1,1,86,103,0.098000," ","int((a+a*cos(d*x+c))^(7/2),x)","\frac{16 a^{4} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \left(5 \left(\cos^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+6 \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+8 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+16\right) \sqrt{2}}{35 \sqrt{a \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, d}"," ",0,"16/35*a^4*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)*(5*cos(1/2*d*x+1/2*c)^6+6*cos(1/2*d*x+1/2*c)^4+8*cos(1/2*d*x+1/2*c)^2+16)*2^(1/2)/(a*cos(1/2*d*x+1/2*c)^2)^(1/2)/d","A"
2,1,73,77,0.106000," ","int((a+a*cos(d*x+c))^(5/2),x)","\frac{8 a^{3} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \left(3 \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+4 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+8\right) \sqrt{2}}{15 \sqrt{a \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, d}"," ",0,"8/15*a^3*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)*(3*cos(1/2*d*x+1/2*c)^4+4*cos(1/2*d*x+1/2*c)^2+8)*2^(1/2)/(a*cos(1/2*d*x+1/2*c)^2)^(1/2)/d","A"
3,1,58,51,0.117000," ","int((a+a*cos(d*x+c))^(3/2),x)","\frac{4 a^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)+2\right) \sqrt{2}}{3 \sqrt{a \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, d}"," ",0,"4/3*a^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)*(cos(1/2*d*x+1/2*c)^2+2)*2^(1/2)/(a*cos(1/2*d*x+1/2*c)^2)^(1/2)/d","A"
4,1,43,24,0.000000," ","int((a+a*cos(d*x+c))^(1/2),x)","\frac{2 a \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2}}{\sqrt{a \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, d}"," ",0,"2*a*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)*2^(1/2)/(a*cos(1/2*d*x+1/2*c)^2)^(1/2)/d","A"
5,1,54,37,0.000000," ","int(1/(a+a*cos(d*x+c))^(1/2),x)","\frac{\sqrt{2}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \mathrm{am}^{-1}\left(\frac{d x}{2}+\frac{c}{2}| 1\right)}{d \sqrt{a \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \mathrm{csgn}\left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}"," ",0,"1/d*2^(1/2)/(a*cos(1/2*d*x+1/2*c)^2)^(1/2)/csgn(cos(1/2*d*x+1/2*c))*cos(1/2*d*x+1/2*c)*InverseJacobiAM(1/2*d*x+1/2*c,1)","C"
6,1,138,62,0.150000," ","int(1/(a+a*cos(d*x+c))^(3/2),x)","\frac{\sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(\sqrt{2}\, \ln \left(\frac{4 \sqrt{a}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}+4 a}{\cos \left(\frac{d x}{2}+\frac{c}{2}\right)}\right) a \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}\right)}{4 a^{\frac{5}{2}} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{a \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, d}"," ",0,"1/4/a^(5/2)/cos(1/2*d*x+1/2*c)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*(2^(1/2)*ln(2*(2*a^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)+2*a)/cos(1/2*d*x+1/2*c))*a*cos(1/2*d*x+1/2*c)^2+2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2))/sin(1/2*d*x+1/2*c)/(a*cos(1/2*d*x+1/2*c)^2)^(1/2)/d","B"
7,1,174,88,0.164000," ","int(1/(a+a*cos(d*x+c))^(5/2),x)","\frac{\sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(3 \sqrt{2}\, \ln \left(\frac{4 \sqrt{a}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}+4 a}{\cos \left(\frac{d x}{2}+\frac{c}{2}\right)}\right) a \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+3 \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \sqrt{a}+2 \sqrt{2}\, \sqrt{a \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{a}\right)}{32 a^{\frac{7}{2}} \cos \left(\frac{d x}{2}+\frac{c}{2}\right)^{3} \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{a \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, d}"," ",0,"1/32/a^(7/2)/cos(1/2*d*x+1/2*c)^3*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*(3*2^(1/2)*ln(2*(2*a^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)+2*a)/cos(1/2*d*x+1/2*c))*a*cos(1/2*d*x+1/2*c)^4+3*2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*cos(1/2*d*x+1/2*c)^2*a^(1/2)+2*2^(1/2)*(a*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^(1/2))/sin(1/2*d*x+1/2*c)/(a*cos(1/2*d*x+1/2*c)^2)^(1/2)/d","A"
8,0,0,53,0.078000," ","int((a+a*cos(d*x+c))^(4/3),x)","\int \left(a +a \cos \left(d x +c \right)\right)^{\frac{4}{3}}\, dx"," ",0,"int((a+a*cos(d*x+c))^(4/3),x)","F"
9,0,0,52,0.146000," ","int((a+a*cos(d*x+c))^(2/3),x)","\int \left(a +a \cos \left(d x +c \right)\right)^{\frac{2}{3}}\, dx"," ",0,"int((a+a*cos(d*x+c))^(2/3),x)","F"
