1,1,66,57,0.175000," ","int(sin(x)^4/(I+tan(x)),x)","\frac{i}{24 \left(i+\tan \left(x \right)\right)^{3}}-\frac{3 i}{16 \left(i+\tan \left(x \right)\right)}-\frac{5}{32 \left(i+\tan \left(x \right)\right)^{2}}+\frac{\ln \left(i+\tan \left(x \right)\right)}{32}+\frac{i}{8 \tan \left(x \right)-8 i}-\frac{1}{32 \left(\tan \left(x \right)-i\right)^{2}}-\frac{\ln \left(\tan \left(x \right)-i\right)}{32}"," ",0,"1/24*I/(I+tan(x))^3-3/16*I/(I+tan(x))-5/32/(I+tan(x))^2+1/32*ln(I+tan(x))+1/8*I/(tan(x)-I)-1/32/(tan(x)-I)^2-1/32*ln(tan(x)-I)","A"
2,1,81,21,0.172000," ","int(sin(x)^3/(I+tan(x)),x)","\frac{i}{\left(\tan \left(\frac{x}{2}\right)+i\right)^{4}}+\frac{2}{5 \left(\tan \left(\frac{x}{2}\right)+i\right)^{5}}-\frac{2}{3 \left(\tan \left(\frac{x}{2}\right)+i\right)^{3}}-\frac{1}{8 \left(\tan \left(\frac{x}{2}\right)+i\right)}-\frac{i}{4 \left(\tan \left(\frac{x}{2}\right)-i\right)^{2}}+\frac{1}{6 \left(\tan \left(\frac{x}{2}\right)-i\right)^{3}}+\frac{1}{8 \tan \left(\frac{x}{2}\right)-8 i}"," ",0,"I/(tan(1/2*x)+I)^4+2/5/(tan(1/2*x)+I)^5-2/3/(tan(1/2*x)+I)^3-1/8/(tan(1/2*x)+I)-1/4*I/(tan(1/2*x)-I)^2+1/6/(tan(1/2*x)-I)^3+1/8/(tan(1/2*x)-I)","B"
3,1,47,36,0.169000," ","int(sin(x)^2/(I+tan(x)),x)","-\frac{i}{4 \left(i+\tan \left(x \right)\right)}-\frac{1}{8 \left(i+\tan \left(x \right)\right)^{2}}+\frac{\ln \left(i+\tan \left(x \right)\right)}{16}+\frac{i}{8 \tan \left(x \right)-8 i}-\frac{\ln \left(\tan \left(x \right)-i\right)}{16}"," ",0,"-1/4*I/(I+tan(x))-1/8/(I+tan(x))^2+1/16*ln(I+tan(x))+1/8*I/(tan(x)-I)-1/16*ln(tan(x)-I)","A"
4,1,47,14,0.165000," ","int(sin(x)/(I+tan(x)),x)","\frac{i}{\left(\tan \left(\frac{x}{2}\right)+i\right)^{2}}+\frac{2}{3 \left(\tan \left(\frac{x}{2}\right)+i\right)^{3}}-\frac{1}{2 \left(\tan \left(\frac{x}{2}\right)+i\right)}+\frac{1}{2 \tan \left(\frac{x}{2}\right)-2 i}"," ",0,"I/(tan(1/2*x)+I)^2+2/3/(tan(1/2*x)+I)^3-1/2/(tan(1/2*x)+I)+1/2/(tan(1/2*x)-I)","B"
5,1,21,14,0.157000," ","int(csc(x)/(I+tan(x)),x)","\frac{2}{\tan \left(\frac{x}{2}\right)+i}-i \ln \left(\tan \left(\frac{x}{2}\right)\right)"," ",0,"2/(tan(1/2*x)+I)-I*ln(tan(1/2*x))","A"
6,1,20,16,0.174000," ","int(csc(x)^2/(I+tan(x)),x)","-\ln \left(i+\tan \left(x \right)\right)+\ln \left(\tan \left(x \right)\right)+\frac{i}{\tan \left(x \right)}"," ",0,"-ln(I+tan(x))+ln(tan(x))+I/tan(x)","A"
7,1,42,18,0.177000," ","int(csc(x)^3/(I+tan(x)),x)","-\frac{\tan \left(\frac{x}{2}\right)}{2}-\frac{i \left(\tan^{2}\left(\frac{x}{2}\right)\right)}{8}+\frac{i}{8 \tan \left(\frac{x}{2}\right)^{2}}+\frac{i \ln \left(\tan \left(\frac{x}{2}\right)\right)}{2}-\frac{1}{2 \tan \left(\frac{x}{2}\right)}"," ",0,"-1/2*tan(1/2*x)-1/8*I*tan(1/2*x)^2+1/8*I/tan(1/2*x)^2+1/2*I*ln(tan(1/2*x))-1/2/tan(1/2*x)","B"
8,1,15,14,0.184000," ","int(csc(x)^4/(I+tan(x)),x)","-\frac{1}{2 \tan \left(x \right)^{2}}+\frac{i}{3 \tan \left(x \right)^{3}}"," ",0,"-1/2/tan(x)^2+1/3*I/tan(x)^3","A"
9,1,58,29,0.189000," ","int(csc(x)^5/(I+tan(x)),x)","-\frac{\tan \left(\frac{x}{2}\right)}{8}-\frac{i \left(\tan^{4}\left(\frac{x}{2}\right)\right)}{64}-\frac{\left(\tan^{3}\left(\frac{x}{2}\right)\right)}{24}-\frac{1}{24 \tan \left(\frac{x}{2}\right)^{3}}+\frac{i}{64 \tan \left(\frac{x}{2}\right)^{4}}+\frac{i \ln \left(\tan \left(\frac{x}{2}\right)\right)}{8}-\frac{1}{8 \tan \left(\frac{x}{2}\right)}"," ",0,"-1/8*tan(1/2*x)-1/64*I*tan(1/2*x)^4-1/24*tan(1/2*x)^3-1/24/tan(1/2*x)^3+1/64*I/tan(1/2*x)^4+1/8*I*ln(tan(1/2*x))-1/8/tan(1/2*x)","A"
10,1,28,27,0.186000," ","int(csc(x)^6/(I+tan(x)),x)","-\frac{1}{2 \tan \left(x \right)^{2}}+\frac{i}{3 \tan \left(x \right)^{3}}-\frac{1}{4 \tan \left(x \right)^{4}}+\frac{i}{5 \tan \left(x \right)^{5}}"," ",0,"-1/2/tan(x)^2+1/3*I/tan(x)^3-1/4/tan(x)^4+1/5*I/tan(x)^5","A"
11,1,113,93,0.320000," ","int(sin(d*x+c)^5*(a+b*tan(d*x+c)),x)","-\frac{8 a \cos \left(d x +c \right)}{15 d}-\frac{a \cos \left(d x +c \right) \left(\sin^{4}\left(d x +c \right)\right)}{5 d}-\frac{4 a \cos \left(d x +c \right) \left(\sin^{2}\left(d x +c \right)\right)}{15 d}-\frac{b \left(\sin^{5}\left(d x +c \right)\right)}{5 d}-\frac{b \left(\sin^{3}\left(d x +c \right)\right)}{3 d}-\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}"," ",0,"-8/15*a*cos(d*x+c)/d-1/5/d*a*cos(d*x+c)*sin(d*x+c)^4-4/15/d*a*cos(d*x+c)*sin(d*x+c)^2-1/5*b*sin(d*x+c)^5/d-1/3*b*sin(d*x+c)^3/d-b*sin(d*x+c)/d+1/d*b*ln(sec(d*x+c)+tan(d*x+c))","A"
12,1,92,77,0.313000," ","int(sin(d*x+c)^4*(a+b*tan(d*x+c)),x)","-\frac{a \cos \left(d x +c \right) \left(\sin^{3}\left(d x +c \right)\right)}{4 d}-\frac{3 a \cos \left(d x +c \right) \sin \left(d x +c \right)}{8 d}+\frac{3 a x}{8}+\frac{3 c a}{8 d}-\frac{b \left(\sin^{4}\left(d x +c \right)\right)}{4 d}-\frac{b \left(\sin^{2}\left(d x +c \right)\right)}{2 d}-\frac{b \ln \left(\cos \left(d x +c \right)\right)}{d}"," ",0,"-1/4/d*a*cos(d*x+c)*sin(d*x+c)^3-3/8*a*cos(d*x+c)*sin(d*x+c)/d+3/8*a*x+3/8/d*c*a-1/4/d*b*sin(d*x+c)^4-1/2/d*b*sin(d*x+c)^2-b*ln(cos(d*x+c))/d","A"
13,1,79,65,0.299000," ","int(sin(d*x+c)^3*(a+b*tan(d*x+c)),x)","-\frac{a \cos \left(d x +c \right) \left(\sin^{2}\left(d x +c \right)\right)}{3 d}-\frac{2 a \cos \left(d x +c \right)}{3 d}-\frac{b \left(\sin^{3}\left(d x +c \right)\right)}{3 d}-\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}"," ",0,"-1/3/d*a*cos(d*x+c)*sin(d*x+c)^2-2/3*a*cos(d*x+c)/d-1/3*b*sin(d*x+c)^3/d-b*sin(d*x+c)/d+1/d*b*ln(sec(d*x+c)+tan(d*x+c))","A"
14,1,58,45,0.184000," ","int(sin(d*x+c)^2*(a+b*tan(d*x+c)),x)","-\frac{a \cos \left(d x +c \right) \sin \left(d x +c \right)}{2 d}+\frac{a x}{2}+\frac{c a}{2 d}-\frac{b \left(\sin^{2}\left(d x +c \right)\right)}{2 d}-\frac{b \ln \left(\cos \left(d x +c \right)\right)}{d}"," ",0,"-1/2*a*cos(d*x+c)*sin(d*x+c)/d+1/2*a*x+1/2/d*c*a-1/2/d*b*sin(d*x+c)^2-b*ln(cos(d*x+c))/d","A"
15,1,45,37,0.182000," ","int(sin(d*x+c)*(a+b*tan(d*x+c)),x)","-\frac{a \cos \left(d x +c \right)}{d}-\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}"," ",0,"-a*cos(d*x+c)/d-b*sin(d*x+c)/d+1/d*b*ln(sec(d*x+c)+tan(d*x+c))","A"
16,1,42,26,0.280000," ","int(csc(d*x+c)*(a+b*tan(d*x+c)),x)","\frac{b \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{a \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{d}"," ",0,"1/d*b*ln(sec(d*x+c)+tan(d*x+c))+1/d*a*ln(csc(d*x+c)-cot(d*x+c))","A"
17,1,26,25,0.366000," ","int(csc(d*x+c)^2*(a+b*tan(d*x+c)),x)","-\frac{a \cot \left(d x +c \right)}{d}+\frac{b \ln \left(\tan \left(d x +c \right)\right)}{d}"," ",0,"-a*cot(d*x+c)/d+b*ln(tan(d*x+c))/d","A"
18,1,75,56,0.386000," ","int(csc(d*x+c)^3*(a+b*tan(d*x+c)),x)","-\frac{a \cot \left(d x +c \right) \csc \left(d x +c \right)}{2 d}+\frac{a \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{2 d}-\frac{b}{d \sin \left(d x +c \right)}+\frac{b \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}"," ",0,"-1/2*a*cot(d*x+c)*csc(d*x+c)/d+1/2/d*a*ln(csc(d*x+c)-cot(d*x+c))-1/d*b/sin(d*x+c)+1/d*b*ln(sec(d*x+c)+tan(d*x+c))","A"
19,1,60,53,0.377000," ","int(csc(d*x+c)^4*(a+b*tan(d*x+c)),x)","-\frac{2 a \cot \left(d x +c \right)}{3 d}-\frac{a \cot \left(d x +c \right) \left(\csc^{2}\left(d x +c \right)\right)}{3 d}-\frac{b}{2 d \sin \left(d x +c \right)^{2}}+\frac{b \ln \left(\tan \left(d x +c \right)\right)}{d}"," ",0,"-2/3*a*cot(d*x+c)/d-1/3/d*a*cot(d*x+c)*csc(d*x+c)^2-1/2/d*b/sin(d*x+c)^2+b*ln(tan(d*x+c))/d","A"
20,1,109,90,0.392000," ","int(csc(d*x+c)^5*(a+b*tan(d*x+c)),x)","-\frac{a \cot \left(d x +c \right) \left(\csc^{3}\left(d x +c \right)\right)}{4 d}-\frac{3 a \cot \left(d x +c \right) \csc \left(d x +c \right)}{8 d}+\frac{3 a \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{8 d}-\frac{b}{3 d \sin \left(d x +c \right)^{3}}-\frac{b}{d \sin \left(d x +c \right)}+\frac{b \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}"," ",0,"-1/4*a*cot(d*x+c)*csc(d*x+c)^3/d-3/8*a*cot(d*x+c)*csc(d*x+c)/d+3/8/d*a*ln(csc(d*x+c)-cot(d*x+c))-1/3/d*b/sin(d*x+c)^3-1/d*b/sin(d*x+c)+1/d*b*ln(sec(d*x+c)+tan(d*x+c))","A"
21,1,94,81,0.401000," ","int(csc(d*x+c)^6*(a+b*tan(d*x+c)),x)","-\frac{8 a \cot \left(d x +c \right)}{15 d}-\frac{a \cot \left(d x +c \right) \left(\csc^{4}\left(d x +c \right)\right)}{5 d}-\frac{4 a \cot \left(d x +c \right) \left(\csc^{2}\left(d x +c \right)\right)}{15 d}-\frac{b}{4 d \sin \left(d x +c \right)^{4}}-\frac{b}{2 d \sin \left(d x +c \right)^{2}}+\frac{b \ln \left(\tan \left(d x +c \right)\right)}{d}"," ",0,"-8/15*a*cot(d*x+c)/d-1/5/d*a*cot(d*x+c)*csc(d*x+c)^4-4/15/d*a*cot(d*x+c)*csc(d*x+c)^2-1/4/d*b/sin(d*x+c)^4-1/2/d*b/sin(d*x+c)^2+b*ln(tan(d*x+c))/d","A"
22,1,204,107,0.418000," ","int(sin(d*x+c)^4*(a+b*tan(d*x+c))^2,x)","-\frac{a^{2} \cos \left(d x +c \right) \left(\sin^{3}\left(d x +c \right)\right)}{4 d}-\frac{3 a^{2} \cos \left(d x +c \right) \sin \left(d x +c \right)}{8 d}+\frac{3 a^{2} x}{8}+\frac{3 a^{2} c}{8 d}-\frac{a b \left(\sin^{4}\left(d x +c \right)\right)}{2 d}-\frac{a b \left(\sin^{2}\left(d x +c \right)\right)}{d}-\frac{2 a b \ln \left(\cos \left(d x +c \right)\right)}{d}+\frac{b^{2} \left(\sin^{7}\left(d x +c \right)\right)}{d \cos \left(d x +c \right)}+\frac{b^{2} \cos \left(d x +c \right) \left(\sin^{5}\left(d x +c \right)\right)}{d}+\frac{5 b^{2} \cos \left(d x +c \right) \left(\sin^{3}\left(d x +c \right)\right)}{4 d}+\frac{15 b^{2} \cos \left(d x +c \right) \sin \left(d x +c \right)}{8 d}-\frac{15 b^{2} x}{8}-\frac{15 c \,b^{2}}{8 d}"," ",0,"-1/4/d*a^2*cos(d*x+c)*sin(d*x+c)^3-3/8/d*a^2*cos(d*x+c)*sin(d*x+c)+3/8*a^2*x+3/8/d*a^2*c-1/2/d*a*b*sin(d*x+c)^4-1/d*a*b*sin(d*x+c)^2-2*a*b*ln(cos(d*x+c))/d+1/d*b^2*sin(d*x+c)^7/cos(d*x+c)+1/d*b^2*cos(d*x+c)*sin(d*x+c)^5+5/4/d*b^2*cos(d*x+c)*sin(d*x+c)^3+15/8/d*b^2*cos(d*x+c)*sin(d*x+c)-15/8*b^2*x-15/8/d*c*b^2","A"
23,1,167,116,0.398000," ","int(sin(d*x+c)^3*(a+b*tan(d*x+c))^2,x)","-\frac{\cos \left(d x +c \right) \left(\sin^{2}\left(d x +c \right)\right) a^{2}}{3 d}-\frac{2 a^{2} \cos \left(d x +c \right)}{3 d}-\frac{2 a b \left(\sin^{3}\left(d x +c \right)\right)}{3 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^{6}\left(d x +c \right)\right)}{d \cos \left(d x +c \right)}+\frac{8 b^{2} \cos \left(d x +c \right)}{3 d}+\frac{b^{2} \cos \left(d x +c \right) \left(\sin^{4}\left(d x +c \right)\right)}{d}+\frac{4 b^{2} \cos \left(d x +c \right) \left(\sin^{2}\left(d x +c \right)\right)}{3 d}"," ",0,"-1/3/d*cos(d*x+c)*sin(d*x+c)^2*a^2-2/3*a^2*cos(d*x+c)/d-2/3*a*b*sin(d*x+c)^3/d-2*a*b*sin(d*x+c)/d+2/d*a*b*ln(sec(d*x+c)+tan(d*x+c))+1/d*b^2*sin(d*x+c)^6/cos(d*x+c)+8/3*b^2*cos(d*x+c)/d+1/d*b^2*cos(d*x+c)*sin(d*x+c)^4+4/3/d*b^2*cos(d*x+c)*sin(d*x+c)^2","A"
24,1,145,70,0.338000," ","int(sin(d*x+c)^2*(a+b*tan(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{a b \left(\sin^{2}\left(d x +c \right)\right)}{d}-\frac{2 a b \ln \left(\cos \left(d x +c \right)\right)}{d}+\frac{b^{2} \left(\sin^{5}\left(d x +c \right)\right)}{d \cos \left(d x +c \right)}+\frac{b^{2} \cos \left(d x +c \right) \left(\sin^{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 c \,b^{2}}{2 d}"," ",0,"-1/2/d*a^2*cos(d*x+c)*sin(d*x+c)+1/2*a^2*x+1/2/d*a^2*c-1/d*a*b*sin(d*x+c)^2-2*a*b*ln(cos(d*x+c))/d+1/d*b^2*sin(d*x+c)^5/cos(d*x+c)+1/d*b^2*cos(d*x+c)*sin(d*x+c)^3+3/2/d*b^2*cos(d*x+c)*sin(d*x+c)-3/2*b^2*x-3/2/d*c*b^2","B"
25,1,108,68,0.311000," ","int(sin(d*x+c)*(a+b*tan(d*x+c))^2,x)","-\frac{a^{2} \cos \left(d x +c \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^{4}\left(d x +c \right)\right)}{d \cos \left(d x +c \right)}+\frac{b^{2} \cos \left(d x +c \right) \left(\sin^{2}\left(d x +c \right)\right)}{d}+\frac{2 b^{2} \cos \left(d x +c \right)}{d}"," ",0,"-a^2*cos(d*x+c)/d-2*a*b*sin(d*x+c)/d+2/d*a*b*ln(sec(d*x+c)+tan(d*x+c))+1/d*b^2*sin(d*x+c)^4/cos(d*x+c)+1/d*b^2*cos(d*x+c)*sin(d*x+c)^2+2*b^2*cos(d*x+c)/d","A"
26,1,61,43,0.327000," ","int(csc(d*x+c)*(a+b*tan(d*x+c))^2,x)","\frac{a^{2} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\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}}{d \cos \left(d x +c \right)}"," ",0,"1/d*a^2*ln(csc(d*x+c)-cot(d*x+c))+2/d*a*b*ln(sec(d*x+c)+tan(d*x+c))+1/d*b^2/cos(d*x+c)","A"
27,1,43,42,0.472000," ","int(csc(d*x+c)^2*(a+b*tan(d*x+c))^2,x)","-\frac{a^{2} \cot \left(d x +c \right)}{d}+\frac{2 a b \ln \left(\tan \left(d x +c \right)\right)}{d}+\frac{b^{2} \tan \left(d x +c \right)}{d}"," ",0,"-a^2*cot(d*x+c)/d+2*a*b*ln(tan(d*x+c))/d+b^2*tan(d*x+c)/d","A"
