1,1,42,27,0.080000," ","int(sin(x)^6/(a-a*cos(x)^2),x)","-\frac{5 \left(\tan^{3}\left(x \right)\right)}{8 a \left(\tan^{2}\left(x \right)+1\right)^{2}}-\frac{3 \tan \left(x \right)}{8 a \left(\tan^{2}\left(x \right)+1\right)^{2}}+\frac{3 \arctan \left(\tan \left(x \right)\right)}{8 a}"," ",0,"-5/8/a/(tan(x)^2+1)^2*tan(x)^3-3/8/a/(tan(x)^2+1)^2*tan(x)+3/8/a*arctan(tan(x))","A"
2,1,16,17,0.069000," ","int(sin(x)^5/(a-a*cos(x)^2),x)","\frac{\frac{\left(\cos^{3}\left(x \right)\right)}{3}-\cos \left(x \right)}{a}"," ",0,"1/a*(1/3*cos(x)^3-cos(x))","A"
3,1,25,16,0.078000," ","int(sin(x)^4/(a-a*cos(x)^2),x)","-\frac{\tan \left(x \right)}{2 a \left(\tan^{2}\left(x \right)+1\right)}+\frac{\arctan \left(\tan \left(x \right)\right)}{2 a}"," ",0,"-1/2/a*tan(x)/(tan(x)^2+1)+1/2/a*arctan(tan(x))","A"
4,1,8,7,0.062000," ","int(sin(x)^3/(a-a*cos(x)^2),x)","-\frac{\cos \left(x \right)}{a}"," ",0,"-cos(x)/a","A"
5,1,8,5,0.086000," ","int(sin(x)^2/(a-a*cos(x)^2),x)","\frac{\arctan \left(\tan \left(x \right)\right)}{a}"," ",0,"1/a*arctan(tan(x))","C"
6,1,9,8,0.052000," ","int(sin(x)/(a-a*cos(x)^2),x)","-\frac{\arctanh \left(\cos \left(x \right)\right)}{a}"," ",0,"-arctanh(cos(x))/a","A"
7,1,44,18,0.103000," ","int(csc(x)/(a-a*cos(x)^2),x)","\frac{1}{4 a \left(-1+\cos \left(x \right)\right)}+\frac{\ln \left(-1+\cos \left(x \right)\right)}{4 a}+\frac{1}{4 a \left(\cos \left(x \right)+1\right)}-\frac{\ln \left(\cos \left(x \right)+1\right)}{4 a}"," ",0,"1/4/a/(-1+cos(x))+1/4/a*ln(-1+cos(x))+1/4/a/(cos(x)+1)-1/4*ln(cos(x)+1)/a","B"
8,1,18,17,0.109000," ","int(csc(x)^2/(a-a*cos(x)^2),x)","\frac{-\frac{1}{3 \tan \left(x \right)^{3}}-\frac{1}{\tan \left(x \right)}}{a}"," ",0,"1/a*(-1/3/tan(x)^3-1/tan(x))","A"
9,1,66,29,0.120000," ","int(csc(x)^3/(a-a*cos(x)^2),x)","-\frac{1}{16 a \left(-1+\cos \left(x \right)\right)^{2}}+\frac{3}{16 a \left(-1+\cos \left(x \right)\right)}+\frac{3 \ln \left(-1+\cos \left(x \right)\right)}{16 a}+\frac{1}{16 a \left(\cos \left(x \right)+1\right)^{2}}+\frac{3}{16 a \left(\cos \left(x \right)+1\right)}-\frac{3 \ln \left(\cos \left(x \right)+1\right)}{16 a}"," ",0,"-1/16/a/(-1+cos(x))^2+3/16/a/(-1+cos(x))+3/16/a*ln(-1+cos(x))+1/16/a/(cos(x)+1)^2+3/16/a/(cos(x)+1)-3/16*ln(cos(x)+1)/a","B"
10,1,138,66,0.076000," ","int(sin(x)^7/(a+b*cos(x)^2),x)","\frac{\cos^{5}\left(x \right)}{5 b}-\frac{\left(\cos^{3}\left(x \right)\right) a}{3 b^{2}}-\frac{\cos^{3}\left(x \right)}{b}+\frac{a^{2} \cos \left(x \right)}{b^{3}}+\frac{3 a \cos \left(x \right)}{b^{2}}+\frac{3 \cos \left(x \right)}{b}-\frac{\arctan \left(\frac{\cos \left(x \right) b}{\sqrt{a b}}\right) a^{3}}{b^{3} \sqrt{a b}}-\frac{3 \arctan \left(\frac{\cos \left(x \right) b}{\sqrt{a b}}\right) a^{2}}{b^{2} \sqrt{a b}}-\frac{3 \arctan \left(\frac{\cos \left(x \right) b}{\sqrt{a b}}\right) a}{b \sqrt{a b}}-\frac{\arctan \left(\frac{\cos \left(x \right) b}{\sqrt{a b}}\right)}{\sqrt{a b}}"," ",0,"1/5*cos(x)^5/b-1/3/b^2*cos(x)^3*a-cos(x)^3/b+1/b^3*a^2*cos(x)+3*a*cos(x)/b^2+3*cos(x)/b-1/b^3/(a*b)^(1/2)*arctan(cos(x)*b/(a*b)^(1/2))*a^3-3/b^2/(a*b)^(1/2)*arctan(cos(x)*b/(a*b)^(1/2))*a^2-3/b/(a*b)^(1/2)*arctan(cos(x)*b/(a*b)^(1/2))*a-1/(a*b)^(1/2)*arctan(cos(x)*b/(a*b)^(1/2))","B"
11,1,86,44,0.066000," ","int(sin(x)^5/(a+b*cos(x)^2),x)","-\frac{\cos^{3}\left(x \right)}{3 b}+\frac{a \cos \left(x \right)}{b^{2}}+\frac{2 \cos \left(x \right)}{b}-\frac{\arctan \left(\frac{\cos \left(x \right) b}{\sqrt{a b}}\right) a^{2}}{b^{2} \sqrt{a b}}-\frac{2 \arctan \left(\frac{\cos \left(x \right) b}{\sqrt{a b}}\right) a}{b \sqrt{a b}}-\frac{\arctan \left(\frac{\cos \left(x \right) b}{\sqrt{a b}}\right)}{\sqrt{a b}}"," ",0,"-1/3*cos(x)^3/b+a*cos(x)/b^2+2*cos(x)/b-1/b^2/(a*b)^(1/2)*arctan(cos(x)*b/(a*b)^(1/2))*a^2-2/b/(a*b)^(1/2)*arctan(cos(x)*b/(a*b)^(1/2))*a-1/(a*b)^(1/2)*arctan(cos(x)*b/(a*b)^(1/2))","A"
12,1,46,28,0.064000," ","int(sin(x)^3/(a+b*cos(x)^2),x)","\frac{\cos \left(x \right)}{b}-\frac{\arctan \left(\frac{\cos \left(x \right) b}{\sqrt{a b}}\right) a}{b \sqrt{a b}}-\frac{\arctan \left(\frac{\cos \left(x \right) b}{\sqrt{a b}}\right)}{\sqrt{a b}}"," ",0,"cos(x)/b-1/b/(a*b)^(1/2)*arctan(cos(x)*b/(a*b)^(1/2))*a-1/(a*b)^(1/2)*arctan(cos(x)*b/(a*b)^(1/2))","A"
13,1,18,18,0.043000," ","int(sin(x)/(a+b*cos(x)^2),x)","-\frac{\arctan \left(\frac{\cos \left(x \right) b}{\sqrt{a b}}\right)}{\sqrt{a b}}"," ",0,"-1/(a*b)^(1/2)*arctan(cos(x)*b/(a*b)^(1/2))","A"
14,1,56,34,0.102000," ","int(csc(x)/(a+b*cos(x)^2),x)","-\frac{b \arctan \left(\frac{\cos \left(x \right) b}{\sqrt{a b}}\right)}{\left(a +b \right) \sqrt{a b}}+\frac{\ln \left(-1+\cos \left(x \right)\right)}{2 a +2 b}-\frac{\ln \left(\cos \left(x \right)+1\right)}{2 a +2 b}"," ",0,"-b/(a+b)/(a*b)^(1/2)*arctan(cos(x)*b/(a*b)^(1/2))+1/(2*a+2*b)*ln(-1+cos(x))-1/(2*a+2*b)*ln(cos(x)+1)","A"
15,1,111,50,0.121000," ","int(csc(x)^3/(a+b*cos(x)^2),x)","-\frac{b^{2} \arctan \left(\frac{\cos \left(x \right) b}{\sqrt{a b}}\right)}{\left(a +b \right)^{2} \sqrt{a b}}+\frac{1}{\left(4 a +4 b \right) \left(-1+\cos \left(x \right)\right)}+\frac{\ln \left(-1+\cos \left(x \right)\right) a}{4 \left(a +b \right)^{2}}+\frac{3 \ln \left(-1+\cos \left(x \right)\right) b}{4 \left(a +b \right)^{2}}+\frac{1}{\left(4 a +4 b \right) \left(\cos \left(x \right)+1\right)}-\frac{\ln \left(\cos \left(x \right)+1\right) a}{4 \left(a +b \right)^{2}}-\frac{3 \ln \left(\cos \left(x \right)+1\right) b}{4 \left(a +b \right)^{2}}"," ",0,"-b^2/(a+b)^2/(a*b)^(1/2)*arctan(cos(x)*b/(a*b)^(1/2))+1/(4*a+4*b)/(-1+cos(x))+1/4/(a+b)^2*ln(-1+cos(x))*a+3/4/(a+b)^2*ln(-1+cos(x))*b+1/(4*a+4*b)/(cos(x)+1)-1/4/(a+b)^2*ln(cos(x)+1)*a-3/4/(a+b)^2*ln(cos(x)+1)*b","B"
16,1,205,80,0.126000," ","int(csc(x)^5/(a+b*cos(x)^2),x)","-\frac{b^{3} \arctan \left(\frac{\cos \left(x \right) b}{\sqrt{a b}}\right)}{\left(a +b \right)^{3} \sqrt{a b}}-\frac{1}{2 \left(8 a +8 b \right) \left(-1+\cos \left(x \right)\right)^{2}}+\frac{3 a}{16 \left(a +b \right)^{2} \left(-1+\cos \left(x \right)\right)}+\frac{7 b}{16 \left(a +b \right)^{2} \left(-1+\cos \left(x \right)\right)}+\frac{3 \ln \left(-1+\cos \left(x \right)\right) a^{2}}{16 \left(a +b \right)^{3}}+\frac{5 \ln \left(-1+\cos \left(x \right)\right) a b}{8 \left(a +b \right)^{3}}+\frac{15 \ln \left(-1+\cos \left(x \right)\right) b^{2}}{16 \left(a +b \right)^{3}}+\frac{1}{2 \left(8 a +8 b \right) \left(\cos \left(x \right)+1\right)^{2}}+\frac{3 a}{16 \left(a +b \right)^{2} \left(\cos \left(x \right)+1\right)}+\frac{7 b}{16 \left(a +b \right)^{2} \left(\cos \left(x \right)+1\right)}-\frac{3 \ln \left(\cos \left(x \right)+1\right) a^{2}}{16 \left(a +b \right)^{3}}-\frac{5 \ln \left(\cos \left(x \right)+1\right) a b}{8 \left(a +b \right)^{3}}-\frac{15 \ln \left(\cos \left(x \right)+1\right) b^{2}}{16 \left(a +b \right)^{3}}"," ",0,"-b^3/(a+b)^3/(a*b)^(1/2)*arctan(cos(x)*b/(a*b)^(1/2))-1/2/(8*a+8*b)/(-1+cos(x))^2+3/16/(a+b)^2/(-1+cos(x))*a+7/16/(a+b)^2/(-1+cos(x))*b+3/16/(a+b)^3*ln(-1+cos(x))*a^2+5/8/(a+b)^3*ln(-1+cos(x))*a*b+15/16/(a+b)^3*ln(-1+cos(x))*b^2+1/2/(8*a+8*b)/(cos(x)+1)^2+3/16/(a+b)^2/(cos(x)+1)*a+7/16/(a+b)^2/(cos(x)+1)*b-3/16/(a+b)^3*ln(cos(x)+1)*a^2-5/8/(a+b)^3*ln(cos(x)+1)*a*b-15/16/(a+b)^3*ln(cos(x)+1)*b^2","B"