10,0,0,51,0.087000," ","int((a+a*cos(d*x+c))^(1/3),x)","\int \left(a +a \cos \left(d x +c \right)\right)^{\frac{1}{3}}\, dx"," ",0,"int((a+a*cos(d*x+c))^(1/3),x)","F"
11,0,0,51,0.099000," ","int(1/(a+a*cos(d*x+c))^(1/3),x)","\int \frac{1}{\left(a +a \cos \left(d x +c \right)\right)^{\frac{1}{3}}}\, dx"," ",0,"int(1/(a+a*cos(d*x+c))^(1/3),x)","F"
12,0,0,52,0.064000," ","int(1/(a+a*cos(d*x+c))^(2/3),x)","\int \frac{1}{\left(a +a \cos \left(d x +c \right)\right)^{\frac{2}{3}}}\, dx"," ",0,"int(1/(a+a*cos(d*x+c))^(2/3),x)","F"
13,0,0,55,0.069000," ","int(1/(a+a*cos(d*x+c))^(4/3),x)","\int \frac{1}{\left(a +a \cos \left(d x +c \right)\right)^{\frac{4}{3}}}\, dx"," ",0,"int(1/(a+a*cos(d*x+c))^(4/3),x)","F"
14,0,0,61,0.334000," ","int((a+a*cos(d*x+c))^n,x)","\int \left(a +a \cos \left(d x +c \right)\right)^{n}\, dx"," ",0,"int((a+a*cos(d*x+c))^n,x)","F"
15,0,0,65,0.355000," ","int((a-a*cos(d*x+c))^n,x)","\int \left(a -a \cos \left(d x +c \right)\right)^{n}\, dx"," ",0,"int((a-a*cos(d*x+c))^n,x)","F"
16,0,0,47,0.252000," ","int((2+2*cos(d*x+c))^n,x)","\int \left(2+2 \cos \left(d x +c \right)\right)^{n}\, dx"," ",0,"int((2+2*cos(d*x+c))^n,x)","F"
17,0,0,50,0.273000," ","int((2-2*cos(d*x+c))^n,x)","\int \left(2-2 \cos \left(d x +c \right)\right)^{n}\, dx"," ",0,"int((2-2*cos(d*x+c))^n,x)","F"
18,1,18,27,0.033000," ","int(1/(5+3*cos(d*x+c)),x)","\frac{\arctan \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2}\right)}{2 d}"," ",0,"1/2/d*arctan(1/2*tan(1/2*d*x+1/2*c))","A"
19,1,48,50,0.037000," ","int(1/(5+3*cos(d*x+c))^2,x)","-\frac{3 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{16 d \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)+4\right)}+\frac{5 \arctan \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2}\right)}{32 d}"," ",0,"-3/16/d*tan(1/2*d*x+1/2*c)/(tan(1/2*d*x+1/2*c)^2+4)+5/32/d*arctan(1/2*tan(1/2*d*x+1/2*c))","A"
20,1,79,73,0.041000," ","int(1/(5+3*cos(d*x+c))^3,x)","-\frac{69 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{512 d \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)+4\right)^{2}}-\frac{51 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{128 d \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)+4\right)^{2}}+\frac{59 \arctan \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2}\right)}{1024 d}"," ",0,"-69/512/d/(tan(1/2*d*x+1/2*c)^2+4)^2*tan(1/2*d*x+1/2*c)^3-51/128/d/(tan(1/2*d*x+1/2*c)^2+4)^2*tan(1/2*d*x+1/2*c)+59/1024/d*arctan(1/2*tan(1/2*d*x+1/2*c))","A"
21,1,110,96,0.033000," ","int(1/(5+3*cos(d*x+c))^4,x)","-\frac{639 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{8192 d \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)+4\right)^{3}}-\frac{117 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{256 d \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)+4\right)^{3}}-\frac{369 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{512 d \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)+4\right)^{3}}+\frac{385 \arctan \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2}\right)}{16384 d}"," ",0,"-639/8192/d/(tan(1/2*d*x+1/2*c)^2+4)^3*tan(1/2*d*x+1/2*c)^5-117/256/d/(tan(1/2*d*x+1/2*c)^2+4)^3*tan(1/2*d*x+1/2*c)^3-369/512/d/(tan(1/2*d*x+1/2*c)^2+4)^3*tan(1/2*d*x+1/2*c)+385/16384/d*arctan(1/2*tan(1/2*d*x+1/2*c))","A"
22,1,18,29,0.027000," ","int(1/(5-3*cos(d*x+c)),x)","\frac{\arctan \left(2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{2 d}"," ",0,"1/2/d*arctan(2*tan(1/2*d*x+1/2*c))","A"
23,1,48,52,0.043000," ","int(1/(5-3*cos(d*x+c))^2,x)","\frac{3 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{64 d \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)+\frac{1}{4}\right)}+\frac{5 \arctan \left(2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{32 d}"," ",0,"3/64/d*tan(1/2*d*x+1/2*c)/(tan(1/2*d*x+1/2*c)^2+1/4)+5/32/d*arctan(2*tan(1/2*d*x+1/2*c))","A"
24,1,83,75,0.034000," ","int(1/(5-3*cos(d*x+c))^3,x)","\frac{51 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{128 d \left(4 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right)^{2}}+\frac{69 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{512 d \left(4 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right)^{2}}+\frac{59 \arctan \left(2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{1024 d}"," ",0,"51/128/d/(4*tan(1/2*d*x+1/2*c)^2+1)^2*tan(1/2*d*x+1/2*c)^3+69/512/d/(4*tan(1/2*d*x+1/2*c)^2+1)^2*tan(1/2*d*x+1/2*c)+59/1024/d*arctan(2*tan(1/2*d*x+1/2*c))","A"