28,1,120,91,0.527000," ","int(csc(d*x+c)^3*(a+b*tan(d*x+c))^2,x)","-\frac{a^{2} \cot \left(d x +c \right) \csc \left(d x +c \right)}{2 d}+\frac{a^{2} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{2 d}-\frac{2 a b}{d \sin \left(d x +c \right)}+\frac{2 a b \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{b^{2}}{d \cos \left(d x +c \right)}+\frac{b^{2} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{d}"," ",0,"-1/2*a^2*cot(d*x+c)*csc(d*x+c)/d+1/2/d*a^2*ln(csc(d*x+c)-cot(d*x+c))-2/d*a*b/sin(d*x+c)+2/d*a*b*ln(sec(d*x+c)+tan(d*x+c))+1/d*b^2/cos(d*x+c)+1/d*b^2*ln(csc(d*x+c)-cot(d*x+c))","A"
29,1,104,77,0.556000," ","int(csc(d*x+c)^4*(a+b*tan(d*x+c))^2,x)","-\frac{2 a^{2} \cot \left(d x +c \right)}{3 d}-\frac{a^{2} \cot \left(d x +c \right) \left(\csc^{2}\left(d x +c \right)\right)}{3 d}-\frac{a b}{d \sin \left(d x +c \right)^{2}}+\frac{2 a b \ln \left(\tan \left(d x +c \right)\right)}{d}+\frac{b^{2}}{d \sin \left(d x +c \right) \cos \left(d x +c \right)}-\frac{2 b^{2} \cot \left(d x +c \right)}{d}"," ",0,"-2/3*a^2*cot(d*x+c)/d-1/3/d*a^2*cot(d*x+c)*csc(d*x+c)^2-1/d*a*b/sin(d*x+c)^2+2*a*b*ln(tan(d*x+c))/d+1/d*b^2/sin(d*x+c)/cos(d*x+c)-2/d*b^2*cot(d*x+c)","A"
30,1,183,151,0.431000," ","int(csc(d*x+c)^5*(a+b*tan(d*x+c))^2,x)","-\frac{a^{2} \cot \left(d x +c \right) \left(\csc^{3}\left(d x +c \right)\right)}{4 d}-\frac{3 a^{2} \cot \left(d x +c \right) \csc \left(d x +c \right)}{8 d}+\frac{3 a^{2} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{8 d}-\frac{2 a b}{3 d \sin \left(d x +c \right)^{3}}-\frac{2 a b}{d \sin \left(d x +c \right)}+\frac{2 a b \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}-\frac{b^{2}}{2 d \sin \left(d x +c \right)^{2} \cos \left(d x +c \right)}+\frac{3 b^{2}}{2 d \cos \left(d x +c \right)}+\frac{3 b^{2} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{2 d}"," ",0,"-1/4*a^2*cot(d*x+c)*csc(d*x+c)^3/d-3/8*a^2*cot(d*x+c)*csc(d*x+c)/d+3/8/d*a^2*ln(csc(d*x+c)-cot(d*x+c))-2/3/d*a*b/sin(d*x+c)^3-2/d*a*b/sin(d*x+c)+2/d*a*b*ln(sec(d*x+c)+tan(d*x+c))-1/2/d*b^2/sin(d*x+c)^2/cos(d*x+c)+3/2/d*b^2/cos(d*x+c)+3/2/d*b^2*ln(csc(d*x+c)-cot(d*x+c))","A"
31,1,166,116,0.522000," ","int(csc(d*x+c)^6*(a+b*tan(d*x+c))^2,x)","-\frac{8 a^{2} \cot \left(d x +c \right)}{15 d}-\frac{a^{2} \cot \left(d x +c \right) \left(\csc^{4}\left(d x +c \right)\right)}{5 d}-\frac{4 a^{2} \cot \left(d x +c \right) \left(\csc^{2}\left(d x +c \right)\right)}{15 d}-\frac{a b}{2 d \sin \left(d x +c \right)^{4}}-\frac{a b}{d \sin \left(d x +c \right)^{2}}+\frac{2 a b \ln \left(\tan \left(d x +c \right)\right)}{d}-\frac{b^{2}}{3 d \sin \left(d x +c \right)^{3} \cos \left(d x +c \right)}+\frac{4 b^{2}}{3 d \sin \left(d x +c \right) \cos \left(d x +c \right)}-\frac{8 b^{2} \cot \left(d x +c \right)}{3 d}"," ",0,"-8/15*a^2*cot(d*x+c)/d-1/5/d*a^2*cot(d*x+c)*csc(d*x+c)^4-4/15/d*a^2*cot(d*x+c)*csc(d*x+c)^2-1/2/d*a*b/sin(d*x+c)^4-1/d*a*b/sin(d*x+c)^2+2*a*b*ln(tan(d*x+c))/d-1/3/d*b^2/sin(d*x+c)^3/cos(d*x+c)+4/3/d*b^2/sin(d*x+c)/cos(d*x+c)-8/3/d*b^2*cot(d*x+c)","A"
32,1,271,195,0.437000," ","int(sin(d*x+c)^3*(a+b*tan(d*x+c))^3,x)","-\frac{\cos \left(d x +c \right) \left(\sin^{2}\left(d x +c \right)\right) a^{3}}{3 d}-\frac{2 a^{3} \cos \left(d x +c \right)}{3 d}-\frac{a^{2} b \left(\sin^{3}\left(d x +c \right)\right)}{d}-\frac{3 a^{2} b \sin \left(d x +c \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 b^{2} a \left(\sin^{6}\left(d x +c \right)\right)}{d \cos \left(d x +c \right)}+\frac{8 a \,b^{2} \cos \left(d x +c \right)}{d}+\frac{3 b^{2} a \cos \left(d x +c \right) \left(\sin^{4}\left(d x +c \right)\right)}{d}+\frac{4 \cos \left(d x +c \right) \left(\sin^{2}\left(d x +c \right)\right) a \,b^{2}}{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,"-1/3/d*cos(d*x+c)*sin(d*x+c)^2*a^3-2/3*a^3*cos(d*x+c)/d-a^2*b*sin(d*x+c)^3/d-3*a^2*b*sin(d*x+c)/d+3/d*a^2*b*ln(sec(d*x+c)+tan(d*x+c))+3/d*b^2*a*sin(d*x+c)^6/cos(d*x+c)+8*a*b^2*cos(d*x+c)/d+3/d*b^2*a*cos(d*x+c)*sin(d*x+c)^4+4/d*cos(d*x+c)*sin(d*x+c)^2*a*b^2+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*b^3*sin(d*x+c)/d-5/2/d*b^3*ln(sec(d*x+c)+tan(d*x+c))","A"
33,1,226,97,0.373000," ","int(sin(d*x+c)^2*(a+b*tan(d*x+c))^3,x)","-\frac{a^{3} \sin \left(d x +c \right) \cos \left(d x +c \right)}{2 d}+\frac{a^{3} x}{2}+\frac{a^{3} c}{2 d}-\frac{3 a^{2} b \left(\sin^{2}\left(d x +c \right)\right)}{2 d}-\frac{3 a^{2} b \ln \left(\cos \left(d x +c \right)\right)}{d}+\frac{3 b^{2} a \left(\sin^{5}\left(d x +c \right)\right)}{d \cos \left(d x +c \right)}+\frac{3 b^{2} a \cos \left(d x +c \right) \left(\sin^{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 b^{2} a x}{2}-\frac{9 a \,b^{2} c}{2 d}+\frac{b^{3} \left(\sin^{6}\left(d x +c \right)\right)}{2 d \cos \left(d x +c \right)^{2}}+\frac{b^{3} \left(\sin^{4}\left(d x +c \right)\right)}{2 d}+\frac{\left(\sin^{2}\left(d x +c \right)\right) b^{3}}{d}+\frac{2 b^{3} \ln \left(\cos \left(d x +c \right)\right)}{d}"," ",0,"-1/2/d*a^3*sin(d*x+c)*cos(d*x+c)+1/2*a^3*x+1/2/d*a^3*c-3/2/d*a^2*b*sin(d*x+c)^2-3/d*a^2*b*ln(cos(d*x+c))+3/d*b^2*a*sin(d*x+c)^5/cos(d*x+c)+3/d*b^2*a*cos(d*x+c)*sin(d*x+c)^3+9/2*a*b^2*cos(d*x+c)*sin(d*x+c)/d-9/2*b^2*a*x-9/2/d*a*b^2*c+1/2/d*b^3*sin(d*x+c)^6/cos(d*x+c)^2+1/2/d*b^3*sin(d*x+c)^4+1/d*sin(d*x+c)^2*b^3+2*b^3*ln(cos(d*x+c))/d","B"
34,1,193,127,0.345000," ","int(sin(d*x+c)*(a+b*tan(d*x+c))^3,x)","-\frac{a^{3} \cos \left(d x +c \right)}{d}-\frac{3 a^{2} b \sin \left(d x +c \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 b^{2} a \left(\sin^{4}\left(d x +c \right)\right)}{d \cos \left(d x +c \right)}+\frac{3 \cos \left(d x +c \right) \left(\sin^{2}\left(d x +c \right)\right) a \,b^{2}}{d}+\frac{6 a \,b^{2} \cos \left(d x +c \right)}{d}+\frac{b^{3} \left(\sin^{5}\left(d x +c \right)\right)}{2 d \cos \left(d x +c \right)^{2}}+\frac{b^{3} \left(\sin^{3}\left(d x +c \right)\right)}{2 d}+\frac{3 b^{3} \sin \left(d x +c \right)}{2 d}-\frac{3 b^{3} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{2 d}"," ",0,"-a^3*cos(d*x+c)/d-3*a^2*b*sin(d*x+c)/d+3/d*a^2*b*ln(sec(d*x+c)+tan(d*x+c))+3/d*b^2*a*sin(d*x+c)^4/cos(d*x+c)+3/d*cos(d*x+c)*sin(d*x+c)^2*a*b^2+6*a*b^2*cos(d*x+c)/d+1/2/d*b^3*sin(d*x+c)^5/cos(d*x+c)^2+1/2*b^3*sin(d*x+c)^3/d+3/2*b^3*sin(d*x+c)/d-3/2/d*b^3*ln(sec(d*x+c)+tan(d*x+c))","A"
35,1,125,82,0.347000," ","int(csc(d*x+c)*(a+b*tan(d*x+c))^3,x)","\frac{a^{3} \ln \left(\csc \left(d x +c \right)-\cot \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 b^{2} a}{d \cos \left(d x +c \right)}+\frac{b^{3} \left(\sin^{3}\left(d x +c \right)\right)}{2 d \cos \left(d x +c \right)^{2}}+\frac{b^{3} \sin \left(d x +c \right)}{2 d}-\frac{b^{3} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{2 d}"," ",0,"1/d*a^3*ln(csc(d*x+c)-cot(d*x+c))+3/d*a^2*b*ln(sec(d*x+c)+tan(d*x+c))+3/d*b^2*a/cos(d*x+c)+1/2/d*b^3*sin(d*x+c)^3/cos(d*x+c)^2+1/2*b^3*sin(d*x+c)/d-1/2/d*b^3*ln(sec(d*x+c)+tan(d*x+c))","A"
36,1,63,62,0.524000," ","int(csc(d*x+c)^2*(a+b*tan(d*x+c))^3,x)","-\frac{a^{3} \cot \left(d x +c \right)}{d}+\frac{3 a^{2} b \ln \left(\tan \left(d x +c \right)\right)}{d}+\frac{3 a \,b^{2} \tan \left(d x +c \right)}{d}+\frac{b^{3}}{2 d \cos \left(d x +c \right)^{2}}"," ",0,"-a^3*cot(d*x+c)/d+3*a^2*b*ln(tan(d*x+c))/d+3*a*b^2*tan(d*x+c)/d+1/2/d*b^3/cos(d*x+c)^2","A"
37,1,170,133,0.515000," ","int(csc(d*x+c)^3*(a+b*tan(d*x+c))^3,x)","-\frac{a^{3} \cot \left(d x +c \right) \csc \left(d x +c \right)}{2 d}+\frac{a^{3} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{2 d}-\frac{3 a^{2} b}{d \sin \left(d x +c \right)}+\frac{3 a^{2} b \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{3 b^{2} a}{d \cos \left(d x +c \right)}+\frac{3 b^{2} a \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{d}+\frac{b^{3} \sec \left(d x +c \right) \tan \left(d x +c \right)}{2 d}+\frac{b^{3} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{2 d}"," ",0,"-1/2*a^3*cot(d*x+c)*csc(d*x+c)/d+1/2/d*a^3*ln(csc(d*x+c)-cot(d*x+c))-3/d*a^2*b/sin(d*x+c)+3/d*a^2*b*ln(sec(d*x+c)+tan(d*x+c))+3/d*b^2*a/cos(d*x+c)+3/d*b^2*a*ln(csc(d*x+c)-cot(d*x+c))+1/2*b^3*sec(d*x+c)*tan(d*x+c)/d+1/2/d*b^3*ln(sec(d*x+c)+tan(d*x+c))","A"
38,1,141,107,0.545000," ","int(csc(d*x+c)^4*(a+b*tan(d*x+c))^3,x)","-\frac{2 a^{3} \cot \left(d x +c \right)}{3 d}-\frac{a^{3} \cot \left(d x +c \right) \left(\csc^{2}\left(d x +c \right)\right)}{3 d}-\frac{3 a^{2} b}{2 d \sin \left(d x +c \right)^{2}}+\frac{3 a^{2} b \ln \left(\tan \left(d x +c \right)\right)}{d}+\frac{3 b^{2} a}{d \sin \left(d x +c \right) \cos \left(d x +c \right)}-\frac{6 b^{2} a \cot \left(d x +c \right)}{d}+\frac{b^{3}}{2 d \cos \left(d x +c \right)^{2}}+\frac{b^{3} \ln \left(\tan \left(d x +c \right)\right)}{d}"," ",0,"-2/3*a^3*cot(d*x+c)/d-1/3/d*a^3*cot(d*x+c)*csc(d*x+c)^2-3/2/d*a^2*b/sin(d*x+c)^2+3*a^2*b*ln(tan(d*x+c))/d+3/d*b^2*a/sin(d*x+c)/cos(d*x+c)-6/d*b^2*a*cot(d*x+c)+1/2/d*b^3/cos(d*x+c)^2+1/d*b^3*ln(tan(d*x+c))","A"
39,1,254,211,0.484000," ","int(csc(d*x+c)^5*(a+b*tan(d*x+c))^3,x)","-\frac{a^{3} \cot \left(d x +c \right) \left(\csc^{3}\left(d x +c \right)\right)}{4 d}-\frac{3 a^{3} \cot \left(d x +c \right) \csc \left(d x +c \right)}{8 d}+\frac{3 a^{3} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{8 d}-\frac{a^{2} b}{d \sin \left(d x +c \right)^{3}}-\frac{3 a^{2} b}{d \sin \left(d x +c \right)}+\frac{3 a^{2} b \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}-\frac{3 b^{2} a}{2 d \sin \left(d x +c \right)^{2} \cos \left(d x +c \right)}+\frac{9 b^{2} a}{2 d \cos \left(d x +c \right)}+\frac{9 b^{2} a \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{2 d}+\frac{b^{3}}{2 d \sin \left(d x +c \right) \cos \left(d x +c \right)^{2}}-\frac{3 b^{3}}{2 d \sin \left(d x +c \right)}+\frac{3 b^{3} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{2 d}"," ",0,"-1/4*a^3*cot(d*x+c)*csc(d*x+c)^3/d-3/8*a^3*cot(d*x+c)*csc(d*x+c)/d+3/8/d*a^3*ln(csc(d*x+c)-cot(d*x+c))-1/d*a^2*b/sin(d*x+c)^3-3/d*a^2*b/sin(d*x+c)+3/d*a^2*b*ln(sec(d*x+c)+tan(d*x+c))-3/2/d*b^2*a/sin(d*x+c)^2/cos(d*x+c)+9/2/d*b^2*a/cos(d*x+c)+9/2/d*b^2*a*ln(csc(d*x+c)-cot(d*x+c))+1/2/d*b^3/sin(d*x+c)/cos(d*x+c)^2-3/2/d*b^3/sin(d*x+c)+3/2/d*b^3*ln(sec(d*x+c)+tan(d*x+c))","A"
40,1,230,157,0.569000," ","int(csc(d*x+c)^6*(a+b*tan(d*x+c))^3,x)","-\frac{8 a^{3} \cot \left(d x +c \right)}{15 d}-\frac{a^{3} \cot \left(d x +c \right) \left(\csc^{4}\left(d x +c \right)\right)}{5 d}-\frac{4 a^{3} \cot \left(d x +c \right) \left(\csc^{2}\left(d x +c \right)\right)}{15 d}-\frac{3 a^{2} b}{4 d \sin \left(d x +c \right)^{4}}-\frac{3 a^{2} b}{2 d \sin \left(d x +c \right)^{2}}+\frac{3 a^{2} b \ln \left(\tan \left(d x +c \right)\right)}{d}-\frac{b^{2} a}{d \sin \left(d x +c \right)^{3} \cos \left(d x +c \right)}+\frac{4 b^{2} a}{d \sin \left(d x +c \right) \cos \left(d x +c \right)}-\frac{8 b^{2} a \cot \left(d x +c \right)}{d}+\frac{b^{3}}{2 d \sin \left(d x +c \right)^{2} \cos \left(d x +c \right)^{2}}-\frac{b^{3}}{d \sin \left(d x +c \right)^{2}}+\frac{2 b^{3} \ln \left(\tan \left(d x +c \right)\right)}{d}"," ",0,"-8/15*a^3*cot(d*x+c)/d-1/5/d*a^3*cot(d*x+c)*csc(d*x+c)^4-4/15/d*a^3*cot(d*x+c)*csc(d*x+c)^2-3/4/d*a^2*b/sin(d*x+c)^4-3/2/d*a^2*b/sin(d*x+c)^2+3*a^2*b*ln(tan(d*x+c))/d-1/d*b^2*a/sin(d*x+c)^3/cos(d*x+c)+4/d*b^2*a/sin(d*x+c)/cos(d*x+c)-8/d*b^2*a*cot(d*x+c)+1/2/d*b^3/sin(d*x+c)^2/cos(d*x+c)^2-1/d*b^3/sin(d*x+c)^2+2/d*b^3*ln(tan(d*x+c))","A"
41,1,412,265,0.533000," ","int(sin(d*x+c)^3*(a+b*tan(d*x+c))^4,x)","-\frac{\cos \left(d x +c \right) \left(\sin^{2}\left(d x +c \right)\right) a^{4}}{3 d}-\frac{2 a^{4} \cos \left(d x +c \right)}{3 d}-\frac{4 a^{3} b \left(\sin^{3}\left(d x +c \right)\right)}{3 d}-\frac{4 a^{3} b \sin \left(d x +c \right)}{d}+\frac{4 a^{3} b \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{6 a^{2} b^{2} \left(\sin^{6}\left(d x +c \right)\right)}{d \cos \left(d x +c \right)}+\frac{16 a^{2} b^{2} \cos \left(d x +c \right)}{d}+\frac{6 a^{2} b^{2} \cos \left(d x +c \right) \left(\sin^{4}\left(d x +c \right)\right)}{d}+\frac{8 a^{2} b^{2} \cos \left(d x +c \right) \left(\sin^{2}\left(d x +c \right)\right)}{d}+\frac{2 a \,b^{3} \left(\sin^{7}\left(d x +c \right)\right)}{d \cos \left(d x +c \right)^{2}}+\frac{2 a \,b^{3} \left(\sin^{5}\left(d x +c \right)\right)}{d}+\frac{10 a \,b^{3} \left(\sin^{3}\left(d x +c \right)\right)}{3 d}+\frac{10 a \,b^{3} \sin \left(d x +c \right)}{d}-\frac{10 a \,b^{3} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{b^{4} \left(\sin^{8}\left(d x +c \right)\right)}{3 d \cos \left(d x +c \right)^{3}}-\frac{5 b^{4} \left(\sin^{8}\left(d x +c \right)\right)}{3 d \cos \left(d x +c \right)}-\frac{16 b^{4} \cos \left(d x +c \right)}{3 d}-\frac{5 b^{4} \cos \left(d x +c \right) \left(\sin^{6}\left(d x +c \right)\right)}{3 d}-\frac{2 b^{4} \cos \left(d x +c \right) \left(\sin^{4}\left(d x +c \right)\right)}{d}-\frac{8 b^{4} \cos \left(d x +c \right) \left(\sin^{2}\left(d x +c \right)\right)}{3 d}"," ",0,"-1/3/d*cos(d*x+c)*sin(d*x+c)^2*a^4-2/3*a^4*cos(d*x+c)/d-4/3*a^3*b*sin(d*x+c)^3/d-4*a^3*b*sin(d*x+c)/d+4/d*a^3*b*ln(sec(d*x+c)+tan(d*x+c))+6/d*a^2*b^2*sin(d*x+c)^6/cos(d*x+c)+16*a^2*b^2*cos(d*x+c)/d+6/d*a^2*b^2*cos(d*x+c)*sin(d*x+c)^4+8/d*a^2*b^2*cos(d*x+c)*sin(d*x+c)^2+2/d*a*b^3*sin(d*x+c)^7/cos(d*x+c)^2+2/d*a*b^3*sin(d*x+c)^5+10/3*a*b^3*sin(d*x+c)^3/d+10*a*b^3*sin(d*x+c)/d-10/d*a*b^3*ln(sec(d*x+c)+tan(d*x+c))+1/3/d*b^4*sin(d*x+c)^8/cos(d*x+c)^3-5/3/d*b^4*sin(d*x+c)^8/cos(d*x+c)-16/3*b^4*cos(d*x+c)/d-5/3/d*b^4*cos(d*x+c)*sin(d*x+c)^6-2/d*b^4*cos(d*x+c)*sin(d*x+c)^4-8/3/d*b^4*cos(d*x+c)*sin(d*x+c)^2","A"