17,1,194,74,0.087000," ","int(sin(x)^6/(a+b*cos(x)^2),x)","\frac{\arctan \left(\frac{a \tan \left(x \right)}{\sqrt{\left(a +b \right) a}}\right) a^{3}}{b^{3} \sqrt{\left(a +b \right) a}}+\frac{3 \arctan \left(\frac{a \tan \left(x \right)}{\sqrt{\left(a +b \right) a}}\right) a^{2}}{b^{2} \sqrt{\left(a +b \right) a}}+\frac{3 \arctan \left(\frac{a \tan \left(x \right)}{\sqrt{\left(a +b \right) a}}\right) a}{b \sqrt{\left(a +b \right) a}}+\frac{\arctan \left(\frac{a \tan \left(x \right)}{\sqrt{\left(a +b \right) a}}\right)}{\sqrt{\left(a +b \right) a}}+\frac{\left(\tan^{3}\left(x \right)\right) a}{2 b^{2} \left(\tan^{2}\left(x \right)+1\right)^{2}}+\frac{9 \left(\tan^{3}\left(x \right)\right)}{8 b \left(\tan^{2}\left(x \right)+1\right)^{2}}+\frac{\tan \left(x \right) a}{2 b^{2} \left(\tan^{2}\left(x \right)+1\right)^{2}}+\frac{7 \tan \left(x \right)}{8 b \left(\tan^{2}\left(x \right)+1\right)^{2}}-\frac{\arctan \left(\tan \left(x \right)\right) a^{2}}{b^{3}}-\frac{5 \arctan \left(\tan \left(x \right)\right) a}{2 b^{2}}-\frac{15 \arctan \left(\tan \left(x \right)\right)}{8 b}"," ",0,"1/b^3/((a+b)*a)^(1/2)*arctan(a*tan(x)/((a+b)*a)^(1/2))*a^3+3/b^2/((a+b)*a)^(1/2)*arctan(a*tan(x)/((a+b)*a)^(1/2))*a^2+3/b/((a+b)*a)^(1/2)*arctan(a*tan(x)/((a+b)*a)^(1/2))*a+1/((a+b)*a)^(1/2)*arctan(a*tan(x)/((a+b)*a)^(1/2))+1/2/b^2/(tan(x)^2+1)^2*tan(x)^3*a+9/8/b/(tan(x)^2+1)^2*tan(x)^3+1/2/b^2/(tan(x)^2+1)^2*tan(x)*a+7/8/b/(tan(x)^2+1)^2*tan(x)-1/b^3*arctan(tan(x))*a^2-5/2/b^2*arctan(tan(x))*a-15/8/b*arctan(tan(x))","B"
18,1,105,48,0.075000," ","int(sin(x)^4/(a+b*cos(x)^2),x)","\frac{\arctan \left(\frac{a \tan \left(x \right)}{\sqrt{\left(a +b \right) a}}\right) a^{2}}{b^{2} \sqrt{\left(a +b \right) a}}+\frac{2 \arctan \left(\frac{a \tan \left(x \right)}{\sqrt{\left(a +b \right) a}}\right) a}{b \sqrt{\left(a +b \right) a}}+\frac{\arctan \left(\frac{a \tan \left(x \right)}{\sqrt{\left(a +b \right) a}}\right)}{\sqrt{\left(a +b \right) a}}+\frac{\tan \left(x \right)}{2 b \left(\tan^{2}\left(x \right)+1\right)}-\frac{3 \arctan \left(\tan \left(x \right)\right)}{2 b}-\frac{\arctan \left(\tan \left(x \right)\right) a}{b^{2}}"," ",0,"1/b^2/((a+b)*a)^(1/2)*arctan(a*tan(x)/((a+b)*a)^(1/2))*a^2+2/b/((a+b)*a)^(1/2)*arctan(a*tan(x)/((a+b)*a)^(1/2))*a+1/((a+b)*a)^(1/2)*arctan(a*tan(x)/((a+b)*a)^(1/2))+1/2/b*tan(x)/(tan(x)^2+1)-3/2/b*arctan(tan(x))-1/b^2*arctan(tan(x))*a","B"
19,1,54,32,0.072000," ","int(sin(x)^2/(a+b*cos(x)^2),x)","\frac{\arctan \left(\frac{a \tan \left(x \right)}{\sqrt{\left(a +b \right) a}}\right) a}{b \sqrt{\left(a +b \right) a}}+\frac{\arctan \left(\frac{a \tan \left(x \right)}{\sqrt{\left(a +b \right) a}}\right)}{\sqrt{\left(a +b \right) a}}-\frac{\arctan \left(\tan \left(x \right)\right)}{b}"," ",0,"1/b/((a+b)*a)^(1/2)*arctan(a*tan(x)/((a+b)*a)^(1/2))*a+1/((a+b)*a)^(1/2)*arctan(a*tan(x)/((a+b)*a)^(1/2))-1/b*arctan(tan(x))","A"
20,1,21,22,0.056000," ","int(1/(a+b*cos(x)^2),x)","\frac{\arctan \left(\frac{a \tan \left(x \right)}{\sqrt{\left(a +b \right) a}}\right)}{\sqrt{\left(a +b \right) a}}"," ",0,"1/((a+b)*a)^(1/2)*arctan(a*tan(x)/((a+b)*a)^(1/2))","A"
21,1,39,33,0.111000," ","int(csc(x)^2/(a+b*cos(x)^2),x)","\frac{b \arctan \left(\frac{a \tan \left(x \right)}{\sqrt{\left(a +b \right) a}}\right)}{\left(a +b \right) \sqrt{\left(a +b \right) a}}-\frac{1}{\left(a +b \right) \tan \left(x \right)}"," ",0,"b/(a+b)/((a+b)*a)^(1/2)*arctan(a*tan(x)/((a+b)*a)^(1/2))-1/(a+b)/tan(x)","A"
22,1,65,51,0.116000," ","int(csc(x)^4/(a+b*cos(x)^2),x)","-\frac{1}{3 \left(a +b \right) \tan \left(x \right)^{3}}-\frac{a}{\left(a +b \right)^{2} \tan \left(x \right)}-\frac{2 b}{\left(a +b \right)^{2} \tan \left(x \right)}+\frac{b^{2} \arctan \left(\frac{a \tan \left(x \right)}{\sqrt{\left(a +b \right) a}}\right)}{\left(a +b \right)^{2} \sqrt{\left(a +b \right) a}}"," ",0,"-1/3/(a+b)/tan(x)^3-1/(a+b)^2/tan(x)*a-2/(a+b)^2/tan(x)*b+b^2/(a+b)^2/((a+b)*a)^(1/2)*arctan(a*tan(x)/((a+b)*a)^(1/2))","A"
23,1,106,77,0.126000," ","int(csc(x)^6/(a+b*cos(x)^2),x)","-\frac{1}{5 \left(a +b \right) \tan \left(x \right)^{5}}-\frac{2 a}{3 \left(a +b \right)^{2} \tan \left(x \right)^{3}}-\frac{b}{\left(a +b \right)^{2} \tan \left(x \right)^{3}}-\frac{a^{2}}{\left(a +b \right)^{3} \tan \left(x \right)}-\frac{3 a b}{\left(a +b \right)^{3} \tan \left(x \right)}-\frac{3 b^{2}}{\left(a +b \right)^{3} \tan \left(x \right)}+\frac{b^{3} \arctan \left(\frac{a \tan \left(x \right)}{\sqrt{\left(a +b \right) a}}\right)}{\left(a +b \right)^{3} \sqrt{\left(a +b \right) a}}"," ",0,"-1/5/(a+b)/tan(x)^5-2/3/(a+b)^2/tan(x)^3*a-1/(a+b)^2/tan(x)^3*b-1/(a+b)^3/tan(x)*a^2-3/(a+b)^3/tan(x)*a*b-3/(a+b)^3/tan(x)*b^2+b^3/(a+b)^3/((a+b)*a)^(1/2)*arctan(a*tan(x)/((a+b)*a)^(1/2))","A"
24,1,80,69,0.053000," ","int(sin(x)/(4-3*cos(x)^3),x)","\frac{4^{\frac{1}{3}} 3^{\frac{2}{3}} \ln \left(\cos \left(x \right)-\frac{4^{\frac{1}{3}} 3^{\frac{2}{3}}}{3}\right)}{36}-\frac{4^{\frac{1}{3}} 3^{\frac{2}{3}} \ln \left(\cos^{2}\left(x \right)+\frac{4^{\frac{1}{3}} 3^{\frac{2}{3}} \cos \left(x \right)}{3}+\frac{4^{\frac{2}{3}} 3^{\frac{1}{3}}}{3}\right)}{72}-\frac{4^{\frac{1}{3}} 3^{\frac{1}{6}} \arctan \left(\frac{\sqrt{3}\, \left(\frac{4^{\frac{2}{3}} 3^{\frac{1}{3}} \cos \left(x \right)}{2}+1\right)}{3}\right)}{12}"," ",0,"1/36*4^(1/3)*3^(2/3)*ln(cos(x)-1/3*4^(1/3)*3^(2/3))-1/72*4^(1/3)*3^(2/3)*ln(cos(x)^2+1/3*4^(1/3)*3^(2/3)*cos(x)+1/3*4^(2/3)*3^(1/3))-1/12*4^(1/3)*3^(1/6)*arctan(1/3*3^(1/2)*(1/2*4^(2/3)*3^(1/3)*cos(x)+1))","A"
25,1,7,4,0.064000," ","int(1/(1-cos(x)^2),x)","-\frac{1}{\tan \left(x \right)}"," ",0,"-1/tan(x)","A"
26,1,14,11,0.072000," ","int(1/(1-cos(x)^2)^2,x)","-\frac{1}{3 \tan \left(x \right)^{3}}-\frac{1}{\tan \left(x \right)}"," ",0,"-1/3/tan(x)^3-1/tan(x)","A"
27,1,20,17,0.071000," ","int(1/(1-cos(x)^2)^3,x)","-\frac{2}{3 \tan \left(x \right)^{3}}-\frac{1}{5 \tan \left(x \right)^{5}}-\frac{1}{\tan \left(x \right)}"," ",0,"-2/3/tan(x)^3-1/5/tan(x)^5-1/tan(x)","A"
28,1,78,66,0.065000," ","int(cos(x)^7/(a+b*cos(x)^2),x)","\frac{\frac{\left(\sin^{5}\left(x \right)\right) b^{2}}{5}+\frac{\left(\sin^{3}\left(x \right)\right) a b}{3}-\frac{2 \left(\sin^{3}\left(x \right)\right) b^{2}}{3}+a^{2} \sin \left(x \right)-a b \sin \left(x \right)+b^{2} \sin \left(x \right)}{b^{3}}-\frac{a^{3} \arctanh \left(\frac{\sin \left(x \right) b}{\sqrt{\left(a +b \right) b}}\right)}{b^{3} \sqrt{\left(a +b \right) b}}"," ",0,"1/b^3*(1/5*sin(x)^5*b^2+1/3*sin(x)^3*a*b-2/3*sin(x)^3*b^2+a^2*sin(x)-a*b*sin(x)+b^2*sin(x))-a^3/b^3/((a+b)*b)^(1/2)*arctanh(sin(x)*b/((a+b)*b)^(1/2))","A"
29,1,50,46,0.058000," ","int(cos(x)^5/(a+b*cos(x)^2),x)","-\frac{\frac{\left(\sin^{3}\left(x \right)\right) b}{3}+\sin \left(x \right) a -\sin \left(x \right) b}{b^{2}}+\frac{a^{2} \arctanh \left(\frac{\sin \left(x \right) b}{\sqrt{\left(a +b \right) b}}\right)}{b^{2} \sqrt{\left(a +b \right) b}}"," ",0,"-1/b^2*(1/3*sin(x)^3*b+sin(x)*a-sin(x)*b)+1/b^2*a^2/((a+b)*b)^(1/2)*arctanh(sin(x)*b/((a+b)*b)^(1/2))","A"