25,1,116,98,0.045000," ","int(1/(5-3*cos(d*x+c))^4,x)","\frac{369 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{512 d \left(4 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right)^{3}}+\frac{117 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{256 d \left(4 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right)^{3}}+\frac{639 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{8192 d \left(4 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right)^{3}}+\frac{385 \arctan \left(2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{16384 d}"," ",0,"369/512/d/(4*tan(1/2*d*x+1/2*c)^2+1)^3*tan(1/2*d*x+1/2*c)^5+117/256/d/(4*tan(1/2*d*x+1/2*c)^2+1)^3*tan(1/2*d*x+1/2*c)^3+639/8192/d/(4*tan(1/2*d*x+1/2*c)^2+1)^3*tan(1/2*d*x+1/2*c)+385/16384/d*arctan(2*tan(1/2*d*x+1/2*c))","A"
26,1,18,29,0.030000," ","int(1/(-5+3*cos(d*x+c)),x)","-\frac{\arctan \left(2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{2 d}"," ",0,"-1/2/d*arctan(2*tan(1/2*d*x+1/2*c))","A"
27,1,48,52,0.036000," ","int(1/(-5+3*cos(d*x+c))^2,x)","\frac{3 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{64 d \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)+\frac{1}{4}\right)}+\frac{5 \arctan \left(2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{32 d}"," ",0,"3/64/d*tan(1/2*d*x+1/2*c)/(tan(1/2*d*x+1/2*c)^2+1/4)+5/32/d*arctan(2*tan(1/2*d*x+1/2*c))","A"
28,1,83,75,0.038000," ","int(1/(-5+3*cos(d*x+c))^3,x)","-\frac{51 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{128 d \left(4 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right)^{2}}-\frac{69 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{512 d \left(4 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right)^{2}}-\frac{59 \arctan \left(2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{1024 d}"," ",0,"-51/128/d/(4*tan(1/2*d*x+1/2*c)^2+1)^2*tan(1/2*d*x+1/2*c)^3-69/512/d/(4*tan(1/2*d*x+1/2*c)^2+1)^2*tan(1/2*d*x+1/2*c)-59/1024/d*arctan(2*tan(1/2*d*x+1/2*c))","A"
29,1,116,98,0.040000," ","int(1/(-5+3*cos(d*x+c))^4,x)","\frac{369 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{512 d \left(4 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right)^{3}}+\frac{117 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{256 d \left(4 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right)^{3}}+\frac{639 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{8192 d \left(4 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right)^{3}}+\frac{385 \arctan \left(2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{16384 d}"," ",0,"369/512/d/(4*tan(1/2*d*x+1/2*c)^2+1)^3*tan(1/2*d*x+1/2*c)^5+117/256/d/(4*tan(1/2*d*x+1/2*c)^2+1)^3*tan(1/2*d*x+1/2*c)^3+639/8192/d/(4*tan(1/2*d*x+1/2*c)^2+1)^3*tan(1/2*d*x+1/2*c)+385/16384/d*arctan(2*tan(1/2*d*x+1/2*c))","A"
30,1,18,27,0.032000," ","int(1/(-5-3*cos(d*x+c)),x)","-\frac{\arctan \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2}\right)}{2 d}"," ",0,"-1/2/d*arctan(1/2*tan(1/2*d*x+1/2*c))","A"
31,1,48,50,0.041000," ","int(1/(-5-3*cos(d*x+c))^2,x)","-\frac{3 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{16 d \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)+4\right)}+\frac{5 \arctan \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2}\right)}{32 d}"," ",0,"-3/16/d*tan(1/2*d*x+1/2*c)/(tan(1/2*d*x+1/2*c)^2+4)+5/32/d*arctan(1/2*tan(1/2*d*x+1/2*c))","A"
32,1,79,73,0.037000," ","int(1/(-5-3*cos(d*x+c))^3,x)","\frac{69 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{512 d \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)+4\right)^{2}}+\frac{51 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{128 d \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)+4\right)^{2}}-\frac{59 \arctan \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2}\right)}{1024 d}"," ",0,"69/512/d/(tan(1/2*d*x+1/2*c)^2+4)^2*tan(1/2*d*x+1/2*c)^3+51/128/d/(tan(1/2*d*x+1/2*c)^2+4)^2*tan(1/2*d*x+1/2*c)-59/1024/d*arctan(1/2*tan(1/2*d*x+1/2*c))","A"
33,1,110,96,0.042000," ","int(1/(-5-3*cos(d*x+c))^4,x)","-\frac{639 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{8192 d \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)+4\right)^{3}}-\frac{117 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{256 d \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)+4\right)^{3}}-\frac{369 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{512 d \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)+4\right)^{3}}+\frac{385 \arctan \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2}\right)}{16384 d}"," ",0,"-639/8192/d/(tan(1/2*d*x+1/2*c)^2+4)^3*tan(1/2*d*x+1/2*c)^5-117/256/d/(tan(1/2*d*x+1/2*c)^2+4)^3*tan(1/2*d*x+1/2*c)^3-369/512/d/(tan(1/2*d*x+1/2*c)^2+4)^3*tan(1/2*d*x+1/2*c)+385/16384/d*arctan(1/2*tan(1/2*d*x+1/2*c))","A"