42,1,368,131,0.469000," ","int(sin(d*x+c)^2*(a+b*tan(d*x+c))^4,x)","-\frac{a^{4} \sin \left(d x +c \right) \cos \left(d x +c \right)}{2 d}+\frac{a^{4} x}{2}+\frac{a^{4} c}{2 d}-\frac{2 a^{3} b \left(\sin^{2}\left(d x +c \right)\right)}{d}-\frac{4 a^{3} b \ln \left(\cos \left(d x +c \right)\right)}{d}+\frac{6 a^{2} b^{2} \left(\sin^{5}\left(d x +c \right)\right)}{d \cos \left(d x +c \right)}+\frac{6 a^{2} b^{2} \cos \left(d x +c \right) \left(\sin^{3}\left(d x +c \right)\right)}{d}+\frac{9 a^{2} b^{2} \sin \left(d x +c \right) \cos \left(d x +c \right)}{d}-9 a^{2} b^{2} x -\frac{9 a^{2} b^{2} c}{d}+\frac{2 a \,b^{3} \left(\sin^{6}\left(d x +c \right)\right)}{d \cos \left(d x +c \right)^{2}}+\frac{2 a \,b^{3} \left(\sin^{4}\left(d x +c \right)\right)}{d}+\frac{4 a \,b^{3} \left(\sin^{2}\left(d x +c \right)\right)}{d}+\frac{8 a \,b^{3} \ln \left(\cos \left(d x +c \right)\right)}{d}+\frac{b^{4} \left(\sin^{7}\left(d x +c \right)\right)}{3 d \cos \left(d x +c \right)^{3}}-\frac{4 b^{4} \left(\sin^{7}\left(d x +c \right)\right)}{3 d \cos \left(d x +c \right)}-\frac{4 b^{4} \cos \left(d x +c \right) \left(\sin^{5}\left(d x +c \right)\right)}{3 d}-\frac{5 b^{4} \cos \left(d x +c \right) \left(\sin^{3}\left(d x +c \right)\right)}{3 d}-\frac{5 b^{4} \sin \left(d x +c \right) \cos \left(d x +c \right)}{2 d}+\frac{5 b^{4} x}{2}+\frac{5 b^{4} c}{2 d}"," ",0,"-1/2/d*a^4*sin(d*x+c)*cos(d*x+c)+1/2*a^4*x+1/2/d*a^4*c-2/d*a^3*b*sin(d*x+c)^2-4/d*a^3*b*ln(cos(d*x+c))+6/d*a^2*b^2*sin(d*x+c)^5/cos(d*x+c)+6/d*a^2*b^2*cos(d*x+c)*sin(d*x+c)^3+9/d*a^2*b^2*sin(d*x+c)*cos(d*x+c)-9*a^2*b^2*x-9/d*a^2*b^2*c+2/d*a*b^3*sin(d*x+c)^6/cos(d*x+c)^2+2/d*a*b^3*sin(d*x+c)^4+4/d*a*b^3*sin(d*x+c)^2+8/d*a*b^3*ln(cos(d*x+c))+1/3/d*b^4*sin(d*x+c)^7/cos(d*x+c)^3-4/3/d*b^4*sin(d*x+c)^7/cos(d*x+c)-4/3/d*b^4*cos(d*x+c)*sin(d*x+c)^5-5/3/d*b^4*cos(d*x+c)*sin(d*x+c)^3-5/2/d*b^4*sin(d*x+c)*cos(d*x+c)+5/2*b^4*x+5/2/d*b^4*c","B"
43,1,309,178,0.438000," ","int(sin(d*x+c)*(a+b*tan(d*x+c))^4,x)","-\frac{a^{4} \cos \left(d x +c \right)}{d}-\frac{4 a^{3} b \sin \left(d x +c \right)}{d}+\frac{4 a^{3} b \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{6 a^{2} b^{2} \left(\sin^{4}\left(d x +c \right)\right)}{d \cos \left(d x +c \right)}+\frac{6 a^{2} b^{2} \cos \left(d x +c \right) \left(\sin^{2}\left(d x +c \right)\right)}{d}+\frac{12 a^{2} b^{2} \cos \left(d x +c \right)}{d}+\frac{2 a \,b^{3} \left(\sin^{5}\left(d x +c \right)\right)}{d \cos \left(d x +c \right)^{2}}+\frac{2 a \,b^{3} \left(\sin^{3}\left(d x +c \right)\right)}{d}+\frac{6 a \,b^{3} \sin \left(d x +c \right)}{d}-\frac{6 a \,b^{3} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{b^{4} \left(\sin^{6}\left(d x +c \right)\right)}{3 d \cos \left(d x +c \right)^{3}}-\frac{b^{4} \left(\sin^{6}\left(d x +c \right)\right)}{d \cos \left(d x +c \right)}-\frac{8 b^{4} \cos \left(d x +c \right)}{3 d}-\frac{b^{4} \cos \left(d x +c \right) \left(\sin^{4}\left(d x +c \right)\right)}{d}-\frac{4 b^{4} \cos \left(d x +c \right) \left(\sin^{2}\left(d x +c \right)\right)}{3 d}"," ",0,"-a^4*cos(d*x+c)/d-4*a^3*b*sin(d*x+c)/d+4/d*a^3*b*ln(sec(d*x+c)+tan(d*x+c))+6/d*a^2*b^2*sin(d*x+c)^4/cos(d*x+c)+6/d*a^2*b^2*cos(d*x+c)*sin(d*x+c)^2+12*a^2*b^2*cos(d*x+c)/d+2/d*a*b^3*sin(d*x+c)^5/cos(d*x+c)^2+2*a*b^3*sin(d*x+c)^3/d+6*a*b^3*sin(d*x+c)/d-6/d*a*b^3*ln(sec(d*x+c)+tan(d*x+c))+1/3/d*b^4*sin(d*x+c)^6/cos(d*x+c)^3-1/d*b^4*sin(d*x+c)^6/cos(d*x+c)-8/3*b^4*cos(d*x+c)/d-1/d*b^4*cos(d*x+c)*sin(d*x+c)^4-4/3/d*b^4*cos(d*x+c)*sin(d*x+c)^2","A"
44,1,214,116,0.464000," ","int(csc(d*x+c)*(a+b*tan(d*x+c))^4,x)","\frac{a^{4} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{d}+\frac{4 a^{3} b \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{6 a^{2} b^{2}}{d \cos \left(d x +c \right)}+\frac{2 a \,b^{3} \left(\sin^{3}\left(d x +c \right)\right)}{d \cos \left(d x +c \right)^{2}}+\frac{2 a \,b^{3} \sin \left(d x +c \right)}{d}-\frac{2 a \,b^{3} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{b^{4} \left(\sin^{4}\left(d x +c \right)\right)}{3 d \cos \left(d x +c \right)^{3}}-\frac{b^{4} \left(\sin^{4}\left(d x +c \right)\right)}{3 d \cos \left(d x +c \right)}-\frac{b^{4} \cos \left(d x +c \right) \left(\sin^{2}\left(d x +c \right)\right)}{3 d}-\frac{2 b^{4} \cos \left(d x +c \right)}{3 d}"," ",0,"1/d*a^4*ln(csc(d*x+c)-cot(d*x+c))+4/d*a^3*b*ln(sec(d*x+c)+tan(d*x+c))+6/d*a^2*b^2/cos(d*x+c)+2/d*a*b^3*sin(d*x+c)^3/cos(d*x+c)^2+2*a*b^3*sin(d*x+c)/d-2/d*a*b^3*ln(sec(d*x+c)+tan(d*x+c))+1/3/d*b^4*sin(d*x+c)^4/cos(d*x+c)^3-1/3/d*b^4*sin(d*x+c)^4/cos(d*x+c)-1/3/d*b^4*cos(d*x+c)*sin(d*x+c)^2-2/3*b^4*cos(d*x+c)/d","A"
45,1,90,81,0.537000," ","int(csc(d*x+c)^2*(a+b*tan(d*x+c))^4,x)","-\frac{a^{4} \cot \left(d x +c \right)}{d}+\frac{4 a^{3} b \ln \left(\tan \left(d x +c \right)\right)}{d}+\frac{6 a^{2} b^{2} \tan \left(d x +c \right)}{d}+\frac{2 a \,b^{3}}{d \cos \left(d x +c \right)^{2}}+\frac{b^{4} \left(\sin^{3}\left(d x +c \right)\right)}{3 d \cos \left(d x +c \right)^{3}}"," ",0,"-a^4*cot(d*x+c)/d+4*a^3*b*ln(tan(d*x+c))/d+6*a^2*b^2*tan(d*x+c)/d+2/d*a*b^3/cos(d*x+c)^2+1/3/d*b^4*sin(d*x+c)^3/cos(d*x+c)^3","A"
46,1,192,155,0.515000," ","int(csc(d*x+c)^3*(a+b*tan(d*x+c))^4,x)","-\frac{a^{4} \cot \left(d x +c \right) \csc \left(d x +c \right)}{2 d}+\frac{a^{4} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{2 d}-\frac{4 a^{3} b}{d \sin \left(d x +c \right)}+\frac{4 a^{3} b \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{6 a^{2} b^{2}}{d \cos \left(d x +c \right)}+\frac{6 a^{2} b^{2} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{d}+\frac{2 a \,b^{3} \sec \left(d x +c \right) \tan \left(d x +c \right)}{d}+\frac{2 a \,b^{3} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{b^{4}}{3 d \cos \left(d x +c \right)^{3}}"," ",0,"-1/2*a^4*cot(d*x+c)*csc(d*x+c)/d+1/2/d*a^4*ln(csc(d*x+c)-cot(d*x+c))-4/d*a^3*b/sin(d*x+c)+4/d*a^3*b*ln(sec(d*x+c)+tan(d*x+c))+6/d*a^2*b^2/cos(d*x+c)+6/d*a^2*b^2*ln(csc(d*x+c)-cot(d*x+c))+2*a*b^3*sec(d*x+c)*tan(d*x+c)/d+2/d*a*b^3*ln(sec(d*x+c)+tan(d*x+c))+1/3/d*b^4/cos(d*x+c)^3","A"
47,1,184,133,0.657000," ","int(csc(d*x+c)^4*(a+b*tan(d*x+c))^4,x)","-\frac{2 a^{4} \cot \left(d x +c \right)}{3 d}-\frac{a^{4} \cot \left(d x +c \right) \left(\csc^{2}\left(d x +c \right)\right)}{3 d}-\frac{2 a^{3} b}{d \sin \left(d x +c \right)^{2}}+\frac{4 a^{3} b \ln \left(\tan \left(d x +c \right)\right)}{d}+\frac{6 a^{2} b^{2}}{d \sin \left(d x +c \right) \cos \left(d x +c \right)}-\frac{12 a^{2} b^{2} \cot \left(d x +c \right)}{d}+\frac{2 a \,b^{3}}{d \cos \left(d x +c \right)^{2}}+\frac{4 a \,b^{3} \ln \left(\tan \left(d x +c \right)\right)}{d}+\frac{2 b^{4} \tan \left(d x +c \right)}{3 d}+\frac{b^{4} \tan \left(d x +c \right) \left(\sec^{2}\left(d x +c \right)\right)}{3 d}"," ",0,"-2/3*a^4*cot(d*x+c)/d-1/3/d*a^4*cot(d*x+c)*csc(d*x+c)^2-2/d*a^3*b/sin(d*x+c)^2+4*a^3*b*ln(tan(d*x+c))/d+6/d*a^2*b^2/sin(d*x+c)/cos(d*x+c)-12/d*a^2*b^2*cot(d*x+c)+2/d*a*b^3/cos(d*x+c)^2+4/d*a*b^3*ln(tan(d*x+c))+2/3/d*b^4*tan(d*x+c)+1/3/d*b^4*tan(d*x+c)*sec(d*x+c)^2","A"
48,1,317,264,0.504000," ","int(csc(d*x+c)^5*(a+b*tan(d*x+c))^4,x)","-\frac{a^{4} \cot \left(d x +c \right) \left(\csc^{3}\left(d x +c \right)\right)}{4 d}-\frac{3 a^{4} \cot \left(d x +c \right) \csc \left(d x +c \right)}{8 d}+\frac{3 a^{4} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{8 d}-\frac{4 a^{3} b}{3 d \sin \left(d x +c \right)^{3}}-\frac{4 a^{3} b}{d \sin \left(d x +c \right)}+\frac{4 a^{3} b \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}-\frac{3 a^{2} b^{2}}{d \sin \left(d x +c \right)^{2} \cos \left(d x +c \right)}+\frac{9 a^{2} b^{2}}{d \cos \left(d x +c \right)}+\frac{9 a^{2} b^{2} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{d}+\frac{2 a \,b^{3}}{d \sin \left(d x +c \right) \cos \left(d x +c \right)^{2}}-\frac{6 a \,b^{3}}{d \sin \left(d x +c \right)}+\frac{6 a \,b^{3} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{b^{4}}{3 d \cos \left(d x +c \right)^{3}}+\frac{b^{4}}{d \cos \left(d x +c \right)}+\frac{b^{4} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{d}"," ",0,"-1/4*a^4*cot(d*x+c)*csc(d*x+c)^3/d-3/8*a^4*cot(d*x+c)*csc(d*x+c)/d+3/8/d*a^4*ln(csc(d*x+c)-cot(d*x+c))-4/3/d*a^3*b/sin(d*x+c)^3-4/d*a^3*b/sin(d*x+c)+4/d*a^3*b*ln(sec(d*x+c)+tan(d*x+c))-3/d*a^2*b^2/sin(d*x+c)^2/cos(d*x+c)+9/d*a^2*b^2/cos(d*x+c)+9/d*a^2*b^2*ln(csc(d*x+c)-cot(d*x+c))+2/d*a*b^3/sin(d*x+c)/cos(d*x+c)^2-6/d*a*b^3/sin(d*x+c)+6/d*a*b^3*ln(sec(d*x+c)+tan(d*x+c))+1/3/d*b^4/cos(d*x+c)^3+1/d*b^4/cos(d*x+c)+1/d*b^4*ln(csc(d*x+c)-cot(d*x+c))","A"
49,1,301,188,0.594000," ","int(csc(d*x+c)^6*(a+b*tan(d*x+c))^4,x)","-\frac{8 a^{4} \cot \left(d x +c \right)}{15 d}-\frac{a^{4} \cot \left(d x +c \right) \left(\csc^{4}\left(d x +c \right)\right)}{5 d}-\frac{4 a^{4} \cot \left(d x +c \right) \left(\csc^{2}\left(d x +c \right)\right)}{15 d}-\frac{a^{3} b}{d \sin \left(d x +c \right)^{4}}-\frac{2 a^{3} b}{d \sin \left(d x +c \right)^{2}}+\frac{4 a^{3} b \ln \left(\tan \left(d x +c \right)\right)}{d}-\frac{2 a^{2} b^{2}}{d \sin \left(d x +c \right)^{3} \cos \left(d x +c \right)}+\frac{8 a^{2} b^{2}}{d \sin \left(d x +c \right) \cos \left(d x +c \right)}-\frac{16 a^{2} b^{2} \cot \left(d x +c \right)}{d}+\frac{2 a \,b^{3}}{d \sin \left(d x +c \right)^{2} \cos \left(d x +c \right)^{2}}-\frac{4 a \,b^{3}}{d \sin \left(d x +c \right)^{2}}+\frac{8 a \,b^{3} \ln \left(\tan \left(d x +c \right)\right)}{d}+\frac{b^{4}}{3 d \sin \left(d x +c \right) \cos \left(d x +c \right)^{3}}+\frac{4 b^{4}}{3 d \sin \left(d x +c \right) \cos \left(d x +c \right)}-\frac{8 b^{4} \cot \left(d x +c \right)}{3 d}"," ",0,"-8/15*a^4*cot(d*x+c)/d-1/5/d*a^4*cot(d*x+c)*csc(d*x+c)^4-4/15/d*a^4*cot(d*x+c)*csc(d*x+c)^2-1/d*a^3*b/sin(d*x+c)^4-2/d*a^3*b/sin(d*x+c)^2+4*a^3*b*ln(tan(d*x+c))/d-2/d*a^2*b^2/sin(d*x+c)^3/cos(d*x+c)+8/d*a^2*b^2/sin(d*x+c)/cos(d*x+c)-16/d*a^2*b^2*cot(d*x+c)+2/d*a*b^3/sin(d*x+c)^2/cos(d*x+c)^2-4/d*a*b^3/sin(d*x+c)^2+8/d*a*b^3*ln(tan(d*x+c))+1/3/d*b^4/sin(d*x+c)/cos(d*x+c)^3+4/3/d*b^4/sin(d*x+c)/cos(d*x+c)-8/3/d*b^4*cot(d*x+c)","A"
50,1,442,372,0.535000," ","int(csc(d*x+c)^7*(a+b*tan(d*x+c))^4,x)","-\frac{a^{4} \cot \left(d x +c \right) \left(\csc^{5}\left(d x +c \right)\right)}{6 d}-\frac{5 a^{4} \cot \left(d x +c \right) \left(\csc^{3}\left(d x +c \right)\right)}{24 d}-\frac{5 a^{4} \cot \left(d x +c \right) \csc \left(d x +c \right)}{16 d}+\frac{5 a^{4} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{16 d}-\frac{4 a^{3} b}{5 d \sin \left(d x +c \right)^{5}}-\frac{4 a^{3} b}{3 d \sin \left(d x +c \right)^{3}}-\frac{4 a^{3} b}{d \sin \left(d x +c \right)}+\frac{4 a^{3} b \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}-\frac{3 a^{2} b^{2}}{2 d \sin \left(d x +c \right)^{4} \cos \left(d x +c \right)}-\frac{15 a^{2} b^{2}}{4 d \sin \left(d x +c \right)^{2} \cos \left(d x +c \right)}+\frac{45 a^{2} b^{2}}{4 d \cos \left(d x +c \right)}+\frac{45 a^{2} b^{2} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{4 d}-\frac{4 a \,b^{3}}{3 d \sin \left(d x +c \right)^{3} \cos \left(d x +c \right)^{2}}+\frac{10 a \,b^{3}}{3 d \sin \left(d x +c \right) \cos \left(d x +c \right)^{2}}-\frac{10 a \,b^{3}}{d \sin \left(d x +c \right)}+\frac{10 a \,b^{3} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{b^{4}}{3 d \sin \left(d x +c \right)^{2} \cos \left(d x +c \right)^{3}}-\frac{5 b^{4}}{6 d \sin \left(d x +c \right)^{2} \cos \left(d x +c \right)}+\frac{5 b^{4}}{2 d \cos \left(d x +c \right)}+\frac{5 b^{4} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{2 d}"," ",0,"-1/6*a^4*cot(d*x+c)*csc(d*x+c)^5/d-5/24*a^4*cot(d*x+c)*csc(d*x+c)^3/d-5/16*a^4*cot(d*x+c)*csc(d*x+c)/d+5/16/d*a^4*ln(csc(d*x+c)-cot(d*x+c))-4/5/d*a^3*b/sin(d*x+c)^5-4/3/d*a^3*b/sin(d*x+c)^3-4/d*a^3*b/sin(d*x+c)+4/d*a^3*b*ln(sec(d*x+c)+tan(d*x+c))-3/2/d*a^2*b^2/sin(d*x+c)^4/cos(d*x+c)-15/4/d*a^2*b^2/sin(d*x+c)^2/cos(d*x+c)+45/4/d*a^2*b^2/cos(d*x+c)+45/4/d*a^2*b^2*ln(csc(d*x+c)-cot(d*x+c))-4/3/d*a*b^3/sin(d*x+c)^3/cos(d*x+c)^2+10/3/d*a*b^3/sin(d*x+c)/cos(d*x+c)^2-10/d*a*b^3/sin(d*x+c)+10/d*a*b^3*ln(sec(d*x+c)+tan(d*x+c))+1/3/d*b^4/sin(d*x+c)^2/cos(d*x+c)^3-5/6/d*b^4/sin(d*x+c)^2/cos(d*x+c)+5/2/d*b^4/cos(d*x+c)+5/2/d*b^4*ln(csc(d*x+c)-cot(d*x+c))","A"
