1,1,117,47,0.059000," ","int((A+B*sin(x))/(a+b*cos(x)),x)","-\frac{\ln \left(a \left(\tan^{2}\left(\frac{x}{2}\right)\right)-\left(\tan^{2}\left(\frac{x}{2}\right)\right) b +a +b \right) a B}{b \left(a -b \right)}+\frac{\ln \left(a \left(\tan^{2}\left(\frac{x}{2}\right)\right)-\left(\tan^{2}\left(\frac{x}{2}\right)\right) b +a +b \right) B}{a -b}+\frac{2 A \arctan \left(\frac{\tan \left(\frac{x}{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)}}+\frac{B \ln \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)}{b}"," ",0,"-1/b/(a-b)*ln(a*tan(1/2*x)^2-tan(1/2*x)^2*b+a+b)*a*B+1/(a-b)*ln(a*tan(1/2*x)^2-tan(1/2*x)^2*b+a+b)*B+2*A/((a-b)*(a+b))^(1/2)*arctan(tan(1/2*x)*(a-b)/((a-b)*(a+b))^(1/2))+B/b*ln(tan(1/2*x)^2+1)","B"
2,1,19,19,0.053000," ","int((A+B*sin(x))/(cos(x)+1),x)","A \tan \left(\frac{x}{2}\right)+B \ln \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)"," ",0,"A*tan(1/2*x)+B*ln(tan(1/2*x)^2+1)","A"
3,1,31,23,0.070000," ","int((A+B*sin(x))/(1-cos(x)),x)","-\frac{A}{\tan \left(\frac{x}{2}\right)}+2 B \ln \left(\tan \left(\frac{x}{2}\right)\right)-B \ln \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)"," ",0,"-A/tan(1/2*x)+2*B*ln(tan(1/2*x))-B*ln(tan(1/2*x)^2+1)","A"
4,1,150,48,0.060000," ","int((b+c+sin(x))/(a+b*cos(x)),x)","-\frac{\ln \left(a \left(\tan^{2}\left(\frac{x}{2}\right)\right)-\left(\tan^{2}\left(\frac{x}{2}\right)\right) b +a +b \right) a}{b \left(a -b \right)}+\frac{\ln \left(a \left(\tan^{2}\left(\frac{x}{2}\right)\right)-\left(\tan^{2}\left(\frac{x}{2}\right)\right) b +a +b \right)}{a -b}+\frac{2 b \arctan \left(\frac{\tan \left(\frac{x}{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)}}+\frac{2 \arctan \left(\frac{\tan \left(\frac{x}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) c}{\sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{\ln \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)}{b}"," ",0,"-1/b/(a-b)*ln(a*tan(1/2*x)^2-tan(1/2*x)^2*b+a+b)*a+1/(a-b)*ln(a*tan(1/2*x)^2-tan(1/2*x)^2*b+a+b)+2*b/((a-b)*(a+b))^(1/2)*arctan(tan(1/2*x)*(a-b)/((a-b)*(a+b))^(1/2))+2/((a-b)*(a+b))^(1/2)*arctan(tan(1/2*x)*(a-b)/((a-b)*(a+b))^(1/2))*c+1/b*ln(tan(1/2*x)^2+1)","B"
5,1,110,48,0.063000," ","int((b+c+sin(x))/(a-b*cos(x)),x)","\frac{\ln \left(a \left(\tan^{2}\left(\frac{x}{2}\right)\right)+\left(\tan^{2}\left(\frac{x}{2}\right)\right) b +a -b \right)}{b}+\frac{2 b \arctan \left(\frac{\left(a +b \right) \tan \left(\frac{x}{2}\right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{2 \arctan \left(\frac{\left(a +b \right) \tan \left(\frac{x}{2}\right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) c}{\sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{\ln \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)}{b}"," ",0,"1/b*ln(a*tan(1/2*x)^2+tan(1/2*x)^2*b+a-b)+2*b/((a-b)*(a+b))^(1/2)*arctan((a+b)*tan(1/2*x)/((a-b)*(a+b))^(1/2))+2/((a-b)*(a+b))^(1/2)*arctan((a+b)*tan(1/2*x)/((a-b)*(a+b))^(1/2))*c-1/b*ln(tan(1/2*x)^2+1)","B"
6,1,129,55,0.103000," ","int((A+B*tan(x))/(a+b*cos(x)),x)","\frac{\ln \left(a \left(\tan^{2}\left(\frac{x}{2}\right)\right)-\left(\tan^{2}\left(\frac{x}{2}\right)\right) b +a +b \right) B}{a -b}-\frac{\ln \left(a \left(\tan^{2}\left(\frac{x}{2}\right)\right)-\left(\tan^{2}\left(\frac{x}{2}\right)\right) b +a +b \right) B b}{a \left(a -b \right)}+\frac{2 A \arctan \left(\frac{\tan \left(\frac{x}{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)}}-\frac{B \ln \left(\tan \left(\frac{x}{2}\right)-1\right)}{a}-\frac{B \ln \left(\tan \left(\frac{x}{2}\right)+1\right)}{a}"," ",0,"1/(a-b)*ln(a*tan(1/2*x)^2-tan(1/2*x)^2*b+a+b)*B-1/a/(a-b)*ln(a*tan(1/2*x)^2-tan(1/2*x)^2*b+a+b)*B*b+2*A/((a-b)*(a+b))^(1/2)*arctan(tan(1/2*x)*(a-b)/((a-b)*(a+b))^(1/2))-B/a*ln(tan(1/2*x)-1)-B/a*ln(tan(1/2*x)+1)","B"
7,1,135,86,0.097000," ","int((A+B*cot(x))/(a+b*cos(x)),x)","-\frac{a B \ln \left(a \left(\tan^{2}\left(\frac{x}{2}\right)\right)-\left(\tan^{2}\left(\frac{x}{2}\right)\right) b +a +b \right)}{\left(a +b \right) \left(a -b \right)}+\frac{2 \arctan \left(\frac{\tan \left(\frac{x}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) a A}{\left(a +b \right) \sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{2 \arctan \left(\frac{\tan \left(\frac{x}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) A b}{\left(a +b \right) \sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{B \ln \left(\tan \left(\frac{x}{2}\right)\right)}{a +b}"," ",0,"-1/(a+b)*a*B/(a-b)*ln(a*tan(1/2*x)^2-tan(1/2*x)^2*b+a+b)+2/(a+b)/((a-b)*(a+b))^(1/2)*arctan(tan(1/2*x)*(a-b)/((a-b)*(a+b))^(1/2))*a*A+2/(a+b)/((a-b)*(a+b))^(1/2)*arctan(tan(1/2*x)*(a-b)/((a-b)*(a+b))^(1/2))*A*b+1/(a+b)*B*ln(tan(1/2*x))","A"
8,1,134,85,0.091000," ","int((A+B*csc(x))/(a+b*cos(x)),x)","\frac{B b \ln \left(a \left(\tan^{2}\left(\frac{x}{2}\right)\right)-\left(\tan^{2}\left(\frac{x}{2}\right)\right) b +a +b \right)}{\left(a +b \right) \left(a -b \right)}+\frac{2 \arctan \left(\frac{\tan \left(\frac{x}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) a A}{\left(a +b \right) \sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{2 \arctan \left(\frac{\tan \left(\frac{x}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) A b}{\left(a +b \right) \sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{B \ln \left(\tan \left(\frac{x}{2}\right)\right)}{a +b}"," ",0,"1/(a+b)*B*b/(a-b)*ln(a*tan(1/2*x)^2-tan(1/2*x)^2*b+a+b)+2/(a+b)/((a-b)*(a+b))^(1/2)*arctan(tan(1/2*x)*(a-b)/((a-b)*(a+b))^(1/2))*a*A+2/(a+b)/((a-b)*(a+b))^(1/2)*arctan(tan(1/2*x)*(a-b)/((a-b)*(a+b))^(1/2))*A*b+1/(a+b)*B*ln(tan(1/2*x))","A"
