1,1,56,81,0.135000," ","int(cos(d*x+c)^7*(a+a*sin(d*x+c)),x)","\frac{-\frac{a \left(\cos^{8}\left(d x +c \right)\right)}{8}+\frac{a \left(\frac{16}{5}+\cos^{6}\left(d x +c \right)+\frac{6 \left(\cos^{4}\left(d x +c \right)\right)}{5}+\frac{8 \left(\cos^{2}\left(d x +c \right)\right)}{5}\right) \sin \left(d x +c \right)}{7}}{d}"," ",0,"1/d*(-1/8*a*cos(d*x+c)^8+1/7*a*(16/5+cos(d*x+c)^6+6/5*cos(d*x+c)^4+8/5*cos(d*x+c)^2)*sin(d*x+c))","A"
2,1,62,77,0.145000," ","int(cos(d*x+c)^6*(a+a*sin(d*x+c)),x)","\frac{-\frac{\left(\cos^{7}\left(d x +c \right)\right) a}{7}+a \left(\frac{\left(\cos^{5}\left(d x +c \right)+\frac{5 \left(\cos^{3}\left(d x +c \right)\right)}{4}+\frac{15 \cos \left(d x +c \right)}{8}\right) \sin \left(d x +c \right)}{6}+\frac{5 d x}{16}+\frac{5 c}{16}\right)}{d}"," ",0,"1/d*(-1/7*cos(d*x+c)^7*a+a*(1/6*(cos(d*x+c)^5+5/4*cos(d*x+c)^3+15/8*cos(d*x+c))*sin(d*x+c)+5/16*d*x+5/16*c))","A"
3,1,46,60,0.135000," ","int(cos(d*x+c)^5*(a+a*sin(d*x+c)),x)","\frac{-\frac{\left(\cos^{6}\left(d x +c \right)\right) a}{6}+\frac{a \left(\frac{8}{3}+\cos^{4}\left(d x +c \right)+\frac{4 \left(\cos^{2}\left(d x +c \right)\right)}{3}\right) \sin \left(d x +c \right)}{5}}{d}"," ",0,"1/d*(-1/6*cos(d*x+c)^6*a+1/5*a*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c))","A"
4,1,52,57,0.143000," ","int(cos(d*x+c)^4*(a+a*sin(d*x+c)),x)","\frac{-\frac{\left(\cos^{5}\left(d x +c \right)\right) a}{5}+a \left(\frac{\left(\cos^{3}\left(d x +c \right)+\frac{3 \cos \left(d x +c \right)}{2}\right) \sin \left(d x +c \right)}{4}+\frac{3 d x}{8}+\frac{3 c}{8}\right)}{d}"," ",0,"1/d*(-1/5*cos(d*x+c)^5*a+a*(1/4*(cos(d*x+c)^3+3/2*cos(d*x+c))*sin(d*x+c)+3/8*d*x+3/8*c))","A"
5,1,36,41,0.131000," ","int(cos(d*x+c)^3*(a+a*sin(d*x+c)),x)","\frac{-\frac{\left(\cos^{4}\left(d x +c \right)\right) a}{4}+\frac{a \left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{3}}{d}"," ",0,"1/d*(-1/4*cos(d*x+c)^4*a+1/3*a*(2+cos(d*x+c)^2)*sin(d*x+c))","A"
6,1,41,37,0.083000," ","int(cos(d*x+c)^2*(a+a*sin(d*x+c)),x)","\frac{-\frac{\left(\cos^{3}\left(d x +c \right)\right) a}{3}+a \left(\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)}{2}+\frac{d x}{2}+\frac{c}{2}\right)}{d}"," ",0,"1/d*(-1/3*cos(d*x+c)^3*a+a*(1/2*cos(d*x+c)*sin(d*x+c)+1/2*d*x+1/2*c))","A"
7,1,25,20,0.043000," ","int(cos(d*x+c)*(a+a*sin(d*x+c)),x)","\frac{\frac{a \left(\sin^{2}\left(d x +c \right)\right)}{2}+a \sin \left(d x +c \right)}{d}"," ",0,"1/d*(1/2*a*sin(d*x+c)^2+a*sin(d*x+c))","A"
8,1,16,17,0.083000," ","int(sec(d*x+c)*(a+a*sin(d*x+c)),x)","-\frac{a \ln \left(\sin \left(d x +c \right)-1\right)}{d}"," ",0,"-1/d*a*ln(sin(d*x+c)-1)","A"
9,1,24,23,0.135000," ","int(sec(d*x+c)^2*(a+a*sin(d*x+c)),x)","\frac{\frac{a}{\cos \left(d x +c \right)}+a \tan \left(d x +c \right)}{d}"," ",0,"1/d*(a/cos(d*x+c)+a*tan(d*x+c))","A"
10,1,54,35,0.168000," ","int(sec(d*x+c)^3*(a+a*sin(d*x+c)),x)","\frac{a}{2 d \cos \left(d x +c \right)^{2}}+\frac{a \sec \left(d x +c \right) \tan \left(d x +c \right)}{2 d}+\frac{a \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{2 d}"," ",0,"1/2/d*a/cos(d*x+c)^2+1/2*a*sec(d*x+c)*tan(d*x+c)/d+1/2/d*a*ln(sec(d*x+c)+tan(d*x+c))","A"
11,1,38,40,0.164000," ","int(sec(d*x+c)^4*(a+a*sin(d*x+c)),x)","\frac{\frac{a}{3 \cos \left(d x +c \right)^{3}}-a \left(-\frac{2}{3}-\frac{\left(\sec^{2}\left(d x +c \right)\right)}{3}\right) \tan \left(d x +c \right)}{d}"," ",0,"1/d*(1/3*a/cos(d*x+c)^3-a*(-2/3-1/3*sec(d*x+c)^2)*tan(d*x+c))","A"
12,1,74,76,0.175000," ","int(sec(d*x+c)^5*(a+a*sin(d*x+c)),x)","\frac{a}{4 d \cos \left(d x +c \right)^{4}}+\frac{a \tan \left(d x +c \right) \left(\sec^{3}\left(d x +c \right)\right)}{4 d}+\frac{3 a \sec \left(d x +c \right) \tan \left(d x +c \right)}{8 d}+\frac{3 a \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{8 d}"," ",0,"1/4/d*a/cos(d*x+c)^4+1/4/d*a*tan(d*x+c)*sec(d*x+c)^3+3/8*a*sec(d*x+c)*tan(d*x+c)/d+3/8/d*a*ln(sec(d*x+c)+tan(d*x+c))","A"
13,1,129,114,0.176000," ","int(cos(d*x+c)^6*(a+a*sin(d*x+c))^2,x)","\frac{a^{2} \left(-\frac{\sin \left(d x +c \right) \left(\cos^{7}\left(d x +c \right)\right)}{8}+\frac{\left(\cos^{5}\left(d x +c \right)+\frac{5 \left(\cos^{3}\left(d x +c \right)\right)}{4}+\frac{15 \cos \left(d x +c \right)}{8}\right) \sin \left(d x +c \right)}{48}+\frac{5 d x}{128}+\frac{5 c}{128}\right)-\frac{2 a^{2} \left(\cos^{7}\left(d x +c \right)\right)}{7}+a^{2} \left(\frac{\left(\cos^{5}\left(d x +c \right)+\frac{5 \left(\cos^{3}\left(d x +c \right)\right)}{4}+\frac{15 \cos \left(d x +c \right)}{8}\right) \sin \left(d x +c \right)}{6}+\frac{5 d x}{16}+\frac{5 c}{16}\right)}{d}"," ",0,"1/d*(a^2*(-1/8*sin(d*x+c)*cos(d*x+c)^7+1/48*(cos(d*x+c)^5+5/4*cos(d*x+c)^3+15/8*cos(d*x+c))*sin(d*x+c)+5/128*d*x+5/128*c)-2/7*a^2*cos(d*x+c)^7+a^2*(1/6*(cos(d*x+c)^5+5/4*cos(d*x+c)^3+15/8*cos(d*x+c))*sin(d*x+c)+5/16*d*x+5/16*c))","A"
14,1,99,61,0.172000," ","int(cos(d*x+c)^5*(a+a*sin(d*x+c))^2,x)","\frac{a^{2} \left(-\frac{\sin \left(d x +c \right) \left(\cos^{6}\left(d x +c \right)\right)}{7}+\frac{\left(\frac{8}{3}+\cos^{4}\left(d x +c \right)+\frac{4 \left(\cos^{2}\left(d x +c \right)\right)}{3}\right) \sin \left(d x +c \right)}{35}\right)-\frac{\left(\cos^{6}\left(d x +c \right)\right) a^{2}}{3}+\frac{a^{2} \left(\frac{8}{3}+\cos^{4}\left(d x +c \right)+\frac{4 \left(\cos^{2}\left(d x +c \right)\right)}{3}\right) \sin \left(d x +c \right)}{5}}{d}"," ",0,"1/d*(a^2*(-1/7*sin(d*x+c)*cos(d*x+c)^6+1/35*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c))-1/3*cos(d*x+c)^6*a^2+1/5*a^2*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c))","A"
15,1,109,92,0.177000," ","int(cos(d*x+c)^4*(a+a*sin(d*x+c))^2,x)","\frac{a^{2} \left(-\frac{\sin \left(d x +c \right) \left(\cos^{5}\left(d x +c \right)\right)}{6}+\frac{\left(\cos^{3}\left(d x +c \right)+\frac{3 \cos \left(d x +c \right)}{2}\right) \sin \left(d x +c \right)}{24}+\frac{d x}{16}+\frac{c}{16}\right)-\frac{2 \left(\cos^{5}\left(d x +c \right)\right) a^{2}}{5}+a^{2} \left(\frac{\left(\cos^{3}\left(d x +c \right)+\frac{3 \cos \left(d x +c \right)}{2}\right) \sin \left(d x +c \right)}{4}+\frac{3 d x}{8}+\frac{3 c}{8}\right)}{d}"," ",0,"1/d*(a^2*(-1/6*sin(d*x+c)*cos(d*x+c)^5+1/24*(cos(d*x+c)^3+3/2*cos(d*x+c))*sin(d*x+c)+1/16*d*x+1/16*c)-2/5*cos(d*x+c)^5*a^2+a^2*(1/4*(cos(d*x+c)^3+3/2*cos(d*x+c))*sin(d*x+c)+3/8*d*x+3/8*c))","A"
16,1,79,41,0.165000," ","int(cos(d*x+c)^3*(a+a*sin(d*x+c))^2,x)","\frac{a^{2} \left(-\frac{\left(\cos^{4}\left(d x +c \right)\right) \sin \left(d x +c \right)}{5}+\frac{\left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{15}\right)-\frac{\left(\cos^{4}\left(d x +c \right)\right) a^{2}}{2}+\frac{a^{2} \left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{3}}{d}"," ",0,"1/d*(a^2*(-1/5*cos(d*x+c)^4*sin(d*x+c)+1/15*(2+cos(d*x+c)^2)*sin(d*x+c))-1/2*cos(d*x+c)^4*a^2+1/3*a^2*(2+cos(d*x+c)^2)*sin(d*x+c))","A"
17,1,87,70,0.120000," ","int(cos(d*x+c)^2*(a+a*sin(d*x+c))^2,x)","\frac{a^{2} \left(-\frac{\sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right)}{4}+\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)}{8}+\frac{d x}{8}+\frac{c}{8}\right)-\frac{2 \left(\cos^{3}\left(d x +c \right)\right) a^{2}}{3}+a^{2} \left(\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)}{2}+\frac{d x}{2}+\frac{c}{2}\right)}{d}"," ",0,"1/d*(a^2*(-1/4*sin(d*x+c)*cos(d*x+c)^3+1/8*cos(d*x+c)*sin(d*x+c)+1/8*d*x+1/8*c)-2/3*cos(d*x+c)^3*a^2+a^2*(1/2*cos(d*x+c)*sin(d*x+c)+1/2*d*x+1/2*c))","A"
18,1,21,20,0.071000," ","int(cos(d*x+c)*(a+a*sin(d*x+c))^2,x)","\frac{\left(a +a \sin \left(d x +c \right)\right)^{3}}{3 d a}"," ",0,"1/3*(a+a*sin(d*x+c))^3/d/a","A"
19,1,53,34,0.144000," ","int(sec(d*x+c)*(a+a*sin(d*x+c))^2,x)","-\frac{a^{2} \sin \left(d x +c \right)}{d}+\frac{2 a^{2} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}-\frac{2 a^{2} \ln \left(\cos \left(d x +c \right)\right)}{d}"," ",0,"-a^2*sin(d*x+c)/d+2/d*a^2*ln(sec(d*x+c)+tan(d*x+c))-2/d*a^2*ln(cos(d*x+c))","A"
20,1,47,38,0.183000," ","int(sec(d*x+c)^2*(a+a*sin(d*x+c))^2,x)","\frac{a^{2} \left(\tan \left(d x +c \right)-d x -c \right)+\frac{2 a^{2}}{\cos \left(d x +c \right)}+a^{2} \tan \left(d x +c \right)}{d}"," ",0,"1/d*(a^2*(tan(d*x+c)-d*x-c)+2*a^2/cos(d*x+c)+a^2*tan(d*x+c))","A"
21,1,75,20,0.213000," ","int(sec(d*x+c)^3*(a+a*sin(d*x+c))^2,x)","\frac{a^{2} \left(\sin^{3}\left(d x +c \right)\right)}{2 d \cos \left(d x +c \right)^{2}}+\frac{a^{2} \sin \left(d x +c \right)}{2 d}+\frac{a^{2}}{d \cos \left(d x +c \right)^{2}}+\frac{a^{2} \sec \left(d x +c \right) \tan \left(d x +c \right)}{2 d}"," ",0,"1/2/d*a^2*sin(d*x+c)^3/cos(d*x+c)^2+1/2*a^2*sin(d*x+c)/d+1/d*a^2/cos(d*x+c)^2+1/2/d*a^2*sec(d*x+c)*tan(d*x+c)","B"
22,1,63,59,0.216000," ","int(sec(d*x+c)^4*(a+a*sin(d*x+c))^2,x)","\frac{\frac{a^{2} \left(\sin^{3}\left(d x +c \right)\right)}{3 \cos \left(d x +c \right)^{3}}+\frac{2 a^{2}}{3 \cos \left(d x +c \right)^{3}}-a^{2} \left(-\frac{2}{3}-\frac{\left(\sec^{2}\left(d x +c \right)\right)}{3}\right) \tan \left(d x +c \right)}{d}"," ",0,"1/d*(1/3*a^2*sin(d*x+c)^3/cos(d*x+c)^3+2/3*a^2/cos(d*x+c)^3-a^2*(-2/3-1/3*sec(d*x+c)^2)*tan(d*x+c))","A"
23,1,144,58,0.227000," ","int(sec(d*x+c)^5*(a+a*sin(d*x+c))^2,x)","\frac{a^{2} \left(\sin^{3}\left(d x +c \right)\right)}{4 d \cos \left(d x +c \right)^{4}}+\frac{a^{2} \left(\sin^{3}\left(d x +c \right)\right)}{8 d \cos \left(d x +c \right)^{2}}+\frac{a^{2} \sin \left(d x +c \right)}{8 d}+\frac{a^{2} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{4 d}+\frac{a^{2}}{2 d \cos \left(d x +c \right)^{4}}+\frac{a^{2} \tan \left(d x +c \right) \left(\sec^{3}\left(d x +c \right)\right)}{4 d}+\frac{3 a^{2} \sec \left(d x +c \right) \tan \left(d x +c \right)}{8 d}"," ",0,"1/4/d*a^2*sin(d*x+c)^3/cos(d*x+c)^4+1/8/d*a^2*sin(d*x+c)^3/cos(d*x+c)^2+1/8*a^2*sin(d*x+c)/d+1/4/d*a^2*ln(sec(d*x+c)+tan(d*x+c))+1/2/d*a^2/cos(d*x+c)^4+1/4/d*a^2*tan(d*x+c)*sec(d*x+c)^3+3/8/d*a^2*sec(d*x+c)*tan(d*x+c)","B"
24,1,93,58,0.223000," ","int(sec(d*x+c)^6*(a+a*sin(d*x+c))^2,x)","\frac{a^{2} \left(\frac{\sin^{3}\left(d x +c \right)}{5 \cos \left(d x +c \right)^{5}}+\frac{2 \left(\sin^{3}\left(d x +c \right)\right)}{15 \cos \left(d x +c \right)^{3}}\right)+\frac{2 a^{2}}{5 \cos \left(d x +c \right)^{5}}-a^{2} \left(-\frac{8}{15}-\frac{\left(\sec^{4}\left(d x +c \right)\right)}{5}-\frac{4 \left(\sec^{2}\left(d x +c \right)\right)}{15}\right) \tan \left(d x +c \right)}{d}"," ",0,"1/d*(a^2*(1/5*sin(d*x+c)^3/cos(d*x+c)^5+2/15*sin(d*x+c)^3/cos(d*x+c)^3)+2/5*a^2/cos(d*x+c)^5-a^2*(-8/15-1/5*sec(d*x+c)^4-4/15*sec(d*x+c)^2)*tan(d*x+c))","A"
25,1,190,99,0.242000," ","int(sec(d*x+c)^7*(a+a*sin(d*x+c))^2,x)","\frac{a^{2} \left(\sin^{3}\left(d x +c \right)\right)}{6 d \cos \left(d x +c \right)^{6}}+\frac{a^{2} \left(\sin^{3}\left(d x +c \right)\right)}{8 d \cos \left(d x +c \right)^{4}}+\frac{a^{2} \left(\sin^{3}\left(d x +c \right)\right)}{16 d \cos \left(d x +c \right)^{2}}+\frac{a^{2} \sin \left(d x +c \right)}{16 d}+\frac{a^{2} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{4 d}+\frac{a^{2}}{3 d \cos \left(d x +c \right)^{6}}+\frac{a^{2} \tan \left(d x +c \right) \left(\sec^{5}\left(d x +c \right)\right)}{6 d}+\frac{5 a^{2} \tan \left(d x +c \right) \left(\sec^{3}\left(d x +c \right)\right)}{24 d}+\frac{5 a^{2} \sec \left(d x +c \right) \tan \left(d x +c \right)}{16 d}"," ",0,"1/6/d*a^2*sin(d*x+c)^3/cos(d*x+c)^6+1/8/d*a^2*sin(d*x+c)^3/cos(d*x+c)^4+1/16/d*a^2*sin(d*x+c)^3/cos(d*x+c)^2+1/16*a^2*sin(d*x+c)/d+1/4/d*a^2*ln(sec(d*x+c)+tan(d*x+c))+1/3/d*a^2/cos(d*x+c)^6+1/6/d*a^2*tan(d*x+c)*sec(d*x+c)^5+5/24/d*a^2*tan(d*x+c)*sec(d*x+c)^3+5/16/d*a^2*sec(d*x+c)*tan(d*x+c)","A"
26,1,121,74,0.237000," ","int(sec(d*x+c)^8*(a+a*sin(d*x+c))^2,x)","\frac{a^{2} \left(\frac{\sin^{3}\left(d x +c \right)}{7 \cos \left(d x +c \right)^{7}}+\frac{4 \left(\sin^{3}\left(d x +c \right)\right)}{35 \cos \left(d x +c \right)^{5}}+\frac{8 \left(\sin^{3}\left(d x +c \right)\right)}{105 \cos \left(d x +c \right)^{3}}\right)+\frac{2 a^{2}}{7 \cos \left(d x +c \right)^{7}}-a^{2} \left(-\frac{16}{35}-\frac{\left(\sec^{6}\left(d x +c \right)\right)}{7}-\frac{6 \left(\sec^{4}\left(d x +c \right)\right)}{35}-\frac{8 \left(\sec^{2}\left(d x +c \right)\right)}{35}\right) \tan \left(d x +c \right)}{d}"," ",0,"1/d*(a^2*(1/7*sin(d*x+c)^3/cos(d*x+c)^7+4/35*sin(d*x+c)^3/cos(d*x+c)^5+8/105*sin(d*x+c)^3/cos(d*x+c)^3)+2/7*a^2/cos(d*x+c)^7-a^2*(-16/35-1/7*sec(d*x+c)^6-6/35*sec(d*x+c)^4-8/35*sec(d*x+c)^2)*tan(d*x+c))","A"
27,1,163,140,0.184000," ","int(cos(d*x+c)^6*(a+a*sin(d*x+c))^3,x)","\frac{a^{3} \left(-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{7}\left(d x +c \right)\right)}{9}-\frac{2 \left(\cos^{7}\left(d x +c \right)\right)}{63}\right)+3 a^{3} \left(-\frac{\sin \left(d x +c \right) \left(\cos^{7}\left(d x +c \right)\right)}{8}+\frac{\left(\cos^{5}\left(d x +c \right)+\frac{5 \left(\cos^{3}\left(d x +c \right)\right)}{4}+\frac{15 \cos \left(d x +c \right)}{8}\right) \sin \left(d x +c \right)}{48}+\frac{5 d x}{128}+\frac{5 c}{128}\right)-\frac{3 a^{3} \left(\cos^{7}\left(d x +c \right)\right)}{7}+a^{3} \left(\frac{\left(\cos^{5}\left(d x +c \right)+\frac{5 \left(\cos^{3}\left(d x +c \right)\right)}{4}+\frac{15 \cos \left(d x +c \right)}{8}\right) \sin \left(d x +c \right)}{6}+\frac{5 d x}{16}+\frac{5 c}{16}\right)}{d}"," ",0,"1/d*(a^3*(-1/9*sin(d*x+c)^2*cos(d*x+c)^7-2/63*cos(d*x+c)^7)+3*a^3*(-1/8*sin(d*x+c)*cos(d*x+c)^7+1/48*(cos(d*x+c)^5+5/4*cos(d*x+c)^3+15/8*cos(d*x+c))*sin(d*x+c)+5/128*d*x+5/128*c)-3/7*a^3*cos(d*x+c)^7+a^3*(1/6*(cos(d*x+c)^5+5/4*cos(d*x+c)^3+15/8*cos(d*x+c))*sin(d*x+c)+5/16*d*x+5/16*c))","A"
28,1,133,61,0.171000," ","int(cos(d*x+c)^5*(a+a*sin(d*x+c))^3,x)","\frac{a^{3} \left(-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{6}\left(d x +c \right)\right)}{8}-\frac{\left(\cos^{6}\left(d x +c \right)\right)}{24}\right)+3 a^{3} \left(-\frac{\sin \left(d x +c \right) \left(\cos^{6}\left(d x +c \right)\right)}{7}+\frac{\left(\frac{8}{3}+\cos^{4}\left(d x +c \right)+\frac{4 \left(\cos^{2}\left(d x +c \right)\right)}{3}\right) \sin \left(d x +c \right)}{35}\right)-\frac{\left(\cos^{6}\left(d x +c \right)\right) a^{3}}{2}+\frac{a^{3} \left(\frac{8}{3}+\cos^{4}\left(d x +c \right)+\frac{4 \left(\cos^{2}\left(d x +c \right)\right)}{3}\right) \sin \left(d x +c \right)}{5}}{d}"," ",0,"1/d*(a^3*(-1/8*sin(d*x+c)^2*cos(d*x+c)^6-1/24*cos(d*x+c)^6)+3*a^3*(-1/7*sin(d*x+c)*cos(d*x+c)^6+1/35*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c))-1/2*cos(d*x+c)^6*a^3+1/5*a^3*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c))","B"
29,1,143,118,0.181000," ","int(cos(d*x+c)^4*(a+a*sin(d*x+c))^3,x)","\frac{a^{3} \left(-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{5}\left(d x +c \right)\right)}{7}-\frac{2 \left(\cos^{5}\left(d x +c \right)\right)}{35}\right)+3 a^{3} \left(-\frac{\sin \left(d x +c \right) \left(\cos^{5}\left(d x +c \right)\right)}{6}+\frac{\left(\cos^{3}\left(d x +c \right)+\frac{3 \cos \left(d x +c \right)}{2}\right) \sin \left(d x +c \right)}{24}+\frac{d x}{16}+\frac{c}{16}\right)-\frac{3 \left(\cos^{5}\left(d x +c \right)\right) a^{3}}{5}+a^{3} \left(\frac{\left(\cos^{3}\left(d x +c \right)+\frac{3 \cos \left(d x +c \right)}{2}\right) \sin \left(d x +c \right)}{4}+\frac{3 d x}{8}+\frac{3 c}{8}\right)}{d}"," ",0,"1/d*(a^3*(-1/7*sin(d*x+c)^2*cos(d*x+c)^5-2/35*cos(d*x+c)^5)+3*a^3*(-1/6*sin(d*x+c)*cos(d*x+c)^5+1/24*(cos(d*x+c)^3+3/2*cos(d*x+c))*sin(d*x+c)+1/16*d*x+1/16*c)-3/5*cos(d*x+c)^5*a^3+a^3*(1/4*(cos(d*x+c)^3+3/2*cos(d*x+c))*sin(d*x+c)+3/8*d*x+3/8*c))","A"
30,1,113,41,0.171000," ","int(cos(d*x+c)^3*(a+a*sin(d*x+c))^3,x)","\frac{a^{3} \left(-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{4}\left(d x +c \right)\right)}{6}-\frac{\left(\cos^{4}\left(d x +c \right)\right)}{12}\right)+3 a^{3} \left(-\frac{\left(\cos^{4}\left(d x +c \right)\right) \sin \left(d x +c \right)}{5}+\frac{\left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{15}\right)-\frac{3 \left(\cos^{4}\left(d x +c \right)\right) a^{3}}{4}+\frac{a^{3} \left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{3}}{d}"," ",0,"1/d*(a^3*(-1/6*sin(d*x+c)^2*cos(d*x+c)^4-1/12*cos(d*x+c)^4)+3*a^3*(-1/5*cos(d*x+c)^4*sin(d*x+c)+1/15*(2+cos(d*x+c)^2)*sin(d*x+c))-3/4*cos(d*x+c)^4*a^3+1/3*a^3*(2+cos(d*x+c)^2)*sin(d*x+c))","B"
31,1,121,96,0.125000," ","int(cos(d*x+c)^2*(a+a*sin(d*x+c))^3,x)","\frac{a^{3} \left(-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{3}\left(d x +c \right)\right)}{5}-\frac{2 \left(\cos^{3}\left(d x +c \right)\right)}{15}\right)+3 a^{3} \left(-\frac{\sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right)}{4}+\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)}{8}+\frac{d x}{8}+\frac{c}{8}\right)-\left(\cos^{3}\left(d x +c \right)\right) a^{3}+a^{3} \left(\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)}{2}+\frac{d x}{2}+\frac{c}{2}\right)}{d}"," ",0,"1/d*(a^3*(-1/5*sin(d*x+c)^2*cos(d*x+c)^3-2/15*cos(d*x+c)^3)+3*a^3*(-1/4*sin(d*x+c)*cos(d*x+c)^3+1/8*cos(d*x+c)*sin(d*x+c)+1/8*d*x+1/8*c)-cos(d*x+c)^3*a^3+a^3*(1/2*cos(d*x+c)*sin(d*x+c)+1/2*d*x+1/2*c))","A"
32,1,21,20,0.073000," ","int(cos(d*x+c)*(a+a*sin(d*x+c))^3,x)","\frac{\left(a +a \sin \left(d x +c \right)\right)^{4}}{4 d a}"," ",0,"1/4*(a+a*sin(d*x+c))^4/d/a","A"
33,1,69,50,0.135000," ","int(sec(d*x+c)*(a+a*sin(d*x+c))^3,x)","-\frac{a^{3} \left(\sin^{2}\left(d x +c \right)\right)}{2 d}-\frac{4 a^{3} \ln \left(\cos \left(d x +c \right)\right)}{d}-\frac{3 a^{3} \sin \left(d x +c \right)}{d}+\frac{4 a^{3} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}"," ",0,"-1/2*a^3*sin(d*x+c)^2/d-4/d*a^3*ln(cos(d*x+c))-3*a^3*sin(d*x+c)/d+4/d*a^3*ln(sec(d*x+c)+tan(d*x+c))","A"
34,1,87,50,0.220000," ","int(sec(d*x+c)^2*(a+a*sin(d*x+c))^3,x)","\frac{a^{3} \left(\frac{\sin^{4}\left(d x +c \right)}{\cos \left(d x +c \right)}+\left(2+\sin^{2}\left(d x +c \right)\right) \cos \left(d x +c \right)\right)+3 a^{3} \left(\tan \left(d x +c \right)-d x -c \right)+\frac{3 a^{3}}{\cos \left(d x +c \right)}+a^{3} \tan \left(d x +c \right)}{d}"," ",0,"1/d*(a^3*(sin(d*x+c)^4/cos(d*x+c)+(2+sin(d*x+c)^2)*cos(d*x+c))+3*a^3*(tan(d*x+c)-d*x-c)+3*a^3/cos(d*x+c)+a^3*tan(d*x+c))","A"
35,1,128,40,0.224000," ","int(sec(d*x+c)^3*(a+a*sin(d*x+c))^3,x)","\frac{a^{3} \left(\tan^{2}\left(d x +c \right)\right)}{2 d}+\frac{a^{3} \ln \left(\cos \left(d x +c \right)\right)}{d}+\frac{3 a^{3} \left(\sin^{3}\left(d x +c \right)\right)}{2 d \cos \left(d x +c \right)^{2}}+\frac{3 a^{3} \sin \left(d x +c \right)}{2 d}-\frac{a^{3} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{3 a^{3}}{2 d \cos \left(d x +c \right)^{2}}+\frac{a^{3} \sec \left(d x +c \right) \tan \left(d x +c \right)}{2 d}"," ",0,"1/2/d*a^3*tan(d*x+c)^2+1/d*a^3*ln(cos(d*x+c))+3/2/d*a^3*sin(d*x+c)^3/cos(d*x+c)^2+3/2*a^3*sin(d*x+c)/d-1/d*a^3*ln(sec(d*x+c)+tan(d*x+c))+3/2/d*a^3/cos(d*x+c)^2+1/2/d*a^3*sec(d*x+c)*tan(d*x+c)","B"
36,1,120,29,0.263000," ","int(sec(d*x+c)^4*(a+a*sin(d*x+c))^3,x)","\frac{a^{3} \left(\frac{\sin^{4}\left(d x +c \right)}{3 \cos \left(d x +c \right)^{3}}-\frac{\sin^{4}\left(d x +c \right)}{3 \cos \left(d x +c \right)}-\frac{\left(2+\sin^{2}\left(d x +c \right)\right) \cos \left(d x +c \right)}{3}\right)+\frac{a^{3} \left(\sin^{3}\left(d x +c \right)\right)}{\cos \left(d x +c \right)^{3}}+\frac{a^{3}}{\cos \left(d x +c \right)^{3}}-a^{3} \left(-\frac{2}{3}-\frac{\left(\sec^{2}\left(d x +c \right)\right)}{3}\right) \tan \left(d x +c \right)}{d}"," ",0,"1/d*(a^3*(1/3*sin(d*x+c)^4/cos(d*x+c)^3-1/3*sin(d*x+c)^4/cos(d*x+c)-1/3*(2+sin(d*x+c)^2)*cos(d*x+c))+a^3/cos(d*x+c)^3*sin(d*x+c)^3+a^3/cos(d*x+c)^3-a^3*(-2/3-1/3*sec(d*x+c)^2)*tan(d*x+c))","B"
37,1,146,21,0.240000," ","int(sec(d*x+c)^5*(a+a*sin(d*x+c))^3,x)","\frac{a^{3} \left(\sin^{4}\left(d x +c \right)\right)}{4 d \cos \left(d x +c \right)^{4}}+\frac{3 a^{3} \left(\sin^{3}\left(d x +c \right)\right)}{4 d \cos \left(d x +c \right)^{4}}+\frac{3 a^{3} \left(\sin^{3}\left(d x +c \right)\right)}{8 d \cos \left(d x +c \right)^{2}}+\frac{3 a^{3} \sin \left(d x +c \right)}{8 d}+\frac{3 a^{3}}{4 d \cos \left(d x +c \right)^{4}}+\frac{a^{3} \tan \left(d x +c \right) \left(\sec^{3}\left(d x +c \right)\right)}{4 d}+\frac{3 a^{3} \sec \left(d x +c \right) \tan \left(d x +c \right)}{8 d}"," ",0,"1/4/d*a^3*sin(d*x+c)^4/cos(d*x+c)^4+3/4/d*a^3*sin(d*x+c)^3/cos(d*x+c)^4+3/8/d*a^3*sin(d*x+c)^3/cos(d*x+c)^2+3/8*a^3*sin(d*x+c)/d+3/4/d*a^3/cos(d*x+c)^4+1/4/d*a^3*tan(d*x+c)*sec(d*x+c)^3+3/8/d*a^3*sec(d*x+c)*tan(d*x+c)","B"
38,1,171,86,0.261000," ","int(sec(d*x+c)^6*(a+a*sin(d*x+c))^3,x)","\frac{a^{3} \left(\frac{\sin^{4}\left(d x +c \right)}{5 \cos \left(d x +c \right)^{5}}+\frac{\sin^{4}\left(d x +c \right)}{15 \cos \left(d x +c \right)^{3}}-\frac{\sin^{4}\left(d x +c \right)}{15 \cos \left(d x +c \right)}-\frac{\left(2+\sin^{2}\left(d x +c \right)\right) \cos \left(d x +c \right)}{15}\right)+3 a^{3} \left(\frac{\sin^{3}\left(d x +c \right)}{5 \cos \left(d x +c \right)^{5}}+\frac{2 \left(\sin^{3}\left(d x +c \right)\right)}{15 \cos \left(d x +c \right)^{3}}\right)+\frac{3 a^{3}}{5 \cos \left(d x +c \right)^{5}}-a^{3} \left(-\frac{8}{15}-\frac{\left(\sec^{4}\left(d x +c \right)\right)}{5}-\frac{4 \left(\sec^{2}\left(d x +c \right)\right)}{15}\right) \tan \left(d x +c \right)}{d}"," ",0,"1/d*(a^3*(1/5*sin(d*x+c)^4/cos(d*x+c)^5+1/15*sin(d*x+c)^4/cos(d*x+c)^3-1/15*sin(d*x+c)^4/cos(d*x+c)-1/15*(2+sin(d*x+c)^2)*cos(d*x+c))+3*a^3*(1/5*sin(d*x+c)^3/cos(d*x+c)^5+2/15*sin(d*x+c)^3/cos(d*x+c)^3)+3/5*a^3/cos(d*x+c)^5-a^3*(-8/15-1/5*sec(d*x+c)^4-4/15*sec(d*x+c)^2)*tan(d*x+c))","A"
39,1,238,79,0.246000," ","int(sec(d*x+c)^7*(a+a*sin(d*x+c))^3,x)","\frac{a^{3} \left(\sin^{4}\left(d x +c \right)\right)}{6 d \cos \left(d x +c \right)^{6}}+\frac{a^{3} \left(\sin^{4}\left(d x +c \right)\right)}{12 d \cos \left(d x +c \right)^{4}}+\frac{a^{3} \left(\sin^{3}\left(d x +c \right)\right)}{2 d \cos \left(d x +c \right)^{6}}+\frac{3 a^{3} \left(\sin^{3}\left(d x +c \right)\right)}{8 d \cos \left(d x +c \right)^{4}}+\frac{3 a^{3} \left(\sin^{3}\left(d x +c \right)\right)}{16 d \cos \left(d x +c \right)^{2}}+\frac{3 a^{3} \sin \left(d x +c \right)}{16 d}+\frac{a^{3} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{8 d}+\frac{a^{3}}{2 d \cos \left(d x +c \right)^{6}}+\frac{a^{3} \tan \left(d x +c \right) \left(\sec^{5}\left(d x +c \right)\right)}{6 d}+\frac{5 a^{3} \tan \left(d x +c \right) \left(\sec^{3}\left(d x +c \right)\right)}{24 d}+\frac{5 a^{3} \sec \left(d x +c \right) \tan \left(d x +c \right)}{16 d}"," ",0,"1/6/d*a^3*sin(d*x+c)^4/cos(d*x+c)^6+1/12/d*a^3*sin(d*x+c)^4/cos(d*x+c)^4+1/2/d*a^3*sin(d*x+c)^3/cos(d*x+c)^6+3/8/d*a^3*sin(d*x+c)^3/cos(d*x+c)^4+3/16/d*a^3*sin(d*x+c)^3/cos(d*x+c)^2+3/16*a^3*sin(d*x+c)/d+1/8/d*a^3*ln(sec(d*x+c)+tan(d*x+c))+1/2/d*a^3/cos(d*x+c)^6+1/6/d*a^3*tan(d*x+c)*sec(d*x+c)^5+5/24/d*a^3*tan(d*x+c)*sec(d*x+c)^3+5/16/d*a^3*sec(d*x+c)*tan(d*x+c)","B"
40,1,217,89,0.271000," ","int(sec(d*x+c)^8*(a+a*sin(d*x+c))^3,x)","\frac{a^{3} \left(\frac{\sin^{4}\left(d x +c \right)}{7 \cos \left(d x +c \right)^{7}}+\frac{3 \left(\sin^{4}\left(d x +c \right)\right)}{35 \cos \left(d x +c \right)^{5}}+\frac{\sin^{4}\left(d x +c \right)}{35 \cos \left(d x +c \right)^{3}}-\frac{\sin^{4}\left(d x +c \right)}{35 \cos \left(d x +c \right)}-\frac{\left(2+\sin^{2}\left(d x +c \right)\right) \cos \left(d x +c \right)}{35}\right)+3 a^{3} \left(\frac{\sin^{3}\left(d x +c \right)}{7 \cos \left(d x +c \right)^{7}}+\frac{4 \left(\sin^{3}\left(d x +c \right)\right)}{35 \cos \left(d x +c \right)^{5}}+\frac{8 \left(\sin^{3}\left(d x +c \right)\right)}{105 \cos \left(d x +c \right)^{3}}\right)+\frac{3 a^{3}}{7 \cos \left(d x +c \right)^{7}}-a^{3} \left(-\frac{16}{35}-\frac{\left(\sec^{6}\left(d x +c \right)\right)}{7}-\frac{6 \left(\sec^{4}\left(d x +c \right)\right)}{35}-\frac{8 \left(\sec^{2}\left(d x +c \right)\right)}{35}\right) \tan \left(d x +c \right)}{d}"," ",0,"1/d*(a^3*(1/7*sin(d*x+c)^4/cos(d*x+c)^7+3/35*sin(d*x+c)^4/cos(d*x+c)^5+1/35*sin(d*x+c)^4/cos(d*x+c)^3-1/35*sin(d*x+c)^4/cos(d*x+c)-1/35*(2+sin(d*x+c)^2)*cos(d*x+c))+3*a^3*(1/7*sin(d*x+c)^3/cos(d*x+c)^7+4/35*sin(d*x+c)^3/cos(d*x+c)^5+8/105*sin(d*x+c)^3/cos(d*x+c)^3)+3/7*a^3/cos(d*x+c)^7-a^3*(-16/35-1/7*sec(d*x+c)^6-6/35*sec(d*x+c)^4-8/35*sec(d*x+c)^2)*tan(d*x+c))","B"
41,1,513,61,0.182000," ","int(cos(d*x+c)^5*(a+a*sin(d*x+c))^8,x)","\frac{a^{8} \left(-\frac{\left(\sin^{7}\left(d x +c \right)\right) \left(\cos^{6}\left(d x +c \right)\right)}{13}-\frac{7 \left(\sin^{5}\left(d x +c \right)\right) \left(\cos^{6}\left(d x +c \right)\right)}{143}-\frac{35 \left(\sin^{3}\left(d x +c \right)\right) \left(\cos^{6}\left(d x +c \right)\right)}{1287}-\frac{5 \sin \left(d x +c \right) \left(\cos^{6}\left(d x +c \right)\right)}{429}+\frac{\left(\frac{8}{3}+\cos^{4}\left(d x +c \right)+\frac{4 \left(\cos^{2}\left(d x +c \right)\right)}{3}\right) \sin \left(d x +c \right)}{429}\right)+8 a^{8} \left(-\frac{\left(\sin^{6}\left(d x +c \right)\right) \left(\cos^{6}\left(d x +c \right)\right)}{12}-\frac{\left(\sin^{4}\left(d x +c \right)\right) \left(\cos^{6}\left(d x +c \right)\right)}{20}-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{6}\left(d x +c \right)\right)}{40}-\frac{\left(\cos^{6}\left(d x +c \right)\right)}{120}\right)+28 a^{8} \left(-\frac{\left(\sin^{5}\left(d x +c \right)\right) \left(\cos^{6}\left(d x +c \right)\right)}{11}-\frac{5 \left(\sin^{3}\left(d x +c \right)\right) \left(\cos^{6}\left(d x +c \right)\right)}{99}-\frac{5 \sin \left(d x +c \right) \left(\cos^{6}\left(d x +c \right)\right)}{231}+\frac{\left(\frac{8}{3}+\cos^{4}\left(d x +c \right)+\frac{4 \left(\cos^{2}\left(d x +c \right)\right)}{3}\right) \sin \left(d x +c \right)}{231}\right)+56 a^{8} \left(-\frac{\left(\sin^{4}\left(d x +c \right)\right) \left(\cos^{6}\left(d x +c \right)\right)}{10}-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{6}\left(d x +c \right)\right)}{20}-\frac{\left(\cos^{6}\left(d x +c \right)\right)}{60}\right)+70 a^{8} \left(-\frac{\left(\sin^{3}\left(d x +c \right)\right) \left(\cos^{6}\left(d x +c \right)\right)}{9}-\frac{\sin \left(d x +c \right) \left(\cos^{6}\left(d x +c \right)\right)}{21}+\frac{\left(\frac{8}{3}+\cos^{4}\left(d x +c \right)+\frac{4 \left(\cos^{2}\left(d x +c \right)\right)}{3}\right) \sin \left(d x +c \right)}{105}\right)+56 a^{8} \left(-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{6}\left(d x +c \right)\right)}{8}-\frac{\left(\cos^{6}\left(d x +c \right)\right)}{24}\right)+28 a^{8} \left(-\frac{\sin \left(d x +c \right) \left(\cos^{6}\left(d x +c \right)\right)}{7}+\frac{\left(\frac{8}{3}+\cos^{4}\left(d x +c \right)+\frac{4 \left(\cos^{2}\left(d x +c \right)\right)}{3}\right) \sin \left(d x +c \right)}{35}\right)-\frac{4 a^{8} \left(\cos^{6}\left(d x +c \right)\right)}{3}+\frac{a^{8} \left(\frac{8}{3}+\cos^{4}\left(d x +c \right)+\frac{4 \left(\cos^{2}\left(d x +c \right)\right)}{3}\right) \sin \left(d x +c \right)}{5}}{d}"," ",0,"1/d*(a^8*(-1/13*sin(d*x+c)^7*cos(d*x+c)^6-7/143*sin(d*x+c)^5*cos(d*x+c)^6-35/1287*sin(d*x+c)^3*cos(d*x+c)^6-5/429*sin(d*x+c)*cos(d*x+c)^6+1/429*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c))+8*a^8*(-1/12*sin(d*x+c)^6*cos(d*x+c)^6-1/20*sin(d*x+c)^4*cos(d*x+c)^6-1/40*sin(d*x+c)^2*cos(d*x+c)^6-1/120*cos(d*x+c)^6)+28*a^8*(-1/11*sin(d*x+c)^5*cos(d*x+c)^6-5/99*sin(d*x+c)^3*cos(d*x+c)^6-5/231*sin(d*x+c)*cos(d*x+c)^6+1/231*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c))+56*a^8*(-1/10*sin(d*x+c)^4*cos(d*x+c)^6-1/20*sin(d*x+c)^2*cos(d*x+c)^6-1/60*cos(d*x+c)^6)+70*a^8*(-1/9*sin(d*x+c)^3*cos(d*x+c)^6-1/21*sin(d*x+c)*cos(d*x+c)^6+1/105*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c))+56*a^8*(-1/8*sin(d*x+c)^2*cos(d*x+c)^6-1/24*cos(d*x+c)^6)+28*a^8*(-1/7*sin(d*x+c)*cos(d*x+c)^6+1/35*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c))-4/3*a^8*cos(d*x+c)^6+1/5*a^8*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c))","B"
42,1,535,264,0.196000," ","int(cos(d*x+c)^4*(a+a*sin(d*x+c))^8,x)","\frac{a^{8} \left(-\frac{\left(\sin^{7}\left(d x +c \right)\right) \left(\cos^{5}\left(d x +c \right)\right)}{12}-\frac{7 \left(\sin^{5}\left(d x +c \right)\right) \left(\cos^{5}\left(d x +c \right)\right)}{120}-\frac{7 \left(\sin^{3}\left(d x +c \right)\right) \left(\cos^{5}\left(d x +c \right)\right)}{192}-\frac{7 \sin \left(d x +c \right) \left(\cos^{5}\left(d x +c \right)\right)}{384}+\frac{7 \left(\cos^{3}\left(d x +c \right)+\frac{3 \cos \left(d x +c \right)}{2}\right) \sin \left(d x +c \right)}{1536}+\frac{7 d x}{1024}+\frac{7 c}{1024}\right)+8 a^{8} \left(-\frac{\left(\sin^{6}\left(d x +c \right)\right) \left(\cos^{5}\left(d x +c \right)\right)}{11}-\frac{2 \left(\sin^{4}\left(d x +c \right)\right) \left(\cos^{5}\left(d x +c \right)\right)}{33}-\frac{8 \left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{5}\left(d x +c \right)\right)}{231}-\frac{16 \left(\cos^{5}\left(d x +c \right)\right)}{1155}\right)+28 a^{8} \left(-\frac{\left(\sin^{5}\left(d x +c \right)\right) \left(\cos^{5}\left(d x +c \right)\right)}{10}-\frac{\left(\sin^{3}\left(d x +c \right)\right) \left(\cos^{5}\left(d x +c \right)\right)}{16}-\frac{\sin \left(d x +c \right) \left(\cos^{5}\left(d x +c \right)\right)}{32}+\frac{\left(\cos^{3}\left(d x +c \right)+\frac{3 \cos \left(d x +c \right)}{2}\right) \sin \left(d x +c \right)}{128}+\frac{3 d x}{256}+\frac{3 c}{256}\right)+56 a^{8} \left(-\frac{\left(\sin^{4}\left(d x +c \right)\right) \left(\cos^{5}\left(d x +c \right)\right)}{9}-\frac{4 \left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{5}\left(d x +c \right)\right)}{63}-\frac{8 \left(\cos^{5}\left(d x +c \right)\right)}{315}\right)+70 a^{8} \left(-\frac{\left(\sin^{3}\left(d x +c \right)\right) \left(\cos^{5}\left(d x +c \right)\right)}{8}-\frac{\sin \left(d x +c \right) \left(\cos^{5}\left(d x +c \right)\right)}{16}+\frac{\left(\cos^{3}\left(d x +c \right)+\frac{3 \cos \left(d x +c \right)}{2}\right) \sin \left(d x +c \right)}{64}+\frac{3 d x}{128}+\frac{3 c}{128}\right)+56 a^{8} \left(-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{5}\left(d x +c \right)\right)}{7}-\frac{2 \left(\cos^{5}\left(d x +c \right)\right)}{35}\right)+28 a^{8} \left(-\frac{\sin \left(d x +c \right) \left(\cos^{5}\left(d x +c \right)\right)}{6}+\frac{\left(\cos^{3}\left(d x +c \right)+\frac{3 \cos \left(d x +c \right)}{2}\right) \sin \left(d x +c \right)}{24}+\frac{d x}{16}+\frac{c}{16}\right)-\frac{8 \left(\cos^{5}\left(d x +c \right)\right) a^{8}}{5}+a^{8} \left(\frac{\left(\cos^{3}\left(d x +c \right)+\frac{3 \cos \left(d x +c \right)}{2}\right) \sin \left(d x +c \right)}{4}+\frac{3 d x}{8}+\frac{3 c}{8}\right)}{d}"," ",0,"1/d*(a^8*(-1/12*sin(d*x+c)^7*cos(d*x+c)^5-7/120*sin(d*x+c)^5*cos(d*x+c)^5-7/192*sin(d*x+c)^3*cos(d*x+c)^5-7/384*sin(d*x+c)*cos(d*x+c)^5+7/1536*(cos(d*x+c)^3+3/2*cos(d*x+c))*sin(d*x+c)+7/1024*d*x+7/1024*c)+8*a^8*(-1/11*sin(d*x+c)^6*cos(d*x+c)^5-2/33*sin(d*x+c)^4*cos(d*x+c)^5-8/231*sin(d*x+c)^2*cos(d*x+c)^5-16/1155*cos(d*x+c)^5)+28*a^8*(-1/10*sin(d*x+c)^5*cos(d*x+c)^5-1/16*sin(d*x+c)^3*cos(d*x+c)^5-1/32*sin(d*x+c)*cos(d*x+c)^5+1/128*(cos(d*x+c)^3+3/2*cos(d*x+c))*sin(d*x+c)+3/256*d*x+3/256*c)+56*a^8*(-1/9*sin(d*x+c)^4*cos(d*x+c)^5-4/63*sin(d*x+c)^2*cos(d*x+c)^5-8/315*cos(d*x+c)^5)+70*a^8*(-1/8*sin(d*x+c)^3*cos(d*x+c)^5-1/16*sin(d*x+c)*cos(d*x+c)^5+1/64*(cos(d*x+c)^3+3/2*cos(d*x+c))*sin(d*x+c)+3/128*d*x+3/128*c)+56*a^8*(-1/7*sin(d*x+c)^2*cos(d*x+c)^5-2/35*cos(d*x+c)^5)+28*a^8*(-1/6*sin(d*x+c)*cos(d*x+c)^5+1/24*(cos(d*x+c)^3+3/2*cos(d*x+c))*sin(d*x+c)+1/16*d*x+1/16*c)-8/5*cos(d*x+c)^5*a^8+a^8*(1/4*(cos(d*x+c)^3+3/2*cos(d*x+c))*sin(d*x+c)+3/8*d*x+3/8*c))","B"
43,1,463,41,0.189000," ","int(cos(d*x+c)^3*(a+a*sin(d*x+c))^8,x)","\frac{a^{8} \left(-\frac{\left(\sin^{7}\left(d x +c \right)\right) \left(\cos^{4}\left(d x +c \right)\right)}{11}-\frac{7 \left(\sin^{5}\left(d x +c \right)\right) \left(\cos^{4}\left(d x +c \right)\right)}{99}-\frac{5 \left(\sin^{3}\left(d x +c \right)\right) \left(\cos^{4}\left(d x +c \right)\right)}{99}-\frac{\left(\cos^{4}\left(d x +c \right)\right) \sin \left(d x +c \right)}{33}+\frac{\left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{99}\right)+8 a^{8} \left(-\frac{\left(\sin^{6}\left(d x +c \right)\right) \left(\cos^{4}\left(d x +c \right)\right)}{10}-\frac{3 \left(\sin^{4}\left(d x +c \right)\right) \left(\cos^{4}\left(d x +c \right)\right)}{40}-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{4}\left(d x +c \right)\right)}{20}-\frac{\left(\cos^{4}\left(d x +c \right)\right)}{40}\right)+28 a^{8} \left(-\frac{\left(\sin^{5}\left(d x +c \right)\right) \left(\cos^{4}\left(d x +c \right)\right)}{9}-\frac{5 \left(\sin^{3}\left(d x +c \right)\right) \left(\cos^{4}\left(d x +c \right)\right)}{63}-\frac{\left(\cos^{4}\left(d x +c \right)\right) \sin \left(d x +c \right)}{21}+\frac{\left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{63}\right)+56 a^{8} \left(-\frac{\left(\sin^{4}\left(d x +c \right)\right) \left(\cos^{4}\left(d x +c \right)\right)}{8}-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{4}\left(d x +c \right)\right)}{12}-\frac{\left(\cos^{4}\left(d x +c \right)\right)}{24}\right)+70 a^{8} \left(-\frac{\left(\sin^{3}\left(d x +c \right)\right) \left(\cos^{4}\left(d x +c \right)\right)}{7}-\frac{3 \left(\cos^{4}\left(d x +c \right)\right) \sin \left(d x +c \right)}{35}+\frac{\left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{35}\right)+56 a^{8} \left(-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{4}\left(d x +c \right)\right)}{6}-\frac{\left(\cos^{4}\left(d x +c \right)\right)}{12}\right)+28 a^{8} \left(-\frac{\left(\cos^{4}\left(d x +c \right)\right) \sin \left(d x +c \right)}{5}+\frac{\left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{15}\right)-2 \left(\cos^{4}\left(d x +c \right)\right) a^{8}+\frac{a^{8} \left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{3}}{d}"," ",0,"1/d*(a^8*(-1/11*sin(d*x+c)^7*cos(d*x+c)^4-7/99*sin(d*x+c)^5*cos(d*x+c)^4-5/99*sin(d*x+c)^3*cos(d*x+c)^4-1/33*cos(d*x+c)^4*sin(d*x+c)+1/99*(2+cos(d*x+c)^2)*sin(d*x+c))+8*a^8*(-1/10*sin(d*x+c)^6*cos(d*x+c)^4-3/40*sin(d*x+c)^4*cos(d*x+c)^4-1/20*sin(d*x+c)^2*cos(d*x+c)^4-1/40*cos(d*x+c)^4)+28*a^8*(-1/9*sin(d*x+c)^5*cos(d*x+c)^4-5/63*sin(d*x+c)^3*cos(d*x+c)^4-1/21*cos(d*x+c)^4*sin(d*x+c)+1/63*(2+cos(d*x+c)^2)*sin(d*x+c))+56*a^8*(-1/8*sin(d*x+c)^4*cos(d*x+c)^4-1/12*sin(d*x+c)^2*cos(d*x+c)^4-1/24*cos(d*x+c)^4)+70*a^8*(-1/7*sin(d*x+c)^3*cos(d*x+c)^4-3/35*cos(d*x+c)^4*sin(d*x+c)+1/35*(2+cos(d*x+c)^2)*sin(d*x+c))+56*a^8*(-1/6*sin(d*x+c)^2*cos(d*x+c)^4-1/12*cos(d*x+c)^4)+28*a^8*(-1/5*cos(d*x+c)^4*sin(d*x+c)+1/15*(2+cos(d*x+c)^2)*sin(d*x+c))-2*cos(d*x+c)^4*a^8+1/3*a^8*(2+cos(d*x+c)^2)*sin(d*x+c))","B"
44,1,480,242,0.141000," ","int(cos(d*x+c)^2*(a+a*sin(d*x+c))^8,x)","\frac{a^{8} \left(-\frac{\left(\sin^{7}\left(d x +c \right)\right) \left(\cos^{3}\left(d x +c \right)\right)}{10}-\frac{7 \left(\sin^{5}\left(d x +c \right)\right) \left(\cos^{3}\left(d x +c \right)\right)}{80}-\frac{7 \left(\sin^{3}\left(d x +c \right)\right) \left(\cos^{3}\left(d x +c \right)\right)}{96}-\frac{7 \sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right)}{128}+\frac{7 \cos \left(d x +c \right) \sin \left(d x +c \right)}{256}+\frac{7 d x}{256}+\frac{7 c}{256}\right)+8 a^{8} \left(-\frac{\left(\sin^{6}\left(d x +c \right)\right) \left(\cos^{3}\left(d x +c \right)\right)}{9}-\frac{2 \left(\sin^{4}\left(d x +c \right)\right) \left(\cos^{3}\left(d x +c \right)\right)}{21}-\frac{8 \left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{3}\left(d x +c \right)\right)}{105}-\frac{16 \left(\cos^{3}\left(d x +c \right)\right)}{315}\right)+28 a^{8} \left(-\frac{\left(\sin^{5}\left(d x +c \right)\right) \left(\cos^{3}\left(d x +c \right)\right)}{8}-\frac{5 \left(\sin^{3}\left(d x +c \right)\right) \left(\cos^{3}\left(d x +c \right)\right)}{48}-\frac{5 \sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right)}{64}+\frac{5 \cos \left(d x +c \right) \sin \left(d x +c \right)}{128}+\frac{5 d x}{128}+\frac{5 c}{128}\right)+56 a^{8} \left(-\frac{\left(\sin^{4}\left(d x +c \right)\right) \left(\cos^{3}\left(d x +c \right)\right)}{7}-\frac{4 \left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{3}\left(d x +c \right)\right)}{35}-\frac{8 \left(\cos^{3}\left(d x +c \right)\right)}{105}\right)+70 a^{8} \left(-\frac{\left(\sin^{3}\left(d x +c \right)\right) \left(\cos^{3}\left(d x +c \right)\right)}{6}-\frac{\sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right)}{8}+\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)}{16}+\frac{d x}{16}+\frac{c}{16}\right)+56 a^{8} \left(-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{3}\left(d x +c \right)\right)}{5}-\frac{2 \left(\cos^{3}\left(d x +c \right)\right)}{15}\right)+28 a^{8} \left(-\frac{\sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right)}{4}+\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)}{8}+\frac{d x}{8}+\frac{c}{8}\right)-\frac{8 \left(\cos^{3}\left(d x +c \right)\right) a^{8}}{3}+a^{8} \left(\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)}{2}+\frac{d x}{2}+\frac{c}{2}\right)}{d}"," ",0,"1/d*(a^8*(-1/10*sin(d*x+c)^7*cos(d*x+c)^3-7/80*sin(d*x+c)^5*cos(d*x+c)^3-7/96*sin(d*x+c)^3*cos(d*x+c)^3-7/128*sin(d*x+c)*cos(d*x+c)^3+7/256*cos(d*x+c)*sin(d*x+c)+7/256*d*x+7/256*c)+8*a^8*(-1/9*sin(d*x+c)^6*cos(d*x+c)^3-2/21*sin(d*x+c)^4*cos(d*x+c)^3-8/105*sin(d*x+c)^2*cos(d*x+c)^3-16/315*cos(d*x+c)^3)+28*a^8*(-1/8*sin(d*x+c)^5*cos(d*x+c)^3-5/48*sin(d*x+c)^3*cos(d*x+c)^3-5/64*sin(d*x+c)*cos(d*x+c)^3+5/128*cos(d*x+c)*sin(d*x+c)+5/128*d*x+5/128*c)+56*a^8*(-1/7*sin(d*x+c)^4*cos(d*x+c)^3-4/35*sin(d*x+c)^2*cos(d*x+c)^3-8/105*cos(d*x+c)^3)+70*a^8*(-1/6*sin(d*x+c)^3*cos(d*x+c)^3-1/8*sin(d*x+c)*cos(d*x+c)^3+1/16*cos(d*x+c)*sin(d*x+c)+1/16*d*x+1/16*c)+56*a^8*(-1/5*sin(d*x+c)^2*cos(d*x+c)^3-2/15*cos(d*x+c)^3)+28*a^8*(-1/4*sin(d*x+c)*cos(d*x+c)^3+1/8*cos(d*x+c)*sin(d*x+c)+1/8*d*x+1/8*c)-8/3*cos(d*x+c)^3*a^8+a^8*(1/2*cos(d*x+c)*sin(d*x+c)+1/2*d*x+1/2*c))","A"
45,1,21,20,0.079000," ","int(cos(d*x+c)*(a+a*sin(d*x+c))^8,x)","\frac{\left(a +a \sin \left(d x +c \right)\right)^{9}}{9 d a}"," ",0,"1/9*(a+a*sin(d*x+c))^9/d/a","A"
46,1,149,154,0.167000," ","int(sec(d*x+c)*(a+a*sin(d*x+c))^8,x)","-\frac{a^{8} \left(\sin^{7}\left(d x +c \right)\right)}{7 d}-\frac{4 a^{8} \left(\sin^{6}\left(d x +c \right)\right)}{3 d}-\frac{29 a^{8} \left(\sin^{5}\left(d x +c \right)\right)}{5 d}-\frac{16 a^{8} \left(\sin^{4}\left(d x +c \right)\right)}{d}-\frac{33 a^{8} \left(\sin^{3}\left(d x +c \right)\right)}{d}-\frac{60 a^{8} \left(\sin^{2}\left(d x +c \right)\right)}{d}-\frac{127 a^{8} \sin \left(d x +c \right)}{d}-\frac{128 a^{8} \ln \left(\cos \left(d x +c \right)\right)}{d}+\frac{128 a^{8} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}"," ",0,"-1/7/d*a^8*sin(d*x+c)^7-4/3/d*a^8*sin(d*x+c)^6-29/5*a^8*sin(d*x+c)^5/d-16*a^8*sin(d*x+c)^4/d-33*a^8*sin(d*x+c)^3/d-60*a^8*sin(d*x+c)^2/d-127*a^8*sin(d*x+c)/d-128/d*a^8*ln(cos(d*x+c))+128/d*a^8*ln(sec(d*x+c)+tan(d*x+c))","A"
47,1,389,189,0.382000," ","int(sec(d*x+c)^2*(a+a*sin(d*x+c))^8,x)","\frac{a^{8} \left(\frac{\sin^{9}\left(d x +c \right)}{\cos \left(d x +c \right)}+\left(\sin^{7}\left(d x +c \right)+\frac{7 \left(\sin^{5}\left(d x +c \right)\right)}{6}+\frac{35 \left(\sin^{3}\left(d x +c \right)\right)}{24}+\frac{35 \sin \left(d x +c \right)}{16}\right) \cos \left(d x +c \right)-\frac{35 d x}{16}-\frac{35 c}{16}\right)+8 a^{8} \left(\frac{\sin^{8}\left(d x +c \right)}{\cos \left(d x +c \right)}+\left(\frac{16}{5}+\sin^{6}\left(d x +c \right)+\frac{6 \left(\sin^{4}\left(d x +c \right)\right)}{5}+\frac{8 \left(\sin^{2}\left(d x +c \right)\right)}{5}\right) \cos \left(d x +c \right)\right)+28 a^{8} \left(\frac{\sin^{7}\left(d x +c \right)}{\cos \left(d x +c \right)}+\left(\sin^{5}\left(d x +c \right)+\frac{5 \left(\sin^{3}\left(d x +c \right)\right)}{4}+\frac{15 \sin \left(d x +c \right)}{8}\right) \cos \left(d x +c \right)-\frac{15 d x}{8}-\frac{15 c}{8}\right)+56 a^{8} \left(\frac{\sin^{6}\left(d x +c \right)}{\cos \left(d x +c \right)}+\left(\frac{8}{3}+\sin^{4}\left(d x +c \right)+\frac{4 \left(\sin^{2}\left(d x +c \right)\right)}{3}\right) \cos \left(d x +c \right)\right)+70 a^{8} \left(\frac{\sin^{5}\left(d x +c \right)}{\cos \left(d x +c \right)}+\left(\sin^{3}\left(d x +c \right)+\frac{3 \sin \left(d x +c \right)}{2}\right) \cos \left(d x +c \right)-\frac{3 d x}{2}-\frac{3 c}{2}\right)+56 a^{8} \left(\frac{\sin^{4}\left(d x +c \right)}{\cos \left(d x +c \right)}+\left(2+\sin^{2}\left(d x +c \right)\right) \cos \left(d x +c \right)\right)+28 a^{8} \left(\tan \left(d x +c \right)-d x -c \right)+\frac{8 a^{8}}{\cos \left(d x +c \right)}+a^{8} \tan \left(d x +c \right)}{d}"," ",0,"1/d*(a^8*(sin(d*x+c)^9/cos(d*x+c)+(sin(d*x+c)^7+7/6*sin(d*x+c)^5+35/24*sin(d*x+c)^3+35/16*sin(d*x+c))*cos(d*x+c)-35/16*d*x-35/16*c)+8*a^8*(sin(d*x+c)^8/cos(d*x+c)+(16/5+sin(d*x+c)^6+6/5*sin(d*x+c)^4+8/5*sin(d*x+c)^2)*cos(d*x+c))+28*a^8*(sin(d*x+c)^7/cos(d*x+c)+(sin(d*x+c)^5+5/4*sin(d*x+c)^3+15/8*sin(d*x+c))*cos(d*x+c)-15/8*d*x-15/8*c)+56*a^8*(sin(d*x+c)^6/cos(d*x+c)+(8/3+sin(d*x+c)^4+4/3*sin(d*x+c)^2)*cos(d*x+c))+70*a^8*(sin(d*x+c)^5/cos(d*x+c)+(sin(d*x+c)^3+3/2*sin(d*x+c))*cos(d*x+c)-3/2*d*x-3/2*c)+56*a^8*(sin(d*x+c)^4/cos(d*x+c)+(2+sin(d*x+c)^2)*cos(d*x+c))+28*a^8*(tan(d*x+c)-d*x-c)+8*a^8/cos(d*x+c)+a^8*tan(d*x+c))","B"
48,1,345,119,0.279000," ","int(sec(d*x+c)^3*(a+a*sin(d*x+c))^8,x)","\frac{a^{8} \left(\sin^{7}\left(d x +c \right)\right)}{2 d}+\frac{4 a^{8} \left(\sin^{6}\left(d x +c \right)\right)}{d}+\frac{147 a^{8} \left(\sin^{5}\left(d x +c \right)\right)}{10 d}+\frac{34 a^{8} \left(\sin^{4}\left(d x +c \right)\right)}{d}+\frac{119 a^{8} \left(\sin^{3}\left(d x +c \right)\right)}{2 d}+\frac{68 a^{8} \left(\sin^{2}\left(d x +c \right)\right)}{d}+\frac{385 a^{8} \sin \left(d x +c \right)}{2 d}+\frac{a^{8} \left(\sin^{9}\left(d x +c \right)\right)}{2 d \cos \left(d x +c \right)^{2}}+\frac{4 a^{8} \left(\sin^{8}\left(d x +c \right)\right)}{d \cos \left(d x +c \right)^{2}}+\frac{14 a^{8} \left(\sin^{7}\left(d x +c \right)\right)}{d \cos \left(d x +c \right)^{2}}+\frac{192 a^{8} \ln \left(\cos \left(d x +c \right)\right)}{d}-\frac{192 a^{8} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{28 a^{8} \left(\sin^{6}\left(d x +c \right)\right)}{d \cos \left(d x +c \right)^{2}}+\frac{35 a^{8} \left(\sin^{5}\left(d x +c \right)\right)}{d \cos \left(d x +c \right)^{2}}+\frac{14 a^{8} \left(\sin^{3}\left(d x +c \right)\right)}{d \cos \left(d x +c \right)^{2}}+\frac{a^{8} \sec \left(d x +c \right) \tan \left(d x +c \right)}{2 d}+\frac{28 a^{8} \left(\tan^{2}\left(d x +c \right)\right)}{d}+\frac{4 a^{8}}{d \cos \left(d x +c \right)^{2}}"," ",0,"1/2/d*a^8*sin(d*x+c)^7+4/d*a^8*sin(d*x+c)^6+147/10*a^8*sin(d*x+c)^5/d+34*a^8*sin(d*x+c)^4/d+119/2*a^8*sin(d*x+c)^3/d+68*a^8*sin(d*x+c)^2/d+385/2*a^8*sin(d*x+c)/d+1/2/d*a^8*sin(d*x+c)^9/cos(d*x+c)^2+4/d*a^8*sin(d*x+c)^8/cos(d*x+c)^2+14/d*a^8*sin(d*x+c)^7/cos(d*x+c)^2+192/d*a^8*ln(cos(d*x+c))-192/d*a^8*ln(sec(d*x+c)+tan(d*x+c))+28/d*a^8*sin(d*x+c)^6/cos(d*x+c)^2+35/d*a^8*sin(d*x+c)^5/cos(d*x+c)^2+14/d*a^8*sin(d*x+c)^3/cos(d*x+c)^2+1/2/d*a^8*sec(d*x+c)*tan(d*x+c)+28/d*a^8*tan(d*x+c)^2+4/d*a^8/cos(d*x+c)^2","B"
49,1,478,167,0.418000," ","int(sec(d*x+c)^4*(a+a*sin(d*x+c))^8,x)","\frac{a^{8} \left(\frac{\sin^{9}\left(d x +c \right)}{3 \cos \left(d x +c \right)^{3}}-\frac{2 \left(\sin^{9}\left(d x +c \right)\right)}{\cos \left(d x +c \right)}-2 \left(\sin^{7}\left(d x +c \right)+\frac{7 \left(\sin^{5}\left(d x +c \right)\right)}{6}+\frac{35 \left(\sin^{3}\left(d x +c \right)\right)}{24}+\frac{35 \sin \left(d x +c \right)}{16}\right) \cos \left(d x +c \right)+\frac{35 d x}{8}+\frac{35 c}{8}\right)+8 a^{8} \left(\frac{\sin^{8}\left(d x +c \right)}{3 \cos \left(d x +c \right)^{3}}-\frac{5 \left(\sin^{8}\left(d x +c \right)\right)}{3 \cos \left(d x +c \right)}-\frac{5 \left(\frac{16}{5}+\sin^{6}\left(d x +c \right)+\frac{6 \left(\sin^{4}\left(d x +c \right)\right)}{5}+\frac{8 \left(\sin^{2}\left(d x +c \right)\right)}{5}\right) \cos \left(d x +c \right)}{3}\right)+28 a^{8} \left(\frac{\sin^{7}\left(d x +c \right)}{3 \cos \left(d x +c \right)^{3}}-\frac{4 \left(\sin^{7}\left(d x +c \right)\right)}{3 \cos \left(d x +c \right)}-\frac{4 \left(\sin^{5}\left(d x +c \right)+\frac{5 \left(\sin^{3}\left(d x +c \right)\right)}{4}+\frac{15 \sin \left(d x +c \right)}{8}\right) \cos \left(d x +c \right)}{3}+\frac{5 d x}{2}+\frac{5 c}{2}\right)+56 a^{8} \left(\frac{\sin^{6}\left(d x +c \right)}{3 \cos \left(d x +c \right)^{3}}-\frac{\sin^{6}\left(d x +c \right)}{\cos \left(d x +c \right)}-\left(\frac{8}{3}+\sin^{4}\left(d x +c \right)+\frac{4 \left(\sin^{2}\left(d x +c \right)\right)}{3}\right) \cos \left(d x +c \right)\right)+70 a^{8} \left(\frac{\left(\tan^{3}\left(d x +c \right)\right)}{3}-\tan \left(d x +c \right)+d x +c \right)+56 a^{8} \left(\frac{\sin^{4}\left(d x +c \right)}{3 \cos \left(d x +c \right)^{3}}-\frac{\sin^{4}\left(d x +c \right)}{3 \cos \left(d x +c \right)}-\frac{\left(2+\sin^{2}\left(d x +c \right)\right) \cos \left(d x +c \right)}{3}\right)+\frac{28 a^{8} \left(\sin^{3}\left(d x +c \right)\right)}{3 \cos \left(d x +c \right)^{3}}+\frac{8 a^{8}}{3 \cos \left(d x +c \right)^{3}}-a^{8} \left(-\frac{2}{3}-\frac{\left(\sec^{2}\left(d x +c \right)\right)}{3}\right) \tan \left(d x +c \right)}{d}"," ",0,"1/d*(a^8*(1/3*sin(d*x+c)^9/cos(d*x+c)^3-2*sin(d*x+c)^9/cos(d*x+c)-2*(sin(d*x+c)^7+7/6*sin(d*x+c)^5+35/24*sin(d*x+c)^3+35/16*sin(d*x+c))*cos(d*x+c)+35/8*d*x+35/8*c)+8*a^8*(1/3*sin(d*x+c)^8/cos(d*x+c)^3-5/3*sin(d*x+c)^8/cos(d*x+c)-5/3*(16/5+sin(d*x+c)^6+6/5*sin(d*x+c)^4+8/5*sin(d*x+c)^2)*cos(d*x+c))+28*a^8*(1/3*sin(d*x+c)^7/cos(d*x+c)^3-4/3*sin(d*x+c)^7/cos(d*x+c)-4/3*(sin(d*x+c)^5+5/4*sin(d*x+c)^3+15/8*sin(d*x+c))*cos(d*x+c)+5/2*d*x+5/2*c)+56*a^8*(1/3*sin(d*x+c)^6/cos(d*x+c)^3-sin(d*x+c)^6/cos(d*x+c)-(8/3+sin(d*x+c)^4+4/3*sin(d*x+c)^2)*cos(d*x+c))+70*a^8*(1/3*tan(d*x+c)^3-tan(d*x+c)+d*x+c)+56*a^8*(1/3*sin(d*x+c)^4/cos(d*x+c)^3-1/3*sin(d*x+c)^4/cos(d*x+c)-1/3*(2+sin(d*x+c)^2)*cos(d*x+c))+28/3*a^8/cos(d*x+c)^3*sin(d*x+c)^3+8/3*a^8/cos(d*x+c)^3-a^8*(-2/3-1/3*sec(d*x+c)^2)*tan(d*x+c))","B"
50,1,503,108,0.279000," ","int(sec(d*x+c)^5*(a+a*sin(d*x+c))^8,x)","-\frac{4 a^{8} \left(\sin^{6}\left(d x +c \right)\right)}{d}+\frac{a^{8} \left(\sin^{9}\left(d x +c \right)\right)}{4 d \cos \left(d x +c \right)^{4}}+\frac{2 a^{8} \left(\sin^{8}\left(d x +c \right)\right)}{d \cos \left(d x +c \right)^{4}}+\frac{7 a^{8} \left(\sin^{7}\left(d x +c \right)\right)}{d \cos \left(d x +c \right)^{4}}+\frac{35 a^{8} \left(\sin^{5}\left(d x +c \right)\right)}{2 d \cos \left(d x +c \right)^{4}}+\frac{7 a^{8} \left(\sin^{3}\left(d x +c \right)\right)}{d \cos \left(d x +c \right)^{4}}+\frac{a^{8} \tan \left(d x +c \right) \left(\sec^{3}\left(d x +c \right)\right)}{4 d}+\frac{14 a^{8} \left(\sin^{4}\left(d x +c \right)\right)}{d \cos \left(d x +c \right)^{4}}-\frac{91 a^{8} \left(\sin^{5}\left(d x +c \right)\right)}{8 d}-\frac{28 a^{8} \left(\tan^{2}\left(d x +c \right)\right)}{d}-\frac{5 a^{8} \left(\sin^{9}\left(d x +c \right)\right)}{8 d \cos \left(d x +c \right)^{2}}-\frac{35 a^{8} \left(\sin^{5}\left(d x +c \right)\right)}{4 d \cos \left(d x +c \right)^{2}}-\frac{6 a^{8} \left(\sin^{4}\left(d x +c \right)\right)}{d}-\frac{637 a^{8} \sin \left(d x +c \right)}{8 d}-\frac{12 a^{8} \left(\sin^{2}\left(d x +c \right)\right)}{d}+\frac{2 a^{8}}{d \cos \left(d x +c \right)^{4}}-\frac{80 a^{8} \ln \left(\cos \left(d x +c \right)\right)}{d}+\frac{80 a^{8} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}-\frac{665 a^{8} \left(\sin^{3}\left(d x +c \right)\right)}{24 d}+\frac{14 a^{8} \left(\tan^{4}\left(d x +c \right)\right)}{d}-\frac{5 a^{8} \left(\sin^{7}\left(d x +c \right)\right)}{8 d}-\frac{4 a^{8} \left(\sin^{8}\left(d x +c \right)\right)}{d \cos \left(d x +c \right)^{2}}-\frac{21 a^{8} \left(\sin^{7}\left(d x +c \right)\right)}{2 d \cos \left(d x +c \right)^{2}}+\frac{7 a^{8} \left(\sin^{3}\left(d x +c \right)\right)}{2 d \cos \left(d x +c \right)^{2}}+\frac{3 a^{8} \sec \left(d x +c \right) \tan \left(d x +c \right)}{8 d}"," ",0,"-637/8*a^8*sin(d*x+c)/d-12*a^8*sin(d*x+c)^2/d-665/24*a^8*sin(d*x+c)^3/d-6*a^8*sin(d*x+c)^4/d-91/8*a^8*sin(d*x+c)^5/d+2/d*a^8/cos(d*x+c)^4+14/d*a^8*tan(d*x+c)^4-5/8/d*a^8*sin(d*x+c)^7-4/d*a^8*sin(d*x+c)^6-80/d*a^8*ln(cos(d*x+c))+80/d*a^8*ln(sec(d*x+c)+tan(d*x+c))+1/4/d*a^8*sin(d*x+c)^9/cos(d*x+c)^4+2/d*a^8*sin(d*x+c)^8/cos(d*x+c)^4+7/d*a^8*sin(d*x+c)^7/cos(d*x+c)^4+35/2/d*a^8*sin(d*x+c)^5/cos(d*x+c)^4+7/d*a^8*sin(d*x+c)^3/cos(d*x+c)^4+1/4/d*a^8*tan(d*x+c)*sec(d*x+c)^3+14/d*a^8/cos(d*x+c)^4*sin(d*x+c)^4-28/d*a^8*tan(d*x+c)^2-5/8/d*a^8*sin(d*x+c)^9/cos(d*x+c)^2-4/d*a^8*sin(d*x+c)^8/cos(d*x+c)^2-21/2/d*a^8*sin(d*x+c)^7/cos(d*x+c)^2-35/4/d*a^8*sin(d*x+c)^5/cos(d*x+c)^2+7/2/d*a^8*sin(d*x+c)^3/cos(d*x+c)^2+3/8/d*a^8*sec(d*x+c)*tan(d*x+c)","B"
51,1,245,65,0.146000," ","int(cos(d*x+c)^6/(a+a*sin(d*x+c)),x)","-\frac{5 \left(\tan^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}+\frac{2 \left(\tan^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}-\frac{\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)}{2 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}+\frac{4 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}+\frac{\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)}{2 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}+\frac{5 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{4 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}+\frac{2}{5 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}+\frac{3 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 a d}"," ",0,"-5/4/a/d/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^9+2/a/d/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^8-1/2/a/d/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^7+4/a/d/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^4+1/2/a/d/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^3+5/4/a/d/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)+2/5/a/d/(1+tan(1/2*d*x+1/2*c)^2)^5+3/4/a/d*arctan(tan(1/2*d*x+1/2*c))","B"
52,1,45,43,0.135000," ","int(cos(d*x+c)^5/(a+a*sin(d*x+c)),x)","\frac{\frac{\left(\sin^{4}\left(d x +c \right)\right)}{4}-\frac{\left(\sin^{3}\left(d x +c \right)\right)}{3}-\frac{\left(\sin^{2}\left(d x +c \right)\right)}{2}+\sin \left(d x +c \right)}{d a}"," ",0,"1/d/a*(1/4*sin(d*x+c)^4-1/3*sin(d*x+c)^3-1/2*sin(d*x+c)^2+sin(d*x+c))","A"
53,1,141,43,0.138000," ","int(cos(d*x+c)^4/(a+a*sin(d*x+c)),x)","-\frac{\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)}{a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}+\frac{2 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}+\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}+\frac{2}{3 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}+\frac{\arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a d}"," ",0,"-1/a/d/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)^5+2/a/d/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)^4+1/a/d/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)+2/3/a/d/(1+tan(1/2*d*x+1/2*c)^2)^3+1/a/d*arctan(tan(1/2*d*x+1/2*c))","B"
54,1,28,30,0.077000," ","int(cos(d*x+c)^3/(a+a*sin(d*x+c)),x)","-\frac{\frac{\left(\sin^{2}\left(d x +c \right)\right)}{2}-\sin \left(d x +c \right)}{a d}"," ",0,"-1/a/d*(1/2*sin(d*x+c)^2-sin(d*x+c))","A"
55,1,43,19,0.125000," ","int(cos(d*x+c)^2/(a+a*sin(d*x+c)),x)","\frac{2}{a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}+\frac{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a d}"," ",0,"2/a/d/(1+tan(1/2*d*x+1/2*c)^2)+2/a/d*arctan(tan(1/2*d*x+1/2*c))","B"
56,1,19,16,0.057000," ","int(cos(d*x+c)/(a+a*sin(d*x+c)),x)","\frac{\ln \left(a +a \sin \left(d x +c \right)\right)}{d a}"," ",0,"1/d*ln(a+a*sin(d*x+c))/a","A"
57,1,54,33,0.145000," ","int(sec(d*x+c)/(a+a*sin(d*x+c)),x)","-\frac{\ln \left(\sin \left(d x +c \right)-1\right)}{4 a d}-\frac{1}{2 a d \left(1+\sin \left(d x +c \right)\right)}+\frac{\ln \left(1+\sin \left(d x +c \right)\right)}{4 a d}"," ",0,"-1/4/a/d*ln(sin(d*x+c)-1)-1/2/a/d/(1+sin(d*x+c))+1/4*ln(1+sin(d*x+c))/a/d","A"
58,1,70,38,0.148000," ","int(sec(d*x+c)^2/(a+a*sin(d*x+c)),x)","\frac{-\frac{1}{2 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{2}{3 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}+\frac{1}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}-\frac{3}{2 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}}{d a}"," ",0,"2/d/a*(-1/4/(tan(1/2*d*x+1/2*c)-1)-1/3/(tan(1/2*d*x+1/2*c)+1)^3+1/2/(tan(1/2*d*x+1/2*c)+1)^2-3/4/(tan(1/2*d*x+1/2*c)+1))","A"
59,1,90,69,0.161000," ","int(sec(d*x+c)^3/(a+a*sin(d*x+c)),x)","-\frac{1}{8 a d \left(\sin \left(d x +c \right)-1\right)}-\frac{3 \ln \left(\sin \left(d x +c \right)-1\right)}{16 a d}-\frac{1}{8 a d \left(1+\sin \left(d x +c \right)\right)^{2}}-\frac{1}{4 a d \left(1+\sin \left(d x +c \right)\right)}+\frac{3 \ln \left(1+\sin \left(d x +c \right)\right)}{16 a d}"," ",0,"-1/8/a/d/(sin(d*x+c)-1)-3/16/a/d*ln(sin(d*x+c)-1)-1/8/a/d/(1+sin(d*x+c))^2-1/4/a/d/(1+sin(d*x+c))+3/16*ln(1+sin(d*x+c))/a/d","A"
60,1,130,56,0.164000," ","int(sec(d*x+c)^4/(a+a*sin(d*x+c)),x)","\frac{-\frac{1}{6 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{3}}-\frac{1}{4 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}-\frac{5}{8 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{2}{5 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{5}}+\frac{1}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{4}}-\frac{5}{3 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}+\frac{3}{2 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}-\frac{11}{8 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}}{d a}"," ",0,"2/d/a*(-1/12/(tan(1/2*d*x+1/2*c)-1)^3-1/8/(tan(1/2*d*x+1/2*c)-1)^2-5/16/(tan(1/2*d*x+1/2*c)-1)-1/5/(tan(1/2*d*x+1/2*c)+1)^5+1/2/(tan(1/2*d*x+1/2*c)+1)^4-5/6/(tan(1/2*d*x+1/2*c)+1)^3+3/4/(tan(1/2*d*x+1/2*c)+1)^2-11/16/(tan(1/2*d*x+1/2*c)+1))","B"
61,1,126,108,0.168000," ","int(sec(d*x+c)^5/(a+a*sin(d*x+c)),x)","\frac{1}{32 a d \left(\sin \left(d x +c \right)-1\right)^{2}}-\frac{1}{8 a d \left(\sin \left(d x +c \right)-1\right)}-\frac{5 \ln \left(\sin \left(d x +c \right)-1\right)}{32 a d}-\frac{1}{24 a d \left(1+\sin \left(d x +c \right)\right)^{3}}-\frac{3}{32 a d \left(1+\sin \left(d x +c \right)\right)^{2}}-\frac{3}{16 a d \left(1+\sin \left(d x +c \right)\right)}+\frac{5 \ln \left(1+\sin \left(d x +c \right)\right)}{32 a d}"," ",0,"1/32/a/d/(sin(d*x+c)-1)^2-1/8/a/d/(sin(d*x+c)-1)-5/32/a/d*ln(sin(d*x+c)-1)-1/24/a/d/(1+sin(d*x+c))^3-3/32/a/d/(1+sin(d*x+c))^2-3/16/a/d/(1+sin(d*x+c))+5/32*ln(1+sin(d*x+c))/a/d","A"
62,1,415,94,0.225000," ","int(cos(d*x+c)^8/(a+a*sin(d*x+c))^2,x)","-\frac{9 \left(\tan^{11}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{8 a^{2} d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}+\frac{4 \left(\tan^{10}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a^{2} d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}-\frac{89 \left(\tan^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{24 a^{2} d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}+\frac{4 \left(\tan^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a^{2} d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}+\frac{11 \left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 a^{2} d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}+\frac{8 \left(\tan^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a^{2} d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}-\frac{11 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 a^{2} d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}+\frac{8 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a^{2} d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}+\frac{89 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{24 a^{2} d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}+\frac{4 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{5 a^{2} d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}+\frac{9 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{8 a^{2} d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}+\frac{4}{5 a^{2} d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}+\frac{7 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{8 a^{2} d}"," ",0,"-9/8/a^2/d/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^11+4/a^2/d/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^10-89/24/a^2/d/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^9+4/a^2/d/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^8+11/4/a^2/d/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^7+8/a^2/d/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^6-11/4/a^2/d/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^5+8/a^2/d/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^4+89/24/a^2/d/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^3+4/5/a^2/d/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^2+9/8/a^2/d/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)+4/5/a^2/d/(1+tan(1/2*d*x+1/2*c)^2)^6+7/8/a^2/d*arctan(tan(1/2*d*x+1/2*c))","B"
63,1,45,43,0.187000," ","int(cos(d*x+c)^7/(a+a*sin(d*x+c))^2,x)","\frac{-\frac{\left(\sin^{5}\left(d x +c \right)\right)}{5}+\frac{\left(\sin^{4}\left(d x +c \right)\right)}{2}-\left(\sin^{2}\left(d x +c \right)\right)+\sin \left(d x +c \right)}{d \,a^{2}}"," ",0,"1/d/a^2*(-1/5*sin(d*x+c)^5+1/2*sin(d*x+c)^4-sin(d*x+c)^2+sin(d*x+c))","A"
64,1,279,72,0.179000," ","int(cos(d*x+c)^6/(a+a*sin(d*x+c))^2,x)","-\frac{3 \left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 a^{2} d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}+\frac{4 \left(\tan^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a^{2} d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{11 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 a^{2} d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}+\frac{4 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a^{2} d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}+\frac{11 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 a^{2} d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}+\frac{4 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 a^{2} d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}+\frac{3 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{4 a^{2} d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}+\frac{4}{3 a^{2} d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}+\frac{5 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 a^{2} d}"," ",0,"-3/4/a^2/d/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^7+4/a^2/d/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^6-11/4/a^2/d/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^5+4/a^2/d/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^4+11/4/a^2/d/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^3+4/3/a^2/d/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^2+3/4/a^2/d/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)+4/3/a^2/d/(1+tan(1/2*d*x+1/2*c)^2)^4+5/4/a^2/d*arctan(tan(1/2*d*x+1/2*c))","B"
65,1,19,21,0.167000," ","int(cos(d*x+c)^5/(a+a*sin(d*x+c))^2,x)","\frac{\left(\sin \left(d x +c \right)-1\right)^{3}}{3 d \,a^{2}}"," ",0,"1/3/d/a^2*(sin(d*x+c)-1)^3","A"
66,1,142,50,0.189000," ","int(cos(d*x+c)^4/(a+a*sin(d*x+c))^2,x)","\frac{\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)}{a^{2} d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{4 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a^{2} d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}-\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{a^{2} d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{4}{a^{2} d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{3 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a^{2} d}"," ",0,"1/a^2/d/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)^3+4/a^2/d/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)^2-1/a^2/d/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)+4/a^2/d/(1+tan(1/2*d*x+1/2*c)^2)^2+3/a^2/d*arctan(tan(1/2*d*x+1/2*c))","B"
67,1,33,32,0.176000," ","int(cos(d*x+c)^3/(a+a*sin(d*x+c))^2,x)","\frac{2 \ln \left(1+\sin \left(d x +c \right)\right)}{a^{2} d}-\frac{\sin \left(d x +c \right)}{a^{2} d}"," ",0,"2*ln(1+sin(d*x+c))/a^2/d-sin(d*x+c)/a^2/d","A"
68,1,41,34,0.200000," ","int(cos(d*x+c)^2/(a+a*sin(d*x+c))^2,x)","-\frac{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a^{2} d}-\frac{4}{a^{2} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}"," ",0,"-2/a^2/d*arctan(tan(1/2*d*x+1/2*c))-4/a^2/d/(tan(1/2*d*x+1/2*c)+1)","A"
69,1,21,21,0.073000," ","int(cos(d*x+c)/(a+a*sin(d*x+c))^2,x)","-\frac{1}{d \left(a +a \sin \left(d x +c \right)\right) a}"," ",0,"-1/d/(a+a*sin(d*x+c))/a","A"
70,1,72,54,0.185000," ","int(sec(d*x+c)/(a+a*sin(d*x+c))^2,x)","-\frac{\ln \left(\sin \left(d x +c \right)-1\right)}{8 a^{2} d}-\frac{1}{4 a^{2} d \left(1+\sin \left(d x +c \right)\right)^{2}}-\frac{1}{4 a^{2} d \left(1+\sin \left(d x +c \right)\right)}+\frac{\ln \left(1+\sin \left(d x +c \right)\right)}{8 a^{2} d}"," ",0,"-1/8/a^2/d*ln(sin(d*x+c)-1)-1/4/a^2/d/(1+sin(d*x+c))^2-1/4/a^2/d/(1+sin(d*x+c))+1/8*ln(1+sin(d*x+c))/a^2/d","A"
71,1,98,65,0.192000," ","int(sec(d*x+c)^2/(a+a*sin(d*x+c))^2,x)","\frac{-\frac{1}{4 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{4}{5 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{5}}+\frac{2}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{4}}-\frac{3}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}+\frac{5}{2 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}-\frac{7}{4 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}}{d \,a^{2}}"," ",0,"2/d/a^2*(-1/8/(tan(1/2*d*x+1/2*c)-1)-2/5/(tan(1/2*d*x+1/2*c)+1)^5+1/(tan(1/2*d*x+1/2*c)+1)^4-3/2/(tan(1/2*d*x+1/2*c)+1)^3+5/4/(tan(1/2*d*x+1/2*c)+1)^2-7/8/(tan(1/2*d*x+1/2*c)+1))","A"
72,1,108,94,0.232000," ","int(sec(d*x+c)^3/(a+a*sin(d*x+c))^2,x)","-\frac{1}{16 a^{2} d \left(\sin \left(d x +c \right)-1\right)}-\frac{\ln \left(\sin \left(d x +c \right)-1\right)}{8 a^{2} d}-\frac{1}{12 a^{2} d \left(1+\sin \left(d x +c \right)\right)^{3}}-\frac{1}{8 a^{2} d \left(1+\sin \left(d x +c \right)\right)^{2}}-\frac{3}{16 a^{2} d \left(1+\sin \left(d x +c \right)\right)}+\frac{\ln \left(1+\sin \left(d x +c \right)\right)}{8 a^{2} d}"," ",0,"-1/16/a^2/d/(sin(d*x+c)-1)-1/8/a^2/d*ln(sin(d*x+c)-1)-1/12/a^2/d/(1+sin(d*x+c))^3-1/8/a^2/d/(1+sin(d*x+c))^2-3/16/a^2/d/(1+sin(d*x+c))+1/8*ln(1+sin(d*x+c))/a^2/d","A"
73,1,158,85,0.233000," ","int(sec(d*x+c)^4/(a+a*sin(d*x+c))^2,x)","\frac{-\frac{1}{12 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{3}}-\frac{1}{8 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}-\frac{3}{8 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{4}{7 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{7}}+\frac{2}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{6}}-\frac{4}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{5}}+\frac{5}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{4}}-\frac{55}{12 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}+\frac{23}{8 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}-\frac{13}{8 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}}{a^{2} d}"," ",0,"2/d/a^2*(-1/24/(tan(1/2*d*x+1/2*c)-1)^3-1/16/(tan(1/2*d*x+1/2*c)-1)^2-3/16/(tan(1/2*d*x+1/2*c)-1)-2/7/(tan(1/2*d*x+1/2*c)+1)^7+1/(tan(1/2*d*x+1/2*c)+1)^6-2/(tan(1/2*d*x+1/2*c)+1)^5+5/2/(tan(1/2*d*x+1/2*c)+1)^4-55/24/(tan(1/2*d*x+1/2*c)+1)^3+23/16/(tan(1/2*d*x+1/2*c)+1)^2-13/16/(tan(1/2*d*x+1/2*c)+1))","A"
74,1,144,132,0.233000," ","int(sec(d*x+c)^5/(a+a*sin(d*x+c))^2,x)","\frac{1}{64 a^{2} d \left(\sin \left(d x +c \right)-1\right)^{2}}-\frac{5}{64 a^{2} d \left(\sin \left(d x +c \right)-1\right)}-\frac{15 \ln \left(\sin \left(d x +c \right)-1\right)}{128 a^{2} d}-\frac{1}{32 a^{2} d \left(1+\sin \left(d x +c \right)\right)^{4}}-\frac{1}{16 a^{2} d \left(1+\sin \left(d x +c \right)\right)^{3}}-\frac{3}{32 a^{2} d \left(1+\sin \left(d x +c \right)\right)^{2}}-\frac{5}{32 a^{2} d \left(1+\sin \left(d x +c \right)\right)}+\frac{15 \ln \left(1+\sin \left(d x +c \right)\right)}{128 a^{2} d}"," ",0,"1/64/a^2/d/(sin(d*x+c)-1)^2-5/64/a^2/d/(sin(d*x+c)-1)-15/128/a^2/d*ln(sin(d*x+c)-1)-1/32/a^2/d/(1+sin(d*x+c))^4-1/16/a^2/d/(1+sin(d*x+c))^3-3/32/a^2/d/(1+sin(d*x+c))^2-5/32/a^2/d/(1+sin(d*x+c))+15/128*ln(1+sin(d*x+c))/a^2/d","A"
75,1,313,93,0.214000," ","int(cos(d*x+c)^8/(a+a*sin(d*x+c))^3,x)","-\frac{\tan^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)}{4 a^{3} d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}+\frac{6 \left(\tan^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a^{3} d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}-\frac{13 \left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{2 a^{3} d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}+\frac{16 \left(\tan^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a^{3} d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}+\frac{20 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 a^{3} d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}+\frac{13 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{2 a^{3} d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}+\frac{16 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 a^{3} d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}+\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{4 a^{3} d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}+\frac{34}{15 a^{3} d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}+\frac{7 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 a^{3} d}"," ",0,"-1/4/a^3/d/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^9+6/a^3/d/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^8-13/2/a^3/d/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^7+16/a^3/d/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^6+20/3/a^3/d/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^4+13/2/a^3/d/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^3+16/3/a^3/d/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^2+1/4/a^3/d/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)+34/15/a^3/d/(1+tan(1/2*d*x+1/2*c)^2)^5+7/4/a^3/d*arctan(tan(1/2*d*x+1/2*c))","B"
76,1,19,21,0.178000," ","int(cos(d*x+c)^7/(a+a*sin(d*x+c))^3,x)","-\frac{\left(\sin \left(d x +c \right)-1\right)^{4}}{4 d \,a^{3}}"," ",0,"-1/4/d/a^3*(sin(d*x+c)-1)^4","A"
77,1,177,71,0.203000," ","int(cos(d*x+c)^6/(a+a*sin(d*x+c))^3,x)","\frac{3 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a^{3} d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}+\frac{6 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a^{3} d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}+\frac{16 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a^{3} d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}-\frac{3 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{a^{3} d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}+\frac{22}{3 a^{3} d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}+\frac{5 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a^{3} d}"," ",0,"3/a^3/d/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)^5+6/a^3/d/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)^4+16/a^3/d/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)^2-3/a^3/d/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)+22/3/a^3/d/(1+tan(1/2*d*x+1/2*c)^2)^3+5/a^3/d*arctan(tan(1/2*d*x+1/2*c))","B"
78,1,49,48,0.185000," ","int(cos(d*x+c)^5/(a+a*sin(d*x+c))^3,x)","\frac{4 \ln \left(1+\sin \left(d x +c \right)\right)}{a^{3} d}-\frac{3 \sin \left(d x +c \right)}{a^{3} d}+\frac{\sin^{2}\left(d x +c \right)}{2 a^{3} d}"," ",0,"4*ln(1+sin(d*x+c))/a^3/d-3*sin(d*x+c)/a^3/d+1/2*sin(d*x+c)^2/a^3/d","A"
79,1,64,49,0.214000," ","int(cos(d*x+c)^4/(a+a*sin(d*x+c))^3,x)","-\frac{2}{a^{3} d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}-\frac{6 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a^{3} d}-\frac{8}{a^{3} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}"," ",0,"-2/a^3/d/(1+tan(1/2*d*x+1/2*c)^2)-6/a^3/d*arctan(tan(1/2*d*x+1/2*c))-8/a^3/d/(tan(1/2*d*x+1/2*c)+1)","A"
80,1,37,39,0.199000," ","int(cos(d*x+c)^3/(a+a*sin(d*x+c))^3,x)","-\frac{\ln \left(1+\sin \left(d x +c \right)\right)}{a^{3} d}-\frac{2}{a^{3} d \left(1+\sin \left(d x +c \right)\right)}"," ",0,"-ln(1+sin(d*x+c))/a^3/d-2/a^3/d/(1+sin(d*x+c))","A"
81,1,55,25,0.223000," ","int(cos(d*x+c)^2/(a+a*sin(d*x+c))^3,x)","\frac{-\frac{8}{3 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}+\frac{4}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}-\frac{2}{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1}}{d \,a^{3}}"," ",0,"2/d/a^3*(-4/3/(tan(1/2*d*x+1/2*c)+1)^3+2/(tan(1/2*d*x+1/2*c)+1)^2-1/(tan(1/2*d*x+1/2*c)+1))","B"
82,1,21,20,0.070000," ","int(cos(d*x+c)/(a+a*sin(d*x+c))^3,x)","-\frac{1}{2 a d \left(a +a \sin \left(d x +c \right)\right)^{2}}"," ",0,"-1/2/a/d/(a+a*sin(d*x+c))^2","A"
83,1,90,74,0.213000," ","int(sec(d*x+c)/(a+a*sin(d*x+c))^3,x)","-\frac{\ln \left(\sin \left(d x +c \right)-1\right)}{16 a^{3} d}-\frac{1}{6 a^{3} d \left(1+\sin \left(d x +c \right)\right)^{3}}-\frac{1}{8 a^{3} d \left(1+\sin \left(d x +c \right)\right)^{2}}-\frac{1}{8 a^{3} d \left(1+\sin \left(d x +c \right)\right)}+\frac{\ln \left(1+\sin \left(d x +c \right)\right)}{16 a^{3} d}"," ",0,"-1/16/a^3/d*ln(sin(d*x+c)-1)-1/6/a^3/d/(1+sin(d*x+c))^3-1/8/a^3/d/(1+sin(d*x+c))^2-1/8/a^3/d/(1+sin(d*x+c))+1/16*ln(1+sin(d*x+c))/a^3/d","A"
84,1,130,91,0.219000," ","int(sec(d*x+c)^2/(a+a*sin(d*x+c))^3,x)","\frac{-\frac{1}{8 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{8}{7 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{7}}+\frac{4}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{6}}-\frac{38}{5 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{5}}+\frac{9}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{4}}-\frac{15}{2 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}+\frac{17}{4 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}-\frac{15}{8 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}}{d \,a^{3}}"," ",0,"2/d/a^3*(-1/16/(tan(1/2*d*x+1/2*c)-1)-4/7/(tan(1/2*d*x+1/2*c)+1)^7+2/(tan(1/2*d*x+1/2*c)+1)^6-19/5/(tan(1/2*d*x+1/2*c)+1)^5+9/2/(tan(1/2*d*x+1/2*c)+1)^4-15/4/(tan(1/2*d*x+1/2*c)+1)^3+17/8/(tan(1/2*d*x+1/2*c)+1)^2-15/16/(tan(1/2*d*x+1/2*c)+1))","A"
85,1,126,114,0.260000," ","int(sec(d*x+c)^3/(a+a*sin(d*x+c))^3,x)","-\frac{1}{32 a^{3} d \left(\sin \left(d x +c \right)-1\right)}-\frac{5 \ln \left(\sin \left(d x +c \right)-1\right)}{64 a^{3} d}-\frac{1}{16 a^{3} d \left(1+\sin \left(d x +c \right)\right)^{4}}-\frac{1}{12 a^{3} d \left(1+\sin \left(d x +c \right)\right)^{3}}-\frac{3}{32 a^{3} d \left(1+\sin \left(d x +c \right)\right)^{2}}-\frac{1}{8 a^{3} d \left(1+\sin \left(d x +c \right)\right)}+\frac{5 \ln \left(1+\sin \left(d x +c \right)\right)}{64 a^{3} d}"," ",0,"-1/32/a^3/d/(sin(d*x+c)-1)-5/64/a^3/d*ln(sin(d*x+c)-1)-1/16/a^3/d/(1+sin(d*x+c))^4-1/12/a^3/d/(1+sin(d*x+c))^3-3/32/a^3/d/(1+sin(d*x+c))^2-1/8/a^3/d/(1+sin(d*x+c))+5/64*ln(1+sin(d*x+c))/a^3/d","A"
86,1,190,113,0.268000," ","int(sec(d*x+c)^4/(a+a*sin(d*x+c))^3,x)","\frac{-\frac{1}{24 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{3}}-\frac{1}{16 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}-\frac{7}{32 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{8}{9 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{9}}+\frac{4}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{8}}-\frac{68}{7 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{7}}+\frac{46}{3 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{6}}-\frac{35}{2 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{5}}+\frac{59}{4 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{4}}-\frac{19}{2 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}+\frac{9}{2 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}-\frac{57}{32 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}}{a^{3} d}"," ",0,"2/d/a^3*(-1/48/(tan(1/2*d*x+1/2*c)-1)^3-1/32/(tan(1/2*d*x+1/2*c)-1)^2-7/64/(tan(1/2*d*x+1/2*c)-1)-4/9/(tan(1/2*d*x+1/2*c)+1)^9+2/(tan(1/2*d*x+1/2*c)+1)^8-34/7/(tan(1/2*d*x+1/2*c)+1)^7+23/3/(tan(1/2*d*x+1/2*c)+1)^6-35/4/(tan(1/2*d*x+1/2*c)+1)^5+59/8/(tan(1/2*d*x+1/2*c)+1)^4-19/4/(tan(1/2*d*x+1/2*c)+1)^3+9/4/(tan(1/2*d*x+1/2*c)+1)^2-57/64/(tan(1/2*d*x+1/2*c)+1))","A"
87,1,162,155,0.270000," ","int(sec(d*x+c)^5/(a+a*sin(d*x+c))^3,x)","\frac{1}{128 a^{3} d \left(\sin \left(d x +c \right)-1\right)^{2}}-\frac{3}{64 a^{3} d \left(\sin \left(d x +c \right)-1\right)}-\frac{21 \ln \left(\sin \left(d x +c \right)-1\right)}{256 a^{3} d}-\frac{1}{40 a^{3} d \left(1+\sin \left(d x +c \right)\right)^{5}}-\frac{3}{64 a^{3} d \left(1+\sin \left(d x +c \right)\right)^{4}}-\frac{1}{16 a^{3} d \left(1+\sin \left(d x +c \right)\right)^{3}}-\frac{5}{64 a^{3} d \left(1+\sin \left(d x +c \right)\right)^{2}}-\frac{15}{128 a^{3} d \left(1+\sin \left(d x +c \right)\right)}+\frac{21 \ln \left(1+\sin \left(d x +c \right)\right)}{256 a^{3} d}"," ",0,"1/128/a^3/d/(sin(d*x+c)-1)^2-3/64/a^3/d/(sin(d*x+c)-1)-21/256/a^3/d*ln(sin(d*x+c)-1)-1/40/a^3/d/(1+sin(d*x+c))^5-3/64/a^3/d/(1+sin(d*x+c))^4-1/16/a^3/d/(1+sin(d*x+c))^3-5/64/a^3/d/(1+sin(d*x+c))^2-15/128/a^3/d/(1+sin(d*x+c))+21/256*ln(1+sin(d*x+c))/a^3/d","A"
88,1,146,121,0.283000," ","int(cos(d*x+c)^8/(a+a*sin(d*x+c))^8,x)","\frac{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a^{8} d}-\frac{256}{7 a^{8} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{7}}+\frac{128}{a^{8} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{6}}-\frac{896}{5 a^{8} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{5}}+\frac{128}{a^{8} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{4}}-\frac{160}{3 a^{8} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}+\frac{16}{a^{8} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}"," ",0,"2/a^8/d*arctan(tan(1/2*d*x+1/2*c))-256/7/a^8/d/(tan(1/2*d*x+1/2*c)+1)^7+128/a^8/d/(tan(1/2*d*x+1/2*c)+1)^6-896/5/a^8/d/(tan(1/2*d*x+1/2*c)+1)^5+128/a^8/d/(tan(1/2*d*x+1/2*c)+1)^4-160/3/a^8/d/(tan(1/2*d*x+1/2*c)+1)^3+16/a^8/d/(tan(1/2*d*x+1/2*c)+1)^2","A"
89,1,55,34,0.250000," ","int(cos(d*x+c)^7/(a+a*sin(d*x+c))^8,x)","\frac{-\frac{3}{\left(1+\sin \left(d x +c \right)\right)^{2}}+\frac{1}{1+\sin \left(d x +c \right)}-\frac{2}{\left(1+\sin \left(d x +c \right)\right)^{4}}+\frac{4}{\left(1+\sin \left(d x +c \right)\right)^{3}}}{d \,a^{8}}"," ",0,"1/d/a^8*(-3/(1+sin(d*x+c))^2+1/(1+sin(d*x+c))-2/(1+sin(d*x+c))^4+4/(1+sin(d*x+c))^3)","A"
90,1,145,54,0.279000," ","int(cos(d*x+c)^6/(a+a*sin(d*x+c))^8,x)","\frac{-\frac{172}{3 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}-\frac{256}{9 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{9}}-\frac{1856}{7 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{7}}+\frac{14}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}-\frac{2}{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1}+\frac{152}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{4}}-\frac{272}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{5}}+\frac{128}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{8}}+\frac{992}{3 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{6}}}{d \,a^{8}}"," ",0,"2/d/a^8*(-86/3/(tan(1/2*d*x+1/2*c)+1)^3-128/9/(tan(1/2*d*x+1/2*c)+1)^9-928/7/(tan(1/2*d*x+1/2*c)+1)^7+7/(tan(1/2*d*x+1/2*c)+1)^2-1/(tan(1/2*d*x+1/2*c)+1)+76/(tan(1/2*d*x+1/2*c)+1)^4-136/(tan(1/2*d*x+1/2*c)+1)^5+64/(tan(1/2*d*x+1/2*c)+1)^8+496/3/(tan(1/2*d*x+1/2*c)+1)^6)","B"
91,1,43,61,0.253000," ","int(cos(d*x+c)^5/(a+a*sin(d*x+c))^8,x)","\frac{-\frac{1}{3 \left(1+\sin \left(d x +c \right)\right)^{3}}+\frac{1}{\left(1+\sin \left(d x +c \right)\right)^{4}}-\frac{4}{5 \left(1+\sin \left(d x +c \right)\right)^{5}}}{d \,a^{8}}"," ",0,"1/d/a^8*(-1/3/(1+sin(d*x+c))^3+1/(1+sin(d*x+c))^4-4/5/(1+sin(d*x+c))^5)","A"
92,1,175,110,0.300000," ","int(cos(d*x+c)^4/(a+a*sin(d*x+c))^8,x)","\frac{\frac{584}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{6}}+\frac{576}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{8}}-\frac{60}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}-\frac{256}{11 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{11}}+\frac{14}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}-\frac{1024}{3 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{9}}-\frac{4752}{7 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{7}}+\frac{128}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{10}}-\frac{2}{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1}+\frac{176}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{4}}-\frac{1864}{5 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{5}}}{d \,a^{8}}"," ",0,"2/d/a^8*(292/(tan(1/2*d*x+1/2*c)+1)^6+288/(tan(1/2*d*x+1/2*c)+1)^8-30/(tan(1/2*d*x+1/2*c)+1)^3-128/11/(tan(1/2*d*x+1/2*c)+1)^11+7/(tan(1/2*d*x+1/2*c)+1)^2-512/3/(tan(1/2*d*x+1/2*c)+1)^9-2376/7/(tan(1/2*d*x+1/2*c)+1)^7+64/(tan(1/2*d*x+1/2*c)+1)^10-1/(tan(1/2*d*x+1/2*c)+1)+88/(tan(1/2*d*x+1/2*c)+1)^4-932/5/(tan(1/2*d*x+1/2*c)+1)^5)","A"
93,1,33,41,0.266000," ","int(cos(d*x+c)^3/(a+a*sin(d*x+c))^8,x)","\frac{\frac{1}{5 \left(1+\sin \left(d x +c \right)\right)^{5}}-\frac{1}{3 \left(1+\sin \left(d x +c \right)\right)^{6}}}{d \,a^{8}}"," ",0,"1/d/a^8*(1/5/(1+sin(d*x+c))^5-1/3/(1+sin(d*x+c))^6)","A"
94,1,205,171,0.302000," ","int(cos(d*x+c)^2/(a+a*sin(d*x+c))^8,x)","\frac{-\frac{480}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{5}}+\frac{864}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{10}}+\frac{1472}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{8}}+\frac{128}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{12}}-\frac{4544}{11 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{11}}-\frac{11680}{9 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{9}}-\frac{9056}{7 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{7}}+\frac{2672}{3 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{6}}+\frac{14}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}-\frac{2}{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1}+\frac{200}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{4}}-\frac{188}{3 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}-\frac{256}{13 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{13}}}{d \,a^{8}}"," ",0,"2/d/a^8*(-240/(tan(1/2*d*x+1/2*c)+1)^5+432/(tan(1/2*d*x+1/2*c)+1)^10+736/(tan(1/2*d*x+1/2*c)+1)^8+64/(tan(1/2*d*x+1/2*c)+1)^12-2272/11/(tan(1/2*d*x+1/2*c)+1)^11-5840/9/(tan(1/2*d*x+1/2*c)+1)^9-4528/7/(tan(1/2*d*x+1/2*c)+1)^7+1336/3/(tan(1/2*d*x+1/2*c)+1)^6+7/(tan(1/2*d*x+1/2*c)+1)^2-1/(tan(1/2*d*x+1/2*c)+1)+100/(tan(1/2*d*x+1/2*c)+1)^4-94/3/(tan(1/2*d*x+1/2*c)+1)^3-128/13/(tan(1/2*d*x+1/2*c)+1)^13)","A"
95,1,21,20,0.095000," ","int(cos(d*x+c)/(a+a*sin(d*x+c))^8,x)","-\frac{1}{7 a d \left(a +a \sin \left(d x +c \right)\right)^{7}}"," ",0,"-1/7/a/d/(a+a*sin(d*x+c))^7","A"
96,1,180,176,0.294000," ","int(sec(d*x+c)/(a+a*sin(d*x+c))^8,x)","-\frac{\ln \left(\sin \left(d x +c \right)-1\right)}{512 a^{8} d}-\frac{1}{16 a^{8} d \left(1+\sin \left(d x +c \right)\right)^{8}}-\frac{1}{28 a^{8} d \left(1+\sin \left(d x +c \right)\right)^{7}}-\frac{1}{48 a^{8} d \left(1+\sin \left(d x +c \right)\right)^{6}}-\frac{1}{80 a^{8} d \left(1+\sin \left(d x +c \right)\right)^{5}}-\frac{1}{128 a^{8} d \left(1+\sin \left(d x +c \right)\right)^{4}}-\frac{1}{192 a^{8} d \left(1+\sin \left(d x +c \right)\right)^{3}}-\frac{1}{256 a^{8} d \left(1+\sin \left(d x +c \right)\right)^{2}}-\frac{1}{256 a^{8} d \left(1+\sin \left(d x +c \right)\right)}+\frac{\ln \left(1+\sin \left(d x +c \right)\right)}{512 a^{8} d}"," ",0,"-1/512/a^8/d*ln(sin(d*x+c)-1)-1/16/a^8/d/(1+sin(d*x+c))^8-1/28/a^8/d/(1+sin(d*x+c))^7-1/48/a^8/d/(1+sin(d*x+c))^6-1/80/a^8/d/(1+sin(d*x+c))^5-1/128/a^8/d/(1+sin(d*x+c))^4-1/192/a^8/d/(1+sin(d*x+c))^3-1/256/a^8/d/(1+sin(d*x+c))^2-1/256/a^8/d/(1+sin(d*x+c))+1/512/a^8/d*ln(1+sin(d*x+c))","A"
97,1,280,227,0.264000," ","int(sec(d*x+c)^2/(a+a*sin(d*x+c))^8,x)","\frac{-\frac{1}{256 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{256}{17 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{17}}+\frac{128}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{16}}-\frac{2752}{5 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{15}}+\frac{1568}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{14}}-\frac{42800}{13 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{13}}+\frac{5384}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{12}}-\frac{77908}{11 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{11}}+\frac{38218}{5 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{10}}-\frac{6847}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{9}}+\frac{10241}{2 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{8}}-\frac{12799}{4 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{7}}+\frac{13313}{8 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{6}}-\frac{57083}{80 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{5}}+\frac{7937}{32 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{4}}-\frac{4351}{64 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}+\frac{1793}{128 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}-\frac{511}{256 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}}{d \,a^{8}}"," ",0,"2/d/a^8*(-1/512/(tan(1/2*d*x+1/2*c)-1)-128/17/(tan(1/2*d*x+1/2*c)+1)^17+64/(tan(1/2*d*x+1/2*c)+1)^16-1376/5/(tan(1/2*d*x+1/2*c)+1)^15+784/(tan(1/2*d*x+1/2*c)+1)^14-21400/13/(tan(1/2*d*x+1/2*c)+1)^13+2692/(tan(1/2*d*x+1/2*c)+1)^12-38954/11/(tan(1/2*d*x+1/2*c)+1)^11+19109/5/(tan(1/2*d*x+1/2*c)+1)^10-6847/2/(tan(1/2*d*x+1/2*c)+1)^9+10241/4/(tan(1/2*d*x+1/2*c)+1)^8-12799/8/(tan(1/2*d*x+1/2*c)+1)^7+13313/16/(tan(1/2*d*x+1/2*c)+1)^6-57083/160/(tan(1/2*d*x+1/2*c)+1)^5+7937/64/(tan(1/2*d*x+1/2*c)+1)^4-4351/128/(tan(1/2*d*x+1/2*c)+1)^3+1793/256/(tan(1/2*d*x+1/2*c)+1)^2-511/512/(tan(1/2*d*x+1/2*c)+1))","A"
98,1,216,216,0.341000," ","int(sec(d*x+c)^3/(a+a*sin(d*x+c))^8,x)","-\frac{1}{1024 a^{8} d \left(\sin \left(d x +c \right)-1\right)}-\frac{5 \ln \left(\sin \left(d x +c \right)-1\right)}{1024 a^{8} d}-\frac{1}{36 a^{8} d \left(1+\sin \left(d x +c \right)\right)^{9}}-\frac{1}{32 a^{8} d \left(1+\sin \left(d x +c \right)\right)^{8}}-\frac{3}{112 a^{8} d \left(1+\sin \left(d x +c \right)\right)^{7}}-\frac{1}{48 a^{8} d \left(1+\sin \left(d x +c \right)\right)^{6}}-\frac{1}{64 a^{8} d \left(1+\sin \left(d x +c \right)\right)^{5}}-\frac{3}{256 a^{8} d \left(1+\sin \left(d x +c \right)\right)^{4}}-\frac{7}{768 a^{8} d \left(1+\sin \left(d x +c \right)\right)^{3}}-\frac{1}{128 a^{8} d \left(1+\sin \left(d x +c \right)\right)^{2}}-\frac{9}{1024 a^{8} d \left(1+\sin \left(d x +c \right)\right)}+\frac{5 \ln \left(1+\sin \left(d x +c \right)\right)}{1024 a^{8} d}"," ",0,"-1/1024/a^8/d/(sin(d*x+c)-1)-5/1024/a^8/d*ln(sin(d*x+c)-1)-1/36/a^8/d/(1+sin(d*x+c))^9-1/32/a^8/d/(1+sin(d*x+c))^8-3/112/a^8/d/(1+sin(d*x+c))^7-1/48/a^8/d/(1+sin(d*x+c))^6-1/64/a^8/d/(1+sin(d*x+c))^5-3/256/a^8/d/(1+sin(d*x+c))^4-7/768/a^8/d/(1+sin(d*x+c))^3-1/128/a^8/d/(1+sin(d*x+c))^2-9/1024/a^8/d/(1+sin(d*x+c))+5/1024/a^8/d*ln(1+sin(d*x+c))","A"
99,1,340,259,0.350000," ","int(sec(d*x+c)^4/(a+a*sin(d*x+c))^8,x)","\frac{-\frac{1}{768 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{3}}-\frac{1}{512 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}-\frac{3}{256 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{256}{19 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{19}}+\frac{128}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{18}}-\frac{10496}{17 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{17}}+\frac{1984}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{16}}-\frac{14192}{3 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{15}}+\frac{8856}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{14}}-\frac{175016}{13 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{13}}+\frac{50936}{3 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{12}}-\frac{18011}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{11}}+\frac{32417}{2 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{10}}-\frac{12430}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{9}}+\frac{32525}{4 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{8}}-\frac{72425}{16 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{7}}+\frac{204605}{96 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{6}}-\frac{26871}{32 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{5}}+\frac{2177}{8 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{4}}-\frac{54229}{768 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}+\frac{7181}{512 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}-\frac{509}{256 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}}{a^{8} d}"," ",0,"2/d/a^8*(-1/1536/(tan(1/2*d*x+1/2*c)-1)^3-1/1024/(tan(1/2*d*x+1/2*c)-1)^2-3/512/(tan(1/2*d*x+1/2*c)-1)-128/19/(tan(1/2*d*x+1/2*c)+1)^19+64/(tan(1/2*d*x+1/2*c)+1)^18-5248/17/(tan(1/2*d*x+1/2*c)+1)^17+992/(tan(1/2*d*x+1/2*c)+1)^16-7096/3/(tan(1/2*d*x+1/2*c)+1)^15+4428/(tan(1/2*d*x+1/2*c)+1)^14-87508/13/(tan(1/2*d*x+1/2*c)+1)^13+25468/3/(tan(1/2*d*x+1/2*c)+1)^12-18011/2/(tan(1/2*d*x+1/2*c)+1)^11+32417/4/(tan(1/2*d*x+1/2*c)+1)^10-6215/(tan(1/2*d*x+1/2*c)+1)^9+32525/8/(tan(1/2*d*x+1/2*c)+1)^8-72425/32/(tan(1/2*d*x+1/2*c)+1)^7+204605/192/(tan(1/2*d*x+1/2*c)+1)^6-26871/64/(tan(1/2*d*x+1/2*c)+1)^5+2177/16/(tan(1/2*d*x+1/2*c)+1)^4-54229/1536/(tan(1/2*d*x+1/2*c)+1)^3+7181/1024/(tan(1/2*d*x+1/2*c)+1)^2-509/512/(tan(1/2*d*x+1/2*c)+1))","A"
100,1,252,258,0.361000," ","int(sec(d*x+c)^5/(a+a*sin(d*x+c))^8,x)","\frac{1}{4096 a^{8} d \left(\sin \left(d x +c \right)-1\right)^{2}}-\frac{11}{4096 a^{8} d \left(\sin \left(d x +c \right)-1\right)}-\frac{33 \ln \left(\sin \left(d x +c \right)-1\right)}{4096 a^{8} d}-\frac{1}{80 a^{8} d \left(1+\sin \left(d x +c \right)\right)^{10}}-\frac{1}{48 a^{8} d \left(1+\sin \left(d x +c \right)\right)^{9}}-\frac{3}{128 a^{8} d \left(1+\sin \left(d x +c \right)\right)^{8}}-\frac{5}{224 a^{8} d \left(1+\sin \left(d x +c \right)\right)^{7}}-\frac{5}{256 a^{8} d \left(1+\sin \left(d x +c \right)\right)^{6}}-\frac{21}{1280 a^{8} d \left(1+\sin \left(d x +c \right)\right)^{5}}-\frac{7}{512 a^{8} d \left(1+\sin \left(d x +c \right)\right)^{4}}-\frac{3}{256 a^{8} d \left(1+\sin \left(d x +c \right)\right)^{3}}-\frac{45}{4096 a^{8} d \left(1+\sin \left(d x +c \right)\right)^{2}}-\frac{55}{4096 a^{8} d \left(1+\sin \left(d x +c \right)\right)}+\frac{33 \ln \left(1+\sin \left(d x +c \right)\right)}{4096 a^{8} d}"," ",0,"1/4096/a^8/d/(sin(d*x+c)-1)^2-11/4096/a^8/d/(sin(d*x+c)-1)-33/4096/a^8/d*ln(sin(d*x+c)-1)-1/80/a^8/d/(1+sin(d*x+c))^10-1/48/a^8/d/(1+sin(d*x+c))^9-3/128/a^8/d/(1+sin(d*x+c))^8-5/224/a^8/d/(1+sin(d*x+c))^7-5/256/a^8/d/(1+sin(d*x+c))^6-21/1280/a^8/d/(1+sin(d*x+c))^5-7/512/a^8/d/(1+sin(d*x+c))^4-3/256/a^8/d/(1+sin(d*x+c))^3-45/4096/a^8/d/(1+sin(d*x+c))^2-55/4096/a^8/d/(1+sin(d*x+c))+33/4096/a^8/d*ln(1+sin(d*x+c))","A"
101,1,57,81,0.198000," ","int(cos(d*x+c)^7*(a+a*sin(d*x+c))^(1/2),x)","\frac{2 \left(a +a \sin \left(d x +c \right)\right)^{\frac{9}{2}} \left(429 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)-1683 \left(\cos^{2}\left(d x +c \right)\right)-2796 \sin \left(d x +c \right)+2924\right)}{6435 a^{4} d}"," ",0,"2/6435/a^4*(a+a*sin(d*x+c))^(9/2)*(429*cos(d*x+c)^2*sin(d*x+c)-1683*cos(d*x+c)^2-2796*sin(d*x+c)+2924)/d","A"
102,1,75,111,0.200000," ","int(cos(d*x+c)^6*(a+a*sin(d*x+c))^(1/2),x)","-\frac{2 \left(1+\sin \left(d x +c \right)\right) a \left(\sin \left(d x +c \right)-1\right)^{4} \left(231 \left(\sin^{3}\left(d x +c \right)\right)+945 \left(\sin^{2}\left(d x +c \right)\right)+1421 \sin \left(d x +c \right)+835\right)}{3003 \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"-2/3003*(1+sin(d*x+c))*a*(sin(d*x+c)-1)^4*(231*sin(d*x+c)^3+945*sin(d*x+c)^2+1421*sin(d*x+c)+835)/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
103,1,41,61,0.161000," ","int(cos(d*x+c)^5*(a+a*sin(d*x+c))^(1/2),x)","-\frac{2 \left(a +a \sin \left(d x +c \right)\right)^{\frac{7}{2}} \left(63 \left(\cos^{2}\left(d x +c \right)\right)+182 \sin \left(d x +c \right)-214\right)}{693 a^{3} d}"," ",0,"-2/693/a^3*(a+a*sin(d*x+c))^(7/2)*(63*cos(d*x+c)^2+182*sin(d*x+c)-214)/d","A"
104,1,65,83,0.197000," ","int(cos(d*x+c)^4*(a+a*sin(d*x+c))^(1/2),x)","\frac{2 \left(1+\sin \left(d x +c \right)\right) a \left(\sin \left(d x +c \right)-1\right)^{3} \left(35 \left(\sin^{2}\left(d x +c \right)\right)+110 \sin \left(d x +c \right)+107\right)}{315 \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"2/315*(1+sin(d*x+c))*a*(sin(d*x+c)-1)^3*(35*sin(d*x+c)^2+110*sin(d*x+c)+107)/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
105,1,31,41,0.150000," ","int(cos(d*x+c)^3*(a+a*sin(d*x+c))^(1/2),x)","-\frac{2 \left(a +a \sin \left(d x +c \right)\right)^{\frac{5}{2}} \left(5 \sin \left(d x +c \right)-9\right)}{35 a^{2} d}"," ",0,"-2/35/a^2*(a+a*sin(d*x+c))^(5/2)*(5*sin(d*x+c)-9)/d","A"
106,1,55,55,0.181000," ","int(cos(d*x+c)^2*(a+a*sin(d*x+c))^(1/2),x)","-\frac{2 \left(1+\sin \left(d x +c \right)\right) a \left(\sin \left(d x +c \right)-1\right)^{2} \left(3 \sin \left(d x +c \right)+7\right)}{15 \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"-2/15*(1+sin(d*x+c))*a*(sin(d*x+c)-1)^2*(3*sin(d*x+c)+7)/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
107,1,21,20,0.041000," ","int(cos(d*x+c)*(a+a*sin(d*x+c))^(1/2),x)","\frac{2 \left(a +a \sin \left(d x +c \right)\right)^{\frac{3}{2}}}{3 d a}"," ",0,"2/3*(a+a*sin(d*x+c))^(3/2)/d/a","A"
108,1,32,31,0.099000," ","int(sec(d*x+c)*(a+a*sin(d*x+c))^(1/2),x)","\frac{\arctanh \left(\frac{\sqrt{a +a \sin \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) \sqrt{2}\, \sqrt{a}}{d}"," ",0,"arctanh(1/2*(a+a*sin(d*x+c))^(1/2)*2^(1/2)/a^(1/2))*2^(1/2)*a^(1/2)/d","A"
109,1,83,61,0.232000," ","int(sec(d*x+c)^2*(a+a*sin(d*x+c))^(1/2),x)","-\frac{\left(1+\sin \left(d x +c \right)\right) \left(\sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a \sqrt{a -a \sin \left(d x +c \right)}-2 a^{\frac{3}{2}}\right)}{2 \sqrt{a}\, \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"-1/2/a^(1/2)*(1+sin(d*x+c))*(2^(1/2)*arctanh(1/2*(a-a*sin(d*x+c))^(1/2)*2^(1/2)/a^(1/2))*a*(a-a*sin(d*x+c))^(1/2)-2*a^(3/2))/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
110,1,90,76,0.263000," ","int(sec(d*x+c)^3*(a+a*sin(d*x+c))^(1/2),x)","\frac{2 a^{3} \left(-\frac{1}{4 a^{2} \sqrt{a +a \sin \left(d x +c \right)}}-\frac{\frac{\sqrt{a +a \sin \left(d x +c \right)}}{2 a \sin \left(d x +c \right)-2 a}-\frac{3 \sqrt{2}\, \arctanh \left(\frac{\sqrt{a +a \sin \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right)}{4 \sqrt{a}}}{4 a^{2}}\right)}{d}"," ",0,"2*a^3*(-1/4/a^2/(a+a*sin(d*x+c))^(1/2)-1/4/a^2*(1/2*(a+a*sin(d*x+c))^(1/2)/(a*sin(d*x+c)-a)-3/4*2^(1/2)/a^(1/2)*arctanh(1/2*(a+a*sin(d*x+c))^(1/2)*2^(1/2)/a^(1/2))))/d","A"
111,1,153,114,0.243000," ","int(sec(d*x+c)^4*(a+a*sin(d*x+c))^(1/2),x)","\frac{\sin \left(d x +c \right) \left(15 \left(a -a \sin \left(d x +c \right)\right)^{\frac{3}{2}} \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a -20 a^{\frac{5}{2}}\right)-30 a^{\frac{5}{2}} \left(\cos^{2}\left(d x +c \right)\right)+15 \left(a -a \sin \left(d x +c \right)\right)^{\frac{3}{2}} \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a +4 a^{\frac{5}{2}}}{48 a^{\frac{3}{2}} \left(\sin \left(d x +c \right)-1\right) \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"1/48/a^(3/2)*(sin(d*x+c)*(15*(a-a*sin(d*x+c))^(3/2)*2^(1/2)*arctanh(1/2*(a-a*sin(d*x+c))^(1/2)*2^(1/2)/a^(1/2))*a-20*a^(5/2))-30*a^(5/2)*cos(d*x+c)^2+15*(a-a*sin(d*x+c))^(3/2)*2^(1/2)*arctanh(1/2*(a-a*sin(d*x+c))^(1/2)*2^(1/2)/a^(1/2))*a+4*a^(5/2))/(sin(d*x+c)-1)/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
112,1,118,122,0.334000," ","int(sec(d*x+c)^5*(a+a*sin(d*x+c))^(1/2),x)","-\frac{2 a^{5} \left(\frac{3}{16 a^{4} \sqrt{a +a \sin \left(d x +c \right)}}+\frac{1}{24 a^{3} \left(a +a \sin \left(d x +c \right)\right)^{\frac{3}{2}}}+\frac{\frac{\sqrt{a +a \sin \left(d x +c \right)}\, a \left(11 \sin \left(d x +c \right)-15\right)}{8 \left(a \sin \left(d x +c \right)-a \right)^{2}}-\frac{35 \sqrt{2}\, \arctanh \left(\frac{\sqrt{a +a \sin \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right)}{16 \sqrt{a}}}{16 a^{4}}\right)}{d}"," ",0,"-2*a^5*(3/16/a^4/(a+a*sin(d*x+c))^(1/2)+1/24/a^3/(a+a*sin(d*x+c))^(3/2)+1/16/a^4*(1/8*(a+a*sin(d*x+c))^(1/2)*a*(11*sin(d*x+c)-15)/(a*sin(d*x+c)-a)^2-35/16*2^(1/2)/a^(1/2)*arctanh(1/2*(a+a*sin(d*x+c))^(1/2)*2^(1/2)/a^(1/2))))/d","A"
113,1,244,166,0.349000," ","int(sec(d*x+c)^6*(a+a*sin(d*x+c))^(1/2),x)","-\frac{-420 a^{\frac{9}{2}} \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right)+\left(630 \left(a -a \sin \left(d x +c \right)\right)^{\frac{5}{2}} \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{2}-288 a^{\frac{9}{2}}\right) \sin \left(d x +c \right)-630 a^{\frac{9}{2}} \left(\cos^{4}\left(d x +c \right)\right)+\left(-315 \left(a -a \sin \left(d x +c \right)\right)^{\frac{5}{2}} \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{2}+84 a^{\frac{9}{2}}\right) \left(\cos^{2}\left(d x +c \right)\right)+630 \left(a -a \sin \left(d x +c \right)\right)^{\frac{5}{2}} \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{2}+32 a^{\frac{9}{2}}}{1280 a^{\frac{7}{2}} \left(\sin \left(d x +c \right)-1\right)^{2} \left(1+\sin \left(d x +c \right)\right) \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"-1/1280/a^(7/2)*(-420*a^(9/2)*sin(d*x+c)*cos(d*x+c)^2+(630*(a-a*sin(d*x+c))^(5/2)*2^(1/2)*arctanh(1/2*(a-a*sin(d*x+c))^(1/2)*2^(1/2)/a^(1/2))*a^2-288*a^(9/2))*sin(d*x+c)-630*a^(9/2)*cos(d*x+c)^4+(-315*(a-a*sin(d*x+c))^(5/2)*2^(1/2)*arctanh(1/2*(a-a*sin(d*x+c))^(1/2)*2^(1/2)/a^(1/2))*a^2+84*a^(9/2))*cos(d*x+c)^2+630*(a-a*sin(d*x+c))^(5/2)*2^(1/2)*arctanh(1/2*(a-a*sin(d*x+c))^(1/2)*2^(1/2)/a^(1/2))*a^2+32*a^(9/2))/(sin(d*x+c)-1)^2/(1+sin(d*x+c))/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