30,1,33,30,0.059000," ","int(cos(x)^3/(a+b*cos(x)^2),x)","\frac{\sin \left(x \right)}{b}-\frac{a \arctanh \left(\frac{\sin \left(x \right) b}{\sqrt{\left(a +b \right) b}}\right)}{b \sqrt{\left(a +b \right) b}}"," ",0,"sin(x)/b-1/b*a/((a+b)*b)^(1/2)*arctanh(sin(x)*b/((a+b)*b)^(1/2))","A"
31,1,21,21,0.046000," ","int(cos(x)/(a+b*cos(x)^2),x)","\frac{\arctanh \left(\frac{\sin \left(x \right) b}{\sqrt{\left(a +b \right) b}}\right)}{\sqrt{\left(a +b \right) b}}"," ",0,"1/((a+b)*b)^(1/2)*arctanh(sin(x)*b/((a+b)*b)^(1/2))","A"
32,1,47,33,0.096000," ","int(sec(x)/(a+b*cos(x)^2),x)","-\frac{b \arctanh \left(\frac{\sin \left(x \right) b}{\sqrt{\left(a +b \right) b}}\right)}{a \sqrt{\left(a +b \right) b}}-\frac{\ln \left(\sin \left(x \right)-1\right)}{2 a}+\frac{\ln \left(\sin \left(x \right)+1\right)}{2 a}"," ",0,"-1/a*b/((a+b)*b)^(1/2)*arctanh(sin(x)*b/((a+b)*b)^(1/2))-1/2/a*ln(sin(x)-1)+1/2/a*ln(sin(x)+1)","A"
33,1,92,47,0.116000," ","int(sec(x)^3/(a+b*cos(x)^2),x)","\frac{b^{2} \arctanh \left(\frac{\sin \left(x \right) b}{\sqrt{\left(a +b \right) b}}\right)}{a^{2} \sqrt{\left(a +b \right) b}}-\frac{1}{4 a \left(\sin \left(x \right)-1\right)}-\frac{\ln \left(\sin \left(x \right)-1\right)}{4 a}+\frac{\ln \left(\sin \left(x \right)-1\right) b}{2 a^{2}}-\frac{1}{4 a \left(\sin \left(x \right)+1\right)}+\frac{\ln \left(\sin \left(x \right)+1\right)}{4 a}-\frac{\ln \left(\sin \left(x \right)+1\right) b}{2 a^{2}}"," ",0,"b^2/a^2/((a+b)*b)^(1/2)*arctanh(sin(x)*b/((a+b)*b)^(1/2))-1/4/a/(sin(x)-1)-1/4/a*ln(sin(x)-1)+1/2/a^2*ln(sin(x)-1)*b-1/4/a/(sin(x)+1)+1/4/a*ln(sin(x)+1)-1/2/a^2*ln(sin(x)+1)*b","A"
34,1,165,76,0.126000," ","int(sec(x)^5/(a+b*cos(x)^2),x)","-\frac{b^{3} \arctanh \left(\frac{\sin \left(x \right) b}{\sqrt{\left(a +b \right) b}}\right)}{a^{3} \sqrt{\left(a +b \right) b}}+\frac{1}{16 a \left(\sin \left(x \right)-1\right)^{2}}-\frac{3}{16 a \left(\sin \left(x \right)-1\right)}+\frac{b}{4 a^{2} \left(\sin \left(x \right)-1\right)}-\frac{3 \ln \left(\sin \left(x \right)-1\right)}{16 a}+\frac{\ln \left(\sin \left(x \right)-1\right) b}{4 a^{2}}-\frac{\ln \left(\sin \left(x \right)-1\right) b^{2}}{2 a^{3}}-\frac{1}{16 a \left(\sin \left(x \right)+1\right)^{2}}-\frac{3}{16 a \left(\sin \left(x \right)+1\right)}+\frac{b}{4 a^{2} \left(\sin \left(x \right)+1\right)}+\frac{3 \ln \left(\sin \left(x \right)+1\right)}{16 a}-\frac{\ln \left(\sin \left(x \right)+1\right) b}{4 a^{2}}+\frac{\ln \left(\sin \left(x \right)+1\right) b^{2}}{2 a^{3}}"," ",0,"-b^3/a^3/((a+b)*b)^(1/2)*arctanh(sin(x)*b/((a+b)*b)^(1/2))+1/16/a/(sin(x)-1)^2-3/16/a/(sin(x)-1)+1/4/a^2/(sin(x)-1)*b-3/16/a*ln(sin(x)-1)+1/4/a^2*ln(sin(x)-1)*b-1/2/a^3*ln(sin(x)-1)*b^2-1/16/a/(sin(x)+1)^2-3/16/a/(sin(x)+1)+1/4/a^2/(sin(x)+1)*b+3/16/a*ln(sin(x)+1)-1/4/a^2*ln(sin(x)+1)*b+1/2/a^3*ln(sin(x)+1)*b^2","B"
35,1,122,73,0.070000," ","int(cos(x)^6/(a+b*cos(x)^2),x)","-\frac{\arctan \left(\frac{a \tan \left(x \right)}{\sqrt{\left(a +b \right) a}}\right) a^{3}}{b^{3} \sqrt{\left(a +b \right) a}}-\frac{\left(\tan^{3}\left(x \right)\right) a}{2 b^{2} \left(\tan^{2}\left(x \right)+1\right)^{2}}+\frac{3 \left(\tan^{3}\left(x \right)\right)}{8 b \left(\tan^{2}\left(x \right)+1\right)^{2}}-\frac{\tan \left(x \right) a}{2 b^{2} \left(\tan^{2}\left(x \right)+1\right)^{2}}+\frac{5 \tan \left(x \right)}{8 b \left(\tan^{2}\left(x \right)+1\right)^{2}}+\frac{\arctan \left(\tan \left(x \right)\right) a^{2}}{b^{3}}-\frac{\arctan \left(\tan \left(x \right)\right) a}{2 b^{2}}+\frac{3 \arctan \left(\tan \left(x \right)\right)}{8 b}"," ",0,"-1/b^3/((a+b)*a)^(1/2)*arctan(a*tan(x)/((a+b)*a)^(1/2))*a^3-1/2/b^2/(tan(x)^2+1)^2*tan(x)^3*a+3/8/b/(tan(x)^2+1)^2*tan(x)^3-1/2/b^2/(tan(x)^2+1)^2*tan(x)*a+5/8/b/(tan(x)^2+1)^2*tan(x)+1/b^3*arctan(tan(x))*a^2-1/2/b^2*arctan(tan(x))*a+3/8/b*arctan(tan(x))","A"
36,1,60,48,0.071000," ","int(cos(x)^4/(a+b*cos(x)^2),x)","\frac{\arctan \left(\frac{a \tan \left(x \right)}{\sqrt{\left(a +b \right) a}}\right) a^{2}}{b^{2} \sqrt{\left(a +b \right) a}}+\frac{\tan \left(x \right)}{2 b \left(\tan^{2}\left(x \right)+1\right)}+\frac{\arctan \left(\tan \left(x \right)\right)}{2 b}-\frac{\arctan \left(\tan \left(x \right)\right) a}{b^{2}}"," ",0,"1/b^2/((a+b)*a)^(1/2)*arctan(a*tan(x)/((a+b)*a)^(1/2))*a^2+1/2/b*tan(x)/(tan(x)^2+1)+1/2/b*arctan(tan(x))-1/b^2*arctan(tan(x))*a","A"
37,1,32,30,0.061000," ","int(cos(x)^2/(a+b*cos(x)^2),x)","-\frac{\arctan \left(\frac{a \tan \left(x \right)}{\sqrt{\left(a +b \right) a}}\right) a}{b \sqrt{\left(a +b \right) a}}+\frac{x}{b}"," ",0,"-1/b/((a+b)*a)^(1/2)*arctan(a*tan(x)/((a+b)*a)^(1/2))*a+x/b","A"
38,1,21,22,0.053000," ","int(1/(a+b*cos(x)^2),x)","\frac{\arctan \left(\frac{a \tan \left(x \right)}{\sqrt{\left(a +b \right) a}}\right)}{\sqrt{\left(a +b \right) a}}"," ",0,"1/((a+b)*a)^(1/2)*arctan(a*tan(x)/((a+b)*a)^(1/2))","A"
39,1,33,29,0.099000," ","int(sec(x)^2/(a+b*cos(x)^2),x)","\frac{\tan \left(x \right)}{a}-\frac{b \arctan \left(\frac{a \tan \left(x \right)}{\sqrt{\left(a +b \right) a}}\right)}{a \sqrt{\left(a +b \right) a}}"," ",0,"tan(x)/a-1/a*b/((a+b)*a)^(1/2)*arctan(a*tan(x)/((a+b)*a)^(1/2))","A"
40,1,51,46,0.109000," ","int(sec(x)^4/(a+b*cos(x)^2),x)","\frac{\tan^{3}\left(x \right)}{3 a}+\frac{\tan \left(x \right)}{a}-\frac{\tan \left(x \right) b}{a^{2}}+\frac{b^{2} \arctan \left(\frac{a \tan \left(x \right)}{\sqrt{\left(a +b \right) a}}\right)}{a^{2} \sqrt{\left(a +b \right) a}}"," ",0,"1/3*tan(x)^3/a+tan(x)/a-1/a^2*tan(x)*b+b^2/a^2/((a+b)*a)^(1/2)*arctan(a*tan(x)/((a+b)*a)^(1/2))","A"
41,1,80,67,0.108000," ","int(sec(x)^6/(a+b*cos(x)^2),x)","\frac{\tan^{5}\left(x \right)}{5 a}+\frac{2 \left(\tan^{3}\left(x \right)\right)}{3 a}-\frac{\left(\tan^{3}\left(x \right)\right) b}{3 a^{2}}+\frac{\tan \left(x \right)}{a}-\frac{\tan \left(x \right) b}{a^{2}}+\frac{b^{2} \tan \left(x \right)}{a^{3}}-\frac{b^{3} \arctan \left(\frac{a \tan \left(x \right)}{\sqrt{\left(a +b \right) a}}\right)}{a^{3} \sqrt{\left(a +b \right) a}}"," ",0,"1/5*tan(x)^5/a+2/3*tan(x)^3/a-1/3/a^2*tan(x)^3*b+tan(x)/a-1/a^2*tan(x)*b+1/a^3*b^2*tan(x)-b^3/a^3/((a+b)*a)^(1/2)*arctan(a*tan(x)/((a+b)*a)^(1/2))","A"
42,1,81,53,0.069000," ","int(1/(a+b*cos(x)^2)^2,x)","-\frac{b \tan \left(x \right)}{2 \left(a +b \right) a \left(a \left(\tan^{2}\left(x \right)\right)+a +b \right)}+\frac{\arctan \left(\frac{a \tan \left(x \right)}{\sqrt{\left(a +b \right) a}}\right)}{\left(a +b \right) \sqrt{\left(a +b \right) a}}+\frac{\arctan \left(\frac{a \tan \left(x \right)}{\sqrt{\left(a +b \right) a}}\right) b}{2 \left(a +b \right) a \sqrt{\left(a +b \right) a}}"," ",0,"-1/2*b/(a+b)/a*tan(x)/(a*tan(x)^2+a+b)+1/(a+b)/((a+b)*a)^(1/2)*arctan(a*tan(x)/((a+b)*a)^(1/2))+1/2/(a+b)/a/((a+b)*a)^(1/2)*arctan(a*tan(x)/((a+b)*a)^(1/2))*b","A"
