cos\left(-a + c\right) - 2 \, \cos\left(b x + c\right)^{2} \cos\left(-a + c\right) + \cos\left(-a + c\right)\right)} \log\left(\frac{1}{2} \, \cos\left(b x + c\right) + \frac{1}{2}\right) \sin\left(b x + c\right) - 15 \, {\left(\cos\left(b x + c\right)^{4} \cos\left(-a + c\right) - 2 \, \cos\left(b x + c\right)^{2} \cos\left(-a + c\right) + \cos\left(-a + c\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(b x + c\right) + \frac{1}{2}\right) \sin\left(b x + c\right) - 10 \, {\left(3 \, \cos\left(b x + c\right)^{3} \cos\left(-a + c\right) - 5 \, \cos\left(b x + c\right) \cos\left(-a + c\right)\right)} \sin\left(b x + c\right) - 16 \, \sin\left(-a + c\right)}{80 \, {\left(b \cos\left(b x + c\right)^{4} - 2 \, b \cos\left(b x + c\right)^{2} + b\right)} \sin\left(b x + c\right)}"," ",0,"-1/80*(15*(cos(b*x + c)^4*cos(-a + c) - 2*cos(b*x + c)^2*cos(-a + c) + cos(-a + c))*log(1/2*cos(b*x + c) + 1/2)*sin(b*x + c) - 15*(cos(b*x + c)^4*cos(-a + c) - 2*cos(b*x + c)^2*cos(-a + c) + cos(-a + c))*log(-1/2*cos(b*x + c) + 1/2)*sin(b*x + c) - 10*(3*cos(b*x + c)^3*cos(-a + c) - 5*cos(b*x + c)*cos(-a + c))*sin(b*x + c) - 16*sin(-a + c))/((b*cos(b*x + c)^4 - 2*b*cos(b*x + c)^2 + b)*sin(b*x + c))","B",0
201,0,0,0,0.431940," ","integrate(sin(b*x+a)^2*sin(d*x+c)^n,x, algorithm=""fricas"")","{\rm integral}\left(-{\left(\cos\left(b x + a\right)^{2} - 1\right)} \sin\left(d x + c\right)^{n}, x\right)"," ",0,"integral(-(cos(b*x + a)^2 - 1)*sin(d*x + c)^n, x)","F",0
202,1,69,0,0.464640," ","integrate(sin(b*x+a)^2*sin(d*x+c),x, algorithm=""fricas"")","-\frac{2 \, b d \cos\left(b x + a\right) \sin\left(b x + a\right) \sin\left(d x + c\right) + {\left(d^{2} \cos\left(b x + a\right)^{2} + 2 \, b^{2} - d^{2}\right)} \cos\left(d x + c\right)}{4 \, b^{2} d - d^{3}}"," ",0,"-(2*b*d*cos(b*x + a)*sin(b*x + a)*sin(d*x + c) + (d^2*cos(b*x + a)^2 + 2*b^2 - d^2)*cos(d*x + c))/(4*b^2*d - d^3)","A",0
203,1,118,0,0.467850," ","integrate(sin(b*x+a)^2*sin(d*x+c)^2,x, algorithm=""fricas"")","-\frac{{\left(2 \, b d^{2} \cos\left(b x + a\right)^{2} + b^{3} - 2 \, b d^{2}\right)} \cos\left(d x + c\right) \sin\left(d x + c\right) - {\left(b^{3} d - b d^{3}\right)} x - {\left(2 \, b^{2} d \cos\left(b x + a\right) \cos\left(d x + c\right)^{2} - {\left(2 \, b^{2} d - d^{3}\right)} \cos\left(b x + a\right)\right)} \sin\left(b x + a\right)}{4 \, {\left(b^{3} d - b d^{3}\right)}}"," ",0,"-1/4*((2*b*d^2*cos(b*x + a)^2 + b^3 - 2*b*d^2)*cos(d*x + c)*sin(d*x + c) - (b^3*d - b*d^3)*x - (2*b^2*d*cos(b*x + a)*cos(d*x + c)^2 - (2*b^2*d - d^3)*cos(b*x + a))*sin(b*x + a))/(b^3*d - b*d^3)","A",0
204,1,192,0,0.611882," ","integrate(sin(b*x+a)^2*sin(d*x+c)^3,x, algorithm=""fricas"")","\frac{{\left(8 \, b^{4} - 38 \, b^{2} d^{2} + 9 \, d^{4} + 9 \, {\left(4 \, b^{2} d^{2} - d^{4}\right)} \cos\left(b x + a\right)^{2}\right)} \cos\left(d x + c\right)^{3} + 6 \, {\left({\left(4 \, b^{3} d - b d^{3}\right)} \cos\left(b x + a\right) \cos\left(d x + c\right)^{2} - {\left(4 \, b^{3} d - 7 \, b d^{3}\right)} \cos\left(b x + a\right)\right)} \sin\left(b x + a\right) \sin\left(d x + c\right) - 3 \, {\left(8 \, b^{4} - 26 \, b^{2} d^{2} + 9 \, d^{4} + 3 \, {\left(4 \, b^{2} d^{2} - 3 \, d^{4}\right)} \cos\left(b x + a\right)^{2}\right)} \cos\left(d x + c\right)}{3 \, {\left(16 \, b^{4} d - 40 \, b^{2} d^{3} + 9 \, d^{5}\right)}}"," ",0,"1/3*((8*b^4 - 38*b^2*d^2 + 9*d^4 + 9*(4*b^2*d^2 - d^4)*cos(b*x + a)^2)*cos(d*x + c)^3 + 6*((4*b^3*d - b*d^3)*cos(b*x + a)*cos(d*x + c)^2 - (4*b^3*d - 7*b*d^3)*cos(b*x + a))*sin(b*x + a)*sin(d*x + c) - 3*(8*b^4 - 26*b^2*d^2 + 9*d^4 + 3*(4*b^2*d^2 - 3*d^4)*cos(b*x + a)^2)*cos(d*x + c))/(16*b^4*d - 40*b^2*d^3 + 9*d^5)","A",0
205,0,0,0,0.658297," ","integrate(sin(b*x+a)^3*sin(d*x+c)^n,x, algorithm=""fricas"")","{\rm integral}\left(-{\left(\cos\left(b x + a\right)^{2} - 1\right)} \sin\left(d x + c\right)^{n} \sin\left(b x + a\right), x\right)"," ",0,"integral(-(cos(b*x + a)^2 - 1)*sin(d*x + c)^n*sin(b*x + a), x)","F",0
206,1,115,0,0.564728," ","integrate(sin(b*x+a)^3*sin(d*x+c),x, algorithm=""fricas"")","\frac{{\left(7 \, b^{2} d - d^{3} - {\left(b^{2} d - d^{3}\right)} \cos\left(b x + a\right)^{2}\right)} \cos\left(d x + c\right) \sin\left(b x + a\right) + 3 \, {\left({\left(b^{3} - b d^{2}\right)} \cos\left(b x + a\right)^{3} - {\left(3 \, b^{3} - b d^{2}\right)} \cos\left(b x + a\right)\right)} \sin\left(d x + c\right)}{9 \, b^{4} - 10 \, b^{2} d^{2} + d^{4}}"," ",0,"((7*b^2*d - d^3 - (b^2*d - d^3)*cos(b*x + a)^2)*cos(d*x + c)*sin(b*x + a) + 3*((b^3 - b*d^2)*cos(b*x + a)^3 - (3*b^3 - b*d^2)*cos(b*x + a))*sin(d*x + c))/(9*b^4 - 10*b^2*d^2 + d^4)","A",0
207,1,189,0,0.472685," ","integrate(sin(b*x+a)^3*sin(d*x+c)^2,x, algorithm=""fricas"")","\frac{{\left(9 \, b^{4} - 38 \, b^{2} d^{2} + 8 \, d^{4}\right)} \cos\left(b x + a\right)^{3} + 6 \, {\left(7 \, b^{3} d - 4 \, b d^{3} - {\left(b^{3} d - 4 \, b d^{3}\right)} \cos\left(b x + a\right)^{2}\right)} \cos\left(d x + c\right) \sin\left(b x + a\right) \sin\left(d x + c\right) - 9 \, {\left({\left(b^{4} - 4 \, b^{2} d^{2}\right)} \cos\left(b x + a\right)^{3} - {\left(3 \, b^{4} - 4 \, b^{2} d^{2}\right)} \cos\left(b x + a\right)\right)} \cos\left(d x + c\right)^{2} - 3 \, {\left(9 \, b^{4} - 26 \, b^{2} d^{2} + 8 \, d^{4}\right)} \cos\left(b x + a\right)}{3 \, {\left(9 \, b^{5} - 40 \, b^{3} d^{2} + 16 \, b d^{4}\right)}}"," ",0,"1/3*((9*b^4 - 38*b^2*d^2 + 8*d^4)*cos(b*x + a)^3 + 6*(7*b^3*d - 4*b*d^3 - (b^3*d - 4*b*d^3)*cos(b*x + a)^2)*cos(d*x + c)*sin(b*x + a)*sin(d*x + c) - 9*((b^4 - 4*b^2*d^2)*cos(b*x + a)^3 - (3*b^4 - 4*b^2*d^2)*cos(b*x + a))*cos(d*x + c)^2 - 3*(9*b^4 - 26*b^2*d^2 + 8*d^4)*cos(b*x + a))/(9*b^5 - 40*b^3*d^2 + 16*b*d^4)","A",0