114,1,57,81,0.175000," ","int(cos(d*x+c)^7*(a+a*sin(d*x+c))^(3/2),x)","\frac{2 \left(a +a \sin \left(d x +c \right)\right)^{\frac{11}{2}} \left(715 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)-2717 \left(\cos^{2}\left(d x +c \right)\right)-4356 \sin \left(d x +c \right)+4484\right)}{12155 a^{4} d}"," ",0,"2/12155/a^4*(a+a*sin(d*x+c))^(11/2)*(715*cos(d*x+c)^2*sin(d*x+c)-2717*cos(d*x+c)^2-4356*sin(d*x+c)+4484)/d","A"
115,1,87,139,0.206000," ","int(cos(d*x+c)^6*(a+a*sin(d*x+c))^(3/2),x)","-\frac{2 \left(1+\sin \left(d x +c \right)\right) a^{2} \left(\sin \left(d x +c \right)-1\right)^{4} \left(3003 \left(\sin^{4}\left(d x +c \right)\right)+15708 \left(\sin^{3}\left(d x +c \right)\right)+33138 \left(\sin^{2}\left(d x +c \right)\right)+34748 \sin \left(d x +c \right)+16363\right)}{45045 \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"-2/45045*(1+sin(d*x+c))*a^2*(sin(d*x+c)-1)^4*(3003*sin(d*x+c)^4+15708*sin(d*x+c)^3+33138*sin(d*x+c)^2+34748*sin(d*x+c)+16363)/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
116,1,41,61,0.166000," ","int(cos(d*x+c)^5*(a+a*sin(d*x+c))^(3/2),x)","-\frac{2 \left(a +a \sin \left(d x +c \right)\right)^{\frac{9}{2}} \left(99 \left(\cos^{2}\left(d x +c \right)\right)+270 \sin \left(d x +c \right)-302\right)}{1287 a^{3} d}"," ",0,"-2/1287/a^3*(a+a*sin(d*x+c))^(9/2)*(99*cos(d*x+c)^2+270*sin(d*x+c)-302)/d","A"
117,1,77,111,0.185000," ","int(cos(d*x+c)^4*(a+a*sin(d*x+c))^(3/2),x)","\frac{2 \left(1+\sin \left(d x +c \right)\right) a^{2} \left(\sin \left(d x +c \right)-1\right)^{3} \left(105 \left(\sin^{3}\left(d x +c \right)\right)+455 \left(\sin^{2}\left(d x +c \right)\right)+755 \sin \left(d x +c \right)+533\right)}{1155 \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"2/1155*(1+sin(d*x+c))*a^2*(sin(d*x+c)-1)^3*(105*sin(d*x+c)^3+455*sin(d*x+c)^2+755*sin(d*x+c)+533)/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
118,1,31,41,0.150000," ","int(cos(d*x+c)^3*(a+a*sin(d*x+c))^(3/2),x)","-\frac{2 \left(a +a \sin \left(d x +c \right)\right)^{\frac{7}{2}} \left(7 \sin \left(d x +c \right)-11\right)}{63 a^{2} d}"," ",0,"-2/63/a^2*(a+a*sin(d*x+c))^(7/2)*(7*sin(d*x+c)-11)/d","A"
119,1,67,83,0.266000," ","int(cos(d*x+c)^2*(a+a*sin(d*x+c))^(3/2),x)","-\frac{2 \left(1+\sin \left(d x +c \right)\right) a^{2} \left(\sin \left(d x +c \right)-1\right)^{2} \left(15 \left(\sin^{2}\left(d x +c \right)\right)+54 \sin \left(d x +c \right)+71\right)}{105 \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"-2/105*(1+sin(d*x+c))*a^2*(sin(d*x+c)-1)^2*(15*sin(d*x+c)^2+54*sin(d*x+c)+71)/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
120,1,21,20,0.042000," ","int(cos(d*x+c)*(a+a*sin(d*x+c))^(3/2),x)","\frac{2 \left(a +a \sin \left(d x +c \right)\right)^{\frac{5}{2}}}{5 d a}"," ",0,"2/5*(a+a*sin(d*x+c))^(5/2)/d/a","A"
121,1,49,51,0.137000," ","int(sec(d*x+c)*(a+a*sin(d*x+c))^(3/2),x)","-\frac{2 a \left(\sqrt{a +a \sin \left(d x +c \right)}-\sqrt{a}\, \sqrt{2}\, \arctanh \left(\frac{\sqrt{a +a \sin \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right)\right)}{d}"," ",0,"-2*a*((a+a*sin(d*x+c))^(1/2)-a^(1/2)*2^(1/2)*arctanh(1/2*(a+a*sin(d*x+c))^(1/2)*2^(1/2)/a^(1/2)))/d","A"
122,1,37,24,0.138000," ","int(sec(d*x+c)^2*(a+a*sin(d*x+c))^(3/2),x)","\frac{2 a^{2} \left(1+\sin \left(d x +c \right)\right)}{\cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"2*a^2*(1+sin(d*x+c))/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
123,1,70,58,0.191000," ","int(sec(d*x+c)^3*(a+a*sin(d*x+c))^(3/2),x)","\frac{2 a^{3} \left(-\frac{\sqrt{a +a \sin \left(d x +c \right)}}{4 a \left(a \sin \left(d x +c \right)-a \right)}+\frac{\sqrt{2}\, \arctanh \left(\frac{\sqrt{a +a \sin \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right)}{8 a^{\frac{3}{2}}}\right)}{d}"," ",0,"2*a^3*(-1/4*(a+a*sin(d*x+c))^(1/2)/a/(a*sin(d*x+c)-a)+1/8/a^(3/2)*2^(1/2)*arctanh(1/2*(a+a*sin(d*x+c))^(1/2)*2^(1/2)/a^(1/2)))/d","A"
124,1,107,88,0.234000," ","int(sec(d*x+c)^4*(a+a*sin(d*x+c))^(3/2),x)","\frac{\left(1+\sin \left(d x +c \right)\right) \left(3 \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{2} \left(a -a \sin \left(d x +c \right)\right)^{\frac{3}{2}}-10 a^{\frac{7}{2}}+6 a^{\frac{7}{2}} \sin \left(d x +c \right)\right)}{12 a^{\frac{3}{2}} \left(\sin \left(d x +c \right)-1\right) \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"1/12/a^(3/2)*(1+sin(d*x+c))/(sin(d*x+c)-1)*(3*2^(1/2)*arctanh(1/2*(a-a*sin(d*x+c))^(1/2)*2^(1/2)/a^(1/2))*a^2*(a-a*sin(d*x+c))^(3/2)-10*a^(7/2)+6*a^(7/2)*sin(d*x+c))/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
125,1,101,104,0.329000," ","int(sec(d*x+c)^5*(a+a*sin(d*x+c))^(3/2),x)","-\frac{2 a^{5} \left(\frac{1}{8 a^{3} \sqrt{a +a \sin \left(d x +c \right)}}+\frac{\frac{\sqrt{a +a \sin \left(d x +c \right)}\, a \left(7 \sin \left(d x +c \right)-11\right)}{8 \left(a \sin \left(d x +c \right)-a \right)^{2}}-\frac{15 \sqrt{2}\, \arctanh \left(\frac{\sqrt{a +a \sin \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right)}{16 \sqrt{a}}}{8 a^{3}}\right)}{d}"," ",0,"-2*a^5*(1/8/a^3/(a+a*sin(d*x+c))^(1/2)+1/8/a^3*(1/8*(a+a*sin(d*x+c))^(1/2)*a*(7*sin(d*x+c)-11)/(a*sin(d*x+c)-a)^2-15/16*2^(1/2)/a^(1/2)*arctanh(1/2*(a+a*sin(d*x+c))^(1/2)*2^(1/2)/a^(1/2))))/d","A"
126,1,172,142,0.253000," ","int(sec(d*x+c)^6*(a+a*sin(d*x+c))^(3/2),x)","-\frac{210 a^{\frac{7}{2}} \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right)+\left(105 \left(a -a \sin \left(d x +c \right)\right)^{\frac{5}{2}} \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a -168 a^{\frac{7}{2}}\right) \sin \left(d x +c \right)-350 a^{\frac{7}{2}} \left(\cos^{2}\left(d x +c \right)\right)+105 \left(a -a \sin \left(d x +c \right)\right)^{\frac{5}{2}} \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a +72 a^{\frac{7}{2}}}{480 a^{\frac{3}{2}} \left(\sin \left(d x +c \right)-1\right)^{2} \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"-1/480/a^(3/2)*(210*a^(7/2)*sin(d*x+c)*cos(d*x+c)^2+(105*(a-a*sin(d*x+c))^(5/2)*2^(1/2)*arctanh(1/2*(a-a*sin(d*x+c))^(1/2)*2^(1/2)/a^(1/2))*a-168*a^(7/2))*sin(d*x+c)-350*a^(7/2)*cos(d*x+c)^2+105*(a-a*sin(d*x+c))^(5/2)*2^(1/2)*arctanh(1/2*(a-a*sin(d*x+c))^(1/2)*2^(1/2)/a^(1/2))*a+72*a^(7/2))/(sin(d*x+c)-1)^2/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
127,1,41,61,0.165000," ","int(cos(d*x+c)^5*(a+a*sin(d*x+c))^(5/2),x)","-\frac{2 \left(a +a \sin \left(d x +c \right)\right)^{\frac{11}{2}} \left(143 \left(\cos^{2}\left(d x +c \right)\right)+374 \sin \left(d x +c \right)-406\right)}{2145 a^{3} d}"," ",0,"-2/2145/a^3*(a+a*sin(d*x+c))^(11/2)*(143*cos(d*x+c)^2+374*sin(d*x+c)-406)/d","A"
128,1,87,139,0.190000," ","int(cos(d*x+c)^4*(a+a*sin(d*x+c))^(5/2),x)","\frac{2 \left(1+\sin \left(d x +c \right)\right) a^{3} \left(\sin \left(d x +c \right)-1\right)^{3} \left(1155 \left(\sin^{4}\left(d x +c \right)\right)+6300 \left(\sin^{3}\left(d x +c \right)\right)+14210 \left(\sin^{2}\left(d x +c \right)\right)+16700 \sin \left(d x +c \right)+9683\right)}{15015 \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"2/15015*(1+sin(d*x+c))*a^3*(sin(d*x+c)-1)^3*(1155*sin(d*x+c)^4+6300*sin(d*x+c)^3+14210*sin(d*x+c)^2+16700*sin(d*x+c)+9683)/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
129,1,31,41,0.161000," ","int(cos(d*x+c)^3*(a+a*sin(d*x+c))^(5/2),x)","-\frac{2 \left(a +a \sin \left(d x +c \right)\right)^{\frac{9}{2}} \left(9 \sin \left(d x +c \right)-13\right)}{99 a^{2} d}"," ",0,"-2/99/a^2*(a+a*sin(d*x+c))^(9/2)*(9*sin(d*x+c)-13)/d","A"
130,1,77,111,0.198000," ","int(cos(d*x+c)^2*(a+a*sin(d*x+c))^(5/2),x)","-\frac{2 \left(1+\sin \left(d x +c \right)\right) a^{3} \left(\sin \left(d x +c \right)-1\right)^{2} \left(35 \left(\sin^{3}\left(d x +c \right)\right)+165 \left(\sin^{2}\left(d x +c \right)\right)+321 \sin \left(d x +c \right)+319\right)}{315 \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"-2/315*(1+sin(d*x+c))*a^3*(sin(d*x+c)-1)^2*(35*sin(d*x+c)^3+165*sin(d*x+c)^2+321*sin(d*x+c)+319)/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
131,1,21,20,0.044000," ","int(cos(d*x+c)*(a+a*sin(d*x+c))^(5/2),x)","\frac{2 \left(a +a \sin \left(d x +c \right)\right)^{\frac{7}{2}}}{7 d a}"," ",0,"2/7*(a+a*sin(d*x+c))^(7/2)/d/a","A"
132,1,66,71,0.167000," ","int(sec(d*x+c)*(a+a*sin(d*x+c))^(5/2),x)","-\frac{2 a \left(\frac{\left(a +a \sin \left(d x +c \right)\right)^{\frac{3}{2}}}{3}+2 a \sqrt{a +a \sin \left(d x +c \right)}-2 a^{\frac{3}{2}} \sqrt{2}\, \arctanh \left(\frac{\sqrt{a +a \sin \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right)\right)}{d}"," ",0,"-2*a*(1/3*(a+a*sin(d*x+c))^(3/2)+2*a*(a+a*sin(d*x+c))^(1/2)-2*a^(3/2)*2^(1/2)*arctanh(1/2*(a+a*sin(d*x+c))^(1/2)*2^(1/2)/a^(1/2)))/d","A"
133,1,45,51,0.168000," ","int(sec(d*x+c)^2*(a+a*sin(d*x+c))^(5/2),x)","-\frac{2 a^{3} \left(1+\sin \left(d x +c \right)\right) \left(\sin \left(d x +c \right)-3\right)}{\cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"-2*a^3*(1+sin(d*x+c))*(sin(d*x+c)-3)/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
134,1,66,58,0.197000," ","int(sec(d*x+c)^3*(a+a*sin(d*x+c))^(5/2),x)","-\frac{a^{3} \left(\frac{\sqrt{a +a \sin \left(d x +c \right)}}{a \sin \left(d x +c \right)-a}+\frac{\sqrt{2}\, \arctanh \left(\frac{\sqrt{a +a \sin \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right)}{2 \sqrt{a}}\right)}{d}"," ",0,"-a^3*((a+a*sin(d*x+c))^(1/2)/(a*sin(d*x+c)-a)+1/2*2^(1/2)/a^(1/2)*arctanh(1/2*(a+a*sin(d*x+c))^(1/2)*2^(1/2)/a^(1/2)))/d","A"
135,1,47,26,0.163000," ","int(sec(d*x+c)^4*(a+a*sin(d*x+c))^(5/2),x)","-\frac{2 a^{3} \left(1+\sin \left(d x +c \right)\right)}{3 \left(\sin \left(d x +c \right)-1\right) \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"-2/3*a^3*(1+sin(d*x+c))/(sin(d*x+c)-1)/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
136,1,107,84,0.262000," ","int(sec(d*x+c)^5*(a+a*sin(d*x+c))^(5/2),x)","-\frac{2 a^{5} \left(-\frac{\sqrt{a +a \sin \left(d x +c \right)}}{8 a \left(a \sin \left(d x +c \right)-a \right)^{2}}-\frac{3 \left(-\frac{\sqrt{a +a \sin \left(d x +c \right)}}{4 a \left(a \sin \left(d x +c \right)-a \right)}+\frac{\sqrt{2}\, \arctanh \left(\frac{\sqrt{a +a \sin \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right)}{8 a^{\frac{3}{2}}}\right)}{8 a}\right)}{d}"," ",0,"-2*a^5*(-1/8*(a+a*sin(d*x+c))^(1/2)/a/(a*sin(d*x+c)-a)^2-3/8/a*(-1/4*(a+a*sin(d*x+c))^(1/2)/a/(a*sin(d*x+c)-a)+1/8/a^(3/2)*2^(1/2)*arctanh(1/2*(a+a*sin(d*x+c))^(1/2)*2^(1/2)/a^(1/2))))/d","A"
137,1,120,116,0.300000," ","int(sec(d*x+c)^6*(a+a*sin(d*x+c))^(5/2),x)","\frac{\left(1+\sin \left(d x +c \right)\right) \left(-30 a^{\frac{11}{2}} \left(\cos^{2}\left(d x +c \right)\right)-80 a^{\frac{11}{2}} \sin \left(d x +c \right)+104 a^{\frac{11}{2}}-15 \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{3} \left(a -a \sin \left(d x +c \right)\right)^{\frac{5}{2}}\right)}{120 a^{\frac{5}{2}} \left(\sin \left(d x +c \right)-1\right)^{2} \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"1/120*(1+sin(d*x+c))*(-30*a^(11/2)*cos(d*x+c)^2-80*a^(11/2)*sin(d*x+c)+104*a^(11/2)-15*2^(1/2)*arctanh(1/2*(a-a*sin(d*x+c))^(1/2)*2^(1/2)/a^(1/2))*a^3*(a-a*sin(d*x+c))^(5/2))/a^(5/2)/(sin(d*x+c)-1)^2/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
138,1,113,132,0.500000," ","int(sec(d*x+c)^7*(a+a*sin(d*x+c))^(5/2),x)","\frac{2 a^{7} \left(-\frac{1}{16 a^{4} \sqrt{a +a \sin \left(d x +c \right)}}-\frac{-\frac{a^{2} \sqrt{a +a \sin \left(d x +c \right)}\, \left(57 \left(\cos^{2}\left(d x +c \right)\right)+158 \sin \left(d x +c \right)-190\right)}{48 \left(a \sin \left(d x +c \right)-a \right)^{3}}-\frac{35 \sqrt{2}\, \arctanh \left(\frac{\sqrt{a +a \sin \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right)}{32 \sqrt{a}}}{16 a^{4}}\right)}{d}"," ",0,"2*a^7*(-1/16/a^4/(a+a*sin(d*x+c))^(1/2)-1/16/a^4*(-1/48*a^2*(a+a*sin(d*x+c))^(1/2)*(57*cos(d*x+c)^2+158*sin(d*x+c)-190)/(a*sin(d*x+c)-a)^3-35/32*2^(1/2)/a^(1/2)*arctanh(1/2*(a+a*sin(d*x+c))^(1/2)*2^(1/2)/a^(1/2))))/d","A"
139,1,57,81,0.220000," ","int(cos(d*x+c)^7*(a+a*sin(d*x+c))^(7/2),x)","\frac{2 \left(a +a \sin \left(d x +c \right)\right)^{\frac{15}{2}} \left(1615 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)-5865 \left(\cos^{2}\left(d x +c \right)\right)-8980 \sin \left(d x +c \right)+9108\right)}{33915 a^{4} d}"," ",0,"2/33915/a^4*(a+a*sin(d*x+c))^(15/2)*(1615*cos(d*x+c)^2*sin(d*x+c)-5865*cos(d*x+c)^2-8980*sin(d*x+c)+9108)/d","A"
140,1,107,195,0.232000," ","int(cos(d*x+c)^6*(a+a*sin(d*x+c))^(7/2),x)","-\frac{2 \left(1+\sin \left(d x +c \right)\right) a^{4} \left(\sin \left(d x +c \right)-1\right)^{4} \left(51051 \left(\sin^{6}\left(d x +c \right)\right)+378378 \left(\sin^{5}\left(d x +c \right)\right)+1222221 \left(\sin^{4}\left(d x +c \right)\right)+2244396 \left(\sin^{3}\left(d x +c \right)\right)+2546901 \left(\sin^{2}\left(d x +c \right)\right)+1778602 \sin \left(d x +c \right)+646739\right)}{969969 \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"-2/969969*(1+sin(d*x+c))*a^4*(sin(d*x+c)-1)^4*(51051*sin(d*x+c)^6+378378*sin(d*x+c)^5+1222221*sin(d*x+c)^4+2244396*sin(d*x+c)^3+2546901*sin(d*x+c)^2+1778602*sin(d*x+c)+646739)/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
141,1,41,61,0.171000," ","int(cos(d*x+c)^5*(a+a*sin(d*x+c))^(7/2),x)","-\frac{2 \left(a +a \sin \left(d x +c \right)\right)^{\frac{13}{2}} \left(195 \left(\cos^{2}\left(d x +c \right)\right)+494 \sin \left(d x +c \right)-526\right)}{3315 a^{3} d}"," ",0,"-2/3315/a^3*(a+a*sin(d*x+c))^(13/2)*(195*cos(d*x+c)^2+494*sin(d*x+c)-526)/d","A"
142,1,97,167,0.203000," ","int(cos(d*x+c)^4*(a+a*sin(d*x+c))^(7/2),x)","\frac{2 \left(1+\sin \left(d x +c \right)\right) a^{4} \left(\sin \left(d x +c \right)-1\right)^{3} \left(3003 \left(\sin^{5}\left(d x +c \right)\right)+19635 \left(\sin^{4}\left(d x +c \right)\right)+55230 \left(\sin^{3}\left(d x +c \right)\right)+86870 \left(\sin^{2}\left(d x +c \right)\right)+81815 \sin \left(d x +c \right)+41735\right)}{45045 \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"2/45045*(1+sin(d*x+c))*a^4*(sin(d*x+c)-1)^3*(3003*sin(d*x+c)^5+19635*sin(d*x+c)^4+55230*sin(d*x+c)^3+86870*sin(d*x+c)^2+81815*sin(d*x+c)+41735)/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
143,1,31,41,0.156000," ","int(cos(d*x+c)^3*(a+a*sin(d*x+c))^(7/2),x)","-\frac{2 \left(a +a \sin \left(d x +c \right)\right)^{\frac{11}{2}} \left(11 \sin \left(d x +c \right)-15\right)}{143 a^{2} d}"," ",0,"-2/143/a^2*(a+a*sin(d*x+c))^(11/2)*(11*sin(d*x+c)-15)/d","A"
144,1,87,139,0.202000," ","int(cos(d*x+c)^2*(a+a*sin(d*x+c))^(7/2),x)","-\frac{2 \left(1+\sin \left(d x +c \right)\right) a^{4} \left(\sin \left(d x +c \right)-1\right)^{2} \left(315 \left(\sin^{4}\left(d x +c \right)\right)+1820 \left(\sin^{3}\left(d x +c \right)\right)+4530 \left(\sin^{2}\left(d x +c \right)\right)+6396 \sin \left(d x +c \right)+5419\right)}{3465 \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"-2/3465*(1+sin(d*x+c))*a^4*(sin(d*x+c)-1)^2*(315*sin(d*x+c)^4+1820*sin(d*x+c)^3+4530*sin(d*x+c)^2+6396*sin(d*x+c)+5419)/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
145,1,21,20,0.040000," ","int(cos(d*x+c)*(a+a*sin(d*x+c))^(7/2),x)","\frac{2 \left(a +a \sin \left(d x +c \right)\right)^{\frac{9}{2}}}{9 d a}"," ",0,"2/9*(a+a*sin(d*x+c))^(9/2)/d/a","A"
146,1,83,91,0.168000," ","int(sec(d*x+c)*(a+a*sin(d*x+c))^(7/2),x)","-\frac{2 a \left(\frac{\left(a +a \sin \left(d x +c \right)\right)^{\frac{5}{2}}}{5}+\frac{2 \left(a +a \sin \left(d x +c \right)\right)^{\frac{3}{2}} a}{3}+4 a^{2} \sqrt{a +a \sin \left(d x +c \right)}-4 a^{\frac{5}{2}} \sqrt{2}\, \arctanh \left(\frac{\sqrt{a +a \sin \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right)\right)}{d}"," ",0,"-2*a*(1/5*(a+a*sin(d*x+c))^(5/2)+2/3*(a+a*sin(d*x+c))^(3/2)*a+4*a^2*(a+a*sin(d*x+c))^(1/2)-4*a^(5/2)*2^(1/2)*arctanh(1/2*(a+a*sin(d*x+c))^(1/2)*2^(1/2)/a^(1/2)))/d","A"
147,1,55,77,0.175000," ","int(sec(d*x+c)^2*(a+a*sin(d*x+c))^(7/2),x)","-\frac{2 a^{4} \left(1+\sin \left(d x +c \right)\right) \left(\sin^{2}\left(d x +c \right)+10 \sin \left(d x +c \right)-23\right)}{3 \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"-2/3*a^4*(1+sin(d*x+c))*(sin(d*x+c)^2+10*sin(d*x+c)-23)/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
148,1,83,78,0.266000," ","int(sec(d*x+c)^3*(a+a*sin(d*x+c))^(7/2),x)","\frac{2 a^{3} \left(\sqrt{a +a \sin \left(d x +c \right)}+4 a \left(-\frac{\sqrt{a +a \sin \left(d x +c \right)}}{4 \left(a \sin \left(d x +c \right)-a \right)}-\frac{3 \sqrt{2}\, \arctanh \left(\frac{\sqrt{a +a \sin \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right)}{8 \sqrt{a}}\right)\right)}{d}"," ",0,"2*a^3*((a+a*sin(d*x+c))^(1/2)+4*a*(-1/4*(a+a*sin(d*x+c))^(1/2)/(a*sin(d*x+c)-a)-3/8*2^(1/2)/a^(1/2)*arctanh(1/2*(a+a*sin(d*x+c))^(1/2)*2^(1/2)/a^(1/2))))/d","A"
149,1,57,55,0.192000," ","int(sec(d*x+c)^4*(a+a*sin(d*x+c))^(7/2),x)","-\frac{2 a^{4} \left(1+\sin \left(d x +c \right)\right) \left(3 \sin \left(d x +c \right)-1\right)}{3 \left(\sin \left(d x +c \right)-1\right) \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"-2/3*a^4*(1+sin(d*x+c))/(sin(d*x+c)-1)*(3*sin(d*x+c)-1)/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
150,1,75,87,0.276000," ","int(sec(d*x+c)^5*(a+a*sin(d*x+c))^(7/2),x)","-\frac{2 a^{5} \left(-\frac{\sqrt{a +a \sin \left(d x +c \right)}\, \left(3+\sin \left(d x +c \right)\right)}{16 \left(a \sin \left(d x +c \right)-a \right)^{2}}+\frac{\sqrt{2}\, \arctanh \left(\frac{\sqrt{a +a \sin \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right)}{32 a^{\frac{3}{2}}}\right)}{d}"," ",0,"-2*a^5*(-1/16*(a+a*sin(d*x+c))^(1/2)*(3+sin(d*x+c))/(a*sin(d*x+c)-a)^2+1/32/a^(3/2)*2^(1/2)*arctanh(1/2*(a+a*sin(d*x+c))^(1/2)*2^(1/2)/a^(1/2)))/d","A"
151,1,47,26,0.178000," ","int(sec(d*x+c)^6*(a+a*sin(d*x+c))^(7/2),x)","\frac{2 a^{4} \left(1+\sin \left(d x +c \right)\right)}{5 \left(\sin \left(d x +c \right)-1\right)^{2} \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"2/5*a^4*(1+sin(d*x+c))/(sin(d*x+c)-1)^2/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
152,1,144,112,0.352000," ","int(sec(d*x+c)^7*(a+a*sin(d*x+c))^(7/2),x)","\frac{2 a^{7} \left(-\frac{\sqrt{a +a \sin \left(d x +c \right)}}{12 a \left(a \sin \left(d x +c \right)-a \right)^{3}}-\frac{5 \left(-\frac{\sqrt{a +a \sin \left(d x +c \right)}}{8 a \left(a \sin \left(d x +c \right)-a \right)^{2}}-\frac{3 \left(-\frac{\sqrt{a +a \sin \left(d x +c \right)}}{4 a \left(a \sin \left(d x +c \right)-a \right)}+\frac{\sqrt{2}\, \arctanh \left(\frac{\sqrt{a +a \sin \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right)}{8 a^{\frac{3}{2}}}\right)}{8 a}\right)}{12 a}\right)}{d}"," ",0,"2*a^7*(-1/12*(a+a*sin(d*x+c))^(1/2)/a/(a*sin(d*x+c)-a)^3-5/12/a*(-1/8*(a+a*sin(d*x+c))^(1/2)/a/(a*sin(d*x+c)-a)^2-3/8/a*(-1/4*(a+a*sin(d*x+c))^(1/2)/a/(a*sin(d*x+c)-a)+1/8/a^(3/2)*2^(1/2)*arctanh(1/2*(a+a*sin(d*x+c))^(1/2)*2^(1/2)/a^(1/2)))))/d","A"
153,1,139,144,0.238000," ","int(sec(d*x+c)^8*(a+a*sin(d*x+c))^(7/2),x)","\frac{\left(1+\sin \left(d x +c \right)\right) \left(-210 a^{\frac{15}{2}} \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right)+770 a^{\frac{15}{2}} \left(\cos^{2}\left(d x +c \right)\right)+1288 a^{\frac{15}{2}} \sin \left(d x +c \right)-1528 a^{\frac{15}{2}}+105 \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{4} \left(a -a \sin \left(d x +c \right)\right)^{\frac{7}{2}}\right)}{1680 a^{\frac{7}{2}} \left(\sin \left(d x +c \right)-1\right)^{3} \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"1/1680/a^(7/2)*(1+sin(d*x+c))/(sin(d*x+c)-1)^3*(-210*a^(15/2)*sin(d*x+c)*cos(d*x+c)^2+770*a^(15/2)*cos(d*x+c)^2+1288*a^(15/2)*sin(d*x+c)-1528*a^(15/2)+105*2^(1/2)*arctanh(1/2*(a-a*sin(d*x+c))^(1/2)*2^(1/2)/a^(1/2))*a^4*(a-a*sin(d*x+c))^(7/2))/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
154,1,129,160,0.416000," ","int(sec(d*x+c)^9*(a+a*sin(d*x+c))^(7/2),x)","-\frac{2 a^{9} \left(\frac{1}{32 a^{5} \sqrt{a +a \sin \left(d x +c \right)}}+\frac{-\frac{\sqrt{a +a \sin \left(d x +c \right)}\, a^{3} \left(187 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)-725 \left(\cos^{2}\left(d x +c \right)\right)-1236 \sin \left(d x +c \right)+1364\right)}{128 \left(a \sin \left(d x +c \right)-a \right)^{4}}-\frac{315 \sqrt{2}\, \arctanh \left(\frac{\sqrt{a +a \sin \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right)}{256 \sqrt{a}}}{32 a^{5}}\right)}{d}"," ",0,"-2*a^9*(1/32/a^5/(a+a*sin(d*x+c))^(1/2)+1/32/a^5*(-1/128*(a+a*sin(d*x+c))^(1/2)*a^3*(187*cos(d*x+c)^2*sin(d*x+c)-725*cos(d*x+c)^2-1236*sin(d*x+c)+1364)/(a*sin(d*x+c)-a)^4-315/256*2^(1/2)/a^(1/2)*arctanh(1/2*(a+a*sin(d*x+c))^(1/2)*2^(1/2)/a^(1/2))))/d","A"
155,1,205,198,0.276000," ","int(sec(d*x+c)^10*(a+a*sin(d*x+c))^(7/2),x)","-\frac{-6930 a^{\frac{11}{2}} \sin \left(d x +c \right) \left(\cos^{4}\left(d x +c \right)\right)+42504 a^{\frac{11}{2}} \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right)+385 \left(9 \left(a -a \sin \left(d x +c \right)\right)^{\frac{9}{2}} \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a -32 a^{\frac{11}{2}}\right) \sin \left(d x +c \right)+25410 a^{\frac{11}{2}} \left(\cos^{4}\left(d x +c \right)\right)-50424 a^{\frac{11}{2}} \left(\cos^{2}\left(d x +c \right)\right)+3465 \left(a -a \sin \left(d x +c \right)\right)^{\frac{9}{2}} \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a +7840 a^{\frac{11}{2}}}{40320 a^{\frac{3}{2}} \left(\sin \left(d x +c \right)-1\right)^{4} \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"-1/40320/a^(3/2)*(-6930*a^(11/2)*sin(d*x+c)*cos(d*x+c)^4+42504*a^(11/2)*sin(d*x+c)*cos(d*x+c)^2+385*(9*(a-a*sin(d*x+c))^(9/2)*2^(1/2)*arctanh(1/2*(a-a*sin(d*x+c))^(1/2)*2^(1/2)/a^(1/2))*a-32*a^(11/2))*sin(d*x+c)+25410*a^(11/2)*cos(d*x+c)^4-50424*a^(11/2)*cos(d*x+c)^2+3465*(a-a*sin(d*x+c))^(9/2)*2^(1/2)*arctanh(1/2*(a-a*sin(d*x+c))^(1/2)*2^(1/2)/a^(1/2))*a+7840*a^(11/2))/(sin(d*x+c)-1)^4/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
156,1,57,81,0.158000," ","int(cos(d*x+c)^7/(a+a*sin(d*x+c))^(1/2),x)","\frac{2 \left(a +a \sin \left(d x +c \right)\right)^{\frac{7}{2}} \left(231 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)-945 \left(\cos^{2}\left(d x +c \right)\right)-1652 \sin \left(d x +c \right)+1780\right)}{3003 a^{4} d}"," ",0,"2/3003/a^4*(a+a*sin(d*x+c))^(7/2)*(231*cos(d*x+c)^2*sin(d*x+c)-945*cos(d*x+c)^2-1652*sin(d*x+c)+1780)/d","A"
157,1,64,83,0.199000," ","int(cos(d*x+c)^6/(a+a*sin(d*x+c))^(1/2),x)","-\frac{2 \left(1+\sin \left(d x +c \right)\right) \left(\sin \left(d x +c \right)-1\right)^{4} \left(63 \left(\sin^{2}\left(d x +c \right)\right)+182 \sin \left(d x +c \right)+151\right)}{693 \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"-2/693*(1+sin(d*x+c))*(sin(d*x+c)-1)^4*(63*sin(d*x+c)^2+182*sin(d*x+c)+151)/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
158,1,41,61,0.154000," ","int(cos(d*x+c)^5/(a+a*sin(d*x+c))^(1/2),x)","-\frac{2 \left(a +a \sin \left(d x +c \right)\right)^{\frac{5}{2}} \left(35 \left(\cos^{2}\left(d x +c \right)\right)+110 \sin \left(d x +c \right)-142\right)}{315 a^{3} d}"," ",0,"-2/315/a^3*(a+a*sin(d*x+c))^(5/2)*(35*cos(d*x+c)^2+110*sin(d*x+c)-142)/d","A"
159,1,54,55,0.176000," ","int(cos(d*x+c)^4/(a+a*sin(d*x+c))^(1/2),x)","\frac{2 \left(1+\sin \left(d x +c \right)\right) \left(\sin \left(d x +c \right)-1\right)^{3} \left(5 \sin \left(d x +c \right)+9\right)}{35 \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"2/35*(1+sin(d*x+c))*(sin(d*x+c)-1)^3*(5*sin(d*x+c)+9)/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
160,1,31,41,0.142000," ","int(cos(d*x+c)^3/(a+a*sin(d*x+c))^(1/2),x)","-\frac{2 \left(a +a \sin \left(d x +c \right)\right)^{\frac{3}{2}} \left(3 \sin \left(d x +c \right)-7\right)}{15 a^{2} d}"," ",0,"-2/15/a^2*(a+a*sin(d*x+c))^(3/2)*(3*sin(d*x+c)-7)/d","A"
161,1,44,26,0.188000," ","int(cos(d*x+c)^2/(a+a*sin(d*x+c))^(1/2),x)","-\frac{2 \left(1+\sin \left(d x +c \right)\right) \left(\sin \left(d x +c \right)-1\right)^{2}}{3 \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"-2/3*(1+sin(d*x+c))*(sin(d*x+c)-1)^2/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
162,1,21,20,0.026000," ","int(cos(d*x+c)/(a+a*sin(d*x+c))^(1/2),x)","\frac{2 \sqrt{a +a \sin \left(d x +c \right)}}{d a}"," ",0,"2*(a+a*sin(d*x+c))^(1/2)/d/a","A"
163,1,54,50,0.148000," ","int(sec(d*x+c)/(a+a*sin(d*x+c))^(1/2),x)","-\frac{2 a \left(\frac{1}{2 a \sqrt{a +a \sin \left(d x +c \right)}}-\frac{\sqrt{2}\, \arctanh \left(\frac{\sqrt{a +a \sin \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right)}{4 a^{\frac{3}{2}}}\right)}{d}"," ",0,"-2*a*(1/2/a/(a+a*sin(d*x+c))^(1/2)-1/4/a^(3/2)*2^(1/2)*arctanh(1/2*(a+a*sin(d*x+c))^(1/2)*2^(1/2)/a^(1/2)))/d","A"
164,1,130,85,0.204000," ","int(sec(d*x+c)^2/(a+a*sin(d*x+c))^(1/2),x)","-\frac{\sin \left(d x +c \right) \left(3 \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a \sqrt{a -a \sin \left(d x +c \right)}-6 a^{\frac{3}{2}}\right)+3 \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a \sqrt{a -a \sin \left(d x +c \right)}-2 a^{\frac{3}{2}}}{8 a^{\frac{3}{2}} \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"-1/8*(sin(d*x+c)*(3*2^(1/2)*arctanh(1/2*(a-a*sin(d*x+c))^(1/2)*2^(1/2)/a^(1/2))*a*(a-a*sin(d*x+c))^(1/2)-6*a^(3/2))+3*2^(1/2)*arctanh(1/2*(a-a*sin(d*x+c))^(1/2)*2^(1/2)/a^(1/2))*a*(a-a*sin(d*x+c))^(1/2)-2*a^(3/2))/a^(3/2)/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
165,1,107,93,0.267000," ","int(sec(d*x+c)^3/(a+a*sin(d*x+c))^(1/2),x)","\frac{2 a^{3} \left(-\frac{1}{4 a^{3} \sqrt{a +a \sin \left(d x +c \right)}}-\frac{1}{12 a^{2} \left(a +a \sin \left(d x +c \right)\right)^{\frac{3}{2}}}-\frac{\frac{\sqrt{a +a \sin \left(d x +c \right)}}{4 a \sin \left(d x +c \right)-4 a}-\frac{5 \sqrt{2}\, \arctanh \left(\frac{\sqrt{a +a \sin \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right)}{8 \sqrt{a}}}{4 a^{3}}\right)}{d}"," ",0,"2*a^3*(-1/4/a^3/(a+a*sin(d*x+c))^(1/2)-1/12/a^2/(a+a*sin(d*x+c))^(3/2)-1/4/a^3*(1/4*(a+a*sin(d*x+c))^(1/2)/(a*sin(d*x+c)-a)-5/8*2^(1/2)/a^(1/2)*arctanh(1/2*(a+a*sin(d*x+c))^(1/2)*2^(1/2)/a^(1/2))))/d","A"
166,1,231,135,0.245000," ","int(sec(d*x+c)^4/(a+a*sin(d*x+c))^(1/2),x)","\frac{-210 a^{\frac{7}{2}} \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right)+\left(210 \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{2} \left(a -a \sin \left(d x +c \right)\right)^{\frac{3}{2}}-112 a^{\frac{7}{2}}\right) \sin \left(d x +c \right)+\left(-105 \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{2} \left(a -a \sin \left(d x +c \right)\right)^{\frac{3}{2}}-70 a^{\frac{7}{2}}\right) \left(\cos^{2}\left(d x +c \right)\right)+210 \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{2} \left(a -a \sin \left(d x +c \right)\right)^{\frac{3}{2}}-16 a^{\frac{7}{2}}}{384 a^{\frac{7}{2}} \left(\sin \left(d x +c \right)-1\right) \left(1+\sin \left(d x +c \right)\right) \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"1/384*(-210*a^(7/2)*sin(d*x+c)*cos(d*x+c)^2+(210*2^(1/2)*arctanh(1/2*(a-a*sin(d*x+c))^(1/2)*2^(1/2)/a^(1/2))*a^2*(a-a*sin(d*x+c))^(3/2)-112*a^(7/2))*sin(d*x+c)+(-105*2^(1/2)*arctanh(1/2*(a-a*sin(d*x+c))^(1/2)*2^(1/2)/a^(1/2))*a^2*(a-a*sin(d*x+c))^(3/2)-70*a^(7/2))*cos(d*x+c)^2+210*2^(1/2)*arctanh(1/2*(a-a*sin(d*x+c))^(1/2)*2^(1/2)/a^(1/2))*a^2*(a-a*sin(d*x+c))^(3/2)-16*a^(7/2))/a^(7/2)/(sin(d*x+c)-1)/(1+sin(d*x+c))/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
167,1,135,144,0.346000," ","int(sec(d*x+c)^5/(a+a*sin(d*x+c))^(1/2),x)","-\frac{2 a^{5} \left(\frac{3}{16 a^{5} \sqrt{a +a \sin \left(d x +c \right)}}+\frac{1}{16 a^{4} \left(a +a \sin \left(d x +c \right)\right)^{\frac{3}{2}}}+\frac{1}{40 a^{3} \left(a +a \sin \left(d x +c \right)\right)^{\frac{5}{2}}}+\frac{\frac{\sqrt{a +a \sin \left(d x +c \right)}\, a \left(15 \sin \left(d x +c \right)-19\right)}{16 \left(a \sin \left(d x +c \right)-a \right)^{2}}-\frac{63 \sqrt{2}\, \arctanh \left(\frac{\sqrt{a +a \sin \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right)}{32 \sqrt{a}}}{16 a^{5}}\right)}{d}"," ",0,"-2*a^5*(3/16/a^5/(a+a*sin(d*x+c))^(1/2)+1/16/a^4/(a+a*sin(d*x+c))^(3/2)+1/40/a^3/(a+a*sin(d*x+c))^(5/2)+1/16/a^5*(1/16*(a+a*sin(d*x+c))^(1/2)*a*(15*sin(d*x+c)-19)/(a*sin(d*x+c)-a)^2-63/32*2^(1/2)/a^(1/2)*arctanh(1/2*(a+a*sin(d*x+c))^(1/2)*2^(1/2)/a^(1/2))))/d","A"
168,1,308,186,0.276000," ","int(sec(d*x+c)^6/(a+a*sin(d*x+c))^(1/2),x)","-\frac{-6930 a^{\frac{11}{2}} \sin \left(d x +c \right) \left(\cos^{4}\left(d x +c \right)\right)+\left(-3696 a^{\frac{11}{2}}-3465 \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{3} \left(a -a \sin \left(d x +c \right)\right)^{\frac{5}{2}}\right) \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+\left(-2816 a^{\frac{11}{2}}+13860 \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{3} \left(a -a \sin \left(d x +c \right)\right)^{\frac{5}{2}}\right) \sin \left(d x +c \right)-2310 a^{\frac{11}{2}} \left(\cos^{4}\left(d x +c \right)\right)+\left(-528 a^{\frac{11}{2}}-10395 \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{3} \left(a -a \sin \left(d x +c \right)\right)^{\frac{5}{2}}\right) \left(\cos^{2}\left(d x +c \right)\right)-256 a^{\frac{11}{2}}+13860 \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{3} \left(a -a \sin \left(d x +c \right)\right)^{\frac{5}{2}}}{15360 a^{\frac{11}{2}} \left(\sin \left(d x +c \right)-1\right)^{2} \left(1+\sin \left(d x +c \right)\right)^{2} \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"-1/15360*(-6930*a^(11/2)*sin(d*x+c)*cos(d*x+c)^4+(-3696*a^(11/2)-3465*2^(1/2)*arctanh(1/2*(a-a*sin(d*x+c))^(1/2)*2^(1/2)/a^(1/2))*a^3*(a-a*sin(d*x+c))^(5/2))*cos(d*x+c)^2*sin(d*x+c)+(-2816*a^(11/2)+13860*2^(1/2)*arctanh(1/2*(a-a*sin(d*x+c))^(1/2)*2^(1/2)/a^(1/2))*a^3*(a-a*sin(d*x+c))^(5/2))*sin(d*x+c)-2310*a^(11/2)*cos(d*x+c)^4+(-528*a^(11/2)-10395*2^(1/2)*arctanh(1/2*(a-a*sin(d*x+c))^(1/2)*2^(1/2)/a^(1/2))*a^3*(a-a*sin(d*x+c))^(5/2))*cos(d*x+c)^2-256*a^(11/2)+13860*2^(1/2)*arctanh(1/2*(a-a*sin(d*x+c))^(1/2)*2^(1/2)/a^(1/2))*a^3*(a-a*sin(d*x+c))^(5/2))/a^(11/2)/(sin(d*x+c)-1)^2/(1+sin(d*x+c))^2/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
169,1,57,81,0.156000," ","int(cos(d*x+c)^7/(a+a*sin(d*x+c))^(3/2),x)","\frac{2 \left(a +a \sin \left(d x +c \right)\right)^{\frac{5}{2}} \left(105 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)-455 \left(\cos^{2}\left(d x +c \right)\right)-860 \sin \left(d x +c \right)+988\right)}{1155 a^{4} d}"," ",0,"2/1155/a^4*(a+a*sin(d*x+c))^(5/2)*(105*cos(d*x+c)^2*sin(d*x+c)-455*cos(d*x+c)^2-860*sin(d*x+c)+988)/d","A"
170,1,57,55,0.195000," ","int(cos(d*x+c)^6/(a+a*sin(d*x+c))^(3/2),x)","-\frac{2 \left(1+\sin \left(d x +c \right)\right) \left(\sin \left(d x +c \right)-1\right)^{4} \left(7 \sin \left(d x +c \right)+11\right)}{63 a \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"-2/63/a*(1+sin(d*x+c))*(sin(d*x+c)-1)^4*(7*sin(d*x+c)+11)/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
171,1,41,61,0.156000," ","int(cos(d*x+c)^5/(a+a*sin(d*x+c))^(3/2),x)","-\frac{2 \left(a +a \sin \left(d x +c \right)\right)^{\frac{3}{2}} \left(15 \left(\cos^{2}\left(d x +c \right)\right)+54 \sin \left(d x +c \right)-86\right)}{105 a^{3} d}"," ",0,"-2/105/a^3*(a+a*sin(d*x+c))^(3/2)*(15*cos(d*x+c)^2+54*sin(d*x+c)-86)/d","A"
172,1,47,26,0.168000," ","int(cos(d*x+c)^4/(a+a*sin(d*x+c))^(3/2),x)","\frac{2 \left(1+\sin \left(d x +c \right)\right) \left(\sin \left(d x +c \right)-1\right)^{3}}{5 a \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"2/5/a*(1+sin(d*x+c))*(sin(d*x+c)-1)^3/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
173,1,29,41,0.132000," ","int(cos(d*x+c)^3/(a+a*sin(d*x+c))^(3/2),x)","-\frac{2 \sqrt{a +a \sin \left(d x +c \right)}\, \left(\sin \left(d x +c \right)-5\right)}{3 a^{2} d}"," ",0,"-2/3/a^2*(a+a*sin(d*x+c))^(1/2)*(sin(d*x+c)-5)/d","A"
174,1,94,65,0.213000," ","int(cos(d*x+c)^2/(a+a*sin(d*x+c))^(3/2),x)","\frac{2 \left(1+\sin \left(d x +c \right)\right) \sqrt{-a \left(\sin \left(d x +c \right)-1\right)}\, \left(\sqrt{a -a \sin \left(d x +c \right)}-\sqrt{a}\, \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right)\right)}{a^{2} \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"2/a^2*(1+sin(d*x+c))*(-a*(sin(d*x+c)-1))^(1/2)*((a-a*sin(d*x+c))^(1/2)-a^(1/2)*2^(1/2)*arctanh(1/2*(a-a*sin(d*x+c))^(1/2)*2^(1/2)/a^(1/2)))/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
175,1,21,20,0.023000," ","int(cos(d*x+c)/(a+a*sin(d*x+c))^(3/2),x)","-\frac{2}{a d \sqrt{a +a \sin \left(d x +c \right)}}"," ",0,"-2/a/d/(a+a*sin(d*x+c))^(1/2)","A"
176,1,71,70,0.172000," ","int(sec(d*x+c)/(a+a*sin(d*x+c))^(3/2),x)","-\frac{a \left(\frac{1}{2 a^{2} \sqrt{a +a \sin \left(d x +c \right)}}+\frac{1}{3 a \left(a +a \sin \left(d x +c \right)\right)^{\frac{3}{2}}}-\frac{\sqrt{2}\, \arctanh \left(\frac{\sqrt{a +a \sin \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right)}{4 a^{\frac{5}{2}}}\right)}{d}"," ",0,"-a*(1/2/a^2/(a+a*sin(d*x+c))^(1/2)+1/3/a/(a+a*sin(d*x+c))^(3/2)-1/4/a^(5/2)*2^(1/2)*arctanh(1/2*(a+a*sin(d*x+c))^(1/2)*2^(1/2)/a^(1/2)))/d","A"
177,1,202,111,0.247000," ","int(sec(d*x+c)^2/(a+a*sin(d*x+c))^(3/2),x)","-\frac{\sin \left(d x +c \right) \left(30 \sqrt{a -a \sin \left(d x +c \right)}\, \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{2}-40 a^{\frac{5}{2}}\right)+\left(-15 \sqrt{a -a \sin \left(d x +c \right)}\, \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{2}+30 a^{\frac{5}{2}}\right) \left(\cos^{2}\left(d x +c \right)\right)+30 \sqrt{a -a \sin \left(d x +c \right)}\, \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{2}-24 a^{\frac{5}{2}}}{64 a^{\frac{7}{2}} \left(1+\sin \left(d x +c \right)\right) \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"-1/64/a^(7/2)*(sin(d*x+c)*(30*(a-a*sin(d*x+c))^(1/2)*2^(1/2)*arctanh(1/2*(a-a*sin(d*x+c))^(1/2)*2^(1/2)/a^(1/2))*a^2-40*a^(5/2))+(-15*(a-a*sin(d*x+c))^(1/2)*2^(1/2)*arctanh(1/2*(a-a*sin(d*x+c))^(1/2)*2^(1/2)/a^(1/2))*a^2+30*a^(5/2))*cos(d*x+c)^2+30*(a-a*sin(d*x+c))^(1/2)*2^(1/2)*arctanh(1/2*(a-a*sin(d*x+c))^(1/2)*2^(1/2)/a^(1/2))*a^2-24*a^(5/2))/(1+sin(d*x+c))/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
178,1,124,123,0.270000," ","int(sec(d*x+c)^3/(a+a*sin(d*x+c))^(3/2),x)","\frac{2 a^{3} \left(-\frac{3}{16 a^{4} \sqrt{a +a \sin \left(d x +c \right)}}-\frac{1}{12 a^{3} \left(a +a \sin \left(d x +c \right)\right)^{\frac{3}{2}}}-\frac{1}{20 a^{2} \left(a +a \sin \left(d x +c \right)\right)^{\frac{5}{2}}}-\frac{\frac{\sqrt{a +a \sin \left(d x +c \right)}}{2 a \sin \left(d x +c \right)-2 a}-\frac{7 \sqrt{2}\, \arctanh \left(\frac{\sqrt{a +a \sin \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right)}{4 \sqrt{a}}}{16 a^{4}}\right)}{d}"," ",0,"2*a^3*(-3/16/a^4/(a+a*sin(d*x+c))^(1/2)-1/12/a^3/(a+a*sin(d*x+c))^(3/2)-1/20/a^2/(a+a*sin(d*x+c))^(5/2)-1/16/a^4*(1/2*(a+a*sin(d*x+c))^(1/2)/(a*sin(d*x+c)-a)-7/4*2^(1/2)/a^(1/2)*arctanh(1/2*(a+a*sin(d*x+c))^(1/2)*2^(1/2)/a^(1/2))))/d","A"
179,1,289,164,0.310000," ","int(sec(d*x+c)^4/(a+a*sin(d*x+c))^(3/2),x)","\frac{\left(-840 a^{\frac{9}{2}}-315 \left(a -a \sin \left(d x +c \right)\right)^{\frac{3}{2}} \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{3}\right) \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right)+\left(-384 a^{\frac{9}{2}}+1260 \left(a -a \sin \left(d x +c \right)\right)^{\frac{3}{2}} \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{3}\right) \sin \left(d x +c \right)+630 a^{\frac{9}{2}} \left(\cos^{4}\left(d x +c \right)\right)+\left(-504 a^{\frac{9}{2}}-945 \left(a -a \sin \left(d x +c \right)\right)^{\frac{3}{2}} \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{3}\right) \left(\cos^{2}\left(d x +c \right)\right)-128 a^{\frac{9}{2}}+1260 \left(a -a \sin \left(d x +c \right)\right)^{\frac{3}{2}} \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{3}}{1536 a^{\frac{11}{2}} \left(\sin \left(d x +c \right)-1\right) \left(1+\sin \left(d x +c \right)\right)^{2} \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"1/1536/a^(11/2)*((-840*a^(9/2)-315*(a-a*sin(d*x+c))^(3/2)*2^(1/2)*arctanh(1/2*(a-a*sin(d*x+c))^(1/2)*2^(1/2)/a^(1/2))*a^3)*sin(d*x+c)*cos(d*x+c)^2+(-384*a^(9/2)+1260*(a-a*sin(d*x+c))^(3/2)*2^(1/2)*arctanh(1/2*(a-a*sin(d*x+c))^(1/2)*2^(1/2)/a^(1/2))*a^3)*sin(d*x+c)+630*a^(9/2)*cos(d*x+c)^4+(-504*a^(9/2)-945*(a-a*sin(d*x+c))^(3/2)*2^(1/2)*arctanh(1/2*(a-a*sin(d*x+c))^(1/2)*2^(1/2)/a^(1/2))*a^3)*cos(d*x+c)^2-128*a^(9/2)+1260*(a-a*sin(d*x+c))^(3/2)*2^(1/2)*arctanh(1/2*(a-a*sin(d*x+c))^(1/2)*2^(1/2)/a^(1/2))*a^3)/(sin(d*x+c)-1)/(1+sin(d*x+c))^2/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
180,1,152,176,0.363000," ","int(sec(d*x+c)^5/(a+a*sin(d*x+c))^(3/2),x)","-\frac{2 a^{5} \left(\frac{5}{32 a^{6} \sqrt{a +a \sin \left(d x +c \right)}}+\frac{1}{16 a^{5} \left(a +a \sin \left(d x +c \right)\right)^{\frac{3}{2}}}+\frac{3}{80 a^{4} \left(a +a \sin \left(d x +c \right)\right)^{\frac{5}{2}}}+\frac{1}{56 a^{3} \left(a +a \sin \left(d x +c \right)\right)^{\frac{7}{2}}}+\frac{\frac{\sqrt{a +a \sin \left(d x +c \right)}\, a \left(19 \sin \left(d x +c \right)-23\right)}{16 \left(a \sin \left(d x +c \right)-a \right)^{2}}-\frac{99 \sqrt{2}\, \arctanh \left(\frac{\sqrt{a +a \sin \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right)}{32 \sqrt{a}}}{32 a^{6}}\right)}{d}"," ",0,"-2*a^5*(5/32/a^6/(a+a*sin(d*x+c))^(1/2)+1/16/a^5/(a+a*sin(d*x+c))^(3/2)+3/80/a^4/(a+a*sin(d*x+c))^(5/2)+1/56/a^3/(a+a*sin(d*x+c))^(7/2)+1/32/a^6*(1/16*(a+a*sin(d*x+c))^(1/2)*a*(19*sin(d*x+c)-23)/(a*sin(d*x+c)-a)^2-99/32*2^(1/2)/a^(1/2)*arctanh(1/2*(a+a*sin(d*x+c))^(1/2)*2^(1/2)/a^(1/2))))/d","A"
181,1,367,217,0.292000," ","int(sec(d*x+c)^6/(a+a*sin(d*x+c))^(3/2),x)","-\frac{-120120 a^{\frac{13}{2}} \sin \left(d x +c \right) \left(\cos^{4}\left(d x +c \right)\right)+\left(-54912 a^{\frac{13}{2}}-180180 \left(a -a \sin \left(d x +c \right)\right)^{\frac{5}{2}} \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{4}\right) \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+\left(-39936 a^{\frac{13}{2}}+360360 \left(a -a \sin \left(d x +c \right)\right)^{\frac{5}{2}} \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{4}\right) \sin \left(d x +c \right)+90090 a^{\frac{13}{2}} \left(\cos^{6}\left(d x +c \right)\right)+9009 \left(-8 a^{\frac{13}{2}}+5 \left(a -a \sin \left(d x +c \right)\right)^{\frac{5}{2}} \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{4}\right) \left(\cos^{4}\left(d x +c \right)\right)+\left(-18304 a^{\frac{13}{2}}-360360 \left(a -a \sin \left(d x +c \right)\right)^{\frac{5}{2}} \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{4}\right) \left(\cos^{2}\left(d x +c \right)\right)-9216 a^{\frac{13}{2}}+360360 \left(a -a \sin \left(d x +c \right)\right)^{\frac{5}{2}} \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{4}}{245760 a^{\frac{15}{2}} \left(\sin \left(d x +c \right)-1\right)^{2} \left(1+\sin \left(d x +c \right)\right)^{3} \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"-1/245760/a^(15/2)*(-120120*a^(13/2)*sin(d*x+c)*cos(d*x+c)^4+(-54912*a^(13/2)-180180*(a-a*sin(d*x+c))^(5/2)*2^(1/2)*arctanh(1/2*(a-a*sin(d*x+c))^(1/2)*2^(1/2)/a^(1/2))*a^4)*cos(d*x+c)^2*sin(d*x+c)+(-39936*a^(13/2)+360360*(a-a*sin(d*x+c))^(5/2)*2^(1/2)*arctanh(1/2*(a-a*sin(d*x+c))^(1/2)*2^(1/2)/a^(1/2))*a^4)*sin(d*x+c)+90090*a^(13/2)*cos(d*x+c)^6+9009*(-8*a^(13/2)+5*(a-a*sin(d*x+c))^(5/2)*2^(1/2)*arctanh(1/2*(a-a*sin(d*x+c))^(1/2)*2^(1/2)/a^(1/2))*a^4)*cos(d*x+c)^4+(-18304*a^(13/2)-360360*(a-a*sin(d*x+c))^(5/2)*2^(1/2)*arctanh(1/2*(a-a*sin(d*x+c))^(1/2)*2^(1/2)/a^(1/2))*a^4)*cos(d*x+c)^2-9216*a^(13/2)+360360*(a-a*sin(d*x+c))^(5/2)*2^(1/2)*arctanh(1/2*(a-a*sin(d*x+c))^(1/2)*2^(1/2)/a^(1/2))*a^4)/(sin(d*x+c)-1)^2/(1+sin(d*x+c))^3/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
182,1,67,83,0.204000," ","int(cos(d*x+c)^10/(a+a*sin(d*x+c))^(5/2),x)","-\frac{2 \left(1+\sin \left(d x +c \right)\right) \left(\sin \left(d x +c \right)-1\right)^{6} \left(143 \left(\sin^{2}\left(d x +c \right)\right)+374 \sin \left(d x +c \right)+263\right)}{2145 a^{2} \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"-2/2145/a^2*(1+sin(d*x+c))*(sin(d*x+c)-1)^6*(143*sin(d*x+c)^2+374*sin(d*x+c)+263)/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
183,1,67,101,0.166000," ","int(cos(d*x+c)^9/(a+a*sin(d*x+c))^(5/2),x)","\frac{2 \left(a +a \sin \left(d x +c \right)\right)^{\frac{5}{2}} \left(1155 \left(\cos^{4}\left(d x +c \right)\right)+6300 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)-16520 \left(\cos^{2}\left(d x +c \right)\right)-23000 \sin \left(d x +c \right)+25048\right)}{15015 a^{5} d}"," ",0,"2/15015/a^5*(a+a*sin(d*x+c))^(5/2)*(1155*cos(d*x+c)^4+6300*cos(d*x+c)^2*sin(d*x+c)-16520*cos(d*x+c)^2-23000*sin(d*x+c)+25048)/d","A"
184,1,57,55,0.208000," ","int(cos(d*x+c)^8/(a+a*sin(d*x+c))^(5/2),x)","\frac{2 \left(1+\sin \left(d x +c \right)\right) \left(\sin \left(d x +c \right)-1\right)^{5} \left(9 \sin \left(d x +c \right)+13\right)}{99 a^{2} \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"2/99/a^2*(1+sin(d*x+c))*(sin(d*x+c)-1)^5*(9*sin(d*x+c)+13)/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
185,1,57,81,0.170000," ","int(cos(d*x+c)^7/(a+a*sin(d*x+c))^(5/2),x)","\frac{2 \left(a +a \sin \left(d x +c \right)\right)^{\frac{3}{2}} \left(35 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)-165 \left(\cos^{2}\left(d x +c \right)\right)-356 \sin \left(d x +c \right)+484\right)}{315 a^{4} d}"," ",0,"2/315/a^4*(a+a*sin(d*x+c))^(3/2)*(35*cos(d*x+c)^2*sin(d*x+c)-165*cos(d*x+c)^2-356*sin(d*x+c)+484)/d","A"
186,1,47,26,0.162000," ","int(cos(d*x+c)^6/(a+a*sin(d*x+c))^(5/2),x)","-\frac{2 \left(1+\sin \left(d x +c \right)\right) \left(\sin \left(d x +c \right)-1\right)^{4}}{7 a^{2} \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"-2/7/a^2*(1+sin(d*x+c))*(sin(d*x+c)-1)^4/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
187,1,41,61,0.368000," ","int(cos(d*x+c)^5/(a+a*sin(d*x+c))^(5/2),x)","-\frac{2 \sqrt{a +a \sin \left(d x +c \right)}\, \left(3 \left(\cos^{2}\left(d x +c \right)\right)+14 \sin \left(d x +c \right)-46\right)}{15 a^{3} d}"," ",0,"-2/15/a^3*(a+a*sin(d*x+c))^(1/2)*(3*cos(d*x+c)^2+14*sin(d*x+c)-46)/d","A"
188,1,112,93,0.234000," ","int(cos(d*x+c)^4/(a+a*sin(d*x+c))^(5/2),x)","-\frac{2 \left(1+\sin \left(d x +c \right)\right) \sqrt{-a \left(\sin \left(d x +c \right)-1\right)}\, \left(6 a^{\frac{3}{2}} \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right)-\left(a -a \sin \left(d x +c \right)\right)^{\frac{3}{2}}-6 a \sqrt{a -a \sin \left(d x +c \right)}\right)}{3 a^{4} \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"-2/3*(1+sin(d*x+c))*(-a*(sin(d*x+c)-1))^(1/2)*(6*a^(3/2)*2^(1/2)*arctanh(1/2*(a-a*sin(d*x+c))^(1/2)*2^(1/2)/a^(1/2))-(a-a*sin(d*x+c))^(3/2)-6*a*(a-a*sin(d*x+c))^(1/2))/a^4/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
189,1,29,41,0.134000," ","int(cos(d*x+c)^3/(a+a*sin(d*x+c))^(5/2),x)","-\frac{2 \left(3+\sin \left(d x +c \right)\right)}{a^{2} \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"-2/a^2/(a+a*sin(d*x+c))^(1/2)*(3+sin(d*x+c))/d","A"
190,1,123,65,0.212000," ","int(cos(d*x+c)^2/(a+a*sin(d*x+c))^(5/2),x)","-\frac{\left(-\sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a \sin \left(d x +c \right)-\sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a +2 \sqrt{a -a \sin \left(d x +c \right)}\, \sqrt{a}\right) \sqrt{-a \left(\sin \left(d x +c \right)-1\right)}}{2 a^{\frac{7}{2}} \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"-1/2/a^(7/2)*(-2^(1/2)*arctanh(1/2*(a-a*sin(d*x+c))^(1/2)*2^(1/2)/a^(1/2))*a*sin(d*x+c)-2^(1/2)*arctanh(1/2*(a-a*sin(d*x+c))^(1/2)*2^(1/2)/a^(1/2))*a+2*(a-a*sin(d*x+c))^(1/2)*a^(1/2))*(-a*(sin(d*x+c)-1))^(1/2)/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
191,1,21,20,0.025000," ","int(cos(d*x+c)/(a+a*sin(d*x+c))^(5/2),x)","-\frac{2}{3 a d \left(a +a \sin \left(d x +c \right)\right)^{\frac{3}{2}}}"," ",0,"-2/3/a/d/(a+a*sin(d*x+c))^(3/2)","A"
192,1,88,90,0.169000," ","int(sec(d*x+c)/(a+a*sin(d*x+c))^(5/2),x)","-\frac{2 a \left(\frac{1}{8 a^{3} \sqrt{a +a \sin \left(d x +c \right)}}+\frac{1}{12 a^{2} \left(a +a \sin \left(d x +c \right)\right)^{\frac{3}{2}}}+\frac{1}{10 a \left(a +a \sin \left(d x +c \right)\right)^{\frac{5}{2}}}-\frac{\sqrt{2}\, \arctanh \left(\frac{\sqrt{a +a \sin \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right)}{16 a^{\frac{7}{2}}}\right)}{d}"," ",0,"-2*a*(1/8/a^3/(a+a*sin(d*x+c))^(1/2)+1/12/a^2/(a+a*sin(d*x+c))^(3/2)+1/10/a/(a+a*sin(d*x+c))^(5/2)-1/16/a^(7/2)*2^(1/2)*arctanh(1/2*(a+a*sin(d*x+c))^(1/2)*2^(1/2)/a^(1/2)))/d","A"
193,1,266,140,0.236000," ","int(sec(d*x+c)^2/(a+a*sin(d*x+c))^(5/2),x)","-\frac{\left(210 a^{\frac{7}{2}}-105 \sqrt{a -a \sin \left(d x +c \right)}\, \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{3}\right) \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right)+\left(-448 a^{\frac{7}{2}}+420 \sqrt{a -a \sin \left(d x +c \right)}\, \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{3}\right) \sin \left(d x +c \right)+\left(490 a^{\frac{7}{2}}-315 \sqrt{a -a \sin \left(d x +c \right)}\, \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{3}\right) \left(\cos^{2}\left(d x +c \right)\right)-320 a^{\frac{7}{2}}+420 \sqrt{a -a \sin \left(d x +c \right)}\, \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{3}}{768 a^{\frac{11}{2}} \left(1+\sin \left(d x +c \right)\right)^{2} \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"-1/768/a^(11/2)*((210*a^(7/2)-105*(a-a*sin(d*x+c))^(1/2)*2^(1/2)*arctanh(1/2*(a-a*sin(d*x+c))^(1/2)*2^(1/2)/a^(1/2))*a^3)*sin(d*x+c)*cos(d*x+c)^2+(-448*a^(7/2)+420*(a-a*sin(d*x+c))^(1/2)*2^(1/2)*arctanh(1/2*(a-a*sin(d*x+c))^(1/2)*2^(1/2)/a^(1/2))*a^3)*sin(d*x+c)+(490*a^(7/2)-315*(a-a*sin(d*x+c))^(1/2)*2^(1/2)*arctanh(1/2*(a-a*sin(d*x+c))^(1/2)*2^(1/2)/a^(1/2))*a^3)*cos(d*x+c)^2-320*a^(7/2)+420*(a-a*sin(d*x+c))^(1/2)*2^(1/2)*arctanh(1/2*(a-a*sin(d*x+c))^(1/2)*2^(1/2)/a^(1/2))*a^3)/(1+sin(d*x+c))^2/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
194,1,141,154,0.296000," ","int(sec(d*x+c)^3/(a+a*sin(d*x+c))^(5/2),x)","\frac{2 a^{3} \left(-\frac{1}{8 a^{5} \sqrt{a +a \sin \left(d x +c \right)}}-\frac{1}{16 a^{4} \left(a +a \sin \left(d x +c \right)\right)^{\frac{3}{2}}}-\frac{1}{20 a^{3} \left(a +a \sin \left(d x +c \right)\right)^{\frac{5}{2}}}-\frac{1}{28 a^{2} \left(a +a \sin \left(d x +c \right)\right)^{\frac{7}{2}}}-\frac{\frac{\sqrt{a +a \sin \left(d x +c \right)}}{4 a \sin \left(d x +c \right)-4 a}-\frac{9 \sqrt{2}\, \arctanh \left(\frac{\sqrt{a +a \sin \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right)}{8 \sqrt{a}}}{16 a^{5}}\right)}{d}"," ",0,"2*a^3*(-1/8/a^5/(a+a*sin(d*x+c))^(1/2)-1/16/a^4/(a+a*sin(d*x+c))^(3/2)-1/20/a^3/(a+a*sin(d*x+c))^(5/2)-1/28/a^2/(a+a*sin(d*x+c))^(7/2)-1/16/a^5*(1/4*(a+a*sin(d*x+c))^(1/2)/(a*sin(d*x+c)-a)-9/8*2^(1/2)/a^(1/2)*arctanh(1/2*(a+a*sin(d*x+c))^(1/2)*2^(1/2)/a^(1/2))))/d","A"
195,1,355,198,0.289000," ","int(sec(d*x+c)^4/(a+a*sin(d*x+c))^(5/2),x)","\frac{6930 a^{\frac{11}{2}} \sin \left(d x +c \right) \left(\cos^{4}\left(d x +c \right)\right)-924 \left(16 a^{\frac{11}{2}}+15 \left(a -a \sin \left(d x +c \right)\right)^{\frac{3}{2}} \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{4}\right) \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+\left(-5632 a^{\frac{11}{2}}+27720 \left(a -a \sin \left(d x +c \right)\right)^{\frac{3}{2}} \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{4}\right) \sin \left(d x +c \right)+\left(16170 a^{\frac{11}{2}}+3465 \left(a -a \sin \left(d x +c \right)\right)^{\frac{3}{2}} \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{4}\right) \left(\cos^{4}\left(d x +c \right)\right)-1320 \left(8 a^{\frac{11}{2}}+21 \left(a -a \sin \left(d x +c \right)\right)^{\frac{3}{2}} \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{4}\right) \left(\cos^{2}\left(d x +c \right)\right)-2560 a^{\frac{11}{2}}+27720 \left(a -a \sin \left(d x +c \right)\right)^{\frac{3}{2}} \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{4}}{24576 a^{\frac{15}{2}} \left(\sin \left(d x +c \right)-1\right) \left(1+\sin \left(d x +c \right)\right)^{3} \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"1/24576/a^(15/2)*(6930*a^(11/2)*sin(d*x+c)*cos(d*x+c)^4-924*(16*a^(11/2)+15*(a-a*sin(d*x+c))^(3/2)*2^(1/2)*arctanh(1/2*(a-a*sin(d*x+c))^(1/2)*2^(1/2)/a^(1/2))*a^4)*cos(d*x+c)^2*sin(d*x+c)+(-5632*a^(11/2)+27720*(a-a*sin(d*x+c))^(3/2)*2^(1/2)*arctanh(1/2*(a-a*sin(d*x+c))^(1/2)*2^(1/2)/a^(1/2))*a^4)*sin(d*x+c)+(16170*a^(11/2)+3465*(a-a*sin(d*x+c))^(3/2)*2^(1/2)*arctanh(1/2*(a-a*sin(d*x+c))^(1/2)*2^(1/2)/a^(1/2))*a^4)*cos(d*x+c)^4-1320*(8*a^(11/2)+21*(a-a*sin(d*x+c))^(3/2)*2^(1/2)*arctanh(1/2*(a-a*sin(d*x+c))^(1/2)*2^(1/2)/a^(1/2))*a^4)*cos(d*x+c)^2-2560*a^(11/2)+27720*(a-a*sin(d*x+c))^(3/2)*2^(1/2)*arctanh(1/2*(a-a*sin(d*x+c))^(1/2)*2^(1/2)/a^(1/2))*a^4)/(sin(d*x+c)-1)/(1+sin(d*x+c))^3/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
196,1,249,132,0.662000," ","int((e*cos(d*x+c))^(7/2)*(a+a*sin(d*x+c)),x)","-\frac{2 a \,e^{4} \left(-224 \left(\sin^{11}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+144 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+560 \left(\sin^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-216 \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-560 \left(\sin^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+168 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+280 \left(\sin^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+15 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}-48 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-70 \left(\sin^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+7 \sin \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{63 \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e +e}\, d}"," ",0,"-2/63/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)*a*e^4*(-224*sin(1/2*d*x+1/2*c)^11+144*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^8+560*sin(1/2*d*x+1/2*c)^9-216*sin(1/2*d*x+1/2*c)^6*cos(1/2*d*x+1/2*c)-560*sin(1/2*d*x+1/2*c)^7+168*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+280*sin(1/2*d*x+1/2*c)^5+15*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)-48*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)-70*sin(1/2*d*x+1/2*c)^3+7*sin(1/2*d*x+1/2*c))/d","A"
197,1,214,107,0.643000," ","int((e*cos(d*x+c))^(5/2)*(a+a*sin(d*x+c)),x)","\frac{2 a \,e^{3} \left(-80 \left(\sin^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+56 \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+160 \left(\sin^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-56 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-120 \left(\sin^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+21 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}+14 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+40 \left(\sin^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-5 \sin \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{35 \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e +e}\, d}"," ",0,"2/35/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)*a*e^3*(-80*sin(1/2*d*x+1/2*c)^9+56*sin(1/2*d*x+1/2*c)^6*cos(1/2*d*x+1/2*c)+160*sin(1/2*d*x+1/2*c)^7-56*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)-120*sin(1/2*d*x+1/2*c)^5+21*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)+14*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+40*sin(1/2*d*x+1/2*c)^3-5*sin(1/2*d*x+1/2*c))/d","A"
198,1,179,107,0.615000," ","int((e*cos(d*x+c))^(3/2)*(a+a*sin(d*x+c)),x)","-\frac{2 a \,e^{2} \left(-24 \left(\sin^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+20 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+36 \left(\sin^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+5 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}-10 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-18 \left(\sin^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+3 \sin \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{15 \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e +e}\, d}"," ",0,"-2/15/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)*a*e^2*(-24*sin(1/2*d*x+1/2*c)^7+20*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+36*sin(1/2*d*x+1/2*c)^5+5*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)-10*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)-18*sin(1/2*d*x+1/2*c)^3+3*sin(1/2*d*x+1/2*c))/d","A"
199,1,120,81,0.601000," ","int((a+a*sin(d*x+c))*(e*cos(d*x+c))^(1/2),x)","\frac{2 a e \left(-4 \left(\sin^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+3 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}+4 \left(\sin^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\sin \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e +e}\, d}"," ",0,"2/3/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)*a*e*(-4*sin(1/2*d*x+1/2*c)^5+3*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)+4*sin(1/2*d*x+1/2*c)^3-sin(1/2*d*x+1/2*c))/d","A"
200,1,103,81,0.384000," ","int((a+a*sin(d*x+c))/(e*cos(d*x+c))^(1/2),x)","-\frac{2 a \left(\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}-2 \left(\sin^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e +e}\, d}"," ",0,"-2/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)*a*((sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)-2*sin(1/2*d*x+1/2*c)^3+sin(1/2*d*x+1/2*c))/d","A"
201,1,117,109,0.779000," ","int((a+a*sin(d*x+c))/(e*cos(d*x+c))^(3/2),x)","-\frac{2 \left(\EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-\sin \left(\frac{d x}{2}+\frac{c}{2}\right)\right) a}{e \sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e +e}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) d}"," ",0,"-2/e/(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)/sin(1/2*d*x+1/2*c)*(EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)-2*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)-sin(1/2*d*x+1/2*c))*a/d","A"
202,1,189,109,0.883000," ","int((a+a*sin(d*x+c))/(e*cos(d*x+c))^(5/2),x)","-\frac{2 \left(2 \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}+2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\sin \left(\frac{d x}{2}+\frac{c}{2}\right)\right) a}{3 \left(2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e +e}\, e^{2} d}"," ",0,"-2/3/(2*sin(1/2*d*x+1/2*c)^2-1)/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)/e^2*(2*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^2-(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)+2*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+sin(1/2*d*x+1/2*c))*a/d","A"
203,1,304,134,1.402000," ","int((a+a*sin(d*x+c))/(e*cos(d*x+c))^(7/2),x)","-\frac{2 \left(12 \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-24 \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-12 \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+24 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+3 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}-8 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-\sin \left(\frac{d x}{2}+\frac{c}{2}\right)\right) a}{5 \left(4 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-4 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e +e}\, e^{3} d}"," ",0,"-2/5/(4*sin(1/2*d*x+1/2*c)^4-4*sin(1/2*d*x+1/2*c)^2+1)/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)/e^3*(12*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*sin(1/2*d*x+1/2*c)^4-24*sin(1/2*d*x+1/2*c)^6*cos(1/2*d*x+1/2*c)-12*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*sin(1/2*d*x+1/2*c)^2+24*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+3*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)-8*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)-sin(1/2*d*x+1/2*c))*a/d","B"
204,1,295,172,0.750000," ","int((e*cos(d*x+c))^(7/2)*(a+a*sin(d*x+c))^2,x)","-\frac{2 a^{2} e^{4} \left(-4032 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{12}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+10080 \left(\sin^{10}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-4928 \left(\sin^{11}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-8208 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+12320 \left(\sin^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+2232 \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-12320 \left(\sin^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+924 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+6160 \left(\sin^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+195 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}-498 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-1540 \left(\sin^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+154 \sin \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{693 \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e +e}\, d}"," ",0,"-2/693/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)*a^2*e^4*(-4032*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^12+10080*sin(1/2*d*x+1/2*c)^10*cos(1/2*d*x+1/2*c)-4928*sin(1/2*d*x+1/2*c)^11-8208*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^8+12320*sin(1/2*d*x+1/2*c)^9+2232*sin(1/2*d*x+1/2*c)^6*cos(1/2*d*x+1/2*c)-12320*sin(1/2*d*x+1/2*c)^7+924*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+6160*sin(1/2*d*x+1/2*c)^5+195*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)-498*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)-1540*sin(1/2*d*x+1/2*c)^3+154*sin(1/2*d*x+1/2*c))/d","A"
205,1,260,145,0.864000," ","int((e*cos(d*x+c))^(5/2)*(a+a*sin(d*x+c))^2,x)","\frac{2 a^{2} e^{3} \left(-1120 \left(\sin^{10}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+2240 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1440 \left(\sin^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1064 \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+2880 \left(\sin^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-56 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-2160 \left(\sin^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+231 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}+84 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+720 \left(\sin^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-90 \sin \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{315 \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e +e}\, d}"," ",0,"2/315/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)*a^2*e^3*(-1120*sin(1/2*d*x+1/2*c)^10*cos(1/2*d*x+1/2*c)+2240*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^8-1440*sin(1/2*d*x+1/2*c)^9-1064*sin(1/2*d*x+1/2*c)^6*cos(1/2*d*x+1/2*c)+2880*sin(1/2*d*x+1/2*c)^7-56*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)-2160*sin(1/2*d*x+1/2*c)^5+231*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)+84*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+720*sin(1/2*d*x+1/2*c)^3-90*sin(1/2*d*x+1/2*c))/d","A"
206,1,203,145,0.747000," ","int((e*cos(d*x+c))^(3/2)*(a+a*sin(d*x+c))^2,x)","-\frac{2 a^{2} e^{2} \left(-80 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+120 \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-112 \left(\sin^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+168 \left(\sin^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+15 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}-20 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-84 \left(\sin^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+14 \sin \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{35 \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e +e}\, d}"," ",0,"-2/35/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)*a^2*e^2*(-80*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^8+120*sin(1/2*d*x+1/2*c)^6*cos(1/2*d*x+1/2*c)-112*sin(1/2*d*x+1/2*c)^7+168*sin(1/2*d*x+1/2*c)^5+15*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)-20*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)-84*sin(1/2*d*x+1/2*c)^3+14*sin(1/2*d*x+1/2*c))/d","A"
207,1,188,117,0.789000," ","int((a+a*sin(d*x+c))^2*(e*cos(d*x+c))^(1/2),x)","\frac{2 a^{2} e \left(-24 \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+24 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-40 \left(\sin^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+21 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}-6 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+40 \left(\sin^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-10 \sin \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{15 \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e +e}\, d}"," ",0,"2/15/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)*a^2*e*(-24*sin(1/2*d*x+1/2*c)^6*cos(1/2*d*x+1/2*c)+24*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)-40*sin(1/2*d*x+1/2*c)^5+21*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)-6*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+40*sin(1/2*d*x+1/2*c)^3-10*sin(1/2*d*x+1/2*c))/d","A"
208,1,152,117,0.571000," ","int((a+a*sin(d*x+c))^2/(e*cos(d*x+c))^(1/2),x)","-\frac{2 a^{2} \left(-4 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+5 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}+2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-12 \left(\sin^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+6 \sin \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e +e}\, d}"," ",0,"-2/3/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)*a^2*(-4*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+5*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)+2*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)-12*sin(1/2*d*x+1/2*c)^3+6*sin(1/2*d*x+1/2*c))/d","A"
209,1,120,105,0.813000," ","int((a+a*sin(d*x+c))^2/(e*cos(d*x+c))^(3/2),x)","-\frac{2 \left(3 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}-4 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-2 \sin \left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{2}}{e \sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e +e}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) d}"," ",0,"-2/e/(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)/sin(1/2*d*x+1/2*c)*(3*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)-4*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)-2*sin(1/2*d*x+1/2*c))*a^2/d","A"
210,1,193,105,1.041000," ","int((a+a*sin(d*x+c))^2/(e*cos(d*x+c))^(5/2),x)","\frac{2 \left(2 \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}-4 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-2 \sin \left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{2}}{3 \left(2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e +e}\, e^{2} d}"," ",0,"2/3/(2*sin(1/2*d*x+1/2*c)^2-1)/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)/e^2*(2*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^2-(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)-4*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)-2*sin(1/2*d*x+1/2*c))*a^2/d","A"
211,1,305,139,1.380000," ","int((a+a*sin(d*x+c))^2/(e*cos(d*x+c))^(7/2),x)","-\frac{2 \left(4 \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-8 \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-4 \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+8 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}-6 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-2 \sin \left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{2}}{5 \left(4 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-4 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e +e}\, e^{3} d}"," ",0,"-2/5/(4*sin(1/2*d*x+1/2*c)^4-4*sin(1/2*d*x+1/2*c)^2+1)/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)/e^3*(4*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*sin(1/2*d*x+1/2*c)^4-8*sin(1/2*d*x+1/2*c)^6*cos(1/2*d*x+1/2*c)-4*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*sin(1/2*d*x+1/2*c)^2+8*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)-6*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)-2*sin(1/2*d*x+1/2*c))*a^2/d","B"
212,1,375,126,1.591000," ","int((a+a*sin(d*x+c))^2/(e*cos(d*x+c))^(9/2),x)","-\frac{2 \left(8 \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-12 \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+8 \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+6 \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-8 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}+6 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+2 \sin \left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{2}}{7 \left(8 \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-12 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+6 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e +e}\, e^{4} d}"," ",0,"-2/7/(8*sin(1/2*d*x+1/2*c)^6-12*sin(1/2*d*x+1/2*c)^4+6*sin(1/2*d*x+1/2*c)^2-1)/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)/e^4*(8*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^6-12*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^4+8*sin(1/2*d*x+1/2*c)^6*cos(1/2*d*x+1/2*c)+6*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^2-8*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)-(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)+6*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+2*sin(1/2*d*x+1/2*c))*a^2/d","B"
213,1,488,153,2.438000," ","int((a+a*sin(d*x+c))^2/(e*cos(d*x+c))^(11/2),x)","-\frac{2 \left(48 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-96 \left(\sin^{10}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-96 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+192 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+72 \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-152 \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-24 \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+56 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+3 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}-12 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-2 \sin \left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{2}}{9 \left(16 \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-32 \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+24 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-8 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e +e}\, e^{5} d}"," ",0,"-2/9/(16*sin(1/2*d*x+1/2*c)^8-32*sin(1/2*d*x+1/2*c)^6+24*sin(1/2*d*x+1/2*c)^4-8*sin(1/2*d*x+1/2*c)^2+1)/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)/e^5*(48*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*sin(1/2*d*x+1/2*c)^8-96*sin(1/2*d*x+1/2*c)^10*cos(1/2*d*x+1/2*c)-96*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*sin(1/2*d*x+1/2*c)^6+192*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^8+72*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*sin(1/2*d*x+1/2*c)^4-152*sin(1/2*d*x+1/2*c)^6*cos(1/2*d*x+1/2*c)-24*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*sin(1/2*d*x+1/2*c)^2+56*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+3*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)-12*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)-2*sin(1/2*d*x+1/2*c))*a^2/d","B"
214,1,321,203,0.941000," ","int((e*cos(d*x+c))^(7/2)*(a+a*sin(d*x+c))^3,x)","-\frac{2 a^{3} e^{4} \left(88704 \left(\sin^{15}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-157248 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{12}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-310464 \left(\sin^{13}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+393120 \left(\sin^{10}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+337568 \left(\sin^{11}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-361296 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-67760 \left(\sin^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+148824 \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-126280 \left(\sin^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-12012 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+101948 \left(\sin^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+3315 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}-5694 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-30338 \left(\sin^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+3311 \sin \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{9009 \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e +e}\, d}"," ",0,"-2/9009/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)*a^3*e^4*(88704*sin(1/2*d*x+1/2*c)^15-157248*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^12-310464*sin(1/2*d*x+1/2*c)^13+393120*sin(1/2*d*x+1/2*c)^10*cos(1/2*d*x+1/2*c)+337568*sin(1/2*d*x+1/2*c)^11-361296*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^8-67760*sin(1/2*d*x+1/2*c)^9+148824*sin(1/2*d*x+1/2*c)^6*cos(1/2*d*x+1/2*c)-126280*sin(1/2*d*x+1/2*c)^7-12012*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+101948*sin(1/2*d*x+1/2*c)^5+3315*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)-5694*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)-30338*sin(1/2*d*x+1/2*c)^3+3311*sin(1/2*d*x+1/2*c))/d","A"
215,1,264,176,1.029000," ","int((e*cos(d*x+c))^(5/2)*(a+a*sin(d*x+c))^3,x)","\frac{2 a^{3} e^{3} \left(1344 \left(\sin^{13}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-2464 \left(\sin^{10}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-4032 \left(\sin^{11}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+4928 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+2928 \left(\sin^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-3080 \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+864 \left(\sin^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+616 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-1908 \left(\sin^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+231 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}+804 \left(\sin^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-111 \sin \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{231 \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e +e}\, d}"," ",0,"2/231/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)*a^3*e^3*(1344*sin(1/2*d*x+1/2*c)^13-2464*sin(1/2*d*x+1/2*c)^10*cos(1/2*d*x+1/2*c)-4032*sin(1/2*d*x+1/2*c)^11+4928*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^8+2928*sin(1/2*d*x+1/2*c)^9-3080*sin(1/2*d*x+1/2*c)^6*cos(1/2*d*x+1/2*c)+864*sin(1/2*d*x+1/2*c)^7+616*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)-1908*sin(1/2*d*x+1/2*c)^5+231*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)+804*sin(1/2*d*x+1/2*c)^3-111*sin(1/2*d*x+1/2*c))/d","A"
216,1,251,176,1.265000," ","int((e*cos(d*x+c))^(3/2)*(a+a*sin(d*x+c))^3,x)","-\frac{2 a^{3} e^{2} \left(1120 \left(\sin^{11}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-2160 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-2800 \left(\sin^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+3240 \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+784 \left(\sin^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-840 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+1624 \left(\sin^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+195 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}-120 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-1162 \left(\sin^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+217 \sin \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{315 \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e +e}\, d}"," ",0,"-2/315/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)*a^3*e^2*(1120*sin(1/2*d*x+1/2*c)^11-2160*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^8-2800*sin(1/2*d*x+1/2*c)^9+3240*sin(1/2*d*x+1/2*c)^6*cos(1/2*d*x+1/2*c)+784*sin(1/2*d*x+1/2*c)^7-840*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+1624*sin(1/2*d*x+1/2*c)^5+195*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)-120*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)-1162*sin(1/2*d*x+1/2*c)^3+217*sin(1/2*d*x+1/2*c))/d","A"
217,1,214,148,0.847000," ","int((a+a*sin(d*x+c))^3*(e*cos(d*x+c))^(1/2),x)","\frac{2 a^{3} e \left(240 \left(\sin^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-504 \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-480 \left(\sin^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+504 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-200 \left(\sin^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+231 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}-126 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+440 \left(\sin^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-125 \sin \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{105 \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e +e}\, d}"," ",0,"2/105/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)*a^3*e*(240*sin(1/2*d*x+1/2*c)^9-504*sin(1/2*d*x+1/2*c)^6*cos(1/2*d*x+1/2*c)-480*sin(1/2*d*x+1/2*c)^7+504*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)-200*sin(1/2*d*x+1/2*c)^5+231*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)-126*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+440*sin(1/2*d*x+1/2*c)^3-125*sin(1/2*d*x+1/2*c))/d","A"
218,1,178,148,0.767000," ","int((a+a*sin(d*x+c))^3/(e*cos(d*x+c))^(1/2),x)","-\frac{2 a^{3} \left(8 \left(\sin^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-20 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-12 \left(\sin^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+15 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}+10 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-34 \left(\sin^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+19 \sin \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{5 \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e +e}\, d}"," ",0,"-2/5/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)*a^3*(8*sin(1/2*d*x+1/2*c)^7-20*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)-12*sin(1/2*d*x+1/2*c)^5+15*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)+10*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)-34*sin(1/2*d*x+1/2*c)^3+19*sin(1/2*d*x+1/2*c))/d","A"
219,1,146,122,1.182000," ","int((a+a*sin(d*x+c))^3/(e*cos(d*x+c))^(3/2),x)","-\frac{2 \left(-4 \left(\sin^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+21 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}-24 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+4 \left(\sin^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-13 \sin \left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{3}}{3 e \sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e +e}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) d}"," ",0,"-2/3/e/(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)/sin(1/2*d*x+1/2*c)*(-4*sin(1/2*d*x+1/2*c)^5+21*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)-24*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+4*sin(1/2*d*x+1/2*c)^3-13*sin(1/2*d*x+1/2*c))*a^3/d","A"
220,1,219,122,1.266000," ","int((a+a*sin(d*x+c))^3/(e*cos(d*x+c))^(5/2),x)","\frac{2 \left(10 \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-12 \left(\sin^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-5 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}-8 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+12 \left(\sin^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-7 \sin \left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{3}}{3 \left(2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e +e}\, e^{2} d}"," ",0,"2/3/(2*sin(1/2*d*x+1/2*c)^2-1)/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)/e^2*(10*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^2-12*sin(1/2*d*x+1/2*c)^5-5*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)-8*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+12*sin(1/2*d*x+1/2*c)^3-7*sin(1/2*d*x+1/2*c))*a^3/d","A"
221,1,332,139,1.884000," ","int((a+a*sin(d*x+c))^3/(e*cos(d*x+c))^(7/2),x)","\frac{2 \left(12 \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-24 \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-12 \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+24 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-20 \left(\sin^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+3 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}+2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+20 \left(\sin^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\sin \left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{3}}{5 \left(4 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-4 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e +e}\, e^{3} d}"," ",0,"2/5/(4*sin(1/2*d*x+1/2*c)^4-4*sin(1/2*d*x+1/2*c)^2+1)/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)/e^3*(12*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*sin(1/2*d*x+1/2*c)^4-24*sin(1/2*d*x+1/2*c)^6*cos(1/2*d*x+1/2*c)-12*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*sin(1/2*d*x+1/2*c)^2+24*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)-20*sin(1/2*d*x+1/2*c)^5+3*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)+2*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+20*sin(1/2*d*x+1/2*c)^3-sin(1/2*d*x+1/2*c))*a^3/d","B"
222,1,401,139,2.002000," ","int((a+a*sin(d*x+c))^3/(e*cos(d*x+c))^(9/2),x)","\frac{2 \left(8 \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-12 \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+8 \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+6 \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-8 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+28 \left(\sin^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}-22 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-28 \left(\sin^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-5 \sin \left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{3}}{21 \left(8 \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-12 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+6 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e +e}\, e^{4} d}"," ",0,"2/21/(8*sin(1/2*d*x+1/2*c)^6-12*sin(1/2*d*x+1/2*c)^4+6*sin(1/2*d*x+1/2*c)^2-1)/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)/e^4*(8*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^6-12*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^4+8*sin(1/2*d*x+1/2*c)^6*cos(1/2*d*x+1/2*c)+6*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^2-8*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+28*sin(1/2*d*x+1/2*c)^5-(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)-22*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)-28*sin(1/2*d*x+1/2*c)^3-5*sin(1/2*d*x+1/2*c))*a^3/d","B"
223,1,514,173,2.684000," ","int((a+a*sin(d*x+c))^3/(e*cos(d*x+c))^(11/2),x)","-\frac{2 \left(48 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-96 \left(\sin^{10}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-96 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+192 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+72 \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-152 \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-24 \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+56 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+36 \left(\sin^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+3 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}-48 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-36 \left(\sin^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-11 \sin \left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{3}}{45 \left(16 \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-32 \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+24 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-8 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e +e}\, e^{5} d}"," ",0,"-2/45/(16*sin(1/2*d*x+1/2*c)^8-32*sin(1/2*d*x+1/2*c)^6+24*sin(1/2*d*x+1/2*c)^4-8*sin(1/2*d*x+1/2*c)^2+1)/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)/e^5*(48*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*sin(1/2*d*x+1/2*c)^8-96*sin(1/2*d*x+1/2*c)^10*cos(1/2*d*x+1/2*c)-96*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*sin(1/2*d*x+1/2*c)^6+192*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^8+72*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*sin(1/2*d*x+1/2*c)^4-152*sin(1/2*d*x+1/2*c)^6*cos(1/2*d*x+1/2*c)-24*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*sin(1/2*d*x+1/2*c)^2+56*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+36*sin(1/2*d*x+1/2*c)^5+3*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)-48*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)-36*sin(1/2*d*x+1/2*c)^3-11*sin(1/2*d*x+1/2*c))*a^3/d","B"
224,1,295,210,0.938000," ","int((e*cos(d*x+c))^(3/2)*(a+a*sin(d*x+c))^4,x)","-\frac{2 a^{4} e^{2} \left(20160 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{12}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-50400 \left(\sin^{10}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+49280 \left(\sin^{11}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-6480 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-123200 \left(\sin^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+60120 \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+78848 \left(\sin^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-23100 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+4928 \left(\sin^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+3315 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}-150 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-17864 \left(\sin^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+4004 \sin \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3465 \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e +e}\, d}"," ",0,"-2/3465/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)*a^4*e^2*(20160*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^12-50400*sin(1/2*d*x+1/2*c)^10*cos(1/2*d*x+1/2*c)+49280*sin(1/2*d*x+1/2*c)^11-6480*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^8-123200*sin(1/2*d*x+1/2*c)^9+60120*sin(1/2*d*x+1/2*c)^6*cos(1/2*d*x+1/2*c)+78848*sin(1/2*d*x+1/2*c)^7-23100*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+4928*sin(1/2*d*x+1/2*c)^5+3315*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)-150*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)-17864*sin(1/2*d*x+1/2*c)^3+4004*sin(1/2*d*x+1/2*c))/d","A"
225,1,258,182,0.982000," ","int((a+a*sin(d*x+c))^4*(e*cos(d*x+c))^(1/2),x)","\frac{2 a^{4} e \left(224 \left(\sin^{10}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-448 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+576 \left(\sin^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-392 \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-1152 \left(\sin^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+616 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+192 \left(\sin^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+231 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}-168 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+384 \left(\sin^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-132 \sin \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{63 \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e +e}\, d}"," ",0,"2/63/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)*a^4*e*(224*sin(1/2*d*x+1/2*c)^10*cos(1/2*d*x+1/2*c)-448*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^8+576*sin(1/2*d*x+1/2*c)^9-392*sin(1/2*d*x+1/2*c)^6*cos(1/2*d*x+1/2*c)-1152*sin(1/2*d*x+1/2*c)^7+616*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+192*sin(1/2*d*x+1/2*c)^5+231*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)-168*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+384*sin(1/2*d*x+1/2*c)^3-132*sin(1/2*d*x+1/2*c))/d","A"
226,1,222,182,0.863000," ","int((a+a*sin(d*x+c))^4/(e*cos(d*x+c))^(1/2),x)","-\frac{2 a^{4} \left(80 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-120 \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+224 \left(\sin^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-280 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-336 \left(\sin^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+195 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}+160 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-392 \left(\sin^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+252 \sin \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{35 \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e +e}\, d}"," ",0,"-2/35/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)*a^4*(80*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^8-120*sin(1/2*d*x+1/2*c)^6*cos(1/2*d*x+1/2*c)+224*sin(1/2*d*x+1/2*c)^7-280*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)-336*sin(1/2*d*x+1/2*c)^5+195*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)+160*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)-392*sin(1/2*d*x+1/2*c)^3+252*sin(1/2*d*x+1/2*c))/d","A"
227,1,190,166,1.146000," ","int((a+a*sin(d*x+c))^4/(e*cos(d*x+c))^(3/2),x)","-\frac{2 \left(-24 \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+24 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-80 \left(\sin^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+231 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}-246 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+80 \left(\sin^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-140 \sin \left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{4}}{15 e \sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e +e}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) d}"," ",0,"-2/15/e/(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)/sin(1/2*d*x+1/2*c)*(-24*sin(1/2*d*x+1/2*c)^6*cos(1/2*d*x+1/2*c)+24*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)-80*sin(1/2*d*x+1/2*c)^5+231*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)-246*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+80*sin(1/2*d*x+1/2*c)^3-140*sin(1/2*d*x+1/2*c))*a^4/d","A"
228,1,263,166,1.282000," ","int((a+a*sin(d*x+c))^4/(e*cos(d*x+c))^(5/2),x)","\frac{2 \left(-8 \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+30 \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+8 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-48 \left(\sin^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-15 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}-18 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+48 \left(\sin^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-20 \sin \left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{4}}{3 \left(2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e +e}\, e^{2} d}"," ",0,"2/3/(2*sin(1/2*d*x+1/2*c)^2-1)/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)/e^2*(-8*sin(1/2*d*x+1/2*c)^6*cos(1/2*d*x+1/2*c)+30*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^2+8*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)-48*sin(1/2*d*x+1/2*c)^5-15*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)-18*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+48*sin(1/2*d*x+1/2*c)^3-20*sin(1/2*d*x+1/2*c))*a^4/d","A"
229,1,332,139,1.795000," ","int((a+a*sin(d*x+c))^4/(e*cos(d*x+c))^(7/2),x)","\frac{2 \left(84 \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-128 \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-84 \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+128 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-80 \left(\sin^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+21 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}-16 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+80 \left(\sin^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-12 \sin \left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{4}}{5 \left(4 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-4 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e +e}\, e^{3} d}"," ",0,"2/5/(4*sin(1/2*d*x+1/2*c)^4-4*sin(1/2*d*x+1/2*c)^2+1)/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)/e^3*(84*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*sin(1/2*d*x+1/2*c)^4-128*sin(1/2*d*x+1/2*c)^6*cos(1/2*d*x+1/2*c)-84*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*sin(1/2*d*x+1/2*c)^2+128*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)-80*sin(1/2*d*x+1/2*c)^5+21*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)-16*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+80*sin(1/2*d*x+1/2*c)^3-12*sin(1/2*d*x+1/2*c))*a^4/d","B"
230,1,401,139,2.001000," ","int((a+a*sin(d*x+c))^4/(e*cos(d*x+c))^(9/2),x)","-\frac{2 \left(40 \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-60 \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-128 \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+30 \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+128 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-112 \left(\sin^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-5 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}+16 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+112 \left(\sin^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-4 \sin \left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{4}}{21 \left(8 \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-12 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+6 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e +e}\, e^{4} d}"," ",0,"-2/21/(8*sin(1/2*d*x+1/2*c)^6-12*sin(1/2*d*x+1/2*c)^4+6*sin(1/2*d*x+1/2*c)^2-1)/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)/e^4*(40*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^6-60*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^4-128*sin(1/2*d*x+1/2*c)^6*cos(1/2*d*x+1/2*c)+30*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^2+128*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)-112*sin(1/2*d*x+1/2*c)^5-5*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)+16*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+112*sin(1/2*d*x+1/2*c)^3-4*sin(1/2*d*x+1/2*c))*a^4/d","B"
231,1,514,177,2.935000," ","int((a+a*sin(d*x+c))^4/(e*cos(d*x+c))^(11/2),x)","\frac{2 \left(48 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-96 \left(\sin^{10}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-96 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+192 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+72 \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-272 \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-24 \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+176 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-144 \left(\sin^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+3 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}+42 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+144 \left(\sin^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+4 \sin \left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{4}}{45 \left(16 \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-32 \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+24 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-8 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e +e}\, e^{5} d}"," ",0,"2/45/(16*sin(1/2*d*x+1/2*c)^8-32*sin(1/2*d*x+1/2*c)^6+24*sin(1/2*d*x+1/2*c)^4-8*sin(1/2*d*x+1/2*c)^2+1)/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)/e^5*(48*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*sin(1/2*d*x+1/2*c)^8-96*sin(1/2*d*x+1/2*c)^10*cos(1/2*d*x+1/2*c)-96*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*sin(1/2*d*x+1/2*c)^6+192*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^8+72*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*sin(1/2*d*x+1/2*c)^4-272*sin(1/2*d*x+1/2*c)^6*cos(1/2*d*x+1/2*c)-24*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*sin(1/2*d*x+1/2*c)^2+176*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)-144*sin(1/2*d*x+1/2*c)^5+3*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)+42*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+144*sin(1/2*d*x+1/2*c)^3+4*sin(1/2*d*x+1/2*c))*a^4/d","B"
