1,1,147,107,0.154000," ","int((a+a*sin(d*x+c))*tan(d*x+c)^5,x)","\frac{a \left(\sin^{7}\left(d x +c \right)\right)}{4 d \cos \left(d x +c \right)^{4}}-\frac{3 a \left(\sin^{7}\left(d x +c \right)\right)}{8 d \cos \left(d x +c \right)^{2}}-\frac{3 a \left(\sin^{5}\left(d x +c \right)\right)}{8 d}-\frac{5 a \left(\sin^{3}\left(d x +c \right)\right)}{8 d}-\frac{15 a \sin \left(d x +c \right)}{8 d}+\frac{15 a \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{8 d}+\frac{a \left(\tan^{4}\left(d x +c \right)\right)}{4 d}-\frac{a \left(\tan^{2}\left(d x +c \right)\right)}{2 d}-\frac{a \ln \left(\cos \left(d x +c \right)\right)}{d}"," ",0,"1/4/d*a*sin(d*x+c)^7/cos(d*x+c)^4-3/8/d*a*sin(d*x+c)^7/cos(d*x+c)^2-3/8*a*sin(d*x+c)^5/d-5/8*a*sin(d*x+c)^3/d-15/8*a*sin(d*x+c)/d+15/8/d*a*ln(sec(d*x+c)+tan(d*x+c))+1/4/d*a*tan(d*x+c)^4-1/2/d*a*tan(d*x+c)^2-1/d*a*ln(cos(d*x+c))","A"
2,1,96,65,0.148000," ","int((a+a*sin(d*x+c))*tan(d*x+c)^3,x)","\frac{a \left(\sin^{5}\left(d x +c \right)\right)}{2 d \cos \left(d x +c \right)^{2}}+\frac{a \left(\sin^{3}\left(d x +c \right)\right)}{2 d}+\frac{3 a \sin \left(d x +c \right)}{2 d}-\frac{3 a \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{2 d}+\frac{a \left(\tan^{2}\left(d x +c \right)\right)}{2 d}+\frac{a \ln \left(\cos \left(d x +c \right)\right)}{d}"," ",0,"1/2/d*a*sin(d*x+c)^5/cos(d*x+c)^2+1/2*a*sin(d*x+c)^3/d+3/2*a*sin(d*x+c)/d-3/2/d*a*ln(sec(d*x+c)+tan(d*x+c))+1/2/d*a*tan(d*x+c)^2+1/d*a*ln(cos(d*x+c))","A"
3,1,29,30,0.100000," ","int((a+a*sin(d*x+c))*tan(d*x+c),x)","-\frac{a \sin \left(d x +c \right)}{d}-\frac{a \ln \left(\sin \left(d x +c \right)-1\right)}{d}"," ",0,"-a*sin(d*x+c)/d-a/d*ln(sin(d*x+c)-1)","A"
4,1,25,24,0.089000," ","int(cot(d*x+c)*(a+a*sin(d*x+c)),x)","\frac{a \ln \left(\sin \left(d x +c \right)\right)}{d}+\frac{a \sin \left(d x +c \right)}{d}"," ",0,"a*ln(sin(d*x+c))/d+a*sin(d*x+c)/d","A"
5,1,83,52,0.204000," ","int(cot(d*x+c)^3*(a+a*sin(d*x+c)),x)","-\frac{a \left(\cos^{4}\left(d x +c \right)\right)}{d \sin \left(d x +c \right)}-\frac{\left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) a}{d}-\frac{2 a \sin \left(d x +c \right)}{d}-\frac{a \left(\cot^{2}\left(d x +c \right)\right)}{2 d}-\frac{a \ln \left(\sin \left(d x +c \right)\right)}{d}"," ",0,"-1/d*a/sin(d*x+c)*cos(d*x+c)^4-1/d*cos(d*x+c)^2*sin(d*x+c)*a-2*a*sin(d*x+c)/d-1/2/d*a*cot(d*x+c)^2-a*ln(sin(d*x+c))/d","A"
6,1,136,77,0.170000," ","int(cot(d*x+c)^5*(a+a*sin(d*x+c)),x)","-\frac{a \left(\cos^{6}\left(d x +c \right)\right)}{3 d \sin \left(d x +c \right)^{3}}+\frac{a \left(\cos^{6}\left(d x +c \right)\right)}{d \sin \left(d x +c \right)}+\frac{8 a \sin \left(d x +c \right)}{3 d}+\frac{\left(\cos^{4}\left(d x +c \right)\right) \sin \left(d x +c \right) a}{d}+\frac{4 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) a}{3 d}-\frac{a \left(\cot^{4}\left(d x +c \right)\right)}{4 d}+\frac{a \left(\cot^{2}\left(d x +c \right)\right)}{2 d}+\frac{a \ln \left(\sin \left(d x +c \right)\right)}{d}"," ",0,"-1/3/d*a/sin(d*x+c)^3*cos(d*x+c)^6+1/d*a/sin(d*x+c)*cos(d*x+c)^6+8/3*a*sin(d*x+c)/d+1/d*cos(d*x+c)^4*sin(d*x+c)*a+4/3/d*cos(d*x+c)^2*sin(d*x+c)*a-1/4/d*a*cot(d*x+c)^4+1/2/d*a*cot(d*x+c)^2+a*ln(sin(d*x+c))/d","A"
7,1,195,107,0.191000," ","int(cot(d*x+c)^7*(a+a*sin(d*x+c)),x)","-\frac{a \left(\cos^{8}\left(d x +c \right)\right)}{5 d \sin \left(d x +c \right)^{5}}+\frac{a \left(\cos^{8}\left(d x +c \right)\right)}{5 d \sin \left(d x +c \right)^{3}}-\frac{a \left(\cos^{8}\left(d x +c \right)\right)}{d \sin \left(d x +c \right)}-\frac{16 a \sin \left(d x +c \right)}{5 d}-\frac{\left(\cos^{6}\left(d x +c \right)\right) \sin \left(d x +c \right) a}{d}-\frac{6 \left(\cos^{4}\left(d x +c \right)\right) \sin \left(d x +c \right) a}{5 d}-\frac{8 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) a}{5 d}-\frac{a \left(\cot^{6}\left(d x +c \right)\right)}{6 d}+\frac{a \left(\cot^{4}\left(d x +c \right)\right)}{4 d}-\frac{a \left(\cot^{2}\left(d x +c \right)\right)}{2 d}-\frac{a \ln \left(\sin \left(d x +c \right)\right)}{d}"," ",0,"-1/5/d*a/sin(d*x+c)^5*cos(d*x+c)^8+1/5/d*a/sin(d*x+c)^3*cos(d*x+c)^8-1/d*a/sin(d*x+c)*cos(d*x+c)^8-16/5*a*sin(d*x+c)/d-1/d*cos(d*x+c)^6*sin(d*x+c)*a-6/5/d*cos(d*x+c)^4*sin(d*x+c)*a-8/5/d*cos(d*x+c)^2*sin(d*x+c)*a-1/6/d*a*cot(d*x+c)^6+1/4/d*a*cot(d*x+c)^4-1/2/d*a*cot(d*x+c)^2-a*ln(sin(d*x+c))/d","A"
8,1,135,95,0.243000," ","int((a+a*sin(d*x+c))*tan(d*x+c)^6,x)","\frac{a \left(\frac{\sin^{8}\left(d x +c \right)}{5 \cos \left(d x +c \right)^{5}}-\frac{\sin^{8}\left(d x +c \right)}{5 \cos \left(d x +c \right)^{3}}+\frac{\sin^{8}\left(d x +c \right)}{\cos \left(d x +c \right)}+\left(\frac{16}{5}+\sin^{6}\left(d x +c \right)+\frac{6 \left(\sin^{4}\left(d x +c \right)\right)}{5}+\frac{8 \left(\sin^{2}\left(d x +c \right)\right)}{5}\right) \cos \left(d x +c \right)\right)+a \left(\frac{\left(\tan^{5}\left(d x +c \right)\right)}{5}-\frac{\left(\tan^{3}\left(d x +c \right)\right)}{3}+\tan \left(d x +c \right)-d x -c \right)}{d}"," ",0,"1/d*(a*(1/5*sin(d*x+c)^8/cos(d*x+c)^5-1/5*sin(d*x+c)^8/cos(d*x+c)^3+sin(d*x+c)^8/cos(d*x+c)+(16/5+sin(d*x+c)^6+6/5*sin(d*x+c)^4+8/5*sin(d*x+c)^2)*cos(d*x+c))+a*(1/5*tan(d*x+c)^5-1/3*tan(d*x+c)^3+tan(d*x+c)-d*x-c))","A"
9,1,98,68,0.207000," ","int((a+a*sin(d*x+c))*tan(d*x+c)^4,x)","\frac{a \left(\frac{\sin^{6}\left(d x +c \right)}{3 \cos \left(d x +c \right)^{3}}-\frac{\sin^{6}\left(d x +c \right)}{\cos \left(d x +c \right)}-\left(\frac{8}{3}+\sin^{4}\left(d x +c \right)+\frac{4 \left(\sin^{2}\left(d x +c \right)\right)}{3}\right) \cos \left(d x +c \right)\right)+a \left(\frac{\left(\tan^{3}\left(d x +c \right)\right)}{3}-\tan \left(d x +c \right)+d x +c \right)}{d}"," ",0,"1/d*(a*(1/3*sin(d*x+c)^6/cos(d*x+c)^3-sin(d*x+c)^6/cos(d*x+c)-(8/3+sin(d*x+c)^4+4/3*sin(d*x+c)^2)*cos(d*x+c))+a*(1/3*tan(d*x+c)^3-tan(d*x+c)+d*x+c))","A"
10,1,59,39,0.171000," ","int((a+a*sin(d*x+c))*tan(d*x+c)^2,x)","\frac{a \left(\frac{\sin^{4}\left(d x +c \right)}{\cos \left(d x +c \right)}+\left(2+\sin^{2}\left(d x +c \right)\right) \cos \left(d x +c \right)\right)+a \left(\tan \left(d x +c \right)-d x -c \right)}{d}"," ",0,"1/d*(a*(sin(d*x+c)^4/cos(d*x+c)+(2+sin(d*x+c)^2)*cos(d*x+c))+a*(tan(d*x+c)-d*x-c))","A"
11,1,57,41,0.101000," ","int(cot(d*x+c)^2*(a+a*sin(d*x+c)),x)","-a x +\frac{a \cos \left(d x +c \right)}{d}-\frac{a \cot \left(d x +c \right)}{d}+\frac{a \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{d}-\frac{c a}{d}"," ",0,"-a*x+a*cos(d*x+c)/d-a*cot(d*x+c)/d+1/d*a*ln(csc(d*x+c)-cot(d*x+c))-1/d*c*a","A"
12,1,106,74,0.120000," ","int(cot(d*x+c)^4*(a+a*sin(d*x+c)),x)","-\frac{a \left(\cos^{5}\left(d x +c \right)\right)}{2 d \sin \left(d x +c \right)^{2}}-\frac{a \left(\cos^{3}\left(d x +c \right)\right)}{2 d}-\frac{3 a \cos \left(d x +c \right)}{2 d}-\frac{3 a \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{2 d}-\frac{a \left(\cot^{3}\left(d x +c \right)\right)}{3 d}+\frac{a \cot \left(d x +c \right)}{d}+a x +\frac{c a}{d}"," ",0,"-1/2/d*a/sin(d*x+c)^2*cos(d*x+c)^5-1/2*a*cos(d*x+c)^3/d-3/2*a*cos(d*x+c)/d-3/2/d*a*ln(csc(d*x+c)-cot(d*x+c))-1/3*a*cot(d*x+c)^3/d+a*cot(d*x+c)/d+a*x+1/d*c*a","A"
13,1,159,110,0.127000," ","int(cot(d*x+c)^6*(a+a*sin(d*x+c)),x)","-\frac{a \left(\cos^{7}\left(d x +c \right)\right)}{4 d \sin \left(d x +c \right)^{4}}+\frac{3 a \left(\cos^{7}\left(d x +c \right)\right)}{8 d \sin \left(d x +c \right)^{2}}+\frac{3 a \left(\cos^{5}\left(d x +c \right)\right)}{8 d}+\frac{5 a \left(\cos^{3}\left(d x +c \right)\right)}{8 d}+\frac{15 a \cos \left(d x +c \right)}{8 d}+\frac{15 a \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{8 d}-\frac{a \left(\cot^{5}\left(d x +c \right)\right)}{5 d}+\frac{a \left(\cot^{3}\left(d x +c \right)\right)}{3 d}-\frac{a \cot \left(d x +c \right)}{d}-a x -\frac{c a}{d}"," ",0,"-1/4/d*a/sin(d*x+c)^4*cos(d*x+c)^7+3/8/d*a/sin(d*x+c)^2*cos(d*x+c)^7+3/8*a*cos(d*x+c)^5/d+5/8*a*cos(d*x+c)^3/d+15/8*a*cos(d*x+c)/d+15/8/d*a*ln(csc(d*x+c)-cot(d*x+c))-1/5*a*cot(d*x+c)^5/d+1/3*a*cot(d*x+c)^3/d-a*cot(d*x+c)/d-a*x-1/d*c*a","A"
14,1,261,109,0.197000," ","int((a+a*sin(d*x+c))^2*tan(d*x+c)^5,x)","\frac{a^{2} \left(\sin^{8}\left(d x +c \right)\right)}{4 d \cos \left(d x +c \right)^{4}}-\frac{a^{2} \left(\sin^{8}\left(d x +c \right)\right)}{2 d \cos \left(d x +c \right)^{2}}-\frac{a^{2} \left(\sin^{6}\left(d x +c \right)\right)}{2 d}-\frac{3 a^{2} \left(\sin^{4}\left(d x +c \right)\right)}{4 d}-\frac{3 a^{2} \left(\sin^{2}\left(d x +c \right)\right)}{2 d}-\frac{4 a^{2} \ln \left(\cos \left(d x +c \right)\right)}{d}+\frac{a^{2} \left(\sin^{7}\left(d x +c \right)\right)}{2 d \cos \left(d x +c \right)^{4}}-\frac{3 a^{2} \left(\sin^{7}\left(d x +c \right)\right)}{4 d \cos \left(d x +c \right)^{2}}-\frac{3 a^{2} \left(\sin^{5}\left(d x +c \right)\right)}{4 d}-\frac{5 a^{2} \left(\sin^{3}\left(d x +c \right)\right)}{4 d}-\frac{15 a^{2} \sin \left(d x +c \right)}{4 d}+\frac{15 a^{2} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{4 d}+\frac{a^{2} \left(\tan^{4}\left(d x +c \right)\right)}{4 d}-\frac{a^{2} \left(\tan^{2}\left(d x +c \right)\right)}{2 d}"," ",0,"1/4/d*a^2*sin(d*x+c)^8/cos(d*x+c)^4-1/2/d*a^2*sin(d*x+c)^8/cos(d*x+c)^2-1/2/d*a^2*sin(d*x+c)^6-3/4/d*a^2*sin(d*x+c)^4-3/2*a^2*sin(d*x+c)^2/d-4/d*a^2*ln(cos(d*x+c))+1/2/d*a^2*sin(d*x+c)^7/cos(d*x+c)^4-3/4/d*a^2*sin(d*x+c)^7/cos(d*x+c)^2-3/4/d*a^2*sin(d*x+c)^5-5/4/d*a^2*sin(d*x+c)^3-15/4*a^2*sin(d*x+c)/d+15/4/d*a^2*ln(sec(d*x+c)+tan(d*x+c))+1/4/d*a^2*tan(d*x+c)^4-1/2/d*a^2*tan(d*x+c)^2","B"
15,1,162,70,0.174000," ","int((a+a*sin(d*x+c))^2*tan(d*x+c)^3,x)","\frac{a^{2} \left(\sin^{6}\left(d x +c \right)\right)}{2 d \cos \left(d x +c \right)^{2}}+\frac{a^{2} \left(\sin^{4}\left(d x +c \right)\right)}{2 d}+\frac{a^{2} \left(\sin^{2}\left(d x +c \right)\right)}{d}+\frac{3 a^{2} \ln \left(\cos \left(d x +c \right)\right)}{d}+\frac{a^{2} \left(\sin^{5}\left(d x +c \right)\right)}{d \cos \left(d x +c \right)^{2}}+\frac{a^{2} \left(\sin^{3}\left(d x +c \right)\right)}{d}+\frac{3 a^{2} \sin \left(d x +c \right)}{d}-\frac{3 a^{2} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{a^{2} \left(\tan^{2}\left(d x +c \right)\right)}{2 d}"," ",0,"1/2/d*a^2*sin(d*x+c)^6/cos(d*x+c)^2+1/2/d*a^2*sin(d*x+c)^4+a^2*sin(d*x+c)^2/d+3/d*a^2*ln(cos(d*x+c))+1/d*a^2*sin(d*x+c)^5/cos(d*x+c)^2+1/d*a^2*sin(d*x+c)^3+3*a^2*sin(d*x+c)/d-3/d*a^2*ln(sec(d*x+c)+tan(d*x+c))+1/2/d*a^2*tan(d*x+c)^2","B"
16,1,69,50,0.141000," ","int((a+a*sin(d*x+c))^2*tan(d*x+c),x)","-\frac{a^{2} \left(\sin^{2}\left(d x +c \right)\right)}{2 d}-\frac{2 a^{2} \ln \left(\cos \left(d x +c \right)\right)}{d}-\frac{2 a^{2} \sin \left(d x +c \right)}{d}+\frac{2 a^{2} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}"," ",0,"-1/2*a^2*sin(d*x+c)^2/d-2/d*a^2*ln(cos(d*x+c))-2*a^2*sin(d*x+c)/d+2/d*a^2*ln(sec(d*x+c)+tan(d*x+c))","A"
17,1,94,28,0.223000," ","int(cot(d*x+c)^3*(a+a*sin(d*x+c))^2,x)","\frac{a^{2} \left(\cos^{2}\left(d x +c \right)\right)}{2 d}-\frac{2 a^{2} \left(\cos^{4}\left(d x +c \right)\right)}{d \sin \left(d x +c \right)}-\frac{2 a^{2} \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{d}-\frac{4 a^{2} \sin \left(d x +c \right)}{d}-\frac{a^{2} \left(\cot^{2}\left(d x +c \right)\right)}{2 d}"," ",0,"1/2/d*a^2*cos(d*x+c)^2-2/d*a^2/sin(d*x+c)*cos(d*x+c)^4-2/d*a^2*cos(d*x+c)^2*sin(d*x+c)-4*a^2*sin(d*x+c)/d-1/2/d*a^2*cot(d*x+c)^2","B"
18,1,313,124,0.212000," ","int(cot(d*x+c)^7*(a+a*sin(d*x+c))^2,x)","-\frac{a^{2} \left(\cos^{8}\left(d x +c \right)\right)}{4 d \sin \left(d x +c \right)^{4}}+\frac{a^{2} \left(\cos^{8}\left(d x +c \right)\right)}{2 d \sin \left(d x +c \right)^{2}}+\frac{a^{2} \left(\cos^{6}\left(d x +c \right)\right)}{2 d}+\frac{3 a^{2} \left(\cos^{4}\left(d x +c \right)\right)}{4 d}+\frac{3 a^{2} \left(\cos^{2}\left(d x +c \right)\right)}{2 d}+\frac{2 a^{2} \ln \left(\sin \left(d x +c \right)\right)}{d}-\frac{2 a^{2} \left(\cos^{8}\left(d x +c \right)\right)}{5 d \sin \left(d x +c \right)^{5}}+\frac{2 a^{2} \left(\cos^{8}\left(d x +c \right)\right)}{5 d \sin \left(d x +c \right)^{3}}-\frac{2 a^{2} \left(\cos^{8}\left(d x +c \right)\right)}{d \sin \left(d x +c \right)}-\frac{32 a^{2} \sin \left(d x +c \right)}{5 d}-\frac{2 a^{2} \sin \left(d x +c \right) \left(\cos^{6}\left(d x +c \right)\right)}{d}-\frac{12 a^{2} \sin \left(d x +c \right) \left(\cos^{4}\left(d x +c \right)\right)}{5 d}-\frac{16 a^{2} \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{5 d}-\frac{a^{2} \left(\cot^{6}\left(d x +c \right)\right)}{6 d}+\frac{a^{2} \left(\cot^{4}\left(d x +c \right)\right)}{4 d}-\frac{a^{2} \left(\cot^{2}\left(d x +c \right)\right)}{2 d}"," ",0,"-1/4/d*a^2/sin(d*x+c)^4*cos(d*x+c)^8+1/2/d*a^2/sin(d*x+c)^2*cos(d*x+c)^8+1/2/d*a^2*cos(d*x+c)^6+3/4/d*a^2*cos(d*x+c)^4+3/2/d*a^2*cos(d*x+c)^2+2*a^2*ln(sin(d*x+c))/d-2/5/d*a^2/sin(d*x+c)^5*cos(d*x+c)^8+2/5/d*a^2/sin(d*x+c)^3*cos(d*x+c)^8-2/d*a^2/sin(d*x+c)*cos(d*x+c)^8-32/5*a^2*sin(d*x+c)/d-2/d*a^2*sin(d*x+c)*cos(d*x+c)^6-12/5/d*a^2*sin(d*x+c)*cos(d*x+c)^4-16/5/d*a^2*cos(d*x+c)^2*sin(d*x+c)-1/6/d*a^2*cot(d*x+c)^6+1/4/d*a^2*cot(d*x+c)^4-1/2/d*a^2*cot(d*x+c)^2","B"
19,1,251,137,0.307000," ","int((a+a*sin(d*x+c))^2*tan(d*x+c)^6,x)","\frac{a^{2} \left(\frac{\sin^{9}\left(d x +c \right)}{5 \cos \left(d x +c \right)^{5}}-\frac{4 \left(\sin^{9}\left(d x +c \right)\right)}{15 \cos \left(d x +c \right)^{3}}+\frac{8 \left(\sin^{9}\left(d x +c \right)\right)}{5 \cos \left(d x +c \right)}+\frac{8 \left(\sin^{7}\left(d x +c \right)+\frac{7 \left(\sin^{5}\left(d x +c \right)\right)}{6}+\frac{35 \left(\sin^{3}\left(d x +c \right)\right)}{24}+\frac{35 \sin \left(d x +c \right)}{16}\right) \cos \left(d x +c \right)}{5}-\frac{7 d x}{2}-\frac{7 c}{2}\right)+2 a^{2} \left(\frac{\sin^{8}\left(d x +c \right)}{5 \cos \left(d x +c \right)^{5}}-\frac{\sin^{8}\left(d x +c \right)}{5 \cos \left(d x +c \right)^{3}}+\frac{\sin^{8}\left(d x +c \right)}{\cos \left(d x +c \right)}+\left(\frac{16}{5}+\sin^{6}\left(d x +c \right)+\frac{6 \left(\sin^{4}\left(d x +c \right)\right)}{5}+\frac{8 \left(\sin^{2}\left(d x +c \right)\right)}{5}\right) \cos \left(d x +c \right)\right)+a^{2} \left(\frac{\left(\tan^{5}\left(d x +c \right)\right)}{5}-\frac{\left(\tan^{3}\left(d x +c \right)\right)}{3}+\tan \left(d x +c \right)-d x -c \right)}{d}"," ",0,"1/d*(a^2*(1/5*sin(d*x+c)^9/cos(d*x+c)^5-4/15*sin(d*x+c)^9/cos(d*x+c)^3+8/5*sin(d*x+c)^9/cos(d*x+c)+8/5*(sin(d*x+c)^7+7/6*sin(d*x+c)^5+35/24*sin(d*x+c)^3+35/16*sin(d*x+c))*cos(d*x+c)-7/2*d*x-7/2*c)+2*a^2*(1/5*sin(d*x+c)^8/cos(d*x+c)^5-1/5*sin(d*x+c)^8/cos(d*x+c)^3+sin(d*x+c)^8/cos(d*x+c)+(16/5+sin(d*x+c)^6+6/5*sin(d*x+c)^4+8/5*sin(d*x+c)^2)*cos(d*x+c))+a^2*(1/5*tan(d*x+c)^5-1/3*tan(d*x+c)^3+tan(d*x+c)-d*x-c))","A"
20,1,186,110,0.292000," ","int((a+a*sin(d*x+c))^2*tan(d*x+c)^4,x)","\frac{a^{2} \left(\frac{\sin^{7}\left(d x +c \right)}{3 \cos \left(d x +c \right)^{3}}-\frac{4 \left(\sin^{7}\left(d x +c \right)\right)}{3 \cos \left(d x +c \right)}-\frac{4 \left(\sin^{5}\left(d x +c \right)+\frac{5 \left(\sin^{3}\left(d x +c \right)\right)}{4}+\frac{15 \sin \left(d x +c \right)}{8}\right) \cos \left(d x +c \right)}{3}+\frac{5 d x}{2}+\frac{5 c}{2}\right)+2 a^{2} \left(\frac{\sin^{6}\left(d x +c \right)}{3 \cos \left(d x +c \right)^{3}}-\frac{\sin^{6}\left(d x +c \right)}{\cos \left(d x +c \right)}-\left(\frac{8}{3}+\sin^{4}\left(d x +c \right)+\frac{4 \left(\sin^{2}\left(d x +c \right)\right)}{3}\right) \cos \left(d x +c \right)\right)+a^{2} \left(\frac{\left(\tan^{3}\left(d x +c \right)\right)}{3}-\tan \left(d x +c \right)+d x +c \right)}{d}"," ",0,"1/d*(a^2*(1/3*sin(d*x+c)^7/cos(d*x+c)^3-4/3*sin(d*x+c)^7/cos(d*x+c)-4/3*(sin(d*x+c)^5+5/4*sin(d*x+c)^3+15/8*sin(d*x+c))*cos(d*x+c)+5/2*d*x+5/2*c)+2*a^2*(1/3*sin(d*x+c)^6/cos(d*x+c)^3-sin(d*x+c)^6/cos(d*x+c)-(8/3+sin(d*x+c)^4+4/3*sin(d*x+c)^2)*cos(d*x+c))+a^2*(1/3*tan(d*x+c)^3-tan(d*x+c)+d*x+c))","A"
21,1,117,67,0.245000," ","int((a+a*sin(d*x+c))^2*tan(d*x+c)^2,x)","\frac{a^{2} \left(\frac{\sin^{5}\left(d x +c \right)}{\cos \left(d x +c \right)}+\left(\sin^{3}\left(d x +c \right)+\frac{3 \sin \left(d x +c \right)}{2}\right) \cos \left(d x +c \right)-\frac{3 d x}{2}-\frac{3 c}{2}\right)+2 a^{2} \left(\frac{\sin^{4}\left(d x +c \right)}{\cos \left(d x +c \right)}+\left(2+\sin^{2}\left(d x +c \right)\right) \cos \left(d x +c \right)\right)+a^{2} \left(\tan \left(d x +c \right)-d x -c \right)}{d}"," ",0,"1/d*(a^2*(sin(d*x+c)^5/cos(d*x+c)+(sin(d*x+c)^3+3/2*sin(d*x+c))*cos(d*x+c)-3/2*d*x-3/2*c)+2*a^2*(sin(d*x+c)^4/cos(d*x+c)+(2+sin(d*x+c)^2)*cos(d*x+c))+a^2*(tan(d*x+c)-d*x-c))","A"
22,1,52,41,0.072000," ","int((a+a*sin(d*x+c))^2,x)","\frac{a^{2} \left(-\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)}{2}+\frac{d x}{2}+\frac{c}{2}\right)-2 a^{2} \cos \left(d x +c \right)+a^{2} \left(d x +c \right)}{d}"," ",0,"1/d*(a^2*(-1/2*cos(d*x+c)*sin(d*x+c)+1/2*d*x+1/2*c)-2*a^2*cos(d*x+c)+a^2*(d*x+c))","A"
23,1,89,70,0.129000," ","int(cot(d*x+c)^2*(a+a*sin(d*x+c))^2,x)","\frac{a^{2} \cos \left(d x +c \right) \sin \left(d x +c \right)}{2 d}-\frac{a^{2} x}{2}-\frac{a^{2} c}{2 d}+\frac{2 a^{2} \cos \left(d x +c \right)}{d}+\frac{2 a^{2} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{d}-\frac{a^{2} \cot \left(d x +c \right)}{d}"," ",0,"1/2*a^2*cos(d*x+c)*sin(d*x+c)/d-1/2*a^2*x-1/2/d*a^2*c+2*a^2*cos(d*x+c)/d+2/d*a^2*ln(csc(d*x+c)-cot(d*x+c))-a^2*cot(d*x+c)/d","A"
24,1,190,92,0.222000," ","int(cot(d*x+c)^4*(a+a*sin(d*x+c))^2,x)","-\frac{a^{2} \left(\cos^{5}\left(d x +c \right)\right)}{d \sin \left(d x +c \right)}-\frac{a^{2} \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)}{d}-\frac{3 a^{2} \cos \left(d x +c \right) \sin \left(d x +c \right)}{2 d}-\frac{a^{2} x}{2}-\frac{a^{2} c}{2 d}-\frac{a^{2} \left(\cos^{5}\left(d x +c \right)\right)}{d \sin \left(d x +c \right)^{2}}-\frac{a^{2} \left(\cos^{3}\left(d x +c \right)\right)}{d}-\frac{3 a^{2} \cos \left(d x +c \right)}{d}-\frac{3 a^{2} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{d}-\frac{a^{2} \left(\cot^{3}\left(d x +c \right)\right)}{3 d}+\frac{a^{2} \cot \left(d x +c \right)}{d}"," ",0,"-1/d*a^2/sin(d*x+c)*cos(d*x+c)^5-a^2*cos(d*x+c)^3*sin(d*x+c)/d-3/2*a^2*cos(d*x+c)*sin(d*x+c)/d-1/2*a^2*x-1/2/d*a^2*c-1/d*a^2/sin(d*x+c)^2*cos(d*x+c)^5-a^2*cos(d*x+c)^3/d-3*a^2*cos(d*x+c)/d-3/d*a^2*ln(csc(d*x+c)-cot(d*x+c))-1/3*a^2*cot(d*x+c)^3/d+a^2*cot(d*x+c)/d","B"
25,1,445,146,0.232000," ","int((a+a*sin(d*x+c))^3*tan(d*x+c)^7,x)","\frac{35 a^{3} \left(\sin^{9}\left(d x +c \right)\right)}{48 d}+\frac{3 a^{3} \left(\sin^{8}\left(d x +c \right)\right)}{2 d}+\frac{15 a^{3} \left(\sin^{7}\left(d x +c \right)\right)}{8 d}+\frac{a^{3} \left(\sin^{10}\left(d x +c \right)\right)}{2 d \cos \left(d x +c \right)^{6}}-\frac{a^{3} \left(\sin^{10}\left(d x +c \right)\right)}{2 d \cos \left(d x +c \right)^{4}}+\frac{3 a^{3} \left(\sin^{10}\left(d x +c \right)\right)}{2 d \cos \left(d x +c \right)^{2}}+\frac{a^{3} \left(\sin^{9}\left(d x +c \right)\right)}{2 d \cos \left(d x +c \right)^{6}}-\frac{3 a^{3} \left(\sin^{9}\left(d x +c \right)\right)}{8 d \cos \left(d x +c \right)^{4}}+\frac{15 a^{3} \left(\sin^{9}\left(d x +c \right)\right)}{16 d \cos \left(d x +c \right)^{2}}+\frac{a^{3} \left(\sin^{11}\left(d x +c \right)\right)}{6 d \cos \left(d x +c \right)^{6}}-\frac{5 a^{3} \left(\sin^{11}\left(d x +c \right)\right)}{24 d \cos \left(d x +c \right)^{4}}+\frac{35 a^{3} \left(\sin^{11}\left(d x +c \right)\right)}{48 d \cos \left(d x +c \right)^{2}}+\frac{21 a^{3} \left(\sin^{5}\left(d x +c \right)\right)}{8 d}+\frac{35 a^{3} \left(\sin^{3}\left(d x +c \right)\right)}{8 d}+\frac{105 a^{3} \sin \left(d x +c \right)}{8 d}-\frac{105 a^{3} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{8 d}+\frac{a^{3} \left(\tan^{6}\left(d x +c \right)\right)}{6 d}-\frac{a^{3} \left(\tan^{4}\left(d x +c \right)\right)}{4 d}+\frac{a^{3} \left(\tan^{2}\left(d x +c \right)\right)}{2 d}+\frac{2 a^{3} \left(\sin^{6}\left(d x +c \right)\right)}{d}+\frac{3 a^{3} \left(\sin^{4}\left(d x +c \right)\right)}{d}+\frac{6 a^{3} \left(\sin^{2}\left(d x +c \right)\right)}{d}+\frac{13 a^{3} \ln \left(\cos \left(d x +c \right)\right)}{d}"," ",0,"35/48/d*a^3*sin(d*x+c)^9+3/2/d*a^3*sin(d*x+c)^8+15/8/d*a^3*sin(d*x+c)^7+1/2/d*a^3*sin(d*x+c)^10/cos(d*x+c)^6-1/2/d*a^3*sin(d*x+c)^10/cos(d*x+c)^4+3/2/d*a^3*sin(d*x+c)^10/cos(d*x+c)^2+1/2/d*a^3*sin(d*x+c)^9/cos(d*x+c)^6-3/8/d*a^3*sin(d*x+c)^9/cos(d*x+c)^4+15/16/d*a^3*sin(d*x+c)^9/cos(d*x+c)^2+1/6/d*a^3*sin(d*x+c)^11/cos(d*x+c)^6-5/24/d*a^3*sin(d*x+c)^11/cos(d*x+c)^4+35/48/d*a^3*sin(d*x+c)^11/cos(d*x+c)^2+21/8/d*a^3*sin(d*x+c)^5+35/8*a^3*sin(d*x+c)^3/d+105/8*a^3*sin(d*x+c)/d-105/8/d*a^3*ln(sec(d*x+c)+tan(d*x+c))+1/6/d*a^3*tan(d*x+c)^6-1/4/d*a^3*tan(d*x+c)^4+1/2/d*a^3*tan(d*x+c)^2+2/d*a^3*sin(d*x+c)^6+3/d*a^3*sin(d*x+c)^4+6*a^3*sin(d*x+c)^2/d+13/d*a^3*ln(cos(d*x+c))","B"
26,1,205,87,0.183000," ","int((a+a*sin(d*x+c))^3*tan(d*x+c)^3,x)","\frac{a^{3} \left(\sin^{7}\left(d x +c \right)\right)}{2 d \cos \left(d x +c \right)^{2}}+\frac{a^{3} \left(\sin^{5}\left(d x +c \right)\right)}{2 d}+\frac{7 a^{3} \left(\sin^{3}\left(d x +c \right)\right)}{3 d}+\frac{7 a^{3} \sin \left(d x +c \right)}{d}-\frac{7 a^{3} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{3 a^{3} \left(\sin^{6}\left(d x +c \right)\right)}{2 d \cos \left(d x +c \right)^{2}}+\frac{3 a^{3} \left(\sin^{4}\left(d x +c \right)\right)}{2 d}+\frac{3 a^{3} \left(\sin^{2}\left(d x +c \right)\right)}{d}+\frac{7 a^{3} \ln \left(\cos \left(d x +c \right)\right)}{d}+\frac{3 a^{3} \left(\sin^{5}\left(d x +c \right)\right)}{2 d \cos \left(d x +c \right)^{2}}+\frac{a^{3} \left(\tan^{2}\left(d x +c \right)\right)}{2 d}"," ",0,"1/2/d*a^3*sin(d*x+c)^7/cos(d*x+c)^2+1/2/d*a^3*sin(d*x+c)^5+7/3*a^3*sin(d*x+c)^3/d+7*a^3*sin(d*x+c)/d-7/d*a^3*ln(sec(d*x+c)+tan(d*x+c))+3/2/d*a^3*sin(d*x+c)^6/cos(d*x+c)^2+3/2/d*a^3*sin(d*x+c)^4+3*a^3*sin(d*x+c)^2/d+7/d*a^3*ln(cos(d*x+c))+3/2/d*a^3*sin(d*x+c)^5/cos(d*x+c)^2+1/2/d*a^3*tan(d*x+c)^2","B"
27,1,85,66,0.144000," ","int((a+a*sin(d*x+c))^3*tan(d*x+c),x)","-\frac{a^{3} \left(\sin^{3}\left(d x +c \right)\right)}{3 d}-\frac{4 a^{3} \sin \left(d x +c \right)}{d}+\frac{4 a^{3} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}-\frac{3 a^{3} \left(\sin^{2}\left(d x +c \right)\right)}{2 d}-\frac{4 a^{3} \ln \left(\cos \left(d x +c \right)\right)}{d}"," ",0,"-1/3*a^3*sin(d*x+c)^3/d-4*a^3*sin(d*x+c)/d+4/d*a^3*ln(sec(d*x+c)+tan(d*x+c))-3/2*a^3*sin(d*x+c)^2/d-4/d*a^3*ln(cos(d*x+c))","A"
28,1,109,92,0.240000," ","int(cot(d*x+c)^3*(a+a*sin(d*x+c))^3,x)","-\frac{8 a^{3} \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{3 d}-\frac{16 a^{3} \sin \left(d x +c \right)}{3 d}+\frac{3 a^{3} \left(\cos^{2}\left(d x +c \right)\right)}{2 d}+\frac{2 a^{3} \ln \left(\sin \left(d x +c \right)\right)}{d}-\frac{3 a^{3} \left(\cos^{4}\left(d x +c \right)\right)}{d \sin \left(d x +c \right)}-\frac{a^{3} \left(\cot^{2}\left(d x +c \right)\right)}{2 d}"," ",0,"-8/3/d*a^3*cos(d*x+c)^2*sin(d*x+c)-16/3*a^3*sin(d*x+c)/d+3/2/d*a^3*cos(d*x+c)^2+2*a^3*ln(sin(d*x+c))/d-3/d*a^3/sin(d*x+c)*cos(d*x+c)^4-1/2/d*a^3*cot(d*x+c)^2","A"
