1,1,28,28,0.839000," ","int(sin(x)^3*(a*cos(x)+b*sin(x)),x)","b \left(-\frac{\left(\sin^{3}\left(x \right)+\frac{3 \sin \left(x \right)}{2}\right) \cos \left(x \right)}{4}+\frac{3 x}{8}\right)+\frac{a \left(\sin^{4}\left(x \right)\right)}{4}"," ",0,"b*(-1/4*(sin(x)^3+3/2*sin(x))*cos(x)+3/8*x)+1/4*a*sin(x)^4","A"
2,1,20,20,0.818000," ","int(sin(x)^2*(a*cos(x)+b*sin(x)),x)","-\frac{b \left(2+\sin^{2}\left(x \right)\right) \cos \left(x \right)}{3}+\frac{a \left(\sin^{3}\left(x \right)\right)}{3}"," ",0,"-1/3*b*(2+sin(x)^2)*cos(x)+1/3*a*sin(x)^3","A"
3,1,21,19,0.157000," ","int(sin(x)*(a*cos(x)+b*sin(x)),x)","b \left(-\frac{\cos \left(x \right) \sin \left(x \right)}{2}+\frac{x}{2}\right)-\frac{a \left(\cos^{2}\left(x \right)\right)}{2}"," ",0,"b*(-1/2*cos(x)*sin(x)+1/2*x)-1/2*a*cos(x)^2","A"
4,1,11,10,0.055000," ","int(a*cos(x)+b*sin(x),x)","-b \cos \left(x \right)+a \sin \left(x \right)"," ",0,"-b*cos(x)+a*sin(x)","A"
5,1,10,9,0.451000," ","int(csc(x)*(a*cos(x)+b*sin(x)),x)","b x +a \ln \left(\sin \left(x \right)\right)"," ",0,"b*x+a*ln(sin(x))","A"
6,1,19,12,0.495000," ","int(csc(x)^2*(a*cos(x)+b*sin(x)),x)","-\frac{a}{\sin \left(x \right)}+b \ln \left(-\cot \left(x \right)+\csc \left(x \right)\right)"," ",0,"-a/sin(x)+b*ln(-cot(x)+csc(x))","A"
7,1,14,13,0.824000," ","int(csc(x)^3*(a*cos(x)+b*sin(x)),x)","-\frac{a}{2 \sin \left(x \right)^{2}}-b \cot \left(x \right)"," ",0,"-1/2*a/sin(x)^2-b*cot(x)","A"
8,1,173,85,0.473000," ","int(sin(x)^3/(a*cos(x)+b*sin(x)),x)","-\frac{a^{3} \ln \left(a +b \tan \left(x \right)\right)}{\left(a^{2}+b^{2}\right)^{2}}-\frac{\tan \left(x \right) a^{2} b}{2 \left(a^{2}+b^{2}\right)^{2} \left(1+\tan^{2}\left(x \right)\right)}-\frac{\tan \left(x \right) b^{3}}{2 \left(a^{2}+b^{2}\right)^{2} \left(1+\tan^{2}\left(x \right)\right)}+\frac{a^{3}}{2 \left(a^{2}+b^{2}\right)^{2} \left(1+\tan^{2}\left(x \right)\right)}+\frac{b^{2} a}{2 \left(a^{2}+b^{2}\right)^{2} \left(1+\tan^{2}\left(x \right)\right)}+\frac{a^{3} \ln \left(1+\tan^{2}\left(x \right)\right)}{2 \left(a^{2}+b^{2}\right)^{2}}+\frac{3 \arctan \left(\tan \left(x \right)\right) a^{2} b}{2 \left(a^{2}+b^{2}\right)^{2}}+\frac{\arctan \left(\tan \left(x \right)\right) b^{3}}{2 \left(a^{2}+b^{2}\right)^{2}}"," ",0,"-a^3/(a^2+b^2)^2*ln(a+b*tan(x))-1/2/(a^2+b^2)^2/(1+tan(x)^2)*tan(x)*a^2*b-1/2/(a^2+b^2)^2/(1+tan(x)^2)*tan(x)*b^3+1/2/(a^2+b^2)^2/(1+tan(x)^2)*a^3+1/2/(a^2+b^2)^2/(1+tan(x)^2)*b^2*a+1/2/(a^2+b^2)^2*a^3*ln(1+tan(x)^2)+3/2/(a^2+b^2)^2*arctan(tan(x))*a^2*b+1/2/(a^2+b^2)^2*arctan(tan(x))*b^3","B"
9,1,84,64,0.486000," ","int(sin(x)^2/(a*cos(x)+b*sin(x)),x)","\frac{8 a^{2} \arctanh \left(\frac{2 a \tan \left(\frac{x}{2}\right)-2 b}{2 \sqrt{a^{2}+b^{2}}}\right)}{\left(4 a^{2}+4 b^{2}\right) \sqrt{a^{2}+b^{2}}}+\frac{-2 a \tan \left(\frac{x}{2}\right)-2 b}{\left(a^{2}+b^{2}\right) \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)}"," ",0,"8*a^2/(4*a^2+4*b^2)/(a^2+b^2)^(1/2)*arctanh(1/2*(2*a*tan(1/2*x)-2*b)/(a^2+b^2)^(1/2))+2/(a^2+b^2)*(-a*tan(1/2*x)-b)/(tan(1/2*x)^2+1)","A"
10,1,54,35,0.458000," ","int(sin(x)/(a*cos(x)+b*sin(x)),x)","-\frac{a \ln \left(a +b \tan \left(x \right)\right)}{a^{2}+b^{2}}+\frac{a \ln \left(1+\tan^{2}\left(x \right)\right)}{2 a^{2}+2 b^{2}}+\frac{b \arctan \left(\tan \left(x \right)\right)}{a^{2}+b^{2}}"," ",0,"-a/(a^2+b^2)*ln(a+b*tan(x))+1/2/(a^2+b^2)*a*ln(1+tan(x)^2)+1/(a^2+b^2)*b*arctan(tan(x))","A"
11,1,35,32,0.488000," ","int(1/(a*cos(x)+b*sin(x)),x)","\frac{2 \arctanh \left(\frac{2 a \tan \left(\frac{x}{2}\right)-2 b}{2 \sqrt{a^{2}+b^{2}}}\right)}{\sqrt{a^{2}+b^{2}}}"," ",0,"2/(a^2+b^2)^(1/2)*arctanh(1/2*(2*a*tan(1/2*x)-2*b)/(a^2+b^2)^(1/2))","A"
12,1,21,23,0.713000," ","int(csc(x)/(a*cos(x)+b*sin(x)),x)","-\frac{\ln \left(a +b \tan \left(x \right)\right)}{a}+\frac{\ln \left(\tan \left(x \right)\right)}{a}"," ",0,"-1/a*ln(a+b*tan(x))+1/a*ln(tan(x))","A"
13,1,107,51,0.787000," ","int(csc(x)^2/(a*cos(x)+b*sin(x)),x)","-\frac{\tan \left(\frac{x}{2}\right)}{2 a}-\frac{1}{2 a \tan \left(\frac{x}{2}\right)}-\frac{b \ln \left(\tan \left(\frac{x}{2}\right)\right)}{a^{2}}+\frac{2 \arctanh \left(\frac{2 a \tan \left(\frac{x}{2}\right)-2 b}{2 \sqrt{a^{2}+b^{2}}}\right)}{\sqrt{a^{2}+b^{2}}}+\frac{2 \arctanh \left(\frac{2 a \tan \left(\frac{x}{2}\right)-2 b}{2 \sqrt{a^{2}+b^{2}}}\right) b^{2}}{a^{2} \sqrt{a^{2}+b^{2}}}"," ",0,"-1/2/a*tan(1/2*x)-1/2/a/tan(1/2*x)-b/a^2*ln(tan(1/2*x))+2/(a^2+b^2)^(1/2)*arctanh(1/2*(2*a*tan(1/2*x)-2*b)/(a^2+b^2)^(1/2))+2/a^2/(a^2+b^2)^(1/2)*arctanh(1/2*(2*a*tan(1/2*x)-2*b)/(a^2+b^2)^(1/2))*b^2","B"
14,1,64,53,11.609000," ","int(csc(x)^3/(a*cos(x)+b*sin(x)),x)","-\frac{\ln \left(a +b \tan \left(x \right)\right)}{a}-\frac{\ln \left(a +b \tan \left(x \right)\right) b^{2}}{a^{3}}-\frac{1}{2 a \tan \left(x \right)^{2}}+\frac{\ln \left(\tan \left(x \right)\right)}{a}+\frac{\ln \left(\tan \left(x \right)\right) b^{2}}{a^{3}}+\frac{b}{a^{2} \tan \left(x \right)}"," ",0,"-1/a*ln(a+b*tan(x))-1/a^3*ln(a+b*tan(x))*b^2-1/2/a/tan(x)^2+1/a*ln(tan(x))+1/a^3*ln(tan(x))*b^2+b/a^2/tan(x)","A"
15,1,141,99,0.551000," ","int(sin(x)^3/(a*cos(x)+b*sin(x))^2,x)","-\frac{4 a^{2} \left(\frac{\frac{\tan \left(\frac{x}{2}\right) b}{2}+\frac{a}{2}}{a \left(\tan^{2}\left(\frac{x}{2}\right)\right)-2 \tan \left(\frac{x}{2}\right) b -a}-\frac{3 b \arctanh \left(\frac{2 a \tan \left(\frac{x}{2}\right)-2 b}{2 \sqrt{a^{2}+b^{2}}}\right)}{2 \sqrt{a^{2}+b^{2}}}\right)}{a^{4}+2 a^{2} b^{2}+b^{4}}+\frac{-4 a b \tan \left(\frac{x}{2}\right)+2 a^{2}-2 b^{2}}{\left(a^{4}+2 a^{2} b^{2}+b^{4}\right) \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)}"," ",0,"-4*a^2/(a^4+2*a^2*b^2+b^4)*((1/2*tan(1/2*x)*b+1/2*a)/(a*tan(1/2*x)^2-2*tan(1/2*x)*b-a)-3/2*b/(a^2+b^2)^(1/2)*arctanh(1/2*(2*a*tan(1/2*x)-2*b)/(a^2+b^2)^(1/2)))+4/(a^4+2*a^2*b^2+b^4)*(-a*b*tan(1/2*x)+1/2*a^2-1/2*b^2)/(tan(1/2*x)^2+1)","A"
16,1,99,64,0.557000," ","int(sin(x)^2/(a*cos(x)+b*sin(x))^2,x)","-\frac{a^{2}}{\left(a^{2}+b^{2}\right) b \left(a +b \tan \left(x \right)\right)}-\frac{2 a b \ln \left(a +b \tan \left(x \right)\right)}{\left(a^{2}+b^{2}\right)^{2}}+\frac{a b \ln \left(1+\tan^{2}\left(x \right)\right)}{\left(a^{2}+b^{2}\right)^{2}}-\frac{\arctan \left(\tan \left(x \right)\right) a^{2}}{\left(a^{2}+b^{2}\right)^{2}}+\frac{\arctan \left(\tan \left(x \right)\right) b^{2}}{\left(a^{2}+b^{2}\right)^{2}}"," ",0,"-a^2/(a^2+b^2)/b/(a+b*tan(x))-2*a*b/(a^2+b^2)^2*ln(a+b*tan(x))+1/(a^2+b^2)^2*a*b*ln(1+tan(x)^2)-1/(a^2+b^2)^2*arctan(tan(x))*a^2+1/(a^2+b^2)^2*arctan(tan(x))*b^2","A"
17,1,97,56,0.547000," ","int(sin(x)/(a*cos(x)+b*sin(x))^2,x)","\frac{8 \tan \left(\frac{x}{2}\right) b +8 a}{\left(-4 a^{2}-4 b^{2}\right) \left(a \left(\tan^{2}\left(\frac{x}{2}\right)\right)-2 \tan \left(\frac{x}{2}\right) b -a \right)}-\frac{8 b \arctanh \left(\frac{2 a \tan \left(\frac{x}{2}\right)-2 b}{2 \sqrt{a^{2}+b^{2}}}\right)}{\left(-4 a^{2}-4 b^{2}\right) \sqrt{a^{2}+b^{2}}}"," ",0,"4*(2*tan(1/2*x)*b+2*a)/(-4*a^2-4*b^2)/(a*tan(1/2*x)^2-2*tan(1/2*x)*b-a)-8*b/(-4*a^2-4*b^2)/(a^2+b^2)^(1/2)*arctanh(1/2*(2*a*tan(1/2*x)-2*b)/(a^2+b^2)^(1/2))","A"
18,1,14,17,0.533000," ","int(1/(a*cos(x)+b*sin(x))^2,x)","-\frac{1}{b \left(a +b \tan \left(x \right)\right)}"," ",0,"-1/b/(a+b*tan(x))","A"
19,1,106,59,0.808000," ","int(csc(x)/(a*cos(x)+b*sin(x))^2,x)","\frac{\ln \left(\tan \left(\frac{x}{2}\right)\right)}{a^{2}}-\frac{2 \tan \left(\frac{x}{2}\right) b}{a^{2} \left(a \left(\tan^{2}\left(\frac{x}{2}\right)\right)-2 \tan \left(\frac{x}{2}\right) b -a \right)}-\frac{2}{a \left(a \left(\tan^{2}\left(\frac{x}{2}\right)\right)-2 \tan \left(\frac{x}{2}\right) b -a \right)}-\frac{2 b \arctanh \left(\frac{2 a \tan \left(\frac{x}{2}\right)-2 b}{2 \sqrt{a^{2}+b^{2}}}\right)}{a^{2} \sqrt{a^{2}+b^{2}}}"," ",0,"1/a^2*ln(tan(1/2*x))-2/a^2/(a*tan(1/2*x)^2-2*tan(1/2*x)*b-a)*tan(1/2*x)*b-2/a/(a*tan(1/2*x)^2-2*tan(1/2*x)*b-a)-2/a^2*b/(a^2+b^2)^(1/2)*arctanh(1/2*(2*a*tan(1/2*x)-2*b)/(a^2+b^2)^(1/2))","A"
20,1,60,51,0.724000," ","int(csc(x)^2/(a*cos(x)+b*sin(x))^2,x)","-\frac{1}{b \left(a +b \tan \left(x \right)\right)}-\frac{b}{a^{2} \left(a +b \tan \left(x \right)\right)}+\frac{2 b \ln \left(a +b \tan \left(x \right)\right)}{a^{3}}-\frac{1}{a^{2} \tan \left(x \right)}-\frac{2 b \ln \left(\tan \left(x \right)\right)}{a^{3}}"," ",0,"-1/b/(a+b*tan(x))-1/a^2*b/(a+b*tan(x))+2*b*ln(a+b*tan(x))/a^3-1/a^2/tan(x)-2*b*ln(tan(x))/a^3","A"
21,1,224,110,0.721000," ","int(csc(x)^3/(a*cos(x)+b*sin(x))^2,x)","\frac{\tan^{2}\left(\frac{x}{2}\right)}{8 a^{2}}+\frac{\tan \left(\frac{x}{2}\right) b}{a^{3}}-\frac{1}{8 a^{2} \tan \left(\frac{x}{2}\right)^{2}}+\frac{3 \ln \left(\tan \left(\frac{x}{2}\right)\right)}{2 a^{2}}+\frac{3 \ln \left(\tan \left(\frac{x}{2}\right)\right) b^{2}}{a^{4}}+\frac{b}{a^{3} \tan \left(\frac{x}{2}\right)}-\frac{2 \tan \left(\frac{x}{2}\right) b}{a^{2} \left(a \left(\tan^{2}\left(\frac{x}{2}\right)\right)-2 \tan \left(\frac{x}{2}\right) b -a \right)}-\frac{2 \tan \left(\frac{x}{2}\right) b^{3}}{a^{4} \left(a \left(\tan^{2}\left(\frac{x}{2}\right)\right)-2 \tan \left(\frac{x}{2}\right) b -a \right)}-\frac{2}{a \left(a \left(\tan^{2}\left(\frac{x}{2}\right)\right)-2 \tan \left(\frac{x}{2}\right) b -a \right)}-\frac{2 b^{2}}{a^{3} \left(a \left(\tan^{2}\left(\frac{x}{2}\right)\right)-2 \tan \left(\frac{x}{2}\right) b -a \right)}-\frac{6 b \sqrt{a^{2}+b^{2}}\, \arctanh \left(\frac{2 a \tan \left(\frac{x}{2}\right)-2 b}{2 \sqrt{a^{2}+b^{2}}}\right)}{a^{4}}"," ",0,"1/8/a^2*tan(1/2*x)^2+1/a^3*tan(1/2*x)*b-1/8/a^2/tan(1/2*x)^2+3/2/a^2*ln(tan(1/2*x))+3/a^4*ln(tan(1/2*x))*b^2+1/a^3*b/tan(1/2*x)-2/a^2/(a*tan(1/2*x)^2-2*tan(1/2*x)*b-a)*tan(1/2*x)*b-2/a^4/(a*tan(1/2*x)^2-2*tan(1/2*x)*b-a)*tan(1/2*x)*b^3-2/a/(a*tan(1/2*x)^2-2*tan(1/2*x)*b-a)-2/a^3/(a*tan(1/2*x)^2-2*tan(1/2*x)*b-a)*b^2-6/a^4*b*(a^2+b^2)^(1/2)*arctanh(1/2*(2*a*tan(1/2*x)-2*b)/(a^2+b^2)^(1/2))","B"
22,1,193,96,0.577000," ","int(sin(x)^3/(a*cos(x)+b*sin(x))^3,x)","\frac{a^{3} \ln \left(a +b \tan \left(x \right)\right)}{\left(a^{2}+b^{2}\right)^{3}}-\frac{3 a \ln \left(a +b \tan \left(x \right)\right) b^{2}}{\left(a^{2}+b^{2}\right)^{3}}-\frac{a^{4}}{\left(a^{2}+b^{2}\right)^{2} b^{2} \left(a +b \tan \left(x \right)\right)}-\frac{3 a^{2}}{\left(a^{2}+b^{2}\right)^{2} \left(a +b \tan \left(x \right)\right)}+\frac{a^{3}}{2 b^{2} \left(a^{2}+b^{2}\right) \left(a +b \tan \left(x \right)\right)^{2}}-\frac{\ln \left(1+\tan^{2}\left(x \right)\right) a^{3}}{2 \left(a^{2}+b^{2}\right)^{3}}+\frac{3 \ln \left(1+\tan^{2}\left(x \right)\right) b^{2} a}{2 \left(a^{2}+b^{2}\right)^{3}}-\frac{3 \arctan \left(\tan \left(x \right)\right) a^{2} b}{\left(a^{2}+b^{2}\right)^{3}}+\frac{\arctan \left(\tan \left(x \right)\right) b^{3}}{\left(a^{2}+b^{2}\right)^{3}}"," ",0,"a^3/(a^2+b^2)^3*ln(a+b*tan(x))-3*a/(a^2+b^2)^3*ln(a+b*tan(x))*b^2-a^4/(a^2+b^2)^2/b^2/(a+b*tan(x))-3*a^2/(a^2+b^2)^2/(a+b*tan(x))+1/2/b^2*a^3/(a^2+b^2)/(a+b*tan(x))^2-1/2/(a^2+b^2)^3*ln(1+tan(x)^2)*a^3+3/2/(a^2+b^2)^3*ln(1+tan(x)^2)*b^2*a-3/(a^2+b^2)^3*arctan(tan(x))*a^2*b+1/(a^2+b^2)^3*arctan(tan(x))*b^3","A"
23,1,212,84,0.587000," ","int(sin(x)^2/(a*cos(x)+b*sin(x))^3,x)","-\frac{8 \left(-\frac{a \left(a^{2}-2 b^{2}\right) \left(\tan^{3}\left(\frac{x}{2}\right)\right)}{8 \left(a^{4}+2 a^{2} b^{2}+b^{4}\right)}+\frac{3 b \left(a^{2}-2 b^{2}\right) \left(\tan^{2}\left(\frac{x}{2}\right)\right)}{8 \left(a^{4}+2 a^{2} b^{2}+b^{4}\right)}-\frac{\left(a^{2}+10 b^{2}\right) a \tan \left(\frac{x}{2}\right)}{8 \left(a^{4}+2 a^{2} b^{2}+b^{4}\right)}-\frac{3 a^{2} b}{8 \left(a^{4}+2 a^{2} b^{2}+b^{4}\right)}\right)}{\left(a \left(\tan^{2}\left(\frac{x}{2}\right)\right)-2 \tan \left(\frac{x}{2}\right) b -a \right)^{2}}-\frac{\left(a^{2}-2 b^{2}\right) \arctanh \left(\frac{2 a \tan \left(\frac{x}{2}\right)-2 b}{2 \sqrt{a^{2}+b^{2}}}\right)}{\left(a^{4}+2 a^{2} b^{2}+b^{4}\right) \sqrt{a^{2}+b^{2}}}"," ",0,"-8*(-1/8*a*(a^2-2*b^2)/(a^4+2*a^2*b^2+b^4)*tan(1/2*x)^3+3/8*b*(a^2-2*b^2)/(a^4+2*a^2*b^2+b^4)*tan(1/2*x)^2-1/8*(a^2+10*b^2)*a/(a^4+2*a^2*b^2+b^4)*tan(1/2*x)-3/8*a^2*b/(a^4+2*a^2*b^2+b^4))/(a*tan(1/2*x)^2-2*tan(1/2*x)*b-a)^2-(a^2-2*b^2)/(a^4+2*a^2*b^2+b^4)/(a^2+b^2)^(1/2)*arctanh(1/2*(2*a*tan(1/2*x)-2*b)/(a^2+b^2)^(1/2))","B"
24,1,29,13,0.691000," ","int(sin(x)/(a*cos(x)+b*sin(x))^3,x)","\frac{a}{2 b^{2} \left(a +b \tan \left(x \right)\right)^{2}}-\frac{1}{b^{2} \left(a +b \tan \left(x \right)\right)}"," ",0,"1/2*a/b^2/(a+b*tan(x))^2-1/b^2/(a+b*tan(x))","B"
25,1,157,65,0.538000," ","int(1/(a*cos(x)+b*sin(x))^3,x)","-\frac{2 \left(-\frac{\left(a^{2}+2 b^{2}\right) \left(\tan^{3}\left(\frac{x}{2}\right)\right)}{2 \left(a^{2}+b^{2}\right) a}-\frac{b \left(a^{2}-2 b^{2}\right) \left(\tan^{2}\left(\frac{x}{2}\right)\right)}{2 a^{2} \left(a^{2}+b^{2}\right)}-\frac{\left(a^{2}-2 b^{2}\right) \tan \left(\frac{x}{2}\right)}{2 \left(a^{2}+b^{2}\right) a}+\frac{b}{2 a^{2}+2 b^{2}}\right)}{\left(a \left(\tan^{2}\left(\frac{x}{2}\right)\right)-2 \tan \left(\frac{x}{2}\right) b -a \right)^{2}}+\frac{\arctanh \left(\frac{2 a \tan \left(\frac{x}{2}\right)-2 b}{2 \sqrt{a^{2}+b^{2}}}\right)}{\left(a^{2}+b^{2}\right)^{\frac{3}{2}}}"," ",0,"-2*(-1/2*(a^2+2*b^2)/(a^2+b^2)/a*tan(1/2*x)^3-1/2*b*(a^2-2*b^2)/a^2/(a^2+b^2)*tan(1/2*x)^2-1/2*(a^2-2*b^2)/(a^2+b^2)/a*tan(1/2*x)+1/2*b/(a^2+b^2))/(a*tan(1/2*x)^2-2*tan(1/2*x)*b-a)^2+1/(a^2+b^2)^(3/2)*arctanh(1/2*(2*a*tan(1/2*x)-2*b)/(a^2+b^2)^(1/2))","B"
26,1,73,57,0.666000," ","int(csc(x)/(a*cos(x)+b*sin(x))^3,x)","\frac{a}{2 b^{2} \left(a +b \tan \left(x \right)\right)^{2}}+\frac{1}{2 a \left(a +b \tan \left(x \right)\right)^{2}}-\frac{1}{b^{2} \left(a +b \tan \left(x \right)\right)}+\frac{1}{a^{2} \left(a +b \tan \left(x \right)\right)}-\frac{\ln \left(a +b \tan \left(x \right)\right)}{a^{3}}+\frac{\ln \left(\tan \left(x \right)\right)}{a^{3}}"," ",0,"1/2*a/b^2/(a+b*tan(x))^2+1/2/a/(a+b*tan(x))^2-1/b^2/(a+b*tan(x))+1/a^2/(a+b*tan(x))-ln(a+b*tan(x))/a^3+ln(tan(x))/a^3","A"
27,1,333,168,0.749000," ","int(csc(x)^2/(a*cos(x)+b*sin(x))^3,x)","-\frac{\tan \left(\frac{x}{2}\right)}{2 a^{3}}-\frac{1}{2 a^{3} \tan \left(\frac{x}{2}\right)}-\frac{3 b \ln \left(\tan \left(\frac{x}{2}\right)\right)}{a^{4}}+\frac{\tan^{3}\left(\frac{x}{2}\right)}{a \left(a \left(\tan^{2}\left(\frac{x}{2}\right)\right)-2 \tan \left(\frac{x}{2}\right) b -a \right)^{2}}+\frac{6 \left(\tan^{3}\left(\frac{x}{2}\right)\right) b^{2}}{a^{3} \left(a \left(\tan^{2}\left(\frac{x}{2}\right)\right)-2 \tan \left(\frac{x}{2}\right) b -a \right)^{2}}+\frac{5 \left(\tan^{2}\left(\frac{x}{2}\right)\right) b}{a^{2} \left(a \left(\tan^{2}\left(\frac{x}{2}\right)\right)-2 \tan \left(\frac{x}{2}\right) b -a \right)^{2}}-\frac{10 \left(\tan^{2}\left(\frac{x}{2}\right)\right) b^{3}}{a^{4} \left(a \left(\tan^{2}\left(\frac{x}{2}\right)\right)-2 \tan \left(\frac{x}{2}\right) b -a \right)^{2}}+\frac{\tan \left(\frac{x}{2}\right)}{a \left(a \left(\tan^{2}\left(\frac{x}{2}\right)\right)-2 \tan \left(\frac{x}{2}\right) b -a \right)^{2}}-\frac{14 \tan \left(\frac{x}{2}\right) b^{2}}{a^{3} \left(a \left(\tan^{2}\left(\frac{x}{2}\right)\right)-2 \tan \left(\frac{x}{2}\right) b -a \right)^{2}}-\frac{5 b}{a^{2} \left(a \left(\tan^{2}\left(\frac{x}{2}\right)\right)-2 \tan \left(\frac{x}{2}\right) b -a \right)^{2}}+\frac{3 \arctanh \left(\frac{2 a \tan \left(\frac{x}{2}\right)-2 b}{2 \sqrt{a^{2}+b^{2}}}\right)}{a^{2} \sqrt{a^{2}+b^{2}}}+\frac{6 \arctanh \left(\frac{2 a \tan \left(\frac{x}{2}\right)-2 b}{2 \sqrt{a^{2}+b^{2}}}\right) b^{2}}{a^{4} \sqrt{a^{2}+b^{2}}}"," ",0,"-1/2/a^3*tan(1/2*x)-1/2/a^3/tan(1/2*x)-3/a^4*b*ln(tan(1/2*x))+1/a/(a*tan(1/2*x)^2-2*tan(1/2*x)*b-a)^2*tan(1/2*x)^3+6/a^3/(a*tan(1/2*x)^2-2*tan(1/2*x)*b-a)^2*tan(1/2*x)^3*b^2+5/a^2/(a*tan(1/2*x)^2-2*tan(1/2*x)*b-a)^2*tan(1/2*x)^2*b-10/a^4/(a*tan(1/2*x)^2-2*tan(1/2*x)*b-a)^2*tan(1/2*x)^2*b^3+1/a/(a*tan(1/2*x)^2-2*tan(1/2*x)*b-a)^2*tan(1/2*x)-14/a^3/(a*tan(1/2*x)^2-2*tan(1/2*x)*b-a)^2*tan(1/2*x)*b^2-5/a^2/(a*tan(1/2*x)^2-2*tan(1/2*x)*b-a)^2*b+3/a^2/(a^2+b^2)^(1/2)*arctanh(1/2*(2*a*tan(1/2*x)-2*b)/(a^2+b^2)^(1/2))+6/a^4/(a^2+b^2)^(1/2)*arctanh(1/2*(2*a*tan(1/2*x)-2*b)/(a^2+b^2)^(1/2))*b^2","A"
28,1,151,113,0.756000," ","int(csc(x)^3/(a*cos(x)+b*sin(x))^3,x)","\frac{a}{2 b^{2} \left(a +b \tan \left(x \right)\right)^{2}}+\frac{1}{a \left(a +b \tan \left(x \right)\right)^{2}}+\frac{b^{2}}{2 a^{3} \left(a +b \tan \left(x \right)\right)^{2}}-\frac{1}{b^{2} \left(a +b \tan \left(x \right)\right)}+\frac{2}{a^{2} \left(a +b \tan \left(x \right)\right)}+\frac{3 b^{2}}{a^{4} \left(a +b \tan \left(x \right)\right)}-\frac{2 \ln \left(a +b \tan \left(x \right)\right)}{a^{3}}-\frac{6 \ln \left(a +b \tan \left(x \right)\right) b^{2}}{a^{5}}-\frac{1}{2 a^{3} \tan \left(x \right)^{2}}+\frac{2 \ln \left(\tan \left(x \right)\right)}{a^{3}}+\frac{6 \ln \left(\tan \left(x \right)\right) b^{2}}{a^{5}}+\frac{3 b}{a^{4} \tan \left(x \right)}"," ",0,"1/2*a/b^2/(a+b*tan(x))^2+1/a/(a+b*tan(x))^2+1/2/a^3*b^2/(a+b*tan(x))^2-1/b^2/(a+b*tan(x))+2/a^2/(a+b*tan(x))+3/a^4*b^2/(a+b*tan(x))-2*ln(a+b*tan(x))/a^3-6/a^5*ln(a+b*tan(x))*b^2-1/2/a^3/tan(x)^2+2*ln(tan(x))/a^3+6/a^5*ln(tan(x))*b^2+3/a^4*b/tan(x)","A"
29,0,0,60,10.852000," ","int((a*cos(d*x+c)+I*a*sin(d*x+c))^n/(sin(d*x+c)^n),x)","\int \left(a \cos \left(d x +c \right)+i a \sin \left(d x +c \right)\right)^{n} \left(\sin^{-n}\left(d x +c \right)\right)\, dx"," ",0,"int((a*cos(d*x+c)+I*a*sin(d*x+c))^n/(sin(d*x+c)^n),x)","F"
30,1,62,77,1.087000," ","int(cos(d*x+c)^5*(a*cos(d*x+c)+b*sin(d*x+c)),x)","\frac{a \left(\frac{\left(\cos^{5}\left(d x +c \right)+\frac{5 \left(\cos^{3}\left(d x +c \right)\right)}{4}+\frac{15 \cos \left(d x +c \right)}{8}\right) \sin \left(d x +c \right)}{6}+\frac{5 d x}{16}+\frac{5 c}{16}\right)-\frac{b \left(\cos^{6}\left(d x +c \right)\right)}{6}}{d}"," ",0,"1/d*(a*(1/6*(cos(d*x+c)^5+5/4*cos(d*x+c)^3+15/8*cos(d*x+c))*sin(d*x+c)+5/16*d*x+5/16*c)-1/6*b*cos(d*x+c)^6)","A"
31,1,46,54,1.053000," ","int(cos(d*x+c)^4*(a*cos(d*x+c)+b*sin(d*x+c)),x)","\frac{\frac{a \left(\frac{8}{3}+\cos^{4}\left(d x +c \right)+\frac{4 \left(\cos^{2}\left(d x +c \right)\right)}{3}\right) \sin \left(d x +c \right)}{5}-\frac{b \left(\cos^{5}\left(d x +c \right)\right)}{5}}{d}"," ",0,"1/d*(1/5*a*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c)-1/5*b*cos(d*x+c)^5)","A"
32,1,52,57,10.813000," ","int(cos(d*x+c)^3*(a*cos(d*x+c)+b*sin(d*x+c)),x)","\frac{a \left(\frac{\left(\cos^{3}\left(d x +c \right)+\frac{3 \cos \left(d x +c \right)}{2}\right) \sin \left(d x +c \right)}{4}+\frac{3 d x}{8}+\frac{3 c}{8}\right)-\frac{b \left(\cos^{4}\left(d x +c \right)\right)}{4}}{d}"," ",0,"1/d*(a*(1/4*(cos(d*x+c)^3+3/2*cos(d*x+c))*sin(d*x+c)+3/8*d*x+3/8*c)-1/4*b*cos(d*x+c)^4)","A"
33,1,36,40,1.028000," ","int(cos(d*x+c)^2*(a*cos(d*x+c)+b*sin(d*x+c)),x)","\frac{\frac{a \left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{3}-\frac{b \left(\cos^{3}\left(d x +c \right)\right)}{3}}{d}"," ",0,"1/d*(1/3*a*(2+cos(d*x+c)^2)*sin(d*x+c)-1/3*b*cos(d*x+c)^3)","A"
34,1,41,37,0.708000," ","int(cos(d*x+c)*(a*cos(d*x+c)+b*sin(d*x+c)),x)","\frac{a \left(\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)}{2}+\frac{d x}{2}+\frac{c}{2}\right)-\frac{\left(\cos^{2}\left(d x +c \right)\right) b}{2}}{d}"," ",0,"1/d*(a*(1/2*cos(d*x+c)*sin(d*x+c)+1/2*d*x+1/2*c)-1/2*cos(d*x+c)^2*b)","A"
35,1,25,24,0.130000," ","int(a*cos(d*x+c)+b*sin(d*x+c),x)","-\frac{b \cos \left(d x +c \right)}{d}+\frac{a \sin \left(d x +c \right)}{d}"," ",0,"-b*cos(d*x+c)/d+a*sin(d*x+c)/d","A"
36,1,24,17,1.338000," ","int(sec(d*x+c)*(a*cos(d*x+c)+b*sin(d*x+c)),x)","a x -\frac{b \ln \left(\cos \left(d x +c \right)\right)}{d}+\frac{c a}{d}"," ",0,"a*x-b*ln(cos(d*x+c))/d+1/d*c*a","A"
37,1,34,24,1.773000," ","int(sec(d*x+c)^2*(a*cos(d*x+c)+b*sin(d*x+c)),x)","\frac{a \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{b}{d \cos \left(d x +c \right)}"," ",0,"1/d*a*ln(sec(d*x+c)+tan(d*x+c))+1/d*b/cos(d*x+c)","A"
38,1,25,26,1.695000," ","int(sec(d*x+c)^3*(a*cos(d*x+c)+b*sin(d*x+c)),x)","\frac{a \tan \left(d x +c \right)+\frac{b}{2 \cos \left(d x +c \right)^{2}}}{d}"," ",0,"1/d*(a*tan(d*x+c)+1/2*b/cos(d*x+c)^2)","A"
39,1,54,46,2.004000," ","int(sec(d*x+c)^4*(a*cos(d*x+c)+b*sin(d*x+c)),x)","\frac{a \sec \left(d x +c \right) \tan \left(d x +c \right)}{2 d}+\frac{a \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{2 d}+\frac{b}{3 d \cos \left(d x +c \right)^{3}}"," ",0,"1/2*a*sec(d*x+c)*tan(d*x+c)/d+1/2/d*a*ln(sec(d*x+c)+tan(d*x+c))+1/3/d*b/cos(d*x+c)^3","A"
40,1,38,40,1.746000," ","int(sec(d*x+c)^5*(a*cos(d*x+c)+b*sin(d*x+c)),x)","\frac{-a \left(-\frac{2}{3}-\frac{\left(\sec^{2}\left(d x +c \right)\right)}{3}\right) \tan \left(d x +c \right)+\frac{b}{4 \cos \left(d x +c \right)^{4}}}{d}"," ",0,"1/d*(-a*(-2/3-1/3*sec(d*x+c)^2)*tan(d*x+c)+1/4*b/cos(d*x+c)^4)","A"
41,1,74,66,11.311000," ","int(sec(d*x+c)^6*(a*cos(d*x+c)+b*sin(d*x+c)),x)","\frac{a \left(\sec^{3}\left(d x +c \right)\right) \tan \left(d x +c \right)}{4 d}+\frac{3 a \sec \left(d x +c \right) \tan \left(d x +c \right)}{8 d}+\frac{3 a \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{8 d}+\frac{b}{5 d \cos \left(d x +c \right)^{5}}"," ",0,"1/4*a*sec(d*x+c)^3*tan(d*x+c)/d+3/8*a*sec(d*x+c)*tan(d*x+c)/d+3/8/d*a*ln(sec(d*x+c)+tan(d*x+c))+1/5/d*b/cos(d*x+c)^5","A"
42,1,48,54,1.952000," ","int(sec(d*x+c)^7*(a*cos(d*x+c)+b*sin(d*x+c)),x)","\frac{-a \left(-\frac{8}{15}-\frac{\left(\sec^{4}\left(d x +c \right)\right)}{5}-\frac{4 \left(\sec^{2}\left(d x +c \right)\right)}{15}\right) \tan \left(d x +c \right)+\frac{b}{6 \cos \left(d x +c \right)^{6}}}{d}"," ",0,"1/d*(-a*(-8/15-1/5*sec(d*x+c)^4-4/15*sec(d*x+c)^2)*tan(d*x+c)+1/6*b/cos(d*x+c)^6)","A"
43,1,108,125,1.672000," ","int(cos(d*x+c)^5*(a*cos(d*x+c)+b*sin(d*x+c))^2,x)","\frac{b^{2} \left(-\frac{\sin \left(d x +c \right) \left(\cos^{6}\left(d x +c \right)\right)}{7}+\frac{\left(\frac{8}{3}+\cos^{4}\left(d x +c \right)+\frac{4 \left(\cos^{2}\left(d x +c \right)\right)}{3}\right) \sin \left(d x +c \right)}{35}\right)-\frac{2 a b \left(\cos^{7}\left(d x +c \right)\right)}{7}+\frac{a^{2} \left(\frac{16}{5}+\cos^{6}\left(d x +c \right)+\frac{6 \left(\cos^{4}\left(d x +c \right)\right)}{5}+\frac{8 \left(\cos^{2}\left(d x +c \right)\right)}{5}\right) \sin \left(d x +c \right)}{7}}{d}"," ",0,"1/d*(b^2*(-1/7*sin(d*x+c)*cos(d*x+c)^6+1/35*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c))-2/7*a*b*cos(d*x+c)^7+1/7*a^2*(16/5+cos(d*x+c)^6+6/5*cos(d*x+c)^4+8/5*cos(d*x+c)^2)*sin(d*x+c))","A"
44,1,118,156,11.253000," ","int(cos(d*x+c)^4*(a*cos(d*x+c)+b*sin(d*x+c))^2,x)","\frac{b^{2} \left(-\frac{\left(\cos^{5}\left(d x +c \right)\right) \sin \left(d x +c \right)}{6}+\frac{\left(\cos^{3}\left(d x +c \right)+\frac{3 \cos \left(d x +c \right)}{2}\right) \sin \left(d x +c \right)}{24}+\frac{d x}{16}+\frac{c}{16}\right)-\frac{a b \left(\cos^{6}\left(d x +c \right)\right)}{3}+a^{2} \left(\frac{\left(\cos^{5}\left(d x +c \right)+\frac{5 \left(\cos^{3}\left(d x +c \right)\right)}{4}+\frac{15 \cos \left(d x +c \right)}{8}\right) \sin \left(d x +c \right)}{6}+\frac{5 d x}{16}+\frac{5 c}{16}\right)}{d}"," ",0,"1/d*(b^2*(-1/6*cos(d*x+c)^5*sin(d*x+c)+1/24*(cos(d*x+c)^3+3/2*cos(d*x+c))*sin(d*x+c)+1/16*d*x+1/16*c)-1/3*a*b*cos(d*x+c)^6+a^2*(1/6*(cos(d*x+c)^5+5/4*cos(d*x+c)^3+15/8*cos(d*x+c))*sin(d*x+c)+5/16*d*x+5/16*c))","A"
45,1,88,93,1.763000," ","int(cos(d*x+c)^3*(a*cos(d*x+c)+b*sin(d*x+c))^2,x)","\frac{b^{2} \left(-\frac{\sin \left(d x +c \right) \left(\cos^{4}\left(d x +c \right)\right)}{5}+\frac{\left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{15}\right)-\frac{2 a b \left(\cos^{5}\left(d x +c \right)\right)}{5}+\frac{a^{2} \left(\frac{8}{3}+\cos^{4}\left(d x +c \right)+\frac{4 \left(\cos^{2}\left(d x +c \right)\right)}{3}\right) \sin \left(d x +c \right)}{5}}{d}"," ",0,"1/d*(b^2*(-1/5*sin(d*x+c)*cos(d*x+c)^4+1/15*(2+cos(d*x+c)^2)*sin(d*x+c))-2/5*a*b*cos(d*x+c)^5+1/5*a^2*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c))","A"
46,1,97,112,1.425000," ","int(cos(d*x+c)^2*(a*cos(d*x+c)+b*sin(d*x+c))^2,x)","\frac{b^{2} \left(-\frac{\left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)}{4}+\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)}{8}+\frac{d x}{8}+\frac{c}{8}\right)-\frac{a b \left(\cos^{4}\left(d x +c \right)\right)}{2}+a^{2} \left(\frac{\left(\cos^{3}\left(d x +c \right)+\frac{3 \cos \left(d x +c \right)}{2}\right) \sin \left(d x +c \right)}{4}+\frac{3 d x}{8}+\frac{3 c}{8}\right)}{d}"," ",0,"1/d*(b^2*(-1/4*cos(d*x+c)^3*sin(d*x+c)+1/8*cos(d*x+c)*sin(d*x+c)+1/8*d*x+1/8*c)-1/2*a*b*cos(d*x+c)^4+a^2*(1/4*(cos(d*x+c)^3+3/2*cos(d*x+c))*sin(d*x+c)+3/8*d*x+3/8*c))","A"
47,1,52,61,1.428000," ","int(cos(d*x+c)*(a*cos(d*x+c)+b*sin(d*x+c))^2,x)","\frac{\frac{b^{2} \left(\sin^{3}\left(d x +c \right)\right)}{3}-\frac{2 \left(\cos^{3}\left(d x +c \right)\right) a b}{3}+\frac{a^{2} \left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{3}}{d}"," ",0,"1/d*(1/3*b^2*sin(d*x+c)^3-2/3*cos(d*x+c)^3*a*b+1/3*a^2*(2+cos(d*x+c)^2)*sin(d*x+c))","A"
48,1,70,51,1.189000," ","int((a*cos(d*x+c)+b*sin(d*x+c))^2,x)","\frac{b^{2} \left(-\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)}{2}+\frac{d x}{2}+\frac{c}{2}\right)-\left(\cos^{2}\left(d x +c \right)\right) a b +a^{2} \left(\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)}{2}+\frac{d x}{2}+\frac{c}{2}\right)}{d}"," ",0,"1/d*(b^2*(-1/2*cos(d*x+c)*sin(d*x+c)+1/2*d*x+1/2*c)-cos(d*x+c)^2*a*b+a^2*(1/2*cos(d*x+c)*sin(d*x+c)+1/2*d*x+1/2*c))","A"
49,1,63,55,1.855000," ","int(sec(d*x+c)*(a*cos(d*x+c)+b*sin(d*x+c))^2,x)","-\frac{2 a b \cos \left(d x +c \right)}{d}+\frac{a^{2} \sin \left(d x +c \right)}{d}-\frac{b^{2} \sin \left(d x +c \right)}{d}+\frac{b^{2} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}"," ",0,"-2*a*b*cos(d*x+c)/d+a^2*sin(d*x+c)/d-b^2*sin(d*x+c)/d+1/d*b^2*ln(sec(d*x+c)+tan(d*x+c))","A"
50,1,57,39,3.741000," ","int(sec(d*x+c)^2*(a*cos(d*x+c)+b*sin(d*x+c))^2,x)","a^{2} x -b^{2} x +\frac{b^{2} \tan \left(d x +c \right)}{d}-\frac{2 a b \ln \left(\cos \left(d x +c \right)\right)}{d}+\frac{a^{2} c}{d}-\frac{c \,b^{2}}{d}"," ",0,"a^2*x-b^2*x+b^2*tan(d*x+c)/d-2*a*b*ln(cos(d*x+c))/d+1/d*a^2*c-1/d*c*b^2","A"
51,1,98,63,1.689000," ","int(sec(d*x+c)^3*(a*cos(d*x+c)+b*sin(d*x+c))^2,x)","\frac{a^{2} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{2 a b}{d \cos \left(d x +c \right)}+\frac{b^{2} \left(\sin^{3}\left(d x +c \right)\right)}{2 d \cos \left(d x +c \right)^{2}}+\frac{b^{2} \sin \left(d x +c \right)}{2 d}-\frac{b^{2} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{2 d}"," ",0,"1/d*a^2*ln(sec(d*x+c)+tan(d*x+c))+2/d*a*b/cos(d*x+c)+1/2/d*b^2*sin(d*x+c)^3/cos(d*x+c)^2+1/2*b^2*sin(d*x+c)/d-1/2/d*b^2*ln(sec(d*x+c)+tan(d*x+c))","A"
52,1,48,28,10.894000," ","int(sec(d*x+c)^4*(a*cos(d*x+c)+b*sin(d*x+c))^2,x)","\frac{a^{2} \tan \left(d x +c \right)+\frac{a b}{\cos \left(d x +c \right)^{2}}+\frac{b^{2} \left(\sin^{3}\left(d x +c \right)\right)}{3 \cos \left(d x +c \right)^{3}}}{d}"," ",0,"1/d*(a^2*tan(d*x+c)+a*b/cos(d*x+c)^2+1/3*b^2*sin(d*x+c)^3/cos(d*x+c)^3)","A"
53,1,143,108,1.961000," ","int(sec(d*x+c)^5*(a*cos(d*x+c)+b*sin(d*x+c))^2,x)","\frac{a^{2} \sec \left(d x +c \right) \tan \left(d x +c \right)}{2 d}+\frac{a^{2} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{2 d}+\frac{2 a b}{3 d \cos \left(d x +c \right)^{3}}+\frac{b^{2} \left(\sin^{3}\left(d x +c \right)\right)}{4 d \cos \left(d x +c \right)^{4}}+\frac{b^{2} \left(\sin^{3}\left(d x +c \right)\right)}{8 d \cos \left(d x +c \right)^{2}}+\frac{b^{2} \sin \left(d x +c \right)}{8 d}-\frac{b^{2} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{8 d}"," ",0,"1/2*a^2*sec(d*x+c)*tan(d*x+c)/d+1/2/d*a^2*ln(sec(d*x+c)+tan(d*x+c))+2/3/d*a*b/cos(d*x+c)^3+1/4/d*b^2*sin(d*x+c)^3/cos(d*x+c)^4+1/8/d*b^2*sin(d*x+c)^3/cos(d*x+c)^2+1/8*b^2*sin(d*x+c)/d-1/8/d*b^2*ln(sec(d*x+c)+tan(d*x+c))","A"
54,1,82,79,1.971000," ","int(sec(d*x+c)^6*(a*cos(d*x+c)+b*sin(d*x+c))^2,x)","\frac{-a^{2} \left(-\frac{2}{3}-\frac{\left(\sec^{2}\left(d x +c \right)\right)}{3}\right) \tan \left(d x +c \right)+\frac{a b}{2 \cos \left(d x +c \right)^{4}}+b^{2} \left(\frac{\sin^{3}\left(d x +c \right)}{5 \cos \left(d x +c \right)^{5}}+\frac{2 \left(\sin^{3}\left(d x +c \right)\right)}{15 \cos \left(d x +c \right)^{3}}\right)}{d}"," ",0,"1/d*(-a^2*(-2/3-1/3*sec(d*x+c)^2)*tan(d*x+c)+1/2*a*b/cos(d*x+c)^4+b^2*(1/5*sin(d*x+c)^3/cos(d*x+c)^5+2/15*sin(d*x+c)^3/cos(d*x+c)^3))","A"
55,1,189,152,10.992000," ","int(sec(d*x+c)^7*(a*cos(d*x+c)+b*sin(d*x+c))^2,x)","\frac{a^{2} \left(\sec^{3}\left(d x +c \right)\right) \tan \left(d x +c \right)}{4 d}+\frac{3 a^{2} \sec \left(d x +c \right) \tan \left(d x +c \right)}{8 d}+\frac{3 a^{2} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{8 d}+\frac{2 a b}{5 d \cos \left(d x +c \right)^{5}}+\frac{b^{2} \left(\sin^{3}\left(d x +c \right)\right)}{6 d \cos \left(d x +c \right)^{6}}+\frac{b^{2} \left(\sin^{3}\left(d x +c \right)\right)}{8 d \cos \left(d x +c \right)^{4}}+\frac{b^{2} \left(\sin^{3}\left(d x +c \right)\right)}{16 d \cos \left(d x +c \right)^{2}}+\frac{b^{2} \sin \left(d x +c \right)}{16 d}-\frac{b^{2} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{16 d}"," ",0,"1/4*a^2*sec(d*x+c)^3*tan(d*x+c)/d+3/8*a^2*sec(d*x+c)*tan(d*x+c)/d+3/8/d*a^2*ln(sec(d*x+c)+tan(d*x+c))+2/5/d*a*b/cos(d*x+c)^5+1/6/d*b^2*sin(d*x+c)^3/cos(d*x+c)^6+1/8/d*b^2*sin(d*x+c)^3/cos(d*x+c)^4+1/16/d*b^2*sin(d*x+c)^3/cos(d*x+c)^2+1/16*b^2*sin(d*x+c)/d-1/16/d*b^2*ln(sec(d*x+c)+tan(d*x+c))","A"
56,1,110,117,2.100000," ","int(sec(d*x+c)^8*(a*cos(d*x+c)+b*sin(d*x+c))^2,x)","\frac{-a^{2} \left(-\frac{8}{15}-\frac{\left(\sec^{4}\left(d x +c \right)\right)}{5}-\frac{4 \left(\sec^{2}\left(d x +c \right)\right)}{15}\right) \tan \left(d x +c \right)+\frac{a b}{3 \cos \left(d x +c \right)^{6}}+b^{2} \left(\frac{\sin^{3}\left(d x +c \right)}{7 \cos \left(d x +c \right)^{7}}+\frac{4 \left(\sin^{3}\left(d x +c \right)\right)}{35 \cos \left(d x +c \right)^{5}}+\frac{8 \left(\sin^{3}\left(d x +c \right)\right)}{105 \cos \left(d x +c \right)^{3}}\right)}{d}"," ",0,"1/d*(-a^2*(-8/15-1/5*sec(d*x+c)^4-4/15*sec(d*x+c)^2)*tan(d*x+c)+1/3*a*b/cos(d*x+c)^6+b^2*(1/7*sin(d*x+c)^3/cos(d*x+c)^7+4/35*sin(d*x+c)^3/cos(d*x+c)^5+8/105*sin(d*x+c)^3/cos(d*x+c)^3))","A"
57,1,175,239,11.011000," ","int(cos(d*x+c)^5*(a*cos(d*x+c)+b*sin(d*x+c))^3,x)","\frac{b^{3} \left(-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{6}\left(d x +c \right)\right)}{8}-\frac{\left(\cos^{6}\left(d x +c \right)\right)}{24}\right)+3 b^{2} a \left(-\frac{\sin \left(d x +c \right) \left(\cos^{7}\left(d x +c \right)\right)}{8}+\frac{\left(\cos^{5}\left(d x +c \right)+\frac{5 \left(\cos^{3}\left(d x +c \right)\right)}{4}+\frac{15 \cos \left(d x +c \right)}{8}\right) \sin \left(d x +c \right)}{48}+\frac{5 d x}{128}+\frac{5 c}{128}\right)-\frac{3 a^{2} b \left(\cos^{8}\left(d x +c \right)\right)}{8}+a^{3} \left(\frac{\left(\cos^{7}\left(d x +c \right)+\frac{7 \left(\cos^{5}\left(d x +c \right)\right)}{6}+\frac{35 \left(\cos^{3}\left(d x +c \right)\right)}{24}+\frac{35 \cos \left(d x +c \right)}{16}\right) \sin \left(d x +c \right)}{8}+\frac{35 d x}{128}+\frac{35 c}{128}\right)}{d}"," ",0,"1/d*(b^3*(-1/8*sin(d*x+c)^2*cos(d*x+c)^6-1/24*cos(d*x+c)^6)+3*b^2*a*(-1/8*sin(d*x+c)*cos(d*x+c)^7+1/48*(cos(d*x+c)^5+5/4*cos(d*x+c)^3+15/8*cos(d*x+c))*sin(d*x+c)+5/128*d*x+5/128*c)-3/8*a^2*b*cos(d*x+c)^8+a^3*(1/8*(cos(d*x+c)^7+7/6*cos(d*x+c)^5+35/24*cos(d*x+c)^3+35/16*cos(d*x+c))*sin(d*x+c)+35/128*d*x+35/128*c))","A"
58,1,145,161,10.379000," ","int(cos(d*x+c)^4*(a*cos(d*x+c)+b*sin(d*x+c))^3,x)","\frac{b^{3} \left(-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{5}\left(d x +c \right)\right)}{7}-\frac{2 \left(\cos^{5}\left(d x +c \right)\right)}{35}\right)+3 b^{2} a \left(-\frac{\sin \left(d x +c \right) \left(\cos^{6}\left(d x +c \right)\right)}{7}+\frac{\left(\frac{8}{3}+\cos^{4}\left(d x +c \right)+\frac{4 \left(\cos^{2}\left(d x +c \right)\right)}{3}\right) \sin \left(d x +c \right)}{35}\right)-\frac{3 a^{2} b \left(\cos^{7}\left(d x +c \right)\right)}{7}+\frac{a^{3} \left(\frac{16}{5}+\cos^{6}\left(d x +c \right)+\frac{6 \left(\cos^{4}\left(d x +c \right)\right)}{5}+\frac{8 \left(\cos^{2}\left(d x +c \right)\right)}{5}\right) \sin \left(d x +c \right)}{7}}{d}"," ",0,"1/d*(b^3*(-1/7*sin(d*x+c)^2*cos(d*x+c)^5-2/35*cos(d*x+c)^5)+3*b^2*a*(-1/7*sin(d*x+c)*cos(d*x+c)^6+1/35*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c))-3/7*a^2*b*cos(d*x+c)^7+1/7*a^3*(16/5+cos(d*x+c)^6+6/5*cos(d*x+c)^4+8/5*cos(d*x+c)^2)*sin(d*x+c))","A"