9,1,1066,232,0.271000," ","int((c+d*sec(f*x+e))^4/(a+b*cos(f*x+e)),x)","\frac{4 d^{3} b c}{f \,a^{2} \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right)}-\frac{8 \arctan \left(\frac{\tan \left(\frac{e}{2}+\frac{f x}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) b \,c^{3} d}{f a \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{8 \arctan \left(\frac{\tan \left(\frac{e}{2}+\frac{f x}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) b^{3} c \,d^{3}}{f \,a^{3} \sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{12 \arctan \left(\frac{\tan \left(\frac{e}{2}+\frac{f x}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) b^{2} c^{2} d^{2}}{f \,a^{2} \sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{2 \arctan \left(\frac{\tan \left(\frac{e}{2}+\frac{f x}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) c^{4}}{f \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{d^{4}}{f a \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right)}-\frac{d^{4}}{2 f a \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right)^{2}}-\frac{d^{4}}{3 f a \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right)^{3}}-\frac{d^{4}}{f a \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right)}+\frac{d^{4}}{2 f a \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right)^{2}}-\frac{d^{4}}{3 f a \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right)^{3}}+\frac{d^{4} \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right) b^{3}}{f \,a^{4}}+\frac{2 d^{3} c}{f a \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right)}-\frac{d^{4} b}{2 f \,a^{2} \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right)}-\frac{4 d \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right) c^{3}}{f a}-\frac{6 d^{2} c^{2}}{f a \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right)}+\frac{2 d^{3} c}{f a \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right)}-\frac{d^{4} b}{2 f \,a^{2} \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right)}-\frac{d^{4} b^{2}}{f \,a^{3} \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right)}-\frac{2 d^{3} c}{f a \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right)^{2}}+\frac{d^{4} b}{2 f \,a^{2} \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right)^{2}}+\frac{4 d \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right) c^{3}}{f a}+\frac{2 d^{3} \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right) c}{f a}-\frac{d^{4} \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right) b}{2 f \,a^{2}}-\frac{d^{4} \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right) b^{3}}{f \,a^{4}}-\frac{d^{4} b^{2}}{f \,a^{3} \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right)}+\frac{2 d^{3} c}{f a \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right)^{2}}-\frac{d^{4} b}{2 f \,a^{2} \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right)^{2}}-\frac{6 d^{2} c^{2}}{f a \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right)}+\frac{d^{4} \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right) b}{2 f \,a^{2}}-\frac{6 d^{2} \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right) b \,c^{2}}{f \,a^{2}}+\frac{4 d^{3} \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right) b^{2} c}{f \,a^{3}}+\frac{4 d^{3} b c}{f \,a^{2} \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right)}+\frac{6 d^{2} \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right) b \,c^{2}}{f \,a^{2}}-\frac{4 d^{3} \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right) b^{2} c}{f \,a^{3}}+\frac{2 \arctan \left(\frac{\tan \left(\frac{e}{2}+\frac{f x}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) b^{4} d^{4}}{f \,a^{4} \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{2 d^{3} \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right) c}{f a}"," ",0,"4/f*d^3/a^2/(tan(1/2*e+1/2*f*x)+1)*b*c-8/f/a/((a-b)*(a+b))^(1/2)*arctan(tan(1/2*e+1/2*f*x)*(a-b)/((a-b)*(a+b))^(1/2))*b*c^3*d-8/f/a^3/((a-b)*(a+b))^(1/2)*arctan(tan(1/2*e+1/2*f*x)*(a-b)/((a-b)*(a+b))^(1/2))*b^3*c*d^3+12/f/a^2/((a-b)*(a+b))^(1/2)*arctan(tan(1/2*e+1/2*f*x)*(a-b)/((a-b)*(a+b))^(1/2))*b^2*c^2*d^2+2/f/((a-b)*(a+b))^(1/2)*arctan(tan(1/2*e+1/2*f*x)*(a-b)/((a-b)*(a+b))^(1/2))*c^4-1/f*d^4/a/(tan(1/2*e+1/2*f*x)-1)-1/2/f*d^4/a/(tan(1/2*e+1/2*f*x)-1)^2-1/3/f*d^4/a/(tan(1/2*e+1/2*f*x)+1)^3-1/f*d^4/a/(tan(1/2*e+1/2*f*x)+1)+1/2/f*d^4/a/(tan(1/2*e+1/2*f*x)+1)^2-1/3/f*d^4/a/(tan(1/2*e+1/2*f*x)-1)^3+1/f*d^4/a^4*ln(tan(1/2*e+1/2*f*x)-1)*b^3+2/f*d^3/a/(tan(1/2*e+1/2*f*x)-1)*c-1/2/f*d^4/a^2/(tan(1/2*e+1/2*f*x)-1)*b-4/f*d/a*ln(tan(1/2*e+1/2*f*x)-1)*c^3-6/f*d^2/a/(tan(1/2*e+1/2*f*x)+1)*c^2+2/f*d^3/a/(tan(1/2*e+1/2*f*x)+1)*c-1/2/f*d^4/a^2/(tan(1/2*e+1/2*f*x)+1)*b-1/f*d^4/a^3/(tan(1/2*e+1/2*f*x)+1)*b^2-2/f*d^3/a/(tan(1/2*e+1/2*f*x)+1)^2*c+1/2/f*d^4/a^2/(tan(1/2*e+1/2*f*x)+1)^2*b+4/f*d/a*ln(tan(1/2*e+1/2*f*x)+1)*c^3+2/f*d^3/a*ln(tan(1/2*e+1/2*f*x)+1)*c-1/2/f*d^4/a^2*ln(tan(1/2*e+1/2*f*x)+1)*b-1/f*d^4/a^4*ln(tan(1/2*e+1/2*f*x)+1)*b^3-1/f*d^4/a^3/(tan(1/2*e+1/2*f*x)-1)*b^2+2/f*d^3/a/(tan(1/2*e+1/2*f*x)-1)^2*c-1/2/f*d^4/a^2/(tan(1/2*e+1/2*f*x)-1)^2*b-6/f*d^2/a/(tan(1/2*e+1/2*f*x)-1)*c^2+1/2/f*d^4/a^2*ln(tan(1/2*e+1/2*f*x)-1)*b-6/f*d^2/a^2*ln(tan(1/2*e+1/2*f*x)+1)*b*c^2+4/f*d^3/a^3*ln(tan(1/2*e+1/2*f*x)+1)*b^2*c+4/f*d^3/a^2/(tan(1/2*e+1/2*f*x)-1)*b*c+6/f*d^2/a^2*ln(tan(1/2*e+1/2*f*x)-1)*b*c^2-4/f*d^3/a^3*ln(tan(1/2*e+1/2*f*x)-1)*b^2*c+2/f/a^4/((a-b)*(a+b))^(1/2)*arctan(tan(1/2*e+1/2*f*x)*(a-b)/((a-b)*(a+b))^(1/2))*b^4*d^4-2/f*d^3/a*ln(tan(1/2*e+1/2*f*x)-1)*c","B"
10,1,593,157,0.265000," ","int((c+d*sec(f*x+e))^3/(a+b*cos(f*x+e)),x)","\frac{2 \arctan \left(\frac{\tan \left(\frac{e}{2}+\frac{f x}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) c^{3}}{f \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{6 \arctan \left(\frac{\tan \left(\frac{e}{2}+\frac{f x}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) b \,c^{2} d}{f a \sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{6 \arctan \left(\frac{\tan \left(\frac{e}{2}+\frac{f x}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) b^{2} c \,d^{2}}{f \,a^{2} \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{2 \arctan \left(\frac{\tan \left(\frac{e}{2}+\frac{f x}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) b^{3} d^{3}}{f \,a^{3} \sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{d^{3}}{2 f a \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right)^{2}}-\frac{3 d \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right) c^{2}}{f a}-\frac{d^{3} \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right)}{2 f a}+\frac{3 d^{2} \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right) b c}{f \,a^{2}}-\frac{d^{3} \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right) b^{2}}{f \,a^{3}}-\frac{3 d^{2} c}{f a \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right)}+\frac{d^{3}}{2 f a \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right)}+\frac{d^{3} b}{f \,a^{2} \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right)}-\frac{d^{3}}{2 f a \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right)^{2}}+\frac{3 