29,1,359,166,0.377000," ","int((a+a*sin(d*x+c))^3*tan(d*x+c)^6,x)","\frac{a^{3} \left(\frac{\sin^{10}\left(d x +c \right)}{5 \cos \left(d x +c \right)^{5}}-\frac{\sin^{10}\left(d x +c \right)}{3 \cos \left(d x +c \right)^{3}}+\frac{7 \left(\sin^{10}\left(d x +c \right)\right)}{3 \cos \left(d x +c \right)}+\frac{7 \left(\frac{128}{35}+\sin^{8}\left(d x +c \right)+\frac{8 \left(\sin^{6}\left(d x +c \right)\right)}{7}+\frac{48 \left(\sin^{4}\left(d x +c \right)\right)}{35}+\frac{64 \left(\sin^{2}\left(d x +c \right)\right)}{35}\right) \cos \left(d x +c \right)}{3}\right)+3 a^{3} \left(\frac{\sin^{9}\left(d x +c \right)}{5 \cos \left(d x +c \right)^{5}}-\frac{4 \left(\sin^{9}\left(d x +c \right)\right)}{15 \cos \left(d x +c \right)^{3}}+\frac{8 \left(\sin^{9}\left(d x +c \right)\right)}{5 \cos \left(d x +c \right)}+\frac{8 \left(\sin^{7}\left(d x +c \right)+\frac{7 \left(\sin^{5}\left(d x +c \right)\right)}{6}+\frac{35 \left(\sin^{3}\left(d x +c \right)\right)}{24}+\frac{35 \sin \left(d x +c \right)}{16}\right) \cos \left(d x +c \right)}{5}-\frac{7 d x}{2}-\frac{7 c}{2}\right)+3 a^{3} \left(\frac{\sin^{8}\left(d x +c \right)}{5 \cos \left(d x +c \right)^{5}}-\frac{\sin^{8}\left(d x +c \right)}{5 \cos \left(d x +c \right)^{3}}+\frac{\sin^{8}\left(d x +c \right)}{\cos \left(d x +c \right)}+\left(\frac{16}{5}+\sin^{6}\left(d x +c \right)+\frac{6 \left(\sin^{4}\left(d x +c \right)\right)}{5}+\frac{8 \left(\sin^{2}\left(d x +c \right)\right)}{5}\right) \cos \left(d x +c \right)\right)+a^{3} \left(\frac{\left(\tan^{5}\left(d x +c \right)\right)}{5}-\frac{\left(\tan^{3}\left(d x +c \right)\right)}{3}+\tan \left(d x +c \right)-d x -c \right)}{d}"," ",0,"1/d*(a^3*(1/5*sin(d*x+c)^10/cos(d*x+c)^5-1/3*sin(d*x+c)^10/cos(d*x+c)^3+7/3*sin(d*x+c)^10/cos(d*x+c)+7/3*(128/35+sin(d*x+c)^8+8/7*sin(d*x+c)^6+48/35*sin(d*x+c)^4+64/35*sin(d*x+c)^2)*cos(d*x+c))+3*a^3*(1/5*sin(d*x+c)^9/cos(d*x+c)^5-4/15*sin(d*x+c)^9/cos(d*x+c)^3+8/5*sin(d*x+c)^9/cos(d*x+c)+8/5*(sin(d*x+c)^7+7/6*sin(d*x+c)^5+35/24*sin(d*x+c)^3+35/16*sin(d*x+c))*cos(d*x+c)-7/2*d*x-7/2*c)+3*a^3*(1/5*sin(d*x+c)^8/cos(d*x+c)^5-1/5*sin(d*x+c)^8/cos(d*x+c)^3+sin(d*x+c)^8/cos(d*x+c)+(16/5+sin(d*x+c)^6+6/5*sin(d*x+c)^4+8/5*sin(d*x+c)^2)*cos(d*x+c))+a^3*(1/5*tan(d*x+c)^5-1/3*tan(d*x+c)^3+tan(d*x+c)-d*x-c))","B"
30,1,266,109,0.359000," ","int((a+a*sin(d*x+c))^3*tan(d*x+c)^4,x)","\frac{a^{3} \left(\frac{\sin^{8}\left(d x +c \right)}{3 \cos \left(d x +c \right)^{3}}-\frac{5 \left(\sin^{8}\left(d x +c \right)\right)}{3 \cos \left(d x +c \right)}-\frac{5 \left(\frac{16}{5}+\sin^{6}\left(d x +c \right)+\frac{6 \left(\sin^{4}\left(d x +c \right)\right)}{5}+\frac{8 \left(\sin^{2}\left(d x +c \right)\right)}{5}\right) \cos \left(d x +c \right)}{3}\right)+3 a^{3} \left(\frac{\sin^{7}\left(d x +c \right)}{3 \cos \left(d x +c \right)^{3}}-\frac{4 \left(\sin^{7}\left(d x +c \right)\right)}{3 \cos \left(d x +c \right)}-\frac{4 \left(\sin^{5}\left(d x +c \right)+\frac{5 \left(\sin^{3}\left(d x +c \right)\right)}{4}+\frac{15 \sin \left(d x +c \right)}{8}\right) \cos \left(d x +c \right)}{3}+\frac{5 d x}{2}+\frac{5 c}{2}\right)+3 a^{3} \left(\frac{\sin^{6}\left(d x +c \right)}{3 \cos \left(d x +c \right)^{3}}-\frac{\sin^{6}\left(d x +c \right)}{\cos \left(d x +c \right)}-\left(\frac{8}{3}+\sin^{4}\left(d x +c \right)+\frac{4 \left(\sin^{2}\left(d x +c \right)\right)}{3}\right) \cos \left(d x +c \right)\right)+a^{3} \left(\frac{\left(\tan^{3}\left(d x +c \right)\right)}{3}-\tan \left(d x +c \right)+d x +c \right)}{d}"," ",0,"1/d*(a^3*(1/3*sin(d*x+c)^8/cos(d*x+c)^3-5/3*sin(d*x+c)^8/cos(d*x+c)-5/3*(16/5+sin(d*x+c)^6+6/5*sin(d*x+c)^4+8/5*sin(d*x+c)^2)*cos(d*x+c))+3*a^3*(1/3*sin(d*x+c)^7/cos(d*x+c)^3-4/3*sin(d*x+c)^7/cos(d*x+c)-4/3*(sin(d*x+c)^5+5/4*sin(d*x+c)^3+15/8*sin(d*x+c))*cos(d*x+c)+5/2*d*x+5/2*c)+3*a^3*(1/3*sin(d*x+c)^6/cos(d*x+c)^3-sin(d*x+c)^6/cos(d*x+c)-(8/3+sin(d*x+c)^4+4/3*sin(d*x+c)^2)*cos(d*x+c))+a^3*(1/3*tan(d*x+c)^3-tan(d*x+c)+d*x+c))","B"
31,1,167,83,0.314000," ","int((a+a*sin(d*x+c))^3*tan(d*x+c)^2,x)","\frac{a^{3} \left(\frac{\sin^{6}\left(d x +c \right)}{\cos \left(d x +c \right)}+\left(\frac{8}{3}+\sin^{4}\left(d x +c \right)+\frac{4 \left(\sin^{2}\left(d x +c \right)\right)}{3}\right) \cos \left(d x +c \right)\right)+3 a^{3} \left(\frac{\sin^{5}\left(d x +c \right)}{\cos \left(d x +c \right)}+\left(\sin^{3}\left(d x +c \right)+\frac{3 \sin \left(d x +c \right)}{2}\right) \cos \left(d x +c \right)-\frac{3 d x}{2}-\frac{3 c}{2}\right)+3 a^{3} \left(\frac{\sin^{4}\left(d x +c \right)}{\cos \left(d x +c \right)}+\left(2+\sin^{2}\left(d x +c \right)\right) \cos \left(d x +c \right)\right)+a^{3} \left(\tan \left(d x +c \right)-d x -c \right)}{d}"," ",0,"1/d*(a^3*(sin(d*x+c)^6/cos(d*x+c)+(8/3+sin(d*x+c)^4+4/3*sin(d*x+c)^2)*cos(d*x+c))+3*a^3*(sin(d*x+c)^5/cos(d*x+c)+(sin(d*x+c)^3+3/2*sin(d*x+c))*cos(d*x+c)-3/2*d*x-3/2*c)+3*a^3*(sin(d*x+c)^4/cos(d*x+c)+(2+sin(d*x+c)^2)*cos(d*x+c))+a^3*(tan(d*x+c)-d*x-c))","A"
32,1,74,57,0.136000," ","int((a+a*sin(d*x+c))^3,x)","\frac{-\frac{a^{3} \left(2+\sin^{2}\left(d x +c \right)\right) \cos \left(d x +c \right)}{3}+3 a^{3} \left(-\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)}{2}+\frac{d x}{2}+\frac{c}{2}\right)-3 a^{3} \cos \left(d x +c \right)+a^{3} \left(d x +c \right)}{d}"," ",0,"1/d*(-1/3*a^3*(2+sin(d*x+c)^2)*cos(d*x+c)+3*a^3*(-1/2*cos(d*x+c)*sin(d*x+c)+1/2*d*x+1/2*c)-3*a^3*cos(d*x+c)+a^3*(d*x+c))","A"
33,1,105,86,0.140000," ","int(cot(d*x+c)^2*(a+a*sin(d*x+c))^3,x)","-\frac{a^{3} \left(\cos^{3}\left(d x +c \right)\right)}{3 d}+\frac{3 a^{3} \cos \left(d x +c \right) \sin \left(d x +c \right)}{2 d}+\frac{a^{3} x}{2}+\frac{a^{3} c}{2 d}+\frac{3 a^{3} \cos \left(d x +c \right)}{d}+\frac{3 a^{3} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{d}-\frac{a^{3} \cot \left(d x +c \right)}{d}"," ",0,"-1/3*a^3*cos(d*x+c)^3/d+3/2*a^3*cos(d*x+c)*sin(d*x+c)/d+1/2*a^3*x+1/2/d*a^3*c+3*a^3*cos(d*x+c)/d+3/d*a^3*ln(csc(d*x+c)-cot(d*x+c))-a^3*cot(d*x+c)/d","A"
34,1,387,123,0.235000," ","int((a+a*sin(d*x+c))^4*tan(d*x+c)^5,x)","-\frac{4 a^{4} \left(\sin^{6}\left(d x +c \right)\right)}{d}-\frac{5 a^{4} \left(\sin^{5}\left(d x +c \right)\right)}{d}-\frac{3 a^{4} \left(\sin^{8}\left(d x +c \right)\right)}{4 d}-\frac{5 a^{4} \left(\sin^{7}\left(d x +c \right)\right)}{2 d}-\frac{25 a^{4} \left(\sin^{3}\left(d x +c \right)\right)}{3 d}-\frac{25 a^{4} \sin \left(d x +c \right)}{d}+\frac{25 a^{4} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{a^{4} \left(\sin^{10}\left(d x +c \right)\right)}{4 d \cos \left(d x +c \right)^{4}}-\frac{3 a^{4} \left(\sin^{10}\left(d x +c \right)\right)}{4 d \cos \left(d x +c \right)^{2}}+\frac{a^{4} \left(\sin^{9}\left(d x +c \right)\right)}{d \cos \left(d x +c \right)^{4}}-\frac{5 a^{4} \left(\sin^{9}\left(d x +c \right)\right)}{2 d \cos \left(d x +c \right)^{2}}+\frac{3 a^{4} \left(\sin^{8}\left(d x +c \right)\right)}{2 d \cos \left(d x +c \right)^{4}}-\frac{3 a^{4} \left(\sin^{8}\left(d x +c \right)\right)}{d \cos \left(d x +c \right)^{2}}+\frac{a^{4} \left(\sin^{7}\left(d x +c \right)\right)}{d \cos \left(d x +c \right)^{4}}-\frac{3 a^{4} \left(\sin^{7}\left(d x +c \right)\right)}{2 d \cos \left(d x +c \right)^{2}}-\frac{6 a^{4} \left(\sin^{4}\left(d x +c \right)\right)}{d}-\frac{12 a^{4} \left(\sin^{2}\left(d x +c \right)\right)}{d}-\frac{25 a^{4} \ln \left(\cos \left(d x +c \right)\right)}{d}+\frac{a^{4} \left(\tan^{4}\left(d x +c \right)\right)}{4 d}-\frac{a^{4} \left(\tan^{2}\left(d x +c \right)\right)}{2 d}"," ",0,"-4/d*a^4*sin(d*x+c)^6-5/d*a^4*sin(d*x+c)^5-3/4/d*a^4*sin(d*x+c)^8-5/2/d*a^4*sin(d*x+c)^7-25/3*a^4*sin(d*x+c)^3/d-25*a^4*sin(d*x+c)/d+25/d*a^4*ln(sec(d*x+c)+tan(d*x+c))+1/4/d*a^4*sin(d*x+c)^10/cos(d*x+c)^4-3/4/d*a^4*sin(d*x+c)^10/cos(d*x+c)^2+1/d*a^4*sin(d*x+c)^9/cos(d*x+c)^4-5/2/d*a^4*sin(d*x+c)^9/cos(d*x+c)^2+3/2/d*a^4*sin(d*x+c)^8/cos(d*x+c)^4-3/d*a^4*sin(d*x+c)^8/cos(d*x+c)^2+1/d*a^4*sin(d*x+c)^7/cos(d*x+c)^4-3/2/d*a^4*sin(d*x+c)^7/cos(d*x+c)^2-6*a^4*sin(d*x+c)^4/d-12*a^4*sin(d*x+c)^2/d-25/d*a^4*ln(cos(d*x+c))+1/4/d*a^4*tan(d*x+c)^4-1/2/d*a^4*tan(d*x+c)^2","B"
35,1,245,103,0.201000," ","int((a+a*sin(d*x+c))^4*tan(d*x+c)^3,x)","\frac{a^{4} \left(\sin^{8}\left(d x +c \right)\right)}{2 d \cos \left(d x +c \right)^{2}}+\frac{a^{4} \left(\sin^{6}\left(d x +c \right)\right)}{2 d}+\frac{15 a^{4} \left(\sin^{4}\left(d x +c \right)\right)}{4 d}+\frac{15 a^{4} \left(\sin^{2}\left(d x +c \right)\right)}{2 d}+\frac{16 a^{4} \ln \left(\cos \left(d x +c \right)\right)}{d}+\frac{2 a^{4} \left(\sin^{7}\left(d x +c \right)\right)}{d \cos \left(d x +c \right)^{2}}+\frac{2 a^{4} \left(\sin^{5}\left(d x +c \right)\right)}{d}+\frac{16 a^{4} \left(\sin^{3}\left(d x +c \right)\right)}{3 d}+\frac{16 a^{4} \sin \left(d x +c \right)}{d}-\frac{16 a^{4} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{3 a^{4} \left(\sin^{6}\left(d x +c \right)\right)}{d \cos \left(d x +c \right)^{2}}+\frac{2 a^{4} \left(\sin^{5}\left(d x +c \right)\right)}{d \cos \left(d x +c \right)^{2}}+\frac{a^{4} \left(\tan^{2}\left(d x +c \right)\right)}{2 d}"," ",0,"1/2/d*a^4*sin(d*x+c)^8/cos(d*x+c)^2+1/2/d*a^4*sin(d*x+c)^6+15/4*a^4*sin(d*x+c)^4/d+15/2*a^4*sin(d*x+c)^2/d+16/d*a^4*ln(cos(d*x+c))+2/d*a^4*sin(d*x+c)^7/cos(d*x+c)^2+2/d*a^4*sin(d*x+c)^5+16/3*a^4*sin(d*x+c)^3/d+16*a^4*sin(d*x+c)/d-16/d*a^4*ln(sec(d*x+c)+tan(d*x+c))+3/d*a^4*sin(d*x+c)^6/cos(d*x+c)^2+2/d*a^4*sin(d*x+c)^5/cos(d*x+c)^2+1/2/d*a^4*tan(d*x+c)^2","B"
36,1,101,82,0.155000," ","int((a+a*sin(d*x+c))^4*tan(d*x+c),x)","-\frac{a^{4} \left(\sin^{4}\left(d x +c \right)\right)}{4 d}-\frac{7 a^{4} \left(\sin^{2}\left(d x +c \right)\right)}{2 d}-\frac{8 a^{4} \ln \left(\cos \left(d x +c \right)\right)}{d}-\frac{4 a^{4} \left(\sin^{3}\left(d x +c \right)\right)}{3 d}-\frac{8 a^{4} \sin \left(d x +c \right)}{d}+\frac{8 a^{4} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}"," ",0,"-1/4*a^4*sin(d*x+c)^4/d-7/2*a^4*sin(d*x+c)^2/d-8/d*a^4*ln(cos(d*x+c))-4/3*a^4*sin(d*x+c)^3/d-8*a^4*sin(d*x+c)/d+8/d*a^4*ln(sec(d*x+c)+tan(d*x+c))","A"
37,1,125,94,0.244000," ","int(cot(d*x+c)^3*(a+a*sin(d*x+c))^4,x)","-\frac{a^{4} \left(\cos^{4}\left(d x +c \right)\right)}{4 d}-\frac{8 a^{4} \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{3 d}-\frac{16 a^{4} \sin \left(d x +c \right)}{3 d}+\frac{3 a^{4} \left(\cos^{2}\left(d x +c \right)\right)}{d}+\frac{5 a^{4} \ln \left(\sin \left(d x +c \right)\right)}{d}-\frac{4 a^{4} \left(\cos^{4}\left(d x +c \right)\right)}{d \sin \left(d x +c \right)}-\frac{a^{4} \left(\cot^{2}\left(d x +c \right)\right)}{2 d}"," ",0,"-1/4/d*a^4*cos(d*x+c)^4-8/3/d*a^4*cos(d*x+c)^2*sin(d*x+c)-16/3*a^4*sin(d*x+c)/d+3/d*a^4*cos(d*x+c)^2+5*a^4*ln(sin(d*x+c))/d-4/d*a^4/sin(d*x+c)*cos(d*x+c)^4-1/2/d*a^4*cot(d*x+c)^2","A"
38,1,360,131,0.408000," ","int((a+a*sin(d*x+c))^4*tan(d*x+c)^4,x)","\frac{a^{4} \left(\frac{\sin^{9}\left(d x +c \right)}{3 \cos \left(d x +c \right)^{3}}-\frac{2 \left(\sin^{9}\left(d x +c \right)\right)}{\cos \left(d x +c \right)}-2 \left(\sin^{7}\left(d x +c \right)+\frac{7 \left(\sin^{5}\left(d x +c \right)\right)}{6}+\frac{35 \left(\sin^{3}\left(d x +c \right)\right)}{24}+\frac{35 \sin \left(d x +c \right)}{16}\right) \cos \left(d x +c \right)+\frac{35 d x}{8}+\frac{35 c}{8}\right)+4 a^{4} \left(\frac{\sin^{8}\left(d x +c \right)}{3 \cos \left(d x +c \right)^{3}}-\frac{5 \left(\sin^{8}\left(d x +c \right)\right)}{3 \cos \left(d x +c \right)}-\frac{5 \left(\frac{16}{5}+\sin^{6}\left(d x +c \right)+\frac{6 \left(\sin^{4}\left(d x +c \right)\right)}{5}+\frac{8 \left(\sin^{2}\left(d x +c \right)\right)}{5}\right) \cos \left(d x +c \right)}{3}\right)+6 a^{4} \left(\frac{\sin^{7}\left(d x +c \right)}{3 \cos \left(d x +c \right)^{3}}-\frac{4 \left(\sin^{7}\left(d x +c \right)\right)}{3 \cos \left(d x +c \right)}-\frac{4 \left(\sin^{5}\left(d x +c \right)+\frac{5 \left(\sin^{3}\left(d x +c \right)\right)}{4}+\frac{15 \sin \left(d x +c \right)}{8}\right) \cos \left(d x +c \right)}{3}+\frac{5 d x}{2}+\frac{5 c}{2}\right)+4 a^{4} \left(\frac{\sin^{6}\left(d x +c \right)}{3 \cos \left(d x +c \right)^{3}}-\frac{\sin^{6}\left(d x +c \right)}{\cos \left(d x +c \right)}-\left(\frac{8}{3}+\sin^{4}\left(d x +c \right)+\frac{4 \left(\sin^{2}\left(d x +c \right)\right)}{3}\right) \cos \left(d x +c \right)\right)+a^{4} \left(\frac{\left(\tan^{3}\left(d x +c \right)\right)}{3}-\tan \left(d x +c \right)+d x +c \right)}{d}"," ",0,"1/d*(a^4*(1/3*sin(d*x+c)^9/cos(d*x+c)^3-2*sin(d*x+c)^9/cos(d*x+c)-2*(sin(d*x+c)^7+7/6*sin(d*x+c)^5+35/24*sin(d*x+c)^3+35/16*sin(d*x+c))*cos(d*x+c)+35/8*d*x+35/8*c)+4*a^4*(1/3*sin(d*x+c)^8/cos(d*x+c)^3-5/3*sin(d*x+c)^8/cos(d*x+c)-5/3*(16/5+sin(d*x+c)^6+6/5*sin(d*x+c)^4+8/5*sin(d*x+c)^2)*cos(d*x+c))+6*a^4*(1/3*sin(d*x+c)^7/cos(d*x+c)^3-4/3*sin(d*x+c)^7/cos(d*x+c)-4/3*(sin(d*x+c)^5+5/4*sin(d*x+c)^3+15/8*sin(d*x+c))*cos(d*x+c)+5/2*d*x+5/2*c)+4*a^4*(1/3*sin(d*x+c)^6/cos(d*x+c)^3-sin(d*x+c)^6/cos(d*x+c)-(8/3+sin(d*x+c)^4+4/3*sin(d*x+c)^2)*cos(d*x+c))+a^4*(1/3*tan(d*x+c)^3-tan(d*x+c)+d*x+c))","B"
39,1,231,105,0.312000," ","int((a+a*sin(d*x+c))^4*tan(d*x+c)^2,x)","\frac{a^{4} \left(\frac{\sin^{7}\left(d x +c \right)}{\cos \left(d x +c \right)}+\left(\sin^{5}\left(d x +c \right)+\frac{5 \left(\sin^{3}\left(d x +c \right)\right)}{4}+\frac{15 \sin \left(d x +c \right)}{8}\right) \cos \left(d x +c \right)-\frac{15 d x}{8}-\frac{15 c}{8}\right)+4 a^{4} \left(\frac{\sin^{6}\left(d x +c \right)}{\cos \left(d x +c \right)}+\left(\frac{8}{3}+\sin^{4}\left(d x +c \right)+\frac{4 \left(\sin^{2}\left(d x +c \right)\right)}{3}\right) \cos \left(d x +c \right)\right)+6 a^{4} \left(\frac{\sin^{5}\left(d x +c \right)}{\cos \left(d x +c \right)}+\left(\sin^{3}\left(d x +c \right)+\frac{3 \sin \left(d x +c \right)}{2}\right) \cos \left(d x +c \right)-\frac{3 d x}{2}-\frac{3 c}{2}\right)+4 a^{4} \left(\frac{\sin^{4}\left(d x +c \right)}{\cos \left(d x +c \right)}+\left(2+\sin^{2}\left(d x +c \right)\right) \cos \left(d x +c \right)\right)+a^{4} \left(\tan \left(d x +c \right)-d x -c \right)}{d}"," ",0,"1/d*(a^4*(sin(d*x+c)^7/cos(d*x+c)+(sin(d*x+c)^5+5/4*sin(d*x+c)^3+15/8*sin(d*x+c))*cos(d*x+c)-15/8*d*x-15/8*c)+4*a^4*(sin(d*x+c)^6/cos(d*x+c)+(8/3+sin(d*x+c)^4+4/3*sin(d*x+c)^2)*cos(d*x+c))+6*a^4*(sin(d*x+c)^5/cos(d*x+c)+(sin(d*x+c)^3+3/2*sin(d*x+c))*cos(d*x+c)-3/2*d*x-3/2*c)+4*a^4*(sin(d*x+c)^4/cos(d*x+c)+(2+sin(d*x+c)^2)*cos(d*x+c))+a^4*(tan(d*x+c)-d*x-c))","B"
40,1,111,79,0.195000," ","int((a+a*sin(d*x+c))^4,x)","\frac{a^{4} \left(-\frac{\left(\sin^{3}\left(d x +c \right)+\frac{3 \sin \left(d x +c \right)}{2}\right) \cos \left(d x +c \right)}{4}+\frac{3 d x}{8}+\frac{3 c}{8}\right)-\frac{4 a^{4} \left(2+\sin^{2}\left(d x +c \right)\right) \cos \left(d x +c \right)}{3}+6 a^{4} \left(-\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)}{2}+\frac{d x}{2}+\frac{c}{2}\right)-4 a^{4} \cos \left(d x +c \right)+a^{4} \left(d x +c \right)}{d}"," ",0,"1/d*(a^4*(-1/4*(sin(d*x+c)^3+3/2*sin(d*x+c))*cos(d*x+c)+3/8*d*x+3/8*c)-4/3*a^4*(2+sin(d*x+c)^2)*cos(d*x+c)+6*a^4*(-1/2*cos(d*x+c)*sin(d*x+c)+1/2*d*x+1/2*c)-4*a^4*cos(d*x+c)+a^4*(d*x+c))","A"
41,1,127,108,0.137000," ","int(cot(d*x+c)^2*(a+a*sin(d*x+c))^4,x)","-\frac{a^{4} \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)}{4 d}+\frac{25 a^{4} \cos \left(d x +c \right) \sin \left(d x +c \right)}{8 d}+\frac{17 a^{4} x}{8}+\frac{17 a^{4} c}{8 d}-\frac{4 a^{4} \left(\cos^{3}\left(d x +c \right)\right)}{3 d}+\frac{4 a^{4} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{d}+\frac{4 a^{4} \cos \left(d x +c \right)}{d}-\frac{a^{4} \cot \left(d x +c \right)}{d}"," ",0,"-1/4/d*a^4*cos(d*x+c)^3*sin(d*x+c)+25/8*a^4*cos(d*x+c)*sin(d*x+c)/d+17/8*a^4*x+17/8/d*a^4*c-4/3*a^4*cos(d*x+c)^3/d+4/d*a^4*ln(csc(d*x+c)-cot(d*x+c))+4*a^4*cos(d*x+c)/d-a^4*cot(d*x+c)/d","A"
42,1,190,130,0.233000," ","int(cot(d*x+c)^4*(a+a*sin(d*x+c))^4,x)","-\frac{23 a^{4} \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)}{4 d}-\frac{69 a^{4} \cos \left(d x +c \right) \sin \left(d x +c \right)}{8 d}-\frac{61 a^{4} x}{8}-\frac{61 a^{4} c}{8 d}-\frac{2 a^{4} \left(\cos^{3}\left(d x +c \right)\right)}{3 d}-\frac{2 a^{4} \cos \left(d x +c \right)}{d}-\frac{2 a^{4} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{d}-\frac{6 a^{4} \left(\cos^{5}\left(d x +c \right)\right)}{d \sin \left(d x +c \right)}-\frac{2 a^{4} \left(\cos^{5}\left(d x +c \right)\right)}{d \sin \left(d x +c \right)^{2}}-\frac{a^{4} \left(\cot^{3}\left(d x +c \right)\right)}{3 d}+\frac{a^{4} \cot \left(d x +c \right)}{d}"," ",0,"-23/4/d*a^4*cos(d*x+c)^3*sin(d*x+c)-69/8*a^4*cos(d*x+c)*sin(d*x+c)/d-61/8*a^4*x-61/8/d*a^4*c-2/3*a^4*cos(d*x+c)^3/d-2*a^4*cos(d*x+c)/d-2/d*a^4*ln(csc(d*x+c)-cot(d*x+c))-6/d*a^4/sin(d*x+c)*cos(d*x+c)^5-2/d*a^4/sin(d*x+c)^2*cos(d*x+c)^5-1/3*a^4*cot(d*x+c)^3/d+a^4*cot(d*x+c)/d","A"
43,1,293,182,0.231000," ","int(cot(d*x+c)^6*(a+a*sin(d*x+c))^4,x)","\frac{97 a^{4} x}{8}+\frac{7 a^{4} \sin \left(d x +c \right) \left(\cos^{5}\left(d x +c \right)\right)}{d}+\frac{97 a^{4} c}{8 d}-\frac{a^{4} \left(\cos^{5}\left(d x +c \right)\right)}{2 d}-\frac{5 a^{4} \left(\cos^{3}\left(d x +c \right)\right)}{6 d}-\frac{a^{4} \left(\cos^{7}\left(d x +c \right)\right)}{d \sin \left(d x +c \right)^{4}}-\frac{2 a^{4} \left(\cos^{7}\left(d x +c \right)\right)}{d \sin \left(d x +c \right)^{3}}+\frac{7 a^{4} \left(\cos^{7}\left(d x +c \right)\right)}{d \sin \left(d x +c \right)}+\frac{35 a^{4} \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)}{4 d}+\frac{105 a^{4} \cos \left(d x +c \right) \sin \left(d x +c \right)}{8 d}-\frac{a^{4} \left(\cos^{7}\left(d x +c \right)\right)}{2 d \sin \left(d x +c \right)^{2}}-\frac{a^{4} \cot \left(d x +c \right)}{d}-\frac{5 a^{4} \cos \left(d x +c \right)}{2 d}-\frac{a^{4} \left(\cot^{5}\left(d x +c \right)\right)}{5 d}+\frac{a^{4} \left(\cot^{3}\left(d x +c \right)\right)}{3 d}-\frac{5 a^{4} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{2 d}"," ",0,"97/8*a^4*x+7/d*a^4*sin(d*x+c)*cos(d*x+c)^5+97/8/d*a^4*c-1/2/d*a^4*cos(d*x+c)^5-5/6*a^4*cos(d*x+c)^3/d-1/d*a^4/sin(d*x+c)^4*cos(d*x+c)^7-2/d*a^4/sin(d*x+c)^3*cos(d*x+c)^7+7/d*a^4/sin(d*x+c)*cos(d*x+c)^7+35/4/d*a^4*cos(d*x+c)^3*sin(d*x+c)+105/8*a^4*cos(d*x+c)*sin(d*x+c)/d-1/2/d*a^4/sin(d*x+c)^2*cos(d*x+c)^7-a^4*cot(d*x+c)/d-5/2*a^4*cos(d*x+c)/d-1/5*a^4*cot(d*x+c)^5/d+1/3*a^4*cot(d*x+c)^3/d-5/2/d*a^4*ln(csc(d*x+c)-cot(d*x+c))","A"
44,1,162,118,0.182000," ","int(tan(d*x+c)^7/(a+a*sin(d*x+c)),x)","-\frac{1}{96 a d \left(\sin \left(d x +c \right)-1\right)^{3}}-\frac{9}{128 a d \left(\sin \left(d x +c \right)-1\right)^{2}}-\frac{29}{128 a d \left(\sin \left(d x +c \right)-1\right)}+\frac{35 \ln \left(\sin \left(d x +c \right)-1\right)}{256 a d}+\frac{1}{64 a d \left(1+\sin \left(d x +c \right)\right)^{4}}-\frac{5}{48 a d \left(1+\sin \left(d x +c \right)\right)^{3}}+\frac{19}{64 a d \left(1+\sin \left(d x +c \right)\right)^{2}}-\frac{1}{2 a d \left(1+\sin \left(d x +c \right)\right)}-\frac{35 \ln \left(1+\sin \left(d x +c \right)\right)}{256 a d}"," ",0,"-1/96/a/d/(sin(d*x+c)-1)^3-9/128/a/d/(sin(d*x+c)-1)^2-29/128/a/d/(sin(d*x+c)-1)+35/256/a/d*ln(sin(d*x+c)-1)+1/64/a/d/(1+sin(d*x+c))^4-5/48/a/d/(1+sin(d*x+c))^3+19/64/a/d/(1+sin(d*x+c))^2-1/2/a/d/(1+sin(d*x+c))-35/256*ln(1+sin(d*x+c))/a/d","A"
45,1,126,96,0.176000," ","int(tan(d*x+c)^5/(a+a*sin(d*x+c)),x)","\frac{1}{32 a d \left(\sin \left(d x +c \right)-1\right)^{2}}+\frac{3}{16 a d \left(\sin \left(d x +c \right)-1\right)}-\frac{5 \ln \left(\sin \left(d x +c \right)-1\right)}{32 a d}+\frac{1}{24 a d \left(1+\sin \left(d x +c \right)\right)^{3}}-\frac{7}{32 a d \left(1+\sin \left(d x +c \right)\right)^{2}}+\frac{1}{2 a d \left(1+\sin \left(d x +c \right)\right)}+\frac{5 \ln \left(1+\sin \left(d x +c \right)\right)}{32 a d}"," ",0,"1/32/a/d/(sin(d*x+c)-1)^2+3/16/a/d/(sin(d*x+c)-1)-5/32/a/d*ln(sin(d*x+c)-1)+1/24/a/d/(1+sin(d*x+c))^3-7/32/a/d/(1+sin(d*x+c))^2+1/2/a/d/(1+sin(d*x+c))+5/32*ln(1+sin(d*x+c))/a/d","A"
46,1,90,74,0.169000," ","int(tan(d*x+c)^3/(a+a*sin(d*x+c)),x)","-\frac{1}{8 a d \left(\sin \left(d x +c \right)-1\right)}+\frac{3 \ln \left(\sin \left(d x +c \right)-1\right)}{16 a d}+\frac{1}{8 a d \left(1+\sin \left(d x +c \right)\right)^{2}}-\frac{1}{2 a d \left(1+\sin \left(d x +c \right)\right)}-\frac{3 \ln \left(1+\sin \left(d x +c \right)\right)}{16 a d}"," ",0,"-1/8/a/d/(sin(d*x+c)-1)+3/16/a/d*ln(sin(d*x+c)-1)+1/8/a/d/(1+sin(d*x+c))^2-1/2/a/d/(1+sin(d*x+c))-3/16*ln(1+sin(d*x+c))/a/d","A"
47,1,54,33,0.178000," ","int(tan(d*x+c)/(a+a*sin(d*x+c)),x)","-\frac{\ln \left(\sin \left(d x +c \right)-1\right)}{4 a d}+\frac{1}{2 a d \left(1+\sin \left(d x +c \right)\right)}+\frac{\ln \left(1+\sin \left(d x +c \right)\right)}{4 a d}"," ",0,"-1/4/a/d*ln(sin(d*x+c)-1)+1/2/a/d/(1+sin(d*x+c))+1/4*ln(1+sin(d*x+c))/a/d","A"
48,1,33,32,0.116000," ","int(cot(d*x+c)/(a+a*sin(d*x+c)),x)","\frac{\ln \left(\sin \left(d x +c \right)\right)}{a d}-\frac{\ln \left(1+\sin \left(d x +c \right)\right)}{a d}"," ",0,"ln(sin(d*x+c))/a/d-ln(1+sin(d*x+c))/a/d","A"
49,1,30,30,0.130000," ","int(cot(d*x+c)^3/(a+a*sin(d*x+c)),x)","-\frac{-\frac{1}{\sin \left(d x +c \right)}+\frac{1}{2 \sin \left(d x +c \right)^{2}}}{a d}"," ",0,"-1/a/d*(-1/sin(d*x+c)+1/2/sin(d*x+c)^2)","A"
50,1,49,47,0.233000," ","int(cot(d*x+c)^5/(a+a*sin(d*x+c)),x)","\frac{-\frac{1}{\sin \left(d x +c \right)}+\frac{1}{2 \sin \left(d x +c \right)^{2}}-\frac{1}{4 \sin \left(d x +c \right)^{4}}+\frac{1}{3 \sin \left(d x +c \right)^{3}}}{d a}"," ",0,"1/d/a*(-1/sin(d*x+c)+1/2/sin(d*x+c)^2-1/4/sin(d*x+c)^4+1/3/sin(d*x+c)^3)","A"
51,1,67,62,0.246000," ","int(cot(d*x+c)^7/(a+a*sin(d*x+c)),x)","\frac{-\frac{1}{6 \sin \left(d x +c \right)^{6}}+\frac{1}{\sin \left(d x +c \right)}+\frac{1}{5 \sin \left(d x +c \right)^{5}}-\frac{1}{2 \sin \left(d x +c \right)^{2}}+\frac{1}{2 \sin \left(d x +c \right)^{4}}-\frac{2}{3 \sin \left(d x +c \right)^{3}}}{d a}"," ",0,"1/d/a*(-1/6/sin(d*x+c)^6+1/sin(d*x+c)+1/5/sin(d*x+c)^5-1/2/sin(d*x+c)^2+1/2/sin(d*x+c)^4-2/3/sin(d*x+c)^3)","A"
52,1,87,78,0.277000," ","int(cot(d*x+c)^9/(a+a*sin(d*x+c)),x)","\frac{\frac{1}{2 \sin \left(d x +c \right)^{6}}-\frac{1}{\sin \left(d x +c \right)}-\frac{3}{5 \sin \left(d x +c \right)^{5}}+\frac{1}{7 \sin \left(d x +c \right)^{7}}+\frac{1}{2 \sin \left(d x +c \right)^{2}}-\frac{1}{8 \sin \left(d x +c \right)^{8}}-\frac{3}{4 \sin \left(d x +c \right)^{4}}+\frac{1}{\sin \left(d x +c \right)^{3}}}{d a}"," ",0,"1/d/a*(1/2/sin(d*x+c)^6-1/sin(d*x+c)-3/5/sin(d*x+c)^5+1/7/sin(d*x+c)^7+1/2/sin(d*x+c)^2-1/8/sin(d*x+c)^8-3/4/sin(d*x+c)^4+1/sin(d*x+c)^3)","A"
53,1,175,78,0.184000," ","int(tan(d*x+c)^6/(a+a*sin(d*x+c)),x)","\frac{-\frac{1}{10 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{5}}-\frac{1}{4 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{4}}+\frac{1}{4 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}-\frac{5}{16 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{2}{7 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{7}}+\frac{1}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{6}}-\frac{9}{10 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{5}}-\frac{1}{4 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{4}}+\frac{1}{4 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}+\frac{3}{8 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}+\frac{5}{16 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}}{d a}"," ",0,"128/d/a*(-1/1280/(tan(1/2*d*x+1/2*c)-1)^5-1/512/(tan(1/2*d*x+1/2*c)-1)^4+1/512/(tan(1/2*d*x+1/2*c)-1)^2-5/2048/(tan(1/2*d*x+1/2*c)-1)-1/448/(tan(1/2*d*x+1/2*c)+1)^7+1/128/(tan(1/2*d*x+1/2*c)+1)^6-9/1280/(tan(1/2*d*x+1/2*c)+1)^5-1/512/(tan(1/2*d*x+1/2*c)+1)^4+1/512/(tan(1/2*d*x+1/2*c)+1)^3+3/1024/(tan(1/2*d*x+1/2*c)+1)^2+5/2048/(tan(1/2*d*x+1/2*c)+1))","B"
