1,1,68,25,0.049000," ","int(sin(x)^4/(a+a*cos(x)),x)","\frac{\tan^{5}\left(\frac{x}{2}\right)}{a \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)^{3}}-\frac{8 \left(\tan^{3}\left(\frac{x}{2}\right)\right)}{3 a \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)^{3}}-\frac{\tan \left(\frac{x}{2}\right)}{a \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)^{3}}+\frac{x}{2 a}"," ",0,"1/a/(tan(1/2*x)^2+1)^3*tan(1/2*x)^5-8/3/a/(tan(1/2*x)^2+1)^3*tan(1/2*x)^3-1/a/(tan(1/2*x)^2+1)^3*tan(1/2*x)+1/2*x/a","B"
2,1,16,17,0.037000," ","int(sin(x)^3/(a+a*cos(x)),x)","\frac{\frac{\left(\cos^{2}\left(x \right)\right)}{2}-\cos \left(x \right)}{a}"," ",0,"1/a*(1/2*cos(x)^2-cos(x))","A"
3,1,31,13,0.043000," ","int(sin(x)^2/(a+a*cos(x)),x)","-\frac{2 \tan \left(\frac{x}{2}\right)}{a \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)}+\frac{2 \arctan \left(\tan \left(\frac{x}{2}\right)\right)}{a}"," ",0,"-2/a*tan(1/2*x)/(tan(1/2*x)^2+1)+2/a*arctan(tan(1/2*x))","B"
4,1,13,10,0.028000," ","int(sin(x)/(a+a*cos(x)),x)","-\frac{\ln \left(a +a \cos \left(x \right)\right)}{a}"," ",0,"-ln(a+a*cos(x))/a","A"
5,1,9,11,0.024000," ","int(1/(a+a*cos(x)),x)","\frac{\tan \left(\frac{x}{2}\right)}{a}"," ",0,"1/a*tan(1/2*x)","A"
6,1,33,19,0.053000," ","int(csc(x)/(a+a*cos(x)),x)","\frac{\ln \left(-1+\cos \left(x \right)\right)}{4 a}+\frac{1}{2 a \left(\cos \left(x \right)+1\right)}-\frac{\ln \left(\cos \left(x \right)+1\right)}{4 a}"," ",0,"1/4/a*ln(-1+cos(x))+1/2/a/(cos(x)+1)-1/4*ln(cos(x)+1)/a","A"
7,1,29,20,0.051000," ","int(csc(x)^2/(a+a*cos(x)),x)","\frac{\frac{\left(\tan^{3}\left(\frac{x}{2}\right)\right)}{3}+2 \tan \left(\frac{x}{2}\right)-\frac{1}{\tan \left(\frac{x}{2}\right)}}{4 a}"," ",0,"1/4/a*(1/3*tan(1/2*x)^3+2*tan(1/2*x)-1/tan(1/2*x))","A"
8,1,55,41,0.062000," ","int(csc(x)^3/(a+a*cos(x)),x)","\frac{1}{8 a \left(-1+\cos \left(x \right)\right)}+\frac{3 \ln \left(-1+\cos \left(x \right)\right)}{16 a}+\frac{1}{8 a \left(\cos \left(x \right)+1\right)^{2}}+\frac{1}{4 a \left(\cos \left(x \right)+1\right)}-\frac{3 \ln \left(\cos \left(x \right)+1\right)}{16 a}"," ",0,"1/8/a/(-1+cos(x))+3/16/a*ln(-1+cos(x))+1/8/a/(cos(x)+1)^2+1/4/a/(cos(x)+1)-3/16*ln(cos(x)+1)/a","A"
9,1,45,31,0.062000," ","int(csc(x)^4/(a+a*cos(x)),x)","\frac{\frac{\left(\tan^{5}\left(\frac{x}{2}\right)\right)}{5}+\frac{4 \left(\tan^{3}\left(\frac{x}{2}\right)\right)}{3}+6 \tan \left(\frac{x}{2}\right)-\frac{1}{3 \tan \left(\frac{x}{2}\right)^{3}}-\frac{4}{\tan \left(\frac{x}{2}\right)}}{16 a}"," ",0,"1/16/a*(1/5*tan(1/2*x)^5+4/3*tan(1/2*x)^3+6*tan(1/2*x)-1/3/tan(1/2*x)^3-4/tan(1/2*x))","A"
10,1,10,5,0.021000," ","int(sin(2*x)/(1+cos(2*x)),x)","-\frac{\ln \left(1+\cos \left(2 x \right)\right)}{2}"," ",0,"-1/2*ln(1+cos(2*x))","A"
11,1,12,3,0.024000," ","int(sin(2*x)/(1-cos(2*x)),x)","\frac{\ln \left(1-\cos \left(2 x \right)\right)}{2}"," ",0,"1/2*ln(1-cos(2*x))","B"
12,1,7,6,0.024000," ","int(sin(x)/(cos(x)+1)^2,x)","\frac{1}{\cos \left(x \right)+1}"," ",0,"1/(cos(x)+1)","A"
13,1,11,10,0.035000," ","int(sin(x)/(1-cos(x))^2,x)","-\frac{1}{1-\cos \left(x \right)}"," ",0,"-1/(1-cos(x))","A"
14,1,11,14,0.044000," ","int(sin(x)^2/(cos(x)+1)^2,x)","2 \tan \left(\frac{x}{2}\right)-x"," ",0,"2*tan(1/2*x)-x","A"
15,1,13,16,0.070000," ","int(sin(x)^2/(1-cos(x))^2,x)","-\frac{2}{\tan \left(\frac{x}{2}\right)}-x"," ",0,"-2/tan(1/2*x)-x","A"
16,1,11,10,0.040000," ","int(sin(x)^3/(cos(x)+1)^2,x)","\cos \left(x \right)-2 \ln \left(\cos \left(x \right)+1\right)"," ",0,"cos(x)-2*ln(cos(x)+1)","A"
17,1,11,12,0.056000," ","int(sin(x)^3/(1-cos(x))^2,x)","\cos \left(x \right)+2 \ln \left(-1+\cos \left(x \right)\right)"," ",0,"cos(x)+2*ln(-1+cos(x))","A"
18,1,9,8,0.025000," ","int(sin(x)/(cos(x)+1)^3,x)","\frac{1}{2 \left(\cos \left(x \right)+1\right)^{2}}"," ",0,"1/2/(cos(x)+1)^2","A"
19,1,11,10,0.039000," ","int(sin(x)/(1-cos(x))^3,x)","-\frac{1}{2 \left(1-\cos \left(x \right)\right)^{2}}"," ",0,"-1/2/(1-cos(x))^2","A"
20,1,9,12,0.050000," ","int(sin(x)^2/(cos(x)+1)^3,x)","\frac{\left(\tan^{3}\left(\frac{x}{2}\right)\right)}{3}"," ",0,"1/3*tan(1/2*x)^3","A"
21,1,9,14,0.073000," ","int(sin(x)^2/(1-cos(x))^3,x)","-\frac{1}{3 \tan \left(\frac{x}{2}\right)^{3}}"," ",0,"-1/3/tan(1/2*x)^3","A"
22,1,15,14,0.053000," ","int(sin(x)^3/(cos(x)+1)^3,x)","\frac{2}{\cos \left(x \right)+1}+\ln \left(\cos \left(x \right)+1\right)"," ",0,"2/(cos(x)+1)+ln(cos(x)+1)","A"
23,1,17,20,0.073000," ","int(sin(x)^3/(1-cos(x))^3,x)","\frac{2}{-1+\cos \left(x \right)}-\ln \left(-1+\cos \left(x \right)\right)"," ",0,"2/(-1+cos(x))-ln(-1+cos(x))","A"
24,1,315,87,0.041000," ","int(sin(x)^4/(a+b*cos(x)),x)","\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^{4}}{b^{4} \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{4 \arctan \left(\frac{\tan \left(\frac{x}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) a^{2}}{b^{2} \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)}{\sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{2 \left(\tan^{5}\left(\frac{x}{2}\right)\right) a^{2}}{b^{3} \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)^{3}}+\frac{\left(\tan^{5}\left(\frac{x}{2}\right)\right) a}{b^{2} \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)^{3}}-\frac{2 \left(\tan^{5}\left(\frac{x}{2}\right)\right)}{b \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)^{3}}+\frac{4 \left(\tan^{3}\left(\frac{x}{2}\right)\right) a^{2}}{b^{3} \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)^{3}}-\frac{20 \left(\tan^{3}\left(\frac{x}{2}\right)\right)}{3 b \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)^{3}}+\frac{2 \tan \left(\frac{x}{2}\right) a^{2}}{b^{3} \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)^{3}}-\frac{2 \tan \left(\frac{x}{2}\right)}{b \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)^{3}}-\frac{\tan \left(\frac{x}{2}\right) a}{b^{2} \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)^{3}}-\frac{2 \arctan \left(\tan \left(\frac{x}{2}\right)\right) a^{3}}{b^{4}}+\frac{3 \arctan \left(\tan \left(\frac{x}{2}\right)\right) a}{b^{2}}"," ",0,"2/b^4/((a-b)*(a+b))^(1/2)*arctan(tan(1/2*x)*(a-b)/((a-b)*(a+b))^(1/2))*a^4-4/b^2/((a-b)*(a+b))^(1/2)*arctan(tan(1/2*x)*(a-b)/((a-b)*(a+b))^(1/2))*a^2+2/((a-b)*(a+b))^(1/2)*arctan(tan(1/2*x)*(a-b)/((a-b)*(a+b))^(1/2))+2/b^3/(tan(1/2*x)^2+1)^3*tan(1/2*x)^5*a^2+1/b^2/(tan(1/2*x)^2+1)^3*tan(1/2*x)^5*a-2/b/(tan(1/2*x)^2+1)^3*tan(1/2*x)^5+4/b^3/(tan(1/2*x)^2+1)^3*tan(1/2*x)^3*a^2-20/3/b/(tan(1/2*x)^2+1)^3*tan(1/2*x)^3+2/b^3/(tan(1/2*x)^2+1)^3*tan(1/2*x)*a^2-2/b/(tan(1/2*x)^2+1)^3*tan(1/2*x)-1/b^2/(tan(1/2*x)^2+1)^3*tan(1/2*x)*a-2/b^4*arctan(tan(1/2*x))*a^3+3/b^2*arctan(tan(1/2*x))*a","B"
25,1,45,38,0.025000," ","int(sin(x)^3/(a+b*cos(x)),x)","\frac{\cos^{2}\left(x \right)}{2 b}-\frac{a \cos \left(x \right)}{b^{2}}+\frac{\ln \left(a +b \cos \left(x \right)\right) a^{2}}{b^{3}}-\frac{\ln \left(a +b \cos \left(x \right)\right)}{b}"," ",0,"1/2*cos(x)^2/b-a*cos(x)/b^2+1/b^3*ln(a+b*cos(x))*a^2-ln(a+b*cos(x))/b","A"
26,1,108,49,0.036000," ","int(sin(x)^2/(a+b*cos(x)),x)","-\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^{2}}{b^{2} \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)}{\sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{2 \tan \left(\frac{x}{2}\right)}{b \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)}+\frac{2 \arctan \left(\tan \left(\frac{x}{2}\right)\right) a}{b^{2}}"," ",0,"-2/b^2/((a-b)*(a+b))^(1/2)*arctan(tan(1/2*x)*(a-b)/((a-b)*(a+b))^(1/2))*a^2+2/((a-b)*(a+b))^(1/2)*arctan(tan(1/2*x)*(a-b)/((a-b)*(a+b))^(1/2))-2/b*tan(1/2*x)/(tan(1/2*x)^2+1)+2/b^2*arctan(tan(1/2*x))*a","B"
27,1,13,12,0.018000," ","int(sin(x)/(a+b*cos(x)),x)","-\frac{\ln \left(a +b \cos \left(x \right)\right)}{b}"," ",0,"-ln(a+b*cos(x))/b","A"
28,1,36,32,0.022000," ","int(1/(a+b*cos(x)),x)","\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)}{\sqrt{\left(a -b \right) \left(a +b \right)}}"," ",0,"2/((a-b)*(a+b))^(1/2)*arctan(tan(1/2*x)*(a-b)/((a-b)*(a+b))^(1/2))","A"
29,1,54,49,0.038000," ","int(csc(x)/(a+b*cos(x)),x)","\frac{b \ln \left(a +b \cos \left(x \right)\right)}{\left(a -b \right) \left(a +b \right)}+\frac{\ln \left(-1+\cos \left(x \right)\right)}{2 a +2 b}-\frac{\ln \left(\cos \left(x \right)+1\right)}{2 a -2 b}"," ",0,"b/(a-b)/(a+b)*ln(a+b*cos(x))+1/(2*a+2*b)*ln(-1+cos(x))-1/(2*a-2*b)*ln(cos(x)+1)","A"
30,1,78,57,0.047000," ","int(csc(x)^2/(a+b*cos(x)),x)","\frac{\tan \left(\frac{x}{2}\right)}{2 a -2 b}-\frac{2 b^{2} \arctan \left(\frac{\tan \left(\frac{x}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right)}{\left(a -b \right) \left(a +b \right) \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{1}{2 \left(a +b \right) \tan \left(\frac{x}{2}\right)}"," ",0,"1/2/(a-b)*tan(1/2*x)-2/(a-b)/(a+b)*b^2/((a-b)*(a+b))^(1/2)*arctan(tan(1/2*x)*(a-b)/((a-b)*(a+b))^(1/2))-1/2/(a+b)/tan(1/2*x)","A"
31,1,114,86,0.056000," ","int(csc(x)^3/(a+b*cos(x)),x)","-\frac{b^{3} \ln \left(a +b \cos \left(x \right)\right)}{\left(a +b \right)^{2} \left(a -b \right)^{2}}+\frac{1}{\left(4 a +4 b \right) \left(-1+\cos \left(x \right)\right)}+\frac{\ln \left(-1+\cos \left(x \right)\right) a}{4 \left(a +b \right)^{2}}+\frac{\ln \left(-1+\cos \left(x \right)\right) b}{2 \left(a +b \right)^{2}}+\frac{1}{\left(4 a -4 b \right) \left(\cos \left(x \right)+1\right)}-\frac{\ln \left(\cos \left(x \right)+1\right) a}{4 \left(a -b \right)^{2}}+\frac{\ln \left(\cos \left(x \right)+1\right) b}{2 \left(a -b \right)^{2}}"," ",0,"-b^3/(a+b)^2/(a-b)^2*ln(a+b*cos(x))+1/(4*a+4*b)/(-1+cos(x))+1/4/(a+b)^2*ln(-1+cos(x))*a+1/2/(a+b)^2*ln(-1+cos(x))*b+1/(4*a-4*b)/(cos(x)+1)-1/4/(a-b)^2*ln(cos(x)+1)*a+1/2/(a-b)^2*ln(cos(x)+1)*b","A"
32,1,153,96,0.056000," ","int(csc(x)^4/(a+b*cos(x)),x)","\frac{a \left(\tan^{3}\left(\frac{x}{2}\right)\right)}{24 \left(a -b \right)^{2}}-\frac{\left(\tan^{3}\left(\frac{x}{2}\right)\right) b}{24 \left(a -b \right)^{2}}+\frac{3 a \tan \left(\frac{x}{2}\right)}{8 \left(a -b \right)^{2}}-\frac{5 \tan \left(\frac{x}{2}\right) b}{8 \left(a -b \right)^{2}}+\frac{2 b^{4} \arctan \left(\frac{\tan \left(\frac{x}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right)}{\left(a -b \right)^{2} \left(a +b \right)^{2} \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{1}{24 \left(a +b \right) \tan \left(\frac{x}{2}\right)^{3}}-\frac{3 a}{8 \left(a +b \right)^{2} \tan \left(\frac{x}{2}\right)}-\frac{5 b}{8 \left(a +b \right)^{2} \tan \left(\frac{x}{2}\right)}"," ",0,"1/24/(a-b)^2*a*tan(1/2*x)^3-1/24/(a-b)^2*tan(1/2*x)^3*b+3/8/(a-b)^2*a*tan(1/2*x)-5/8/(a-b)^2*tan(1/2*x)*b+2/(a-b)^2/(a+b)^2*b^4/((a-b)*(a+b))^(1/2)*arctan(tan(1/2*x)*(a-b)/((a-b)*(a+b))^(1/2))-1/24/(a+b)/tan(1/2*x)^3-3/8/(a+b)^2/tan(1/2*x)*a-5/8/(a+b)^2/tan(1/2*x)*b","A"
33,1,127,141,0.224000," ","int((a+b*cos(d*x+c))*(e*sin(d*x+c))^(7/2),x)","\frac{\frac{2 b \left(e \sin \left(d x +c \right)\right)^{\frac{9}{2}}}{9 e}-\frac{e^{4} a \left(-6 \left(\sin^{5}\left(d x +c \right)\right)+5 \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticF \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right)-4 \left(\sin^{3}\left(d x +c \right)\right)+10 \sin \left(d x +c \right)\right)}{21 \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}}}{d}"," ",0,"(2/9/e*b*(e*sin(d*x+c))^(9/2)-1/21*e^4*a*(-6*sin(d*x+c)^5+5*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))-4*sin(d*x+c)^3+10*sin(d*x+c))/cos(d*x+c)/(e*sin(d*x+c))^(1/2))/d","A"
34,1,171,116,0.237000," ","int((a+b*cos(d*x+c))*(e*sin(d*x+c))^(5/2),x)","\frac{\frac{2 b \left(e \sin \left(d x +c \right)\right)^{\frac{7}{2}}}{7 e}-\frac{e^{3} a \left(6 \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticE \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right)-3 \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticF \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right)-2 \left(\sin^{4}\left(d x +c \right)\right)+2 \left(\sin^{2}\left(d x +c \right)\right)\right)}{5 \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}}}{d}"," ",0,"(2/7/e*b*(e*sin(d*x+c))^(7/2)-1/5*e^3*a*(6*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticE((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))-3*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))-2*sin(d*x+c)^4+2*sin(d*x+c)^2)/cos(d*x+c)/(e*sin(d*x+c))^(1/2))/d","A"
35,1,116,116,0.208000," ","int((a+b*cos(d*x+c))*(e*sin(d*x+c))^(3/2),x)","\frac{\frac{2 b \left(e \sin \left(d x +c \right)\right)^{\frac{5}{2}}}{5 e}-\frac{e^{2} a \left(\sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticF \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right)-2 \left(\sin^{3}\left(d x +c \right)\right)+2 \sin \left(d x +c \right)\right)}{3 \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}}}{d}"," ",0,"(2/5/e*b*(e*sin(d*x+c))^(5/2)-1/3*e^2*a*((-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))-2*sin(d*x+c)^3+2*sin(d*x+c))/cos(d*x+c)/(e*sin(d*x+c))^(1/2))/d","A"
36,1,117,90,0.229000," ","int((a+b*cos(d*x+c))*(e*sin(d*x+c))^(1/2),x)","\frac{\frac{2 b \left(e \sin \left(d x +c \right)\right)^{\frac{3}{2}}}{3 e}-\frac{a e \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \left(2 \EllipticE \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right)-\EllipticF \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right)\right)}{\cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}}}{d}"," ",0,"(2/3*b/e*(e*sin(d*x+c))^(3/2)-a*e*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*(2*EllipticE((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))-EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2)))/cos(d*x+c)/(e*sin(d*x+c))^(1/2))/d","A"
37,1,92,90,0.156000," ","int((a+b*cos(d*x+c))/(e*sin(d*x+c))^(1/2),x)","-\frac{a \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticF \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right)-2 \sin \left(d x +c \right) \cos \left(d x +c \right) b}{\cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, d}"," ",0,"-1/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*(a*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))-2*sin(d*x+c)*cos(d*x+c)*b)/d","A"
38,1,153,118,0.218000," ","int((a+b*cos(d*x+c))/(e*sin(d*x+c))^(3/2),x)","\frac{2 \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticE \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right) a -a \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticF \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right)-2 a \left(\cos^{2}\left(d x +c \right)\right)-2 b \cos \left(d x +c \right)}{e \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, d}"," ",0,"(2*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticE((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))*a-a*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))-2*a*cos(d*x+c)^2-2*b*cos(d*x+c))/e/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/d","A"
39,1,124,118,0.242000," ","int((a+b*cos(d*x+c))/(e*sin(d*x+c))^(5/2),x)","\frac{-\frac{2 b}{3 e \left(e \sin \left(d x +c \right)\right)^{\frac{3}{2}}}-\frac{a \left(\sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sin^{\frac{5}{2}}\left(d x +c \right)\right) \EllipticF \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right)-2 \left(\sin^{3}\left(d x +c \right)\right)+2 \sin \left(d x +c \right)\right)}{3 e^{2} \sin \left(d x +c \right)^{2} \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}}}{d}"," ",0,"(-2/3*b/e/(e*sin(d*x+c))^(3/2)-1/3*a/e^2*((-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(5/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))-2*sin(d*x+c)^3+2*sin(d*x+c))/sin(d*x+c)^2/cos(d*x+c)/(e*sin(d*x+c))^(1/2))/d","A"
40,1,187,143,0.299000," ","int((a+b*cos(d*x+c))/(e*sin(d*x+c))^(7/2),x)","\frac{-\frac{2 b}{5 e \left(e \sin \left(d x +c \right)\right)^{\frac{5}{2}}}+\frac{a \left(6 \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sin^{\frac{7}{2}}\left(d x +c \right)\right) \EllipticE \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right)-3 \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sin^{\frac{7}{2}}\left(d x +c \right)\right) \EllipticF \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right)+6 \left(\sin^{5}\left(d x +c \right)\right)-4 \left(\sin^{3}\left(d x +c \right)\right)-2 \sin \left(d x +c \right)\right)}{5 e^{3} \sin \left(d x +c \right)^{3} \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}}}{d}"," ",0,"(-2/5*b/e/(e*sin(d*x+c))^(5/2)+1/5*a/e^3*(6*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(7/2)*EllipticE((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))-3*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(7/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))+6*sin(d*x+c)^5-4*sin(d*x+c)^3-2*sin(d*x+c))/sin(d*x+c)^3/cos(d*x+c)/(e*sin(d*x+c))^(1/2))/d","A"
41,1,228,201,0.240000," ","int((a+b*cos(d*x+c))^2*(e*sin(d*x+c))^(7/2),x)","\frac{\frac{4 a b \left(e \sin \left(d x +c \right)\right)^{\frac{9}{2}}}{9 e}-\frac{e^{4} \left(-42 b^{2} \sin \left(d x +c \right) \left(\cos^{6}\left(d x +c \right)\right)+\left(-66 a^{2}+72 b^{2}\right) \left(\cos^{4}\left(d x +c \right)\right) \sin \left(d x +c \right)+\left(176 a^{2}-10 b^{2}\right) \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+55 \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticF \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right) a^{2}+10 \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticF \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right) b^{2}\right)}{231 \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}}}{d}"," ",0,"(4/9/e*a*b*(e*sin(d*x+c))^(9/2)-1/231*e^4*(-42*b^2*sin(d*x+c)*cos(d*x+c)^6+(-66*a^2+72*b^2)*cos(d*x+c)^4*sin(d*x+c)+(176*a^2-10*b^2)*cos(d*x+c)^2*sin(d*x+c)+55*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))*a^2+10*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))*b^2)/cos(d*x+c)/(e*sin(d*x+c))^(1/2))/d","A"
42,1,332,166,0.265000," ","int((a+b*cos(d*x+c))^2*(e*sin(d*x+c))^(5/2),x)","\frac{\frac{4 a b \left(e \sin \left(d x +c \right)\right)^{\frac{7}{2}}}{7 e}-\frac{e^{3} \left(10 b^{2} \left(\sin^{6}\left(d x +c \right)\right)+54 \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticE \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right) a^{2}+12 \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticE \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right) b^{2}-27 \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticF \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right) a^{2}-6 \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticF \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right) b^{2}-18 a^{2} \left(\sin^{4}\left(d x +c \right)\right)-14 \left(\sin^{4}\left(d x +c \right)\right) b^{2}+18 \left(\sin^{2}\left(d x +c \right)\right) a^{2}+4 \left(\sin^{2}\left(d x +c \right)\right) b^{2}\right)}{45 \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}}}{d}"," ",0,"(4/7/e*a*b*(e*sin(d*x+c))^(7/2)-1/45*e^3*(10*b^2*sin(d*x+c)^6+54*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticE((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))*a^2+12*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticE((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))*b^2-27*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))*a^2-6*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))*b^2-18*a^2*sin(d*x+c)^4-14*sin(d*x+c)^4*b^2+18*sin(d*x+c)^2*a^2+4*sin(d*x+c)^2*b^2)/cos(d*x+c)/(e*sin(d*x+c))^(1/2))/d","A"
43,1,229,166,0.242000," ","int((a+b*cos(d*x+c))^2*(e*sin(d*x+c))^(3/2),x)","-\frac{e^{2} \left(30 b^{2} \sin \left(d x +c \right) \left(\cos^{4}\left(d x +c \right)\right)+35 \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticF \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right) a^{2}+10 \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticF \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right) b^{2}+84 a b \sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right)+70 a^{2} \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right)-10 b^{2} \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right)-84 a b \sin \left(d x +c \right) \cos \left(d x +c \right)\right)}{105 \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, d}"," ",0,"-1/105/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*e^2*(30*b^2*sin(d*x+c)*cos(d*x+c)^4+35*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))*a^2+10*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))*b^2+84*a*b*sin(d*x+c)*cos(d*x+c)^3+70*a^2*sin(d*x+c)*cos(d*x+c)^2-10*b^2*sin(d*x+c)*cos(d*x+c)^2-84*a*b*sin(d*x+c)*cos(d*x+c))/d","A"
44,1,294,130,0.247000," ","int((a+b*cos(d*x+c))^2*(e*sin(d*x+c))^(1/2),x)","-\frac{e \left(30 \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticE \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right) a^{2}+12 \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticE \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right) b^{2}-15 \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticF \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right) a^{2}-6 \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticF \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right) b^{2}+6 b^{2} \left(\cos^{4}\left(d x +c \right)\right)+20 a b \left(\cos^{3}\left(d x +c \right)\right)-6 \left(\cos^{2}\left(d x +c \right)\right) b^{2}-20 a b \cos \left(d x +c \right)\right)}{15 \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, d}"," ",0,"-1/15/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*e*(30*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticE((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))*a^2+12*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticE((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))*b^2-15*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))*a^2-6*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))*b^2+6*b^2*cos(d*x+c)^4+20*a*b*cos(d*x+c)^3-6*cos(d*x+c)^2*b^2-20*a*b*cos(d*x+c))/d","B"
45,1,170,130,0.216000," ","int((a+b*cos(d*x+c))^2/(e*sin(d*x+c))^(1/2),x)","-\frac{3 \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticF \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right) a^{2}+2 \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticF \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right) b^{2}-2 b^{2} \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right)-12 a b \sin \left(d x +c \right) \cos \left(d x +c \right)}{3 \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, d}"," ",0,"-1/3/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*(3*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))*a^2+2*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))*b^2-2*b^2*sin(d*x+c)*cos(d*x+c)^2-12*a*b*sin(d*x+c)*cos(d*x+c))/d","A"
46,1,277,140,0.229000," ","int((a+b*cos(d*x+c))^2/(e*sin(d*x+c))^(3/2),x)","\frac{\left(-2 a^{2}-2 b^{2}\right) \left(\cos^{2}\left(d x +c \right)\right)-4 a b \cos \left(d x +c \right)+2 \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticE \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right) a^{2}+4 \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticE \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right) b^{2}-\sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticF \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right) a^{2}-2 \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticF \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right) b^{2}}{e \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, d}"," ",0,"((-2*a^2-2*b^2)*cos(d*x+c)^2-4*a*b*cos(d*x+c)+2*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticE((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))*a^2+4*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticE((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))*b^2-(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))*a^2-2*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))*b^2)/e/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/d","A"
47,1,190,140,0.228000," ","int((a+b*cos(d*x+c))^2/(e*sin(d*x+c))^(5/2),x)","\frac{-\frac{4 a b}{3 e \left(e \sin \left(d x +c \right)\right)^{\frac{3}{2}}}-\frac{\left(2 a^{2}+2 b^{2}\right) \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right)+\sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sin^{\frac{5}{2}}\left(d x +c \right)\right) \EllipticF \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right) a^{2}-2 b^{2} \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sin^{\frac{5}{2}}\left(d x +c \right)\right) \EllipticF \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right)}{3 e^{2} \sin \left(d x +c \right)^{2} \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}}}{d}"," ",0,"(-4/3*a*b/e/(e*sin(d*x+c))^(3/2)-1/3/e^2*((2*a^2+2*b^2)*sin(d*x+c)*cos(d*x+c)^2+(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(5/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))*a^2-2*b^2*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(5/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2)))/sin(d*x+c)^2/cos(d*x+c)/(e*sin(d*x+c))^(1/2))/d","A"
48,1,327,177,0.262000," ","int((a+b*cos(d*x+c))^2/(e*sin(d*x+c))^(7/2),x)","\frac{-\frac{4 a b}{5 e \left(e \sin \left(d x +c \right)\right)^{\frac{5}{2}}}+\frac{\left(6 a^{2}-4 b^{2}\right) \sin \left(d x +c \right) \left(\cos^{4}\left(d x +c \right)\right)+\left(-8 a^{2}+2 b^{2}\right) \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+6 \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sin^{\frac{7}{2}}\left(d x +c \right)\right) \EllipticE \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right) a^{2}-4 \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sin^{\frac{7}{2}}\left(d x +c \right)\right) \EllipticE \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right) b^{2}-3 \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sin^{\frac{7}{2}}\left(d x +c \right)\right) \EllipticF \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right) a^{2}+2 \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sin^{\frac{7}{2}}\left(d x +c \right)\right) \EllipticF \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right) b^{2}}{5 e^{3} \sin \left(d x +c \right)^{3} \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}}}{d}"," ",0,"(-4/5*a*b/e/(e*sin(d*x+c))^(5/2)+1/5/e^3*((6*a^2-4*b^2)*sin(d*x+c)*cos(d*x+c)^4+(-8*a^2+2*b^2)*cos(d*x+c)^2*sin(d*x+c)+6*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(7/2)*EllipticE((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))*a^2-4*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(7/2)*EllipticE((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))*b^2-3*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(7/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))*a^2+2*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(7/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))*b^2)/sin(d*x+c)^3/cos(d*x+c)/(e*sin(d*x+c))^(1/2))/d","A"
