1,1,111,53,1.945000," ","int(sin(b*x+a)*sin(2*b*x+2*a)^7,x)","\frac{35 \sin \left(b x +a \right)}{128 b}-\frac{35 \sin \left(3 b x +3 a \right)}{384 b}-\frac{21 \sin \left(5 b x +5 a \right)}{640 b}+\frac{3 \sin \left(7 b x +7 a \right)}{128 b}+\frac{7 \sin \left(9 b x +9 a \right)}{1152 b}-\frac{7 \sin \left(11 b x +11 a \right)}{1408 b}-\frac{\sin \left(13 b x +13 a \right)}{1664 b}+\frac{\sin \left(15 b x +15 a \right)}{1920 b}"," ",0,"35/128*sin(b*x+a)/b-35/384*sin(3*b*x+3*a)/b-21/640/b*sin(5*b*x+5*a)+3/128/b*sin(7*b*x+7*a)+7/1152/b*sin(9*b*x+9*a)-7/1408/b*sin(11*b*x+11*a)-1/1664/b*sin(13*b*x+13*a)+1/1920/b*sin(15*b*x+15*a)","B"
2,1,97,53,0.261000," ","int(sin(b*x+a)*sin(2*b*x+2*a)^6,x)","-\frac{5 \cos \left(b x +a \right)}{16 b}-\frac{5 \cos \left(3 b x +3 a \right)}{64 b}+\frac{3 \cos \left(5 b x +5 a \right)}{64 b}+\frac{3 \cos \left(7 b x +7 a \right)}{224 b}-\frac{\cos \left(9 b x +9 a \right)}{96 b}-\frac{\cos \left(11 b x +11 a \right)}{704 b}+\frac{\cos \left(13 b x +13 a \right)}{832 b}"," ",0,"-5/16*cos(b*x+a)/b-5/64*cos(3*b*x+3*a)/b+3/64*cos(5*b*x+5*a)/b+3/224*cos(7*b*x+7*a)/b-1/96*cos(9*b*x+9*a)/b-1/704*cos(11*b*x+11*a)/b+1/832*cos(13*b*x+13*a)/b","A"
3,1,83,40,1.287000," ","int(sin(b*x+a)*sin(2*b*x+2*a)^5,x)","\frac{5 \sin \left(b x +a \right)}{16 b}-\frac{5 \sin \left(3 b x +3 a \right)}{48 b}-\frac{\sin \left(5 b x +5 a \right)}{32 b}+\frac{5 \sin \left(7 b x +7 a \right)}{224 b}+\frac{\sin \left(9 b x +9 a \right)}{288 b}-\frac{\sin \left(11 b x +11 a \right)}{352 b}"," ",0,"5/16*sin(b*x+a)/b-5/48*sin(3*b*x+3*a)/b-1/32/b*sin(5*b*x+5*a)+5/224/b*sin(7*b*x+7*a)+1/288/b*sin(9*b*x+9*a)-1/352/b*sin(11*b*x+11*a)","B"
4,1,69,40,0.243000," ","int(sin(b*x+a)*sin(2*b*x+2*a)^4,x)","-\frac{3 \cos \left(b x +a \right)}{8 b}-\frac{\cos \left(3 b x +3 a \right)}{12 b}+\frac{\cos \left(5 b x +5 a \right)}{20 b}+\frac{\cos \left(7 b x +7 a \right)}{112 b}-\frac{\cos \left(9 b x +9 a \right)}{144 b}"," ",0,"-3/8*cos(b*x+a)/b-1/12*cos(3*b*x+3*a)/b+1/20*cos(5*b*x+5*a)/b+1/112*cos(7*b*x+7*a)/b-1/144*cos(9*b*x+9*a)/b","A"
5,1,55,27,0.930000," ","int(sin(b*x+a)*sin(2*b*x+2*a)^3,x)","\frac{3 \sin \left(b x +a \right)}{8 b}-\frac{\sin \left(3 b x +3 a \right)}{8 b}-\frac{\sin \left(5 b x +5 a \right)}{40 b}+\frac{\sin \left(7 b x +7 a \right)}{56 b}"," ",0,"3/8*sin(b*x+a)/b-1/8*sin(3*b*x+3*a)/b-1/40/b*sin(5*b*x+5*a)+1/56/b*sin(7*b*x+7*a)","A"
6,1,41,27,0.266000," ","int(sin(b*x+a)*sin(2*b*x+2*a)^2,x)","-\frac{\cos \left(b x +a \right)}{2 b}-\frac{\cos \left(3 b x +3 a \right)}{12 b}+\frac{\cos \left(5 b x +5 a \right)}{20 b}"," ",0,"-1/2*cos(b*x+a)/b-1/12*cos(3*b*x+3*a)/b+1/20*cos(5*b*x+5*a)/b","A"
7,1,27,26,0.483000," ","int(sin(b*x+a)*sin(2*b*x+2*a),x)","\frac{\sin \left(b x +a \right)}{2 b}-\frac{\sin \left(3 b x +3 a \right)}{6 b}"," ",0,"1/2*sin(b*x+a)/b-1/6*sin(3*b*x+3*a)/b","A"
8,1,20,12,0.681000," ","int(csc(2*b*x+2*a)*sin(b*x+a),x)","\frac{\ln \left(\sec \left(b x +a \right)+\tan \left(b x +a \right)\right)}{2 b}"," ",0,"1/2/b*ln(sec(b*x+a)+tan(b*x+a))","A"
9,1,36,24,0.975000," ","int(csc(2*b*x+2*a)^2*sin(b*x+a),x)","\frac{1}{4 b \cos \left(b x +a \right)}+\frac{\ln \left(\csc \left(b x +a \right)-\cot \left(b x +a \right)\right)}{4 b}"," ",0,"1/4/b/cos(b*x+a)+1/4/b*ln(csc(b*x+a)-cot(b*x+a))","A"
10,1,55,43,0.985000," ","int(csc(2*b*x+2*a)^3*sin(b*x+a),x)","\frac{1}{16 b \sin \left(b x +a \right) \cos \left(b x +a \right)^{2}}-\frac{3}{16 b \sin \left(b x +a \right)}+\frac{3 \ln \left(\sec \left(b x +a \right)+\tan \left(b x +a \right)\right)}{16 b}"," ",0,"1/16/b/sin(b*x+a)/cos(b*x+a)^2-3/16/b/sin(b*x+a)+3/16/b*ln(sec(b*x+a)+tan(b*x+a))","A"
11,1,78,58,0.866000," ","int(csc(2*b*x+2*a)^4*sin(b*x+a),x)","\frac{1}{48 b \sin \left(b x +a \right)^{2} \cos \left(b x +a \right)^{3}}-\frac{5}{96 b \sin \left(b x +a \right)^{2} \cos \left(b x +a \right)}+\frac{5}{32 b \cos \left(b x +a \right)}+\frac{5 \ln \left(\csc \left(b x +a \right)-\cot \left(b x +a \right)\right)}{32 b}"," ",0,"1/48/b/sin(b*x+a)^2/cos(b*x+a)^3-5/96/b/sin(b*x+a)^2/cos(b*x+a)+5/32/b/cos(b*x+a)+5/32/b*ln(csc(b*x+a)-cot(b*x+a))","A"
12,1,97,79,0.979000," ","int(csc(2*b*x+2*a)^5*sin(b*x+a),x)","\frac{1}{128 b \sin \left(b x +a \right)^{3} \cos \left(b x +a \right)^{4}}-\frac{7}{384 b \sin \left(b x +a \right)^{3} \cos \left(b x +a \right)^{2}}+\frac{35}{768 b \sin \left(b x +a \right) \cos \left(b x +a \right)^{2}}-\frac{35}{256 b \sin \left(b x +a \right)}+\frac{35 \ln \left(\sec \left(b x +a \right)+\tan \left(b x +a \right)\right)}{256 b}"," ",0,"1/128/b/sin(b*x+a)^3/cos(b*x+a)^4-7/384/b/sin(b*x+a)^3/cos(b*x+a)^2+35/768/b/sin(b*x+a)/cos(b*x+a)^2-35/256/b/sin(b*x+a)+35/256/b*ln(sec(b*x+a)+tan(b*x+a))","A"
13,1,86,40,0.393000," ","int(sin(b*x+a)^2*sin(2*b*x+2*a)^5,x)","-\frac{5 \cos \left(2 b x +2 a \right)}{32 b}+\frac{5 \cos \left(4 b x +4 a \right)}{256 b}+\frac{5 \cos \left(6 b x +6 a \right)}{192 b}-\frac{\cos \left(8 b x +8 a \right)}{128 b}-\frac{\cos \left(10 b x +10 a \right)}{320 b}+\frac{\cos \left(12 b x +12 a \right)}{768 b}"," ",0,"-5/32*cos(2*b*x+2*a)/b+5/256*cos(4*b*x+4*a)/b+5/192*cos(6*b*x+6*a)/b-1/128*cos(8*b*x+8*a)/b-1/320*cos(10*b*x+10*a)/b+1/768*cos(12*b*x+12*a)/b","B"
14,1,75,68,0.959000," ","int(sin(b*x+a)^2*sin(2*b*x+2*a)^4,x)","\frac{3 x}{16}-\frac{\sin \left(2 b x +2 a \right)}{32 b}-\frac{\sin \left(4 b x +4 a \right)}{16 b}+\frac{\sin \left(6 b x +6 a \right)}{64 b}+\frac{\sin \left(8 b x +8 a \right)}{128 b}-\frac{\sin \left(10 b x +10 a \right)}{320 b}"," ",0,"3/16*x-1/32*sin(2*b*x+2*a)/b-1/16/b*sin(4*b*x+4*a)+1/64/b*sin(6*b*x+6*a)+1/128/b*sin(8*b*x+8*a)-1/320/b*sin(10*b*x+10*a)","A"
15,1,58,27,0.292000," ","int(sin(b*x+a)^2*sin(2*b*x+2*a)^3,x)","-\frac{3 \cos \left(2 b x +2 a \right)}{16 b}+\frac{\cos \left(4 b x +4 a \right)}{32 b}+\frac{\cos \left(6 b x +6 a \right)}{48 b}-\frac{\cos \left(8 b x +8 a \right)}{128 b}"," ",0,"-3/16*cos(2*b*x+2*a)/b+1/32*cos(4*b*x+4*a)/b+1/48*cos(6*b*x+6*a)/b-1/128*cos(8*b*x+8*a)/b","B"
16,1,47,43,0.669000," ","int(sin(b*x+a)^2*sin(2*b*x+2*a)^2,x)","\frac{x}{4}-\frac{\sin \left(2 b x +2 a \right)}{16 b}-\frac{\sin \left(4 b x +4 a \right)}{16 b}+\frac{\sin \left(6 b x +6 a \right)}{48 b}"," ",0,"1/4*x-1/16*sin(2*b*x+2*a)/b-1/16/b*sin(4*b*x+4*a)+1/48/b*sin(6*b*x+6*a)","A"
17,1,30,13,0.142000," ","int(sin(b*x+a)^2*sin(2*b*x+2*a),x)","-\frac{\cos \left(2 b x +2 a \right)}{4 b}+\frac{\cos \left(4 b x +4 a \right)}{16 b}"," ",0,"-1/4*cos(2*b*x+2*a)/b+1/16*cos(4*b*x+4*a)/b","B"
18,1,13,12,0.396000," ","int(csc(2*b*x+2*a)*sin(b*x+a)^2,x)","-\frac{\ln \left(\cos \left(b x +a \right)\right)}{2 b}"," ",0,"-1/2*ln(cos(b*x+a))/b","A"
19,1,12,11,1.071000," ","int(csc(2*b*x+2*a)^2*sin(b*x+a)^2,x)","\frac{\tan \left(b x +a \right)}{4 b}"," ",0,"1/4*tan(b*x+a)/b","A"
20,1,27,26,0.872000," ","int(csc(2*b*x+2*a)^3*sin(b*x+a)^2,x)","\frac{1}{16 b \cos \left(b x +a \right)^{2}}+\frac{\ln \left(\tan \left(b x +a \right)\right)}{8 b}"," ",0,"1/16/b/cos(b*x+a)^2+1/8*ln(tan(b*x+a))/b","A"
21,1,51,36,1.217000," ","int(csc(2*b*x+2*a)^4*sin(b*x+a)^2,x)","\frac{\frac{1}{3 \sin \left(b x +a \right) \cos \left(b x +a \right)^{3}}+\frac{4}{3 \sin \left(b x +a \right) \cos \left(b x +a \right)}-\frac{8 \cot \left(b x +a \right)}{3}}{16 b}"," ",0,"1/16/b*(1/3/sin(b*x+a)/cos(b*x+a)^3+4/3/sin(b*x+a)/cos(b*x+a)-8/3*cot(b*x+a))","A"
22,1,69,52,0.922000," ","int(csc(2*b*x+2*a)^5*sin(b*x+a)^2,x)","\frac{1}{128 b \sin \left(b x +a \right)^{2} \cos \left(b x +a \right)^{4}}+\frac{3}{128 b \sin \left(b x +a \right)^{2} \cos \left(b x +a \right)^{2}}-\frac{3}{64 b \sin \left(b x +a \right)^{2}}+\frac{3 \ln \left(\tan \left(b x +a \right)\right)}{32 b}"," ",0,"1/128/b/sin(b*x+a)^2/cos(b*x+a)^4+3/128/b/sin(b*x+a)^2/cos(b*x+a)^2-3/64/b/sin(b*x+a)^2+3/32*ln(tan(b*x+a))/b","A"
23,1,97,40,1.478000," ","int(sin(b*x+a)^3*sin(2*b*x+2*a)^5,x)","\frac{5 \sin \left(b x +a \right)}{32 b}-\frac{25 \sin \left(3 b x +3 a \right)}{384 b}-\frac{\sin \left(5 b x +5 a \right)}{128 b}+\frac{\sin \left(7 b x +7 a \right)}{64 b}-\frac{\sin \left(9 b x +9 a \right)}{576 b}-\frac{3 \sin \left(11 b x +11 a \right)}{1408 b}+\frac{\sin \left(13 b x +13 a \right)}{1664 b}"," ",0,"5/32*sin(b*x+a)/b-25/384*sin(3*b*x+3*a)/b-1/128/b*sin(5*b*x+5*a)+1/64/b*sin(7*b*x+7*a)-1/576/b*sin(9*b*x+9*a)-3/1408/b*sin(11*b*x+11*a)+1/1664/b*sin(13*b*x+13*a)","B"
24,1,83,53,0.305000," ","int(sin(b*x+a)^3*sin(2*b*x+2*a)^4,x)","-\frac{7 \cos \left(b x +a \right)}{32 b}-\frac{\cos \left(3 b x +3 a \right)}{32 b}+\frac{11 \cos \left(5 b x +5 a \right)}{320 b}-\frac{\cos \left(7 b x +7 a \right)}{448 b}-\frac{\cos \left(9 b x +9 a \right)}{192 b}+\frac{\cos \left(11 b x +11 a \right)}{704 b}"," ",0,"-7/32*cos(b*x+a)/b-1/32*cos(3*b*x+3*a)/b+11/320*cos(5*b*x+5*a)/b-1/448*cos(7*b*x+7*a)/b-1/192*cos(9*b*x+9*a)/b+1/704*cos(11*b*x+11*a)/b","A"
25,1,55,27,0.882000," ","int(sin(b*x+a)^3*sin(2*b*x+2*a)^3,x)","\frac{3 \sin \left(b x +a \right)}{16 b}-\frac{\sin \left(3 b x +3 a \right)}{12 b}+\frac{3 \sin \left(7 b x +7 a \right)}{224 b}-\frac{\sin \left(9 b x +9 a \right)}{288 b}"," ",0,"3/16*sin(b*x+a)/b-1/12*sin(3*b*x+3*a)/b+3/224/b*sin(7*b*x+7*a)-1/288/b*sin(9*b*x+9*a)","A"
26,1,55,40,0.302000," ","int(sin(b*x+a)^3*sin(2*b*x+2*a)^2,x)","-\frac{5 \cos \left(b x +a \right)}{16 b}-\frac{\cos \left(3 b x +3 a \right)}{48 b}+\frac{3 \cos \left(5 b x +5 a \right)}{80 b}-\frac{\cos \left(7 b x +7 a \right)}{112 b}"," ",0,"-5/16*cos(b*x+a)/b-1/48*cos(3*b*x+3*a)/b+3/80*cos(5*b*x+5*a)/b-1/112*cos(7*b*x+7*a)/b","A"
27,1,41,13,0.582000," ","int(sin(b*x+a)^3*sin(2*b*x+2*a),x)","\frac{\sin \left(b x +a \right)}{4 b}-\frac{\sin \left(3 b x +3 a \right)}{8 b}+\frac{\sin \left(5 b x +5 a \right)}{40 b}"," ",0,"1/4*sin(b*x+a)/b-1/8*sin(3*b*x+3*a)/b+1/40/b*sin(5*b*x+5*a)","B"
28,1,32,24,0.523000," ","int(csc(2*b*x+2*a)*sin(b*x+a)^3,x)","-\frac{\sin \left(b x +a \right)}{2 b}+\frac{\ln \left(\sec \left(b x +a \right)+\tan \left(b x +a \right)\right)}{2 b}"," ",0,"-1/2*sin(b*x+a)/b+1/2/b*ln(sec(b*x+a)+tan(b*x+a))","A"
29,1,14,11,0.685000," ","int(csc(2*b*x+2*a)^2*sin(b*x+a)^3,x)","\frac{1}{4 b \cos \left(b x +a \right)}"," ",0,"1/4/b/cos(b*x+a)","A"
30,1,38,30,10.773000," ","int(csc(2*b*x+2*a)^3*sin(b*x+a)^3,x)","\frac{\sec \left(b x +a \right) \tan \left(b x +a \right)}{16 b}+\frac{\ln \left(\sec \left(b x +a \right)+\tan \left(b x +a \right)\right)}{16 b}"," ",0,"1/16*sec(b*x+a)*tan(b*x+a)/b+1/16/b*ln(sec(b*x+a)+tan(b*x+a))","A"
31,1,49,37,0.917000," ","int(csc(2*b*x+2*a)^4*sin(b*x+a)^3,x)","\frac{1}{48 b \cos \left(b x +a \right)^{3}}+\frac{1}{16 b \cos \left(b x +a \right)}+\frac{\ln \left(\csc \left(b x +a \right)-\cot \left(b x +a \right)\right)}{16 b}"," ",0,"1/48/b/cos(b*x+a)^3+1/16/b/cos(b*x+a)+1/16/b*ln(csc(b*x+a)-cot(b*x+a))","A"
32,1,76,62,0.916000," ","int(csc(2*b*x+2*a)^5*sin(b*x+a)^3,x)","\frac{1}{128 b \sin \left(b x +a \right) \cos \left(b x +a \right)^{4}}+\frac{5}{256 b \sin \left(b x +a \right) \cos \left(b x +a \right)^{2}}-\frac{15}{256 b \sin \left(b x +a \right)}+\frac{15 \ln \left(\sec \left(b x +a \right)+\tan \left(b x +a \right)\right)}{256 b}"," ",0,"1/128/b/sin(b*x+a)/cos(b*x+a)^4+5/256/b/sin(b*x+a)/cos(b*x+a)^2-15/256/b/sin(b*x+a)+15/256/b*ln(sec(b*x+a)+tan(b*x+a))","A"
33,1,71,53,0.834000," ","int(csc(b*x+a)*sin(2*b*x+2*a)^8,x)","\frac{-\frac{256 \left(\sin^{6}\left(b x +a \right)\right) \left(\cos^{9}\left(b x +a \right)\right)}{15}-\frac{512 \left(\sin^{4}\left(b x +a \right)\right) \left(\cos^{9}\left(b x +a \right)\right)}{65}-\frac{2048 \left(\sin^{2}\left(b x +a \right)\right) \left(\cos^{9}\left(b x +a \right)\right)}{715}-\frac{4096 \left(\cos^{9}\left(b x +a \right)\right)}{6435}}{b}"," ",0,"256/b*(-1/15*sin(b*x+a)^6*cos(b*x+a)^9-2/65*sin(b*x+a)^4*cos(b*x+a)^9-8/715*sin(b*x+a)^2*cos(b*x+a)^9-16/6435*cos(b*x+a)^9)","A"
34,1,97,53,1.262000," ","int(csc(b*x+a)*sin(2*b*x+2*a)^7,x)","\frac{-\frac{128 \left(\sin^{5}\left(b x +a \right)\right) \left(\cos^{8}\left(b x +a \right)\right)}{13}-\frac{640 \left(\sin^{3}\left(b x +a \right)\right) \left(\cos^{8}\left(b x +a \right)\right)}{143}-\frac{640 \sin \left(b x +a \right) \left(\cos^{8}\left(b x +a \right)\right)}{429}+\frac{640 \left(\frac{16}{5}+\cos^{6}\left(b x +a \right)+\frac{6 \left(\cos^{4}\left(b x +a \right)\right)}{5}+\frac{8 \left(\cos^{2}\left(b x +a \right)\right)}{5}\right) \sin \left(b x +a \right)}{3003}}{b}"," ",0,"128/b*(-1/13*sin(b*x+a)^5*cos(b*x+a)^8-5/143*sin(b*x+a)^3*cos(b*x+a)^8-5/429*sin(b*x+a)*cos(b*x+a)^8+5/3003*(16/5+cos(b*x+a)^6+6/5*cos(b*x+a)^4+8/5*cos(b*x+a)^2)*sin(b*x+a))","A"
35,1,53,40,1.009000," ","int(csc(b*x+a)*sin(2*b*x+2*a)^6,x)","\frac{-\frac{64 \left(\sin^{4}\left(b x +a \right)\right) \left(\cos^{7}\left(b x +a \right)\right)}{11}-\frac{256 \left(\sin^{2}\left(b x +a \right)\right) \left(\cos^{7}\left(b x +a \right)\right)}{99}-\frac{512 \left(\cos^{7}\left(b x +a \right)\right)}{693}}{b}"," ",0,"64/b*(-1/11*sin(b*x+a)^4*cos(b*x+a)^7-4/99*sin(b*x+a)^2*cos(b*x+a)^7-8/693*cos(b*x+a)^7)","A"
36,1,69,40,0.972000," ","int(csc(b*x+a)*sin(2*b*x+2*a)^5,x)","\frac{-\frac{32 \left(\sin^{3}\left(b x +a \right)\right) \left(\cos^{6}\left(b x +a \right)\right)}{9}-\frac{32 \sin \left(b x +a \right) \left(\cos^{6}\left(b x +a \right)\right)}{21}+\frac{32 \left(\frac{8}{3}+\cos^{4}\left(b x +a \right)+\frac{4 \left(\cos^{2}\left(b x +a \right)\right)}{3}\right) \sin \left(b x +a \right)}{105}}{b}"," ",0,"32/b*(-1/9*sin(b*x+a)^3*cos(b*x+a)^6-1/21*sin(b*x+a)*cos(b*x+a)^6+1/105*(8/3+cos(b*x+a)^4+4/3*cos(b*x+a)^2)*sin(b*x+a))","A"
37,1,35,27,0.662000," ","int(csc(b*x+a)*sin(2*b*x+2*a)^4,x)","\frac{-\frac{16 \left(\sin^{2}\left(b x +a \right)\right) \left(\cos^{5}\left(b x +a \right)\right)}{7}-\frac{32 \left(\cos^{5}\left(b x +a \right)\right)}{35}}{b}"," ",0,"16/b*(-1/7*sin(b*x+a)^2*cos(b*x+a)^5-2/35*cos(b*x+a)^5)","A"
38,1,41,27,1.049000," ","int(csc(b*x+a)*sin(2*b*x+2*a)^3,x)","\frac{-\frac{8 \sin \left(b x +a \right) \left(\cos^{4}\left(b x +a \right)\right)}{5}+\frac{8 \left(2+\cos^{2}\left(b x +a \right)\right) \sin \left(b x +a \right)}{15}}{b}"," ",0,"8/b*(-1/5*sin(b*x+a)*cos(b*x+a)^4+1/15*(2+cos(b*x+a)^2)*sin(b*x+a))","A"
39,1,14,13,0.499000," ","int(csc(b*x+a)*sin(2*b*x+2*a)^2,x)","-\frac{4 \left(\cos^{3}\left(b x +a \right)\right)}{3 b}"," ",0,"-4/3*cos(b*x+a)^3/b","A"
40,1,12,11,0.339000," ","int(csc(b*x+a)*sin(2*b*x+2*a),x)","\frac{2 \sin \left(b x +a \right)}{b}"," ",0,"2*sin(b*x+a)/b","A"
41,1,34,24,0.673000," ","int(csc(b*x+a)*csc(2*b*x+2*a),x)","-\frac{1}{2 b \sin \left(b x +a \right)}+\frac{\ln \left(\sec \left(b x +a \right)+\tan \left(b x +a \right)\right)}{2 b}"," ",0,"-1/2/b/sin(b*x+a)+1/2/b*ln(sec(b*x+a)+tan(b*x+a))","A"
42,1,57,43,0.915000," ","int(csc(b*x+a)*csc(2*b*x+2*a)^2,x)","-\frac{1}{8 b \sin \left(b x +a \right)^{2} \cos \left(b x +a \right)}+\frac{3}{8 b \cos \left(b x +a \right)}+\frac{3 \ln \left(\csc \left(b x +a \right)-\cot \left(b x +a \right)\right)}{8 b}"," ",0,"-1/8/b/sin(b*x+a)^2/cos(b*x+a)+3/8/b/cos(b*x+a)+3/8/b*ln(csc(b*x+a)-cot(b*x+a))","A"
43,1,76,58,0.765000," ","int(csc(b*x+a)*csc(2*b*x+2*a)^3,x)","-\frac{1}{24 b \sin \left(b x +a \right)^{3} \cos \left(b x +a \right)^{2}}+\frac{5}{48 b \sin \left(b x +a \right) \cos \left(b x +a \right)^{2}}-\frac{5}{16 b \sin \left(b x +a \right)}+\frac{5 \ln \left(\sec \left(b x +a \right)+\tan \left(b x +a \right)\right)}{16 b}"," ",0,"-1/24/b/sin(b*x+a)^3/cos(b*x+a)^2+5/48/b/sin(b*x+a)/cos(b*x+a)^2-5/16/b/sin(b*x+a)+5/16/b*ln(sec(b*x+a)+tan(b*x+a))","A"
44,1,99,79,0.954000," ","int(csc(b*x+a)*csc(2*b*x+2*a)^4,x)","-\frac{1}{64 b \sin \left(b x +a \right)^{4} \cos \left(b x +a \right)^{3}}+\frac{7}{192 b \sin \left(b x +a \right)^{2} \cos \left(b x +a \right)^{3}}-\frac{35}{384 b \sin \left(b x +a \right)^{2} \cos \left(b x +a \right)}+\frac{35}{128 b \cos \left(b x +a \right)}+\frac{35 \ln \left(\csc \left(b x +a \right)-\cot \left(b x +a \right)\right)}{128 b}"," ",0,"-1/64/b/sin(b*x+a)^4/cos(b*x+a)^3+7/192/b/sin(b*x+a)^2/cos(b*x+a)^3-35/384/b/sin(b*x+a)^2/cos(b*x+a)+35/128/b/cos(b*x+a)+35/128/b*ln(csc(b*x+a)-cot(b*x+a))","A"
45,1,111,139,1.411000," ","int(csc(b*x+a)^2*sin(2*b*x+2*a)^8,x)","\frac{-\frac{128 \left(\sin^{5}\left(b x +a \right)\right) \left(\cos^{9}\left(b x +a \right)\right)}{7}-\frac{160 \left(\sin^{3}\left(b x +a \right)\right) \left(\cos^{9}\left(b x +a \right)\right)}{21}-\frac{16 \sin \left(b x +a \right) \left(\cos^{9}\left(b x +a \right)\right)}{7}+\frac{2 \left(\cos^{7}\left(b x +a \right)+\frac{7 \left(\cos^{5}\left(b x +a \right)\right)}{6}+\frac{35 \left(\cos^{3}\left(b x +a \right)\right)}{24}+\frac{35 \cos \left(b x +a \right)}{16}\right) \sin \left(b x +a \right)}{7}+\frac{5 b x}{8}+\frac{5 a}{8}}{b}"," ",0,"256/b*(-1/14*sin(b*x+a)^5*cos(b*x+a)^9-5/168*sin(b*x+a)^3*cos(b*x+a)^9-1/112*sin(b*x+a)*cos(b*x+a)^9+1/896*(cos(b*x+a)^7+7/6*cos(b*x+a)^5+35/24*cos(b*x+a)^3+35/16*cos(b*x+a))*sin(b*x+a)+5/2048*b*x+5/2048*a)","A"
46,1,53,40,0.728000," ","int(csc(b*x+a)^2*sin(2*b*x+2*a)^7,x)","\frac{-\frac{32 \left(\sin^{4}\left(b x +a \right)\right) \left(\cos^{8}\left(b x +a \right)\right)}{3}-\frac{64 \left(\sin^{2}\left(b x +a \right)\right) \left(\cos^{8}\left(b x +a \right)\right)}{15}-\frac{16 \left(\cos^{8}\left(b x +a \right)\right)}{15}}{b}"," ",0,"128/b*(-1/12*sin(b*x+a)^4*cos(b*x+a)^8-1/30*sin(b*x+a)^2*cos(b*x+a)^8-1/120*cos(b*x+a)^8)","A"
47,1,83,99,0.972000," ","int(csc(b*x+a)^2*sin(2*b*x+2*a)^6,x)","\frac{-\frac{32 \left(\sin^{3}\left(b x +a \right)\right) \left(\cos^{7}\left(b x +a \right)\right)}{5}-\frac{12 \sin \left(b x +a \right) \left(\cos^{7}\left(b x +a \right)\right)}{5}+\frac{2 \left(\cos^{5}\left(b x +a \right)+\frac{5 \left(\cos^{3}\left(b x +a \right)\right)}{4}+\frac{15 \cos \left(b x +a \right)}{8}\right) \sin \left(b x +a \right)}{5}+\frac{3 b x}{4}+\frac{3 a}{4}}{b}"," ",0,"64/b*(-1/10*sin(b*x+a)^3*cos(b*x+a)^7-3/80*sin(b*x+a)*cos(b*x+a)^7+1/160*(cos(b*x+a)^5+5/4*cos(b*x+a)^3+15/8*cos(b*x+a))*sin(b*x+a)+3/256*b*x+3/256*a)","A"
48,1,35,27,0.576000," ","int(csc(b*x+a)^2*sin(2*b*x+2*a)^5,x)","\frac{-4 \left(\sin^{2}\left(b x +a \right)\right) \left(\cos^{6}\left(b x +a \right)\right)-\frac{4 \left(\cos^{6}\left(b x +a \right)\right)}{3}}{b}"," ",0,"32/b*(-1/8*sin(b*x+a)^2*cos(b*x+a)^6-1/24*cos(b*x+a)^6)","A"
49,1,55,56,0.912000," ","int(csc(b*x+a)^2*sin(2*b*x+2*a)^4,x)","\frac{-\frac{8 \sin \left(b x +a \right) \left(\cos^{5}\left(b x +a \right)\right)}{3}+\frac{2 \left(\cos^{3}\left(b x +a \right)+\frac{3 \cos \left(b x +a \right)}{2}\right) \sin \left(b x +a \right)}{3}+b x +a}{b}"," ",0,"16/b*(-1/6*sin(b*x+a)*cos(b*x+a)^5+1/24*(cos(b*x+a)^3+3/2*cos(b*x+a))*sin(b*x+a)+1/16*b*x+1/16*a)","A"
50,1,14,13,0.569000," ","int(csc(b*x+a)^2*sin(2*b*x+2*a)^3,x)","-\frac{2 \left(\cos^{4}\left(b x +a \right)\right)}{b}"," ",0,"-2*cos(b*x+a)^4/b","A"
51,1,28,21,0.592000," ","int(csc(b*x+a)^2*sin(2*b*x+2*a)^2,x)","\frac{2 \cos \left(b x +a \right) \sin \left(b x +a \right)+2 b x +2 a}{b}"," ",0,"4/b*(1/2*cos(b*x+a)*sin(b*x+a)+1/2*b*x+1/2*a)","A"
52,1,13,12,0.281000," ","int(csc(b*x+a)^2*sin(2*b*x+2*a),x)","\frac{2 \ln \left(\sin \left(b x +a \right)\right)}{b}"," ",0,"2*ln(sin(b*x+a))/b","A"
53,1,27,26,0.728000," ","int(csc(b*x+a)^2*csc(2*b*x+2*a),x)","-\frac{1}{4 b \sin \left(b x +a \right)^{2}}+\frac{\ln \left(\tan \left(b x +a \right)\right)}{2 b}"," ",0,"-1/4/b/sin(b*x+a)^2+1/2*ln(tan(b*x+a))/b","A"
54,1,51,36,1.107000," ","int(csc(b*x+a)^2*csc(2*b*x+2*a)^2,x)","\frac{-\frac{1}{3 \sin \left(b x +a \right)^{3} \cos \left(b x +a \right)}+\frac{4}{3 \sin \left(b x +a \right) \cos \left(b x +a \right)}-\frac{8 \cot \left(b x +a \right)}{3}}{4 b}"," ",0,"1/4/b*(-1/3/sin(b*x+a)^3/cos(b*x+a)+4/3/sin(b*x+a)/cos(b*x+a)-8/3*cot(b*x+a))","A"
55,1,69,52,0.862000," ","int(csc(b*x+a)^2*csc(2*b*x+2*a)^3,x)","-\frac{1}{32 b \sin \left(b x +a \right)^{4} \cos \left(b x +a \right)^{2}}+\frac{3}{32 b \sin \left(b x +a \right)^{2} \cos \left(b x +a \right)^{2}}-\frac{3}{16 b \sin \left(b x +a \right)^{2}}+\frac{3 \ln \left(\tan \left(b x +a \right)\right)}{8 b}"," ",0,"-1/32/b/sin(b*x+a)^4/cos(b*x+a)^2+3/32/b/sin(b*x+a)^2/cos(b*x+a)^2-3/16/b/sin(b*x+a)^2+3/8*ln(tan(b*x+a))/b","A"
56,1,87,62,1.235000," ","int(csc(b*x+a)^2*csc(2*b*x+2*a)^4,x)","\frac{-\frac{1}{5 \sin \left(b x +a \right)^{5} \cos \left(b x +a \right)^{3}}+\frac{8}{15 \sin \left(b x +a \right)^{3} \cos \left(b x +a \right)^{3}}-\frac{16}{15 \sin \left(b x +a \right)^{3} \cos \left(b x +a \right)}+\frac{64}{15 \sin \left(b x +a \right) \cos \left(b x +a \right)}-\frac{128 \cot \left(b x +a \right)}{15}}{16 b}"," ",0,"1/16/b*(-1/5/sin(b*x+a)^5/cos(b*x+a)^3+8/15/sin(b*x+a)^3/cos(b*x+a)^3-16/15/sin(b*x+a)^3/cos(b*x+a)+64/15/sin(b*x+a)/cos(b*x+a)-128/15*cot(b*x+a))","A"
57,1,111,78,0.842000," ","int(csc(b*x+a)^2*csc(2*b*x+2*a)^5,x)","-\frac{1}{192 b \sin \left(b x +a \right)^{6} \cos \left(b x +a \right)^{4}}+\frac{5}{384 b \sin \left(b x +a \right)^{4} \cos \left(b x +a \right)^{4}}-\frac{5}{192 b \sin \left(b x +a \right)^{4} \cos \left(b x +a \right)^{2}}+\frac{5}{64 b \sin \left(b x +a \right)^{2} \cos \left(b x +a \right)^{2}}-\frac{5}{32 b \sin \left(b x +a \right)^{2}}+\frac{5 \ln \left(\tan \left(b x +a \right)\right)}{16 b}"," ",0,"-1/192/b/sin(b*x+a)^6/cos(b*x+a)^4+5/384/b/sin(b*x+a)^4/cos(b*x+a)^4-5/192/b/sin(b*x+a)^4/cos(b*x+a)^2+5/64/b/sin(b*x+a)^2/cos(b*x+a)^2-5/32/b/sin(b*x+a)^2+5/16*ln(tan(b*x+a))/b","A"
58,1,123,88,1.261000," ","int(csc(b*x+a)^2*csc(2*b*x+2*a)^6,x)","\frac{-\frac{1}{7 \sin \left(b x +a \right)^{7} \cos \left(b x +a \right)^{5}}+\frac{12}{35 \sin \left(b x +a \right)^{5} \cos \left(b x +a \right)^{5}}-\frac{24}{35 \sin \left(b x +a \right)^{5} \cos \left(b x +a \right)^{3}}+\frac{64}{35 \sin \left(b x +a \right)^{3} \cos \left(b x +a \right)^{3}}-\frac{128}{35 \sin \left(b x +a \right)^{3} \cos \left(b x +a \right)}+\frac{512}{35 \sin \left(b x +a \right) \cos \left(b x +a \right)}-\frac{1024 \cot \left(b x +a \right)}{35}}{64 b}"," ",0,"1/64/b*(-1/7/sin(b*x+a)^7/cos(b*x+a)^5+12/35/sin(b*x+a)^5/cos(b*x+a)^5-24/35/sin(b*x+a)^5/cos(b*x+a)^3+64/35/sin(b*x+a)^3/cos(b*x+a)^3-128/35/sin(b*x+a)^3/cos(b*x+a)+512/35/sin(b*x+a)/cos(b*x+a)-1024/35*cot(b*x+a))","A"
59,1,71,53,0.949000," ","int(csc(b*x+a)^3*sin(2*b*x+2*a)^10,x)","\frac{-\frac{1024 \left(\sin^{6}\left(b x +a \right)\right) \left(\cos^{11}\left(b x +a \right)\right)}{17}-\frac{2048 \left(\sin^{4}\left(b x +a \right)\right) \left(\cos^{11}\left(b x +a \right)\right)}{85}-\frac{8192 \left(\sin^{2}\left(b x +a \right)\right) \left(\cos^{11}\left(b x +a \right)\right)}{1105}-\frac{16384 \left(\cos^{11}\left(b x +a \right)\right)}{12155}}{b}"," ",0,"1024/b*(-1/17*sin(b*x+a)^6*cos(b*x+a)^11-2/85*sin(b*x+a)^4*cos(b*x+a)^11-8/1105*sin(b*x+a)^2*cos(b*x+a)^11-16/12155*cos(b*x+a)^11)","A"
60,1,107,66,1.330000," ","int(csc(b*x+a)^3*sin(2*b*x+2*a)^9,x)","\frac{-\frac{512 \left(\sin^{5}\left(b x +a \right)\right) \left(\cos^{10}\left(b x +a \right)\right)}{15}-\frac{512 \left(\sin^{3}\left(b x +a \right)\right) \left(\cos^{10}\left(b x +a \right)\right)}{39}-\frac{512 \sin \left(b x +a \right) \left(\cos^{10}\left(b x +a \right)\right)}{143}+\frac{512 \left(\frac{128}{35}+\cos^{8}\left(b x +a \right)+\frac{8 \left(\cos^{6}\left(b x +a \right)\right)}{7}+\frac{48 \left(\cos^{4}\left(b x +a \right)\right)}{35}+\frac{64 \left(\cos^{2}\left(b x +a \right)\right)}{35}\right) \sin \left(b x +a \right)}{1287}}{b}"," ",0,"512/b*(-1/15*sin(b*x+a)^5*cos(b*x+a)^10-1/39*sin(b*x+a)^3*cos(b*x+a)^10-1/143*sin(b*x+a)*cos(b*x+a)^10+1/1287*(128/35+cos(b*x+a)^8+8/7*cos(b*x+a)^6+48/35*cos(b*x+a)^4+64/35*cos(b*x+a)^2)*sin(b*x+a))","A"
61,1,53,40,0.768000," ","int(csc(b*x+a)^3*sin(2*b*x+2*a)^8,x)","\frac{-\frac{256 \left(\sin^{4}\left(b x +a \right)\right) \left(\cos^{9}\left(b x +a \right)\right)}{13}-\frac{1024 \left(\sin^{2}\left(b x +a \right)\right) \left(\cos^{9}\left(b x +a \right)\right)}{143}-\frac{2048 \left(\cos^{9}\left(b x +a \right)\right)}{1287}}{b}"," ",0,"256/b*(-1/13*sin(b*x+a)^4*cos(b*x+a)^9-4/143*sin(b*x+a)^2*cos(b*x+a)^9-8/1287*cos(b*x+a)^9)","A"