54,1,130,63,0.170000," ","int(tan(d*x+c)^4/(a+a*sin(d*x+c)),x)","\frac{-\frac{1}{6 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{3}}-\frac{1}{4 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}+\frac{3}{8 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{2}{5 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{5}}+\frac{1}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{4}}-\frac{1}{3 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}-\frac{1}{2 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}-\frac{3}{8 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}}{d a}"," ",0,"32/d/a*(-1/192/(tan(1/2*d*x+1/2*c)-1)^3-1/128/(tan(1/2*d*x+1/2*c)-1)^2+3/256/(tan(1/2*d*x+1/2*c)-1)-1/80/(tan(1/2*d*x+1/2*c)+1)^5+1/32/(tan(1/2*d*x+1/2*c)+1)^4-1/96/(tan(1/2*d*x+1/2*c)+1)^3-1/64/(tan(1/2*d*x+1/2*c)+1)^2-3/256/(tan(1/2*d*x+1/2*c)+1))","B"
55,1,70,46,0.145000," ","int(tan(d*x+c)^2/(a+a*sin(d*x+c)),x)","\frac{-\frac{1}{2 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{2}{3 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}+\frac{1}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}+\frac{8}{16 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+16}}{d a}"," ",0,"8/d/a*(-1/16/(tan(1/2*d*x+1/2*c)-1)-1/12/(tan(1/2*d*x+1/2*c)+1)^3+1/8/(tan(1/2*d*x+1/2*c)+1)^2+1/16/(tan(1/2*d*x+1/2*c)+1))","A"
56,1,22,23,0.074000," ","int(1/(a+a*sin(d*x+c)),x)","-\frac{2}{a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}"," ",0,"-2/a/d/(tan(1/2*d*x+1/2*c)+1)","A"
57,1,56,29,0.185000," ","int(cot(d*x+c)^2/(a+a*sin(d*x+c)),x)","\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 a d}-\frac{1}{2 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}-\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a d}"," ",0,"1/2/a/d*tan(1/2*d*x+1/2*c)-1/2/a/d/tan(1/2*d*x+1/2*c)-1/a/d*ln(tan(1/2*d*x+1/2*c))","A"
58,1,132,52,0.200000," ","int(cot(d*x+c)^4/(a+a*sin(d*x+c)),x)","\frac{\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)}{24 a d}-\frac{\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}{8 a d}-\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{8 a d}+\frac{1}{8 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}+\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{2 a d}+\frac{1}{8 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}-\frac{1}{24 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{3}}"," ",0,"1/24/a/d*tan(1/2*d*x+1/2*c)^3-1/8/a/d*tan(1/2*d*x+1/2*c)^2-1/8/a/d*tan(1/2*d*x+1/2*c)+1/8/a/d/tan(1/2*d*x+1/2*c)+1/2/a/d*ln(tan(1/2*d*x+1/2*c))+1/8/a/d/tan(1/2*d*x+1/2*c)^2-1/24/a/d/tan(1/2*d*x+1/2*c)^3","B"
59,1,208,74,0.239000," ","int(cot(d*x+c)^6/(a+a*sin(d*x+c)),x)","\frac{\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)}{160 a d}-\frac{\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)}{64 a d}-\frac{\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)}{32 a d}+\frac{\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}{8 a d}+\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{16 a d}-\frac{1}{16 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}-\frac{3 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{8 a d}-\frac{1}{160 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{5}}-\frac{1}{8 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}+\frac{1}{64 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{4}}+\frac{1}{32 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{3}}"," ",0,"1/160/a/d*tan(1/2*d*x+1/2*c)^5-1/64/a/d*tan(1/2*d*x+1/2*c)^4-1/32/a/d*tan(1/2*d*x+1/2*c)^3+1/8/a/d*tan(1/2*d*x+1/2*c)^2+1/16/a/d*tan(1/2*d*x+1/2*c)-1/16/a/d/tan(1/2*d*x+1/2*c)-3/8/a/d*ln(tan(1/2*d*x+1/2*c))-1/160/a/d/tan(1/2*d*x+1/2*c)^5-1/8/a/d/tan(1/2*d*x+1/2*c)^2+1/64/a/d/tan(1/2*d*x+1/2*c)^4+1/32/a/d/tan(1/2*d*x+1/2*c)^3","B"
60,1,284,96,0.324000," ","int(cot(d*x+c)^8/(a+a*sin(d*x+c)),x)","\frac{\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)}{896 a d}-\frac{\tan^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)}{384 a d}-\frac{\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)}{128 a d}+\frac{3 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{128 a d}+\frac{3 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{128 a d}-\frac{15 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{128 a d}-\frac{5 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{128 a d}+\frac{1}{384 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{6}}+\frac{5}{128 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}+\frac{5 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{16 a d}+\frac{1}{128 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{5}}-\frac{1}{896 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{7}}+\frac{15}{128 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}-\frac{3}{128 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{4}}-\frac{3}{128 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{3}}"," ",0,"1/896/a/d*tan(1/2*d*x+1/2*c)^7-1/384/a/d*tan(1/2*d*x+1/2*c)^6-1/128/a/d*tan(1/2*d*x+1/2*c)^5+3/128/a/d*tan(1/2*d*x+1/2*c)^4+3/128/a/d*tan(1/2*d*x+1/2*c)^3-15/128/a/d*tan(1/2*d*x+1/2*c)^2-5/128/a/d*tan(1/2*d*x+1/2*c)+1/384/a/d/tan(1/2*d*x+1/2*c)^6+5/128/a/d/tan(1/2*d*x+1/2*c)+5/16/a/d*ln(tan(1/2*d*x+1/2*c))+1/128/a/d/tan(1/2*d*x+1/2*c)^5-1/896/a/d/tan(1/2*d*x+1/2*c)^7+15/128/a/d/tan(1/2*d*x+1/2*c)^2-3/128/a/d/tan(1/2*d*x+1/2*c)^4-3/128/a/d/tan(1/2*d*x+1/2*c)^3","B"
61,1,180,171,0.248000," ","int(tan(d*x+c)^7/(a+a*sin(d*x+c))^2,x)","-\frac{1}{192 a^{2} d \left(\sin \left(d x +c \right)-1\right)^{3}}-\frac{1}{32 a^{2} d \left(\sin \left(d x +c \right)-1\right)^{2}}-\frac{21}{256 a^{2} d \left(\sin \left(d x +c \right)-1\right)}+\frac{7 \ln \left(\sin \left(d x +c \right)-1\right)}{256 a^{2} d}+\frac{1}{80 a^{2} d \left(1+\sin \left(d x +c \right)\right)^{5}}-\frac{5}{64 a^{2} d \left(1+\sin \left(d x +c \right)\right)^{4}}+\frac{19}{96 a^{2} d \left(1+\sin \left(d x +c \right)\right)^{3}}-\frac{1}{4 a^{2} d \left(1+\sin \left(d x +c \right)\right)^{2}}+\frac{35}{256 a^{2} d \left(1+\sin \left(d x +c \right)\right)}-\frac{7 \ln \left(1+\sin \left(d x +c \right)\right)}{256 a^{2} d}"," ",0,"-1/192/a^2/d/(sin(d*x+c)-1)^3-1/32/a^2/d/(sin(d*x+c)-1)^2-21/256/a^2/d/(sin(d*x+c)-1)+7/256/a^2/d*ln(sin(d*x+c)-1)+1/80/a^2/d/(1+sin(d*x+c))^5-5/64/a^2/d/(1+sin(d*x+c))^4+19/96/a^2/d/(1+sin(d*x+c))^3-1/4/a^2/d/(1+sin(d*x+c))^2+35/256/a^2/d/(1+sin(d*x+c))-7/256*ln(1+sin(d*x+c))/a^2/d","A"
62,1,144,132,0.235000," ","int(tan(d*x+c)^5/(a+a*sin(d*x+c))^2,x)","\frac{1}{64 a^{2} d \left(\sin \left(d x +c \right)-1\right)^{2}}+\frac{5}{64 a^{2} d \left(\sin \left(d x +c \right)-1\right)}-\frac{5 \ln \left(\sin \left(d x +c \right)-1\right)}{128 a^{2} d}+\frac{1}{32 a^{2} d \left(1+\sin \left(d x +c \right)\right)^{4}}-\frac{7}{48 a^{2} d \left(1+\sin \left(d x +c \right)\right)^{3}}+\frac{1}{4 a^{2} d \left(1+\sin \left(d x +c \right)\right)^{2}}-\frac{5}{32 a^{2} d \left(1+\sin \left(d x +c \right)\right)}+\frac{5 \ln \left(1+\sin \left(d x +c \right)\right)}{128 a^{2} d}"," ",0,"1/64/a^2/d/(sin(d*x+c)-1)^2+5/64/a^2/d/(sin(d*x+c)-1)-5/128/a^2/d*ln(sin(d*x+c)-1)+1/32/a^2/d/(1+sin(d*x+c))^4-7/48/a^2/d/(1+sin(d*x+c))^3+1/4/a^2/d/(1+sin(d*x+c))^2-5/32/a^2/d/(1+sin(d*x+c))+5/128*ln(1+sin(d*x+c))/a^2/d","A"
63,1,108,94,0.236000," ","int(tan(d*x+c)^3/(a+a*sin(d*x+c))^2,x)","-\frac{1}{16 a^{2} d \left(\sin \left(d x +c \right)-1\right)}+\frac{\ln \left(\sin \left(d x +c \right)-1\right)}{16 a^{2} d}+\frac{1}{12 a^{2} d \left(1+\sin \left(d x +c \right)\right)^{3}}-\frac{1}{4 a^{2} d \left(1+\sin \left(d x +c \right)\right)^{2}}+\frac{3}{16 a^{2} d \left(1+\sin \left(d x +c \right)\right)}-\frac{\ln \left(1+\sin \left(d x +c \right)\right)}{16 a^{2} d}"," ",0,"-1/16/a^2/d/(sin(d*x+c)-1)+1/16/a^2/d*ln(sin(d*x+c)-1)+1/12/a^2/d/(1+sin(d*x+c))^3-1/4/a^2/d/(1+sin(d*x+c))^2+3/16/a^2/d/(1+sin(d*x+c))-1/16*ln(1+sin(d*x+c))/a^2/d","A"
64,1,72,54,0.239000," ","int(tan(d*x+c)/(a+a*sin(d*x+c))^2,x)","-\frac{\ln \left(\sin \left(d x +c \right)-1\right)}{8 a^{2} d}+\frac{1}{4 a^{2} d \left(1+\sin \left(d x +c \right)\right)^{2}}-\frac{1}{4 a^{2} d \left(1+\sin \left(d x +c \right)\right)}+\frac{\ln \left(1+\sin \left(d x +c \right)\right)}{8 a^{2} d}"," ",0,"-1/8/a^2/d*ln(sin(d*x+c)-1)+1/4/a^2/d/(1+sin(d*x+c))^2-1/4/a^2/d/(1+sin(d*x+c))+1/8*ln(1+sin(d*x+c))/a^2/d","A"
65,1,50,52,0.152000," ","int(cot(d*x+c)/(a+a*sin(d*x+c))^2,x)","\frac{\ln \left(\sin \left(d x +c \right)\right)}{a^{2} d}+\frac{1}{a^{2} d \left(1+\sin \left(d x +c \right)\right)}-\frac{\ln \left(1+\sin \left(d x +c \right)\right)}{a^{2} d}"," ",0,"ln(sin(d*x+c))/a^2/d+1/a^2/d/(1+sin(d*x+c))-ln(1+sin(d*x+c))/a^2/d","A"
66,1,66,63,0.323000," ","int(cot(d*x+c)^3/(a+a*sin(d*x+c))^2,x)","-\frac{1}{2 a^{2} d \sin \left(d x +c \right)^{2}}+\frac{2}{a^{2} d \sin \left(d x +c \right)}+\frac{2 \ln \left(\sin \left(d x +c \right)\right)}{a^{2} d}-\frac{2 \ln \left(1+\sin \left(d x +c \right)\right)}{a^{2} d}"," ",0,"-1/2/a^2/d/sin(d*x+c)^2+2/a^2/d/sin(d*x+c)+2*ln(sin(d*x+c))/a^2/d-2*ln(1+sin(d*x+c))/a^2/d","A"
67,1,39,49,0.247000," ","int(cot(d*x+c)^5/(a+a*sin(d*x+c))^2,x)","\frac{-\frac{1}{2 \sin \left(d x +c \right)^{2}}-\frac{1}{4 \sin \left(d x +c \right)^{4}}+\frac{2}{3 \sin \left(d x +c \right)^{3}}}{d \,a^{2}}"," ",0,"1/d/a^2*(-1/2/sin(d*x+c)^2-1/4/sin(d*x+c)^4+2/3/sin(d*x+c)^3)","A"
68,1,49,65,0.287000," ","int(cot(d*x+c)^7/(a+a*sin(d*x+c))^2,x)","\frac{-\frac{1}{6 \sin \left(d x +c \right)^{6}}+\frac{2}{5 \sin \left(d x +c \right)^{5}}+\frac{1}{2 \sin \left(d x +c \right)^{2}}-\frac{2}{3 \sin \left(d x +c \right)^{3}}}{d \,a^{2}}"," ",0,"1/d/a^2*(-1/6/sin(d*x+c)^6+2/5/sin(d*x+c)^5+1/2/sin(d*x+c)^2-2/3/sin(d*x+c)^3)","A"
69,1,79,113,0.325000," ","int(cot(d*x+c)^9/(a+a*sin(d*x+c))^2,x)","\frac{\frac{1}{6 \sin \left(d x +c \right)^{6}}-\frac{4}{5 \sin \left(d x +c \right)^{5}}+\frac{2}{7 \sin \left(d x +c \right)^{7}}-\frac{1}{2 \sin \left(d x +c \right)^{2}}-\frac{1}{8 \sin \left(d x +c \right)^{8}}+\frac{1}{4 \sin \left(d x +c \right)^{4}}+\frac{2}{3 \sin \left(d x +c \right)^{3}}}{d \,a^{2}}"," ",0,"1/d/a^2*(1/6/sin(d*x+c)^6-4/5/sin(d*x+c)^5+2/7/sin(d*x+c)^7-1/2/sin(d*x+c)^2-1/8/sin(d*x+c)^8+1/4/sin(d*x+c)^4+2/3/sin(d*x+c)^3)","A"
70,1,89,129,0.378000," ","int(cot(d*x+c)^11/(a+a*sin(d*x+c))^2,x)","\frac{\frac{6}{5 \sin \left(d x +c \right)^{5}}-\frac{6}{7 \sin \left(d x +c \right)^{7}}+\frac{1}{2 \sin \left(d x +c \right)^{2}}+\frac{2}{9 \sin \left(d x +c \right)^{9}}+\frac{1}{4 \sin \left(d x +c \right)^{8}}-\frac{1}{2 \sin \left(d x +c \right)^{4}}-\frac{2}{3 \sin \left(d x +c \right)^{3}}-\frac{1}{10 \sin \left(d x +c \right)^{10}}}{d \,a^{2}}"," ",0,"1/d/a^2*(6/5/sin(d*x+c)^5-6/7/sin(d*x+c)^7+1/2/sin(d*x+c)^2+2/9/sin(d*x+c)^9+1/4/sin(d*x+c)^8-1/2/sin(d*x+c)^4-2/3/sin(d*x+c)^3-1/10/sin(d*x+c)^10)","A"
71,1,119,177,0.422000," ","int(cot(d*x+c)^13/(a+a*sin(d*x+c))^2,x)","\frac{-\frac{1}{3 \sin \left(d x +c \right)^{6}}-\frac{8}{5 \sin \left(d x +c \right)^{5}}-\frac{1}{12 \sin \left(d x +c \right)^{12}}+\frac{12}{7 \sin \left(d x +c \right)^{7}}-\frac{1}{2 \sin \left(d x +c \right)^{2}}-\frac{8}{9 \sin \left(d x +c \right)^{9}}-\frac{1}{4 \sin \left(d x +c \right)^{8}}+\frac{3}{4 \sin \left(d x +c \right)^{4}}+\frac{2}{11 \sin \left(d x +c \right)^{11}}+\frac{2}{3 \sin \left(d x +c \right)^{3}}+\frac{3}{10 \sin \left(d x +c \right)^{10}}}{d \,a^{2}}"," ",0,"1/d/a^2*(-1/3/sin(d*x+c)^6-8/5/sin(d*x+c)^5-1/12/sin(d*x+c)^12+12/7/sin(d*x+c)^7-1/2/sin(d*x+c)^2-8/9/sin(d*x+c)^9-1/4/sin(d*x+c)^8+3/4/sin(d*x+c)^4+2/11/sin(d*x+c)^11+2/3/sin(d*x+c)^3+3/10/sin(d*x+c)^10)","A"
72,1,162,155,0.259000," ","int(tan(d*x+c)^5/(a+a*sin(d*x+c))^3,x)","\frac{1}{128 a^{3} d \left(\sin \left(d x +c \right)-1\right)^{2}}+\frac{1}{32 a^{3} d \left(\sin \left(d x +c \right)-1\right)}-\frac{\ln \left(\sin \left(d x +c \right)-1\right)}{256 a^{3} d}+\frac{1}{40 a^{3} d \left(1+\sin \left(d x +c \right)\right)^{5}}-\frac{7}{64 a^{3} d \left(1+\sin \left(d x +c \right)\right)^{4}}+\frac{1}{6 a^{3} d \left(1+\sin \left(d x +c \right)\right)^{3}}-\frac{5}{64 a^{3} d \left(1+\sin \left(d x +c \right)\right)^{2}}-\frac{5}{128 a^{3} d \left(1+\sin \left(d x +c \right)\right)}+\frac{\ln \left(1+\sin \left(d x +c \right)\right)}{256 a^{3} d}"," ",0,"1/128/a^3/d/(sin(d*x+c)-1)^2+1/32/a^3/d/(sin(d*x+c)-1)-1/256/a^3/d*ln(sin(d*x+c)-1)+1/40/a^3/d/(1+sin(d*x+c))^5-7/64/a^3/d/(1+sin(d*x+c))^4+1/6/a^3/d/(1+sin(d*x+c))^3-5/64/a^3/d/(1+sin(d*x+c))^2-5/128/a^3/d/(1+sin(d*x+c))+1/256*ln(1+sin(d*x+c))/a^3/d","A"
73,1,126,114,0.265000," ","int(tan(d*x+c)^3/(a+a*sin(d*x+c))^3,x)","-\frac{1}{32 a^{3} d \left(\sin \left(d x +c \right)-1\right)}+\frac{\ln \left(\sin \left(d x +c \right)-1\right)}{64 a^{3} d}+\frac{1}{16 a^{3} d \left(1+\sin \left(d x +c \right)\right)^{4}}-\frac{1}{6 a^{3} d \left(1+\sin \left(d x +c \right)\right)^{3}}+\frac{3}{32 a^{3} d \left(1+\sin \left(d x +c \right)\right)^{2}}+\frac{1}{16 a^{3} d \left(1+\sin \left(d x +c \right)\right)}-\frac{\ln \left(1+\sin \left(d x +c \right)\right)}{64 a^{3} d}"," ",0,"-1/32/a^3/d/(sin(d*x+c)-1)+1/64/a^3/d*ln(sin(d*x+c)-1)+1/16/a^3/d/(1+sin(d*x+c))^4-1/6/a^3/d/(1+sin(d*x+c))^3+3/32/a^3/d/(1+sin(d*x+c))^2+1/16/a^3/d/(1+sin(d*x+c))-1/64*ln(1+sin(d*x+c))/a^3/d","A"
74,1,90,74,0.244000," ","int(tan(d*x+c)/(a+a*sin(d*x+c))^3,x)","-\frac{\ln \left(\sin \left(d x +c \right)-1\right)}{16 a^{3} d}+\frac{1}{6 a^{3} d \left(1+\sin \left(d x +c \right)\right)^{3}}-\frac{1}{8 a^{3} d \left(1+\sin \left(d x +c \right)\right)^{2}}-\frac{1}{8 a^{3} d \left(1+\sin \left(d x +c \right)\right)}+\frac{\ln \left(1+\sin \left(d x +c \right)\right)}{16 a^{3} d}"," ",0,"-1/16/a^3/d*ln(sin(d*x+c)-1)+1/6/a^3/d/(1+sin(d*x+c))^3-1/8/a^3/d/(1+sin(d*x+c))^2-1/8/a^3/d/(1+sin(d*x+c))+1/16*ln(1+sin(d*x+c))/a^3/d","A"
75,1,68,72,0.167000," ","int(cot(d*x+c)/(a+a*sin(d*x+c))^3,x)","\frac{\ln \left(\sin \left(d x +c \right)\right)}{a^{3} d}+\frac{1}{2 a^{3} d \left(1+\sin \left(d x +c \right)\right)^{2}}+\frac{1}{a^{3} d \left(1+\sin \left(d x +c \right)\right)}-\frac{\ln \left(1+\sin \left(d x +c \right)\right)}{a^{3} d}"," ",0,"ln(sin(d*x+c))/a^3/d+1/2/a^3/d/(1+sin(d*x+c))^2+1/a^3/d/(1+sin(d*x+c))-ln(1+sin(d*x+c))/a^3/d","A"
76,1,84,84,0.474000," ","int(cot(d*x+c)^3/(a+a*sin(d*x+c))^3,x)","-\frac{1}{2 a^{3} d \sin \left(d x +c \right)^{2}}+\frac{3}{a^{3} d \sin \left(d x +c \right)}+\frac{5 \ln \left(\sin \left(d x +c \right)\right)}{a^{3} d}+\frac{2}{a^{3} d \left(1+\sin \left(d x +c \right)\right)}-\frac{5 \ln \left(1+\sin \left(d x +c \right)\right)}{a^{3} d}"," ",0,"-1/2/a^3/d/sin(d*x+c)^2+3/a^3/d/sin(d*x+c)+5*ln(sin(d*x+c))/a^3/d+2/a^3/d/(1+sin(d*x+c))-5*ln(1+sin(d*x+c))/a^3/d","A"
77,1,97,94,0.343000," ","int(cot(d*x+c)^5/(a+a*sin(d*x+c))^3,x)","-\frac{1}{4 a^{3} d \sin \left(d x +c \right)^{4}}+\frac{1}{a^{3} d \sin \left(d x +c \right)^{3}}-\frac{2}{a^{3} d \sin \left(d x +c \right)^{2}}+\frac{4}{a^{3} d \sin \left(d x +c \right)}+\frac{4 \ln \left(\sin \left(d x +c \right)\right)}{a^{3} d}-\frac{4 \ln \left(1+\sin \left(d x +c \right)\right)}{a^{3} d}"," ",0,"-1/4/a^3/d/sin(d*x+c)^4+1/a^3/d/sin(d*x+c)^3-2/a^3/d/sin(d*x+c)^2+4/a^3/d/sin(d*x+c)+4*ln(sin(d*x+c))/a^3/d-4*ln(1+sin(d*x+c))/a^3/d","A"
78,1,49,65,0.331000," ","int(cot(d*x+c)^7/(a+a*sin(d*x+c))^3,x)","\frac{-\frac{1}{6 \sin \left(d x +c \right)^{6}}+\frac{3}{5 \sin \left(d x +c \right)^{5}}-\frac{3}{4 \sin \left(d x +c \right)^{4}}+\frac{1}{3 \sin \left(d x +c \right)^{3}}}{d \,a^{3}}"," ",0,"1/d/a^3*(-1/6/sin(d*x+c)^6+3/5/sin(d*x+c)^5-3/4/sin(d*x+c)^4+1/3/sin(d*x+c)^3)","A"
79,1,69,97,0.355000," ","int(cot(d*x+c)^9/(a+a*sin(d*x+c))^3,x)","\frac{-\frac{1}{3 \sin \left(d x +c \right)^{6}}-\frac{2}{5 \sin \left(d x +c \right)^{5}}+\frac{3}{7 \sin \left(d x +c \right)^{7}}-\frac{1}{8 \sin \left(d x +c \right)^{8}}+\frac{3}{4 \sin \left(d x +c \right)^{4}}-\frac{1}{3 \sin \left(d x +c \right)^{3}}}{d \,a^{3}}"," ",0,"1/d/a^3*(-1/3/sin(d*x+c)^6-2/5/sin(d*x+c)^5+3/7/sin(d*x+c)^7-1/8/sin(d*x+c)^8+3/4/sin(d*x+c)^4-1/3/sin(d*x+c)^3)","A"
80,1,89,129,0.385000," ","int(cot(d*x+c)^11/(a+a*sin(d*x+c))^3,x)","\frac{\frac{5}{6 \sin \left(d x +c \right)^{6}}+\frac{1}{5 \sin \left(d x +c \right)^{5}}-\frac{5}{7 \sin \left(d x +c \right)^{7}}+\frac{1}{3 \sin \left(d x +c \right)^{9}}-\frac{1}{8 \sin \left(d x +c \right)^{8}}-\frac{3}{4 \sin \left(d x +c \right)^{4}}+\frac{1}{3 \sin \left(d x +c \right)^{3}}-\frac{1}{10 \sin \left(d x +c \right)^{10}}}{d \,a^{3}}"," ",0,"1/d/a^3*(5/6/sin(d*x+c)^6+1/5/sin(d*x+c)^5-5/7/sin(d*x+c)^7+1/3/sin(d*x+c)^9-1/8/sin(d*x+c)^8-3/4/sin(d*x+c)^4+1/3/sin(d*x+c)^3-1/10/sin(d*x+c)^10)","A"
81,1,89,129,0.427000," ","int(cot(d*x+c)^13/(a+a*sin(d*x+c))^3,x)","\frac{-\frac{4}{3 \sin \left(d x +c \right)^{6}}-\frac{1}{12 \sin \left(d x +c \right)^{12}}+\frac{6}{7 \sin \left(d x +c \right)^{7}}-\frac{8}{9 \sin \left(d x +c \right)^{9}}+\frac{3}{4 \sin \left(d x +c \right)^{8}}+\frac{3}{4 \sin \left(d x +c \right)^{4}}+\frac{3}{11 \sin \left(d x +c \right)^{11}}-\frac{1}{3 \sin \left(d x +c \right)^{3}}}{d \,a^{3}}"," ",0,"1/d/a^3*(-4/3/sin(d*x+c)^6-1/12/sin(d*x+c)^12+6/7/sin(d*x+c)^7-8/9/sin(d*x+c)^9+3/4/sin(d*x+c)^8+3/4/sin(d*x+c)^4+3/11/sin(d*x+c)^11-1/3/sin(d*x+c)^3)","A"
82,1,180,177,0.240000," ","int(tan(d*x+c)^5/(a+a*sin(d*x+c))^4,x)","\frac{1}{256 a^{4} d \left(\sin \left(d x +c \right)-1\right)^{2}}+\frac{3}{256 a^{4} d \left(\sin \left(d x +c \right)-1\right)}+\frac{\ln \left(\sin \left(d x +c \right)-1\right)}{256 a^{4} d}+\frac{1}{48 a^{4} d \left(1+\sin \left(d x +c \right)\right)^{6}}-\frac{7}{80 a^{4} d \left(1+\sin \left(d x +c \right)\right)^{5}}+\frac{1}{8 a^{4} d \left(1+\sin \left(d x +c \right)\right)^{4}}-\frac{5}{96 a^{4} d \left(1+\sin \left(d x +c \right)\right)^{3}}-\frac{5}{256 a^{4} d \left(1+\sin \left(d x +c \right)\right)^{2}}-\frac{1}{256 a^{4} d \left(1+\sin \left(d x +c \right)\right)}-\frac{\ln \left(1+\sin \left(d x +c \right)\right)}{256 a^{4} d}"," ",0,"1/256/a^4/d/(sin(d*x+c)-1)^2+3/256/a^4/d/(sin(d*x+c)-1)+1/256/a^4/d*ln(sin(d*x+c)-1)+1/48/a^4/d/(1+sin(d*x+c))^6-7/80/a^4/d/(1+sin(d*x+c))^5+1/8/a^4/d/(1+sin(d*x+c))^4-5/96/a^4/d/(1+sin(d*x+c))^3-5/256/a^4/d/(1+sin(d*x+c))^2-1/256/a^4/d/(1+sin(d*x+c))-1/256*ln(1+sin(d*x+c))/a^4/d","A"
83,1,81,120,0.239000," ","int(tan(d*x+c)^3/(a+a*sin(d*x+c))^4,x)","\frac{-\frac{1}{64 \left(\sin \left(d x +c \right)-1\right)}+\frac{1}{20 \left(1+\sin \left(d x +c \right)\right)^{5}}-\frac{1}{8 \left(1+\sin \left(d x +c \right)\right)^{4}}+\frac{1}{16 \left(1+\sin \left(d x +c \right)\right)^{3}}+\frac{1}{32 \left(1+\sin \left(d x +c \right)\right)^{2}}+\frac{1}{64+64 \sin \left(d x +c \right)}}{d \,a^{4}}"," ",0,"1/d/a^4*(-1/64/(sin(d*x+c)-1)+1/20/(1+sin(d*x+c))^5-1/8/(1+sin(d*x+c))^4+1/16/(1+sin(d*x+c))^3+1/32/(1+sin(d*x+c))^2+1/64/(1+sin(d*x+c)))","A"
84,1,108,95,0.249000," ","int(tan(d*x+c)/(a+a*sin(d*x+c))^4,x)","-\frac{\ln \left(\sin \left(d x +c \right)-1\right)}{32 a^{4} d}+\frac{1}{8 a^{4} d \left(1+\sin \left(d x +c \right)\right)^{4}}-\frac{1}{12 a^{4} d \left(1+\sin \left(d x +c \right)\right)^{3}}-\frac{1}{16 a^{4} d \left(1+\sin \left(d x +c \right)\right)^{2}}-\frac{1}{16 a^{4} d \left(1+\sin \left(d x +c \right)\right)}+\frac{\ln \left(1+\sin \left(d x +c \right)\right)}{32 a^{4} d}"," ",0,"-1/32/a^4/d*ln(sin(d*x+c)-1)+1/8/a^4/d/(1+sin(d*x+c))^4-1/12/a^4/d/(1+sin(d*x+c))^3-1/16/a^4/d/(1+sin(d*x+c))^2-1/16/a^4/d/(1+sin(d*x+c))+1/32*ln(1+sin(d*x+c))/a^4/d","A"
85,1,101,104,0.337000," ","int(cot(d*x+c)^3/(a+a*sin(d*x+c))^4,x)","-\frac{1}{2 a^{4} d \sin \left(d x +c \right)^{2}}+\frac{4}{a^{4} d \sin \left(d x +c \right)}+\frac{9 \ln \left(\sin \left(d x +c \right)\right)}{a^{4} d}+\frac{1}{a^{4} d \left(1+\sin \left(d x +c \right)\right)^{2}}+\frac{5}{a^{4} d \left(1+\sin \left(d x +c \right)\right)}-\frac{9 \ln \left(1+\sin \left(d x +c \right)\right)}{a^{4} d}"," ",0,"-1/2/a^4/d/sin(d*x+c)^2+4/a^4/d/sin(d*x+c)+9*ln(sin(d*x+c))/a^4/d+1/a^4/d/(1+sin(d*x+c))^2+5/a^4/d/(1+sin(d*x+c))-9*ln(1+sin(d*x+c))/a^4/d","A"
86,1,130,127,0.334000," ","int(cot(d*x+c)^7/(a+a*sin(d*x+c))^4,x)","-\frac{1}{6 a^{4} d \sin \left(d x +c \right)^{6}}+\frac{4}{5 a^{4} d \sin \left(d x +c \right)^{5}}-\frac{7}{4 a^{4} d \sin \left(d x +c \right)^{4}}+\frac{8}{3 a^{4} d \sin \left(d x +c \right)^{3}}-\frac{4}{a^{4} d \sin \left(d x +c \right)^{2}}+\frac{8}{a^{4} d \sin \left(d x +c \right)}+\frac{8 \ln \left(\sin \left(d x +c \right)\right)}{a^{4} d}-\frac{8 \ln \left(1+\sin \left(d x +c \right)\right)}{a^{4} d}"," ",0,"-1/6/a^4/d/sin(d*x+c)^6+4/5/a^4/d/sin(d*x+c)^5-7/4/a^4/d/sin(d*x+c)^4+8/3/a^4/d/sin(d*x+c)^3-4/a^4/d/sin(d*x+c)^2+8/a^4/d/sin(d*x+c)+8*ln(sin(d*x+c))/a^4/d-8*ln(1+sin(d*x+c))/a^4/d","A"
87,1,158,113,0.213000," ","int(tan(d*x+c)^2/(a+a*sin(d*x+c))^4,x)","\frac{-\frac{1}{16 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{16}{9 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{9}}+\frac{8}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{8}}-\frac{116}{7 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{7}}+\frac{62}{3 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{6}}-\frac{83}{5 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{5}}+\frac{17}{2 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{4}}-\frac{29}{12 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}+\frac{1}{8 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}+\frac{8}{128 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+128}}{d \,a^{4}}"," ",0,"8/d/a^4*(-1/128/(tan(1/2*d*x+1/2*c)-1)-2/9/(tan(1/2*d*x+1/2*c)+1)^9+1/(tan(1/2*d*x+1/2*c)+1)^8-29/14/(tan(1/2*d*x+1/2*c)+1)^7+31/12/(tan(1/2*d*x+1/2*c)+1)^6-83/40/(tan(1/2*d*x+1/2*c)+1)^5+17/16/(tan(1/2*d*x+1/2*c)+1)^4-29/96/(tan(1/2*d*x+1/2*c)+1)^3+1/64/(tan(1/2*d*x+1/2*c)+1)^2+1/128/(tan(1/2*d*x+1/2*c)+1))","A"
88,1,161,102,0.306000," ","int(cot(d*x+c)^2/(a+a*sin(d*x+c))^4,x)","\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 a^{4} d}-\frac{1}{2 a^{4} d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}-\frac{4 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a^{4} d}-\frac{16}{5 a^{4} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{5}}+\frac{8}{a^{4} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{4}}-\frac{44}{3 a^{4} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}+\frac{14}{a^{4} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}-\frac{18}{a^{4} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}"," ",0,"1/2/a^4/d*tan(1/2*d*x+1/2*c)-1/2/a^4/d/tan(1/2*d*x+1/2*c)-4/a^4/d*ln(tan(1/2*d*x+1/2*c))-16/5/a^4/d/(tan(1/2*d*x+1/2*c)+1)^5+8/a^4/d/(tan(1/2*d*x+1/2*c)+1)^4-44/3/a^4/d/(tan(1/2*d*x+1/2*c)+1)^3+14/a^4/d/(tan(1/2*d*x+1/2*c)+1)^2-18/a^4/d/(tan(1/2*d*x+1/2*c)+1)","A"