51,1,361,260,0.404000," ","int(sin(d*x+c)^5/(a+b*tan(d*x+c)),x)","\frac{-\frac{64 a^{5} b \arctanh \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)-2 b}{2 \sqrt{a^{2}+b^{2}}}\right)}{\left(32 a^{6}+96 a^{4} b^{2}+96 b^{4} a^{2}+32 b^{6}\right) \sqrt{a^{2}+b^{2}}}-\frac{2 \left(-\left(\tan^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{4} b -b^{2} a^{3} \left(\tan^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(-\frac{16}{3} b \,a^{4}-\frac{4}{3} a^{2} b^{3}\right) \left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(-6 b^{2} a^{3}-2 a \,b^{4}\right) \left(\tan^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(-\frac{178}{15} b \,a^{4}-\frac{136}{15} a^{2} b^{3}-\frac{16}{5} b^{5}\right) \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(\frac{16}{3} a^{5}+\frac{2}{3} a \,b^{4}\right) \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(-\frac{16}{3} b \,a^{4}-\frac{4}{3} a^{2} b^{3}\right) \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(-2 b^{2} a^{3}+\frac{8}{3} a^{5}-\frac{2}{3} a \,b^{4}\right) \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\tan \left(\frac{d x}{2}+\frac{c}{2}\right) a^{4} b +\frac{8 a^{5}}{15}-\frac{3 b^{2} a^{3}}{5}-\frac{2 a \,b^{4}}{15}\right)}{\left(a^{4}+2 a^{2} b^{2}+b^{4}\right) \left(a^{2}+b^{2}\right) \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}}{d}"," ",0,"1/d*(-64*a^5*b/(32*a^6+96*a^4*b^2+96*a^2*b^4+32*b^6)/(a^2+b^2)^(1/2)*arctanh(1/2*(2*a*tan(1/2*d*x+1/2*c)-2*b)/(a^2+b^2)^(1/2))-2/(a^4+2*a^2*b^2+b^4)/(a^2+b^2)*(-tan(1/2*d*x+1/2*c)^9*a^4*b-b^2*a^3*tan(1/2*d*x+1/2*c)^8+(-16/3*b*a^4-4/3*a^2*b^3)*tan(1/2*d*x+1/2*c)^7+(-6*a^3*b^2-2*a*b^4)*tan(1/2*d*x+1/2*c)^6+(-178/15*b*a^4-136/15*a^2*b^3-16/5*b^5)*tan(1/2*d*x+1/2*c)^5+(16/3*a^5+2/3*a*b^4)*tan(1/2*d*x+1/2*c)^4+(-16/3*b*a^4-4/3*a^2*b^3)*tan(1/2*d*x+1/2*c)^3+(-2*b^2*a^3+8/3*a^5-2/3*a*b^4)*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)*a^4*b+8/15*a^5-3/5*b^2*a^3-2/15*a*b^4)/(1+tan(1/2*d*x+1/2*c)^2)^5)","A"
52,1,565,152,0.365000," ","int(sin(d*x+c)^4/(a+b*tan(d*x+c)),x)","\frac{b \,a^{4} \ln \left(a +b \tan \left(d x +c \right)\right)}{d \left(a^{2}+b^{2}\right)^{3}}-\frac{5 \left(\tan^{3}\left(d x +c \right)\right) a^{5}}{8 d \left(a^{2}+b^{2}\right)^{3} \left(1+\tan^{2}\left(d x +c \right)\right)^{2}}-\frac{3 \left(\tan^{3}\left(d x +c \right)\right) b^{2} a^{3}}{4 d \left(a^{2}+b^{2}\right)^{3} \left(1+\tan^{2}\left(d x +c \right)\right)^{2}}-\frac{\left(\tan^{3}\left(d x +c \right)\right) a \,b^{4}}{8 d \left(a^{2}+b^{2}\right)^{3} \left(1+\tan^{2}\left(d x +c \right)\right)^{2}}-\frac{\left(\tan^{2}\left(d x +c \right)\right) b \,a^{4}}{d \left(a^{2}+b^{2}\right)^{3} \left(1+\tan^{2}\left(d x +c \right)\right)^{2}}-\frac{3 \left(\tan^{2}\left(d x +c \right)\right) a^{2} b^{3}}{2 d \left(a^{2}+b^{2}\right)^{3} \left(1+\tan^{2}\left(d x +c \right)\right)^{2}}-\frac{\left(\tan^{2}\left(d x +c \right)\right) b^{5}}{2 d \left(a^{2}+b^{2}\right)^{3} \left(1+\tan^{2}\left(d x +c \right)\right)^{2}}-\frac{3 \tan \left(d x +c \right) a^{5}}{8 d \left(a^{2}+b^{2}\right)^{3} \left(1+\tan^{2}\left(d x +c \right)\right)^{2}}-\frac{\tan \left(d x +c \right) b^{2} a^{3}}{4 d \left(a^{2}+b^{2}\right)^{3} \left(1+\tan^{2}\left(d x +c \right)\right)^{2}}+\frac{\tan \left(d x +c \right) a \,b^{4}}{8 d \left(a^{2}+b^{2}\right)^{3} \left(1+\tan^{2}\left(d x +c \right)\right)^{2}}-\frac{3 b \,a^{4}}{4 d \left(a^{2}+b^{2}\right)^{3} \left(1+\tan^{2}\left(d x +c \right)\right)^{2}}-\frac{a^{2} b^{3}}{d \left(a^{2}+b^{2}\right)^{3} \left(1+\tan^{2}\left(d x +c \right)\right)^{2}}-\frac{b^{5}}{4 d \left(a^{2}+b^{2}\right)^{3} \left(1+\tan^{2}\left(d x +c \right)\right)^{2}}+\frac{3 \arctan \left(\tan \left(d x +c \right)\right) a^{5}}{8 d \left(a^{2}+b^{2}\right)^{3}}-\frac{3 \arctan \left(\tan \left(d x +c \right)\right) a^{3} b^{2}}{4 d \left(a^{2}+b^{2}\right)^{3}}-\frac{\arctan \left(\tan \left(d x +c \right)\right) a \,b^{4}}{8 d \left(a^{2}+b^{2}\right)^{3}}-\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right) a^{4} b}{2 d \left(a^{2}+b^{2}\right)^{3}}"," ",0,"1/d*b*a^4/(a^2+b^2)^3*ln(a+b*tan(d*x+c))-5/8/d/(a^2+b^2)^3/(1+tan(d*x+c)^2)^2*tan(d*x+c)^3*a^5-3/4/d/(a^2+b^2)^3/(1+tan(d*x+c)^2)^2*tan(d*x+c)^3*b^2*a^3-1/8/d/(a^2+b^2)^3/(1+tan(d*x+c)^2)^2*tan(d*x+c)^3*a*b^4-1/d/(a^2+b^2)^3/(1+tan(d*x+c)^2)^2*tan(d*x+c)^2*b*a^4-3/2/d/(a^2+b^2)^3/(1+tan(d*x+c)^2)^2*tan(d*x+c)^2*a^2*b^3-1/2/d/(a^2+b^2)^3/(1+tan(d*x+c)^2)^2*tan(d*x+c)^2*b^5-3/8/d/(a^2+b^2)^3/(1+tan(d*x+c)^2)^2*tan(d*x+c)*a^5-1/4/d/(a^2+b^2)^3/(1+tan(d*x+c)^2)^2*tan(d*x+c)*b^2*a^3+1/8/d/(a^2+b^2)^3/(1+tan(d*x+c)^2)^2*tan(d*x+c)*a*b^4-3/4/d/(a^2+b^2)^3/(1+tan(d*x+c)^2)^2*b*a^4-1/d/(a^2+b^2)^3/(1+tan(d*x+c)^2)^2*a^2*b^3-1/4/d/(a^2+b^2)^3/(1+tan(d*x+c)^2)^2*b^5+3/8/d/(a^2+b^2)^3*arctan(tan(d*x+c))*a^5-3/4/d/(a^2+b^2)^3*arctan(tan(d*x+c))*a^3*b^2-1/8/d/(a^2+b^2)^3*arctan(tan(d*x+c))*a*b^4-1/2/d/(a^2+b^2)^3*ln(1+tan(d*x+c)^2)*a^4*b","B"
53,1,205,160,0.359000," ","int(sin(d*x+c)^3/(a+b*tan(d*x+c)),x)","\frac{-\frac{16 a^{3} b \arctanh \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)-2 b}{2 \sqrt{a^{2}+b^{2}}}\right)}{\left(8 a^{4}+16 a^{2} b^{2}+8 b^{4}\right) \sqrt{a^{2}+b^{2}}}-\frac{2 \left(-\left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{2} b -b^{2} a \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(-\frac{10}{3} a^{2} b -\frac{4}{3} b^{3}\right) \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+2 a^{3} \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-a^{2} b \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+\frac{2 a^{3}}{3}-\frac{b^{2} a}{3}\right)}{\left(a^{4}+2 a^{2} b^{2}+b^{4}\right) \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}}{d}"," ",0,"1/d*(-16*a^3*b/(8*a^4+16*a^2*b^2+8*b^4)/(a^2+b^2)^(1/2)*arctanh(1/2*(2*a*tan(1/2*d*x+1/2*c)-2*b)/(a^2+b^2)^(1/2))-2/(a^4+2*a^2*b^2+b^4)*(-tan(1/2*d*x+1/2*c)^5*a^2*b-b^2*a*tan(1/2*d*x+1/2*c)^4+(-10/3*a^2*b-4/3*b^3)*tan(1/2*d*x+1/2*c)^3+2*a^3*tan(1/2*d*x+1/2*c)^2-a^2*b*tan(1/2*d*x+1/2*c)+2/3*a^3-1/3*b^2*a)/(1+tan(1/2*d*x+1/2*c)^2)^3)","A"
54,1,238,90,0.362000," ","int(sin(d*x+c)^2/(a+b*tan(d*x+c)),x)","\frac{b \,a^{2} \ln \left(a +b \tan \left(d x +c \right)\right)}{d \left(a^{2}+b^{2}\right)^{2}}-\frac{\tan \left(d x +c \right) a^{3}}{2 d \left(a^{2}+b^{2}\right)^{2} \left(1+\tan^{2}\left(d x +c \right)\right)}-\frac{\tan \left(d x +c \right) b^{2} a}{2 d \left(a^{2}+b^{2}\right)^{2} \left(1+\tan^{2}\left(d x +c \right)\right)}-\frac{a^{2} b}{2 d \left(a^{2}+b^{2}\right)^{2} \left(1+\tan^{2}\left(d x +c \right)\right)}-\frac{b^{3}}{2 d \left(a^{2}+b^{2}\right)^{2} \left(1+\tan^{2}\left(d x +c \right)\right)}-\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right) a^{2} b}{2 d \left(a^{2}+b^{2}\right)^{2}}+\frac{\arctan \left(\tan \left(d x +c \right)\right) a^{3}}{2 d \left(a^{2}+b^{2}\right)^{2}}-\frac{\arctan \left(\tan \left(d x +c \right)\right) a \,b^{2}}{2 d \left(a^{2}+b^{2}\right)^{2}}"," ",0,"1/d*b*a^2/(a^2+b^2)^2*ln(a+b*tan(d*x+c))-1/2/d/(a^2+b^2)^2/(1+tan(d*x+c)^2)*tan(d*x+c)*a^3-1/2/d/(a^2+b^2)^2/(1+tan(d*x+c)^2)*tan(d*x+c)*b^2*a-1/2/d/(a^2+b^2)^2/(1+tan(d*x+c)^2)*a^2*b-1/2/d/(a^2+b^2)^2/(1+tan(d*x+c)^2)*b^3-1/2/d/(a^2+b^2)^2*ln(1+tan(d*x+c)^2)*a^2*b+1/2/d/(a^2+b^2)^2*arctan(tan(d*x+c))*a^3-1/2/d/(a^2+b^2)^2*arctan(tan(d*x+c))*a*b^2","B"
55,1,100,86,0.315000," ","int(sin(d*x+c)/(a+b*tan(d*x+c)),x)","\frac{-\frac{4 a b \arctanh \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)-2 b}{2 \sqrt{a^{2}+b^{2}}}\right)}{\left(2 a^{2}+2 b^{2}\right) \sqrt{a^{2}+b^{2}}}-\frac{2 \left(-\tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)}{\left(a^{2}+b^{2}\right) \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}}{d}"," ",0,"1/d*(-4*a*b/(2*a^2+2*b^2)/(a^2+b^2)^(1/2)*arctanh(1/2*(2*a*tan(1/2*d*x+1/2*c)-2*b)/(a^2+b^2)^(1/2))-2/(a^2+b^2)*(-tan(1/2*d*x+1/2*c)*b+a)/(1+tan(1/2*d*x+1/2*c)^2))","A"
56,1,65,62,0.364000," ","int(csc(d*x+c)/(a+b*tan(d*x+c)),x)","\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d a}-\frac{2 b \arctanh \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}}}"," ",0,"1/d/a*ln(tan(1/2*d*x+1/2*c))-2/d/a*b/(a^2+b^2)^(1/2)*arctanh(1/2*(2*a*tan(1/2*d*x+1/2*c)-2*b)/(a^2+b^2)^(1/2))","A"
57,1,53,50,0.353000," ","int(csc(d*x+c)^2/(a+b*tan(d*x+c)),x)","\frac{b \ln \left(a +b \tan \left(d x +c \right)\right)}{a^{2} d}-\frac{1}{d a \tan \left(d x +c \right)}-\frac{b \ln \left(\tan \left(d x +c \right)\right)}{a^{2} d}"," ",0,"b*ln(a+b*tan(d*x+c))/a^2/d-1/d/a/tan(d*x+c)-b*ln(tan(d*x+c))/a^2/d","A"
58,1,162,114,0.414000," ","int(csc(d*x+c)^3/(a+b*tan(d*x+c)),x)","\frac{\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}{8 d a}+\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) b}{2 d \,a^{2}}-\frac{1}{8 d a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}+\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{2 d a}+\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{2}}{d \,a^{3}}+\frac{b}{2 d \,a^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}-\frac{2 b \sqrt{a^{2}+b^{2}}\, \arctanh \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^{3}}"," ",0,"1/8/d/a*tan(1/2*d*x+1/2*c)^2+1/2/d/a^2*tan(1/2*d*x+1/2*c)*b-1/8/d/a/tan(1/2*d*x+1/2*c)^2+1/2/d/a*ln(tan(1/2*d*x+1/2*c))+1/d/a^3*ln(tan(1/2*d*x+1/2*c))*b^2+1/2/d*b/a^2/tan(1/2*d*x+1/2*c)-2/d*b*(a^2+b^2)^(1/2)/a^3*arctanh(1/2*(2*a*tan(1/2*d*x+1/2*c)-2*b)/(a^2+b^2)^(1/2))","A"
59,1,144,104,0.392000," ","int(csc(d*x+c)^4/(a+b*tan(d*x+c)),x)","\frac{b \ln \left(a +b \tan \left(d x +c \right)\right)}{a^{2} d}+\frac{b^{3} \ln \left(a +b \tan \left(d x +c \right)\right)}{d \,a^{4}}-\frac{1}{3 d a \tan \left(d x +c \right)^{3}}-\frac{1}{d a \tan \left(d x +c \right)}-\frac{b^{2}}{d \,a^{3} \tan \left(d x +c \right)}+\frac{b}{2 d \,a^{2} \tan \left(d x +c \right)^{2}}-\frac{b \ln \left(\tan \left(d x +c \right)\right)}{a^{2} d}-\frac{b^{3} \ln \left(\tan \left(d x +c \right)\right)}{d \,a^{4}}"," ",0,"b*ln(a+b*tan(d*x+c))/a^2/d+1/d/a^4*b^3*ln(a+b*tan(d*x+c))-1/3/d/a/tan(d*x+c)^3-1/d/a/tan(d*x+c)-1/d/a^3/tan(d*x+c)*b^2+1/2/d*b/a^2/tan(d*x+c)^2-b*ln(tan(d*x+c))/a^2/d-1/d/a^4*b^3*ln(tan(d*x+c))","A"
60,1,273,161,0.409000," ","int(csc(d*x+c)^6/(a+b*tan(d*x+c)),x)","\frac{b \ln \left(a +b \tan \left(d x +c \right)\right)}{a^{2} d}+\frac{2 b^{3} \ln \left(a +b \tan \left(d x +c \right)\right)}{d \,a^{4}}+\frac{b^{5} \ln \left(a +b \tan \left(d x +c \right)\right)}{d \,a^{6}}-\frac{1}{5 d a \tan \left(d x +c \right)^{5}}-\frac{2}{3 d a \tan \left(d x +c \right)^{3}}-\frac{b^{2}}{3 d \,a^{3} \tan \left(d x +c \right)^{3}}-\frac{1}{d a \tan \left(d x +c \right)}-\frac{2 b^{2}}{d \,a^{3} \tan \left(d x +c \right)}-\frac{b^{4}}{d \,a^{5} \tan \left(d x +c \right)}+\frac{b}{4 d \,a^{2} \tan \left(d x +c \right)^{4}}+\frac{b}{d \,a^{2} \tan \left(d x +c \right)^{2}}+\frac{b^{3}}{2 d \,a^{4} \tan \left(d x +c \right)^{2}}-\frac{b \ln \left(\tan \left(d x +c \right)\right)}{a^{2} d}-\frac{2 b^{3} \ln \left(\tan \left(d x +c \right)\right)}{d \,a^{4}}-\frac{b^{5} \ln \left(\tan \left(d x +c \right)\right)}{d \,a^{6}}"," ",0,"b*ln(a+b*tan(d*x+c))/a^2/d+2/d/a^4*b^3*ln(a+b*tan(d*x+c))+1/d/a^6*b^5*ln(a+b*tan(d*x+c))-1/5/d/a/tan(d*x+c)^5-2/3/d/a/tan(d*x+c)^3-1/3/d/a^3/tan(d*x+c)^3*b^2-1/d/a/tan(d*x+c)-2/d/a^3/tan(d*x+c)*b^2-1/d/a^5/tan(d*x+c)*b^4+1/4/d*b/a^2/tan(d*x+c)^4+1/d*b/a^2/tan(d*x+c)^2+1/2/d/a^4*b^3/tan(d*x+c)^2-b*ln(tan(d*x+c))/a^2/d-2/d/a^4*b^3*ln(tan(d*x+c))-1/d/a^6*b^5*ln(tan(d*x+c))","A"