34,1,36,57,0.033000," ","int(1/(3+5*cos(d*x+c)),x)","\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2\right)}{4 d}-\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-2\right)}{4 d}"," ",0,"1/4/d*ln(tan(1/2*d*x+1/2*c)+2)-1/4/d*ln(tan(1/2*d*x+1/2*c)-2)","A"
35,1,72,80,0.037000," ","int(1/(3+5*cos(d*x+c))^2,x)","-\frac{5}{32 d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2\right)}-\frac{3 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2\right)}{64 d}-\frac{5}{32 d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-2\right)}+\frac{3 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-2\right)}{64 d}"," ",0,"-5/32/d/(tan(1/2*d*x+1/2*c)+2)-3/64/d*ln(tan(1/2*d*x+1/2*c)+2)-5/32/d/(tan(1/2*d*x+1/2*c)-2)+3/64/d*ln(tan(1/2*d*x+1/2*c)-2)","A"
36,1,108,103,0.036000," ","int(1/(3+5*cos(d*x+c))^3,x)","-\frac{25}{512 d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2\right)^{2}}+\frac{85}{1024 d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2\right)}+\frac{43 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2\right)}{2048 d}+\frac{25}{512 d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-2\right)^{2}}+\frac{85}{1024 d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-2\right)}-\frac{43 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-2\right)}{2048 d}"," ",0,"-25/512/d/(tan(1/2*d*x+1/2*c)+2)^2+85/1024/d/(tan(1/2*d*x+1/2*c)+2)+43/2048/d*ln(tan(1/2*d*x+1/2*c)+2)+25/512/d/(tan(1/2*d*x+1/2*c)-2)^2+85/1024/d/(tan(1/2*d*x+1/2*c)-2)-43/2048/d*ln(tan(1/2*d*x+1/2*c)-2)","A"
37,1,144,126,0.038000," ","int(1/(3+5*cos(d*x+c))^4,x)","-\frac{125}{6144 d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2\right)^{3}}+\frac{175}{4096 d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2\right)^{2}}-\frac{745}{16384 d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2\right)}-\frac{279 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2\right)}{32768 d}-\frac{125}{6144 d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-2\right)^{3}}-\frac{175}{4096 d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-2\right)^{2}}-\frac{745}{16384 d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-2\right)}+\frac{279 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-2\right)}{32768 d}"," ",0,"-125/6144/d/(tan(1/2*d*x+1/2*c)+2)^3+175/4096/d/(tan(1/2*d*x+1/2*c)+2)^2-745/16384/d/(tan(1/2*d*x+1/2*c)+2)-279/32768/d*ln(tan(1/2*d*x+1/2*c)+2)-125/6144/d/(tan(1/2*d*x+1/2*c)-2)^3-175/4096/d/(tan(1/2*d*x+1/2*c)-2)^2-745/16384/d/(tan(1/2*d*x+1/2*c)-2)+279/32768/d*ln(tan(1/2*d*x+1/2*c)-2)","A"
38,1,40,55,0.034000," ","int(1/(3-5*cos(d*x+c)),x)","-\frac{\ln \left(2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}{4 d}+\frac{\ln \left(2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}{4 d}"," ",0,"-1/4/d*ln(2*tan(1/2*d*x+1/2*c)+1)+1/4/d*ln(2*tan(1/2*d*x+1/2*c)-1)","A"
39,1,80,78,0.040000," ","int(1/(3-5*cos(d*x+c))^2,x)","-\frac{5}{64 d \left(2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}+\frac{3 \ln \left(2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}{64 d}-\frac{5}{64 d \left(2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{3 \ln \left(2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}{64 d}"," ",0,"-5/64/d/(2*tan(1/2*d*x+1/2*c)+1)+3/64/d*ln(2*tan(1/2*d*x+1/2*c)+1)-5/64/d/(2*tan(1/2*d*x+1/2*c)-1)-3/64/d*ln(2*tan(1/2*d*x+1/2*c)-1)","A"
40,1,120,101,0.042000," ","int(1/(3-5*cos(d*x+c))^3,x)","\frac{25}{2048 d \left(2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}+\frac{35}{2048 d \left(2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}-\frac{43 \ln \left(2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}{2048 d}-\frac{25}{2048 d \left(2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}+\frac{35}{2048 d \left(2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}+\frac{43 \ln \left(2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}{2048 d}"," ",0,"25/2048/d/(2*tan(1/2*d*x+1/2*c)+1)^2+35/2048/d/(2*tan(1/2*d*x+1/2*c)+1)-43/2048/d*ln(2*tan(1/2*d*x+1/2*c)+1)-25/2048/d/(2*tan(1/2*d*x+1/2*c)-1)^2+35/2048/d/(2*tan(1/2*d*x+1/2*c)-1)+43/2048/d*ln(2*tan(1/2*d*x+1/2*c)-1)","A"