89,1,195,130,0.315000," ","int(cot(d*x+c)^4/(a+a*sin(d*x+c))^4,x)","\frac{\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)}{24 a^{4} d}-\frac{\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}{2 a^{4} d}+\frac{35 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{8 a^{4} d}-\frac{1}{24 a^{4} d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{3}}+\frac{1}{2 a^{4} d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}-\frac{35}{8 a^{4} d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}-\frac{14 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a^{4} d}-\frac{16}{3 a^{4} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}+\frac{8}{a^{4} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}-\frac{32}{a^{4} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}"," ",0,"1/24/a^4/d*tan(1/2*d*x+1/2*c)^3-1/2/a^4/d*tan(1/2*d*x+1/2*c)^2+35/8/a^4/d*tan(1/2*d*x+1/2*c)-1/24/a^4/d/tan(1/2*d*x+1/2*c)^3+1/2/a^4/d/tan(1/2*d*x+1/2*c)^2-35/8/a^4/d/tan(1/2*d*x+1/2*c)-14/a^4/d*ln(tan(1/2*d*x+1/2*c))-16/3/a^4/d/(tan(1/2*d*x+1/2*c)+1)^3+8/a^4/d/(tan(1/2*d*x+1/2*c)+1)^2-32/a^4/d/(tan(1/2*d*x+1/2*c)+1)","A"
90,1,229,136,0.337000," ","int(cot(d*x+c)^6/(a+a*sin(d*x+c))^4,x)","\frac{\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)}{160 a^{4} d}-\frac{\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)}{16 a^{4} d}+\frac{11 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{32 a^{4} d}-\frac{3 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{2 a^{4} d}+\frac{111 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{16 a^{4} d}-\frac{1}{160 a^{4} d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{5}}+\frac{1}{16 a^{4} d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{4}}-\frac{11}{32 a^{4} d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{3}}+\frac{3}{2 a^{4} d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}-\frac{111}{16 a^{4} d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}-\frac{27 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{2 a^{4} d}-\frac{16}{a^{4} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}"," ",0,"1/160/a^4/d*tan(1/2*d*x+1/2*c)^5-1/16/a^4/d*tan(1/2*d*x+1/2*c)^4+11/32/a^4/d*tan(1/2*d*x+1/2*c)^3-3/2/a^4/d*tan(1/2*d*x+1/2*c)^2+111/16/a^4/d*tan(1/2*d*x+1/2*c)-1/160/a^4/d/tan(1/2*d*x+1/2*c)^5+1/16/a^4/d/tan(1/2*d*x+1/2*c)^4-11/32/a^4/d/tan(1/2*d*x+1/2*c)^3+3/2/a^4/d/tan(1/2*d*x+1/2*c)^2-111/16/a^4/d/tan(1/2*d*x+1/2*c)-27/2/a^4/d*ln(tan(1/2*d*x+1/2*c))-16/a^4/d/(tan(1/2*d*x+1/2*c)+1)","A"
91,1,172,135,0.697000," ","int((a+a*sin(f*x+e))^(1/2)*tan(f*x+e)^4,x)","-\frac{96 a^{\frac{5}{2}} \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right)+\left(33 \left(a -a \sin \left(f x +e \right)\right)^{\frac{3}{2}} \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a +20 a^{\frac{5}{2}}\right) \sin \left(f x +e \right)-162 a^{\frac{5}{2}} \left(\cos^{2}\left(f x +e \right)\right)+33 \left(a -a \sin \left(f x +e \right)\right)^{\frac{3}{2}} \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a -4 a^{\frac{5}{2}}}{48 a^{\frac{3}{2}} \left(\sin \left(f x +e \right)-1\right) \cos \left(f x +e \right) \sqrt{a +a \sin \left(f x +e \right)}\, f}"," ",0,"-1/48/a^(3/2)*(96*a^(5/2)*sin(f*x+e)*cos(f*x+e)^2+(33*(a-a*sin(f*x+e))^(3/2)*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a+20*a^(5/2))*sin(f*x+e)-162*a^(5/2)*cos(f*x+e)^2+33*(a-a*sin(f*x+e))^(3/2)*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a-4*a^(5/2))/(sin(f*x+e)-1)/cos(f*x+e)/(a+a*sin(f*x+e))^(1/2)/f","A"
92,1,89,88,0.728000," ","int((a+a*sin(f*x+e))^(1/2)*tan(f*x+e)^2,x)","-\frac{\left(1+\sin \left(f x +e \right)\right) \left(\sqrt{a}\, \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) \sqrt{a -a \sin \left(f x +e \right)}+4 a \sin \left(f x +e \right)-6 a \right)}{2 \cos \left(f x +e \right) \sqrt{a +a \sin \left(f x +e \right)}\, f}"," ",0,"-1/2*(1+sin(f*x+e))*(a^(1/2)*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*(a-a*sin(f*x+e))^(1/2)+4*a*sin(f*x+e)-6*a)/cos(f*x+e)/(a+a*sin(f*x+e))^(1/2)/f","A"
93,1,125,79,0.793000," ","int(cot(f*x+e)^2*(a+a*sin(f*x+e))^(1/2),x)","\frac{\left(1+\sin \left(f x +e \right)\right) \sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, \left(\sin \left(f x +e \right) \left(2 \sqrt{a -a \sin \left(f x +e \right)}\, a^{\frac{3}{2}}-\arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}}{\sqrt{a}}\right) a^{2}\right)-\sqrt{a -a \sin \left(f x +e \right)}\, a^{\frac{3}{2}}\right)}{\sin \left(f x +e \right) a^{\frac{3}{2}} \cos \left(f x +e \right) \sqrt{a +a \sin \left(f x +e \right)}\, f}"," ",0,"(1+sin(f*x+e))*(-a*(sin(f*x+e)-1))^(1/2)*(sin(f*x+e)*(2*(a-a*sin(f*x+e))^(1/2)*a^(3/2)-arctanh((a-a*sin(f*x+e))^(1/2)/a^(1/2))*a^2)-(a-a*sin(f*x+e))^(1/2)*a^(3/2))/sin(f*x+e)/a^(3/2)/cos(f*x+e)/(a+a*sin(f*x+e))^(1/2)/f","A"
94,1,170,141,0.929000," ","int(cot(f*x+e)^4*(a+a*sin(f*x+e))^(1/2),x)","-\frac{\left(1+\sin \left(f x +e \right)\right) \sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, \left(48 \sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, a^{\frac{7}{2}} \left(\sin^{3}\left(f x +e \right)\right)-15 \sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, a^{\frac{7}{2}}+56 \left(-a \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{3}{2}} a^{\frac{5}{2}}-33 \left(-a \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{5}{2}} a^{\frac{3}{2}}-33 \arctanh \left(\frac{\sqrt{-a \left(\sin \left(f x +e \right)-1\right)}}{\sqrt{a}}\right) a^{4} \left(\sin^{3}\left(f x +e \right)\right)\right)}{24 a^{\frac{7}{2}} \sin \left(f x +e \right)^{3} \cos \left(f x +e \right) \sqrt{a +a \sin \left(f x +e \right)}\, f}"," ",0,"-1/24*(1+sin(f*x+e))*(-a*(sin(f*x+e)-1))^(1/2)*(48*(-a*(sin(f*x+e)-1))^(1/2)*a^(7/2)*sin(f*x+e)^3-15*(-a*(sin(f*x+e)-1))^(1/2)*a^(7/2)+56*(-a*(sin(f*x+e)-1))^(3/2)*a^(5/2)-33*(-a*(sin(f*x+e)-1))^(5/2)*a^(3/2)-33*arctanh((-a*(sin(f*x+e)-1))^(1/2)/a^(1/2))*a^4*sin(f*x+e)^3)/a^(7/2)/sin(f*x+e)^3/cos(f*x+e)/(a+a*sin(f*x+e))^(1/2)/f","A"
95,1,139,142,0.750000," ","int((a+a*sin(f*x+e))^(3/2)*tan(f*x+e)^4,x)","\frac{\left(1+\sin \left(f x +e \right)\right) \left(3 a^{\frac{3}{2}} \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) \left(a -a \sin \left(f x +e \right)\right)^{\frac{3}{2}}-8 a^{3} \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right)-24 a^{3} \left(\cos^{2}\left(f x +e \right)\right)-106 \sin \left(f x +e \right) a^{3}+102 a^{3}\right)}{12 a \left(\sin \left(f x +e \right)-1\right) \cos \left(f x +e \right) \sqrt{a +a \sin \left(f x +e \right)}\, f}"," ",0,"1/12*(1+sin(f*x+e))/a/(sin(f*x+e)-1)*(3*a^(3/2)*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*(a-a*sin(f*x+e))^(3/2)-8*a^3*sin(f*x+e)*cos(f*x+e)^2-24*a^3*cos(f*x+e)^2-106*sin(f*x+e)*a^3+102*a^3)/cos(f*x+e)/(a+a*sin(f*x+e))^(1/2)/f","A"
96,1,55,76,0.580000," ","int((a+a*sin(f*x+e))^(3/2)*tan(f*x+e)^2,x)","-\frac{2 a^{2} \left(1+\sin \left(f x +e \right)\right) \left(\sin^{2}\left(f x +e \right)+4 \sin \left(f x +e \right)-8\right)}{3 \cos \left(f x +e \right) \sqrt{a +a \sin \left(f x +e \right)}\, f}"," ",0,"-2/3*a^2*(1+sin(f*x+e))*(sin(f*x+e)^2+4*sin(f*x+e)-8)/cos(f*x+e)/(a+a*sin(f*x+e))^(1/2)/f","A"
97,1,144,105,0.898000," ","int(cot(f*x+e)^2*(a+a*sin(f*x+e))^(3/2),x)","\frac{\left(1+\sin \left(f x +e \right)\right) \sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, \left(\sin \left(f x +e \right) \left(12 \sqrt{a -a \sin \left(f x +e \right)}\, a^{\frac{3}{2}}-2 \sqrt{a}\, \left(a -a \sin \left(f x +e \right)\right)^{\frac{3}{2}}-9 \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}}{\sqrt{a}}\right) a^{2}\right)-3 \sqrt{a -a \sin \left(f x +e \right)}\, a^{\frac{3}{2}}\right)}{3 \sin \left(f x +e \right) \sqrt{a}\, \cos \left(f x +e \right) \sqrt{a +a \sin \left(f x +e \right)}\, f}"," ",0,"1/3*(1+sin(f*x+e))*(-a*(sin(f*x+e)-1))^(1/2)*(sin(f*x+e)*(12*(a-a*sin(f*x+e))^(1/2)*a^(3/2)-2*a^(1/2)*(a-a*sin(f*x+e))^(3/2)-9*arctanh((a-a*sin(f*x+e))^(1/2)/a^(1/2))*a^2)-3*(a-a*sin(f*x+e))^(1/2)*a^(3/2))/sin(f*x+e)/a^(1/2)/cos(f*x+e)/(a+a*sin(f*x+e))^(1/2)/f","A"
98,1,196,169,1.002000," ","int(cot(f*x+e)^4*(a+a*sin(f*x+e))^(3/2),x)","\frac{\left(1+\sin \left(f x +e \right)\right) \sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, \left(16 \left(-a \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{3}{2}} \left(\sin^{3}\left(f x +e \right)\right) a^{\frac{3}{2}}-96 a^{\frac{5}{2}} \sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, \left(\sin^{3}\left(f x +e \right)\right)+111 \arctanh \left(\frac{\sqrt{-a \left(\sin \left(f x +e \right)-1\right)}}{\sqrt{a}}\right) \left(\sin^{3}\left(f x +e \right)\right) a^{3}+15 \left(-a \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{5}{2}} \sqrt{a}-8 \left(-a \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{3}{2}} a^{\frac{3}{2}}-15 \sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, a^{\frac{5}{2}}\right)}{24 a^{\frac{3}{2}} \sin \left(f x +e \right)^{3} \cos \left(f x +e \right) \sqrt{a +a \sin \left(f x +e \right)}\, f}"," ",0,"1/24*(1+sin(f*x+e))*(-a*(sin(f*x+e)-1))^(1/2)/a^(3/2)*(16*(-a*(sin(f*x+e)-1))^(3/2)*sin(f*x+e)^3*a^(3/2)-96*a^(5/2)*(-a*(sin(f*x+e)-1))^(1/2)*sin(f*x+e)^3+111*arctanh((-a*(sin(f*x+e)-1))^(1/2)/a^(1/2))*sin(f*x+e)^3*a^3+15*(-a*(sin(f*x+e)-1))^(5/2)*a^(1/2)-8*(-a*(sin(f*x+e)-1))^(3/2)*a^(3/2)-15*(-a*(sin(f*x+e)-1))^(1/2)*a^(5/2))/sin(f*x+e)^3/cos(f*x+e)/(a+a*sin(f*x+e))^(1/2)/f","A"
99,1,87,135,0.693000," ","int((a+a*sin(f*x+e))^(5/2)*tan(f*x+e)^4,x)","\frac{2 a^{3} \left(1+\sin \left(f x +e \right)\right) \left(3 \left(\sin^{4}\left(f x +e \right)\right)+8 \left(\sin^{3}\left(f x +e \right)\right)+48 \left(\sin^{2}\left(f x +e \right)\right)-192 \sin \left(f x +e \right)+128\right)}{15 \left(\sin \left(f x +e \right)-1\right) \cos \left(f x +e \right) \sqrt{a +a \sin \left(f x +e \right)}\, f}"," ",0,"2/15*a^3*(1+sin(f*x+e))/(sin(f*x+e)-1)*(3*sin(f*x+e)^4+8*sin(f*x+e)^3+48*sin(f*x+e)^2-192*sin(f*x+e)+128)/cos(f*x+e)/(a+a*sin(f*x+e))^(1/2)/f","A"
100,1,67,102,0.491000," ","int((a+a*sin(f*x+e))^(5/2)*tan(f*x+e)^2,x)","-\frac{2 a^{3} \left(1+\sin \left(f x +e \right)\right) \left(3 \left(\sin^{3}\left(f x +e \right)\right)+11 \left(\sin^{2}\left(f x +e \right)\right)+44 \sin \left(f x +e \right)-88\right)}{15 \cos \left(f x +e \right) \sqrt{a +a \sin \left(f x +e \right)}\, f}"," ",0,"-2/15*a^3*(1+sin(f*x+e))*(3*sin(f*x+e)^3+11*sin(f*x+e)^2+44*sin(f*x+e)-88)/cos(f*x+e)/(a+a*sin(f*x+e))^(1/2)/f","A"
101,1,162,131,0.726000," ","int(cot(f*x+e)^2*(a+a*sin(f*x+e))^(5/2),x)","\frac{\left(1+\sin \left(f x +e \right)\right) \sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, \left(\sin \left(f x +e \right) \left(90 \sqrt{a -a \sin \left(f x +e \right)}\, a^{\frac{5}{2}}-40 a^{\frac{3}{2}} \left(a -a \sin \left(f x +e \right)\right)^{\frac{3}{2}}+6 \sqrt{a}\, \left(a -a \sin \left(f x +e \right)\right)^{\frac{5}{2}}-75 \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}}{\sqrt{a}}\right) a^{3}\right)-15 \sqrt{a -a \sin \left(f x +e \right)}\, a^{\frac{5}{2}}\right)}{15 \sin \left(f x +e \right) \sqrt{a}\, \cos \left(f x +e \right) \sqrt{a +a \sin \left(f x +e \right)}\, f}"," ",0,"1/15*(1+sin(f*x+e))*(-a*(sin(f*x+e)-1))^(1/2)*(sin(f*x+e)*(90*(a-a*sin(f*x+e))^(1/2)*a^(5/2)-40*a^(3/2)*(a-a*sin(f*x+e))^(3/2)+6*a^(1/2)*(a-a*sin(f*x+e))^(5/2)-75*arctanh((a-a*sin(f*x+e))^(1/2)/a^(1/2))*a^3)-15*(a-a*sin(f*x+e))^(1/2)*a^(5/2))/sin(f*x+e)/a^(1/2)/cos(f*x+e)/(a+a*sin(f*x+e))^(1/2)/f","A"
102,1,222,195,0.909000," ","int(cot(f*x+e)^4*(a+a*sin(f*x+e))^(5/2),x)","-\frac{\left(1+\sin \left(f x +e \right)\right) \sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, \left(48 \left(-a \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{5}{2}} \left(\sin^{3}\left(f x +e \right)\right) \sqrt{a}-320 \left(-a \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{3}{2}} \left(\sin^{3}\left(f x +e \right)\right) a^{\frac{3}{2}}+480 a^{\frac{5}{2}} \sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, \left(\sin^{3}\left(f x +e \right)\right)-825 \arctanh \left(\frac{\sqrt{-a \left(\sin \left(f x +e \right)-1\right)}}{\sqrt{a}}\right) \left(\sin^{3}\left(f x +e \right)\right) a^{3}+135 \left(-a \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{5}{2}} \sqrt{a}-440 \left(-a \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{3}{2}} a^{\frac{3}{2}}+345 \sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, a^{\frac{5}{2}}\right)}{120 \sin \left(f x +e \right)^{3} \sqrt{a}\, \cos \left(f x +e \right) \sqrt{a +a \sin \left(f x +e \right)}\, f}"," ",0,"-1/120*(1+sin(f*x+e))*(-a*(sin(f*x+e)-1))^(1/2)*(48*(-a*(sin(f*x+e)-1))^(5/2)*sin(f*x+e)^3*a^(1/2)-320*(-a*(sin(f*x+e)-1))^(3/2)*sin(f*x+e)^3*a^(3/2)+480*a^(5/2)*(-a*(sin(f*x+e)-1))^(1/2)*sin(f*x+e)^3-825*arctanh((-a*(sin(f*x+e)-1))^(1/2)/a^(1/2))*sin(f*x+e)^3*a^3+135*(-a*(sin(f*x+e)-1))^(5/2)*a^(1/2)-440*(-a*(sin(f*x+e)-1))^(3/2)*a^(3/2)+345*(-a*(sin(f*x+e)-1))^(1/2)*a^(5/2))/sin(f*x+e)^3/a^(1/2)/cos(f*x+e)/(a+a*sin(f*x+e))^(1/2)/f","A"
103,1,231,127,1.010000," ","int(tan(f*x+e)^4/(a+a*sin(f*x+e))^(1/2),x)","\frac{366 a^{\frac{7}{2}} \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right)+\left(402 \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) \left(a -a \sin \left(f x +e \right)\right)^{\frac{3}{2}} a^{2}-112 a^{\frac{7}{2}}\right) \sin \left(f x +e \right)+\left(-201 \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) \left(a -a \sin \left(f x +e \right)\right)^{\frac{3}{2}} a^{2}+122 a^{\frac{7}{2}}\right) \left(\cos^{2}\left(f x +e \right)\right)+402 \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) \left(a -a \sin \left(f x +e \right)\right)^{\frac{3}{2}} a^{2}-16 a^{\frac{7}{2}}}{384 a^{\frac{7}{2}} \left(\sin \left(f x +e \right)-1\right) \left(1+\sin \left(f x +e \right)\right) \cos \left(f x +e \right) \sqrt{a +a \sin \left(f x +e \right)}\, f}"," ",0,"1/384*(366*a^(7/2)*sin(f*x+e)*cos(f*x+e)^2+(402*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*(a-a*sin(f*x+e))^(3/2)*a^2-112*a^(7/2))*sin(f*x+e)+(-201*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*(a-a*sin(f*x+e))^(3/2)*a^2+122*a^(7/2))*cos(f*x+e)^2+402*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*(a-a*sin(f*x+e))^(3/2)*a^2-16*a^(7/2))/a^(7/2)/(sin(f*x+e)-1)/(1+sin(f*x+e))/cos(f*x+e)/(a+a*sin(f*x+e))^(1/2)/f","A"
104,1,130,88,0.576000," ","int(tan(f*x+e)^2/(a+a*sin(f*x+e))^(1/2),x)","\frac{\sin \left(f x +e \right) \left(5 \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) \sqrt{a -a \sin \left(f x +e \right)}\, a +6 a^{\frac{3}{2}}\right)+5 \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) \sqrt{a -a \sin \left(f x +e \right)}\, a +2 a^{\frac{3}{2}}}{8 a^{\frac{3}{2}} \cos \left(f x +e \right) \sqrt{a +a \sin \left(f x +e \right)}\, f}"," ",0,"1/8*(sin(f*x+e)*(5*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*(a-a*sin(f*x+e))^(1/2)*a+6*a^(3/2))+5*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*(a-a*sin(f*x+e))^(1/2)*a+2*a^(3/2))/a^(3/2)/cos(f*x+e)/(a+a*sin(f*x+e))^(1/2)/f","A"
105,1,103,54,0.691000," ","int(cot(f*x+e)^2/(a+a*sin(f*x+e))^(1/2),x)","-\frac{\left(1+\sin \left(f x +e \right)\right) \sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, \left(-\arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}}{\sqrt{a}}\right) a \sin \left(f x +e \right)+\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{a}\right)}{a^{\frac{3}{2}} \sin \left(f x +e \right) \cos \left(f x +e \right) \sqrt{a +a \sin \left(f x +e \right)}\, f}"," ",0,"-(1+sin(f*x+e))*(-a*(sin(f*x+e)-1))^(1/2)*(-arctanh((a-a*sin(f*x+e))^(1/2)/a^(1/2))*a*sin(f*x+e)+(a-a*sin(f*x+e))^(1/2)*a^(1/2))/a^(3/2)/sin(f*x+e)/cos(f*x+e)/(a+a*sin(f*x+e))^(1/2)/f","A"
106,1,144,115,0.822000," ","int(cot(f*x+e)^4/(a+a*sin(f*x+e))^(1/2),x)","\frac{\left(1+\sin \left(f x +e \right)\right) \sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, \left(-21 \arctanh \left(\frac{\sqrt{-a \left(\sin \left(f x +e \right)-1\right)}}{\sqrt{a}}\right) \left(\sin^{3}\left(f x +e \right)\right) a^{3}+27 \left(-a \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{5}{2}} \sqrt{a}-56 \left(-a \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{3}{2}} a^{\frac{3}{2}}+21 \sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, a^{\frac{5}{2}}\right)}{24 \sin \left(f x +e \right)^{3} a^{\frac{7}{2}} \cos \left(f x +e \right) \sqrt{a +a \sin \left(f x +e \right)}\, f}"," ",0,"1/24*(1+sin(f*x+e))*(-a*(sin(f*x+e)-1))^(1/2)*(-21*arctanh((-a*(sin(f*x+e)-1))^(1/2)/a^(1/2))*sin(f*x+e)^3*a^3+27*(-a*(sin(f*x+e)-1))^(5/2)*a^(1/2)-56*(-a*(sin(f*x+e)-1))^(3/2)*a^(3/2)+21*(-a*(sin(f*x+e)-1))^(1/2)*a^(5/2))/sin(f*x+e)^3/a^(7/2)/cos(f*x+e)/(a+a*sin(f*x+e))^(1/2)/f","A"
107,1,289,150,0.802000," ","int(tan(f*x+e)^4/(a+a*sin(f*x+e))^(3/2),x)","-\frac{\left(-1080 a^{\frac{9}{2}}-21 \left(a -a \sin \left(f x +e \right)\right)^{\frac{3}{2}} \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{3}\right) \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right)+\left(384 a^{\frac{9}{2}}+84 \left(a -a \sin \left(f x +e \right)\right)^{\frac{3}{2}} \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{3}\right) \sin \left(f x +e \right)+42 a^{\frac{9}{2}} \left(\cos^{4}\left(f x +e \right)\right)+\left(-648 a^{\frac{9}{2}}-63 \left(a -a \sin \left(f x +e \right)\right)^{\frac{3}{2}} \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{3}\right) \left(\cos^{2}\left(f x +e \right)\right)+128 a^{\frac{9}{2}}+84 \left(a -a \sin \left(f x +e \right)\right)^{\frac{3}{2}} \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{3}}{1536 a^{\frac{11}{2}} \left(\sin \left(f x +e \right)-1\right) \left(1+\sin \left(f x +e \right)\right)^{2} \cos \left(f x +e \right) \sqrt{a +a \sin \left(f x +e \right)}\, f}"," ",0,"-1/1536/a^(11/2)*((-1080*a^(9/2)-21*(a-a*sin(f*x+e))^(3/2)*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a^3)*sin(f*x+e)*cos(f*x+e)^2+(384*a^(9/2)+84*(a-a*sin(f*x+e))^(3/2)*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a^3)*sin(f*x+e)+42*a^(9/2)*cos(f*x+e)^4+(-648*a^(9/2)-63*(a-a*sin(f*x+e))^(3/2)*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a^3)*cos(f*x+e)^2+128*a^(9/2)+84*(a-a*sin(f*x+e))^(3/2)*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a^3)/(sin(f*x+e)-1)/(1+sin(f*x+e))^2/cos(f*x+e)/(a+a*sin(f*x+e))^(1/2)/f","A"
108,1,202,111,0.698000," ","int(tan(f*x+e)^2/(a+a*sin(f*x+e))^(3/2),x)","\frac{\sin \left(f x +e \right) \left(2 \sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{2}+40 a^{\frac{5}{2}}\right)+\left(-\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{2}+2 a^{\frac{5}{2}}\right) \left(\cos^{2}\left(f x +e \right)\right)+2 \sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{2}+24 a^{\frac{5}{2}}}{64 a^{\frac{7}{2}} \left(1+\sin \left(f x +e \right)\right) \cos \left(f x +e \right) \sqrt{a +a \sin \left(f x +e \right)}\, f}"," ",0,"1/64/a^(7/2)*(sin(f*x+e)*(2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a^2+40*a^(5/2))+(-(a-a*sin(f*x+e))^(1/2)*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a^2+2*a^(5/2))*cos(f*x+e)^2+2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a^2+24*a^(5/2))/(1+sin(f*x+e))/cos(f*x+e)/(a+a*sin(f*x+e))^(1/2)/f","A"
109,1,134,96,0.801000," ","int(cot(f*x+e)^2/(a+a*sin(f*x+e))^(3/2),x)","-\frac{\left(1+\sin \left(f x +e \right)\right) \sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, \left(\sin \left(f x +e \right) a^{2} \left(2 \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right)-3 \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}}{\sqrt{a}}\right)\right)+\sqrt{a -a \sin \left(f x +e \right)}\, a^{\frac{3}{2}}\right)}{a^{\frac{7}{2}} \sin \left(f x +e \right) \cos \left(f x +e \right) \sqrt{a +a \sin \left(f x +e \right)}\, f}"," ",0,"-1/a^(7/2)*(1+sin(f*x+e))*(-a*(sin(f*x+e)-1))^(1/2)*(sin(f*x+e)*a^2*(2*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))-3*arctanh((a-a*sin(f*x+e))^(1/2)/a^(1/2)))+(a-a*sin(f*x+e))^(1/2)*a^(3/2))/sin(f*x+e)/cos(f*x+e)/(a+a*sin(f*x+e))^(1/2)/f","A"
110,1,144,124,0.892000," ","int(cot(f*x+e)^4/(a+a*sin(f*x+e))^(3/2),x)","-\frac{\left(1+\sin \left(f x +e \right)\right) \sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, \left(3 \left(-a \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{5}{2}} a^{\frac{3}{2}}+3 \arctanh \left(\frac{\sqrt{-a \left(\sin \left(f x +e \right)-1\right)}}{\sqrt{a}}\right) a^{4} \left(\sin^{3}\left(f x +e \right)\right)+8 \left(-a \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{3}{2}} a^{\frac{5}{2}}-3 \sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, a^{\frac{7}{2}}\right)}{24 a^{\frac{11}{2}} \sin \left(f x +e \right)^{3} \cos \left(f x +e \right) \sqrt{a +a \sin \left(f x +e \right)}\, f}"," ",0,"-1/24/a^(11/2)*(1+sin(f*x+e))*(-a*(sin(f*x+e)-1))^(1/2)*(3*(-a*(sin(f*x+e)-1))^(5/2)*a^(3/2)+3*arctanh((-a*(sin(f*x+e)-1))^(1/2)/a^(1/2))*a^4*sin(f*x+e)^3+8*(-a*(sin(f*x+e)-1))^(3/2)*a^(5/2)-3*(-a*(sin(f*x+e)-1))^(1/2)*a^(7/2))/sin(f*x+e)^3/cos(f*x+e)/(a+a*sin(f*x+e))^(1/2)/f","A"
111,1,353,176,0.989000," ","int(tan(f*x+e)^4/(a+a*sin(f*x+e))^(5/2),x)","-\frac{1902 a^{\frac{11}{2}} \sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right)+\left(-13888 a^{\frac{11}{2}}-3804 \left(a -a \sin \left(f x +e \right)\right)^{\frac{3}{2}} \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{4}\right) \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+\left(5632 a^{\frac{11}{2}}+7608 \left(a -a \sin \left(f x +e \right)\right)^{\frac{3}{2}} \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{4}\right) \sin \left(f x +e \right)+\left(4438 a^{\frac{11}{2}}+951 \left(a -a \sin \left(f x +e \right)\right)^{\frac{3}{2}} \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{4}\right) \left(\cos^{4}\left(f x +e \right)\right)+\left(-9920 a^{\frac{11}{2}}-7608 \left(a -a \sin \left(f x +e \right)\right)^{\frac{3}{2}} \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{4}\right) \left(\cos^{2}\left(f x +e \right)\right)+2560 a^{\frac{11}{2}}+7608 \left(a -a \sin \left(f x +e \right)\right)^{\frac{3}{2}} \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{4}}{24576 a^{\frac{15}{2}} \left(\sin \left(f x +e \right)-1\right) \left(1+\sin \left(f x +e \right)\right)^{3} \cos \left(f x +e \right) \sqrt{a +a \sin \left(f x +e \right)}\, f}"," ",0,"-1/24576/a^(15/2)*(1902*a^(11/2)*sin(f*x+e)*cos(f*x+e)^4+(-13888*a^(11/2)-3804*(a-a*sin(f*x+e))^(3/2)*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a^4)*cos(f*x+e)^2*sin(f*x+e)+(5632*a^(11/2)+7608*(a-a*sin(f*x+e))^(3/2)*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a^4)*sin(f*x+e)+(4438*a^(11/2)+951*(a-a*sin(f*x+e))^(3/2)*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a^4)*cos(f*x+e)^4+(-9920*a^(11/2)-7608*(a-a*sin(f*x+e))^(3/2)*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a^4)*cos(f*x+e)^2+2560*a^(11/2)+7608*(a-a*sin(f*x+e))^(3/2)*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a^4)/(sin(f*x+e)-1)/(1+sin(f*x+e))^3/cos(f*x+e)/(a+a*sin(f*x+e))^(1/2)/f","A"