49,1,252,246,0.318000," ","int((a+b*cos(d*x+c))^3*(e*sin(d*x+c))^(7/2),x)","\frac{\frac{2 b \left(e \sin \left(d x +c \right)\right)^{\frac{9}{2}} \left(9 \left(\cos^{2}\left(d x +c \right)\right) b^{2}+39 a^{2}+4 b^{2}\right)}{117 e}-\frac{e^{4} a \left(-126 b^{2} \sin \left(d x +c \right) \left(\cos^{6}\left(d x +c \right)\right)+\left(-66 a^{2}+216 b^{2}\right) \left(\cos^{4}\left(d x +c \right)\right) \sin \left(d x +c \right)+\left(176 a^{2}-30 b^{2}\right) \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+55 \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticF \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right) a^{2}+30 \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticF \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right) b^{2}\right)}{231 \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}}}{d}"," ",0,"(2/117/e*b*(e*sin(d*x+c))^(9/2)*(9*cos(d*x+c)^2*b^2+39*a^2+4*b^2)-1/231*e^4*a*(-126*b^2*sin(d*x+c)*cos(d*x+c)^6+(-66*a^2+216*b^2)*cos(d*x+c)^4*sin(d*x+c)+(176*a^2-30*b^2)*cos(d*x+c)^2*sin(d*x+c)+55*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))*a^2+30*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))*b^2)/cos(d*x+c)/(e*sin(d*x+c))^(1/2))/d","A"
50,1,356,210,0.434000," ","int((a+b*cos(d*x+c))^3*(e*sin(d*x+c))^(5/2),x)","\frac{\frac{2 b \left(e \sin \left(d x +c \right)\right)^{\frac{7}{2}} \left(7 \left(\cos^{2}\left(d x +c \right)\right) b^{2}+33 a^{2}+4 b^{2}\right)}{77 e}-\frac{e^{3} a \left(10 b^{2} \left(\sin^{6}\left(d x +c \right)\right)+18 \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticE \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right) a^{2}+12 \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticE \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right) b^{2}-9 \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticF \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right) a^{2}-6 \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticF \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right) b^{2}-6 a^{2} \left(\sin^{4}\left(d x +c \right)\right)-14 \left(\sin^{4}\left(d x +c \right)\right) b^{2}+6 \left(\sin^{2}\left(d x +c \right)\right) a^{2}+4 \left(\sin^{2}\left(d x +c \right)\right) b^{2}\right)}{15 \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}}}{d}"," ",0,"(2/77/e*b*(e*sin(d*x+c))^(7/2)*(7*cos(d*x+c)^2*b^2+33*a^2+4*b^2)-1/15*e^3*a*(10*b^2*sin(d*x+c)^6+18*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticE((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))*a^2+12*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticE((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))*b^2-9*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))*a^2-6*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))*b^2-6*a^2*sin(d*x+c)^4-14*sin(d*x+c)^4*b^2+6*sin(d*x+c)^2*a^2+4*sin(d*x+c)^2*b^2)/cos(d*x+c)/(e*sin(d*x+c))^(1/2))/d","A"
51,1,226,210,0.298000," ","int((a+b*cos(d*x+c))^3*(e*sin(d*x+c))^(3/2),x)","\frac{\frac{2 b \left(e \sin \left(d x +c \right)\right)^{\frac{5}{2}} \left(5 \left(\cos^{2}\left(d x +c \right)\right) b^{2}+27 a^{2}+4 b^{2}\right)}{45 e}-\frac{e^{2} a \left(18 b^{2} \sin \left(d x +c \right) \left(\cos^{4}\left(d x +c \right)\right)+\left(14 a^{2}-6 b^{2}\right) \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+7 \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticF \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right) a^{2}+6 \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticF \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right) b^{2}\right)}{21 \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}}}{d}"," ",0,"(2/45/e*b*(e*sin(d*x+c))^(5/2)*(5*cos(d*x+c)^2*b^2+27*a^2+4*b^2)-1/21*e^2*a*(18*b^2*sin(d*x+c)*cos(d*x+c)^4+(14*a^2-6*b^2)*cos(d*x+c)^2*sin(d*x+c)+7*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))*a^2+6*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))*b^2)/cos(d*x+c)/(e*sin(d*x+c))^(1/2))/d","A"
52,1,315,173,0.399000," ","int((a+b*cos(d*x+c))^3*(e*sin(d*x+c))^(1/2),x)","\frac{\frac{2 b \left(e \sin \left(d x +c \right)\right)^{\frac{3}{2}} \left(3 \left(\cos^{2}\left(d x +c \right)\right) b^{2}+21 a^{2}+4 b^{2}\right)}{21 e}-\frac{a e \left(10 \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticE \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right) a^{2}+12 \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticE \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right) b^{2}-5 \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticF \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right) a^{2}-6 \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticF \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right) b^{2}+6 \left(\sin^{4}\left(d x +c \right)\right) b^{2}-6 \left(\sin^{2}\left(d x +c \right)\right) b^{2}\right)}{5 \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}}}{d}"," ",0,"(2/21/e*b*(e*sin(d*x+c))^(3/2)*(3*cos(d*x+c)^2*b^2+21*a^2+4*b^2)-1/5*a*e*(10*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticE((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))*a^2+12*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticE((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))*b^2-5*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))*a^2-6*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))*b^2+6*sin(d*x+c)^4*b^2-6*sin(d*x+c)^2*b^2)/cos(d*x+c)/(e*sin(d*x+c))^(1/2))/d","A"
53,1,210,171,0.268000," ","int((a+b*cos(d*x+c))^3/(e*sin(d*x+c))^(1/2),x)","-\frac{5 \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticF \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right) a^{3}+10 \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticF \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right) a \,b^{2}-2 b^{3} \sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right)-10 a \,b^{2} \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right)-30 a^{2} b \sin \left(d x +c \right) \cos \left(d x +c \right)-8 b^{3} \sin \left(d x +c \right) \cos \left(d x +c \right)}{5 \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, d}"," ",0,"-1/5/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*(5*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))*a^3+10*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))*a*b^2-2*b^3*sin(d*x+c)*cos(d*x+c)^3-10*a*b^2*sin(d*x+c)*cos(d*x+c)^2-30*a^2*b*sin(d*x+c)*cos(d*x+c)-8*b^3*sin(d*x+c)*cos(d*x+c))/d","A"
54,1,313,183,0.322000," ","int((a+b*cos(d*x+c))^3/(e*sin(d*x+c))^(3/2),x)","\frac{6 \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticE \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right) a^{3}+36 \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticE \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right) a \,b^{2}-3 \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticF \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right) a^{3}-18 \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticF \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right) a \,b^{2}+2 b^{3} \left(\cos^{3}\left(d x +c \right)\right)-6 a^{3} \left(\cos^{2}\left(d x +c \right)\right)-18 b^{2} a \left(\cos^{2}\left(d x +c \right)\right)-18 a^{2} b \cos \left(d x +c \right)-8 b^{3} \cos \left(d x +c \right)}{3 e \sqrt{e \sin \left(d x +c \right)}\, \cos \left(d x +c \right) d}"," ",0,"1/3/e/(e*sin(d*x+c))^(1/2)/cos(d*x+c)*(6*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticE((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))*a^3+36*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticE((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))*a*b^2-3*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))*a^3-18*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))*a*b^2+2*b^3*cos(d*x+c)^3-6*a^3*cos(d*x+c)^2-18*b^2*a*cos(d*x+c)^2-18*a^2*b*cos(d*x+c)-8*b^3*cos(d*x+c))/d","A"
55,1,214,181,0.312000," ","int((a+b*cos(d*x+c))^3/(e*sin(d*x+c))^(5/2),x)","\frac{-\frac{2 b \left(-3 \left(\cos^{2}\left(d x +c \right)\right) b^{2}+3 a^{2}+4 b^{2}\right)}{3 e \left(e \sin \left(d x +c \right)\right)^{\frac{3}{2}}}-\frac{a \left(\left(2 a^{2}+6 b^{2}\right) \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right)+\sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sin^{\frac{5}{2}}\left(d x +c \right)\right) \EllipticF \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right) a^{2}-6 b^{2} \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sin^{\frac{5}{2}}\left(d x +c \right)\right) \EllipticF \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right)\right)}{3 e^{2} \sin \left(d x +c \right)^{2} \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}}}{d}"," ",0,"(-2/3*b/e/(e*sin(d*x+c))^(3/2)*(-3*cos(d*x+c)^2*b^2+3*a^2+4*b^2)-1/3*a/e^2*((2*a^2+6*b^2)*sin(d*x+c)*cos(d*x+c)^2+(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(5/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))*a^2-6*b^2*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(5/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2)))/sin(d*x+c)^2/cos(d*x+c)/(e*sin(d*x+c))^(1/2))/d","A"
56,1,351,204,0.340000," ","int((a+b*cos(d*x+c))^3/(e*sin(d*x+c))^(7/2),x)","\frac{-\frac{2 b \left(5 \left(\cos^{2}\left(d x +c \right)\right) b^{2}+3 a^{2}-4 b^{2}\right)}{5 e \left(e \sin \left(d x +c \right)\right)^{\frac{5}{2}}}+\frac{a \left(\left(6 a^{2}-12 b^{2}\right) \sin \left(d x +c \right) \left(\cos^{4}\left(d x +c \right)\right)+\left(-8 a^{2}+6 b^{2}\right) \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+6 \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sin^{\frac{7}{2}}\left(d x +c \right)\right) \EllipticE \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right) a^{2}-12 \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sin^{\frac{7}{2}}\left(d x +c \right)\right) \EllipticE \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right) b^{2}-3 \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sin^{\frac{7}{2}}\left(d x +c \right)\right) \EllipticF \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right) a^{2}+6 \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sin^{\frac{7}{2}}\left(d x +c \right)\right) \EllipticF \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right) b^{2}\right)}{5 e^{3} \sin \left(d x +c \right)^{3} \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}}}{d}"," ",0,"(-2/5*b/e/(e*sin(d*x+c))^(5/2)*(5*cos(d*x+c)^2*b^2+3*a^2-4*b^2)+1/5*a/e^3*((6*a^2-12*b^2)*sin(d*x+c)*cos(d*x+c)^4+(-8*a^2+6*b^2)*cos(d*x+c)^2*sin(d*x+c)+6*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(7/2)*EllipticE((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))*a^2-12*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(7/2)*EllipticE((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))*b^2-3*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(7/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))*a^2+6*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(7/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))*b^2)/sin(d*x+c)^3/cos(d*x+c)/(e*sin(d*x+c))^(1/2))/d","A"
57,1,241,205,0.334000," ","int((a+b*cos(d*x+c))^3/(e*sin(d*x+c))^(9/2),x)","\frac{-\frac{2 b \left(7 \left(\cos^{2}\left(d x +c \right)\right) b^{2}+9 a^{2}-4 b^{2}\right)}{21 e \left(e \sin \left(d x +c \right)\right)^{\frac{7}{2}}}-\frac{a \left(\left(-10 a^{2}+12 b^{2}\right) \sin \left(d x +c \right) \left(\cos^{4}\left(d x +c \right)\right)+\left(16 a^{2}+6 b^{2}\right) \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+5 \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sin^{\frac{9}{2}}\left(d x +c \right)\right) \EllipticF \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right) a^{2}-6 \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sin^{\frac{9}{2}}\left(d x +c \right)\right) \EllipticF \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right) b^{2}\right)}{21 e^{4} \sin \left(d x +c \right)^{4} \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}}}{d}"," ",0,"(-2/21*b/e/(e*sin(d*x+c))^(7/2)*(7*cos(d*x+c)^2*b^2+9*a^2-4*b^2)-1/21*a/e^4*((-10*a^2+12*b^2)*sin(d*x+c)*cos(d*x+c)^4+(16*a^2+6*b^2)*cos(d*x+c)^2*sin(d*x+c)+5*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(9/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))*a^2-6*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(9/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))*b^2)/sin(d*x+c)^4/cos(d*x+c)/(e*sin(d*x+c))^(1/2))/d","A"
58,1,2930,569,1.112000," ","int((e*sin(d*x+c))^(11/2)/(a+b*cos(d*x+c)),x)","\text{output too large to display}"," ",0,"-3/2/d*e^6*a^3/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/b^3/(-a^2+b^2)^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1+(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1+(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))+1/2/d*e^6*a/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/(-a^2+b^2)^(1/2)/b*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1+(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1+(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))+1/2/d*e^6*a^7/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/b^7/(-a^2+b^2)^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1-(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1-(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))-3/2/d*e^6*a^5/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/b^5/(-a^2+b^2)^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1-(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1-(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))+3/2/d*e^6*a^3/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/b^3/(-a^2+b^2)^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1-(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1-(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))-1/2/d*e^6*a/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/(-a^2+b^2)^(1/2)/b*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1-(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1-(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))-1/2/d*e^6*a^7/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/b^7/(-a^2+b^2)^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1+(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1+(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))+3/2/d*e^6*a^5/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/b^5/(-a^2+b^2)^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1+(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1+(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))+3/2/d/b*e^7*(e^2*(a^2-b^2)/b^2)^(1/4)/(a^2*e^2-b^2*e^2)*2^(1/2)*arctan(2^(1/2)/(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)+1)*a^2+1/2/d/b^5*e^7*(e^2*(a^2-b^2)/b^2)^(1/4)/(a^2*e^2-b^2*e^2)*2^(1/2)*arctan(2^(1/2)/(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)-1)*a^6-3/2/d/b^3*e^7*(e^2*(a^2-b^2)/b^2)^(1/4)/(a^2*e^2-b^2*e^2)*2^(1/2)*arctan(2^(1/2)/(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)-1)*a^4+3/2/d/b*e^7*(e^2*(a^2-b^2)/b^2)^(1/4)/(a^2*e^2-b^2*e^2)*2^(1/2)*arctan(2^(1/2)/(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)-1)*a^2+1/4/d/b^5*e^7*(e^2*(a^2-b^2)/b^2)^(1/4)/(a^2*e^2-b^2*e^2)*2^(1/2)*ln((e*sin(d*x+c)+(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)*2^(1/2)+(e^2*(a^2-b^2)/b^2)^(1/2))/(e*sin(d*x+c)-(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)*2^(1/2)+(e^2*(a^2-b^2)/b^2)^(1/2)))*a^6-3/4/d/b^3*e^7*(e^2*(a^2-b^2)/b^2)^(1/4)/(a^2*e^2-b^2*e^2)*2^(1/2)*ln((e*sin(d*x+c)+(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)*2^(1/2)+(e^2*(a^2-b^2)/b^2)^(1/2))/(e*sin(d*x+c)-(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)*2^(1/2)+(e^2*(a^2-b^2)/b^2)^(1/2)))*a^4+3/4/d/b*e^7*(e^2*(a^2-b^2)/b^2)^(1/4)/(a^2*e^2-b^2*e^2)*2^(1/2)*ln((e*sin(d*x+c)+(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)*2^(1/2)+(e^2*(a^2-b^2)/b^2)^(1/2))/(e*sin(d*x+c)-(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)*2^(1/2)+(e^2*(a^2-b^2)/b^2)^(1/2)))*a^2+1/2/d/b^5*e^7*(e^2*(a^2-b^2)/b^2)^(1/4)/(a^2*e^2-b^2*e^2)*2^(1/2)*arctan(2^(1/2)/(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)+1)*a^6-3/2/d/b^3*e^7*(e^2*(a^2-b^2)/b^2)^(1/4)/(a^2*e^2-b^2*e^2)*2^(1/2)*arctan(2^(1/2)/(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)+1)*a^4-11/7/d*e^6*a/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/b^2*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))-1/d*e^6*a^5/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/b^6*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))+7/3/d*e^6*a^3/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/b^4*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))+2/5/d/b^3*e^3*(e*sin(d*x+c))^(5/2)*a^2+4/d/b^3*e^5*a^2*(e*sin(d*x+c))^(1/2)-2/d/b^5*e^5*a^4*(e*sin(d*x+c))^(1/2)-2/5/d/b*e^3*(e*sin(d*x+c))^(5/2)-2/d/b*e^5*(e*sin(d*x+c))^(1/2)-2/9*e*(e*sin(d*x+c))^(9/2)/b/d-1/2/d*b*e^7*(e^2*(a^2-b^2)/b^2)^(1/4)/(a^2*e^2-b^2*e^2)*2^(1/2)*arctan(2^(1/2)/(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)-1)-1/4/d*b*e^7*(e^2*(a^2-b^2)/b^2)^(1/4)/(a^2*e^2-b^2*e^2)*2^(1/2)*ln((e*sin(d*x+c)+(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)*2^(1/2)+(e^2*(a^2-b^2)/b^2)^(1/2))/(e*sin(d*x+c)-(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)*2^(1/2)+(e^2*(a^2-b^2)/b^2)^(1/2)))-1/2/d*b*e^7*(e^2*(a^2-b^2)/b^2)^(1/4)/(a^2*e^2-b^2*e^2)*2^(1/2)*arctan(2^(1/2)/(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)+1)+2/7/d*e^6*a*cos(d*x+c)^3/(e*sin(d*x+c))^(1/2)/b^2*sin(d*x+c)+2/3/d*e^6*a^3*cos(d*x+c)/(e*sin(d*x+c))^(1/2)/b^4*sin(d*x+c)-10/7/d*e^6*a*cos(d*x+c)/(e*sin(d*x+c))^(1/2)/b^2*sin(d*x+c)","B"
59,1,2051,494,1.068000," ","int((e*sin(d*x+c))^(9/2)/(a+b*cos(d*x+c)),x)","-\frac{2 e \left(e \sin \left(d x +c \right)\right)^{\frac{7}{2}}}{7 b d}+\frac{2 e^{3} \left(e \sin \left(d x +c \right)\right)^{\frac{3}{2}} a^{2}}{3 d \,b^{3}}-\frac{2 e^{3} \left(e \sin \left(d x +c \right)\right)^{\frac{3}{2}}}{3 d b}-\frac{e^{5} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \sin \left(d x +c \right)}}{\left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}\right)^{\frac{1}{4}}}-1\right) a^{4}}{2 d \,b^{5} \left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}\right)^{\frac{1}{4}}}+\frac{e^{5} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \sin \left(d x +c \right)}}{\left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}\right)^{\frac{1}{4}}}-1\right) a^{2}}{d \,b^{3} \left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}\right)^{\frac{1}{4}}}-\frac{e^{5} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \sin \left(d x +c \right)}}{\left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}\right)^{\frac{1}{4}}}-1\right)}{2 d b \left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}\right)^{\frac{1}{4}}}-\frac{e^{5} \sqrt{2}\, \ln \left(\frac{e \sin \left(d x +c \right)-\left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}\right)^{\frac{1}{4}} \sqrt{e \sin \left(d x +c \right)}\, \sqrt{2}+\sqrt{\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}}}{e \sin \left(d x +c \right)+\left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}\right)^{\frac{1}{4}} \sqrt{e \sin \left(d x +c \right)}\, \sqrt{2}+\sqrt{\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}}}\right) a^{4}}{4 d \,b^{5} \left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}\right)^{\frac{1}{4}}}+\frac{e^{5} \sqrt{2}\, \ln \left(\frac{e \sin \left(d x +c \right)-\left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}\right)^{\frac{1}{4}} \sqrt{e \sin \left(d x +c \right)}\, \sqrt{2}+\sqrt{\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}}}{e \sin \left(d x +c \right)+\left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}\right)^{\frac{1}{4}} \sqrt{e \sin \left(d x +c \right)}\, \sqrt{2}+\sqrt{\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}}}\right) a^{2}}{2 d \,b^{3} \left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}\right)^{\frac{1}{4}}}-\frac{e^{5} \sqrt{2}\, \ln \left(\frac{e \sin \left(d x +c \right)-\left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}\right)^{\frac{1}{4}} \sqrt{e \sin \left(d x +c \right)}\, \sqrt{2}+\sqrt{\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}}}{e \sin \left(d x +c \right)+\left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}\right)^{\frac{1}{4}} \sqrt{e \sin \left(d x +c \right)}\, \sqrt{2}+\sqrt{\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}}}\right)}{4 d b \left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}\right)^{\frac{1}{4}}}-\frac{e^{5} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \sin \left(d x +c \right)}}{\left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}\right)^{\frac{1}{4}}}+1\right) a^{4}}{2 d \,b^{5} \left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}\right)^{\frac{1}{4}}}+\frac{e^{5} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \sin \left(d x +c \right)}}{\left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}\right)^{\frac{1}{4}}}+1\right) a^{2}}{d \,b^{3} \left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}\right)^{\frac{1}{4}}}-\frac{e^{5} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \sin \left(d x +c \right)}}{\left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}\right)^{\frac{1}{4}}}+1\right)}{2 d b \left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}\right)^{\frac{1}{4}}}+\frac{2 e^{5} a \left(\cos^{3}\left(d x +c \right)\right)}{5 d \sqrt{e \sin \left(d x +c \right)}\, b^{2}}+\frac{2 e^{5} a^{3} \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticE \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right)}{d \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, b^{4}}-\frac{16 e^{5} a \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticE \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right)}{5 d \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, b^{2}}-\frac{e^{5} a^{3} \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticF \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right)}{d \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, b^{4}}+\frac{8 e^{5} a \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticF \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right)}{5 d \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, b^{2}}-\frac{2 e^{5} a \cos \left(d x +c \right)}{5 d \sqrt{e \sin \left(d x +c \right)}\, b^{2}}-\frac{e^{5} a^{5} \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{1}{1-\frac{\sqrt{-a^{2}+b^{2}}}{b}}, \frac{\sqrt{2}}{2}\right)}{2 d \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, b^{6} \left(1-\frac{\sqrt{-a^{2}+b^{2}}}{b}\right)}+\frac{e^{5} a^{3} \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{1}{1-\frac{\sqrt{-a^{2}+b^{2}}}{b}}, \frac{\sqrt{2}}{2}\right)}{d \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, b^{4} \left(1-\frac{\sqrt{-a^{2}+b^{2}}}{b}\right)}-\frac{e^{5} a \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{1}{1-\frac{\sqrt{-a^{2}+b^{2}}}{b}}, \frac{\sqrt{2}}{2}\right)}{2 d \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, b^{2} \left(1-\frac{\sqrt{-a^{2}+b^{2}}}{b}\right)}-\frac{e^{5} a^{5} \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{1}{1+\frac{\sqrt{-a^{2}+b^{2}}}{b}}, \frac{\sqrt{2}}{2}\right)}{2 d \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, b^{6} \left(1+\frac{\sqrt{-a^{2}+b^{2}}}{b}\right)}+\frac{e^{5} a^{3} \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{1}{1+\frac{\sqrt{-a^{2}+b^{2}}}{b}}, \frac{\sqrt{2}}{2}\right)}{d \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, b^{4} \left(1+\frac{\sqrt{-a^{2}+b^{2}}}{b}\right)}-\frac{e^{5} a \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{1}{1+\frac{\sqrt{-a^{2}+b^{2}}}{b}}, \frac{\sqrt{2}}{2}\right)}{2 d \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, b^{2} \left(1+\frac{\sqrt{-a^{2}+b^{2}}}{b}\right)}"," ",0,"-2/7*e*(e*sin(d*x+c))^(7/2)/b/d+2/3/d*e^3/b^3*(e*sin(d*x+c))^(3/2)*a^2-2/3/d*e^3/b*(e*sin(d*x+c))^(3/2)-1/2/d*e^5/b^5/(e^2*(a^2-b^2)/b^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)-1)*a^4+1/d*e^5/b^3/(e^2*(a^2-b^2)/b^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)-1)*a^2-1/2/d*e^5/b/(e^2*(a^2-b^2)/b^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)-1)-1/4/d*e^5/b^5/(e^2*(a^2-b^2)/b^2)^(1/4)*2^(1/2)*ln((e*sin(d*x+c)-(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)*2^(1/2)+(e^2*(a^2-b^2)/b^2)^(1/2))/(e*sin(d*x+c)+(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)*2^(1/2)+(e^2*(a^2-b^2)/b^2)^(1/2)))*a^4+1/2/d*e^5/b^3/(e^2*(a^2-b^2)/b^2)^(1/4)*2^(1/2)*ln((e*sin(d*x+c)-(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)*2^(1/2)+(e^2*(a^2-b^2)/b^2)^(1/2))/(e*sin(d*x+c)+(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)*2^(1/2)+(e^2*(a^2-b^2)/b^2)^(1/2)))*a^2-1/4/d*e^5/b/(e^2*(a^2-b^2)/b^2)^(1/4)*2^(1/2)*ln((e*sin(d*x+c)-(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)*2^(1/2)+(e^2*(a^2-b^2)/b^2)^(1/2))/(e*sin(d*x+c)+(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)*2^(1/2)+(e^2*(a^2-b^2)/b^2)^(1/2)))-1/2/d*e^5/b^5/(e^2*(a^2-b^2)/b^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)+1)*a^4+1/d*e^5/b^3/(e^2*(a^2-b^2)/b^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)+1)*a^2-1/2/d*e^5/b/(e^2*(a^2-b^2)/b^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)+1)+2/5/d*e^5*a*cos(d*x+c)^3/(e*sin(d*x+c))^(1/2)/b^2+2/d*e^5*a^3/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/b^4*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticE((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))-16/5/d*e^5*a/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/b^2*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticE((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))-1/d*e^5*a^3/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/b^4*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))+8/5/d*e^5*a/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/b^2*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))-2/5/d*e^5*a*cos(d*x+c)/(e*sin(d*x+c))^(1/2)/b^2-1/2/d*e^5*a^5/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/b^6*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1-(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1-(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))+1/d*e^5*a^3/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/b^4*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1-(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1-(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))-1/2/d*e^5*a/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/b^2*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1-(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1-(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))-1/2/d*e^5*a^5/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/b^6*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1+(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1+(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))+1/d*e^5*a^3/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/b^4*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1+(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1+(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))-1/2/d*e^5*a/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/b^2*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1+(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1+(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))","B"