232,1,583,177,3.241000," ","int((a+a*sin(d*x+c))^4/(e*cos(d*x+c))^(13/2),x)","\frac{2 \left(32 \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \left(\sin^{10}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-80 \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+32 \left(\sin^{10}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+80 \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-64 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-40 \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+176 \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+10 \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-144 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+176 \left(\sin^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}-78 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-176 \left(\sin^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-12 \sin \left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{4}}{77 \left(32 \left(\sin^{10}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-80 \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+80 \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-40 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+10 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e +e}\, e^{6} d}"," ",0,"2/77/(32*sin(1/2*d*x+1/2*c)^10-80*sin(1/2*d*x+1/2*c)^8+80*sin(1/2*d*x+1/2*c)^6-40*sin(1/2*d*x+1/2*c)^4+10*sin(1/2*d*x+1/2*c)^2-1)/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)/e^6*(32*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*sin(1/2*d*x+1/2*c)^10-80*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*sin(1/2*d*x+1/2*c)^8+32*sin(1/2*d*x+1/2*c)^10*cos(1/2*d*x+1/2*c)+80*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^6-64*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^8-40*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^4+176*sin(1/2*d*x+1/2*c)^6*cos(1/2*d*x+1/2*c)+10*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^2-144*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+176*sin(1/2*d*x+1/2*c)^5-(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)-78*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)-176*sin(1/2*d*x+1/2*c)^3-12*sin(1/2*d*x+1/2*c))*a^4/d","B"
233,1,251,140,0.888000," ","int((e*cos(d*x+c))^(11/2)/(a+a*sin(d*x+c)),x)","-\frac{2 e^{6} \left(224 \left(\sin^{11}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+144 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-560 \left(\sin^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-216 \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+560 \left(\sin^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+168 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-280 \left(\sin^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+15 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}-48 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+70 \left(\sin^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-7 \sin \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{63 a \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e +e}\, d}"," ",0,"-2/63/a/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)*e^6*(224*sin(1/2*d*x+1/2*c)^11+144*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^8-560*sin(1/2*d*x+1/2*c)^9-216*sin(1/2*d*x+1/2*c)^6*cos(1/2*d*x+1/2*c)+560*sin(1/2*d*x+1/2*c)^7+168*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)-280*sin(1/2*d*x+1/2*c)^5+15*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)-48*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+70*sin(1/2*d*x+1/2*c)^3-7*sin(1/2*d*x+1/2*c))/d","A"
234,1,216,113,0.793000," ","int((e*cos(d*x+c))^(9/2)/(a+a*sin(d*x+c)),x)","\frac{2 e^{5} \left(80 \left(\sin^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+56 \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-160 \left(\sin^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-56 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+120 \left(\sin^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+21 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}+14 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-40 \left(\sin^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+5 \sin \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{35 a \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e +e}\, d}"," ",0,"2/35/a/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)*e^5*(80*sin(1/2*d*x+1/2*c)^9+56*sin(1/2*d*x+1/2*c)^6*cos(1/2*d*x+1/2*c)-160*sin(1/2*d*x+1/2*c)^7-56*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+120*sin(1/2*d*x+1/2*c)^5+21*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)+14*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)-40*sin(1/2*d*x+1/2*c)^3+5*sin(1/2*d*x+1/2*c))/d","A"
235,1,181,113,1.086000," ","int((e*cos(d*x+c))^(7/2)/(a+a*sin(d*x+c)),x)","-\frac{2 e^{4} \left(24 \left(\sin^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+20 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-36 \left(\sin^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+5 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}-10 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+18 \left(\sin^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-3 \sin \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{15 a \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e +e}\, d}"," ",0,"-2/15/a/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)*e^4*(24*sin(1/2*d*x+1/2*c)^7+20*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)-36*sin(1/2*d*x+1/2*c)^5+5*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)-10*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+18*sin(1/2*d*x+1/2*c)^3-3*sin(1/2*d*x+1/2*c))/d","A"
236,1,122,86,0.711000," ","int((e*cos(d*x+c))^(5/2)/(a+a*sin(d*x+c)),x)","\frac{2 e^{3} \left(4 \left(\sin^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+3 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}-4 \left(\sin^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 a \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e +e}\, d}"," ",0,"2/3/a/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)*e^3*(4*sin(1/2*d*x+1/2*c)^5+3*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)-4*sin(1/2*d*x+1/2*c)^3+sin(1/2*d*x+1/2*c))/d","A"
237,1,110,86,0.517000," ","int((e*cos(d*x+c))^(3/2)/(a+a*sin(d*x+c)),x)","-\frac{2 e^{2} \left(\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}+2 \left(\sin^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\sin \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e +e}\, d}"," ",0,"-2/a/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)*e^2*((sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)+2*sin(1/2*d*x+1/2*c)^3-sin(1/2*d*x+1/2*c))/d","A"
238,1,115,94,1.143000," ","int((e*cos(d*x+c))^(1/2)/(a+a*sin(d*x+c)),x)","-\frac{2 \left(\EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\sin \left(\frac{d x}{2}+\frac{c}{2}\right)\right) e}{\sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e +e}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) a d}"," ",0,"-2/(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)/sin(1/2*d*x+1/2*c)/a*(EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)-2*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+sin(1/2*d*x+1/2*c))*e/d","A"
239,1,190,94,1.479000," ","int(1/(a+a*sin(d*x+c))/(e*cos(d*x+c))^(1/2),x)","-\frac{2 \left(2 \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}+2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-\sin \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 \left(2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) a \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e +e}\, d}"," ",0,"-2/3/(2*sin(1/2*d*x+1/2*c)^2-1)/a/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)*(2*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^2-(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)+2*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)-sin(1/2*d*x+1/2*c))/d","B"
240,1,304,124,2.003000," ","int(1/(e*cos(d*x+c))^(3/2)/(a+a*sin(d*x+c)),x)","-\frac{2 \left(12 \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-24 \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-12 \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+24 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+3 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}-8 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\sin \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{5 \left(4 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-4 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) a \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e +e}\, e d}"," ",0,"-2/5/(4*sin(1/2*d*x+1/2*c)^4-4*sin(1/2*d*x+1/2*c)^2+1)/a/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)/e*(12*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*sin(1/2*d*x+1/2*c)^4-24*sin(1/2*d*x+1/2*c)^6*cos(1/2*d*x+1/2*c)-12*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*sin(1/2*d*x+1/2*c)^2+24*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+3*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)-8*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+sin(1/2*d*x+1/2*c))/d","B"
241,1,375,124,2.248000," ","int(1/(e*cos(d*x+c))^(5/2)/(a+a*sin(d*x+c)),x)","-\frac{2 \left(40 \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-60 \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+40 \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+30 \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-40 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-5 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}+16 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-3 \sin \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{21 \left(8 \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-12 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+6 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) a \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e +e}\, e^{2} d}"," ",0,"-2/21/(8*sin(1/2*d*x+1/2*c)^6-12*sin(1/2*d*x+1/2*c)^4+6*sin(1/2*d*x+1/2*c)^2-1)/a/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)/e^2*(40*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^6-60*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^4+40*sin(1/2*d*x+1/2*c)^6*cos(1/2*d*x+1/2*c)+30*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^2-40*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)-5*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)+16*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)-3*sin(1/2*d*x+1/2*c))/d","B"
242,1,488,151,2.719000," ","int(1/(e*cos(d*x+c))^(7/2)/(a+a*sin(d*x+c)),x)","-\frac{2 \left(336 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-672 \left(\sin^{10}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-672 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1344 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+504 \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1064 \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-168 \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+392 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+21 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}-66 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+5 \sin \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{45 \left(16 \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-32 \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+24 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-8 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) a \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e +e}\, e^{3} d}"," ",0,"-2/45/(16*sin(1/2*d*x+1/2*c)^8-32*sin(1/2*d*x+1/2*c)^6+24*sin(1/2*d*x+1/2*c)^4-8*sin(1/2*d*x+1/2*c)^2+1)/a/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)/e^3*(336*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*sin(1/2*d*x+1/2*c)^8-672*sin(1/2*d*x+1/2*c)^10*cos(1/2*d*x+1/2*c)-672*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*sin(1/2*d*x+1/2*c)^6+1344*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^8+504*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*sin(1/2*d*x+1/2*c)^4-1064*sin(1/2*d*x+1/2*c)^6*cos(1/2*d*x+1/2*c)-168*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*sin(1/2*d*x+1/2*c)^2+392*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+21*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)-66*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+5*sin(1/2*d*x+1/2*c))/d","B"
243,1,203,153,0.921000," ","int((e*cos(d*x+c))^(11/2)/(a+a*sin(d*x+c))^2,x)","-\frac{2 e^{6} \left(-80 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+120 \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+112 \left(\sin^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-168 \left(\sin^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+15 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}-20 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+84 \left(\sin^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-14 \sin \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{35 a^{2} \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e +e}\, d}"," ",0,"-2/35/a^2/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)*e^6*(-80*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^8+120*sin(1/2*d*x+1/2*c)^6*cos(1/2*d*x+1/2*c)+112*sin(1/2*d*x+1/2*c)^7-168*sin(1/2*d*x+1/2*c)^5+15*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)-20*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+84*sin(1/2*d*x+1/2*c)^3-14*sin(1/2*d*x+1/2*c))/d","A"
244,1,190,126,1.001000," ","int((e*cos(d*x+c))^(9/2)/(a+a*sin(d*x+c))^2,x)","\frac{2 e^{5} \left(-24 \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+24 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+40 \left(\sin^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+21 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}-6 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-40 \left(\sin^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+10 \sin \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{15 a^{2} \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e +e}\, d}"," ",0,"2/15/a^2/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)*e^5*(-24*sin(1/2*d*x+1/2*c)^6*cos(1/2*d*x+1/2*c)+24*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+40*sin(1/2*d*x+1/2*c)^5+21*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)-6*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)-40*sin(1/2*d*x+1/2*c)^3+10*sin(1/2*d*x+1/2*c))/d","A"
245,1,155,126,0.755000," ","int((e*cos(d*x+c))^(7/2)/(a+a*sin(d*x+c))^2,x)","-\frac{2 e^{4} \left(-4 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+5 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}+2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+12 \left(\sin^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-6 \sin \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 a^{2} \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e +e}\, d}"," ",0,"-2/3/a^2/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)*e^4*(-4*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+5*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)+2*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+12*sin(1/2*d*x+1/2*c)^3-6*sin(1/2*d*x+1/2*c))/d","A"
246,1,120,99,1.152000," ","int((e*cos(d*x+c))^(5/2)/(a+a*sin(d*x+c))^2,x)","-\frac{2 \left(3 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}-4 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+2 \sin \left(\frac{d x}{2}+\frac{c}{2}\right)\right) e^{3}}{\sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e +e}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) a^{2} d}"," ",0,"-2/(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)/sin(1/2*d*x+1/2*c)/a^2*(3*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)-4*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+2*sin(1/2*d*x+1/2*c))*e^3/d","A"
247,1,193,99,1.395000," ","int((e*cos(d*x+c))^(3/2)/(a+a*sin(d*x+c))^2,x)","\frac{2 \left(2 \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}-4 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+2 \sin \left(\frac{d x}{2}+\frac{c}{2}\right)\right) e^{2}}{3 \left(2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) a^{2} \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e +e}\, d}"," ",0,"2/3/(2*sin(1/2*d*x+1/2*c)^2-1)/a^2/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)*(2*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^2-(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)-4*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+2*sin(1/2*d*x+1/2*c))*e^2/d","A"
248,1,303,128,2.172000," ","int((e*cos(d*x+c))^(1/2)/(a+a*sin(d*x+c))^2,x)","-\frac{2 \left(4 \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-8 \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-4 \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+8 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}-6 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+2 \sin \left(\frac{d x}{2}+\frac{c}{2}\right)\right) e}{5 \left(4 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-4 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) a^{2} \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e +e}\, d}"," ",0,"-2/5/(4*sin(1/2*d*x+1/2*c)^4-4*sin(1/2*d*x+1/2*c)^2+1)/a^2/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)*(4*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*sin(1/2*d*x+1/2*c)^4-8*sin(1/2*d*x+1/2*c)^6*cos(1/2*d*x+1/2*c)-4*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*sin(1/2*d*x+1/2*c)^2+8*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)-6*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+2*sin(1/2*d*x+1/2*c))*e/d","B"
249,1,372,128,2.245000," ","int(1/(a+a*sin(d*x+c))^2/(e*cos(d*x+c))^(1/2),x)","-\frac{2 \left(8 \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-12 \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+8 \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+6 \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-8 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}+6 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-2 \sin \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{7 \left(8 \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-12 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+6 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) a^{2} \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e +e}\, d}"," ",0,"-2/7/(8*sin(1/2*d*x+1/2*c)^6-12*sin(1/2*d*x+1/2*c)^4+6*sin(1/2*d*x+1/2*c)^2-1)/a^2/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)*(8*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^6-12*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^4+8*sin(1/2*d*x+1/2*c)^6*cos(1/2*d*x+1/2*c)+6*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^2-8*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)-(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)+6*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)-2*sin(1/2*d*x+1/2*c))/d","B"
250,1,488,158,3.078000," ","int(1/(e*cos(d*x+c))^(3/2)/(a+a*sin(d*x+c))^2,x)","-\frac{2 \left(48 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-96 \left(\sin^{10}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-96 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+192 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+72 \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-152 \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-24 \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+56 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+3 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}-12 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+2 \sin \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{9 \left(16 \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-32 \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+24 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-8 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) a^{2} \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e +e}\, e d}"," ",0,"-2/9/(16*sin(1/2*d*x+1/2*c)^8-32*sin(1/2*d*x+1/2*c)^6+24*sin(1/2*d*x+1/2*c)^4-8*sin(1/2*d*x+1/2*c)^2+1)/a^2/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)/e*(48*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*sin(1/2*d*x+1/2*c)^8-96*sin(1/2*d*x+1/2*c)^10*cos(1/2*d*x+1/2*c)-96*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*sin(1/2*d*x+1/2*c)^6+192*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^8+72*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*sin(1/2*d*x+1/2*c)^4-152*sin(1/2*d*x+1/2*c)^6*cos(1/2*d*x+1/2*c)-24*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*sin(1/2*d*x+1/2*c)^2+56*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+3*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)-12*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+2*sin(1/2*d*x+1/2*c))/d","B"
251,1,557,158,3.652000," ","int(1/(e*cos(d*x+c))^(5/2)/(a+a*sin(d*x+c))^2,x)","-\frac{2 \left(160 \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \left(\sin^{10}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-400 \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+160 \left(\sin^{10}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+400 \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-320 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-200 \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+264 \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+50 \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-104 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-5 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}+28 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-6 \sin \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{33 \left(32 \left(\sin^{10}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-80 \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+80 \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-40 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+10 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) a^{2} \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e +e}\, e^{2} d}"," ",0,"-2/33/(32*sin(1/2*d*x+1/2*c)^10-80*sin(1/2*d*x+1/2*c)^8+80*sin(1/2*d*x+1/2*c)^6-40*sin(1/2*d*x+1/2*c)^4+10*sin(1/2*d*x+1/2*c)^2-1)/a^2/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)/e^2*(160*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*sin(1/2*d*x+1/2*c)^10-400*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*sin(1/2*d*x+1/2*c)^8+160*sin(1/2*d*x+1/2*c)^10*cos(1/2*d*x+1/2*c)+400*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^6-320*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^8-200*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^4+264*sin(1/2*d*x+1/2*c)^6*cos(1/2*d*x+1/2*c)+50*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^2-104*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)-5*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)+28*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)-6*sin(1/2*d*x+1/2*c))/d","B"
252,1,670,185,4.586000," ","int(1/(e*cos(d*x+c))^(7/2)/(a+a*sin(d*x+c))^2,x)","-\frac{2 \left(1344 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\sin^{12}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-2688 \left(\sin^{14}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-4032 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\sin^{10}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+8064 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{12}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+5040 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-10304 \left(\sin^{10}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-3360 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+7168 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1260 \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-2896 \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-252 \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+656 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+21 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}-86 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+10 \sin \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{65 \left(64 \left(\sin^{12}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-192 \left(\sin^{10}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+240 \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-160 \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+60 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-12 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) a^{2} \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e +e}\, e^{3} d}"," ",0,"-2/65/(64*sin(1/2*d*x+1/2*c)^12-192*sin(1/2*d*x+1/2*c)^10+240*sin(1/2*d*x+1/2*c)^8-160*sin(1/2*d*x+1/2*c)^6+60*sin(1/2*d*x+1/2*c)^4-12*sin(1/2*d*x+1/2*c)^2+1)/a^2/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)/e^3*(1344*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^12-2688*sin(1/2*d*x+1/2*c)^14*cos(1/2*d*x+1/2*c)-4032*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^10+8064*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^12+5040*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*sin(1/2*d*x+1/2*c)^8-10304*sin(1/2*d*x+1/2*c)^10*cos(1/2*d*x+1/2*c)-3360*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*sin(1/2*d*x+1/2*c)^6+7168*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^8+1260*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*sin(1/2*d*x+1/2*c)^4-2896*sin(1/2*d*x+1/2*c)^6*cos(1/2*d*x+1/2*c)-252*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*sin(1/2*d*x+1/2*c)^2+656*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+21*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)-86*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+10*sin(1/2*d*x+1/2*c))/d","B"
253,1,251,173,1.191000," ","int((e*cos(d*x+c))^(15/2)/(a+a*sin(d*x+c))^3,x)","-\frac{2 e^{8} \left(-1120 \left(\sin^{11}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-2160 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+2800 \left(\sin^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+3240 \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-784 \left(\sin^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-840 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-1624 \left(\sin^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+195 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}-120 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+1162 \left(\sin^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-217 \sin \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{315 a^{3} \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e +e}\, d}"," ",0,"-2/315/a^3/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)*e^8*(-1120*sin(1/2*d*x+1/2*c)^11-2160*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^8+2800*sin(1/2*d*x+1/2*c)^9+3240*sin(1/2*d*x+1/2*c)^6*cos(1/2*d*x+1/2*c)-784*sin(1/2*d*x+1/2*c)^7-840*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)-1624*sin(1/2*d*x+1/2*c)^5+195*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)-120*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+1162*sin(1/2*d*x+1/2*c)^3-217*sin(1/2*d*x+1/2*c))/d","A"
254,1,216,146,1.104000," ","int((e*cos(d*x+c))^(13/2)/(a+a*sin(d*x+c))^3,x)","\frac{2 e^{7} \left(-240 \left(\sin^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-504 \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+480 \left(\sin^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+504 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+200 \left(\sin^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+231 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}-126 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-440 \left(\sin^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+125 \sin \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{105 a^{3} \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e +e}\, d}"," ",0,"2/105/a^3/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)*e^7*(-240*sin(1/2*d*x+1/2*c)^9-504*sin(1/2*d*x+1/2*c)^6*cos(1/2*d*x+1/2*c)+480*sin(1/2*d*x+1/2*c)^7+504*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+200*sin(1/2*d*x+1/2*c)^5+231*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)-126*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)-440*sin(1/2*d*x+1/2*c)^3+125*sin(1/2*d*x+1/2*c))/d","A"
255,1,181,146,0.927000," ","int((e*cos(d*x+c))^(11/2)/(a+a*sin(d*x+c))^3,x)","-\frac{2 e^{6} \left(-8 \left(\sin^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-20 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+12 \left(\sin^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+15 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}+10 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+34 \left(\sin^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-19 \sin \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{5 a^{3} \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e +e}\, d}"," ",0,"-2/5/a^3/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)*e^6*(-8*sin(1/2*d*x+1/2*c)^7-20*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+12*sin(1/2*d*x+1/2*c)^5+15*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)+10*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+34*sin(1/2*d*x+1/2*c)^3-19*sin(1/2*d*x+1/2*c))/d","A"
256,1,146,119,1.262000," ","int((e*cos(d*x+c))^(9/2)/(a+a*sin(d*x+c))^3,x)","-\frac{2 \left(4 \left(\sin^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+21 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}-24 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-4 \left(\sin^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+13 \sin \left(\frac{d x}{2}+\frac{c}{2}\right)\right) e^{5}}{3 \sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e +e}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) a^{3} d}"," ",0,"-2/3/(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)/sin(1/2*d*x+1/2*c)/a^3*(4*sin(1/2*d*x+1/2*c)^5+21*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)-24*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)-4*sin(1/2*d*x+1/2*c)^3+13*sin(1/2*d*x+1/2*c))*e^5/d","A"
257,1,219,119,1.369000," ","int((e*cos(d*x+c))^(7/2)/(a+a*sin(d*x+c))^3,x)","\frac{2 \left(10 \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+12 \left(\sin^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-5 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}-8 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-12 \left(\sin^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+7 \sin \left(\frac{d x}{2}+\frac{c}{2}\right)\right) e^{4}}{3 \left(2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) a^{3} \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e +e}\, d}"," ",0,"2/3/(2*sin(1/2*d*x+1/2*c)^2-1)/a^3/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)*(10*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^2+12*sin(1/2*d*x+1/2*c)^5-5*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)-8*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)-12*sin(1/2*d*x+1/2*c)^3+7*sin(1/2*d*x+1/2*c))*e^4/d","A"
258,1,330,130,2.142000," ","int((e*cos(d*x+c))^(5/2)/(a+a*sin(d*x+c))^3,x)","\frac{2 \left(12 \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-24 \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-12 \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+24 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+20 \left(\sin^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+3 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}+2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-20 \left(\sin^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin \left(\frac{d x}{2}+\frac{c}{2}\right)\right) e^{3}}{5 \left(4 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-4 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) a^{3} \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e +e}\, d}"," ",0,"2/5/(4*sin(1/2*d*x+1/2*c)^4-4*sin(1/2*d*x+1/2*c)^2+1)/a^3/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)*(12*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*sin(1/2*d*x+1/2*c)^4-24*sin(1/2*d*x+1/2*c)^6*cos(1/2*d*x+1/2*c)-12*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*sin(1/2*d*x+1/2*c)^2+24*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+20*sin(1/2*d*x+1/2*c)^5+3*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)+2*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)-20*sin(1/2*d*x+1/2*c)^3+sin(1/2*d*x+1/2*c))*e^3/d","B"
259,1,401,130,2.316000," ","int((e*cos(d*x+c))^(3/2)/(a+a*sin(d*x+c))^3,x)","\frac{2 \left(8 \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-12 \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+8 \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+6 \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-8 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-28 \left(\sin^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}-22 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+28 \left(\sin^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+5 \sin \left(\frac{d x}{2}+\frac{c}{2}\right)\right) e^{2}}{21 \left(8 \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-12 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+6 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) a^{3} \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e +e}\, d}"," ",0,"2/21/(8*sin(1/2*d*x+1/2*c)^6-12*sin(1/2*d*x+1/2*c)^4+6*sin(1/2*d*x+1/2*c)^2-1)/a^3/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)*(8*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^6-12*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^4+8*sin(1/2*d*x+1/2*c)^6*cos(1/2*d*x+1/2*c)+6*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^2-8*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)-28*sin(1/2*d*x+1/2*c)^5-(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)-22*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+28*sin(1/2*d*x+1/2*c)^3+5*sin(1/2*d*x+1/2*c))*e^2/d","B"
260,1,512,161,3.409000," ","int((e*cos(d*x+c))^(1/2)/(a+a*sin(d*x+c))^3,x)","-\frac{2 \left(48 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-96 \left(\sin^{10}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-96 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+192 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+72 \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-152 \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-24 \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+56 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-36 \left(\sin^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+3 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}-48 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+36 \left(\sin^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+11 \sin \left(\frac{d x}{2}+\frac{c}{2}\right)\right) e}{45 \left(16 \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-32 \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+24 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-8 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) a^{3} \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e +e}\, d}"," ",0,"-2/45/(16*sin(1/2*d*x+1/2*c)^8-32*sin(1/2*d*x+1/2*c)^6+24*sin(1/2*d*x+1/2*c)^4-8*sin(1/2*d*x+1/2*c)^2+1)/a^3/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)*(48*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*sin(1/2*d*x+1/2*c)^8-96*sin(1/2*d*x+1/2*c)^10*cos(1/2*d*x+1/2*c)-96*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*sin(1/2*d*x+1/2*c)^6+192*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^8+72*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*sin(1/2*d*x+1/2*c)^4-152*sin(1/2*d*x+1/2*c)^6*cos(1/2*d*x+1/2*c)-24*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*sin(1/2*d*x+1/2*c)^2+56*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)-36*sin(1/2*d*x+1/2*c)^5+3*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)-48*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+36*sin(1/2*d*x+1/2*c)^3+11*sin(1/2*d*x+1/2*c))*e/d","B"
261,1,580,161,3.991000," ","int(1/(a+a*sin(d*x+c))^3/(e*cos(d*x+c))^(1/2),x)","-\frac{2 \left(160 \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \left(\sin^{10}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-400 \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+160 \left(\sin^{10}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+400 \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-320 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-200 \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+264 \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+50 \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-104 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+44 \left(\sin^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-5 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}+72 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-44 \left(\sin^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-17 \sin \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{77 \left(32 \left(\sin^{10}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-80 \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+80 \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-40 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+10 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) a^{3} \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e +e}\, d}"," ",0,"-2/77/(32*sin(1/2*d*x+1/2*c)^10-80*sin(1/2*d*x+1/2*c)^8+80*sin(1/2*d*x+1/2*c)^6-40*sin(1/2*d*x+1/2*c)^4+10*sin(1/2*d*x+1/2*c)^2-1)/a^3/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)*(160*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*sin(1/2*d*x+1/2*c)^10-400*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*sin(1/2*d*x+1/2*c)^8+160*sin(1/2*d*x+1/2*c)^10*cos(1/2*d*x+1/2*c)+400*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^6-320*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^8-200*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^4+264*sin(1/2*d*x+1/2*c)^6*cos(1/2*d*x+1/2*c)+50*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^2-104*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+44*sin(1/2*d*x+1/2*c)^5-5*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)+72*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)-44*sin(1/2*d*x+1/2*c)^3-17*sin(1/2*d*x+1/2*c))/d","B"
262,1,696,191,4.732000," ","int(1/(e*cos(d*x+c))^(3/2)/(a+a*sin(d*x+c))^3,x)","-\frac{2 \left(1344 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\sin^{12}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-2688 \left(\sin^{14}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-4032 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\sin^{10}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+8064 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{12}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+5040 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-10304 \left(\sin^{10}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-3360 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+7168 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1260 \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-2896 \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-252 \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+656 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-52 \left(\sin^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+21 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}-138 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+52 \left(\sin^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+23 \sin \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{117 \left(64 \left(\sin^{12}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-192 \left(\sin^{10}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+240 \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-160 \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+60 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-12 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) a^{3} \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e +e}\, e d}"," ",0,"-2/117/(64*sin(1/2*d*x+1/2*c)^12-192*sin(1/2*d*x+1/2*c)^10+240*sin(1/2*d*x+1/2*c)^8-160*sin(1/2*d*x+1/2*c)^6+60*sin(1/2*d*x+1/2*c)^4-12*sin(1/2*d*x+1/2*c)^2+1)/a^3/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)/e*(1344*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^12-2688*sin(1/2*d*x+1/2*c)^14*cos(1/2*d*x+1/2*c)-4032*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^10+8064*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^12+5040*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*sin(1/2*d*x+1/2*c)^8-10304*sin(1/2*d*x+1/2*c)^10*cos(1/2*d*x+1/2*c)-3360*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*sin(1/2*d*x+1/2*c)^6+7168*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^8+1260*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*sin(1/2*d*x+1/2*c)^4-2896*sin(1/2*d*x+1/2*c)^6*cos(1/2*d*x+1/2*c)-252*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*sin(1/2*d*x+1/2*c)^2+656*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)-52*sin(1/2*d*x+1/2*c)^5+21*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)-138*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+52*sin(1/2*d*x+1/2*c)^3+23*sin(1/2*d*x+1/2*c))/d","B"
263,1,225,186,1.081000," ","int((e*cos(d*x+c))^(15/2)/(a+a*sin(d*x+c))^4,x)","-\frac{2 e^{8} \left(80 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-120 \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-224 \left(\sin^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-280 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+336 \left(\sin^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+195 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}+160 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+392 \left(\sin^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-252 \sin \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{35 a^{4} \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e +e}\, d}"," ",0,"-2/35/a^4/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)*e^8*(80*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^8-120*sin(1/2*d*x+1/2*c)^6*cos(1/2*d*x+1/2*c)-224*sin(1/2*d*x+1/2*c)^7-280*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+336*sin(1/2*d*x+1/2*c)^5+195*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)+160*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+392*sin(1/2*d*x+1/2*c)^3-252*sin(1/2*d*x+1/2*c))/d","A"
264,1,190,159,1.653000," ","int((e*cos(d*x+c))^(13/2)/(a+a*sin(d*x+c))^4,x)","-\frac{2 \left(-24 \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+24 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+80 \left(\sin^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+231 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}-246 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-80 \left(\sin^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+140 \sin \left(\frac{d x}{2}+\frac{c}{2}\right)\right) e^{7}}{15 \sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e +e}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) a^{4} d}"," ",0,"-2/15/(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)/sin(1/2*d*x+1/2*c)/a^4*(-24*sin(1/2*d*x+1/2*c)^6*cos(1/2*d*x+1/2*c)+24*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+80*sin(1/2*d*x+1/2*c)^5+231*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)-246*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)-80*sin(1/2*d*x+1/2*c)^3+140*sin(1/2*d*x+1/2*c))*e^7/d","A"
265,1,263,159,1.683000," ","int((e*cos(d*x+c))^(11/2)/(a+a*sin(d*x+c))^4,x)","\frac{2 \left(-8 \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+30 \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+8 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+48 \left(\sin^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-15 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}-18 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-48 \left(\sin^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+20 \sin \left(\frac{d x}{2}+\frac{c}{2}\right)\right) e^{6}}{3 \left(2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) a^{4} \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e +e}\, d}"," ",0,"2/3/(2*sin(1/2*d*x+1/2*c)^2-1)/a^4/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)*(-8*sin(1/2*d*x+1/2*c)^6*cos(1/2*d*x+1/2*c)+30*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^2+8*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+48*sin(1/2*d*x+1/2*c)^5-15*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)-18*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)-48*sin(1/2*d*x+1/2*c)^3+20*sin(1/2*d*x+1/2*c))*e^6/d","A"
266,1,332,132,2.471000," ","int((e*cos(d*x+c))^(9/2)/(a+a*sin(d*x+c))^4,x)","\frac{2 \left(84 \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-128 \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-84 \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+128 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+80 \left(\sin^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+21 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}-16 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-80 \left(\sin^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+12 \sin \left(\frac{d x}{2}+\frac{c}{2}\right)\right) e^{5}}{5 \left(4 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-4 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) a^{4} \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e +e}\, d}"," ",0,"2/5/(4*sin(1/2*d*x+1/2*c)^4-4*sin(1/2*d*x+1/2*c)^2+1)/a^4/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)*(84*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*sin(1/2*d*x+1/2*c)^4-128*sin(1/2*d*x+1/2*c)^6*cos(1/2*d*x+1/2*c)-84*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*sin(1/2*d*x+1/2*c)^2+128*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+80*sin(1/2*d*x+1/2*c)^5+21*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)-16*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)-80*sin(1/2*d*x+1/2*c)^3+12*sin(1/2*d*x+1/2*c))*e^5/d","B"
267,1,401,132,2.692000," ","int((e*cos(d*x+c))^(7/2)/(a+a*sin(d*x+c))^4,x)","-\frac{2 \left(40 \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-60 \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-128 \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+30 \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+128 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+112 \left(\sin^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-5 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}+16 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-112 \left(\sin^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+4 \sin \left(\frac{d x}{2}+\frac{c}{2}\right)\right) e^{4}}{21 \left(8 \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-12 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+6 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) a^{4} \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e +e}\, d}"," ",0,"-2/21/(8*sin(1/2*d*x+1/2*c)^6-12*sin(1/2*d*x+1/2*c)^4+6*sin(1/2*d*x+1/2*c)^2-1)/a^4/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)*(40*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^6-60*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^4-128*sin(1/2*d*x+1/2*c)^6*cos(1/2*d*x+1/2*c)+30*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^2+128*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+112*sin(1/2*d*x+1/2*c)^5-5*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)+16*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)-112*sin(1/2*d*x+1/2*c)^3+4*sin(1/2*d*x+1/2*c))*e^4/d","B"
268,1,514,162,3.403000," ","int((e*cos(d*x+c))^(5/2)/(a+a*sin(d*x+c))^4,x)","\frac{2 \left(48 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-96 \left(\sin^{10}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-96 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+192 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+72 \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-272 \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-24 \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+176 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+144 \left(\sin^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+3 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}+42 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-144 \left(\sin^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-4 \sin \left(\frac{d x}{2}+\frac{c}{2}\right)\right) e^{3}}{45 \left(16 \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-32 \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+24 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-8 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) a^{4} \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e +e}\, d}"," ",0,"2/45/(16*sin(1/2*d*x+1/2*c)^8-32*sin(1/2*d*x+1/2*c)^6+24*sin(1/2*d*x+1/2*c)^4-8*sin(1/2*d*x+1/2*c)^2+1)/a^4/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)*(48*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*sin(1/2*d*x+1/2*c)^8-96*sin(1/2*d*x+1/2*c)^10*cos(1/2*d*x+1/2*c)-96*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*sin(1/2*d*x+1/2*c)^6+192*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^8+72*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*sin(1/2*d*x+1/2*c)^4-272*sin(1/2*d*x+1/2*c)^6*cos(1/2*d*x+1/2*c)-24*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*sin(1/2*d*x+1/2*c)^2+176*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+144*sin(1/2*d*x+1/2*c)^5+3*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)+42*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)-144*sin(1/2*d*x+1/2*c)^3-4*sin(1/2*d*x+1/2*c))*e^3/d","B"
269,1,583,162,4.367000," ","int((e*cos(d*x+c))^(3/2)/(a+a*sin(d*x+c))^4,x)","\frac{2 \left(32 \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \left(\sin^{10}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-80 \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+32 \left(\sin^{10}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+80 \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-64 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-40 \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+176 \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+10 \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-144 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-176 \left(\sin^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}-78 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+176 \left(\sin^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+12 \sin \left(\frac{d x}{2}+\frac{c}{2}\right)\right) e^{2}}{77 \left(32 \left(\sin^{10}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-80 \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+80 \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-40 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+10 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) a^{4} \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e +e}\, d}"," ",0,"2/77/(32*sin(1/2*d*x+1/2*c)^10-80*sin(1/2*d*x+1/2*c)^8+80*sin(1/2*d*x+1/2*c)^6-40*sin(1/2*d*x+1/2*c)^4+10*sin(1/2*d*x+1/2*c)^2-1)/a^4/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)*(32*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*sin(1/2*d*x+1/2*c)^10-80*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*sin(1/2*d*x+1/2*c)^8+32*sin(1/2*d*x+1/2*c)^10*cos(1/2*d*x+1/2*c)+80*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^6-64*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^8-40*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^4+176*sin(1/2*d*x+1/2*c)^6*cos(1/2*d*x+1/2*c)+10*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^2-144*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)-176*sin(1/2*d*x+1/2*c)^5-(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)-78*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+176*sin(1/2*d*x+1/2*c)^3+12*sin(1/2*d*x+1/2*c))*e^2/d","B"
270,1,694,195,5.337000," ","int((e*cos(d*x+c))^(1/2)/(a+a*sin(d*x+c))^4,x)","-\frac{2 \left(192 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\sin^{12}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-384 \left(\sin^{14}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-576 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\sin^{10}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1152 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{12}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+720 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1472 \left(\sin^{10}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-480 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1024 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+180 \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-280 \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-36 \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-40 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-208 \left(\sin^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+3 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}-120 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+208 \left(\sin^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+20 \sin \left(\frac{d x}{2}+\frac{c}{2}\right)\right) e}{117 \left(64 \left(\sin^{12}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-192 \left(\sin^{10}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+240 \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-160 \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+60 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-12 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) a^{4} \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e +e}\, d}"," ",0,"-2/117/(64*sin(1/2*d*x+1/2*c)^12-192*sin(1/2*d*x+1/2*c)^10+240*sin(1/2*d*x+1/2*c)^8-160*sin(1/2*d*x+1/2*c)^6+60*sin(1/2*d*x+1/2*c)^4-12*sin(1/2*d*x+1/2*c)^2+1)/a^4/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)*(192*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^12-384*sin(1/2*d*x+1/2*c)^14*cos(1/2*d*x+1/2*c)-576*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^10+1152*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^12+720*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*sin(1/2*d*x+1/2*c)^8-1472*sin(1/2*d*x+1/2*c)^10*cos(1/2*d*x+1/2*c)-480*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*sin(1/2*d*x+1/2*c)^6+1024*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^8+180*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*sin(1/2*d*x+1/2*c)^4-280*sin(1/2*d*x+1/2*c)^6*cos(1/2*d*x+1/2*c)-36*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*sin(1/2*d*x+1/2*c)^2-40*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)-208*sin(1/2*d*x+1/2*c)^5+3*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)-120*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+208*sin(1/2*d*x+1/2*c)^3+20*sin(1/2*d*x+1/2*c))*e/d","B"
271,1,762,195,5.291000," ","int(1/(a+a*sin(d*x+c))^4/(e*cos(d*x+c))^(1/2),x)","-\frac{2 \left(640 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \left(\sin^{14}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-2240 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \left(\sin^{12}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+640 \left(\sin^{14}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+3360 \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \left(\sin^{10}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1920 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{12}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-2800 \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+2496 \left(\sin^{10}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+1400 \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1792 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-420 \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+616 \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+70 \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-40 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+240 \left(\sin^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-5 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}+160 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-240 \left(\sin^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-28 \sin \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{165 \left(128 \left(\sin^{14}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-448 \left(\sin^{12}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+672 \left(\sin^{10}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-560 \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+280 \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-84 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+14 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) a^{4} \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e +e}\, d}"," ",0,"-2/165/(128*sin(1/2*d*x+1/2*c)^14-448*sin(1/2*d*x+1/2*c)^12+672*sin(1/2*d*x+1/2*c)^10-560*sin(1/2*d*x+1/2*c)^8+280*sin(1/2*d*x+1/2*c)^6-84*sin(1/2*d*x+1/2*c)^4+14*sin(1/2*d*x+1/2*c)^2-1)/a^4/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)*(640*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*sin(1/2*d*x+1/2*c)^14-2240*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*sin(1/2*d*x+1/2*c)^12+640*sin(1/2*d*x+1/2*c)^14*cos(1/2*d*x+1/2*c)+3360*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*sin(1/2*d*x+1/2*c)^10-1920*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^12-2800*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*sin(1/2*d*x+1/2*c)^8+2496*sin(1/2*d*x+1/2*c)^10*cos(1/2*d*x+1/2*c)+1400*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^6-1792*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^8-420*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^4+616*sin(1/2*d*x+1/2*c)^6*cos(1/2*d*x+1/2*c)+70*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^2-40*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+240*sin(1/2*d*x+1/2*c)^5-5*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)+160*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)-240*sin(1/2*d*x+1/2*c)^3-28*sin(1/2*d*x+1/2*c))/d","B"
272,1,878,225,6.760000," ","int(1/(e*cos(d*x+c))^(3/2)/(a+a*sin(d*x+c))^4,x)","-\frac{2 \left(5376 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\sin^{16}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-10752 \left(\sin^{18}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-21504 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\sin^{14}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+43008 \left(\sin^{16}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+37632 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\sin^{12}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-76160 \left(\sin^{14}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-37632 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\sin^{10}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+77952 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{12}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+23520 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-50560 \left(\sin^{10}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-9408 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+21376 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+2352 \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-5656 \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-336 \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+792 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-272 \left(\sin^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+21 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}-242 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+272 \left(\sin^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+36 \sin \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{221 \left(256 \left(\sin^{16}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1024 \left(\sin^{14}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1792 \left(\sin^{12}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1792 \left(\sin^{10}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1120 \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-448 \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+112 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-16 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) a^{4} \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e +e}\, e d}"," ",0,"-2/221/(256*sin(1/2*d*x+1/2*c)^16-1024*sin(1/2*d*x+1/2*c)^14+1792*sin(1/2*d*x+1/2*c)^12-1792*sin(1/2*d*x+1/2*c)^10+1120*sin(1/2*d*x+1/2*c)^8-448*sin(1/2*d*x+1/2*c)^6+112*sin(1/2*d*x+1/2*c)^4-16*sin(1/2*d*x+1/2*c)^2+1)/a^4/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)/e*(5376*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^16-10752*sin(1/2*d*x+1/2*c)^18*cos(1/2*d*x+1/2*c)-21504*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^14+43008*sin(1/2*d*x+1/2*c)^16*cos(1/2*d*x+1/2*c)+37632*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^12-76160*sin(1/2*d*x+1/2*c)^14*cos(1/2*d*x+1/2*c)-37632*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^10+77952*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^12+23520*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*sin(1/2*d*x+1/2*c)^8-50560*sin(1/2*d*x+1/2*c)^10*cos(1/2*d*x+1/2*c)-9408*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*sin(1/2*d*x+1/2*c)^6+21376*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^8+2352*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*sin(1/2*d*x+1/2*c)^4-5656*sin(1/2*d*x+1/2*c)^6*cos(1/2*d*x+1/2*c)-336*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*sin(1/2*d*x+1/2*c)^2+792*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)-272*sin(1/2*d*x+1/2*c)^5+21*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)-242*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+272*sin(1/2*d*x+1/2*c)^3+36*sin(1/2*d*x+1/2*c))/d","B"
273,1,241,198,0.350000," ","int((e*cos(d*x+c))^(3/2)*(a+a*sin(d*x+c))^(1/2),x)","-\frac{\left(3 \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \sin \left(d x +c \right)-3 \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sin \left(d x +c \right)-4 \left(\cos^{3}\left(d x +c \right)\right)-4 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)-2 \left(\cos^{2}\left(d x +c \right)\right)+6 \cos \left(d x +c \right) \sin \left(d x +c \right)+6 \cos \left(d x +c \right)\right) \left(e \cos \left(d x +c \right)\right)^{\frac{3}{2}} \sqrt{a \left(1+\sin \left(d x +c \right)\right)}}{8 d \left(-1+\cos \left(d x +c \right)-\sin \left(d x +c \right)\right) \cos \left(d x +c \right)^{2}}"," ",0,"-1/8/d*(3*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*sin(d*x+c)-3*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*sin(d*x+c)-4*cos(d*x+c)^3-4*cos(d*x+c)^2*sin(d*x+c)-2*cos(d*x+c)^2+6*cos(d*x+c)*sin(d*x+c)+6*cos(d*x+c))*(e*cos(d*x+c))^(3/2)*(a*(1+sin(d*x+c)))^(1/2)/(-1+cos(d*x+c)-sin(d*x+c))/cos(d*x+c)^2","A"
274,1,213,168,0.271000," ","int((e*cos(d*x+c))^(1/2)*(a+a*sin(d*x+c))^(1/2),x)","-\frac{\left(\sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \sin \left(d x +c \right)+\sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sin \left(d x +c \right)+2 \cos \left(d x +c \right) \sin \left(d x +c \right)+2 \left(\cos^{2}\left(d x +c \right)\right)-2 \cos \left(d x +c \right)\right) \sqrt{e \cos \left(d x +c \right)}\, \sqrt{a \left(1+\sin \left(d x +c \right)\right)}}{2 d \left(1-\cos \left(d x +c \right)+\sin \left(d x +c \right)\right) \cos \left(d x +c \right)}"," ",0,"-1/2/d*(2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*sin(d*x+c)+2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*sin(d*x+c)+2*cos(d*x+c)*sin(d*x+c)+2*cos(d*x+c)^2-2*cos(d*x+c))*(e*cos(d*x+c))^(1/2)*(a*(1+sin(d*x+c)))^(1/2)/(1-cos(d*x+c)+sin(d*x+c))/cos(d*x+c)","A"
275,1,142,139,0.190000," ","int((a+a*sin(d*x+c))^(1/2)/(e*cos(d*x+c))^(1/2),x)","-\frac{\left(\arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right)-\arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right)\right) \sqrt{a \left(1+\sin \left(d x +c \right)\right)}\, \left(-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)\right) \sqrt{2}}{d \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{e \cos \left(d x +c \right)}}"," ",0,"-1/d*(arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))-arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2)))*(a*(1+sin(d*x+c)))^(1/2)*(-1+cos(d*x+c)+sin(d*x+c))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)/(e*cos(d*x+c))^(1/2)*2^(1/2)","A"
276,1,34,30,0.206000," ","int((a+a*sin(d*x+c))^(1/2)/(e*cos(d*x+c))^(3/2),x)","\frac{2 \cos \left(d x +c \right) \sqrt{a \left(1+\sin \left(d x +c \right)\right)}}{d \left(e \cos \left(d x +c \right)\right)^{\frac{3}{2}}}"," ",0,"2/d*cos(d*x+c)*(a*(1+sin(d*x+c)))^(1/2)/(e*cos(d*x+c))^(3/2)","A"
277,1,44,64,0.211000," ","int((a+a*sin(d*x+c))^(1/2)/(e*cos(d*x+c))^(5/2),x)","\frac{2 \left(2 \sin \left(d x +c \right)-1\right) \sqrt{a \left(1+\sin \left(d x +c \right)\right)}\, \cos \left(d x +c \right)}{3 d \left(e \cos \left(d x +c \right)\right)^{\frac{5}{2}}}"," ",0,"2/3/d*(2*sin(d*x+c)-1)*(a*(1+sin(d*x+c)))^(1/2)*cos(d*x+c)/(e*cos(d*x+c))^(5/2)","A"
278,1,54,97,0.211000," ","int((a+a*sin(d*x+c))^(1/2)/(e*cos(d*x+c))^(7/2),x)","\frac{2 \left(8 \left(\cos^{2}\left(d x +c \right)\right)+4 \sin \left(d x +c \right)-1\right) \sqrt{a \left(1+\sin \left(d x +c \right)\right)}\, \cos \left(d x +c \right)}{15 d \left(e \cos \left(d x +c \right)\right)^{\frac{7}{2}}}"," ",0,"2/15/d*(8*cos(d*x+c)^2+4*sin(d*x+c)-1)*(a*(1+sin(d*x+c)))^(1/2)*cos(d*x+c)/(e*cos(d*x+c))^(7/2)","A"
279,1,70,130,0.228000," ","int((a+a*sin(d*x+c))^(1/2)/(e*cos(d*x+c))^(9/2),x)","\frac{2 \left(16 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)-8 \left(\cos^{2}\left(d x +c \right)\right)+6 \sin \left(d x +c \right)-1\right) \sqrt{a \left(1+\sin \left(d x +c \right)\right)}\, \cos \left(d x +c \right)}{35 d \left(e \cos \left(d x +c \right)\right)^{\frac{9}{2}}}"," ",0,"2/35/d*(16*cos(d*x+c)^2*sin(d*x+c)-8*cos(d*x+c)^2+6*sin(d*x+c)-1)*(a*(1+sin(d*x+c)))^(1/2)*cos(d*x+c)/(e*cos(d*x+c))^(9/2)","A"
280,1,314,269,0.340000," ","int((e*cos(d*x+c))^(5/2)*(a+a*sin(d*x+c))^(3/2),x)","\frac{\left(32 \sin \left(d x +c \right) \left(\cos^{4}\left(d x +c \right)\right)-32 \left(\cos^{5}\left(d x +c \right)\right)+45 \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sin \left(d x +c \right)+45 \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \sin \left(d x +c \right)+48 \sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right)+80 \left(\cos^{4}\left(d x +c \right)\right)-60 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+12 \left(\cos^{3}\left(d x +c \right)\right)+90 \cos \left(d x +c \right) \sin \left(d x +c \right)+30 \left(\cos^{2}\left(d x +c \right)\right)-90 \cos \left(d x +c \right)\right) \left(e \cos \left(d x +c \right)\right)^{\frac{5}{2}} \left(a \left(1+\sin \left(d x +c \right)\right)\right)^{\frac{3}{2}}}{128 d \left(\cos \left(d x +c \right) \sin \left(d x +c \right)+\cos^{2}\left(d x +c \right)-2 \sin \left(d x +c \right)+\cos \left(d x +c \right)-2\right) \cos \left(d x +c \right)^{3}}"," ",0,"1/128/d*(32*sin(d*x+c)*cos(d*x+c)^4-32*cos(d*x+c)^5+45*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*sin(d*x+c)+45*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*sin(d*x+c)+48*sin(d*x+c)*cos(d*x+c)^3+80*cos(d*x+c)^4-60*cos(d*x+c)^2*sin(d*x+c)+12*cos(d*x+c)^3+90*cos(d*x+c)*sin(d*x+c)+30*cos(d*x+c)^2-90*cos(d*x+c))*(e*cos(d*x+c))^(5/2)*(a*(1+sin(d*x+c)))^(3/2)/(cos(d*x+c)*sin(d*x+c)+cos(d*x+c)^2-2*sin(d*x+c)+cos(d*x+c)-2)/cos(d*x+c)^3","A"
281,1,288,234,0.326000," ","int((e*cos(d*x+c))^(3/2)*(a+a*sin(d*x+c))^(3/2),x)","\frac{\left(16 \sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right)+21 \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sin \left(d x +c \right)-21 \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \sin \left(d x +c \right)-16 \left(\cos^{4}\left(d x +c \right)\right)+28 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+44 \left(\cos^{3}\left(d x +c \right)\right)-42 \cos \left(d x +c \right) \sin \left(d x +c \right)+14 \left(\cos^{2}\left(d x +c \right)\right)-42 \cos \left(d x +c \right)\right) \left(e \cos \left(d x +c \right)\right)^{\frac{3}{2}} \left(a \left(1+\sin \left(d x +c \right)\right)\right)^{\frac{3}{2}}}{48 d \left(\cos \left(d x +c \right) \sin \left(d x +c \right)+\cos^{2}\left(d x +c \right)-2 \sin \left(d x +c \right)+\cos \left(d x +c \right)-2\right) \cos \left(d x +c \right)^{2}}"," ",0,"1/48/d*(16*sin(d*x+c)*cos(d*x+c)^3+21*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*sin(d*x+c)-21*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*sin(d*x+c)-16*cos(d*x+c)^4+28*cos(d*x+c)^2*sin(d*x+c)+44*cos(d*x+c)^3-42*cos(d*x+c)*sin(d*x+c)+14*cos(d*x+c)^2-42*cos(d*x+c))*(e*cos(d*x+c))^(3/2)*(a*(1+sin(d*x+c)))^(3/2)/(cos(d*x+c)*sin(d*x+c)+cos(d*x+c)^2-2*sin(d*x+c)+cos(d*x+c)-2)/cos(d*x+c)^2","A"
282,1,262,205,0.298000," ","int((a+a*sin(d*x+c))^(3/2)*(e*cos(d*x+c))^(1/2),x)","\frac{\left(5 \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sin \left(d x +c \right)+5 \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \sin \left(d x +c \right)+4 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)-4 \left(\cos^{3}\left(d x +c \right)\right)+10 \cos \left(d x +c \right) \sin \left(d x +c \right)+14 \left(\cos^{2}\left(d x +c \right)\right)-10 \cos \left(d x +c \right)\right) \left(a \left(1+\sin \left(d x +c \right)\right)\right)^{\frac{3}{2}} \sqrt{e \cos \left(d x +c \right)}}{8 d \left(\cos \left(d x +c \right) \sin \left(d x +c \right)+\cos^{2}\left(d x +c \right)-2 \sin \left(d x +c \right)+\cos \left(d x +c \right)-2\right) \cos \left(d x +c \right)}"," ",0,"1/8/d*(5*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*sin(d*x+c)+5*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*sin(d*x+c)+4*cos(d*x+c)^2*sin(d*x+c)-4*cos(d*x+c)^3+10*cos(d*x+c)*sin(d*x+c)+14*cos(d*x+c)^2-10*cos(d*x+c))*(a*(1+sin(d*x+c)))^(3/2)*(e*cos(d*x+c))^(1/2)/(cos(d*x+c)*sin(d*x+c)+cos(d*x+c)^2-2*sin(d*x+c)+cos(d*x+c)-2)/cos(d*x+c)","A"
283,1,228,172,0.261000," ","int((a+a*sin(d*x+c))^(3/2)/(e*cos(d*x+c))^(1/2),x)","-\frac{\left(3 \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \sin \left(d x +c \right)-3 \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sin \left(d x +c \right)-2 \cos \left(d x +c \right) \sin \left(d x +c \right)+2 \left(\cos^{2}\left(d x +c \right)\right)-2 \cos \left(d x +c \right)\right) \left(a \left(1+\sin \left(d x +c \right)\right)\right)^{\frac{3}{2}}}{2 d \left(\cos \left(d x +c \right) \sin \left(d x +c \right)+\cos^{2}\left(d x +c \right)-2 \sin \left(d x +c \right)+\cos \left(d x +c \right)-2\right) \sqrt{e \cos \left(d x +c \right)}}"," ",0,"-1/2/d*(3*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*sin(d*x+c)-3*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*sin(d*x+c)-2*cos(d*x+c)*sin(d*x+c)+2*cos(d*x+c)^2-2*cos(d*x+c))*(a*(1+sin(d*x+c)))^(3/2)/(cos(d*x+c)*sin(d*x+c)+cos(d*x+c)^2-2*sin(d*x+c)+cos(d*x+c)-2)/(e*cos(d*x+c))^(1/2)","A"
284,1,323,184,0.209000," ","int((a+a*sin(d*x+c))^(3/2)/(e*cos(d*x+c))^(3/2),x)","-\frac{2 \left(a \left(1+\sin \left(d x +c \right)\right)\right)^{\frac{3}{2}} \left(-1+\cos \left(d x +c \right)\right) \left(\sqrt{2}\, \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \sin \left(d x +c \right)+\sqrt{2}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sin \left(d x +c \right)-2 \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+2 \cos \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}-\sqrt{2}\, \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right)-\sqrt{2}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right)+2 \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\right)}{d \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \left(1-\cos \left(d x +c \right)+\sin \left(d x +c \right)\right) \left(e \cos \left(d x +c \right)\right)^{\frac{3}{2}}}"," ",0,"-2/d*(a*(1+sin(d*x+c)))^(3/2)*(-1+cos(d*x+c))*(2^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*sin(d*x+c)+2^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*sin(d*x+c)-2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+2*cos(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)-2^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))-2^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))+2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)/(1-cos(d*x+c)+sin(d*x+c))/(e*cos(d*x+c))^(3/2)","A"
285,1,34,30,0.178000," ","int((a+a*sin(d*x+c))^(3/2)/(e*cos(d*x+c))^(5/2),x)","\frac{2 \cos \left(d x +c \right) \left(a \left(1+\sin \left(d x +c \right)\right)\right)^{\frac{3}{2}}}{3 d \left(e \cos \left(d x +c \right)\right)^{\frac{5}{2}}}"," ",0,"2/3/d*cos(d*x+c)*(a*(1+sin(d*x+c)))^(3/2)/(e*cos(d*x+c))^(5/2)","A"
286,1,44,64,0.193000," ","int((a+a*sin(d*x+c))^(3/2)/(e*cos(d*x+c))^(7/2),x)","-\frac{2 \left(2 \sin \left(d x +c \right)-3\right) \left(a \left(1+\sin \left(d x +c \right)\right)\right)^{\frac{3}{2}} \cos \left(d x +c \right)}{5 d \left(e \cos \left(d x +c \right)\right)^{\frac{7}{2}}}"," ",0,"-2/5/d*(2*sin(d*x+c)-3)*(a*(1+sin(d*x+c)))^(3/2)*cos(d*x+c)/(e*cos(d*x+c))^(7/2)","A"
287,1,54,97,0.201000," ","int((a+a*sin(d*x+c))^(3/2)/(e*cos(d*x+c))^(9/2),x)","\frac{2 \left(8 \left(\cos^{2}\left(d x +c \right)\right)+12 \sin \left(d x +c \right)-9\right) \left(a \left(1+\sin \left(d x +c \right)\right)\right)^{\frac{3}{2}} \cos \left(d x +c \right)}{21 d \left(e \cos \left(d x +c \right)\right)^{\frac{9}{2}}}"," ",0,"2/21/d*(8*cos(d*x+c)^2+12*sin(d*x+c)-9)*(a*(1+sin(d*x+c)))^(3/2)*cos(d*x+c)/(e*cos(d*x+c))^(9/2)","A"
288,1,70,130,0.203000," ","int((a+a*sin(d*x+c))^(3/2)/(e*cos(d*x+c))^(11/2),x)","-\frac{2 \left(16 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)-24 \left(\cos^{2}\left(d x +c \right)\right)-10 \sin \left(d x +c \right)+5\right) \left(a \left(1+\sin \left(d x +c \right)\right)\right)^{\frac{3}{2}} \cos \left(d x +c \right)}{45 d \left(e \cos \left(d x +c \right)\right)^{\frac{11}{2}}}"," ",0,"-2/45/d*(16*cos(d*x+c)^2*sin(d*x+c)-24*cos(d*x+c)^2-10*sin(d*x+c)+5)*(a*(1+sin(d*x+c)))^(3/2)*cos(d*x+c)/(e*cos(d*x+c))^(11/2)","A"
289,1,344,273,0.326000," ","int((e*cos(d*x+c))^(3/2)*(a+a*sin(d*x+c))^(5/2),x)","-\frac{\left(96 \sin \left(d x +c \right) \left(\cos^{4}\left(d x +c \right)\right)+96 \left(\cos^{5}\left(d x +c \right)\right)-368 \sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right)-231 \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sin \left(d x +c \right)+231 \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \sin \left(d x +c \right)+272 \left(\cos^{4}\left(d x +c \right)\right)-308 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)-676 \left(\cos^{3}\left(d x +c \right)\right)+462 \cos \left(d x +c \right) \sin \left(d x +c \right)-154 \left(\cos^{2}\left(d x +c \right)\right)+462 \cos \left(d x +c \right)\right) \left(e \cos \left(d x +c \right)\right)^{\frac{3}{2}} \left(a \left(1+\sin \left(d x +c \right)\right)\right)^{\frac{5}{2}}}{384 d \left(\left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)-\left(\cos^{3}\left(d x +c \right)\right)+2 \cos \left(d x +c \right) \sin \left(d x +c \right)+3 \left(\cos^{2}\left(d x +c \right)\right)-4 \sin \left(d x +c \right)+2 \cos \left(d x +c \right)-4\right) \cos \left(d x +c \right)^{2}}"," ",0,"-1/384/d*(96*sin(d*x+c)*cos(d*x+c)^4+96*cos(d*x+c)^5-368*sin(d*x+c)*cos(d*x+c)^3-231*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*sin(d*x+c)+231*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*sin(d*x+c)+272*cos(d*x+c)^4-308*cos(d*x+c)^2*sin(d*x+c)-676*cos(d*x+c)^3+462*cos(d*x+c)*sin(d*x+c)-154*cos(d*x+c)^2+462*cos(d*x+c))*(e*cos(d*x+c))^(3/2)*(a*(1+sin(d*x+c)))^(5/2)/(cos(d*x+c)^2*sin(d*x+c)-cos(d*x+c)^3+2*cos(d*x+c)*sin(d*x+c)+3*cos(d*x+c)^2-4*sin(d*x+c)+2*cos(d*x+c)-4)/cos(d*x+c)^2","A"
290,1,318,242,0.338000," ","int((a+a*sin(d*x+c))^(5/2)*(e*cos(d*x+c))^(1/2),x)","-\frac{\left(16 \sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right)-45 \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \sin \left(d x +c \right)-45 \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sin \left(d x +c \right)+16 \left(\cos^{4}\left(d x +c \right)\right)-68 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+52 \left(\cos^{3}\left(d x +c \right)\right)-90 \cos \left(d x +c \right) \sin \left(d x +c \right)-158 \left(\cos^{2}\left(d x +c \right)\right)+90 \cos \left(d x +c \right)\right) \left(a \left(1+\sin \left(d x +c \right)\right)\right)^{\frac{5}{2}} \sqrt{e \cos \left(d x +c \right)}}{48 d \left(\left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)-\left(\cos^{3}\left(d x +c \right)\right)+2 \cos \left(d x +c \right) \sin \left(d x +c \right)+3 \left(\cos^{2}\left(d x +c \right)\right)-4 \sin \left(d x +c \right)+2 \cos \left(d x +c \right)-4\right) \cos \left(d x +c \right)}"," ",0,"-1/48/d*(16*sin(d*x+c)*cos(d*x+c)^3-45*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*sin(d*x+c)-45*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*sin(d*x+c)+16*cos(d*x+c)^4-68*cos(d*x+c)^2*sin(d*x+c)+52*cos(d*x+c)^3-90*cos(d*x+c)*sin(d*x+c)-158*cos(d*x+c)^2+90*cos(d*x+c))*(a*(1+sin(d*x+c)))^(5/2)*(e*cos(d*x+c))^(1/2)/(cos(d*x+c)^2*sin(d*x+c)-cos(d*x+c)^3+2*cos(d*x+c)*sin(d*x+c)+3*cos(d*x+c)^2-4*sin(d*x+c)+2*cos(d*x+c)-4)/cos(d*x+c)","A"
291,1,284,209,0.299000," ","int((a+a*sin(d*x+c))^(5/2)/(e*cos(d*x+c))^(1/2),x)","\frac{\left(a \left(1+\sin \left(d x +c \right)\right)\right)^{\frac{5}{2}} \left(21 \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sin \left(d x +c \right)-21 \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \sin \left(d x +c \right)-4 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)-4 \left(\cos^{3}\left(d x +c \right)\right)+22 \cos \left(d x +c \right) \sin \left(d x +c \right)-18 \left(\cos^{2}\left(d x +c \right)\right)+22 \cos \left(d x +c \right)\right)}{8 d \left(\left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)-\left(\cos^{3}\left(d x +c \right)\right)+2 \cos \left(d x +c \right) \sin \left(d x +c \right)+3 \left(\cos^{2}\left(d x +c \right)\right)-4 \sin \left(d x +c \right)+2 \cos \left(d x +c \right)-4\right) \sqrt{e \cos \left(d x +c \right)}}"," ",0,"1/8/d*(a*(1+sin(d*x+c)))^(5/2)*(21*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*sin(d*x+c)-21*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*sin(d*x+c)-4*cos(d*x+c)^2*sin(d*x+c)-4*cos(d*x+c)^3+22*cos(d*x+c)*sin(d*x+c)-18*cos(d*x+c)^2+22*cos(d*x+c))/(cos(d*x+c)^2*sin(d*x+c)-cos(d*x+c)^3+2*cos(d*x+c)*sin(d*x+c)+3*cos(d*x+c)^2-4*sin(d*x+c)+2*cos(d*x+c)-4)/(e*cos(d*x+c))^(1/2)","A"
292,1,445,209,0.250000," ","int((a+a*sin(d*x+c))^(5/2)/(e*cos(d*x+c))^(3/2),x)","-\frac{\left(5 \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \sin \left(d x +c \right)+5 \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sin \left(d x +c \right)-5 \cos \left(d x +c \right) \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}-5 \cos \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sqrt{2}-5 \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}-5 \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sqrt{2}+4 \cos \left(d x +c \right) \sin \left(d x +c \right)-36 \cos \left(d x +c \right)\right) \left(a \left(1+\sin \left(d x +c \right)\right)\right)^{\frac{5}{2}}}{4 d \left(-\left(\cos^{2}\left(d x +c \right)\right)+2 \sin \left(d x +c \right)+2\right) \left(e \cos \left(d x +c \right)\right)^{\frac{3}{2}}}"," ",0,"-1/4/d*(5*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*sin(d*x+c)+5*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*sin(d*x+c)-5*cos(d*x+c)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2)-5*cos(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*2^(1/2)-5*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2)-5*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*2^(1/2)+4*cos(d*x+c)*sin(d*x+c)-36*cos(d*x+c))*(a*(1+sin(d*x+c)))^(5/2)/(-cos(d*x+c)^2+2*sin(d*x+c)+2)/(e*cos(d*x+c))^(3/2)","B"
293,1,545,176,0.242000," ","int((a+a*sin(d*x+c))^(5/2)/(e*cos(d*x+c))^(5/2),x)","-\frac{\left(3 \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \sqrt{2}\, \sin \left(d x +c \right) \cos \left(d x +c \right)-3 \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sqrt{2}\, \sin \left(d x +c \right) \cos \left(d x +c \right)-3 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}\, \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right)+3 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right)-4 \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \cos \left(d x +c \right)-6 \sqrt{2}\, \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \sin \left(d x +c \right)+6 \sqrt{2}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sin \left(d x +c \right)-3 \cos \left(d x +c \right) \sqrt{2}\, \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right)+3 \cos \left(d x +c \right) \sqrt{2}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right)+6 \sqrt{2}\, \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right)-6 \sqrt{2}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right)\right) \left(a \left(1+\sin \left(d x +c \right)\right)\right)^{\frac{5}{2}}}{3 d \left(1+\sin \left(d x +c \right)\right) \sin \left(d x +c \right) \left(e \cos \left(d x +c \right)\right)^{\frac{5}{2}} \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}"," ",0,"-1/3/d*(3*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)*sin(d*x+c)*cos(d*x+c)-3*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*2^(1/2)*sin(d*x+c)*cos(d*x+c)-3*cos(d*x+c)^2*2^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))+3*cos(d*x+c)^2*2^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))-4*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)*cos(d*x+c)-6*2^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*sin(d*x+c)+6*2^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*sin(d*x+c)-3*cos(d*x+c)*2^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))+3*cos(d*x+c)*2^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))+6*2^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))-6*2^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2)))*(a*(1+sin(d*x+c)))^(5/2)/(1+sin(d*x+c))/sin(d*x+c)/(e*cos(d*x+c))^(5/2)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)","B"
294,1,34,30,0.177000," ","int((a+a*sin(d*x+c))^(5/2)/(e*cos(d*x+c))^(7/2),x)","\frac{2 \cos \left(d x +c \right) \left(a \left(1+\sin \left(d x +c \right)\right)\right)^{\frac{5}{2}}}{5 d \left(e \cos \left(d x +c \right)\right)^{\frac{7}{2}}}"," ",0,"2/5/d*cos(d*x+c)*(a*(1+sin(d*x+c)))^(5/2)/(e*cos(d*x+c))^(7/2)","A"
295,1,44,64,0.205000," ","int((a+a*sin(d*x+c))^(5/2)/(e*cos(d*x+c))^(9/2),x)","-\frac{2 \left(2 \sin \left(d x +c \right)-5\right) \left(a \left(1+\sin \left(d x +c \right)\right)\right)^{\frac{5}{2}} \cos \left(d x +c \right)}{21 d \left(e \cos \left(d x +c \right)\right)^{\frac{9}{2}}}"," ",0,"-2/21/d*(2*sin(d*x+c)-5)*(a*(1+sin(d*x+c)))^(5/2)*cos(d*x+c)/(e*cos(d*x+c))^(9/2)","A"
296,1,54,97,0.199000," ","int((a+a*sin(d*x+c))^(5/2)/(e*cos(d*x+c))^(11/2),x)","-\frac{2 \left(8 \left(\cos^{2}\left(d x +c \right)\right)+20 \sin \left(d x +c \right)-25\right) \left(a \left(1+\sin \left(d x +c \right)\right)\right)^{\frac{5}{2}} \cos \left(d x +c \right)}{45 d \left(e \cos \left(d x +c \right)\right)^{\frac{11}{2}}}"," ",0,"-2/45/d*(8*cos(d*x+c)^2+20*sin(d*x+c)-25)*(a*(1+sin(d*x+c)))^(5/2)*cos(d*x+c)/(e*cos(d*x+c))^(11/2)","A"
297,1,70,130,0.211000," ","int((a+a*sin(d*x+c))^(5/2)/(e*cos(d*x+c))^(13/2),x)","-\frac{2 \left(16 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)-40 \left(\cos^{2}\left(d x +c \right)\right)-42 \sin \left(d x +c \right)+35\right) \left(a \left(1+\sin \left(d x +c \right)\right)\right)^{\frac{5}{2}} \cos \left(d x +c \right)}{77 d \left(e \cos \left(d x +c \right)\right)^{\frac{13}{2}}}"," ",0,"-2/77/d*(16*cos(d*x+c)^2*sin(d*x+c)-40*cos(d*x+c)^2-42*sin(d*x+c)+35)*(a*(1+sin(d*x+c)))^(5/2)*cos(d*x+c)/(e*cos(d*x+c))^(13/2)","A"
298,1,239,206,0.282000," ","int((e*cos(d*x+c))^(5/2)/(a+a*sin(d*x+c))^(1/2),x)","-\frac{\left(3 \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \sin \left(d x +c \right)+3 \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sin \left(d x +c \right)+4 \left(\cos^{3}\left(d x +c \right)\right)-4 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+2 \left(\cos^{2}\left(d x +c \right)\right)+6 \cos \left(d x +c \right) \sin \left(d x +c \right)-6 \cos \left(d x +c \right)\right) \left(e \cos \left(d x +c \right)\right)^{\frac{5}{2}}}{8 d \left(-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)\right) \cos \left(d x +c \right)^{2} \sqrt{a \left(1+\sin \left(d x +c \right)\right)}}"," ",0,"-1/8/d*(3*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*sin(d*x+c)+3*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*sin(d*x+c)+4*cos(d*x+c)^3-4*cos(d*x+c)^2*sin(d*x+c)+2*cos(d*x+c)^2+6*cos(d*x+c)*sin(d*x+c)-6*cos(d*x+c))*(e*cos(d*x+c))^(5/2)/(-1+cos(d*x+c)+sin(d*x+c))/cos(d*x+c)^2/(a*(1+sin(d*x+c)))^(1/2)","A"
299,1,212,174,0.237000," ","int((e*cos(d*x+c))^(3/2)/(a+a*sin(d*x+c))^(1/2),x)","\frac{\left(\sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \sin \left(d x +c \right)-\sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sin \left(d x +c \right)+2 \cos \left(d x +c \right) \sin \left(d x +c \right)-2 \left(\cos^{2}\left(d x +c \right)\right)+2 \cos \left(d x +c \right)\right) \left(e \cos \left(d x +c \right)\right)^{\frac{3}{2}}}{2 d \left(-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)\right) \sqrt{a \left(1+\sin \left(d x +c \right)\right)}\, \cos \left(d x +c \right)}"," ",0,"1/2/d*(2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*sin(d*x+c)-2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*sin(d*x+c)+2*cos(d*x+c)*sin(d*x+c)-2*cos(d*x+c)^2+2*cos(d*x+c))*(e*cos(d*x+c))^(3/2)/(-1+cos(d*x+c)+sin(d*x+c))/(a*(1+sin(d*x+c)))^(1/2)/cos(d*x+c)","A"
300,1,141,147,0.182000," ","int((e*cos(d*x+c))^(1/2)/(a+a*sin(d*x+c))^(1/2),x)","\frac{\sqrt{e \cos \left(d x +c \right)}\, \left(1-\cos \left(d x +c \right)+\sin \left(d x +c \right)\right) \left(\arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right)+\arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right)\right) \sqrt{2}}{d \sqrt{a \left(1+\sin \left(d x +c \right)\right)}\, \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}"," ",0,"1/d*(e*cos(d*x+c))^(1/2)*(1-cos(d*x+c)+sin(d*x+c))*(arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))+arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2)))/(a*(1+sin(d*x+c)))^(1/2)/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2)","A"
301,1,34,30,0.174000," ","int(1/(e*cos(d*x+c))^(1/2)/(a+a*sin(d*x+c))^(1/2),x)","-\frac{2 \cos \left(d x +c \right)}{d \sqrt{e \cos \left(d x +c \right)}\, \sqrt{a \left(1+\sin \left(d x +c \right)\right)}}"," ",0,"-2/d*cos(d*x+c)/(e*cos(d*x+c))^(1/2)/(a*(1+sin(d*x+c)))^(1/2)","A"
302,1,44,64,0.177000," ","int(1/(e*cos(d*x+c))^(3/2)/(a+a*sin(d*x+c))^(1/2),x)","\frac{2 \left(2 \sin \left(d x +c \right)+1\right) \cos \left(d x +c \right)}{3 d \left(e \cos \left(d x +c \right)\right)^{\frac{3}{2}} \sqrt{a \left(1+\sin \left(d x +c \right)\right)}}"," ",0,"2/3/d*(2*sin(d*x+c)+1)*cos(d*x+c)/(e*cos(d*x+c))^(3/2)/(a*(1+sin(d*x+c)))^(1/2)","A"
303,1,54,97,0.196000," ","int(1/(e*cos(d*x+c))^(5/2)/(a+a*sin(d*x+c))^(1/2),x)","\frac{2 \left(-8 \left(\cos^{2}\left(d x +c \right)\right)+4 \sin \left(d x +c \right)+1\right) \cos \left(d x +c \right)}{15 d \left(e \cos \left(d x +c \right)\right)^{\frac{5}{2}} \sqrt{a \left(1+\sin \left(d x +c \right)\right)}}"," ",0,"2/15/d*(-8*cos(d*x+c)^2+4*sin(d*x+c)+1)*cos(d*x+c)/(e*cos(d*x+c))^(5/2)/(a*(1+sin(d*x+c)))^(1/2)","A"
304,1,70,130,0.191000," ","int(1/(e*cos(d*x+c))^(7/2)/(a+a*sin(d*x+c))^(1/2),x)","\frac{2 \left(16 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+8 \left(\cos^{2}\left(d x +c \right)\right)+6 \sin \left(d x +c \right)+1\right) \cos \left(d x +c \right)}{35 d \left(e \cos \left(d x +c \right)\right)^{\frac{7}{2}} \sqrt{a \left(1+\sin \left(d x +c \right)\right)}}"," ",0,"2/35/d*(16*cos(d*x+c)^2*sin(d*x+c)+8*cos(d*x+c)^2+6*sin(d*x+c)+1)*cos(d*x+c)/(e*cos(d*x+c))^(7/2)/(a*(1+sin(d*x+c)))^(1/2)","A"
305,1,266,209,0.272000," ","int((e*cos(d*x+c))^(7/2)/(a+a*sin(d*x+c))^(3/2),x)","-\frac{\left(e \cos \left(d x +c \right)\right)^{\frac{7}{2}} \left(5 \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \sin \left(d x +c \right)-5 \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sin \left(d x +c \right)+4 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+4 \left(\cos^{3}\left(d x +c \right)\right)+10 \cos \left(d x +c \right) \sin \left(d x +c \right)-14 \left(\cos^{2}\left(d x +c \right)\right)+10 \cos \left(d x +c \right)\right)}{8 d \left(\cos \left(d x +c \right) \sin \left(d x +c \right)-\left(\cos^{2}\left(d x +c \right)\right)-2 \sin \left(d x +c \right)-\cos \left(d x +c \right)+2\right) \left(a \left(1+\sin \left(d x +c \right)\right)\right)^{\frac{3}{2}} \cos \left(d x +c \right)}"," ",0,"-1/8/d*(e*cos(d*x+c))^(7/2)*(5*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*sin(d*x+c)-5*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*sin(d*x+c)+4*cos(d*x+c)^2*sin(d*x+c)+4*cos(d*x+c)^3+10*cos(d*x+c)*sin(d*x+c)-14*cos(d*x+c)^2+10*cos(d*x+c))/(cos(d*x+c)*sin(d*x+c)-cos(d*x+c)^2-2*sin(d*x+c)-cos(d*x+c)+2)/(a*(1+sin(d*x+c)))^(3/2)/cos(d*x+c)","A"
306,1,232,189,0.240000," ","int((e*cos(d*x+c))^(5/2)/(a+a*sin(d*x+c))^(3/2),x)","-\frac{\left(e \cos \left(d x +c \right)\right)^{\frac{5}{2}} \left(-3 \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \sin \left(d x +c \right)-3 \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sin \left(d x +c \right)+2 \cos \left(d x +c \right) \sin \left(d x +c \right)+2 \left(\cos^{2}\left(d x +c \right)\right)-2 \cos \left(d x +c \right)\right)}{2 d \left(\cos \left(d x +c \right) \sin \left(d x +c \right)-\left(\cos^{2}\left(d x +c \right)\right)-2 \sin \left(d x +c \right)-\cos \left(d x +c \right)+2\right) \left(a \left(1+\sin \left(d x +c \right)\right)\right)^{\frac{3}{2}}}"," ",0,"-1/2/d*(e*cos(d*x+c))^(5/2)*(-3*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*sin(d*x+c)-3*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*sin(d*x+c)+2*cos(d*x+c)*sin(d*x+c)+2*cos(d*x+c)^2-2*cos(d*x+c))/(cos(d*x+c)*sin(d*x+c)-cos(d*x+c)^2-2*sin(d*x+c)-cos(d*x+c)+2)/(a*(1+sin(d*x+c)))^(3/2)","A"
307,1,321,206,0.199000," ","int((e*cos(d*x+c))^(3/2)/(a+a*sin(d*x+c))^(3/2),x)","-\frac{2 \left(e \cos \left(d x +c \right)\right)^{\frac{3}{2}} \left(-1+\cos \left(d x +c \right)\right) \left(\sqrt{2}\, \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \sin \left(d x +c \right)-\sqrt{2}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sin \left(d x +c \right)-2 \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-2 \cos \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+\sqrt{2}\, \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right)-\sqrt{2}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right)-2 \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\right)}{d \sin \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \left(a \left(1+\sin \left(d x +c \right)\right)\right)^{\frac{3}{2}} \left(-1+\cos \left(d x +c \right)+\sin \left(d x +c \right)\right)}"," ",0,"-2/d*(e*cos(d*x+c))^(3/2)*(-1+cos(d*x+c))*(2^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*sin(d*x+c)-2^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*sin(d*x+c)-2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-2*cos(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+2^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))-2^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))-2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))/sin(d*x+c)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)/(a*(1+sin(d*x+c)))^(3/2)/(-1+cos(d*x+c)+sin(d*x+c))","A"
308,1,34,30,0.187000," ","int((e*cos(d*x+c))^(1/2)/(a+a*sin(d*x+c))^(3/2),x)","-\frac{2 \sqrt{e \cos \left(d x +c \right)}\, \cos \left(d x +c \right)}{3 d \left(a \left(1+\sin \left(d x +c \right)\right)\right)^{\frac{3}{2}}}"," ",0,"-2/3/d*(e*cos(d*x+c))^(1/2)*cos(d*x+c)/(a*(1+sin(d*x+c)))^(3/2)","A"
309,1,44,64,0.186000," ","int(1/(a+a*sin(d*x+c))^(3/2)/(e*cos(d*x+c))^(1/2),x)","-\frac{2 \left(2 \sin \left(d x +c \right)+3\right) \cos \left(d x +c \right)}{5 d \left(a \left(1+\sin \left(d x +c \right)\right)\right)^{\frac{3}{2}} \sqrt{e \cos \left(d x +c \right)}}"," ",0,"-2/5/d*(2*sin(d*x+c)+3)*cos(d*x+c)/(a*(1+sin(d*x+c)))^(3/2)/(e*cos(d*x+c))^(1/2)","A"
310,1,54,97,0.173000," ","int(1/(e*cos(d*x+c))^(3/2)/(a+a*sin(d*x+c))^(3/2),x)","\frac{2 \left(-8 \left(\cos^{2}\left(d x +c \right)\right)+12 \sin \left(d x +c \right)+9\right) \cos \left(d x +c \right)}{21 d \left(e \cos \left(d x +c \right)\right)^{\frac{3}{2}} \left(a \left(1+\sin \left(d x +c \right)\right)\right)^{\frac{3}{2}}}"," ",0,"2/21/d*(-8*cos(d*x+c)^2+12*sin(d*x+c)+9)*cos(d*x+c)/(e*cos(d*x+c))^(3/2)/(a*(1+sin(d*x+c)))^(3/2)","A"
311,1,70,130,0.184000," ","int(1/(e*cos(d*x+c))^(5/2)/(a+a*sin(d*x+c))^(3/2),x)","-\frac{2 \left(16 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+24 \left(\cos^{2}\left(d x +c \right)\right)-10 \sin \left(d x +c \right)-5\right) \cos \left(d x +c \right)}{45 d \left(e \cos \left(d x +c \right)\right)^{\frac{5}{2}} \left(a \left(1+\sin \left(d x +c \right)\right)\right)^{\frac{3}{2}}}"," ",0,"-2/45/d*(16*cos(d*x+c)^2*sin(d*x+c)+24*cos(d*x+c)^2-10*sin(d*x+c)-5)*cos(d*x+c)/(e*cos(d*x+c))^(5/2)/(a*(1+sin(d*x+c)))^(3/2)","A"
