1,1,89,49,0.280000," ","int(csc(x)^5/(a+a*csc(x)),x)","\frac{\tan^{3}\left(\frac{x}{2}\right)}{24 a}-\frac{\tan^{2}\left(\frac{x}{2}\right)}{8 a}+\frac{7 \tan \left(\frac{x}{2}\right)}{8 a}-\frac{1}{24 a \tan \left(\frac{x}{2}\right)^{3}}+\frac{1}{8 a \tan \left(\frac{x}{2}\right)^{2}}-\frac{7}{8 a \tan \left(\frac{x}{2}\right)}-\frac{3 \ln \left(\tan \left(\frac{x}{2}\right)\right)}{2 a}-\frac{2}{a \left(\tan \left(\frac{x}{2}\right)+1\right)}"," ",0,"1/24/a*tan(1/2*x)^3-1/8/a*tan(1/2*x)^2+7/8/a*tan(1/2*x)-1/24/a/tan(1/2*x)^3+1/8/a/tan(1/2*x)^2-7/8/a/tan(1/2*x)-3/2/a*ln(tan(1/2*x))-2/a/(tan(1/2*x)+1)","A"
2,1,67,40,0.274000," ","int(csc(x)^4/(a+a*csc(x)),x)","\frac{\tan^{2}\left(\frac{x}{2}\right)}{8 a}-\frac{\tan \left(\frac{x}{2}\right)}{2 a}-\frac{1}{8 a \tan \left(\frac{x}{2}\right)^{2}}+\frac{1}{2 a \tan \left(\frac{x}{2}\right)}+\frac{3 \ln \left(\tan \left(\frac{x}{2}\right)\right)}{2 a}+\frac{2}{a \left(\tan \left(\frac{x}{2}\right)+1\right)}"," ",0,"1/8/a*tan(1/2*x)^2-1/2/a*tan(1/2*x)-1/8/a/tan(1/2*x)^2+1/2/a/tan(1/2*x)+3/2/a*ln(tan(1/2*x))+2/a/(tan(1/2*x)+1)","A"
3,1,45,27,0.228000," ","int(csc(x)^3/(a+a*csc(x)),x)","\frac{\tan \left(\frac{x}{2}\right)}{2 a}-\frac{1}{2 a \tan \left(\frac{x}{2}\right)}-\frac{\ln \left(\tan \left(\frac{x}{2}\right)\right)}{a}-\frac{2}{a \left(\tan \left(\frac{x}{2}\right)+1\right)}"," ",0,"1/2/a*tan(1/2*x)-1/2/a/tan(1/2*x)-1/a*ln(tan(1/2*x))-2/a/(tan(1/2*x)+1)","A"
4,1,24,20,0.248000," ","int(csc(x)^2/(a+a*csc(x)),x)","\frac{2}{a \left(\tan \left(\frac{x}{2}\right)+1\right)}+\frac{\ln \left(\tan \left(\frac{x}{2}\right)\right)}{a}"," ",0,"2/a/(tan(1/2*x)+1)+1/a*ln(tan(1/2*x))","A"
5,1,14,12,0.204000," ","int(csc(x)/(a+a*csc(x)),x)","-\frac{2}{a \left(\tan \left(\frac{x}{2}\right)+1\right)}"," ",0,"-2/a/(tan(1/2*x)+1)","A"
6,1,41,28,0.525000," ","int(1/(a+a*csc(d*x+c)),x)","\frac{2}{a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}+\frac{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a d}"," ",0,"2/a/d/(tan(1/2*d*x+1/2*c)+1)+2/a/d*arctan(tan(1/2*d*x+1/2*c))","A"
7,1,40,25,0.396000," ","int(sin(x)/(a+a*csc(x)),x)","-\frac{2}{a \left(\tan \left(\frac{x}{2}\right)+1\right)}-\frac{2}{a \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)}-\frac{2 \arctan \left(\tan \left(\frac{x}{2}\right)\right)}{a}"," ",0,"-2/a/(tan(1/2*x)+1)-2/a/(tan(1/2*x)^2+1)-2/a*arctan(tan(1/2*x))","A"
8,1,100,36,0.522000," ","int(sin(x)^2/(a+a*csc(x)),x)","\frac{2}{a \left(\tan \left(\frac{x}{2}\right)+1\right)}+\frac{\tan^{3}\left(\frac{x}{2}\right)}{a \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)^{2}}+\frac{2 \left(\tan^{2}\left(\frac{x}{2}\right)\right)}{a \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)^{2}}-\frac{\tan \left(\frac{x}{2}\right)}{a \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)^{2}}+\frac{2}{a \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)^{2}}+\frac{3 \arctan \left(\tan \left(\frac{x}{2}\right)\right)}{a}"," ",0,"2/a/(tan(1/2*x)+1)+1/a/(tan(1/2*x)^2+1)^2*tan(1/2*x)^3+2/a/(tan(1/2*x)^2+1)^2*tan(1/2*x)^2-1/a/(tan(1/2*x)^2+1)^2*tan(1/2*x)+2/a/(tan(1/2*x)^2+1)^2+3/a*arctan(tan(1/2*x))","B"
9,1,121,47,0.507000," ","int(sin(x)^3/(a+a*csc(x)),x)","-\frac{2}{a \left(\tan \left(\frac{x}{2}\right)+1\right)}-\frac{\tan^{5}\left(\frac{x}{2}\right)}{a \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)^{3}}-\frac{2 \left(\tan^{4}\left(\frac{x}{2}\right)\right)}{a \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)^{3}}-\frac{8 \left(\tan^{2}\left(\frac{x}{2}\right)\right)}{a \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)^{3}}+\frac{\tan \left(\frac{x}{2}\right)}{a \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)^{3}}-\frac{10}{3 a \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)^{3}}-\frac{3 \arctan \left(\tan \left(\frac{x}{2}\right)\right)}{a}"," ",0,"-2/a/(tan(1/2*x)+1)-1/a/(tan(1/2*x)^2+1)^3*tan(1/2*x)^5-2/a/(tan(1/2*x)^2+1)^3*tan(1/2*x)^4-8/a/(tan(1/2*x)^2+1)^3*tan(1/2*x)^2+1/a/(tan(1/2*x)^2+1)^3*tan(1/2*x)-10/3/a/(tan(1/2*x)^2+1)^3-3/a*arctan(tan(1/2*x))","B"
10,1,185,58,0.434000," ","int(sin(x)^4/(a+a*csc(x)),x)","\frac{2}{a \left(\tan \left(\frac{x}{2}\right)+1\right)}+\frac{7 \left(\tan^{7}\left(\frac{x}{2}\right)\right)}{4 a \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)^{4}}+\frac{2 \left(\tan^{6}\left(\frac{x}{2}\right)\right)}{a \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)^{4}}+\frac{15 \left(\tan^{5}\left(\frac{x}{2}\right)\right)}{4 a \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)^{4}}+\frac{10 \left(\tan^{4}\left(\frac{x}{2}\right)\right)}{a \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)^{4}}-\frac{15 \left(\tan^{3}\left(\frac{x}{2}\right)\right)}{4 a \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)^{4}}+\frac{34 \left(\tan^{2}\left(\frac{x}{2}\right)\right)}{3 a \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)^{4}}-\frac{7 \tan \left(\frac{x}{2}\right)}{4 a \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)^{4}}+\frac{10}{3 a \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)^{4}}+\frac{15 \arctan \left(\tan \left(\frac{x}{2}\right)\right)}{4 a}"," ",0,"2/a/(tan(1/2*x)+1)+7/4/a/(tan(1/2*x)^2+1)^4*tan(1/2*x)^7+2/a/(tan(1/2*x)^2+1)^4*tan(1/2*x)^6+15/4/a/(tan(1/2*x)^2+1)^4*tan(1/2*x)^5+10/a/(tan(1/2*x)^2+1)^4*tan(1/2*x)^4-15/4/a/(tan(1/2*x)^2+1)^4*tan(1/2*x)^3+34/3/a/(tan(1/2*x)^2+1)^4*tan(1/2*x)^2-7/4/a/(tan(1/2*x)^2+1)^4*tan(1/2*x)+10/3/a/(tan(1/2*x)^2+1)^4+15/4/a*arctan(tan(1/2*x))","B"
11,1,83,53,0.709000," ","int(1/(a+a*csc(d*x+c))^2,x)","-\frac{4}{3 d \,a^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}+\frac{2}{d \,a^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}+\frac{2}{d \,a^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}+\frac{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{2}}"," ",0,"-4/3/d/a^2/(tan(1/2*d*x+1/2*c)+1)^3+2/d/a^2/(tan(1/2*d*x+1/2*c)+1)^2+2/d/a^2/(tan(1/2*d*x+1/2*c)+1)+2/d/a^2*arctan(tan(1/2*d*x+1/2*c))","A"
12,1,125,82,0.794000," ","int(1/(a+a*csc(d*x+c))^3,x)","-\frac{4}{d \,a^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{4}}+\frac{8}{5 d \,a^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{5}}+\frac{4}{3 d \,a^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}+\frac{2}{d \,a^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}+\frac{2}{d \,a^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}+\frac{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{3}}"," ",0,"-4/d/a^3/(tan(1/2*d*x+1/2*c)+1)^4+8/5/d/a^3/(tan(1/2*d*x+1/2*c)+1)^5+4/3/d/a^3/(tan(1/2*d*x+1/2*c)+1)^3+2/d/a^3/(tan(1/2*d*x+1/2*c)+1)^2+2/d/a^3/(tan(1/2*d*x+1/2*c)+1)+2/d/a^3*arctan(tan(1/2*d*x+1/2*c))","A"