61,1,1211,289,0.497000," ","int(sin(d*x+c)^6/(a+b*tan(d*x+c))^2,x)","-\frac{\tan \left(d x +c \right) a^{2} b^{6}}{2 d \left(a^{2}+b^{2}\right)^{5} \left(1+\tan^{2}\left(d x +c \right)\right)^{3}}+\frac{2 \tan \left(d x +c \right) a^{6} b^{2}}{d \left(a^{2}+b^{2}\right)^{5} \left(1+\tan^{2}\left(d x +c \right)\right)^{3}}+\frac{15 \tan \left(d x +c \right) a^{4} b^{4}}{8 d \left(a^{2}+b^{2}\right)^{5} \left(1+\tan^{2}\left(d x +c \right)\right)^{3}}-\frac{3 \left(\tan^{4}\left(d x +c \right)\right) a^{7} b}{d \left(a^{2}+b^{2}\right)^{5} \left(1+\tan^{2}\left(d x +c \right)\right)^{3}}+\frac{2 \left(\tan^{5}\left(d x +c \right)\right) a^{6} b^{2}}{d \left(a^{2}+b^{2}\right)^{5} \left(1+\tan^{2}\left(d x +c \right)\right)^{3}}-\frac{a^{6} b}{\left(a^{2}+b^{2}\right)^{4} d \left(a +b \tan \left(d x +c \right)\right)}-\frac{\left(\tan^{3}\left(d x +c \right)\right) b^{8}}{6 d \left(a^{2}+b^{2}\right)^{5} \left(1+\tan^{2}\left(d x +c \right)\right)^{3}}-\frac{5 \tan \left(d x +c \right) a^{8}}{16 d \left(a^{2}+b^{2}\right)^{5} \left(1+\tan^{2}\left(d x +c \right)\right)^{3}}-\frac{\tan \left(d x +c \right) b^{8}}{16 d \left(a^{2}+b^{2}\right)^{5} \left(1+\tan^{2}\left(d x +c \right)\right)^{3}}+\frac{3 a^{3} b^{5}}{2 d \left(a^{2}+b^{2}\right)^{5} \left(1+\tan^{2}\left(d x +c \right)\right)^{3}}-\frac{b^{3} a^{5}}{2 d \left(a^{2}+b^{2}\right)^{5} \left(1+\tan^{2}\left(d x +c \right)\right)^{3}}-\frac{11 a^{7} b}{6 d \left(a^{2}+b^{2}\right)^{5} \left(1+\tan^{2}\left(d x +c \right)\right)^{3}}+\frac{a \,b^{7}}{6 d \left(a^{2}+b^{2}\right)^{5} \left(1+\tan^{2}\left(d x +c \right)\right)^{3}}+\frac{3 \ln \left(1+\tan^{2}\left(d x +c \right)\right) a^{5} b^{3}}{d \left(a^{2}+b^{2}\right)^{5}}+\frac{5 \arctan \left(\tan \left(d x +c \right)\right) a^{8}}{16 d \left(a^{2}+b^{2}\right)^{5}}+\frac{\arctan \left(\tan \left(d x +c \right)\right) b^{8}}{16 d \left(a^{2}+b^{2}\right)^{5}}-\frac{5 \arctan \left(\tan \left(d x +c \right)\right) a^{6} b^{2}}{d \left(a^{2}+b^{2}\right)^{5}}+\frac{\arctan \left(\tan \left(d x +c \right)\right) a^{2} b^{6}}{2 d \left(a^{2}+b^{2}\right)^{5}}-\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right) a^{7} b}{d \left(a^{2}+b^{2}\right)^{5}}-\frac{11 \left(\tan^{5}\left(d x +c \right)\right) a^{8}}{16 d \left(a^{2}+b^{2}\right)^{5} \left(1+\tan^{2}\left(d x +c \right)\right)^{3}}+\frac{\left(\tan^{5}\left(d x +c \right)\right) b^{8}}{16 d \left(a^{2}+b^{2}\right)^{5} \left(1+\tan^{2}\left(d x +c \right)\right)^{3}}-\frac{5 \left(\tan^{3}\left(d x +c \right)\right) a^{8}}{6 d \left(a^{2}+b^{2}\right)^{5} \left(1+\tan^{2}\left(d x +c \right)\right)^{3}}-\frac{\left(\tan^{3}\left(d x +c \right)\right) a^{2} b^{6}}{3 d \left(a^{2}+b^{2}\right)^{5} \left(1+\tan^{2}\left(d x +c \right)\right)^{3}}+\frac{\left(\tan^{5}\left(d x +c \right)\right) a^{2} b^{6}}{2 d \left(a^{2}+b^{2}\right)^{5} \left(1+\tan^{2}\left(d x +c \right)\right)^{3}}+\frac{5 \left(\tan^{2}\left(d x +c \right)\right) a^{3} b^{5}}{2 d \left(a^{2}+b^{2}\right)^{5} \left(1+\tan^{2}\left(d x +c \right)\right)^{3}}+\frac{\left(\tan^{2}\left(d x +c \right)\right) a \,b^{7}}{2 d \left(a^{2}+b^{2}\right)^{5} \left(1+\tan^{2}\left(d x +c \right)\right)^{3}}-\frac{5 \left(\tan^{2}\left(d x +c \right)\right) b^{3} a^{5}}{2 d \left(a^{2}+b^{2}\right)^{5} \left(1+\tan^{2}\left(d x +c \right)\right)^{3}}+\frac{13 \left(\tan^{3}\left(d x +c \right)\right) a^{6} b^{2}}{3 d \left(a^{2}+b^{2}\right)^{5} \left(1+\tan^{2}\left(d x +c \right)\right)^{3}}+\frac{5 \left(\tan^{3}\left(d x +c \right)\right) a^{4} b^{4}}{d \left(a^{2}+b^{2}\right)^{5} \left(1+\tan^{2}\left(d x +c \right)\right)^{3}}-\frac{9 \left(\tan^{2}\left(d x +c \right)\right) a^{7} b}{2 d \left(a^{2}+b^{2}\right)^{5} \left(1+\tan^{2}\left(d x +c \right)\right)^{3}}+\frac{25 \left(\tan^{5}\left(d x +c \right)\right) a^{4} b^{4}}{8 d \left(a^{2}+b^{2}\right)^{5} \left(1+\tan^{2}\left(d x +c \right)\right)^{3}}-\frac{3 \left(\tan^{4}\left(d x +c \right)\right) a^{5} b^{3}}{d \left(a^{2}+b^{2}\right)^{5} \left(1+\tan^{2}\left(d x +c \right)\right)^{3}}+\frac{2 b \,a^{7} \ln \left(a +b \tan \left(d x +c \right)\right)}{d \left(a^{2}+b^{2}\right)^{5}}-\frac{6 b^{3} a^{5} \ln \left(a +b \tan \left(d x +c \right)\right)}{d \left(a^{2}+b^{2}\right)^{5}}+\frac{25 \arctan \left(\tan \left(d x +c \right)\right) a^{4} b^{4}}{8 d \left(a^{2}+b^{2}\right)^{5}}"," ",0,"-a^6*b/(a^2+b^2)^4/d/(a+b*tan(d*x+c))+5/16/d/(a^2+b^2)^5*arctan(tan(d*x+c))*a^8+1/16/d/(a^2+b^2)^5*arctan(tan(d*x+c))*b^8-1/d/(a^2+b^2)^5*ln(1+tan(d*x+c)^2)*a^7*b-5/d/(a^2+b^2)^5*arctan(tan(d*x+c))*a^6*b^2-11/16/d/(a^2+b^2)^5/(1+tan(d*x+c)^2)^3*tan(d*x+c)^5*a^8+1/16/d/(a^2+b^2)^5/(1+tan(d*x+c)^2)^3*tan(d*x+c)^5*b^8-5/6/d/(a^2+b^2)^5/(1+tan(d*x+c)^2)^3*tan(d*x+c)^3*a^8-1/6/d/(a^2+b^2)^5/(1+tan(d*x+c)^2)^3*tan(d*x+c)^3*b^8-5/16/d/(a^2+b^2)^5/(1+tan(d*x+c)^2)^3*tan(d*x+c)*a^8-1/16/d/(a^2+b^2)^5/(1+tan(d*x+c)^2)^3*tan(d*x+c)*b^8+3/2/d/(a^2+b^2)^5/(1+tan(d*x+c)^2)^3*a^3*b^5-1/2/d/(a^2+b^2)^5/(1+tan(d*x+c)^2)^3*b^3*a^5+1/2/d/(a^2+b^2)^5*arctan(tan(d*x+c))*a^2*b^6-11/6/d/(a^2+b^2)^5/(1+tan(d*x+c)^2)^3*a^7*b+1/6/d/(a^2+b^2)^5/(1+tan(d*x+c)^2)^3*a*b^7+2/d*b*a^7/(a^2+b^2)^5*ln(a+b*tan(d*x+c))-6/d*b^3*a^5/(a^2+b^2)^5*ln(a+b*tan(d*x+c))+25/8/d/(a^2+b^2)^5*arctan(tan(d*x+c))*a^4*b^4+3/d/(a^2+b^2)^5*ln(1+tan(d*x+c)^2)*a^5*b^3-1/3/d/(a^2+b^2)^5/(1+tan(d*x+c)^2)^3*tan(d*x+c)^3*a^2*b^6+1/2/d/(a^2+b^2)^5/(1+tan(d*x+c)^2)^3*tan(d*x+c)^5*a^2*b^6+5/2/d/(a^2+b^2)^5/(1+tan(d*x+c)^2)^3*tan(d*x+c)^2*a^3*b^5+1/2/d/(a^2+b^2)^5/(1+tan(d*x+c)^2)^3*tan(d*x+c)^2*a*b^7-5/2/d/(a^2+b^2)^5/(1+tan(d*x+c)^2)^3*tan(d*x+c)^2*b^3*a^5+13/3/d/(a^2+b^2)^5/(1+tan(d*x+c)^2)^3*tan(d*x+c)^3*a^6*b^2+5/d/(a^2+b^2)^5/(1+tan(d*x+c)^2)^3*tan(d*x+c)^3*a^4*b^4-9/2/d/(a^2+b^2)^5/(1+tan(d*x+c)^2)^3*tan(d*x+c)^2*a^7*b+25/8/d/(a^2+b^2)^5/(1+tan(d*x+c)^2)^3*tan(d*x+c)^5*a^4*b^4-3/d/(a^2+b^2)^5/(1+tan(d*x+c)^2)^3*tan(d*x+c)^4*a^5*b^3+2/d/(a^2+b^2)^5/(1+tan(d*x+c)^2)^3*tan(d*x+c)^5*a^6*b^2-1/2/d/(a^2+b^2)^5/(1+tan(d*x+c)^2)^3*tan(d*x+c)*a^2*b^6+2/d/(a^2+b^2)^5/(1+tan(d*x+c)^2)^3*tan(d*x+c)*a^6*b^2+15/8/d/(a^2+b^2)^5/(1+tan(d*x+c)^2)^3*tan(d*x+c)*a^4*b^4-3/d/(a^2+b^2)^5/(1+tan(d*x+c)^2)^3*tan(d*x+c)^4*a^7*b","B"
62,1,724,211,0.484000," ","int(sin(d*x+c)^4/(a+b*tan(d*x+c))^2,x)","-\frac{a^{4} b}{\left(a^{2}+b^{2}\right)^{3} d \left(a +b \tan \left(d x +c \right)\right)}+\frac{2 b \,a^{5} \ln \left(a +b \tan \left(d x +c \right)\right)}{d \left(a^{2}+b^{2}\right)^{4}}-\frac{4 b^{3} a^{3} \ln \left(a +b \tan \left(d x +c \right)\right)}{d \left(a^{2}+b^{2}\right)^{4}}-\frac{5 \left(\tan^{3}\left(d x +c \right)\right) a^{6}}{8 d \left(a^{2}+b^{2}\right)^{4} \left(1+\tan^{2}\left(d x +c \right)\right)^{2}}+\frac{7 \left(\tan^{3}\left(d x +c \right)\right) a^{4} b^{2}}{8 d \left(a^{2}+b^{2}\right)^{4} \left(1+\tan^{2}\left(d x +c \right)\right)^{2}}+\frac{13 \left(\tan^{3}\left(d x +c \right)\right) b^{4} a^{2}}{8 d \left(a^{2}+b^{2}\right)^{4} \left(1+\tan^{2}\left(d x +c \right)\right)^{2}}+\frac{\left(\tan^{3}\left(d x +c \right)\right) b^{6}}{8 d \left(a^{2}+b^{2}\right)^{4} \left(1+\tan^{2}\left(d x +c \right)\right)^{2}}-\frac{2 \left(\tan^{2}\left(d x +c \right)\right) a^{5} b}{d \left(a^{2}+b^{2}\right)^{4} \left(1+\tan^{2}\left(d x +c \right)\right)^{2}}-\frac{2 \left(\tan^{2}\left(d x +c \right)\right) a^{3} b^{3}}{d \left(a^{2}+b^{2}\right)^{4} \left(1+\tan^{2}\left(d x +c \right)\right)^{2}}-\frac{3 \tan \left(d x +c \right) a^{6}}{8 d \left(a^{2}+b^{2}\right)^{4} \left(1+\tan^{2}\left(d x +c \right)\right)^{2}}+\frac{9 \tan \left(d x +c \right) a^{4} b^{2}}{8 d \left(a^{2}+b^{2}\right)^{4} \left(1+\tan^{2}\left(d x +c \right)\right)^{2}}+\frac{11 \tan \left(d x +c \right) b^{4} a^{2}}{8 d \left(a^{2}+b^{2}\right)^{4} \left(1+\tan^{2}\left(d x +c \right)\right)^{2}}-\frac{\tan \left(d x +c \right) b^{6}}{8 d \left(a^{2}+b^{2}\right)^{4} \left(1+\tan^{2}\left(d x +c \right)\right)^{2}}-\frac{3 a^{5} b}{2 d \left(a^{2}+b^{2}\right)^{4} \left(1+\tan^{2}\left(d x +c \right)\right)^{2}}-\frac{b^{3} a^{3}}{d \left(a^{2}+b^{2}\right)^{4} \left(1+\tan^{2}\left(d x +c \right)\right)^{2}}+\frac{a \,b^{5}}{2 d \left(a^{2}+b^{2}\right)^{4} \left(1+\tan^{2}\left(d x +c \right)\right)^{2}}-\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right) a^{5} b}{d \left(a^{2}+b^{2}\right)^{4}}+\frac{2 \ln \left(1+\tan^{2}\left(d x +c \right)\right) a^{3} b^{3}}{d \left(a^{2}+b^{2}\right)^{4}}+\frac{3 \arctan \left(\tan \left(d x +c \right)\right) a^{6}}{8 d \left(a^{2}+b^{2}\right)^{4}}-\frac{33 \arctan \left(\tan \left(d x +c \right)\right) a^{4} b^{2}}{8 d \left(a^{2}+b^{2}\right)^{4}}+\frac{13 \arctan \left(\tan \left(d x +c \right)\right) b^{4} a^{2}}{8 d \left(a^{2}+b^{2}\right)^{4}}+\frac{\arctan \left(\tan \left(d x +c \right)\right) b^{6}}{8 d \left(a^{2}+b^{2}\right)^{4}}"," ",0,"-a^4*b/(a^2+b^2)^3/d/(a+b*tan(d*x+c))+2/d*b*a^5/(a^2+b^2)^4*ln(a+b*tan(d*x+c))-4/d*b^3*a^3/(a^2+b^2)^4*ln(a+b*tan(d*x+c))-5/8/d/(a^2+b^2)^4/(1+tan(d*x+c)^2)^2*tan(d*x+c)^3*a^6+7/8/d/(a^2+b^2)^4/(1+tan(d*x+c)^2)^2*tan(d*x+c)^3*a^4*b^2+13/8/d/(a^2+b^2)^4/(1+tan(d*x+c)^2)^2*tan(d*x+c)^3*b^4*a^2+1/8/d/(a^2+b^2)^4/(1+tan(d*x+c)^2)^2*tan(d*x+c)^3*b^6-2/d/(a^2+b^2)^4/(1+tan(d*x+c)^2)^2*tan(d*x+c)^2*a^5*b-2/d/(a^2+b^2)^4/(1+tan(d*x+c)^2)^2*tan(d*x+c)^2*a^3*b^3-3/8/d/(a^2+b^2)^4/(1+tan(d*x+c)^2)^2*tan(d*x+c)*a^6+9/8/d/(a^2+b^2)^4/(1+tan(d*x+c)^2)^2*tan(d*x+c)*a^4*b^2+11/8/d/(a^2+b^2)^4/(1+tan(d*x+c)^2)^2*tan(d*x+c)*b^4*a^2-1/8/d/(a^2+b^2)^4/(1+tan(d*x+c)^2)^2*tan(d*x+c)*b^6-3/2/d/(a^2+b^2)^4/(1+tan(d*x+c)^2)^2*a^5*b-1/d/(a^2+b^2)^4/(1+tan(d*x+c)^2)^2*b^3*a^3+1/2/d/(a^2+b^2)^4/(1+tan(d*x+c)^2)^2*a*b^5-1/d/(a^2+b^2)^4*ln(1+tan(d*x+c)^2)*a^5*b+2/d/(a^2+b^2)^4*ln(1+tan(d*x+c)^2)*a^3*b^3+3/8/d/(a^2+b^2)^4*arctan(tan(d*x+c))*a^6-33/8/d/(a^2+b^2)^4*arctan(tan(d*x+c))*a^4*b^2+13/8/d/(a^2+b^2)^4*arctan(tan(d*x+c))*b^4*a^2+1/8/d/(a^2+b^2)^4*arctan(tan(d*x+c))*b^6","B"
63,1,352,144,0.456000," ","int(sin(d*x+c)^2/(a+b*tan(d*x+c))^2,x)","-\frac{a^{2} b}{\left(a^{2}+b^{2}\right)^{2} d \left(a +b \tan \left(d x +c \right)\right)}+\frac{2 a^{3} b \ln \left(a +b \tan \left(d x +c \right)\right)}{d \left(a^{2}+b^{2}\right)^{3}}-\frac{2 a \,b^{3} \ln \left(a +b \tan \left(d x +c \right)\right)}{d \left(a^{2}+b^{2}\right)^{3}}-\frac{\tan \left(d x +c \right) a^{4}}{2 d \left(a^{2}+b^{2}\right)^{3} \left(1+\tan^{2}\left(d x +c \right)\right)}+\frac{\tan \left(d x +c \right) b^{4}}{2 d \left(a^{2}+b^{2}\right)^{3} \left(1+\tan^{2}\left(d x +c \right)\right)}-\frac{a^{3} b}{d \left(a^{2}+b^{2}\right)^{3} \left(1+\tan^{2}\left(d x +c \right)\right)}-\frac{a \,b^{3}}{d \left(a^{2}+b^{2}\right)^{3} \left(1+\tan^{2}\left(d x +c \right)\right)}-\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right) a^{3} b}{d \left(a^{2}+b^{2}\right)^{3}}+\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right) a \,b^{3}}{d \left(a^{2}+b^{2}\right)^{3}}-\frac{3 \arctan \left(\tan \left(d x +c \right)\right) a^{2} b^{2}}{d \left(a^{2}+b^{2}\right)^{3}}+\frac{\arctan \left(\tan \left(d x +c \right)\right) b^{4}}{2 d \left(a^{2}+b^{2}\right)^{3}}+\frac{\arctan \left(\tan \left(d x +c \right)\right) a^{4}}{2 d \left(a^{2}+b^{2}\right)^{3}}"," ",0,"-a^2*b/(a^2+b^2)^2/d/(a+b*tan(d*x+c))+2/d*a^3*b/(a^2+b^2)^3*ln(a+b*tan(d*x+c))-2/d*a*b^3/(a^2+b^2)^3*ln(a+b*tan(d*x+c))-1/2/d/(a^2+b^2)^3/(1+tan(d*x+c)^2)*tan(d*x+c)*a^4+1/2/d/(a^2+b^2)^3/(1+tan(d*x+c)^2)*tan(d*x+c)*b^4-1/d/(a^2+b^2)^3/(1+tan(d*x+c)^2)*a^3*b-1/d/(a^2+b^2)^3/(1+tan(d*x+c)^2)*a*b^3-1/d/(a^2+b^2)^3*ln(1+tan(d*x+c)^2)*a^3*b+1/d/(a^2+b^2)^3*ln(1+tan(d*x+c)^2)*a*b^3-3/d/(a^2+b^2)^3*arctan(tan(d*x+c))*a^2*b^2+1/2/d/(a^2+b^2)^3*arctan(tan(d*x+c))*b^4+1/2/d/(a^2+b^2)^3*arctan(tan(d*x+c))*a^4","B"
64,1,75,72,0.467000," ","int(csc(d*x+c)^2/(a+b*tan(d*x+c))^2,x)","-\frac{b}{a^{2} d \left(a +b \tan \left(d x +c \right)\right)}+\frac{2 b \ln \left(a +b \tan \left(d x +c \right)\right)}{a^{3} d}-\frac{1}{d \,a^{2} \tan \left(d x +c \right)}-\frac{2 b \ln \left(\tan \left(d x +c \right)\right)}{a^{3} d}"," ",0,"-b/a^2/d/(a+b*tan(d*x+c))+2*b*ln(a+b*tan(d*x+c))/a^3/d-1/d/a^2/tan(d*x+c)-2*b*ln(tan(d*x+c))/a^3/d","A"