312,1,80,163,0.215000," ","int(1/(e*cos(d*x+c))^(7/2)/(a+a*sin(d*x+c))^(3/2),x)","\frac{2 \left(-128 \left(\cos^{4}\left(d x +c \right)\right)+192 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+144 \left(\cos^{2}\left(d x +c \right)\right)+56 \sin \left(d x +c \right)+21\right) \cos \left(d x +c \right)}{385 d \left(e \cos \left(d x +c \right)\right)^{\frac{7}{2}} \left(a \left(1+\sin \left(d x +c \right)\right)\right)^{\frac{3}{2}}}"," ",0,"2/385/d*(-128*cos(d*x+c)^4+192*cos(d*x+c)^2*sin(d*x+c)+144*cos(d*x+c)^2+56*sin(d*x+c)+21)*cos(d*x+c)/(e*cos(d*x+c))^(7/2)/(a*(1+sin(d*x+c)))^(3/2)","A"
313,1,282,223,0.285000," ","int((e*cos(d*x+c))^(9/2)/(a+a*sin(d*x+c))^(5/2),x)","\frac{\left(e \cos \left(d x +c \right)\right)^{\frac{9}{2}} \left(21 \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \sin \left(d x +c \right)+21 \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sin \left(d x +c \right)+4 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)-4 \left(\cos^{3}\left(d x +c \right)\right)-22 \cos \left(d x +c \right) \sin \left(d x +c \right)-18 \left(\cos^{2}\left(d x +c \right)\right)+22 \cos \left(d x +c \right)\right)}{8 d \left(\left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+\cos^{3}\left(d x +c \right)+2 \cos \left(d x +c \right) \sin \left(d x +c \right)-3 \left(\cos^{2}\left(d x +c \right)\right)-4 \sin \left(d x +c \right)-2 \cos \left(d x +c \right)+4\right) \left(a \left(1+\sin \left(d x +c \right)\right)\right)^{\frac{5}{2}}}"," ",0,"1/8/d*(e*cos(d*x+c))^(9/2)*(21*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*sin(d*x+c)+21*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*sin(d*x+c)+4*cos(d*x+c)^2*sin(d*x+c)-4*cos(d*x+c)^3-22*cos(d*x+c)*sin(d*x+c)-18*cos(d*x+c)^2+22*cos(d*x+c))/(cos(d*x+c)^2*sin(d*x+c)+cos(d*x+c)^3+2*cos(d*x+c)*sin(d*x+c)-3*cos(d*x+c)^2-4*sin(d*x+c)-2*cos(d*x+c)+4)/(a*(1+sin(d*x+c)))^(5/2)","A"
314,1,443,209,0.234000," ","int((e*cos(d*x+c))^(7/2)/(a+a*sin(d*x+c))^(5/2),x)","\frac{\left(5 \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \sin \left(d x +c \right)-5 \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sin \left(d x +c \right)+5 \cos \left(d x +c \right) \sqrt{2}\, \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}-5 \cos \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sqrt{2}+5 \sqrt{2}\, \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}-5 \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right)+4 \cos \left(d x +c \right) \sin \left(d x +c \right)+36 \cos \left(d x +c \right)\right) \left(e \cos \left(d x +c \right)\right)^{\frac{7}{2}}}{4 d \left(\cos^{2}\left(d x +c \right)+2 \sin \left(d x +c \right)-2\right) \left(a \left(1+\sin \left(d x +c \right)\right)\right)^{\frac{5}{2}}}"," ",0,"1/4/d*(5*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*sin(d*x+c)-5*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*sin(d*x+c)+5*cos(d*x+c)*2^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)-5*cos(d*x+c)*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))+5*2^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)-5*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))+4*cos(d*x+c)*sin(d*x+c)+36*cos(d*x+c))*(e*cos(d*x+c))^(7/2)/(cos(d*x+c)^2+2*sin(d*x+c)-2)/(a*(1+sin(d*x+c)))^(5/2)","B"
315,1,545,190,0.224000," ","int((e*cos(d*x+c))^(5/2)/(a+a*sin(d*x+c))^(5/2),x)","-\frac{\left(3 \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \sqrt{2}\, \sin \left(d x +c \right) \cos \left(d x +c \right)+3 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}\, \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right)+3 \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sqrt{2}\, \sin \left(d x +c \right) \cos \left(d x +c \right)+3 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right)-6 \sqrt{2}\, \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \sin \left(d x +c \right)+3 \cos \left(d x +c \right) \sqrt{2}\, \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right)-6 \sqrt{2}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sin \left(d x +c \right)+3 \cos \left(d x +c \right) \sqrt{2}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right)-4 \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \cos \left(d x +c \right)-6 \sqrt{2}\, \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right)-6 \sqrt{2}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right)\right) \left(e \cos \left(d x +c \right)\right)^{\frac{5}{2}}}{3 d \left(\sin \left(d x +c \right)-1\right) \left(a \left(1+\sin \left(d x +c \right)\right)\right)^{\frac{5}{2}} \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)}"," ",0,"-1/3/d*(3*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*2^(1/2)*sin(d*x+c)*cos(d*x+c)+3*cos(d*x+c)^2*2^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))+3*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*2^(1/2)*sin(d*x+c)*cos(d*x+c)+3*cos(d*x+c)^2*2^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))-6*2^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*sin(d*x+c)+3*cos(d*x+c)*2^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))-6*2^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*sin(d*x+c)+3*cos(d*x+c)*2^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))-4*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)*cos(d*x+c)-6*2^(1/2)*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))-6*2^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2)))*(e*cos(d*x+c))^(5/2)/(sin(d*x+c)-1)/(a*(1+sin(d*x+c)))^(5/2)/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)/sin(d*x+c)","B"
316,1,34,30,0.191000," ","int((e*cos(d*x+c))^(3/2)/(a+a*sin(d*x+c))^(5/2),x)","-\frac{2 \left(e \cos \left(d x +c \right)\right)^{\frac{3}{2}} \cos \left(d x +c \right)}{5 d \left(a \left(1+\sin \left(d x +c \right)\right)\right)^{\frac{5}{2}}}"," ",0,"-2/5/d*(e*cos(d*x+c))^(3/2)*cos(d*x+c)/(a*(1+sin(d*x+c)))^(5/2)","A"
317,1,44,64,0.200000," ","int((e*cos(d*x+c))^(1/2)/(a+a*sin(d*x+c))^(5/2),x)","-\frac{2 \left(2 \sin \left(d x +c \right)+5\right) \cos \left(d x +c \right) \sqrt{e \cos \left(d x +c \right)}}{21 d \left(a \left(1+\sin \left(d x +c \right)\right)\right)^{\frac{5}{2}}}"," ",0,"-2/21/d*(2*sin(d*x+c)+5)*cos(d*x+c)*(e*cos(d*x+c))^(1/2)/(a*(1+sin(d*x+c)))^(5/2)","A"
318,1,54,97,0.194000," ","int(1/(a+a*sin(d*x+c))^(5/2)/(e*cos(d*x+c))^(1/2),x)","-\frac{2 \left(-8 \left(\cos^{2}\left(d x +c \right)\right)+20 \sin \left(d x +c \right)+25\right) \cos \left(d x +c \right)}{45 d \left(a \left(1+\sin \left(d x +c \right)\right)\right)^{\frac{5}{2}} \sqrt{e \cos \left(d x +c \right)}}"," ",0,"-2/45/d*(-8*cos(d*x+c)^2+20*sin(d*x+c)+25)*cos(d*x+c)/(a*(1+sin(d*x+c)))^(5/2)/(e*cos(d*x+c))^(1/2)","A"
319,1,70,130,0.189000," ","int(1/(e*cos(d*x+c))^(3/2)/(a+a*sin(d*x+c))^(5/2),x)","-\frac{2 \left(16 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+40 \left(\cos^{2}\left(d x +c \right)\right)-42 \sin \left(d x +c \right)-35\right) \cos \left(d x +c \right)}{77 d \left(e \cos \left(d x +c \right)\right)^{\frac{3}{2}} \left(a \left(1+\sin \left(d x +c \right)\right)\right)^{\frac{5}{2}}}"," ",0,"-2/77/d*(16*cos(d*x+c)^2*sin(d*x+c)+40*cos(d*x+c)^2-42*sin(d*x+c)-35)*cos(d*x+c)/(e*cos(d*x+c))^(3/2)/(a*(1+sin(d*x+c)))^(5/2)","A"
320,1,80,163,0.199000," ","int(1/(e*cos(d*x+c))^(5/2)/(a+a*sin(d*x+c))^(5/2),x)","-\frac{2 \left(-128 \left(\cos^{4}\left(d x +c \right)\right)+320 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+400 \left(\cos^{2}\left(d x +c \right)\right)-120 \sin \left(d x +c \right)-75\right) \cos \left(d x +c \right)}{585 d \left(e \cos \left(d x +c \right)\right)^{\frac{5}{2}} \left(a \left(1+\sin \left(d x +c \right)\right)\right)^{\frac{5}{2}}}"," ",0,"-2/585/d*(-128*cos(d*x+c)^4+320*cos(d*x+c)^2*sin(d*x+c)+400*cos(d*x+c)^2-120*sin(d*x+c)-75)*cos(d*x+c)/(e*cos(d*x+c))^(5/2)/(a*(1+sin(d*x+c)))^(5/2)","A"
321,0,0,60,0.236000," ","int((e*cos(d*x+c))^(7/3)/(a+a*sin(d*x+c))^(1/2),x)","\int \frac{\left(e \cos \left(d x +c \right)\right)^{\frac{7}{3}}}{\sqrt{a +a \sin \left(d x +c \right)}}\, dx"," ",0,"int((e*cos(d*x+c))^(7/3)/(a+a*sin(d*x+c))^(1/2),x)","F"
322,0,0,60,0.221000," ","int((e*cos(d*x+c))^(5/3)/(a+a*sin(d*x+c))^(1/2),x)","\int \frac{\left(e \cos \left(d x +c \right)\right)^{\frac{5}{3}}}{\sqrt{a +a \sin \left(d x +c \right)}}\, dx"," ",0,"int((e*cos(d*x+c))^(5/3)/(a+a*sin(d*x+c))^(1/2),x)","F"
323,0,0,60,0.221000," ","int((e*cos(d*x+c))^(2/3)/(a+a*sin(d*x+c))^(1/2),x)","\int \frac{\left(e \cos \left(d x +c \right)\right)^{\frac{2}{3}}}{\sqrt{a +a \sin \left(d x +c \right)}}\, dx"," ",0,"int((e*cos(d*x+c))^(2/3)/(a+a*sin(d*x+c))^(1/2),x)","F"
324,0,0,60,0.225000," ","int((e*cos(d*x+c))^(1/3)/(a+a*sin(d*x+c))^(1/2),x)","\int \frac{\left(e \cos \left(d x +c \right)\right)^{\frac{1}{3}}}{\sqrt{a +a \sin \left(d x +c \right)}}\, dx"," ",0,"int((e*cos(d*x+c))^(1/3)/(a+a*sin(d*x+c))^(1/2),x)","F"
325,0,0,59,0.210000," ","int(1/(e*cos(d*x+c))^(1/3)/(a+a*sin(d*x+c))^(1/2),x)","\int \frac{1}{\left(e \cos \left(d x +c \right)\right)^{\frac{1}{3}} \sqrt{a +a \sin \left(d x +c \right)}}\, dx"," ",0,"int(1/(e*cos(d*x+c))^(1/3)/(a+a*sin(d*x+c))^(1/2),x)","F"
326,0,0,59,0.204000," ","int(1/(e*cos(d*x+c))^(4/3)/(a+a*sin(d*x+c))^(1/2),x)","\int \frac{1}{\left(e \cos \left(d x +c \right)\right)^{\frac{4}{3}} \sqrt{a +a \sin \left(d x +c \right)}}\, dx"," ",0,"int(1/(e*cos(d*x+c))^(4/3)/(a+a*sin(d*x+c))^(1/2),x)","F"
327,0,0,77,14.571000," ","int((e*cos(d*x+c))^p*(a+a*sin(d*x+c))^8,x)","\int \left(e \cos \left(d x +c \right)\right)^{p} \left(a +a \sin \left(d x +c \right)\right)^{8}\, dx"," ",0,"int((e*cos(d*x+c))^p*(a+a*sin(d*x+c))^8,x)","F"
328,0,0,77,5.356000," ","int((e*cos(d*x+c))^p*(a+a*sin(d*x+c))^3,x)","\int \left(e \cos \left(d x +c \right)\right)^{p} \left(a +a \sin \left(d x +c \right)\right)^{3}\, dx"," ",0,"int((e*cos(d*x+c))^p*(a+a*sin(d*x+c))^3,x)","F"
329,0,0,77,4.298000," ","int((e*cos(d*x+c))^p*(a+a*sin(d*x+c))^2,x)","\int \left(e \cos \left(d x +c \right)\right)^{p} \left(a +a \sin \left(d x +c \right)\right)^{2}\, dx"," ",0,"int((e*cos(d*x+c))^p*(a+a*sin(d*x+c))^2,x)","F"
330,0,0,75,1.487000," ","int((e*cos(d*x+c))^p*(a+a*sin(d*x+c)),x)","\int \left(e \cos \left(d x +c \right)\right)^{p} \left(a +a \sin \left(d x +c \right)\right)\, dx"," ",0,"int((e*cos(d*x+c))^p*(a+a*sin(d*x+c)),x)","F"
331,0,0,77,0.290000," ","int((e*cos(d*x+c))^p/(a+a*sin(d*x+c)),x)","\int \frac{\left(e \cos \left(d x +c \right)\right)^{p}}{a +a \sin \left(d x +c \right)}\, dx"," ",0,"int((e*cos(d*x+c))^p/(a+a*sin(d*x+c)),x)","F"
332,0,0,77,0.693000," ","int((e*cos(d*x+c))^p/(a+a*sin(d*x+c))^2,x)","\int \frac{\left(e \cos \left(d x +c \right)\right)^{p}}{\left(a +a \sin \left(d x +c \right)\right)^{2}}\, dx"," ",0,"int((e*cos(d*x+c))^p/(a+a*sin(d*x+c))^2,x)","F"
333,0,0,77,0.658000," ","int((e*cos(d*x+c))^p/(a+a*sin(d*x+c))^3,x)","\int \frac{\left(e \cos \left(d x +c \right)\right)^{p}}{\left(a +a \sin \left(d x +c \right)\right)^{3}}\, dx"," ",0,"int((e*cos(d*x+c))^p/(a+a*sin(d*x+c))^3,x)","F"
334,0,0,77,3.306000," ","int((e*cos(d*x+c))^p/(a+a*sin(d*x+c))^8,x)","\int \frac{\left(e \cos \left(d x +c \right)\right)^{p}}{\left(a +a \sin \left(d x +c \right)\right)^{8}}\, dx"," ",0,"int((e*cos(d*x+c))^p/(a+a*sin(d*x+c))^8,x)","F"
335,0,0,89,0.210000," ","int((e*cos(d*x+c))^p*(a+a*sin(d*x+c))^(7/2),x)","\int \left(e \cos \left(d x +c \right)\right)^{p} \left(a +a \sin \left(d x +c \right)\right)^{\frac{7}{2}}\, dx"," ",0,"int((e*cos(d*x+c))^p*(a+a*sin(d*x+c))^(7/2),x)","F"
336,0,0,89,0.198000," ","int((e*cos(d*x+c))^p*(a+a*sin(d*x+c))^(5/2),x)","\int \left(e \cos \left(d x +c \right)\right)^{p} \left(a +a \sin \left(d x +c \right)\right)^{\frac{5}{2}}\, dx"," ",0,"int((e*cos(d*x+c))^p*(a+a*sin(d*x+c))^(5/2),x)","F"
337,0,0,89,0.210000," ","int((e*cos(d*x+c))^p*(a+a*sin(d*x+c))^(3/2),x)","\int \left(e \cos \left(d x +c \right)\right)^{p} \left(a +a \sin \left(d x +c \right)\right)^{\frac{3}{2}}\, dx"," ",0,"int((e*cos(d*x+c))^p*(a+a*sin(d*x+c))^(3/2),x)","F"
338,0,0,85,0.202000," ","int((e*cos(d*x+c))^p*(a+a*sin(d*x+c))^(1/2),x)","\int \left(e \cos \left(d x +c \right)\right)^{p} \sqrt{a +a \sin \left(d x +c \right)}\, dx"," ",0,"int((e*cos(d*x+c))^p*(a+a*sin(d*x+c))^(1/2),x)","F"
339,0,0,85,0.170000," ","int((e*cos(d*x+c))^p/(a+a*sin(d*x+c))^(1/2),x)","\int \frac{\left(e \cos \left(d x +c \right)\right)^{p}}{\sqrt{a +a \sin \left(d x +c \right)}}\, dx"," ",0,"int((e*cos(d*x+c))^p/(a+a*sin(d*x+c))^(1/2),x)","F"
340,0,0,86,0.168000," ","int((e*cos(d*x+c))^p/(a+a*sin(d*x+c))^(3/2),x)","\int \frac{\left(e \cos \left(d x +c \right)\right)^{p}}{\left(a +a \sin \left(d x +c \right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int((e*cos(d*x+c))^p/(a+a*sin(d*x+c))^(3/2),x)","F"
341,0,0,89,0.167000," ","int((e*cos(d*x+c))^p/(a+a*sin(d*x+c))^(5/2),x)","\int \frac{\left(e \cos \left(d x +c \right)\right)^{p}}{\left(a +a \sin \left(d x +c \right)\right)^{\frac{5}{2}}}\, dx"," ",0,"int((e*cos(d*x+c))^p/(a+a*sin(d*x+c))^(5/2),x)","F"
342,0,0,96,1.345000," ","int((e*cos(d*x+c))^p*(a+a*sin(d*x+c))^m,x)","\int \left(e \cos \left(d x +c \right)\right)^{p} \left(a +a \sin \left(d x +c \right)\right)^{m}\, dx"," ",0,"int((e*cos(d*x+c))^p*(a+a*sin(d*x+c))^m,x)","F"
343,0,0,109,6.771000," ","int(cos(d*x+c)^7*(a+a*sin(d*x+c))^m,x)","\int \left(\cos^{7}\left(d x +c \right)\right) \left(a +a \sin \left(d x +c \right)\right)^{m}\, dx"," ",0,"int(cos(d*x+c)^7*(a+a*sin(d*x+c))^m,x)","F"
344,0,0,81,3.224000," ","int(cos(d*x+c)^5*(a+a*sin(d*x+c))^m,x)","\int \left(\cos^{5}\left(d x +c \right)\right) \left(a +a \sin \left(d x +c \right)\right)^{m}\, dx"," ",0,"int(cos(d*x+c)^5*(a+a*sin(d*x+c))^m,x)","F"
345,0,0,55,1.738000," ","int(cos(d*x+c)^3*(a+a*sin(d*x+c))^m,x)","\int \left(\cos^{3}\left(d x +c \right)\right) \left(a +a \sin \left(d x +c \right)\right)^{m}\, dx"," ",0,"int(cos(d*x+c)^3*(a+a*sin(d*x+c))^m,x)","F"
346,1,27,26,0.024000," ","int(cos(d*x+c)*(a+a*sin(d*x+c))^m,x)","\frac{\left(a +a \sin \left(d x +c \right)\right)^{1+m}}{a d \left(1+m \right)}"," ",0,"(a+a*sin(d*x+c))^(1+m)/a/d/(1+m)","A"
347,0,0,38,0.921000," ","int(sec(d*x+c)*(a+a*sin(d*x+c))^m,x)","\int \sec \left(d x +c \right) \left(a +a \sin \left(d x +c \right)\right)^{m}\, dx"," ",0,"int(sec(d*x+c)*(a+a*sin(d*x+c))^m,x)","F"
348,0,0,45,0.203000," ","int(sec(d*x+c)^3*(a+a*sin(d*x+c))^m,x)","\int \left(\sec^{3}\left(d x +c \right)\right) \left(a +a \sin \left(d x +c \right)\right)^{m}\, dx"," ",0,"int(sec(d*x+c)^3*(a+a*sin(d*x+c))^m,x)","F"
349,0,0,49,0.231000," ","int(sec(d*x+c)^5*(a+a*sin(d*x+c))^m,x)","\int \left(\sec^{5}\left(d x +c \right)\right) \left(a +a \sin \left(d x +c \right)\right)^{m}\, dx"," ",0,"int(sec(d*x+c)^5*(a+a*sin(d*x+c))^m,x)","F"
350,0,0,69,2.444000," ","int(cos(d*x+c)^4*(a+a*sin(d*x+c))^m,x)","\int \left(\cos^{4}\left(d x +c \right)\right) \left(a +a \sin \left(d x +c \right)\right)^{m}\, dx"," ",0,"int(cos(d*x+c)^4*(a+a*sin(d*x+c))^m,x)","F"
351,0,0,67,1.342000," ","int(cos(d*x+c)^2*(a+a*sin(d*x+c))^m,x)","\int \left(\cos^{2}\left(d x +c \right)\right) \left(a +a \sin \left(d x +c \right)\right)^{m}\, dx"," ",0,"int(cos(d*x+c)^2*(a+a*sin(d*x+c))^m,x)","F"
352,0,0,61,0.156000," ","int(sec(d*x+c)^2*(a+a*sin(d*x+c))^m,x)","\int \left(\sec^{2}\left(d x +c \right)\right) \left(a +a \sin \left(d x +c \right)\right)^{m}\, dx"," ",0,"int(sec(d*x+c)^2*(a+a*sin(d*x+c))^m,x)","F"
353,0,0,69,0.196000," ","int(sec(d*x+c)^4*(a+a*sin(d*x+c))^m,x)","\int \left(\sec^{4}\left(d x +c \right)\right) \left(a +a \sin \left(d x +c \right)\right)^{m}\, dx"," ",0,"int(sec(d*x+c)^4*(a+a*sin(d*x+c))^m,x)","F"
354,0,0,72,0.204000," ","int((e*cos(d*x+c))^(5/2)*(a+a*sin(d*x+c))^m,x)","\int \left(e \cos \left(d x +c \right)\right)^{\frac{5}{2}} \left(a +a \sin \left(d x +c \right)\right)^{m}\, dx"," ",0,"int((e*cos(d*x+c))^(5/2)*(a+a*sin(d*x+c))^m,x)","F"
355,0,0,72,0.196000," ","int((e*cos(d*x+c))^(3/2)*(a+a*sin(d*x+c))^m,x)","\int \left(e \cos \left(d x +c \right)\right)^{\frac{3}{2}} \left(a +a \sin \left(d x +c \right)\right)^{m}\, dx"," ",0,"int((e*cos(d*x+c))^(3/2)*(a+a*sin(d*x+c))^m,x)","F"
356,0,0,72,0.219000," ","int((e*cos(d*x+c))^(1/2)*(a+a*sin(d*x+c))^m,x)","\int \sqrt{e \cos \left(d x +c \right)}\, \left(a +a \sin \left(d x +c \right)\right)^{m}\, dx"," ",0,"int((e*cos(d*x+c))^(1/2)*(a+a*sin(d*x+c))^m,x)","F"
357,0,0,72,0.189000," ","int((a+a*sin(d*x+c))^m/(e*cos(d*x+c))^(1/2),x)","\int \frac{\left(a +a \sin \left(d x +c \right)\right)^{m}}{\sqrt{e \cos \left(d x +c \right)}}\, dx"," ",0,"int((a+a*sin(d*x+c))^m/(e*cos(d*x+c))^(1/2),x)","F"
358,0,0,68,0.181000," ","int((a+a*sin(d*x+c))^m/(e*cos(d*x+c))^(3/2),x)","\int \frac{\left(a +a \sin \left(d x +c \right)\right)^{m}}{\left(e \cos \left(d x +c \right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int((a+a*sin(d*x+c))^m/(e*cos(d*x+c))^(3/2),x)","F"
359,0,0,69,0.186000," ","int((a+a*sin(d*x+c))^m/(e*cos(d*x+c))^(5/2),x)","\int \frac{\left(a +a \sin \left(d x +c \right)\right)^{m}}{\left(e \cos \left(d x +c \right)\right)^{\frac{5}{2}}}\, dx"," ",0,"int((a+a*sin(d*x+c))^m/(e*cos(d*x+c))^(5/2),x)","F"
360,0,0,201,0.344000," ","int((e*cos(d*x+c))^(-4-m)*(a+a*sin(d*x+c))^m,x)","\int \left(e \cos \left(d x +c \right)\right)^{-4-m} \left(a +a \sin \left(d x +c \right)\right)^{m}\, dx"," ",0,"int((e*cos(d*x+c))^(-4-m)*(a+a*sin(d*x+c))^m,x)","F"
361,0,0,142,0.309000," ","int((e*cos(d*x+c))^(-3-m)*(a+a*sin(d*x+c))^m,x)","\int \left(e \cos \left(d x +c \right)\right)^{-3-m} \left(a +a \sin \left(d x +c \right)\right)^{m}\, dx"," ",0,"int((e*cos(d*x+c))^(-3-m)*(a+a*sin(d*x+c))^m,x)","F"
362,0,0,89,0.320000," ","int((e*cos(d*x+c))^(-2-m)*(a+a*sin(d*x+c))^m,x)","\int \left(e \cos \left(d x +c \right)\right)^{-2-m} \left(a +a \sin \left(d x +c \right)\right)^{m}\, dx"," ",0,"int((e*cos(d*x+c))^(-2-m)*(a+a*sin(d*x+c))^m,x)","F"
363,0,0,34,0.303000," ","int((e*cos(d*x+c))^(-1-m)*(a+a*sin(d*x+c))^m,x)","\int \left(e \cos \left(d x +c \right)\right)^{-1-m} \left(a +a \sin \left(d x +c \right)\right)^{m}\, dx"," ",0,"int((e*cos(d*x+c))^(-1-m)*(a+a*sin(d*x+c))^m,x)","F"
364,0,0,93,0.565000," ","int((a+a*sin(d*x+c))^m/((e*cos(d*x+c))^m),x)","\int \left(a +a \sin \left(d x +c \right)\right)^{m} \left(e \cos \left(d x +c \right)\right)^{-m}\, dx"," ",0,"int((a+a*sin(d*x+c))^m/((e*cos(d*x+c))^m),x)","F"
365,0,0,87,0.308000," ","int((e*cos(d*x+c))^(1-m)*(a+a*sin(d*x+c))^m,x)","\int \left(e \cos \left(d x +c \right)\right)^{1-m} \left(a +a \sin \left(d x +c \right)\right)^{m}\, dx"," ",0,"int((e*cos(d*x+c))^(1-m)*(a+a*sin(d*x+c))^m,x)","F"
366,0,0,93,0.314000," ","int((e*cos(d*x+c))^(2-m)*(a+a*sin(d*x+c))^m,x)","\int \left(e \cos \left(d x +c \right)\right)^{2-m} \left(a +a \sin \left(d x +c \right)\right)^{m}\, dx"," ",0,"int((e*cos(d*x+c))^(2-m)*(a+a*sin(d*x+c))^m,x)","F"
367,0,0,154,1.678000," ","int((e*cos(d*x+c))^(5-2*m)*(a+a*sin(d*x+c))^m,x)","\int \left(e \cos \left(d x +c \right)\right)^{5-2 m} \left(a +a \sin \left(d x +c \right)\right)^{m}\, dx"," ",0,"int((e*cos(d*x+c))^(5-2*m)*(a+a*sin(d*x+c))^m,x)","F"
368,0,0,98,1.573000," ","int((e*cos(d*x+c))^(3-2*m)*(a+a*sin(d*x+c))^m,x)","\int \left(e \cos \left(d x +c \right)\right)^{3-2 m} \left(a +a \sin \left(d x +c \right)\right)^{m}\, dx"," ",0,"int((e*cos(d*x+c))^(3-2*m)*(a+a*sin(d*x+c))^m,x)","F"
369,0,0,44,2.197000," ","int((e*cos(d*x+c))^(1-2*m)*(a+a*sin(d*x+c))^m,x)","\int \left(e \cos \left(d x +c \right)\right)^{1-2 m} \left(a +a \sin \left(d x +c \right)\right)^{m}\, dx"," ",0,"int((e*cos(d*x+c))^(1-2*m)*(a+a*sin(d*x+c))^m,x)","F"
370,0,0,59,1.332000," ","int((e*cos(d*x+c))^(-1-2*m)*(a+a*sin(d*x+c))^m,x)","\int \left(e \cos \left(d x +c \right)\right)^{-1-2 m} \left(a +a \sin \left(d x +c \right)\right)^{m}\, dx"," ",0,"int((e*cos(d*x+c))^(-1-2*m)*(a+a*sin(d*x+c))^m,x)","F"
371,0,0,68,1.368000," ","int((e*cos(d*x+c))^(-3-2*m)*(a+a*sin(d*x+c))^m,x)","\int \left(e \cos \left(d x +c \right)\right)^{-3-2 m} \left(a +a \sin \left(d x +c \right)\right)^{m}\, dx"," ",0,"int((e*cos(d*x+c))^(-3-2*m)*(a+a*sin(d*x+c))^m,x)","F"
372,0,0,73,1.843000," ","int((e*cos(d*x+c))^(4-2*m)*(a+a*sin(d*x+c))^m,x)","\int \left(e \cos \left(d x +c \right)\right)^{4-2 m} \left(a +a \sin \left(d x +c \right)\right)^{m}\, dx"," ",0,"int((e*cos(d*x+c))^(4-2*m)*(a+a*sin(d*x+c))^m,x)","F"
373,0,0,73,1.711000," ","int((e*cos(d*x+c))^(2-2*m)*(a+a*sin(d*x+c))^m,x)","\int \left(e \cos \left(d x +c \right)\right)^{2-2 m} \left(a +a \sin \left(d x +c \right)\right)^{m}\, dx"," ",0,"int((e*cos(d*x+c))^(2-2*m)*(a+a*sin(d*x+c))^m,x)","F"
374,0,0,72,0.753000," ","int((a+a*sin(d*x+c))^m/((e*cos(d*x+c))^(2*m)),x)","\int \left(a +a \sin \left(d x +c \right)\right)^{m} \left(e \cos \left(d x +c \right)\right)^{-2 m}\, dx"," ",0,"int((a+a*sin(d*x+c))^m/((e*cos(d*x+c))^(2*m)),x)","F"
375,0,0,73,1.287000," ","int((e*cos(d*x+c))^(-2-2*m)*(a+a*sin(d*x+c))^m,x)","\int \left(e \cos \left(d x +c \right)\right)^{-2-2 m} \left(a +a \sin \left(d x +c \right)\right)^{m}\, dx"," ",0,"int((e*cos(d*x+c))^(-2-2*m)*(a+a*sin(d*x+c))^m,x)","F"
376,1,46,54,0.146000," ","int(cos(d*x+c)^5*(a+b*sin(d*x+c)),x)","\frac{-\frac{b \left(\cos^{6}\left(d x +c \right)\right)}{6}+\frac{a \left(\frac{8}{3}+\cos^{4}\left(d x +c \right)+\frac{4 \left(\cos^{2}\left(d x +c \right)\right)}{3}\right) \sin \left(d x +c \right)}{5}}{d}"," ",0,"1/d*(-1/6*b*cos(d*x+c)^6+1/5*a*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c))","A"
377,1,36,40,0.143000," ","int(cos(d*x+c)^3*(a+b*sin(d*x+c)),x)","\frac{-\frac{\left(\cos^{4}\left(d x +c \right)\right) b}{4}+\frac{a \left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{3}}{d}"," ",0,"1/d*(-1/4*cos(d*x+c)^4*b+1/3*a*(2+cos(d*x+c)^2)*sin(d*x+c))","A"
378,1,25,20,0.053000," ","int(cos(d*x+c)*(a+b*sin(d*x+c)),x)","\frac{\frac{\left(\sin^{2}\left(d x +c \right)\right) b}{2}+a \sin \left(d x +c \right)}{d}"," ",0,"1/d*(1/2*sin(d*x+c)^2*b+a*sin(d*x+c))","A"
379,1,34,39,0.099000," ","int(sec(d*x+c)*(a+b*sin(d*x+c)),x)","-\frac{b \ln \left(\cos \left(d x +c \right)\right)}{d}+\frac{a \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}"," ",0,"-1/d*b*ln(cos(d*x+c))+1/d*a*ln(sec(d*x+c)+tan(d*x+c))","A"
380,1,54,37,0.166000," ","int(sec(d*x+c)^3*(a+b*sin(d*x+c)),x)","\frac{a \sec \left(d x +c \right) \tan \left(d x +c \right)}{2 d}+\frac{a \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{2 d}+\frac{b}{2 d \cos \left(d x +c \right)^{2}}"," ",0,"1/2*a*sec(d*x+c)*tan(d*x+c)/d+1/2/d*a*ln(sec(d*x+c)+tan(d*x+c))+1/2/d*b/cos(d*x+c)^2","A"
381,1,74,55,0.168000," ","int(sec(d*x+c)^5*(a+b*sin(d*x+c)),x)","\frac{a \tan \left(d x +c \right) \left(\sec^{3}\left(d x +c \right)\right)}{4 d}+\frac{3 a \sec \left(d x +c \right) \tan \left(d x +c \right)}{8 d}+\frac{3 a \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{8 d}+\frac{b}{4 d \cos \left(d x +c \right)^{4}}"," ",0,"1/4/d*a*tan(d*x+c)*sec(d*x+c)^3+3/8*a*sec(d*x+c)*tan(d*x+c)/d+3/8/d*a*ln(sec(d*x+c)+tan(d*x+c))+1/4/d*b/cos(d*x+c)^4","A"
382,1,52,57,0.149000," ","int(cos(d*x+c)^4*(a+b*sin(d*x+c)),x)","\frac{-\frac{b \left(\cos^{5}\left(d x +c \right)\right)}{5}+a \left(\frac{\left(\cos^{3}\left(d x +c \right)+\frac{3 \cos \left(d x +c \right)}{2}\right) \sin \left(d x +c \right)}{4}+\frac{3 d x}{8}+\frac{3 c}{8}\right)}{d}"," ",0,"1/d*(-1/5*b*cos(d*x+c)^5+a*(1/4*(cos(d*x+c)^3+3/2*cos(d*x+c))*sin(d*x+c)+3/8*d*x+3/8*c))","A"
383,1,41,37,0.087000," ","int(cos(d*x+c)^2*(a+b*sin(d*x+c)),x)","\frac{-\frac{b \left(\cos^{3}\left(d x +c \right)\right)}{3}+a \left(\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)}{2}+\frac{d x}{2}+\frac{c}{2}\right)}{d}"," ",0,"1/d*(-1/3*b*cos(d*x+c)^3+a*(1/2*cos(d*x+c)*sin(d*x+c)+1/2*d*x+1/2*c))","A"
384,1,24,23,0.150000," ","int(sec(d*x+c)^2*(a+b*sin(d*x+c)),x)","\frac{\tan \left(d x +c \right) a +\frac{b}{\cos \left(d x +c \right)}}{d}"," ",0,"1/d*(tan(d*x+c)*a+b/cos(d*x+c))","A"
385,1,38,40,0.159000," ","int(sec(d*x+c)^4*(a+b*sin(d*x+c)),x)","\frac{-a \left(-\frac{2}{3}-\frac{\left(\sec^{2}\left(d x +c \right)\right)}{3}\right) \tan \left(d x +c \right)+\frac{b}{3 \cos \left(d x +c \right)^{3}}}{d}"," ",0,"1/d*(-a*(-2/3-1/3*sec(d*x+c)^2)*tan(d*x+c)+1/3*b/cos(d*x+c)^3)","A"
386,1,48,54,0.160000," ","int(sec(d*x+c)^6*(a+b*sin(d*x+c)),x)","\frac{-a \left(-\frac{8}{15}-\frac{\left(\sec^{4}\left(d x +c \right)\right)}{5}-\frac{4 \left(\sec^{2}\left(d x +c \right)\right)}{15}\right) \tan \left(d x +c \right)+\frac{b}{5 \cos \left(d x +c \right)^{5}}}{d}"," ",0,"1/d*(-a*(-8/15-1/5*sec(d*x+c)^4-4/15*sec(d*x+c)^2)*tan(d*x+c)+1/5*b/cos(d*x+c)^5)","A"
387,1,98,91,0.202000," ","int(cos(d*x+c)^5*(a+b*sin(d*x+c))^2,x)","\frac{b^{2} \left(-\frac{\left(\cos^{6}\left(d x +c \right)\right) \sin \left(d x +c \right)}{7}+\frac{\left(\frac{8}{3}+\cos^{4}\left(d x +c \right)+\frac{4 \left(\cos^{2}\left(d x +c \right)\right)}{3}\right) \sin \left(d x +c \right)}{35}\right)-\frac{a b \left(\cos^{6}\left(d x +c \right)\right)}{3}+\frac{a^{2} \left(\frac{8}{3}+\cos^{4}\left(d x +c \right)+\frac{4 \left(\cos^{2}\left(d x +c \right)\right)}{3}\right) \sin \left(d x +c \right)}{5}}{d}"," ",0,"1/d*(b^2*(-1/7*cos(d*x+c)^6*sin(d*x+c)+1/35*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c))-1/3*a*b*cos(d*x+c)^6+1/5*a^2*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c))","A"
388,1,78,71,0.200000," ","int(cos(d*x+c)^3*(a+b*sin(d*x+c))^2,x)","\frac{b^{2} \left(-\frac{\sin \left(d x +c \right) \left(\cos^{4}\left(d x +c \right)\right)}{5}+\frac{\left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{15}\right)-\frac{a b \left(\cos^{4}\left(d x +c \right)\right)}{2}+\frac{a^{2} \left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{3}}{d}"," ",0,"1/d*(b^2*(-1/5*sin(d*x+c)*cos(d*x+c)^4+1/15*(2+cos(d*x+c)^2)*sin(d*x+c))-1/2*a*b*cos(d*x+c)^4+1/3*a^2*(2+cos(d*x+c)^2)*sin(d*x+c))","A"
389,1,21,20,0.085000," ","int(cos(d*x+c)*(a+b*sin(d*x+c))^2,x)","\frac{\left(a +b \sin \left(d x +c \right)\right)^{3}}{3 b d}"," ",0,"1/3*(a+b*sin(d*x+c))^3/b/d","A"
390,1,72,57,0.145000," ","int(sec(d*x+c)*(a+b*sin(d*x+c))^2,x)","-\frac{b^{2} \sin \left(d x +c \right)}{d}+\frac{a^{2} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{b^{2} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}-\frac{2 a b \ln \left(\cos \left(d x +c \right)\right)}{d}"," ",0,"-b^2*sin(d*x+c)/d+1/d*a^2*ln(sec(d*x+c)+tan(d*x+c))+1/d*b^2*ln(sec(d*x+c)+tan(d*x+c))-2/d*a*b*ln(cos(d*x+c))","A"
391,1,118,55,0.254000," ","int(sec(d*x+c)^3*(a+b*sin(d*x+c))^2,x)","\frac{a^{2} \sec \left(d x +c \right) \tan \left(d x +c \right)}{2 d}+\frac{a^{2} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{2 d}+\frac{a b}{d \cos \left(d x +c \right)^{2}}+\frac{b^{2} \left(\sin^{3}\left(d x +c \right)\right)}{2 d \cos \left(d x +c \right)^{2}}+\frac{b^{2} \sin \left(d x +c \right)}{2 d}-\frac{b^{2} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{2 d}"," ",0,"1/2/d*a^2*sec(d*x+c)*tan(d*x+c)+1/2/d*a^2*ln(sec(d*x+c)+tan(d*x+c))+1/d*a*b/cos(d*x+c)^2+1/2/d*b^2*sin(d*x+c)^3/cos(d*x+c)^2+1/2*b^2*sin(d*x+c)/d-1/2/d*b^2*ln(sec(d*x+c)+tan(d*x+c))","B"
392,1,165,93,0.253000," ","int(sec(d*x+c)^5*(a+b*sin(d*x+c))^2,x)","\frac{a^{2} \tan \left(d x +c \right) \left(\sec^{3}\left(d x +c \right)\right)}{4 d}+\frac{3 a^{2} \sec \left(d x +c \right) \tan \left(d x +c \right)}{8 d}+\frac{3 a^{2} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{8 d}+\frac{a b}{2 d \cos \left(d x +c \right)^{4}}+\frac{b^{2} \left(\sin^{3}\left(d x +c \right)\right)}{4 d \cos \left(d x +c \right)^{4}}+\frac{b^{2} \left(\sin^{3}\left(d x +c \right)\right)}{8 d \cos \left(d x +c \right)^{2}}+\frac{b^{2} \sin \left(d x +c \right)}{8 d}-\frac{b^{2} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{8 d}"," ",0,"1/4/d*a^2*tan(d*x+c)*sec(d*x+c)^3+3/8/d*a^2*sec(d*x+c)*tan(d*x+c)+3/8/d*a^2*ln(sec(d*x+c)+tan(d*x+c))+1/2/d*a*b/cos(d*x+c)^4+1/4/d*b^2*sin(d*x+c)^3/cos(d*x+c)^4+1/8/d*b^2*sin(d*x+c)^3/cos(d*x+c)^2+1/8*b^2*sin(d*x+c)/d-1/8/d*b^2*ln(sec(d*x+c)+tan(d*x+c))","A"
393,1,128,134,0.227000," ","int(cos(d*x+c)^6*(a+b*sin(d*x+c))^2,x)","\frac{b^{2} \left(-\frac{\sin \left(d x +c \right) \left(\cos^{7}\left(d x +c \right)\right)}{8}+\frac{\left(\cos^{5}\left(d x +c \right)+\frac{5 \left(\cos^{3}\left(d x +c \right)\right)}{4}+\frac{15 \cos \left(d x +c \right)}{8}\right) \sin \left(d x +c \right)}{48}+\frac{5 d x}{128}+\frac{5 c}{128}\right)-\frac{2 a b \left(\cos^{7}\left(d x +c \right)\right)}{7}+a^{2} \left(\frac{\left(\cos^{5}\left(d x +c \right)+\frac{5 \left(\cos^{3}\left(d x +c \right)\right)}{4}+\frac{15 \cos \left(d x +c \right)}{8}\right) \sin \left(d x +c \right)}{6}+\frac{5 d x}{16}+\frac{5 c}{16}\right)}{d}"," ",0,"1/d*(b^2*(-1/8*sin(d*x+c)*cos(d*x+c)^7+1/48*(cos(d*x+c)^5+5/4*cos(d*x+c)^3+15/8*cos(d*x+c))*sin(d*x+c)+5/128*d*x+5/128*c)-2/7*a*b*cos(d*x+c)^7+a^2*(1/6*(cos(d*x+c)^5+5/4*cos(d*x+c)^3+15/8*cos(d*x+c))*sin(d*x+c)+5/16*d*x+5/16*c))","A"
394,1,108,106,0.217000," ","int(cos(d*x+c)^4*(a+b*sin(d*x+c))^2,x)","\frac{b^{2} \left(-\frac{\sin \left(d x +c \right) \left(\cos^{5}\left(d x +c \right)\right)}{6}+\frac{\left(\cos^{3}\left(d x +c \right)+\frac{3 \cos \left(d x +c \right)}{2}\right) \sin \left(d x +c \right)}{24}+\frac{d x}{16}+\frac{c}{16}\right)-\frac{2 a b \left(\cos^{5}\left(d x +c \right)\right)}{5}+a^{2} \left(\frac{\left(\cos^{3}\left(d x +c \right)+\frac{3 \cos \left(d x +c \right)}{2}\right) \sin \left(d x +c \right)}{4}+\frac{3 d x}{8}+\frac{3 c}{8}\right)}{d}"," ",0,"1/d*(b^2*(-1/6*sin(d*x+c)*cos(d*x+c)^5+1/24*(cos(d*x+c)^3+3/2*cos(d*x+c))*sin(d*x+c)+1/16*d*x+1/16*c)-2/5*a*b*cos(d*x+c)^5+a^2*(1/4*(cos(d*x+c)^3+3/2*cos(d*x+c))*sin(d*x+c)+3/8*d*x+3/8*c))","A"
395,1,86,78,0.153000," ","int(cos(d*x+c)^2*(a+b*sin(d*x+c))^2,x)","\frac{b^{2} \left(-\frac{\sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right)}{4}+\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)}{8}+\frac{d x}{8}+\frac{c}{8}\right)-\frac{2 a b \left(\cos^{3}\left(d x +c \right)\right)}{3}+a^{2} \left(\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)}{2}+\frac{d x}{2}+\frac{c}{2}\right)}{d}"," ",0,"1/d*(b^2*(-1/4*sin(d*x+c)*cos(d*x+c)^3+1/8*cos(d*x+c)*sin(d*x+c)+1/8*d*x+1/8*c)-2/3*a*b*cos(d*x+c)^3+a^2*(1/2*cos(d*x+c)*sin(d*x+c)+1/2*d*x+1/2*c))","A"
396,1,46,49,0.191000," ","int(sec(d*x+c)^2*(a+b*sin(d*x+c))^2,x)","\frac{a^{2} \tan \left(d x +c \right)+\frac{2 a b}{\cos \left(d x +c \right)}+b^{2} \left(\tan \left(d x +c \right)-d x -c \right)}{d}"," ",0,"1/d*(a^2*tan(d*x+c)+2*a*b/cos(d*x+c)+b^2*(tan(d*x+c)-d*x-c))","A"
397,1,62,69,0.283000," ","int(sec(d*x+c)^4*(a+b*sin(d*x+c))^2,x)","\frac{-a^{2} \left(-\frac{2}{3}-\frac{\left(\sec^{2}\left(d x +c \right)\right)}{3}\right) \tan \left(d x +c \right)+\frac{2 a b}{3 \cos \left(d x +c \right)^{3}}+\frac{b^{2} \left(\sin^{3}\left(d x +c \right)\right)}{3 \cos \left(d x +c \right)^{3}}}{d}"," ",0,"1/d*(-a^2*(-2/3-1/3*sec(d*x+c)^2)*tan(d*x+c)+2/3*a*b/cos(d*x+c)^3+1/3*b^2*sin(d*x+c)^3/cos(d*x+c)^3)","A"
398,1,92,95,0.250000," ","int(sec(d*x+c)^6*(a+b*sin(d*x+c))^2,x)","\frac{-a^{2} \left(-\frac{8}{15}-\frac{\left(\sec^{4}\left(d x +c \right)\right)}{5}-\frac{4 \left(\sec^{2}\left(d x +c \right)\right)}{15}\right) \tan \left(d x +c \right)+\frac{2 a b}{5 \cos \left(d x +c \right)^{5}}+b^{2} \left(\frac{\sin^{3}\left(d x +c \right)}{5 \cos \left(d x +c \right)^{5}}+\frac{2 \left(\sin^{3}\left(d x +c \right)\right)}{15 \cos \left(d x +c \right)^{3}}\right)}{d}"," ",0,"1/d*(-a^2*(-8/15-1/5*sec(d*x+c)^4-4/15*sec(d*x+c)^2)*tan(d*x+c)+2/5*a*b/cos(d*x+c)^5+b^2*(1/5*sin(d*x+c)^3/cos(d*x+c)^5+2/15*sin(d*x+c)^3/cos(d*x+c)^3))","A"
399,1,120,119,0.296000," ","int(sec(d*x+c)^8*(a+b*sin(d*x+c))^2,x)","\frac{-a^{2} \left(-\frac{16}{35}-\frac{\left(\sec^{6}\left(d x +c \right)\right)}{7}-\frac{6 \left(\sec^{4}\left(d x +c \right)\right)}{35}-\frac{8 \left(\sec^{2}\left(d x +c \right)\right)}{35}\right) \tan \left(d x +c \right)+\frac{2 a b}{7 \cos \left(d x +c \right)^{7}}+b^{2} \left(\frac{\sin^{3}\left(d x +c \right)}{7 \cos \left(d x +c \right)^{7}}+\frac{4 \left(\sin^{3}\left(d x +c \right)\right)}{35 \cos \left(d x +c \right)^{5}}+\frac{8 \left(\sin^{3}\left(d x +c \right)\right)}{105 \cos \left(d x +c \right)^{3}}\right)}{d}"," ",0,"1/d*(-a^2*(-16/35-1/7*sec(d*x+c)^6-6/35*sec(d*x+c)^4-8/35*sec(d*x+c)^2)*tan(d*x+c)+2/7*a*b/cos(d*x+c)^7+b^2*(1/7*sin(d*x+c)^3/cos(d*x+c)^7+4/35*sin(d*x+c)^3/cos(d*x+c)^5+8/105*sin(d*x+c)^3/cos(d*x+c)^3))","A"
400,1,135,134,0.233000," ","int(cos(d*x+c)^5*(a+b*sin(d*x+c))^3,x)","\frac{b^{3} \left(-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{6}\left(d x +c \right)\right)}{8}-\frac{\left(\cos^{6}\left(d x +c \right)\right)}{24}\right)+3 a \,b^{2} \left(-\frac{\left(\cos^{6}\left(d x +c \right)\right) \sin \left(d x +c \right)}{7}+\frac{\left(\frac{8}{3}+\cos^{4}\left(d x +c \right)+\frac{4 \left(\cos^{2}\left(d x +c \right)\right)}{3}\right) \sin \left(d x +c \right)}{35}\right)-\frac{a^{2} b \left(\cos^{6}\left(d x +c \right)\right)}{2}+\frac{a^{3} \left(\frac{8}{3}+\cos^{4}\left(d x +c \right)+\frac{4 \left(\cos^{2}\left(d x +c \right)\right)}{3}\right) \sin \left(d x +c \right)}{5}}{d}"," ",0,"1/d*(b^3*(-1/8*sin(d*x+c)^2*cos(d*x+c)^6-1/24*cos(d*x+c)^6)+3*a*b^2*(-1/7*cos(d*x+c)^6*sin(d*x+c)+1/35*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c))-1/2*a^2*b*cos(d*x+c)^6+1/5*a^3*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c))","A"
401,1,115,71,0.230000," ","int(cos(d*x+c)^3*(a+b*sin(d*x+c))^3,x)","\frac{b^{3} \left(-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{4}\left(d x +c \right)\right)}{6}-\frac{\left(\cos^{4}\left(d x +c \right)\right)}{12}\right)+3 a \,b^{2} \left(-\frac{\sin \left(d x +c \right) \left(\cos^{4}\left(d x +c \right)\right)}{5}+\frac{\left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{15}\right)-\frac{3 a^{2} b \left(\cos^{4}\left(d x +c \right)\right)}{4}+\frac{a^{3} \left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{3}}{d}"," ",0,"1/d*(b^3*(-1/6*cos(d*x+c)^4*sin(d*x+c)^2-1/12*cos(d*x+c)^4)+3*a*b^2*(-1/5*sin(d*x+c)*cos(d*x+c)^4+1/15*(2+cos(d*x+c)^2)*sin(d*x+c))-3/4*a^2*b*cos(d*x+c)^4+1/3*a^3*(2+cos(d*x+c)^2)*sin(d*x+c))","A"
402,1,21,20,0.096000," ","int(cos(d*x+c)*(a+b*sin(d*x+c))^3,x)","\frac{\left(a +b \sin \left(d x +c \right)\right)^{4}}{4 b d}"," ",0,"1/4*(a+b*sin(d*x+c))^4/b/d","A"
403,1,108,74,0.184000," ","int(sec(d*x+c)*(a+b*sin(d*x+c))^3,x)","\frac{a^{3} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}-\frac{3 a^{2} b \ln \left(\cos \left(d x +c \right)\right)}{d}-\frac{3 a \,b^{2} \sin \left(d x +c \right)}{d}+\frac{3 a \,b^{2} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}-\frac{b^{3} \left(\sin^{2}\left(d x +c \right)\right)}{2 d}-\frac{b^{3} \ln \left(\cos \left(d x +c \right)\right)}{d}"," ",0,"1/d*a^3*ln(sec(d*x+c)+tan(d*x+c))-3/d*a^2*b*ln(cos(d*x+c))-3*a*b^2*sin(d*x+c)/d+3/d*a*b^2*ln(sec(d*x+c)+tan(d*x+c))-1/2*b^3*sin(d*x+c)^2/d-1/d*b^3*ln(cos(d*x+c))","A"
404,1,154,103,0.285000," ","int(sec(d*x+c)^3*(a+b*sin(d*x+c))^3,x)","\frac{a^{3} \sec \left(d x +c \right) \tan \left(d x +c \right)}{2 d}+\frac{a^{3} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{2 d}+\frac{3 a^{2} b}{2 d \cos \left(d x +c \right)^{2}}+\frac{3 a \,b^{2} \left(\sin^{3}\left(d x +c \right)\right)}{2 d \cos \left(d x +c \right)^{2}}+\frac{3 a \,b^{2} \sin \left(d x +c \right)}{2 d}-\frac{3 a \,b^{2} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{2 d}+\frac{b^{3} \left(\tan^{2}\left(d x +c \right)\right)}{2 d}+\frac{b^{3} \ln \left(\cos \left(d x +c \right)\right)}{d}"," ",0,"1/2/d*a^3*sec(d*x+c)*tan(d*x+c)+1/2/d*a^3*ln(sec(d*x+c)+tan(d*x+c))+3/2/d*a^2*b/cos(d*x+c)^2+3/2/d*a*b^2*sin(d*x+c)^3/cos(d*x+c)^2+3/2*a*b^2*sin(d*x+c)/d-3/2/d*a*b^2*ln(sec(d*x+c)+tan(d*x+c))+1/2/d*b^3*tan(d*x+c)^2+1/d*b^3*ln(cos(d*x+c))","A"
405,1,195,88,0.268000," ","int(sec(d*x+c)^5*(a+b*sin(d*x+c))^3,x)","\frac{a^{3} \tan \left(d x +c \right) \left(\sec^{3}\left(d x +c \right)\right)}{4 d}+\frac{3 a^{3} \sec \left(d x +c \right) \tan \left(d x +c \right)}{8 d}+\frac{3 a^{3} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{8 d}+\frac{3 a^{2} b}{4 d \cos \left(d x +c \right)^{4}}+\frac{3 a \,b^{2} \left(\sin^{3}\left(d x +c \right)\right)}{4 d \cos \left(d x +c \right)^{4}}+\frac{3 a \,b^{2} \left(\sin^{3}\left(d x +c \right)\right)}{8 d \cos \left(d x +c \right)^{2}}+\frac{3 a \,b^{2} \sin \left(d x +c \right)}{8 d}-\frac{3 a \,b^{2} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{8 d}+\frac{b^{3} \left(\sin^{4}\left(d x +c \right)\right)}{4 d \cos \left(d x +c \right)^{4}}"," ",0,"1/4/d*a^3*tan(d*x+c)*sec(d*x+c)^3+3/8/d*a^3*sec(d*x+c)*tan(d*x+c)+3/8/d*a^3*ln(sec(d*x+c)+tan(d*x+c))+3/4/d*a^2*b/cos(d*x+c)^4+3/4/d*a*b^2*sin(d*x+c)^3/cos(d*x+c)^4+3/8/d*a*b^2*sin(d*x+c)^3/cos(d*x+c)^2+3/8*a*b^2*sin(d*x+c)/d-3/8/d*a*b^2*ln(sec(d*x+c)+tan(d*x+c))+1/4/d*b^3*sin(d*x+c)^4/cos(d*x+c)^4","B"
406,1,145,146,0.277000," ","int(cos(d*x+c)^4*(a+b*sin(d*x+c))^3,x)","\frac{b^{3} \left(-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{5}\left(d x +c \right)\right)}{7}-\frac{2 \left(\cos^{5}\left(d x +c \right)\right)}{35}\right)+3 a \,b^{2} \left(-\frac{\sin \left(d x +c \right) \left(\cos^{5}\left(d x +c \right)\right)}{6}+\frac{\left(\cos^{3}\left(d x +c \right)+\frac{3 \cos \left(d x +c \right)}{2}\right) \sin \left(d x +c \right)}{24}+\frac{d x}{16}+\frac{c}{16}\right)-\frac{3 a^{2} b \left(\cos^{5}\left(d x +c \right)\right)}{5}+a^{3} \left(\frac{\left(\cos^{3}\left(d x +c \right)+\frac{3 \cos \left(d x +c \right)}{2}\right) \sin \left(d x +c \right)}{4}+\frac{3 d x}{8}+\frac{3 c}{8}\right)}{d}"," ",0,"1/d*(b^3*(-1/7*sin(d*x+c)^2*cos(d*x+c)^5-2/35*cos(d*x+c)^5)+3*a*b^2*(-1/6*sin(d*x+c)*cos(d*x+c)^5+1/24*(cos(d*x+c)^3+3/2*cos(d*x+c))*sin(d*x+c)+1/16*d*x+1/16*c)-3/5*a^2*b*cos(d*x+c)^5+a^3*(1/4*(cos(d*x+c)^3+3/2*cos(d*x+c))*sin(d*x+c)+3/8*d*x+3/8*c))","A"
407,1,123,121,0.205000," ","int(cos(d*x+c)^2*(a+b*sin(d*x+c))^3,x)","\frac{b^{3} \left(-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{3}\left(d x +c \right)\right)}{5}-\frac{2 \left(\cos^{3}\left(d x +c \right)\right)}{15}\right)+3 a \,b^{2} \left(-\frac{\sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right)}{4}+\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)}{8}+\frac{d x}{8}+\frac{c}{8}\right)-a^{2} b \left(\cos^{3}\left(d x +c \right)\right)+a^{3} \left(\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)}{2}+\frac{d x}{2}+\frac{c}{2}\right)}{d}"," ",0,"1/d*(b^3*(-1/5*sin(d*x+c)^2*cos(d*x+c)^3-2/15*cos(d*x+c)^3)+3*a*b^2*(-1/4*sin(d*x+c)*cos(d*x+c)^3+1/8*cos(d*x+c)*sin(d*x+c)+1/8*d*x+1/8*c)-a^2*b*cos(d*x+c)^3+a^3*(1/2*cos(d*x+c)*sin(d*x+c)+1/2*d*x+1/2*c))","A"
408,1,89,79,0.396000," ","int(sec(d*x+c)^2*(a+b*sin(d*x+c))^3,x)","\frac{a^{3} \tan \left(d x +c \right)+\frac{3 a^{2} b}{\cos \left(d x +c \right)}+3 a \,b^{2} \left(\tan \left(d x +c \right)-d x -c \right)+b^{3} \left(\frac{\sin^{4}\left(d x +c \right)}{\cos \left(d x +c \right)}+\left(2+\sin^{2}\left(d x +c \right)\right) \cos \left(d x +c \right)\right)}{d}"," ",0,"1/d*(a^3*tan(d*x+c)+3*a^2*b/cos(d*x+c)+3*a*b^2*(tan(d*x+c)-d*x-c)+b^3*(sin(d*x+c)^4/cos(d*x+c)+(2+sin(d*x+c)^2)*cos(d*x+c)))","A"
409,1,122,78,0.404000," ","int(sec(d*x+c)^4*(a+b*sin(d*x+c))^3,x)","\frac{-a^{3} \left(-\frac{2}{3}-\frac{\left(\sec^{2}\left(d x +c \right)\right)}{3}\right) \tan \left(d x +c \right)+\frac{a^{2} b}{\cos \left(d x +c \right)^{3}}+\frac{a \,b^{2} \left(\sin^{3}\left(d x +c \right)\right)}{\cos \left(d x +c \right)^{3}}+b^{3} \left(\frac{\sin^{4}\left(d x +c \right)}{3 \cos \left(d x +c \right)^{3}}-\frac{\sin^{4}\left(d x +c \right)}{3 \cos \left(d x +c \right)}-\frac{\left(2+\sin^{2}\left(d x +c \right)\right) \cos \left(d x +c \right)}{3}\right)}{d}"," ",0,"1/d*(-a^3*(-2/3-1/3*sec(d*x+c)^2)*tan(d*x+c)+a^2*b/cos(d*x+c)^3+a*b^2*sin(d*x+c)^3/cos(d*x+c)^3+b^3*(1/3*sin(d*x+c)^4/cos(d*x+c)^3-1/3*sin(d*x+c)^4/cos(d*x+c)-1/3*(2+sin(d*x+c)^2)*cos(d*x+c)))","A"
410,1,173,127,0.318000," ","int(sec(d*x+c)^6*(a+b*sin(d*x+c))^3,x)","\frac{-a^{3} \left(-\frac{8}{15}-\frac{\left(\sec^{4}\left(d x +c \right)\right)}{5}-\frac{4 \left(\sec^{2}\left(d x +c \right)\right)}{15}\right) \tan \left(d x +c \right)+\frac{3 a^{2} b}{5 \cos \left(d x +c \right)^{5}}+3 a \,b^{2} \left(\frac{\sin^{3}\left(d x +c \right)}{5 \cos \left(d x +c \right)^{5}}+\frac{2 \left(\sin^{3}\left(d x +c \right)\right)}{15 \cos \left(d x +c \right)^{3}}\right)+b^{3} \left(\frac{\sin^{4}\left(d x +c \right)}{5 \cos \left(d x +c \right)^{5}}+\frac{\sin^{4}\left(d x +c \right)}{15 \cos \left(d x +c \right)^{3}}-\frac{\sin^{4}\left(d x +c \right)}{15 \cos \left(d x +c \right)}-\frac{\left(2+\sin^{2}\left(d x +c \right)\right) \cos \left(d x +c \right)}{15}\right)}{d}"," ",0,"1/d*(-a^3*(-8/15-1/5*sec(d*x+c)^4-4/15*sec(d*x+c)^2)*tan(d*x+c)+3/5*a^2*b/cos(d*x+c)^5+3*a*b^2*(1/5*sin(d*x+c)^3/cos(d*x+c)^5+2/15*sin(d*x+c)^3/cos(d*x+c)^3)+b^3*(1/5*sin(d*x+c)^4/cos(d*x+c)^5+1/15*sin(d*x+c)^4/cos(d*x+c)^3-1/15*sin(d*x+c)^4/cos(d*x+c)-1/15*(2+sin(d*x+c)^2)*cos(d*x+c)))","A"
411,1,219,155,0.366000," ","int(sec(d*x+c)^8*(a+b*sin(d*x+c))^3,x)","\frac{-a^{3} \left(-\frac{16}{35}-\frac{\left(\sec^{6}\left(d x +c \right)\right)}{7}-\frac{6 \left(\sec^{4}\left(d x +c \right)\right)}{35}-\frac{8 \left(\sec^{2}\left(d x +c \right)\right)}{35}\right) \tan \left(d x +c \right)+\frac{3 a^{2} b}{7 \cos \left(d x +c \right)^{7}}+3 a \,b^{2} \left(\frac{\sin^{3}\left(d x +c \right)}{7 \cos \left(d x +c \right)^{7}}+\frac{4 \left(\sin^{3}\left(d x +c \right)\right)}{35 \cos \left(d x +c \right)^{5}}+\frac{8 \left(\sin^{3}\left(d x +c \right)\right)}{105 \cos \left(d x +c \right)^{3}}\right)+b^{3} \left(\frac{\sin^{4}\left(d x +c \right)}{7 \cos \left(d x +c \right)^{7}}+\frac{3 \left(\sin^{4}\left(d x +c \right)\right)}{35 \cos \left(d x +c \right)^{5}}+\frac{\sin^{4}\left(d x +c \right)}{35 \cos \left(d x +c \right)^{3}}-\frac{\sin^{4}\left(d x +c \right)}{35 \cos \left(d x +c \right)}-\frac{\left(2+\sin^{2}\left(d x +c \right)\right) \cos \left(d x +c \right)}{35}\right)}{d}"," ",0,"1/d*(-a^3*(-16/35-1/7*sec(d*x+c)^6-6/35*sec(d*x+c)^4-8/35*sec(d*x+c)^2)*tan(d*x+c)+3/7*a^2*b/cos(d*x+c)^7+3*a*b^2*(1/7*sin(d*x+c)^3/cos(d*x+c)^7+4/35*sin(d*x+c)^3/cos(d*x+c)^5+8/105*sin(d*x+c)^3/cos(d*x+c)^3)+b^3*(1/7*sin(d*x+c)^4/cos(d*x+c)^7+3/35*sin(d*x+c)^4/cos(d*x+c)^5+1/35*sin(d*x+c)^4/cos(d*x+c)^3-1/35*sin(d*x+c)^4/cos(d*x+c)-1/35*(2+sin(d*x+c)^2)*cos(d*x+c)))","A"
412,1,265,180,0.383000," ","int(sec(d*x+c)^10*(a+b*sin(d*x+c))^3,x)","\frac{-a^{3} \left(-\frac{128}{315}-\frac{\left(\sec^{8}\left(d x +c \right)\right)}{9}-\frac{8 \left(\sec^{6}\left(d x +c \right)\right)}{63}-\frac{16 \left(\sec^{4}\left(d x +c \right)\right)}{105}-\frac{64 \left(\sec^{2}\left(d x +c \right)\right)}{315}\right) \tan \left(d x +c \right)+\frac{a^{2} b}{3 \cos \left(d x +c \right)^{9}}+3 a \,b^{2} \left(\frac{\sin^{3}\left(d x +c \right)}{9 \cos \left(d x +c \right)^{9}}+\frac{2 \left(\sin^{3}\left(d x +c \right)\right)}{21 \cos \left(d x +c \right)^{7}}+\frac{8 \left(\sin^{3}\left(d x +c \right)\right)}{105 \cos \left(d x +c \right)^{5}}+\frac{16 \left(\sin^{3}\left(d x +c \right)\right)}{315 \cos \left(d x +c \right)^{3}}\right)+b^{3} \left(\frac{\sin^{4}\left(d x +c \right)}{9 \cos \left(d x +c \right)^{9}}+\frac{5 \left(\sin^{4}\left(d x +c \right)\right)}{63 \cos \left(d x +c \right)^{7}}+\frac{\sin^{4}\left(d x +c \right)}{21 \cos \left(d x +c \right)^{5}}+\frac{\sin^{4}\left(d x +c \right)}{63 \cos \left(d x +c \right)^{3}}-\frac{\sin^{4}\left(d x +c \right)}{63 \cos \left(d x +c \right)}-\frac{\left(2+\sin^{2}\left(d x +c \right)\right) \cos \left(d x +c \right)}{63}\right)}{d}"," ",0,"1/d*(-a^3*(-128/315-1/9*sec(d*x+c)^8-8/63*sec(d*x+c)^6-16/105*sec(d*x+c)^4-64/315*sec(d*x+c)^2)*tan(d*x+c)+1/3*a^2*b/cos(d*x+c)^9+3*a*b^2*(1/9*sin(d*x+c)^3/cos(d*x+c)^9+2/21*sin(d*x+c)^3/cos(d*x+c)^7+8/105*sin(d*x+c)^3/cos(d*x+c)^5+16/315*sin(d*x+c)^3/cos(d*x+c)^3)+b^3*(1/9*sin(d*x+c)^4/cos(d*x+c)^9+5/63*sin(d*x+c)^4/cos(d*x+c)^7+1/21*sin(d*x+c)^4/cos(d*x+c)^5+1/63*sin(d*x+c)^4/cos(d*x+c)^3-1/63*sin(d*x+c)^4/cos(d*x+c)-1/63*(2+sin(d*x+c)^2)*cos(d*x+c)))","A"
413,1,530,134,0.266000," ","int(cos(d*x+c)^5*(a+b*sin(d*x+c))^8,x)","\frac{b^{8} \left(-\frac{\left(\sin^{7}\left(d x +c \right)\right) \left(\cos^{6}\left(d x +c \right)\right)}{13}-\frac{7 \left(\sin^{5}\left(d x +c \right)\right) \left(\cos^{6}\left(d x +c \right)\right)}{143}-\frac{35 \left(\sin^{3}\left(d x +c \right)\right) \left(\cos^{6}\left(d x +c \right)\right)}{1287}-\frac{5 \left(\cos^{6}\left(d x +c \right)\right) \sin \left(d x +c \right)}{429}+\frac{\left(\frac{8}{3}+\cos^{4}\left(d x +c \right)+\frac{4 \left(\cos^{2}\left(d x +c \right)\right)}{3}\right) \sin \left(d x +c \right)}{429}\right)+8 a \,b^{7} \left(-\frac{\left(\sin^{6}\left(d x +c \right)\right) \left(\cos^{6}\left(d x +c \right)\right)}{12}-\frac{\left(\sin^{4}\left(d x +c \right)\right) \left(\cos^{6}\left(d x +c \right)\right)}{20}-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{6}\left(d x +c \right)\right)}{40}-\frac{\left(\cos^{6}\left(d x +c \right)\right)}{120}\right)+28 a^{2} b^{6} \left(-\frac{\left(\sin^{5}\left(d x +c \right)\right) \left(\cos^{6}\left(d x +c \right)\right)}{11}-\frac{5 \left(\sin^{3}\left(d x +c \right)\right) \left(\cos^{6}\left(d x +c \right)\right)}{99}-\frac{5 \left(\cos^{6}\left(d x +c \right)\right) \sin \left(d x +c \right)}{231}+\frac{\left(\frac{8}{3}+\cos^{4}\left(d x +c \right)+\frac{4 \left(\cos^{2}\left(d x +c \right)\right)}{3}\right) \sin \left(d x +c \right)}{231}\right)+56 a^{3} b^{5} \left(-\frac{\left(\sin^{4}\left(d x +c \right)\right) \left(\cos^{6}\left(d x +c \right)\right)}{10}-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{6}\left(d x +c \right)\right)}{20}-\frac{\left(\cos^{6}\left(d x +c \right)\right)}{60}\right)+70 a^{4} b^{4} \left(-\frac{\left(\sin^{3}\left(d x +c \right)\right) \left(\cos^{6}\left(d x +c \right)\right)}{9}-\frac{\left(\cos^{6}\left(d x +c \right)\right) \sin \left(d x +c \right)}{21}+\frac{\left(\frac{8}{3}+\cos^{4}\left(d x +c \right)+\frac{4 \left(\cos^{2}\left(d x +c \right)\right)}{3}\right) \sin \left(d x +c \right)}{105}\right)+56 a^{5} b^{3} \left(-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{6}\left(d x +c \right)\right)}{8}-\frac{\left(\cos^{6}\left(d x +c \right)\right)}{24}\right)+28 a^{6} b^{2} \left(-\frac{\left(\cos^{6}\left(d x +c \right)\right) \sin \left(d x +c \right)}{7}+\frac{\left(\frac{8}{3}+\cos^{4}\left(d x +c \right)+\frac{4 \left(\cos^{2}\left(d x +c \right)\right)}{3}\right) \sin \left(d x +c \right)}{35}\right)-\frac{4 a^{7} b \left(\cos^{6}\left(d x +c \right)\right)}{3}+\frac{a^{8} \left(\frac{8}{3}+\cos^{4}\left(d x +c \right)+\frac{4 \left(\cos^{2}\left(d x +c \right)\right)}{3}\right) \sin \left(d x +c \right)}{5}}{d}"," ",0,"1/d*(b^8*(-1/13*sin(d*x+c)^7*cos(d*x+c)^6-7/143*sin(d*x+c)^5*cos(d*x+c)^6-35/1287*sin(d*x+c)^3*cos(d*x+c)^6-5/429*cos(d*x+c)^6*sin(d*x+c)+1/429*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c))+8*a*b^7*(-1/12*sin(d*x+c)^6*cos(d*x+c)^6-1/20*sin(d*x+c)^4*cos(d*x+c)^6-1/40*sin(d*x+c)^2*cos(d*x+c)^6-1/120*cos(d*x+c)^6)+28*a^2*b^6*(-1/11*sin(d*x+c)^5*cos(d*x+c)^6-5/99*sin(d*x+c)^3*cos(d*x+c)^6-5/231*cos(d*x+c)^6*sin(d*x+c)+1/231*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c))+56*a^3*b^5*(-1/10*sin(d*x+c)^4*cos(d*x+c)^6-1/20*sin(d*x+c)^2*cos(d*x+c)^6-1/60*cos(d*x+c)^6)+70*a^4*b^4*(-1/9*sin(d*x+c)^3*cos(d*x+c)^6-1/21*cos(d*x+c)^6*sin(d*x+c)+1/105*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c))+56*a^5*b^3*(-1/8*sin(d*x+c)^2*cos(d*x+c)^6-1/24*cos(d*x+c)^6)+28*a^6*b^2*(-1/7*cos(d*x+c)^6*sin(d*x+c)+1/35*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c))-4/3*a^7*b*cos(d*x+c)^6+1/5*a^8*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c))","B"
414,1,480,71,0.257000," ","int(cos(d*x+c)^3*(a+b*sin(d*x+c))^8,x)","\frac{b^{8} \left(-\frac{\left(\sin^{7}\left(d x +c \right)\right) \left(\cos^{4}\left(d x +c \right)\right)}{11}-\frac{7 \left(\sin^{5}\left(d x +c \right)\right) \left(\cos^{4}\left(d x +c \right)\right)}{99}-\frac{5 \left(\sin^{3}\left(d x +c \right)\right) \left(\cos^{4}\left(d x +c \right)\right)}{99}-\frac{\sin \left(d x +c \right) \left(\cos^{4}\left(d x +c \right)\right)}{33}+\frac{\left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{99}\right)+8 a \,b^{7} \left(-\frac{\left(\sin^{6}\left(d x +c \right)\right) \left(\cos^{4}\left(d x +c \right)\right)}{10}-\frac{3 \left(\sin^{4}\left(d x +c \right)\right) \left(\cos^{4}\left(d x +c \right)\right)}{40}-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{4}\left(d x +c \right)\right)}{20}-\frac{\left(\cos^{4}\left(d x +c \right)\right)}{40}\right)+28 a^{2} b^{6} \left(-\frac{\left(\sin^{5}\left(d x +c \right)\right) \left(\cos^{4}\left(d x +c \right)\right)}{9}-\frac{5 \left(\sin^{3}\left(d x +c \right)\right) \left(\cos^{4}\left(d x +c \right)\right)}{63}-\frac{\sin \left(d x +c \right) \left(\cos^{4}\left(d x +c \right)\right)}{21}+\frac{\left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{63}\right)+56 a^{3} b^{5} \left(-\frac{\left(\sin^{4}\left(d x +c \right)\right) \left(\cos^{4}\left(d x +c \right)\right)}{8}-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{4}\left(d x +c \right)\right)}{12}-\frac{\left(\cos^{4}\left(d x +c \right)\right)}{24}\right)+70 a^{4} b^{4} \left(-\frac{\left(\sin^{3}\left(d x +c \right)\right) \left(\cos^{4}\left(d x +c \right)\right)}{7}-\frac{3 \sin \left(d x +c \right) \left(\cos^{4}\left(d x +c \right)\right)}{35}+\frac{\left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{35}\right)+56 a^{5} b^{3} \left(-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{4}\left(d x +c \right)\right)}{6}-\frac{\left(\cos^{4}\left(d x +c \right)\right)}{12}\right)+28 a^{6} b^{2} \left(-\frac{\sin \left(d x +c \right) \left(\cos^{4}\left(d x +c \right)\right)}{5}+\frac{\left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{15}\right)-2 a^{7} b \left(\cos^{4}\left(d x +c \right)\right)+\frac{a^{8} \left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{3}}{d}"," ",0,"1/d*(b^8*(-1/11*sin(d*x+c)^7*cos(d*x+c)^4-7/99*sin(d*x+c)^5*cos(d*x+c)^4-5/99*sin(d*x+c)^3*cos(d*x+c)^4-1/33*sin(d*x+c)*cos(d*x+c)^4+1/99*(2+cos(d*x+c)^2)*sin(d*x+c))+8*a*b^7*(-1/10*sin(d*x+c)^6*cos(d*x+c)^4-3/40*sin(d*x+c)^4*cos(d*x+c)^4-1/20*cos(d*x+c)^4*sin(d*x+c)^2-1/40*cos(d*x+c)^4)+28*a^2*b^6*(-1/9*sin(d*x+c)^5*cos(d*x+c)^4-5/63*sin(d*x+c)^3*cos(d*x+c)^4-1/21*sin(d*x+c)*cos(d*x+c)^4+1/63*(2+cos(d*x+c)^2)*sin(d*x+c))+56*a^3*b^5*(-1/8*sin(d*x+c)^4*cos(d*x+c)^4-1/12*cos(d*x+c)^4*sin(d*x+c)^2-1/24*cos(d*x+c)^4)+70*a^4*b^4*(-1/7*sin(d*x+c)^3*cos(d*x+c)^4-3/35*sin(d*x+c)*cos(d*x+c)^4+1/35*(2+cos(d*x+c)^2)*sin(d*x+c))+56*a^5*b^3*(-1/6*cos(d*x+c)^4*sin(d*x+c)^2-1/12*cos(d*x+c)^4)+28*a^6*b^2*(-1/5*sin(d*x+c)*cos(d*x+c)^4+1/15*(2+cos(d*x+c)^2)*sin(d*x+c))-2*a^7*b*cos(d*x+c)^4+1/3*a^8*(2+cos(d*x+c)^2)*sin(d*x+c))","B"
415,1,21,20,0.109000," ","int(cos(d*x+c)*(a+b*sin(d*x+c))^8,x)","\frac{\left(a +b \sin \left(d x +c \right)\right)^{9}}{9 b d}"," ",0,"1/9*(a+b*sin(d*x+c))^9/b/d","A"
416,1,465,233,0.232000," ","int(sec(d*x+c)*(a+b*sin(d*x+c))^8,x)","-\frac{b^{8} \left(\sin^{7}\left(d x +c \right)\right)}{7 d}-\frac{28 a^{2} b^{6} \left(\sin^{5}\left(d x +c \right)\right)}{5 d}-\frac{28 a^{2} b^{6} \left(\sin^{3}\left(d x +c \right)\right)}{3 d}-\frac{2 a \,b^{7} \left(\sin^{4}\left(d x +c \right)\right)}{d}-\frac{4 a \,b^{7} \left(\sin^{2}\left(d x +c \right)\right)}{d}-\frac{14 a^{3} b^{5} \left(\sin^{4}\left(d x +c \right)\right)}{d}-\frac{28 a^{3} b^{5} \left(\sin^{2}\left(d x +c \right)\right)}{d}-\frac{70 a^{4} b^{4} \left(\sin^{3}\left(d x +c \right)\right)}{3 d}-\frac{28 a^{5} b^{3} \left(\sin^{2}\left(d x +c \right)\right)}{d}-\frac{\sin \left(d x +c \right) b^{8}}{d}+\frac{b^{8} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{a^{8} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}-\frac{28 a^{2} b^{6} \sin \left(d x +c \right)}{d}+\frac{28 a^{2} b^{6} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}-\frac{8 a \,b^{7} \ln \left(\cos \left(d x +c \right)\right)}{d}-\frac{56 a^{3} b^{5} \ln \left(\cos \left(d x +c \right)\right)}{d}-\frac{70 a^{4} b^{4} \sin \left(d x +c \right)}{d}+\frac{70 a^{4} b^{4} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}-\frac{8 a^{7} b \ln \left(\cos \left(d x +c \right)\right)}{d}-\frac{28 a^{6} b^{2} \sin \left(d x +c \right)}{d}+\frac{28 a^{6} b^{2} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}-\frac{56 a^{5} b^{3} \ln \left(\cos \left(d x +c \right)\right)}{d}-\frac{4 a \,b^{7} \left(\sin^{6}\left(d x +c \right)\right)}{3 d}-\frac{b^{8} \left(\sin^{3}\left(d x +c \right)\right)}{3 d}-\frac{b^{8} \left(\sin^{5}\left(d x +c \right)\right)}{5 d}"," ",0,"-4/3*a*b^7*sin(d*x+c)^6/d-1/7*b^8*sin(d*x+c)^7/d-1/d*sin(d*x+c)*b^8-1/5/d*b^8*sin(d*x+c)^5-1/3/d*b^8*sin(d*x+c)^3+1/d*b^8*ln(sec(d*x+c)+tan(d*x+c))+1/d*a^8*ln(sec(d*x+c)+tan(d*x+c))-28/5/d*a^2*b^6*sin(d*x+c)^5-28/3/d*a^2*b^6*sin(d*x+c)^3-28/d*a^2*b^6*sin(d*x+c)+28/d*a^2*b^6*ln(sec(d*x+c)+tan(d*x+c))-2/d*a*b^7*sin(d*x+c)^4-4/d*a*b^7*sin(d*x+c)^2-8/d*a*b^7*ln(cos(d*x+c))-14/d*a^3*b^5*sin(d*x+c)^4-28/d*a^3*b^5*sin(d*x+c)^2-56/d*a^3*b^5*ln(cos(d*x+c))-70/3/d*a^4*b^4*sin(d*x+c)^3-70/d*a^4*b^4*sin(d*x+c)+70/d*a^4*b^4*ln(sec(d*x+c)+tan(d*x+c))-8/d*a^7*b*ln(cos(d*x+c))-28/d*a^6*b^2*sin(d*x+c)+28/d*a^6*b^2*ln(sec(d*x+c)+tan(d*x+c))-28/d*a^5*b^3*sin(d*x+c)^2-56/d*a^5*b^3*ln(cos(d*x+c))","A"
417,1,645,266,0.334000," ","int(sec(d*x+c)^3*(a+b*sin(d*x+c))^8,x)","\frac{b^{8} \left(\sin^{7}\left(d x +c \right)\right)}{2 d}+\frac{14 a^{2} b^{6} \left(\sin^{5}\left(d x +c \right)\right)}{d}+\frac{70 a^{2} b^{6} \left(\sin^{3}\left(d x +c \right)\right)}{3 d}+\frac{6 a \,b^{7} \left(\sin^{4}\left(d x +c \right)\right)}{d}+\frac{12 a \,b^{7} \left(\sin^{2}\left(d x +c \right)\right)}{d}+\frac{28 a^{3} b^{5} \left(\sin^{4}\left(d x +c \right)\right)}{d}+\frac{56 a^{3} b^{5} \left(\sin^{2}\left(d x +c \right)\right)}{d}+\frac{35 a^{4} b^{4} \left(\sin^{3}\left(d x +c \right)\right)}{d}+\frac{7 \sin \left(d x +c \right) b^{8}}{2 d}-\frac{7 b^{8} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{2 d}+\frac{a^{8} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{2 d}+\frac{14 a^{6} b^{2} \left(\sin^{3}\left(d x +c \right)\right)}{d \cos \left(d x +c \right)^{2}}+\frac{35 a^{4} b^{4} \left(\sin^{5}\left(d x +c \right)\right)}{d \cos \left(d x +c \right)^{2}}+\frac{28 a^{3} b^{5} \left(\sin^{6}\left(d x +c \right)\right)}{d \cos \left(d x +c \right)^{2}}+\frac{14 a^{2} b^{6} \left(\sin^{7}\left(d x +c \right)\right)}{d \cos \left(d x +c \right)^{2}}+\frac{70 a^{2} b^{6} \sin \left(d x +c \right)}{d}-\frac{70 a^{2} b^{6} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{24 a \,b^{7} \ln \left(\cos \left(d x +c \right)\right)}{d}+\frac{112 a^{3} b^{5} \ln \left(\cos \left(d x +c \right)\right)}{d}+\frac{105 a^{4} b^{4} \sin \left(d x +c \right)}{d}-\frac{105 a^{4} b^{4} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{14 a^{6} b^{2} \sin \left(d x +c \right)}{d}-\frac{14 a^{6} b^{2} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{56 a^{5} b^{3} \ln \left(\cos \left(d x +c \right)\right)}{d}+\frac{4 a \,b^{7} \left(\sin^{6}\left(d x +c \right)\right)}{d}+\frac{7 b^{8} \left(\sin^{3}\left(d x +c \right)\right)}{6 d}+\frac{7 b^{8} \left(\sin^{5}\left(d x +c \right)\right)}{10 d}+\frac{4 a \,b^{7} \left(\sin^{8}\left(d x +c \right)\right)}{d \cos \left(d x +c \right)^{2}}+\frac{b^{8} \left(\sin^{9}\left(d x +c \right)\right)}{2 d \cos \left(d x +c \right)^{2}}+\frac{28 a^{5} b^{3} \left(\tan^{2}\left(d x +c \right)\right)}{d}+\frac{a^{8} \sec \left(d x +c \right) \tan \left(d x +c \right)}{2 d}+\frac{4 a^{7} b}{d \cos \left(d x +c \right)^{2}}"," ",0,"4*a*b^7*sin(d*x+c)^6/d+1/2*b^8*sin(d*x+c)^7/d+7/2/d*sin(d*x+c)*b^8+7/10/d*b^8*sin(d*x+c)^5+7/6/d*b^8*sin(d*x+c)^3-7/2/d*b^8*ln(sec(d*x+c)+tan(d*x+c))+1/2/d*a^8*ln(sec(d*x+c)+tan(d*x+c))+14/d*a^2*b^6*sin(d*x+c)^5+70/3/d*a^2*b^6*sin(d*x+c)^3+70/d*a^2*b^6*sin(d*x+c)-70/d*a^2*b^6*ln(sec(d*x+c)+tan(d*x+c))+6/d*a*b^7*sin(d*x+c)^4+12/d*a*b^7*sin(d*x+c)^2+24/d*a*b^7*ln(cos(d*x+c))+28/d*a^3*b^5*sin(d*x+c)^4+56/d*a^3*b^5*sin(d*x+c)^2+112/d*a^3*b^5*ln(cos(d*x+c))+35/d*a^4*b^4*sin(d*x+c)^3+105/d*a^4*b^4*sin(d*x+c)-105/d*a^4*b^4*ln(sec(d*x+c)+tan(d*x+c))+14/d*a^6*b^2*sin(d*x+c)-14/d*a^6*b^2*ln(sec(d*x+c)+tan(d*x+c))+56/d*a^5*b^3*ln(cos(d*x+c))+14/d*a^6*b^2*sin(d*x+c)^3/cos(d*x+c)^2+35/d*a^4*b^4*sin(d*x+c)^5/cos(d*x+c)^2+28/d*a^3*b^5*sin(d*x+c)^6/cos(d*x+c)^2+14/d*a^2*b^6*sin(d*x+c)^7/cos(d*x+c)^2+4/d*a*b^7*sin(d*x+c)^8/cos(d*x+c)^2+1/2/d*b^8*sin(d*x+c)^9/cos(d*x+c)^2+1/2/d*a^8*sec(d*x+c)*tan(d*x+c)+4/d*a^7*b/cos(d*x+c)^2+28/d*a^5*b^3*tan(d*x+c)^2","B"
418,1,760,304,0.347000," ","int(sec(d*x+c)^5*(a+b*sin(d*x+c))^8,x)","-\frac{5 b^{8} \left(\sin^{7}\left(d x +c \right)\right)}{8 d}-\frac{21 a^{2} b^{6} \left(\sin^{5}\left(d x +c \right)\right)}{2 d}-\frac{35 a^{2} b^{6} \left(\sin^{3}\left(d x +c \right)\right)}{2 d}-\frac{6 a \,b^{7} \left(\sin^{4}\left(d x +c \right)\right)}{d}-\frac{12 a \,b^{7} \left(\sin^{2}\left(d x +c \right)\right)}{d}-\frac{35 a^{4} b^{4} \left(\sin^{3}\left(d x +c \right)\right)}{4 d}-\frac{35 \sin \left(d x +c \right) b^{8}}{8 d}+\frac{35 b^{8} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{8 d}+\frac{3 a^{8} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{8 d}+\frac{7 a^{6} b^{2} \left(\sin^{3}\left(d x +c \right)\right)}{2 d \cos \left(d x +c \right)^{2}}-\frac{35 a^{4} b^{4} \left(\sin^{5}\left(d x +c \right)\right)}{4 d \cos \left(d x +c \right)^{2}}-\frac{21 a^{2} b^{6} \left(\sin^{7}\left(d x +c \right)\right)}{2 d \cos \left(d x +c \right)^{2}}+\frac{14 a^{5} b^{3} \left(\sin^{4}\left(d x +c \right)\right)}{d \cos \left(d x +c \right)^{4}}+\frac{7 a^{6} b^{2} \left(\sin^{3}\left(d x +c \right)\right)}{d \cos \left(d x +c \right)^{4}}+\frac{35 a^{4} b^{4} \left(\sin^{5}\left(d x +c \right)\right)}{2 d \cos \left(d x +c \right)^{4}}+\frac{7 a^{2} b^{6} \left(\sin^{7}\left(d x +c \right)\right)}{d \cos \left(d x +c \right)^{4}}+\frac{2 a \,b^{7} \left(\sin^{8}\left(d x +c \right)\right)}{d \cos \left(d x +c \right)^{4}}-\frac{105 a^{2} b^{6} \sin \left(d x +c \right)}{2 d}+\frac{105 a^{2} b^{6} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{2 d}-\frac{24 a \,b^{7} \ln \left(\cos \left(d x +c \right)\right)}{d}-\frac{56 a^{3} b^{5} \ln \left(\cos \left(d x +c \right)\right)}{d}-\frac{105 a^{4} b^{4} \sin \left(d x +c \right)}{4 d}+\frac{105 a^{4} b^{4} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{4 d}+\frac{7 a^{6} b^{2} \sin \left(d x +c \right)}{2 d}-\frac{7 a^{6} b^{2} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{2 d}-\frac{4 a \,b^{7} \left(\sin^{6}\left(d x +c \right)\right)}{d}-\frac{35 b^{8} \left(\sin^{3}\left(d x +c \right)\right)}{24 d}-\frac{7 b^{8} \left(\sin^{5}\left(d x +c \right)\right)}{8 d}-\frac{4 a \,b^{7} \left(\sin^{8}\left(d x +c \right)\right)}{d \cos \left(d x +c \right)^{2}}-\frac{28 a^{3} b^{5} \left(\tan^{2}\left(d x +c \right)\right)}{d}+\frac{a^{8} \tan \left(d x +c \right) \left(\sec^{3}\left(d x +c \right)\right)}{4 d}+\frac{b^{8} \left(\sin^{9}\left(d x +c \right)\right)}{4 d \cos \left(d x +c \right)^{4}}+\frac{14 a^{3} b^{5} \left(\tan^{4}\left(d x +c \right)\right)}{d}+\frac{2 a^{7} b}{d \cos \left(d x +c \right)^{4}}-\frac{5 b^{8} \left(\sin^{9}\left(d x +c \right)\right)}{8 d \cos \left(d x +c \right)^{2}}+\frac{3 a^{8} \sec \left(d x +c \right) \tan \left(d x +c \right)}{8 d}"," ",0,"-4*a*b^7*sin(d*x+c)^6/d-5/8*b^8*sin(d*x+c)^7/d-35/8/d*sin(d*x+c)*b^8-7/8/d*b^8*sin(d*x+c)^5-35/24/d*b^8*sin(d*x+c)^3+35/8/d*b^8*ln(sec(d*x+c)+tan(d*x+c))+3/8/d*a^8*ln(sec(d*x+c)+tan(d*x+c))+14/d*a^5*b^3*sin(d*x+c)^4/cos(d*x+c)^4+7/d*a^6*b^2*sin(d*x+c)^3/cos(d*x+c)^4+35/2/d*a^4*b^4*sin(d*x+c)^5/cos(d*x+c)^4+7/d*a^2*b^6*sin(d*x+c)^7/cos(d*x+c)^4+2/d*a*b^7*sin(d*x+c)^8/cos(d*x+c)^4-21/2/d*a^2*b^6*sin(d*x+c)^5-35/2/d*a^2*b^6*sin(d*x+c)^3-105/2/d*a^2*b^6*sin(d*x+c)+105/2/d*a^2*b^6*ln(sec(d*x+c)+tan(d*x+c))-6/d*a*b^7*sin(d*x+c)^4-12/d*a*b^7*sin(d*x+c)^2-24/d*a*b^7*ln(cos(d*x+c))-56/d*a^3*b^5*ln(cos(d*x+c))-35/4/d*a^4*b^4*sin(d*x+c)^3-105/4/d*a^4*b^4*sin(d*x+c)+105/4/d*a^4*b^4*ln(sec(d*x+c)+tan(d*x+c))+7/2/d*a^6*b^2*sin(d*x+c)-7/2/d*a^6*b^2*ln(sec(d*x+c)+tan(d*x+c))+7/2/d*a^6*b^2*sin(d*x+c)^3/cos(d*x+c)^2-35/4/d*a^4*b^4*sin(d*x+c)^5/cos(d*x+c)^2-21/2/d*a^2*b^6*sin(d*x+c)^7/cos(d*x+c)^2-4/d*a*b^7*sin(d*x+c)^8/cos(d*x+c)^2+14/d*a^3*b^5*tan(d*x+c)^4-28/d*a^3*b^5*tan(d*x+c)^2+1/4/d*a^8*tan(d*x+c)*sec(d*x+c)^3+2/d*a^7*b/cos(d*x+c)^4+1/4/d*b^8*sin(d*x+c)^9/cos(d*x+c)^4-5/8/d*b^8*sin(d*x+c)^9/cos(d*x+c)^2+3/8/d*a^8*sec(d*x+c)*tan(d*x+c)","B"
419,1,497,403,0.201000," ","int(cos(d*x+c)^2*(a+b*sin(d*x+c))^8,x)","\frac{b^{8} \left(-\frac{\left(\sin^{7}\left(d x +c \right)\right) \left(\cos^{3}\left(d x +c \right)\right)}{10}-\frac{7 \left(\sin^{5}\left(d x +c \right)\right) \left(\cos^{3}\left(d x +c \right)\right)}{80}-\frac{7 \left(\sin^{3}\left(d x +c \right)\right) \left(\cos^{3}\left(d x +c \right)\right)}{96}-\frac{7 \sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right)}{128}+\frac{7 \cos \left(d x +c \right) \sin \left(d x +c \right)}{256}+\frac{7 d x}{256}+\frac{7 c}{256}\right)+8 a \,b^{7} \left(-\frac{\left(\sin^{6}\left(d x +c \right)\right) \left(\cos^{3}\left(d x +c \right)\right)}{9}-\frac{2 \left(\sin^{4}\left(d x +c \right)\right) \left(\cos^{3}\left(d x +c \right)\right)}{21}-\frac{8 \left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{3}\left(d x +c \right)\right)}{105}-\frac{16 \left(\cos^{3}\left(d x +c \right)\right)}{315}\right)+28 a^{2} b^{6} \left(-\frac{\left(\sin^{5}\left(d x +c \right)\right) \left(\cos^{3}\left(d x +c \right)\right)}{8}-\frac{5 \left(\sin^{3}\left(d x +c \right)\right) \left(\cos^{3}\left(d x +c \right)\right)}{48}-\frac{5 \sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right)}{64}+\frac{5 \cos \left(d x +c \right) \sin \left(d x +c \right)}{128}+\frac{5 d x}{128}+\frac{5 c}{128}\right)+56 a^{3} b^{5} \left(-\frac{\left(\sin^{4}\left(d x +c \right)\right) \left(\cos^{3}\left(d x +c \right)\right)}{7}-\frac{4 \left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{3}\left(d x +c \right)\right)}{35}-\frac{8 \left(\cos^{3}\left(d x +c \right)\right)}{105}\right)+70 a^{4} b^{4} \left(-\frac{\left(\sin^{3}\left(d x +c \right)\right) \left(\cos^{3}\left(d x +c \right)\right)}{6}-\frac{\sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right)}{8}+\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)}{16}+\frac{d x}{16}+\frac{c}{16}\right)+56 a^{5} b^{3} \left(-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{3}\left(d x +c \right)\right)}{5}-\frac{2 \left(\cos^{3}\left(d x +c \right)\right)}{15}\right)+28 a^{6} b^{2} \left(-\frac{\sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right)}{4}+\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)}{8}+\frac{d x}{8}+\frac{c}{8}\right)-\frac{8 a^{7} b \left(\cos^{3}\left(d x +c \right)\right)}{3}+a^{8} \left(\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)}{2}+\frac{d x}{2}+\frac{c}{2}\right)}{d}"," ",0,"1/d*(b^8*(-1/10*sin(d*x+c)^7*cos(d*x+c)^3-7/80*sin(d*x+c)^5*cos(d*x+c)^3-7/96*sin(d*x+c)^3*cos(d*x+c)^3-7/128*sin(d*x+c)*cos(d*x+c)^3+7/256*cos(d*x+c)*sin(d*x+c)+7/256*d*x+7/256*c)+8*a*b^7*(-1/9*sin(d*x+c)^6*cos(d*x+c)^3-2/21*sin(d*x+c)^4*cos(d*x+c)^3-8/105*sin(d*x+c)^2*cos(d*x+c)^3-16/315*cos(d*x+c)^3)+28*a^2*b^6*(-1/8*sin(d*x+c)^5*cos(d*x+c)^3-5/48*sin(d*x+c)^3*cos(d*x+c)^3-5/64*sin(d*x+c)*cos(d*x+c)^3+5/128*cos(d*x+c)*sin(d*x+c)+5/128*d*x+5/128*c)+56*a^3*b^5*(-1/7*sin(d*x+c)^4*cos(d*x+c)^3-4/35*sin(d*x+c)^2*cos(d*x+c)^3-8/105*cos(d*x+c)^3)+70*a^4*b^4*(-1/6*sin(d*x+c)^3*cos(d*x+c)^3-1/8*sin(d*x+c)*cos(d*x+c)^3+1/16*cos(d*x+c)*sin(d*x+c)+1/16*d*x+1/16*c)+56*a^5*b^3*(-1/5*sin(d*x+c)^2*cos(d*x+c)^3-2/15*cos(d*x+c)^3)+28*a^6*b^2*(-1/4*sin(d*x+c)*cos(d*x+c)^3+1/8*cos(d*x+c)*sin(d*x+c)+1/8*d*x+1/8*c)-8/3*a^7*b*cos(d*x+c)^3+a^8*(1/2*cos(d*x+c)*sin(d*x+c)+1/2*d*x+1/2*c))","A"
420,1,406,335,0.422000," ","int(sec(d*x+c)^2*(a+b*sin(d*x+c))^8,x)","\frac{a^{8} \tan \left(d x +c \right)+\frac{8 a^{7} b}{\cos \left(d x +c \right)}+28 a^{6} b^{2} \left(\tan \left(d x +c \right)-d x -c \right)+56 a^{5} b^{3} \left(\frac{\sin^{4}\left(d x +c \right)}{\cos \left(d x +c \right)}+\left(2+\sin^{2}\left(d x +c \right)\right) \cos \left(d x +c \right)\right)+70 a^{4} b^{4} \left(\frac{\sin^{5}\left(d x +c \right)}{\cos \left(d x +c \right)}+\left(\sin^{3}\left(d x +c \right)+\frac{3 \sin \left(d x +c \right)}{2}\right) \cos \left(d x +c \right)-\frac{3 d x}{2}-\frac{3 c}{2}\right)+56 a^{3} b^{5} \left(\frac{\sin^{6}\left(d x +c \right)}{\cos \left(d x +c \right)}+\left(\frac{8}{3}+\sin^{4}\left(d x +c \right)+\frac{4 \left(\sin^{2}\left(d x +c \right)\right)}{3}\right) \cos \left(d x +c \right)\right)+28 a^{2} b^{6} \left(\frac{\sin^{7}\left(d x +c \right)}{\cos \left(d x +c \right)}+\left(\sin^{5}\left(d x +c \right)+\frac{5 \left(\sin^{3}\left(d x +c \right)\right)}{4}+\frac{15 \sin \left(d x +c \right)}{8}\right) \cos \left(d x +c \right)-\frac{15 d x}{8}-\frac{15 c}{8}\right)+8 a \,b^{7} \left(\frac{\sin^{8}\left(d x +c \right)}{\cos \left(d x +c \right)}+\left(\frac{16}{5}+\sin^{6}\left(d x +c \right)+\frac{6 \left(\sin^{4}\left(d x +c \right)\right)}{5}+\frac{8 \left(\sin^{2}\left(d x +c \right)\right)}{5}\right) \cos \left(d x +c \right)\right)+b^{8} \left(\frac{\sin^{9}\left(d x +c \right)}{\cos \left(d x +c \right)}+\left(\sin^{7}\left(d x +c \right)+\frac{7 \left(\sin^{5}\left(d x +c \right)\right)}{6}+\frac{35 \left(\sin^{3}\left(d x +c \right)\right)}{24}+\frac{35 \sin \left(d x +c \right)}{16}\right) \cos \left(d x +c \right)-\frac{35 d x}{16}-\frac{35 c}{16}\right)}{d}"," ",0,"1/d*(a^8*tan(d*x+c)+8*a^7*b/cos(d*x+c)+28*a^6*b^2*(tan(d*x+c)-d*x-c)+56*a^5*b^3*(sin(d*x+c)^4/cos(d*x+c)+(2+sin(d*x+c)^2)*cos(d*x+c))+70*a^4*b^4*(sin(d*x+c)^5/cos(d*x+c)+(sin(d*x+c)^3+3/2*sin(d*x+c))*cos(d*x+c)-3/2*d*x-3/2*c)+56*a^3*b^5*(sin(d*x+c)^6/cos(d*x+c)+(8/3+sin(d*x+c)^4+4/3*sin(d*x+c)^2)*cos(d*x+c))+28*a^2*b^6*(sin(d*x+c)^7/cos(d*x+c)+(sin(d*x+c)^5+5/4*sin(d*x+c)^3+15/8*sin(d*x+c))*cos(d*x+c)-15/8*d*x-15/8*c)+8*a*b^7*(sin(d*x+c)^8/cos(d*x+c)+(16/5+sin(d*x+c)^6+6/5*sin(d*x+c)^4+8/5*sin(d*x+c)^2)*cos(d*x+c))+b^8*(sin(d*x+c)^9/cos(d*x+c)+(sin(d*x+c)^7+7/6*sin(d*x+c)^5+35/24*sin(d*x+c)^3+35/16*sin(d*x+c))*cos(d*x+c)-35/16*d*x-35/16*c))","A"
421,1,495,351,0.457000," ","int(sec(d*x+c)^4*(a+b*sin(d*x+c))^8,x)","\frac{-a^{8} \left(-\frac{2}{3}-\frac{\left(\sec^{2}\left(d x +c \right)\right)}{3}\right) \tan \left(d x +c \right)+\frac{8 a^{7} b}{3 \cos \left(d x +c \right)^{3}}+\frac{28 a^{6} b^{2} \left(\sin^{3}\left(d x +c \right)\right)}{3 \cos \left(d x +c \right)^{3}}+56 a^{5} b^{3} \left(\frac{\sin^{4}\left(d x +c \right)}{3 \cos \left(d x +c \right)^{3}}-\frac{\sin^{4}\left(d x +c \right)}{3 \cos \left(d x +c \right)}-\frac{\left(2+\sin^{2}\left(d x +c \right)\right) \cos \left(d x +c \right)}{3}\right)+70 a^{4} b^{4} \left(\frac{\left(\tan^{3}\left(d x +c \right)\right)}{3}-\tan \left(d x +c \right)+d x +c \right)+56 a^{3} b^{5} \left(\frac{\sin^{6}\left(d x +c \right)}{3 \cos \left(d x +c \right)^{3}}-\frac{\sin^{6}\left(d x +c \right)}{\cos \left(d x +c \right)}-\left(\frac{8}{3}+\sin^{4}\left(d x +c \right)+\frac{4 \left(\sin^{2}\left(d x +c \right)\right)}{3}\right) \cos \left(d x +c \right)\right)+28 a^{2} b^{6} \left(\frac{\sin^{7}\left(d x +c \right)}{3 \cos \left(d x +c \right)^{3}}-\frac{4 \left(\sin^{7}\left(d x +c \right)\right)}{3 \cos \left(d x +c \right)}-\frac{4 \left(\sin^{5}\left(d x +c \right)+\frac{5 \left(\sin^{3}\left(d x +c \right)\right)}{4}+\frac{15 \sin \left(d x +c \right)}{8}\right) \cos \left(d x +c \right)}{3}+\frac{5 d x}{2}+\frac{5 c}{2}\right)+8 a \,b^{7} \left(\frac{\sin^{8}\left(d x +c \right)}{3 \cos \left(d x +c \right)^{3}}-\frac{5 \left(\sin^{8}\left(d x +c \right)\right)}{3 \cos \left(d x +c \right)}-\frac{5 \left(\frac{16}{5}+\sin^{6}\left(d x +c \right)+\frac{6 \left(\sin^{4}\left(d x +c \right)\right)}{5}+\frac{8 \left(\sin^{2}\left(d x +c \right)\right)}{5}\right) \cos \left(d x +c \right)}{3}\right)+b^{8} \left(\frac{\sin^{9}\left(d x +c \right)}{3 \cos \left(d x +c \right)^{3}}-\frac{2 \left(\sin^{9}\left(d x +c \right)\right)}{\cos \left(d x +c \right)}-2 \left(\sin^{7}\left(d x +c \right)+\frac{7 \left(\sin^{5}\left(d x +c \right)\right)}{6}+\frac{35 \left(\sin^{3}\left(d x +c \right)\right)}{24}+\frac{35 \sin \left(d x +c \right)}{16}\right) \cos \left(d x +c \right)+\frac{35 d x}{8}+\frac{35 c}{8}\right)}{d}"," ",0,"1/d*(-a^8*(-2/3-1/3*sec(d*x+c)^2)*tan(d*x+c)+8/3*a^7*b/cos(d*x+c)^3+28/3*a^6*b^2*sin(d*x+c)^3/cos(d*x+c)^3+56*a^5*b^3*(1/3*sin(d*x+c)^4/cos(d*x+c)^3-1/3*sin(d*x+c)^4/cos(d*x+c)-1/3*(2+sin(d*x+c)^2)*cos(d*x+c))+70*a^4*b^4*(1/3*tan(d*x+c)^3-tan(d*x+c)+d*x+c)+56*a^3*b^5*(1/3*sin(d*x+c)^6/cos(d*x+c)^3-sin(d*x+c)^6/cos(d*x+c)-(8/3+sin(d*x+c)^4+4/3*sin(d*x+c)^2)*cos(d*x+c))+28*a^2*b^6*(1/3*sin(d*x+c)^7/cos(d*x+c)^3-4/3*sin(d*x+c)^7/cos(d*x+c)-4/3*(sin(d*x+c)^5+5/4*sin(d*x+c)^3+15/8*sin(d*x+c))*cos(d*x+c)+5/2*d*x+5/2*c)+8*a*b^7*(1/3*sin(d*x+c)^8/cos(d*x+c)^3-5/3*sin(d*x+c)^8/cos(d*x+c)-5/3*(16/5+sin(d*x+c)^6+6/5*sin(d*x+c)^4+8/5*sin(d*x+c)^2)*cos(d*x+c))+b^8*(1/3*sin(d*x+c)^9/cos(d*x+c)^3-2*sin(d*x+c)^9/cos(d*x+c)-2*(sin(d*x+c)^7+7/6*sin(d*x+c)^5+35/24*sin(d*x+c)^3+35/16*sin(d*x+c))*cos(d*x+c)+35/8*d*x+35/8*c))","A"
422,1,544,363,0.523000," ","int(sec(d*x+c)^6*(a+b*sin(d*x+c))^8,x)","\frac{-a^{8} \left(-\frac{8}{15}-\frac{\left(\sec^{4}\left(d x +c \right)\right)}{5}-\frac{4 \left(\sec^{2}\left(d x +c \right)\right)}{15}\right) \tan \left(d x +c \right)+\frac{8 a^{7} b}{5 \cos \left(d x +c \right)^{5}}+28 a^{6} b^{2} \left(\frac{\sin^{3}\left(d x +c \right)}{5 \cos \left(d x +c \right)^{5}}+\frac{2 \left(\sin^{3}\left(d x +c \right)\right)}{15 \cos \left(d x +c \right)^{3}}\right)+56 a^{5} b^{3} \left(\frac{\sin^{4}\left(d x +c \right)}{5 \cos \left(d x +c \right)^{5}}+\frac{\sin^{4}\left(d x +c \right)}{15 \cos \left(d x +c \right)^{3}}-\frac{\sin^{4}\left(d x +c \right)}{15 \cos \left(d x +c \right)}-\frac{\left(2+\sin^{2}\left(d x +c \right)\right) \cos \left(d x +c \right)}{15}\right)+\frac{14 a^{4} b^{4} \left(\sin^{5}\left(d x +c \right)\right)}{\cos \left(d x +c \right)^{5}}+56 a^{3} b^{5} \left(\frac{\sin^{6}\left(d x +c \right)}{5 \cos \left(d x +c \right)^{5}}-\frac{\sin^{6}\left(d x +c \right)}{15 \cos \left(d x +c \right)^{3}}+\frac{\sin^{6}\left(d x +c \right)}{5 \cos \left(d x +c \right)}+\frac{\left(\frac{8}{3}+\sin^{4}\left(d x +c \right)+\frac{4 \left(\sin^{2}\left(d x +c \right)\right)}{3}\right) \cos \left(d x +c \right)}{5}\right)+28 a^{2} b^{6} \left(\frac{\left(\tan^{5}\left(d x +c \right)\right)}{5}-\frac{\left(\tan^{3}\left(d x +c \right)\right)}{3}+\tan \left(d x +c \right)-d x -c \right)+8 a \,b^{7} \left(\frac{\sin^{8}\left(d x +c \right)}{5 \cos \left(d x +c \right)^{5}}-\frac{\sin^{8}\left(d x +c \right)}{5 \cos \left(d x +c \right)^{3}}+\frac{\sin^{8}\left(d x +c \right)}{\cos \left(d x +c \right)}+\left(\frac{16}{5}+\sin^{6}\left(d x +c \right)+\frac{6 \left(\sin^{4}\left(d x +c \right)\right)}{5}+\frac{8 \left(\sin^{2}\left(d x +c \right)\right)}{5}\right) \cos \left(d x +c \right)\right)+b^{8} \left(\frac{\sin^{9}\left(d x +c \right)}{5 \cos \left(d x +c \right)^{5}}-\frac{4 \left(\sin^{9}\left(d x +c \right)\right)}{15 \cos \left(d x +c \right)^{3}}+\frac{8 \left(\sin^{9}\left(d x +c \right)\right)}{5 \cos \left(d x +c \right)}+\frac{8 \left(\sin^{7}\left(d x +c \right)+\frac{7 \left(\sin^{5}\left(d x +c \right)\right)}{6}+\frac{35 \left(\sin^{3}\left(d x +c \right)\right)}{24}+\frac{35 \sin \left(d x +c \right)}{16}\right) \cos \left(d x +c \right)}{5}-\frac{7 d x}{2}-\frac{7 c}{2}\right)}{d}"," ",0,"1/d*(-a^8*(-8/15-1/5*sec(d*x+c)^4-4/15*sec(d*x+c)^2)*tan(d*x+c)+8/5*a^7*b/cos(d*x+c)^5+28*a^6*b^2*(1/5*sin(d*x+c)^3/cos(d*x+c)^5+2/15*sin(d*x+c)^3/cos(d*x+c)^3)+56*a^5*b^3*(1/5*sin(d*x+c)^4/cos(d*x+c)^5+1/15*sin(d*x+c)^4/cos(d*x+c)^3-1/15*sin(d*x+c)^4/cos(d*x+c)-1/15*(2+sin(d*x+c)^2)*cos(d*x+c))+14*a^4*b^4*sin(d*x+c)^5/cos(d*x+c)^5+56*a^3*b^5*(1/5*sin(d*x+c)^6/cos(d*x+c)^5-1/15*sin(d*x+c)^6/cos(d*x+c)^3+1/5*sin(d*x+c)^6/cos(d*x+c)+1/5*(8/3+sin(d*x+c)^4+4/3*sin(d*x+c)^2)*cos(d*x+c))+28*a^2*b^6*(1/5*tan(d*x+c)^5-1/3*tan(d*x+c)^3+tan(d*x+c)-d*x-c)+8*a*b^7*(1/5*sin(d*x+c)^8/cos(d*x+c)^5-1/5*sin(d*x+c)^8/cos(d*x+c)^3+sin(d*x+c)^8/cos(d*x+c)+(16/5+sin(d*x+c)^6+6/5*sin(d*x+c)^4+8/5*sin(d*x+c)^2)*cos(d*x+c))+b^8*(1/5*sin(d*x+c)^9/cos(d*x+c)^5-4/15*sin(d*x+c)^9/cos(d*x+c)^3+8/5*sin(d*x+c)^9/cos(d*x+c)+8/5*(sin(d*x+c)^7+7/6*sin(d*x+c)^5+35/24*sin(d*x+c)^3+35/16*sin(d*x+c))*cos(d*x+c)-7/2*d*x-7/2*c))","A"
423,1,567,388,0.410000," ","int(sec(d*x+c)^8*(a+b*sin(d*x+c))^8,x)","\frac{-a^{8} \left(-\frac{16}{35}-\frac{\left(\sec^{6}\left(d x +c \right)\right)}{7}-\frac{6 \left(\sec^{4}\left(d x +c \right)\right)}{35}-\frac{8 \left(\sec^{2}\left(d x +c \right)\right)}{35}\right) \tan \left(d x +c \right)+\frac{8 a^{7} b}{7 \cos \left(d x +c \right)^{7}}+28 a^{6} b^{2} \left(\frac{\sin^{3}\left(d x +c \right)}{7 \cos \left(d x +c \right)^{7}}+\frac{4 \left(\sin^{3}\left(d x +c \right)\right)}{35 \cos \left(d x +c \right)^{5}}+\frac{8 \left(\sin^{3}\left(d x +c \right)\right)}{105 \cos \left(d x +c \right)^{3}}\right)+56 a^{5} b^{3} \left(\frac{\sin^{4}\left(d x +c \right)}{7 \cos \left(d x +c \right)^{7}}+\frac{3 \left(\sin^{4}\left(d x +c \right)\right)}{35 \cos \left(d x +c \right)^{5}}+\frac{\sin^{4}\left(d x +c \right)}{35 \cos \left(d x +c \right)^{3}}-\frac{\sin^{4}\left(d x +c \right)}{35 \cos \left(d x +c \right)}-\frac{\left(2+\sin^{2}\left(d x +c \right)\right) \cos \left(d x +c \right)}{35}\right)+70 a^{4} b^{4} \left(\frac{\sin^{5}\left(d x +c \right)}{7 \cos \left(d x +c \right)^{7}}+\frac{2 \left(\sin^{5}\left(d x +c \right)\right)}{35 \cos \left(d x +c \right)^{5}}\right)+56 a^{3} b^{5} \left(\frac{\sin^{6}\left(d x +c \right)}{7 \cos \left(d x +c \right)^{7}}+\frac{\sin^{6}\left(d x +c \right)}{35 \cos \left(d x +c \right)^{5}}-\frac{\sin^{6}\left(d x +c \right)}{105 \cos \left(d x +c \right)^{3}}+\frac{\sin^{6}\left(d x +c \right)}{35 \cos \left(d x +c \right)}+\frac{\left(\frac{8}{3}+\sin^{4}\left(d x +c \right)+\frac{4 \left(\sin^{2}\left(d x +c \right)\right)}{3}\right) \cos \left(d x +c \right)}{35}\right)+\frac{4 a^{2} b^{6} \left(\sin^{7}\left(d x +c \right)\right)}{\cos \left(d x +c \right)^{7}}+8 a \,b^{7} \left(\frac{\sin^{8}\left(d x +c \right)}{7 \cos \left(d x +c \right)^{7}}-\frac{\sin^{8}\left(d x +c \right)}{35 \cos \left(d x +c \right)^{5}}+\frac{\sin^{8}\left(d x +c \right)}{35 \cos \left(d x +c \right)^{3}}-\frac{\sin^{8}\left(d x +c \right)}{7 \cos \left(d x +c \right)}-\frac{\left(\frac{16}{5}+\sin^{6}\left(d x +c \right)+\frac{6 \left(\sin^{4}\left(d x +c \right)\right)}{5}+\frac{8 \left(\sin^{2}\left(d x +c \right)\right)}{5}\right) \cos \left(d x +c \right)}{7}\right)+b^{8} \left(\frac{\left(\tan^{7}\left(d x +c \right)\right)}{7}-\frac{\left(\tan^{5}\left(d x +c \right)\right)}{5}+\frac{\left(\tan^{3}\left(d x +c \right)\right)}{3}-\tan \left(d x +c \right)+d x +c \right)}{d}"," ",0,"1/d*(-a^8*(-16/35-1/7*sec(d*x+c)^6-6/35*sec(d*x+c)^4-8/35*sec(d*x+c)^2)*tan(d*x+c)+8/7*a^7*b/cos(d*x+c)^7+28*a^6*b^2*(1/7*sin(d*x+c)^3/cos(d*x+c)^7+4/35*sin(d*x+c)^3/cos(d*x+c)^5+8/105*sin(d*x+c)^3/cos(d*x+c)^3)+56*a^5*b^3*(1/7*sin(d*x+c)^4/cos(d*x+c)^7+3/35*sin(d*x+c)^4/cos(d*x+c)^5+1/35*sin(d*x+c)^4/cos(d*x+c)^3-1/35*sin(d*x+c)^4/cos(d*x+c)-1/35*(2+sin(d*x+c)^2)*cos(d*x+c))+70*a^4*b^4*(1/7*sin(d*x+c)^5/cos(d*x+c)^7+2/35*sin(d*x+c)^5/cos(d*x+c)^5)+56*a^3*b^5*(1/7*sin(d*x+c)^6/cos(d*x+c)^7+1/35*sin(d*x+c)^6/cos(d*x+c)^5-1/105*sin(d*x+c)^6/cos(d*x+c)^3+1/35*sin(d*x+c)^6/cos(d*x+c)+1/35*(8/3+sin(d*x+c)^4+4/3*sin(d*x+c)^2)*cos(d*x+c))+4*a^2*b^6*sin(d*x+c)^7/cos(d*x+c)^7+8*a*b^7*(1/7*sin(d*x+c)^8/cos(d*x+c)^7-1/35*sin(d*x+c)^8/cos(d*x+c)^5+1/35*sin(d*x+c)^8/cos(d*x+c)^3-1/7*sin(d*x+c)^8/cos(d*x+c)-1/7*(16/5+sin(d*x+c)^6+6/5*sin(d*x+c)^4+8/5*sin(d*x+c)^2)*cos(d*x+c))+b^8*(1/7*tan(d*x+c)^7-1/5*tan(d*x+c)^5+1/3*tan(d*x+c)^3-tan(d*x+c)+d*x+c))","A"
424,1,662,224,0.395000," ","int(sec(d*x+c)^10*(a+b*sin(d*x+c))^8,x)","\frac{-a^{8} \left(-\frac{128}{315}-\frac{\left(\sec^{8}\left(d x +c \right)\right)}{9}-\frac{8 \left(\sec^{6}\left(d x +c \right)\right)}{63}-\frac{16 \left(\sec^{4}\left(d x +c \right)\right)}{105}-\frac{64 \left(\sec^{2}\left(d x +c \right)\right)}{315}\right) \tan \left(d x +c \right)+\frac{8 a^{7} b}{9 \cos \left(d x +c \right)^{9}}+28 a^{6} b^{2} \left(\frac{\sin^{3}\left(d x +c \right)}{9 \cos \left(d x +c \right)^{9}}+\frac{2 \left(\sin^{3}\left(d x +c \right)\right)}{21 \cos \left(d x +c \right)^{7}}+\frac{8 \left(\sin^{3}\left(d x +c \right)\right)}{105 \cos \left(d x +c \right)^{5}}+\frac{16 \left(\sin^{3}\left(d x +c \right)\right)}{315 \cos \left(d x +c \right)^{3}}\right)+56 a^{5} b^{3} \left(\frac{\sin^{4}\left(d x +c \right)}{9 \cos \left(d x +c \right)^{9}}+\frac{5 \left(\sin^{4}\left(d x +c \right)\right)}{63 \cos \left(d x +c \right)^{7}}+\frac{\sin^{4}\left(d x +c \right)}{21 \cos \left(d x +c \right)^{5}}+\frac{\sin^{4}\left(d x +c \right)}{63 \cos \left(d x +c \right)^{3}}-\frac{\sin^{4}\left(d x +c \right)}{63 \cos \left(d x +c \right)}-\frac{\left(2+\sin^{2}\left(d x +c \right)\right) \cos \left(d x +c \right)}{63}\right)+70 a^{4} b^{4} \left(\frac{\sin^{5}\left(d x +c \right)}{9 \cos \left(d x +c \right)^{9}}+\frac{4 \left(\sin^{5}\left(d x +c \right)\right)}{63 \cos \left(d x +c \right)^{7}}+\frac{8 \left(\sin^{5}\left(d x +c \right)\right)}{315 \cos \left(d x +c \right)^{5}}\right)+56 a^{3} b^{5} \left(\frac{\sin^{6}\left(d x +c \right)}{9 \cos \left(d x +c \right)^{9}}+\frac{\sin^{6}\left(d x +c \right)}{21 \cos \left(d x +c \right)^{7}}+\frac{\sin^{6}\left(d x +c \right)}{105 \cos \left(d x +c \right)^{5}}-\frac{\sin^{6}\left(d x +c \right)}{315 \cos \left(d x +c \right)^{3}}+\frac{\sin^{6}\left(d x +c \right)}{105 \cos \left(d x +c \right)}+\frac{\left(\frac{8}{3}+\sin^{4}\left(d x +c \right)+\frac{4 \left(\sin^{2}\left(d x +c \right)\right)}{3}\right) \cos \left(d x +c \right)}{105}\right)+28 a^{2} b^{6} \left(\frac{\sin^{7}\left(d x +c \right)}{9 \cos \left(d x +c \right)^{9}}+\frac{2 \left(\sin^{7}\left(d x +c \right)\right)}{63 \cos \left(d x +c \right)^{7}}\right)+8 a \,b^{7} \left(\frac{\sin^{8}\left(d x +c \right)}{9 \cos \left(d x +c \right)^{9}}+\frac{\sin^{8}\left(d x +c \right)}{63 \cos \left(d x +c \right)^{7}}-\frac{\sin^{8}\left(d x +c \right)}{315 \cos \left(d x +c \right)^{5}}+\frac{\sin^{8}\left(d x +c \right)}{315 \cos \left(d x +c \right)^{3}}-\frac{\sin^{8}\left(d x +c \right)}{63 \cos \left(d x +c \right)}-\frac{\left(\frac{16}{5}+\sin^{6}\left(d x +c \right)+\frac{6 \left(\sin^{4}\left(d x +c \right)\right)}{5}+\frac{8 \left(\sin^{2}\left(d x +c \right)\right)}{5}\right) \cos \left(d x +c \right)}{63}\right)+\frac{b^{8} \left(\sin^{9}\left(d x +c \right)\right)}{9 \cos \left(d x +c \right)^{9}}}{d}"," ",0,"1/d*(-a^8*(-128/315-1/9*sec(d*x+c)^8-8/63*sec(d*x+c)^6-16/105*sec(d*x+c)^4-64/315*sec(d*x+c)^2)*tan(d*x+c)+8/9*a^7*b/cos(d*x+c)^9+28*a^6*b^2*(1/9*sin(d*x+c)^3/cos(d*x+c)^9+2/21*sin(d*x+c)^3/cos(d*x+c)^7+8/105*sin(d*x+c)^3/cos(d*x+c)^5+16/315*sin(d*x+c)^3/cos(d*x+c)^3)+56*a^5*b^3*(1/9*sin(d*x+c)^4/cos(d*x+c)^9+5/63*sin(d*x+c)^4/cos(d*x+c)^7+1/21*sin(d*x+c)^4/cos(d*x+c)^5+1/63*sin(d*x+c)^4/cos(d*x+c)^3-1/63*sin(d*x+c)^4/cos(d*x+c)-1/63*(2+sin(d*x+c)^2)*cos(d*x+c))+70*a^4*b^4*(1/9*sin(d*x+c)^5/cos(d*x+c)^9+4/63*sin(d*x+c)^5/cos(d*x+c)^7+8/315*sin(d*x+c)^5/cos(d*x+c)^5)+56*a^3*b^5*(1/9*sin(d*x+c)^6/cos(d*x+c)^9+1/21*sin(d*x+c)^6/cos(d*x+c)^7+1/105*sin(d*x+c)^6/cos(d*x+c)^5-1/315*sin(d*x+c)^6/cos(d*x+c)^3+1/105*sin(d*x+c)^6/cos(d*x+c)+1/105*(8/3+sin(d*x+c)^4+4/3*sin(d*x+c)^2)*cos(d*x+c))+28*a^2*b^6*(1/9*sin(d*x+c)^7/cos(d*x+c)^9+2/63*sin(d*x+c)^7/cos(d*x+c)^7)+8*a*b^7*(1/9*sin(d*x+c)^8/cos(d*x+c)^9+1/63*sin(d*x+c)^8/cos(d*x+c)^7-1/315*sin(d*x+c)^8/cos(d*x+c)^5+1/315*sin(d*x+c)^8/cos(d*x+c)^3-1/63*sin(d*x+c)^8/cos(d*x+c)-1/63*(16/5+sin(d*x+c)^6+6/5*sin(d*x+c)^4+8/5*sin(d*x+c)^2)*cos(d*x+c))+1/9*b^8*sin(d*x+c)^9/cos(d*x+c)^9)","B"
425,1,163,112,0.147000," ","int(cos(d*x+c)^5/(a+b*sin(d*x+c)),x)","\frac{\sin^{4}\left(d x +c \right)}{4 b d}-\frac{a \left(\sin^{3}\left(d x +c \right)\right)}{3 b^{2} d}+\frac{\left(\sin^{2}\left(d x +c \right)\right) a^{2}}{2 d \,b^{3}}-\frac{\sin^{2}\left(d x +c \right)}{b d}-\frac{a^{3} \sin \left(d x +c \right)}{d \,b^{4}}+\frac{2 a \sin \left(d x +c \right)}{b^{2} d}+\frac{\ln \left(a +b \sin \left(d x +c \right)\right) a^{4}}{d \,b^{5}}-\frac{2 \ln \left(a +b \sin \left(d x +c \right)\right) a^{2}}{d \,b^{3}}+\frac{\ln \left(a +b \sin \left(d x +c \right)\right)}{b d}"," ",0,"1/4*sin(d*x+c)^4/b/d-1/3*a*sin(d*x+c)^3/b^2/d+1/2/d/b^3*sin(d*x+c)^2*a^2-sin(d*x+c)^2/b/d-1/d/b^4*a^3*sin(d*x+c)+2*a*sin(d*x+c)/b^2/d+1/d/b^5*ln(a+b*sin(d*x+c))*a^4-2/d/b^3*ln(a+b*sin(d*x+c))*a^2+ln(a+b*sin(d*x+c))/b/d","A"
426,1,72,59,0.144000," ","int(cos(d*x+c)^3/(a+b*sin(d*x+c)),x)","-\frac{\sin^{2}\left(d x +c \right)}{2 b d}+\frac{a \sin \left(d x +c \right)}{b^{2} d}-\frac{\ln \left(a +b \sin \left(d x +c \right)\right) a^{2}}{d \,b^{3}}+\frac{\ln \left(a +b \sin \left(d x +c \right)\right)}{b d}"," ",0,"-1/2*sin(d*x+c)^2/b/d+a*sin(d*x+c)/b^2/d-1/d/b^3*ln(a+b*sin(d*x+c))*a^2+ln(a+b*sin(d*x+c))/b/d","A"
427,1,19,18,0.085000," ","int(cos(d*x+c)/(a+b*sin(d*x+c)),x)","\frac{\ln \left(a +b \sin \left(d x +c \right)\right)}{b d}"," ",0,"ln(a+b*sin(d*x+c))/b/d","A"
428,1,76,71,0.149000," ","int(sec(d*x+c)/(a+b*sin(d*x+c)),x)","-\frac{\ln \left(\sin \left(d x +c \right)-1\right)}{d \left(2 a +2 b \right)}-\frac{b \ln \left(a +b \sin \left(d x +c \right)\right)}{d \left(a +b \right) \left(a -b \right)}+\frac{\ln \left(1+\sin \left(d x +c \right)\right)}{d \left(2 a -2 b \right)}"," ",0,"-1/d/(2*a+2*b)*ln(sin(d*x+c)-1)-1/d*b/(a+b)/(a-b)*ln(a+b*sin(d*x+c))+1/d/(2*a-2*b)*ln(1+sin(d*x+c))","A"
429,1,164,117,0.181000," ","int(sec(d*x+c)^3/(a+b*sin(d*x+c)),x)","-\frac{1}{d \left(4 a +4 b \right) \left(\sin \left(d x +c \right)-1\right)}-\frac{\ln \left(\sin \left(d x +c \right)-1\right) a}{4 d \left(a +b \right)^{2}}-\frac{\ln \left(\sin \left(d x +c \right)-1\right) b}{2 d \left(a +b \right)^{2}}+\frac{b^{3} \ln \left(a +b \sin \left(d x +c \right)\right)}{d \left(a +b \right)^{2} \left(a -b \right)^{2}}-\frac{1}{d \left(4 a -4 b \right) \left(1+\sin \left(d x +c \right)\right)}+\frac{\ln \left(1+\sin \left(d x +c \right)\right) a}{4 d \left(a -b \right)^{2}}-\frac{\ln \left(1+\sin \left(d x +c \right)\right) b}{2 d \left(a -b \right)^{2}}"," ",0,"-1/d/(4*a+4*b)/(sin(d*x+c)-1)-1/4/d/(a+b)^2*ln(sin(d*x+c)-1)*a-1/2/d/(a+b)^2*ln(sin(d*x+c)-1)*b+1/d*b^3/(a+b)^2/(a-b)^2*ln(a+b*sin(d*x+c))-1/d/(4*a-4*b)/(1+sin(d*x+c))+1/4/d/(a-b)^2*ln(1+sin(d*x+c))*a-1/2/d/(a-b)^2*ln(1+sin(d*x+c))*b","A"
430,1,305,187,0.179000," ","int(sec(d*x+c)^5/(a+b*sin(d*x+c)),x)","\frac{1}{2 d \left(8 a +8 b \right) \left(\sin \left(d x +c \right)-1\right)^{2}}-\frac{3 a}{16 d \left(a +b \right)^{2} \left(\sin \left(d x +c \right)-1\right)}-\frac{5 b}{16 d \left(a +b \right)^{2} \left(\sin \left(d x +c \right)-1\right)}-\frac{3 \ln \left(\sin \left(d x +c \right)-1\right) a^{2}}{16 d \left(a +b \right)^{3}}-\frac{9 \ln \left(\sin \left(d x +c \right)-1\right) a b}{16 d \left(a +b \right)^{3}}-\frac{\ln \left(\sin \left(d x +c \right)-1\right) b^{2}}{2 d \left(a +b \right)^{3}}-\frac{b^{5} \ln \left(a +b \sin \left(d x +c \right)\right)}{d \left(a +b \right)^{3} \left(a -b \right)^{3}}-\frac{1}{2 d \left(8 a -8 b \right) \left(1+\sin \left(d x +c \right)\right)^{2}}-\frac{3 a}{16 d \left(a -b \right)^{2} \left(1+\sin \left(d x +c \right)\right)}+\frac{5 b}{16 d \left(a -b \right)^{2} \left(1+\sin \left(d x +c \right)\right)}+\frac{3 \ln \left(1+\sin \left(d x +c \right)\right) a^{2}}{16 d \left(a -b \right)^{3}}-\frac{9 \ln \left(1+\sin \left(d x +c \right)\right) a b}{16 d \left(a -b \right)^{3}}+\frac{\ln \left(1+\sin \left(d x +c \right)\right) b^{2}}{2 d \left(a -b \right)^{3}}"," ",0,"1/2/d/(8*a+8*b)/(sin(d*x+c)-1)^2-3/16/d/(a+b)^2/(sin(d*x+c)-1)*a-5/16/d/(a+b)^2/(sin(d*x+c)-1)*b-3/16/d/(a+b)^3*ln(sin(d*x+c)-1)*a^2-9/16/d/(a+b)^3*ln(sin(d*x+c)-1)*a*b-1/2/d/(a+b)^3*ln(sin(d*x+c)-1)*b^2-1/d*b^5/(a+b)^3/(a-b)^3*ln(a+b*sin(d*x+c))-1/2/d/(8*a-8*b)/(1+sin(d*x+c))^2-3/16/d/(a-b)^2/(1+sin(d*x+c))*a+5/16/d/(a-b)^2/(1+sin(d*x+c))*b+3/16/d/(a-b)^3*ln(1+sin(d*x+c))*a^2-9/16/d/(a-b)^3*ln(1+sin(d*x+c))*a*b+1/2/d/(a-b)^3*ln(1+sin(d*x+c))*b^2","A"
431,1,1055,174,0.164000," ","int(cos(d*x+c)^6/(a+b*sin(d*x+c)),x)","-\frac{9 \left(\tan^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a}{4 d \,b^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}+\frac{15 a \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 d \,b^{2}}+\frac{2 \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \sqrt{a^{2}-b^{2}}}+\frac{12 \left(\tan^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d b \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}+\frac{2 a^{4}}{d \,b^{5} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}+\frac{28 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 d b \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}-\frac{14 a^{2}}{3 d \,b^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}+\frac{56 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 d b \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}+\frac{6 \left(\tan^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d b \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}+\frac{46}{15 d b \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}-\frac{2 \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right) a^{6}}{d \,b^{6} \sqrt{a^{2}-b^{2}}}+\frac{6 \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right) a^{4}}{d \,b^{4} \sqrt{a^{2}-b^{2}}}+\frac{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{5}}{d \,b^{6}}-\frac{5 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{3}}{d \,b^{4}}+\frac{8 \left(\tan^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{4}}{d \,b^{5} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}-\frac{6 \left(\tan^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{2}}{d \,b^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}+\frac{2 \left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{3}}{d \,b^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}-\frac{6 \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right) a^{2}}{d \,b^{2} \sqrt{a^{2}-b^{2}}}+\frac{12 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{4}}{d \,b^{5} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}+\frac{2 \left(\tan^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{4}}{d \,b^{5} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}-\frac{80 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{2}}{3 d \,b^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}-\frac{2 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{3}}{d \,b^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}-\frac{5 \left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a}{2 d \,b^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}-\frac{20 \left(\tan^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{2}}{d \,b^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}+\frac{5 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a}{2 d \,b^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}+\frac{8 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{4}}{d \,b^{5} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}-\frac{52 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{2}}{3 d \,b^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}-\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) a^{3}}{d \,b^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}+\frac{9 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) a}{4 d \,b^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}+\frac{\left(\tan^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{3}}{d \,b^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}"," ",0,"15/4/d/b^2*a*arctan(tan(1/2*d*x+1/2*c))+2/d/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))+12/d/b^5/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^4*a^4-80/3/d/b^3/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^4*a^2-2/d/b^4/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^3*a^3+5/2/d/b^2/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^3*a+8/d/b^5/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^2*a^4-52/3/d/b^3/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^2*a^2-1/d/b^4/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)*a^3+9/4/d/b^2/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)*a+1/d/b^4/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^9*a^3-9/4/d/b^2/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^9*a+2/d/b^5/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^8*a^4+8/d/b^5/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^6*a^4-6/d/b^3/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^8*a^2+2/d/b^4/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^7*a^3-5/2/d/b^2/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^7*a-20/d/b^3/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^6*a^2-2/d/b^6/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))*a^6+6/d/b^4/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))*a^4+12/d/b/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^6+2/d/b^5/(1+tan(1/2*d*x+1/2*c)^2)^5*a^4+2/d/b^6*arctan(tan(1/2*d*x+1/2*c))*a^5+28/3/d/b/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^2-5/d/b^4*arctan(tan(1/2*d*x+1/2*c))*a^3-14/3/d/b^3/(1+tan(1/2*d*x+1/2*c)^2)^5*a^2+56/3/d/b/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^4-6/d/b^2/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))*a^2+46/15/d/b/(1+tan(1/2*d*x+1/2*c)^2)^5+6/d/b/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^8","B"
432,1,450,115,0.148000," ","int(cos(d*x+c)^4/(a+b*sin(d*x+c)),x)","-\frac{a \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,b^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}-\frac{2 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{2}}{d \,b^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}+\frac{4 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d b \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}-\frac{4 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{2}}{d \,b^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}+\frac{4 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d b \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}+\frac{a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,b^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}-\frac{2 a^{2}}{d \,b^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}+\frac{8}{3 d b \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}-\frac{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{3}}{d \,b^{4}}+\frac{3 a \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,b^{2}}+\frac{2 \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right) a^{4}}{d \,b^{4} \sqrt{a^{2}-b^{2}}}-\frac{4 \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right) a^{2}}{d \,b^{2} \sqrt{a^{2}-b^{2}}}+\frac{2 \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \sqrt{a^{2}-b^{2}}}"," ",0,"-1/d/b^2/(1+tan(1/2*d*x+1/2*c)^2)^3*a*tan(1/2*d*x+1/2*c)^5-2/d/b^3/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)^4*a^2+4/d/b/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)^4-4/d/b^3/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)^2*a^2+4/d/b/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)^2+1/d/b^2/(1+tan(1/2*d*x+1/2*c)^2)^3*a*tan(1/2*d*x+1/2*c)-2/d/b^3/(1+tan(1/2*d*x+1/2*c)^2)^3*a^2+8/3/d/b/(1+tan(1/2*d*x+1/2*c)^2)^3-2/d/b^4*arctan(tan(1/2*d*x+1/2*c))*a^3+3/d/b^2*a*arctan(tan(1/2*d*x+1/2*c))+2/d/b^4/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))*a^4-4/d/b^2/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))*a^2+2/d/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))","B"
433,1,142,65,0.145000," ","int(cos(d*x+c)^2/(a+b*sin(d*x+c)),x)","-\frac{2 \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right) a^{2}}{d \,b^{2} \sqrt{a^{2}-b^{2}}}+\frac{2 \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \sqrt{a^{2}-b^{2}}}+\frac{2}{d b \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}+\frac{2 a \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,b^{2}}"," ",0,"-2/d/b^2/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))*a^2+2/d/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))+2/d/b/(1+tan(1/2*d*x+1/2*c)^2)+2/d/b^2*a*arctan(tan(1/2*d*x+1/2*c))","B"
434,1,117,79,0.157000," ","int(sec(d*x+c)^2/(a+b*sin(d*x+c)),x)","-\frac{2}{d \left(2 a +2 b \right) \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{2}{d \left(2 a -2 b \right) \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}-\frac{2 b^{2} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \left(a -b \right) \left(a +b \right) \sqrt{a^{2}-b^{2}}}"," ",0,"-2/d/(2*a+2*b)/(tan(1/2*d*x+1/2*c)-1)-2/d/(2*a-2*b)/(tan(1/2*d*x+1/2*c)+1)-2/d*b^2/(a-b)/(a+b)/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))","A"