112,1,266,140,0.958000," ","int(tan(f*x+e)^2/(a+a*sin(f*x+e))^(5/2),x)","-\frac{\left(66 a^{\frac{7}{2}}-33 \sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{3}\right) \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right)+\left(-448 a^{\frac{7}{2}}+132 \sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{3}\right) \sin \left(f x +e \right)+\left(154 a^{\frac{7}{2}}-99 \sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{3}\right) \left(\cos^{2}\left(f x +e \right)\right)-320 a^{\frac{7}{2}}+132 \sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(f x +e \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{3}}{768 a^{\frac{11}{2}} \left(1+\sin \left(f x +e \right)\right)^{2} \cos \left(f x +e \right) \sqrt{a +a \sin \left(f x +e \right)}\, f}"," ",0,"-1/768/a^(11/2)*((66*a^(7/2)-33*(a-a*sin(f*x+e))^(1/2)*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a^3)*sin(f*x+e)*cos(f*x+e)^2+(-448*a^(7/2)+132*(a-a*sin(f*x+e))^(1/2)*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a^3)*sin(f*x+e)+(154*a^(7/2)-99*(a-a*sin(f*x+e))^(1/2)*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a^3)*cos(f*x+e)^2-320*a^(7/2)+132*(a-a*sin(f*x+e))^(1/2)*2^(1/2)*arctanh(1/2*(a-a*sin(f*x+e))^(1/2)*2^(1/2)/a^(1/2))*a^3)/(1+sin(f*x+e))^2/cos(f*x+e)/(a+a*sin(f*x+e))^(1/2)/f","A"
113,1,219,122,0.688000," ","int(cot(f*x+e)^2/(a+a*sin(f*x+e))^(5/2),x)","-\frac{\left(7 \sqrt{2}\, \arctanh \left(\frac{\sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, \sqrt{2}}{2 \sqrt{a}}\right) \left(\sin^{2}\left(f x +e \right)\right) a -10 \arctanh \left(\frac{\sqrt{-a \left(\sin \left(f x +e \right)-1\right)}}{\sqrt{a}}\right) \left(\sin^{2}\left(f x +e \right)\right) a +7 \sqrt{2}\, \arctanh \left(\frac{\sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a \sin \left(f x +e \right)+4 \sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, \sqrt{a}\, \sin \left(f x +e \right)-10 \arctanh \left(\frac{\sqrt{-a \left(\sin \left(f x +e \right)-1\right)}}{\sqrt{a}}\right) a \sin \left(f x +e \right)+2 \sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, \sqrt{a}\right) \sqrt{-a \left(\sin \left(f x +e \right)-1\right)}}{2 a^{\frac{7}{2}} \sin \left(f x +e \right) \cos \left(f x +e \right) \sqrt{a +a \sin \left(f x +e \right)}\, f}"," ",0,"-1/2/a^(7/2)*(7*2^(1/2)*arctanh(1/2*(-a*(sin(f*x+e)-1))^(1/2)*2^(1/2)/a^(1/2))*sin(f*x+e)^2*a-10*arctanh((-a*(sin(f*x+e)-1))^(1/2)/a^(1/2))*sin(f*x+e)^2*a+7*2^(1/2)*arctanh(1/2*(-a*(sin(f*x+e)-1))^(1/2)*2^(1/2)/a^(1/2))*a*sin(f*x+e)+4*(-a*(sin(f*x+e)-1))^(1/2)*a^(1/2)*sin(f*x+e)-10*arctanh((-a*(sin(f*x+e)-1))^(1/2)/a^(1/2))*a*sin(f*x+e)+2*(-a*(sin(f*x+e)-1))^(1/2)*a^(1/2))*(-a*(sin(f*x+e)-1))^(1/2)/sin(f*x+e)/cos(f*x+e)/(a+a*sin(f*x+e))^(1/2)/f","A"
114,1,182,162,1.007000," ","int(cot(f*x+e)^4/(a+a*sin(f*x+e))^(5/2),x)","\frac{\left(1+\sin \left(f x +e \right)\right) \sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, \left(-96 \sqrt{2}\, \arctanh \left(\frac{\sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{5} \left(\sin^{3}\left(f x +e \right)\right)-57 \left(-a \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{5}{2}} a^{\frac{5}{2}}+88 \left(-a \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{3}{2}} a^{\frac{7}{2}}-39 \sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, a^{\frac{9}{2}}+135 a^{5} \arctanh \left(\frac{\sqrt{-a \left(\sin \left(f x +e \right)-1\right)}}{\sqrt{a}}\right) \left(\sin^{3}\left(f x +e \right)\right)\right)}{24 a^{\frac{15}{2}} \sin \left(f x +e \right)^{3} \cos \left(f x +e \right) \sqrt{a +a \sin \left(f x +e \right)}\, f}"," ",0,"1/24*(1+sin(f*x+e))*(-a*(sin(f*x+e)-1))^(1/2)*(-96*2^(1/2)*arctanh(1/2*(-a*(sin(f*x+e)-1))^(1/2)*2^(1/2)/a^(1/2))*a^5*sin(f*x+e)^3-57*(-a*(sin(f*x+e)-1))^(5/2)*a^(5/2)+88*(-a*(sin(f*x+e)-1))^(3/2)*a^(7/2)-39*(-a*(sin(f*x+e)-1))^(1/2)*a^(9/2)+135*a^5*arctanh((-a*(sin(f*x+e)-1))^(1/2)/a^(1/2))*sin(f*x+e)^3)/a^(15/2)/sin(f*x+e)^3/cos(f*x+e)/(a+a*sin(f*x+e))^(1/2)/f","A"
115,0,0,1058,0.273000," ","int((a+a*sin(f*x+e))^(1/3)*tan(f*x+e)^4,x)","\int \left(a +a \sin \left(f x +e \right)\right)^{\frac{1}{3}} \left(\tan^{4}\left(f x +e \right)\right)\, dx"," ",0,"int((a+a*sin(f*x+e))^(1/3)*tan(f*x+e)^4,x)","F"
116,0,0,103,0.222000," ","int((a+a*sin(f*x+e))^(1/3)*tan(f*x+e)^2,x)","\int \left(a +a \sin \left(f x +e \right)\right)^{\frac{1}{3}} \left(\tan^{2}\left(f x +e \right)\right)\, dx"," ",0,"int((a+a*sin(f*x+e))^(1/3)*tan(f*x+e)^2,x)","F"
117,0,0,64,0.195000," ","int(cot(f*x+e)^2*(a+a*sin(f*x+e))^(1/3),x)","\int \left(\cot^{2}\left(f x +e \right)\right) \left(a +a \sin \left(f x +e \right)\right)^{\frac{1}{3}}\, dx"," ",0,"int(cot(f*x+e)^2*(a+a*sin(f*x+e))^(1/3),x)","F"
118,0,0,64,0.227000," ","int(cot(f*x+e)^4*(a+a*sin(f*x+e))^(1/3),x)","\int \left(\cot^{4}\left(f x +e \right)\right) \left(a +a \sin \left(f x +e \right)\right)^{\frac{1}{3}}\, dx"," ",0,"int(cot(f*x+e)^4*(a+a*sin(f*x+e))^(1/3),x)","F"
119,0,0,588,0.233000," ","int(tan(f*x+e)^4/(a+a*sin(f*x+e))^(1/3),x)","\int \frac{\tan^{4}\left(f x +e \right)}{\left(a +a \sin \left(f x +e \right)\right)^{\frac{1}{3}}}\, dx"," ",0,"int(tan(f*x+e)^4/(a+a*sin(f*x+e))^(1/3),x)","F"
120,0,0,102,0.213000," ","int(tan(f*x+e)^2/(a+a*sin(f*x+e))^(1/3),x)","\int \frac{\tan^{2}\left(f x +e \right)}{\left(a +a \sin \left(f x +e \right)\right)^{\frac{1}{3}}}\, dx"," ",0,"int(tan(f*x+e)^2/(a+a*sin(f*x+e))^(1/3),x)","F"
121,0,0,64,0.199000," ","int(cot(f*x+e)^2/(a+a*sin(f*x+e))^(1/3),x)","\int \frac{\cot^{2}\left(f x +e \right)}{\left(a +a \sin \left(f x +e \right)\right)^{\frac{1}{3}}}\, dx"," ",0,"int(cot(f*x+e)^2/(a+a*sin(f*x+e))^(1/3),x)","F"
122,0,0,64,0.253000," ","int(cot(f*x+e)^4/(a+a*sin(f*x+e))^(1/3),x)","\int \frac{\cot^{4}\left(f x +e \right)}{\left(a +a \sin \left(f x +e \right)\right)^{\frac{1}{3}}}\, dx"," ",0,"int(cot(f*x+e)^4/(a+a*sin(f*x+e))^(1/3),x)","F"
123,0,0,253,2.675000," ","int((a+a*sin(f*x+e))^3*(g*tan(f*x+e))^p,x)","\int \left(a +a \sin \left(f x +e \right)\right)^{3} \left(g \tan \left(f x +e \right)\right)^{p}\, dx"," ",0,"int((a+a*sin(f*x+e))^3*(g*tan(f*x+e))^p,x)","F"
124,0,0,177,2.243000," ","int((a+a*sin(f*x+e))^2*(g*tan(f*x+e))^p,x)","\int \left(a +a \sin \left(f x +e \right)\right)^{2} \left(g \tan \left(f x +e \right)\right)^{p}\, dx"," ",0,"int((a+a*sin(f*x+e))^2*(g*tan(f*x+e))^p,x)","F"
125,0,0,121,1.522000," ","int((a+a*sin(f*x+e))*(g*tan(f*x+e))^p,x)","\int \left(a +a \sin \left(f x +e \right)\right) \left(g \tan \left(f x +e \right)\right)^{p}\, dx"," ",0,"int((a+a*sin(f*x+e))*(g*tan(f*x+e))^p,x)","F"
126,0,0,102,0.466000," ","int((g*tan(f*x+e))^p/(a+a*sin(f*x+e)),x)","\int \frac{\left(g \tan \left(f x +e \right)\right)^{p}}{a +a \sin \left(f x +e \right)}\, dx"," ",0,"int((g*tan(f*x+e))^p/(a+a*sin(f*x+e)),x)","F"
127,0,0,132,1.022000," ","int((g*tan(f*x+e))^p/(a+a*sin(f*x+e))^2,x)","\int \frac{\left(g \tan \left(f x +e \right)\right)^{p}}{\left(a +a \sin \left(f x +e \right)\right)^{2}}\, dx"," ",0,"int((g*tan(f*x+e))^p/(a+a*sin(f*x+e))^2,x)","F"
128,0,0,236,1.002000," ","int((g*tan(f*x+e))^p/(a+a*sin(f*x+e))^3,x)","\int \frac{\left(g \tan \left(f x +e \right)\right)^{p}}{\left(a +a \sin \left(f x +e \right)\right)^{3}}\, dx"," ",0,"int((g*tan(f*x+e))^p/(a+a*sin(f*x+e))^3,x)","F"
129,0,0,103,1.324000," ","int((a+a*sin(f*x+e))^m*(g*tan(f*x+e))^p,x)","\int \left(a +a \sin \left(f x +e \right)\right)^{m} \left(g \tan \left(f x +e \right)\right)^{p}\, dx"," ",0,"int((a+a*sin(f*x+e))^m*(g*tan(f*x+e))^p,x)","F"
130,0,0,159,0.265000," ","int((a+a*sin(f*x+e))^m*tan(f*x+e)^3,x)","\int \left(a +a \sin \left(f x +e \right)\right)^{m} \left(\tan^{3}\left(f x +e \right)\right)\, dx"," ",0,"int((a+a*sin(f*x+e))^m*tan(f*x+e)^3,x)","F"
131,0,0,68,1.368000," ","int((a+a*sin(f*x+e))^m*tan(f*x+e),x)","\int \left(a +a \sin \left(f x +e \right)\right)^{m} \tan \left(f x +e \right)\, dx"," ",0,"int((a+a*sin(f*x+e))^m*tan(f*x+e),x)","F"
132,0,0,45,1.425000," ","int(cot(f*x+e)*(a+a*sin(f*x+e))^m,x)","\int \cot \left(f x +e \right) \left(a +a \sin \left(f x +e \right)\right)^{m}\, dx"," ",0,"int(cot(f*x+e)*(a+a*sin(f*x+e))^m,x)","F"
133,0,0,81,0.418000," ","int(cot(f*x+e)^3*(a+a*sin(f*x+e))^m,x)","\int \left(\cot^{3}\left(f x +e \right)\right) \left(a +a \sin \left(f x +e \right)\right)^{m}\, dx"," ",0,"int(cot(f*x+e)^3*(a+a*sin(f*x+e))^m,x)","F"
134,0,0,119,0.529000," ","int(cot(f*x+e)^5*(a+a*sin(f*x+e))^m,x)","\int \left(\cot^{5}\left(f x +e \right)\right) \left(a +a \sin \left(f x +e \right)\right)^{m}\, dx"," ",0,"int(cot(f*x+e)^5*(a+a*sin(f*x+e))^m,x)","F"
135,0,0,295,0.259000," ","int((a+a*sin(f*x+e))^m*tan(f*x+e)^4,x)","\int \left(a +a \sin \left(f x +e \right)\right)^{m} \left(\tan^{4}\left(f x +e \right)\right)\, dx"," ",0,"int((a+a*sin(f*x+e))^m*tan(f*x+e)^4,x)","F"
136,0,0,145,0.219000," ","int((a+a*sin(f*x+e))^m*tan(f*x+e)^2,x)","\int \left(a +a \sin \left(f x +e \right)\right)^{m} \left(\tan^{2}\left(f x +e \right)\right)\, dx"," ",0,"int((a+a*sin(f*x+e))^m*tan(f*x+e)^2,x)","F"
137,0,0,62,0.450000," ","int((a+a*sin(f*x+e))^m,x)","\int \left(a +a \sin \left(f x +e \right)\right)^{m}\, dx"," ",0,"int((a+a*sin(f*x+e))^m,x)","F"
138,0,0,77,0.351000," ","int(cot(f*x+e)^2*(a+a*sin(f*x+e))^m,x)","\int \left(\cot^{2}\left(f x +e \right)\right) \left(a +a \sin \left(f x +e \right)\right)^{m}\, dx"," ",0,"int(cot(f*x+e)^2*(a+a*sin(f*x+e))^m,x)","F"
139,0,0,77,0.442000," ","int(cot(f*x+e)^4*(a+a*sin(f*x+e))^m,x)","\int \left(\cot^{4}\left(f x +e \right)\right) \left(a +a \sin \left(f x +e \right)\right)^{m}\, dx"," ",0,"int(cot(f*x+e)^4*(a+a*sin(f*x+e))^m,x)","F"
140,1,96,80,0.095000," ","int((a+b*sin(d*x+c))*tan(d*x+c)^3,x)","\frac{a \left(\tan^{2}\left(d x +c \right)\right)}{2 d}+\frac{a \ln \left(\cos \left(d x +c \right)\right)}{d}+\frac{b \left(\sin^{5}\left(d x +c \right)\right)}{2 d \cos \left(d x +c \right)^{2}}+\frac{b \left(\sin^{3}\left(d x +c \right)\right)}{2 d}+\frac{3 b \sin \left(d x +c \right)}{2 d}-\frac{3 b \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{2 d}"," ",0,"1/2/d*a*tan(d*x+c)^2+1/d*a*ln(cos(d*x+c))+1/2/d*b*sin(d*x+c)^5/cos(d*x+c)^2+1/2/d*b*sin(d*x+c)^3+3/2*b*sin(d*x+c)/d-3/2/d*b*ln(sec(d*x+c)+tan(d*x+c))","A"
141,1,46,51,0.084000," ","int((a+b*sin(d*x+c))*tan(d*x+c),x)","-\frac{b \sin \left(d x +c \right)}{d}+\frac{b \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}-\frac{a \ln \left(\cos \left(d x +c \right)\right)}{d}"," ",0,"-b*sin(d*x+c)/d+1/d*b*ln(sec(d*x+c)+tan(d*x+c))-1/d*a*ln(cos(d*x+c))","A"
142,1,25,24,0.080000," ","int(cot(d*x+c)*(a+b*sin(d*x+c)),x)","\frac{a \ln \left(\sin \left(d x +c \right)\right)}{d}+\frac{b \sin \left(d x +c \right)}{d}"," ",0,"a*ln(sin(d*x+c))/d+b*sin(d*x+c)/d","A"
143,1,83,52,0.189000," ","int(cot(d*x+c)^3*(a+b*sin(d*x+c)),x)","-\frac{a \left(\cot^{2}\left(d x +c \right)\right)}{2 d}-\frac{a \ln \left(\sin \left(d x +c \right)\right)}{d}-\frac{b \left(\cos^{4}\left(d x +c \right)\right)}{d \sin \left(d x +c \right)}-\frac{\left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) b}{d}-\frac{2 b \sin \left(d x +c \right)}{d}"," ",0,"-1/2/d*a*cot(d*x+c)^2-a*ln(sin(d*x+c))/d-1/d*b/sin(d*x+c)*cos(d*x+c)^4-1/d*cos(d*x+c)^2*sin(d*x+c)*b-2*b*sin(d*x+c)/d","A"
144,1,136,77,0.177000," ","int(cot(d*x+c)^5*(a+b*sin(d*x+c)),x)","-\frac{a \left(\cot^{4}\left(d x +c \right)\right)}{4 d}+\frac{a \left(\cot^{2}\left(d x +c \right)\right)}{2 d}+\frac{a \ln \left(\sin \left(d x +c \right)\right)}{d}-\frac{b \left(\cos^{6}\left(d x +c \right)\right)}{3 d \sin \left(d x +c \right)^{3}}+\frac{b \left(\cos^{6}\left(d x +c \right)\right)}{d \sin \left(d x +c \right)}+\frac{8 b \sin \left(d x +c \right)}{3 d}+\frac{\left(\cos^{4}\left(d x +c \right)\right) \sin \left(d x +c \right) b}{d}+\frac{4 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) b}{3 d}"," ",0,"-1/4/d*a*cot(d*x+c)^4+1/2/d*a*cot(d*x+c)^2+a*ln(sin(d*x+c))/d-1/3/d*b/sin(d*x+c)^3*cos(d*x+c)^6+1/d*b/sin(d*x+c)*cos(d*x+c)^6+8/3*b*sin(d*x+c)/d+1/d*cos(d*x+c)^4*sin(d*x+c)*b+4/3/d*cos(d*x+c)^2*sin(d*x+c)*b","A"
145,1,98,68,0.155000," ","int((a+b*sin(d*x+c))*tan(d*x+c)^4,x)","\frac{a \left(\frac{\left(\tan^{3}\left(d x +c \right)\right)}{3}-\tan \left(d x +c \right)+d x +c \right)+b \left(\frac{\sin^{6}\left(d x +c \right)}{3 \cos \left(d x +c \right)^{3}}-\frac{\sin^{6}\left(d x +c \right)}{\cos \left(d x +c \right)}-\left(\frac{8}{3}+\sin^{4}\left(d x +c \right)+\frac{4 \left(\sin^{2}\left(d x +c \right)\right)}{3}\right) \cos \left(d x +c \right)\right)}{d}"," ",0,"1/d*(a*(1/3*tan(d*x+c)^3-tan(d*x+c)+d*x+c)+b*(1/3*sin(d*x+c)^6/cos(d*x+c)^3-sin(d*x+c)^6/cos(d*x+c)-(8/3+sin(d*x+c)^4+4/3*sin(d*x+c)^2)*cos(d*x+c)))","A"
146,1,59,38,0.136000," ","int((a+b*sin(d*x+c))*tan(d*x+c)^2,x)","\frac{a \left(\tan \left(d x +c \right)-d x -c \right)+b \left(\frac{\sin^{4}\left(d x +c \right)}{\cos \left(d x +c \right)}+\left(2+\sin^{2}\left(d x +c \right)\right) \cos \left(d x +c \right)\right)}{d}"," ",0,"1/d*(a*(tan(d*x+c)-d*x-c)+b*(sin(d*x+c)^4/cos(d*x+c)+(2+sin(d*x+c)^2)*cos(d*x+c)))","A"
147,1,57,41,0.098000," ","int(cot(d*x+c)^2*(a+b*sin(d*x+c)),x)","-a x +\frac{b \cos \left(d x +c \right)}{d}-\frac{a \cot \left(d x +c \right)}{d}+\frac{b \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{d}-\frac{c a}{d}"," ",0,"-a*x+b*cos(d*x+c)/d-a*cot(d*x+c)/d+1/d*b*ln(csc(d*x+c)-cot(d*x+c))-1/d*c*a","A"
148,1,106,74,0.115000," ","int(cot(d*x+c)^4*(a+b*sin(d*x+c)),x)","-\frac{a \left(\cot^{3}\left(d x +c \right)\right)}{3 d}+\frac{a \cot \left(d x +c \right)}{d}+a x +\frac{c a}{d}-\frac{b \left(\cos^{5}\left(d x +c \right)\right)}{2 d \sin \left(d x +c \right)^{2}}-\frac{b \left(\cos^{3}\left(d x +c \right)\right)}{2 d}-\frac{3 b \cos \left(d x +c \right)}{2 d}-\frac{3 b \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{2 d}"," ",0,"-1/3*a*cot(d*x+c)^3/d+a*cot(d*x+c)/d+a*x+1/d*c*a-1/2/d*b/sin(d*x+c)^2*cos(d*x+c)^5-1/2*b*cos(d*x+c)^3/d-3/2*b*cos(d*x+c)/d-3/2/d*b*ln(csc(d*x+c)-cot(d*x+c))","A"
149,1,159,110,0.129000," ","int(cot(d*x+c)^6*(a+b*sin(d*x+c)),x)","-\frac{a \left(\cot^{5}\left(d x +c \right)\right)}{5 d}+\frac{a \left(\cot^{3}\left(d x +c \right)\right)}{3 d}-\frac{a \cot \left(d x +c \right)}{d}-a x -\frac{c a}{d}-\frac{b \left(\cos^{7}\left(d x +c \right)\right)}{4 d \sin \left(d x +c \right)^{4}}+\frac{3 b \left(\cos^{7}\left(d x +c \right)\right)}{8 d \sin \left(d x +c \right)^{2}}+\frac{3 b \left(\cos^{5}\left(d x +c \right)\right)}{8 d}+\frac{5 b \left(\cos^{3}\left(d x +c \right)\right)}{8 d}+\frac{15 b \cos \left(d x +c \right)}{8 d}+\frac{15 b \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{8 d}"," ",0,"-1/5*a*cot(d*x+c)^5/d+1/3*a*cot(d*x+c)^3/d-a*cot(d*x+c)/d-a*x-1/d*c*a-1/4/d*b/sin(d*x+c)^4*cos(d*x+c)^7+3/8/d*b/sin(d*x+c)^2*cos(d*x+c)^7+3/8*b*cos(d*x+c)^5/d+5/8*b*cos(d*x+c)^3/d+15/8*b*cos(d*x+c)/d+15/8/d*b*ln(csc(d*x+c)-cot(d*x+c))","A"
150,1,172,103,0.146000," ","int((a+b*sin(d*x+c))^2*tan(d*x+c)^3,x)","\frac{a^{2} \left(\tan^{2}\left(d x +c \right)\right)}{2 d}+\frac{a^{2} \ln \left(\cos \left(d x +c \right)\right)}{d}+\frac{a b \left(\sin^{5}\left(d x +c \right)\right)}{d \cos \left(d x +c \right)^{2}}+\frac{a b \left(\sin^{3}\left(d x +c \right)\right)}{d}+\frac{3 a b \sin \left(d x +c \right)}{d}-\frac{3 a b \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{b^{2} \left(\sin^{6}\left(d x +c \right)\right)}{2 d \cos \left(d x +c \right)^{2}}+\frac{b^{2} \left(\sin^{4}\left(d x +c \right)\right)}{2 d}+\frac{b^{2} \left(\sin^{2}\left(d x +c \right)\right)}{d}+\frac{2 b^{2} \ln \left(\cos \left(d x +c \right)\right)}{d}"," ",0,"1/2/d*a^2*tan(d*x+c)^2+1/d*a^2*ln(cos(d*x+c))+1/d*a*b*sin(d*x+c)^5/cos(d*x+c)^2+1/d*a*b*sin(d*x+c)^3+3*a*b*sin(d*x+c)/d-3/d*a*b*ln(sec(d*x+c)+tan(d*x+c))+1/2/d*b^2*sin(d*x+c)^6/cos(d*x+c)^2+1/2/d*b^2*sin(d*x+c)^4+b^2*sin(d*x+c)^2/d+2/d*b^2*ln(cos(d*x+c))","A"
151,1,82,72,0.148000," ","int((a+b*sin(d*x+c))^2*tan(d*x+c),x)","-\frac{a^{2} \ln \left(\cos \left(d x +c \right)\right)}{d}-\frac{2 a b \sin \left(d x +c \right)}{d}+\frac{2 a b \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}-\frac{b^{2} \left(\sin^{2}\left(d x +c \right)\right)}{2 d}-\frac{b^{2} \ln \left(\cos \left(d x +c \right)\right)}{d}"," ",0,"-1/d*a^2*ln(cos(d*x+c))-2*a*b*sin(d*x+c)/d+2/d*a*b*ln(sec(d*x+c)+tan(d*x+c))-1/2*b^2*sin(d*x+c)^2/d-1/d*b^2*ln(cos(d*x+c))","A"
152,1,45,44,0.099000," ","int(cot(d*x+c)*(a+b*sin(d*x+c))^2,x)","\frac{a^{2} \ln \left(\sin \left(d x +c \right)\right)}{d}+\frac{2 a b \sin \left(d x +c \right)}{d}+\frac{b^{2} \left(\sin^{2}\left(d x +c \right)\right)}{2 d}"," ",0,"a^2*ln(sin(d*x+c))/d+2*a*b*sin(d*x+c)/d+1/2*b^2*sin(d*x+c)^2/d","A"
153,1,120,80,0.237000," ","int(cot(d*x+c)^3*(a+b*sin(d*x+c))^2,x)","-\frac{a^{2} \left(\cot^{2}\left(d x +c \right)\right)}{2 d}-\frac{a^{2} \ln \left(\sin \left(d x +c \right)\right)}{d}-\frac{2 a b \left(\cos^{4}\left(d x +c \right)\right)}{d \sin \left(d x +c \right)}-\frac{2 a b \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{d}-\frac{4 a b \sin \left(d x +c \right)}{d}+\frac{b^{2} \left(\cos^{2}\left(d x +c \right)\right)}{2 d}+\frac{b^{2} \ln \left(\sin \left(d x +c \right)\right)}{d}"," ",0,"-1/2/d*a^2*cot(d*x+c)^2-a^2*ln(sin(d*x+c))/d-2/d*a*b/sin(d*x+c)*cos(d*x+c)^4-2/d*a*b*cos(d*x+c)^2*sin(d*x+c)-4*a*b*sin(d*x+c)/d+1/2/d*b^2*cos(d*x+c)^2+1/d*b^2*ln(sin(d*x+c))","A"
154,1,220,118,0.278000," ","int(cot(d*x+c)^5*(a+b*sin(d*x+c))^2,x)","-\frac{a^{2} \left(\cot^{4}\left(d x +c \right)\right)}{4 d}+\frac{a^{2} \left(\cot^{2}\left(d x +c \right)\right)}{2 d}+\frac{a^{2} \ln \left(\sin \left(d x +c \right)\right)}{d}-\frac{2 a b \left(\cos^{6}\left(d x +c \right)\right)}{3 d \sin \left(d x +c \right)^{3}}+\frac{2 a b \left(\cos^{6}\left(d x +c \right)\right)}{d \sin \left(d x +c \right)}+\frac{16 a b \sin \left(d x +c \right)}{3 d}+\frac{2 a b \sin \left(d x +c \right) \left(\cos^{4}\left(d x +c \right)\right)}{d}+\frac{8 a b \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{3 d}-\frac{b^{2} \left(\cos^{6}\left(d x +c \right)\right)}{2 d \sin \left(d x +c \right)^{2}}-\frac{b^{2} \left(\cos^{4}\left(d x +c \right)\right)}{2 d}-\frac{b^{2} \left(\cos^{2}\left(d x +c \right)\right)}{d}-\frac{2 b^{2} \ln \left(\sin \left(d x +c \right)\right)}{d}"," ",0,"-1/4/d*a^2*cot(d*x+c)^4+1/2/d*a^2*cot(d*x+c)^2+a^2*ln(sin(d*x+c))/d-2/3/d*a*b/sin(d*x+c)^3*cos(d*x+c)^6+2/d*a*b/sin(d*x+c)*cos(d*x+c)^6+16/3*a*b*sin(d*x+c)/d+2/d*a*b*sin(d*x+c)*cos(d*x+c)^4+8/3/d*a*b*cos(d*x+c)^2*sin(d*x+c)-1/2/d*b^2/sin(d*x+c)^2*cos(d*x+c)^6-1/2/d*b^2*cos(d*x+c)^4-1/d*b^2*cos(d*x+c)^2-2/d*b^2*ln(sin(d*x+c))","A"
155,1,185,137,0.197000," ","int((a+b*sin(d*x+c))^2*tan(d*x+c)^4,x)","\frac{a^{2} \left(\frac{\left(\tan^{3}\left(d x +c \right)\right)}{3}-\tan \left(d x +c \right)+d x +c \right)+2 a b \left(\frac{\sin^{6}\left(d x +c \right)}{3 \cos \left(d x +c \right)^{3}}-\frac{\sin^{6}\left(d x +c \right)}{\cos \left(d x +c \right)}-\left(\frac{8}{3}+\sin^{4}\left(d x +c \right)+\frac{4 \left(\sin^{2}\left(d x +c \right)\right)}{3}\right) \cos \left(d x +c \right)\right)+b^{2} \left(\frac{\sin^{7}\left(d x +c \right)}{3 \cos \left(d x +c \right)^{3}}-\frac{4 \left(\sin^{7}\left(d x +c \right)\right)}{3 \cos \left(d x +c \right)}-\frac{4 \left(\sin^{5}\left(d x +c \right)+\frac{5 \left(\sin^{3}\left(d x +c \right)\right)}{4}+\frac{15 \sin \left(d x +c \right)}{8}\right) \cos \left(d x +c \right)}{3}+\frac{5 d x}{2}+\frac{5 c}{2}\right)}{d}"," ",0,"1/d*(a^2*(1/3*tan(d*x+c)^3-tan(d*x+c)+d*x+c)+2*a*b*(1/3*sin(d*x+c)^6/cos(d*x+c)^3-sin(d*x+c)^6/cos(d*x+c)-(8/3+sin(d*x+c)^4+4/3*sin(d*x+c)^2)*cos(d*x+c))+b^2*(1/3*sin(d*x+c)^7/cos(d*x+c)^3-4/3*sin(d*x+c)^7/cos(d*x+c)-4/3*(sin(d*x+c)^5+5/4*sin(d*x+c)^3+15/8*sin(d*x+c))*cos(d*x+c)+5/2*d*x+5/2*c))","A"
156,1,116,88,0.227000," ","int((a+b*sin(d*x+c))^2*tan(d*x+c)^2,x)","\frac{a^{2} \left(\tan \left(d x +c \right)-d x -c \right)+2 a b \left(\frac{\sin^{4}\left(d x +c \right)}{\cos \left(d x +c \right)}+\left(2+\sin^{2}\left(d x +c \right)\right) \cos \left(d x +c \right)\right)+b^{2} \left(\frac{\sin^{5}\left(d x +c \right)}{\cos \left(d x +c \right)}+\left(\sin^{3}\left(d x +c \right)+\frac{3 \sin \left(d x +c \right)}{2}\right) \cos \left(d x +c \right)-\frac{3 d x}{2}-\frac{3 c}{2}\right)}{d}"," ",0,"1/d*(a^2*(tan(d*x+c)-d*x-c)+2*a*b*(sin(d*x+c)^4/cos(d*x+c)+(2+sin(d*x+c)^2)*cos(d*x+c))+b^2*(sin(d*x+c)^5/cos(d*x+c)+(sin(d*x+c)^3+3/2*sin(d*x+c))*cos(d*x+c)-3/2*d*x-3/2*c))","A"
157,1,102,74,0.131000," ","int(cot(d*x+c)^2*(a+b*sin(d*x+c))^2,x)","-a^{2} x -\frac{a^{2} \cot \left(d x +c \right)}{d}-\frac{a^{2} c}{d}+\frac{2 a b \cos \left(d x +c \right)}{d}+\frac{2 a b \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{d}+\frac{b^{2} \cos \left(d x +c \right) \sin \left(d x +c \right)}{2 d}+\frac{b^{2} x}{2}+\frac{b^{2} c}{2 d}"," ",0,"-a^2*x-a^2*cot(d*x+c)/d-1/d*a^2*c+2*a*b*cos(d*x+c)/d+2/d*a*b*ln(csc(d*x+c)-cot(d*x+c))+1/2*b^2*cos(d*x+c)*sin(d*x+c)/d+1/2*b^2*x+1/2/d*b^2*c","A"
158,1,199,125,0.246000," ","int(cot(d*x+c)^4*(a+b*sin(d*x+c))^2,x)","-\frac{a^{2} \left(\cot^{3}\left(d x +c \right)\right)}{3 d}+\frac{a^{2} \cot \left(d x +c \right)}{d}+a^{2} x +\frac{a^{2} c}{d}-\frac{a b \left(\cos^{5}\left(d x +c \right)\right)}{d \sin \left(d x +c \right)^{2}}-\frac{a b \left(\cos^{3}\left(d x +c \right)\right)}{d}-\frac{3 a b \cos \left(d x +c \right)}{d}-\frac{3 a b \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{d}-\frac{b^{2} \left(\cos^{5}\left(d x +c \right)\right)}{d \sin \left(d x +c \right)}-\frac{b^{2} \sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right)}{d}-\frac{3 b^{2} \cos \left(d x +c \right) \sin \left(d x +c \right)}{2 d}-\frac{3 b^{2} x}{2}-\frac{3 b^{2} c}{2 d}"," ",0,"-1/3*a^2*cot(d*x+c)^3/d+a^2*cot(d*x+c)/d+a^2*x+1/d*a^2*c-1/d*a*b/sin(d*x+c)^2*cos(d*x+c)^5-a*b*cos(d*x+c)^3/d-3*a*b*cos(d*x+c)/d-3/d*a*b*ln(csc(d*x+c)-cot(d*x+c))-1/d*b^2/sin(d*x+c)*cos(d*x+c)^5-1/d*b^2*sin(d*x+c)*cos(d*x+c)^3-3/2*b^2*cos(d*x+c)*sin(d*x+c)/d-3/2*b^2*x-3/2/d*b^2*c","A"
159,1,302,182,0.233000," ","int(cot(d*x+c)^6*(a+b*sin(d*x+c))^2,x)","-\frac{a^{2} \left(\cot^{5}\left(d x +c \right)\right)}{5 d}+\frac{a^{2} \left(\cot^{3}\left(d x +c \right)\right)}{3 d}-\frac{a^{2} \cot \left(d x +c \right)}{d}-a^{2} x -\frac{a^{2} c}{d}-\frac{a b \left(\cos^{7}\left(d x +c \right)\right)}{2 d \sin \left(d x +c \right)^{4}}+\frac{3 a b \left(\cos^{7}\left(d x +c \right)\right)}{4 d \sin \left(d x +c \right)^{2}}+\frac{3 a b \left(\cos^{5}\left(d x +c \right)\right)}{4 d}+\frac{5 a b \left(\cos^{3}\left(d x +c \right)\right)}{4 d}+\frac{15 a b \cos \left(d x +c \right)}{4 d}+\frac{15 a b \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{4 d}-\frac{b^{2} \left(\cos^{7}\left(d x +c \right)\right)}{3 d \sin \left(d x +c \right)^{3}}+\frac{4 b^{2} \left(\cos^{7}\left(d x +c \right)\right)}{3 d \sin \left(d x +c \right)}+\frac{4 b^{2} \sin \left(d x +c \right) \left(\cos^{5}\left(d x +c \right)\right)}{3 d}+\frac{5 b^{2} \sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right)}{3 d}+\frac{5 b^{2} \cos \left(d x +c \right) \sin \left(d x +c \right)}{2 d}+\frac{5 b^{2} x}{2}+\frac{5 b^{2} c}{2 d}"," ",0,"-1/5*a^2*cot(d*x+c)^5/d+1/3*a^2*cot(d*x+c)^3/d-a^2*cot(d*x+c)/d-a^2*x-1/d*a^2*c-1/2/d*a*b/sin(d*x+c)^4*cos(d*x+c)^7+3/4/d*a*b/sin(d*x+c)^2*cos(d*x+c)^7+3/4*a*b*cos(d*x+c)^5/d+5/4*a*b*cos(d*x+c)^3/d+15/4*a*b*cos(d*x+c)/d+15/4/d*a*b*ln(csc(d*x+c)-cot(d*x+c))-1/3/d*b^2/sin(d*x+c)^3*cos(d*x+c)^7+4/3/d*b^2/sin(d*x+c)*cos(d*x+c)^7+4/3/d*b^2*sin(d*x+c)*cos(d*x+c)^5+5/3/d*b^2*sin(d*x+c)*cos(d*x+c)^3+5/2*b^2*cos(d*x+c)*sin(d*x+c)/d+5/2*b^2*x+5/2/d*b^2*c","A"