62,1,79,53,0.986000," ","int(csc(b*x+a)^3*sin(2*b*x+2*a)^7,x)","\frac{-\frac{128 \left(\sin^{3}\left(b x +a \right)\right) \left(\cos^{8}\left(b x +a \right)\right)}{11}-\frac{128 \sin \left(b x +a \right) \left(\cos^{8}\left(b x +a \right)\right)}{33}+\frac{128 \left(\frac{16}{5}+\cos^{6}\left(b x +a \right)+\frac{6 \left(\cos^{4}\left(b x +a \right)\right)}{5}+\frac{8 \left(\cos^{2}\left(b x +a \right)\right)}{5}\right) \sin \left(b x +a \right)}{231}}{b}"," ",0,"128/b*(-1/11*sin(b*x+a)^3*cos(b*x+a)^8-1/33*sin(b*x+a)*cos(b*x+a)^8+1/231*(16/5+cos(b*x+a)^6+6/5*cos(b*x+a)^4+8/5*cos(b*x+a)^2)*sin(b*x+a))","A"
63,1,35,27,0.671000," ","int(csc(b*x+a)^3*sin(2*b*x+2*a)^6,x)","\frac{-\frac{64 \left(\sin^{2}\left(b x +a \right)\right) \left(\cos^{7}\left(b x +a \right)\right)}{9}-\frac{128 \left(\cos^{7}\left(b x +a \right)\right)}{63}}{b}"," ",0,"64/b*(-1/9*sin(b*x+a)^2*cos(b*x+a)^7-2/63*cos(b*x+a)^7)","A"
64,1,51,40,0.959000," ","int(csc(b*x+a)^3*sin(2*b*x+2*a)^5,x)","\frac{-\frac{32 \sin \left(b x +a \right) \left(\cos^{6}\left(b x +a \right)\right)}{7}+\frac{32 \left(\frac{8}{3}+\cos^{4}\left(b x +a \right)+\frac{4 \left(\cos^{2}\left(b x +a \right)\right)}{3}\right) \sin \left(b x +a \right)}{35}}{b}"," ",0,"32/b*(-1/7*sin(b*x+a)*cos(b*x+a)^6+1/35*(8/3+cos(b*x+a)^4+4/3*cos(b*x+a)^2)*sin(b*x+a))","A"
65,1,14,13,0.582000," ","int(csc(b*x+a)^3*sin(2*b*x+2*a)^4,x)","-\frac{16 \left(\cos^{5}\left(b x +a \right)\right)}{5 b}"," ",0,"-16/5*cos(b*x+a)^5/b","A"
66,1,22,25,0.819000," ","int(csc(b*x+a)^3*sin(2*b*x+2*a)^3,x)","\frac{8 \left(2+\cos^{2}\left(b x +a \right)\right) \sin \left(b x +a \right)}{3 b}"," ",0,"8/3/b*(2+cos(b*x+a)^2)*sin(b*x+a)","A"
67,1,34,24,0.568000," ","int(csc(b*x+a)^3*sin(2*b*x+2*a)^2,x)","\frac{4 \cos \left(b x +a \right)}{b}+\frac{4 \ln \left(\csc \left(b x +a \right)-\cot \left(b x +a \right)\right)}{b}"," ",0,"4*cos(b*x+a)/b+4/b*ln(csc(b*x+a)-cot(b*x+a))","A"
68,1,14,11,0.294000," ","int(csc(b*x+a)^3*sin(2*b*x+2*a),x)","-\frac{2}{b \sin \left(b x +a \right)}"," ",0,"-2/b/sin(b*x+a)","A"
69,1,47,37,0.893000," ","int(csc(b*x+a)^3*csc(2*b*x+2*a),x)","-\frac{1}{6 b \sin \left(b x +a \right)^{3}}-\frac{1}{2 b \sin \left(b x +a \right)}+\frac{\ln \left(\sec \left(b x +a \right)+\tan \left(b x +a \right)\right)}{2 b}"," ",0,"-1/6/b/sin(b*x+a)^3-1/2/b/sin(b*x+a)+1/2/b*ln(sec(b*x+a)+tan(b*x+a))","A"
70,1,78,62,0.738000," ","int(csc(b*x+a)^3*csc(2*b*x+2*a)^2,x)","-\frac{1}{16 b \sin \left(b x +a \right)^{4} \cos \left(b x +a \right)}-\frac{5}{32 b \sin \left(b x +a \right)^{2} \cos \left(b x +a \right)}+\frac{15}{32 b \cos \left(b x +a \right)}+\frac{15 \ln \left(\csc \left(b x +a \right)-\cot \left(b x +a \right)\right)}{32 b}"," ",0,"-1/16/b/sin(b*x+a)^4/cos(b*x+a)-5/32/b/sin(b*x+a)^2/cos(b*x+a)+15/32/b/cos(b*x+a)+15/32/b*ln(csc(b*x+a)-cot(b*x+a))","A"
71,1,97,71,0.706000," ","int(csc(b*x+a)^3*csc(2*b*x+2*a)^3,x)","-\frac{1}{40 b \sin \left(b x +a \right)^{5} \cos \left(b x +a \right)^{2}}-\frac{7}{120 b \sin \left(b x +a \right)^{3} \cos \left(b x +a \right)^{2}}+\frac{7}{48 b \sin \left(b x +a \right) \cos \left(b x +a \right)^{2}}-\frac{7}{16 b \sin \left(b x +a \right)}+\frac{7 \ln \left(\sec \left(b x +a \right)+\tan \left(b x +a \right)\right)}{16 b}"," ",0,"-1/40/b/sin(b*x+a)^5/cos(b*x+a)^2-7/120/b/sin(b*x+a)^3/cos(b*x+a)^2+7/48/b/sin(b*x+a)/cos(b*x+a)^2-7/16/b/sin(b*x+a)+7/16/b*ln(sec(b*x+a)+tan(b*x+a))","A"
72,1,120,100,0.854000," ","int(csc(b*x+a)^3*csc(2*b*x+2*a)^4,x)","-\frac{1}{96 b \sin \left(b x +a \right)^{6} \cos \left(b x +a \right)^{3}}-\frac{3}{128 b \sin \left(b x +a \right)^{4} \cos \left(b x +a \right)^{3}}+\frac{7}{128 b \sin \left(b x +a \right)^{2} \cos \left(b x +a \right)^{3}}-\frac{35}{256 b \sin \left(b x +a \right)^{2} \cos \left(b x +a \right)}+\frac{105}{256 b \cos \left(b x +a \right)}+\frac{105 \ln \left(\csc \left(b x +a \right)-\cot \left(b x +a \right)\right)}{256 b}"," ",0,"-1/96/b/sin(b*x+a)^6/cos(b*x+a)^3-3/128/b/sin(b*x+a)^4/cos(b*x+a)^3+7/128/b/sin(b*x+a)^2/cos(b*x+a)^3-35/256/b/sin(b*x+a)^2/cos(b*x+a)+105/256/b/cos(b*x+a)+105/256/b*ln(csc(b*x+a)-cot(b*x+a))","A"
73,1,183661406,118,89.385000," ","int(sin(b*x+a)*sin(2*b*x+2*a)^(5/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
74,1,65166862,96,25.674000," ","int(sin(b*x+a)*sin(2*b*x+2*a)^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
75,1,6214674,74,2.853000," ","int(sin(b*x+a)*sin(2*b*x+2*a)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
76,1,15972263,52,3.214000," ","int(sin(b*x+a)/sin(2*b*x+2*a)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
77,1,59119746,21,11.404000," ","int(sin(b*x+a)/sin(2*b*x+2*a)^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
78,1,597,45,41.618000," ","int(sin(b*x+a)/sin(2*b*x+2*a)^(5/2),x)","\frac{\sqrt{-\frac{\tan \left(\frac{b x}{2}+\frac{a}{2}\right)}{\tan^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)-1}}\, \left(6 \sqrt{\tan \left(\frac{b x}{2}+\frac{a}{2}\right) \left(\tan^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)-1\right)}\, \sqrt{\tan \left(\frac{b x}{2}+\frac{a}{2}\right)+1}\, \sqrt{-2 \tan \left(\frac{b x}{2}+\frac{a}{2}\right)+2}\, \sqrt{-\tan \left(\frac{b x}{2}+\frac{a}{2}\right)}\, \EllipticE \left(\sqrt{\tan \left(\frac{b x}{2}+\frac{a}{2}\right)+1}, \frac{\sqrt{2}}{2}\right) \left(\tan^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-3 \sqrt{\tan \left(\frac{b x}{2}+\frac{a}{2}\right) \left(\tan^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)-1\right)}\, \sqrt{\tan \left(\frac{b x}{2}+\frac{a}{2}\right)+1}\, \sqrt{-2 \tan \left(\frac{b x}{2}+\frac{a}{2}\right)+2}\, \sqrt{-\tan \left(\frac{b x}{2}+\frac{a}{2}\right)}\, \EllipticF \left(\sqrt{\tan \left(\frac{b x}{2}+\frac{a}{2}\right)+1}, \frac{\sqrt{2}}{2}\right) \left(\tan^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+6 \sqrt{\tan \left(\frac{b x}{2}+\frac{a}{2}\right) \left(\tan^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)-1\right)}\, \sqrt{\tan \left(\frac{b x}{2}+\frac{a}{2}\right)+1}\, \sqrt{-2 \tan \left(\frac{b x}{2}+\frac{a}{2}\right)+2}\, \sqrt{-\tan \left(\frac{b x}{2}+\frac{a}{2}\right)}\, \EllipticE \left(\sqrt{\tan \left(\frac{b x}{2}+\frac{a}{2}\right)+1}, \frac{\sqrt{2}}{2}\right)-3 \sqrt{\tan \left(\frac{b x}{2}+\frac{a}{2}\right) \left(\tan^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)-1\right)}\, \sqrt{\tan \left(\frac{b x}{2}+\frac{a}{2}\right)+1}\, \sqrt{-2 \tan \left(\frac{b x}{2}+\frac{a}{2}\right)+2}\, \sqrt{-\tan \left(\frac{b x}{2}+\frac{a}{2}\right)}\, \EllipticF \left(\sqrt{\tan \left(\frac{b x}{2}+\frac{a}{2}\right)+1}, \frac{\sqrt{2}}{2}\right)+2 \sqrt{\tan \left(\frac{b x}{2}+\frac{a}{2}\right) \left(\tan^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)-1\right)}\, \left(\tan^{4}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+2 \left(\tan^{4}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) \sqrt{\tan^{3}\left(\frac{b x}{2}+\frac{a}{2}\right)-\tan \left(\frac{b x}{2}+\frac{a}{2}\right)}-2 \sqrt{\tan \left(\frac{b x}{2}+\frac{a}{2}\right) \left(\tan^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)-1\right)}\, \left(\tan^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-2 \sqrt{\tan^{3}\left(\frac{b x}{2}+\frac{a}{2}\right)-\tan \left(\frac{b x}{2}+\frac{a}{2}\right)}\right)}{8 b \tan \left(\frac{b x}{2}+\frac{a}{2}\right) \left(1+\tan^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) \sqrt{\tan^{3}\left(\frac{b x}{2}+\frac{a}{2}\right)-\tan \left(\frac{b x}{2}+\frac{a}{2}\right)}}"," ",0,"1/8/b*(-tan(1/2*b*x+1/2*a)/(tan(1/2*b*x+1/2*a)^2-1))^(1/2)*(6*(tan(1/2*b*x+1/2*a)*(tan(1/2*b*x+1/2*a)^2-1))^(1/2)*(tan(1/2*b*x+1/2*a)+1)^(1/2)*(-2*tan(1/2*b*x+1/2*a)+2)^(1/2)*(-tan(1/2*b*x+1/2*a))^(1/2)*EllipticE((tan(1/2*b*x+1/2*a)+1)^(1/2),1/2*2^(1/2))*tan(1/2*b*x+1/2*a)^2-3*(tan(1/2*b*x+1/2*a)*(tan(1/2*b*x+1/2*a)^2-1))^(1/2)*(tan(1/2*b*x+1/2*a)+1)^(1/2)*(-2*tan(1/2*b*x+1/2*a)+2)^(1/2)*(-tan(1/2*b*x+1/2*a))^(1/2)*EllipticF((tan(1/2*b*x+1/2*a)+1)^(1/2),1/2*2^(1/2))*tan(1/2*b*x+1/2*a)^2+6*(tan(1/2*b*x+1/2*a)*(tan(1/2*b*x+1/2*a)^2-1))^(1/2)*(tan(1/2*b*x+1/2*a)+1)^(1/2)*(-2*tan(1/2*b*x+1/2*a)+2)^(1/2)*(-tan(1/2*b*x+1/2*a))^(1/2)*EllipticE((tan(1/2*b*x+1/2*a)+1)^(1/2),1/2*2^(1/2))-3*(tan(1/2*b*x+1/2*a)*(tan(1/2*b*x+1/2*a)^2-1))^(1/2)*(tan(1/2*b*x+1/2*a)+1)^(1/2)*(-2*tan(1/2*b*x+1/2*a)+2)^(1/2)*(-tan(1/2*b*x+1/2*a))^(1/2)*EllipticF((tan(1/2*b*x+1/2*a)+1)^(1/2),1/2*2^(1/2))+2*(tan(1/2*b*x+1/2*a)*(tan(1/2*b*x+1/2*a)^2-1))^(1/2)*tan(1/2*b*x+1/2*a)^4+2*tan(1/2*b*x+1/2*a)^4*(tan(1/2*b*x+1/2*a)^3-tan(1/2*b*x+1/2*a))^(1/2)-2*(tan(1/2*b*x+1/2*a)*(tan(1/2*b*x+1/2*a)^2-1))^(1/2)*tan(1/2*b*x+1/2*a)^2-2*(tan(1/2*b*x+1/2*a)^3-tan(1/2*b*x+1/2*a))^(1/2))/tan(1/2*b*x+1/2*a)/(1+tan(1/2*b*x+1/2*a)^2)/(tan(1/2*b*x+1/2*a)^3-tan(1/2*b*x+1/2*a))^(1/2)","C"
79,-1,0,67,180.000000," ","int(sin(b*x+a)/sin(2*b*x+2*a)^(7/2),x)","\int \frac{\sin \left(b x +a \right)}{\sin \left(2 b x +2 a \right)^{\frac{7}{2}}}\, dx"," ",0,"int(sin(b*x+a)/sin(2*b*x+2*a)^(7/2),x)","F"
80,-1,0,89,180.000000," ","int(sin(b*x+a)/sin(2*b*x+2*a)^(9/2),x)","\int \frac{\sin \left(b x +a \right)}{\sin \left(2 b x +2 a \right)^{\frac{9}{2}}}\, dx"," ",0,"int(sin(b*x+a)/sin(2*b*x+2*a)^(9/2),x)","F"
81,-1,0,109,180.000000," ","int(sin(b*x+a)^2*sin(2*b*x+2*a)^(7/2),x)","\int \left(\sin^{2}\left(b x +a \right)\right) \left(\sin^{\frac{7}{2}}\left(2 b x +2 a \right)\right)\, dx"," ",0,"int(sin(b*x+a)^2*sin(2*b*x+2*a)^(7/2),x)","F"
82,1,278615779,84,167.057000," ","int(sin(b*x+a)^2*sin(2*b*x+2*a)^(5/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
83,1,172368074,84,71.760000," ","int(sin(b*x+a)^2*sin(2*b*x+2*a)^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
84,1,16549859,59,5.709000," ","int(sin(b*x+a)^2*sin(2*b*x+2*a)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
85,1,53360209,59,13.507000," ","int(sin(b*x+a)^2/sin(2*b*x+2*a)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
86,1,83175028,66,15.515000," ","int(sin(b*x+a)^2/sin(2*b*x+2*a)^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
87,1,123,67,59.888000," ","int(sin(b*x+a)^2/sin(2*b*x+2*a)^(5/2),x)","\frac{\sqrt{1+\sin \left(2 b x +2 a \right)}\, \sqrt{-2 \sin \left(2 b x +2 a \right)+2}\, \sqrt{-\sin \left(2 b x +2 a \right)}\, \EllipticF \left(\sqrt{1+\sin \left(2 b x +2 a \right)}, \frac{\sqrt{2}}{2}\right) \sin \left(2 b x +2 a \right)-2 \left(\cos^{2}\left(2 b x +2 a \right)\right)+2 \cos \left(2 b x +2 a \right)}{12 \sin \left(2 b x +2 a \right)^{\frac{3}{2}} \cos \left(2 b x +2 a \right) b}"," ",0,"1/12/sin(2*b*x+2*a)^(3/2)/cos(2*b*x+2*a)*((1+sin(2*b*x+2*a))^(1/2)*(-2*sin(2*b*x+2*a)+2)^(1/2)*(-sin(2*b*x+2*a))^(1/2)*EllipticF((1+sin(2*b*x+2*a))^(1/2),1/2*2^(1/2))*sin(2*b*x+2*a)-2*cos(2*b*x+2*a)^2+2*cos(2*b*x+2*a))/b","A"
88,-1,0,92,180.000000," ","int(sin(b*x+a)^2/sin(2*b*x+2*a)^(7/2),x)","\int \frac{\sin^{2}\left(b x +a \right)}{\sin \left(2 b x +2 a \right)^{\frac{7}{2}}}\, dx"," ",0,"int(sin(b*x+a)^2/sin(2*b*x+2*a)^(7/2),x)","F"
89,1,322540527,118,194.690000," ","int(sin(b*x+a)^3*sin(2*b*x+2*a)^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
90,1,47453403,96,23.188000," ","int(sin(b*x+a)^3*sin(2*b*x+2*a)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
91,1,155804040,74,46.944000," ","int(sin(b*x+a)^3/sin(2*b*x+2*a)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
92,1,149378290,73,52.777000," ","int(sin(b*x+a)^3/sin(2*b*x+2*a)^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
93,1,727,24,183.929000," ","int(sin(b*x+a)^3/sin(2*b*x+2*a)^(5/2),x)","-\frac{\sqrt{-\frac{\tan \left(\frac{b x}{2}+\frac{a}{2}\right)}{\tan^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)-1}}\, \left(\tan^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)-1\right) \left(6 \sqrt{\tan \left(\frac{b x}{2}+\frac{a}{2}\right)+1}\, \sqrt{-2 \tan \left(\frac{b x}{2}+\frac{a}{2}\right)+2}\, \sqrt{-\tan \left(\frac{b x}{2}+\frac{a}{2}\right)}\, \EllipticE \left(\sqrt{\tan \left(\frac{b x}{2}+\frac{a}{2}\right)+1}, \frac{\sqrt{2}}{2}\right) \left(\tan^{6}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-3 \sqrt{\tan \left(\frac{b x}{2}+\frac{a}{2}\right)+1}\, \sqrt{-2 \tan \left(\frac{b x}{2}+\frac{a}{2}\right)+2}\, \sqrt{-\tan \left(\frac{b x}{2}+\frac{a}{2}\right)}\, \EllipticF \left(\sqrt{\tan \left(\frac{b x}{2}+\frac{a}{2}\right)+1}, \frac{\sqrt{2}}{2}\right) \left(\tan^{6}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+18 \sqrt{\tan \left(\frac{b x}{2}+\frac{a}{2}\right)+1}\, \sqrt{-2 \tan \left(\frac{b x}{2}+\frac{a}{2}\right)+2}\, \sqrt{-\tan \left(\frac{b x}{2}+\frac{a}{2}\right)}\, \EllipticE \left(\sqrt{\tan \left(\frac{b x}{2}+\frac{a}{2}\right)+1}, \frac{\sqrt{2}}{2}\right) \left(\tan^{4}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-9 \sqrt{\tan \left(\frac{b x}{2}+\frac{a}{2}\right)+1}\, \sqrt{-2 \tan \left(\frac{b x}{2}+\frac{a}{2}\right)+2}\, \sqrt{-\tan \left(\frac{b x}{2}+\frac{a}{2}\right)}\, \EllipticF \left(\sqrt{\tan \left(\frac{b x}{2}+\frac{a}{2}\right)+1}, \frac{\sqrt{2}}{2}\right) \left(\tan^{4}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+6 \left(\tan^{8}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+18 \sqrt{\tan \left(\frac{b x}{2}+\frac{a}{2}\right)+1}\, \sqrt{-2 \tan \left(\frac{b x}{2}+\frac{a}{2}\right)+2}\, \sqrt{-\tan \left(\frac{b x}{2}+\frac{a}{2}\right)}\, \EllipticE \left(\sqrt{\tan \left(\frac{b x}{2}+\frac{a}{2}\right)+1}, \frac{\sqrt{2}}{2}\right) \left(\tan^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-9 \sqrt{\tan \left(\frac{b x}{2}+\frac{a}{2}\right)+1}\, \sqrt{-2 \tan \left(\frac{b x}{2}+\frac{a}{2}\right)+2}\, \sqrt{-\tan \left(\frac{b x}{2}+\frac{a}{2}\right)}\, \EllipticF \left(\sqrt{\tan \left(\frac{b x}{2}+\frac{a}{2}\right)+1}, \frac{\sqrt{2}}{2}\right) \left(\tan^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-2 \left(\tan^{6}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+6 \sqrt{\tan \left(\frac{b x}{2}+\frac{a}{2}\right)+1}\, \sqrt{-2 \tan \left(\frac{b x}{2}+\frac{a}{2}\right)+2}\, \sqrt{-\tan \left(\frac{b x}{2}+\frac{a}{2}\right)}\, \EllipticE \left(\sqrt{\tan \left(\frac{b x}{2}+\frac{a}{2}\right)+1}, \frac{\sqrt{2}}{2}\right)-3 \sqrt{\tan \left(\frac{b x}{2}+\frac{a}{2}\right)+1}\, \sqrt{-2 \tan \left(\frac{b x}{2}+\frac{a}{2}\right)+2}\, \sqrt{-\tan \left(\frac{b x}{2}+\frac{a}{2}\right)}\, \EllipticF \left(\sqrt{\tan \left(\frac{b x}{2}+\frac{a}{2}\right)+1}, \frac{\sqrt{2}}{2}\right)+10 \left(\tan^{4}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-14 \left(\tan^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)\right)}{48 \sqrt{\tan \left(\frac{b x}{2}+\frac{a}{2}\right) \left(\tan^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)-1\right)}\, \left(1+\tan^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)^{3} \sqrt{\tan^{3}\left(\frac{b x}{2}+\frac{a}{2}\right)-\tan \left(\frac{b x}{2}+\frac{a}{2}\right)}\, b}"," ",0,"-1/48*(-tan(1/2*b*x+1/2*a)/(tan(1/2*b*x+1/2*a)^2-1))^(1/2)*(tan(1/2*b*x+1/2*a)^2-1)*(6*(tan(1/2*b*x+1/2*a)+1)^(1/2)*(-2*tan(1/2*b*x+1/2*a)+2)^(1/2)*(-tan(1/2*b*x+1/2*a))^(1/2)*EllipticE((tan(1/2*b*x+1/2*a)+1)^(1/2),1/2*2^(1/2))*tan(1/2*b*x+1/2*a)^6-3*(tan(1/2*b*x+1/2*a)+1)^(1/2)*(-2*tan(1/2*b*x+1/2*a)+2)^(1/2)*(-tan(1/2*b*x+1/2*a))^(1/2)*EllipticF((tan(1/2*b*x+1/2*a)+1)^(1/2),1/2*2^(1/2))*tan(1/2*b*x+1/2*a)^6+18*(tan(1/2*b*x+1/2*a)+1)^(1/2)*(-2*tan(1/2*b*x+1/2*a)+2)^(1/2)*(-tan(1/2*b*x+1/2*a))^(1/2)*EllipticE((tan(1/2*b*x+1/2*a)+1)^(1/2),1/2*2^(1/2))*tan(1/2*b*x+1/2*a)^4-9*(tan(1/2*b*x+1/2*a)+1)^(1/2)*(-2*tan(1/2*b*x+1/2*a)+2)^(1/2)*(-tan(1/2*b*x+1/2*a))^(1/2)*EllipticF((tan(1/2*b*x+1/2*a)+1)^(1/2),1/2*2^(1/2))*tan(1/2*b*x+1/2*a)^4+6*tan(1/2*b*x+1/2*a)^8+18*(tan(1/2*b*x+1/2*a)+1)^(1/2)*(-2*tan(1/2*b*x+1/2*a)+2)^(1/2)*(-tan(1/2*b*x+1/2*a))^(1/2)*EllipticE((tan(1/2*b*x+1/2*a)+1)^(1/2),1/2*2^(1/2))*tan(1/2*b*x+1/2*a)^2-9*(tan(1/2*b*x+1/2*a)+1)^(1/2)*(-2*tan(1/2*b*x+1/2*a)+2)^(1/2)*(-tan(1/2*b*x+1/2*a))^(1/2)*EllipticF((tan(1/2*b*x+1/2*a)+1)^(1/2),1/2*2^(1/2))*tan(1/2*b*x+1/2*a)^2-2*tan(1/2*b*x+1/2*a)^6+6*(tan(1/2*b*x+1/2*a)+1)^(1/2)*(-2*tan(1/2*b*x+1/2*a)+2)^(1/2)*(-tan(1/2*b*x+1/2*a))^(1/2)*EllipticE((tan(1/2*b*x+1/2*a)+1)^(1/2),1/2*2^(1/2))-3*(tan(1/2*b*x+1/2*a)+1)^(1/2)*(-2*tan(1/2*b*x+1/2*a)+2)^(1/2)*(-tan(1/2*b*x+1/2*a))^(1/2)*EllipticF((tan(1/2*b*x+1/2*a)+1)^(1/2),1/2*2^(1/2))+10*tan(1/2*b*x+1/2*a)^4-14*tan(1/2*b*x+1/2*a)^2)/(tan(1/2*b*x+1/2*a)*(tan(1/2*b*x+1/2*a)^2-1))^(1/2)/(1+tan(1/2*b*x+1/2*a)^2)^3/(tan(1/2*b*x+1/2*a)^3-tan(1/2*b*x+1/2*a))^(1/2)/b","C"
94,-1,0,47,180.000000," ","int(sin(b*x+a)^3/sin(2*b*x+2*a)^(7/2),x)","\int \frac{\sin^{3}\left(b x +a \right)}{\sin \left(2 b x +2 a \right)^{\frac{7}{2}}}\, dx"," ",0,"int(sin(b*x+a)^3/sin(2*b*x+2*a)^(7/2),x)","F"
95,-1,0,69,180.000000," ","int(sin(b*x+a)^3/sin(2*b*x+2*a)^(9/2),x)","\int \frac{\sin^{3}\left(b x +a \right)}{\sin \left(2 b x +2 a \right)^{\frac{9}{2}}}\, dx"," ",0,"int(sin(b*x+a)^3/sin(2*b*x+2*a)^(9/2),x)","F"
96,-1,0,91,180.000000," ","int(sin(b*x+a)^3/sin(2*b*x+2*a)^(11/2),x)","\int \frac{\sin^{3}\left(b x +a \right)}{\sin \left(2 b x +2 a \right)^{\frac{11}{2}}}\, dx"," ",0,"int(sin(b*x+a)^3/sin(2*b*x+2*a)^(11/2),x)","F"
97,1,973,118,19.859000," ","int(csc(b*x+a)*sin(2*b*x+2*a)^(7/2),x)","-\frac{16 \sqrt{-\frac{\tan \left(\frac{b x}{2}+\frac{a}{2}\right)}{\tan^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)-1}}\, \left(6 \sqrt{\tan \left(\frac{b x}{2}+\frac{a}{2}\right) \left(\tan \left(\frac{b x}{2}+\frac{a}{2}\right)-1\right) \left(\tan \left(\frac{b x}{2}+\frac{a}{2}\right)+1\right)}\, \sqrt{\tan \left(\frac{b x}{2}+\frac{a}{2}\right)+1}\, \sqrt{-2 \tan \left(\frac{b x}{2}+\frac{a}{2}\right)+2}\, \sqrt{-\tan \left(\frac{b x}{2}+\frac{a}{2}\right)}\, \EllipticE \left(\sqrt{\tan \left(\frac{b x}{2}+\frac{a}{2}\right)+1}, \frac{\sqrt{2}}{2}\right) \left(\tan^{4}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-3 \sqrt{\tan \left(\frac{b x}{2}+\frac{a}{2}\right) \left(\tan \left(\frac{b x}{2}+\frac{a}{2}\right)-1\right) \left(\tan \left(\frac{b x}{2}+\frac{a}{2}\right)+1\right)}\, \sqrt{\tan \left(\frac{b x}{2}+\frac{a}{2}\right)+1}\, \sqrt{-2 \tan \left(\frac{b x}{2}+\frac{a}{2}\right)+2}\, \sqrt{-\tan \left(\frac{b x}{2}+\frac{a}{2}\right)}\, \EllipticF \left(\sqrt{\tan \left(\frac{b x}{2}+\frac{a}{2}\right)+1}, \frac{\sqrt{2}}{2}\right) \left(\tan^{4}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-12 \sqrt{\tan \left(\frac{b x}{2}+\frac{a}{2}\right) \left(\tan \left(\frac{b x}{2}+\frac{a}{2}\right)-1\right) \left(\tan \left(\frac{b x}{2}+\frac{a}{2}\right)+1\right)}\, \sqrt{\tan \left(\frac{b x}{2}+\frac{a}{2}\right)+1}\, \sqrt{-2 \tan \left(\frac{b x}{2}+\frac{a}{2}\right)+2}\, \sqrt{-\tan \left(\frac{b x}{2}+\frac{a}{2}\right)}\, \EllipticE \left(\sqrt{\tan \left(\frac{b x}{2}+\frac{a}{2}\right)+1}, \frac{\sqrt{2}}{2}\right) \left(\tan^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+6 \sqrt{\tan \left(\frac{b x}{2}+\frac{a}{2}\right) \left(\tan \left(\frac{b x}{2}+\frac{a}{2}\right)-1\right) \left(\tan \left(\frac{b x}{2}+\frac{a}{2}\right)+1\right)}\, \sqrt{\tan \left(\frac{b x}{2}+\frac{a}{2}\right)+1}\, \sqrt{-2 \tan \left(\frac{b x}{2}+\frac{a}{2}\right)+2}\, \sqrt{-\tan \left(\frac{b x}{2}+\frac{a}{2}\right)}\, \EllipticF \left(\sqrt{\tan \left(\frac{b x}{2}+\frac{a}{2}\right)+1}, \frac{\sqrt{2}}{2}\right) \left(\tan^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+6 \left(\tan^{6}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) \sqrt{\tan^{3}\left(\frac{b x}{2}+\frac{a}{2}\right)-\tan \left(\frac{b x}{2}+\frac{a}{2}\right)}+6 \sqrt{\tan \left(\frac{b x}{2}+\frac{a}{2}\right) \left(\tan \left(\frac{b x}{2}+\frac{a}{2}\right)-1\right) \left(\tan \left(\frac{b x}{2}+\frac{a}{2}\right)+1\right)}\, \sqrt{\tan \left(\frac{b x}{2}+\frac{a}{2}\right)+1}\, \sqrt{-2 \tan \left(\frac{b x}{2}+\frac{a}{2}\right)+2}\, \sqrt{-\tan \left(\frac{b x}{2}+\frac{a}{2}\right)}\, \EllipticE \left(\sqrt{\tan \left(\frac{b x}{2}+\frac{a}{2}\right)+1}, \frac{\sqrt{2}}{2}\right)-3 \sqrt{\tan \left(\frac{b x}{2}+\frac{a}{2}\right) \left(\tan \left(\frac{b x}{2}+\frac{a}{2}\right)-1\right) \left(\tan \left(\frac{b x}{2}+\frac{a}{2}\right)+1\right)}\, \sqrt{\tan \left(\frac{b x}{2}+\frac{a}{2}\right)+1}\, \sqrt{-2 \tan \left(\frac{b x}{2}+\frac{a}{2}\right)+2}\, \sqrt{-\tan \left(\frac{b x}{2}+\frac{a}{2}\right)}\, \EllipticF \left(\sqrt{\tan \left(\frac{b x}{2}+\frac{a}{2}\right)+1}, \frac{\sqrt{2}}{2}\right)-4 \sqrt{\tan \left(\frac{b x}{2}+\frac{a}{2}\right) \left(\tan \left(\frac{b x}{2}+\frac{a}{2}\right)-1\right) \left(\tan \left(\frac{b x}{2}+\frac{a}{2}\right)+1\right)}\, \left(\tan^{4}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-12 \left(\tan^{4}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) \sqrt{\tan^{3}\left(\frac{b x}{2}+\frac{a}{2}\right)-\tan \left(\frac{b x}{2}+\frac{a}{2}\right)}-4 \sqrt{\tan \left(\frac{b x}{2}+\frac{a}{2}\right) \left(\tan \left(\frac{b x}{2}+\frac{a}{2}\right)-1\right) \left(\tan \left(\frac{b x}{2}+\frac{a}{2}\right)+1\right)}\, \left(\tan^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+6 \left(\tan^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) \sqrt{\tan^{3}\left(\frac{b x}{2}+\frac{a}{2}\right)-\tan \left(\frac{b x}{2}+\frac{a}{2}\right)}\right)}{5 b \sqrt{\tan \left(\frac{b x}{2}+\frac{a}{2}\right) \left(\tan^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)-1\right)}\, \sqrt{\tan \left(\frac{b x}{2}+\frac{a}{2}\right) \left(\tan \left(\frac{b x}{2}+\frac{a}{2}\right)-1\right) \left(\tan \left(\frac{b x}{2}+\frac{a}{2}\right)+1\right)}\, \sqrt{\tan^{3}\left(\frac{b x}{2}+\frac{a}{2}\right)-\tan \left(\frac{b x}{2}+\frac{a}{2}\right)}\, \left(\tan \left(\frac{b x}{2}+\frac{a}{2}\right)-1\right) \left(\tan \left(\frac{b x}{2}+\frac{a}{2}\right)+1\right)}"," ",0,"-16/5/b*(-tan(1/2*b*x+1/2*a)/(tan(1/2*b*x+1/2*a)^2-1))^(1/2)*(6*(tan(1/2*b*x+1/2*a)*(tan(1/2*b*x+1/2*a)-1)*(tan(1/2*b*x+1/2*a)+1))^(1/2)*(tan(1/2*b*x+1/2*a)+1)^(1/2)*(-2*tan(1/2*b*x+1/2*a)+2)^(1/2)*(-tan(1/2*b*x+1/2*a))^(1/2)*EllipticE((tan(1/2*b*x+1/2*a)+1)^(1/2),1/2*2^(1/2))*tan(1/2*b*x+1/2*a)^4-3*(tan(1/2*b*x+1/2*a)*(tan(1/2*b*x+1/2*a)-1)*(tan(1/2*b*x+1/2*a)+1))^(1/2)*(tan(1/2*b*x+1/2*a)+1)^(1/2)*(-2*tan(1/2*b*x+1/2*a)+2)^(1/2)*(-tan(1/2*b*x+1/2*a))^(1/2)*EllipticF((tan(1/2*b*x+1/2*a)+1)^(1/2),1/2*2^(1/2))*tan(1/2*b*x+1/2*a)^4-12*(tan(1/2*b*x+1/2*a)*(tan(1/2*b*x+1/2*a)-1)*(tan(1/2*b*x+1/2*a)+1))^(1/2)*(tan(1/2*b*x+1/2*a)+1)^(1/2)*(-2*tan(1/2*b*x+1/2*a)+2)^(1/2)*(-tan(1/2*b*x+1/2*a))^(1/2)*EllipticE((tan(1/2*b*x+1/2*a)+1)^(1/2),1/2*2^(1/2))*tan(1/2*b*x+1/2*a)^2+6*(tan(1/2*b*x+1/2*a)*(tan(1/2*b*x+1/2*a)-1)*(tan(1/2*b*x+1/2*a)+1))^(1/2)*(tan(1/2*b*x+1/2*a)+1)^(1/2)*(-2*tan(1/2*b*x+1/2*a)+2)^(1/2)*(-tan(1/2*b*x+1/2*a))^(1/2)*EllipticF((tan(1/2*b*x+1/2*a)+1)^(1/2),1/2*2^(1/2))*tan(1/2*b*x+1/2*a)^2+6*tan(1/2*b*x+1/2*a)^6*(tan(1/2*b*x+1/2*a)^3-tan(1/2*b*x+1/2*a))^(1/2)+6*(tan(1/2*b*x+1/2*a)*(tan(1/2*b*x+1/2*a)-1)*(tan(1/2*b*x+1/2*a)+1))^(1/2)*(tan(1/2*b*x+1/2*a)+1)^(1/2)*(-2*tan(1/2*b*x+1/2*a)+2)^(1/2)*(-tan(1/2*b*x+1/2*a))^(1/2)*EllipticE((tan(1/2*b*x+1/2*a)+1)^(1/2),1/2*2^(1/2))-3*(tan(1/2*b*x+1/2*a)*(tan(1/2*b*x+1/2*a)-1)*(tan(1/2*b*x+1/2*a)+1))^(1/2)*(tan(1/2*b*x+1/2*a)+1)^(1/2)*(-2*tan(1/2*b*x+1/2*a)+2)^(1/2)*(-tan(1/2*b*x+1/2*a))^(1/2)*EllipticF((tan(1/2*b*x+1/2*a)+1)^(1/2),1/2*2^(1/2))-4*(tan(1/2*b*x+1/2*a)*(tan(1/2*b*x+1/2*a)-1)*(tan(1/2*b*x+1/2*a)+1))^(1/2)*tan(1/2*b*x+1/2*a)^4-12*tan(1/2*b*x+1/2*a)^4*(tan(1/2*b*x+1/2*a)^3-tan(1/2*b*x+1/2*a))^(1/2)-4*(tan(1/2*b*x+1/2*a)*(tan(1/2*b*x+1/2*a)-1)*(tan(1/2*b*x+1/2*a)+1))^(1/2)*tan(1/2*b*x+1/2*a)^2+6*tan(1/2*b*x+1/2*a)^2*(tan(1/2*b*x+1/2*a)^3-tan(1/2*b*x+1/2*a))^(1/2))/(tan(1/2*b*x+1/2*a)*(tan(1/2*b*x+1/2*a)^2-1))^(1/2)/(tan(1/2*b*x+1/2*a)*(tan(1/2*b*x+1/2*a)-1)*(tan(1/2*b*x+1/2*a)+1))^(1/2)/(tan(1/2*b*x+1/2*a)^3-tan(1/2*b*x+1/2*a))^(1/2)/(tan(1/2*b*x+1/2*a)-1)/(tan(1/2*b*x+1/2*a)+1)","C"