60,1,2087,507,0.849000," ","int((e*sin(d*x+c))^(7/2)/(a+b*cos(d*x+c)),x)","-\frac{2 e \left(e \sin \left(d x +c \right)\right)^{\frac{5}{2}}}{5 b d}+\frac{2 e^{3} a^{2} \sqrt{e \sin \left(d x +c \right)}}{d \,b^{3}}-\frac{2 e^{3} \sqrt{e \sin \left(d x +c \right)}}{d b}-\frac{e^{5} \left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \sin \left(d x +c \right)}}{\left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}\right)^{\frac{1}{4}}}+1\right) a^{4}}{2 d \,b^{3} \left(a^{2} e^{2}-b^{2} e^{2}\right)}+\frac{e^{5} \left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \sin \left(d x +c \right)}}{\left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}\right)^{\frac{1}{4}}}+1\right) a^{2}}{d b \left(a^{2} e^{2}-b^{2} e^{2}\right)}-\frac{e^{5} b \left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \sin \left(d x +c \right)}}{\left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}\right)^{\frac{1}{4}}}+1\right)}{2 d \left(a^{2} e^{2}-b^{2} e^{2}\right)}-\frac{e^{5} \left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \sin \left(d x +c \right)}}{\left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}\right)^{\frac{1}{4}}}-1\right) a^{4}}{2 d \,b^{3} \left(a^{2} e^{2}-b^{2} e^{2}\right)}+\frac{e^{5} \left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \sin \left(d x +c \right)}}{\left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}\right)^{\frac{1}{4}}}-1\right) a^{2}}{d b \left(a^{2} e^{2}-b^{2} e^{2}\right)}-\frac{e^{5} b \left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \sin \left(d x +c \right)}}{\left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}\right)^{\frac{1}{4}}}-1\right)}{2 d \left(a^{2} e^{2}-b^{2} e^{2}\right)}-\frac{e^{5} \left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{e \sin \left(d x +c \right)+\left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}\right)^{\frac{1}{4}} \sqrt{e \sin \left(d x +c \right)}\, \sqrt{2}+\sqrt{\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}}}{e \sin \left(d x +c \right)-\left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}\right)^{\frac{1}{4}} \sqrt{e \sin \left(d x +c \right)}\, \sqrt{2}+\sqrt{\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}}}\right) a^{4}}{4 d \,b^{3} \left(a^{2} e^{2}-b^{2} e^{2}\right)}+\frac{e^{5} \left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{e \sin \left(d x +c \right)+\left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}\right)^{\frac{1}{4}} \sqrt{e \sin \left(d x +c \right)}\, \sqrt{2}+\sqrt{\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}}}{e \sin \left(d x +c \right)-\left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}\right)^{\frac{1}{4}} \sqrt{e \sin \left(d x +c \right)}\, \sqrt{2}+\sqrt{\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}}}\right) a^{2}}{2 d b \left(a^{2} e^{2}-b^{2} e^{2}\right)}-\frac{e^{5} b \left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{e \sin \left(d x +c \right)+\left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}\right)^{\frac{1}{4}} \sqrt{e \sin \left(d x +c \right)}\, \sqrt{2}+\sqrt{\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}}}{e \sin \left(d x +c \right)-\left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}\right)^{\frac{1}{4}} \sqrt{e \sin \left(d x +c \right)}\, \sqrt{2}+\sqrt{\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}}}\right)}{4 d \left(a^{2} e^{2}-b^{2} e^{2}\right)}+\frac{e^{4} a^{3} \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticF \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right)}{d \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, b^{4}}-\frac{4 e^{4} a \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticF \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right)}{3 d \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, b^{2}}-\frac{2 e^{4} a \cos \left(d x +c \right) \sin \left(d x +c \right)}{3 d \sqrt{e \sin \left(d x +c \right)}\, b^{2}}-\frac{e^{4} a^{5} \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{1}{1-\frac{\sqrt{-a^{2}+b^{2}}}{b}}, \frac{\sqrt{2}}{2}\right)}{2 d \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, b^{5} \sqrt{-a^{2}+b^{2}}\, \left(1-\frac{\sqrt{-a^{2}+b^{2}}}{b}\right)}+\frac{e^{4} a^{3} \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{1}{1-\frac{\sqrt{-a^{2}+b^{2}}}{b}}, \frac{\sqrt{2}}{2}\right)}{d \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, b^{3} \sqrt{-a^{2}+b^{2}}\, \left(1-\frac{\sqrt{-a^{2}+b^{2}}}{b}\right)}-\frac{e^{4} a \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{1}{1-\frac{\sqrt{-a^{2}+b^{2}}}{b}}, \frac{\sqrt{2}}{2}\right)}{2 d \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, \sqrt{-a^{2}+b^{2}}\, b \left(1-\frac{\sqrt{-a^{2}+b^{2}}}{b}\right)}+\frac{e^{4} a^{5} \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{1}{1+\frac{\sqrt{-a^{2}+b^{2}}}{b}}, \frac{\sqrt{2}}{2}\right)}{2 d \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, b^{5} \sqrt{-a^{2}+b^{2}}\, \left(1+\frac{\sqrt{-a^{2}+b^{2}}}{b}\right)}-\frac{e^{4} a^{3} \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{1}{1+\frac{\sqrt{-a^{2}+b^{2}}}{b}}, \frac{\sqrt{2}}{2}\right)}{d \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, b^{3} \sqrt{-a^{2}+b^{2}}\, \left(1+\frac{\sqrt{-a^{2}+b^{2}}}{b}\right)}+\frac{e^{4} a \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{1}{1+\frac{\sqrt{-a^{2}+b^{2}}}{b}}, \frac{\sqrt{2}}{2}\right)}{2 d \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, \sqrt{-a^{2}+b^{2}}\, b \left(1+\frac{\sqrt{-a^{2}+b^{2}}}{b}\right)}"," ",0,"-2/5*e*(e*sin(d*x+c))^(5/2)/b/d+2/d*e^3/b^3*a^2*(e*sin(d*x+c))^(1/2)-2/d*e^3/b*(e*sin(d*x+c))^(1/2)-1/2/d*e^5/b^3*(e^2*(a^2-b^2)/b^2)^(1/4)/(a^2*e^2-b^2*e^2)*2^(1/2)*arctan(2^(1/2)/(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)+1)*a^4+1/d*e^5/b*(e^2*(a^2-b^2)/b^2)^(1/4)/(a^2*e^2-b^2*e^2)*2^(1/2)*arctan(2^(1/2)/(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)+1)*a^2-1/2/d*e^5*b*(e^2*(a^2-b^2)/b^2)^(1/4)/(a^2*e^2-b^2*e^2)*2^(1/2)*arctan(2^(1/2)/(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)+1)-1/2/d*e^5/b^3*(e^2*(a^2-b^2)/b^2)^(1/4)/(a^2*e^2-b^2*e^2)*2^(1/2)*arctan(2^(1/2)/(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)-1)*a^4+1/d*e^5/b*(e^2*(a^2-b^2)/b^2)^(1/4)/(a^2*e^2-b^2*e^2)*2^(1/2)*arctan(2^(1/2)/(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)-1)*a^2-1/2/d*e^5*b*(e^2*(a^2-b^2)/b^2)^(1/4)/(a^2*e^2-b^2*e^2)*2^(1/2)*arctan(2^(1/2)/(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)-1)-1/4/d*e^5/b^3*(e^2*(a^2-b^2)/b^2)^(1/4)/(a^2*e^2-b^2*e^2)*2^(1/2)*ln((e*sin(d*x+c)+(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)*2^(1/2)+(e^2*(a^2-b^2)/b^2)^(1/2))/(e*sin(d*x+c)-(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)*2^(1/2)+(e^2*(a^2-b^2)/b^2)^(1/2)))*a^4+1/2/d*e^5/b*(e^2*(a^2-b^2)/b^2)^(1/4)/(a^2*e^2-b^2*e^2)*2^(1/2)*ln((e*sin(d*x+c)+(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)*2^(1/2)+(e^2*(a^2-b^2)/b^2)^(1/2))/(e*sin(d*x+c)-(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)*2^(1/2)+(e^2*(a^2-b^2)/b^2)^(1/2)))*a^2-1/4/d*e^5*b*(e^2*(a^2-b^2)/b^2)^(1/4)/(a^2*e^2-b^2*e^2)*2^(1/2)*ln((e*sin(d*x+c)+(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)*2^(1/2)+(e^2*(a^2-b^2)/b^2)^(1/2))/(e*sin(d*x+c)-(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)*2^(1/2)+(e^2*(a^2-b^2)/b^2)^(1/2)))+1/d*e^4*a^3/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/b^4*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))-4/3/d*e^4*a/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/b^2*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))-2/3/d*e^4*a*cos(d*x+c)/(e*sin(d*x+c))^(1/2)/b^2*sin(d*x+c)-1/2/d*e^4*a^5/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/b^5/(-a^2+b^2)^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1-(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1-(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))+1/d*e^4*a^3/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/b^3/(-a^2+b^2)^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1-(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1-(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))-1/2/d*e^4*a/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/(-a^2+b^2)^(1/2)/b*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1-(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1-(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))+1/2/d*e^4*a^5/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/b^5/(-a^2+b^2)^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1+(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1+(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))-1/d*e^4*a^3/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/b^3/(-a^2+b^2)^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1+(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1+(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))+1/2/d*e^4*a/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/(-a^2+b^2)^(1/2)/b*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1+(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1+(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))","B"
61,1,1247,435,0.866000," ","int((e*sin(d*x+c))^(5/2)/(a+b*cos(d*x+c)),x)","-\frac{2 e \left(e \sin \left(d x +c \right)\right)^{\frac{3}{2}}}{3 b d}+\frac{e^{3} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \sin \left(d x +c \right)}}{\left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}\right)^{\frac{1}{4}}}-1\right) a^{2}}{2 d \,b^{3} \left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}\right)^{\frac{1}{4}}}-\frac{e^{3} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \sin \left(d x +c \right)}}{\left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}\right)^{\frac{1}{4}}}-1\right)}{2 d b \left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}\right)^{\frac{1}{4}}}+\frac{e^{3} \sqrt{2}\, \ln \left(\frac{e \sin \left(d x +c \right)-\left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}\right)^{\frac{1}{4}} \sqrt{e \sin \left(d x +c \right)}\, \sqrt{2}+\sqrt{\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}}}{e \sin \left(d x +c \right)+\left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}\right)^{\frac{1}{4}} \sqrt{e \sin \left(d x +c \right)}\, \sqrt{2}+\sqrt{\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}}}\right) a^{2}}{4 d \,b^{3} \left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}\right)^{\frac{1}{4}}}-\frac{e^{3} \sqrt{2}\, \ln \left(\frac{e \sin \left(d x +c \right)-\left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}\right)^{\frac{1}{4}} \sqrt{e \sin \left(d x +c \right)}\, \sqrt{2}+\sqrt{\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}}}{e \sin \left(d x +c \right)+\left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}\right)^{\frac{1}{4}} \sqrt{e \sin \left(d x +c \right)}\, \sqrt{2}+\sqrt{\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}}}\right)}{4 d b \left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}\right)^{\frac{1}{4}}}+\frac{e^{3} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \sin \left(d x +c \right)}}{\left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}\right)^{\frac{1}{4}}}+1\right) a^{2}}{2 d \,b^{3} \left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}\right)^{\frac{1}{4}}}-\frac{e^{3} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \sin \left(d x +c \right)}}{\left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}\right)^{\frac{1}{4}}}+1\right)}{2 d b \left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}\right)^{\frac{1}{4}}}-\frac{2 e^{3} a \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticE \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right)}{d \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, b^{2}}+\frac{e^{3} a \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticF \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right)}{d \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, b^{2}}+\frac{e^{3} a^{3} \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{1}{1-\frac{\sqrt{-a^{2}+b^{2}}}{b}}, \frac{\sqrt{2}}{2}\right)}{2 d \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, b^{4} \left(1-\frac{\sqrt{-a^{2}+b^{2}}}{b}\right)}-\frac{e^{3} a \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{1}{1-\frac{\sqrt{-a^{2}+b^{2}}}{b}}, \frac{\sqrt{2}}{2}\right)}{2 d \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, b^{2} \left(1-\frac{\sqrt{-a^{2}+b^{2}}}{b}\right)}+\frac{e^{3} a^{3} \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{1}{1+\frac{\sqrt{-a^{2}+b^{2}}}{b}}, \frac{\sqrt{2}}{2}\right)}{2 d \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, b^{4} \left(1+\frac{\sqrt{-a^{2}+b^{2}}}{b}\right)}-\frac{e^{3} a \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{1}{1+\frac{\sqrt{-a^{2}+b^{2}}}{b}}, \frac{\sqrt{2}}{2}\right)}{2 d \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, b^{2} \left(1+\frac{\sqrt{-a^{2}+b^{2}}}{b}\right)}"," ",0,"-2/3*e*(e*sin(d*x+c))^(3/2)/b/d+1/2/d*e^3/b^3/(e^2*(a^2-b^2)/b^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)-1)*a^2-1/2/d*e^3/b/(e^2*(a^2-b^2)/b^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)-1)+1/4/d*e^3/b^3/(e^2*(a^2-b^2)/b^2)^(1/4)*2^(1/2)*ln((e*sin(d*x+c)-(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)*2^(1/2)+(e^2*(a^2-b^2)/b^2)^(1/2))/(e*sin(d*x+c)+(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)*2^(1/2)+(e^2*(a^2-b^2)/b^2)^(1/2)))*a^2-1/4/d*e^3/b/(e^2*(a^2-b^2)/b^2)^(1/4)*2^(1/2)*ln((e*sin(d*x+c)-(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)*2^(1/2)+(e^2*(a^2-b^2)/b^2)^(1/2))/(e*sin(d*x+c)+(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)*2^(1/2)+(e^2*(a^2-b^2)/b^2)^(1/2)))+1/2/d*e^3/b^3/(e^2*(a^2-b^2)/b^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)+1)*a^2-1/2/d*e^3/b/(e^2*(a^2-b^2)/b^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)+1)-2/d*e^3*a/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/b^2*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticE((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))+1/d*e^3*a/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/b^2*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))+1/2/d*e^3*a^3/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/b^4*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1-(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1-(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))-1/2/d*e^3*a/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/b^2*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1-(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1-(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))+1/2/d*e^3*a^3/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/b^4*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1+(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1+(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))-1/2/d*e^3*a/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/b^2*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1+(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1+(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))","B"
62,1,1314,448,0.868000," ","int((e*sin(d*x+c))^(3/2)/(a+b*cos(d*x+c)),x)","-\frac{2 e \sqrt{e \sin \left(d x +c \right)}}{b d}+\frac{e^{3} \left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \sin \left(d x +c \right)}}{\left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}\right)^{\frac{1}{4}}}+1\right) a^{2}}{2 d b \left(a^{2} e^{2}-b^{2} e^{2}\right)}-\frac{e^{3} b \left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \sin \left(d x +c \right)}}{\left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}\right)^{\frac{1}{4}}}+1\right)}{2 d \left(a^{2} e^{2}-b^{2} e^{2}\right)}+\frac{e^{3} \left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \sin \left(d x +c \right)}}{\left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}\right)^{\frac{1}{4}}}-1\right) a^{2}}{2 d b \left(a^{2} e^{2}-b^{2} e^{2}\right)}-\frac{e^{3} b \left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \sin \left(d x +c \right)}}{\left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}\right)^{\frac{1}{4}}}-1\right)}{2 d \left(a^{2} e^{2}-b^{2} e^{2}\right)}+\frac{e^{3} \left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{e \sin \left(d x +c \right)+\left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}\right)^{\frac{1}{4}} \sqrt{e \sin \left(d x +c \right)}\, \sqrt{2}+\sqrt{\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}}}{e \sin \left(d x +c \right)-\left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}\right)^{\frac{1}{4}} \sqrt{e \sin \left(d x +c \right)}\, \sqrt{2}+\sqrt{\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}}}\right) a^{2}}{4 d b \left(a^{2} e^{2}-b^{2} e^{2}\right)}-\frac{e^{3} b \left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{e \sin \left(d x +c \right)+\left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}\right)^{\frac{1}{4}} \sqrt{e \sin \left(d x +c \right)}\, \sqrt{2}+\sqrt{\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}}}{e \sin \left(d x +c \right)-\left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}\right)^{\frac{1}{4}} \sqrt{e \sin \left(d x +c \right)}\, \sqrt{2}+\sqrt{\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}}}\right)}{4 d \left(a^{2} e^{2}-b^{2} e^{2}\right)}-\frac{e^{2} a \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticF \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right)}{d \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, b^{2}}+\frac{e^{2} a^{3} \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{1}{1-\frac{\sqrt{-a^{2}+b^{2}}}{b}}, \frac{\sqrt{2}}{2}\right)}{2 d \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, b^{3} \sqrt{-a^{2}+b^{2}}\, \left(1-\frac{\sqrt{-a^{2}+b^{2}}}{b}\right)}-\frac{e^{2} a \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{1}{1-\frac{\sqrt{-a^{2}+b^{2}}}{b}}, \frac{\sqrt{2}}{2}\right)}{2 d \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, \sqrt{-a^{2}+b^{2}}\, b \left(1-\frac{\sqrt{-a^{2}+b^{2}}}{b}\right)}-\frac{e^{2} a^{3} \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{1}{1+\frac{\sqrt{-a^{2}+b^{2}}}{b}}, \frac{\sqrt{2}}{2}\right)}{2 d \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, b^{3} \sqrt{-a^{2}+b^{2}}\, \left(1+\frac{\sqrt{-a^{2}+b^{2}}}{b}\right)}+\frac{e^{2} a \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{1}{1+\frac{\sqrt{-a^{2}+b^{2}}}{b}}, \frac{\sqrt{2}}{2}\right)}{2 d \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, \sqrt{-a^{2}+b^{2}}\, b \left(1+\frac{\sqrt{-a^{2}+b^{2}}}{b}\right)}"," ",0,"-2*e*(e*sin(d*x+c))^(1/2)/b/d+1/2/d*e^3/b*(e^2*(a^2-b^2)/b^2)^(1/4)/(a^2*e^2-b^2*e^2)*2^(1/2)*arctan(2^(1/2)/(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)+1)*a^2-1/2/d*e^3*b*(e^2*(a^2-b^2)/b^2)^(1/4)/(a^2*e^2-b^2*e^2)*2^(1/2)*arctan(2^(1/2)/(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)+1)+1/2/d*e^3/b*(e^2*(a^2-b^2)/b^2)^(1/4)/(a^2*e^2-b^2*e^2)*2^(1/2)*arctan(2^(1/2)/(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)-1)*a^2-1/2/d*e^3*b*(e^2*(a^2-b^2)/b^2)^(1/4)/(a^2*e^2-b^2*e^2)*2^(1/2)*arctan(2^(1/2)/(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)-1)+1/4/d*e^3/b*(e^2*(a^2-b^2)/b^2)^(1/4)/(a^2*e^2-b^2*e^2)*2^(1/2)*ln((e*sin(d*x+c)+(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)*2^(1/2)+(e^2*(a^2-b^2)/b^2)^(1/2))/(e*sin(d*x+c)-(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)*2^(1/2)+(e^2*(a^2-b^2)/b^2)^(1/2)))*a^2-1/4/d*e^3*b*(e^2*(a^2-b^2)/b^2)^(1/4)/(a^2*e^2-b^2*e^2)*2^(1/2)*ln((e*sin(d*x+c)+(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)*2^(1/2)+(e^2*(a^2-b^2)/b^2)^(1/2))/(e*sin(d*x+c)-(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)*2^(1/2)+(e^2*(a^2-b^2)/b^2)^(1/2)))-1/d*e^2*a/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/b^2*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))+1/2/d*e^2*a^3/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/b^3/(-a^2+b^2)^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1-(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1-(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))-1/2/d*e^2*a/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/(-a^2+b^2)^(1/2)/b*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1-(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1-(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))-1/2/d*e^2*a^3/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/b^3/(-a^2+b^2)^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1+(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1+(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))+1/2/d*e^2*a/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/(-a^2+b^2)^(1/2)/b*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1+(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1+(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))","B"
63,1,815,320,0.870000," ","int((e*sin(d*x+c))^(1/2)/(a+b*cos(d*x+c)),x)","-\frac{e \sqrt{2}\, \ln \left(\frac{e \sin \left(d x +c \right)-\left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}\right)^{\frac{1}{4}} \sqrt{e \sin \left(d x +c \right)}\, \sqrt{2}+\sqrt{\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}}}{e \sin \left(d x +c \right)+\left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}\right)^{\frac{1}{4}} \sqrt{e \sin \left(d x +c \right)}\, \sqrt{2}+\sqrt{\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}}}\right)}{4 d b \left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}\right)^{\frac{1}{4}}}-\frac{e \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \sin \left(d x +c \right)}}{\left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}\right)^{\frac{1}{4}}}+1\right)}{2 d b \left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}\right)^{\frac{1}{4}}}-\frac{e \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \sin \left(d x +c \right)}}{\left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}\right)^{\frac{1}{4}}}-1\right)}{2 d b \left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}\right)^{\frac{1}{4}}}+\frac{e a \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{-\sin \left(d x +c \right)+1}, -\frac{b}{\sqrt{-a^{2}+b^{2}}-b}, \frac{\sqrt{2}}{2}\right) \sqrt{-a^{2}+b^{2}}}{2 d b \left(\sqrt{-a^{2}+b^{2}}-b \right) \left(b +\sqrt{-a^{2}+b^{2}}\right) \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}}-\frac{e a \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{b}{b +\sqrt{-a^{2}+b^{2}}}, \frac{\sqrt{2}}{2}\right) \sqrt{-a^{2}+b^{2}}}{2 d b \left(\sqrt{-a^{2}+b^{2}}-b \right) \left(b +\sqrt{-a^{2}+b^{2}}\right) \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}}+\frac{e a \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{-\sin \left(d x +c \right)+1}, -\frac{b}{\sqrt{-a^{2}+b^{2}}-b}, \frac{\sqrt{2}}{2}\right)}{2 d \left(\sqrt{-a^{2}+b^{2}}-b \right) \left(b +\sqrt{-a^{2}+b^{2}}\right) \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}}+\frac{e a \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{b}{b +\sqrt{-a^{2}+b^{2}}}, \frac{\sqrt{2}}{2}\right)}{2 d \left(\sqrt{-a^{2}+b^{2}}-b \right) \left(b +\sqrt{-a^{2}+b^{2}}\right) \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}}"," ",0,"-1/4/d*e/b/(e^2*(a^2-b^2)/b^2)^(1/4)*2^(1/2)*ln((e*sin(d*x+c)-(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)*2^(1/2)+(e^2*(a^2-b^2)/b^2)^(1/2))/(e*sin(d*x+c)+(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)*2^(1/2)+(e^2*(a^2-b^2)/b^2)^(1/2)))-1/2/d*e/b/(e^2*(a^2-b^2)/b^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)+1)-1/2/d*e/b/(e^2*(a^2-b^2)/b^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)-1)+1/2/d*e*a*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/b/((-a^2+b^2)^(1/2)-b)/(b+(-a^2+b^2)^(1/2))/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*EllipticPi((-sin(d*x+c)+1)^(1/2),-b/((-a^2+b^2)^(1/2)-b),1/2*2^(1/2))*(-a^2+b^2)^(1/2)-1/2/d*e*a*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/b/((-a^2+b^2)^(1/2)-b)/(b+(-a^2+b^2)^(1/2))/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*EllipticPi((-sin(d*x+c)+1)^(1/2),b/(b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))*(-a^2+b^2)^(1/2)+1/2/d*e*a*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/((-a^2+b^2)^(1/2)-b)/(b+(-a^2+b^2)^(1/2))/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*EllipticPi((-sin(d*x+c)+1)^(1/2),-b/((-a^2+b^2)^(1/2)-b),1/2*2^(1/2))+1/2/d*e*a*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/((-a^2+b^2)^(1/2)-b)/(b+(-a^2+b^2)^(1/2))/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*EllipticPi((-sin(d*x+c)+1)^(1/2),b/(b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))","B"