59,1,155,194,9.716000," ","int(cos(d*x+c)^3*(a*cos(d*x+c)+b*sin(d*x+c))^3,x)","\frac{b^{3} \left(-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{4}\left(d x +c \right)\right)}{6}-\frac{\left(\cos^{4}\left(d x +c \right)\right)}{12}\right)+3 b^{2} a \left(-\frac{\left(\cos^{5}\left(d x +c \right)\right) \sin \left(d x +c \right)}{6}+\frac{\left(\cos^{3}\left(d x +c \right)+\frac{3 \cos \left(d x +c \right)}{2}\right) \sin \left(d x +c \right)}{24}+\frac{d x}{16}+\frac{c}{16}\right)-\frac{a^{2} b \left(\cos^{6}\left(d x +c \right)\right)}{2}+a^{3} \left(\frac{\left(\cos^{5}\left(d x +c \right)+\frac{5 \left(\cos^{3}\left(d x +c \right)\right)}{4}+\frac{15 \cos \left(d x +c \right)}{8}\right) \sin \left(d x +c \right)}{6}+\frac{5 d x}{16}+\frac{5 c}{16}\right)}{d}"," ",0,"1/d*(b^3*(-1/6*sin(d*x+c)^2*cos(d*x+c)^4-1/12*cos(d*x+c)^4)+3*b^2*a*(-1/6*cos(d*x+c)^5*sin(d*x+c)+1/24*(cos(d*x+c)^3+3/2*cos(d*x+c))*sin(d*x+c)+1/16*d*x+1/16*c)-1/2*a^2*b*cos(d*x+c)^6+a^3*(1/6*(cos(d*x+c)^5+5/4*cos(d*x+c)^3+15/8*cos(d*x+c))*sin(d*x+c)+5/16*d*x+5/16*c))","A"
60,1,125,128,10.500000," ","int(cos(d*x+c)^2*(a*cos(d*x+c)+b*sin(d*x+c))^3,x)","\frac{b^{3} \left(-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{3}\left(d x +c \right)\right)}{5}-\frac{2 \left(\cos^{3}\left(d x +c \right)\right)}{15}\right)+3 b^{2} a \left(-\frac{\sin \left(d x +c \right) \left(\cos^{4}\left(d x +c \right)\right)}{5}+\frac{\left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{15}\right)-\frac{3 a^{2} b \left(\cos^{5}\left(d x +c \right)\right)}{5}+\frac{a^{3} \left(\frac{8}{3}+\cos^{4}\left(d x +c \right)+\frac{4 \left(\cos^{2}\left(d x +c \right)\right)}{3}\right) \sin \left(d x +c \right)}{5}}{d}"," ",0,"1/d*(b^3*(-1/5*sin(d*x+c)^2*cos(d*x+c)^3-2/15*cos(d*x+c)^3)+3*b^2*a*(-1/5*sin(d*x+c)*cos(d*x+c)^4+1/15*(2+cos(d*x+c)^2)*sin(d*x+c))-3/5*a^2*b*cos(d*x+c)^5+1/5*a^3*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c))","A"
61,1,114,72,1.383000," ","int(cos(d*x+c)*(a*cos(d*x+c)+b*sin(d*x+c))^3,x)","\frac{\frac{b^{3} \left(\sin^{4}\left(d x +c \right)\right)}{4}+3 b^{2} a \left(-\frac{\left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)}{4}+\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)}{8}+\frac{d x}{8}+\frac{c}{8}\right)-\frac{3 a^{2} b \left(\cos^{4}\left(d x +c \right)\right)}{4}+a^{3} \left(\frac{\left(\cos^{3}\left(d x +c \right)+\frac{3 \cos \left(d x +c \right)}{2}\right) \sin \left(d x +c \right)}{4}+\frac{3 d x}{8}+\frac{3 c}{8}\right)}{d}"," ",0,"1/d*(1/4*b^3*sin(d*x+c)^4+3*b^2*a*(-1/4*cos(d*x+c)^3*sin(d*x+c)+1/8*cos(d*x+c)*sin(d*x+c)+1/8*d*x+1/8*c)-3/4*a^2*b*cos(d*x+c)^4+a^3*(1/4*(cos(d*x+c)^3+3/2*cos(d*x+c))*sin(d*x+c)+3/8*d*x+3/8*c))","A"
62,1,75,56,9.743000," ","int((a*cos(d*x+c)+b*sin(d*x+c))^3,x)","\frac{-\frac{b^{3} \left(2+\sin^{2}\left(d x +c \right)\right) \cos \left(d x +c \right)}{3}+b^{2} a \left(\sin^{3}\left(d x +c \right)\right)-\left(\cos^{3}\left(d x +c \right)\right) a^{2} b +\frac{a^{3} \left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{3}}{d}"," ",0,"1/d*(-1/3*b^3*(2+sin(d*x+c)^2)*cos(d*x+c)+b^2*a*sin(d*x+c)^3-cos(d*x+c)^3*a^2*b+1/3*a^3*(2+cos(d*x+c)^2)*sin(d*x+c))","A"
63,1,123,87,1.592000," ","int(sec(d*x+c)*(a*cos(d*x+c)+b*sin(d*x+c))^3,x)","\frac{a^{3} \cos \left(d x +c \right) \sin \left(d x +c \right)}{2 d}+\frac{a^{3} x}{2}+\frac{a^{3} c}{2 d}-\frac{3 a^{2} b \left(\cos^{2}\left(d x +c \right)\right)}{2 d}-\frac{3 a \,b^{2} \cos \left(d x +c \right) \sin \left(d x +c \right)}{2 d}+\frac{3 a \,b^{2} x}{2}+\frac{3 a \,b^{2} c}{2 d}-\frac{\left(\sin^{2}\left(d x +c \right)\right) b^{3}}{2 d}-\frac{b^{3} \ln \left(\cos \left(d x +c \right)\right)}{d}"," ",0,"1/2*a^3*cos(d*x+c)*sin(d*x+c)/d+1/2*a^3*x+1/2/d*a^3*c-3/2*a^2*b*cos(d*x+c)^2/d-3/2*a*b^2*cos(d*x+c)*sin(d*x+c)/d+3/2*a*b^2*x+3/2/d*a*b^2*c-1/2/d*sin(d*x+c)^2*b^3-b^3*ln(cos(d*x+c))/d","A"
64,1,126,86,10.959000," ","int(sec(d*x+c)^2*(a*cos(d*x+c)+b*sin(d*x+c))^3,x)","\frac{a^{3} \sin \left(d x +c \right)}{d}-\frac{3 a^{2} b \cos \left(d x +c \right)}{d}-\frac{3 a \,b^{2} \sin \left(d x +c \right)}{d}+\frac{3 b^{2} a \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{b^{3} \left(\sin^{4}\left(d x +c \right)\right)}{d \cos \left(d x +c \right)}+\frac{b^{3} \cos \left(d x +c \right) \left(\sin^{2}\left(d x +c \right)\right)}{d}+\frac{2 b^{3} \cos \left(d x +c \right)}{d}"," ",0,"a^3*sin(d*x+c)/d-3*a^2*b*cos(d*x+c)/d-3*a*b^2*sin(d*x+c)/d+3/d*b^2*a*ln(sec(d*x+c)+tan(d*x+c))+1/d*b^3*sin(d*x+c)^4/cos(d*x+c)+1/d*b^3*cos(d*x+c)*sin(d*x+c)^2+2*b^3*cos(d*x+c)/d","A"
65,1,93,70,1.796000," ","int(sec(d*x+c)^3*(a*cos(d*x+c)+b*sin(d*x+c))^3,x)","a^{3} x +\frac{a^{3} c}{d}-\frac{3 a^{2} b \ln \left(\cos \left(d x +c \right)\right)}{d}-3 a \,b^{2} x +\frac{3 a \,b^{2} \tan \left(d x +c \right)}{d}-\frac{3 a \,b^{2} c}{d}+\frac{b^{3} \left(\tan^{2}\left(d x +c \right)\right)}{2 d}+\frac{b^{3} \ln \left(\cos \left(d x +c \right)\right)}{d}"," ",0,"a^3*x+1/d*a^3*c-3*a^2*b*ln(cos(d*x+c))/d-3*a*b^2*x+3*a*b^2*tan(d*x+c)/d-3/d*a*b^2*c+1/2*b^3*tan(d*x+c)^2/d+b^3*ln(cos(d*x+c))/d","A"
66,1,187,97,10.246000," ","int(sec(d*x+c)^4*(a*cos(d*x+c)+b*sin(d*x+c))^3,x)","\frac{a^{3} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{3 a^{2} b}{d \cos \left(d x +c \right)}+\frac{3 b^{2} a \left(\sin^{3}\left(d x +c \right)\right)}{2 d \cos \left(d x +c \right)^{2}}+\frac{3 a \,b^{2} \sin \left(d x +c \right)}{2 d}-\frac{3 b^{2} a \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{2 d}+\frac{b^{3} \left(\sin^{4}\left(d x +c \right)\right)}{3 d \cos \left(d x +c \right)^{3}}-\frac{b^{3} \left(\sin^{4}\left(d x +c \right)\right)}{3 d \cos \left(d x +c \right)}-\frac{b^{3} \cos \left(d x +c \right) \left(\sin^{2}\left(d x +c \right)\right)}{3 d}-\frac{2 b^{3} \cos \left(d x +c \right)}{3 d}"," ",0,"1/d*a^3*ln(sec(d*x+c)+tan(d*x+c))+3/d*a^2*b/cos(d*x+c)+3/2/d*b^2*a*sin(d*x+c)^3/cos(d*x+c)^2+3/2*a*b^2*sin(d*x+c)/d-3/2/d*b^2*a*ln(sec(d*x+c)+tan(d*x+c))+1/3/d*b^3*sin(d*x+c)^4/cos(d*x+c)^3-1/3/d*b^3*sin(d*x+c)^4/cos(d*x+c)-1/3/d*b^3*cos(d*x+c)*sin(d*x+c)^2-2/3*b^3*cos(d*x+c)/d","A"
67,1,72,28,11.415000," ","int(sec(d*x+c)^5*(a*cos(d*x+c)+b*sin(d*x+c))^3,x)","\frac{a^{3} \tan \left(d x +c \right)+\frac{3 a^{2} b}{2 \cos \left(d x +c \right)^{2}}+\frac{b^{2} a \left(\sin^{3}\left(d x +c \right)\right)}{\cos \left(d x +c \right)^{3}}+\frac{b^{3} \left(\sin^{4}\left(d x +c \right)\right)}{4 \cos \left(d x +c \right)^{4}}}{d}"," ",0,"1/d*(a^3*tan(d*x+c)+3/2*a^2*b/cos(d*x+c)^2+b^2*a*sin(d*x+c)^3/cos(d*x+c)^3+1/4*b^3*sin(d*x+c)^4/cos(d*x+c)^4)","B"
68,1,256,144,2.360000," ","int(sec(d*x+c)^6*(a*cos(d*x+c)+b*sin(d*x+c))^3,x)","\frac{a^{3} \sec \left(d x +c \right) \tan \left(d x +c \right)}{2 d}+\frac{a^{3} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{2 d}+\frac{a^{2} b}{d \cos \left(d x +c \right)^{3}}+\frac{3 b^{2} a \left(\sin^{3}\left(d x +c \right)\right)}{4 d \cos \left(d x +c \right)^{4}}+\frac{3 b^{2} a \left(\sin^{3}\left(d x +c \right)\right)}{8 d \cos \left(d x +c \right)^{2}}+\frac{3 a \,b^{2} \sin \left(d x +c \right)}{8 d}-\frac{3 b^{2} a \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{8 d}+\frac{b^{3} \left(\sin^{4}\left(d x +c \right)\right)}{5 d \cos \left(d x +c \right)^{5}}+\frac{b^{3} \left(\sin^{4}\left(d x +c \right)\right)}{15 d \cos \left(d x +c \right)^{3}}-\frac{b^{3} \left(\sin^{4}\left(d x +c \right)\right)}{15 d \cos \left(d x +c \right)}-\frac{b^{3} \cos \left(d x +c \right) \left(\sin^{2}\left(d x +c \right)\right)}{15 d}-\frac{2 b^{3} \cos \left(d x +c \right)}{15 d}"," ",0,"1/2*a^3*sec(d*x+c)*tan(d*x+c)/d+1/2/d*a^3*ln(sec(d*x+c)+tan(d*x+c))+1/d*a^2*b/cos(d*x+c)^3+3/4/d*b^2*a*sin(d*x+c)^3/cos(d*x+c)^4+3/8/d*b^2*a*sin(d*x+c)^3/cos(d*x+c)^2+3/8*a*b^2*sin(d*x+c)/d-3/8/d*b^2*a*ln(sec(d*x+c)+tan(d*x+c))+1/5/d*b^3*sin(d*x+c)^4/cos(d*x+c)^5+1/15/d*b^3*sin(d*x+c)^4/cos(d*x+c)^3-1/15/d*b^3*sin(d*x+c)^4/cos(d*x+c)-1/15/d*b^3*cos(d*x+c)*sin(d*x+c)^2-2/15*b^3*cos(d*x+c)/d","A"
69,1,127,110,20.798000," ","int(sec(d*x+c)^7*(a*cos(d*x+c)+b*sin(d*x+c))^3,x)","\frac{-a^{3} \left(-\frac{2}{3}-\frac{\left(\sec^{2}\left(d x +c \right)\right)}{3}\right) \tan \left(d x +c \right)+\frac{3 a^{2} b}{4 \cos \left(d x +c \right)^{4}}+3 b^{2} a \left(\frac{\sin^{3}\left(d x +c \right)}{5 \cos \left(d x +c \right)^{5}}+\frac{2 \left(\sin^{3}\left(d x +c \right)\right)}{15 \cos \left(d x +c \right)^{3}}\right)+b^{3} \left(\frac{\sin^{4}\left(d x +c \right)}{6 \cos \left(d x +c \right)^{6}}+\frac{\sin^{4}\left(d x +c \right)}{12 \cos \left(d x +c \right)^{4}}\right)}{d}"," ",0,"1/d*(-a^3*(-2/3-1/3*sec(d*x+c)^2)*tan(d*x+c)+3/4*a^2*b/cos(d*x+c)^4+3*b^2*a*(1/5*sin(d*x+c)^3/cos(d*x+c)^5+2/15*sin(d*x+c)^3/cos(d*x+c)^3)+b^3*(1/6*sin(d*x+c)^4/cos(d*x+c)^6+1/12*sin(d*x+c)^4/cos(d*x+c)^4))","A"
70,1,328,190,11.101000," ","int(sec(d*x+c)^8*(a*cos(d*x+c)+b*sin(d*x+c))^3,x)","\frac{a^{3} \left(\sec^{3}\left(d x +c \right)\right) \tan \left(d x +c \right)}{4 d}+\frac{3 a^{3} \sec \left(d x +c \right) \tan \left(d x +c \right)}{8 d}+\frac{3 a^{3} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{8 d}+\frac{3 a^{2} b}{5 d \cos \left(d x +c \right)^{5}}+\frac{b^{2} a \left(\sin^{3}\left(d x +c \right)\right)}{2 d \cos \left(d x +c \right)^{6}}+\frac{3 b^{2} a \left(\sin^{3}\left(d x +c \right)\right)}{8 d \cos \left(d x +c \right)^{4}}+\frac{3 b^{2} a \left(\sin^{3}\left(d x +c \right)\right)}{16 d \cos \left(d x +c \right)^{2}}+\frac{3 a \,b^{2} \sin \left(d x +c \right)}{16 d}-\frac{3 b^{2} a \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{16 d}+\frac{b^{3} \left(\sin^{4}\left(d x +c \right)\right)}{7 d \cos \left(d x +c \right)^{7}}+\frac{3 b^{3} \left(\sin^{4}\left(d x +c \right)\right)}{35 d \cos \left(d x +c \right)^{5}}+\frac{b^{3} \left(\sin^{4}\left(d x +c \right)\right)}{35 d \cos \left(d x +c \right)^{3}}-\frac{b^{3} \left(\sin^{4}\left(d x +c \right)\right)}{35 d \cos \left(d x +c \right)}-\frac{b^{3} \cos \left(d x +c \right) \left(\sin^{2}\left(d x +c \right)\right)}{35 d}-\frac{2 b^{3} \cos \left(d x +c \right)}{35 d}"," ",0,"1/4*a^3*sec(d*x+c)^3*tan(d*x+c)/d+3/8*a^3*sec(d*x+c)*tan(d*x+c)/d+3/8/d*a^3*ln(sec(d*x+c)+tan(d*x+c))+3/5/d*a^2*b/cos(d*x+c)^5+1/2/d*b^2*a*sin(d*x+c)^3/cos(d*x+c)^6+3/8/d*b^2*a*sin(d*x+c)^3/cos(d*x+c)^4+3/16/d*b^2*a*sin(d*x+c)^3/cos(d*x+c)^2+3/16*a*b^2*sin(d*x+c)/d-3/16/d*b^2*a*ln(sec(d*x+c)+tan(d*x+c))+1/7/d*b^3*sin(d*x+c)^4/cos(d*x+c)^7+3/35/d*b^3*sin(d*x+c)^4/cos(d*x+c)^5+1/35/d*b^3*sin(d*x+c)^4/cos(d*x+c)^3-1/35/d*b^3*sin(d*x+c)^4/cos(d*x+c)-1/35/d*b^3*cos(d*x+c)*sin(d*x+c)^2-2/35*b^3*cos(d*x+c)/d","A"
71,1,173,160,9.661000," ","int(sec(d*x+c)^9*(a*cos(d*x+c)+b*sin(d*x+c))^3,x)","\frac{-a^{3} \left(-\frac{8}{15}-\frac{\left(\sec^{4}\left(d x +c \right)\right)}{5}-\frac{4 \left(\sec^{2}\left(d x +c \right)\right)}{15}\right) \tan \left(d x +c \right)+\frac{a^{2} b}{2 \cos \left(d x +c \right)^{6}}+3 b^{2} a \left(\frac{\sin^{3}\left(d x +c \right)}{7 \cos \left(d x +c \right)^{7}}+\frac{4 \left(\sin^{3}\left(d x +c \right)\right)}{35 \cos \left(d x +c \right)^{5}}+\frac{8 \left(\sin^{3}\left(d x +c \right)\right)}{105 \cos \left(d x +c \right)^{3}}\right)+b^{3} \left(\frac{\sin^{4}\left(d x +c \right)}{8 \cos \left(d x +c \right)^{8}}+\frac{\sin^{4}\left(d x +c \right)}{12 \cos \left(d x +c \right)^{6}}+\frac{\sin^{4}\left(d x +c \right)}{24 \cos \left(d x +c \right)^{4}}\right)}{d}"," ",0,"1/d*(-a^3*(-8/15-1/5*sec(d*x+c)^4-4/15*sec(d*x+c)^2)*tan(d*x+c)+1/2*a^2*b/cos(d*x+c)^6+3*b^2*a*(1/7*sin(d*x+c)^3/cos(d*x+c)^7+4/35*sin(d*x+c)^3/cos(d*x+c)^5+8/105*sin(d*x+c)^3/cos(d*x+c)^3)+b^3*(1/8*sin(d*x+c)^4/cos(d*x+c)^8+1/12*sin(d*x+c)^4/cos(d*x+c)^6+1/24*sin(d*x+c)^4/cos(d*x+c)^4))","A"
72,1,399,235,21.070000," ","int(sec(d*x+c)^10*(a*cos(d*x+c)+b*sin(d*x+c))^3,x)","\frac{a^{3} \left(\sec^{5}\left(d x +c \right)\right) \tan \left(d x +c \right)}{6 d}+\frac{5 a^{3} \left(\sec^{3}\left(d x +c \right)\right) \tan \left(d x +c \right)}{24 d}+\frac{5 a^{3} \sec \left(d x +c \right) \tan \left(d x +c \right)}{16 d}+\frac{5 a^{3} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{16 d}+\frac{3 a^{2} b}{7 d \cos \left(d x +c \right)^{7}}+\frac{3 b^{2} a \left(\sin^{3}\left(d x +c \right)\right)}{8 d \cos \left(d x +c \right)^{8}}+\frac{5 b^{2} a \left(\sin^{3}\left(d x +c \right)\right)}{16 d \cos \left(d x +c \right)^{6}}+\frac{15 b^{2} a \left(\sin^{3}\left(d x +c \right)\right)}{64 d \cos \left(d x +c \right)^{4}}+\frac{15 b^{2} a \left(\sin^{3}\left(d x +c \right)\right)}{128 d \cos \left(d x +c \right)^{2}}+\frac{15 a \,b^{2} \sin \left(d x +c \right)}{128 d}-\frac{15 b^{2} a \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{128 d}+\frac{b^{3} \left(\sin^{4}\left(d x +c \right)\right)}{9 d \cos \left(d x +c \right)^{9}}+\frac{5 b^{3} \left(\sin^{4}\left(d x +c \right)\right)}{63 d \cos \left(d x +c \right)^{7}}+\frac{b^{3} \left(\sin^{4}\left(d x +c \right)\right)}{21 d \cos \left(d x +c \right)^{5}}+\frac{b^{3} \left(\sin^{4}\left(d x +c \right)\right)}{63 d \cos \left(d x +c \right)^{3}}-\frac{b^{3} \left(\sin^{4}\left(d x +c \right)\right)}{63 d \cos \left(d x +c \right)}-\frac{b^{3} \cos \left(d x +c \right) \left(\sin^{2}\left(d x +c \right)\right)}{63 d}-\frac{2 b^{3} \cos \left(d x +c \right)}{63 d}"," ",0,"1/6*a^3*sec(d*x+c)^5*tan(d*x+c)/d+5/24*a^3*sec(d*x+c)^3*tan(d*x+c)/d+5/16*a^3*sec(d*x+c)*tan(d*x+c)/d+5/16/d*a^3*ln(sec(d*x+c)+tan(d*x+c))+3/7/d*a^2*b/cos(d*x+c)^7+3/8/d*b^2*a*sin(d*x+c)^3/cos(d*x+c)^8+5/16/d*b^2*a*sin(d*x+c)^3/cos(d*x+c)^6+15/64/d*b^2*a*sin(d*x+c)^3/cos(d*x+c)^4+15/128/d*b^2*a*sin(d*x+c)^3/cos(d*x+c)^2+15/128*a*b^2*sin(d*x+c)/d-15/128/d*b^2*a*ln(sec(d*x+c)+tan(d*x+c))+1/9/d*b^3*sin(d*x+c)^4/cos(d*x+c)^9+5/63/d*b^3*sin(d*x+c)^4/cos(d*x+c)^7+1/21/d*b^3*sin(d*x+c)^4/cos(d*x+c)^5+1/63/d*b^3*sin(d*x+c)^4/cos(d*x+c)^3-1/63/d*b^3*sin(d*x+c)^4/cos(d*x+c)-1/63/d*b^3*cos(d*x+c)*sin(d*x+c)^2-2/63*b^3*cos(d*x+c)/d","A"
73,1,219,197,20.739000," ","int(sec(d*x+c)^11*(a*cos(d*x+c)+b*sin(d*x+c))^3,x)","\frac{-a^{3} \left(-\frac{16}{35}-\frac{\left(\sec^{6}\left(d x +c \right)\right)}{7}-\frac{6 \left(\sec^{4}\left(d x +c \right)\right)}{35}-\frac{8 \left(\sec^{2}\left(d x +c \right)\right)}{35}\right) \tan \left(d x +c \right)+\frac{3 a^{2} b}{8 \cos \left(d x +c \right)^{8}}+3 b^{2} a \left(\frac{\sin^{3}\left(d x +c \right)}{9 \cos \left(d x +c \right)^{9}}+\frac{2 \left(\sin^{3}\left(d x +c \right)\right)}{21 \cos \left(d x +c \right)^{7}}+\frac{8 \left(\sin^{3}\left(d x +c \right)\right)}{105 \cos \left(d x +c \right)^{5}}+\frac{16 \left(\sin^{3}\left(d x +c \right)\right)}{315 \cos \left(d x +c \right)^{3}}\right)+b^{3} \left(\frac{\sin^{4}\left(d x +c \right)}{10 \cos \left(d x +c \right)^{10}}+\frac{3 \left(\sin^{4}\left(d x +c \right)\right)}{40 \cos \left(d x +c \right)^{8}}+\frac{\sin^{4}\left(d x +c \right)}{20 \cos \left(d x +c \right)^{6}}+\frac{\sin^{4}\left(d x +c \right)}{40 \cos \left(d x +c \right)^{4}}\right)}{d}"," ",0,"1/d*(-a^3*(-16/35-1/7*sec(d*x+c)^6-6/35*sec(d*x+c)^4-8/35*sec(d*x+c)^2)*tan(d*x+c)+3/8*a^2*b/cos(d*x+c)^8+3*b^2*a*(1/9*sin(d*x+c)^3/cos(d*x+c)^9+2/21*sin(d*x+c)^3/cos(d*x+c)^7+8/105*sin(d*x+c)^3/cos(d*x+c)^5+16/315*sin(d*x+c)^3/cos(d*x+c)^3)+b^3*(1/10*sin(d*x+c)^4/cos(d*x+c)^10+3/40*sin(d*x+c)^4/cos(d*x+c)^8+1/20*sin(d*x+c)^4/cos(d*x+c)^6+1/40*sin(d*x+c)^4/cos(d*x+c)^4))","A"
74,1,236,253,11.184000," ","int(cos(d*x+c)^5*(a*cos(d*x+c)+b*sin(d*x+c))^4,x)","\frac{b^{4} \left(-\frac{\left(\sin^{3}\left(d x +c \right)\right) \left(\cos^{6}\left(d x +c \right)\right)}{9}-\frac{\sin \left(d x +c \right) \left(\cos^{6}\left(d x +c \right)\right)}{21}+\frac{\left(\frac{8}{3}+\cos^{4}\left(d x +c \right)+\frac{4 \left(\cos^{2}\left(d x +c \right)\right)}{3}\right) \sin \left(d x +c \right)}{105}\right)+4 a \,b^{3} \left(-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{7}\left(d x +c \right)\right)}{9}-\frac{2 \left(\cos^{7}\left(d x +c \right)\right)}{63}\right)+6 a^{2} b^{2} \left(-\frac{\sin \left(d x +c \right) \left(\cos^{8}\left(d x +c \right)\right)}{9}+\frac{\left(\frac{16}{5}+\cos^{6}\left(d x +c \right)+\frac{6 \left(\cos^{4}\left(d x +c \right)\right)}{5}+\frac{8 \left(\cos^{2}\left(d x +c \right)\right)}{5}\right) \sin \left(d x +c \right)}{63}\right)-\frac{4 a^{3} b \left(\cos^{9}\left(d x +c \right)\right)}{9}+\frac{a^{4} \left(\frac{128}{35}+\cos^{8}\left(d x +c \right)+\frac{8 \left(\cos^{6}\left(d x +c \right)\right)}{7}+\frac{48 \left(\cos^{4}\left(d x +c \right)\right)}{35}+\frac{64 \left(\cos^{2}\left(d x +c \right)\right)}{35}\right) \sin \left(d x +c \right)}{9}}{d}"," ",0,"1/d*(b^4*(-1/9*sin(d*x+c)^3*cos(d*x+c)^6-1/21*sin(d*x+c)*cos(d*x+c)^6+1/105*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c))+4*a*b^3*(-1/9*sin(d*x+c)^2*cos(d*x+c)^7-2/63*cos(d*x+c)^7)+6*a^2*b^2*(-1/9*sin(d*x+c)*cos(d*x+c)^8+1/63*(16/5+cos(d*x+c)^6+6/5*cos(d*x+c)^4+8/5*cos(d*x+c)^2)*sin(d*x+c))-4/9*a^3*b*cos(d*x+c)^9+1/9*a^4*(128/35+cos(d*x+c)^8+8/7*cos(d*x+c)^6+48/35*cos(d*x+c)^4+64/35*cos(d*x+c)^2)*sin(d*x+c))","A"
75,1,250,345,21.237000," ","int(cos(d*x+c)^4*(a*cos(d*x+c)+b*sin(d*x+c))^4,x)","\frac{b^{4} \left(-\frac{\left(\sin^{3}\left(d x +c \right)\right) \left(\cos^{5}\left(d x +c \right)\right)}{8}-\frac{\left(\cos^{5}\left(d x +c \right)\right) \sin \left(d x +c \right)}{16}+\frac{\left(\cos^{3}\left(d x +c \right)+\frac{3 \cos \left(d x +c \right)}{2}\right) \sin \left(d x +c \right)}{64}+\frac{3 d x}{128}+\frac{3 c}{128}\right)+4 a \,b^{3} \left(-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{6}\left(d x +c \right)\right)}{8}-\frac{\left(\cos^{6}\left(d x +c \right)\right)}{24}\right)+6 a^{2} b^{2} \left(-\frac{\sin \left(d x +c \right) \left(\cos^{7}\left(d x +c \right)\right)}{8}+\frac{\left(\cos^{5}\left(d x +c \right)+\frac{5 \left(\cos^{3}\left(d x +c \right)\right)}{4}+\frac{15 \cos \left(d x +c \right)}{8}\right) \sin \left(d x +c \right)}{48}+\frac{5 d x}{128}+\frac{5 c}{128}\right)-\frac{a^{3} b \left(\cos^{8}\left(d x +c \right)\right)}{2}+a^{4} \left(\frac{\left(\cos^{7}\left(d x +c \right)+\frac{7 \left(\cos^{5}\left(d x +c \right)\right)}{6}+\frac{35 \left(\cos^{3}\left(d x +c \right)\right)}{24}+\frac{35 \cos \left(d x +c \right)}{16}\right) \sin \left(d x +c \right)}{8}+\frac{35 d x}{128}+\frac{35 c}{128}\right)}{d}"," ",0,"1/d*(b^4*(-1/8*sin(d*x+c)^3*cos(d*x+c)^5-1/16*cos(d*x+c)^5*sin(d*x+c)+1/64*(cos(d*x+c)^3+3/2*cos(d*x+c))*sin(d*x+c)+3/128*d*x+3/128*c)+4*a*b^3*(-1/8*sin(d*x+c)^2*cos(d*x+c)^6-1/24*cos(d*x+c)^6)+6*a^2*b^2*(-1/8*sin(d*x+c)*cos(d*x+c)^7+1/48*(cos(d*x+c)^5+5/4*cos(d*x+c)^3+15/8*cos(d*x+c))*sin(d*x+c)+5/128*d*x+5/128*c)-1/2*a^3*b*cos(d*x+c)^8+a^4*(1/8*(cos(d*x+c)^7+7/6*cos(d*x+c)^5+35/24*cos(d*x+c)^3+35/16*cos(d*x+c))*sin(d*x+c)+35/128*d*x+35/128*c))","A"
76,1,206,202,39.350000," ","int(cos(d*x+c)^3*(a*cos(d*x+c)+b*sin(d*x+c))^4,x)","\frac{b^{4} \left(-\frac{\left(\sin^{3}\left(d x +c \right)\right) \left(\cos^{4}\left(d x +c \right)\right)}{7}-\frac{3 \sin \left(d x +c \right) \left(\cos^{4}\left(d x +c \right)\right)}{35}+\frac{\left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{35}\right)+4 a \,b^{3} \left(-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{5}\left(d x +c \right)\right)}{7}-\frac{2 \left(\cos^{5}\left(d x +c \right)\right)}{35}\right)+6 a^{2} b^{2} \left(-\frac{\sin \left(d x +c \right) \left(\cos^{6}\left(d x +c \right)\right)}{7}+\frac{\left(\frac{8}{3}+\cos^{4}\left(d x +c \right)+\frac{4 \left(\cos^{2}\left(d x +c \right)\right)}{3}\right) \sin \left(d x +c \right)}{35}\right)-\frac{4 a^{3} b \left(\cos^{7}\left(d x +c \right)\right)}{7}+\frac{a^{4} \left(\frac{16}{5}+\cos^{6}\left(d x +c \right)+\frac{6 \left(\cos^{4}\left(d x +c \right)\right)}{5}+\frac{8 \left(\cos^{2}\left(d x +c \right)\right)}{5}\right) \sin \left(d x +c \right)}{7}}{d}"," ",0,"1/d*(b^4*(-1/7*sin(d*x+c)^3*cos(d*x+c)^4-3/35*sin(d*x+c)*cos(d*x+c)^4+1/35*(2+cos(d*x+c)^2)*sin(d*x+c))+4*a*b^3*(-1/7*sin(d*x+c)^2*cos(d*x+c)^5-2/35*cos(d*x+c)^5)+6*a^2*b^2*(-1/7*sin(d*x+c)*cos(d*x+c)^6+1/35*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c))-4/7*a^3*b*cos(d*x+c)^7+1/7*a^4*(16/5+cos(d*x+c)^6+6/5*cos(d*x+c)^4+8/5*cos(d*x+c)^2)*sin(d*x+c))","A"
77,1,219,275,28.973000," ","int(cos(d*x+c)^2*(a*cos(d*x+c)+b*sin(d*x+c))^4,x)","\frac{b^{4} \left(-\frac{\left(\sin^{3}\left(d x +c \right)\right) \left(\cos^{3}\left(d x +c \right)\right)}{6}-\frac{\left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)}{8}+\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)}{16}+\frac{d x}{16}+\frac{c}{16}\right)+4 a \,b^{3} \left(-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{4}\left(d x +c \right)\right)}{6}-\frac{\left(\cos^{4}\left(d x +c \right)\right)}{12}\right)+6 a^{2} b^{2} \left(-\frac{\left(\cos^{5}\left(d x +c \right)\right) \sin \left(d x +c \right)}{6}+\frac{\left(\cos^{3}\left(d x +c \right)+\frac{3 \cos \left(d x +c \right)}{2}\right) \sin \left(d x +c \right)}{24}+\frac{d x}{16}+\frac{c}{16}\right)-\frac{2 a^{3} b \left(\cos^{6}\left(d x +c \right)\right)}{3}+a^{4} \left(\frac{\left(\cos^{5}\left(d x +c \right)+\frac{5 \left(\cos^{3}\left(d x +c \right)\right)}{4}+\frac{15 \cos \left(d x +c \right)}{8}\right) \sin \left(d x +c \right)}{6}+\frac{5 d x}{16}+\frac{5 c}{16}\right)}{d}"," ",0,"1/d*(b^4*(-1/6*sin(d*x+c)^3*cos(d*x+c)^3-1/8*cos(d*x+c)^3*sin(d*x+c)+1/16*cos(d*x+c)*sin(d*x+c)+1/16*d*x+1/16*c)+4*a*b^3*(-1/6*sin(d*x+c)^2*cos(d*x+c)^4-1/12*cos(d*x+c)^4)+6*a^2*b^2*(-1/6*cos(d*x+c)^5*sin(d*x+c)+1/24*(cos(d*x+c)^3+3/2*cos(d*x+c))*sin(d*x+c)+1/16*d*x+1/16*c)-2/3*a^3*b*cos(d*x+c)^6+a^4*(1/6*(cos(d*x+c)^5+5/4*cos(d*x+c)^3+15/8*cos(d*x+c))*sin(d*x+c)+5/16*d*x+5/16*c))","A"
78,1,142,151,39.384000," ","int(cos(d*x+c)*(a*cos(d*x+c)+b*sin(d*x+c))^4,x)","\frac{\frac{b^{4} \left(\sin^{5}\left(d x +c \right)\right)}{5}+4 a \,b^{3} \left(-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{3}\left(d x +c \right)\right)}{5}-\frac{2 \left(\cos^{3}\left(d x +c \right)\right)}{15}\right)+6 a^{2} b^{2} \left(-\frac{\sin \left(d x +c \right) \left(\cos^{4}\left(d x +c \right)\right)}{5}+\frac{\left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{15}\right)-\frac{4 a^{3} b \left(\cos^{5}\left(d x +c \right)\right)}{5}+\frac{a^{4} \left(\frac{8}{3}+\cos^{4}\left(d x +c \right)+\frac{4 \left(\cos^{2}\left(d x +c \right)\right)}{3}\right) \sin \left(d x +c \right)}{5}}{d}"," ",0,"1/d*(1/5*b^4*sin(d*x+c)^5+4*a*b^3*(-1/5*sin(d*x+c)^2*cos(d*x+c)^3-2/15*cos(d*x+c)^3)+6*a^2*b^2*(-1/5*sin(d*x+c)*cos(d*x+c)^4+1/15*(2+cos(d*x+c)^2)*sin(d*x+c))-4/5*a^3*b*cos(d*x+c)^5+1/5*a^4*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c))","A"
79,1,153,102,30.891000," ","int((a*cos(d*x+c)+b*sin(d*x+c))^4,x)","\frac{b^{4} \left(-\frac{\left(\sin^{3}\left(d x +c \right)+\frac{3 \sin \left(d x +c \right)}{2}\right) \cos \left(d x +c \right)}{4}+\frac{3 d x}{8}+\frac{3 c}{8}\right)+a \,b^{3} \left(\sin^{4}\left(d x +c \right)\right)+6 a^{2} b^{2} \left(-\frac{\left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)}{4}+\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)}{8}+\frac{d x}{8}+\frac{c}{8}\right)-\left(\cos^{4}\left(d x +c \right)\right) a^{3} b +a^{4} \left(\frac{\left(\cos^{3}\left(d x +c \right)+\frac{3 \cos \left(d x +c \right)}{2}\right) \sin \left(d x +c \right)}{4}+\frac{3 d x}{8}+\frac{3 c}{8}\right)}{d}"," ",0,"1/d*(b^4*(-1/4*(sin(d*x+c)^3+3/2*sin(d*x+c))*cos(d*x+c)+3/8*d*x+3/8*c)+a*b^3*sin(d*x+c)^4+6*a^2*b^2*(-1/4*cos(d*x+c)^3*sin(d*x+c)+1/8*cos(d*x+c)*sin(d*x+c)+1/8*d*x+1/8*c)-cos(d*x+c)^4*a^3*b+a^4*(1/4*(cos(d*x+c)^3+3/2*cos(d*x+c))*sin(d*x+c)+3/8*d*x+3/8*c))","A"
80,1,163,142,11.205000," ","int(sec(d*x+c)*(a*cos(d*x+c)+b*sin(d*x+c))^4,x)","\frac{\sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) a^{4}}{3 d}+\frac{2 a^{4} \sin \left(d x +c \right)}{3 d}-\frac{4 a^{3} b \left(\cos^{3}\left(d x +c \right)\right)}{3 d}+\frac{2 a^{2} b^{2} \left(\sin^{3}\left(d x +c \right)\right)}{d}-\frac{4 \left(\sin^{2}\left(d x +c \right)\right) \cos \left(d x +c \right) a \,b^{3}}{3 d}-\frac{8 a \,b^{3} \cos \left(d x +c \right)}{3 d}-\frac{b^{4} \left(\sin^{3}\left(d x +c \right)\right)}{3 d}-\frac{b^{4} \sin \left(d x +c \right)}{d}+\frac{b^{4} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}"," ",0,"1/3/d*sin(d*x+c)*cos(d*x+c)^2*a^4+2/3*a^4*sin(d*x+c)/d-4/3*a^3*b*cos(d*x+c)^3/d+2*a^2*b^2*sin(d*x+c)^3/d-4/3/d*sin(d*x+c)^2*cos(d*x+c)*a*b^3-8/3*a*b^3*cos(d*x+c)/d-1/3*b^4*sin(d*x+c)^3/d-b^4*sin(d*x+c)/d+1/d*b^4*ln(sec(d*x+c)+tan(d*x+c))","A"
81,1,210,115,52.301000," ","int(sec(d*x+c)^2*(a*cos(d*x+c)+b*sin(d*x+c))^4,x)","\frac{a^{4} \cos \left(d x +c \right) \sin \left(d x +c \right)}{2 d}+\frac{a^{4} x}{2}+\frac{a^{4} c}{2 d}-\frac{2 \left(\cos^{2}\left(d x +c \right)\right) a^{3} b}{d}-\frac{3 a^{2} b^{2} \cos \left(d x +c \right) \sin \left(d x +c \right)}{d}+3 a^{2} b^{2} x +\frac{3 a^{2} b^{2} c}{d}-\frac{2 a \,b^{3} \left(\sin^{2}\left(d x +c \right)\right)}{d}-\frac{4 a \,b^{3} \ln \left(\cos \left(d x +c \right)\right)}{d}+\frac{b^{4} \left(\sin^{5}\left(d x +c \right)\right)}{d \cos \left(d x +c \right)}+\frac{b^{4} \cos \left(d x +c \right) \left(\sin^{3}\left(d x +c \right)\right)}{d}+\frac{3 b^{4} \cos \left(d x +c \right) \sin \left(d x +c \right)}{2 d}-\frac{3 b^{4} x}{2}-\frac{3 b^{4} c}{2 d}"," ",0,"1/2*a^4*cos(d*x+c)*sin(d*x+c)/d+1/2*a^4*x+1/2/d*a^4*c-2/d*cos(d*x+c)^2*a^3*b-3*a^2*b^2*cos(d*x+c)*sin(d*x+c)/d+3*a^2*b^2*x+3/d*a^2*b^2*c-2/d*a*b^3*sin(d*x+c)^2-4*a*b^3*ln(cos(d*x+c))/d+1/d*b^4*sin(d*x+c)^5/cos(d*x+c)+1/d*b^4*cos(d*x+c)*sin(d*x+c)^3+3/2*b^4*cos(d*x+c)*sin(d*x+c)/d-3/2*b^4*x-3/2/d*b^4*c","A"
82,1,211,145,29.434000," ","int(sec(d*x+c)^3*(a*cos(d*x+c)+b*sin(d*x+c))^4,x)","\frac{a^{4} \sin \left(d x +c \right)}{d}-\frac{4 a^{3} b \cos \left(d x +c \right)}{d}+\frac{6 a^{2} b^{2} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}-\frac{6 a^{2} b^{2} \sin \left(d x +c \right)}{d}+\frac{4 a \,b^{3} \left(\sin^{4}\left(d x +c \right)\right)}{d \cos \left(d x +c \right)}+\frac{4 \left(\sin^{2}\left(d x +c \right)\right) \cos \left(d x +c \right) a \,b^{3}}{d}+\frac{8 a \,b^{3} \cos \left(d x +c \right)}{d}+\frac{b^{4} \left(\sin^{5}\left(d x +c \right)\right)}{2 d \cos \left(d x +c \right)^{2}}+\frac{b^{4} \left(\sin^{3}\left(d x +c \right)\right)}{2 d}+\frac{3 b^{4} \sin \left(d x +c \right)}{2 d}-\frac{3 b^{4} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{2 d}"," ",0,"a^4*sin(d*x+c)/d-4*a^3*b*cos(d*x+c)/d+6/d*a^2*b^2*ln(sec(d*x+c)+tan(d*x+c))-6*a^2*b^2*sin(d*x+c)/d+4/d*a*b^3*sin(d*x+c)^4/cos(d*x+c)+4/d*sin(d*x+c)^2*cos(d*x+c)*a*b^3+8*a*b^3*cos(d*x+c)/d+1/2/d*b^4*sin(d*x+c)^5/cos(d*x+c)^2+1/2*b^4*sin(d*x+c)^3/d+3/2*b^4*sin(d*x+c)/d-3/2/d*b^4*ln(sec(d*x+c)+tan(d*x+c))","A"
83,1,145,101,1.921000," ","int(sec(d*x+c)^4*(a*cos(d*x+c)+b*sin(d*x+c))^4,x)","a^{4} x +\frac{a^{4} c}{d}-\frac{4 a^{3} b \ln \left(\cos \left(d x +c \right)\right)}{d}-6 a^{2} b^{2} x +\frac{6 a^{2} b^{2} \tan \left(d x +c \right)}{d}-\frac{6 a^{2} b^{2} c}{d}+\frac{2 a \,b^{3} \left(\tan^{2}\left(d x +c \right)\right)}{d}+\frac{4 a \,b^{3} \ln \left(\cos \left(d x +c \right)\right)}{d}+\frac{b^{4} \left(\tan^{3}\left(d x +c \right)\right)}{3 d}-\frac{b^{4} \tan \left(d x +c \right)}{d}+b^{4} x +\frac{b^{4} c}{d}"," ",0,"a^4*x+1/d*a^4*c-4/d*a^3*b*ln(cos(d*x+c))-6*a^2*b^2*x+6*a^2*b^2*tan(d*x+c)/d-6/d*a^2*b^2*c+2*a*b^3*tan(d*x+c)^2/d+4*a*b^3*ln(cos(d*x+c))/d+1/3*b^4*tan(d*x+c)^3/d-b^4*tan(d*x+c)/d+b^4*x+1/d*b^4*c","A"
84,1,297,160,37.628000," ","int(sec(d*x+c)^5*(a*cos(d*x+c)+b*sin(d*x+c))^4,x)","\frac{a^{4} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{4 a^{3} b}{d \cos \left(d x +c \right)}+\frac{3 a^{2} b^{2} \left(\sin^{3}\left(d x +c \right)\right)}{d \cos \left(d x +c \right)^{2}}+\frac{3 a^{2} b^{2} \sin \left(d x +c \right)}{d}-\frac{3 a^{2} b^{2} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{4 a \,b^{3} \left(\sin^{4}\left(d x +c \right)\right)}{3 d \cos \left(d x +c \right)^{3}}-\frac{4 a \,b^{3} \left(\sin^{4}\left(d x +c \right)\right)}{3 d \cos \left(d x +c \right)}-\frac{4 \left(\sin^{2}\left(d x +c \right)\right) \cos \left(d x +c \right) a \,b^{3}}{3 d}-\frac{8 a \,b^{3} \cos \left(d x +c \right)}{3 d}+\frac{b^{4} \left(\sin^{5}\left(d x +c \right)\right)}{4 d \cos \left(d x +c \right)^{4}}-\frac{b^{4} \left(\sin^{5}\left(d x +c \right)\right)}{8 d \cos \left(d x +c \right)^{2}}-\frac{b^{4} \left(\sin^{3}\left(d x +c \right)\right)}{8 d}-\frac{3 b^{4} \sin \left(d x +c \right)}{8 d}+\frac{3 b^{4} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{8 d}"," ",0,"1/d*a^4*ln(sec(d*x+c)+tan(d*x+c))+4/d*a^3*b/cos(d*x+c)+3/d*a^2*b^2*sin(d*x+c)^3/cos(d*x+c)^2+3*a^2*b^2*sin(d*x+c)/d-3/d*a^2*b^2*ln(sec(d*x+c)+tan(d*x+c))+4/3/d*a*b^3*sin(d*x+c)^4/cos(d*x+c)^3-4/3/d*a*b^3*sin(d*x+c)^4/cos(d*x+c)-4/3/d*sin(d*x+c)^2*cos(d*x+c)*a*b^3-8/3*a*b^3*cos(d*x+c)/d+1/4/d*b^4*sin(d*x+c)^5/cos(d*x+c)^4-1/8/d*b^4*sin(d*x+c)^5/cos(d*x+c)^2-1/8*b^4*sin(d*x+c)^3/d-3/8*b^4*sin(d*x+c)/d+3/8/d*b^4*ln(sec(d*x+c)+tan(d*x+c))","A"
85,1,96,28,27.471000," ","int(sec(d*x+c)^6*(a*cos(d*x+c)+b*sin(d*x+c))^4,x)","\frac{a^{4} \tan \left(d x +c \right)+\frac{2 a^{3} b}{\cos \left(d x +c \right)^{2}}+\frac{2 a^{2} b^{2} \left(\sin^{3}\left(d x +c \right)\right)}{\cos \left(d x +c \right)^{3}}+\frac{a \,b^{3} \left(\sin^{4}\left(d x +c \right)\right)}{\cos \left(d x +c \right)^{4}}+\frac{b^{4} \left(\sin^{5}\left(d x +c \right)\right)}{5 \cos \left(d x +c \right)^{5}}}{d}"," ",0,"1/d*(a^4*tan(d*x+c)+2*a^3*b/cos(d*x+c)^2+2*a^2*b^2*sin(d*x+c)^3/cos(d*x+c)^3+a*b^3*sin(d*x+c)^4/cos(d*x+c)^4+1/5*b^4*sin(d*x+c)^5/cos(d*x+c)^5)","B"
86,1,394,234,65.240000," ","int(sec(d*x+c)^7*(a*cos(d*x+c)+b*sin(d*x+c))^4,x)","\frac{a^{4} \sec \left(d x +c \right) \tan \left(d x +c \right)}{2 d}+\frac{a^{4} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{2 d}+\frac{4 a^{3} b}{3 d \cos \left(d x +c \right)^{3}}+\frac{3 a^{2} b^{2} \left(\sin^{3}\left(d x +c \right)\right)}{2 d \cos \left(d x +c \right)^{4}}+\frac{3 a^{2} b^{2} \left(\sin^{3}\left(d x +c \right)\right)}{4 d \cos \left(d x +c \right)^{2}}+\frac{3 a^{2} b^{2} \sin \left(d x +c \right)}{4 d}-\frac{3 a^{2} b^{2} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{4 d}+\frac{4 a \,b^{3} \left(\sin^{4}\left(d x +c \right)\right)}{5 d \cos \left(d x +c \right)^{5}}+\frac{4 a \,b^{3} \left(\sin^{4}\left(d x +c \right)\right)}{15 d \cos \left(d x +c \right)^{3}}-\frac{4 a \,b^{3} \left(\sin^{4}\left(d x +c \right)\right)}{15 d \cos \left(d x +c \right)}-\frac{4 \left(\sin^{2}\left(d x +c \right)\right) \cos \left(d x +c \right) a \,b^{3}}{15 d}-\frac{8 a \,b^{3} \cos \left(d x +c \right)}{15 d}+\frac{b^{4} \left(\sin^{5}\left(d x +c \right)\right)}{6 d \cos \left(d x +c \right)^{6}}+\frac{b^{4} \left(\sin^{5}\left(d x +c \right)\right)}{24 d \cos \left(d x +c \right)^{4}}-\frac{b^{4} \left(\sin^{5}\left(d x +c \right)\right)}{48 d \cos \left(d x +c \right)^{2}}-\frac{b^{4} \left(\sin^{3}\left(d x +c \right)\right)}{48 d}-\frac{b^{4} \sin \left(d x +c \right)}{16 d}+\frac{b^{4} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{16 d}"," ",0,"1/2*a^4*sec(d*x+c)*tan(d*x+c)/d+1/2/d*a^4*ln(sec(d*x+c)+tan(d*x+c))+4/3/d*a^3*b/cos(d*x+c)^3+3/2/d*a^2*b^2*sin(d*x+c)^3/cos(d*x+c)^4+3/4/d*a^2*b^2*sin(d*x+c)^3/cos(d*x+c)^2+3/4*a^2*b^2*sin(d*x+c)/d-3/4/d*a^2*b^2*ln(sec(d*x+c)+tan(d*x+c))+4/5/d*a*b^3*sin(d*x+c)^4/cos(d*x+c)^5+4/15/d*a*b^3*sin(d*x+c)^4/cos(d*x+c)^3-4/15/d*a*b^3*sin(d*x+c)^4/cos(d*x+c)-4/15/d*sin(d*x+c)^2*cos(d*x+c)*a*b^3-8/15*a*b^3*cos(d*x+c)/d+1/6/d*b^4*sin(d*x+c)^5/cos(d*x+c)^6+1/24/d*b^4*sin(d*x+c)^5/cos(d*x+c)^4-1/48/d*b^4*sin(d*x+c)^5/cos(d*x+c)^2-1/48*b^4*sin(d*x+c)^3/d-1/16*b^4*sin(d*x+c)/d+1/16/d*b^4*ln(sec(d*x+c)+tan(d*x+c))","A"
87,1,171,135,52.372000," ","int(sec(d*x+c)^8*(a*cos(d*x+c)+b*sin(d*x+c))^4,x)","\frac{-a^{4} \left(-\frac{2}{3}-\frac{\left(\sec^{2}\left(d x +c \right)\right)}{3}\right) \tan \left(d x +c \right)+\frac{a^{3} b}{\cos \left(d x +c \right)^{4}}+6 a^{2} b^{2} \left(\frac{\sin^{3}\left(d x +c \right)}{5 \cos \left(d x +c \right)^{5}}+\frac{2 \left(\sin^{3}\left(d x +c \right)\right)}{15 \cos \left(d x +c \right)^{3}}\right)+4 a \,b^{3} \left(\frac{\sin^{4}\left(d x +c \right)}{6 \cos \left(d x +c \right)^{6}}+\frac{\sin^{4}\left(d x +c \right)}{12 \cos \left(d x +c \right)^{4}}\right)+b^{4} \left(\frac{\sin^{5}\left(d x +c \right)}{7 \cos \left(d x +c \right)^{7}}+\frac{2 \left(\sin^{5}\left(d x +c \right)\right)}{35 \cos \left(d x +c \right)^{5}}\right)}{d}"," ",0,"1/d*(-a^4*(-2/3-1/3*sec(d*x+c)^2)*tan(d*x+c)+a^3*b/cos(d*x+c)^4+6*a^2*b^2*(1/5*sin(d*x+c)^3/cos(d*x+c)^5+2/15*sin(d*x+c)^3/cos(d*x+c)^3)+4*a*b^3*(1/6*sin(d*x+c)^4/cos(d*x+c)^6+1/12*sin(d*x+c)^4/cos(d*x+c)^4)+b^4*(1/7*sin(d*x+c)^5/cos(d*x+c)^7+2/35*sin(d*x+c)^5/cos(d*x+c)^5))","A"