98,1,243,96,20.549000," ","int(csc(b*x+a)*sin(2*b*x+2*a)^(5/2),x)","-\frac{8 \sqrt{-\frac{\tan \left(\frac{b x}{2}+\frac{a}{2}\right)}{\tan^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)-1}}\, \left(\sqrt{\tan \left(\frac{b x}{2}+\frac{a}{2}\right)+1}\, \sqrt{-2 \tan \left(\frac{b x}{2}+\frac{a}{2}\right)+2}\, \sqrt{-\tan \left(\frac{b x}{2}+\frac{a}{2}\right)}\, \EllipticF \left(\sqrt{\tan \left(\frac{b x}{2}+\frac{a}{2}\right)+1}, \frac{\sqrt{2}}{2}\right) \left(\tan^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-\sqrt{\tan \left(\frac{b x}{2}+\frac{a}{2}\right)+1}\, \sqrt{-2 \tan \left(\frac{b x}{2}+\frac{a}{2}\right)+2}\, \sqrt{-\tan \left(\frac{b x}{2}+\frac{a}{2}\right)}\, \EllipticF \left(\sqrt{\tan \left(\frac{b x}{2}+\frac{a}{2}\right)+1}, \frac{\sqrt{2}}{2}\right)+2 \left(\tan^{3}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+2 \tan \left(\frac{b x}{2}+\frac{a}{2}\right)\right)}{3 b \sqrt{\tan \left(\frac{b x}{2}+\frac{a}{2}\right) \left(\tan^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)-1\right)}\, \sqrt{\tan^{3}\left(\frac{b x}{2}+\frac{a}{2}\right)-\tan \left(\frac{b x}{2}+\frac{a}{2}\right)}}"," ",0,"-8/3/b*(-tan(1/2*b*x+1/2*a)/(tan(1/2*b*x+1/2*a)^2-1))^(1/2)*((tan(1/2*b*x+1/2*a)+1)^(1/2)*(-2*tan(1/2*b*x+1/2*a)+2)^(1/2)*(-tan(1/2*b*x+1/2*a))^(1/2)*EllipticF((tan(1/2*b*x+1/2*a)+1)^(1/2),1/2*2^(1/2))*tan(1/2*b*x+1/2*a)^2-(tan(1/2*b*x+1/2*a)+1)^(1/2)*(-2*tan(1/2*b*x+1/2*a)+2)^(1/2)*(-tan(1/2*b*x+1/2*a))^(1/2)*EllipticF((tan(1/2*b*x+1/2*a)+1)^(1/2),1/2*2^(1/2))+2*tan(1/2*b*x+1/2*a)^3+2*tan(1/2*b*x+1/2*a))/(tan(1/2*b*x+1/2*a)*(tan(1/2*b*x+1/2*a)^2-1))^(1/2)/(tan(1/2*b*x+1/2*a)^3-tan(1/2*b*x+1/2*a))^(1/2)","C"
99,1,362,73,10.365000," ","int(csc(b*x+a)*sin(2*b*x+2*a)^(3/2),x)","\frac{4 \sqrt{-\frac{\tan \left(\frac{b x}{2}+\frac{a}{2}\right)}{\tan^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)-1}}\, \left(\tan^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)-1\right) \left(2 \sqrt{\tan \left(\frac{b x}{2}+\frac{a}{2}\right) \left(\tan \left(\frac{b x}{2}+\frac{a}{2}\right)-1\right) \left(\tan \left(\frac{b x}{2}+\frac{a}{2}\right)+1\right)}\, \sqrt{\tan \left(\frac{b x}{2}+\frac{a}{2}\right)+1}\, \sqrt{-2 \tan \left(\frac{b x}{2}+\frac{a}{2}\right)+2}\, \sqrt{-\tan \left(\frac{b x}{2}+\frac{a}{2}\right)}\, \EllipticE \left(\sqrt{\tan \left(\frac{b x}{2}+\frac{a}{2}\right)+1}, \frac{\sqrt{2}}{2}\right)-\sqrt{\tan \left(\frac{b x}{2}+\frac{a}{2}\right) \left(\tan \left(\frac{b x}{2}+\frac{a}{2}\right)-1\right) \left(\tan \left(\frac{b x}{2}+\frac{a}{2}\right)+1\right)}\, \sqrt{\tan \left(\frac{b x}{2}+\frac{a}{2}\right)+1}\, \sqrt{-2 \tan \left(\frac{b x}{2}+\frac{a}{2}\right)+2}\, \sqrt{-\tan \left(\frac{b x}{2}+\frac{a}{2}\right)}\, \EllipticF \left(\sqrt{\tan \left(\frac{b x}{2}+\frac{a}{2}\right)+1}, \frac{\sqrt{2}}{2}\right)+2 \left(\tan^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) \sqrt{\tan^{3}\left(\frac{b x}{2}+\frac{a}{2}\right)-\tan \left(\frac{b x}{2}+\frac{a}{2}\right)}\right)}{b \sqrt{\tan \left(\frac{b x}{2}+\frac{a}{2}\right) \left(\tan^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)-1\right)}\, \sqrt{\tan \left(\frac{b x}{2}+\frac{a}{2}\right) \left(\tan \left(\frac{b x}{2}+\frac{a}{2}\right)-1\right) \left(\tan \left(\frac{b x}{2}+\frac{a}{2}\right)+1\right)}\, \sqrt{\tan^{3}\left(\frac{b x}{2}+\frac{a}{2}\right)-\tan \left(\frac{b x}{2}+\frac{a}{2}\right)}}"," ",0,"4/b*(-tan(1/2*b*x+1/2*a)/(tan(1/2*b*x+1/2*a)^2-1))^(1/2)*(tan(1/2*b*x+1/2*a)^2-1)*(2*(tan(1/2*b*x+1/2*a)*(tan(1/2*b*x+1/2*a)-1)*(tan(1/2*b*x+1/2*a)+1))^(1/2)*(tan(1/2*b*x+1/2*a)+1)^(1/2)*(-2*tan(1/2*b*x+1/2*a)+2)^(1/2)*(-tan(1/2*b*x+1/2*a))^(1/2)*EllipticE((tan(1/2*b*x+1/2*a)+1)^(1/2),1/2*2^(1/2))-(tan(1/2*b*x+1/2*a)*(tan(1/2*b*x+1/2*a)-1)*(tan(1/2*b*x+1/2*a)+1))^(1/2)*(tan(1/2*b*x+1/2*a)+1)^(1/2)*(-2*tan(1/2*b*x+1/2*a)+2)^(1/2)*(-tan(1/2*b*x+1/2*a))^(1/2)*EllipticF((tan(1/2*b*x+1/2*a)+1)^(1/2),1/2*2^(1/2))+2*tan(1/2*b*x+1/2*a)^2*(tan(1/2*b*x+1/2*a)^3-tan(1/2*b*x+1/2*a))^(1/2))/(tan(1/2*b*x+1/2*a)*(tan(1/2*b*x+1/2*a)^2-1))^(1/2)/(tan(1/2*b*x+1/2*a)*(tan(1/2*b*x+1/2*a)-1)*(tan(1/2*b*x+1/2*a)+1))^(1/2)/(tan(1/2*b*x+1/2*a)^3-tan(1/2*b*x+1/2*a))^(1/2)","C"
100,1,157,51,8.587000," ","int(csc(b*x+a)*sin(2*b*x+2*a)^(1/2),x)","\frac{2 \sqrt{-\frac{\tan \left(\frac{b x}{2}+\frac{a}{2}\right)}{\tan^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)-1}}\, \left(\tan^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)-1\right) \sqrt{\tan \left(\frac{b x}{2}+\frac{a}{2}\right)+1}\, \sqrt{-2 \tan \left(\frac{b x}{2}+\frac{a}{2}\right)+2}\, \sqrt{-\tan \left(\frac{b x}{2}+\frac{a}{2}\right)}\, \EllipticF \left(\sqrt{\tan \left(\frac{b x}{2}+\frac{a}{2}\right)+1}, \frac{\sqrt{2}}{2}\right)}{b \sqrt{\tan \left(\frac{b x}{2}+\frac{a}{2}\right) \left(\tan^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)-1\right)}\, \sqrt{\tan^{3}\left(\frac{b x}{2}+\frac{a}{2}\right)-\tan \left(\frac{b x}{2}+\frac{a}{2}\right)}}"," ",0,"2/b*(-tan(1/2*b*x+1/2*a)/(tan(1/2*b*x+1/2*a)^2-1))^(1/2)*(tan(1/2*b*x+1/2*a)^2-1)/(tan(1/2*b*x+1/2*a)*(tan(1/2*b*x+1/2*a)^2-1))^(1/2)*(tan(1/2*b*x+1/2*a)+1)^(1/2)*(-2*tan(1/2*b*x+1/2*a)+2)^(1/2)*(-tan(1/2*b*x+1/2*a))^(1/2)/(tan(1/2*b*x+1/2*a)^3-tan(1/2*b*x+1/2*a))^(1/2)*EllipticF((tan(1/2*b*x+1/2*a)+1)^(1/2),1/2*2^(1/2))","C"
101,1,308,22,9.957000," ","int(csc(b*x+a)/sin(2*b*x+2*a)^(1/2),x)","\frac{\sqrt{-\frac{\tan \left(\frac{b x}{2}+\frac{a}{2}\right)}{\tan^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)-1}}\, \left(2 \sqrt{\tan \left(\frac{b x}{2}+\frac{a}{2}\right) \left(\tan^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)-1\right)}\, \sqrt{\tan \left(\frac{b x}{2}+\frac{a}{2}\right)+1}\, \sqrt{-2 \tan \left(\frac{b x}{2}+\frac{a}{2}\right)+2}\, \sqrt{-\tan \left(\frac{b x}{2}+\frac{a}{2}\right)}\, \EllipticE \left(\sqrt{\tan \left(\frac{b x}{2}+\frac{a}{2}\right)+1}, \frac{\sqrt{2}}{2}\right)-\sqrt{\tan \left(\frac{b x}{2}+\frac{a}{2}\right) \left(\tan^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)-1\right)}\, \sqrt{\tan \left(\frac{b x}{2}+\frac{a}{2}\right)+1}\, \sqrt{-2 \tan \left(\frac{b x}{2}+\frac{a}{2}\right)+2}\, \sqrt{-\tan \left(\frac{b x}{2}+\frac{a}{2}\right)}\, \EllipticF \left(\sqrt{\tan \left(\frac{b x}{2}+\frac{a}{2}\right)+1}, \frac{\sqrt{2}}{2}\right)+\left(\tan^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) \sqrt{\tan^{3}\left(\frac{b x}{2}+\frac{a}{2}\right)-\tan \left(\frac{b x}{2}+\frac{a}{2}\right)}-\sqrt{\tan^{3}\left(\frac{b x}{2}+\frac{a}{2}\right)-\tan \left(\frac{b x}{2}+\frac{a}{2}\right)}\right)}{b \tan \left(\frac{b x}{2}+\frac{a}{2}\right) \sqrt{\tan^{3}\left(\frac{b x}{2}+\frac{a}{2}\right)-\tan \left(\frac{b x}{2}+\frac{a}{2}\right)}}"," ",0,"1/b*(-tan(1/2*b*x+1/2*a)/(tan(1/2*b*x+1/2*a)^2-1))^(1/2)*(2*(tan(1/2*b*x+1/2*a)*(tan(1/2*b*x+1/2*a)^2-1))^(1/2)*(tan(1/2*b*x+1/2*a)+1)^(1/2)*(-2*tan(1/2*b*x+1/2*a)+2)^(1/2)*(-tan(1/2*b*x+1/2*a))^(1/2)*EllipticE((tan(1/2*b*x+1/2*a)+1)^(1/2),1/2*2^(1/2))-(tan(1/2*b*x+1/2*a)*(tan(1/2*b*x+1/2*a)^2-1))^(1/2)*(tan(1/2*b*x+1/2*a)+1)^(1/2)*(-2*tan(1/2*b*x+1/2*a)+2)^(1/2)*(-tan(1/2*b*x+1/2*a))^(1/2)*EllipticF((tan(1/2*b*x+1/2*a)+1)^(1/2),1/2*2^(1/2))+tan(1/2*b*x+1/2*a)^2*(tan(1/2*b*x+1/2*a)^3-tan(1/2*b*x+1/2*a))^(1/2)-(tan(1/2*b*x+1/2*a)^3-tan(1/2*b*x+1/2*a))^(1/2))/tan(1/2*b*x+1/2*a)/(tan(1/2*b*x+1/2*a)^3-tan(1/2*b*x+1/2*a))^(1/2)","C"
102,1,194,45,13.100000," ","int(csc(b*x+a)/sin(2*b*x+2*a)^(3/2),x)","-\frac{\sqrt{-\frac{\tan \left(\frac{b x}{2}+\frac{a}{2}\right)}{\tan^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)-1}}\, \left(\tan^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)-1\right) \left(2 \sqrt{\tan \left(\frac{b x}{2}+\frac{a}{2}\right)+1}\, \sqrt{-2 \tan \left(\frac{b x}{2}+\frac{a}{2}\right)+2}\, \sqrt{-\tan \left(\frac{b x}{2}+\frac{a}{2}\right)}\, \EllipticF \left(\sqrt{\tan \left(\frac{b x}{2}+\frac{a}{2}\right)+1}, \frac{\sqrt{2}}{2}\right) \tan \left(\frac{b x}{2}+\frac{a}{2}\right)-\left(\tan^{4}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+1\right)}{12 b \tan \left(\frac{b x}{2}+\frac{a}{2}\right) \sqrt{\tan \left(\frac{b x}{2}+\frac{a}{2}\right) \left(\tan^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)-1\right)}\, \sqrt{\tan^{3}\left(\frac{b x}{2}+\frac{a}{2}\right)-\tan \left(\frac{b x}{2}+\frac{a}{2}\right)}}"," ",0,"-1/12/b*(-tan(1/2*b*x+1/2*a)/(tan(1/2*b*x+1/2*a)^2-1))^(1/2)*(tan(1/2*b*x+1/2*a)^2-1)/tan(1/2*b*x+1/2*a)*(2*(tan(1/2*b*x+1/2*a)+1)^(1/2)*(-2*tan(1/2*b*x+1/2*a)+2)^(1/2)*(-tan(1/2*b*x+1/2*a))^(1/2)*EllipticF((tan(1/2*b*x+1/2*a)+1)^(1/2),1/2*2^(1/2))*tan(1/2*b*x+1/2*a)-tan(1/2*b*x+1/2*a)^4+1)/(tan(1/2*b*x+1/2*a)*(tan(1/2*b*x+1/2*a)^2-1))^(1/2)/(tan(1/2*b*x+1/2*a)^3-tan(1/2*b*x+1/2*a))^(1/2)","C"
103,1,481,67,37.234000," ","int(csc(b*x+a)/sin(2*b*x+2*a)^(5/2),x)","-\frac{\sqrt{-\frac{\tan \left(\frac{b x}{2}+\frac{a}{2}\right)}{\tan^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)-1}}\, \left(24 \sqrt{\tan \left(\frac{b x}{2}+\frac{a}{2}\right) \left(\tan^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)-1\right)}\, \sqrt{\tan \left(\frac{b x}{2}+\frac{a}{2}\right)+1}\, \sqrt{-2 \tan \left(\frac{b x}{2}+\frac{a}{2}\right)+2}\, \sqrt{-\tan \left(\frac{b x}{2}+\frac{a}{2}\right)}\, \EllipticE \left(\sqrt{\tan \left(\frac{b x}{2}+\frac{a}{2}\right)+1}, \frac{\sqrt{2}}{2}\right) \left(\tan^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-12 \sqrt{\tan \left(\frac{b x}{2}+\frac{a}{2}\right) \left(\tan^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)-1\right)}\, \sqrt{\tan \left(\frac{b x}{2}+\frac{a}{2}\right)+1}\, \sqrt{-2 \tan \left(\frac{b x}{2}+\frac{a}{2}\right)+2}\, \sqrt{-\tan \left(\frac{b x}{2}+\frac{a}{2}\right)}\, \EllipticF \left(\sqrt{\tan \left(\frac{b x}{2}+\frac{a}{2}\right)+1}, \frac{\sqrt{2}}{2}\right) \left(\tan^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+\sqrt{\tan \left(\frac{b x}{2}+\frac{a}{2}\right) \left(\tan^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)-1\right)}\, \left(\tan^{6}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-\sqrt{\tan \left(\frac{b x}{2}+\frac{a}{2}\right) \left(\tan^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)-1\right)}\, \left(\tan^{4}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+12 \left(\tan^{4}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) \sqrt{\tan^{3}\left(\frac{b x}{2}+\frac{a}{2}\right)-\tan \left(\frac{b x}{2}+\frac{a}{2}\right)}-\sqrt{\tan \left(\frac{b x}{2}+\frac{a}{2}\right) \left(\tan^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)-1\right)}\, \left(\tan^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-12 \left(\tan^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) \sqrt{\tan^{3}\left(\frac{b x}{2}+\frac{a}{2}\right)-\tan \left(\frac{b x}{2}+\frac{a}{2}\right)}+\sqrt{\tan \left(\frac{b x}{2}+\frac{a}{2}\right) \left(\tan^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)-1\right)}\right)}{80 b \tan \left(\frac{b x}{2}+\frac{a}{2}\right)^{3} \sqrt{\tan^{3}\left(\frac{b x}{2}+\frac{a}{2}\right)-\tan \left(\frac{b x}{2}+\frac{a}{2}\right)}}"," ",0,"-1/80/b*(-tan(1/2*b*x+1/2*a)/(tan(1/2*b*x+1/2*a)^2-1))^(1/2)/tan(1/2*b*x+1/2*a)^3*(24*(tan(1/2*b*x+1/2*a)*(tan(1/2*b*x+1/2*a)^2-1))^(1/2)*(tan(1/2*b*x+1/2*a)+1)^(1/2)*(-2*tan(1/2*b*x+1/2*a)+2)^(1/2)*(-tan(1/2*b*x+1/2*a))^(1/2)*EllipticE((tan(1/2*b*x+1/2*a)+1)^(1/2),1/2*2^(1/2))*tan(1/2*b*x+1/2*a)^2-12*(tan(1/2*b*x+1/2*a)*(tan(1/2*b*x+1/2*a)^2-1))^(1/2)*(tan(1/2*b*x+1/2*a)+1)^(1/2)*(-2*tan(1/2*b*x+1/2*a)+2)^(1/2)*(-tan(1/2*b*x+1/2*a))^(1/2)*EllipticF((tan(1/2*b*x+1/2*a)+1)^(1/2),1/2*2^(1/2))*tan(1/2*b*x+1/2*a)^2+(tan(1/2*b*x+1/2*a)*(tan(1/2*b*x+1/2*a)^2-1))^(1/2)*tan(1/2*b*x+1/2*a)^6-(tan(1/2*b*x+1/2*a)*(tan(1/2*b*x+1/2*a)^2-1))^(1/2)*tan(1/2*b*x+1/2*a)^4+12*tan(1/2*b*x+1/2*a)^4*(tan(1/2*b*x+1/2*a)^3-tan(1/2*b*x+1/2*a))^(1/2)-(tan(1/2*b*x+1/2*a)*(tan(1/2*b*x+1/2*a)^2-1))^(1/2)*tan(1/2*b*x+1/2*a)^2-12*tan(1/2*b*x+1/2*a)^2*(tan(1/2*b*x+1/2*a)^3-tan(1/2*b*x+1/2*a))^(1/2)+(tan(1/2*b*x+1/2*a)*(tan(1/2*b*x+1/2*a)^2-1))^(1/2))/(tan(1/2*b*x+1/2*a)^3-tan(1/2*b*x+1/2*a))^(1/2)","C"
104,-1,0,89,180.000000," ","int(csc(b*x+a)/sin(2*b*x+2*a)^(7/2),x)","\int \frac{\csc \left(b x +a \right)}{\sin \left(2 b x +2 a \right)^{\frac{7}{2}}}\, dx"," ",0,"int(csc(b*x+a)/sin(2*b*x+2*a)^(7/2),x)","F"
105,1,204,117,29.075000," ","int(csc(b*x+a)^2*sin(2*b*x+2*a)^(9/2),x)","\frac{8 \sqrt{2}\, \left(\frac{\sqrt{2}\, \left(\sin^{\frac{7}{2}}\left(2 b x +2 a \right)\right)}{56}-\frac{\sqrt{2}\, \left(6 \sqrt{1+\sin \left(2 b x +2 a \right)}\, \sqrt{-2 \sin \left(2 b x +2 a \right)+2}\, \sqrt{-\sin \left(2 b x +2 a \right)}\, \EllipticE \left(\sqrt{1+\sin \left(2 b x +2 a \right)}, \frac{\sqrt{2}}{2}\right)-3 \sqrt{1+\sin \left(2 b x +2 a \right)}\, \sqrt{-2 \sin \left(2 b x +2 a \right)+2}\, \sqrt{-\sin \left(2 b x +2 a \right)}\, \EllipticF \left(\sqrt{1+\sin \left(2 b x +2 a \right)}, \frac{\sqrt{2}}{2}\right)-2 \left(\sin^{4}\left(2 b x +2 a \right)\right)+2 \left(\sin^{2}\left(2 b x +2 a \right)\right)\right)}{80 \cos \left(2 b x +2 a \right) \sqrt{\sin \left(2 b x +2 a \right)}}\right)}{b}"," ",0,"8*2^(1/2)*(1/56*2^(1/2)*sin(2*b*x+2*a)^(7/2)-1/80*2^(1/2)*(6*(1+sin(2*b*x+2*a))^(1/2)*(-2*sin(2*b*x+2*a)+2)^(1/2)*(-sin(2*b*x+2*a))^(1/2)*EllipticE((1+sin(2*b*x+2*a))^(1/2),1/2*2^(1/2))-3*(1+sin(2*b*x+2*a))^(1/2)*(-2*sin(2*b*x+2*a)+2)^(1/2)*(-sin(2*b*x+2*a))^(1/2)*EllipticF((1+sin(2*b*x+2*a))^(1/2),1/2*2^(1/2))-2*sin(2*b*x+2*a)^4+2*sin(2*b*x+2*a)^2)/cos(2*b*x+2*a)/sin(2*b*x+2*a)^(1/2))/b","A"
106,1,139,117,25.250000," ","int(csc(b*x+a)^2*sin(2*b*x+2*a)^(7/2),x)","\frac{4 \sqrt{2}\, \left(\frac{\sqrt{2}\, \left(\sin^{\frac{5}{2}}\left(2 b x +2 a \right)\right)}{20}+\frac{\sqrt{2}\, \left(\sqrt{1+\sin \left(2 b x +2 a \right)}\, \sqrt{-2 \sin \left(2 b x +2 a \right)+2}\, \sqrt{-\sin \left(2 b x +2 a \right)}\, \EllipticF \left(\sqrt{1+\sin \left(2 b x +2 a \right)}, \frac{\sqrt{2}}{2}\right)+2 \left(\sin^{3}\left(2 b x +2 a \right)\right)-2 \sin \left(2 b x +2 a \right)\right)}{24 \cos \left(2 b x +2 a \right) \sqrt{\sin \left(2 b x +2 a \right)}}\right)}{b}"," ",0,"4*2^(1/2)*(1/20*2^(1/2)*sin(2*b*x+2*a)^(5/2)+1/24*2^(1/2)*((1+sin(2*b*x+2*a))^(1/2)*(-2*sin(2*b*x+2*a)+2)^(1/2)*(-sin(2*b*x+2*a))^(1/2)*EllipticF((1+sin(2*b*x+2*a))^(1/2),1/2*2^(1/2))+2*sin(2*b*x+2*a)^3-2*sin(2*b*x+2*a))/cos(2*b*x+2*a)/sin(2*b*x+2*a)^(1/2))/b","A"
107,1,137,92,22.392000," ","int(csc(b*x+a)^2*sin(2*b*x+2*a)^(5/2),x)","\frac{2 \sqrt{2}\, \left(\frac{\sqrt{2}\, \left(\sin^{\frac{3}{2}}\left(2 b x +2 a \right)\right)}{6}-\frac{\sqrt{2}\, \sqrt{1+\sin \left(2 b x +2 a \right)}\, \sqrt{-2 \sin \left(2 b x +2 a \right)+2}\, \sqrt{-\sin \left(2 b x +2 a \right)}\, \left(2 \EllipticE \left(\sqrt{1+\sin \left(2 b x +2 a \right)}, \frac{\sqrt{2}}{2}\right)-\EllipticF \left(\sqrt{1+\sin \left(2 b x +2 a \right)}, \frac{\sqrt{2}}{2}\right)\right)}{4 \cos \left(2 b x +2 a \right) \sqrt{\sin \left(2 b x +2 a \right)}}\right)}{b}"," ",0,"2*2^(1/2)*(1/6*2^(1/2)*sin(2*b*x+2*a)^(3/2)-1/4*2^(1/2)*(1+sin(2*b*x+2*a))^(1/2)*(-2*sin(2*b*x+2*a)+2)^(1/2)*(-sin(2*b*x+2*a))^(1/2)*(2*EllipticE((1+sin(2*b*x+2*a))^(1/2),1/2*2^(1/2))-EllipticF((1+sin(2*b*x+2*a))^(1/2),1/2*2^(1/2)))/cos(2*b*x+2*a)/sin(2*b*x+2*a)^(1/2))/b","A"
108,1,111,91,15.645000," ","int(csc(b*x+a)^2*sin(2*b*x+2*a)^(3/2),x)","\frac{\sqrt{2}\, \left(\sqrt{2}\, \left(\sqrt{\sin}\left(2 b x +2 a \right)\right)+\frac{\sqrt{2}\, \sqrt{1+\sin \left(2 b x +2 a \right)}\, \sqrt{-2 \sin \left(2 b x +2 a \right)+2}\, \sqrt{-\sin \left(2 b x +2 a \right)}\, \EllipticF \left(\sqrt{1+\sin \left(2 b x +2 a \right)}, \frac{\sqrt{2}}{2}\right)}{2 \cos \left(2 b x +2 a \right) \sqrt{\sin \left(2 b x +2 a \right)}}\right)}{b}"," ",0,"2^(1/2)*(2^(1/2)*sin(2*b*x+2*a)^(1/2)+1/2*2^(1/2)*(1+sin(2*b*x+2*a))^(1/2)*(-2*sin(2*b*x+2*a)+2)^(1/2)*(-sin(2*b*x+2*a))^(1/2)*EllipticF((1+sin(2*b*x+2*a))^(1/2),1/2*2^(1/2))/cos(2*b*x+2*a)/sin(2*b*x+2*a)^(1/2))/b","A"
109,1,176,67,17.731000," ","int(csc(b*x+a)^2*sin(2*b*x+2*a)^(1/2),x)","\frac{2 \sqrt{1+\sin \left(2 b x +2 a \right)}\, \sqrt{-2 \sin \left(2 b x +2 a \right)+2}\, \sqrt{-\sin \left(2 b x +2 a \right)}\, \EllipticE \left(\sqrt{1+\sin \left(2 b x +2 a \right)}, \frac{\sqrt{2}}{2}\right)-\sqrt{1+\sin \left(2 b x +2 a \right)}\, \sqrt{-2 \sin \left(2 b x +2 a \right)+2}\, \sqrt{-\sin \left(2 b x +2 a \right)}\, \EllipticF \left(\sqrt{1+\sin \left(2 b x +2 a \right)}, \frac{\sqrt{2}}{2}\right)-2 \left(\cos^{2}\left(2 b x +2 a \right)\right)-2 \cos \left(2 b x +2 a \right)}{\cos \left(2 b x +2 a \right) \sqrt{\sin \left(2 b x +2 a \right)}\, b}"," ",0,"1/cos(2*b*x+2*a)/sin(2*b*x+2*a)^(1/2)*(2*(1+sin(2*b*x+2*a))^(1/2)*(-2*sin(2*b*x+2*a)+2)^(1/2)*(-sin(2*b*x+2*a))^(1/2)*EllipticE((1+sin(2*b*x+2*a))^(1/2),1/2*2^(1/2))-(1+sin(2*b*x+2*a))^(1/2)*(-2*sin(2*b*x+2*a)+2)^(1/2)*(-sin(2*b*x+2*a))^(1/2)*EllipticF((1+sin(2*b*x+2*a))^(1/2),1/2*2^(1/2))-2*cos(2*b*x+2*a)^2-2*cos(2*b*x+2*a))/b","B"
110,-2,0,67,180.000000," ","int(csc(b*x+a)^2/sin(2*b*x+2*a)^(1/2),x)","\int \frac{\csc^{2}\left(b x +a \right)}{\sqrt{\sin \left(2 b x +2 a \right)}}\, dx"," ",0,"int(csc(b*x+a)^2/sin(2*b*x+2*a)^(1/2),x)","F"
111,1,227,92,59.936000," ","int(csc(b*x+a)^2/sin(2*b*x+2*a)^(3/2),x)","\frac{\sqrt{2}\, \left(-\frac{8 \sqrt{2}}{5 \sin \left(2 b x +2 a \right)^{\frac{5}{2}}}+\frac{4 \sqrt{2}\, \left(6 \sqrt{1+\sin \left(2 b x +2 a \right)}\, \sqrt{-2 \sin \left(2 b x +2 a \right)+2}\, \sqrt{-\sin \left(2 b x +2 a \right)}\, \left(\sin^{2}\left(2 b x +2 a \right)\right) \EllipticE \left(\sqrt{1+\sin \left(2 b x +2 a \right)}, \frac{\sqrt{2}}{2}\right)-3 \sqrt{1+\sin \left(2 b x +2 a \right)}\, \sqrt{-2 \sin \left(2 b x +2 a \right)+2}\, \sqrt{-\sin \left(2 b x +2 a \right)}\, \left(\sin^{2}\left(2 b x +2 a \right)\right) \EllipticF \left(\sqrt{1+\sin \left(2 b x +2 a \right)}, \frac{\sqrt{2}}{2}\right)+6 \left(\sin^{4}\left(2 b x +2 a \right)\right)-4 \left(\sin^{2}\left(2 b x +2 a \right)\right)-2\right)}{5 \sin \left(2 b x +2 a \right)^{\frac{5}{2}} \cos \left(2 b x +2 a \right)}\right)}{8 b}"," ",0,"1/8*2^(1/2)*(-8/5*2^(1/2)/sin(2*b*x+2*a)^(5/2)+4/5*2^(1/2)/sin(2*b*x+2*a)^(5/2)*(6*(1+sin(2*b*x+2*a))^(1/2)*(-2*sin(2*b*x+2*a)+2)^(1/2)*(-sin(2*b*x+2*a))^(1/2)*sin(2*b*x+2*a)^2*EllipticE((1+sin(2*b*x+2*a))^(1/2),1/2*2^(1/2))-3*(1+sin(2*b*x+2*a))^(1/2)*(-2*sin(2*b*x+2*a)+2)^(1/2)*(-sin(2*b*x+2*a))^(1/2)*sin(2*b*x+2*a)^2*EllipticF((1+sin(2*b*x+2*a))^(1/2),1/2*2^(1/2))+6*sin(2*b*x+2*a)^4-4*sin(2*b*x+2*a)^2-2)/cos(2*b*x+2*a))/b","B"
112,1,154,92,90.513000," ","int(csc(b*x+a)^2/sin(2*b*x+2*a)^(5/2),x)","\frac{\sqrt{2}\, \left(-\frac{16 \sqrt{2}}{7 \sin \left(2 b x +2 a \right)^{\frac{7}{2}}}+\frac{8 \sqrt{2}\, \left(5 \sqrt{1+\sin \left(2 b x +2 a \right)}\, \sqrt{-2 \sin \left(2 b x +2 a \right)+2}\, \sqrt{-\sin \left(2 b x +2 a \right)}\, \EllipticF \left(\sqrt{1+\sin \left(2 b x +2 a \right)}, \frac{\sqrt{2}}{2}\right) \left(\sin^{3}\left(2 b x +2 a \right)\right)+10 \left(\sin^{4}\left(2 b x +2 a \right)\right)-4 \left(\sin^{2}\left(2 b x +2 a \right)\right)-6\right)}{21 \sin \left(2 b x +2 a \right)^{\frac{7}{2}} \cos \left(2 b x +2 a \right)}\right)}{16 b}"," ",0,"1/16*2^(1/2)*(-16/7*2^(1/2)/sin(2*b*x+2*a)^(7/2)+8/21*2^(1/2)/sin(2*b*x+2*a)^(7/2)*(5*(1+sin(2*b*x+2*a))^(1/2)*(-2*sin(2*b*x+2*a)+2)^(1/2)*(-sin(2*b*x+2*a))^(1/2)*EllipticF((1+sin(2*b*x+2*a))^(1/2),1/2*2^(1/2))*sin(2*b*x+2*a)^3+10*sin(2*b*x+2*a)^4-4*sin(2*b*x+2*a)^2-6)/cos(2*b*x+2*a))/b","A"
113,-1,0,117,180.000000," ","int(csc(b*x+a)^2/sin(2*b*x+2*a)^(7/2),x)","\int \frac{\csc^{2}\left(b x +a \right)}{\sin \left(2 b x +2 a \right)^{\frac{7}{2}}}\, dx"," ",0,"int(csc(b*x+a)^2/sin(2*b*x+2*a)^(7/2),x)","F"
114,-1,0,117,180.000000," ","int(csc(b*x+a)^2/sin(2*b*x+2*a)^(9/2),x)","\int \frac{\csc^{2}\left(b x +a \right)}{\sin \left(2 b x +2 a \right)^{\frac{9}{2}}}\, dx"," ",0,"int(csc(b*x+a)^2/sin(2*b*x+2*a)^(9/2),x)","F"
115,1,441,164,211.099000," ","int(csc(b*x+a)^3*sin(2*b*x+2*a)^(9/2),x)","-\frac{64 \sqrt{-\frac{\tan \left(\frac{b x}{2}+\frac{a}{2}\right)}{\tan^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)-1}}\, \left(\sqrt{\tan \left(\frac{b x}{2}+\frac{a}{2}\right)+1}\, \sqrt{-2 \tan \left(\frac{b x}{2}+\frac{a}{2}\right)+2}\, \sqrt{-\tan \left(\frac{b x}{2}+\frac{a}{2}\right)}\, \EllipticF \left(\sqrt{\tan \left(\frac{b x}{2}+\frac{a}{2}\right)+1}, \frac{\sqrt{2}}{2}\right) \left(\tan^{6}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-3 \sqrt{\tan \left(\frac{b x}{2}+\frac{a}{2}\right)+1}\, \sqrt{-2 \tan \left(\frac{b x}{2}+\frac{a}{2}\right)+2}\, \sqrt{-\tan \left(\frac{b x}{2}+\frac{a}{2}\right)}\, \EllipticF \left(\sqrt{\tan \left(\frac{b x}{2}+\frac{a}{2}\right)+1}, \frac{\sqrt{2}}{2}\right) \left(\tan^{4}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+2 \left(\tan^{7}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+3 \sqrt{\tan \left(\frac{b x}{2}+\frac{a}{2}\right)+1}\, \sqrt{-2 \tan \left(\frac{b x}{2}+\frac{a}{2}\right)+2}\, \sqrt{-\tan \left(\frac{b x}{2}+\frac{a}{2}\right)}\, \EllipticF \left(\sqrt{\tan \left(\frac{b x}{2}+\frac{a}{2}\right)+1}, \frac{\sqrt{2}}{2}\right) \left(\tan^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+10 \left(\tan^{5}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-\sqrt{\tan \left(\frac{b x}{2}+\frac{a}{2}\right)+1}\, \sqrt{-2 \tan \left(\frac{b x}{2}+\frac{a}{2}\right)+2}\, \sqrt{-\tan \left(\frac{b x}{2}+\frac{a}{2}\right)}\, \EllipticF \left(\sqrt{\tan \left(\frac{b x}{2}+\frac{a}{2}\right)+1}, \frac{\sqrt{2}}{2}\right)+10 \left(\tan^{3}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+2 \tan \left(\frac{b x}{2}+\frac{a}{2}\right)\right)}{21 \sqrt{\tan \left(\frac{b x}{2}+\frac{a}{2}\right) \left(\tan^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)-1\right)}\, \left(\tan \left(\frac{b x}{2}+\frac{a}{2}\right)+1\right)^{2} \sqrt{\tan^{3}\left(\frac{b x}{2}+\frac{a}{2}\right)-\tan \left(\frac{b x}{2}+\frac{a}{2}\right)}\, \left(\tan \left(\frac{b x}{2}+\frac{a}{2}\right)-1\right)^{2} b}"," ",0,"-64/21*(-tan(1/2*b*x+1/2*a)/(tan(1/2*b*x+1/2*a)^2-1))^(1/2)*((tan(1/2*b*x+1/2*a)+1)^(1/2)*(-2*tan(1/2*b*x+1/2*a)+2)^(1/2)*(-tan(1/2*b*x+1/2*a))^(1/2)*EllipticF((tan(1/2*b*x+1/2*a)+1)^(1/2),1/2*2^(1/2))*tan(1/2*b*x+1/2*a)^6-3*(tan(1/2*b*x+1/2*a)+1)^(1/2)*(-2*tan(1/2*b*x+1/2*a)+2)^(1/2)*(-tan(1/2*b*x+1/2*a))^(1/2)*EllipticF((tan(1/2*b*x+1/2*a)+1)^(1/2),1/2*2^(1/2))*tan(1/2*b*x+1/2*a)^4+2*tan(1/2*b*x+1/2*a)^7+3*(tan(1/2*b*x+1/2*a)+1)^(1/2)*(-2*tan(1/2*b*x+1/2*a)+2)^(1/2)*(-tan(1/2*b*x+1/2*a))^(1/2)*EllipticF((tan(1/2*b*x+1/2*a)+1)^(1/2),1/2*2^(1/2))*tan(1/2*b*x+1/2*a)^2+10*tan(1/2*b*x+1/2*a)^5-(tan(1/2*b*x+1/2*a)+1)^(1/2)*(-2*tan(1/2*b*x+1/2*a)+2)^(1/2)*(-tan(1/2*b*x+1/2*a))^(1/2)*EllipticF((tan(1/2*b*x+1/2*a)+1)^(1/2),1/2*2^(1/2))+10*tan(1/2*b*x+1/2*a)^3+2*tan(1/2*b*x+1/2*a))/(tan(1/2*b*x+1/2*a)*(tan(1/2*b*x+1/2*a)^2-1))^(1/2)/(tan(1/2*b*x+1/2*a)+1)^2/(tan(1/2*b*x+1/2*a)^3-tan(1/2*b*x+1/2*a))^(1/2)/(tan(1/2*b*x+1/2*a)-1)^2/b","C"