64,1,855,325,0.825000," ","int(1/(a+b*cos(d*x+c))/(e*sin(d*x+c))^(1/2),x)","-\frac{b e \left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{e \sin \left(d x +c \right)+\left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}\right)^{\frac{1}{4}} \sqrt{e \sin \left(d x +c \right)}\, \sqrt{2}+\sqrt{\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}}}{e \sin \left(d x +c \right)-\left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}\right)^{\frac{1}{4}} \sqrt{e \sin \left(d x +c \right)}\, \sqrt{2}+\sqrt{\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}}}\right)}{4 d \left(a^{2} e^{2}-b^{2} e^{2}\right)}-\frac{b e \left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \sin \left(d x +c \right)}}{\left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}\right)^{\frac{1}{4}}}+1\right)}{2 d \left(a^{2} e^{2}-b^{2} e^{2}\right)}-\frac{b e \left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \sin \left(d x +c \right)}}{\left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}\right)^{\frac{1}{4}}}-1\right)}{2 d \left(a^{2} e^{2}-b^{2} e^{2}\right)}+\frac{a \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{-\sin \left(d x +c \right)+1}, -\frac{b}{\sqrt{-a^{2}+b^{2}}-b}, \frac{\sqrt{2}}{2}\right)}{2 d \left(\sqrt{-a^{2}+b^{2}}-b \right) \left(b +\sqrt{-a^{2}+b^{2}}\right) \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}}+\frac{a \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{b}{b +\sqrt{-a^{2}+b^{2}}}, \frac{\sqrt{2}}{2}\right)}{2 d \left(\sqrt{-a^{2}+b^{2}}-b \right) \left(b +\sqrt{-a^{2}+b^{2}}\right) \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}}+\frac{a \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{-\sin \left(d x +c \right)+1}, -\frac{b}{\sqrt{-a^{2}+b^{2}}-b}, \frac{\sqrt{2}}{2}\right) b}{2 d \sqrt{-a^{2}+b^{2}}\, \left(\sqrt{-a^{2}+b^{2}}-b \right) \left(b +\sqrt{-a^{2}+b^{2}}\right) \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}}-\frac{a \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{b}{b +\sqrt{-a^{2}+b^{2}}}, \frac{\sqrt{2}}{2}\right) b}{2 d \sqrt{-a^{2}+b^{2}}\, \left(\sqrt{-a^{2}+b^{2}}-b \right) \left(b +\sqrt{-a^{2}+b^{2}}\right) \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}}"," ",0,"-1/4/d*b*e*(e^2*(a^2-b^2)/b^2)^(1/4)/(a^2*e^2-b^2*e^2)*2^(1/2)*ln((e*sin(d*x+c)+(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)*2^(1/2)+(e^2*(a^2-b^2)/b^2)^(1/2))/(e*sin(d*x+c)-(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)*2^(1/2)+(e^2*(a^2-b^2)/b^2)^(1/2)))-1/2/d*b*e*(e^2*(a^2-b^2)/b^2)^(1/4)/(a^2*e^2-b^2*e^2)*2^(1/2)*arctan(2^(1/2)/(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)+1)-1/2/d*b*e*(e^2*(a^2-b^2)/b^2)^(1/4)/(a^2*e^2-b^2*e^2)*2^(1/2)*arctan(2^(1/2)/(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)-1)+1/2/d*a*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/((-a^2+b^2)^(1/2)-b)/(b+(-a^2+b^2)^(1/2))/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*EllipticPi((-sin(d*x+c)+1)^(1/2),-b/((-a^2+b^2)^(1/2)-b),1/2*2^(1/2))+1/2/d*a*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/((-a^2+b^2)^(1/2)-b)/(b+(-a^2+b^2)^(1/2))/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*EllipticPi((-sin(d*x+c)+1)^(1/2),b/(b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))+1/2/d*a*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(-a^2+b^2)^(1/2)/((-a^2+b^2)^(1/2)-b)/(b+(-a^2+b^2)^(1/2))/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*EllipticPi((-sin(d*x+c)+1)^(1/2),-b/((-a^2+b^2)^(1/2)-b),1/2*2^(1/2))*b-1/2/d*a*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(-a^2+b^2)^(1/2)/((-a^2+b^2)^(1/2)-b)/(b+(-a^2+b^2)^(1/2))/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*EllipticPi((-sin(d*x+c)+1)^(1/2),b/(b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))*b","B"
65,1,1248,464,0.868000," ","int(1/(a+b*cos(d*x+c))/(e*sin(d*x+c))^(3/2),x)","\frac{b \sqrt{2}\, \ln \left(\frac{e \sin \left(d x +c \right)-\left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}\right)^{\frac{1}{4}} \sqrt{e \sin \left(d x +c \right)}\, \sqrt{2}+\sqrt{\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}}}{e \sin \left(d x +c \right)+\left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}\right)^{\frac{1}{4}} \sqrt{e \sin \left(d x +c \right)}\, \sqrt{2}+\sqrt{\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}}}\right)}{4 d e \left(a -b \right) \left(a +b \right) \left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}\right)^{\frac{1}{4}}}+\frac{b \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \sin \left(d x +c \right)}}{\left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}\right)^{\frac{1}{4}}}+1\right)}{2 d e \left(a -b \right) \left(a +b \right) \left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}\right)^{\frac{1}{4}}}+\frac{b \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \sin \left(d x +c \right)}}{\left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}\right)^{\frac{1}{4}}}-1\right)}{2 d e \left(a -b \right) \left(a +b \right) \left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}\right)^{\frac{1}{4}}}+\frac{2 b}{d e \left(a^{2}-b^{2}\right) \sqrt{e \sin \left(d x +c \right)}}-\frac{a \sqrt{-a^{2}+b^{2}}\, \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{-\sin \left(d x +c \right)+1}, -\frac{b}{\sqrt{-a^{2}+b^{2}}-b}, \frac{\sqrt{2}}{2}\right) b}{2 d e \left(a^{2}-b^{2}\right) \left(b +\sqrt{-a^{2}+b^{2}}\right) \left(\sqrt{-a^{2}+b^{2}}-b \right) \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}}+\frac{a \sqrt{-a^{2}+b^{2}}\, \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{b}{b +\sqrt{-a^{2}+b^{2}}}, \frac{\sqrt{2}}{2}\right) b}{2 d e \left(a^{2}-b^{2}\right) \left(b +\sqrt{-a^{2}+b^{2}}\right) \left(\sqrt{-a^{2}+b^{2}}-b \right) \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}}-\frac{a \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{-\sin \left(d x +c \right)+1}, -\frac{b}{\sqrt{-a^{2}+b^{2}}-b}, \frac{\sqrt{2}}{2}\right) b^{2}}{2 d e \left(a^{2}-b^{2}\right) \left(b +\sqrt{-a^{2}+b^{2}}\right) \left(\sqrt{-a^{2}+b^{2}}-b \right) \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}}-\frac{a \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{b}{b +\sqrt{-a^{2}+b^{2}}}, \frac{\sqrt{2}}{2}\right) b^{2}}{2 d e \left(a^{2}-b^{2}\right) \left(b +\sqrt{-a^{2}+b^{2}}\right) \left(\sqrt{-a^{2}+b^{2}}-b \right) \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}}-\frac{2 a^{3} \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticE \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right)}{d e \left(a^{2}-b^{2}\right) \left(b +\sqrt{-a^{2}+b^{2}}\right) \left(\sqrt{-a^{2}+b^{2}}-b \right) \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}}+\frac{a^{3} \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticF \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right)}{d e \left(a^{2}-b^{2}\right) \left(b +\sqrt{-a^{2}+b^{2}}\right) \left(\sqrt{-a^{2}+b^{2}}-b \right) \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}}+\frac{2 a^{3} \cos \left(d x +c \right)}{d e \left(a^{2}-b^{2}\right) \left(b +\sqrt{-a^{2}+b^{2}}\right) \left(\sqrt{-a^{2}+b^{2}}-b \right) \sqrt{e \sin \left(d x +c \right)}}"," ",0,"1/4/d/e*b/(a-b)/(a+b)/(e^2*(a^2-b^2)/b^2)^(1/4)*2^(1/2)*ln((e*sin(d*x+c)-(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)*2^(1/2)+(e^2*(a^2-b^2)/b^2)^(1/2))/(e*sin(d*x+c)+(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)*2^(1/2)+(e^2*(a^2-b^2)/b^2)^(1/2)))+1/2/d/e*b/(a-b)/(a+b)/(e^2*(a^2-b^2)/b^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)+1)+1/2/d/e*b/(a-b)/(a+b)/(e^2*(a^2-b^2)/b^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)-1)+2/d/e*b/(a^2-b^2)/(e*sin(d*x+c))^(1/2)-1/2/d*a/e/(a^2-b^2)/(b+(-a^2+b^2)^(1/2))/((-a^2+b^2)^(1/2)-b)/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*(-a^2+b^2)^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticPi((-sin(d*x+c)+1)^(1/2),-b/((-a^2+b^2)^(1/2)-b),1/2*2^(1/2))*b+1/2/d*a/e/(a^2-b^2)/(b+(-a^2+b^2)^(1/2))/((-a^2+b^2)^(1/2)-b)/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*(-a^2+b^2)^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticPi((-sin(d*x+c)+1)^(1/2),b/(b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))*b-1/2/d*a/e/(a^2-b^2)/(b+(-a^2+b^2)^(1/2))/((-a^2+b^2)^(1/2)-b)/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticPi((-sin(d*x+c)+1)^(1/2),-b/((-a^2+b^2)^(1/2)-b),1/2*2^(1/2))*b^2-1/2/d*a/e/(a^2-b^2)/(b+(-a^2+b^2)^(1/2))/((-a^2+b^2)^(1/2)-b)/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticPi((-sin(d*x+c)+1)^(1/2),b/(b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))*b^2-2/d*a^3/e/(a^2-b^2)/(b+(-a^2+b^2)^(1/2))/((-a^2+b^2)^(1/2)-b)/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticE((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))+1/d*a^3/e/(a^2-b^2)/(b+(-a^2+b^2)^(1/2))/((-a^2+b^2)^(1/2)-b)/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))+2/d*a^3/e/(a^2-b^2)/(b+(-a^2+b^2)^(1/2))/((-a^2+b^2)^(1/2)-b)*cos(d*x+c)/(e*sin(d*x+c))^(1/2)","B"
66,1,845,481,0.984000," ","int(1/(a+b*cos(d*x+c))/(e*sin(d*x+c))^(5/2),x)","\frac{2 b}{3 d e \left(a^{2}-b^{2}\right) \left(e \sin \left(d x +c \right)\right)^{\frac{3}{2}}}+\frac{b^{3} \left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{e \sin \left(d x +c \right)+\left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}\right)^{\frac{1}{4}} \sqrt{e \sin \left(d x +c \right)}\, \sqrt{2}+\sqrt{\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}}}{e \sin \left(d x +c \right)-\left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}\right)^{\frac{1}{4}} \sqrt{e \sin \left(d x +c \right)}\, \sqrt{2}+\sqrt{\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}}}\right)}{4 d e \left(a -b \right) \left(a +b \right) \left(a^{2} e^{2}-b^{2} e^{2}\right)}+\frac{b^{3} \left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \sin \left(d x +c \right)}}{\left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}\right)^{\frac{1}{4}}}+1\right)}{2 d e \left(a -b \right) \left(a +b \right) \left(a^{2} e^{2}-b^{2} e^{2}\right)}+\frac{b^{3} \left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \sin \left(d x +c \right)}}{\left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}\right)^{\frac{1}{4}}}-1\right)}{2 d e \left(a -b \right) \left(a +b \right) \left(a^{2} e^{2}-b^{2} e^{2}\right)}+\frac{a b \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{1}{1-\frac{\sqrt{-a^{2}+b^{2}}}{b}}, \frac{\sqrt{2}}{2}\right)}{2 d \,e^{2} \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, \left(a -b \right) \left(a +b \right) \sqrt{-a^{2}+b^{2}}\, \left(1-\frac{\sqrt{-a^{2}+b^{2}}}{b}\right)}-\frac{a b \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{1}{1+\frac{\sqrt{-a^{2}+b^{2}}}{b}}, \frac{\sqrt{2}}{2}\right)}{2 d \,e^{2} \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, \left(a -b \right) \left(a +b \right) \sqrt{-a^{2}+b^{2}}\, \left(1+\frac{\sqrt{-a^{2}+b^{2}}}{b}\right)}+\frac{a \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sin^{\frac{5}{2}}\left(d x +c \right)\right) \EllipticF \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right)}{3 d \,e^{2} \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, \left(a^{2}-b^{2}\right) \left(\cos^{2}\left(d x +c \right)-1\right)}+\frac{2 a \cos \left(d x +c \right) \sin \left(d x +c \right)}{3 d \,e^{2} \sqrt{e \sin \left(d x +c \right)}\, \left(a^{2}-b^{2}\right) \left(\cos^{2}\left(d x +c \right)-1\right)}"," ",0,"2/3/d/e*b/(a^2-b^2)/(e*sin(d*x+c))^(3/2)+1/4/d/e*b^3/(a-b)/(a+b)*(e^2*(a^2-b^2)/b^2)^(1/4)/(a^2*e^2-b^2*e^2)*2^(1/2)*ln((e*sin(d*x+c)+(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)*2^(1/2)+(e^2*(a^2-b^2)/b^2)^(1/2))/(e*sin(d*x+c)-(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)*2^(1/2)+(e^2*(a^2-b^2)/b^2)^(1/2)))+1/2/d/e*b^3/(a-b)/(a+b)*(e^2*(a^2-b^2)/b^2)^(1/4)/(a^2*e^2-b^2*e^2)*2^(1/2)*arctan(2^(1/2)/(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)+1)+1/2/d/e*b^3/(a-b)/(a+b)*(e^2*(a^2-b^2)/b^2)^(1/4)/(a^2*e^2-b^2*e^2)*2^(1/2)*arctan(2^(1/2)/(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)-1)+1/2/d/e^2*a/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/(a-b)/(a+b)*b/(-a^2+b^2)^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1-(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1-(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))-1/2/d/e^2*a/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/(a-b)/(a+b)*b/(-a^2+b^2)^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1+(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1+(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))+1/3/d/e^2*a/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/(a^2-b^2)/(cos(d*x+c)^2-1)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(5/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))+2/3/d/e^2*a*cos(d*x+c)/(e*sin(d*x+c))^(1/2)/(a^2-b^2)/(cos(d*x+c)^2-1)*sin(d*x+c)","A"
67,1,1807,535,0.790000," ","int(1/(a+b*cos(d*x+c))/(e*sin(d*x+c))^(7/2),x)","-\frac{b^{3} \sqrt{2}\, \ln \left(\frac{e \sin \left(d x +c \right)-\left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}\right)^{\frac{1}{4}} \sqrt{e \sin \left(d x +c \right)}\, \sqrt{2}+\sqrt{\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}}}{e \sin \left(d x +c \right)+\left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}\right)^{\frac{1}{4}} \sqrt{e \sin \left(d x +c \right)}\, \sqrt{2}+\sqrt{\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}}}\right)}{4 d \,e^{3} \left(a -b \right)^{2} \left(a +b \right)^{2} \left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}\right)^{\frac{1}{4}}}-\frac{b^{3} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \sin \left(d x +c \right)}}{\left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}\right)^{\frac{1}{4}}}+1\right)}{2 d \,e^{3} \left(a -b \right)^{2} \left(a +b \right)^{2} \left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}\right)^{\frac{1}{4}}}-\frac{b^{3} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \sin \left(d x +c \right)}}{\left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}\right)^{\frac{1}{4}}}-1\right)}{2 d \,e^{3} \left(a -b \right)^{2} \left(a +b \right)^{2} \left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}\right)^{\frac{1}{4}}}+\frac{2 b}{5 d e \left(a +b \right) \left(a -b \right) \left(e \sin \left(d x +c \right)\right)^{\frac{5}{2}}}-\frac{2 b^{3}}{d \,e^{3} \left(a -b \right)^{2} \left(a +b \right)^{2} \sqrt{e \sin \left(d x +c \right)}}+\frac{a \left(\sqrt{\sin}\left(d x +c \right)\right) \sqrt{-a^{2}+b^{2}}\, \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \EllipticPi \left(\sqrt{-\sin \left(d x +c \right)+1}, -\frac{b}{\sqrt{-a^{2}+b^{2}}-b}, \frac{\sqrt{2}}{2}\right) b^{3}}{2 d \,e^{3} \left(b +\sqrt{-a^{2}+b^{2}}\right) \left(\sqrt{-a^{2}+b^{2}}-b \right) \left(a +b \right)^{2} \left(a -b \right)^{2} \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}}-\frac{a \left(\sqrt{\sin}\left(d x +c \right)\right) \sqrt{-a^{2}+b^{2}}\, \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \EllipticPi \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{b}{b +\sqrt{-a^{2}+b^{2}}}, \frac{\sqrt{2}}{2}\right) b^{3}}{2 d \,e^{3} \left(b +\sqrt{-a^{2}+b^{2}}\right) \left(\sqrt{-a^{2}+b^{2}}-b \right) \left(a +b \right)^{2} \left(a -b \right)^{2} \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}}+\frac{a \left(\sqrt{\sin}\left(d x +c \right)\right) \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \EllipticPi \left(\sqrt{-\sin \left(d x +c \right)+1}, -\frac{b}{\sqrt{-a^{2}+b^{2}}-b}, \frac{\sqrt{2}}{2}\right) b^{4}}{2 d \,e^{3} \left(b +\sqrt{-a^{2}+b^{2}}\right) \left(\sqrt{-a^{2}+b^{2}}-b \right) \left(a +b \right)^{2} \left(a -b \right)^{2} \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}}+\frac{a \left(\sqrt{\sin}\left(d x +c \right)\right) \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \EllipticPi \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{b}{b +\sqrt{-a^{2}+b^{2}}}, \frac{\sqrt{2}}{2}\right) b^{4}}{2 d \,e^{3} \left(b +\sqrt{-a^{2}+b^{2}}\right) \left(\sqrt{-a^{2}+b^{2}}-b \right) \left(a +b \right)^{2} \left(a -b \right)^{2} \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}}-\frac{6 a^{5} \left(\sqrt{\sin}\left(d x +c \right)\right) \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \EllipticE \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right)}{5 d \,e^{3} \left(b +\sqrt{-a^{2}+b^{2}}\right) \left(\sqrt{-a^{2}+b^{2}}-b \right) \left(a +b \right)^{2} \left(a -b \right)^{2} \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}}+\frac{16 a^{3} \left(\sqrt{\sin}\left(d x +c \right)\right) \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \EllipticE \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right) b^{2}}{5 d \,e^{3} \left(b +\sqrt{-a^{2}+b^{2}}\right) \left(\sqrt{-a^{2}+b^{2}}-b \right) \left(a +b \right)^{2} \left(a -b \right)^{2} \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}}+\frac{3 a^{5} \left(\sqrt{\sin}\left(d x +c \right)\right) \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \EllipticF \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right)}{5 d \,e^{3} \left(b +\sqrt{-a^{2}+b^{2}}\right) \left(\sqrt{-a^{2}+b^{2}}-b \right) \left(a +b \right)^{2} \left(a -b \right)^{2} \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}}-\frac{8 a^{3} \left(\sqrt{\sin}\left(d x +c \right)\right) \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \EllipticF \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right) b^{2}}{5 d \,e^{3} \left(b +\sqrt{-a^{2}+b^{2}}\right) \left(\sqrt{-a^{2}+b^{2}}-b \right) \left(a +b \right)^{2} \left(a -b \right)^{2} \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}}-\frac{6 a^{5} \left(\cos^{3}\left(d x +c \right)\right)}{5 d \,e^{3} \left(b +\sqrt{-a^{2}+b^{2}}\right) \left(\sqrt{-a^{2}+b^{2}}-b \right) \left(a +b \right)^{2} \left(a -b \right)^{2} \sin \left(d x +c \right)^{2} \sqrt{e \sin \left(d x +c \right)}}+\frac{16 a^{3} \left(\cos^{3}\left(d x +c \right)\right) b^{2}}{5 d \,e^{3} \left(b +\sqrt{-a^{2}+b^{2}}\right) \left(\sqrt{-a^{2}+b^{2}}-b \right) \left(a +b \right)^{2} \left(a -b \right)^{2} \sin \left(d x +c \right)^{2} \sqrt{e \sin \left(d x +c \right)}}+\frac{8 a^{5} \cos \left(d x +c \right)}{5 d \,e^{3} \left(b +\sqrt{-a^{2}+b^{2}}\right) \left(\sqrt{-a^{2}+b^{2}}-b \right) \left(a +b \right)^{2} \left(a -b \right)^{2} \sin \left(d x +c \right)^{2} \sqrt{e \sin \left(d x +c \right)}}-\frac{18 a^{3} \cos \left(d x +c \right) b^{2}}{5 d \,e^{3} \left(b +\sqrt{-a^{2}+b^{2}}\right) \left(\sqrt{-a^{2}+b^{2}}-b \right) \left(a +b \right)^{2} \left(a -b \right)^{2} \sin \left(d x +c \right)^{2} \sqrt{e \sin \left(d x +c \right)}}"," ",0,"-1/4/d/e^3*b^3/(a-b)^2/(a+b)^2/(e^2*(a^2-b^2)/b^2)^(1/4)*2^(1/2)*ln((e*sin(d*x+c)-(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)*2^(1/2)+(e^2*(a^2-b^2)/b^2)^(1/2))/(e*sin(d*x+c)+(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)*2^(1/2)+(e^2*(a^2-b^2)/b^2)^(1/2)))-1/2/d/e^3*b^3/(a-b)^2/(a+b)^2/(e^2*(a^2-b^2)/b^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)+1)-1/2/d/e^3*b^3/(a-b)^2/(a+b)^2/(e^2*(a^2-b^2)/b^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)-1)+2/5/d/e*b/(a+b)/(a-b)/(e*sin(d*x+c))^(5/2)-2/d/e^3*b^3/(a-b)^2/(a+b)^2/(e*sin(d*x+c))^(1/2)+1/2/d/e^3*a/(b+(-a^2+b^2)^(1/2))/((-a^2+b^2)^(1/2)-b)/(a+b)^2/(a-b)^2*sin(d*x+c)^(1/2)/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*(-a^2+b^2)^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*EllipticPi((-sin(d*x+c)+1)^(1/2),-b/((-a^2+b^2)^(1/2)-b),1/2*2^(1/2))*b^3-1/2/d/e^3*a/(b+(-a^2+b^2)^(1/2))/((-a^2+b^2)^(1/2)-b)/(a+b)^2/(a-b)^2*sin(d*x+c)^(1/2)/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*(-a^2+b^2)^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*EllipticPi((-sin(d*x+c)+1)^(1/2),b/(b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))*b^3+1/2/d/e^3*a/(b+(-a^2+b^2)^(1/2))/((-a^2+b^2)^(1/2)-b)/(a+b)^2/(a-b)^2*sin(d*x+c)^(1/2)/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*EllipticPi((-sin(d*x+c)+1)^(1/2),-b/((-a^2+b^2)^(1/2)-b),1/2*2^(1/2))*b^4+1/2/d/e^3*a/(b+(-a^2+b^2)^(1/2))/((-a^2+b^2)^(1/2)-b)/(a+b)^2/(a-b)^2*sin(d*x+c)^(1/2)/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*EllipticPi((-sin(d*x+c)+1)^(1/2),b/(b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))*b^4-6/5/d/e^3*a^5/(b+(-a^2+b^2)^(1/2))/((-a^2+b^2)^(1/2)-b)/(a+b)^2/(a-b)^2*sin(d*x+c)^(1/2)/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*EllipticE((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))+16/5/d/e^3*a^3/(b+(-a^2+b^2)^(1/2))/((-a^2+b^2)^(1/2)-b)/(a+b)^2/(a-b)^2*sin(d*x+c)^(1/2)/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*EllipticE((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))*b^2+3/5/d/e^3*a^5/(b+(-a^2+b^2)^(1/2))/((-a^2+b^2)^(1/2)-b)/(a+b)^2/(a-b)^2*sin(d*x+c)^(1/2)/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))-8/5/d/e^3*a^3/(b+(-a^2+b^2)^(1/2))/((-a^2+b^2)^(1/2)-b)/(a+b)^2/(a-b)^2*sin(d*x+c)^(1/2)/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))*b^2-6/5/d/e^3*a^5/(b+(-a^2+b^2)^(1/2))/((-a^2+b^2)^(1/2)-b)/(a+b)^2/(a-b)^2/sin(d*x+c)^2*cos(d*x+c)^3/(e*sin(d*x+c))^(1/2)+16/5/d/e^3*a^3/(b+(-a^2+b^2)^(1/2))/((-a^2+b^2)^(1/2)-b)/(a+b)^2/(a-b)^2/sin(d*x+c)^2*cos(d*x+c)^3/(e*sin(d*x+c))^(1/2)*b^2+8/5/d/e^3*a^5/(b+(-a^2+b^2)^(1/2))/((-a^2+b^2)^(1/2)-b)/(a+b)^2/(a-b)^2/sin(d*x+c)^2*cos(d*x+c)/(e*sin(d*x+c))^(1/2)-18/5/d/e^3*a^3/(b+(-a^2+b^2)^(1/2))/((-a^2+b^2)^(1/2)-b)/(a+b)^2/(a-b)^2/sin(d*x+c)^2*cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^2","B"
68,1,4706,579,1.596000," ","int((e*sin(d*x+c))^(11/2)/(a+b*cos(d*x+c))^2,x)","\text{output too large to display}"," ",0,"-2/7/d*e^6*cos(d*x+c)^3/(e*sin(d*x+c))^(1/2)/b^2*sin(d*x+c)+10/7/d*e^6*cos(d*x+c)/(e*sin(d*x+c))^(1/2)/b^2*sin(d*x+c)+1/d*e^7*a/b*(e*sin(d*x+c))^(1/2)/(-b^2*cos(d*x+c)^2*e^2+a^2*e^2)+1/d*e^7*a^5/b^5*(e*sin(d*x+c))^(1/2)/(-b^2*cos(d*x+c)^2*e^2+a^2*e^2)-2/d*e^7*a^3/b^3*(e*sin(d*x+c))^(1/2)/(-b^2*cos(d*x+c)^2*e^2+a^2*e^2)+8/d*e^5*a^3/b^5*(e*sin(d*x+c))^(1/2)-8/d*e^5*a/b^3*(e*sin(d*x+c))^(1/2)+3/2/d*e^6/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*a^4/b^4/(a^2-b^2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))-1/2/d*e^6/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/(-a^2+b^2)^(1/2)/b*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1+(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1+(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))+1/2/d*e^6/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/(-a^2+b^2)^(1/2)/b*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1-(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1-(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))-1/2/d*e^6/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*a^6/b^6/(a^2-b^2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))-3/2/d*e^6/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*a^2/b^2/(a^2-b^2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))+7/2/d*e^6/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/b^7/(-a^2+b^2)^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1+(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1+(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))*a^6-15/2/d*e^6/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/b^5/(-a^2+b^2)^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1+(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1+(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))*a^4+9/2/d*e^6/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/b^3/(-a^2+b^2)^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1+(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1+(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))*a^2+1/2/d*e^6/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b/(a^2-b^2)/(-a^2+b^2)^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1-(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1-(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))-1/2/d*e^6/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b/(a^2-b^2)/(-a^2+b^2)^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1+(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1+(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))-9/2/d*e^6/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/b^3/(-a^2+b^2)^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1-(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1-(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))*a^2+15/2/d*e^6/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/b^5/(-a^2+b^2)^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1-(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1-(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))*a^4-7/2/d*e^6/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/b^7/(-a^2+b^2)^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1-(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1-(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))*a^6-4/5/d*e^3*a/b^3*(e*sin(d*x+c))^(5/2)-9/4/d*e^7*a^5/b^5*(e^2*(a^2-b^2)/b^2)^(1/4)/(a^2*e^2-b^2*e^2)*2^(1/2)*arctan(2^(1/2)/(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)+1)+9/2/d*e^7*a^3/b^3*(e^2*(a^2-b^2)/b^2)^(1/4)/(a^2*e^2-b^2*e^2)*2^(1/2)*arctan(2^(1/2)/(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)+1)-9/4/d*e^7*a/b*(e^2*(a^2-b^2)/b^2)^(1/4)/(a^2*e^2-b^2*e^2)*2^(1/2)*arctan(2^(1/2)/(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)+1)-9/4/d*e^7*a^5/b^5*(e^2*(a^2-b^2)/b^2)^(1/4)/(a^2*e^2-b^2*e^2)*2^(1/2)*arctan(2^(1/2)/(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)-1)+9/2/d*e^7*a^3/b^3*(e^2*(a^2-b^2)/b^2)^(1/4)/(a^2*e^2-b^2*e^2)*2^(1/2)*arctan(2^(1/2)/(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)-1)-9/4/d*e^7*a/b*(e^2*(a^2-b^2)/b^2)^(1/4)/(a^2*e^2-b^2*e^2)*2^(1/2)*arctan(2^(1/2)/(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)-1)-9/8/d*e^7*a^5/b^5*(e^2*(a^2-b^2)/b^2)^(1/4)/(a^2*e^2-b^2*e^2)*2^(1/2)*ln((e*sin(d*x+c)+(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)*2^(1/2)+(e^2*(a^2-b^2)/b^2)^(1/2))/(e*sin(d*x+c)-(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)*2^(1/2)+(e^2*(a^2-b^2)/b^2)^(1/2)))+9/4/d*e^7*a^3/b^3*(e^2*(a^2-b^2)/b^2)^(1/4)/(a^2*e^2-b^2*e^2)*2^(1/2)*ln((e*sin(d*x+c)+(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)*2^(1/2)+(e^2*(a^2-b^2)/b^2)^(1/2))/(e*sin(d*x+c)-(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)*2^(1/2)+(e^2*(a^2-b^2)/b^2)^(1/2)))-9/8/d*e^7*a/b*(e^2*(a^2-b^2)/b^2)^(1/4)/(a^2*e^2-b^2*e^2)*2^(1/2)*ln((e*sin(d*x+c)+(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)*2^(1/2)+(e^2*(a^2-b^2)/b^2)^(1/2))/(e*sin(d*x+c)-(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)*2^(1/2)+(e^2*(a^2-b^2)/b^2)^(1/2)))-3/d*e^6*sin(d*x+c)*cos(d*x+c)/(e*sin(d*x+c))^(1/2)*a^2/(a^2-b^2)/(-cos(d*x+c)^2*b^2+a^2)+1/d*e^6*sin(d*x+c)*cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^2/(a^2-b^2)/(-cos(d*x+c)^2*b^2+a^2)-17/4/d*e^6/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*a^6/b^5/(a^2-b^2)/(-a^2+b^2)^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1-(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1-(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))+21/4/d*e^6/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*a^4/b^3/(a^2-b^2)/(-a^2+b^2)^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1-(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1-(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))-11/4/d*e^6/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*a^2/b/(a^2-b^2)/(-a^2+b^2)^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1-(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1-(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))-5/4/d*e^6/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*a^8/b^7/(a^2-b^2)/(-a^2+b^2)^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1+(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1+(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))+17/4/d*e^6/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*a^6/b^5/(a^2-b^2)/(-a^2+b^2)^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1+(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1+(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))-21/4/d*e^6/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*a^4/b^3/(a^2-b^2)/(-a^2+b^2)^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1+(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1+(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))+11/4/d*e^6/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*a^2/b/(a^2-b^2)/(-a^2+b^2)^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1+(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1+(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))+5/4/d*e^6/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*a^8/b^7/(a^2-b^2)/(-a^2+b^2)^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1-(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1-(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))+5/d*e^6/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/b^6*a^4*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))-7/d*e^6/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/b^4*a^2*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))-2/d*e^6*cos(d*x+c)/(e*sin(d*x+c))^(1/2)/b^4*a^2*sin(d*x+c)+3/d*e^6*sin(d*x+c)*cos(d*x+c)/(e*sin(d*x+c))^(1/2)*a^4/b^2/(a^2-b^2)/(-cos(d*x+c)^2*b^2+a^2)-1/d*e^6*sin(d*x+c)*cos(d*x+c)/(e*sin(d*x+c))^(1/2)*a^6/b^4/(a^2-b^2)/(-cos(d*x+c)^2*b^2+a^2)+1/2/d*e^6/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/(a^2-b^2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))+11/7/d*e^6/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/b^2*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))","B"