88,1,491,302,68.458000," ","int(sec(d*x+c)^9*(a*cos(d*x+c)+b*sin(d*x+c))^4,x)","\frac{a^{4} \left(\sec^{3}\left(d x +c \right)\right) \tan \left(d x +c \right)}{4 d}+\frac{3 a^{4} \sec \left(d x +c \right) \tan \left(d x +c \right)}{8 d}+\frac{3 a^{4} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{8 d}+\frac{4 a^{3} b}{5 d \cos \left(d x +c \right)^{5}}+\frac{a^{2} b^{2} \left(\sin^{3}\left(d x +c \right)\right)}{d \cos \left(d x +c \right)^{6}}+\frac{3 a^{2} b^{2} \left(\sin^{3}\left(d x +c \right)\right)}{4 d \cos \left(d x +c \right)^{4}}+\frac{3 a^{2} b^{2} \left(\sin^{3}\left(d x +c \right)\right)}{8 d \cos \left(d x +c \right)^{2}}+\frac{3 a^{2} b^{2} \sin \left(d x +c \right)}{8 d}-\frac{3 a^{2} b^{2} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{8 d}+\frac{4 a \,b^{3} \left(\sin^{4}\left(d x +c \right)\right)}{7 d \cos \left(d x +c \right)^{7}}+\frac{12 a \,b^{3} \left(\sin^{4}\left(d x +c \right)\right)}{35 d \cos \left(d x +c \right)^{5}}+\frac{4 a \,b^{3} \left(\sin^{4}\left(d x +c \right)\right)}{35 d \cos \left(d x +c \right)^{3}}-\frac{4 a \,b^{3} \left(\sin^{4}\left(d x +c \right)\right)}{35 d \cos \left(d x +c \right)}-\frac{4 \left(\sin^{2}\left(d x +c \right)\right) \cos \left(d x +c \right) a \,b^{3}}{35 d}-\frac{8 a \,b^{3} \cos \left(d x +c \right)}{35 d}+\frac{b^{4} \left(\sin^{5}\left(d x +c \right)\right)}{8 d \cos \left(d x +c \right)^{8}}+\frac{b^{4} \left(\sin^{5}\left(d x +c \right)\right)}{16 d \cos \left(d x +c \right)^{6}}+\frac{b^{4} \left(\sin^{5}\left(d x +c \right)\right)}{64 d \cos \left(d x +c \right)^{4}}-\frac{b^{4} \left(\sin^{5}\left(d x +c \right)\right)}{128 d \cos \left(d x +c \right)^{2}}-\frac{b^{4} \left(\sin^{3}\left(d x +c \right)\right)}{128 d}-\frac{3 b^{4} \sin \left(d x +c \right)}{128 d}+\frac{3 b^{4} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{128 d}"," ",0,"1/4*a^4*sec(d*x+c)^3*tan(d*x+c)/d+3/8*a^4*sec(d*x+c)*tan(d*x+c)/d+3/8/d*a^4*ln(sec(d*x+c)+tan(d*x+c))+4/5/d*a^3*b/cos(d*x+c)^5+1/d*a^2*b^2*sin(d*x+c)^3/cos(d*x+c)^6+3/4/d*a^2*b^2*sin(d*x+c)^3/cos(d*x+c)^4+3/8/d*a^2*b^2*sin(d*x+c)^3/cos(d*x+c)^2+3/8*a^2*b^2*sin(d*x+c)/d-3/8/d*a^2*b^2*ln(sec(d*x+c)+tan(d*x+c))+4/7/d*a*b^3*sin(d*x+c)^4/cos(d*x+c)^7+12/35/d*a*b^3*sin(d*x+c)^4/cos(d*x+c)^5+4/35/d*a*b^3*sin(d*x+c)^4/cos(d*x+c)^3-4/35/d*a*b^3*sin(d*x+c)^4/cos(d*x+c)-4/35/d*sin(d*x+c)^2*cos(d*x+c)*a*b^3-8/35*a*b^3*cos(d*x+c)/d+1/8/d*b^4*sin(d*x+c)^5/cos(d*x+c)^8+1/16/d*b^4*sin(d*x+c)^5/cos(d*x+c)^6+1/64/d*b^4*sin(d*x+c)^5/cos(d*x+c)^4-1/128/d*b^4*sin(d*x+c)^5/cos(d*x+c)^2-1/128*b^4*sin(d*x+c)^3/d-3/128*b^4*sin(d*x+c)/d+3/128/d*b^4*ln(sec(d*x+c)+tan(d*x+c))","A"
89,1,236,189,75.918000," ","int(sec(d*x+c)^10*(a*cos(d*x+c)+b*sin(d*x+c))^4,x)","\frac{-a^{4} \left(-\frac{8}{15}-\frac{\left(\sec^{4}\left(d x +c \right)\right)}{5}-\frac{4 \left(\sec^{2}\left(d x +c \right)\right)}{15}\right) \tan \left(d x +c \right)+\frac{2 a^{3} b}{3 \cos \left(d x +c \right)^{6}}+6 a^{2} b^{2} \left(\frac{\sin^{3}\left(d x +c \right)}{7 \cos \left(d x +c \right)^{7}}+\frac{4 \left(\sin^{3}\left(d x +c \right)\right)}{35 \cos \left(d x +c \right)^{5}}+\frac{8 \left(\sin^{3}\left(d x +c \right)\right)}{105 \cos \left(d x +c \right)^{3}}\right)+4 a \,b^{3} \left(\frac{\sin^{4}\left(d x +c \right)}{8 \cos \left(d x +c \right)^{8}}+\frac{\sin^{4}\left(d x +c \right)}{12 \cos \left(d x +c \right)^{6}}+\frac{\sin^{4}\left(d x +c \right)}{24 \cos \left(d x +c \right)^{4}}\right)+b^{4} \left(\frac{\sin^{5}\left(d x +c \right)}{9 \cos \left(d x +c \right)^{9}}+\frac{4 \left(\sin^{5}\left(d x +c \right)\right)}{63 \cos \left(d x +c \right)^{7}}+\frac{8 \left(\sin^{5}\left(d x +c \right)\right)}{315 \cos \left(d x +c \right)^{5}}\right)}{d}"," ",0,"1/d*(-a^4*(-8/15-1/5*sec(d*x+c)^4-4/15*sec(d*x+c)^2)*tan(d*x+c)+2/3*a^3*b/cos(d*x+c)^6+6*a^2*b^2*(1/7*sin(d*x+c)^3/cos(d*x+c)^7+4/35*sin(d*x+c)^3/cos(d*x+c)^5+8/105*sin(d*x+c)^3/cos(d*x+c)^3)+4*a*b^3*(1/8*sin(d*x+c)^4/cos(d*x+c)^8+1/12*sin(d*x+c)^4/cos(d*x+c)^6+1/24*sin(d*x+c)^4/cos(d*x+c)^4)+b^4*(1/9*sin(d*x+c)^5/cos(d*x+c)^9+4/63*sin(d*x+c)^5/cos(d*x+c)^7+8/315*sin(d*x+c)^5/cos(d*x+c)^5))","A"
90,1,590,372,74.032000," ","int(sec(d*x+c)^11*(a*cos(d*x+c)+b*sin(d*x+c))^4,x)","\frac{b^{4} \left(\sin^{5}\left(d x +c \right)\right)}{10 d \cos \left(d x +c \right)^{10}}+\frac{a^{4} \left(\sec^{5}\left(d x +c \right)\right) \tan \left(d x +c \right)}{6 d}+\frac{b^{4} \left(\sin^{5}\left(d x +c \right)\right)}{32 d \cos \left(d x +c \right)^{6}}+\frac{4 a^{3} b}{7 d \cos \left(d x +c \right)^{7}}-\frac{15 a^{2} b^{2} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{64 d}+\frac{b^{4} \left(\sin^{5}\left(d x +c \right)\right)}{128 d \cos \left(d x +c \right)^{4}}+\frac{3 b^{4} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{256 d}+\frac{5 a^{4} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{16 d}+\frac{5 a^{4} \sec \left(d x +c \right) \tan \left(d x +c \right)}{16 d}-\frac{8 a \,b^{3} \cos \left(d x +c \right)}{63 d}+\frac{15 a^{2} b^{2} \sin \left(d x +c \right)}{64 d}-\frac{b^{4} \left(\sin^{3}\left(d x +c \right)\right)}{256 d}-\frac{3 b^{4} \sin \left(d x +c \right)}{256 d}-\frac{4 \left(\sin^{2}\left(d x +c \right)\right) \cos \left(d x +c \right) a \,b^{3}}{63 d}-\frac{4 a \,b^{3} \left(\sin^{4}\left(d x +c \right)\right)}{63 d \cos \left(d x +c \right)}+\frac{5 a^{2} b^{2} \left(\sin^{3}\left(d x +c \right)\right)}{8 d \cos \left(d x +c \right)^{6}}+\frac{15 a^{2} b^{2} \left(\sin^{3}\left(d x +c \right)\right)}{64 d \cos \left(d x +c \right)^{2}}+\frac{4 a \,b^{3} \left(\sin^{4}\left(d x +c \right)\right)}{63 d \cos \left(d x +c \right)^{3}}+\frac{15 a^{2} b^{2} \left(\sin^{3}\left(d x +c \right)\right)}{32 d \cos \left(d x +c \right)^{4}}+\frac{4 a \,b^{3} \left(\sin^{4}\left(d x +c \right)\right)}{21 d \cos \left(d x +c \right)^{5}}+\frac{3 a^{2} b^{2} \left(\sin^{3}\left(d x +c \right)\right)}{4 d \cos \left(d x +c \right)^{8}}+\frac{20 a \,b^{3} \left(\sin^{4}\left(d x +c \right)\right)}{63 d \cos \left(d x +c \right)^{7}}+\frac{4 a \,b^{3} \left(\sin^{4}\left(d x +c \right)\right)}{9 d \cos \left(d x +c \right)^{9}}+\frac{5 a^{4} \left(\sec^{3}\left(d x +c \right)\right) \tan \left(d x +c \right)}{24 d}-\frac{b^{4} \left(\sin^{5}\left(d x +c \right)\right)}{256 d \cos \left(d x +c \right)^{2}}+\frac{b^{4} \left(\sin^{5}\left(d x +c \right)\right)}{16 d \cos \left(d x +c \right)^{8}}"," ",0,"4/7/d*a^3*b/cos(d*x+c)^7+1/10/d*b^4*sin(d*x+c)^5/cos(d*x+c)^10-15/64/d*a^2*b^2*ln(sec(d*x+c)+tan(d*x+c))-1/256/d*b^4*sin(d*x+c)^5/cos(d*x+c)^2+3/256/d*b^4*ln(sec(d*x+c)+tan(d*x+c))+5/16/d*a^4*ln(sec(d*x+c)+tan(d*x+c))+5/16*a^4*sec(d*x+c)*tan(d*x+c)/d+5/24*a^4*sec(d*x+c)^3*tan(d*x+c)/d+1/6*a^4*sec(d*x+c)^5*tan(d*x+c)/d-8/63*a*b^3*cos(d*x+c)/d+15/64*a^2*b^2*sin(d*x+c)/d+20/63/d*a*b^3*sin(d*x+c)^4/cos(d*x+c)^7+15/64/d*a^2*b^2*sin(d*x+c)^3/cos(d*x+c)^2-4/63/d*sin(d*x+c)^2*cos(d*x+c)*a*b^3-1/256*b^4*sin(d*x+c)^3/d-3/256*b^4*sin(d*x+c)/d+1/32/d*b^4*sin(d*x+c)^5/cos(d*x+c)^6+4/21/d*a*b^3*sin(d*x+c)^4/cos(d*x+c)^5+4/63/d*a*b^3*sin(d*x+c)^4/cos(d*x+c)^3-4/63/d*a*b^3*sin(d*x+c)^4/cos(d*x+c)+15/32/d*a^2*b^2*sin(d*x+c)^3/cos(d*x+c)^4+5/8/d*a^2*b^2*sin(d*x+c)^3/cos(d*x+c)^6+1/16/d*b^4*sin(d*x+c)^5/cos(d*x+c)^8+3/4/d*a^2*b^2*sin(d*x+c)^3/cos(d*x+c)^8+4/9/d*a*b^3*sin(d*x+c)^4/cos(d*x+c)^9+1/128/d*b^4*sin(d*x+c)^5/cos(d*x+c)^4","A"
91,1,300,242,78.721000," ","int(sec(d*x+c)^12*(a*cos(d*x+c)+b*sin(d*x+c))^4,x)","\frac{-a^{4} \left(-\frac{16}{35}-\frac{\left(\sec^{6}\left(d x +c \right)\right)}{7}-\frac{6 \left(\sec^{4}\left(d x +c \right)\right)}{35}-\frac{8 \left(\sec^{2}\left(d x +c \right)\right)}{35}\right) \tan \left(d x +c \right)+\frac{a^{3} b}{2 \cos \left(d x +c \right)^{8}}+6 a^{2} b^{2} \left(\frac{\sin^{3}\left(d x +c \right)}{9 \cos \left(d x +c \right)^{9}}+\frac{2 \left(\sin^{3}\left(d x +c \right)\right)}{21 \cos \left(d x +c \right)^{7}}+\frac{8 \left(\sin^{3}\left(d x +c \right)\right)}{105 \cos \left(d x +c \right)^{5}}+\frac{16 \left(\sin^{3}\left(d x +c \right)\right)}{315 \cos \left(d x +c \right)^{3}}\right)+4 a \,b^{3} \left(\frac{\sin^{4}\left(d x +c \right)}{10 \cos \left(d x +c \right)^{10}}+\frac{3 \left(\sin^{4}\left(d x +c \right)\right)}{40 \cos \left(d x +c \right)^{8}}+\frac{\sin^{4}\left(d x +c \right)}{20 \cos \left(d x +c \right)^{6}}+\frac{\sin^{4}\left(d x +c \right)}{40 \cos \left(d x +c \right)^{4}}\right)+b^{4} \left(\frac{\sin^{5}\left(d x +c \right)}{11 \cos \left(d x +c \right)^{11}}+\frac{2 \left(\sin^{5}\left(d x +c \right)\right)}{33 \cos \left(d x +c \right)^{9}}+\frac{8 \left(\sin^{5}\left(d x +c \right)\right)}{231 \cos \left(d x +c \right)^{7}}+\frac{16 \left(\sin^{5}\left(d x +c \right)\right)}{1155 \cos \left(d x +c \right)^{5}}\right)}{d}"," ",0,"1/d*(-a^4*(-16/35-1/7*sec(d*x+c)^6-6/35*sec(d*x+c)^4-8/35*sec(d*x+c)^2)*tan(d*x+c)+1/2*a^3*b/cos(d*x+c)^8+6*a^2*b^2*(1/9*sin(d*x+c)^3/cos(d*x+c)^9+2/21*sin(d*x+c)^3/cos(d*x+c)^7+8/105*sin(d*x+c)^3/cos(d*x+c)^5+16/315*sin(d*x+c)^3/cos(d*x+c)^3)+4*a*b^3*(1/10*sin(d*x+c)^4/cos(d*x+c)^10+3/40*sin(d*x+c)^4/cos(d*x+c)^8+1/20*sin(d*x+c)^4/cos(d*x+c)^6+1/40*sin(d*x+c)^4/cos(d*x+c)^4)+b^4*(1/11*sin(d*x+c)^5/cos(d*x+c)^11+2/33*sin(d*x+c)^5/cos(d*x+c)^9+8/231*sin(d*x+c)^5/cos(d*x+c)^7+16/1155*sin(d*x+c)^5/cos(d*x+c)^5))","A"
92,1,335,471,0.329000," ","int(cos(d*x+c)^5*(a*cos(d*x+c)+b*sin(d*x+c))^5,x)","\frac{b^{5} \left(-\frac{\left(\sin^{4}\left(d x +c \right)\right) \left(\cos^{6}\left(d x +c \right)\right)}{10}-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{6}\left(d x +c \right)\right)}{20}-\frac{\left(\cos^{6}\left(d x +c \right)\right)}{60}\right)+5 a \,b^{4} \left(-\frac{\left(\sin^{3}\left(d x +c \right)\right) \left(\cos^{7}\left(d x +c \right)\right)}{10}-\frac{3 \sin \left(d x +c \right) \left(\cos^{7}\left(d x +c \right)\right)}{80}+\frac{\left(\cos^{5}\left(d x +c \right)+\frac{5 \left(\cos^{3}\left(d x +c \right)\right)}{4}+\frac{15 \cos \left(d x +c \right)}{8}\right) \sin \left(d x +c \right)}{160}+\frac{3 d x}{256}+\frac{3 c}{256}\right)+10 a^{2} b^{3} \left(-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{8}\left(d x +c \right)\right)}{10}-\frac{\left(\cos^{8}\left(d x +c \right)\right)}{40}\right)+10 a^{3} b^{2} \left(-\frac{\sin \left(d x +c \right) \left(\cos^{9}\left(d x +c \right)\right)}{10}+\frac{\left(\cos^{7}\left(d x +c \right)+\frac{7 \left(\cos^{5}\left(d x +c \right)\right)}{6}+\frac{35 \left(\cos^{3}\left(d x +c \right)\right)}{24}+\frac{35 \cos \left(d x +c \right)}{16}\right) \sin \left(d x +c \right)}{80}+\frac{7 d x}{256}+\frac{7 c}{256}\right)-\frac{a^{4} b \left(\cos^{10}\left(d x +c \right)\right)}{2}+a^{5} \left(\frac{\left(\cos^{9}\left(d x +c \right)+\frac{9 \left(\cos^{7}\left(d x +c \right)\right)}{8}+\frac{21 \left(\cos^{5}\left(d x +c \right)\right)}{16}+\frac{105 \left(\cos^{3}\left(d x +c \right)\right)}{64}+\frac{315 \cos \left(d x +c \right)}{128}\right) \sin \left(d x +c \right)}{10}+\frac{63 d x}{256}+\frac{63 c}{256}\right)}{d}"," ",0,"1/d*(b^5*(-1/10*sin(d*x+c)^4*cos(d*x+c)^6-1/20*sin(d*x+c)^2*cos(d*x+c)^6-1/60*cos(d*x+c)^6)+5*a*b^4*(-1/10*sin(d*x+c)^3*cos(d*x+c)^7-3/80*sin(d*x+c)*cos(d*x+c)^7+1/160*(cos(d*x+c)^5+5/4*cos(d*x+c)^3+15/8*cos(d*x+c))*sin(d*x+c)+3/256*d*x+3/256*c)+10*a^2*b^3*(-1/10*sin(d*x+c)^2*cos(d*x+c)^8-1/40*cos(d*x+c)^8)+10*a^3*b^2*(-1/10*sin(d*x+c)*cos(d*x+c)^9+1/80*(cos(d*x+c)^7+7/6*cos(d*x+c)^5+35/24*cos(d*x+c)^3+35/16*cos(d*x+c))*sin(d*x+c)+7/256*d*x+7/256*c)-1/2*a^4*b*cos(d*x+c)^10+a^5*(1/10*(cos(d*x+c)^9+9/8*cos(d*x+c)^7+21/16*cos(d*x+c)^5+105/64*cos(d*x+c)^3+315/128*cos(d*x+c))*sin(d*x+c)+63/256*d*x+63/256*c))","A"
93,1,291,307,0.237000," ","int(cos(d*x+c)^4*(a*cos(d*x+c)+b*sin(d*x+c))^5,x)","\frac{b^{5} \left(-\frac{\left(\sin^{4}\left(d x +c \right)\right) \left(\cos^{5}\left(d x +c \right)\right)}{9}-\frac{4 \left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{5}\left(d x +c \right)\right)}{63}-\frac{8 \left(\cos^{5}\left(d x +c \right)\right)}{315}\right)+5 a \,b^{4} \left(-\frac{\left(\sin^{3}\left(d x +c \right)\right) \left(\cos^{6}\left(d x +c \right)\right)}{9}-\frac{\sin \left(d x +c \right) \left(\cos^{6}\left(d x +c \right)\right)}{21}+\frac{\left(\frac{8}{3}+\cos^{4}\left(d x +c \right)+\frac{4 \left(\cos^{2}\left(d x +c \right)\right)}{3}\right) \sin \left(d x +c \right)}{105}\right)+10 a^{2} b^{3} \left(-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{7}\left(d x +c \right)\right)}{9}-\frac{2 \left(\cos^{7}\left(d x +c \right)\right)}{63}\right)+10 a^{3} b^{2} \left(-\frac{\sin \left(d x +c \right) \left(\cos^{8}\left(d x +c \right)\right)}{9}+\frac{\left(\frac{16}{5}+\cos^{6}\left(d x +c \right)+\frac{6 \left(\cos^{4}\left(d x +c \right)\right)}{5}+\frac{8 \left(\cos^{2}\left(d x +c \right)\right)}{5}\right) \sin \left(d x +c \right)}{63}\right)-\frac{5 a^{4} b \left(\cos^{9}\left(d x +c \right)\right)}{9}+\frac{a^{5} \left(\frac{128}{35}+\cos^{8}\left(d x +c \right)+\frac{8 \left(\cos^{6}\left(d x +c \right)\right)}{7}+\frac{48 \left(\cos^{4}\left(d x +c \right)\right)}{35}+\frac{64 \left(\cos^{2}\left(d x +c \right)\right)}{35}\right) \sin \left(d x +c \right)}{9}}{d}"," ",0,"1/d*(b^5*(-1/9*sin(d*x+c)^4*cos(d*x+c)^5-4/63*sin(d*x+c)^2*cos(d*x+c)^5-8/315*cos(d*x+c)^5)+5*a*b^4*(-1/9*sin(d*x+c)^3*cos(d*x+c)^6-1/21*sin(d*x+c)*cos(d*x+c)^6+1/105*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c))+10*a^2*b^3*(-1/9*sin(d*x+c)^2*cos(d*x+c)^7-2/63*cos(d*x+c)^7)+10*a^3*b^2*(-1/9*sin(d*x+c)*cos(d*x+c)^8+1/63*(16/5+cos(d*x+c)^6+6/5*cos(d*x+c)^4+8/5*cos(d*x+c)^2)*sin(d*x+c))-5/9*a^4*b*cos(d*x+c)^9+1/9*a^5*(128/35+cos(d*x+c)^8+8/7*cos(d*x+c)^6+48/35*cos(d*x+c)^4+64/35*cos(d*x+c)^2)*sin(d*x+c))","A"
94,1,305,386,0.178000," ","int(cos(d*x+c)^3*(a*cos(d*x+c)+b*sin(d*x+c))^5,x)","\frac{b^{5} \left(-\frac{\left(\sin^{4}\left(d x +c \right)\right) \left(\cos^{4}\left(d x +c \right)\right)}{8}-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{4}\left(d x +c \right)\right)}{12}-\frac{\left(\cos^{4}\left(d x +c \right)\right)}{24}\right)+5 a \,b^{4} \left(-\frac{\left(\sin^{3}\left(d x +c \right)\right) \left(\cos^{5}\left(d x +c \right)\right)}{8}-\frac{\sin \left(d x +c \right) \left(\cos^{5}\left(d x +c \right)\right)}{16}+\frac{\left(\cos^{3}\left(d x +c \right)+\frac{3 \cos \left(d x +c \right)}{2}\right) \sin \left(d x +c \right)}{64}+\frac{3 d x}{128}+\frac{3 c}{128}\right)+10 a^{2} b^{3} \left(-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{6}\left(d x +c \right)\right)}{8}-\frac{\left(\cos^{6}\left(d x +c \right)\right)}{24}\right)+10 a^{3} b^{2} \left(-\frac{\sin \left(d x +c \right) \left(\cos^{7}\left(d x +c \right)\right)}{8}+\frac{\left(\cos^{5}\left(d x +c \right)+\frac{5 \left(\cos^{3}\left(d x +c \right)\right)}{4}+\frac{15 \cos \left(d x +c \right)}{8}\right) \sin \left(d x +c \right)}{48}+\frac{5 d x}{128}+\frac{5 c}{128}\right)-\frac{5 a^{4} b \left(\cos^{8}\left(d x +c \right)\right)}{8}+a^{5} \left(\frac{\left(\cos^{7}\left(d x +c \right)+\frac{7 \left(\cos^{5}\left(d x +c \right)\right)}{6}+\frac{35 \left(\cos^{3}\left(d x +c \right)\right)}{24}+\frac{35 \cos \left(d x +c \right)}{16}\right) \sin \left(d x +c \right)}{8}+\frac{35 d x}{128}+\frac{35 c}{128}\right)}{d}"," ",0,"1/d*(b^5*(-1/8*sin(d*x+c)^4*cos(d*x+c)^4-1/12*sin(d*x+c)^2*cos(d*x+c)^4-1/24*cos(d*x+c)^4)+5*a*b^4*(-1/8*sin(d*x+c)^3*cos(d*x+c)^5-1/16*sin(d*x+c)*cos(d*x+c)^5+1/64*(cos(d*x+c)^3+3/2*cos(d*x+c))*sin(d*x+c)+3/128*d*x+3/128*c)+10*a^2*b^3*(-1/8*sin(d*x+c)^2*cos(d*x+c)^6-1/24*cos(d*x+c)^6)+10*a^3*b^2*(-1/8*sin(d*x+c)*cos(d*x+c)^7+1/48*(cos(d*x+c)^5+5/4*cos(d*x+c)^3+15/8*cos(d*x+c))*sin(d*x+c)+5/128*d*x+5/128*c)-5/8*a^4*b*cos(d*x+c)^8+a^5*(1/8*(cos(d*x+c)^7+7/6*cos(d*x+c)^5+35/24*cos(d*x+c)^3+35/16*cos(d*x+c))*sin(d*x+c)+35/128*d*x+35/128*c))","A"
95,1,261,255,0.159000," ","int(cos(d*x+c)^2*(a*cos(d*x+c)+b*sin(d*x+c))^5,x)","\frac{b^{5} \left(-\frac{\left(\sin^{4}\left(d x +c \right)\right) \left(\cos^{3}\left(d x +c \right)\right)}{7}-\frac{4 \left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{3}\left(d x +c \right)\right)}{35}-\frac{8 \left(\cos^{3}\left(d x +c \right)\right)}{105}\right)+5 a \,b^{4} \left(-\frac{\left(\sin^{3}\left(d x +c \right)\right) \left(\cos^{4}\left(d x +c \right)\right)}{7}-\frac{3 \sin \left(d x +c \right) \left(\cos^{4}\left(d x +c \right)\right)}{35}+\frac{\left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{35}\right)+10 a^{2} b^{3} \left(-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{5}\left(d x +c \right)\right)}{7}-\frac{2 \left(\cos^{5}\left(d x +c \right)\right)}{35}\right)+10 a^{3} b^{2} \left(-\frac{\sin \left(d x +c \right) \left(\cos^{6}\left(d x +c \right)\right)}{7}+\frac{\left(\frac{8}{3}+\cos^{4}\left(d x +c \right)+\frac{4 \left(\cos^{2}\left(d x +c \right)\right)}{3}\right) \sin \left(d x +c \right)}{35}\right)-\frac{5 a^{4} b \left(\cos^{7}\left(d x +c \right)\right)}{7}+\frac{a^{5} \left(\frac{16}{5}+\cos^{6}\left(d x +c \right)+\frac{6 \left(\cos^{4}\left(d x +c \right)\right)}{5}+\frac{8 \left(\cos^{2}\left(d x +c \right)\right)}{5}\right) \sin \left(d x +c \right)}{7}}{d}"," ",0,"1/d*(b^5*(-1/7*sin(d*x+c)^4*cos(d*x+c)^3-4/35*sin(d*x+c)^2*cos(d*x+c)^3-8/105*cos(d*x+c)^3)+5*a*b^4*(-1/7*sin(d*x+c)^3*cos(d*x+c)^4-3/35*sin(d*x+c)*cos(d*x+c)^4+1/35*(2+cos(d*x+c)^2)*sin(d*x+c))+10*a^2*b^3*(-1/7*sin(d*x+c)^2*cos(d*x+c)^5-2/35*cos(d*x+c)^5)+10*a^3*b^2*(-1/7*sin(d*x+c)*cos(d*x+c)^6+1/35*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c))-5/7*a^4*b*cos(d*x+c)^7+1/7*a^5*(16/5+cos(d*x+c)^6+6/5*cos(d*x+c)^4+8/5*cos(d*x+c)^2)*sin(d*x+c))","A"
96,1,236,118,0.115000," ","int(cos(d*x+c)*(a*cos(d*x+c)+b*sin(d*x+c))^5,x)","\frac{\frac{b^{5} \left(\sin^{6}\left(d x +c \right)\right)}{6}+5 a \,b^{4} \left(-\frac{\left(\sin^{3}\left(d x +c \right)\right) \left(\cos^{3}\left(d x +c \right)\right)}{6}-\frac{\sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right)}{8}+\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)}{16}+\frac{d x}{16}+\frac{c}{16}\right)+10 a^{2} b^{3} \left(-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{4}\left(d x +c \right)\right)}{6}-\frac{\left(\cos^{4}\left(d x +c \right)\right)}{12}\right)+10 a^{3} b^{2} \left(-\frac{\sin \left(d x +c \right) \left(\cos^{5}\left(d x +c \right)\right)}{6}+\frac{\left(\cos^{3}\left(d x +c \right)+\frac{3 \cos \left(d x +c \right)}{2}\right) \sin \left(d x +c \right)}{24}+\frac{d x}{16}+\frac{c}{16}\right)-\frac{5 a^{4} b \left(\cos^{6}\left(d x +c \right)\right)}{6}+a^{5} \left(\frac{\left(\cos^{5}\left(d x +c \right)+\frac{5 \left(\cos^{3}\left(d x +c \right)\right)}{4}+\frac{15 \cos \left(d x +c \right)}{8}\right) \sin \left(d x +c \right)}{6}+\frac{5 d x}{16}+\frac{5 c}{16}\right)}{d}"," ",0,"1/d*(1/6*b^5*sin(d*x+c)^6+5*a*b^4*(-1/6*sin(d*x+c)^3*cos(d*x+c)^3-1/8*sin(d*x+c)*cos(d*x+c)^3+1/16*cos(d*x+c)*sin(d*x+c)+1/16*d*x+1/16*c)+10*a^2*b^3*(-1/6*sin(d*x+c)^2*cos(d*x+c)^4-1/12*cos(d*x+c)^4)+10*a^3*b^2*(-1/6*sin(d*x+c)*cos(d*x+c)^5+1/24*(cos(d*x+c)^3+3/2*cos(d*x+c))*sin(d*x+c)+1/16*d*x+1/16*c)-5/6*a^4*b*cos(d*x+c)^6+a^5*(1/6*(cos(d*x+c)^5+5/4*cos(d*x+c)^3+15/8*cos(d*x+c))*sin(d*x+c)+5/16*d*x+5/16*c))","A"
97,1,175,90,0.150000," ","int((a*cos(d*x+c)+b*sin(d*x+c))^5,x)","\frac{-\frac{b^{5} \left(\frac{8}{3}+\sin^{4}\left(d x +c \right)+\frac{4 \left(\sin^{2}\left(d x +c \right)\right)}{3}\right) \cos \left(d x +c \right)}{5}+a \,b^{4} \left(\sin^{5}\left(d x +c \right)\right)+10 a^{2} b^{3} \left(-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{3}\left(d x +c \right)\right)}{5}-\frac{2 \left(\cos^{3}\left(d x +c \right)\right)}{15}\right)+10 a^{3} b^{2} \left(-\frac{\sin \left(d x +c \right) \left(\cos^{4}\left(d x +c \right)\right)}{5}+\frac{\left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{15}\right)-a^{4} b \left(\cos^{5}\left(d x +c \right)\right)+\frac{a^{5} \left(\frac{8}{3}+\cos^{4}\left(d x +c \right)+\frac{4 \left(\cos^{2}\left(d x +c \right)\right)}{3}\right) \sin \left(d x +c \right)}{5}}{d}"," ",0,"1/d*(-1/5*b^5*(8/3+sin(d*x+c)^4+4/3*sin(d*x+c)^2)*cos(d*x+c)+a*b^4*sin(d*x+c)^5+10*a^2*b^3*(-1/5*sin(d*x+c)^2*cos(d*x+c)^3-2/15*cos(d*x+c)^3)+10*a^3*b^2*(-1/5*sin(d*x+c)*cos(d*x+c)^4+1/15*(2+cos(d*x+c)^2)*sin(d*x+c))-a^4*b*cos(d*x+c)^5+1/5*a^5*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c))","A"
98,1,272,164,0.237000," ","int(sec(d*x+c)*(a*cos(d*x+c)+b*sin(d*x+c))^5,x)","\frac{a^{5} \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)}{4 d}+\frac{3 a^{5} \cos \left(d x +c \right) \sin \left(d x +c \right)}{8 d}+\frac{3 a^{5} x}{8}+\frac{3 a^{5} c}{8 d}-\frac{5 a^{4} \left(\cos^{4}\left(d x +c \right)\right) b}{4 d}-\frac{5 a^{3} b^{2} \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)}{2 d}+\frac{5 a^{3} b^{2} \cos \left(d x +c \right) \sin \left(d x +c \right)}{4 d}+\frac{5 a^{3} b^{2} x}{4}+\frac{5 a^{3} b^{2} c}{4 d}+\frac{5 a^{2} b^{3} \left(\sin^{4}\left(d x +c \right)\right)}{2 d}-\frac{5 a \,b^{4} \cos \left(d x +c \right) \left(\sin^{3}\left(d x +c \right)\right)}{4 d}-\frac{15 a \,b^{4} \cos \left(d x +c \right) \sin \left(d x +c \right)}{8 d}+\frac{15 a \,b^{4} x}{8}+\frac{15 a \,b^{4} c}{8 d}-\frac{b^{5} \left(\sin^{4}\left(d x +c \right)\right)}{4 d}-\frac{\left(\sin^{2}\left(d x +c \right)\right) b^{5}}{2 d}-\frac{b^{5} \ln \left(\cos \left(d x +c \right)\right)}{d}"," ",0,"1/4*a^5*cos(d*x+c)^3*sin(d*x+c)/d+3/8*a^5*cos(d*x+c)*sin(d*x+c)/d+3/8*a^5*x+3/8/d*a^5*c-5/4/d*a^4*cos(d*x+c)^4*b-5/2*a^3*b^2*cos(d*x+c)^3*sin(d*x+c)/d+5/4*a^3*b^2*cos(d*x+c)*sin(d*x+c)/d+5/4*a^3*b^2*x+5/4/d*a^3*b^2*c+5/2/d*a^2*b^3*sin(d*x+c)^4-5/4/d*a*b^4*cos(d*x+c)*sin(d*x+c)^3-15/8*a*b^4*cos(d*x+c)*sin(d*x+c)/d+15/8*a*b^4*x+15/8/d*a*b^4*c-1/4/d*b^5*sin(d*x+c)^4-1/2/d*sin(d*x+c)^2*b^5-1/d*b^5*ln(cos(d*x+c))","A"
99,1,251,193,0.239000," ","int(sec(d*x+c)^2*(a*cos(d*x+c)+b*sin(d*x+c))^5,x)","\frac{\left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) a^{5}}{3 d}+\frac{2 a^{5} \sin \left(d x +c \right)}{3 d}-\frac{5 a^{4} b \left(\cos^{3}\left(d x +c \right)\right)}{3 d}+\frac{10 a^{3} b^{2} \left(\sin^{3}\left(d x +c \right)\right)}{3 d}-\frac{10 \cos \left(d x +c \right) \left(\sin^{2}\left(d x +c \right)\right) a^{2} b^{3}}{3 d}-\frac{20 a^{2} b^{3} \cos \left(d x +c \right)}{3 d}-\frac{5 a \,b^{4} \left(\sin^{3}\left(d x +c \right)\right)}{3 d}-\frac{5 a \,b^{4} \sin \left(d x +c \right)}{d}+\frac{5 a \,b^{4} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{b^{5} \left(\sin^{6}\left(d x +c \right)\right)}{d \cos \left(d x +c \right)}+\frac{8 b^{5} \cos \left(d x +c \right)}{3 d}+\frac{b^{5} \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) b^{5}}{3 d}"," ",0,"1/3/d*cos(d*x+c)^2*sin(d*x+c)*a^5+2/3*a^5*sin(d*x+c)/d-5/3*a^4*b*cos(d*x+c)^3/d+10/3*a^3*b^2*sin(d*x+c)^3/d-10/3/d*cos(d*x+c)*sin(d*x+c)^2*a^2*b^3-20/3*a^2*b^3*cos(d*x+c)/d-5/3*a*b^4*sin(d*x+c)^3/d-5*a*b^4*sin(d*x+c)/d+5/d*a*b^4*ln(sec(d*x+c)+tan(d*x+c))+1/d*b^5*sin(d*x+c)^6/cos(d*x+c)+8/3*b^5*cos(d*x+c)/d+1/d*b^5*cos(d*x+c)*sin(d*x+c)^4+4/3/d*cos(d*x+c)*sin(d*x+c)^2*b^5","A"
100,1,291,163,0.241000," ","int(sec(d*x+c)^3*(a*cos(d*x+c)+b*sin(d*x+c))^5,x)","\frac{a^{5} \cos \left(d x +c \right) \sin \left(d x +c \right)}{2 d}+\frac{a^{5} x}{2}+\frac{a^{5} c}{2 d}-\frac{5 a^{4} b \left(\cos^{2}\left(d x +c \right)\right)}{2 d}-\frac{5 a^{3} b^{2} \cos \left(d x +c \right) \sin \left(d x +c \right)}{d}+5 a^{3} b^{2} x +\frac{5 a^{3} b^{2} c}{d}-\frac{5 a^{2} b^{3} \left(\sin^{2}\left(d x +c \right)\right)}{d}-\frac{10 a^{2} b^{3} \ln \left(\cos \left(d x +c \right)\right)}{d}+\frac{5 a \,b^{4} \left(\sin^{5}\left(d x +c \right)\right)}{d \cos \left(d x +c \right)}+\frac{5 a \,b^{4} \cos \left(d x +c \right) \left(\sin^{3}\left(d x +c \right)\right)}{d}+\frac{15 a \,b^{4} \cos \left(d x +c \right) \sin \left(d x +c \right)}{2 d}-\frac{15 a \,b^{4} x}{2}-\frac{15 a \,b^{4} c}{2 d}+\frac{b^{5} \left(\sin^{6}\left(d x +c \right)\right)}{2 d \cos \left(d x +c \right)^{2}}+\frac{b^{5} \left(\sin^{4}\left(d x +c \right)\right)}{2 d}+\frac{\left(\sin^{2}\left(d x +c \right)\right) b^{5}}{d}+\frac{2 b^{5} \ln \left(\cos \left(d x +c \right)\right)}{d}"," ",0,"1/2*a^5*cos(d*x+c)*sin(d*x+c)/d+1/2*a^5*x+1/2/d*a^5*c-5/2/d*a^4*b*cos(d*x+c)^2-5*a^3*b^2*cos(d*x+c)*sin(d*x+c)/d+5*a^3*b^2*x+5/d*a^3*b^2*c-5/d*a^2*b^3*sin(d*x+c)^2-10/d*a^2*b^3*ln(cos(d*x+c))+5/d*a*b^4*sin(d*x+c)^5/cos(d*x+c)+5/d*a*b^4*cos(d*x+c)*sin(d*x+c)^3+15/2*a*b^4*cos(d*x+c)*sin(d*x+c)/d-15/2*a*b^4*x-15/2/d*a*b^4*c+1/2/d*b^5*sin(d*x+c)^6/cos(d*x+c)^2+1/2/d*b^5*sin(d*x+c)^4+1/d*sin(d*x+c)^2*b^5+2/d*b^5*ln(cos(d*x+c))","A"
101,1,327,196,0.233000," ","int(sec(d*x+c)^4*(a*cos(d*x+c)+b*sin(d*x+c))^5,x)","\frac{a^{5} \sin \left(d x +c \right)}{d}-\frac{5 a^{4} b \cos \left(d x +c \right)}{d}-\frac{10 a^{3} b^{2} \sin \left(d x +c \right)}{d}+\frac{10 a^{3} b^{2} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{10 a^{2} b^{3} \left(\sin^{4}\left(d x +c \right)\right)}{d \cos \left(d x +c \right)}+\frac{10 \cos \left(d x +c \right) \left(\sin^{2}\left(d x +c \right)\right) a^{2} b^{3}}{d}+\frac{20 a^{2} b^{3} \cos \left(d x +c \right)}{d}+\frac{5 a \,b^{4} \left(\sin^{5}\left(d x +c \right)\right)}{2 d \cos \left(d x +c \right)^{2}}+\frac{5 a \,b^{4} \left(\sin^{3}\left(d x +c \right)\right)}{2 d}+\frac{15 a \,b^{4} \sin \left(d x +c \right)}{2 d}-\frac{15 a \,b^{4} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{2 d}+\frac{b^{5} \left(\sin^{6}\left(d x +c \right)\right)}{3 d \cos \left(d x +c \right)^{3}}-\frac{b^{5} \left(\sin^{6}\left(d x +c \right)\right)}{d \cos \left(d x +c \right)}-\frac{8 b^{5} \cos \left(d x +c \right)}{3 d}-\frac{b^{5} \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) b^{5}}{3 d}"," ",0,"a^5*sin(d*x+c)/d-5*a^4*b*cos(d*x+c)/d-10*a^3*b^2*sin(d*x+c)/d+10/d*a^3*b^2*ln(sec(d*x+c)+tan(d*x+c))+10/d*a^2*b^3*sin(d*x+c)^4/cos(d*x+c)+10/d*cos(d*x+c)*sin(d*x+c)^2*a^2*b^3+20*a^2*b^3*cos(d*x+c)/d+5/2/d*a*b^4*sin(d*x+c)^5/cos(d*x+c)^2+5/2*a*b^4*sin(d*x+c)^3/d+15/2*a*b^4*sin(d*x+c)/d-15/2/d*a*b^4*ln(sec(d*x+c)+tan(d*x+c))+1/3/d*b^5*sin(d*x+c)^6/cos(d*x+c)^3-1/d*b^5*sin(d*x+c)^6/cos(d*x+c)-8/3*b^5*cos(d*x+c)/d-1/d*b^5*cos(d*x+c)*sin(d*x+c)^4-4/3/d*cos(d*x+c)*sin(d*x+c)^2*b^5","A"
102,1,202,141,0.234000," ","int(sec(d*x+c)^5*(a*cos(d*x+c)+b*sin(d*x+c))^5,x)","a^{5} x +\frac{a^{5} c}{d}-\frac{5 a^{4} b \ln \left(\cos \left(d x +c \right)\right)}{d}-10 a^{3} b^{2} x +\frac{10 \tan \left(d x +c \right) a^{3} b^{2}}{d}-\frac{10 a^{3} b^{2} c}{d}+\frac{5 a^{2} b^{3} \left(\tan^{2}\left(d x +c \right)\right)}{d}+\frac{10 a^{2} b^{3} \ln \left(\cos \left(d x +c \right)\right)}{d}+\frac{5 a \,b^{4} \left(\tan^{3}\left(d x +c \right)\right)}{3 d}-\frac{5 a \,b^{4} \tan \left(d x +c \right)}{d}+5 a \,b^{4} x +\frac{5 a \,b^{4} c}{d}+\frac{b^{5} \left(\tan^{4}\left(d x +c \right)\right)}{4 d}-\frac{b^{5} \left(\tan^{2}\left(d x +c \right)\right)}{2 d}-\frac{b^{5} \ln \left(\cos \left(d x +c \right)\right)}{d}"," ",0,"a^5*x+1/d*a^5*c-5/d*a^4*b*ln(cos(d*x+c))-10*a^3*b^2*x+10/d*tan(d*x+c)*a^3*b^2-10/d*a^3*b^2*c+5/d*a^2*b^3*tan(d*x+c)^2+10/d*a^2*b^3*ln(cos(d*x+c))+5/3/d*a*b^4*tan(d*x+c)^3-5*a*b^4*tan(d*x+c)/d+5*a*b^4*x+5/d*a*b^4*c+1/4/d*b^5*tan(d*x+c)^4-1/2*b^5*tan(d*x+c)^2/d-1/d*b^5*ln(cos(d*x+c))","A"
103,1,440,212,0.227000," ","int(sec(d*x+c)^6*(a*cos(d*x+c)+b*sin(d*x+c))^5,x)","\frac{a^{5} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{5 a^{4} b}{d \cos \left(d x +c \right)}+\frac{5 a^{3} b^{2} \left(\sin^{3}\left(d x +c \right)\right)}{d \cos \left(d x +c \right)^{2}}+\frac{5 a^{3} b^{2} \sin \left(d x +c \right)}{d}-\frac{5 a^{3} b^{2} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{10 a^{2} b^{3} \left(\sin^{4}\left(d x +c \right)\right)}{3 d \cos \left(d x +c \right)^{3}}-\frac{10 a^{2} b^{3} \left(\sin^{4}\left(d x +c \right)\right)}{3 d \cos \left(d x +c \right)}-\frac{10 \cos \left(d x +c \right) \left(\sin^{2}\left(d x +c \right)\right) a^{2} b^{3}}{3 d}-\frac{20 a^{2} b^{3} \cos \left(d x +c \right)}{3 d}+\frac{5 a \,b^{4} \left(\sin^{5}\left(d x +c \right)\right)}{4 d \cos \left(d x +c \right)^{4}}-\frac{5 a \,b^{4} \left(\sin^{5}\left(d x +c \right)\right)}{8 d \cos \left(d x +c \right)^{2}}-\frac{5 a \,b^{4} \left(\sin^{3}\left(d x +c \right)\right)}{8 d}-\frac{15 a \,b^{4} \sin \left(d x +c \right)}{8 d}+\frac{15 a \,b^{4} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{8 d}+\frac{b^{5} \left(\sin^{6}\left(d x +c \right)\right)}{5 d \cos \left(d x +c \right)^{5}}-\frac{b^{5} \left(\sin^{6}\left(d x +c \right)\right)}{15 d \cos \left(d x +c \right)^{3}}+\frac{b^{5} \left(\sin^{6}\left(d x +c \right)\right)}{5 d \cos \left(d x +c \right)}+\frac{8 b^{5} \cos \left(d x +c \right)}{15 d}+\frac{b^{5} \cos \left(d x +c \right) \left(\sin^{4}\left(d x +c \right)\right)}{5 d}+\frac{4 \cos \left(d x +c \right) \left(\sin^{2}\left(d x +c \right)\right) b^{5}}{15 d}"," ",0,"1/d*a^5*ln(sec(d*x+c)+tan(d*x+c))+5/d*a^4*b/cos(d*x+c)+5/d*a^3*b^2*sin(d*x+c)^3/cos(d*x+c)^2+5*a^3*b^2*sin(d*x+c)/d-5/d*a^3*b^2*ln(sec(d*x+c)+tan(d*x+c))+10/3/d*a^2*b^3*sin(d*x+c)^4/cos(d*x+c)^3-10/3/d*a^2*b^3*sin(d*x+c)^4/cos(d*x+c)-10/3/d*cos(d*x+c)*sin(d*x+c)^2*a^2*b^3-20/3*a^2*b^3*cos(d*x+c)/d+5/4/d*a*b^4*sin(d*x+c)^5/cos(d*x+c)^4-5/8/d*a*b^4*sin(d*x+c)^5/cos(d*x+c)^2-5/8*a*b^4*sin(d*x+c)^3/d-15/8*a*b^4*sin(d*x+c)/d+15/8/d*a*b^4*ln(sec(d*x+c)+tan(d*x+c))+1/5/d*b^5*sin(d*x+c)^6/cos(d*x+c)^5-1/15/d*b^5*sin(d*x+c)^6/cos(d*x+c)^3+1/5/d*b^5*sin(d*x+c)^6/cos(d*x+c)+8/15*b^5*cos(d*x+c)/d+1/5/d*b^5*cos(d*x+c)*sin(d*x+c)^4+4/15/d*cos(d*x+c)*sin(d*x+c)^2*b^5","B"
104,1,120,28,0.282000," ","int(sec(d*x+c)^7*(a*cos(d*x+c)+b*sin(d*x+c))^5,x)","\frac{a^{5} \tan \left(d x +c \right)+\frac{5 a^{4} b}{2 \cos \left(d x +c \right)^{2}}+\frac{10 a^{3} b^{2} \left(\sin^{3}\left(d x +c \right)\right)}{3 \cos \left(d x +c \right)^{3}}+\frac{5 a^{2} b^{3} \left(\sin^{4}\left(d x +c \right)\right)}{2 \cos \left(d x +c \right)^{4}}+\frac{a \,b^{4} \left(\sin^{5}\left(d x +c \right)\right)}{\cos \left(d x +c \right)^{5}}+\frac{b^{5} \left(\sin^{6}\left(d x +c \right)\right)}{6 \cos \left(d x +c \right)^{6}}}{d}"," ",0,"1/d*(a^5*tan(d*x+c)+5/2*a^4*b/cos(d*x+c)^2+10/3*a^3*b^2*sin(d*x+c)^3/cos(d*x+c)^3+5/2*a^2*b^3*sin(d*x+c)^4/cos(d*x+c)^4+a*b^4*sin(d*x+c)^5/cos(d*x+c)^5+1/6*b^5*sin(d*x+c)^6/cos(d*x+c)^6)","B"
105,1,564,290,0.285000," ","int(sec(d*x+c)^8*(a*cos(d*x+c)+b*sin(d*x+c))^5,x)","\frac{8 b^{5} \cos \left(d x +c \right)}{105 d}-\frac{5 a \,b^{4} \sin \left(d x +c \right)}{16 d}+\frac{5 a^{3} b^{2} \sin \left(d x +c \right)}{4 d}+\frac{a^{5} \sec \left(d x +c \right) \tan \left(d x +c \right)}{2 d}-\frac{4 a^{2} b^{3} \cos \left(d x +c \right)}{3 d}-\frac{2 \cos \left(d x +c \right) \left(\sin^{2}\left(d x +c \right)\right) a^{2} b^{3}}{3 d}-\frac{b^{5} \left(\sin^{6}\left(d x +c \right)\right)}{105 d \cos \left(d x +c \right)^{3}}-\frac{5 a^{3} b^{2} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{4 d}+\frac{5 a^{3} b^{2} \left(\sin^{3}\left(d x +c \right)\right)}{4 d \cos \left(d x +c \right)^{2}}+\frac{2 a^{2} b^{3} \left(\sin^{4}\left(d x +c \right)\right)}{3 d \cos \left(d x +c \right)^{3}}+\frac{5 a \,b^{4} \left(\sin^{5}\left(d x +c \right)\right)}{24 d \cos \left(d x +c \right)^{4}}+\frac{a^{5} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{2 d}+\frac{5 a \,b^{4} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{16 d}-\frac{5 a \,b^{4} \left(\sin^{3}\left(d x +c \right)\right)}{48 d}+\frac{b^{5} \left(\sin^{6}\left(d x +c \right)\right)}{35 d \cos \left(d x +c \right)}+\frac{b^{5} \cos \left(d x +c \right) \left(\sin^{4}\left(d x +c \right)\right)}{35 d}+\frac{4 \cos \left(d x +c \right) \left(\sin^{2}\left(d x +c \right)\right) b^{5}}{105 d}+\frac{b^{5} \left(\sin^{6}\left(d x +c \right)\right)}{35 d \cos \left(d x +c \right)^{5}}+\frac{5 a^{4} b}{3 d \cos \left(d x +c \right)^{3}}+\frac{b^{5} \left(\sin^{6}\left(d x +c \right)\right)}{7 d \cos \left(d x +c \right)^{7}}-\frac{5 a \,b^{4} \left(\sin^{5}\left(d x +c \right)\right)}{48 d \cos \left(d x +c \right)^{2}}+\frac{5 a^{3} b^{2} \left(\sin^{3}\left(d x +c \right)\right)}{2 d \cos \left(d x +c \right)^{4}}+\frac{2 a^{2} b^{3} \left(\sin^{4}\left(d x +c \right)\right)}{d \cos \left(d x +c \right)^{5}}+\frac{5 a \,b^{4} \left(\sin^{5}\left(d x +c \right)\right)}{6 d \cos \left(d x +c \right)^{6}}-\frac{2 a^{2} b^{3} \left(\sin^{4}\left(d x +c \right)\right)}{3 d \cos \left(d x +c \right)}"," ",0,"8/105*b^5*cos(d*x+c)/d-5/16*a*b^4*sin(d*x+c)/d-5/48*a*b^4*sin(d*x+c)^3/d+5/4*a^3*b^2*sin(d*x+c)/d+1/2*a^5*sec(d*x+c)*tan(d*x+c)/d-4/3*a^2*b^3*cos(d*x+c)/d+1/35/d*b^5*sin(d*x+c)^6/cos(d*x+c)^5-5/4/d*a^3*b^2*ln(sec(d*x+c)+tan(d*x+c))-1/105/d*b^5*sin(d*x+c)^6/cos(d*x+c)^3+5/4/d*a^3*b^2*sin(d*x+c)^3/cos(d*x+c)^2+2/3/d*a^2*b^3*sin(d*x+c)^4/cos(d*x+c)^3+5/24/d*a*b^4*sin(d*x+c)^5/cos(d*x+c)^4-2/3/d*cos(d*x+c)*sin(d*x+c)^2*a^2*b^3+5/2/d*a^3*b^2*sin(d*x+c)^3/cos(d*x+c)^4+2/d*a^2*b^3*sin(d*x+c)^4/cos(d*x+c)^5+5/6/d*a*b^4*sin(d*x+c)^5/cos(d*x+c)^6+1/2/d*a^5*ln(sec(d*x+c)+tan(d*x+c))+5/16/d*a*b^4*ln(sec(d*x+c)+tan(d*x+c))+1/35/d*b^5*sin(d*x+c)^6/cos(d*x+c)+1/35/d*b^5*cos(d*x+c)*sin(d*x+c)^4+4/105/d*cos(d*x+c)*sin(d*x+c)^2*b^5-2/3/d*a^2*b^3*sin(d*x+c)^4/cos(d*x+c)-5/48/d*a*b^4*sin(d*x+c)^5/cos(d*x+c)^2+5/3/d*a^4*b/cos(d*x+c)^3+1/7/d*b^5*sin(d*x+c)^6/cos(d*x+c)^7","A"