116,1,973,142,81.756000," ","int(csc(b*x+a)^3*sin(2*b*x+2*a)^(7/2),x)","\frac{32 \sqrt{-\frac{\tan \left(\frac{b x}{2}+\frac{a}{2}\right)}{\tan^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)-1}}\, \left(2 \sqrt{\tan \left(\frac{b x}{2}+\frac{a}{2}\right) \left(\tan \left(\frac{b x}{2}+\frac{a}{2}\right)-1\right) \left(\tan \left(\frac{b x}{2}+\frac{a}{2}\right)+1\right)}\, \sqrt{\tan \left(\frac{b x}{2}+\frac{a}{2}\right)+1}\, \sqrt{-2 \tan \left(\frac{b x}{2}+\frac{a}{2}\right)+2}\, \sqrt{-\tan \left(\frac{b x}{2}+\frac{a}{2}\right)}\, \EllipticE \left(\sqrt{\tan \left(\frac{b x}{2}+\frac{a}{2}\right)+1}, \frac{\sqrt{2}}{2}\right) \left(\tan^{4}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-\sqrt{\tan \left(\frac{b x}{2}+\frac{a}{2}\right) \left(\tan \left(\frac{b x}{2}+\frac{a}{2}\right)-1\right) \left(\tan \left(\frac{b x}{2}+\frac{a}{2}\right)+1\right)}\, \sqrt{\tan \left(\frac{b x}{2}+\frac{a}{2}\right)+1}\, \sqrt{-2 \tan \left(\frac{b x}{2}+\frac{a}{2}\right)+2}\, \sqrt{-\tan \left(\frac{b x}{2}+\frac{a}{2}\right)}\, \EllipticF \left(\sqrt{\tan \left(\frac{b x}{2}+\frac{a}{2}\right)+1}, \frac{\sqrt{2}}{2}\right) \left(\tan^{4}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-4 \sqrt{\tan \left(\frac{b x}{2}+\frac{a}{2}\right) \left(\tan \left(\frac{b x}{2}+\frac{a}{2}\right)-1\right) \left(\tan \left(\frac{b x}{2}+\frac{a}{2}\right)+1\right)}\, \sqrt{\tan \left(\frac{b x}{2}+\frac{a}{2}\right)+1}\, \sqrt{-2 \tan \left(\frac{b x}{2}+\frac{a}{2}\right)+2}\, \sqrt{-\tan \left(\frac{b x}{2}+\frac{a}{2}\right)}\, \EllipticE \left(\sqrt{\tan \left(\frac{b x}{2}+\frac{a}{2}\right)+1}, \frac{\sqrt{2}}{2}\right) \left(\tan^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+2 \sqrt{\tan \left(\frac{b x}{2}+\frac{a}{2}\right) \left(\tan \left(\frac{b x}{2}+\frac{a}{2}\right)-1\right) \left(\tan \left(\frac{b x}{2}+\frac{a}{2}\right)+1\right)}\, \sqrt{\tan \left(\frac{b x}{2}+\frac{a}{2}\right)+1}\, \sqrt{-2 \tan \left(\frac{b x}{2}+\frac{a}{2}\right)+2}\, \sqrt{-\tan \left(\frac{b x}{2}+\frac{a}{2}\right)}\, \EllipticF \left(\sqrt{\tan \left(\frac{b x}{2}+\frac{a}{2}\right)+1}, \frac{\sqrt{2}}{2}\right) \left(\tan^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+2 \left(\tan^{6}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) \sqrt{\tan^{3}\left(\frac{b x}{2}+\frac{a}{2}\right)-\tan \left(\frac{b x}{2}+\frac{a}{2}\right)}+2 \sqrt{\tan \left(\frac{b x}{2}+\frac{a}{2}\right) \left(\tan \left(\frac{b x}{2}+\frac{a}{2}\right)-1\right) \left(\tan \left(\frac{b x}{2}+\frac{a}{2}\right)+1\right)}\, \sqrt{\tan \left(\frac{b x}{2}+\frac{a}{2}\right)+1}\, \sqrt{-2 \tan \left(\frac{b x}{2}+\frac{a}{2}\right)+2}\, \sqrt{-\tan \left(\frac{b x}{2}+\frac{a}{2}\right)}\, \EllipticE \left(\sqrt{\tan \left(\frac{b x}{2}+\frac{a}{2}\right)+1}, \frac{\sqrt{2}}{2}\right)-\sqrt{\tan \left(\frac{b x}{2}+\frac{a}{2}\right) \left(\tan \left(\frac{b x}{2}+\frac{a}{2}\right)-1\right) \left(\tan \left(\frac{b x}{2}+\frac{a}{2}\right)+1\right)}\, \sqrt{\tan \left(\frac{b x}{2}+\frac{a}{2}\right)+1}\, \sqrt{-2 \tan \left(\frac{b x}{2}+\frac{a}{2}\right)+2}\, \sqrt{-\tan \left(\frac{b x}{2}+\frac{a}{2}\right)}\, \EllipticF \left(\sqrt{\tan \left(\frac{b x}{2}+\frac{a}{2}\right)+1}, \frac{\sqrt{2}}{2}\right)+2 \sqrt{\tan \left(\frac{b x}{2}+\frac{a}{2}\right) \left(\tan \left(\frac{b x}{2}+\frac{a}{2}\right)-1\right) \left(\tan \left(\frac{b x}{2}+\frac{a}{2}\right)+1\right)}\, \left(\tan^{4}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-4 \left(\tan^{4}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) \sqrt{\tan^{3}\left(\frac{b x}{2}+\frac{a}{2}\right)-\tan \left(\frac{b x}{2}+\frac{a}{2}\right)}+2 \sqrt{\tan \left(\frac{b x}{2}+\frac{a}{2}\right) \left(\tan \left(\frac{b x}{2}+\frac{a}{2}\right)-1\right) \left(\tan \left(\frac{b x}{2}+\frac{a}{2}\right)+1\right)}\, \left(\tan^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+2 \left(\tan^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) \sqrt{\tan^{3}\left(\frac{b x}{2}+\frac{a}{2}\right)-\tan \left(\frac{b x}{2}+\frac{a}{2}\right)}\right)}{5 \sqrt{\tan \left(\frac{b x}{2}+\frac{a}{2}\right) \left(\tan^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)-1\right)}\, \sqrt{\tan \left(\frac{b x}{2}+\frac{a}{2}\right) \left(\tan \left(\frac{b x}{2}+\frac{a}{2}\right)-1\right) \left(\tan \left(\frac{b x}{2}+\frac{a}{2}\right)+1\right)}\, \sqrt{\tan^{3}\left(\frac{b x}{2}+\frac{a}{2}\right)-\tan \left(\frac{b x}{2}+\frac{a}{2}\right)}\, \left(\tan \left(\frac{b x}{2}+\frac{a}{2}\right)-1\right) \left(\tan \left(\frac{b x}{2}+\frac{a}{2}\right)+1\right) b}"," ",0,"32/5*(-tan(1/2*b*x+1/2*a)/(tan(1/2*b*x+1/2*a)^2-1))^(1/2)*(2*(tan(1/2*b*x+1/2*a)*(tan(1/2*b*x+1/2*a)-1)*(tan(1/2*b*x+1/2*a)+1))^(1/2)*(tan(1/2*b*x+1/2*a)+1)^(1/2)*(-2*tan(1/2*b*x+1/2*a)+2)^(1/2)*(-tan(1/2*b*x+1/2*a))^(1/2)*EllipticE((tan(1/2*b*x+1/2*a)+1)^(1/2),1/2*2^(1/2))*tan(1/2*b*x+1/2*a)^4-(tan(1/2*b*x+1/2*a)*(tan(1/2*b*x+1/2*a)-1)*(tan(1/2*b*x+1/2*a)+1))^(1/2)*(tan(1/2*b*x+1/2*a)+1)^(1/2)*(-2*tan(1/2*b*x+1/2*a)+2)^(1/2)*(-tan(1/2*b*x+1/2*a))^(1/2)*EllipticF((tan(1/2*b*x+1/2*a)+1)^(1/2),1/2*2^(1/2))*tan(1/2*b*x+1/2*a)^4-4*(tan(1/2*b*x+1/2*a)*(tan(1/2*b*x+1/2*a)-1)*(tan(1/2*b*x+1/2*a)+1))^(1/2)*(tan(1/2*b*x+1/2*a)+1)^(1/2)*(-2*tan(1/2*b*x+1/2*a)+2)^(1/2)*(-tan(1/2*b*x+1/2*a))^(1/2)*EllipticE((tan(1/2*b*x+1/2*a)+1)^(1/2),1/2*2^(1/2))*tan(1/2*b*x+1/2*a)^2+2*(tan(1/2*b*x+1/2*a)*(tan(1/2*b*x+1/2*a)-1)*(tan(1/2*b*x+1/2*a)+1))^(1/2)*(tan(1/2*b*x+1/2*a)+1)^(1/2)*(-2*tan(1/2*b*x+1/2*a)+2)^(1/2)*(-tan(1/2*b*x+1/2*a))^(1/2)*EllipticF((tan(1/2*b*x+1/2*a)+1)^(1/2),1/2*2^(1/2))*tan(1/2*b*x+1/2*a)^2+2*tan(1/2*b*x+1/2*a)^6*(tan(1/2*b*x+1/2*a)^3-tan(1/2*b*x+1/2*a))^(1/2)+2*(tan(1/2*b*x+1/2*a)*(tan(1/2*b*x+1/2*a)-1)*(tan(1/2*b*x+1/2*a)+1))^(1/2)*(tan(1/2*b*x+1/2*a)+1)^(1/2)*(-2*tan(1/2*b*x+1/2*a)+2)^(1/2)*(-tan(1/2*b*x+1/2*a))^(1/2)*EllipticE((tan(1/2*b*x+1/2*a)+1)^(1/2),1/2*2^(1/2))-(tan(1/2*b*x+1/2*a)*(tan(1/2*b*x+1/2*a)-1)*(tan(1/2*b*x+1/2*a)+1))^(1/2)*(tan(1/2*b*x+1/2*a)+1)^(1/2)*(-2*tan(1/2*b*x+1/2*a)+2)^(1/2)*(-tan(1/2*b*x+1/2*a))^(1/2)*EllipticF((tan(1/2*b*x+1/2*a)+1)^(1/2),1/2*2^(1/2))+2*(tan(1/2*b*x+1/2*a)*(tan(1/2*b*x+1/2*a)-1)*(tan(1/2*b*x+1/2*a)+1))^(1/2)*tan(1/2*b*x+1/2*a)^4-4*tan(1/2*b*x+1/2*a)^4*(tan(1/2*b*x+1/2*a)^3-tan(1/2*b*x+1/2*a))^(1/2)+2*(tan(1/2*b*x+1/2*a)*(tan(1/2*b*x+1/2*a)-1)*(tan(1/2*b*x+1/2*a)+1))^(1/2)*tan(1/2*b*x+1/2*a)^2+2*tan(1/2*b*x+1/2*a)^2*(tan(1/2*b*x+1/2*a)^3-tan(1/2*b*x+1/2*a))^(1/2))/(tan(1/2*b*x+1/2*a)*(tan(1/2*b*x+1/2*a)^2-1))^(1/2)/(tan(1/2*b*x+1/2*a)*(tan(1/2*b*x+1/2*a)-1)*(tan(1/2*b*x+1/2*a)+1))^(1/2)/(tan(1/2*b*x+1/2*a)^3-tan(1/2*b*x+1/2*a))^(1/2)/(tan(1/2*b*x+1/2*a)-1)/(tan(1/2*b*x+1/2*a)+1)/b","C"
117,1,243,119,41.222000," ","int(csc(b*x+a)^3*sin(2*b*x+2*a)^(5/2),x)","\frac{16 \sqrt{-\frac{\tan \left(\frac{b x}{2}+\frac{a}{2}\right)}{\tan^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)-1}}\, \left(\sqrt{\tan \left(\frac{b x}{2}+\frac{a}{2}\right)+1}\, \sqrt{-2 \tan \left(\frac{b x}{2}+\frac{a}{2}\right)+2}\, \sqrt{-\tan \left(\frac{b x}{2}+\frac{a}{2}\right)}\, \EllipticF \left(\sqrt{\tan \left(\frac{b x}{2}+\frac{a}{2}\right)+1}, \frac{\sqrt{2}}{2}\right) \left(\tan^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-\sqrt{\tan \left(\frac{b x}{2}+\frac{a}{2}\right)+1}\, \sqrt{-2 \tan \left(\frac{b x}{2}+\frac{a}{2}\right)+2}\, \sqrt{-\tan \left(\frac{b x}{2}+\frac{a}{2}\right)}\, \EllipticF \left(\sqrt{\tan \left(\frac{b x}{2}+\frac{a}{2}\right)+1}, \frac{\sqrt{2}}{2}\right)-\left(\tan^{3}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-\tan \left(\frac{b x}{2}+\frac{a}{2}\right)\right)}{3 \sqrt{\tan^{3}\left(\frac{b x}{2}+\frac{a}{2}\right)-\tan \left(\frac{b x}{2}+\frac{a}{2}\right)}\, \sqrt{\tan \left(\frac{b x}{2}+\frac{a}{2}\right) \left(\tan^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)-1\right)}\, b}"," ",0,"16/3*(-tan(1/2*b*x+1/2*a)/(tan(1/2*b*x+1/2*a)^2-1))^(1/2)*((tan(1/2*b*x+1/2*a)+1)^(1/2)*(-2*tan(1/2*b*x+1/2*a)+2)^(1/2)*(-tan(1/2*b*x+1/2*a))^(1/2)*EllipticF((tan(1/2*b*x+1/2*a)+1)^(1/2),1/2*2^(1/2))*tan(1/2*b*x+1/2*a)^2-(tan(1/2*b*x+1/2*a)+1)^(1/2)*(-2*tan(1/2*b*x+1/2*a)+2)^(1/2)*(-tan(1/2*b*x+1/2*a))^(1/2)*EllipticF((tan(1/2*b*x+1/2*a)+1)^(1/2),1/2*2^(1/2))-tan(1/2*b*x+1/2*a)^3-tan(1/2*b*x+1/2*a))/(tan(1/2*b*x+1/2*a)^3-tan(1/2*b*x+1/2*a))^(1/2)/(tan(1/2*b*x+1/2*a)*(tan(1/2*b*x+1/2*a)^2-1))^(1/2)/b","C"
118,1,542,98,86.501000," ","int(csc(b*x+a)^3*sin(2*b*x+2*a)^(3/2),x)","\frac{4 \sqrt{-\frac{\tan \left(\frac{b x}{2}+\frac{a}{2}\right)}{\tan^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)-1}}\, \left(4 \sqrt{\tan \left(\frac{b x}{2}+\frac{a}{2}\right)+1}\, \sqrt{-2 \tan \left(\frac{b x}{2}+\frac{a}{2}\right)+2}\, \sqrt{-\tan \left(\frac{b x}{2}+\frac{a}{2}\right)}\, \sqrt{\tan \left(\frac{b x}{2}+\frac{a}{2}\right) \left(\tan \left(\frac{b x}{2}+\frac{a}{2}\right)-1\right) \left(\tan \left(\frac{b x}{2}+\frac{a}{2}\right)+1\right)}\, \sqrt{\tan \left(\frac{b x}{2}+\frac{a}{2}\right) \left(\tan^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)-1\right)}\, \EllipticE \left(\sqrt{\tan \left(\frac{b x}{2}+\frac{a}{2}\right)+1}, \frac{\sqrt{2}}{2}\right)-2 \sqrt{\tan \left(\frac{b x}{2}+\frac{a}{2}\right)+1}\, \sqrt{-2 \tan \left(\frac{b x}{2}+\frac{a}{2}\right)+2}\, \sqrt{-\tan \left(\frac{b x}{2}+\frac{a}{2}\right)}\, \sqrt{\tan \left(\frac{b x}{2}+\frac{a}{2}\right) \left(\tan \left(\frac{b x}{2}+\frac{a}{2}\right)-1\right) \left(\tan \left(\frac{b x}{2}+\frac{a}{2}\right)+1\right)}\, \sqrt{\tan \left(\frac{b x}{2}+\frac{a}{2}\right) \left(\tan^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)-1\right)}\, \EllipticF \left(\sqrt{\tan \left(\frac{b x}{2}+\frac{a}{2}\right)+1}, \frac{\sqrt{2}}{2}\right)+2 \left(\tan^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right) \sqrt{\tan^{3}\left(\frac{b x}{2}+\frac{a}{2}\right)-\tan \left(\frac{b x}{2}+\frac{a}{2}\right)}\, \sqrt{\tan \left(\frac{b x}{2}+\frac{a}{2}\right) \left(\tan^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)-1\right)}+\sqrt{\tan \left(\frac{b x}{2}+\frac{a}{2}\right) \left(\tan \left(\frac{b x}{2}+\frac{a}{2}\right)-1\right) \left(\tan \left(\frac{b x}{2}+\frac{a}{2}\right)+1\right)}\, \sqrt{\tan^{3}\left(\frac{b x}{2}+\frac{a}{2}\right)-\tan \left(\frac{b x}{2}+\frac{a}{2}\right)}\, \left(\tan^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-\sqrt{\tan \left(\frac{b x}{2}+\frac{a}{2}\right) \left(\tan \left(\frac{b x}{2}+\frac{a}{2}\right)-1\right) \left(\tan \left(\frac{b x}{2}+\frac{a}{2}\right)+1\right)}\, \sqrt{\tan^{3}\left(\frac{b x}{2}+\frac{a}{2}\right)-\tan \left(\frac{b x}{2}+\frac{a}{2}\right)}\right)}{\tan \left(\frac{b x}{2}+\frac{a}{2}\right) \sqrt{\tan \left(\frac{b x}{2}+\frac{a}{2}\right) \left(\tan \left(\frac{b x}{2}+\frac{a}{2}\right)-1\right) \left(\tan \left(\frac{b x}{2}+\frac{a}{2}\right)+1\right)}\, \sqrt{\tan^{3}\left(\frac{b x}{2}+\frac{a}{2}\right)-\tan \left(\frac{b x}{2}+\frac{a}{2}\right)}\, b}"," ",0,"4*(-tan(1/2*b*x+1/2*a)/(tan(1/2*b*x+1/2*a)^2-1))^(1/2)*(4*(tan(1/2*b*x+1/2*a)+1)^(1/2)*(-2*tan(1/2*b*x+1/2*a)+2)^(1/2)*(-tan(1/2*b*x+1/2*a))^(1/2)*(tan(1/2*b*x+1/2*a)*(tan(1/2*b*x+1/2*a)-1)*(tan(1/2*b*x+1/2*a)+1))^(1/2)*(tan(1/2*b*x+1/2*a)*(tan(1/2*b*x+1/2*a)^2-1))^(1/2)*EllipticE((tan(1/2*b*x+1/2*a)+1)^(1/2),1/2*2^(1/2))-2*(tan(1/2*b*x+1/2*a)+1)^(1/2)*(-2*tan(1/2*b*x+1/2*a)+2)^(1/2)*(-tan(1/2*b*x+1/2*a))^(1/2)*(tan(1/2*b*x+1/2*a)*(tan(1/2*b*x+1/2*a)-1)*(tan(1/2*b*x+1/2*a)+1))^(1/2)*(tan(1/2*b*x+1/2*a)*(tan(1/2*b*x+1/2*a)^2-1))^(1/2)*EllipticF((tan(1/2*b*x+1/2*a)+1)^(1/2),1/2*2^(1/2))+2*tan(1/2*b*x+1/2*a)^2*(tan(1/2*b*x+1/2*a)^3-tan(1/2*b*x+1/2*a))^(1/2)*(tan(1/2*b*x+1/2*a)*(tan(1/2*b*x+1/2*a)^2-1))^(1/2)+(tan(1/2*b*x+1/2*a)*(tan(1/2*b*x+1/2*a)-1)*(tan(1/2*b*x+1/2*a)+1))^(1/2)*(tan(1/2*b*x+1/2*a)^3-tan(1/2*b*x+1/2*a))^(1/2)*tan(1/2*b*x+1/2*a)^2-(tan(1/2*b*x+1/2*a)*(tan(1/2*b*x+1/2*a)-1)*(tan(1/2*b*x+1/2*a)+1))^(1/2)*(tan(1/2*b*x+1/2*a)^3-tan(1/2*b*x+1/2*a))^(1/2))/tan(1/2*b*x+1/2*a)/(tan(1/2*b*x+1/2*a)*(tan(1/2*b*x+1/2*a)-1)*(tan(1/2*b*x+1/2*a)+1))^(1/2)/(tan(1/2*b*x+1/2*a)^3-tan(1/2*b*x+1/2*a))^(1/2)/b","C"
119,1,192,24,31.018000," ","int(csc(b*x+a)^3*sin(2*b*x+2*a)^(1/2),x)","\frac{\sqrt{-\frac{\tan \left(\frac{b x}{2}+\frac{a}{2}\right)}{\tan^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)-1}}\, \left(\tan^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)-1\right) \left(4 \sqrt{\tan \left(\frac{b x}{2}+\frac{a}{2}\right)+1}\, \sqrt{-2 \tan \left(\frac{b x}{2}+\frac{a}{2}\right)+2}\, \sqrt{-\tan \left(\frac{b x}{2}+\frac{a}{2}\right)}\, \EllipticF \left(\sqrt{\tan \left(\frac{b x}{2}+\frac{a}{2}\right)+1}, \frac{\sqrt{2}}{2}\right) \tan \left(\frac{b x}{2}+\frac{a}{2}\right)+\tan^{4}\left(\frac{b x}{2}+\frac{a}{2}\right)-1\right)}{3 \tan \left(\frac{b x}{2}+\frac{a}{2}\right) \sqrt{\tan \left(\frac{b x}{2}+\frac{a}{2}\right) \left(\tan^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)-1\right)}\, \sqrt{\tan^{3}\left(\frac{b x}{2}+\frac{a}{2}\right)-\tan \left(\frac{b x}{2}+\frac{a}{2}\right)}\, b}"," ",0,"1/3*(-tan(1/2*b*x+1/2*a)/(tan(1/2*b*x+1/2*a)^2-1))^(1/2)*(tan(1/2*b*x+1/2*a)^2-1)/tan(1/2*b*x+1/2*a)*(4*(tan(1/2*b*x+1/2*a)+1)^(1/2)*(-2*tan(1/2*b*x+1/2*a)+2)^(1/2)*(-tan(1/2*b*x+1/2*a))^(1/2)*EllipticF((tan(1/2*b*x+1/2*a)+1)^(1/2),1/2*2^(1/2))*tan(1/2*b*x+1/2*a)+tan(1/2*b*x+1/2*a)^4-1)/(tan(1/2*b*x+1/2*a)*(tan(1/2*b*x+1/2*a)^2-1))^(1/2)/(tan(1/2*b*x+1/2*a)^3-tan(1/2*b*x+1/2*a))^(1/2)/b","C"
120,-2,0,47,180.000000," ","int(csc(b*x+a)^3/sin(2*b*x+2*a)^(1/2),x)","\int \frac{\csc^{3}\left(b x +a \right)}{\sqrt{\sin \left(2 b x +2 a \right)}}\, dx"," ",0,"int(csc(b*x+a)^3/sin(2*b*x+2*a)^(1/2),x)","F"
121,1,222,69,107.667000," ","int(csc(b*x+a)^3/sin(2*b*x+2*a)^(3/2),x)","-\frac{\sqrt{-\frac{\tan \left(\frac{b x}{2}+\frac{a}{2}\right)}{\tan^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)-1}}\, \left(\tan^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)-1\right) \left(-3 \left(\tan^{8}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+16 \sqrt{\tan \left(\frac{b x}{2}+\frac{a}{2}\right)+1}\, \sqrt{-2 \tan \left(\frac{b x}{2}+\frac{a}{2}\right)+2}\, \sqrt{-\tan \left(\frac{b x}{2}+\frac{a}{2}\right)}\, \EllipticF \left(\sqrt{\tan \left(\frac{b x}{2}+\frac{a}{2}\right)+1}, \frac{\sqrt{2}}{2}\right) \left(\tan^{3}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)-2 \left(\tan^{6}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+2 \left(\tan^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+3\right)}{336 \tan \left(\frac{b x}{2}+\frac{a}{2}\right)^{3} \sqrt{\tan \left(\frac{b x}{2}+\frac{a}{2}\right) \left(\tan^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)-1\right)}\, \sqrt{\tan^{3}\left(\frac{b x}{2}+\frac{a}{2}\right)-\tan \left(\frac{b x}{2}+\frac{a}{2}\right)}\, b}"," ",0,"-1/336*(-tan(1/2*b*x+1/2*a)/(tan(1/2*b*x+1/2*a)^2-1))^(1/2)*(tan(1/2*b*x+1/2*a)^2-1)/tan(1/2*b*x+1/2*a)^3*(-3*tan(1/2*b*x+1/2*a)^8+16*(tan(1/2*b*x+1/2*a)+1)^(1/2)*(-2*tan(1/2*b*x+1/2*a)+2)^(1/2)*(-tan(1/2*b*x+1/2*a))^(1/2)*EllipticF((tan(1/2*b*x+1/2*a)+1)^(1/2),1/2*2^(1/2))*tan(1/2*b*x+1/2*a)^3-2*tan(1/2*b*x+1/2*a)^6+2*tan(1/2*b*x+1/2*a)^2+3)/(tan(1/2*b*x+1/2*a)*(tan(1/2*b*x+1/2*a)^2-1))^(1/2)/(tan(1/2*b*x+1/2*a)^3-tan(1/2*b*x+1/2*a))^(1/2)/b","C"
122,-1,0,91,180.000000," ","int(csc(b*x+a)^3/sin(2*b*x+2*a)^(5/2),x)","\int \frac{\csc^{3}\left(b x +a \right)}{\sin \left(2 b x +2 a \right)^{\frac{5}{2}}}\, dx"," ",0,"int(csc(b*x+a)^3/sin(2*b*x+2*a)^(5/2),x)","F"
123,0,0,74,10.162000," ","int(sin(b*x+a)^3*sin(2*b*x+2*a)^m,x)","\int \left(\sin^{3}\left(b x +a \right)\right) \left(\sin^{m}\left(2 b x +2 a \right)\right)\, dx"," ",0,"int(sin(b*x+a)^3*sin(2*b*x+2*a)^m,x)","F"
124,0,0,74,6.229000," ","int(sin(b*x+a)^2*sin(2*b*x+2*a)^m,x)","\int \left(\sin^{2}\left(b x +a \right)\right) \left(\sin^{m}\left(2 b x +2 a \right)\right)\, dx"," ",0,"int(sin(b*x+a)^2*sin(2*b*x+2*a)^m,x)","F"
125,0,0,72,5.039000," ","int(sin(b*x+a)*sin(2*b*x+2*a)^m,x)","\int \sin \left(b x +a \right) \left(\sin^{m}\left(2 b x +2 a \right)\right)\, dx"," ",0,"int(sin(b*x+a)*sin(2*b*x+2*a)^m,x)","F"
126,0,0,62,4.345000," ","int(csc(b*x+a)*sin(2*b*x+2*a)^m,x)","\int \csc \left(b x +a \right) \left(\sin^{m}\left(2 b x +2 a \right)\right)\, dx"," ",0,"int(csc(b*x+a)*sin(2*b*x+2*a)^m,x)","F"
127,0,0,75,4.280000," ","int(csc(b*x+a)^2*sin(2*b*x+2*a)^m,x)","\int \left(\csc^{2}\left(b x +a \right)\right) \left(\sin^{m}\left(2 b x +2 a \right)\right)\, dx"," ",0,"int(csc(b*x+a)^2*sin(2*b*x+2*a)^m,x)","F"
128,0,0,75,3.849000," ","int(csc(b*x+a)^3*sin(2*b*x+2*a)^m,x)","\int \left(\csc^{3}\left(b x +a \right)\right) \left(\sin^{m}\left(2 b x +2 a \right)\right)\, dx"," ",0,"int(csc(b*x+a)^3*sin(2*b*x+2*a)^m,x)","F"
129,1,111,53,0.413000," ","int(cos(b*x+a)*sin(2*b*x+2*a)^7,x)","-\frac{35 \cos \left(b x +a \right)}{128 b}-\frac{35 \cos \left(3 b x +3 a \right)}{384 b}+\frac{21 \cos \left(5 b x +5 a \right)}{640 b}+\frac{3 \cos \left(7 b x +7 a \right)}{128 b}-\frac{7 \cos \left(9 b x +9 a \right)}{1152 b}-\frac{7 \cos \left(11 b x +11 a \right)}{1408 b}+\frac{\cos \left(13 b x +13 a \right)}{1664 b}+\frac{\cos \left(15 b x +15 a \right)}{1920 b}"," ",0,"-35/128*cos(b*x+a)/b-35/384*cos(3*b*x+3*a)/b+21/640*cos(5*b*x+5*a)/b+3/128*cos(7*b*x+7*a)/b-7/1152*cos(9*b*x+9*a)/b-7/1408*cos(11*b*x+11*a)/b+1/1664*cos(13*b*x+13*a)/b+1/1920*cos(15*b*x+15*a)/b","B"
130,1,97,53,1.760000," ","int(cos(b*x+a)*sin(2*b*x+2*a)^6,x)","\frac{5 \sin \left(b x +a \right)}{16 b}-\frac{5 \sin \left(3 b x +3 a \right)}{64 b}-\frac{3 \sin \left(5 b x +5 a \right)}{64 b}+\frac{3 \sin \left(7 b x +7 a \right)}{224 b}+\frac{\sin \left(9 b x +9 a \right)}{96 b}-\frac{\sin \left(11 b x +11 a \right)}{704 b}-\frac{\sin \left(13 b x +13 a \right)}{832 b}"," ",0,"5/16*sin(b*x+a)/b-5/64*sin(3*b*x+3*a)/b-3/64/b*sin(5*b*x+5*a)+3/224/b*sin(7*b*x+7*a)+1/96/b*sin(9*b*x+9*a)-1/704/b*sin(11*b*x+11*a)-1/832/b*sin(13*b*x+13*a)","A"
131,1,83,40,0.458000," ","int(cos(b*x+a)*sin(2*b*x+2*a)^5,x)","-\frac{5 \cos \left(b x +a \right)}{16 b}-\frac{5 \cos \left(3 b x +3 a \right)}{48 b}+\frac{\cos \left(5 b x +5 a \right)}{32 b}+\frac{5 \cos \left(7 b x +7 a \right)}{224 b}-\frac{\cos \left(9 b x +9 a \right)}{288 b}-\frac{\cos \left(11 b x +11 a \right)}{352 b}"," ",0,"-5/16*cos(b*x+a)/b-5/48*cos(3*b*x+3*a)/b+1/32*cos(5*b*x+5*a)/b+5/224*cos(7*b*x+7*a)/b-1/288*cos(9*b*x+9*a)/b-1/352*cos(11*b*x+11*a)/b","B"
132,1,69,40,1.223000," ","int(cos(b*x+a)*sin(2*b*x+2*a)^4,x)","\frac{3 \sin \left(b x +a \right)}{8 b}-\frac{\sin \left(3 b x +3 a \right)}{12 b}-\frac{\sin \left(5 b x +5 a \right)}{20 b}+\frac{\sin \left(7 b x +7 a \right)}{112 b}+\frac{\sin \left(9 b x +9 a \right)}{144 b}"," ",0,"3/8*sin(b*x+a)/b-1/12*sin(3*b*x+3*a)/b-1/20/b*sin(5*b*x+5*a)+1/112/b*sin(7*b*x+7*a)+1/144/b*sin(9*b*x+9*a)","A"
133,1,55,27,0.409000," ","int(cos(b*x+a)*sin(2*b*x+2*a)^3,x)","-\frac{3 \cos \left(b x +a \right)}{8 b}-\frac{\cos \left(3 b x +3 a \right)}{8 b}+\frac{\cos \left(5 b x +5 a \right)}{40 b}+\frac{\cos \left(7 b x +7 a \right)}{56 b}"," ",0,"-3/8*cos(b*x+a)/b-1/8*cos(3*b*x+3*a)/b+1/40*cos(5*b*x+5*a)/b+1/56*cos(7*b*x+7*a)/b","A"
134,1,41,27,0.622000," ","int(cos(b*x+a)*sin(2*b*x+2*a)^2,x)","\frac{\sin \left(b x +a \right)}{2 b}-\frac{\sin \left(3 b x +3 a \right)}{12 b}-\frac{\sin \left(5 b x +5 a \right)}{20 b}"," ",0,"1/2*sin(b*x+a)/b-1/12*sin(3*b*x+3*a)/b-1/20/b*sin(5*b*x+5*a)","A"
135,1,27,26,0.219000," ","int(cos(b*x+a)*sin(2*b*x+2*a),x)","-\frac{\cos \left(b x +a \right)}{2 b}-\frac{\cos \left(3 b x +3 a \right)}{6 b}"," ",0,"-1/2*cos(b*x+a)/b-1/6*cos(3*b*x+3*a)/b","A"
136,1,22,12,0.551000," ","int(cos(b*x+a)/sin(2*b*x+2*a),x)","\frac{\ln \left(\csc \left(b x +a \right)-\cot \left(b x +a \right)\right)}{2 b}"," ",0,"1/2/b*ln(csc(b*x+a)-cot(b*x+a))","A"
137,1,34,24,0.861000," ","int(cos(b*x+a)/sin(2*b*x+2*a)^2,x)","-\frac{1}{4 b \sin \left(b x +a \right)}+\frac{\ln \left(\sec \left(b x +a \right)+\tan \left(b x +a \right)\right)}{4 b}"," ",0,"-1/4/b/sin(b*x+a)+1/4/b*ln(sec(b*x+a)+tan(b*x+a))","A"
138,1,57,43,0.947000," ","int(cos(b*x+a)/sin(2*b*x+2*a)^3,x)","-\frac{1}{16 b \sin \left(b x +a \right)^{2} \cos \left(b x +a \right)}+\frac{3}{16 b \cos \left(b x +a \right)}+\frac{3 \ln \left(\csc \left(b x +a \right)-\cot \left(b x +a \right)\right)}{16 b}"," ",0,"-1/16/b/sin(b*x+a)^2/cos(b*x+a)+3/16/b/cos(b*x+a)+3/16/b*ln(csc(b*x+a)-cot(b*x+a))","A"
139,1,76,58,1.113000," ","int(cos(b*x+a)/sin(2*b*x+2*a)^4,x)","-\frac{1}{48 b \sin \left(b x +a \right)^{3} \cos \left(b x +a \right)^{2}}+\frac{5}{96 b \sin \left(b x +a \right) \cos \left(b x +a \right)^{2}}-\frac{5}{32 b \sin \left(b x +a \right)}+\frac{5 \ln \left(\sec \left(b x +a \right)+\tan \left(b x +a \right)\right)}{32 b}"," ",0,"-1/48/b/sin(b*x+a)^3/cos(b*x+a)^2+5/96/b/sin(b*x+a)/cos(b*x+a)^2-5/32/b/sin(b*x+a)+5/32/b*ln(sec(b*x+a)+tan(b*x+a))","A"
140,1,99,79,0.963000," ","int(cos(b*x+a)/sin(2*b*x+2*a)^5,x)","-\frac{1}{128 b \sin \left(b x +a \right)^{4} \cos \left(b x +a \right)^{3}}+\frac{7}{384 b \sin \left(b x +a \right)^{2} \cos \left(b x +a \right)^{3}}-\frac{35}{768 b \sin \left(b x +a \right)^{2} \cos \left(b x +a \right)}+\frac{35}{256 b \cos \left(b x +a \right)}+\frac{35 \ln \left(\csc \left(b x +a \right)-\cot \left(b x +a \right)\right)}{256 b}"," ",0,"-1/128/b/sin(b*x+a)^4/cos(b*x+a)^3+7/384/b/sin(b*x+a)^2/cos(b*x+a)^3-35/768/b/sin(b*x+a)^2/cos(b*x+a)+35/256/b/cos(b*x+a)+35/256/b*ln(csc(b*x+a)-cot(b*x+a))","A"
141,1,86,40,0.339000," ","int(cos(b*x+a)^2*sin(2*b*x+2*a)^5,x)","-\frac{5 \cos \left(2 b x +2 a \right)}{32 b}-\frac{5 \cos \left(4 b x +4 a \right)}{256 b}+\frac{5 \cos \left(6 b x +6 a \right)}{192 b}+\frac{\cos \left(8 b x +8 a \right)}{128 b}-\frac{\cos \left(10 b x +10 a \right)}{320 b}-\frac{\cos \left(12 b x +12 a \right)}{768 b}"," ",0,"-5/32*cos(2*b*x+2*a)/b-5/256*cos(4*b*x+4*a)/b+5/192*cos(6*b*x+6*a)/b+1/128*cos(8*b*x+8*a)/b-1/320*cos(10*b*x+10*a)/b-1/768*cos(12*b*x+12*a)/b","B"
142,1,75,68,1.652000," ","int(cos(b*x+a)^2*sin(2*b*x+2*a)^4,x)","\frac{3 x}{16}+\frac{\sin \left(2 b x +2 a \right)}{32 b}-\frac{\sin \left(4 b x +4 a \right)}{16 b}-\frac{\sin \left(6 b x +6 a \right)}{64 b}+\frac{\sin \left(8 b x +8 a \right)}{128 b}+\frac{\sin \left(10 b x +10 a \right)}{320 b}"," ",0,"3/16*x+1/32*sin(2*b*x+2*a)/b-1/16/b*sin(4*b*x+4*a)-1/64/b*sin(6*b*x+6*a)+1/128/b*sin(8*b*x+8*a)+1/320/b*sin(10*b*x+10*a)","A"
143,1,58,26,0.416000," ","int(cos(b*x+a)^2*sin(2*b*x+2*a)^3,x)","-\frac{3 \cos \left(2 b x +2 a \right)}{16 b}-\frac{\cos \left(4 b x +4 a \right)}{32 b}+\frac{\cos \left(6 b x +6 a \right)}{48 b}+\frac{\cos \left(8 b x +8 a \right)}{128 b}"," ",0,"-3/16*cos(2*b*x+2*a)/b-1/32*cos(4*b*x+4*a)/b+1/48*cos(6*b*x+6*a)/b+1/128*cos(8*b*x+8*a)/b","B"
144,1,47,43,0.962000," ","int(cos(b*x+a)^2*sin(2*b*x+2*a)^2,x)","\frac{x}{4}+\frac{\sin \left(2 b x +2 a \right)}{16 b}-\frac{\sin \left(4 b x +4 a \right)}{16 b}-\frac{\sin \left(6 b x +6 a \right)}{48 b}"," ",0,"1/4*x+1/16*sin(2*b*x+2*a)/b-1/16/b*sin(4*b*x+4*a)-1/48/b*sin(6*b*x+6*a)","A"
145,1,30,13,0.240000," ","int(cos(b*x+a)^2*sin(2*b*x+2*a),x)","-\frac{\cos \left(2 b x +2 a \right)}{4 b}-\frac{\cos \left(4 b x +4 a \right)}{16 b}"," ",0,"-1/4*cos(2*b*x+2*a)/b-1/16*cos(4*b*x+4*a)/b","B"
146,1,13,12,0.644000," ","int(cos(b*x+a)^2/sin(2*b*x+2*a),x)","\frac{\ln \left(\sin \left(b x +a \right)\right)}{2 b}"," ",0,"1/2*ln(sin(b*x+a))/b","A"
147,1,12,11,1.128000," ","int(cos(b*x+a)^2/sin(2*b*x+2*a)^2,x)","-\frac{\cot \left(b x +a \right)}{4 b}"," ",0,"-1/4*cot(b*x+a)/b","A"
148,1,27,26,1.075000," ","int(cos(b*x+a)^2/sin(2*b*x+2*a)^3,x)","-\frac{1}{16 b \sin \left(b x +a \right)^{2}}+\frac{\ln \left(\tan \left(b x +a \right)\right)}{8 b}"," ",0,"-1/16/b/sin(b*x+a)^2+1/8*ln(tan(b*x+a))/b","A"
149,1,51,36,1.625000," ","int(cos(b*x+a)^2/sin(2*b*x+2*a)^4,x)","\frac{-\frac{1}{3 \sin \left(b x +a \right)^{3} \cos \left(b x +a \right)}+\frac{4}{3 \sin \left(b x +a \right) \cos \left(b x +a \right)}-\frac{8 \cot \left(b x +a \right)}{3}}{16 b}"," ",0,"1/16/b*(-1/3/sin(b*x+a)^3/cos(b*x+a)+4/3/sin(b*x+a)/cos(b*x+a)-8/3*cot(b*x+a))","A"
150,1,69,52,1.265000," ","int(cos(b*x+a)^2/sin(2*b*x+2*a)^5,x)","-\frac{1}{128 b \sin \left(b x +a \right)^{4} \cos \left(b x +a \right)^{2}}+\frac{3}{128 b \sin \left(b x +a \right)^{2} \cos \left(b x +a \right)^{2}}-\frac{3}{64 b \sin \left(b x +a \right)^{2}}+\frac{3 \ln \left(\tan \left(b x +a \right)\right)}{32 b}"," ",0,"-1/128/b/sin(b*x+a)^4/cos(b*x+a)^2+3/128/b/sin(b*x+a)^2/cos(b*x+a)^2-3/64/b/sin(b*x+a)^2+3/32*ln(tan(b*x+a))/b","A"
151,1,97,40,0.397000," ","int(cos(b*x+a)^3*sin(2*b*x+2*a)^5,x)","-\frac{5 \cos \left(b x +a \right)}{32 b}-\frac{25 \cos \left(3 b x +3 a \right)}{384 b}+\frac{\cos \left(5 b x +5 a \right)}{128 b}+\frac{\cos \left(7 b x +7 a \right)}{64 b}+\frac{\cos \left(9 b x +9 a \right)}{576 b}-\frac{3 \cos \left(11 b x +11 a \right)}{1408 b}-\frac{\cos \left(13 b x +13 a \right)}{1664 b}"," ",0,"-5/32*cos(b*x+a)/b-25/384*cos(3*b*x+3*a)/b+1/128*cos(5*b*x+5*a)/b+1/64*cos(7*b*x+7*a)/b+1/576*cos(9*b*x+9*a)/b-3/1408*cos(11*b*x+11*a)/b-1/1664*cos(13*b*x+13*a)/b","B"
152,1,83,53,1.251000," ","int(cos(b*x+a)^3*sin(2*b*x+2*a)^4,x)","\frac{7 \sin \left(b x +a \right)}{32 b}-\frac{\sin \left(3 b x +3 a \right)}{32 b}-\frac{11 \sin \left(5 b x +5 a \right)}{320 b}-\frac{\sin \left(7 b x +7 a \right)}{448 b}+\frac{\sin \left(9 b x +9 a \right)}{192 b}+\frac{\sin \left(11 b x +11 a \right)}{704 b}"," ",0,"7/32*sin(b*x+a)/b-1/32*sin(3*b*x+3*a)/b-11/320/b*sin(5*b*x+5*a)-1/448/b*sin(7*b*x+7*a)+1/192/b*sin(9*b*x+9*a)+1/704/b*sin(11*b*x+11*a)","A"
153,1,55,27,0.454000," ","int(cos(b*x+a)^3*sin(2*b*x+2*a)^3,x)","-\frac{3 \cos \left(b x +a \right)}{16 b}-\frac{\cos \left(3 b x +3 a \right)}{12 b}+\frac{3 \cos \left(7 b x +7 a \right)}{224 b}+\frac{\cos \left(9 b x +9 a \right)}{288 b}"," ",0,"-3/16*cos(b*x+a)/b-1/12*cos(3*b*x+3*a)/b+3/224*cos(7*b*x+7*a)/b+1/288*cos(9*b*x+9*a)/b","A"
154,1,55,40,0.987000," ","int(cos(b*x+a)^3*sin(2*b*x+2*a)^2,x)","\frac{5 \sin \left(b x +a \right)}{16 b}-\frac{\sin \left(3 b x +3 a \right)}{48 b}-\frac{3 \sin \left(5 b x +5 a \right)}{80 b}-\frac{\sin \left(7 b x +7 a \right)}{112 b}"," ",0,"5/16*sin(b*x+a)/b-1/48*sin(3*b*x+3*a)/b-3/80/b*sin(5*b*x+5*a)-1/112/b*sin(7*b*x+7*a)","A"