208,1,291,0,0.590334," ","integrate(sin(b*x+a)^3*sin(d*x+c)^3,x, algorithm=""fricas"")","-\frac{{\left({\left(63 \, b^{4} d - 88 \, b^{2} d^{3} + 9 \, d^{5} - {\left(9 \, b^{4} d - 82 \, b^{2} d^{3} + 9 \, d^{5}\right)} \cos\left(b x + a\right)^{2}\right)} \cos\left(d x + c\right)^{3} - 3 \, {\left(21 \, b^{4} d - 70 \, b^{2} d^{3} + 9 \, d^{5} - {\left(3 \, b^{4} d - 28 \, b^{2} d^{3} + 9 \, d^{5}\right)} \cos\left(b x + a\right)^{2}\right)} \cos\left(d x + c\right)\right)} \sin\left(b x + a\right) - {\left({\left(9 \, b^{5} - 88 \, b^{3} d^{2} + 63 \, b d^{4}\right)} \cos\left(b x + a\right)^{3} - {\left({\left(9 \, b^{5} - 82 \, b^{3} d^{2} + 9 \, b d^{4}\right)} \cos\left(b x + a\right)^{3} - 3 \, {\left(9 \, b^{5} - 28 \, b^{3} d^{2} + 3 \, b d^{4}\right)} \cos\left(b x + a\right)\right)} \cos\left(d x + c\right)^{2} - 3 \, {\left(9 \, b^{5} - 70 \, b^{3} d^{2} + 21 \, b d^{4}\right)} \cos\left(b x + a\right)\right)} \sin\left(d x + c\right)}{3 \, {\left(9 \, b^{6} - 91 \, b^{4} d^{2} + 91 \, b^{2} d^{4} - 9 \, d^{6}\right)}}"," ",0,"-1/3*(((63*b^4*d - 88*b^2*d^3 + 9*d^5 - (9*b^4*d - 82*b^2*d^3 + 9*d^5)*cos(b*x + a)^2)*cos(d*x + c)^3 - 3*(21*b^4*d - 70*b^2*d^3 + 9*d^5 - (3*b^4*d - 28*b^2*d^3 + 9*d^5)*cos(b*x + a)^2)*cos(d*x + c))*sin(b*x + a) - ((9*b^5 - 88*b^3*d^2 + 63*b*d^4)*cos(b*x + a)^3 - ((9*b^5 - 82*b^3*d^2 + 9*b*d^4)*cos(b*x + a)^3 - 3*(9*b^5 - 28*b^3*d^2 + 3*b*d^4)*cos(b*x + a))*cos(d*x + c)^2 - 3*(9*b^5 - 70*b^3*d^2 + 21*b*d^4)*cos(b*x + a))*sin(d*x + c))/(9*b^6 - 91*b^4*d^2 + 91*b^2*d^4 - 9*d^6)","A",0
209,0,0,0,0.579461," ","integrate(cos(d*x+c)^n*sin(b*x+a),x, algorithm=""fricas"")","{\rm integral}\left(\cos\left(d x + c\right)^{n} \sin\left(b x + a\right), x\right)"," ",0,"integral(cos(d*x + c)^n*sin(b*x + a), x)","F",0
210,1,106,0,0.416305," ","integrate(cos(d*x+c)^3*sin(b*x+a),x, algorithm=""fricas"")","\frac{6 \, b d^{2} \cos\left(b x + a\right) \cos\left(d x + c\right) - {\left(b^{3} - b d^{2}\right)} \cos\left(b x + a\right) \cos\left(d x + c\right)^{3} + 3 \, {\left(2 \, d^{3} - {\left(b^{2} d - d^{3}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(b x + a\right) \sin\left(d x + c\right)}{b^{4} - 10 \, b^{2} d^{2} + 9 \, d^{4}}"," ",0,"(6*b*d^2*cos(b*x + a)*cos(d*x + c) - (b^3 - b*d^2)*cos(b*x + a)*cos(d*x + c)^3 + 3*(2*d^3 - (b^2*d - d^3)*cos(d*x + c)^2)*sin(b*x + a)*sin(d*x + c))/(b^4 - 10*b^2*d^2 + 9*d^4)","A",0
211,1,66,0,0.502311," ","integrate(cos(d*x+c)^2*sin(b*x+a),x, algorithm=""fricas"")","-\frac{b^{2} \cos\left(b x + a\right) \cos\left(d x + c\right)^{2} + 2 \, b d \cos\left(d x + c\right) \sin\left(b x + a\right) \sin\left(d x + c\right) - 2 \, d^{2} \cos\left(b x + a\right)}{b^{3} - 4 \, b d^{2}}"," ",0,"-(b^2*cos(b*x + a)*cos(d*x + c)^2 + 2*b*d*cos(d*x + c)*sin(b*x + a)*sin(d*x + c) - 2*d^2*cos(b*x + a))/(b^3 - 4*b*d^2)","A",0
212,1,42,0,0.462744," ","integrate(cos(d*x+c)*sin(b*x+a),x, algorithm=""fricas"")","-\frac{b \cos\left(b x + a\right) \cos\left(d x + c\right) + d \sin\left(b x + a\right) \sin\left(d x + c\right)}{b^{2} - d^{2}}"," ",0,"-(b*cos(b*x + a)*cos(d*x + c) + d*sin(b*x + a)*sin(d*x + c))/(b^2 - d^2)","A",0
213,1,31,0,0.457184," ","integrate(sec(b*x+c)*sin(b*x+a),x, algorithm=""fricas"")","-\frac{b x \sin\left(-a + c\right) + \cos\left(-a + c\right) \log\left(-\cos\left(b x + c\right)\right)}{b}"," ",0,"-(b*x*sin(-a + c) + cos(-a + c)*log(-cos(b*x + c)))/b","A",0
214,1,69,0,0.480359," ","integrate(sec(b*x+c)^2*sin(b*x+a),x, algorithm=""fricas"")","-\frac{\cos\left(b x + c\right) \log\left(\sin\left(b x + c\right) + 1\right) \sin\left(-a + c\right) - \cos\left(b x + c\right) \log\left(-\sin\left(b x + c\right) + 1\right) \sin\left(-a + c\right) - 2 \, \cos\left(-a + c\right)}{2 \, b \cos\left(b x + c\right)}"," ",0,"-1/2*(cos(b*x + c)*log(sin(b*x + c) + 1)*sin(-a + c) - cos(b*x + c)*log(-sin(b*x + c) + 1)*sin(-a + c) - 2*cos(-a + c))/(b*cos(b*x + c))","B",0
215,1,42,0,0.536434," ","integrate(sec(b*x+c)^3*sin(b*x+a),x, algorithm=""fricas"")","-\frac{2 \, \cos\left(b x + c\right) \sin\left(b x + c\right) \sin\left(-a + c\right) - \cos\left(-a + c\right)}{2 \, b \cos\left(b x + c\right)^{2}}"," ",0,"-1/2*(2*cos(b*x + c)*sin(b*x + c)*sin(-a + c) - cos(-a + c))/(b*cos(b*x + c)^2)","A",0
216,1,94,0,0.526458," ","integrate(sec(b*x+c)^4*sin(b*x+a),x, algorithm=""fricas"")","-\frac{3 \, \cos\left(b x + c\right)^{3} \log\left(\sin\left(b x + c\right) + 1\right) \sin\left(-a + c\right) - 3 \, \cos\left(b x + c\right)^{3} \log\left(-\sin\left(b x + c\right) + 1\right) \sin\left(-a + c\right) + 6 \, \cos\left(b x + c\right) \sin\left(b x + c\right) \sin\left(-a + c\right) - 4 \, \cos\left(-a + c\right)}{12 \, b \cos\left(b x + c\right)^{3}}"," ",0,"-1/12*(3*cos(b*x + c)^3*log(sin(b*x + c) + 1)*sin(-a + c) - 3*cos(b*x + c)^3*log(-sin(b*x + c) + 1)*sin(-a + c) + 6*cos(b*x + c)*sin(b*x + c)*sin(-a + c) - 4*cos(-a + c))/(b*cos(b*x + c)^3)","A",0
217,1,53,0,0.483006," ","integrate(sec(b*x+c)^5*sin(b*x+a),x, algorithm=""fricas"")","-\frac{4 \, {\left(2 \, \cos\left(b x + c\right)^{3} + \cos\left(b x + c\right)\right)} \sin\left(b x + c\right) \sin\left(-a + c\right) - 3 \, \cos\left(-a + c\right)}{12 \, b \cos\left(b x + c\right)^{4}}"," ",0,"-1/12*(4*(2*cos(b*x + c)^3 + cos(b*x + c))*sin(b*x + c)*sin(-a + c) - 3*cos(-a + c))/(b*cos(b*x + c)^4)","A",0
218,1,107,0,0.496041," ","integrate(sec(b*x+c)^6*sin(b*x+a),x, algorithm=""fricas"")","-\frac{15 \, \cos\left(b x + c\right)^{5} \log\left(\sin\left(b x + c\right) + 1\right) \sin\left(-a + c\right) - 15 \, \cos\left(b x + c\right)^{5} \log\left(-\sin\left(b x + c\right) + 1\right) \sin\left(-a + c\right) + 10 \, {\left(3 \, \cos\left(b x + c\right)^{3} + 2 \, \cos\left(b x + c\right)\right)} \sin\left(b x + c\right) \sin\left(-a + c\right) - 16 \, \cos\left(-a + c\right)}{80 \, b \cos\left(b x + c\right)^{5}}"," ",0,"-1/80*(15*cos(b*x + c)^5*log(sin(b*x + c) + 1)*sin(-a + c) - 15*cos(b*x + c)^5*log(-sin(b*x + c) + 1)*sin(-a + c) + 10*(3*cos(b*x + c)^3 + 2*cos(b*x + c))*sin(b*x + c)*sin(-a + c) - 16*cos(-a + c))/(b*cos(b*x + c)^5)","A",0
219,0,0,0,0.489011," ","integrate(cos(d*x+c)^n*sin(b*x+a)^2,x, algorithm=""fricas"")","{\rm integral}\left(-{\left(\cos\left(b x + a\right)^{2} - 1\right)} \cos\left(d x + c\right)^{n}, x\right)"," ",0,"integral(-(cos(b*x + a)^2 - 1)*cos(d*x + c)^n, x)","F",0