13,1,535,51,0.920000," ","int((a+a*csc(x))^(5/2),x)","\frac{\left(-3 \sin \left(x \right) \cos \left(x \right) \left(-\frac{-1+\cos \left(x \right)}{\sin \left(x \right)}\right)^{\frac{3}{2}} \ln \left(-\frac{\sqrt{2}\, \sqrt{-\frac{-1+\cos \left(x \right)}{\sin \left(x \right)}}\, \sin \left(x \right)+\sin \left(x \right)-\cos \left(x \right)+1}{\sqrt{2}\, \sqrt{-\frac{-1+\cos \left(x \right)}{\sin \left(x \right)}}\, \sin \left(x \right)-\sin \left(x \right)+\cos \left(x \right)-1}\right)-12 \sin \left(x \right) \cos \left(x \right) \left(-\frac{-1+\cos \left(x \right)}{\sin \left(x \right)}\right)^{\frac{3}{2}} \arctan \left(\sqrt{2}\, \sqrt{-\frac{-1+\cos \left(x \right)}{\sin \left(x \right)}}+1\right)-12 \sin \left(x \right) \cos \left(x \right) \left(-\frac{-1+\cos \left(x \right)}{\sin \left(x \right)}\right)^{\frac{3}{2}} \arctan \left(\sqrt{2}\, \sqrt{-\frac{-1+\cos \left(x \right)}{\sin \left(x \right)}}-1\right)-3 \sin \left(x \right) \cos \left(x \right) \left(-\frac{-1+\cos \left(x \right)}{\sin \left(x \right)}\right)^{\frac{3}{2}} \ln \left(-\frac{\sqrt{2}\, \sqrt{-\frac{-1+\cos \left(x \right)}{\sin \left(x \right)}}\, \sin \left(x \right)-\sin \left(x \right)+\cos \left(x \right)-1}{\sqrt{2}\, \sqrt{-\frac{-1+\cos \left(x \right)}{\sin \left(x \right)}}\, \sin \left(x \right)+\sin \left(x \right)-\cos \left(x \right)+1}\right)-3 \sin \left(x \right) \left(-\frac{-1+\cos \left(x \right)}{\sin \left(x \right)}\right)^{\frac{3}{2}} \ln \left(-\frac{\sqrt{2}\, \sqrt{-\frac{-1+\cos \left(x \right)}{\sin \left(x \right)}}\, \sin \left(x \right)+\sin \left(x \right)-\cos \left(x \right)+1}{\sqrt{2}\, \sqrt{-\frac{-1+\cos \left(x \right)}{\sin \left(x \right)}}\, \sin \left(x \right)-\sin \left(x \right)+\cos \left(x \right)-1}\right)-12 \sin \left(x \right) \left(-\frac{-1+\cos \left(x \right)}{\sin \left(x \right)}\right)^{\frac{3}{2}} \arctan \left(\sqrt{2}\, \sqrt{-\frac{-1+\cos \left(x \right)}{\sin \left(x \right)}}+1\right)-12 \sin \left(x \right) \left(-\frac{-1+\cos \left(x \right)}{\sin \left(x \right)}\right)^{\frac{3}{2}} \arctan \left(\sqrt{2}\, \sqrt{-\frac{-1+\cos \left(x \right)}{\sin \left(x \right)}}-1\right)-3 \sin \left(x \right) \left(-\frac{-1+\cos \left(x \right)}{\sin \left(x \right)}\right)^{\frac{3}{2}} \ln \left(-\frac{\sqrt{2}\, \sqrt{-\frac{-1+\cos \left(x \right)}{\sin \left(x \right)}}\, \sin \left(x \right)-\sin \left(x \right)+\cos \left(x \right)-1}{\sqrt{2}\, \sqrt{-\frac{-1+\cos \left(x \right)}{\sin \left(x \right)}}\, \sin \left(x \right)+\sin \left(x \right)-\cos \left(x \right)+1}\right)+16 \sin \left(x \right) \cos \left(x \right) \sqrt{2}-16 \left(\cos^{2}\left(x \right)\right) \sqrt{2}-14 \sin \left(x \right) \sqrt{2}+2 \cos \left(x \right) \sqrt{2}+14 \sqrt{2}\right) \sin \left(x \right) \left(\frac{a \left(1+\sin \left(x \right)\right)}{\sin \left(x \right)}\right)^{\frac{5}{2}} \sqrt{2}}{6 \left(\cos^{2}\left(x \right)\right) \sin \left(x \right)-6 \left(\cos^{3}\left(x \right)\right)+12 \cos \left(x \right) \sin \left(x \right)+18 \left(\cos^{2}\left(x \right)\right)-24 \sin \left(x \right)+12 \cos \left(x \right)-24}"," ",0,"1/6*(-3*sin(x)*cos(x)*(-(-1+cos(x))/sin(x))^(3/2)*ln(-(2^(1/2)*(-(-1+cos(x))/sin(x))^(1/2)*sin(x)+sin(x)-cos(x)+1)/(2^(1/2)*(-(-1+cos(x))/sin(x))^(1/2)*sin(x)-sin(x)+cos(x)-1))-12*sin(x)*cos(x)*(-(-1+cos(x))/sin(x))^(3/2)*arctan(2^(1/2)*(-(-1+cos(x))/sin(x))^(1/2)+1)-12*sin(x)*cos(x)*(-(-1+cos(x))/sin(x))^(3/2)*arctan(2^(1/2)*(-(-1+cos(x))/sin(x))^(1/2)-1)-3*sin(x)*cos(x)*(-(-1+cos(x))/sin(x))^(3/2)*ln(-(2^(1/2)*(-(-1+cos(x))/sin(x))^(1/2)*sin(x)-sin(x)+cos(x)-1)/(2^(1/2)*(-(-1+cos(x))/sin(x))^(1/2)*sin(x)+sin(x)-cos(x)+1))-3*sin(x)*(-(-1+cos(x))/sin(x))^(3/2)*ln(-(2^(1/2)*(-(-1+cos(x))/sin(x))^(1/2)*sin(x)+sin(x)-cos(x)+1)/(2^(1/2)*(-(-1+cos(x))/sin(x))^(1/2)*sin(x)-sin(x)+cos(x)-1))-12*sin(x)*(-(-1+cos(x))/sin(x))^(3/2)*arctan(2^(1/2)*(-(-1+cos(x))/sin(x))^(1/2)+1)-12*sin(x)*(-(-1+cos(x))/sin(x))^(3/2)*arctan(2^(1/2)*(-(-1+cos(x))/sin(x))^(1/2)-1)-3*sin(x)*(-(-1+cos(x))/sin(x))^(3/2)*ln(-(2^(1/2)*(-(-1+cos(x))/sin(x))^(1/2)*sin(x)-sin(x)+cos(x)-1)/(2^(1/2)*(-(-1+cos(x))/sin(x))^(1/2)*sin(x)+sin(x)-cos(x)+1))+16*sin(x)*cos(x)*2^(1/2)-16*cos(x)^2*2^(1/2)-14*sin(x)*2^(1/2)+2*cos(x)*2^(1/2)+14*2^(1/2))*sin(x)*(a*(1+sin(x))/sin(x))^(5/2)/(cos(x)^2*sin(x)-cos(x)^3+2*cos(x)*sin(x)+3*cos(x)^2-4*sin(x)+2*cos(x)-4)*2^(1/2)","B"
14,1,273,36,0.631000," ","int((a+a*csc(x))^(3/2),x)","-\frac{\left(\sqrt{-\frac{-1+\cos \left(x \right)}{\sin \left(x \right)}}\, \ln \left(-\frac{\sqrt{2}\, \sqrt{-\frac{-1+\cos \left(x \right)}{\sin \left(x \right)}}\, \sin \left(x \right)+\sin \left(x \right)-\cos \left(x \right)+1}{\sqrt{2}\, \sqrt{-\frac{-1+\cos \left(x \right)}{\sin \left(x \right)}}\, \sin \left(x \right)-\sin \left(x \right)+\cos \left(x \right)-1}\right) \sin \left(x \right)+4 \sqrt{-\frac{-1+\cos \left(x \right)}{\sin \left(x \right)}}\, \arctan \left(\sqrt{2}\, \sqrt{-\frac{-1+\cos \left(x \right)}{\sin \left(x \right)}}+1\right) \sin \left(x \right)+4 \sqrt{-\frac{-1+\cos \left(x \right)}{\sin \left(x \right)}}\, \arctan \left(\sqrt{2}\, \sqrt{-\frac{-1+\cos \left(x \right)}{\sin \left(x \right)}}-1\right) \sin \left(x \right)+\sqrt{-\frac{-1+\cos \left(x \right)}{\sin \left(x \right)}}\, \ln \left(-\frac{\sqrt{2}\, \sqrt{-\frac{-1+\cos \left(x \right)}{\sin \left(x \right)}}\, \sin \left(x \right)-\sin \left(x \right)+\cos \left(x \right)-1}{\sqrt{2}\, \sqrt{-\frac{-1+\cos \left(x \right)}{\sin \left(x \right)}}\, \sin \left(x \right)+\sin \left(x \right)-\cos \left(x \right)+1}\right) \sin \left(x \right)-2 \sin \left(x \right) \sqrt{2}-2 \cos \left(x \right) \sqrt{2}+2 \sqrt{2}\right) \sin \left(x \right) \left(\frac{a \left(1+\sin \left(x \right)\right)}{\sin \left(x \right)}\right)^{\frac{3}{2}} \sqrt{2}}{2 \left(\cos \left(x \right) \sin \left(x \right)+\cos^{2}\left(x \right)-2 \sin \left(x \right)+\cos \left(x \right)-2\right)}"," ",0,"-1/2*((-(-1+cos(x))/sin(x))^(1/2)*ln(-(2^(1/2)*(-(-1+cos(x))/sin(x))^(1/2)*sin(x)+sin(x)-cos(x)+1)/(2^(1/2)*(-(-1+cos(x))/sin(x))^(1/2)*sin(x)-sin(x)+cos(x)-1))*sin(x)+4*(-(-1+cos(x))/sin(x))^(1/2)*arctan(2^(1/2)*(-(-1+cos(x))/sin(x))^(1/2)+1)*sin(x)+4*(-(-1+cos(x))/sin(x))^(1/2)*arctan(2^(1/2)*(-(-1+cos(x))/sin(x))^(1/2)-1)*sin(x)+(-(-1+cos(x))/sin(x))^(1/2)*ln(-(2^(1/2)*(-(-1+cos(x))/sin(x))^(1/2)*sin(x)-sin(x)+cos(x)-1)/(2^(1/2)*(-(-1+cos(x))/sin(x))^(1/2)*sin(x)+sin(x)-cos(x)+1))*sin(x)-2*sin(x)*2^(1/2)-2*cos(x)*2^(1/2)+2*2^(1/2))*sin(x)*(a*(1+sin(x))/sin(x))^(3/2)/(cos(x)*sin(x)+cos(x)^2-2*sin(x)+cos(x)-2)*2^(1/2)","B"
15,1,199,20,0.716000," ","int((a+a*csc(x))^(1/2),x)","\frac{\sqrt{2}\, \sqrt{\frac{a \left(1+\sin \left(x \right)\right)}{\sin \left(x \right)}}\, \sin \left(x \right) \sqrt{-\frac{-1+\cos \left(x \right)}{\sin \left(x \right)}}\, \left(\ln \left(-\frac{\sqrt{2}\, \sqrt{-\frac{-1+\cos \left(x \right)}{\sin \left(x \right)}}\, \sin \left(x \right)+\sin \left(x \right)-\cos \left(x \right)+1}{\sqrt{2}\, \sqrt{-\frac{-1+\cos \left(x \right)}{\sin \left(x \right)}}\, \sin \left(x \right)-\sin \left(x \right)+\cos \left(x \right)-1}\right)+4 \arctan \left(\sqrt{2}\, \sqrt{-\frac{-1+\cos \left(x \right)}{\sin \left(x \right)}}+1\right)+4 \arctan \left(\sqrt{2}\, \sqrt{-\frac{-1+\cos \left(x \right)}{\sin \left(x \right)}}-1\right)+\ln \left(-\frac{\sqrt{2}\, \sqrt{-\frac{-1+\cos \left(x \right)}{\sin \left(x \right)}}\, \sin \left(x \right)-\sin \left(x \right)+\cos \left(x \right)-1}{\sqrt{2}\, \sqrt{-\frac{-1+\cos \left(x \right)}{\sin \left(x \right)}}\, \sin \left(x \right)+\sin \left(x \right)-\cos \left(x \right)+1}\right)\right)}{2-2 \cos \left(x \right)+2 \sin \left(x \right)}"," ",0,"1/2*2^(1/2)*(a*(1+sin(x))/sin(x))^(1/2)*sin(x)*(-(-1+cos(x))/sin(x))^(1/2)*(ln(-(2^(1/2)*(-(-1+cos(x))/sin(x))^(1/2)*sin(x)+sin(x)-cos(x)+1)/(2^(1/2)*(-(-1+cos(x))/sin(x))^(1/2)*sin(x)-sin(x)+cos(x)-1))+4*arctan(2^(1/2)*(-(-1+cos(x))/sin(x))^(1/2)+1)+4*arctan(2^(1/2)*(-(-1+cos(x))/sin(x))^(1/2)-1)+ln(-(2^(1/2)*(-(-1+cos(x))/sin(x))^(1/2)*sin(x)-sin(x)+cos(x)-1)/(2^(1/2)*(-(-1+cos(x))/sin(x))^(1/2)*sin(x)+sin(x)-cos(x)+1)))/(1-cos(x)+sin(x))","B"