65,1,189,138,0.513000," ","int(csc(d*x+c)^4/(a+b*tan(d*x+c))^2,x)","-\frac{b}{a^{2} d \left(a +b \tan \left(d x +c \right)\right)}-\frac{b^{3}}{d \,a^{4} \left(a +b \tan \left(d x +c \right)\right)}+\frac{2 b \ln \left(a +b \tan \left(d x +c \right)\right)}{a^{3} d}+\frac{4 b^{3} \ln \left(a +b \tan \left(d x +c \right)\right)}{d \,a^{5}}-\frac{1}{3 d \,a^{2} \tan \left(d x +c \right)^{3}}-\frac{1}{d \,a^{2} \tan \left(d x +c \right)}-\frac{3 b^{2}}{d \,a^{4} \tan \left(d x +c \right)}+\frac{b}{d \,a^{3} \tan \left(d x +c \right)^{2}}-\frac{2 b \ln \left(\tan \left(d x +c \right)\right)}{a^{3} d}-\frac{4 b^{3} \ln \left(\tan \left(d x +c \right)\right)}{d \,a^{5}}"," ",0,"-b/a^2/d/(a+b*tan(d*x+c))-1/d*b^3/a^4/(a+b*tan(d*x+c))+2*b*ln(a+b*tan(d*x+c))/a^3/d+4/d*b^3/a^5*ln(a+b*tan(d*x+c))-1/3/d/a^2/tan(d*x+c)^3-1/d/a^2/tan(d*x+c)-3/d/a^4/tan(d*x+c)*b^2+1/d/a^3*b/tan(d*x+c)^2-2*b*ln(tan(d*x+c))/a^3/d-4/d*b^3/a^5*ln(tan(d*x+c))","A"
66,1,343,213,0.518000," ","int(csc(d*x+c)^6/(a+b*tan(d*x+c))^2,x)","-\frac{b}{a^{2} d \left(a +b \tan \left(d x +c \right)\right)}-\frac{2 b^{3}}{d \,a^{4} \left(a +b \tan \left(d x +c \right)\right)}-\frac{b^{5}}{d \,a^{6} \left(a +b \tan \left(d x +c \right)\right)}+\frac{2 b \ln \left(a +b \tan \left(d x +c \right)\right)}{a^{3} d}+\frac{8 b^{3} \ln \left(a +b \tan \left(d x +c \right)\right)}{d \,a^{5}}+\frac{6 b^{5} \ln \left(a +b \tan \left(d x +c \right)\right)}{d \,a^{7}}-\frac{1}{5 d \,a^{2} \tan \left(d x +c \right)^{5}}-\frac{2}{3 d \,a^{2} \tan \left(d x +c \right)^{3}}-\frac{b^{2}}{d \,a^{4} \tan \left(d x +c \right)^{3}}-\frac{1}{d \,a^{2} \tan \left(d x +c \right)}-\frac{6 b^{2}}{d \,a^{4} \tan \left(d x +c \right)}-\frac{5 b^{4}}{d \,a^{6} \tan \left(d x +c \right)}+\frac{b}{2 d \,a^{3} \tan \left(d x +c \right)^{4}}+\frac{2 b}{d \,a^{3} \tan \left(d x +c \right)^{2}}+\frac{2 b^{3}}{d \,a^{5} \tan \left(d x +c \right)^{2}}-\frac{2 b \ln \left(\tan \left(d x +c \right)\right)}{a^{3} d}-\frac{8 b^{3} \ln \left(\tan \left(d x +c \right)\right)}{d \,a^{5}}-\frac{6 b^{5} \ln \left(\tan \left(d x +c \right)\right)}{d \,a^{7}}"," ",0,"-b/a^2/d/(a+b*tan(d*x+c))-2/d*b^3/a^4/(a+b*tan(d*x+c))-1/d*b^5/a^6/(a+b*tan(d*x+c))+2*b*ln(a+b*tan(d*x+c))/a^3/d+8/d*b^3/a^5*ln(a+b*tan(d*x+c))+6/d*b^5/a^7*ln(a+b*tan(d*x+c))-1/5/d/a^2/tan(d*x+c)^5-2/3/d/a^2/tan(d*x+c)^3-1/d/a^4/tan(d*x+c)^3*b^2-1/d/a^2/tan(d*x+c)-6/d/a^4/tan(d*x+c)*b^2-5/d/a^6/tan(d*x+c)*b^4+1/2/d/a^3*b/tan(d*x+c)^4+2/d/a^3*b/tan(d*x+c)^2+2/d*b^3/a^5/tan(d*x+c)^2-2*b*ln(tan(d*x+c))/a^3/d-8/d*b^3/a^5*ln(tan(d*x+c))-6/d*b^5/a^7*ln(tan(d*x+c))","A"
67,1,1449,372,0.503000," ","int(sin(d*x+c)^6/(a+b*tan(d*x+c))^3,x)","-\frac{a^{6} b}{2 \left(a^{2}+b^{2}\right)^{4} d \left(a +b \tan \left(d x +c \right)\right)^{2}}-\frac{b^{9}}{12 d \left(a^{2}+b^{2}\right)^{6} \left(1+\tan^{2}\left(d x +c \right)\right)^{3}}-\frac{3 \ln \left(1+\tan^{2}\left(d x +c \right)\right) a^{8} b}{2 d \left(a^{2}+b^{2}\right)^{6}}+\frac{11 \ln \left(1+\tan^{2}\left(d x +c \right)\right) a^{6} b^{3}}{d \left(a^{2}+b^{2}\right)^{6}}-\frac{15 \ln \left(1+\tan^{2}\left(d x +c \right)\right) a^{4} b^{5}}{2 d \left(a^{2}+b^{2}\right)^{6}}-\frac{3 a^{2} b^{7}}{2 d \left(a^{2}+b^{2}\right)^{6} \left(1+\tan^{2}\left(d x +c \right)\right)^{3}}-\frac{5 \left(\tan^{3}\left(d x +c \right)\right) a^{9}}{6 d \left(a^{2}+b^{2}\right)^{6} \left(1+\tan^{2}\left(d x +c \right)\right)^{3}}+\frac{13 a^{4} b^{5}}{2 d \left(a^{2}+b^{2}\right)^{6} \left(1+\tan^{2}\left(d x +c \right)\right)^{3}}+\frac{31 a^{6} b^{3}}{6 d \left(a^{2}+b^{2}\right)^{6} \left(1+\tan^{2}\left(d x +c \right)\right)^{3}}-\frac{11 a^{8} b}{4 d \left(a^{2}+b^{2}\right)^{6} \left(1+\tan^{2}\left(d x +c \right)\right)^{3}}-\frac{11 \left(\tan^{5}\left(d x +c \right)\right) a^{9}}{16 d \left(a^{2}+b^{2}\right)^{6} \left(1+\tan^{2}\left(d x +c \right)\right)^{3}}+\frac{3 a^{8} b \ln \left(a +b \tan \left(d x +c \right)\right)}{d \left(a^{2}+b^{2}\right)^{6}}-\frac{22 a^{6} b^{3} \ln \left(a +b \tan \left(d x +c \right)\right)}{d \left(a^{2}+b^{2}\right)^{6}}+\frac{15 a^{4} b^{5} \ln \left(a +b \tan \left(d x +c \right)\right)}{d \left(a^{2}+b^{2}\right)^{6}}-\frac{2 b \,a^{7}}{d \left(a^{2}+b^{2}\right)^{5} \left(a +b \tan \left(d x +c \right)\right)}+\frac{6 b^{3} a^{5}}{d \left(a^{2}+b^{2}\right)^{5} \left(a +b \tan \left(d x +c \right)\right)}-\frac{45 \arctan \left(\tan \left(d x +c \right)\right) a^{7} b^{2}}{4 d \left(a^{2}+b^{2}\right)^{6}}+\frac{195 \arctan \left(\tan \left(d x +c \right)\right) a^{5} b^{4}}{8 d \left(a^{2}+b^{2}\right)^{6}}-\frac{17 \arctan \left(\tan \left(d x +c \right)\right) a^{3} b^{6}}{4 d \left(a^{2}+b^{2}\right)^{6}}-\frac{3 \arctan \left(\tan \left(d x +c \right)\right) a \,b^{8}}{16 d \left(a^{2}+b^{2}\right)^{6}}-\frac{\left(\tan^{2}\left(d x +c \right)\right) b^{9}}{4 d \left(a^{2}+b^{2}\right)^{6} \left(1+\tan^{2}\left(d x +c \right)\right)^{3}}-\frac{5 \tan \left(d x +c \right) a^{9}}{16 d \left(a^{2}+b^{2}\right)^{6} \left(1+\tan^{2}\left(d x +c \right)\right)^{3}}+\frac{5 \arctan \left(\tan \left(d x +c \right)\right) a^{9}}{16 d \left(a^{2}+b^{2}\right)^{6}}-\frac{23 \tan \left(d x +c \right) a^{3} b^{6}}{4 d \left(a^{2}+b^{2}\right)^{6} \left(1+\tan^{2}\left(d x +c \right)\right)^{3}}+\frac{3 \tan \left(d x +c \right) a \,b^{8}}{16 d \left(a^{2}+b^{2}\right)^{6} \left(1+\tan^{2}\left(d x +c \right)\right)^{3}}+\frac{15 \left(\tan^{4}\left(d x +c \right)\right) a^{4} b^{5}}{2 d \left(a^{2}+b^{2}\right)^{6} \left(1+\tan^{2}\left(d x +c \right)\right)^{3}}+\frac{12 \left(\tan^{3}\left(d x +c \right)\right) a^{7} b^{2}}{d \left(a^{2}+b^{2}\right)^{6} \left(1+\tan^{2}\left(d x +c \right)\right)^{3}}+\frac{2 \left(\tan^{3}\left(d x +c \right)\right) a^{5} b^{4}}{d \left(a^{2}+b^{2}\right)^{6} \left(1+\tan^{2}\left(d x +c \right)\right)^{3}}+\frac{27 \left(\tan^{5}\left(d x +c \right)\right) a^{5} b^{4}}{8 d \left(a^{2}+b^{2}\right)^{6} \left(1+\tan^{2}\left(d x +c \right)\right)^{3}}-\frac{17 \left(\tan^{5}\left(d x +c \right)\right) a^{3} b^{6}}{4 d \left(a^{2}+b^{2}\right)^{6} \left(1+\tan^{2}\left(d x +c \right)\right)^{3}}+\frac{19 \left(\tan^{2}\left(d x +c \right)\right) a^{6} b^{3}}{2 d \left(a^{2}+b^{2}\right)^{6} \left(1+\tan^{2}\left(d x +c \right)\right)^{3}}+\frac{15 \left(\tan^{2}\left(d x +c \right)\right) a^{4} b^{5}}{d \left(a^{2}+b^{2}\right)^{6} \left(1+\tan^{2}\left(d x +c \right)\right)^{3}}-\frac{3 \left(\tan^{2}\left(d x +c \right)\right) a^{2} b^{7}}{2 d \left(a^{2}+b^{2}\right)^{6} \left(1+\tan^{2}\left(d x +c \right)\right)^{3}}-\frac{3 \tan \left(d x +c \right) a^{5} b^{4}}{8 d \left(a^{2}+b^{2}\right)^{6} \left(1+\tan^{2}\left(d x +c \right)\right)^{3}}+\frac{21 \tan \left(d x +c \right) a^{7} b^{2}}{4 d \left(a^{2}+b^{2}\right)^{6} \left(1+\tan^{2}\left(d x +c \right)\right)^{3}}-\frac{34 \left(\tan^{3}\left(d x +c \right)\right) a^{3} b^{6}}{3 d \left(a^{2}+b^{2}\right)^{6} \left(1+\tan^{2}\left(d x +c \right)\right)^{3}}-\frac{\left(\tan^{3}\left(d x +c \right)\right) a \,b^{8}}{2 d \left(a^{2}+b^{2}\right)^{6} \left(1+\tan^{2}\left(d x +c \right)\right)^{3}}-\frac{27 \left(\tan^{2}\left(d x +c \right)\right) a^{8} b}{4 d \left(a^{2}+b^{2}\right)^{6} \left(1+\tan^{2}\left(d x +c \right)\right)^{3}}-\frac{3 \left(\tan^{5}\left(d x +c \right)\right) a \,b^{8}}{16 d \left(a^{2}+b^{2}\right)^{6} \left(1+\tan^{2}\left(d x +c \right)\right)^{3}}-\frac{9 \left(\tan^{4}\left(d x +c \right)\right) a^{8} b}{2 d \left(a^{2}+b^{2}\right)^{6} \left(1+\tan^{2}\left(d x +c \right)\right)^{3}}+\frac{3 \left(\tan^{4}\left(d x +c \right)\right) a^{6} b^{3}}{d \left(a^{2}+b^{2}\right)^{6} \left(1+\tan^{2}\left(d x +c \right)\right)^{3}}+\frac{27 \left(\tan^{5}\left(d x +c \right)\right) a^{7} b^{2}}{4 d \left(a^{2}+b^{2}\right)^{6} \left(1+\tan^{2}\left(d x +c \right)\right)^{3}}"," ",0,"-1/2*a^6*b/(a^2+b^2)^4/d/(a+b*tan(d*x+c))^2-3/2/d/(a^2+b^2)^6*ln(1+tan(d*x+c)^2)*a^8*b+11/d/(a^2+b^2)^6*ln(1+tan(d*x+c)^2)*a^6*b^3-15/2/d/(a^2+b^2)^6*ln(1+tan(d*x+c)^2)*a^4*b^5+3/d*a^8*b/(a^2+b^2)^6*ln(a+b*tan(d*x+c))-22/d*a^6*b^3/(a^2+b^2)^6*ln(a+b*tan(d*x+c))+15/d*a^4*b^5/(a^2+b^2)^6*ln(a+b*tan(d*x+c))-2/d*b*a^7/(a^2+b^2)^5/(a+b*tan(d*x+c))+6/d*b^3*a^5/(a^2+b^2)^5/(a+b*tan(d*x+c))-3/2/d/(a^2+b^2)^6/(1+tan(d*x+c)^2)^3*a^2*b^7+13/2/d/(a^2+b^2)^6/(1+tan(d*x+c)^2)^3*a^4*b^5+31/6/d/(a^2+b^2)^6/(1+tan(d*x+c)^2)^3*a^6*b^3-11/4/d/(a^2+b^2)^6/(1+tan(d*x+c)^2)^3*a^8*b-11/16/d/(a^2+b^2)^6/(1+tan(d*x+c)^2)^3*tan(d*x+c)^5*a^9-5/6/d/(a^2+b^2)^6/(1+tan(d*x+c)^2)^3*tan(d*x+c)^3*a^9-1/4/d/(a^2+b^2)^6/(1+tan(d*x+c)^2)^3*tan(d*x+c)^2*b^9-5/16/d/(a^2+b^2)^6/(1+tan(d*x+c)^2)^3*tan(d*x+c)*a^9-45/4/d/(a^2+b^2)^6*arctan(tan(d*x+c))*a^7*b^2+195/8/d/(a^2+b^2)^6*arctan(tan(d*x+c))*a^5*b^4-17/4/d/(a^2+b^2)^6*arctan(tan(d*x+c))*a^3*b^6-3/16/d/(a^2+b^2)^6*arctan(tan(d*x+c))*a*b^8+5/16/d/(a^2+b^2)^6*arctan(tan(d*x+c))*a^9-1/12/d/(a^2+b^2)^6/(1+tan(d*x+c)^2)^3*b^9-23/4/d/(a^2+b^2)^6/(1+tan(d*x+c)^2)^3*tan(d*x+c)*a^3*b^6+3/16/d/(a^2+b^2)^6/(1+tan(d*x+c)^2)^3*tan(d*x+c)*a*b^8+15/2/d/(a^2+b^2)^6/(1+tan(d*x+c)^2)^3*tan(d*x+c)^4*a^4*b^5+12/d/(a^2+b^2)^6/(1+tan(d*x+c)^2)^3*tan(d*x+c)^3*a^7*b^2+2/d/(a^2+b^2)^6/(1+tan(d*x+c)^2)^3*tan(d*x+c)^3*a^5*b^4+27/8/d/(a^2+b^2)^6/(1+tan(d*x+c)^2)^3*tan(d*x+c)^5*a^5*b^4-17/4/d/(a^2+b^2)^6/(1+tan(d*x+c)^2)^3*tan(d*x+c)^5*a^3*b^6+19/2/d/(a^2+b^2)^6/(1+tan(d*x+c)^2)^3*tan(d*x+c)^2*a^6*b^3+15/d/(a^2+b^2)^6/(1+tan(d*x+c)^2)^3*tan(d*x+c)^2*a^4*b^5-3/2/d/(a^2+b^2)^6/(1+tan(d*x+c)^2)^3*tan(d*x+c)^2*a^2*b^7-3/8/d/(a^2+b^2)^6/(1+tan(d*x+c)^2)^3*tan(d*x+c)*a^5*b^4+21/4/d/(a^2+b^2)^6/(1+tan(d*x+c)^2)^3*tan(d*x+c)*a^7*b^2-34/3/d/(a^2+b^2)^6/(1+tan(d*x+c)^2)^3*tan(d*x+c)^3*a^3*b^6-1/2/d/(a^2+b^2)^6/(1+tan(d*x+c)^2)^3*tan(d*x+c)^3*a*b^8-27/4/d/(a^2+b^2)^6/(1+tan(d*x+c)^2)^3*tan(d*x+c)^2*a^8*b-3/16/d/(a^2+b^2)^6/(1+tan(d*x+c)^2)^3*tan(d*x+c)^5*a*b^8-9/2/d/(a^2+b^2)^6/(1+tan(d*x+c)^2)^3*tan(d*x+c)^4*a^8*b+3/d/(a^2+b^2)^6/(1+tan(d*x+c)^2)^3*tan(d*x+c)^4*a^6*b^3+27/4/d/(a^2+b^2)^6/(1+tan(d*x+c)^2)^3*tan(d*x+c)^5*a^7*b^2","B"
68,1,882,277,0.493000," ","int(sin(d*x+c)^4/(a+b*tan(d*x+c))^3,x)","\frac{3 \left(\tan^{2}\left(d x +c \right)\right) a^{2} b^{5}}{d \left(a^{2}+b^{2}\right)^{5} \left(1+\tan^{2}\left(d x +c \right)\right)^{2}}+\frac{29 \left(\tan^{3}\left(d x +c \right)\right) a^{5} b^{2}}{8 d \left(a^{2}+b^{2}\right)^{5} \left(1+\tan^{2}\left(d x +c \right)\right)^{2}}-\frac{3 \ln \left(1+\tan^{2}\left(d x +c \right)\right) a^{2} b^{5}}{d \left(a^{2}+b^{2}\right)^{5}}+\frac{5 a^{4} b^{3}}{4 d \left(a^{2}+b^{2}\right)^{5} \left(1+\tan^{2}\left(d x +c \right)\right)^{2}}+\frac{13 a^{2} b^{5}}{4 d \left(a^{2}+b^{2}\right)^{5} \left(1+\tan^{2}\left(d x +c \right)\right)^{2}}-\frac{3 \ln \left(1+\tan^{2}\left(d x +c \right)\right) a^{6} b}{2 d \left(a^{2}+b^{2}\right)^{5}}+\frac{15 \ln \left(1+\tan^{2}\left(d x +c \right)\right) a^{4} b^{3}}{2 d \left(a^{2}+b^{2}\right)^{5}}-\frac{5 \left(\tan^{3}\left(d x +c \right)\right) a^{7}}{8 d \left(a^{2}+b^{2}\right)^{5} \left(1+\tan^{2}\left(d x +c \right)\right)^{2}}-\frac{3 \tan \left(d x +c \right) a^{7}}{8 d \left(a^{2}+b^{2}\right)^{5} \left(1+\tan^{2}\left(d x +c \right)\right)^{2}}-\frac{9 a^{6} b}{4 d \left(a^{2}+b^{2}\right)^{5} \left(1+\tan^{2}\left(d x +c \right)\right)^{2}}+\frac{3 \arctan \left(\tan \left(d x +c \right)\right) a^{7}}{8 d \left(a^{2}+b^{2}\right)^{5}}-\frac{2 b \,a^{5}}{d \left(a^{2}+b^{2}\right)^{4} \left(a +b \tan \left(d x +c \right)\right)}+\frac{4 b^{3} a^{3}}{d \left(a^{2}+b^{2}\right)^{4} \left(a +b \tan \left(d x +c \right)\right)}+\frac{3 a^{6} b \ln \left(a +b \tan \left(d x +c \right)\right)}{d \left(a^{2}+b^{2}\right)^{5}}-\frac{9 \arctan \left(\tan \left(d x +c \right)\right) a \,b^{6}}{8 d \left(a^{2}+b^{2}\right)^{5}}-\frac{75 \arctan \left(\tan \left(d x +c \right)\right) a^{5} b^{2}}{8 d \left(a^{2}+b^{2}\right)^{5}}+\frac{105 \arctan \left(\tan \left(d x +c \right)\right) a^{3} b^{4}}{8 d \left(a^{2}+b^{2}\right)^{5}}-\frac{3 \left(\tan^{2}\left(d x +c \right)\right) a^{6} b}{d \left(a^{2}+b^{2}\right)^{5} \left(1+\tan^{2}\left(d x +c \right)\right)^{2}}+\frac{27 \tan \left(d x +c \right) a^{5} b^{2}}{8 d \left(a^{2}+b^{2}\right)^{5} \left(1+\tan^{2}\left(d x +c \right)\right)^{2}}-\frac{a^{4} b}{2 \left(a^{2}+b^{2}\right)^{3} d \left(a +b \tan \left(d x +c \right)\right)^{2}}-\frac{b^{7}}{4 d \left(a^{2}+b^{2}\right)^{5} \left(1+\tan^{2}\left(d x +c \right)\right)^{2}}+\frac{6 a^{2} b^{5} \ln \left(a +b \tan \left(d x +c \right)\right)}{d \left(a^{2}+b^{2}\right)^{5}}-\frac{15 a^{4} b^{3} \ln \left(a +b \tan \left(d x +c \right)\right)}{d \left(a^{2}+b^{2}\right)^{5}}-\frac{9 \left(\tan^{3}\left(d x +c \right)\right) a \,b^{6}}{8 d \left(a^{2}+b^{2}\right)^{5} \left(1+\tan^{2}\left(d x +c \right)\right)^{2}}+\frac{25 \left(\tan^{3}\left(d x +c \right)\right) a^{3} b^{4}}{8 d \left(a^{2}+b^{2}\right)^{5} \left(1+\tan^{2}\left(d x +c \right)\right)^{2}}-\frac{15 \tan \left(d x +c \right) a \,b^{6}}{8 d \left(a^{2}+b^{2}\right)^{5} \left(1+\tan^{2}\left(d x +c \right)\right)^{2}}+\frac{15 \tan \left(d x +c \right) a^{3} b^{4}}{8 d \left(a^{2}+b^{2}\right)^{5} \left(1+\tan^{2}\left(d x +c \right)\right)^{2}}"," ",0,"3/d/(a^2+b^2)^5/(1+tan(d*x+c)^2)^2*tan(d*x+c)^2*a^2*b^5+29/8/d/(a^2+b^2)^5/(1+tan(d*x+c)^2)^2*tan(d*x+c)^3*a^5*b^2-3/d/(a^2+b^2)^5/(1+tan(d*x+c)^2)^2*tan(d*x+c)^2*a^6*b+27/8/d/(a^2+b^2)^5/(1+tan(d*x+c)^2)^2*tan(d*x+c)*a^5*b^2-9/8/d/(a^2+b^2)^5/(1+tan(d*x+c)^2)^2*tan(d*x+c)^3*a*b^6+25/8/d/(a^2+b^2)^5/(1+tan(d*x+c)^2)^2*tan(d*x+c)^3*a^3*b^4-15/8/d/(a^2+b^2)^5/(1+tan(d*x+c)^2)^2*tan(d*x+c)*a*b^6-1/4/d/(a^2+b^2)^5/(1+tan(d*x+c)^2)^2*b^7+3/8/d/(a^2+b^2)^5*arctan(tan(d*x+c))*a^7+15/8/d/(a^2+b^2)^5/(1+tan(d*x+c)^2)^2*tan(d*x+c)*a^3*b^4-2/d*b*a^5/(a^2+b^2)^4/(a+b*tan(d*x+c))+4/d*b^3*a^3/(a^2+b^2)^4/(a+b*tan(d*x+c))-3/d/(a^2+b^2)^5*ln(1+tan(d*x+c)^2)*a^2*b^5+3/d*a^6*b/(a^2+b^2)^5*ln(a+b*tan(d*x+c))-9/8/d/(a^2+b^2)^5*arctan(tan(d*x+c))*a*b^6-75/8/d/(a^2+b^2)^5*arctan(tan(d*x+c))*a^5*b^2+105/8/d/(a^2+b^2)^5*arctan(tan(d*x+c))*a^3*b^4+5/4/d/(a^2+b^2)^5/(1+tan(d*x+c)^2)^2*a^4*b^3+13/4/d/(a^2+b^2)^5/(1+tan(d*x+c)^2)^2*a^2*b^5-3/2/d/(a^2+b^2)^5*ln(1+tan(d*x+c)^2)*a^6*b+15/2/d/(a^2+b^2)^5*ln(1+tan(d*x+c)^2)*a^4*b^3-1/2*a^4*b/(a^2+b^2)^3/d/(a+b*tan(d*x+c))^2+6/d*a^2*b^5/(a^2+b^2)^5*ln(a+b*tan(d*x+c))-15/d*a^4*b^3/(a^2+b^2)^5*ln(a+b*tan(d*x+c))-5/8/d/(a^2+b^2)^5/(1+tan(d*x+c)^2)^2*tan(d*x+c)^3*a^7-3/8/d/(a^2+b^2)^5/(1+tan(d*x+c)^2)^2*tan(d*x+c)*a^7-9/4/d/(a^2+b^2)^5/(1+tan(d*x+c)^2)^2*a^6*b","B"