106,1,217,165,0.279000," ","int(sec(d*x+c)^9*(a*cos(d*x+c)+b*sin(d*x+c))^5,x)","\frac{-a^{5} \left(-\frac{2}{3}-\frac{\left(\sec^{2}\left(d x +c \right)\right)}{3}\right) \tan \left(d x +c \right)+\frac{5 a^{4} b}{4 \cos \left(d x +c \right)^{4}}+10 a^{3} b^{2} \left(\frac{\sin^{3}\left(d x +c \right)}{5 \cos \left(d x +c \right)^{5}}+\frac{2 \left(\sin^{3}\left(d x +c \right)\right)}{15 \cos \left(d x +c \right)^{3}}\right)+10 a^{2} b^{3} \left(\frac{\sin^{4}\left(d x +c \right)}{6 \cos \left(d x +c \right)^{6}}+\frac{\sin^{4}\left(d x +c \right)}{12 \cos \left(d x +c \right)^{4}}\right)+5 a \,b^{4} \left(\frac{\sin^{5}\left(d x +c \right)}{7 \cos \left(d x +c \right)^{7}}+\frac{2 \left(\sin^{5}\left(d x +c \right)\right)}{35 \cos \left(d x +c \right)^{5}}\right)+b^{5} \left(\frac{\sin^{6}\left(d x +c \right)}{8 \cos \left(d x +c \right)^{8}}+\frac{\sin^{6}\left(d x +c \right)}{24 \cos \left(d x +c \right)^{6}}\right)}{d}"," ",0,"1/d*(-a^5*(-2/3-1/3*sec(d*x+c)^2)*tan(d*x+c)+5/4*a^4*b/cos(d*x+c)^4+10*a^3*b^2*(1/5*sin(d*x+c)^3/cos(d*x+c)^5+2/15*sin(d*x+c)^3/cos(d*x+c)^3)+10*a^2*b^3*(1/6*sin(d*x+c)^4/cos(d*x+c)^6+1/12*sin(d*x+c)^4/cos(d*x+c)^4)+5*a*b^4*(1/7*sin(d*x+c)^5/cos(d*x+c)^7+2/35*sin(d*x+c)^5/cos(d*x+c)^5)+b^5*(1/8*sin(d*x+c)^6/cos(d*x+c)^8+1/24*sin(d*x+c)^6/cos(d*x+c)^6))","A"
107,1,688,359,0.280000," ","int(sec(d*x+c)^10*(a*cos(d*x+c)+b*sin(d*x+c))^5,x)","\frac{8 b^{5} \cos \left(d x +c \right)}{315 d}-\frac{15 a \,b^{4} \sin \left(d x +c \right)}{128 d}+\frac{5 a^{3} b^{2} \sin \left(d x +c \right)}{8 d}+\frac{3 a^{5} \sec \left(d x +c \right) \tan \left(d x +c \right)}{8 d}-\frac{4 a^{2} b^{3} \cos \left(d x +c \right)}{7 d}-\frac{2 \cos \left(d x +c \right) \left(\sin^{2}\left(d x +c \right)\right) a^{2} b^{3}}{7 d}+\frac{a^{4} b}{d \cos \left(d x +c \right)^{5}}+\frac{a^{5} \left(\sec^{3}\left(d x +c \right)\right) \tan \left(d x +c \right)}{4 d}+\frac{b^{5} \left(\sin^{6}\left(d x +c \right)\right)}{9 d \cos \left(d x +c \right)^{9}}-\frac{b^{5} \left(\sin^{6}\left(d x +c \right)\right)}{315 d \cos \left(d x +c \right)^{3}}-\frac{5 a^{3} b^{2} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{8 d}+\frac{5 a^{3} b^{2} \left(\sin^{3}\left(d x +c \right)\right)}{3 d \cos \left(d x +c \right)^{6}}+\frac{10 a^{2} b^{3} \left(\sin^{4}\left(d x +c \right)\right)}{7 d \cos \left(d x +c \right)^{7}}+\frac{5 a \,b^{4} \left(\sin^{5}\left(d x +c \right)\right)}{8 d \cos \left(d x +c \right)^{8}}+\frac{5 a^{3} b^{2} \left(\sin^{3}\left(d x +c \right)\right)}{8 d \cos \left(d x +c \right)^{2}}+\frac{2 a^{2} b^{3} \left(\sin^{4}\left(d x +c \right)\right)}{7 d \cos \left(d x +c \right)^{3}}+\frac{5 a \,b^{4} \left(\sin^{5}\left(d x +c \right)\right)}{64 d \cos \left(d x +c \right)^{4}}+\frac{3 a^{5} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{8 d}+\frac{15 a \,b^{4} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{128 d}-\frac{5 a \,b^{4} \left(\sin^{3}\left(d x +c \right)\right)}{128 d}+\frac{b^{5} \left(\sin^{6}\left(d x +c \right)\right)}{105 d \cos \left(d x +c \right)}+\frac{b^{5} \cos \left(d x +c \right) \left(\sin^{4}\left(d x +c \right)\right)}{105 d}+\frac{4 \cos \left(d x +c \right) \left(\sin^{2}\left(d x +c \right)\right) b^{5}}{315 d}+\frac{b^{5} \left(\sin^{6}\left(d x +c \right)\right)}{105 d \cos \left(d x +c \right)^{5}}+\frac{b^{5} \left(\sin^{6}\left(d x +c \right)\right)}{21 d \cos \left(d x +c \right)^{7}}-\frac{5 a \,b^{4} \left(\sin^{5}\left(d x +c \right)\right)}{128 d \cos \left(d x +c \right)^{2}}+\frac{5 a^{3} b^{2} \left(\sin^{3}\left(d x +c \right)\right)}{4 d \cos \left(d x +c \right)^{4}}+\frac{6 a^{2} b^{3} \left(\sin^{4}\left(d x +c \right)\right)}{7 d \cos \left(d x +c \right)^{5}}+\frac{5 a \,b^{4} \left(\sin^{5}\left(d x +c \right)\right)}{16 d \cos \left(d x +c \right)^{6}}-\frac{2 a^{2} b^{3} \left(\sin^{4}\left(d x +c \right)\right)}{7 d \cos \left(d x +c \right)}"," ",0,"8/315*b^5*cos(d*x+c)/d-15/128*a*b^4*sin(d*x+c)/d-5/128*a*b^4*sin(d*x+c)^3/d+5/8*a^3*b^2*sin(d*x+c)/d+3/8*a^5*sec(d*x+c)*tan(d*x+c)/d+1/4*a^5*sec(d*x+c)^3*tan(d*x+c)/d-4/7*a^2*b^3*cos(d*x+c)/d+1/d*a^4*b/cos(d*x+c)^5+1/9/d*b^5*sin(d*x+c)^6/cos(d*x+c)^9+1/105/d*b^5*sin(d*x+c)^6/cos(d*x+c)^5-5/8/d*a^3*b^2*ln(sec(d*x+c)+tan(d*x+c))-1/315/d*b^5*sin(d*x+c)^6/cos(d*x+c)^3+5/8/d*a^3*b^2*sin(d*x+c)^3/cos(d*x+c)^2+2/7/d*a^2*b^3*sin(d*x+c)^4/cos(d*x+c)^3+5/64/d*a*b^4*sin(d*x+c)^5/cos(d*x+c)^4-2/7/d*cos(d*x+c)*sin(d*x+c)^2*a^2*b^3+5/4/d*a^3*b^2*sin(d*x+c)^3/cos(d*x+c)^4+6/7/d*a^2*b^3*sin(d*x+c)^4/cos(d*x+c)^5+5/16/d*a*b^4*sin(d*x+c)^5/cos(d*x+c)^6+3/8/d*a^5*ln(sec(d*x+c)+tan(d*x+c))+15/128/d*a*b^4*ln(sec(d*x+c)+tan(d*x+c))+1/105/d*b^5*sin(d*x+c)^6/cos(d*x+c)+1/105/d*b^5*cos(d*x+c)*sin(d*x+c)^4+4/315/d*cos(d*x+c)*sin(d*x+c)^2*b^5-2/7/d*a^2*b^3*sin(d*x+c)^4/cos(d*x+c)-5/128/d*a*b^4*sin(d*x+c)^5/cos(d*x+c)^2+1/21/d*b^5*sin(d*x+c)^6/cos(d*x+c)^7+5/3/d*a^3*b^2*sin(d*x+c)^3/cos(d*x+c)^6+10/7/d*a^2*b^3*sin(d*x+c)^4/cos(d*x+c)^7+5/8/d*a*b^4*sin(d*x+c)^5/cos(d*x+c)^8","A"
108,1,299,224,0.271000," ","int(sec(d*x+c)^11*(a*cos(d*x+c)+b*sin(d*x+c))^5,x)","\frac{-a^{5} \left(-\frac{8}{15}-\frac{\left(\sec^{4}\left(d x +c \right)\right)}{5}-\frac{4 \left(\sec^{2}\left(d x +c \right)\right)}{15}\right) \tan \left(d x +c \right)+\frac{5 a^{4} b}{6 \cos \left(d x +c \right)^{6}}+10 a^{3} b^{2} \left(\frac{\sin^{3}\left(d x +c \right)}{7 \cos \left(d x +c \right)^{7}}+\frac{4 \left(\sin^{3}\left(d x +c \right)\right)}{35 \cos \left(d x +c \right)^{5}}+\frac{8 \left(\sin^{3}\left(d x +c \right)\right)}{105 \cos \left(d x +c \right)^{3}}\right)+10 a^{2} b^{3} \left(\frac{\sin^{4}\left(d x +c \right)}{8 \cos \left(d x +c \right)^{8}}+\frac{\sin^{4}\left(d x +c \right)}{12 \cos \left(d x +c \right)^{6}}+\frac{\sin^{4}\left(d x +c \right)}{24 \cos \left(d x +c \right)^{4}}\right)+5 a \,b^{4} \left(\frac{\sin^{5}\left(d x +c \right)}{9 \cos \left(d x +c \right)^{9}}+\frac{4 \left(\sin^{5}\left(d x +c \right)\right)}{63 \cos \left(d x +c \right)^{7}}+\frac{8 \left(\sin^{5}\left(d x +c \right)\right)}{315 \cos \left(d x +c \right)^{5}}\right)+b^{5} \left(\frac{\sin^{6}\left(d x +c \right)}{10 \cos \left(d x +c \right)^{10}}+\frac{\sin^{6}\left(d x +c \right)}{20 \cos \left(d x +c \right)^{8}}+\frac{\sin^{6}\left(d x +c \right)}{60 \cos \left(d x +c \right)^{6}}\right)}{d}"," ",0,"1/d*(-a^5*(-8/15-1/5*sec(d*x+c)^4-4/15*sec(d*x+c)^2)*tan(d*x+c)+5/6*a^4*b/cos(d*x+c)^6+10*a^3*b^2*(1/7*sin(d*x+c)^3/cos(d*x+c)^7+4/35*sin(d*x+c)^3/cos(d*x+c)^5+8/105*sin(d*x+c)^3/cos(d*x+c)^3)+10*a^2*b^3*(1/8*sin(d*x+c)^4/cos(d*x+c)^8+1/12*sin(d*x+c)^4/cos(d*x+c)^6+1/24*sin(d*x+c)^4/cos(d*x+c)^4)+5*a*b^4*(1/9*sin(d*x+c)^5/cos(d*x+c)^9+4/63*sin(d*x+c)^5/cos(d*x+c)^7+8/315*sin(d*x+c)^5/cos(d*x+c)^5)+b^5*(1/10*sin(d*x+c)^6/cos(d*x+c)^10+1/20*sin(d*x+c)^6/cos(d*x+c)^8+1/60*sin(d*x+c)^6/cos(d*x+c)^6))","A"
109,1,814,430,0.282000," ","int(sec(d*x+c)^12*(a*cos(d*x+c)+b*sin(d*x+c))^5,x)","\frac{8 b^{5} \cos \left(d x +c \right)}{693 d}-\frac{15 a \,b^{4} \sin \left(d x +c \right)}{256 d}+\frac{25 a^{3} b^{2} \sin \left(d x +c \right)}{64 d}+\frac{5 a^{5} \sec \left(d x +c \right) \tan \left(d x +c \right)}{16 d}-\frac{20 a^{2} b^{3} \cos \left(d x +c \right)}{63 d}-\frac{10 \cos \left(d x +c \right) \left(\sin^{2}\left(d x +c \right)\right) a^{2} b^{3}}{63 d}+\frac{5 a^{5} \left(\sec^{3}\left(d x +c \right)\right) \tan \left(d x +c \right)}{24 d}+\frac{5 b^{5} \left(\sin^{6}\left(d x +c \right)\right)}{99 d \cos \left(d x +c \right)^{9}}+\frac{5 a^{4} b}{7 d \cos \left(d x +c \right)^{7}}+\frac{a^{5} \left(\sec^{5}\left(d x +c \right)\right) \tan \left(d x +c \right)}{6 d}+\frac{b^{5} \left(\sin^{6}\left(d x +c \right)\right)}{11 d \cos \left(d x +c \right)^{11}}-\frac{b^{5} \left(\sin^{6}\left(d x +c \right)\right)}{693 d \cos \left(d x +c \right)^{3}}-\frac{25 a^{3} b^{2} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{64 d}+\frac{25 a^{3} b^{2} \left(\sin^{3}\left(d x +c \right)\right)}{24 d \cos \left(d x +c \right)^{6}}+\frac{50 a^{2} b^{3} \left(\sin^{4}\left(d x +c \right)\right)}{63 d \cos \left(d x +c \right)^{7}}+\frac{5 a \,b^{4} \left(\sin^{5}\left(d x +c \right)\right)}{16 d \cos \left(d x +c \right)^{8}}+\frac{25 a^{3} b^{2} \left(\sin^{3}\left(d x +c \right)\right)}{64 d \cos \left(d x +c \right)^{2}}+\frac{10 a^{2} b^{3} \left(\sin^{4}\left(d x +c \right)\right)}{63 d \cos \left(d x +c \right)^{3}}+\frac{5 a \,b^{4} \left(\sin^{5}\left(d x +c \right)\right)}{128 d \cos \left(d x +c \right)^{4}}+\frac{a \,b^{4} \left(\sin^{5}\left(d x +c \right)\right)}{2 d \cos \left(d x +c \right)^{10}}+\frac{5 a^{5} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{16 d}+\frac{15 a \,b^{4} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{256 d}-\frac{5 a \,b^{4} \left(\sin^{3}\left(d x +c \right)\right)}{256 d}+\frac{b^{5} \left(\sin^{6}\left(d x +c \right)\right)}{231 d \cos \left(d x +c \right)}+\frac{b^{5} \cos \left(d x +c \right) \left(\sin^{4}\left(d x +c \right)\right)}{231 d}+\frac{4 \cos \left(d x +c \right) \left(\sin^{2}\left(d x +c \right)\right) b^{5}}{693 d}+\frac{b^{5} \left(\sin^{6}\left(d x +c \right)\right)}{231 d \cos \left(d x +c \right)^{5}}+\frac{5 b^{5} \left(\sin^{6}\left(d x +c \right)\right)}{231 d \cos \left(d x +c \right)^{7}}-\frac{5 a \,b^{4} \left(\sin^{5}\left(d x +c \right)\right)}{256 d \cos \left(d x +c \right)^{2}}+\frac{25 a^{3} b^{2} \left(\sin^{3}\left(d x +c \right)\right)}{32 d \cos \left(d x +c \right)^{4}}+\frac{10 a^{2} b^{3} \left(\sin^{4}\left(d x +c \right)\right)}{21 d \cos \left(d x +c \right)^{5}}+\frac{5 a \,b^{4} \left(\sin^{5}\left(d x +c \right)\right)}{32 d \cos \left(d x +c \right)^{6}}-\frac{10 a^{2} b^{3} \left(\sin^{4}\left(d x +c \right)\right)}{63 d \cos \left(d x +c \right)}+\frac{5 a^{3} b^{2} \left(\sin^{3}\left(d x +c \right)\right)}{4 d \cos \left(d x +c \right)^{8}}+\frac{10 a^{2} b^{3} \left(\sin^{4}\left(d x +c \right)\right)}{9 d \cos \left(d x +c \right)^{9}}"," ",0,"8/693*b^5*cos(d*x+c)/d-15/256*a*b^4*sin(d*x+c)/d-5/256*a*b^4*sin(d*x+c)^3/d+25/64*a^3*b^2*sin(d*x+c)/d+5/16*a^5*sec(d*x+c)*tan(d*x+c)/d+5/24*a^5*sec(d*x+c)^3*tan(d*x+c)/d+1/6*a^5*sec(d*x+c)^5*tan(d*x+c)/d-20/63*a^2*b^3*cos(d*x+c)/d+5/99/d*b^5*sin(d*x+c)^6/cos(d*x+c)^9+5/7/d*a^4*b/cos(d*x+c)^7+1/11/d*b^5*sin(d*x+c)^6/cos(d*x+c)^11+5/4/d*a^3*b^2*sin(d*x+c)^3/cos(d*x+c)^8+10/9/d*a^2*b^3*sin(d*x+c)^4/cos(d*x+c)^9+1/2/d*a*b^4*sin(d*x+c)^5/cos(d*x+c)^10+1/231/d*b^5*sin(d*x+c)^6/cos(d*x+c)^5-25/64/d*a^3*b^2*ln(sec(d*x+c)+tan(d*x+c))-1/693/d*b^5*sin(d*x+c)^6/cos(d*x+c)^3+25/64/d*a^3*b^2*sin(d*x+c)^3/cos(d*x+c)^2+10/63/d*a^2*b^3*sin(d*x+c)^4/cos(d*x+c)^3+5/128/d*a*b^4*sin(d*x+c)^5/cos(d*x+c)^4-10/63/d*cos(d*x+c)*sin(d*x+c)^2*a^2*b^3+25/32/d*a^3*b^2*sin(d*x+c)^3/cos(d*x+c)^4+10/21/d*a^2*b^3*sin(d*x+c)^4/cos(d*x+c)^5+5/32/d*a*b^4*sin(d*x+c)^5/cos(d*x+c)^6+5/16/d*a^5*ln(sec(d*x+c)+tan(d*x+c))+15/256/d*a*b^4*ln(sec(d*x+c)+tan(d*x+c))+1/231/d*b^5*sin(d*x+c)^6/cos(d*x+c)+1/231/d*b^5*cos(d*x+c)*sin(d*x+c)^4+4/693/d*cos(d*x+c)*sin(d*x+c)^2*b^5-10/63/d*a^2*b^3*sin(d*x+c)^4/cos(d*x+c)-5/256/d*a*b^4*sin(d*x+c)^5/cos(d*x+c)^2+5/231/d*b^5*sin(d*x+c)^6/cos(d*x+c)^7+25/24/d*a^3*b^2*sin(d*x+c)^3/cos(d*x+c)^6+50/63/d*a^2*b^3*sin(d*x+c)^4/cos(d*x+c)^7+5/16/d*a*b^4*sin(d*x+c)^5/cos(d*x+c)^8","A"
110,1,524,213,0.210000," ","int(cos(d*x+c)^5/(a*cos(d*x+c)+b*sin(d*x+c)),x)","\frac{b^{5} \ln \left(a +b \tan \left(d x +c \right)\right)}{d \left(a^{2}+b^{2}\right)^{3}}+\frac{3 \left(\tan^{3}\left(d x +c \right)\right) a^{5}}{8 d \left(a^{2}+b^{2}\right)^{3} \left(\tan^{2}\left(d x +c \right)+1\right)^{2}}+\frac{5 \left(\tan^{3}\left(d x +c \right)\right) a^{3} b^{2}}{4 d \left(a^{2}+b^{2}\right)^{3} \left(\tan^{2}\left(d x +c \right)+1\right)^{2}}+\frac{7 \left(\tan^{3}\left(d x +c \right)\right) a \,b^{4}}{8 d \left(a^{2}+b^{2}\right)^{3} \left(\tan^{2}\left(d x +c \right)+1\right)^{2}}+\frac{\left(\tan^{2}\left(d x +c \right)\right) a^{2} b^{3}}{2 d \left(a^{2}+b^{2}\right)^{3} \left(\tan^{2}\left(d x +c \right)+1\right)^{2}}+\frac{\left(\tan^{2}\left(d x +c \right)\right) b^{5}}{2 d \left(a^{2}+b^{2}\right)^{3} \left(\tan^{2}\left(d x +c \right)+1\right)^{2}}+\frac{7 \tan \left(d x +c \right) a^{3} b^{2}}{4 d \left(a^{2}+b^{2}\right)^{3} \left(\tan^{2}\left(d x +c \right)+1\right)^{2}}+\frac{9 \tan \left(d x +c \right) a \,b^{4}}{8 d \left(a^{2}+b^{2}\right)^{3} \left(\tan^{2}\left(d x +c \right)+1\right)^{2}}+\frac{5 \tan \left(d x +c \right) a^{5}}{8 d \left(a^{2}+b^{2}\right)^{3} \left(\tan^{2}\left(d x +c \right)+1\right)^{2}}+\frac{a^{4} b}{4 d \left(a^{2}+b^{2}\right)^{3} \left(\tan^{2}\left(d x +c \right)+1\right)^{2}}+\frac{a^{2} b^{3}}{d \left(a^{2}+b^{2}\right)^{3} \left(\tan^{2}\left(d x +c \right)+1\right)^{2}}+\frac{3 b^{5}}{4 d \left(a^{2}+b^{2}\right)^{3} \left(\tan^{2}\left(d x +c \right)+1\right)^{2}}-\frac{b^{5} \ln \left(\tan^{2}\left(d x +c \right)+1\right)}{2 d \left(a^{2}+b^{2}\right)^{3}}+\frac{15 \arctan \left(\tan \left(d x +c \right)\right) a \,b^{4}}{8 d \left(a^{2}+b^{2}\right)^{3}}+\frac{3 \arctan \left(\tan \left(d x +c \right)\right) a^{5}}{8 d \left(a^{2}+b^{2}\right)^{3}}+\frac{5 \arctan \left(\tan \left(d x +c \right)\right) a^{3} b^{2}}{4 d \left(a^{2}+b^{2}\right)^{3}}"," ",0,"1/d*b^5/(a^2+b^2)^3*ln(a+b*tan(d*x+c))+3/8/d/(a^2+b^2)^3/(tan(d*x+c)^2+1)^2*tan(d*x+c)^3*a^5+5/4/d/(a^2+b^2)^3/(tan(d*x+c)^2+1)^2*tan(d*x+c)^3*a^3*b^2+7/8/d/(a^2+b^2)^3/(tan(d*x+c)^2+1)^2*tan(d*x+c)^3*a*b^4+1/2/d/(a^2+b^2)^3/(tan(d*x+c)^2+1)^2*tan(d*x+c)^2*a^2*b^3+1/2/d/(a^2+b^2)^3/(tan(d*x+c)^2+1)^2*tan(d*x+c)^2*b^5+7/4/d/(a^2+b^2)^3/(tan(d*x+c)^2+1)^2*tan(d*x+c)*a^3*b^2+9/8/d/(a^2+b^2)^3/(tan(d*x+c)^2+1)^2*tan(d*x+c)*a*b^4+5/8/d/(a^2+b^2)^3/(tan(d*x+c)^2+1)^2*tan(d*x+c)*a^5+1/4/d/(a^2+b^2)^3/(tan(d*x+c)^2+1)^2*a^4*b+1/d/(a^2+b^2)^3/(tan(d*x+c)^2+1)^2*a^2*b^3+3/4/d/(a^2+b^2)^3/(tan(d*x+c)^2+1)^2*b^5-1/2/d/(a^2+b^2)^3*b^5*ln(tan(d*x+c)^2+1)+15/8/d/(a^2+b^2)^3*arctan(tan(d*x+c))*a*b^4+3/8/d/(a^2+b^2)^3*arctan(tan(d*x+c))*a^5+5/4/d/(a^2+b^2)^3*arctan(tan(d*x+c))*a^3*b^2","B"
111,1,221,158,0.179000," ","int(cos(d*x+c)^4/(a*cos(d*x+c)+b*sin(d*x+c)),x)","\frac{-\frac{2 \left(\left(-a^{3}-2 a \,b^{2}\right) \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(-a^{2} b -2 b^{3}\right) \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(-\frac{2}{3} a^{3}-\frac{8}{3} a \,b^{2}\right) \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-2 b^{3} \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(-a^{3}-2 a \,b^{2}\right) \tan \left(\frac{d x}{2}+\frac{c}{2}\right)-\frac{a^{2} b}{3}-\frac{4 b^{3}}{3}\right)}{\left(a^{4}+2 a^{2} b^{2}+b^{4}\right) \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}+\frac{2 b^{4} \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(a^{4}+2 a^{2} b^{2}+b^{4}\right) \sqrt{a^{2}+b^{2}}}}{d}"," ",0,"1/d*(-2/(a^4+2*a^2*b^2+b^4)*((-a^3-2*a*b^2)*tan(1/2*d*x+1/2*c)^5+(-a^2*b-2*b^3)*tan(1/2*d*x+1/2*c)^4+(-2/3*a^3-8/3*a*b^2)*tan(1/2*d*x+1/2*c)^3-2*b^3*tan(1/2*d*x+1/2*c)^2+(-a^3-2*a*b^2)*tan(1/2*d*x+1/2*c)-1/3*a^2*b-4/3*b^3)/(tan(1/2*d*x+1/2*c)^2+1)^3+2*b^4/(a^4+2*a^2*b^2+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)))","A"
112,1,236,113,0.162000," ","int(cos(d*x+c)^3/(a*cos(d*x+c)+b*sin(d*x+c)),x)","\frac{b^{3} \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(\tan^{2}\left(d x +c \right)+1\right)}+\frac{\tan \left(d x +c \right) a \,b^{2}}{2 d \left(a^{2}+b^{2}\right)^{2} \left(\tan^{2}\left(d x +c \right)+1\right)}+\frac{a^{2} b}{2 d \left(a^{2}+b^{2}\right)^{2} \left(\tan^{2}\left(d x +c \right)+1\right)}+\frac{b^{3}}{2 d \left(a^{2}+b^{2}\right)^{2} \left(\tan^{2}\left(d x +c \right)+1\right)}-\frac{b^{3} \ln \left(\tan^{2}\left(d x +c \right)+1\right)}{2 d \left(a^{2}+b^{2}\right)^{2}}+\frac{3 \arctan \left(\tan \left(d x +c \right)\right) a \,b^{2}}{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}}"," ",0,"1/d*b^3/(a^2+b^2)^2*ln(a+b*tan(d*x+c))+1/2/d/(a^2+b^2)^2/(tan(d*x+c)^2+1)*tan(d*x+c)*a^3+1/2/d/(a^2+b^2)^2/(tan(d*x+c)^2+1)*tan(d*x+c)*a*b^2+1/2/d/(a^2+b^2)^2/(tan(d*x+c)^2+1)*a^2*b+1/2/d/(a^2+b^2)^2/(tan(d*x+c)^2+1)*b^3-1/2/d/(a^2+b^2)^2*b^3*ln(tan(d*x+c)^2+1)+3/2/d/(a^2+b^2)^2*arctan(tan(d*x+c))*a*b^2+1/2/d/(a^2+b^2)^2*arctan(tan(d*x+c))*a^3","B"
113,1,90,87,0.161000," ","int(cos(d*x+c)^2/(a*cos(d*x+c)+b*sin(d*x+c)),x)","\frac{-\frac{2 \left(-a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)-b \right)}{\left(a^{2}+b^{2}\right) \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}+\frac{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)}{\left(a^{2}+b^{2}\right)^{\frac{3}{2}}}}{d}"," ",0,"1/d*(-2/(a^2+b^2)*(-a*tan(1/2*d*x+1/2*c)-b)/(tan(1/2*d*x+1/2*c)^2+1)+2*b^2/(a^2+b^2)^(3/2)*arctanh(1/2*(2*a*tan(1/2*d*x+1/2*c)-2*b)/(a^2+b^2)^(1/2)))","A"
114,1,74,45,0.151000," ","int(cos(d*x+c)/(a*cos(d*x+c)+b*sin(d*x+c)),x)","\frac{b \ln \left(a +b \tan \left(d x +c \right)\right)}{d \left(a^{2}+b^{2}\right)}-\frac{b \ln \left(\tan^{2}\left(d x +c \right)+1\right)}{2 d \left(a^{2}+b^{2}\right)}+\frac{a \arctan \left(\tan \left(d x +c \right)\right)}{d \left(a^{2}+b^{2}\right)}"," ",0,"1/d*b/(a^2+b^2)*ln(a+b*tan(d*x+c))-1/2/d/(a^2+b^2)*b*ln(tan(d*x+c)^2+1)+1/d/(a^2+b^2)*a*arctan(tan(d*x+c))","A"
115,1,43,43,0.144000," ","int(1/(a*cos(d*x+c)+b*sin(d*x+c)),x)","\frac{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 \sqrt{a^{2}+b^{2}}}"," ",0,"2/d/(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"
116,1,19,41,0.213000," ","int(sec(d*x+c)/(a*cos(d*x+c)+b*sin(d*x+c)),x)","\frac{\ln \left(a +b \tan \left(d x +c \right)\right)}{d b}"," ",0,"1/d/b*ln(a+b*tan(d*x+c))","A"
117,1,174,76,0.227000," ","int(sec(d*x+c)^2/(a*cos(d*x+c)+b*sin(d*x+c)),x)","-\frac{1}{d b \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}+\frac{a \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}{d \,b^{2}}+\frac{1}{d b \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}-\frac{a \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}{d \,b^{2}}+\frac{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) a^{2}}{d \,b^{2} \sqrt{a^{2}+b^{2}}}+\frac{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 \sqrt{a^{2}+b^{2}}}"," ",0,"-1/d/b/(tan(1/2*d*x+1/2*c)-1)+1/d*a/b^2*ln(tan(1/2*d*x+1/2*c)-1)+1/d/b/(tan(1/2*d*x+1/2*c)+1)-1/d*a/b^2*ln(tan(1/2*d*x+1/2*c)+1)+2/d/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))*a^2+2/d/(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))","B"
118,1,72,86,0.234000," ","int(sec(d*x+c)^3/(a*cos(d*x+c)+b*sin(d*x+c)),x)","\frac{\tan^{2}\left(d x +c \right)}{2 d b}-\frac{a \tan \left(d x +c \right)}{b^{2} d}+\frac{\ln \left(a +b \tan \left(d x +c \right)\right) a^{2}}{d \,b^{3}}+\frac{\ln \left(a +b \tan \left(d x +c \right)\right)}{d b}"," ",0,"1/2/d/b*tan(d*x+c)^2-a*tan(d*x+c)/b^2/d+1/d/b^3*ln(a+b*tan(d*x+c))*a^2+1/d/b*ln(a+b*tan(d*x+c))","A"
119,1,488,143,0.244000," ","int(sec(d*x+c)^4/(a*cos(d*x+c)+b*sin(d*x+c)),x)","-\frac{1}{3 d b \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{3}}-\frac{a}{2 d \,b^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}-\frac{1}{2 d b \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}-\frac{a^{2}}{d \,b^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{a}{2 d \,b^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{3}{2 d b \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}+\frac{a^{3} \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}{d \,b^{4}}+\frac{3 a \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}{2 d \,b^{2}}+\frac{1}{3 d b \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}-\frac{1}{2 d b \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}+\frac{a}{2 d \,b^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}+\frac{a^{2}}{d \,b^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}-\frac{a}{2 d \,b^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}+\frac{3}{2 d b \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}-\frac{a^{3} \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}{d \,b^{4}}-\frac{3 a \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}{2 d \,b^{2}}+\frac{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) a^{4}}{d \,b^{4} \sqrt{a^{2}+b^{2}}}+\frac{4 \arctanh \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)-2 b}{2 \sqrt{a^{2}+b^{2}}}\right) a^{2}}{d \,b^{2} \sqrt{a^{2}+b^{2}}}+\frac{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 \sqrt{a^{2}+b^{2}}}"," ",0,"-1/3/d/b/(tan(1/2*d*x+1/2*c)-1)^3-1/2/d/b^2/(tan(1/2*d*x+1/2*c)-1)^2*a-1/2/d/b/(tan(1/2*d*x+1/2*c)-1)^2-1/d/b^3/(tan(1/2*d*x+1/2*c)-1)*a^2-1/2/d/b^2/(tan(1/2*d*x+1/2*c)-1)*a-3/2/d/b/(tan(1/2*d*x+1/2*c)-1)+1/d*a^3/b^4*ln(tan(1/2*d*x+1/2*c)-1)+3/2/d*a/b^2*ln(tan(1/2*d*x+1/2*c)-1)+1/3/d/b/(tan(1/2*d*x+1/2*c)+1)^3-1/2/d/b/(tan(1/2*d*x+1/2*c)+1)^2+1/2/d/b^2/(tan(1/2*d*x+1/2*c)+1)^2*a+1/d/b^3/(tan(1/2*d*x+1/2*c)+1)*a^2-1/2/d/b^2/(tan(1/2*d*x+1/2*c)+1)*a+3/2/d/b/(tan(1/2*d*x+1/2*c)+1)-1/d*a^3/b^4*ln(tan(1/2*d*x+1/2*c)+1)-3/2/d*a/b^2*ln(tan(1/2*d*x+1/2*c)+1)+2/d/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))*a^4+4/d/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))*a^2+2/d/(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))","B"
120,1,162,152,0.231000," ","int(sec(d*x+c)^5/(a*cos(d*x+c)+b*sin(d*x+c)),x)","\frac{\tan^{4}\left(d x +c \right)}{4 d b}-\frac{a \left(\tan^{3}\left(d x +c \right)\right)}{3 b^{2} d}+\frac{\left(\tan^{2}\left(d x +c \right)\right) a^{2}}{2 d \,b^{3}}+\frac{\tan^{2}\left(d x +c \right)}{d b}-\frac{\tan \left(d x +c \right) a^{3}}{d \,b^{4}}-\frac{2 a \tan \left(d x +c \right)}{b^{2} d}+\frac{\ln \left(a +b \tan \left(d x +c \right)\right) a^{4}}{d \,b^{5}}+\frac{2 \ln \left(a +b \tan \left(d x +c \right)\right) a^{2}}{d \,b^{3}}+\frac{\ln \left(a +b \tan \left(d x +c \right)\right)}{d b}"," ",0,"1/4/d/b*tan(d*x+c)^4-1/3*a*tan(d*x+c)^3/b^2/d+1/2/d/b^3*tan(d*x+c)^2*a^2+1/d/b*tan(d*x+c)^2-1/d/b^4*tan(d*x+c)*a^3-2*a*tan(d*x+c)/b^2/d+1/d/b^5*ln(a+b*tan(d*x+c))*a^4+2/d/b^3*ln(a+b*tan(d*x+c))*a^2+1/d/b*ln(a+b*tan(d*x+c))","A"
121,1,994,244,0.257000," ","int(sec(d*x+c)^6/(a*cos(d*x+c)+b*sin(d*x+c)),x)","\frac{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 \sqrt{a^{2}+b^{2}}}-\frac{15}{8 d b \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}+\frac{15}{8 d b \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}+\frac{6 \arctanh \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)-2 b}{2 \sqrt{a^{2}+b^{2}}}\right) a^{4}}{d \,b^{4} \sqrt{a^{2}+b^{2}}}+\frac{6 \arctanh \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)-2 b}{2 \sqrt{a^{2}+b^{2}}}\right) a^{2}}{d \,b^{2} \sqrt{a^{2}+b^{2}}}+\frac{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) a^{6}}{d \,b^{6} \sqrt{a^{2}+b^{2}}}-\frac{13}{12 d b \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{3}}-\frac{9}{8 d b \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}+\frac{13}{12 d b \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}-\frac{9}{8 d b \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}-\frac{a}{4 d \,b^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{4}}-\frac{a^{2}}{3 d \,b^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{3}}-\frac{a}{2 d \,b^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{3}}-\frac{a^{3}}{2 d \,b^{4} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}-\frac{a^{2}}{2 d \,b^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}-\frac{a^{4}}{d \,b^{5} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{a^{3}}{2 d \,b^{4} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}+\frac{a^{5} \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}{d \,b^{6}}+\frac{a}{4 d \,b^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{4}}+\frac{a^{2}}{3 d \,b^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}-\frac{a}{2 d \,b^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}+\frac{a^{3}}{2 d \,b^{4} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}-\frac{a^{2}}{2 d \,b^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}+\frac{a^{4}}{d \,b^{5} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}-\frac{a^{3}}{2 d \,b^{4} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}-\frac{5 a^{2}}{2 d \,b^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{9 a}{8 d \,b^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}+\frac{5 a^{3} \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}{2 d \,b^{4}}+\frac{11 a}{8 d \,b^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}+\frac{5 a^{2}}{2 d \,b^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}-\frac{9 a}{8 d \,b^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}-\frac{5 a^{3} \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}{2 d \,b^{4}}-\frac{11 a}{8 d \,b^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}-\frac{a^{5} \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}{d \,b^{6}}-\frac{1}{5 d b \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{5}}-\frac{1}{2 d b \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{4}}+\frac{1}{5 d b \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{5}}-\frac{1}{2 d b \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{4}}+\frac{15 a \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}{8 d \,b^{2}}-\frac{15 a \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}{8 d \,b^{2}}"," ",0,"2/d/(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))-15/8/d/b/(tan(1/2*d*x+1/2*c)-1)+15/8/d/b/(tan(1/2*d*x+1/2*c)+1)+6/d/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))*a^4+6/d/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))*a^2+2/d/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))*a^6-13/12/d/b/(tan(1/2*d*x+1/2*c)-1)^3-9/8/d/b/(tan(1/2*d*x+1/2*c)-1)^2+13/12/d/b/(tan(1/2*d*x+1/2*c)+1)^3-9/8/d/b/(tan(1/2*d*x+1/2*c)+1)^2-1/4/d/b^2/(tan(1/2*d*x+1/2*c)-1)^4*a-1/3/d/b^3/(tan(1/2*d*x+1/2*c)-1)^3*a^2-1/2/d/b^2/(tan(1/2*d*x+1/2*c)-1)^3*a-1/2/d/b^4/(tan(1/2*d*x+1/2*c)-1)^2*a^3-1/2/d/b^3/(tan(1/2*d*x+1/2*c)-1)^2*a^2-1/d/b^5/(tan(1/2*d*x+1/2*c)-1)*a^4-1/2/d/b^4/(tan(1/2*d*x+1/2*c)-1)*a^3+1/d*a^5/b^6*ln(tan(1/2*d*x+1/2*c)-1)+1/4/d/b^2/(tan(1/2*d*x+1/2*c)+1)^4*a+1/3/d/b^3/(tan(1/2*d*x+1/2*c)+1)^3*a^2-1/2/d/b^2/(tan(1/2*d*x+1/2*c)+1)^3*a+1/2/d/b^4/(tan(1/2*d*x+1/2*c)+1)^2*a^3-1/2/d/b^3/(tan(1/2*d*x+1/2*c)+1)^2*a^2+1/d/b^5/(tan(1/2*d*x+1/2*c)+1)*a^4-1/2/d/b^4/(tan(1/2*d*x+1/2*c)+1)*a^3-5/2/d/b^3/(tan(1/2*d*x+1/2*c)-1)*a^2-9/8/d/b^2/(tan(1/2*d*x+1/2*c)-1)*a+5/2/d*a^3/b^4*ln(tan(1/2*d*x+1/2*c)-1)+11/8/d/b^2/(tan(1/2*d*x+1/2*c)+1)^2*a+5/2/d/b^3/(tan(1/2*d*x+1/2*c)+1)*a^2-9/8/d/b^2/(tan(1/2*d*x+1/2*c)+1)*a-5/2/d*a^3/b^4*ln(tan(1/2*d*x+1/2*c)+1)-11/8/d/b^2/(tan(1/2*d*x+1/2*c)-1)^2*a-1/d*a^5/b^6*ln(tan(1/2*d*x+1/2*c)+1)-1/5/d/b/(tan(1/2*d*x+1/2*c)-1)^5-1/2/d/b/(tan(1/2*d*x+1/2*c)-1)^4+1/5/d/b/(tan(1/2*d*x+1/2*c)+1)^5-1/2/d/b/(tan(1/2*d*x+1/2*c)+1)^4+15/8/d*a/b^2*ln(tan(1/2*d*x+1/2*c)-1)-15/8/d*a/b^2*ln(tan(1/2*d*x+1/2*c)+1)","B"
122,1,292,141,0.230000," ","int(cos(d*x+c)^4/(a*cos(d*x+c)+b*sin(d*x+c))^2,x)","-\frac{b^{3}}{d \left(a^{2}+b^{2}\right)^{2} \left(a +b \tan \left(d x +c \right)\right)}+\frac{4 b^{3} a \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(\tan^{2}\left(d x +c \right)+1\right)}-\frac{\tan \left(d x +c \right) b^{4}}{2 d \left(a^{2}+b^{2}\right)^{3} \left(\tan^{2}\left(d x +c \right)+1\right)}+\frac{a^{3} b}{d \left(a^{2}+b^{2}\right)^{3} \left(\tan^{2}\left(d x +c \right)+1\right)}+\frac{b^{3} a}{d \left(a^{2}+b^{2}\right)^{3} \left(\tan^{2}\left(d x +c \right)+1\right)}-\frac{2 b^{3} a \ln \left(\tan^{2}\left(d x +c \right)+1\right)}{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{3 \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,"-1/d*b^3/(a^2+b^2)^2/(a+b*tan(d*x+c))+4/d*b^3/(a^2+b^2)^3*a*ln(a+b*tan(d*x+c))+1/2/d/(a^2+b^2)^3/(tan(d*x+c)^2+1)*tan(d*x+c)*a^4-1/2/d/(a^2+b^2)^3/(tan(d*x+c)^2+1)*tan(d*x+c)*b^4+1/d/(a^2+b^2)^3/(tan(d*x+c)^2+1)*a^3*b+1/d/(a^2+b^2)^3/(tan(d*x+c)^2+1)*b^3*a-2/d/(a^2+b^2)^3*b^3*a*ln(tan(d*x+c)^2+1)+3/d/(a^2+b^2)^3*arctan(tan(d*x+c))*a^2*b^2-3/2/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"
123,1,172,134,0.235000," ","int(cos(d*x+c)^3/(a*cos(d*x+c)+b*sin(d*x+c))^2,x)","\frac{-\frac{2 \left(\left(-a^{2}+b^{2}\right) \tan \left(\frac{d x}{2}+\frac{c}{2}\right)-2 a b \right)}{\left(a^{4}+2 a^{2} b^{2}+b^{4}\right) \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}-\frac{2 b^{2} \left(\frac{-\frac{b^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{a}-b}{\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)-a}-\frac{3 a \arctanh \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)-2 b}{2 \sqrt{a^{2}+b^{2}}}\right)}{\sqrt{a^{2}+b^{2}}}\right)}{\left(a^{2}+b^{2}\right)^{2}}}{d}"," ",0,"1/d*(-2/(a^4+2*a^2*b^2+b^4)*((-a^2+b^2)*tan(1/2*d*x+1/2*c)-2*a*b)/(tan(1/2*d*x+1/2*c)^2+1)-2*b^2/(a^2+b^2)^2*((-b^2/a*tan(1/2*d*x+1/2*c)-b)/(tan(1/2*d*x+1/2*c)^2*a-2*b*tan(1/2*d*x+1/2*c)-a)-3*a/(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"
124,1,130,82,0.211000," ","int(cos(d*x+c)^2/(a*cos(d*x+c)+b*sin(d*x+c))^2,x)","-\frac{b}{\left(a^{2}+b^{2}\right) d \left(a +b \tan \left(d x +c \right)\right)}+\frac{2 b a \ln \left(a +b \tan \left(d x +c \right)\right)}{d \left(a^{2}+b^{2}\right)^{2}}-\frac{a b \ln \left(\tan^{2}\left(d x +c \right)+1\right)}{d \left(a^{2}+b^{2}\right)^{2}}+\frac{\arctan \left(\tan \left(d x +c \right)\right) a^{2}}{d \left(a^{2}+b^{2}\right)^{2}}-\frac{\arctan \left(\tan \left(d x +c \right)\right) b^{2}}{d \left(a^{2}+b^{2}\right)^{2}}"," ",0,"-b/(a^2+b^2)/d/(a+b*tan(d*x+c))+2/d*b*a/(a^2+b^2)^2*ln(a+b*tan(d*x+c))-1/d/(a^2+b^2)^2*a*b*ln(tan(d*x+c)^2+1)+1/d/(a^2+b^2)^2*arctan(tan(d*x+c))*a^2-1/d/(a^2+b^2)^2*arctan(tan(d*x+c))*b^2","A"
125,1,118,79,0.207000," ","int(cos(d*x+c)/(a*cos(d*x+c)+b*sin(d*x+c))^2,x)","\frac{-\frac{2 \left(-\frac{b^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{a \left(a^{2}+b^{2}\right)}-\frac{b}{a^{2}+b^{2}}\right)}{\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)-a}+\frac{2 a \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(a^{2}+b^{2}\right)^{\frac{3}{2}}}}{d}"," ",0,"1/d*(-2*(-b^2/a/(a^2+b^2)*tan(1/2*d*x+1/2*c)-b/(a^2+b^2))/(tan(1/2*d*x+1/2*c)^2*a-2*b*tan(1/2*d*x+1/2*c)-a)+2*a/(a^2+b^2)^(3/2)*arctanh(1/2*(2*a*tan(1/2*d*x+1/2*c)-2*b)/(a^2+b^2)^(1/2)))","A"
126,1,21,32,0.196000," ","int(1/(a*cos(d*x+c)+b*sin(d*x+c))^2,x)","-\frac{1}{d b \left(a +b \tan \left(d x +c \right)\right)}"," ",0,"-1/d/b/(a+b*tan(d*x+c))","A"
127,1,174,88,0.276000," ","int(sec(d*x+c)/(a*cos(d*x+c)+b*sin(d*x+c))^2,x)","-\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}{d \,b^{2}}+\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}{d \,b^{2}}+\frac{2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \left(\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)-a \right) a}+\frac{2}{d b \left(\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)-a \right)}-\frac{2 a \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 \,b^{2} \sqrt{a^{2}+b^{2}}}"," ",0,"-1/d/b^2*ln(tan(1/2*d*x+1/2*c)-1)+1/d/b^2*ln(tan(1/2*d*x+1/2*c)+1)+2/d/(tan(1/2*d*x+1/2*c)^2*a-2*b*tan(1/2*d*x+1/2*c)-a)/a*tan(1/2*d*x+1/2*c)+2/d/b/(tan(1/2*d*x+1/2*c)^2*a-2*b*tan(1/2*d*x+1/2*c)-a)-2/d/b^2*a/(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"
128,1,78,75,0.306000," ","int(sec(d*x+c)^2/(a*cos(d*x+c)+b*sin(d*x+c))^2,x)","\frac{\tan \left(d x +c \right)}{b^{2} d}-\frac{2 a \ln \left(a +b \tan \left(d x +c \right)\right)}{d \,b^{3}}-\frac{a^{2}}{d \,b^{3} \left(a +b \tan \left(d x +c \right)\right)}-\frac{1}{d b \left(a +b \tan \left(d x +c \right)\right)}"," ",0,"tan(d*x+c)/b^2/d-2/d*a/b^3*ln(a+b*tan(d*x+c))-1/d/b^3/(a+b*tan(d*x+c))*a^2-1/d/b/(a+b*tan(d*x+c))","A"
129,1,440,174,0.323000," ","int(sec(d*x+c)^3/(a*cos(d*x+c)+b*sin(d*x+c))^2,x)","\frac{1}{2 d \,b^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}+\frac{2 a}{d \,b^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}+\frac{1}{2 d \,b^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{3 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right) a^{2}}{d \,b^{4}}-\frac{3 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}{2 d \,b^{2}}-\frac{1}{2 d \,b^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}-\frac{2 a}{d \,b^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}+\frac{1}{2 d \,b^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}+\frac{3 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right) a^{2}}{d \,b^{4}}+\frac{3 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}{2 d \,b^{2}}+\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,b^{2} \left(\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)-a \right)}+\frac{2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \left(\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)-a \right) a}+\frac{2 a^{2}}{d \,b^{3} \left(\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)-a \right)}+\frac{2}{d b \left(\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)-a \right)}-\frac{6 a \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 \,b^{4}}"," ",0,"1/2/d/b^2/(tan(1/2*d*x+1/2*c)-1)^2+2/d/b^3/(tan(1/2*d*x+1/2*c)-1)*a+1/2/d/b^2/(tan(1/2*d*x+1/2*c)-1)-3/d/b^4*ln(tan(1/2*d*x+1/2*c)-1)*a^2-3/2/d/b^2*ln(tan(1/2*d*x+1/2*c)-1)-1/2/d/b^2/(tan(1/2*d*x+1/2*c)+1)^2-2/d/b^3/(tan(1/2*d*x+1/2*c)+1)*a+1/2/d/b^2/(tan(1/2*d*x+1/2*c)+1)+3/d/b^4*ln(tan(1/2*d*x+1/2*c)+1)*a^2+3/2/d/b^2*ln(tan(1/2*d*x+1/2*c)+1)+2/d/b^2/(tan(1/2*d*x+1/2*c)^2*a-2*b*tan(1/2*d*x+1/2*c)-a)*a*tan(1/2*d*x+1/2*c)+2/d/(tan(1/2*d*x+1/2*c)^2*a-2*b*tan(1/2*d*x+1/2*c)-a)/a*tan(1/2*d*x+1/2*c)+2/d/b^3/(tan(1/2*d*x+1/2*c)^2*a-2*b*tan(1/2*d*x+1/2*c)-a)*a^2+2/d/b/(tan(1/2*d*x+1/2*c)^2*a-2*b*tan(1/2*d*x+1/2*c)-a)-6/d/b^4*a*(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))","B"