435,1,270,128,0.188000," ","int(sec(d*x+c)^4/(a+b*sin(d*x+c)),x)","-\frac{2}{3 d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{3} \left(2 a +2 b \right)}-\frac{1}{d \left(2 a +2 b \right) \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}-\frac{a}{d \left(a +b \right)^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{3 b}{2 d \left(a +b \right)^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}+\frac{2 b^{4} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \left(a -b \right)^{2} \left(a +b \right)^{2} \sqrt{a^{2}-b^{2}}}-\frac{2}{3 d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3} \left(2 a -2 b \right)}+\frac{1}{d \left(2 a -2 b \right) \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}-\frac{a}{d \left(a -b \right)^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}+\frac{3 b}{2 d \left(a -b \right)^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}"," ",0,"-2/3/d/(tan(1/2*d*x+1/2*c)-1)^3/(2*a+2*b)-1/d/(2*a+2*b)/(tan(1/2*d*x+1/2*c)-1)^2-1/d/(a+b)^2/(tan(1/2*d*x+1/2*c)-1)*a-3/2/d/(a+b)^2/(tan(1/2*d*x+1/2*c)-1)*b+2/d*b^4/(a-b)^2/(a+b)^2/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))-2/3/d/(tan(1/2*d*x+1/2*c)+1)^3/(2*a-2*b)+1/d/(2*a-2*b)/(tan(1/2*d*x+1/2*c)+1)^2-1/d/(a-b)^2/(tan(1/2*d*x+1/2*c)+1)*a+3/2/d/(a-b)^2/(tan(1/2*d*x+1/2*c)+1)*b","B"
436,1,525,186,0.184000," ","int(sec(d*x+c)^6/(a+b*sin(d*x+c)),x)","-\frac{2}{5 d \left(2 a +2 b \right) \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{5}}-\frac{1}{2 d \left(a +b \right) \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{4}}-\frac{7 a}{8 d \left(a +b \right)^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}-\frac{9 b}{8 d \left(a +b \right)^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}-\frac{11 a}{12 d \left(a +b \right)^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{3}}-\frac{13 b}{12 d \left(a +b \right)^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{3}}-\frac{a^{2}}{d \left(a +b \right)^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{21 a b}{8 d \left(a +b \right)^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{15 b^{2}}{8 d \left(a +b \right)^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{2 b^{6} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \left(a -b \right)^{3} \left(a +b \right)^{3} \sqrt{a^{2}-b^{2}}}-\frac{2}{5 d \left(2 a -2 b \right) \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{5}}+\frac{1}{2 d \left(a -b \right) \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{4}}+\frac{7 a}{8 d \left(a -b \right)^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}-\frac{9 b}{8 d \left(a -b \right)^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}-\frac{11 a}{12 d \left(a -b \right)^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}+\frac{13 b}{12 d \left(a -b \right)^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}-\frac{a^{2}}{d \left(a -b \right)^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}+\frac{21 a b}{8 d \left(a -b \right)^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}-\frac{15 b^{2}}{8 d \left(a -b \right)^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}"," ",0,"-2/5/d/(2*a+2*b)/(tan(1/2*d*x+1/2*c)-1)^5-1/2/d/(a+b)/(tan(1/2*d*x+1/2*c)-1)^4-7/8/d/(a+b)^2/(tan(1/2*d*x+1/2*c)-1)^2*a-9/8/d/(a+b)^2/(tan(1/2*d*x+1/2*c)-1)^2*b-11/12/d/(a+b)^2/(tan(1/2*d*x+1/2*c)-1)^3*a-13/12/d/(a+b)^2/(tan(1/2*d*x+1/2*c)-1)^3*b-1/d/(a+b)^3/(tan(1/2*d*x+1/2*c)-1)*a^2-21/8/d/(a+b)^3/(tan(1/2*d*x+1/2*c)-1)*a*b-15/8/d/(a+b)^3/(tan(1/2*d*x+1/2*c)-1)*b^2-2/d*b^6/(a-b)^3/(a+b)^3/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))-2/5/d/(2*a-2*b)/(tan(1/2*d*x+1/2*c)+1)^5+1/2/d/(a-b)/(tan(1/2*d*x+1/2*c)+1)^4+7/8/d/(a-b)^2/(tan(1/2*d*x+1/2*c)+1)^2*a-9/8/d/(a-b)^2/(tan(1/2*d*x+1/2*c)+1)^2*b-11/12/d/(a-b)^2/(tan(1/2*d*x+1/2*c)+1)^3*a+13/12/d/(a-b)^2/(tan(1/2*d*x+1/2*c)+1)^3*b-1/d/(a-b)^3/(tan(1/2*d*x+1/2*c)+1)*a^2+21/8/d/(a-b)^3/(tan(1/2*d*x+1/2*c)+1)*a*b-15/8/d/(a-b)^3/(tan(1/2*d*x+1/2*c)+1)*b^2","B"
437,1,305,180,0.246000," ","int(cos(d*x+c)^7/(a+b*sin(d*x+c))^2,x)","-\frac{\sin^{5}\left(d x +c \right)}{5 b^{2} d}+\frac{a \left(\sin^{4}\left(d x +c \right)\right)}{2 b^{3} d}-\frac{\left(\sin^{3}\left(d x +c \right)\right) a^{2}}{d \,b^{4}}+\frac{\sin^{3}\left(d x +c \right)}{b^{2} d}+\frac{2 \left(\sin^{2}\left(d x +c \right)\right) a^{3}}{d \,b^{5}}-\frac{3 a \left(\sin^{2}\left(d x +c \right)\right)}{b^{3} d}-\frac{5 a^{4} \sin \left(d x +c \right)}{d \,b^{6}}+\frac{9 a^{2} \sin \left(d x +c \right)}{d \,b^{4}}-\frac{3 \sin \left(d x +c \right)}{b^{2} d}+\frac{6 a^{5} \ln \left(a +b \sin \left(d x +c \right)\right)}{d \,b^{7}}-\frac{12 a^{3} \ln \left(a +b \sin \left(d x +c \right)\right)}{d \,b^{5}}+\frac{6 a \ln \left(a +b \sin \left(d x +c \right)\right)}{b^{3} d}+\frac{a^{6}}{d \,b^{7} \left(a +b \sin \left(d x +c \right)\right)}-\frac{3 a^{4}}{d \,b^{5} \left(a +b \sin \left(d x +c \right)\right)}+\frac{3 a^{2}}{d \,b^{3} \left(a +b \sin \left(d x +c \right)\right)}-\frac{1}{b d \left(a +b \sin \left(d x +c \right)\right)}"," ",0,"-1/5*sin(d*x+c)^5/b^2/d+1/2*a*sin(d*x+c)^4/b^3/d-1/d/b^4*sin(d*x+c)^3*a^2+sin(d*x+c)^3/b^2/d+2/d/b^5*sin(d*x+c)^2*a^3-3*a*sin(d*x+c)^2/b^3/d-5/d/b^6*a^4*sin(d*x+c)+9/d/b^4*a^2*sin(d*x+c)-3*sin(d*x+c)/b^2/d+6/d*a^5/b^7*ln(a+b*sin(d*x+c))-12/d*a^3/b^5*ln(a+b*sin(d*x+c))+6*a*ln(a+b*sin(d*x+c))/b^3/d+1/d/b^7/(a+b*sin(d*x+c))*a^6-3/d/b^5/(a+b*sin(d*x+c))*a^4+3/d/b^3/(a+b*sin(d*x+c))*a^2-1/b/d/(a+b*sin(d*x+c))","A"
438,1,174,118,0.252000," ","int(cos(d*x+c)^5/(a+b*sin(d*x+c))^2,x)","\frac{\sin^{3}\left(d x +c \right)}{3 b^{2} d}-\frac{a \left(\sin^{2}\left(d x +c \right)\right)}{b^{3} d}+\frac{3 a^{2} \sin \left(d x +c \right)}{d \,b^{4}}-\frac{2 \sin \left(d x +c \right)}{b^{2} d}-\frac{4 a^{3} \ln \left(a +b \sin \left(d x +c \right)\right)}{d \,b^{5}}+\frac{4 a \ln \left(a +b \sin \left(d x +c \right)\right)}{b^{3} d}-\frac{a^{4}}{d \,b^{5} \left(a +b \sin \left(d x +c \right)\right)}+\frac{2 a^{2}}{d \,b^{3} \left(a +b \sin \left(d x +c \right)\right)}-\frac{1}{b d \left(a +b \sin \left(d x +c \right)\right)}"," ",0,"1/3*sin(d*x+c)^3/b^2/d-a*sin(d*x+c)^2/b^3/d+3/d/b^4*a^2*sin(d*x+c)-2*sin(d*x+c)/b^2/d-4/d*a^3/b^5*ln(a+b*sin(d*x+c))+4*a*ln(a+b*sin(d*x+c))/b^3/d-1/d/b^5/(a+b*sin(d*x+c))*a^4+2/d/b^3/(a+b*sin(d*x+c))*a^2-1/b/d/(a+b*sin(d*x+c))","A"
439,1,78,63,0.239000," ","int(cos(d*x+c)^3/(a+b*sin(d*x+c))^2,x)","-\frac{\sin \left(d x +c \right)}{b^{2} d}+\frac{2 a \ln \left(a +b \sin \left(d x +c \right)\right)}{b^{3} d}+\frac{a^{2}}{d \,b^{3} \left(a +b \sin \left(d x +c \right)\right)}-\frac{1}{b d \left(a +b \sin \left(d x +c \right)\right)}"," ",0,"-sin(d*x+c)/b^2/d+2*a*ln(a+b*sin(d*x+c))/b^3/d+1/d/b^3/(a+b*sin(d*x+c))*a^2-1/b/d/(a+b*sin(d*x+c))","A"
440,1,21,20,0.127000," ","int(cos(d*x+c)/(a+b*sin(d*x+c))^2,x)","-\frac{1}{b d \left(a +b \sin \left(d x +c \right)\right)}"," ",0,"-1/b/d/(a+b*sin(d*x+c))","A"
441,1,101,100,0.265000," ","int(sec(d*x+c)/(a+b*sin(d*x+c))^2,x)","-\frac{\ln \left(\sin \left(d x +c \right)-1\right)}{2 d \left(a +b \right)^{2}}+\frac{b}{d \left(a +b \right) \left(a -b \right) \left(a +b \sin \left(d x +c \right)\right)}-\frac{2 a b \ln \left(a +b \sin \left(d x +c \right)\right)}{d \left(a +b \right)^{2} \left(a -b \right)^{2}}+\frac{\ln \left(1+\sin \left(d x +c \right)\right)}{2 \left(a -b \right)^{2} d}"," ",0,"-1/2/d/(a+b)^2*ln(sin(d*x+c)-1)+1/d*b/(a+b)/(a-b)/(a+b*sin(d*x+c))-2/d*a*b/(a+b)^2/(a-b)^2*ln(a+b*sin(d*x+c))+1/2*ln(1+sin(d*x+c))/(a-b)^2/d","A"
442,1,192,169,0.325000," ","int(sec(d*x+c)^3/(a+b*sin(d*x+c))^2,x)","-\frac{1}{4 d \left(a +b \right)^{2} \left(\sin \left(d x +c \right)-1\right)}-\frac{\ln \left(\sin \left(d x +c \right)-1\right) a}{4 d \left(a +b \right)^{3}}-\frac{3 \ln \left(\sin \left(d x +c \right)-1\right) b}{4 d \left(a +b \right)^{3}}-\frac{b^{3}}{d \left(a +b \right)^{2} \left(a -b \right)^{2} \left(a +b \sin \left(d x +c \right)\right)}+\frac{4 b^{3} a \ln \left(a +b \sin \left(d x +c \right)\right)}{d \left(a +b \right)^{3} \left(a -b \right)^{3}}-\frac{1}{4 d \left(a -b \right)^{2} \left(1+\sin \left(d x +c \right)\right)}+\frac{\ln \left(1+\sin \left(d x +c \right)\right) a}{4 d \left(a -b \right)^{3}}-\frac{3 \ln \left(1+\sin \left(d x +c \right)\right) b}{4 d \left(a -b \right)^{3}}"," ",0,"-1/4/d/(a+b)^2/(sin(d*x+c)-1)-1/4/d/(a+b)^3*ln(sin(d*x+c)-1)*a-3/4/d/(a+b)^3*ln(sin(d*x+c)-1)*b-1/d*b^3/(a+b)^2/(a-b)^2/(a+b*sin(d*x+c))+4/d*b^3*a/(a+b)^3/(a-b)^3*ln(a+b*sin(d*x+c))-1/4/d/(a-b)^2/(1+sin(d*x+c))+1/4/d/(a-b)^3*ln(1+sin(d*x+c))*a-3/4/d/(a-b)^3*ln(1+sin(d*x+c))*b","A"
443,1,331,259,0.309000," ","int(sec(d*x+c)^5/(a+b*sin(d*x+c))^2,x)","\frac{1}{16 d \left(a +b \right)^{2} \left(\sin \left(d x +c \right)-1\right)^{2}}-\frac{7 b}{16 d \left(a +b \right)^{3} \left(\sin \left(d x +c \right)-1\right)}-\frac{3 a}{16 d \left(a +b \right)^{3} \left(\sin \left(d x +c \right)-1\right)}-\frac{3 \ln \left(\sin \left(d x +c \right)-1\right) a^{2}}{16 d \left(a +b \right)^{4}}-\frac{3 \ln \left(\sin \left(d x +c \right)-1\right) a b}{4 d \left(a +b \right)^{4}}-\frac{15 \ln \left(\sin \left(d x +c \right)-1\right) b^{2}}{16 d \left(a +b \right)^{4}}+\frac{b^{5}}{d \left(a +b \right)^{3} \left(a -b \right)^{3} \left(a +b \sin \left(d x +c \right)\right)}-\frac{6 b^{5} a \ln \left(a +b \sin \left(d x +c \right)\right)}{d \left(a +b \right)^{4} \left(a -b \right)^{4}}-\frac{1}{16 d \left(a -b \right)^{2} \left(1+\sin \left(d x +c \right)\right)^{2}}+\frac{7 b}{16 d \left(a -b \right)^{3} \left(1+\sin \left(d x +c \right)\right)}-\frac{3 a}{16 d \left(a -b \right)^{3} \left(1+\sin \left(d x +c \right)\right)}+\frac{3 \ln \left(1+\sin \left(d x +c \right)\right) a^{2}}{16 d \left(a -b \right)^{4}}-\frac{3 \ln \left(1+\sin \left(d x +c \right)\right) a b}{4 d \left(a -b \right)^{4}}+\frac{15 \ln \left(1+\sin \left(d x +c \right)\right) b^{2}}{16 d \left(a -b \right)^{4}}"," ",0,"1/16/d/(a+b)^2/(sin(d*x+c)-1)^2-7/16/d/(a+b)^3/(sin(d*x+c)-1)*b-3/16/d/(a+b)^3/(sin(d*x+c)-1)*a-3/16/d/(a+b)^4*ln(sin(d*x+c)-1)*a^2-3/4/d/(a+b)^4*ln(sin(d*x+c)-1)*a*b-15/16/d/(a+b)^4*ln(sin(d*x+c)-1)*b^2+1/d*b^5/(a+b)^3/(a-b)^3/(a+b*sin(d*x+c))-6/d*b^5*a/(a+b)^4/(a-b)^4*ln(a+b*sin(d*x+c))-1/16/d/(a-b)^2/(1+sin(d*x+c))^2+7/16/d/(a-b)^3/(1+sin(d*x+c))*b-3/16/d/(a-b)^3/(1+sin(d*x+c))*a+3/16/d/(a-b)^4*ln(1+sin(d*x+c))*a^2-3/4/d/(a-b)^4*ln(1+sin(d*x+c))*a*b+15/16/d/(a-b)^4*ln(1+sin(d*x+c))*b^2","A"
444,1,1021,176,0.254000," ","int(cos(d*x+c)^6/(a+b*sin(d*x+c))^2,x)","-\frac{2}{d b \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)}-\frac{8 a^{3}}{d \,b^{5} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}+\frac{28 a}{3 d \,b^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{2 a^{4}}{d \,b^{5} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)}-\frac{9 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{4 d \,b^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}+\frac{4 a^{2}}{d \,b^{3} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)}-\frac{2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right) a}+\frac{9 \left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 d \,b^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}+\frac{\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)}{4 d \,b^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)}{4 d \,b^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{10 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{4}}{d \,b^{6}}+\frac{15 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{2}}{d \,b^{4}}-\frac{15 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 d \,b^{2}}+\frac{10 a^{5} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,b^{6} \sqrt{a^{2}-b^{2}}}-\frac{20 a^{3} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,b^{4} \sqrt{a^{2}-b^{2}}}+\frac{10 a \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,b^{2} \sqrt{a^{2}-b^{2}}}+\frac{4 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,b^{2} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)}-\frac{3 \left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{2}}{d \,b^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{8 \left(\tan^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{3}}{d \,b^{5} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}+\frac{12 \left(\tan^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a}{d \,b^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{3 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{2}}{d \,b^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{24 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{3}}{d \,b^{5} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}+\frac{28 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a}{d \,b^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}+\frac{3 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{2}}{d \,b^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{24 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{3}}{d \,b^{5} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}+\frac{76 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a}{3 d \,b^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}+\frac{3 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) a^{2}}{d \,b^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{2 a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,b^{4} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)}"," ",0,"4/d/b^3/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)*a^2-2/d/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)/a*tan(1/2*d*x+1/2*c)+9/4/d/b^2/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^7+1/4/d/b^2/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^5-1/4/d/b^2/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^3-9/4/d/b^2/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)-8/d/b^5/(1+tan(1/2*d*x+1/2*c)^2)^4*a^3+28/3/d/b^3/(1+tan(1/2*d*x+1/2*c)^2)^4*a-10/d/b^6*arctan(tan(1/2*d*x+1/2*c))*a^4+15/d/b^4*arctan(tan(1/2*d*x+1/2*c))*a^2-2/d/b^5/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)*a^4-15/4/d/b^2*arctan(tan(1/2*d*x+1/2*c))-2/d/b/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)+4/d/b^2/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)*a*tan(1/2*d*x+1/2*c)+10/d/b^6*a^5/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))-20/d/b^4*a^3/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))+10/d/b^2*a/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))-3/d/b^4/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^7*a^2-8/d/b^5/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^6*a^3+12/d/b^3/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^6*a-3/d/b^4/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^5*a^2-24/d/b^5/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^4*a^3+28/d/b^3/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^4*a+3/d/b^4/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^3*a^2-24/d/b^5/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^2*a^3+76/3/d/b^3/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^2*a+3/d/b^4/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)*a^2-2/d/b^4/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)*a^3*tan(1/2*d*x+1/2*c)","B"
445,1,385,119,0.243000," ","int(cos(d*x+c)^4/(a+b*sin(d*x+c))^2,x)","\frac{\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,b^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{4 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a}{d \,b^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}-\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,b^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{4 a}{d \,b^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{6 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{2}}{d \,b^{4}}-\frac{3 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,b^{2}}+\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,b^{2} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)}-\frac{2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right) a}+\frac{2 a^{2}}{d \,b^{3} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)}-\frac{2}{d b \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)}-\frac{6 a \sqrt{a^{2}-b^{2}}\, \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,b^{4}}"," ",0,"1/d/b^2/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)^3+4/d/b^3/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)^2*a-1/d/b^2/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)+4/d/b^3/(1+tan(1/2*d*x+1/2*c)^2)^2*a+6/d/b^4*arctan(tan(1/2*d*x+1/2*c))*a^2-3/d/b^2*arctan(tan(1/2*d*x+1/2*c))+2/d/b^2/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)*a*tan(1/2*d*x+1/2*c)-2/d/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)/a*tan(1/2*d*x+1/2*c)+2/d/b^3/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)*a^2-2/d/b/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)-6/d/b^4*a*(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))","B"
446,1,153,79,0.231000," ","int(cos(d*x+c)^2/(a+b*sin(d*x+c))^2,x)","-\frac{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,b^{2}}-\frac{2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right) a}-\frac{2}{d b \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)}+\frac{2 a \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,b^{2} \sqrt{a^{2}-b^{2}}}"," ",0,"-2/d/b^2*arctan(tan(1/2*d*x+1/2*c))-2/d/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)/a*tan(1/2*d*x+1/2*c)-2/d/b/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)+2/d/b^2*a/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))","A"
447,1,222,125,0.225000," ","int(sec(d*x+c)^2/(a+b*sin(d*x+c))^2,x)","-\frac{1}{d \left(a +b \right)^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{2 b^{4} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \left(a -b \right)^{2} \left(a +b \right)^{2} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right) a}-\frac{2 b^{3}}{d \left(a -b \right)^{2} \left(a +b \right)^{2} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)}-\frac{6 b^{2} a \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \left(a -b \right)^{2} \left(a +b \right)^{2} \sqrt{a^{2}-b^{2}}}-\frac{1}{d \left(a -b \right)^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}"," ",0,"-1/d/(a+b)^2/(tan(1/2*d*x+1/2*c)-1)-2/d*b^4/(a-b)^2/(a+b)^2/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)/a*tan(1/2*d*x+1/2*c)-2/d*b^3/(a-b)^2/(a+b)^2/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)-6/d*b^2/(a-b)^2/(a+b)^2*a/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))-1/d/(a-b)^2/(tan(1/2*d*x+1/2*c)+1)","A"
448,1,370,184,0.318000," ","int(sec(d*x+c)^4/(a+b*sin(d*x+c))^2,x)","-\frac{1}{3 d \left(a +b \right)^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{3}}-\frac{1}{2 d \left(a +b \right)^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}-\frac{a}{d \left(a +b \right)^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{2 b}{d \left(a +b \right)^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}+\frac{2 b^{6} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \left(a -b \right)^{3} \left(a +b \right)^{3} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right) a}+\frac{2 b^{5}}{d \left(a -b \right)^{3} \left(a +b \right)^{3} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)}+\frac{10 b^{4} a \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \left(a -b \right)^{3} \left(a +b \right)^{3} \sqrt{a^{2}-b^{2}}}-\frac{1}{3 d \left(a -b \right)^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}+\frac{1}{2 d \left(a -b \right)^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}-\frac{a}{d \left(a -b \right)^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}+\frac{2 b}{d \left(a -b \right)^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}"," ",0,"-1/3/d/(a+b)^2/(tan(1/2*d*x+1/2*c)-1)^3-1/2/d/(a+b)^2/(tan(1/2*d*x+1/2*c)-1)^2-1/d/(a+b)^3/(tan(1/2*d*x+1/2*c)-1)*a-2/d/(a+b)^3/(tan(1/2*d*x+1/2*c)-1)*b+2/d*b^6/(a-b)^3/(a+b)^3/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)/a*tan(1/2*d*x+1/2*c)+2/d*b^5/(a-b)^3/(a+b)^3/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)+10/d*b^4/(a-b)^3/(a+b)^3*a/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))-1/3/d/(a-b)^2/(tan(1/2*d*x+1/2*c)+1)^3+1/2/d/(a-b)^2/(tan(1/2*d*x+1/2*c)+1)^2-1/d/(a-b)^3/(tan(1/2*d*x+1/2*c)+1)*a+2/d/(a-b)^3/(tan(1/2*d*x+1/2*c)+1)*b","B"
449,1,320,184,0.285000," ","int(cos(d*x+c)^7/(a+b*sin(d*x+c))^3,x)","-\frac{\sin^{4}\left(d x +c \right)}{4 b^{3} d}+\frac{a \left(\sin^{3}\left(d x +c \right)\right)}{b^{4} d}-\frac{3 \left(\sin^{2}\left(d x +c \right)\right) a^{2}}{d \,b^{5}}+\frac{3 \left(\sin^{2}\left(d x +c \right)\right)}{2 b^{3} d}+\frac{10 \sin \left(d x +c \right) a^{3}}{d \,b^{6}}-\frac{9 a \sin \left(d x +c \right)}{b^{4} d}-\frac{15 \ln \left(a +b \sin \left(d x +c \right)\right) a^{4}}{d \,b^{7}}+\frac{18 \ln \left(a +b \sin \left(d x +c \right)\right) a^{2}}{d \,b^{5}}-\frac{3 \ln \left(a +b \sin \left(d x +c \right)\right)}{b^{3} d}-\frac{6 a^{5}}{d \,b^{7} \left(a +b \sin \left(d x +c \right)\right)}+\frac{12 a^{3}}{d \,b^{5} \left(a +b \sin \left(d x +c \right)\right)}-\frac{6 a}{b^{3} d \left(a +b \sin \left(d x +c \right)\right)}+\frac{a^{6}}{2 d \,b^{7} \left(a +b \sin \left(d x +c \right)\right)^{2}}-\frac{3 a^{4}}{2 d \,b^{5} \left(a +b \sin \left(d x +c \right)\right)^{2}}+\frac{3 a^{2}}{2 d \,b^{3} \left(a +b \sin \left(d x +c \right)\right)^{2}}-\frac{1}{2 b d \left(a +b \sin \left(d x +c \right)\right)^{2}}"," ",0,"-1/4*sin(d*x+c)^4/b^3/d+a*sin(d*x+c)^3/b^4/d-3/d/b^5*sin(d*x+c)^2*a^2+3/2*sin(d*x+c)^2/b^3/d+10/d/b^6*sin(d*x+c)*a^3-9*a*sin(d*x+c)/b^4/d-15/d/b^7*ln(a+b*sin(d*x+c))*a^4+18/d/b^5*ln(a+b*sin(d*x+c))*a^2-3*ln(a+b*sin(d*x+c))/b^3/d-6/d*a^5/b^7/(a+b*sin(d*x+c))+12/d*a^3/b^5/(a+b*sin(d*x+c))-6*a/b^3/d/(a+b*sin(d*x+c))+1/2/d/b^7/(a+b*sin(d*x+c))^2*a^6-3/2/d/b^5/(a+b*sin(d*x+c))^2*a^4+3/2/d/b^3/(a+b*sin(d*x+c))^2*a^2-1/2/b/d/(a+b*sin(d*x+c))^2","A"
450,1,183,123,0.289000," ","int(cos(d*x+c)^5/(a+b*sin(d*x+c))^3,x)","\frac{\sin^{2}\left(d x +c \right)}{2 b^{3} d}-\frac{3 a \sin \left(d x +c \right)}{b^{4} d}+\frac{6 \ln \left(a +b \sin \left(d x +c \right)\right) a^{2}}{d \,b^{5}}-\frac{2 \ln \left(a +b \sin \left(d x +c \right)\right)}{b^{3} d}+\frac{4 a^{3}}{d \,b^{5} \left(a +b \sin \left(d x +c \right)\right)}-\frac{4 a}{b^{3} d \left(a +b \sin \left(d x +c \right)\right)}-\frac{a^{4}}{2 d \,b^{5} \left(a +b \sin \left(d x +c \right)\right)^{2}}+\frac{a^{2}}{d \,b^{3} \left(a +b \sin \left(d x +c \right)\right)^{2}}-\frac{1}{2 b d \left(a +b \sin \left(d x +c \right)\right)^{2}}"," ",0,"1/2*sin(d*x+c)^2/b^3/d-3*a*sin(d*x+c)/b^4/d+6/d/b^5*ln(a+b*sin(d*x+c))*a^2-2*ln(a+b*sin(d*x+c))/b^3/d+4/d*a^3/b^5/(a+b*sin(d*x+c))-4*a/b^3/d/(a+b*sin(d*x+c))-1/2/d/b^5/(a+b*sin(d*x+c))^2*a^4+1/d/b^3/(a+b*sin(d*x+c))^2*a^2-1/2/b/d/(a+b*sin(d*x+c))^2","A"
451,1,85,70,0.260000," ","int(cos(d*x+c)^3/(a+b*sin(d*x+c))^3,x)","-\frac{\ln \left(a +b \sin \left(d x +c \right)\right)}{b^{3} d}-\frac{2 a}{b^{3} d \left(a +b \sin \left(d x +c \right)\right)}+\frac{a^{2}}{2 d \,b^{3} \left(a +b \sin \left(d x +c \right)\right)^{2}}-\frac{1}{2 b d \left(a +b \sin \left(d x +c \right)\right)^{2}}"," ",0,"-ln(a+b*sin(d*x+c))/b^3/d-2*a/b^3/d/(a+b*sin(d*x+c))+1/2/d/b^3/(a+b*sin(d*x+c))^2*a^2-1/2/b/d/(a+b*sin(d*x+c))^2","A"
452,1,21,20,0.110000," ","int(cos(d*x+c)/(a+b*sin(d*x+c))^3,x)","-\frac{1}{2 b d \left(a +b \sin \left(d x +c \right)\right)^{2}}"," ",0,"-1/2/b/d/(a+b*sin(d*x+c))^2","A"
453,1,166,139,0.290000," ","int(sec(d*x+c)/(a+b*sin(d*x+c))^3,x)","-\frac{\ln \left(\sin \left(d x +c \right)-1\right)}{2 d \left(a +b \right)^{3}}+\frac{b}{2 d \left(a +b \right) \left(a -b \right) \left(a +b \sin \left(d x +c \right)\right)^{2}}+\frac{2 a b}{d \left(a +b \right)^{2} \left(a -b \right)^{2} \left(a +b \sin \left(d x +c \right)\right)}-\frac{3 b \ln \left(a +b \sin \left(d x +c \right)\right) a^{2}}{d \left(a +b \right)^{3} \left(a -b \right)^{3}}-\frac{b^{3} \ln \left(a +b \sin \left(d x +c \right)\right)}{d \left(a +b \right)^{3} \left(a -b \right)^{3}}+\frac{\ln \left(1+\sin \left(d x +c \right)\right)}{2 \left(a -b \right)^{3} d}"," ",0,"-1/2/d/(a+b)^3*ln(sin(d*x+c)-1)+1/2/d*b/(a+b)/(a-b)/(a+b*sin(d*x+c))^2+2/d*a*b/(a+b)^2/(a-b)^2/(a+b*sin(d*x+c))-3/d*b/(a+b)^3/(a-b)^3*ln(a+b*sin(d*x+c))*a^2-1/d*b^3/(a+b)^3/(a-b)^3*ln(a+b*sin(d*x+c))+1/2*ln(1+sin(d*x+c))/(a-b)^3/d","A"
454,1,258,216,0.324000," ","int(sec(d*x+c)^3/(a+b*sin(d*x+c))^3,x)","-\frac{1}{4 d \left(a +b \right)^{3} \left(\sin \left(d x +c \right)-1\right)}-\frac{\ln \left(\sin \left(d x +c \right)-1\right) a}{4 d \left(a +b \right)^{4}}-\frac{\ln \left(\sin \left(d x +c \right)-1\right) b}{d \left(a +b \right)^{4}}-\frac{b^{3}}{2 d \left(a +b \right)^{2} \left(a -b \right)^{2} \left(a +b \sin \left(d x +c \right)\right)^{2}}-\frac{4 a \,b^{3}}{d \left(a +b \right)^{3} \left(a -b \right)^{3} \left(a +b \sin \left(d x +c \right)\right)}+\frac{10 b^{3} \ln \left(a +b \sin \left(d x +c \right)\right) a^{2}}{d \left(a +b \right)^{4} \left(a -b \right)^{4}}+\frac{2 b^{5} \ln \left(a +b \sin \left(d x +c \right)\right)}{d \left(a +b \right)^{4} \left(a -b \right)^{4}}-\frac{1}{4 d \left(a -b \right)^{3} \left(1+\sin \left(d x +c \right)\right)}+\frac{\ln \left(1+\sin \left(d x +c \right)\right) a}{4 d \left(a -b \right)^{4}}-\frac{\ln \left(1+\sin \left(d x +c \right)\right) b}{d \left(a -b \right)^{4}}"," ",0,"-1/4/d/(a+b)^3/(sin(d*x+c)-1)-1/4/d/(a+b)^4*ln(sin(d*x+c)-1)*a-1/d/(a+b)^4*ln(sin(d*x+c)-1)*b-1/2/d*b^3/(a+b)^2/(a-b)^2/(a+b*sin(d*x+c))^2-4/d*a*b^3/(a+b)^3/(a-b)^3/(a+b*sin(d*x+c))+10/d*b^3/(a+b)^4/(a-b)^4*ln(a+b*sin(d*x+c))*a^2+2/d*b^5/(a+b)^4/(a-b)^4*ln(a+b*sin(d*x+c))-1/4/d/(a-b)^3/(1+sin(d*x+c))+1/4/d/(a-b)^4*ln(1+sin(d*x+c))*a-1/d/(a-b)^4*ln(1+sin(d*x+c))*b","A"
455,1,398,316,0.336000," ","int(sec(d*x+c)^5/(a+b*sin(d*x+c))^3,x)","\frac{1}{16 d \left(a +b \right)^{3} \left(\sin \left(d x +c \right)-1\right)^{2}}-\frac{3 a}{16 d \left(a +b \right)^{4} \left(\sin \left(d x +c \right)-1\right)}-\frac{9 b}{16 d \left(a +b \right)^{4} \left(\sin \left(d x +c \right)-1\right)}-\frac{3 \ln \left(\sin \left(d x +c \right)-1\right) a^{2}}{16 d \left(a +b \right)^{5}}-\frac{15 \ln \left(\sin \left(d x +c \right)-1\right) a b}{16 d \left(a +b \right)^{5}}-\frac{3 \ln \left(\sin \left(d x +c \right)-1\right) b^{2}}{2 d \left(a +b \right)^{5}}+\frac{b^{5}}{2 d \left(a +b \right)^{3} \left(a -b \right)^{3} \left(a +b \sin \left(d x +c \right)\right)^{2}}+\frac{6 b^{5} a}{d \left(a +b \right)^{4} \left(a -b \right)^{4} \left(a +b \sin \left(d x +c \right)\right)}-\frac{21 b^{5} \ln \left(a +b \sin \left(d x +c \right)\right) a^{2}}{d \left(a +b \right)^{5} \left(a -b \right)^{5}}-\frac{3 b^{7} \ln \left(a +b \sin \left(d x +c \right)\right)}{d \left(a +b \right)^{5} \left(a -b \right)^{5}}-\frac{1}{16 d \left(a -b \right)^{3} \left(1+\sin \left(d x +c \right)\right)^{2}}-\frac{3 a}{16 d \left(a -b \right)^{4} \left(1+\sin \left(d x +c \right)\right)}+\frac{9 b}{16 d \left(a -b \right)^{4} \left(1+\sin \left(d x +c \right)\right)}+\frac{3 \ln \left(1+\sin \left(d x +c \right)\right) a^{2}}{16 d \left(a -b \right)^{5}}-\frac{15 \ln \left(1+\sin \left(d x +c \right)\right) a b}{16 d \left(a -b \right)^{5}}+\frac{3 \ln \left(1+\sin \left(d x +c \right)\right) b^{2}}{2 d \left(a -b \right)^{5}}"," ",0,"1/16/d/(a+b)^3/(sin(d*x+c)-1)^2-3/16/d/(a+b)^4/(sin(d*x+c)-1)*a-9/16/d/(a+b)^4/(sin(d*x+c)-1)*b-3/16/d/(a+b)^5*ln(sin(d*x+c)-1)*a^2-15/16/d/(a+b)^5*ln(sin(d*x+c)-1)*a*b-3/2/d/(a+b)^5*ln(sin(d*x+c)-1)*b^2+1/2/d*b^5/(a+b)^3/(a-b)^3/(a+b*sin(d*x+c))^2+6/d*b^5*a/(a+b)^4/(a-b)^4/(a+b*sin(d*x+c))-21/d*b^5/(a+b)^5/(a-b)^5*ln(a+b*sin(d*x+c))*a^2-3/d*b^7/(a+b)^5/(a-b)^5*ln(a+b*sin(d*x+c))-1/16/d/(a-b)^3/(1+sin(d*x+c))^2-3/16/d/(a-b)^4/(1+sin(d*x+c))*a+9/16/d/(a-b)^4/(1+sin(d*x+c))*b+3/16/d/(a-b)^5*ln(1+sin(d*x+c))*a^2-15/16/d/(a-b)^5*ln(1+sin(d*x+c))*a*b+3/2/d/(a-b)^5*ln(1+sin(d*x+c))*b^2","A"
456,1,1060,184,0.308000," ","int(cos(d*x+c)^6/(a+b*sin(d*x+c))^3,x)","\frac{7 a^{3} \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,b^{4} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}+\frac{20 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{3}}{d \,b^{6}}-\frac{15 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) a}{d \,b^{4}}-\frac{1}{d b \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}-\frac{14}{3 d \,b^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}-\frac{5 \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,b^{2} \sqrt{a^{2}-b^{2}}}-\frac{6 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,b^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}-\frac{8 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,b^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}-\frac{5 a \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,b^{2} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}+\frac{8 a^{4} \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,b^{5} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}+\frac{9 a^{2} \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,b^{3} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}-\frac{2 b \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2} a^{2}}+\frac{25 a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,b^{4} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}-\frac{23 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,b^{2} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}+\frac{3 a \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,b^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}+\frac{12 a^{2}}{d \,b^{5} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}-\frac{2 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2} a}-\frac{2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2} a}-\frac{15 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d b \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}+\frac{8 a^{4}}{d \,b^{5} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}-\frac{7 a^{2}}{d \,b^{3} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}-\frac{20 \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right) a^{4}}{d \,b^{6} \sqrt{a^{2}-b^{2}}}+\frac{25 \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right) a^{2}}{d \,b^{4} \sqrt{a^{2}-b^{2}}}+\frac{12 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{2}}{d \,b^{5} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}+\frac{24 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{2}}{d \,b^{5} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}-\frac{3 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,b^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}"," ",0,"-6/d/b^3/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)^4-8/d/b^3/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)^2+12/d/b^5/(1+tan(1/2*d*x+1/2*c)^2)^3*a^2+20/d/b^6*arctan(tan(1/2*d*x+1/2*c))*a^3-15/d/b^4*arctan(tan(1/2*d*x+1/2*c))*a-2/d/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2/a*tan(1/2*d*x+1/2*c)^3-2/d/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2/a*tan(1/2*d*x+1/2*c)-15/d/b/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)^2+8/d/b^5/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*a^4-7/d/b^3/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*a^2-5/d/b^2/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))+7/d/b^4/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*a^3*tan(1/2*d*x+1/2*c)^3-5/d/b^2/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*a*tan(1/2*d*x+1/2*c)^3+8/d/b^5/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*a^4*tan(1/2*d*x+1/2*c)^2+9/d/b^3/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*a^2*tan(1/2*d*x+1/2*c)^2-2/d*b/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2/a^2*tan(1/2*d*x+1/2*c)^2+25/d/b^4/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*a^3*tan(1/2*d*x+1/2*c)-23/d/b^2/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*a*tan(1/2*d*x+1/2*c)-20/d/b^6/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))*a^4+25/d/b^4/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))*a^2+3/d/b^4/(1+tan(1/2*d*x+1/2*c)^2)^3*a*tan(1/2*d*x+1/2*c)^5+12/d/b^5/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)^4*a^2+24/d/b^5/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)^2*a^2-3/d/b^4/(1+tan(1/2*d*x+1/2*c)^2)^3*a*tan(1/2*d*x+1/2*c)-14/3/d/b^3/(1+tan(1/2*d*x+1/2*c)^2)^3-1/d/b/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2","B"
457,1,560,130,0.306000," ","int(cos(d*x+c)^4/(a+b*sin(d*x+c))^3,x)","-\frac{2}{d \,b^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}-\frac{6 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) a}{d \,b^{4}}-\frac{3 a \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,b^{2} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}-\frac{2 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2} a}-\frac{4 a^{2} \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,b^{3} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}-\frac{9 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d b \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}-\frac{2 b \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2} a^{2}}-\frac{13 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,b^{2} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}-\frac{2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2} a}-\frac{4 a^{2}}{d \,b^{3} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}-\frac{1}{d b \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}+\frac{6 \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right) a^{2}}{d \,b^{4} \sqrt{a^{2}-b^{2}}}-\frac{3 \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,b^{2} \sqrt{a^{2}-b^{2}}}"," ",0,"-2/d/b^3/(1+tan(1/2*d*x+1/2*c)^2)-6/d/b^4*arctan(tan(1/2*d*x+1/2*c))*a-3/d/b^2/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*a*tan(1/2*d*x+1/2*c)^3-2/d/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2/a*tan(1/2*d*x+1/2*c)^3-4/d/b^3/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*a^2*tan(1/2*d*x+1/2*c)^2-9/d/b/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)^2-2/d*b/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2/a^2*tan(1/2*d*x+1/2*c)^2-13/d/b^2/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*a*tan(1/2*d*x+1/2*c)-2/d/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2/a*tan(1/2*d*x+1/2*c)-4/d/b^3/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*a^2-1/d/b/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2+6/d/b^4/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))*a^2-3/d/b^2/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))","B"
458,1,443,106,0.298000," ","int(cos(d*x+c)^2/(a+b*sin(d*x+c))^3,x)","-\frac{a \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2} \left(a^{2}-b^{2}\right)}+\frac{2 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{2}}{d \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2} a \left(a^{2}-b^{2}\right)}+\frac{b \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2} \left(a^{2}-b^{2}\right)}+\frac{2 b^{3} \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2} \left(a^{2}-b^{2}\right) a^{2}}+\frac{a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2} \left(a^{2}-b^{2}\right)}+\frac{2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b^{2}}{d \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2} a \left(a^{2}-b^{2}\right)}+\frac{b}{d \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2} \left(a^{2}-b^{2}\right)}+\frac{\arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \left(a^{2}-b^{2}\right)^{\frac{3}{2}}}"," ",0,"-1/d/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*a/(a^2-b^2)*tan(1/2*d*x+1/2*c)^3+2/d/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2/a/(a^2-b^2)*tan(1/2*d*x+1/2*c)^3*b^2+1/d/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*b/(a^2-b^2)*tan(1/2*d*x+1/2*c)^2+2/d/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*b^3/(a^2-b^2)/a^2*tan(1/2*d*x+1/2*c)^2+1/d/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*a/(a^2-b^2)*tan(1/2*d*x+1/2*c)+2/d/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2/a/(a^2-b^2)*tan(1/2*d*x+1/2*c)*b^2+1/d/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*b/(a^2-b^2)+1/d/(a^2-b^2)^(3/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))","B"
459,1,705,181,0.276000," ","int(sec(d*x+c)^2/(a+b*sin(d*x+c))^3,x)","-\frac{1}{d \left(a +b \right)^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{9 b^{4} a \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \left(a -b \right)^{3} \left(a +b \right)^{3} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}+\frac{2 b^{6} \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \left(a -b \right)^{3} \left(a +b \right)^{3} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2} a}-\frac{8 b^{3} a^{2} \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \left(a -b \right)^{3} \left(a +b \right)^{3} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}-\frac{15 b^{5} \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \left(a -b \right)^{3} \left(a +b \right)^{3} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}+\frac{2 b^{7} \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \left(a -b \right)^{3} \left(a +b \right)^{3} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2} a^{2}}-\frac{23 b^{4} a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \left(a -b \right)^{3} \left(a +b \right)^{3} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}+\frac{2 b^{6} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \left(a -b \right)^{3} \left(a +b \right)^{3} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2} a}-\frac{8 b^{3} a^{2}}{d \left(a -b \right)^{3} \left(a +b \right)^{3} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}+\frac{b^{5}}{d \left(a -b \right)^{3} \left(a +b \right)^{3} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}-\frac{12 b^{2} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right) a^{2}}{d \left(a -b \right)^{3} \left(a +b \right)^{3} \sqrt{a^{2}-b^{2}}}-\frac{3 b^{4} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \left(a -b \right)^{3} \left(a +b \right)^{3} \sqrt{a^{2}-b^{2}}}-\frac{1}{d \left(a -b \right)^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}"," ",0,"-1/d/(a+b)^3/(tan(1/2*d*x+1/2*c)-1)-9/d*b^4/(a-b)^3/(a+b)^3/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*a*tan(1/2*d*x+1/2*c)^3+2/d*b^6/(a-b)^3/(a+b)^3/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2/a*tan(1/2*d*x+1/2*c)^3-8/d*b^3/(a-b)^3/(a+b)^3/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*a^2*tan(1/2*d*x+1/2*c)^2-15/d*b^5/(a-b)^3/(a+b)^3/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)^2+2/d*b^7/(a-b)^3/(a+b)^3/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2/a^2*tan(1/2*d*x+1/2*c)^2-23/d*b^4/(a-b)^3/(a+b)^3/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*a*tan(1/2*d*x+1/2*c)+2/d*b^6/(a-b)^3/(a+b)^3/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2/a*tan(1/2*d*x+1/2*c)-8/d*b^3/(a-b)^3/(a+b)^3/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*a^2+1/d*b^5/(a-b)^3/(a+b)^3/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2-12/d*b^2/(a-b)^3/(a+b)^3/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))*a^2-3/d*b^4/(a-b)^3/(a+b)^3/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))-1/d/(a-b)^3/(tan(1/2*d*x+1/2*c)+1)","B"
460,1,854,251,0.338000," ","int(sec(d*x+c)^4/(a+b*sin(d*x+c))^3,x)","-\frac{1}{3 d \left(a +b \right)^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{3}}-\frac{1}{2 d \left(a +b \right)^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}-\frac{a}{d \left(a +b \right)^{4} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{5 b}{2 d \left(a +b \right)^{4} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}+\frac{13 b^{6} a \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \left(a -b \right)^{4} \left(a +b \right)^{4} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}-\frac{2 b^{8} \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \left(a -b \right)^{4} \left(a +b \right)^{4} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2} a}+\frac{12 b^{5} a^{2} \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \left(a -b \right)^{4} \left(a +b \right)^{4} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}+\frac{23 b^{7} \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \left(a -b \right)^{4} \left(a +b \right)^{4} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}-\frac{2 b^{9} \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \left(a -b \right)^{4} \left(a +b \right)^{4} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2} a^{2}}+\frac{35 b^{6} a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \left(a -b \right)^{4} \left(a +b \right)^{4} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}-\frac{2 b^{8} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \left(a -b \right)^{4} \left(a +b \right)^{4} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2} a}+\frac{12 b^{5} a^{2}}{d \left(a -b \right)^{4} \left(a +b \right)^{4} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}-\frac{b^{7}}{d \left(a -b \right)^{4} \left(a +b \right)^{4} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}+\frac{30 b^{4} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right) a^{2}}{d \left(a -b \right)^{4} \left(a +b \right)^{4} \sqrt{a^{2}-b^{2}}}+\frac{5 b^{6} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \left(a -b \right)^{4} \left(a +b \right)^{4} \sqrt{a^{2}-b^{2}}}-\frac{1}{3 d \left(a -b \right)^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}+\frac{1}{2 d \left(a -b \right)^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}-\frac{a}{d \left(a -b \right)^{4} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}+\frac{5 b}{2 d \left(a -b \right)^{4} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}"," ",0,"-1/3/d/(a+b)^3/(tan(1/2*d*x+1/2*c)-1)^3-1/2/d/(a+b)^3/(tan(1/2*d*x+1/2*c)-1)^2-1/d/(a+b)^4/(tan(1/2*d*x+1/2*c)-1)*a-5/2/d/(a+b)^4/(tan(1/2*d*x+1/2*c)-1)*b+13/d*b^6/(a-b)^4/(a+b)^4/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*a*tan(1/2*d*x+1/2*c)^3-2/d*b^8/(a-b)^4/(a+b)^4/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2/a*tan(1/2*d*x+1/2*c)^3+12/d*b^5/(a-b)^4/(a+b)^4/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*a^2*tan(1/2*d*x+1/2*c)^2+23/d*b^7/(a-b)^4/(a+b)^4/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)^2-2/d*b^9/(a-b)^4/(a+b)^4/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2/a^2*tan(1/2*d*x+1/2*c)^2+35/d*b^6/(a-b)^4/(a+b)^4/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*a*tan(1/2*d*x+1/2*c)-2/d*b^8/(a-b)^4/(a+b)^4/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2/a*tan(1/2*d*x+1/2*c)+12/d*b^5/(a-b)^4/(a+b)^4/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*a^2-1/d*b^7/(a-b)^4/(a+b)^4/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2+30/d*b^4/(a-b)^4/(a+b)^4/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))*a^2+5/d*b^6/(a-b)^4/(a+b)^4/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))-1/3/d/(a-b)^3/(tan(1/2*d*x+1/2*c)+1)^3+1/2/d/(a-b)^3/(tan(1/2*d*x+1/2*c)+1)^2-1/d/(a-b)^4/(tan(1/2*d*x+1/2*c)+1)*a+5/2/d/(a-b)^4/(tan(1/2*d*x+1/2*c)+1)*b","B"
461,1,208,203,0.357000," ","int(cos(d*x+c)^7/(a+b*sin(d*x+c))^8,x)","\frac{-\frac{a \left(5 a^{2}-3 b^{2}\right)}{b^{7} \left(a +b \sin \left(d x +c \right)\right)^{4}}-\frac{-a^{6}+3 a^{4} b^{2}-3 a^{2} b^{4}+b^{6}}{7 b^{7} \left(a +b \sin \left(d x +c \right)\right)^{7}}+\frac{1}{b^{7} \left(a +b \sin \left(d x +c \right)\right)}-\frac{-15 a^{4}+18 a^{2} b^{2}-3 b^{4}}{5 b^{7} \left(a +b \sin \left(d x +c \right)\right)^{5}}-\frac{a \left(a^{4}-2 a^{2} b^{2}+b^{4}\right)}{b^{7} \left(a +b \sin \left(d x +c \right)\right)^{6}}-\frac{3 a}{b^{7} \left(a +b \sin \left(d x +c \right)\right)^{2}}-\frac{-15 a^{2}+3 b^{2}}{3 b^{7} \left(a +b \sin \left(d x +c \right)\right)^{3}}}{d}"," ",0,"1/d*(-a*(5*a^2-3*b^2)/b^7/(a+b*sin(d*x+c))^4-1/7*(-a^6+3*a^4*b^2-3*a^2*b^4+b^6)/b^7/(a+b*sin(d*x+c))^7+1/b^7/(a+b*sin(d*x+c))-1/5*(-15*a^4+18*a^2*b^2-3*b^4)/b^7/(a+b*sin(d*x+c))^5-a*(a^4-2*a^2*b^2+b^4)/b^7/(a+b*sin(d*x+c))^6-3*a/b^7/(a+b*sin(d*x+c))^2-1/3*(-15*a^2+3*b^2)/b^7/(a+b*sin(d*x+c))^3)","A"
462,1,127,133,0.342000," ","int(cos(d*x+c)^5/(a+b*sin(d*x+c))^8,x)","\frac{-\frac{a^{4}-2 a^{2} b^{2}+b^{4}}{7 b^{5} \left(a +b \sin \left(d x +c \right)\right)^{7}}-\frac{1}{3 b^{5} \left(a +b \sin \left(d x +c \right)\right)^{3}}-\frac{6 a^{2}-2 b^{2}}{5 b^{5} \left(a +b \sin \left(d x +c \right)\right)^{5}}+\frac{2 a \left(a^{2}-b^{2}\right)}{3 b^{5} \left(a +b \sin \left(d x +c \right)\right)^{6}}+\frac{a}{b^{5} \left(a +b \sin \left(d x +c \right)\right)^{4}}}{d}"," ",0,"1/d*(-1/7*(a^4-2*a^2*b^2+b^4)/b^5/(a+b*sin(d*x+c))^7-1/3/b^5/(a+b*sin(d*x+c))^3-1/5*(6*a^2-2*b^2)/b^5/(a+b*sin(d*x+c))^5+2/3*a*(a^2-b^2)/b^5/(a+b*sin(d*x+c))^6+a/b^5/(a+b*sin(d*x+c))^4)","A"
463,1,67,71,0.335000," ","int(cos(d*x+c)^3/(a+b*sin(d*x+c))^8,x)","\frac{-\frac{-a^{2}+b^{2}}{7 b^{3} \left(a +b \sin \left(d x +c \right)\right)^{7}}+\frac{1}{5 b^{3} \left(a +b \sin \left(d x +c \right)\right)^{5}}-\frac{a}{3 b^{3} \left(a +b \sin \left(d x +c \right)\right)^{6}}}{d}"," ",0,"1/d*(-1/7*(-a^2+b^2)/b^3/(a+b*sin(d*x+c))^7+1/5/b^3/(a+b*sin(d*x+c))^5-1/3*a/b^3/(a+b*sin(d*x+c))^6)","A"
464,1,21,20,0.138000," ","int(cos(d*x+c)/(a+b*sin(d*x+c))^8,x)","-\frac{1}{7 b d \left(a +b \sin \left(d x +c \right)\right)^{7}}"," ",0,"-1/7/b/d/(a+b*sin(d*x+c))^7","A"
465,1,699,374,0.438000," ","int(sec(d*x+c)/(a+b*sin(d*x+c))^8,x)","-\frac{\ln \left(\sin \left(d x +c \right)-1\right)}{2 d \left(a +b \right)^{8}}+\frac{b}{7 d \left(a +b \right) \left(a -b \right) \left(a +b \sin \left(d x +c \right)\right)^{7}}+\frac{a b}{3 d \left(a +b \right)^{2} \left(a -b \right)^{2} \left(a +b \sin \left(d x +c \right)\right)^{6}}+\frac{3 b \,a^{2}}{5 d \left(a +b \right)^{3} \left(a -b \right)^{3} \left(a +b \sin \left(d x +c \right)\right)^{5}}+\frac{b^{3}}{5 d \left(a +b \right)^{3} \left(a -b \right)^{3} \left(a +b \sin \left(d x +c \right)\right)^{5}}+\frac{5 b \,a^{4}}{3 d \left(a +b \right)^{5} \left(a -b \right)^{5} \left(a +b \sin \left(d x +c \right)\right)^{3}}+\frac{10 b^{3} a^{2}}{3 d \left(a +b \right)^{5} \left(a -b \right)^{5} \left(a +b \sin \left(d x +c \right)\right)^{3}}+\frac{b^{5}}{3 d \left(a +b \right)^{5} \left(a -b \right)^{5} \left(a +b \sin \left(d x +c \right)\right)^{3}}+\frac{7 b \,a^{6}}{d \left(a +b \right)^{7} \left(a -b \right)^{7} \left(a +b \sin \left(d x +c \right)\right)}+\frac{35 b^{3} a^{4}}{d \left(a +b \right)^{7} \left(a -b \right)^{7} \left(a +b \sin \left(d x +c \right)\right)}+\frac{21 b^{5} a^{2}}{d \left(a +b \right)^{7} \left(a -b \right)^{7} \left(a +b \sin \left(d x +c \right)\right)}+\frac{b^{7}}{d \left(a +b \right)^{7} \left(a -b \right)^{7} \left(a +b \sin \left(d x +c \right)\right)}+\frac{b \,a^{3}}{d \left(a +b \right)^{4} \left(a -b \right)^{4} \left(a +b \sin \left(d x +c \right)\right)^{4}}+\frac{b^{3} a}{d \left(a +b \right)^{4} \left(a -b \right)^{4} \left(a +b \sin \left(d x +c \right)\right)^{4}}+\frac{3 b \,a^{5}}{d \left(a +b \right)^{6} \left(a -b \right)^{6} \left(a +b \sin \left(d x +c \right)\right)^{2}}+\frac{10 b^{3} a^{3}}{d \left(a +b \right)^{6} \left(a -b \right)^{6} \left(a +b \sin \left(d x +c \right)\right)^{2}}+\frac{3 b^{5} a}{d \left(a +b \right)^{6} \left(a -b \right)^{6} \left(a +b \sin \left(d x +c \right)\right)^{2}}-\frac{8 b \,a^{7} \ln \left(a +b \sin \left(d x +c \right)\right)}{d \left(a +b \right)^{8} \left(a -b \right)^{8}}-\frac{56 b^{3} a^{5} \ln \left(a +b \sin \left(d x +c \right)\right)}{d \left(a +b \right)^{8} \left(a -b \right)^{8}}-\frac{56 b^{5} a^{3} \ln \left(a +b \sin \left(d x +c \right)\right)}{d \left(a +b \right)^{8} \left(a -b \right)^{8}}-\frac{8 b^{7} a \ln \left(a +b \sin \left(d x +c \right)\right)}{d \left(a +b \right)^{8} \left(a -b \right)^{8}}+\frac{\ln \left(1+\sin \left(d x +c \right)\right)}{2 \left(a -b \right)^{8} d}"," ",0,"-1/2/d/(a+b)^8*ln(sin(d*x+c)-1)+1/7/d*b/(a+b)/(a-b)/(a+b*sin(d*x+c))^7+1/3/d*a*b/(a+b)^2/(a-b)^2/(a+b*sin(d*x+c))^6+3/5/d*b/(a+b)^3/(a-b)^3/(a+b*sin(d*x+c))^5*a^2+1/5/d*b^3/(a+b)^3/(a-b)^3/(a+b*sin(d*x+c))^5+5/3/d*b/(a+b)^5/(a-b)^5/(a+b*sin(d*x+c))^3*a^4+10/3/d*b^3/(a+b)^5/(a-b)^5/(a+b*sin(d*x+c))^3*a^2+1/3/d*b^5/(a+b)^5/(a-b)^5/(a+b*sin(d*x+c))^3+7/d*b/(a+b)^7/(a-b)^7/(a+b*sin(d*x+c))*a^6+35/d*b^3/(a+b)^7/(a-b)^7/(a+b*sin(d*x+c))*a^4+21/d*b^5/(a+b)^7/(a-b)^7/(a+b*sin(d*x+c))*a^2+1/d*b^7/(a+b)^7/(a-b)^7/(a+b*sin(d*x+c))+1/d*b*a^3/(a+b)^4/(a-b)^4/(a+b*sin(d*x+c))^4+1/d*b^3*a/(a+b)^4/(a-b)^4/(a+b*sin(d*x+c))^4+3/d*b*a^5/(a+b)^6/(a-b)^6/(a+b*sin(d*x+c))^2+10/d*b^3*a^3/(a+b)^6/(a-b)^6/(a+b*sin(d*x+c))^2+3/d*b^5*a/(a+b)^6/(a-b)^6/(a+b*sin(d*x+c))^2-8/d*b*a^7/(a+b)^8/(a-b)^8*ln(a+b*sin(d*x+c))-56/d*b^3*a^5/(a+b)^8/(a-b)^8*ln(a+b*sin(d*x+c))-56/d*b^5*a^3/(a+b)^8/(a-b)^8*ln(a+b*sin(d*x+c))-8/d*b^7*a/(a+b)^8/(a-b)^8*ln(a+b*sin(d*x+c))+1/2*ln(1+sin(d*x+c))/(a-b)^8/d","A"
466,1,804,507,0.481000," ","int(sec(d*x+c)^3/(a+b*sin(d*x+c))^8,x)","-\frac{b^{7}}{d \left(a +b \right)^{6} \left(a -b \right)^{6} \left(a +b \sin \left(d x +c \right)\right)^{3}}-\frac{\ln \left(\sin \left(d x +c \right)-1\right) a}{4 d \left(a +b \right)^{9}}-\frac{9 \ln \left(\sin \left(d x +c \right)-1\right) b}{4 d \left(a +b \right)^{9}}+\frac{\ln \left(1+\sin \left(d x +c \right)\right) a}{4 d \left(a -b \right)^{9}}-\frac{9 \ln \left(1+\sin \left(d x +c \right)\right) b}{4 d \left(a -b \right)^{9}}-\frac{2 b^{5}}{5 d \left(a +b \right)^{4} \left(a -b \right)^{4} \left(a +b \sin \left(d x +c \right)\right)^{5}}-\frac{4 b^{9}}{d \left(a +b \right)^{8} \left(a -b \right)^{8} \left(a +b \sin \left(d x +c \right)\right)}-\frac{b^{3}}{7 d \left(a +b \right)^{2} \left(a -b \right)^{2} \left(a +b \sin \left(d x +c \right)\right)^{7}}-\frac{5 b^{3} a^{3}}{d \left(a +b \right)^{5} \left(a -b \right)^{5} \left(a +b \sin \left(d x +c \right)\right)^{4}}-\frac{3 b^{5} a}{d \left(a +b \right)^{5} \left(a -b \right)^{5} \left(a +b \sin \left(d x +c \right)\right)^{4}}-\frac{28 b^{3} a^{5}}{d \left(a +b \right)^{7} \left(a -b \right)^{7} \left(a +b \sin \left(d x +c \right)\right)^{2}}-\frac{56 b^{5} a^{3}}{d \left(a +b \right)^{7} \left(a -b \right)^{7} \left(a +b \sin \left(d x +c \right)\right)^{2}}-\frac{12 b^{7} a}{d \left(a +b \right)^{7} \left(a -b \right)^{7} \left(a +b \sin \left(d x +c \right)\right)^{2}}+\frac{120 b^{3} a^{7} \ln \left(a +b \sin \left(d x +c \right)\right)}{d \left(a +b \right)^{9} \left(a -b \right)^{9}}+\frac{504 b^{5} a^{5} \ln \left(a +b \sin \left(d x +c \right)\right)}{d \left(a +b \right)^{9} \left(a -b \right)^{9}}+\frac{360 b^{7} a^{3} \ln \left(a +b \sin \left(d x +c \right)\right)}{d \left(a +b \right)^{9} \left(a -b \right)^{9}}-\frac{1}{4 d \left(a +b \right)^{8} \left(\sin \left(d x +c \right)-1\right)}-\frac{1}{4 d \left(a -b \right)^{8} \left(1+\sin \left(d x +c \right)\right)}+\frac{40 b^{9} a \ln \left(a +b \sin \left(d x +c \right)\right)}{d \left(a +b \right)^{9} \left(a -b \right)^{9}}-\frac{35 b^{3} a^{4}}{3 d \left(a +b \right)^{6} \left(a -b \right)^{6} \left(a +b \sin \left(d x +c \right)\right)^{3}}-\frac{14 b^{5} a^{2}}{d \left(a +b \right)^{6} \left(a -b \right)^{6} \left(a +b \sin \left(d x +c \right)\right)^{3}}-\frac{2 a \,b^{3}}{3 d \left(a +b \right)^{3} \left(a -b \right)^{3} \left(a +b \sin \left(d x +c \right)\right)^{6}}-\frac{2 b^{3} a^{2}}{d \left(a +b \right)^{4} \left(a -b \right)^{4} \left(a +b \sin \left(d x +c \right)\right)^{5}}-\frac{84 b^{3} a^{6}}{d \left(a +b \right)^{8} \left(a -b \right)^{8} \left(a +b \sin \left(d x +c \right)\right)}-\frac{252 b^{5} a^{4}}{d \left(a +b \right)^{8} \left(a -b \right)^{8} \left(a +b \sin \left(d x +c \right)\right)}-\frac{108 b^{7} a^{2}}{d \left(a +b \right)^{8} \left(a -b \right)^{8} \left(a +b \sin \left(d x +c \right)\right)}"," ",0,"-1/d*b^7/(a+b)^6/(a-b)^6/(a+b*sin(d*x+c))^3-1/4/d/(a+b)^9*ln(sin(d*x+c)-1)*a-9/4/d/(a+b)^9*ln(sin(d*x+c)-1)*b+1/4/d/(a-b)^9*ln(1+sin(d*x+c))*a-9/4/d/(a-b)^9*ln(1+sin(d*x+c))*b-2/5/d*b^5/(a+b)^4/(a-b)^4/(a+b*sin(d*x+c))^5-4/d*b^9/(a+b)^8/(a-b)^8/(a+b*sin(d*x+c))-1/7/d*b^3/(a+b)^2/(a-b)^2/(a+b*sin(d*x+c))^7-5/d*b^3*a^3/(a+b)^5/(a-b)^5/(a+b*sin(d*x+c))^4-3/d*b^5*a/(a+b)^5/(a-b)^5/(a+b*sin(d*x+c))^4-28/d*b^3*a^5/(a+b)^7/(a-b)^7/(a+b*sin(d*x+c))^2-56/d*b^5*a^3/(a+b)^7/(a-b)^7/(a+b*sin(d*x+c))^2-12/d*b^7*a/(a+b)^7/(a-b)^7/(a+b*sin(d*x+c))^2+120/d*b^3*a^7/(a+b)^9/(a-b)^9*ln(a+b*sin(d*x+c))+504/d*b^5*a^5/(a+b)^9/(a-b)^9*ln(a+b*sin(d*x+c))+360/d*b^7*a^3/(a+b)^9/(a-b)^9*ln(a+b*sin(d*x+c))-1/4/d/(a+b)^8/(sin(d*x+c)-1)-1/4/d/(a-b)^8/(1+sin(d*x+c))+40/d*b^9*a/(a+b)^9/(a-b)^9*ln(a+b*sin(d*x+c))-35/3/d*b^3/(a+b)^6/(a-b)^6/(a+b*sin(d*x+c))^3*a^4-14/d*b^5/(a+b)^6/(a-b)^6/(a+b*sin(d*x+c))^3*a^2-2/3/d*a*b^3/(a+b)^3/(a-b)^3/(a+b*sin(d*x+c))^6-2/d*b^3/(a+b)^4/(a-b)^4/(a+b*sin(d*x+c))^5*a^2-84/d*b^3/(a+b)^8/(a-b)^8/(a+b*sin(d*x+c))*a^6-252/d*b^5/(a+b)^8/(a-b)^8/(a+b*sin(d*x+c))*a^4-108/d*b^7/(a+b)^8/(a-b)^8/(a+b*sin(d*x+c))*a^2","A"
467,1,9454,469,0.424000," ","int(cos(d*x+c)^8/(a+b*sin(d*x+c))^8,x)","\text{output too large to display}"," ",0,"result too large to display","B"
468,1,6933,386,0.408000," ","int(cos(d*x+c)^6/(a+b*sin(d*x+c))^8,x)","\text{output too large to display}"," ",0,"result too large to display","B"
469,1,9171,390,0.391000," ","int(cos(d*x+c)^4/(a+b*sin(d*x+c))^8,x)","\text{output too large to display}"," ",0,"result too large to display","B"
470,1,11250,401,0.407000," ","int(cos(d*x+c)^2/(a+b*sin(d*x+c))^8,x)","\text{output too large to display}"," ",0,"result too large to display","B"
471,1,7675,506,0.385000," ","int(sec(d*x+c)^2/(a+b*sin(d*x+c))^8,x)","\text{output too large to display}"," ",0,"result too large to display","B"
472,1,7823,628,0.587000," ","int(sec(d*x+c)^4/(a+b*sin(d*x+c))^8,x)","\text{output too large to display}"," ",0,"result too large to display","B"
473,1,126,134,0.605000," ","int(cos(d*x+c)^5*(a+b*sin(d*x+c))^(1/2),x)","\frac{2 \left(a +b \sin \left(d x +c \right)\right)^{\frac{3}{2}} \left(315 b^{4} \left(\cos^{4}\left(d x +c \right)\right)+280 a \,b^{3} \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)-240 a^{2} b^{2} \left(\cos^{2}\left(d x +c \right)\right)+360 b^{4} \left(\cos^{2}\left(d x +c \right)\right)-192 a^{3} b \sin \left(d x +c \right)+512 a \,b^{3} \sin \left(d x +c \right)+128 a^{4}-288 a^{2} b^{2}+480 b^{4}\right)}{3465 b^{5} d}"," ",0,"2/3465/b^5*(a+b*sin(d*x+c))^(3/2)*(315*b^4*cos(d*x+c)^4+280*a*b^3*cos(d*x+c)^2*sin(d*x+c)-240*a^2*b^2*cos(d*x+c)^2+360*b^4*cos(d*x+c)^2-192*a^3*b*sin(d*x+c)+512*a*b^3*sin(d*x+c)+128*a^4-288*a^2*b^2+480*b^4)/d","A"
474,1,55,71,0.376000," ","int(cos(d*x+c)^3*(a+b*sin(d*x+c))^(1/2),x)","-\frac{2 \left(a +b \sin \left(d x +c \right)\right)^{\frac{3}{2}} \left(-15 b^{2} \left(\cos^{2}\left(d x +c \right)\right)-12 a b \sin \left(d x +c \right)+8 a^{2}-20 b^{2}\right)}{105 b^{3} d}"," ",0,"-2/105/b^3*(a+b*sin(d*x+c))^(3/2)*(-15*b^2*cos(d*x+c)^2-12*a*b*sin(d*x+c)+8*a^2-20*b^2)/d","A"
475,1,21,20,0.043000," ","int(cos(d*x+c)*(a+b*sin(d*x+c))^(1/2),x)","\frac{2 \left(a +b \sin \left(d x +c \right)\right)^{\frac{3}{2}}}{3 b d}"," ",0,"2/3*(a+b*sin(d*x+c))^(3/2)/b/d","A"
476,1,63,62,0.389000," ","int(sec(d*x+c)*(a+b*sin(d*x+c))^(1/2),x)","\frac{\arctanh \left(\frac{\sqrt{a +b \sin \left(d x +c \right)}}{\sqrt{a +b}}\right) \sqrt{a +b}}{d}-\frac{\sqrt{-a +b}\, \arctan \left(\frac{\sqrt{a +b \sin \left(d x +c \right)}}{\sqrt{-a +b}}\right)}{d}"," ",0,"arctanh((a+b*sin(d*x+c))^(1/2)/(a+b)^(1/2))*(a+b)^(1/2)/d-1/d*(-a+b)^(1/2)*arctan((a+b*sin(d*x+c))^(1/2)/(-a+b)^(1/2))","A"
477,1,185,104,0.609000," ","int(sec(d*x+c)^3*(a+b*sin(d*x+c))^(1/2),x)","\frac{2 \sqrt{a +b \sin \left(d x +c \right)}\, \sqrt{-a +b}\, \sqrt{a +b}\, \sin \left(d x +c \right)-\left(-2 \arctanh \left(\frac{\sqrt{a +b \sin \left(d x +c \right)}}{\sqrt{a +b}}\right) a \sqrt{-a +b}-\arctanh \left(\frac{\sqrt{a +b \sin \left(d x +c \right)}}{\sqrt{a +b}}\right) b \sqrt{-a +b}-2 \arctan \left(\frac{\sqrt{a +b \sin \left(d x +c \right)}}{\sqrt{-a +b}}\right) a \sqrt{a +b}+\arctan \left(\frac{\sqrt{a +b \sin \left(d x +c \right)}}{\sqrt{-a +b}}\right) b \sqrt{a +b}\right) \left(\cos^{2}\left(d x +c \right)\right)}{4 \sqrt{-a +b}\, \sqrt{a +b}\, \cos \left(d x +c \right)^{2} d}"," ",0,"1/4*(2*(a+b*sin(d*x+c))^(1/2)*(-a+b)^(1/2)*(a+b)^(1/2)*sin(d*x+c)-(-2*arctanh((a+b*sin(d*x+c))^(1/2)/(a+b)^(1/2))*a*(-a+b)^(1/2)-arctanh((a+b*sin(d*x+c))^(1/2)/(a+b)^(1/2))*b*(-a+b)^(1/2)-2*arctan((a+b*sin(d*x+c))^(1/2)/(-a+b)^(1/2))*a*(a+b)^(1/2)+arctan((a+b*sin(d*x+c))^(1/2)/(-a+b)^(1/2))*b*(a+b)^(1/2))*cos(d*x+c)^2)/(-a+b)^(1/2)/(a+b)^(1/2)/cos(d*x+c)^2/d","A"
478,1,509,183,0.880000," ","int(sec(d*x+c)^5*(a+b*sin(d*x+c))^(1/2),x)","-\frac{3 b \left(a +b \sin \left(d x +c \right)\right)^{\frac{3}{2}} a}{16 d \left(b \sin \left(d x +c \right)+b \right)^{2} \left(a -b \right)}+\frac{5 b^{2} \left(a +b \sin \left(d x +c \right)\right)^{\frac{3}{2}}}{32 d \left(b \sin \left(d x +c \right)+b \right)^{2} \left(a -b \right)}+\frac{3 b \sqrt{a +b \sin \left(d x +c \right)}\, a}{16 d \left(b \sin \left(d x +c \right)+b \right)^{2}}-\frac{7 b^{2} \sqrt{a +b \sin \left(d x +c \right)}}{32 d \left(b \sin \left(d x +c \right)+b \right)^{2}}+\frac{3 \arctan \left(\frac{\sqrt{a +b \sin \left(d x +c \right)}}{\sqrt{-a +b}}\right) a^{2}}{8 d \left(a -b \right) \sqrt{-a +b}}-\frac{9 \arctan \left(\frac{\sqrt{a +b \sin \left(d x +c \right)}}{\sqrt{-a +b}}\right) a b}{16 d \left(a -b \right) \sqrt{-a +b}}+\frac{5 \arctan \left(\frac{\sqrt{a +b \sin \left(d x +c \right)}}{\sqrt{-a +b}}\right) b^{2}}{32 d \left(a -b \right) \sqrt{-a +b}}-\frac{3 b \left(a +b \sin \left(d x +c \right)\right)^{\frac{3}{2}} a}{16 d \left(b \sin \left(d x +c \right)-b \right)^{2} \left(a +b \right)}-\frac{5 b^{2} \left(a +b \sin \left(d x +c \right)\right)^{\frac{3}{2}}}{32 d \left(b \sin \left(d x +c \right)-b \right)^{2} \left(a +b \right)}+\frac{3 b \sqrt{a +b \sin \left(d x +c \right)}\, a}{16 d \left(b \sin \left(d x +c \right)-b \right)^{2}}+\frac{7 b^{2} \sqrt{a +b \sin \left(d x +c \right)}}{32 d \left(b \sin \left(d x +c \right)-b \right)^{2}}+\frac{3 \arctanh \left(\frac{\sqrt{a +b \sin \left(d x +c \right)}}{\sqrt{a +b}}\right) a^{2}}{8 d \left(a +b \right)^{\frac{3}{2}}}+\frac{9 \arctanh \left(\frac{\sqrt{a +b \sin \left(d x +c \right)}}{\sqrt{a +b}}\right) a b}{16 d \left(a +b \right)^{\frac{3}{2}}}+\frac{5 \arctanh \left(\frac{\sqrt{a +b \sin \left(d x +c \right)}}{\sqrt{a +b}}\right) b^{2}}{32 d \left(a +b \right)^{\frac{3}{2}}}"," ",0,"-3/16/d/(b*sin(d*x+c)+b)^2*b/(a-b)*(a+b*sin(d*x+c))^(3/2)*a+5/32/d/(b*sin(d*x+c)+b)^2*b^2/(a-b)*(a+b*sin(d*x+c))^(3/2)+3/16/d/(b*sin(d*x+c)+b)^2*b*(a+b*sin(d*x+c))^(1/2)*a-7/32/d/(b*sin(d*x+c)+b)^2*b^2*(a+b*sin(d*x+c))^(1/2)+3/8/d/(a-b)/(-a+b)^(1/2)*arctan((a+b*sin(d*x+c))^(1/2)/(-a+b)^(1/2))*a^2-9/16/d/(a-b)/(-a+b)^(1/2)*arctan((a+b*sin(d*x+c))^(1/2)/(-a+b)^(1/2))*a*b+5/32/d/(a-b)/(-a+b)^(1/2)*arctan((a+b*sin(d*x+c))^(1/2)/(-a+b)^(1/2))*b^2-3/16/d/(b*sin(d*x+c)-b)^2*b/(a+b)*(a+b*sin(d*x+c))^(3/2)*a-5/32/d/(b*sin(d*x+c)-b)^2*b^2/(a+b)*(a+b*sin(d*x+c))^(3/2)+3/16/d/(b*sin(d*x+c)-b)^2*b*(a+b*sin(d*x+c))^(1/2)*a+7/32/d/(b*sin(d*x+c)-b)^2*b^2*(a+b*sin(d*x+c))^(1/2)+3/8/d/(a+b)^(3/2)*arctanh((a+b*sin(d*x+c))^(1/2)/(a+b)^(1/2))*a^2+9/16/d/(a+b)^(3/2)*arctanh((a+b*sin(d*x+c))^(1/2)/(a+b)^(1/2))*a*b+5/32/d/(a+b)^(3/2)*arctanh((a+b*sin(d*x+c))^(1/2)/(a+b)^(1/2))*b^2","B"
479,1,1189,340,0.690000," ","int(cos(d*x+c)^4*(a+b*sin(d*x+c))^(1/2),x)","-\frac{2 \left(-35 b^{6} \left(\sin^{6}\left(d x +c \right)\right)-40 a \,b^{5} \left(\sin^{5}\left(d x +c \right)\right)+16 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{5} b -12 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{4} b^{2}-64 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{3} b^{3}-72 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{2} b^{4}+48 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{5}+84 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) b^{6}-16 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{6}+76 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{4} b^{2}+24 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{2} b^{4}-84 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) b^{6}+a^{2} b^{4} \left(\sin^{4}\left(d x +c \right)\right)+112 b^{6} \left(\sin^{4}\left(d x +c \right)\right)-2 a^{3} b^{3} \left(\sin^{3}\left(d x +c \right)\right)+146 a \,b^{5} \left(\sin^{3}\left(d x +c \right)\right)-8 a^{4} b^{2} \left(\sin^{2}\left(d x +c \right)\right)+28 a^{2} b^{4} \left(\sin^{2}\left(d x +c \right)\right)-77 b^{6} \left(\sin^{2}\left(d x +c \right)\right)+2 a^{3} b^{3} \sin \left(d x +c \right)-106 a \,b^{5} \sin \left(d x +c \right)+8 a^{4} b^{2}-29 a^{2} b^{4}\right)}{315 b^{5} \cos \left(d x +c \right) \sqrt{a +b \sin \left(d x +c \right)}\, d}"," ",0,"-2/315*(-35*b^6*sin(d*x+c)^6-40*a*b^5*sin(d*x+c)^5+16*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^5*b-12*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^4*b^2-64*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^3*b^3-72*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^2*b^4+48*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a*b^5+84*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*b^6-16*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^6+76*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^4*b^2+24*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^2*b^4-84*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*b^6+a^2*b^4*sin(d*x+c)^4+112*b^6*sin(d*x+c)^4-2*a^3*b^3*sin(d*x+c)^3+146*a*b^5*sin(d*x+c)^3-8*a^4*b^2*sin(d*x+c)^2+28*a^2*b^4*sin(d*x+c)^2-77*b^6*sin(d*x+c)^2+2*a^3*b^3*sin(d*x+c)-106*a*b^5*sin(d*x+c)+8*a^4*b^2-29*a^2*b^4)/b^5/cos(d*x+c)/(a+b*sin(d*x+c))^(1/2)/d","B"
480,1,792,261,0.715000," ","int(cos(d*x+c)^2*(a+b*sin(d*x+c))^(1/2),x)","\frac{\frac{4 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{3} b}{15}+\frac{4 a^{2} \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) b^{2}}{5}-\frac{4 a \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) b^{3}}{15}-\frac{4 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) b^{4}}{5}-\frac{4 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{4}}{15}-\frac{8 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{2} b^{2}}{15}+\frac{4 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) b^{4}}{5}-\frac{2 b^{4} \left(\sin^{4}\left(d x +c \right)\right)}{5}-\frac{8 a \,b^{3} \left(\sin^{3}\left(d x +c \right)\right)}{15}-\frac{2 a^{2} b^{2} \left(\sin^{2}\left(d x +c \right)\right)}{15}+\frac{2 b^{4} \left(\sin^{2}\left(d x +c \right)\right)}{5}+\frac{8 a \,b^{3} \sin \left(d x +c \right)}{15}+\frac{2 a^{2} b^{2}}{15}}{b^{3} \cos \left(d x +c \right) \sqrt{a +b \sin \left(d x +c \right)}\, d}"," ",0,"2/15*(2*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^3*b+6*a^2*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*b^2-2*a*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*b^3-6*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*b^4-2*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^4-4*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^2*b^2+6*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*b^4-3*b^4*sin(d*x+c)^4-4*a*b^3*sin(d*x+c)^3-a^2*b^2*sin(d*x+c)^2+3*b^4*sin(d*x+c)^2+4*a*b^3*sin(d*x+c)+a^2*b^2)/b^3/cos(d*x+c)/(a+b*sin(d*x+c))^(1/2)/d","B"
481,1,614,205,1.007000," ","int(sec(d*x+c)^2*(a+b*sin(d*x+c))^(1/2),x)","\frac{\sqrt{\left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) b +\left(\cos^{2}\left(d x +c \right)\right) a}\, \left(\EllipticE \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) \sqrt{-\frac{b \sin \left(d x +c \right)}{a +b}+\frac{b}{a +b}}\, \sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}\, \sqrt{-\frac{b \sin \left(d x +c \right)}{a -b}-\frac{b}{a -b}}\, a^{2}-\EllipticE \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) \sqrt{-\frac{b \sin \left(d x +c \right)}{a +b}+\frac{b}{a +b}}\, \sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}\, \sqrt{-\frac{b \sin \left(d x +c \right)}{a -b}-\frac{b}{a -b}}\, b^{2}-\sqrt{-\frac{b \sin \left(d x +c \right)}{a +b}+\frac{b}{a +b}}\, \sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}\, \EllipticF \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) \sqrt{-\frac{b \sin \left(d x +c \right)}{a -b}-\frac{b}{a -b}}\, a b +\sqrt{-\frac{b \sin \left(d x +c \right)}{a +b}+\frac{b}{a +b}}\, \sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}\, \EllipticF \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) \sqrt{-\frac{b \sin \left(d x +c \right)}{a -b}-\frac{b}{a -b}}\, b^{2}-b^{2} \left(\cos^{2}\left(d x +c \right)\right)+a b \sin \left(d x +c \right)+b^{2}\right)}{b \sqrt{-\left(a +b \sin \left(d x +c \right)\right) \left(\sin \left(d x +c \right)-1\right) \left(1+\sin \left(d x +c \right)\right)}\, \cos \left(d x +c \right) \sqrt{a +b \sin \left(d x +c \right)}\, d}"," ",0,"1/b*(cos(d*x+c)^2*sin(d*x+c)*b+cos(d*x+c)^2*a)^(1/2)*(EllipticE((b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2),((a-b)/(a+b))^(1/2))*(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*(b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2)*(-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*a^2-EllipticE((b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2),((a-b)/(a+b))^(1/2))*(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*(b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2)*(-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*b^2-(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*(b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2)*EllipticF((b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2),((a-b)/(a+b))^(1/2))*(-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*a*b+(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*(b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2)*EllipticF((b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2),((a-b)/(a+b))^(1/2))*(-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*b^2-b^2*cos(d*x+c)^2+a*b*sin(d*x+c)+b^2)/(-(a+b*sin(d*x+c))*(sin(d*x+c)-1)*(1+sin(d*x+c)))^(1/2)/cos(d*x+c)/(a+b*sin(d*x+c))^(1/2)/d","B"
482,1,1259,294,0.846000," ","int(sec(d*x+c)^4*(a+b*sin(d*x+c))^(1/2),x)","\frac{-4 \sqrt{\left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) b +\left(\cos^{2}\left(d x +c \right)\right) a}\, a b \left(a^{2}-b^{2}\right) \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right)-2 \sqrt{\left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) b +\left(\cos^{2}\left(d x +c \right)\right) a}\, a b \left(a^{2}-b^{2}\right) \sin \left(d x +c \right)+\sqrt{\left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) b +\left(\cos^{2}\left(d x +c \right)\right) a}\, b^{2} \left(4 a^{2}-3 b^{2}\right) \left(\cos^{4}\left(d x +c \right)\right)+\sqrt{\left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) b +\left(\cos^{2}\left(d x +c \right)\right) a}\, \left(4 \sqrt{-\frac{b \sin \left(d x +c \right)}{a -b}-\frac{b}{a -b}}\, \sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}\, \EllipticF \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) \sqrt{-\frac{b \sin \left(d x +c \right)}{a +b}+\frac{b}{a +b}}\, a^{3} b -3 \sqrt{-\frac{b \sin \left(d x +c \right)}{a -b}-\frac{b}{a -b}}\, \sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}\, \EllipticF \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) \sqrt{-\frac{b \sin \left(d x +c \right)}{a +b}+\frac{b}{a +b}}\, a^{2} b^{2}-4 \sqrt{-\frac{b \sin \left(d x +c \right)}{a -b}-\frac{b}{a -b}}\, \sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}\, \EllipticF \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) \sqrt{-\frac{b \sin \left(d x +c \right)}{a +b}+\frac{b}{a +b}}\, a \,b^{3}+3 \sqrt{-\frac{b \sin \left(d x +c \right)}{a -b}-\frac{b}{a -b}}\, \sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}\, \EllipticF \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) \sqrt{-\frac{b \sin \left(d x +c \right)}{a +b}+\frac{b}{a +b}}\, b^{4}-4 \sqrt{-\frac{b \sin \left(d x +c \right)}{a -b}-\frac{b}{a -b}}\, \sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}\, \EllipticE \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) \sqrt{-\frac{b \sin \left(d x +c \right)}{a +b}+\frac{b}{a +b}}\, a^{4}+7 \sqrt{-\frac{b \sin \left(d x +c \right)}{a -b}-\frac{b}{a -b}}\, \sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}\, \EllipticE \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) \sqrt{-\frac{b \sin \left(d x +c \right)}{a +b}+\frac{b}{a +b}}\, a^{2} b^{2}-3 \sqrt{-\frac{b \sin \left(d x +c \right)}{a -b}-\frac{b}{a -b}}\, \sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}\, \EllipticE \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) \sqrt{-\frac{b \sin \left(d x +c \right)}{a +b}+\frac{b}{a +b}}\, b^{4}-a^{2} b^{2}+b^{4}\right) \left(\cos^{2}\left(d x +c \right)\right)-2 \sqrt{\left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) b +\left(\cos^{2}\left(d x +c \right)\right) a}\, a^{2} b^{2}+2 \sqrt{\left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) b +\left(\cos^{2}\left(d x +c \right)\right) a}\, b^{4}}{6 \sqrt{-\left(a +b \sin \left(d x +c \right)\right) \left(\sin \left(d x +c \right)-1\right) \left(1+\sin \left(d x +c \right)\right)}\, \left(a +b \right) \left(\sin \left(d x +c \right)-1\right) \left(a -b \right) \left(1+\sin \left(d x +c \right)\right) b \cos \left(d x +c \right) \sqrt{a +b \sin \left(d x +c \right)}\, d}"," ",0,"1/6*(-4*(cos(d*x+c)^2*sin(d*x+c)*b+cos(d*x+c)^2*a)^(1/2)*a*b*(a^2-b^2)*sin(d*x+c)*cos(d*x+c)^2-2*(cos(d*x+c)^2*sin(d*x+c)*b+cos(d*x+c)^2*a)^(1/2)*a*b*(a^2-b^2)*sin(d*x+c)+(cos(d*x+c)^2*sin(d*x+c)*b+cos(d*x+c)^2*a)^(1/2)*b^2*(4*a^2-3*b^2)*cos(d*x+c)^4+(cos(d*x+c)^2*sin(d*x+c)*b+cos(d*x+c)^2*a)^(1/2)*(4*(-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*(b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2)*EllipticF((b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2),((a-b)/(a+b))^(1/2))*(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*a^3*b-3*(-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*(b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2)*EllipticF((b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2),((a-b)/(a+b))^(1/2))*(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*a^2*b^2-4*(-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*(b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2)*EllipticF((b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2),((a-b)/(a+b))^(1/2))*(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*a*b^3+3*(-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*(b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2)*EllipticF((b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2),((a-b)/(a+b))^(1/2))*(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*b^4-4*(-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*(b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2)*EllipticE((b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2),((a-b)/(a+b))^(1/2))*(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*a^4+7*(-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*(b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2)*EllipticE((b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2),((a-b)/(a+b))^(1/2))*(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*a^2*b^2-3*(-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*(b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2)*EllipticE((b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2),((a-b)/(a+b))^(1/2))*(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*b^4-a^2*b^2+b^4)*cos(d*x+c)^2-2*(cos(d*x+c)^2*sin(d*x+c)*b+cos(d*x+c)^2*a)^(1/2)*a^2*b^2+2*(cos(d*x+c)^2*sin(d*x+c)*b+cos(d*x+c)^2*a)^(1/2)*b^4)/(-(a+b*sin(d*x+c))*(sin(d*x+c)-1)*(1+sin(d*x+c)))^(1/2)/(a+b)/(sin(d*x+c)-1)/(a-b)/(1+sin(d*x+c))/b/cos(d*x+c)/(a+b*sin(d*x+c))^(1/2)/d","B"
483,1,126,134,0.696000," ","int(cos(d*x+c)^5*(a+b*sin(d*x+c))^(3/2),x)","\frac{2 \left(a +b \sin \left(d x +c \right)\right)^{\frac{5}{2}} \left(3465 b^{4} \left(\cos^{4}\left(d x +c \right)\right)+2520 a \,b^{3} \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)-1680 a^{2} b^{2} \left(\cos^{2}\left(d x +c \right)\right)+3080 b^{4} \left(\cos^{2}\left(d x +c \right)\right)-960 a^{3} b \sin \left(d x +c \right)+3200 a \,b^{3} \sin \left(d x +c \right)+384 a^{4}-608 a^{2} b^{2}+2464 b^{4}\right)}{45045 b^{5} d}"," ",0,"2/45045/b^5*(a+b*sin(d*x+c))^(5/2)*(3465*b^4*cos(d*x+c)^4+2520*a*b^3*cos(d*x+c)^2*sin(d*x+c)-1680*a^2*b^2*cos(d*x+c)^2+3080*b^4*cos(d*x+c)^2-960*a^3*b*sin(d*x+c)+3200*a*b^3*sin(d*x+c)+384*a^4-608*a^2*b^2+2464*b^4)/d","A"
484,1,55,71,0.327000," ","int(cos(d*x+c)^3*(a+b*sin(d*x+c))^(3/2),x)","-\frac{2 \left(a +b \sin \left(d x +c \right)\right)^{\frac{5}{2}} \left(-35 b^{2} \left(\cos^{2}\left(d x +c \right)\right)-20 a b \sin \left(d x +c \right)+8 a^{2}-28 b^{2}\right)}{315 b^{3} d}"," ",0,"-2/315/b^3*(a+b*sin(d*x+c))^(5/2)*(-35*b^2*cos(d*x+c)^2-20*a*b*sin(d*x+c)+8*a^2-28*b^2)/d","A"
485,1,21,20,0.045000," ","int(cos(d*x+c)*(a+b*sin(d*x+c))^(3/2),x)","\frac{2 \left(a +b \sin \left(d x +c \right)\right)^{\frac{5}{2}}}{5 b d}"," ",0,"2/5*(a+b*sin(d*x+c))^(5/2)/b/d","A"
486,1,218,80,0.477000," ","int(sec(d*x+c)*(a+b*sin(d*x+c))^(3/2),x)","-\frac{2 b \sqrt{a +b \sin \left(d x +c \right)}}{d}+\frac{\arctan \left(\frac{\sqrt{a +b \sin \left(d x +c \right)}}{\sqrt{-a +b}}\right) a^{2}}{d \sqrt{-a +b}}-\frac{2 b \arctan \left(\frac{\sqrt{a +b \sin \left(d x +c \right)}}{\sqrt{-a +b}}\right) a}{d \sqrt{-a +b}}+\frac{b^{2} \arctan \left(\frac{\sqrt{a +b \sin \left(d x +c \right)}}{\sqrt{-a +b}}\right)}{d \sqrt{-a +b}}+\frac{\arctanh \left(\frac{\sqrt{a +b \sin \left(d x +c \right)}}{\sqrt{a +b}}\right) a^{2}}{d \sqrt{a +b}}+\frac{2 b \arctanh \left(\frac{\sqrt{a +b \sin \left(d x +c \right)}}{\sqrt{a +b}}\right) a}{d \sqrt{a +b}}+\frac{b^{2} \arctanh \left(\frac{\sqrt{a +b \sin \left(d x +c \right)}}{\sqrt{a +b}}\right)}{d \sqrt{a +b}}"," ",0,"-2*b*(a+b*sin(d*x+c))^(1/2)/d+1/d/(-a+b)^(1/2)*arctan((a+b*sin(d*x+c))^(1/2)/(-a+b)^(1/2))*a^2-2/d*b/(-a+b)^(1/2)*arctan((a+b*sin(d*x+c))^(1/2)/(-a+b)^(1/2))*a+1/d*b^2/(-a+b)^(1/2)*arctan((a+b*sin(d*x+c))^(1/2)/(-a+b)^(1/2))+1/d/(a+b)^(1/2)*arctanh((a+b*sin(d*x+c))^(1/2)/(a+b)^(1/2))*a^2+2/d*b/(a+b)^(1/2)*arctanh((a+b*sin(d*x+c))^(1/2)/(a+b)^(1/2))*a+1/d*b^2/(a+b)^(1/2)*arctanh((a+b*sin(d*x+c))^(1/2)/(a+b)^(1/2))","B"
487,1,279,110,0.683000," ","int(sec(d*x+c)^3*(a+b*sin(d*x+c))^(3/2),x)","\frac{2 a \sqrt{a +b \sin \left(d x +c \right)}\, \sqrt{-a +b}\, \sqrt{a +b}\, \sin \left(d x +c \right)-\left(-2 \arctanh \left(\frac{\sqrt{a +b \sin \left(d x +c \right)}}{\sqrt{a +b}}\right) a^{2} \sqrt{-a +b}-b \arctanh \left(\frac{\sqrt{a +b \sin \left(d x +c \right)}}{\sqrt{a +b}}\right) a \sqrt{-a +b}+b^{2} \arctanh \left(\frac{\sqrt{a +b \sin \left(d x +c \right)}}{\sqrt{a +b}}\right) \sqrt{-a +b}-2 \arctan \left(\frac{\sqrt{a +b \sin \left(d x +c \right)}}{\sqrt{-a +b}}\right) a^{2} \sqrt{a +b}+b \arctan \left(\frac{\sqrt{a +b \sin \left(d x +c \right)}}{\sqrt{-a +b}}\right) a \sqrt{a +b}+b^{2} \arctan \left(\frac{\sqrt{a +b \sin \left(d x +c \right)}}{\sqrt{-a +b}}\right) \sqrt{a +b}\right) \left(\cos^{2}\left(d x +c \right)\right)+2 \sqrt{a +b \sin \left(d x +c \right)}\, b \sqrt{-a +b}\, \sqrt{a +b}}{4 \sqrt{-a +b}\, \sqrt{a +b}\, \cos \left(d x +c \right)^{2} d}"," ",0,"1/4*(2*a*(a+b*sin(d*x+c))^(1/2)*(-a+b)^(1/2)*(a+b)^(1/2)*sin(d*x+c)-(-2*arctanh((a+b*sin(d*x+c))^(1/2)/(a+b)^(1/2))*a^2*(-a+b)^(1/2)-b*arctanh((a+b*sin(d*x+c))^(1/2)/(a+b)^(1/2))*a*(-a+b)^(1/2)+b^2*arctanh((a+b*sin(d*x+c))^(1/2)/(a+b)^(1/2))*(-a+b)^(1/2)-2*arctan((a+b*sin(d*x+c))^(1/2)/(-a+b)^(1/2))*a^2*(a+b)^(1/2)+b*arctan((a+b*sin(d*x+c))^(1/2)/(-a+b)^(1/2))*a*(a+b)^(1/2)+b^2*arctan((a+b*sin(d*x+c))^(1/2)/(-a+b)^(1/2))*(a+b)^(1/2))*cos(d*x+c)^2+2*(a+b*sin(d*x+c))^(1/2)*b*(-a+b)^(1/2)*(a+b)^(1/2))/(-a+b)^(1/2)/(a+b)^(1/2)/cos(d*x+c)^2/d","B"
488,1,409,164,1.019000," ","int(sec(d*x+c)^5*(a+b*sin(d*x+c))^(3/2),x)","\frac{4 \sqrt{a +b \sin \left(d x +c \right)}\, \sqrt{-a +b}\, \sqrt{a +b}\, b \left(b \left(\cos^{2}\left(d x +c \right)\right)+8 a \sin \left(d x +c \right)-b \right)+3 b \left(4 \arctanh \left(\frac{\sqrt{a +b \sin \left(d x +c \right)}}{\sqrt{a +b}}\right) a^{2} \sqrt{-a +b}+2 b \arctanh \left(\frac{\sqrt{a +b \sin \left(d x +c \right)}}{\sqrt{a +b}}\right) a \sqrt{-a +b}-b^{2} \arctanh \left(\frac{\sqrt{a +b \sin \left(d x +c \right)}}{\sqrt{a +b}}\right) \sqrt{-a +b}+4 \arctan \left(\frac{\sqrt{a +b \sin \left(d x +c \right)}}{\sqrt{-a +b}}\right) a^{2} \sqrt{a +b}-2 b \arctan \left(\frac{\sqrt{a +b \sin \left(d x +c \right)}}{\sqrt{-a +b}}\right) a \sqrt{a +b}-b^{2} \arctan \left(\frac{\sqrt{a +b \sin \left(d x +c \right)}}{\sqrt{-a +b}}\right) \sqrt{a +b}\right) \left(\cos^{4}\left(d x +c \right)\right)+6 \sqrt{a +b \sin \left(d x +c \right)}\, \sqrt{-a +b}\, \sqrt{a +b}\, b \left(2 a \sin \left(d x +c \right)-b \right) \left(\cos^{2}\left(d x +c \right)\right)-24 \left(a +b \sin \left(d x +c \right)\right)^{\frac{3}{2}} a \sqrt{-a +b}\, \sqrt{a +b}+24 \sqrt{a +b \sin \left(d x +c \right)}\, a^{2} \sqrt{-a +b}\, \sqrt{a +b}+12 \sqrt{a +b \sin \left(d x +c \right)}\, b^{2} \sqrt{-a +b}\, \sqrt{a +b}}{32 \sqrt{-a +b}\, \sqrt{a +b}\, b \cos \left(d x +c \right)^{4} d}"," ",0,"1/32*(4*(a+b*sin(d*x+c))^(1/2)*(-a+b)^(1/2)*(a+b)^(1/2)*b*(b*cos(d*x+c)^2+8*a*sin(d*x+c)-b)+3*b*(4*arctanh((a+b*sin(d*x+c))^(1/2)/(a+b)^(1/2))*a^2*(-a+b)^(1/2)+2*b*arctanh((a+b*sin(d*x+c))^(1/2)/(a+b)^(1/2))*a*(-a+b)^(1/2)-b^2*arctanh((a+b*sin(d*x+c))^(1/2)/(a+b)^(1/2))*(-a+b)^(1/2)+4*arctan((a+b*sin(d*x+c))^(1/2)/(-a+b)^(1/2))*a^2*(a+b)^(1/2)-2*b*arctan((a+b*sin(d*x+c))^(1/2)/(-a+b)^(1/2))*a*(a+b)^(1/2)-b^2*arctan((a+b*sin(d*x+c))^(1/2)/(-a+b)^(1/2))*(a+b)^(1/2))*cos(d*x+c)^4+6*(a+b*sin(d*x+c))^(1/2)*(-a+b)^(1/2)*(a+b)^(1/2)*b*(2*a*sin(d*x+c)-b)*cos(d*x+c)^2-24*(a+b*sin(d*x+c))^(3/2)*a*(-a+b)^(1/2)*(a+b)^(1/2)+24*(a+b*sin(d*x+c))^(1/2)*a^2*(-a+b)^(1/2)*(a+b)^(1/2)+12*(a+b*sin(d*x+c))^(1/2)*b^2*(-a+b)^(1/2)*(a+b)^(1/2))/(-a+b)^(1/2)/(a+b)^(1/2)/b/cos(d*x+c)^4/d","B"
489,1,1355,371,0.802000," ","int(cos(d*x+c)^4*(a+b*sin(d*x+c))^(3/2),x)","-\frac{2 \left(-255 b^{7} \left(\sin^{3}\left(d x +c \right)\right)+300 b^{7} \left(\sin^{5}\left(d x +c \right)\right)-581 a \,b^{6} \left(\sin^{2}\left(d x +c \right)\right)+2 a^{4} b^{3} \sin \left(d x +c \right)-373 a^{2} b^{5} \sin \left(d x +c \right)+60 b^{7} \sin \left(d x +c \right)-245 a \,b^{6} \left(\sin^{6}\left(d x +c \right)\right)-8 a^{5} b^{2} \left(\sin^{2}\left(d x +c \right)\right)-145 a^{2} b^{5} \left(\sin^{5}\left(d x +c \right)\right)+8 a^{5} b^{2}-47 a^{3} b^{4}+60 a \,b^{6}+518 a^{2} b^{5} \left(\sin^{3}\left(d x +c \right)\right)+766 a \,b^{6} \left(\sin^{4}\left(d x +c \right)\right)+a^{3} b^{4} \left(\sin^{4}\left(d x +c \right)\right)+46 a^{3} b^{4} \left(\sin^{2}\left(d x +c \right)\right)-2 a^{4} b^{3} \left(\sin^{3}\left(d x +c \right)\right)+60 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) b^{7}-16 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{7}-105 b^{7} \left(\sin^{7}\left(d x +c \right)\right)+16 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{6} b -12 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{5} b^{2}-100 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{4} b^{3}-360 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{3} b^{4}+24 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{2} b^{5}+372 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{6}+112 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{5} b^{2}+336 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{3} b^{4}-432 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{6}\right)}{1155 b^{5} \cos \left(d x +c \right) \sqrt{a +b \sin \left(d x +c \right)}\, d}"," ",0,"-2/1155*(16*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^6*b-581*a*b^6*sin(d*x+c)^2+2*a^4*b^3*sin(d*x+c)-373*a^2*b^5*sin(d*x+c)-245*a*b^6*sin(d*x+c)^6-145*a^2*b^5*sin(d*x+c)^5+a^3*b^4*sin(d*x+c)^4+766*a*b^6*sin(d*x+c)^4-2*a^4*b^3*sin(d*x+c)^3+518*a^2*b^5*sin(d*x+c)^3-8*a^5*b^2*sin(d*x+c)^2+46*a^3*b^4*sin(d*x+c)^2+300*b^7*sin(d*x+c)^5-255*b^7*sin(d*x+c)^3+60*b^7*sin(d*x+c)-105*b^7*sin(d*x+c)^7+8*a^5*b^2-47*a^3*b^4+60*a*b^6+60*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*b^7-16*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^7-12*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^5*b^2-100*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^4*b^3-360*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^3*b^4+24*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^2*b^5+372*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a*b^6+112*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^5*b^2+336*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^3*b^4-432*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a*b^6)/b^5/cos(d*x+c)/(a+b*sin(d*x+c))^(1/2)/d","B"
490,1,943,293,0.722000," ","int(cos(d*x+c)^2*(a+b*sin(d*x+c))^(3/2),x)","\frac{-\frac{2 b^{5} \left(\sin^{5}\left(d x +c \right)\right)}{7}+\frac{4 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{4} b}{35}+\frac{32 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{3} b^{2}}{35}+\frac{8 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{2} b^{3}}{105}-\frac{32 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{4}}{35}-\frac{4 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) b^{5}}{21}-\frac{4 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{5}}{35}-\frac{104 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{3} b^{2}}{105}+\frac{116 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{4}}{105}-\frac{26 a \,b^{4} \left(\sin^{4}\left(d x +c \right)\right)}{35}-\frac{18 a^{2} b^{3} \left(\sin^{3}\left(d x +c \right)\right)}{35}+\frac{10 b^{5} \left(\sin^{3}\left(d x +c \right)\right)}{21}-\frac{2 a^{3} b^{2} \left(\sin^{2}\left(d x +c \right)\right)}{35}+\frac{14 a \,b^{4} \left(\sin^{2}\left(d x +c \right)\right)}{15}+\frac{18 a^{2} b^{3} \sin \left(d x +c \right)}{35}-\frac{4 b^{5} \sin \left(d x +c \right)}{21}+\frac{2 a^{3} b^{2}}{35}-\frac{4 a \,b^{4}}{21}}{b^{3} \cos \left(d x +c \right) \sqrt{a +b \sin \left(d x +c \right)}\, d}"," ",0,"2/105*(-15*b^5*sin(d*x+c)^5+6*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^4*b+48*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^3*b^2+4*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^2*b^3-48*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a*b^4-10*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*b^5-6*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^5-52*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^3*b^2+58*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a*b^4-39*a*b^4*sin(d*x+c)^4-27*a^2*b^3*sin(d*x+c)^3+25*b^5*sin(d*x+c)^3-3*a^3*b^2*sin(d*x+c)^2+49*a*b^4*sin(d*x+c)^2+27*a^2*b^3*sin(d*x+c)-10*b^5*sin(d*x+c)+3*a^3*b^2-10*a*b^4)/b^3/cos(d*x+c)/(a+b*sin(d*x+c))^(1/2)/d","B"
491,1,635,224,0.789000," ","int(sec(d*x+c)^2*(a+b*sin(d*x+c))^(3/2),x)","-\frac{\sqrt{\left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) b +\left(\cos^{2}\left(d x +c \right)\right) a}\, \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}\, \sqrt{-\frac{b \sin \left(d x +c \right)}{a +b}+\frac{b}{a +b}}\, \sqrt{-\frac{b \sin \left(d x +c \right)}{a -b}-\frac{b}{a -b}}\, \EllipticF \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{2} b -\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}\, \sqrt{-\frac{b \sin \left(d x +c \right)}{a +b}+\frac{b}{a +b}}\, \sqrt{-\frac{b \sin \left(d x +c \right)}{a -b}-\frac{b}{a -b}}\, \EllipticF \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) b^{3}-\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}\, \sqrt{-\frac{b \sin \left(d x +c \right)}{a +b}+\frac{b}{a +b}}\, \sqrt{-\frac{b \sin \left(d x +c \right)}{a -b}-\frac{b}{a -b}}\, \EllipticE \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{3}+\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}\, \sqrt{-\frac{b \sin \left(d x +c \right)}{a +b}+\frac{b}{a +b}}\, \sqrt{-\frac{b \sin \left(d x +c \right)}{a -b}-\frac{b}{a -b}}\, \EllipticE \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{2}+a \,b^{2} \left(\cos^{2}\left(d x +c \right)\right)-a^{2} b \sin \left(d x +c \right)-b^{3} \sin \left(d x +c \right)-2 a \,b^{2}\right)}{b \sqrt{-\left(a +b \sin \left(d x +c \right)\right) \left(\sin \left(d x +c \right)-1\right) \left(1+\sin \left(d x +c \right)\right)}\, \cos \left(d x +c \right) \sqrt{a +b \sin \left(d x +c \right)}\, d}"," ",0,"-1/b*(cos(d*x+c)^2*sin(d*x+c)*b+cos(d*x+c)^2*a)^(1/2)*((b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2)*(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*(-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*EllipticF((b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2),((a-b)/(a+b))^(1/2))*a^2*b-(b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2)*(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*(-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*EllipticF((b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2),((a-b)/(a+b))^(1/2))*b^3-(b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2)*(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*(-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*EllipticE((b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2),((a-b)/(a+b))^(1/2))*a^3+(b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2)*(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*(-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*EllipticE((b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2),((a-b)/(a+b))^(1/2))*a*b^2+a*b^2*cos(d*x+c)^2-a^2*b*sin(d*x+c)-b^3*sin(d*x+c)-2*a*b^2)/(-(a+b*sin(d*x+c))*(sin(d*x+c)-1)*(1+sin(d*x+c)))^(1/2)/cos(d*x+c)/(a+b*sin(d*x+c))^(1/2)/d","B"
492,1,938,264,1.196000," ","int(sec(d*x+c)^4*(a+b*sin(d*x+c))^(3/2),x)","\frac{-\sqrt{\left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) b +\left(\cos^{2}\left(d x +c \right)\right) a}\, b \left(4 a^{2}-b^{2}\right) \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right)-2 \sqrt{\left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) b +\left(\cos^{2}\left(d x +c \right)\right) a}\, b \left(a^{2}+b^{2}\right) \sin \left(d x +c \right)+4 \sqrt{\left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) b +\left(\cos^{2}\left(d x +c \right)\right) a}\, a \,b^{2} \left(\cos^{4}\left(d x +c \right)\right)+\sqrt{\left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) b +\left(\cos^{2}\left(d x +c \right)\right) a}\, \left(4 \sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}\, \sqrt{-\frac{b \sin \left(d x +c \right)}{a +b}+\frac{b}{a +b}}\, \sqrt{-\frac{b \sin \left(d x +c \right)}{a -b}-\frac{b}{a -b}}\, \EllipticF \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{2} b -3 \EllipticF \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) \sqrt{-\frac{b \sin \left(d x +c \right)}{a -b}-\frac{b}{a -b}}\, \sqrt{-\frac{b \sin \left(d x +c \right)}{a +b}+\frac{b}{a +b}}\, \sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}\, a \,b^{2}-\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}\, \sqrt{-\frac{b \sin \left(d x +c \right)}{a +b}+\frac{b}{a +b}}\, \sqrt{-\frac{b \sin \left(d x +c \right)}{a -b}-\frac{b}{a -b}}\, \EllipticF \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) b^{3}-4 \sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}\, \sqrt{-\frac{b \sin \left(d x +c \right)}{a +b}+\frac{b}{a +b}}\, \sqrt{-\frac{b \sin \left(d x +c \right)}{a -b}-\frac{b}{a -b}}\, \EllipticE \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{3}+4 \sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}\, \sqrt{-\frac{b \sin \left(d x +c \right)}{a +b}+\frac{b}{a +b}}\, \sqrt{-\frac{b \sin \left(d x +c \right)}{a -b}-\frac{b}{a -b}}\, \EllipticE \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{2}-a \,b^{2}\right) \left(\cos^{2}\left(d x +c \right)\right)-4 \sqrt{\left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) b +\left(\cos^{2}\left(d x +c \right)\right) a}\, a \,b^{2}}{6 \sqrt{-\left(a +b \sin \left(d x +c \right)\right) \left(\sin \left(d x +c \right)-1\right) \left(1+\sin \left(d x +c \right)\right)}\, \left(\sin \left(d x +c \right)-1\right) \left(1+\sin \left(d x +c \right)\right) b \cos \left(d x +c \right) \sqrt{a +b \sin \left(d x +c \right)}\, d}"," ",0,"1/6*(-(cos(d*x+c)^2*sin(d*x+c)*b+cos(d*x+c)^2*a)^(1/2)*b*(4*a^2-b^2)*sin(d*x+c)*cos(d*x+c)^2-2*(cos(d*x+c)^2*sin(d*x+c)*b+cos(d*x+c)^2*a)^(1/2)*b*(a^2+b^2)*sin(d*x+c)+4*(cos(d*x+c)^2*sin(d*x+c)*b+cos(d*x+c)^2*a)^(1/2)*a*b^2*cos(d*x+c)^4+(cos(d*x+c)^2*sin(d*x+c)*b+cos(d*x+c)^2*a)^(1/2)*(4*(b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2)*(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*(-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*EllipticF((b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2),((a-b)/(a+b))^(1/2))*a^2*b-3*EllipticF((b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2),((a-b)/(a+b))^(1/2))*(-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*(b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2)*a*b^2-(b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2)*(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*(-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*EllipticF((b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2),((a-b)/(a+b))^(1/2))*b^3-4*(b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2)*(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*(-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*EllipticE((b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2),((a-b)/(a+b))^(1/2))*a^3+4*(b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2)*(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*(-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*EllipticE((b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2),((a-b)/(a+b))^(1/2))*a*b^2-a*b^2)*cos(d*x+c)^2-4*(cos(d*x+c)^2*sin(d*x+c)*b+cos(d*x+c)^2*a)^(1/2)*a*b^2)/(-(a+b*sin(d*x+c))*(sin(d*x+c)-1)*(1+sin(d*x+c)))^(1/2)/(sin(d*x+c)-1)/(1+sin(d*x+c))/b/cos(d*x+c)/(a+b*sin(d*x+c))^(1/2)/d","B"