41,1,160,124,0.042000," ","int(1/(3-5*cos(d*x+c))^4,x)","-\frac{125}{49152 d \left(2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}-\frac{25}{8192 d \left(2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}-\frac{295}{32768 d \left(2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}+\frac{279 \ln \left(2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}{32768 d}-\frac{125}{49152 d \left(2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{3}}+\frac{25}{8192 d \left(2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}-\frac{295}{32768 d \left(2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{279 \ln \left(2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}{32768 d}"," ",0,"-125/49152/d/(2*tan(1/2*d*x+1/2*c)+1)^3-25/8192/d/(2*tan(1/2*d*x+1/2*c)+1)^2-295/32768/d/(2*tan(1/2*d*x+1/2*c)+1)+279/32768/d*ln(2*tan(1/2*d*x+1/2*c)+1)-125/49152/d/(2*tan(1/2*d*x+1/2*c)-1)^3+25/8192/d/(2*tan(1/2*d*x+1/2*c)-1)^2-295/32768/d/(2*tan(1/2*d*x+1/2*c)-1)-279/32768/d*ln(2*tan(1/2*d*x+1/2*c)-1)","A"
42,1,40,55,0.029000," ","int(1/(-3+5*cos(d*x+c)),x)","\frac{\ln \left(2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}{4 d}-\frac{\ln \left(2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}{4 d}"," ",0,"1/4/d*ln(2*tan(1/2*d*x+1/2*c)+1)-1/4/d*ln(2*tan(1/2*d*x+1/2*c)-1)","A"
43,1,80,78,0.037000," ","int(1/(-3+5*cos(d*x+c))^2,x)","-\frac{5}{64 d \left(2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}+\frac{3 \ln \left(2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}{64 d}-\frac{5}{64 d \left(2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{3 \ln \left(2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}{64 d}"," ",0,"-5/64/d/(2*tan(1/2*d*x+1/2*c)+1)+3/64/d*ln(2*tan(1/2*d*x+1/2*c)+1)-5/64/d/(2*tan(1/2*d*x+1/2*c)-1)-3/64/d*ln(2*tan(1/2*d*x+1/2*c)-1)","A"
44,1,120,101,0.040000," ","int(1/(-3+5*cos(d*x+c))^3,x)","-\frac{25}{2048 d \left(2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}-\frac{35}{2048 d \left(2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}+\frac{43 \ln \left(2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}{2048 d}+\frac{25}{2048 d \left(2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}-\frac{35}{2048 d \left(2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{43 \ln \left(2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}{2048 d}"," ",0,"-25/2048/d/(2*tan(1/2*d*x+1/2*c)+1)^2-35/2048/d/(2*tan(1/2*d*x+1/2*c)+1)+43/2048/d*ln(2*tan(1/2*d*x+1/2*c)+1)+25/2048/d/(2*tan(1/2*d*x+1/2*c)-1)^2-35/2048/d/(2*tan(1/2*d*x+1/2*c)-1)-43/2048/d*ln(2*tan(1/2*d*x+1/2*c)-1)","A"
45,1,160,124,0.039000," ","int(1/(-3+5*cos(d*x+c))^4,x)","-\frac{125}{49152 d \left(2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}-\frac{25}{8192 d \left(2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}-\frac{295}{32768 d \left(2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}+\frac{279 \ln \left(2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}{32768 d}-\frac{125}{49152 d \left(2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{3}}+\frac{25}{8192 d \left(2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}-\frac{295}{32768 d \left(2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{279 \ln \left(2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}{32768 d}"," ",0,"-125/49152/d/(2*tan(1/2*d*x+1/2*c)+1)^3-25/8192/d/(2*tan(1/2*d*x+1/2*c)+1)^2-295/32768/d/(2*tan(1/2*d*x+1/2*c)+1)+279/32768/d*ln(2*tan(1/2*d*x+1/2*c)+1)-125/49152/d/(2*tan(1/2*d*x+1/2*c)-1)^3+25/8192/d/(2*tan(1/2*d*x+1/2*c)-1)^2-295/32768/d/(2*tan(1/2*d*x+1/2*c)-1)-279/32768/d*ln(2*tan(1/2*d*x+1/2*c)-1)","A"
46,1,36,57,0.033000," ","int(1/(-3-5*cos(d*x+c)),x)","-\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2\right)}{4 d}+\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-2\right)}{4 d}"," ",0,"-1/4/d*ln(tan(1/2*d*x+1/2*c)+2)+1/4/d*ln(tan(1/2*d*x+1/2*c)-2)","A"
47,1,72,80,0.040000," ","int(1/(-3-5*cos(d*x+c))^2,x)","-\frac{5}{32 d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2\right)}-\frac{3 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2\right)}{64 d}-\frac{5}{32 d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-2\right)}+\frac{3 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-2\right)}{64 d}"," ",0,"-5/32/d/(tan(1/2*d*x+1/2*c)+2)-3/64/d*ln(tan(1/2*d*x+1/2*c)+2)-5/32/d/(tan(1/2*d*x+1/2*c)-2)+3/64/d*ln(tan(1/2*d*x+1/2*c)-2)","A"