220,1,70,0,0.454576," ","integrate(cos(d*x+c)*sin(b*x+a)^2,x, algorithm=""fricas"")","-\frac{2 \, b d \cos\left(b x + a\right) \cos\left(d x + c\right) \sin\left(b x + a\right) - {\left(d^{2} \cos\left(b x + a\right)^{2} + 2 \, b^{2} - d^{2}\right)} \sin\left(d x + c\right)}{4 \, b^{2} d - d^{3}}"," ",0,"-(2*b*d*cos(b*x + a)*cos(d*x + c)*sin(b*x + a) - (d^2*cos(b*x + a)^2 + 2*b^2 - d^2)*sin(d*x + c))/(4*b^2*d - d^3)","A",0
221,1,108,0,0.435293," ","integrate(cos(d*x+c)^2*sin(b*x+a)^2,x, algorithm=""fricas"")","\frac{{\left(2 \, b d^{2} \cos\left(b x + a\right)^{2} + b^{3} - 2 \, b d^{2}\right)} \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(b^{3} d - b d^{3}\right)} x - {\left(2 \, b^{2} d \cos\left(b x + a\right) \cos\left(d x + c\right)^{2} - d^{3} \cos\left(b x + a\right)\right)} \sin\left(b x + a\right)}{4 \, {\left(b^{3} d - b d^{3}\right)}}"," ",0,"1/4*((2*b*d^2*cos(b*x + a)^2 + b^3 - 2*b*d^2)*cos(d*x + c)*sin(d*x + c) + (b^3*d - b*d^3)*x - (2*b^2*d*cos(b*x + a)*cos(d*x + c)^2 - d^3*cos(b*x + a))*sin(b*x + a))/(b^3*d - b*d^3)","A",0
222,1,174,0,0.431713," ","integrate(cos(d*x+c)^3*sin(b*x+a)^2,x, algorithm=""fricas"")","\frac{6 \, {\left(6 \, b d^{3} \cos\left(b x + a\right) \cos\left(d x + c\right) - {\left(4 \, b^{3} d - b d^{3}\right)} \cos\left(b x + a\right) \cos\left(d x + c\right)^{3}\right)} \sin\left(b x + a\right) - {\left(18 \, d^{4} \cos\left(b x + a\right)^{2} - 16 \, b^{4} + 40 \, b^{2} d^{2} - 18 \, d^{4} - {\left(8 \, b^{4} - 38 \, b^{2} d^{2} + 9 \, d^{4} + 9 \, {\left(4 \, b^{2} d^{2} - d^{4}\right)} \cos\left(b x + a\right)^{2}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{3 \, {\left(16 \, b^{4} d - 40 \, b^{2} d^{3} + 9 \, d^{5}\right)}}"," ",0,"1/3*(6*(6*b*d^3*cos(b*x + a)*cos(d*x + c) - (4*b^3*d - b*d^3)*cos(b*x + a)*cos(d*x + c)^3)*sin(b*x + a) - (18*d^4*cos(b*x + a)^2 - 16*b^4 + 40*b^2*d^2 - 18*d^4 - (8*b^4 - 38*b^2*d^2 + 9*d^4 + 9*(4*b^2*d^2 - d^4)*cos(b*x + a)^2)*cos(d*x + c)^2)*sin(d*x + c))/(16*b^4*d - 40*b^2*d^3 + 9*d^5)","A",0
223,0,0,0,0.540214," ","integrate(cos(d*x+c)^n*sin(b*x+a)^3,x, algorithm=""fricas"")","{\rm integral}\left(-{\left(\cos\left(b x + a\right)^{2} - 1\right)} \cos\left(d x + c\right)^{n} \sin\left(b x + a\right), x\right)"," ",0,"integral(-(cos(b*x + a)^2 - 1)*cos(d*x + c)^n*sin(b*x + a), x)","F",0
224,1,116,0,0.441125," ","integrate(cos(d*x+c)*sin(b*x+a)^3,x, algorithm=""fricas"")","-\frac{{\left(7 \, b^{2} d - d^{3} - {\left(b^{2} d - d^{3}\right)} \cos\left(b x + a\right)^{2}\right)} \sin\left(b x + a\right) \sin\left(d x + c\right) - 3 \, {\left({\left(b^{3} - b d^{2}\right)} \cos\left(b x + a\right)^{3} - {\left(3 \, b^{3} - b d^{2}\right)} \cos\left(b x + a\right)\right)} \cos\left(d x + c\right)}{9 \, b^{4} - 10 \, b^{2} d^{2} + d^{4}}"," ",0,"-((7*b^2*d - d^3 - (b^2*d - d^3)*cos(b*x + a)^2)*sin(b*x + a)*sin(d*x + c) - 3*((b^3 - b*d^2)*cos(b*x + a)^3 - (3*b^3 - b*d^2)*cos(b*x + a))*cos(d*x + c))/(9*b^4 - 10*b^2*d^2 + d^4)","A",0
225,1,179,0,0.438241," ","integrate(cos(d*x+c)^2*sin(b*x+a)^3,x, algorithm=""fricas"")","-\frac{2 \, {\left(b^{2} d^{2} - 4 \, d^{4}\right)} \cos\left(b x + a\right)^{3} + 6 \, {\left(7 \, b^{3} d - 4 \, b d^{3} - {\left(b^{3} d - 4 \, b d^{3}\right)} \cos\left(b x + a\right)^{2}\right)} \cos\left(d x + c\right) \sin\left(b x + a\right) \sin\left(d x + c\right) - 9 \, {\left({\left(b^{4} - 4 \, b^{2} d^{2}\right)} \cos\left(b x + a\right)^{3} - {\left(3 \, b^{4} - 4 \, b^{2} d^{2}\right)} \cos\left(b x + a\right)\right)} \cos\left(d x + c\right)^{2} - 6 \, {\left(7 \, b^{2} d^{2} - 4 \, d^{4}\right)} \cos\left(b x + a\right)}{3 \, {\left(9 \, b^{5} - 40 \, b^{3} d^{2} + 16 \, b d^{4}\right)}}"," ",0,"-1/3*(2*(b^2*d^2 - 4*d^4)*cos(b*x + a)^3 + 6*(7*b^3*d - 4*b*d^3 - (b^3*d - 4*b*d^3)*cos(b*x + a)^2)*cos(d*x + c)*sin(b*x + a)*sin(d*x + c) - 9*((b^4 - 4*b^2*d^2)*cos(b*x + a)^3 - (3*b^4 - 4*b^2*d^2)*cos(b*x + a))*cos(d*x + c)^2 - 6*(7*b^2*d^2 - 4*d^4)*cos(b*x + a))/(9*b^5 - 40*b^3*d^2 + 16*b*d^4)","A",0
226,1,264,0,0.496900," ","integrate(cos(d*x+c)^3*sin(b*x+a)^3,x, algorithm=""fricas"")","\frac{{\left({\left(9 \, b^{5} - 82 \, b^{3} d^{2} + 9 \, b d^{4}\right)} \cos\left(b x + a\right)^{3} - 3 \, {\left(9 \, b^{5} - 28 \, b^{3} d^{2} + 3 \, b d^{4}\right)} \cos\left(b x + a\right)\right)} \cos\left(d x + c\right)^{3} + {\left(122 \, b^{2} d^{3} - 18 \, d^{5} - 2 \, {\left(b^{2} d^{3} - 9 \, d^{5}\right)} \cos\left(b x + a\right)^{2} - {\left(63 \, b^{4} d - 88 \, b^{2} d^{3} + 9 \, d^{5} - {\left(9 \, b^{4} d - 82 \, b^{2} d^{3} + 9 \, d^{5}\right)} \cos\left(b x + a\right)^{2}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(b x + a\right) \sin\left(d x + c\right) - 6 \, {\left({\left(b^{3} d^{2} - 9 \, b d^{4}\right)} \cos\left(b x + a\right)^{3} - 3 \, {\left(7 \, b^{3} d^{2} - 3 \, b d^{4}\right)} \cos\left(b x + a\right)\right)} \cos\left(d x + c\right)}{3 \, {\left(9 \, b^{6} - 91 \, b^{4} d^{2} + 91 \, b^{2} d^{4} - 9 \, d^{6}\right)}}"," ",0,"1/3*(((9*b^5 - 82*b^3*d^2 + 9*b*d^4)*cos(b*x + a)^3 - 3*(9*b^5 - 28*b^3*d^2 + 3*b*d^4)*cos(b*x + a))*cos(d*x + c)^3 + (122*b^2*d^3 - 18*d^5 - 2*(b^2*d^3 - 9*d^5)*cos(b*x + a)^2 - (63*b^4*d - 88*b^2*d^3 + 9*d^5 - (9*b^4*d - 82*b^2*d^3 + 9*d^5)*cos(b*x + a)^2)*cos(d*x + c)^2)*sin(b*x + a)*sin(d*x + c) - 6*((b^3*d^2 - 9*b*d^4)*cos(b*x + a)^3 - 3*(7*b^3*d^2 - 3*b*d^4)*cos(b*x + a))*cos(d*x + c))/(9*b^6 - 91*b^4*d^2 + 91*b^2*d^4 - 9*d^6)","A",0
227,1,30,0,0.478285," ","integrate(cos(b*x+a)/sin(b*x+c),x, algorithm=""fricas"")","\frac{b x \sin\left(-a + c\right) + \cos\left(-a + c\right) \log\left(\frac{1}{2} \, \sin\left(b x + c\right)\right)}{b}"," ",0,"(b*x*sin(-a + c) + cos(-a + c)*log(1/2*sin(b*x + c)))/b","A",0