493,1,1519,372,1.035000," ","int(sec(d*x+c)^6*(a+b*sin(d*x+c))^(3/2),x)","-\frac{-2 \sqrt{\left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) b +\left(\cos^{2}\left(d x +c \right)\right) a}\, b \left(32 a^{4}-37 a^{2} b^{2}+5 b^{4}\right) \sin \left(d x +c \right) \left(\cos^{4}\left(d x +c \right)\right)-4 \sqrt{\left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) b +\left(\cos^{2}\left(d x +c \right)\right) a}\, b \left(8 a^{4}-9 a^{2} b^{2}+b^{4}\right) \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)-24 \sqrt{\left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) b +\left(\cos^{2}\left(d x +c \right)\right) a}\, b \left(a^{4}-b^{4}\right) \sin \left(d x +c \right)+2 \sqrt{\left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) b +\left(\cos^{2}\left(d x +c \right)\right) a}\, a \,b^{2} \left(32 a^{2}-29 b^{2}\right) \left(\cos^{6}\left(d x +c \right)\right)+2 \sqrt{\left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) b +\left(\cos^{2}\left(d x +c \right)\right) a}\, \left(32 \sqrt{-\frac{b \sin \left(d x +c \right)}{a -b}-\frac{b}{a -b}}\, \sqrt{-\frac{b \sin \left(d x +c \right)}{a +b}+\frac{b}{a +b}}\, \EllipticF \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) \sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}\, a^{4} b -24 \sqrt{-\frac{b \sin \left(d x +c \right)}{a -b}-\frac{b}{a -b}}\, \sqrt{-\frac{b \sin \left(d x +c \right)}{a +b}+\frac{b}{a +b}}\, \EllipticF \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) \sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}\, a^{3} b^{2}-37 \sqrt{-\frac{b \sin \left(d x +c \right)}{a -b}-\frac{b}{a -b}}\, \sqrt{-\frac{b \sin \left(d x +c \right)}{a +b}+\frac{b}{a +b}}\, \EllipticF \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) \sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}\, a^{2} b^{3}+24 \sqrt{-\frac{b \sin \left(d x +c \right)}{a -b}-\frac{b}{a -b}}\, \sqrt{-\frac{b \sin \left(d x +c \right)}{a +b}+\frac{b}{a +b}}\, \EllipticF \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) \sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}\, a \,b^{4}+5 \sqrt{-\frac{b \sin \left(d x +c \right)}{a -b}-\frac{b}{a -b}}\, \sqrt{-\frac{b \sin \left(d x +c \right)}{a +b}+\frac{b}{a +b}}\, \EllipticF \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) \sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}\, b^{5}-32 \sqrt{-\frac{b \sin \left(d x +c \right)}{a -b}-\frac{b}{a -b}}\, \sqrt{-\frac{b \sin \left(d x +c \right)}{a +b}+\frac{b}{a +b}}\, \sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}\, \EllipticE \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{5}+61 \sqrt{-\frac{b \sin \left(d x +c \right)}{a -b}-\frac{b}{a -b}}\, \sqrt{-\frac{b \sin \left(d x +c \right)}{a +b}+\frac{b}{a +b}}\, \sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}\, \EllipticE \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{3} b^{2}-29 \sqrt{-\frac{b \sin \left(d x +c \right)}{a -b}-\frac{b}{a -b}}\, \sqrt{-\frac{b \sin \left(d x +c \right)}{a +b}+\frac{b}{a +b}}\, \sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}\, \EllipticE \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{4}-8 a^{3} b^{2}+8 a \,b^{4}\right) \left(\cos^{4}\left(d x +c \right)\right)-4 \sqrt{\left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) b +\left(\cos^{2}\left(d x +c \right)\right) a}\, a \,b^{2} \left(a^{2}-b^{2}\right) \left(\cos^{2}\left(d x +c \right)\right)-48 \sqrt{\left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) b +\left(\cos^{2}\left(d x +c \right)\right) a}\, a^{3} b^{2}+48 \sqrt{\left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) b +\left(\cos^{2}\left(d x +c \right)\right) a}\, a \,b^{4}}{120 \sqrt{-\left(a +b \sin \left(d x +c \right)\right) \left(\sin \left(d x +c \right)-1\right) \left(1+\sin \left(d x +c \right)\right)}\, \left(a +b \right) \left(a -b \right) \left(1+\sin \left(d x +c \right)\right)^{2} \left(\sin \left(d x +c \right)-1\right)^{2} b \cos \left(d x +c \right) \sqrt{a +b \sin \left(d x +c \right)}\, d}"," ",0,"-1/120*(-2*(cos(d*x+c)^2*sin(d*x+c)*b+cos(d*x+c)^2*a)^(1/2)*b*(32*a^4-37*a^2*b^2+5*b^4)*sin(d*x+c)*cos(d*x+c)^4-4*(cos(d*x+c)^2*sin(d*x+c)*b+cos(d*x+c)^2*a)^(1/2)*b*(8*a^4-9*a^2*b^2+b^4)*cos(d*x+c)^2*sin(d*x+c)-24*(cos(d*x+c)^2*sin(d*x+c)*b+cos(d*x+c)^2*a)^(1/2)*b*(a^4-b^4)*sin(d*x+c)+2*(cos(d*x+c)^2*sin(d*x+c)*b+cos(d*x+c)^2*a)^(1/2)*a*b^2*(32*a^2-29*b^2)*cos(d*x+c)^6+2*(cos(d*x+c)^2*sin(d*x+c)*b+cos(d*x+c)^2*a)^(1/2)*(32*(-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*EllipticF((b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2),((a-b)/(a+b))^(1/2))*(b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2)*a^4*b-24*(-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*EllipticF((b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2),((a-b)/(a+b))^(1/2))*(b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2)*a^3*b^2-37*(-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*EllipticF((b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2),((a-b)/(a+b))^(1/2))*(b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2)*a^2*b^3+24*(-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*EllipticF((b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2),((a-b)/(a+b))^(1/2))*(b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2)*a*b^4+5*(-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*EllipticF((b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2),((a-b)/(a+b))^(1/2))*(b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2)*b^5-32*(-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*(b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2)*EllipticE((b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2),((a-b)/(a+b))^(1/2))*a^5+61*(-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*(b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2)*EllipticE((b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2),((a-b)/(a+b))^(1/2))*a^3*b^2-29*(-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*(b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2)*EllipticE((b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2),((a-b)/(a+b))^(1/2))*a*b^4-8*a^3*b^2+8*a*b^4)*cos(d*x+c)^4-4*(cos(d*x+c)^2*sin(d*x+c)*b+cos(d*x+c)^2*a)^(1/2)*a*b^2*(a^2-b^2)*cos(d*x+c)^2-48*(cos(d*x+c)^2*sin(d*x+c)*b+cos(d*x+c)^2*a)^(1/2)*a^3*b^2+48*(cos(d*x+c)^2*sin(d*x+c)*b+cos(d*x+c)^2*a)^(1/2)*a*b^4)/(-(a+b*sin(d*x+c))*(sin(d*x+c)-1)*(1+sin(d*x+c)))^(1/2)/(a+b)/(a-b)/(1+sin(d*x+c))^2/(sin(d*x+c)-1)^2/b/cos(d*x+c)/(a+b*sin(d*x+c))^(1/2)/d","B"
494,1,126,134,0.642000," ","int(cos(d*x+c)^5*(a+b*sin(d*x+c))^(5/2),x)","\frac{2 \left(a +b \sin \left(d x +c \right)\right)^{\frac{7}{2}} \left(3003 b^{4} \left(\cos^{4}\left(d x +c \right)\right)+1848 a \,b^{3} \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)-1008 a^{2} b^{2} \left(\cos^{2}\left(d x +c \right)\right)+2184 b^{4} \left(\cos^{2}\left(d x +c \right)\right)-448 a^{3} b \sin \left(d x +c \right)+1792 a \,b^{3} \sin \left(d x +c \right)+128 a^{4}-32 a^{2} b^{2}+1248 b^{4}\right)}{45045 b^{5} d}"," ",0,"2/45045/b^5*(a+b*sin(d*x+c))^(7/2)*(3003*b^4*cos(d*x+c)^4+1848*a*b^3*cos(d*x+c)^2*sin(d*x+c)-1008*a^2*b^2*cos(d*x+c)^2+2184*b^4*cos(d*x+c)^2-448*a^3*b*sin(d*x+c)+1792*a*b^3*sin(d*x+c)+128*a^4-32*a^2*b^2+1248*b^4)/d","A"
495,1,55,71,0.485000," ","int(cos(d*x+c)^3*(a+b*sin(d*x+c))^(5/2),x)","-\frac{2 \left(a +b \sin \left(d x +c \right)\right)^{\frac{7}{2}} \left(-63 b^{2} \left(\cos^{2}\left(d x +c \right)\right)-28 a b \sin \left(d x +c \right)+8 a^{2}-36 b^{2}\right)}{693 b^{3} d}"," ",0,"-2/693/b^3*(a+b*sin(d*x+c))^(7/2)*(-63*b^2*cos(d*x+c)^2-28*a*b*sin(d*x+c)+8*a^2-36*b^2)/d","A"
496,1,21,20,0.041000," ","int(cos(d*x+c)*(a+b*sin(d*x+c))^(5/2),x)","\frac{2 \left(a +b \sin \left(d x +c \right)\right)^{\frac{7}{2}}}{7 b d}"," ",0,"2/7*(a+b*sin(d*x+c))^(7/2)/b/d","A"
497,1,312,99,0.522000," ","int(sec(d*x+c)*(a+b*sin(d*x+c))^(5/2),x)","-\frac{2 b \left(a +b \sin \left(d x +c \right)\right)^{\frac{3}{2}}}{3 d}-\frac{4 a b \sqrt{a +b \sin \left(d x +c \right)}}{d}+\frac{\arctan \left(\frac{\sqrt{a +b \sin \left(d x +c \right)}}{\sqrt{-a +b}}\right) a^{3}}{d \sqrt{-a +b}}-\frac{3 b \arctan \left(\frac{\sqrt{a +b \sin \left(d x +c \right)}}{\sqrt{-a +b}}\right) a^{2}}{d \sqrt{-a +b}}+\frac{3 b^{2} \arctan \left(\frac{\sqrt{a +b \sin \left(d x +c \right)}}{\sqrt{-a +b}}\right) a}{d \sqrt{-a +b}}-\frac{b^{3} \arctan \left(\frac{\sqrt{a +b \sin \left(d x +c \right)}}{\sqrt{-a +b}}\right)}{d \sqrt{-a +b}}+\frac{\arctanh \left(\frac{\sqrt{a +b \sin \left(d x +c \right)}}{\sqrt{a +b}}\right) a^{3}}{d \sqrt{a +b}}+\frac{3 b \arctanh \left(\frac{\sqrt{a +b \sin \left(d x +c \right)}}{\sqrt{a +b}}\right) a^{2}}{d \sqrt{a +b}}+\frac{3 b^{2} \arctanh \left(\frac{\sqrt{a +b \sin \left(d x +c \right)}}{\sqrt{a +b}}\right) a}{d \sqrt{a +b}}+\frac{b^{3} \arctanh \left(\frac{\sqrt{a +b \sin \left(d x +c \right)}}{\sqrt{a +b}}\right)}{d \sqrt{a +b}}"," ",0,"-2/3*b*(a+b*sin(d*x+c))^(3/2)/d-4*a*b*(a+b*sin(d*x+c))^(1/2)/d+1/d/(-a+b)^(1/2)*arctan((a+b*sin(d*x+c))^(1/2)/(-a+b)^(1/2))*a^3-3/d*b/(-a+b)^(1/2)*arctan((a+b*sin(d*x+c))^(1/2)/(-a+b)^(1/2))*a^2+3/d*b^2/(-a+b)^(1/2)*arctan((a+b*sin(d*x+c))^(1/2)/(-a+b)^(1/2))*a-1/d*b^3/(-a+b)^(1/2)*arctan((a+b*sin(d*x+c))^(1/2)/(-a+b)^(1/2))+1/d/(a+b)^(1/2)*arctanh((a+b*sin(d*x+c))^(1/2)/(a+b)^(1/2))*a^3+3/d*b/(a+b)^(1/2)*arctanh((a+b*sin(d*x+c))^(1/2)/(a+b)^(1/2))*a^2+3/d*b^2/(a+b)^(1/2)*arctanh((a+b*sin(d*x+c))^(1/2)/(a+b)^(1/2))*a+1/d*b^3/(a+b)^(1/2)*arctanh((a+b*sin(d*x+c))^(1/2)/(a+b)^(1/2))","B"
498,1,356,131,0.672000," ","int(sec(d*x+c)^3*(a+b*sin(d*x+c))^(5/2),x)","\frac{2 \sin \left(d x +c \right) \sqrt{-a +b}\, \sqrt{a +b}\, \sqrt{a +b \sin \left(d x +c \right)}\, \left(a^{2}+b^{2}\right)-\left(-2 \arctanh \left(\frac{\sqrt{a +b \sin \left(d x +c \right)}}{\sqrt{a +b}}\right) a^{3} \sqrt{-a +b}-b \arctanh \left(\frac{\sqrt{a +b \sin \left(d x +c \right)}}{\sqrt{a +b}}\right) a^{2} \sqrt{-a +b}+4 b^{2} \arctanh \left(\frac{\sqrt{a +b \sin \left(d x +c \right)}}{\sqrt{a +b}}\right) a \sqrt{-a +b}+3 b^{3} \arctanh \left(\frac{\sqrt{a +b \sin \left(d x +c \right)}}{\sqrt{a +b}}\right) \sqrt{-a +b}-2 \arctan \left(\frac{\sqrt{a +b \sin \left(d x +c \right)}}{\sqrt{-a +b}}\right) a^{3} \sqrt{a +b}+b \arctan \left(\frac{\sqrt{a +b \sin \left(d x +c \right)}}{\sqrt{-a +b}}\right) a^{2} \sqrt{a +b}+4 b^{2} \arctan \left(\frac{\sqrt{a +b \sin \left(d x +c \right)}}{\sqrt{-a +b}}\right) a \sqrt{a +b}-3 b^{3} \arctan \left(\frac{\sqrt{a +b \sin \left(d x +c \right)}}{\sqrt{-a +b}}\right) \sqrt{a +b}\right) \left(\cos^{2}\left(d x +c \right)\right)+4 \sqrt{a +b \sin \left(d x +c \right)}\, b a \sqrt{-a +b}\, \sqrt{a +b}}{4 \sqrt{-a +b}\, \sqrt{a +b}\, \cos \left(d x +c \right)^{2} d}"," ",0,"1/4*(2*sin(d*x+c)*(-a+b)^(1/2)*(a+b)^(1/2)*(a+b*sin(d*x+c))^(1/2)*(a^2+b^2)-(-2*arctanh((a+b*sin(d*x+c))^(1/2)/(a+b)^(1/2))*a^3*(-a+b)^(1/2)-b*arctanh((a+b*sin(d*x+c))^(1/2)/(a+b)^(1/2))*a^2*(-a+b)^(1/2)+4*b^2*arctanh((a+b*sin(d*x+c))^(1/2)/(a+b)^(1/2))*a*(-a+b)^(1/2)+3*b^3*arctanh((a+b*sin(d*x+c))^(1/2)/(a+b)^(1/2))*(-a+b)^(1/2)-2*arctan((a+b*sin(d*x+c))^(1/2)/(-a+b)^(1/2))*a^3*(a+b)^(1/2)+b*arctan((a+b*sin(d*x+c))^(1/2)/(-a+b)^(1/2))*a^2*(a+b)^(1/2)+4*b^2*arctan((a+b*sin(d*x+c))^(1/2)/(-a+b)^(1/2))*a*(a+b)^(1/2)-3*b^3*arctan((a+b*sin(d*x+c))^(1/2)/(-a+b)^(1/2))*(a+b)^(1/2))*cos(d*x+c)^2+4*(a+b*sin(d*x+c))^(1/2)*b*a*(-a+b)^(1/2)*(a+b)^(1/2))/(-a+b)^(1/2)/(a+b)^(1/2)/cos(d*x+c)^2/d","B"
499,1,538,175,1.787000," ","int(sec(d*x+c)^5*(a+b*sin(d*x+c))^(5/2),x)","\frac{4 \sqrt{-a +b}\, \sqrt{a +b}\, \sqrt{a +b \sin \left(d x +c \right)}\, b \left(3 a b \left(\cos^{2}\left(d x +c \right)\right)+8 a^{2} \sin \left(d x +c \right)-b^{2} \sin \left(d x +c \right)-3 a b \right)+3 b \left(4 \arctanh \left(\frac{\sqrt{a +b \sin \left(d x +c \right)}}{\sqrt{a +b}}\right) a^{3} \sqrt{-a +b}+2 b \arctanh \left(\frac{\sqrt{a +b \sin \left(d x +c \right)}}{\sqrt{a +b}}\right) a^{2} \sqrt{-a +b}-3 b^{2} \arctanh \left(\frac{\sqrt{a +b \sin \left(d x +c \right)}}{\sqrt{a +b}}\right) a \sqrt{-a +b}-b^{3} \arctanh \left(\frac{\sqrt{a +b \sin \left(d x +c \right)}}{\sqrt{a +b}}\right) \sqrt{-a +b}+4 \arctan \left(\frac{\sqrt{a +b \sin \left(d x +c \right)}}{\sqrt{-a +b}}\right) a^{3} \sqrt{a +b}-2 b \arctan \left(\frac{\sqrt{a +b \sin \left(d x +c \right)}}{\sqrt{-a +b}}\right) a^{2} \sqrt{a +b}-3 b^{2} \arctan \left(\frac{\sqrt{a +b \sin \left(d x +c \right)}}{\sqrt{-a +b}}\right) a \sqrt{a +b}+b^{3} \arctan \left(\frac{\sqrt{a +b \sin \left(d x +c \right)}}{\sqrt{-a +b}}\right) \sqrt{a +b}\right) \left(\cos^{4}\left(d x +c \right)\right)+2 \sqrt{-a +b}\, \sqrt{a +b}\, \sqrt{a +b \sin \left(d x +c \right)}\, b \left(6 a^{2} \sin \left(d x +c \right)-3 b^{2} \sin \left(d x +c \right)-7 a b \right) \left(\cos^{2}\left(d x +c \right)\right)-24 \left(a +b \sin \left(d x +c \right)\right)^{\frac{3}{2}} a^{2} \sqrt{-a +b}\, \sqrt{a +b}+12 \left(a +b \sin \left(d x +c \right)\right)^{\frac{3}{2}} b^{2} \sqrt{-a +b}\, \sqrt{a +b}+24 \sqrt{a +b \sin \left(d x +c \right)}\, a^{3} \sqrt{-a +b}\, \sqrt{a +b}+16 a \sqrt{a +b \sin \left(d x +c \right)}\, b^{2} \sqrt{-a +b}\, \sqrt{a +b}}{32 \sqrt{-a +b}\, \sqrt{a +b}\, b \cos \left(d x +c \right)^{4} d}"," ",0,"1/32*(4*(-a+b)^(1/2)*(a+b)^(1/2)*(a+b*sin(d*x+c))^(1/2)*b*(3*a*b*cos(d*x+c)^2+8*a^2*sin(d*x+c)-b^2*sin(d*x+c)-3*a*b)+3*b*(4*arctanh((a+b*sin(d*x+c))^(1/2)/(a+b)^(1/2))*a^3*(-a+b)^(1/2)+2*b*arctanh((a+b*sin(d*x+c))^(1/2)/(a+b)^(1/2))*a^2*(-a+b)^(1/2)-3*b^2*arctanh((a+b*sin(d*x+c))^(1/2)/(a+b)^(1/2))*a*(-a+b)^(1/2)-b^3*arctanh((a+b*sin(d*x+c))^(1/2)/(a+b)^(1/2))*(-a+b)^(1/2)+4*arctan((a+b*sin(d*x+c))^(1/2)/(-a+b)^(1/2))*a^3*(a+b)^(1/2)-2*b*arctan((a+b*sin(d*x+c))^(1/2)/(-a+b)^(1/2))*a^2*(a+b)^(1/2)-3*b^2*arctan((a+b*sin(d*x+c))^(1/2)/(-a+b)^(1/2))*a*(a+b)^(1/2)+b^3*arctan((a+b*sin(d*x+c))^(1/2)/(-a+b)^(1/2))*(a+b)^(1/2))*cos(d*x+c)^4+2*(-a+b)^(1/2)*(a+b)^(1/2)*(a+b*sin(d*x+c))^(1/2)*b*(6*a^2*sin(d*x+c)-3*b^2*sin(d*x+c)-7*a*b)*cos(d*x+c)^2-24*(a+b*sin(d*x+c))^(3/2)*a^2*(-a+b)^(1/2)*(a+b)^(1/2)+12*(a+b*sin(d*x+c))^(3/2)*b^2*(-a+b)^(1/2)*(a+b)^(1/2)+24*(a+b*sin(d*x+c))^(1/2)*a^3*(-a+b)^(1/2)*(a+b)^(1/2)+16*a*(a+b*sin(d*x+c))^(1/2)*b^2*(-a+b)^(1/2)*(a+b)^(1/2))/(-a+b)^(1/2)/(a+b)^(1/2)/b/cos(d*x+c)^4/d","B"
500,1,1619,436,0.965000," ","int(cos(d*x+c)^4*(a+b*sin(d*x+c))^(5/2),x)","-\frac{2 \left(40 a^{6} b^{2}+5 a^{4} b^{4} \left(\sin^{4}\left(d x +c \right)\right)+3080 b^{8} \left(\sin^{6}\left(d x +c \right)\right)-2233 b^{8} \left(\sin^{4}\left(d x +c \right)\right)+308 b^{8} \left(\sin^{2}\left(d x +c \right)\right)+14500 a^{2} b^{6} \left(\sin^{4}\left(d x +c \right)\right)-11606 a^{2} b^{6} \left(\sin^{2}\left(d x +c \right)\right)+11290 a \,b^{7} \left(\sin^{5}\left(d x +c \right)\right)-1880 a^{3} b^{5} \left(\sin^{5}\left(d x +c \right)\right)+10 a^{5} b^{3} \sin \left(d x +c \right)-4780 a^{3} b^{5} \sin \left(d x +c \right)+2104 a \,b^{7} \sin \left(d x +c \right)+4236 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{2} b^{6}+1488 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{7}+780 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{6} b^{2}+5948 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{4} b^{4}-5724 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{2} b^{6}-3990 a \,b^{7} \left(\sin^{7}\left(d x +c \right)\right)+6660 a^{3} b^{5} \left(\sin^{3}\left(d x +c \right)\right)+340 a^{4} b^{4} \left(\sin^{2}\left(d x +c \right)\right)-40 a^{6} b^{2} \left(\sin^{2}\left(d x +c \right)\right)-10 a^{5} b^{3} \left(\sin^{3}\left(d x +c \right)\right)-9404 a \,b^{7} \left(\sin^{3}\left(d x +c \right)\right)-924 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) b^{8}+924 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) b^{8}-80 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{8}-4690 a^{2} b^{6} \left(\sin^{6}\left(d x +c \right)\right)-1155 b^{8} \left(\sin^{8}\left(d x +c \right)\right)-345 a^{4} b^{4}+1796 a^{2} b^{6}+80 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{7} b -60 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{6} b^{2}-720 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{5} b^{3}-5100 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{4} b^{4}-848 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{3} b^{5}\right)}{15015 b^{5} \cos \left(d x +c \right) \sqrt{a +b \sin \left(d x +c \right)}\, d}"," ",0,"-2/15015*(40*a^6*b^2-3990*a*b^7*sin(d*x+c)^7+80*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^7*b-11606*a^2*b^6*sin(d*x+c)^2+10*a^5*b^3*sin(d*x+c)-4780*a^3*b^5*sin(d*x+c)+2104*a*b^7*sin(d*x+c)-4690*a^2*b^6*sin(d*x+c)^6-1880*a^3*b^5*sin(d*x+c)^5+11290*a*b^7*sin(d*x+c)^5+5*a^4*b^4*sin(d*x+c)^4+14500*a^2*b^6*sin(d*x+c)^4-10*a^5*b^3*sin(d*x+c)^3+6660*a^3*b^5*sin(d*x+c)^3-9404*a*b^7*sin(d*x+c)^3-40*a^6*b^2*sin(d*x+c)^2+340*a^4*b^4*sin(d*x+c)^2-924*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*b^8-1155*b^8*sin(d*x+c)^8+3080*b^8*sin(d*x+c)^6-2233*b^8*sin(d*x+c)^4+308*b^8*sin(d*x+c)^2-345*a^4*b^4+1796*a^2*b^6+924*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*b^8-80*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^8-60*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^6*b^2-720*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^5*b^3-5100*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^4*b^4-848*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^3*b^5+4236*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^2*b^6+1488*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a*b^7+780*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^6*b^2+5948*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^4*b^4-5724*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^2*b^6)/b^5/cos(d*x+c)/(a+b*sin(d*x+c))^(1/2)/d","B"
501,1,1190,341,0.888000," ","int(cos(d*x+c)^2*(a+b*sin(d*x+c))^(5/2),x)","\frac{-\frac{2 b^{6} \left(\sin^{6}\left(d x +c \right)\right)}{9}-\frac{52 a \,b^{5} \left(\sin^{5}\left(d x +c \right)\right)}{63}+\frac{4 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{5} b}{63}+\frac{20 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{4} b^{2}}{21}+\frac{88 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{3} b^{3}}{315}-\frac{24 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{2} b^{4}}{35}-\frac{12 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{5}}{35}-\frac{4 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) b^{6}}{15}-\frac{4 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{6}}{63}-\frac{388 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{4} b^{2}}{315}+\frac{36 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{2} b^{4}}{35}+\frac{4 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) b^{6}}{15}-\frac{68 a^{2} b^{4} \left(\sin^{4}\left(d x +c \right)\right)}{63}+\frac{14 b^{6} \left(\sin^{4}\left(d x +c \right)\right)}{45}-\frac{32 a^{3} b^{3} \left(\sin^{3}\left(d x +c \right)\right)}{63}+\frac{424 a \,b^{5} \left(\sin^{3}\left(d x +c \right)\right)}{315}-\frac{2 a^{4} b^{2} \left(\sin^{2}\left(d x +c \right)\right)}{63}+\frac{68 a^{2} b^{4} \left(\sin^{2}\left(d x +c \right)\right)}{45}-\frac{4 b^{6} \left(\sin^{2}\left(d x +c \right)\right)}{45}+\frac{32 a^{3} b^{3} \sin \left(d x +c \right)}{63}-\frac{164 a \,b^{5} \sin \left(d x +c \right)}{315}+\frac{2 a^{4} b^{2}}{63}-\frac{136 a^{2} b^{4}}{315}}{b^{3} \cos \left(d x +c \right) \sqrt{a +b \sin \left(d x +c \right)}\, d}"," ",0,"2/315*(-35*b^6*sin(d*x+c)^6-130*a*b^5*sin(d*x+c)^5+10*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^5*b+150*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^4*b^2+44*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^3*b^3-108*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^2*b^4-54*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a*b^5-42*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*b^6-10*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^6-194*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^4*b^2+162*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^2*b^4+42*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*b^6-170*a^2*b^4*sin(d*x+c)^4+49*b^6*sin(d*x+c)^4-80*a^3*b^3*sin(d*x+c)^3+212*a*b^5*sin(d*x+c)^3-5*a^4*b^2*sin(d*x+c)^2+238*a^2*b^4*sin(d*x+c)^2-14*b^6*sin(d*x+c)^2+80*a^3*b^3*sin(d*x+c)-82*a*b^5*sin(d*x+c)+5*a^4*b^2-68*a^2*b^4)/b^3/cos(d*x+c)/(a+b*sin(d*x+c))^(1/2)/d","B"
502,1,1042,257,0.876000," ","int(sec(d*x+c)^2*(a+b*sin(d*x+c))^(5/2),x)","-\frac{\sqrt{\left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) b +\left(\cos^{2}\left(d x +c \right)\right) a}\, \left(\sqrt{-\frac{b \sin \left(d x +c \right)}{a -b}-\frac{b}{a -b}}\, \sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}\, \EllipticF \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) \sqrt{-\frac{b \sin \left(d x +c \right)}{a +b}+\frac{b}{a +b}}\, a^{3} b +3 \sqrt{-\frac{b \sin \left(d x +c \right)}{a -b}-\frac{b}{a -b}}\, \sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}\, \EllipticF \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) \sqrt{-\frac{b \sin \left(d x +c \right)}{a +b}+\frac{b}{a +b}}\, a^{2} b^{2}-\sqrt{-\frac{b \sin \left(d x +c \right)}{a -b}-\frac{b}{a -b}}\, \sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}\, \EllipticF \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) \sqrt{-\frac{b \sin \left(d x +c \right)}{a +b}+\frac{b}{a +b}}\, a \,b^{3}-3 \sqrt{-\frac{b \sin \left(d x +c \right)}{a -b}-\frac{b}{a -b}}\, \sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}\, \EllipticF \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) \sqrt{-\frac{b \sin \left(d x +c \right)}{a +b}+\frac{b}{a +b}}\, b^{4}-\sqrt{-\frac{b \sin \left(d x +c \right)}{a -b}-\frac{b}{a -b}}\, \sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}\, \EllipticE \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) \sqrt{-\frac{b \sin \left(d x +c \right)}{a +b}+\frac{b}{a +b}}\, a^{4}-2 \sqrt{-\frac{b \sin \left(d x +c \right)}{a -b}-\frac{b}{a -b}}\, \sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}\, \EllipticE \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) \sqrt{-\frac{b \sin \left(d x +c \right)}{a +b}+\frac{b}{a +b}}\, a^{2} b^{2}+3 \sqrt{-\frac{b \sin \left(d x +c \right)}{a -b}-\frac{b}{a -b}}\, \sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}\, \EllipticE \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) \sqrt{-\frac{b \sin \left(d x +c \right)}{a +b}+\frac{b}{a +b}}\, b^{4}+a^{2} b^{2} \left(\cos^{2}\left(d x +c \right)\right)+b^{4} \left(\cos^{2}\left(d x +c \right)\right)-a^{3} b \sin \left(d x +c \right)-3 a \,b^{3} \sin \left(d x +c \right)-3 a^{2} b^{2}-b^{4}\right)}{b \sqrt{-\left(a +b \sin \left(d x +c \right)\right) \left(\sin \left(d x +c \right)-1\right) \left(1+\sin \left(d x +c \right)\right)}\, \cos \left(d x +c \right) \sqrt{a +b \sin \left(d x +c \right)}\, d}"," ",0,"-1/b*(cos(d*x+c)^2*sin(d*x+c)*b+cos(d*x+c)^2*a)^(1/2)*((-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*(b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2)*EllipticF((b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2),((a-b)/(a+b))^(1/2))*(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*a^3*b+3*(-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*(b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2)*EllipticF((b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2),((a-b)/(a+b))^(1/2))*(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*a^2*b^2-(-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*(b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2)*EllipticF((b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2),((a-b)/(a+b))^(1/2))*(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*a*b^3-3*(-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*(b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2)*EllipticF((b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2),((a-b)/(a+b))^(1/2))*(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*b^4-(-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*(b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2)*EllipticE((b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2),((a-b)/(a+b))^(1/2))*(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*a^4-2*(-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*(b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2)*EllipticE((b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2),((a-b)/(a+b))^(1/2))*(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*a^2*b^2+3*(-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*(b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2)*EllipticE((b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2),((a-b)/(a+b))^(1/2))*(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*b^4+a^2*b^2*cos(d*x+c)^2+b^4*cos(d*x+c)^2-a^3*b*sin(d*x+c)-3*a*b^3*sin(d*x+c)-3*a^2*b^2-b^4)/(-(a+b*sin(d*x+c))*(sin(d*x+c)-1)*(1+sin(d*x+c)))^(1/2)/cos(d*x+c)/(a+b*sin(d*x+c))^(1/2)/d","B"
503,1,1249,284,0.910000," ","int(sec(d*x+c)^4*(a+b*sin(d*x+c))^(5/2),x)","\frac{-4 \sqrt{\left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) b +\left(\cos^{2}\left(d x +c \right)\right) a}\, a b \left(a^{2}-b^{2}\right) \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right)-2 \sqrt{\left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) b +\left(\cos^{2}\left(d x +c \right)\right) a}\, a b \left(a^{2}+3 b^{2}\right) \sin \left(d x +c \right)+\sqrt{\left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) b +\left(\cos^{2}\left(d x +c \right)\right) a}\, b^{2} \left(4 a^{2}-3 b^{2}\right) \left(\cos^{4}\left(d x +c \right)\right)-\sqrt{\left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) b +\left(\cos^{2}\left(d x +c \right)\right) a}\, \left(4 \sqrt{-\frac{b \sin \left(d x +c \right)}{a -b}-\frac{b}{a -b}}\, \sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}\, \EllipticE \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) \sqrt{-\frac{b \sin \left(d x +c \right)}{a +b}+\frac{b}{a +b}}\, a^{4}-7 \sqrt{-\frac{b \sin \left(d x +c \right)}{a -b}-\frac{b}{a -b}}\, \sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}\, \EllipticE \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) \sqrt{-\frac{b \sin \left(d x +c \right)}{a +b}+\frac{b}{a +b}}\, a^{2} b^{2}+3 \sqrt{-\frac{b \sin \left(d x +c \right)}{a -b}-\frac{b}{a -b}}\, \sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}\, \EllipticE \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) \sqrt{-\frac{b \sin \left(d x +c \right)}{a +b}+\frac{b}{a +b}}\, b^{4}-4 \sqrt{-\frac{b \sin \left(d x +c \right)}{a -b}-\frac{b}{a -b}}\, \sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}\, \EllipticF \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) \sqrt{-\frac{b \sin \left(d x +c \right)}{a +b}+\frac{b}{a +b}}\, a^{3} b +3 \sqrt{-\frac{b \sin \left(d x +c \right)}{a -b}-\frac{b}{a -b}}\, \sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}\, \EllipticF \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) \sqrt{-\frac{b \sin \left(d x +c \right)}{a +b}+\frac{b}{a +b}}\, a^{2} b^{2}+4 \sqrt{-\frac{b \sin \left(d x +c \right)}{a -b}-\frac{b}{a -b}}\, \sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}\, \EllipticF \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) \sqrt{-\frac{b \sin \left(d x +c \right)}{a +b}+\frac{b}{a +b}}\, a \,b^{3}-3 \sqrt{-\frac{b \sin \left(d x +c \right)}{a -b}-\frac{b}{a -b}}\, \sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}\, \EllipticF \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) \sqrt{-\frac{b \sin \left(d x +c \right)}{a +b}+\frac{b}{a +b}}\, b^{4}+a^{2} b^{2}-5 b^{4}\right) \left(\cos^{2}\left(d x +c \right)\right)-6 \sqrt{\left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) b +\left(\cos^{2}\left(d x +c \right)\right) a}\, a^{2} b^{2}-2 \sqrt{\left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) b +\left(\cos^{2}\left(d x +c \right)\right) a}\, b^{4}}{6 \sqrt{-\left(a +b \sin \left(d x +c \right)\right) \left(\sin \left(d x +c \right)-1\right) \left(1+\sin \left(d x +c \right)\right)}\, \left(\sin \left(d x +c \right)-1\right) \left(1+\sin \left(d x +c \right)\right) b \cos \left(d x +c \right) \sqrt{a +b \sin \left(d x +c \right)}\, d}"," ",0,"1/6*(-4*(cos(d*x+c)^2*sin(d*x+c)*b+cos(d*x+c)^2*a)^(1/2)*a*b*(a^2-b^2)*sin(d*x+c)*cos(d*x+c)^2-2*(cos(d*x+c)^2*sin(d*x+c)*b+cos(d*x+c)^2*a)^(1/2)*a*b*(a^2+3*b^2)*sin(d*x+c)+(cos(d*x+c)^2*sin(d*x+c)*b+cos(d*x+c)^2*a)^(1/2)*b^2*(4*a^2-3*b^2)*cos(d*x+c)^4-(cos(d*x+c)^2*sin(d*x+c)*b+cos(d*x+c)^2*a)^(1/2)*(4*(-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*(b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2)*EllipticE((b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2),((a-b)/(a+b))^(1/2))*(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*a^4-7*(-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*(b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2)*EllipticE((b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2),((a-b)/(a+b))^(1/2))*(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*a^2*b^2+3*(-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*(b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2)*EllipticE((b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2),((a-b)/(a+b))^(1/2))*(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*b^4-4*(-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*(b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2)*EllipticF((b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2),((a-b)/(a+b))^(1/2))*(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*a^3*b+3*(-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*(b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2)*EllipticF((b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2),((a-b)/(a+b))^(1/2))*(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*a^2*b^2+4*(-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*(b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2)*EllipticF((b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2),((a-b)/(a+b))^(1/2))*(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*a*b^3-3*(-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*(b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2)*EllipticF((b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2),((a-b)/(a+b))^(1/2))*(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*b^4+a^2*b^2-5*b^4)*cos(d*x+c)^2-6*(cos(d*x+c)^2*sin(d*x+c)*b+cos(d*x+c)^2*a)^(1/2)*a^2*b^2-2*(cos(d*x+c)^2*sin(d*x+c)*b+cos(d*x+c)^2*a)^(1/2)*b^4)/(-(a+b*sin(d*x+c))*(sin(d*x+c)-1)*(1+sin(d*x+c)))^(1/2)/(sin(d*x+c)-1)/(1+sin(d*x+c))/b/cos(d*x+c)/(a+b*sin(d*x+c))^(1/2)/d","B"
504,1,1360,364,0.945000," ","int(sec(d*x+c)^6*(a+b*sin(d*x+c))^(5/2),x)","\frac{\sqrt{\left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) b +\left(\cos^{2}\left(d x +c \right)\right) a}\, a b \left(32 a^{2}-17 b^{2}\right) \sin \left(d x +c \right) \left(\cos^{4}\left(d x +c \right)\right)+8 \sqrt{\left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) b +\left(\cos^{2}\left(d x +c \right)\right) a}\, a b \left(2 a^{2}-b^{2}\right) \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+12 \sqrt{\left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) b +\left(\cos^{2}\left(d x +c \right)\right) a}\, a b \left(a^{2}+3 b^{2}\right) \sin \left(d x +c \right)-\sqrt{\left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) b +\left(\cos^{2}\left(d x +c \right)\right) a}\, b^{2} \left(32 a^{2}-9 b^{2}\right) \left(\cos^{6}\left(d x +c \right)\right)+\sqrt{\left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) b +\left(\cos^{2}\left(d x +c \right)\right) a}\, \left(32 \sqrt{-\frac{b \sin \left(d x +c \right)}{a -b}-\frac{b}{a -b}}\, \sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}\, \EllipticE \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) \sqrt{-\frac{b \sin \left(d x +c \right)}{a +b}+\frac{b}{a +b}}\, a^{4}-41 \sqrt{-\frac{b \sin \left(d x +c \right)}{a -b}-\frac{b}{a -b}}\, \sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}\, \EllipticE \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) \sqrt{-\frac{b \sin \left(d x +c \right)}{a +b}+\frac{b}{a +b}}\, a^{2} b^{2}+9 \sqrt{-\frac{b \sin \left(d x +c \right)}{a -b}-\frac{b}{a -b}}\, \sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}\, \EllipticE \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) \sqrt{-\frac{b \sin \left(d x +c \right)}{a +b}+\frac{b}{a +b}}\, b^{4}-32 \sqrt{-\frac{b \sin \left(d x +c \right)}{a -b}-\frac{b}{a -b}}\, \sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}\, \EllipticF \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) \sqrt{-\frac{b \sin \left(d x +c \right)}{a +b}+\frac{b}{a +b}}\, a^{3} b +24 \sqrt{-\frac{b \sin \left(d x +c \right)}{a -b}-\frac{b}{a -b}}\, \sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}\, \EllipticF \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) \sqrt{-\frac{b \sin \left(d x +c \right)}{a +b}+\frac{b}{a +b}}\, a^{2} b^{2}+17 \sqrt{-\frac{b \sin \left(d x +c \right)}{a -b}-\frac{b}{a -b}}\, \sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}\, \EllipticF \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) \sqrt{-\frac{b \sin \left(d x +c \right)}{a +b}+\frac{b}{a +b}}\, a \,b^{3}-9 \sqrt{-\frac{b \sin \left(d x +c \right)}{a -b}-\frac{b}{a -b}}\, \sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}\, \EllipticF \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) \sqrt{-\frac{b \sin \left(d x +c \right)}{a +b}+\frac{b}{a +b}}\, b^{4}+8 a^{2} b^{2}-3 b^{4}\right) \left(\cos^{4}\left(d x +c \right)\right)+2 \sqrt{\left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) b +\left(\cos^{2}\left(d x +c \right)\right) a}\, b^{2} \left(a^{2}-9 b^{2}\right) \left(\cos^{2}\left(d x +c \right)\right)+36 \sqrt{\left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) b +\left(\cos^{2}\left(d x +c \right)\right) a}\, a^{2} b^{2}+12 \sqrt{\left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) b +\left(\cos^{2}\left(d x +c \right)\right) a}\, b^{4}}{60 \sqrt{-\left(a +b \sin \left(d x +c \right)\right) \left(\sin \left(d x +c \right)-1\right) \left(1+\sin \left(d x +c \right)\right)}\, \left(\sin \left(d x +c \right)-1\right)^{2} \left(1+\sin \left(d x +c \right)\right)^{2} b \cos \left(d x +c \right) \sqrt{a +b \sin \left(d x +c \right)}\, d}"," ",0,"1/60*((cos(d*x+c)^2*sin(d*x+c)*b+cos(d*x+c)^2*a)^(1/2)*a*b*(32*a^2-17*b^2)*sin(d*x+c)*cos(d*x+c)^4+8*(cos(d*x+c)^2*sin(d*x+c)*b+cos(d*x+c)^2*a)^(1/2)*a*b*(2*a^2-b^2)*cos(d*x+c)^2*sin(d*x+c)+12*(cos(d*x+c)^2*sin(d*x+c)*b+cos(d*x+c)^2*a)^(1/2)*a*b*(a^2+3*b^2)*sin(d*x+c)-(cos(d*x+c)^2*sin(d*x+c)*b+cos(d*x+c)^2*a)^(1/2)*b^2*(32*a^2-9*b^2)*cos(d*x+c)^6+(cos(d*x+c)^2*sin(d*x+c)*b+cos(d*x+c)^2*a)^(1/2)*(32*(-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*(b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2)*EllipticE((b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2),((a-b)/(a+b))^(1/2))*(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*a^4-41*(-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*(b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2)*EllipticE((b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2),((a-b)/(a+b))^(1/2))*(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*a^2*b^2+9*(-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*(b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2)*EllipticE((b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2),((a-b)/(a+b))^(1/2))*(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*b^4-32*(-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*(b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2)*EllipticF((b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2),((a-b)/(a+b))^(1/2))*(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*a^3*b+24*(-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*(b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2)*EllipticF((b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2),((a-b)/(a+b))^(1/2))*(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*a^2*b^2+17*(-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*(b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2)*EllipticF((b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2),((a-b)/(a+b))^(1/2))*(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*a*b^3-9*(-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*(b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2)*EllipticF((b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2),((a-b)/(a+b))^(1/2))*(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*b^4+8*a^2*b^2-3*b^4)*cos(d*x+c)^4+2*(cos(d*x+c)^2*sin(d*x+c)*b+cos(d*x+c)^2*a)^(1/2)*b^2*(a^2-9*b^2)*cos(d*x+c)^2+36*(cos(d*x+c)^2*sin(d*x+c)*b+cos(d*x+c)^2*a)^(1/2)*a^2*b^2+12*(cos(d*x+c)^2*sin(d*x+c)*b+cos(d*x+c)^2*a)^(1/2)*b^4)/(-(a+b*sin(d*x+c))*(sin(d*x+c)-1)*(1+sin(d*x+c)))^(1/2)/(sin(d*x+c)-1)^2/(1+sin(d*x+c))^2/b/cos(d*x+c)/(a+b*sin(d*x+c))^(1/2)/d","B"
505,1,1888,477,8.633000," ","int(sec(d*x+c)^8*(a+b*sin(d*x+c))^(5/2),x)","\frac{\sqrt{-\left(-a -b \sin \left(d x +c \right)\right) \left(\cos^{2}\left(d x +c \right)\right)}\, \left(2 \left(\cos^{4}\left(d x +c \right)\right) \sqrt{\left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) b +\left(\cos^{2}\left(d x +c \right)\right) a}\, b^{2} \left(4 a^{4}-5 a^{2} b^{2}+b^{4}\right)+40 \sqrt{\left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) b +\left(\cos^{2}\left(d x +c \right)\right) a}\, b^{2} \left(3 a^{4}-2 a^{2} b^{2}-b^{4}\right)+4 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) b +\left(\cos^{2}\left(d x +c \right)\right) a}\, b^{2} \left(a^{4}-14 a^{2} b^{2}+13 b^{4}\right)-\left(\cos^{8}\left(d x +c \right)\right) \sqrt{\left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) b +\left(\cos^{2}\left(d x +c \right)\right) a}\, b^{2} \left(128 a^{4}-144 a^{2} b^{2}+21 b^{4}\right)+16 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) b +\left(\cos^{2}\left(d x +c \right)\right) a}\, a b \left(3 a^{4}-4 a^{2} b^{2}+b^{4}\right) \sin \left(d x +c \right)+40 \sqrt{\left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) b +\left(\cos^{2}\left(d x +c \right)\right) a}\, a b \left(a^{4}+2 a^{2} b^{2}-3 b^{4}\right) \sin \left(d x +c \right)+16 \left(\cos^{6}\left(d x +c \right)\right) \sqrt{\left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) b +\left(\cos^{2}\left(d x +c \right)\right) a}\, a b \left(8 a^{4}-11 a^{2} b^{2}+3 b^{4}\right) \sin \left(d x +c \right)+2 \left(\cos^{4}\left(d x +c \right)\right) \sqrt{\left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) b +\left(\cos^{2}\left(d x +c \right)\right) a}\, a b \left(32 a^{4}-43 a^{2} b^{2}+11 b^{4}\right) \sin \left(d x +c \right)-\left(\cos^{6}\left(d x +c \right)\right) \sqrt{\left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) b +\left(\cos^{2}\left(d x +c \right)\right) a}\, \left(128 \EllipticF \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) \sqrt{-\frac{b \sin \left(d x +c \right)}{a +b}+\frac{b}{a +b}}\, \sqrt{-\frac{b \sin \left(d x +c \right)}{a -b}-\frac{b}{a -b}}\, \sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}\, a^{5} b -96 \EllipticF \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) \sqrt{-\frac{b \sin \left(d x +c \right)}{a +b}+\frac{b}{a +b}}\, \sqrt{-\frac{b \sin \left(d x +c \right)}{a -b}-\frac{b}{a -b}}\, \sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}\, a^{4} b^{2}-176 \EllipticF \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) \sqrt{-\frac{b \sin \left(d x +c \right)}{a +b}+\frac{b}{a +b}}\, \sqrt{-\frac{b \sin \left(d x +c \right)}{a -b}-\frac{b}{a -b}}\, \sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}\, a^{3} b^{3}+117 \EllipticF \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) \sqrt{-\frac{b \sin \left(d x +c \right)}{a +b}+\frac{b}{a +b}}\, \sqrt{-\frac{b \sin \left(d x +c \right)}{a -b}-\frac{b}{a -b}}\, \sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}\, a^{2} b^{4}+48 \EllipticF \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) \sqrt{-\frac{b \sin \left(d x +c \right)}{a +b}+\frac{b}{a +b}}\, \sqrt{-\frac{b \sin \left(d x +c \right)}{a -b}-\frac{b}{a -b}}\, \sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}\, a \,b^{5}-21 \EllipticF \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) \sqrt{-\frac{b \sin \left(d x +c \right)}{a +b}+\frac{b}{a +b}}\, \sqrt{-\frac{b \sin \left(d x +c \right)}{a -b}-\frac{b}{a -b}}\, \sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}\, b^{6}-128 \sqrt{-\frac{b \sin \left(d x +c \right)}{a +b}+\frac{b}{a +b}}\, \EllipticE \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) \sqrt{-\frac{b \sin \left(d x +c \right)}{a -b}-\frac{b}{a -b}}\, \sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}\, a^{6}+272 \sqrt{-\frac{b \sin \left(d x +c \right)}{a +b}+\frac{b}{a +b}}\, \EllipticE \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) \sqrt{-\frac{b \sin \left(d x +c \right)}{a -b}-\frac{b}{a -b}}\, \sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}\, a^{4} b^{2}-165 \sqrt{-\frac{b \sin \left(d x +c \right)}{a +b}+\frac{b}{a +b}}\, \EllipticE \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) \sqrt{-\frac{b \sin \left(d x +c \right)}{a -b}-\frac{b}{a -b}}\, \sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}\, a^{2} b^{4}+21 \sqrt{-\frac{b \sin \left(d x +c \right)}{a +b}+\frac{b}{a +b}}\, \EllipticE \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) \sqrt{-\frac{b \sin \left(d x +c \right)}{a -b}-\frac{b}{a -b}}\, \sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}\, b^{6}-32 a^{4} b^{2}+39 a^{2} b^{4}-7 b^{6}\right)\right)}{280 \cos \left(d x +c \right)^{9} \left(a +b \sin \left(d x +c \right)\right)^{\frac{3}{2}} b \left(a^{2}-b^{2}\right) d}"," ",0,"1/280*(-(-a-b*sin(d*x+c))*cos(d*x+c)^2)^(1/2)/cos(d*x+c)^9/(a+b*sin(d*x+c))^(3/2)/b/(a^2-b^2)*(2*cos(d*x+c)^4*(cos(d*x+c)^2*sin(d*x+c)*b+cos(d*x+c)^2*a)^(1/2)*b^2*(4*a^4-5*a^2*b^2+b^4)+40*(cos(d*x+c)^2*sin(d*x+c)*b+cos(d*x+c)^2*a)^(1/2)*b^2*(3*a^4-2*a^2*b^2-b^4)+4*cos(d*x+c)^2*(cos(d*x+c)^2*sin(d*x+c)*b+cos(d*x+c)^2*a)^(1/2)*b^2*(a^4-14*a^2*b^2+13*b^4)-cos(d*x+c)^8*(cos(d*x+c)^2*sin(d*x+c)*b+cos(d*x+c)^2*a)^(1/2)*b^2*(128*a^4-144*a^2*b^2+21*b^4)+16*cos(d*x+c)^2*(cos(d*x+c)^2*sin(d*x+c)*b+cos(d*x+c)^2*a)^(1/2)*a*b*(3*a^4-4*a^2*b^2+b^4)*sin(d*x+c)+40*(cos(d*x+c)^2*sin(d*x+c)*b+cos(d*x+c)^2*a)^(1/2)*a*b*(a^4+2*a^2*b^2-3*b^4)*sin(d*x+c)+16*cos(d*x+c)^6*(cos(d*x+c)^2*sin(d*x+c)*b+cos(d*x+c)^2*a)^(1/2)*a*b*(8*a^4-11*a^2*b^2+3*b^4)*sin(d*x+c)+2*cos(d*x+c)^4*(cos(d*x+c)^2*sin(d*x+c)*b+cos(d*x+c)^2*a)^(1/2)*a*b*(32*a^4-43*a^2*b^2+11*b^4)*sin(d*x+c)-cos(d*x+c)^6*(cos(d*x+c)^2*sin(d*x+c)*b+cos(d*x+c)^2*a)^(1/2)*(128*EllipticF((b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2),((a-b)/(a+b))^(1/2))*(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*(-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*(b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2)*a^5*b-96*EllipticF((b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2),((a-b)/(a+b))^(1/2))*(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*(-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*(b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2)*a^4*b^2-176*EllipticF((b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2),((a-b)/(a+b))^(1/2))*(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*(-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*(b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2)*a^3*b^3+117*EllipticF((b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2),((a-b)/(a+b))^(1/2))*(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*(-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*(b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2)*a^2*b^4+48*EllipticF((b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2),((a-b)/(a+b))^(1/2))*(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*(-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*(b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2)*a*b^5-21*EllipticF((b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2),((a-b)/(a+b))^(1/2))*(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*(-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*(b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2)*b^6-128*(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*EllipticE((b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2),((a-b)/(a+b))^(1/2))*(-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*(b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2)*a^6+272*(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*EllipticE((b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2),((a-b)/(a+b))^(1/2))*(-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*(b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2)*a^4*b^2-165*(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*EllipticE((b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2),((a-b)/(a+b))^(1/2))*(-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*(b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2)*a^2*b^4+21*(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*EllipticE((b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2),((a-b)/(a+b))^(1/2))*(-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*(b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2)*b^6-32*a^4*b^2+39*a^2*b^4-7*b^6))/d","B"
506,1,126,134,0.334000," ","int(cos(d*x+c)^5/(a+b*sin(d*x+c))^(1/2),x)","\frac{2 \sqrt{a +b \sin \left(d x +c \right)}\, \left(35 b^{4} \left(\cos^{4}\left(d x +c \right)\right)+40 a \,b^{3} \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)-48 a^{2} b^{2} \left(\cos^{2}\left(d x +c \right)\right)+56 b^{4} \left(\cos^{2}\left(d x +c \right)\right)-64 a^{3} b \sin \left(d x +c \right)+128 a \,b^{3} \sin \left(d x +c \right)+128 a^{4}-288 a^{2} b^{2}+224 b^{4}\right)}{315 b^{5} d}"," ",0,"2/315/b^5*(a+b*sin(d*x+c))^(1/2)*(35*b^4*cos(d*x+c)^4+40*a*b^3*cos(d*x+c)^2*sin(d*x+c)-48*a^2*b^2*cos(d*x+c)^2+56*b^4*cos(d*x+c)^2-64*a^3*b*sin(d*x+c)+128*a*b^3*sin(d*x+c)+128*a^4-288*a^2*b^2+224*b^4)/d","A"
507,1,55,71,0.296000," ","int(cos(d*x+c)^3/(a+b*sin(d*x+c))^(1/2),x)","-\frac{2 \sqrt{a +b \sin \left(d x +c \right)}\, \left(-3 b^{2} \left(\cos^{2}\left(d x +c \right)\right)-4 a b \sin \left(d x +c \right)+8 a^{2}-12 b^{2}\right)}{15 b^{3} d}"," ",0,"-2/15/b^3*(a+b*sin(d*x+c))^(1/2)*(-3*b^2*cos(d*x+c)^2-4*a*b*sin(d*x+c)+8*a^2-12*b^2)/d","A"
508,1,21,20,0.021000," ","int(cos(d*x+c)/(a+b*sin(d*x+c))^(1/2),x)","\frac{2 \sqrt{a +b \sin \left(d x +c \right)}}{b d}"," ",0,"2*(a+b*sin(d*x+c))^(1/2)/b/d","A"
509,1,62,62,0.473000," ","int(sec(d*x+c)/(a+b*sin(d*x+c))^(1/2),x)","\frac{\arctan \left(\frac{\sqrt{a +b \sin \left(d x +c \right)}}{\sqrt{-a +b}}\right)}{d \sqrt{-a +b}}+\frac{\arctanh \left(\frac{\sqrt{a +b \sin \left(d x +c \right)}}{\sqrt{a +b}}\right)}{d \sqrt{a +b}}"," ",0,"1/d/(-a+b)^(1/2)*arctan((a+b*sin(d*x+c))^(1/2)/(-a+b)^(1/2))+arctanh((a+b*sin(d*x+c))^(1/2)/(a+b)^(1/2))/d/(a+b)^(1/2)","A"
510,1,218,124,0.816000," ","int(sec(d*x+c)^3/(a+b*sin(d*x+c))^(1/2),x)","-\frac{b \sqrt{a +b \sin \left(d x +c \right)}}{4 d \left(a -b \right) \left(b \sin \left(d x +c \right)+b \right)}+\frac{\arctan \left(\frac{\sqrt{a +b \sin \left(d x +c \right)}}{\sqrt{-a +b}}\right) a}{2 d \left(a -b \right) \sqrt{-a +b}}-\frac{3 \arctan \left(\frac{\sqrt{a +b \sin \left(d x +c \right)}}{\sqrt{-a +b}}\right) b}{4 d \left(a -b \right) \sqrt{-a +b}}-\frac{b \sqrt{a +b \sin \left(d x +c \right)}}{4 d \left(a +b \right) \left(b \sin \left(d x +c \right)-b \right)}+\frac{\arctanh \left(\frac{\sqrt{a +b \sin \left(d x +c \right)}}{\sqrt{a +b}}\right) a}{2 d \left(a +b \right)^{\frac{3}{2}}}+\frac{3 \arctanh \left(\frac{\sqrt{a +b \sin \left(d x +c \right)}}{\sqrt{a +b}}\right) b}{4 d \left(a +b \right)^{\frac{3}{2}}}"," ",0,"-1/4/d*b/(a-b)*(a+b*sin(d*x+c))^(1/2)/(b*sin(d*x+c)+b)+1/2/d/(a-b)/(-a+b)^(1/2)*arctan((a+b*sin(d*x+c))^(1/2)/(-a+b)^(1/2))*a-3/4/d/(a-b)/(-a+b)^(1/2)*arctan((a+b*sin(d*x+c))^(1/2)/(-a+b)^(1/2))*b-1/4/d*b/(a+b)*(a+b*sin(d*x+c))^(1/2)/(b*sin(d*x+c)-b)+1/2/d/(a+b)^(3/2)*arctanh((a+b*sin(d*x+c))^(1/2)/(a+b)^(1/2))*a+3/4/d/(a+b)^(3/2)*arctanh((a+b*sin(d*x+c))^(1/2)/(a+b)^(1/2))*b","A"
511,1,618,206,1.112000," ","int(sec(d*x+c)^5/(a+b*sin(d*x+c))^(1/2),x)","-\frac{3 b \left(a +b \sin \left(d x +c \right)\right)^{\frac{3}{2}} a}{16 d \left(b \sin \left(d x +c \right)+b \right)^{2} \left(a^{2}-2 a b +b^{2}\right)}+\frac{9 b^{2} \left(a +b \sin \left(d x +c \right)\right)^{\frac{3}{2}}}{32 d \left(b \sin \left(d x +c \right)+b \right)^{2} \left(a^{2}-2 a b +b^{2}\right)}+\frac{3 b \sqrt{a +b \sin \left(d x +c \right)}\, a}{16 d \left(b \sin \left(d x +c \right)+b \right)^{2} \left(a -b \right)}-\frac{11 b^{2} \sqrt{a +b \sin \left(d x +c \right)}}{32 d \left(b \sin \left(d x +c \right)+b \right)^{2} \left(a -b \right)}+\frac{3 \arctan \left(\frac{\sqrt{a +b \sin \left(d x +c \right)}}{\sqrt{-a +b}}\right) a^{2}}{8 d \left(a^{2}-2 a b +b^{2}\right) \sqrt{-a +b}}-\frac{15 \arctan \left(\frac{\sqrt{a +b \sin \left(d x +c \right)}}{\sqrt{-a +b}}\right) a b}{16 d \left(a^{2}-2 a b +b^{2}\right) \sqrt{-a +b}}+\frac{21 \arctan \left(\frac{\sqrt{a +b \sin \left(d x +c \right)}}{\sqrt{-a +b}}\right) b^{2}}{32 d \left(a^{2}-2 a b +b^{2}\right) \sqrt{-a +b}}-\frac{3 b \left(a +b \sin \left(d x +c \right)\right)^{\frac{3}{2}} a}{16 d \left(b \sin \left(d x +c \right)-b \right)^{2} \left(a^{2}+2 a b +b^{2}\right)}-\frac{9 b^{2} \left(a +b \sin \left(d x +c \right)\right)^{\frac{3}{2}}}{32 d \left(b \sin \left(d x +c \right)-b \right)^{2} \left(a^{2}+2 a b +b^{2}\right)}+\frac{3 b \sqrt{a +b \sin \left(d x +c \right)}\, a}{16 d \left(b \sin \left(d x +c \right)-b \right)^{2} \left(a +b \right)}+\frac{11 b^{2} \sqrt{a +b \sin \left(d x +c \right)}}{32 d \left(b \sin \left(d x +c \right)-b \right)^{2} \left(a +b \right)}+\frac{3 \arctanh \left(\frac{\sqrt{a +b \sin \left(d x +c \right)}}{\sqrt{a +b}}\right) a^{2}}{8 d \left(a^{2}+2 a b +b^{2}\right) \sqrt{a +b}}+\frac{15 \arctanh \left(\frac{\sqrt{a +b \sin \left(d x +c \right)}}{\sqrt{a +b}}\right) a b}{16 d \left(a^{2}+2 a b +b^{2}\right) \sqrt{a +b}}+\frac{21 \arctanh \left(\frac{\sqrt{a +b \sin \left(d x +c \right)}}{\sqrt{a +b}}\right) b^{2}}{32 d \left(a^{2}+2 a b +b^{2}\right) \sqrt{a +b}}"," ",0,"-3/16/d/(b*sin(d*x+c)+b)^2*b/(a^2-2*a*b+b^2)*(a+b*sin(d*x+c))^(3/2)*a+9/32/d/(b*sin(d*x+c)+b)^2*b^2/(a^2-2*a*b+b^2)*(a+b*sin(d*x+c))^(3/2)+3/16/d/(b*sin(d*x+c)+b)^2*b/(a-b)*(a+b*sin(d*x+c))^(1/2)*a-11/32/d/(b*sin(d*x+c)+b)^2*b^2/(a-b)*(a+b*sin(d*x+c))^(1/2)+3/8/d/(a^2-2*a*b+b^2)/(-a+b)^(1/2)*arctan((a+b*sin(d*x+c))^(1/2)/(-a+b)^(1/2))*a^2-15/16/d/(a^2-2*a*b+b^2)/(-a+b)^(1/2)*arctan((a+b*sin(d*x+c))^(1/2)/(-a+b)^(1/2))*a*b+21/32/d/(a^2-2*a*b+b^2)/(-a+b)^(1/2)*arctan((a+b*sin(d*x+c))^(1/2)/(-a+b)^(1/2))*b^2-3/16/d/(b*sin(d*x+c)-b)^2*b/(a^2+2*a*b+b^2)*(a+b*sin(d*x+c))^(3/2)*a-9/32/d/(b*sin(d*x+c)-b)^2*b^2/(a^2+2*a*b+b^2)*(a+b*sin(d*x+c))^(3/2)+3/16/d/(b*sin(d*x+c)-b)^2*b/(a+b)*(a+b*sin(d*x+c))^(1/2)*a+11/32/d/(b*sin(d*x+c)-b)^2*b^2/(a+b)*(a+b*sin(d*x+c))^(1/2)+3/8/d/(a^2+2*a*b+b^2)/(a+b)^(1/2)*arctanh((a+b*sin(d*x+c))^(1/2)/(a+b)^(1/2))*a^2+15/16/d/(a^2+2*a*b+b^2)/(a+b)^(1/2)*arctanh((a+b*sin(d*x+c))^(1/2)/(a+b)^(1/2))*a*b+21/32/d/(a^2+2*a*b+b^2)/(a+b)^(1/2)*arctanh((a+b*sin(d*x+c))^(1/2)/(a+b)^(1/2))*b^2","B"
512,1,942,293,0.853000," ","int(cos(d*x+c)^4/(a+b*sin(d*x+c))^(1/2),x)","-\frac{2 \left(-5 b^{5} \left(\sin^{5}\left(d x +c \right)\right)+16 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{4} b -12 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{3} b^{2}-36 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{2} b^{3}+12 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{4}+20 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) b^{5}-16 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{5}+48 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{3} b^{2}-32 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{4}+a \,b^{4} \left(\sin^{4}\left(d x +c \right)\right)-2 a^{2} b^{3} \left(\sin^{3}\left(d x +c \right)\right)+20 b^{5} \left(\sin^{3}\left(d x +c \right)\right)-8 a^{3} b^{2} \left(\sin^{2}\left(d x +c \right)\right)+14 a \,b^{4} \left(\sin^{2}\left(d x +c \right)\right)+2 a^{2} b^{3} \sin \left(d x +c \right)-15 b^{5} \sin \left(d x +c \right)+8 a^{3} b^{2}-15 a \,b^{4}\right)}{35 b^{5} \cos \left(d x +c \right) \sqrt{a +b \sin \left(d x +c \right)}\, d}"," ",0,"-2/35*(-5*b^5*sin(d*x+c)^5+16*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^4*b-12*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^3*b^2-36*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^2*b^3+12*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a*b^4+20*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*b^5-16*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^5+48*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^3*b^2-32*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a*b^4+a*b^4*sin(d*x+c)^4-2*a^2*b^3*sin(d*x+c)^3+20*b^5*sin(d*x+c)^3-8*a^3*b^2*sin(d*x+c)^2+14*a*b^4*sin(d*x+c)^2+2*a^2*b^3*sin(d*x+c)-15*b^5*sin(d*x+c)+8*a^3*b^2-15*a*b^4)/b^5/cos(d*x+c)/(a+b*sin(d*x+c))^(1/2)/d","B"
513,1,462,225,0.743000," ","int(cos(d*x+c)^2/(a+b*sin(d*x+c))^(1/2),x)","\frac{\frac{4 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{2} b}{3}-\frac{4 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) b^{3}}{3}-\frac{4 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{3}}{3}+\frac{4 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{2}}{3}-\frac{2 b^{3} \left(\sin^{3}\left(d x +c \right)\right)}{3}-\frac{2 a \,b^{2} \left(\sin^{2}\left(d x +c \right)\right)}{3}+\frac{2 b^{3} \sin \left(d x +c \right)}{3}+\frac{2 a \,b^{2}}{3}}{b^{3} \cos \left(d x +c \right) \sqrt{a +b \sin \left(d x +c \right)}\, d}"," ",0,"2/3*(2*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^2*b-2*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*b^3-2*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^3+2*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a*b^2-b^3*sin(d*x+c)^3-a*b^2*sin(d*x+c)^2+b^3*sin(d*x+c)+a*b^2)/b^3/cos(d*x+c)/(a+b*sin(d*x+c))^(1/2)/d","B"
514,1,640,239,0.798000," ","int(sec(d*x+c)^2/(a+b*sin(d*x+c))^(1/2),x)","\frac{\sqrt{\left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) b +\left(\cos^{2}\left(d x +c \right)\right) a}\, \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}\, \sqrt{-\frac{b \sin \left(d x +c \right)}{a +b}+\frac{b}{a +b}}\, \sqrt{-\frac{b \sin \left(d x +c \right)}{a -b}-\frac{b}{a -b}}\, \EllipticE \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{3}-\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}\, \sqrt{-\frac{b \sin \left(d x +c \right)}{a +b}+\frac{b}{a +b}}\, \sqrt{-\frac{b \sin \left(d x +c \right)}{a -b}-\frac{b}{a -b}}\, \EllipticE \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{2}-\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}\, \sqrt{-\frac{b \sin \left(d x +c \right)}{a +b}+\frac{b}{a +b}}\, \sqrt{-\frac{b \sin \left(d x +c \right)}{a -b}-\frac{b}{a -b}}\, \EllipticF \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{2} b +\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}\, \sqrt{-\frac{b \sin \left(d x +c \right)}{a +b}+\frac{b}{a +b}}\, \sqrt{-\frac{b \sin \left(d x +c \right)}{a -b}-\frac{b}{a -b}}\, \EllipticF \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) b^{3}-a \,b^{2} \left(\cos^{2}\left(d x +c \right)\right)+a^{2} b \sin \left(d x +c \right)-b^{3} \sin \left(d x +c \right)\right)}{b \left(a +b \right) \sqrt{-\left(a +b \sin \left(d x +c \right)\right) \left(\sin \left(d x +c \right)-1\right) \left(1+\sin \left(d x +c \right)\right)}\, \left(a -b \right) \cos \left(d x +c \right) \sqrt{a +b \sin \left(d x +c \right)}\, d}"," ",0,"1/b*(cos(d*x+c)^2*sin(d*x+c)*b+cos(d*x+c)^2*a)^(1/2)*((b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2)*(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*(-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*EllipticE((b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2),((a-b)/(a+b))^(1/2))*a^3-(b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2)*(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*(-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*EllipticE((b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2),((a-b)/(a+b))^(1/2))*a*b^2-(b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2)*(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*(-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*EllipticF((b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2),((a-b)/(a+b))^(1/2))*a^2*b+(b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2)*(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*(-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*EllipticF((b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2),((a-b)/(a+b))^(1/2))*b^3-a*b^2*cos(d*x+c)^2+a^2*b*sin(d*x+c)-b^3*sin(d*x+c))/(a+b)/(-(a+b*sin(d*x+c))*(sin(d*x+c)-1)*(1+sin(d*x+c)))^(1/2)/(a-b)/cos(d*x+c)/(a+b*sin(d*x+c))^(1/2)/d","B"
515,1,1314,337,2.258000," ","int(sec(d*x+c)^4/(a+b*sin(d*x+c))^(1/2),x)","\frac{\sqrt{-\left(-a -b \sin \left(d x +c \right)\right) \left(\cos^{2}\left(d x +c \right)\right)}\, \left(-4 \left(\cos^{4}\left(d x +c \right)\right) \sqrt{\left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) b +\left(\cos^{2}\left(d x +c \right)\right) a}\, a \,b^{2} \left(a^{2}-2 b^{2}\right)+\left(\cos^{2}\left(d x +c \right)\right) \sqrt{\left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) b +\left(\cos^{2}\left(d x +c \right)\right) a}\, b \left(4 a^{4}-9 a^{2} b^{2}+5 b^{4}\right) \sin \left(d x +c \right)+2 \sqrt{\left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) b +\left(\cos^{2}\left(d x +c \right)\right) a}\, b \left(a^{4}-2 a^{2} b^{2}+b^{4}\right) \sin \left(d x +c \right)-\left(\cos^{2}\left(d x +c \right)\right) \sqrt{\left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) b +\left(\cos^{2}\left(d x +c \right)\right) a}\, \left(4 \sqrt{-\frac{b \sin \left(d x +c \right)}{a -b}-\frac{b}{a -b}}\, \sqrt{-\frac{b \sin \left(d x +c \right)}{a +b}+\frac{b}{a +b}}\, \EllipticF \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) \sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}\, a^{4} b -3 \sqrt{-\frac{b \sin \left(d x +c \right)}{a -b}-\frac{b}{a -b}}\, \sqrt{-\frac{b \sin \left(d x +c \right)}{a +b}+\frac{b}{a +b}}\, \EllipticF \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) \sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}\, a^{3} b^{2}-9 \sqrt{-\frac{b \sin \left(d x +c \right)}{a -b}-\frac{b}{a -b}}\, \sqrt{-\frac{b \sin \left(d x +c \right)}{a +b}+\frac{b}{a +b}}\, \EllipticF \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) \sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}\, a^{2} b^{3}+3 \sqrt{-\frac{b \sin \left(d x +c \right)}{a -b}-\frac{b}{a -b}}\, \sqrt{-\frac{b \sin \left(d x +c \right)}{a +b}+\frac{b}{a +b}}\, \EllipticF \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) \sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}\, a \,b^{4}+5 \sqrt{-\frac{b \sin \left(d x +c \right)}{a -b}-\frac{b}{a -b}}\, \sqrt{-\frac{b \sin \left(d x +c \right)}{a +b}+\frac{b}{a +b}}\, \EllipticF \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) \sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}\, b^{5}-4 \sqrt{-\frac{b \sin \left(d x +c \right)}{a -b}-\frac{b}{a -b}}\, \sqrt{-\frac{b \sin \left(d x +c \right)}{a +b}+\frac{b}{a +b}}\, \sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}\, \EllipticE \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{5}+12 \sqrt{-\frac{b \sin \left(d x +c \right)}{a -b}-\frac{b}{a -b}}\, \sqrt{-\frac{b \sin \left(d x +c \right)}{a +b}+\frac{b}{a +b}}\, \sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}\, \EllipticE \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{3} b^{2}-8 \sqrt{-\frac{b \sin \left(d x +c \right)}{a -b}-\frac{b}{a -b}}\, \sqrt{-\frac{b \sin \left(d x +c \right)}{a +b}+\frac{b}{a +b}}\, \sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}\, \EllipticE \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{4}-a^{3} b^{2}+a \,b^{4}\right)\right)}{6 \cos \left(d x +c \right)^{5} \left(a +b \sin \left(d x +c \right)\right)^{\frac{3}{2}} b \left(a^{4}-2 a^{2} b^{2}+b^{4}\right) d}"," ",0,"1/6*(-(-a-b*sin(d*x+c))*cos(d*x+c)^2)^(1/2)/cos(d*x+c)^5/(a+b*sin(d*x+c))^(3/2)/b/(a^4-2*a^2*b^2+b^4)*(-4*cos(d*x+c)^4*(cos(d*x+c)^2*sin(d*x+c)*b+cos(d*x+c)^2*a)^(1/2)*a*b^2*(a^2-2*b^2)+cos(d*x+c)^2*(cos(d*x+c)^2*sin(d*x+c)*b+cos(d*x+c)^2*a)^(1/2)*b*(4*a^4-9*a^2*b^2+5*b^4)*sin(d*x+c)+2*(cos(d*x+c)^2*sin(d*x+c)*b+cos(d*x+c)^2*a)^(1/2)*b*(a^4-2*a^2*b^2+b^4)*sin(d*x+c)-cos(d*x+c)^2*(cos(d*x+c)^2*sin(d*x+c)*b+cos(d*x+c)^2*a)^(1/2)*(4*(-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*EllipticF((b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2),((a-b)/(a+b))^(1/2))*(b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2)*a^4*b-3*(-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*EllipticF((b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2),((a-b)/(a+b))^(1/2))*(b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2)*a^3*b^2-9*(-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*EllipticF((b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2),((a-b)/(a+b))^(1/2))*(b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2)*a^2*b^3+3*(-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*EllipticF((b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2),((a-b)/(a+b))^(1/2))*(b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2)*a*b^4+5*(-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*EllipticF((b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2),((a-b)/(a+b))^(1/2))*(b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2)*b^5-4*(-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*(b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2)*EllipticE((b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2),((a-b)/(a+b))^(1/2))*a^5+12*(-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*(b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2)*EllipticE((b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2),((a-b)/(a+b))^(1/2))*a^3*b^2-8*(-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*(b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2)*EllipticE((b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2),((a-b)/(a+b))^(1/2))*a*b^4-a^3*b^2+a*b^4))/d","B"
516,1,116,134,0.354000," ","int(cos(d*x+c)^5/(a+b*sin(d*x+c))^(3/2),x)","\frac{\frac{16 a \,b^{3} \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{35}+\frac{2 \left(-192 a^{3} b +256 a \,b^{3}\right) \sin \left(d x +c \right)}{105}+\frac{2 b^{4} \left(\cos^{4}\left(d x +c \right)\right)}{7}+\frac{2 \left(-48 a^{2} b^{2}+40 b^{4}\right) \left(\cos^{2}\left(d x +c \right)\right)}{105}-\frac{256 a^{4}}{35}+\frac{1216 a^{2} b^{2}}{105}-\frac{64 b^{4}}{21}}{b^{5} \sqrt{a +b \sin \left(d x +c \right)}\, d}"," ",0,"2/105/b^5*(24*a*b^3*cos(d*x+c)^2*sin(d*x+c)+(-192*a^3*b+256*a*b^3)*sin(d*x+c)+15*b^4*cos(d*x+c)^4+(-48*a^2*b^2+40*b^4)*cos(d*x+c)^2-384*a^4+608*a^2*b^2-160*b^4)/(a+b*sin(d*x+c))^(1/2)/d","A"
517,1,54,71,0.326000," ","int(cos(d*x+c)^3/(a+b*sin(d*x+c))^(3/2),x)","\frac{\frac{2 b^{2} \left(\cos^{2}\left(d x +c \right)\right)}{3}+\frac{8 a b \sin \left(d x +c \right)}{3}+\frac{16 a^{2}}{3}-\frac{8 b^{2}}{3}}{b^{3} \sqrt{a +b \sin \left(d x +c \right)}\, d}"," ",0,"2/3/b^3/(a+b*sin(d*x+c))^(1/2)*(b^2*cos(d*x+c)^2+4*a*b*sin(d*x+c)+8*a^2-4*b^2)/d","A"
518,1,21,20,0.020000," ","int(cos(d*x+c)/(a+b*sin(d*x+c))^(3/2),x)","-\frac{2}{b d \sqrt{a +b \sin \left(d x +c \right)}}"," ",0,"-2/b/d/(a+b*sin(d*x+c))^(1/2)","A"
519,1,99,91,0.558000," ","int(sec(d*x+c)/(a+b*sin(d*x+c))^(3/2),x)","\frac{2 b}{d \left(a -b \right) \left(a +b \right) \sqrt{a +b \sin \left(d x +c \right)}}+\frac{\arctan \left(\frac{\sqrt{a +b \sin \left(d x +c \right)}}{\sqrt{-a +b}}\right)}{d \left(a -b \right) \sqrt{-a +b}}+\frac{\arctanh \left(\frac{\sqrt{a +b \sin \left(d x +c \right)}}{\sqrt{a +b}}\right)}{\left(a +b \right)^{\frac{3}{2}} d}"," ",0,"2/d*b/(a-b)/(a+b)/(a+b*sin(d*x+c))^(1/2)+1/d/(a-b)/(-a+b)^(1/2)*arctan((a+b*sin(d*x+c))^(1/2)/(-a+b)^(1/2))+arctanh((a+b*sin(d*x+c))^(1/2)/(a+b)^(1/2))/(a+b)^(3/2)/d","A"
520,1,250,162,0.894000," ","int(sec(d*x+c)^3/(a+b*sin(d*x+c))^(3/2),x)","-\frac{2 b^{3}}{d \left(a +b \right)^{2} \left(a -b \right)^{2} \sqrt{a +b \sin \left(d x +c \right)}}-\frac{b \sqrt{a +b \sin \left(d x +c \right)}}{4 d \left(a -b \right)^{2} \left(b \sin \left(d x +c \right)+b \right)}+\frac{\arctan \left(\frac{\sqrt{a +b \sin \left(d x +c \right)}}{\sqrt{-a +b}}\right) a}{2 d \left(a -b \right)^{2} \sqrt{-a +b}}-\frac{5 b \arctan \left(\frac{\sqrt{a +b \sin \left(d x +c \right)}}{\sqrt{-a +b}}\right)}{4 d \left(a -b \right)^{2} \sqrt{-a +b}}-\frac{b \sqrt{a +b \sin \left(d x +c \right)}}{4 d \left(a +b \right)^{2} \left(b \sin \left(d x +c \right)-b \right)}+\frac{\arctanh \left(\frac{\sqrt{a +b \sin \left(d x +c \right)}}{\sqrt{a +b}}\right) a}{2 d \left(a +b \right)^{\frac{5}{2}}}+\frac{5 b \arctanh \left(\frac{\sqrt{a +b \sin \left(d x +c \right)}}{\sqrt{a +b}}\right)}{4 d \left(a +b \right)^{\frac{5}{2}}}"," ",0,"-2/d*b^3/(a+b)^2/(a-b)^2/(a+b*sin(d*x+c))^(1/2)-1/4/d*b/(a-b)^2*(a+b*sin(d*x+c))^(1/2)/(b*sin(d*x+c)+b)+1/2/d/(a-b)^2/(-a+b)^(1/2)*arctan((a+b*sin(d*x+c))^(1/2)/(-a+b)^(1/2))*a-5/4/d*b/(a-b)^2/(-a+b)^(1/2)*arctan((a+b*sin(d*x+c))^(1/2)/(-a+b)^(1/2))-1/4/d*b/(a+b)^2*(a+b*sin(d*x+c))^(1/2)/(b*sin(d*x+c)-b)+1/2/d/(a+b)^(5/2)*arctanh((a+b*sin(d*x+c))^(1/2)/(a+b)^(1/2))*a+5/4/d*b/(a+b)^(5/2)*arctanh((a+b*sin(d*x+c))^(1/2)/(a+b)^(1/2))","A"
521,1,649,256,1.101000," ","int(sec(d*x+c)^5/(a+b*sin(d*x+c))^(3/2),x)","\frac{2 b^{5}}{d \left(a -b \right)^{3} \left(a +b \right)^{3} \sqrt{a +b \sin \left(d x +c \right)}}-\frac{3 b \left(a +b \sin \left(d x +c \right)\right)^{\frac{3}{2}} a}{16 d \left(a -b \right)^{3} \left(b \sin \left(d x +c \right)+b \right)^{2}}+\frac{13 b^{2} \left(a +b \sin \left(d x +c \right)\right)^{\frac{3}{2}}}{32 d \left(a -b \right)^{3} \left(b \sin \left(d x +c \right)+b \right)^{2}}+\frac{3 b \sqrt{a +b \sin \left(d x +c \right)}\, a^{2}}{16 d \left(a -b \right)^{3} \left(b \sin \left(d x +c \right)+b \right)^{2}}-\frac{21 b^{2} \sqrt{a +b \sin \left(d x +c \right)}\, a}{32 d \left(a -b \right)^{3} \left(b \sin \left(d x +c \right)+b \right)^{2}}+\frac{15 b^{3} \sqrt{a +b \sin \left(d x +c \right)}}{32 d \left(a -b \right)^{3} \left(b \sin \left(d x +c \right)+b \right)^{2}}+\frac{3 \arctan \left(\frac{\sqrt{a +b \sin \left(d x +c \right)}}{\sqrt{-a +b}}\right) a^{2}}{8 d \left(a -b \right)^{3} \sqrt{-a +b}}-\frac{21 b \arctan \left(\frac{\sqrt{a +b \sin \left(d x +c \right)}}{\sqrt{-a +b}}\right) a}{16 d \left(a -b \right)^{3} \sqrt{-a +b}}+\frac{45 b^{2} \arctan \left(\frac{\sqrt{a +b \sin \left(d x +c \right)}}{\sqrt{-a +b}}\right)}{32 d \left(a -b \right)^{3} \sqrt{-a +b}}-\frac{3 b \left(a +b \sin \left(d x +c \right)\right)^{\frac{3}{2}} a}{16 d \left(a +b \right)^{3} \left(b \sin \left(d x +c \right)-b \right)^{2}}-\frac{13 b^{2} \left(a +b \sin \left(d x +c \right)\right)^{\frac{3}{2}}}{32 d \left(a +b \right)^{3} \left(b \sin \left(d x +c \right)-b \right)^{2}}+\frac{3 b \sqrt{a +b \sin \left(d x +c \right)}\, a^{2}}{16 d \left(a +b \right)^{3} \left(b \sin \left(d x +c \right)-b \right)^{2}}+\frac{21 b^{2} \sqrt{a +b \sin \left(d x +c \right)}\, a}{32 d \left(a +b \right)^{3} \left(b \sin \left(d x +c \right)-b \right)^{2}}+\frac{15 b^{3} \sqrt{a +b \sin \left(d x +c \right)}}{32 d \left(a +b \right)^{3} \left(b \sin \left(d x +c \right)-b \right)^{2}}+\frac{3 \arctanh \left(\frac{\sqrt{a +b \sin \left(d x +c \right)}}{\sqrt{a +b}}\right) a^{2}}{8 d \left(a +b \right)^{\frac{7}{2}}}+\frac{21 b \arctanh \left(\frac{\sqrt{a +b \sin \left(d x +c \right)}}{\sqrt{a +b}}\right) a}{16 d \left(a +b \right)^{\frac{7}{2}}}+\frac{45 b^{2} \arctanh \left(\frac{\sqrt{a +b \sin \left(d x +c \right)}}{\sqrt{a +b}}\right)}{32 d \left(a +b \right)^{\frac{7}{2}}}"," ",0,"2/d*b^5/(a-b)^3/(a+b)^3/(a+b*sin(d*x+c))^(1/2)-3/16/d*b/(a-b)^3/(b*sin(d*x+c)+b)^2*(a+b*sin(d*x+c))^(3/2)*a+13/32/d*b^2/(a-b)^3/(b*sin(d*x+c)+b)^2*(a+b*sin(d*x+c))^(3/2)+3/16/d*b/(a-b)^3/(b*sin(d*x+c)+b)^2*(a+b*sin(d*x+c))^(1/2)*a^2-21/32/d*b^2/(a-b)^3/(b*sin(d*x+c)+b)^2*(a+b*sin(d*x+c))^(1/2)*a+15/32/d*b^3/(a-b)^3/(b*sin(d*x+c)+b)^2*(a+b*sin(d*x+c))^(1/2)+3/8/d/(a-b)^3/(-a+b)^(1/2)*arctan((a+b*sin(d*x+c))^(1/2)/(-a+b)^(1/2))*a^2-21/16/d*b/(a-b)^3/(-a+b)^(1/2)*arctan((a+b*sin(d*x+c))^(1/2)/(-a+b)^(1/2))*a+45/32/d*b^2/(a-b)^3/(-a+b)^(1/2)*arctan((a+b*sin(d*x+c))^(1/2)/(-a+b)^(1/2))-3/16/d*b/(a+b)^3/(b*sin(d*x+c)-b)^2*(a+b*sin(d*x+c))^(3/2)*a-13/32/d*b^2/(a+b)^3/(b*sin(d*x+c)-b)^2*(a+b*sin(d*x+c))^(3/2)+3/16/d*b/(a+b)^3/(b*sin(d*x+c)-b)^2*(a+b*sin(d*x+c))^(1/2)*a^2+21/32/d*b^2/(a+b)^3/(b*sin(d*x+c)-b)^2*(a+b*sin(d*x+c))^(1/2)*a+15/32/d*b^3/(a+b)^3/(b*sin(d*x+c)-b)^2*(a+b*sin(d*x+c))^(1/2)+3/8/d/(a+b)^(7/2)*arctanh((a+b*sin(d*x+c))^(1/2)/(a+b)^(1/2))*a^2+21/16/d*b/(a+b)^(7/2)*arctanh((a+b*sin(d*x+c))^(1/2)/(a+b)^(1/2))*a+45/32/d*b^2/(a+b)^(7/2)*arctanh((a+b*sin(d*x+c))^(1/2)/(a+b)^(1/2))","B"
522,1,1195,357,0.825000," ","int(cos(d*x+c)^6/(a+b*sin(d*x+c))^(3/2),x)","-\frac{2 \left(7 b^{6} \left(\sin^{6}\left(d x +c \right)\right)-10 a \,b^{5} \left(\sin^{5}\left(d x +c \right)\right)+256 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{5} b -192 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{4} b^{2}-520 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{3} b^{3}+360 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{2} b^{4}+264 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{5}-168 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) b^{6}-256 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{6}+712 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{4} b^{2}-624 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{2} b^{4}+168 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) b^{6}+16 a^{2} b^{4} \left(\sin^{4}\left(d x +c \right)\right)-35 b^{6} \left(\sin^{4}\left(d x +c \right)\right)-32 a^{3} b^{3} \left(\sin^{3}\left(d x +c \right)\right)+68 a \,b^{5} \left(\sin^{3}\left(d x +c \right)\right)-128 a^{4} b^{2} \left(\sin^{2}\left(d x +c \right)\right)+196 a^{2} b^{4} \left(\sin^{2}\left(d x +c \right)\right)-35 b^{6} \left(\sin^{2}\left(d x +c \right)\right)+32 a^{3} b^{3} \sin \left(d x +c \right)-58 a \,b^{5} \sin \left(d x +c \right)+128 a^{4} b^{2}-212 a^{2} b^{4}+63 b^{6}\right)}{63 b^{7} \cos \left(d x +c \right) \sqrt{a +b \sin \left(d x +c \right)}\, d}"," ",0,"-2/63*(7*b^6*sin(d*x+c)^6-10*a*b^5*sin(d*x+c)^5+256*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^5*b-192*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^4*b^2-520*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^3*b^3+360*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^2*b^4+264*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a*b^5-168*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*b^6-256*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^6+712*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^4*b^2-624*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^2*b^4+168*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*b^6+16*a^2*b^4*sin(d*x+c)^4-35*b^6*sin(d*x+c)^4-32*a^3*b^3*sin(d*x+c)^3+68*a*b^5*sin(d*x+c)^3-128*a^4*b^2*sin(d*x+c)^2+196*a^2*b^4*sin(d*x+c)^2-35*b^6*sin(d*x+c)^2+32*a^3*b^3*sin(d*x+c)-58*a*b^5*sin(d*x+c)+128*a^4*b^2-212*a^2*b^4+63*b^6)/b^7/cos(d*x+c)/(a+b*sin(d*x+c))^(1/2)/d","B"
523,1,797,277,0.697000," ","int(cos(d*x+c)^4/(a+b*sin(d*x+c))^(3/2),x)","\frac{\frac{32 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{3} b}{5}-\frac{24 a^{2} \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) b^{2}}{5}-\frac{32 a \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) b^{3}}{5}+\frac{24 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) b^{4}}{5}-\frac{32 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{4}}{5}+\frac{56 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{2} b^{2}}{5}-\frac{24 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) b^{4}}{5}+\frac{2 b^{4} \left(\sin^{4}\left(d x +c \right)\right)}{5}-\frac{4 a \,b^{3} \left(\sin^{3}\left(d x +c \right)\right)}{5}-\frac{16 a^{2} b^{2} \left(\sin^{2}\left(d x +c \right)\right)}{5}+\frac{8 b^{4} \left(\sin^{2}\left(d x +c \right)\right)}{5}+\frac{4 a \,b^{3} \sin \left(d x +c \right)}{5}+\frac{16 a^{2} b^{2}}{5}-2 b^{4}}{b^{5} \cos \left(d x +c \right) \sqrt{a +b \sin \left(d x +c \right)}\, d}"," ",0,"2/5*(16*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^3*b-12*a^2*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*b^2-16*a*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*b^3+12*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*b^4-16*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^4+28*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^2*b^2-12*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*b^4+b^4*sin(d*x+c)^4-2*a*b^3*sin(d*x+c)^3-8*a^2*b^2*sin(d*x+c)^2+4*b^4*sin(d*x+c)^2+2*a*b^3*sin(d*x+c)+8*a^2*b^2-5*b^4)/b^5/cos(d*x+c)/(a+b*sin(d*x+c))^(1/2)/d","B"
524,1,434,216,0.749000," ","int(cos(d*x+c)^2/(a+b*sin(d*x+c))^(3/2),x)","\frac{4 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{2}-4 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) b^{2}-4 a \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) b +4 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) b^{2}+2 b^{2} \left(\sin^{2}\left(d x +c \right)\right)-2 b^{2}}{b^{3} \cos \left(d x +c \right) \sqrt{a +b \sin \left(d x +c \right)}\, d}"," ",0,"2*(2*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^2-2*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*b^2-2*a*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*b+2*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*b^2+b^2*sin(d*x+c)^2-b^2)/b^3/cos(d*x+c)/(a+b*sin(d*x+c))^(1/2)/d","B"
525,1,1062,305,1.121000," ","int(sec(d*x+c)^2/(a+b*sin(d*x+c))^(3/2),x)","\frac{\sqrt{\left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) b +\left(\cos^{2}\left(d x +c \right)\right) a}\, \left(\sqrt{-\frac{b \sin \left(d x +c \right)}{a -b}-\frac{b}{a -b}}\, \sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}\, \EllipticE \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) \sqrt{-\frac{b \sin \left(d x +c \right)}{a +b}+\frac{b}{a +b}}\, a^{4}+2 \sqrt{-\frac{b \sin \left(d x +c \right)}{a -b}-\frac{b}{a -b}}\, \sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}\, \EllipticE \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) \sqrt{-\frac{b \sin \left(d x +c \right)}{a +b}+\frac{b}{a +b}}\, a^{2} b^{2}-3 \sqrt{-\frac{b \sin \left(d x +c \right)}{a -b}-\frac{b}{a -b}}\, \sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}\, \EllipticE \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) \sqrt{-\frac{b \sin \left(d x +c \right)}{a +b}+\frac{b}{a +b}}\, b^{4}-\sqrt{-\frac{b \sin \left(d x +c \right)}{a -b}-\frac{b}{a -b}}\, \sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}\, \EllipticF \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) \sqrt{-\frac{b \sin \left(d x +c \right)}{a +b}+\frac{b}{a +b}}\, a^{3} b -3 \sqrt{-\frac{b \sin \left(d x +c \right)}{a -b}-\frac{b}{a -b}}\, \sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}\, \EllipticF \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) \sqrt{-\frac{b \sin \left(d x +c \right)}{a +b}+\frac{b}{a +b}}\, a^{2} b^{2}+\sqrt{-\frac{b \sin \left(d x +c \right)}{a -b}-\frac{b}{a -b}}\, \sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}\, \EllipticF \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) \sqrt{-\frac{b \sin \left(d x +c \right)}{a +b}+\frac{b}{a +b}}\, a \,b^{3}+3 \sqrt{-\frac{b \sin \left(d x +c \right)}{a -b}-\frac{b}{a -b}}\, \sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}\, \EllipticF \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) \sqrt{-\frac{b \sin \left(d x +c \right)}{a +b}+\frac{b}{a +b}}\, b^{4}-a^{2} b^{2} \left(\cos^{2}\left(d x +c \right)\right)-3 b^{4} \left(\cos^{2}\left(d x +c \right)\right)+a^{3} b \sin \left(d x +c \right)-a \,b^{3} \sin \left(d x +c \right)-a^{2} b^{2}+b^{4}\right)}{b \left(a^{2}-b^{2}\right) \left(a -b \right) \left(a +b \right) \sqrt{-\left(a +b \sin \left(d x +c \right)\right) \left(\sin \left(d x +c \right)-1\right) \left(1+\sin \left(d x +c \right)\right)}\, \cos \left(d x +c \right) \sqrt{a +b \sin \left(d x +c \right)}\, d}"," ",0,"1/b*(cos(d*x+c)^2*sin(d*x+c)*b+cos(d*x+c)^2*a)^(1/2)*((-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*(b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2)*EllipticE((b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2),((a-b)/(a+b))^(1/2))*(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*a^4+2*(-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*(b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2)*EllipticE((b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2),((a-b)/(a+b))^(1/2))*(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*a^2*b^2-3*(-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*(b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2)*EllipticE((b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2),((a-b)/(a+b))^(1/2))*(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*b^4-(-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*(b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2)*EllipticF((b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2),((a-b)/(a+b))^(1/2))*(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*a^3*b-3*(-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*(b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2)*EllipticF((b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2),((a-b)/(a+b))^(1/2))*(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*a^2*b^2+(-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*(b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2)*EllipticF((b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2),((a-b)/(a+b))^(1/2))*(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*a*b^3+3*(-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*(b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2)*EllipticF((b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2),((a-b)/(a+b))^(1/2))*(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*b^4-a^2*b^2*cos(d*x+c)^2-3*b^4*cos(d*x+c)^2+a^3*b*sin(d*x+c)-a*b^3*sin(d*x+c)-a^2*b^2+b^4)/(a^2-b^2)/(a-b)/(a+b)/(-(a+b*sin(d*x+c))*(sin(d*x+c)-1)*(1+sin(d*x+c)))^(1/2)/cos(d*x+c)/(a+b*sin(d*x+c))^(1/2)/d","B"
526,1,1646,403,4.731000," ","int(sec(d*x+c)^4/(a+b*sin(d*x+c))^(3/2),x)","\frac{\sqrt{-\left(-a -b \sin \left(d x +c \right)\right) \left(\cos^{2}\left(d x +c \right)\right)}\, \left(-2 \sqrt{\left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) b +\left(\cos^{2}\left(d x +c \right)\right) a}\, b^{2} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right)-\left(\cos^{4}\left(d x +c \right)\right) \sqrt{\left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) b +\left(\cos^{2}\left(d x +c \right)\right) a}\, b^{2} \left(4 a^{4}-15 a^{2} b^{2}-21 b^{4}\right)+4 \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) b +\left(\cos^{2}\left(d x +c \right)\right) a}\, a b \left(a^{4}-4 a^{2} b^{2}+3 b^{4}\right) \sin \left(d x +c \right)+2 \sqrt{\left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) b +\left(\cos^{2}\left(d x +c \right)\right) a}\, a b \left(a^{4}-2 a^{2} b^{2}+b^{4}\right) \sin \left(d x +c \right)+\left(\cos^{2}\left(d x +c \right)\right) \sqrt{\left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) b +\left(\cos^{2}\left(d x +c \right)\right) a}\, \left(4 \sqrt{-\frac{b \sin \left(d x +c \right)}{a +b}+\frac{b}{a +b}}\, \EllipticE \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) \sqrt{-\frac{b \sin \left(d x +c \right)}{a -b}-\frac{b}{a -b}}\, \sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}\, a^{6}-19 \sqrt{-\frac{b \sin \left(d x +c \right)}{a +b}+\frac{b}{a +b}}\, \EllipticE \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) \sqrt{-\frac{b \sin \left(d x +c \right)}{a -b}-\frac{b}{a -b}}\, \sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}\, a^{4} b^{2}-6 \sqrt{-\frac{b \sin \left(d x +c \right)}{a +b}+\frac{b}{a +b}}\, \EllipticE \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) \sqrt{-\frac{b \sin \left(d x +c \right)}{a -b}-\frac{b}{a -b}}\, \sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}\, a^{2} b^{4}+21 \sqrt{-\frac{b \sin \left(d x +c \right)}{a +b}+\frac{b}{a +b}}\, \EllipticE \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) \sqrt{-\frac{b \sin \left(d x +c \right)}{a -b}-\frac{b}{a -b}}\, \sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}\, b^{6}-4 \EllipticF \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) \sqrt{-\frac{b \sin \left(d x +c \right)}{a +b}+\frac{b}{a +b}}\, \sqrt{-\frac{b \sin \left(d x +c \right)}{a -b}-\frac{b}{a -b}}\, \sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}\, a^{5} b +3 \EllipticF \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) \sqrt{-\frac{b \sin \left(d x +c \right)}{a +b}+\frac{b}{a +b}}\, \sqrt{-\frac{b \sin \left(d x +c \right)}{a -b}-\frac{b}{a -b}}\, \sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}\, a^{4} b^{2}+16 \EllipticF \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) \sqrt{-\frac{b \sin \left(d x +c \right)}{a +b}+\frac{b}{a +b}}\, \sqrt{-\frac{b \sin \left(d x +c \right)}{a -b}-\frac{b}{a -b}}\, \sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}\, a^{3} b^{3}+18 \EllipticF \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) \sqrt{-\frac{b \sin \left(d x +c \right)}{a +b}+\frac{b}{a +b}}\, \sqrt{-\frac{b \sin \left(d x +c \right)}{a -b}-\frac{b}{a -b}}\, \sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}\, a^{2} b^{4}-12 \EllipticF \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) \sqrt{-\frac{b \sin \left(d x +c \right)}{a +b}+\frac{b}{a +b}}\, \sqrt{-\frac{b \sin \left(d x +c \right)}{a -b}-\frac{b}{a -b}}\, \sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}\, a \,b^{5}-21 \EllipticF \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) \sqrt{-\frac{b \sin \left(d x +c \right)}{a +b}+\frac{b}{a +b}}\, \sqrt{-\frac{b \sin \left(d x +c \right)}{a -b}-\frac{b}{a -b}}\, \sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}\, b^{6}+a^{4} b^{2}+6 a^{2} b^{4}-7 b^{6}\right)\right)}{6 \cos \left(d x +c \right)^{5} \left(a +b \sin \left(d x +c \right)\right)^{\frac{3}{2}} b \left(a^{6}-3 a^{4} b^{2}+3 a^{2} b^{4}-b^{6}\right) d}"," ",0,"1/6*(-(-a-b*sin(d*x+c))*cos(d*x+c)^2)^(1/2)/cos(d*x+c)^5/(a+b*sin(d*x+c))^(3/2)/b/(a^6-3*a^4*b^2+3*a^2*b^4-b^6)*(-2*(cos(d*x+c)^2*sin(d*x+c)*b+cos(d*x+c)^2*a)^(1/2)*b^2*(a^4-2*a^2*b^2+b^4)-cos(d*x+c)^4*(cos(d*x+c)^2*sin(d*x+c)*b+cos(d*x+c)^2*a)^(1/2)*b^2*(4*a^4-15*a^2*b^2-21*b^4)+4*cos(d*x+c)^2*(cos(d*x+c)^2*sin(d*x+c)*b+cos(d*x+c)^2*a)^(1/2)*a*b*(a^4-4*a^2*b^2+3*b^4)*sin(d*x+c)+2*(cos(d*x+c)^2*sin(d*x+c)*b+cos(d*x+c)^2*a)^(1/2)*a*b*(a^4-2*a^2*b^2+b^4)*sin(d*x+c)+cos(d*x+c)^2*(cos(d*x+c)^2*sin(d*x+c)*b+cos(d*x+c)^2*a)^(1/2)*(4*(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*EllipticE((b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2),((a-b)/(a+b))^(1/2))*(-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*(b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2)*a^6-19*(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*EllipticE((b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2),((a-b)/(a+b))^(1/2))*(-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*(b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2)*a^4*b^2-6*(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*EllipticE((b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2),((a-b)/(a+b))^(1/2))*(-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*(b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2)*a^2*b^4+21*(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*EllipticE((b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2),((a-b)/(a+b))^(1/2))*(-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*(b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2)*b^6-4*EllipticF((b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2),((a-b)/(a+b))^(1/2))*(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*(-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*(b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2)*a^5*b+3*EllipticF((b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2),((a-b)/(a+b))^(1/2))*(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*(-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*(b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2)*a^4*b^2+16*EllipticF((b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2),((a-b)/(a+b))^(1/2))*(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*(-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*(b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2)*a^3*b^3+18*EllipticF((b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2),((a-b)/(a+b))^(1/2))*(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*(-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*(b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2)*a^2*b^4-12*EllipticF((b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2),((a-b)/(a+b))^(1/2))*(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*(-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*(b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2)*a*b^5-21*EllipticF((b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2),((a-b)/(a+b))^(1/2))*(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*(-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*(b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2)*b^6+a^4*b^2+6*a^2*b^4-7*b^6))/d","B"
527,1,116,134,0.432000," ","int(cos(d*x+c)^5/(a+b*sin(d*x+c))^(5/2),x)","\frac{\frac{16 a \,b^{3} \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{15}+\frac{2 \left(192 a^{3} b -128 a \,b^{3}\right) \sin \left(d x +c \right)}{15}+\frac{2 b^{4} \left(\cos^{4}\left(d x +c \right)\right)}{5}+\frac{2 \left(-48 a^{2} b^{2}+24 b^{4}\right) \left(\cos^{2}\left(d x +c \right)\right)}{15}+\frac{256 a^{4}}{15}-\frac{64 a^{2} b^{2}}{15}-\frac{64 b^{4}}{15}}{b^{5} \left(a +b \sin \left(d x +c \right)\right)^{\frac{3}{2}} d}"," ",0,"2/15/b^5*(8*a*b^3*cos(d*x+c)^2*sin(d*x+c)+(192*a^3*b-128*a*b^3)*sin(d*x+c)+3*b^4*cos(d*x+c)^4+(-48*a^2*b^2+24*b^4)*cos(d*x+c)^2+128*a^4-32*a^2*b^2-32*b^4)/(a+b*sin(d*x+c))^(3/2)/d","A"
528,1,55,71,0.392000," ","int(cos(d*x+c)^3/(a+b*sin(d*x+c))^(5/2),x)","-\frac{2 \left(-3 b^{2} \left(\cos^{2}\left(d x +c \right)\right)+12 a b \sin \left(d x +c \right)+8 a^{2}+4 b^{2}\right)}{3 b^{3} \left(a +b \sin \left(d x +c \right)\right)^{\frac{3}{2}} d}"," ",0,"-2/3/b^3*(-3*b^2*cos(d*x+c)^2+12*a*b*sin(d*x+c)+8*a^2+4*b^2)/(a+b*sin(d*x+c))^(3/2)/d","A"
529,1,21,20,0.024000," ","int(cos(d*x+c)/(a+b*sin(d*x+c))^(5/2),x)","-\frac{2}{3 b d \left(a +b \sin \left(d x +c \right)\right)^{\frac{3}{2}}}"," ",0,"-2/3/b/d/(a+b*sin(d*x+c))^(3/2)","A"
530,1,130,121,0.747000," ","int(sec(d*x+c)/(a+b*sin(d*x+c))^(5/2),x)","\frac{2 b}{3 d \left(a -b \right) \left(a +b \right) \left(a +b \sin \left(d x +c \right)\right)^{\frac{3}{2}}}+\frac{4 b a}{d \left(a -b \right)^{2} \left(a +b \right)^{2} \sqrt{a +b \sin \left(d x +c \right)}}+\frac{\arctan \left(\frac{\sqrt{a +b \sin \left(d x +c \right)}}{\sqrt{-a +b}}\right)}{d \left(a -b \right)^{2} \sqrt{-a +b}}+\frac{\arctanh \left(\frac{\sqrt{a +b \sin \left(d x +c \right)}}{\sqrt{a +b}}\right)}{\left(a +b \right)^{\frac{5}{2}} d}"," ",0,"2/3/d*b/(a-b)/(a+b)/(a+b*sin(d*x+c))^(3/2)+4/d*b*a/(a-b)^2/(a+b)^2/(a+b*sin(d*x+c))^(1/2)+1/d/(a-b)^2/(-a+b)^(1/2)*arctan((a+b*sin(d*x+c))^(1/2)/(-a+b)^(1/2))+arctanh((a+b*sin(d*x+c))^(1/2)/(a+b)^(1/2))/(a+b)^(5/2)/d","A"
531,1,283,203,0.934000," ","int(sec(d*x+c)^3/(a+b*sin(d*x+c))^(5/2),x)","-\frac{2 b^{3}}{3 d \left(a +b \right)^{2} \left(a -b \right)^{2} \left(a +b \sin \left(d x +c \right)\right)^{\frac{3}{2}}}-\frac{8 b^{3} a}{d \left(a +b \right)^{3} \left(a -b \right)^{3} \sqrt{a +b \sin \left(d x +c \right)}}-\frac{b \sqrt{a +b \sin \left(d x +c \right)}}{4 d \left(a -b \right)^{3} \left(b \sin \left(d x +c \right)+b \right)}+\frac{\arctan \left(\frac{\sqrt{a +b \sin \left(d x +c \right)}}{\sqrt{-a +b}}\right) a}{2 d \left(a -b \right)^{3} \sqrt{-a +b}}-\frac{7 b \arctan \left(\frac{\sqrt{a +b \sin \left(d x +c \right)}}{\sqrt{-a +b}}\right)}{4 d \left(a -b \right)^{3} \sqrt{-a +b}}-\frac{b \sqrt{a +b \sin \left(d x +c \right)}}{4 d \left(a +b \right)^{3} \left(b \sin \left(d x +c \right)-b \right)}+\frac{\arctanh \left(\frac{\sqrt{a +b \sin \left(d x +c \right)}}{\sqrt{a +b}}\right) a}{2 d \left(a +b \right)^{\frac{7}{2}}}+\frac{7 b \arctanh \left(\frac{\sqrt{a +b \sin \left(d x +c \right)}}{\sqrt{a +b}}\right)}{4 d \left(a +b \right)^{\frac{7}{2}}}"," ",0,"-2/3/d*b^3/(a+b)^2/(a-b)^2/(a+b*sin(d*x+c))^(3/2)-8/d*b^3*a/(a+b)^3/(a-b)^3/(a+b*sin(d*x+c))^(1/2)-1/4/d*b/(a-b)^3*(a+b*sin(d*x+c))^(1/2)/(b*sin(d*x+c)+b)+1/2/d/(a-b)^3/(-a+b)^(1/2)*arctan((a+b*sin(d*x+c))^(1/2)/(-a+b)^(1/2))*a-7/4/d*b/(a-b)^3/(-a+b)^(1/2)*arctan((a+b*sin(d*x+c))^(1/2)/(-a+b)^(1/2))-1/4/d*b/(a+b)^3*(a+b*sin(d*x+c))^(1/2)/(b*sin(d*x+c)-b)+1/2/d/(a+b)^(7/2)*arctanh((a+b*sin(d*x+c))^(1/2)/(a+b)^(1/2))*a+7/4/d*b/(a+b)^(7/2)*arctanh((a+b*sin(d*x+c))^(1/2)/(a+b)^(1/2))","A"
532,1,682,307,1.054000," ","int(sec(d*x+c)^5/(a+b*sin(d*x+c))^(5/2),x)","\frac{2 b^{5}}{3 d \left(a -b \right)^{3} \left(a +b \right)^{3} \left(a +b \sin \left(d x +c \right)\right)^{\frac{3}{2}}}+\frac{12 b^{5} a}{d \left(a -b \right)^{4} \left(a +b \right)^{4} \sqrt{a +b \sin \left(d x +c \right)}}-\frac{3 b \left(a +b \sin \left(d x +c \right)\right)^{\frac{3}{2}} a}{16 d \left(a -b \right)^{4} \left(b \sin \left(d x +c \right)+b \right)^{2}}+\frac{17 b^{2} \left(a +b \sin \left(d x +c \right)\right)^{\frac{3}{2}}}{32 d \left(a -b \right)^{4} \left(b \sin \left(d x +c \right)+b \right)^{2}}+\frac{3 b \sqrt{a +b \sin \left(d x +c \right)}\, a^{2}}{16 d \left(a -b \right)^{4} \left(b \sin \left(d x +c \right)+b \right)^{2}}-\frac{25 b^{2} \sqrt{a +b \sin \left(d x +c \right)}\, a}{32 d \left(a -b \right)^{4} \left(b \sin \left(d x +c \right)+b \right)^{2}}+\frac{19 b^{3} \sqrt{a +b \sin \left(d x +c \right)}}{32 d \left(a -b \right)^{4} \left(b \sin \left(d x +c \right)+b \right)^{2}}+\frac{3 \arctan \left(\frac{\sqrt{a +b \sin \left(d x +c \right)}}{\sqrt{-a +b}}\right) a^{2}}{8 d \left(a -b \right)^{4} \sqrt{-a +b}}-\frac{27 b \arctan \left(\frac{\sqrt{a +b \sin \left(d x +c \right)}}{\sqrt{-a +b}}\right) a}{16 d \left(a -b \right)^{4} \sqrt{-a +b}}+\frac{77 b^{2} \arctan \left(\frac{\sqrt{a +b \sin \left(d x +c \right)}}{\sqrt{-a +b}}\right)}{32 d \left(a -b \right)^{4} \sqrt{-a +b}}-\frac{3 b \left(a +b \sin \left(d x +c \right)\right)^{\frac{3}{2}} a}{16 d \left(a +b \right)^{4} \left(b \sin \left(d x +c \right)-b \right)^{2}}-\frac{17 b^{2} \left(a +b \sin \left(d x +c \right)\right)^{\frac{3}{2}}}{32 d \left(a +b \right)^{4} \left(b \sin \left(d x +c \right)-b \right)^{2}}+\frac{3 b \sqrt{a +b \sin \left(d x +c \right)}\, a^{2}}{16 d \left(a +b \right)^{4} \left(b \sin \left(d x +c \right)-b \right)^{2}}+\frac{25 b^{2} \sqrt{a +b \sin \left(d x +c \right)}\, a}{32 d \left(a +b \right)^{4} \left(b \sin \left(d x +c \right)-b \right)^{2}}+\frac{19 b^{3} \sqrt{a +b \sin \left(d x +c \right)}}{32 d \left(a +b \right)^{4} \left(b \sin \left(d x +c \right)-b \right)^{2}}+\frac{3 \arctanh \left(\frac{\sqrt{a +b \sin \left(d x +c \right)}}{\sqrt{a +b}}\right) a^{2}}{8 d \left(a +b \right)^{\frac{9}{2}}}+\frac{27 b \arctanh \left(\frac{\sqrt{a +b \sin \left(d x +c \right)}}{\sqrt{a +b}}\right) a}{16 d \left(a +b \right)^{\frac{9}{2}}}+\frac{77 b^{2} \arctanh \left(\frac{\sqrt{a +b \sin \left(d x +c \right)}}{\sqrt{a +b}}\right)}{32 d \left(a +b \right)^{\frac{9}{2}}}"," ",0,"2/3/d*b^5/(a-b)^3/(a+b)^3/(a+b*sin(d*x+c))^(3/2)+12/d*b^5*a/(a-b)^4/(a+b)^4/(a+b*sin(d*x+c))^(1/2)-3/16/d*b/(a-b)^4/(b*sin(d*x+c)+b)^2*(a+b*sin(d*x+c))^(3/2)*a+17/32/d*b^2/(a-b)^4/(b*sin(d*x+c)+b)^2*(a+b*sin(d*x+c))^(3/2)+3/16/d*b/(a-b)^4/(b*sin(d*x+c)+b)^2*(a+b*sin(d*x+c))^(1/2)*a^2-25/32/d*b^2/(a-b)^4/(b*sin(d*x+c)+b)^2*(a+b*sin(d*x+c))^(1/2)*a+19/32/d*b^3/(a-b)^4/(b*sin(d*x+c)+b)^2*(a+b*sin(d*x+c))^(1/2)+3/8/d/(a-b)^4/(-a+b)^(1/2)*arctan((a+b*sin(d*x+c))^(1/2)/(-a+b)^(1/2))*a^2-27/16/d*b/(a-b)^4/(-a+b)^(1/2)*arctan((a+b*sin(d*x+c))^(1/2)/(-a+b)^(1/2))*a+77/32/d*b^2/(a-b)^4/(-a+b)^(1/2)*arctan((a+b*sin(d*x+c))^(1/2)/(-a+b)^(1/2))-3/16/d*b/(a+b)^4/(b*sin(d*x+c)-b)^2*(a+b*sin(d*x+c))^(3/2)*a-17/32/d*b^2/(a+b)^4/(b*sin(d*x+c)-b)^2*(a+b*sin(d*x+c))^(3/2)+3/16/d*b/(a+b)^4/(b*sin(d*x+c)-b)^2*(a+b*sin(d*x+c))^(1/2)*a^2+25/32/d*b^2/(a+b)^4/(b*sin(d*x+c)-b)^2*(a+b*sin(d*x+c))^(1/2)*a+19/32/d*b^3/(a+b)^4/(b*sin(d*x+c)-b)^2*(a+b*sin(d*x+c))^(1/2)+3/8/d/(a+b)^(9/2)*arctanh((a+b*sin(d*x+c))^(1/2)/(a+b)^(1/2))*a^2+27/16/d*b/(a+b)^(9/2)*arctanh((a+b*sin(d*x+c))^(1/2)/(a+b)^(1/2))*a+77/32/d*b^2/(a+b)^(9/2)*arctanh((a+b*sin(d*x+c))^(1/2)/(a+b)^(1/2))","B"