48,1,108,103,0.036000," ","int(1/(-3-5*cos(d*x+c))^3,x)","\frac{25}{512 d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2\right)^{2}}-\frac{85}{1024 d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2\right)}-\frac{43 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2\right)}{2048 d}-\frac{25}{512 d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-2\right)^{2}}-\frac{85}{1024 d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-2\right)}+\frac{43 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-2\right)}{2048 d}"," ",0,"25/512/d/(tan(1/2*d*x+1/2*c)+2)^2-85/1024/d/(tan(1/2*d*x+1/2*c)+2)-43/2048/d*ln(tan(1/2*d*x+1/2*c)+2)-25/512/d/(tan(1/2*d*x+1/2*c)-2)^2-85/1024/d/(tan(1/2*d*x+1/2*c)-2)+43/2048/d*ln(tan(1/2*d*x+1/2*c)-2)","A"
49,1,144,126,0.043000," ","int(1/(-3-5*cos(d*x+c))^4,x)","-\frac{125}{6144 d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2\right)^{3}}+\frac{175}{4096 d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2\right)^{2}}-\frac{745}{16384 d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2\right)}-\frac{279 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2\right)}{32768 d}-\frac{125}{6144 d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-2\right)^{3}}-\frac{175}{4096 d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-2\right)^{2}}-\frac{745}{16384 d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-2\right)}+\frac{279 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-2\right)}{32768 d}"," ",0,"-125/6144/d/(tan(1/2*d*x+1/2*c)+2)^3+175/4096/d/(tan(1/2*d*x+1/2*c)+2)^2-745/16384/d/(tan(1/2*d*x+1/2*c)+2)-279/32768/d*ln(tan(1/2*d*x+1/2*c)+2)-125/6144/d/(tan(1/2*d*x+1/2*c)-2)^3-175/4096/d/(tan(1/2*d*x+1/2*c)-2)^2-745/16384/d/(tan(1/2*d*x+1/2*c)-2)+279/32768/d*ln(tan(1/2*d*x+1/2*c)-2)","A"
50,1,662,235,0.305000," ","int((a+b*cos(d*x+c))^(5/2),x)","-\frac{2 \sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(24 \left(\cos^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{3}+56 \left(\cos^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a \,b^{2}-48 \left(\cos^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{3}+22 \left(\cos^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{2} b -84 \left(\cos^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a \,b^{2}+30 \left(\cos^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{3}-8 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{\frac{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b}{a -b}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{3}+8 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{\frac{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b}{a -b}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a \,b^{2}+23 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{\frac{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b}{a -b}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{3}-23 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{\frac{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b}{a -b}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{2} b +9 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{\frac{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b}{a -b}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a \,b^{2}-9 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{\frac{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b}{a -b}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) b^{3}-22 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) a^{2} b +28 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) a \,b^{2}-6 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) b^{3}\right)}{15 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(a +b \right) \left(\sin^{2}\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) b +a +b}\, d}"," ",0,"-2/15*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(24*cos(1/2*d*x+1/2*c)^7*b^3+56*cos(1/2*d*x+1/2*c)^5*a*b^2-48*cos(1/2*d*x+1/2*c)^5*b^3+22*cos(1/2*d*x+1/2*c)^3*a^2*b-84*cos(1/2*d*x+1/2*c)^3*a*b^2+30*cos(1/2*d*x+1/2*c)^3*b^3-8*(sin(1/2*d*x+1/2*c)^2)^(1/2)*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)/(a-b))^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a^3+8*(sin(1/2*d*x+1/2*c)^2)^(1/2)*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)/(a-b))^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a*b^2+23*(sin(1/2*d*x+1/2*c)^2)^(1/2)*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)/(a-b))^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a^3-23*(sin(1/2*d*x+1/2*c)^2)^(1/2)*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)/(a-b))^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a^2*b+9*(sin(1/2*d*x+1/2*c)^2)^(1/2)*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)/(a-b))^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a*b^2-9*(sin(1/2*d*x+1/2*c)^2)^(1/2)*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)/(a-b))^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*b^3-22*cos(1/2*d*x+1/2*c)*a^2*b+28*cos(1/2*d*x+1/2*c)*a*b^2-6*cos(1/2*d*x+1/2*c)*b^3)/(-2*sin(1/2*d*x+1/2*c)^4*b+(a+b)*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*b+a+b)^(1/2)/d","B"
51,1,450,199,0.246000," ","int((a+b*cos(d*x+c))^(3/2),x)","-\frac{2 \sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(4 \left(\cos^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{2}+2 \left(\cos^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a b -6 \left(\cos^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{2}-\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{\frac{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b}{a -b}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{2}+\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{\frac{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b}{a -b}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) b^{2}+4 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{\frac{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b}{a -b}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a^{2}-4 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{\frac{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b}{a -b}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) a b -2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) a b +2 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) b^{2}\right)}{3 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(a +b \right) \left(\sin^{2}\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) b +a +b}\, d}"," ",0,"-2/3*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(4*cos(1/2*d*x+1/2*c)^5*b^2+2*cos(1/2*d*x+1/2*c)^3*a*b-6*cos(1/2*d*x+1/2*c)^3*b^2-(sin(1/2*d*x+1/2*c)^2)^(1/2)*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)/(a-b))^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a^2+(sin(1/2*d*x+1/2*c)^2)^(1/2)*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)/(a-b))^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*b^2+4*(sin(1/2*d*x+1/2*c)^2)^(1/2)*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)/(a-b))^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a^2-4*(sin(1/2*d*x+1/2*c)^2)^(1/2)*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)/(a-b))^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*a*b-2*cos(1/2*d*x+1/2*c)*a*b+2*cos(1/2*d*x+1/2*c)*b^2)/(-2*sin(1/2*d*x+1/2*c)^4*b+(a+b)*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*b+a+b)^(1/2)/d","B"
52,1,170,82,0.250000," ","int((a+b*cos(d*x+c))^(1/2),x)","-\frac{2 \sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b \right) \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{\frac{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b}{a -b}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) \left(a -b \right)}{\sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(a +b \right) \left(\sin^{2}\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) b +a +b}\, d}"," ",0,"-2*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)/(a-b))^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*(a-b)/(-2*sin(1/2*d*x+1/2*c)^4*b+(a+b)*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*b+a+b)^(1/2)/d","B"
53,1,75,82,0.104000," ","int(1/(a+b*cos(d*x+c))^(1/2),x)","\frac{2 \sqrt{\frac{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b}{a +b}}\, \mathrm{am}^{-1}\left(\frac{d x}{2}+\frac{c}{2}\bigg| \frac{\sqrt{2}\, \sqrt{b}}{\sqrt{a +b}}\right)}{d \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b}}"," ",0,"2/d/(2*cos(1/2*d*x+1/2*c)^2*b+a-b)^(1/2)*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)/(a+b))^(1/2)*InverseJacobiAM(1/2*d*x+1/2*c,2^(1/2)/(a+b)^(1/2)*b^(1/2))","C"