16,1,221,47,0.745000," ","int(1/(a+a*csc(x))^(1/2),x)","-\frac{\left(4 \sqrt{2}\, \arctan \left(\sqrt{-\frac{-1+\cos \left(x \right)}{\sin \left(x \right)}}\right)-\ln \left(-\frac{\sqrt{2}\, \sqrt{-\frac{-1+\cos \left(x \right)}{\sin \left(x \right)}}\, \sin \left(x \right)+\sin \left(x \right)-\cos \left(x \right)+1}{\sqrt{2}\, \sqrt{-\frac{-1+\cos \left(x \right)}{\sin \left(x \right)}}\, \sin \left(x \right)-\sin \left(x \right)+\cos \left(x \right)-1}\right)-4 \arctan \left(\sqrt{2}\, \sqrt{-\frac{-1+\cos \left(x \right)}{\sin \left(x \right)}}+1\right)-4 \arctan \left(\sqrt{2}\, \sqrt{-\frac{-1+\cos \left(x \right)}{\sin \left(x \right)}}-1\right)-\ln \left(-\frac{\sqrt{2}\, \sqrt{-\frac{-1+\cos \left(x \right)}{\sin \left(x \right)}}\, \sin \left(x \right)-\sin \left(x \right)+\cos \left(x \right)-1}{\sqrt{2}\, \sqrt{-\frac{-1+\cos \left(x \right)}{\sin \left(x \right)}}\, \sin \left(x \right)+\sin \left(x \right)-\cos \left(x \right)+1}\right)\right) \left(1-\cos \left(x \right)+\sin \left(x \right)\right) \sqrt{2}}{4 \sqrt{\frac{a \left(1+\sin \left(x \right)\right)}{\sin \left(x \right)}}\, \sin \left(x \right) \sqrt{-\frac{-1+\cos \left(x \right)}{\sin \left(x \right)}}}"," ",0,"-1/4*(4*2^(1/2)*arctan((-(-1+cos(x))/sin(x))^(1/2))-ln(-(2^(1/2)*(-(-1+cos(x))/sin(x))^(1/2)*sin(x)+sin(x)-cos(x)+1)/(2^(1/2)*(-(-1+cos(x))/sin(x))^(1/2)*sin(x)-sin(x)+cos(x)-1))-4*arctan(2^(1/2)*(-(-1+cos(x))/sin(x))^(1/2)+1)-4*arctan(2^(1/2)*(-(-1+cos(x))/sin(x))^(1/2)-1)-ln(-(2^(1/2)*(-(-1+cos(x))/sin(x))^(1/2)*sin(x)-sin(x)+cos(x)-1)/(2^(1/2)*(-(-1+cos(x))/sin(x))^(1/2)*sin(x)+sin(x)-cos(x)+1)))*(1-cos(x)+sin(x))/(a*(1+sin(x))/sin(x))^(1/2)/sin(x)/(-(-1+cos(x))/sin(x))^(1/2)*2^(1/2)","B"
17,1,1141,60,0.811000," ","int(1/(a+a*csc(x))^(3/2),x)","-\frac{\left(-1+\cos \left(x \right)\right) \left(\sqrt{2}\, \sqrt{-\frac{-1+\cos \left(x \right)}{\sin \left(x \right)}}\, \sin \left(x \right)+4 \ln \left(-\frac{\sqrt{2}\, \sqrt{-\frac{-1+\cos \left(x \right)}{\sin \left(x \right)}}\, \sin \left(x \right)+\sin \left(x \right)-\cos \left(x \right)+1}{\sqrt{2}\, \sqrt{-\frac{-1+\cos \left(x \right)}{\sin \left(x \right)}}\, \sin \left(x \right)-\sin \left(x \right)+\cos \left(x \right)-1}\right)+16 \arctan \left(\sqrt{2}\, \sqrt{-\frac{-1+\cos \left(x \right)}{\sin \left(x \right)}}+1\right)+10 \sqrt{2}\, \cos \left(x \right) \sin \left(x \right) \arctan \left(\sqrt{-\frac{-1+\cos \left(x \right)}{\sin \left(x \right)}}\right)-\sqrt{2}\, \cos \left(x \right) \sin \left(x \right) \left(-\frac{-1+\cos \left(x \right)}{\sin \left(x \right)}\right)^{\frac{3}{2}}+\sqrt{2}\, \cos \left(x \right) \sin \left(x \right) \sqrt{-\frac{-1+\cos \left(x \right)}{\sin \left(x \right)}}+4 \ln \left(-\frac{\sqrt{2}\, \sqrt{-\frac{-1+\cos \left(x \right)}{\sin \left(x \right)}}\, \sin \left(x \right)-\sin \left(x \right)+\cos \left(x \right)-1}{\sqrt{2}\, \sqrt{-\frac{-1+\cos \left(x \right)}{\sin \left(x \right)}}\, \sin \left(x \right)+\sin \left(x \right)-\cos \left(x \right)+1}\right)+16 \arctan \left(\sqrt{2}\, \sqrt{-\frac{-1+\cos \left(x \right)}{\sin \left(x \right)}}-1\right)-\sqrt{2}\, \left(\cos^{2}\left(x \right)\right) \sqrt{-\frac{-1+\cos \left(x \right)}{\sin \left(x \right)}}+10 \sqrt{2}\, \left(\cos^{2}\left(x \right)\right) \arctan \left(\sqrt{-\frac{-1+\cos \left(x \right)}{\sin \left(x \right)}}\right)+\sqrt{2}\, \left(\cos^{2}\left(x \right)\right) \left(-\frac{-1+\cos \left(x \right)}{\sin \left(x \right)}\right)^{\frac{3}{2}}-2 \cos \left(x \right) \sin \left(x \right) \ln \left(-\frac{\sqrt{2}\, \sqrt{-\frac{-1+\cos \left(x \right)}{\sin \left(x \right)}}\, \sin \left(x \right)-\sin \left(x \right)+\cos \left(x \right)-1}{\sqrt{2}\, \sqrt{-\frac{-1+\cos \left(x \right)}{\sin \left(x \right)}}\, \sin \left(x \right)+\sin \left(x \right)-\cos \left(x \right)+1}\right)-2 \cos \left(x \right) \sin \left(x \right) \ln \left(-\frac{\sqrt{2}\, \sqrt{-\frac{-1+\cos \left(x \right)}{\sin \left(x \right)}}\, \sin \left(x \right)+\sin \left(x \right)-\cos \left(x \right)+1}{\sqrt{2}\, \sqrt{-\frac{-1+\cos \left(x \right)}{\sin \left(x \right)}}\, \sin \left(x \right)-\sin \left(x \right)+\cos \left(x \right)-1}\right)-8 \cos \left(x \right) \sin \left(x \right) \arctan \left(\sqrt{2}\, \sqrt{-\frac{-1+\cos \left(x \right)}{\sin \left(x \right)}}+1\right)-8 \cos \left(x \right) \sin \left(x \right) \arctan \left(\sqrt{2}\, \sqrt{-\frac{-1+\cos \left(x \right)}{\sin \left(x \right)}}-1\right)+10 \sqrt{2}\, \cos \left(x \right) \arctan \left(\sqrt{-\frac{-1+\cos \left(x \right)}{\sin \left(x \right)}}\right)-20 \sqrt{2}\, \sin \left(x \right) \arctan \left(\sqrt{-\frac{-1+\cos \left(x \right)}{\sin \left(x \right)}}\right)-\sqrt{2}\, \sin \left(x \right) \left(-\frac{-1+\cos \left(x \right)}{\sin \left(x \right)}\right)^{\frac{3}{2}}-20 \sqrt{2}\, \arctan \left(\sqrt{-\frac{-1+\cos \left(x \right)}{\sin \left(x \right)}}\right)-2 \left(\cos^{2}\left(x \right)\right) \ln \left(-\frac{\sqrt{2}\, \sqrt{-\frac{-1+\cos \left(x \right)}{\sin \left(x \right)}}\, \sin \left(x \right)+\sin \left(x \right)-\cos \left(x \right)+1}{\sqrt{2}\, \sqrt{-\frac{-1+\cos \left(x \right)}{\sin \left(x \right)}}\, \sin \left(x \right)-\sin \left(x \right)+\cos \left(x \right)-1}\right)-8 \left(\cos^{2}\left(x \right)\right) \arctan \left(\sqrt{2}\, \sqrt{-\frac{-1+\cos \left(x \right)}{\sin \left(x \right)}}+1\right)-8 \left(\cos^{2}\left(x \right)\right) \arctan \left(\sqrt{2}\, \sqrt{-\frac{-1+\cos \left(x \right)}{\sin \left(x \right)}}-1\right)-2 \cos \left(x \right) \ln \left(-\frac{\sqrt{2}\, \sqrt{-\frac{-1+\cos \left(x \right)}{\sin \left(x \right)}}\, \sin \left(x \right)-\sin \left(x \right)+\cos \left(x \right)-1}{\sqrt{2}\, \sqrt{-\frac{-1+\cos \left(x \right)}{\sin \left(x \right)}}\, \sin \left(x \right)+\sin \left(x \right)-\cos \left(x \right)+1}\right)-2 \cos \left(x \right) \ln \left(-\frac{\sqrt{2}\, \sqrt{-\frac{-1+\cos \left(x \right)}{\sin \left(x \right)}}\, \sin \left(x \right)+\sin \left(x \right)-\cos \left(x \right)+1}{\sqrt{2}\, \sqrt{-\frac{-1+\cos \left(x \right)}{\sin \left(x \right)}}\, \sin \left(x \right)-\sin \left(x \right)+\cos \left(x \right)-1}\right)-8 \cos \left(x \right) \arctan \left(\sqrt{2}\, \sqrt{-\frac{-1+\cos \left(x \right)}{\sin \left(x \right)}}+1\right)-8 \cos \left(x \right) \arctan \left(\sqrt{2}\, \sqrt{-\frac{-1+\cos \left(x \right)}{\sin \left(x \right)}}-1\right)+4 \sin \left(x \right) \ln \left(-\frac{\sqrt{2}\, \sqrt{-\frac{-1+\cos \left(x \right)}{\sin \left(x \right)}}\, \sin \left(x \right)-\sin \left(x \right)+\cos \left(x \right)-1}{\sqrt{2}\, \sqrt{-\frac{-1+\cos \left(x \right)}{\sin \left(x \right)}}\, \sin \left(x \right)+\sin \left(x \right)-\cos \left(x \right)+1}\right)+4 \sin \left(x \right) \ln \left(-\frac{\sqrt{2}\, \sqrt{-\frac{-1+\cos \left(x \right)}{\sin \left(x \right)}}\, \sin \left(x \right)+\sin \left(x \right)-\cos \left(x \right)+1}{\sqrt{2}\, \sqrt{-\frac{-1+\cos \left(x \right)}{\sin \left(x \right)}}\, \sin \left(x \right)-\sin \left(x \right)+\cos \left(x \right)-1}\right)+16 \sin \left(x \right) \arctan \left(\sqrt{2}\, \sqrt{-\frac{-1+\cos \left(x \right)}{\sin \left(x \right)}}+1\right)+16 \sin \left(x \right) \arctan \left(\sqrt{2}\, \sqrt{-\frac{-1+\cos \left(x \right)}{\sin \left(x \right)}}-1\right)-\sqrt{2}\, \left(-\frac{-1+\cos \left(x \right)}{\sin \left(x \right)}\right)^{\frac{3}{2}}-2 \left(\cos^{2}\left(x \right)\right) \ln \left(-\frac{\sqrt{2}\, \sqrt{-\frac{-1+\cos \left(x \right)}{\sin \left(x \right)}}\, \sin \left(x \right)-\sin \left(x \right)+\cos \left(x \right)-1}{\sqrt{2}\, \sqrt{-\frac{-1+\cos \left(x \right)}{\sin \left(x \right)}}\, \sin \left(x \right)+\sin \left(x \right)-\cos \left(x \right)+1}\right)+\sqrt{2}\, \sqrt{-\frac{-1+\cos \left(x \right)}{\sin \left(x \right)}}\right) \sqrt{2}}{8 \left(\frac{a \left(1+\sin \left(x \right)\right)}{\sin \left(x \right)}\right)^{\frac{3}{2}} \sin \left(x \right)^{3} \left(-\frac{-1+\cos \left(x \right)}{\sin \left(x \right)}\right)^{\frac{3}{2}}}"," ",0,"-1/8*(-1+cos(x))*(2^(1/2)*(-(-1+cos(x))/sin(x))^(1/2)*sin(x)+4*ln(-(2^(1/2)*(-(-1+cos(x))/sin(x))^(1/2)*sin(x)+sin(x)-cos(x)+1)/(2^(1/2)*(-(-1+cos(x))/sin(x))^(1/2)*sin(x)-sin(x)+cos(x)-1))+16*arctan(2^(1/2)*(-(-1+cos(x))/sin(x))^(1/2)+1)+10*2^(1/2)*cos(x)*sin(x)*arctan((-(-1+cos(x))/sin(x))^(1/2))-2^(1/2)*cos(x)*sin(x)*(-(-1+cos(x))/sin(x))^(3/2)+2^(1/2)*cos(x)*sin(x)*(-(-1+cos(x))/sin(x))^(1/2)+4*ln(-(2^(1/2)*(-(-1+cos(x))/sin(x))^(1/2)*sin(x)-sin(x)+cos(x)-1)/(2^(1/2)*(-(-1+cos(x))/sin(x))^(1/2)*sin(x)+sin(x)-cos(x)+1))+16*arctan(2^(1/2)*(-(-1+cos(x))/sin(x))^(1/2)-1)+2^(1/2)*cos(x)^2*(-(-1+cos(x))/sin(x))^(3/2)-2*cos(x)*sin(x)*ln(-(2^(1/2)*(-(-1+cos(x))/sin(x))^(1/2)*sin(x)-sin(x)+cos(x)-1)/(2^(1/2)*(-(-1+cos(x))/sin(x))^(1/2)*sin(x)+sin(x)-cos(x)+1))-2*cos(x)*sin(x)*ln(-(2^(1/2)*(-(-1+cos(x))/sin(x))^(1/2)*sin(x)+sin(x)-cos(x)+1)/(2^(1/2)*(-(-1+cos(x))/sin(x))^(1/2)*sin(x)-sin(x)+cos(x)-1))-8*cos(x)*sin(x)*arctan(2^(1/2)*(-(-1+cos(x))/sin(x))^(1/2)+1)-8*cos(x)*sin(x)*arctan(2^(1/2)*(-(-1+cos(x))/sin(x))^(1/2)-1)+10*2^(1/2)*cos(x)*arctan((-(-1+cos(x))/sin(x))^(1/2))-20*2^(1/2)*sin(x)*arctan((-(-1+cos(x))/sin(x))^(1/2))+10*2^(1/2)*cos(x)^2*arctan((-(-1+cos(x))/sin(x))^(1/2))-2^(1/2)*sin(x)*(-(-1+cos(x))/sin(x))^(3/2)-2^(1/2)*cos(x)^2*(-(-1+cos(x))/sin(x))^(1/2)-20*2^(1/2)*arctan((-(-1+cos(x))/sin(x))^(1/2))-2*cos(x)^2*ln(-(2^(1/2)*(-(-1+cos(x))/sin(x))^(1/2)*sin(x)-sin(x)+cos(x)-1)/(2^(1/2)*(-(-1+cos(x))/sin(x))^(1/2)*sin(x)+sin(x)-cos(x)+1))-2*cos(x)^2*ln(-(2^(1/2)*(-(-1+cos(x))/sin(x))^(1/2)*sin(x)+sin(x)-cos(x)+1)/(2^(1/2)*(-(-1+cos(x))/sin(x))^(1/2)*sin(x)-sin(x)+cos(x)-1))-8*cos(x)^2*arctan(2^(1/2)*(-(-1+cos(x))/sin(x))^(1/2)+1)-8*cos(x)^2*arctan(2^(1/2)*(-(-1+cos(x))/sin(x))^(1/2)-1)-2*cos(x)*ln(-(2^(1/2)*(-(-1+cos(x))/sin(x))^(1/2)*sin(x)-sin(x)+cos(x)-1)/(2^(1/2)*(-(-1+cos(x))/sin(x))^(1/2)*sin(x)+sin(x)-cos(x)+1))-2*cos(x)*ln(-(2^(1/2)*(-(-1+cos(x))/sin(x))^(1/2)*sin(x)+sin(x)-cos(x)+1)/(2^(1/2)*(-(-1+cos(x))/sin(x))^(1/2)*sin(x)-sin(x)+cos(x)-1))-8*cos(x)*arctan(2^(1/2)*(-(-1+cos(x))/sin(x))^(1/2)+1)-8*cos(x)*arctan(2^(1/2)*(-(-1+cos(x))/sin(x))^(1/2)-1)+4*sin(x)*ln(-(2^(1/2)*(-(-1+cos(x))/sin(x))^(1/2)*sin(x)-sin(x)+cos(x)-1)/(2^(1/2)*(-(-1+cos(x))/sin(x))^(1/2)*sin(x)+sin(x)-cos(x)+1))+4*sin(x)*ln(-(2^(1/2)*(-(-1+cos(x))/sin(x))^(1/2)*sin(x)+sin(x)-cos(x)+1)/(2^(1/2)*(-(-1+cos(x))/sin(x))^(1/2)*sin(x)-sin(x)+cos(x)-1))+16*sin(x)*arctan(2^(1/2)*(-(-1+cos(x))/sin(x))^(1/2)+1)+16*sin(x)*arctan(2^(1/2)*(-(-1+cos(x))/sin(x))^(1/2)-1)-2^(1/2)*(-(-1+cos(x))/sin(x))^(3/2)+2^(1/2)*(-(-1+cos(x))/sin(x))^(1/2))/(a*(1+sin(x))/sin(x))^(3/2)/sin(x)^3/(-(-1+cos(x))/sin(x))^(3/2)*2^(1/2)","B"
18,1,1961,75,0.614000," ","int(1/(a+a*csc(x))^(5/2),x)","\text{Expression too large to display}"," ",0,"-1/128*(-1+cos(x))^2*(-11*2^(1/2)*(-(-1+cos(x))/sin(x))^(1/2)*sin(x)-19*sin(x)*cos(x)^2*(-(-1+cos(x))/sin(x))^(3/2)*2^(1/2)-11*sin(x)*cos(x)^2*(-(-1+cos(x))/sin(x))^(1/2)*2^(1/2)+11*sin(x)*cos(x)^2*(-(-1+cos(x))/sin(x))^(7/2)*2^(1/2)+19*sin(x)*cos(x)^2*(-(-1+cos(x))/sin(x))^(5/2)*2^(1/2)-172*sin(x)*cos(x)^2*2^(1/2)*arctan((-(-1+cos(x))/sin(x))^(1/2))-11*cos(x)^3*(-(-1+cos(x))/sin(x))^(7/2)*2^(1/2)-11*cos(x)^2*(-(-1+cos(x))/sin(x))^(7/2)*2^(1/2)+32*sin(x)*cos(x)^2*ln(-(2^(1/2)*(-(-1+cos(x))/sin(x))^(1/2)*sin(x)+sin(x)-cos(x)+1)/(2^(1/2)*(-(-1+cos(x))/sin(x))^(1/2)*sin(x)-sin(x)+cos(x)-1))+128*sin(x)*cos(x)^2*arctan(2^(1/2)*(-(-1+cos(x))/sin(x))^(1/2)-1)-128*ln(-(2^(1/2)*(-(-1+cos(x))/sin(x))^(1/2)*sin(x)+sin(x)-cos(x)+1)/(2^(1/2)*(-(-1+cos(x))/sin(x))^(1/2)*sin(x)-sin(x)+cos(x)-1))-512*arctan(2^(1/2)*(-(-1+cos(x))/sin(x))^(1/2)+1)-344*2^(1/2)*cos(x)*sin(x)*arctan((-(-1+cos(x))/sin(x))^(1/2))-38*2^(1/2)*cos(x)*sin(x)*(-(-1+cos(x))/sin(x))^(3/2)-22*2^(1/2)*cos(x)*sin(x)*(-(-1+cos(x))/sin(x))^(1/2)+38*sin(x)*cos(x)*(-(-1+cos(x))/sin(x))^(5/2)*2^(1/2)+22*sin(x)*cos(x)*(-(-1+cos(x))/sin(x))^(7/2)*2^(1/2)-128*ln(-(2^(1/2)*(-(-1+cos(x))/sin(x))^(1/2)*sin(x)-sin(x)+cos(x)-1)/(2^(1/2)*(-(-1+cos(x))/sin(x))^(1/2)*sin(x)+sin(x)-cos(x)+1))-512*arctan(2^(1/2)*(-(-1+cos(x))/sin(x))^(1/2)-1)+32*sin(x)*cos(x)^2*ln(-(2^(1/2)*(-(-1+cos(x))/sin(x))^(1/2)*sin(x)-sin(x)+cos(x)-1)/(2^(1/2)*(-(-1+cos(x))/sin(x))^(1/2)*sin(x)+sin(x)-cos(x)+1))+128*sin(x)*cos(x)^2*arctan(2^(1/2)*(-(-1+cos(x))/sin(x))^(1/2)+1)+11*sin(x)*(-(-1+cos(x))/sin(x))^(7/2)*2^(1/2)-19*cos(x)^3*(-(-1+cos(x))/sin(x))^(5/2)*2^(1/2)+11*cos(x)*(-(-1+cos(x))/sin(x))^(7/2)*2^(1/2)-19*cos(x)^2*(-(-1+cos(x))/sin(x))^(5/2)*2^(1/2)+19*sin(x)*(-(-1+cos(x))/sin(x))^(5/2)*2^(1/2)+19*cos(x)^3*(-(-1+cos(x))/sin(x))^(3/2)*2^(1/2)+19*cos(x)*(-(-1+cos(x))/sin(x))^(5/2)*2^(1/2)+11*cos(x)^3*(-(-1+cos(x))/sin(x))^(1/2)*2^(1/2)-19*cos(x)*(-(-1+cos(x))/sin(x))^(3/2)*2^(1/2)+172*cos(x)^3*2^(1/2)*arctan((-(-1+cos(x))/sin(x))^(1/2))-11*cos(x)*(-(-1+cos(x))/sin(x))^(1/2)*2^(1/2)+19*2^(1/2)*cos(x)^2*(-(-1+cos(x))/sin(x))^(3/2)+64*cos(x)*sin(x)*ln(-(2^(1/2)*(-(-1+cos(x))/sin(x))^(1/2)*sin(x)-sin(x)+cos(x)-1)/(2^(1/2)*(-(-1+cos(x))/sin(x))^(1/2)*sin(x)+sin(x)-cos(x)+1))+64*cos(x)*sin(x)*ln(-(2^(1/2)*(-(-1+cos(x))/sin(x))^(1/2)*sin(x)+sin(x)-cos(x)+1)/(2^(1/2)*(-(-1+cos(x))/sin(x))^(1/2)*sin(x)-sin(x)+cos(x)-1))+256*cos(x)*sin(x)*arctan(2^(1/2)*(-(-1+cos(x))/sin(x))^(1/2)+1)+256*cos(x)*sin(x)*arctan(2^(1/2)*(-(-1+cos(x))/sin(x))^(1/2)-1)-344*2^(1/2)*cos(x)*arctan((-(-1+cos(x))/sin(x))^(1/2))+688*2^(1/2)*sin(x)*arctan((-(-1+cos(x))/sin(x))^(1/2))-516*2^(1/2)*cos(x)^2*arctan((-(-1+cos(x))/sin(x))^(1/2))-19*2^(1/2)*sin(x)*(-(-1+cos(x))/sin(x))^(3/2)+11*2^(1/2)*cos(x)^2*(-(-1+cos(x))/sin(x))^(1/2)+688*2^(1/2)*arctan((-(-1+cos(x))/sin(x))^(1/2))+96*cos(x)^2*ln(-(2^(1/2)*(-(-1+cos(x))/sin(x))^(1/2)*sin(x)-sin(x)+cos(x)-1)/(2^(1/2)*(-(-1+cos(x))/sin(x))^(1/2)*sin(x)+sin(x)-cos(x)+1))+96*cos(x)^2*ln(-(2^(1/2)*(-(-1+cos(x))/sin(x))^(1/2)*sin(x)+sin(x)-cos(x)+1)/(2^(1/2)*(-(-1+cos(x))/sin(x))^(1/2)*sin(x)-sin(x)+cos(x)-1))+384*cos(x)^2*arctan(2^(1/2)*(-(-1+cos(x))/sin(x))^(1/2)+1)+384*cos(x)^2*arctan(2^(1/2)*(-(-1+cos(x))/sin(x))^(1/2)-1)+64*cos(x)*ln(-(2^(1/2)*(-(-1+cos(x))/sin(x))^(1/2)*sin(x)-sin(x)+cos(x)-1)/(2^(1/2)*(-(-1+cos(x))/sin(x))^(1/2)*sin(x)+sin(x)-cos(x)+1))+64*cos(x)*ln(-(2^(1/2)*(-(-1+cos(x))/sin(x))^(1/2)*sin(x)+sin(x)-cos(x)+1)/(2^(1/2)*(-(-1+cos(x))/sin(x))^(1/2)*sin(x)-sin(x)+cos(x)-1))+256*cos(x)*arctan(2^(1/2)*(-(-1+cos(x))/sin(x))^(1/2)+1)+256*cos(x)*arctan(2^(1/2)*(-(-1+cos(x))/sin(x))^(1/2)-1)-128*sin(x)*ln(-(2^(1/2)*(-(-1+cos(x))/sin(x))^(1/2)*sin(x)-sin(x)+cos(x)-1)/(2^(1/2)*(-(-1+cos(x))/sin(x))^(1/2)*sin(x)+sin(x)-cos(x)+1))-128*sin(x)*ln(-(2^(1/2)*(-(-1+cos(x))/sin(x))^(1/2)*sin(x)+sin(x)-cos(x)+1)/(2^(1/2)*(-(-1+cos(x))/sin(x))^(1/2)*sin(x)-sin(x)+cos(x)-1))-512*sin(x)*arctan(2^(1/2)*(-(-1+cos(x))/sin(x))^(1/2)+1)-512*sin(x)*arctan(2^(1/2)*(-(-1+cos(x))/sin(x))^(1/2)-1)-19*2^(1/2)*(-(-1+cos(x))/sin(x))^(3/2)-32*cos(x)^3*ln(-(2^(1/2)*(-(-1+cos(x))/sin(x))^(1/2)*sin(x)+sin(x)-cos(x)+1)/(2^(1/2)*(-(-1+cos(x))/sin(x))^(1/2)*sin(x)-sin(x)+cos(x)-1))-128*cos(x)^3*arctan(2^(1/2)*(-(-1+cos(x))/sin(x))^(1/2)-1)-32*cos(x)^3*ln(-(2^(1/2)*(-(-1+cos(x))/sin(x))^(1/2)*sin(x)-sin(x)+cos(x)-1)/(2^(1/2)*(-(-1+cos(x))/sin(x))^(1/2)*sin(x)+sin(x)-cos(x)+1))-128*cos(x)^3*arctan(2^(1/2)*(-(-1+cos(x))/sin(x))^(1/2)+1)+19*(-(-1+cos(x))/sin(x))^(5/2)*2^(1/2)+11*(-(-1+cos(x))/sin(x))^(7/2)*2^(1/2)-11*2^(1/2)*(-(-1+cos(x))/sin(x))^(1/2))/(a*(1+sin(x))/sin(x))^(5/2)/sin(x)^5/(-(-1+cos(x))/sin(x))^(5/2)*2^(1/2)","B"