155,1,41,13,0.169000," ","int(cos(b*x+a)^3*sin(2*b*x+2*a),x)","-\frac{\cos \left(b x +a \right)}{4 b}-\frac{\cos \left(3 b x +3 a \right)}{8 b}-\frac{\cos \left(5 b x +5 a \right)}{40 b}"," ",0,"-1/4*cos(b*x+a)/b-1/8*cos(3*b*x+3*a)/b-1/40*cos(5*b*x+5*a)/b","B"
156,1,34,24,0.565000," ","int(cos(b*x+a)^3/sin(2*b*x+2*a),x)","\frac{\cos \left(b x +a \right)}{2 b}+\frac{\ln \left(\csc \left(b x +a \right)-\cot \left(b x +a \right)\right)}{2 b}"," ",0,"1/2*cos(b*x+a)/b+1/2/b*ln(csc(b*x+a)-cot(b*x+a))","A"
157,1,14,11,0.472000," ","int(cos(b*x+a)^3/sin(2*b*x+2*a)^2,x)","-\frac{1}{4 b \sin \left(b x +a \right)}"," ",0,"-1/4/b/sin(b*x+a)","A"
158,1,40,30,0.857000," ","int(cos(b*x+a)^3/sin(2*b*x+2*a)^3,x)","-\frac{\cot \left(b x +a \right) \csc \left(b x +a \right)}{16 b}+\frac{\ln \left(\csc \left(b x +a \right)-\cot \left(b x +a \right)\right)}{16 b}"," ",0,"-1/16*cot(b*x+a)*csc(b*x+a)/b+1/16/b*ln(csc(b*x+a)-cot(b*x+a))","A"
159,1,47,37,1.214000," ","int(cos(b*x+a)^3/sin(2*b*x+2*a)^4,x)","-\frac{1}{48 b \sin \left(b x +a \right)^{3}}-\frac{1}{16 b \sin \left(b x +a \right)}+\frac{\ln \left(\sec \left(b x +a \right)+\tan \left(b x +a \right)\right)}{16 b}"," ",0,"-1/48/b/sin(b*x+a)^3-1/16/b/sin(b*x+a)+1/16/b*ln(sec(b*x+a)+tan(b*x+a))","A"
160,1,78,62,1.120000," ","int(cos(b*x+a)^3/sin(2*b*x+2*a)^5,x)","-\frac{1}{128 b \sin \left(b x +a \right)^{4} \cos \left(b x +a \right)}-\frac{5}{256 b \sin \left(b x +a \right)^{2} \cos \left(b x +a \right)}+\frac{15}{256 b \cos \left(b x +a \right)}+\frac{15 \ln \left(\csc \left(b x +a \right)-\cot \left(b x +a \right)\right)}{256 b}"," ",0,"-1/128/b/sin(b*x+a)^4/cos(b*x+a)-5/256/b/sin(b*x+a)^2/cos(b*x+a)+15/256/b/cos(b*x+a)+15/256/b*ln(csc(b*x+a)-cot(b*x+a))","A"
161,1,199880292,118,91.921000," ","int(cos(b*x+a)*sin(2*b*x+2*a)^(5/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
162,1,74316382,96,24.515000," ","int(cos(b*x+a)*sin(2*b*x+2*a)^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
163,1,5342284,74,2.750000," ","int(cos(b*x+a)*sin(2*b*x+2*a)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
164,1,16154758,52,3.185000," ","int(cos(b*x+a)/sin(2*b*x+2*a)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
165,1,55902198,22,10.737000," ","int(cos(b*x+a)/sin(2*b*x+2*a)^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
166,1,194,45,33.699000," ","int(cos(b*x+a)/sin(2*b*x+2*a)^(5/2),x)","-\frac{\sqrt{-\frac{\tan \left(\frac{b x}{2}+\frac{a}{2}\right)}{\tan^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)-1}}\, \left(\tan^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)-1\right) \left(2 \sqrt{\tan \left(\frac{b x}{2}+\frac{a}{2}\right)+1}\, \sqrt{-2 \tan \left(\frac{b x}{2}+\frac{a}{2}\right)+2}\, \sqrt{-\tan \left(\frac{b x}{2}+\frac{a}{2}\right)}\, \EllipticF \left(\sqrt{\tan \left(\frac{b x}{2}+\frac{a}{2}\right)+1}, \frac{\sqrt{2}}{2}\right) \tan \left(\frac{b x}{2}+\frac{a}{2}\right)-\left(\tan^{4}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+1\right)}{24 b \tan \left(\frac{b x}{2}+\frac{a}{2}\right) \sqrt{\tan \left(\frac{b x}{2}+\frac{a}{2}\right) \left(\tan^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)-1\right)}\, \sqrt{\tan^{3}\left(\frac{b x}{2}+\frac{a}{2}\right)-\tan \left(\frac{b x}{2}+\frac{a}{2}\right)}}"," ",0,"-1/24/b*(-tan(1/2*b*x+1/2*a)/(tan(1/2*b*x+1/2*a)^2-1))^(1/2)*(tan(1/2*b*x+1/2*a)^2-1)/tan(1/2*b*x+1/2*a)*(2*(tan(1/2*b*x+1/2*a)+1)^(1/2)*(-2*tan(1/2*b*x+1/2*a)+2)^(1/2)*(-tan(1/2*b*x+1/2*a))^(1/2)*EllipticF((tan(1/2*b*x+1/2*a)+1)^(1/2),1/2*2^(1/2))*tan(1/2*b*x+1/2*a)-tan(1/2*b*x+1/2*a)^4+1)/(tan(1/2*b*x+1/2*a)*(tan(1/2*b*x+1/2*a)^2-1))^(1/2)/(tan(1/2*b*x+1/2*a)^3-tan(1/2*b*x+1/2*a))^(1/2)","C"
167,-1,0,67,180.000000," ","int(cos(b*x+a)/sin(2*b*x+2*a)^(7/2),x)","\int \frac{\cos \left(b x +a \right)}{\sin \left(2 b x +2 a \right)^{\frac{7}{2}}}\, dx"," ",0,"int(cos(b*x+a)/sin(2*b*x+2*a)^(7/2),x)","F"
168,-1,0,89,180.000000," ","int(cos(b*x+a)/sin(2*b*x+2*a)^(9/2),x)","\int \frac{\cos \left(b x +a \right)}{\sin \left(2 b x +2 a \right)^{\frac{9}{2}}}\, dx"," ",0,"int(cos(b*x+a)/sin(2*b*x+2*a)^(9/2),x)","F"
169,-1,0,109,180.000000," ","int(cos(b*x+a)^2*sin(2*b*x+2*a)^(7/2),x)","\int \left(\cos^{2}\left(b x +a \right)\right) \left(\sin^{\frac{7}{2}}\left(2 b x +2 a \right)\right)\, dx"," ",0,"int(cos(b*x+a)^2*sin(2*b*x+2*a)^(7/2),x)","F"
170,1,336654856,84,196.388000," ","int(cos(b*x+a)^2*sin(2*b*x+2*a)^(5/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
171,1,174364216,84,61.350000," ","int(cos(b*x+a)^2*sin(2*b*x+2*a)^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
172,1,24858211,59,7.574000," ","int(cos(b*x+a)^2*sin(2*b*x+2*a)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
173,1,59624230,59,15.386000," ","int(cos(b*x+a)^2/sin(2*b*x+2*a)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
174,1,94273592,67,17.328000," ","int(cos(b*x+a)^2/sin(2*b*x+2*a)^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
175,1,123,67,59.046000," ","int(cos(b*x+a)^2/sin(2*b*x+2*a)^(5/2),x)","\frac{\sqrt{1+\sin \left(2 b x +2 a \right)}\, \sqrt{-2 \sin \left(2 b x +2 a \right)+2}\, \sqrt{-\sin \left(2 b x +2 a \right)}\, \EllipticF \left(\sqrt{1+\sin \left(2 b x +2 a \right)}, \frac{\sqrt{2}}{2}\right) \sin \left(2 b x +2 a \right)-2 \left(\cos^{2}\left(2 b x +2 a \right)\right)-2 \cos \left(2 b x +2 a \right)}{12 \sin \left(2 b x +2 a \right)^{\frac{3}{2}} \cos \left(2 b x +2 a \right) b}"," ",0,"1/12/sin(2*b*x+2*a)^(3/2)/cos(2*b*x+2*a)*((1+sin(2*b*x+2*a))^(1/2)*(-2*sin(2*b*x+2*a)+2)^(1/2)*(-sin(2*b*x+2*a))^(1/2)*EllipticF((1+sin(2*b*x+2*a))^(1/2),1/2*2^(1/2))*sin(2*b*x+2*a)-2*cos(2*b*x+2*a)^2-2*cos(2*b*x+2*a))/b","A"
176,1,227,92,212.846000," ","int(cos(b*x+a)^2/sin(2*b*x+2*a)^(7/2),x)","\frac{\sqrt{2}\, \left(-\frac{8 \sqrt{2}}{5 \sin \left(2 b x +2 a \right)^{\frac{5}{2}}}+\frac{4 \sqrt{2}\, \left(6 \sqrt{1+\sin \left(2 b x +2 a \right)}\, \sqrt{-2 \sin \left(2 b x +2 a \right)+2}\, \sqrt{-\sin \left(2 b x +2 a \right)}\, \left(\sin^{2}\left(2 b x +2 a \right)\right) \EllipticE \left(\sqrt{1+\sin \left(2 b x +2 a \right)}, \frac{\sqrt{2}}{2}\right)-3 \sqrt{1+\sin \left(2 b x +2 a \right)}\, \sqrt{-2 \sin \left(2 b x +2 a \right)+2}\, \sqrt{-\sin \left(2 b x +2 a \right)}\, \left(\sin^{2}\left(2 b x +2 a \right)\right) \EllipticF \left(\sqrt{1+\sin \left(2 b x +2 a \right)}, \frac{\sqrt{2}}{2}\right)+6 \left(\sin^{4}\left(2 b x +2 a \right)\right)-4 \left(\sin^{2}\left(2 b x +2 a \right)\right)-2\right)}{5 \sin \left(2 b x +2 a \right)^{\frac{5}{2}} \cos \left(2 b x +2 a \right)}\right)}{32 b}"," ",0,"1/32*2^(1/2)*(-8/5*2^(1/2)/sin(2*b*x+2*a)^(5/2)+4/5*2^(1/2)/sin(2*b*x+2*a)^(5/2)*(6*(1+sin(2*b*x+2*a))^(1/2)*(-2*sin(2*b*x+2*a)+2)^(1/2)*(-sin(2*b*x+2*a))^(1/2)*sin(2*b*x+2*a)^2*EllipticE((1+sin(2*b*x+2*a))^(1/2),1/2*2^(1/2))-3*(1+sin(2*b*x+2*a))^(1/2)*(-2*sin(2*b*x+2*a)+2)^(1/2)*(-sin(2*b*x+2*a))^(1/2)*sin(2*b*x+2*a)^2*EllipticF((1+sin(2*b*x+2*a))^(1/2),1/2*2^(1/2))+6*sin(2*b*x+2*a)^4-4*sin(2*b*x+2*a)^2-2)/cos(2*b*x+2*a))/b","B"
177,-1,0,118,180.000000," ","int(cos(b*x+a)^3*sin(2*b*x+2*a)^(3/2),x)","\int \left(\cos^{3}\left(b x +a \right)\right) \left(\sin^{\frac{3}{2}}\left(2 b x +2 a \right)\right)\, dx"," ",0,"int(cos(b*x+a)^3*sin(2*b*x+2*a)^(3/2),x)","F"
178,1,88680892,96,32.658000," ","int(cos(b*x+a)^3*sin(2*b*x+2*a)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
179,1,191110780,74,69.299000," ","int(cos(b*x+a)^3/sin(2*b*x+2*a)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
180,1,179323229,74,32.122000," ","int(cos(b*x+a)^3/sin(2*b*x+2*a)^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
181,1,192,24,167.451000," ","int(cos(b*x+a)^3/sin(2*b*x+2*a)^(5/2),x)","\frac{\sqrt{-\frac{\tan \left(\frac{b x}{2}+\frac{a}{2}\right)}{\tan^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)-1}}\, \left(\tan^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)-1\right) \left(4 \sqrt{\tan \left(\frac{b x}{2}+\frac{a}{2}\right)+1}\, \sqrt{-2 \tan \left(\frac{b x}{2}+\frac{a}{2}\right)+2}\, \sqrt{-\tan \left(\frac{b x}{2}+\frac{a}{2}\right)}\, \EllipticF \left(\sqrt{\tan \left(\frac{b x}{2}+\frac{a}{2}\right)+1}, \frac{\sqrt{2}}{2}\right) \tan \left(\frac{b x}{2}+\frac{a}{2}\right)+\tan^{4}\left(\frac{b x}{2}+\frac{a}{2}\right)-1\right)}{24 \tan \left(\frac{b x}{2}+\frac{a}{2}\right) \sqrt{\tan \left(\frac{b x}{2}+\frac{a}{2}\right) \left(\tan^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)-1\right)}\, \sqrt{\tan^{3}\left(\frac{b x}{2}+\frac{a}{2}\right)-\tan \left(\frac{b x}{2}+\frac{a}{2}\right)}\, b}"," ",0,"1/24*(-tan(1/2*b*x+1/2*a)/(tan(1/2*b*x+1/2*a)^2-1))^(1/2)*(tan(1/2*b*x+1/2*a)^2-1)/tan(1/2*b*x+1/2*a)*(4*(tan(1/2*b*x+1/2*a)+1)^(1/2)*(-2*tan(1/2*b*x+1/2*a)+2)^(1/2)*(-tan(1/2*b*x+1/2*a))^(1/2)*EllipticF((tan(1/2*b*x+1/2*a)+1)^(1/2),1/2*2^(1/2))*tan(1/2*b*x+1/2*a)+tan(1/2*b*x+1/2*a)^4-1)/(tan(1/2*b*x+1/2*a)*(tan(1/2*b*x+1/2*a)^2-1))^(1/2)/(tan(1/2*b*x+1/2*a)^3-tan(1/2*b*x+1/2*a))^(1/2)/b","C"
182,-1,0,47,180.000000," ","int(cos(b*x+a)^3/sin(2*b*x+2*a)^(7/2),x)","\int \frac{\cos^{3}\left(b x +a \right)}{\sin \left(2 b x +2 a \right)^{\frac{7}{2}}}\, dx"," ",0,"int(cos(b*x+a)^3/sin(2*b*x+2*a)^(7/2),x)","F"
183,-1,0,69,180.000000," ","int(cos(b*x+a)^3/sin(2*b*x+2*a)^(9/2),x)","\int \frac{\cos^{3}\left(b x +a \right)}{\sin \left(2 b x +2 a \right)^{\frac{9}{2}}}\, dx"," ",0,"int(cos(b*x+a)^3/sin(2*b*x+2*a)^(9/2),x)","F"
184,-1,0,91,180.000000," ","int(cos(b*x+a)^3/sin(2*b*x+2*a)^(11/2),x)","\int \frac{\cos^{3}\left(b x +a \right)}{\sin \left(2 b x +2 a \right)^{\frac{11}{2}}}\, dx"," ",0,"int(cos(b*x+a)^3/sin(2*b*x+2*a)^(11/2),x)","F"
185,1,98,25,0.814000," ","int(cos(x)/sin(2*x)^(1/2),x)","\frac{\sqrt{-\frac{\tan \left(\frac{x}{2}\right)}{\tan^{2}\left(\frac{x}{2}\right)-1}}\, \left(\tan^{2}\left(\frac{x}{2}\right)-1\right) \sqrt{\tan \left(\frac{x}{2}\right)+1}\, \sqrt{-2 \tan \left(\frac{x}{2}\right)+2}\, \sqrt{-\tan \left(\frac{x}{2}\right)}\, \EllipticF \left(\sqrt{\tan \left(\frac{x}{2}\right)+1}, \frac{\sqrt{2}}{2}\right)}{\sqrt{\tan \left(\frac{x}{2}\right) \left(\tan^{2}\left(\frac{x}{2}\right)-1\right)}\, \sqrt{\tan^{3}\left(\frac{x}{2}\right)-\tan \left(\frac{x}{2}\right)}}"," ",0,"(-tan(1/2*x)/(tan(1/2*x)^2-1))^(1/2)*(tan(1/2*x)^2-1)/(tan(1/2*x)*(tan(1/2*x)^2-1))^(1/2)*(tan(1/2*x)+1)^(1/2)*(-2*tan(1/2*x)+2)^(1/2)*(-tan(1/2*x))^(1/2)/(tan(1/2*x)^3-tan(1/2*x))^(1/2)*EllipticF((tan(1/2*x)+1)^(1/2),1/2*2^(1/2))","C"
186,1,99,23,2.461000," ","int(csc(x)*sin(2*x)^(1/2),x)","\frac{2 \sqrt{-\frac{\tan \left(\frac{x}{2}\right)}{\tan^{2}\left(\frac{x}{2}\right)-1}}\, \left(\tan^{2}\left(\frac{x}{2}\right)-1\right) \sqrt{\tan \left(\frac{x}{2}\right)+1}\, \sqrt{-2 \tan \left(\frac{x}{2}\right)+2}\, \sqrt{-\tan \left(\frac{x}{2}\right)}\, \EllipticF \left(\sqrt{\tan \left(\frac{x}{2}\right)+1}, \frac{\sqrt{2}}{2}\right)}{\sqrt{\tan \left(\frac{x}{2}\right) \left(\tan^{2}\left(\frac{x}{2}\right)-1\right)}\, \sqrt{\tan^{3}\left(\frac{x}{2}\right)-\tan \left(\frac{x}{2}\right)}}"," ",0,"2*(-tan(1/2*x)/(tan(1/2*x)^2-1))^(1/2)*(tan(1/2*x)^2-1)/(tan(1/2*x)*(tan(1/2*x)^2-1))^(1/2)*(tan(1/2*x)+1)^(1/2)*(-2*tan(1/2*x)+2)^(1/2)*(-tan(1/2*x))^(1/2)/(tan(1/2*x)^3-tan(1/2*x))^(1/2)*EllipticF((tan(1/2*x)+1)^(1/2),1/2*2^(1/2))","C"
187,0,0,75,6.181000," ","int(cos(b*x+a)^3*sin(2*b*x+2*a)^m,x)","\int \left(\cos^{3}\left(b x +a \right)\right) \left(\sin^{m}\left(2 b x +2 a \right)\right)\, dx"," ",0,"int(cos(b*x+a)^3*sin(2*b*x+2*a)^m,x)","F"
188,0,0,75,5.900000," ","int(cos(b*x+a)^2*sin(2*b*x+2*a)^m,x)","\int \left(\cos^{2}\left(b x +a \right)\right) \left(\sin^{m}\left(2 b x +2 a \right)\right)\, dx"," ",0,"int(cos(b*x+a)^2*sin(2*b*x+2*a)^m,x)","F"
189,0,0,73,5.358000," ","int(cos(b*x+a)*sin(2*b*x+2*a)^m,x)","\int \cos \left(b x +a \right) \left(\sin^{m}\left(2 b x +2 a \right)\right)\, dx"," ",0,"int(cos(b*x+a)*sin(2*b*x+2*a)^m,x)","F"
190,1,69,40,0.426000," ","int(cos(b*x+a)^2*sin(b*x+a)^3*sin(2*b*x+2*a)^2,x)","-\frac{3 \cos \left(b x +a \right)}{32 b}-\frac{\cos \left(3 b x +3 a \right)}{48 b}+\frac{\cos \left(5 b x +5 a \right)}{80 b}+\frac{\cos \left(7 b x +7 a \right)}{448 b}-\frac{\cos \left(9 b x +9 a \right)}{576 b}"," ",0,"-3/32*cos(b*x+a)/b-1/48*cos(3*b*x+3*a)/b+1/80*cos(5*b*x+5*a)/b+1/448*cos(7*b*x+7*a)/b-1/576*cos(9*b*x+9*a)/b","A"
191,0,0,268,14.316000," ","int(sin(b*x+a)*sin(d*x+c)^n,x)","\int \sin \left(b x +a \right) \left(\sin^{n}\left(d x +c \right)\right)\, dx"," ",0,"int(sin(b*x+a)*sin(d*x+c)^n,x)","F"
192,1,84,83,0.856000," ","int(sin(b*x+a)*sin(d*x+c)^3,x)","-\frac{\sin \left(a -3 c +\left(b -3 d \right) x \right)}{8 \left(b -3 d \right)}+\frac{3 \sin \left(a -c +\left(b -d \right) x \right)}{8 \left(b -d \right)}-\frac{3 \sin \left(a +c +\left(b +d \right) x \right)}{8 \left(b +d \right)}+\frac{\sin \left(a +3 c +\left(b +3 d \right) x \right)}{8 b +24 d}"," ",0,"-1/8*sin(a-3*c+(b-3*d)*x)/(b-3*d)+3/8*sin(a-c+(b-d)*x)/(b-d)-3/8*sin(a+c+(b+d)*x)/(b+d)+1/8*sin(a+3*c+(b+3*d)*x)/(b+3*d)","A"
193,1,57,56,0.200000," ","int(sin(b*x+a)*sin(d*x+c)^2,x)","-\frac{\cos \left(b x +a \right)}{2 b}+\frac{\cos \left(a -2 c +\left(b -2 d \right) x \right)}{4 b -8 d}+\frac{\cos \left(a +2 c +\left(b +2 d \right) x \right)}{4 b +8 d}"," ",0,"-1/2*cos(b*x+a)/b+1/4*cos(a-2*c+(b-2*d)*x)/(b-2*d)+1/4*cos(a+2*c+(b+2*d)*x)/(b+2*d)","A"
194,1,40,39,0.418000," ","int(sin(b*x+a)*sin(d*x+c),x)","\frac{\sin \left(a -c +\left(b -d \right) x \right)}{2 b -2 d}-\frac{\sin \left(a +c +\left(b +d \right) x \right)}{2 \left(b +d \right)}"," ",0,"1/2*sin(a-c+(b-d)*x)/(b-d)-1/2*sin(a+c+(b+d)*x)/(b+d)","A"
195,1,325,26,1.549000," ","int(csc(b*x+c)*sin(b*x+a),x)","-\frac{\ln \left(\tan \left(b x +a \right) \cos \left(a \right) \cos \left(c \right)+\tan \left(b x +a \right) \sin \left(a \right) \sin \left(c \right)+\cos \left(a \right) \sin \left(c \right)-\sin \left(a \right) \cos \left(c \right)\right) \cos \left(a \right) \sin \left(c \right)}{b \left(\left(\cos^{2}\left(a \right)\right) \left(\cos^{2}\left(c \right)\right)+\left(\cos^{2}\left(a \right)\right) \left(\sin^{2}\left(c \right)\right)+\left(\cos^{2}\left(c \right)\right) \left(\sin^{2}\left(a \right)\right)+\left(\sin^{2}\left(a \right)\right) \left(\sin^{2}\left(c \right)\right)\right)}+\frac{\ln \left(\tan \left(b x +a \right) \cos \left(a \right) \cos \left(c \right)+\tan \left(b x +a \right) \sin \left(a \right) \sin \left(c \right)+\cos \left(a \right) \sin \left(c \right)-\sin \left(a \right) \cos \left(c \right)\right) \sin \left(a \right) \cos \left(c \right)}{b \left(\left(\cos^{2}\left(a \right)\right) \left(\cos^{2}\left(c \right)\right)+\left(\cos^{2}\left(a \right)\right) \left(\sin^{2}\left(c \right)\right)+\left(\cos^{2}\left(c \right)\right) \left(\sin^{2}\left(a \right)\right)+\left(\sin^{2}\left(a \right)\right) \left(\sin^{2}\left(c \right)\right)\right)}+\frac{\ln \left(1+\tan^{2}\left(b x +a \right)\right) \cos \left(a \right) \sin \left(c \right)}{2 b \left(\cos^{2}\left(c \right)+\sin^{2}\left(c \right)\right) \left(\cos^{2}\left(a \right)+\sin^{2}\left(a \right)\right)}-\frac{\ln \left(1+\tan^{2}\left(b x +a \right)\right) \sin \left(a \right) \cos \left(c \right)}{2 b \left(\cos^{2}\left(c \right)+\sin^{2}\left(c \right)\right) \left(\cos^{2}\left(a \right)+\sin^{2}\left(a \right)\right)}+\frac{\arctan \left(\tan \left(b x +a \right)\right) \cos \left(a \right) \cos \left(c \right)}{b \left(\cos^{2}\left(c \right)+\sin^{2}\left(c \right)\right) \left(\cos^{2}\left(a \right)+\sin^{2}\left(a \right)\right)}+\frac{\arctan \left(\tan \left(b x +a \right)\right) \sin \left(a \right) \sin \left(c \right)}{b \left(\cos^{2}\left(c \right)+\sin^{2}\left(c \right)\right) \left(\cos^{2}\left(a \right)+\sin^{2}\left(a \right)\right)}"," ",0,"-1/b/(cos(a)^2*cos(c)^2+cos(a)^2*sin(c)^2+cos(c)^2*sin(a)^2+sin(a)^2*sin(c)^2)*ln(tan(b*x+a)*cos(a)*cos(c)+tan(b*x+a)*sin(a)*sin(c)+cos(a)*sin(c)-sin(a)*cos(c))*cos(a)*sin(c)+1/b/(cos(a)^2*cos(c)^2+cos(a)^2*sin(c)^2+cos(c)^2*sin(a)^2+sin(a)^2*sin(c)^2)*ln(tan(b*x+a)*cos(a)*cos(c)+tan(b*x+a)*sin(a)*sin(c)+cos(a)*sin(c)-sin(a)*cos(c))*sin(a)*cos(c)+1/2/b/(cos(c)^2+sin(c)^2)/(cos(a)^2+sin(a)^2)*ln(1+tan(b*x+a)^2)*cos(a)*sin(c)-1/2/b/(cos(c)^2+sin(c)^2)/(cos(a)^2+sin(a)^2)*ln(1+tan(b*x+a)^2)*sin(a)*cos(c)+1/b/(cos(c)^2+sin(c)^2)/(cos(a)^2+sin(a)^2)*arctan(tan(b*x+a))*cos(a)*cos(c)+1/b/(cos(c)^2+sin(c)^2)/(cos(a)^2+sin(a)^2)*arctan(tan(b*x+a))*sin(a)*sin(c)","B"
196,1,890,36,2.226000," ","int(csc(b*x+c)^2*sin(b*x+a),x)","-\frac{8 \tan \left(\frac{b x}{2}+\frac{a}{2}\right) \cos \left(a \right) \cos \left(c \right)}{b \left(-4 \left(\cos^{2}\left(a \right)\right) \left(\cos^{2}\left(c \right)\right)-4 \left(\cos^{2}\left(a \right)\right) \left(\sin^{2}\left(c \right)\right)-4 \left(\cos^{2}\left(c \right)\right) \left(\sin^{2}\left(a \right)\right)-4 \left(\sin^{2}\left(a \right)\right) \left(\sin^{2}\left(c \right)\right)\right) \left(-\cos \left(a \right) \sin \left(c \right) \left(\tan^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+\cos \left(c \right) \sin \left(a \right) \left(\tan^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+2 \tan \left(\frac{b x}{2}+\frac{a}{2}\right) \cos \left(a \right) \cos \left(c \right)+2 \tan \left(\frac{b x}{2}+\frac{a}{2}\right) \sin \left(a \right) \sin \left(c \right)+\cos \left(a \right) \sin \left(c \right)-\sin \left(a \right) \cos \left(c \right)\right)}-\frac{8 \tan \left(\frac{b x}{2}+\frac{a}{2}\right) \sin \left(a \right) \sin \left(c \right)}{b \left(-4 \left(\cos^{2}\left(a \right)\right) \left(\cos^{2}\left(c \right)\right)-4 \left(\cos^{2}\left(a \right)\right) \left(\sin^{2}\left(c \right)\right)-4 \left(\cos^{2}\left(c \right)\right) \left(\sin^{2}\left(a \right)\right)-4 \left(\sin^{2}\left(a \right)\right) \left(\sin^{2}\left(c \right)\right)\right) \left(-\cos \left(a \right) \sin \left(c \right) \left(\tan^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+\cos \left(c \right) \sin \left(a \right) \left(\tan^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+2 \tan \left(\frac{b x}{2}+\frac{a}{2}\right) \cos \left(a \right) \cos \left(c \right)+2 \tan \left(\frac{b x}{2}+\frac{a}{2}\right) \sin \left(a \right) \sin \left(c \right)+\cos \left(a \right) \sin \left(c \right)-\sin \left(a \right) \cos \left(c \right)\right)}-\frac{8 \cos \left(a \right) \sin \left(c \right)}{b \left(-4 \left(\cos^{2}\left(a \right)\right) \left(\cos^{2}\left(c \right)\right)-4 \left(\cos^{2}\left(a \right)\right) \left(\sin^{2}\left(c \right)\right)-4 \left(\cos^{2}\left(c \right)\right) \left(\sin^{2}\left(a \right)\right)-4 \left(\sin^{2}\left(a \right)\right) \left(\sin^{2}\left(c \right)\right)\right) \left(-\cos \left(a \right) \sin \left(c \right) \left(\tan^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+\cos \left(c \right) \sin \left(a \right) \left(\tan^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+2 \tan \left(\frac{b x}{2}+\frac{a}{2}\right) \cos \left(a \right) \cos \left(c \right)+2 \tan \left(\frac{b x}{2}+\frac{a}{2}\right) \sin \left(a \right) \sin \left(c \right)+\cos \left(a \right) \sin \left(c \right)-\sin \left(a \right) \cos \left(c \right)\right)}+\frac{8 \sin \left(a \right) \cos \left(c \right)}{b \left(-4 \left(\cos^{2}\left(a \right)\right) \left(\cos^{2}\left(c \right)\right)-4 \left(\cos^{2}\left(a \right)\right) \left(\sin^{2}\left(c \right)\right)-4 \left(\cos^{2}\left(c \right)\right) \left(\sin^{2}\left(a \right)\right)-4 \left(\sin^{2}\left(a \right)\right) \left(\sin^{2}\left(c \right)\right)\right) \left(-\cos \left(a \right) \sin \left(c \right) \left(\tan^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+\cos \left(c \right) \sin \left(a \right) \left(\tan^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+2 \tan \left(\frac{b x}{2}+\frac{a}{2}\right) \cos \left(a \right) \cos \left(c \right)+2 \tan \left(\frac{b x}{2}+\frac{a}{2}\right) \sin \left(a \right) \sin \left(c \right)+\cos \left(a \right) \sin \left(c \right)-\sin \left(a \right) \cos \left(c \right)\right)}-\frac{8 \arctan \left(\frac{2 \left(\sin \left(a \right) \cos \left(c \right)-\cos \left(a \right) \sin \left(c \right)\right) \tan \left(\frac{b x}{2}+\frac{a}{2}\right)+2 \cos \left(a \right) \cos \left(c \right)+2 \sin \left(a \right) \sin \left(c \right)}{2 \sqrt{-\left(\cos^{2}\left(a \right)\right) \left(\cos^{2}\left(c \right)\right)-\left(\cos^{2}\left(a \right)\right) \left(\sin^{2}\left(c \right)\right)-\left(\cos^{2}\left(c \right)\right) \left(\sin^{2}\left(a \right)\right)-\left(\sin^{2}\left(a \right)\right) \left(\sin^{2}\left(c \right)\right)}}\right) \cos \left(a \right) \cos \left(c \right)}{b \left(-4 \left(\cos^{2}\left(a \right)\right) \left(\cos^{2}\left(c \right)\right)-4 \left(\cos^{2}\left(a \right)\right) \left(\sin^{2}\left(c \right)\right)-4 \left(\cos^{2}\left(c \right)\right) \left(\sin^{2}\left(a \right)\right)-4 \left(\sin^{2}\left(a \right)\right) \left(\sin^{2}\left(c \right)\right)\right) \sqrt{-\left(\cos^{2}\left(a \right)\right) \left(\cos^{2}\left(c \right)\right)-\left(\cos^{2}\left(a \right)\right) \left(\sin^{2}\left(c \right)\right)-\left(\cos^{2}\left(c \right)\right) \left(\sin^{2}\left(a \right)\right)-\left(\sin^{2}\left(a \right)\right) \left(\sin^{2}\left(c \right)\right)}}-\frac{8 \arctan \left(\frac{2 \left(\sin \left(a \right) \cos \left(c \right)-\cos \left(a \right) \sin \left(c \right)\right) \tan \left(\frac{b x}{2}+\frac{a}{2}\right)+2 \cos \left(a \right) \cos \left(c \right)+2 \sin \left(a \right) \sin \left(c \right)}{2 \sqrt{-\left(\cos^{2}\left(a \right)\right) \left(\cos^{2}\left(c \right)\right)-\left(\cos^{2}\left(a \right)\right) \left(\sin^{2}\left(c \right)\right)-\left(\cos^{2}\left(c \right)\right) \left(\sin^{2}\left(a \right)\right)-\left(\sin^{2}\left(a \right)\right) \left(\sin^{2}\left(c \right)\right)}}\right) \sin \left(a \right) \sin \left(c \right)}{b \left(-4 \left(\cos^{2}\left(a \right)\right) \left(\cos^{2}\left(c \right)\right)-4 \left(\cos^{2}\left(a \right)\right) \left(\sin^{2}\left(c \right)\right)-4 \left(\cos^{2}\left(c \right)\right) \left(\sin^{2}\left(a \right)\right)-4 \left(\sin^{2}\left(a \right)\right) \left(\sin^{2}\left(c \right)\right)\right) \sqrt{-\left(\cos^{2}\left(a \right)\right) \left(\cos^{2}\left(c \right)\right)-\left(\cos^{2}\left(a \right)\right) \left(\sin^{2}\left(c \right)\right)-\left(\cos^{2}\left(c \right)\right) \left(\sin^{2}\left(a \right)\right)-\left(\sin^{2}\left(a \right)\right) \left(\sin^{2}\left(c \right)\right)}}"," ",0,"-8/b/(-4*cos(a)^2*cos(c)^2-4*cos(a)^2*sin(c)^2-4*cos(c)^2*sin(a)^2-4*sin(a)^2*sin(c)^2)/(-cos(a)*sin(c)*tan(1/2*b*x+1/2*a)^2+cos(c)*sin(a)*tan(1/2*b*x+1/2*a)^2+2*tan(1/2*b*x+1/2*a)*cos(a)*cos(c)+2*tan(1/2*b*x+1/2*a)*sin(a)*sin(c)+cos(a)*sin(c)-sin(a)*cos(c))*tan(1/2*b*x+1/2*a)*cos(a)*cos(c)-8/b/(-4*cos(a)^2*cos(c)^2-4*cos(a)^2*sin(c)^2-4*cos(c)^2*sin(a)^2-4*sin(a)^2*sin(c)^2)/(-cos(a)*sin(c)*tan(1/2*b*x+1/2*a)^2+cos(c)*sin(a)*tan(1/2*b*x+1/2*a)^2+2*tan(1/2*b*x+1/2*a)*cos(a)*cos(c)+2*tan(1/2*b*x+1/2*a)*sin(a)*sin(c)+cos(a)*sin(c)-sin(a)*cos(c))*tan(1/2*b*x+1/2*a)*sin(a)*sin(c)-8/b/(-4*cos(a)^2*cos(c)^2-4*cos(a)^2*sin(c)^2-4*cos(c)^2*sin(a)^2-4*sin(a)^2*sin(c)^2)/(-cos(a)*sin(c)*tan(1/2*b*x+1/2*a)^2+cos(c)*sin(a)*tan(1/2*b*x+1/2*a)^2+2*tan(1/2*b*x+1/2*a)*cos(a)*cos(c)+2*tan(1/2*b*x+1/2*a)*sin(a)*sin(c)+cos(a)*sin(c)-sin(a)*cos(c))*cos(a)*sin(c)+8/b/(-4*cos(a)^2*cos(c)^2-4*cos(a)^2*sin(c)^2-4*cos(c)^2*sin(a)^2-4*sin(a)^2*sin(c)^2)/(-cos(a)*sin(c)*tan(1/2*b*x+1/2*a)^2+cos(c)*sin(a)*tan(1/2*b*x+1/2*a)^2+2*tan(1/2*b*x+1/2*a)*cos(a)*cos(c)+2*tan(1/2*b*x+1/2*a)*sin(a)*sin(c)+cos(a)*sin(c)-sin(a)*cos(c))*sin(a)*cos(c)-8/b/(-4*cos(a)^2*cos(c)^2-4*cos(a)^2*sin(c)^2-4*cos(c)^2*sin(a)^2-4*sin(a)^2*sin(c)^2)/(-cos(a)^2*cos(c)^2-cos(a)^2*sin(c)^2-cos(c)^2*sin(a)^2-sin(a)^2*sin(c)^2)^(1/2)*arctan(1/2*(2*(sin(a)*cos(c)-cos(a)*sin(c))*tan(1/2*b*x+1/2*a)+2*cos(a)*cos(c)+2*sin(a)*sin(c))/(-cos(a)^2*cos(c)^2-cos(a)^2*sin(c)^2-cos(c)^2*sin(a)^2-sin(a)^2*sin(c)^2)^(1/2))*cos(a)*cos(c)-8/b/(-4*cos(a)^2*cos(c)^2-4*cos(a)^2*sin(c)^2-4*cos(c)^2*sin(a)^2-4*sin(a)^2*sin(c)^2)/(-cos(a)^2*cos(c)^2-cos(a)^2*sin(c)^2-cos(c)^2*sin(a)^2-sin(a)^2*sin(c)^2)^(1/2)*arctan(1/2*(2*(sin(a)*cos(c)-cos(a)*sin(c))*tan(1/2*b*x+1/2*a)+2*cos(a)*cos(c)+2*sin(a)*sin(c))/(-cos(a)^2*cos(c)^2-cos(a)^2*sin(c)^2-cos(c)^2*sin(a)^2-sin(a)^2*sin(c)^2)^(1/2))*sin(a)*sin(c)","B"