d \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right) c^{2}}{f a}+\frac{d^{3} \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right)}{2 f a}-\frac{3 d^{2} \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right) b c}{f \,a^{2}}+\frac{d^{3} \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right) b^{2}}{f \,a^{3}}-\frac{3 d^{2} c}{f a \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right)}+\frac{d^{3}}{2 f a \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right)}+\frac{d^{3} b}{f \,a^{2} \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right)}"," ",0,"2/f/((a-b)*(a+b))^(1/2)*arctan(tan(1/2*e+1/2*f*x)*(a-b)/((a-b)*(a+b))^(1/2))*c^3-6/f/a/((a-b)*(a+b))^(1/2)*arctan(tan(1/2*e+1/2*f*x)*(a-b)/((a-b)*(a+b))^(1/2))*b*c^2*d+6/f/a^2/((a-b)*(a+b))^(1/2)*arctan(tan(1/2*e+1/2*f*x)*(a-b)/((a-b)*(a+b))^(1/2))*b^2*c*d^2-2/f/a^3/((a-b)*(a+b))^(1/2)*arctan(tan(1/2*e+1/2*f*x)*(a-b)/((a-b)*(a+b))^(1/2))*b^3*d^3+1/2/f*d^3/a/(tan(1/2*e+1/2*f*x)-1)^2-3/f*d/a*ln(tan(1/2*e+1/2*f*x)-1)*c^2-1/2/f*d^3/a*ln(tan(1/2*e+1/2*f*x)-1)+3/f*d^2/a^2*ln(tan(1/2*e+1/2*f*x)-1)*b*c-1/f*d^3/a^3*ln(tan(1/2*e+1/2*f*x)-1)*b^2-3/f*d^2/a/(tan(1/2*e+1/2*f*x)-1)*c+1/2/f*d^3/a/(tan(1/2*e+1/2*f*x)-1)+1/f*d^3/a^2/(tan(1/2*e+1/2*f*x)-1)*b-1/2/f*d^3/a/(tan(1/2*e+1/2*f*x)+1)^2+3/f*d/a*ln(tan(1/2*e+1/2*f*x)+1)*c^2+1/2/f*d^3/a*ln(tan(1/2*e+1/2*f*x)+1)-3/f*d^2/a^2*ln(tan(1/2*e+1/2*f*x)+1)*b*c+1/f*d^3/a^3*ln(tan(1/2*e+1/2*f*x)+1)*b^2-3/f*d^2/a/(tan(1/2*e+1/2*f*x)+1)*c+1/2/f*d^3/a/(tan(1/2*e+1/2*f*x)+1)+1/f*d^3/a^2/(tan(1/2*e+1/2*f*x)+1)*b","B"
11,1,288,94,0.227000," ","int((c+d*sec(f*x+e))^2/(a+b*cos(f*x+e)),x)","\frac{2 \arctan \left(\frac{\tan \left(\frac{e}{2}+\frac{f x}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) c^{2}}{f \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{4 \arctan \left(\frac{\tan \left(\frac{e}{2}+\frac{f x}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) b c d}{f a \sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{2 \arctan \left(\frac{\tan \left(\frac{e}{2}+\frac{f x}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) b^{2} d^{2}}{f \,a^{2} \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{d^{2}}{f a \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right)}-\frac{2 d \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right) c}{f a}+\frac{d^{2} \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right) b}{f \,a^{2}}-\frac{d^{2}}{f a \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right)}+\frac{2 d \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right) c}{f a}-\frac{d^{2} \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right) b}{f \,a^{2}}"," ",0,"2/f/((a-b)*(a+b))^(1/2)*arctan(tan(1/2*e+1/2*f*x)*(a-b)/((a-b)*(a+b))^(1/2))*c^2-4/f/a/((a-b)*(a+b))^(1/2)*arctan(tan(1/2*e+1/2*f*x)*(a-b)/((a-b)*(a+b))^(1/2))*b*c*d+2/f/a^2/((a-b)*(a+b))^(1/2)*arctan(tan(1/2*e+1/2*f*x)*(a-b)/((a-b)*(a+b))^(1/2))*b^2*d^2-1/f*d^2/a/(tan(1/2*e+1/2*f*x)-1)-2/f*d/a*ln(tan(1/2*e+1/2*f*x)-1)*c+1/f*d^2/a^2*ln(tan(1/2*e+1/2*f*x)-1)*b-1/f*d^2/a/(tan(1/2*e+1/2*f*x)+1)+2/f*d/a*ln(tan(1/2*e+1/2*f*x)+1)*c-1/f*d^2/a^2*ln(tan(1/2*e+1/2*f*x)+1)*b","B"
12,1,135,67,0.213000," ","int((c+d*sec(f*x+e))/(a+b*cos(f*x+e)),x)","\frac{2 \arctan \left(\frac{\tan \left(\frac{e}{2}+\frac{f x}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) c}{f \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{2 \arctan \left(\frac{\tan \left(\frac{e}{2}+\frac{f x}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) b d}{f a \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{d \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)-1\right)}{f a}+\frac{d \ln \left(\tan \left(\frac{e}{2}+\frac{f x}{2}\right)+1\right)}{f a}"," ",0,"2/f/((a-b)*(a+b))^(1/2)*arctan(tan(1/2*e+1/2*f*x)*(a-b)/((a-b)*(a+b))^(1/2))*c-2/f/a/((a-b)*(a+b))^(1/2)*arctan(tan(1/2*e+1/2*f*x)*(a-b)/((a-b)*(a+b))^(1/2))*b*d-1/f*d/a*ln(tan(1/2*e+1/2*f*x)-1)+1/f*d/a*ln(tan(1/2*e+1/2*f*x)+1)","A"
13,1,110,103,0.264000," ","int(1/(a+b*cos(f*x+e))/(c+d*sec(f*x+e)),x)","-\frac{2 d \arctanh \left(\frac{\left(c -d \right) \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{\sqrt{\left(c +d \right) \left(c -d \right)}}\right)}{f \left(c a -b d \right) \sqrt{\left(c +d \right) \left(c -d \right)}}+\frac{2 a \arctan \left(\frac{\tan \left(\frac{e}{2}+\frac{f x}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right)}{f \left(c a -b d \right) \sqrt{\left(a -b \right) \left(a +b \right)}}"," ",0,"-2/f*d/(a*c-b*d)/((c+d)*(c-d))^(1/2)*arctanh((c-d)*tan(1/2*e+1/2*f*x)/((c+d)*(c-d))^(1/2))+2/f*a/(a*c-b*d)/((a-b)*(a+b))^(1/2)*arctan(tan(1/2*e+1/2*f*x)*(a-b)/((a-b)*(a+b))^(1/2))","A"
14,1,418,169,0.277000," ","int(1/(a+b*cos(f*x+e))/(c+d*sec(f*x+e))^2,x)","-\frac{2 d^{2} \tan \left(\frac{e}{2}+\frac{f x}{2}\right) c a}{f \left(c a -b d \right)^{2} \left(c^{2}-d^{2}\right) \left(\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) c -\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) d -c -d \right)}+\frac{2 d^{3} \tan \left(\frac{e}{2}+\frac{f x}{2}\right) b}{f \left(c a -b d \right)^{2} \left(c^{2}-d^{2}\right) \left(\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) c -\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) d -c -d \right)}-\frac{4 d \arctanh \left(\frac{\left(c -d \right) \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{\sqrt{\left(c +d \right) \left(c -d \right)}}\right) a \,c^{2}}{f \left(c a -b d \right)^{2} \left(c +d \right) \left(c -d \right) \sqrt{\left(c +d \right) \left(c -d \right)}}+\frac{2 d^{3} \arctanh \left(\frac{\left(c -d \right) \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{\sqrt{\left(c +d \right) \left(c -d \right)}}\right) a}{f \left(c a -b d \right)^{2} \left(c +d \right) \left(c -d \right) \sqrt{\left(c +d \right) \left(c -d \right)}}+\frac{2 d^{2} \arctanh \left(\frac{\left(c -d \right) \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{\sqrt{\left(c +d \right) \left(c -d \right)}}\right) b c}{f \left(c a -b d \right)^{2} \left(c +d \right) \left(c -d \right) \sqrt{\left(c +d \right) \left(c -d \right)}}+\frac{2 a^{2} \arctan \left(\frac{\tan \left(\frac{e}{2}+\frac{f x}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right)}{f \left(c a -b d \right)^{2} \sqrt{\left(a -b \right) \left(a +b \right)}}"," ",0,"-2/f*d^2/(a*c-b*d)^2/(c^2-d^2)*tan(1/2*e+1/2*f*x)/(tan(1/2*e+1/2*f*x)^2*c-tan(1/2*e+1/2*f*x)^2*d-c-d)*c*a+2/f*d^3/(a*c-b*d)^2/(c^2-d^2)*tan(1/2*e+1/2*f*x)/(tan(1/2*e+1/2*f*x)^2*c-tan(1/2*e+1/2*f*x)^2*d-c-d)*b-4/f*d/(a*c-b*d)^2/(c+d)/(c-d)/((c+d)*(c-d))^(1/2)*arctanh((c-d)*tan(1/2*e+1/2*f*x)/((c+d)*(c-d))^(1/2))*a*c^2+2/f*d^3/(a*c-b*d)^2/(c+d)/(c-d)/((c+d)*(c-d))^(1/2)*arctanh((c-d)*tan(1/2*e+1/2*f*x)/((c+d)*(c-d))^(1/2))*a+2/f*d^2/(a*c-b*d)^2/(c+d)/(c-d)/((c+d)*(c-d))^(1/2)*arctanh((c-d)*tan(1/2*e+1/2*f*x)/((c+d)*(c-d))^(1/2))*b*c+2/f*a^2/(a*c-b*d)^2/((a-b)*(a+b))^(1/2)*arctan(tan(1/2*e+1/2*f*x)*(a-b)/((a-b)*(a+b))^(1/2))","B"