130,1,174,139,0.342000," ","int(sec(d*x+c)^4/(a*cos(d*x+c)+b*sin(d*x+c))^2,x)","\frac{\tan^{3}\left(d x +c \right)}{3 b^{2} d}-\frac{a \left(\tan^{2}\left(d x +c \right)\right)}{b^{3} d}+\frac{3 a^{2} \tan \left(d x +c \right)}{d \,b^{4}}+\frac{2 \tan \left(d x +c \right)}{b^{2} d}-\frac{4 a^{3} \ln \left(a +b \tan \left(d x +c \right)\right)}{d \,b^{5}}-\frac{4 a \ln \left(a +b \tan \left(d x +c \right)\right)}{d \,b^{3}}-\frac{a^{4}}{d \,b^{5} \left(a +b \tan \left(d x +c \right)\right)}-\frac{2 a^{2}}{d \,b^{3} \left(a +b \tan \left(d x +c \right)\right)}-\frac{1}{d b \left(a +b \tan \left(d x +c \right)\right)}"," ",0,"1/3*tan(d*x+c)^3/b^2/d-a*tan(d*x+c)^2/b^3/d+3/d/b^4*a^2*tan(d*x+c)+2*tan(d*x+c)/b^2/d-4/d*a^3/b^5*ln(a+b*tan(d*x+c))-4/d*a/b^3*ln(a+b*tan(d*x+c))-1/d/b^5/(a+b*tan(d*x+c))*a^4-2/d/b^3/(a+b*tan(d*x+c))*a^2-1/d/b/(a+b*tan(d*x+c))","A"
131,1,283,207,0.269000," ","int(cos(d*x+c)^4/(a*cos(d*x+c)+b*sin(d*x+c))^3,x)","\frac{-\frac{2 \left(\left(-a^{3}+3 a \,b^{2}\right) \tan \left(\frac{d x}{2}+\frac{c}{2}\right)-3 a^{2} b +b^{3}\right)}{\left(a^{6}+3 a^{4} b^{2}+3 a^{2} b^{4}+b^{6}\right) \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}-\frac{2 b^{2} \left(\frac{-\frac{b^{2} \left(9 a^{2}+2 b^{2}\right) \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{2 a}-\frac{b \left(8 a^{4}-15 a^{2} b^{2}-2 b^{4}\right) \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{2 a^{2}}+\frac{b^{2} \left(23 a^{2}+2 b^{2}\right) \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 a}+4 a^{2} b +\frac{b^{3}}{2}}{\left(\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)-a \right)^{2}}-\frac{3 \left(4 a^{2}-b^{2}\right) \arctanh \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)-2 b}{2 \sqrt{a^{2}+b^{2}}}\right)}{2 \sqrt{a^{2}+b^{2}}}\right)}{\left(a^{2}+b^{2}\right)^{3}}}{d}"," ",0,"1/d*(-2/(a^6+3*a^4*b^2+3*a^2*b^4+b^6)*((-a^3+3*a*b^2)*tan(1/2*d*x+1/2*c)-3*a^2*b+b^3)/(tan(1/2*d*x+1/2*c)^2+1)-2*b^2/(a^2+b^2)^3*((-1/2*b^2*(9*a^2+2*b^2)/a*tan(1/2*d*x+1/2*c)^3-1/2*b*(8*a^4-15*a^2*b^2-2*b^4)/a^2*tan(1/2*d*x+1/2*c)^2+1/2*b^2*(23*a^2+2*b^2)/a*tan(1/2*d*x+1/2*c)+4*a^2*b+1/2*b^3)/(tan(1/2*d*x+1/2*c)^2*a-2*b*tan(1/2*d*x+1/2*c)-a)^2-3/2*(4*a^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))))","A"
132,1,219,120,0.253000," ","int(cos(d*x+c)^3/(a*cos(d*x+c)+b*sin(d*x+c))^3,x)","-\frac{b}{2 \left(a^{2}+b^{2}\right) 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^{2}}{d \left(a^{2}+b^{2}\right)^{3}}-\frac{b^{3} \ln \left(a +b \tan \left(d x +c \right)\right)}{d \left(a^{2}+b^{2}\right)^{3}}-\frac{2 a b}{\left(a^{2}+b^{2}\right)^{2} d \left(a +b \tan \left(d x +c \right)\right)}-\frac{3 \ln \left(\tan^{2}\left(d x +c \right)+1\right) a^{2} b}{2 d \left(a^{2}+b^{2}\right)^{3}}+\frac{\ln \left(\tan^{2}\left(d x +c \right)+1\right) b^{3}}{2 d \left(a^{2}+b^{2}\right)^{3}}+\frac{\arctan \left(\tan \left(d x +c \right)\right) a^{3}}{d \left(a^{2}+b^{2}\right)^{3}}-\frac{3 \arctan \left(\tan \left(d x +c \right)\right) a \,b^{2}}{d \left(a^{2}+b^{2}\right)^{3}}"," ",0,"-1/2*b/(a^2+b^2)/d/(a+b*tan(d*x+c))^2+3/d*b/(a^2+b^2)^3*ln(a+b*tan(d*x+c))*a^2-1/d*b^3/(a^2+b^2)^3*ln(a+b*tan(d*x+c))-2*a*b/(a^2+b^2)^2/d/(a+b*tan(d*x+c))-3/2/d/(a^2+b^2)^3*ln(tan(d*x+c)^2+1)*a^2*b+1/2/d/(a^2+b^2)^3*ln(tan(d*x+c)^2+1)*b^3+1/d/(a^2+b^2)^3*arctan(tan(d*x+c))*a^3-3/d/(a^2+b^2)^3*arctan(tan(d*x+c))*a*b^2","A"
133,1,280,112,0.248000," ","int(cos(d*x+c)^2/(a*cos(d*x+c)+b*sin(d*x+c))^3,x)","\frac{-\frac{2 \left(-\frac{b^{2} \left(5 a^{2}+2 b^{2}\right) \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{2 a \left(a^{4}+2 a^{2} b^{2}+b^{4}\right)}-\frac{b \left(4 a^{4}-7 a^{2} b^{2}-2 b^{4}\right) \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{2 \left(a^{4}+2 a^{2} b^{2}+b^{4}\right) a^{2}}+\frac{b^{2} \left(11 a^{2}+2 b^{2}\right) \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 \left(a^{4}+2 a^{2} b^{2}+b^{4}\right) a}+\frac{b \left(4 a^{2}+b^{2}\right)}{2 a^{4}+4 a^{2} b^{2}+2 b^{4}}\right)}{\left(\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)-a \right)^{2}}+\frac{\left(2 a^{2}-b^{2}\right) \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(a^{4}+2 a^{2} b^{2}+b^{4}\right) \sqrt{a^{2}+b^{2}}}}{d}"," ",0,"1/d*(-2*(-1/2*b^2*(5*a^2+2*b^2)/a/(a^4+2*a^2*b^2+b^4)*tan(1/2*d*x+1/2*c)^3-1/2*b*(4*a^4-7*a^2*b^2-2*b^4)/(a^4+2*a^2*b^2+b^4)/a^2*tan(1/2*d*x+1/2*c)^2+1/2*b^2*(11*a^2+2*b^2)/(a^4+2*a^2*b^2+b^4)/a*tan(1/2*d*x+1/2*c)+1/2*b*(4*a^2+b^2)/(a^4+2*a^2*b^2+b^4))/(tan(1/2*d*x+1/2*c)^2*a-2*b*tan(1/2*d*x+1/2*c)-a)^2+(2*a^2-b^2)/(a^4+2*a^2*b^2+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)))","B"
134,1,21,20,0.230000," ","int(cos(d*x+c)/(a*cos(d*x+c)+b*sin(d*x+c))^3,x)","-\frac{1}{2 b d \left(a +b \tan \left(d x +c \right)\right)^{2}}"," ",0,"-1/2/b/d/(a+b*tan(d*x+c))^2","A"
135,1,191,95,0.256000," ","int(1/(a*cos(d*x+c)+b*sin(d*x+c))^3,x)","\frac{-\frac{2 \left(-\frac{\left(a^{2}+2 b^{2}\right) \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{2 a \left(a^{2}+b^{2}\right)}-\frac{b \left(a^{2}-2 b^{2}\right) \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{2 \left(a^{2}+b^{2}\right) a^{2}}-\frac{\left(a^{2}-2 b^{2}\right) \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 a \left(a^{2}+b^{2}\right)}+\frac{b}{2 a^{2}+2 b^{2}}\right)}{\left(\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)-a \right)^{2}}+\frac{\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(a^{2}+b^{2}\right)^{\frac{3}{2}}}}{d}"," ",0,"1/d*(-2*(-1/2*(a^2+2*b^2)/a/(a^2+b^2)*tan(1/2*d*x+1/2*c)^3-1/2*b*(a^2-2*b^2)/(a^2+b^2)/a^2*tan(1/2*d*x+1/2*c)^2-1/2*(a^2-2*b^2)/a/(a^2+b^2)*tan(1/2*d*x+1/2*c)+1/2*b/(a^2+b^2))/(tan(1/2*d*x+1/2*c)^2*a-2*b*tan(1/2*d*x+1/2*c)-a)^2+1/(a^2+b^2)^(3/2)*arctanh(1/2*(2*a*tan(1/2*d*x+1/2*c)-2*b)/(a^2+b^2)^(1/2)))","A"
136,1,84,87,0.394000," ","int(sec(d*x+c)/(a*cos(d*x+c)+b*sin(d*x+c))^3,x)","\frac{\ln \left(a +b \tan \left(d x +c \right)\right)}{d \,b^{3}}+\frac{2 a}{d \,b^{3} \left(a +b \tan \left(d x +c \right)\right)}-\frac{a^{2}}{2 d \,b^{3} \left(a +b \tan \left(d x +c \right)\right)^{2}}-\frac{1}{2 b d \left(a +b \tan \left(d x +c \right)\right)^{2}}"," ",0,"1/d/b^3*ln(a+b*tan(d*x+c))+2/d*a/b^3/(a+b*tan(d*x+c))-1/2/d/b^3/(a+b*tan(d*x+c))^2*a^2-1/2/b/d/(a+b*tan(d*x+c))^2","A"
137,1,611,244,0.409000," ","int(sec(d*x+c)^2/(a*cos(d*x+c)+b*sin(d*x+c))^3,x)","-\frac{1}{d \,b^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}+\frac{3 a \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}{d \,b^{4}}+\frac{1}{d \,b^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}-\frac{3 a \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}{d \,b^{4}}-\frac{3 a \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,b^{2} \left(\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)-a \right)^{2}}+\frac{2 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a -2 b \tan \left(\frac{d x}{2}+\frac{c}{2}\right)-a \right)^{2} a}-\frac{4 a^{2} \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,b^{3} \left(\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)-a \right)^{2}}+\frac{9 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d b \left(\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)-a \right)^{2}}-\frac{2 b \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a -2 b \tan \left(\frac{d x}{2}+\frac{c}{2}\right)-a \right)^{2} a^{2}}+\frac{13 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,b^{2} \left(\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)-a \right)^{2}}-\frac{2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \left(\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)-a \right)^{2} a}+\frac{4 a^{2}}{d \,b^{3} \left(\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)-a \right)^{2}}-\frac{1}{d b \left(\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)-a \right)^{2}}+\frac{6 \arctanh \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)-2 b}{2 \sqrt{a^{2}+b^{2}}}\right) a^{2}}{d \,b^{4} \sqrt{a^{2}+b^{2}}}+\frac{3 \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 \,b^{2} \sqrt{a^{2}+b^{2}}}"," ",0,"-1/d/b^3/(tan(1/2*d*x+1/2*c)-1)+3/d*a/b^4*ln(tan(1/2*d*x+1/2*c)-1)+1/d/b^3/(tan(1/2*d*x+1/2*c)+1)-3/d*a/b^4*ln(tan(1/2*d*x+1/2*c)+1)-3/d/b^2/(tan(1/2*d*x+1/2*c)^2*a-2*b*tan(1/2*d*x+1/2*c)-a)^2*a*tan(1/2*d*x+1/2*c)^3+2/d/(tan(1/2*d*x+1/2*c)^2*a-2*b*tan(1/2*d*x+1/2*c)-a)^2/a*tan(1/2*d*x+1/2*c)^3-4/d/b^3/(tan(1/2*d*x+1/2*c)^2*a-2*b*tan(1/2*d*x+1/2*c)-a)^2*a^2*tan(1/2*d*x+1/2*c)^2+9/d/b/(tan(1/2*d*x+1/2*c)^2*a-2*b*tan(1/2*d*x+1/2*c)-a)^2*tan(1/2*d*x+1/2*c)^2-2/d*b/(tan(1/2*d*x+1/2*c)^2*a-2*b*tan(1/2*d*x+1/2*c)-a)^2/a^2*tan(1/2*d*x+1/2*c)^2+13/d/b^2/(tan(1/2*d*x+1/2*c)^2*a-2*b*tan(1/2*d*x+1/2*c)-a)^2*a*tan(1/2*d*x+1/2*c)-2/d/(tan(1/2*d*x+1/2*c)^2*a-2*b*tan(1/2*d*x+1/2*c)-a)^2/a*tan(1/2*d*x+1/2*c)+4/d/b^3/(tan(1/2*d*x+1/2*c)^2*a-2*b*tan(1/2*d*x+1/2*c)-a)^2*a^2-1/d/b/(tan(1/2*d*x+1/2*c)^2*a-2*b*tan(1/2*d*x+1/2*c)-a)^2+6/d/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))*a^2+3/d/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))","B"
138,1,184,157,0.404000," ","int(sec(d*x+c)^3/(a*cos(d*x+c)+b*sin(d*x+c))^3,x)","\frac{\tan^{2}\left(d x +c \right)}{2 b^{3} d}-\frac{3 a \tan \left(d x +c \right)}{b^{4} d}+\frac{4 a^{3}}{d \,b^{5} \left(a +b \tan \left(d x +c \right)\right)}+\frac{4 a}{d \,b^{3} \left(a +b \tan \left(d x +c \right)\right)}+\frac{6 \ln \left(a +b \tan \left(d x +c \right)\right) a^{2}}{d \,b^{5}}+\frac{2 \ln \left(a +b \tan \left(d x +c \right)\right)}{d \,b^{3}}-\frac{a^{4}}{2 d \,b^{5} \left(a +b \tan \left(d x +c \right)\right)^{2}}-\frac{a^{2}}{d \,b^{3} \left(a +b \tan \left(d x +c \right)\right)^{2}}-\frac{1}{2 b d \left(a +b \tan \left(d x +c \right)\right)^{2}}"," ",0,"1/2*tan(d*x+c)^2/b^3/d-3*a*tan(d*x+c)/b^4/d+4/d*a^3/b^5/(a+b*tan(d*x+c))+4/d*a/b^3/(a+b*tan(d*x+c))+6/d/b^5*ln(a+b*tan(d*x+c))*a^2+2/d/b^3*ln(a+b*tan(d*x+c))-1/2/d/b^5/(a+b*tan(d*x+c))^2*a^4-1/d/b^3/(a+b*tan(d*x+c))^2*a^2-1/2/b/d/(a+b*tan(d*x+c))^2","A"
139,1,1125,361,0.397000," ","int(sec(d*x+c)^4/(a*cos(d*x+c)+b*sin(d*x+c))^3,x)","\frac{15 a \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}{2 d \,b^{4}}-\frac{15 a \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}{2 d \,b^{4}}+\frac{5 \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 \,b^{2} \sqrt{a^{2}+b^{2}}}+\frac{2 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a -2 b \tan \left(\frac{d x}{2}+\frac{c}{2}\right)-a \right)^{2} a}+\frac{15 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d b \left(\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)-a \right)^{2}}-\frac{2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \left(\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)-a \right)^{2} a}+\frac{7 a^{2}}{d \,b^{3} \left(\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)-a \right)^{2}}-\frac{5}{2 d \,b^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}+\frac{5}{2 d \,b^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}-\frac{3 a}{2 d \,b^{4} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}-\frac{6 a^{2}}{d \,b^{5} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{3 a}{2 d \,b^{4} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}+\frac{10 a^{3} \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}{d \,b^{6}}+\frac{3 a}{2 d \,b^{4} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}+\frac{6 a^{2}}{d \,b^{5} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}-\frac{3 a}{2 d \,b^{4} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}-\frac{10 a^{3} \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}{d \,b^{6}}+\frac{8 a^{4}}{d \,b^{5} \left(\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)-a \right)^{2}}-\frac{1}{d b \left(\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)-a \right)^{2}}-\frac{5 a \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,b^{2} \left(\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)-a \right)^{2}}+\frac{9 a^{2} \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,b^{3} \left(\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)-a \right)^{2}}-\frac{2 b \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a -2 b \tan \left(\frac{d x}{2}+\frac{c}{2}\right)-a \right)^{2} a^{2}}+\frac{23 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,b^{2} \left(\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)-a \right)^{2}}-\frac{1}{3 d \,b^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{3}}-\frac{1}{2 d \,b^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}+\frac{1}{3 d \,b^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}-\frac{1}{2 d \,b^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}+\frac{25 \arctanh \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)-2 b}{2 \sqrt{a^{2}+b^{2}}}\right) a^{2}}{d \,b^{4} \sqrt{a^{2}+b^{2}}}+\frac{20 \arctanh \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)-2 b}{2 \sqrt{a^{2}+b^{2}}}\right) a^{4}}{d \,b^{6} \sqrt{a^{2}+b^{2}}}+\frac{25 a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,b^{4} \left(\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)-a \right)^{2}}-\frac{7 a^{3} \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,b^{4} \left(\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)-a \right)^{2}}-\frac{8 a^{4} \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,b^{5} \left(\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)-a \right)^{2}}"," ",0,"15/2/d*a/b^4*ln(tan(1/2*d*x+1/2*c)-1)-15/2/d*a/b^4*ln(tan(1/2*d*x+1/2*c)+1)+2/d/(tan(1/2*d*x+1/2*c)^2*a-2*b*tan(1/2*d*x+1/2*c)-a)^2/a*tan(1/2*d*x+1/2*c)^3+15/d/b/(tan(1/2*d*x+1/2*c)^2*a-2*b*tan(1/2*d*x+1/2*c)-a)^2*tan(1/2*d*x+1/2*c)^2-2/d/(tan(1/2*d*x+1/2*c)^2*a-2*b*tan(1/2*d*x+1/2*c)-a)^2/a*tan(1/2*d*x+1/2*c)+7/d/b^3/(tan(1/2*d*x+1/2*c)^2*a-2*b*tan(1/2*d*x+1/2*c)-a)^2*a^2+5/d/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))-5/2/d/b^3/(tan(1/2*d*x+1/2*c)-1)+5/2/d/b^3/(tan(1/2*d*x+1/2*c)+1)-1/d/b/(tan(1/2*d*x+1/2*c)^2*a-2*b*tan(1/2*d*x+1/2*c)-a)^2+8/d/b^5/(tan(1/2*d*x+1/2*c)^2*a-2*b*tan(1/2*d*x+1/2*c)-a)^2*a^4-3/2/d/b^4/(tan(1/2*d*x+1/2*c)-1)^2*a-6/d/b^5/(tan(1/2*d*x+1/2*c)-1)*a^2-3/2/d/b^4/(tan(1/2*d*x+1/2*c)-1)*a+10/d*a^3/b^6*ln(tan(1/2*d*x+1/2*c)-1)+3/2/d/b^4/(tan(1/2*d*x+1/2*c)+1)^2*a+6/d/b^5/(tan(1/2*d*x+1/2*c)+1)*a^2-3/2/d/b^4/(tan(1/2*d*x+1/2*c)+1)*a-10/d*a^3/b^6*ln(tan(1/2*d*x+1/2*c)+1)-1/3/d/b^3/(tan(1/2*d*x+1/2*c)-1)^3-1/2/d/b^3/(tan(1/2*d*x+1/2*c)-1)^2+1/3/d/b^3/(tan(1/2*d*x+1/2*c)+1)^3-1/2/d/b^3/(tan(1/2*d*x+1/2*c)+1)^2-5/d/b^2/(tan(1/2*d*x+1/2*c)^2*a-2*b*tan(1/2*d*x+1/2*c)-a)^2*a*tan(1/2*d*x+1/2*c)^3+9/d/b^3/(tan(1/2*d*x+1/2*c)^2*a-2*b*tan(1/2*d*x+1/2*c)-a)^2*a^2*tan(1/2*d*x+1/2*c)^2-2/d*b/(tan(1/2*d*x+1/2*c)^2*a-2*b*tan(1/2*d*x+1/2*c)-a)^2/a^2*tan(1/2*d*x+1/2*c)^2+23/d/b^2/(tan(1/2*d*x+1/2*c)^2*a-2*b*tan(1/2*d*x+1/2*c)-a)^2*a*tan(1/2*d*x+1/2*c)+25/d/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))*a^2+25/d/b^4/(tan(1/2*d*x+1/2*c)^2*a-2*b*tan(1/2*d*x+1/2*c)-a)^2*a^3*tan(1/2*d*x+1/2*c)+20/d/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))*a^4-7/d/b^4/(tan(1/2*d*x+1/2*c)^2*a-2*b*tan(1/2*d*x+1/2*c)-a)^2*a^3*tan(1/2*d*x+1/2*c)^3-8/d/b^5/(tan(1/2*d*x+1/2*c)^2*a-2*b*tan(1/2*d*x+1/2*c)-a)^2*a^4*tan(1/2*d*x+1/2*c)^2","B"
140,1,321,226,0.431000," ","int(sec(d*x+c)^5/(a*cos(d*x+c)+b*sin(d*x+c))^3,x)","\frac{\tan^{4}\left(d x +c \right)}{4 b^{3} d}-\frac{a \left(\tan^{3}\left(d x +c \right)\right)}{b^{4} d}+\frac{3 \left(\tan^{2}\left(d x +c \right)\right) a^{2}}{d \,b^{5}}+\frac{3 \left(\tan^{2}\left(d x +c \right)\right)}{2 b^{3} d}-\frac{10 \tan \left(d x +c \right) a^{3}}{d \,b^{6}}-\frac{9 a \tan \left(d x +c \right)}{b^{4} d}+\frac{15 \ln \left(a +b \tan \left(d x +c \right)\right) a^{4}}{d \,b^{7}}+\frac{18 \ln \left(a +b \tan \left(d x +c \right)\right) a^{2}}{d \,b^{5}}+\frac{3 \ln \left(a +b \tan \left(d x +c \right)\right)}{d \,b^{3}}-\frac{a^{6}}{2 d \,b^{7} \left(a +b \tan \left(d x +c \right)\right)^{2}}-\frac{3 a^{4}}{2 d \,b^{5} \left(a +b \tan \left(d x +c \right)\right)^{2}}-\frac{3 a^{2}}{2 d \,b^{3} \left(a +b \tan \left(d x +c \right)\right)^{2}}-\frac{1}{2 b d \left(a +b \tan \left(d x +c \right)\right)^{2}}+\frac{6 a^{5}}{d \,b^{7} \left(a +b \tan \left(d x +c \right)\right)}+\frac{12 a^{3}}{d \,b^{5} \left(a +b \tan \left(d x +c \right)\right)}+\frac{6 a}{d \,b^{3} \left(a +b \tan \left(d x +c \right)\right)}"," ",0,"1/4*tan(d*x+c)^4/b^3/d-a*tan(d*x+c)^3/b^4/d+3/d/b^5*tan(d*x+c)^2*a^2+3/2*tan(d*x+c)^2/b^3/d-10/d/b^6*tan(d*x+c)*a^3-9*a*tan(d*x+c)/b^4/d+15/d/b^7*ln(a+b*tan(d*x+c))*a^4+18/d/b^5*ln(a+b*tan(d*x+c))*a^2+3/d/b^3*ln(a+b*tan(d*x+c))-1/2/d/b^7/(a+b*tan(d*x+c))^2*a^6-3/2/d/b^5/(a+b*tan(d*x+c))^2*a^4-3/2/d/b^3/(a+b*tan(d*x+c))^2*a^2-1/2/b/d/(a+b*tan(d*x+c))^2+6/d*a^5/b^7/(a+b*tan(d*x+c))+12/d*a^3/b^5/(a+b*tan(d*x+c))+6/d*a/b^3/(a+b*tan(d*x+c))","A"
141,1,304,163,0.303000," ","int(cos(d*x+c)^4/(a*cos(d*x+c)+b*sin(d*x+c))^4,x)","-\frac{b}{3 \left(a^{2}+b^{2}\right) d \left(a +b \tan \left(d x +c \right)\right)^{3}}-\frac{3 b \,a^{2}}{d \left(a^{2}+b^{2}\right)^{3} \left(a +b \tan \left(d x +c \right)\right)}+\frac{b^{3}}{d \left(a^{2}+b^{2}\right)^{3} \left(a +b \tan \left(d x +c \right)\right)}-\frac{a b}{\left(a^{2}+b^{2}\right)^{2} d \left(a +b \tan \left(d x +c \right)\right)^{2}}+\frac{4 b \,a^{3} \ln \left(a +b \tan \left(d x +c \right)\right)}{d \left(a^{2}+b^{2}\right)^{4}}-\frac{4 b^{3} a \ln \left(a +b \tan \left(d x +c \right)\right)}{d \left(a^{2}+b^{2}\right)^{4}}-\frac{2 \ln \left(\tan^{2}\left(d x +c \right)+1\right) a^{3} b}{d \left(a^{2}+b^{2}\right)^{4}}+\frac{2 \ln \left(\tan^{2}\left(d x +c \right)+1\right) a \,b^{3}}{d \left(a^{2}+b^{2}\right)^{4}}+\frac{\arctan \left(\tan \left(d x +c \right)\right) a^{4}}{d \left(a^{2}+b^{2}\right)^{4}}-\frac{6 \arctan \left(\tan \left(d x +c \right)\right) a^{2} b^{2}}{d \left(a^{2}+b^{2}\right)^{4}}+\frac{\arctan \left(\tan \left(d x +c \right)\right) b^{4}}{d \left(a^{2}+b^{2}\right)^{4}}"," ",0,"-1/3*b/(a^2+b^2)/d/(a+b*tan(d*x+c))^3-3/d*b/(a^2+b^2)^3/(a+b*tan(d*x+c))*a^2+1/d*b^3/(a^2+b^2)^3/(a+b*tan(d*x+c))-a*b/(a^2+b^2)^2/d/(a+b*tan(d*x+c))^2+4/d*b*a^3/(a^2+b^2)^4*ln(a+b*tan(d*x+c))-4/d*b^3*a/(a^2+b^2)^4*ln(a+b*tan(d*x+c))-2/d/(a^2+b^2)^4*ln(tan(d*x+c)^2+1)*a^3*b+2/d/(a^2+b^2)^4*ln(tan(d*x+c)^2+1)*a*b^3+1/d/(a^2+b^2)^4*arctan(tan(d*x+c))*a^4-6/d/(a^2+b^2)^4*arctan(tan(d*x+c))*a^2*b^2+1/d/(a^2+b^2)^4*arctan(tan(d*x+c))*b^4","A"
142,1,494,151,0.309000," ","int(cos(d*x+c)^3/(a*cos(d*x+c)+b*sin(d*x+c))^4,x)","\frac{-\frac{2 \left(-\frac{b^{2} \left(9 a^{4}+6 a^{2} b^{2}+2 b^{4}\right) \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{2 a \left(a^{6}+3 a^{4} b^{2}+3 a^{2} b^{4}+b^{6}\right)}-\frac{b \left(6 a^{6}-27 a^{4} b^{2}-12 a^{2} b^{4}-4 b^{6}\right) \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{2 a^{2} \left(a^{6}+3 a^{4} b^{2}+3 a^{2} b^{4}+b^{6}\right)}+\frac{b^{2} \left(54 a^{6}-21 a^{4} b^{2}-4 a^{2} b^{4}-4 b^{6}\right) \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 a^{3} \left(a^{6}+3 a^{4} b^{2}+3 a^{2} b^{4}+b^{6}\right)}+\frac{b \left(6 a^{6}-20 a^{4} b^{2}-3 a^{2} b^{4}-2 b^{6}\right) \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a^{2} \left(a^{6}+3 a^{4} b^{2}+3 a^{2} b^{4}+b^{6}\right)}-\frac{b^{2} \left(27 a^{4}+4 a^{2} b^{2}+2 b^{4}\right) \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 a \left(a^{6}+3 a^{4} b^{2}+3 a^{2} b^{4}+b^{6}\right)}-\frac{b \left(18 a^{4}+5 a^{2} b^{2}+2 b^{4}\right)}{6 \left(a^{6}+3 a^{4} b^{2}+3 a^{2} b^{4}+b^{6}\right)}\right)}{\left(\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)-a \right)^{3}}+\frac{a \left(2 a^{2}-3 b^{2}\right) \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(a^{6}+3 a^{4} b^{2}+3 a^{2} b^{4}+b^{6}\right) \sqrt{a^{2}+b^{2}}}}{d}"," ",0,"1/d*(-2*(-1/2*b^2*(9*a^4+6*a^2*b^2+2*b^4)/a/(a^6+3*a^4*b^2+3*a^2*b^4+b^6)*tan(1/2*d*x+1/2*c)^5-1/2*b*(6*a^6-27*a^4*b^2-12*a^2*b^4-4*b^6)/a^2/(a^6+3*a^4*b^2+3*a^2*b^4+b^6)*tan(1/2*d*x+1/2*c)^4+1/3/a^3*b^2*(54*a^6-21*a^4*b^2-4*a^2*b^4-4*b^6)/(a^6+3*a^4*b^2+3*a^2*b^4+b^6)*tan(1/2*d*x+1/2*c)^3+1/a^2*b*(6*a^6-20*a^4*b^2-3*a^2*b^4-2*b^6)/(a^6+3*a^4*b^2+3*a^2*b^4+b^6)*tan(1/2*d*x+1/2*c)^2-1/2/a*b^2*(27*a^4+4*a^2*b^2+2*b^4)/(a^6+3*a^4*b^2+3*a^2*b^4+b^6)*tan(1/2*d*x+1/2*c)-1/6*b*(18*a^4+5*a^2*b^2+2*b^4)/(a^6+3*a^4*b^2+3*a^2*b^4+b^6))/(tan(1/2*d*x+1/2*c)^2*a-2*b*tan(1/2*d*x+1/2*c)-a)^3+a*(2*a^2-3*b^2)/(a^6+3*a^4*b^2+3*a^2*b^4+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)))","B"
143,1,21,28,0.302000," ","int(cos(d*x+c)^2/(a*cos(d*x+c)+b*sin(d*x+c))^4,x)","-\frac{1}{3 d b \left(a +b \tan \left(d x +c \right)\right)^{3}}"," ",0,"-1/3/d/b/(a+b*tan(d*x+c))^3","A"
144,1,383,131,0.303000," ","int(cos(d*x+c)/(a*cos(d*x+c)+b*sin(d*x+c))^4,x)","\frac{-\frac{2 \left(-\frac{\left(a^{4}+4 a^{2} b^{2}+2 b^{4}\right) \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{2 a \left(a^{4}+2 a^{2} b^{2}+b^{4}\right)}-\frac{b \left(a^{4}-8 a^{2} b^{2}-4 b^{4}\right) \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{2 a^{2} \left(a^{4}+2 a^{2} b^{2}+b^{4}\right)}+\frac{b^{2} \left(15 a^{4}-4 a^{2} b^{2}-4 b^{4}\right) \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 a^{3} \left(a^{4}+2 a^{2} b^{2}+b^{4}\right)}+\frac{b \left(2 a^{4}-5 a^{2} b^{2}-2 b^{4}\right) \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a^{2} \left(a^{4}+2 a^{2} b^{2}+b^{4}\right)}+\frac{\left(a^{4}-6 a^{2} b^{2}-2 b^{4}\right) \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 a \left(a^{4}+2 a^{2} b^{2}+b^{4}\right)}-\frac{b \left(5 a^{2}+2 b^{2}\right)}{6 \left(a^{4}+2 a^{2} b^{2}+b^{4}\right)}\right)}{\left(\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)-a \right)^{3}}+\frac{a \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(a^{4}+2 a^{2} b^{2}+b^{4}\right) \sqrt{a^{2}+b^{2}}}}{d}"," ",0,"1/d*(-2*(-1/2*(a^4+4*a^2*b^2+2*b^4)/a/(a^4+2*a^2*b^2+b^4)*tan(1/2*d*x+1/2*c)^5-1/2*b*(a^4-8*a^2*b^2-4*b^4)/a^2/(a^4+2*a^2*b^2+b^4)*tan(1/2*d*x+1/2*c)^4+1/3/a^3*b^2*(15*a^4-4*a^2*b^2-4*b^4)/(a^4+2*a^2*b^2+b^4)*tan(1/2*d*x+1/2*c)^3+1/a^2*b*(2*a^4-5*a^2*b^2-2*b^4)/(a^4+2*a^2*b^2+b^4)*tan(1/2*d*x+1/2*c)^2+1/2/a*(a^4-6*a^2*b^2-2*b^4)/(a^4+2*a^2*b^2+b^4)*tan(1/2*d*x+1/2*c)-1/6*b*(5*a^2+2*b^2)/(a^4+2*a^2*b^2+b^4))/(tan(1/2*d*x+1/2*c)^2*a-2*b*tan(1/2*d*x+1/2*c)-a)^3+a/(a^4+2*a^2*b^2+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)))","B"
145,1,64,94,0.279000," ","int(1/(a*cos(d*x+c)+b*sin(d*x+c))^4,x)","\frac{-\frac{1}{b^{3} \left(a +b \tan \left(d x +c \right)\right)}-\frac{a^{2}+b^{2}}{3 b^{3} \left(a +b \tan \left(d x +c \right)\right)^{3}}+\frac{a}{b^{3} \left(a +b \tan \left(d x +c \right)\right)^{2}}}{d}"," ",0,"1/d*(-1/b^3/(a+b*tan(d*x+c))-1/3*(a^2+b^2)/b^3/(a+b*tan(d*x+c))^3+a/b^3/(a+b*tan(d*x+c))^2)","A"
146,1,1367,217,0.420000," ","int(sec(d*x+c)/(a*cos(d*x+c)+b*sin(d*x+c))^4,x)","\frac{16 a^{2} \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d b \left(\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)-a \right)^{3} \left(a^{2}+b^{2}\right)}+\frac{4 b^{3} \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a -2 b \tan \left(\frac{d x}{2}+\frac{c}{2}\right)-a \right)^{3} a^{2} \left(a^{2}+b^{2}\right)}+\frac{11 a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,b^{2} \left(\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)-a \right)^{3} \left(a^{2}+b^{2}\right)}+\frac{2 b^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \left(\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)-a \right)^{3} a \left(a^{2}+b^{2}\right)}+\frac{a^{3} \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,b^{2} \left(\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)-a \right)^{3} \left(a^{2}+b^{2}\right)}+\frac{2 b^{2} \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a -2 b \tan \left(\frac{d x}{2}+\frac{c}{2}\right)-a \right)^{3} a \left(a^{2}+b^{2}\right)}+\frac{2 a^{4} \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,b^{3} \left(\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)-a \right)^{3} \left(a^{2}+b^{2}\right)}-\frac{3 a^{2} \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d b \left(\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)-a \right)^{3} \left(a^{2}+b^{2}\right)}-\frac{4 b^{3} \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a -2 b \tan \left(\frac{d x}{2}+\frac{c}{2}\right)-a \right)^{3} \left(a^{2}+b^{2}\right) a^{2}}-\frac{12 a^{3} \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,b^{2} \left(\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)-a \right)^{3} \left(a^{2}+b^{2}\right)}+\frac{8 b^{2} \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 d \left(\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)-a \right)^{3} a \left(a^{2}+b^{2}\right)}+\frac{8 b^{4} \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 d \left(\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)-a \right)^{3} a^{3} \left(a^{2}+b^{2}\right)}-\frac{4 a^{4} \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,b^{3} \left(\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)-a \right)^{3} \left(a^{2}+b^{2}\right)}-\frac{2 a \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a -2 b \tan \left(\frac{d x}{2}+\frac{c}{2}\right)-a \right)^{3} \left(a^{2}+b^{2}\right)}+\frac{8 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \left(\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)-a \right)^{3} \left(a^{2}+b^{2}\right)}-\frac{4 b \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a -2 b \tan \left(\frac{d x}{2}+\frac{c}{2}\right)-a \right)^{3} \left(a^{2}+b^{2}\right)}+\frac{14 b \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a -2 b \tan \left(\frac{d x}{2}+\frac{c}{2}\right)-a \right)^{3} \left(a^{2}+b^{2}\right)}+\frac{2 a^{4}}{d \,b^{3} \left(\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)-a \right)^{3} \left(a^{2}+b^{2}\right)}+\frac{5 a^{2}}{3 d b \left(\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)-a \right)^{3} \left(a^{2}+b^{2}\right)}+\frac{2 a \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a -2 b \tan \left(\frac{d x}{2}+\frac{c}{2}\right)-a \right)^{3} \left(a^{2}+b^{2}\right)}-\frac{2 a^{3} \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 \,b^{4} \left(a^{2}+b^{2}\right)^{\frac{3}{2}}}-\frac{3 a \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 \,b^{2} \left(a^{2}+b^{2}\right)^{\frac{3}{2}}}+\frac{2 b}{3 d \left(\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)-a \right)^{3} \left(a^{2}+b^{2}\right)}-\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}{d \,b^{4}}+\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}{d \,b^{4}}"," ",0,"2/d/(tan(1/2*d*x+1/2*c)^2*a-2*b*tan(1/2*d*x+1/2*c)-a)^3*a/(a^2+b^2)*tan(1/2*d*x+1/2*c)^5+16/d/b/(tan(1/2*d*x+1/2*c)^2*a-2*b*tan(1/2*d*x+1/2*c)-a)^3*a^2/(a^2+b^2)*tan(1/2*d*x+1/2*c)^2+4/d*b^3/(tan(1/2*d*x+1/2*c)^2*a-2*b*tan(1/2*d*x+1/2*c)-a)^3/a^2/(a^2+b^2)*tan(1/2*d*x+1/2*c)^2+11/d/b^2/(tan(1/2*d*x+1/2*c)^2*a-2*b*tan(1/2*d*x+1/2*c)-a)^3*a^3/(a^2+b^2)*tan(1/2*d*x+1/2*c)+2/d*b^2/(tan(1/2*d*x+1/2*c)^2*a-2*b*tan(1/2*d*x+1/2*c)-a)^3/a/(a^2+b^2)*tan(1/2*d*x+1/2*c)+1/d/b^2/(tan(1/2*d*x+1/2*c)^2*a-2*b*tan(1/2*d*x+1/2*c)-a)^3*a^3/(a^2+b^2)*tan(1/2*d*x+1/2*c)^5+2/d*b^2/(tan(1/2*d*x+1/2*c)^2*a-2*b*tan(1/2*d*x+1/2*c)-a)^3/a/(a^2+b^2)*tan(1/2*d*x+1/2*c)^5+2/d/b^3/(tan(1/2*d*x+1/2*c)^2*a-2*b*tan(1/2*d*x+1/2*c)-a)^3/(a^2+b^2)*a^4*tan(1/2*d*x+1/2*c)^4-3/d/b/(tan(1/2*d*x+1/2*c)^2*a-2*b*tan(1/2*d*x+1/2*c)-a)^3/(a^2+b^2)*a^2*tan(1/2*d*x+1/2*c)^4-4/d*b^3/(tan(1/2*d*x+1/2*c)^2*a-2*b*tan(1/2*d*x+1/2*c)-a)^3/(a^2+b^2)/a^2*tan(1/2*d*x+1/2*c)^4-12/d/b^2/(tan(1/2*d*x+1/2*c)^2*a-2*b*tan(1/2*d*x+1/2*c)-a)^3*a^3/(a^2+b^2)*tan(1/2*d*x+1/2*c)^3+8/3/d*b^2/(tan(1/2*d*x+1/2*c)^2*a-2*b*tan(1/2*d*x+1/2*c)-a)^3/a/(a^2+b^2)*tan(1/2*d*x+1/2*c)^3+8/3/d*b^4/(tan(1/2*d*x+1/2*c)^2*a-2*b*tan(1/2*d*x+1/2*c)-a)^3/a^3/(a^2+b^2)*tan(1/2*d*x+1/2*c)^3-4/d/b^3/(tan(1/2*d*x+1/2*c)^2*a-2*b*tan(1/2*d*x+1/2*c)-a)^3*a^4/(a^2+b^2)*tan(1/2*d*x+1/2*c)^2+2/3/d*b/(tan(1/2*d*x+1/2*c)^2*a-2*b*tan(1/2*d*x+1/2*c)-a)^3/(a^2+b^2)-2/d/(tan(1/2*d*x+1/2*c)^2*a-2*b*tan(1/2*d*x+1/2*c)-a)^3*a/(a^2+b^2)*tan(1/2*d*x+1/2*c)^3+8/d/(tan(1/2*d*x+1/2*c)^2*a-2*b*tan(1/2*d*x+1/2*c)-a)^3*a/(a^2+b^2)*tan(1/2*d*x+1/2*c)-4/d*b/(tan(1/2*d*x+1/2*c)^2*a-2*b*tan(1/2*d*x+1/2*c)-a)^3/(a^2+b^2)*tan(1/2*d*x+1/2*c)^4+14/d*b/(tan(1/2*d*x+1/2*c)^2*a-2*b*tan(1/2*d*x+1/2*c)-a)^3/(a^2+b^2)*tan(1/2*d*x+1/2*c)^2+2/d/b^3/(tan(1/2*d*x+1/2*c)^2*a-2*b*tan(1/2*d*x+1/2*c)-a)^3/(a^2+b^2)*a^4+5/3/d/b/(tan(1/2*d*x+1/2*c)^2*a-2*b*tan(1/2*d*x+1/2*c)-a)^3/(a^2+b^2)*a^2-2/d/b^4*a^3/(a^2+b^2)^(3/2)*arctanh(1/2*(2*a*tan(1/2*d*x+1/2*c)-2*b)/(a^2+b^2)^(1/2))-3/d/b^2*a/(a^2+b^2)^(3/2)*arctanh(1/2*(2*a*tan(1/2*d*x+1/2*c)-2*b)/(a^2+b^2)^(1/2))-1/d/b^4*ln(tan(1/2*d*x+1/2*c)-1)+1/d/b^4*ln(tan(1/2*d*x+1/2*c)+1)","B"
147,1,188,136,0.411000," ","int(sec(d*x+c)^2/(a*cos(d*x+c)+b*sin(d*x+c))^4,x)","\frac{\tan \left(d x +c \right)}{b^{4} d}-\frac{4 a \ln \left(a +b \tan \left(d x +c \right)\right)}{d \,b^{5}}-\frac{6 a^{2}}{d \,b^{5} \left(a +b \tan \left(d x +c \right)\right)}-\frac{2}{d \,b^{3} \left(a +b \tan \left(d x +c \right)\right)}-\frac{a^{4}}{3 d \,b^{5} \left(a +b \tan \left(d x +c \right)\right)^{3}}-\frac{2 a^{2}}{3 d \,b^{3} \left(a +b \tan \left(d x +c \right)\right)^{3}}-\frac{1}{3 d b \left(a +b \tan \left(d x +c \right)\right)^{3}}+\frac{2 a^{3}}{d \,b^{5} \left(a +b \tan \left(d x +c \right)\right)^{2}}+\frac{2 a}{d \,b^{3} \left(a +b \tan \left(d x +c \right)\right)^{2}}"," ",0,"tan(d*x+c)/b^4/d-4/d*a/b^5*ln(a+b*tan(d*x+c))-6/d/b^5/(a+b*tan(d*x+c))*a^2-2/d/b^3/(a+b*tan(d*x+c))-1/3/d/b^5/(a+b*tan(d*x+c))^3*a^4-2/3/d/b^3/(a+b*tan(d*x+c))^3*a^2-1/3/d/b/(a+b*tan(d*x+c))^3+2/d*a^3/b^5/(a+b*tan(d*x+c))^2+2/d*a/b^3/(a+b*tan(d*x+c))^2","A"