160,1,279,138,0.161000," ","int((a+b*sin(d*x+c))^3*tan(d*x+c)^3,x)","\frac{a^{3} \left(\tan^{2}\left(d x +c \right)\right)}{2 d}+\frac{a^{3} \ln \left(\cos \left(d x +c \right)\right)}{d}+\frac{3 a^{2} b \left(\sin^{5}\left(d x +c \right)\right)}{2 d \cos \left(d x +c \right)^{2}}+\frac{3 a^{2} b \left(\sin^{3}\left(d x +c \right)\right)}{2 d}+\frac{9 a^{2} b \sin \left(d x +c \right)}{2 d}-\frac{9 a^{2} b \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{2 d}+\frac{3 a \,b^{2} \left(\sin^{6}\left(d x +c \right)\right)}{2 d \cos \left(d x +c \right)^{2}}+\frac{3 a \,b^{2} \left(\sin^{4}\left(d x +c \right)\right)}{2 d}+\frac{3 a \,b^{2} \left(\sin^{2}\left(d x +c \right)\right)}{d}+\frac{6 a \,b^{2} \ln \left(\cos \left(d x +c \right)\right)}{d}+\frac{b^{3} \left(\sin^{7}\left(d x +c \right)\right)}{2 d \cos \left(d x +c \right)^{2}}+\frac{b^{3} \left(\sin^{5}\left(d x +c \right)\right)}{2 d}+\frac{5 b^{3} \left(\sin^{3}\left(d x +c \right)\right)}{6 d}+\frac{5 b^{3} \sin \left(d x +c \right)}{2 d}-\frac{5 b^{3} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{2 d}"," ",0,"1/2/d*a^3*tan(d*x+c)^2+1/d*a^3*ln(cos(d*x+c))+3/2/d*a^2*b*sin(d*x+c)^5/cos(d*x+c)^2+3/2/d*a^2*b*sin(d*x+c)^3+9/2*a^2*b*sin(d*x+c)/d-9/2/d*a^2*b*ln(sec(d*x+c)+tan(d*x+c))+3/2/d*a*b^2*sin(d*x+c)^6/cos(d*x+c)^2+3/2/d*a*b^2*sin(d*x+c)^4+3*a*b^2*sin(d*x+c)^2/d+6/d*a*b^2*ln(cos(d*x+c))+1/2/d*b^3*sin(d*x+c)^7/cos(d*x+c)^2+1/2/d*b^3*sin(d*x+c)^5+5/6*b^3*sin(d*x+c)^3/d+5/2/d*b^3*sin(d*x+c)-5/2/d*b^3*ln(sec(d*x+c)+tan(d*x+c))","B"
161,1,139,97,0.145000," ","int((a+b*sin(d*x+c))^3*tan(d*x+c),x)","-\frac{a^{3} \ln \left(\cos \left(d x +c \right)\right)}{d}+\frac{3 a^{2} b \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}-\frac{3 a^{2} b \sin \left(d x +c \right)}{d}-\frac{3 a \,b^{2} \left(\sin^{2}\left(d x +c \right)\right)}{2 d}-\frac{3 a \,b^{2} \ln \left(\cos \left(d x +c \right)\right)}{d}-\frac{b^{3} \left(\sin^{3}\left(d x +c \right)\right)}{3 d}-\frac{b^{3} \sin \left(d x +c \right)}{d}+\frac{b^{3} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}"," ",0,"-1/d*a^3*ln(cos(d*x+c))+3/d*a^2*b*ln(sec(d*x+c)+tan(d*x+c))-3*a^2*b*sin(d*x+c)/d-3/2*a*b^2*sin(d*x+c)^2/d-3/d*a*b^2*ln(cos(d*x+c))-1/3*b^3*sin(d*x+c)^3/d-1/d*b^3*sin(d*x+c)+1/d*b^3*ln(sec(d*x+c)+tan(d*x+c))","A"
162,1,64,63,0.104000," ","int(cot(d*x+c)*(a+b*sin(d*x+c))^3,x)","\frac{a^{3} \ln \left(\sin \left(d x +c \right)\right)}{d}+\frac{3 a^{2} b \sin \left(d x +c \right)}{d}+\frac{3 a \,b^{2} \left(\sin^{2}\left(d x +c \right)\right)}{2 d}+\frac{b^{3} \left(\sin^{3}\left(d x +c \right)\right)}{3 d}"," ",0,"a^3*ln(sin(d*x+c))/d+3*a^2*b*sin(d*x+c)/d+3/2*a*b^2*sin(d*x+c)^2/d+1/3*b^3*sin(d*x+c)^3/d","A"
163,1,165,110,0.257000," ","int(cot(d*x+c)^3*(a+b*sin(d*x+c))^3,x)","-\frac{a^{3} \left(\cot^{2}\left(d x +c \right)\right)}{2 d}-\frac{a^{3} \ln \left(\sin \left(d x +c \right)\right)}{d}-\frac{3 a^{2} b \left(\cos^{4}\left(d x +c \right)\right)}{d \sin \left(d x +c \right)}-\frac{3 a^{2} b \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{d}-\frac{6 a^{2} b \sin \left(d x +c \right)}{d}+\frac{3 a \,b^{2} \left(\cos^{2}\left(d x +c \right)\right)}{2 d}+\frac{3 a \,b^{2} \ln \left(\sin \left(d x +c \right)\right)}{d}+\frac{b^{3} \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{3 d}+\frac{2 b^{3} \sin \left(d x +c \right)}{3 d}"," ",0,"-1/2/d*a^3*cot(d*x+c)^2-a^3*ln(sin(d*x+c))/d-3/d*a^2*b/sin(d*x+c)*cos(d*x+c)^4-3/d*a^2*b*cos(d*x+c)^2*sin(d*x+c)-6*a^2*b*sin(d*x+c)/d+3/2/d*a*b^2*cos(d*x+c)^2+3/d*a*b^2*ln(sin(d*x+c))+1/3/d*b^3*cos(d*x+c)^2*sin(d*x+c)+2/3/d*b^3*sin(d*x+c)","A"
164,1,316,157,0.230000," ","int(cot(d*x+c)^5*(a+b*sin(d*x+c))^3,x)","-\frac{a^{3} \left(\cot^{4}\left(d x +c \right)\right)}{4 d}+\frac{a^{3} \left(\cot^{2}\left(d x +c \right)\right)}{2 d}+\frac{a^{3} \ln \left(\sin \left(d x +c \right)\right)}{d}-\frac{a^{2} b \left(\cos^{6}\left(d x +c \right)\right)}{d \sin \left(d x +c \right)^{3}}+\frac{3 a^{2} b \left(\cos^{6}\left(d x +c \right)\right)}{d \sin \left(d x +c \right)}+\frac{8 a^{2} b \sin \left(d x +c \right)}{d}+\frac{3 a^{2} b \sin \left(d x +c \right) \left(\cos^{4}\left(d x +c \right)\right)}{d}+\frac{4 a^{2} b \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{d}-\frac{3 a \,b^{2} \left(\cos^{6}\left(d x +c \right)\right)}{2 d \sin \left(d x +c \right)^{2}}-\frac{3 a \,b^{2} \left(\cos^{4}\left(d x +c \right)\right)}{2 d}-\frac{3 a \,b^{2} \left(\cos^{2}\left(d x +c \right)\right)}{d}-\frac{6 a \,b^{2} \ln \left(\sin \left(d x +c \right)\right)}{d}-\frac{b^{3} \left(\cos^{6}\left(d x +c \right)\right)}{d \sin \left(d x +c \right)}-\frac{8 b^{3} \sin \left(d x +c \right)}{3 d}-\frac{b^{3} \sin \left(d x +c \right) \left(\cos^{4}\left(d x +c \right)\right)}{d}-\frac{4 b^{3} \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{3 d}"," ",0,"-1/4/d*a^3*cot(d*x+c)^4+1/2/d*a^3*cot(d*x+c)^2+a^3*ln(sin(d*x+c))/d-1/d*a^2*b/sin(d*x+c)^3*cos(d*x+c)^6+3/d*a^2*b/sin(d*x+c)*cos(d*x+c)^6+8*a^2*b*sin(d*x+c)/d+3/d*a^2*b*sin(d*x+c)*cos(d*x+c)^4+4/d*a^2*b*cos(d*x+c)^2*sin(d*x+c)-3/2/d*a*b^2/sin(d*x+c)^2*cos(d*x+c)^6-3/2/d*a*b^2*cos(d*x+c)^4-3/d*a*b^2*cos(d*x+c)^2-6/d*a*b^2*ln(sin(d*x+c))-1/d*b^3/sin(d*x+c)*cos(d*x+c)^6-8/3/d*b^3*sin(d*x+c)-1/d*b^3*sin(d*x+c)*cos(d*x+c)^4-4/3/d*b^3*cos(d*x+c)^2*sin(d*x+c)","B"
165,1,268,206,0.252000," ","int((a+b*sin(d*x+c))^3*tan(d*x+c)^4,x)","\frac{a^{3} \left(\frac{\left(\tan^{3}\left(d x +c \right)\right)}{3}-\tan \left(d x +c \right)+d x +c \right)+3 a^{2} b \left(\frac{\sin^{6}\left(d x +c \right)}{3 \cos \left(d x +c \right)^{3}}-\frac{\sin^{6}\left(d x +c \right)}{\cos \left(d x +c \right)}-\left(\frac{8}{3}+\sin^{4}\left(d x +c \right)+\frac{4 \left(\sin^{2}\left(d x +c \right)\right)}{3}\right) \cos \left(d x +c \right)\right)+3 a \,b^{2} \left(\frac{\sin^{7}\left(d x +c \right)}{3 \cos \left(d x +c \right)^{3}}-\frac{4 \left(\sin^{7}\left(d x +c \right)\right)}{3 \cos \left(d x +c \right)}-\frac{4 \left(\sin^{5}\left(d x +c \right)+\frac{5 \left(\sin^{3}\left(d x +c \right)\right)}{4}+\frac{15 \sin \left(d x +c \right)}{8}\right) \cos \left(d x +c \right)}{3}+\frac{5 d x}{2}+\frac{5 c}{2}\right)+b^{3} \left(\frac{\sin^{8}\left(d x +c \right)}{3 \cos \left(d x +c \right)^{3}}-\frac{5 \left(\sin^{8}\left(d x +c \right)\right)}{3 \cos \left(d x +c \right)}-\frac{5 \left(\frac{16}{5}+\sin^{6}\left(d x +c \right)+\frac{6 \left(\sin^{4}\left(d x +c \right)\right)}{5}+\frac{8 \left(\sin^{2}\left(d x +c \right)\right)}{5}\right) \cos \left(d x +c \right)}{3}\right)}{d}"," ",0,"1/d*(a^3*(1/3*tan(d*x+c)^3-tan(d*x+c)+d*x+c)+3*a^2*b*(1/3*sin(d*x+c)^6/cos(d*x+c)^3-sin(d*x+c)^6/cos(d*x+c)-(8/3+sin(d*x+c)^4+4/3*sin(d*x+c)^2)*cos(d*x+c))+3*a*b^2*(1/3*sin(d*x+c)^7/cos(d*x+c)^3-4/3*sin(d*x+c)^7/cos(d*x+c)-4/3*(sin(d*x+c)^5+5/4*sin(d*x+c)^3+15/8*sin(d*x+c))*cos(d*x+c)+5/2*d*x+5/2*c)+b^3*(1/3*sin(d*x+c)^8/cos(d*x+c)^3-5/3*sin(d*x+c)^8/cos(d*x+c)-5/3*(16/5+sin(d*x+c)^6+6/5*sin(d*x+c)^4+8/5*sin(d*x+c)^2)*cos(d*x+c)))","A"
166,1,169,138,0.286000," ","int((a+b*sin(d*x+c))^3*tan(d*x+c)^2,x)","\frac{a^{3} \left(\tan \left(d x +c \right)-d x -c \right)+3 a^{2} b \left(\frac{\sin^{4}\left(d x +c \right)}{\cos \left(d x +c \right)}+\left(2+\sin^{2}\left(d x +c \right)\right) \cos \left(d x +c \right)\right)+3 a \,b^{2} \left(\frac{\sin^{5}\left(d x +c \right)}{\cos \left(d x +c \right)}+\left(\sin^{3}\left(d x +c \right)+\frac{3 \sin \left(d x +c \right)}{2}\right) \cos \left(d x +c \right)-\frac{3 d x}{2}-\frac{3 c}{2}\right)+b^{3} \left(\frac{\sin^{6}\left(d x +c \right)}{\cos \left(d x +c \right)}+\left(\frac{8}{3}+\sin^{4}\left(d x +c \right)+\frac{4 \left(\sin^{2}\left(d x +c \right)\right)}{3}\right) \cos \left(d x +c \right)\right)}{d}"," ",0,"1/d*(a^3*(tan(d*x+c)-d*x-c)+3*a^2*b*(sin(d*x+c)^4/cos(d*x+c)+(2+sin(d*x+c)^2)*cos(d*x+c))+3*a*b^2*(sin(d*x+c)^5/cos(d*x+c)+(sin(d*x+c)^3+3/2*sin(d*x+c))*cos(d*x+c)-3/2*d*x-3/2*c)+b^3*(sin(d*x+c)^6/cos(d*x+c)+(8/3+sin(d*x+c)^4+4/3*sin(d*x+c)^2)*cos(d*x+c)))","A"
167,1,125,96,0.143000," ","int(cot(d*x+c)^2*(a+b*sin(d*x+c))^3,x)","-a^{3} x -\frac{a^{3} \cot \left(d x +c \right)}{d}-\frac{a^{3} c}{d}+\frac{3 a^{2} b \cos \left(d x +c \right)}{d}+\frac{3 a^{2} b \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{d}+\frac{3 a \,b^{2} \cos \left(d x +c \right) \sin \left(d x +c \right)}{2 d}+\frac{3 a \,b^{2} x}{2}+\frac{3 a \,b^{2} c}{2 d}-\frac{b^{3} \left(\cos^{3}\left(d x +c \right)\right)}{3 d}"," ",0,"-a^3*x-a^3*cot(d*x+c)/d-1/d*a^3*c+3*a^2*b*cos(d*x+c)/d+3/d*a^2*b*ln(csc(d*x+c)-cot(d*x+c))+3/2*a*b^2*cos(d*x+c)*sin(d*x+c)/d+3/2*a*b^2*x+3/2/d*a*b^2*c-1/3*b^3*cos(d*x+c)^3/d","A"
168,1,264,178,0.228000," ","int(cot(d*x+c)^4*(a+b*sin(d*x+c))^3,x)","-\frac{a^{3} \left(\cot^{3}\left(d x +c \right)\right)}{3 d}+\frac{a^{3} \cot \left(d x +c \right)}{d}+a^{3} x +\frac{a^{3} c}{d}-\frac{3 a^{2} b \left(\cos^{5}\left(d x +c \right)\right)}{2 d \sin \left(d x +c \right)^{2}}-\frac{3 a^{2} b \left(\cos^{3}\left(d x +c \right)\right)}{2 d}-\frac{9 a^{2} b \cos \left(d x +c \right)}{2 d}-\frac{9 a^{2} b \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{2 d}-\frac{3 a \,b^{2} \left(\cos^{5}\left(d x +c \right)\right)}{d \sin \left(d x +c \right)}-\frac{3 a \,b^{2} \sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right)}{d}-\frac{9 a \,b^{2} \cos \left(d x +c \right) \sin \left(d x +c \right)}{2 d}-\frac{9 a \,b^{2} x}{2}-\frac{9 a \,b^{2} c}{2 d}+\frac{b^{3} \left(\cos^{3}\left(d x +c \right)\right)}{3 d}+\frac{b^{3} \cos \left(d x +c \right)}{d}+\frac{b^{3} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{d}"," ",0,"-1/3*a^3*cot(d*x+c)^3/d+a^3*cot(d*x+c)/d+a^3*x+1/d*a^3*c-3/2/d*a^2*b/sin(d*x+c)^2*cos(d*x+c)^5-3/2/d*a^2*b*cos(d*x+c)^3-9/2*a^2*b*cos(d*x+c)/d-9/2/d*a^2*b*ln(csc(d*x+c)-cot(d*x+c))-3/d*a*b^2/sin(d*x+c)*cos(d*x+c)^5-3/d*a*b^2*sin(d*x+c)*cos(d*x+c)^3-9/2*a*b^2*cos(d*x+c)*sin(d*x+c)/d-9/2*a*b^2*x-9/2/d*a*b^2*c+1/3*b^3*cos(d*x+c)^3/d+b^3*cos(d*x+c)/d+1/d*b^3*ln(csc(d*x+c)-cot(d*x+c))","A"
169,1,415,263,0.258000," ","int(cot(d*x+c)^6*(a+b*sin(d*x+c))^3,x)","-\frac{a^{3} \left(\cot^{5}\left(d x +c \right)\right)}{5 d}+\frac{a^{3} \left(\cot^{3}\left(d x +c \right)\right)}{3 d}-\frac{a^{3} \cot \left(d x +c \right)}{d}-a^{3} x -\frac{a^{3} c}{d}-\frac{3 a^{2} b \left(\cos^{7}\left(d x +c \right)\right)}{4 d \sin \left(d x +c \right)^{4}}+\frac{9 a^{2} b \left(\cos^{7}\left(d x +c \right)\right)}{8 d \sin \left(d x +c \right)^{2}}+\frac{9 a^{2} b \left(\cos^{5}\left(d x +c \right)\right)}{8 d}+\frac{15 a^{2} b \left(\cos^{3}\left(d x +c \right)\right)}{8 d}+\frac{45 a^{2} b \cos \left(d x +c \right)}{8 d}+\frac{45 a^{2} b \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{8 d}-\frac{a \,b^{2} \left(\cos^{7}\left(d x +c \right)\right)}{d \sin \left(d x +c \right)^{3}}+\frac{4 a \,b^{2} \left(\cos^{7}\left(d x +c \right)\right)}{d \sin \left(d x +c \right)}+\frac{4 a \,b^{2} \sin \left(d x +c \right) \left(\cos^{5}\left(d x +c \right)\right)}{d}+\frac{5 a \,b^{2} \sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right)}{d}+\frac{15 a \,b^{2} \cos \left(d x +c \right) \sin \left(d x +c \right)}{2 d}+\frac{15 a \,b^{2} x}{2}+\frac{15 a \,b^{2} c}{2 d}-\frac{b^{3} \left(\cos^{7}\left(d x +c \right)\right)}{2 d \sin \left(d x +c \right)^{2}}-\frac{b^{3} \left(\cos^{5}\left(d x +c \right)\right)}{2 d}-\frac{5 b^{3} \left(\cos^{3}\left(d x +c \right)\right)}{6 d}-\frac{5 b^{3} \cos \left(d x +c \right)}{2 d}-\frac{5 b^{3} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{2 d}"," ",0,"-1/5*a^3*cot(d*x+c)^5/d+1/3*a^3*cot(d*x+c)^3/d-a^3*cot(d*x+c)/d-a^3*x-1/d*a^3*c-3/4/d*a^2*b/sin(d*x+c)^4*cos(d*x+c)^7+9/8/d*a^2*b/sin(d*x+c)^2*cos(d*x+c)^7+9/8/d*a^2*b*cos(d*x+c)^5+15/8/d*a^2*b*cos(d*x+c)^3+45/8*a^2*b*cos(d*x+c)/d+45/8/d*a^2*b*ln(csc(d*x+c)-cot(d*x+c))-1/d*a*b^2/sin(d*x+c)^3*cos(d*x+c)^7+4/d*a*b^2/sin(d*x+c)*cos(d*x+c)^7+4/d*a*b^2*sin(d*x+c)*cos(d*x+c)^5+5/d*a*b^2*sin(d*x+c)*cos(d*x+c)^3+15/2*a*b^2*cos(d*x+c)*sin(d*x+c)/d+15/2*a*b^2*x+15/2/d*a*b^2*c-1/2/d*b^3/sin(d*x+c)^2*cos(d*x+c)^7-1/2/d*b^3*cos(d*x+c)^5-5/6*b^3*cos(d*x+c)^3/d-5/2*b^3*cos(d*x+c)/d-5/2/d*b^3*ln(csc(d*x+c)-cot(d*x+c))","A"
170,1,304,196,0.180000," ","int(tan(d*x+c)^5/(a+b*sin(d*x+c)),x)","\frac{1}{2 d \left(8 a +8 b \right) \left(\sin \left(d x +c \right)-1\right)^{2}}+\frac{7 a}{16 d \left(a +b \right)^{2} \left(\sin \left(d x +c \right)-1\right)}+\frac{5 b}{16 d \left(a +b \right)^{2} \left(\sin \left(d x +c \right)-1\right)}-\frac{\ln \left(\sin \left(d x +c \right)-1\right) a^{2}}{2 d \left(a +b \right)^{3}}-\frac{9 \ln \left(\sin \left(d x +c \right)-1\right) a b}{16 d \left(a +b \right)^{3}}-\frac{3 \ln \left(\sin \left(d x +c \right)-1\right) b^{2}}{16 d \left(a +b \right)^{3}}+\frac{a^{5} \ln \left(a +b \sin \left(d x +c \right)\right)}{d \left(a +b \right)^{3} \left(a -b \right)^{3}}+\frac{1}{2 d \left(8 a -8 b \right) \left(1+\sin \left(d x +c \right)\right)^{2}}-\frac{7 a}{16 d \left(a -b \right)^{2} \left(1+\sin \left(d x +c \right)\right)}+\frac{5 b}{16 d \left(a -b \right)^{2} \left(1+\sin \left(d x +c \right)\right)}-\frac{\ln \left(1+\sin \left(d x +c \right)\right) a^{2}}{2 d \left(a -b \right)^{3}}+\frac{9 \ln \left(1+\sin \left(d x +c \right)\right) a b}{16 d \left(a -b \right)^{3}}-\frac{3 \ln \left(1+\sin \left(d x +c \right)\right) b^{2}}{16 d \left(a -b \right)^{3}}"," ",0,"1/2/d/(8*a+8*b)/(sin(d*x+c)-1)^2+7/16/d/(a+b)^2/(sin(d*x+c)-1)*a+5/16/d/(a+b)^2/(sin(d*x+c)-1)*b-1/2/d/(a+b)^3*ln(sin(d*x+c)-1)*a^2-9/16/d/(a+b)^3*ln(sin(d*x+c)-1)*a*b-3/16/d/(a+b)^3*ln(sin(d*x+c)-1)*b^2+1/d*a^5/(a+b)^3/(a-b)^3*ln(a+b*sin(d*x+c))+1/2/d/(8*a-8*b)/(1+sin(d*x+c))^2-7/16/d/(a-b)^2/(1+sin(d*x+c))*a+5/16/d/(a-b)^2/(1+sin(d*x+c))*b-1/2/d/(a-b)^3*ln(1+sin(d*x+c))*a^2+9/16/d/(a-b)^3*ln(1+sin(d*x+c))*a*b-3/16/d/(a-b)^3*ln(1+sin(d*x+c))*b^2","A"
171,1,164,120,0.180000," ","int(tan(d*x+c)^3/(a+b*sin(d*x+c)),x)","-\frac{1}{d \left(4 a +4 b \right) \left(\sin \left(d x +c \right)-1\right)}+\frac{\ln \left(\sin \left(d x +c \right)-1\right) a}{2 d \left(a +b \right)^{2}}+\frac{\ln \left(\sin \left(d x +c \right)-1\right) b}{4 d \left(a +b \right)^{2}}-\frac{a^{3} \ln \left(a +b \sin \left(d x +c \right)\right)}{d \left(a +b \right)^{2} \left(a -b \right)^{2}}+\frac{1}{d \left(4 a -4 b \right) \left(1+\sin \left(d x +c \right)\right)}+\frac{\ln \left(1+\sin \left(d x +c \right)\right) a}{2 d \left(a -b \right)^{2}}-\frac{\ln \left(1+\sin \left(d x +c \right)\right) b}{4 d \left(a -b \right)^{2}}"," ",0,"-1/d/(4*a+4*b)/(sin(d*x+c)-1)+1/2/d/(a+b)^2*ln(sin(d*x+c)-1)*a+1/4/d/(a+b)^2*ln(sin(d*x+c)-1)*b-1/d*a^3/(a+b)^2/(a-b)^2*ln(a+b*sin(d*x+c))+1/d/(4*a-4*b)/(1+sin(d*x+c))+1/2/d/(a-b)^2*ln(1+sin(d*x+c))*a-1/4/d/(a-b)^2*ln(1+sin(d*x+c))*b","A"
172,1,76,70,0.180000," ","int(tan(d*x+c)/(a+b*sin(d*x+c)),x)","-\frac{\ln \left(\sin \left(d x +c \right)-1\right)}{d \left(2 a +2 b \right)}+\frac{a \ln \left(a +b \sin \left(d x +c \right)\right)}{d \left(a +b \right) \left(a -b \right)}-\frac{\ln \left(1+\sin \left(d x +c \right)\right)}{d \left(2 a -2 b \right)}"," ",0,"-1/d/(2*a+2*b)*ln(sin(d*x+c)-1)+1/d*a/(a+b)/(a-b)*ln(a+b*sin(d*x+c))-1/d/(2*a-2*b)*ln(1+sin(d*x+c))","A"
173,1,35,34,0.112000," ","int(cot(d*x+c)/(a+b*sin(d*x+c)),x)","\frac{\ln \left(\sin \left(d x +c \right)\right)}{a d}-\frac{\ln \left(a +b \sin \left(d x +c \right)\right)}{d a}"," ",0,"ln(sin(d*x+c))/a/d-1/d/a*ln(a+b*sin(d*x+c))","A"
174,1,106,82,0.221000," ","int(cot(d*x+c)^3/(a+b*sin(d*x+c)),x)","\frac{\ln \left(a +b \sin \left(d x +c \right)\right)}{d a}-\frac{\ln \left(a +b \sin \left(d x +c \right)\right) b^{2}}{d \,a^{3}}-\frac{1}{2 d a \sin \left(d x +c \right)^{2}}-\frac{\ln \left(\sin \left(d x +c \right)\right)}{a d}+\frac{\ln \left(\sin \left(d x +c \right)\right) b^{2}}{d \,a^{3}}+\frac{b}{d \,a^{2} \sin \left(d x +c \right)}"," ",0,"1/d/a*ln(a+b*sin(d*x+c))-1/d/a^3*ln(a+b*sin(d*x+c))*b^2-1/2/d/a/sin(d*x+c)^2-ln(sin(d*x+c))/a/d+1/d/a^3*ln(sin(d*x+c))*b^2+1/d/a^2*b/sin(d*x+c)","A"
175,1,216,142,0.202000," ","int(cot(d*x+c)^5/(a+b*sin(d*x+c)),x)","-\frac{\ln \left(a +b \sin \left(d x +c \right)\right)}{d a}+\frac{2 \ln \left(a +b \sin \left(d x +c \right)\right) b^{2}}{d \,a^{3}}-\frac{\ln \left(a +b \sin \left(d x +c \right)\right) b^{4}}{d \,a^{5}}-\frac{1}{4 d a \sin \left(d x +c \right)^{4}}+\frac{1}{d a \sin \left(d x +c \right)^{2}}-\frac{b^{2}}{2 d \,a^{3} \sin \left(d x +c \right)^{2}}+\frac{\ln \left(\sin \left(d x +c \right)\right)}{a d}-\frac{2 \ln \left(\sin \left(d x +c \right)\right) b^{2}}{d \,a^{3}}+\frac{\ln \left(\sin \left(d x +c \right)\right) b^{4}}{d \,a^{5}}-\frac{2 b}{d \,a^{2} \sin \left(d x +c \right)}+\frac{b^{3}}{d \,a^{4} \sin \left(d x +c \right)}+\frac{b}{3 d \,a^{2} \sin \left(d x +c \right)^{3}}"," ",0,"-1/d/a*ln(a+b*sin(d*x+c))+2/d/a^3*ln(a+b*sin(d*x+c))*b^2-1/d/a^5*ln(a+b*sin(d*x+c))*b^4-1/4/d/a/sin(d*x+c)^4+1/d/a/sin(d*x+c)^2-1/2/d/a^3/sin(d*x+c)^2*b^2+ln(sin(d*x+c))/a/d-2/d/a^3*ln(sin(d*x+c))*b^2+1/d/a^5*ln(sin(d*x+c))*b^4-2/d/a^2*b/sin(d*x+c)+1/d/a^4*b^3/sin(d*x+c)+1/3/d/a^2*b/sin(d*x+c)^3","A"
176,1,269,168,0.193000," ","int(tan(d*x+c)^4/(a+b*sin(d*x+c)),x)","-\frac{32}{3 d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{3} \left(32 a +32 b \right)}-\frac{16}{d \left(32 a +32 b \right) \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}+\frac{a}{d \left(a +b \right)^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}+\frac{b}{2 d \left(a +b \right)^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{32}{3 d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3} \left(32 a -32 b \right)}+\frac{16}{d \left(32 a -32 b \right) \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}+\frac{a}{d \left(a -b \right)^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}-\frac{b}{2 d \left(a -b \right)^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}+\frac{2 a^{4} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \left(a -b \right)^{2} \left(a +b \right)^{2} \sqrt{a^{2}-b^{2}}}"," ",0,"-32/3/d/(tan(1/2*d*x+1/2*c)-1)^3/(32*a+32*b)-16/d/(32*a+32*b)/(tan(1/2*d*x+1/2*c)-1)^2+1/d/(a+b)^2/(tan(1/2*d*x+1/2*c)-1)*a+1/2/d/(a+b)^2/(tan(1/2*d*x+1/2*c)-1)*b-32/3/d/(tan(1/2*d*x+1/2*c)+1)^3/(32*a-32*b)+16/d/(32*a-32*b)/(tan(1/2*d*x+1/2*c)+1)^2+1/d/(a-b)^2/(tan(1/2*d*x+1/2*c)+1)*a-1/2/d/(a-b)^2/(tan(1/2*d*x+1/2*c)+1)*b+2/d*a^4/(a-b)^2/(a+b)^2/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))","A"
177,1,117,91,0.158000," ","int(tan(d*x+c)^2/(a+b*sin(d*x+c)),x)","-\frac{8}{d \left(8 a +8 b \right) \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{8}{d \left(8 a -8 b \right) \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}-\frac{2 a^{2} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \left(a -b \right) \left(a +b \right) \sqrt{a^{2}-b^{2}}}"," ",0,"-8/d/(8*a+8*b)/(tan(1/2*d*x+1/2*c)-1)-8/d/(8*a-8*b)/(tan(1/2*d*x+1/2*c)+1)-2/d*a^2/(a-b)/(a+b)/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))","A"
178,1,155,75,0.172000," ","int(cot(d*x+c)^2/(a+b*sin(d*x+c)),x)","\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 a d}-\frac{1}{2 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}-\frac{b \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{2}}-\frac{2 \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \sqrt{a^{2}-b^{2}}}+\frac{2 b^{2} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,a^{2} \sqrt{a^{2}-b^{2}}}"," ",0,"1/2/a/d*tan(1/2*d*x+1/2*c)-1/2/a/d/tan(1/2*d*x+1/2*c)-1/d/a^2*b*ln(tan(1/2*d*x+1/2*c))-2/d/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))+2/d*b^2/a^2/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))","B"
179,1,348,141,0.198000," ","int(cot(d*x+c)^4/(a+b*sin(d*x+c)),x)","\frac{\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)}{24 a d}-\frac{b \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{8 d \,a^{2}}-\frac{5 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{8 a d}+\frac{b^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 d \,a^{3}}-\frac{1}{24 d a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{3}}+\frac{5}{8 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}-\frac{b^{2}}{2 d \,a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}+\frac{b}{8 d \,a^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}+\frac{3 b \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{2 d \,a^{2}}-\frac{b^{3} \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{4}}+\frac{2 \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \sqrt{a^{2}-b^{2}}}-\frac{4 b^{2} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,a^{2} \sqrt{a^{2}-b^{2}}}+\frac{2 \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right) b^{4}}{d \,a^{4} \sqrt{a^{2}-b^{2}}}"," ",0,"1/24/d/a*tan(1/2*d*x+1/2*c)^3-1/8/d/a^2*b*tan(1/2*d*x+1/2*c)^2-5/8/a/d*tan(1/2*d*x+1/2*c)+1/2/d/a^3*b^2*tan(1/2*d*x+1/2*c)-1/24/d/a/tan(1/2*d*x+1/2*c)^3+5/8/a/d/tan(1/2*d*x+1/2*c)-1/2/d/a^3/tan(1/2*d*x+1/2*c)*b^2+1/8/d/a^2*b/tan(1/2*d*x+1/2*c)^2+3/2/d/a^2*b*ln(tan(1/2*d*x+1/2*c))-1/d/a^4*b^3*ln(tan(1/2*d*x+1/2*c))+2/d/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))-4/d*b^2/a^2/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))+2/d/a^4/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))*b^4","B"
180,1,629,288,0.206000," ","int(cot(d*x+c)^6/(a+b*sin(d*x+c)),x)","-\frac{b \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{64 d \,a^{2}}+\frac{b^{2} \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{24 d \,a^{3}}-\frac{\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{3}}{8 d \,a^{4}}+\frac{6 b^{2} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,a^{2} \sqrt{a^{2}-b^{2}}}-\frac{15 b \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{8 d \,a^{2}}-\frac{2 \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \sqrt{a^{2}-b^{2}}}+\frac{b^{4} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 d \,a^{5}}-\frac{b^{2}}{24 d \,a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{3}}-\frac{b^{4}}{2 d \,a^{5} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}+\frac{b}{64 d \,a^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{4}}+\frac{b^{3}}{8 d \,a^{4} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}-\frac{b^{5} \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{6}}+\frac{b \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 d \,a^{2}}-\frac{9 b^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{8 d \,a^{3}}+\frac{9 b^{2}}{8 d \,a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}-\frac{b}{4 d \,a^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}+\frac{5 b^{3} \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{2 d \,a^{4}}+\frac{11 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{16 a d}-\frac{11}{16 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}-\frac{1}{160 d a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{5}}+\frac{\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)}{160 a d}+\frac{7}{96 d a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{3}}-\frac{7 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{96 a d}+\frac{2 \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right) b^{6}}{d \,a^{6} \sqrt{a^{2}-b^{2}}}-\frac{6 \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right) b^{4}}{d \,a^{4} \sqrt{a^{2}-b^{2}}}"," ",0,"6/d*b^2/a^2/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))-15/8/d/a^2*b*ln(tan(1/2*d*x+1/2*c))-2/d/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))+1/2/d/a^5*b^4*tan(1/2*d*x+1/2*c)-1/24/d/a^3/tan(1/2*d*x+1/2*c)^3*b^2-1/2/d/a^5/tan(1/2*d*x+1/2*c)*b^4+1/64/d/a^2*b/tan(1/2*d*x+1/2*c)^4+1/8/d/a^4*b^3/tan(1/2*d*x+1/2*c)^2-1/d/a^6*b^5*ln(tan(1/2*d*x+1/2*c))-1/64/d/a^2*b*tan(1/2*d*x+1/2*c)^4+1/24/d/a^3*b^2*tan(1/2*d*x+1/2*c)^3-1/8/d/a^4*tan(1/2*d*x+1/2*c)^2*b^3+1/4/d/a^2*b*tan(1/2*d*x+1/2*c)^2-9/8/d/a^3*b^2*tan(1/2*d*x+1/2*c)+9/8/d/a^3/tan(1/2*d*x+1/2*c)*b^2-1/4/d/a^2*b/tan(1/2*d*x+1/2*c)^2+5/2/d/a^4*b^3*ln(tan(1/2*d*x+1/2*c))+11/16/a/d*tan(1/2*d*x+1/2*c)-11/16/a/d/tan(1/2*d*x+1/2*c)+1/160/d/a*tan(1/2*d*x+1/2*c)^5-1/160/d/a/tan(1/2*d*x+1/2*c)^5-7/96/d/a*tan(1/2*d*x+1/2*c)^3+7/96/d/a/tan(1/2*d*x+1/2*c)^3+2/d/a^6/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))*b^6-6/d/a^4/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))*b^4","B"