19,1,113,31,2.354000," ","int(csc(f*x+e)^(1/2)*(a+a*csc(f*x+e))^(1/2),x)","\frac{\sqrt{2}\, \sqrt{\frac{1}{\sin \left(f x +e \right)}}\, \left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{a \left(1+\sin \left(f x +e \right)\right)}{\sin \left(f x +e \right)}}\, \left(\arcsinh \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+\arctanh \left(\frac{\sqrt{2}}{2 \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}}\right)\right)}{f \left(1-\cos \left(f x +e \right)+\sin \left(f x +e \right)\right) \sqrt{\frac{1}{1+\cos \left(f x +e \right)}}}"," ",0,"1/f*2^(1/2)*(1/sin(f*x+e))^(1/2)*(-1+cos(f*x+e))*(a*(1+sin(f*x+e))/sin(f*x+e))^(1/2)*(arcsinh((-1+cos(f*x+e))/sin(f*x+e))+arctanh(1/2*2^(1/2)/(1/(1+cos(f*x+e)))^(1/2)))/(1-cos(f*x+e)+sin(f*x+e))/(1/(1+cos(f*x+e)))^(1/2)","B"
20,1,117,32,2.108000," ","int((-csc(f*x+e))^(1/2)*(a-a*csc(f*x+e))^(1/2),x)","-\frac{2 \sqrt{-\frac{1}{\sin \left(f x +e \right)}}\, \left(-1+\cos \left(f x +e \right)\right) \sqrt{\frac{a \left(\sin \left(f x +e \right)-1\right)}{\sin \left(f x +e \right)}}\, \left(\arctan \left(\frac{1}{\sqrt{-\frac{2}{1+\cos \left(f x +e \right)}}}\right)-\arctan \left(\frac{\sin \left(f x +e \right) \sqrt{-\frac{2}{1+\cos \left(f x +e \right)}}}{2}\right)\right)}{f \left(-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)\right) \sqrt{-\frac{2}{1+\cos \left(f x +e \right)}}}"," ",0,"-2/f*(-1/sin(f*x+e))^(1/2)*(-1+cos(f*x+e))*(a*(sin(f*x+e)-1)/sin(f*x+e))^(1/2)*(arctan(1/(-2/(1+cos(f*x+e)))^(1/2))-arctan(1/2*sin(f*x+e)*(-2/(1+cos(f*x+e)))^(1/2)))/(-1+cos(f*x+e)+sin(f*x+e))/(-2/(1+cos(f*x+e)))^(1/2)","B"
21,0,0,213,2.641000," ","int(csc(d*x+c)^(4/3)*(a+a*csc(d*x+c))^(1/2),x)","\int \left(\csc^{\frac{4}{3}}\left(d x +c \right)\right) \sqrt{a +a \csc \left(d x +c \right)}\, dx"," ",0,"int(csc(d*x+c)^(4/3)*(a+a*csc(d*x+c))^(1/2),x)","F"
22,0,0,180,4.174000," ","int(csc(d*x+c)^(1/3)*(a+a*csc(d*x+c))^(1/2),x)","\int \left(\csc^{\frac{1}{3}}\left(d x +c \right)\right) \sqrt{a +a \csc \left(d x +c \right)}\, dx"," ",0,"int(csc(d*x+c)^(1/3)*(a+a*csc(d*x+c))^(1/2),x)","F"
23,0,0,213,2.982000," ","int((a+a*csc(d*x+c))^(1/2)/csc(d*x+c)^(2/3),x)","\int \frac{\sqrt{a +a \csc \left(d x +c \right)}}{\csc \left(d x +c \right)^{\frac{2}{3}}}\, dx"," ",0,"int((a+a*csc(d*x+c))^(1/2)/csc(d*x+c)^(2/3),x)","F"
24,0,0,426,2.413000," ","int(csc(d*x+c)^(5/3)*(a+a*csc(d*x+c))^(1/2),x)","\int \left(\csc^{\frac{5}{3}}\left(d x +c \right)\right) \sqrt{a +a \csc \left(d x +c \right)}\, dx"," ",0,"int(csc(d*x+c)^(5/3)*(a+a*csc(d*x+c))^(1/2),x)","F"
25,0,0,394,2.178000," ","int(csc(d*x+c)^(2/3)*(a+a*csc(d*x+c))^(1/2),x)","\int \left(\csc^{\frac{2}{3}}\left(d x +c \right)\right) \sqrt{a +a \csc \left(d x +c \right)}\, dx"," ",0,"int(csc(d*x+c)^(2/3)*(a+a*csc(d*x+c))^(1/2),x)","F"
26,0,0,426,2.682000," ","int((a+a*csc(d*x+c))^(1/2)/csc(d*x+c)^(1/3),x)","\int \frac{\sqrt{a +a \csc \left(d x +c \right)}}{\csc \left(d x +c \right)^{\frac{1}{3}}}\, dx"," ",0,"int((a+a*csc(d*x+c))^(1/2)/csc(d*x+c)^(1/3),x)","F"
27,0,0,458,1.804000," ","int((a+a*csc(d*x+c))^(1/2)/csc(d*x+c)^(4/3),x)","\int \frac{\sqrt{a +a \csc \left(d x +c \right)}}{\csc \left(d x +c \right)^{\frac{4}{3}}}\, dx"," ",0,"int((a+a*csc(d*x+c))^(1/2)/csc(d*x+c)^(4/3),x)","F"
28,0,0,44,1.950000," ","int(csc(d*x+c)^n*(a+a*csc(d*x+c))^(1/2),x)","\int \left(\csc^{n}\left(d x +c \right)\right) \sqrt{a +a \csc \left(d x +c \right)}\, dx"," ",0,"int(csc(d*x+c)^n*(a+a*csc(d*x+c))^(1/2),x)","F"
29,0,0,65,2.448000," ","int(csc(d*x+c)^n*(a-a*csc(d*x+c))^(1/2),x)","\int \left(\csc^{n}\left(d x +c \right)\right) \sqrt{a -a \csc \left(d x +c \right)}\, dx"," ",0,"int(csc(d*x+c)^n*(a-a*csc(d*x+c))^(1/2),x)","F"
30,0,0,144,3.273000," ","int(csc(f*x+e)^3*(a+a*csc(f*x+e))^m,x)","\int \left(\csc^{3}\left(f x +e \right)\right) \left(a +a \csc \left(f x +e \right)\right)^{m}\, dx"," ",0,"int(csc(f*x+e)^3*(a+a*csc(f*x+e))^m,x)","F"
31,0,0,97,1.997000," ","int(csc(f*x+e)^2*(a+a*csc(f*x+e))^m,x)","\int \left(\csc^{2}\left(f x +e \right)\right) \left(a +a \csc \left(f x +e \right)\right)^{m}\, dx"," ",0,"int(csc(f*x+e)^2*(a+a*csc(f*x+e))^m,x)","F"
32,0,0,62,1.544000," ","int(csc(f*x+e)*(a+a*csc(f*x+e))^m,x)","\int \csc \left(f x +e \right) \left(a +a \csc \left(f x +e \right)\right)^{m}\, dx"," ",0,"int(csc(f*x+e)*(a+a*csc(f*x+e))^m,x)","F"
33,0,0,72,1.204000," ","int((a+a*csc(f*x+e))^m,x)","\int \left(a +a \csc \left(f x +e \right)\right)^{m}\, dx"," ",0,"int((a+a*csc(f*x+e))^m,x)","F"
34,0,0,71,2.262000," ","int((a+a*csc(f*x+e))^m*sin(f*x+e),x)","\int \left(a +a \csc \left(f x +e \right)\right)^{m} \sin \left(f x +e \right)\, dx"," ",0,"int((a+a*csc(f*x+e))^m*sin(f*x+e),x)","F"
35,0,0,72,4.686000," ","int((a+a*csc(f*x+e))^m*sin(f*x+e)^2,x)","\int \left(a +a \csc \left(f x +e \right)\right)^{m} \left(\sin^{2}\left(f x +e \right)\right)\, dx"," ",0,"int((a+a*csc(f*x+e))^m*sin(f*x+e)^2,x)","F"
36,1,139,101,1.389000," ","int((a+b*csc(d*x+c))^4,x)","a^{4} x +\frac{a^{4} c}{d}+\frac{4 a^{3} b \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{d}-\frac{6 a^{2} b^{2} \cot \left(d x +c \right)}{d}-\frac{2 a \,b^{3} \cot \left(d x +c \right) \csc \left(d x +c \right)}{d}+\frac{2 a \,b^{3} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{d}-\frac{2 b^{4} \cot \left(d x +c \right)}{3 d}-\frac{b^{4} \cot \left(d x +c \right) \left(\csc^{2}\left(d x +c \right)\right)}{3 d}"," ",0,"a^4*x+1/d*a^4*c+4/d*a^3*b*ln(csc(d*x+c)-cot(d*x+c))-6/d*a^2*b^2*cot(d*x+c)-2*a*b^3*cot(d*x+c)*csc(d*x+c)/d+2/d*a*b^3*ln(csc(d*x+c)-cot(d*x+c))-2/3/d*b^4*cot(d*x+c)-1/3/d*b^4*cot(d*x+c)*csc(d*x+c)^2","A"
37,1,99,67,1.368000," ","int((a+b*csc(d*x+c))^3,x)","a^{3} x +\frac{a^{3} c}{d}+\frac{3 a^{2} b \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{d}-\frac{3 a \,b^{2} \cot \left(d x +c \right)}{d}-\frac{b^{3} \csc \left(d x +c \right) \cot \left(d x +c \right)}{2 d}+\frac{b^{3} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{2 d}"," ",0,"a^3*x+1/d*a^3*c+3/d*a^2*b*ln(csc(d*x+c)-cot(d*x+c))-3*a*b^2*cot(d*x+c)/d-1/2/d*b^3*csc(d*x+c)*cot(d*x+c)+1/2/d*b^3*ln(csc(d*x+c)-cot(d*x+c))","A"
38,1,52,34,0.831000," ","int((a+b*csc(d*x+c))^2,x)","a^{2} x -\frac{b^{2} \cot \left(d x +c \right)}{d}+\frac{2 a b \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{d}+\frac{a^{2} c}{d}"," ",0,"a^2*x-1/d*b^2*cot(d*x+c)+2/d*a*b*ln(csc(d*x+c)-cot(d*x+c))+1/d*a^2*c","A"
39,1,162,98,0.272000," ","int(csc(x)^5/(a+b*csc(x)),x)","\frac{\tan^{3}\left(\frac{x}{2}\right)}{24 b}-\frac{a \left(\tan^{2}\left(\frac{x}{2}\right)\right)}{8 b^{2}}+\frac{a^{2} \tan \left(\frac{x}{2}\right)}{2 b^{3}}+\frac{3 \tan \left(\frac{x}{2}\right)}{8 b}+\frac{2 a^{4} \arctan \left(\frac{2 \tan \left(\frac{x}{2}\right) b +2 a}{2 \sqrt{-a^{2}+b^{2}}}\right)}{b^{4} \sqrt{-a^{2}+b^{2}}}-\frac{1}{24 b \tan \left(\frac{x}{2}\right)^{3}}-\frac{a^{2}}{2 b^{3} \tan \left(\frac{x}{2}\right)}-\frac{3}{8 b \tan \left(\frac{x}{2}\right)}+\frac{a}{8 b^{2} \tan \left(\frac{x}{2}\right)^{2}}-\frac{a^{3} \ln \left(\tan \left(\frac{x}{2}\right)\right)}{b^{4}}-\frac{a \ln \left(\tan \left(\frac{x}{2}\right)\right)}{2 b^{2}}"," ",0,"1/24/b*tan(1/2*x)^3-1/8/b^2*a*tan(1/2*x)^2+1/2/b^3*a^2*tan(1/2*x)+3/8/b*tan(1/2*x)+2/b^4*a^4/(-a^2+b^2)^(1/2)*arctan(1/2*(2*tan(1/2*x)*b+2*a)/(-a^2+b^2)^(1/2))-1/24/b/tan(1/2*x)^3-1/2/b^3/tan(1/2*x)*a^2-3/8/b/tan(1/2*x)+1/8*a/b^2/tan(1/2*x)^2-1/b^4*a^3*ln(tan(1/2*x))-1/2/b^2*a*ln(tan(1/2*x))","A"