15,1,1869,418,0.330000," ","int(1/(a+b*cos(f*x+e))/(c+d*sec(f*x+e))^3,x)","-\frac{6 d^{2} \left(\tan^{3}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) a^{2} c^{3}}{f \left(c a -b d \right)^{3} \left(\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) c -\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) d -c -d \right)^{2} \left(c -d \right) \left(c^{2}+2 c d +d^{2}\right)}-\frac{d^{3} \left(\tan^{3}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) a^{2} c^{2}}{f \left(c a -b d \right)^{3} \left(\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) c -\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) d -c -d \right)^{2} \left(c -d \right) \left(c^{2}+2 c d +d^{2}\right)}+\frac{2 d^{4} \left(\tan^{3}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) a^{2} c}{f \left(c a -b d \right)^{3} \left(\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) c -\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) d -c -d \right)^{2} \left(c -d \right) \left(c^{2}+2 c d +d^{2}\right)}+\frac{10 d^{3} \left(\tan^{3}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) a b \,c^{2}}{f \left(c a -b d \right)^{3} \left(\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) c -\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) d -c -d \right)^{2} \left(c -d \right) \left(c^{2}+2 c d +d^{2}\right)}+\frac{2 d^{4} \left(\tan^{3}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) a b c}{f \left(c a -b d \right)^{3} \left(\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) c -\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) d -c -d \right)^{2} \left(c -d \right) \left(c^{2}+2 c d +d^{2}\right)}-\frac{2 d^{5} \left(\tan^{3}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) a b}{f \left(c a -b d \right)^{3} \left(\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) c -\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) d -c -d \right)^{2} \left(c -d \right) \left(c^{2}+2 c d +d^{2}\right)}-\frac{4 d^{4} \left(\tan^{3}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) b^{2} c}{f \left(c a -b d \right)^{3} \left(\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) c -\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) d -c -d \right)^{2} \left(c -d \right) \left(c^{2}+2 c d +d^{2}\right)}-\frac{d^{5} \left(\tan^{3}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) b^{2}}{f \left(c a -b d \right)^{3} \left(\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) c -\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) d -c -d \right)^{2} \left(c -d \right) \left(c^{2}+2 c d +d^{2}\right)}+\frac{6 d^{2} \tan \left(\frac{e}{2}+\frac{f x}{2}\right) a^{2} c^{3}}{f \left(c a -b d \right)^{3} \left(\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) c -\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) d -c -d \right)^{2} \left(c +d \right) \left(c -d \right)^{2}}-\frac{d^{3} \tan \left(\frac{e}{2}+\frac{f x}{2}\right) a^{2} c^{2}}{f \left(c a -b d \right)^{3} \left(\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) c -\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) d -c -d \right)^{2} \left(c +d \right) \left(c -d \right)^{2}}-\frac{2 d^{4} \tan \left(\frac{e}{2}+\frac{f x}{2}\right) a^{2} c}{f \left(c a -b d \right)^{3} \left(\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) c -\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) d -c -d \right)^{2} \left(c +d \right) \left(c -d \right)^{2}}-\frac{10 d^{3} \tan \left(\frac{e}{2}+\frac{f x}{2}\right) a b \,c^{2}}{f \left(c a -b d \right)^{3} \left(\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) c -\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) d -c -d \right)^{2} \left(c +d \right) \left(c -d \right)^{2}}+\frac{2 d^{4} \tan \left(\frac{e}{2}+\frac{f x}{2}\right) a b c}{f \left(c a -b d \right)^{3} \left(\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) c -\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) d -c -d \right)^{2} \left(c +d \right) \left(c -d \right)^{2}}+\frac{2 d^{5} \tan \left(\frac{e}{2}+\frac{f x}{2}\right) a b}{f \left(c a -b d \right)^{3} \left(\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) c -\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) d -c -d \right)^{2} \left(c +d \right) \left(c -d \right)^{2}}+\frac{4 d^{4} \tan \left(\frac{e}{2}+\frac{f x}{2}\right) b^{2} c}{f \left(c a -b d \right)^{3} \left(\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) c -\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) d -c -d \right)^{2} \left(c +d \right) \left(c -d \right)^{2}}-\frac{d^{5} \tan \left(\frac{e}{2}+\frac{f x}{2}\right) b^{2}}{f \left(c a -b d \right)^{3} \left(\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) c -\left(\tan^{2}\left(\frac{e}{2}+\frac{f x}{2}\right)\right) d -c -d \right)^{2} \left(c +d \right) \left(c -d \right)^{2}}-\frac{6 d \arctanh \left(\frac{\left(c -d \right) \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{\sqrt{\left(c +d \right) \left(c -d \right)}}\right) a^{2} c^{4}}{f \left(c a -b d \right)^{3} \left(c^{4}-2 c^{2} d^{2}+d^{4}\right) \sqrt{\left(c +d \right) \left(c -d \right)}}+\frac{5 d^{3} \arctanh \left(\frac{\left(c -d \right) \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{\sqrt{\left(c +d \right) \left(c -d \right)}}\right) a^{2} c^{2}}{f \left(c a -b d \right)^{3} \left(c^{4}-2 c^{2} d^{2}+d^{4}\right) \sqrt{\left(c +d \right) \left(c -d \right)}}-\frac{2 d^{5} \arctanh \left(\frac{\left(c -d \right) \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{\sqrt{\left(c +d \right) \left(c -d \right)}}\right) a^{2}}{f \left(c a -b d \right)^{3} \left(c^{4}-2 c^{2} d^{2}+d^{4}\right) \sqrt{\left(c +d \right) \left(c -d \right)}}+\frac{6 d^{2} \arctanh \left(\frac{\left(c -d \right) \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{\sqrt{\left(c +d \right) \left(c -d \right)}}\right) a b \,c^{3}}{f \left(c a -b d \right)^{3} \left(c^{4}-2 c^{2} d^{2}+d^{4}\right) \sqrt{\left(c +d \right) \left(c -d \right)}}-\frac{2 d^{3} \arctanh \left(\frac{\left(c -d \right) \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{\sqrt{\left(c +d \right) \left(c -d \right)}}\right) b^{2} c^{2}}{f \left(c a -b d \right)^{3} \left(c^{4}-2 c^{2} d^{2}+d^{4}\right) \sqrt{\left(c +d \right) \left(c -d \right)}}-\frac{d^{5} \arctanh \left(\frac{\left(c -d \right) \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{\sqrt{\left(c +d \right) \left(c -d \right)}}\right) b^{2}}{f \left(c a -b d \right)^{3} \left(c^{4}-2 c^{2} d^{2}+d^{4}\right) \sqrt{\left(c +d \right) \left(c -d \right)}}+\frac{2 a^{3} \arctan \left(\frac{\tan \left(\frac{e}{2}+\frac{f x}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right)}{f \left(c a -b d \right)^{3} \sqrt{\left(a -b \right) \left(a +b \right)}}"," ",0,"-6/f*d^2/(a*c-b*d)^3/(tan(1/2*e+1/2*f*x)^2*c-tan(1/2*e+1/2*f*x)^2*d-c-d)^2/(c-d)/(c^2+2*c*d+d^2)*tan(1/2*e+1/2*f*x)^3*a^2*c^3-1/f*d^3/(a*c-b*d)^3/(tan(1/2*e+1/2*f*x)^2*c-tan(1/2*e+1/2*f*x)^2*d-c-d)^2/(c-d)/(c^2+2*c*d+d^2)*tan(1/2*e+1/2*f*x)^3*a^2*c^2+2/f*d^4/(a*c-b*d)^3/(tan(1/2*e+1/2*f*x)^2*c-tan(1/2*e+1/2*f*x)^2*d-c-d)^2/(c-d)/(c^2+2*c*d+d^2)*tan(1/2*e+1/2*f*x)^3*a^2*c+10/f*d^3/(a*c-b*d)^3/(tan(1/2*e+1/2*f*x)^2*c-tan(1/2*e+1/2*f*x)^2*d-c-d)^2/(c-d)/(c^2+2*c*d+d^2)*tan(1/2*e+1/2*f*x)^3*a*b*c^2+2/f*d^4/(a*c-b*d)^3/(tan(1/2*e+1/2*f*x)^2*c-tan(1/2*e+1/2*f*x)^2*d-c-d)^2/(c-d)/(c^2+2*c*d+d^2)*tan(1/2*e+1/2*f*x)^3*a*b*c-2/f*d^5/(a*c-b*d)^3/(tan(1/2*e+1/2*f*x)^2*c-tan(1/2*e+1/2*f*x)^2*d-c-d)^2/(c-d)/(c^2+2*c*d+d^2)*tan(1/2*e+1/2*f*x)^3*a*b-4/f*d^4/(a*c-b*d)^3/(tan(1/2*e+1/2*f*x)^2*c-tan(1/2*e+1/2*f*x)^2*d-c-d)^2/(c-d)/(c^2+2*c*d+d^2)*tan(1/2*e+1/2*f*x)^3*b^2*c-1/f*d^5/(a*c-b*d)^3/(tan(1/2*e+1/2*f*x)^2*c-tan(1/2*e+1/2*f*x)^2*d-c-d)^2/(c-d)/(c^2+2*c*d+d^2)*tan(1/2*e+1/2*f*x)^3*b^2+6/f*d^2/(a*c-b*d)^3/(tan(1/2*e+1/2*f*x)^2*c-tan(1/2*e+1/2*f*x)^2*d-c-d)^2/(c+d)/(c-d)^2*tan(1/2*e+1/2*f*x)*a^2*c^3-1/f*d^3/(a*c-b*d)^3/(tan(1/2*e+1/2*f*x)^2*c-tan(1/2*e+1/2*f*x)^2*d-c-d)^2/(c+d)/(c-d)^2*tan(1/2*e+1/2*f*x)*a^2*c^2-2/f*d^4/(a*c-b*d)^3/(tan(1/2*e+1/2*f*x)^2*c-tan(1/2*e+1/2*f*x)^2*d-c-d)^2/(c+d)/(c-d)^2*tan(1/2*e+1/2*f*x)*a^2*c-10/f*d^3/(a*c-b*d)^3/(tan(1/2*e+1/2*f*x)^2*c-tan(1/2*e+1/2*f*x)^2*d-c-d)^2/(c+d)/(c-d)^2*tan(1/2*e+1/2*f*x)*a*b*c^2+2/f*d^4/(a*c-b*d)^3/(tan(1/2*e+1/2*f*x)^2*c-tan(1/2*e+1/2*f*x)^2*d-c-d)^2/(c+d)/(c-d)^2*tan(1/2*e+1/2*f*x)*a*b*c+2/f*d^5/(a*c-b*d)^3/(tan(1/2*e+1/2*f*x)^2*c-tan(1/2*e+1/2*f*x)^2*d-c-d)^2/(c+d)/(c-d)^2*tan(1/2*e+1/2*f*x)*a*b+4/f*d^4/(a*c-b*d)^3/(tan(1/2*e+1/2*f*x)^2*c-tan(1/2*e+1/2*f*x)^2*d-c-d)^2/(c+d)/(c-d)^2*tan(1/2*e+1/2*f*x)*b^2*c-1/f*d^5/(a*c-b*d)^3/(tan(1/2*e+1/2*f*x)^2*c-tan(1/2*e+1/2*f*x)^2*d-c-d)^2/(c+d)/(c-d)^2*tan(1/2*e+1/2*f*x)*b^2-6/f*d/(a*c-b*d)^3/(c^4-2*c^2*d^2+d^4)/((c+d)*(c-d))^(1/2)*arctanh((c-d)*tan(1/2*e+1/2*f*x)/((c+d)*(c-d))^(1/2))*a^2*c^4+5/f*d^3/(a*c-b*d)^3/(c^4-2*c^2*d^2+d^4)/((c+d)*(c-d))^(1/2)*arctanh((c-d)*tan(1/2*e+1/2*f*x)/((c+d)*(c-d))^(1/2))*a^2*c^2-2/f*d^5/(a*c-b*d)^3/(c^4-2*c^2*d^2+d^4)/((c+d)*(c-d))^(1/2)*arctanh((c-d)*tan(1/2*e+1/2*f*x)/((c+d)*(c-d))^(1/2))*a^2+6/f*d^2/(a*c-b*d)^3/(c^4-2*c^2*d^2+d^4)/((c+d)*(c-d))^(1/2)*arctanh((c-d)*tan(1/2*e+1/2*f*x)/((c+d)*(c-d))^(1/2))*a*b*c^3-2/f*d^3/(a*c-b*d)^3/(c^4-2*c^2*d^2+d^4)/((c+d)*(c-d))^(1/2)*arctanh((c-d)*tan(1/2*e+1/2*f*x)/((c+d)*(c-d))^(1/2))*b^2*c^2-1/f*d^5/(a*c-b*d)^3/(c^4-2*c^2*d^2+d^4)/((c+d)*(c-d))^(1/2)*arctanh((c-d)*tan(1/2*e+1/2*f*x)/((c+d)*(c-d))^(1/2))*b^2+2/f*a^3/(a*c-b*d)^3/((a-b)*(a+b))^(1/2)*arctan(tan(1/2*e+1/2*f*x)*(a-b)/((a-b)*(a+b))^(1/2))","B"
16,1,357,199,0.676000," ","int((c+d*sec(f*x+e))^(1/2)/(a+b*cos(f*x+e)),x)","-\frac{2 \sqrt{\frac{d +c \cos \left(f x +e \right)}{\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{d +c \cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right) \left(c +d \right)}}\, \left(1+\cos \left(f x +e \right)\right)^{2} \left(-1+\cos \left(f x +e \right)\right) \left(\EllipticF \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, \sqrt{\frac{c -d}{c +d}}\right) a c -\EllipticF \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, \sqrt{\frac{c -d}{c +d}}\right) a d +\EllipticF \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, \sqrt{\frac{c -d}{c +d}}\right) b c -\EllipticF \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, \sqrt{\frac{c -d}{c +d}}\right) b d -2 \EllipticPi \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, -\frac{a -b}{a +b}, \sqrt{\frac{c -d}{c +d}}\right) a c +2 \EllipticPi \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, -\frac{a -b}{a +b}, \sqrt{\frac{c -d}{c +d}}\right) b d \right)}{f \left(d +c \cos \left(f x +e \right)\right) \sin \left(f x +e \right)^{2} \left(a -b \right) \left(a +b \right)}"," ",0,"-2/f*((d+c*cos(f*x+e))/cos(f*x+e))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((d+c*cos(f*x+e))/(1+cos(f*x+e))/(c+d))^(1/2)*(1+cos(f*x+e))^2*(-1+cos(f*x+e))*(EllipticF((-1+cos(f*x+e))/sin(f*x+e),((c-d)/(c+d))^(1/2))*a*c-EllipticF((-1+cos(f*x+e))/sin(f*x+e),((c-d)/(c+d))^(1/2))*a*d+EllipticF((-1+cos(f*x+e))/sin(f*x+e),((c-d)/(c+d))^(1/2))*b*c-EllipticF((-1+cos(f*x+e))/sin(f*x+e),((c-d)/(c+d))^(1/2))*b*d-2*EllipticPi((-1+cos(f*x+e))/sin(f*x+e),-(a-b)/(a+b),((c-d)/(c+d))^(1/2))*a*c+2*EllipticPi((-1+cos(f*x+e))/sin(f*x+e),-(a-b)/(a+b),((c-d)/(c+d))^(1/2))*b*d)/(d+c*cos(f*x+e))/sin(f*x+e)^2/(a-b)/(a+b)","A"
17,1,239,97,0.576000," ","int(1/(a+b*cos(f*x+e))/(c+d*sec(f*x+e))^(1/2),x)","\frac{2 \sqrt{\frac{d +c \cos \left(f x +e \right)}{\cos \left(f x +e \right)}}\, \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{d +c \cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right) \left(c +d \right)}}\, \left(1+\cos \left(f x +e \right)\right)^{2} \left(2 a \EllipticPi \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, -\frac{a -b}{a +b}, \sqrt{\frac{c -d}{c +d}}\right)-a \EllipticF \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, \sqrt{\frac{c -d}{c +d}}\right)-b \EllipticF \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, \sqrt{\frac{c -d}{c +d}}\right)\right) \left(-1+\cos \left(f x +e \right)\right)}{f \left(d +c \cos \left(f x +e \right)\right) \sin \left(f x +e \right)^{2} \left(a -b \right) \left(a +b \right)}"," ",0,"2/f*((d+c*cos(f*x+e))/cos(f*x+e))^(1/2)*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((d+c*cos(f*x+e))/(1+cos(f*x+e))/(c+d))^(1/2)*(1+cos(f*x+e))^2*(2*a*EllipticPi((-1+cos(f*x+e))/sin(f*x+e),-(a-b)/(a+b),((c-d)/(c+d))^(1/2))-a*EllipticF((-1+cos(f*x+e))/sin(f*x+e),((c-d)/(c+d))^(1/2))-b*EllipticF((-1+cos(f*x+e))/sin(f*x+e),((c-d)/(c+d))^(1/2)))*(-1+cos(f*x+e))/(d+c*cos(f*x+e))/sin(f*x+e)^2/(a-b)/(a+b)","B"