197,1,120,37,2.343000," ","int(csc(b*x+c)^3*sin(b*x+a),x)","\frac{-\frac{1}{\left(\cos \left(a \right) \cos \left(c \right)+\sin \left(a \right) \sin \left(c \right)\right)^{2} \left(\tan \left(b x +a \right) \cos \left(a \right) \cos \left(c \right)+\tan \left(b x +a \right) \sin \left(a \right) \sin \left(c \right)+\cos \left(a \right) \sin \left(c \right)-\sin \left(a \right) \cos \left(c \right)\right)}-\frac{\sin \left(a \right) \cos \left(c \right)-\cos \left(a \right) \sin \left(c \right)}{2 \left(\cos \left(a \right) \cos \left(c \right)+\sin \left(a \right) \sin \left(c \right)\right)^{2} \left(\tan \left(b x +a \right) \cos \left(a \right) \cos \left(c \right)+\tan \left(b x +a \right) \sin \left(a \right) \sin \left(c \right)+\cos \left(a \right) \sin \left(c \right)-\sin \left(a \right) \cos \left(c \right)\right)^{2}}}{b}"," ",0,"1/b*(-1/(cos(a)*cos(c)+sin(a)*sin(c))^2/(tan(b*x+a)*cos(a)*cos(c)+tan(b*x+a)*sin(a)*sin(c)+cos(a)*sin(c)-sin(a)*cos(c))-1/2*(sin(a)*cos(c)-cos(a)*sin(c))/(cos(a)*cos(c)+sin(a)*sin(c))^2/(tan(b*x+a)*cos(a)*cos(c)+tan(b*x+a)*sin(a)*sin(c)+cos(a)*sin(c)-sin(a)*cos(c))^2)","B"
198,1,14880,61,4.898000," ","int(csc(b*x+c)^4*sin(b*x+a),x)","\text{output too large to display}"," ",0,"result too large to display","B"
199,1,321,56,4.635000," ","int(csc(b*x+c)^5*sin(b*x+a),x)","\frac{\frac{\left(\cos \left(a \right) \sin \left(c \right)-\sin \left(a \right) \cos \left(c \right)\right) \left(\left(\cos^{2}\left(a \right)\right) \left(\cos^{2}\left(c \right)\right)+\left(\cos^{2}\left(a \right)\right) \left(\sin^{2}\left(c \right)\right)+\left(\cos^{2}\left(c \right)\right) \left(\sin^{2}\left(a \right)\right)+\left(\sin^{2}\left(a \right)\right) \left(\sin^{2}\left(c \right)\right)\right)}{4 \left(\cos \left(a \right) \cos \left(c \right)+\sin \left(a \right) \sin \left(c \right)\right)^{4} \left(\tan \left(b x +a \right) \cos \left(a \right) \cos \left(c \right)+\tan \left(b x +a \right) \sin \left(a \right) \sin \left(c \right)+\cos \left(a \right) \sin \left(c \right)-\sin \left(a \right) \cos \left(c \right)\right)^{4}}-\frac{1}{\left(\cos \left(a \right) \cos \left(c \right)+\sin \left(a \right) \sin \left(c \right)\right)^{4} \left(\tan \left(b x +a \right) \cos \left(a \right) \cos \left(c \right)+\tan \left(b x +a \right) \sin \left(a \right) \sin \left(c \right)+\cos \left(a \right) \sin \left(c \right)-\sin \left(a \right) \cos \left(c \right)\right)}-\frac{-3 \cos \left(a \right) \sin \left(c \right)+3 \sin \left(a \right) \cos \left(c \right)}{2 \left(\cos \left(a \right) \cos \left(c \right)+\sin \left(a \right) \sin \left(c \right)\right)^{4} \left(\tan \left(b x +a \right) \cos \left(a \right) \cos \left(c \right)+\tan \left(b x +a \right) \sin \left(a \right) \sin \left(c \right)+\cos \left(a \right) \sin \left(c \right)-\sin \left(a \right) \cos \left(c \right)\right)^{2}}-\frac{\left(\cos^{2}\left(a \right)\right) \left(\cos^{2}\left(c \right)\right)+3 \left(\cos^{2}\left(a \right)\right) \left(\sin^{2}\left(c \right)\right)-4 \cos \left(a \right) \cos \left(c \right) \sin \left(a \right) \sin \left(c \right)+3 \left(\cos^{2}\left(c \right)\right) \left(\sin^{2}\left(a \right)\right)+\left(\sin^{2}\left(a \right)\right) \left(\sin^{2}\left(c \right)\right)}{3 \left(\cos \left(a \right) \cos \left(c \right)+\sin \left(a \right) \sin \left(c \right)\right)^{4} \left(\tan \left(b x +a \right) \cos \left(a \right) \cos \left(c \right)+\tan \left(b x +a \right) \sin \left(a \right) \sin \left(c \right)+\cos \left(a \right) \sin \left(c \right)-\sin \left(a \right) \cos \left(c \right)\right)^{3}}}{b}"," ",0,"1/b*(1/4*(cos(a)*sin(c)-sin(a)*cos(c))*(cos(a)^2*cos(c)^2+cos(a)^2*sin(c)^2+cos(c)^2*sin(a)^2+sin(a)^2*sin(c)^2)/(cos(a)*cos(c)+sin(a)*sin(c))^4/(tan(b*x+a)*cos(a)*cos(c)+tan(b*x+a)*sin(a)*sin(c)+cos(a)*sin(c)-sin(a)*cos(c))^4-1/(cos(a)*cos(c)+sin(a)*sin(c))^4/(tan(b*x+a)*cos(a)*cos(c)+tan(b*x+a)*sin(a)*sin(c)+cos(a)*sin(c)-sin(a)*cos(c))-1/2*(-3*cos(a)*sin(c)+3*sin(a)*cos(c))/(cos(a)*cos(c)+sin(a)*sin(c))^4/(tan(b*x+a)*cos(a)*cos(c)+tan(b*x+a)*sin(a)*sin(c)+cos(a)*sin(c)-sin(a)*cos(c))^2-1/3*(cos(a)^2*cos(c)^2+3*cos(a)^2*sin(c)^2-4*cos(a)*cos(c)*sin(a)*sin(c)+3*cos(c)^2*sin(a)^2+sin(a)^2*sin(c)^2)/(cos(a)*cos(c)+sin(a)*sin(c))^4/(tan(b*x+a)*cos(a)*cos(c)+tan(b*x+a)*sin(a)*sin(c)+cos(a)*sin(c)-sin(a)*cos(c))^3)","B"
200,1,97954,86,14.958000," ","int(csc(b*x+c)^6*sin(b*x+a),x)","\text{output too large to display}"," ",0,"result too large to display","B"
201,0,0,357,7.184000," ","int(sin(b*x+a)^2*sin(d*x+c)^n,x)","\int \left(\sin^{2}\left(b x +a \right)\right) \left(\sin^{n}\left(d x +c \right)\right)\, dx"," ",0,"int(sin(b*x+a)^2*sin(d*x+c)^n,x)","F"
202,1,63,62,0.152000," ","int(sin(b*x+a)^2*sin(d*x+c),x)","-\frac{\cos \left(2 a -c +\left(2 b -d \right) x \right)}{4 \left(2 b -d \right)}-\frac{\cos \left(d x +c \right)}{2 d}+\frac{\cos \left(2 a +c +\left(2 b +d \right) x \right)}{8 b +4 d}"," ",0,"-1/4*cos(2*a-c+(2*b-d)*x)/(2*b-d)-1/2*cos(d*x+c)/d+1/4*cos(2*a+c+(2*b+d)*x)/(2*b+d)","A"
203,1,83,78,1.078000," ","int(sin(b*x+a)^2*sin(d*x+c)^2,x)","\frac{x}{4}-\frac{\sin \left(2 b x +2 a \right)}{8 b}-\frac{\sin \left(2 d x +2 c \right)}{8 d}+\frac{\sin \left(\left(2 b -2 d \right) x +2 a -2 c \right)}{16 b -16 d}+\frac{\sin \left(\left(2 b +2 d \right) x +2 a +2 c \right)}{16 b +16 d}"," ",0,"1/4*x-1/8*sin(2*b*x+2*a)/b-1/8*sin(2*d*x+2*c)/d+1/16/(b-d)*sin((2*b-2*d)*x+2*a-2*c)+1/16/(b+d)*sin((2*b+2*d)*x+2*a+2*c)","A"
204,1,133,132,0.276000," ","int(sin(b*x+a)^2*sin(d*x+c)^3,x)","\frac{\cos \left(2 a -3 c +\left(2 b -3 d \right) x \right)}{32 b -48 d}-\frac{3 \cos \left(2 a -c +\left(2 b -d \right) x \right)}{16 \left(2 b -d \right)}-\frac{3 \cos \left(d x +c \right)}{8 d}+\frac{\cos \left(3 d x +3 c \right)}{24 d}+\frac{3 \cos \left(2 a +c +\left(2 b +d \right) x \right)}{16 \left(2 b +d \right)}-\frac{\cos \left(2 a +3 c +\left(2 b +3 d \right) x \right)}{16 \left(2 b +3 d \right)}"," ",0,"1/16*cos(2*a-3*c+(2*b-3*d)*x)/(2*b-3*d)-3/16*cos(2*a-c+(2*b-d)*x)/(2*b-d)-3/8*cos(d*x+c)/d+1/24*cos(3*d*x+3*c)/d+3/16*cos(2*a+c+(2*b+d)*x)/(2*b+d)-1/16*cos(2*a+3*c+(2*b+3*d)*x)/(2*b+3*d)","A"
205,0,0,540,6.415000," ","int(sin(b*x+a)^3*sin(d*x+c)^n,x)","\int \left(\sin^{3}\left(b x +a \right)\right) \left(\sin^{n}\left(d x +c \right)\right)\, dx"," ",0,"int(sin(b*x+a)^3*sin(d*x+c)^n,x)","F"
206,1,90,89,0.993000," ","int(sin(b*x+a)^3*sin(d*x+c),x)","\frac{3 \sin \left(a -c +\left(b -d \right) x \right)}{8 \left(b -d \right)}-\frac{\sin \left(3 a -c +\left(3 b -d \right) x \right)}{8 \left(3 b -d \right)}-\frac{3 \sin \left(a +c +\left(b +d \right) x \right)}{8 \left(b +d \right)}+\frac{\sin \left(3 a +c +\left(3 b +d \right) x \right)}{24 b +8 d}"," ",0,"3/8*sin(a-c+(b-d)*x)/(b-d)-1/8*sin(3*a-c+(3*b-d)*x)/(3*b-d)-3/8*sin(a+c+(b+d)*x)/(b+d)+1/8*sin(3*a+c+(3*b+d)*x)/(3*b+d)","A"
207,1,127,126,0.293000," ","int(sin(b*x+a)^3*sin(d*x+c)^2,x)","-\frac{3 \cos \left(b x +a \right)}{8 b}+\frac{\cos \left(3 b x +3 a \right)}{24 b}+\frac{3 \cos \left(a -2 c +\left(b -2 d \right) x \right)}{16 \left(b -2 d \right)}-\frac{\cos \left(3 a -2 c +\left(3 b -2 d \right) x \right)}{16 \left(3 b -2 d \right)}+\frac{3 \cos \left(a +2 c +\left(b +2 d \right) x \right)}{16 \left(b +2 d \right)}-\frac{\cos \left(3 a +2 c +\left(3 b +2 d \right) x \right)}{16 \left(3 b +2 d \right)}"," ",0,"-3/8*cos(b*x+a)/b+1/24*cos(3*b*x+3*a)/b+3/16*cos(a-2*c+(b-2*d)*x)/(b-2*d)-1/16*cos(3*a-2*c+(3*b-2*d)*x)/(3*b-2*d)+3/16*cos(a+2*c+(b+2*d)*x)/(b+2*d)-1/16*cos(3*a+2*c+(3*b+2*d)*x)/(3*b+2*d)","A"
208,1,184,179,2.019000," ","int(sin(b*x+a)^3*sin(d*x+c)^3,x)","-\frac{3 \sin \left(a -3 c +\left(b -3 d \right) x \right)}{32 \left(b -3 d \right)}+\frac{9 \sin \left(a -c +\left(b -d \right) x \right)}{32 \left(b -d \right)}-\frac{9 \sin \left(a +c +\left(b +d \right) x \right)}{32 \left(b +d \right)}+\frac{3 \sin \left(a +3 c +\left(b +3 d \right) x \right)}{32 \left(b +3 d \right)}+\frac{\sin \left(\left(3 b -3 d \right) x +3 a -3 c \right)}{96 b -96 d}-\frac{3 \sin \left(3 a -c +\left(3 b -d \right) x \right)}{32 \left(3 b -d \right)}+\frac{3 \sin \left(3 a +c +\left(3 b +d \right) x \right)}{32 \left(3 b +d \right)}-\frac{\sin \left(\left(3 b +3 d \right) x +3 a +3 c \right)}{96 \left(b +d \right)}"," ",0,"-3/32*sin(a-3*c+(b-3*d)*x)/(b-3*d)+9/32*sin(a-c+(b-d)*x)/(b-d)-9/32*sin(a+c+(b+d)*x)/(b+d)+3/32*sin(a+3*c+(b+3*d)*x)/(b+3*d)+1/96/(b-d)*sin((3*b-3*d)*x+3*a-3*c)-3/32*sin(3*a-c+(3*b-d)*x)/(3*b-d)+3/32*sin(3*a+c+(3*b+d)*x)/(3*b+d)-1/96/(b+d)*sin((3*b+3*d)*x+3*a+3*c)","A"
209,0,0,252,3.262000," ","int(cos(d*x+c)^n*sin(b*x+a),x)","\int \left(\cos^{n}\left(d x +c \right)\right) \sin \left(b x +a \right)\, dx"," ",0,"int(cos(d*x+c)^n*sin(b*x+a),x)","F"
210,1,84,83,0.173000," ","int(cos(d*x+c)^3*sin(b*x+a),x)","-\frac{\cos \left(a -3 c +\left(b -3 d \right) x \right)}{8 \left(b -3 d \right)}-\frac{3 \cos \left(a -c +\left(b -d \right) x \right)}{8 \left(b -d \right)}-\frac{3 \cos \left(a +c +\left(b +d \right) x \right)}{8 \left(b +d \right)}-\frac{\cos \left(a +3 c +\left(b +3 d \right) x \right)}{8 \left(b +3 d \right)}"," ",0,"-1/8*cos(a-3*c+(b-3*d)*x)/(b-3*d)-3/8*cos(a-c+(b-d)*x)/(b-d)-3/8*cos(a+c+(b+d)*x)/(b+d)-1/8*cos(a+3*c+(b+3*d)*x)/(b+3*d)","A"
211,1,57,56,0.169000," ","int(cos(d*x+c)^2*sin(b*x+a),x)","-\frac{\cos \left(b x +a \right)}{2 b}-\frac{\cos \left(a -2 c +\left(b -2 d \right) x \right)}{4 \left(b -2 d \right)}-\frac{\cos \left(a +2 c +\left(b +2 d \right) x \right)}{4 \left(b +2 d \right)}"," ",0,"-1/2*cos(b*x+a)/b-1/4*cos(a-2*c+(b-2*d)*x)/(b-2*d)-1/4*cos(a+2*c+(b+2*d)*x)/(b+2*d)","A"
212,1,40,39,0.176000," ","int(cos(d*x+c)*sin(b*x+a),x)","-\frac{\cos \left(a -c +\left(b -d \right) x \right)}{2 \left(b -d \right)}-\frac{\cos \left(a +c +\left(b +d \right) x \right)}{2 \left(b +d \right)}"," ",0,"-1/2*cos(a-c+(b-d)*x)/(b-d)-1/2*cos(a+c+(b+d)*x)/(b+d)","A"
213,1,563,27,1.558000," ","int(sec(b*x+c)*sin(b*x+a),x)","\frac{\ln \left(-\tan \left(b x +a \right) \cos \left(a \right) \sin \left(c \right)+\tan \left(b x +a \right) \sin \left(a \right) \cos \left(c \right)+\cos \left(a \right) \cos \left(c \right)+\sin \left(a \right) \sin \left(c \right)\right) \left(\cos^{2}\left(a \right)\right) \cos \left(c \right) \sin \left(c \right)}{b \left(\left(\cos^{2}\left(a \right)\right) \left(\cos^{2}\left(c \right)\right)+\left(\cos^{2}\left(a \right)\right) \left(\sin^{2}\left(c \right)\right)+\left(\cos^{2}\left(c \right)\right) \left(\sin^{2}\left(a \right)\right)+\left(\sin^{2}\left(a \right)\right) \left(\sin^{2}\left(c \right)\right)\right) \left(\sin \left(a \right) \cos \left(c \right)-\cos \left(a \right) \sin \left(c \right)\right)}-\frac{\ln \left(-\tan \left(b x +a \right) \cos \left(a \right) \sin \left(c \right)+\tan \left(b x +a \right) \sin \left(a \right) \cos \left(c \right)+\cos \left(a \right) \cos \left(c \right)+\sin \left(a \right) \sin \left(c \right)\right) \cos \left(a \right) \left(\cos^{2}\left(c \right)\right) \sin \left(a \right)}{b \left(\left(\cos^{2}\left(a \right)\right) \left(\cos^{2}\left(c \right)\right)+\left(\cos^{2}\left(a \right)\right) \left(\sin^{2}\left(c \right)\right)+\left(\cos^{2}\left(c \right)\right) \left(\sin^{2}\left(a \right)\right)+\left(\sin^{2}\left(a \right)\right) \left(\sin^{2}\left(c \right)\right)\right) \left(\sin \left(a \right) \cos \left(c \right)-\cos \left(a \right) \sin \left(c \right)\right)}+\frac{\ln \left(-\tan \left(b x +a \right) \cos \left(a \right) \sin \left(c \right)+\tan \left(b x +a \right) \sin \left(a \right) \cos \left(c \right)+\cos \left(a \right) \cos \left(c \right)+\sin \left(a \right) \sin \left(c \right)\right) \cos \left(a \right) \sin \left(a \right) \left(\sin^{2}\left(c \right)\right)}{b \left(\left(\cos^{2}\left(a \right)\right) \left(\cos^{2}\left(c \right)\right)+\left(\cos^{2}\left(a \right)\right) \left(\sin^{2}\left(c \right)\right)+\left(\cos^{2}\left(c \right)\right) \left(\sin^{2}\left(a \right)\right)+\left(\sin^{2}\left(a \right)\right) \left(\sin^{2}\left(c \right)\right)\right) \left(\sin \left(a \right) \cos \left(c \right)-\cos \left(a \right) \sin \left(c \right)\right)}-\frac{\ln \left(-\tan \left(b x +a \right) \cos \left(a \right) \sin \left(c \right)+\tan \left(b x +a \right) \sin \left(a \right) \cos \left(c \right)+\cos \left(a \right) \cos \left(c \right)+\sin \left(a \right) \sin \left(c \right)\right) \cos \left(c \right) \left(\sin^{2}\left(a \right)\right) \sin \left(c \right)}{b \left(\left(\cos^{2}\left(a \right)\right) \left(\cos^{2}\left(c \right)\right)+\left(\cos^{2}\left(a \right)\right) \left(\sin^{2}\left(c \right)\right)+\left(\cos^{2}\left(c \right)\right) \left(\sin^{2}\left(a \right)\right)+\left(\sin^{2}\left(a \right)\right) \left(\sin^{2}\left(c \right)\right)\right) \left(\sin \left(a \right) \cos \left(c \right)-\cos \left(a \right) \sin \left(c \right)\right)}+\frac{\ln \left(1+\tan^{2}\left(b x +a \right)\right) \cos \left(a \right) \cos \left(c \right)}{2 b \left(\cos^{2}\left(c \right)+\sin^{2}\left(c \right)\right) \left(\cos^{2}\left(a \right)+\sin^{2}\left(a \right)\right)}+\frac{\ln \left(1+\tan^{2}\left(b x +a \right)\right) \sin \left(a \right) \sin \left(c \right)}{2 b \left(\cos^{2}\left(c \right)+\sin^{2}\left(c \right)\right) \left(\cos^{2}\left(a \right)+\sin^{2}\left(a \right)\right)}-\frac{\cos \left(a \right) \sin \left(c \right) \arctan \left(\tan \left(b x +a \right)\right)}{b \left(\cos^{2}\left(c \right)+\sin^{2}\left(c \right)\right) \left(\cos^{2}\left(a \right)+\sin^{2}\left(a \right)\right)}+\frac{\cos \left(c \right) \sin \left(a \right) \arctan \left(\tan \left(b x +a \right)\right)}{b \left(\cos^{2}\left(c \right)+\sin^{2}\left(c \right)\right) \left(\cos^{2}\left(a \right)+\sin^{2}\left(a \right)\right)}"," ",0,"1/b/(cos(a)^2*cos(c)^2+cos(a)^2*sin(c)^2+cos(c)^2*sin(a)^2+sin(a)^2*sin(c)^2)/(sin(a)*cos(c)-cos(a)*sin(c))*ln(-tan(b*x+a)*cos(a)*sin(c)+tan(b*x+a)*sin(a)*cos(c)+cos(a)*cos(c)+sin(a)*sin(c))*cos(a)^2*cos(c)*sin(c)-1/b/(cos(a)^2*cos(c)^2+cos(a)^2*sin(c)^2+cos(c)^2*sin(a)^2+sin(a)^2*sin(c)^2)/(sin(a)*cos(c)-cos(a)*sin(c))*ln(-tan(b*x+a)*cos(a)*sin(c)+tan(b*x+a)*sin(a)*cos(c)+cos(a)*cos(c)+sin(a)*sin(c))*cos(a)*cos(c)^2*sin(a)+1/b/(cos(a)^2*cos(c)^2+cos(a)^2*sin(c)^2+cos(c)^2*sin(a)^2+sin(a)^2*sin(c)^2)/(sin(a)*cos(c)-cos(a)*sin(c))*ln(-tan(b*x+a)*cos(a)*sin(c)+tan(b*x+a)*sin(a)*cos(c)+cos(a)*cos(c)+sin(a)*sin(c))*cos(a)*sin(a)*sin(c)^2-1/b/(cos(a)^2*cos(c)^2+cos(a)^2*sin(c)^2+cos(c)^2*sin(a)^2+sin(a)^2*sin(c)^2)/(sin(a)*cos(c)-cos(a)*sin(c))*ln(-tan(b*x+a)*cos(a)*sin(c)+tan(b*x+a)*sin(a)*cos(c)+cos(a)*cos(c)+sin(a)*sin(c))*cos(c)*sin(a)^2*sin(c)+1/2/b/(cos(c)^2+sin(c)^2)/(cos(a)^2+sin(a)^2)*ln(1+tan(b*x+a)^2)*cos(a)*cos(c)+1/2/b/(cos(c)^2+sin(c)^2)/(cos(a)^2+sin(a)^2)*ln(1+tan(b*x+a)^2)*sin(a)*sin(c)-1/b/(cos(c)^2+sin(c)^2)/(cos(a)^2+sin(a)^2)*cos(a)*sin(c)*arctan(tan(b*x+a))+1/b/(cos(c)^2+sin(c)^2)/(cos(a)^2+sin(a)^2)*cos(c)*sin(a)*arctan(tan(b*x+a))","B"
214,1,888,34,1.969000," ","int(sec(b*x+c)^2*sin(b*x+a),x)","-\frac{8 \tan \left(\frac{b x}{2}+\frac{a}{2}\right) \cos \left(a \right) \sin \left(c \right)}{b \left(-4 \left(\cos^{2}\left(a \right)\right) \left(\cos^{2}\left(c \right)\right)-4 \left(\cos^{2}\left(a \right)\right) \left(\sin^{2}\left(c \right)\right)-4 \left(\cos^{2}\left(c \right)\right) \left(\sin^{2}\left(a \right)\right)-4 \left(\sin^{2}\left(a \right)\right) \left(\sin^{2}\left(c \right)\right)\right) \left(\cos \left(a \right) \cos \left(c \right) \left(\tan^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+\sin \left(a \right) \sin \left(c \right) \left(\tan^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+2 \tan \left(\frac{b x}{2}+\frac{a}{2}\right) \cos \left(a \right) \sin \left(c \right)-2 \tan \left(\frac{b x}{2}+\frac{a}{2}\right) \sin \left(a \right) \cos \left(c \right)-\cos \left(a \right) \cos \left(c \right)-\sin \left(a \right) \sin \left(c \right)\right)}+\frac{8 \tan \left(\frac{b x}{2}+\frac{a}{2}\right) \sin \left(a \right) \cos \left(c \right)}{b \left(-4 \left(\cos^{2}\left(a \right)\right) \left(\cos^{2}\left(c \right)\right)-4 \left(\cos^{2}\left(a \right)\right) \left(\sin^{2}\left(c \right)\right)-4 \left(\cos^{2}\left(c \right)\right) \left(\sin^{2}\left(a \right)\right)-4 \left(\sin^{2}\left(a \right)\right) \left(\sin^{2}\left(c \right)\right)\right) \left(\cos \left(a \right) \cos \left(c \right) \left(\tan^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+\sin \left(a \right) \sin \left(c \right) \left(\tan^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+2 \tan \left(\frac{b x}{2}+\frac{a}{2}\right) \cos \left(a \right) \sin \left(c \right)-2 \tan \left(\frac{b x}{2}+\frac{a}{2}\right) \sin \left(a \right) \cos \left(c \right)-\cos \left(a \right) \cos \left(c \right)-\sin \left(a \right) \sin \left(c \right)\right)}+\frac{8 \cos \left(a \right) \cos \left(c \right)}{b \left(-4 \left(\cos^{2}\left(a \right)\right) \left(\cos^{2}\left(c \right)\right)-4 \left(\cos^{2}\left(a \right)\right) \left(\sin^{2}\left(c \right)\right)-4 \left(\cos^{2}\left(c \right)\right) \left(\sin^{2}\left(a \right)\right)-4 \left(\sin^{2}\left(a \right)\right) \left(\sin^{2}\left(c \right)\right)\right) \left(\cos \left(a \right) \cos \left(c \right) \left(\tan^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+\sin \left(a \right) \sin \left(c \right) \left(\tan^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+2 \tan \left(\frac{b x}{2}+\frac{a}{2}\right) \cos \left(a \right) \sin \left(c \right)-2 \tan \left(\frac{b x}{2}+\frac{a}{2}\right) \sin \left(a \right) \cos \left(c \right)-\cos \left(a \right) \cos \left(c \right)-\sin \left(a \right) \sin \left(c \right)\right)}+\frac{8 \sin \left(a \right) \sin \left(c \right)}{b \left(-4 \left(\cos^{2}\left(a \right)\right) \left(\cos^{2}\left(c \right)\right)-4 \left(\cos^{2}\left(a \right)\right) \left(\sin^{2}\left(c \right)\right)-4 \left(\cos^{2}\left(c \right)\right) \left(\sin^{2}\left(a \right)\right)-4 \left(\sin^{2}\left(a \right)\right) \left(\sin^{2}\left(c \right)\right)\right) \left(\cos \left(a \right) \cos \left(c \right) \left(\tan^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+\sin \left(a \right) \sin \left(c \right) \left(\tan^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+2 \tan \left(\frac{b x}{2}+\frac{a}{2}\right) \cos \left(a \right) \sin \left(c \right)-2 \tan \left(\frac{b x}{2}+\frac{a}{2}\right) \sin \left(a \right) \cos \left(c \right)-\cos \left(a \right) \cos \left(c \right)-\sin \left(a \right) \sin \left(c \right)\right)}-\frac{8 \arctan \left(\frac{2 \left(\cos \left(a \right) \cos \left(c \right)+\sin \left(a \right) \sin \left(c \right)\right) \tan \left(\frac{b x}{2}+\frac{a}{2}\right)+2 \cos \left(a \right) \sin \left(c \right)-2 \sin \left(a \right) \cos \left(c \right)}{2 \sqrt{-\left(\cos^{2}\left(a \right)\right) \left(\cos^{2}\left(c \right)\right)-\left(\cos^{2}\left(a \right)\right) \left(\sin^{2}\left(c \right)\right)-\left(\cos^{2}\left(c \right)\right) \left(\sin^{2}\left(a \right)\right)-\left(\sin^{2}\left(a \right)\right) \left(\sin^{2}\left(c \right)\right)}}\right) \cos \left(a \right) \sin \left(c \right)}{b \left(-4 \left(\cos^{2}\left(a \right)\right) \left(\cos^{2}\left(c \right)\right)-4 \left(\cos^{2}\left(a \right)\right) \left(\sin^{2}\left(c \right)\right)-4 \left(\cos^{2}\left(c \right)\right) \left(\sin^{2}\left(a \right)\right)-4 \left(\sin^{2}\left(a \right)\right) \left(\sin^{2}\left(c \right)\right)\right) \sqrt{-\left(\cos^{2}\left(a \right)\right) \left(\cos^{2}\left(c \right)\right)-\left(\cos^{2}\left(a \right)\right) \left(\sin^{2}\left(c \right)\right)-\left(\cos^{2}\left(c \right)\right) \left(\sin^{2}\left(a \right)\right)-\left(\sin^{2}\left(a \right)\right) \left(\sin^{2}\left(c \right)\right)}}+\frac{8 \arctan \left(\frac{2 \left(\cos \left(a \right) \cos \left(c \right)+\sin \left(a \right) \sin \left(c \right)\right) \tan \left(\frac{b x}{2}+\frac{a}{2}\right)+2 \cos \left(a \right) \sin \left(c \right)-2 \sin \left(a \right) \cos \left(c \right)}{2 \sqrt{-\left(\cos^{2}\left(a \right)\right) \left(\cos^{2}\left(c \right)\right)-\left(\cos^{2}\left(a \right)\right) \left(\sin^{2}\left(c \right)\right)-\left(\cos^{2}\left(c \right)\right) \left(\sin^{2}\left(a \right)\right)-\left(\sin^{2}\left(a \right)\right) \left(\sin^{2}\left(c \right)\right)}}\right) \sin \left(a \right) \cos \left(c \right)}{b \left(-4 \left(\cos^{2}\left(a \right)\right) \left(\cos^{2}\left(c \right)\right)-4 \left(\cos^{2}\left(a \right)\right) \left(\sin^{2}\left(c \right)\right)-4 \left(\cos^{2}\left(c \right)\right) \left(\sin^{2}\left(a \right)\right)-4 \left(\sin^{2}\left(a \right)\right) \left(\sin^{2}\left(c \right)\right)\right) \sqrt{-\left(\cos^{2}\left(a \right)\right) \left(\cos^{2}\left(c \right)\right)-\left(\cos^{2}\left(a \right)\right) \left(\sin^{2}\left(c \right)\right)-\left(\cos^{2}\left(c \right)\right) \left(\sin^{2}\left(a \right)\right)-\left(\sin^{2}\left(a \right)\right) \left(\sin^{2}\left(c \right)\right)}}"," ",0,"-8/b/(-4*cos(a)^2*cos(c)^2-4*cos(a)^2*sin(c)^2-4*cos(c)^2*sin(a)^2-4*sin(a)^2*sin(c)^2)/(cos(a)*cos(c)*tan(1/2*b*x+1/2*a)^2+sin(a)*sin(c)*tan(1/2*b*x+1/2*a)^2+2*tan(1/2*b*x+1/2*a)*cos(a)*sin(c)-2*tan(1/2*b*x+1/2*a)*sin(a)*cos(c)-cos(a)*cos(c)-sin(a)*sin(c))*tan(1/2*b*x+1/2*a)*cos(a)*sin(c)+8/b/(-4*cos(a)^2*cos(c)^2-4*cos(a)^2*sin(c)^2-4*cos(c)^2*sin(a)^2-4*sin(a)^2*sin(c)^2)/(cos(a)*cos(c)*tan(1/2*b*x+1/2*a)^2+sin(a)*sin(c)*tan(1/2*b*x+1/2*a)^2+2*tan(1/2*b*x+1/2*a)*cos(a)*sin(c)-2*tan(1/2*b*x+1/2*a)*sin(a)*cos(c)-cos(a)*cos(c)-sin(a)*sin(c))*tan(1/2*b*x+1/2*a)*sin(a)*cos(c)+8/b/(-4*cos(a)^2*cos(c)^2-4*cos(a)^2*sin(c)^2-4*cos(c)^2*sin(a)^2-4*sin(a)^2*sin(c)^2)/(cos(a)*cos(c)*tan(1/2*b*x+1/2*a)^2+sin(a)*sin(c)*tan(1/2*b*x+1/2*a)^2+2*tan(1/2*b*x+1/2*a)*cos(a)*sin(c)-2*tan(1/2*b*x+1/2*a)*sin(a)*cos(c)-cos(a)*cos(c)-sin(a)*sin(c))*cos(a)*cos(c)+8/b/(-4*cos(a)^2*cos(c)^2-4*cos(a)^2*sin(c)^2-4*cos(c)^2*sin(a)^2-4*sin(a)^2*sin(c)^2)/(cos(a)*cos(c)*tan(1/2*b*x+1/2*a)^2+sin(a)*sin(c)*tan(1/2*b*x+1/2*a)^2+2*tan(1/2*b*x+1/2*a)*cos(a)*sin(c)-2*tan(1/2*b*x+1/2*a)*sin(a)*cos(c)-cos(a)*cos(c)-sin(a)*sin(c))*sin(a)*sin(c)-8/b/(-4*cos(a)^2*cos(c)^2-4*cos(a)^2*sin(c)^2-4*cos(c)^2*sin(a)^2-4*sin(a)^2*sin(c)^2)/(-cos(a)^2*cos(c)^2-cos(a)^2*sin(c)^2-cos(c)^2*sin(a)^2-sin(a)^2*sin(c)^2)^(1/2)*arctan(1/2*(2*(cos(a)*cos(c)+sin(a)*sin(c))*tan(1/2*b*x+1/2*a)+2*cos(a)*sin(c)-2*sin(a)*cos(c))/(-cos(a)^2*cos(c)^2-cos(a)^2*sin(c)^2-cos(c)^2*sin(a)^2-sin(a)^2*sin(c)^2)^(1/2))*cos(a)*sin(c)+8/b/(-4*cos(a)^2*cos(c)^2-4*cos(a)^2*sin(c)^2-4*cos(c)^2*sin(a)^2-4*sin(a)^2*sin(c)^2)/(-cos(a)^2*cos(c)^2-cos(a)^2*sin(c)^2-cos(c)^2*sin(a)^2-sin(a)^2*sin(c)^2)^(1/2)*arctan(1/2*(2*(cos(a)*cos(c)+sin(a)*sin(c))*tan(1/2*b*x+1/2*a)+2*cos(a)*sin(c)-2*sin(a)*cos(c))/(-cos(a)^2*cos(c)^2-cos(a)^2*sin(c)^2-cos(c)^2*sin(a)^2-sin(a)^2*sin(c)^2)^(1/2))*sin(a)*cos(c)","B"
215,1,150,36,3.140000," ","int(sec(b*x+c)^3*sin(b*x+a),x)","\frac{\frac{1}{\left(\cos \left(a \right) \sin \left(c \right)-\sin \left(a \right) \cos \left(c \right)\right) \left(\sin \left(a \right) \cos \left(c \right)-\cos \left(a \right) \sin \left(c \right)\right) \left(-\tan \left(b x +a \right) \cos \left(a \right) \sin \left(c \right)+\tan \left(b x +a \right) \sin \left(a \right) \cos \left(c \right)+\cos \left(a \right) \cos \left(c \right)+\sin \left(a \right) \sin \left(c \right)\right)}+\frac{-\cos \left(a \right) \cos \left(c \right)-\sin \left(a \right) \sin \left(c \right)}{2 \left(\cos \left(a \right) \sin \left(c \right)-\sin \left(a \right) \cos \left(c \right)\right) \left(\sin \left(a \right) \cos \left(c \right)-\cos \left(a \right) \sin \left(c \right)\right) \left(-\tan \left(b x +a \right) \cos \left(a \right) \sin \left(c \right)+\tan \left(b x +a \right) \sin \left(a \right) \cos \left(c \right)+\cos \left(a \right) \cos \left(c \right)+\sin \left(a \right) \sin \left(c \right)\right)^{2}}}{b}"," ",0,"1/b*(1/(cos(a)*sin(c)-sin(a)*cos(c))/(sin(a)*cos(c)-cos(a)*sin(c))/(-tan(b*x+a)*cos(a)*sin(c)+tan(b*x+a)*sin(a)*cos(c)+cos(a)*cos(c)+sin(a)*sin(c))+1/2*(-cos(a)*cos(c)-sin(a)*sin(c))/(cos(a)*sin(c)-sin(a)*cos(c))/(sin(a)*cos(c)-cos(a)*sin(c))/(-tan(b*x+a)*cos(a)*sin(c)+tan(b*x+a)*sin(a)*cos(c)+cos(a)*cos(c)+sin(a)*sin(c))^2)","B"