228,1,71,0,0.472537," ","integrate(cos(b*x+a)/sin(b*x+c)^2,x, algorithm=""fricas"")","-\frac{\log\left(\frac{1}{2} \, \cos\left(b x + c\right) + \frac{1}{2}\right) \sin\left(b x + c\right) \sin\left(-a + c\right) - \log\left(-\frac{1}{2} \, \cos\left(b x + c\right) + \frac{1}{2}\right) \sin\left(b x + c\right) \sin\left(-a + c\right) + 2 \, \cos\left(-a + c\right)}{2 \, b \sin\left(b x + c\right)}"," ",0,"-1/2*(log(1/2*cos(b*x + c) + 1/2)*sin(b*x + c)*sin(-a + c) - log(-1/2*cos(b*x + c) + 1/2)*sin(b*x + c)*sin(-a + c) + 2*cos(-a + c))/(b*sin(b*x + c))","B",0
229,1,45,0,0.470521," ","integrate(cos(b*x+a)/sin(b*x+c)^3,x, algorithm=""fricas"")","\frac{2 \, \cos\left(b x + c\right) \sin\left(b x + c\right) \sin\left(-a + c\right) + \cos\left(-a + c\right)}{2 \, {\left(b \cos\left(b x + c\right)^{2} - b\right)}}"," ",0,"1/2*(2*cos(b*x + c)*sin(b*x + c)*sin(-a + c) + cos(-a + c))/(b*cos(b*x + c)^2 - b)","A",0
230,1,376,0,0.534847," ","integrate(sin(b*x+a)*tan(b*x+c)^3,x, algorithm=""fricas"")","-\frac{\frac{3 \, \sqrt{2} {\left(2 \, {\left(\cos\left(-2 \, a + 2 \, c\right) + 1\right)} \cos\left(b x + a\right) \sin\left(b x + a\right) \sin\left(-2 \, a + 2 \, c\right) - 2 \, {\left(\cos\left(-2 \, a + 2 \, c\right)^{2} + \cos\left(-2 \, a + 2 \, c\right)\right)} \cos\left(b x + a\right)^{2} + \cos\left(-2 \, a + 2 \, c\right)^{2} - 1\right)} \log\left(-\frac{2 \, \cos\left(b x + a\right)^{2} \cos\left(-2 \, a + 2 \, c\right) - 2 \, \cos\left(b x + a\right) \sin\left(b x + a\right) \sin\left(-2 \, a + 2 \, c\right) + \frac{2 \, \sqrt{2} {\left({\left(\cos\left(-2 \, a + 2 \, c\right) + 1\right)} \sin\left(b x + a\right) + \cos\left(b x + a\right) \sin\left(-2 \, a + 2 \, c\right)\right)}}{\sqrt{\cos\left(-2 \, a + 2 \, c\right) + 1}} - \cos\left(-2 \, a + 2 \, c\right) - 3}{2 \, \cos\left(b x + a\right)^{2} \cos\left(-2 \, a + 2 \, c\right) - 2 \, \cos\left(b x + a\right) \sin\left(b x + a\right) \sin\left(-2 \, a + 2 \, c\right) - \cos\left(-2 \, a + 2 \, c\right) + 1}\right)}{\sqrt{\cos\left(-2 \, a + 2 \, c\right) + 1}} - 4 \, {\left(4 \, \cos\left(b x + a\right)^{2} \cos\left(-2 \, a + 2 \, c\right) - 3 \, \cos\left(-2 \, a + 2 \, c\right) + 5\right)} \sin\left(b x + a\right) - 4 \, {\left(4 \, \cos\left(b x + a\right)^{3} - 5 \, \cos\left(b x + a\right)\right)} \sin\left(-2 \, a + 2 \, c\right)}{8 \, {\left(2 \, b \cos\left(b x + a\right)^{2} \cos\left(-2 \, a + 2 \, c\right) - 2 \, b \cos\left(b x + a\right) \sin\left(b x + a\right) \sin\left(-2 \, a + 2 \, c\right) - b \cos\left(-2 \, a + 2 \, c\right) + b\right)}}"," ",0,"-1/8*(3*sqrt(2)*(2*(cos(-2*a + 2*c) + 1)*cos(b*x + a)*sin(b*x + a)*sin(-2*a + 2*c) - 2*(cos(-2*a + 2*c)^2 + cos(-2*a + 2*c))*cos(b*x + a)^2 + cos(-2*a + 2*c)^2 - 1)*log(-(2*cos(b*x + a)^2*cos(-2*a + 2*c) - 2*cos(b*x + a)*sin(b*x + a)*sin(-2*a + 2*c) + 2*sqrt(2)*((cos(-2*a + 2*c) + 1)*sin(b*x + a) + cos(b*x + a)*sin(-2*a + 2*c))/sqrt(cos(-2*a + 2*c) + 1) - cos(-2*a + 2*c) - 3)/(2*cos(b*x + a)^2*cos(-2*a + 2*c) - 2*cos(b*x + a)*sin(b*x + a)*sin(-2*a + 2*c) - cos(-2*a + 2*c) + 1))/sqrt(cos(-2*a + 2*c) + 1) - 4*(4*cos(b*x + a)^2*cos(-2*a + 2*c) - 3*cos(-2*a + 2*c) + 5)*sin(b*x + a) - 4*(4*cos(b*x + a)^3 - 5*cos(b*x + a))*sin(-2*a + 2*c))/(2*b*cos(b*x + a)^2*cos(-2*a + 2*c) - 2*b*cos(b*x + a)*sin(b*x + a)*sin(-2*a + 2*c) - b*cos(-2*a + 2*c) + b)","B",0
231,1,315,0,0.466933," ","integrate(sin(b*x+a)*tan(b*x+c)^2,x, algorithm=""fricas"")","-\frac{4 \, {\left(\cos\left(-2 \, a + 2 \, c\right) + 1\right)} \cos\left(b x + a\right)^{2} - 4 \, \cos\left(b x + a\right) \sin\left(b x + a\right) \sin\left(-2 \, a + 2 \, c\right) + \frac{\sqrt{2} {\left({\left(\cos\left(-2 \, a + 2 \, c\right) + 1\right)} \cos\left(b x + a\right) \sin\left(-2 \, a + 2 \, c\right) + {\left(\cos\left(-2 \, a + 2 \, c\right)^{2} - 1\right)} \sin\left(b x + a\right)\right)} \log\left(-\frac{2 \, \cos\left(b x + a\right)^{2} \cos\left(-2 \, a + 2 \, c\right) - 2 \, \cos\left(b x + a\right) \sin\left(b x + a\right) \sin\left(-2 \, a + 2 \, c\right) + \frac{2 \, \sqrt{2} {\left({\left(\cos\left(-2 \, a + 2 \, c\right) + 1\right)} \sin\left(b x + a\right) + \cos\left(b x + a\right) \sin\left(-2 \, a + 2 \, c\right)\right)}}{\sqrt{\cos\left(-2 \, a + 2 \, c\right) + 1}} - \cos\left(-2 \, a + 2 \, c\right) - 3}{2 \, \cos\left(b x + a\right)^{2} \cos\left(-2 \, a + 2 \, c\right) - 2 \, \cos\left(b x + a\right) \sin\left(b x + a\right) \sin\left(-2 \, a + 2 \, c\right) - \cos\left(-2 \, a + 2 \, c\right) + 1}\right)}{\sqrt{\cos\left(-2 \, a + 2 \, c\right) + 1}} + 4 \, \cos\left(-2 \, a + 2 \, c\right) + 4}{4 \, {\left(b \sin\left(b x + a\right) \sin\left(-2 \, a + 2 \, c\right) - {\left(b \cos\left(-2 \, a + 2 \, c\right) + b\right)} \cos\left(b x + a\right)\right)}}"," ",0,"-1/4*(4*(cos(-2*a + 2*c) + 1)*cos(b*x + a)^2 - 4*cos(b*x + a)*sin(b*x + a)*sin(-2*a + 2*c) + sqrt(2)*((cos(-2*a + 2*c) + 1)*cos(b*x + a)*sin(-2*a + 2*c) + (cos(-2*a + 2*c)^2 - 1)*sin(b*x + a))*log(-(2*cos(b*x + a)^2*cos(-2*a + 2*c) - 2*cos(b*x + a)*sin(b*x + a)*sin(-2*a + 2*c) + 2*sqrt(2)*((cos(-2*a + 2*c) + 1)*sin(b*x + a) + cos(b*x + a)*sin(-2*a + 2*c))/sqrt(cos(-2*a + 2*c) + 1) - cos(-2*a + 2*c) - 3)/(2*cos(b*x + a)^2*cos(-2*a + 2*c) - 2*cos(b*x + a)*sin(b*x + a)*sin(-2*a + 2*c) - cos(-2*a + 2*c) + 1))/sqrt(cos(-2*a + 2*c) + 1) + 4*cos(-2*a + 2*c) + 4)/(b*sin(b*x + a)*sin(-2*a + 2*c) - (b*cos(-2*a + 2*c) + b)*cos(b*x + a))","B",0
232,1,188,0,0.451469," ","integrate(sin(b*x+a)*tan(b*x+c),x, algorithm=""fricas"")","\frac{\sqrt{2} \sqrt{\cos\left(-2 \, a + 2 \, c\right) + 1} \log\left(\frac{2 \, \cos\left(b x + a\right)^{2} \cos\left(-2 \, a + 2 \, c\right) - 2 \, \cos\left(b x + a\right) \sin\left(b x + a\right) \sin\left(-2 \, a + 2 \, c\right) - \frac{2 \, \sqrt{2} {\left({\left(\cos\left(-2 \, a + 2 \, c\right) + 1\right)} \sin\left(b x + a\right) + \cos\left(b x + a\right) \sin\left(-2 \, a + 2 \, c\right)\right)}}{\sqrt{\cos\left(-2 \, a + 2 \, c\right) + 1}} - \cos\left(-2 \, a + 2 \, c\right) - 3}{2 \, \cos\left(b x + a\right)^{2} \cos\left(-2 \, a + 2 \, c\right) - 2 \, \cos\left(b x + a\right) \sin\left(b x + a\right) \sin\left(-2 \, a + 2 \, c\right) - \cos\left(-2 \, a + 2 \, c\right) + 1}\right) - 4 \, \sin\left(b x + a\right)}{4 \, b}"," ",0,"1/4*(sqrt(2)*sqrt(cos(-2*a + 2*c) + 1)*log((2*cos(b*x + a)^2*cos(-2*a + 2*c) - 2*cos(b*x + a)*sin(b*x + a)*sin(-2*a + 2*c) - 2*sqrt(2)*((cos(-2*a + 2*c) + 1)*sin(b*x + a) + cos(b*x + a)*sin(-2*a + 2*c))/sqrt(cos(-2*a + 2*c) + 1) - cos(-2*a + 2*c) - 3)/(2*cos(b*x + a)^2*cos(-2*a + 2*c) - 2*cos(b*x + a)*sin(b*x + a)*sin(-2*a + 2*c) - cos(-2*a + 2*c) + 1)) - 4*sin(b*x + a))/b","B",0