18,1,226,78,0.181000," ","int((A+B*cos(e*x+d)+C*sin(e*x+d))/(a+b*cos(e*x+d)),x)","-\frac{\ln \left(a \left(\tan^{2}\left(\frac{e x}{2}+\frac{d}{2}\right)\right)-\left(\tan^{2}\left(\frac{e x}{2}+\frac{d}{2}\right)\right) b +a +b \right) a C}{e b \left(a -b \right)}+\frac{\ln \left(a \left(\tan^{2}\left(\frac{e x}{2}+\frac{d}{2}\right)\right)-\left(\tan^{2}\left(\frac{e x}{2}+\frac{d}{2}\right)\right) b +a +b \right) C}{e \left(a -b \right)}+\frac{2 \arctan \left(\frac{\tan \left(\frac{e x}{2}+\frac{d}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) A}{e \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{2 \arctan \left(\frac{\tan \left(\frac{e x}{2}+\frac{d}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) a B}{e b \sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{C \ln \left(\tan^{2}\left(\frac{e x}{2}+\frac{d}{2}\right)+1\right)}{e b}+\frac{2 B \arctan \left(\tan \left(\frac{e x}{2}+\frac{d}{2}\right)\right)}{e b}"," ",0,"-1/e/b/(a-b)*ln(a*tan(1/2*e*x+1/2*d)^2-tan(1/2*e*x+1/2*d)^2*b+a+b)*a*C+1/e/(a-b)*ln(a*tan(1/2*e*x+1/2*d)^2-tan(1/2*e*x+1/2*d)^2*b+a+b)*C+2/e/((a-b)*(a+b))^(1/2)*arctan(tan(1/2*e*x+1/2*d)*(a-b)/((a-b)*(a+b))^(1/2))*A-2/e/b/((a-b)*(a+b))^(1/2)*arctan(tan(1/2*e*x+1/2*d)*(a-b)/((a-b)*(a+b))^(1/2))*a*B+1/e/b*C*ln(tan(1/2*e*x+1/2*d)^2+1)+2/e/b*B*arctan(tan(1/2*e*x+1/2*d))","B"
19,1,279,111,0.174000," ","int((A+B*cos(e*x+d)+C*sin(e*x+d))/(a+b*cos(e*x+d))^2,x)","-\frac{2 \tan \left(\frac{e x}{2}+\frac{d}{2}\right) A b}{e \left(a \left(\tan^{2}\left(\frac{e x}{2}+\frac{d}{2}\right)\right)-\left(\tan^{2}\left(\frac{e x}{2}+\frac{d}{2}\right)\right) b +a +b \right) \left(a^{2}-b^{2}\right)}+\frac{2 \tan \left(\frac{e x}{2}+\frac{d}{2}\right) a B}{e \left(a \left(\tan^{2}\left(\frac{e x}{2}+\frac{d}{2}\right)\right)-\left(\tan^{2}\left(\frac{e x}{2}+\frac{d}{2}\right)\right) b +a +b \right) \left(a^{2}-b^{2}\right)}-\frac{2 C}{e \left(a \left(\tan^{2}\left(\frac{e x}{2}+\frac{d}{2}\right)\right)-\left(\tan^{2}\left(\frac{e x}{2}+\frac{d}{2}\right)\right) b +a +b \right) \left(a -b \right)}+\frac{2 \arctan \left(\frac{\tan \left(\frac{e x}{2}+\frac{d}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) a A}{e \left(a -b \right) \left(a +b \right) \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{2 \arctan \left(\frac{\tan \left(\frac{e x}{2}+\frac{d}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) B b}{e \left(a -b \right) \left(a +b \right) \sqrt{\left(a -b \right) \left(a +b \right)}}"," ",0,"-2/e/(a*tan(1/2*e*x+1/2*d)^2-tan(1/2*e*x+1/2*d)^2*b+a+b)/(a^2-b^2)*tan(1/2*e*x+1/2*d)*A*b+2/e/(a*tan(1/2*e*x+1/2*d)^2-tan(1/2*e*x+1/2*d)^2*b+a+b)/(a^2-b^2)*tan(1/2*e*x+1/2*d)*a*B-2/e/(a*tan(1/2*e*x+1/2*d)^2-tan(1/2*e*x+1/2*d)^2*b+a+b)*C/(a-b)+2/e/(a-b)/(a+b)/((a-b)*(a+b))^(1/2)*arctan(tan(1/2*e*x+1/2*d)*(a-b)/((a-b)*(a+b))^(1/2))*a*A-2/e/(a-b)/(a+b)/((a-b)*(a+b))^(1/2)*arctan(tan(1/2*e*x+1/2*d)*(a-b)/((a-b)*(a+b))^(1/2))*B*b","B"
20,1,994,172,0.182000," ","int((A+B*cos(e*x+d)+C*sin(e*x+d))/(a+b*cos(e*x+d))^3,x)","-\frac{4 \left(\tan^{3}\left(\frac{e x}{2}+\frac{d}{2}\right)\right) A a b}{e \left(a \left(\tan^{2}\left(\frac{e x}{2}+\frac{d}{2}\right)\right)-\left(\tan^{2}\left(\frac{e x}{2}+\frac{d}{2}\right)\right) b +a +b \right)^{2} \left(a -b \right) \left(a^{2}+2 a b +b^{2}\right)}-\frac{\left(\tan^{3}\left(\frac{e x}{2}+\frac{d}{2}\right)\right) A \,b^{2}}{e \left(a \left(\tan^{2}\left(\frac{e x}{2}+\frac{d}{2}\right)\right)-\left(\tan^{2}\left(\frac{e x}{2}+\frac{d}{2}\right)\right) b +a +b \right)^{2} \left(a -b \right) \left(a^{2}+2 a b +b^{2}\right)}+\frac{2 \left(\tan^{3}\left(\frac{e x}{2}+\frac{d}{2}\right)\right) a^{2} B}{e \left(a \left(\tan^{2}\left(\frac{e x}{2}+\frac{d}{2}\right)\right)-\left(\tan^{2}\left(\frac{e x}{2}+\frac{d}{2}\right)\right) b +a +b \right)^{2} \left(a -b \right) \left(a^{2}+2 a b +b^{2}\right)}+\frac{\left(\tan^{3}\left(\frac{e x}{2}+\frac{d}{2}\right)\right) B a b}{e \left(a \left(\tan^{2}\left(\frac{e x}{2}+\frac{d}{2}\right)\right)-\left(\tan^{2}\left(\frac{e x}{2}+\frac{d}{2}\right)\right) b +a +b \right)^{2} \left(a -b \right) \left(a^{2}+2 a b +b^{2}\right)}+\frac{2 \left(\tan^{3}\left(\frac{e x}{2}+\frac{d}{2}\right)\right) b^{2} B}{e \left(a \left(\tan^{2}\left(\frac{e x}{2}+\frac{d}{2}\right)\right)-\left(\tan^{2}\left(\frac{e x}{2}+\frac{d}{2}\right)\right) b +a +b \right)^{2} \left(a -b \right) \left(a^{2}+2 a b +b^{2}\right)}-\frac{2 C \left(\tan^{2}\left(\frac{e x}{2}+\frac{d}{2}\right)\right)}{e \left(a \left(\tan^{2}\left(\frac{e x}{2}+\frac{d}{2}\right)\right)-\left(\tan^{2}\left(\frac{e x}{2}+\frac{d}{2}\right)\right) b +a +b \right)^{2} \left(a -b \right)}-\frac{4 \tan \left(\frac{e x}{2}+\frac{d}{2}\right) A a b}{e \left(a \left(\tan^{2}\left(\frac{e x}{2}+\frac{d}{2}\right)\right)-\left(\tan^{2}\left(\frac{e x}{2}+\frac{d}{2}\right)\right) b +a +b \right)^{2} \left(a +b \right) \left(a^{2}-2 a b +b^{2}\right)}+\frac{\tan \left(\frac{e x}{2}+\frac{d}{2}\right) A \,b^{2}}{e \left(a \left(\tan^{2}\left(\frac{e x}{2}+\frac{d}{2}\right)\right)-\left(\tan^{2}\left(\frac{e x}{2}+\frac{d}{2}\right)\right) b +a +b \right)^{2} \left(a +b \right) \left(a^{2}-2 a b +b^{2}\right)}+\frac{2 \tan \left(\frac{e x}{2}+\frac{d}{2}\right) a^{2} B}{e \left(a \left(\tan^{2}\left(\frac{e x}{2}+\frac{d}{2}\right)\right)-\left(\tan^{2}\left(\frac{e x}{2}+\frac{d}{2}\right)\right) b +a +b \right)^{2} \left(a +b \right) \left(a^{2}-2 a b +b^{2}\right)}-\frac{\tan \left(\frac{e x}{2}+\frac{d}{2}\right) B a b}{e \left(a \left(\tan^{2}\left(\frac{e x}{2}+\frac{d}{2}\right)\right)-\left(\tan^{2}\left(\frac{e x}{2}+\frac{d}{2}\right)\right) b +a +b \right)^{2} \left(a +b \right) \left(a^{2}-2 a b +b^{2}\right)}+\frac{2 \tan \left(\frac{e x}{2}+\frac{d}{2}\right) b^{2} B}{e \left(a \left(\tan^{2}\left(\frac{e x}{2}+\frac{d}{2}\right)\right)-\left(\tan^{2}\left(\frac{e