216,1,14825,61,8.843000," ","int(sec(b*x+c)^4*sin(b*x+a),x)","\text{output too large to display}"," ",0,"result too large to display","B"
217,1,333,55,13.273000," ","int(sec(b*x+c)^5*sin(b*x+a),x)","\frac{\frac{\left(\cos \left(a \right) \cos \left(c \right)+\sin \left(a \right) \sin \left(c \right)\right) \left(\left(\cos^{2}\left(a \right)\right) \left(\cos^{2}\left(c \right)\right)+\left(\cos^{2}\left(a \right)\right) \left(\sin^{2}\left(c \right)\right)+\left(\cos^{2}\left(c \right)\right) \left(\sin^{2}\left(a \right)\right)+\left(\sin^{2}\left(a \right)\right) \left(\sin^{2}\left(c \right)\right)\right)}{4 \left(\cos \left(a \right) \sin \left(c \right)-\sin \left(a \right) \cos \left(c \right)\right)^{4} \left(\tan \left(b x +a \right) \cos \left(a \right) \sin \left(c \right)-\tan \left(b x +a \right) \sin \left(a \right) \cos \left(c \right)-\sin \left(a \right) \sin \left(c \right)-\cos \left(a \right) \cos \left(c \right)\right)^{4}}-\frac{-3 \cos \left(a \right) \cos \left(c \right)-3 \sin \left(a \right) \sin \left(c \right)}{2 \left(\cos \left(a \right) \sin \left(c \right)-\sin \left(a \right) \cos \left(c \right)\right)^{4} \left(\tan \left(b x +a \right) \cos \left(a \right) \sin \left(c \right)-\tan \left(b x +a \right) \sin \left(a \right) \cos \left(c \right)-\sin \left(a \right) \sin \left(c \right)-\cos \left(a \right) \cos \left(c \right)\right)^{2}}+\frac{1}{\left(\cos \left(a \right) \sin \left(c \right)-\sin \left(a \right) \cos \left(c \right)\right)^{4} \left(\tan \left(b x +a \right) \cos \left(a \right) \sin \left(c \right)-\tan \left(b x +a \right) \sin \left(a \right) \cos \left(c \right)-\sin \left(a \right) \sin \left(c \right)-\cos \left(a \right) \cos \left(c \right)\right)}-\frac{-\left(\cos^{2}\left(a \right)\right) \left(\sin^{2}\left(c \right)\right)-3 \left(\sin^{2}\left(a \right)\right) \left(\sin^{2}\left(c \right)\right)-4 \cos \left(a \right) \cos \left(c \right) \sin \left(a \right) \sin \left(c \right)-3 \left(\cos^{2}\left(a \right)\right) \left(\cos^{2}\left(c \right)\right)-\left(\cos^{2}\left(c \right)\right) \left(\sin^{2}\left(a \right)\right)}{3 \left(\cos \left(a \right) \sin \left(c \right)-\sin \left(a \right) \cos \left(c \right)\right)^{4} \left(\tan \left(b x +a \right) \cos \left(a \right) \sin \left(c \right)-\tan \left(b x +a \right) \sin \left(a \right) \cos \left(c \right)-\sin \left(a \right) \sin \left(c \right)-\cos \left(a \right) \cos \left(c \right)\right)^{3}}}{b}"," ",0,"1/b*(1/4*(cos(a)*cos(c)+sin(a)*sin(c))*(cos(a)^2*cos(c)^2+cos(a)^2*sin(c)^2+cos(c)^2*sin(a)^2+sin(a)^2*sin(c)^2)/(cos(a)*sin(c)-sin(a)*cos(c))^4/(tan(b*x+a)*cos(a)*sin(c)-tan(b*x+a)*sin(a)*cos(c)-sin(a)*sin(c)-cos(a)*cos(c))^4-1/2*(-3*cos(a)*cos(c)-3*sin(a)*sin(c))/(cos(a)*sin(c)-sin(a)*cos(c))^4/(tan(b*x+a)*cos(a)*sin(c)-tan(b*x+a)*sin(a)*cos(c)-sin(a)*sin(c)-cos(a)*cos(c))^2+1/(cos(a)*sin(c)-sin(a)*cos(c))^4/(tan(b*x+a)*cos(a)*sin(c)-tan(b*x+a)*sin(a)*cos(c)-sin(a)*sin(c)-cos(a)*cos(c))-1/3*(-cos(a)^2*sin(c)^2-3*sin(a)^2*sin(c)^2-4*cos(a)*cos(c)*sin(a)*sin(c)-3*cos(a)^2*cos(c)^2-cos(c)^2*sin(a)^2)/(cos(a)*sin(c)-sin(a)*cos(c))^4/(tan(b*x+a)*cos(a)*sin(c)-tan(b*x+a)*sin(a)*cos(c)-sin(a)*sin(c)-cos(a)*cos(c))^3)","B"
218,1,97703,86,14.867000," ","int(sec(b*x+c)^6*sin(b*x+a),x)","\text{output too large to display}"," ",0,"result too large to display","B"
219,0,0,333,5.432000," ","int(cos(d*x+c)^n*sin(b*x+a)^2,x)","\int \left(\cos^{n}\left(d x +c \right)\right) \left(\sin^{2}\left(b x +a \right)\right)\, dx"," ",0,"int(cos(d*x+c)^n*sin(b*x+a)^2,x)","F"
220,1,63,62,0.631000," ","int(cos(d*x+c)*sin(b*x+a)^2,x)","-\frac{\sin \left(2 a -c +\left(2 b -d \right) x \right)}{4 \left(2 b -d \right)}+\frac{\sin \left(d x +c \right)}{2 d}-\frac{\sin \left(2 a +c +\left(2 b +d \right) x \right)}{4 \left(2 b +d \right)}"," ",0,"-1/4*sin(2*a-c+(2*b-d)*x)/(2*b-d)+1/2*sin(d*x+c)/d-1/4*sin(2*a+c+(2*b+d)*x)/(2*b+d)","A"
221,1,83,78,1.231000," ","int(cos(d*x+c)^2*sin(b*x+a)^2,x)","\frac{x}{4}-\frac{\sin \left(2 b x +2 a \right)}{8 b}+\frac{\sin \left(2 d x +2 c \right)}{8 d}-\frac{\sin \left(\left(2 b -2 d \right) x +2 a -2 c \right)}{16 \left(b -d \right)}-\frac{\sin \left(\left(2 b +2 d \right) x +2 a +2 c \right)}{16 \left(b +d \right)}"," ",0,"1/4*x-1/8*sin(2*b*x+2*a)/b+1/8*sin(2*d*x+2*c)/d-1/16/(b-d)*sin((2*b-2*d)*x+2*a-2*c)-1/16/(b+d)*sin((2*b+2*d)*x+2*a+2*c)","A"
222,1,133,132,1.194000," ","int(cos(d*x+c)^3*sin(b*x+a)^2,x)","-\frac{\sin \left(2 a -3 c +\left(2 b -3 d \right) x \right)}{16 \left(2 b -3 d \right)}-\frac{3 \sin \left(2 a -c +\left(2 b -d \right) x \right)}{16 \left(2 b -d \right)}+\frac{3 \sin \left(d x +c \right)}{8 d}+\frac{\sin \left(3 d x +3 c \right)}{24 d}-\frac{3 \sin \left(2 a +c +\left(2 b +d \right) x \right)}{16 \left(2 b +d \right)}-\frac{\sin \left(2 a +3 c +\left(2 b +3 d \right) x \right)}{16 \left(2 b +3 d \right)}"," ",0,"-1/16*sin(2*a-3*c+(2*b-3*d)*x)/(2*b-3*d)-3/16*sin(2*a-c+(2*b-d)*x)/(2*b-d)+3/8*sin(d*x+c)/d+1/24*sin(3*d*x+3*c)/d-3/16*sin(2*a+c+(2*b+d)*x)/(2*b+d)-1/16*sin(2*a+3*c+(2*b+3*d)*x)/(2*b+3*d)","A"
223,0,0,508,5.522000," ","int(cos(d*x+c)^n*sin(b*x+a)^3,x)","\int \left(\cos^{n}\left(d x +c \right)\right) \left(\sin^{3}\left(b x +a \right)\right)\, dx"," ",0,"int(cos(d*x+c)^n*sin(b*x+a)^3,x)","F"
224,1,90,89,0.266000," ","int(cos(d*x+c)*sin(b*x+a)^3,x)","-\frac{3 \cos \left(a -c +\left(b -d \right) x \right)}{8 \left(b -d \right)}+\frac{\cos \left(3 a -c +\left(3 b -d \right) x \right)}{24 b -8 d}-\frac{3 \cos \left(a +c +\left(b +d \right) x \right)}{8 \left(b +d \right)}+\frac{\cos \left(3 a +c +\left(3 b +d \right) x \right)}{24 b +8 d}"," ",0,"-3/8*cos(a-c+(b-d)*x)/(b-d)+1/8*cos(3*a-c+(3*b-d)*x)/(3*b-d)-3/8*cos(a+c+(b+d)*x)/(b+d)+1/8*cos(3*a+c+(3*b+d)*x)/(3*b+d)","A"
225,1,127,126,0.288000," ","int(cos(d*x+c)^2*sin(b*x+a)^3,x)","-\frac{3 \cos \left(b x +a \right)}{8 b}+\frac{\cos \left(3 b x +3 a \right)}{24 b}-\frac{3 \cos \left(a -2 c +\left(b -2 d \right) x \right)}{16 \left(b -2 d \right)}+\frac{\cos \left(3 a -2 c +\left(3 b -2 d \right) x \right)}{48 b -32 d}-\frac{3 \cos \left(a +2 c +\left(b +2 d \right) x \right)}{16 \left(b +2 d \right)}+\frac{\cos \left(3 a +2 c +\left(3 b +2 d \right) x \right)}{48 b +32 d}"," ",0,"-3/8*cos(b*x+a)/b+1/24*cos(3*b*x+3*a)/b-3/16*cos(a-2*c+(b-2*d)*x)/(b-2*d)+1/16*cos(3*a-2*c+(3*b-2*d)*x)/(3*b-2*d)-3/16*cos(a+2*c+(b+2*d)*x)/(b+2*d)+1/16*cos(3*a+2*c+(3*b+2*d)*x)/(3*b+2*d)","A"
226,1,184,179,0.312000," ","int(cos(d*x+c)^3*sin(b*x+a)^3,x)","-\frac{3 \cos \left(a -3 c +\left(b -3 d \right) x \right)}{32 \left(b -3 d \right)}-\frac{9 \cos \left(a -c +\left(b -d \right) x \right)}{32 \left(b -d \right)}-\frac{9 \cos \left(a +c +\left(b +d \right) x \right)}{32 \left(b +d \right)}-\frac{3 \cos \left(a +3 c +\left(b +3 d \right) x \right)}{32 \left(b +3 d \right)}+\frac{\cos \left(\left(3 b -3 d \right) x +3 a -3 c \right)}{96 b -96 d}+\frac{3 \cos \left(3 a -c +\left(3 b -d \right) x \right)}{32 \left(3 b -d \right)}+\frac{3 \cos \left(3 a +c +\left(3 b +d \right) x \right)}{32 \left(3 b +d \right)}+\frac{\cos \left(\left(3 b +3 d \right) x +3 a +3 c \right)}{96 b +96 d}"," ",0,"-3/32*cos(a-3*c+(b-3*d)*x)/(b-3*d)-9/32*cos(a-c+(b-d)*x)/(b-d)-9/32*cos(a+c+(b+d)*x)/(b+d)-3/32*cos(a+3*c+(b+3*d)*x)/(b+3*d)+1/96/(b-d)*cos((3*b-3*d)*x+3*a-3*c)+3/32*cos(3*a-c+(3*b-d)*x)/(3*b-d)+3/32*cos(3*a+c+(3*b+d)*x)/(3*b+d)+1/96/(b+d)*cos((3*b+3*d)*x+3*a+3*c)","A"
227,1,325,27,1.935000," ","int(cos(b*x+a)/sin(b*x+c),x)","\frac{\ln \left(\tan \left(b x +a \right) \cos \left(a \right) \cos \left(c \right)+\tan \left(b x +a \right) \sin \left(a \right) \sin \left(c \right)+\cos \left(a \right) \sin \left(c \right)-\sin \left(a \right) \cos \left(c \right)\right) \cos \left(a \right) \cos \left(c \right)}{b \left(\left(\cos^{2}\left(a \right)\right) \left(\cos^{2}\left(c \right)\right)+\left(\cos^{2}\left(a \right)\right) \left(\sin^{2}\left(c \right)\right)+\left(\cos^{2}\left(c \right)\right) \left(\sin^{2}\left(a \right)\right)+\left(\sin^{2}\left(a \right)\right) \left(\sin^{2}\left(c \right)\right)\right)}+\frac{\ln \left(\tan \left(b x +a \right) \cos \left(a \right) \cos \left(c \right)+\tan \left(b x +a \right) \sin \left(a \right) \sin \left(c \right)+\cos \left(a \right) \sin \left(c \right)-\sin \left(a \right) \cos \left(c \right)\right) \sin \left(a \right) \sin \left(c \right)}{b \left(\left(\cos^{2}\left(a \right)\right) \left(\cos^{2}\left(c \right)\right)+\left(\cos^{2}\left(a \right)\right) \left(\sin^{2}\left(c \right)\right)+\left(\cos^{2}\left(c \right)\right) \left(\sin^{2}\left(a \right)\right)+\left(\sin^{2}\left(a \right)\right) \left(\sin^{2}\left(c \right)\right)\right)}-\frac{\ln \left(1+\tan^{2}\left(b x +a \right)\right) \cos \left(a \right) \cos \left(c \right)}{2 b \left(\cos^{2}\left(c \right)+\sin^{2}\left(c \right)\right) \left(\cos^{2}\left(a \right)+\sin^{2}\left(a \right)\right)}-\frac{\ln \left(1+\tan^{2}\left(b x +a \right)\right) \sin \left(a \right) \sin \left(c \right)}{2 b \left(\cos^{2}\left(c \right)+\sin^{2}\left(c \right)\right) \left(\cos^{2}\left(a \right)+\sin^{2}\left(a \right)\right)}+\frac{\cos \left(a \right) \sin \left(c \right) \arctan \left(\tan \left(b x +a \right)\right)}{b \left(\cos^{2}\left(c \right)+\sin^{2}\left(c \right)\right) \left(\cos^{2}\left(a \right)+\sin^{2}\left(a \right)\right)}-\frac{\cos \left(c \right) \sin \left(a \right) \arctan \left(\tan \left(b x +a \right)\right)}{b \left(\cos^{2}\left(c \right)+\sin^{2}\left(c \right)\right) \left(\cos^{2}\left(a \right)+\sin^{2}\left(a \right)\right)}"," ",0,"1/b/(cos(a)^2*cos(c)^2+cos(a)^2*sin(c)^2+cos(c)^2*sin(a)^2+sin(a)^2*sin(c)^2)*ln(tan(b*x+a)*cos(a)*cos(c)+tan(b*x+a)*sin(a)*sin(c)+cos(a)*sin(c)-sin(a)*cos(c))*cos(a)*cos(c)+1/b/(cos(a)^2*cos(c)^2+cos(a)^2*sin(c)^2+cos(c)^2*sin(a)^2+sin(a)^2*sin(c)^2)*ln(tan(b*x+a)*cos(a)*cos(c)+tan(b*x+a)*sin(a)*sin(c)+cos(a)*sin(c)-sin(a)*cos(c))*sin(a)*sin(c)-1/2/b/(cos(c)^2+sin(c)^2)/(cos(a)^2+sin(a)^2)*ln(1+tan(b*x+a)^2)*cos(a)*cos(c)-1/2/b/(cos(c)^2+sin(c)^2)/(cos(a)^2+sin(a)^2)*ln(1+tan(b*x+a)^2)*sin(a)*sin(c)+1/b/(cos(c)^2+sin(c)^2)/(cos(a)^2+sin(a)^2)*cos(a)*sin(c)*arctan(tan(b*x+a))-1/b/(cos(c)^2+sin(c)^2)/(cos(a)^2+sin(a)^2)*cos(c)*sin(a)*arctan(tan(b*x+a))","B"
228,1,1062,35,2.163000," ","int(cos(b*x+a)/sin(b*x+c)^2,x)","-\frac{\tan \left(\frac{b x}{2}+\frac{a}{2}\right) \left(\cos^{2}\left(a \right)\right) \left(\cos^{2}\left(c \right)\right)}{b \left(-\frac{\cos \left(a \right) \sin \left(c \right) \left(\tan^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)}{2}+\frac{\cos \left(c \right) \sin \left(a \right) \left(\tan^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)}{2}+\tan \left(\frac{b x}{2}+\frac{a}{2}\right) \cos \left(a \right) \cos \left(c \right)+\tan \left(\frac{b x}{2}+\frac{a}{2}\right) \sin \left(a \right) \sin \left(c \right)+\frac{\cos \left(a \right) \sin \left(c \right)}{2}-\frac{\sin \left(a \right) \cos \left(c \right)}{2}\right) \left(\left(\cos^{2}\left(a \right)\right) \left(\cos^{2}\left(c \right)\right)+\left(\cos^{2}\left(a \right)\right) \left(\sin^{2}\left(c \right)\right)+\left(\cos^{2}\left(c \right)\right) \left(\sin^{2}\left(a \right)\right)+\left(\sin^{2}\left(a \right)\right) \left(\sin^{2}\left(c \right)\right)\right) \left(\cos \left(a \right) \sin \left(c \right)-\sin \left(a \right) \cos \left(c \right)\right)}-\frac{2 \tan \left(\frac{b x}{2}+\frac{a}{2}\right) \cos \left(a \right) \cos \left(c \right) \sin \left(a \right) \sin \left(c \right)}{b \left(-\frac{\cos \left(a \right) \sin \left(c \right) \left(\tan^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)}{2}+\frac{\cos \left(c \right) \sin \left(a \right) \left(\tan^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)}{2}+\tan \left(\frac{b x}{2}+\frac{a}{2}\right) \cos \left(a \right) \cos \left(c \right)+\tan \left(\frac{b x}{2}+\frac{a}{2}\right) \sin \left(a \right) \sin \left(c \right)+\frac{\cos \left(a \right) \sin \left(c \right)}{2}-\frac{\sin \left(a \right) \cos \left(c \right)}{2}\right) \left(\left(\cos^{2}\left(a \right)\right) \left(\cos^{2}\left(c \right)\right)+\left(\cos^{2}\left(a \right)\right) \left(\sin^{2}\left(c \right)\right)+\left(\cos^{2}\left(c \right)\right) \left(\sin^{2}\left(a \right)\right)+\left(\sin^{2}\left(a \right)\right) \left(\sin^{2}\left(c \right)\right)\right) \left(\cos \left(a \right) \sin \left(c \right)-\sin \left(a \right) \cos \left(c \right)\right)}-\frac{\tan \left(\frac{b x}{2}+\frac{a}{2}\right) \left(\sin^{2}\left(a \right)\right) \left(\sin^{2}\left(c \right)\right)}{b \left(-\frac{\cos \left(a \right) \sin \left(c \right) \left(\tan^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)}{2}+\frac{\cos \left(c \right) \sin \left(a \right) \left(\tan^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)}{2}+\tan \left(\frac{b x}{2}+\frac{a}{2}\right) \cos \left(a \right) \cos \left(c \right)+\tan \left(\frac{b x}{2}+\frac{a}{2}\right) \sin \left(a \right) \sin \left(c \right)+\frac{\cos \left(a \right) \sin \left(c \right)}{2}-\frac{\sin \left(a \right) \cos \left(c \right)}{2}\right) \left(\left(\cos^{2}\left(a \right)\right) \left(\cos^{2}\left(c \right)\right)+\left(\cos^{2}\left(a \right)\right) \left(\sin^{2}\left(c \right)\right)+\left(\cos^{2}\left(c \right)\right) \left(\sin^{2}\left(a \right)\right)+\left(\sin^{2}\left(a \right)\right) \left(\sin^{2}\left(c \right)\right)\right) \left(\cos \left(a \right) \sin \left(c \right)-\sin \left(a \right) \cos \left(c \right)\right)}-\frac{\cos \left(a \right) \cos \left(c \right)}{b \left(-\frac{\cos \left(a \right) \sin \left(c \right) \left(\tan^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)}{2}+\frac{\cos \left(c \right) \sin \left(a \right) \left(\tan^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)}{2}+\tan \left(\frac{b x}{2}+\frac{a}{2}\right) \cos \left(a \right) \cos \left(c \right)+\tan \left(\frac{b x}{2}+\frac{a}{2}\right) \sin \left(a \right) \sin \left(c \right)+\frac{\cos \left(a \right) \sin \left(c \right)}{2}-\frac{\sin \left(a \right) \cos \left(c \right)}{2}\right) \left(\left(\cos^{2}\left(a \right)\right) \left(\cos^{2}\left(c \right)\right)+\left(\cos^{2}\left(a \right)\right) \left(\sin^{2}\left(c \right)\right)+\left(\cos^{2}\left(c \right)\right) \left(\sin^{2}\left(a \right)\right)+\left(\sin^{2}\left(a \right)\right) \left(\sin^{2}\left(c \right)\right)\right)}-\frac{\sin \left(a \right) \sin \left(c \right)}{b \left(-\frac{\cos \left(a \right) \sin \left(c \right) \left(\tan^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)}{2}+\frac{\cos \left(c \right) \sin \left(a \right) \left(\tan^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)}{2}+\tan \left(\frac{b x}{2}+\frac{a}{2}\right) \cos \left(a \right) \cos \left(c \right)+\tan \left(\frac{b x}{2}+\frac{a}{2}\right) \sin \left(a \right) \sin \left(c \right)+\frac{\cos \left(a \right) \sin \left(c \right)}{2}-\frac{\sin \left(a \right) \cos \left(c \right)}{2}\right) \left(\left(\cos^{2}\left(a \right)\right) \left(\cos^{2}\left(c \right)\right)+\left(\cos^{2}\left(a \right)\right) \left(\sin^{2}\left(c \right)\right)+\left(\cos^{2}\left(c \right)\right) \left(\sin^{2}\left(a \right)\right)+\left(\sin^{2}\left(a \right)\right) \left(\sin^{2}\left(c \right)\right)\right)}+\frac{4 \arctan \left(\frac{2 \left(\sin \left(a \right) \cos \left(c \right)-\cos \left(a \right) \sin \left(c \right)\right) \tan \left(\frac{b x}{2}+\frac{a}{2}\right)+2 \cos \left(a \right) \cos \left(c \right)+2 \sin \left(a \right) \sin \left(c \right)}{2 \sqrt{-\left(\cos^{2}\left(a \right)\right) \left(\cos^{2}\left(c \right)\right)-\left(\cos^{2}\left(a \right)\right) \left(\sin^{2}\left(c \right)\right)-\left(\cos^{2}\left(c \right)\right) \left(\sin^{2}\left(a \right)\right)-\left(\sin^{2}\left(a \right)\right) \left(\sin^{2}\left(c \right)\right)}}\right) \cos \left(a \right) \sin \left(c \right)}{b \left(2 \left(\cos^{2}\left(a \right)\right) \left(\cos^{2}\left(c \right)\right)+2 \left(\cos^{2}\left(a \right)\right) \left(\sin^{2}\left(c \right)\right)+2 \left(\cos^{2}\left(c \right)\right) \left(\sin^{2}\left(a \right)\right)+2 \left(\sin^{2}\left(a \right)\right) \left(\sin^{2}\left(c \right)\right)\right) \sqrt{-\left(\cos^{2}\left(a \right)\right) \left(\cos^{2}\left(c \right)\right)-\left(\cos^{2}\left(a \right)\right) \left(\sin^{2}\left(c \right)\right)-\left(\cos^{2}\left(c \right)\right) \left(\sin^{2}\left(a \right)\right)-\left(\sin^{2}\left(a \right)\right) \left(\sin^{2}\left(c \right)\right)}}-\frac{4 \arctan \left(\frac{2 \left(\sin \left(a \right) \cos \left(c \right)-\cos \left(a \right) \sin \left(c \right)\right) \tan \left(\frac{b x}{2}+\frac{a}{2}\right)+2 \cos \left(a \right) \cos \left(c \right)+2 \sin \left(a \right) \sin \left(c \right)}{2 \sqrt{-\left(\cos^{2}\left(a \right)\right) \left(\cos^{2}\left(c \right)\right)-\left(\cos^{2}\left(a \right)\right) \left(\sin^{2}\left(c \right)\right)-\left(\cos^{2}\left(c \right)\right) \left(\sin^{2}\left(a \right)\right)-\left(\sin^{2}\left(a \right)\right) \left(\sin^{2}\left(c \right)\right)}}\right) \sin \left(a \right) \cos \left(c \right)}{b \left(2 \left(\cos^{2}\left(a \right)\right) \left(\cos^{2}\left(c \right)\right)+2 \left(\cos^{2}\left(a \right)\right) \left(\sin^{2}\left(c \right)\right)+2 \left(\cos^{2}\left(c \right)\right) \left(\sin^{2}\left(a \right)\right)+2 \left(\sin^{2}\left(a \right)\right) \left(\sin^{2}\left(c \right)\right)\right) \sqrt{-\left(\cos^{2}\left(a \right)\right) \left(\cos^{2}\left(c \right)\right)-\left(\cos^{2}\left(a \right)\right) \left(\sin^{2}\left(c \right)\right)-\left(\cos^{2}\left(c \right)\right) \left(\sin^{2}\left(a \right)\right)-\left(\sin^{2}\left(a \right)\right) \left(\sin^{2}\left(c \right)\right)}}"," ",0,"-1/b/(-1/2*cos(a)*sin(c)*tan(1/2*b*x+1/2*a)^2+1/2*cos(c)*sin(a)*tan(1/2*b*x+1/2*a)^2+tan(1/2*b*x+1/2*a)*cos(a)*cos(c)+tan(1/2*b*x+1/2*a)*sin(a)*sin(c)+1/2*cos(a)*sin(c)-1/2*sin(a)*cos(c))/(cos(a)^2*cos(c)^2+cos(a)^2*sin(c)^2+cos(c)^2*sin(a)^2+sin(a)^2*sin(c)^2)/(cos(a)*sin(c)-sin(a)*cos(c))*tan(1/2*b*x+1/2*a)*cos(a)^2*cos(c)^2-2/b/(-1/2*cos(a)*sin(c)*tan(1/2*b*x+1/2*a)^2+1/2*cos(c)*sin(a)*tan(1/2*b*x+1/2*a)^2+tan(1/2*b*x+1/2*a)*cos(a)*cos(c)+tan(1/2*b*x+1/2*a)*sin(a)*sin(c)+1/2*cos(a)*sin(c)-1/2*sin(a)*cos(c))/(cos(a)^2*cos(c)^2+cos(a)^2*sin(c)^2+cos(c)^2*sin(a)^2+sin(a)^2*sin(c)^2)/(cos(a)*sin(c)-sin(a)*cos(c))*tan(1/2*b*x+1/2*a)*cos(a)*cos(c)*sin(a)*sin(c)-1/b/(-1/2*cos(a)*sin(c)*tan(1/2*b*x+1/2*a)^2+1/2*cos(c)*sin(a)*tan(1/2*b*x+1/2*a)^2+tan(1/2*b*x+1/2*a)*cos(a)*cos(c)+tan(1/2*b*x+1/2*a)*sin(a)*sin(c)+1/2*cos(a)*sin(c)-1/2*sin(a)*cos(c))/(cos(a)^2*cos(c)^2+cos(a)^2*sin(c)^2+cos(c)^2*sin(a)^2+sin(a)^2*sin(c)^2)/(cos(a)*sin(c)-sin(a)*cos(c))*tan(1/2*b*x+1/2*a)*sin(a)^2*sin(c)^2-1/b/(-1/2*cos(a)*sin(c)*tan(1/2*b*x+1/2*a)^2+1/2*cos(c)*sin(a)*tan(1/2*b*x+1/2*a)^2+tan(1/2*b*x+1/2*a)*cos(a)*cos(c)+tan(1/2*b*x+1/2*a)*sin(a)*sin(c)+1/2*cos(a)*sin(c)-1/2*sin(a)*cos(c))/(cos(a)^2*cos(c)^2+cos(a)^2*sin(c)^2+cos(c)^2*sin(a)^2+sin(a)^2*sin(c)^2)*cos(a)*cos(c)-1/b/(-1/2*cos(a)*sin(c)*tan(1/2*b*x+1/2*a)^2+1/2*cos(c)*sin(a)*tan(1/2*b*x+1/2*a)^2+tan(1/2*b*x+1/2*a)*cos(a)*cos(c)+tan(1/2*b*x+1/2*a)*sin(a)*sin(c)+1/2*cos(a)*sin(c)-1/2*sin(a)*cos(c))/(cos(a)^2*cos(c)^2+cos(a)^2*sin(c)^2+cos(c)^2*sin(a)^2+sin(a)^2*sin(c)^2)*sin(a)*sin(c)+4/b/(2*cos(a)^2*cos(c)^2+2*cos(a)^2*sin(c)^2+2*cos(c)^2*sin(a)^2+2*sin(a)^2*sin(c)^2)/(-cos(a)^2*cos(c)^2-cos(a)^2*sin(c)^2-cos(c)^2*sin(a)^2-sin(a)^2*sin(c)^2)^(1/2)*arctan(1/2*(2*(sin(a)*cos(c)-cos(a)*sin(c))*tan(1/2*b*x+1/2*a)+2*cos(a)*cos(c)+2*sin(a)*sin(c))/(-cos(a)^2*cos(c)^2-cos(a)^2*sin(c)^2-cos(c)^2*sin(a)^2-sin(a)^2*sin(c)^2)^(1/2))*cos(a)*sin(c)-4/b/(2*cos(a)^2*cos(c)^2+2*cos(a)^2*sin(c)^2+2*cos(c)^2*sin(a)^2+2*sin(a)^2*sin(c)^2)/(-cos(a)^2*cos(c)^2-cos(a)^2*sin(c)^2-cos(c)^2*sin(a)^2-sin(a)^2*sin(c)^2)^(1/2)*arctan(1/2*(2*(sin(a)*cos(c)-cos(a)*sin(c))*tan(1/2*b*x+1/2*a)+2*cos(a)*cos(c)+2*sin(a)*sin(c))/(-cos(a)^2*cos(c)^2-cos(a)^2*sin(c)^2-cos(c)^2*sin(a)^2-sin(a)^2*sin(c)^2)^(1/2))*sin(a)*cos(c)","B"
229,1,55,36,12.388000," ","int(cos(b*x+a)/sin(b*x+c)^3,x)","-\frac{1}{2 b \left(\cos \left(a \right) \cos \left(c \right)+\sin \left(a \right) \sin \left(c \right)\right) \left(\tan \left(b x +a \right) \cos \left(a \right) \cos \left(c \right)+\tan \left(b x +a \right) \sin \left(a \right) \sin \left(c \right)+\cos \left(a \right) \sin \left(c \right)-\sin \left(a \right) \cos \left(c \right)\right)^{2}}"," ",0,"-1/2/b/(cos(a)*cos(c)+sin(a)*sin(c))/(tan(b*x+a)*cos(a)*cos(c)+tan(b*x+a)*sin(a)*sin(c)+cos(a)*sin(c)-sin(a)*cos(c))^2","A"
230,1,186,68,1.005000," ","int(sin(b*x+a)*tan(b*x+c)^3,x)","-\frac{i {\mathrm e}^{i \left(b x +a \right)}}{2 b}+\frac{i {\mathrm e}^{-i \left(b x +a \right)}}{2 b}-\frac{i \left(3 \,{\mathrm e}^{i \left(3 b x +5 a +2 c \right)}-{\mathrm e}^{i \left(3 b x +3 a +4 c \right)}+{\mathrm e}^{i \left(b x +5 a \right)}-3 \,{\mathrm e}^{i \left(b x +3 a +2 c \right)}\right)}{2 b \left({\mathrm e}^{2 i \left(b x +a +c \right)}+{\mathrm e}^{2 i a}\right)^{2}}+\frac{3 \ln \left({\mathrm e}^{i \left(b x +a \right)}-i {\mathrm e}^{i \left(a -c \right)}\right) \cos \left(a -c \right)}{2 b}-\frac{3 \ln \left({\mathrm e}^{i \left(b x +a \right)}+i {\mathrm e}^{i \left(a -c \right)}\right) \cos \left(a -c \right)}{2 b}"," ",0,"-1/2*I*exp(I*(b*x+a))/b+1/2*I/b*exp(-I*(b*x+a))-1/2*I/b/(exp(2*I*(b*x+a+c))+exp(2*I*a))^2*(3*exp(I*(3*b*x+5*a+2*c))-exp(I*(3*b*x+3*a+4*c))+exp(I*(b*x+5*a))-3*exp(I*(b*x+3*a+2*c)))+3/2*ln(exp(I*(b*x+a))-I*exp(I*(a-c)))/b*cos(a-c)-3/2*ln(exp(I*(b*x+a))+I*exp(I*(a-c)))/b*cos(a-c)","C"
231,1,143,44,0.792000," ","int(sin(b*x+a)*tan(b*x+c)^2,x)","\frac{{\mathrm e}^{i \left(b x +a \right)}}{2 b}+\frac{{\mathrm e}^{-i \left(b x +a \right)}}{2 b}+\frac{{\mathrm e}^{i \left(b x +3 a \right)}+{\mathrm e}^{i \left(b x +a +2 c \right)}}{b \left({\mathrm e}^{2 i \left(b x +a +c \right)}+{\mathrm e}^{2 i a}\right)}+\frac{\ln \left({\mathrm e}^{i \left(b x +a \right)}+i {\mathrm e}^{i \left(a -c \right)}\right) \sin \left(a -c \right)}{b}-\frac{\ln \left({\mathrm e}^{i \left(b x +a \right)}-i {\mathrm e}^{i \left(a -c \right)}\right) \sin \left(a -c \right)}{b}"," ",0,"1/2*exp(I*(b*x+a))/b+1/2/b*exp(-I*(b*x+a))+1/b/(exp(2*I*(b*x+a+c))+exp(2*I*a))*(exp(I*(b*x+3*a))+exp(I*(b*x+a+2*c)))+ln(exp(I*(b*x+a))+I*exp(I*(a-c)))/b*sin(a-c)-ln(exp(I*(b*x+a))-I*exp(I*(a-c)))/b*sin(a-c)","C"
232,1,99,29,0.515000," ","int(sin(b*x+a)*tan(b*x+c),x)","\frac{i {\mathrm e}^{i \left(b x +a \right)}}{2 b}-\frac{i {\mathrm e}^{-i \left(b x +a \right)}}{2 b}+\frac{\ln \left({\mathrm e}^{i \left(b x +a \right)}+i {\mathrm e}^{i \left(a -c \right)}\right) \cos \left(a -c \right)}{b}-\frac{\ln \left({\mathrm e}^{i \left(b x +a \right)}-i {\mathrm e}^{i \left(a -c \right)}\right) \cos \left(a -c \right)}{b}"," ",0,"1/2*I*exp(I*(b*x+a))/b-1/2*I/b*exp(-I*(b*x+a))+ln(exp(I*(b*x+a))+I*exp(I*(a-c)))/b*cos(a-c)-ln(exp(I*(b*x+a))-I*exp(I*(a-c)))/b*cos(a-c)","C"
233,1,95,29,0.799000," ","int(cot(b*x+c)*sin(b*x+a),x)","-\frac{i {\mathrm e}^{i \left(b x +a \right)}}{2 b}+\frac{i {\mathrm e}^{-i \left(b x +a \right)}}{2 b}-\frac{\ln \left({\mathrm e}^{i \left(b x +a \right)}+{\mathrm e}^{i \left(a -c \right)}\right) \sin \left(a -c \right)}{b}+\frac{\ln \left({\mathrm e}^{i \left(b x +a \right)}-{\mathrm e}^{i \left(a -c \right)}\right) \sin \left(a -c \right)}{b}"," ",0,"-1/2*I*exp(I*(b*x+a))/b+1/2*I/b*exp(-I*(b*x+a))-ln(exp(I*(b*x+a))+exp(I*(a-c)))/b*sin(a-c)+ln(exp(I*(b*x+a))-exp(I*(a-c)))/b*sin(a-c)","C"