54,1,217,129,0.488000," ","int(1/(a+b*cos(d*x+c))^(3/2),x)","-\frac{2 \left(\EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-\frac{2 b \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a -b}+\frac{a +b}{a -b}}\, a -\EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-\frac{2 b \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a -b}+\frac{a +b}{a -b}}\, b +2 b \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}{\left(a -b \right) \left(a +b \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) b +a +b}\, d}"," ",0,"-2*(EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*b/(a-b)*sin(1/2*d*x+1/2*c)^2+(a+b)/(a-b))^(1/2)*a-EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*b/(a-b)*sin(1/2*d*x+1/2*c)^2+(a+b)/(a-b))^(1/2)*b+2*b*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2)/(a-b)/(a+b)/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*b+a+b)^(1/2)/d","A"
55,1,489,259,0.579000," ","int(1/(a+b*cos(d*x+c))^(5/2),x)","-\frac{\sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a +b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(\frac{\cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(a +b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}}{3 b \left(a -b \right) \left(a +b \right) \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)+\frac{a -b}{2 b}\right)^{2}}+\frac{16 b \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right) a}{3 \left(a -b \right)^{2} \left(a +b \right)^{2} \sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a +b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}}+\frac{2 \left(3 a -b \right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{\frac{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b}{a -b}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right)}{\left(3 a^{3}+3 a^{2} b -3 b^{2} a -3 b^{3}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(a +b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}}-\frac{8 a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{\frac{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a -b}{a -b}}\, \left(\EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right)-\EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{-\frac{2 b}{a -b}}\right)\right)}{3 \left(a -b \right) \left(a +b \right)^{2} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +\left(a +b \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{-2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a +b}\, d}"," ",0,"-(-(-2*cos(1/2*d*x+1/2*c)^2*b-a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(1/3/b/(a-b)/(a+b)*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4*b+(a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)/(cos(1/2*d*x+1/2*c)^2+1/2/b*(a-b))^2+16/3*b*sin(1/2*d*x+1/2*c)^2/(a-b)^2/(a+b)^2*cos(1/2*d*x+1/2*c)*a/(-(-2*cos(1/2*d*x+1/2*c)^2*b-a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)+2*(3*a-b)/(3*a^3+3*a^2*b-3*a*b^2-3*b^3)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)/(a-b))^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4*b+(a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))-8/3*a/(a-b)/(a+b)^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*((2*cos(1/2*d*x+1/2*c)^2*b+a-b)/(a-b))^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4*b+(a+b)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(EllipticF(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))-EllipticE(cos(1/2*d*x+1/2*c),(-2*b/(a-b))^(1/2))))/sin(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^2*b+a+b)^(1/2)/d","A"
56,0,0,88,0.079000," ","int((a+b*cos(d*x+c))^(4/3),x)","\int \left(a +b \cos \left(d x +c \right)\right)^{\frac{4}{3}}\, dx"," ",0,"int((a+b*cos(d*x+c))^(4/3),x)","F"
57,0,0,85,0.207000," ","int((a+b*cos(d*x+c))^(2/3),x)","\int \left(a +b \cos \left(d x +c \right)\right)^{\frac{2}{3}}\, dx"," ",0,"int((a+b*cos(d*x+c))^(2/3),x)","F"
58,0,0,85,0.168000," ","int((a+b*cos(d*x+c))^(1/3),x)","\int \left(a +b \cos \left(d x +c \right)\right)^{\frac{1}{3}}\, dx"," ",0,"int((a+b*cos(d*x+c))^(1/3),x)","F"
59,0,0,85,0.105000," ","int(1/(a+b*cos(d*x+c))^(1/3),x)","\int \frac{1}{\left(a +b \cos \left(d x +c \right)\right)^{\frac{1}{3}}}\, dx"," ",0,"int(1/(a+b*cos(d*x+c))^(1/3),x)","F"
60,0,0,85,0.084000," ","int(1/(a+b*cos(d*x+c))^(2/3),x)","\int \frac{1}{\left(a +b \cos \left(d x +c \right)\right)^{\frac{2}{3}}}\, dx"," ",0,"int(1/(a+b*cos(d*x+c))^(2/3),x)","F"
61,0,0,90,0.073000," ","int(1/(a+b*cos(d*x+c))^(4/3),x)","\int \frac{1}{\left(a +b \cos \left(d x +c \right)\right)^{\frac{4}{3}}}\, dx"," ",0,"int(1/(a+b*cos(d*x+c))^(4/3),x)","F"
62,0,0,89,0.408000," ","int((a+b*cos(d*x+c))^n,x)","\int \left(a +b \cos \left(d x +c \right)\right)^{n}\, dx"," ",0,"int((a+b*cos(d*x+c))^n,x)","F"