181,1,318,231,0.270000," ","int(tan(d*x+c)^5/(a+b*sin(d*x+c))^2,x)","\frac{1}{16 d \left(a +b \right)^{2} \left(\sin \left(d x +c \right)-1\right)^{2}}+\frac{3 b}{16 d \left(a +b \right)^{3} \left(\sin \left(d x +c \right)-1\right)}+\frac{7 a}{16 d \left(a +b \right)^{3} \left(\sin \left(d x +c \right)-1\right)}-\frac{a^{2} \ln \left(\sin \left(d x +c \right)-1\right)}{2 d \left(a +b \right)^{4}}-\frac{a \ln \left(\sin \left(d x +c \right)-1\right) b}{8 d \left(a +b \right)^{4}}-\frac{a^{5}}{d \left(a +b \right)^{3} \left(a -b \right)^{3} \left(a +b \sin \left(d x +c \right)\right)}+\frac{a^{6} \ln \left(a +b \sin \left(d x +c \right)\right)}{d \left(a +b \right)^{4} \left(a -b \right)^{4}}+\frac{5 a^{4} \ln \left(a +b \sin \left(d x +c \right)\right) b^{2}}{d \left(a +b \right)^{4} \left(a -b \right)^{4}}+\frac{1}{16 d \left(a -b \right)^{2} \left(1+\sin \left(d x +c \right)\right)^{2}}+\frac{3 b}{16 d \left(a -b \right)^{3} \left(1+\sin \left(d x +c \right)\right)}-\frac{7 a}{16 d \left(a -b \right)^{3} \left(1+\sin \left(d x +c \right)\right)}-\frac{a^{2} \ln \left(1+\sin \left(d x +c \right)\right)}{2 d \left(a -b \right)^{4}}+\frac{a \ln \left(1+\sin \left(d x +c \right)\right) b}{8 d \left(a -b \right)^{4}}"," ",0,"1/16/d/(a+b)^2/(sin(d*x+c)-1)^2+3/16/d/(a+b)^3/(sin(d*x+c)-1)*b+7/16/d/(a+b)^3/(sin(d*x+c)-1)*a-1/2/d*a^2/(a+b)^4*ln(sin(d*x+c)-1)-1/8/d*a/(a+b)^4*ln(sin(d*x+c)-1)*b-1/d*a^5/(a+b)^3/(a-b)^3/(a+b*sin(d*x+c))+1/d*a^6/(a+b)^4/(a-b)^4*ln(a+b*sin(d*x+c))+5/d*a^4/(a+b)^4/(a-b)^4*ln(a+b*sin(d*x+c))*b^2+1/16/d/(a-b)^2/(1+sin(d*x+c))^2+3/16/d/(a-b)^3/(1+sin(d*x+c))*b-7/16/d/(a-b)^3/(1+sin(d*x+c))*a-1/2/d*a^2/(a-b)^4*ln(1+sin(d*x+c))+1/8/d*a/(a-b)^4*ln(1+sin(d*x+c))*b","A"
182,1,182,155,0.264000," ","int(tan(d*x+c)^3/(a+b*sin(d*x+c))^2,x)","-\frac{1}{4 d \left(a +b \right)^{2} \left(\sin \left(d x +c \right)-1\right)}+\frac{a \ln \left(\sin \left(d x +c \right)-1\right)}{2 d \left(a +b \right)^{3}}+\frac{a^{3}}{d \left(a +b \right)^{2} \left(a -b \right)^{2} \left(a +b \sin \left(d x +c \right)\right)}-\frac{a^{4} \ln \left(a +b \sin \left(d x +c \right)\right)}{d \left(a +b \right)^{3} \left(a -b \right)^{3}}-\frac{3 a^{2} \ln \left(a +b \sin \left(d x +c \right)\right) b^{2}}{d \left(a +b \right)^{3} \left(a -b \right)^{3}}+\frac{1}{4 d \left(a -b \right)^{2} \left(1+\sin \left(d x +c \right)\right)}+\frac{a \ln \left(1+\sin \left(d x +c \right)\right)}{2 \left(a -b \right)^{3} d}"," ",0,"-1/4/d/(a+b)^2/(sin(d*x+c)-1)+1/2/d*a/(a+b)^3*ln(sin(d*x+c)-1)+1/d*a^3/(a+b)^2/(a-b)^2/(a+b*sin(d*x+c))-1/d*a^4/(a+b)^3/(a-b)^3*ln(a+b*sin(d*x+c))-3/d*a^2/(a+b)^3/(a-b)^3*ln(a+b*sin(d*x+c))*b^2+1/4/d/(a-b)^2/(1+sin(d*x+c))+1/2*a*ln(1+sin(d*x+c))/(a-b)^3/d","A"
183,1,132,105,0.243000," ","int(tan(d*x+c)/(a+b*sin(d*x+c))^2,x)","-\frac{\ln \left(\sin \left(d x +c \right)-1\right)}{2 d \left(a +b \right)^{2}}-\frac{a}{d \left(a +b \right) \left(a -b \right) \left(a +b \sin \left(d x +c \right)\right)}+\frac{\ln \left(a +b \sin \left(d x +c \right)\right) a^{2}}{d \left(a +b \right)^{2} \left(a -b \right)^{2}}+\frac{\ln \left(a +b \sin \left(d x +c \right)\right) b^{2}}{d \left(a +b \right)^{2} \left(a -b \right)^{2}}-\frac{\ln \left(1+\sin \left(d x +c \right)\right)}{2 \left(a -b \right)^{2} d}"," ",0,"-1/2/d/(a+b)^2*ln(sin(d*x+c)-1)-1/d*a/(a+b)/(a-b)/(a+b*sin(d*x+c))+1/d/(a+b)^2/(a-b)^2*ln(a+b*sin(d*x+c))*a^2+1/d/(a+b)^2/(a-b)^2*ln(a+b*sin(d*x+c))*b^2-1/2*ln(1+sin(d*x+c))/(a-b)^2/d","A"
184,1,54,53,0.146000," ","int(cot(d*x+c)/(a+b*sin(d*x+c))^2,x)","\frac{\ln \left(\sin \left(d x +c \right)\right)}{a^{2} d}-\frac{\ln \left(a +b \sin \left(d x +c \right)\right)}{a^{2} d}+\frac{1}{a d \left(a +b \sin \left(d x +c \right)\right)}"," ",0,"ln(sin(d*x+c))/a^2/d-ln(a+b*sin(d*x+c))/a^2/d+1/a/d/(a+b*sin(d*x+c))","A"
185,1,150,111,0.291000," ","int(cot(d*x+c)^3/(a+b*sin(d*x+c))^2,x)","\frac{\ln \left(a +b \sin \left(d x +c \right)\right)}{a^{2} d}-\frac{3 \ln \left(a +b \sin \left(d x +c \right)\right) b^{2}}{d \,a^{4}}-\frac{1}{a d \left(a +b \sin \left(d x +c \right)\right)}+\frac{b^{2}}{d \,a^{3} \left(a +b \sin \left(d x +c \right)\right)}-\frac{1}{2 d \,a^{2} \sin \left(d x +c \right)^{2}}-\frac{\ln \left(\sin \left(d x +c \right)\right)}{a^{2} d}+\frac{3 \ln \left(\sin \left(d x +c \right)\right) b^{2}}{d \,a^{4}}+\frac{2 b}{d \,a^{3} \sin \left(d x +c \right)}"," ",0,"ln(a+b*sin(d*x+c))/a^2/d-3/d/a^4*ln(a+b*sin(d*x+c))*b^2-1/a/d/(a+b*sin(d*x+c))+1/d/a^3/(a+b*sin(d*x+c))*b^2-1/2/d/a^2/sin(d*x+c)^2-ln(sin(d*x+c))/a^2/d+3/d/a^4*ln(sin(d*x+c))*b^2+2/d/a^3*b/sin(d*x+c)","A"
186,1,282,182,0.273000," ","int(cot(d*x+c)^5/(a+b*sin(d*x+c))^2,x)","-\frac{\ln \left(a +b \sin \left(d x +c \right)\right)}{a^{2} d}+\frac{6 \ln \left(a +b \sin \left(d x +c \right)\right) b^{2}}{d \,a^{4}}-\frac{5 \ln \left(a +b \sin \left(d x +c \right)\right) b^{4}}{d \,a^{6}}+\frac{1}{a d \left(a +b \sin \left(d x +c \right)\right)}-\frac{2 b^{2}}{d \,a^{3} \left(a +b \sin \left(d x +c \right)\right)}+\frac{b^{4}}{d \,a^{5} \left(a +b \sin \left(d x +c \right)\right)}-\frac{1}{4 d \,a^{2} \sin \left(d x +c \right)^{4}}+\frac{1}{d \,a^{2} \sin \left(d x +c \right)^{2}}-\frac{3 b^{2}}{2 d \,a^{4} \sin \left(d x +c \right)^{2}}+\frac{\ln \left(\sin \left(d x +c \right)\right)}{a^{2} d}-\frac{6 \ln \left(\sin \left(d x +c \right)\right) b^{2}}{d \,a^{4}}+\frac{5 \ln \left(\sin \left(d x +c \right)\right) b^{4}}{d \,a^{6}}+\frac{2 b}{3 d \,a^{3} \sin \left(d x +c \right)^{3}}-\frac{4 b}{d \,a^{3} \sin \left(d x +c \right)}+\frac{4 b^{3}}{d \,a^{5} \sin \left(d x +c \right)}"," ",0,"-ln(a+b*sin(d*x+c))/a^2/d+6/d/a^4*ln(a+b*sin(d*x+c))*b^2-5/d/a^6*ln(a+b*sin(d*x+c))*b^4+1/a/d/(a+b*sin(d*x+c))-2/d/a^3/(a+b*sin(d*x+c))*b^2+1/d/a^5/(a+b*sin(d*x+c))*b^4-1/4/d/a^2/sin(d*x+c)^4+1/d/a^2/sin(d*x+c)^2-3/2/d/a^4/sin(d*x+c)^2*b^2+ln(sin(d*x+c))/a^2/d-6/d/a^4*ln(sin(d*x+c))*b^2+5/d/a^6*ln(sin(d*x+c))*b^4+2/3/d/a^3*b/sin(d*x+c)^3-4/d/a^3*b/sin(d*x+c)+4/d*b^3/a^5/sin(d*x+c)","A"
187,1,382,311,0.259000," ","int(tan(d*x+c)^4/(a+b*sin(d*x+c))^2,x)","-\frac{1}{3 d \left(a +b \right)^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{3}}-\frac{1}{2 d \left(a +b \right)^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}+\frac{a}{d \left(a +b \right)^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{1}{3 d \left(a -b \right)^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}+\frac{1}{2 d \left(a -b \right)^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}+\frac{a}{d \left(a -b \right)^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}+\frac{2 a^{3} b^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \left(a -b \right)^{3} \left(a +b \right)^{3} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)}+\frac{2 a^{4} b}{d \left(a -b \right)^{3} \left(a +b \right)^{3} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)}+\frac{2 a^{5} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \left(a -b \right)^{3} \left(a +b \right)^{3} \sqrt{a^{2}-b^{2}}}+\frac{8 a^{3} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right) b^{2}}{d \left(a -b \right)^{3} \left(a +b \right)^{3} \sqrt{a^{2}-b^{2}}}"," ",0,"-1/3/d/(a+b)^2/(tan(1/2*d*x+1/2*c)-1)^3-1/2/d/(a+b)^2/(tan(1/2*d*x+1/2*c)-1)^2+1/d*a/(a+b)^3/(tan(1/2*d*x+1/2*c)-1)-1/3/d/(a-b)^2/(tan(1/2*d*x+1/2*c)+1)^3+1/2/d/(a-b)^2/(tan(1/2*d*x+1/2*c)+1)^2+1/d*a/(a-b)^3/(tan(1/2*d*x+1/2*c)+1)+2/d*a^3/(a-b)^3/(a+b)^3/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)*b^2*tan(1/2*d*x+1/2*c)+2/d*a^4/(a-b)^3/(a+b)^3/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)*b+2/d*a^5/(a-b)^3/(a+b)^3/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))+8/d*a^3/(a-b)^3/(a+b)^3/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))*b^2","A"
188,1,282,186,0.306000," ","int(tan(d*x+c)^2/(a+b*sin(d*x+c))^2,x)","-\frac{1}{d \left(a +b \right)^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{1}{d \left(a -b \right)^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}-\frac{2 a \,b^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \left(a -b \right)^{2} \left(a +b \right)^{2} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)}-\frac{2 a^{2} b}{d \left(a -b \right)^{2} \left(a +b \right)^{2} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)}-\frac{2 a^{3} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \left(a -b \right)^{2} \left(a +b \right)^{2} \sqrt{a^{2}-b^{2}}}-\frac{4 a \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right) b^{2}}{d \left(a -b \right)^{2} \left(a +b \right)^{2} \sqrt{a^{2}-b^{2}}}"," ",0,"-1/d/(a+b)^2/(tan(1/2*d*x+1/2*c)-1)-1/d/(a-b)^2/(tan(1/2*d*x+1/2*c)+1)-2/d*a/(a-b)^2/(a+b)^2/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)*b^2*tan(1/2*d*x+1/2*c)-2/d*a^2/(a-b)^2/(a+b)^2/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)*b-2/d*a^3/(a-b)^2/(a+b)^2/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))-4/d*a/(a-b)^2/(a+b)^2/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))*b^2","A"
189,1,245,110,0.279000," ","int(cot(d*x+c)^2/(a+b*sin(d*x+c))^2,x)","\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 d \,a^{2}}-\frac{1}{2 d \,a^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}-\frac{2 b \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{3}}-\frac{2 b^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,a^{3} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)}-\frac{2 b}{d \,a^{2} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)}-\frac{2 \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d a \sqrt{a^{2}-b^{2}}}+\frac{4 \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right) b^{2}}{d \,a^{3} \sqrt{a^{2}-b^{2}}}"," ",0,"1/2/d/a^2*tan(1/2*d*x+1/2*c)-1/2/d/a^2/tan(1/2*d*x+1/2*c)-2/d/a^3*b*ln(tan(1/2*d*x+1/2*c))-2/d/a^3/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)*b^2*tan(1/2*d*x+1/2*c)-2/d/a^2/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)*b-2/d/a/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))+4/d/a^3/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))*b^2","B"
190,1,527,227,0.287000," ","int(cot(d*x+c)^4/(a+b*sin(d*x+c))^2,x)","\frac{\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)}{24 d \,a^{2}}-\frac{b \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 d \,a^{3}}-\frac{5 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{8 d \,a^{2}}+\frac{3 b^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 d \,a^{4}}-\frac{1}{24 d \,a^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{3}}+\frac{5}{8 d \,a^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}-\frac{3 b^{2}}{2 d \,a^{4} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}+\frac{b}{4 d \,a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}+\frac{3 b \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{3}}-\frac{4 b^{3} \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{5}}+\frac{2 b^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,a^{3} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)}-\frac{2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b^{4}}{d \,a^{5} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)}+\frac{2 b}{d \,a^{2} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)}-\frac{2 b^{3}}{d \,a^{4} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)}+\frac{2 \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d a \sqrt{a^{2}-b^{2}}}-\frac{10 \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right) b^{2}}{d \,a^{3} \sqrt{a^{2}-b^{2}}}+\frac{8 \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right) b^{4}}{d \,a^{5} \sqrt{a^{2}-b^{2}}}"," ",0,"1/24/d/a^2*tan(1/2*d*x+1/2*c)^3-1/4/d/a^3*b*tan(1/2*d*x+1/2*c)^2-5/8/d/a^2*tan(1/2*d*x+1/2*c)+3/2/d/a^4*b^2*tan(1/2*d*x+1/2*c)-1/24/d/a^2/tan(1/2*d*x+1/2*c)^3+5/8/d/a^2/tan(1/2*d*x+1/2*c)-3/2/d/a^4/tan(1/2*d*x+1/2*c)*b^2+1/4/d/a^3*b/tan(1/2*d*x+1/2*c)^2+3/d/a^3*b*ln(tan(1/2*d*x+1/2*c))-4/d/a^5*b^3*ln(tan(1/2*d*x+1/2*c))+2/d/a^3/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)*b^2*tan(1/2*d*x+1/2*c)-2/d/a^5/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)*tan(1/2*d*x+1/2*c)*b^4+2/d/a^2/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)*b-2/d/a^4/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)*b^3+2/d/a/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))-10/d/a^3/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))*b^2+8/d/a^5/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))*b^4","B"
191,1,897,401,0.323000," ","int(cot(d*x+c)^6/(a+b*sin(d*x+c))^2,x)","\frac{\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)}{160 d \,a^{2}}+\frac{b^{3}}{2 d \,a^{5} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}-\frac{6 b^{5} \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{7}}+\frac{5 b^{4} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 d \,a^{6}}-\frac{b^{2}}{8 d \,a^{4} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{3}}-\frac{5 b^{4}}{2 d \,a^{6} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}+\frac{b}{32 d \,a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{4}}-\frac{2 b}{d \,a^{2} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)}-\frac{15 b \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 d \,a^{3}}-\frac{2 \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d a \sqrt{a^{2}-b^{2}}}-\frac{7 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{96 d \,a^{2}}+\frac{16 \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right) b^{2}}{d \,a^{3} \sqrt{a^{2}-b^{2}}}+\frac{11 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{16 d \,a^{2}}-\frac{11}{16 d \,a^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}-\frac{b \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{32 d \,a^{3}}+\frac{b^{2} \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{8 d \,a^{4}}-\frac{\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{3}}{2 d \,a^{5}}-\frac{2 b^{5}}{d \,a^{6} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)}-\frac{27 b^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{8 d \,a^{4}}+\frac{27 b^{2}}{8 d \,a^{4} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}-\frac{b}{2 d \,a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}+\frac{10 b^{3} \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{5}}+\frac{b \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{2 d \,a^{3}}+\frac{4 b^{3}}{d \,a^{4} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)}-\frac{1}{160 d \,a^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{5}}+\frac{7}{96 d \,a^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{3}}-\frac{26 \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right) b^{4}}{d \,a^{5} \sqrt{a^{2}-b^{2}}}-\frac{2 b^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,a^{3} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)}+\frac{4 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b^{4}}{d \,a^{5} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)}-\frac{2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b^{6}}{d \,a^{7} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)}+\frac{12 \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right) b^{6}}{d \,a^{7} \sqrt{a^{2}-b^{2}}}"," ",0,"1/2/d/a^5*b^3/tan(1/2*d*x+1/2*c)^2-6/d/a^7*b^5*ln(tan(1/2*d*x+1/2*c))-1/32/d/a^3*b*tan(1/2*d*x+1/2*c)^4+1/8/d/a^4*b^2*tan(1/2*d*x+1/2*c)^3-1/2/d/a^5*tan(1/2*d*x+1/2*c)^2*b^3+5/2/d/a^6*b^4*tan(1/2*d*x+1/2*c)-1/8/d/a^4/tan(1/2*d*x+1/2*c)^3*b^2-2/d/a^6/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)*b^5-5/2/d/a^6/tan(1/2*d*x+1/2*c)*b^4+1/32/d/a^3*b/tan(1/2*d*x+1/2*c)^4-15/4/d/a^3*b*ln(tan(1/2*d*x+1/2*c))-2/d/a^2/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)*b-2/d/a/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))-2/d/a^3/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)*b^2*tan(1/2*d*x+1/2*c)+16/d/a^3/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))*b^2+11/16/d/a^2*tan(1/2*d*x+1/2*c)-11/16/d/a^2/tan(1/2*d*x+1/2*c)+1/2/d/a^3*b*tan(1/2*d*x+1/2*c)^2-27/8/d/a^4*b^2*tan(1/2*d*x+1/2*c)+27/8/d/a^4/tan(1/2*d*x+1/2*c)*b^2-1/2/d/a^3*b/tan(1/2*d*x+1/2*c)^2+10/d/a^5*b^3*ln(tan(1/2*d*x+1/2*c))+4/d/a^4/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)*b^3+4/d/a^5/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)*tan(1/2*d*x+1/2*c)*b^4+1/160/d/a^2*tan(1/2*d*x+1/2*c)^5-1/160/d/a^2/tan(1/2*d*x+1/2*c)^5-7/96/d/a^2*tan(1/2*d*x+1/2*c)^3+7/96/d/a^2/tan(1/2*d*x+1/2*c)^3-26/d/a^5/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))*b^4-2/d/a^7/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)*tan(1/2*d*x+1/2*c)*b^6+12/d/a^7/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))*b^6","B"
192,1,465,311,0.327000," ","int(tan(d*x+c)^5/(a+b*sin(d*x+c))^3,x)","\frac{1}{16 d \left(a +b \right)^{3} \left(\sin \left(d x +c \right)-1\right)^{2}}+\frac{b}{16 d \left(a +b \right)^{4} \left(\sin \left(d x +c \right)-1\right)}+\frac{7 a}{16 d \left(a +b \right)^{4} \left(\sin \left(d x +c \right)-1\right)}-\frac{\ln \left(\sin \left(d x +c \right)-1\right) a^{2}}{2 d \left(a +b \right)^{5}}+\frac{5 \ln \left(\sin \left(d x +c \right)-1\right) a b}{16 d \left(a +b \right)^{5}}+\frac{\ln \left(\sin \left(d x +c \right)-1\right) b^{2}}{16 d \left(a +b \right)^{5}}-\frac{a^{5}}{2 d \left(a +b \right)^{3} \left(a -b \right)^{3} \left(a +b \sin \left(d x +c \right)\right)^{2}}+\frac{a^{7} \ln \left(a +b \sin \left(d x +c \right)\right)}{d \left(a +b \right)^{5} \left(a -b \right)^{5}}+\frac{13 a^{5} \ln \left(a +b \sin \left(d x +c \right)\right) b^{2}}{d \left(a +b \right)^{5} \left(a -b \right)^{5}}+\frac{10 a^{3} \ln \left(a +b \sin \left(d x +c \right)\right) b^{4}}{d \left(a +b \right)^{5} \left(a -b \right)^{5}}-\frac{a^{6}}{d \left(a +b \right)^{4} \left(a -b \right)^{4} \left(a +b \sin \left(d x +c \right)\right)}-\frac{5 a^{4} b^{2}}{d \left(a +b \right)^{4} \left(a -b \right)^{4} \left(a +b \sin \left(d x +c \right)\right)}+\frac{1}{16 d \left(a -b \right)^{3} \left(1+\sin \left(d x +c \right)\right)^{2}}+\frac{b}{16 d \left(a -b \right)^{4} \left(1+\sin \left(d x +c \right)\right)}-\frac{7 a}{16 d \left(a -b \right)^{4} \left(1+\sin \left(d x +c \right)\right)}-\frac{\ln \left(1+\sin \left(d x +c \right)\right) a^{2}}{2 d \left(a -b \right)^{5}}-\frac{5 \ln \left(1+\sin \left(d x +c \right)\right) a b}{16 d \left(a -b \right)^{5}}+\frac{\ln \left(1+\sin \left(d x +c \right)\right) b^{2}}{16 d \left(a -b \right)^{5}}"," ",0,"1/16/d/(a+b)^3/(sin(d*x+c)-1)^2+1/16/d/(a+b)^4/(sin(d*x+c)-1)*b+7/16/d/(a+b)^4/(sin(d*x+c)-1)*a-1/2/d/(a+b)^5*ln(sin(d*x+c)-1)*a^2+5/16/d/(a+b)^5*ln(sin(d*x+c)-1)*a*b+1/16/d/(a+b)^5*ln(sin(d*x+c)-1)*b^2-1/2/d*a^5/(a+b)^3/(a-b)^3/(a+b*sin(d*x+c))^2+1/d*a^7/(a+b)^5/(a-b)^5*ln(a+b*sin(d*x+c))+13/d*a^5/(a+b)^5/(a-b)^5*ln(a+b*sin(d*x+c))*b^2+10/d*a^3/(a+b)^5/(a-b)^5*ln(a+b*sin(d*x+c))*b^4-1/d*a^6/(a+b)^4/(a-b)^4/(a+b*sin(d*x+c))-5/d*a^4/(a+b)^4/(a-b)^4/(a+b*sin(d*x+c))*b^2+1/16/d/(a-b)^3/(1+sin(d*x+c))^2+1/16/d/(a-b)^4/(1+sin(d*x+c))*b-7/16/d/(a-b)^4/(1+sin(d*x+c))*a-1/2/d/(a-b)^5*ln(1+sin(d*x+c))*a^2-5/16/d/(a-b)^5*ln(1+sin(d*x+c))*a*b+1/16/d/(a-b)^5*ln(1+sin(d*x+c))*b^2","A"
193,1,323,224,0.305000," ","int(tan(d*x+c)^3/(a+b*sin(d*x+c))^3,x)","-\frac{1}{4 d \left(a +b \right)^{3} \left(\sin \left(d x +c \right)-1\right)}+\frac{\ln \left(\sin \left(d x +c \right)-1\right) a}{2 d \left(a +b \right)^{4}}-\frac{\ln \left(\sin \left(d x +c \right)-1\right) b}{4 d \left(a +b \right)^{4}}+\frac{a^{3}}{2 d \left(a +b \right)^{2} \left(a -b \right)^{2} \left(a +b \sin \left(d x +c \right)\right)^{2}}-\frac{a^{5} \ln \left(a +b \sin \left(d x +c \right)\right)}{d \left(a +b \right)^{4} \left(a -b \right)^{4}}-\frac{8 a^{3} \ln \left(a +b \sin \left(d x +c \right)\right) b^{2}}{d \left(a +b \right)^{4} \left(a -b \right)^{4}}-\frac{3 a \ln \left(a +b \sin \left(d x +c \right)\right) b^{4}}{d \left(a +b \right)^{4} \left(a -b \right)^{4}}+\frac{a^{4}}{d \left(a +b \right)^{3} \left(a -b \right)^{3} \left(a +b \sin \left(d x +c \right)\right)}+\frac{3 a^{2} b^{2}}{d \left(a +b \right)^{3} \left(a -b \right)^{3} \left(a +b \sin \left(d x +c \right)\right)}+\frac{1}{4 d \left(a -b \right)^{3} \left(1+\sin \left(d x +c \right)\right)}+\frac{\ln \left(1+\sin \left(d x +c \right)\right) a}{2 d \left(a -b \right)^{4}}+\frac{\ln \left(1+\sin \left(d x +c \right)\right) b}{4 d \left(a -b \right)^{4}}"," ",0,"-1/4/d/(a+b)^3/(sin(d*x+c)-1)+1/2/d/(a+b)^4*ln(sin(d*x+c)-1)*a-1/4/d/(a+b)^4*ln(sin(d*x+c)-1)*b+1/2/d*a^3/(a+b)^2/(a-b)^2/(a+b*sin(d*x+c))^2-1/d*a^5/(a+b)^4/(a-b)^4*ln(a+b*sin(d*x+c))-8/d*a^3/(a+b)^4/(a-b)^4*ln(a+b*sin(d*x+c))*b^2-3/d*a/(a+b)^4/(a-b)^4*ln(a+b*sin(d*x+c))*b^4+1/d*a^4/(a+b)^3/(a-b)^3/(a+b*sin(d*x+c))+3/d*a^2/(a+b)^3/(a-b)^3/(a+b*sin(d*x+c))*b^2+1/4/d/(a-b)^3/(1+sin(d*x+c))+1/2/d/(a-b)^4*ln(1+sin(d*x+c))*a+1/4/d/(a-b)^4*ln(1+sin(d*x+c))*b","A"
194,1,198,146,0.293000," ","int(tan(d*x+c)/(a+b*sin(d*x+c))^3,x)","-\frac{\ln \left(\sin \left(d x +c \right)-1\right)}{2 d \left(a +b \right)^{3}}-\frac{a}{2 d \left(a +b \right) \left(a -b \right) \left(a +b \sin \left(d x +c \right)\right)^{2}}-\frac{a^{2}}{d \left(a +b \right)^{2} \left(a -b \right)^{2} \left(a +b \sin \left(d x +c \right)\right)}-\frac{b^{2}}{d \left(a +b \right)^{2} \left(a -b \right)^{2} \left(a +b \sin \left(d x +c \right)\right)}+\frac{a^{3} \ln \left(a +b \sin \left(d x +c \right)\right)}{d \left(a +b \right)^{3} \left(a -b \right)^{3}}+\frac{3 a \ln \left(a +b \sin \left(d x +c \right)\right) b^{2}}{d \left(a +b \right)^{3} \left(a -b \right)^{3}}-\frac{\ln \left(1+\sin \left(d x +c \right)\right)}{2 \left(a -b \right)^{3} d}"," ",0,"-1/2/d/(a+b)^3*ln(sin(d*x+c)-1)-1/2/d*a/(a+b)/(a-b)/(a+b*sin(d*x+c))^2-1/d/(a+b)^2/(a-b)^2/(a+b*sin(d*x+c))*a^2-1/d/(a+b)^2/(a-b)^2/(a+b*sin(d*x+c))*b^2+1/d*a^3/(a+b)^3/(a-b)^3*ln(a+b*sin(d*x+c))+3/d*a/(a+b)^3/(a-b)^3*ln(a+b*sin(d*x+c))*b^2-1/2*ln(1+sin(d*x+c))/(a-b)^3/d","A"
195,1,74,73,0.175000," ","int(cot(d*x+c)/(a+b*sin(d*x+c))^3,x)","\frac{\ln \left(\sin \left(d x +c \right)\right)}{a^{3} d}-\frac{\ln \left(a +b \sin \left(d x +c \right)\right)}{a^{3} d}+\frac{1}{2 a d \left(a +b \sin \left(d x +c \right)\right)^{2}}+\frac{1}{a^{2} d \left(a +b \sin \left(d x +c \right)\right)}"," ",0,"ln(sin(d*x+c))/a^3/d-ln(a+b*sin(d*x+c))/a^3/d+1/2/a/d/(a+b*sin(d*x+c))^2+1/a^2/d/(a+b*sin(d*x+c))","A"