43,1,175,93,0.070000," ","int(1/(a+b*cos(x)^2)^3,x)","\frac{-\frac{b \left(8 a +5 b \right) \left(\tan^{3}\left(x \right)\right)}{8 a \left(a^{2}+2 a b +b^{2}\right)}-\frac{\left(8 a +3 b \right) b \tan \left(x \right)}{8 a^{2} \left(a +b \right)}}{\left(a \left(\tan^{2}\left(x \right)\right)+a +b \right)^{2}}+\frac{\arctan \left(\frac{a \tan \left(x \right)}{\sqrt{\left(a +b \right) a}}\right)}{\left(a^{2}+2 a b +b^{2}\right) \sqrt{\left(a +b \right) a}}+\frac{\arctan \left(\frac{a \tan \left(x \right)}{\sqrt{\left(a +b \right) a}}\right) b}{\left(a^{2}+2 a b +b^{2}\right) a \sqrt{\left(a +b \right) a}}+\frac{3 \arctan \left(\frac{a \tan \left(x \right)}{\sqrt{\left(a +b \right) a}}\right) b^{2}}{8 \left(a^{2}+2 a b +b^{2}\right) a^{2} \sqrt{\left(a +b \right) a}}"," ",0,"(-1/8*b*(8*a+5*b)/a/(a^2+2*a*b+b^2)*tan(x)^3-1/8*(8*a+3*b)/a^2*b/(a+b)*tan(x))/(a*tan(x)^2+a+b)^2+1/(a^2+2*a*b+b^2)/((a+b)*a)^(1/2)*arctan(a*tan(x)/((a+b)*a)^(1/2))+1/(a^2+2*a*b+b^2)/a/((a+b)*a)^(1/2)*arctan(a*tan(x)/((a+b)*a)^(1/2))*b+3/8/(a^2+2*a*b+b^2)/a^2/((a+b)*a)^(1/2)*arctan(a*tan(x)/((a+b)*a)^(1/2))*b^2","A"
44,1,14,29,0.052000," ","int(1/(1+cos(x)^2),x)","\frac{\arctan \left(\frac{\tan \left(x \right) \sqrt{2}}{2}\right) \sqrt{2}}{2}"," ",0,"1/2*arctan(1/2*tan(x)*2^(1/2))*2^(1/2)","A"
45,1,27,43,0.059000," ","int(1/(1+cos(x)^2)^2,x)","-\frac{\tan \left(x \right)}{4 \left(\tan^{2}\left(x \right)+2\right)}+\frac{3 \arctan \left(\frac{\tan \left(x \right) \sqrt{2}}{2}\right) \sqrt{2}}{8}"," ",0,"-1/4*tan(x)/(tan(x)^2+2)+3/8*arctan(1/2*tan(x)*2^(1/2))*2^(1/2)","A"
46,1,35,57,0.060000," ","int(1/(1+cos(x)^2)^3,x)","\frac{-\frac{13 \left(\tan^{3}\left(x \right)\right)}{32}-\frac{11 \tan \left(x \right)}{16}}{\left(\tan^{2}\left(x \right)+2\right)^{2}}+\frac{19 \arctan \left(\frac{\tan \left(x \right) \sqrt{2}}{2}\right) \sqrt{2}}{64}"," ",0,"(-13/32*tan(x)^3-11/16*tan(x))/(tan(x)^2+2)^2+19/64*arctan(1/2*tan(x)*2^(1/2))*2^(1/2)","A"
47,1,13,10,0.863000," ","int((1-cos(x)^2)^(1/2),x)","-\frac{2 \sin \left(x \right) \cos \left(x \right)}{\sqrt{2-2 \cos \left(2 x \right)}}"," ",0,"-sin(x)*cos(x)/(sin(x)^2)^(1/2)","A"
48,1,14,12,0.535000," ","int((-1+cos(x)^2)^(1/2),x)","\frac{\sin \left(x \right) \cos \left(x \right)}{\sqrt{-\left(\sin^{2}\left(x \right)\right)}}"," ",0,"sin(x)*cos(x)/(-sin(x)^2)^(1/2)","A"
49,1,19,21,1.432000," ","int((1-cos(x)^2)^(3/2),x)","\frac{2 \sin \left(x \right) \cos \left(x \right) \left(\cos^{2}\left(x \right)-3\right)}{3 \sqrt{2-2 \cos \left(2 x \right)}}"," ",0,"1/3*sin(x)*cos(x)*(cos(x)^2-3)/(sin(x)^2)^(1/2)","A"
50,1,21,25,0.990000," ","int((-1+cos(x)^2)^(3/2),x)","-\frac{\sin \left(x \right) \cos \left(x \right) \left(\sin^{2}\left(x \right)+2\right)}{3 \sqrt{-\left(\sin^{2}\left(x \right)\right)}}"," ",0,"-1/3*sin(x)*cos(x)*(sin(x)^2+2)/(-sin(x)^2)^(1/2)","A"
51,1,14,13,0.709000," ","int(1/(1-cos(x)^2)^(1/2),x)","-\frac{2 \arctanh \left(\cos \left(x \right)\right) \sin \left(x \right)}{\sqrt{2-2 \cos \left(2 x \right)}}"," ",0,"-arctanh(cos(x))*sin(x)/(sin(x)^2)^(1/2)","A"
52,1,34,15,0.412000," ","int(1/(-1+cos(x)^2)^(1/2),x)","-\frac{\sin \left(x \right) \sqrt{-\left(\cos^{2}\left(x \right)\right)}\, \arctan \left(\frac{1}{\sqrt{-\left(\cos^{2}\left(x \right)\right)}}\right)}{\cos \left(x \right) \sqrt{-\left(\sin^{2}\left(x \right)\right)}}"," ",0,"-sin(x)*(-cos(x)^2)^(1/2)*arctan(1/(-cos(x)^2)^(1/2))/cos(x)/(-sin(x)^2)^(1/2)","B"
53,1,37,24,1.565000," ","int(1/(1-cos(x)^2)^(3/2),x)","-\frac{2 \left(\frac{\cos \left(x \right)}{2}+\frac{\left(-\ln \left(-1+\cos \left(x \right)\right)+\ln \left(\cos \left(x \right)+1\right)\right) \left(\sin^{2}\left(x \right)\right)}{4}\right)}{\sin \left(x \right) \sqrt{2-2 \cos \left(2 x \right)}}"," ",0,"-(1/2*cos(x)+1/4*(-ln(-1+cos(x))+ln(cos(x)+1))*sin(x)^2)/sin(x)/(sin(x)^2)^(1/2)","A"
54,1,51,28,1.176000," ","int(1/(-1+cos(x)^2)^(3/2),x)","-\frac{\sqrt{-\left(\cos^{2}\left(x \right)\right)}\, \left(-\arctan \left(\frac{1}{\sqrt{-\left(\cos^{2}\left(x \right)\right)}}\right) \left(\sin^{2}\left(x \right)\right)+\sqrt{-\left(\cos^{2}\left(x \right)\right)}\right)}{2 \sin \left(x \right) \cos \left(x \right) \sqrt{-\left(\sin^{2}\left(x \right)\right)}}"," ",0,"-1/2/sin(x)*(-cos(x)^2)^(1/2)*(-arctan(1/(-cos(x)^2)^(1/2))*sin(x)^2+(-cos(x)^2)^(1/2))/cos(x)/(-sin(x)^2)^(1/2)","A"
55,1,41,17,1.556000," ","int((1+cos(x)^2)^(1/2),x)","-\frac{\sqrt{\left(1+\cos^{2}\left(x \right)\right) \left(\sin^{2}\left(x \right)\right)}\, \sqrt{\frac{1}{2}-\frac{\cos \left(2 x \right)}{2}}\, \EllipticE \left(\cos \left(x \right), i\right)}{\sqrt{1-\left(\cos^{4}\left(x \right)\right)}\, \sin \left(x \right)}"," ",0,"-((1+cos(x)^2)*sin(x)^2)^(1/2)*(sin(x)^2)^(1/2)*EllipticE(cos(x),I)/(1-cos(x)^4)^(1/2)/sin(x)","B"
56,1,75,35,2.405000," ","int((-1-cos(x)^2)^(1/2),x)","-\frac{i \sqrt{-\left(1+\cos^{2}\left(x \right)\right) \left(\sin^{2}\left(x \right)\right)}\, \sqrt{1+\cos^{2}\left(x \right)}\, \sqrt{\frac{1}{2}-\frac{\cos \left(2 x \right)}{2}}\, \left(2 \EllipticF \left(i \cos \left(x \right), i\right)-\EllipticE \left(i \cos \left(x \right), i\right)\right)}{\sqrt{\cos^{4}\left(x \right)-1}\, \sin \left(x \right) \sqrt{-1-\left(\cos^{2}\left(x \right)\right)}}"," ",0,"-I*(-(1+cos(x)^2)*sin(x)^2)^(1/2)*(1+cos(x)^2)^(1/2)*(sin(x)^2)^(1/2)*(2*EllipticF(I*cos(x),I)-EllipticE(I*cos(x),I))/(cos(x)^4-1)^(1/2)/sin(x)/(-1-cos(x)^2)^(1/2)","B"
57,1,49,46,0.974000," ","int((a+b*cos(x)^2)^(1/2),x)","-\frac{a \sqrt{\frac{1}{2}-\frac{\cos \left(2 x \right)}{2}}\, \sqrt{\frac{a +b \left(\cos^{2}\left(x \right)\right)}{a}}\, \EllipticE \left(\cos \left(x \right), \sqrt{-\frac{b}{a}}\right)}{\sin \left(x \right) \sqrt{a +b \left(\cos^{2}\left(x \right)\right)}}"," ",0,"-a*(sin(x)^2)^(1/2)*((a+b*cos(x)^2)/a)^(1/2)*EllipticE(cos(x),(-1/a*b)^(1/2))/sin(x)/(a+b*cos(x)^2)^(1/2)","A"
58,1,101,49,2.339000," ","int((1+cos(x)^2)^(3/2),x)","\frac{\sqrt{\left(1+\cos^{2}\left(x \right)\right) \left(\sin^{2}\left(x \right)\right)}\, \left(-\cos \left(x \right) \left(\sin^{4}\left(x \right)\right)+2 \sqrt{\frac{1}{2}-\frac{\cos \left(2 x \right)}{2}}\, \sqrt{-\left(\sin^{2}\left(x \right)\right)+2}\, \EllipticF \left(\cos \left(x \right), i\right)-6 \sqrt{\frac{1}{2}-\frac{\cos \left(2 x \right)}{2}}\, \sqrt{-\left(\sin^{2}\left(x \right)\right)+2}\, \EllipticE \left(\cos \left(x \right), i\right)+2 \left(\sin^{2}\left(x \right)\right) \cos \left(x \right)\right)}{3 \sqrt{1-\left(\cos^{4}\left(x \right)\right)}\, \sin \left(x \right) \sqrt{1+\cos^{2}\left(x \right)}}"," ",0,"1/3*((1+cos(x)^2)*sin(x)^2)^(1/2)*(-cos(x)*sin(x)^4+2*(sin(x)^2)^(1/2)*(-sin(x)^2+2)^(1/2)*EllipticF(cos(x),I)-6*(sin(x)^2)^(1/2)*(-sin(x)^2+2)^(1/2)*EllipticE(cos(x),I)+2*sin(x)^2*cos(x))/(1-cos(x)^4)^(1/2)/sin(x)/(1+cos(x)^2)^(1/2)","B"
59,1,110,87,2.622000," ","int((-1-cos(x)^2)^(3/2),x)","\frac{\sqrt{-\left(1+\cos^{2}\left(x \right)\right) \left(\sin^{2}\left(x \right)\right)}\, \left(-\cos \left(x \right) \left(\sin^{4}\left(x \right)\right)+10 i \sqrt{-\left(\sin^{2}\left(x \right)\right)+2}\, \sqrt{\frac{1}{2}-\frac{\cos \left(2 x \right)}{2}}\, \EllipticF \left(i \cos \left(x \right), i\right)-6 i \sqrt{-\left(\sin^{2}\left(x \right)\right)+2}\, \sqrt{\frac{1}{2}-\frac{\cos \left(2 x \right)}{2}}\, \EllipticE \left(i \cos \left(x \right), i\right)+2 \left(\sin^{2}\left(x \right)\right) \cos \left(x \right)\right)}{3 \sqrt{\cos^{4}\left(x \right)-1}\, \sin \left(x \right) \sqrt{-1-\left(\cos^{2}\left(x \right)\right)}}"," ",0,"1/3*(-(1+cos(x)^2)*sin(x)^2)^(1/2)*(-cos(x)*sin(x)^4+10*I*(-sin(x)^2+2)^(1/2)*(sin(x)^2)^(1/2)*EllipticF(I*cos(x),I)-6*I*(-sin(x)^2+2)^(1/2)*(sin(x)^2)^(1/2)*EllipticE(I*cos(x),I)+2*sin(x)^2*cos(x))/(cos(x)^4-1)^(1/2)/sin(x)/(-1-cos(x)^2)^(1/2)","A"