148,1,1255,382,0.473000," ","int(sec(d*x+c)^3/(a*cos(d*x+c)+b*sin(d*x+c))^4,x)","\frac{2}{3 d b \left(\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)-a \right)^{3}}+\frac{1}{2 d \,b^{4} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}+\frac{1}{2 d \,b^{4} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{1}{2 d \,b^{4} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}+\frac{1}{2 d \,b^{4} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}+\frac{4 a}{d \,b^{5} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{10 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right) a^{2}}{d \,b^{6}}-\frac{4 a}{d \,b^{5} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}+\frac{10 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right) a^{2}}{d \,b^{6}}+\frac{18 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d b \left(\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)-a \right)^{3}}+\frac{12 a^{4}}{d \,b^{5} \left(\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)-a \right)^{3}}+\frac{5 a^{2}}{3 d \,b^{3} \left(\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)-a \right)^{3}}+\frac{2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \left(\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)-a \right)^{3} a}+\frac{2 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a -2 b \tan \left(\frac{d x}{2}+\frac{c}{2}\right)-a \right)^{3} a}+\frac{8 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 d \left(\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)-a \right)^{3} a}-\frac{20 a^{3} \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 \,b^{6} \sqrt{a^{2}+b^{2}}}-\frac{15 a \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 \,b^{4} \sqrt{a^{2}+b^{2}}}+\frac{8 b^{2} \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 d \left(\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)-a \right)^{3} a^{3}}-\frac{24 a^{4} \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,b^{5} \left(\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)-a \right)^{3}}+\frac{100 a^{2} \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,b^{3} \left(\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)-a \right)^{3}}+\frac{4 b \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a -2 b \tan \left(\frac{d x}{2}+\frac{c}{2}\right)-a \right)^{3} a^{2}}+\frac{63 a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,b^{4} \left(\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)-a \right)^{3}}+\frac{10 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,b^{2} \left(\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)-a \right)^{3}}+\frac{9 a^{3} \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,b^{4} \left(\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)-a \right)^{3}}+\frac{12 a^{4} \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,b^{5} \left(\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)-a \right)^{3}}-\frac{39 a^{2} \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,b^{3} \left(\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)-a \right)^{3}}-\frac{4 b \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a -2 b \tan \left(\frac{d x}{2}+\frac{c}{2}\right)-a \right)^{3} a^{2}}-\frac{72 a^{3} \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,b^{4} \left(\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)-a \right)^{3}}+\frac{38 a \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,b^{2} \left(\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)-a \right)^{3}}-\frac{5 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}{2 d \,b^{4}}+\frac{5 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}{2 d \,b^{4}}"," ",0,"2/3/d/b/(tan(1/2*d*x+1/2*c)^2*a-2*b*tan(1/2*d*x+1/2*c)-a)^3+1/2/d/b^4/(tan(1/2*d*x+1/2*c)-1)^2+1/2/d/b^4/(tan(1/2*d*x+1/2*c)-1)-1/2/d/b^4/(tan(1/2*d*x+1/2*c)+1)^2+1/2/d/b^4/(tan(1/2*d*x+1/2*c)+1)+18/d/b/(tan(1/2*d*x+1/2*c)^2*a-2*b*tan(1/2*d*x+1/2*c)-a)^3*tan(1/2*d*x+1/2*c)^2+12/d/b^5/(tan(1/2*d*x+1/2*c)^2*a-2*b*tan(1/2*d*x+1/2*c)-a)^3*a^4+5/3/d/b^3/(tan(1/2*d*x+1/2*c)^2*a-2*b*tan(1/2*d*x+1/2*c)-a)^3*a^2+2/d/(tan(1/2*d*x+1/2*c)^2*a-2*b*tan(1/2*d*x+1/2*c)-a)^3/a*tan(1/2*d*x+1/2*c)+2/d/(tan(1/2*d*x+1/2*c)^2*a-2*b*tan(1/2*d*x+1/2*c)-a)^3/a*tan(1/2*d*x+1/2*c)^5+8/3/d/(tan(1/2*d*x+1/2*c)^2*a-2*b*tan(1/2*d*x+1/2*c)-a)^3/a*tan(1/2*d*x+1/2*c)^3+4/d/b^5/(tan(1/2*d*x+1/2*c)-1)*a-10/d/b^6*ln(tan(1/2*d*x+1/2*c)-1)*a^2-4/d/b^5/(tan(1/2*d*x+1/2*c)+1)*a+10/d/b^6*ln(tan(1/2*d*x+1/2*c)+1)*a^2+8/3/d*b^2/(tan(1/2*d*x+1/2*c)^2*a-2*b*tan(1/2*d*x+1/2*c)-a)^3/a^3*tan(1/2*d*x+1/2*c)^3-24/d/b^5/(tan(1/2*d*x+1/2*c)^2*a-2*b*tan(1/2*d*x+1/2*c)-a)^3*a^4*tan(1/2*d*x+1/2*c)^2+100/d/b^3/(tan(1/2*d*x+1/2*c)^2*a-2*b*tan(1/2*d*x+1/2*c)-a)^3*a^2*tan(1/2*d*x+1/2*c)^2+4/d*b/(tan(1/2*d*x+1/2*c)^2*a-2*b*tan(1/2*d*x+1/2*c)-a)^3/a^2*tan(1/2*d*x+1/2*c)^2+63/d/b^4/(tan(1/2*d*x+1/2*c)^2*a-2*b*tan(1/2*d*x+1/2*c)-a)^3*a^3*tan(1/2*d*x+1/2*c)+10/d/b^2/(tan(1/2*d*x+1/2*c)^2*a-2*b*tan(1/2*d*x+1/2*c)-a)^3*a*tan(1/2*d*x+1/2*c)-20/d/b^6*a^3/(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))-15/d/b^4*a/(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))+9/d/b^4/(tan(1/2*d*x+1/2*c)^2*a-2*b*tan(1/2*d*x+1/2*c)-a)^3*a^3*tan(1/2*d*x+1/2*c)^5+12/d/b^5/(tan(1/2*d*x+1/2*c)^2*a-2*b*tan(1/2*d*x+1/2*c)-a)^3*a^4*tan(1/2*d*x+1/2*c)^4-39/d/b^3/(tan(1/2*d*x+1/2*c)^2*a-2*b*tan(1/2*d*x+1/2*c)-a)^3*a^2*tan(1/2*d*x+1/2*c)^4-4/d*b/(tan(1/2*d*x+1/2*c)^2*a-2*b*tan(1/2*d*x+1/2*c)-a)^3/a^2*tan(1/2*d*x+1/2*c)^4-72/d/b^4/(tan(1/2*d*x+1/2*c)^2*a-2*b*tan(1/2*d*x+1/2*c)-a)^3*a^3*tan(1/2*d*x+1/2*c)^3+38/d/b^2/(tan(1/2*d*x+1/2*c)^2*a-2*b*tan(1/2*d*x+1/2*c)-a)^3*a*tan(1/2*d*x+1/2*c)^3-5/2/d/b^4*ln(tan(1/2*d*x+1/2*c)-1)+5/2/d/b^4*ln(tan(1/2*d*x+1/2*c)+1)","B"
149,1,330,228,0.428000," ","int(sec(d*x+c)^4/(a*cos(d*x+c)+b*sin(d*x+c))^4,x)","\frac{\tan^{3}\left(d x +c \right)}{3 b^{4} d}-\frac{2 a \left(\tan^{2}\left(d x +c \right)\right)}{b^{5} d}+\frac{10 a^{2} \tan \left(d x +c \right)}{d \,b^{6}}+\frac{3 \tan \left(d x +c \right)}{b^{4} d}-\frac{20 a^{3} \ln \left(a +b \tan \left(d x +c \right)\right)}{d \,b^{7}}-\frac{12 a \ln \left(a +b \tan \left(d x +c \right)\right)}{d \,b^{5}}+\frac{3 a^{5}}{d \,b^{7} \left(a +b \tan \left(d x +c \right)\right)^{2}}+\frac{6 a^{3}}{d \,b^{5} \left(a +b \tan \left(d x +c \right)\right)^{2}}+\frac{3 a}{d \,b^{3} \left(a +b \tan \left(d x +c \right)\right)^{2}}-\frac{a^{6}}{3 d \,b^{7} \left(a +b \tan \left(d x +c \right)\right)^{3}}-\frac{a^{4}}{d \,b^{5} \left(a +b \tan \left(d x +c \right)\right)^{3}}-\frac{a^{2}}{d \,b^{3} \left(a +b \tan \left(d x +c \right)\right)^{3}}-\frac{1}{3 d b \left(a +b \tan \left(d x +c \right)\right)^{3}}-\frac{15 a^{4}}{d \,b^{7} \left(a +b \tan \left(d x +c \right)\right)}-\frac{18 a^{2}}{d \,b^{5} \left(a +b \tan \left(d x +c \right)\right)}-\frac{3}{d \,b^{3} \left(a +b \tan \left(d x +c \right)\right)}"," ",0,"1/3*tan(d*x+c)^3/b^4/d-2*a*tan(d*x+c)^2/b^5/d+10/d/b^6*a^2*tan(d*x+c)+3*tan(d*x+c)/b^4/d-20/d/b^7*a^3*ln(a+b*tan(d*x+c))-12/d*a/b^5*ln(a+b*tan(d*x+c))+3/d*a^5/b^7/(a+b*tan(d*x+c))^2+6/d*a^3/b^5/(a+b*tan(d*x+c))^2+3/d*a/b^3/(a+b*tan(d*x+c))^2-1/3/d/b^7/(a+b*tan(d*x+c))^3*a^6-1/d/b^5/(a+b*tan(d*x+c))^3*a^4-1/d/b^3/(a+b*tan(d*x+c))^3*a^2-1/3/d/b/(a+b*tan(d*x+c))^3-15/d/b^7/(a+b*tan(d*x+c))*a^4-18/d/b^5/(a+b*tan(d*x+c))*a^2-3/d/b^3/(a+b*tan(d*x+c))","A"
150,1,137,88,0.231000," ","int(cos(d*x+c)^5/(a*cos(d*x+c)+I*a*sin(d*x+c)),x)","\frac{i}{32 a d \left(\tan \left(d x +c \right)+i\right)^{2}}+\frac{5 i \ln \left(\tan \left(d x +c \right)+i\right)}{32 a d}+\frac{1}{8 a d \left(\tan \left(d x +c \right)+i\right)}-\frac{5 i \ln \left(\tan \left(d x +c \right)-i\right)}{32 a d}-\frac{3 i}{32 a d \left(\tan \left(d x +c \right)-i\right)^{2}}-\frac{1}{24 a d \left(\tan \left(d x +c \right)-i\right)^{3}}+\frac{3}{16 a d \left(\tan \left(d x +c \right)-i\right)}"," ",0,"1/32*I/a/d/(tan(d*x+c)+I)^2+5/32*I/a/d*ln(tan(d*x+c)+I)+1/8/a/d/(tan(d*x+c)+I)-5/32*I/a/d*ln(tan(d*x+c)-I)-3/32*I/a/d/(tan(d*x+c)-I)^2-1/24/a/d/(tan(d*x+c)-I)^3+3/16/a/d/(tan(d*x+c)-I)","A"
151,1,141,63,0.165000," ","int(cos(d*x+c)^4/(a*cos(d*x+c)+I*a*sin(d*x+c)),x)","\frac{-\frac{i}{4 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+i\right)^{2}}-\frac{1}{6 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+i\right)^{3}}+\frac{5}{8 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+i\right)}-\frac{i}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{4}}+\frac{3 i}{2 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{2}}+\frac{2}{5 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{5}}-\frac{5}{3 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{3}}+\frac{11}{8 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)}}{a d}"," ",0,"2/d/a*(-1/8*I/(tan(1/2*d*x+1/2*c)+I)^2-1/12/(tan(1/2*d*x+1/2*c)+I)^3+5/16/(tan(1/2*d*x+1/2*c)+I)-1/2*I/(tan(1/2*d*x+1/2*c)-I)^4+3/4*I/(tan(1/2*d*x+1/2*c)-I)^2+1/5/(tan(1/2*d*x+1/2*c)-I)^5-5/6/(tan(1/2*d*x+1/2*c)-I)^3+11/16/(tan(1/2*d*x+1/2*c)-I))","B"
152,1,98,66,0.161000," ","int(cos(d*x+c)^3/(a*cos(d*x+c)+I*a*sin(d*x+c)),x)","\frac{3 i \ln \left(\tan \left(d x +c \right)+i\right)}{16 a d}+\frac{1}{8 a d \left(\tan \left(d x +c \right)+i\right)}-\frac{3 i \ln \left(\tan \left(d x +c \right)-i\right)}{16 a d}-\frac{i}{8 a d \left(\tan \left(d x +c \right)-i\right)^{2}}+\frac{1}{4 a d \left(\tan \left(d x +c \right)-i\right)}"," ",0,"3/16*I/a/d*ln(tan(d*x+c)+I)+1/8/a/d/(tan(d*x+c)+I)-3/16*I/a/d*ln(tan(d*x+c)-I)-1/8*I/a/d/(tan(d*x+c)-I)^2+1/4/a/d/(tan(d*x+c)-I)","A"
153,1,75,47,0.161000," ","int(cos(d*x+c)^2/(a*cos(d*x+c)+I*a*sin(d*x+c)),x)","\frac{\frac{2}{4 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+4 i}-\frac{2}{3 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{3}}+\frac{i}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{2}}+\frac{3}{2 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)}}{a d}"," ",0,"2/d/a*(1/4/(tan(1/2*d*x+1/2*c)+I)-1/3/(tan(1/2*d*x+1/2*c)-I)^3+1/2*I/(tan(1/2*d*x+1/2*c)-I)^2+3/4/(tan(1/2*d*x+1/2*c)-I))","A"
154,1,59,40,0.148000," ","int(cos(d*x+c)/(a*cos(d*x+c)+I*a*sin(d*x+c)),x)","\frac{i \ln \left(\tan \left(d x +c \right)+i\right)}{4 a d}-\frac{i \ln \left(\tan \left(d x +c \right)-i\right)}{4 a d}+\frac{1}{2 a d \left(\tan \left(d x +c \right)-i\right)}"," ",0,"1/4*I/a/d*ln(tan(d*x+c)+I)-1/4*I/a/d*ln(tan(d*x+c)-I)+1/2/a/d/(tan(d*x+c)-I)","A"
155,1,23,27,0.134000," ","int(1/(a*cos(d*x+c)+I*a*sin(d*x+c)),x)","\frac{2}{d a \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)}"," ",0,"2/d/a/(tan(1/2*d*x+1/2*c)-I)","A"
156,1,22,22,0.181000," ","int(sec(d*x+c)/(a*cos(d*x+c)+I*a*sin(d*x+c)),x)","-\frac{i \ln \left(i \tan \left(d x +c \right)+1\right)}{d a}"," ",0,"-I/d/a*ln(I*tan(d*x+c)+1)","A"
157,1,85,30,0.211000," ","int(sec(d*x+c)^2/(a*cos(d*x+c)+I*a*sin(d*x+c)),x)","\frac{i}{a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}{a d}-\frac{i}{a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}+\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}{a d}"," ",0,"I/a/d/(tan(1/2*d*x+1/2*c)-1)-1/a/d*ln(tan(1/2*d*x+1/2*c)-1)-I/a/d/(tan(1/2*d*x+1/2*c)+1)+1/a/d*ln(tan(1/2*d*x+1/2*c)+1)","B"
158,1,26,31,0.220000," ","int(sec(d*x+c)^3/(a*cos(d*x+c)+I*a*sin(d*x+c)),x)","\frac{\tan \left(d x +c \right)-\frac{i \left(\tan^{2}\left(d x +c \right)\right)}{2}}{d a}"," ",0,"1/d/a*(tan(d*x+c)-1/2*I*tan(d*x+c)^2)","A"
159,1,258,53,0.231000," ","int(sec(d*x+c)^4/(a*cos(d*x+c)+I*a*sin(d*x+c)),x)","\frac{i}{3 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{3}}+\frac{1}{2 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}+\frac{i}{2 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}+\frac{1}{2 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}+\frac{i}{2 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}{2 a d}-\frac{i}{3 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}+\frac{1}{2 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}-\frac{i}{2 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}-\frac{1}{2 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}+\frac{i}{2 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}+\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}{2 a d}"," ",0,"1/3*I/a/d/(tan(1/2*d*x+1/2*c)-1)^3+1/2/a/d/(tan(1/2*d*x+1/2*c)-1)^2+1/2*I/a/d/(tan(1/2*d*x+1/2*c)-1)^2+1/2/a/d/(tan(1/2*d*x+1/2*c)-1)+1/2*I/a/d/(tan(1/2*d*x+1/2*c)-1)-1/2/a/d*ln(tan(1/2*d*x+1/2*c)-1)-1/3*I/a/d/(tan(1/2*d*x+1/2*c)+1)^3+1/2/a/d/(tan(1/2*d*x+1/2*c)+1)-1/2*I/a/d/(tan(1/2*d*x+1/2*c)+1)-1/2/a/d/(tan(1/2*d*x+1/2*c)+1)^2+1/2*I/a/d/(tan(1/2*d*x+1/2*c)+1)^2+1/2/a/d*ln(tan(1/2*d*x+1/2*c)+1)","B"
160,1,47,47,0.223000," ","int(sec(d*x+c)^5/(a*cos(d*x+c)+I*a*sin(d*x+c)),x)","\frac{\tan \left(d x +c \right)-\frac{i \left(\tan^{4}\left(d x +c \right)\right)}{4}+\frac{\left(\tan^{3}\left(d x +c \right)\right)}{3}-\frac{i \left(\tan^{2}\left(d x +c \right)\right)}{2}}{d a}"," ",0,"1/d/a*(tan(d*x+c)-1/4*I*tan(d*x+c)^4+1/3*tan(d*x+c)^3-1/2*I*tan(d*x+c)^2)","A"
161,1,430,75,0.237000," ","int(sec(d*x+c)^6/(a*cos(d*x+c)+I*a*sin(d*x+c)),x)","\frac{5 i}{8 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}+\frac{7}{8 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}-\frac{3 i}{4 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}+\frac{5}{8 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}+\frac{i}{5 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{5}}+\frac{1}{2 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{3}}-\frac{i}{5 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{5}}+\frac{1}{4 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{4}}+\frac{3 i}{8 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{3 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}{8 a d}+\frac{i}{2 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{4}}+\frac{5}{8 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}+\frac{3 i}{4 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{3}}+\frac{1}{2 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}+\frac{i}{2 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{4}}-\frac{1}{4 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{4}}-\frac{3 i}{8 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}-\frac{7}{8 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}+\frac{5 i}{8 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}+\frac{3 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}{8 a d}"," ",0,"5/8*I/a/d/(tan(1/2*d*x+1/2*c)-1)^2+7/8/a/d/(tan(1/2*d*x+1/2*c)-1)^2-3/4*I/a/d/(tan(1/2*d*x+1/2*c)+1)^3+5/8/a/d/(tan(1/2*d*x+1/2*c)-1)+1/5*I/a/d/(tan(1/2*d*x+1/2*c)-1)^5+1/2/a/d/(tan(1/2*d*x+1/2*c)-1)^3-1/5*I/a/d/(tan(1/2*d*x+1/2*c)+1)^5+1/4/a/d/(tan(1/2*d*x+1/2*c)-1)^4+3/8*I/a/d/(tan(1/2*d*x+1/2*c)-1)-3/8/a/d*ln(tan(1/2*d*x+1/2*c)-1)+1/2*I/a/d/(tan(1/2*d*x+1/2*c)+1)^4+5/8/a/d/(tan(1/2*d*x+1/2*c)+1)+3/4*I/a/d/(tan(1/2*d*x+1/2*c)-1)^3+1/2/a/d/(tan(1/2*d*x+1/2*c)+1)^3+1/2*I/a/d/(tan(1/2*d*x+1/2*c)-1)^4-1/4/a/d/(tan(1/2*d*x+1/2*c)+1)^4-3/8*I/a/d/(tan(1/2*d*x+1/2*c)+1)-7/8/a/d/(tan(1/2*d*x+1/2*c)+1)^2+5/8*I/a/d/(tan(1/2*d*x+1/2*c)+1)^2+3/8/a/d*ln(tan(1/2*d*x+1/2*c)+1)","B"
162,1,68,63,0.231000," ","int(sec(d*x+c)^7/(a*cos(d*x+c)+I*a*sin(d*x+c)),x)","\frac{\tan \left(d x +c \right)-\frac{i \left(\tan^{6}\left(d x +c \right)\right)}{6}+\frac{\left(\tan^{5}\left(d x +c \right)\right)}{5}-\frac{i \left(\tan^{4}\left(d x +c \right)\right)}{2}+\frac{2 \left(\tan^{3}\left(d x +c \right)\right)}{3}-\frac{i \left(\tan^{2}\left(d x +c \right)\right)}{2}}{d a}"," ",0,"1/d/a*(tan(d*x+c)-1/6*I*tan(d*x+c)^6+1/5*tan(d*x+c)^5-1/2*I*tan(d*x+c)^4+2/3*tan(d*x+c)^3-1/2*I*tan(d*x+c)^2)","A"
163,1,174,78,0.194000," ","int(cos(d*x+c)^5/(a*cos(d*x+c)+I*a*sin(d*x+c))^2,x)","\frac{-\frac{i}{8 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+i\right)^{2}}-\frac{1}{12 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+i\right)^{3}}+\frac{3}{8 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+i\right)}+\frac{2 i}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{6}}-\frac{5 i}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{4}}+\frac{23 i}{8 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{2}}-\frac{4}{7 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{7}}+\frac{4}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{5}}-\frac{55}{12 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{3}}+\frac{13}{8 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)}}{d \,a^{2}}"," ",0,"2/d/a^2*(-1/16*I/(tan(1/2*d*x+1/2*c)+I)^2-1/24/(tan(1/2*d*x+1/2*c)+I)^3+3/16/(tan(1/2*d*x+1/2*c)+I)+I/(tan(1/2*d*x+1/2*c)-I)^6-5/2*I/(tan(1/2*d*x+1/2*c)-I)^4+23/16*I/(tan(1/2*d*x+1/2*c)-I)^2-2/7/(tan(1/2*d*x+1/2*c)-I)^7+2/(tan(1/2*d*x+1/2*c)-I)^5-55/24/(tan(1/2*d*x+1/2*c)-I)^3+13/16/(tan(1/2*d*x+1/2*c)-I))","B"
164,1,117,86,0.201000," ","int(cos(d*x+c)^4/(a*cos(d*x+c)+I*a*sin(d*x+c))^2,x)","\frac{i \ln \left(\tan \left(d x +c \right)+i\right)}{8 a^{2} d}+\frac{1}{16 a^{2} d \left(\tan \left(d x +c \right)+i\right)}-\frac{i \ln \left(\tan \left(d x +c \right)-i\right)}{8 a^{2} d}-\frac{i}{8 a^{2} d \left(\tan \left(d x +c \right)-i\right)^{2}}-\frac{1}{12 a^{2} d \left(\tan \left(d x +c \right)-i\right)^{3}}+\frac{3}{16 a^{2} d \left(\tan \left(d x +c \right)-i\right)}"," ",0,"1/8*I/a^2/d*ln(tan(d*x+c)+I)+1/16/a^2/d/(tan(d*x+c)+I)-1/8*I/a^2/d*ln(tan(d*x+c)-I)-1/8*I/a^2/d/(tan(d*x+c)-I)^2-1/12/a^2/d/(tan(d*x+c)-I)^3+3/16/a^2/d/(tan(d*x+c)-I)","A"
165,1,108,63,0.184000," ","int(cos(d*x+c)^3/(a*cos(d*x+c)+I*a*sin(d*x+c))^2,x)","\frac{\frac{2}{8 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+8 i}-\frac{2 i}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{4}}+\frac{5 i}{2 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{2}}+\frac{4}{5 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{5}}-\frac{3}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{3}}+\frac{7}{4 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)}}{d \,a^{2}}"," ",0,"2/d/a^2*(1/8/(tan(1/2*d*x+1/2*c)+I)-I/(tan(1/2*d*x+1/2*c)-I)^4+5/4*I/(tan(1/2*d*x+1/2*c)-I)^2+2/5/(tan(1/2*d*x+1/2*c)-I)^5-3/2/(tan(1/2*d*x+1/2*c)-I)^3+7/8/(tan(1/2*d*x+1/2*c)-I))","A"
166,1,79,79,0.190000," ","int(cos(d*x+c)^2/(a*cos(d*x+c)+I*a*sin(d*x+c))^2,x)","\frac{i \ln \left(\tan \left(d x +c \right)+i\right)}{8 a^{2} d}-\frac{i \ln \left(\tan \left(d x +c \right)-i\right)}{8 a^{2} d}-\frac{i}{4 a^{2} d \left(\tan \left(d x +c \right)-i\right)^{2}}+\frac{1}{4 a^{2} d \left(\tan \left(d x +c \right)-i\right)}"," ",0,"1/8*I/a^2/d*ln(tan(d*x+c)+I)-1/8*I/a^2/d*ln(tan(d*x+c)-I)-1/4*I/a^2/d/(tan(d*x+c)-I)^2+1/4/a^2/d/(tan(d*x+c)-I)","A"
167,1,57,47,0.168000," ","int(cos(d*x+c)/(a*cos(d*x+c)+I*a*sin(d*x+c))^2,x)","\frac{\frac{2}{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i}+\frac{2 i}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{2}}-\frac{4}{3 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{3}}}{d \,a^{2}}"," ",0,"2/d/a^2*(1/(tan(1/2*d*x+1/2*c)-I)+I/(tan(1/2*d*x+1/2*c)-I)^2-2/3/(tan(1/2*d*x+1/2*c)-I)^3)","A"
168,1,23,27,0.154000," ","int(1/(a*cos(d*x+c)+I*a*sin(d*x+c))^2,x)","\frac{i}{d \,a^{2} \left(i \tan \left(d x +c \right)+1\right)}"," ",0,"I/d/a^2/(I*tan(d*x+c)+1)","A"
169,1,63,45,0.227000," ","int(sec(d*x+c)/(a*cos(d*x+c)+I*a*sin(d*x+c))^2,x)","\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}{a^{2} d}-\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}{a^{2} d}+\frac{4}{a^{2} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)}"," ",0,"1/a^2/d*ln(tan(1/2*d*x+1/2*c)-1)-1/a^2/d*ln(tan(1/2*d*x+1/2*c)+1)+4/a^2/d/(tan(1/2*d*x+1/2*c)-I)","A"
170,1,35,53,0.241000," ","int(sec(d*x+c)^2/(a*cos(d*x+c)+I*a*sin(d*x+c))^2,x)","-\frac{2 i \ln \left(\tan \left(d x +c \right)-i\right)}{a^{2} d}-\frac{\tan \left(d x +c \right)}{a^{2} d}"," ",0,"-2*I/a^2/d*ln(tan(d*x+c)-I)-tan(d*x+c)/a^2/d","A"
171,1,170,51,0.250000," ","int(sec(d*x+c)^3/(a*cos(d*x+c)+I*a*sin(d*x+c))^2,x)","-\frac{1}{2 a^{2} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}+\frac{2 i}{a^{2} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{1}{2 a^{2} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}-\frac{3 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}{2 a^{2} d}-\frac{1}{2 a^{2} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}-\frac{2 i}{a^{2} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}+\frac{1}{2 a^{2} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}+\frac{3 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}{2 a^{2} d}"," ",0,"-1/2/a^2/d/(tan(1/2*d*x+1/2*c)-1)+2*I/a^2/d/(tan(1/2*d*x+1/2*c)-1)-1/2/a^2/d/(tan(1/2*d*x+1/2*c)-1)^2-3/2/a^2/d*ln(tan(1/2*d*x+1/2*c)-1)-1/2/a^2/d/(tan(1/2*d*x+1/2*c)+1)-2*I/a^2/d/(tan(1/2*d*x+1/2*c)+1)+1/2/a^2/d/(tan(1/2*d*x+1/2*c)+1)^2+3/2/a^2/d*ln(tan(1/2*d*x+1/2*c)+1)","B"
172,1,36,30,0.257000," ","int(sec(d*x+c)^4/(a*cos(d*x+c)+I*a*sin(d*x+c))^2,x)","\frac{\tan \left(d x +c \right)-\frac{\left(\tan^{3}\left(d x +c \right)\right)}{3}-i \left(\tan^{2}\left(d x +c \right)\right)}{d \,a^{2}}"," ",0,"1/d/a^2*(tan(d*x+c)-1/3*tan(d*x+c)^3-I*tan(d*x+c)^2)","A"
173,1,342,75,0.275000," ","int(sec(d*x+c)^5/(a*cos(d*x+c)+I*a*sin(d*x+c))^2,x)","\frac{3}{8 a^{2} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}+\frac{i}{a^{2} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}+\frac{1}{8 a^{2} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}-\frac{2 i}{3 a^{2} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}-\frac{1}{2 a^{2} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{3}}-\frac{i}{a^{2} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}-\frac{1}{4 a^{2} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{4}}-\frac{5 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}{8 a^{2} d}+\frac{3}{8 a^{2} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}+\frac{i}{a^{2} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}-\frac{1}{8 a^{2} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}+\frac{i}{a^{2} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{1}{2 a^{2} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}+\frac{2 i}{3 a^{2} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{3}}+\frac{1}{4 a^{2} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{4}}+\frac{5 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}{8 a^{2} d}"," ",0,"3/8/a^2/d/(tan(1/2*d*x+1/2*c)-1)+I/a^2/d/(tan(1/2*d*x+1/2*c)+1)^2+1/8/a^2/d/(tan(1/2*d*x+1/2*c)-1)^2-2/3*I/a^2/d/(tan(1/2*d*x+1/2*c)+1)^3-1/2/a^2/d/(tan(1/2*d*x+1/2*c)-1)^3-I/a^2/d/(tan(1/2*d*x+1/2*c)+1)-1/4/a^2/d/(tan(1/2*d*x+1/2*c)-1)^4-5/8/a^2/d*ln(tan(1/2*d*x+1/2*c)-1)+3/8/a^2/d/(tan(1/2*d*x+1/2*c)+1)+I/a^2/d/(tan(1/2*d*x+1/2*c)-1)^2-1/8/a^2/d/(tan(1/2*d*x+1/2*c)+1)^2+I/a^2/d/(tan(1/2*d*x+1/2*c)-1)-1/2/a^2/d/(tan(1/2*d*x+1/2*c)+1)^3+2/3*I/a^2/d/(tan(1/2*d*x+1/2*c)-1)^3+1/4/a^2/d/(tan(1/2*d*x+1/2*c)+1)^4+5/8/a^2/d*ln(tan(1/2*d*x+1/2*c)+1)","B"
174,1,47,64,0.254000," ","int(sec(d*x+c)^6/(a*cos(d*x+c)+I*a*sin(d*x+c))^2,x)","\frac{\tan \left(d x +c \right)-\frac{\left(\tan^{5}\left(d x +c \right)\right)}{5}-\frac{i \left(\tan^{4}\left(d x +c \right)\right)}{2}-i \left(\tan^{2}\left(d x +c \right)\right)}{d \,a^{2}}"," ",0,"1/d/a^2*(tan(d*x+c)-1/5*tan(d*x+c)^5-1/2*I*tan(d*x+c)^4-I*tan(d*x+c)^2)","A"
175,1,137,106,0.198000," ","int(cos(d*x+c)^5/(a*cos(d*x+c)+I*a*sin(d*x+c))^3,x)","\frac{5 i \ln \left(\tan \left(d x +c \right)+i\right)}{64 a^{3} d}+\frac{1}{32 a^{3} d \left(\tan \left(d x +c \right)+i\right)}-\frac{5 i \ln \left(\tan \left(d x +c \right)-i\right)}{64 a^{3} d}+\frac{i}{16 a^{3} d \left(\tan \left(d x +c \right)-i\right)^{4}}-\frac{3 i}{32 a^{3} d \left(\tan \left(d x +c \right)-i\right)^{2}}-\frac{1}{12 a^{3} d \left(\tan \left(d x +c \right)-i\right)^{3}}+\frac{1}{8 a^{3} d \left(\tan \left(d x +c \right)-i\right)}"," ",0,"5/64*I/a^3/d*ln(tan(d*x+c)+I)+1/32/a^3/d/(tan(d*x+c)+I)-5/64*I/a^3/d*ln(tan(d*x+c)-I)+1/16*I/a^3/d/(tan(d*x+c)-I)^4-3/32*I/a^3/d/(tan(d*x+c)-I)^2-1/12/a^3/d/(tan(d*x+c)-I)^3+1/8/a^3/d/(tan(d*x+c)-I)","A"
176,1,141,96,0.194000," ","int(cos(d*x+c)^4/(a*cos(d*x+c)+I*a*sin(d*x+c))^3,x)","\frac{\frac{2}{16 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+16 i}+\frac{4 i}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{6}}-\frac{9 i}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{4}}+\frac{17 i}{4 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{2}}-\frac{8}{7 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{7}}+\frac{38}{5 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{5}}-\frac{15}{2 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{3}}+\frac{15}{8 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)}}{d \,a^{3}}"," ",0,"2/d/a^3*(1/16/(tan(1/2*d*x+1/2*c)+I)+2*I/(tan(1/2*d*x+1/2*c)-I)^6-9/2*I/(tan(1/2*d*x+1/2*c)-I)^4+17/8*I/(tan(1/2*d*x+1/2*c)-I)^2-4/7/(tan(1/2*d*x+1/2*c)-I)^7+19/5/(tan(1/2*d*x+1/2*c)-I)^5-15/4/(tan(1/2*d*x+1/2*c)-I)^3+15/16/(tan(1/2*d*x+1/2*c)-I))","A"
177,1,98,117,0.194000," ","int(cos(d*x+c)^3/(a*cos(d*x+c)+I*a*sin(d*x+c))^3,x)","\frac{i \ln \left(\tan \left(d x +c \right)+i\right)}{16 a^{3} d}-\frac{i \ln \left(\tan \left(d x +c \right)-i\right)}{16 a^{3} d}-\frac{i}{8 a^{3} d \left(\tan \left(d x +c \right)-i\right)^{2}}-\frac{1}{6 a^{3} d \left(\tan \left(d x +c \right)-i\right)^{3}}+\frac{1}{8 a^{3} d \left(\tan \left(d x +c \right)-i\right)}"," ",0,"1/16*I/a^3/d*ln(tan(d*x+c)+I)-1/16*I/a^3/d*ln(tan(d*x+c)-I)-1/8*I/a^3/d/(tan(d*x+c)-I)^2-1/6/a^3/d/(tan(d*x+c)-I)^3+1/8/a^3/d/(tan(d*x+c)-I)","A"
178,1,90,80,0.191000," ","int(cos(d*x+c)^2/(a*cos(d*x+c)+I*a*sin(d*x+c))^3,x)","\frac{-\frac{16}{3 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{3}}-\frac{4 i}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{4}}+\frac{4 i}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{2}}+\frac{2}{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i}+\frac{8}{5 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{5}}}{d \,a^{3}}"," ",0,"2/d/a^3*(-8/3/(tan(1/2*d*x+1/2*c)-I)^3-2*I/(tan(1/2*d*x+1/2*c)-I)^4+2*I/(tan(1/2*d*x+1/2*c)-I)^2+1/(tan(1/2*d*x+1/2*c)-I)+4/5/(tan(1/2*d*x+1/2*c)-I)^5)","A"
179,1,23,28,0.167000," ","int(cos(d*x+c)/(a*cos(d*x+c)+I*a*sin(d*x+c))^3,x)","\frac{i}{2 d \,a^{3} \left(i \tan \left(d x +c \right)+1\right)^{2}}"," ",0,"1/2*I/d/a^3/(I*tan(d*x+c)+1)^2","A"
180,1,57,27,0.172000," ","int(1/(a*cos(d*x+c)+I*a*sin(d*x+c))^3,x)","\frac{\frac{4 i}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{2}}+\frac{2}{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i}-\frac{8}{3 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)^{3}}}{d \,a^{3}}"," ",0,"2/d/a^3*(2*I/(tan(1/2*d*x+1/2*c)-I)^2+1/(tan(1/2*d*x+1/2*c)-I)-4/3/(tan(1/2*d*x+1/2*c)-I)^3)","B"
181,1,40,58,0.257000," ","int(sec(d*x+c)/(a*cos(d*x+c)+I*a*sin(d*x+c))^3,x)","\frac{2}{a^{3} d \left(\tan \left(d x +c \right)-i\right)}+\frac{i \ln \left(\tan \left(d x +c \right)-i\right)}{a^{3} d}"," ",0,"2/a^3/d/(tan(d*x+c)-I)+I/a^3/d*ln(tan(d*x+c)-I)","A"
182,1,108,60,0.279000," ","int(sec(d*x+c)^2/(a*cos(d*x+c)+I*a*sin(d*x+c))^3,x)","-\frac{i}{a^{3} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}+\frac{3 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}{a^{3} d}+\frac{i}{a^{3} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}-\frac{3 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}{a^{3} d}+\frac{8}{a^{3} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-i\right)}"," ",0,"-I/a^3/d/(tan(1/2*d*x+1/2*c)-1)+3/a^3/d*ln(tan(1/2*d*x+1/2*c)-1)+I/a^3/d/(tan(1/2*d*x+1/2*c)+1)-3/a^3/d*ln(tan(1/2*d*x+1/2*c)+1)+8/a^3/d/(tan(1/2*d*x+1/2*c)-I)","A"
183,1,52,70,0.294000," ","int(sec(d*x+c)^3/(a*cos(d*x+c)+I*a*sin(d*x+c))^3,x)","-\frac{3 \tan \left(d x +c \right)}{a^{3} d}+\frac{i \left(\tan^{2}\left(d x +c \right)\right)}{2 a^{3} d}-\frac{4 i \ln \left(\tan \left(d x +c \right)-i\right)}{a^{3} d}"," ",0,"-3*tan(d*x+c)/a^3/d+1/2*I*tan(d*x+c)^2/a^3/d-4*I/a^3/d*ln(tan(d*x+c)-I)","A"
184,1,258,68,0.294000," ","int(sec(d*x+c)^4/(a*cos(d*x+c)+I*a*sin(d*x+c))^3,x)","-\frac{i}{3 a^{3} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{3}}-\frac{3}{2 a^{3} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}-\frac{i}{2 a^{3} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}-\frac{3}{2 a^{3} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}+\frac{7 i}{2 a^{3} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{5 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}{2 a^{3} d}+\frac{i}{3 a^{3} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}+\frac{3}{2 a^{3} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}-\frac{i}{2 a^{3} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}-\frac{3}{2 a^{3} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}-\frac{7 i}{2 a^{3} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}+\frac{5 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}{2 a^{3} d}"," ",0,"-1/3*I/a^3/d/(tan(1/2*d*x+1/2*c)-1)^3-3/2/a^3/d/(tan(1/2*d*x+1/2*c)-1)^2-1/2*I/a^3/d/(tan(1/2*d*x+1/2*c)-1)^2-3/2/a^3/d/(tan(1/2*d*x+1/2*c)-1)+7/2*I/a^3/d/(tan(1/2*d*x+1/2*c)-1)-5/2/a^3/d*ln(tan(1/2*d*x+1/2*c)-1)+1/3*I/a^3/d/(tan(1/2*d*x+1/2*c)+1)^3+3/2/a^3/d/(tan(1/2*d*x+1/2*c)+1)^2-1/2*I/a^3/d/(tan(1/2*d*x+1/2*c)+1)^2-3/2/a^3/d/(tan(1/2*d*x+1/2*c)+1)-7/2*I/a^3/d/(tan(1/2*d*x+1/2*c)+1)+5/2/a^3/d*ln(tan(1/2*d*x+1/2*c)+1)","B"
185,1,47,30,0.301000," ","int(sec(d*x+c)^5/(a*cos(d*x+c)+I*a*sin(d*x+c))^3,x)","\frac{\tan \left(d x +c \right)+\frac{i \left(\tan^{4}\left(d x +c \right)\right)}{4}-\left(\tan^{3}\left(d x +c \right)\right)-\frac{3 i \left(\tan^{2}\left(d x +c \right)\right)}{2}}{d \,a^{3}}"," ",0,"1/d/a^3*(tan(d*x+c)+1/4*I*tan(d*x+c)^4-tan(d*x+c)^3-3/2*I*tan(d*x+c)^2)","A"
186,1,430,92,0.305000," ","int(sec(d*x+c)^6/(a*cos(d*x+c)+I*a*sin(d*x+c))^3,x)","\frac{i}{5 a^{3} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{5}}+\frac{1}{8 a^{3} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{13 i}{8 a^{3} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}-\frac{3}{4 a^{3} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{4}}-\frac{i}{5 a^{3} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{5}}-\frac{5}{8 a^{3} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}+\frac{7 i}{12 a^{3} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{3}}-\frac{3}{2 a^{3} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{3}}+\frac{11 i}{8 a^{3} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}-\frac{7 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}{8 a^{3} d}-\frac{i}{2 a^{3} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{4}}+\frac{5}{8 a^{3} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}+\frac{13 i}{8 a^{3} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}+\frac{3}{4 a^{3} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{4}}-\frac{7 i}{12 a^{3} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}+\frac{1}{8 a^{3} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}+\frac{11 i}{8 a^{3} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}-\frac{3}{2 a^{3} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}-\frac{i}{2 a^{3} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{4}}+\frac{7 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}{8 a^{3} d}"," ",0,"1/5*I/a^3/d/(tan(1/2*d*x+1/2*c)+1)^5+1/8/a^3/d/(tan(1/2*d*x+1/2*c)-1)-13/8*I/a^3/d/(tan(1/2*d*x+1/2*c)+1)-3/4/a^3/d/(tan(1/2*d*x+1/2*c)-1)^4-1/5*I/a^3/d/(tan(1/2*d*x+1/2*c)-1)^5-5/8/a^3/d/(tan(1/2*d*x+1/2*c)-1)^2+7/12*I/a^3/d/(tan(1/2*d*x+1/2*c)-1)^3-3/2/a^3/d/(tan(1/2*d*x+1/2*c)-1)^3+11/8*I/a^3/d/(tan(1/2*d*x+1/2*c)-1)^2-7/8/a^3/d*ln(tan(1/2*d*x+1/2*c)-1)-1/2*I/a^3/d/(tan(1/2*d*x+1/2*c)-1)^4+5/8/a^3/d/(tan(1/2*d*x+1/2*c)+1)^2+13/8*I/a^3/d/(tan(1/2*d*x+1/2*c)-1)+3/4/a^3/d/(tan(1/2*d*x+1/2*c)+1)^4-7/12*I/a^3/d/(tan(1/2*d*x+1/2*c)+1)^3+1/8/a^3/d/(tan(1/2*d*x+1/2*c)+1)+11/8*I/a^3/d/(tan(1/2*d*x+1/2*c)+1)^2-3/2/a^3/d/(tan(1/2*d*x+1/2*c)+1)^3-1/2*I/a^3/d/(tan(1/2*d*x+1/2*c)+1)^4+7/8/a^3/d*ln(tan(1/2*d*x+1/2*c)+1)","B"
187,0,0,59,0.678000," ","int((a*cos(d*x+c)+I*a*sin(d*x+c))^n/(cos(d*x+c)^n),x)","\int \left(a \cos \left(d x +c \right)+i a \sin \left(d x +c \right)\right)^{n} \left(\cos^{-n}\left(d x +c \right)\right)\, dx"," ",0,"int((a*cos(d*x+c)+I*a*sin(d*x+c))^n/(cos(d*x+c)^n),x)","F"
188,1,6,5,0.080000," ","int(1/(sec(x)+tan(x)),x)","\ln \left(1+\sin \left(x \right)\right)"," ",0,"ln(1+sin(x))","A"
189,1,11,10,0.106000," ","int(sin(x)/(sec(x)+tan(x)),x)","-\ln \left(1+\sin \left(x \right)\right)+\sin \left(x \right)"," ",0,"-ln(1+sin(x))+sin(x)","A"
190,1,15,4,0.109000," ","int(cos(x)/(sec(x)+tan(x)),x)","\frac{2}{\tan^{2}\left(\frac{x}{2}\right)+1}+x"," ",0,"2/(tan(1/2*x)^2+1)+x","B"
191,1,13,11,0.077000," ","int(tan(x)/(sec(x)+tan(x)),x)","\frac{2}{\tan \left(\frac{x}{2}\right)+1}+x"," ",0,"2/(tan(1/2*x)+1)+x","A"
192,1,10,9,0.130000," ","int(cot(x)/(sec(x)+tan(x)),x)","\ln \left(\tan \left(\frac{x}{2}\right)\right)-x"," ",0,"ln(tan(1/2*x))-x","A"
193,1,11,10,0.072000," ","int(sec(x)/(sec(x)+tan(x)),x)","-\frac{2}{\tan \left(\frac{x}{2}\right)+1}"," ",0,"-2/(tan(1/2*x)+1)","A"
194,1,8,11,0.119000," ","int(csc(x)/(sec(x)+tan(x)),x)","-\ln \left(1+\csc \left(x \right)\right)"," ",0,"-ln(1+csc(x))","A"
195,1,8,9,0.085000," ","int(1/(sec(x)-tan(x)),x)","-\ln \left(\sin \left(x \right)-1\right)"," ",0,"-ln(sin(x)-1)","A"
196,1,13,14,0.105000," ","int(sin(x)/(sec(x)-tan(x)),x)","-\sin \left(x \right)-\ln \left(\sin \left(x \right)-1\right)"," ",0,"-sin(x)-ln(sin(x)-1)","A"
197,1,15,6,0.114000," ","int(cos(x)/(sec(x)-tan(x)),x)","-\frac{2}{\tan^{2}\left(\frac{x}{2}\right)+1}+x"," ",0,"-2/(tan(1/2*x)^2+1)+x","B"
198,1,15,15,0.070000," ","int(tan(x)/(sec(x)-tan(x)),x)","-\frac{2}{\tan \left(\frac{x}{2}\right)-1}-x"," ",0,"-2/(tan(1/2*x)-1)-x","A"
199,1,8,7,0.129000," ","int(cot(x)/(sec(x)-tan(x)),x)","\ln \left(\tan \left(\frac{x}{2}\right)\right)+x"," ",0,"ln(tan(1/2*x))+x","A"
200,1,11,11,0.070000," ","int(sec(x)/(sec(x)-tan(x)),x)","-\frac{2}{\tan \left(\frac{x}{2}\right)-1}"," ",0,"-2/(tan(1/2*x)-1)","A"
201,1,8,13,0.107000," ","int(csc(x)/(sec(x)-tan(x)),x)","-\ln \left(-1+\csc \left(x \right)\right)"," ",0,"-ln(-1+csc(x))","A"
202,1,24,23,0.103000," ","int(csc(d*x+c)*(cot(d*x+c)+csc(d*x+c)),x)","\frac{-\frac{1}{\sin \left(d x +c \right)}-\cot \left(d x +c \right)}{d}"," ",0,"1/d*(-1/sin(d*x+c)-cot(d*x+c))","A"
203,1,19,6,0.104000," ","int(sin(x)/(cot(x)+csc(x)),x)","-\frac{2 \tan \left(\frac{x}{2}\right)}{\tan^{2}\left(\frac{x}{2}\right)+1}+x"," ",0,"-2*tan(1/2*x)/(tan(1/2*x)^2+1)+x","B"
204,1,11,10,0.097000," ","int(cos(x)/(cot(x)+csc(x)),x)","-\cos \left(x \right)+\ln \left(1+\cos \left(x \right)\right)"," ",0,"-cos(x)+ln(1+cos(x))","A"
205,1,21,7,0.112000," ","int(tan(x)/(cot(x)+csc(x)),x)","-\ln \left(\tan \left(\frac{x}{2}\right)-1\right)+\ln \left(\tan \left(\frac{x}{2}\right)+1\right)-x"," ",0,"-ln(tan(1/2*x)-1)+ln(tan(1/2*x)+1)-x","B"
206,1,9,12,0.065000," ","int(cot(x)/(cot(x)+csc(x)),x)","-\tan \left(\frac{x}{2}\right)+x"," ",0,"-tan(1/2*x)+x","A"
207,1,6,11,0.089000," ","int(sec(x)/(cot(x)+csc(x)),x)","\ln \left(1+\sec \left(x \right)\right)"," ",0,"ln(1+sec(x))","A"
208,1,5,9,0.059000," ","int(csc(x)/(cot(x)+csc(x)),x)","\tan \left(\frac{x}{2}\right)"," ",0,"tan(1/2*x)","A"
209,1,19,4,0.096000," ","int(sin(x)/(-cot(x)+csc(x)),x)","\frac{2 \tan \left(\frac{x}{2}\right)}{\tan^{2}\left(\frac{x}{2}\right)+1}+x"," ",0,"2*tan(1/2*x)/(tan(1/2*x)^2+1)+x","B"
210,1,9,10,0.096000," ","int(cos(x)/(-cot(x)+csc(x)),x)","\cos \left(x \right)+\ln \left(\cos \left(x \right)-1\right)"," ",0,"cos(x)+ln(cos(x)-1)","A"