69,1,542,200,0.488000," ","int(sin(d*x+c)^2/(a+b*tan(d*x+c))^3,x)","-\frac{a^{2} b}{2 \left(a^{2}+b^{2}\right)^{2} d \left(a +b \tan \left(d x +c \right)\right)^{2}}+\frac{3 b \ln \left(a +b \tan \left(d x +c \right)\right) a^{4}}{d \left(a^{2}+b^{2}\right)^{4}}-\frac{8 b^{3} \ln \left(a +b \tan \left(d x +c \right)\right) a^{2}}{d \left(a^{2}+b^{2}\right)^{4}}+\frac{b^{5} \ln \left(a +b \tan \left(d x +c \right)\right)}{d \left(a^{2}+b^{2}\right)^{4}}-\frac{2 a^{3} b}{d \left(a^{2}+b^{2}\right)^{3} \left(a +b \tan \left(d x +c \right)\right)}+\frac{2 a \,b^{3}}{d \left(a^{2}+b^{2}\right)^{3} \left(a +b \tan \left(d x +c \right)\right)}-\frac{\tan \left(d x +c \right) a^{5}}{2 d \left(a^{2}+b^{2}\right)^{4} \left(1+\tan^{2}\left(d x +c \right)\right)}+\frac{\tan \left(d x +c \right) b^{2} a^{3}}{d \left(a^{2}+b^{2}\right)^{4} \left(1+\tan^{2}\left(d x +c \right)\right)}+\frac{3 \tan \left(d x +c \right) a \,b^{4}}{2 d \left(a^{2}+b^{2}\right)^{4} \left(1+\tan^{2}\left(d x +c \right)\right)}-\frac{3 b \,a^{4}}{2 d \left(a^{2}+b^{2}\right)^{4} \left(1+\tan^{2}\left(d x +c \right)\right)}-\frac{a^{2} b^{3}}{d \left(a^{2}+b^{2}\right)^{4} \left(1+\tan^{2}\left(d x +c \right)\right)}+\frac{b^{5}}{2 d \left(a^{2}+b^{2}\right)^{4} \left(1+\tan^{2}\left(d x +c \right)\right)}-\frac{3 \ln \left(1+\tan^{2}\left(d x +c \right)\right) b \,a^{4}}{2 d \left(a^{2}+b^{2}\right)^{4}}+\frac{4 \ln \left(1+\tan^{2}\left(d x +c \right)\right) a^{2} b^{3}}{d \left(a^{2}+b^{2}\right)^{4}}-\frac{\ln \left(1+\tan^{2}\left(d x +c \right)\right) b^{5}}{2 d \left(a^{2}+b^{2}\right)^{4}}-\frac{7 \arctan \left(\tan \left(d x +c \right)\right) b^{2} a^{3}}{d \left(a^{2}+b^{2}\right)^{4}}+\frac{9 \arctan \left(\tan \left(d x +c \right)\right) a \,b^{4}}{2 d \left(a^{2}+b^{2}\right)^{4}}+\frac{\arctan \left(\tan \left(d x +c \right)\right) a^{5}}{2 d \left(a^{2}+b^{2}\right)^{4}}"," ",0,"-1/2*a^2*b/(a^2+b^2)^2/d/(a+b*tan(d*x+c))^2+3/d*b/(a^2+b^2)^4*ln(a+b*tan(d*x+c))*a^4-8/d*b^3/(a^2+b^2)^4*ln(a+b*tan(d*x+c))*a^2+1/d*b^5/(a^2+b^2)^4*ln(a+b*tan(d*x+c))-2/d*a^3*b/(a^2+b^2)^3/(a+b*tan(d*x+c))+2/d*a*b^3/(a^2+b^2)^3/(a+b*tan(d*x+c))-1/2/d/(a^2+b^2)^4/(1+tan(d*x+c)^2)*tan(d*x+c)*a^5+1/d/(a^2+b^2)^4/(1+tan(d*x+c)^2)*tan(d*x+c)*b^2*a^3+3/2/d/(a^2+b^2)^4/(1+tan(d*x+c)^2)*tan(d*x+c)*a*b^4-3/2/d/(a^2+b^2)^4/(1+tan(d*x+c)^2)*b*a^4-1/d/(a^2+b^2)^4/(1+tan(d*x+c)^2)*a^2*b^3+1/2/d/(a^2+b^2)^4/(1+tan(d*x+c)^2)*b^5-3/2/d/(a^2+b^2)^4*ln(1+tan(d*x+c)^2)*b*a^4+4/d/(a^2+b^2)^4*ln(1+tan(d*x+c)^2)*a^2*b^3-1/2/d/(a^2+b^2)^4*ln(1+tan(d*x+c)^2)*b^5-7/d/(a^2+b^2)^4*arctan(tan(d*x+c))*b^2*a^3+9/2/d/(a^2+b^2)^4*arctan(tan(d*x+c))*a*b^4+1/2/d/(a^2+b^2)^4*arctan(tan(d*x+c))*a^5","B"
70,1,96,93,0.516000," ","int(csc(d*x+c)^2/(a+b*tan(d*x+c))^3,x)","-\frac{b}{2 a^{2} d \left(a +b \tan \left(d x +c \right)\right)^{2}}+\frac{3 b \ln \left(a +b \tan \left(d x +c \right)\right)}{a^{4} d}-\frac{2 b}{a^{3} d \left(a +b \tan \left(d x +c \right)\right)}-\frac{1}{d \,a^{3} \tan \left(d x +c \right)}-\frac{3 b \ln \left(\tan \left(d x +c \right)\right)}{a^{4} d}"," ",0,"-1/2*b/a^2/d/(a+b*tan(d*x+c))^2+3*b*ln(a+b*tan(d*x+c))/a^4/d-2*b/a^3/d/(a+b*tan(d*x+c))-1/d/a^3/tan(d*x+c)-3*b*ln(tan(d*x+c))/a^4/d","A"
71,1,234,172,0.552000," ","int(csc(d*x+c)^4/(a+b*tan(d*x+c))^3,x)","\frac{3 b \ln \left(a +b \tan \left(d x +c \right)\right)}{a^{4} d}+\frac{10 b^{3} \ln \left(a +b \tan \left(d x +c \right)\right)}{d \,a^{6}}-\frac{b}{2 a^{2} d \left(a +b \tan \left(d x +c \right)\right)^{2}}-\frac{b^{3}}{2 d \,a^{4} \left(a +b \tan \left(d x +c \right)\right)^{2}}-\frac{2 b}{a^{3} d \left(a +b \tan \left(d x +c \right)\right)}-\frac{4 b^{3}}{d \,a^{5} \left(a +b \tan \left(d x +c \right)\right)}-\frac{1}{3 d \,a^{3} \tan \left(d x +c \right)^{3}}-\frac{1}{d \,a^{3} \tan \left(d x +c \right)}-\frac{6 b^{2}}{d \,a^{5} \tan \left(d x +c \right)}+\frac{3 b}{2 d \,a^{4} \tan \left(d x +c \right)^{2}}-\frac{3 b \ln \left(\tan \left(d x +c \right)\right)}{a^{4} d}-\frac{10 b^{3} \ln \left(\tan \left(d x +c \right)\right)}{d \,a^{6}}"," ",0,"3*b*ln(a+b*tan(d*x+c))/a^4/d+10/d*b^3/a^6*ln(a+b*tan(d*x+c))-1/2*b/a^2/d/(a+b*tan(d*x+c))^2-1/2/d*b^3/a^4/(a+b*tan(d*x+c))^2-2*b/a^3/d/(a+b*tan(d*x+c))-4/d*b^3/a^5/(a+b*tan(d*x+c))-1/3/d/a^3/tan(d*x+c)^3-1/d/a^3/tan(d*x+c)-6/d/a^5/tan(d*x+c)*b^2+3/2/d/a^4*b/tan(d*x+c)^2-3*b*ln(tan(d*x+c))/a^4/d-10/d*b^3/a^6*ln(tan(d*x+c))","A"
72,1,410,257,0.566000," ","int(csc(d*x+c)^6/(a+b*tan(d*x+c))^3,x)","\frac{3 b \ln \left(a +b \tan \left(d x +c \right)\right)}{a^{4} d}+\frac{20 b^{3} \ln \left(a +b \tan \left(d x +c \right)\right)}{d \,a^{6}}+\frac{21 b^{5} \ln \left(a +b \tan \left(d x +c \right)\right)}{d \,a^{8}}-\frac{b}{2 a^{2} d \left(a +b \tan \left(d x +c \right)\right)^{2}}-\frac{b^{3}}{d \,a^{4} \left(a +b \tan \left(d x +c \right)\right)^{2}}-\frac{b^{5}}{2 d \,a^{6} \left(a +b \tan \left(d x +c \right)\right)^{2}}-\frac{2 b}{a^{3} d \left(a +b \tan \left(d x +c \right)\right)}-\frac{8 b^{3}}{d \,a^{5} \left(a +b \tan \left(d x +c \right)\right)}-\frac{6 b^{5}}{d \,a^{7} \left(a +b \tan \left(d x +c \right)\right)}-\frac{1}{5 d \,a^{3} \tan \left(d x +c \right)^{5}}-\frac{2}{3 d \,a^{3} \tan \left(d x +c \right)^{3}}-\frac{2 b^{2}}{d \,a^{5} \tan \left(d x +c \right)^{3}}-\frac{1}{d \,a^{3} \tan \left(d x +c \right)}-\frac{12 b^{2}}{d \,a^{5} \tan \left(d x +c \right)}-\frac{15 b^{4}}{d \,a^{7} \tan \left(d x +c \right)}+\frac{3 b}{4 d \,a^{4} \tan \left(d x +c \right)^{4}}+\frac{3 b}{d \,a^{4} \tan \left(d x +c \right)^{2}}+\frac{5 b^{3}}{d \,a^{6} \tan \left(d x +c \right)^{2}}-\frac{3 b \ln \left(\tan \left(d x +c \right)\right)}{a^{4} d}-\frac{20 b^{3} \ln \left(\tan \left(d x +c \right)\right)}{d \,a^{6}}-\frac{21 b^{5} \ln \left(\tan \left(d x +c \right)\right)}{d \,a^{8}}"," ",0,"3*b*ln(a+b*tan(d*x+c))/a^4/d+20/d*b^3/a^6*ln(a+b*tan(d*x+c))+21/d*b^5/a^8*ln(a+b*tan(d*x+c))-1/2*b/a^2/d/(a+b*tan(d*x+c))^2-1/d*b^3/a^4/(a+b*tan(d*x+c))^2-1/2/d*b^5/a^6/(a+b*tan(d*x+c))^2-2*b/a^3/d/(a+b*tan(d*x+c))-8/d*b^3/a^5/(a+b*tan(d*x+c))-6/d*b^5/a^7/(a+b*tan(d*x+c))-1/5/d/a^3/tan(d*x+c)^5-2/3/d/a^3/tan(d*x+c)^3-2/d/a^5/tan(d*x+c)^3*b^2-1/d/a^3/tan(d*x+c)-12/d/a^5/tan(d*x+c)*b^2-15/d/a^7/tan(d*x+c)*b^4+3/4/d/a^4*b/tan(d*x+c)^4+3/d/a^4*b/tan(d*x+c)^2+5/d*b^3/a^6/tan(d*x+c)^2-3*b*ln(tan(d*x+c))/a^4/d-20/d*b^3/a^6*ln(tan(d*x+c))-21/d*b^5/a^8*ln(tan(d*x+c))","A"
73,1,1215,358,0.539000," ","int(sin(d*x+c)^4/(a+b*tan(d*x+c))^4,x)","-\frac{4 b^{7} a \ln \left(a +b \tan \left(d x +c \right)\right)}{d \left(a^{2}+b^{2}\right)^{6}}-\frac{b \,a^{5}}{d \left(a^{2}+b^{2}\right)^{4} \left(a +b \tan \left(d x +c \right)\right)^{2}}+\frac{18 \ln \left(1+\tan^{2}\left(d x +c \right)\right) a^{5} b^{3}}{d \left(a^{2}+b^{2}\right)^{6}}-\frac{18 \ln \left(1+\tan^{2}\left(d x +c \right)\right) a^{3} b^{5}}{d \left(a^{2}+b^{2}\right)^{6}}-\frac{6 a^{2} b^{5}}{d \left(a^{2}+b^{2}\right)^{5} \left(a +b \tan \left(d x +c \right)\right)}+\frac{4 b \,a^{7} \ln \left(a +b \tan \left(d x +c \right)\right)}{d \left(a^{2}+b^{2}\right)^{6}}-\frac{2 \left(\tan^{2}\left(d x +c \right)\right) a \,b^{7}}{d \left(a^{2}+b^{2}\right)^{6} \left(1+\tan^{2}\left(d x +c \right)\right)^{2}}+\frac{13 \tan \left(d x +c \right) a^{6} b^{2}}{2 d \left(a^{2}+b^{2}\right)^{6} \left(1+\tan^{2}\left(d x +c \right)\right)^{2}}-\frac{15 \tan \left(d x +c \right) a^{2} b^{6}}{2 d \left(a^{2}+b^{2}\right)^{6} \left(1+\tan^{2}\left(d x +c \right)\right)^{2}}-\frac{5 \tan \left(d x +c \right) a^{4} b^{4}}{4 d \left(a^{2}+b^{2}\right)^{6} \left(1+\tan^{2}\left(d x +c \right)\right)^{2}}+\frac{15 \left(\tan^{3}\left(d x +c \right)\right) a^{6} b^{2}}{2 d \left(a^{2}+b^{2}\right)^{6} \left(1+\tan^{2}\left(d x +c \right)\right)^{2}}+\frac{5 \left(\tan^{3}\left(d x +c \right)\right) a^{4} b^{4}}{4 d \left(a^{2}+b^{2}\right)^{6} \left(1+\tan^{2}\left(d x +c \right)\right)^{2}}-\frac{13 \left(\tan^{3}\left(d x +c \right)\right) a^{2} b^{6}}{2 d \left(a^{2}+b^{2}\right)^{6} \left(1+\tan^{2}\left(d x +c \right)\right)^{2}}-\frac{4 \left(\tan^{2}\left(d x +c \right)\right) a^{7} b}{d \left(a^{2}+b^{2}\right)^{6} \left(1+\tan^{2}\left(d x +c \right)\right)^{2}}+\frac{6 \left(\tan^{2}\left(d x +c \right)\right) a^{5} b^{3}}{d \left(a^{2}+b^{2}\right)^{6} \left(1+\tan^{2}\left(d x +c \right)\right)^{2}}+\frac{8 \left(\tan^{2}\left(d x +c \right)\right) a^{3} b^{5}}{d \left(a^{2}+b^{2}\right)^{6} \left(1+\tan^{2}\left(d x +c \right)\right)^{2}}+\frac{2 b^{3} a^{3}}{d \left(a^{2}+b^{2}\right)^{4} \left(a +b \tan \left(d x +c \right)\right)^{2}}-\frac{33 \arctan \left(\tan \left(d x +c \right)\right) a^{2} b^{6}}{2 d \left(a^{2}+b^{2}\right)^{6}}+\frac{7 a^{3} b^{5}}{d \left(a^{2}+b^{2}\right)^{6} \left(1+\tan^{2}\left(d x +c \right)\right)^{2}}-\frac{3 a \,b^{7}}{d \left(a^{2}+b^{2}\right)^{6} \left(1+\tan^{2}\left(d x +c \right)\right)^{2}}+\frac{3 \arctan \left(\tan \left(d x +c \right)\right) b^{8}}{8 d \left(a^{2}+b^{2}\right)^{6}}+\frac{3 \arctan \left(\tan \left(d x +c \right)\right) a^{8}}{8 d \left(a^{2}+b^{2}\right)^{6}}-\frac{2 \ln \left(1+\tan^{2}\left(d x +c \right)\right) a^{7} b}{d \left(a^{2}+b^{2}\right)^{6}}-\frac{5 \left(\tan^{3}\left(d x +c \right)\right) a^{8}}{8 d \left(a^{2}+b^{2}\right)^{6} \left(1+\tan^{2}\left(d x +c \right)\right)^{2}}-\frac{36 b^{3} a^{5} \ln \left(a +b \tan \left(d x +c \right)\right)}{d \left(a^{2}+b^{2}\right)^{6}}+\frac{36 b^{5} a^{3} \ln \left(a +b \tan \left(d x +c \right)\right)}{d \left(a^{2}+b^{2}\right)^{6}}-\frac{a^{4} b}{3 \left(a^{2}+b^{2}\right)^{3} d \left(a +b \tan \left(d x +c \right)\right)^{3}}-\frac{33 \arctan \left(\tan \left(d x +c \right)\right) a^{6} b^{2}}{2 d \left(a^{2}+b^{2}\right)^{6}}+\frac{185 \arctan \left(\tan \left(d x +c \right)\right) a^{4} b^{4}}{4 d \left(a^{2}+b^{2}\right)^{6}}-\frac{3 a^{6} b}{d \left(a^{2}+b^{2}\right)^{5} \left(a +b \tan \left(d x +c \right)\right)}+\frac{15 a^{4} b^{3}}{d \left(a^{2}+b^{2}\right)^{5} \left(a +b \tan \left(d x +c \right)\right)}-\frac{3 \tan \left(d x +c \right) a^{8}}{8 d \left(a^{2}+b^{2}\right)^{6} \left(1+\tan^{2}\left(d x +c \right)\right)^{2}}+\frac{5 \tan \left(d x +c \right) b^{8}}{8 d \left(a^{2}+b^{2}\right)^{6} \left(1+\tan^{2}\left(d x +c \right)\right)^{2}}+\frac{2 \ln \left(1+\tan^{2}\left(d x +c \right)\right) a \,b^{7}}{d \left(a^{2}+b^{2}\right)^{6}}+\frac{3 \left(\tan^{3}\left(d x +c \right)\right) b^{8}}{8 d \left(a^{2}+b^{2}\right)^{6} \left(1+\tan^{2}\left(d x +c \right)\right)^{2}}-\frac{3 a^{7} b}{d \left(a^{2}+b^{2}\right)^{6} \left(1+\tan^{2}\left(d x +c \right)\right)^{2}}+\frac{7 b^{3} a^{5}}{d \left(a^{2}+b^{2}\right)^{6} \left(1+\tan^{2}\left(d x +c \right)\right)^{2}}"," ",0,"-4/d*b^7*a/(a^2+b^2)^6*ln(a+b*tan(d*x+c))-1/d*b*a^5/(a^2+b^2)^4/(a+b*tan(d*x+c))^2-6/d*a^2*b^5/(a^2+b^2)^5/(a+b*tan(d*x+c))+4/d*b*a^7/(a^2+b^2)^6*ln(a+b*tan(d*x+c))+2/d*b^3*a^3/(a^2+b^2)^4/(a+b*tan(d*x+c))^2-33/2/d/(a^2+b^2)^6*arctan(tan(d*x+c))*a^2*b^6-5/8/d/(a^2+b^2)^6/(1+tan(d*x+c)^2)^2*tan(d*x+c)^3*a^8+3/8/d/(a^2+b^2)^6*arctan(tan(d*x+c))*b^8+3/8/d/(a^2+b^2)^6*arctan(tan(d*x+c))*a^8-2/d/(a^2+b^2)^6/(1+tan(d*x+c)^2)^2*tan(d*x+c)^2*a*b^7+13/2/d/(a^2+b^2)^6/(1+tan(d*x+c)^2)^2*tan(d*x+c)*a^6*b^2-15/2/d/(a^2+b^2)^6/(1+tan(d*x+c)^2)^2*tan(d*x+c)*a^2*b^6-5/4/d/(a^2+b^2)^6/(1+tan(d*x+c)^2)^2*tan(d*x+c)*a^4*b^4+15/2/d/(a^2+b^2)^6/(1+tan(d*x+c)^2)^2*tan(d*x+c)^3*a^6*b^2+5/4/d/(a^2+b^2)^6/(1+tan(d*x+c)^2)^2*tan(d*x+c)^3*a^4*b^4-13/2/d/(a^2+b^2)^6/(1+tan(d*x+c)^2)^2*tan(d*x+c)^3*a^2*b^6-4/d/(a^2+b^2)^6/(1+tan(d*x+c)^2)^2*tan(d*x+c)^2*a^7*b+6/d/(a^2+b^2)^6/(1+tan(d*x+c)^2)^2*tan(d*x+c)^2*a^5*b^3+8/d/(a^2+b^2)^6/(1+tan(d*x+c)^2)^2*tan(d*x+c)^2*a^3*b^5-36/d*b^3*a^5/(a^2+b^2)^6*ln(a+b*tan(d*x+c))+7/d/(a^2+b^2)^6/(1+tan(d*x+c)^2)^2*a^3*b^5-3/d/(a^2+b^2)^6/(1+tan(d*x+c)^2)^2*a*b^7-2/d/(a^2+b^2)^6*ln(1+tan(d*x+c)^2)*a^7*b+18/d/(a^2+b^2)^6*ln(1+tan(d*x+c)^2)*a^5*b^3-18/d/(a^2+b^2)^6*ln(1+tan(d*x+c)^2)*a^3*b^5+36/d*b^5*a^3/(a^2+b^2)^6*ln(a+b*tan(d*x+c))-1/3*a^4*b/(a^2+b^2)^3/d/(a+b*tan(d*x+c))^3+2/d/(a^2+b^2)^6*ln(1+tan(d*x+c)^2)*a*b^7-33/2/d/(a^2+b^2)^6*arctan(tan(d*x+c))*a^6*b^2+185/4/d/(a^2+b^2)^6*arctan(tan(d*x+c))*a^4*b^4+3/8/d/(a^2+b^2)^6/(1+tan(d*x+c)^2)^2*tan(d*x+c)^3*b^8-3/8/d/(a^2+b^2)^6/(1+tan(d*x+c)^2)^2*tan(d*x+c)*a^8+5/8/d/(a^2+b^2)^6/(1+tan(d*x+c)^2)^2*tan(d*x+c)*b^8-3/d/(a^2+b^2)^6/(1+tan(d*x+c)^2)^2*a^7*b+7/d/(a^2+b^2)^6/(1+tan(d*x+c)^2)^2*b^3*a^5-3/d*a^6*b/(a^2+b^2)^5/(a+b*tan(d*x+c))+15/d*a^4*b^3/(a^2+b^2)^5/(a+b*tan(d*x+c))","B"