60,1,192,119,1.793000," ","int((a+b*cos(x)^2)^(3/2),x)","-\frac{-\frac{\sqrt{\frac{1}{2}-\frac{\cos \left(2 x \right)}{2}}\, \sqrt{\frac{a +b \left(\cos^{2}\left(x \right)\right)}{a}}\, \EllipticF \left(\cos \left(x \right), \sqrt{-\frac{b}{a}}\right) a^{2}}{3}-\frac{a \sqrt{\frac{1}{2}-\frac{\cos \left(2 x \right)}{2}}\, \sqrt{\frac{a +b \left(\cos^{2}\left(x \right)\right)}{a}}\, \EllipticF \left(\cos \left(x \right), \sqrt{-\frac{b}{a}}\right) b}{3}+\frac{4 \sqrt{\frac{1}{2}-\frac{\cos \left(2 x \right)}{2}}\, \sqrt{\frac{a +b \left(\cos^{2}\left(x \right)\right)}{a}}\, \EllipticE \left(\cos \left(x \right), \sqrt{-\frac{b}{a}}\right) a^{2}}{3}+\frac{2 \sqrt{\frac{1}{2}-\frac{\cos \left(2 x \right)}{2}}\, \sqrt{\frac{a +b \left(\cos^{2}\left(x \right)\right)}{a}}\, \EllipticE \left(\cos \left(x \right), \sqrt{-\frac{b}{a}}\right) a b}{3}+\frac{\left(\cos^{5}\left(x \right)\right) b^{2}}{3}+\frac{\left(\cos^{3}\left(x \right)\right) a b}{3}-\frac{\left(\cos^{3}\left(x \right)\right) b^{2}}{3}-\frac{a b \cos \left(x \right)}{3}}{\sin \left(x \right) \sqrt{a +b \left(\cos^{2}\left(x \right)\right)}}"," ",0,"-(-1/3*(sin(x)^2)^(1/2)*((a+b*cos(x)^2)/a)^(1/2)*EllipticF(cos(x),(-1/a*b)^(1/2))*a^2-1/3*a*(sin(x)^2)^(1/2)*((a+b*cos(x)^2)/a)^(1/2)*EllipticF(cos(x),(-1/a*b)^(1/2))*b+4/3*(sin(x)^2)^(1/2)*((a+b*cos(x)^2)/a)^(1/2)*EllipticE(cos(x),(-1/a*b)^(1/2))*a^2+2/3*(sin(x)^2)^(1/2)*((a+b*cos(x)^2)/a)^(1/2)*EllipticE(cos(x),(-1/a*b)^(1/2))*a*b+1/3*cos(x)^5*b^2+1/3*cos(x)^3*a*b-1/3*cos(x)^3*b^2-1/3*a*b*cos(x))/sin(x)/(a+b*cos(x)^2)^(1/2)","A"
61,1,41,17,1.813000," ","int(1/(1+cos(x)^2)^(1/2),x)","-\frac{\sqrt{\left(1+\cos^{2}\left(x \right)\right) \left(\sin^{2}\left(x \right)\right)}\, \sqrt{\frac{1}{2}-\frac{\cos \left(2 x \right)}{2}}\, \EllipticF \left(\cos \left(x \right), i\right)}{\sqrt{1-\left(\cos^{4}\left(x \right)\right)}\, \sin \left(x \right)}"," ",0,"-((1+cos(x)^2)*sin(x)^2)^(1/2)*(sin(x)^2)^(1/2)/(1-cos(x)^4)^(1/2)*EllipticF(cos(x),I)/sin(x)","B"
62,1,62,35,2.138000," ","int(1/(-1-cos(x)^2)^(1/2),x)","\frac{i \sqrt{-\left(1+\cos^{2}\left(x \right)\right) \left(\sin^{2}\left(x \right)\right)}\, \sqrt{1+\cos^{2}\left(x \right)}\, \sqrt{\frac{1}{2}-\frac{\cos \left(2 x \right)}{2}}\, \EllipticF \left(i \cos \left(x \right), i\right)}{\sqrt{\cos^{4}\left(x \right)-1}\, \sin \left(x \right) \sqrt{-1-\left(\cos^{2}\left(x \right)\right)}}"," ",0,"I*(-(1+cos(x)^2)*sin(x)^2)^(1/2)*(1+cos(x)^2)^(1/2)*(sin(x)^2)^(1/2)/(cos(x)^4-1)^(1/2)*EllipticF(I*cos(x),I)/sin(x)/(-1-cos(x)^2)^(1/2)","A"
63,1,48,46,0.695000," ","int(1/(a+b*cos(x)^2)^(1/2),x)","-\frac{\sqrt{\frac{1}{2}-\frac{\cos \left(2 x \right)}{2}}\, \sqrt{\frac{a +b \left(\cos^{2}\left(x \right)\right)}{a}}\, \EllipticF \left(\cos \left(x \right), \sqrt{-\frac{b}{a}}\right)}{\sin \left(x \right) \sqrt{a +b \left(\cos^{2}\left(x \right)\right)}}"," ",0,"-(sin(x)^2)^(1/2)*((a+b*cos(x)^2)/a)^(1/2)*EllipticF(cos(x),(-1/a*b)^(1/2))/sin(x)/(a+b*cos(x)^2)^(1/2)","A"
64,1,70,32,2.338000," ","int(1/(1+cos(x)^2)^(3/2),x)","-\frac{\sqrt{-\left(\sin^{4}\left(x \right)\right)+2 \left(\sin^{2}\left(x \right)\right)}\, \left(\sqrt{\frac{1}{2}-\frac{\cos \left(2 x \right)}{2}}\, \sqrt{-\left(\sin^{2}\left(x \right)\right)+2}\, \EllipticE \left(\cos \left(x \right), i\right)+\left(\sin^{2}\left(x \right)\right) \cos \left(x \right)\right)}{2 \sqrt{1-\left(\cos^{4}\left(x \right)\right)}\, \sin \left(x \right) \sqrt{1+\cos^{2}\left(x \right)}}"," ",0,"-1/2*(-sin(x)^4+2*sin(x)^2)^(1/2)*((sin(x)^2)^(1/2)*(-sin(x)^2+2)^(1/2)*EllipticE(cos(x),I)+sin(x)^2*cos(x))/(1-cos(x)^4)^(1/2)/sin(x)/(1+cos(x)^2)^(1/2)","B"
65,1,101,52,2.820000," ","int(1/(-1-cos(x)^2)^(3/2),x)","-\frac{\sqrt{\sin^{4}\left(x \right)-2 \left(\sin^{2}\left(x \right)\right)}\, \left(2 i \sqrt{-\left(\sin^{2}\left(x \right)\right)+2}\, \sqrt{\frac{1}{2}-\frac{\cos \left(2 x \right)}{2}}\, \EllipticF \left(i \cos \left(x \right), i\right)-i \sqrt{-\left(\sin^{2}\left(x \right)\right)+2}\, \sqrt{\frac{1}{2}-\frac{\cos \left(2 x \right)}{2}}\, \EllipticE \left(i \cos \left(x \right), i\right)-\left(\sin^{2}\left(x \right)\right) \cos \left(x \right)\right)}{2 \sqrt{\cos^{4}\left(x \right)-1}\, \sin \left(x \right) \sqrt{-1-\left(\cos^{2}\left(x \right)\right)}}"," ",0,"-1/2*(sin(x)^4-2*sin(x)^2)^(1/2)*(2*I*EllipticF(I*cos(x),I)*(sin(x)^2)^(1/2)*(-sin(x)^2+2)^(1/2)-I*EllipticE(I*cos(x),I)*(sin(x)^2)^(1/2)*(-sin(x)^2+2)^(1/2)-sin(x)^2*cos(x))/(cos(x)^4-1)^(1/2)/sin(x)/(-1-cos(x)^2)^(1/2)","A"
66,1,73,80,1.851000," ","int(1/(a+b*cos(x)^2)^(3/2),x)","-\frac{\sqrt{\frac{1}{2}-\frac{\cos \left(2 x \right)}{2}}\, \sqrt{-\frac{b \left(\sin^{2}\left(x \right)\right)}{a}+\frac{a +b}{a}}\, a \EllipticE \left(\cos \left(x \right), \sqrt{-\frac{b}{a}}\right)+b \cos \left(x \right) \left(\sin^{2}\left(x \right)\right)}{a \left(a +b \right) \sin \left(x \right) \sqrt{a +b \left(\cos^{2}\left(x \right)\right)}}"," ",0,"-((sin(x)^2)^(1/2)*(-b/a*sin(x)^2+(a+b)/a)^(1/2)*a*EllipticE(cos(x),(-1/a*b)^(1/2))+b*cos(x)*sin(x)^2)/a/(a+b)/sin(x)/(a+b*cos(x)^2)^(1/2)","A"
67,1,33,8,0.875000," ","int(cos(x)/(1+cos(x)^2)^(1/2),x)","-\frac{\sqrt{\left(1+\cos^{2}\left(x \right)\right) \left(\sin^{2}\left(x \right)\right)}\, \arcsin \left(\cos^{2}\left(x \right)\right)}{2 \sin \left(x \right) \sqrt{1+\cos^{2}\left(x \right)}}"," ",0,"-1/2*((1+cos(x)^2)*sin(x)^2)^(1/2)*arcsin(cos(x)^2)/sin(x)/(1+cos(x)^2)^(1/2)","B"
68,1,57,11,1.043000," ","int(cos(5+3*x)/(3+cos(5+3*x)^2)^(1/2),x)","\frac{\sqrt{\left(3+\cos^{2}\left(5+3 x \right)\right) \left(\sin^{2}\left(5+3 x \right)\right)}\, \arcsin \left(-1+\frac{\left(\sin^{2}\left(5+3 x \right)\right)}{2}\right)}{6 \sin \left(5+3 x \right) \sqrt{3+\cos^{2}\left(5+3 x \right)}}"," ",0,"1/6*((3+cos(5+3*x)^2)*sin(5+3*x)^2)^(1/2)*arcsin(-1+1/2*sin(5+3*x)^2)/sin(5+3*x)/(3+cos(5+3*x)^2)^(1/2)","B"
69,1,53,8,2.153000," ","int(cos(x)/(4-cos(x)^2)^(1/2),x)","-\frac{\sqrt{-\left(-4+\cos^{2}\left(x \right)\right) \left(\sin^{2}\left(x \right)\right)}\, \ln \left(-\left(\sin^{2}\left(x \right)\right)+\sqrt{\sin^{4}\left(x \right)+3 \left(\sin^{2}\left(x \right)\right)}-\frac{3}{2}\right)}{2 \sin \left(x \right) \sqrt{4-\left(\cos^{2}\left(x \right)\right)}}"," ",0,"-1/2*(-(-4+cos(x)^2)*sin(x)^2)^(1/2)*ln(-sin(x)^2+(sin(x)^4+3*sin(x)^2)^(1/2)-3/2)/sin(x)/(4-cos(x)^2)^(1/2)","B"