211,1,19,5,0.113000," ","int(tan(x)/(-cot(x)+csc(x)),x)","-\ln \left(\tan \left(\frac{x}{2}\right)-1\right)+\ln \left(\tan \left(\frac{x}{2}\right)+1\right)+x"," ",0,"-ln(tan(1/2*x)-1)+ln(tan(1/2*x)+1)+x","B"
212,1,13,16,0.069000," ","int(cot(x)/(-cot(x)+csc(x)),x)","-\frac{1}{\tan \left(\frac{x}{2}\right)}-x"," ",0,"-1/tan(1/2*x)-x","A"
213,1,6,13,0.094000," ","int(sec(x)/(-cot(x)+csc(x)),x)","\ln \left(-1+\sec \left(x \right)\right)"," ",0,"ln(-1+sec(x))","A"
214,1,9,12,0.059000," ","int(csc(x)/(-cot(x)+csc(x)),x)","-\frac{1}{\tan \left(\frac{x}{2}\right)}"," ",0,"-1/tan(1/2*x)","A"
215,1,21,20,0.115000," ","int(1/(csc(d*x+c)+sin(d*x+c)),x)","-\frac{\arctanh \left(\frac{\cos \left(d x +c \right) \sqrt{2}}{2}\right) \sqrt{2}}{2 d}"," ",0,"-1/2*arctanh(1/2*cos(d*x+c)*2^(1/2))/d*2^(1/2)","A"
216,1,30,45,0.131000," ","int(sin(d*x+c)/(csc(d*x+c)+sin(d*x+c)),x)","-\frac{\sqrt{2}\, \arctan \left(\tan \left(d x +c \right) \sqrt{2}\right)}{2 d}+\frac{d x +c}{d}"," ",0,"-1/2/d*2^(1/2)*arctan(tan(d*x+c)*2^(1/2))+1/d*(d*x+c)","A"
217,1,17,16,0.064000," ","int(cos(d*x+c)/(csc(d*x+c)+sin(d*x+c)),x)","\frac{\ln \left(\cos^{2}\left(d x +c \right)-2\right)}{2 d}"," ",0,"1/2/d*ln(cos(d*x+c)^2-2)","A"
218,1,42,25,0.158000," ","int(tan(d*x+c)/(csc(d*x+c)+sin(d*x+c)),x)","-\frac{\ln \left(\sin \left(d x +c \right)-1\right)}{4 d}+\frac{\ln \left(\sin \left(d x +c \right)+1\right)}{4 d}-\frac{\arctan \left(\sin \left(d x +c \right)\right)}{2 d}"," ",0,"-1/4/d*ln(sin(d*x+c)-1)+1/4/d*ln(sin(d*x+c)+1)-1/2*arctan(sin(d*x+c))/d","A"
219,1,13,11,0.074000," ","int(cot(d*x+c)/(csc(d*x+c)+sin(d*x+c)),x)","-\frac{\arctan \left(\csc \left(d x +c \right)\right)}{d}"," ",0,"-1/d*arctan(csc(d*x+c))","A"
220,1,19,14,0.088000," ","int(sec(d*x+c)/(csc(d*x+c)+sin(d*x+c)),x)","\frac{\ln \left(2 \left(\sec^{2}\left(d x +c \right)\right)-1\right)}{4 d}"," ",0,"1/4/d*ln(2*sec(d*x+c)^2-1)","A"
221,1,20,44,0.109000," ","int(csc(d*x+c)/(csc(d*x+c)+sin(d*x+c)),x)","\frac{\sqrt{2}\, \arctan \left(\tan \left(d x +c \right) \sqrt{2}\right)}{2 d}"," ",0,"1/2/d*2^(1/2)*arctan(tan(d*x+c)*2^(1/2))","A"
222,1,13,10,0.121000," ","int(1/(csc(d*x+c)-sin(d*x+c)),x)","\frac{1}{d \cos \left(d x +c \right)}"," ",0,"1/d/cos(d*x+c)","A"
223,1,24,14,0.124000," ","int(sin(d*x+c)/(csc(d*x+c)-sin(d*x+c)),x)","\frac{\tan \left(d x +c \right)}{d}-\frac{\arctan \left(\tan \left(d x +c \right)\right)}{d}"," ",0,"tan(d*x+c)/d-1/d*arctan(tan(d*x+c))","A"
224,1,13,12,0.063000," ","int(cos(d*x+c)/(csc(d*x+c)-sin(d*x+c)),x)","-\frac{\ln \left(\cos \left(d x +c \right)\right)}{d}"," ",0,"-ln(cos(d*x+c))/d","A"
225,1,60,30,0.158000," ","int(tan(d*x+c)/(csc(d*x+c)-sin(d*x+c)),x)","-\frac{1}{4 d \left(\sin \left(d x +c \right)-1\right)}+\frac{\ln \left(\sin \left(d x +c \right)-1\right)}{4 d}-\frac{1}{4 d \left(\sin \left(d x +c \right)+1\right)}-\frac{\ln \left(\sin \left(d x +c \right)+1\right)}{4 d}"," ",0,"-1/4/d/(sin(d*x+c)-1)+1/4/d*ln(sin(d*x+c)-1)-1/4/d/(sin(d*x+c)+1)-1/4/d*ln(sin(d*x+c)+1)","A"
226,1,12,11,0.118000," ","int(cot(d*x+c)/(csc(d*x+c)-sin(d*x+c)),x)","\frac{\arctanh \left(\sin \left(d x +c \right)\right)}{d}"," ",0,"arctanh(sin(d*x+c))/d","A"
227,1,14,13,0.076000," ","int(sec(d*x+c)/(csc(d*x+c)-sin(d*x+c)),x)","\frac{\sec^{2}\left(d x +c \right)}{2 d}"," ",0,"1/2*sec(d*x+c)^2/d","A"
228,1,11,10,0.107000," ","int(csc(d*x+c)/(csc(d*x+c)-sin(d*x+c)),x)","\frac{\tan \left(d x +c \right)}{d}"," ",0,"tan(d*x+c)/d","A"
229,1,29,29,0.051000," ","int(cos(d*x+c)^3*(a*sin(d*x+c)+b*tan(d*x+c)),x)","-\frac{\frac{a \left(\cos^{4}\left(d x +c \right)\right)}{4}+\frac{b \left(\cos^{3}\left(d x +c \right)\right)}{3}}{d}"," ",0,"-1/d*(1/4*a*cos(d*x+c)^4+1/3*b*cos(d*x+c)^3)","A"
230,1,29,29,0.044000," ","int(cos(d*x+c)^2*(a*sin(d*x+c)+b*tan(d*x+c)),x)","-\frac{\frac{a \left(\cos^{3}\left(d x +c \right)\right)}{3}+\frac{b \left(\cos^{2}\left(d x +c \right)\right)}{2}}{d}"," ",0,"-1/d*(1/3*a*cos(d*x+c)^3+1/2*b*cos(d*x+c)^2)","A"
231,1,26,20,0.034000," ","int(cos(d*x+c)*(a*sin(d*x+c)+b*tan(d*x+c)),x)","-\frac{\frac{\left(\cos^{2}\left(d x +c \right)\right) a}{2}+b \cos \left(d x +c \right)}{d}"," ",0,"-1/d*(1/2*cos(d*x+c)^2*a+b*cos(d*x+c))","A"
232,1,31,26,0.008000," ","int(a*sin(d*x+c)+b*tan(d*x+c),x)","\frac{b \ln \left(\tan^{2}\left(d x +c \right)+1\right)}{2 d}-\frac{a \cos \left(d x +c \right)}{d}"," ",0,"1/2*b/d*ln(tan(d*x+c)^2+1)-a*cos(d*x+c)/d","A"
233,1,25,25,0.035000," ","int(sec(d*x+c)*(a*sin(d*x+c)+b*tan(d*x+c)),x)","\frac{b \sec \left(d x +c \right)}{d}+\frac{a \ln \left(\sec \left(d x +c \right)\right)}{d}"," ",0,"b*sec(d*x+c)/d+1/d*a*ln(sec(d*x+c))","A"
234,1,25,26,0.039000," ","int(sec(d*x+c)^2*(a*sin(d*x+c)+b*tan(d*x+c)),x)","\frac{\frac{b \left(\sec^{2}\left(d x +c \right)\right)}{2}+a \sec \left(d x +c \right)}{d}"," ",0,"1/d*(1/2*b*sec(d*x+c)^2+a*sec(d*x+c))","A"
235,1,28,29,0.043000," ","int(sec(d*x+c)^3*(a*sin(d*x+c)+b*tan(d*x+c)),x)","\frac{\frac{\left(\sec^{3}\left(d x +c \right)\right) b}{3}+\frac{\left(\sec^{2}\left(d x +c \right)\right) a}{2}}{d}"," ",0,"1/d*(1/3*sec(d*x+c)^3*b+1/2*sec(d*x+c)^2*a)","A"
236,1,100,96,0.092000," ","int(cos(d*x+c)^3*(a*sin(d*x+c)+b*tan(d*x+c))^2,x)","\frac{a^{2} \left(-\frac{\sin \left(d x +c \right) \left(\cos^{4}\left(d x +c \right)\right)}{5}+\frac{\left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{15}\right)+2 a b \left(-\frac{\sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right)}{4}+\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)}{8}+\frac{d x}{8}+\frac{c}{8}\right)+\frac{b^{2} \left(\sin^{3}\left(d x +c \right)\right)}{3}}{d}"," ",0,"1/d*(a^2*(-1/5*sin(d*x+c)*cos(d*x+c)^4+1/15*(2+cos(d*x+c)^2)*sin(d*x+c))+2*a*b*(-1/4*sin(d*x+c)*cos(d*x+c)^3+1/8*cos(d*x+c)*sin(d*x+c)+1/8*d*x+1/8*c)+1/3*b^2*sin(d*x+c)^3)","A"
237,1,86,78,0.082000," ","int(cos(d*x+c)^2*(a*sin(d*x+c)+b*tan(d*x+c))^2,x)","\frac{a^{2} \left(-\frac{\sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right)}{4}+\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)}{8}+\frac{d x}{8}+\frac{c}{8}\right)+\frac{2 a b \left(\sin^{3}\left(d x +c \right)\right)}{3}+b^{2} \left(-\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)}{2}+\frac{d x}{2}+\frac{c}{2}\right)}{d}"," ",0,"1/d*(a^2*(-1/4*sin(d*x+c)*cos(d*x+c)^3+1/8*cos(d*x+c)*sin(d*x+c)+1/8*d*x+1/8*c)+2/3*a*b*sin(d*x+c)^3+b^2*(-1/2*cos(d*x+c)*sin(d*x+c)+1/2*d*x+1/2*c))","A"
238,1,83,81,0.074000," ","int(cos(d*x+c)*(a*sin(d*x+c)+b*tan(d*x+c))^2,x)","\frac{a^{2} \left(\sin^{3}\left(d x +c \right)\right)}{3 d}-\frac{a b \cos \left(d x +c \right) \sin \left(d x +c \right)}{d}+a b x +\frac{a b c}{d}-\frac{b^{2} \sin \left(d x +c \right)}{d}+\frac{b^{2} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}"," ",0,"1/3*a^2*sin(d*x+c)^3/d-a*b*cos(d*x+c)*sin(d*x+c)/d+a*b*x+1/d*a*b*c-b^2*sin(d*x+c)/d+1/d*b^2*ln(sec(d*x+c)+tan(d*x+c))","A"
239,1,99,73,0.059000," ","int((a*sin(d*x+c)+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{2 a b \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}-\frac{2 a b \sin \left(d x +c \right)}{d}-b^{2} x +\frac{b^{2} \tan \left(d x +c \right)}{d}-\frac{b^{2} c}{d}"," ",0,"-1/2*a^2*cos(d*x+c)*sin(d*x+c)/d+1/2*a^2*x+1/2/d*a^2*c+2/d*a*b*ln(sec(d*x+c)+tan(d*x+c))-2*a*b*sin(d*x+c)/d-b^2*x+b^2*tan(d*x+c)/d-1/d*b^2*c","A"
240,1,123,84,0.092000," ","int(sec(d*x+c)*(a*sin(d*x+c)+b*tan(d*x+c))^2,x)","-\frac{a^{2} \sin \left(d x +c \right)}{d}+\frac{a^{2} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}-2 a b x +\frac{2 a b \tan \left(d x +c \right)}{d}-\frac{2 a b c}{d}+\frac{b^{2} \left(\sin^{3}\left(d x +c \right)\right)}{2 d \cos \left(d x +c \right)^{2}}+\frac{b^{2} \sin \left(d x +c \right)}{2 d}-\frac{b^{2} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{2 d}"," ",0,"-a^2*sin(d*x+c)/d+1/d*a^2*ln(sec(d*x+c)+tan(d*x+c))-2*a*b*x+2*a*b*tan(d*x+c)/d-2/d*a*b*c+1/2/d*b^2*sin(d*x+c)^3/cos(d*x+c)^2+1/2*b^2*sin(d*x+c)/d-1/2/d*b^2*ln(sec(d*x+c)+tan(d*x+c))","A"
241,1,109,93,0.108000," ","int(sec(d*x+c)^2*(a*sin(d*x+c)+b*tan(d*x+c))^2,x)","-a^{2} x +\frac{a^{2} \tan \left(d x +c \right)}{d}-\frac{a^{2} c}{d}+\frac{a b \left(\sin^{3}\left(d x +c \right)\right)}{d \cos \left(d x +c \right)^{2}}+\frac{a b \sin \left(d x +c \right)}{d}-\frac{a b \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{b^{2} \left(\sin^{3}\left(d x +c \right)\right)}{3 d \cos \left(d x +c \right)^{3}}"," ",0,"-a^2*x+a^2*tan(d*x+c)/d-1/d*a^2*c+1/d*a*b*sin(d*x+c)^3/cos(d*x+c)^2+a*b*sin(d*x+c)/d-1/d*a*b*ln(sec(d*x+c)+tan(d*x+c))+1/3/d*b^2*sin(d*x+c)^3/cos(d*x+c)^3","A"
242,1,169,115,0.112000," ","int(sec(d*x+c)^3*(a*sin(d*x+c)+b*tan(d*x+c))^2,x)","\frac{a^{2} \left(\sin^{3}\left(d x +c \right)\right)}{2 d \cos \left(d x +c \right)^{2}}+\frac{a^{2} \sin \left(d x +c \right)}{2 d}-\frac{a^{2} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{2 d}+\frac{2 a b \left(\sin^{3}\left(d x +c \right)\right)}{3 d \cos \left(d x +c \right)^{3}}+\frac{b^{2} \left(\sin^{3}\left(d x +c \right)\right)}{4 d \cos \left(d x +c \right)^{4}}+\frac{b^{2} \left(\sin^{3}\left(d x +c \right)\right)}{8 d \cos \left(d x +c \right)^{2}}+\frac{b^{2} \sin \left(d x +c \right)}{8 d}-\frac{b^{2} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{8 d}"," ",0,"1/2/d*a^2*sin(d*x+c)^3/cos(d*x+c)^2+1/2*a^2*sin(d*x+c)/d-1/2/d*a^2*ln(sec(d*x+c)+tan(d*x+c))+2/3/d*a*b*sin(d*x+c)^3/cos(d*x+c)^3+1/4/d*b^2*sin(d*x+c)^3/cos(d*x+c)^4+1/8/d*b^2*sin(d*x+c)^3/cos(d*x+c)^2+1/8*b^2*sin(d*x+c)/d-1/8/d*b^2*ln(sec(d*x+c)+tan(d*x+c))","A"
243,1,109,71,0.106000," ","int(cos(d*x+c)^3*(a*sin(d*x+c)+b*tan(d*x+c))^3,x)","\frac{a^{3} \left(-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{4}\left(d x +c \right)\right)}{6}-\frac{\left(\cos^{4}\left(d x +c \right)\right)}{12}\right)+3 a^{2} b \left(-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{3}\left(d x +c \right)\right)}{5}-\frac{2 \left(\cos^{3}\left(d x +c \right)\right)}{15}\right)+\frac{3 a \,b^{2} \left(\sin^{4}\left(d x +c \right)\right)}{4}-\frac{b^{3} \left(2+\sin^{2}\left(d x +c \right)\right) \cos \left(d x +c \right)}{3}}{d}"," ",0,"1/d*(a^3*(-1/6*sin(d*x+c)^2*cos(d*x+c)^4-1/12*cos(d*x+c)^4)+3*a^2*b*(-1/5*sin(d*x+c)^2*cos(d*x+c)^3-2/15*cos(d*x+c)^3)+3/4*a*b^2*sin(d*x+c)^4-1/3*b^3*(2+sin(d*x+c)^2)*cos(d*x+c))","A"
244,1,128,112,0.106000," ","int(cos(d*x+c)^2*(a*sin(d*x+c)+b*tan(d*x+c))^3,x)","-\frac{a^{3} \left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{3}\left(d x +c \right)\right)}{5 d}-\frac{2 a^{3} \left(\cos^{3}\left(d x +c \right)\right)}{15 d}+\frac{3 a^{2} b \left(\sin^{4}\left(d x +c \right)\right)}{4 d}-\frac{\cos \left(d x +c \right) \left(\sin^{2}\left(d x +c \right)\right) a \,b^{2}}{d}-\frac{2 a \,b^{2} \cos \left(d x +c \right)}{d}-\frac{b^{3} \left(\sin^{2}\left(d x +c \right)\right)}{2 d}-\frac{b^{3} \ln \left(\cos \left(d x +c \right)\right)}{d}"," ",0,"-1/5/d*a^3*sin(d*x+c)^2*cos(d*x+c)^3-2/15*a^3*cos(d*x+c)^3/d+3/4/d*a^2*b*sin(d*x+c)^4-1/d*cos(d*x+c)*sin(d*x+c)^2*a*b^2-2*a*b^2*cos(d*x+c)/d-1/2/d*b^3*sin(d*x+c)^2-b^3*ln(cos(d*x+c))/d","A"
245,1,147,108,0.078000," ","int(cos(d*x+c)*(a*sin(d*x+c)+b*tan(d*x+c))^3,x)","\frac{a^{3} \left(\sin^{4}\left(d x +c \right)\right)}{4 d}-\frac{\cos \left(d x +c \right) \left(\sin^{2}\left(d x +c \right)\right) a^{2} b}{d}-\frac{2 a^{2} b \cos \left(d x +c \right)}{d}-\frac{3 a \,b^{2} \left(\sin^{2}\left(d x +c \right)\right)}{2 d}-\frac{3 a \,b^{2} \ln \left(\cos \left(d x +c \right)\right)}{d}+\frac{b^{3} \left(\sin^{4}\left(d x +c \right)\right)}{d \cos \left(d x +c \right)}+\frac{b^{3} \cos \left(d x +c \right) \left(\sin^{2}\left(d x +c \right)\right)}{d}+\frac{2 b^{3} \cos \left(d x +c \right)}{d}"," ",0,"1/4/d*a^3*sin(d*x+c)^4-1/d*cos(d*x+c)*sin(d*x+c)^2*a^2*b-2*a^2*b*cos(d*x+c)/d-3/2/d*a*b^2*sin(d*x+c)^2-3*a*b^2*ln(cos(d*x+c))/d+1/d*b^3*sin(d*x+c)^4/cos(d*x+c)+1/d*b^3*cos(d*x+c)*sin(d*x+c)^2+2*b^3*cos(d*x+c)/d","A"
246,1,164,110,0.076000," ","int((a*sin(d*x+c)+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{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 a \,b^{2} \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(\tan^{2}\left(d x +c \right)\right)}{2 d}+\frac{b^{3} \ln \left(\cos \left(d x +c \right)\right)}{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-3/2/d*a^2*b*sin(d*x+c)^2-3*a^2*b*ln(cos(d*x+c))/d+3/d*a*b^2*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*tan(d*x+c)^2+b^3*ln(cos(d*x+c))/d","A"
247,1,213,109,0.114000," ","int(sec(d*x+c)*(a*sin(d*x+c)+b*tan(d*x+c))^3,x)","-\frac{a^{3} \left(\sin^{2}\left(d x +c \right)\right)}{2 d}-\frac{a^{3} \ln \left(\cos \left(d x +c \right)\right)}{d}+\frac{3 a^{2} b \left(\sin^{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^{2} b}{d}+\frac{6 a^{2} b \cos \left(d x +c \right)}{d}+\frac{3 a \,b^{2} \left(\tan^{2}\left(d x +c \right)\right)}{2 d}+\frac{3 a \,b^{2} \ln \left(\cos \left(d x +c \right)\right)}{d}+\frac{b^{3} \left(\sin^{4}\left(d x +c \right)\right)}{3 d \cos \left(d x +c \right)^{3}}-\frac{b^{3} \left(\sin^{4}\left(d x +c \right)\right)}{3 d \cos \left(d x +c \right)}-\frac{b^{3} \cos \left(d x +c \right) \left(\sin^{2}\left(d x +c \right)\right)}{3 d}-\frac{2 b^{3} \cos \left(d x +c \right)}{3 d}"," ",0,"-1/2/d*a^3*sin(d*x+c)^2-a^3*ln(cos(d*x+c))/d+3/d*a^2*b*sin(d*x+c)^4/cos(d*x+c)+3/d*cos(d*x+c)*sin(d*x+c)^2*a^2*b+6*a^2*b*cos(d*x+c)/d+3/2/d*a*b^2*tan(d*x+c)^2+3*a*b^2*ln(cos(d*x+c))/d+1/3/d*b^3*sin(d*x+c)^4/cos(d*x+c)^3-1/3/d*b^3*sin(d*x+c)^4/cos(d*x+c)-1/3/d*b^3*cos(d*x+c)*sin(d*x+c)^2-2/3*b^3*cos(d*x+c)/d","A"
248,1,204,107,0.137000," ","int(sec(d*x+c)^2*(a*sin(d*x+c)+b*tan(d*x+c))^3,x)","\frac{a^{3} \left(\sin^{4}\left(d x +c \right)\right)}{d \cos \left(d x +c \right)}+\frac{\cos \left(d x +c \right) \left(\sin^{2}\left(d x +c \right)\right) a^{3}}{d}+\frac{2 a^{3} \cos \left(d x +c \right)}{d}+\frac{3 a^{2} b \left(\tan^{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{a \,b^{2} \left(\sin^{4}\left(d x +c \right)\right)}{d \cos \left(d x +c \right)^{3}}-\frac{a \,b^{2} \left(\sin^{4}\left(d x +c \right)\right)}{d \cos \left(d x +c \right)}-\frac{\cos \left(d x +c \right) \left(\sin^{2}\left(d x +c \right)\right) a \,b^{2}}{d}-\frac{2 a \,b^{2} \cos \left(d x +c \right)}{d}+\frac{b^{3} \left(\sin^{4}\left(d x +c \right)\right)}{4 d \cos \left(d x +c \right)^{4}}"," ",0,"1/d*a^3*sin(d*x+c)^4/cos(d*x+c)+1/d*cos(d*x+c)*sin(d*x+c)^2*a^3+2*a^3*cos(d*x+c)/d+3/2*a^2*b*tan(d*x+c)^2/d+3*a^2*b*ln(cos(d*x+c))/d+1/d*a*b^2*sin(d*x+c)^4/cos(d*x+c)^3-1/d*a*b^2*sin(d*x+c)^4/cos(d*x+c)-1/d*cos(d*x+c)*sin(d*x+c)^2*a*b^2-2*a*b^2*cos(d*x+c)/d+1/4/d*b^3*sin(d*x+c)^4/cos(d*x+c)^4","A"
249,1,252,111,0.138000," ","int(sec(d*x+c)^3*(a*sin(d*x+c)+b*tan(d*x+c))^3,x)","\frac{a^{3} \left(\tan^{2}\left(d x +c \right)\right)}{2 d}+\frac{a^{3} \ln \left(\cos \left(d x +c \right)\right)}{d}+\frac{a^{2} b \left(\sin^{4}\left(d x +c \right)\right)}{d \cos \left(d x +c \right)^{3}}-\frac{a^{2} b \left(\sin^{4}\left(d x +c \right)\right)}{d \cos \left(d x +c \right)}-\frac{\cos \left(d x +c \right) \left(\sin^{2}\left(d x +c \right)\right) a^{2} b}{d}-\frac{2 a^{2} b \cos \left(d x +c \right)}{d}+\frac{3 a \,b^{2} \left(\sin^{4}\left(d x +c \right)\right)}{4 d \cos \left(d x +c \right)^{4}}+\frac{b^{3} \left(\sin^{4}\left(d x +c \right)\right)}{5 d \cos \left(d x +c \right)^{5}}+\frac{b^{3} \left(\sin^{4}\left(d x +c \right)\right)}{15 d \cos \left(d x +c \right)^{3}}-\frac{b^{3} \left(\sin^{4}\left(d x +c \right)\right)}{15 d \cos \left(d x +c \right)}-\frac{b^{3} \cos \left(d x +c \right) \left(\sin^{2}\left(d x +c \right)\right)}{15 d}-\frac{2 b^{3} \cos \left(d x +c \right)}{15 d}"," ",0,"1/2/d*a^3*tan(d*x+c)^2+a^3*ln(cos(d*x+c))/d+1/d*a^2*b*sin(d*x+c)^4/cos(d*x+c)^3-1/d*a^2*b*sin(d*x+c)^4/cos(d*x+c)-1/d*cos(d*x+c)*sin(d*x+c)^2*a^2*b-2*a^2*b*cos(d*x+c)/d+3/4/d*a*b^2*sin(d*x+c)^4/cos(d*x+c)^4+1/5/d*b^3*sin(d*x+c)^4/cos(d*x+c)^5+1/15/d*b^3*sin(d*x+c)^4/cos(d*x+c)^3-1/15/d*b^3*sin(d*x+c)^4/cos(d*x+c)-1/15/d*b^3*cos(d*x+c)*sin(d*x+c)^2-2/15*b^3*cos(d*x+c)/d","B"
250,1,111,107,0.184000," ","int(cos(d*x+c)^3/(a*sin(d*x+c)+b*tan(d*x+c)),x)","\frac{\cos^{2}\left(d x +c \right)}{2 a d}-\frac{b \cos \left(d x +c \right)}{a^{2} d}-\frac{b^{4} \ln \left(b +a \cos \left(d x +c \right)\right)}{d \,a^{3} \left(a +b \right) \left(a -b \right)}+\frac{\ln \left(\cos \left(d x +c \right)-1\right)}{d \left(2 a +2 b \right)}+\frac{\ln \left(1+\cos \left(d x +c \right)\right)}{d \left(2 a -2 b \right)}"," ",0,"1/2*cos(d*x+c)^2/a/d-b*cos(d*x+c)/a^2/d-1/d/a^3*b^4/(a+b)/(a-b)*ln(b+a*cos(d*x+c))+1/d/(2*a+2*b)*ln(cos(d*x+c)-1)+1/d/(2*a-2*b)*ln(1+cos(d*x+c))","A"
251,1,93,88,0.180000," ","int(cos(d*x+c)^2/(a*sin(d*x+c)+b*tan(d*x+c)),x)","\frac{\cos \left(d x +c \right)}{a d}+\frac{b^{3} \ln \left(b +a \cos \left(d x +c \right)\right)}{d \,a^{2} \left(a +b \right) \left(a -b \right)}+\frac{\ln \left(\cos \left(d x +c \right)-1\right)}{d \left(2 a +2 b \right)}-\frac{\ln \left(1+\cos \left(d x +c \right)\right)}{d \left(2 a -2 b \right)}"," ",0,"cos(d*x+c)/a/d+1/d/a^2*b^3/(a+b)/(a-b)*ln(b+a*cos(d*x+c))+1/d/(2*a+2*b)*ln(cos(d*x+c)-1)-1/d/(2*a-2*b)*ln(1+cos(d*x+c))","A"
252,1,80,76,0.154000," ","int(cos(d*x+c)/(a*sin(d*x+c)+b*tan(d*x+c)),x)","-\frac{b^{2} \ln \left(b +a \cos \left(d x +c \right)\right)}{d \left(a +b \right) \left(a -b \right) a}+\frac{\ln \left(\cos \left(d x +c \right)-1\right)}{d \left(2 a +2 b \right)}+\frac{\ln \left(1+\cos \left(d x +c \right)\right)}{d \left(2 a -2 b \right)}"," ",0,"-1/d*b^2/(a+b)/(a-b)/a*ln(b+a*cos(d*x+c))+1/d/(2*a+2*b)*ln(cos(d*x+c)-1)+1/d/(2*a-2*b)*ln(1+cos(d*x+c))","A"
253,1,75,70,0.146000," ","int(1/(a*sin(d*x+c)+b*tan(d*x+c)),x)","\frac{b \ln \left(b +a \cos \left(d x +c \right)\right)}{d \left(a +b \right) \left(a -b \right)}+\frac{\ln \left(\cos \left(d x +c \right)-1\right)}{d \left(2 a +2 b \right)}-\frac{\ln \left(1+\cos \left(d x +c \right)\right)}{d \left(2 a -2 b \right)}"," ",0,"1/d*b/(a+b)/(a-b)*ln(b+a*cos(d*x+c))+1/d/(2*a+2*b)*ln(cos(d*x+c)-1)-1/d/(2*a-2*b)*ln(1+cos(d*x+c))","A"
254,1,75,71,0.190000," ","int(sec(d*x+c)/(a*sin(d*x+c)+b*tan(d*x+c)),x)","-\frac{a \ln \left(b +a \cos \left(d x +c \right)\right)}{d \left(a +b \right) \left(a -b \right)}+\frac{\ln \left(\cos \left(d x +c \right)-1\right)}{d \left(2 a +2 b \right)}+\frac{\ln \left(1+\cos \left(d x +c \right)\right)}{d \left(2 a -2 b \right)}"," ",0,"-1/d*a/(a+b)/(a-b)*ln(b+a*cos(d*x+c))+1/d/(2*a+2*b)*ln(cos(d*x+c)-1)+1/d/(2*a-2*b)*ln(1+cos(d*x+c))","A"
255,1,95,90,0.195000," ","int(sec(d*x+c)^2/(a*sin(d*x+c)+b*tan(d*x+c)),x)","\frac{a^{2} \ln \left(b +a \cos \left(d x +c \right)\right)}{d \left(a +b \right) \left(a -b \right) b}+\frac{\ln \left(\cos \left(d x +c \right)-1\right)}{d \left(2 a +2 b \right)}-\frac{\ln \left(1+\cos \left(d x +c \right)\right)}{d \left(2 a -2 b \right)}-\frac{\ln \left(\cos \left(d x +c \right)\right)}{b d}"," ",0,"1/d*a^2/(a+b)/(a-b)/b*ln(b+a*cos(d*x+c))+1/d/(2*a+2*b)*ln(cos(d*x+c)-1)-1/d/(2*a-2*b)*ln(1+cos(d*x+c))-ln(cos(d*x+c))/b/d","A"
256,1,110,104,0.197000," ","int(sec(d*x+c)^3/(a*sin(d*x+c)+b*tan(d*x+c)),x)","-\frac{a^{3} \ln \left(b +a \cos \left(d x +c \right)\right)}{d \left(a +b \right) \left(a -b \right) b^{2}}+\frac{\ln \left(\cos \left(d x +c \right)-1\right)}{d \left(2 a +2 b \right)}+\frac{\ln \left(1+\cos \left(d x +c \right)\right)}{d \left(2 a -2 b \right)}+\frac{a \ln \left(\cos \left(d x +c \right)\right)}{b^{2} d}+\frac{1}{d b \cos \left(d x +c \right)}"," ",0,"-1/d*a^3/(a+b)/(a-b)/b^2*ln(b+a*cos(d*x+c))+1/d/(2*a+2*b)*ln(cos(d*x+c)-1)+1/d/(2*a-2*b)*ln(1+cos(d*x+c))+a*ln(cos(d*x+c))/b^2/d+1/d/b/cos(d*x+c)","A"
257,1,291,221,0.235000," ","int(cos(d*x+c)^3/(a*sin(d*x+c)+b*tan(d*x+c))^2,x)","-\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 d \left(a^{2}-2 a b +b^{2}\right)}+\frac{2 b^{5} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \left(a +b \right)^{2} \left(a -b \right)^{2} a^{2} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a -b \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-a -b \right)}+\frac{10 b^{4} \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a +b \right) \left(a -b \right)}}\right)}{d \left(a +b \right)^{2} \left(a -b \right)^{2} a \sqrt{\left(a +b \right) \left(a -b \right)}}-\frac{4 b^{6} \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a +b \right) \left(a -b \right)}}\right)}{d \left(a +b \right)^{2} \left(a -b \right)^{2} a^{3} \sqrt{\left(a +b \right) \left(a -b \right)}}-\frac{2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,a^{2} \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}+\frac{4 b \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{3}}-\frac{1}{2 d \left(a +b \right)^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}"," ",0,"-1/2/d/(a^2-2*a*b+b^2)*tan(1/2*d*x+1/2*c)+2/d*b^5/(a+b)^2/(a-b)^2/a^2*tan(1/2*d*x+1/2*c)/(tan(1/2*d*x+1/2*c)^2*a-b*tan(1/2*d*x+1/2*c)^2-a-b)+10/d*b^4/(a+b)^2/(a-b)^2/a/((a+b)*(a-b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a+b)*(a-b))^(1/2))-4/d*b^6/(a+b)^2/(a-b)^2/a^3/((a+b)*(a-b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a+b)*(a-b))^(1/2))-2/d/a^2*tan(1/2*d*x+1/2*c)/(tan(1/2*d*x+1/2*c)^2+1)+4/d/a^3*b*arctan(tan(1/2*d*x+1/2*c))-1/2/d/(a+b)^2/tan(1/2*d*x+1/2*c)","A"
258,1,255,205,0.210000," ","int(cos(d*x+c)^2/(a*sin(d*x+c)+b*tan(d*x+c))^2,x)","\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 d \left(a^{2}-2 a b +b^{2}\right)}-\frac{2 b^{4} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \left(a +b \right)^{2} \left(a -b \right)^{2} a \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a -b \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-a -b \right)}-\frac{8 b^{3} \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a +b \right) \left(a -b \right)}}\right)}{d \left(a +b \right)^{2} \left(a -b \right)^{2} \sqrt{\left(a +b \right) \left(a -b \right)}}+\frac{2 b^{5} \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a +b \right) \left(a -b \right)}}\right)}{d \left(a +b \right)^{2} \left(a -b \right)^{2} a^{2} \sqrt{\left(a +b \right) \left(a -b \right)}}-\frac{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{2}}-\frac{1}{2 d \left(a +b \right)^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}"," ",0,"1/2/d/(a^2-2*a*b+b^2)*tan(1/2*d*x+1/2*c)-2/d*b^4/(a+b)^2/(a-b)^2/a*tan(1/2*d*x+1/2*c)/(tan(1/2*d*x+1/2*c)^2*a-b*tan(1/2*d*x+1/2*c)^2-a-b)-8/d*b^3/(a+b)^2/(a-b)^2/((a+b)*(a-b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a+b)*(a-b))^(1/2))+2/d*b^5/(a+b)^2/(a-b)^2/a^2/((a+b)*(a-b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a+b)*(a-b))^(1/2))-2/d/a^2*arctan(tan(1/2*d*x+1/2*c))-1/2/d/(a+b)^2/tan(1/2*d*x+1/2*c)","A"
259,1,155,197,0.175000," ","int(cos(d*x+c)/(a*sin(d*x+c)+b*tan(d*x+c))^2,x)","\frac{-\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 \left(a^{2}-2 a b +b^{2}\right)}-\frac{2 b^{2} \left(-\frac{b \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a -b \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-a -b}-\frac{3 a \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a +b \right) \left(a -b \right)}}\right)}{\sqrt{\left(a +b \right) \left(a -b \right)}}\right)}{\left(a -b \right)^{2} \left(a +b \right)^{2}}-\frac{1}{2 \left(a +b \right)^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}}{d}"," ",0,"1/d*(-1/2/(a^2-2*a*b+b^2)*tan(1/2*d*x+1/2*c)-2*b^2/(a-b)^2/(a+b)^2*(-b*tan(1/2*d*x+1/2*c)/(tan(1/2*d*x+1/2*c)^2*a-b*tan(1/2*d*x+1/2*c)^2-a-b)-3*a/((a+b)*(a-b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a+b)*(a-b))^(1/2)))-1/2/(a+b)^2/tan(1/2*d*x+1/2*c))","A"
260,1,162,181,0.180000," ","int(1/(a*sin(d*x+c)+b*tan(d*x+c))^2,x)","\frac{\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 a^{2}-4 a b +2 b^{2}}+\frac{2 b \left(-\frac{a b \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a -b \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-a -b}-\frac{\left(2 a^{2}+b^{2}\right) \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a +b \right) \left(a -b \right)}}\right)}{\sqrt{\left(a +b \right) \left(a -b \right)}}\right)}{\left(a -b \right)^{2} \left(a +b \right)^{2}}-\frac{1}{2 \left(a +b \right)^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}}{d}"," ",0,"1/d*(1/2/(a^2-2*a*b+b^2)*tan(1/2*d*x+1/2*c)+2*b/(a-b)^2/(a+b)^2*(-a*b*tan(1/2*d*x+1/2*c)/(tan(1/2*d*x+1/2*c)^2*a-b*tan(1/2*d*x+1/2*c)^2-a-b)-(2*a^2+b^2)/((a+b)*(a-b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a+b)*(a-b))^(1/2)))-1/2/(a+b)^2/tan(1/2*d*x+1/2*c))","A"
261,1,162,127,0.220000," ","int(sec(d*x+c)/(a*sin(d*x+c)+b*tan(d*x+c))^2,x)","\frac{-\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 \left(a^{2}-2 a b +b^{2}\right)}-\frac{2 a \left(-\frac{a b \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a -b \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-a -b}-\frac{\left(a^{2}+2 b^{2}\right) \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a +b \right) \left(a -b \right)}}\right)}{\sqrt{\left(a +b \right) \left(a -b \right)}}\right)}{\left(a -b \right)^{2} \left(a +b \right)^{2}}-\frac{1}{2 \left(a +b \right)^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}}{d}"," ",0,"1/d*(-1/2/(a^2-2*a*b+b^2)*tan(1/2*d*x+1/2*c)-2*a/(a-b)^2/(a+b)^2*(-a*b*tan(1/2*d*x+1/2*c)/(tan(1/2*d*x+1/2*c)^2*a-b*tan(1/2*d*x+1/2*c)^2-a-b)-(a^2+2*b^2)/((a+b)*(a-b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a+b)*(a-b))^(1/2)))-1/2/(a+b)^2/tan(1/2*d*x+1/2*c))","A"
262,1,155,122,0.219000," ","int(sec(d*x+c)^2/(a*sin(d*x+c)+b*tan(d*x+c))^2,x)","\frac{\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 a^{2}-4 a b +2 b^{2}}+\frac{2 a^{2} \left(-\frac{a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a -b \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-a -b}-\frac{3 b \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a +b \right) \left(a -b \right)}}\right)}{\sqrt{\left(a +b \right) \left(a -b \right)}}\right)}{\left(a -b \right)^{2} \left(a +b \right)^{2}}-\frac{1}{2 \left(a +b \right)^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}}{d}"," ",0,"1/d*(1/2/(a^2-2*a*b+b^2)*tan(1/2*d*x+1/2*c)+2*a^2/(a-b)^2/(a+b)^2*(-a*tan(1/2*d*x+1/2*c)/(tan(1/2*d*x+1/2*c)^2*a-b*tan(1/2*d*x+1/2*c)^2-a-b)-3*b/((a+b)*(a-b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a+b)*(a-b))^(1/2)))-1/2/(a+b)^2/tan(1/2*d*x+1/2*c))","A"
263,1,276,209,0.244000," ","int(sec(d*x+c)^3/(a*sin(d*x+c)+b*tan(d*x+c))^2,x)","-\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 d \left(a^{2}-2 a b +b^{2}\right)}-\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}{d \,b^{2}}+\frac{2 a^{4} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \left(a -b \right)^{2} b \left(a +b \right)^{2} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a -b \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-a -b \right)}-\frac{2 a^{5} \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a +b \right) \left(a -b \right)}}\right)}{d \left(a -b \right)^{2} b^{2} \left(a +b \right)^{2} \sqrt{\left(a +b \right) \left(a -b \right)}}+\frac{8 a^{3} \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a +b \right) \left(a -b \right)}}\right)}{d \left(a -b \right)^{2} \left(a +b \right)^{2} \sqrt{\left(a +b \right) \left(a -b \right)}}+\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}{d \,b^{2}}-\frac{1}{2 d \left(a +b \right)^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}"," ",0,"-1/2/d/(a^2-2*a*b+b^2)*tan(1/2*d*x+1/2*c)-1/d/b^2*ln(tan(1/2*d*x+1/2*c)-1)+2/d*a^4/(a-b)^2/b/(a+b)^2*tan(1/2*d*x+1/2*c)/(tan(1/2*d*x+1/2*c)^2*a-b*tan(1/2*d*x+1/2*c)^2-a-b)-2/d*a^5/(a-b)^2/b^2/(a+b)^2/((a+b)*(a-b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a+b)*(a-b))^(1/2))+8/d*a^3/(a-b)^2/(a+b)^2/((a+b)*(a-b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a+b)*(a-b))^(1/2))+1/d/b^2*ln(tan(1/2*d*x+1/2*c)+1)-1/2/d/(a+b)^2/tan(1/2*d*x+1/2*c)","A"
264,1,333,240,0.227000," ","int(cos(d*x+c)^3/(a*sin(d*x+c)+b*tan(d*x+c))^3,x)","\frac{b^{6}}{2 d \,a^{3} \left(a +b \right)^{2} \left(a -b \right)^{2} \left(b +a \cos \left(d x +c \right)\right)^{2}}-\frac{15 b^{4} a \ln \left(b +a \cos \left(d x +c \right)\right)}{d \left(a +b \right)^{4} \left(a -b \right)^{4}}+\frac{4 b^{6} \ln \left(b +a \cos \left(d x +c \right)\right)}{d \left(a +b \right)^{4} \left(a -b \right)^{4} a}-\frac{b^{8} \ln \left(b +a \cos \left(d x +c \right)\right)}{d \left(a +b \right)^{4} \left(a -b \right)^{4} a^{3}}-\frac{6 b^{5}}{d a \left(a +b \right)^{3} \left(a -b \right)^{3} \left(b +a \cos \left(d x +c \right)\right)}+\frac{2 b^{7}}{d \,a^{3} \left(a +b \right)^{3} \left(a -b \right)^{3} \left(b +a \cos \left(d x +c \right)\right)}+\frac{1}{4 d \left(a +b \right)^{3} \left(\cos \left(d x +c \right)-1\right)}-\frac{\ln \left(\cos \left(d x +c \right)-1\right) a}{2 d \left(a +b \right)^{4}}-\frac{5 \ln \left(\cos \left(d x +c \right)-1\right) b}{4 d \left(a +b \right)^{4}}-\frac{1}{4 d \left(a -b \right)^{3} \left(1+\cos \left(d x +c \right)\right)}-\frac{a \ln \left(1+\cos \left(d x +c \right)\right)}{2 \left(a -b \right)^{4} d}+\frac{5 b \ln \left(1+\cos \left(d x +c \right)\right)}{4 \left(a -b \right)^{4} d}"," ",0,"1/2/d*b^6/a^3/(a+b)^2/(a-b)^2/(b+a*cos(d*x+c))^2-15/d*b^4/(a+b)^4/(a-b)^4*a*ln(b+a*cos(d*x+c))+4/d*b^6/(a+b)^4/(a-b)^4/a*ln(b+a*cos(d*x+c))-1/d*b^8/(a+b)^4/(a-b)^4/a^3*ln(b+a*cos(d*x+c))-6/d*b^5/a/(a+b)^3/(a-b)^3/(b+a*cos(d*x+c))+2/d*b^7/a^3/(a+b)^3/(a-b)^3/(b+a*cos(d*x+c))+1/4/d/(a+b)^3/(cos(d*x+c)-1)-1/2/d/(a+b)^4*ln(cos(d*x+c)-1)*a-5/4/d/(a+b)^4*ln(cos(d*x+c)-1)*b-1/4/d/(a-b)^3/(1+cos(d*x+c))-1/2*a*ln(1+cos(d*x+c))/(a-b)^4/d+5/4*b*ln(1+cos(d*x+c))/(a-b)^4/d","A"
265,1,295,224,0.229000," ","int(cos(d*x+c)^2/(a*sin(d*x+c)+b*tan(d*x+c))^3,x)","-\frac{b^{5}}{2 d \,a^{2} \left(a +b \right)^{2} \left(a -b \right)^{2} \left(b +a \cos \left(d x +c \right)\right)^{2}}+\frac{10 b^{3} \ln \left(b +a \cos \left(d x +c \right)\right) a^{2}}{d \left(a +b \right)^{4} \left(a -b \right)^{4}}+\frac{2 b^{5} \ln \left(b +a \cos \left(d x +c \right)\right)}{d \left(a +b \right)^{4} \left(a -b \right)^{4}}+\frac{5 b^{4}}{d \left(a +b \right)^{3} \left(a -b \right)^{3} \left(b +a \cos \left(d x +c \right)\right)}-\frac{b^{6}}{d \left(a +b \right)^{3} \left(a -b \right)^{3} a^{2} \left(b +a \cos \left(d x +c \right)\right)}+\frac{1}{4 d \left(a +b \right)^{3} \left(\cos \left(d x +c \right)-1\right)}-\frac{\ln \left(\cos \left(d x +c \right)-1\right) a}{4 d \left(a +b \right)^{4}}-\frac{\ln \left(\cos \left(d x +c \right)-1\right) b}{d \left(a +b \right)^{4}}+\frac{1}{4 d \left(a -b \right)^{3} \left(1+\cos \left(d x +c \right)\right)}+\frac{a \ln \left(1+\cos \left(d x +c \right)\right)}{4 \left(a -b \right)^{4} d}-\frac{b \ln \left(1+\cos \left(d x +c \right)\right)}{\left(a -b \right)^{4} d}"," ",0,"-1/2/d*b^5/a^2/(a+b)^2/(a-b)^2/(b+a*cos(d*x+c))^2+10/d*b^3/(a+b)^4/(a-b)^4*ln(b+a*cos(d*x+c))*a^2+2/d*b^5/(a+b)^4/(a-b)^4*ln(b+a*cos(d*x+c))+5/d*b^4/(a+b)^3/(a-b)^3/(b+a*cos(d*x+c))-1/d*b^6/(a+b)^3/(a-b)^3/a^2/(b+a*cos(d*x+c))+1/4/d/(a+b)^3/(cos(d*x+c)-1)-1/4/d/(a+b)^4*ln(cos(d*x+c)-1)*a-1/d/(a+b)^4*ln(cos(d*x+c)-1)*b+1/4/d/(a-b)^3/(1+cos(d*x+c))+1/4*a*ln(1+cos(d*x+c))/(a-b)^4/d-b*ln(1+cos(d*x+c))/(a-b)^4/d","A"
266,1,220,203,0.191000," ","int(cos(d*x+c)/(a*sin(d*x+c)+b*tan(d*x+c))^3,x)","\frac{b^{4}}{2 d \left(a +b \right)^{2} \left(a -b \right)^{2} a \left(b +a \cos \left(d x +c \right)\right)^{2}}-\frac{4 a \,b^{3}}{d \left(a +b \right)^{3} \left(a -b \right)^{3} \left(b +a \cos \left(d x +c \right)\right)}-\frac{6 a^{3} b^{2} \ln \left(b +a \cos \left(d x +c \right)\right)}{d \left(a +b \right)^{4} \left(a -b \right)^{4}}-\frac{6 b^{4} a \ln \left(b +a \cos \left(d x +c \right)\right)}{d \left(a +b \right)^{4} \left(a -b \right)^{4}}+\frac{1}{4 d \left(a +b \right)^{3} \left(\cos \left(d x +c \right)-1\right)}-\frac{3 \ln \left(\cos \left(d x +c \right)-1\right) b}{4 d \left(a +b \right)^{4}}-\frac{1}{4 d \left(a -b \right)^{3} \left(1+\cos \left(d x +c \right)\right)}+\frac{3 b \ln \left(1+\cos \left(d x +c \right)\right)}{4 \left(a -b \right)^{4} d}"," ",0,"1/2/d*b^4/(a+b)^2/(a-b)^2/a/(b+a*cos(d*x+c))^2-4/d*a*b^3/(a+b)^3/(a-b)^3/(b+a*cos(d*x+c))-6/d*a^3*b^2/(a+b)^4/(a-b)^4*ln(b+a*cos(d*x+c))-6/d*b^4/(a+b)^4/(a-b)^4*a*ln(b+a*cos(d*x+c))+1/4/d/(a+b)^3/(cos(d*x+c)-1)-3/4/d/(a+b)^4*ln(cos(d*x+c)-1)*b-1/4/d/(a-b)^3/(1+cos(d*x+c))+3/4*b*ln(1+cos(d*x+c))/(a-b)^4/d","A"