40,1,112,74,0.233000," ","int(csc(x)^4/(a+b*csc(x)),x)","\frac{\tan^{2}\left(\frac{x}{2}\right)}{8 b}-\frac{a \tan \left(\frac{x}{2}\right)}{2 b^{2}}-\frac{2 a^{3} \arctan \left(\frac{2 \tan \left(\frac{x}{2}\right) b +2 a}{2 \sqrt{-a^{2}+b^{2}}}\right)}{b^{3} \sqrt{-a^{2}+b^{2}}}-\frac{1}{8 b \tan \left(\frac{x}{2}\right)^{2}}+\frac{\ln \left(\tan \left(\frac{x}{2}\right)\right) a^{2}}{b^{3}}+\frac{\ln \left(\tan \left(\frac{x}{2}\right)\right)}{2 b}+\frac{a}{2 b^{2} \tan \left(\frac{x}{2}\right)}"," ",0,"1/8/b*tan(1/2*x)^2-1/2/b^2*a*tan(1/2*x)-2/b^3*a^3/(-a^2+b^2)^(1/2)*arctan(1/2*(2*tan(1/2*x)*b+2*a)/(-a^2+b^2)^(1/2))-1/8/b/tan(1/2*x)^2+1/b^3*ln(tan(1/2*x))*a^2+1/2/b*ln(tan(1/2*x))+1/2*a/b^2/tan(1/2*x)","A"
41,1,77,56,0.214000," ","int(csc(x)^3/(a+b*csc(x)),x)","\frac{\tan \left(\frac{x}{2}\right)}{2 b}+\frac{2 a^{2} \arctan \left(\frac{2 \tan \left(\frac{x}{2}\right) b +2 a}{2 \sqrt{-a^{2}+b^{2}}}\right)}{b^{2} \sqrt{-a^{2}+b^{2}}}-\frac{1}{2 b \tan \left(\frac{x}{2}\right)}-\frac{a \ln \left(\tan \left(\frac{x}{2}\right)\right)}{b^{2}}"," ",0,"1/2/b*tan(1/2*x)+2/b^2*a^2/(-a^2+b^2)^(1/2)*arctan(1/2*(2*tan(1/2*x)*b+2*a)/(-a^2+b^2)^(1/2))-1/2/b/tan(1/2*x)-1/b^2*a*ln(tan(1/2*x))","A"
42,1,53,47,0.219000," ","int(csc(x)^2/(a+b*csc(x)),x)","-\frac{2 a \arctan \left(\frac{2 \tan \left(\frac{x}{2}\right) b +2 a}{2 \sqrt{-a^{2}+b^{2}}}\right)}{b \sqrt{-a^{2}+b^{2}}}+\frac{\ln \left(\tan \left(\frac{x}{2}\right)\right)}{b}"," ",0,"-2/b*a/(-a^2+b^2)^(1/2)*arctan(1/2*(2*tan(1/2*x)*b+2*a)/(-a^2+b^2)^(1/2))+1/b*ln(tan(1/2*x))","A"
43,1,39,34,0.180000," ","int(csc(x)/(a+b*csc(x)),x)","\frac{2 \arctan \left(\frac{2 \tan \left(\frac{x}{2}\right) b +2 a}{2 \sqrt{-a^{2}+b^{2}}}\right)}{\sqrt{-a^{2}+b^{2}}}"," ",0,"2/(-a^2+b^2)^(1/2)*arctan(1/2*(2*tan(1/2*x)*b+2*a)/(-a^2+b^2)^(1/2))","A"
44,1,70,52,0.567000," ","int(1/(a+b*csc(d*x+c)),x)","-\frac{2 b \arctan \left(\frac{2 b \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 a}{2 \sqrt{-a^{2}+b^{2}}}\right)}{d a \sqrt{-a^{2}+b^{2}}}+\frac{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d a}"," ",0,"-2/d/a*b/(-a^2+b^2)^(1/2)*arctan(1/2*(2*b*tan(1/2*d*x+1/2*c)+2*a)/(-a^2+b^2)^(1/2))+2/d/a*arctan(tan(1/2*d*x+1/2*c))","A"
45,1,72,55,0.457000," ","int(sin(x)/(a+b*csc(x)),x)","\frac{2 b^{2} \arctan \left(\frac{2 \tan \left(\frac{x}{2}\right) b +2 a}{2 \sqrt{-a^{2}+b^{2}}}\right)}{a^{2} \sqrt{-a^{2}+b^{2}}}-\frac{2}{a \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)}-\frac{2 b \arctan \left(\tan \left(\frac{x}{2}\right)\right)}{a^{2}}"," ",0,"2*b^2/a^2/(-a^2+b^2)^(1/2)*arctan(1/2*(2*tan(1/2*x)*b+2*a)/(-a^2+b^2)^(1/2))-2/a/(tan(1/2*x)^2+1)-2/a^2*b*arctan(tan(1/2*x))","A"
46,1,142,72,0.488000," ","int(sin(x)^2/(a+b*csc(x)),x)","-\frac{2 b^{3} \arctan \left(\frac{2 \tan \left(\frac{x}{2}\right) b +2 a}{2 \sqrt{-a^{2}+b^{2}}}\right)}{a^{3} \sqrt{-a^{2}+b^{2}}}+\frac{\tan^{3}\left(\frac{x}{2}\right)}{a \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)^{2}}+\frac{2 b \left(\tan^{2}\left(\frac{x}{2}\right)\right)}{a^{2} \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)^{2}}-\frac{\tan \left(\frac{x}{2}\right)}{a \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)^{2}}+\frac{2 b}{a^{2} \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)^{2}}+\frac{2 \arctan \left(\tan \left(\frac{x}{2}\right)\right) b^{2}}{a^{3}}+\frac{x}{2 a}"," ",0,"-2/a^3*b^3/(-a^2+b^2)^(1/2)*arctan(1/2*(2*tan(1/2*x)*b+2*a)/(-a^2+b^2)^(1/2))+1/a/(tan(1/2*x)^2+1)^2*tan(1/2*x)^3+2/a^2/(tan(1/2*x)^2+1)^2*b*tan(1/2*x)^2-1/a/(tan(1/2*x)^2+1)^2*tan(1/2*x)+2/a^2/(tan(1/2*x)^2+1)^2*b+2/a^3*arctan(tan(1/2*x))*b^2+1/2*x/a","A"
47,1,213,96,0.436000," ","int(sin(x)^3/(a+b*csc(x)),x)","\frac{2 b^{4} \arctan \left(\frac{2 \tan \left(\frac{x}{2}\right) b +2 a}{2 \sqrt{-a^{2}+b^{2}}}\right)}{a^{4} \sqrt{-a^{2}+b^{2}}}-\frac{\left(\tan^{5}\left(\frac{x}{2}\right)\right) b}{a^{2} \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)^{3}}-\frac{2 b^{2} \left(\tan^{4}\left(\frac{x}{2}\right)\right)}{a^{3} \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)^{3}}-\frac{4 \left(\tan^{2}\left(\frac{x}{2}\right)\right)}{a \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)^{3}}-\frac{4 \left(\tan^{2}\left(\frac{x}{2}\right)\right) b^{2}}{a^{3} \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)^{3}}+\frac{b \tan \left(\frac{x}{2}\right)}{a^{2} \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)^{3}}-\frac{4}{3 a \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)^{3}}-\frac{2 b^{2}}{a^{3} \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)^{3}}-\frac{b \arctan \left(\tan \left(\frac{x}{2}\right)\right)}{a^{2}}-\frac{2 \arctan \left(\tan \left(\frac{x}{2}\right)\right) b^{3}}{a^{4}}"," ",0,"2/a^4*b^4/(-a^2+b^2)^(1/2)*arctan(1/2*(2*tan(1/2*x)*b+2*a)/(-a^2+b^2)^(1/2))-1/a^2/(tan(1/2*x)^2+1)^3*tan(1/2*x)^5*b-2/a^3/(tan(1/2*x)^2+1)^3*b^2*tan(1/2*x)^4-4/a/(tan(1/2*x)^2+1)^3*tan(1/2*x)^2-4/a^3/(tan(1/2*x)^2+1)^3*tan(1/2*x)^2*b^2+1/a^2/(tan(1/2*x)^2+1)^3*b*tan(1/2*x)-4/3/a/(tan(1/2*x)^2+1)^3-2/a^3/(tan(1/2*x)^2+1)^3*b^2-1/a^2*b*arctan(tan(1/2*x))-2/a^4*arctan(tan(1/2*x))*b^3","B"
48,1,405,128,0.378000," ","int(sin(x)^4/(a+b*csc(x)),x)","-\frac{2 b^{5} \arctan \left(\frac{2 \tan \left(\frac{x}{2}\right) b +2 a}{2 \sqrt{-a^{2}+b^{2}}}\right)}{a^{5} \sqrt{-a^{2}+b^{2}}}+\frac{3 \left(\tan^{7}\left(\frac{x}{2}\right)\right)}{4 a \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)^{4}}+\frac{\left(\tan^{7}\left(\frac{x}{2}\right)\right) b^{2}}{a^{3} \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)^{4}}+\frac{2 b^{3} \left(\tan^{6}\left(\frac{x}{2}\right)\right)}{a^{4} \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)^{4}}+\frac{\left(\tan^{5}\left(\frac{x}{2}\right)\right) b^{2}}{a^{3} \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)^{4}}+\frac{11 \left(\tan^{5}\left(\frac{x}{2}\right)\right)}{4 a \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)^{4}}+\frac{4 \left(\tan^{4}\left(\frac{x}{2}\right)\right) b}{a^{2} \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)^{4}}+\frac{6 \left(\tan^{4}\left(\frac{x}{2}\right)\right) b^{3}}{a^{4} \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)^{4}}-\frac{\left(\tan^{3}\left(\frac{x}{2}\right)\right) b^{2}}{a^{3} \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)^{4}}-\frac{11 \left(\tan^{3}\left(\frac{x}{2}\right)\right)}{4 a \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)^{4}}+\frac{6 \left(\tan^{2}\left(\frac{x}{2}\right)\right) b^{3}}{a^{4} \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)^{4}}+\frac{16 \left(\tan^{2}\left(\frac{x}{2}\right)\right) b}{3 a^{2} \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)^{4}}-\frac{3 \tan \left(\frac{x}{2}\right)}{4 a \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)^{4}}-\frac{\tan \left(\frac{x}{2}\right) b^{2}}{a^{3} \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)^{4}}+\frac{4 b}{3 a^{2} \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)^{4}}+\frac{2 b^{3}}{a^{4} \left(\tan^{2}\left(\frac{x}{2}\right)+1\right)^{4}}+\frac{2 \arctan \left(\tan \left(\frac{x}{2}\right)\right) b^{4}}{a^{5}}+\frac{3 \arctan \left(\tan \left(\frac{x}{2}\right)\right)}{4 a}+\frac{\arctan \left(\tan \left(\frac{x}{2}\right)\right) b^{2}}{a^{3}}"," ",0,"-2*b^5/a^5/(-a^2+b^2)^(1/2)*arctan(1/2*(2*tan(1/2*x)*b+2*a)/(-a^2+b^2)^(1/2))+3/4/a/(tan(1/2*x)^2+1)^4*tan(1/2*x)^7+1/a^3/(tan(1/2*x)^2+1)^4*tan(1/2*x)^7*b^2+2/a^4/(tan(1/2*x)^2+1)^4*b^3*tan(1/2*x)^6+1/a^3/(tan(1/2*x)^2+1)^4*tan(1/2*x)^5*b^2+11/4/a/(tan(1/2*x)^2+1)^4*tan(1/2*x)^5+4/a^2/(tan(1/2*x)^2+1)^4*tan(1/2*x)^4*b+6/a^4/(tan(1/2*x)^2+1)^4*tan(1/2*x)^4*b^3-1/a^3/(tan(1/2*x)^2+1)^4*tan(1/2*x)^3*b^2-11/4/a/(tan(1/2*x)^2+1)^4*tan(1/2*x)^3+6/a^4/(tan(1/2*x)^2+1)^4*tan(1/2*x)^2*b^3+16/3/a^2/(tan(1/2*x)^2+1)^4*tan(1/2*x)^2*b-3/4/a/(tan(1/2*x)^2+1)^4*tan(1/2*x)-1/a^3/(tan(1/2*x)^2+1)^4*tan(1/2*x)*b^2+4/3/a^2/(tan(1/2*x)^2+1)^4*b+2/a^4/(tan(1/2*x)^2+1)^4*b^3+2/a^5*arctan(tan(1/2*x))*b^4+3/4/a*arctan(tan(1/2*x))+1/a^3*arctan(tan(1/2*x))*b^2","B"