70,1,3350,343,0.227000," ","int(1/(a+b*cos(x)^4),x)","\text{output too large to display}"," ",0,"-1/8/(a+b)^(3/2)*ln(a^(1/2)*tan(x)^2-tan(x)*(2*((a+b)*a)^(1/2)-2*a)^(1/2)+(a+b)^(1/2))*(2*(a^2+a*b)^(1/2)-2*a)^(1/2)+1/8/(a+b)^(3/2)*ln(a^(1/2)*tan(x)^2+tan(x)*(2*((a+b)*a)^(1/2)-2*a)^(1/2)+(a+b)^(1/2))*(2*(a^2+a*b)^(1/2)-2*a)^(1/2)+a/(a+b)^(3/2)/(4*a^(1/2)*(a+b)^(1/2)-2*((a+b)*a)^(1/2)+2*a)^(1/2)*arctan((2*a^(1/2)*tan(x)-(2*((a+b)*a)^(1/2)-2*a)^(1/2))/(4*a^(1/2)*(a+b)^(1/2)-2*((a+b)*a)^(1/2)+2*a)^(1/2))+b/(a+b)^(3/2)/(4*a^(1/2)*(a+b)^(1/2)-2*((a+b)*a)^(1/2)+2*a)^(1/2)*arctan((2*a^(1/2)*tan(x)-(2*((a+b)*a)^(1/2)-2*a)^(1/2))/(4*a^(1/2)*(a+b)^(1/2)-2*((a+b)*a)^(1/2)+2*a)^(1/2))+a/(a+b)^(3/2)/(4*a^(1/2)*(a+b)^(1/2)-2*((a+b)*a)^(1/2)+2*a)^(1/2)*arctan((2*a^(1/2)*tan(x)+(2*((a+b)*a)^(1/2)-2*a)^(1/2))/(4*a^(1/2)*(a+b)^(1/2)-2*((a+b)*a)^(1/2)+2*a)^(1/2))+b/(a+b)^(3/2)/(4*a^(1/2)*(a+b)^(1/2)-2*((a+b)*a)^(1/2)+2*a)^(1/2)*arctan((2*a^(1/2)*tan(x)+(2*((a+b)*a)^(1/2)-2*a)^(1/2))/(4*a^(1/2)*(a+b)^(1/2)-2*((a+b)*a)^(1/2)+2*a)^(1/2))-1/8/a^(1/2)/(a+b)*ln(a^(1/2)*tan(x)^2+tan(x)*(2*((a+b)*a)^(1/2)-2*a)^(1/2)+(a+b)^(1/2))*(2*(a^2+a*b)^(1/2)-2*a)^(1/2)+1/8/a^(1/2)/(a+b)*ln(a^(1/2)*tan(x)^2-tan(x)*(2*((a+b)*a)^(1/2)-2*a)^(1/2)+(a+b)^(1/2))*(2*(a^2+a*b)^(1/2)-2*a)^(1/2)+1/8*a/b/(a+b)^(3/2)*ln(a^(1/2)*tan(x)^2+tan(x)*(2*((a+b)*a)^(1/2)-2*a)^(1/2)+(a+b)^(1/2))*(2*(a^2+a*b)^(1/2)-2*a)^(1/2)+1/8/b/(a+b)^(3/2)*ln(a^(1/2)*tan(x)^2+tan(x)*(2*((a+b)*a)^(1/2)-2*a)^(1/2)+(a+b)^(1/2))*(2*(a^2+a*b)^(1/2)-2*a)^(1/2)*(a^2+a*b)^(1/2)+1/8/a/(a+b)^(3/2)*ln(a^(1/2)*tan(x)^2+tan(x)*(2*((a+b)*a)^(1/2)-2*a)^(1/2)+(a+b)^(1/2))*(2*(a^2+a*b)^(1/2)-2*a)^(1/2)*(a^2+a*b)^(1/2)+1/4/a^(1/2)/b/(a+b)/(4*a^(1/2)*(a+b)^(1/2)-2*((a+b)*a)^(1/2)+2*a)^(1/2)*arctan((2*a^(1/2)*tan(x)+(2*((a+b)*a)^(1/2)-2*a)^(1/2))/(4*a^(1/2)*(a+b)^(1/2)-2*((a+b)*a)^(1/2)+2*a)^(1/2))*(2*((a+b)*a)^(1/2)-2*a)^(1/2)*(2*(a^2+a*b)^(1/2)-2*a)^(1/2)*(a^2+a*b)^(1/2)+1/4/a^(1/2)/b/(a+b)/(4*a^(1/2)*(a+b)^(1/2)-2*((a+b)*a)^(1/2)+2*a)^(1/2)*arctan((2*a^(1/2)*tan(x)-(2*((a+b)*a)^(1/2)-2*a)^(1/2))/(4*a^(1/2)*(a+b)^(1/2)-2*((a+b)*a)^(1/2)+2*a)^(1/2))*(2*((a+b)*a)^(1/2)-2*a)^(1/2)*(2*(a^2+a*b)^(1/2)-2*a)^(1/2)*(a^2+a*b)^(1/2)-1/4/a/(a+b)^(3/2)/(4*a^(1/2)*(a+b)^(1/2)-2*((a+b)*a)^(1/2)+2*a)^(1/2)*arctan((2*a^(1/2)*tan(x)-(2*((a+b)*a)^(1/2)-2*a)^(1/2))/(4*a^(1/2)*(a+b)^(1/2)-2*((a+b)*a)^(1/2)+2*a)^(1/2))*(2*((a+b)*a)^(1/2)-2*a)^(1/2)*(2*(a^2+a*b)^(1/2)-2*a)^(1/2)*(a^2+a*b)^(1/2)+1/4/a^(3/2)/(a+b)/(4*a^(1/2)*(a+b)^(1/2)-2*((a+b)*a)^(1/2)+2*a)^(1/2)*arctan((2*a^(1/2)*tan(x)-(2*((a+b)*a)^(1/2)-2*a)^(1/2))/(4*a^(1/2)*(a+b)^(1/2)-2*((a+b)*a)^(1/2)+2*a)^(1/2))*(2*((a+b)*a)^(1/2)-2*a)^(1/2)*(2*(a^2+a*b)^(1/2)-2*a)^(1/2)*(a^2+a*b)^(1/2)+1/4*a^(1/2)/b/(a+b)/(4*a^(1/2)*(a+b)^(1/2)-2*((a+b)*a)^(1/2)+2*a)^(1/2)*arctan((2*a^(1/2)*tan(x)-(2*((a+b)*a)^(1/2)-2*a)^(1/2))/(4*a^(1/2)*(a+b)^(1/2)-2*((a+b)*a)^(1/2)+2*a)^(1/2))*(2*((a+b)*a)^(1/2)-2*a)^(1/2)*(2*(a^2+a*b)^(1/2)-2*a)^(1/2)+1/4/a^(3/2)/(a+b)/(4*a^(1/2)*(a+b)^(1/2)-2*((a+b)*a)^(1/2)+2*a)^(1/2)*arctan((2*a^(1/2)*tan(x)+(2*((a+b)*a)^(1/2)-2*a)^(1/2))/(4*a^(1/2)*(a+b)^(1/2)-2*((a+b)*a)^(1/2)+2*a)^(1/2))*(2*((a+b)*a)^(1/2)-2*a)^(1/2)*(2*(a^2+a*b)^(1/2)-2*a)^(1/2)*(a^2+a*b)^(1/2)+1/4*a^(1/2)/b/(a+b)/(4*a^(1/2)*(a+b)^(1/2)-2*((a+b)*a)^(1/2)+2*a)^(1/2)*arctan((2*a^(1/2)*tan(x)+(2*((a+b)*a)^(1/2)-2*a)^(1/2))/(4*a^(1/2)*(a+b)^(1/2)-2*((a+b)*a)^(1/2)+2*a)^(1/2))*(2*((a+b)*a)^(1/2)-2*a)^(1/2)*(2*(a^2+a*b)^(1/2)-2*a)^(1/2)-1/4*a/b/(a+b)^(3/2)/(4*a^(1/2)*(a+b)^(1/2)-2*((a+b)*a)^(1/2)+2*a)^(1/2)*arctan((2*a^(1/2)*tan(x)-(2*((a+b)*a)^(1/2)-2*a)^(1/2))/(4*a^(1/2)*(a+b)^(1/2)-2*((a+b)*a)^(1/2)+2*a)^(1/2))*(2*((a+b)*a)^(1/2)-2*a)^(1/2)*(2*(a^2+a*b)^(1/2)-2*a)^(1/2)-1/4/b/(a+b)^(3/2)/(4*a^(1/2)*(a+b)^(1/2)-2*((a+b)*a)^(1/2)+2*a)^(1/2)*arctan((2*a^(1/2)*tan(x)-(2*((a+b)*a)^(1/2)-2*a)^(1/2))/(4*a^(1/2)*(a+b)^(1/2)-2*((a+b)*a)^(1/2)+2*a)^(1/2))*(2*((a+b)*a)^(1/2)-2*a)^(1/2)*(2*(a^2+a*b)^(1/2)-2*a)^(1/2)*(a^2+a*b)^(1/2)-1/4*a/b/(a+b)^(3/2)/(4*a^(1/2)*(a+b)^(1/2)-2*((a+b)*a)^(1/2)+2*a)^(1/2)*arctan((2*a^(1/2)*tan(x)+(2*((a+b)*a)^(1/2)-2*a)^(1/2))/(4*a^(1/2)*(a+b)^(1/2)-2*((a+b)*a)^(1/2)+2*a)^(1/2))*(2*((a+b)*a)^(1/2)-2*a)^(1/2)*(2*(a^2+a*b)^(1/2)-2*a)^(1/2)-1/4/b/(a+b)^(3/2)/(4*a^(1/2)*(a+b)^(1/2)-2*((a+b)*a)^(1/2)+2*a)^(1/2)*arctan((2*a^(1/2)*tan(x)+(2*((a+b)*a)^(1/2)-2*a)^(1/2))/(4*a^(1/2)*(a+b)^(1/2)-2*((a+b)*a)^(1/2)+2*a)^(1/2))*(2*((a+b)*a)^(1/2)-2*a)^(1/2)*(2*(a^2+a*b)^(1/2)-2*a)^(1/2)*(a^2+a*b)^(1/2)-1/4/a/(a+b)^(3/2)/(4*a^(1/2)*(a+b)^(1/2)-2*((a+b)*a)^(1/2)+2*a)^(1/2)*arctan((2*a^(1/2)*tan(x)+(2*((a+b)*a)^(1/2)-2*a)^(1/2))/(4*a^(1/2)*(a+b)^(1/2)-2*((a+b)*a)^(1/2)+2*a)^(1/2))*(2*((a+b)*a)^(1/2)-2*a)^(1/2)*(2*(a^2+a*b)^(1/2)-2*a)^(1/2)*(a^2+a*b)^(1/2)-1/8/a^(3/2)/(a+b)*ln(a^(1/2)*tan(x)^2+tan(x)*(2*((a+b)*a)^(1/2)-2*a)^(1/2)+(a+b)^(1/2))*(2*(a^2+a*b)^(1/2)-2*a)^(1/2)*(a^2+a*b)^(1/2)-1/8*a^(1/2)/b/(a+b)*ln(a^(1/2)*tan(x)^2+tan(x)*(2*((a+b)*a)^(1/2)-2*a)^(1/2)+(a+b)^(1/2))*(2*(a^2+a*b)^(1/2)-2*a)^(1/2)-1/4/(a+b)^(3/2)/(4*a^(1/2)*(a+b)^(1/2)-2*((a+b)*a)^(1/2)+2*a)^(1/2)*arctan((2*a^(1/2)*tan(x)+(2*((a+b)*a)^(1/2)-2*a)^(1/2))/(4*a^(1/2)*(a+b)^(1/2)-2*((a+b)*a)^(1/2)+2*a)^(1/2))*(2*((a+b)*a)^(1/2)-2*a)^(1/2)*(2*(a^2+a*b)^(1/2)-2*a)^(1/2)+1/8*a^(1/2)/b/(a+b)*ln(a^(1/2)*tan(x)^2-tan(x)*(2*((a+b)*a)^(1/2)-2*a)^(1/2)+(a+b)^(1/2))*(2*(a^2+a*b)^(1/2)-2*a)^(1/2)+1/4/a^(1/2)/(a+b)/(4*a^(1/2)*(a+b)^(1/2)-2*((a+b)*a)^(1/2)+2*a)^(1/2)*arctan((2*a^(1/2)*tan(x)+(2*((a+b)*a)^(1/2)-2*a)^(1/2))/(4*a^(1/2)*(a+b)^(1/2)-2*((a+b)*a)^(1/2)+2*a)^(1/2))*(2*((a+b)*a)^(1/2)-2*a)^(1/2)*(2*(a^2+a*b)^(1/2)-2*a)^(1/2)-1/8*a/b/(a+b)^(3/2)*ln(a^(1/2)*tan(x)^2-tan(x)*(2*((a+b)*a)^(1/2)-2*a)^(1/2)+(a+b)^(1/2))*(2*(a^2+a*b)^(1/2)-2*a)^(1/2)-1/8/b/(a+b)^(3/2)*ln(a^(1/2)*tan(x)^2-tan(x)*(2*((a+b)*a)^(1/2)-2*a)^(1/2)+(a+b)^(1/2))*(2*(a^2+a*b)^(1/2)-2*a)^(1/2)*(a^2+a*b)^(1/2)-1/8/a/(a+b)^(3/2)*ln(a^(1/2)*tan(x)^2-tan(x)*(2*((a+b)*a)^(1/2)-2*a)^(1/2)+(a+b)^(1/2))*(2*(a^2+a*b)^(1/2)-2*a)^(1/2)*(a^2+a*b)^(1/2)-1/4/(a+b)^(3/2)/(4*a^(1/2)*(a+b)^(1/2)-2*((a+b)*a)^(1/2)+2*a)^(1/2)*arctan((2*a^(1/2)*tan(x)-(2*((a+b)*a)^(1/2)-2*a)^(1/2))/(4*a^(1/2)*(a+b)^(1/2)-2*((a+b)*a)^(1/2)+2*a)^(1/2))*(2*((a+b)*a)^(1/2)-2*a)^(1/2)*(2*(a^2+a*b)^(1/2)-2*a)^(1/2)+1/8/a^(3/2)/(a+b)*ln(a^(1/2)*tan(x)^2-tan(x)*(2*((a+b)*a)^(1/2)-2*a)^(1/2)+(a+b)^(1/2))*(2*(a^2+a*b)^(1/2)-2*a)^(1/2)*(a^2+a*b)^(1/2)+1/8/a^(1/2)/b/(a+b)*ln(a^(1/2)*tan(x)^2-tan(x)*(2*((a+b)*a)^(1/2)-2*a)^(1/2)+(a+b)^(1/2))*(2*(a^2+a*b)^(1/2)-2*a)^(1/2)*(a^2+a*b)^(1/2)-1/8/a^(1/2)/b/(a+b)*ln(a^(1/2)*tan(x)^2+tan(x)*(2*((a+b)*a)^(1/2)-2*a)^(1/2)+(a+b)^(1/2))*(2*(a^2+a*b)^(1/2)-2*a)^(1/2)*(a^2+a*b)^(1/2)+1/4/a^(1/2)/(a+b)/(4*a^(1/2)*(a+b)^(1/2)-2*((a+b)*a)^(1/2)+2*a)^(1/2)*arctan((2*a^(1/2)*tan(x)-(2*((a+b)*a)^(1/2)-2*a)^(1/2))/(4*a^(1/2)*(a+b)^(1/2)-2*((a+b)*a)^(1/2)+2*a)^(1/2))*(2*((a+b)*a)^(1/2)-2*a)^(1/2)*(2*(a^2+a*b)^(1/2)-2*a)^(1/2)","B"
71,1,64,65,0.089000," ","int(1/(a-b*cos(x)^4),x)","-\frac{\arctanh \left(\frac{a \tan \left(x \right)}{\sqrt{\left(\sqrt{a b}-a \right) a}}\right)}{2 \sqrt{\left(\sqrt{a b}-a \right) a}}+\frac{\arctan \left(\frac{a \tan \left(x \right)}{\sqrt{\left(\sqrt{a b}+a \right) a}}\right)}{2 \sqrt{\left(\sqrt{a b}+a \right) a}}"," ",0,"-1/2/(((a*b)^(1/2)-a)*a)^(1/2)*arctanh(a*tan(x)/(((a*b)^(1/2)-a)*a)^(1/2))+1/2/(((a*b)^(1/2)+a)*a)^(1/2)*arctan(a*tan(x)/(((a*b)^(1/2)+a)*a)^(1/2))","A"