233,1,197,0,0.447451," ","integrate(cot(b*x+c)*sin(b*x+a),x, algorithm=""fricas"")","\frac{\frac{\sqrt{2} \log\left(\frac{2 \, \cos\left(b x + a\right)^{2} \cos\left(-2 \, a + 2 \, c\right) - 2 \, \cos\left(b x + a\right) \sin\left(b x + a\right) \sin\left(-2 \, a + 2 \, c\right) + \frac{2 \, \sqrt{2} {\left({\left(\cos\left(-2 \, a + 2 \, c\right) + 1\right)} \cos\left(b x + a\right) - \sin\left(b x + a\right) \sin\left(-2 \, a + 2 \, c\right)\right)}}{\sqrt{\cos\left(-2 \, a + 2 \, c\right) + 1}} - \cos\left(-2 \, a + 2 \, c\right) + 3}{2 \, \cos\left(b x + a\right)^{2} \cos\left(-2 \, a + 2 \, c\right) - 2 \, \cos\left(b x + a\right) \sin\left(b x + a\right) \sin\left(-2 \, a + 2 \, c\right) - \cos\left(-2 \, a + 2 \, c\right) - 1}\right) \sin\left(-2 \, a + 2 \, c\right)}{\sqrt{\cos\left(-2 \, a + 2 \, c\right) + 1}} + 4 \, \sin\left(b x + a\right)}{4 \, b}"," ",0,"1/4*(sqrt(2)*log((2*cos(b*x + a)^2*cos(-2*a + 2*c) - 2*cos(b*x + a)*sin(b*x + a)*sin(-2*a + 2*c) + 2*sqrt(2)*((cos(-2*a + 2*c) + 1)*cos(b*x + a) - sin(b*x + a)*sin(-2*a + 2*c))/sqrt(cos(-2*a + 2*c) + 1) - cos(-2*a + 2*c) + 3)/(2*cos(b*x + a)^2*cos(-2*a + 2*c) - 2*cos(b*x + a)*sin(b*x + a)*sin(-2*a + 2*c) - cos(-2*a + 2*c) - 1))*sin(-2*a + 2*c)/sqrt(cos(-2*a + 2*c) + 1) + 4*sin(b*x + a))/b","B",0
234,1,316,0,0.450648," ","integrate(cot(b*x+c)^2*sin(b*x+a),x, algorithm=""fricas"")","\frac{4 \, {\left(\cos\left(-2 \, a + 2 \, c\right) + 1\right)} \cos\left(b x + a\right) \sin\left(b x + a\right) + \frac{\sqrt{2} {\left({\left(\cos\left(-2 \, a + 2 \, c\right) + 1\right)} \cos\left(b x + a\right) \sin\left(-2 \, a + 2 \, c\right) + {\left(\cos\left(-2 \, a + 2 \, c\right)^{2} + 2 \, \cos\left(-2 \, a + 2 \, c\right) + 1\right)} \sin\left(b x + a\right)\right)} \log\left(-\frac{2 \, \cos\left(b x + a\right)^{2} \cos\left(-2 \, a + 2 \, c\right) - 2 \, \cos\left(b x + a\right) \sin\left(b x + a\right) \sin\left(-2 \, a + 2 \, c\right) - \frac{2 \, \sqrt{2} {\left({\left(\cos\left(-2 \, a + 2 \, c\right) + 1\right)} \cos\left(b x + a\right) - \sin\left(b x + a\right) \sin\left(-2 \, a + 2 \, c\right)\right)}}{\sqrt{\cos\left(-2 \, a + 2 \, c\right) + 1}} - \cos\left(-2 \, a + 2 \, c\right) + 3}{2 \, \cos\left(b x + a\right)^{2} \cos\left(-2 \, a + 2 \, c\right) - 2 \, \cos\left(b x + a\right) \sin\left(b x + a\right) \sin\left(-2 \, a + 2 \, c\right) - \cos\left(-2 \, a + 2 \, c\right) - 1}\right)}{\sqrt{\cos\left(-2 \, a + 2 \, c\right) + 1}} + 4 \, {\left(\cos\left(b x + a\right)^{2} + 1\right)} \sin\left(-2 \, a + 2 \, c\right)}{4 \, {\left(b \cos\left(b x + a\right) \sin\left(-2 \, a + 2 \, c\right) + {\left(b \cos\left(-2 \, a + 2 \, c\right) + b\right)} \sin\left(b x + a\right)\right)}}"," ",0,"1/4*(4*(cos(-2*a + 2*c) + 1)*cos(b*x + a)*sin(b*x + a) + sqrt(2)*((cos(-2*a + 2*c) + 1)*cos(b*x + a)*sin(-2*a + 2*c) + (cos(-2*a + 2*c)^2 + 2*cos(-2*a + 2*c) + 1)*sin(b*x + a))*log(-(2*cos(b*x + a)^2*cos(-2*a + 2*c) - 2*cos(b*x + a)*sin(b*x + a)*sin(-2*a + 2*c) - 2*sqrt(2)*((cos(-2*a + 2*c) + 1)*cos(b*x + a) - sin(b*x + a)*sin(-2*a + 2*c))/sqrt(cos(-2*a + 2*c) + 1) - cos(-2*a + 2*c) + 3)/(2*cos(b*x + a)^2*cos(-2*a + 2*c) - 2*cos(b*x + a)*sin(b*x + a)*sin(-2*a + 2*c) - cos(-2*a + 2*c) - 1))/sqrt(cos(-2*a + 2*c) + 1) + 4*(cos(b*x + a)^2 + 1)*sin(-2*a + 2*c))/(b*cos(b*x + a)*sin(-2*a + 2*c) + (b*cos(-2*a + 2*c) + b)*sin(b*x + a))","B",0
235,1,372,0,0.507838," ","integrate(cot(b*x+c)^3*sin(b*x+a),x, algorithm=""fricas"")","\frac{\frac{3 \, \sqrt{2} {\left(2 \, {\left(\cos\left(-2 \, a + 2 \, c\right)^{2} - 1\right)} \cos\left(b x + a\right) \sin\left(b x + a\right) + {\left(2 \, \cos\left(b x + a\right)^{2} \cos\left(-2 \, a + 2 \, c\right) - \cos\left(-2 \, a + 2 \, c\right) - 1\right)} \sin\left(-2 \, a + 2 \, c\right)\right)} \log\left(-\frac{2 \, \cos\left(b x + a\right)^{2} \cos\left(-2 \, a + 2 \, c\right) - 2 \, \cos\left(b x + a\right) \sin\left(b x + a\right) \sin\left(-2 \, a + 2 \, c\right) - \frac{2 \, \sqrt{2} {\left({\left(\cos\left(-2 \, a + 2 \, c\right) + 1\right)} \cos\left(b x + a\right) - \sin\left(b x + a\right) \sin\left(-2 \, a + 2 \, c\right)\right)}}{\sqrt{\cos\left(-2 \, a + 2 \, c\right) + 1}} - \cos\left(-2 \, a + 2 \, c\right) + 3}{2 \, \cos\left(b x + a\right)^{2} \cos\left(-2 \, a + 2 \, c\right) - 2 \, \cos\left(b x + a\right) \sin\left(b x + a\right) \sin\left(-2 \, a + 2 \, c\right) - \cos\left(-2 \, a + 2 \, c\right) - 1}\right)}{\sqrt{\cos\left(-2 \, a + 2 \, c\right) + 1}} - 4 \, {\left(4 \, \cos\left(b x + a\right)^{2} \cos\left(-2 \, a + 2 \, c\right) - 3 \, \cos\left(-2 \, a + 2 \, c\right) - 5\right)} \sin\left(b x + a\right) - 4 \, {\left(4 \, \cos\left(b x + a\right)^{3} - 5 \, \cos\left(b x + a\right)\right)} \sin\left(-2 \, a + 2 \, c\right)}{8 \, {\left(2 \, b \cos\left(b x + a\right)^{2} \cos\left(-2 \, a + 2 \, c\right) - 2 \, b \cos\left(b x + a\right) \sin\left(b x + a\right) \sin\left(-2 \, a + 2 \, c\right) - b \cos\left(-2 \, a + 2 \, c\right) - b\right)}}"," ",0,"1/8*(3*sqrt(2)*(2*(cos(-2*a + 2*c)^2 - 1)*cos(b*x + a)*sin(b*x + a) + (2*cos(b*x + a)^2*cos(-2*a + 2*c) - cos(-2*a + 2*c) - 1)*sin(-2*a + 2*c))*log(-(2*cos(b*x + a)^2*cos(-2*a + 2*c) - 2*cos(b*x + a)*sin(b*x + a)*sin(-2*a + 2*c) - 2*sqrt(2)*((cos(-2*a + 2*c) + 1)*cos(b*x + a) - sin(b*x + a)*sin(-2*a + 2*c))/sqrt(cos(-2*a + 2*c) + 1) - cos(-2*a + 2*c) + 3)/(2*cos(b*x + a)^2*cos(-2*a + 2*c) - 2*cos(b*x + a)*sin(b*x + a)*sin(-2*a + 2*c) - cos(-2*a + 2*c) - 1))/sqrt(cos(-2*a + 2*c) + 1) - 4*(4*cos(b*x + a)^2*cos(-2*a + 2*c) - 3*cos(-2*a + 2*c) - 5)*sin(b*x + a) - 4*(4*cos(b*x + a)^3 - 5*cos(b*x + a))*sin(-2*a + 2*c))/(2*b*cos(b*x + a)^2*cos(-2*a + 2*c) - 2*b*cos(b*x + a)*sin(b*x + a)*sin(-2*a + 2*c) - b*cos(-2*a + 2*c) - b)","B",0