533,1,2253,422,0.887000," ","int(cos(d*x+c)^8/(a+b*sin(d*x+c))^(5/2),x)","-\frac{2 \left(-14 a \,b^{7} \sin \left(d x +c \right) \left(\cos^{6}\left(d x +c \right)\right)+\left(48 a^{3} b^{5}-64 a \,b^{7}\right) \left(\cos^{4}\left(d x +c \right)\right) \sin \left(d x +c \right)+\left(1280 a^{5} b^{3}-2328 a^{3} b^{5}+984 a \,b^{7}\right) \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)-16 \sqrt{-\frac{b \sin \left(d x +c \right)}{a -b}-\frac{b}{a -b}}\, \sqrt{-\frac{b \sin \left(d x +c \right)}{a +b}+\frac{b}{a +b}}\, \sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}\, b \left(128 \EllipticE \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{7}-368 \EllipticE \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{5} b^{2}+348 \EllipticE \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{3} b^{4}-108 \EllipticE \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{6}-128 \EllipticF \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{6} b +96 \EllipticF \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{5} b^{2}+272 \EllipticF \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{4} b^{3}-189 \EllipticF \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{3} b^{4}-159 \EllipticF \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{2} b^{5}+93 \EllipticF \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{6}+15 \EllipticF \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) b^{7}\right) \sin \left(d x +c \right)-9 b^{8} \left(\cos^{8}\left(d x +c \right)\right)+\left(24 a^{2} b^{6}-18 b^{8}\right) \left(\cos^{6}\left(d x +c \right)\right)+\left(-128 a^{4} b^{4}+204 a^{2} b^{6}-60 b^{8}\right) \left(\cos^{4}\left(d x +c \right)\right)+\left(1024 a^{6} b^{2}-1664 a^{4} b^{4}+456 a^{2} b^{6}+120 b^{8}\right) \left(\cos^{2}\left(d x +c \right)\right)+2048 \sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}\, \sqrt{-\frac{b \sin \left(d x +c \right)}{a +b}+\frac{b}{a +b}}\, \sqrt{-\frac{b \sin \left(d x +c \right)}{a -b}-\frac{b}{a -b}}\, \EllipticF \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{7} b -1536 \sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}\, \sqrt{-\frac{b \sin \left(d x +c \right)}{a +b}+\frac{b}{a +b}}\, \sqrt{-\frac{b \sin \left(d x +c \right)}{a -b}-\frac{b}{a -b}}\, \EllipticF \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{6} b^{2}-4352 \sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}\, \sqrt{-\frac{b \sin \left(d x +c \right)}{a +b}+\frac{b}{a +b}}\, \sqrt{-\frac{b \sin \left(d x +c \right)}{a -b}-\frac{b}{a -b}}\, \EllipticF \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{5} b^{3}+3024 \sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}\, \sqrt{-\frac{b \sin \left(d x +c \right)}{a +b}+\frac{b}{a +b}}\, \sqrt{-\frac{b \sin \left(d x +c \right)}{a -b}-\frac{b}{a -b}}\, \EllipticF \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{4} b^{4}+2544 \sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}\, \sqrt{-\frac{b \sin \left(d x +c \right)}{a +b}+\frac{b}{a +b}}\, \sqrt{-\frac{b \sin \left(d x +c \right)}{a -b}-\frac{b}{a -b}}\, \EllipticF \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{3} b^{5}-1488 \sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}\, \sqrt{-\frac{b \sin \left(d x +c \right)}{a +b}+\frac{b}{a +b}}\, \sqrt{-\frac{b \sin \left(d x +c \right)}{a -b}-\frac{b}{a -b}}\, \EllipticF \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{2} b^{6}-240 \sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}\, \sqrt{-\frac{b \sin \left(d x +c \right)}{a +b}+\frac{b}{a +b}}\, \sqrt{-\frac{b \sin \left(d x +c \right)}{a -b}-\frac{b}{a -b}}\, \EllipticF \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{7}-2048 \sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}\, \sqrt{-\frac{b \sin \left(d x +c \right)}{a +b}+\frac{b}{a +b}}\, \sqrt{-\frac{b \sin \left(d x +c \right)}{a -b}-\frac{b}{a -b}}\, \EllipticE \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{8}+5888 \sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}\, \sqrt{-\frac{b \sin \left(d x +c \right)}{a +b}+\frac{b}{a +b}}\, \sqrt{-\frac{b \sin \left(d x +c \right)}{a -b}-\frac{b}{a -b}}\, \EllipticE \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{6} b^{2}-5568 \sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}\, \sqrt{-\frac{b \sin \left(d x +c \right)}{a +b}+\frac{b}{a +b}}\, \sqrt{-\frac{b \sin \left(d x +c \right)}{a -b}-\frac{b}{a -b}}\, \EllipticE \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{4} b^{4}+1728 \sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}\, \sqrt{-\frac{b \sin \left(d x +c \right)}{a +b}+\frac{b}{a +b}}\, \sqrt{-\frac{b \sin \left(d x +c \right)}{a -b}-\frac{b}{a -b}}\, \EllipticE \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{2} b^{6}\right)}{99 \left(a +b \sin \left(d x +c \right)\right)^{\frac{3}{2}} b^{9} \cos \left(d x +c \right) d}"," ",0,"-2/99*(-14*a*b^7*sin(d*x+c)*cos(d*x+c)^6+(48*a^3*b^5-64*a*b^7)*cos(d*x+c)^4*sin(d*x+c)+(1280*a^5*b^3-2328*a^3*b^5+984*a*b^7)*cos(d*x+c)^2*sin(d*x+c)-16*(-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*(b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2)*b*(128*EllipticE((b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2),((a-b)/(a+b))^(1/2))*a^7-368*EllipticE((b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2),((a-b)/(a+b))^(1/2))*a^5*b^2+348*EllipticE((b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2),((a-b)/(a+b))^(1/2))*a^3*b^4-108*EllipticE((b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2),((a-b)/(a+b))^(1/2))*a*b^6-128*EllipticF((b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2),((a-b)/(a+b))^(1/2))*a^6*b+96*EllipticF((b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2),((a-b)/(a+b))^(1/2))*a^5*b^2+272*EllipticF((b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2),((a-b)/(a+b))^(1/2))*a^4*b^3-189*EllipticF((b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2),((a-b)/(a+b))^(1/2))*a^3*b^4-159*EllipticF((b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2),((a-b)/(a+b))^(1/2))*a^2*b^5+93*EllipticF((b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2),((a-b)/(a+b))^(1/2))*a*b^6+15*EllipticF((b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2),((a-b)/(a+b))^(1/2))*b^7)*sin(d*x+c)-9*b^8*cos(d*x+c)^8+(24*a^2*b^6-18*b^8)*cos(d*x+c)^6+(-128*a^4*b^4+204*a^2*b^6-60*b^8)*cos(d*x+c)^4+(1024*a^6*b^2-1664*a^4*b^4+456*a^2*b^6+120*b^8)*cos(d*x+c)^2+2048*(b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2)*(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*(-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*EllipticF((b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2),((a-b)/(a+b))^(1/2))*a^7*b-1536*(b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2)*(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*(-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*EllipticF((b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2),((a-b)/(a+b))^(1/2))*a^6*b^2-4352*(b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2)*(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*(-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*EllipticF((b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2),((a-b)/(a+b))^(1/2))*a^5*b^3+3024*(b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2)*(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*(-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*EllipticF((b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2),((a-b)/(a+b))^(1/2))*a^4*b^4+2544*(b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2)*(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*(-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*EllipticF((b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2),((a-b)/(a+b))^(1/2))*a^3*b^5-1488*(b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2)*(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*(-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*EllipticF((b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2),((a-b)/(a+b))^(1/2))*a^2*b^6-240*(b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2)*(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*(-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*EllipticF((b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2),((a-b)/(a+b))^(1/2))*a*b^7-2048*(b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2)*(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*(-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*EllipticE((b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2),((a-b)/(a+b))^(1/2))*a^8+5888*(b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2)*(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*(-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*EllipticE((b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2),((a-b)/(a+b))^(1/2))*a^6*b^2-5568*(b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2)*(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*(-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*EllipticE((b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2),((a-b)/(a+b))^(1/2))*a^4*b^4+1728*(b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2)*(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*(-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*EllipticE((b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2),((a-b)/(a+b))^(1/2))*a^2*b^6)/(a+b*sin(d*x+c))^(3/2)/b^9/cos(d*x+c)/d","B"
534,1,1642,335,0.783000," ","int(cos(d*x+c)^6/(a+b*sin(d*x+c))^(5/2),x)","\frac{\frac{4 a \,b^{5} \sin \left(d x +c \right) \left(\cos^{4}\left(d x +c \right)\right)}{7}+\frac{2 \left(160 a^{3} b^{3}-136 a \,b^{5}\right) \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{21}+\frac{16 \sqrt{-\frac{b \sin \left(d x +c \right)}{a -b}-\frac{b}{a -b}}\, \sqrt{-\frac{b \sin \left(d x +c \right)}{a +b}+\frac{b}{a +b}}\, \sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}\, b \left(32 \EllipticF \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{4} b -24 \EllipticF \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{3} b^{2}-37 \EllipticF \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{2} b^{3}+24 \EllipticF \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{4}+5 \EllipticF \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) b^{5}-32 \EllipticE \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{5}+61 \EllipticE \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{3} b^{2}-29 \EllipticE \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{4}\right) \sin \left(d x +c \right)}{21}+\frac{2 b^{6} \left(\cos^{6}\left(d x +c \right)\right)}{7}+\frac{2 \left(-16 a^{2} b^{4}+10 b^{6}\right) \left(\cos^{4}\left(d x +c \right)\right)}{21}+\frac{2 \left(128 a^{4} b^{2}-84 a^{2} b^{4}-20 b^{6}\right) \left(\cos^{2}\left(d x +c \right)\right)}{21}-\frac{512 \sqrt{-\frac{b \sin \left(d x +c \right)}{a +b}+\frac{b}{a +b}}\, \EllipticE \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) \sqrt{-\frac{b \sin \left(d x +c \right)}{a -b}-\frac{b}{a -b}}\, \sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}\, a^{6}}{21}+\frac{976 \sqrt{-\frac{b \sin \left(d x +c \right)}{a +b}+\frac{b}{a +b}}\, \EllipticE \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) \sqrt{-\frac{b \sin \left(d x +c \right)}{a -b}-\frac{b}{a -b}}\, \sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}\, a^{4} b^{2}}{21}-\frac{464 \sqrt{-\frac{b \sin \left(d x +c \right)}{a +b}+\frac{b}{a +b}}\, \EllipticE \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) \sqrt{-\frac{b \sin \left(d x +c \right)}{a -b}-\frac{b}{a -b}}\, \sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}\, a^{2} b^{4}}{21}+\frac{512 \EllipticF \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) \sqrt{-\frac{b \sin \left(d x +c \right)}{a +b}+\frac{b}{a +b}}\, \sqrt{-\frac{b \sin \left(d x +c \right)}{a -b}-\frac{b}{a -b}}\, \sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}\, a^{5} b}{21}-\frac{128 \EllipticF \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) \sqrt{-\frac{b \sin \left(d x +c \right)}{a +b}+\frac{b}{a +b}}\, \sqrt{-\frac{b \sin \left(d x +c \right)}{a -b}-\frac{b}{a -b}}\, \sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}\, a^{4} b^{2}}{7}-\frac{592 \EllipticF \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) \sqrt{-\frac{b \sin \left(d x +c \right)}{a +b}+\frac{b}{a +b}}\, \sqrt{-\frac{b \sin \left(d x +c \right)}{a -b}-\frac{b}{a -b}}\, \sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}\, a^{3} b^{3}}{21}+\frac{128 \EllipticF \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) \sqrt{-\frac{b \sin \left(d x +c \right)}{a +b}+\frac{b}{a +b}}\, \sqrt{-\frac{b \sin \left(d x +c \right)}{a -b}-\frac{b}{a -b}}\, \sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}\, a^{2} b^{4}}{7}+\frac{80 \EllipticF \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) \sqrt{-\frac{b \sin \left(d x +c \right)}{a +b}+\frac{b}{a +b}}\, \sqrt{-\frac{b \sin \left(d x +c \right)}{a -b}-\frac{b}{a -b}}\, \sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}\, a \,b^{5}}{21}}{\left(a +b \sin \left(d x +c \right)\right)^{\frac{3}{2}} b^{7} \cos \left(d x +c \right) d}"," ",0,"2/21*(6*a*b^5*sin(d*x+c)*cos(d*x+c)^4+(160*a^3*b^3-136*a*b^5)*cos(d*x+c)^2*sin(d*x+c)+8*(-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*(b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2)*b*(32*EllipticF((b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2),((a-b)/(a+b))^(1/2))*a^4*b-24*EllipticF((b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2),((a-b)/(a+b))^(1/2))*a^3*b^2-37*EllipticF((b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2),((a-b)/(a+b))^(1/2))*a^2*b^3+24*EllipticF((b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2),((a-b)/(a+b))^(1/2))*a*b^4+5*EllipticF((b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2),((a-b)/(a+b))^(1/2))*b^5-32*EllipticE((b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2),((a-b)/(a+b))^(1/2))*a^5+61*EllipticE((b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2),((a-b)/(a+b))^(1/2))*a^3*b^2-29*EllipticE((b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2),((a-b)/(a+b))^(1/2))*a*b^4)*sin(d*x+c)+3*b^6*cos(d*x+c)^6+(-16*a^2*b^4+10*b^6)*cos(d*x+c)^4+(128*a^4*b^2-84*a^2*b^4-20*b^6)*cos(d*x+c)^2-256*(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*EllipticE((b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2),((a-b)/(a+b))^(1/2))*(-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*(b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2)*a^6+488*(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*EllipticE((b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2),((a-b)/(a+b))^(1/2))*(-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*(b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2)*a^4*b^2-232*(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*EllipticE((b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2),((a-b)/(a+b))^(1/2))*(-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*(b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2)*a^2*b^4+256*EllipticF((b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2),((a-b)/(a+b))^(1/2))*(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*(-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*(b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2)*a^5*b-192*EllipticF((b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2),((a-b)/(a+b))^(1/2))*(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*(-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*(b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2)*a^4*b^2-296*EllipticF((b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2),((a-b)/(a+b))^(1/2))*(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*(-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*(b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2)*a^3*b^3+192*EllipticF((b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2),((a-b)/(a+b))^(1/2))*(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*(-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*(b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2)*a^2*b^4+40*EllipticF((b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2),((a-b)/(a+b))^(1/2))*(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*(-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*(b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2)*a*b^5)/(a+b*sin(d*x+c))^(3/2)/b^7/cos(d*x+c)/d","B"
535,1,1047,267,0.778000," ","int(cos(d*x+c)^4/(a+b*sin(d*x+c))^(5/2),x)","-\frac{2 \left(10 a \,b^{3} \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+4 \sqrt{-\frac{b \sin \left(d x +c \right)}{a -b}-\frac{b}{a -b}}\, \sqrt{-\frac{b \sin \left(d x +c \right)}{a +b}+\frac{b}{a +b}}\, \sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}\, b \left(4 \EllipticF \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{2} b -3 \EllipticF \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{2}-\EllipticF \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) b^{3}-4 \EllipticE \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{3}+4 \EllipticE \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{2}\right) \sin \left(d x +c \right)-b^{4} \left(\cos^{4}\left(d x +c \right)\right)+\left(8 a^{2} b^{2}+2 b^{4}\right) \left(\cos^{2}\left(d x +c \right)\right)+16 \sqrt{-\frac{b \sin \left(d x +c \right)}{a -b}-\frac{b}{a -b}}\, \sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}\, \EllipticF \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) \sqrt{-\frac{b \sin \left(d x +c \right)}{a +b}+\frac{b}{a +b}}\, a^{3} b -12 \sqrt{-\frac{b \sin \left(d x +c \right)}{a -b}-\frac{b}{a -b}}\, \sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}\, \EllipticF \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) \sqrt{-\frac{b \sin \left(d x +c \right)}{a +b}+\frac{b}{a +b}}\, a^{2} b^{2}-4 \sqrt{-\frac{b \sin \left(d x +c \right)}{a -b}-\frac{b}{a -b}}\, \sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}\, \EllipticF \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) \sqrt{-\frac{b \sin \left(d x +c \right)}{a +b}+\frac{b}{a +b}}\, a \,b^{3}-16 \sqrt{-\frac{b \sin \left(d x +c \right)}{a -b}-\frac{b}{a -b}}\, \sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}\, \EllipticE \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) \sqrt{-\frac{b \sin \left(d x +c \right)}{a +b}+\frac{b}{a +b}}\, a^{4}+16 \sqrt{-\frac{b \sin \left(d x +c \right)}{a -b}-\frac{b}{a -b}}\, \sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}\, \EllipticE \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) \sqrt{-\frac{b \sin \left(d x +c \right)}{a +b}+\frac{b}{a +b}}\, a^{2} b^{2}\right)}{3 \left(a +b \sin \left(d x +c \right)\right)^{\frac{3}{2}} b^{5} \cos \left(d x +c \right) d}"," ",0,"-2/3*(10*a*b^3*cos(d*x+c)^2*sin(d*x+c)+4*(-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*(b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2)*b*(4*EllipticF((b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2),((a-b)/(a+b))^(1/2))*a^2*b-3*EllipticF((b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2),((a-b)/(a+b))^(1/2))*a*b^2-EllipticF((b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2),((a-b)/(a+b))^(1/2))*b^3-4*EllipticE((b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2),((a-b)/(a+b))^(1/2))*a^3+4*EllipticE((b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2),((a-b)/(a+b))^(1/2))*a*b^2)*sin(d*x+c)-b^4*cos(d*x+c)^4+(8*a^2*b^2+2*b^4)*cos(d*x+c)^2+16*(-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*(b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2)*EllipticF((b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2),((a-b)/(a+b))^(1/2))*(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*a^3*b-12*(-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*(b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2)*EllipticF((b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2),((a-b)/(a+b))^(1/2))*(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*a^2*b^2-4*(-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*(b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2)*EllipticF((b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2),((a-b)/(a+b))^(1/2))*(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*a*b^3-16*(-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*(b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2)*EllipticE((b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2),((a-b)/(a+b))^(1/2))*(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*a^4+16*(-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*(b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2)*EllipticE((b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2),((a-b)/(a+b))^(1/2))*(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*a^2*b^2)/(a+b*sin(d*x+c))^(3/2)/b^5/cos(d*x+c)/d","B"
536,1,864,265,0.822000," ","int(cos(d*x+c)^2/(a+b*sin(d*x+c))^(5/2),x)","\frac{\frac{4 a \,b^{3} \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{3}+\frac{4 \sqrt{-\frac{b \sin \left(d x +c \right)}{a +b}+\frac{b}{a +b}}\, \sqrt{-\frac{b \sin \left(d x +c \right)}{a -b}-\frac{b}{a -b}}\, \sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}\, b \left(\EllipticF \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{2} b -\EllipticF \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) b^{3}-\EllipticE \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{3}+\EllipticE \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{2}\right) \sin \left(d x +c \right)}{3}+\frac{2 \left(a^{2} b^{2}+b^{4}\right) \left(\cos^{2}\left(d x +c \right)\right)}{3}+\frac{4 \sqrt{-\frac{b \sin \left(d x +c \right)}{a -b}-\frac{b}{a -b}}\, \sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}\, \EllipticF \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) \sqrt{-\frac{b \sin \left(d x +c \right)}{a +b}+\frac{b}{a +b}}\, a^{3} b}{3}-\frac{4 \sqrt{-\frac{b \sin \left(d x +c \right)}{a -b}-\frac{b}{a -b}}\, \sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}\, \EllipticF \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) \sqrt{-\frac{b \sin \left(d x +c \right)}{a +b}+\frac{b}{a +b}}\, a \,b^{3}}{3}-\frac{4 \sqrt{-\frac{b \sin \left(d x +c \right)}{a -b}-\frac{b}{a -b}}\, \sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}\, \EllipticE \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) \sqrt{-\frac{b \sin \left(d x +c \right)}{a +b}+\frac{b}{a +b}}\, a^{4}}{3}+\frac{4 \sqrt{-\frac{b \sin \left(d x +c \right)}{a -b}-\frac{b}{a -b}}\, \sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}\, \EllipticE \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) \sqrt{-\frac{b \sin \left(d x +c \right)}{a +b}+\frac{b}{a +b}}\, a^{2} b^{2}}{3}}{\left(a^{2}-b^{2}\right) \left(a +b \sin \left(d x +c \right)\right)^{\frac{3}{2}} b^{3} \cos \left(d x +c \right) d}"," ",0,"2/3*(2*a*b^3*cos(d*x+c)^2*sin(d*x+c)+2*(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*(-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*(b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2)*b*(EllipticF((b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2),((a-b)/(a+b))^(1/2))*a^2*b-EllipticF((b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2),((a-b)/(a+b))^(1/2))*b^3-EllipticE((b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2),((a-b)/(a+b))^(1/2))*a^3+EllipticE((b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2),((a-b)/(a+b))^(1/2))*a*b^2)*sin(d*x+c)+(a^2*b^2+b^4)*cos(d*x+c)^2+2*(-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*(b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2)*EllipticF((b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2),((a-b)/(a+b))^(1/2))*(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*a^3*b-2*(-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*(b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2)*EllipticF((b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2),((a-b)/(a+b))^(1/2))*(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*a*b^3-2*(-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*(b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2)*EllipticE((b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2),((a-b)/(a+b))^(1/2))*(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*a^4+2*(-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*(b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2)*EllipticE((b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2),((a-b)/(a+b))^(1/2))*(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*a^2*b^2)/(a^2-b^2)/(a+b*sin(d*x+c))^(3/2)/b^3/cos(d*x+c)/d","B"
537,1,1653,367,3.851000," ","int(sec(d*x+c)^2/(a+b*sin(d*x+c))^(5/2),x)","\frac{\sqrt{-\left(-a -b \sin \left(d x +c \right)\right) \left(\cos^{2}\left(d x +c \right)\right)}\, \left(\frac{\sqrt{\left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) b +\left(\cos^{2}\left(d x +c \right)\right) a}\, \left(\EllipticE \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) \sqrt{-\frac{b \sin \left(d x +c \right)}{a +b}+\frac{b}{a +b}}\, \sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}\, \sqrt{-\frac{b \sin \left(d x +c \right)}{a -b}-\frac{b}{a -b}}\, a^{2}-\EllipticE \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) \sqrt{-\frac{b \sin \left(d x +c \right)}{a +b}+\frac{b}{a +b}}\, \sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}\, \sqrt{-\frac{b \sin \left(d x +c \right)}{a -b}-\frac{b}{a -b}}\, b^{2}-b^{2} \left(\cos^{2}\left(d x +c \right)\right)+a b \sin \left(d x +c \right)+b^{2} \sin \left(d x +c \right)+a b +b^{2}\right)}{2 \left(a +b \right)^{3} b \cos \left(d x +c \right)^{2} \left(a +b \sin \left(d x +c \right)\right)}-\frac{2 a \,b^{2} \left(\frac{2 b \left(\cos^{2}\left(d x +c \right)\right)}{\left(a^{2}-b^{2}\right) \sqrt{-\left(-a -b \sin \left(d x +c \right)\right) \left(\cos^{2}\left(d x +c \right)\right)}}+\frac{2 a \left(\frac{a}{b}-1\right) \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{\frac{b \left(1-\sin \left(d x +c \right)\right)}{a +b}}\, \sqrt{\frac{\left(-1-\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right)}{\left(a^{2}-b^{2}\right) \sqrt{-\left(-a -b \sin \left(d x +c \right)\right) \left(\cos^{2}\left(d x +c \right)\right)}}+\frac{2 b \left(\frac{a}{b}-1\right) \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{\frac{b \left(1-\sin \left(d x +c \right)\right)}{a +b}}\, \sqrt{\frac{\left(-1-\sin \left(d x +c \right)\right) b}{a -b}}\, \left(\left(-\frac{a}{b}-1\right) \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right)+\EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right)\right)}{\left(a^{2}-b^{2}\right) \sqrt{-\left(-a -b \sin \left(d x +c \right)\right) \left(\cos^{2}\left(d x +c \right)\right)}}\right)}{\left(a +b \right)^{2} \left(a -b \right)^{2}}-\frac{b^{2} \left(\frac{2 \sqrt{-\left(-a -b \sin \left(d x +c \right)\right) \left(\cos^{2}\left(d x +c \right)\right)}}{3 b \left(a^{2}-b^{2}\right) \left(\sin \left(d x +c \right)+\frac{a}{b}\right)^{2}}+\frac{8 b \left(\cos^{2}\left(d x +c \right)\right) a}{3 \left(a^{2}-b^{2}\right)^{2} \sqrt{-\left(-a -b \sin \left(d x +c \right)\right) \left(\cos^{2}\left(d x +c \right)\right)}}+\frac{2 \left(3 a^{2}+b^{2}\right) \left(\frac{a}{b}-1\right) \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{\frac{b \left(1-\sin \left(d x +c \right)\right)}{a +b}}\, \sqrt{\frac{\left(-1-\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right)}{\left(3 a^{4}-6 a^{2} b^{2}+3 b^{4}\right) \sqrt{-\left(-a -b \sin \left(d x +c \right)\right) \left(\cos^{2}\left(d x +c \right)\right)}}+\frac{8 a b \left(\frac{a}{b}-1\right) \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{\frac{b \left(1-\sin \left(d x +c \right)\right)}{a +b}}\, \sqrt{\frac{\left(-1-\sin \left(d x +c \right)\right) b}{a -b}}\, \left(\left(-\frac{a}{b}-1\right) \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right)+\EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right)\right)}{3 \left(a^{2}-b^{2}\right)^{2} \sqrt{-\left(-a -b \sin \left(d x +c \right)\right) \left(\cos^{2}\left(d x +c \right)\right)}}\right)}{\left(a +b \right) \left(a -b \right)}+\frac{-\frac{-\left(\sin^{2}\left(d x +c \right)\right) b -a \sin \left(d x +c \right)+b \sin \left(d x +c \right)+a}{\left(a -b \right) \sqrt{\left(-a -b \sin \left(d x +c \right)\right) \left(\sin \left(d x +c \right)-1\right) \left(1+\sin \left(d x +c \right)\right)}}-\frac{2 b \left(\frac{a}{b}-1\right) \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{\frac{b \left(1-\sin \left(d x +c \right)\right)}{a +b}}\, \sqrt{\frac{\left(-1-\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right)}{\left(2 a -2 b \right) \sqrt{-\left(-a -b \sin \left(d x +c \right)\right) \left(\cos^{2}\left(d x +c \right)\right)}}-\frac{b \left(\frac{a}{b}-1\right) \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{\frac{b \left(1-\sin \left(d x +c \right)\right)}{a +b}}\, \sqrt{\frac{\left(-1-\sin \left(d x +c \right)\right) b}{a -b}}\, \left(\left(-\frac{a}{b}-1\right) \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right)+\EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right)\right)}{\left(a -b \right) \sqrt{-\left(-a -b \sin \left(d x +c \right)\right) \left(\cos^{2}\left(d x +c \right)\right)}}}{2 \left(a -b \right)^{2}}\right)}{\cos \left(d x +c \right) \sqrt{a +b \sin \left(d x +c \right)}\, d}"," ",0,"(-(-a-b*sin(d*x+c))*cos(d*x+c)^2)^(1/2)*(1/2/(a+b)^3/b/cos(d*x+c)^2/(a+b*sin(d*x+c))*(cos(d*x+c)^2*sin(d*x+c)*b+cos(d*x+c)^2*a)^(1/2)*(EllipticE((b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2),((a-b)/(a+b))^(1/2))*(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*(b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2)*(-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*a^2-EllipticE((b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2),((a-b)/(a+b))^(1/2))*(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*(b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2)*(-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*b^2-b^2*cos(d*x+c)^2+a*b*sin(d*x+c)+b^2*sin(d*x+c)+a*b+b^2)-2*a*b^2/(a+b)^2/(a-b)^2*(2*b*cos(d*x+c)^2/(a^2-b^2)/(-(-a-b*sin(d*x+c))*cos(d*x+c)^2)^(1/2)+2*a/(a^2-b^2)*(a/b-1)*((a+b*sin(d*x+c))/(a-b))^(1/2)*(b*(1-sin(d*x+c))/(a+b))^(1/2)*((-1-sin(d*x+c))*b/(a-b))^(1/2)/(-(-a-b*sin(d*x+c))*cos(d*x+c)^2)^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))+2*b/(a^2-b^2)*(a/b-1)*((a+b*sin(d*x+c))/(a-b))^(1/2)*(b*(1-sin(d*x+c))/(a+b))^(1/2)*((-1-sin(d*x+c))*b/(a-b))^(1/2)/(-(-a-b*sin(d*x+c))*cos(d*x+c)^2)^(1/2)*((-a/b-1)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))+EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))))-b^2/(a+b)/(a-b)*(2/3/b/(a^2-b^2)*(-(-a-b*sin(d*x+c))*cos(d*x+c)^2)^(1/2)/(sin(d*x+c)+a/b)^2+8/3*b*cos(d*x+c)^2/(a^2-b^2)^2*a/(-(-a-b*sin(d*x+c))*cos(d*x+c)^2)^(1/2)+2*(3*a^2+b^2)/(3*a^4-6*a^2*b^2+3*b^4)*(a/b-1)*((a+b*sin(d*x+c))/(a-b))^(1/2)*(b*(1-sin(d*x+c))/(a+b))^(1/2)*((-1-sin(d*x+c))*b/(a-b))^(1/2)/(-(-a-b*sin(d*x+c))*cos(d*x+c)^2)^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))+8/3*a*b/(a^2-b^2)^2*(a/b-1)*((a+b*sin(d*x+c))/(a-b))^(1/2)*(b*(1-sin(d*x+c))/(a+b))^(1/2)*((-1-sin(d*x+c))*b/(a-b))^(1/2)/(-(-a-b*sin(d*x+c))*cos(d*x+c)^2)^(1/2)*((-a/b-1)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))+EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))))+1/2/(a-b)^2*(-(-sin(d*x+c)^2*b-a*sin(d*x+c)+b*sin(d*x+c)+a)/(a-b)/((-a-b*sin(d*x+c))*(sin(d*x+c)-1)*(1+sin(d*x+c)))^(1/2)-2*b/(2*a-2*b)*(a/b-1)*((a+b*sin(d*x+c))/(a-b))^(1/2)*(b*(1-sin(d*x+c))/(a+b))^(1/2)*((-1-sin(d*x+c))*b/(a-b))^(1/2)/(-(-a-b*sin(d*x+c))*cos(d*x+c)^2)^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))-b/(a-b)*(a/b-1)*((a+b*sin(d*x+c))/(a-b))^(1/2)*(b*(1-sin(d*x+c))/(a+b))^(1/2)*((-1-sin(d*x+c))*b/(a-b))^(1/2)/(-(-a-b*sin(d*x+c))*cos(d*x+c)^2)^(1/2)*((-a/b-1)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))+EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2)))))/cos(d*x+c)/(a+b*sin(d*x+c))^(1/2)/d","B"
538,1,2585,465,5.841000," ","int(sec(d*x+c)^4/(a+b*sin(d*x+c))^(5/2),x)","\text{Expression too large to display}"," ",0,"(-(-a-b*sin(d*x+c))*cos(d*x+c)^2)^(1/2)*(-1/4*(-a-3*b)/(a+b)^4/b/cos(d*x+c)^2/(a+b*sin(d*x+c))*(cos(d*x+c)^2*sin(d*x+c)*b+cos(d*x+c)^2*a)^(1/2)*(EllipticE((b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2),((a-b)/(a+b))^(1/2))*(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*(b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2)*(-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*a^2-EllipticE((b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2),((a-b)/(a+b))^(1/2))*(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*(b/(a-b)*sin(d*x+c)+1/(a-b)*a)^(1/2)*(-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*b^2-b^2*cos(d*x+c)^2+a*b*sin(d*x+c)+b^2*sin(d*x+c)+a*b+b^2)+4*a*b^4/(a+b)^3/(a-b)^3*(2*b*cos(d*x+c)^2/(a^2-b^2)/(-(-a-b*sin(d*x+c))*cos(d*x+c)^2)^(1/2)+2*a/(a^2-b^2)*(a/b-1)*((a+b*sin(d*x+c))/(a-b))^(1/2)*(b*(1-sin(d*x+c))/(a+b))^(1/2)*((-1-sin(d*x+c))*b/(a-b))^(1/2)/(-(-a-b*sin(d*x+c))*cos(d*x+c)^2)^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))+2*b/(a^2-b^2)*(a/b-1)*((a+b*sin(d*x+c))/(a-b))^(1/2)*(b*(1-sin(d*x+c))/(a+b))^(1/2)*((-1-sin(d*x+c))*b/(a-b))^(1/2)/(-(-a-b*sin(d*x+c))*cos(d*x+c)^2)^(1/2)*((-a/b-1)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))+EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))))+1/4/(a+b)^2*(1/3/(a+b)*(-(-a-b*sin(d*x+c))*cos(d*x+c)^2)^(1/2)/(sin(d*x+c)-1)^2-1/3*(-sin(d*x+c)^2*b-a*sin(d*x+c)-b*sin(d*x+c)-a)/(a+b)^2*(a+3*b)/((-a-b*sin(d*x+c))*(sin(d*x+c)-1)*(1+sin(d*x+c)))^(1/2)+2*b^2/(3*a^2+6*a*b+3*b^2)*(a/b-1)*((a+b*sin(d*x+c))/(a-b))^(1/2)*(b*(1-sin(d*x+c))/(a+b))^(1/2)*((-1-sin(d*x+c))*b/(a-b))^(1/2)/(-(-a-b*sin(d*x+c))*cos(d*x+c)^2)^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))-1/3*b*(a+3*b)/(a+b)^2*(a/b-1)*((a+b*sin(d*x+c))/(a-b))^(1/2)*(b*(1-sin(d*x+c))/(a+b))^(1/2)*((-1-sin(d*x+c))*b/(a-b))^(1/2)/(-(-a-b*sin(d*x+c))*cos(d*x+c)^2)^(1/2)*((-a/b-1)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))+EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))))+b^4/(a+b)^2/(a-b)^2*(2/3/b/(a^2-b^2)*(-(-a-b*sin(d*x+c))*cos(d*x+c)^2)^(1/2)/(sin(d*x+c)+a/b)^2+8/3*b*cos(d*x+c)^2/(a^2-b^2)^2*a/(-(-a-b*sin(d*x+c))*cos(d*x+c)^2)^(1/2)+2*(3*a^2+b^2)/(3*a^4-6*a^2*b^2+3*b^4)*(a/b-1)*((a+b*sin(d*x+c))/(a-b))^(1/2)*(b*(1-sin(d*x+c))/(a+b))^(1/2)*((-1-sin(d*x+c))*b/(a-b))^(1/2)/(-(-a-b*sin(d*x+c))*cos(d*x+c)^2)^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))+8/3*a*b/(a^2-b^2)^2*(a/b-1)*((a+b*sin(d*x+c))/(a-b))^(1/2)*(b*(1-sin(d*x+c))/(a+b))^(1/2)*((-1-sin(d*x+c))*b/(a-b))^(1/2)/(-(-a-b*sin(d*x+c))*cos(d*x+c)^2)^(1/2)*((-a/b-1)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))+EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))))+1/4*(a-3*b)/(a-b)^3*(-(-sin(d*x+c)^2*b-a*sin(d*x+c)+b*sin(d*x+c)+a)/(a-b)/((-a-b*sin(d*x+c))*(sin(d*x+c)-1)*(1+sin(d*x+c)))^(1/2)-2*b/(2*a-2*b)*(a/b-1)*((a+b*sin(d*x+c))/(a-b))^(1/2)*(b*(1-sin(d*x+c))/(a+b))^(1/2)*((-1-sin(d*x+c))*b/(a-b))^(1/2)/(-(-a-b*sin(d*x+c))*cos(d*x+c)^2)^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))-b/(a-b)*(a/b-1)*((a+b*sin(d*x+c))/(a-b))^(1/2)*(b*(1-sin(d*x+c))/(a+b))^(1/2)*((-1-sin(d*x+c))*b/(a-b))^(1/2)/(-(-a-b*sin(d*x+c))*cos(d*x+c)^2)^(1/2)*((-a/b-1)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))+EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))))+1/4/(a-b)^2*(-1/3/(a-b)*(-(-a-b*sin(d*x+c))*cos(d*x+c)^2)^(1/2)/(1+sin(d*x+c))^2-1/3*(-sin(d*x+c)^2*b-a*sin(d*x+c)+b*sin(d*x+c)+a)/(a-b)^2*(a-3*b)/((-a-b*sin(d*x+c))*(sin(d*x+c)-1)*(1+sin(d*x+c)))^(1/2)+2*b^2/(3*a^2-6*a*b+3*b^2)*(a/b-1)*((a+b*sin(d*x+c))/(a-b))^(1/2)*(b*(1-sin(d*x+c))/(a+b))^(1/2)*((-1-sin(d*x+c))*b/(a-b))^(1/2)/(-(-a-b*sin(d*x+c))*cos(d*x+c)^2)^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))-1/3*b*(a-3*b)/(a-b)^2*(a/b-1)*((a+b*sin(d*x+c))/(a-b))^(1/2)*(b*(1-sin(d*x+c))/(a+b))^(1/2)*((-1-sin(d*x+c))*b/(a-b))^(1/2)/(-(-a-b*sin(d*x+c))*cos(d*x+c)^2)^(1/2)*((-a/b-1)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))+EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2)))))/cos(d*x+c)/(a+b*sin(d*x+c))^(1/2)/d","B"
539,1,259,132,1.395000," ","int((e*cos(d*x+c))^(7/2)*(a+b*sin(d*x+c)),x)","-\frac{2 e^{4} \left(-224 b \left(\sin^{11}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+144 a \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+560 b \left(\sin^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-216 a \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-560 b \left(\sin^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+168 a \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+280 b \left(\sin^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+15 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a -48 a \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-70 b \left(\sin^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+7 b \sin \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{63 \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e +e}\, d}"," ",0,"-2/63/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)*e^4*(-224*b*sin(1/2*d*x+1/2*c)^11+144*a*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^8+560*b*sin(1/2*d*x+1/2*c)^9-216*a*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6-560*b*sin(1/2*d*x+1/2*c)^7+168*a*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^4+280*b*sin(1/2*d*x+1/2*c)^5+15*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*a-48*a*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2-70*b*sin(1/2*d*x+1/2*c)^3+7*b*sin(1/2*d*x+1/2*c))/d","A"
540,1,222,107,1.412000," ","int((e*cos(d*x+c))^(5/2)*(a+b*sin(d*x+c)),x)","\frac{2 e^{3} \left(-80 b \left(\sin^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+56 a \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+160 b \left(\sin^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-56 a \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-120 b \left(\sin^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+21 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a +14 a \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+40 b \left(\sin^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-5 b \sin \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{35 \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e +e}\, d}"," ",0,"2/35/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)*e^3*(-80*b*sin(1/2*d*x+1/2*c)^9+56*a*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6+160*b*sin(1/2*d*x+1/2*c)^7-56*a*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^4-120*b*sin(1/2*d*x+1/2*c)^5+21*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*a+14*a*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2+40*b*sin(1/2*d*x+1/2*c)^3-5*b*sin(1/2*d*x+1/2*c))/d","B"
541,1,185,107,1.288000," ","int((e*cos(d*x+c))^(3/2)*(a+b*sin(d*x+c)),x)","-\frac{2 e^{2} \left(-24 b \left(\sin^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+20 a \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+36 b \left(\sin^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+5 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a -10 a \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-18 b \left(\sin^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+3 b \sin \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{15 \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e +e}\, d}"," ",0,"-2/15/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)*e^2*(-24*b*sin(1/2*d*x+1/2*c)^7+20*a*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^4+36*b*sin(1/2*d*x+1/2*c)^5+5*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*a-10*a*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2-18*b*sin(1/2*d*x+1/2*c)^3+3*b*sin(1/2*d*x+1/2*c))/d","A"
542,1,123,81,1.116000," ","int((a+b*sin(d*x+c))*(e*cos(d*x+c))^(1/2),x)","\frac{2 e \left(-4 b \left(\sin^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+3 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a +4 b \left(\sin^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-b \sin \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e +e}\, d}"," ",0,"2/3/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)*e*(-4*b*sin(1/2*d*x+1/2*c)^5+3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*a+4*b*sin(1/2*d*x+1/2*c)^3-b*sin(1/2*d*x+1/2*c))/d","A"
543,1,106,81,0.844000," ","int((a+b*sin(d*x+c))/(e*cos(d*x+c))^(1/2),x)","-\frac{2 \left(\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a -2 b \left(\sin^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+b \sin \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e +e}\, d}"," ",0,"-2/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)*((sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*a-2*b*sin(1/2*d*x+1/2*c)^3+b*sin(1/2*d*x+1/2*c))/d","A"
544,1,119,109,1.623000," ","int((a+b*sin(d*x+c))/(e*cos(d*x+c))^(3/2),x)","-\frac{2 \left(\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a -2 a \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-b \sin \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{e \sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e +e}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) d}"," ",0,"-2/e/(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)/sin(1/2*d*x+1/2*c)*((sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*a-2*a*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2-b*sin(1/2*d*x+1/2*c))/d","A"
545,1,193,109,2.084000," ","int((a+b*sin(d*x+c))/(e*cos(d*x+c))^(5/2),x)","-\frac{2 \left(2 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a +2 a \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+b \sin \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 \left(2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e +e}\, e^{2} d}"," ",0,"-2/3/(2*sin(1/2*d*x+1/2*c)^2-1)/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)/e^2*(2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*a*sin(1/2*d*x+1/2*c)^2-(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*a+2*a*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2+b*sin(1/2*d*x+1/2*c))/d","A"
546,1,310,134,3.237000," ","int((a+b*sin(d*x+c))/(e*cos(d*x+c))^(7/2),x)","-\frac{2 \left(12 \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-24 a \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-12 \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+24 a \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+3 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a -8 a \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-b \sin \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{5 \left(4 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-4 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e +e}\, e^{3} d}"," ",0,"-2/5/(4*sin(1/2*d*x+1/2*c)^4-4*sin(1/2*d*x+1/2*c)^2+1)/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)/e^3*(12*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*a*sin(1/2*d*x+1/2*c)^4-24*a*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6-12*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*a*sin(1/2*d*x+1/2*c)^2+24*a*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^4+3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*a-8*a*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2-b*sin(1/2*d*x+1/2*c))/d","B"
547,1,473,192,1.751000," ","int((e*cos(d*x+c))^(7/2)*(a+b*sin(d*x+c))^2,x)","-\frac{2 e^{4} \left(-4032 b^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{12}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-4928 a b \left(\sin^{11}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+10080 b^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{10}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1584 a^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+12320 a b \left(\sin^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-9792 b^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-2376 a^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-12320 a b \left(\sin^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+4608 b^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1848 a^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+6160 a b \left(\sin^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-924 b^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+165 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a^{2}+30 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) b^{2}-528 a^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1540 a b \left(\sin^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+30 b^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+154 a b \sin \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{693 \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e +e}\, d}"," ",0,"-2/693/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)*e^4*(-4032*b^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^12-4928*a*b*sin(1/2*d*x+1/2*c)^11+10080*b^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^10+1584*a^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^8+12320*a*b*sin(1/2*d*x+1/2*c)^9-9792*b^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^8-2376*a^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6-12320*a*b*sin(1/2*d*x+1/2*c)^7+4608*b^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6+1848*a^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^4+6160*a*b*sin(1/2*d*x+1/2*c)^5-924*b^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^4+165*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*a^2+30*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*b^2-528*a^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2-1540*a*b*sin(1/2*d*x+1/2*c)^3+30*b^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2+154*a*b*sin(1/2*d*x+1/2*c))/d","B"
548,1,408,157,1.514000," ","int((e*cos(d*x+c))^(5/2)*(a+b*sin(d*x+c))^2,x)","\frac{2 e^{3} \left(-1120 b^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{10}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1440 a b \left(\sin^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+2240 b^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+504 a^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+2880 a b \left(\sin^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1568 b^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-504 a^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-2160 a b \left(\sin^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+448 b^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+189 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a^{2}+42 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) b^{2}+126 a^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+720 a b \left(\sin^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-42 b^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-90 a b \sin \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{315 \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e +e}\, d}"," ",0,"2/315/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)*e^3*(-1120*b^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^10-1440*a*b*sin(1/2*d*x+1/2*c)^9+2240*b^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^8+504*a^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6+2880*a*b*sin(1/2*d*x+1/2*c)^7-1568*b^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6-504*a^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^4-2160*a*b*sin(1/2*d*x+1/2*c)^5+448*b^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^4+189*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*a^2+42*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*b^2+126*a^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2+720*a*b*sin(1/2*d*x+1/2*c)^3-42*b^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2-90*a*b*sin(1/2*d*x+1/2*c))/d","B"
549,1,343,157,1.725000," ","int((e*cos(d*x+c))^(3/2)*(a+b*sin(d*x+c))^2,x)","-\frac{2 e^{2} \left(-240 b^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-336 a b \left(\sin^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+360 b^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+140 a^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+504 a b \left(\sin^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-140 b^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+35 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a^{2}+10 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) b^{2}-70 a^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-252 a b \left(\sin^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+10 b^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+42 a b \sin \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{105 \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e +e}\, d}"," ",0,"-2/105/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)*e^2*(-240*b^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^8-336*a*b*sin(1/2*d*x+1/2*c)^7+360*b^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6+140*a^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^4+504*a*b*sin(1/2*d*x+1/2*c)^5-140*b^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^4+35*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*a^2+10*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*b^2-70*a^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2-252*a*b*sin(1/2*d*x+1/2*c)^3+10*b^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2+42*a*b*sin(1/2*d*x+1/2*c))/d","B"
550,1,251,121,1.727000," ","int((a+b*sin(d*x+c))^2*(e*cos(d*x+c))^(1/2),x)","\frac{2 e \left(-24 b^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-40 a b \left(\sin^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+24 b^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+15 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a^{2}+6 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) b^{2}+40 a b \left(\sin^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-6 b^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-10 a b \sin \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{15 \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e +e}\, d}"," ",0,"2/15/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)*e*(-24*b^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6-40*a*b*sin(1/2*d*x+1/2*c)^5+24*b^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^4+15*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*a^2+6*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*b^2+40*a*b*sin(1/2*d*x+1/2*c)^3-6*b^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2-10*a*b*sin(1/2*d*x+1/2*c))/d","B"
551,1,210,121,1.069000," ","int((a+b*sin(d*x+c))^2/(e*cos(d*x+c))^(1/2),x)","-\frac{2 \left(-4 b^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+3 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a^{2}+2 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) b^{2}-12 a b \left(\sin^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+2 b^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+6 a b \sin \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e +e}\, d}"," ",0,"-2/3/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)*(-4*b^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^4+3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*a^2+2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*b^2-12*a*b*sin(1/2*d*x+1/2*c)^3+2*b^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2+6*a*b*sin(1/2*d*x+1/2*c))/d","A"
552,1,197,131,1.799000," ","int((a+b*sin(d*x+c))^2/(e*cos(d*x+c))^(3/2),x)","-\frac{2 \left(\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a^{2}+2 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) b^{2}-2 a^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-2 b^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-2 a b \sin \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{e \sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e +e}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) d}"," ",0,"-2/e/(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)/sin(1/2*d*x+1/2*c)*((sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*a^2+2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*b^2-2*a^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2-2*b^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2-2*a*b*sin(1/2*d*x+1/2*c))/d","A"
553,1,333,131,2.181000," ","int((a+b*sin(d*x+c))^2/(e*cos(d*x+c))^(5/2),x)","-\frac{2 \left(2 \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, a^{2} \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-4 \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, b^{2} \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a^{2}+2 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) b^{2}+2 a^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+2 b^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+2 a b \sin \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 \left(2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e +e}\, e^{2} d}"," ",0,"-2/3/(2*sin(1/2*d*x+1/2*c)^2-1)/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)/e^2*(2*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*a^2*sin(1/2*d*x+1/2*c)^2-4*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*b^2*sin(1/2*d*x+1/2*c)^2-(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*a^2+2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*b^2+2*a^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2+2*b^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2+2*a*b*sin(1/2*d*x+1/2*c))/d","B"
554,1,564,168,3.995000," ","int((a+b*sin(d*x+c))^2/(e*cos(d*x+c))^(7/2),x)","-\frac{2 \left(12 \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, a^{2} \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-8 \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, b^{2} \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-24 a^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+16 b^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-12 \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, a^{2} \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+8 \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, b^{2} \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+24 a^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-16 b^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+3 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a^{2}-2 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) b^{2}-8 a^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+2 b^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-2 a b \sin \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{5 \left(4 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-4 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e +e}\, e^{3} d}"," ",0,"-2/5/(4*sin(1/2*d*x+1/2*c)^4-4*sin(1/2*d*x+1/2*c)^2+1)/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)/e^3*(12*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(sin(1/2*d*x+1/2*c)^2)^(1/2)*a^2*sin(1/2*d*x+1/2*c)^4-8*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(sin(1/2*d*x+1/2*c)^2)^(1/2)*b^2*sin(1/2*d*x+1/2*c)^4-24*a^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6+16*b^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6-12*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(sin(1/2*d*x+1/2*c)^2)^(1/2)*a^2*sin(1/2*d*x+1/2*c)^2+8*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(sin(1/2*d*x+1/2*c)^2)^(1/2)*b^2*sin(1/2*d*x+1/2*c)^2+24*a^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^4-16*b^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^4+3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*a^2-2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*b^2-8*a^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2+2*b^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2-2*a*b*sin(1/2*d*x+1/2*c))/d","B"
555,1,618,237,3.471000," ","int((e*cos(d*x+c))^(7/2)*(a+b*sin(d*x+c))^3,x)","-\frac{2 e^{4} \left(3003 a^{2} b \sin \left(\frac{d x}{2}+\frac{c}{2}\right)-308 b^{3} \left(\sin^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+433664 b^{3} \left(\sin^{11}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-310464 b^{3} \left(\sin^{13}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+120120 a^{2} b \left(\sin^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-240240 a^{2} b \left(\sin^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-30030 a^{2} b \left(\sin^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-6864 a^{3} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+240240 a^{2} b \left(\sin^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+24024 a^{3} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-96096 a^{2} b \left(\sin^{11}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+20592 a^{3} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+308 b^{3} \sin \left(\frac{d x}{2}+\frac{c}{2}\right)-18172 b^{3} \left(\sin^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-30888 a^{3} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+2145 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a^{3}-381888 a \,b^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+179712 a \,b^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-36036 a \,b^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1170 a \,b^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-157248 a \,b^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{12}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+393120 a \,b^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{10}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+88704 b^{3} \left(\sin^{15}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-308000 b^{3} \left(\sin^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+113960 b^{3} \left(\sin^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1170 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a \,b^{2}\right)}{9009 \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e +e}\, d}"," ",0,"-2/9009/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)*e^4*(3003*a^2*b*sin(1/2*d*x+1/2*c)+308*b^3*sin(1/2*d*x+1/2*c)+88704*b^3*sin(1/2*d*x+1/2*c)^15-308000*b^3*sin(1/2*d*x+1/2*c)^9+113960*b^3*sin(1/2*d*x+1/2*c)^7-18172*b^3*sin(1/2*d*x+1/2*c)^5-308*b^3*sin(1/2*d*x+1/2*c)^3+433664*b^3*sin(1/2*d*x+1/2*c)^11-310464*b^3*sin(1/2*d*x+1/2*c)^13+20592*a^3*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^8-30888*a^3*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6+24024*a^3*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^4-6864*a^3*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2-96096*a^2*b*sin(1/2*d*x+1/2*c)^11+240240*a^2*b*sin(1/2*d*x+1/2*c)^9-240240*a^2*b*sin(1/2*d*x+1/2*c)^7+120120*a^2*b*sin(1/2*d*x+1/2*c)^5-30030*a^2*b*sin(1/2*d*x+1/2*c)^3+1170*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*a*b^2-381888*a*b^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^8+179712*a*b^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6-36036*a*b^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^4+1170*a*b^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2+2145*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*a^3-157248*a*b^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^12+393120*a*b^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^10)/d","B"
556,1,534,201,3.090000," ","int((e*cos(d*x+c))^(5/2)*(a+b*sin(d*x+c))^3,x)","\frac{2 e^{3} \left(6720 b^{3} \left(\sin^{13}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-12320 a \,b^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{10}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-20160 b^{3} \left(\sin^{11}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-7920 a^{2} b \left(\sin^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+24640 a \,b^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+22560 b^{3} \left(\sin^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1848 a^{3} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+15840 a^{2} b \left(\sin^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-17248 a \,b^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-11520 b^{3} \left(\sin^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1848 a^{3} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-11880 a^{2} b \left(\sin^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+4928 a \,b^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+2340 b^{3} \left(\sin^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+693 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a^{3}+462 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a \,b^{2}+462 a^{3} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+3960 a^{2} b \left(\sin^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-462 a \,b^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+60 b^{3} \left(\sin^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-495 a^{2} b \sin \left(\frac{d x}{2}+\frac{c}{2}\right)-60 b^{3} \sin \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{1155 \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e +e}\, d}"," ",0,"2/1155/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)*e^3*(6720*b^3*sin(1/2*d*x+1/2*c)^13-12320*a*b^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^10-20160*b^3*sin(1/2*d*x+1/2*c)^11-7920*a^2*b*sin(1/2*d*x+1/2*c)^9+24640*a*b^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^8+22560*b^3*sin(1/2*d*x+1/2*c)^9+1848*a^3*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6+15840*a^2*b*sin(1/2*d*x+1/2*c)^7-17248*a*b^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6-11520*b^3*sin(1/2*d*x+1/2*c)^7-1848*a^3*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^4-11880*a^2*b*sin(1/2*d*x+1/2*c)^5+4928*a*b^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^4+2340*b^3*sin(1/2*d*x+1/2*c)^5+693*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*a^3+462*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*a*b^2+462*a^3*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2+3960*a^2*b*sin(1/2*d*x+1/2*c)^3-462*a*b^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2+60*b^3*sin(1/2*d*x+1/2*c)^3-495*a^2*b*sin(1/2*d*x+1/2*c)-60*b^3*sin(1/2*d*x+1/2*c))/d","B"
557,1,450,201,2.625000," ","int((e*cos(d*x+c))^(3/2)*(a+b*sin(d*x+c))^3,x)","-\frac{2 e^{2} \left(1120 b^{3} \left(\sin^{11}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-2160 a \,b^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-2800 b^{3} \left(\sin^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1512 a^{2} b \left(\sin^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+3240 a \,b^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+2296 b^{3} \left(\sin^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+420 a^{3} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+2268 a^{2} b \left(\sin^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1260 a \,b^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-644 b^{3} \left(\sin^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+105 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a^{3}+90 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a \,b^{2}-210 a^{3} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1134 a^{2} b \left(\sin^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+90 a \,b^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-28 b^{3} \left(\sin^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+189 a^{2} b \sin \left(\frac{d x}{2}+\frac{c}{2}\right)+28 b^{3} \sin \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{315 \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e +e}\, d}"," ",0,"-2/315/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)*e^2*(1120*b^3*sin(1/2*d*x+1/2*c)^11-2160*a*b^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^8-2800*b^3*sin(1/2*d*x+1/2*c)^9-1512*a^2*b*sin(1/2*d*x+1/2*c)^7+3240*a*b^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6+2296*b^3*sin(1/2*d*x+1/2*c)^7+420*a^3*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^4+2268*a^2*b*sin(1/2*d*x+1/2*c)^5-1260*a*b^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^4-644*b^3*sin(1/2*d*x+1/2*c)^5+105*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*a^3+90*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*a*b^2-210*a^3*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2-1134*a^2*b*sin(1/2*d*x+1/2*c)^3+90*a*b^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2-28*b^3*sin(1/2*d*x+1/2*c)^3+189*a^2*b*sin(1/2*d*x+1/2*c)+28*b^3*sin(1/2*d*x+1/2*c))/d","B"
558,1,339,164,2.122000," ","int((a+b*sin(d*x+c))^3*(e*cos(d*x+c))^(1/2),x)","\frac{2 e \left(240 b^{3} \left(\sin^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-504 a \,b^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-480 b^{3} \left(\sin^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-420 a^{2} b \left(\sin^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+504 a \,b^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+220 b^{3} \left(\sin^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+105 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a^{3}+126 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a \,b^{2}+420 a^{2} b \left(\sin^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-126 a \,b^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+20 b^{3} \left(\sin^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-105 a^{2} b \sin \left(\frac{d x}{2}+\frac{c}{2}\right)-20 b^{3} \sin \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{105 \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e +e}\, d}"," ",0,"2/105/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)*e*(240*b^3*sin(1/2*d*x+1/2*c)^9-504*a*b^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6-480*b^3*sin(1/2*d*x+1/2*c)^7-420*a^2*b*sin(1/2*d*x+1/2*c)^5+504*a*b^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^4+220*b^3*sin(1/2*d*x+1/2*c)^5+105*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*a^3+126*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*a*b^2+420*a^2*b*sin(1/2*d*x+1/2*c)^3-126*a*b^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2+20*b^3*sin(1/2*d*x+1/2*c)^3-105*a^2*b*sin(1/2*d*x+1/2*c)-20*b^3*sin(1/2*d*x+1/2*c))/d","B"
559,1,279,162,1.760000," ","int((a+b*sin(d*x+c))^3/(e*cos(d*x+c))^(1/2),x)","-\frac{2 \left(8 b^{3} \left(\sin^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-20 a \,b^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-12 b^{3} \left(\sin^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+5 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a^{3}+10 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a \,b^{2}-30 a^{2} b \left(\sin^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+10 a \,b^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-4 b^{3} \left(\sin^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+15 a^{2} b \sin \left(\frac{d x}{2}+\frac{c}{2}\right)+4 b^{3} \sin \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{5 \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e +e}\, d}"," ",0,"-2/5/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)*(8*b^3*sin(1/2*d*x+1/2*c)^7-20*a*b^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^4-12*b^3*sin(1/2*d*x+1/2*c)^5+5*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*a^3+10*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*a*b^2-30*a^2*b*sin(1/2*d*x+1/2*c)^3+10*a*b^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2-4*b^3*sin(1/2*d*x+1/2*c)^3+15*a^2*b*sin(1/2*d*x+1/2*c)+4*b^3*sin(1/2*d*x+1/2*c))/d","A"
560,1,248,174,2.693000," ","int((a+b*sin(d*x+c))^3/(e*cos(d*x+c))^(3/2),x)","-\frac{2 \left(-4 b^{3} \left(\sin^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+3 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a^{3}+18 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a \,b^{2}-6 a^{3} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-18 a \,b^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+4 b^{3} \left(\sin^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-9 a^{2} b \sin \left(\frac{d x}{2}+\frac{c}{2}\right)-4 b^{3} \sin \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 e \sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e +e}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) d}"," ",0,"-2/3/e/(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)/sin(1/2*d*x+1/2*c)*(-4*b^3*sin(1/2*d*x+1/2*c)^5+3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*a^3+18*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*a*b^2-6*a^3*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2-18*a*b^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2+4*b^3*sin(1/2*d*x+1/2*c)^3-9*a^2*b*sin(1/2*d*x+1/2*c)-4*b^3*sin(1/2*d*x+1/2*c))/d","A"
561,1,384,172,2.600000," ","int((a+b*sin(d*x+c))^3/(e*cos(d*x+c))^(5/2),x)","-\frac{2 \left(2 \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, a^{3} \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-12 \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, a \,b^{2} \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+12 b^{3} \left(\sin^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a^{3}+6 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a \,b^{2}+2 a^{3} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+6 a \,b^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-12 b^{3} \left(\sin^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+3 a^{2} b \sin \left(\frac{d x}{2}+\frac{c}{2}\right)+4 b^{3} \sin \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 \left(2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e +e}\, e^{2} d}"," ",0,"-2/3/(2*sin(1/2*d*x+1/2*c)^2-1)/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)/e^2*(2*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*a^3*sin(1/2*d*x+1/2*c)^2-12*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*a*b^2*sin(1/2*d*x+1/2*c)^2+12*b^3*sin(1/2*d*x+1/2*c)^5-(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*a^3+6*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*a*b^2+2*a^3*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2+6*a*b^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2-12*b^3*sin(1/2*d*x+1/2*c)^3+3*a^2*b*sin(1/2*d*x+1/2*c)+4*b^3*sin(1/2*d*x+1/2*c))/d","B"
562,1,618,195,5.149000," ","int((a+b*sin(d*x+c))^3/(e*cos(d*x+c))^(7/2),x)","-\frac{2 \left(12 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, a^{3} \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-24 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, a \,b^{2} \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-24 a^{3} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+48 a \,b^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-12 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, a^{3} \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+24 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, a \,b^{2} \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+24 a^{3} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-48 a \,b^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+20 b^{3} \left(\sin^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+3 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a^{3}-6 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a \,b^{2}-8 a^{3} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+6 a \,b^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-20 b^{3} \left(\sin^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-3 a^{2} b \sin \left(\frac{d x}{2}+\frac{c}{2}\right)+4 b^{3} \sin \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{5 \left(4 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-4 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e +e}\, e^{3} d}"," ",0,"-2/5/(4*sin(1/2*d*x+1/2*c)^4-4*sin(1/2*d*x+1/2*c)^2+1)/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)/e^3*(12*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*a^3*sin(1/2*d*x+1/2*c)^4-24*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*a*b^2*sin(1/2*d*x+1/2*c)^4-24*a^3*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6+48*a*b^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6-12*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*a^3*sin(1/2*d*x+1/2*c)^2+24*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*a*b^2*sin(1/2*d*x+1/2*c)^2+24*a^3*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^4-48*a*b^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^4+20*b^3*sin(1/2*d*x+1/2*c)^5+3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*a^3-6*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*a*b^2-8*a^3*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2+6*a*b^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2-20*b^3*sin(1/2*d*x+1/2*c)^3-3*a^2*b*sin(1/2*d*x+1/2*c)+4*b^3*sin(1/2*d*x+1/2*c))/d","B"
563,1,750,196,5.731000," ","int((a+b*sin(d*x+c))^3/(e*cos(d*x+c))^(9/2),x)","-\frac{2 \left(40 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, a^{3} \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-48 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, a \,b^{2} \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-60 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, a^{3} \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+72 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, a \,b^{2} \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+40 a^{3} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-48 a \,b^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+30 \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, a^{3} \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-36 \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, a \,b^{2} \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-40 a^{3} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+48 a \,b^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-28 b^{3} \left(\sin^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-5 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a^{3}+6 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a \,b^{2}+16 a^{3} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+6 a \,b^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+28 b^{3} \left(\sin^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+9 a^{2} b \sin \left(\frac{d x}{2}+\frac{c}{2}\right)-4 b^{3} \sin \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{21 \left(8 \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-12 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+6 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e +e}\, e^{4} d}"," ",0,"-2/21/(8*sin(1/2*d*x+1/2*c)^6-12*sin(1/2*d*x+1/2*c)^4+6*sin(1/2*d*x+1/2*c)^2-1)/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)/e^4*(40*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*a^3*sin(1/2*d*x+1/2*c)^6-48*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*a*b^2*sin(1/2*d*x+1/2*c)^6-60*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*a^3*sin(1/2*d*x+1/2*c)^4+72*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*a*b^2*sin(1/2*d*x+1/2*c)^4+40*a^3*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6-48*a*b^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6+30*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*a^3*sin(1/2*d*x+1/2*c)^2-36*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*a*b^2*sin(1/2*d*x+1/2*c)^2-40*a^3*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^4+48*a*b^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^4-28*b^3*sin(1/2*d*x+1/2*c)^5-5*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*a^3+6*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*a*b^2+16*a^3*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2+6*a*b^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2+28*b^3*sin(1/2*d*x+1/2*c)^3+9*a^2*b*sin(1/2*d*x+1/2*c)-4*b^3*sin(1/2*d*x+1/2*c))/d","B"
564,1,863,301,3.413000," ","int((e*cos(d*x+c))^(7/2)*(a+b*sin(d*x+c))^4,x)","-\frac{2 e^{4} \left(-6160 a \,b^{3} \left(\sin^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-200200 a^{3} b \left(\sin^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-6209280 a \,b^{3} \left(\sin^{13}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+8673280 a \,b^{3} \left(\sin^{11}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1572480 a^{2} b^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{12}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+3931200 a^{2} b^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{10}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-3818880 a^{2} b^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1797120 a^{2} b^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-360360 a^{2} b^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+11700 a^{2} b^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+10725 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a^{4}+780 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) b^{4}+2279200 a \,b^{3} \left(\sin^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1601600 a^{3} b \left(\sin^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-144456 b^{4} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-154440 a^{4} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-363440 a \,b^{3} \left(\sin^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+800800 a^{3} b \left(\sin^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1601600 a^{3} b \left(\sin^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+3739008 b^{4} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{12}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+946608 b^{4} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+102960 a^{4} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+11700 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a^{2} b^{2}-6160000 a \,b^{3} \left(\sin^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+20020 a^{3} b \sin \left(\frac{d x}{2}+\frac{c}{2}\right)+6160 a \,b^{3} \sin \left(\frac{d x}{2}+\frac{c}{2}\right)-34320 a^{4} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+120120 a^{4} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+780 b^{4} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-640640 a^{3} b \left(\sin^{11}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1774080 a \,b^{3} \left(\sin^{15}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-2620800 b^{4} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{10}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+768768 b^{4} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{16}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-2690688 b^{4} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{14}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}{45045 \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e +e}\, d}"," ",0,"-2/45045/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)*e^4*(3739008*b^4*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^12-2620800*b^4*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^10+102960*a^4*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^8+946608*b^4*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^8-154440*a^4*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6-144456*b^4*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6+120120*a^4*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^4-34320*a^4*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2+780*b^4*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2-2690688*b^4*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^14+768768*b^4*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^16+8673280*a*b^3*sin(1/2*d*x+1/2*c)^11-6209280*a*b^3*sin(1/2*d*x+1/2*c)^13+1774080*a*b^3*sin(1/2*d*x+1/2*c)^15-640640*a^3*b*sin(1/2*d*x+1/2*c)^11+1601600*a^3*b*sin(1/2*d*x+1/2*c)^9-6160000*a*b^3*sin(1/2*d*x+1/2*c)^9-1601600*a^3*b*sin(1/2*d*x+1/2*c)^7+2279200*a*b^3*sin(1/2*d*x+1/2*c)^7+800800*a^3*b*sin(1/2*d*x+1/2*c)^5-363440*a*b^3*sin(1/2*d*x+1/2*c)^5-200200*a^3*b*sin(1/2*d*x+1/2*c)^3-6160*a*b^3*sin(1/2*d*x+1/2*c)^3+20020*a^3*b*sin(1/2*d*x+1/2*c)+6160*a*b^3*sin(1/2*d*x+1/2*c)+11700*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*a^2*b^2-1572480*a^2*b^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^12+3931200*a^2*b^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^10-3818880*a^2*b^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^8+1797120*a^2*b^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6-360360*a^2*b^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^4+11700*a^2*b^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2+10725*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*a^4+780*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*b^4)/d","B"
565,1,776,258,2.999000," ","int((e*cos(d*x+c))^(5/2)*(a+b*sin(d*x+c))^4,x)","\frac{2 e^{3} \left(3120 a \,b^{3} \left(\sin^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+68640 a^{3} b \left(\sin^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+349440 a \,b^{3} \left(\sin^{13}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1048320 a \,b^{3} \left(\sin^{11}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-320320 a^{2} b^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{10}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+640640 a^{2} b^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-448448 a^{2} b^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+128128 a^{2} b^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-12012 a^{2} b^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-599040 a \,b^{3} \left(\sin^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+274560 a^{3} b \left(\sin^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+48664 b^{4} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+24024 a^{4} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+121680 a \,b^{3} \left(\sin^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-205920 a^{3} b \left(\sin^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-137280 a^{3} b \left(\sin^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-443520 b^{4} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{12}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-246400 b^{4} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1173120 a \,b^{3} \left(\sin^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-8580 a^{3} b \sin \left(\frac{d x}{2}+\frac{c}{2}\right)-3120 a \,b^{3} \sin \left(\frac{d x}{2}+\frac{c}{2}\right)+6006 a^{4} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-24024 a^{4} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-924 b^{4} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+9009 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a^{4}+924 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) b^{4}+492800 b^{4} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{10}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+147840 b^{4} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{14}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+616 b^{4} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+12012 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a^{2} b^{2}\right)}{15015 \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e +e}\, d}"," ",0,"2/15015/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)*e^3*(-443520*b^4*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^12+12012*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*a^2*b^2+9009*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*a^4+924*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*b^4+492800*b^4*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^10-246400*b^4*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^8+24024*a^4*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6+48664*b^4*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6-24024*a^4*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^4+6006*a^4*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2-924*b^4*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2+147840*b^4*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^14-1048320*a*b^3*sin(1/2*d*x+1/2*c)^11+349440*a*b^3*sin(1/2*d*x+1/2*c)^13-137280*a^3*b*sin(1/2*d*x+1/2*c)^9+1173120*a*b^3*sin(1/2*d*x+1/2*c)^9+274560*a^3*b*sin(1/2*d*x+1/2*c)^7-599040*a*b^3*sin(1/2*d*x+1/2*c)^7-205920*a^3*b*sin(1/2*d*x+1/2*c)^5+121680*a*b^3*sin(1/2*d*x+1/2*c)^5+68640*a^3*b*sin(1/2*d*x+1/2*c)^3+3120*a*b^3*sin(1/2*d*x+1/2*c)^3-8580*a^3*b*sin(1/2*d*x+1/2*c)-3120*a*b^3*sin(1/2*d*x+1/2*c)+616*b^4*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^4-320320*a^2*b^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^10+640640*a^2*b^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^8-448448*a^2*b^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6+128128*a^2*b^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^4-12012*a^2*b^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2)/d","B"
566,1,639,258,2.756000," ","int((e*cos(d*x+c))^(3/2)*(a+b*sin(d*x+c))^4,x)","-\frac{2 e^{2} \left(20160 b^{4} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{12}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+49280 a \,b^{3} \left(\sin^{11}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-50400 b^{4} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{10}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-47520 a^{2} b^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-123200 a \,b^{3} \left(\sin^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+41040 b^{4} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-22176 a^{3} b \left(\sin^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+71280 a^{2} b^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+101024 a \,b^{3} \left(\sin^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-11160 b^{4} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+4620 a^{4} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+33264 a^{3} b \left(\sin^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-27720 a^{2} b^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-28336 a \,b^{3} \left(\sin^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1155 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a^{4}+1980 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a^{2} b^{2}+180 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) b^{4}-2310 a^{4} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-16632 a^{3} b \left(\sin^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1980 a^{2} b^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1232 a \,b^{3} \left(\sin^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+180 b^{4} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+2772 a^{3} b \sin \left(\frac{d x}{2}+\frac{c}{2}\right)+1232 a \,b^{3} \sin \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3465 \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e +e}\, d}"," ",0,"-2/3465/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)*e^2*(20160*b^4*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^12+49280*a*b^3*sin(1/2*d*x+1/2*c)^11-50400*b^4*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^10-47520*a^2*b^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^8-123200*a*b^3*sin(1/2*d*x+1/2*c)^9+41040*b^4*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^8-22176*a^3*b*sin(1/2*d*x+1/2*c)^7+71280*a^2*b^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6+101024*a*b^3*sin(1/2*d*x+1/2*c)^7-11160*b^4*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6+4620*a^4*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^4+33264*a^3*b*sin(1/2*d*x+1/2*c)^5-27720*a^2*b^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^4-28336*a*b^3*sin(1/2*d*x+1/2*c)^5+1155*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*a^4+1980*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*a^2*b^2+180*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*b^4-2310*a^4*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2-16632*a^3*b*sin(1/2*d*x+1/2*c)^3+1980*a^2*b^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2-1232*a*b^3*sin(1/2*d*x+1/2*c)^3+180*b^4*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2+2772*a^3*b*sin(1/2*d*x+1/2*c)+1232*a*b^3*sin(1/2*d*x+1/2*c))/d","B"
567,1,525,214,2.593000," ","int((a+b*sin(d*x+c))^4*(e*cos(d*x+c))^(1/2),x)","\frac{2 e \left(1120 b^{4} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{10}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+2880 a \,b^{3} \left(\sin^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-2240 b^{4} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-3024 a^{2} b^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-5760 a \,b^{3} \left(\sin^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1064 b^{4} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1680 a^{3} b \left(\sin^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+3024 a^{2} b^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+2640 a \,b^{3} \left(\sin^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+56 b^{4} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+315 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a^{4}+756 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a^{2} b^{2}+84 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) b^{4}+1680 a^{3} b \left(\sin^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-756 a^{2} b^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+240 a \,b^{3} \left(\sin^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-84 b^{4} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-420 a^{3} b \sin \left(\frac{d x}{2}+\frac{c}{2}\right)-240 a \,b^{3} \sin \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{315 \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e +e}\, d}"," ",0,"2/315/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)*e*(1120*b^4*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^10+2880*a*b^3*sin(1/2*d*x+1/2*c)^9-2240*b^4*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^8-3024*a^2*b^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6-5760*a*b^3*sin(1/2*d*x+1/2*c)^7+1064*b^4*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6-1680*a^3*b*sin(1/2*d*x+1/2*c)^5+3024*a^2*b^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^4+2640*a*b^3*sin(1/2*d*x+1/2*c)^5+56*b^4*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^4+315*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*a^4+756*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*a^2*b^2+84*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*b^4+1680*a^3*b*sin(1/2*d*x+1/2*c)^3-756*a^2*b^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2+240*a*b^3*sin(1/2*d*x+1/2*c)^3-84*b^4*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2-420*a^3*b*sin(1/2*d*x+1/2*c)-240*a*b^3*sin(1/2*d*x+1/2*c))/d","B"
568,1,412,214,2.022000," ","int((a+b*sin(d*x+c))^4/(e*cos(d*x+c))^(1/2),x)","-\frac{2 \left(80 b^{4} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+224 a \,b^{3} \left(\sin^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-120 b^{4} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-280 a^{2} b^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-336 a \,b^{3} \left(\sin^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+35 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a^{4}+140 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a^{2} b^{2}+20 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) b^{4}-280 a^{3} b \left(\sin^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+140 a^{2} b^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-112 a \,b^{3} \left(\sin^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+20 b^{4} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+140 a^{3} b \sin \left(\frac{d x}{2}+\frac{c}{2}\right)+112 a \,b^{3} \sin \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{35 \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e +e}\, d}"," ",0,"-2/35/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)*(80*b^4*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^8+224*a*b^3*sin(1/2*d*x+1/2*c)^7-120*b^4*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6-280*a^2*b^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^4-336*a*b^3*sin(1/2*d*x+1/2*c)^5+35*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*a^4+140*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*a^2*b^2+20*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*b^4-280*a^3*b*sin(1/2*d*x+1/2*c)^3+140*a^2*b^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2-112*a*b^3*sin(1/2*d*x+1/2*c)^3+20*b^4*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2+140*a^3*b*sin(1/2*d*x+1/2*c)+112*a*b^3*sin(1/2*d*x+1/2*c))/d","A"
569,1,378,226,3.015000," ","int((a+b*sin(d*x+c))^4/(e*cos(d*x+c))^(3/2),x)","-\frac{2 \left(-24 b^{4} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-80 a \,b^{3} \left(\sin^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+24 b^{4} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+15 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a^{4}+180 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a^{2} b^{2}+36 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) b^{4}-30 a^{4} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-180 a^{2} b^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+80 a \,b^{3} \left(\sin^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-36 b^{4} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-60 a^{3} b \sin \left(\frac{d x}{2}+\frac{c}{2}\right)-80 a \,b^{3} \sin \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{15 e \sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e +e}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) d}"," ",0,"-2/15/e/(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)/sin(1/2*d*x+1/2*c)*(-24*b^4*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6-80*a*b^3*sin(1/2*d*x+1/2*c)^5+24*b^4*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^4+15*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*a^4+180*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*a^2*b^2+36*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*b^4-30*a^4*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2-180*a^2*b^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2+80*a*b^3*sin(1/2*d*x+1/2*c)^3-36*b^4*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2-60*a^3*b*sin(1/2*d*x+1/2*c)-80*a*b^3*sin(1/2*d*x+1/2*c))/d","A"