72,1,227,218,0.216000," ","int(1/(1+cos(x)^4),x)","\frac{\sqrt{2}\, \sqrt{-2+2 \sqrt{2}}\, \ln \left(\tan^{2}\left(x \right)-\tan \left(x \right) \sqrt{-2+2 \sqrt{2}}+\sqrt{2}\right)}{16}+\frac{\arctan \left(\frac{2 \tan \left(x \right)-\sqrt{-2+2 \sqrt{2}}}{\sqrt{2 \sqrt{2}+2}}\right) \sqrt{2}}{4 \sqrt{2 \sqrt{2}+2}}+\frac{\arctan \left(\frac{2 \tan \left(x \right)-\sqrt{-2+2 \sqrt{2}}}{\sqrt{2 \sqrt{2}+2}}\right)}{2 \sqrt{2 \sqrt{2}+2}}-\frac{\sqrt{2}\, \sqrt{-2+2 \sqrt{2}}\, \ln \left(\tan^{2}\left(x \right)+\tan \left(x \right) \sqrt{-2+2 \sqrt{2}}+\sqrt{2}\right)}{16}+\frac{\arctan \left(\frac{2 \tan \left(x \right)+\sqrt{-2+2 \sqrt{2}}}{\sqrt{2 \sqrt{2}+2}}\right) \sqrt{2}}{4 \sqrt{2 \sqrt{2}+2}}+\frac{\arctan \left(\frac{2 \tan \left(x \right)+\sqrt{-2+2 \sqrt{2}}}{\sqrt{2 \sqrt{2}+2}}\right)}{2 \sqrt{2 \sqrt{2}+2}}"," ",0,"1/16*2^(1/2)*(-2+2*2^(1/2))^(1/2)*ln(tan(x)^2-tan(x)*(-2+2*2^(1/2))^(1/2)+2^(1/2))+1/4/(2*2^(1/2)+2)^(1/2)*arctan((2*tan(x)-(-2+2*2^(1/2))^(1/2))/(2*2^(1/2)+2)^(1/2))*2^(1/2)+1/2/(2*2^(1/2)+2)^(1/2)*arctan((2*tan(x)-(-2+2*2^(1/2))^(1/2))/(2*2^(1/2)+2)^(1/2))-1/16*2^(1/2)*(-2+2*2^(1/2))^(1/2)*ln(tan(x)^2+tan(x)*(-2+2*2^(1/2))^(1/2)+2^(1/2))+1/4/(2*2^(1/2)+2)^(1/2)*arctan((2*tan(x)+(-2+2*2^(1/2))^(1/2))/(2*2^(1/2)+2)^(1/2))*2^(1/2)+1/2/(2*2^(1/2)+2)^(1/2)*arctan((2*tan(x)+(-2+2*2^(1/2))^(1/2))/(2*2^(1/2)+2)^(1/2))","A"
73,1,21,33,0.081000," ","int(1/(1-cos(x)^4),x)","\frac{\arctan \left(\frac{\tan \left(x \right) \sqrt{2}}{2}\right) \sqrt{2}}{4}-\frac{1}{2 \tan \left(x \right)}"," ",0,"1/4*arctan(1/2*tan(x)*2^(1/2))*2^(1/2)-1/2/tan(x)","A"
74,1,150,312,0.099000," ","int(1/(a+b*cos(x)^5),x)","\frac{\left(\munderset{\textit{\_R} =\RootOf \left(\left(a -b \right) \textit{\_Z}^{10}+\left(5 a +5 b \right) \textit{\_Z}^{8}+\left(10 a -10 b \right) \textit{\_Z}^{6}+\left(10 a +10 b \right) \textit{\_Z}^{4}+\left(5 a -5 b \right) \textit{\_Z}^{2}+a +b \right)}{\sum}\frac{\left(\textit{\_R}^{8}+4 \textit{\_R}^{6}+6 \textit{\_R}^{4}+4 \textit{\_R}^{2}+1\right) \ln \left(\tan \left(\frac{x}{2}\right)-\textit{\_R} \right)}{\textit{\_R}^{9} a -\textit{\_R}^{9} b +4 \textit{\_R}^{7} a +4 \textit{\_R}^{7} b +6 \textit{\_R}^{5} a -6 \textit{\_R}^{5} b +4 \textit{\_R}^{3} a +4 \textit{\_R}^{3} b +\textit{\_R} a -\textit{\_R} b}\right)}{5}"," ",0,"1/5*sum((_R^8+4*_R^6+6*_R^4+4*_R^2+1)/(_R^9*a-_R^9*b+4*_R^7*a+4*_R^7*b+6*_R^5*a-6*_R^5*b+4*_R^3*a+4*_R^3*b+_R*a-_R*b)*ln(tan(1/2*x)-_R),_R=RootOf((a-b)*_Z^10+(5*a+5*b)*_Z^8+(10*a-10*b)*_Z^6+(10*a+10*b)*_Z^4+(5*a-5*b)*_Z^2+a+b))","C"
75,1,60,109,0.464000," ","int(1/(a+b*cos(x)^6),x)","\frac{\munderset{\textit{\_R} =\RootOf \left(a \,\textit{\_Z}^{6}+3 a \,\textit{\_Z}^{4}+3 a \,\textit{\_Z}^{2}+a +b \right)}{\sum}\frac{\left(\textit{\_R}^{4}+2 \textit{\_R}^{2}+1\right) \ln \left(\tan \left(x \right)-\textit{\_R} \right)}{\textit{\_R}^{5}+2 \textit{\_R}^{3}+\textit{\_R}}}{6 a}"," ",0,"1/6/a*sum((_R^4+2*_R^2+1)/(_R^5+2*_R^3+_R)*ln(tan(x)-_R),_R=RootOf(_Z^6*a+3*_Z^4*a+3*_Z^2*a+a+b))","C"
76,1,76,169,0.218000," ","int(1/(a+b*cos(x)^8),x)","\frac{\munderset{\textit{\_R} =\RootOf \left(a \,\textit{\_Z}^{8}+4 a \,\textit{\_Z}^{6}+6 a \,\textit{\_Z}^{4}+4 a \,\textit{\_Z}^{2}+a +b \right)}{\sum}\frac{\left(\textit{\_R}^{6}+3 \textit{\_R}^{4}+3 \textit{\_R}^{2}+1\right) \ln \left(\tan \left(x \right)-\textit{\_R} \right)}{\textit{\_R}^{7}+3 \textit{\_R}^{5}+3 \textit{\_R}^{3}+\textit{\_R}}}{8 a}"," ",0,"1/8/a*sum((_R^6+3*_R^4+3*_R^2+1)/(_R^7+3*_R^5+3*_R^3+_R)*ln(tan(x)-_R),_R=RootOf(_Z^8*a+4*_Z^6*a+6*_Z^4*a+4*_Z^2*a+a+b))","C"
77,1,148,312,0.095000," ","int(1/(a-b*cos(x)^5),x)","\frac{\left(\munderset{\textit{\_R} =\RootOf \left(\left(a +b \right) \textit{\_Z}^{10}+\left(5 a -5 b \right) \textit{\_Z}^{8}+\left(10 a +10 b \right) \textit{\_Z}^{6}+\left(10 a -10 b \right) \textit{\_Z}^{4}+\left(5 a +5 b \right) \textit{\_Z}^{2}+a -b \right)}{\sum}\frac{\left(\textit{\_R}^{8}+4 \textit{\_R}^{6}+6 \textit{\_R}^{4}+4 \textit{\_R}^{2}+1\right) \ln \left(\tan \left(\frac{x}{2}\right)-\textit{\_R} \right)}{\textit{\_R}^{9} a +\textit{\_R}^{9} b +4 \textit{\_R}^{7} a -4 \textit{\_R}^{7} b +6 \textit{\_R}^{5} a +6 \textit{\_R}^{5} b +4 \textit{\_R}^{3} a -4 \textit{\_R}^{3} b +\textit{\_R} a +\textit{\_R} b}\right)}{5}"," ",0,"1/5*sum((_R^8+4*_R^6+6*_R^4+4*_R^2+1)/(_R^9*a+_R^9*b+4*_R^7*a-4*_R^7*b+6*_R^5*a+6*_R^5*b+4*_R^3*a-4*_R^3*b+_R*a+_R*b)*ln(tan(1/2*x)-_R),_R=RootOf((a+b)*_Z^10+(5*a-5*b)*_Z^8+(10*a+10*b)*_Z^6+(10*a-10*b)*_Z^4+(5*a+5*b)*_Z^2+a-b))","C"
78,1,62,113,0.429000," ","int(1/(a-b*cos(x)^6),x)","\frac{\munderset{\textit{\_R} =\RootOf \left(a \,\textit{\_Z}^{6}+3 a \,\textit{\_Z}^{4}+3 a \,\textit{\_Z}^{2}+a -b \right)}{\sum}\frac{\left(\textit{\_R}^{4}+2 \textit{\_R}^{2}+1\right) \ln \left(\tan \left(x \right)-\textit{\_R} \right)}{\textit{\_R}^{5}+2 \textit{\_R}^{3}+\textit{\_R}}}{6 a}"," ",0,"1/6/a*sum((_R^4+2*_R^2+1)/(_R^5+2*_R^3+_R)*ln(tan(x)-_R),_R=RootOf(_Z^6*a+3*_Z^4*a+3*_Z^2*a+a-b))","C"
79,1,78,137,0.221000," ","int(1/(a-b*cos(x)^8),x)","\frac{\munderset{\textit{\_R} =\RootOf \left(a \,\textit{\_Z}^{8}+4 a \,\textit{\_Z}^{6}+6 a \,\textit{\_Z}^{4}+4 a \,\textit{\_Z}^{2}+a -b \right)}{\sum}\frac{\left(\textit{\_R}^{6}+3 \textit{\_R}^{4}+3 \textit{\_R}^{2}+1\right) \ln \left(\tan \left(x \right)-\textit{\_R} \right)}{\textit{\_R}^{7}+3 \textit{\_R}^{5}+3 \textit{\_R}^{3}+\textit{\_R}}}{8 a}"," ",0,"1/8/a*sum((_R^6+3*_R^4+3*_R^2+1)/(_R^7+3*_R^5+3*_R^3+_R)*ln(tan(x)-_R),_R=RootOf(_Z^8*a+4*_Z^6*a+6*_Z^4*a+4*_Z^2*a+a-b))","C"
80,1,62,160,0.071000," ","int(1/(1+cos(x)^5),x)","\frac{\tan \left(\frac{x}{2}\right)}{5}+\frac{\left(\munderset{\textit{\_R} =\RootOf \left(5 \textit{\_Z}^{8}+10 \textit{\_Z}^{4}+1\right)}{\sum}\frac{\left(5 \textit{\_R}^{6}+5 \textit{\_R}^{4}+5 \textit{\_R}^{2}+1\right) \ln \left(\tan \left(\frac{x}{2}\right)-\textit{\_R} \right)}{\textit{\_R}^{7}+\textit{\_R}^{3}}\right)}{50}"," ",0,"1/5*tan(1/2*x)+1/50*sum((5*_R^6+5*_R^4+5*_R^2+1)/(_R^7+_R^3)*ln(tan(1/2*x)-_R),_R=RootOf(5*_Z^8+10*_Z^4+1))","C"
81,1,73,58,0.069000," ","int(1/(1+cos(x)^6),x)","-\frac{\ln \left(\tan^{2}\left(x \right)+\tan \left(x \right)+1\right)}{12}+\frac{\sqrt{3}\, \arctan \left(\frac{\left(2 \tan \left(x \right)+1\right) \sqrt{3}}{3}\right)}{6}+\frac{\arctan \left(\frac{\tan \left(x \right) \sqrt{2}}{2}\right) \sqrt{2}}{6}+\frac{\ln \left(\tan^{2}\left(x \right)-\tan \left(x \right)+1\right)}{12}+\frac{\sqrt{3}\, \arctan \left(\frac{\left(2 \tan \left(x \right)-1\right) \sqrt{3}}{3}\right)}{6}"," ",0,"-1/12*ln(tan(x)^2+tan(x)+1)+1/6*3^(1/2)*arctan(1/3*(2*tan(x)+1)*3^(1/2))+1/6*arctan(1/2*tan(x)*2^(1/2))*2^(1/2)+1/12*ln(tan(x)^2-tan(x)+1)+1/6*3^(1/2)*arctan(1/3*(2*tan(x)-1)*3^(1/2))","A"
82,1,67,89,0.071000," ","int(1/(1+cos(x)^8),x)","\frac{\left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{8}+4 \textit{\_Z}^{6}+6 \textit{\_Z}^{4}+4 \textit{\_Z}^{2}+2\right)}{\sum}\frac{\left(\textit{\_R}^{6}+3 \textit{\_R}^{4}+3 \textit{\_R}^{2}+1\right) \ln \left(\tan \left(x \right)-\textit{\_R} \right)}{\textit{\_R}^{7}+3 \textit{\_R}^{5}+3 \textit{\_R}^{3}+\textit{\_R}}\right)}{8}"," ",0,"1/8*sum((_R^6+3*_R^4+3*_R^2+1)/(_R^7+3*_R^5+3*_R^3+_R)*ln(tan(x)-_R),_R=RootOf(_Z^8+4*_Z^6+6*_Z^4+4*_Z^2+2))","C"
83,1,62,145,0.076000," ","int(1/(1-cos(x)^5),x)","\frac{\left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{8}+10 \textit{\_Z}^{4}+5\right)}{\sum}\frac{\left(\textit{\_R}^{6}+5 \textit{\_R}^{4}+5 \textit{\_R}^{2}+5\right) \ln \left(\tan \left(\frac{x}{2}\right)-\textit{\_R} \right)}{\textit{\_R}^{7}+5 \textit{\_R}^{3}}\right)}{10}-\frac{1}{5 \tan \left(\frac{x}{2}\right)}"," ",0,"1/10*sum((_R^6+5*_R^4+5*_R^2+5)/(_R^7+5*_R^3)*ln(tan(1/2*x)-_R),_R=RootOf(_Z^8+10*_Z^4+5))-1/5/tan(1/2*x)","C"