236,0,0,0,0.477236," ","integrate(sin(b*x+a)*tan(d*x+c),x, algorithm=""fricas"")","{\rm integral}\left(\sin\left(b x + a\right) \tan\left(d x + c\right), x\right)"," ",0,"integral(sin(b*x + a)*tan(d*x + c), x)","F",0
237,0,0,0,0.540292," ","integrate(cot(d*x+c)*sin(b*x+a),x, algorithm=""fricas"")","{\rm integral}\left(\cot\left(d x + c\right) \sin\left(b x + a\right), x\right)"," ",0,"integral(cot(d*x + c)*sin(b*x + a), x)","F",0
238,1,109,0,0.431321," ","integrate(cos(b*x+a)*cos(d*x+c)^3,x, algorithm=""fricas"")","-\frac{{\left(6 \, b d^{2} \cos\left(d x + c\right) - {\left(b^{3} - b d^{2}\right)} \cos\left(d x + c\right)^{3}\right)} \sin\left(b x + a\right) - 3 \, {\left(2 \, d^{3} \cos\left(b x + a\right) - {\left(b^{2} d - d^{3}\right)} \cos\left(b x + a\right) \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{b^{4} - 10 \, b^{2} d^{2} + 9 \, d^{4}}"," ",0,"-((6*b*d^2*cos(d*x + c) - (b^3 - b*d^2)*cos(d*x + c)^3)*sin(b*x + a) - 3*(2*d^3*cos(b*x + a) - (b^2*d - d^3)*cos(b*x + a)*cos(d*x + c)^2)*sin(d*x + c))/(b^4 - 10*b^2*d^2 + 9*d^4)","A",0
239,1,63,0,0.454199," ","integrate(cos(b*x+a)*cos(d*x+c)^2,x, algorithm=""fricas"")","-\frac{2 \, b d \cos\left(b x + a\right) \cos\left(d x + c\right) \sin\left(d x + c\right) - {\left(b^{2} \cos\left(d x + c\right)^{2} - 2 \, d^{2}\right)} \sin\left(b x + a\right)}{b^{3} - 4 \, b d^{2}}"," ",0,"-(2*b*d*cos(b*x + a)*cos(d*x + c)*sin(d*x + c) - (b^2*cos(d*x + c)^2 - 2*d^2)*sin(b*x + a))/(b^3 - 4*b*d^2)","A",0
240,1,42,0,0.447777," ","integrate(cos(b*x+a)*cos(d*x+c),x, algorithm=""fricas"")","\frac{b \cos\left(d x + c\right) \sin\left(b x + a\right) - d \cos\left(b x + a\right) \sin\left(d x + c\right)}{b^{2} - d^{2}}"," ",0,"(b*cos(d*x + c)*sin(b*x + a) - d*cos(b*x + a)*sin(d*x + c))/(b^2 - d^2)","A",0
241,1,31,0,0.536089," ","integrate(cos(b*x+a)*sec(b*x+c),x, algorithm=""fricas"")","\frac{b x \cos\left(-a + c\right) - \log\left(-\cos\left(b x + c\right)\right) \sin\left(-a + c\right)}{b}"," ",0,"(b*x*cos(-a + c) - log(-cos(b*x + c))*sin(-a + c))/b","A",0
242,1,69,0,0.458293," ","integrate(cos(b*x+a)*sec(b*x+c)^2,x, algorithm=""fricas"")","\frac{\cos\left(b x + c\right) \cos\left(-a + c\right) \log\left(\sin\left(b x + c\right) + 1\right) - \cos\left(b x + c\right) \cos\left(-a + c\right) \log\left(-\sin\left(b x + c\right) + 1\right) + 2 \, \sin\left(-a + c\right)}{2 \, b \cos\left(b x + c\right)}"," ",0,"1/2*(cos(b*x + c)*cos(-a + c)*log(sin(b*x + c) + 1) - cos(b*x + c)*cos(-a + c)*log(-sin(b*x + c) + 1) + 2*sin(-a + c))/(b*cos(b*x + c))","A",0
243,1,40,0,0.505386," ","integrate(cos(b*x+a)*sec(b*x+c)^3,x, algorithm=""fricas"")","\frac{2 \, \cos\left(b x + c\right) \cos\left(-a + c\right) \sin\left(b x + c\right) + \sin\left(-a + c\right)}{2 \, b \cos\left(b x + c\right)^{2}}"," ",0,"1/2*(2*cos(b*x + c)*cos(-a + c)*sin(b*x + c) + sin(-a + c))/(b*cos(b*x + c)^2)","A",0
244,1,163,0,0.630955," ","integrate(cos(b*x+a)^2*cos(d*x+c)^3,x, algorithm=""fricas"")","-\frac{6 \, {\left(6 \, b d^{3} \cos\left(b x + a\right) \cos\left(d x + c\right) - {\left(4 \, b^{3} d - b d^{3}\right)} \cos\left(b x + a\right) \cos\left(d x + c\right)^{3}\right)} \sin\left(b x + a\right) - {\left(18 \, d^{4} \cos\left(b x + a\right)^{2} + 16 \, b^{4} - 40 \, b^{2} d^{2} + {\left(8 \, b^{4} - 2 \, b^{2} d^{2} - 9 \, {\left(4 \, b^{2} d^{2} - d^{4}\right)} \cos\left(b x + a\right)^{2}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{3 \, {\left(16 \, b^{4} d - 40 \, b^{2} d^{3} + 9 \, d^{5}\right)}}"," ",0,"-1/3*(6*(6*b*d^3*cos(b*x + a)*cos(d*x + c) - (4*b^3*d - b*d^3)*cos(b*x + a)*cos(d*x + c)^3)*sin(b*x + a) - (18*d^4*cos(b*x + a)^2 + 16*b^4 - 40*b^2*d^2 + (8*b^4 - 2*b^2*d^2 - 9*(4*b^2*d^2 - d^4)*cos(b*x + a)^2)*cos(d*x + c)^2)*sin(d*x + c))/(16*b^4*d - 40*b^2*d^3 + 9*d^5)","A",0
245,1,105,0,0.443646," ","integrate(cos(b*x+a)^2*cos(d*x+c)^2,x, algorithm=""fricas"")","-\frac{{\left(2 \, b d^{2} \cos\left(b x + a\right)^{2} - b^{3}\right)} \cos\left(d x + c\right) \sin\left(d x + c\right) - {\left(b^{3} d - b d^{3}\right)} x - {\left(2 \, b^{2} d \cos\left(b x + a\right) \cos\left(d x + c\right)^{2} - d^{3} \cos\left(b x + a\right)\right)} \sin\left(b x + a\right)}{4 \, {\left(b^{3} d - b d^{3}\right)}}"," ",0,"-1/4*((2*b*d^2*cos(b*x + a)^2 - b^3)*cos(d*x + c)*sin(d*x + c) - (b^3*d - b*d^3)*x - (2*b^2*d*cos(b*x + a)*cos(d*x + c)^2 - d^3*cos(b*x + a))*sin(b*x + a))/(b^3*d - b*d^3)","A",0
246,1,240,0,0.479945," ","integrate(cos(b*x+a)^3*cos(d*x+c)^3,x, algorithm=""fricas"")","\frac{{\left({\left(18 \, b^{5} - 2 \, b^{3} d^{2} + {\left(9 \, b^{5} - 82 \, b^{3} d^{2} + 9 \, b d^{4}\right)} \cos\left(b x + a\right)^{2}\right)} \cos\left(d x + c\right)^{3} - 6 \, {\left(20 \, b^{3} d^{2} + {\left(b^{3} d^{2} - 9 \, b d^{4}\right)} \cos\left(b x + a\right)^{2}\right)} \cos\left(d x + c\right)\right)} \sin\left(b x + a\right) + {\left(120 \, b^{2} d^{3} \cos\left(b x + a\right) + 2 \, {\left(b^{2} d^{3} - 9 \, d^{5}\right)} \cos\left(b x + a\right)^{3} - {\left({\left(9 \, b^{4} d - 82 \, b^{2} d^{3} + 9 \, d^{5}\right)} \cos\left(b x + a\right)^{3} + 6 \, {\left(9 \, b^{4} d - b^{2} d^{3}\right)} \cos\left(b x + a\right)\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{3 \, {\left(9 \, b^{6} - 91 \, b^{4} d^{2} + 91 \, b^{2} d^{4} - 9 \, d^{6}\right)}}"," ",0,"1/3*(((18*b^5 - 2*b^3*d^2 + (9*b^5 - 82*b^3*d^2 + 9*b*d^4)*cos(b*x + a)^2)*cos(d*x + c)^3 - 6*(20*b^3*d^2 + (b^3*d^2 - 9*b*d^4)*cos(b*x + a)^2)*cos(d*x + c))*sin(b*x + a) + (120*b^2*d^3*cos(b*x + a) + 2*(b^2*d^3 - 9*d^5)*cos(b*x + a)^3 - ((9*b^4*d - 82*b^2*d^3 + 9*d^5)*cos(b*x + a)^3 + 6*(9*b^4*d - b^2*d^3)*cos(b*x + a))*cos(d*x + c)^2)*sin(d*x + c))/(9*b^6 - 91*b^4*d^2 + 91*b^2*d^4 - 9*d^6)","A",0