49,1,247,103,0.691000," ","int(1/(a+b*csc(d*x+c))^2,x)","-\frac{2 b \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+b \right) \left(a^{2}-b^{2}\right)}-\frac{2 b^{2}}{d a \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+b \right) \left(a^{2}-b^{2}\right)}-\frac{4 b \arctan \left(\frac{2 b \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 a}{2 \sqrt{-a^{2}+b^{2}}}\right)}{d \left(a^{2}-b^{2}\right) \sqrt{-a^{2}+b^{2}}}+\frac{2 b^{3} \arctan \left(\frac{2 b \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 a}{2 \sqrt{-a^{2}+b^{2}}}\right)}{d \,a^{2} \left(a^{2}-b^{2}\right) \sqrt{-a^{2}+b^{2}}}+\frac{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{2}}"," ",0,"-2/d*b/(tan(1/2*d*x+1/2*c)^2*b+2*a*tan(1/2*d*x+1/2*c)+b)/(a^2-b^2)*tan(1/2*d*x+1/2*c)-2/d*b^2/a/(tan(1/2*d*x+1/2*c)^2*b+2*a*tan(1/2*d*x+1/2*c)+b)/(a^2-b^2)-4/d*b/(a^2-b^2)/(-a^2+b^2)^(1/2)*arctan(1/2*(2*b*tan(1/2*d*x+1/2*c)+2*a)/(-a^2+b^2)^(1/2))+2/d*b^3/a^2/(a^2-b^2)/(-a^2+b^2)^(1/2)*arctan(1/2*(2*b*tan(1/2*d*x+1/2*c)+2*a)/(-a^2+b^2)^(1/2))+2/d/a^2*arctan(tan(1/2*d*x+1/2*c))","B"
50,1,796,161,0.775000," ","int(1/(a+b*csc(d*x+c))^3,x)","-\frac{4 a \,b^{2} \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+b \right)^{2} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right)}+\frac{b^{4} \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d a \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+b \right)^{2} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right)}-\frac{10 a^{2} b \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+b \right)^{2} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right)}-\frac{b^{3} \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+b \right)^{2} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right)}+\frac{2 b^{5} \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{2} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+b \right)^{2} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right)}-\frac{16 a \,b^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+b \right)^{2} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right)}+\frac{7 b^{4} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d a \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+b \right)^{2} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right)}-\frac{5 b^{3}}{d \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+b \right)^{2} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right)}+\frac{2 b^{5}}{d \,a^{2} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+b \right)^{2} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right)}-\frac{6 a b \arctan \left(\frac{2 b \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 a}{2 \sqrt{-a^{2}+b^{2}}}\right)}{d \left(a^{4}-2 a^{2} b^{2}+b^{4}\right) \sqrt{-a^{2}+b^{2}}}+\frac{5 b^{3} \arctan \left(\frac{2 b \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 a}{2 \sqrt{-a^{2}+b^{2}}}\right)}{d a \left(a^{4}-2 a^{2} b^{2}+b^{4}\right) \sqrt{-a^{2}+b^{2}}}-\frac{2 b^{5} \arctan \left(\frac{2 b \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 a}{2 \sqrt{-a^{2}+b^{2}}}\right)}{d \,a^{3} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right) \sqrt{-a^{2}+b^{2}}}+\frac{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{3}}"," ",0,"-4/d*a*b^2/(tan(1/2*d*x+1/2*c)^2*b+2*a*tan(1/2*d*x+1/2*c)+b)^2/(a^4-2*a^2*b^2+b^4)*tan(1/2*d*x+1/2*c)^3+1/d/a*b^4/(tan(1/2*d*x+1/2*c)^2*b+2*a*tan(1/2*d*x+1/2*c)+b)^2/(a^4-2*a^2*b^2+b^4)*tan(1/2*d*x+1/2*c)^3-10/d*a^2*b/(tan(1/2*d*x+1/2*c)^2*b+2*a*tan(1/2*d*x+1/2*c)+b)^2/(a^4-2*a^2*b^2+b^4)*tan(1/2*d*x+1/2*c)^2-1/d*b^3/(tan(1/2*d*x+1/2*c)^2*b+2*a*tan(1/2*d*x+1/2*c)+b)^2/(a^4-2*a^2*b^2+b^4)*tan(1/2*d*x+1/2*c)^2+2/d/a^2*b^5/(tan(1/2*d*x+1/2*c)^2*b+2*a*tan(1/2*d*x+1/2*c)+b)^2/(a^4-2*a^2*b^2+b^4)*tan(1/2*d*x+1/2*c)^2-16/d*a*b^2/(tan(1/2*d*x+1/2*c)^2*b+2*a*tan(1/2*d*x+1/2*c)+b)^2/(a^4-2*a^2*b^2+b^4)*tan(1/2*d*x+1/2*c)+7/d/a*b^4/(tan(1/2*d*x+1/2*c)^2*b+2*a*tan(1/2*d*x+1/2*c)+b)^2/(a^4-2*a^2*b^2+b^4)*tan(1/2*d*x+1/2*c)-5/d*b^3/(tan(1/2*d*x+1/2*c)^2*b+2*a*tan(1/2*d*x+1/2*c)+b)^2/(a^4-2*a^2*b^2+b^4)+2/d/a^2*b^5/(tan(1/2*d*x+1/2*c)^2*b+2*a*tan(1/2*d*x+1/2*c)+b)^2/(a^4-2*a^2*b^2+b^4)-6/d*a*b/(a^4-2*a^2*b^2+b^4)/(-a^2+b^2)^(1/2)*arctan(1/2*(2*b*tan(1/2*d*x+1/2*c)+2*a)/(-a^2+b^2)^(1/2))+5/d/a*b^3/(a^4-2*a^2*b^2+b^4)/(-a^2+b^2)^(1/2)*arctan(1/2*(2*b*tan(1/2*d*x+1/2*c)+2*a)/(-a^2+b^2)^(1/2))-2/d/a^3*b^5/(a^4-2*a^2*b^2+b^4)/(-a^2+b^2)^(1/2)*arctan(1/2*(2*b*tan(1/2*d*x+1/2*c)+2*a)/(-a^2+b^2)^(1/2))+2/d/a^3*arctan(tan(1/2*d*x+1/2*c))","B"
51,1,1912,228,0.823000," ","int(1/(a+b*csc(d*x+c))^4,x)","\frac{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{4}}-\frac{46 a^{2} b^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+b \right)^{3} \left(a^{6}-3 a^{4} b^{2}+3 b^{4} a^{2}-b^{6}\right)}+\frac{4 a \,b^{4} \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+b \right)^{3} \left(a^{6}-3 a^{4} b^{2}+3 b^{4} a^{2}-b^{6}\right)}-\frac{8 a^{2} b \arctan \left(\frac{2 b \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 a}{2 \sqrt{-a^{2}+b^{2}}}\right)}{d \left(a^{6}-3 a^{4} b^{2}+3 b^{4} a^{2}-b^{6}\right) \sqrt{-a^{2}+b^{2}}}-\frac{88 a^{2} b^{3} \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 d \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+b \right)^{3} \left(a^{6}-3 a^{4} b^{2}+3 b^{4} a^{2}-b^{6}\right)}+\frac{38 a \,b^{4} \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+b \right)^{3} \left(a^{6}-3 a^{4} b^{2}+3 b^{4} a^{2}-b^{6}\right)}-\frac{b^{7} \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{2} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+b \right)^{3} \left(a^{6}-3 a^{4} b^{2}+3 b^{4} a^{2}-b^{6}\right)}-\frac{104 a^{4} b \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 d \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+b \right)^{3} \left(a^{6}-3 a^{4} b^{2}+3 b^{4} a^{2}-b^{6}\right)}-\frac{2 b^{8} \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{3} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+b \right)^{3} \left(a^{6}-3 a^{4} b^{2}+3 b^{4} a^{2}-b^{6}\right)}-\frac{11 b^{7} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,a^{2} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+b \right)^{3} \left(a^{6}-3 a^{4} b^{2}+3 b^{4} a^{2}-b^{6}\right)}-\frac{28 