267,1,322,221,0.205000," ","int(1/(a*sin(d*x+c)+b*tan(d*x+c))^3,x)","-\frac{b^{3}}{2 d \left(a +b \right)^{2} \left(a -b \right)^{2} \left(b +a \cos \left(d x +c \right)\right)^{2}}+\frac{3 b \ln \left(b +a \cos \left(d x +c \right)\right) a^{4}}{d \left(a +b \right)^{4} \left(a -b \right)^{4}}+\frac{8 b^{3} \ln \left(b +a \cos \left(d x +c \right)\right) a^{2}}{d \left(a +b \right)^{4} \left(a -b \right)^{4}}+\frac{b^{5} \ln \left(b +a \cos \left(d x +c \right)\right)}{d \left(a +b \right)^{4} \left(a -b \right)^{4}}+\frac{3 b^{2} a^{2}}{d \left(a +b \right)^{3} \left(a -b \right)^{3} \left(b +a \cos \left(d x +c \right)\right)}+\frac{b^{4}}{d \left(a +b \right)^{3} \left(a -b \right)^{3} \left(b +a \cos \left(d x +c \right)\right)}+\frac{1}{4 d \left(a +b \right)^{3} \left(\cos \left(d x +c \right)-1\right)}+\frac{\ln \left(\cos \left(d x +c \right)-1\right) a}{4 d \left(a +b \right)^{4}}-\frac{\ln \left(\cos \left(d x +c \right)-1\right) b}{2 d \left(a +b \right)^{4}}+\frac{1}{4 d \left(a -b \right)^{3} \left(1+\cos \left(d x +c \right)\right)}-\frac{a \ln \left(1+\cos \left(d x +c \right)\right)}{4 \left(a -b \right)^{4} d}-\frac{b \ln \left(1+\cos \left(d x +c \right)\right)}{2 \left(a -b \right)^{4} d}"," ",0,"-1/2/d*b^3/(a+b)^2/(a-b)^2/(b+a*cos(d*x+c))^2+3/d*b/(a+b)^4/(a-b)^4*ln(b+a*cos(d*x+c))*a^4+8/d*b^3/(a+b)^4/(a-b)^4*ln(b+a*cos(d*x+c))*a^2+1/d*b^5/(a+b)^4/(a-b)^4*ln(b+a*cos(d*x+c))+3/d*b^2/(a+b)^3/(a-b)^3/(b+a*cos(d*x+c))*a^2+1/d*b^4/(a+b)^3/(a-b)^3/(b+a*cos(d*x+c))+1/4/d/(a+b)^3/(cos(d*x+c)-1)+1/4/d/(a+b)^4*ln(cos(d*x+c)-1)*a-1/2/d/(a+b)^4*ln(cos(d*x+c)-1)*b+1/4/d/(a-b)^3/(1+cos(d*x+c))-1/4*a*ln(1+cos(d*x+c))/(a-b)^4/d-1/2*b*ln(1+cos(d*x+c))/(a-b)^4/d","A"
268,1,324,223,0.234000," ","int(sec(d*x+c)/(a*sin(d*x+c)+b*tan(d*x+c))^3,x)","-\frac{a^{5} \ln \left(b +a \cos \left(d x +c \right)\right)}{d \left(a +b \right)^{4} \left(a -b \right)^{4}}-\frac{8 a^{3} b^{2} \ln \left(b +a \cos \left(d x +c \right)\right)}{d \left(a +b \right)^{4} \left(a -b \right)^{4}}-\frac{3 b^{4} a \ln \left(b +a \cos \left(d x +c \right)\right)}{d \left(a +b \right)^{4} \left(a -b \right)^{4}}+\frac{b^{2} a}{2 d \left(a +b \right)^{2} \left(a -b \right)^{2} \left(b +a \cos \left(d x +c \right)\right)^{2}}-\frac{2 a^{3} b}{d \left(a +b \right)^{3} \left(a -b \right)^{3} \left(b +a \cos \left(d x +c \right)\right)}-\frac{2 a \,b^{3}}{d \left(a +b \right)^{3} \left(a -b \right)^{3} \left(b +a \cos \left(d x +c \right)\right)}+\frac{1}{4 d \left(a +b \right)^{3} \left(\cos \left(d x +c \right)-1\right)}+\frac{\ln \left(\cos \left(d x +c \right)-1\right) a}{2 d \left(a +b \right)^{4}}-\frac{\ln \left(\cos \left(d x +c \right)-1\right) b}{4 d \left(a +b \right)^{4}}-\frac{1}{4 d \left(a -b \right)^{3} \left(1+\cos \left(d x +c \right)\right)}+\frac{a \ln \left(1+\cos \left(d x +c \right)\right)}{2 \left(a -b \right)^{4} d}+\frac{b \ln \left(1+\cos \left(d x +c \right)\right)}{4 \left(a -b \right)^{4} d}"," ",0,"-1/d*a^5/(a+b)^4/(a-b)^4*ln(b+a*cos(d*x+c))-8/d*a^3*b^2/(a+b)^4/(a-b)^4*ln(b+a*cos(d*x+c))-3/d*b^4/(a+b)^4/(a-b)^4*a*ln(b+a*cos(d*x+c))+1/2/d*b^2/(a+b)^2*a/(a-b)^2/(b+a*cos(d*x+c))^2-2/d*a^3*b/(a+b)^3/(a-b)^3/(b+a*cos(d*x+c))-2/d*a*b^3/(a+b)^3/(a-b)^3/(b+a*cos(d*x+c))+1/4/d/(a+b)^3/(cos(d*x+c)-1)+1/2/d/(a+b)^4*ln(cos(d*x+c)-1)*a-1/4/d/(a+b)^4*ln(cos(d*x+c)-1)*b-1/4/d/(a-b)^3/(1+cos(d*x+c))+1/2*a*ln(1+cos(d*x+c))/(a-b)^4/d+1/4*b*ln(1+cos(d*x+c))/(a-b)^4/d","A"
269,1,251,202,0.249000," ","int(sec(d*x+c)^2/(a*sin(d*x+c)+b*tan(d*x+c))^3,x)","-\frac{b \,a^{2}}{2 d \left(a +b \right)^{2} \left(a -b \right)^{2} \left(b +a \cos \left(d x +c \right)\right)^{2}}+\frac{a^{4}}{d \left(a +b \right)^{3} \left(a -b \right)^{3} \left(b +a \cos \left(d x +c \right)\right)}+\frac{3 b^{2} a^{2}}{d \left(a +b \right)^{3} \left(a -b \right)^{3} \left(b +a \cos \left(d x +c \right)\right)}+\frac{6 b \ln \left(b +a \cos \left(d x +c \right)\right) a^{4}}{d \left(a +b \right)^{4} \left(a -b \right)^{4}}+\frac{6 b^{3} \ln \left(b +a \cos \left(d x +c \right)\right) a^{2}}{d \left(a +b \right)^{4} \left(a -b \right)^{4}}+\frac{1}{4 d \left(a +b \right)^{3} \left(\cos \left(d x +c \right)-1\right)}+\frac{3 \ln \left(\cos \left(d x +c \right)-1\right) a}{4 d \left(a +b \right)^{4}}+\frac{1}{4 d \left(a -b \right)^{3} \left(1+\cos \left(d x +c \right)\right)}-\frac{3 a \ln \left(1+\cos \left(d x +c \right)\right)}{4 \left(a -b \right)^{4} d}"," ",0,"-1/2/d*b*a^2/(a+b)^2/(a-b)^2/(b+a*cos(d*x+c))^2+1/d*a^4/(a+b)^3/(a-b)^3/(b+a*cos(d*x+c))+3/d*b^2/(a+b)^3/(a-b)^3/(b+a*cos(d*x+c))*a^2+6/d*b/(a+b)^4/(a-b)^4*ln(b+a*cos(d*x+c))*a^4+6/d*b^3/(a+b)^4/(a-b)^4*ln(b+a*cos(d*x+c))*a^2+1/4/d/(a+b)^3/(cos(d*x+c)-1)+3/4/d/(a+b)^4*ln(cos(d*x+c)-1)*a+1/4/d/(a-b)^3/(1+cos(d*x+c))-3/4*a*ln(1+cos(d*x+c))/(a-b)^4/d","A"
270,1,256,218,0.248000," ","int(sec(d*x+c)^3/(a*sin(d*x+c)+b*tan(d*x+c))^3,x)","\frac{a^{3}}{2 d \left(a +b \right)^{2} \left(a -b \right)^{2} \left(b +a \cos \left(d x +c \right)\right)^{2}}-\frac{4 a^{3} b}{d \left(a +b \right)^{3} \left(a -b \right)^{3} \left(b +a \cos \left(d x +c \right)\right)}-\frac{2 a^{5} \ln \left(b +a \cos \left(d x +c \right)\right)}{d \left(a +b \right)^{4} \left(a -b \right)^{4}}-\frac{10 a^{3} b^{2} \ln \left(b +a \cos \left(d x +c \right)\right)}{d \left(a +b \right)^{4} \left(a -b \right)^{4}}+\frac{1}{4 d \left(a +b \right)^{3} \left(\cos \left(d x +c \right)-1\right)}+\frac{\ln \left(\cos \left(d x +c \right)-1\right) a}{d \left(a +b \right)^{4}}+\frac{\ln \left(\cos \left(d x +c \right)-1\right) b}{4 d \left(a +b \right)^{4}}-\frac{1}{4 d \left(a -b \right)^{3} \left(1+\cos \left(d x +c \right)\right)}+\frac{a \ln \left(1+\cos \left(d x +c \right)\right)}{\left(a -b \right)^{4} d}-\frac{b \ln \left(1+\cos \left(d x +c \right)\right)}{4 \left(a -b \right)^{4} d}"," ",0,"1/2/d*a^3/(a+b)^2/(a-b)^2/(b+a*cos(d*x+c))^2-4/d*a^3*b/(a+b)^3/(a-b)^3/(b+a*cos(d*x+c))-2/d*a^5/(a+b)^4/(a-b)^4*ln(b+a*cos(d*x+c))-10/d*a^3*b^2/(a+b)^4/(a-b)^4*ln(b+a*cos(d*x+c))+1/4/d/(a+b)^3/(cos(d*x+c)-1)+1/d/(a+b)^4*ln(cos(d*x+c)-1)*a+1/4/d/(a+b)^4*ln(cos(d*x+c)-1)*b-1/4/d/(a-b)^3/(1+cos(d*x+c))+a*ln(1+cos(d*x+c))/(a-b)^4/d-1/4*b*ln(1+cos(d*x+c))/(a-b)^4/d","A"
271,0,0,155,4.639000," ","int(cos(d*x+c)^m*(a*sin(d*x+c)+b*tan(d*x+c))^3,x)","\int \left(\cos^{m}\left(d x +c \right)\right) \left(a \sin \left(d x +c \right)+b \tan \left(d x +c \right)\right)^{3}\, dx"," ",0,"int(cos(d*x+c)^m*(a*sin(d*x+c)+b*tan(d*x+c))^3,x)","F"
272,0,0,252,2.247000," ","int(cos(d*x+c)^m*(a*sin(d*x+c)+b*tan(d*x+c))^2,x)","\int \left(\cos^{m}\left(d x +c \right)\right) \left(a \sin \left(d x +c \right)+b \tan \left(d x +c \right)\right)^{2}\, dx"," ",0,"int(cos(d*x+c)^m*(a*sin(d*x+c)+b*tan(d*x+c))^2,x)","F"
273,1,40,39,0.088000," ","int(cos(d*x+c)^m*(a*sin(d*x+c)+b*tan(d*x+c)),x)","-\frac{b \left(\cos^{m}\left(d x +c \right)\right)}{d m}-\frac{a \left(\cos^{1+m}\left(d x +c \right)\right)}{d \left(1+m \right)}"," ",0,"-b*cos(d*x+c)^m/d/m-a*cos(d*x+c)^(1+m)/d/(1+m)","A"
274,0,0,146,0.646000," ","int(cos(d*x+c)^m/(a*sin(d*x+c)+b*tan(d*x+c)),x)","\int \frac{\cos^{m}\left(d x +c \right)}{a \sin \left(d x +c \right)+b \tan \left(d x +c \right)}\, dx"," ",0,"int(cos(d*x+c)^m/(a*sin(d*x+c)+b*tan(d*x+c)),x)","F"
275,1,81,61,0.075000," ","int(cos(x)*sin(x)/(a*cos(x)+b*sin(x)),x)","-\frac{4 a b \arctanh \left(\frac{2 a \tan \left(\frac{x}{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(-b \tan \left(\frac{x}{2}\right)+a \right)}{\left(a^{2}+b^{2}\right) \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)}"," ",0,"-4*a*b/(2*a^2+2*b^2)/(a^2+b^2)^(1/2)*arctanh(1/2*(2*a*tan(1/2*x)-2*b)/(a^2+b^2)^(1/2))-2/(a^2+b^2)*(-b*tan(1/2*x)+a)/(tan(1/2*x)^2+1)","A"
276,1,174,86,0.085000," ","int(cos(x)*sin(x)^2/(a*cos(x)+b*sin(x)),x)","-\frac{\tan \left(x \right) a^{3}}{2 \left(a^{2}+b^{2}\right)^{2} \left(\tan^{2}\left(x \right)+1\right)}-\frac{\tan \left(x \right) a \,b^{2}}{2 \left(a^{2}+b^{2}\right)^{2} \left(\tan^{2}\left(x \right)+1\right)}-\frac{a^{2} b}{2 \left(a^{2}+b^{2}\right)^{2} \left(\tan^{2}\left(x \right)+1\right)}-\frac{b^{3}}{2 \left(a^{2}+b^{2}\right)^{2} \left(\tan^{2}\left(x \right)+1\right)}-\frac{\ln \left(\tan^{2}\left(x \right)+1\right) a^{2} b}{2 \left(a^{2}+b^{2}\right)^{2}}+\frac{\arctan \left(\tan \left(x \right)\right) a^{3}}{2 \left(a^{2}+b^{2}\right)^{2}}-\frac{\arctan \left(\tan \left(x \right)\right) a \,b^{2}}{2 \left(a^{2}+b^{2}\right)^{2}}+\frac{b \,a^{2} \ln \left(a +b \tan \left(x \right)\right)}{\left(a^{2}+b^{2}\right)^{2}}"," ",0,"-1/2/(a^2+b^2)^2/(tan(x)^2+1)*tan(x)*a^3-1/2/(a^2+b^2)^2/(tan(x)^2+1)*tan(x)*a*b^2-1/2/(a^2+b^2)^2/(tan(x)^2+1)*a^2*b-1/2/(a^2+b^2)^2/(tan(x)^2+1)*b^3-1/2/(a^2+b^2)^2*ln(tan(x)^2+1)*a^2*b+1/2/(a^2+b^2)^2*arctan(tan(x))*a^3-1/2/(a^2+b^2)^2*arctan(tan(x))*a*b^2+b*a^2/(a^2+b^2)^2*ln(a+b*tan(x))","B"
277,1,166,114,0.088000," ","int(cos(x)*sin(x)^3/(a*cos(x)+b*sin(x)),x)","-\frac{16 a^{3} b \arctanh \left(\frac{2 a \tan \left(\frac{x}{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(-a^{2} b \left(\tan^{5}\left(\frac{x}{2}\right)\right)-a \,b^{2} \left(\tan^{4}\left(\frac{x}{2}\right)\right)+\left(-\frac{10}{3} a^{2} b -\frac{4}{3} b^{3}\right) \left(\tan^{3}\left(\frac{x}{2}\right)\right)+2 a^{3} \left(\tan^{2}\left(\frac{x}{2}\right)\right)-a^{2} b \tan \left(\frac{x}{2}\right)+\frac{2 a^{3}}{3}-\frac{a \,b^{2}}{3}\right)}{\left(a^{4}+2 a^{2} b^{2}+b^{4}\right) \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)^{3}}"," ",0,"-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*x)-2*b)/(a^2+b^2)^(1/2))-2/(a^4+2*a^2*b^2+b^4)*(-a^2*b*tan(1/2*x)^5-a*b^2*tan(1/2*x)^4+(-10/3*a^2*b-4/3*b^3)*tan(1/2*x)^3+2*a^3*tan(1/2*x)^2-a^2*b*tan(1/2*x)+2/3*a^3-1/3*a*b^2)/(tan(1/2*x)^2+1)^3","A"
278,1,175,87,0.082000," ","int(cos(x)^2*sin(x)/(a*cos(x)+b*sin(x)),x)","\frac{\tan \left(x \right) a^{2} b}{2 \left(a^{2}+b^{2}\right)^{2} \left(\tan^{2}\left(x \right)+1\right)}+\frac{\tan \left(x \right) b^{3}}{2 \left(a^{2}+b^{2}\right)^{2} \left(\tan^{2}\left(x \right)+1\right)}-\frac{a^{3}}{2 \left(a^{2}+b^{2}\right)^{2} \left(\tan^{2}\left(x \right)+1\right)}-\frac{a \,b^{2}}{2 \left(a^{2}+b^{2}\right)^{2} \left(\tan^{2}\left(x \right)+1\right)}+\frac{\ln \left(\tan^{2}\left(x \right)+1\right) a \,b^{2}}{2 \left(a^{2}+b^{2}\right)^{2}}-\frac{\arctan \left(\tan \left(x \right)\right) a^{2} b}{2 \left(a^{2}+b^{2}\right)^{2}}+\frac{\arctan \left(\tan \left(x \right)\right) b^{3}}{2 \left(a^{2}+b^{2}\right)^{2}}-\frac{b^{2} a \ln \left(a +b \tan \left(x \right)\right)}{\left(a^{2}+b^{2}\right)^{2}}"," ",0,"1/2/(a^2+b^2)^2/(tan(x)^2+1)*tan(x)*a^2*b+1/2/(a^2+b^2)^2/(tan(x)^2+1)*tan(x)*b^3-1/2/(a^2+b^2)^2/(tan(x)^2+1)*a^3-1/2/(a^2+b^2)^2/(tan(x)^2+1)*a*b^2+1/2/(a^2+b^2)^2*ln(tan(x)^2+1)*a*b^2-1/2/(a^2+b^2)^2*arctan(tan(x))*a^2*b+1/2/(a^2+b^2)^2*arctan(tan(x))*b^3-b^2*a/(a^2+b^2)^2*ln(a+b*tan(x))","A"
279,1,168,104,0.087000," ","int(cos(x)^2*sin(x)^2/(a*cos(x)+b*sin(x)),x)","\frac{8 a^{2} b^{2} \arctanh \left(\frac{2 a \tan \left(\frac{x}{2}\right)-2 b}{2 \sqrt{a^{2}+b^{2}}}\right)}{\left(4 a^{4}+8 a^{2} b^{2}+4 b^{4}\right) \sqrt{a^{2}+b^{2}}}+\frac{-2 a \,b^{2} \left(\tan^{5}\left(\frac{x}{2}\right)\right)-2 b^{3} \left(\tan^{4}\left(\frac{x}{2}\right)\right)+2 \left(\frac{4}{3} a^{3}-\frac{2}{3} a \,b^{2}\right) \left(\tan^{3}\left(\frac{x}{2}\right)\right)+4 a^{2} b \left(\tan^{2}\left(\frac{x}{2}\right)\right)-2 a \,b^{2} \tan \left(\frac{x}{2}\right)+\frac{4 a^{2} b}{3}-\frac{2 b^{3}}{3}}{\left(a^{4}+2 a^{2} b^{2}+b^{4}\right) \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)^{3}}"," ",0,"8*a^2*b^2/(4*a^4+8*a^2*b^2+4*b^4)/(a^2+b^2)^(1/2)*arctanh(1/2*(2*a*tan(1/2*x)-2*b)/(a^2+b^2)^(1/2))+2/(a^4+2*a^2*b^2+b^4)*(-a*b^2*tan(1/2*x)^5-b^3*tan(1/2*x)^4+(4/3*a^3-2/3*a*b^2)*tan(1/2*x)^3+2*a^2*b*tan(1/2*x)^2-a*b^2*tan(1/2*x)+2/3*a^2*b-1/3*b^3)/(tan(1/2*x)^2+1)^3","A"
280,1,363,162,0.086000," ","int(cos(x)^2*sin(x)^3/(a*cos(x)+b*sin(x)),x)","\frac{3 \left(\tan^{3}\left(x \right)\right) a^{2} b^{3}}{4 \left(a^{2}+b^{2}\right)^{3} \left(\tan^{2}\left(x \right)+1\right)^{2}}+\frac{\left(\tan^{3}\left(x \right)\right) b^{5}}{8 \left(a^{2}+b^{2}\right)^{3} \left(\tan^{2}\left(x \right)+1\right)^{2}}+\frac{5 \left(\tan^{3}\left(x \right)\right) a^{4} b}{8 \left(a^{2}+b^{2}\right)^{3} \left(\tan^{2}\left(x \right)+1\right)^{2}}-\frac{\left(\tan^{2}\left(x \right)\right) a^{5}}{2 \left(a^{2}+b^{2}\right)^{3} \left(\tan^{2}\left(x \right)+1\right)^{2}}-\frac{\left(\tan^{2}\left(x \right)\right) a^{3} b^{2}}{2 \left(a^{2}+b^{2}\right)^{3} \left(\tan^{2}\left(x \right)+1\right)^{2}}+\frac{3 \tan \left(x \right) a^{4} b}{8 \left(a^{2}+b^{2}\right)^{3} \left(\tan^{2}\left(x \right)+1\right)^{2}}+\frac{\tan \left(x \right) a^{2} b^{3}}{4 \left(a^{2}+b^{2}\right)^{3} \left(\tan^{2}\left(x \right)+1\right)^{2}}-\frac{\tan \left(x \right) b^{5}}{8 \left(a^{2}+b^{2}\right)^{3} \left(\tan^{2}\left(x \right)+1\right)^{2}}-\frac{a^{5}}{4 \left(a^{2}+b^{2}\right)^{3} \left(\tan^{2}\left(x \right)+1\right)^{2}}+\frac{a \,b^{4}}{4 \left(a^{2}+b^{2}\right)^{3} \left(\tan^{2}\left(x \right)+1\right)^{2}}+\frac{\ln \left(\tan^{2}\left(x \right)+1\right) a^{3} b^{2}}{2 \left(a^{2}+b^{2}\right)^{3}}-\frac{3 \arctan \left(\tan \left(x \right)\right) a^{4} b}{8 \left(a^{2}+b^{2}\right)^{3}}+\frac{3 \arctan \left(\tan \left(x \right)\right) a^{2} b^{3}}{4 \left(a^{2}+b^{2}\right)^{3}}+\frac{\arctan \left(\tan \left(x \right)\right) b^{5}}{8 \left(a^{2}+b^{2}\right)^{3}}-\frac{a^{3} b^{2} \ln \left(a +b \tan \left(x \right)\right)}{\left(a^{2}+b^{2}\right)^{3}}"," ",0,"3/4/(a^2+b^2)^3/(tan(x)^2+1)^2*tan(x)^3*a^2*b^3+1/8/(a^2+b^2)^3/(tan(x)^2+1)^2*tan(x)^3*b^5+5/8/(a^2+b^2)^3/(tan(x)^2+1)^2*tan(x)^3*a^4*b-1/2/(a^2+b^2)^3/(tan(x)^2+1)^2*tan(x)^2*a^5-1/2/(a^2+b^2)^3/(tan(x)^2+1)^2*tan(x)^2*a^3*b^2+3/8/(a^2+b^2)^3/(tan(x)^2+1)^2*tan(x)*a^4*b+1/4/(a^2+b^2)^3/(tan(x)^2+1)^2*tan(x)*a^2*b^3-1/8/(a^2+b^2)^3/(tan(x)^2+1)^2*tan(x)*b^5-1/4/(a^2+b^2)^3/(tan(x)^2+1)^2*a^5+1/4/(a^2+b^2)^3/(tan(x)^2+1)^2*a*b^4+1/2/(a^2+b^2)^3*ln(tan(x)^2+1)*a^3*b^2-3/8/(a^2+b^2)^3*arctan(tan(x))*a^4*b+3/4/(a^2+b^2)^3*arctan(tan(x))*a^2*b^3+1/8/(a^2+b^2)^3*arctan(tan(x))*b^5-a^3*b^2/(a^2+b^2)^3*ln(a+b*tan(x))","B"
281,1,170,115,0.092000," ","int(cos(x)^3*sin(x)/(a*cos(x)+b*sin(x)),x)","-\frac{4 b^{3} a \arctanh \left(\frac{2 a \tan \left(\frac{x}{2}\right)-2 b}{2 \sqrt{a^{2}+b^{2}}}\right)}{\left(2 a^{4}+4 a^{2} b^{2}+2 b^{4}\right) \sqrt{a^{2}+b^{2}}}-\frac{2 \left(-b^{3} \left(\tan^{5}\left(\frac{x}{2}\right)\right)+\left(a^{3}+2 a \,b^{2}\right) \left(\tan^{4}\left(\frac{x}{2}\right)\right)+\left(\frac{4}{3} a^{2} b -\frac{2}{3} b^{3}\right) \left(\tan^{3}\left(\frac{x}{2}\right)\right)+2 a \,b^{2} \left(\tan^{2}\left(\frac{x}{2}\right)\right)-b^{3} \tan \left(\frac{x}{2}\right)+\frac{a^{3}}{3}+\frac{4 a \,b^{2}}{3}\right)}{\left(a^{4}+2 a^{2} b^{2}+b^{4}\right) \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)^{3}}"," ",0,"-4*b^3*a/(2*a^4+4*a^2*b^2+2*b^4)/(a^2+b^2)^(1/2)*arctanh(1/2*(2*a*tan(1/2*x)-2*b)/(a^2+b^2)^(1/2))-2/(a^4+2*a^2*b^2+b^4)*(-b^3*tan(1/2*x)^5+(a^3+2*a*b^2)*tan(1/2*x)^4+(4/3*a^2*b-2/3*b^3)*tan(1/2*x)^3+2*a*b^2*tan(1/2*x)^2-b^3*tan(1/2*x)+1/3*a^3+4/3*a*b^2)/(tan(1/2*x)^2+1)^3","A"
282,1,363,161,0.090000," ","int(cos(x)^3*sin(x)^2/(a*cos(x)+b*sin(x)),x)","\frac{\left(\tan^{3}\left(x \right)\right) a^{5}}{8 \left(a^{2}+b^{2}\right)^{3} \left(\tan^{2}\left(x \right)+1\right)^{2}}-\frac{\left(\tan^{3}\left(x \right)\right) a^{3} b^{2}}{4 \left(a^{2}+b^{2}\right)^{3} \left(\tan^{2}\left(x \right)+1\right)^{2}}-\frac{3 \left(\tan^{3}\left(x \right)\right) a \,b^{4}}{8 \left(a^{2}+b^{2}\right)^{3} \left(\tan^{2}\left(x \right)+1\right)^{2}}+\frac{\left(\tan^{2}\left(x \right)\right) a^{4} b}{2 \left(a^{2}+b^{2}\right)^{3} \left(\tan^{2}\left(x \right)+1\right)^{2}}+\frac{\left(\tan^{2}\left(x \right)\right) a^{2} b^{3}}{2 \left(a^{2}+b^{2}\right)^{3} \left(\tan^{2}\left(x \right)+1\right)^{2}}-\frac{3 \tan \left(x \right) a^{3} b^{2}}{4 \left(a^{2}+b^{2}\right)^{3} \left(\tan^{2}\left(x \right)+1\right)^{2}}-\frac{5 \tan \left(x \right) a \,b^{4}}{8 \left(a^{2}+b^{2}\right)^{3} \left(\tan^{2}\left(x \right)+1\right)^{2}}-\frac{\tan \left(x \right) a^{5}}{8 \left(a^{2}+b^{2}\right)^{3} \left(\tan^{2}\left(x \right)+1\right)^{2}}+\frac{a^{4} b}{4 \left(a^{2}+b^{2}\right)^{3} \left(\tan^{2}\left(x \right)+1\right)^{2}}-\frac{b^{5}}{4 \left(a^{2}+b^{2}\right)^{3} \left(\tan^{2}\left(x \right)+1\right)^{2}}-\frac{\ln \left(\tan^{2}\left(x \right)+1\right) a^{2} b^{3}}{2 \left(a^{2}+b^{2}\right)^{3}}+\frac{\arctan \left(\tan \left(x \right)\right) a^{5}}{8 \left(a^{2}+b^{2}\right)^{3}}+\frac{3 \arctan \left(\tan \left(x \right)\right) a^{3} b^{2}}{4 \left(a^{2}+b^{2}\right)^{3}}-\frac{3 \arctan \left(\tan \left(x \right)\right) a \,b^{4}}{8 \left(a^{2}+b^{2}\right)^{3}}+\frac{a^{2} b^{3} \ln \left(a +b \tan \left(x \right)\right)}{\left(a^{2}+b^{2}\right)^{3}}"," ",0,"1/8/(a^2+b^2)^3/(tan(x)^2+1)^2*tan(x)^3*a^5-1/4/(a^2+b^2)^3/(tan(x)^2+1)^2*tan(x)^3*a^3*b^2-3/8/(a^2+b^2)^3/(tan(x)^2+1)^2*tan(x)^3*a*b^4+1/2/(a^2+b^2)^3/(tan(x)^2+1)^2*tan(x)^2*a^4*b+1/2/(a^2+b^2)^3/(tan(x)^2+1)^2*tan(x)^2*a^2*b^3-3/4/(a^2+b^2)^3/(tan(x)^2+1)^2*tan(x)*a^3*b^2-5/8/(a^2+b^2)^3/(tan(x)^2+1)^2*tan(x)*a*b^4-1/8/(a^2+b^2)^3/(tan(x)^2+1)^2*tan(x)*a^5+1/4/(a^2+b^2)^3/(tan(x)^2+1)^2*a^4*b-1/4/(a^2+b^2)^3/(tan(x)^2+1)^2*b^5-1/2/(a^2+b^2)^3*ln(tan(x)^2+1)*a^2*b^3+1/8/(a^2+b^2)^3*arctan(tan(x))*a^5+3/4/(a^2+b^2)^3*arctan(tan(x))*a^3*b^2-3/8/(a^2+b^2)^3*arctan(tan(x))*a*b^4+a^2*b^3/(a^2+b^2)^3*ln(a+b*tan(x))","B"
283,1,305,177,0.110000," ","int(cos(x)^3*sin(x)^3/(a*cos(x)+b*sin(x)),x)","-\frac{16 a^{3} b^{3} \arctanh \left(\frac{2 a \tan \left(\frac{x}{2}\right)-2 b}{2 \sqrt{a^{2}+b^{2}}}\right)}{\left(8 a^{6}+24 a^{4} b^{2}+24 a^{2} b^{4}+8 b^{6}\right) \sqrt{a^{2}+b^{2}}}-\frac{2 \left(-a^{2} b^{3} \left(\tan^{9}\left(\frac{x}{2}\right)\right)-a \,b^{4} \left(\tan^{8}\left(\frac{x}{2}\right)\right)+\left(-\frac{16}{3} a^{2} b^{3}-\frac{4}{3} b^{5}\right) \left(\tan^{7}\left(\frac{x}{2}\right)\right)+\left(2 a^{5}+6 a^{3} b^{2}\right) \left(\tan^{6}\left(\frac{x}{2}\right)\right)+\left(\frac{16}{5} a^{4} b -\frac{34}{15} a^{2} b^{3}+\frac{8}{15} b^{5}\right) \left(\tan^{5}\left(\frac{x}{2}\right)\right)+\left(-\frac{2}{3} a^{5}+\frac{10}{3} a^{3} b^{2}-2 a \,b^{4}\right) \left(\tan^{4}\left(\frac{x}{2}\right)\right)+\left(-\frac{16}{3} a^{2} b^{3}-\frac{4}{3} b^{5}\right) \left(\tan^{3}\left(\frac{x}{2}\right)\right)+\left(\frac{2}{3} a^{5}+\frac{14}{3} a^{3} b^{2}\right) \left(\tan^{2}\left(\frac{x}{2}\right)\right)-a^{2} b^{3} \tan \left(\frac{x}{2}\right)+\frac{2 a^{5}}{15}+\frac{14 a^{3} b^{2}}{15}-\frac{a \,b^{4}}{5}\right)}{\left(a^{4}+2 a^{2} b^{2}+b^{4}\right) \left(a^{2}+b^{2}\right) \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)^{5}}"," ",0,"-16*a^3*b^3/(8*a^6+24*a^4*b^2+24*a^2*b^4+8*b^6)/(a^2+b^2)^(1/2)*arctanh(1/2*(2*a*tan(1/2*x)-2*b)/(a^2+b^2)^(1/2))-2/(a^4+2*a^2*b^2+b^4)/(a^2+b^2)*(-a^2*b^3*tan(1/2*x)^9-a*b^4*tan(1/2*x)^8+(-16/3*a^2*b^3-4/3*b^5)*tan(1/2*x)^7+(2*a^5+6*a^3*b^2)*tan(1/2*x)^6+(16/5*a^4*b-34/15*a^2*b^3+8/15*b^5)*tan(1/2*x)^5+(-2/3*a^5+10/3*a^3*b^2-2*a*b^4)*tan(1/2*x)^4+(-16/3*a^2*b^3-4/3*b^5)*tan(1/2*x)^3+(2/3*a^5+14/3*a^3*b^2)*tan(1/2*x)^2-a^2*b^3*tan(1/2*x)+2/15*a^5+14/15*a^3*b^2-1/5*a*b^4)/(tan(1/2*x)^2+1)^5","A"
284,1,120,70,0.103000," ","int(cos(x)*sin(x)/(a*cos(x)+b*sin(x))^2,x)","\frac{\ln \left(\tan^{2}\left(x \right)+1\right) a^{2}}{2 \left(a^{2}+b^{2}\right)^{2}}-\frac{\ln \left(\tan^{2}\left(x \right)+1\right) b^{2}}{2 \left(a^{2}+b^{2}\right)^{2}}+\frac{2 a b \arctan \left(\tan \left(x \right)\right)}{\left(a^{2}+b^{2}\right)^{2}}+\frac{a}{\left(a^{2}+b^{2}\right) \left(a +b \tan \left(x \right)\right)}-\frac{\ln \left(a +b \tan \left(x \right)\right) a^{2}}{\left(a^{2}+b^{2}\right)^{2}}+\frac{\ln \left(a +b \tan \left(x \right)\right) b^{2}}{\left(a^{2}+b^{2}\right)^{2}}"," ",0,"1/2/(a^2+b^2)^2*ln(tan(x)^2+1)*a^2-1/2/(a^2+b^2)^2*ln(tan(x)^2+1)*b^2+2/(a^2+b^2)^2*a*b*arctan(tan(x))+a/(a^2+b^2)/(a+b*tan(x))-1/(a^2+b^2)^2*ln(a+b*tan(x))*a^2+1/(a^2+b^2)^2*ln(a+b*tan(x))*b^2","A"
285,1,142,106,0.121000," ","int(cos(x)*sin(x)^2/(a*cos(x)+b*sin(x))^2,x)","-\frac{2 a \left(\frac{-\tan \left(\frac{x}{2}\right) b^{2}-a b}{\left(\tan^{2}\left(\frac{x}{2}\right)\right) a -2 b \tan \left(\frac{x}{2}\right)-a}-\frac{\left(a^{2}-2 b^{2}\right) \arctanh \left(\frac{2 a \tan \left(\frac{x}{2}\right)-2 b}{2 \sqrt{a^{2}+b^{2}}}\right)}{\sqrt{a^{2}+b^{2}}}\right)}{\left(a^{2}+b^{2}\right)^{2}}+\frac{2 \left(-a^{2}+b^{2}\right) \tan \left(\frac{x}{2}\right)-4 a b}{\left(a^{4}+2 a^{2} b^{2}+b^{4}\right) \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)}"," ",0,"-2*a/(a^2+b^2)^2*((-tan(1/2*x)*b^2-a*b)/(tan(1/2*x)^2*a-2*b*tan(1/2*x)-a)-(a^2-2*b^2)/(a^2+b^2)^(1/2)*arctanh(1/2*(2*a*tan(1/2*x)-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*x)-2*a*b)/(tan(1/2*x)^2+1)","A"
286,1,243,127,0.114000," ","int(cos(x)*sin(x)^3/(a*cos(x)+b*sin(x))^2,x)","-\frac{\tan \left(x \right) a^{3} b}{\left(a^{2}+b^{2}\right)^{3} \left(\tan^{2}\left(x \right)+1\right)}-\frac{\tan \left(x \right) a \,b^{3}}{\left(a^{2}+b^{2}\right)^{3} \left(\tan^{2}\left(x \right)+1\right)}+\frac{a^{4}}{2 \left(a^{2}+b^{2}\right)^{3} \left(\tan^{2}\left(x \right)+1\right)}-\frac{b^{4}}{2 \left(a^{2}+b^{2}\right)^{3} \left(\tan^{2}\left(x \right)+1\right)}+\frac{\ln \left(\tan^{2}\left(x \right)+1\right) a^{4}}{2 \left(a^{2}+b^{2}\right)^{3}}-\frac{3 \ln \left(\tan^{2}\left(x \right)+1\right) a^{2} b^{2}}{2 \left(a^{2}+b^{2}\right)^{3}}+\frac{3 \arctan \left(\tan \left(x \right)\right) a^{3} b}{\left(a^{2}+b^{2}\right)^{3}}-\frac{a \arctan \left(\tan \left(x \right)\right) b^{3}}{\left(a^{2}+b^{2}\right)^{3}}+\frac{a^{3}}{\left(a^{2}+b^{2}\right)^{2} \left(a +b \tan \left(x \right)\right)}-\frac{a^{4} \ln \left(a +b \tan \left(x \right)\right)}{\left(a^{2}+b^{2}\right)^{3}}+\frac{3 a^{2} \ln \left(a +b \tan \left(x \right)\right) b^{2}}{\left(a^{2}+b^{2}\right)^{3}}"," ",0,"-1/(a^2+b^2)^3/(tan(x)^2+1)*tan(x)*a^3*b-1/(a^2+b^2)^3/(tan(x)^2+1)*tan(x)*a*b^3+1/2/(a^2+b^2)^3/(tan(x)^2+1)*a^4-1/2/(a^2+b^2)^3/(tan(x)^2+1)*b^4+1/2/(a^2+b^2)^3*ln(tan(x)^2+1)*a^4-3/2/(a^2+b^2)^3*ln(tan(x)^2+1)*a^2*b^2+3/(a^2+b^2)^3*arctan(tan(x))*a^3*b-1/(a^2+b^2)^3*a*arctan(tan(x))*b^3+a^3/(a^2+b^2)^2/(a+b*tan(x))-a^4/(a^2+b^2)^3*ln(a+b*tan(x))+3*a^2/(a^2+b^2)^3*ln(a+b*tan(x))*b^2","A"
287,1,152,105,0.112000," ","int(cos(x)^2*sin(x)/(a*cos(x)+b*sin(x))^2,x)","\frac{4 b \left(\frac{-\frac{\tan \left(\frac{x}{2}\right) b^{2}}{2}-\frac{a b}{2}}{\left(\tan^{2}\left(\frac{x}{2}\right)\right) a -2 b \tan \left(\frac{x}{2}\right)-a}-\frac{\left(2 a^{2}-b^{2}\right) \arctanh \left(\frac{2 a \tan \left(\frac{x}{2}\right)-2 b}{2 \sqrt{a^{2}+b^{2}}}\right)}{2 \sqrt{a^{2}+b^{2}}}\right)}{a^{4}+2 a^{2} b^{2}+b^{4}}-\frac{4 \left(-a b \tan \left(\frac{x}{2}\right)+\frac{a^{2}}{2}-\frac{b^{2}}{2}\right)}{\left(a^{4}+2 a^{2} b^{2}+b^{4}\right) \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)}"," ",0,"4*b/(a^4+2*a^2*b^2+b^4)*((-1/2*tan(1/2*x)*b^2-1/2*a*b)/(tan(1/2*x)^2*a-2*b*tan(1/2*x)-a)-1/2*(2*a^2-b^2)/(a^2+b^2)^(1/2)*arctanh(1/2*(2*a*tan(1/2*x)-2*b)/(a^2+b^2)^(1/2)))-4/(a^4+2*a^2*b^2+b^4)*(-a*b*tan(1/2*x)+1/2*a^2-1/2*b^2)/(tan(1/2*x)^2+1)","A"
288,1,260,127,0.124000," ","int(cos(x)^2*sin(x)^2/(a*cos(x)+b*sin(x))^2,x)","-\frac{\tan \left(x \right) a^{4}}{2 \left(a^{2}+b^{2}\right)^{3} \left(\tan^{2}\left(x \right)+1\right)}+\frac{\tan \left(x \right) b^{4}}{2 \left(a^{2}+b^{2}\right)^{3} \left(\tan^{2}\left(x \right)+1\right)}-\frac{a^{3} b}{\left(a^{2}+b^{2}\right)^{3} \left(\tan^{2}\left(x \right)+1\right)}-\frac{b^{3} a}{\left(a^{2}+b^{2}\right)^{3} \left(\tan^{2}\left(x \right)+1\right)}-\frac{\ln \left(\tan^{2}\left(x \right)+1\right) a^{3} b}{\left(a^{2}+b^{2}\right)^{3}}+\frac{\ln \left(\tan^{2}\left(x \right)+1\right) a \,b^{3}}{\left(a^{2}+b^{2}\right)^{3}}-\frac{3 \arctan \left(\tan \left(x \right)\right) a^{2} b^{2}}{\left(a^{2}+b^{2}\right)^{3}}+\frac{\arctan \left(\tan \left(x \right)\right) b^{4}}{2 \left(a^{2}+b^{2}\right)^{3}}+\frac{\arctan \left(\tan \left(x \right)\right) a^{4}}{2 \left(a^{2}+b^{2}\right)^{3}}-\frac{b \,a^{2}}{\left(a^{2}+b^{2}\right)^{2} \left(a +b \tan \left(x \right)\right)}+\frac{2 b \,a^{3} \ln \left(a +b \tan \left(x \right)\right)}{\left(a^{2}+b^{2}\right)^{3}}-\frac{2 b^{3} a \ln \left(a +b \tan \left(x \right)\right)}{\left(a^{2}+b^{2}\right)^{3}}"," ",0,"-1/2/(a^2+b^2)^3/(tan(x)^2+1)*tan(x)*a^4+1/2/(a^2+b^2)^3/(tan(x)^2+1)*tan(x)*b^4-1/(a^2+b^2)^3/(tan(x)^2+1)*a^3*b-1/(a^2+b^2)^3/(tan(x)^2+1)*b^3*a-1/(a^2+b^2)^3*ln(tan(x)^2+1)*a^3*b+1/(a^2+b^2)^3*ln(tan(x)^2+1)*a*b^3-3/(a^2+b^2)^3*arctan(tan(x))*a^2*b^2+1/2/(a^2+b^2)^3*arctan(tan(x))*b^4+1/2/(a^2+b^2)^3*arctan(tan(x))*a^4-b*a^2/(a^2+b^2)^2/(a+b*tan(x))+2*b*a^3/(a^2+b^2)^3*ln(a+b*tan(x))-2*b^3*a/(a^2+b^2)^3*ln(a+b*tan(x))","B"
289,1,269,164,0.139000," ","int(cos(x)^2*sin(x)^3/(a*cos(x)+b*sin(x))^2,x)","\frac{4 a^{2} b \left(\frac{-\frac{\tan \left(\frac{x}{2}\right) b^{2}}{2}-\frac{a b}{2}}{\left(\tan^{2}\left(\frac{x}{2}\right)\right) a -2 b \tan \left(\frac{x}{2}\right)-a}-\frac{\left(2 a^{2}-3 b^{2}\right) \arctanh \left(\frac{2 a \tan \left(\frac{x}{2}\right)-2 b}{2 \sqrt{a^{2}+b^{2}}}\right)}{2 \sqrt{a^{2}+b^{2}}}\right)}{\left(a^{4}+2 a^{2} b^{2}+b^{4}\right) \left(a^{2}+b^{2}\right)}-\frac{4 \left(\left(-a^{3} b +b^{3} a \right) \left(\tan^{5}\left(\frac{x}{2}\right)\right)+\left(-\frac{3}{2} a^{2} b^{2}+\frac{1}{2} b^{4}\right) \left(\tan^{4}\left(\frac{x}{2}\right)\right)+\left(-\frac{10}{3} a^{3} b +\frac{2}{3} b^{3} a \right) \left(\tan^{3}\left(\frac{x}{2}\right)\right)+\left(a^{4}-3 a^{2} b^{2}\right) \left(\tan^{2}\left(\frac{x}{2}\right)\right)+\left(-a^{3} b +b^{3} a \right) \tan \left(\frac{x}{2}\right)+\frac{a^{4}}{3}-\frac{3 a^{2} b^{2}}{2}+\frac{b^{4}}{6}\right)}{\left(a^{2}+b^{2}\right) \left(a^{4}+2 a^{2} b^{2}+b^{4}\right) \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)^{3}}"," ",0,"4*a^2*b/(a^4+2*a^2*b^2+b^4)/(a^2+b^2)*((-1/2*tan(1/2*x)*b^2-1/2*a*b)/(tan(1/2*x)^2*a-2*b*tan(1/2*x)-a)-1/2*(2*a^2-3*b^2)/(a^2+b^2)^(1/2)*arctanh(1/2*(2*a*tan(1/2*x)-2*b)/(a^2+b^2)^(1/2)))-4/(a^2+b^2)/(a^4+2*a^2*b^2+b^4)*((-a^3*b+a*b^3)*tan(1/2*x)^5+(-3/2*a^2*b^2+1/2*b^4)*tan(1/2*x)^4+(-10/3*a^3*b+2/3*b^3*a)*tan(1/2*x)^3+(a^4-3*a^2*b^2)*tan(1/2*x)^2+(-a^3*b+a*b^3)*tan(1/2*x)+1/3*a^4-3/2*a^2*b^2+1/6*b^4)/(tan(1/2*x)^2+1)^3","A"
290,1,241,126,0.115000," ","int(cos(x)^3*sin(x)/(a*cos(x)+b*sin(x))^2,x)","\frac{\tan \left(x \right) a^{3} b}{\left(a^{2}+b^{2}\right)^{3} \left(\tan^{2}\left(x \right)+1\right)}+\frac{\tan \left(x \right) a \,b^{3}}{\left(a^{2}+b^{2}\right)^{3} \left(\tan^{2}\left(x \right)+1\right)}-\frac{a^{4}}{2 \left(a^{2}+b^{2}\right)^{3} \left(\tan^{2}\left(x \right)+1\right)}+\frac{b^{4}}{2 \left(a^{2}+b^{2}\right)^{3} \left(\tan^{2}\left(x \right)+1\right)}+\frac{3 \ln \left(\tan^{2}\left(x \right)+1\right) a^{2} b^{2}}{2 \left(a^{2}+b^{2}\right)^{3}}-\frac{\ln \left(\tan^{2}\left(x \right)+1\right) b^{4}}{2 \left(a^{2}+b^{2}\right)^{3}}-\frac{\arctan \left(\tan \left(x \right)\right) a^{3} b}{\left(a^{2}+b^{2}\right)^{3}}+\frac{3 a \arctan \left(\tan \left(x \right)\right) b^{3}}{\left(a^{2}+b^{2}\right)^{3}}+\frac{a \,b^{2}}{\left(a^{2}+b^{2}\right)^{2} \left(a +b \tan \left(x \right)\right)}-\frac{3 a^{2} \ln \left(a +b \tan \left(x \right)\right) b^{2}}{\left(a^{2}+b^{2}\right)^{3}}+\frac{b^{4} \ln \left(a +b \tan \left(x \right)\right)}{\left(a^{2}+b^{2}\right)^{3}}"," ",0,"1/(a^2+b^2)^3/(tan(x)^2+1)*tan(x)*a^3*b+1/(a^2+b^2)^3/(tan(x)^2+1)*tan(x)*a*b^3-1/2/(a^2+b^2)^3/(tan(x)^2+1)*a^4+1/2/(a^2+b^2)^3/(tan(x)^2+1)*b^4+3/2/(a^2+b^2)^3*ln(tan(x)^2+1)*a^2*b^2-1/2/(a^2+b^2)^3*ln(tan(x)^2+1)*b^4-1/(a^2+b^2)^3*arctan(tan(x))*a^3*b+3/(a^2+b^2)^3*a*arctan(tan(x))*b^3+a*b^2/(a^2+b^2)^2/(a+b*tan(x))-3*a^2/(a^2+b^2)^3*ln(a+b*tan(x))*b^2+b^4/(a^2+b^2)^3*ln(a+b*tan(x))","A"
291,1,261,168,0.142000," ","int(cos(x)^3*sin(x)^2/(a*cos(x)+b*sin(x))^2,x)","-\frac{2 a \,b^{2} \left(\frac{-\tan \left(\frac{x}{2}\right) b^{2}-a b}{\left(\tan^{2}\left(\frac{x}{2}\right)\right) a -2 b \tan \left(\frac{x}{2}\right)-a}-\frac{\left(3 a^{2}-2 b^{2}\right) \arctanh \left(\frac{2 a \tan \left(\frac{x}{2}\right)-2 b}{2 \sqrt{a^{2}+b^{2}}}\right)}{\sqrt{a^{2}+b^{2}}}\right)}{\left(a^{4}+2 a^{2} b^{2}+b^{4}\right) \left(a^{2}+b^{2}\right)}+\frac{2 \left(-3 a^{2} b^{2}+b^{4}\right) \left(\tan^{5}\left(\frac{x}{2}\right)\right)-8 b^{3} a \left(\tan^{4}\left(\frac{x}{2}\right)\right)+2 \left(\frac{4}{3} a^{4}-6 a^{2} b^{2}+\frac{2}{3} b^{4}\right) \left(\tan^{3}\left(\frac{x}{2}\right)\right)+2 \left(4 a^{3} b -4 b^{3} a \right) \left(\tan^{2}\left(\frac{x}{2}\right)\right)+2 \left(-3 a^{2} b^{2}+b^{4}\right) \tan \left(\frac{x}{2}\right)+\frac{8 a^{3} b}{3}-\frac{16 b^{3} a}{3}}{\left(a^{2}+b^{2}\right) \left(a^{4}+2 a^{2} b^{2}+b^{4}\right) \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)^{3}}"," ",0,"-2*a*b^2/(a^4+2*a^2*b^2+b^4)/(a^2+b^2)*((-tan(1/2*x)*b^2-a*b)/(tan(1/2*x)^2*a-2*b*tan(1/2*x)-a)-(3*a^2-2*b^2)/(a^2+b^2)^(1/2)*arctanh(1/2*(2*a*tan(1/2*x)-2*b)/(a^2+b^2)^(1/2)))+2/(a^2+b^2)/(a^4+2*a^2*b^2+b^4)*((-3*a^2*b^2+b^4)*tan(1/2*x)^5-4*b^3*a*tan(1/2*x)^4+(4/3*a^4-6*a^2*b^2+2/3*b^4)*tan(1/2*x)^3+(4*a^3*b-4*a*b^3)*tan(1/2*x)^2+(-3*a^2*b^2+b^4)*tan(1/2*x)+4/3*a^3*b-8/3*b^3*a)/(tan(1/2*x)^2+1)^3","A"
292,1,515,200,0.130000," ","int(cos(x)^3*sin(x)^3/(a*cos(x)+b*sin(x))^2,x)","\frac{\left(\tan^{3}\left(x \right)\right) a^{3} b^{3}}{2 \left(a^{2}+b^{2}\right)^{4} \left(\tan^{2}\left(x \right)+1\right)^{2}}-\frac{3 \left(\tan^{3}\left(x \right)\right) a \,b^{5}}{4 \left(a^{2}+b^{2}\right)^{4} \left(\tan^{2}\left(x \right)+1\right)^{2}}+\frac{5 \left(\tan^{3}\left(x \right)\right) a^{5} b}{4 \left(a^{2}+b^{2}\right)^{4} \left(\tan^{2}\left(x \right)+1\right)^{2}}-\frac{\left(\tan^{2}\left(x \right)\right) a^{6}}{2 \left(a^{2}+b^{2}\right)^{4} \left(\tan^{2}\left(x \right)+1\right)^{2}}+\frac{\left(\tan^{2}\left(x \right)\right) a^{4} b^{2}}{\left(a^{2}+b^{2}\right)^{4} \left(\tan^{2}\left(x \right)+1\right)^{2}}+\frac{3 \left(\tan^{2}\left(x \right)\right) a^{2} b^{4}}{2 \left(a^{2}+b^{2}\right)^{4} \left(\tan^{2}\left(x \right)+1\right)^{2}}+\frac{3 \tan \left(x \right) a^{5} b}{4 \left(a^{2}+b^{2}\right)^{4} \left(\tan^{2}\left(x \right)+1\right)^{2}}-\frac{\tan \left(x \right) a^{3} b^{3}}{2 \left(a^{2}+b^{2}\right)^{4} \left(\tan^{2}\left(x \right)+1\right)^{2}}-\frac{5 \tan \left(x \right) a \,b^{5}}{4 \left(a^{2}+b^{2}\right)^{4} \left(\tan^{2}\left(x \right)+1\right)^{2}}-\frac{a^{6}}{4 \left(a^{2}+b^{2}\right)^{4} \left(\tan^{2}\left(x \right)+1\right)^{2}}+\frac{5 a^{4} b^{2}}{4 \left(a^{2}+b^{2}\right)^{4} \left(\tan^{2}\left(x \right)+1\right)^{2}}+\frac{5 a^{2} b^{4}}{4 \left(a^{2}+b^{2}\right)^{4} \left(\tan^{2}\left(x \right)+1\right)^{2}}-\frac{b^{6}}{4 \left(a^{2}+b^{2}\right)^{4} \left(\tan^{2}\left(x \right)+1\right)^{2}}+\frac{3 \ln \left(\tan^{2}\left(x \right)+1\right) a^{4} b^{2}}{2 \left(a^{2}+b^{2}\right)^{4}}-\frac{3 \ln \left(\tan^{2}\left(x \right)+1\right) a^{2} b^{4}}{2 \left(a^{2}+b^{2}\right)^{4}}-\frac{3 \arctan \left(\tan \left(x \right)\right) a^{5} b}{4 \left(a^{2}+b^{2}\right)^{4}}+\frac{9 \arctan \left(\tan \left(x \right)\right) a^{3} b^{3}}{2 \left(a^{2}+b^{2}\right)^{4}}-\frac{3 \arctan \left(\tan \left(x \right)\right) a \,b^{5}}{4 \left(a^{2}+b^{2}\right)^{4}}+\frac{a^{3} b^{2}}{\left(a^{2}+b^{2}\right)^{3} \left(a +b \tan \left(x \right)\right)}-\frac{3 a^{4} b^{2} \ln \left(a +b \tan \left(x \right)\right)}{\left(a^{2}+b^{2}\right)^{4}}+\frac{3 a^{2} b^{4} \ln \left(a +b \tan \left(x \right)\right)}{\left(a^{2}+b^{2}\right)^{4}}"," ",0,"1/2/(a^2+b^2)^4/(tan(x)^2+1)^2*tan(x)^3*a^3*b^3-3/4/(a^2+b^2)^4/(tan(x)^2+1)^2*tan(x)^3*a*b^5+5/4/(a^2+b^2)^4/(tan(x)^2+1)^2*tan(x)^3*a^5*b-1/2/(a^2+b^2)^4/(tan(x)^2+1)^2*tan(x)^2*a^6+1/(a^2+b^2)^4/(tan(x)^2+1)^2*tan(x)^2*a^4*b^2+3/2/(a^2+b^2)^4/(tan(x)^2+1)^2*tan(x)^2*a^2*b^4+3/4/(a^2+b^2)^4/(tan(x)^2+1)^2*tan(x)*a^5*b-1/2/(a^2+b^2)^4/(tan(x)^2+1)^2*tan(x)*a^3*b^3-5/4/(a^2+b^2)^4/(tan(x)^2+1)^2*tan(x)*a*b^5-1/4/(a^2+b^2)^4/(tan(x)^2+1)^2*a^6+5/4/(a^2+b^2)^4/(tan(x)^2+1)^2*a^4*b^2+5/4/(a^2+b^2)^4/(tan(x)^2+1)^2*a^2*b^4-1/4/(a^2+b^2)^4/(tan(x)^2+1)^2*b^6+3/2/(a^2+b^2)^4*ln(tan(x)^2+1)*a^4*b^2-3/2/(a^2+b^2)^4*ln(tan(x)^2+1)*a^2*b^4-3/4/(a^2+b^2)^4*arctan(tan(x))*a^5*b+9/2/(a^2+b^2)^4*arctan(tan(x))*a^3*b^3-3/4/(a^2+b^2)^4*arctan(tan(x))*a*b^5+a^3*b^2/(a^2+b^2)^3/(a+b*tan(x))-3*a^4*b^2/(a^2+b^2)^4*ln(a+b*tan(x))+3*a^2*b^4/(a^2+b^2)^4*ln(a+b*tan(x))","B"
293,1,63,43,0.111000," ","int(tan(x)/(b*cos(x)+a*sin(x)),x)","-\frac{\ln \left(\tan \left(\frac{x}{2}\right)-1\right)}{a}-\frac{2 b \arctanh \left(\frac{2 b \tan \left(\frac{x}{2}\right)-2 a}{2 \sqrt{a^{2}+b^{2}}}\right)}{a \sqrt{a^{2}+b^{2}}}+\frac{\ln \left(\tan \left(\frac{x}{2}\right)+1\right)}{a}"," ",0,"-1/a*ln(tan(1/2*x)-1)-2*b/a/(a^2+b^2)^(1/2)*arctanh(1/2*(2*b*tan(1/2*x)-2*a)/(a^2+b^2)^(1/2))+1/a*ln(tan(1/2*x)+1)","A"
294,1,49,44,0.101000," ","int(cot(x)/(b*cos(x)+a*sin(x)),x)","-\frac{2 a \arctanh \left(\frac{2 b \tan \left(\frac{x}{2}\right)-2 a}{2 \sqrt{a^{2}+b^{2}}}\right)}{b \sqrt{a^{2}+b^{2}}}+\frac{\ln \left(\tan \left(\frac{x}{2}\right)\right)}{b}"," ",0,"-2*a/b/(a^2+b^2)^(1/2)*arctanh(1/2*(2*b*tan(1/2*x)-2*a)/(a^2+b^2)^(1/2))+1/b*ln(tan(1/2*x))","A"