247,1,366,0,0.490062," ","integrate(cos(b*x+a)*tan(b*x+c)^3,x, algorithm=""fricas"")","\frac{16 \, \cos\left(b x + a\right)^{3} \cos\left(-2 \, a + 2 \, c\right) - 4 \, {\left(4 \, \cos\left(b x + a\right)^{2} + 1\right)} \sin\left(b x + a\right) \sin\left(-2 \, a + 2 \, c\right) - 4 \, {\left(\cos\left(-2 \, a + 2 \, c\right) - 5\right)} \cos\left(b x + a\right) + \frac{3 \, \sqrt{2} {\left(2 \, {\left(\cos\left(-2 \, a + 2 \, c\right)^{2} - 1\right)} \cos\left(b x + a\right) \sin\left(b x + a\right) + {\left(2 \, \cos\left(b x + a\right)^{2} \cos\left(-2 \, a + 2 \, c\right) - \cos\left(-2 \, a + 2 \, c\right) + 1\right)} \sin\left(-2 \, a + 2 \, c\right)\right)} \log\left(-\frac{2 \, \cos\left(b x + a\right)^{2} \cos\left(-2 \, a + 2 \, c\right) - 2 \, \cos\left(b x + a\right) \sin\left(b x + a\right) \sin\left(-2 \, a + 2 \, c\right) + \frac{2 \, \sqrt{2} {\left({\left(\cos\left(-2 \, a + 2 \, c\right) + 1\right)} \sin\left(b x + a\right) + \cos\left(b x + a\right) \sin\left(-2 \, a + 2 \, c\right)\right)}}{\sqrt{\cos\left(-2 \, a + 2 \, c\right) + 1}} - \cos\left(-2 \, a + 2 \, c\right) - 3}{2 \, \cos\left(b x + a\right)^{2} \cos\left(-2 \, a + 2 \, c\right) - 2 \, \cos\left(b x + a\right) \sin\left(b x + a\right) \sin\left(-2 \, a + 2 \, c\right) - \cos\left(-2 \, a + 2 \, c\right) + 1}\right)}{\sqrt{\cos\left(-2 \, a + 2 \, c\right) + 1}}}{8 \, {\left(2 \, b \cos\left(b x + a\right)^{2} \cos\left(-2 \, a + 2 \, c\right) - 2 \, b \cos\left(b x + a\right) \sin\left(b x + a\right) \sin\left(-2 \, a + 2 \, c\right) - b \cos\left(-2 \, a + 2 \, c\right) + b\right)}}"," ",0,"1/8*(16*cos(b*x + a)^3*cos(-2*a + 2*c) - 4*(4*cos(b*x + a)^2 + 1)*sin(b*x + a)*sin(-2*a + 2*c) - 4*(cos(-2*a + 2*c) - 5)*cos(b*x + a) + 3*sqrt(2)*(2*(cos(-2*a + 2*c)^2 - 1)*cos(b*x + a)*sin(b*x + a) + (2*cos(b*x + a)^2*cos(-2*a + 2*c) - cos(-2*a + 2*c) + 1)*sin(-2*a + 2*c))*log(-(2*cos(b*x + a)^2*cos(-2*a + 2*c) - 2*cos(b*x + a)*sin(b*x + a)*sin(-2*a + 2*c) + 2*sqrt(2)*((cos(-2*a + 2*c) + 1)*sin(b*x + a) + cos(b*x + a)*sin(-2*a + 2*c))/sqrt(cos(-2*a + 2*c) + 1) - cos(-2*a + 2*c) - 3)/(2*cos(b*x + a)^2*cos(-2*a + 2*c) - 2*cos(b*x + a)*sin(b*x + a)*sin(-2*a + 2*c) - cos(-2*a + 2*c) + 1))/sqrt(cos(-2*a + 2*c) + 1))/(2*b*cos(b*x + a)^2*cos(-2*a + 2*c) - 2*b*cos(b*x + a)*sin(b*x + a)*sin(-2*a + 2*c) - b*cos(-2*a + 2*c) + b)","B",0
248,1,316,0,0.508548," ","integrate(cos(b*x+a)*tan(b*x+c)^2,x, algorithm=""fricas"")","\frac{4 \, {\left(\cos\left(-2 \, a + 2 \, c\right) + 1\right)} \cos\left(b x + a\right) \sin\left(b x + a\right) + \frac{\sqrt{2} {\left({\left(\cos\left(-2 \, a + 2 \, c\right) + 1\right)} \sin\left(b x + a\right) \sin\left(-2 \, a + 2 \, c\right) - {\left(\cos\left(-2 \, a + 2 \, c\right)^{2} + 2 \, \cos\left(-2 \, a + 2 \, c\right) + 1\right)} \cos\left(b x + a\right)\right)} \log\left(\frac{2 \, \cos\left(b x + a\right)^{2} \cos\left(-2 \, a + 2 \, c\right) - 2 \, \cos\left(b x + a\right) \sin\left(b x + a\right) \sin\left(-2 \, a + 2 \, c\right) - \frac{2 \, \sqrt{2} {\left({\left(\cos\left(-2 \, a + 2 \, c\right) + 1\right)} \sin\left(b x + a\right) + \cos\left(b x + a\right) \sin\left(-2 \, a + 2 \, c\right)\right)}}{\sqrt{\cos\left(-2 \, a + 2 \, c\right) + 1}} - \cos\left(-2 \, a + 2 \, c\right) - 3}{2 \, \cos\left(b x + a\right)^{2} \cos\left(-2 \, a + 2 \, c\right) - 2 \, \cos\left(b x + a\right) \sin\left(b x + a\right) \sin\left(-2 \, a + 2 \, c\right) - \cos\left(-2 \, a + 2 \, c\right) + 1}\right)}{\sqrt{\cos\left(-2 \, a + 2 \, c\right) + 1}} + 4 \, {\left(\cos\left(b x + a\right)^{2} - 2\right)} \sin\left(-2 \, a + 2 \, c\right)}{4 \, {\left(b \sin\left(b x + a\right) \sin\left(-2 \, a + 2 \, c\right) - {\left(b \cos\left(-2 \, a + 2 \, c\right) + b\right)} \cos\left(b x + a\right)\right)}}"," ",0,"1/4*(4*(cos(-2*a + 2*c) + 1)*cos(b*x + a)*sin(b*x + a) + sqrt(2)*((cos(-2*a + 2*c) + 1)*sin(b*x + a)*sin(-2*a + 2*c) - (cos(-2*a + 2*c)^2 + 2*cos(-2*a + 2*c) + 1)*cos(b*x + a))*log((2*cos(b*x + a)^2*cos(-2*a + 2*c) - 2*cos(b*x + a)*sin(b*x + a)*sin(-2*a + 2*c) - 2*sqrt(2)*((cos(-2*a + 2*c) + 1)*sin(b*x + a) + cos(b*x + a)*sin(-2*a + 2*c))/sqrt(cos(-2*a + 2*c) + 1) - cos(-2*a + 2*c) - 3)/(2*cos(b*x + a)^2*cos(-2*a + 2*c) - 2*cos(b*x + a)*sin(b*x + a)*sin(-2*a + 2*c) - cos(-2*a + 2*c) + 1))/sqrt(cos(-2*a + 2*c) + 1) + 4*(cos(b*x + a)^2 - 2)*sin(-2*a + 2*c))/(b*sin(b*x + a)*sin(-2*a + 2*c) - (b*cos(-2*a + 2*c) + b)*cos(b*x + a))","B",0
249,1,196,0,0.467332," ","integrate(cos(b*x+a)*tan(b*x+c),x, algorithm=""fricas"")","\frac{\frac{\sqrt{2} \log\left(\frac{2 \, \cos\left(b x + a\right)^{2} \cos\left(-2 \, a + 2 \, c\right) - 2 \, \cos\left(b x + a\right) \sin\left(b x + a\right) \sin\left(-2 \, a + 2 \, c\right) - \frac{2 \, \sqrt{2} {\left({\left(\cos\left(-2 \, a + 2 \, c\right) + 1\right)} \sin\left(b x + a\right) + \cos\left(b x + a\right) \sin\left(-2 \, a + 2 \, c\right)\right)}}{\sqrt{\cos\left(-2 \, a + 2 \, c\right) + 1}} - \cos\left(-2 \, a + 2 \, c\right) - 3}{2 \, \cos\left(b x + a\right)^{2} \cos\left(-2 \, a + 2 \, c\right) - 2 \, \cos\left(b x + a\right) \sin\left(b x + a\right) \sin\left(-2 \, a + 2 \, c\right) - \cos\left(-2 \, a + 2 \, c\right) + 1}\right) \sin\left(-2 \, a + 2 \, c\right)}{\sqrt{\cos\left(-2 \, a + 2 \, c\right) + 1}} - 4 \, \cos\left(b x + a\right)}{4 \, b}"," ",0,"1/4*(sqrt(2)*log((2*cos(b*x + a)^2*cos(-2*a + 2*c) - 2*cos(b*x + a)*sin(b*x + a)*sin(-2*a + 2*c) - 2*sqrt(2)*((cos(-2*a + 2*c) + 1)*sin(b*x + a) + cos(b*x + a)*sin(-2*a + 2*c))/sqrt(cos(-2*a + 2*c) + 1) - cos(-2*a + 2*c) - 3)/(2*cos(b*x + a)^2*cos(-2*a + 2*c) - 2*cos(b*x + a)*sin(b*x + a)*sin(-2*a + 2*c) - cos(-2*a + 2*c) + 1))*sin(-2*a + 2*c)/sqrt(cos(-2*a + 2*c) + 1) - 4*cos(b*x + a))/b","B",0