x}{2}+\frac{d}{2}\right)\right) b +a +b \right)^{2} \left(a +b \right) \left(a^{2}-2 a b +b^{2}\right)}-\frac{2 a C}{e \left(a \left(\tan^{2}\left(\frac{e x}{2}+\frac{d}{2}\right)\right)-\left(\tan^{2}\left(\frac{e x}{2}+\frac{d}{2}\right)\right) b +a +b \right)^{2} \left(a^{2}-2 a b +b^{2}\right)}+\frac{2 \arctan \left(\frac{\tan \left(\frac{e x}{2}+\frac{d}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) a^{2} A}{e \left(a^{4}-2 a^{2} b^{2}+b^{4}\right) \sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{\arctan \left(\frac{\tan \left(\frac{e x}{2}+\frac{d}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) A \,b^{2}}{e \left(a^{4}-2 a^{2} b^{2}+b^{4}\right) \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{3 \arctan \left(\frac{\tan \left(\frac{e x}{2}+\frac{d}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) B a b}{e \left(a^{4}-2 a^{2} b^{2}+b^{4}\right) \sqrt{\left(a -b \right) \left(a +b \right)}}"," ",0,"-4/e/(a*tan(1/2*e*x+1/2*d)^2-tan(1/2*e*x+1/2*d)^2*b+a+b)^2/(a-b)/(a^2+2*a*b+b^2)*tan(1/2*e*x+1/2*d)^3*A*a*b-1/e/(a*tan(1/2*e*x+1/2*d)^2-tan(1/2*e*x+1/2*d)^2*b+a+b)^2/(a-b)/(a^2+2*a*b+b^2)*tan(1/2*e*x+1/2*d)^3*A*b^2+2/e/(a*tan(1/2*e*x+1/2*d)^2-tan(1/2*e*x+1/2*d)^2*b+a+b)^2/(a-b)/(a^2+2*a*b+b^2)*tan(1/2*e*x+1/2*d)^3*a^2*B+1/e/(a*tan(1/2*e*x+1/2*d)^2-tan(1/2*e*x+1/2*d)^2*b+a+b)^2/(a-b)/(a^2+2*a*b+b^2)*tan(1/2*e*x+1/2*d)^3*B*a*b+2/e/(a*tan(1/2*e*x+1/2*d)^2-tan(1/2*e*x+1/2*d)^2*b+a+b)^2/(a-b)/(a^2+2*a*b+b^2)*tan(1/2*e*x+1/2*d)^3*b^2*B-2/e/(a*tan(1/2*e*x+1/2*d)^2-tan(1/2*e*x+1/2*d)^2*b+a+b)^2*C/(a-b)*tan(1/2*e*x+1/2*d)^2-4/e/(a*tan(1/2*e*x+1/2*d)^2-tan(1/2*e*x+1/2*d)^2*b+a+b)^2/(a+b)/(a^2-2*a*b+b^2)*tan(1/2*e*x+1/2*d)*A*a*b+1/e/(a*tan(1/2*e*x+1/2*d)^2-tan(1/2*e*x+1/2*d)^2*b+a+b)^2/(a+b)/(a^2-2*a*b+b^2)*tan(1/2*e*x+1/2*d)*A*b^2+2/e/(a*tan(1/2*e*x+1/2*d)^2-tan(1/2*e*x+1/2*d)^2*b+a+b)^2/(a+b)/(a^2-2*a*b+b^2)*tan(1/2*e*x+1/2*d)*a^2*B-1/e/(a*tan(1/2*e*x+1/2*d)^2-tan(1/2*e*x+1/2*d)^2*b+a+b)^2/(a+b)/(a^2-2*a*b+b^2)*tan(1/2*e*x+1/2*d)*B*a*b+2/e/(a*tan(1/2*e*x+1/2*d)^2-tan(1/2*e*x+1/2*d)^2*b+a+b)^2/(a+b)/(a^2-2*a*b+b^2)*tan(1/2*e*x+1/2*d)*b^2*B-2/e/(a*tan(1/2*e*x+1/2*d)^2-tan(1/2*e*x+1/2*d)^2*b+a+b)^2*a*C/(a^2-2*a*b+b^2)+2/e/(a^4-2*a^2*b^2+b^4)/((a-b)*(a+b))^(1/2)*arctan(tan(1/2*e*x+1/2*d)*(a-b)/((a-b)*(a+b))^(1/2))*a^2*A+1/e/(a^4-2*a^2*b^2+b^4)/((a-b)*(a+b))^(1/2)*arctan(tan(1/2*e*x+1/2*d)*(a-b)/((a-b)*(a+b))^(1/2))*A*b^2-3/e/(a^4-2*a^2*b^2+b^4)/((a-b)*(a+b))^(1/2)*arctan(tan(1/2*e*x+1/2*d)*(a-b)/((a-b)*(a+b))^(1/2))*B*a*b","B"
21,1,1974,243,0.188000," ","int((A+B*cos(e*x+d)+C*sin(e*x+d))/(a+b*cos(e*x+d))^4,x)","\frac{3 \tan \left(\frac{e x}{2}+\frac{d}{2}\right) A a \,b^{2}}{e \left(a \left(\tan^{2}\left(\frac{e x}{2}+\frac{d}{2}\right)\right)-\left(\tan^{2}\left(\frac{e x}{2}+\frac{d}{2}\right)\right) b +a +b \right)^{3} \left(a +b \right) \left(a^{3}-3 a^{2} b +3 b^{2} a -b^{3}\right)}+\frac{28 \left(\tan^{3}\left(\frac{e x}{2}+\frac{d}{2}\right)\right) B a \,b^{2}}{3 e \left(a \left(\tan^{2}\left(\frac{e x}{2}+\frac{d}{2}\right)\right)-\left(\tan^{2}\left(\frac{e x}{2}+\frac{d}{2}\right)\right) b +a +b \right)^{3} \left(a^{2}-2 a b +b^{2}\right) \left(a^{2}+2 a b +b^{2}\right)}-\frac{6 \tan \left(\frac{e x}{2}+\frac{d}{2}\right) A \,a^{2} b}{e \left(a \left(\tan^{2}\left(\frac{e x}{2}+\frac{d}{2}\right)\right)-\left(\tan^{2}\left(\frac{e x}{2}+\frac{d}{2}\right)\right) b +a +b \right)^{3} \left(a +b \right) \left(a^{3}-3 a^{2} b +3 b^{2} a -b^{3}\right)}-\frac{12 \left(\tan^{3}\left(\frac{e x}{2}+\frac{d}{2}\right)\right) A \,a^{2} b}{e \left(a \left(\tan^{2}\left(\frac{e x}{2}+\frac{d}{2}\right)\right)-\left(\tan^{2}\left(\frac{e x}{2}+\frac{d}{2}\right)\right) b +a +b \right)^{3} \left(a^{2}-2 a b +b^{2}\right) \left(a^{2}+2 a b +b^{2}\right)}+\frac{2 \left(\tan^{5}\left(\frac{e x}{2}+\frac{d}{2}\right)\right) a^{2} b B}{e \left(a \left(\tan^{2}\left(\frac{e x}{2}+\frac{d}{2}\right)\right)-\left(\tan^{2}\left(\frac{e x}{2}+\frac{d}{2}\right)\right) b +a +b \right)^{3} \left(a -b \right) \left(a^{3}+3 a^{2} b +3 b^{2} a +b^{3}\right)}+\frac{6 \left(\tan^{5}\left(\frac{e x}{2}+\frac{d}{2}\right)\right) B a \,b^{2}}{e \left(a \left(\tan^{2}\left(\frac{e x}{2}+\frac{d}{2}\right)\right)-\left(\tan^{2}\left(\frac{e x}{2}+\frac{d}{2}\right)\right) b +a +b \right)^{3} \left(a -b \right) \left(a^{3}+3 a^{2} b +3 b^{2} a +b^{3}\right)}-\frac{3 \left(\tan^{5}\left(\frac{e x}{2}+\frac{d}{2}\right)\right) A a \,b^{2}}{e \left(a \left(\tan^{2}\left(\frac{e x}{2}+\frac{d}{2}\right)\right)-\left(\tan^{2}\left(\frac{e x}{2}+\frac{d}{2}\right)\right) b +a +b \right)^{3} \left(a -b \right) \left(a^{3}+3 a^{2} b +3 b^{2} a +b^{3}\right)}-\frac{6 \left(\tan^{5}\left(\frac{e x}{2}+\frac{d}{2}\right)\right) A \,a^{2} b}{e \left(a \left(\tan^{2}\left(\frac{e x}{2}+\frac{d}{2}\right)\right)-\left(\tan^{2}\left(\frac{e x}{2}+\frac{d}{2}\right)\right) b +a +b \right)^{3} \left(a -b \right) \left(a^{3}+3 a^{2} b +3 b^{2} a +b^{3}\right)}-\frac{2 C \,b^{2}}{3 e \left(a \left(\tan^{2}\left(\frac{e x}{2}+\frac{d}{2}\right)\right)-\left(\tan^{2}\left(\frac{e x}{2}+\frac{d}{2}\right)\right) b +a +b \right)^{3} \left(a^{3}-3 a^{2} b +3 b^{2} a -b^{3}\right)}-\frac{2 C \left(\tan^{4}\left(\frac{e x}{2}+\frac{d}{2}\right)\right)}{e \left(a \left(\tan^{2}\left(\frac{e x}{2}+\frac{d}{2}\right)\right)-\left(\tan^{2}\left(\frac{e x}{2}+\frac{d}{2}\right)\right) b +a +b \right)^{3} \left(a -b \right)}+\frac{2 \left(\tan^{5}\left(\frac{e x}{2}+\frac{d}{2}\right)\right) a^{3} B}{e \left(a \left(\tan^{2}\left(\frac{e x}{2}+\frac{d}{2}\right)\right)-\left(\tan^{2}\left(\frac{e x}{2}+\frac{d}{2}\right)\right) b +a +b \right)^{3} \left(a -b \right) \left(a^{3}+3 a^{2} b +3 b^{2} a +b^{3}\right)}+\frac{\left(\tan^{5}\left(\frac{e x}{2}+\frac{d}{2}\right)\right) b^{3} B}{e \left(a \left(\tan^{2}\left(\frac{e x}{2}+\frac{d}{2}\right)\right)-\left(\tan^{2}\left(\frac{e x}{2}+\frac{d}{2}\right)\right) b +a +b \right)^{3} \left(a -b \right) \left(a^{3}+3 a^{2} b +3 b^{2} a +b^{3}\right)}-\frac{4 \left(\tan^{3}\left(\frac{e x}{2}+\frac{d}{2}\right)\right) A \,b^{3}}{3 e \left(a \left(\tan^{2}\left(\frac{e x}{2}+\frac{d}{2}\right)\right)-\left(\tan^{2}\left(\frac{e x}{2}+\frac{d}{2}\right)\right) b +a +b \right)^{3} \left(a^{2}-2 a b +b^{2}\right) \left(a^{2}+2 a b +b^{2}\right)}+\frac{4 \left(\tan^{3}\left(\frac{e x}{2}+\frac{d}{2}\right)\right) a^{3} B}{e \left(a \left(\tan^{2}\left(\frac{e x}{2}+\frac{d}{2}\right)\right)-\left(\tan^{2}\left(\frac{e x}{2}+\frac{d}{2}\right)\right) b +a +b \right)^{3} \left(a^{2}-2 a b +b^{2}\right) \left(a^{2}+2 a b +b^{2}\right)}-\frac{2 \tan \left(\frac{e x}{2}+\frac{d}{2}\right) A \,b^{3}}{e \left(a \left(\tan^{2}\left(\frac{e x}{2}+\frac{d}{2}\right)\right)-\left(\tan^{2}\left(\frac{e x}{2}+\frac{d}{2}\right)\right) b +a +b \right)^{3} \left(a +b \right) \left(a^{3}-3 a^{2} b +3 b^{2} a -b^{3}\right)}+\frac{2 \tan \left(\frac{e x}{2}+\frac{d}{2}\right) a^{3} B}{e \left(a \left(\tan^{2}\left(\frac{e x}{2}+\frac{d}{2}\right)\right)-\left(\tan^{2}\left(\frac{e x}{2}+\frac{d}{2}\right)\right) b +a +b \right)^{3} \left(a +b \right) \left(a^{3}-3 a^{2} b +3 b^{2} a -b^{3}\right)}-\frac{\tan \left(\frac{e x}{2}+\frac{d}{2}\right) b^{3} B}{e \left(a \left(\tan^{2}\left(\frac{e x}{2}+\frac{d}{2}\right)\right)-\left(\tan^{2}\left(\frac{e x}{2}+\frac{d}{2}\right)\right) b +a +b \right)^{3} \left(a +b \right) \left(a^{3}-3 a^{2} b +3 b^{2} a -b^{3}\right)}-\frac{2 \left(\tan^{5}\left(\frac{e x}{2}+\frac{d}{2}\right)\right) A \,b^{3}}{e \left(a \left(\tan^{2}\left(\frac{e x}{2}+\frac{d}{2}\right)\right)-\left(\tan^{2}\left(\frac{e x}{2}+\frac{d}{2}\right)\right) b +a +b \right)^{3} \left(a -b \right) \left(a^{3}+3 a^{2} b +3 b^{2} a +b^{3}\right)}-\frac{2 \tan \left(\frac{e x}{2}+\frac{d}{2}\right) a^{2} b B}{e \left(a \left(\tan^{2}\left(\frac{e x}{2}+\frac{d}{2}\right)\right)-\left(\tan^{2}\left(\frac{e x}{2}+\frac{d}{2}\right)\right) b +a +b \right)^{3} \left(a +b \right) \left(a^{3}-3 a^{2} b +3 b^{2} a -b^{3}\right)}+\frac{6 \tan \left(\frac{e x}{2}+\frac{d}{2}\right) B a \,b^{2}}{e \left(a \left(\tan^{2}\left(\frac{e x}{2}+\frac{d}{2}\right)\right)-\left(\tan^{2}\left(\frac{e x}{2}+\frac{d}{2}\right)\right) b +a +b \right)^{3} \left(a +b \right) \left(a^{3}-3 a^{2} b +3 b^{2} a -b^{3}\right)}+\frac{3 \arctan \left(\frac{\tan \left(\frac{e x}{2}+\frac{d}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) A a \,b^{2}}{e \left(a^{6}-3 b^{2} a^{4}+3 b^{4} a^{2}-b^{6}\right) \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{4 \arctan \left(\frac{\tan \left(\frac{e x}{2}+\frac{d}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) a^{2} b B}{e \left(a^{6}-3 b^{2} a^{4}+3 b^{4} a^{2}-b^{6}\right) \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{2 C \,a^{2}}{e \left(a \left(\tan^{2}\left(\frac{e x}{2}+\frac{d}{2}\right)\right)-\left(\tan^{2}\left(\frac{e x}{2}+\frac{d}{2}\right)\right) b +a +b \right)^{3} \left(a^{3}-3 a^{2} b +3 b^{2} a -b^{3}\right)}-\frac{4 a C \left(\tan^{2}\left(\frac{e x}{2}+\frac{d}{2}\right)\right)}{e \left(a \left(\tan^{2}\left(\frac{e x}{2}+\frac{d}{2}\right)\right)-\left(\tan^{2}\left(\frac{e x}{2}+\frac{d}{2}\right)\right) b +a +b \right)^{3} \left(a^{2}-2 a b +b^{2}\right)}+\frac{2 \arctan \left(\frac{\tan \left(\frac{e x}{2}+\frac{d}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) A \,a^{3}}{e \left(a^{6}-3 b^{2} a^{4}+3 b^{4} a^{2}-b^{6}\right) \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{\arctan \left(\frac{\tan \left(\frac{e x}{2}+\frac{d}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) b^{3} B}{e \left(a^{6}-3 b^{2} a^{4}+3 b^{4} a^{2}-b^{6}\right) \sqrt{\left(a -b \right) \left(a +b \right)}}"," ",0,"-6/e/(a*tan(1/2*e*x+1/2*d)^2-tan(1/2*e*x+1/2*d)^2*b+a+b)^3/(a-b)/(a^3+3*a^2*b+3*a*b^2+b^3)*tan(1/2*e*x+1/2*d)^5*A*a^2*b-3/e/(a*tan(1/2*e*x+1/2*d)^2-tan(1/2*e*x+1/2*d)^2*b+a+b)^3/(a-b)/(a^3+3*a^2*b+3*a*b^2+b^3)*tan(1/2*e*x+1/2*d)^5*A*a*b^2+2/e/(a*tan(1/2*e*x+1/2*d)^2-tan(1/2*e*x+1/2*d)^2*b+a+b)^3/(a-b)/(a^3+3*a^2*b+3*a*b^2+b^3)*tan(1/2*e*x+1/2*d)^5*a^2*b*B+6/e/(a*tan(1/2*e*x+1/2*d)^2-tan(1/2*e*x+1/2*d)^2*b+a+b)^3/(a-b)/(a^3+3*a^2*b+3*a*b^2+b^3)*tan(1/2*e*x+1/2*d)^5*B*a*b^2-12/e/(a*tan(1/2*e*x+1/2*d)^2-tan(1/2*e*x+1/2*d)^2*b+a+b)^3/(a^2-2*a*b+b^2)/(a^2+2*a*b+b^2)*tan(1/2*e*x+1/2*d)^3*A*a^2*b+28/3/e/(a*tan(1/2*e*x+1/2*d)^2-tan(1/2*e*x+1/2*d)^2*b+a+b)^3/(a^2-2*a*b+b^2)/(a^2+2*a*b+b^2)*tan(1/2*e*x+1/2*d)^3*B*a*b^2-6/e/(a*tan(1/2*e*x+1/2*d)^2-tan(1/2*e*x+1/2*d)^2*b+a+b)^3/(a+b)/(a^3-3*a^2*b+3*a*b^2-b^3)*tan(1/2*e*x+1/2*d)*A*a^2*b+3/e/(a*tan(1/2*e*x+1/2*d)^2-tan(1/2*e*x+1/2*d)^2*b+a+b)^3/(a+b)/(a^3-3*a^2*b+3*a*b^2-b^3)*tan(1/2*e*x+1/2*d)*A*a*b^2-2/e/(a*tan(1/2*e*x+1/2*d)^2-tan(1/2*e*x+1/2*d)^2*b+a+b)^3/(a+b)/(a^3-3*a^2*b+3*a*b^2-b^3)*tan(1/2*e*x+1/2*d)*a^2*b*B+6/e/(a*tan(1/2*e*x+1/2*d)^2-tan(1/2*e*x+1/2*d)^2*b+a+b)^3/(a+b)/(a^3-3*a^2*b+3*a*b^2-b^3)*tan(1/2*e*x+1/2*d)*B*a*b^2-2/3/e/(a*tan(1/2*e*x+1/2*d)^2-tan(1/2*e*x+1/2*d)^2*b+a+b)^3*C/(a^3-3*a^2*b+3*a*b^2-b^3)*b^2-2/e/(a*tan(1/2*e*x+1/2*d)^2-tan(1/2*e*x+1/2*d)^2*b+a+b)^3*C/(a-b)*tan(1/2*e*x+1/2*d)^4+2/e/(a*tan(1/2*e*x+1/2*d)^2-tan(1/2*e*x+1/2*d)^2*b+a+b)^3/(a-b)/(a^3+3*a^2*b+3*a*b^2+b^3)*tan(1/2*e*x+1/2*d)^5*a^3*B+1/e/(a*tan(1/2*e*x+1/2*d)^2-tan(1/2*e*x+1/2*d)^2*b+a+b)^3/(a-b)/(a^3+3*a^2*b+3*a*b^2+b^3)*tan(1/2*e*x+1/2*d)^5*b^3*B-4/3/e/(a*tan(1/2*e*x+1/2*d)^2-tan(1/2*e*x+1/2*d)^2*b+a+b)^3/(a^2-2*a*b+b^2)/(a^2+2*a*b+b^2)*tan(1/2*e*x+1/2*d)^3*A*b^3+4/e/(a*tan(1/2*e*x+1/2*d)^2-tan(1/2*e*x+1/2*d)^2*b+a+b)^3/(a^2-2*a*b+b^2)/(a^2+2*a*b+b^2)*tan(1/2*e*x+1/2*d)^3*a^3*B-2/e/(a*tan(1/2*e*x+1/2*d)^2-tan(1/2*e*x+1/2*d)^2*b+a+b)^3/(a+b)/(a^3-3*a^2*b+3*a*b^2-b^3)*tan(1/2*e*x+1/2*d)*A*b^3+2/e/(a*tan(1/2*e*x+1/2*d)^2-tan(1/2*e*x+1/2*d)^2*b+a+b)^3/(a+b)/(a^3-3*a^2*b+3*a*b^2-b^3)*tan(1/2*e*x+1/2*d)*a^3*B-1/e/(a*tan(1/2*e*x+1/2*d)^2-tan(1/2*e*x+1/2*d)^2*b+a+b)^3/(a+b)/(a^3-3*a^2*b+3*a*b^2-b^3)*tan(1/2*e*x+1/2*d)*b^3*B+3/e/(a^6-3*a^4*b^2+3*a^2*b^4-b^6)/((a-b)*(a+b))^(1/2)*arctan(tan(1/2*e*x+1/2*d)*(a-b)/((a-b)*(a+b))^(1/2))*A*a*b^2-2/e/(a*tan(1/2*e*x+1/2*d)^2-tan(1/2*e*x+1/2*d)^2*b+a+b)^3/(a-b)/(a^3+3*a^2*b+3*a*b^2+b^3)*tan(1/2*e*x+1/2*d)^5*A*b^3-4/e/(a^6-3*a^4*b^2+3*a^2*b^4-b^6)/((a-b)*(a+b))^(1/2)*arctan(tan(1/2*e*x+1/2*d)*(a-b)/((a-b)*(a+b))^(1/2))*a^2*b*B-2/e/(a*tan(1/2*e*x+1/2*d)^2-tan(1/2*e*x+1/2*d)^2*b+a+b)^3*C/(a^3-3*a^2*b+3*a*b^2-b^3)*a^2+2/e/(a^6-3*a^4*b^2+3*a^2*b^4-b^6)/((a-b)*(a+b))^(1/2)*arctan(tan(1/2*e*x+1/2*d)*(a-b)/((a-b)*(a+b))^(1/2))*A*a^3-1/e/(a^6-3*a^4*b^2+3*a^2*b^4-b^6)/((a-b)*(a+b))^(1/2)*arctan(tan(1/2*e*x+1/2*d)*(a-b)/((a-b)*(a+b))^(1/2))*b^3*B-4/e/(a*tan(1/2*e*x+1/2*d)^2-tan(1/2*e*x+1/2*d)^2*b+a+b)^3*a*C/(a^2-2*a*b+b^2)*tan(1/2*e*x+1/2*d)^2","B"