84,1,233,49,0.237000," ","int(1/(1-cos(x)^6),x)","-\frac{\sqrt{3}\, \sqrt{2 \sqrt{3}-3}\, \ln \left(\tan^{2}\left(x \right)+\tan \left(x \right) \sqrt{2 \sqrt{3}-3}+\sqrt{3}\right)}{36}+\frac{\arctan \left(\frac{2 \tan \left(x \right)+\sqrt{2 \sqrt{3}-3}}{\sqrt{2 \sqrt{3}+3}}\right)}{3 \sqrt{2 \sqrt{3}+3}}+\frac{\arctan \left(\frac{2 \tan \left(x \right)+\sqrt{2 \sqrt{3}-3}}{\sqrt{2 \sqrt{3}+3}}\right) \sqrt{3}}{6 \sqrt{2 \sqrt{3}+3}}+\frac{\sqrt{3}\, \sqrt{2 \sqrt{3}-3}\, \ln \left(\tan^{2}\left(x \right)-\tan \left(x \right) \sqrt{2 \sqrt{3}-3}+\sqrt{3}\right)}{36}+\frac{\arctan \left(\frac{2 \tan \left(x \right)-\sqrt{2 \sqrt{3}-3}}{\sqrt{2 \sqrt{3}+3}}\right)}{3 \sqrt{2 \sqrt{3}+3}}+\frac{\arctan \left(\frac{2 \tan \left(x \right)-\sqrt{2 \sqrt{3}-3}}{\sqrt{2 \sqrt{3}+3}}\right) \sqrt{3}}{6 \sqrt{2 \sqrt{3}+3}}-\frac{1}{3 \tan \left(x \right)}"," ",0,"-1/36*3^(1/2)*(2*3^(1/2)-3)^(1/2)*ln(tan(x)^2+tan(x)*(2*3^(1/2)-3)^(1/2)+3^(1/2))+1/3/(2*3^(1/2)+3)^(1/2)*arctan((2*tan(x)+(2*3^(1/2)-3)^(1/2))/(2*3^(1/2)+3)^(1/2))+1/6/(2*3^(1/2)+3)^(1/2)*arctan((2*tan(x)+(2*3^(1/2)-3)^(1/2))/(2*3^(1/2)+3)^(1/2))*3^(1/2)+1/36*3^(1/2)*(2*3^(1/2)-3)^(1/2)*ln(tan(x)^2-tan(x)*(2*3^(1/2)-3)^(1/2)+3^(1/2))+1/3/(2*3^(1/2)+3)^(1/2)*arctan((2*tan(x)-(2*3^(1/2)-3)^(1/2))/(2*3^(1/2)+3)^(1/2))+1/6/(2*3^(1/2)+3)^(1/2)*arctan((2*tan(x)-(2*3^(1/2)-3)^(1/2))/(2*3^(1/2)+3)^(1/2))*3^(1/2)-1/3/tan(x)","B"
85,1,246,65,0.112000," ","int(1/(1-cos(x)^8),x)","\frac{\arctan \left(\frac{\tan \left(x \right) \sqrt{2}}{2}\right) \sqrt{2}}{8}+\frac{\sqrt{2}\, \sqrt{-2+2 \sqrt{2}}\, \ln \left(\tan^{2}\left(x \right)-\tan \left(x \right) \sqrt{-2+2 \sqrt{2}}+\sqrt{2}\right)}{32}+\frac{\arctan \left(\frac{2 \tan \left(x \right)-\sqrt{-2+2 \sqrt{2}}}{\sqrt{2 \sqrt{2}+2}}\right) \sqrt{2}}{8 \sqrt{2 \sqrt{2}+2}}+\frac{\arctan \left(\frac{2 \tan \left(x \right)-\sqrt{-2+2 \sqrt{2}}}{\sqrt{2 \sqrt{2}+2}}\right)}{4 \sqrt{2 \sqrt{2}+2}}-\frac{\sqrt{2}\, \sqrt{-2+2 \sqrt{2}}\, \ln \left(\tan^{2}\left(x \right)+\tan \left(x \right) \sqrt{-2+2 \sqrt{2}}+\sqrt{2}\right)}{32}+\frac{\arctan \left(\frac{2 \tan \left(x \right)+\sqrt{-2+2 \sqrt{2}}}{\sqrt{2 \sqrt{2}+2}}\right) \sqrt{2}}{8 \sqrt{2 \sqrt{2}+2}}+\frac{\arctan \left(\frac{2 \tan \left(x \right)+\sqrt{-2+2 \sqrt{2}}}{\sqrt{2 \sqrt{2}+2}}\right)}{4 \sqrt{2 \sqrt{2}+2}}-\frac{1}{4 \tan \left(x \right)}"," ",0,"1/8*arctan(1/2*tan(x)*2^(1/2))*2^(1/2)+1/32*2^(1/2)*(-2+2*2^(1/2))^(1/2)*ln(tan(x)^2-tan(x)*(-2+2*2^(1/2))^(1/2)+2^(1/2))+1/8/(2*2^(1/2)+2)^(1/2)*arctan((2*tan(x)-(-2+2*2^(1/2))^(1/2))/(2*2^(1/2)+2)^(1/2))*2^(1/2)+1/4/(2*2^(1/2)+2)^(1/2)*arctan((2*tan(x)-(-2+2*2^(1/2))^(1/2))/(2*2^(1/2)+2)^(1/2))-1/32*2^(1/2)*(-2+2*2^(1/2))^(1/2)*ln(tan(x)^2+tan(x)*(-2+2*2^(1/2))^(1/2)+2^(1/2))+1/8/(2*2^(1/2)+2)^(1/2)*arctan((2*tan(x)+(-2+2*2^(1/2))^(1/2))/(2*2^(1/2)+2)^(1/2))*2^(1/2)+1/4/(2*2^(1/2)+2)^(1/2)*arctan((2*tan(x)+(-2+2*2^(1/2))^(1/2))/(2*2^(1/2)+2)^(1/2))-1/4/tan(x)","B"
86,1,16,15,0.101000," ","int(tan(x)/(1+cos(x)^2),x)","-\ln \left(\cos \left(x \right)\right)+\frac{\ln \left(1+\cos^{2}\left(x \right)\right)}{2}"," ",0,"-ln(cos(x))+1/2*ln(1+cos(x)^2)","A"
87,1,43,32,0.085000," ","int((a+b*cos(x)^2)^(1/2)*tan(x),x)","-\sqrt{a +b \left(\cos^{2}\left(x \right)\right)}+\sqrt{a}\, \ln \left(\frac{2 a +2 \sqrt{a}\, \sqrt{a +b \left(\cos^{2}\left(x \right)\right)}}{\cos \left(x \right)}\right)"," ",0,"-(a+b*cos(x)^2)^(1/2)+a^(1/2)*ln((2*a+2*a^(1/2)*(a+b*cos(x)^2)^(1/2))/cos(x))","A"
88,1,17,16,0.987000," ","int((1-cos(x)^2)^(1/2)*tan(x),x)","-\sqrt{\frac{1}{2}-\frac{\cos \left(2 x \right)}{2}}+\arctanh \left(\frac{2}{\sqrt{2-2 \cos \left(2 x \right)}}\right)"," ",0,"-(sin(x)^2)^(1/2)+arctanh(1/(sin(x)^2)^(1/2))","A"
89,1,30,19,0.095000," ","int(tan(x)/(a+b*cos(x)^2)^(1/2),x)","\frac{\ln \left(\frac{2 a +2 \sqrt{a}\, \sqrt{a +b \left(\cos^{2}\left(x \right)\right)}}{\cos \left(x \right)}\right)}{\sqrt{a}}"," ",0,"1/a^(1/2)*ln((2*a+2*a^(1/2)*(a+b*cos(x)^2)^(1/2))/cos(x))","A"
90,1,10,9,0.087000," ","int(tan(x)/(1+cos(x)^2)^(1/2),x)","\arctanh \left(\frac{1}{\sqrt{1+\cos^{2}\left(x \right)}}\right)"," ",0,"arctanh(1/(1+cos(x)^2)^(1/2))","A"
91,1,8,7,0.440000," ","int(tan(x)/(1-cos(x)^2)^(1/2),x)","\arctanh \left(\frac{2}{\sqrt{2-2 \cos \left(2 x \right)}}\right)"," ",0,"arctanh(1/(sin(x)^2)^(1/2))","A"
92,1,125,112,0.109000," ","int(tan(x)^3/(a+b*cos(x)^3),x)","\frac{\ln \left(\cos \left(x \right)+\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 a \left(\frac{a}{b}\right)^{\frac{2}{3}}}-\frac{\ln \left(\cos^{2}\left(x \right)-\left(\frac{a}{b}\right)^{\frac{1}{3}} \cos \left(x \right)+\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 a \left(\frac{a}{b}\right)^{\frac{2}{3}}}+\frac{\sqrt{3}\, \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 \cos \left(x \right)}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 a \left(\frac{a}{b}\right)^{\frac{2}{3}}}-\frac{\ln \left(a +b \left(\cos^{3}\left(x \right)\right)\right)}{3 a}+\frac{\ln \left(\cos \left(x \right)\right)}{a}+\frac{1}{2 a \cos \left(x \right)^{2}}"," ",0,"1/3/a/(1/b*a)^(2/3)*ln(cos(x)+(1/b*a)^(1/3))-1/6/a/(1/b*a)^(2/3)*ln(cos(x)^2-(1/b*a)^(1/3)*cos(x)+(1/b*a)^(2/3))+1/3/a/(1/b*a)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(1/b*a)^(1/3)*cos(x)-1))-1/3*ln(a+b*cos(x)^3)/a+ln(cos(x))/a+1/2/a/cos(x)^2","A"
93,1,34,33,0.697000," ","int((a+b*cos(x)^3)^(1/2)*tan(x),x)","\frac{2 \arctanh \left(\frac{\sqrt{a +b \left(\cos^{3}\left(x \right)\right)}}{\sqrt{a}}\right) \sqrt{a}}{3}-\frac{2 \sqrt{a +b \left(\cos^{3}\left(x \right)\right)}}{3}"," ",0,"2/3*arctanh((a+b*cos(x)^3)^(1/2)/a^(1/2))*a^(1/2)-2/3*(a+b*cos(x)^3)^(1/2)","A"
94,1,21,20,0.125000," ","int(tan(x)/(a+b*cos(x)^3)^(1/2),x)","\frac{2 \arctanh \left(\frac{\sqrt{a +b \left(\cos^{3}\left(x \right)\right)}}{\sqrt{a}}\right)}{3 \sqrt{a}}"," ",0,"2/3*arctanh((a+b*cos(x)^3)^(1/2)/a^(1/2))/a^(1/2)","A"
95,1,44,33,0.121000," ","int((a+b*cos(x)^4)^(1/2)*tan(x),x)","-\frac{\sqrt{a +b \left(\cos^{4}\left(x \right)\right)}}{2}+\frac{\sqrt{a}\, \ln \left(\frac{2 a +2 \sqrt{a}\, \sqrt{a +b \left(\cos^{4}\left(x \right)\right)}}{\cos \left(x \right)^{2}}\right)}{2}"," ",0,"-1/2*(a+b*cos(x)^4)^(1/2)+1/2*a^(1/2)*ln((2*a+2*a^(1/2)*(a+b*cos(x)^4)^(1/2))/cos(x)^2)","A"
96,1,31,20,0.122000," ","int(tan(x)/(a+b*cos(x)^4)^(1/2),x)","\frac{\ln \left(\frac{2 a +2 \sqrt{a}\, \sqrt{a +b \left(\cos^{4}\left(x \right)\right)}}{\cos \left(x \right)^{2}}\right)}{2 \sqrt{a}}"," ",0,"1/2/a^(1/2)*ln((2*a+2*a^(1/2)*(a+b*cos(x)^4)^(1/2))/cos(x)^2)","A"
97,1,39,39,0.050000," ","int((a+b*cos(x)^n)^(1/2)*tan(x),x)","-\frac{2 \sqrt{a +b \left(\cos^{n}\left(x \right)\right)}-2 \sqrt{a}\, \arctanh \left(\frac{\sqrt{a +b \left(\cos^{n}\left(x \right)\right)}}{\sqrt{a}}\right)}{n}"," ",0,"-1/n*(2*(a+b*cos(x)^n)^(1/2)-2*a^(1/2)*arctanh((a+b*cos(x)^n)^(1/2)/a^(1/2)))","A"
98,1,24,23,0.061000," ","int(tan(x)/(a+b*cos(x)^n)^(1/2),x)","\frac{2 \arctanh \left(\frac{\sqrt{a +b \left(\cos^{n}\left(x \right)\right)}}{\sqrt{a}}\right)}{n \sqrt{a}}"," ",0,"2*arctanh((a+b*cos(x)^n)^(1/2)/a^(1/2))/n/a^(1/2)","A"