74,1,668,258,0.549000," ","int(sin(d*x+c)^2/(a+b*tan(d*x+c))^4,x)","-\frac{a^{2} b}{3 \left(a^{2}+b^{2}\right)^{2} d \left(a +b \tan \left(d x +c \right)\right)^{3}}-\frac{3 b \,a^{4}}{d \left(a^{2}+b^{2}\right)^{4} \left(a +b \tan \left(d x +c \right)\right)}+\frac{8 b^{3} a^{2}}{d \left(a^{2}+b^{2}\right)^{4} \left(a +b \tan \left(d x +c \right)\right)}-\frac{b^{5}}{d \left(a^{2}+b^{2}\right)^{4} \left(a +b \tan \left(d x +c \right)\right)}-\frac{a^{3} b}{d \left(a^{2}+b^{2}\right)^{3} \left(a +b \tan \left(d x +c \right)\right)^{2}}+\frac{a \,b^{3}}{d \left(a^{2}+b^{2}\right)^{3} \left(a +b \tan \left(d x +c \right)\right)^{2}}+\frac{4 a^{5} b \ln \left(a +b \tan \left(d x +c \right)\right)}{d \left(a^{2}+b^{2}\right)^{5}}-\frac{20 a^{3} b^{3} \ln \left(a +b \tan \left(d x +c \right)\right)}{d \left(a^{2}+b^{2}\right)^{5}}+\frac{8 a \,b^{5} \ln \left(a +b \tan \left(d x +c \right)\right)}{d \left(a^{2}+b^{2}\right)^{5}}-\frac{\tan \left(d x +c \right) a^{6}}{2 d \left(a^{2}+b^{2}\right)^{5} \left(1+\tan^{2}\left(d x +c \right)\right)}+\frac{5 \tan \left(d x +c \right) a^{4} b^{2}}{2 d \left(a^{2}+b^{2}\right)^{5} \left(1+\tan^{2}\left(d x +c \right)\right)}+\frac{5 \tan \left(d x +c \right) b^{4} a^{2}}{2 d \left(a^{2}+b^{2}\right)^{5} \left(1+\tan^{2}\left(d x +c \right)\right)}-\frac{\tan \left(d x +c \right) b^{6}}{2 d \left(a^{2}+b^{2}\right)^{5} \left(1+\tan^{2}\left(d x +c \right)\right)}-\frac{2 a^{5} b}{d \left(a^{2}+b^{2}\right)^{5} \left(1+\tan^{2}\left(d x +c \right)\right)}+\frac{2 a \,b^{5}}{d \left(a^{2}+b^{2}\right)^{5} \left(1+\tan^{2}\left(d x +c \right)\right)}-\frac{2 \ln \left(1+\tan^{2}\left(d x +c \right)\right) a^{5} b}{d \left(a^{2}+b^{2}\right)^{5}}+\frac{10 \ln \left(1+\tan^{2}\left(d x +c \right)\right) a^{3} b^{3}}{d \left(a^{2}+b^{2}\right)^{5}}-\frac{4 \ln \left(1+\tan^{2}\left(d x +c \right)\right) a \,b^{5}}{d \left(a^{2}+b^{2}\right)^{5}}-\frac{25 \arctan \left(\tan \left(d x +c \right)\right) a^{4} b^{2}}{2 d \left(a^{2}+b^{2}\right)^{5}}+\frac{35 \arctan \left(\tan \left(d x +c \right)\right) b^{4} a^{2}}{2 d \left(a^{2}+b^{2}\right)^{5}}-\frac{3 \arctan \left(\tan \left(d x +c \right)\right) b^{6}}{2 d \left(a^{2}+b^{2}\right)^{5}}+\frac{\arctan \left(\tan \left(d x +c \right)\right) a^{6}}{2 d \left(a^{2}+b^{2}\right)^{5}}"," ",0,"-1/3*a^2*b/(a^2+b^2)^2/d/(a+b*tan(d*x+c))^3-3/d*b/(a^2+b^2)^4/(a+b*tan(d*x+c))*a^4+8/d*b^3/(a^2+b^2)^4/(a+b*tan(d*x+c))*a^2-1/d*b^5/(a^2+b^2)^4/(a+b*tan(d*x+c))-1/d*a^3*b/(a^2+b^2)^3/(a+b*tan(d*x+c))^2+1/d*a*b^3/(a^2+b^2)^3/(a+b*tan(d*x+c))^2+4/d*a^5*b/(a^2+b^2)^5*ln(a+b*tan(d*x+c))-20/d*a^3*b^3/(a^2+b^2)^5*ln(a+b*tan(d*x+c))+8/d*a*b^5/(a^2+b^2)^5*ln(a+b*tan(d*x+c))-1/2/d/(a^2+b^2)^5/(1+tan(d*x+c)^2)*tan(d*x+c)*a^6+5/2/d/(a^2+b^2)^5/(1+tan(d*x+c)^2)*tan(d*x+c)*a^4*b^2+5/2/d/(a^2+b^2)^5/(1+tan(d*x+c)^2)*tan(d*x+c)*b^4*a^2-1/2/d/(a^2+b^2)^5/(1+tan(d*x+c)^2)*tan(d*x+c)*b^6-2/d/(a^2+b^2)^5/(1+tan(d*x+c)^2)*a^5*b+2/d/(a^2+b^2)^5/(1+tan(d*x+c)^2)*a*b^5-2/d/(a^2+b^2)^5*ln(1+tan(d*x+c)^2)*a^5*b+10/d/(a^2+b^2)^5*ln(1+tan(d*x+c)^2)*a^3*b^3-4/d/(a^2+b^2)^5*ln(1+tan(d*x+c)^2)*a*b^5-25/2/d/(a^2+b^2)^5*arctan(tan(d*x+c))*a^4*b^2+35/2/d/(a^2+b^2)^5*arctan(tan(d*x+c))*b^4*a^2-3/2/d/(a^2+b^2)^5*arctan(tan(d*x+c))*b^6+1/2/d/(a^2+b^2)^5*arctan(tan(d*x+c))*a^6","B"
75,1,117,114,0.531000," ","int(csc(d*x+c)^2/(a+b*tan(d*x+c))^4,x)","-\frac{b}{3 a^{2} d \left(a +b \tan \left(d x +c \right)\right)^{3}}+\frac{4 b \ln \left(a +b \tan \left(d x +c \right)\right)}{a^{5} d}-\frac{3 b}{a^{4} d \left(a +b \tan \left(d x +c \right)\right)}-\frac{b}{a^{3} d \left(a +b \tan \left(d x +c \right)\right)^{2}}-\frac{1}{d \,a^{4} \tan \left(d x +c \right)}-\frac{4 b \ln \left(\tan \left(d x +c \right)\right)}{a^{5} d}"," ",0,"-1/3*b/a^2/d/(a+b*tan(d*x+c))^3+4*b*ln(a+b*tan(d*x+c))/a^5/d-3*b/a^4/d/(a+b*tan(d*x+c))-b/a^3/d/(a+b*tan(d*x+c))^2-1/d/a^4/tan(d*x+c)-4*b*ln(tan(d*x+c))/a^5/d","A"
76,1,278,201,0.588000," ","int(csc(d*x+c)^4/(a+b*tan(d*x+c))^4,x)","-\frac{3 b}{a^{4} d \left(a +b \tan \left(d x +c \right)\right)}-\frac{10 b^{3}}{d \,a^{6} \left(a +b \tan \left(d x +c \right)\right)}-\frac{b}{3 a^{2} d \left(a +b \tan \left(d x +c \right)\right)^{3}}-\frac{b^{3}}{3 d \,a^{4} \left(a +b \tan \left(d x +c \right)\right)^{3}}-\frac{b}{a^{3} d \left(a +b \tan \left(d x +c \right)\right)^{2}}-\frac{2 b^{3}}{d \,a^{5} \left(a +b \tan \left(d x +c \right)\right)^{2}}+\frac{4 b \ln \left(a +b \tan \left(d x +c \right)\right)}{a^{5} d}+\frac{20 b^{3} \ln \left(a +b \tan \left(d x +c \right)\right)}{d \,a^{7}}-\frac{1}{3 d \,a^{4} \tan \left(d x +c \right)^{3}}-\frac{1}{d \,a^{4} \tan \left(d x +c \right)}-\frac{10 b^{2}}{d \,a^{6} \tan \left(d x +c \right)}+\frac{2 b}{d \,a^{5} \tan \left(d x +c \right)^{2}}-\frac{4 b \ln \left(\tan \left(d x +c \right)\right)}{a^{5} d}-\frac{20 b^{3} \ln \left(\tan \left(d x +c \right)\right)}{d \,a^{7}}"," ",0,"-3*b/a^4/d/(a+b*tan(d*x+c))-10/d*b^3/a^6/(a+b*tan(d*x+c))-1/3*b/a^2/d/(a+b*tan(d*x+c))^3-1/3/d*b^3/a^4/(a+b*tan(d*x+c))^3-b/a^3/d/(a+b*tan(d*x+c))^2-2/d*b^3/a^5/(a+b*tan(d*x+c))^2+4*b*ln(a+b*tan(d*x+c))/a^5/d+20/d*b^3/a^7*ln(a+b*tan(d*x+c))-1/3/d/a^4/tan(d*x+c)^3-1/d/a^4/tan(d*x+c)-10/d/a^6/tan(d*x+c)*b^2+2/d/a^5*b/tan(d*x+c)^2-4*b*ln(tan(d*x+c))/a^5/d-20/d*b^3/a^7*ln(tan(d*x+c))","A"
77,1,476,294,0.599000," ","int(csc(d*x+c)^6/(a+b*tan(d*x+c))^4,x)","-\frac{3 b}{a^{4} d \left(a +b \tan \left(d x +c \right)\right)}-\frac{20 b^{3}}{d \,a^{6} \left(a +b \tan \left(d x +c \right)\right)}-\frac{21 b^{5}}{d \,a^{8} \left(a +b \tan \left(d x +c \right)\right)}-\frac{b}{3 a^{2} d \left(a +b \tan \left(d x +c \right)\right)^{3}}-\frac{2 b^{3}}{3 d \,a^{4} \left(a +b \tan \left(d x +c \right)\right)^{3}}-\frac{b^{5}}{3 d \,a^{6} \left(a +b \tan \left(d x +c \right)\right)^{3}}-\frac{b}{a^{3} d \left(a +b \tan \left(d x +c \right)\right)^{2}}-\frac{4 b^{3}}{d \,a^{5} \left(a +b \tan \left(d x +c \right)\right)^{2}}-\frac{3 b^{5}}{d \,a^{7} \left(a +b \tan \left(d x +c \right)\right)^{2}}+\frac{4 b \ln \left(a +b \tan \left(d x +c \right)\right)}{a^{5} d}+\frac{40 b^{3} \ln \left(a +b \tan \left(d x +c \right)\right)}{d \,a^{7}}+\frac{56 b^{5} \ln \left(a +b \tan \left(d x +c \right)\right)}{d \,a^{9}}-\frac{1}{5 d \,a^{4} \tan \left(d x +c \right)^{5}}-\frac{2}{3 d \,a^{4} \tan \left(d x +c \right)^{3}}-\frac{10 b^{2}}{3 d \,a^{6} \tan \left(d x +c \right)^{3}}-\frac{1}{d \,a^{4} \tan \left(d x +c \right)}-\frac{20 b^{2}}{d \,a^{6} \tan \left(d x +c \right)}-\frac{35 b^{4}}{d \,a^{8} \tan \left(d x +c \right)}+\frac{b}{d \,a^{5} \tan \left(d x +c \right)^{4}}+\frac{4 b}{d \,a^{5} \tan \left(d x +c \right)^{2}}+\frac{10 b^{3}}{d \,a^{7} \tan \left(d x +c \right)^{2}}-\frac{4 b \ln \left(\tan \left(d x +c \right)\right)}{a^{5} d}-\frac{40 b^{3} \ln \left(\tan \left(d x +c \right)\right)}{d \,a^{7}}-\frac{56 b^{5} \ln \left(\tan \left(d x +c \right)\right)}{d \,a^{9}}"," ",0,"-3*b/a^4/d/(a+b*tan(d*x+c))-20/d*b^3/a^6/(a+b*tan(d*x+c))-21/d*b^5/a^8/(a+b*tan(d*x+c))-1/3*b/a^2/d/(a+b*tan(d*x+c))^3-2/3/d*b^3/a^4/(a+b*tan(d*x+c))^3-1/3/d*b^5/a^6/(a+b*tan(d*x+c))^3-b/a^3/d/(a+b*tan(d*x+c))^2-4/d*b^3/a^5/(a+b*tan(d*x+c))^2-3/d*b^5/a^7/(a+b*tan(d*x+c))^2+4*b*ln(a+b*tan(d*x+c))/a^5/d+40/d*b^3/a^7*ln(a+b*tan(d*x+c))+56/d*b^5/a^9*ln(a+b*tan(d*x+c))-1/5/d/a^4/tan(d*x+c)^5-2/3/d/a^4/tan(d*x+c)^3-10/3/d/a^6/tan(d*x+c)^3*b^2-1/d/a^4/tan(d*x+c)-20/d/a^6/tan(d*x+c)*b^2-35/d/a^8/tan(d*x+c)*b^4+1/d/a^5*b/tan(d*x+c)^4+4/d/a^5*b/tan(d*x+c)^2+10/d*b^3/a^7/tan(d*x+c)^2-4*b*ln(tan(d*x+c))/a^5/d-40/d*b^3/a^7*ln(tan(d*x+c))-56/d*b^5/a^9*ln(tan(d*x+c))","A"
78,1,26,24,0.121000," ","int(csc(x)/(1+tan(x)),x)","-\sqrt{2}\, \arctanh \left(\frac{\left(2 \tan \left(\frac{x}{2}\right)-2\right) \sqrt{2}}{4}\right)+\ln \left(\tan \left(\frac{x}{2}\right)\right)"," ",0,"-2^(1/2)*arctanh(1/4*(2*tan(1/2*x)-2)*2^(1/2))+ln(tan(1/2*x))","A"
79,0,0,213,1.202000," ","int(sin(d*x+c)^m*(a+b*tan(d*x+c))^3,x)","\int \left(\sin^{m}\left(d x +c \right)\right) \left(a +b \tan \left(d x +c \right)\right)^{3}\, dx"," ",0,"int(sin(d*x+c)^m*(a+b*tan(d*x+c))^3,x)","F"
80,0,0,165,0.941000," ","int(sin(d*x+c)^m*(a+b*tan(d*x+c))^2,x)","\int \left(\sin^{m}\left(d x +c \right)\right) \left(a +b \tan \left(d x +c \right)\right)^{2}\, dx"," ",0,"int(sin(d*x+c)^m*(a+b*tan(d*x+c))^2,x)","F"
81,0,0,101,1.399000," ","int(sin(d*x+c)^m*(a+b*tan(d*x+c)),x)","\int \left(\sin^{m}\left(d x +c \right)\right) \left(a +b \tan \left(d x +c \right)\right)\, dx"," ",0,"int(sin(d*x+c)^m*(a+b*tan(d*x+c)),x)","F"
82,0,0,694,1.083000," ","int(sin(d*x+c)^m/(a+b*tan(d*x+c)),x)","\int \frac{\sin^{m}\left(d x +c \right)}{a +b \tan \left(d x +c \right)}\, dx"," ",0,"int(sin(d*x+c)^m/(a+b*tan(d*x+c)),x)","F"
83,0,0,23,1.551000," ","int(sin(d*x+c)^m*(a+b*tan(d*x+c))^n,x)","\int \left(\sin^{m}\left(d x +c \right)\right) \left(a +b \tan \left(d x +c \right)\right)^{n}\, dx"," ",0,"int(sin(d*x+c)^m*(a+b*tan(d*x+c))^n,x)","F"
84,0,0,419,3.519000," ","int(sin(d*x+c)^4*(a+b*tan(d*x+c))^n,x)","\int \left(\sin^{4}\left(d x +c \right)\right) \left(a +b \tan \left(d x +c \right)\right)^{n}\, dx"," ",0,"int(sin(d*x+c)^4*(a+b*tan(d*x+c))^n,x)","F"
85,0,0,262,1.999000," ","int(sin(d*x+c)^2*(a+b*tan(d*x+c))^n,x)","\int \left(\sin^{2}\left(d x +c \right)\right) \left(a +b \tan \left(d x +c \right)\right)^{n}\, dx"," ",0,"int(sin(d*x+c)^2*(a+b*tan(d*x+c))^n,x)","F"
86,0,0,50,0.873000," ","int(csc(d*x+c)^2*(a+b*tan(d*x+c))^n,x)","\int \left(\csc^{2}\left(d x +c \right)\right) \left(a +b \tan \left(d x +c \right)\right)^{n}\, dx"," ",0,"int(csc(d*x+c)^2*(a+b*tan(d*x+c))^n,x)","F"
87,0,0,136,0.741000," ","int(csc(d*x+c)^4*(a+b*tan(d*x+c))^n,x)","\int \left(\csc^{4}\left(d x +c \right)\right) \left(a +b \tan \left(d x +c \right)\right)^{n}\, dx"," ",0,"int(csc(d*x+c)^4*(a+b*tan(d*x+c))^n,x)","F"
88,0,0,23,1.869000," ","int(sin(d*x+c)^3*(a+b*tan(d*x+c))^n,x)","\int \left(\sin^{3}\left(d x +c \right)\right) \left(a +b \tan \left(d x +c \right)\right)^{n}\, dx"," ",0,"int(sin(d*x+c)^3*(a+b*tan(d*x+c))^n,x)","F"
89,0,0,21,0.460000," ","int(sin(d*x+c)*(a+b*tan(d*x+c))^n,x)","\int \sin \left(d x +c \right) \left(a +b \tan \left(d x +c \right)\right)^{n}\, dx"," ",0,"int(sin(d*x+c)*(a+b*tan(d*x+c))^n,x)","F"
90,0,0,21,0.867000," ","int(csc(d*x+c)*(a+b*tan(d*x+c))^n,x)","\int \csc \left(d x +c \right) \left(a +b \tan \left(d x +c \right)\right)^{n}\, dx"," ",0,"int(csc(d*x+c)*(a+b*tan(d*x+c))^n,x)","F"
91,0,0,23,0.752000," ","int(csc(d*x+c)^3*(a+b*tan(d*x+c))^n,x)","\int \left(\csc^{3}\left(d x +c \right)\right) \left(a +b \tan \left(d x +c \right)\right)^{n}\, dx"," ",0,"int(csc(d*x+c)^3*(a+b*tan(d*x+c))^n,x)","F"