69,1,3595,499,1.724000," ","int((e*sin(d*x+c))^(9/2)/(a+b*cos(d*x+c))^2,x)","\text{output too large to display}"," ",0,"1/d*e^5*a/b*(e*sin(d*x+c))^(3/2)/(-b^2*cos(d*x+c)^2*e^2+a^2*e^2)-1/d*e^5*a^3/b^3*(e*sin(d*x+c))^(3/2)/(-b^2*cos(d*x+c)^2*e^2+a^2*e^2)+2/d*e^5/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*a^2/b^2/(a^2-b^2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticE((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))+5/2/d*e^5/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/b^6*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1+(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1+(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))*a^4-3/d*e^5/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/b^4*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1+(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1+(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))*a^2-1/d*e^5/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*a^4/b^4/(a^2-b^2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticE((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))+1/d*e^5*sin(d*x+c)^2*cos(d*x+c)/(e*sin(d*x+c))^(1/2)*a^4/b^2/(a^2-b^2)/(-cos(d*x+c)^2*b^2+a^2)-1/d*e^5/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/(a^2-b^2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticE((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))+1/2/d*e^5/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/(a^2-b^2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))+16/5/d*e^5/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/b^2*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticE((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))-8/5/d*e^5/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/b^2*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))-7/4/d*e^5/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*a^2/b^2/(a^2-b^2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1-(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1-(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))-3/4/d*e^5/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*a^6/b^6/(a^2-b^2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1+(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1+(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))+2/d*e^5/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*a^4/b^4/(a^2-b^2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1+(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1+(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))-7/4/d*e^5/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*a^2/b^2/(a^2-b^2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1+(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1+(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))-3/4/d*e^5/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*a^6/b^6/(a^2-b^2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1-(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1-(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))+2/d*e^5/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*a^4/b^4/(a^2-b^2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1-(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1-(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))-2/d*e^5*sin(d*x+c)^2*cos(d*x+c)/(e*sin(d*x+c))^(1/2)*a^2/(a^2-b^2)/(-cos(d*x+c)^2*b^2+a^2)+1/d*e^5*sin(d*x+c)^2*cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^2/(a^2-b^2)/(-cos(d*x+c)^2*b^2+a^2)-1/d*e^5/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*a^2/b^2/(a^2-b^2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))+5/2/d*e^5/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/b^6*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1-(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1-(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))*a^4-3/d*e^5/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/b^4*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1-(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1-(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))*a^2+1/2/d*e^5/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*a^4/b^4/(a^2-b^2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))-2/5/d*e^5*cos(d*x+c)^3/(e*sin(d*x+c))^(1/2)/b^2+2/5/d*e^5*cos(d*x+c)/(e*sin(d*x+c))^(1/2)/b^2+1/2/d*e^5/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/(a^2-b^2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1-(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1-(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))+1/2/d*e^5/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/(a^2-b^2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1+(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1+(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))-6/d*e^5/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/b^4*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticE((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))*a^2+3/d*e^5/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/b^4*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))*a^2+1/2/d*e^5/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/b^2*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1-(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1-(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))+1/2/d*e^5/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/b^2*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1+(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1+(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))+7/8/d*e^5*a^3/b^5/(e^2*(a^2-b^2)/b^2)^(1/4)*2^(1/2)*ln((e*sin(d*x+c)-(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)*2^(1/2)+(e^2*(a^2-b^2)/b^2)^(1/2))/(e*sin(d*x+c)+(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)*2^(1/2)+(e^2*(a^2-b^2)/b^2)^(1/2)))+7/4/d*e^5*a^3/b^5/(e^2*(a^2-b^2)/b^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)+1)+7/4/d*e^5*a^3/b^5/(e^2*(a^2-b^2)/b^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)-1)-7/8/d*e^5*a/b^3/(e^2*(a^2-b^2)/b^2)^(1/4)*2^(1/2)*ln((e*sin(d*x+c)-(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)*2^(1/2)+(e^2*(a^2-b^2)/b^2)^(1/2))/(e*sin(d*x+c)+(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)*2^(1/2)+(e^2*(a^2-b^2)/b^2)^(1/2)))-7/4/d*e^5*a/b^3/(e^2*(a^2-b^2)/b^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)+1)-7/4/d*e^5*a/b^3/(e^2*(a^2-b^2)/b^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)-1)-4/3/d*e^3*a/b^3*(e*sin(d*x+c))^(3/2)","B"
70,1,3396,513,1.543000," ","int((e*sin(d*x+c))^(7/2)/(a+b*cos(d*x+c))^2,x)","\text{output too large to display}"," ",0,"-4/d*e^3*a/b^3*(e*sin(d*x+c))^(1/2)+5/4/d*e^5*a^3/b^3*(e^2*(a^2-b^2)/b^2)^(1/4)/(a^2*e^2-b^2*e^2)*2^(1/2)*arctan(2^(1/2)/(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)+1)-5/4/d*e^5*a/b*(e^2*(a^2-b^2)/b^2)^(1/4)/(a^2*e^2-b^2*e^2)*2^(1/2)*arctan(2^(1/2)/(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)+1)-1/d*e^4/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*a^2/b^2/(a^2-b^2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))+1/2/d*e^4/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/(-a^2+b^2)^(1/2)/b*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1-(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1-(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))-1/2/d*e^4/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/(-a^2+b^2)^(1/2)/b*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1+(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1+(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))+1/2/d*e^4/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*a^4/b^4/(a^2-b^2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))+3/d*e^4/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/b^3/(-a^2+b^2)^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1+(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1+(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))*a^2+1/2/d*e^4/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b/(a^2-b^2)/(-a^2+b^2)^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1-(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1-(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))-1/2/d*e^4/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b/(a^2-b^2)/(-a^2+b^2)^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1+(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1+(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))+5/2/d*e^4/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/b^5/(-a^2+b^2)^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1-(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1-(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))*a^4-3/d*e^4/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/b^3/(-a^2+b^2)^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1-(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1-(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))*a^2-5/2/d*e^4/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/b^5/(-a^2+b^2)^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1+(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1+(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))*a^4-1/d*e^5*a^3/b^3*(e*sin(d*x+c))^(1/2)/(-b^2*cos(d*x+c)^2*e^2+a^2*e^2)+1/d*e^5*a/b*(e*sin(d*x+c))^(1/2)/(-b^2*cos(d*x+c)^2*e^2+a^2*e^2)+2/3/d*e^4*cos(d*x+c)/(e*sin(d*x+c))^(1/2)/b^2*sin(d*x+c)+5/4/d*e^5*a^3/b^3*(e^2*(a^2-b^2)/b^2)^(1/4)/(a^2*e^2-b^2*e^2)*2^(1/2)*arctan(2^(1/2)/(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)-1)-5/4/d*e^5*a/b*(e^2*(a^2-b^2)/b^2)^(1/4)/(a^2*e^2-b^2*e^2)*2^(1/2)*arctan(2^(1/2)/(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)-1)+5/8/d*e^5*a^3/b^3*(e^2*(a^2-b^2)/b^2)^(1/4)/(a^2*e^2-b^2*e^2)*2^(1/2)*ln((e*sin(d*x+c)+(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)*2^(1/2)+(e^2*(a^2-b^2)/b^2)^(1/2))/(e*sin(d*x+c)-(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)*2^(1/2)+(e^2*(a^2-b^2)/b^2)^(1/2)))-5/8/d*e^5*a/b*(e^2*(a^2-b^2)/b^2)^(1/4)/(a^2*e^2-b^2*e^2)*2^(1/2)*ln((e*sin(d*x+c)+(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)*2^(1/2)+(e^2*(a^2-b^2)/b^2)^(1/2))/(e*sin(d*x+c)-(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)*2^(1/2)+(e^2*(a^2-b^2)/b^2)^(1/2)))-2/d*e^4*sin(d*x+c)*cos(d*x+c)/(e*sin(d*x+c))^(1/2)*a^2/(a^2-b^2)/(-cos(d*x+c)^2*b^2+a^2)+1/d*e^4*sin(d*x+c)*cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^2/(a^2-b^2)/(-cos(d*x+c)^2*b^2+a^2)+3/d*e^4/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*a^4/b^3/(a^2-b^2)/(-a^2+b^2)^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1-(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1-(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))-9/4/d*e^4/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*a^2/b/(a^2-b^2)/(-a^2+b^2)^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1-(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1-(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))+5/4/d*e^4/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*a^6/b^5/(a^2-b^2)/(-a^2+b^2)^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1+(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1+(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))-3/d*e^4/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*a^4/b^3/(a^2-b^2)/(-a^2+b^2)^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1+(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1+(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))+9/4/d*e^4/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*a^2/b/(a^2-b^2)/(-a^2+b^2)^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1+(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1+(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))-5/4/d*e^4/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*a^6/b^5/(a^2-b^2)/(-a^2+b^2)^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1-(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1-(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))-3/d*e^4/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/b^4*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))*a^2+1/d*e^4*sin(d*x+c)*cos(d*x+c)/(e*sin(d*x+c))^(1/2)*a^4/b^2/(a^2-b^2)/(-cos(d*x+c)^2*b^2+a^2)+1/2/d*e^4/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/(a^2-b^2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))+4/3/d*e^4/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/b^2*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))","B"
71,1,3174,436,0.919000," ","int((e*sin(d*x+c))^(5/2)/(a+b*cos(d*x+c))^2,x)","\text{output too large to display}"," ",0,"1/d*e^3*a/b*(e*sin(d*x+c))^(3/2)/(-b^2*cos(d*x+c)^2*e^2+a^2*e^2)-3/8/d*e^3*a/b^3/(e^2*(a^2-b^2)/b^2)^(1/4)*2^(1/2)*ln((e*sin(d*x+c)-(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)*2^(1/2)+(e^2*(a^2-b^2)/b^2)^(1/2))/(e*sin(d*x+c)+(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)*2^(1/2)+(e^2*(a^2-b^2)/b^2)^(1/2)))-3/4/d*e^3*a/b^3/(e^2*(a^2-b^2)/b^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)+1)-3/4/d*e^3*a/b^3/(e^2*(a^2-b^2)/b^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)-1)-3/d*e^3*a^2/(b+(-a^2+b^2)^(1/2))/((-a^2+b^2)^(1/2)-b)/(-cos(d*x+c)^2*b^2+a^2)/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(5/2)*EllipticE((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))+3/2/d*e^3*a^2/(b+(-a^2+b^2)^(1/2))/((-a^2+b^2)^(1/2)-b)/(-cos(d*x+c)^2*b^2+a^2)/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(5/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))+3/4/d*e^3*a^2/b/(b+(-a^2+b^2)^(1/2))/((-a^2+b^2)^(1/2)-b)/(-cos(d*x+c)^2*b^2+a^2)/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(5/2)*EllipticPi((-sin(d*x+c)+1)^(1/2),-b/((-a^2+b^2)^(1/2)-b),1/2*2^(1/2))*(-a^2+b^2)^(1/2)+3/4/d*e^3*a^2/(b+(-a^2+b^2)^(1/2))/((-a^2+b^2)^(1/2)-b)/(-cos(d*x+c)^2*b^2+a^2)/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(5/2)*EllipticPi((-sin(d*x+c)+1)^(1/2),-b/((-a^2+b^2)^(1/2)-b),1/2*2^(1/2))-3/4/d*e^3*a^2/b/(b+(-a^2+b^2)^(1/2))/((-a^2+b^2)^(1/2)-b)/(-cos(d*x+c)^2*b^2+a^2)/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(5/2)*EllipticPi((-sin(d*x+c)+1)^(1/2),b/(b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))*(-a^2+b^2)^(1/2)+3/4/d*e^3*a^2/(b+(-a^2+b^2)^(1/2))/((-a^2+b^2)^(1/2)-b)/(-cos(d*x+c)^2*b^2+a^2)/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(5/2)*EllipticPi((-sin(d*x+c)+1)^(1/2),b/(b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))-1/d*e^3*a^2/(b+(-a^2+b^2)^(1/2))/((-a^2+b^2)^(1/2)-b)/(-cos(d*x+c)^2*b^2+a^2)/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*sin(d*x+c)^4-3/d*e^3*a^4/b^2/(b+(-a^2+b^2)^(1/2))/((-a^2+b^2)^(1/2)-b)/(-cos(d*x+c)^2*b^2+a^2)/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticE((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))+3/d*e^3*a^2/(b+(-a^2+b^2)^(1/2))/((-a^2+b^2)^(1/2)-b)/(-cos(d*x+c)^2*b^2+a^2)/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticE((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))+3/2/d*e^3*a^4/b^2/(b+(-a^2+b^2)^(1/2))/((-a^2+b^2)^(1/2)-b)/(-cos(d*x+c)^2*b^2+a^2)/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))-3/2/d*e^3*a^2/(b+(-a^2+b^2)^(1/2))/((-a^2+b^2)^(1/2)-b)/(-cos(d*x+c)^2*b^2+a^2)/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))+3/4/d*e^3*a^4/b^3/(b+(-a^2+b^2)^(1/2))/((-a^2+b^2)^(1/2)-b)/(-cos(d*x+c)^2*b^2+a^2)/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticPi((-sin(d*x+c)+1)^(1/2),-b/((-a^2+b^2)^(1/2)-b),1/2*2^(1/2))*(-a^2+b^2)^(1/2)-3/4/d*e^3*a^2/b/(b+(-a^2+b^2)^(1/2))/((-a^2+b^2)^(1/2)-b)/(-cos(d*x+c)^2*b^2+a^2)/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticPi((-sin(d*x+c)+1)^(1/2),-b/((-a^2+b^2)^(1/2)-b),1/2*2^(1/2))*(-a^2+b^2)^(1/2)+3/4/d*e^3*a^4/b^2/(b+(-a^2+b^2)^(1/2))/((-a^2+b^2)^(1/2)-b)/(-cos(d*x+c)^2*b^2+a^2)/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticPi((-sin(d*x+c)+1)^(1/2),-b/((-a^2+b^2)^(1/2)-b),1/2*2^(1/2))-3/4/d*e^3*a^2/(b+(-a^2+b^2)^(1/2))/((-a^2+b^2)^(1/2)-b)/(-cos(d*x+c)^2*b^2+a^2)/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticPi((-sin(d*x+c)+1)^(1/2),-b/((-a^2+b^2)^(1/2)-b),1/2*2^(1/2))-3/4/d*e^3*a^4/b^3/(b+(-a^2+b^2)^(1/2))/((-a^2+b^2)^(1/2)-b)/(-cos(d*x+c)^2*b^2+a^2)/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticPi((-sin(d*x+c)+1)^(1/2),b/(b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))*(-a^2+b^2)^(1/2)+3/4/d*e^3*a^2/b/(b+(-a^2+b^2)^(1/2))/((-a^2+b^2)^(1/2)-b)/(-cos(d*x+c)^2*b^2+a^2)/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticPi((-sin(d*x+c)+1)^(1/2),b/(b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))*(-a^2+b^2)^(1/2)+3/4/d*e^3*a^4/b^2/(b+(-a^2+b^2)^(1/2))/((-a^2+b^2)^(1/2)-b)/(-cos(d*x+c)^2*b^2+a^2)/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticPi((-sin(d*x+c)+1)^(1/2),b/(b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))-3/4/d*e^3*a^2/(b+(-a^2+b^2)^(1/2))/((-a^2+b^2)^(1/2)-b)/(-cos(d*x+c)^2*b^2+a^2)/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticPi((-sin(d*x+c)+1)^(1/2),b/(b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))+1/d*e^3*a^2/(b+(-a^2+b^2)^(1/2))/((-a^2+b^2)^(1/2)-b)/(-cos(d*x+c)^2*b^2+a^2)/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*sin(d*x+c)^2","B"
72,1,2148,449,1.556000," ","int((e*sin(d*x+c))^(3/2)/(a+b*cos(d*x+c))^2,x)","\frac{e^{3} a \sqrt{e \sin \left(d x +c \right)}}{d b \left(-b^{2} \left(\cos^{2}\left(d x +c \right)\right) e^{2}+a^{2} e^{2}\right)}-\frac{e^{3} a \left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{e \sin \left(d x +c \right)+\left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}\right)^{\frac{1}{4}} \sqrt{e \sin \left(d x +c \right)}\, \sqrt{2}+\sqrt{\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}}}{e \sin \left(d x +c \right)-\left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}\right)^{\frac{1}{4}} \sqrt{e \sin \left(d x +c \right)}\, \sqrt{2}+\sqrt{\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}}}\right)}{8 d b \left(a^{2} e^{2}-b^{2} e^{2}\right)}-\frac{e^{3} a \left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \sin \left(d x +c \right)}}{\left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}\right)^{\frac{1}{4}}}+1\right)}{4 d b \left(a^{2} e^{2}-b^{2} e^{2}\right)}-\frac{e^{3} a \left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \sin \left(d x +c \right)}}{\left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}\right)^{\frac{1}{4}}}-1\right)}{4 d b \left(a^{2} e^{2}-b^{2} e^{2}\right)}+\frac{e^{2} \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticF \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right)}{d \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, b^{2}}-\frac{3 e^{2} \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{1}{1-\frac{\sqrt{-a^{2}+b^{2}}}{b}}, \frac{\sqrt{2}}{2}\right) a^{2}}{2 d \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, b^{3} \sqrt{-a^{2}+b^{2}}\, \left(1-\frac{\sqrt{-a^{2}+b^{2}}}{b}\right)}+\frac{e^{2} \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{1}{1-\frac{\sqrt{-a^{2}+b^{2}}}{b}}, \frac{\sqrt{2}}{2}\right)}{2 d \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, \sqrt{-a^{2}+b^{2}}\, b \left(1-\frac{\sqrt{-a^{2}+b^{2}}}{b}\right)}+\frac{3 e^{2} \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{1}{1+\frac{\sqrt{-a^{2}+b^{2}}}{b}}, \frac{\sqrt{2}}{2}\right) a^{2}}{2 d \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, b^{3} \sqrt{-a^{2}+b^{2}}\, \left(1+\frac{\sqrt{-a^{2}+b^{2}}}{b}\right)}-\frac{e^{2} \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{1}{1+\frac{\sqrt{-a^{2}+b^{2}}}{b}}, \frac{\sqrt{2}}{2}\right)}{2 d \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, \sqrt{-a^{2}+b^{2}}\, b \left(1+\frac{\sqrt{-a^{2}+b^{2}}}{b}\right)}-\frac{e^{2} \sin \left(d x +c \right) \cos \left(d x +c \right) a^{2}}{d \sqrt{e \sin \left(d x +c \right)}\, \left(a^{2}-b^{2}\right) \left(-\left(\cos^{2}\left(d x +c \right)\right) b^{2}+a^{2}\right)}+\frac{e^{2} \sin \left(d x +c \right) \cos \left(d x +c \right) b^{2}}{d \sqrt{e \sin \left(d x +c \right)}\, \left(a^{2}-b^{2}\right) \left(-\left(\cos^{2}\left(d x +c \right)\right) b^{2}+a^{2}\right)}-\frac{e^{2} a^{2} \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticF \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right)}{2 d \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, b^{2} \left(a^{2}-b^{2}\right)}+\frac{e^{2} \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticF \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right)}{2 d \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, \left(a^{2}-b^{2}\right)}+\frac{5 e^{2} a^{4} \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{1}{1-\frac{\sqrt{-a^{2}+b^{2}}}{b}}, \frac{\sqrt{2}}{2}\right)}{4 d \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, b^{3} \left(a^{2}-b^{2}\right) \sqrt{-a^{2}+b^{2}}\, \left(1-\frac{\sqrt{-a^{2}+b^{2}}}{b}\right)}-\frac{7 e^{2} \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{1}{1-\frac{\sqrt{-a^{2}+b^{2}}}{b}}, \frac{\sqrt{2}}{2}\right) a^{2}}{4 d \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, \left(a^{2}-b^{2}\right) \sqrt{-a^{2}+b^{2}}\, b \left(1-\frac{\sqrt{-a^{2}+b^{2}}}{b}\right)}+\frac{e^{2} b \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{1}{1-\frac{\sqrt{-a^{2}+b^{2}}}{b}}, \frac{\sqrt{2}}{2}\right)}{2 d \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, \left(a^{2}-b^{2}\right) \sqrt{-a^{2}+b^{2}}\, \left(1-\frac{\sqrt{-a^{2}+b^{2}}}{b}\right)}-\frac{5 e^{2} a^{4} \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{1}{1+\frac{\sqrt{-a^{2}+b^{2}}}{b}}, \frac{\sqrt{2}}{2}\right)}{4 d \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, b^{3} \left(a^{2}-b^{2}\right) \sqrt{-a^{2}+b^{2}}\, \left(1+\frac{\sqrt{-a^{2}+b^{2}}}{b}\right)}+\frac{7 e^{2} \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{1}{1+\frac{\sqrt{-a^{2}+b^{2}}}{b}}, \frac{\sqrt{2}}{2}\right) a^{2}}{4 d \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, \left(a^{2}-b^{2}\right) \sqrt{-a^{2}+b^{2}}\, b \left(1+\frac{\sqrt{-a^{2}+b^{2}}}{b}\right)}-\frac{e^{2} b \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{1}{1+\frac{\sqrt{-a^{2}+b^{2}}}{b}}, \frac{\sqrt{2}}{2}\right)}{2 d \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, \left(a^{2}-b^{2}\right) \sqrt{-a^{2}+b^{2}}\, \left(1+\frac{\sqrt{-a^{2}+b^{2}}}{b}\right)}"," ",0,"1/d*e^3*a/b*(e*sin(d*x+c))^(1/2)/(-b^2*cos(d*x+c)^2*e^2+a^2*e^2)-1/8/d*e^3*a/b*(e^2*(a^2-b^2)/b^2)^(1/4)/(a^2*e^2-b^2*e^2)*2^(1/2)*ln((e*sin(d*x+c)+(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)*2^(1/2)+(e^2*(a^2-b^2)/b^2)^(1/2))/(e*sin(d*x+c)-(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)*2^(1/2)+(e^2*(a^2-b^2)/b^2)^(1/2)))-1/4/d*e^3*a/b*(e^2*(a^2-b^2)/b^2)^(1/4)/(a^2*e^2-b^2*e^2)*2^(1/2)*arctan(2^(1/2)/(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)+1)-1/4/d*e^3*a/b*(e^2*(a^2-b^2)/b^2)^(1/4)/(a^2*e^2-b^2*e^2)*2^(1/2)*arctan(2^(1/2)/(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)-1)+1/d*e^2/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/b^2*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))-3/2/d*e^2/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/b^3/(-a^2+b^2)^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1-(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1-(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))*a^2+1/2/d*e^2/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/(-a^2+b^2)^(1/2)/b*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1-(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1-(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))+3/2/d*e^2/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/b^3/(-a^2+b^2)^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1+(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1+(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))*a^2-1/2/d*e^2/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/(-a^2+b^2)^(1/2)/b*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1+(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1+(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))-1/d*e^2*sin(d*x+c)*cos(d*x+c)/(e*sin(d*x+c))^(1/2)*a^2/(a^2-b^2)/(-cos(d*x+c)^2*b^2+a^2)+1/d*e^2*sin(d*x+c)*cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^2/(a^2-b^2)/(-cos(d*x+c)^2*b^2+a^2)-1/2/d*e^2/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*a^2/b^2/(a^2-b^2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))+1/2/d*e^2/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/(a^2-b^2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))+5/4/d*e^2/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*a^4/b^3/(a^2-b^2)/(-a^2+b^2)^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1-(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1-(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))-7/4/d*e^2/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/(a^2-b^2)/(-a^2+b^2)^(1/2)/b*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1-(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1-(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))*a^2+1/2/d*e^2/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/(a^2-b^2)/(-a^2+b^2)^(1/2)*b*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1-(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1-(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))-5/4/d*e^2/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*a^4/b^3/(a^2-b^2)/(-a^2+b^2)^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1+(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1+(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))+7/4/d*e^2/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/(a^2-b^2)/(-a^2+b^2)^(1/2)/b*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1+(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1+(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))*a^2-1/2/d*e^2/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/(a^2-b^2)/(-a^2+b^2)^(1/2)*b*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1+(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1+(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))","B"