250,1,190,0,0.458599," ","integrate(cos(b*x+a)*cot(b*x+c),x, algorithm=""fricas"")","\frac{\sqrt{2} \sqrt{\cos\left(-2 \, a + 2 \, c\right) + 1} \log\left(-\frac{2 \, \cos\left(b x + a\right)^{2} \cos\left(-2 \, a + 2 \, c\right) - 2 \, \cos\left(b x + a\right) \sin\left(b x + a\right) \sin\left(-2 \, a + 2 \, c\right) - \frac{2 \, \sqrt{2} {\left({\left(\cos\left(-2 \, a + 2 \, c\right) + 1\right)} \cos\left(b x + a\right) - \sin\left(b x + a\right) \sin\left(-2 \, a + 2 \, c\right)\right)}}{\sqrt{\cos\left(-2 \, a + 2 \, c\right) + 1}} - \cos\left(-2 \, a + 2 \, c\right) + 3}{2 \, \cos\left(b x + a\right)^{2} \cos\left(-2 \, a + 2 \, c\right) - 2 \, \cos\left(b x + a\right) \sin\left(b x + a\right) \sin\left(-2 \, a + 2 \, c\right) - \cos\left(-2 \, a + 2 \, c\right) - 1}\right) + 4 \, \cos\left(b x + a\right)}{4 \, b}"," ",0,"1/4*(sqrt(2)*sqrt(cos(-2*a + 2*c) + 1)*log(-(2*cos(b*x + a)^2*cos(-2*a + 2*c) - 2*cos(b*x + a)*sin(b*x + a)*sin(-2*a + 2*c) - 2*sqrt(2)*((cos(-2*a + 2*c) + 1)*cos(b*x + a) - sin(b*x + a)*sin(-2*a + 2*c))/sqrt(cos(-2*a + 2*c) + 1) - cos(-2*a + 2*c) + 3)/(2*cos(b*x + a)^2*cos(-2*a + 2*c) - 2*cos(b*x + a)*sin(b*x + a)*sin(-2*a + 2*c) - cos(-2*a + 2*c) - 1)) + 4*cos(b*x + a))/b","B",0
251,1,316,0,0.493269," ","integrate(cos(b*x+a)*cot(b*x+c)^2,x, algorithm=""fricas"")","\frac{4 \, {\left(\cos\left(-2 \, a + 2 \, c\right) + 1\right)} \cos\left(b x + a\right)^{2} - 4 \, \cos\left(b x + a\right) \sin\left(b x + a\right) \sin\left(-2 \, a + 2 \, c\right) + \frac{\sqrt{2} {\left({\left(\cos\left(-2 \, a + 2 \, c\right) + 1\right)} \sin\left(b x + a\right) \sin\left(-2 \, a + 2 \, c\right) - {\left(\cos\left(-2 \, a + 2 \, c\right)^{2} - 1\right)} \cos\left(b x + a\right)\right)} \log\left(-\frac{2 \, \cos\left(b x + a\right)^{2} \cos\left(-2 \, a + 2 \, c\right) - 2 \, \cos\left(b x + a\right) \sin\left(b x + a\right) \sin\left(-2 \, a + 2 \, c\right) - \frac{2 \, \sqrt{2} {\left({\left(\cos\left(-2 \, a + 2 \, c\right) + 1\right)} \cos\left(b x + a\right) - \sin\left(b x + a\right) \sin\left(-2 \, a + 2 \, c\right)\right)}}{\sqrt{\cos\left(-2 \, a + 2 \, c\right) + 1}} - \cos\left(-2 \, a + 2 \, c\right) + 3}{2 \, \cos\left(b x + a\right)^{2} \cos\left(-2 \, a + 2 \, c\right) - 2 \, \cos\left(b x + a\right) \sin\left(b x + a\right) \sin\left(-2 \, a + 2 \, c\right) - \cos\left(-2 \, a + 2 \, c\right) - 1}\right)}{\sqrt{\cos\left(-2 \, a + 2 \, c\right) + 1}} - 8 \, \cos\left(-2 \, a + 2 \, c\right) - 8}{4 \, {\left(b \cos\left(b x + a\right) \sin\left(-2 \, a + 2 \, c\right) + {\left(b \cos\left(-2 \, a + 2 \, c\right) + b\right)} \sin\left(b x + a\right)\right)}}"," ",0,"1/4*(4*(cos(-2*a + 2*c) + 1)*cos(b*x + a)^2 - 4*cos(b*x + a)*sin(b*x + a)*sin(-2*a + 2*c) + sqrt(2)*((cos(-2*a + 2*c) + 1)*sin(b*x + a)*sin(-2*a + 2*c) - (cos(-2*a + 2*c)^2 - 1)*cos(b*x + a))*log(-(2*cos(b*x + a)^2*cos(-2*a + 2*c) - 2*cos(b*x + a)*sin(b*x + a)*sin(-2*a + 2*c) - 2*sqrt(2)*((cos(-2*a + 2*c) + 1)*cos(b*x + a) - sin(b*x + a)*sin(-2*a + 2*c))/sqrt(cos(-2*a + 2*c) + 1) - cos(-2*a + 2*c) + 3)/(2*cos(b*x + a)^2*cos(-2*a + 2*c) - 2*cos(b*x + a)*sin(b*x + a)*sin(-2*a + 2*c) - cos(-2*a + 2*c) - 1))/sqrt(cos(-2*a + 2*c) + 1) - 8*cos(-2*a + 2*c) - 8)/(b*cos(b*x + a)*sin(-2*a + 2*c) + (b*cos(-2*a + 2*c) + b)*sin(b*x + a))","B",0
252,1,385,0,0.514191," ","integrate(cos(b*x+a)*cot(b*x+c)^3,x, algorithm=""fricas"")","-\frac{16 \, \cos\left(b x + a\right)^{3} \cos\left(-2 \, a + 2 \, c\right) - 4 \, {\left(4 \, \cos\left(b x + a\right)^{2} + 1\right)} \sin\left(b x + a\right) \sin\left(-2 \, a + 2 \, c\right) - 4 \, {\left(\cos\left(-2 \, a + 2 \, c\right) + 5\right)} \cos\left(b x + a\right) + \frac{3 \, \sqrt{2} {\left(2 \, {\left(\cos\left(-2 \, a + 2 \, c\right) + 1\right)} \cos\left(b x + a\right) \sin\left(b x + a\right) \sin\left(-2 \, a + 2 \, c\right) - 2 \, {\left(\cos\left(-2 \, a + 2 \, c\right)^{2} + \cos\left(-2 \, a + 2 \, c\right)\right)} \cos\left(b x + a\right)^{2} + \cos\left(-2 \, a + 2 \, c\right)^{2} + 2 \, \cos\left(-2 \, a + 2 \, c\right) + 1\right)} \log\left(\frac{2 \, \cos\left(b x + a\right)^{2} \cos\left(-2 \, a + 2 \, c\right) - 2 \, \cos\left(b x + a\right) \sin\left(b x + a\right) \sin\left(-2 \, a + 2 \, c\right) + \frac{2 \, \sqrt{2} {\left({\left(\cos\left(-2 \, a + 2 \, c\right) + 1\right)} \cos\left(b x + a\right) - \sin\left(b x + a\right) \sin\left(-2 \, a + 2 \, c\right)\right)}}{\sqrt{\cos\left(-2 \, a + 2 \, c\right) + 1}} - \cos\left(-2 \, a + 2 \, c\right) + 3}{2 \, \cos\left(b x + a\right)^{2} \cos\left(-2 \, a + 2 \, c\right) - 2 \, \cos\left(b x + a\right) \sin\left(b x + a\right) \sin\left(-2 \, a + 2 \, c\right) - \cos\left(-2 \, a + 2 \, c\right) - 1}\right)}{\sqrt{\cos\left(-2 \, a + 2 \, c\right) + 1}}}{8 \, {\left(2 \, b \cos\left(b x + a\right)^{2} \cos\left(-2 \, a + 2 \, c\right) - 2 \, b \cos\left(b x + a\right) \sin\left(b x + a\right) \sin\left(-2 \, a + 2 \, c\right) - b \cos\left(-2 \, a + 2 \, c\right) - b\right)}}"," ",0,"-1/8*(16*cos(b*x + a)^3*cos(-2*a + 2*c) - 4*(4*cos(b*x + a)^2 + 1)*sin(b*x + a)*sin(-2*a + 2*c) - 4*(cos(-2*a + 2*c) + 5)*cos(b*x + a) + 3*sqrt(2)*(2*(cos(-2*a + 2*c) + 1)*cos(b*x + a)*sin(b*x + a)*sin(-2*a + 2*c) - 2*(cos(-2*a + 2*c)^2 + cos(-2*a + 2*c))*cos(b*x + a)^2 + cos(-2*a + 2*c)^2 + 2*cos(-2*a + 2*c) + 1)*log((2*cos(b*x + a)^2*cos(-2*a + 2*c) - 2*cos(b*x + a)*sin(b*x + a)*sin(-2*a + 2*c) + 2*sqrt(2)*((cos(-2*a + 2*c) + 1)*cos(b*x + a) - sin(b*x + a)*sin(-2*a + 2*c))/sqrt(cos(-2*a + 2*c) + 1) - cos(-2*a + 2*c) + 3)/(2*cos(b*x + a)^2*cos(-2*a + 2*c) - 2*cos(b*x + a)*sin(b*x + a)*sin(-2*a + 2*c) - cos(-2*a + 2*c) - 1))/sqrt(cos(-2*a + 2*c) + 1))/(2*b*cos(b*x + a)^2*cos(-2*a + 2*c) - 2*b*cos(b*x + a)*sin(b*x + a)*sin(-2*a + 2*c) - b*cos(-2*a + 2*c) - b)","B",0
253,0,0,0,0.454930," ","integrate(cos(b*x+a)*tan(d*x+c),x, algorithm=""fricas"")","{\rm integral}\left(\cos\left(b x + a\right) \tan\left(d x + c\right), x\right)"," ",0,"integral(cos(b*x + a)*tan(d*x + c), x)","F",0
254,0,0,0,0.410861," ","integrate(cos(b*x+a)*cot(d*x+c),x, algorithm=""fricas"")","{\rm integral}\left(\cos\left(b x + a\right) \cot\left(d x + c\right), x\right)"," ",0,"integral(cos(b*x + a)*cot(d*x + c), x)","F",0