570,1,575,220,2.661000," ","int((a+b*sin(d*x+c))^4/(e*cos(d*x+c))^(5/2),x)","-\frac{2 \left(8 b^{4} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+2 \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, a^{4} \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-24 \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, a^{2} b^{2} \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-8 \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, b^{4} \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+48 a \,b^{3} \left(\sin^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-8 b^{4} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a^{4}+12 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a^{2} b^{2}+4 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) b^{4}+2 a^{4} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+12 a^{2} b^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-48 a \,b^{3} \left(\sin^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+4 b^{4} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+4 a^{3} b \sin \left(\frac{d x}{2}+\frac{c}{2}\right)+16 a \,b^{3} \sin \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 \left(2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e +e}\, e^{2} d}"," ",0,"-2/3/(2*sin(1/2*d*x+1/2*c)^2-1)/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)/e^2*(8*b^4*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6+2*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(sin(1/2*d*x+1/2*c)^2)^(1/2)*a^4*sin(1/2*d*x+1/2*c)^2-24*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(sin(1/2*d*x+1/2*c)^2)^(1/2)*a^2*b^2*sin(1/2*d*x+1/2*c)^2-8*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(sin(1/2*d*x+1/2*c)^2)^(1/2)*b^4*sin(1/2*d*x+1/2*c)^2+48*a*b^3*sin(1/2*d*x+1/2*c)^5-8*b^4*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^4-(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*a^4+12*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*a^2*b^2+4*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*b^4+2*a^4*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2+12*a^2*b^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2-48*a*b^3*sin(1/2*d*x+1/2*c)^3+4*b^4*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2+4*a^3*b*sin(1/2*d*x+1/2*c)+16*a*b^3*sin(1/2*d*x+1/2*c))/d","B"
571,1,874,241,5.958000," ","int((a+b*sin(d*x+c))^4/(e*cos(d*x+c))^(7/2),x)","-\frac{2 \left(12 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, a^{4} \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-48 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, a^{2} b^{2} \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-48 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, b^{4} \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-24 a^{4} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+96 a^{2} b^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+56 b^{4} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-12 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, a^{4} \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+48 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, a^{2} b^{2} \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+48 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, b^{4} \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+24 a^{4} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-96 a^{2} b^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+80 a \,b^{3} \left(\sin^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-56 b^{4} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+3 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a^{4}-12 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a^{2} b^{2}-12 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) b^{4}-8 a^{4} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+12 a^{2} b^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-80 a \,b^{3} \left(\sin^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+12 b^{4} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-4 a^{3} b \sin \left(\frac{d x}{2}+\frac{c}{2}\right)+16 a \,b^{3} \sin \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{5 \left(4 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-4 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e +e}\, e^{3} d}"," ",0,"-2/5/(4*sin(1/2*d*x+1/2*c)^4-4*sin(1/2*d*x+1/2*c)^2+1)/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)/e^3*(12*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*a^4*sin(1/2*d*x+1/2*c)^4-48*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*a^2*b^2*sin(1/2*d*x+1/2*c)^4-48*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*b^4*sin(1/2*d*x+1/2*c)^4-24*a^4*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6+96*a^2*b^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6+56*b^4*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6-12*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*a^4*sin(1/2*d*x+1/2*c)^2+48*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*a^2*b^2*sin(1/2*d*x+1/2*c)^2+48*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*b^4*sin(1/2*d*x+1/2*c)^2+24*a^4*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^4-96*a^2*b^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^4+80*a*b^3*sin(1/2*d*x+1/2*c)^5-56*b^4*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^4+3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*a^4-12*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*a^2*b^2-12*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*b^4-8*a^4*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2+12*a^2*b^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2-80*a*b^3*sin(1/2*d*x+1/2*c)^3+12*b^4*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2-4*a^3*b*sin(1/2*d*x+1/2*c)+16*a*b^3*sin(1/2*d*x+1/2*c))/d","B"
572,1,1067,245,7.290000," ","int((a+b*sin(d*x+c))^4/(e*cos(d*x+c))^(9/2),x)","-\frac{2 \left(112 a \,b^{3} \left(\sin^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-96 a^{2} b^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+96 a^{2} b^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+12 a^{2} b^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-5 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a^{4}-12 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) b^{4}+72 \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, b^{4} \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-72 b^{4} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+40 a^{4} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-112 a \,b^{3} \left(\sin^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+12 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a^{2} b^{2}+12 a^{3} b \sin \left(\frac{d x}{2}+\frac{c}{2}\right)-16 a \,b^{3} \sin \left(\frac{d x}{2}+\frac{c}{2}\right)+16 a^{4} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-40 a^{4} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-12 b^{4} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+30 \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, a^{4} \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+72 b^{4} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-72 \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, a^{2} b^{2} \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+40 \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, a^{4} \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+96 \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, b^{4} \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-60 \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, a^{4} \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-144 \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, b^{4} \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+144 \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, a^{2} b^{2} \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-96 \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, a^{2} b^{2} \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}{21 \left(8 \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-12 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+6 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e +e}\, e^{4} d}"," ",0,"-2/21/(8*sin(1/2*d*x+1/2*c)^6-12*sin(1/2*d*x+1/2*c)^4+6*sin(1/2*d*x+1/2*c)^2-1)/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)/e^4*(30*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(sin(1/2*d*x+1/2*c)^2)^(1/2)*a^4*sin(1/2*d*x+1/2*c)^2+72*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(sin(1/2*d*x+1/2*c)^2)^(1/2)*b^4*sin(1/2*d*x+1/2*c)^2+144*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(sin(1/2*d*x+1/2*c)^2)^(1/2)*a^2*b^2*sin(1/2*d*x+1/2*c)^4-96*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(sin(1/2*d*x+1/2*c)^2)^(1/2)*a^2*b^2*sin(1/2*d*x+1/2*c)^6+40*a^4*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6-72*b^4*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6-40*a^4*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^4+16*a^4*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2-12*b^4*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2-112*a*b^3*sin(1/2*d*x+1/2*c)^5+112*a*b^3*sin(1/2*d*x+1/2*c)^3+12*a^3*b*sin(1/2*d*x+1/2*c)-16*a*b^3*sin(1/2*d*x+1/2*c)+12*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*a^2*b^2+72*b^4*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^4-96*a^2*b^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6+96*a^2*b^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^4+12*a^2*b^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2-5*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*a^4-12*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*b^4-72*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(sin(1/2*d*x+1/2*c)^2)^(1/2)*a^2*b^2*sin(1/2*d*x+1/2*c)^2+40*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(sin(1/2*d*x+1/2*c)^2)^(1/2)*a^4*sin(1/2*d*x+1/2*c)^6+96*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(sin(1/2*d*x+1/2*c)^2)^(1/2)*b^4*sin(1/2*d*x+1/2*c)^6-60*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(sin(1/2*d*x+1/2*c)^2)^(1/2)*a^4*sin(1/2*d*x+1/2*c)^4-144*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(sin(1/2*d*x+1/2*c)^2)^(1/2)*b^4*sin(1/2*d*x+1/2*c)^4)/d","B"
573,1,1416,268,9.879000," ","int((a+b*sin(d*x+c))^4/(e*cos(d*x+c))^(11/2),x)","-\frac{2 \left(-144 a \,b^{3} \left(\sin^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1344 a^{4} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+504 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, a^{4} \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+288 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, b^{4} \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-168 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, a^{4} \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-96 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, b^{4} \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1152 a^{2} b^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{10}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-2304 a^{2} b^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1824 a^{2} b^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-672 a^{2} b^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+36 a^{2} b^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-672 a^{4} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{10}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-488 b^{4} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1064 a^{4} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+144 a \,b^{3} \left(\sin^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+768 b^{4} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-20 a^{3} b \sin \left(\frac{d x}{2}+\frac{c}{2}\right)+16 a \,b^{3} \sin \left(\frac{d x}{2}+\frac{c}{2}\right)-576 \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a^{2} b^{2} \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1152 \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a^{2} b^{2} \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-864 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, a^{2} b^{2} \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+288 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, a^{2} b^{2} \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-66 a^{4} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+392 a^{4} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-12 b^{4} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-384 \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) b^{4} \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+21 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a^{4}+12 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) b^{4}-384 b^{4} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{10}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+104 b^{4} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-36 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a^{2} b^{2}+336 \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a^{4} \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+192 \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) b^{4} \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-672 \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a^{4} \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}{45 \left(16 \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-32 \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+24 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-8 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e +e}\, e^{5} d}"," ",0,"-2/45/(16*sin(1/2*d*x+1/2*c)^8-32*sin(1/2*d*x+1/2*c)^6+24*sin(1/2*d*x+1/2*c)^4-8*sin(1/2*d*x+1/2*c)^2+1)/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)/e^5*(-36*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*a^2*b^2+21*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*a^4+12*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*b^4-384*b^4*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^10+1344*a^4*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^8+768*b^4*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^8-1064*a^4*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6-488*b^4*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6+392*a^4*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^4-66*a^4*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2-12*b^4*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2+144*a*b^3*sin(1/2*d*x+1/2*c)^5-144*a*b^3*sin(1/2*d*x+1/2*c)^3-20*a^3*b*sin(1/2*d*x+1/2*c)+16*a*b^3*sin(1/2*d*x+1/2*c)-672*a^4*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^10+104*b^4*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^4+1152*a^2*b^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^10-2304*a^2*b^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^8+1824*a^2*b^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6-672*a^2*b^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^4+36*a^2*b^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2-576*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*a^2*b^2*sin(1/2*d*x+1/2*c)^8+1152*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*a^2*b^2*sin(1/2*d*x+1/2*c)^6-384*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*b^4*sin(1/2*d*x+1/2*c)^6-864*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*a^2*b^2*sin(1/2*d*x+1/2*c)^4+288*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*a^2*b^2*sin(1/2*d*x+1/2*c)^2+504*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*a^4*sin(1/2*d*x+1/2*c)^4+288*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*b^4*sin(1/2*d*x+1/2*c)^4-168*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*a^4*sin(1/2*d*x+1/2*c)^2-96*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*b^4*sin(1/2*d*x+1/2*c)^2+336*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*a^4*sin(1/2*d*x+1/2*c)^8+192*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*b^4*sin(1/2*d*x+1/2*c)^8-672*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*a^4*sin(1/2*d*x+1/2*c)^6)/d","B"
574,1,3711,546,5.135000," ","int((e*cos(d*x+c))^(11/2)/(a+b*sin(d*x+c)),x)","\text{output too large to display}"," ",0,"-2/d*(e*(2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*e^6*a^5/sin(1/2*d*x+1/2*c)/(e*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)/b^6/(-2*sin(1/2*d*x+1/2*c)^4*e+sin(1/2*d*x+1/2*c)^2*e)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+14/3/d*(e*(2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*e^6*a^3/sin(1/2*d*x+1/2*c)/(e*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)/b^4/(-2*sin(1/2*d*x+1/2*c)^4*e+sin(1/2*d*x+1/2*c)^2*e)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-22/7/d*(e*(2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*e^6*a/sin(1/2*d*x+1/2*c)/(e*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)/b^2/(-2*sin(1/2*d*x+1/2*c)^4*e+sin(1/2*d*x+1/2*c)^2*e)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-6/d*e^5/b^3*(e*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)*a^2-2/d*e^7/b^5*sum((_R^4+_R^2*e)/(_R^7*b^2-3*_R^5*b^2*e+8*_R^3*a^2*e^2-5*_R^3*b^2*e^2-_R*b^2*e^3)*ln((-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)-e^(1/2)*cos(1/2*d*x+1/2*c)*2^(1/2)-_R),_R=RootOf(b^2*_Z^8-4*b^2*e*_Z^6+(16*a^2*e^2-10*b^2*e^2)*_Z^4-4*b^2*e^3*_Z^2+b^2*e^4))*a^6+6/d*e^7/b^3*sum((_R^4+_R^2*e)/(_R^7*b^2-3*_R^5*b^2*e+8*_R^3*a^2*e^2-5*_R^3*b^2*e^2-_R*b^2*e^3)*ln((-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)-e^(1/2)*cos(1/2*d*x+1/2*c)*2^(1/2)-_R),_R=RootOf(b^2*_Z^8-4*b^2*e*_Z^6+(16*a^2*e^2-10*b^2*e^2)*_Z^4-4*b^2*e^3*_Z^2+b^2*e^4))*a^4-6/d*e^7/b*sum((_R^4+_R^2*e)/(_R^7*b^2-3*_R^5*b^2*e+8*_R^3*a^2*e^2-5*_R^3*b^2*e^2-_R*b^2*e^3)*ln((-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)-e^(1/2)*cos(1/2*d*x+1/2*c)*2^(1/2)-_R),_R=RootOf(b^2*_Z^8-4*b^2*e*_Z^6+(16*a^2*e^2-10*b^2*e^2)*_Z^4-4*b^2*e^3*_Z^2+b^2*e^4))*a^2+32/9/d*e^5/b*cos(1/2*d*x+1/2*c)^8*(2*cos(1/2*d*x+1/2*c)^2*e-e)^(1/2)-64/9/d*e^5/b*cos(1/2*d*x+1/2*c)^6*(2*cos(1/2*d*x+1/2*c)^2*e-e)^(1/2)+104/15/d*e^5/b*cos(1/2*d*x+1/2*c)^4*(2*cos(1/2*d*x+1/2*c)^2*e-e)^(1/2)-152/45/d*e^5/b*cos(1/2*d*x+1/2*c)^2*(2*cos(1/2*d*x+1/2*c)^2*e-e)^(1/2)+8/5/d*e^5/b^3*(2*cos(1/2*d*x+1/2*c)^2*e-e)^(1/2)*a^2+2/d*e^5/b^5*(e*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)*a^4+1/8/d*(e*(2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*e^6*a^7/sin(1/2*d*x+1/2*c)/(e*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)/b^8*sum(1/_alpha/(2*_alpha^2-1)*(2^(1/2)/(e*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)*arctanh(1/2*e*(4*_alpha^2-3)/(4*a^2-3*b^2)*(4*cos(1/2*d*x+1/2*c)^2*a^2-3*b^2*cos(1/2*d*x+1/2*c)^2+b^2*_alpha^2-3*a^2+2*b^2)*2^(1/2)/(e*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)/(-e*(2*sin(1/2*d*x+1/2*c)^4-sin(1/2*d*x+1/2*c)^2))^(1/2))+8*b^2/a^2*_alpha*(_alpha^2-1)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-sin(1/2*d*x+1/2*c)^2*e*(2*sin(1/2*d*x+1/2*c)^2-1))^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),-4*b^2/a^2*(_alpha^2-1),2^(1/2))),_alpha=RootOf(4*_Z^4*b^2-4*_Z^2*b^2+a^2))-3/8/d*(e*(2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*e^6*a^5/sin(1/2*d*x+1/2*c)/(e*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)/b^6*sum(1/_alpha/(2*_alpha^2-1)*(2^(1/2)/(e*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)*arctanh(1/2*e*(4*_alpha^2-3)/(4*a^2-3*b^2)*(4*cos(1/2*d*x+1/2*c)^2*a^2-3*b^2*cos(1/2*d*x+1/2*c)^2+b^2*_alpha^2-3*a^2+2*b^2)*2^(1/2)/(e*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)/(-e*(2*sin(1/2*d*x+1/2*c)^4-sin(1/2*d*x+1/2*c)^2))^(1/2))+8*b^2/a^2*_alpha*(_alpha^2-1)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-sin(1/2*d*x+1/2*c)^2*e*(2*sin(1/2*d*x+1/2*c)^2-1))^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),-4*b^2/a^2*(_alpha^2-1),2^(1/2))),_alpha=RootOf(4*_Z^4*b^2-4*_Z^2*b^2+a^2))+3/8/d*(e*(2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*e^6*a^3/sin(1/2*d*x+1/2*c)/(e*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)/b^4*sum(1/_alpha/(2*_alpha^2-1)*(2^(1/2)/(e*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)*arctanh(1/2*e*(4*_alpha^2-3)/(4*a^2-3*b^2)*(4*cos(1/2*d*x+1/2*c)^2*a^2-3*b^2*cos(1/2*d*x+1/2*c)^2+b^2*_alpha^2-3*a^2+2*b^2)*2^(1/2)/(e*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)/(-e*(2*sin(1/2*d*x+1/2*c)^4-sin(1/2*d*x+1/2*c)^2))^(1/2))+8*b^2/a^2*_alpha*(_alpha^2-1)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-sin(1/2*d*x+1/2*c)^2*e*(2*sin(1/2*d*x+1/2*c)^2-1))^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),-4*b^2/a^2*(_alpha^2-1),2^(1/2))),_alpha=RootOf(4*_Z^4*b^2-4*_Z^2*b^2+a^2))-1/8/d*(e*(2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*e^6*a/sin(1/2*d*x+1/2*c)/(e*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)/b^2*sum(1/_alpha/(2*_alpha^2-1)*(2^(1/2)/(e*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)*arctanh(1/2*e*(4*_alpha^2-3)/(4*a^2-3*b^2)*(4*cos(1/2*d*x+1/2*c)^2*a^2-3*b^2*cos(1/2*d*x+1/2*c)^2+b^2*_alpha^2-3*a^2+2*b^2)*2^(1/2)/(e*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)/(-e*(2*sin(1/2*d*x+1/2*c)^4-sin(1/2*d*x+1/2*c)^2))^(1/2))+8*b^2/a^2*_alpha*(_alpha^2-1)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-sin(1/2*d*x+1/2*c)^2*e*(2*sin(1/2*d*x+1/2*c)^2-1))^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),-4*b^2/a^2*(_alpha^2-1),2^(1/2))),_alpha=RootOf(4*_Z^4*b^2-4*_Z^2*b^2+a^2))-152/45/d*e^5/b*(2*cos(1/2*d*x+1/2*c)^2*e-e)^(1/2)+6/d*e^5/b*(e*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)+2/d*e^7*b*sum((_R^4+_R^2*e)/(_R^7*b^2-3*_R^5*b^2*e+8*_R^3*a^2*e^2-5*_R^3*b^2*e^2-_R*b^2*e^3)*ln((-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)-e^(1/2)*cos(1/2*d*x+1/2*c)*2^(1/2)-_R),_R=RootOf(b^2*_Z^8-4*b^2*e*_Z^6+(16*a^2*e^2-10*b^2*e^2)*_Z^4-4*b^2*e^3*_Z^2+b^2*e^4))+8/5/d*e^5/b^3*cos(1/2*d*x+1/2*c)^2*(2*cos(1/2*d*x+1/2*c)^2*e-e)^(1/2)*a^2-8/5/d*e^5/b^3*cos(1/2*d*x+1/2*c)^4*(2*cos(1/2*d*x+1/2*c)^2*e-e)^(1/2)*a^2+48/7/d*(e*(2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*e^6*a*sin(1/2*d*x+1/2*c)^5/(e*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)/b^2/(-2*sin(1/2*d*x+1/2*c)^4*e+sin(1/2*d*x+1/2*c)^2*e)^(1/2)*cos(1/2*d*x+1/2*c)-32/7/d*(e*(2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*e^6*a*sin(1/2*d*x+1/2*c)^7/(e*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)/b^2/(-2*sin(1/2*d*x+1/2*c)^4*e+sin(1/2*d*x+1/2*c)^2*e)^(1/2)*cos(1/2*d*x+1/2*c)+8/3/d*(e*(2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*e^6*a^3*sin(1/2*d*x+1/2*c)^3/(e*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)/b^4/(-2*sin(1/2*d*x+1/2*c)^4*e+sin(1/2*d*x+1/2*c)^2*e)^(1/2)*cos(1/2*d*x+1/2*c)-8/d*(e*(2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*e^6*a*sin(1/2*d*x+1/2*c)^3/(e*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)/b^2/(-2*sin(1/2*d*x+1/2*c)^4*e+sin(1/2*d*x+1/2*c)^2*e)^(1/2)*cos(1/2*d*x+1/2*c)-4/3/d*(e*(2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*e^6*a^3*sin(1/2*d*x+1/2*c)/(e*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)/b^4/(-2*sin(1/2*d*x+1/2*c)^4*e+sin(1/2*d*x+1/2*c)^2*e)^(1/2)*cos(1/2*d*x+1/2*c)+20/7/d*(e*(2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*e^6*a*sin(1/2*d*x+1/2*c)/(e*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)/b^2/(-2*sin(1/2*d*x+1/2*c)^4*e+sin(1/2*d*x+1/2*c)^2*e)^(1/2)*cos(1/2*d*x+1/2*c)","C"
575,1,2126,465,3.569000," ","int((e*cos(d*x+c))^(9/2)/(a+b*sin(d*x+c)),x)","\text{Expression too large to display}"," ",0,"16/7/d*e^4/b*cos(1/2*d*x+1/2*c)^6*(2*cos(1/2*d*x+1/2*c)^2*e-e)^(1/2)-24/7/d*e^4/b*cos(1/2*d*x+1/2*c)^4*(2*cos(1/2*d*x+1/2*c)^2*e-e)^(1/2)+64/21/d*e^4/b*cos(1/2*d*x+1/2*c)^2*(2*cos(1/2*d*x+1/2*c)^2*e-e)^(1/2)+64/21/d*e^4/b*(2*cos(1/2*d*x+1/2*c)^2*e-e)^(1/2)-4/3/d*e^4/b^3*cos(1/2*d*x+1/2*c)^2*(2*cos(1/2*d*x+1/2*c)^2*e-e)^(1/2)*a^2-4/3/d*e^4/b^3*(2*cos(1/2*d*x+1/2*c)^2*e-e)^(1/2)*a^2+2/d*e^4/b^3*(e*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)*a^2-4/d*e^4/b*(e*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)+1/2/d*e^5/b^3*sum((_R^6-_R^4*e-_R^2*e^2+e^3)/(_R^7*b^2-3*_R^5*b^2*e+8*_R^3*a^2*e^2-5*_R^3*b^2*e^2-_R*b^2*e^3)*ln((-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)-e^(1/2)*cos(1/2*d*x+1/2*c)*2^(1/2)-_R),_R=RootOf(b^2*_Z^8-4*b^2*e*_Z^6+(16*a^2*e^2-10*b^2*e^2)*_Z^4-4*b^2*e^3*_Z^2+b^2*e^4))*a^4-1/d*e^5/b*sum((_R^6-_R^4*e-_R^2*e^2+e^3)/(_R^7*b^2-3*_R^5*b^2*e+8*_R^3*a^2*e^2-5*_R^3*b^2*e^2-_R*b^2*e^3)*ln((-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)-e^(1/2)*cos(1/2*d*x+1/2*c)*2^(1/2)-_R),_R=RootOf(b^2*_Z^8-4*b^2*e*_Z^6+(16*a^2*e^2-10*b^2*e^2)*_Z^4-4*b^2*e^3*_Z^2+b^2*e^4))*a^2+1/2/d*e^5*b*sum((_R^6-_R^4*e-_R^2*e^2+e^3)/(_R^7*b^2-3*_R^5*b^2*e+8*_R^3*a^2*e^2-5*_R^3*b^2*e^2-_R*b^2*e^3)*ln((-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)-e^(1/2)*cos(1/2*d*x+1/2*c)*2^(1/2)-_R),_R=RootOf(b^2*_Z^8-4*b^2*e*_Z^6+(16*a^2*e^2-10*b^2*e^2)*_Z^4-4*b^2*e^3*_Z^2+b^2*e^4))-16/5/d*(e*(2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*e^5*a/b^2/(-e*(2*sin(1/2*d*x+1/2*c)^4-sin(1/2*d*x+1/2*c)^2))^(1/2)/sin(1/2*d*x+1/2*c)/(e*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)*cos(1/2*d*x+1/2*c)^7+32/5/d*(e*(2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*e^5*a/b^2/(-e*(2*sin(1/2*d*x+1/2*c)^4-sin(1/2*d*x+1/2*c)^2))^(1/2)/sin(1/2*d*x+1/2*c)/(e*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)*cos(1/2*d*x+1/2*c)^5-4/d*(e*(2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*e^5*a/b^2/(-e*(2*sin(1/2*d*x+1/2*c)^4-sin(1/2*d*x+1/2*c)^2))^(1/2)/sin(1/2*d*x+1/2*c)/(e*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)*cos(1/2*d*x+1/2*c)^3-2/d*(e*(2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*e^5*a^3/b^4/(-e*(2*sin(1/2*d*x+1/2*c)^4-sin(1/2*d*x+1/2*c)^2))^(1/2)/sin(1/2*d*x+1/2*c)/(e*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+16/5/d*(e*(2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*e^5*a/b^2/(-e*(2*sin(1/2*d*x+1/2*c)^4-sin(1/2*d*x+1/2*c)^2))^(1/2)/sin(1/2*d*x+1/2*c)/(e*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+4/5/d*(e*(2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*e^5*a/b^2/(-e*(2*sin(1/2*d*x+1/2*c)^4-sin(1/2*d*x+1/2*c)^2))^(1/2)/sin(1/2*d*x+1/2*c)/(e*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)*cos(1/2*d*x+1/2*c)-1/8/d*(e*(2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*e^5/a/b^6/sin(1/2*d*x+1/2*c)/(e*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)*sum((a^4-2*a^2*b^2+b^4)/_alpha*(8*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),-4*b^2/a^2*(_alpha^2-1),2^(1/2))*(e*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)*_alpha^3*b^2-8*b^2*_alpha*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),-4*b^2/a^2*(_alpha^2-1),2^(1/2))*(e*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)+a^2*2^(1/2)*arctanh(1/2*e*(4*_alpha^2-3)/(4*a^2-3*b^2)*(4*cos(1/2*d*x+1/2*c)^2*a^2-3*b^2*cos(1/2*d*x+1/2*c)^2+b^2*_alpha^2-3*a^2+2*b^2)*2^(1/2)/(e*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)/(-e*(2*sin(1/2*d*x+1/2*c)^4-sin(1/2*d*x+1/2*c)^2))^(1/2))*(-sin(1/2*d*x+1/2*c)^2*e*(2*sin(1/2*d*x+1/2*c)^2-1))^(1/2))/(e*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)/(-sin(1/2*d*x+1/2*c)^2*e*(2*sin(1/2*d*x+1/2*c)^2-1))^(1/2),_alpha=RootOf(4*_Z^4*b^2-4*_Z^2*b^2+a^2))","C"
576,1,2329,480,4.467000," ","int((e*cos(d*x+c))^(7/2)/(a+b*sin(d*x+c)),x)","\text{Expression too large to display}"," ",0,"8/5/d*e^3/b*cos(1/2*d*x+1/2*c)^4*(2*cos(1/2*d*x+1/2*c)^2*e-e)^(1/2)-8/5/d*e^3/b*cos(1/2*d*x+1/2*c)^2*(2*cos(1/2*d*x+1/2*c)^2*e-e)^(1/2)-8/5/d*e^3/b*(2*cos(1/2*d*x+1/2*c)^2*e-e)^(1/2)-2/d*e^3/b^3*(e*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)*a^2+4/d*e^3/b*(e*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)+2/d*e^5/b^3*sum((_R^4+_R^2*e)/(_R^7*b^2-3*_R^5*b^2*e+8*_R^3*a^2*e^2-5*_R^3*b^2*e^2-_R*b^2*e^3)*ln((-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)-e^(1/2)*cos(1/2*d*x+1/2*c)*2^(1/2)-_R),_R=RootOf(b^2*_Z^8-4*b^2*e*_Z^6+(16*a^2*e^2-10*b^2*e^2)*_Z^4-4*b^2*e^3*_Z^2+b^2*e^4))*a^4-4/d*e^5/b*sum((_R^4+_R^2*e)/(_R^7*b^2-3*_R^5*b^2*e+8*_R^3*a^2*e^2-5*_R^3*b^2*e^2-_R*b^2*e^3)*ln((-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)-e^(1/2)*cos(1/2*d*x+1/2*c)*2^(1/2)-_R),_R=RootOf(b^2*_Z^8-4*b^2*e*_Z^6+(16*a^2*e^2-10*b^2*e^2)*_Z^4-4*b^2*e^3*_Z^2+b^2*e^4))*a^2+2/d*e^5*b*sum((_R^4+_R^2*e)/(_R^7*b^2-3*_R^5*b^2*e+8*_R^3*a^2*e^2-5*_R^3*b^2*e^2-_R*b^2*e^3)*ln((-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)-e^(1/2)*cos(1/2*d*x+1/2*c)*2^(1/2)-_R),_R=RootOf(b^2*_Z^8-4*b^2*e*_Z^6+(16*a^2*e^2-10*b^2*e^2)*_Z^4-4*b^2*e^3*_Z^2+b^2*e^4))-8/3/d*(e*(2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*e^4*a*sin(1/2*d*x+1/2*c)^3/(e*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)/b^2/(-2*sin(1/2*d*x+1/2*c)^4*e+sin(1/2*d*x+1/2*c)^2*e)^(1/2)*cos(1/2*d*x+1/2*c)+4/3/d*(e*(2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*e^4*a*sin(1/2*d*x+1/2*c)/(e*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)/b^2/(-2*sin(1/2*d*x+1/2*c)^4*e+sin(1/2*d*x+1/2*c)^2*e)^(1/2)*cos(1/2*d*x+1/2*c)+2/d*(e*(2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*e^4*a^3/sin(1/2*d*x+1/2*c)/(e*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)/b^4/(-2*sin(1/2*d*x+1/2*c)^4*e+sin(1/2*d*x+1/2*c)^2*e)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-8/3/d*(e*(2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*e^4*a/sin(1/2*d*x+1/2*c)/(e*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)/b^2/(-2*sin(1/2*d*x+1/2*c)^4*e+sin(1/2*d*x+1/2*c)^2*e)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-1/8/d*(e*(2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*e^4*a^5/sin(1/2*d*x+1/2*c)/(e*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)/b^6*sum(1/_alpha/(2*_alpha^2-1)*(2^(1/2)/(e*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)*arctanh(1/2*e*(4*_alpha^2-3)/(4*a^2-3*b^2)*(4*cos(1/2*d*x+1/2*c)^2*a^2-3*b^2*cos(1/2*d*x+1/2*c)^2+b^2*_alpha^2-3*a^2+2*b^2)*2^(1/2)/(e*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)/(-e*(2*sin(1/2*d*x+1/2*c)^4-sin(1/2*d*x+1/2*c)^2))^(1/2))+8*b^2/a^2*_alpha*(_alpha^2-1)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-sin(1/2*d*x+1/2*c)^2*e*(2*sin(1/2*d*x+1/2*c)^2-1))^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),-4*b^2/a^2*(_alpha^2-1),2^(1/2))),_alpha=RootOf(4*_Z^4*b^2-4*_Z^2*b^2+a^2))+1/4/d*(e*(2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*e^4*a^3/sin(1/2*d*x+1/2*c)/(e*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)/b^4*sum(1/_alpha/(2*_alpha^2-1)*(2^(1/2)/(e*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)*arctanh(1/2*e*(4*_alpha^2-3)/(4*a^2-3*b^2)*(4*cos(1/2*d*x+1/2*c)^2*a^2-3*b^2*cos(1/2*d*x+1/2*c)^2+b^2*_alpha^2-3*a^2+2*b^2)*2^(1/2)/(e*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)/(-e*(2*sin(1/2*d*x+1/2*c)^4-sin(1/2*d*x+1/2*c)^2))^(1/2))+8*b^2/a^2*_alpha*(_alpha^2-1)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-sin(1/2*d*x+1/2*c)^2*e*(2*sin(1/2*d*x+1/2*c)^2-1))^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),-4*b^2/a^2*(_alpha^2-1),2^(1/2))),_alpha=RootOf(4*_Z^4*b^2-4*_Z^2*b^2+a^2))-1/8/d*(e*(2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*e^4*a/sin(1/2*d*x+1/2*c)/(e*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)/b^2*sum(1/_alpha/(2*_alpha^2-1)*(2^(1/2)/(e*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)*arctanh(1/2*e*(4*_alpha^2-3)/(4*a^2-3*b^2)*(4*cos(1/2*d*x+1/2*c)^2*a^2-3*b^2*cos(1/2*d*x+1/2*c)^2+b^2*_alpha^2-3*a^2+2*b^2)*2^(1/2)/(e*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)/(-e*(2*sin(1/2*d*x+1/2*c)^4-sin(1/2*d*x+1/2*c)^2))^(1/2))+8*b^2/a^2*_alpha*(_alpha^2-1)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-sin(1/2*d*x+1/2*c)^2*e*(2*sin(1/2*d*x+1/2*c)^2-1))^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),-4*b^2/a^2*(_alpha^2-1),2^(1/2))),_alpha=RootOf(4*_Z^4*b^2-4*_Z^2*b^2+a^2))","C"
577,1,1131,410,3.668000," ","int((e*cos(d*x+c))^(5/2)/(a+b*sin(d*x+c)),x)","\frac{4 e^{2} \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e -e}}{3 d b}+\frac{4 e^{2} \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e -e}}{3 d b}-\frac{2 e^{2} \sqrt{e \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}}{d b}-\frac{e^{3} \left(\munderset{\textit{\_R} =\RootOf \left(b^{2} \textit{\_Z}^{8}-4 b^{2} e \,\textit{\_Z}^{6}+\left(16 a^{2} e^{2}-10 b^{2} e^{2}\right) \textit{\_Z}^{4}-4 b^{2} e^{3} \textit{\_Z}^{2}+b^{2} e^{4}\right)}{\sum}\frac{\left(\textit{\_R}^{6}-\textit{\_R}^{4} e -\textit{\_R}^{2} e^{2}+e^{3}\right) \ln \left(\sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e +e}-\sqrt{e}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2}-\textit{\_R} \right)}{\textit{\_R}^{7} b^{2}-3 \textit{\_R}^{5} b^{2} e +8 \textit{\_R}^{3} a^{2} e^{2}-5 \textit{\_R}^{3} b^{2} e^{2}-\textit{\_R} \,b^{2} e^{3}}\right) a^{2}}{2 d b}+\frac{e^{3} b \left(\munderset{\textit{\_R} =\RootOf \left(b^{2} \textit{\_Z}^{8}-4 b^{2} e \,\textit{\_Z}^{6}+\left(16 a^{2} e^{2}-10 b^{2} e^{2}\right) \textit{\_Z}^{4}-4 b^{2} e^{3} \textit{\_Z}^{2}+b^{2} e^{4}\right)}{\sum}\frac{\left(\textit{\_R}^{6}-\textit{\_R}^{4} e -\textit{\_R}^{2} e^{2}+e^{3}\right) \ln \left(\sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e +e}-\sqrt{e}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2}-\textit{\_R} \right)}{\textit{\_R}^{7} b^{2}-3 \textit{\_R}^{5} b^{2} e +8 \textit{\_R}^{3} a^{2} e^{2}-5 \textit{\_R}^{3} b^{2} e^{2}-\textit{\_R} \,b^{2} e^{3}}\right)}{2 d}+\frac{2 \sqrt{e \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, e^{3} a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{d \,b^{2} \sqrt{-e \left(2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{e \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}}+\frac{\sqrt{e \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, e^{3} \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(4 b^{2} \textit{\_Z}^{4}-4 b^{2} \textit{\_Z}^{2}+a^{2}\right)}{\sum}\frac{\left(a^{2}-b^{2}\right) \left(8 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), -\frac{4 b^{2} \left(\underline{\hspace{1.25 ex}}\alpha^{2}-1\right)}{a^{2}}, \sqrt{2}\right) \sqrt{\frac{e \left(2 b^{2} \underline{\hspace{1.25 ex}}\alpha^{2}+a^{2}-2 b^{2}\right)}{b^{2}}}\, \underline{\hspace{1.25 ex}}\alpha^{3} b^{2}-8 b^{2} \underline{\hspace{1.25 ex}}\alpha  \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), -\frac{4 b^{2} \left(\underline{\hspace{1.25 ex}}\alpha^{2}-1\right)}{a^{2}}, \sqrt{2}\right) \sqrt{\frac{e \left(2 b^{2} \underline{\hspace{1.25 ex}}\alpha^{2}+a^{2}-2 b^{2}\right)}{b^{2}}}+a^{2} \sqrt{2}\, \arctanh \left(\frac{e \left(4 \underline{\hspace{1.25 ex}}\alpha^{2}-3\right) \left(4 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{2}-3 b^{2} \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+b^{2} \underline{\hspace{1.25 ex}}\alpha^{2}-3 a^{2}+2 b^{2}\right) \sqrt{2}}{2 \left(4 a^{2}-3 b^{2}\right) \sqrt{\frac{e \left(2 b^{2} \underline{\hspace{1.25 ex}}\alpha^{2}+a^{2}-2 b^{2}\right)}{b^{2}}}\, \sqrt{-e \left(2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}}\right) \sqrt{-\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e \left(2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}\right)}{\underline{\hspace{1.25 ex}}\alpha  \sqrt{\frac{e \left(2 b^{2} \underline{\hspace{1.25 ex}}\alpha^{2}+a^{2}-2 b^{2}\right)}{b^{2}}}\, \sqrt{-\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e \left(2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}}\right)}{8 d a \,b^{4} \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{e \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}}"," ",0,"4/3/d*e^2/b*cos(1/2*d*x+1/2*c)^2*(2*cos(1/2*d*x+1/2*c)^2*e-e)^(1/2)+4/3/d*e^2/b*(2*cos(1/2*d*x+1/2*c)^2*e-e)^(1/2)-2/d*e^2/b*(e*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)-1/2/d*e^3/b*sum((_R^6-_R^4*e-_R^2*e^2+e^3)/(_R^7*b^2-3*_R^5*b^2*e+8*_R^3*a^2*e^2-5*_R^3*b^2*e^2-_R*b^2*e^3)*ln((-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)-e^(1/2)*cos(1/2*d*x+1/2*c)*2^(1/2)-_R),_R=RootOf(b^2*_Z^8-4*b^2*e*_Z^6+(16*a^2*e^2-10*b^2*e^2)*_Z^4-4*b^2*e^3*_Z^2+b^2*e^4))*a^2+1/2/d*e^3*b*sum((_R^6-_R^4*e-_R^2*e^2+e^3)/(_R^7*b^2-3*_R^5*b^2*e+8*_R^3*a^2*e^2-5*_R^3*b^2*e^2-_R*b^2*e^3)*ln((-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)-e^(1/2)*cos(1/2*d*x+1/2*c)*2^(1/2)-_R),_R=RootOf(b^2*_Z^8-4*b^2*e*_Z^6+(16*a^2*e^2-10*b^2*e^2)*_Z^4-4*b^2*e^3*_Z^2+b^2*e^4))+2/d*(e*(2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*e^3*a/b^2/(-e*(2*sin(1/2*d*x+1/2*c)^4-sin(1/2*d*x+1/2*c)^2))^(1/2)/sin(1/2*d*x+1/2*c)/(e*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+1/8/d*(e*(2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*e^3/a/b^4/sin(1/2*d*x+1/2*c)/(e*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)*sum((a^2-b^2)/_alpha*(8*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),-4*b^2/a^2*(_alpha^2-1),2^(1/2))*(e*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)*_alpha^3*b^2-8*b^2*_alpha*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),-4*b^2/a^2*(_alpha^2-1),2^(1/2))*(e*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)+a^2*2^(1/2)*arctanh(1/2*e*(4*_alpha^2-3)/(4*a^2-3*b^2)*(4*cos(1/2*d*x+1/2*c)^2*a^2-3*b^2*cos(1/2*d*x+1/2*c)^2+b^2*_alpha^2-3*a^2+2*b^2)*2^(1/2)/(e*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)/(-e*(2*sin(1/2*d*x+1/2*c)^4-sin(1/2*d*x+1/2*c)^2))^(1/2))*(-sin(1/2*d*x+1/2*c)^2*e*(2*sin(1/2*d*x+1/2*c)^2-1))^(1/2))/(e*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)/(-sin(1/2*d*x+1/2*c)^2*e*(2*sin(1/2*d*x+1/2*c)^2-1))^(1/2),_alpha=RootOf(4*_Z^4*b^2-4*_Z^2*b^2+a^2))","C"
578,1,1266,425,3.233000," ","int((e*cos(d*x+c))^(3/2)/(a+b*sin(d*x+c)),x)","\frac{2 e \sqrt{e \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}}{d b}-\frac{2 e^{3} \left(\munderset{\textit{\_R} =\RootOf \left(b^{2} \textit{\_Z}^{8}-4 b^{2} e \,\textit{\_Z}^{6}+\left(16 a^{2} e^{2}-10 b^{2} e^{2}\right) \textit{\_Z}^{4}-4 b^{2} e^{3} \textit{\_Z}^{2}+b^{2} e^{4}\right)}{\sum}\frac{\left(\textit{\_R}^{4}+\textit{\_R}^{2} e \right) \ln \left(\sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e +e}-\sqrt{e}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2}-\textit{\_R} \right)}{\textit{\_R}^{7} b^{2}-3 \textit{\_R}^{5} b^{2} e +8 \textit{\_R}^{3} a^{2} e^{2}-5 \textit{\_R}^{3} b^{2} e^{2}-\textit{\_R} \,b^{2} e^{3}}\right) a^{2}}{d b}+\frac{2 e^{3} b \left(\munderset{\textit{\_R} =\RootOf \left(b^{2} \textit{\_Z}^{8}-4 b^{2} e \,\textit{\_Z}^{6}+\left(16 a^{2} e^{2}-10 b^{2} e^{2}\right) \textit{\_Z}^{4}-4 b^{2} e^{3} \textit{\_Z}^{2}+b^{2} e^{4}\right)}{\sum}\frac{\left(\textit{\_R}^{4}+\textit{\_R}^{2} e \right) \ln \left(\sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e +e}-\sqrt{e}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2}-\textit{\_R} \right)}{\textit{\_R}^{7} b^{2}-3 \textit{\_R}^{5} b^{2} e +8 \textit{\_R}^{3} a^{2} e^{2}-5 \textit{\_R}^{3} b^{2} e^{2}-\textit{\_R} \,b^{2} e^{3}}\right)}{d}-\frac{2 \sqrt{e \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, a \,e^{2} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{d \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{e \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}\, b^{2} \sqrt{-e \left(2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}}+\frac{\sqrt{e \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, a^{3} e^{2} \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(4 b^{2} \textit{\_Z}^{4}-4 b^{2} \textit{\_Z}^{2}+a^{2}\right)}{\sum}\frac{\frac{\sqrt{2}\, \arctanh \left(\frac{e \left(4 \underline{\hspace{1.25 ex}}\alpha^{2}-3\right) \left(4 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{2}-3 b^{2} \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+b^{2} \underline{\hspace{1.25 ex}}\alpha^{2}-3 a^{2}+2 b^{2}\right) \sqrt{2}}{2 \left(4 a^{2}-3 b^{2}\right) \sqrt{\frac{e \left(2 b^{2} \underline{\hspace{1.25 ex}}\alpha^{2}+a^{2}-2 b^{2}\right)}{b^{2}}}\, \sqrt{-e \left(2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}}\right)}{\sqrt{\frac{e \left(2 b^{2} \underline{\hspace{1.25 ex}}\alpha^{2}+a^{2}-2 b^{2}\right)}{b^{2}}}}+\frac{8 b^{2} \underline{\hspace{1.25 ex}}\alpha  \left(\underline{\hspace{1.25 ex}}\alpha^{2}-1\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), -\frac{4 b^{2} \left(\underline{\hspace{1.25 ex}}\alpha^{2}-1\right)}{a^{2}}, \sqrt{2}\right)}{a^{2} \sqrt{-\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e \left(2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}}}{\underline{\hspace{1.25 ex}}\alpha  \left(2 \underline{\hspace{1.25 ex}}\alpha^{2}-1\right)}\right)}{8 d \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{e \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}\, b^{4}}-\frac{\sqrt{e \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, a \,e^{2} \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(4 b^{2} \textit{\_Z}^{4}-4 b^{2} \textit{\_Z}^{2}+a^{2}\right)}{\sum}\frac{\frac{\sqrt{2}\, \arctanh \left(\frac{e \left(4 \underline{\hspace{1.25 ex}}\alpha^{2}-3\right) \left(4 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{2}-3 b^{2} \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+b^{2} \underline{\hspace{1.25 ex}}\alpha^{2}-3 a^{2}+2 b^{2}\right) \sqrt{2}}{2 \left(4 a^{2}-3 b^{2}\right) \sqrt{\frac{e \left(2 b^{2} \underline{\hspace{1.25 ex}}\alpha^{2}+a^{2}-2 b^{2}\right)}{b^{2}}}\, \sqrt{-e \left(2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}}\right)}{\sqrt{\frac{e \left(2 b^{2} \underline{\hspace{1.25 ex}}\alpha^{2}+a^{2}-2 b^{2}\right)}{b^{2}}}}+\frac{8 b^{2} \underline{\hspace{1.25 ex}}\alpha  \left(\underline{\hspace{1.25 ex}}\alpha^{2}-1\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), -\frac{4 b^{2} \left(\underline{\hspace{1.25 ex}}\alpha^{2}-1\right)}{a^{2}}, \sqrt{2}\right)}{a^{2} \sqrt{-\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e \left(2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}}}{\underline{\hspace{1.25 ex}}\alpha  \left(2 \underline{\hspace{1.25 ex}}\alpha^{2}-1\right)}\right)}{8 d \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{e \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}\, b^{2}}"," ",0,"2/d*e/b*(e*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)-2/d*e^3/b*sum((_R^4+_R^2*e)/(_R^7*b^2-3*_R^5*b^2*e+8*_R^3*a^2*e^2-5*_R^3*b^2*e^2-_R*b^2*e^3)*ln((-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)-e^(1/2)*cos(1/2*d*x+1/2*c)*2^(1/2)-_R),_R=RootOf(b^2*_Z^8-4*b^2*e*_Z^6+(16*a^2*e^2-10*b^2*e^2)*_Z^4-4*b^2*e^3*_Z^2+b^2*e^4))*a^2+2/d*e^3*b*sum((_R^4+_R^2*e)/(_R^7*b^2-3*_R^5*b^2*e+8*_R^3*a^2*e^2-5*_R^3*b^2*e^2-_R*b^2*e^3)*ln((-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)-e^(1/2)*cos(1/2*d*x+1/2*c)*2^(1/2)-_R),_R=RootOf(b^2*_Z^8-4*b^2*e*_Z^6+(16*a^2*e^2-10*b^2*e^2)*_Z^4-4*b^2*e^3*_Z^2+b^2*e^4))-2/d*(e*(2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*a*e^2/sin(1/2*d*x+1/2*c)/(e*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)/b^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-e*(2*sin(1/2*d*x+1/2*c)^4-sin(1/2*d*x+1/2*c)^2))^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+1/8/d*(e*(2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^3*e^2/sin(1/2*d*x+1/2*c)/(e*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)/b^4*sum(1/_alpha/(2*_alpha^2-1)*(2^(1/2)/(e*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)*arctanh(1/2*e*(4*_alpha^2-3)/(4*a^2-3*b^2)*(4*cos(1/2*d*x+1/2*c)^2*a^2-3*b^2*cos(1/2*d*x+1/2*c)^2+b^2*_alpha^2-3*a^2+2*b^2)*2^(1/2)/(e*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)/(-e*(2*sin(1/2*d*x+1/2*c)^4-sin(1/2*d*x+1/2*c)^2))^(1/2))+8*b^2/a^2*_alpha*(_alpha^2-1)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-sin(1/2*d*x+1/2*c)^2*e*(2*sin(1/2*d*x+1/2*c)^2-1))^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),-4*b^2/a^2*(_alpha^2-1),2^(1/2))),_alpha=RootOf(4*_Z^4*b^2-4*_Z^2*b^2+a^2))-1/8/d*(e*(2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*a*e^2/sin(1/2*d*x+1/2*c)/(e*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)/b^2*sum(1/_alpha/(2*_alpha^2-1)*(2^(1/2)/(e*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)*arctanh(1/2*e*(4*_alpha^2-3)/(4*a^2-3*b^2)*(4*cos(1/2*d*x+1/2*c)^2*a^2-3*b^2*cos(1/2*d*x+1/2*c)^2+b^2*_alpha^2-3*a^2+2*b^2)*2^(1/2)/(e*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)/(-e*(2*sin(1/2*d*x+1/2*c)^4-sin(1/2*d*x+1/2*c)^2))^(1/2))+8*b^2/a^2*_alpha*(_alpha^2-1)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-sin(1/2*d*x+1/2*c)^2*e*(2*sin(1/2*d*x+1/2*c)^2-1))^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),-4*b^2/a^2*(_alpha^2-1),2^(1/2))),_alpha=RootOf(4*_Z^4*b^2-4*_Z^2*b^2+a^2))","C"
579,1,682,300,2.844000," ","int((e*cos(d*x+c))^(1/2)/(a+b*sin(d*x+c)),x)","\frac{e b \left(\munderset{\textit{\_R} =\RootOf \left(b^{2} \textit{\_Z}^{8}-4 b^{2} e \,\textit{\_Z}^{6}+\left(16 a^{2} e^{2}-10 b^{2} e^{2}\right) \textit{\_Z}^{4}-4 b^{2} e^{3} \textit{\_Z}^{2}+b^{2} e^{4}\right)}{\sum}\frac{\left(\textit{\_R}^{6}-\textit{\_R}^{4} e -\textit{\_R}^{2} e^{2}+e^{3}\right) \ln \left(\sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e +e}-\sqrt{e}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2}-\textit{\_R} \right)}{\textit{\_R}^{7} b^{2}-3 \textit{\_R}^{5} b^{2} e +8 \textit{\_R}^{3} a^{2} e^{2}-5 \textit{\_R}^{3} b^{2} e^{2}-\textit{\_R} \,b^{2} e^{3}}\right)}{2 d}-\frac{\sqrt{e \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, e \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(4 b^{2} \textit{\_Z}^{4}-4 b^{2} \textit{\_Z}^{2}+a^{2}\right)}{\sum}\frac{8 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), -\frac{4 b^{2} \left(\underline{\hspace{1.25 ex}}\alpha^{2}-1\right)}{a^{2}}, \sqrt{2}\right) \sqrt{\frac{e \left(2 b^{2} \underline{\hspace{1.25 ex}}\alpha^{2}+a^{2}-2 b^{2}\right)}{b^{2}}}\, \underline{\hspace{1.25 ex}}\alpha^{3} b^{2}-8 b^{2} \underline{\hspace{1.25 ex}}\alpha  \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), -\frac{4 b^{2} \left(\underline{\hspace{1.25 ex}}\alpha^{2}-1\right)}{a^{2}}, \sqrt{2}\right) \sqrt{\frac{e \left(2 b^{2} \underline{\hspace{1.25 ex}}\alpha^{2}+a^{2}-2 b^{2}\right)}{b^{2}}}+a^{2} \sqrt{2}\, \arctanh \left(\frac{e \left(4 \underline{\hspace{1.25 ex}}\alpha^{2}-3\right) \left(4 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{2}-3 b^{2} \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+b^{2} \underline{\hspace{1.25 ex}}\alpha^{2}-3 a^{2}+2 b^{2}\right) \sqrt{2}}{2 \left(4 a^{2}-3 b^{2}\right) \sqrt{\frac{e \left(2 b^{2} \underline{\hspace{1.25 ex}}\alpha^{2}+a^{2}-2 b^{2}\right)}{b^{2}}}\, \sqrt{-e \left(2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}}\right) \sqrt{-\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e \left(2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}}{\underline{\hspace{1.25 ex}}\alpha  \sqrt{\frac{e \left(2 b^{2} \underline{\hspace{1.25 ex}}\alpha^{2}+a^{2}-2 b^{2}\right)}{b^{2}}}\, \sqrt{-\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e \left(2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}}\right)}{8 d a \,b^{2} \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{e \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}}"," ",0,"1/2/d*e*b*sum((_R^6-_R^4*e-_R^2*e^2+e^3)/(_R^7*b^2-3*_R^5*b^2*e+8*_R^3*a^2*e^2-5*_R^3*b^2*e^2-_R*b^2*e^3)*ln((-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)-e^(1/2)*cos(1/2*d*x+1/2*c)*2^(1/2)-_R),_R=RootOf(b^2*_Z^8-4*b^2*e*_Z^6+(16*a^2*e^2-10*b^2*e^2)*_Z^4-4*b^2*e^3*_Z^2+b^2*e^4))-1/8/d*(e*(2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*e/a/b^2*sum(1/_alpha*(8*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),-4*b^2/a^2*(_alpha^2-1),2^(1/2))*(e*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)*_alpha^3*b^2-8*b^2*_alpha*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),-4*b^2/a^2*(_alpha^2-1),2^(1/2))*(e*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)+a^2*2^(1/2)*arctanh(1/2*e*(4*_alpha^2-3)/(4*a^2-3*b^2)*(4*cos(1/2*d*x+1/2*c)^2*a^2-3*b^2*cos(1/2*d*x+1/2*c)^2+b^2*_alpha^2-3*a^2+2*b^2)*2^(1/2)/(e*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)/(-e*(2*sin(1/2*d*x+1/2*c)^4-sin(1/2*d*x+1/2*c)^2))^(1/2))*(-sin(1/2*d*x+1/2*c)^2*e*(2*sin(1/2*d*x+1/2*c)^2-1))^(1/2))/(e*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)/(-sin(1/2*d*x+1/2*c)^2*e*(2*sin(1/2*d*x+1/2*c)^2-1))^(1/2),_alpha=RootOf(4*_Z^4*b^2-4*_Z^2*b^2+a^2))/sin(1/2*d*x+1/2*c)/(e*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)","C"
580,1,678,307,2.766000," ","int(1/(a+b*sin(d*x+c))/(e*cos(d*x+c))^(1/2),x)","\frac{2 b e \left(\munderset{\textit{\_R} =\RootOf \left(b^{2} \textit{\_Z}^{8}-4 b^{2} e \,\textit{\_Z}^{6}+\left(16 a^{2} e^{2}-10 b^{2} e^{2}\right) \textit{\_Z}^{4}-4 b^{2} e^{3} \textit{\_Z}^{2}+b^{2} e^{4}\right)}{\sum}\frac{\left(\textit{\_R}^{4}+\textit{\_R}^{2} e \right) \ln \left(\sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e +e}-\sqrt{e}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2}-\textit{\_R} \right)}{\textit{\_R}^{7} b^{2}-3 \textit{\_R}^{5} b^{2} e +8 \textit{\_R}^{3} a^{2} e^{2}-5 \textit{\_R}^{3} b^{2} e^{2}-\textit{\_R} \,b^{2} e^{3}}\right)}{d}-\frac{\sqrt{e \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(4 b^{2} \textit{\_Z}^{4}-4 b^{2} \textit{\_Z}^{2}+a^{2}\right)}{\sum}\frac{8 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), -\frac{4 b^{2} \left(\underline{\hspace{1.25 ex}}\alpha^{2}-1\right)}{a^{2}}, \sqrt{2}\right) \sqrt{\frac{e \left(2 b^{2} \underline{\hspace{1.25 ex}}\alpha^{2}+a^{2}-2 b^{2}\right)}{b^{2}}}\, \underline{\hspace{1.25 ex}}\alpha^{3} b^{2}-8 b^{2} \underline{\hspace{1.25 ex}}\alpha  \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), -\frac{4 b^{2} \left(\underline{\hspace{1.25 ex}}\alpha^{2}-1\right)}{a^{2}}, \sqrt{2}\right) \sqrt{\frac{e \left(2 b^{2} \underline{\hspace{1.25 ex}}\alpha^{2}+a^{2}-2 b^{2}\right)}{b^{2}}}+a^{2} \sqrt{2}\, \arctanh \left(\frac{e \left(4 \underline{\hspace{1.25 ex}}\alpha^{2}-3\right) \left(4 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{2}-3 b^{2} \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+b^{2} \underline{\hspace{1.25 ex}}\alpha^{2}-3 a^{2}+2 b^{2}\right) \sqrt{2}}{2 \left(4 a^{2}-3 b^{2}\right) \sqrt{\frac{e \left(2 b^{2} \underline{\hspace{1.25 ex}}\alpha^{2}+a^{2}-2 b^{2}\right)}{b^{2}}}\, \sqrt{-e \left(2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}}\right) \sqrt{-\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e \left(2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}}{\underline{\hspace{1.25 ex}}\alpha  \left(2 \underline{\hspace{1.25 ex}}\alpha^{2}-1\right) \sqrt{\frac{e \left(2 b^{2} \underline{\hspace{1.25 ex}}\alpha^{2}+a^{2}-2 b^{2}\right)}{b^{2}}}\, \sqrt{-\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e \left(2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}}\right)}{8 d a \,b^{2} \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{e \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}}"," ",0,"2/d*b*e*sum((_R^4+_R^2*e)/(_R^7*b^2-3*_R^5*b^2*e+8*_R^3*a^2*e^2-5*_R^3*b^2*e^2-_R*b^2*e^3)*ln((-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)-e^(1/2)*cos(1/2*d*x+1/2*c)*2^(1/2)-_R),_R=RootOf(b^2*_Z^8-4*b^2*e*_Z^6+(16*a^2*e^2-10*b^2*e^2)*_Z^4-4*b^2*e^3*_Z^2+b^2*e^4))-1/8/d*(e*(2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)/a/b^2*sum(1/_alpha/(2*_alpha^2-1)*(8*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),-4*b^2/a^2*(_alpha^2-1),2^(1/2))*(e*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)*_alpha^3*b^2-8*b^2*_alpha*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),-4*b^2/a^2*(_alpha^2-1),2^(1/2))*(e*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)+a^2*2^(1/2)*arctanh(1/2*e*(4*_alpha^2-3)/(4*a^2-3*b^2)*(4*cos(1/2*d*x+1/2*c)^2*a^2-3*b^2*cos(1/2*d*x+1/2*c)^2+b^2*_alpha^2-3*a^2+2*b^2)*2^(1/2)/(e*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)/(-e*(2*sin(1/2*d*x+1/2*c)^4-sin(1/2*d*x+1/2*c)^2))^(1/2))*(-sin(1/2*d*x+1/2*c)^2*e*(2*sin(1/2*d*x+1/2*c)^2-1))^(1/2))/(e*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)/(-sin(1/2*d*x+1/2*c)^2*e*(2*sin(1/2*d*x+1/2*c)^2-1))^(1/2),_alpha=RootOf(4*_Z^4*b^2-4*_Z^2*b^2+a^2))/sin(1/2*d*x+1/2*c)/(e*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)","C"
581,1,1103,439,4.299000," ","int(1/(e*cos(d*x+c))^(3/2)/(a+b*sin(d*x+c)),x)","\frac{b \sqrt{2}\, \sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e +e}}{2 d \,e^{2} \left(a^{2}-b^{2}\right) \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\frac{\sqrt{2}}{2}\right)}-\frac{b^{3} \left(\munderset{\textit{\_R} =\RootOf \left(b^{2} \textit{\_Z}^{8}-4 b^{2} e \,\textit{\_Z}^{6}+\left(16 a^{2} e^{2}-10 b^{2} e^{2}\right) \textit{\_Z}^{4}-4 b^{2} e^{3} \textit{\_Z}^{2}+b^{2} e^{4}\right)}{\sum}\frac{\left(\textit{\_R}^{6}-\textit{\_R}^{4} e -\textit{\_R}^{2} e^{2}+e^{3}\right) \ln \left(\sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e +e}-\sqrt{e}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2}-\textit{\_R} \right)}{\textit{\_R}^{7} b^{2}-3 \textit{\_R}^{5} b^{2} e +8 \textit{\_R}^{3} a^{2} e^{2}-5 \textit{\_R}^{3} b^{2} e^{2}-\textit{\_R} \,b^{2} e^{3}}\right)}{2 d e \left(a -b \right) \left(a +b \right)}-\frac{b \sqrt{2}\, \sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e +e}}{2 d \,e^{2} \left(a^{2}-b^{2}\right) \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right)-\frac{\sqrt{2}}{2}\right)}-\frac{4 a \left(\cos^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d e \left(a +b \right) \left(a -b \right) \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{e \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}}-\frac{2 a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \sqrt{e \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{d e \left(a +b \right) \left(a -b \right) \sqrt{-e \left(2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{e \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}}+\frac{4 a \cos \left(\frac{d x}{2}+\frac{c}{2}\right)}{d e \left(a +b \right) \left(a -b \right) \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{e \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}}+\frac{\left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(4 b^{2} \textit{\_Z}^{4}-4 b^{2} \textit{\_Z}^{2}+a^{2}\right)}{\sum}\frac{8 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), -\frac{4 b^{2} \left(\underline{\hspace{1.25 ex}}\alpha^{2}-1\right)}{a^{2}}, \sqrt{2}\right) \sqrt{\frac{e \left(2 b^{2} \underline{\hspace{1.25 ex}}\alpha^{2}+a^{2}-2 b^{2}\right)}{b^{2}}}\, \underline{\hspace{1.25 ex}}\alpha^{3} b^{2}-8 b^{2} \underline{\hspace{1.25 ex}}\alpha  \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), -\frac{4 b^{2} \left(\underline{\hspace{1.25 ex}}\alpha^{2}-1\right)}{a^{2}}, \sqrt{2}\right) \sqrt{\frac{e \left(2 b^{2} \underline{\hspace{1.25 ex}}\alpha^{2}+a^{2}-2 b^{2}\right)}{b^{2}}}+a^{2} \sqrt{2}\, \arctanh \left(\frac{e \left(4 \underline{\hspace{1.25 ex}}\alpha^{2}-3\right) \left(4 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{2}-3 b^{2} \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+b^{2} \underline{\hspace{1.25 ex}}\alpha^{2}-3 a^{2}+2 b^{2}\right) \sqrt{2}}{2 \left(4 a^{2}-3 b^{2}\right) \sqrt{\frac{e \left(2 b^{2} \underline{\hspace{1.25 ex}}\alpha^{2}+a^{2}-2 b^{2}\right)}{b^{2}}}\, \sqrt{-e \left(2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}}\right) \sqrt{-\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e \left(2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}}{\underline{\hspace{1.25 ex}}\alpha  \sqrt{\frac{e \left(2 b^{2} \underline{\hspace{1.25 ex}}\alpha^{2}+a^{2}-2 b^{2}\right)}{b^{2}}}\, \sqrt{-\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e \left(2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}}\right) \sqrt{e \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}}{8 d e a \left(a +b \right) \left(a -b \right) \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{e \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}}"," ",0,"1/2/d/e^2*b/(a^2-b^2)*2^(1/2)/(cos(1/2*d*x+1/2*c)+1/2*2^(1/2))*(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)-1/2/d/e*b^3/(a-b)/(a+b)*sum((_R^6-_R^4*e-_R^2*e^2+e^3)/(_R^7*b^2-3*_R^5*b^2*e+8*_R^3*a^2*e^2-5*_R^3*b^2*e^2-_R*b^2*e^3)*ln((-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)-e^(1/2)*cos(1/2*d*x+1/2*c)*2^(1/2)-_R),_R=RootOf(b^2*_Z^8-4*b^2*e*_Z^6+(16*a^2*e^2-10*b^2*e^2)*_Z^4-4*b^2*e^3*_Z^2+b^2*e^4))-1/2/d/e^2*b/(a^2-b^2)*2^(1/2)/(cos(1/2*d*x+1/2*c)-1/2*2^(1/2))*(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)-4/d/e*a/(a+b)/(a-b)/sin(1/2*d*x+1/2*c)/(e*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)*cos(1/2*d*x+1/2*c)^3-2/d/e*a/(a+b)/(a-b)/(-e*(2*sin(1/2*d*x+1/2*c)^4-sin(1/2*d*x+1/2*c)^2))^(1/2)/sin(1/2*d*x+1/2*c)/(e*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*(e*(2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+4/d/e*a/(a+b)/(a-b)/sin(1/2*d*x+1/2*c)/(e*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)*cos(1/2*d*x+1/2*c)+1/8/d/e/a/(a+b)/(a-b)/sin(1/2*d*x+1/2*c)/(e*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)*sum(1/_alpha*(8*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),-4*b^2/a^2*(_alpha^2-1),2^(1/2))*(e*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)*_alpha^3*b^2-8*b^2*_alpha*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),-4*b^2/a^2*(_alpha^2-1),2^(1/2))*(e*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)+a^2*2^(1/2)*arctanh(1/2*e*(4*_alpha^2-3)/(4*a^2-3*b^2)*(4*cos(1/2*d*x+1/2*c)^2*a^2-3*b^2*cos(1/2*d*x+1/2*c)^2+b^2*_alpha^2-3*a^2+2*b^2)*2^(1/2)/(e*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)/(-e*(2*sin(1/2*d*x+1/2*c)^4-sin(1/2*d*x+1/2*c)^2))^(1/2))*(-sin(1/2*d*x+1/2*c)^2*e*(2*sin(1/2*d*x+1/2*c)^2-1))^(1/2))/(e*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)/(-sin(1/2*d*x+1/2*c)^2*e*(2*sin(1/2*d*x+1/2*c)^2-1))^(1/2),_alpha=RootOf(4*_Z^4*b^2-4*_Z^2*b^2+a^2))*(e*(2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)","C"
582,1,1083,458,4.960000," ","int(1/(e*cos(d*x+c))^(5/2)/(a+b*sin(d*x+c)),x)","-\frac{2 b^{3} \left(\munderset{\textit{\_R} =\RootOf \left(b^{2} \textit{\_Z}^{8}-4 b^{2} e \,\textit{\_Z}^{6}+\left(16 a^{2} e^{2}-10 b^{2} e^{2}\right) \textit{\_Z}^{4}-4 b^{2} e^{3} \textit{\_Z}^{2}+b^{2} e^{4}\right)}{\sum}\frac{\left(\textit{\_R}^{4}+\textit{\_R}^{2} e \right) \ln \left(\sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e +e}-\sqrt{e}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2}-\textit{\_R} \right)}{\textit{\_R}^{7} b^{2}-3 \textit{\_R}^{5} b^{2} e +8 \textit{\_R}^{3} a^{2} e^{2}-5 \textit{\_R}^{3} b^{2} e^{2}-\textit{\_R} \,b^{2} e^{3}}\right)}{d e \left(a -b \right) \left(a +b \right)}-\frac{b \sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e +e}}{12 d \,e^{3} \left(a^{2}-b^{2}\right) \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\frac{\sqrt{2}}{2}\right)^{2}}-\frac{b \sqrt{2}\, \sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e +e}}{12 d \,e^{3} \left(a^{2}-b^{2}\right) \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\frac{\sqrt{2}}{2}\right)}-\frac{b \sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e +e}}{12 d \,e^{3} \left(a^{2}-b^{2}\right) \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right)-\frac{\sqrt{2}}{2}\right)^{2}}+\frac{b \sqrt{2}\, \sqrt{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e +e}}{12 d \,e^{3} \left(a^{2}-b^{2}\right) \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right)-\frac{\sqrt{2}}{2}\right)}+\frac{\sqrt{e \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, a \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(4 b^{2} \textit{\_Z}^{4}-4 b^{2} \textit{\_Z}^{2}+a^{2}\right)}{\sum}\frac{\frac{\sqrt{2}\, \arctanh \left(\frac{e \left(4 \underline{\hspace{1.25 ex}}\alpha^{2}-3\right) \left(4 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{2}-3 b^{2} \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+b^{2} \underline{\hspace{1.25 ex}}\alpha^{2}-3 a^{2}+2 b^{2}\right) \sqrt{2}}{2 \left(4 a^{2}-3 b^{2}\right) \sqrt{\frac{e \left(2 b^{2} \underline{\hspace{1.25 ex}}\alpha^{2}+a^{2}-2 b^{2}\right)}{b^{2}}}\, \sqrt{-e \left(2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}}\right)}{\sqrt{\frac{e \left(2 b^{2} \underline{\hspace{1.25 ex}}\alpha^{2}+a^{2}-2 b^{2}\right)}{b^{2}}}}+\frac{8 b^{2} \underline{\hspace{1.25 ex}}\alpha  \left(\underline{\hspace{1.25 ex}}\alpha^{2}-1\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), -\frac{4 b^{2} \left(\underline{\hspace{1.25 ex}}\alpha^{2}-1\right)}{a^{2}}, \sqrt{2}\right)}{a^{2} \sqrt{-\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) e \left(2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}}}{\underline{\hspace{1.25 ex}}\alpha  \left(2 \underline{\hspace{1.25 ex}}\alpha^{2}-1\right)}\right)}{8 d \,e^{2} \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{e \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}\, \left(a -b \right) \left(a +b \right)}+\frac{\sqrt{e \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, a \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-e \left(2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}}{3 d \,e^{3} \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{e \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}\, \left(a^{2}-b^{2}\right) \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)-\frac{1}{2}\right)^{2}}-\frac{2 \sqrt{e \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{3 d \,e^{2} \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{e \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}\, \left(a^{2}-b^{2}\right) \sqrt{-e \left(2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}}"," ",0,"-2/d/e*b^3/(a-b)/(a+b)*sum((_R^4+_R^2*e)/(_R^7*b^2-3*_R^5*b^2*e+8*_R^3*a^2*e^2-5*_R^3*b^2*e^2-_R*b^2*e^3)*ln((-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)-e^(1/2)*cos(1/2*d*x+1/2*c)*2^(1/2)-_R),_R=RootOf(b^2*_Z^8-4*b^2*e*_Z^6+(16*a^2*e^2-10*b^2*e^2)*_Z^4-4*b^2*e^3*_Z^2+b^2*e^4))-1/12/d/e^3*b/(a^2-b^2)/(cos(1/2*d*x+1/2*c)+1/2*2^(1/2))^2*(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)-1/12/d/e^3*b*2^(1/2)/(a^2-b^2)/(cos(1/2*d*x+1/2*c)+1/2*2^(1/2))*(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)-1/12/d/e^3*b/(a^2-b^2)/(cos(1/2*d*x+1/2*c)-1/2*2^(1/2))^2*(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)+1/12/d/e^3*b*2^(1/2)/(a^2-b^2)/(cos(1/2*d*x+1/2*c)-1/2*2^(1/2))*(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)+1/8/d*(e*(2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*a/e^2/sin(1/2*d*x+1/2*c)/(e*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)/(a-b)/(a+b)*sum(1/_alpha/(2*_alpha^2-1)*(2^(1/2)/(e*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)*arctanh(1/2*e*(4*_alpha^2-3)/(4*a^2-3*b^2)*(4*cos(1/2*d*x+1/2*c)^2*a^2-3*b^2*cos(1/2*d*x+1/2*c)^2+b^2*_alpha^2-3*a^2+2*b^2)*2^(1/2)/(e*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)/(-e*(2*sin(1/2*d*x+1/2*c)^4-sin(1/2*d*x+1/2*c)^2))^(1/2))+8*b^2/a^2*_alpha*(_alpha^2-1)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-sin(1/2*d*x+1/2*c)^2*e*(2*sin(1/2*d*x+1/2*c)^2-1))^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),-4*b^2/a^2*(_alpha^2-1),2^(1/2))),_alpha=RootOf(4*_Z^4*b^2-4*_Z^2*b^2+a^2))+1/3/d*(e*(2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*a/e^3/sin(1/2*d*x+1/2*c)/(e*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)/(a^2-b^2)*cos(1/2*d*x+1/2*c)*(-e*(2*sin(1/2*d*x+1/2*c)^4-sin(1/2*d*x+1/2*c)^2))^(1/2)/(cos(1/2*d*x+1/2*c)^2-1/2)^2-2/3/d*(e*(2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*a/e^2/sin(1/2*d*x+1/2*c)/(e*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)/(a^2-b^2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-e*(2*sin(1/2*d*x+1/2*c)^4-sin(1/2*d*x+1/2*c)^2))^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))","C"
583,1,2399,506,7.173000," ","int(1/(e*cos(d*x+c))^(7/2)/(a+b*sin(d*x+c)),x)","\text{Expression too large to display}"," ",0,"1/80/d/e^4*b/(a^2-b^2)*2^(1/2)/(cos(1/2*d*x+1/2*c)+1/2*2^(1/2))^3*(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)+3/80/d/e^4*b/(a^2-b^2)/(cos(1/2*d*x+1/2*c)+1/2*2^(1/2))^2*(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)+3/80/d/e^4*b/(a^2-b^2)*2^(1/2)/(cos(1/2*d*x+1/2*c)+1/2*2^(1/2))*(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)-1/2/d/e^4*b^3/(a^2-b^2)^2*2^(1/2)/(cos(1/2*d*x+1/2*c)+1/2*2^(1/2))*(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)+1/2/d/e^3*b^5/(a-b)^2/(a+b)^2*sum((_R^6-_R^4*e-_R^2*e^2+e^3)/(_R^7*b^2-3*_R^5*b^2*e+8*_R^3*a^2*e^2-5*_R^3*b^2*e^2-_R*b^2*e^3)*ln((-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)-e^(1/2)*cos(1/2*d*x+1/2*c)*2^(1/2)-_R),_R=RootOf(b^2*_Z^8-4*b^2*e*_Z^6+(16*a^2*e^2-10*b^2*e^2)*_Z^4-4*b^2*e^3*_Z^2+b^2*e^4))+3/80/d/e^4*b/(a^2-b^2)/(cos(1/2*d*x+1/2*c)-1/2*2^(1/2))^2*(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)-3/80/d/e^4*b*2^(1/2)/(a^2-b^2)/(cos(1/2*d*x+1/2*c)-1/2*2^(1/2))*(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)-1/80/d/e^4*b/(a^2-b^2)*2^(1/2)/(cos(1/2*d*x+1/2*c)-1/2*2^(1/2))^3*(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)+1/2/d/e^4*b^3/(a^2-b^2)^2*2^(1/2)/(cos(1/2*d*x+1/2*c)-1/2*2^(1/2))*(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)+4/d*(e*(2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)/e^4*a/sin(1/2*d*x+1/2*c)/(e*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)/(a^2-b^2)^2*b^2/(2*sin(1/2*d*x+1/2*c)^2-1)*(-2*sin(1/2*d*x+1/2*c)^4*e+sin(1/2*d*x+1/2*c)^2*e)^(1/2)*cos(1/2*d*x+1/2*c)-2/d*(e*(2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)/e^4*a/sin(1/2*d*x+1/2*c)^3/(e*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)/(a^2-b^2)^2*b^2/(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*sin(1/2*d*x+1/2*c)^4*e+sin(1/2*d*x+1/2*c)^2*e)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-1/8/d*(e*(2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)/e^3*a/sin(1/2*d*x+1/2*c)/(e*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)*b^2/(a-b)^2/(a+b)^2*sum(1/_alpha*(2^(1/2)/(e*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)*arctanh(1/2*e*(4*_alpha^2-3)/(4*a^2-3*b^2)*(4*cos(1/2*d*x+1/2*c)^2*a^2-3*b^2*cos(1/2*d*x+1/2*c)^2+b^2*_alpha^2-3*a^2+2*b^2)*2^(1/2)/(e*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)/(-e*(2*sin(1/2*d*x+1/2*c)^4-sin(1/2*d*x+1/2*c)^2))^(1/2))+8*b^2/a^2*_alpha*(_alpha^2-1)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-sin(1/2*d*x+1/2*c)^2*e*(2*sin(1/2*d*x+1/2*c)^2-1))^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),-4*b^2/a^2*(_alpha^2-1),2^(1/2))),_alpha=RootOf(4*_Z^4*b^2-4*_Z^2*b^2+a^2))-48/5/d*(e*(2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)/e^4*a*sin(1/2*d*x+1/2*c)^3/(e*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)/(a^2-b^2)/(8*sin(1/2*d*x+1/2*c)^6-12*sin(1/2*d*x+1/2*c)^4+6*sin(1/2*d*x+1/2*c)^2-1)*(-2*sin(1/2*d*x+1/2*c)^4*e+sin(1/2*d*x+1/2*c)^2*e)^(1/2)*cos(1/2*d*x+1/2*c)+24/5/d*(e*(2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)/e^4*a*sin(1/2*d*x+1/2*c)/(e*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)/(a^2-b^2)/(8*sin(1/2*d*x+1/2*c)^6-12*sin(1/2*d*x+1/2*c)^4+6*sin(1/2*d*x+1/2*c)^2-1)*(-2*sin(1/2*d*x+1/2*c)^4*e+sin(1/2*d*x+1/2*c)^2*e)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(sin(1/2*d*x+1/2*c)^2)^(1/2)+48/5/d*(e*(2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)/e^4*a*sin(1/2*d*x+1/2*c)/(e*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)/(a^2-b^2)/(8*sin(1/2*d*x+1/2*c)^6-12*sin(1/2*d*x+1/2*c)^4+6*sin(1/2*d*x+1/2*c)^2-1)*(-2*sin(1/2*d*x+1/2*c)^4*e+sin(1/2*d*x+1/2*c)^2*e)^(1/2)*cos(1/2*d*x+1/2*c)-24/5/d*(e*(2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)/e^4*a/sin(1/2*d*x+1/2*c)/(e*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)/(a^2-b^2)/(8*sin(1/2*d*x+1/2*c)^6-12*sin(1/2*d*x+1/2*c)^4+6*sin(1/2*d*x+1/2*c)^2-1)*(-2*sin(1/2*d*x+1/2*c)^4*e+sin(1/2*d*x+1/2*c)^2*e)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(sin(1/2*d*x+1/2*c)^2)^(1/2)-16/5/d*(e*(2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)/e^4*a/sin(1/2*d*x+1/2*c)/(e*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)/(a^2-b^2)/(8*sin(1/2*d*x+1/2*c)^6-12*sin(1/2*d*x+1/2*c)^4+6*sin(1/2*d*x+1/2*c)^2-1)*(-2*sin(1/2*d*x+1/2*c)^4*e+sin(1/2*d*x+1/2*c)^2*e)^(1/2)*cos(1/2*d*x+1/2*c)+6/5/d*(e*(2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)/e^4*a/sin(1/2*d*x+1/2*c)^3/(e*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)/(a^2-b^2)/(8*sin(1/2*d*x+1/2*c)^6-12*sin(1/2*d*x+1/2*c)^4+6*sin(1/2*d*x+1/2*c)^2-1)*(-2*sin(1/2*d*x+1/2*c)^4*e+sin(1/2*d*x+1/2*c)^2*e)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(sin(1/2*d*x+1/2*c)^2)^(1/2)","C"
584,1,19829,553,13.797000," ","int((e*cos(d*x+c))^(11/2)/(a+b*sin(d*x+c))^2,x)","\text{output too large to display}"," ",0,"result too large to display","C"
585,1,20346,473,10.696000," ","int((e*cos(d*x+c))^(9/2)/(a+b*sin(d*x+c))^2,x)","\text{output too large to display}"," ",0,"result too large to display","C"
586,1,14392,487,10.765000," ","int((e*cos(d*x+c))^(7/2)/(a+b*sin(d*x+c))^2,x)","\text{output too large to display}"," ",0,"result too large to display","C"
587,1,13221,410,8.143000," ","int((e*cos(d*x+c))^(5/2)/(a+b*sin(d*x+c))^2,x)","\text{output too large to display}"," ",0,"result too large to display","C"
588,1,9301,424,8.237000," ","int((e*cos(d*x+c))^(3/2)/(a+b*sin(d*x+c))^2,x)","\text{output too large to display}"," ",0,"result too large to display","C"
589,1,7033,442,9.147000," ","int((e*cos(d*x+c))^(1/2)/(a+b*sin(d*x+c))^2,x)","\text{output too large to display}"," ",0,"result too large to display","C"
590,1,4457,449,8.897000," ","int(1/(a+b*sin(d*x+c))^2/(e*cos(d*x+c))^(1/2),x)","\text{output too large to display}"," ",0,"-512/d*a*b*e^(7/2)/(1024*e^(7/2)*2^(1/2)*(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)*b^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6-1792*e^(7/2)*2^(1/2)*(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)*b^2*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+256*e^(7/2)*2^(1/2)*(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)*a^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2+768*e^(7/2)*2^(1/2)*(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)*b^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2+2048*b^2*e^4*sin(1/2*d*x+1/2*c)^8-192*e^(7/2)*2^(1/2)*(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)*a^2*cos(1/2*d*x+1/2*c)-5120*b^2*e^4*sin(1/2*d*x+1/2*c)^6+512*a^2*e^4*sin(1/2*d*x+1/2*c)^4+4160*b^2*e^4*sin(1/2*d*x+1/2*c)^4-768*a^2*e^4*sin(1/2*d*x+1/2*c)^2-1088*b^2*e^4*sin(1/2*d*x+1/2*c)^2+272*e^4*a^2)/(a^2-b^2)*2^(1/2)*cos(1/2*d*x+1/2*c)^5+160/d*a*b*e^3/(1024*e^(7/2)*2^(1/2)*(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)*b^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6-1792*e^(7/2)*2^(1/2)*(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)*b^2*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+256*e^(7/2)*2^(1/2)*(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)*a^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2+768*e^(7/2)*2^(1/2)*(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)*b^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2+2048*b^2*e^4*sin(1/2*d*x+1/2*c)^8-192*e^(7/2)*2^(1/2)*(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)*a^2*cos(1/2*d*x+1/2*c)-5120*b^2*e^4*sin(1/2*d*x+1/2*c)^6+512*a^2*e^4*sin(1/2*d*x+1/2*c)^4+4160*b^2*e^4*sin(1/2*d*x+1/2*c)^4-768*a^2*e^4*sin(1/2*d*x+1/2*c)^2-1088*b^2*e^4*sin(1/2*d*x+1/2*c)^2+272*e^4*a^2)/(a^2-b^2)*(e*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)*cos(1/2*d*x+1/2*c)^4+384/d*a*b*e^(7/2)/(1024*e^(7/2)*2^(1/2)*(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)*b^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6-1792*e^(7/2)*2^(1/2)*(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)*b^2*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+256*e^(7/2)*2^(1/2)*(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)*a^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2+768*e^(7/2)*2^(1/2)*(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)*b^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2+2048*b^2*e^4*sin(1/2*d*x+1/2*c)^8-192*e^(7/2)*2^(1/2)*(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)*a^2*cos(1/2*d*x+1/2*c)-5120*b^2*e^4*sin(1/2*d*x+1/2*c)^6+512*a^2*e^4*sin(1/2*d*x+1/2*c)^4+4160*b^2*e^4*sin(1/2*d*x+1/2*c)^4-768*a^2*e^4*sin(1/2*d*x+1/2*c)^2-1088*b^2*e^4*sin(1/2*d*x+1/2*c)^2+272*e^4*a^2)/(a^2-b^2)*2^(1/2)*cos(1/2*d*x+1/2*c)^3+160/d*a*b*e^2/(1024*e^(7/2)*2^(1/2)*(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)*b^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6-1792*e^(7/2)*2^(1/2)*(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)*b^2*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+256*e^(7/2)*2^(1/2)*(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)*a^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2+768*e^(7/2)*2^(1/2)*(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)*b^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2+2048*b^2*e^4*sin(1/2*d*x+1/2*c)^8-192*e^(7/2)*2^(1/2)*(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)*a^2*cos(1/2*d*x+1/2*c)-5120*b^2*e^4*sin(1/2*d*x+1/2*c)^6+512*a^2*e^4*sin(1/2*d*x+1/2*c)^4+4160*b^2*e^4*sin(1/2*d*x+1/2*c)^4-768*a^2*e^4*sin(1/2*d*x+1/2*c)^2-1088*b^2*e^4*sin(1/2*d*x+1/2*c)^2+272*e^4*a^2)/(a^2-b^2)*(e*(2*cos(1/2*d*x+1/2*c)^2-1))^(3/2)*cos(1/2*d*x+1/2*c)^2-64/d*a*b*e^(7/2)/(1024*e^(7/2)*2^(1/2)*(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)*b^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6-1792*e^(7/2)*2^(1/2)*(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)*b^2*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+256*e^(7/2)*2^(1/2)*(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)*a^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2+768*e^(7/2)*2^(1/2)*(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)*b^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2+2048*b^2*e^4*sin(1/2*d*x+1/2*c)^8-192*e^(7/2)*2^(1/2)*(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)*a^2*cos(1/2*d*x+1/2*c)-5120*b^2*e^4*sin(1/2*d*x+1/2*c)^6+512*a^2*e^4*sin(1/2*d*x+1/2*c)^4+4160*b^2*e^4*sin(1/2*d*x+1/2*c)^4-768*a^2*e^4*sin(1/2*d*x+1/2*c)^2-1088*b^2*e^4*sin(1/2*d*x+1/2*c)^2+272*e^4*a^2)/(a^2-b^2)*2^(1/2)*cos(1/2*d*x+1/2*c)+8/d*a*b*e/(1024*e^(7/2)*2^(1/2)*(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)*b^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6-1792*e^(7/2)*2^(1/2)*(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)*b^2*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+256*e^(7/2)*2^(1/2)*(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)*a^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2+768*e^(7/2)*2^(1/2)*(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)*b^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2+2048*b^2*e^4*sin(1/2*d*x+1/2*c)^8-192*e^(7/2)*2^(1/2)*(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)*a^2*cos(1/2*d*x+1/2*c)-5120*b^2*e^4*sin(1/2*d*x+1/2*c)^6+512*a^2*e^4*sin(1/2*d*x+1/2*c)^4+4160*b^2*e^4*sin(1/2*d*x+1/2*c)^4-768*a^2*e^4*sin(1/2*d*x+1/2*c)^2-1088*b^2*e^4*sin(1/2*d*x+1/2*c)^2+272*e^4*a^2)/(a^2-b^2)*(e*(2*cos(1/2*d*x+1/2*c)^2-1))^(5/2)-48/d*a*b*e^3/(1024*e^(7/2)*2^(1/2)*(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)*b^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6-1792*e^(7/2)*2^(1/2)*(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)*b^2*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+256*e^(7/2)*2^(1/2)*(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)*a^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2+768*e^(7/2)*2^(1/2)*(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)*b^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2+2048*b^2*e^4*sin(1/2*d*x+1/2*c)^8-192*e^(7/2)*2^(1/2)*(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)*a^2*cos(1/2*d*x+1/2*c)-5120*b^2*e^4*sin(1/2*d*x+1/2*c)^6+512*a^2*e^4*sin(1/2*d*x+1/2*c)^4+4160*b^2*e^4*sin(1/2*d*x+1/2*c)^4-768*a^2*e^4*sin(1/2*d*x+1/2*c)^2-1088*b^2*e^4*sin(1/2*d*x+1/2*c)^2+272*e^4*a^2)/(a^2-b^2)*(e*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)*cos(1/2*d*x+1/2*c)^2-8/d*a*b*e^2/(1024*e^(7/2)*2^(1/2)*(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)*b^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6-1792*e^(7/2)*2^(1/2)*(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)*b^2*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+256*e^(7/2)*2^(1/2)*(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)*a^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2+768*e^(7/2)*2^(1/2)*(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)*b^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2+2048*b^2*e^4*sin(1/2*d*x+1/2*c)^8-192*e^(7/2)*2^(1/2)*(-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)*a^2*cos(1/2*d*x+1/2*c)-5120*b^2*e^4*sin(1/2*d*x+1/2*c)^6+512*a^2*e^4*sin(1/2*d*x+1/2*c)^4+4160*b^2*e^4*sin(1/2*d*x+1/2*c)^4-768*a^2*e^4*sin(1/2*d*x+1/2*c)^2-1088*b^2*e^4*sin(1/2*d*x+1/2*c)^2+272*e^4*a^2)/(a^2-b^2)*(e*(2*cos(1/2*d*x+1/2*c)^2-1))^(3/2)+3/d*a*b*e/(a^2-b^2)*sum((_R^4+_R^2*e)/(_R^7*b^2-3*_R^5*b^2*e+8*_R^3*a^2*e^2-5*_R^3*b^2*e^2-_R*b^2*e^3)*ln((-2*sin(1/2*d*x+1/2*c)^2*e+e)^(1/2)-e^(1/2)*cos(1/2*d*x+1/2*c)*2^(1/2)-_R),_R=RootOf(b^2*_Z^8-4*b^2*e*_Z^6+(16*a^2*e^2-10*b^2*e^2)*_Z^4-4*b^2*e^3*_Z^2+b^2*e^4))+1/8/d*(e*(2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(e*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)/b^2*sum(1/_alpha/(2*_alpha^2-1)*(2^(1/2)/(e*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)*arctanh(1/2*e*(4*_alpha^2-3)/(4*a^2-3*b^2)*(4*cos(1/2*d*x+1/2*c)^2*a^2-3*b^2*cos(1/2*d*x+1/2*c)^2+b^2*_alpha^2-3*a^2+2*b^2)*2^(1/2)/(e*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)/(-e*(2*sin(1/2*d*x+1/2*c)^4-sin(1/2*d*x+1/2*c)^2))^(1/2))+8*b^2/a^2*_alpha*(_alpha^2-1)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-sin(1/2*d*x+1/2*c)^2*e*(2*sin(1/2*d*x+1/2*c)^2-1))^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),-4*b^2/a^2*(_alpha^2-1),2^(1/2))),_alpha=RootOf(4*_Z^4*b^2-4*_Z^2*b^2+a^2))-2/d*(e*(2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(e*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)*b^2/(a^2-b^2)/e*cos(1/2*d*x+1/2*c)*(-e*(2*sin(1/2*d*x+1/2*c)^4-sin(1/2*d*x+1/2*c)^2))^(1/2)/(4*b^2*cos(1/2*d*x+1/2*c)^4-4*b^2*cos(1/2*d*x+1/2*c)^2+a^2)+1/d*(e*(2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(e*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)/(a^2-b^2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-e*(2*sin(1/2*d*x+1/2*c)^4-sin(1/2*d*x+1/2*c)^2))^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+1/16/d*(e*(2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(e*(2*cos(1/2*d*x+1/2*c)^2-1))^(1/2)/b^2*sum((-5*a^2+2*b^2)/(a-b)/(a+b)/(2*_alpha^2-1)/_alpha*(2^(1/2)/(e*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)*arctanh(1/2*e*(4*_alpha^2-3)/(4*a^2-3*b^2)*(4*cos(1/2*d*x+1/2*c)^2*a^2-3*b^2*cos(1/2*d*x+1/2*c)^2+b^2*_alpha^2-3*a^2+2*b^2)*2^(1/2)/(e*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)/(-e*(2*sin(1/2*d*x+1/2*c)^4-sin(1/2*d*x+1/2*c)^2))^(1/2))+8*b^2/a^2*_alpha*(_alpha^2-1)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-sin(1/2*d*x+1/2*c)^2*e*(2*sin(1/2*d*x+1/2*c)^2-1))^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),-4*b^2/a^2*(_alpha^2-1),2^(1/2))),_alpha=RootOf(4*_Z^4*b^2-4*_Z^2*b^2+a^2))","C"
591,1,8216,508,13.270000," ","int(1/(e*cos(d*x+c))^(3/2)/(a+b*sin(d*x+c))^2,x)","\text{output too large to display}"," ",0,"result too large to display","C"
592,1,6022,527,17.258000," ","int(1/(e*cos(d*x+c))^(5/2)/(a+b*sin(d*x+c))^2,x)","\text{output too large to display}"," ",0,"result too large to display","C"
593,1,10743,583,25.885000," ","int(1/(e*cos(d*x+c))^(7/2)/(a+b*sin(d*x+c))^2,x)","\text{output too large to display}"," ",0,"result too large to display","C"
594,1,111631,580,36.489000," ","int((e*cos(d*x+c))^(13/2)/(a+b*sin(d*x+c))^3,x)","\text{output too large to display}"," ",0,"result too large to display","C"
595,1,85607,594,39.143000," ","int((e*cos(d*x+c))^(11/2)/(a+b*sin(d*x+c))^3,x)","\text{output too large to display}"," ",0,"result too large to display","C"
596,1,85489,495,29.464000," ","int((e*cos(d*x+c))^(9/2)/(a+b*sin(d*x+c))^3,x)","\text{output too large to display}"," ",0,"result too large to display","C"
597,1,65216,509,29.355000," ","int((e*cos(d*x+c))^(7/2)/(a+b*sin(d*x+c))^3,x)","\text{output too large to display}"," ",0,"result too large to display","C"
598,1,63272,517,31.065000," ","int((e*cos(d*x+c))^(5/2)/(a+b*sin(d*x+c))^3,x)","\text{output too large to display}"," ",0,"result too large to display","C"
599,1,45147,531,30.135000," ","int((e*cos(d*x+c))^(3/2)/(a+b*sin(d*x+c))^3,x)","\text{output too large to display}"," ",0,"result too large to display","C"
600,1,36688,526,30.272000," ","int((e*cos(d*x+c))^(1/2)/(a+b*sin(d*x+c))^3,x)","\text{output too large to display}"," ",0,"result too large to display","C"
601,1,25322,532,28.635000," ","int(1/(a+b*sin(d*x+c))^3/(e*cos(d*x+c))^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
602,1,46134,603,57.541000," ","int(1/(e*cos(d*x+c))^(3/2)/(a+b*sin(d*x+c))^3,x)","\text{output too large to display}"," ",0,"result too large to display","C"
603,1,32645,621,78.670000," ","int(1/(e*cos(d*x+c))^(5/2)/(a+b*sin(d*x+c))^3,x)","\text{output too large to display}"," ",0,"result too large to display","C"
604,1,49016,688,111.396000," ","int(1/(e*cos(d*x+c))^(7/2)/(a+b*sin(d*x+c))^3,x)","\text{output too large to display}"," ",0,"result too large to display","C"
605,1,300244,675,139.890000," ","int((e*cos(d*x+c))^(15/2)/(a+b*sin(d*x+c))^4,x)","\text{output too large to display}"," ",0,"result too large to display","C"
606,1,180834,565,94.455000," ","int((e*cos(d*x+c))^(13/2)/(a+b*sin(d*x+c))^4,x)","\text{output too large to display}"," ",0,"result too large to display","C"
607,1,144252,579,111.918000," ","int((e*cos(d*x+c))^(11/2)/(a+b*sin(d*x+c))^4,x)","\text{output too large to display}"," ",0,"result too large to display","C"
608,1,237416,599,100.678000," ","int((e*cos(d*x+c))^(9/2)/(a+b*sin(d*x+c))^4,x)","\text{output too large to display}"," ",0,"result too large to display","C"
609,1,192036,605,114.161000," ","int((e*cos(d*x+c))^(7/2)/(a+b*sin(d*x+c))^4,x)","\text{output too large to display}"," ",0,"result too large to display","C"
610,1,179434,582,115.350000," ","int((e*cos(d*x+c))^(5/2)/(a+b*sin(d*x+c))^4,x)","\text{output too large to display}"," ",0,"result too large to display","C"
611,1,138380,600,116.408000," ","int((e*cos(d*x+c))^(3/2)/(a+b*sin(d*x+c))^4,x)","\text{output too large to display}"," ",0,"result too large to display","C"
612,1,112960,587,110.043000," ","int((e*cos(d*x+c))^(1/2)/(a+b*sin(d*x+c))^4,x)","\text{output too large to display}"," ",0,"result too large to display","C"
613,1,85165,601,104.026000," ","int(1/(a+b*sin(d*x+c))^4/(e*cos(d*x+c))^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
614,1,150599,677,184.058000," ","int(1/(e*cos(d*x+c))^(3/2)/(a+b*sin(d*x+c))^4,x)","\text{output too large to display}"," ",0,"result too large to display","C"
615,1,442,163,0.609000," ","int(1/(c*cos(f*x+e))^(1/2)/(a+b*sin(f*x+e))^(1/2),x)","\frac{4 \EllipticF \left(\sqrt{\frac{\left(\sin \left(f x +e \right)-1\right) \left(b +\sqrt{-a^{2}+b^{2}}-a \right)}{\cos \left(f x +e \right) \left(b +\sqrt{-a^{2}+b^{2}}+a \right)}}, \sqrt{\frac{\left(a -b +\sqrt{-a^{2}+b^{2}}\right) \left(b +\sqrt{-a^{2}+b^{2}}+a \right)}{\left(-b +\sqrt{-a^{2}+b^{2}}-a \right) \left(b +\sqrt{-a^{2}+b^{2}}-a \right)}}\right) \sqrt{\frac{\cos \left(f x +e \right) \sqrt{-a^{2}+b^{2}}+a \sin \left(f x +e \right)+b \cos \left(f x +e \right)+\sqrt{-a^{2}+b^{2}}+b}{\left(1+\cos \left(f x +e \right)+\sin \left(f x +e \right)\right) \left(b +\sqrt{-a^{2}+b^{2}}+a \right)}}\, \sqrt{\frac{\left(\sin \left(f x +e \right)-1\right) \left(b +\sqrt{-a^{2}+b^{2}}-a \right)}{\cos \left(f x +e \right) \left(b +\sqrt{-a^{2}+b^{2}}+a \right)}}\, \sqrt{-\frac{a \sin \left(f x +e \right)-\cos \left(f x +e \right) \sqrt{-a^{2}+b^{2}}+b \cos \left(f x +e \right)-\sqrt{-a^{2}+b^{2}}+b}{\left(1+\cos \left(f x +e \right)+\sin \left(f x +e \right)\right) \left(-b +\sqrt{-a^{2}+b^{2}}-a \right)}}\, \left(\cos \left(f x +e \right)+1\right)^{2} \left(-1+\cos \left(f x +e \right)\right)^{2} \left(b +\sqrt{-a^{2}+b^{2}}+a \right) \left(1+\sin \left(f x +e \right)\right)}{f \sqrt{a +b \sin \left(f x +e \right)}\, \sin \left(f x +e \right)^{4} \sqrt{c \cos \left(f x +e \right)}\, \left(b +\sqrt{-a^{2}+b^{2}}-a \right)}"," ",0,"4/f*EllipticF(((sin(f*x+e)-1)/cos(f*x+e)*(b+(-a^2+b^2)^(1/2)-a)/(b+(-a^2+b^2)^(1/2)+a))^(1/2),((a-b+(-a^2+b^2)^(1/2))*(b+(-a^2+b^2)^(1/2)+a)/(-b+(-a^2+b^2)^(1/2)-a)/(b+(-a^2+b^2)^(1/2)-a))^(1/2))*((cos(f*x+e)*(-a^2+b^2)^(1/2)+a*sin(f*x+e)+b*cos(f*x+e)+(-a^2+b^2)^(1/2)+b)/(1+cos(f*x+e)+sin(f*x+e))/(b+(-a^2+b^2)^(1/2)+a))^(1/2)*((sin(f*x+e)-1)/cos(f*x+e)*(b+(-a^2+b^2)^(1/2)-a)/(b+(-a^2+b^2)^(1/2)+a))^(1/2)*(-(a*sin(f*x+e)-cos(f*x+e)*(-a^2+b^2)^(1/2)+b*cos(f*x+e)-(-a^2+b^2)^(1/2)+b)/(1+cos(f*x+e)+sin(f*x+e))/(-b+(-a^2+b^2)^(1/2)-a))^(1/2)*(cos(f*x+e)+1)^2*(-1+cos(f*x+e))^2*(b+(-a^2+b^2)^(1/2)+a)*(1+sin(f*x+e))/(a+b*sin(f*x+e))^(1/2)/sin(f*x+e)^4/(c*cos(f*x+e))^(1/2)/(b+(-a^2+b^2)^(1/2)-a)","B"
616,0,0,223,6.004000," ","int((e*cos(d*x+c))^p*(a+b*sin(d*x+c))^3,x)","\int \left(e \cos \left(d x +c \right)\right)^{p} \left(a +b \sin \left(d x +c \right)\right)^{3}\, dx"," ",0,"int((e*cos(d*x+c))^p*(a+b*sin(d*x+c))^3,x)","F"
617,0,0,151,4.431000," ","int((e*cos(d*x+c))^p*(a+b*sin(d*x+c))^2,x)","\int \left(e \cos \left(d x +c \right)\right)^{p} \left(a +b \sin \left(d x +c \right)\right)^{2}\, dx"," ",0,"int((e*cos(d*x+c))^p*(a+b*sin(d*x+c))^2,x)","F"
618,0,0,91,1.772000," ","int((e*cos(d*x+c))^p*(a+b*sin(d*x+c)),x)","\int \left(e \cos \left(d x +c \right)\right)^{p} \left(a +b \sin \left(d x +c \right)\right)\, dx"," ",0,"int((e*cos(d*x+c))^p*(a+b*sin(d*x+c)),x)","F"
619,0,0,142,1.054000," ","int((e*cos(d*x+c))^p/(a+b*sin(d*x+c)),x)","\int \frac{\left(e \cos \left(d x +c \right)\right)^{p}}{a +b \sin \left(d x +c \right)}\, dx"," ",0,"int((e*cos(d*x+c))^p/(a+b*sin(d*x+c)),x)","F"
620,0,0,154,1.115000," ","int((e*cos(d*x+c))^p/(a+b*sin(d*x+c))^2,x)","\int \frac{\left(e \cos \left(d x +c \right)\right)^{p}}{\left(a +b \sin \left(d x +c \right)\right)^{2}}\, dx"," ",0,"int((e*cos(d*x+c))^p/(a+b*sin(d*x+c))^2,x)","F"
621,0,0,154,1.398000," ","int((e*cos(d*x+c))^p/(a+b*sin(d*x+c))^3,x)","\int \frac{\left(e \cos \left(d x +c \right)\right)^{p}}{\left(a +b \sin \left(d x +c \right)\right)^{3}}\, dx"," ",0,"int((e*cos(d*x+c))^p/(a+b*sin(d*x+c))^3,x)","F"
622,0,0,154,8.120000," ","int((e*cos(d*x+c))^p/(a+b*sin(d*x+c))^8,x)","\int \frac{\left(e \cos \left(d x +c \right)\right)^{p}}{\left(a +b \sin \left(d x +c \right)\right)^{8}}\, dx"," ",0,"int((e*cos(d*x+c))^p/(a+b*sin(d*x+c))^8,x)","F"
623,0,0,136,0.276000," ","int((e*cos(d*x+c))^p*(a+b*sin(d*x+c))^(5/2),x)","\int \left(e \cos \left(d x +c \right)\right)^{p} \left(a +b \sin \left(d x +c \right)\right)^{\frac{5}{2}}\, dx"," ",0,"int((e*cos(d*x+c))^p*(a+b*sin(d*x+c))^(5/2),x)","F"
624,0,0,136,0.219000," ","int((e*cos(d*x+c))^p*(a+b*sin(d*x+c))^(3/2),x)","\int \left(e \cos \left(d x +c \right)\right)^{p} \left(a +b \sin \left(d x +c \right)\right)^{\frac{3}{2}}\, dx"," ",0,"int((e*cos(d*x+c))^p*(a+b*sin(d*x+c))^(3/2),x)","F"
625,0,0,136,0.215000," ","int((e*cos(d*x+c))^p*(a+b*sin(d*x+c))^(1/2),x)","\int \left(e \cos \left(d x +c \right)\right)^{p} \sqrt{a +b \sin \left(d x +c \right)}\, dx"," ",0,"int((e*cos(d*x+c))^p*(a+b*sin(d*x+c))^(1/2),x)","F"
626,0,0,136,0.174000," ","int((e*cos(d*x+c))^p/(a+b*sin(d*x+c))^(1/2),x)","\int \frac{\left(e \cos \left(d x +c \right)\right)^{p}}{\sqrt{a +b \sin \left(d x +c \right)}}\, dx"," ",0,"int((e*cos(d*x+c))^p/(a+b*sin(d*x+c))^(1/2),x)","F"
627,0,0,136,0.197000," ","int((e*cos(d*x+c))^p/(a+b*sin(d*x+c))^(3/2),x)","\int \frac{\left(e \cos \left(d x +c \right)\right)^{p}}{\left(a +b \sin \left(d x +c \right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int((e*cos(d*x+c))^p/(a+b*sin(d*x+c))^(3/2),x)","F"
628,0,0,136,0.181000," ","int((e*cos(d*x+c))^p/(a+b*sin(d*x+c))^(5/2),x)","\int \frac{\left(e \cos \left(d x +c \right)\right)^{p}}{\left(a +b \sin \left(d x +c \right)\right)^{\frac{5}{2}}}\, dx"," ",0,"int((e*cos(d*x+c))^p/(a+b*sin(d*x+c))^(5/2),x)","F"
629,0,0,146,1.331000," ","int((e*cos(d*x+c))^p*(a+b*sin(d*x+c))^m,x)","\int \left(e \cos \left(d x +c \right)\right)^{p} \left(a +b \sin \left(d x +c \right)\right)^{m}\, dx"," ",0,"int((e*cos(d*x+c))^p*(a+b*sin(d*x+c))^m,x)","F"
630,0,0,254,0.735000," ","int(cos(d*x+c)^7*(a+b*sin(d*x+c))^m,x)","\int \left(\cos^{7}\left(d x +c \right)\right) \left(a +b \sin \left(d x +c \right)\right)^{m}\, dx"," ",0,"int(cos(d*x+c)^7*(a+b*sin(d*x+c))^m,x)","F"
631,0,0,167,0.613000," ","int(cos(d*x+c)^5*(a+b*sin(d*x+c))^m,x)","\int \left(\cos^{5}\left(d x +c \right)\right) \left(a +b \sin \left(d x +c \right)\right)^{m}\, dx"," ",0,"int(cos(d*x+c)^5*(a+b*sin(d*x+c))^m,x)","F"
632,0,0,92,0.489000," ","int(cos(d*x+c)^3*(a+b*sin(d*x+c))^m,x)","\int \left(\cos^{3}\left(d x +c \right)\right) \left(a +b \sin \left(d x +c \right)\right)^{m}\, dx"," ",0,"int(cos(d*x+c)^3*(a+b*sin(d*x+c))^m,x)","F"
633,1,27,26,0.027000," ","int(cos(d*x+c)*(a+b*sin(d*x+c))^m,x)","\frac{\left(a +b \sin \left(d x +c \right)\right)^{1+m}}{b d \left(1+m \right)}"," ",0,"(a+b*sin(d*x+c))^(1+m)/b/d/(1+m)","A"
634,0,0,115,1.010000," ","int(sec(d*x+c)*(a+b*sin(d*x+c))^m,x)","\int \sec \left(d x +c \right) \left(a +b \sin \left(d x +c \right)\right)^{m}\, dx"," ",0,"int(sec(d*x+c)*(a+b*sin(d*x+c))^m,x)","F"
635,0,0,181,0.515000," ","int(sec(d*x+c)^3*(a+b*sin(d*x+c))^m,x)","\int \left(\sec^{3}\left(d x +c \right)\right) \left(a +b \sin \left(d x +c \right)\right)^{m}\, dx"," ",0,"int(sec(d*x+c)^3*(a+b*sin(d*x+c))^m,x)","F"
636,0,0,301,0.845000," ","int(sec(d*x+c)^5*(a+b*sin(d*x+c))^m,x)","\int \left(\sec^{5}\left(d x +c \right)\right) \left(a +b \sin \left(d x +c \right)\right)^{m}\, dx"," ",0,"int(sec(d*x+c)^5*(a+b*sin(d*x+c))^m,x)","F"
637,0,0,125,0.391000," ","int(cos(d*x+c)^4*(a+b*sin(d*x+c))^m,x)","\int \left(\cos^{4}\left(d x +c \right)\right) \left(a +b \sin \left(d x +c \right)\right)^{m}\, dx"," ",0,"int(cos(d*x+c)^4*(a+b*sin(d*x+c))^m,x)","F"
638,0,0,123,0.313000," ","int(cos(d*x+c)^2*(a+b*sin(d*x+c))^m,x)","\int \left(\cos^{2}\left(d x +c \right)\right) \left(a +b \sin \left(d x +c \right)\right)^{m}\, dx"," ",0,"int(cos(d*x+c)^2*(a+b*sin(d*x+c))^m,x)","F"
639,0,0,125,0.149000," ","int(sec(d*x+c)^2*(a+b*sin(d*x+c))^m,x)","\int \left(\sec^{2}\left(d x +c \right)\right) \left(a +b \sin \left(d x +c \right)\right)^{m}\, dx"," ",0,"int(sec(d*x+c)^2*(a+b*sin(d*x+c))^m,x)","F"
640,0,0,125,0.328000," ","int(sec(d*x+c)^4*(a+b*sin(d*x+c))^m,x)","\int \left(\sec^{4}\left(d x +c \right)\right) \left(a +b \sin \left(d x +c \right)\right)^{m}\, dx"," ",0,"int(sec(d*x+c)^4*(a+b*sin(d*x+c))^m,x)","F"
641,0,0,128,0.204000," ","int((e*cos(d*x+c))^(5/2)*(a+b*sin(d*x+c))^m,x)","\int \left(e \cos \left(d x +c \right)\right)^{\frac{5}{2}} \left(a +b \sin \left(d x +c \right)\right)^{m}\, dx"," ",0,"int((e*cos(d*x+c))^(5/2)*(a+b*sin(d*x+c))^m,x)","F"
642,0,0,128,0.188000," ","int((e*cos(d*x+c))^(3/2)*(a+b*sin(d*x+c))^m,x)","\int \left(e \cos \left(d x +c \right)\right)^{\frac{3}{2}} \left(a +b \sin \left(d x +c \right)\right)^{m}\, dx"," ",0,"int((e*cos(d*x+c))^(3/2)*(a+b*sin(d*x+c))^m,x)","F"
643,0,0,128,0.204000," ","int((e*cos(d*x+c))^(1/2)*(a+b*sin(d*x+c))^m,x)","\int \sqrt{e \cos \left(d x +c \right)}\, \left(a +b \sin \left(d x +c \right)\right)^{m}\, dx"," ",0,"int((e*cos(d*x+c))^(1/2)*(a+b*sin(d*x+c))^m,x)","F"
644,0,0,128,0.176000," ","int((a+b*sin(d*x+c))^m/(e*cos(d*x+c))^(1/2),x)","\int \frac{\left(a +b \sin \left(d x +c \right)\right)^{m}}{\sqrt{e \cos \left(d x +c \right)}}\, dx"," ",0,"int((a+b*sin(d*x+c))^m/(e*cos(d*x+c))^(1/2),x)","F"
645,0,0,128,0.173000," ","int((a+b*sin(d*x+c))^m/(e*cos(d*x+c))^(3/2),x)","\int \frac{\left(a +b \sin \left(d x +c \right)\right)^{m}}{\left(e \cos \left(d x +c \right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int((a+b*sin(d*x+c))^m/(e*cos(d*x+c))^(3/2),x)","F"
646,0,0,128,0.181000," ","int((a+b*sin(d*x+c))^m/(e*cos(d*x+c))^(5/2),x)","\int \frac{\left(a +b \sin \left(d x +c \right)\right)^{m}}{\left(e \cos \left(d x +c \right)\right)^{\frac{5}{2}}}\, dx"," ",0,"int((a+b*sin(d*x+c))^m/(e*cos(d*x+c))^(5/2),x)","F"
647,0,0,566,0.365000," ","int((e*cos(d*x+c))^(-4-m)*(a+b*sin(d*x+c))^m,x)","\int \left(e \cos \left(d x +c \right)\right)^{-4-m} \left(a +b \sin \left(d x +c \right)\right)^{m}\, dx"," ",0,"int((e*cos(d*x+c))^(-4-m)*(a+b*sin(d*x+c))^m,x)","F"
648,0,0,309,0.332000," ","int((e*cos(d*x+c))^(-3-m)*(a+b*sin(d*x+c))^m,x)","\int \left(e \cos \left(d x +c \right)\right)^{-3-m} \left(a +b \sin \left(d x +c \right)\right)^{m}\, dx"," ",0,"int((e*cos(d*x+c))^(-3-m)*(a+b*sin(d*x+c))^m,x)","F"
649,0,0,185,0.336000," ","int((e*cos(d*x+c))^(-2-m)*(a+b*sin(d*x+c))^m,x)","\int \left(e \cos \left(d x +c \right)\right)^{-2-m} \left(a +b \sin \left(d x +c \right)\right)^{m}\, dx"," ",0,"int((e*cos(d*x+c))^(-2-m)*(a+b*sin(d*x+c))^m,x)","F"
650,0,0,130,0.322000," ","int((e*cos(d*x+c))^(-1-m)*(a+b*sin(d*x+c))^m,x)","\int \left(e \cos \left(d x +c \right)\right)^{-1-m} \left(a +b \sin \left(d x +c \right)\right)^{m}\, dx"," ",0,"int((e*cos(d*x+c))^(-1-m)*(a+b*sin(d*x+c))^m,x)","F"
651,0,0,148,0.594000," ","int((a+b*sin(d*x+c))^m/((e*cos(d*x+c))^m),x)","\int \left(a +b \sin \left(d x +c \right)\right)^{m} \left(e \cos \left(d x +c \right)\right)^{-m}\, dx"," ",0,"int((a+b*sin(d*x+c))^m/((e*cos(d*x+c))^m),x)","F"
652,0,0,138,0.327000," ","int((e*cos(d*x+c))^(1-m)*(a+b*sin(d*x+c))^m,x)","\int \left(e \cos \left(d x +c \right)\right)^{1-m} \left(a +b \sin \left(d x +c \right)\right)^{m}\, dx"," ",0,"int((e*cos(d*x+c))^(1-m)*(a+b*sin(d*x+c))^m,x)","F"
653,0,0,148,0.328000," ","int((e*cos(d*x+c))^(2-m)*(a+b*sin(d*x+c))^m,x)","\int \left(e \cos \left(d x +c \right)\right)^{2-m} \left(a +b \sin \left(d x +c \right)\right)^{m}\, dx"," ",0,"int((e*cos(d*x+c))^(2-m)*(a+b*sin(d*x+c))^m,x)","F"