73,1,1384,471,1.210000," ","int((e*sin(d*x+c))^(1/2)/(a+b*cos(d*x+c))^2,x)","-\frac{e^{3} a b \left(e \sin \left(d x +c \right)\right)^{\frac{3}{2}}}{d \left(a^{2} e^{2}-b^{2} e^{2}\right) \left(-b^{2} \left(\cos^{2}\left(d x +c \right)\right) e^{2}+a^{2} e^{2}\right)}-\frac{e^{3} a \sqrt{2}\, \ln \left(\frac{e \sin \left(d x +c \right)-\left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}\right)^{\frac{1}{4}} \sqrt{e \sin \left(d x +c \right)}\, \sqrt{2}+\sqrt{\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}}}{e \sin \left(d x +c \right)+\left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}\right)^{\frac{1}{4}} \sqrt{e \sin \left(d x +c \right)}\, \sqrt{2}+\sqrt{\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}}}\right)}{8 d b \left(a^{2} e^{2}-b^{2} e^{2}\right) \left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}\right)^{\frac{1}{4}}}-\frac{e^{3} a \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \sin \left(d x +c \right)}}{\left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}\right)^{\frac{1}{4}}}+1\right)}{4 d b \left(a^{2} e^{2}-b^{2} e^{2}\right) \left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}\right)^{\frac{1}{4}}}-\frac{e^{3} a \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \sin \left(d x +c \right)}}{\left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}\right)^{\frac{1}{4}}}-1\right)}{4 d b \left(a^{2} e^{2}-b^{2} e^{2}\right) \left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}\right)^{\frac{1}{4}}}+\frac{e \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{1}{1-\frac{\sqrt{-a^{2}+b^{2}}}{b}}, \frac{\sqrt{2}}{2}\right)}{2 d \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, b^{2} \left(1-\frac{\sqrt{-a^{2}+b^{2}}}{b}\right)}+\frac{e \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{1}{1+\frac{\sqrt{-a^{2}+b^{2}}}{b}}, \frac{\sqrt{2}}{2}\right)}{2 d \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, b^{2} \left(1+\frac{\sqrt{-a^{2}+b^{2}}}{b}\right)}+\frac{e \left(\sin^{2}\left(d x +c \right)\right) \cos \left(d x +c \right) b^{2}}{d \sqrt{e \sin \left(d x +c \right)}\, \left(a^{2}-b^{2}\right) \left(-\left(\cos^{2}\left(d x +c \right)\right) b^{2}+a^{2}\right)}-\frac{e \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticE \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right)}{d \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, \left(a^{2}-b^{2}\right)}+\frac{e \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticF \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right)}{2 d \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, \left(a^{2}-b^{2}\right)}-\frac{3 e \,a^{2} \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{1}{1-\frac{\sqrt{-a^{2}+b^{2}}}{b}}, \frac{\sqrt{2}}{2}\right)}{4 d \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, \left(a^{2}-b^{2}\right) b^{2} \left(1-\frac{\sqrt{-a^{2}+b^{2}}}{b}\right)}+\frac{e \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{1}{1-\frac{\sqrt{-a^{2}+b^{2}}}{b}}, \frac{\sqrt{2}}{2}\right)}{2 d \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, \left(a^{2}-b^{2}\right) \left(1-\frac{\sqrt{-a^{2}+b^{2}}}{b}\right)}-\frac{3 e \,a^{2} \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{1}{1+\frac{\sqrt{-a^{2}+b^{2}}}{b}}, \frac{\sqrt{2}}{2}\right)}{4 d \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, \left(a^{2}-b^{2}\right) b^{2} \left(1+\frac{\sqrt{-a^{2}+b^{2}}}{b}\right)}+\frac{e \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{1}{1+\frac{\sqrt{-a^{2}+b^{2}}}{b}}, \frac{\sqrt{2}}{2}\right)}{2 d \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, \left(a^{2}-b^{2}\right) \left(1+\frac{\sqrt{-a^{2}+b^{2}}}{b}\right)}"," ",0,"-1/d*e^3*a*b*(e*sin(d*x+c))^(3/2)/(a^2*e^2-b^2*e^2)/(-b^2*cos(d*x+c)^2*e^2+a^2*e^2)-1/8/d*e^3*a/b/(a^2*e^2-b^2*e^2)/(e^2*(a^2-b^2)/b^2)^(1/4)*2^(1/2)*ln((e*sin(d*x+c)-(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)*2^(1/2)+(e^2*(a^2-b^2)/b^2)^(1/2))/(e*sin(d*x+c)+(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)*2^(1/2)+(e^2*(a^2-b^2)/b^2)^(1/2)))-1/4/d*e^3*a/b/(a^2*e^2-b^2*e^2)/(e^2*(a^2-b^2)/b^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)+1)-1/4/d*e^3*a/b/(a^2*e^2-b^2*e^2)/(e^2*(a^2-b^2)/b^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)-1)+1/2/d*e/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/b^2*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1-(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1-(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))+1/2/d*e/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/b^2*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1+(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1+(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))+1/d*e*sin(d*x+c)^2*cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^2/(a^2-b^2)/(-cos(d*x+c)^2*b^2+a^2)-1/d*e/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/(a^2-b^2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticE((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))+1/2/d*e/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/(a^2-b^2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))-3/4/d*e/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*a^2/(a^2-b^2)/b^2*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1-(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1-(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))+1/2/d*e/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/(a^2-b^2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1-(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1-(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))-3/4/d*e/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*a^2/(a^2-b^2)/b^2*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1+(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1+(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))+1/2/d*e/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/(a^2-b^2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1+(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1+(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))","B"
74,1,1351,476,1.256000," ","int(1/(a+b*cos(d*x+c))^2/(e*sin(d*x+c))^(1/2),x)","-\frac{a b \,e^{3} \sqrt{e \sin \left(d x +c \right)}}{d \left(a^{2} e^{2}-b^{2} e^{2}\right) \left(-b^{2} \left(\cos^{2}\left(d x +c \right)\right) e^{2}+a^{2} e^{2}\right)}-\frac{3 a b \,e^{3} \left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{e \sin \left(d x +c \right)+\left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}\right)^{\frac{1}{4}} \sqrt{e \sin \left(d x +c \right)}\, \sqrt{2}+\sqrt{\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}}}{e \sin \left(d x +c \right)-\left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}\right)^{\frac{1}{4}} \sqrt{e \sin \left(d x +c \right)}\, \sqrt{2}+\sqrt{\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}}}\right)}{8 d \left(a^{2} e^{2}-b^{2} e^{2}\right)^{2}}-\frac{3 a b \,e^{3} \left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \sin \left(d x +c \right)}}{\left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}\right)^{\frac{1}{4}}}+1\right)}{4 d \left(a^{2} e^{2}-b^{2} e^{2}\right)^{2}}-\frac{3 a b \,e^{3} \left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \sin \left(d x +c \right)}}{\left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}\right)^{\frac{1}{4}}}-1\right)}{4 d \left(a^{2} e^{2}-b^{2} e^{2}\right)^{2}}+\frac{\sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{1}{1-\frac{\sqrt{-a^{2}+b^{2}}}{b}}, \frac{\sqrt{2}}{2}\right)}{2 d \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, \sqrt{-a^{2}+b^{2}}\, b \left(1-\frac{\sqrt{-a^{2}+b^{2}}}{b}\right)}-\frac{\sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{1}{1+\frac{\sqrt{-a^{2}+b^{2}}}{b}}, \frac{\sqrt{2}}{2}\right)}{2 d \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, \sqrt{-a^{2}+b^{2}}\, b \left(1+\frac{\sqrt{-a^{2}+b^{2}}}{b}\right)}+\frac{\sin \left(d x +c \right) \cos \left(d x +c \right) b^{2}}{d \sqrt{e \sin \left(d x +c \right)}\, \left(a^{2}-b^{2}\right) \left(-\left(\cos^{2}\left(d x +c \right)\right) b^{2}+a^{2}\right)}+\frac{\sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticF \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right)}{2 d \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, \left(a^{2}-b^{2}\right)}-\frac{5 a^{2} \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{1}{1-\frac{\sqrt{-a^{2}+b^{2}}}{b}}, \frac{\sqrt{2}}{2}\right)}{4 d \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, \left(a^{2}-b^{2}\right) \sqrt{-a^{2}+b^{2}}\, b \left(1-\frac{\sqrt{-a^{2}+b^{2}}}{b}\right)}+\frac{b \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{1}{1-\frac{\sqrt{-a^{2}+b^{2}}}{b}}, \frac{\sqrt{2}}{2}\right)}{2 d \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, \left(a^{2}-b^{2}\right) \sqrt{-a^{2}+b^{2}}\, \left(1-\frac{\sqrt{-a^{2}+b^{2}}}{b}\right)}+\frac{5 a^{2} \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{1}{1+\frac{\sqrt{-a^{2}+b^{2}}}{b}}, \frac{\sqrt{2}}{2}\right)}{4 d \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, \left(a^{2}-b^{2}\right) \sqrt{-a^{2}+b^{2}}\, b \left(1+\frac{\sqrt{-a^{2}+b^{2}}}{b}\right)}-\frac{b \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{1}{1+\frac{\sqrt{-a^{2}+b^{2}}}{b}}, \frac{\sqrt{2}}{2}\right)}{2 d \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, \left(a^{2}-b^{2}\right) \sqrt{-a^{2}+b^{2}}\, \left(1+\frac{\sqrt{-a^{2}+b^{2}}}{b}\right)}"," ",0,"-1/d*a*b*e^3*(e*sin(d*x+c))^(1/2)/(a^2*e^2-b^2*e^2)/(-b^2*cos(d*x+c)^2*e^2+a^2*e^2)-3/8/d*a*b*e^3/(a^2*e^2-b^2*e^2)^2*(e^2*(a^2-b^2)/b^2)^(1/4)*2^(1/2)*ln((e*sin(d*x+c)+(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)*2^(1/2)+(e^2*(a^2-b^2)/b^2)^(1/2))/(e*sin(d*x+c)-(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)*2^(1/2)+(e^2*(a^2-b^2)/b^2)^(1/2)))-3/4/d*a*b*e^3/(a^2*e^2-b^2*e^2)^2*(e^2*(a^2-b^2)/b^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)+1)-3/4/d*a*b*e^3/(a^2*e^2-b^2*e^2)^2*(e^2*(a^2-b^2)/b^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)-1)+1/2/d/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/(-a^2+b^2)^(1/2)/b*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1-(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1-(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))-1/2/d/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/(-a^2+b^2)^(1/2)/b*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1+(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1+(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))+1/d*sin(d*x+c)*cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^2/(a^2-b^2)/(-cos(d*x+c)^2*b^2+a^2)+1/2/d/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/(a^2-b^2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))-5/4/d/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*a^2/(a^2-b^2)/(-a^2+b^2)^(1/2)/b*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1-(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1-(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))+1/2/d/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/(a^2-b^2)/(-a^2+b^2)^(1/2)*b*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1-(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1-(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))+5/4/d/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*a^2/(a^2-b^2)/(-a^2+b^2)^(1/2)/b*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1+(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1+(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))-1/2/d/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/(a^2-b^2)/(-a^2+b^2)^(1/2)*b*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1+(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1+(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))","B"
75,1,4318,536,1.132000," ","int(1/(a+b*cos(d*x+c))^2/(e*sin(d*x+c))^(3/2),x)","\text{output too large to display}"," ",0,"1/d/e*a*b^3/(a-b)^2/(a+b)^2*(e*sin(d*x+c))^(3/2)/(-b^2*cos(d*x+c)^2*e^2+a^2*e^2)+5/8/d/e*a*b/(a-b)^2/(a+b)^2/(e^2*(a^2-b^2)/b^2)^(1/4)*2^(1/2)*ln((e*sin(d*x+c)-(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)*2^(1/2)+(e^2*(a^2-b^2)/b^2)^(1/2))/(e*sin(d*x+c)+(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)*2^(1/2)+(e^2*(a^2-b^2)/b^2)^(1/2)))+5/4/d/e*a^2/(-cos(d*x+c)^2*b^2+a^2)/(a^2-b^2)^2/(b+(-a^2+b^2)^(1/2))/((-a^2+b^2)^(1/2)-b)/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticPi((-sin(d*x+c)+1)^(1/2),-b/((-a^2+b^2)^(1/2)-b),1/2*2^(1/2))*b^4-5/4/d/e*a^4/(-cos(d*x+c)^2*b^2+a^2)/(a^2-b^2)^2/(b+(-a^2+b^2)^(1/2))/((-a^2+b^2)^(1/2)-b)/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticPi((-sin(d*x+c)+1)^(1/2),b/(b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))*b^2+5/4/d/e*a^2/(-cos(d*x+c)^2*b^2+a^2)/(a^2-b^2)^2/(b+(-a^2+b^2)^(1/2))/((-a^2+b^2)^(1/2)-b)/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticPi((-sin(d*x+c)+1)^(1/2),b/(b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))*b^4-1/d/e*a^4/(-cos(d*x+c)^2*b^2+a^2)/(a^2-b^2)^2/(b+(-a^2+b^2)^(1/2))/((-a^2+b^2)^(1/2)-b)/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticE((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))*b^2+3/d/e*a^2/(-cos(d*x+c)^2*b^2+a^2)/(a^2-b^2)^2/(b+(-a^2+b^2)^(1/2))/((-a^2+b^2)^(1/2)-b)/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticE((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))*b^4-5/4/d/e*a^4/(-cos(d*x+c)^2*b^2+a^2)/(a^2-b^2)^2/(b+(-a^2+b^2)^(1/2))/((-a^2+b^2)^(1/2)-b)/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticPi((-sin(d*x+c)+1)^(1/2),-b/((-a^2+b^2)^(1/2)-b),1/2*2^(1/2))*b^2-3/d/e*a^2/(-cos(d*x+c)^2*b^2+a^2)/(a^2-b^2)^2/(b+(-a^2+b^2)^(1/2))/((-a^2+b^2)^(1/2)-b)/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(5/2)*EllipticE((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))*b^4+1/d/e*a^4/(-cos(d*x+c)^2*b^2+a^2)/(a^2-b^2)^2/(b+(-a^2+b^2)^(1/2))/((-a^2+b^2)^(1/2)-b)/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(5/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))*b^2+3/2/d/e*a^2/(-cos(d*x+c)^2*b^2+a^2)/(a^2-b^2)^2/(b+(-a^2+b^2)^(1/2))/((-a^2+b^2)^(1/2)-b)/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(5/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))*b^4-2/d/e*a^4/(-cos(d*x+c)^2*b^2+a^2)/(a^2-b^2)^2/(b+(-a^2+b^2)^(1/2))/((-a^2+b^2)^(1/2)-b)/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(5/2)*EllipticE((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))*b^2+1/2/d/e*a^4/(-cos(d*x+c)^2*b^2+a^2)/(a^2-b^2)^2/(b+(-a^2+b^2)^(1/2))/((-a^2+b^2)^(1/2)-b)/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^2*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))-3/2/d/e*a^2/(-cos(d*x+c)^2*b^2+a^2)/(a^2-b^2)^2/(b+(-a^2+b^2)^(1/2))/((-a^2+b^2)^(1/2)-b)/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^4*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))-5/4/d/e*a^2/(-cos(d*x+c)^2*b^2+a^2)/(a^2-b^2)^2/(b+(-a^2+b^2)^(1/2))/((-a^2+b^2)^(1/2)-b)/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(5/2)*EllipticPi((-sin(d*x+c)+1)^(1/2),-b/((-a^2+b^2)^(1/2)-b),1/2*2^(1/2))*b^4-5/4/d/e*a^2/(-cos(d*x+c)^2*b^2+a^2)/(a^2-b^2)^2/(b+(-a^2+b^2)^(1/2))/((-a^2+b^2)^(1/2)-b)/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(5/2)*EllipticPi((-sin(d*x+c)+1)^(1/2),b/(b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))*b^4+4/d/e*a*b/(a^2-b^2)^2/(e*sin(d*x+c))^(1/2)-5/4/d/e*a^2/(-cos(d*x+c)^2*b^2+a^2)/(a^2-b^2)^2/(b+(-a^2+b^2)^(1/2))/((-a^2+b^2)^(1/2)-b)/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticPi((-sin(d*x+c)+1)^(1/2),b/(b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))*(-a^2+b^2)^(1/2)*b^3-5/4/d/e*a^2/(-cos(d*x+c)^2*b^2+a^2)/(a^2-b^2)^2/(b+(-a^2+b^2)^(1/2))/((-a^2+b^2)^(1/2)-b)/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(5/2)*EllipticPi((-sin(d*x+c)+1)^(1/2),-b/((-a^2+b^2)^(1/2)-b),1/2*2^(1/2))*(-a^2+b^2)^(1/2)*b^3+5/4/d/e*a^2/(-cos(d*x+c)^2*b^2+a^2)/(a^2-b^2)^2/(b+(-a^2+b^2)^(1/2))/((-a^2+b^2)^(1/2)-b)/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(5/2)*EllipticPi((-sin(d*x+c)+1)^(1/2),b/(b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))*(-a^2+b^2)^(1/2)*b^3-5/4/d/e*a^4/(-cos(d*x+c)^2*b^2+a^2)/(a^2-b^2)^2/(b+(-a^2+b^2)^(1/2))/((-a^2+b^2)^(1/2)-b)/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticPi((-sin(d*x+c)+1)^(1/2),-b/((-a^2+b^2)^(1/2)-b),1/2*2^(1/2))*(-a^2+b^2)^(1/2)*b+5/4/d/e*a^2/(-cos(d*x+c)^2*b^2+a^2)/(a^2-b^2)^2/(b+(-a^2+b^2)^(1/2))/((-a^2+b^2)^(1/2)-b)/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticPi((-sin(d*x+c)+1)^(1/2),-b/((-a^2+b^2)^(1/2)-b),1/2*2^(1/2))*(-a^2+b^2)^(1/2)*b^3+5/4/d/e*a^4/(-cos(d*x+c)^2*b^2+a^2)/(a^2-b^2)^2/(b+(-a^2+b^2)^(1/2))/((-a^2+b^2)^(1/2)-b)/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticPi((-sin(d*x+c)+1)^(1/2),b/(b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))*(-a^2+b^2)^(1/2)*b-2/d/e*a^6/(-cos(d*x+c)^2*b^2+a^2)/(a^2-b^2)^2/(b+(-a^2+b^2)^(1/2))/((-a^2+b^2)^(1/2)-b)/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticE((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))+1/d/e*a^6/(-cos(d*x+c)^2*b^2+a^2)/(a^2-b^2)^2/(b+(-a^2+b^2)^(1/2))/((-a^2+b^2)^(1/2)-b)/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))+5/4/d/e*a*b/(a-b)^2/(a+b)^2/(e^2*(a^2-b^2)/b^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)-1)+2/d/e*a^6/(-cos(d*x+c)^2*b^2+a^2)/(a^2-b^2)^2/(b+(-a^2+b^2)^(1/2))/((-a^2+b^2)^(1/2)-b)*cos(d*x+c)/(e*sin(d*x+c))^(1/2)+5/4/d/e*a*b/(a-b)^2/(a+b)^2/(e^2*(a^2-b^2)/b^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)+1)-3/d/e*a^2/(-cos(d*x+c)^2*b^2+a^2)/(a^2-b^2)^2/(b+(-a^2+b^2)^(1/2))/((-a^2+b^2)^(1/2)-b)*cos(d*x+c)^3/(e*sin(d*x+c))^(1/2)*b^4+2/d/e*a^4/(-cos(d*x+c)^2*b^2+a^2)/(a^2-b^2)^2/(b+(-a^2+b^2)^(1/2))/((-a^2+b^2)^(1/2)-b)*cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^2+1/d/e*a^2/(-cos(d*x+c)^2*b^2+a^2)/(a^2-b^2)^2/(b+(-a^2+b^2)^(1/2))/((-a^2+b^2)^(1/2)-b)*cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^4-2/d/e*a^4/(-cos(d*x+c)^2*b^2+a^2)/(a^2-b^2)^2/(b+(-a^2+b^2)^(1/2))/((-a^2+b^2)^(1/2)-b)*cos(d*x+c)^3/(e*sin(d*x+c))^(1/2)*b^2","B"
76,1,2143,556,1.671000," ","int(1/(a+b*cos(d*x+c))^2/(e*sin(d*x+c))^(5/2),x)","\frac{a \,b^{3} \sqrt{e \sin \left(d x +c \right)}}{d e \left(a -b \right)^{2} \left(a +b \right)^{2} \left(-b^{2} \left(\cos^{2}\left(d x +c \right)\right) e^{2}+a^{2} e^{2}\right)}+\frac{7 a \,b^{3} \left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{e \sin \left(d x +c \right)+\left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}\right)^{\frac{1}{4}} \sqrt{e \sin \left(d x +c \right)}\, \sqrt{2}+\sqrt{\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}}}{e \sin \left(d x +c \right)-\left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}\right)^{\frac{1}{4}} \sqrt{e \sin \left(d x +c \right)}\, \sqrt{2}+\sqrt{\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}}}\right)}{8 d e \left(a -b \right)^{2} \left(a +b \right)^{2} \left(a^{2} e^{2}-b^{2} e^{2}\right)}+\frac{7 a \,b^{3} \left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \sin \left(d x +c \right)}}{\left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}\right)^{\frac{1}{4}}}+1\right)}{4 d e \left(a -b \right)^{2} \left(a +b \right)^{2} \left(a^{2} e^{2}-b^{2} e^{2}\right)}+\frac{7 a \,b^{3} \left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{e \sin \left(d x +c \right)}}{\left(\frac{e^{2} \left(a^{2}-b^{2}\right)}{b^{2}}\right)^{\frac{1}{4}}}-1\right)}{4 d e \left(a -b \right)^{2} \left(a +b \right)^{2} \left(a^{2} e^{2}-b^{2} e^{2}\right)}+\frac{4 a b}{3 d e \left(a^{2}-b^{2}\right)^{2} \left(e \sin \left(d x +c \right)\right)^{\frac{3}{2}}}+\frac{b \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{1}{1-\frac{\sqrt{-a^{2}+b^{2}}}{b}}, \frac{\sqrt{2}}{2}\right) a^{2}}{2 d \,e^{2} \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, \left(a -b \right)^{2} \left(a +b \right)^{2} \sqrt{-a^{2}+b^{2}}\, \left(1-\frac{\sqrt{-a^{2}+b^{2}}}{b}\right)}+\frac{b^{3} \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{1}{1-\frac{\sqrt{-a^{2}+b^{2}}}{b}}, \frac{\sqrt{2}}{2}\right)}{2 d \,e^{2} \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, \left(a -b \right)^{2} \left(a +b \right)^{2} \sqrt{-a^{2}+b^{2}}\, \left(1-\frac{\sqrt{-a^{2}+b^{2}}}{b}\right)}-\frac{b \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{1}{1+\frac{\sqrt{-a^{2}+b^{2}}}{b}}, \frac{\sqrt{2}}{2}\right) a^{2}}{2 d \,e^{2} \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, \left(a -b \right)^{2} \left(a +b \right)^{2} \sqrt{-a^{2}+b^{2}}\, \left(1+\frac{\sqrt{-a^{2}+b^{2}}}{b}\right)}-\frac{b^{3} \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{1}{1+\frac{\sqrt{-a^{2}+b^{2}}}{b}}, \frac{\sqrt{2}}{2}\right)}{2 d \,e^{2} \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, \left(a -b \right)^{2} \left(a +b \right)^{2} \sqrt{-a^{2}+b^{2}}\, \left(1+\frac{\sqrt{-a^{2}+b^{2}}}{b}\right)}-\frac{\sin \left(d x +c \right) \cos \left(d x +c \right) b^{4}}{d \,e^{2} \sqrt{e \sin \left(d x +c \right)}\, \left(a -b \right) \left(a +b \right) \left(a^{2}-b^{2}\right) \left(-\left(\cos^{2}\left(d x +c \right)\right) b^{2}+a^{2}\right)}-\frac{b^{2} \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticF \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right)}{2 d \,e^{2} \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, \left(a -b \right) \left(a +b \right) \left(a^{2}-b^{2}\right)}+\frac{5 a^{2} b \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{1}{1-\frac{\sqrt{-a^{2}+b^{2}}}{b}}, \frac{\sqrt{2}}{2}\right)}{4 d \,e^{2} \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, \left(a -b \right) \left(a +b \right) \left(a^{2}-b^{2}\right) \sqrt{-a^{2}+b^{2}}\, \left(1-\frac{\sqrt{-a^{2}+b^{2}}}{b}\right)}-\frac{b^{3} \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{1}{1-\frac{\sqrt{-a^{2}+b^{2}}}{b}}, \frac{\sqrt{2}}{2}\right)}{2 d \,e^{2} \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, \left(a -b \right) \left(a +b \right) \left(a^{2}-b^{2}\right) \sqrt{-a^{2}+b^{2}}\, \left(1-\frac{\sqrt{-a^{2}+b^{2}}}{b}\right)}-\frac{5 a^{2} b \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{1}{1+\frac{\sqrt{-a^{2}+b^{2}}}{b}}, \frac{\sqrt{2}}{2}\right)}{4 d \,e^{2} \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, \left(a -b \right) \left(a +b \right) \left(a^{2}-b^{2}\right) \sqrt{-a^{2}+b^{2}}\, \left(1+\frac{\sqrt{-a^{2}+b^{2}}}{b}\right)}+\frac{b^{3} \sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sqrt{\sin}\left(d x +c \right)\right) \EllipticPi \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{1}{1+\frac{\sqrt{-a^{2}+b^{2}}}{b}}, \frac{\sqrt{2}}{2}\right)}{2 d \,e^{2} \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, \left(a -b \right) \left(a +b \right) \left(a^{2}-b^{2}\right) \sqrt{-a^{2}+b^{2}}\, \left(1+\frac{\sqrt{-a^{2}+b^{2}}}{b}\right)}+\frac{\sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sin^{\frac{5}{2}}\left(d x +c \right)\right) \EllipticF \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right) a^{2}}{3 d \,e^{2} \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, \left(a^{2}-b^{2}\right)^{2} \left(\cos^{2}\left(d x +c \right)-1\right)}+\frac{\sqrt{-\sin \left(d x +c \right)+1}\, \sqrt{2 \sin \left(d x +c \right)+2}\, \left(\sin^{\frac{5}{2}}\left(d x +c \right)\right) \EllipticF \left(\sqrt{-\sin \left(d x +c \right)+1}, \frac{\sqrt{2}}{2}\right) b^{2}}{3 d \,e^{2} \cos \left(d x +c \right) \sqrt{e \sin \left(d x +c \right)}\, \left(a^{2}-b^{2}\right)^{2} \left(\cos^{2}\left(d x +c \right)-1\right)}+\frac{2 \cos \left(d x +c \right) \sin \left(d x +c \right) a^{2}}{3 d \,e^{2} \sqrt{e \sin \left(d x +c \right)}\, \left(a^{2}-b^{2}\right)^{2} \left(\cos^{2}\left(d x +c \right)-1\right)}+\frac{2 \cos \left(d x +c \right) \sin \left(d x +c \right) b^{2}}{3 d \,e^{2} \sqrt{e \sin \left(d x +c \right)}\, \left(a^{2}-b^{2}\right)^{2} \left(\cos^{2}\left(d x +c \right)-1\right)}"," ",0,"1/d/e*a*b^3/(a-b)^2/(a+b)^2*(e*sin(d*x+c))^(1/2)/(-b^2*cos(d*x+c)^2*e^2+a^2*e^2)+7/8/d/e*a*b^3/(a-b)^2/(a+b)^2*(e^2*(a^2-b^2)/b^2)^(1/4)/(a^2*e^2-b^2*e^2)*2^(1/2)*ln((e*sin(d*x+c)+(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)*2^(1/2)+(e^2*(a^2-b^2)/b^2)^(1/2))/(e*sin(d*x+c)-(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)*2^(1/2)+(e^2*(a^2-b^2)/b^2)^(1/2)))+7/4/d/e*a*b^3/(a-b)^2/(a+b)^2*(e^2*(a^2-b^2)/b^2)^(1/4)/(a^2*e^2-b^2*e^2)*2^(1/2)*arctan(2^(1/2)/(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)+1)+7/4/d/e*a*b^3/(a-b)^2/(a+b)^2*(e^2*(a^2-b^2)/b^2)^(1/4)/(a^2*e^2-b^2*e^2)*2^(1/2)*arctan(2^(1/2)/(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)-1)+4/3/d/e*a*b/(a^2-b^2)^2/(e*sin(d*x+c))^(3/2)+1/2/d/e^2/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b/(a-b)^2/(a+b)^2/(-a^2+b^2)^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1-(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1-(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))*a^2+1/2/d/e^2/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^3/(a-b)^2/(a+b)^2/(-a^2+b^2)^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1-(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1-(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))-1/2/d/e^2/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b/(a-b)^2/(a+b)^2/(-a^2+b^2)^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1+(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1+(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))*a^2-1/2/d/e^2/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^3/(a-b)^2/(a+b)^2/(-a^2+b^2)^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1+(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1+(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))-1/d/e^2*sin(d*x+c)*cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^4/(a-b)/(a+b)/(a^2-b^2)/(-cos(d*x+c)^2*b^2+a^2)-1/2/d/e^2/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^2/(a-b)/(a+b)/(a^2-b^2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))+5/4/d/e^2/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*a^2*b/(a-b)/(a+b)/(a^2-b^2)/(-a^2+b^2)^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1-(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1-(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))-1/2/d/e^2/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^3/(a-b)/(a+b)/(a^2-b^2)/(-a^2+b^2)^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1-(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1-(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))-5/4/d/e^2/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*a^2*b/(a-b)/(a+b)/(a^2-b^2)/(-a^2+b^2)^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1+(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1+(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))+1/2/d/e^2/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^3/(a-b)/(a+b)/(a^2-b^2)/(-a^2+b^2)^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1+(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1+(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))+1/3/d/e^2/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/(a^2-b^2)^2/(cos(d*x+c)^2-1)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(5/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))*a^2+1/3/d/e^2/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/(a^2-b^2)^2/(cos(d*x+c)^2-1)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(5/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))*b^2+2/3/d/e^2*cos(d*x+c)/(e*sin(d*x+c))^(1/2)/(a^2-b^2)^2/(cos(d*x+c)^2-1)*sin(d*x+c)*a^2+2/3/d/e^2*cos(d*x+c)/(e*sin(d*x+c))^(1/2)/(a^2-b^2)^2/(cos(d*x+c)^2-1)*sin(d*x+c)*b^2","B"
77,1,2888,612,2.082000," ","int(1/(a+b*cos(d*x+c))^2/(e*sin(d*x+c))^(7/2),x)","\text{output too large to display}"," ",0,"6/d/e^3*cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^2/(a^2-b^2)^3*a^2-6/5/d/e^3*cos(d*x+c)^3/(e*sin(d*x+c))^(1/2)/(a^2-b^2)^2/(cos(d*x+c)^2-1)*a^2-6/5/d/e^3*cos(d*x+c)^3/(e*sin(d*x+c))^(1/2)/(a^2-b^2)^2/(cos(d*x+c)^2-1)*b^2+8/5/d/e^3*cos(d*x+c)/(e*sin(d*x+c))^(1/2)/(a^2-b^2)^2/(cos(d*x+c)^2-1)*a^2+8/5/d/e^3*cos(d*x+c)/(e*sin(d*x+c))^(1/2)/(a^2-b^2)^2/(cos(d*x+c)^2-1)*b^2+4/5/d/e*a*b/(a+b)^2/(a-b)^2/(e*sin(d*x+c))^(5/2)-8/d/e^3*a*b^3/(a-b)^3/(a+b)^3/(e*sin(d*x+c))^(1/2)-3/4/d/e^3/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*a^2*b^2/(a-b)^2/(a+b)^2/(a^2-b^2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1-(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1-(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))-3/4/d/e^3/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*a^2*b^2/(a-b)^2/(a+b)^2/(a^2-b^2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1+(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1+(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))-6/d/e^3/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^2/(a^2-b^2)^3*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticE((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))*a^2+3/d/e^3/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^2/(a^2-b^2)^3*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))*a^2+3/5/d/e^3/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/(a^2-b^2)^2*sin(d*x+c)^(5/2)/(cos(d*x+c)^2-1)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))*b^2-1/2/d/e^3/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^4/(a-b)^3/(a+b)^3*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1-(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1-(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))-1/2/d/e^3/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^4/(a-b)^3/(a+b)^3*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1+(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1+(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))-1/d/e^3/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^4/(a-b)^2/(a+b)^2/(a^2-b^2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticE((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))+1/2/d/e^3/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^4/(a-b)^2/(a+b)^2/(a^2-b^2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))+1/2/d/e^3/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^4/(a-b)^2/(a+b)^2/(a^2-b^2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1-(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1-(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))+1/2/d/e^3/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^4/(a-b)^2/(a+b)^2/(a^2-b^2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1+(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1+(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))-3/2/d/e^3/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^2/(a-b)^3/(a+b)^3*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1-(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1-(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))*a^2-3/2/d/e^3/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^2/(a-b)^3/(a+b)^3*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1+(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1+(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))*a^2-6/5/d/e^3/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/(a^2-b^2)^2*sin(d*x+c)^(5/2)/(cos(d*x+c)^2-1)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*EllipticE((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))*a^2-6/5/d/e^3/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/(a^2-b^2)^2*sin(d*x+c)^(5/2)/(cos(d*x+c)^2-1)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*EllipticE((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))*b^2+3/5/d/e^3/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/(a^2-b^2)^2*sin(d*x+c)^(5/2)/(cos(d*x+c)^2-1)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))*a^2-1/d/e^3*a*b^5/(a-b)^3/(a+b)^3*(e*sin(d*x+c))^(3/2)/(-b^2*cos(d*x+c)^2*e^2+a^2*e^2)+2/d/e^3*cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^4/(a^2-b^2)^3-9/4/d/e^3*a*b^3/(a-b)^3/(a+b)^3/(e^2*(a^2-b^2)/b^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)+1)-9/4/d/e^3*a*b^3/(a-b)^3/(a+b)^3/(e^2*(a^2-b^2)/b^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)-1)-9/8/d/e^3*a*b^3/(a-b)^3/(a+b)^3/(e^2*(a^2-b^2)/b^2)^(1/4)*2^(1/2)*ln((e*sin(d*x+c)-(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)*2^(1/2)+(e^2*(a^2-b^2)/b^2)^(1/2))/(e*sin(d*x+c)+(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)*2^(1/2)+(e^2*(a^2-b^2)/b^2)^(1/2)))+1/d/e^3*sin(d*x+c)^2*cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^6/(a-b)^2/(a+b)^2/(a^2-b^2)/(-cos(d*x+c)^2*b^2+a^2)-2/d/e^3/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^4/(a^2-b^2)^3*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticE((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))+1/d/e^3/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^4/(a^2-b^2)^3*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))","B"
78,1,7803,607,2.882000," ","int((e*sin(d*x+c))^(13/2)/(a+b*cos(d*x+c))^3,x)","\text{output too large to display}"," ",0,"result too large to display","B"
79,1,7238,621,2.677000," ","int((e*sin(d*x+c))^(11/2)/(a+b*cos(d*x+c))^3,x)","\text{output too large to display}"," ",0,"result too large to display","B"
80,1,5791,522,2.385000," ","int((e*sin(d*x+c))^(9/2)/(a+b*cos(d*x+c))^3,x)","\text{output too large to display}"," ",0,"result too large to display","B"
81,1,5404,536,2.458000," ","int((e*sin(d*x+c))^(7/2)/(a+b*cos(d*x+c))^3,x)","\text{output too large to display}"," ",0,"result too large to display","B"
82,1,4303,544,2.227000," ","int((e*sin(d*x+c))^(5/2)/(a+b*cos(d*x+c))^3,x)","\text{output too large to display}"," ",0,"23/8/d*e^3*a/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/(a^2-b^2)/b^2*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1+(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1+(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))-3/8/d*e^3/b/(a^2-b^2)/(e^2*(a^2-b^2)/b^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)+1)-3/8/d*e^3/b/(a^2-b^2)/(e^2*(a^2-b^2)/b^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)-1)-3/16/d*e^3/b/(a^2-b^2)/(e^2*(a^2-b^2)/b^2)^(1/4)*2^(1/2)*ln((e*sin(d*x+c)-(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)*2^(1/2)+(e^2*(a^2-b^2)/b^2)^(1/2))/(e*sin(d*x+c)+(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)*2^(1/2)+(e^2*(a^2-b^2)/b^2)^(1/2)))-5/4/d*e^3*b/(-b^2*cos(d*x+c)^2*e^2+a^2*e^2)^2/(a^2-b^2)*(e*sin(d*x+c))^(7/2)*a^2-3/2/d*e^3*sin(d*x+c)^2*cos(d*x+c)/a/(e*sin(d*x+c))^(1/2)*b^2/(a^2-b^2)/(-cos(d*x+c)^2*b^2+a^2)+1/d*e^3*sin(d*x+c)^2*cos(d*x+c)*a/(e*sin(d*x+c))^(1/2)*b^2/(a^2-b^2)/(-cos(d*x+c)^2*b^2+a^2)^2+17/4/d*e^3*sin(d*x+c)^2*cos(d*x+c)*a/(e*sin(d*x+c))^(1/2)*b^2/(a^2-b^2)^2/(-cos(d*x+c)^2*b^2+a^2)-3/2/d*e^3*sin(d*x+c)^2*cos(d*x+c)/a/(e*sin(d*x+c))^(1/2)*b^4/(a^2-b^2)^2/(-cos(d*x+c)^2*b^2+a^2)+3/2/d*e^3/a/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/(a^2-b^2)^2*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticE((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))*b^2-3/4/d*e^3/a/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/(a^2-b^2)^2*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))*b^2+5/2/d*e^3*a/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/(a^2-b^2)^2*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1-(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1-(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))+5/2/d*e^3*a/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/(a^2-b^2)^2*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1+(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1+(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))+11/4/d*e^3*a^3/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/b^2/(a^2-b^2)^2*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticE((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))-3/4/d*e^3/a/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/(a^2-b^2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1-(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1-(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))-3/4/d*e^3/a/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/(a^2-b^2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1+(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1+(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))-49/16/d*e^3*a^3/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/(a^2-b^2)^2/b^2*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1-(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1-(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))-3/4/d*e^3/a/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/(a^2-b^2)^2*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1-(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1-(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))*b^2+23/8/d*e^3*a/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/(a^2-b^2)/b^2*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1-(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1-(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))-49/16/d*e^3*a^3/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/(a^2-b^2)^2/b^2*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1+(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1+(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))-3/4/d*e^3/a/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/(a^2-b^2)^2*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1+(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1+(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))*b^2+1/2/d*e^5*b/(-b^2*cos(d*x+c)^2*e^2+a^2*e^2)^2*(e*sin(d*x+c))^(3/2)-11/8/d*e^3*a^3/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/b^2/(a^2-b^2)^2*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))+3/2/d*e^3*a/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/b^4*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1-(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1-(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))+3/2/d*e^3*a/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/b^4*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1+(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1+(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))-7/2/d*e^3*a/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/b^2/(a^2-b^2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticE((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))+7/4/d*e^3*a/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/b^2/(a^2-b^2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))+21/16/d*e^3*a^5/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/b^4/(a^2-b^2)^2*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1+(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1+(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))+21/16/d*e^3*a^5/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/b^4/(a^2-b^2)^2*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1-(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1-(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))-21/8/d*e^3*a^3/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/b^4/(a^2-b^2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1-(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1-(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))-21/8/d*e^3*a^3/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/b^4/(a^2-b^2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1+(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1+(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))-1/d*e^3*sin(d*x+c)^2*cos(d*x+c)*a^3/(e*sin(d*x+c))^(1/2)/(a^2-b^2)/(-cos(d*x+c)^2*b^2+a^2)^2+7/2/d*e^3*sin(d*x+c)^2*cos(d*x+c)*a/(e*sin(d*x+c))^(1/2)/(a^2-b^2)/(-cos(d*x+c)^2*b^2+a^2)-11/4/d*e^3*sin(d*x+c)^2*cos(d*x+c)*a^3/(e*sin(d*x+c))^(1/2)/(a^2-b^2)^2/(-cos(d*x+c)^2*b^2+a^2)+3/16/d*e^3/b^3/(a^2-b^2)/(e^2*(a^2-b^2)/b^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)+1)*a^2+3/16/d*e^3/b^3/(a^2-b^2)/(e^2*(a^2-b^2)/b^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)-1)*a^2+3/32/d*e^3/b^3/(a^2-b^2)/(e^2*(a^2-b^2)/b^2)^(1/4)*2^(1/2)*ln((e*sin(d*x+c)-(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)*2^(1/2)+(e^2*(a^2-b^2)/b^2)^(1/2))/(e*sin(d*x+c)+(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)*2^(1/2)+(e^2*(a^2-b^2)/b^2)^(1/2)))*a^2+3/2/d*e^3/a/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/(a^2-b^2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticE((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))-3/4/d*e^3/a/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/(a^2-b^2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))-17/4/d*e^3*a/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/(a^2-b^2)^2*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticE((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))+17/8/d*e^3*a/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/(a^2-b^2)^2*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))-1/4/d*e^5/b/(-b^2*cos(d*x+c)^2*e^2+a^2*e^2)^2*(e*sin(d*x+c))^(3/2)*a^2+1/2/d*e^3*b^3/(-b^2*cos(d*x+c)^2*e^2+a^2*e^2)^2/(a^2-b^2)*(e*sin(d*x+c))^(7/2)","B"
83,1,4116,558,2.240000," ","int((e*sin(d*x+c))^(3/2)/(a+b*cos(d*x+c))^3,x)","\text{output too large to display}"," ",0,"-35/8/d*e^2*a^3/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/b^3/(a^2-b^2)/(-a^2+b^2)^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1-(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1-(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))-3/4/d*e^2/a/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/(a^2-b^2)/(-a^2+b^2)^(1/2)*b*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1-(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1-(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))+3/4/d*e^2/a/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/(a^2-b^2)/(-a^2+b^2)^(1/2)*b*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1+(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1+(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))-81/16/d*e^2*a^3/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/(a^2-b^2)^2/(-a^2+b^2)^(1/2)/b*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1-(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1-(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))-3/4/d*e^2/a/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/(a^2-b^2)^2/(-a^2+b^2)^(1/2)*b^3*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1-(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1-(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))+29/8/d*e^2*a/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/(a^2-b^2)/(-a^2+b^2)^(1/2)/b*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1-(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1-(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))-29/8/d*e^2*a/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/(a^2-b^2)/(-a^2+b^2)^(1/2)/b*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1+(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1+(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))+3/d*e^2*a/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/(a^2-b^2)^2/(-a^2+b^2)^(1/2)*b*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1-(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1-(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))-3/4/d*e^2/a/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/(a^2-b^2)^2*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))*b^2-13/8/d*e^2*a^3/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/b^2/(a^2-b^2)^2*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))+7/4/d*e^2*a/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/b^2/(a^2-b^2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))-3/2/d*e^2*a/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/b^3/(-a^2+b^2)^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1+(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1+(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))+3/2/d*e^2*a/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/b^3/(-a^2+b^2)^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1-(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1-(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))-3/4/d*e^2/a/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/(a^2-b^2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))+19/8/d*e^2*a/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/(a^2-b^2)^2*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))-3/d*e^2*a/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/(a^2-b^2)^2/(-a^2+b^2)^(1/2)*b*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1+(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1+(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))+35/8/d*e^2*a^3/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/b^3/(a^2-b^2)/(-a^2+b^2)^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1+(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1+(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))+81/16/d*e^2*a^3/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/(a^2-b^2)^2/(-a^2+b^2)^(1/2)/b*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1+(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1+(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))+3/4/d*e^2/a/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/(a^2-b^2)^2/(-a^2+b^2)^(1/2)*b^3*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1+(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1+(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))+45/16/d*e^2*a^5/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/b^3/(a^2-b^2)^2/(-a^2+b^2)^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1-(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1-(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))-45/16/d*e^2*a^5/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/b^3/(a^2-b^2)^2/(-a^2+b^2)^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1+(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1+(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))+1/2/d*e^5*b/(-b^2*cos(d*x+c)^2*e^2+a^2*e^2)^2*(e*sin(d*x+c))^(1/2)+7/2/d*e^2*sin(d*x+c)*cos(d*x+c)*a/(e*sin(d*x+c))^(1/2)/(a^2-b^2)/(-cos(d*x+c)^2*b^2+a^2)-1/d*e^2*sin(d*x+c)*cos(d*x+c)*a^3/(e*sin(d*x+c))^(1/2)/(a^2-b^2)/(-cos(d*x+c)^2*b^2+a^2)^2-13/4/d*e^2*sin(d*x+c)*cos(d*x+c)*a^3/(e*sin(d*x+c))^(1/2)/(a^2-b^2)^2/(-cos(d*x+c)^2*b^2+a^2)-1/8/d*e^3*b/(a^2-b^2)*(e^2*(a^2-b^2)/b^2)^(1/4)/(a^2*e^2-b^2*e^2)*2^(1/2)*arctan(2^(1/2)/(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)+1)-1/8/d*e^3*b/(a^2-b^2)*(e^2*(a^2-b^2)/b^2)^(1/4)/(a^2*e^2-b^2*e^2)*2^(1/2)*arctan(2^(1/2)/(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)-1)-1/16/d*e^3*b/(a^2-b^2)*(e^2*(a^2-b^2)/b^2)^(1/4)/(a^2*e^2-b^2*e^2)*2^(1/2)*ln((e*sin(d*x+c)+(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)*2^(1/2)+(e^2*(a^2-b^2)/b^2)^(1/2))/(e*sin(d*x+c)-(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)*2^(1/2)+(e^2*(a^2-b^2)/b^2)^(1/2)))-3/4/d*e^3*b/(-b^2*cos(d*x+c)^2*e^2+a^2*e^2)^2/(a^2-b^2)*(e*sin(d*x+c))^(5/2)*a^2+1/2/d*e^3*b^3/(-b^2*cos(d*x+c)^2*e^2+a^2*e^2)^2/(a^2-b^2)*(e*sin(d*x+c))^(5/2)+1/4/d*e^5/b/(-b^2*cos(d*x+c)^2*e^2+a^2*e^2)^2*(e*sin(d*x+c))^(1/2)*a^2-3/2/d*e^2*sin(d*x+c)*cos(d*x+c)/a/(e*sin(d*x+c))^(1/2)*b^2/(a^2-b^2)/(-cos(d*x+c)^2*b^2+a^2)+1/d*e^2*sin(d*x+c)*cos(d*x+c)*a/(e*sin(d*x+c))^(1/2)*b^2/(a^2-b^2)/(-cos(d*x+c)^2*b^2+a^2)^2+19/4/d*e^2*sin(d*x+c)*cos(d*x+c)*a/(e*sin(d*x+c))^(1/2)*b^2/(a^2-b^2)^2/(-cos(d*x+c)^2*b^2+a^2)-3/2/d*e^2*sin(d*x+c)*cos(d*x+c)/a/(e*sin(d*x+c))^(1/2)*b^4/(a^2-b^2)^2/(-cos(d*x+c)^2*b^2+a^2)-1/16/d*e^3/b/(a^2-b^2)*(e^2*(a^2-b^2)/b^2)^(1/4)/(a^2*e^2-b^2*e^2)*2^(1/2)*arctan(2^(1/2)/(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)-1)*a^2-1/32/d*e^3/b/(a^2-b^2)*(e^2*(a^2-b^2)/b^2)^(1/4)/(a^2*e^2-b^2*e^2)*2^(1/2)*ln((e*sin(d*x+c)+(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)*2^(1/2)+(e^2*(a^2-b^2)/b^2)^(1/2))/(e*sin(d*x+c)-(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)*2^(1/2)+(e^2*(a^2-b^2)/b^2)^(1/2)))*a^2-1/16/d*e^3/b/(a^2-b^2)*(e^2*(a^2-b^2)/b^2)^(1/4)/(a^2*e^2-b^2*e^2)*2^(1/2)*arctan(2^(1/2)/(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)+1)*a^2","B"