a^{3} b^{2} \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+b \right)^{3} \left(a^{6}-3 a^{4} b^{2}+3 b^{4} a^{2}-b^{6}\right)}-\frac{7 b^{5} \arctan \left(\frac{2 b \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 a}{2 \sqrt{-a^{2}+b^{2}}}\right)}{d \,a^{2} \left(a^{6}-3 a^{4} b^{2}+3 b^{4} a^{2}-b^{6}\right) \sqrt{-a^{2}+b^{2}}}-\frac{4 b^{8} \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{3} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+b \right)^{3} \left(a^{6}-3 a^{4} b^{2}+3 b^{4} a^{2}-b^{6}\right)}+\frac{b^{6} \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d a \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+b \right)^{3} \left(a^{6}-3 a^{4} b^{2}+3 b^{4} a^{2}-b^{6}\right)}-\frac{12 b^{7} \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{2} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+b \right)^{3} \left(a^{6}-3 a^{4} b^{2}+3 b^{4} a^{2}-b^{6}\right)}-\frac{76 a^{3} b^{2} \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+b \right)^{3} \left(a^{6}-3 a^{4} b^{2}+3 b^{4} a^{2}-b^{6}\right)}-\frac{6 a^{2} b^{3} \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+b \right)^{3} \left(a^{6}-3 a^{4} b^{2}+3 b^{4} a^{2}-b^{6}\right)}+\frac{2 b^{7} \arctan \left(\frac{2 b \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 a}{2 \sqrt{-a^{2}+b^{2}}}\right)}{d \,a^{4} \left(a^{6}-3 a^{4} b^{2}+3 b^{4} a^{2}-b^{6}\right) \sqrt{-a^{2}+b^{2}}}-\frac{8 b^{6} \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d a \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+b \right)^{3} \left(a^{6}-3 a^{4} b^{2}+3 b^{4} a^{2}-b^{6}\right)}-\frac{26 a \,b^{4}}{3 d \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+b \right)^{3} \left(a^{6}-3 a^{4} b^{2}+3 b^{4} a^{2}-b^{6}\right)}+\frac{17 b^{6}}{3 d a \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+b \right)^{3} \left(a^{6}-3 a^{4} b^{2}+3 b^{4} a^{2}-b^{6}\right)}-\frac{2 b^{8}}{d \,a^{3} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+b \right)^{3} \left(a^{6}-3 a^{4} b^{2}+3 b^{4} a^{2}-b^{6}\right)}+\frac{2 b^{5} \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+b \right)^{3} \left(a^{6}-3 a^{4} b^{2}+3 b^{4} a^{2}-b^{6}\right)}+\frac{32 b^{5} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+b \right)^{3} \left(a^{6}-3 a^{4} b^{2}+3 b^{4} a^{2}-b^{6}\right)}+\frac{26 b^{5} \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+b \right)^{3} \left(a^{6}-3 a^{4} b^{2}+3 b^{4} a^{2}-b^{6}\right)}+\frac{8 b^{3} \arctan \left(\frac{2 b \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 a}{2 \sqrt{-a^{2}+b^{2}}}\right)}{d \left(a^{6}-3 a^{4} b^{2}+3 b^{4} a^{2}-b^{6}\right) \sqrt{-a^{2}+b^{2}}}"," ",0,"-88/3/d*a^2*b^3/(tan(1/2*d*x+1/2*c)^2*b+2*a*tan(1/2*d*x+1/2*c)+b)^3/(a^6-3*a^4*b^2+3*a^2*b^4-b^6)*tan(1/2*d*x+1/2*c)^3-46/d*a^2*b^3/(tan(1/2*d*x+1/2*c)^2*b+2*a*tan(1/2*d*x+1/2*c)+b)^3/(a^6-3*a^4*b^2+3*a^2*b^4-b^6)*tan(1/2*d*x+1/2*c)+4/d*a*b^4/(tan(1/2*d*x+1/2*c)^2*b+2*a*tan(1/2*d*x+1/2*c)+b)^3/(a^6-3*a^4*b^2+3*a^2*b^4-b^6)*tan(1/2*d*x+1/2*c)^4+2/d/a^4*arctan(tan(1/2*d*x+1/2*c))-8/d/a*b^6/(tan(1/2*d*x+1/2*c)^2*b+2*a*tan(1/2*d*x+1/2*c)+b)^3/(a^6-3*a^4*b^2+3*a^2*b^4-b^6)*tan(1/2*d*x+1/2*c)^2-8/d*a^2*b/(a^6-3*a^4*b^2+3*a^2*b^4-b^6)/(-a^2+b^2)^(1/2)*arctan(1/2*(2*b*tan(1/2*d*x+1/2*c)+2*a)/(-a^2+b^2)^(1/2))-6/d*a^2*b^3/(tan(1/2*d*x+1/2*c)^2*b+2*a*tan(1/2*d*x+1/2*c)+b)^3/(a^6-3*a^4*b^2+3*a^2*b^4-b^6)*tan(1/2*d*x+1/2*c)^5+38/d*a*b^4/(tan(1/2*d*x+1/2*c)^2*b+2*a*tan(1/2*d*x+1/2*c)+b)^3/(a^6-3*a^4*b^2+3*a^2*b^4-b^6)*tan(1/2*d*x+1/2*c)^2-1/d/a^2*b^7/(tan(1/2*d*x+1/2*c)^2*b+2*a*tan(1/2*d*x+1/2*c)+b)^3/(a^6-3*a^4*b^2+3*a^2*b^4-b^6)*tan(1/2*d*x+1/2*c)^5-104/3/d*a^4*b/(tan(1/2*d*x+1/2*c)^2*b+2*a*tan(1/2*d*x+1/2*c)+b)^3/(a^6-3*a^4*b^2+3*a^2*b^4-b^6)*tan(1/2*d*x+1/2*c)^3-7/d/a^2*b^5/(a^6-3*a^4*b^2+3*a^2*b^4-b^6)/(-a^2+b^2)^(1/2)*arctan(1/2*(2*b*tan(1/2*d*x+1/2*c)+2*a)/(-a^2+b^2)^(1/2))-2/d/a^3*b^8/(tan(1/2*d*x+1/2*c)^2*b+2*a*tan(1/2*d*x+1/2*c)+b)^3/(a^6-3*a^4*b^2+3*a^2*b^4-b^6)*tan(1/2*d*x+1/2*c)^4-11/d/a^2*b^7/(tan(1/2*d*x+1/2*c)^2*b+2*a*tan(1/2*d*x+1/2*c)+b)^3/(a^6-3*a^4*b^2+3*a^2*b^4-b^6)*tan(1/2*d*x+1/2*c)-28/d*a^3*b^2/(tan(1/2*d*x+1/2*c)^2*b+2*a*tan(1/2*d*x+1/2*c)+b)^3/(a^6-3*a^4*b^2+3*a^2*b^4-b^6)*tan(1/2*d*x+1/2*c)^4-4/d/a^3*b^8/(tan(1/2*d*x+1/2*c)^2*b+2*a*tan(1/2*d*x+1/2*c)+b)^3/(a^6-3*a^4*b^2+3*a^2*b^4-b^6)*tan(1/2*d*x+1/2*c)^2-26/3/d*a*b^4/(tan(1/2*d*x+1/2*c)^2*b+2*a*tan(1/2*d*x+1/2*c)+b)^3/(a^6-3*a^4*b^2+3*a^2*b^4-b^6)+17/3/d/a*b^6/(tan(1/2*d*x+1/2*c)^2*b+2*a*tan(1/2*d*x+1/2*c)+b)^3/(a^6-3*a^4*b^2+3*a^2*b^4-b^6)+2/d/a^4*b^7/(a^6-3*a^4*b^2+3*a^2*b^4-b^6)/(-a^2+b^2)^(1/2)*arctan(1/2*(2*b*tan(1/2*d*x+1/2*c)+2*a)/(-a^2+b^2)^(1/2))+1/d/a*b^6/(tan(1/2*d*x+1/2*c)^2*b+2*a*tan(1/2*d*x+1/2*c)+b)^3/(a^6-3*a^4*b^2+3*a^2*b^4-b^6)*tan(1/2*d*x+1/2*c)^4-12/d/a^2*b^7/(tan(1/2*d*x+1/2*c)^2*b+2*a*tan(1/2*d*x+1/2*c)+b)^3/(a^6-3*a^4*b^2+3*a^2*b^4-b^6)*tan(1/2*d*x+1/2*c)^3-76/d*a^3*b^2/(tan(1/2*d*x+1/2*c)^2*b+2*a*tan(1/2*d*x+1/2*c)+b)^3/(a^6-3*a^4*b^2+3*a^2*b^4-b^6)*tan(1/2*d*x+1/2*c)^2-2/d/a^3*b^8/(tan(1/2*d*x+1/2*c)^2*b+2*a*tan(1/2*d*x+1/2*c)+b)^3/(a^6-3*a^4*b^2+3*a^2*b^4-b^6)+8/d*b^3/(a^6-3*a^4*b^2+3*a^2*b^4-b^6)/(-a^2+b^2)^(1/2)*arctan(1/2*(2*b*tan(1/2*d*x+1/2*c)+2*a)/(-a^2+b^2)^(1/2))+2/d*b^5/(tan(1/2*d*x+1/2*c)^2*b+2*a*tan(1/2*d*x+1/2*c)+b)^3/(a^6-3*a^4*b^2+3*a^2*b^4-b^6)*tan(1/2*d*x+1/2*c)^5+32/d*b^5/(tan(1/2*d*x+1/2*c)^2*b+2*a*tan(1/2*d*x+1/2*c)+b)^3/(a^6-3*a^4*b^2+3*a^2*b^4-b^6)*tan(1/2*d*x+1/2*c)+26/d*b^5/(tan(1/2*d*x+1/2*c)^2*b+2*a*tan(1/2*d*x+1/2*c)+b)^3/(a^6-3*a^4*b^2+3*a^2*b^4-b^6)*tan(1/2*d*x+1/2*c)^3","B"
52,1,36,27,0.565000," ","int(1/(3+5*csc(d*x+c)),x)","-\frac{5 \arctan \left(\frac{5 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{4}+\frac{3}{4}\right)}{6 d}+\frac{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 d}"," ",0,"-5/6/d*arctan(5/4*tan(1/2*d*x+1/2*c)+3/4)+2/3/d*arctan(tan(1/2*d*x+1/2*c))","A"
53,1,53,58,0.635000," ","int(1/(5+3*csc(d*x+c)),x)","-\frac{3 \ln \left(1+3 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{20 d}+\frac{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{5 d}+\frac{3 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+3\right)}{20 d}"," ",0,"-3/20/d*ln(1+3*tan(1/2*d*x+1/2*c))+2/5/d*arctan(tan(1/2*d*x+1/2*c))+3/20/d*ln(tan(1/2*d*x+1/2*c)+3)","A"
54,0,0,246,2.102000," ","int(csc(f*x+e)^3*(a+b*csc(f*x+e))^m,x)","\int \left(\csc^{3}\left(f x +e \right)\right) \left(a +b \csc \left(f x +e \right)\right)^{m}\, dx"," ",0,"int(csc(f*x+e)^3*(a+b*csc(f*x+e))^m,x)","F"
55,0,0,192,1.316000," ","int(csc(f*x+e)^2*(a+b*csc(f*x+e))^m,x)","\int \left(\csc^{2}\left(f x +e \right)\right) \left(a +b \csc \left(f x +e \right)\right)^{m}\, dx"," ",0,"int(csc(f*x+e)^2*(a+b*csc(f*x+e))^m,x)","F"
56,0,0,90,1.721000," ","int(csc(f*x+e)*(a+b*csc(f*x+e))^m,x)","\int \csc \left(f x +e \right) \left(a +b \csc \left(f x +e \right)\right)^{m}\, dx"," ",0,"int(csc(f*x+e)*(a+b*csc(f*x+e))^m,x)","F"
57,0,0,14,1.238000," ","int((a+b*csc(f*x+e))^m,x)","\int \left(a +b \csc \left(f x +e \right)\right)^{m}\, dx"," ",0,"int((a+b*csc(f*x+e))^m,x)","F"
58,0,0,21,1.067000," ","int((a+b*csc(f*x+e))^m*sin(f*x+e),x)","\int \left(a +b \csc \left(f x +e \right)\right)^{m} \sin \left(f x +e \right)\, dx"," ",0,"int((a+b*csc(f*x+e))^m*sin(f*x+e),x)","F"
59,0,0,23,4.447000," ","int((a+b*csc(f*x+e))^m*sin(f*x+e)^2,x)","\int \left(a +b \csc \left(f x +e \right)\right)^{m} \left(\sin^{2}\left(f x +e \right)\right)\, dx"," ",0,"int((a+b*csc(f*x+e))^m*sin(f*x+e)^2,x)","F"