196,1,194,142,0.329000," ","int(cot(d*x+c)^3/(a+b*sin(d*x+c))^3,x)","\frac{\ln \left(a +b \sin \left(d x +c \right)\right)}{a^{3} d}-\frac{6 \ln \left(a +b \sin \left(d x +c \right)\right) b^{2}}{d \,a^{5}}-\frac{1}{a^{2} d \left(a +b \sin \left(d x +c \right)\right)}+\frac{3 b^{2}}{d \,a^{4} \left(a +b \sin \left(d x +c \right)\right)}-\frac{1}{2 a d \left(a +b \sin \left(d x +c \right)\right)^{2}}+\frac{b^{2}}{2 d \,a^{3} \left(a +b \sin \left(d x +c \right)\right)^{2}}-\frac{1}{2 a^{3} d \sin \left(d x +c \right)^{2}}-\frac{\ln \left(\sin \left(d x +c \right)\right)}{a^{3} d}+\frac{6 \ln \left(\sin \left(d x +c \right)\right) b^{2}}{d \,a^{5}}+\frac{3 b}{d \,a^{4} \sin \left(d x +c \right)}"," ",0,"ln(a+b*sin(d*x+c))/a^3/d-6/d/a^5*ln(a+b*sin(d*x+c))*b^2-1/a^2/d/(a+b*sin(d*x+c))+3/d/a^4/(a+b*sin(d*x+c))*b^2-1/2/a/d/(a+b*sin(d*x+c))^2+1/2/d/a^3/(a+b*sin(d*x+c))^2*b^2-1/2/a^3/d/sin(d*x+c)^2-ln(sin(d*x+c))/a^3/d+6/d/a^5*ln(sin(d*x+c))*b^2+3/d/a^4*b/sin(d*x+c)","A"
197,1,348,217,0.350000," ","int(cot(d*x+c)^5/(a+b*sin(d*x+c))^3,x)","-\frac{\ln \left(a +b \sin \left(d x +c \right)\right)}{a^{3} d}+\frac{12 \ln \left(a +b \sin \left(d x +c \right)\right) b^{2}}{d \,a^{5}}-\frac{15 \ln \left(a +b \sin \left(d x +c \right)\right) b^{4}}{d \,a^{7}}+\frac{1}{a^{2} d \left(a +b \sin \left(d x +c \right)\right)}-\frac{6 b^{2}}{d \,a^{4} \left(a +b \sin \left(d x +c \right)\right)}+\frac{5 b^{4}}{d \,a^{6} \left(a +b \sin \left(d x +c \right)\right)}+\frac{1}{2 a d \left(a +b \sin \left(d x +c \right)\right)^{2}}-\frac{b^{2}}{d \,a^{3} \left(a +b \sin \left(d x +c \right)\right)^{2}}+\frac{b^{4}}{2 d \,a^{5} \left(a +b \sin \left(d x +c \right)\right)^{2}}-\frac{1}{4 d \,a^{3} \sin \left(d x +c \right)^{4}}+\frac{1}{a^{3} d \sin \left(d x +c \right)^{2}}-\frac{3 b^{2}}{d \,a^{5} \sin \left(d x +c \right)^{2}}+\frac{\ln \left(\sin \left(d x +c \right)\right)}{a^{3} d}-\frac{12 \ln \left(\sin \left(d x +c \right)\right) b^{2}}{d \,a^{5}}+\frac{15 \ln \left(\sin \left(d x +c \right)\right) b^{4}}{d \,a^{7}}+\frac{b}{d \,a^{4} \sin \left(d x +c \right)^{3}}-\frac{6 b}{d \,a^{4} \sin \left(d x +c \right)}+\frac{10 b^{3}}{d \,a^{6} \sin \left(d x +c \right)}"," ",0,"-ln(a+b*sin(d*x+c))/a^3/d+12/d/a^5*ln(a+b*sin(d*x+c))*b^2-15/d/a^7*ln(a+b*sin(d*x+c))*b^4+1/a^2/d/(a+b*sin(d*x+c))-6/d/a^4/(a+b*sin(d*x+c))*b^2+5/d/a^6/(a+b*sin(d*x+c))*b^4+1/2/a/d/(a+b*sin(d*x+c))^2-1/d/a^3/(a+b*sin(d*x+c))^2*b^2+1/2/d/a^5/(a+b*sin(d*x+c))^2*b^4-1/4/d/a^3/sin(d*x+c)^4+1/a^3/d/sin(d*x+c)^2-3/d/a^5/sin(d*x+c)^2*b^2+ln(sin(d*x+c))/a^3/d-12/d/a^5*ln(sin(d*x+c))*b^2+15/d/a^7*ln(sin(d*x+c))*b^4+1/d/a^4*b/sin(d*x+c)^3-6/d/a^4*b/sin(d*x+c)+10/d*b^3/a^6/sin(d*x+c)","A"
198,1,922,443,0.316000," ","int(tan(d*x+c)^4/(a+b*sin(d*x+c))^3,x)","-\frac{1}{3 d \left(a +b \right)^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{3}}-\frac{1}{2 d \left(a +b \right)^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}+\frac{a}{d \left(a +b \right)^{4} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{b}{2 d \left(a +b \right)^{4} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{1}{3 d \left(a -b \right)^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}+\frac{1}{2 d \left(a -b \right)^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}+\frac{a}{d \left(a -b \right)^{4} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}+\frac{b}{2 d \left(a -b \right)^{4} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}+\frac{5 a^{5} \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{2}}{d \left(a -b \right)^{4} \left(a +b \right)^{4} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}+\frac{6 a^{3} \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{4}}{d \left(a -b \right)^{4} \left(a +b \right)^{4} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}+\frac{4 a^{6} \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b}{d \left(a -b \right)^{4} \left(a +b \right)^{4} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}+\frac{15 a^{4} \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{3}}{d \left(a -b \right)^{4} \left(a +b \right)^{4} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}+\frac{14 a^{2} \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{5}}{d \left(a -b \right)^{4} \left(a +b \right)^{4} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}+\frac{11 a^{5} \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b^{2}}{d \left(a -b \right)^{4} \left(a +b \right)^{4} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}+\frac{22 a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b^{4}}{d \left(a -b \right)^{4} \left(a +b \right)^{4} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}+\frac{4 a^{6} b}{d \left(a -b \right)^{4} \left(a +b \right)^{4} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}+\frac{7 a^{4} b^{3}}{d \left(a -b \right)^{4} \left(a +b \right)^{4} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}+\frac{2 a^{6} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \left(a -b \right)^{4} \left(a +b \right)^{4} \sqrt{a^{2}-b^{2}}}+\frac{21 a^{4} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right) b^{2}}{d \left(a -b \right)^{4} \left(a +b \right)^{4} \sqrt{a^{2}-b^{2}}}+\frac{12 a^{2} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right) b^{4}}{d \left(a -b \right)^{4} \left(a +b \right)^{4} \sqrt{a^{2}-b^{2}}}"," ",0,"-1/3/d/(a+b)^3/(tan(1/2*d*x+1/2*c)-1)^3-1/2/d/(a+b)^3/(tan(1/2*d*x+1/2*c)-1)^2+1/d/(a+b)^4/(tan(1/2*d*x+1/2*c)-1)*a-1/2/d/(a+b)^4/(tan(1/2*d*x+1/2*c)-1)*b-1/3/d/(a-b)^3/(tan(1/2*d*x+1/2*c)+1)^3+1/2/d/(a-b)^3/(tan(1/2*d*x+1/2*c)+1)^2+1/d/(a-b)^4/(tan(1/2*d*x+1/2*c)+1)*a+1/2/d/(a-b)^4/(tan(1/2*d*x+1/2*c)+1)*b+5/d*a^5/(a-b)^4/(a+b)^4/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)^3*b^2+6/d*a^3/(a-b)^4/(a+b)^4/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)^3*b^4+4/d*a^6/(a-b)^4/(a+b)^4/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)^2*b+15/d*a^4/(a-b)^4/(a+b)^4/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)^2*b^3+14/d*a^2/(a-b)^4/(a+b)^4/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)^2*b^5+11/d*a^5/(a-b)^4/(a+b)^4/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)*b^2+22/d*a^3/(a-b)^4/(a+b)^4/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)*b^4+4/d*a^6/(a-b)^4/(a+b)^4/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*b+7/d*a^4/(a-b)^4/(a+b)^4/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*b^3+2/d*a^6/(a-b)^4/(a+b)^4/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))+21/d*a^4/(a-b)^4/(a+b)^4/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))*b^2+12/d*a^2/(a-b)^4/(a+b)^4/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))*b^4","B"
199,1,766,327,0.289000," ","int(tan(d*x+c)^2/(a+b*sin(d*x+c))^3,x)","-\frac{1}{d \left(a +b \right)^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{1}{d \left(a -b \right)^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}-\frac{5 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{3} b^{2}}{d \left(a -b \right)^{3} \left(a +b \right)^{3} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}-\frac{2 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a \,b^{4}}{d \left(a -b \right)^{3} \left(a +b \right)^{3} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}-\frac{4 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{4} b}{d \left(a -b \right)^{3} \left(a +b \right)^{3} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}-\frac{11 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{2} b^{3}}{d \left(a -b \right)^{3} \left(a +b \right)^{3} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}-\frac{6 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{5}}{d \left(a -b \right)^{3} \left(a +b \right)^{3} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}-\frac{11 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) a^{3} b^{2}}{d \left(a -b \right)^{3} \left(a +b \right)^{3} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}-\frac{10 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) a \,b^{4}}{d \left(a -b \right)^{3} \left(a +b \right)^{3} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}-\frac{4 a^{4} b}{d \left(a -b \right)^{3} \left(a +b \right)^{3} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}-\frac{3 a^{2} b^{3}}{d \left(a -b \right)^{3} \left(a +b \right)^{3} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}-\frac{2 \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right) a^{4}}{d \left(a -b \right)^{3} \left(a +b \right)^{3} \sqrt{a^{2}-b^{2}}}-\frac{11 \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right) a^{2} b^{2}}{d \left(a -b \right)^{3} \left(a +b \right)^{3} \sqrt{a^{2}-b^{2}}}-\frac{2 \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right) b^{4}}{d \left(a -b \right)^{3} \left(a +b \right)^{3} \sqrt{a^{2}-b^{2}}}"," ",0,"-1/d/(a+b)^3/(tan(1/2*d*x+1/2*c)-1)-1/d/(a-b)^3/(tan(1/2*d*x+1/2*c)+1)-5/d/(a-b)^3/(a+b)^3/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)^3*a^3*b^2-2/d/(a-b)^3/(a+b)^3/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)^3*a*b^4-4/d/(a-b)^3/(a+b)^3/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)^2*a^4*b-11/d/(a-b)^3/(a+b)^3/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)^2*a^2*b^3-6/d/(a-b)^3/(a+b)^3/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)^2*b^5-11/d/(a-b)^3/(a+b)^3/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)*a^3*b^2-10/d/(a-b)^3/(a+b)^3/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)*a*b^4-4/d/(a-b)^3/(a+b)^3/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*a^4*b-3/d/(a-b)^3/(a+b)^3/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*a^2*b^3-2/d/(a-b)^3/(a+b)^3/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))*a^4-11/d/(a-b)^3/(a+b)^3/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))*a^2*b^2-2/d/(a-b)^3/(a+b)^3/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))*b^4","B"
200,1,729,191,0.303000," ","int(cot(d*x+c)^2/(a+b*sin(d*x+c))^3,x)","\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 d \,a^{3}}-\frac{1}{2 d \,a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}-\frac{3 b \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{4}}-\frac{5 b^{2} \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d a \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2} \left(a^{2}-b^{2}\right)}+\frac{6 b^{4} \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{3} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2} \left(a^{2}-b^{2}\right)}-\frac{4 b \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2} \left(a^{2}-b^{2}\right)}-\frac{3 b^{3} \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{2} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2} \left(a^{2}-b^{2}\right)}+\frac{10 b^{5} \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{4} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2} \left(a^{2}-b^{2}\right)}-\frac{11 b^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d a \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2} \left(a^{2}-b^{2}\right)}+\frac{14 b^{4} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,a^{3} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2} \left(a^{2}-b^{2}\right)}-\frac{4 b}{d \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2} \left(a^{2}-b^{2}\right)}+\frac{5 b^{3}}{d \,a^{2} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2} \left(a^{2}-b^{2}\right)}-\frac{2 \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \left(a^{2}-b^{2}\right)^{\frac{3}{2}}}+\frac{9 \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right) b^{2}}{d \,a^{2} \left(a^{2}-b^{2}\right)^{\frac{3}{2}}}-\frac{6 \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right) b^{4}}{d \,a^{4} \left(a^{2}-b^{2}\right)^{\frac{3}{2}}}"," ",0,"1/2/d/a^3*tan(1/2*d*x+1/2*c)-1/2/d/a^3/tan(1/2*d*x+1/2*c)-3/d/a^4*b*ln(tan(1/2*d*x+1/2*c))-5/d/a/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*b^2/(a^2-b^2)*tan(1/2*d*x+1/2*c)^3+6/d/a^3/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*b^4/(a^2-b^2)*tan(1/2*d*x+1/2*c)^3-4/d/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*b/(a^2-b^2)*tan(1/2*d*x+1/2*c)^2-3/d/a^2/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*b^3/(a^2-b^2)*tan(1/2*d*x+1/2*c)^2+10/d/a^4/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*b^5/(a^2-b^2)*tan(1/2*d*x+1/2*c)^2-11/d/a/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*b^2/(a^2-b^2)*tan(1/2*d*x+1/2*c)+14/d/a^3/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*b^4/(a^2-b^2)*tan(1/2*d*x+1/2*c)-4/d/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*b/(a^2-b^2)+5/d/a^2/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*b^3/(a^2-b^2)-2/d/(a^2-b^2)^(3/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))+9/d/a^2/(a^2-b^2)^(3/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))*b^2-6/d/a^4/(a^2-b^2)^(3/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))*b^4","B"
201,1,780,274,0.332000," ","int(cot(d*x+c)^4/(a+b*sin(d*x+c))^3,x)","\frac{\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)}{24 d \,a^{3}}-\frac{3 b \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{8 d \,a^{4}}-\frac{5 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{8 d \,a^{3}}+\frac{3 b^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,a^{5}}-\frac{1}{24 d \,a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{3}}+\frac{5}{8 d \,a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}-\frac{3 b^{2}}{d \,a^{5} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}+\frac{3 b}{8 d \,a^{4} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}+\frac{9 b \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{2 d \,a^{4}}-\frac{10 b^{3} \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{6}}+\frac{5 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{2}}{d \,a^{3} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}-\frac{10 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{4}}{d \,a^{5} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}+\frac{4 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b}{d \,a^{2} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}-\frac{\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{3}}{d \,a^{4} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}-\frac{18 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{5}}{d \,a^{6} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}+\frac{11 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b^{2}}{d \,a^{3} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}-\frac{26 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b^{4}}{d \,a^{5} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}+\frac{4 b}{d \,a^{2} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}-\frac{9 b^{3}}{d \,a^{4} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}+\frac{2 \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,a^{2} \sqrt{a^{2}-b^{2}}}-\frac{19 \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right) b^{2}}{d \,a^{4} \sqrt{a^{2}-b^{2}}}+\frac{20 \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right) b^{4}}{d \,a^{6} \sqrt{a^{2}-b^{2}}}"," ",0,"1/24/d/a^3*tan(1/2*d*x+1/2*c)^3-3/8/d/a^4*b*tan(1/2*d*x+1/2*c)^2-5/8/d/a^3*tan(1/2*d*x+1/2*c)+3/d/a^5*b^2*tan(1/2*d*x+1/2*c)-1/24/d/a^3/tan(1/2*d*x+1/2*c)^3+5/8/d/a^3/tan(1/2*d*x+1/2*c)-3/d/a^5/tan(1/2*d*x+1/2*c)*b^2+3/8/d/a^4*b/tan(1/2*d*x+1/2*c)^2+9/2/d/a^4*b*ln(tan(1/2*d*x+1/2*c))-10/d/a^6*b^3*ln(tan(1/2*d*x+1/2*c))+5/d/a^3/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)^3*b^2-10/d/a^5/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)^3*b^4+4/d/a^2/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)^2*b-1/d/a^4/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)^2*b^3-18/d/a^6/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)^2*b^5+11/d/a^3/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)*b^2-26/d/a^5/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)*b^4+4/d/a^2/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*b-9/d/a^4/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*b^3+2/d/a^2/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))-19/d/a^4/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))*b^2+20/d/a^6/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))*b^4","B"
202,1,1252,467,0.411000," ","int(cot(d*x+c)^6/(a+b*sin(d*x+c))^3,x)","\frac{\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)}{160 d \,a^{3}}-\frac{1}{160 d \,a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{5}}-\frac{13 b^{5}}{d \,a^{6} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}-\frac{3 b \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{64 d \,a^{4}}-\frac{45 b \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{8 d \,a^{4}}+\frac{17 b^{3}}{d \,a^{4} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}+\frac{11 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{16 d \,a^{3}}-\frac{11}{16 d \,a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}-\frac{27 b^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{4 d \,a^{5}}+\frac{27 b^{2}}{4 d \,a^{5} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}-\frac{3 b}{4 d \,a^{4} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}+\frac{25 b^{3} \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{6}}-\frac{2 \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,a^{2} \sqrt{a^{2}-b^{2}}}+\frac{3 b \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 d \,a^{4}}-\frac{4 b}{d \,a^{2} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}+\frac{b^{2} \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 d \,a^{5}}-\frac{5 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{3}}{4 d \,a^{6}}+\frac{3 b}{64 d \,a^{4} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{4}}+\frac{5 b^{3}}{4 d \,a^{6} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}-\frac{21 b^{5} \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{8}}+\frac{15 b^{4} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 d \,a^{7}}-\frac{b^{2}}{4 d \,a^{5} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{3}}-\frac{15 b^{4}}{2 d \,a^{7} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}+\frac{42 \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right) b^{6}}{d \,a^{8} \sqrt{a^{2}-b^{2}}}-\frac{26 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{7}}{d \,a^{8} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}-\frac{38 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b^{6}}{d \,a^{7} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}-\frac{14 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{6}}{d \,a^{7} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}+\frac{7}{96 d \,a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{3}}-\frac{7 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{96 d \,a^{3}}-\frac{5 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{2}}{d \,a^{3} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}+\frac{19 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{4}}{d \,a^{5} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}-\frac{4 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b}{d \,a^{2} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}+\frac{9 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{3}}{d \,a^{4} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}+\frac{21 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{5}}{d \,a^{6} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}-\frac{11 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b^{2}}{d \,a^{3} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}+\frac{49 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b^{4}}{d \,a^{5} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}+\frac{31 \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right) b^{2}}{d \,a^{4} \sqrt{a^{2}-b^{2}}}-\frac{71 \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right) b^{4}}{d \,a^{6} \sqrt{a^{2}-b^{2}}}"," ",0,"1/160/d/a^3*tan(1/2*d*x+1/2*c)^5-1/160/d/a^3/tan(1/2*d*x+1/2*c)^5-45/8/d/a^4*b*ln(tan(1/2*d*x+1/2*c))+11/16/d/a^3*tan(1/2*d*x+1/2*c)-11/16/d/a^3/tan(1/2*d*x+1/2*c)+3/4/d/a^4*b*tan(1/2*d*x+1/2*c)^2-27/4/d/a^5*b^2*tan(1/2*d*x+1/2*c)+27/4/d/a^5/tan(1/2*d*x+1/2*c)*b^2-3/4/d/a^4*b/tan(1/2*d*x+1/2*c)^2+25/d/a^6*b^3*ln(tan(1/2*d*x+1/2*c))-4/d/a^2/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*b+17/d/a^4/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*b^3-2/d/a^2/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))-13/d/a^6/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*b^5+3/64/d/a^4*b/tan(1/2*d*x+1/2*c)^4+5/4/d/a^6*b^3/tan(1/2*d*x+1/2*c)^2-21/d/a^8*b^5*ln(tan(1/2*d*x+1/2*c))-3/64/d/a^4*b*tan(1/2*d*x+1/2*c)^4+1/4/d/a^5*b^2*tan(1/2*d*x+1/2*c)^3-5/4/d/a^6*tan(1/2*d*x+1/2*c)^2*b^3+15/2/d/a^7*b^4*tan(1/2*d*x+1/2*c)-1/4/d/a^5/tan(1/2*d*x+1/2*c)^3*b^2-15/2/d/a^7/tan(1/2*d*x+1/2*c)*b^4-26/d/a^8/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)^2*b^7-38/d/a^7/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)*b^6+42/d/a^8/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))*b^6-14/d/a^7/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)^3*b^6-7/96/d/a^3*tan(1/2*d*x+1/2*c)^3+7/96/d/a^3/tan(1/2*d*x+1/2*c)^3+31/d/a^4/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))*b^2-71/d/a^6/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))*b^4+19/d/a^5/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)^3*b^4-4/d/a^2/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)^2*b+9/d/a^4/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)^2*b^3+21/d/a^6/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)^2*b^5-11/d/a^3/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)*b^2+49/d/a^5/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)*b^4-5/d/a^3/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)^3*b^2","B"
203,0,0,255,2.629000," ","int((a+b*sin(f*x+e))^3*(g*tan(f*x+e))^p,x)","\int \left(a +b \sin \left(f x +e \right)\right)^{3} \left(g \tan \left(f x +e \right)\right)^{p}\, dx"," ",0,"int((a+b*sin(f*x+e))^3*(g*tan(f*x+e))^p,x)","F"
204,0,0,176,2.489000," ","int((a+b*sin(f*x+e))^2*(g*tan(f*x+e))^p,x)","\int \left(a +b \sin \left(f x +e \right)\right)^{2} \left(g \tan \left(f x +e \right)\right)^{p}\, dx"," ",0,"int((a+b*sin(f*x+e))^2*(g*tan(f*x+e))^p,x)","F"
205,0,0,121,1.533000," ","int((a+b*sin(f*x+e))*(g*tan(f*x+e))^p,x)","\int \left(a +b \sin \left(f x +e \right)\right) \left(g \tan \left(f x +e \right)\right)^{p}\, dx"," ",0,"int((a+b*sin(f*x+e))*(g*tan(f*x+e))^p,x)","F"
206,0,0,256,0.796000," ","int((g*tan(f*x+e))^p/(a+b*sin(f*x+e)),x)","\int \frac{\left(g \tan \left(f x +e \right)\right)^{p}}{a +b \sin \left(f x +e \right)}\, dx"," ",0,"int((g*tan(f*x+e))^p/(a+b*sin(f*x+e)),x)","F"
207,0,0,679,1.567000," ","int((g*tan(f*x+e))^p/(a+b*sin(f*x+e))^2,x)","\int \frac{\left(g \tan \left(f x +e \right)\right)^{p}}{\left(a +b \sin \left(f x +e \right)\right)^{2}}\, dx"," ",0,"int((g*tan(f*x+e))^p/(a+b*sin(f*x+e))^2,x)","F"
208,0,0,25,1.523000," ","int((a+b*sin(f*x+e))^m*(g*tan(f*x+e))^p,x)","\int \left(a +b \sin \left(f x +e \right)\right)^{m} \left(g \tan \left(f x +e \right)\right)^{p}\, dx"," ",0,"int((a+b*sin(f*x+e))^m*(g*tan(f*x+e))^p,x)","F"