84,1,2986,553,1.947000," ","int((e*sin(d*x+c))^(1/2)/(a+b*cos(d*x+c))^3,x)","\text{output too large to display}"," ",0,"3/2/d*e/a/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/(a^2-b^2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticE((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))-3/4/d*e/a/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/(a^2-b^2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))-11/4/d*e*a/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/(a^2-b^2)^2*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticE((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))+11/8/d*e*a/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/(a^2-b^2)^2*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))+3/2/d*e/a/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/(a^2-b^2)^2*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticE((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))*b^2-3/4/d*e/a/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/(a^2-b^2)^2*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))*b^2+7/4/d*e*a/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/(a^2-b^2)^2*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1-(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1-(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))+7/4/d*e*a/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/(a^2-b^2)^2*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1+(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1+(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))-3/4/d*e/a/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/(a^2-b^2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1-(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1-(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))-3/4/d*e/a/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/(a^2-b^2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1+(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1+(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))-1/8/d*e*b/(a^4-2*a^2*b^2+b^4)/(e^2*(a^2-b^2)/b^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)+1)-1/8/d*e*b/(a^4-2*a^2*b^2+b^4)/(e^2*(a^2-b^2)/b^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)-1)-1/16/d*e*b/(a^4-2*a^2*b^2+b^4)/(e^2*(a^2-b^2)/b^2)^(1/4)*2^(1/2)*ln((e*sin(d*x+c)-(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)*2^(1/2)+(e^2*(a^2-b^2)/b^2)^(1/2))/(e*sin(d*x+c)+(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)*2^(1/2)+(e^2*(a^2-b^2)/b^2)^(1/2)))-3/4/d*e*b^3/(-b^2*cos(d*x+c)^2*e^2+a^2*e^2)^2/(a^4-2*a^2*b^2+b^4)*(e*sin(d*x+c))^(7/2)*a^2-7/4/d*e^3*b/(-b^2*cos(d*x+c)^2*e^2+a^2*e^2)^2/(a^2-b^2)*(e*sin(d*x+c))^(3/2)*a^2-3/4/d*e/a/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/(a^2-b^2)^2*b^2*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1+(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1+(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))+9/8/d*e*a/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/(a^2-b^2)/b^2*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1-(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1-(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))+9/8/d*e*a/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/(a^2-b^2)/b^2*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1+(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1+(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))-21/16/d*e*a^3/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/(a^2-b^2)^2/b^2*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1-(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1-(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))-3/4/d*e/a/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/(a^2-b^2)^2*b^2*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1-(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1-(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))-21/16/d*e*a^3/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/(a^2-b^2)^2/b^2*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1+(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1+(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))-3/16/d*e/b/(a^4-2*a^2*b^2+b^4)/(e^2*(a^2-b^2)/b^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)+1)*a^2-3/16/d*e/b/(a^4-2*a^2*b^2+b^4)/(e^2*(a^2-b^2)/b^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)-1)*a^2-3/32/d*e/b/(a^4-2*a^2*b^2+b^4)/(e^2*(a^2-b^2)/b^2)^(1/4)*2^(1/2)*ln((e*sin(d*x+c)-(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)*2^(1/2)+(e^2*(a^2-b^2)/b^2)^(1/2))/(e*sin(d*x+c)+(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)*2^(1/2)+(e^2*(a^2-b^2)/b^2)^(1/2)))*a^2-1/2/d*e*b^5/(-b^2*cos(d*x+c)^2*e^2+a^2*e^2)^2/(a^4-2*a^2*b^2+b^4)*(e*sin(d*x+c))^(7/2)-1/2/d*e^3*b^3/(-b^2*cos(d*x+c)^2*e^2+a^2*e^2)^2/(a^2-b^2)*(e*sin(d*x+c))^(3/2)-3/2/d*e*sin(d*x+c)^2*cos(d*x+c)/a/(e*sin(d*x+c))^(1/2)*b^2/(a^2-b^2)/(-cos(d*x+c)^2*b^2+a^2)+1/d*e*sin(d*x+c)^2*cos(d*x+c)*a/(e*sin(d*x+c))^(1/2)*b^2/(a^2-b^2)/(-cos(d*x+c)^2*b^2+a^2)^2+11/4/d*e*sin(d*x+c)^2*cos(d*x+c)*a/(e*sin(d*x+c))^(1/2)*b^2/(a^2-b^2)^2/(-cos(d*x+c)^2*b^2+a^2)-3/2/d*e*sin(d*x+c)^2*cos(d*x+c)/a/(e*sin(d*x+c))^(1/2)*b^4/(a^2-b^2)^2/(-cos(d*x+c)^2*b^2+a^2)","B"
85,1,2918,559,2.118000," ","int(1/(a+b*cos(d*x+c))^3/(e*sin(d*x+c))^(1/2),x)","\text{output too large to display}"," ",0,"-3/4/d/a/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/(a^2-b^2)/(-a^2+b^2)^(1/2)*b*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1-(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1-(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))-3/4/d/a/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/(a^2-b^2)^2/(-a^2+b^2)^(1/2)*b^3*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1-(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1-(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))-45/16/d*a^3/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/(a^2-b^2)^2/(-a^2+b^2)^(1/2)/b*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1-(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1-(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))+9/4/d*a/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/(a^2-b^2)^2/(-a^2+b^2)^(1/2)*b*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1-(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1-(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))-15/8/d*a/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/(a^2-b^2)/(-a^2+b^2)^(1/2)/b*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1+(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1+(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))+3/4/d/a/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/(a^2-b^2)/(-a^2+b^2)^(1/2)*b*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1+(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1+(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))+45/16/d*a^3/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/(a^2-b^2)^2/(-a^2+b^2)^(1/2)/b*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1+(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1+(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))-9/4/d*a/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/(a^2-b^2)^2/(-a^2+b^2)^(1/2)*b*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1+(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1+(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))+3/4/d/a/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/(a^2-b^2)^2/(-a^2+b^2)^(1/2)*b^3*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1+(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1+(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))-15/16/d*b*e/(a^4-2*a^2*b^2+b^4)*(e^2*(a^2-b^2)/b^2)^(1/4)/(a^2*e^2-b^2*e^2)*2^(1/2)*arctan(2^(1/2)/(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)+1)*a^2+13/8/d*a/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/(a^2-b^2)^2*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))-3/4/d/a/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/(a^2-b^2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))-15/16/d*b*e/(a^4-2*a^2*b^2+b^4)*(e^2*(a^2-b^2)/b^2)^(1/4)/(a^2*e^2-b^2*e^2)*2^(1/2)*arctan(2^(1/2)/(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)-1)*a^2-15/32/d*b*e/(a^4-2*a^2*b^2+b^4)*(e^2*(a^2-b^2)/b^2)^(1/4)/(a^2*e^2-b^2*e^2)*2^(1/2)*ln((e*sin(d*x+c)+(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)*2^(1/2)+(e^2*(a^2-b^2)/b^2)^(1/2))/(e*sin(d*x+c)-(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)*2^(1/2)+(e^2*(a^2-b^2)/b^2)^(1/2)))*a^2+15/8/d*a/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/(a^2-b^2)/(-a^2+b^2)^(1/2)/b*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1-(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1-(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))+1/d*sin(d*x+c)*cos(d*x+c)*a/(e*sin(d*x+c))^(1/2)*b^2/(a^2-b^2)/(-cos(d*x+c)^2*b^2+a^2)^2+13/4/d*sin(d*x+c)*cos(d*x+c)*a/(e*sin(d*x+c))^(1/2)*b^2/(a^2-b^2)^2/(-cos(d*x+c)^2*b^2+a^2)-3/2/d*sin(d*x+c)*cos(d*x+c)/a/(e*sin(d*x+c))^(1/2)*b^4/(a^2-b^2)^2/(-cos(d*x+c)^2*b^2+a^2)-3/2/d*sin(d*x+c)*cos(d*x+c)/a/(e*sin(d*x+c))^(1/2)*b^2/(a^2-b^2)/(-cos(d*x+c)^2*b^2+a^2)-3/8/d*b^3*e/(a^4-2*a^2*b^2+b^4)*(e^2*(a^2-b^2)/b^2)^(1/4)/(a^2*e^2-b^2*e^2)*2^(1/2)*arctan(2^(1/2)/(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)+1)-3/8/d*b^3*e/(a^4-2*a^2*b^2+b^4)*(e^2*(a^2-b^2)/b^2)^(1/4)/(a^2*e^2-b^2*e^2)*2^(1/2)*arctan(2^(1/2)/(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)-1)-3/16/d*b^3*e/(a^4-2*a^2*b^2+b^4)*(e^2*(a^2-b^2)/b^2)^(1/4)/(a^2*e^2-b^2*e^2)*2^(1/2)*ln((e*sin(d*x+c)+(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)*2^(1/2)+(e^2*(a^2-b^2)/b^2)^(1/2))/(e*sin(d*x+c)-(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)*2^(1/2)+(e^2*(a^2-b^2)/b^2)^(1/2)))-3/4/d/a/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/(a^2-b^2)^2*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))*b^2-5/4/d*b^3*e/(-b^2*cos(d*x+c)^2*e^2+a^2*e^2)^2/(a^4-2*a^2*b^2+b^4)*(e*sin(d*x+c))^(5/2)*a^2-9/4/d*b*e^3/(-b^2*cos(d*x+c)^2*e^2+a^2*e^2)^2/(a^2-b^2)*(e*sin(d*x+c))^(1/2)*a^2-1/2/d*b^5*e/(-b^2*cos(d*x+c)^2*e^2+a^2*e^2)^2/(a^4-2*a^2*b^2+b^4)*(e*sin(d*x+c))^(5/2)-1/2/d*b^3*e^3/(-b^2*cos(d*x+c)^2*e^2+a^2*e^2)^2/(a^2-b^2)*(e*sin(d*x+c))^(1/2)","B"
86,1,4913,631,2.845000," ","int(1/(a+b*cos(d*x+c))^3/(e*sin(d*x+c))^(3/2),x)","\text{output too large to display}"," ",0,"-2/d/e*a^3*cos(d*x+c)/(e*sin(d*x+c))^(1/2)/(a^2-b^2)^3+6/d/e*b/(a^2-b^2)^3/(e*sin(d*x+c))^(1/2)*a^2+6/d/e*a/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/(a^2-b^2)^3*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticE((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))*b^2-3/d/e*a/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/(a^2-b^2)^3*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))*b^2+3/2/d/e*sin(d*x+c)^2*cos(d*x+c)/a/(e*sin(d*x+c))^(1/2)*b^6/(a-b)/(a+b)/(a^2-b^2)^2/(-cos(d*x+c)^2*b^2+a^2)-3/2/d/e*sin(d*x+c)^2*cos(d*x+c)/a/(e*sin(d*x+c))^(1/2)*b^6/(a+b)^2/(a-b)^2/(a^2-b^2)/(-cos(d*x+c)^2*b^2+a^2)-1/2/d/e*sin(d*x+c)^2*cos(d*x+c)*a/(e*sin(d*x+c))^(1/2)*b^4/(a+b)^2/(a-b)^2/(a^2-b^2)/(-cos(d*x+c)^2*b^2+a^2)-1/d/e*sin(d*x+c)^2*cos(d*x+c)*a/(e*sin(d*x+c))^(1/2)*b^4/(a-b)/(a+b)/(a^2-b^2)/(-cos(d*x+c)^2*b^2+a^2)^2-11/4/d/e*sin(d*x+c)^2*cos(d*x+c)*a/(e*sin(d*x+c))^(1/2)*b^4/(a-b)/(a+b)/(a^2-b^2)^2/(-cos(d*x+c)^2*b^2+a^2)-3/4/d/e/a/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^4/(a+b)^2/(a-b)^2/(a^2-b^2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1-(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1-(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))+7/8/d/e*a/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^2/(a+b)^2/(a-b)^2/(a^2-b^2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1-(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1-(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))+7/8/d/e*a/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^2/(a+b)^2/(a-b)^2/(a^2-b^2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1+(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1+(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))+3/4/d/e/a/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^4/(a-b)/(a+b)/(a^2-b^2)^2*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1-(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1-(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))-7/4/d/e*a/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^2/(a-b)/(a+b)/(a^2-b^2)^2*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1+(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1+(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))+3/4/d/e/a/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^4/(a-b)/(a+b)/(a^2-b^2)^2*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1+(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1+(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))-7/4/d/e*a/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^2/(a-b)/(a+b)/(a^2-b^2)^2*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1-(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1-(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))-3/4/d/e/a/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^4/(a+b)^2/(a-b)^2/(a^2-b^2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1+(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1+(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))+5/16/d/e*b^3/(a-b)^3/(a+b)^3/(e^2*(a^2-b^2)/b^2)^(1/4)*2^(1/2)*ln((e*sin(d*x+c)-(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)*2^(1/2)+(e^2*(a^2-b^2)/b^2)^(1/2))/(e*sin(d*x+c)+(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)*2^(1/2)+(e^2*(a^2-b^2)/b^2)^(1/2)))+5/8/d/e*b^3/(a-b)^3/(a+b)^3/(e^2*(a^2-b^2)/b^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)+1)+5/8/d/e*b^3/(a-b)^3/(a+b)^3/(e^2*(a^2-b^2)/b^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)-1)+11/4/d/e*b^5/(a-b)^3/(a+b)^3/(-b^2*cos(d*x+c)^2*e^2+a^2*e^2)^2*(e*sin(d*x+c))^(7/2)*a^2+15/4/d*e*b^3/(a-b)^3/(a+b)^3/(-b^2*cos(d*x+c)^2*e^2+a^2*e^2)^2*(e*sin(d*x+c))^(3/2)*a^4-13/4/d*e*b^5/(a-b)^3/(a+b)^3/(-b^2*cos(d*x+c)^2*e^2+a^2*e^2)^2*(e*sin(d*x+c))^(3/2)*a^2+2/d/e*a^3/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/(a^2-b^2)^3*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticE((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))-1/d/e*a^3/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/(a^2-b^2)^3*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))-1/4/d/e*a/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^2/(a+b)^2/(a-b)^2/(a^2-b^2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))+21/16/d/e*a^3/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/(a-b)/(a+b)/(a^2-b^2)^2*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1-(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1-(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))+21/16/d/e*a^3/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/(a-b)/(a+b)/(a^2-b^2)^2*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1+(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1+(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))+3/8/d/e*a^3/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/(a+b)^2/(a-b)^2/(a^2-b^2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1-(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1-(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))+3/8/d/e*a^3/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/(a+b)^2/(a-b)^2/(a^2-b^2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1+(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1+(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))+11/4/d/e*a/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^2/(a-b)/(a+b)/(a^2-b^2)^2*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticE((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))-3/2/d/e/a/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^4/(a-b)/(a+b)/(a^2-b^2)^2*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticE((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))-11/8/d/e*a/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^2/(a-b)/(a+b)/(a^2-b^2)^2*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))+3/4/d/e/a/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^4/(a-b)/(a+b)/(a^2-b^2)^2*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))+3/2/d/e/a/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^4/(a+b)^2/(a-b)^2/(a^2-b^2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticE((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))-3/4/d/e/a/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^4/(a+b)^2/(a-b)^2/(a^2-b^2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))+3/2/d/e*a/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^2/(a-b)^3/(a+b)^3*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1-(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1-(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))+3/2/d/e*a/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^2/(a-b)^3/(a+b)^3*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1+(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1+(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))+1/2/d/e*a/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^2/(a+b)^2/(a-b)^2/(a^2-b^2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticE((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))+2/d/e*b^3/(a^2-b^2)^3/(e*sin(d*x+c))^(1/2)+1/2/d/e*b^7/(a-b)^3/(a+b)^3/(-b^2*cos(d*x+c)^2*e^2+a^2*e^2)^2*(e*sin(d*x+c))^(7/2)-1/2/d*e*b^7/(a-b)^3/(a+b)^3/(-b^2*cos(d*x+c)^2*e^2+a^2*e^2)^2*(e*sin(d*x+c))^(3/2)-6/d/e*a*cos(d*x+c)/(e*sin(d*x+c))^(1/2)/(a^2-b^2)^3*b^2+1/2/d/e*a^3/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/(a-b)^3/(a+b)^3*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1-(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1-(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))+1/2/d/e*a^3/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/(a-b)^3/(a+b)^3*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1+(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1+(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))+35/32/d/e*b/(a-b)^3/(a+b)^3/(e^2*(a^2-b^2)/b^2)^(1/4)*2^(1/2)*a^2*ln((e*sin(d*x+c)-(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)*2^(1/2)+(e^2*(a^2-b^2)/b^2)^(1/2))/(e*sin(d*x+c)+(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)*2^(1/2)+(e^2*(a^2-b^2)/b^2)^(1/2)))+35/16/d/e*b/(a-b)^3/(a+b)^3/(e^2*(a^2-b^2)/b^2)^(1/4)*2^(1/2)*a^2*arctan(2^(1/2)/(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)+1)+35/16/d/e*b/(a-b)^3/(a+b)^3/(e^2*(a^2-b^2)/b^2)^(1/4)*2^(1/2)*a^2*arctan(2^(1/2)/(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)-1)","B"
87,1,4661,649,3.143000," ","int(1/(a+b*cos(d*x+c))^3/(e*sin(d*x+c))^(5/2),x)","\text{output too large to display}"," ",0,"63/16/d/e*b^3/(a-b)^3/(a+b)^3*(e^2*(a^2-b^2)/b^2)^(1/4)/(a^2*e^2-b^2*e^2)*2^(1/2)*arctan(2^(1/2)/(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)+1)*a^2+63/16/d/e*b^3/(a-b)^3/(a+b)^3*(e^2*(a^2-b^2)/b^2)^(1/4)/(a^2*e^2-b^2*e^2)*2^(1/2)*arctan(2^(1/2)/(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)-1)*a^2+63/32/d/e*b^3/(a-b)^3/(a+b)^3*(e^2*(a^2-b^2)/b^2)^(1/4)/(a^2*e^2-b^2*e^2)*2^(1/2)*ln((e*sin(d*x+c)+(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)*2^(1/2)+(e^2*(a^2-b^2)/b^2)^(1/2))/(e*sin(d*x+c)-(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)*2^(1/2)+(e^2*(a^2-b^2)/b^2)^(1/2)))*a^2+1/d/e^2*a/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/(a^2-b^2)^3/(cos(d*x+c)^2-1)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(5/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))*b^2-1/2/d/e^2*sin(d*x+c)*cos(d*x+c)*a/(e*sin(d*x+c))^(1/2)*b^4/(a+b)^2/(a-b)^2/(a^2-b^2)/(-cos(d*x+c)^2*b^2+a^2)-1/d/e^2*sin(d*x+c)*cos(d*x+c)*a/(e*sin(d*x+c))^(1/2)*b^4/(a+b)/(a-b)/(a^2-b^2)/(-cos(d*x+c)^2*b^2+a^2)^2-13/4/d/e^2*sin(d*x+c)*cos(d*x+c)*a/(e*sin(d*x+c))^(1/2)*b^4/(a+b)/(a-b)/(a^2-b^2)^2/(-cos(d*x+c)^2*b^2+a^2)+3/2/d/e^2*sin(d*x+c)*cos(d*x+c)/a/(e*sin(d*x+c))^(1/2)*b^6/(a+b)/(a-b)/(a^2-b^2)^2/(-cos(d*x+c)^2*b^2+a^2)-3/2/d/e^2*sin(d*x+c)*cos(d*x+c)/a/(e*sin(d*x+c))^(1/2)*b^6/(a+b)^2/(a-b)^2/(a^2-b^2)/(-cos(d*x+c)^2*b^2+a^2)+2/3/d/e*b^3/(a^2-b^2)^3/(e*sin(d*x+c))^(3/2)+1/2/d/e^2*a^3/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b/(a-b)^3/(a+b)^3/(-a^2+b^2)^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1-(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1-(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))-1/2/d/e^2*a^3/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b/(a-b)^3/(a+b)^3/(-a^2+b^2)^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1+(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1+(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))+3/2/d/e^2*a/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^3/(a-b)^3/(a+b)^3/(-a^2+b^2)^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1-(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1-(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))-3/2/d/e^2*a/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^3/(a-b)^3/(a+b)^3/(-a^2+b^2)^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1+(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1+(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))+13/8/d/e^2*a/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^3/(a+b)^2/(a-b)^2/(a^2-b^2)/(-a^2+b^2)^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1-(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1-(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))+9/4/d/e^2*a/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^3/(a+b)/(a-b)/(a^2-b^2)^2/(-a^2+b^2)^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1+(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1+(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))-3/4/d/e^2/a/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^5/(a+b)/(a-b)/(a^2-b^2)^2/(-a^2+b^2)^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1+(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1+(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))+5/8/d/e^2*a^3/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b/(a+b)^2/(a-b)^2/(a^2-b^2)/(-a^2+b^2)^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1-(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1-(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))-3/4/d/e^2/a/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^5/(a+b)^2/(a-b)^2/(a^2-b^2)/(-a^2+b^2)^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1-(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1-(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))-5/8/d/e^2*a^3/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b/(a+b)^2/(a-b)^2/(a^2-b^2)/(-a^2+b^2)^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1+(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1+(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))+3/4/d/e^2/a/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^5/(a+b)^2/(a-b)^2/(a^2-b^2)/(-a^2+b^2)^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1+(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1+(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))+45/16/d/e^2*a^3/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b/(a+b)/(a-b)/(a^2-b^2)^2/(-a^2+b^2)^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1-(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1-(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))-9/4/d/e^2*a/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^3/(a+b)/(a-b)/(a^2-b^2)^2/(-a^2+b^2)^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1-(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1-(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))+3/4/d/e^2/a/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^5/(a+b)/(a-b)/(a^2-b^2)^2/(-a^2+b^2)^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1-(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1-(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))-45/16/d/e^2*a^3/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b/(a+b)/(a-b)/(a^2-b^2)^2/(-a^2+b^2)^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1+(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1+(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))-13/8/d/e^2*a/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^3/(a+b)^2/(a-b)^2/(a^2-b^2)/(-a^2+b^2)^(1/2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)/(1+(-a^2+b^2)^(1/2)/b)*EllipticPi((-sin(d*x+c)+1)^(1/2),1/(1+(-a^2+b^2)^(1/2)/b),1/2*2^(1/2))+1/3/d/e^2*a^3/cos(d*x+c)/(e*sin(d*x+c))^(1/2)/(a^2-b^2)^3/(cos(d*x+c)^2-1)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(5/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))+2/d/e^2*a*cos(d*x+c)/(e*sin(d*x+c))^(1/2)/(a^2-b^2)^3/(cos(d*x+c)^2-1)*sin(d*x+c)*b^2+7/8/d/e*b^5/(a-b)^3/(a+b)^3*(e^2*(a^2-b^2)/b^2)^(1/4)/(a^2*e^2-b^2*e^2)*2^(1/2)*arctan(2^(1/2)/(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)+1)+7/8/d/e*b^5/(a-b)^3/(a+b)^3*(e^2*(a^2-b^2)/b^2)^(1/4)/(a^2*e^2-b^2*e^2)*2^(1/2)*arctan(2^(1/2)/(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)-1)+7/16/d/e*b^5/(a-b)^3/(a+b)^3*(e^2*(a^2-b^2)/b^2)^(1/4)/(a^2*e^2-b^2*e^2)*2^(1/2)*ln((e*sin(d*x+c)+(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)*2^(1/2)+(e^2*(a^2-b^2)/b^2)^(1/2))/(e*sin(d*x+c)-(e^2*(a^2-b^2)/b^2)^(1/4)*(e*sin(d*x+c))^(1/2)*2^(1/2)+(e^2*(a^2-b^2)/b^2)^(1/2)))+2/d/e*b/(a^2-b^2)^3/(e*sin(d*x+c))^(3/2)*a^2+1/2/d/e*b^7/(a-b)^3/(a+b)^3/(-b^2*cos(d*x+c)^2*e^2+a^2*e^2)^2*(e*sin(d*x+c))^(5/2)-1/2/d*e*b^7/(a-b)^3/(a+b)^3/(-b^2*cos(d*x+c)^2*e^2+a^2*e^2)^2*(e*sin(d*x+c))^(1/2)-1/4/d/e^2*a/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^2/(a+b)^2/(a-b)^2/(a^2-b^2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))-13/8/d/e^2*a/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^2/(a+b)/(a-b)/(a^2-b^2)^2*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))+3/4/d/e^2/a/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^4/(a+b)/(a-b)/(a^2-b^2)^2*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))-3/4/d/e^2/a/cos(d*x+c)/(e*sin(d*x+c))^(1/2)*b^4/(a+b)^2/(a-b)^2/(a^2-b^2)*(-sin(d*x+c)+1)^(1/2)*(2*sin(d*x+c)+2)^(1/2)*sin(d*x+c)^(1/2)*EllipticF((-sin(d*x+c)+1)^(1/2),1/2*2^(1/2))-15/4/d*e*b^5/(a-b)^3/(a+b)^3/(-b^2*cos(d*x+c)^2*e^2+a^2*e^2)^2*(e*sin(d*x+c))^(1/2)*a^2+13/4/d/e*b^5/(a-b)^3/(a+b)^3/(-b^2*cos(d*x+c)^2*e^2+a^2*e^2)^2*(e*sin(d*x+c))^(5/2)*a^2+17/4/d*e*b^3/(a-b)^3/(a+b)^3/(-b^2*cos(d*x+c)^2*e^2+a^2*e^2)^2*(e*sin(d*x+c))^(1/2)*a^4+2/3/d/e^2*a^3*cos(d*x+c)/(e*sin(d*x+c))^(1/2)/(a^2-b^2)^3/(cos(d*x+c)^2-1)*sin(d*x+c)","B"
88,1,5638,716,3.374000," ","int(1/(a+b*cos(d*x+c))^3/(e*sin(d*x+c))^(7/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"