234,1,143,46,1.007000," ","int(cot(b*x+c)^2*sin(b*x+a),x)","\frac{{\mathrm e}^{i \left(b x +a \right)}}{2 b}+\frac{{\mathrm e}^{-i \left(b x +a \right)}}{2 b}+\frac{{\mathrm e}^{i \left(b x +3 a \right)}-{\mathrm e}^{i \left(b x +a +2 c \right)}}{b \left(-{\mathrm e}^{2 i \left(b x +a +c \right)}+{\mathrm e}^{2 i a}\right)}+\frac{\ln \left({\mathrm e}^{i \left(b x +a \right)}-{\mathrm e}^{i \left(a -c \right)}\right) \cos \left(a -c \right)}{b}-\frac{\ln \left({\mathrm e}^{i \left(b x +a \right)}+{\mathrm e}^{i \left(a -c \right)}\right) \cos \left(a -c \right)}{b}"," ",0,"1/2*exp(I*(b*x+a))/b+1/2/b*exp(-I*(b*x+a))+1/b/(-exp(2*I*(b*x+a+c))+exp(2*I*a))*(exp(I*(b*x+3*a))-exp(I*(b*x+a+2*c)))+ln(exp(I*(b*x+a))-exp(I*(a-c)))/b*cos(a-c)-ln(exp(I*(b*x+a))+exp(I*(a-c)))/b*cos(a-c)","C"
235,1,184,70,0.880000," ","int(cot(b*x+c)^3*sin(b*x+a),x)","\frac{i {\mathrm e}^{i \left(b x +a \right)}}{2 b}-\frac{i {\mathrm e}^{-i \left(b x +a \right)}}{2 b}+\frac{i \left(-3 \,{\mathrm e}^{i \left(3 b x +5 a +2 c \right)}-{\mathrm e}^{i \left(3 b x +3 a +4 c \right)}+{\mathrm e}^{i \left(b x +5 a \right)}+3 \,{\mathrm e}^{i \left(b x +3 a +2 c \right)}\right)}{2 b \left(-{\mathrm e}^{2 i \left(b x +a +c \right)}+{\mathrm e}^{2 i a}\right)^{2}}+\frac{3 \ln \left({\mathrm e}^{i \left(b x +a \right)}+{\mathrm e}^{i \left(a -c \right)}\right) \sin \left(a -c \right)}{2 b}-\frac{3 \ln \left({\mathrm e}^{i \left(b x +a \right)}-{\mathrm e}^{i \left(a -c \right)}\right) \sin \left(a -c \right)}{2 b}"," ",0,"1/2*I*exp(I*(b*x+a))/b-1/2*I/b*exp(-I*(b*x+a))+1/2*I/b/(-exp(2*I*(b*x+a+c))+exp(2*I*a))^2*(-3*exp(I*(3*b*x+5*a+2*c))-exp(I*(3*b*x+3*a+4*c))+exp(I*(b*x+5*a))+3*exp(I*(b*x+3*a+2*c)))+3/2*ln(exp(I*(b*x+a))+exp(I*(a-c)))/b*sin(a-c)-3/2*ln(exp(I*(b*x+a))-exp(I*(a-c)))/b*sin(a-c)","C"
236,0,0,123,1.465000," ","int(sin(b*x+a)*tan(d*x+c),x)","\int \sin \left(b x +a \right) \tan \left(d x +c \right)\, dx"," ",0,"int(sin(b*x+a)*tan(d*x+c),x)","F"
237,0,0,119,1.770000," ","int(cot(d*x+c)*sin(b*x+a),x)","\int \cot \left(d x +c \right) \sin \left(b x +a \right)\, dx"," ",0,"int(cot(d*x+c)*sin(b*x+a),x)","F"
238,1,84,83,0.942000," ","int(cos(b*x+a)*cos(d*x+c)^3,x)","\frac{\sin \left(a -3 c +\left(b -3 d \right) x \right)}{8 b -24 d}+\frac{3 \sin \left(a -c +\left(b -d \right) x \right)}{8 \left(b -d \right)}+\frac{3 \sin \left(a +c +\left(b +d \right) x \right)}{8 \left(b +d \right)}+\frac{\sin \left(a +3 c +\left(b +3 d \right) x \right)}{8 b +24 d}"," ",0,"1/8*sin(a-3*c+(b-3*d)*x)/(b-3*d)+3/8*sin(a-c+(b-d)*x)/(b-d)+3/8*sin(a+c+(b+d)*x)/(b+d)+1/8*sin(a+3*c+(b+3*d)*x)/(b+3*d)","A"
239,1,57,56,0.648000," ","int(cos(b*x+a)*cos(d*x+c)^2,x)","\frac{\sin \left(b x +a \right)}{2 b}+\frac{\sin \left(a -2 c +\left(b -2 d \right) x \right)}{4 b -8 d}+\frac{\sin \left(a +2 c +\left(b +2 d \right) x \right)}{4 b +8 d}"," ",0,"1/2*sin(b*x+a)/b+1/4*sin(a-2*c+(b-2*d)*x)/(b-2*d)+1/4*sin(a+2*c+(b+2*d)*x)/(b+2*d)","A"
240,1,40,39,0.663000," ","int(cos(b*x+a)*cos(d*x+c),x)","\frac{\sin \left(a -c +\left(b -d \right) x \right)}{2 b -2 d}+\frac{\sin \left(a +c +\left(b +d \right) x \right)}{2 b +2 d}"," ",0,"1/2*sin(a-c+(b-d)*x)/(b-d)+1/2*sin(a+c+(b+d)*x)/(b+d)","A"
241,1,461,26,1.572000," ","int(cos(b*x+a)*sec(b*x+c),x)","\frac{\ln \left(-\tan \left(b x +a \right) \cos \left(a \right) \sin \left(c \right)+\tan \left(b x +a \right) \sin \left(a \right) \cos \left(c \right)+\cos \left(a \right) \cos \left(c \right)+\sin \left(a \right) \sin \left(c \right)\right) \left(\cos^{2}\left(a \right)\right) \left(\sin^{2}\left(c \right)\right)}{b \left(\left(\cos^{2}\left(a \right)\right) \left(\cos^{2}\left(c \right)\right)+\left(\cos^{2}\left(a \right)\right) \left(\sin^{2}\left(c \right)\right)+\left(\cos^{2}\left(c \right)\right) \left(\sin^{2}\left(a \right)\right)+\left(\sin^{2}\left(a \right)\right) \left(\sin^{2}\left(c \right)\right)\right) \left(\sin \left(a \right) \cos \left(c \right)-\cos \left(a \right) \sin \left(c \right)\right)}-\frac{2 \ln \left(-\tan \left(b x +a \right) \cos \left(a \right) \sin \left(c \right)+\tan \left(b x +a \right) \sin \left(a \right) \cos \left(c \right)+\cos \left(a \right) \cos \left(c \right)+\sin \left(a \right) \sin \left(c \right)\right) \cos \left(a \right) \cos \left(c \right) \sin \left(a \right) \sin \left(c \right)}{b \left(\left(\cos^{2}\left(a \right)\right) \left(\cos^{2}\left(c \right)\right)+\left(\cos^{2}\left(a \right)\right) \left(\sin^{2}\left(c \right)\right)+\left(\cos^{2}\left(c \right)\right) \left(\sin^{2}\left(a \right)\right)+\left(\sin^{2}\left(a \right)\right) \left(\sin^{2}\left(c \right)\right)\right) \left(\sin \left(a \right) \cos \left(c \right)-\cos \left(a \right) \sin \left(c \right)\right)}+\frac{\ln \left(-\tan \left(b x +a \right) \cos \left(a \right) \sin \left(c \right)+\tan \left(b x +a \right) \sin \left(a \right) \cos \left(c \right)+\cos \left(a \right) \cos \left(c \right)+\sin \left(a \right) \sin \left(c \right)\right) \left(\cos^{2}\left(c \right)\right) \left(\sin^{2}\left(a \right)\right)}{b \left(\left(\cos^{2}\left(a \right)\right) \left(\cos^{2}\left(c \right)\right)+\left(\cos^{2}\left(a \right)\right) \left(\sin^{2}\left(c \right)\right)+\left(\cos^{2}\left(c \right)\right) \left(\sin^{2}\left(a \right)\right)+\left(\sin^{2}\left(a \right)\right) \left(\sin^{2}\left(c \right)\right)\right) \left(\sin \left(a \right) \cos \left(c \right)-\cos \left(a \right) \sin \left(c \right)\right)}+\frac{\ln \left(1+\tan^{2}\left(b x +a \right)\right) \cos \left(a \right) \sin \left(c \right)}{2 b \left(\cos^{2}\left(c \right)+\sin^{2}\left(c \right)\right) \left(\cos^{2}\left(a \right)+\sin^{2}\left(a \right)\right)}-\frac{\ln \left(1+\tan^{2}\left(b x +a \right)\right) \sin \left(a \right) \cos \left(c \right)}{2 b \left(\cos^{2}\left(c \right)+\sin^{2}\left(c \right)\right) \left(\cos^{2}\left(a \right)+\sin^{2}\left(a \right)\right)}+\frac{\cos \left(a \right) \cos \left(c \right) \arctan \left(\tan \left(b x +a \right)\right)}{b \left(\cos^{2}\left(c \right)+\sin^{2}\left(c \right)\right) \left(\cos^{2}\left(a \right)+\sin^{2}\left(a \right)\right)}+\frac{\sin \left(a \right) \sin \left(c \right) \arctan \left(\tan \left(b x +a \right)\right)}{b \left(\cos^{2}\left(c \right)+\sin^{2}\left(c \right)\right) \left(\cos^{2}\left(a \right)+\sin^{2}\left(a \right)\right)}"," ",0,"1/b/(cos(a)^2*cos(c)^2+cos(a)^2*sin(c)^2+cos(c)^2*sin(a)^2+sin(a)^2*sin(c)^2)/(sin(a)*cos(c)-cos(a)*sin(c))*ln(-tan(b*x+a)*cos(a)*sin(c)+tan(b*x+a)*sin(a)*cos(c)+cos(a)*cos(c)+sin(a)*sin(c))*cos(a)^2*sin(c)^2-2/b/(cos(a)^2*cos(c)^2+cos(a)^2*sin(c)^2+cos(c)^2*sin(a)^2+sin(a)^2*sin(c)^2)/(sin(a)*cos(c)-cos(a)*sin(c))*ln(-tan(b*x+a)*cos(a)*sin(c)+tan(b*x+a)*sin(a)*cos(c)+cos(a)*cos(c)+sin(a)*sin(c))*cos(a)*cos(c)*sin(a)*sin(c)+1/b/(cos(a)^2*cos(c)^2+cos(a)^2*sin(c)^2+cos(c)^2*sin(a)^2+sin(a)^2*sin(c)^2)/(sin(a)*cos(c)-cos(a)*sin(c))*ln(-tan(b*x+a)*cos(a)*sin(c)+tan(b*x+a)*sin(a)*cos(c)+cos(a)*cos(c)+sin(a)*sin(c))*cos(c)^2*sin(a)^2+1/2/b/(cos(c)^2+sin(c)^2)/(cos(a)^2+sin(a)^2)*ln(1+tan(b*x+a)^2)*cos(a)*sin(c)-1/2/b/(cos(c)^2+sin(c)^2)/(cos(a)^2+sin(a)^2)*ln(1+tan(b*x+a)^2)*sin(a)*cos(c)+1/b/(cos(c)^2+sin(c)^2)/(cos(a)^2+sin(a)^2)*cos(a)*cos(c)*arctan(tan(b*x+a))+1/b/(cos(c)^2+sin(c)^2)/(cos(a)^2+sin(a)^2)*sin(a)*sin(c)*arctan(tan(b*x+a))","B"
242,1,1049,35,2.252000," ","int(cos(b*x+a)*sec(b*x+c)^2,x)","\frac{2 \tan \left(\frac{b x}{2}+\frac{a}{2}\right) \left(\cos^{2}\left(a \right)\right) \left(\sin^{2}\left(c \right)\right)}{b \left(\cos \left(a \right) \cos \left(c \right) \left(\tan^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+\sin \left(a \right) \sin \left(c \right) \left(\tan^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+2 \tan \left(\frac{b x}{2}+\frac{a}{2}\right) \cos \left(a \right) \sin \left(c \right)-2 \tan \left(\frac{b x}{2}+\frac{a}{2}\right) \sin \left(a \right) \cos \left(c \right)-\cos \left(a \right) \cos \left(c \right)-\sin \left(a \right) \sin \left(c \right)\right) \left(\left(\cos^{2}\left(a \right)\right) \left(\cos^{2}\left(c \right)\right)+\left(\cos^{2}\left(a \right)\right) \left(\sin^{2}\left(c \right)\right)+\left(\cos^{2}\left(c \right)\right) \left(\sin^{2}\left(a \right)\right)+\left(\sin^{2}\left(a \right)\right) \left(\sin^{2}\left(c \right)\right)\right) \left(\cos \left(a \right) \cos \left(c \right)+\sin \left(a \right) \sin \left(c \right)\right)}-\frac{4 \tan \left(\frac{b x}{2}+\frac{a}{2}\right) \cos \left(a \right) \cos \left(c \right) \sin \left(a \right) \sin \left(c \right)}{b \left(\cos \left(a \right) \cos \left(c \right) \left(\tan^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+\sin \left(a \right) \sin \left(c \right) \left(\tan^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+2 \tan \left(\frac{b x}{2}+\frac{a}{2}\right) \cos \left(a \right) \sin \left(c \right)-2 \tan \left(\frac{b x}{2}+\frac{a}{2}\right) \sin \left(a \right) \cos \left(c \right)-\cos \left(a \right) \cos \left(c \right)-\sin \left(a \right) \sin \left(c \right)\right) \left(\left(\cos^{2}\left(a \right)\right) \left(\cos^{2}\left(c \right)\right)+\left(\cos^{2}\left(a \right)\right) \left(\sin^{2}\left(c \right)\right)+\left(\cos^{2}\left(c \right)\right) \left(\sin^{2}\left(a \right)\right)+\left(\sin^{2}\left(a \right)\right) \left(\sin^{2}\left(c \right)\right)\right) \left(\cos \left(a \right) \cos \left(c \right)+\sin \left(a \right) \sin \left(c \right)\right)}+\frac{2 \tan \left(\frac{b x}{2}+\frac{a}{2}\right) \left(\cos^{2}\left(c \right)\right) \left(\sin^{2}\left(a \right)\right)}{b \left(\cos \left(a \right) \cos \left(c \right) \left(\tan^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+\sin \left(a \right) \sin \left(c \right) \left(\tan^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+2 \tan \left(\frac{b x}{2}+\frac{a}{2}\right) \cos \left(a \right) \sin \left(c \right)-2 \tan \left(\frac{b x}{2}+\frac{a}{2}\right) \sin \left(a \right) \cos \left(c \right)-\cos \left(a \right) \cos \left(c \right)-\sin \left(a \right) \sin \left(c \right)\right) \left(\left(\cos^{2}\left(a \right)\right) \left(\cos^{2}\left(c \right)\right)+\left(\cos^{2}\left(a \right)\right) \left(\sin^{2}\left(c \right)\right)+\left(\cos^{2}\left(c \right)\right) \left(\sin^{2}\left(a \right)\right)+\left(\sin^{2}\left(a \right)\right) \left(\sin^{2}\left(c \right)\right)\right) \left(\cos \left(a \right) \cos \left(c \right)+\sin \left(a \right) \sin \left(c \right)\right)}-\frac{2 \cos \left(a \right) \sin \left(c \right)}{b \left(\cos \left(a \right) \cos \left(c \right) \left(\tan^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+\sin \left(a \right) \sin \left(c \right) \left(\tan^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+2 \tan \left(\frac{b x}{2}+\frac{a}{2}\right) \cos \left(a \right) \sin \left(c \right)-2 \tan \left(\frac{b x}{2}+\frac{a}{2}\right) \sin \left(a \right) \cos \left(c \right)-\cos \left(a \right) \cos \left(c \right)-\sin \left(a \right) \sin \left(c \right)\right) \left(\left(\cos^{2}\left(a \right)\right) \left(\cos^{2}\left(c \right)\right)+\left(\cos^{2}\left(a \right)\right) \left(\sin^{2}\left(c \right)\right)+\left(\cos^{2}\left(c \right)\right) \left(\sin^{2}\left(a \right)\right)+\left(\sin^{2}\left(a \right)\right) \left(\sin^{2}\left(c \right)\right)\right)}+\frac{2 \sin \left(a \right) \cos \left(c \right)}{b \left(\cos \left(a \right) \cos \left(c \right) \left(\tan^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+\sin \left(a \right) \sin \left(c \right) \left(\tan^{2}\left(\frac{b x}{2}+\frac{a}{2}\right)\right)+2 \tan \left(\frac{b x}{2}+\frac{a}{2}\right) \cos \left(a \right) \sin \left(c \right)-2 \tan \left(\frac{b x}{2}+\frac{a}{2}\right) \sin \left(a \right) \cos \left(c \right)-\cos \left(a \right) \cos \left(c \right)-\sin \left(a \right) \sin \left(c \right)\right) \left(\left(\cos^{2}\left(a \right)\right) \left(\cos^{2}\left(c \right)\right)+\left(\cos^{2}\left(a \right)\right) \left(\sin^{2}\left(c \right)\right)+\left(\cos^{2}\left(c \right)\right) \left(\sin^{2}\left(a \right)\right)+\left(\sin^{2}\left(a \right)\right) \left(\sin^{2}\left(c \right)\right)\right)}-\frac{2 \arctan \left(\frac{2 \left(\cos \left(a \right) \cos \left(c \right)+\sin \left(a \right) \sin \left(c \right)\right) \tan \left(\frac{b x}{2}+\frac{a}{2}\right)+2 \cos \left(a \right) \sin \left(c \right)-2 \sin \left(a \right) \cos \left(c \right)}{2 \sqrt{-\left(\cos^{2}\left(a \right)\right) \left(\cos^{2}\left(c \right)\right)-\left(\cos^{2}\left(a \right)\right) \left(\sin^{2}\left(c \right)\right)-\left(\cos^{2}\left(c \right)\right) \left(\sin^{2}\left(a \right)\right)-\left(\sin^{2}\left(a \right)\right) \left(\sin^{2}\left(c \right)\right)}}\right) \cos \left(a \right) \cos \left(c \right)}{b \left(\left(\cos^{2}\left(a \right)\right) \left(\cos^{2}\left(c \right)\right)+\left(\cos^{2}\left(a \right)\right) \left(\sin^{2}\left(c \right)\right)+\left(\cos^{2}\left(c \right)\right) \left(\sin^{2}\left(a \right)\right)+\left(\sin^{2}\left(a \right)\right) \left(\sin^{2}\left(c \right)\right)\right) \sqrt{-\left(\cos^{2}\left(a \right)\right) \left(\cos^{2}\left(c \right)\right)-\left(\cos^{2}\left(a \right)\right) \left(\sin^{2}\left(c \right)\right)-\left(\cos^{2}\left(c \right)\right) \left(\sin^{2}\left(a \right)\right)-\left(\sin^{2}\left(a \right)\right) \left(\sin^{2}\left(c \right)\right)}}-\frac{2 \arctan \left(\frac{2 \left(\cos \left(a \right) \cos \left(c \right)+\sin \left(a \right) \sin \left(c \right)\right) \tan \left(\frac{b x}{2}+\frac{a}{2}\right)+2 \cos \left(a \right) \sin \left(c \right)-2 \sin \left(a \right) \cos \left(c \right)}{2 \sqrt{-\left(\cos^{2}\left(a \right)\right) \left(\cos^{2}\left(c \right)\right)-\left(\cos^{2}\left(a \right)\right) \left(\sin^{2}\left(c \right)\right)-\left(\cos^{2}\left(c \right)\right) \left(\sin^{2}\left(a \right)\right)-\left(\sin^{2}\left(a \right)\right) \left(\sin^{2}\left(c \right)\right)}}\right) \sin \left(a \right) \sin \left(c \right)}{b \left(\left(\cos^{2}\left(a \right)\right) \left(\cos^{2}\left(c \right)\right)+\left(\cos^{2}\left(a \right)\right) \left(\sin^{2}\left(c \right)\right)+\left(\cos^{2}\left(c \right)\right) \left(\sin^{2}\left(a \right)\right)+\left(\sin^{2}\left(a \right)\right) \left(\sin^{2}\left(c \right)\right)\right) \sqrt{-\left(\cos^{2}\left(a \right)\right) \left(\cos^{2}\left(c \right)\right)-\left(\cos^{2}\left(a \right)\right) \left(\sin^{2}\left(c \right)\right)-\left(\cos^{2}\left(c \right)\right) \left(\sin^{2}\left(a \right)\right)-\left(\sin^{2}\left(a \right)\right) \left(\sin^{2}\left(c \right)\right)}}"," ",0,"2/b/(cos(a)*cos(c)*tan(1/2*b*x+1/2*a)^2+sin(a)*sin(c)*tan(1/2*b*x+1/2*a)^2+2*tan(1/2*b*x+1/2*a)*cos(a)*sin(c)-2*tan(1/2*b*x+1/2*a)*sin(a)*cos(c)-cos(a)*cos(c)-sin(a)*sin(c))/(cos(a)^2*cos(c)^2+cos(a)^2*sin(c)^2+cos(c)^2*sin(a)^2+sin(a)^2*sin(c)^2)/(cos(a)*cos(c)+sin(a)*sin(c))*tan(1/2*b*x+1/2*a)*cos(a)^2*sin(c)^2-4/b/(cos(a)*cos(c)*tan(1/2*b*x+1/2*a)^2+sin(a)*sin(c)*tan(1/2*b*x+1/2*a)^2+2*tan(1/2*b*x+1/2*a)*cos(a)*sin(c)-2*tan(1/2*b*x+1/2*a)*sin(a)*cos(c)-cos(a)*cos(c)-sin(a)*sin(c))/(cos(a)^2*cos(c)^2+cos(a)^2*sin(c)^2+cos(c)^2*sin(a)^2+sin(a)^2*sin(c)^2)/(cos(a)*cos(c)+sin(a)*sin(c))*tan(1/2*b*x+1/2*a)*cos(a)*cos(c)*sin(a)*sin(c)+2/b/(cos(a)*cos(c)*tan(1/2*b*x+1/2*a)^2+sin(a)*sin(c)*tan(1/2*b*x+1/2*a)^2+2*tan(1/2*b*x+1/2*a)*cos(a)*sin(c)-2*tan(1/2*b*x+1/2*a)*sin(a)*cos(c)-cos(a)*cos(c)-sin(a)*sin(c))/(cos(a)^2*cos(c)^2+cos(a)^2*sin(c)^2+cos(c)^2*sin(a)^2+sin(a)^2*sin(c)^2)/(cos(a)*cos(c)+sin(a)*sin(c))*tan(1/2*b*x+1/2*a)*cos(c)^2*sin(a)^2-2/b/(cos(a)*cos(c)*tan(1/2*b*x+1/2*a)^2+sin(a)*sin(c)*tan(1/2*b*x+1/2*a)^2+2*tan(1/2*b*x+1/2*a)*cos(a)*sin(c)-2*tan(1/2*b*x+1/2*a)*sin(a)*cos(c)-cos(a)*cos(c)-sin(a)*sin(c))/(cos(a)^2*cos(c)^2+cos(a)^2*sin(c)^2+cos(c)^2*sin(a)^2+sin(a)^2*sin(c)^2)*cos(a)*sin(c)+2/b/(cos(a)*cos(c)*tan(1/2*b*x+1/2*a)^2+sin(a)*sin(c)*tan(1/2*b*x+1/2*a)^2+2*tan(1/2*b*x+1/2*a)*cos(a)*sin(c)-2*tan(1/2*b*x+1/2*a)*sin(a)*cos(c)-cos(a)*cos(c)-sin(a)*sin(c))/(cos(a)^2*cos(c)^2+cos(a)^2*sin(c)^2+cos(c)^2*sin(a)^2+sin(a)^2*sin(c)^2)*sin(a)*cos(c)-2/b/(cos(a)^2*cos(c)^2+cos(a)^2*sin(c)^2+cos(c)^2*sin(a)^2+sin(a)^2*sin(c)^2)/(-cos(a)^2*cos(c)^2-cos(a)^2*sin(c)^2-cos(c)^2*sin(a)^2-sin(a)^2*sin(c)^2)^(1/2)*arctan(1/2*(2*(cos(a)*cos(c)+sin(a)*sin(c))*tan(1/2*b*x+1/2*a)+2*cos(a)*sin(c)-2*sin(a)*cos(c))/(-cos(a)^2*cos(c)^2-cos(a)^2*sin(c)^2-cos(c)^2*sin(a)^2-sin(a)^2*sin(c)^2)^(1/2))*cos(a)*cos(c)-2/b/(cos(a)^2*cos(c)^2+cos(a)^2*sin(c)^2+cos(c)^2*sin(a)^2+sin(a)^2*sin(c)^2)/(-cos(a)^2*cos(c)^2-cos(a)^2*sin(c)^2-cos(c)^2*sin(a)^2-sin(a)^2*sin(c)^2)^(1/2)*arctan(1/2*(2*(cos(a)*cos(c)+sin(a)*sin(c))*tan(1/2*b*x+1/2*a)+2*cos(a)*sin(c)-2*sin(a)*cos(c))/(-cos(a)^2*cos(c)^2-cos(a)^2*sin(c)^2-cos(c)^2*sin(a)^2-sin(a)^2*sin(c)^2)^(1/2))*sin(a)*sin(c)","B"
243,1,56,36,3.672000," ","int(cos(b*x+a)*sec(b*x+c)^3,x)","\frac{1}{2 b \left(\cos \left(a \right) \sin \left(c \right)-\sin \left(a \right) \cos \left(c \right)\right) \left(-\tan \left(b x +a \right) \cos \left(a \right) \sin \left(c \right)+\tan \left(b x +a \right) \sin \left(a \right) \cos \left(c \right)+\cos \left(a \right) \cos \left(c \right)+\sin \left(a \right) \sin \left(c \right)\right)^{2}}"," ",0,"1/2/b/(cos(a)*sin(c)-sin(a)*cos(c))/(-tan(b*x+a)*cos(a)*sin(c)+tan(b*x+a)*sin(a)*cos(c)+cos(a)*cos(c)+sin(a)*sin(c))^2","A"
244,1,133,132,1.286000," ","int(cos(b*x+a)^2*cos(d*x+c)^3,x)","\frac{\sin \left(2 a -3 c +\left(2 b -3 d \right) x \right)}{32 b -48 d}+\frac{3 \sin \left(2 a -c +\left(2 b -d \right) x \right)}{16 \left(2 b -d \right)}+\frac{3 \sin \left(d x +c \right)}{8 d}+\frac{\sin \left(3 d x +3 c \right)}{24 d}+\frac{3 \sin \left(2 a +c +\left(2 b +d \right) x \right)}{16 \left(2 b +d \right)}+\frac{\sin \left(2 a +3 c +\left(2 b +3 d \right) x \right)}{32 b +48 d}"," ",0,"1/16*sin(2*a-3*c+(2*b-3*d)*x)/(2*b-3*d)+3/16*sin(2*a-c+(2*b-d)*x)/(2*b-d)+3/8*sin(d*x+c)/d+1/24*sin(3*d*x+3*c)/d+3/16*sin(2*a+c+(2*b+d)*x)/(2*b+d)+1/16*sin(2*a+3*c+(2*b+3*d)*x)/(2*b+3*d)","A"
245,1,83,78,1.689000," ","int(cos(b*x+a)^2*cos(d*x+c)^2,x)","\frac{x}{4}+\frac{\sin \left(2 b x +2 a \right)}{8 b}+\frac{\sin \left(2 d x +2 c \right)}{8 d}+\frac{\sin \left(\left(2 b -2 d \right) x +2 a -2 c \right)}{16 b -16 d}+\frac{\sin \left(\left(2 b +2 d \right) x +2 a +2 c \right)}{16 b +16 d}"," ",0,"1/4*x+1/8*sin(2*b*x+2*a)/b+1/8*sin(2*d*x+2*c)/d+1/16/(b-d)*sin((2*b-2*d)*x+2*a-2*c)+1/16/(b+d)*sin((2*b+2*d)*x+2*a+2*c)","A"
246,1,184,179,1.999000," ","int(cos(b*x+a)^3*cos(d*x+c)^3,x)","\frac{3 \sin \left(a -3 c +\left(b -3 d \right) x \right)}{32 \left(b -3 d \right)}+\frac{9 \sin \left(a -c +\left(b -d \right) x \right)}{32 \left(b -d \right)}+\frac{9 \sin \left(a +c +\left(b +d \right) x \right)}{32 \left(b +d \right)}+\frac{3 \sin \left(a +3 c +\left(b +3 d \right) x \right)}{32 \left(b +3 d \right)}+\frac{\sin \left(\left(3 b -3 d \right) x +3 a -3 c \right)}{96 b -96 d}+\frac{3 \sin \left(3 a -c +\left(3 b -d \right) x \right)}{32 \left(3 b -d \right)}+\frac{3 \sin \left(3 a +c +\left(3 b +d \right) x \right)}{32 \left(3 b +d \right)}+\frac{\sin \left(\left(3 b +3 d \right) x +3 a +3 c \right)}{96 b +96 d}"," ",0,"3/32*sin(a-3*c+(b-3*d)*x)/(b-3*d)+9/32*sin(a-c+(b-d)*x)/(b-d)+9/32*sin(a+c+(b+d)*x)/(b+d)+3/32*sin(a+3*c+(b+3*d)*x)/(b+3*d)+1/96/(b-d)*sin((3*b-3*d)*x+3*a-3*c)+3/32*sin(3*a-c+(3*b-d)*x)/(3*b-d)+3/32*sin(3*a+c+(3*b+d)*x)/(3*b+d)+1/96/(b+d)*sin((3*b+3*d)*x+3*a+3*c)","A"
247,1,181,68,0.958000," ","int(cos(b*x+a)*tan(b*x+c)^3,x)","\frac{{\mathrm e}^{i \left(b x +a \right)}}{2 b}+\frac{{\mathrm e}^{-i \left(b x +a \right)}}{2 b}+\frac{3 \,{\mathrm e}^{i \left(3 b x +5 a +2 c \right)}+{\mathrm e}^{i \left(3 b x +3 a +4 c \right)}+{\mathrm e}^{i \left(b x +5 a \right)}+3 \,{\mathrm e}^{i \left(b x +3 a +2 c \right)}}{2 b \left({\mathrm e}^{2 i \left(b x +a +c \right)}+{\mathrm e}^{2 i a}\right)^{2}}-\frac{3 \ln \left({\mathrm e}^{i \left(b x +a \right)}-i {\mathrm e}^{i \left(a -c \right)}\right) \sin \left(a -c \right)}{2 b}+\frac{3 \ln \left({\mathrm e}^{i \left(b x +a \right)}+i {\mathrm e}^{i \left(a -c \right)}\right) \sin \left(a -c \right)}{2 b}"," ",0,"1/2*exp(I*(b*x+a))/b+1/2/b*exp(-I*(b*x+a))+1/2/b/(exp(2*I*(b*x+a+c))+exp(2*I*a))^2*(3*exp(I*(3*b*x+5*a+2*c))+exp(I*(3*b*x+3*a+4*c))+exp(I*(b*x+5*a))+3*exp(I*(b*x+3*a+2*c)))-3/2*ln(exp(I*(b*x+a))-I*exp(I*(a-c)))/b*sin(a-c)+3/2*ln(exp(I*(b*x+a))+I*exp(I*(a-c)))/b*sin(a-c)","C"
248,1,149,46,0.859000," ","int(cos(b*x+a)*tan(b*x+c)^2,x)","\frac{i {\mathrm e}^{i \left(b x +a \right)}}{2 b}-\frac{i {\mathrm e}^{-i \left(b x +a \right)}}{2 b}-\frac{i \left(-{\mathrm e}^{i \left(b x +3 a \right)}+{\mathrm e}^{i \left(b x +a +2 c \right)}\right)}{b \left({\mathrm e}^{2 i \left(b x +a +c \right)}+{\mathrm e}^{2 i a}\right)}+\frac{\ln \left({\mathrm e}^{i \left(b x +a \right)}+i {\mathrm e}^{i \left(a -c \right)}\right) \cos \left(a -c \right)}{b}-\frac{\ln \left({\mathrm e}^{i \left(b x +a \right)}-i {\mathrm e}^{i \left(a -c \right)}\right) \cos \left(a -c \right)}{b}"," ",0,"1/2*I*exp(I*(b*x+a))/b-1/2*I/b*exp(-I*(b*x+a))-I/b/(exp(2*I*(b*x+a+c))+exp(2*I*a))*(-exp(I*(b*x+3*a))+exp(I*(b*x+a+2*c)))+ln(exp(I*(b*x+a))+I*exp(I*(a-c)))/b*cos(a-c)-ln(exp(I*(b*x+a))-I*exp(I*(a-c)))/b*cos(a-c)","C"
249,1,97,30,0.608000," ","int(cos(b*x+a)*tan(b*x+c),x)","-\frac{{\mathrm e}^{i \left(b x +a \right)}}{2 b}-\frac{{\mathrm e}^{-i \left(b x +a \right)}}{2 b}-\frac{\ln \left({\mathrm e}^{i \left(b x +a \right)}+i {\mathrm e}^{i \left(a -c \right)}\right) \sin \left(a -c \right)}{b}+\frac{\ln \left({\mathrm e}^{i \left(b x +a \right)}-i {\mathrm e}^{i \left(a -c \right)}\right) \sin \left(a -c \right)}{b}"," ",0,"-1/2*exp(I*(b*x+a))/b-1/2/b*exp(-I*(b*x+a))-ln(exp(I*(b*x+a))+I*exp(I*(a-c)))/b*sin(a-c)+ln(exp(I*(b*x+a))-I*exp(I*(a-c)))/b*sin(a-c)","C"
250,1,93,29,0.753000," ","int(cos(b*x+a)*cot(b*x+c),x)","\frac{{\mathrm e}^{i \left(b x +a \right)}}{2 b}+\frac{{\mathrm e}^{-i \left(b x +a \right)}}{2 b}+\frac{\ln \left({\mathrm e}^{i \left(b x +a \right)}-{\mathrm e}^{i \left(a -c \right)}\right) \cos \left(a -c \right)}{b}-\frac{\ln \left({\mathrm e}^{i \left(b x +a \right)}+{\mathrm e}^{i \left(a -c \right)}\right) \cos \left(a -c \right)}{b}"," ",0,"1/2*exp(I*(b*x+a))/b+1/2/b*exp(-I*(b*x+a))+ln(exp(I*(b*x+a))-exp(I*(a-c)))/b*cos(a-c)-ln(exp(I*(b*x+a))+exp(I*(a-c)))/b*cos(a-c)","C"
251,1,145,46,0.842000," ","int(cos(b*x+a)*cot(b*x+c)^2,x)","\frac{i {\mathrm e}^{i \left(b x +a \right)}}{2 b}-\frac{i {\mathrm e}^{-i \left(b x +a \right)}}{2 b}+\frac{i \left({\mathrm e}^{i \left(b x +3 a \right)}+{\mathrm e}^{i \left(b x +a +2 c \right)}\right)}{b \left(-{\mathrm e}^{2 i \left(b x +a +c \right)}+{\mathrm e}^{2 i a}\right)}+\frac{\ln \left({\mathrm e}^{i \left(b x +a \right)}+{\mathrm e}^{i \left(a -c \right)}\right) \sin \left(a -c \right)}{b}-\frac{\ln \left({\mathrm e}^{i \left(b x +a \right)}-{\mathrm e}^{i \left(a -c \right)}\right) \sin \left(a -c \right)}{b}"," ",0,"1/2*I*exp(I*(b*x+a))/b-1/2*I/b*exp(-I*(b*x+a))+I/b/(-exp(2*I*(b*x+a+c))+exp(2*I*a))*(exp(I*(b*x+3*a))+exp(I*(b*x+a+2*c)))+ln(exp(I*(b*x+a))+exp(I*(a-c)))/b*sin(a-c)-ln(exp(I*(b*x+a))-exp(I*(a-c)))/b*sin(a-c)","C"
252,1,179,69,1.006000," ","int(cos(b*x+a)*cot(b*x+c)^3,x)","-\frac{{\mathrm e}^{i \left(b x +a \right)}}{2 b}-\frac{{\mathrm e}^{-i \left(b x +a \right)}}{2 b}-\frac{-3 \,{\mathrm e}^{i \left(3 b x +5 a +2 c \right)}+{\mathrm e}^{i \left(3 b x +3 a +4 c \right)}+{\mathrm e}^{i \left(b x +5 a \right)}-3 \,{\mathrm e}^{i \left(b x +3 a +2 c \right)}}{2 b \left(-{\mathrm e}^{2 i \left(b x +a +c \right)}+{\mathrm e}^{2 i a}\right)^{2}}+\frac{3 \ln \left({\mathrm e}^{i \left(b x +a \right)}+{\mathrm e}^{i \left(a -c \right)}\right) \cos \left(a -c \right)}{2 b}-\frac{3 \ln \left({\mathrm e}^{i \left(b x +a \right)}-{\mathrm e}^{i \left(a -c \right)}\right) \cos \left(a -c \right)}{2 b}"," ",0,"-1/2*exp(I*(b*x+a))/b-1/2/b*exp(-I*(b*x+a))-1/2/b/(-exp(2*I*(b*x+a+c))+exp(2*I*a))^2*(-3*exp(I*(3*b*x+5*a+2*c))+exp(I*(3*b*x+3*a+4*c))+exp(I*(b*x+5*a))-3*exp(I*(b*x+3*a+2*c)))+3/2*ln(exp(I*(b*x+a))+exp(I*(a-c)))/b*cos(a-c)-3/2*ln(exp(I*(b*x+a))-exp(I*(a-c)))/b*cos(a-c)","C"
253,0,0,118,1.591000," ","int(cos(b*x+a)*tan(d*x+c),x)","\int \cos \left(b x +a \right) \tan \left(d x +c \right)\, dx"," ",0,"int(cos(b*x+a)*tan(d*x+c),x)","F"
254,0,0,114,1.766000," ","int(cos(b*x+a)*cot(d*x+c),x)","\int \cos \left(b x +a \right) \cot \left(d x +c \right)\, dx"," ",0,"int(cos(b*x+a)*cot(d*x+c),x)","F"